id	sid	tid	token	lemma	pos
ejpam-2338	1	1	compile	compile	NOUN
ejpam-2338	1	2	/	/	SYM
ejpam-2338	1	3	output.dvi	output.dvi	NOUN
ejpam-2338	1	4	european	european	ADJ
ejpam-2338	1	5	journal	journal	NOUN
ejpam-2338	1	6	of	of	ADP
ejpam-2338	1	7	pure	pure	ADJ
ejpam-2338	1	8	and	and	CCONJ
ejpam-2338	1	9	applied	apply	VERB
ejpam-2338	1	10	mathematics	mathematic	NOUN
ejpam-2338	1	11	vol	vol	NOUN
ejpam-2338	1	12	.	.	PROPN
ejpam-2338	1	13	8	8	NUM
ejpam-2338	1	14	,	,	PUNCT
ejpam-2338	1	15	no	no	INTJ
ejpam-2338	1	16	.	.	NOUN
ejpam-2338	1	17	3	3	NUM
ejpam-2338	1	18	,	,	PUNCT
ejpam-2338	1	19	2015	2015	NUM
ejpam-2338	1	20	,	,	PUNCT
ejpam-2338	1	21	294	294	NUM
ejpam-2338	1	22	-	-	SYM
ejpam-2338	1	23	323	323	NUM
ejpam-2338	1	24	issn	issn	PROPN
ejpam-2338	1	25	1307	1307	NUM
ejpam-2338	1	26	-	-	SYM
ejpam-2338	1	27	5543	5543	NUM
ejpam-2338	1	28	–	–	PUNCT
ejpam-2338	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2338	1	30	three	three	NUM
ejpam-2338	1	31	approaches	approach	NOUN
ejpam-2338	1	32	to	to	ADP
ejpam-2338	1	33	inverse	inverse	NOUN
ejpam-2338	1	34	semigroups	semigroup	NOUN
ejpam-2338	1	35	christopher	christopher	PROPN
ejpam-2338	1	36	hollings	hollings	PROPN
ejpam-2338	1	37	mathematical	mathematical	PROPN
ejpam-2338	1	38	institute	institute	PROPN
ejpam-2338	1	39	,	,	PUNCT
ejpam-2338	1	40	university	university	PROPN
ejpam-2338	1	41	of	of	ADP
ejpam-2338	1	42	oxford	oxford	PROPN
ejpam-2338	1	43	,	,	PUNCT
ejpam-2338	1	44	andrew	andrew	PROPN
ejpam-2338	1	45	wiles	wile	NOUN
ejpam-2338	1	46	building	building	NOUN
ejpam-2338	1	47	,	,	PUNCT
ejpam-2338	1	48	radcliffe	radcliffe	PROPN
ejpam-2338	1	49	observatory	observatory	ADJ
ejpam-2338	1	50	quarter	quarter	NOUN
ejpam-2338	1	51	,	,	PUNCT
ejpam-2338	1	52	woodstock	woodstock	PROPN
ejpam-2338	1	53	road	road	PROPN
ejpam-2338	1	54	,	,	PUNCT
ejpam-2338	1	55	oxford	oxford	PROPN
ejpam-2338	1	56	,	,	PUNCT
ejpam-2338	1	57	ox2	ox2	PROPN
ejpam-2338	1	58	6gg	6gg	NOUN
ejpam-2338	1	59	,	,	PUNCT
ejpam-2338	1	60	uk	uk	PROPN
ejpam-2338	1	61	abstract	abstract	NOUN
ejpam-2338	1	62	.	.	PUNCT
ejpam-2338	2	1	i	i	PRON
ejpam-2338	2	2	give	give	VERB
ejpam-2338	2	3	a	a	DET
ejpam-2338	2	4	historical	historical	ADJ
ejpam-2338	2	5	survey	survey	NOUN
ejpam-2338	2	6	of	of	ADP
ejpam-2338	2	7	the	the	DET
ejpam-2338	2	8	three	three	NUM
ejpam-2338	2	9	main	main	ADJ
ejpam-2338	2	10	approaches	approach	NOUN
ejpam-2338	2	11	to	to	ADP
ejpam-2338	2	12	the	the	DET
ejpam-2338	2	13	study	study	NOUN
ejpam-2338	2	14	of	of	ADP
ejpam-2338	2	15	the	the	DET
ejpam-2338	2	16	structure	structure	NOUN
ejpam-2338	2	17	of	of	ADP
ejpam-2338	2	18	inverse	inverse	NOUN
ejpam-2338	2	19	semigroups	semigroup	NOUN
ejpam-2338	2	20	.	.	PUNCT
ejpam-2338	3	1	the	the	DET
ejpam-2338	3	2	first	first	ADJ
ejpam-2338	3	3	is	be	AUX
ejpam-2338	3	4	that	that	SCONJ
ejpam-2338	3	5	via	via	ADP
ejpam-2338	3	6	inductive	inductive	ADJ
ejpam-2338	3	7	groupoids	groupoid	NOUN
ejpam-2338	3	8	,	,	PUNCT
ejpam-2338	3	9	as	as	SCONJ
ejpam-2338	3	10	studied	study	VERB
ejpam-2338	3	11	by	by	ADP
ejpam-2338	3	12	charles	charles	PROPN
ejpam-2338	3	13	ehresmann	ehresmann	PROPN
ejpam-2338	3	14	.	.	PUNCT
ejpam-2338	4	1	the	the	DET
ejpam-2338	4	2	second	second	ADJ
ejpam-2338	4	3	concerns	concern	VERB
ejpam-2338	4	4	the	the	DET
ejpam-2338	4	5	notion	notion	NOUN
ejpam-2338	4	6	of	of	ADP
ejpam-2338	4	7	a	a	DET
ejpam-2338	4	8	fundamental	fundamental	ADJ
ejpam-2338	4	9	inverse	inverse	NOUN
ejpam-2338	4	10	semigroup	semigroup	NOUN
ejpam-2338	4	11	and	and	CCONJ
ejpam-2338	4	12	its	its	PRON
ejpam-2338	4	13	munn	munn	PROPN
ejpam-2338	4	14	representation	representation	NOUN
ejpam-2338	4	15	.	.	PUNCT
ejpam-2338	5	1	finally	finally	ADV
ejpam-2338	5	2	,	,	PUNCT
ejpam-2338	5	3	the	the	DET
ejpam-2338	5	4	third	third	ADJ
ejpam-2338	5	5	centres	centre	NOUN
ejpam-2338	5	6	upon	upon	SCONJ
ejpam-2338	5	7	the	the	DET
ejpam-2338	5	8	concept	concept	NOUN
ejpam-2338	5	9	of	of	ADP
ejpam-2338	5	10	an	an	DET
ejpam-2338	5	11	e	e	NOUN
ejpam-2338	5	12	-	-	NOUN
ejpam-2338	5	13	unitary	unitary	ADJ
ejpam-2338	5	14	or	or	CCONJ
ejpam-2338	5	15	proper	proper	ADJ
ejpam-2338	5	16	inverse	inverse	NOUN
ejpam-2338	5	17	semigroup	semigroup	NOUN
ejpam-2338	5	18	and	and	CCONJ
ejpam-2338	5	19	its	its	PRON
ejpam-2338	5	20	representation	representation	NOUN
ejpam-2338	5	21	(	(	PUNCT
ejpam-2338	5	22	due	due	ADP
ejpam-2338	5	23	to	to	ADP
ejpam-2338	5	24	mcalister	mcalister	NOUN
ejpam-2338	5	25	)	)	PUNCT
ejpam-2338	5	26	by	by	ADP
ejpam-2338	5	27	a	a	DET
ejpam-2338	5	28	so	so	ADV
ejpam-2338	5	29	-	-	PUNCT
ejpam-2338	5	30	called	call	VERB
ejpam-2338	5	31	p	p	NOUN
ejpam-2338	5	32	-	-	PUNCT
ejpam-2338	5	33	semigroup	semigroup	NOUN
ejpam-2338	5	34	.	.	PUNCT
ejpam-2338	6	1	2010	2010	NUM
ejpam-2338	6	2	mathematics	mathematic	NOUN
ejpam-2338	6	3	subject	subject	NOUN
ejpam-2338	6	4	classifications	classification	NOUN
ejpam-2338	6	5	:	:	PUNCT
ejpam-2338	6	6	01a60	01a60	NUM
ejpam-2338	6	7	,	,	PUNCT
ejpam-2338	6	8	20	20	NUM
ejpam-2338	6	9	-	-	SYM
ejpam-2338	6	10	03	03	NUM
ejpam-2338	6	11	,	,	PUNCT
ejpam-2338	6	12	20m18	20m18	NUM
ejpam-2338	6	13	,	,	PUNCT
ejpam-2338	6	14	20l05	20l05	NUM
ejpam-2338	6	15	key	key	ADJ
ejpam-2338	6	16	words	word	NOUN
ejpam-2338	6	17	and	and	CCONJ
ejpam-2338	6	18	phrases	phrase	NOUN
ejpam-2338	6	19	:	:	PUNCT
ejpam-2338	6	20	inverse	inverse	NOUN
ejpam-2338	6	21	semigroup	semigroup	NOUN
ejpam-2338	6	22	(	(	PUNCT
ejpam-2338	6	23	fundamental	fundamental	ADJ
ejpam-2338	6	24	,	,	PUNCT
ejpam-2338	6	25	e	e	NOUN
ejpam-2338	6	26	-	-	NOUN
ejpam-2338	6	27	unitary	unitary	ADJ
ejpam-2338	6	28	,	,	PUNCT
ejpam-2338	6	29	proper	proper	ADJ
ejpam-2338	6	30	)	)	PUNCT
ejpam-2338	6	31	,	,	PUNCT
ejpam-2338	6	32	inductive	inductive	ADJ
ejpam-2338	6	33	groupoid	groupoid	PROPN
ejpam-2338	6	34	,	,	PUNCT
ejpam-2338	6	35	idempotent	idempotent	NOUN
ejpam-2338	6	36	-	-	PUNCT
ejpam-2338	6	37	separating	separate	VERB
ejpam-2338	6	38	congruence	congruence	NOUN
ejpam-2338	6	39	,	,	PUNCT
ejpam-2338	6	40	munn	munn	PROPN
ejpam-2338	6	41	representation	representation	NOUN
ejpam-2338	6	42	,	,	PUNCT
ejpam-2338	6	43	e	e	NOUN
ejpam-2338	6	44	-	-	ADJ
ejpam-2338	6	45	unitary	unitary	ADJ
ejpam-2338	6	46	cover	cover	NOUN
ejpam-2338	6	47	,	,	PUNCT
ejpam-2338	6	48	minimum	minimum	ADJ
ejpam-2338	6	49	group	group	NOUN
ejpam-2338	6	50	congruence	congruence	NOUN
ejpam-2338	6	51	,	,	PUNCT
ejpam-2338	6	52	maximum	maximum	ADJ
ejpam-2338	6	53	group	group	NOUN
ejpam-2338	6	54	image	image	NOUN
ejpam-2338	6	55	,	,	PUNCT
ejpam-2338	6	56	p	p	NOUN
ejpam-2338	6	57	-	-	PUNCT
ejpam-2338	6	58	semigroup	semigroup	NOUN
ejpam-2338	6	59	,	,	PUNCT
ejpam-2338	6	60	p	p	NOUN
ejpam-2338	6	61	-	-	PUNCT
ejpam-2338	6	62	theorem	theorem	ADJ
ejpam-2338	6	63	1	1	NUM
ejpam-2338	6	64	.	.	NOUN
ejpam-2338	6	65	introduction	introduction	NOUN
ejpam-2338	6	66	since	since	SCONJ
ejpam-2338	6	67	their	their	PRON
ejpam-2338	6	68	introduction	introduction	NOUN
ejpam-2338	6	69	into	into	ADP
ejpam-2338	6	70	the	the	DET
ejpam-2338	6	71	mathematical	mathematical	ADJ
ejpam-2338	6	72	literature	literature	NOUN
ejpam-2338	6	73	in	in	ADP
ejpam-2338	6	74	the	the	DET
ejpam-2338	6	75	early	early	ADJ
ejpam-2338	6	76	1950s	1950s	NUM
ejpam-2338	6	77	,	,	PUNCT
ejpam-2338	6	78	inverse	inverse	NOUN
ejpam-2338	6	79	semigroups	semigroup	NOUN
ejpam-2338	6	80	have	have	AUX
ejpam-2338	6	81	become	become	VERB
ejpam-2338	6	82	one	one	NUM
ejpam-2338	6	83	of	of	ADP
ejpam-2338	6	84	the	the	DET
ejpam-2338	6	85	most	most	ADV
ejpam-2338	6	86	-	-	PUNCT
ejpam-2338	6	87	studied	study	VERB
ejpam-2338	6	88	classes	class	NOUN
ejpam-2338	6	89	of	of	ADP
ejpam-2338	6	90	semigroups	semigroup	NOUN
ejpam-2338	6	91	,	,	PUNCT
ejpam-2338	6	92	with	with	ADP
ejpam-2338	6	93	entire	entire	ADJ
ejpam-2338	6	94	monographs	monograph	NOUN
ejpam-2338	7	1	[	[	X
ejpam-2338	7	2	51	51	NUM
ejpam-2338	7	3	,	,	PUNCT
ejpam-2338	7	4	72	72	NUM
ejpam-2338	7	5	]	]	PUNCT
ejpam-2338	7	6	devoted	devote	VERB
ejpam-2338	7	7	to	to	ADP
ejpam-2338	7	8	their	their	PRON
ejpam-2338	7	9	understanding	understanding	NOUN
ejpam-2338	7	10	.	.	PUNCT
ejpam-2338	8	1	such	such	ADJ
ejpam-2338	8	2	important	important	ADJ
ejpam-2338	8	3	objects	object	NOUN
ejpam-2338	8	4	of	of	ADP
ejpam-2338	8	5	study	study	NOUN
ejpam-2338	8	6	have	have	AUX
ejpam-2338	8	7	naturally	naturally	ADV
ejpam-2338	8	8	given	give	VERB
ejpam-2338	8	9	rise	rise	NOUN
ejpam-2338	8	10	to	to	ADP
ejpam-2338	8	11	a	a	DET
ejpam-2338	8	12	number	number	NOUN
ejpam-2338	8	13	of	of	ADP
ejpam-2338	8	14	different	different	ADJ
ejpam-2338	8	15	methods	method	NOUN
ejpam-2338	8	16	for	for	ADP
ejpam-2338	8	17	their	their	PRON
ejpam-2338	8	18	investigation	investigation	NOUN
ejpam-2338	8	19	.	.	PUNCT
ejpam-2338	9	1	in	in	ADP
ejpam-2338	9	2	this	this	DET
ejpam-2338	9	3	article	article	NOUN
ejpam-2338	9	4	,	,	PUNCT
ejpam-2338	9	5	i	i	PRON
ejpam-2338	9	6	provide	provide	VERB
ejpam-2338	9	7	a	a	DET
ejpam-2338	9	8	historical	historical	ADJ
ejpam-2338	9	9	survey	survey	NOUN
ejpam-2338	9	10	,	,	PUNCT
ejpam-2338	9	11	together	together	ADV
ejpam-2338	9	12	with	with	ADP
ejpam-2338	9	13	an	an	DET
ejpam-2338	9	14	intuitive	intuitive	ADJ
ejpam-2338	9	15	sketch	sketch	NOUN
ejpam-2338	9	16	,	,	PUNCT
ejpam-2338	9	17	of	of	ADP
ejpam-2338	9	18	the	the	DET
ejpam-2338	9	19	three	three	NUM
ejpam-2338	9	20	main	main	ADJ
ejpam-2338	9	21	approaches	approach	NOUN
ejpam-2338	9	22	,	,	PUNCT
ejpam-2338	9	23	as	as	SCONJ
ejpam-2338	9	24	identified	identify	VERB
ejpam-2338	9	25	by	by	ADP
ejpam-2338	9	26	fountain	fountain	NOUN
ejpam-2338	9	27	[	[	X
ejpam-2338	9	28	20	20	NUM
ejpam-2338	9	29	,	,	PUNCT
ejpam-2338	9	30	p.	p.	NOUN
ejpam-2338	9	31	12	12	NUM
ejpam-2338	10	1	]	]	X
ejpam-2338	10	2	:	:	PUNCT
ejpam-2338	10	3	those	those	PRON
ejpam-2338	10	4	via	via	ADP
ejpam-2338	10	5	inductive	inductive	ADJ
ejpam-2338	10	6	groupoids	groupoid	NOUN
ejpam-2338	10	7	,	,	PUNCT
ejpam-2338	10	8	the	the	DET
ejpam-2338	10	9	munn	munn	PROPN
ejpam-2338	10	10	representation	representation	NOUN
ejpam-2338	10	11	,	,	PUNCT
ejpam-2338	10	12	and	and	CCONJ
ejpam-2338	10	13	proper	proper	ADJ
ejpam-2338	10	14	inverse	inverse	NOUN
ejpam-2338	10	15	semigroups	semigroup	NOUN
ejpam-2338	10	16	.	.	PUNCT
ejpam-2338	11	1	the	the	DET
ejpam-2338	11	2	present	present	ADJ
ejpam-2338	11	3	article	article	NOUN
ejpam-2338	11	4	is	be	AUX
ejpam-2338	11	5	a	a	DET
ejpam-2338	11	6	companion	companion	NOUN
ejpam-2338	11	7	piece	piece	NOUN
ejpam-2338	11	8	to	to	ADP
ejpam-2338	11	9	my	my	PRON
ejpam-2338	11	10	earlier	early	ADJ
ejpam-2338	11	11	articles	article	NOUN
ejpam-2338	11	12	[	[	X
ejpam-2338	11	13	36	36	NUM
ejpam-2338	11	14	,	,	PUNCT
ejpam-2338	11	15	40	40	NUM
ejpam-2338	11	16	]	]	PUNCT
ejpam-2338	11	17	,	,	PUNCT
ejpam-2338	11	18	and	and	CCONJ
ejpam-2338	11	19	can	can	AUX
ejpam-2338	11	20	also	also	ADV
ejpam-2338	11	21	be	be	AUX
ejpam-2338	11	22	read	read	VERB
ejpam-2338	11	23	as	as	ADP
ejpam-2338	11	24	a	a	DET
ejpam-2338	11	25	technical	technical	ADJ
ejpam-2338	11	26	addendum	addendum	NOUN
ejpam-2338	11	27	to	to	ADP
ejpam-2338	11	28	[	[	X
ejpam-2338	11	29	41	41	NUM
ejpam-2338	11	30	,	,	PUNCT
ejpam-2338	11	31	chapter	chapter	NOUN
ejpam-2338	11	32	10	10	NUM
ejpam-2338	11	33	]	]	PUNCT
ejpam-2338	11	34	.	.	PUNCT
ejpam-2338	12	1	the	the	DET
ejpam-2338	12	2	investigation	investigation	NOUN
ejpam-2338	12	3	of	of	ADP
ejpam-2338	12	4	inverse	inverse	NOUN
ejpam-2338	12	5	semigroups	semigroup	NOUN
ejpam-2338	12	6	by	by	ADP
ejpam-2338	12	7	means	mean	NOUN
ejpam-2338	12	8	of	of	ADP
ejpam-2338	12	9	their	their	PRON
ejpam-2338	12	10	corresponding	corresponding	ADJ
ejpam-2338	12	11	inductive	inductive	ADJ
ejpam-2338	12	12	groupoids	groupoid	NOUN
ejpam-2338	12	13	(	(	PUNCT
ejpam-2338	12	14	on	on	ADP
ejpam-2338	12	15	the	the	DET
ejpam-2338	12	16	history	history	NOUN
ejpam-2338	12	17	of	of	ADP
ejpam-2338	12	18	which	which	PRON
ejpam-2338	12	19	,	,	PUNCT
ejpam-2338	12	20	i	i	PRON
ejpam-2338	12	21	have	have	AUX
ejpam-2338	12	22	already	already	ADV
ejpam-2338	12	23	written	write	VERB
ejpam-2338	12	24	in	in	ADP
ejpam-2338	12	25	detail	detail	NOUN
ejpam-2338	12	26	in	in	ADP
ejpam-2338	12	27	[	[	X
ejpam-2338	12	28	40	40	NUM
ejpam-2338	12	29	]	]	PUNCT
ejpam-2338	12	30	)	)	PUNCT
ejpam-2338	12	31	goes	go	VERB
ejpam-2338	12	32	back	back	ADV
ejpam-2338	12	33	to	to	ADP
ejpam-2338	12	34	the	the	DET
ejpam-2338	12	35	historical	historical	ADJ
ejpam-2338	12	36	roots	root	NOUN
ejpam-2338	12	37	of	of	ADP
ejpam-2338	12	38	the	the	DET
ejpam-2338	12	39	notion	notion	NOUN
ejpam-2338	12	40	of	of	ADP
ejpam-2338	12	41	an	an	DET
ejpam-2338	12	42	inverse	inverse	NOUN
ejpam-2338	12	43	semigroup	semigroup	NOUN
ejpam-2338	12	44	.	.	PUNCT
ejpam-2338	13	1	the	the	DET
ejpam-2338	13	2	problem	problem	NOUN
ejpam-2338	13	3	arose	arise	VERB
ejpam-2338	13	4	in	in	ADP
ejpam-2338	13	5	the	the	DET
ejpam-2338	13	6	1930s	1930	NOUN
ejpam-2338	13	7	of	of	ADP
ejpam-2338	13	8	giving	give	VERB
ejpam-2338	13	9	an	an	DET
ejpam-2338	13	10	abstract	abstract	ADJ
ejpam-2338	13	11	characterisation	characterisation	NOUN
ejpam-2338	13	12	of	of	ADP
ejpam-2338	13	13	systems	system	NOUN
ejpam-2338	13	14	of	of	ADP
ejpam-2338	13	15	partial	partial	ADJ
ejpam-2338	13	16	transformations	transformation	NOUN
ejpam-2338	13	17	of	of	ADP
ejpam-2338	13	18	a	a	DET
ejpam-2338	13	19	set	set	NOUN
ejpam-2338	13	20	equipped	equip	VERB
ejpam-2338	13	21	with	with	ADP
ejpam-2338	13	22	a	a	DET
ejpam-2338	13	23	partially	partially	ADV
ejpam-2338	13	24	-	-	PUNCT
ejpam-2338	13	25	defined	define	VERB
ejpam-2338	13	26	binary	binary	ADJ
ejpam-2338	13	27	operation	operation	NOUN
ejpam-2338	13	28	.	.	PUNCT
ejpam-2338	14	1	many	many	ADJ
ejpam-2338	14	2	mathematicians	mathematician	NOUN
ejpam-2338	14	3	sought	seek	VERB
ejpam-2338	14	4	to	to	PART
ejpam-2338	14	5	‘	'	PUNCT
ejpam-2338	14	6	complete	complete	ADJ
ejpam-2338	14	7	’	'	PUNCT
ejpam-2338	14	8	this	this	DET
ejpam-2338	14	9	operation	operation	NOUN
ejpam-2338	14	10	to	to	ADP
ejpam-2338	14	11	an	an	DET
ejpam-2338	14	12	everywhere	everywhere	ADV
ejpam-2338	14	13	-	-	PUNCT
ejpam-2338	14	14	defined	define	VERB
ejpam-2338	14	15	one	one	NUM
ejpam-2338	14	16	before	before	ADP
ejpam-2338	14	17	axiomatising	axiomatise	VERB
ejpam-2338	14	18	,	,	PUNCT
ejpam-2338	14	19	eventually	eventually	ADV
ejpam-2338	14	20	giving	give	VERB
ejpam-2338	14	21	rise	rise	NOUN
ejpam-2338	14	22	to	to	ADP
ejpam-2338	14	23	the	the	DET
ejpam-2338	14	24	abstract	abstract	ADJ
ejpam-2338	14	25	notion	notion	NOUN
ejpam-2338	14	26	of	of	ADP
ejpam-2338	14	27	an	an	DET
ejpam-2338	14	28	inverse	inverse	NOUN
ejpam-2338	14	29	semigroup	semigroup	NOUN
ejpam-2338	14	30	.	.	PUNCT
ejpam-2338	15	1	if	if	SCONJ
ejpam-2338	15	2	,	,	PUNCT
ejpam-2338	15	3	on	on	ADP
ejpam-2338	15	4	the	the	DET
ejpam-2338	15	5	other	other	ADJ
ejpam-2338	15	6	hand	hand	NOUN
ejpam-2338	15	7	,	,	PUNCT
ejpam-2338	15	8	we	we	PRON
ejpam-2338	15	9	are	be	AUX
ejpam-2338	15	10	content	content	ADJ
ejpam-2338	15	11	to	to	PART
ejpam-2338	15	12	retain	retain	VERB
ejpam-2338	15	13	the	the	DET
ejpam-2338	15	14	original	original	ADJ
ejpam-2338	15	15	partial	partial	ADJ
ejpam-2338	15	16	email	email	NOUN
ejpam-2338	15	17	address	address	NOUN
ejpam-2338	15	18	:	:	PUNCT
ejpam-2338	15	19	christopher.hollings@maths.ox.ac.uk	christopher.hollings@maths.ox.ac.uk	ADJ
ejpam-2338	15	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2338	15	21	294	294	NUM
ejpam-2338	16	1	c	c	NOUN
ejpam-2338	16	2	©	©	PROPN
ejpam-2338	16	3	2015	2015	NUM
ejpam-2338	16	4	ejpam	ejpam	NOUN
ejpam-2338	16	5	all	all	DET
ejpam-2338	16	6	rights	right	NOUN
ejpam-2338	16	7	reserved	reserve	VERB
ejpam-2338	16	8	.	.	PUNCT
ejpam-2338	17	1	christopher	christopher	PROPN
ejpam-2338	17	2	hollings	hollings	PROPN
ejpam-2338	17	3	/	/	SYM
ejpam-2338	17	4	eur	eur	PROPN
ejpam-2338	17	5	.	.	PUNCT
ejpam-2338	18	1	j.	j.	PROPN
ejpam-2338	18	2	pure	pure	PROPN
ejpam-2338	18	3	appl	appl	PROPN
ejpam-2338	18	4	.	.	PROPN
ejpam-2338	18	5	math	math	PROPN
ejpam-2338	18	6	,	,	PUNCT
ejpam-2338	18	7	8	8	NUM
ejpam-2338	18	8	(	(	PUNCT
ejpam-2338	18	9	2015	2015	NUM
ejpam-2338	18	10	)	)	PUNCT
ejpam-2338	18	11	,	,	PUNCT
ejpam-2338	18	12	294	294	NUM
ejpam-2338	18	13	-	-	SYM
ejpam-2338	18	14	323	323	NUM
ejpam-2338	18	15	295	295	NUM
ejpam-2338	18	16	operation	operation	NOUN
ejpam-2338	18	17	,	,	PUNCT
ejpam-2338	18	18	then	then	ADV
ejpam-2338	18	19	the	the	DET
ejpam-2338	18	20	abstract	abstract	ADJ
ejpam-2338	18	21	object	object	NOUN
ejpam-2338	18	22	that	that	PRON
ejpam-2338	18	23	results	result	VERB
ejpam-2338	18	24	is	be	AUX
ejpam-2338	18	25	a	a	DET
ejpam-2338	18	26	so	so	ADV
ejpam-2338	18	27	-	-	PUNCT
ejpam-2338	18	28	called	call	VERB
ejpam-2338	18	29	inductive	inductive	ADJ
ejpam-2338	18	30	groupoid	groupoid	PROPN
ejpam-2338	18	31	.	.	PUNCT
ejpam-2338	19	1	the	the	DET
ejpam-2338	19	2	fundamental	fundamental	ADJ
ejpam-2338	19	3	connection	connection	NOUN
ejpam-2338	19	4	between	between	ADP
ejpam-2338	19	5	inverse	inverse	NOUN
ejpam-2338	19	6	semigroups	semigroup	NOUN
ejpam-2338	19	7	and	and	CCONJ
ejpam-2338	19	8	inductive	inductive	ADJ
ejpam-2338	19	9	groupoids	groupoid	NOUN
ejpam-2338	19	10	is	be	AUX
ejpam-2338	19	11	enshrined	enshrine	VERB
ejpam-2338	19	12	in	in	ADP
ejpam-2338	19	13	the	the	DET
ejpam-2338	19	14	celebrated	celebrate	VERB
ejpam-2338	19	15	ehresmann	ehresmann	PROPN
ejpam-2338	19	16	–	–	PUNCT
ejpam-2338	19	17	schein	schein	PROPN
ejpam-2338	19	18	–	–	PUNCT
ejpam-2338	19	19	nambooripad	nambooripad	NOUN
ejpam-2338	19	20	theorem	theorem	NOUN
ejpam-2338	19	21	,	,	PUNCT
ejpam-2338	19	22	which	which	PRON
ejpam-2338	19	23	,	,	PUNCT
ejpam-2338	19	24	at	at	ADP
ejpam-2338	19	25	its	its	PRON
ejpam-2338	19	26	simplest	simple	ADJ
ejpam-2338	19	27	,	,	PUNCT
ejpam-2338	19	28	states	state	VERB
ejpam-2338	19	29	that	that	SCONJ
ejpam-2338	19	30	any	any	DET
ejpam-2338	19	31	inverse	inverse	NOUN
ejpam-2338	19	32	semigroup	semigroup	NOUN
ejpam-2338	19	33	gives	give	VERB
ejpam-2338	19	34	rise	rise	NOUN
ejpam-2338	19	35	to	to	ADP
ejpam-2338	19	36	a	a	DET
ejpam-2338	19	37	(	(	PUNCT
ejpam-2338	19	38	unique	unique	ADJ
ejpam-2338	19	39	)	)	PUNCT
ejpam-2338	19	40	inductive	inductive	ADJ
ejpam-2338	19	41	groupoid	groupoid	PROPN
ejpam-2338	19	42	,	,	PUNCT
ejpam-2338	19	43	and	and	CCONJ
ejpam-2338	19	44	vice	vice	ADV
ejpam-2338	19	45	versa	versa	ADV
ejpam-2338	19	46	,	,	PUNCT
ejpam-2338	19	47	thus	thus	ADV
ejpam-2338	19	48	enabling	enable	VERB
ejpam-2338	19	49	us	we	PRON
ejpam-2338	19	50	to	to	PART
ejpam-2338	19	51	use	use	VERB
ejpam-2338	19	52	the	the	DET
ejpam-2338	19	53	structure	structure	NOUN
ejpam-2338	19	54	of	of	ADP
ejpam-2338	19	55	the	the	DET
ejpam-2338	19	56	corresponding	corresponding	ADJ
ejpam-2338	19	57	groupoid	groupoid	NOUN
ejpam-2338	19	58	to	to	PART
ejpam-2338	19	59	inform	inform	VERB
ejpam-2338	19	60	our	our	PRON
ejpam-2338	19	61	investigation	investigation	NOUN
ejpam-2338	19	62	of	of	ADP
ejpam-2338	19	63	the	the	DET
ejpam-2338	19	64	original	original	ADJ
ejpam-2338	19	65	inverse	inverse	NOUN
ejpam-2338	19	66	semigroup	semigroup	NOUN
ejpam-2338	19	67	(	(	PUNCT
ejpam-2338	19	68	or	or	CCONJ
ejpam-2338	19	69	,	,	PUNCT
ejpam-2338	19	70	indeed	indeed	ADV
ejpam-2338	19	71	,	,	PUNCT
ejpam-2338	19	72	to	to	PART
ejpam-2338	19	73	use	use	VERB
ejpam-2338	19	74	the	the	DET
ejpam-2338	19	75	structure	structure	NOUN
ejpam-2338	19	76	of	of	ADP
ejpam-2338	19	77	the	the	DET
ejpam-2338	19	78	inverse	inverse	NOUN
ejpam-2338	19	79	semigroup	semigroup	NOUN
ejpam-2338	19	80	to	to	PART
ejpam-2338	19	81	assist	assist	VERB
ejpam-2338	19	82	in	in	ADP
ejpam-2338	19	83	the	the	DET
ejpam-2338	19	84	study	study	NOUN
ejpam-2338	19	85	of	of	ADP
ejpam-2338	19	86	the	the	DET
ejpam-2338	19	87	inductive	inductive	ADJ
ejpam-2338	19	88	groupoid	groupoid	PROPN
ejpam-2338	19	89	)	)	PUNCT
ejpam-2338	19	90	.	.	PUNCT
ejpam-2338	20	1	the	the	DET
ejpam-2338	20	2	order	order	NOUN
ejpam-2338	20	3	relations	relation	NOUN
ejpam-2338	20	4	in	in	ADP
ejpam-2338	20	5	inverse	inverse	NOUN
ejpam-2338	20	6	semigroups	semigroup	NOUN
ejpam-2338	20	7	and	and	CCONJ
ejpam-2338	20	8	in	in	ADP
ejpam-2338	20	9	inductive	inductive	ADJ
ejpam-2338	20	10	groupoids	groupoid	NOUN
ejpam-2338	20	11	have	have	VERB
ejpam-2338	20	12	a	a	DET
ejpam-2338	20	13	key	key	ADJ
ejpam-2338	20	14	role	role	NOUN
ejpam-2338	20	15	to	to	PART
ejpam-2338	20	16	play	play	VERB
ejpam-2338	20	17	here	here	ADV
ejpam-2338	20	18	.	.	PUNCT
ejpam-2338	21	1	the	the	DET
ejpam-2338	21	2	second	second	ADJ
ejpam-2338	21	3	approach	approach	NOUN
ejpam-2338	21	4	to	to	ADP
ejpam-2338	21	5	inverse	inverse	NOUN
ejpam-2338	21	6	semigroups	semigroup	NOUN
ejpam-2338	21	7	is	be	AUX
ejpam-2338	21	8	that	that	SCONJ
ejpam-2338	21	9	via	via	ADP
ejpam-2338	21	10	the	the	DET
ejpam-2338	21	11	so	so	ADV
ejpam-2338	21	12	-	-	PUNCT
ejpam-2338	21	13	called	call	VERB
ejpam-2338	21	14	munn	munn	PROPN
ejpam-2338	21	15	representation	representation	NOUN
ejpam-2338	21	16	.	.	PUNCT
ejpam-2338	22	1	here	here	ADV
ejpam-2338	22	2	,	,	PUNCT
ejpam-2338	22	3	an	an	DET
ejpam-2338	22	4	inverse	inverse	NOUN
ejpam-2338	22	5	semigroup	semigroup	NOUN
ejpam-2338	22	6	s	s	PART
ejpam-2338	22	7	is	be	AUX
ejpam-2338	22	8	represented	represent	VERB
ejpam-2338	22	9	not	not	PART
ejpam-2338	22	10	merely	merely	ADV
ejpam-2338	22	11	by	by	ADP
ejpam-2338	22	12	partial	partial	ADJ
ejpam-2338	22	13	bijections	bijection	NOUN
ejpam-2338	22	14	of	of	ADP
ejpam-2338	22	15	an	an	DET
ejpam-2338	22	16	arbitrary	arbitrary	ADJ
ejpam-2338	22	17	set	set	NOUN
ejpam-2338	22	18	but	but	CCONJ
ejpam-2338	22	19	by	by	ADP
ejpam-2338	22	20	partial	partial	ADJ
ejpam-2338	22	21	bijections	bijection	NOUN
ejpam-2338	22	22	of	of	ADP
ejpam-2338	22	23	its	its	PRON
ejpam-2338	22	24	semilattice	semilattice	NOUN
ejpam-2338	22	25	of	of	ADP
ejpam-2338	22	26	idempotents	idempotent	NOUN
ejpam-2338	22	27	.	.	PUNCT
ejpam-2338	23	1	intimately	intimately	ADV
ejpam-2338	23	2	connected	connect	VERB
ejpam-2338	23	3	with	with	ADP
ejpam-2338	23	4	the	the	DET
ejpam-2338	23	5	notion	notion	NOUN
ejpam-2338	23	6	of	of	ADP
ejpam-2338	23	7	a	a	DET
ejpam-2338	23	8	munn	munn	PROPN
ejpam-2338	23	9	representation	representation	NOUN
ejpam-2338	23	10	are	be	AUX
ejpam-2338	23	11	those	those	PRON
ejpam-2338	23	12	of	of	ADP
ejpam-2338	23	13	fundamental	fundamental	ADJ
ejpam-2338	23	14	inverse	inverse	NOUN
ejpam-2338	23	15	semigroups	semigroup	NOUN
ejpam-2338	23	16	,	,	PUNCT
ejpam-2338	23	17	and	and	CCONJ
ejpam-2338	23	18	also	also	ADV
ejpam-2338	23	19	idempotentseparating	idempotentseparate	VERB
ejpam-2338	23	20	congruences	congruence	NOUN
ejpam-2338	23	21	and	and	CCONJ
ejpam-2338	23	22	morphisms	morphism	NOUN
ejpam-2338	23	23	.	.	PUNCT
ejpam-2338	24	1	as	as	SCONJ
ejpam-2338	24	2	the	the	DET
ejpam-2338	24	3	name	name	NOUN
ejpam-2338	24	4	suggests	suggest	VERB
ejpam-2338	24	5	,	,	PUNCT
ejpam-2338	24	6	fundamental	fundamental	ADJ
ejpam-2338	24	7	inverse	inverse	NOUN
ejpam-2338	24	8	semigroups	semigroup	NOUN
ejpam-2338	24	9	may	may	AUX
ejpam-2338	24	10	be	be	AUX
ejpam-2338	24	11	used	use	VERB
ejpam-2338	24	12	,	,	PUNCT
ejpam-2338	24	13	in	in	ADP
ejpam-2338	24	14	conjunction	conjunction	NOUN
ejpam-2338	24	15	with	with	ADP
ejpam-2338	24	16	the	the	DET
ejpam-2338	24	17	other	other	ADJ
ejpam-2338	24	18	notions	notion	NOUN
ejpam-2338	24	19	mentioned	mention	VERB
ejpam-2338	24	20	here	here	ADV
ejpam-2338	24	21	,	,	PUNCT
ejpam-2338	24	22	as	as	ADP
ejpam-2338	24	23	a	a	DET
ejpam-2338	24	24	basis	basis	NOUN
ejpam-2338	24	25	for	for	ADP
ejpam-2338	24	26	the	the	DET
ejpam-2338	24	27	characterisation	characterisation	NOUN
ejpam-2338	24	28	of	of	ADP
ejpam-2338	24	29	any	any	DET
ejpam-2338	24	30	given	give	VERB
ejpam-2338	24	31	class	class	NOUN
ejpam-2338	24	32	of	of	ADP
ejpam-2338	24	33	inverse	inverse	NOUN
ejpam-2338	24	34	semigroups	semigroup	NOUN
ejpam-2338	24	35	.	.	PUNCT
ejpam-2338	25	1	the	the	DET
ejpam-2338	25	2	third	third	ADJ
ejpam-2338	25	3	and	and	CCONJ
ejpam-2338	25	4	final	final	ADJ
ejpam-2338	25	5	of	of	ADP
ejpam-2338	25	6	our	our	PRON
ejpam-2338	25	7	three	three	NUM
ejpam-2338	25	8	approaches	approach	NOUN
ejpam-2338	25	9	to	to	ADP
ejpam-2338	25	10	inverse	inverse	NOUN
ejpam-2338	25	11	semigroups	semigroup	NOUN
ejpam-2338	25	12	—	—	PUNCT
ejpam-2338	25	13	that	that	SCONJ
ejpam-2338	25	14	via	via	ADP
ejpam-2338	25	15	p	p	NOUN
ejpam-2338	25	16	-	-	PUNCT
ejpam-2338	25	17	semigroups	semigroup	NOUN
ejpam-2338	25	18	and	and	CCONJ
ejpam-2338	25	19	related	related	ADJ
ejpam-2338	25	20	concepts	concept	NOUN
ejpam-2338	25	21	,	,	PUNCT
ejpam-2338	25	22	as	as	SCONJ
ejpam-2338	25	23	espoused	espouse	VERB
ejpam-2338	25	24	by	by	ADP
ejpam-2338	25	25	mcalister	mcalister	PROPN
ejpam-2338	25	26	—	—	PUNCT
ejpam-2338	25	27	is	be	AUX
ejpam-2338	25	28	,	,	PUNCT
ejpam-2338	25	29	at	at	ADP
ejpam-2338	25	30	its	its	PRON
ejpam-2338	25	31	heart	heart	NOUN
ejpam-2338	25	32	,	,	PUNCT
ejpam-2338	25	33	an	an	DET
ejpam-2338	25	34	attempt	attempt	NOUN
ejpam-2338	25	35	to	to	PART
ejpam-2338	25	36	adapt	adapt	VERB
ejpam-2338	25	37	to	to	ADP
ejpam-2338	25	38	inverse	inverse	NOUN
ejpam-2338	25	39	semigroups	semigroup	NOUN
ejpam-2338	25	40	certain	certain	ADJ
ejpam-2338	25	41	methods	method	NOUN
ejpam-2338	25	42	that	that	PRON
ejpam-2338	25	43	had	have	AUX
ejpam-2338	25	44	proved	prove	VERB
ejpam-2338	25	45	particularly	particularly	ADV
ejpam-2338	25	46	useful	useful	ADJ
ejpam-2338	25	47	in	in	ADP
ejpam-2338	25	48	the	the	DET
ejpam-2338	25	49	early	early	ADJ
ejpam-2338	25	50	theory	theory	NOUN
ejpam-2338	25	51	of	of	ADP
ejpam-2338	25	52	semigroups	semigroup	NOUN
ejpam-2338	25	53	.	.	PUNCT
ejpam-2338	26	1	in	in	ADP
ejpam-2338	26	2	the	the	DET
ejpam-2338	26	3	early	early	ADJ
ejpam-2338	26	4	1940s	1940	NOUN
ejpam-2338	26	5	,	,	PUNCT
ejpam-2338	26	6	both	both	PRON
ejpam-2338	26	7	rees	ree	NOUN
ejpam-2338	26	8	[	[	X
ejpam-2338	26	9	80	80	NUM
ejpam-2338	26	10	]	]	PUNCT
ejpam-2338	26	11	and	and	CCONJ
ejpam-2338	26	12	clifford	clifford	PROPN
ejpam-2338	27	1	[	[	X
ejpam-2338	27	2	6	6	NUM
ejpam-2338	27	3	]	]	PUNCT
ejpam-2338	27	4	had	have	AUX
ejpam-2338	27	5	characterised	characterise	VERB
ejpam-2338	27	6	certain	certain	ADJ
ejpam-2338	27	7	classes	class	NOUN
ejpam-2338	27	8	of	of	ADP
ejpam-2338	27	9	regular	regular	ADJ
ejpam-2338	27	10	semigroups	semigroup	NOUN
ejpam-2338	27	11	in	in	ADP
ejpam-2338	27	12	terms	term	NOUN
ejpam-2338	27	13	of	of	ADP
ejpam-2338	27	14	(	(	PUNCT
ejpam-2338	27	15	amongst	amongst	ADP
ejpam-2338	27	16	other	other	ADJ
ejpam-2338	27	17	things	thing	NOUN
ejpam-2338	27	18	)	)	PUNCT
ejpam-2338	27	19	groups	group	NOUN
ejpam-2338	27	20	and	and	CCONJ
ejpam-2338	27	21	semilattices	semilattice	NOUN
ejpam-2338	27	22	—	—	PUNCT
ejpam-2338	27	23	structures	structure	VERB
ejpam-2338	27	24	that	that	PRON
ejpam-2338	27	25	,	,	PUNCT
ejpam-2338	27	26	at	at	ADP
ejpam-2338	27	27	least	least	ADJ
ejpam-2338	27	28	from	from	ADP
ejpam-2338	27	29	the	the	DET
ejpam-2338	27	30	semigroup	semigroup	PROPN
ejpam-2338	27	31	theorist	theorist	NOUN
ejpam-2338	27	32	’s	’s	PART
ejpam-2338	27	33	point	point	NOUN
ejpam-2338	27	34	of	of	ADP
ejpam-2338	27	35	view	view	NOUN
ejpam-2338	27	36	,	,	PUNCT
ejpam-2338	27	37	are	be	AUX
ejpam-2338	27	38	simple	simple	ADJ
ejpam-2338	27	39	and	and	CCONJ
ejpam-2338	27	40	known	known	ADJ
ejpam-2338	27	41	(	(	PUNCT
ejpam-2338	27	42	on	on	ADP
ejpam-2338	27	43	the	the	DET
ejpam-2338	27	44	work	work	NOUN
ejpam-2338	27	45	of	of	ADP
ejpam-2338	27	46	rees	ree	NOUN
ejpam-2338	27	47	and	and	CCONJ
ejpam-2338	27	48	clifford	clifford	PROPN
ejpam-2338	27	49	,	,	PUNCT
ejpam-2338	27	50	see	see	VERB
ejpam-2338	27	51	[	[	X
ejpam-2338	27	52	37	37	NUM
ejpam-2338	27	53	]	]	PUNCT
ejpam-2338	27	54	or	or	CCONJ
ejpam-2338	27	55	[	[	X
ejpam-2338	27	56	41	41	NUM
ejpam-2338	27	57	,	,	PUNCT
ejpam-2338	27	58	chapter	chapter	NOUN
ejpam-2338	27	59	6	6	NUM
ejpam-2338	27	60	]	]	PUNCT
ejpam-2338	27	61	)	)	PUNCT
ejpam-2338	27	62	.	.	PUNCT
ejpam-2338	28	1	mcalister	mcalister	PROPN
ejpam-2338	28	2	thus	thus	ADV
ejpam-2338	28	3	attempted	attempt	VERB
ejpam-2338	28	4	to	to	PART
ejpam-2338	28	5	characterise	characterise	VERB
ejpam-2338	28	6	inverse	inverse	NOUN
ejpam-2338	28	7	semigroups	semigroup	NOUN
ejpam-2338	28	8	in	in	ADP
ejpam-2338	28	9	similar	similar	ADJ
ejpam-2338	28	10	terms	term	NOUN
ejpam-2338	28	11	;	;	PUNCT
ejpam-2338	28	12	his	his	PRON
ejpam-2338	28	13	structure	structure	NOUN
ejpam-2338	28	14	theorem	theorem	NOUN
ejpam-2338	28	15	(	(	PUNCT
ejpam-2338	28	16	the	the	DET
ejpam-2338	28	17	so	so	ADV
ejpam-2338	28	18	-	-	PUNCT
ejpam-2338	28	19	called	call	VERB
ejpam-2338	28	20	p	p	NOUN
ejpam-2338	28	21	-	-	PUNCT
ejpam-2338	28	22	theorem	theorem	VERB
ejpam-2338	28	23	)	)	PUNCT
ejpam-2338	28	24	does	do	AUX
ejpam-2338	28	25	not	not	PART
ejpam-2338	28	26	in	in	ADP
ejpam-2338	28	27	fact	fact	NOUN
ejpam-2338	28	28	characterise	characterise	NOUN
ejpam-2338	28	29	all	all	DET
ejpam-2338	28	30	inverse	inverse	NOUN
ejpam-2338	28	31	semigroups	semigroup	NOUN
ejpam-2338	28	32	,	,	PUNCT
ejpam-2338	28	33	but	but	CCONJ
ejpam-2338	28	34	an	an	DET
ejpam-2338	28	35	important	important	ADJ
ejpam-2338	28	36	subclass	subclass	NOUN
ejpam-2338	28	37	termed	term	VERB
ejpam-2338	28	38	e	e	NOUN
ejpam-2338	28	39	-	-	NOUN
ejpam-2338	28	40	unitary	unitary	ADJ
ejpam-2338	28	41	(	(	PUNCT
ejpam-2338	28	42	or	or	CCONJ
ejpam-2338	28	43	proper	proper	ADJ
ejpam-2338	28	44	)	)	PUNCT
ejpam-2338	28	45	inverse	inverse	NOUN
ejpam-2338	28	46	semigroups	semigroup	NOUN
ejpam-2338	28	47	.	.	PUNCT
ejpam-2338	29	1	just	just	ADV
ejpam-2338	29	2	as	as	SCONJ
ejpam-2338	29	3	rees	ree	NOUN
ejpam-2338	29	4	had	have	AUX
ejpam-2338	29	5	given	give	VERB
ejpam-2338	29	6	a	a	DET
ejpam-2338	29	7	simple	simple	ADJ
ejpam-2338	29	8	recipe	recipe	NOUN
ejpam-2338	29	9	for	for	ADP
ejpam-2338	29	10	what	what	PRON
ejpam-2338	29	11	we	we	PRON
ejpam-2338	29	12	now	now	ADV
ejpam-2338	29	13	term	term	NOUN
ejpam-2338	29	14	rees	ree	NOUN
ejpam-2338	29	15	matrix	matrix	VERB
ejpam-2338	29	16	semigroups	semigroup	NOUN
ejpam-2338	29	17	and	and	CCONJ
ejpam-2338	29	18	proved	prove	VERB
ejpam-2338	29	19	that	that	SCONJ
ejpam-2338	29	20	any	any	DET
ejpam-2338	29	21	one	one	NUM
ejpam-2338	29	22	of	of	ADP
ejpam-2338	29	23	his	his	PRON
ejpam-2338	29	24	semigroups	semigroup	NOUN
ejpam-2338	29	25	of	of	ADP
ejpam-2338	29	26	interest	interest	NOUN
ejpam-2338	29	27	is	be	AUX
ejpam-2338	29	28	isomorphic	isomorphic	ADJ
ejpam-2338	29	29	to	to	ADP
ejpam-2338	29	30	an	an	DET
ejpam-2338	29	31	appropriate	appropriate	ADJ
ejpam-2338	29	32	one	one	NUM
ejpam-2338	29	33	of	of	ADP
ejpam-2338	29	34	these	these	PRON
ejpam-2338	29	35	,	,	PUNCT
ejpam-2338	29	36	mcalister	mcalister	PROPN
ejpam-2338	29	37	gave	give	VERB
ejpam-2338	29	38	a	a	DET
ejpam-2338	29	39	slightly	slightly	ADV
ejpam-2338	29	40	more	more	ADV
ejpam-2338	29	41	involved	involved	ADJ
ejpam-2338	29	42	recipe	recipe	NOUN
ejpam-2338	29	43	for	for	ADP
ejpam-2338	29	44	a	a	DET
ejpam-2338	29	45	so	so	ADV
ejpam-2338	29	46	-	-	PUNCT
ejpam-2338	29	47	called	call	VERB
ejpam-2338	29	48	p	p	NOUN
ejpam-2338	29	49	-	-	PUNCT
ejpam-2338	29	50	semigroup	semigroup	NOUN
ejpam-2338	29	51	and	and	CCONJ
ejpam-2338	29	52	proved	prove	VERB
ejpam-2338	29	53	that	that	SCONJ
ejpam-2338	29	54	any	any	DET
ejpam-2338	29	55	e	e	NOUN
ejpam-2338	29	56	-	-	ADJ
ejpam-2338	29	57	unitary	unitary	ADJ
ejpam-2338	29	58	inverse	inverse	NOUN
ejpam-2338	29	59	semigroup	semigroup	NOUN
ejpam-2338	29	60	is	be	AUX
ejpam-2338	29	61	isomorphic	isomorphic	ADJ
ejpam-2338	29	62	to	to	ADP
ejpam-2338	29	63	one	one	NUM
ejpam-2338	29	64	of	of	ADP
ejpam-2338	29	65	these	these	PRON
ejpam-2338	29	66	.	.	PUNCT
ejpam-2338	30	1	once	once	ADV
ejpam-2338	30	2	again	again	ADV
ejpam-2338	30	3	,	,	PUNCT
ejpam-2338	30	4	the	the	DET
ejpam-2338	30	5	natural	natural	ADJ
ejpam-2338	30	6	order	order	NOUN
ejpam-2338	30	7	relation	relation	NOUN
ejpam-2338	30	8	in	in	ADP
ejpam-2338	30	9	an	an	DET
ejpam-2338	30	10	inverse	inverse	NOUN
ejpam-2338	30	11	semigroup	semigroup	NOUN
ejpam-2338	30	12	has	have	VERB
ejpam-2338	30	13	an	an	DET
ejpam-2338	30	14	important	important	ADJ
ejpam-2338	30	15	role	role	NOUN
ejpam-2338	30	16	to	to	PART
ejpam-2338	30	17	play	play	VERB
ejpam-2338	30	18	in	in	ADP
ejpam-2338	30	19	mcalister	mcalister	PROPN
ejpam-2338	30	20	’s	’s	PART
ejpam-2338	30	21	construction	construction	NOUN
ejpam-2338	30	22	,	,	PUNCT
ejpam-2338	30	23	as	as	SCONJ
ejpam-2338	30	24	indeed	indeed	ADV
ejpam-2338	30	25	it	it	PRON
ejpam-2338	30	26	does	do	VERB
ejpam-2338	30	27	in	in	ADP
ejpam-2338	30	28	the	the	DET
ejpam-2338	30	29	other	other	ADJ
ejpam-2338	30	30	approaches	approach	NOUN
ejpam-2338	30	31	to	to	ADP
ejpam-2338	30	32	inverse	inverse	NOUN
ejpam-2338	30	33	semigroups	semigroup	NOUN
ejpam-2338	30	34	that	that	PRON
ejpam-2338	30	35	are	be	AUX
ejpam-2338	30	36	discussed	discuss	VERB
ejpam-2338	30	37	here	here	ADV
ejpam-2338	30	38	.	.	PUNCT
ejpam-2338	31	1	the	the	DET
ejpam-2338	31	2	philosophy	philosophy	NOUN
ejpam-2338	31	3	of	of	ADP
ejpam-2338	31	4	mcalister	mcalister	PROPN
ejpam-2338	31	5	’s	’s	PART
ejpam-2338	31	6	approach	approach	NOUN
ejpam-2338	31	7	is	be	AUX
ejpam-2338	31	8	,	,	PUNCT
ejpam-2338	31	9	however	however	ADV
ejpam-2338	31	10	,	,	PUNCT
ejpam-2338	31	11	rather	rather	ADV
ejpam-2338	31	12	different	different	ADJ
ejpam-2338	31	13	from	from	ADP
ejpam-2338	31	14	that	that	PRON
ejpam-2338	31	15	of	of	ADP
ejpam-2338	31	16	munn	munn	PROPN
ejpam-2338	31	17	’s	’s	X
ejpam-2338	31	18	,	,	PUNCT
ejpam-2338	31	19	for	for	ADP
ejpam-2338	31	20	whilst	whilst	ADV
ejpam-2338	31	21	,	,	PUNCT
ejpam-2338	31	22	via	via	ADP
ejpam-2338	31	23	so	so	ADV
ejpam-2338	31	24	-	-	PUNCT
ejpam-2338	31	25	called	call	VERB
ejpam-2338	31	26	‘	'	PUNCT
ejpam-2338	31	27	covers	cover	NOUN
ejpam-2338	31	28	’	'	PUNCT
ejpam-2338	31	29	(	(	PUNCT
ejpam-2338	31	30	see	see	VERB
ejpam-2338	31	31	section	section	NOUN
ejpam-2338	31	32	5.2	5.2	NUM
ejpam-2338	31	33	)	)	PUNCT
ejpam-2338	31	34	,	,	PUNCT
ejpam-2338	31	35	mcalister	mcalister	NOUN
ejpam-2338	31	36	compared	compare	VERB
ejpam-2338	31	37	his	his	PRON
ejpam-2338	31	38	inverse	inverse	NOUN
ejpam-2338	31	39	semigroups	semigroup	NOUN
ejpam-2338	31	40	to	to	ADP
ejpam-2338	31	41	other	other	ADJ
ejpam-2338	31	42	semigroups	semigroup	NOUN
ejpam-2338	31	43	that	that	PRON
ejpam-2338	31	44	are	be	AUX
ejpam-2338	31	45	,	,	PUNCT
ejpam-2338	31	46	in	in	ADP
ejpam-2338	31	47	a	a	DET
ejpam-2338	31	48	sense	sense	NOUN
ejpam-2338	31	49	,	,	PUNCT
ejpam-2338	31	50	‘	'	PUNCT
ejpam-2338	31	51	larger	large	ADJ
ejpam-2338	31	52	’	'	PUNCT
ejpam-2338	31	53	,	,	PUNCT
ejpam-2338	31	54	munn	munn	PROPN
ejpam-2338	31	55	took	take	VERB
ejpam-2338	31	56	the	the	DET
ejpam-2338	31	57	opposite	opposite	ADJ
ejpam-2338	31	58	tack	tack	NOUN
ejpam-2338	31	59	by	by	ADP
ejpam-2338	31	60	considering	consider	VERB
ejpam-2338	31	61	quotients	quotient	NOUN
ejpam-2338	31	62	,	,	PUNCT
ejpam-2338	31	63	hence	hence	ADV
ejpam-2338	31	64	semigroups	semigroup	VERB
ejpam-2338	31	65	that	that	PRON
ejpam-2338	31	66	are	be	AUX
ejpam-2338	31	67	‘	'	PUNCT
ejpam-2338	31	68	smaller	small	ADJ
ejpam-2338	31	69	’	'	PUNCT
ejpam-2338	31	70	than	than	ADP
ejpam-2338	31	71	those	those	PRON
ejpam-2338	31	72	under	under	ADP
ejpam-2338	31	73	initial	initial	ADJ
ejpam-2338	31	74	consideration	consideration	NOUN
ejpam-2338	31	75	.	.	PUNCT
ejpam-2338	32	1	the	the	DET
ejpam-2338	32	2	present	present	ADJ
ejpam-2338	32	3	article	article	NOUN
ejpam-2338	32	4	is	be	AUX
ejpam-2338	32	5	structured	structure	VERB
ejpam-2338	32	6	as	as	SCONJ
ejpam-2338	32	7	follows	follow	VERB
ejpam-2338	32	8	.	.	PUNCT
ejpam-2338	33	1	in	in	ADP
ejpam-2338	33	2	section	section	NOUN
ejpam-2338	33	3	2	2	NUM
ejpam-2338	33	4	,	,	PUNCT
ejpam-2338	33	5	i	i	PRON
ejpam-2338	33	6	give	give	VERB
ejpam-2338	33	7	a	a	DET
ejpam-2338	33	8	very	very	ADV
ejpam-2338	33	9	brief	brief	ADJ
ejpam-2338	33	10	sketch	sketch	NOUN
ejpam-2338	33	11	of	of	ADP
ejpam-2338	33	12	those	those	DET
ejpam-2338	33	13	details	detail	NOUN
ejpam-2338	33	14	of	of	ADP
ejpam-2338	33	15	the	the	DET
ejpam-2338	33	16	development	development	NOUN
ejpam-2338	33	17	of	of	ADP
ejpam-2338	33	18	the	the	DET
ejpam-2338	33	19	notion	notion	NOUN
ejpam-2338	33	20	of	of	ADP
ejpam-2338	33	21	an	an	DET
ejpam-2338	33	22	inverse	inverse	NOUN
ejpam-2338	33	23	semigroup	semigroup	NOUN
ejpam-2338	33	24	that	that	SCONJ
ejpam-2338	33	25	it	it	PRON
ejpam-2338	33	26	will	will	AUX
ejpam-2338	33	27	be	be	AUX
ejpam-2338	33	28	useful	useful	ADJ
ejpam-2338	33	29	for	for	SCONJ
ejpam-2338	33	30	us	we	PRON
ejpam-2338	33	31	to	to	PART
ejpam-2338	33	32	bear	bear	VERB
ejpam-2338	33	33	in	in	ADP
ejpam-2338	33	34	mind	mind	NOUN
ejpam-2338	33	35	as	as	SCONJ
ejpam-2338	33	36	we	we	PRON
ejpam-2338	33	37	proceed	proceed	VERB
ejpam-2338	33	38	through	through	ADP
ejpam-2338	33	39	the	the	DET
ejpam-2338	33	40	rest	rest	NOUN
ejpam-2338	33	41	of	of	ADP
ejpam-2338	33	42	the	the	DET
ejpam-2338	33	43	article	article	NOUN
ejpam-2338	33	44	.	.	PUNCT
ejpam-2338	34	1	the	the	DET
ejpam-2338	34	2	three	three	NUM
ejpam-2338	34	3	approaches	approach	NOUN
ejpam-2338	34	4	to	to	ADP
ejpam-2338	34	5	inverse	inverse	NOUN
ejpam-2338	34	6	semigroups	semigroup	NOUN
ejpam-2338	34	7	outlined	outline	VERB
ejpam-2338	34	8	above	above	ADV
ejpam-2338	34	9	are	be	AUX
ejpam-2338	34	10	then	then	ADV
ejpam-2338	34	11	dealt	deal	VERB
ejpam-2338	34	12	with	with	ADP
ejpam-2338	34	13	in	in	ADP
ejpam-2338	34	14	turn	turn	NOUN
ejpam-2338	34	15	in	in	ADP
ejpam-2338	34	16	sections	section	NOUN
ejpam-2338	34	17	3	3	NUM
ejpam-2338	34	18	,	,	PUNCT
ejpam-2338	34	19	4	4	NUM
ejpam-2338	34	20	and	and	CCONJ
ejpam-2338	34	21	5	5	NUM
ejpam-2338	34	22	.	.	PUNCT
ejpam-2338	35	1	at	at	ADP
ejpam-2338	35	2	the	the	DET
ejpam-2338	35	3	end	end	NOUN
ejpam-2338	35	4	of	of	ADP
ejpam-2338	35	5	the	the	DET
ejpam-2338	35	6	article	article	NOUN
ejpam-2338	35	7	(	(	PUNCT
ejpam-2338	35	8	in	in	ADP
ejpam-2338	35	9	section	section	NOUN
ejpam-2338	35	10	6	6	NUM
ejpam-2338	35	11	)	)	PUNCT
ejpam-2338	35	12	,	,	PUNCT
ejpam-2338	35	13	i	i	PRON
ejpam-2338	35	14	give	give	VERB
ejpam-2338	35	15	a	a	DET
ejpam-2338	35	16	rough	rough	ADJ
ejpam-2338	35	17	indication	indication	NOUN
ejpam-2338	35	18	of	of	ADP
ejpam-2338	35	19	the	the	DET
ejpam-2338	35	20	ways	way	NOUN
ejpam-2338	35	21	in	in	ADP
ejpam-2338	35	22	which	which	PRON
ejpam-2338	35	23	these	these	DET
ejpam-2338	35	24	approaches	approach	NOUN
ejpam-2338	35	25	have	have	AUX
ejpam-2338	35	26	been	be	AUX
ejpam-2338	35	27	adapted	adapt	VERB
ejpam-2338	35	28	to	to	ADP
ejpam-2338	35	29	some	some	DET
ejpam-2338	35	30	classes	class	NOUN
ejpam-2338	35	31	of	of	ADP
ejpam-2338	35	32	semigroups	semigroup	NOUN
ejpam-2338	35	33	more	more	ADV
ejpam-2338	35	34	general	general	ADJ
ejpam-2338	35	35	than	than	ADP
ejpam-2338	35	36	inverse	inverse	NOUN
ejpam-2338	35	37	semigroups	semigroup	NOUN
ejpam-2338	35	38	(	(	PUNCT
ejpam-2338	35	39	specifically	specifically	ADV
ejpam-2338	35	40	,	,	PUNCT
ejpam-2338	35	41	those	those	PRON
ejpam-2338	35	42	described	describe	VERB
ejpam-2338	35	43	in	in	ADP
ejpam-2338	35	44	[	[	X
ejpam-2338	35	45	36	36	NUM
ejpam-2338	35	46	]	]	NUM
ejpam-2338	35	47	)	)	PUNCT
ejpam-2338	35	48	.	.	PUNCT
ejpam-2338	36	1	i	i	PRON
ejpam-2338	36	2	assume	assume	VERB
ejpam-2338	36	3	that	that	SCONJ
ejpam-2338	36	4	the	the	DET
ejpam-2338	36	5	reader	reader	NOUN
ejpam-2338	36	6	is	be	AUX
ejpam-2338	36	7	familiar	familiar	ADJ
ejpam-2338	36	8	with	with	ADP
ejpam-2338	36	9	the	the	DET
ejpam-2338	36	10	basic	basic	ADJ
ejpam-2338	36	11	concepts	concept	NOUN
ejpam-2338	36	12	of	of	ADP
ejpam-2338	36	13	the	the	DET
ejpam-2338	36	14	theories	theory	NOUN
ejpam-2338	36	15	of	of	ADP
ejpam-2338	36	16	inverse	inverse	NOUN
ejpam-2338	36	17	semigroups	semigroup	NOUN
ejpam-2338	36	18	and	and	CCONJ
ejpam-2338	36	19	partial	partial	ADJ
ejpam-2338	36	20	bijections	bijection	NOUN
ejpam-2338	36	21	;	;	PUNCT
ejpam-2338	36	22	further	further	ADJ
ejpam-2338	36	23	details	detail	NOUN
ejpam-2338	36	24	of	of	ADP
ejpam-2338	36	25	these	these	PRON
ejpam-2338	36	26	may	may	AUX
ejpam-2338	36	27	be	be	AUX
ejpam-2338	36	28	found	find	VERB
ejpam-2338	36	29	in	in	ADP
ejpam-2338	36	30	christopher	christopher	PROPN
ejpam-2338	36	31	hollings	hollings	PROPN
ejpam-2338	36	32	/	/	SYM
ejpam-2338	36	33	eur	eur	PROPN
ejpam-2338	36	34	.	.	PUNCT
ejpam-2338	37	1	j.	j.	PROPN
ejpam-2338	37	2	pure	pure	PROPN
ejpam-2338	37	3	appl	appl	PROPN
ejpam-2338	37	4	.	.	PROPN
ejpam-2338	37	5	math	math	PROPN
ejpam-2338	37	6	,	,	PUNCT
ejpam-2338	37	7	8	8	NUM
ejpam-2338	37	8	(	(	PUNCT
ejpam-2338	37	9	2015	2015	NUM
ejpam-2338	37	10	)	)	PUNCT
ejpam-2338	37	11	,	,	PUNCT
ejpam-2338	37	12	294	294	NUM
ejpam-2338	37	13	-	-	SYM
ejpam-2338	37	14	323	323	NUM
ejpam-2338	37	15	296	296	NUM
ejpam-2338	37	16	[	[	SYM
ejpam-2338	37	17	44	44	NUM
ejpam-2338	37	18	,	,	PUNCT
ejpam-2338	37	19	chapter	chapter	NOUN
ejpam-2338	37	20	5	5	NUM
ejpam-2338	37	21	]	]	PUNCT
ejpam-2338	37	22	and	and	CCONJ
ejpam-2338	37	23	[	[	X
ejpam-2338	37	24	51	51	NUM
ejpam-2338	37	25	]	]	PUNCT
ejpam-2338	37	26	.	.	PUNCT
ejpam-2338	38	1	2	2	X
ejpam-2338	38	2	.	.	X
ejpam-2338	38	3	a	a	DET
ejpam-2338	38	4	sketch	sketch	NOUN
ejpam-2338	38	5	of	of	ADP
ejpam-2338	38	6	the	the	DET
ejpam-2338	38	7	development	development	NOUN
ejpam-2338	38	8	of	of	ADP
ejpam-2338	38	9	inverse	inverse	NOUN
ejpam-2338	38	10	semigroups	semigroup	NOUN
ejpam-2338	38	11	in	in	ADP
ejpam-2338	38	12	order	order	NOUN
ejpam-2338	38	13	to	to	PART
ejpam-2338	38	14	set	set	VERB
ejpam-2338	38	15	the	the	DET
ejpam-2338	38	16	scene	scene	NOUN
ejpam-2338	38	17	for	for	ADP
ejpam-2338	38	18	what	what	PRON
ejpam-2338	38	19	follows	follow	VERB
ejpam-2338	38	20	,	,	PUNCT
ejpam-2338	38	21	it	it	PRON
ejpam-2338	38	22	is	be	AUX
ejpam-2338	38	23	necessary	necessary	ADJ
ejpam-2338	38	24	first	first	ADV
ejpam-2338	38	25	to	to	PART
ejpam-2338	38	26	give	give	VERB
ejpam-2338	38	27	a	a	DET
ejpam-2338	38	28	brief	brief	ADJ
ejpam-2338	38	29	indication	indication	NOUN
ejpam-2338	38	30	of	of	ADP
ejpam-2338	38	31	the	the	DET
ejpam-2338	38	32	origins	origin	NOUN
ejpam-2338	38	33	of	of	ADP
ejpam-2338	38	34	the	the	DET
ejpam-2338	38	35	notion	notion	NOUN
ejpam-2338	38	36	of	of	ADP
ejpam-2338	38	37	an	an	DET
ejpam-2338	38	38	inverse	inverse	NOUN
ejpam-2338	38	39	semigroup	semigroup	NOUN
ejpam-2338	38	40	.	.	PUNCT
ejpam-2338	39	1	however	however	ADV
ejpam-2338	39	2	,	,	PUNCT
ejpam-2338	39	3	since	since	SCONJ
ejpam-2338	39	4	i	i	PRON
ejpam-2338	39	5	have	have	AUX
ejpam-2338	39	6	already	already	ADV
ejpam-2338	39	7	done	do	VERB
ejpam-2338	39	8	this	this	PRON
ejpam-2338	39	9	elsewhere	elsewhere	ADV
ejpam-2338	39	10	,	,	PUNCT
ejpam-2338	39	11	i	i	PRON
ejpam-2338	39	12	endeavour	endeavour	VERB
ejpam-2338	39	13	to	to	PART
ejpam-2338	39	14	keep	keep	VERB
ejpam-2338	39	15	this	this	DET
ejpam-2338	39	16	section	section	NOUN
ejpam-2338	39	17	as	as	ADV
ejpam-2338	39	18	short	short	ADJ
ejpam-2338	39	19	as	as	ADP
ejpam-2338	39	20	possible	possible	ADJ
ejpam-2338	39	21	.	.	PUNCT
ejpam-2338	40	1	for	for	ADP
ejpam-2338	40	2	a	a	DET
ejpam-2338	40	3	considerably	considerably	ADV
ejpam-2338	40	4	more	more	ADV
ejpam-2338	40	5	detailed	detailed	ADJ
ejpam-2338	40	6	treatment	treatment	NOUN
ejpam-2338	40	7	,	,	PUNCT
ejpam-2338	40	8	see	see	VERB
ejpam-2338	40	9	[	[	X
ejpam-2338	40	10	41	41	NUM
ejpam-2338	40	11	,	,	PUNCT
ejpam-2338	40	12	chapter	chapter	NOUN
ejpam-2338	40	13	10	10	NUM
ejpam-2338	40	14	]	]	PUNCT
ejpam-2338	40	15	;	;	PUNCT
ejpam-2338	40	16	the	the	DET
ejpam-2338	40	17	present	present	ADJ
ejpam-2338	40	18	account	account	NOUN
ejpam-2338	40	19	consists	consist	VERB
ejpam-2338	40	20	largely	largely	ADV
ejpam-2338	40	21	of	of	ADP
ejpam-2338	40	22	a	a	DET
ejpam-2338	40	23	shortened	shorten	VERB
ejpam-2338	40	24	version	version	NOUN
ejpam-2338	40	25	of	of	ADP
ejpam-2338	40	26	[	[	X
ejpam-2338	40	27	40	40	NUM
ejpam-2338	40	28	,	,	PUNCT
ejpam-2338	40	29	§	§	NOUN
ejpam-2338	40	30	2	2	NUM
ejpam-2338	40	31	]	]	PUNCT
ejpam-2338	40	32	.	.	PUNCT
ejpam-2338	41	1	although	although	SCONJ
ejpam-2338	41	2	the	the	DET
ejpam-2338	41	3	fully	fully	ADV
ejpam-2338	41	4	-	-	PUNCT
ejpam-2338	41	5	formed	form	VERB
ejpam-2338	41	6	notion	notion	NOUN
ejpam-2338	41	7	of	of	ADP
ejpam-2338	41	8	an	an	DET
ejpam-2338	41	9	inverse	inverse	NOUN
ejpam-2338	41	10	semigroup	semigroup	NOUN
ejpam-2338	41	11	did	do	AUX
ejpam-2338	41	12	not	not	PART
ejpam-2338	41	13	emerge	emerge	VERB
ejpam-2338	41	14	until	until	ADP
ejpam-2338	41	15	the	the	DET
ejpam-2338	41	16	1950s	1950s	NUM
ejpam-2338	41	17	,	,	PUNCT
ejpam-2338	41	18	the	the	DET
ejpam-2338	41	19	story	story	NOUN
ejpam-2338	41	20	of	of	ADP
ejpam-2338	41	21	its	its	PRON
ejpam-2338	41	22	development	development	NOUN
ejpam-2338	41	23	begins	begin	VERB
ejpam-2338	41	24	in	in	ADP
ejpam-2338	41	25	the	the	DET
ejpam-2338	41	26	nineteenth	nineteenth	ADJ
ejpam-2338	41	27	century	century	NOUN
ejpam-2338	41	28	with	with	ADP
ejpam-2338	41	29	the	the	DET
ejpam-2338	41	30	erlanger	erlanger	PROPN
ejpam-2338	41	31	programm	programm	PROPN
ejpam-2338	41	32	:	:	PUNCT
ejpam-2338	41	33	the	the	DET
ejpam-2338	41	34	principle	principle	NOUN
ejpam-2338	41	35	,	,	PUNCT
ejpam-2338	41	36	advocated	advocate	VERB
ejpam-2338	41	37	by	by	ADP
ejpam-2338	41	38	felix	felix	PROPN
ejpam-2338	41	39	klein	klein	PROPN
ejpam-2338	41	40	,	,	PUNCT
ejpam-2338	41	41	that	that	SCONJ
ejpam-2338	41	42	every	every	DET
ejpam-2338	41	43	geometry	geometry	NOUN
ejpam-2338	41	44	can	can	AUX
ejpam-2338	41	45	be	be	AUX
ejpam-2338	41	46	viewed	view	VERB
ejpam-2338	41	47	as	as	ADP
ejpam-2338	41	48	the	the	DET
ejpam-2338	41	49	theory	theory	NOUN
ejpam-2338	41	50	of	of	ADP
ejpam-2338	41	51	invariants	invariant	NOUN
ejpam-2338	41	52	of	of	ADP
ejpam-2338	41	53	a	a	DET
ejpam-2338	41	54	particular	particular	ADJ
ejpam-2338	41	55	group	group	NOUN
ejpam-2338	41	56	of	of	ADP
ejpam-2338	41	57	transformations	transformation	NOUN
ejpam-2338	41	58	,	,	PUNCT
ejpam-2338	41	59	and	and	CCONJ
ejpam-2338	41	60	,	,	PUNCT
ejpam-2338	41	61	conversely	conversely	ADV
ejpam-2338	41	62	,	,	PUNCT
ejpam-2338	41	63	that	that	SCONJ
ejpam-2338	41	64	any	any	DET
ejpam-2338	41	65	such	such	ADJ
ejpam-2338	41	66	group	group	NOUN
ejpam-2338	41	67	defines	define	VERB
ejpam-2338	41	68	a	a	DET
ejpam-2338	41	69	corresponding	correspond	VERB
ejpam-2338	41	70	geometry	geometry	NOUN
ejpam-2338	41	71	(	(	PUNCT
ejpam-2338	41	72	see	see	VERB
ejpam-2338	41	73	[	[	X
ejpam-2338	41	74	2	2	NUM
ejpam-2338	41	75	,	,	PUNCT
ejpam-2338	41	76	34	34	NUM
ejpam-2338	41	77	]	]	PUNCT
ejpam-2338	41	78	)	)	PUNCT
ejpam-2338	41	79	.	.	PUNCT
ejpam-2338	42	1	the	the	DET
ejpam-2338	42	2	inextricable	inextricable	PROPN
ejpam-2338	42	3	link	link	NOUN
ejpam-2338	42	4	between	between	ADP
ejpam-2338	42	5	groups	group	NOUN
ejpam-2338	42	6	and	and	CCONJ
ejpam-2338	42	7	the	the	DET
ejpam-2338	42	8	geometrical	geometrical	ADJ
ejpam-2338	42	9	notion	notion	NOUN
ejpam-2338	42	10	of	of	ADP
ejpam-2338	42	11	symmetry	symmetry	NOUN
ejpam-2338	42	12	,	,	PUNCT
ejpam-2338	42	13	which	which	PRON
ejpam-2338	42	14	we	we	PRON
ejpam-2338	42	15	now	now	ADV
ejpam-2338	42	16	take	take	VERB
ejpam-2338	42	17	for	for	SCONJ
ejpam-2338	42	18	granted	grant	VERB
ejpam-2338	42	19	,	,	PUNCT
ejpam-2338	42	20	was	be	AUX
ejpam-2338	42	21	thus	thus	ADV
ejpam-2338	42	22	forged	forge	VERB
ejpam-2338	42	23	.	.	PUNCT
ejpam-2338	43	1	however	however	ADV
ejpam-2338	43	2	,	,	PUNCT
ejpam-2338	43	3	it	it	PRON
ejpam-2338	43	4	was	be	AUX
ejpam-2338	43	5	quickly	quickly	ADV
ejpam-2338	43	6	realised	realise	VERB
ejpam-2338	43	7	that	that	SCONJ
ejpam-2338	43	8	the	the	DET
ejpam-2338	43	9	scheme	scheme	NOUN
ejpam-2338	43	10	provided	provide	VERB
ejpam-2338	43	11	by	by	ADP
ejpam-2338	43	12	the	the	DET
ejpam-2338	43	13	erlanger	erlanger	PROPN
ejpam-2338	43	14	programm	programm	PROPN
ejpam-2338	43	15	was	be	AUX
ejpam-2338	43	16	not	not	PART
ejpam-2338	43	17	entirely	entirely	ADV
ejpam-2338	43	18	useful	useful	ADJ
ejpam-2338	43	19	in	in	ADP
ejpam-2338	43	20	all	all	DET
ejpam-2338	43	21	cases	case	NOUN
ejpam-2338	43	22	,	,	PUNCT
ejpam-2338	43	23	for	for	ADP
ejpam-2338	43	24	there	there	PRON
ejpam-2338	43	25	exist	exist	VERB
ejpam-2338	43	26	geometries	geometry	NOUN
ejpam-2338	43	27	(	(	PUNCT
ejpam-2338	43	28	for	for	ADP
ejpam-2338	43	29	example	example	NOUN
ejpam-2338	43	30	,	,	PUNCT
ejpam-2338	43	31	riemannian	riemannian	ADJ
ejpam-2338	43	32	geometries	geometry	NOUN
ejpam-2338	43	33	)	)	PUNCT
ejpam-2338	43	34	whose	whose	DET
ejpam-2338	43	35	groups	group	NOUN
ejpam-2338	43	36	of	of	ADP
ejpam-2338	43	37	automorphisms	automorphism	NOUN
ejpam-2338	43	38	are	be	AUX
ejpam-2338	43	39	trivial	trivial	ADJ
ejpam-2338	43	40	.	.	PUNCT
ejpam-2338	44	1	nevertheless	nevertheless	ADV
ejpam-2338	44	2	,	,	PUNCT
ejpam-2338	44	3	the	the	DET
ejpam-2338	44	4	earlier	early	ADJ
ejpam-2338	44	5	success	success	NOUN
ejpam-2338	44	6	of	of	ADP
ejpam-2338	44	7	the	the	DET
ejpam-2338	44	8	erlanger	erlanger	PROPN
ejpam-2338	44	9	programm	programm	PROPN
ejpam-2338	44	10	meant	mean	VERB
ejpam-2338	44	11	that	that	SCONJ
ejpam-2338	44	12	it	it	PRON
ejpam-2338	44	13	was	be	AUX
ejpam-2338	44	14	not	not	PART
ejpam-2338	44	15	simply	simply	ADV
ejpam-2338	44	16	discarded	discard	VERB
ejpam-2338	44	17	:	:	PUNCT
ejpam-2338	44	18	efforts	effort	NOUN
ejpam-2338	44	19	were	be	AUX
ejpam-2338	44	20	made	make	VERB
ejpam-2338	44	21	to	to	PART
ejpam-2338	44	22	extend	extend	VERB
ejpam-2338	44	23	it	it	PRON
ejpam-2338	44	24	to	to	ADP
ejpam-2338	44	25	these	these	DET
ejpam-2338	44	26	other	other	ADJ
ejpam-2338	44	27	geometries	geometry	NOUN
ejpam-2338	44	28	by	by	ADP
ejpam-2338	44	29	using	use	VERB
ejpam-2338	44	30	a	a	DET
ejpam-2338	44	31	different	different	ADJ
ejpam-2338	44	32	algebraic	algebraic	ADJ
ejpam-2338	44	33	structure	structure	NOUN
ejpam-2338	44	34	,	,	PUNCT
ejpam-2338	44	35	necessarily	necessarily	ADV
ejpam-2338	44	36	more	more	ADV
ejpam-2338	44	37	general	general	ADJ
ejpam-2338	44	38	than	than	ADP
ejpam-2338	44	39	a	a	DET
ejpam-2338	44	40	group	group	NOUN
ejpam-2338	44	41	,	,	PUNCT
ejpam-2338	44	42	to	to	PART
ejpam-2338	44	43	describe	describe	VERB
ejpam-2338	44	44	their	their	PRON
ejpam-2338	44	45	symmetries	symmetry	NOUN
ejpam-2338	44	46	.	.	PUNCT
ejpam-2338	45	1	in	in	ADP
ejpam-2338	45	2	the	the	DET
ejpam-2338	45	3	case	case	NOUN
ejpam-2338	45	4	of	of	ADP
ejpam-2338	45	5	differential	differential	ADJ
ejpam-2338	45	6	geometry	geometry	NOUN
ejpam-2338	45	7	,	,	PUNCT
ejpam-2338	45	8	the	the	DET
ejpam-2338	45	9	problem	problem	NOUN
ejpam-2338	45	10	was	be	AUX
ejpam-2338	45	11	addressed	address	VERB
ejpam-2338	45	12	by	by	ADP
ejpam-2338	45	13	oswald	oswald	PROPN
ejpam-2338	45	14	veblen	veblen	PROPN
ejpam-2338	45	15	(	(	PUNCT
ejpam-2338	45	16	1880–1960	1880–1960	NUM
ejpam-2338	45	17	)	)	PUNCT
ejpam-2338	45	18	and	and	CCONJ
ejpam-2338	45	19	j.	j.	PROPN
ejpam-2338	45	20	h.	h.	PROPN
ejpam-2338	45	21	c.	c.	PROPN
ejpam-2338	45	22	whitehead	whitehead	PROPN
ejpam-2338	45	23	(	(	PUNCT
ejpam-2338	45	24	1904–1960	1904–1960	NUM
ejpam-2338	45	25	)	)	PUNCT
ejpam-2338	45	26	,	,	PUNCT
ejpam-2338	45	27	in	in	ADP
ejpam-2338	45	28	their	their	PRON
ejpam-2338	45	29	1932	1932	NUM
ejpam-2338	45	30	text	text	NOUN
ejpam-2338	45	31	the	the	DET
ejpam-2338	45	32	foundations	foundation	NOUN
ejpam-2338	45	33	of	of	ADP
ejpam-2338	45	34	differential	differential	ADJ
ejpam-2338	45	35	geometry	geometry	NOUN
ejpam-2338	45	36	,	,	PUNCT
ejpam-2338	45	37	with	with	ADP
ejpam-2338	45	38	the	the	DET
ejpam-2338	45	39	introduction	introduction	NOUN
ejpam-2338	45	40	of	of	ADP
ejpam-2338	45	41	the	the	DET
ejpam-2338	45	42	notion	notion	NOUN
ejpam-2338	45	43	of	of	ADP
ejpam-2338	45	44	a	a	DET
ejpam-2338	45	45	pseudogroup	pseudogroup	NOUN
ejpam-2338	45	46	.	.	PUNCT
ejpam-2338	46	1	this	this	PRON
ejpam-2338	46	2	was	be	AUX
ejpam-2338	46	3	based	base	VERB
ejpam-2338	46	4	,	,	PUNCT
ejpam-2338	46	5	in	in	ADP
ejpam-2338	46	6	part	part	NOUN
ejpam-2338	46	7	,	,	PUNCT
ejpam-2338	46	8	upon	upon	SCONJ
ejpam-2338	46	9	the	the	DET
ejpam-2338	46	10	concept	concept	NOUN
ejpam-2338	46	11	of	of	ADP
ejpam-2338	46	12	a	a	DET
ejpam-2338	46	13	‘	'	PUNCT
ejpam-2338	46	14	continuous	continuous	ADJ
ejpam-2338	46	15	transformation	transformation	NOUN
ejpam-2338	46	16	group	group	NOUN
ejpam-2338	46	17	’	'	PUNCT
ejpam-2338	46	18	,	,	PUNCT
ejpam-2338	46	19	as	as	SCONJ
ejpam-2338	46	20	introduced	introduce	VERB
ejpam-2338	46	21	by	by	ADP
ejpam-2338	46	22	sophus	sophus	PROPN
ejpam-2338	46	23	lie	lie	NOUN
ejpam-2338	46	24	(	(	PUNCT
ejpam-2338	46	25	1842–1899	1842–1899	NUM
ejpam-2338	46	26	)	)	PUNCT
ejpam-2338	47	1	[	[	X
ejpam-2338	47	2	53	53	NUM
ejpam-2338	47	3	]	]	PUNCT
ejpam-2338	47	4	(	(	PUNCT
ejpam-2338	47	5	on	on	ADP
ejpam-2338	47	6	the	the	DET
ejpam-2338	47	7	history	history	NOUN
ejpam-2338	47	8	of	of	ADP
ejpam-2338	47	9	these	these	PRON
ejpam-2338	47	10	,	,	PUNCT
ejpam-2338	47	11	see	see	VERB
ejpam-2338	47	12	[	[	X
ejpam-2338	47	13	7	7	NUM
ejpam-2338	47	14	]	]	NUM
ejpam-2338	47	15	)	)	PUNCT
ejpam-2338	47	16	.	.	PUNCT
ejpam-2338	48	1	definition	definition	NOUN
ejpam-2338	48	2	1	1	NUM
ejpam-2338	48	3	(	(	PUNCT
ejpam-2338	48	4	[	[	X
ejpam-2338	48	5	95	95	NUM
ejpam-2338	48	6	,	,	PUNCT
ejpam-2338	48	7	p.	p.	NOUN
ejpam-2338	48	8	38	38	NUM
ejpam-2338	48	9	]	]	PUNCT
ejpam-2338	48	10	)	)	PUNCT
ejpam-2338	48	11	.	.	PUNCT
ejpam-2338	49	1	a	a	DET
ejpam-2338	49	2	pseudogroup	pseudogroup	NOUN
ejpam-2338	49	3	γ	γ	NOUN
ejpam-2338	49	4	is	be	AUX
ejpam-2338	49	5	a	a	DET
ejpam-2338	49	6	collection	collection	NOUN
ejpam-2338	49	7	of	of	ADP
ejpam-2338	49	8	partial	partial	ADJ
ejpam-2338	49	9	homeomorphisms	homeomorphism	NOUN
ejpam-2338	49	10	between	between	ADP
ejpam-2338	49	11	open	open	ADJ
ejpam-2338	49	12	subsets	subset	NOUN
ejpam-2338	49	13	of	of	ADP
ejpam-2338	49	14	a	a	DET
ejpam-2338	49	15	topological	topological	ADJ
ejpam-2338	49	16	space	space	NOUN
ejpam-2338	49	17	such	such	ADJ
ejpam-2338	49	18	that	that	SCONJ
ejpam-2338	49	19	γ	γ	PROPN
ejpam-2338	49	20	is	be	AUX
ejpam-2338	49	21	closed	close	VERB
ejpam-2338	49	22	under	under	ADP
ejpam-2338	49	23	composition	composition	NOUN
ejpam-2338	49	24	and	and	CCONJ
ejpam-2338	49	25	inverses	inverse	NOUN
ejpam-2338	49	26	,	,	PUNCT
ejpam-2338	49	27	where	where	SCONJ
ejpam-2338	49	28	we	we	PRON
ejpam-2338	49	29	compose	compose	VERB
ejpam-2338	49	30	α	α	PRON
ejpam-2338	49	31	,	,	PUNCT
ejpam-2338	49	32	β	β	PROPN
ejpam-2338	49	33	∈	∈	NOUN
ejpam-2338	49	34	γ	γ	NOUN
ejpam-2338	49	35	only	only	ADV
ejpam-2338	49	36	if	if	SCONJ
ejpam-2338	49	37	i	i	PRON
ejpam-2338	49	38	m	m	VERB
ejpam-2338	49	39	α=	α=	VERB
ejpam-2338	49	40	dom	dom	NOUN
ejpam-2338	49	41	β	β	X
ejpam-2338	49	42	.	.	PUNCT
ejpam-2338	50	1	in	in	ADP
ejpam-2338	50	2	the	the	DET
ejpam-2338	50	3	nineteenth	nineteenth	ADJ
ejpam-2338	50	4	century	century	NOUN
ejpam-2338	50	5	,	,	PUNCT
ejpam-2338	50	6	the	the	DET
ejpam-2338	50	7	study	study	NOUN
ejpam-2338	50	8	of	of	ADP
ejpam-2338	50	9	groups	group	NOUN
ejpam-2338	50	10	of	of	ADP
ejpam-2338	50	11	permutations	permutation	NOUN
ejpam-2338	50	12	had	have	AUX
ejpam-2338	50	13	gradually	gradually	ADV
ejpam-2338	50	14	given	give	VERB
ejpam-2338	50	15	rise	rise	NOUN
ejpam-2338	50	16	to	to	ADP
ejpam-2338	50	17	the	the	DET
ejpam-2338	50	18	notion	notion	NOUN
ejpam-2338	50	19	of	of	ADP
ejpam-2338	50	20	an	an	DET
ejpam-2338	50	21	abstract	abstract	ADJ
ejpam-2338	50	22	group	group	NOUN
ejpam-2338	50	23	.	.	PUNCT
ejpam-2338	51	1	it	it	PRON
ejpam-2338	51	2	was	be	AUX
ejpam-2338	51	3	natural	natural	ADJ
ejpam-2338	51	4	,	,	PUNCT
ejpam-2338	51	5	therefore	therefore	ADV
ejpam-2338	51	6	,	,	PUNCT
ejpam-2338	51	7	for	for	ADP
ejpam-2338	51	8	mathematicians	mathematician	NOUN
ejpam-2338	51	9	next	next	ADJ
ejpam-2338	51	10	to	to	PART
ejpam-2338	51	11	seek	seek	VERB
ejpam-2338	51	12	the	the	DET
ejpam-2338	51	13	corresponding	corresponding	ADJ
ejpam-2338	51	14	abstract	abstract	ADJ
ejpam-2338	51	15	structure	structure	NOUN
ejpam-2338	51	16	for	for	ADP
ejpam-2338	51	17	a	a	DET
ejpam-2338	51	18	pseudogroup	pseudogroup	NOUN
ejpam-2338	51	19	.	.	PUNCT
ejpam-2338	52	1	as	as	SCONJ
ejpam-2338	52	2	i	i	PRON
ejpam-2338	52	3	have	have	AUX
ejpam-2338	52	4	discussed	discuss	VERB
ejpam-2338	52	5	elsewhere	elsewhere	ADV
ejpam-2338	52	6	(	(	PUNCT
ejpam-2338	52	7	see	see	VERB
ejpam-2338	52	8	,	,	PUNCT
ejpam-2338	52	9	for	for	ADP
ejpam-2338	52	10	example	example	NOUN
ejpam-2338	52	11	,	,	PUNCT
ejpam-2338	52	12	[	[	X
ejpam-2338	52	13	40	40	NUM
ejpam-2338	52	14	]	]	PUNCT
ejpam-2338	52	15	)	)	PUNCT
ejpam-2338	52	16	,	,	PUNCT
ejpam-2338	52	17	there	there	PRON
ejpam-2338	52	18	turned	turn	VERB
ejpam-2338	52	19	out	out	ADP
ejpam-2338	52	20	to	to	PART
ejpam-2338	52	21	be	be	AUX
ejpam-2338	52	22	two	two	NUM
ejpam-2338	52	23	distinct	distinct	ADJ
ejpam-2338	52	24	(	(	PUNCT
ejpam-2338	52	25	though	though	SCONJ
ejpam-2338	52	26	closely	closely	ADV
ejpam-2338	52	27	connected	connect	VERB
ejpam-2338	52	28	)	)	PUNCT
ejpam-2338	52	29	solutions	solution	NOUN
ejpam-2338	52	30	to	to	ADP
ejpam-2338	52	31	this	this	DET
ejpam-2338	52	32	problem	problem	NOUN
ejpam-2338	52	33	:	:	PUNCT
ejpam-2338	52	34	one	one	NUM
ejpam-2338	52	35	where	where	SCONJ
ejpam-2338	52	36	we	we	PRON
ejpam-2338	52	37	retain	retain	VERB
ejpam-2338	52	38	the	the	DET
ejpam-2338	52	39	partial	partial	ADJ
ejpam-2338	52	40	composition	composition	NOUN
ejpam-2338	52	41	present	present	ADJ
ejpam-2338	52	42	in	in	ADP
ejpam-2338	52	43	definition	definition	NOUN
ejpam-2338	52	44	1	1	NUM
ejpam-2338	52	45	,	,	PUNCT
ejpam-2338	52	46	and	and	CCONJ
ejpam-2338	52	47	one	one	NUM
ejpam-2338	52	48	where	where	SCONJ
ejpam-2338	52	49	we	we	PRON
ejpam-2338	52	50	complete	complete	VERB
ejpam-2338	52	51	it	it	PRON
ejpam-2338	52	52	to	to	ADP
ejpam-2338	52	53	a	a	DET
ejpam-2338	52	54	fully	fully	ADV
ejpam-2338	52	55	-	-	PUNCT
ejpam-2338	52	56	defined	define	VERB
ejpam-2338	52	57	composition	composition	NOUN
ejpam-2338	52	58	.	.	PUNCT
ejpam-2338	53	1	in	in	ADP
ejpam-2338	53	2	the	the	DET
ejpam-2338	53	3	case	case	NOUN
ejpam-2338	53	4	of	of	ADP
ejpam-2338	53	5	a	a	DET
ejpam-2338	53	6	partial	partial	ADJ
ejpam-2338	53	7	composition	composition	NOUN
ejpam-2338	53	8	,	,	PUNCT
ejpam-2338	53	9	we	we	PRON
ejpam-2338	53	10	arrive	arrive	VERB
ejpam-2338	53	11	at	at	ADP
ejpam-2338	53	12	the	the	DET
ejpam-2338	53	13	notion	notion	NOUN
ejpam-2338	53	14	of	of	ADP
ejpam-2338	53	15	an	an	DET
ejpam-2338	53	16	inductive	inductive	ADJ
ejpam-2338	53	17	groupoid	groupoid	NOUN
ejpam-2338	53	18	,	,	PUNCT
ejpam-2338	53	19	which	which	PRON
ejpam-2338	53	20	i	i	PRON
ejpam-2338	53	21	will	will	AUX
ejpam-2338	53	22	discuss	discuss	VERB
ejpam-2338	53	23	further	far	ADV
ejpam-2338	53	24	in	in	ADP
ejpam-2338	53	25	section	section	NOUN
ejpam-2338	53	26	3	3	NUM
ejpam-2338	53	27	.	.	PUNCT
ejpam-2338	54	1	for	for	ADP
ejpam-2338	54	2	a	a	DET
ejpam-2338	54	3	fully	fully	ADV
ejpam-2338	54	4	-	-	PUNCT
ejpam-2338	54	5	defined	define	VERB
ejpam-2338	54	6	composition	composition	NOUN
ejpam-2338	54	7	,	,	PUNCT
ejpam-2338	54	8	however	however	ADV
ejpam-2338	54	9	,	,	PUNCT
ejpam-2338	54	10	the	the	DET
ejpam-2338	54	11	problem	problem	NOUN
ejpam-2338	54	12	took	take	VERB
ejpam-2338	54	13	rather	rather	ADV
ejpam-2338	54	14	more	more	ADJ
ejpam-2338	54	15	effort	effort	NOUN
ejpam-2338	54	16	to	to	PART
ejpam-2338	54	17	solve	solve	VERB
ejpam-2338	54	18	,	,	PUNCT
ejpam-2338	54	19	for	for	SCONJ
ejpam-2338	54	20	it	it	PRON
ejpam-2338	54	21	was	be	AUX
ejpam-2338	54	22	not	not	PART
ejpam-2338	54	23	immediately	immediately	ADV
ejpam-2338	54	24	clear	clear	ADJ
ejpam-2338	54	25	to	to	ADP
ejpam-2338	54	26	researchers	researcher	NOUN
ejpam-2338	54	27	how	how	SCONJ
ejpam-2338	54	28	they	they	PRON
ejpam-2338	54	29	should	should	AUX
ejpam-2338	54	30	go	go	VERB
ejpam-2338	54	31	about	about	ADP
ejpam-2338	54	32	‘	'	PUNCT
ejpam-2338	54	33	completing	complete	VERB
ejpam-2338	54	34	’	'	PUNCT
ejpam-2338	54	35	the	the	DET
ejpam-2338	54	36	partial	partial	ADJ
ejpam-2338	54	37	composition	composition	NOUN
ejpam-2338	54	38	above	above	ADV
ejpam-2338	54	39	:	:	PUNCT
ejpam-2338	54	40	a	a	DET
ejpam-2338	54	41	psychological	psychological	ADJ
ejpam-2338	54	42	bar	bar	NOUN
ejpam-2338	54	43	appears	appear	VERB
ejpam-2338	54	44	to	to	PART
ejpam-2338	54	45	have	have	AUX
ejpam-2338	54	46	existed	exist	VERB
ejpam-2338	54	47	with	with	ADP
ejpam-2338	54	48	regard	regard	NOUN
ejpam-2338	54	49	to	to	ADP
ejpam-2338	54	50	the	the	DET
ejpam-2338	54	51	admission	admission	NOUN
ejpam-2338	54	52	of	of	ADP
ejpam-2338	54	53	the	the	DET
ejpam-2338	54	54	empty	empty	ADJ
ejpam-2338	54	55	transformation	transformation	NOUN
ejpam-2338	54	56	into	into	ADP
ejpam-2338	54	57	consideration	consideration	NOUN
ejpam-2338	54	58	(	(	PUNCT
ejpam-2338	54	59	see	see	VERB
ejpam-2338	54	60	[	[	X
ejpam-2338	54	61	41	41	NUM
ejpam-2338	54	62	,	,	PUNCT
ejpam-2338	54	63	§	§	PROPN
ejpam-2338	54	64	10.2	10.2	NUM
ejpam-2338	54	65	]	]	PUNCT
ejpam-2338	54	66	)	)	PUNCT
ejpam-2338	54	67	.	.	PUNCT
ejpam-2338	55	1	this	this	DET
ejpam-2338	55	2	obstacle	obstacle	NOUN
ejpam-2338	55	3	was	be	AUX
ejpam-2338	55	4	finally	finally	ADV
ejpam-2338	55	5	overcome	overcome	VERB
ejpam-2338	55	6	in	in	ADP
ejpam-2338	55	7	the	the	DET
ejpam-2338	55	8	early	early	ADJ
ejpam-2338	55	9	1950s	1950s	NUM
ejpam-2338	55	10	by	by	ADP
ejpam-2338	55	11	the	the	DET
ejpam-2338	55	12	russian	russian	ADJ
ejpam-2338	55	13	mathematician	mathematician	NOUN
ejpam-2338	55	14	v.	v.	PROPN
ejpam-2338	55	15	v.	v.	PROPN
ejpam-2338	55	16	wagner	wagner	PROPN
ejpam-2338	55	17	(	(	PUNCT
ejpam-2338	55	18	1908–1981	1908–1981	NUM
ejpam-2338	55	19	)	)	PUNCT
ejpam-2338	55	20	,	,	PUNCT
ejpam-2338	55	21	who	who	PRON
ejpam-2338	55	22	defined	define	VERB
ejpam-2338	55	23	the	the	DET
ejpam-2338	55	24	notion	notion	NOUN
ejpam-2338	55	25	of	of	ADP
ejpam-2338	55	26	what	what	PRON
ejpam-2338	55	27	he	he	PRON
ejpam-2338	55	28	called	call	VERB
ejpam-2338	55	29	a	a	DET
ejpam-2338	55	30	‘	'	PUNCT
ejpam-2338	55	31	generalised	generalised	ADJ
ejpam-2338	55	32	group	group	NOUN
ejpam-2338	55	33	’	'	PUNCT
ejpam-2338	56	1	[	[	X
ejpam-2338	56	2	96–98	96–98	NUM
ejpam-2338	56	3	]	]	X
ejpam-2338	56	4	:	:	PUNCT
ejpam-2338	56	5	an	an	DET
ejpam-2338	56	6	axiomatisation	axiomatisation	NOUN
ejpam-2338	56	7	of	of	ADP
ejpam-2338	56	8	the	the	DET
ejpam-2338	56	9	christopher	christopher	PROPN
ejpam-2338	56	10	hollings	hollings	PROPN
ejpam-2338	56	11	/	/	SYM
ejpam-2338	56	12	eur	eur	PROPN
ejpam-2338	56	13	.	.	PUNCT
ejpam-2338	57	1	j.	j.	PROPN
ejpam-2338	57	2	pure	pure	PROPN
ejpam-2338	57	3	appl	appl	PROPN
ejpam-2338	57	4	.	.	PROPN
ejpam-2338	57	5	math	math	PROPN
ejpam-2338	57	6	,	,	PUNCT
ejpam-2338	57	7	8	8	NUM
ejpam-2338	57	8	(	(	PUNCT
ejpam-2338	57	9	2015	2015	NUM
ejpam-2338	57	10	)	)	PUNCT
ejpam-2338	57	11	,	,	PUNCT
ejpam-2338	57	12	294	294	NUM
ejpam-2338	57	13	-	-	SYM
ejpam-2338	57	14	323	323	NUM
ejpam-2338	57	15	297	297	NUM
ejpam-2338	57	16	collection	collection	NOUN
ejpam-2338	57	17	of	of	ADP
ejpam-2338	57	18	all	all	DET
ejpam-2338	57	19	partial	partial	ADJ
ejpam-2338	57	20	bijections	bijection	NOUN
ejpam-2338	57	21	of	of	ADP
ejpam-2338	57	22	a	a	DET
ejpam-2338	57	23	set	set	NOUN
ejpam-2338	57	24	,	,	PUNCT
ejpam-2338	57	25	under	under	ADP
ejpam-2338	57	26	the	the	DET
ejpam-2338	57	27	now	now	ADV
ejpam-2338	57	28	-	-	PUNCT
ejpam-2338	57	29	familiar	familiar	ADJ
ejpam-2338	57	30	(	(	PUNCT
ejpam-2338	57	31	left	leave	VERB
ejpam-2338	57	32	to	to	ADP
ejpam-2338	57	33	right	right	ADJ
ejpam-2338	57	34	)	)	PUNCT
ejpam-2338	57	35	composition	composition	NOUN
ejpam-2338	57	36	of	of	ADP
ejpam-2338	57	37	such	such	ADJ
ejpam-2338	57	38	functions	function	NOUN
ejpam-2338	57	39	:	:	PUNCT
ejpam-2338	57	40	domαβ	domαβ	NOUN
ejpam-2338	57	41	=	=	SYM
ejpam-2338	57	42	�	�	PROPN
ejpam-2338	57	43	imα∩	imα∩	PROPN
ejpam-2338	57	44	domβ	domβ	PROPN
ejpam-2338	57	45	�	�	PROPN
ejpam-2338	57	46	α−1	α−1	PROPN
ejpam-2338	57	47	,	,	PUNCT
ejpam-2338	57	48	x(αβ	x(αβ	NUM
ejpam-2338	57	49	)	)	PUNCT
ejpam-2338	57	50	=	=	SYM
ejpam-2338	58	1	(	(	PUNCT
ejpam-2338	58	2	xα)β	xα)β	PROPN
ejpam-2338	58	3	,	,	PUNCT
ejpam-2338	58	4	for	for	ADP
ejpam-2338	58	5	any	any	DET
ejpam-2338	58	6	x	x	SYM
ejpam-2338	58	7	∈	∈	PROPN
ejpam-2338	58	8	domαβ	domαβ	NOUN
ejpam-2338	58	9	.	.	PUNCT
ejpam-2338	59	1	(	(	PUNCT
ejpam-2338	59	2	1	1	X
ejpam-2338	59	3	)	)	PUNCT
ejpam-2338	59	4	the	the	DET
ejpam-2338	59	5	same	same	ADJ
ejpam-2338	59	6	notion	notion	NOUN
ejpam-2338	59	7	was	be	AUX
ejpam-2338	59	8	arrived	arrive	VERB
ejpam-2338	59	9	at	at	ADP
ejpam-2338	59	10	independently	independently	ADV
ejpam-2338	59	11	by	by	ADP
ejpam-2338	59	12	the	the	DET
ejpam-2338	59	13	british	british	ADJ
ejpam-2338	59	14	mathematician	mathematician	PROPN
ejpam-2338	59	15	g.	g.	PROPN
ejpam-2338	59	16	b.	b.	PROPN
ejpam-2338	59	17	preston	preston	PROPN
ejpam-2338	59	18	(	(	PUNCT
ejpam-2338	59	19	1925–2015	1925–2015	NUM
ejpam-2338	59	20	)	)	PUNCT
ejpam-2338	59	21	at	at	ADP
ejpam-2338	59	22	around	around	ADP
ejpam-2338	59	23	the	the	DET
ejpam-2338	59	24	same	same	ADJ
ejpam-2338	59	25	time	time	NOUN
ejpam-2338	60	1	[	[	X
ejpam-2338	60	2	74–77	74–77	NOUN
ejpam-2338	60	3	]	]	PUNCT
ejpam-2338	60	4	;	;	PUNCT
ejpam-2338	60	5	it	it	PRON
ejpam-2338	60	6	was	be	AUX
ejpam-2338	60	7	preston	preston	PROPN
ejpam-2338	60	8	who	who	PRON
ejpam-2338	60	9	dubbed	dub	VERB
ejpam-2338	60	10	them	they	PRON
ejpam-2338	60	11	‘	'	PUNCT
ejpam-2338	60	12	inverse	inverse	ADJ
ejpam-2338	60	13	semigroups	semigroup	NOUN
ejpam-2338	60	14	’	'	PUNCT
ejpam-2338	60	15	.	.	PUNCT
ejpam-2338	61	1	for	for	ADP
ejpam-2338	61	2	a	a	DET
ejpam-2338	61	3	more	more	ADV
ejpam-2338	61	4	detailed	detailed	ADJ
ejpam-2338	61	5	account	account	NOUN
ejpam-2338	61	6	of	of	ADP
ejpam-2338	61	7	the	the	DET
ejpam-2338	61	8	development	development	NOUN
ejpam-2338	61	9	of	of	ADP
ejpam-2338	61	10	inverse	inverse	NOUN
ejpam-2338	61	11	semigroups	semigroup	NOUN
ejpam-2338	61	12	,	,	PUNCT
ejpam-2338	61	13	see	see	VERB
ejpam-2338	61	14	[	[	X
ejpam-2338	61	15	41	41	NUM
ejpam-2338	61	16	,	,	PUNCT
ejpam-2338	61	17	chapter	chapter	NOUN
ejpam-2338	61	18	10	10	NUM
ejpam-2338	61	19	]	]	PUNCT
ejpam-2338	61	20	;	;	PUNCT
ejpam-2338	61	21	other	other	ADJ
ejpam-2338	61	22	(	(	PUNCT
ejpam-2338	61	23	shorter	short	ADJ
ejpam-2338	61	24	)	)	PUNCT
ejpam-2338	61	25	accounts	account	NOUN
ejpam-2338	61	26	may	may	AUX
ejpam-2338	61	27	be	be	AUX
ejpam-2338	61	28	found	find	VERB
ejpam-2338	61	29	in	in	ADP
ejpam-2338	61	30	[	[	NOUN
ejpam-2338	61	31	79	79	NUM
ejpam-2338	61	32	,	,	PUNCT
ejpam-2338	61	33	91	91	NUM
ejpam-2338	61	34	,	,	PUNCT
ejpam-2338	61	35	92	92	NUM
ejpam-2338	61	36	]	]	PUNCT
ejpam-2338	61	37	.	.	PUNCT
ejpam-2338	62	1	3	3	X
ejpam-2338	62	2	.	.	X
ejpam-2338	62	3	inverse	inverse	NOUN
ejpam-2338	62	4	semigroups	semigroup	NOUN
ejpam-2338	62	5	and	and	CCONJ
ejpam-2338	62	6	inductive	inductive	ADJ
ejpam-2338	62	7	groupoids	groupoid	NOUN
ejpam-2338	62	8	our	our	PRON
ejpam-2338	62	9	first	first	ADJ
ejpam-2338	62	10	approach	approach	NOUN
ejpam-2338	62	11	to	to	ADP
ejpam-2338	62	12	the	the	DET
ejpam-2338	62	13	study	study	NOUN
ejpam-2338	62	14	of	of	ADP
ejpam-2338	62	15	inverse	inverse	NOUN
ejpam-2338	62	16	semigroups	semigroup	NOUN
ejpam-2338	62	17	is	be	AUX
ejpam-2338	62	18	that	that	SCONJ
ejpam-2338	62	19	via	via	ADP
ejpam-2338	62	20	inductive	inductive	ADJ
ejpam-2338	62	21	groupoids	groupoid	NOUN
ejpam-2338	62	22	,	,	PUNCT
ejpam-2338	62	23	which	which	PRON
ejpam-2338	62	24	has	have	VERB
ejpam-2338	62	25	its	its	PRON
ejpam-2338	62	26	origins	origin	NOUN
ejpam-2338	62	27	in	in	ADP
ejpam-2338	62	28	the	the	DET
ejpam-2338	62	29	work	work	NOUN
ejpam-2338	62	30	of	of	ADP
ejpam-2338	62	31	the	the	DET
ejpam-2338	62	32	french	french	ADJ
ejpam-2338	62	33	mathematician	mathematician	NOUN
ejpam-2338	62	34	charles	charles	PROPN
ejpam-2338	62	35	ehresmann	ehresmann	PROPN
ejpam-2338	62	36	(	(	PUNCT
ejpam-2338	62	37	1905–1979	1905–1979	NUM
ejpam-2338	62	38	)	)	PUNCT
ejpam-2338	62	39	.	.	PUNCT
ejpam-2338	63	1	this	this	DET
ejpam-2338	63	2	approach	approach	NOUN
ejpam-2338	63	3	has	have	AUX
ejpam-2338	63	4	been	be	AUX
ejpam-2338	63	5	exploited	exploit	VERB
ejpam-2338	63	6	,	,	PUNCT
ejpam-2338	63	7	and	and	CCONJ
ejpam-2338	63	8	indeed	indeed	ADV
ejpam-2338	63	9	championed	champion	VERB
ejpam-2338	63	10	,	,	PUNCT
ejpam-2338	63	11	by	by	ADP
ejpam-2338	63	12	lawson	lawson	PROPN
ejpam-2338	64	1	[	[	X
ejpam-2338	64	2	51	51	NUM
ejpam-2338	64	3	]	]	PUNCT
ejpam-2338	64	4	in	in	ADP
ejpam-2338	64	5	particular	particular	ADJ
ejpam-2338	64	6	.	.	PUNCT
ejpam-2338	65	1	it	it	PRON
ejpam-2338	65	2	is	be	AUX
ejpam-2338	65	3	also	also	ADV
ejpam-2338	65	4	the	the	DET
ejpam-2338	65	5	central	central	ADJ
ejpam-2338	65	6	theme	theme	NOUN
ejpam-2338	65	7	of	of	ADP
ejpam-2338	65	8	[	[	X
ejpam-2338	65	9	40	40	NUM
ejpam-2338	65	10	]	]	PUNCT
ejpam-2338	65	11	,	,	PUNCT
ejpam-2338	65	12	although	although	SCONJ
ejpam-2338	65	13	that	that	PRON
ejpam-2338	65	14	earlier	early	ADJ
ejpam-2338	65	15	article	article	NOUN
ejpam-2338	65	16	focused	focus	VERB
ejpam-2338	65	17	largely	largely	ADV
ejpam-2338	65	18	upon	upon	SCONJ
ejpam-2338	65	19	the	the	DET
ejpam-2338	65	20	so	so	ADV
ejpam-2338	65	21	-	-	PUNCT
ejpam-2338	65	22	called	call	VERB
ejpam-2338	65	23	ehresmann	ehresmann	PROPN
ejpam-2338	65	24	–	–	PUNCT
ejpam-2338	65	25	schein	schein	PROPN
ejpam-2338	65	26	–	–	PUNCT
ejpam-2338	65	27	nambooripad	nambooripad	NOUN
ejpam-2338	65	28	theorem	theorem	PROPN
ejpam-2338	65	29	;	;	PUNCT
ejpam-2338	65	30	the	the	DET
ejpam-2338	65	31	present	present	ADJ
ejpam-2338	65	32	article	article	NOUN
ejpam-2338	65	33	takes	take	VERB
ejpam-2338	65	34	a	a	DET
ejpam-2338	65	35	slightly	slightly	ADV
ejpam-2338	65	36	broader	broad	ADJ
ejpam-2338	65	37	view	view	NOUN
ejpam-2338	65	38	.	.	PUNCT
ejpam-2338	66	1	as	as	SCONJ
ejpam-2338	66	2	noted	note	VERB
ejpam-2338	66	3	in	in	ADP
ejpam-2338	66	4	section	section	NOUN
ejpam-2338	66	5	2	2	NUM
ejpam-2338	66	6	,	,	PUNCT
ejpam-2338	66	7	the	the	DET
ejpam-2338	66	8	drive	drive	NOUN
ejpam-2338	66	9	to	to	ADP
ejpam-2338	66	10	‘	'	PUNCT
ejpam-2338	66	11	complete	complete	ADJ
ejpam-2338	66	12	’	'	PUNCT
ejpam-2338	66	13	the	the	DET
ejpam-2338	66	14	partial	partial	ADJ
ejpam-2338	66	15	operation	operation	NOUN
ejpam-2338	66	16	of	of	ADP
ejpam-2338	66	17	definition	definition	NOUN
ejpam-2338	66	18	1	1	NUM
ejpam-2338	66	19	and	and	CCONJ
ejpam-2338	66	20	then	then	ADV
ejpam-2338	66	21	axiomatise	axiomatise	VERB
ejpam-2338	66	22	the	the	DET
ejpam-2338	66	23	resulting	result	VERB
ejpam-2338	66	24	system	system	NOUN
ejpam-2338	66	25	led	lead	VERB
ejpam-2338	66	26	to	to	ADP
ejpam-2338	66	27	the	the	DET
ejpam-2338	66	28	notion	notion	NOUN
ejpam-2338	66	29	of	of	ADP
ejpam-2338	66	30	an	an	DET
ejpam-2338	66	31	inverse	inverse	NOUN
ejpam-2338	66	32	semigroup	semigroup	NOUN
ejpam-2338	66	33	.	.	PUNCT
ejpam-2338	67	1	however	however	ADV
ejpam-2338	67	2	,	,	PUNCT
ejpam-2338	67	3	if	if	SCONJ
ejpam-2338	67	4	we	we	PRON
ejpam-2338	67	5	axiomatise	axiomatise	VERB
ejpam-2338	67	6	with	with	ADP
ejpam-2338	67	7	the	the	DET
ejpam-2338	67	8	partial	partial	ADJ
ejpam-2338	67	9	operation	operation	NOUN
ejpam-2338	67	10	still	still	ADV
ejpam-2338	67	11	in	in	ADP
ejpam-2338	67	12	place	place	NOUN
ejpam-2338	67	13	(	(	PUNCT
ejpam-2338	67	14	and	and	CCONJ
ejpam-2338	67	15	take	take	VERB
ejpam-2338	67	16	into	into	ADP
ejpam-2338	67	17	account	account	NOUN
ejpam-2338	67	18	the	the	DET
ejpam-2338	67	19	natural	natural	ADJ
ejpam-2338	67	20	ordering	ordering	NOUN
ejpam-2338	67	21	possessed	possess	VERB
ejpam-2338	67	22	by	by	ADP
ejpam-2338	67	23	a	a	DET
ejpam-2338	67	24	pseudogroup	pseudogroup	NOUN
ejpam-2338	67	25	:	:	PUNCT
ejpam-2338	67	26	that	that	SCONJ
ejpam-2338	67	27	by	by	ADP
ejpam-2338	67	28	restriction	restriction	NOUN
ejpam-2338	67	29	of	of	ADP
ejpam-2338	67	30	mappings	mapping	NOUN
ejpam-2338	67	31	)	)	PUNCT
ejpam-2338	67	32	,	,	PUNCT
ejpam-2338	67	33	the	the	DET
ejpam-2338	67	34	abstract	abstract	ADJ
ejpam-2338	67	35	description	description	NOUN
ejpam-2338	67	36	of	of	ADP
ejpam-2338	67	37	a	a	DET
ejpam-2338	67	38	pseudogroup	pseudogroup	NOUN
ejpam-2338	67	39	that	that	PRON
ejpam-2338	67	40	we	we	PRON
ejpam-2338	67	41	arrive	arrive	VERB
ejpam-2338	67	42	at	at	ADP
ejpam-2338	67	43	is	be	AUX
ejpam-2338	67	44	an	an	DET
ejpam-2338	67	45	inductive	inductive	ADJ
ejpam-2338	67	46	groupoid	groupoid	NOUN
ejpam-2338	67	47	:	:	PUNCT
ejpam-2338	67	48	a	a	DET
ejpam-2338	67	49	special	special	ADJ
ejpam-2338	67	50	type	type	NOUN
ejpam-2338	67	51	of	of	ADP
ejpam-2338	67	52	small	small	ADJ
ejpam-2338	67	53	ordered	order	VERB
ejpam-2338	67	54	category	category	NOUN
ejpam-2338	67	55	in	in	ADP
ejpam-2338	67	56	which	which	PRON
ejpam-2338	67	57	all	all	DET
ejpam-2338	67	58	arrows	arrow	NOUN
ejpam-2338	67	59	are	be	AUX
ejpam-2338	67	60	invertible	invertible	ADJ
ejpam-2338	67	61	.	.	PUNCT
ejpam-2338	68	1	as	as	SCONJ
ejpam-2338	68	2	one	one	PRON
ejpam-2338	68	3	might	might	AUX
ejpam-2338	68	4	expect	expect	VERB
ejpam-2338	68	5	,	,	PUNCT
ejpam-2338	68	6	given	give	VERB
ejpam-2338	68	7	their	their	PRON
ejpam-2338	68	8	common	common	ADJ
ejpam-2338	68	9	origin	origin	NOUN
ejpam-2338	68	10	,	,	PUNCT
ejpam-2338	68	11	inverse	inverse	NOUN
ejpam-2338	68	12	semigroups	semigroup	NOUN
ejpam-2338	68	13	and	and	CCONJ
ejpam-2338	68	14	inductive	inductive	ADJ
ejpam-2338	68	15	groupoids	groupoid	NOUN
ejpam-2338	68	16	are	be	AUX
ejpam-2338	68	17	very	very	ADV
ejpam-2338	68	18	closely	closely	ADV
ejpam-2338	68	19	connected	connect	VERB
ejpam-2338	68	20	;	;	PUNCT
ejpam-2338	68	21	it	it	PRON
ejpam-2338	68	22	is	be	AUX
ejpam-2338	68	23	largely	largely	ADV
ejpam-2338	68	24	via	via	ADP
ejpam-2338	68	25	the	the	DET
ejpam-2338	68	26	ordering	ordering	NOUN
ejpam-2338	68	27	on	on	ADP
ejpam-2338	68	28	each	each	PRON
ejpam-2338	68	29	that	that	PRON
ejpam-2338	68	30	we	we	PRON
ejpam-2338	68	31	may	may	AUX
ejpam-2338	68	32	make	make	VERB
ejpam-2338	68	33	the	the	DET
ejpam-2338	68	34	link	link	NOUN
ejpam-2338	68	35	.	.	PUNCT
ejpam-2338	69	1	as	as	SCONJ
ejpam-2338	69	2	indicated	indicate	VERB
ejpam-2338	69	3	above	above	ADV
ejpam-2338	69	4	,	,	PUNCT
ejpam-2338	69	5	the	the	DET
ejpam-2338	69	6	leading	lead	VERB
ejpam-2338	69	7	light	light	NOUN
ejpam-2338	69	8	in	in	ADP
ejpam-2338	69	9	the	the	DET
ejpam-2338	69	10	development	development	NOUN
ejpam-2338	69	11	of	of	ADP
ejpam-2338	69	12	the	the	DET
ejpam-2338	69	13	inductive	inductive	ADJ
ejpam-2338	69	14	groupoid	groupoid	PROPN
ejpam-2338	69	15	concept	concept	NOUN
ejpam-2338	69	16	was	be	AUX
ejpam-2338	69	17	ehresmann	ehresmann	PROPN
ejpam-2338	69	18	,	,	PUNCT
ejpam-2338	69	19	who	who	PRON
ejpam-2338	69	20	realised	realise	VERB
ejpam-2338	69	21	that	that	SCONJ
ejpam-2338	69	22	the	the	DET
ejpam-2338	69	23	ordering	ordering	NOUN
ejpam-2338	69	24	of	of	ADP
ejpam-2338	69	25	a	a	DET
ejpam-2338	69	26	pseudogroup	pseudogroup	NOUN
ejpam-2338	69	27	(	(	PUNCT
ejpam-2338	69	28	that	that	PRON
ejpam-2338	69	29	is	is	ADV
ejpam-2338	69	30	,	,	PUNCT
ejpam-2338	69	31	by	by	ADP
ejpam-2338	69	32	restriction	restriction	NOUN
ejpam-2338	69	33	of	of	ADP
ejpam-2338	69	34	mappings	mapping	NOUN
ejpam-2338	69	35	—	—	PUNCT
ejpam-2338	69	36	just	just	ADV
ejpam-2338	69	37	as	as	ADP
ejpam-2338	69	38	in	in	ADP
ejpam-2338	69	39	a	a	DET
ejpam-2338	69	40	symmetric	symmetric	ADJ
ejpam-2338	69	41	inverse	inverse	NOUN
ejpam-2338	69	42	semigroup	semigroup	PROPN
ejpam-2338	69	43	)	)	PUNCT
ejpam-2338	69	44	has	have	VERB
ejpam-2338	69	45	a	a	DET
ejpam-2338	69	46	crucial	crucial	ADJ
ejpam-2338	69	47	role	role	NOUN
ejpam-2338	69	48	to	to	PART
ejpam-2338	69	49	play	play	VERB
ejpam-2338	69	50	.	.	PUNCT
ejpam-2338	70	1	lawson	lawson	PROPN
ejpam-2338	71	1	[	[	X
ejpam-2338	71	2	51	51	NUM
ejpam-2338	71	3	,	,	PUNCT
ejpam-2338	71	4	p.	p.	NOUN
ejpam-2338	71	5	9	9	NUM
ejpam-2338	71	6	]	]	PUNCT
ejpam-2338	71	7	puts	put	VERB
ejpam-2338	71	8	it	it	PRON
ejpam-2338	71	9	succinctly	succinctly	ADV
ejpam-2338	71	10	when	when	SCONJ
ejpam-2338	71	11	he	he	PRON
ejpam-2338	71	12	observes	observe	VERB
ejpam-2338	71	13	that	that	SCONJ
ejpam-2338	71	14	both	both	PRON
ejpam-2338	71	15	wagner	wagner	PROPN
ejpam-2338	71	16	and	and	CCONJ
ejpam-2338	71	17	preston	preston	PROPN
ejpam-2338	71	18	axiomatised	axiomatise	VERB
ejpam-2338	71	19	(	(	PUNCT
ejpam-2338	71	20	ix	ix	ADV
ejpam-2338	71	21	,	,	PUNCT
ejpam-2338	71	22	◦	◦	NOUN
ejpam-2338	71	23	)	)	PUNCT
ejpam-2338	71	24	,	,	PUNCT
ejpam-2338	71	25	where	where	SCONJ
ejpam-2338	71	26	◦	◦	NOUN
ejpam-2338	71	27	is	be	AUX
ejpam-2338	71	28	the	the	DET
ejpam-2338	71	29	composition	composition	NOUN
ejpam-2338	71	30	of	of	ADP
ejpam-2338	71	31	(	(	PUNCT
ejpam-2338	71	32	1	1	NUM
ejpam-2338	71	33	)	)	PUNCT
ejpam-2338	71	34	,	,	PUNCT
ejpam-2338	72	1	whilst	whilst	SCONJ
ejpam-2338	72	2	ehresmann	ehresmann	PROPN
ejpam-2338	72	3	axiomatised	axiomatise	VERB
ejpam-2338	72	4	(	(	PUNCT
ejpam-2338	72	5	ix	ix	ADV
ejpam-2338	72	6	,	,	PUNCT
ejpam-2338	72	7	·	·	PUNCT
ejpam-2338	72	8	,	,	PUNCT
ejpam-2338	72	9	⊆	⊆	NUM
ejpam-2338	72	10	)	)	PUNCT
ejpam-2338	72	11	,	,	PUNCT
ejpam-2338	72	12	where	where	SCONJ
ejpam-2338	72	13	·	·	PUNCT
ejpam-2338	72	14	is	be	AUX
ejpam-2338	72	15	veblen	veblen	PROPN
ejpam-2338	72	16	and	and	CCONJ
ejpam-2338	72	17	whitehead	whitehead	PROPN
ejpam-2338	72	18	’s	’s	PART
ejpam-2338	72	19	partial	partial	ADJ
ejpam-2338	72	20	composition	composition	NOUN
ejpam-2338	72	21	,	,	PUNCT
ejpam-2338	72	22	and	and	CCONJ
ejpam-2338	72	23	⊆	⊆	NUM
ejpam-2338	72	24	denotes	denote	VERB
ejpam-2338	72	25	the	the	DET
ejpam-2338	72	26	ordering	ordering	NOUN
ejpam-2338	72	27	of	of	ADP
ejpam-2338	72	28	partial	partial	ADJ
ejpam-2338	72	29	transformations	transformation	NOUN
ejpam-2338	72	30	by	by	ADP
ejpam-2338	72	31	restriction	restriction	NOUN
ejpam-2338	72	32	.	.	PUNCT
ejpam-2338	73	1	the	the	DET
ejpam-2338	73	2	motivation	motivation	NOUN
ejpam-2338	73	3	for	for	ADP
ejpam-2338	73	4	ehresmann	ehresmann	PROPN
ejpam-2338	73	5	’s	’s	PART
ejpam-2338	73	6	work	work	NOUN
ejpam-2338	73	7	came	come	VERB
ejpam-2338	73	8	from	from	ADP
ejpam-2338	73	9	the	the	DET
ejpam-2338	73	10	study	study	NOUN
ejpam-2338	73	11	of	of	ADP
ejpam-2338	73	12	so	so	ADV
ejpam-2338	73	13	-	-	PUNCT
ejpam-2338	73	14	called	call	VERB
ejpam-2338	73	15	local	local	ADJ
ejpam-2338	73	16	structures	structure	NOUN
ejpam-2338	73	17	:	:	PUNCT
ejpam-2338	73	18	structures	structure	NOUN
ejpam-2338	73	19	defined	define	VERB
ejpam-2338	73	20	on	on	ADP
ejpam-2338	73	21	topological	topological	ADJ
ejpam-2338	73	22	spaces	space	NOUN
ejpam-2338	73	23	by	by	ADP
ejpam-2338	73	24	using	use	VERB
ejpam-2338	73	25	pseudogroups	pseudogroup	NOUN
ejpam-2338	73	26	in	in	ADP
ejpam-2338	73	27	a	a	DET
ejpam-2338	73	28	manner	manner	NOUN
ejpam-2338	73	29	analogous	analogous	ADJ
ejpam-2338	73	30	to	to	ADP
ejpam-2338	73	31	the	the	DET
ejpam-2338	73	32	way	way	NOUN
ejpam-2338	73	33	in	in	ADP
ejpam-2338	73	34	which	which	PRON
ejpam-2338	73	35	groups	group	NOUN
ejpam-2338	73	36	are	be	AUX
ejpam-2338	73	37	used	use	VERB
ejpam-2338	73	38	to	to	PART
ejpam-2338	73	39	define	define	VERB
ejpam-2338	73	40	geometries	geometry	NOUN
ejpam-2338	73	41	.	.	PUNCT
ejpam-2338	74	1	we	we	PRON
ejpam-2338	74	2	therefore	therefore	ADV
ejpam-2338	74	3	begin	begin	VERB
ejpam-2338	74	4	with	with	ADP
ejpam-2338	74	5	a	a	DET
ejpam-2338	74	6	brief	brief	ADJ
ejpam-2338	74	7	introduction	introduction	NOUN
ejpam-2338	74	8	to	to	ADP
ejpam-2338	74	9	local	local	ADJ
ejpam-2338	74	10	structures	structure	NOUN
ejpam-2338	74	11	.	.	PUNCT
ejpam-2338	75	1	the	the	DET
ejpam-2338	75	2	discussion	discussion	NOUN
ejpam-2338	75	3	here	here	ADV
ejpam-2338	75	4	is	be	AUX
ejpam-2338	75	5	based	base	VERB
ejpam-2338	75	6	upon	upon	SCONJ
ejpam-2338	75	7	that	that	PRON
ejpam-2338	75	8	of	of	ADP
ejpam-2338	75	9	[	[	X
ejpam-2338	75	10	51	51	NUM
ejpam-2338	75	11	,	,	PUNCT
ejpam-2338	75	12	§	§	NOUN
ejpam-2338	75	13	1.2	1.2	NUM
ejpam-2338	75	14	]	]	PUNCT
ejpam-2338	75	15	;	;	PUNCT
ejpam-2338	75	16	however	however	ADV
ejpam-2338	75	17	,	,	PUNCT
ejpam-2338	75	18	in	in	ADP
ejpam-2338	75	19	contrast	contrast	NOUN
ejpam-2338	75	20	to	to	ADP
ejpam-2338	75	21	[	[	X
ejpam-2338	75	22	51	51	NUM
ejpam-2338	75	23	]	]	PUNCT
ejpam-2338	75	24	,	,	PUNCT
ejpam-2338	75	25	we	we	PRON
ejpam-2338	75	26	will	will	AUX
ejpam-2338	75	27	compose	compose	VERB
ejpam-2338	75	28	functions	function	NOUN
ejpam-2338	75	29	from	from	ADP
ejpam-2338	75	30	left	leave	VERB
ejpam-2338	75	31	to	to	ADP
ejpam-2338	75	32	right	right	NOUN
ejpam-2338	75	33	,	,	PUNCT
ejpam-2338	75	34	for	for	ADP
ejpam-2338	75	35	consistency	consistency	NOUN
ejpam-2338	75	36	with	with	ADP
ejpam-2338	75	37	the	the	DET
ejpam-2338	75	38	rest	rest	NOUN
ejpam-2338	75	39	of	of	ADP
ejpam-2338	75	40	the	the	DET
ejpam-2338	75	41	article	article	NOUN
ejpam-2338	75	42	.	.	PUNCT
ejpam-2338	76	1	3.1	3.1	NUM
ejpam-2338	76	2	.	.	PUNCT
ejpam-2338	77	1	local	local	ADJ
ejpam-2338	77	2	structures	structure	NOUN
ejpam-2338	77	3	let	let	VERB
ejpam-2338	77	4	x	x	PRON
ejpam-2338	77	5	and	and	CCONJ
ejpam-2338	77	6	y	y	PROPN
ejpam-2338	77	7	be	be	AUX
ejpam-2338	77	8	topological	topological	ADJ
ejpam-2338	77	9	spaces	space	NOUN
ejpam-2338	77	10	.	.	PUNCT
ejpam-2338	78	1	we	we	PRON
ejpam-2338	78	2	call	call	VERB
ejpam-2338	78	3	x	x	VERB
ejpam-2338	78	4	our	our	PRON
ejpam-2338	78	5	model	model	NOUN
ejpam-2338	78	6	space	space	NOUN
ejpam-2338	78	7	—	—	PUNCT
ejpam-2338	78	8	so	so	ADV
ejpam-2338	78	9	-	-	PUNCT
ejpam-2338	78	10	called	call	VERB
ejpam-2338	78	11	because	because	SCONJ
ejpam-2338	78	12	our	our	PRON
ejpam-2338	78	13	goal	goal	NOUN
ejpam-2338	78	14	is	be	AUX
ejpam-2338	78	15	to	to	PART
ejpam-2338	78	16	build	build	VERB
ejpam-2338	78	17	‘	'	PUNCT
ejpam-2338	78	18	structures	structure	NOUN
ejpam-2338	78	19	’	'	PUNCT
ejpam-2338	78	20	on	on	ADP
ejpam-2338	78	21	y	y	PRON
ejpam-2338	78	22	which	which	PRON
ejpam-2338	78	23	look	look	VERB
ejpam-2338	78	24	locally	locally	ADV
ejpam-2338	78	25	like	like	ADP
ejpam-2338	78	26	pieces	piece	NOUN
ejpam-2338	78	27	of	of	ADP
ejpam-2338	78	28	x	x	PRON
ejpam-2338	78	29	,	,	PUNCT
ejpam-2338	78	30	and	and	CCONJ
ejpam-2338	78	31	thereby	thereby	ADV
ejpam-2338	78	32	use	use	VERB
ejpam-2338	78	33	x	x	PUNCT
ejpam-2338	78	34	to	to	ADP
ejpam-2338	78	35	‘	'	PUNCT
ejpam-2338	78	36	model	model	NOUN
ejpam-2338	78	37	’	'	PUNCT
ejpam-2338	78	38	y	y	PROPN
ejpam-2338	78	39	.	.	PUNCT
ejpam-2338	79	1	we	we	PRON
ejpam-2338	79	2	define	define	VERB
ejpam-2338	79	3	a	a	DET
ejpam-2338	79	4	chart	chart	NOUN
ejpam-2338	79	5	from	from	ADP
ejpam-2338	79	6	x	x	PUNCT
ejpam-2338	79	7	to	to	ADP
ejpam-2338	79	8	y	y	PROPN
ejpam-2338	79	9	(	(	PUNCT
ejpam-2338	79	10	hereafter	hereafter	ADV
ejpam-2338	79	11	,	,	PUNCT
ejpam-2338	79	12	x	x	PUNCT
ejpam-2338	79	13	→	→	SYM
ejpam-2338	79	14	y	y	PROPN
ejpam-2338	79	15	)	)	PUNCT
ejpam-2338	79	16	to	to	PART
ejpam-2338	79	17	be	be	AUX
ejpam-2338	79	18	a	a	DET
ejpam-2338	79	19	homeomorphism	homeomorphism	PROPN
ejpam-2338	79	20	φ	φ	NOUN
ejpam-2338	79	21	:	:	PUNCT
ejpam-2338	79	22	u	u	PROPN
ejpam-2338	79	23	→	→	SYM
ejpam-2338	79	24	v	v	PROPN
ejpam-2338	79	25	christopher	christopher	PROPN
ejpam-2338	79	26	hollings	hollings	PROPN
ejpam-2338	79	27	/	/	SYM
ejpam-2338	79	28	eur	eur	PROPN
ejpam-2338	79	29	.	.	PUNCT
ejpam-2338	80	1	j.	j.	PROPN
ejpam-2338	80	2	pure	pure	PROPN
ejpam-2338	80	3	appl	appl	PROPN
ejpam-2338	80	4	.	.	PROPN
ejpam-2338	80	5	math	math	PROPN
ejpam-2338	80	6	,	,	PUNCT
ejpam-2338	80	7	8	8	NUM
ejpam-2338	80	8	(	(	PUNCT
ejpam-2338	80	9	2015	2015	NUM
ejpam-2338	80	10	)	)	PUNCT
ejpam-2338	80	11	,	,	PUNCT
ejpam-2338	80	12	294	294	NUM
ejpam-2338	80	13	-	-	SYM
ejpam-2338	80	14	323	323	NUM
ejpam-2338	80	15	298	298	NUM
ejpam-2338	80	16	between	between	ADP
ejpam-2338	80	17	open	open	ADJ
ejpam-2338	80	18	subsets	subset	NOUN
ejpam-2338	80	19	of	of	ADP
ejpam-2338	80	20	x	x	X
ejpam-2338	80	21	and	and	CCONJ
ejpam-2338	80	22	y	y	PROPN
ejpam-2338	80	23	.	.	PUNCT
ejpam-2338	81	1	an	an	PRON
ejpam-2338	81	2	atlas	atlas	PROPN
ejpam-2338	81	3	a	a	X
ejpam-2338	81	4	(	(	PUNCT
ejpam-2338	81	5	x	x	PROPN
ejpam-2338	81	6	→	→	SYM
ejpam-2338	81	7	y	y	PROPN
ejpam-2338	81	8	)	)	PUNCT
ejpam-2338	81	9	is	be	AUX
ejpam-2338	81	10	a	a	DET
ejpam-2338	81	11	collection	collection	NOUN
ejpam-2338	81	12	of	of	ADP
ejpam-2338	81	13	charts	chart	NOUN
ejpam-2338	81	14	x	x	PUNCT
ejpam-2338	82	1	→	→	PUNCT
ejpam-2338	82	2	y	y	PROPN
ejpam-2338	82	3	such	such	ADJ
ejpam-2338	82	4	that	that	DET
ejpam-2338	82	5	1y	1y	NOUN
ejpam-2338	82	6	=	=	SYM
ejpam-2338	82	7	⋃	⋃	NOUN
ejpam-2338	82	8	φ∈a	φ∈a	ADJ
ejpam-2338	82	9	φ−1φ	φ−1φ	NOUN
ejpam-2338	82	10	.	.	PUNCT
ejpam-2338	83	1	(	(	PUNCT
ejpam-2338	83	2	2	2	X
ejpam-2338	83	3	)	)	PUNCT
ejpam-2338	83	4	a	a	DET
ejpam-2338	83	5	partial	partial	ADJ
ejpam-2338	83	6	atlas	atlas	PROPN
ejpam-2338	83	7	is	be	AUX
ejpam-2338	83	8	a	a	DET
ejpam-2338	83	9	collection	collection	NOUN
ejpam-2338	83	10	of	of	ADP
ejpam-2338	83	11	charts	chart	NOUN
ejpam-2338	83	12	which	which	PRON
ejpam-2338	83	13	lacks	lack	VERB
ejpam-2338	83	14	property	property	NOUN
ejpam-2338	83	15	(	(	PUNCT
ejpam-2338	83	16	2	2	NUM
ejpam-2338	83	17	)	)	PUNCT
ejpam-2338	83	18	.	.	PUNCT
ejpam-2338	84	1	let	let	VERB
ejpam-2338	84	2	z	z	PRON
ejpam-2338	84	3	be	be	AUX
ejpam-2338	84	4	a	a	DET
ejpam-2338	84	5	third	third	ADJ
ejpam-2338	84	6	topological	topological	ADJ
ejpam-2338	84	7	space	space	NOUN
ejpam-2338	84	8	and	and	CCONJ
ejpam-2338	84	9	suppose	suppose	VERB
ejpam-2338	84	10	thata	thata	PROPN
ejpam-2338	84	11	is	be	AUX
ejpam-2338	84	12	a	a	DET
ejpam-2338	84	13	partial	partial	ADJ
ejpam-2338	84	14	atlas	atlas	NOUN
ejpam-2338	84	15	x	x	PROPN
ejpam-2338	84	16	→	→	SYM
ejpam-2338	84	17	y	y	PROPN
ejpam-2338	84	18	and	and	CCONJ
ejpam-2338	84	19	thatb	thatb	NOUN
ejpam-2338	84	20	is	be	AUX
ejpam-2338	84	21	a	a	DET
ejpam-2338	84	22	partial	partial	ADJ
ejpam-2338	84	23	atlas	atlas	PROPN
ejpam-2338	84	24	y	y	PROPN
ejpam-2338	84	25	→	→	PROPN
ejpam-2338	84	26	z	z	PROPN
ejpam-2338	84	27	.	.	PUNCT
ejpam-2338	85	1	then	then	ADV
ejpam-2338	85	2	we	we	PRON
ejpam-2338	85	3	may	may	AUX
ejpam-2338	85	4	compose	compose	VERB
ejpam-2338	85	5	atlases	atlas	NOUN
ejpam-2338	85	6	to	to	PART
ejpam-2338	85	7	obtain	obtain	VERB
ejpam-2338	85	8	a	a	DET
ejpam-2338	85	9	new	new	ADJ
ejpam-2338	85	10	partial	partial	ADJ
ejpam-2338	85	11	atlas	atlas	NOUN
ejpam-2338	85	12	x	x	PUNCT
ejpam-2338	85	13	→	→	SYM
ejpam-2338	85	14	z	z	NOUN
ejpam-2338	85	15	,	,	PUNCT
ejpam-2338	85	16	given	give	VERB
ejpam-2338	85	17	by	by	ADP
ejpam-2338	85	18	ab	ab	PROPN
ejpam-2338	85	19	=	=	PUNCT
ejpam-2338	85	20	{	{	PUNCT
ejpam-2338	85	21	φψ	φψ	PUNCT
ejpam-2338	85	22	:	:	PUNCT
ejpam-2338	85	23	φ	φ	PROPN
ejpam-2338	85	24	∈a	∈a	PROPN
ejpam-2338	85	25	,	,	PUNCT
ejpam-2338	85	26	ψ	ψ	X
ejpam-2338	85	27	∈b	∈b	NOUN
ejpam-2338	85	28	}	}	PUNCT
ejpam-2338	85	29	.	.	PUNCT
ejpam-2338	86	1	we	we	PRON
ejpam-2338	86	2	may	may	AUX
ejpam-2338	86	3	also	also	ADV
ejpam-2338	86	4	‘	'	PUNCT
ejpam-2338	86	5	invert	invert	VERB
ejpam-2338	86	6	’	'	PUNCT
ejpam-2338	86	7	the	the	DET
ejpam-2338	86	8	partial	partial	ADJ
ejpam-2338	86	9	atlas	atlas	PROPN
ejpam-2338	86	10	a	a	PRON
ejpam-2338	86	11	to	to	PART
ejpam-2338	86	12	obtain	obtain	VERB
ejpam-2338	86	13	a	a	DET
ejpam-2338	86	14	−1	−1	NOUN
ejpam-2338	86	15	=	=	PUNCT
ejpam-2338	86	16	{	{	PUNCT
ejpam-2338	86	17	φ−1	φ−1	PROPN
ejpam-2338	86	18	:	:	PUNCT
ejpam-2338	86	19	φ	φ	PROPN
ejpam-2338	86	20	∈	∈	PROPN
ejpam-2338	86	21	a	a	PRON
ejpam-2338	86	22	}	}	PUNCT
ejpam-2338	86	23	:	:	PUNCT
ejpam-2338	86	24	a	a	DET
ejpam-2338	86	25	partial	partial	ADJ
ejpam-2338	86	26	atlas	atlas	PROPN
ejpam-2338	86	27	y	y	PROPN
ejpam-2338	86	28	→	→	PUNCT
ejpam-2338	86	29	x	x	X
ejpam-2338	86	30	.	.	PUNCT
ejpam-2338	87	1	lawson	lawson	PROPN
ejpam-2338	88	1	[	[	X
ejpam-2338	88	2	51	51	NUM
ejpam-2338	88	3	,	,	PUNCT
ejpam-2338	88	4	pp	pp	ADJ
ejpam-2338	88	5	.	.	PUNCT
ejpam-2338	89	1	10–11	10–11	NUM
ejpam-2338	89	2	]	]	PUNCT
ejpam-2338	89	3	comments	comment	NOUN
ejpam-2338	89	4	:	:	PUNCT
ejpam-2338	89	5	intuitively	intuitively	ADV
ejpam-2338	89	6	,	,	PUNCT
ejpam-2338	89	7	the	the	DET
ejpam-2338	89	8	existence	existence	NOUN
ejpam-2338	89	9	of	of	ADP
ejpam-2338	89	10	an	an	DET
ejpam-2338	89	11	atlas	atlas	NOUN
ejpam-2338	89	12	from	from	ADP
ejpam-2338	89	13	x	x	PROPN
ejpam-2338	89	14	to	to	ADP
ejpam-2338	89	15	y	y	PROPN
ejpam-2338	89	16	means	mean	VERB
ejpam-2338	89	17	that	that	SCONJ
ejpam-2338	89	18	y	y	PROPN
ejpam-2338	89	19	can	can	AUX
ejpam-2338	89	20	be	be	AUX
ejpam-2338	89	21	described	describe	VERB
ejpam-2338	89	22	by	by	ADP
ejpam-2338	89	23	a	a	DET
ejpam-2338	89	24	family	family	NOUN
ejpam-2338	89	25	of	of	ADP
ejpam-2338	89	26	overlapping	overlap	VERB
ejpam-2338	89	27	sets	set	NOUN
ejpam-2338	89	28	each	each	PRON
ejpam-2338	89	29	of	of	ADP
ejpam-2338	89	30	which	which	PRON
ejpam-2338	89	31	looks	look	VERB
ejpam-2338	89	32	like	like	ADP
ejpam-2338	89	33	a	a	DET
ejpam-2338	89	34	piece	piece	NOUN
ejpam-2338	89	35	of	of	ADP
ejpam-2338	89	36	x	x	PROPN
ejpam-2338	89	37	.	.	PUNCT
ejpam-2338	90	1	an	an	DET
ejpam-2338	90	2	atlas	atlas	PROPN
ejpam-2338	90	3	,	,	PUNCT
ejpam-2338	90	4	in	in	ADP
ejpam-2338	90	5	the	the	DET
ejpam-2338	90	6	geographical	geographical	ADJ
ejpam-2338	90	7	sense	sense	NOUN
ejpam-2338	90	8	,	,	PUNCT
ejpam-2338	90	9	provides	provide	VERB
ejpam-2338	90	10	a	a	DET
ejpam-2338	90	11	good	good	ADJ
ejpam-2338	90	12	example	example	NOUN
ejpam-2338	90	13	of	of	ADP
ejpam-2338	90	14	an	an	DET
ejpam-2338	90	15	atlas	atlas	PROPN
ejpam-2338	90	16	in	in	ADP
ejpam-2338	90	17	our	our	PRON
ejpam-2338	90	18	sense	sense	NOUN
ejpam-2338	90	19	from	from	ADP
ejpam-2338	90	20	rn	rn	PROPN
ejpam-2338	90	21	to	to	ADP
ejpam-2338	90	22	a	a	DET
ejpam-2338	90	23	sphere	sphere	NOUN
ejpam-2338	90	24	.	.	PUNCT
ejpam-2338	90	25	.	.	PUNCT
ejpam-2338	90	26	.	.	PUNCT
ejpam-2338	91	1	.	.	PUNCT
ejpam-2338	92	1	the	the	DET
ejpam-2338	92	2	problem	problem	NOUN
ejpam-2338	92	3	now	now	ADV
ejpam-2338	92	4	arises	arise	VERB
ejpam-2338	92	5	of	of	ADP
ejpam-2338	92	6	dealing	deal	VERB
ejpam-2338	92	7	with	with	ADP
ejpam-2338	92	8	the	the	DET
ejpam-2338	92	9	overlaps	overlap	NOUN
ejpam-2338	92	10	between	between	ADP
ejpam-2338	92	11	different	different	ADJ
ejpam-2338	92	12	charts	chart	NOUN
ejpam-2338	92	13	,	,	PUNCT
ejpam-2338	92	14	and	and	CCONJ
ejpam-2338	92	15	it	it	PRON
ejpam-2338	92	16	is	be	AUX
ejpam-2338	92	17	here	here	ADV
ejpam-2338	92	18	that	that	SCONJ
ejpam-2338	92	19	pseudogroups	pseudogroup	NOUN
ejpam-2338	92	20	get	get	VERB
ejpam-2338	92	21	into	into	ADP
ejpam-2338	92	22	the	the	DET
ejpam-2338	92	23	picture	picture	NOUN
ejpam-2338	92	24	.	.	PUNCT
ejpam-2338	93	1	let	let	VERB
ejpam-2338	93	2	φi	φi	ADV
ejpam-2338	93	3	:	:	PUNCT
ejpam-2338	93	4	ui	ui	PROPN
ejpam-2338	93	5	→	→	SYM
ejpam-2338	93	6	vi	vi	PROPN
ejpam-2338	94	1	and	and	CCONJ
ejpam-2338	94	2	φ	φ	NUM
ejpam-2338	94	3	j	j	PROPN
ejpam-2338	94	4	:	:	PUNCT
ejpam-2338	94	5	u	u	PROPN
ejpam-2338	94	6	j	j	PROPN
ejpam-2338	94	7	→	→	SYM
ejpam-2338	94	8	vj	vj	X
ejpam-2338	94	9	be	be	AUX
ejpam-2338	94	10	charts	chart	NOUN
ejpam-2338	94	11	in	in	ADP
ejpam-2338	94	12	a	a	DET
ejpam-2338	94	13	(	(	PUNCT
ejpam-2338	94	14	partial	partial	ADJ
ejpam-2338	94	15	)	)	PUNCT
ejpam-2338	94	16	atlas	atlas	PROPN
ejpam-2338	94	17	x	x	PUNCT
ejpam-2338	94	18	→	→	PUNCT
ejpam-2338	94	19	y	y	PROPN
ejpam-2338	94	20	.	.	PUNCT
ejpam-2338	95	1	we	we	PRON
ejpam-2338	95	2	compose	compose	VERB
ejpam-2338	95	3	φi	φi	ADV
ejpam-2338	95	4	with	with	ADP
ejpam-2338	95	5	φ−1	φ−1	PROPN
ejpam-2338	95	6	j	j	PROPN
ejpam-2338	95	7	to	to	PART
ejpam-2338	95	8	obtain	obtain	VERB
ejpam-2338	95	9	the	the	DET
ejpam-2338	95	10	partial	partial	ADJ
ejpam-2338	95	11	homeomorphism	homeomorphism	PROPN
ejpam-2338	95	12	φiφ	φiφ	PROPN
ejpam-2338	95	13	−1	−1	NOUN
ejpam-2338	95	14	j	j	PROPN
ejpam-2338	95	15	:	:	PUNCT
ejpam-2338	95	16	(	(	PUNCT
ejpam-2338	95	17	vi	vi	X
ejpam-2338	95	18	∩	∩	ADJ
ejpam-2338	95	19	vj)φ	vj)φ	NOUN
ejpam-2338	95	20	−1	−1	NOUN
ejpam-2338	95	21	i	i	PRON
ejpam-2338	95	22	→	→	PUNCT
ejpam-2338	95	23	(	(	PUNCT
ejpam-2338	95	24	vi	vi	X
ejpam-2338	95	25	∩	∩	ADJ
ejpam-2338	95	26	vj)φ	vj)φ	NOUN
ejpam-2338	95	27	−1	−1	NOUN
ejpam-2338	95	28	j	j	PROPN
ejpam-2338	95	29	.	.	PUNCT
ejpam-2338	96	1	lawson	lawson	PROPN
ejpam-2338	96	2	calls	call	VERB
ejpam-2338	96	3	this	this	PRON
ejpam-2338	96	4	a	a	DET
ejpam-2338	96	5	transition	transition	NOUN
ejpam-2338	96	6	function	function	NOUN
ejpam-2338	96	7	of	of	ADP
ejpam-2338	96	8	the	the	DET
ejpam-2338	96	9	atlas	atlas	PROPN
ejpam-2338	96	10	a	a	PROPN
ejpam-2338	96	11	.	.	PUNCT
ejpam-2338	97	1	we	we	PRON
ejpam-2338	97	2	see	see	VERB
ejpam-2338	97	3	that	that	SCONJ
ejpam-2338	97	4	the	the	DET
ejpam-2338	97	5	collection	collection	NOUN
ejpam-2338	97	6	of	of	ADP
ejpam-2338	97	7	all	all	DET
ejpam-2338	97	8	such	such	ADJ
ejpam-2338	97	9	transition	transition	NOUN
ejpam-2338	97	10	functions	function	NOUN
ejpam-2338	97	11	of	of	ADP
ejpam-2338	97	12	a	a	DET
ejpam-2338	97	13	(	(	PUNCT
ejpam-2338	97	14	partial	partial	NOUN
ejpam-2338	97	15	)	)	PUNCT
ejpam-2338	97	16	atlas	atlas	PROPN
ejpam-2338	97	17	a	a	PROPN
ejpam-2338	97	18	is	be	AUX
ejpam-2338	97	19	contained	contain	VERB
ejpam-2338	97	20	in	in	ADP
ejpam-2338	97	21	the	the	DET
ejpam-2338	97	22	pseudogroup	pseudogroup	NOUN
ejpam-2338	97	23	γ(x	γ(x	PROPN
ejpam-2338	97	24	)	)	PUNCT
ejpam-2338	97	25	of	of	ADP
ejpam-2338	97	26	all	all	DET
ejpam-2338	97	27	partial	partial	ADJ
ejpam-2338	97	28	homeomorphisms	homeomorphism	NOUN
ejpam-2338	97	29	between	between	ADP
ejpam-2338	97	30	open	open	ADJ
ejpam-2338	97	31	subsets	subset	NOUN
ejpam-2338	97	32	of	of	ADP
ejpam-2338	97	33	x	x	PRON
ejpam-2338	97	34	,	,	PUNCT
ejpam-2338	97	35	that	that	ADV
ejpam-2338	97	36	is	is	ADV
ejpam-2338	97	37	,	,	PUNCT
ejpam-2338	97	38	aa	aa	PROPN
ejpam-2338	97	39	−1	−1	NOUN
ejpam-2338	97	40	⊆	⊆	NUM
ejpam-2338	97	41	γ(x	γ(x	NOUN
ejpam-2338	97	42	)	)	PUNCT
ejpam-2338	97	43	.	.	PUNCT
ejpam-2338	98	1	in	in	ADP
ejpam-2338	98	2	the	the	DET
ejpam-2338	98	3	specific	specific	ADJ
ejpam-2338	98	4	case	case	NOUN
ejpam-2338	98	5	of	of	ADP
ejpam-2338	98	6	differential	differential	ADJ
ejpam-2338	98	7	geometry	geometry	NOUN
ejpam-2338	98	8	,	,	PUNCT
ejpam-2338	98	9	we	we	PRON
ejpam-2338	98	10	would	would	AUX
ejpam-2338	98	11	take	take	VERB
ejpam-2338	98	12	x	x	INTJ
ejpam-2338	98	13	to	to	ADP
ejpam-2338	98	14	bern	bern	PROPN
ejpam-2338	98	15	and	and	CCONJ
ejpam-2338	98	16	y	y	PROPN
ejpam-2338	98	17	to	to	PART
ejpam-2338	98	18	be	be	AUX
ejpam-2338	98	19	some	some	DET
ejpam-2338	98	20	n	n	ADV
ejpam-2338	98	21	-	-	PUNCT
ejpam-2338	98	22	dimensional	dimensional	ADJ
ejpam-2338	98	23	differentiable	differentiable	ADJ
ejpam-2338	98	24	manifold	manifold	ADJ
ejpam-2338	98	25	m	m	NOUN
ejpam-2338	98	26	.	.	PUNCT
ejpam-2338	99	1	we	we	PRON
ejpam-2338	99	2	would	would	AUX
ejpam-2338	99	3	then	then	ADV
ejpam-2338	99	4	be	be	AUX
ejpam-2338	99	5	able	able	ADJ
ejpam-2338	99	6	to	to	PART
ejpam-2338	99	7	use	use	VERB
ejpam-2338	99	8	pieces	piece	NOUN
ejpam-2338	99	9	of	of	ADP
ejpam-2338	99	10	rn	rn	NOUN
ejpam-2338	99	11	to	to	ADP
ejpam-2338	99	12	‘	'	PUNCT
ejpam-2338	99	13	model	model	NOUN
ejpam-2338	99	14	’	'	PUNCT
ejpam-2338	99	15	pieces	piece	NOUN
ejpam-2338	99	16	of	of	ADP
ejpam-2338	99	17	m	m	PRON
ejpam-2338	99	18	,	,	PUNCT
ejpam-2338	99	19	hence	hence	ADV
ejpam-2338	99	20	the	the	DET
ejpam-2338	99	21	following	follow	VERB
ejpam-2338	99	22	comment	comment	NOUN
ejpam-2338	99	23	from	from	ADP
ejpam-2338	99	24	lawson	lawson	PROPN
ejpam-2338	99	25	[	[	X
ejpam-2338	99	26	51	51	NUM
ejpam-2338	99	27	,	,	PUNCT
ejpam-2338	99	28	p.	p.	NOUN
ejpam-2338	99	29	10	10	NUM
ejpam-2338	99	30	]	]	PUNCT
ejpam-2338	99	31	:	:	PUNCT
ejpam-2338	100	1	[	[	X
ejpam-2338	100	2	a]t	a]t	ADJ
ejpam-2338	100	3	its	its	PRON
ejpam-2338	100	4	simplest	simple	ADJ
ejpam-2338	100	5	,	,	PUNCT
ejpam-2338	100	6	differential	differential	ADJ
ejpam-2338	100	7	geometry	geometry	NOUN
ejpam-2338	100	8	concerns	concern	NOUN
ejpam-2338	100	9	spaces	space	NOUN
ejpam-2338	100	10	which	which	PRON
ejpam-2338	100	11	look	look	VERB
ejpam-2338	100	12	locally	locally	ADV
ejpam-2338	100	13	like	like	ADP
ejpam-2338	100	14	pieces	piece	NOUN
ejpam-2338	100	15	of	of	ADP
ejpam-2338	100	16	rn	rn	PROPN
ejpam-2338	100	17	and	and	CCONJ
ejpam-2338	100	18	pseudogroups	pseudogroup	NOUN
ejpam-2338	100	19	provide	provide	VERB
ejpam-2338	100	20	the	the	DET
ejpam-2338	100	21	glue	glue	NOUN
ejpam-2338	100	22	to	to	PART
ejpam-2338	100	23	hold	hold	VERB
ejpam-2338	100	24	these	these	DET
ejpam-2338	100	25	pieces	piece	NOUN
ejpam-2338	100	26	together	together	ADV
ejpam-2338	100	27	.	.	PUNCT
ejpam-2338	101	1	remaining	remain	VERB
ejpam-2338	101	2	in	in	ADP
ejpam-2338	101	3	the	the	DET
ejpam-2338	101	4	general	general	ADJ
ejpam-2338	101	5	setting	setting	NOUN
ejpam-2338	101	6	,	,	PUNCT
ejpam-2338	101	7	we	we	PRON
ejpam-2338	101	8	now	now	ADV
ejpam-2338	101	9	let	let	VERB
ejpam-2338	101	10	f	f	PRON
ejpam-2338	101	11	,	,	PUNCT
ejpam-2338	101	12	g	g	PROPN
ejpam-2338	101	13	be	be	AUX
ejpam-2338	101	14	arbitrary	arbitrary	ADJ
ejpam-2338	101	15	partial	partial	ADJ
ejpam-2338	101	16	bijections	bijection	NOUN
ejpam-2338	101	17	on	on	ADP
ejpam-2338	101	18	a	a	DET
ejpam-2338	101	19	set	set	NOUN
ejpam-2338	101	20	a.	a.	NOUN
ejpam-2338	101	21	we	we	PRON
ejpam-2338	101	22	attempt	attempt	VERB
ejpam-2338	101	23	to	to	PART
ejpam-2338	101	24	define	define	VERB
ejpam-2338	101	25	a	a	DET
ejpam-2338	101	26	new	new	ADJ
ejpam-2338	101	27	partial	partial	ADJ
ejpam-2338	101	28	bijection	bijection	NOUN
ejpam-2338	101	29	f	f	PROPN
ejpam-2338	101	30	∪	∪	ADP
ejpam-2338	101	31	g	g	PROPN
ejpam-2338	101	32	on	on	ADP
ejpam-2338	101	33	dom	dom	NOUN
ejpam-2338	101	34	f	f	PROPN
ejpam-2338	101	35	∪dom	∪dom	PROPN
ejpam-2338	101	36	g	g	PROPN
ejpam-2338	101	37	⊆	⊆	NUM
ejpam-2338	101	38	a.	a.	NOUN
ejpam-2338	101	39	however	however	ADV
ejpam-2338	101	40	,	,	PUNCT
ejpam-2338	101	41	f	f	PROPN
ejpam-2338	101	42	∪	∪	PROPN
ejpam-2338	101	43	g	g	PROPN
ejpam-2338	101	44	may	may	AUX
ejpam-2338	101	45	fail	fail	VERB
ejpam-2338	101	46	to	to	PART
ejpam-2338	101	47	be	be	AUX
ejpam-2338	101	48	a	a	DET
ejpam-2338	101	49	partial	partial	ADJ
ejpam-2338	101	50	bijection	bijection	NOUN
ejpam-2338	101	51	for	for	ADP
ejpam-2338	101	52	two	two	NUM
ejpam-2338	101	53	reasons	reason	NOUN
ejpam-2338	101	54	:	:	PUNCT
ejpam-2338	101	55	(	(	PUNCT
ejpam-2338	101	56	1	1	X
ejpam-2338	101	57	)	)	PUNCT
ejpam-2338	101	58	if	if	SCONJ
ejpam-2338	101	59	dom	dom	NOUN
ejpam-2338	101	60	f	f	PROPN
ejpam-2338	101	61	∩	∩	PROPN
ejpam-2338	101	62	dom	dom	NOUN
ejpam-2338	101	63	g	g	PROPN
ejpam-2338	101	64	6=	6=	PROPN
ejpam-2338	101	65	;	;	PUNCT
ejpam-2338	101	66	,	,	PUNCT
ejpam-2338	101	67	then	then	ADV
ejpam-2338	101	68	f	f	PROPN
ejpam-2338	101	69	and	and	CCONJ
ejpam-2338	101	70	g	g	PROPN
ejpam-2338	101	71	may	may	AUX
ejpam-2338	101	72	differ	differ	VERB
ejpam-2338	101	73	on	on	ADP
ejpam-2338	101	74	this	this	DET
ejpam-2338	101	75	set	set	NOUN
ejpam-2338	101	76	,	,	PUNCT
ejpam-2338	101	77	in	in	ADP
ejpam-2338	101	78	which	which	DET
ejpam-2338	101	79	case	case	NOUN
ejpam-2338	101	80	‘	'	PUNCT
ejpam-2338	101	81	f	f	X
ejpam-2338	101	82	∪	∪	ADP
ejpam-2338	101	83	g	g	NOUN
ejpam-2338	101	84	’	'	PUNCT
ejpam-2338	101	85	simply	simply	ADV
ejpam-2338	101	86	does	do	AUX
ejpam-2338	101	87	not	not	PART
ejpam-2338	101	88	make	make	VERB
ejpam-2338	101	89	sense	sense	NOUN
ejpam-2338	101	90	;	;	PUNCT
ejpam-2338	101	91	(	(	PUNCT
ejpam-2338	101	92	2	2	X
ejpam-2338	101	93	)	)	PUNCT
ejpam-2338	101	94	f	f	NOUN
ejpam-2338	101	95	may	may	AUX
ejpam-2338	101	96	map	map	VERB
ejpam-2338	101	97	x	x	PUNCT
ejpam-2338	101	98	∈	∈	PROPN
ejpam-2338	101	99	dom	dom	NOUN
ejpam-2338	101	100	f	f	PROPN
ejpam-2338	101	101	\	\	PROPN
ejpam-2338	102	1	(	(	PUNCT
ejpam-2338	102	2	dom	dom	NOUN
ejpam-2338	102	3	f	f	PROPN
ejpam-2338	102	4	∩	∩	PROPN
ejpam-2338	102	5	dom	dom	NOUN
ejpam-2338	102	6	g	g	NOUN
ejpam-2338	102	7	)	)	PUNCT
ejpam-2338	102	8	to	to	ADP
ejpam-2338	102	9	the	the	DET
ejpam-2338	102	10	same	same	ADJ
ejpam-2338	102	11	value	value	NOUN
ejpam-2338	102	12	as	as	ADP
ejpam-2338	102	13	g	g	PROPN
ejpam-2338	102	14	maps	map	NOUN
ejpam-2338	102	15	y	y	PROPN
ejpam-2338	102	16	∈	∈	PROPN
ejpam-2338	102	17	dom	dom	NOUN
ejpam-2338	102	18	g	g	PROPN
ejpam-2338	102	19	\	\	PROPN
ejpam-2338	103	1	(	(	PUNCT
ejpam-2338	103	2	dom	dom	NOUN
ejpam-2338	103	3	f	f	PROPN
ejpam-2338	103	4	∩	∩	PROPN
ejpam-2338	103	5	dom	dom	NOUN
ejpam-2338	103	6	g	g	NOUN
ejpam-2338	103	7	)	)	PUNCT
ejpam-2338	103	8	,	,	PUNCT
ejpam-2338	103	9	in	in	ADP
ejpam-2338	103	10	which	which	DET
ejpam-2338	103	11	case	case	NOUN
ejpam-2338	103	12	f	f	PROPN
ejpam-2338	103	13	∪	∪	VERB
ejpam-2338	103	14	g	g	PROPN
ejpam-2338	103	15	fails	fail	VERB
ejpam-2338	103	16	to	to	PART
ejpam-2338	103	17	be	be	AUX
ejpam-2338	103	18	one	one	NUM
ejpam-2338	103	19	-	-	PUNCT
ejpam-2338	103	20	one	one	NUM
ejpam-2338	103	21	.	.	PUNCT
ejpam-2338	104	1	if	if	SCONJ
ejpam-2338	104	2	,	,	PUNCT
ejpam-2338	104	3	however	however	ADV
ejpam-2338	104	4	,	,	PUNCT
ejpam-2338	104	5	f	f	PROPN
ejpam-2338	104	6	∪	∪	PROPN
ejpam-2338	104	7	g	g	PROPN
ejpam-2338	104	8	does	do	AUX
ejpam-2338	104	9	form	form	VERB
ejpam-2338	104	10	a	a	DET
ejpam-2338	104	11	partial	partial	ADJ
ejpam-2338	104	12	bijection	bijection	NOUN
ejpam-2338	104	13	,	,	PUNCT
ejpam-2338	104	14	we	we	PRON
ejpam-2338	104	15	say	say	VERB
ejpam-2338	104	16	that	that	SCONJ
ejpam-2338	104	17	f	f	PROPN
ejpam-2338	104	18	and	and	CCONJ
ejpam-2338	104	19	g	g	PROPN
ejpam-2338	104	20	are	be	AUX
ejpam-2338	104	21	compatible	compatible	ADJ
ejpam-2338	104	22	,	,	PUNCT
ejpam-2338	104	23	and	and	CCONJ
ejpam-2338	104	24	denote	denote	VERB
ejpam-2338	104	25	the	the	DET
ejpam-2338	104	26	fact	fact	NOUN
ejpam-2338	104	27	by	by	ADP
ejpam-2338	104	28	f	f	PROPN
ejpam-2338	104	29	∼	∼	NOUN
ejpam-2338	104	30	g.	g.	PROPN
ejpam-2338	104	31	a	a	DET
ejpam-2338	104	32	set	set	NOUN
ejpam-2338	104	33	of	of	ADP
ejpam-2338	104	34	partial	partial	ADJ
ejpam-2338	104	35	bijections	bijection	NOUN
ejpam-2338	104	36	is	be	AUX
ejpam-2338	104	37	said	say	VERB
ejpam-2338	104	38	to	to	PART
ejpam-2338	104	39	be	be	AUX
ejpam-2338	104	40	compatible	compatible	ADJ
ejpam-2338	104	41	if	if	SCONJ
ejpam-2338	104	42	its	its	PRON
ejpam-2338	104	43	elements	element	NOUN
ejpam-2338	104	44	christopher	christopher	PROPN
ejpam-2338	104	45	hollings	hollings	PROPN
ejpam-2338	104	46	/	/	SYM
ejpam-2338	104	47	eur	eur	PROPN
ejpam-2338	104	48	.	.	PUNCT
ejpam-2338	105	1	j.	j.	PROPN
ejpam-2338	105	2	pure	pure	PROPN
ejpam-2338	105	3	appl	appl	PROPN
ejpam-2338	105	4	.	.	PROPN
ejpam-2338	105	5	math	math	PROPN
ejpam-2338	105	6	,	,	PUNCT
ejpam-2338	105	7	8	8	NUM
ejpam-2338	105	8	(	(	PUNCT
ejpam-2338	105	9	2015	2015	NUM
ejpam-2338	105	10	)	)	PUNCT
ejpam-2338	105	11	,	,	PUNCT
ejpam-2338	105	12	294	294	NUM
ejpam-2338	105	13	-	-	SYM
ejpam-2338	105	14	323	323	NUM
ejpam-2338	105	15	299	299	NUM
ejpam-2338	105	16	are	be	AUX
ejpam-2338	105	17	pairwise	pairwise	NOUN
ejpam-2338	105	18	compatible	compatible	ADJ
ejpam-2338	105	19	.	.	PUNCT
ejpam-2338	106	1	the	the	DET
ejpam-2338	106	2	compatibility	compatibility	NOUN
ejpam-2338	106	3	relation	relation	NOUN
ejpam-2338	106	4	will	will	AUX
ejpam-2338	106	5	appear	appear	VERB
ejpam-2338	106	6	again	again	ADV
ejpam-2338	106	7	in	in	ADP
ejpam-2338	106	8	section	section	NOUN
ejpam-2338	106	9	5	5	NUM
ejpam-2338	106	10	.	.	PUNCT
ejpam-2338	106	11	returning	return	VERB
ejpam-2338	106	12	to	to	ADP
ejpam-2338	106	13	considerations	consideration	NOUN
ejpam-2338	106	14	of	of	ADP
ejpam-2338	106	15	pseudogroups	pseudogroup	NOUN
ejpam-2338	106	16	,	,	PUNCT
ejpam-2338	106	17	we	we	PRON
ejpam-2338	106	18	define	define	VERB
ejpam-2338	106	19	a	a	DET
ejpam-2338	106	20	complete	complete	ADJ
ejpam-2338	106	21	pseudogroup	pseudogroup	NOUN
ejpam-2338	106	22	on	on	ADP
ejpam-2338	106	23	a	a	DET
ejpam-2338	106	24	set	set	NOUN
ejpam-2338	106	25	x	x	PART
ejpam-2338	106	26	to	to	PART
ejpam-2338	106	27	be	be	AUX
ejpam-2338	106	28	an	an	DET
ejpam-2338	106	29	inverse	inverse	NOUN
ejpam-2338	106	30	subsemigroup	subsemigroup	NOUN
ejpam-2338	106	31	γ′	γ′	PROPN
ejpam-2338	106	32	of	of	ADP
ejpam-2338	106	33	γ(x	γ(x	PROPN
ejpam-2338	106	34	)	)	PUNCT
ejpam-2338	106	35	such	such	ADJ
ejpam-2338	106	36	that	that	SCONJ
ejpam-2338	106	37	the	the	DET
ejpam-2338	106	38	union	union	NOUN
ejpam-2338	106	39	of	of	ADP
ejpam-2338	106	40	every	every	DET
ejpam-2338	106	41	non	non	ADJ
ejpam-2338	106	42	-	-	ADJ
ejpam-2338	106	43	empty	empty	ADJ
ejpam-2338	106	44	compatible	compatible	ADJ
ejpam-2338	106	45	subset	subset	NOUN
ejpam-2338	106	46	of	of	ADP
ejpam-2338	106	47	γ′	γ′	PROPN
ejpam-2338	106	48	belongs	belong	VERB
ejpam-2338	106	49	to	to	ADP
ejpam-2338	106	50	γ′.	γ′.	PROPN
ejpam-2338	106	51	we	we	PRON
ejpam-2338	106	52	are	be	AUX
ejpam-2338	106	53	now	now	ADV
ejpam-2338	106	54	finally	finally	ADV
ejpam-2338	106	55	in	in	ADP
ejpam-2338	106	56	a	a	DET
ejpam-2338	106	57	position	position	NOUN
ejpam-2338	106	58	to	to	PART
ejpam-2338	106	59	define	define	VERB
ejpam-2338	106	60	the	the	DET
ejpam-2338	106	61	notion	notion	NOUN
ejpam-2338	106	62	of	of	ADP
ejpam-2338	106	63	a	a	DET
ejpam-2338	106	64	local	local	ADJ
ejpam-2338	106	65	structure	structure	NOUN
ejpam-2338	106	66	.	.	PUNCT
ejpam-2338	107	1	let	let	VERB
ejpam-2338	107	2	x	x	PRON
ejpam-2338	107	3	and	and	CCONJ
ejpam-2338	107	4	y	y	PROPN
ejpam-2338	107	5	be	be	AUX
ejpam-2338	107	6	topological	topological	ADJ
ejpam-2338	107	7	spaces	space	NOUN
ejpam-2338	107	8	,	,	PUNCT
ejpam-2338	107	9	with	with	ADP
ejpam-2338	107	10	x	x	PUNCT
ejpam-2338	107	11	our	our	PRON
ejpam-2338	107	12	model	model	NOUN
ejpam-2338	107	13	space	space	NOUN
ejpam-2338	107	14	,	,	PUNCT
ejpam-2338	107	15	and	and	CCONJ
ejpam-2338	107	16	let	let	VERB
ejpam-2338	107	17	γ′	γ′	PRON
ejpam-2338	107	18	be	be	AUX
ejpam-2338	107	19	a	a	DET
ejpam-2338	107	20	complete	complete	ADJ
ejpam-2338	107	21	pseudogroup	pseudogroup	NOUN
ejpam-2338	107	22	on	on	ADP
ejpam-2338	107	23	x	x	X
ejpam-2338	107	24	.	.	PUNCT
ejpam-2338	108	1	an	an	DET
ejpam-2338	108	2	atlasa	atlasa	NOUN
ejpam-2338	108	3	(	(	PUNCT
ejpam-2338	108	4	x	x	PROPN
ejpam-2338	108	5	→	→	SYM
ejpam-2338	108	6	y	y	PROPN
ejpam-2338	108	7	)	)	PUNCT
ejpam-2338	108	8	is	be	AUX
ejpam-2338	108	9	compatible	compatible	ADJ
ejpam-2338	108	10	with	with	ADP
ejpam-2338	108	11	γ′	γ′	PROPN
ejpam-2338	108	12	ifaa	ifaa	VERB
ejpam-2338	108	13	−1	−1	NOUN
ejpam-2338	108	14	⊆	⊆	NUM
ejpam-2338	108	15	γ′	γ′	PROPN
ejpam-2338	108	16	,	,	PUNCT
ejpam-2338	108	17	that	that	ADV
ejpam-2338	108	18	is	is	ADV
ejpam-2338	108	19	,	,	PUNCT
ejpam-2338	108	20	we	we	PRON
ejpam-2338	108	21	require	require	VERB
ejpam-2338	108	22	all	all	DET
ejpam-2338	108	23	transition	transition	NOUN
ejpam-2338	108	24	functions	function	NOUN
ejpam-2338	108	25	to	to	PART
ejpam-2338	108	26	belong	belong	VERB
ejpam-2338	108	27	to	to	ADP
ejpam-2338	108	28	γ′.	γ′.	PROPN
ejpam-2338	108	29	leta	leta	PROPN
ejpam-2338	108	30	,	,	PUNCT
ejpam-2338	108	31	b	b	X
ejpam-2338	108	32	be	be	AUX
ejpam-2338	108	33	atlases	atlas	NOUN
ejpam-2338	108	34	x	x	PUNCT
ejpam-2338	108	35	→	→	SYM
ejpam-2338	108	36	y	y	PROPN
ejpam-2338	108	37	which	which	PRON
ejpam-2338	108	38	are	be	AUX
ejpam-2338	108	39	both	both	CCONJ
ejpam-2338	108	40	compatible	compatible	ADJ
ejpam-2338	108	41	with	with	ADP
ejpam-2338	108	42	γ′.	γ′.	PROPN
ejpam-2338	108	43	ifab−1	ifab−1	NOUN
ejpam-2338	108	44	⊆	⊆	NUM
ejpam-2338	108	45	γ′	γ′	NUM
ejpam-2338	108	46	,	,	PUNCT
ejpam-2338	108	47	we	we	PRON
ejpam-2338	108	48	say	say	VERB
ejpam-2338	108	49	thata	thata	PROPN
ejpam-2338	108	50	andb	andb	PROPN
ejpam-2338	108	51	are	be	AUX
ejpam-2338	108	52	compatible	compatible	ADJ
ejpam-2338	108	53	modulo	modulo	NOUN
ejpam-2338	108	54	γ′.	γ′.	AUX
ejpam-2338	108	55	let	let	VERB
ejpam-2338	108	56	γ′(x	γ′(x	X
ejpam-2338	108	57	,	,	PUNCT
ejpam-2338	108	58	y	y	PROPN
ejpam-2338	108	59	)	)	PUNCT
ejpam-2338	108	60	denote	denote	VERB
ejpam-2338	108	61	the	the	DET
ejpam-2338	108	62	collection	collection	NOUN
ejpam-2338	108	63	of	of	ADP
ejpam-2338	108	64	all	all	DET
ejpam-2338	108	65	atlases	atlas	NOUN
ejpam-2338	108	66	x	x	PUNCT
ejpam-2338	108	67	→	→	SYM
ejpam-2338	108	68	y	y	PROPN
ejpam-2338	108	69	which	which	PRON
ejpam-2338	108	70	are	be	AUX
ejpam-2338	108	71	compatible	compatible	ADJ
ejpam-2338	108	72	with	with	ADP
ejpam-2338	108	73	γ′.	γ′.	VERB
ejpam-2338	108	74	it	it	PRON
ejpam-2338	108	75	is	be	AUX
ejpam-2338	108	76	possible	possible	ADJ
ejpam-2338	108	77	to	to	PART
ejpam-2338	108	78	show	show	VERB
ejpam-2338	108	79	that	that	SCONJ
ejpam-2338	108	80	‘	'	PUNCT
ejpam-2338	108	81	compatibility	compatibility	NOUN
ejpam-2338	108	82	modulo	modulo	NOUN
ejpam-2338	108	83	γ′	γ′	NOUN
ejpam-2338	108	84	’	'	PUNCT
ejpam-2338	108	85	is	be	AUX
ejpam-2338	108	86	an	an	DET
ejpam-2338	108	87	equivalence	equivalence	NOUN
ejpam-2338	108	88	relation	relation	NOUN
ejpam-2338	108	89	on	on	ADP
ejpam-2338	108	90	γ′(x	γ′(x	X
ejpam-2338	108	91	,	,	PUNCT
ejpam-2338	108	92	y	y	PROPN
ejpam-2338	108	93	)	)	PUNCT
ejpam-2338	108	94	,	,	PUNCT
ejpam-2338	108	95	and	and	CCONJ
ejpam-2338	108	96	that	that	SCONJ
ejpam-2338	108	97	every	every	DET
ejpam-2338	108	98	equivalence	equivalence	NOUN
ejpam-2338	108	99	class	class	NOUN
ejpam-2338	108	100	has	have	VERB
ejpam-2338	108	101	a	a	DET
ejpam-2338	108	102	maximum	maximum	ADJ
ejpam-2338	108	103	element	element	NOUN
ejpam-2338	108	104	[	[	X
ejpam-2338	108	105	51	51	NUM
ejpam-2338	108	106	,	,	PUNCT
ejpam-2338	108	107	proposition	proposition	NOUN
ejpam-2338	108	108	1.2.2	1.2.2	NUM
ejpam-2338	108	109	]	]	PUNCT
ejpam-2338	108	110	.	.	PUNCT
ejpam-2338	109	1	this	this	DET
ejpam-2338	109	2	maximum	maximum	ADJ
ejpam-2338	109	3	element	element	NOUN
ejpam-2338	109	4	is	be	AUX
ejpam-2338	109	5	called	call	VERB
ejpam-2338	109	6	a	a	DET
ejpam-2338	109	7	complete	complete	ADJ
ejpam-2338	109	8	atlas	atlas	PROPN
ejpam-2338	109	9	compatible	compatible	ADJ
ejpam-2338	109	10	with	with	ADP
ejpam-2338	109	11	γ′	γ′	PRON
ejpam-2338	109	12	and	and	CCONJ
ejpam-2338	109	13	is	be	AUX
ejpam-2338	109	14	said	say	VERB
ejpam-2338	109	15	,	,	PUNCT
ejpam-2338	109	16	finally	finally	ADV
ejpam-2338	109	17	,	,	PUNCT
ejpam-2338	109	18	to	to	PART
ejpam-2338	109	19	define	define	VERB
ejpam-2338	109	20	a	a	DET
ejpam-2338	109	21	γ′-structure	γ′-structure	NUM
ejpam-2338	109	22	(	(	PUNCT
ejpam-2338	109	23	or	or	CCONJ
ejpam-2338	109	24	local	local	ADJ
ejpam-2338	109	25	structure	structure	NOUN
ejpam-2338	109	26	)	)	PUNCT
ejpam-2338	109	27	on	on	ADP
ejpam-2338	109	28	y	y	PROPN
ejpam-2338	109	29	.	.	PUNCT
ejpam-2338	110	1	any	any	DET
ejpam-2338	110	2	atlasa	atlasa	NOUN
ejpam-2338	110	3	(	(	PUNCT
ejpam-2338	110	4	x	x	PROPN
ejpam-2338	110	5	→	→	SYM
ejpam-2338	110	6	y	y	PROPN
ejpam-2338	110	7	)	)	PUNCT
ejpam-2338	110	8	determines	determine	VERB
ejpam-2338	110	9	a	a	DET
ejpam-2338	110	10	local	local	ADJ
ejpam-2338	110	11	structure	structure	NOUN
ejpam-2338	110	12	on	on	ADP
ejpam-2338	110	13	y	y	PROPN
ejpam-2338	110	14	in	in	ADP
ejpam-2338	110	15	this	this	DET
ejpam-2338	110	16	way	way	NOUN
ejpam-2338	110	17	,	,	PUNCT
ejpam-2338	110	18	namely	namely	ADV
ejpam-2338	110	19	,	,	PUNCT
ejpam-2338	110	20	that	that	PRON
ejpam-2338	110	21	determined	determine	VERB
ejpam-2338	110	22	by	by	ADP
ejpam-2338	110	23	the	the	DET
ejpam-2338	110	24	maximum	maximum	ADJ
ejpam-2338	110	25	element	element	NOUN
ejpam-2338	110	26	of	of	ADP
ejpam-2338	110	27	the	the	DET
ejpam-2338	110	28	equivalence	equivalence	NOUN
ejpam-2338	110	29	class	class	NOUN
ejpam-2338	110	30	containinga	containinga	NOUN
ejpam-2338	110	31	.	.	PUNCT
ejpam-2338	111	1	lawson	lawson	PROPN
ejpam-2338	112	1	[	[	X
ejpam-2338	112	2	51	51	NUM
ejpam-2338	112	3	,	,	PUNCT
ejpam-2338	112	4	p.	p.	NOUN
ejpam-2338	112	5	14	14	NUM
ejpam-2338	112	6	]	]	PUNCT
ejpam-2338	112	7	says	say	VERB
ejpam-2338	112	8	of	of	ADP
ejpam-2338	112	9	local	local	ADJ
ejpam-2338	112	10	structures	structure	NOUN
ejpam-2338	112	11	that	that	SCONJ
ejpam-2338	112	12	they	they	PRON
ejpam-2338	112	13	are	be	AUX
ejpam-2338	112	14	analogues	analogue	NOUN
ejpam-2338	112	15	of	of	ADP
ejpam-2338	112	16	the	the	DET
ejpam-2338	112	17	geometries	geometry	NOUN
ejpam-2338	112	18	in	in	ADP
ejpam-2338	112	19	the	the	DET
ejpam-2338	112	20	erlanger	erlanger	NOUN
ejpam-2338	112	21	programm	programm	PROPN
ejpam-2338	112	22	and	and	CCONJ
ejpam-2338	112	23	the	the	DET
ejpam-2338	112	24	pseudogroup	pseudogroup	NOUN
ejpam-2338	112	25	γ′	γ′	PROPN
ejpam-2338	112	26	replaces	replace	VERB
ejpam-2338	112	27	the	the	DET
ejpam-2338	112	28	group	group	NOUN
ejpam-2338	112	29	.	.	PUNCT
ejpam-2338	113	1	lawson	lawson	PROPN
ejpam-2338	113	2	gives	give	VERB
ejpam-2338	113	3	two	two	NUM
ejpam-2338	113	4	examples	example	NOUN
ejpam-2338	113	5	of	of	ADP
ejpam-2338	113	6	local	local	ADJ
ejpam-2338	113	7	structures	structure	NOUN
ejpam-2338	113	8	on	on	ADP
ejpam-2338	113	9	the	the	DET
ejpam-2338	113	10	same	same	ADJ
ejpam-2338	113	11	page	page	NOUN
ejpam-2338	113	12	.	.	PUNCT
ejpam-2338	114	1	it	it	PRON
ejpam-2338	114	2	was	be	AUX
ejpam-2338	114	3	the	the	DET
ejpam-2338	114	4	abstract	abstract	ADJ
ejpam-2338	114	5	study	study	NOUN
ejpam-2338	114	6	of	of	ADP
ejpam-2338	114	7	such	such	ADJ
ejpam-2338	114	8	notions	notion	NOUN
ejpam-2338	114	9	that	that	PRON
ejpam-2338	114	10	led	lead	VERB
ejpam-2338	114	11	ehresmann	ehresmann	NOUN
ejpam-2338	114	12	to	to	ADP
ejpam-2338	114	13	the	the	DET
ejpam-2338	114	14	concept	concept	NOUN
ejpam-2338	114	15	of	of	ADP
ejpam-2338	114	16	an	an	DET
ejpam-2338	114	17	inductive	inductive	ADJ
ejpam-2338	114	18	groupoid	groupoid	NOUN
ejpam-2338	114	19	,	,	PUNCT
ejpam-2338	114	20	beginning	begin	VERB
ejpam-2338	114	21	in	in	ADP
ejpam-2338	114	22	around	around	ADP
ejpam-2338	114	23	1947	1947	NUM
ejpam-2338	114	24	(	(	PUNCT
ejpam-2338	114	25	see	see	VERB
ejpam-2338	114	26	[	[	X
ejpam-2338	114	27	14	14	NUM
ejpam-2338	114	28	]	]	X
ejpam-2338	114	29	,	,	PUNCT
ejpam-2338	114	30	together	together	ADV
ejpam-2338	114	31	with	with	ADP
ejpam-2338	114	32	[	[	X
ejpam-2338	114	33	3–5	3–5	X
ejpam-2338	114	34	]	]	PUNCT
ejpam-2338	114	35	on	on	ADP
ejpam-2338	114	36	the	the	DET
ejpam-2338	114	37	history	history	NOUN
ejpam-2338	114	38	of	of	ADP
ejpam-2338	114	39	groupoids	groupoid	NOUN
ejpam-2338	114	40	)	)	PUNCT
ejpam-2338	114	41	.	.	PUNCT
ejpam-2338	115	1	3.2	3.2	NUM
ejpam-2338	115	2	.	.	PUNCT
ejpam-2338	115	3	inductive	inductive	ADJ
ejpam-2338	115	4	groupoids	groupoid	NOUN
ejpam-2338	116	1	i	i	PRON
ejpam-2338	116	2	have	have	AUX
ejpam-2338	116	3	so	so	ADV
ejpam-2338	116	4	far	far	ADV
ejpam-2338	116	5	made	make	VERB
ejpam-2338	116	6	repeated	repeat	VERB
ejpam-2338	116	7	use	use	NOUN
ejpam-2338	116	8	of	of	ADP
ejpam-2338	116	9	the	the	DET
ejpam-2338	116	10	term	term	NOUN
ejpam-2338	116	11	‘	'	PUNCT
ejpam-2338	116	12	inductive	inductive	ADJ
ejpam-2338	116	13	groupoid	groupoid	NOUN
ejpam-2338	116	14	’	'	PUNCT
ejpam-2338	116	15	without	without	ADP
ejpam-2338	116	16	actually	actually	ADV
ejpam-2338	116	17	defining	define	VERB
ejpam-2338	116	18	it	it	PRON
ejpam-2338	116	19	.	.	PUNCT
ejpam-2338	117	1	in	in	ADP
ejpam-2338	117	2	fact	fact	NOUN
ejpam-2338	117	3	,	,	PUNCT
ejpam-2338	117	4	i	i	PRON
ejpam-2338	117	5	am	be	AUX
ejpam-2338	117	6	not	not	PART
ejpam-2338	117	7	going	go	VERB
ejpam-2338	117	8	to	to	PART
ejpam-2338	117	9	give	give	VERB
ejpam-2338	117	10	a	a	DET
ejpam-2338	117	11	precise	precise	ADJ
ejpam-2338	117	12	definition	definition	NOUN
ejpam-2338	117	13	(	(	PUNCT
ejpam-2338	117	14	since	since	SCONJ
ejpam-2338	117	15	this	this	PRON
ejpam-2338	117	16	may	may	AUX
ejpam-2338	117	17	be	be	AUX
ejpam-2338	117	18	found	find	VERB
ejpam-2338	117	19	elsewhere	elsewhere	ADV
ejpam-2338	117	20	;	;	PUNCT
ejpam-2338	117	21	see	see	VERB
ejpam-2338	117	22	,	,	PUNCT
ejpam-2338	117	23	for	for	ADP
ejpam-2338	117	24	example	example	NOUN
ejpam-2338	117	25	,	,	PUNCT
ejpam-2338	118	1	[	[	X
ejpam-2338	118	2	51	51	NUM
ejpam-2338	118	3	]	]	PUNCT
ejpam-2338	118	4	and	and	CCONJ
ejpam-2338	118	5	[	[	X
ejpam-2338	118	6	40	40	NUM
ejpam-2338	118	7	]	]	NUM
ejpam-2338	118	8	)	)	PUNCT
ejpam-2338	118	9	,	,	PUNCT
ejpam-2338	118	10	but	but	CCONJ
ejpam-2338	118	11	attempt	attempt	VERB
ejpam-2338	118	12	rather	rather	ADV
ejpam-2338	118	13	to	to	PART
ejpam-2338	118	14	give	give	VERB
ejpam-2338	118	15	a	a	DET
ejpam-2338	118	16	more	more	ADV
ejpam-2338	118	17	intuitive	intuitive	ADJ
ejpam-2338	118	18	idea	idea	NOUN
ejpam-2338	118	19	of	of	ADP
ejpam-2338	118	20	what	what	PRON
ejpam-2338	118	21	an	an	DET
ejpam-2338	118	22	inductive	inductive	ADJ
ejpam-2338	118	23	groupoid	groupoid	NOUN
ejpam-2338	118	24	is	be	AUX
ejpam-2338	118	25	.	.	PUNCT
ejpam-2338	119	1	as	as	SCONJ
ejpam-2338	119	2	i	i	PRON
ejpam-2338	119	3	stated	state	VERB
ejpam-2338	119	4	earlier	early	ADV
ejpam-2338	119	5	,	,	PUNCT
ejpam-2338	119	6	an	an	DET
ejpam-2338	119	7	inductive	inductive	ADJ
ejpam-2338	119	8	groupoid	groupoid	NOUN
ejpam-2338	119	9	is	be	AUX
ejpam-2338	119	10	a	a	DET
ejpam-2338	119	11	special	special	ADJ
ejpam-2338	119	12	type	type	NOUN
ejpam-2338	119	13	of	of	ADP
ejpam-2338	119	14	small	small	ADJ
ejpam-2338	119	15	ordered	order	VERB
ejpam-2338	119	16	category	category	NOUN
ejpam-2338	119	17	in	in	ADP
ejpam-2338	119	18	which	which	PRON
ejpam-2338	119	19	all	all	DET
ejpam-2338	119	20	arrows	arrow	NOUN
ejpam-2338	119	21	are	be	AUX
ejpam-2338	119	22	invertible	invertible	ADJ
ejpam-2338	119	23	.	.	PUNCT
ejpam-2338	120	1	let	let	VERB
ejpam-2338	120	2	us	we	PRON
ejpam-2338	120	3	start	start	VERB
ejpam-2338	120	4	with	with	ADP
ejpam-2338	120	5	the	the	DET
ejpam-2338	120	6	notion	notion	NOUN
ejpam-2338	120	7	of	of	ADP
ejpam-2338	120	8	a	a	DET
ejpam-2338	120	9	category	category	NOUN
ejpam-2338	120	10	.	.	PUNCT
ejpam-2338	121	1	there	there	PRON
ejpam-2338	121	2	are	be	VERB
ejpam-2338	121	3	a	a	DET
ejpam-2338	121	4	couple	couple	NOUN
ejpam-2338	121	5	of	of	ADP
ejpam-2338	121	6	different	different	ADJ
ejpam-2338	121	7	ways	way	NOUN
ejpam-2338	121	8	of	of	ADP
ejpam-2338	121	9	viewing	view	VERB
ejpam-2338	121	10	a	a	DET
ejpam-2338	121	11	category	category	NOUN
ejpam-2338	121	12	(	(	PUNCT
ejpam-2338	121	13	contrast	contrast	VERB
ejpam-2338	121	14	those	those	PRON
ejpam-2338	121	15	of	of	ADP
ejpam-2338	121	16	[	[	X
ejpam-2338	121	17	45	45	NUM
ejpam-2338	121	18	]	]	PUNCT
ejpam-2338	121	19	and	and	CCONJ
ejpam-2338	121	20	[	[	X
ejpam-2338	121	21	51	51	NUM
ejpam-2338	121	22	]	]	PUNCT
ejpam-2338	121	23	,	,	PUNCT
ejpam-2338	121	24	for	for	ADP
ejpam-2338	121	25	example	example	NOUN
ejpam-2338	121	26	)	)	PUNCT
ejpam-2338	121	27	,	,	PUNCT
ejpam-2338	121	28	but	but	CCONJ
ejpam-2338	121	29	we	we	PRON
ejpam-2338	121	30	will	will	AUX
ejpam-2338	121	31	adopt	adopt	VERB
ejpam-2338	121	32	a	a	DET
ejpam-2338	121	33	particularly	particularly	ADV
ejpam-2338	121	34	algebraic	algebraic	ADJ
ejpam-2338	121	35	point	point	NOUN
ejpam-2338	121	36	of	of	ADP
ejpam-2338	121	37	view	view	NOUN
ejpam-2338	121	38	,	,	PUNCT
ejpam-2338	121	39	which	which	PRON
ejpam-2338	121	40	also	also	ADV
ejpam-2338	121	41	enables	enable	VERB
ejpam-2338	121	42	us	we	PRON
ejpam-2338	121	43	to	to	PART
ejpam-2338	121	44	view	view	VERB
ejpam-2338	121	45	a	a	DET
ejpam-2338	121	46	category	category	NOUN
ejpam-2338	121	47	as	as	ADP
ejpam-2338	121	48	a	a	DET
ejpam-2338	121	49	directed	direct	VERB
ejpam-2338	121	50	graph	graph	NOUN
ejpam-2338	121	51	.	.	PUNCT
ejpam-2338	122	1	from	from	ADP
ejpam-2338	122	2	this	this	DET
ejpam-2338	122	3	viewpoint	viewpoint	NOUN
ejpam-2338	122	4	,	,	PUNCT
ejpam-2338	122	5	a	a	DET
ejpam-2338	122	6	category	category	NOUN
ejpam-2338	122	7	is	be	AUX
ejpam-2338	122	8	a	a	DET
ejpam-2338	122	9	class	class	NOUN
ejpam-2338	122	10	upon	upon	SCONJ
ejpam-2338	122	11	which	which	PRON
ejpam-2338	122	12	there	there	PRON
ejpam-2338	122	13	is	be	VERB
ejpam-2338	122	14	given	give	VERB
ejpam-2338	122	15	a	a	DET
ejpam-2338	122	16	partially	partially	ADV
ejpam-2338	122	17	-	-	PUNCT
ejpam-2338	122	18	defined	define	VERB
ejpam-2338	122	19	binary	binary	ADJ
ejpam-2338	122	20	operation	operation	NOUN
ejpam-2338	122	21	.	.	PUNCT
ejpam-2338	123	1	a	a	DET
ejpam-2338	123	2	category	category	NOUN
ejpam-2338	123	3	which	which	PRON
ejpam-2338	123	4	is	be	AUX
ejpam-2338	123	5	based	base	VERB
ejpam-2338	123	6	upon	upon	SCONJ
ejpam-2338	123	7	a	a	DET
ejpam-2338	123	8	set	set	NOUN
ejpam-2338	123	9	rather	rather	ADV
ejpam-2338	123	10	than	than	ADP
ejpam-2338	123	11	a	a	DET
ejpam-2338	123	12	class	class	NOUN
ejpam-2338	123	13	is	be	AUX
ejpam-2338	123	14	termed	term	VERB
ejpam-2338	123	15	a	a	DET
ejpam-2338	123	16	small	small	ADJ
ejpam-2338	123	17	category	category	NOUN
ejpam-2338	123	18	.	.	PUNCT
ejpam-2338	124	1	all	all	DET
ejpam-2338	124	2	categories	category	NOUN
ejpam-2338	124	3	considered	consider	VERB
ejpam-2338	124	4	from	from	ADP
ejpam-2338	124	5	here	here	ADV
ejpam-2338	124	6	on	on	ADV
ejpam-2338	124	7	will	will	AUX
ejpam-2338	124	8	be	be	AUX
ejpam-2338	124	9	small	small	ADJ
ejpam-2338	124	10	categories	category	NOUN
ejpam-2338	124	11	.	.	PUNCT
ejpam-2338	125	1	within	within	ADP
ejpam-2338	125	2	a	a	DET
ejpam-2338	125	3	category	category	NOUN
ejpam-2338	125	4	,	,	PUNCT
ejpam-2338	125	5	we	we	PRON
ejpam-2338	125	6	distinguish	distinguish	VERB
ejpam-2338	125	7	two	two	NUM
ejpam-2338	125	8	types	type	NOUN
ejpam-2338	125	9	of	of	ADP
ejpam-2338	125	10	elements	element	NOUN
ejpam-2338	125	11	:	:	PUNCT
ejpam-2338	125	12	identities	identity	NOUN
ejpam-2338	125	13	(	(	PUNCT
ejpam-2338	125	14	or	or	CCONJ
ejpam-2338	125	15	objects	object	VERB
ejpam-2338	125	16	)	)	PUNCT
ejpam-2338	125	17	on	on	ADP
ejpam-2338	125	18	the	the	DET
ejpam-2338	125	19	one	one	NUM
ejpam-2338	125	20	hand	hand	NOUN
ejpam-2338	125	21	,	,	PUNCT
ejpam-2338	125	22	and	and	CCONJ
ejpam-2338	125	23	arrows	arrow	NOUN
ejpam-2338	125	24	(	(	PUNCT
ejpam-2338	125	25	or	or	CCONJ
ejpam-2338	125	26	morphisms	morphism	VERB
ejpam-2338	125	27	)	)	PUNCT
ejpam-2338	125	28	on	on	ADP
ejpam-2338	125	29	the	the	DET
ejpam-2338	125	30	other	other	ADJ
ejpam-2338	125	31	.	.	PUNCT
ejpam-2338	126	1	in	in	ADP
ejpam-2338	126	2	the	the	DET
ejpam-2338	126	3	representation	representation	NOUN
ejpam-2338	126	4	of	of	ADP
ejpam-2338	126	5	a	a	DET
ejpam-2338	126	6	category	category	NOUN
ejpam-2338	126	7	as	as	ADP
ejpam-2338	126	8	a	a	DET
ejpam-2338	126	9	directed	direct	VERB
ejpam-2338	126	10	graph	graph	NOUN
ejpam-2338	126	11	,	,	PUNCT
ejpam-2338	126	12	the	the	DET
ejpam-2338	126	13	identities	identity	NOUN
ejpam-2338	126	14	become	become	VERB
ejpam-2338	126	15	the	the	DET
ejpam-2338	126	16	vertices	vertex	NOUN
ejpam-2338	126	17	,	,	PUNCT
ejpam-2338	126	18	whilst	whilst	SCONJ
ejpam-2338	126	19	the	the	DET
ejpam-2338	126	20	arrows	arrow	NOUN
ejpam-2338	126	21	become	become	VERB
ejpam-2338	126	22	the	the	DET
ejpam-2338	126	23	edges	edge	NOUN
ejpam-2338	126	24	.	.	PUNCT
ejpam-2338	127	1	thus	thus	ADV
ejpam-2338	127	2	,	,	PUNCT
ejpam-2338	127	3	there	there	PRON
ejpam-2338	127	4	are	be	VERB
ejpam-2338	127	5	two	two	NUM
ejpam-2338	127	6	identities	identity	NOUN
ejpam-2338	127	7	associated	associate	VERB
ejpam-2338	127	8	with	with	ADP
ejpam-2338	127	9	each	each	DET
ejpam-2338	127	10	arrow	arrow	NOUN
ejpam-2338	127	11	,	,	PUNCT
ejpam-2338	127	12	namely	namely	ADV
ejpam-2338	127	13	,	,	PUNCT
ejpam-2338	127	14	its	its	PRON
ejpam-2338	127	15	initial	initial	ADJ
ejpam-2338	127	16	and	and	CCONJ
ejpam-2338	127	17	terminal	terminal	ADJ
ejpam-2338	127	18	vertices	vertex	NOUN
ejpam-2338	127	19	.	.	PUNCT
ejpam-2338	128	1	for	for	ADP
ejpam-2338	128	2	an	an	DET
ejpam-2338	128	3	arrow	arrow	NOUN
ejpam-2338	128	4	x	x	NOUN
ejpam-2338	128	5	,	,	PUNCT
ejpam-2338	128	6	the	the	DET
ejpam-2338	128	7	initial	initial	ADJ
ejpam-2338	128	8	vertex	vertex	NOUN
ejpam-2338	128	9	/	/	SYM
ejpam-2338	128	10	identity	identity	NOUN
ejpam-2338	128	11	is	be	AUX
ejpam-2338	128	12	denoted	denote	VERB
ejpam-2338	128	13	by	by	ADP
ejpam-2338	128	14	d(x	d(x	PROPN
ejpam-2338	128	15	)	)	PUNCT
ejpam-2338	128	16	(	(	PUNCT
ejpam-2338	128	17	‘	'	PUNCT
ejpam-2338	128	18	d	d	NOUN
ejpam-2338	128	19	’	'	PUNCT
ejpam-2338	128	20	for	for	ADP
ejpam-2338	128	21	‘	'	PUNCT
ejpam-2338	128	22	domain	domain	NOUN
ejpam-2338	128	23	’	'	PUNCT
ejpam-2338	128	24	)	)	PUNCT
ejpam-2338	128	25	,	,	PUNCT
ejpam-2338	128	26	whilst	whilst	SCONJ
ejpam-2338	128	27	the	the	DET
ejpam-2338	128	28	terminal	terminal	ADJ
ejpam-2338	128	29	vertex	vertex	NOUN
ejpam-2338	128	30	/	/	SYM
ejpam-2338	128	31	identity	identity	NOUN
ejpam-2338	128	32	is	be	AUX
ejpam-2338	128	33	denoted	denote	VERB
ejpam-2338	128	34	by	by	ADP
ejpam-2338	128	35	r(x	r(x	PROPN
ejpam-2338	128	36	)	)	PUNCT
ejpam-2338	128	37	(	(	PUNCT
ejpam-2338	128	38	‘	'	PUNCT
ejpam-2338	128	39	r	r	NOUN
ejpam-2338	128	40	’	'	PUNCT
ejpam-2338	128	41	for	for	ADP
ejpam-2338	128	42	‘	'	PUNCT
ejpam-2338	128	43	range	range	NOUN
ejpam-2338	128	44	’	'	PUNCT
ejpam-2338	128	45	)	)	PUNCT
ejpam-2338	128	46	.	.	PUNCT
ejpam-2338	129	1	we	we	PRON
ejpam-2338	129	2	see	see	VERB
ejpam-2338	129	3	that	that	SCONJ
ejpam-2338	129	4	in	in	ADP
ejpam-2338	129	5	figure	figure	NOUN
ejpam-2338	129	6	1	1	NUM
ejpam-2338	129	7	,	,	PUNCT
ejpam-2338	129	8	f	f	PROPN
ejpam-2338	129	9	=	=	SYM
ejpam-2338	129	10	d(y	d(y	PROPN
ejpam-2338	129	11	)	)	PUNCT
ejpam-2338	129	12	,	,	PUNCT
ejpam-2338	129	13	g	g	NOUN
ejpam-2338	129	14	=	=	PUNCT
ejpam-2338	129	15	r(y	r(y	VERB
ejpam-2338	129	16	)	)	PUNCT
ejpam-2338	129	17	,	,	PUNCT
ejpam-2338	129	18	and	and	CCONJ
ejpam-2338	129	19	so	so	ADV
ejpam-2338	129	20	on	on	ADV
ejpam-2338	129	21	.	.	PUNCT
ejpam-2338	130	1	we	we	PRON
ejpam-2338	130	2	note	note	VERB
ejpam-2338	130	3	that	that	SCONJ
ejpam-2338	130	4	the	the	DET
ejpam-2338	130	5	composition	composition	NOUN
ejpam-2338	130	6	of	of	ADP
ejpam-2338	130	7	two	two	NUM
ejpam-2338	130	8	arrows	arrow	NOUN
ejpam-2338	130	9	is	be	AUX
ejpam-2338	130	10	defined	define	VERB
ejpam-2338	130	11	only	only	ADV
ejpam-2338	130	12	when	when	SCONJ
ejpam-2338	130	13	the	the	DET
ejpam-2338	130	14	range	range	NOUN
ejpam-2338	130	15	of	of	ADP
ejpam-2338	130	16	the	the	DET
ejpam-2338	130	17	first	first	ADJ
ejpam-2338	130	18	coincides	coincide	NOUN
ejpam-2338	130	19	with	with	ADP
ejpam-2338	130	20	the	the	DET
ejpam-2338	130	21	domain	domain	NOUN
ejpam-2338	130	22	of	of	ADP
ejpam-2338	130	23	the	the	DET
ejpam-2338	130	24	second	second	ADJ
ejpam-2338	130	25	(	(	PUNCT
ejpam-2338	130	26	cf	cf	NOUN
ejpam-2338	130	27	.	.	PUNCT
ejpam-2338	130	28	definition	definition	NOUN
ejpam-2338	130	29	1	1	NUM
ejpam-2338	130	30	)	)	PUNCT
ejpam-2338	130	31	.	.	PUNCT
ejpam-2338	131	1	thus	thus	ADV
ejpam-2338	131	2	,	,	PUNCT
ejpam-2338	131	3	for	for	ADP
ejpam-2338	131	4	example	example	NOUN
ejpam-2338	131	5	,	,	PUNCT
ejpam-2338	131	6	in	in	ADP
ejpam-2338	131	7	christopher	christopher	PROPN
ejpam-2338	131	8	hollings	hollings	PROPN
ejpam-2338	131	9	/	/	SYM
ejpam-2338	131	10	eur	eur	PROPN
ejpam-2338	131	11	.	.	PUNCT
ejpam-2338	132	1	j.	j.	PROPN
ejpam-2338	132	2	pure	pure	PROPN
ejpam-2338	132	3	appl	appl	PROPN
ejpam-2338	132	4	.	.	PROPN
ejpam-2338	132	5	math	math	PROPN
ejpam-2338	132	6	,	,	PUNCT
ejpam-2338	132	7	8	8	NUM
ejpam-2338	132	8	(	(	PUNCT
ejpam-2338	132	9	2015	2015	NUM
ejpam-2338	132	10	)	)	PUNCT
ejpam-2338	132	11	,	,	PUNCT
ejpam-2338	132	12	294	294	NUM
ejpam-2338	132	13	-	-	SYM
ejpam-2338	132	14	323	323	NUM
ejpam-2338	132	15	300	300	NUM
ejpam-2338	132	16	figure	figure	NOUN
ejpam-2338	132	17	1	1	NUM
ejpam-2338	132	18	,	,	PUNCT
ejpam-2338	132	19	we	we	PRON
ejpam-2338	132	20	may	may	AUX
ejpam-2338	132	21	compose	compose	VERB
ejpam-2338	132	22	y	y	PROPN
ejpam-2338	132	23	with	with	ADP
ejpam-2338	132	24	z	z	PROPN
ejpam-2338	132	25	and	and	CCONJ
ejpam-2338	132	26	z	z	PROPN
ejpam-2338	132	27	with	with	ADP
ejpam-2338	132	28	u	u	NOUN
ejpam-2338	132	29	,	,	PUNCT
ejpam-2338	132	30	but	but	CCONJ
ejpam-2338	132	31	we	we	PRON
ejpam-2338	132	32	may	may	AUX
ejpam-2338	132	33	not	not	PART
ejpam-2338	132	34	compose	compose	VERB
ejpam-2338	132	35	y	y	PROPN
ejpam-2338	132	36	with	with	ADP
ejpam-2338	132	37	u.	u.	NOUN
ejpam-2338	132	38	the	the	DET
ejpam-2338	132	39	pictorial	pictorial	ADJ
ejpam-2338	132	40	representation	representation	NOUN
ejpam-2338	132	41	of	of	ADP
ejpam-2338	132	42	a	a	DET
ejpam-2338	132	43	category	category	NOUN
ejpam-2338	132	44	breaks	break	VERB
ejpam-2338	132	45	down	down	ADP
ejpam-2338	132	46	slightly	slightly	ADV
ejpam-2338	132	47	when	when	SCONJ
ejpam-2338	132	48	we	we	PRON
ejpam-2338	132	49	consider	consider	VERB
ejpam-2338	132	50	the	the	DET
ejpam-2338	132	51	composition	composition	NOUN
ejpam-2338	132	52	of	of	ADP
ejpam-2338	132	53	identities	identity	NOUN
ejpam-2338	132	54	.	.	PUNCT
ejpam-2338	133	1	that	that	SCONJ
ejpam-2338	133	2	we	we	PRON
ejpam-2338	133	3	may	may	AUX
ejpam-2338	133	4	not	not	PART
ejpam-2338	133	5	compose	compose	VERB
ejpam-2338	133	6	distinct	distinct	ADJ
ejpam-2338	133	7	identities	identity	NOUN
ejpam-2338	133	8	is	be	AUX
ejpam-2338	133	9	reasonably	reasonably	ADV
ejpam-2338	133	10	clear	clear	ADJ
ejpam-2338	133	11	from	from	ADP
ejpam-2338	133	12	the	the	DET
ejpam-2338	133	13	diagram	diagram	NOUN
ejpam-2338	133	14	,	,	PUNCT
ejpam-2338	133	15	but	but	CCONJ
ejpam-2338	133	16	what	what	PRON
ejpam-2338	133	17	is	be	AUX
ejpam-2338	133	18	not	not	PART
ejpam-2338	133	19	obvious	obvious	ADJ
ejpam-2338	133	20	is	be	AUX
ejpam-2338	133	21	that	that	SCONJ
ejpam-2338	133	22	we	we	PRON
ejpam-2338	133	23	may	may	AUX
ejpam-2338	133	24	compose	compose	VERB
ejpam-2338	133	25	any	any	DET
ejpam-2338	133	26	identity	identity	NOUN
ejpam-2338	133	27	j	j	NOUN
ejpam-2338	133	28	with	with	ADP
ejpam-2338	133	29	itself	itself	PRON
ejpam-2338	133	30	,	,	PUNCT
ejpam-2338	133	31	and	and	CCONJ
ejpam-2338	133	32	that	that	SCONJ
ejpam-2338	133	33	j	j	PROPN
ejpam-2338	133	34	·	·	PUNCT
ejpam-2338	133	35	j	j	PROPN
ejpam-2338	133	36	=	=	PUNCT
ejpam-2338	133	37	j.	j.	PROPN
ejpam-2338	133	38	furthermore	furthermore	ADV
ejpam-2338	133	39	,	,	PUNCT
ejpam-2338	133	40	we	we	PRON
ejpam-2338	133	41	may	may	AUX
ejpam-2338	133	42	compose	compose	VERB
ejpam-2338	133	43	any	any	DET
ejpam-2338	133	44	arrow	arrow	NOUN
ejpam-2338	133	45	with	with	ADP
ejpam-2338	133	46	its	its	PRON
ejpam-2338	133	47	domain	domain	NOUN
ejpam-2338	133	48	on	on	ADP
ejpam-2338	133	49	the	the	DET
ejpam-2338	133	50	left	left	NOUN
ejpam-2338	133	51	,	,	PUNCT
ejpam-2338	133	52	and	and	CCONJ
ejpam-2338	133	53	with	with	ADP
ejpam-2338	133	54	its	its	PRON
ejpam-2338	133	55	range	range	NOUN
ejpam-2338	133	56	on	on	ADP
ejpam-2338	133	57	the	the	DET
ejpam-2338	133	58	right	right	NOUN
ejpam-2338	133	59	;	;	PUNCT
ejpam-2338	133	60	the	the	DET
ejpam-2338	133	61	domain	domain	NOUN
ejpam-2338	133	62	serves	serve	VERB
ejpam-2338	133	63	as	as	ADP
ejpam-2338	133	64	a	a	DET
ejpam-2338	133	65	left	left	ADJ
ejpam-2338	133	66	identity	identity	NOUN
ejpam-2338	133	67	for	for	ADP
ejpam-2338	133	68	the	the	DET
ejpam-2338	133	69	arrow	arrow	NOUN
ejpam-2338	133	70	,	,	PUNCT
ejpam-2338	133	71	and	and	CCONJ
ejpam-2338	133	72	the	the	DET
ejpam-2338	133	73	range	range	NOUN
ejpam-2338	133	74	as	as	ADP
ejpam-2338	133	75	a	a	DET
ejpam-2338	133	76	right	right	ADJ
ejpam-2338	133	77	identity	identity	NOUN
ejpam-2338	133	78	.	.	PUNCT
ejpam-2338	134	1	thus	thus	ADV
ejpam-2338	134	2	,	,	PUNCT
ejpam-2338	134	3	again	again	ADV
ejpam-2338	134	4	referring	refer	VERB
ejpam-2338	134	5	to	to	PART
ejpam-2338	134	6	figure	figure	VERB
ejpam-2338	134	7	1	1	NUM
ejpam-2338	134	8	,	,	PUNCT
ejpam-2338	134	9	we	we	PRON
ejpam-2338	134	10	have	have	VERB
ejpam-2338	134	11	that	that	SCONJ
ejpam-2338	134	12	the	the	DET
ejpam-2338	134	13	composition	composition	NOUN
ejpam-2338	134	14	f	f	X
ejpam-2338	134	15	·	·	PUNCT
ejpam-2338	134	16	y	y	PROPN
ejpam-2338	134	17	exists	exist	VERB
ejpam-2338	134	18	and	and	CCONJ
ejpam-2338	134	19	is	be	AUX
ejpam-2338	134	20	equal	equal	ADJ
ejpam-2338	134	21	to	to	ADP
ejpam-2338	134	22	y	y	PRON
ejpam-2338	134	23	;	;	PUNCT
ejpam-2338	134	24	similarly	similarly	ADV
ejpam-2338	134	25	,	,	PUNCT
ejpam-2338	134	26	we	we	PRON
ejpam-2338	134	27	may	may	AUX
ejpam-2338	134	28	compose	compose	VERB
ejpam-2338	134	29	y	y	PROPN
ejpam-2338	134	30	with	with	ADP
ejpam-2338	134	31	g	g	PROPN
ejpam-2338	134	32	,	,	PUNCT
ejpam-2338	134	33	with	with	ADP
ejpam-2338	134	34	y	y	PROPN
ejpam-2338	134	35	as	as	ADP
ejpam-2338	134	36	the	the	DET
ejpam-2338	134	37	result	result	NOUN
ejpam-2338	134	38	,	,	PUNCT
ejpam-2338	134	39	and	and	CCONJ
ejpam-2338	134	40	so	so	ADV
ejpam-2338	134	41	on	on	ADV
ejpam-2338	134	42	—	—	PUNCT
ejpam-2338	134	43	by	by	ADP
ejpam-2338	134	44	the	the	DET
ejpam-2338	134	45	above	above	ADJ
ejpam-2338	134	46	comments	comment	NOUN
ejpam-2338	134	47	,	,	PUNCT
ejpam-2338	134	48	e	e	NOUN
ejpam-2338	134	49	·	·	PUNCT
ejpam-2338	134	50	e	e	NOUN
ejpam-2338	134	51	exists	exist	VERB
ejpam-2338	134	52	and	and	CCONJ
ejpam-2338	134	53	is	be	AUX
ejpam-2338	134	54	equal	equal	ADJ
ejpam-2338	134	55	to	to	ADP
ejpam-2338	134	56	e.	e.	PROPN
ejpam-2338	134	57	furthermore	furthermore	ADV
ejpam-2338	134	58	,	,	PUNCT
ejpam-2338	134	59	one	one	NUM
ejpam-2338	134	60	of	of	ADP
ejpam-2338	134	61	the	the	DET
ejpam-2338	134	62	features	feature	NOUN
ejpam-2338	134	63	of	of	ADP
ejpam-2338	134	64	composition	composition	NOUN
ejpam-2338	134	65	in	in	ADP
ejpam-2338	134	66	a	a	DET
ejpam-2338	134	67	category	category	NOUN
ejpam-2338	134	68	is	be	AUX
ejpam-2338	134	69	that	that	SCONJ
ejpam-2338	134	70	it	it	PRON
ejpam-2338	134	71	must	must	AUX
ejpam-2338	134	72	be	be	AUX
ejpam-2338	134	73	associative	associative	ADJ
ejpam-2338	134	74	wherever	wherever	SCONJ
ejpam-2338	134	75	it	it	PRON
ejpam-2338	134	76	is	be	AUX
ejpam-2338	134	77	defined	define	VERB
ejpam-2338	134	78	,	,	PUNCT
ejpam-2338	134	79	such	such	ADJ
ejpam-2338	134	80	as	as	ADP
ejpam-2338	134	81	in	in	ADP
ejpam-2338	134	82	the	the	DET
ejpam-2338	134	83	case	case	NOUN
ejpam-2338	134	84	of	of	ADP
ejpam-2338	134	85	the	the	DET
ejpam-2338	134	86	composition	composition	NOUN
ejpam-2338	134	87	y	y	PROPN
ejpam-2338	134	88	·	·	SYM
ejpam-2338	134	89	z	z	X
ejpam-2338	134	90	·	·	PUNCT
ejpam-2338	134	91	u	u	NOUN
ejpam-2338	134	92	in	in	ADP
ejpam-2338	134	93	figure	figure	NOUN
ejpam-2338	134	94	1	1	NUM
ejpam-2338	134	95	;	;	PUNCT
ejpam-2338	134	96	it	it	PRON
ejpam-2338	134	97	is	be	AUX
ejpam-2338	134	98	also	also	ADV
ejpam-2338	134	99	clear	clear	ADJ
ejpam-2338	134	100	from	from	ADP
ejpam-2338	134	101	the	the	DET
ejpam-2338	134	102	diagram	diagram	NOUN
ejpam-2338	134	103	that	that	SCONJ
ejpam-2338	134	104	a	a	DET
ejpam-2338	134	105	composition	composition	NOUN
ejpam-2338	134	106	a	a	PRON
ejpam-2338	134	107	·	·	SYM
ejpam-2338	134	108	b	b	X
ejpam-2338	134	109	·	·	PUNCT
ejpam-2338	134	110	c	c	NOUN
ejpam-2338	134	111	is	be	AUX
ejpam-2338	134	112	defined	define	VERB
ejpam-2338	134	113	precisely	precisely	ADV
ejpam-2338	134	114	when	when	SCONJ
ejpam-2338	134	115	the	the	DET
ejpam-2338	134	116	compositions	composition	NOUN
ejpam-2338	134	117	a	a	DET
ejpam-2338	134	118	·	·	SYM
ejpam-2338	134	119	b	b	NOUN
ejpam-2338	134	120	and	and	CCONJ
ejpam-2338	134	121	b	b	PROPN
ejpam-2338	134	122	·	·	PUNCT
ejpam-2338	134	123	c	c	NOUN
ejpam-2338	134	124	are	be	AUX
ejpam-2338	134	125	defined	define	VERB
ejpam-2338	134	126	.	.	PUNCT
ejpam-2338	135	1	•e	•e	VERB
ejpam-2338	135	2	•	•	NUM
ejpam-2338	135	3	•	•	NOUN
ejpam-2338	135	4	•	•	NUM
ejpam-2338	135	5	•f	•f	NOUN
ejpam-2338	135	6	g	g	INTJ
ejpam-2338	135	7	hi	hi	INTJ
ejpam-2338	136	1	y	y	PROPN
ejpam-2338	136	2	z	z	PROPN
ejpam-2338	136	3	u	u	PROPN
ejpam-2338	136	4	v	v	NUM
ejpam-2338	136	5	figure	figure	NOUN
ejpam-2338	136	6	1	1	NUM
ejpam-2338	136	7	:	:	PUNCT
ejpam-2338	136	8	part	part	NOUN
ejpam-2338	136	9	of	of	ADP
ejpam-2338	136	10	a	a	DET
ejpam-2338	136	11	small	small	ADJ
ejpam-2338	136	12	category	category	NOUN
ejpam-2338	136	13	represented	represent	VERB
ejpam-2338	136	14	as	as	ADP
ejpam-2338	136	15	a	a	DET
ejpam-2338	136	16	directed	direct	VERB
ejpam-2338	136	17	graph	graph	NOUN
ejpam-2338	136	18	,	,	PUNCT
ejpam-2338	136	19	featuring	feature	VERB
ejpam-2338	136	20	identities	identity	NOUN
ejpam-2338	136	21	e	e	NOUN
ejpam-2338	136	22	,	,	PUNCT
ejpam-2338	136	23	f	f	PROPN
ejpam-2338	136	24	,	,	PUNCT
ejpam-2338	136	25	g	g	PROPN
ejpam-2338	136	26	,	,	PUNCT
ejpam-2338	136	27	h	h	NOUN
ejpam-2338	136	28	,	,	PUNCT
ejpam-2338	136	29	i	i	PRON
ejpam-2338	136	30	and	and	CCONJ
ejpam-2338	136	31	arrows	arrow	NOUN
ejpam-2338	136	32	y	y	PROPN
ejpam-2338	136	33	,	,	PUNCT
ejpam-2338	136	34	z	z	PROPN
ejpam-2338	136	35	,	,	PUNCT
ejpam-2338	136	36	u	u	NOUN
ejpam-2338	136	37	,	,	PUNCT
ejpam-2338	136	38	v	v	ADP
ejpam-2338	136	39	now	now	ADV
ejpam-2338	136	40	that	that	SCONJ
ejpam-2338	136	41	we	we	PRON
ejpam-2338	136	42	have	have	VERB
ejpam-2338	136	43	an	an	DET
ejpam-2338	136	44	intuitive	intuitive	ADJ
ejpam-2338	136	45	idea	idea	NOUN
ejpam-2338	136	46	of	of	ADP
ejpam-2338	136	47	what	what	PRON
ejpam-2338	136	48	constitutes	constitute	VERB
ejpam-2338	136	49	a	a	DET
ejpam-2338	136	50	category	category	NOUN
ejpam-2338	136	51	,	,	PUNCT
ejpam-2338	136	52	it	it	PRON
ejpam-2338	136	53	is	be	AUX
ejpam-2338	136	54	an	an	DET
ejpam-2338	136	55	easy	easy	ADJ
ejpam-2338	136	56	next	next	ADJ
ejpam-2338	136	57	step	step	NOUN
ejpam-2338	136	58	to	to	PART
ejpam-2338	136	59	grasp	grasp	VERB
ejpam-2338	136	60	the	the	DET
ejpam-2338	136	61	notion	notion	NOUN
ejpam-2338	136	62	of	of	ADP
ejpam-2338	136	63	a	a	DET
ejpam-2338	136	64	groupoid	groupoid	NOUN
ejpam-2338	136	65	,	,	PUNCT
ejpam-2338	136	66	for	for	ADP
ejpam-2338	136	67	a	a	DET
ejpam-2338	136	68	groupoid	groupoid	NOUN
ejpam-2338	136	69	is	be	AUX
ejpam-2338	136	70	simply	simply	ADV
ejpam-2338	136	71	a	a	DET
ejpam-2338	136	72	small	small	ADJ
ejpam-2338	136	73	category	category	NOUN
ejpam-2338	136	74	in	in	ADP
ejpam-2338	136	75	which	which	PRON
ejpam-2338	136	76	all	all	DET
ejpam-2338	136	77	arrows	arrow	NOUN
ejpam-2338	136	78	are	be	AUX
ejpam-2338	136	79	invertible	invertible	ADJ
ejpam-2338	136	80	.	.	PUNCT
ejpam-2338	137	1	more	more	ADV
ejpam-2338	137	2	precisely	precisely	ADV
ejpam-2338	137	3	,	,	PUNCT
ejpam-2338	137	4	for	for	ADP
ejpam-2338	137	5	any	any	DET
ejpam-2338	137	6	arrow	arrow	NOUN
ejpam-2338	137	7	a	a	PRON
ejpam-2338	137	8	with	with	ADP
ejpam-2338	137	9	domain	domain	NOUN
ejpam-2338	137	10	d	d	NOUN
ejpam-2338	137	11	and	and	CCONJ
ejpam-2338	137	12	range	range	NOUN
ejpam-2338	137	13	r	r	NOUN
ejpam-2338	137	14	,	,	PUNCT
ejpam-2338	137	15	there	there	PRON
ejpam-2338	137	16	must	must	AUX
ejpam-2338	137	17	exist	exist	VERB
ejpam-2338	137	18	an	an	DET
ejpam-2338	137	19	arrow	arrow	NOUN
ejpam-2338	137	20	a−1	a−1	PROPN
ejpam-2338	137	21	with	with	ADP
ejpam-2338	137	22	domain	domain	NOUN
ejpam-2338	137	23	r	r	NOUN
ejpam-2338	137	24	and	and	CCONJ
ejpam-2338	137	25	range	range	NOUN
ejpam-2338	137	26	d	d	X
ejpam-2338	137	27	such	such	ADJ
ejpam-2338	137	28	that	that	SCONJ
ejpam-2338	137	29	the	the	DET
ejpam-2338	137	30	compositions	composition	NOUN
ejpam-2338	137	31	a	a	DET
ejpam-2338	137	32	·	·	PUNCT
ejpam-2338	137	33	a−1	a−1	PROPN
ejpam-2338	137	34	and	and	CCONJ
ejpam-2338	137	35	a−1	a−1	PROPN
ejpam-2338	137	36	·	·	PUNCT
ejpam-2338	137	37	a	a	PRON
ejpam-2338	137	38	are	be	AUX
ejpam-2338	137	39	defined	define	VERB
ejpam-2338	137	40	,	,	PUNCT
ejpam-2338	137	41	and	and	CCONJ
ejpam-2338	137	42	are	be	AUX
ejpam-2338	137	43	equal	equal	ADJ
ejpam-2338	137	44	to	to	ADP
ejpam-2338	137	45	d	d	PROPN
ejpam-2338	137	46	and	and	CCONJ
ejpam-2338	137	47	r	r	NOUN
ejpam-2338	137	48	,	,	PUNCT
ejpam-2338	137	49	respectively.∗	respectively.∗	PUNCT
ejpam-2338	137	50	we	we	PRON
ejpam-2338	137	51	see	see	VERB
ejpam-2338	137	52	that	that	SCONJ
ejpam-2338	137	53	in	in	ADP
ejpam-2338	137	54	figure	figure	NOUN
ejpam-2338	137	55	1	1	NUM
ejpam-2338	137	56	,	,	PUNCT
ejpam-2338	137	57	u	u	NOUN
ejpam-2338	137	58	and	and	CCONJ
ejpam-2338	137	59	v	v	NOUN
ejpam-2338	137	60	may	may	AUX
ejpam-2338	137	61	be	be	AUX
ejpam-2338	137	62	inverses	inverse	NOUN
ejpam-2338	137	63	for	for	ADP
ejpam-2338	137	64	each	each	DET
ejpam-2338	137	65	other	other	ADJ
ejpam-2338	137	66	(	(	PUNCT
ejpam-2338	137	67	we	we	PRON
ejpam-2338	137	68	require	require	VERB
ejpam-2338	137	69	additional	additional	ADJ
ejpam-2338	137	70	information	information	NOUN
ejpam-2338	137	71	in	in	ADP
ejpam-2338	137	72	order	order	NOUN
ejpam-2338	137	73	to	to	PART
ejpam-2338	137	74	say	say	VERB
ejpam-2338	137	75	whether	whether	SCONJ
ejpam-2338	137	76	or	or	CCONJ
ejpam-2338	137	77	not	not	PART
ejpam-2338	137	78	they	they	PRON
ejpam-2338	137	79	are	be	AUX
ejpam-2338	137	80	in	in	ADP
ejpam-2338	137	81	fact	fact	NOUN
ejpam-2338	137	82	inverses	inverse	NOUN
ejpam-2338	137	83	)	)	PUNCT
ejpam-2338	137	84	,	,	PUNCT
ejpam-2338	137	85	but	but	CCONJ
ejpam-2338	137	86	y	y	PROPN
ejpam-2338	137	87	and	and	CCONJ
ejpam-2338	137	88	z	z	PROPN
ejpam-2338	137	89	do	do	AUX
ejpam-2338	137	90	not	not	PART
ejpam-2338	137	91	have	have	VERB
ejpam-2338	137	92	inverses	inverse	NOUN
ejpam-2338	137	93	;	;	PUNCT
ejpam-2338	137	94	e	e	NOUN
ejpam-2338	137	95	and	and	CCONJ
ejpam-2338	137	96	all	all	DET
ejpam-2338	137	97	the	the	DET
ejpam-2338	137	98	other	other	ADJ
ejpam-2338	137	99	identities	identity	NOUN
ejpam-2338	137	100	are	be	AUX
ejpam-2338	137	101	self	self	NOUN
ejpam-2338	137	102	-	-	PUNCT
ejpam-2338	137	103	inverse	inverse	NOUN
ejpam-2338	137	104	.	.	PUNCT
ejpam-2338	138	1	an	an	DET
ejpam-2338	138	2	inductive	inductive	ADJ
ejpam-2338	138	3	groupoid	groupoid	NOUN
ejpam-2338	138	4	is	be	AUX
ejpam-2338	138	5	a	a	DET
ejpam-2338	138	6	special	special	ADJ
ejpam-2338	138	7	type	type	NOUN
ejpam-2338	138	8	of	of	ADP
ejpam-2338	138	9	ordered	order	VERB
ejpam-2338	138	10	groupoid	groupoid	PROPN
ejpam-2338	138	11	,	,	PUNCT
ejpam-2338	138	12	that	that	ADV
ejpam-2338	138	13	is	is	ADV
ejpam-2338	138	14	,	,	PUNCT
ejpam-2338	138	15	a	a	DET
ejpam-2338	138	16	groupoid	groupoid	NOUN
ejpam-2338	138	17	whose	whose	DET
ejpam-2338	138	18	underlying	underlying	ADJ
ejpam-2338	138	19	set	set	NOUN
ejpam-2338	138	20	is	be	AUX
ejpam-2338	138	21	endowed	endow	VERB
ejpam-2338	138	22	with	with	ADP
ejpam-2338	138	23	a	a	DET
ejpam-2338	138	24	partial	partial	ADJ
ejpam-2338	138	25	ordering	ordering	NOUN
ejpam-2338	138	26	which	which	PRON
ejpam-2338	138	27	satisfies	satisfy	VERB
ejpam-2338	138	28	certain	certain	ADJ
ejpam-2338	138	29	conditions	condition	NOUN
ejpam-2338	138	30	.	.	PUNCT
ejpam-2338	139	1	for	for	ADP
ejpam-2338	139	2	example	example	NOUN
ejpam-2338	139	3	,	,	PUNCT
ejpam-2338	139	4	∗note	∗note	INTJ
ejpam-2338	139	5	that	that	SCONJ
ejpam-2338	139	6	we	we	PRON
ejpam-2338	139	7	differ	differ	VERB
ejpam-2338	139	8	here	here	ADV
ejpam-2338	139	9	from	from	ADP
ejpam-2338	139	10	lawson	lawson	PROPN
ejpam-2338	140	1	[	[	X
ejpam-2338	140	2	51	51	NUM
ejpam-2338	140	3	]	]	X
ejpam-2338	140	4	:	:	PUNCT
ejpam-2338	140	5	the	the	DET
ejpam-2338	140	6	fact	fact	NOUN
ejpam-2338	140	7	that	that	SCONJ
ejpam-2338	140	8	he	he	PRON
ejpam-2338	140	9	composes	compose	VERB
ejpam-2338	140	10	functions	function	NOUN
ejpam-2338	140	11	from	from	ADP
ejpam-2338	140	12	right	right	ADJ
ejpam-2338	140	13	to	to	ADP
ejpam-2338	140	14	left	left	ADJ
ejpam-2338	140	15	means	mean	VERB
ejpam-2338	140	16	that	that	SCONJ
ejpam-2338	140	17	,	,	PUNCT
ejpam-2338	140	18	for	for	ADP
ejpam-2338	140	19	him	he	PRON
ejpam-2338	140	20	,	,	PUNCT
ejpam-2338	140	21	d(a	d(a	PROPN
ejpam-2338	140	22	)	)	PUNCT
ejpam-2338	140	23	=	=	SYM
ejpam-2338	140	24	a−1	a−1	PROPN
ejpam-2338	140	25	·	·	PUNCT
ejpam-2338	140	26	a	a	PRON
ejpam-2338	140	27	and	and	CCONJ
ejpam-2338	140	28	r(a	r(a	ADJ
ejpam-2338	140	29	)	)	PUNCT
ejpam-2338	140	30	=	=	SYM
ejpam-2338	140	31	a	a	PRON
ejpam-2338	140	32	·	·	PUNCT
ejpam-2338	140	33	a−1	a−1	PROPN
ejpam-2338	140	34	.	.	PUNCT
ejpam-2338	141	1	christopher	christopher	PROPN
ejpam-2338	141	2	hollings	hollings	PROPN
ejpam-2338	141	3	/	/	SYM
ejpam-2338	141	4	eur	eur	PROPN
ejpam-2338	141	5	.	.	PUNCT
ejpam-2338	142	1	j.	j.	PROPN
ejpam-2338	142	2	pure	pure	PROPN
ejpam-2338	142	3	appl	appl	PROPN
ejpam-2338	142	4	.	.	PROPN
ejpam-2338	142	5	math	math	PROPN
ejpam-2338	142	6	,	,	PUNCT
ejpam-2338	142	7	8	8	NUM
ejpam-2338	142	8	(	(	PUNCT
ejpam-2338	142	9	2015	2015	NUM
ejpam-2338	142	10	)	)	PUNCT
ejpam-2338	142	11	,	,	PUNCT
ejpam-2338	142	12	294	294	NUM
ejpam-2338	142	13	-	-	SYM
ejpam-2338	142	14	323	323	NUM
ejpam-2338	142	15	301	301	NUM
ejpam-2338	142	16	we	we	PRON
ejpam-2338	142	17	demand	demand	VERB
ejpam-2338	142	18	that	that	SCONJ
ejpam-2338	142	19	the	the	DET
ejpam-2338	142	20	ordering	ordering	NOUN
ejpam-2338	142	21	be	be	AUX
ejpam-2338	142	22	compatible	compatible	ADJ
ejpam-2338	142	23	with	with	ADP
ejpam-2338	142	24	composition	composition	NOUN
ejpam-2338	142	25	wherever	wherever	SCONJ
ejpam-2338	142	26	the	the	DET
ejpam-2338	142	27	latter	latter	ADJ
ejpam-2338	142	28	is	be	AUX
ejpam-2338	142	29	defined	define	VERB
ejpam-2338	142	30	.	.	PUNCT
ejpam-2338	143	1	another	another	DET
ejpam-2338	143	2	condition	condition	NOUN
ejpam-2338	143	3	on	on	ADP
ejpam-2338	143	4	the	the	DET
ejpam-2338	143	5	ordering	ordering	NOUN
ejpam-2338	143	6	deals	deal	NOUN
ejpam-2338	143	7	,	,	PUNCT
ejpam-2338	143	8	intuitively	intuitively	ADV
ejpam-2338	143	9	,	,	PUNCT
ejpam-2338	143	10	with	with	ADP
ejpam-2338	143	11	‘	'	PUNCT
ejpam-2338	143	12	restriction	restriction	NOUN
ejpam-2338	143	13	’	'	PUNCT
ejpam-2338	143	14	of	of	ADP
ejpam-2338	143	15	domains	domain	NOUN
ejpam-2338	143	16	.	.	PUNCT
ejpam-2338	143	17	suppose	suppose	VERB
ejpam-2338	143	18	that	that	SCONJ
ejpam-2338	143	19	a	a	PRON
ejpam-2338	143	20	is	be	AUX
ejpam-2338	143	21	an	an	DET
ejpam-2338	143	22	arrow	arrow	NOUN
ejpam-2338	143	23	in	in	ADP
ejpam-2338	143	24	a	a	DET
ejpam-2338	143	25	category	category	NOUN
ejpam-2338	143	26	and	and	CCONJ
ejpam-2338	143	27	that	that	SCONJ
ejpam-2338	143	28	a	a	PRON
ejpam-2338	143	29	has	have	VERB
ejpam-2338	143	30	domain	domain	NOUN
ejpam-2338	143	31	d.	d.	PROPN
ejpam-2338	143	32	suppose	suppose	VERB
ejpam-2338	143	33	also	also	ADV
ejpam-2338	143	34	that	that	SCONJ
ejpam-2338	143	35	e	e	NOUN
ejpam-2338	143	36	is	be	AUX
ejpam-2338	143	37	some	some	DET
ejpam-2338	143	38	other	other	ADJ
ejpam-2338	143	39	identity	identity	NOUN
ejpam-2338	143	40	in	in	ADP
ejpam-2338	143	41	the	the	DET
ejpam-2338	143	42	category	category	NOUN
ejpam-2338	143	43	,	,	PUNCT
ejpam-2338	143	44	with	with	ADP
ejpam-2338	143	45	e	e	PROPN
ejpam-2338	143	46	≤	≤	PROPN
ejpam-2338	143	47	d.	d.	PROPN
ejpam-2338	143	48	then	then	ADV
ejpam-2338	143	49	there	there	PRON
ejpam-2338	143	50	exists	exist	VERB
ejpam-2338	143	51	a	a	DET
ejpam-2338	143	52	unique	unique	ADJ
ejpam-2338	143	53	arrow	arrow	NOUN
ejpam-2338	143	54	b	b	PROPN
ejpam-2338	143	55	≤	≤	NOUN
ejpam-2338	143	56	a	a	PRON
ejpam-2338	143	57	whose	whose	DET
ejpam-2338	143	58	domain	domain	NOUN
ejpam-2338	143	59	is	be	AUX
ejpam-2338	143	60	e	e	NOUN
ejpam-2338	143	61	;	;	PUNCT
ejpam-2338	143	62	such	such	DET
ejpam-2338	143	63	an	an	DET
ejpam-2338	143	64	arrow	arrow	NOUN
ejpam-2338	143	65	b	b	NOUN
ejpam-2338	143	66	is	be	AUX
ejpam-2338	143	67	usually	usually	ADV
ejpam-2338	143	68	denoted	denote	VERB
ejpam-2338	143	69	by	by	ADP
ejpam-2338	143	70	e|a	e|a	PROPN
ejpam-2338	143	71	(	(	PUNCT
ejpam-2338	143	72	see	see	VERB
ejpam-2338	143	73	figure	figure	NOUN
ejpam-2338	143	74	2	2	NUM
ejpam-2338	143	75	)	)	PUNCT
ejpam-2338	143	76	.	.	PUNCT
ejpam-2338	144	1	≤	≤	NUM
ejpam-2338	144	2	•	•	NUM
ejpam-2338	144	3	•	•	NUM
ejpam-2338	144	4	•	•	NOUN
ejpam-2338	144	5	•	•	NOUN
ejpam-2338	144	6	d	d	X
ejpam-2338	144	7	e	e	PROPN
ejpam-2338	144	8	a	a	DET
ejpam-2338	144	9	e|a	e|a	X
ejpam-2338	144	10	figure	figure	NOUN
ejpam-2338	144	11	2	2	NUM
ejpam-2338	144	12	:	:	PUNCT
ejpam-2338	144	13	illustration	illustration	NOUN
ejpam-2338	144	14	of	of	ADP
ejpam-2338	144	15	the	the	DET
ejpam-2338	144	16	‘	'	PUNCT
ejpam-2338	144	17	restriction	restriction	NOUN
ejpam-2338	144	18	’	'	PUNCT
ejpam-2338	144	19	of	of	ADP
ejpam-2338	144	20	domains	domain	NOUN
ejpam-2338	144	21	in	in	ADP
ejpam-2338	144	22	an	an	DET
ejpam-2338	144	23	ordered	order	VERB
ejpam-2338	144	24	category	category	NOUN
ejpam-2338	144	25	other	other	ADJ
ejpam-2338	144	26	similarly	similarly	ADV
ejpam-2338	144	27	natural	natural	ADJ
ejpam-2338	144	28	conditions	condition	NOUN
ejpam-2338	144	29	are	be	AUX
ejpam-2338	144	30	also	also	ADV
ejpam-2338	144	31	required	require	VERB
ejpam-2338	144	32	for	for	ADP
ejpam-2338	144	33	an	an	DET
ejpam-2338	144	34	ordered	order	VERB
ejpam-2338	144	35	groupoid	groupoid	NOUN
ejpam-2338	144	36	.	.	PUNCT
ejpam-2338	145	1	an	an	DET
ejpam-2338	145	2	inductive	inductive	ADJ
ejpam-2338	145	3	groupoid	groupoid	NOUN
ejpam-2338	145	4	is	be	AUX
ejpam-2338	145	5	an	an	DET
ejpam-2338	145	6	ordered	order	VERB
ejpam-2338	145	7	groupoid	groupoid	NOUN
ejpam-2338	145	8	in	in	ADP
ejpam-2338	145	9	which	which	PRON
ejpam-2338	145	10	every	every	DET
ejpam-2338	145	11	pair	pair	NOUN
ejpam-2338	145	12	of	of	ADP
ejpam-2338	145	13	identities	identity	NOUN
ejpam-2338	145	14	has	have	VERB
ejpam-2338	145	15	a	a	DET
ejpam-2338	145	16	greatest	greatest	ADV
ejpam-2338	145	17	lower	lower	ADV
ejpam-2338	145	18	bound	bind	VERB
ejpam-2338	145	19	(	(	PUNCT
ejpam-2338	145	20	which	which	PRON
ejpam-2338	145	21	is	be	AUX
ejpam-2338	145	22	also	also	ADV
ejpam-2338	145	23	an	an	DET
ejpam-2338	145	24	identity	identity	NOUN
ejpam-2338	145	25	)	)	PUNCT
ejpam-2338	145	26	.	.	PUNCT
ejpam-2338	146	1	the	the	DET
ejpam-2338	146	2	intuitive	intuitive	ADJ
ejpam-2338	146	3	definition	definition	NOUN
ejpam-2338	146	4	that	that	PRON
ejpam-2338	146	5	we	we	PRON
ejpam-2338	146	6	have	have	AUX
ejpam-2338	146	7	given	give	VERB
ejpam-2338	146	8	for	for	ADP
ejpam-2338	146	9	an	an	DET
ejpam-2338	146	10	inductive	inductive	ADJ
ejpam-2338	146	11	groupoid	groupoid	NOUN
ejpam-2338	146	12	may	may	AUX
ejpam-2338	146	13	seem	seem	VERB
ejpam-2338	146	14	a	a	DET
ejpam-2338	146	15	little	little	ADJ
ejpam-2338	146	16	contrived	contrived	ADJ
ejpam-2338	146	17	upon	upon	SCONJ
ejpam-2338	146	18	first	first	ADJ
ejpam-2338	146	19	glance	glance	NOUN
ejpam-2338	146	20	.	.	PUNCT
ejpam-2338	147	1	however	however	ADV
ejpam-2338	147	2	,	,	PUNCT
ejpam-2338	147	3	when	when	SCONJ
ejpam-2338	147	4	we	we	PRON
ejpam-2338	147	5	remember	remember	VERB
ejpam-2338	147	6	where	where	SCONJ
ejpam-2338	147	7	this	this	DET
ejpam-2338	147	8	idea	idea	NOUN
ejpam-2338	147	9	comes	come	VERB
ejpam-2338	147	10	from	from	ADP
ejpam-2338	147	11	,	,	PUNCT
ejpam-2338	147	12	it	it	PRON
ejpam-2338	147	13	begins	begin	VERB
ejpam-2338	147	14	to	to	PART
ejpam-2338	147	15	seem	seem	VERB
ejpam-2338	147	16	much	much	ADV
ejpam-2338	147	17	more	more	ADV
ejpam-2338	147	18	natural	natural	ADJ
ejpam-2338	147	19	.	.	PUNCT
ejpam-2338	148	1	recall	recall	PROPN
ejpam-2338	148	2	lawson	lawson	PROPN
ejpam-2338	148	3	’s	’s	PART
ejpam-2338	148	4	observation	observation	NOUN
ejpam-2338	148	5	that	that	PRON
ejpam-2338	148	6	inductive	inductive	ADJ
ejpam-2338	148	7	groupoids	groupoid	NOUN
ejpam-2338	148	8	emerged	emerge	VERB
ejpam-2338	148	9	as	as	ADP
ejpam-2338	148	10	a	a	DET
ejpam-2338	148	11	result	result	NOUN
ejpam-2338	148	12	of	of	ADP
ejpam-2338	148	13	ehresmann	ehresmann	PROPN
ejpam-2338	148	14	’s	’s	PART
ejpam-2338	148	15	axiomatisation	axiomatisation	NOUN
ejpam-2338	148	16	of	of	ADP
ejpam-2338	148	17	(	(	PUNCT
ejpam-2338	148	18	ix	ix	ADV
ejpam-2338	148	19	,	,	PUNCT
ejpam-2338	148	20	·	·	PUNCT
ejpam-2338	148	21	,	,	PUNCT
ejpam-2338	148	22	⊆	⊆	NUM
ejpam-2338	148	23	)	)	PUNCT
ejpam-2338	148	24	.	.	PUNCT
ejpam-2338	149	1	it	it	PRON
ejpam-2338	149	2	is	be	AUX
ejpam-2338	149	3	not	not	PART
ejpam-2338	149	4	too	too	ADV
ejpam-2338	149	5	difficult	difficult	ADJ
ejpam-2338	149	6	to	to	PART
ejpam-2338	149	7	see	see	VERB
ejpam-2338	149	8	that	that	PRON
ejpam-2338	149	9	(	(	PUNCT
ejpam-2338	149	10	ix	ix	INTJ
ejpam-2338	149	11	,	,	PUNCT
ejpam-2338	149	12	·	·	PUNCT
ejpam-2338	149	13	,	,	PUNCT
ejpam-2338	149	14	⊆	⊆	NUM
ejpam-2338	149	15	)	)	PUNCT
ejpam-2338	149	16	does	do	AUX
ejpam-2338	149	17	indeed	indeed	ADV
ejpam-2338	149	18	form	form	VERB
ejpam-2338	149	19	an	an	DET
ejpam-2338	149	20	inductive	inductive	ADJ
ejpam-2338	149	21	groupoid	groupoid	NOUN
ejpam-2338	149	22	,	,	PUNCT
ejpam-2338	149	23	often	often	ADV
ejpam-2338	149	24	denoted	denote	VERB
ejpam-2338	149	25	by	by	ADP
ejpam-2338	149	26	gx	gx	PROPN
ejpam-2338	149	27	and	and	CCONJ
ejpam-2338	149	28	termed	term	VERB
ejpam-2338	149	29	the	the	DET
ejpam-2338	149	30	symmetric	symmetric	ADJ
ejpam-2338	149	31	groupoid	groupoid	NOUN
ejpam-2338	149	32	on	on	ADP
ejpam-2338	149	33	x	x	X
ejpam-2338	149	34	—	—	PUNCT
ejpam-2338	149	35	see	see	VERB
ejpam-2338	149	36	[	[	X
ejpam-2338	149	37	22	22	NUM
ejpam-2338	149	38	]	]	PUNCT
ejpam-2338	149	39	,	,	PUNCT
ejpam-2338	149	40	for	for	ADP
ejpam-2338	149	41	example	example	NOUN
ejpam-2338	149	42	.	.	PUNCT
ejpam-2338	150	1	the	the	DET
ejpam-2338	150	2	identities	identity	NOUN
ejpam-2338	150	3	in	in	ADP
ejpam-2338	150	4	gx	gx	PROPN
ejpam-2338	150	5	are	be	AUX
ejpam-2338	150	6	none	none	NOUN
ejpam-2338	150	7	other	other	ADJ
ejpam-2338	150	8	than	than	ADP
ejpam-2338	150	9	the	the	DET
ejpam-2338	150	10	partial	partial	ADJ
ejpam-2338	150	11	identity	identity	NOUN
ejpam-2338	150	12	transformations	transformation	NOUN
ejpam-2338	150	13	ia	ia	PROPN
ejpam-2338	150	14	,	,	PUNCT
ejpam-2338	150	15	for	for	ADP
ejpam-2338	150	16	a⊆	a⊆	PROPN
ejpam-2338	150	17	x	x	X
ejpam-2338	150	18	.	.	PUNCT
ejpam-2338	151	1	thus	thus	ADV
ejpam-2338	151	2	,	,	PUNCT
ejpam-2338	151	3	the	the	DET
ejpam-2338	151	4	fact	fact	NOUN
ejpam-2338	151	5	that	that	SCONJ
ejpam-2338	151	6	the	the	DET
ejpam-2338	151	7	composition	composition	NOUN
ejpam-2338	151	8	α·β	α·β	NOUN
ejpam-2338	151	9	is	be	AUX
ejpam-2338	151	10	defined	define	VERB
ejpam-2338	151	11	only	only	ADV
ejpam-2338	151	12	if	if	SCONJ
ejpam-2338	151	13	imα	imα	NOUN
ejpam-2338	151	14	=	=	SYM
ejpam-2338	151	15	domβ	domβ	PROPN
ejpam-2338	151	16	corresponds	correspond	VERB
ejpam-2338	151	17	to	to	ADP
ejpam-2338	151	18	the	the	DET
ejpam-2338	151	19	abstract	abstract	ADJ
ejpam-2338	151	20	condition	condition	NOUN
ejpam-2338	151	21	r(α	r(α	PROPN
ejpam-2338	151	22	)	)	PUNCT
ejpam-2338	151	23	=	=	SYM
ejpam-2338	151	24	d(β	d(β	PROPN
ejpam-2338	151	25	)	)	PUNCT
ejpam-2338	151	26	,	,	PUNCT
ejpam-2338	151	27	where	where	SCONJ
ejpam-2338	151	28	r(α	r(α	PROPN
ejpam-2338	151	29	)	)	PUNCT
ejpam-2338	151	30	=	=	SYM
ejpam-2338	151	31	iimα	iimα	PROPN
ejpam-2338	151	32	and	and	CCONJ
ejpam-2338	151	33	d(β	d(β	PROPN
ejpam-2338	151	34	)	)	PUNCT
ejpam-2338	151	35	=	=	SYM
ejpam-2338	151	36	idomβ	idomβ	NOUN
ejpam-2338	151	37	.	.	PUNCT
ejpam-2338	152	1	moreover	moreover	ADV
ejpam-2338	152	2	,	,	PUNCT
ejpam-2338	152	3	restriction	restriction	NOUN
ejpam-2338	152	4	of	of	ADP
ejpam-2338	152	5	mappings	mapping	NOUN
ejpam-2338	152	6	can	can	AUX
ejpam-2338	152	7	be	be	AUX
ejpam-2338	152	8	shown	show	VERB
ejpam-2338	152	9	to	to	PART
ejpam-2338	152	10	satisfy	satisfy	VERB
ejpam-2338	152	11	the	the	DET
ejpam-2338	152	12	various	various	ADJ
ejpam-2338	152	13	properties	property	NOUN
ejpam-2338	152	14	required	require	VERB
ejpam-2338	152	15	of	of	ADP
ejpam-2338	152	16	the	the	DET
ejpam-2338	152	17	partial	partial	ADJ
ejpam-2338	152	18	ordering	ordering	NOUN
ejpam-2338	152	19	in	in	ADP
ejpam-2338	152	20	the	the	DET
ejpam-2338	152	21	abstract	abstract	ADJ
ejpam-2338	152	22	definition	definition	NOUN
ejpam-2338	152	23	.	.	PUNCT
ejpam-2338	153	1	the	the	DET
ejpam-2338	153	2	‘	'	PUNCT
ejpam-2338	153	3	inductive	inductive	ADJ
ejpam-2338	153	4	’	'	PUNCT
ejpam-2338	153	5	condition	condition	NOUN
ejpam-2338	153	6	holds	hold	VERB
ejpam-2338	153	7	because	because	SCONJ
ejpam-2338	153	8	ia∩b	ia∩b	PROPN
ejpam-2338	153	9	is	be	AUX
ejpam-2338	153	10	the	the	DET
ejpam-2338	153	11	greatest	greatest	ADV
ejpam-2338	153	12	lower	low	ADJ
ejpam-2338	153	13	bound	bind	VERB
ejpam-2338	153	14	of	of	ADP
ejpam-2338	153	15	ia	ia	PROPN
ejpam-2338	153	16	and	and	CCONJ
ejpam-2338	153	17	ib	ib	PROPN
ejpam-2338	153	18	.	.	PUNCT
ejpam-2338	154	1	under	under	ADP
ejpam-2338	154	2	the	the	DET
ejpam-2338	154	3	ehresmann	ehresmann	PROPN
ejpam-2338	154	4	–	–	PUNCT
ejpam-2338	154	5	schein	schein	PROPN
ejpam-2338	154	6	–	–	PUNCT
ejpam-2338	154	7	nambooripad	nambooripad	NOUN
ejpam-2338	154	8	theorem	theorem	NOUN
ejpam-2338	154	9	(	(	PUNCT
ejpam-2338	154	10	see	see	VERB
ejpam-2338	154	11	below	below	ADV
ejpam-2338	154	12	)	)	PUNCT
ejpam-2338	154	13	,	,	PUNCT
ejpam-2338	154	14	gx	gx	PROPN
ejpam-2338	154	15	corresponds	correspond	VERB
ejpam-2338	154	16	to	to	ADP
ejpam-2338	154	17	the	the	DET
ejpam-2338	154	18	symmetric	symmetric	ADJ
ejpam-2338	154	19	inverse	inverse	NOUN
ejpam-2338	154	20	semigroup	semigroup	NOUN
ejpam-2338	154	21	ix	ix	ADV
ejpam-2338	154	22	.	.	PUNCT
ejpam-2338	155	1	the	the	DET
ejpam-2338	155	2	development	development	NOUN
ejpam-2338	155	3	of	of	ADP
ejpam-2338	155	4	this	this	DET
ejpam-2338	155	5	abstract	abstract	ADJ
ejpam-2338	155	6	,	,	PUNCT
ejpam-2338	155	7	category	category	NOUN
ejpam-2338	155	8	-	-	PUNCT
ejpam-2338	155	9	theoretic	theoretic	NOUN
ejpam-2338	155	10	description	description	NOUN
ejpam-2338	155	11	of	of	ADP
ejpam-2338	155	12	partial	partial	ADJ
ejpam-2338	155	13	bijections	bijection	NOUN
ejpam-2338	155	14	of	of	ADP
ejpam-2338	155	15	a	a	DET
ejpam-2338	155	16	set	set	NOUN
ejpam-2338	155	17	has	have	VERB
ejpam-2338	155	18	its	its	PRON
ejpam-2338	155	19	origins	origin	NOUN
ejpam-2338	155	20	in	in	ADP
ejpam-2338	155	21	a	a	DET
ejpam-2338	155	22	1957	1957	NUM
ejpam-2338	155	23	paper	paper	NOUN
ejpam-2338	155	24	by	by	ADP
ejpam-2338	155	25	ehresmann	ehresmann	PROPN
ejpam-2338	156	1	[	[	X
ejpam-2338	156	2	13	13	NUM
ejpam-2338	156	3	]	]	PUNCT
ejpam-2338	156	4	,	,	PUNCT
ejpam-2338	156	5	in	in	ADP
ejpam-2338	156	6	which	which	PRON
ejpam-2338	156	7	the	the	DET
ejpam-2338	156	8	notion	notion	NOUN
ejpam-2338	156	9	of	of	ADP
ejpam-2338	156	10	a	a	DET
ejpam-2338	156	11	local	local	ADJ
ejpam-2338	156	12	structure	structure	NOUN
ejpam-2338	156	13	was	be	AUX
ejpam-2338	156	14	treated	treat	VERB
ejpam-2338	156	15	rigorously	rigorously	ADV
ejpam-2338	156	16	:	:	PUNCT
ejpam-2338	156	17	schein	schein	PROPN
ejpam-2338	157	1	[	[	X
ejpam-2338	157	2	90	90	NUM
ejpam-2338	157	3	,	,	PUNCT
ejpam-2338	157	4	p.	p.	NOUN
ejpam-2338	157	5	194	194	NUM
ejpam-2338	158	1	]	]	PUNCT
ejpam-2338	158	2	comments	comment	NOUN
ejpam-2338	158	3	that	that	PRON
ejpam-2338	158	4	christopher	christopher	PROPN
ejpam-2338	158	5	hollings	hollings	PROPN
ejpam-2338	158	6	/	/	SYM
ejpam-2338	158	7	eur	eur	PROPN
ejpam-2338	158	8	.	.	PUNCT
ejpam-2338	159	1	j.	j.	PROPN
ejpam-2338	159	2	pure	pure	PROPN
ejpam-2338	159	3	appl	appl	PROPN
ejpam-2338	159	4	.	.	PROPN
ejpam-2338	159	5	math	math	PROPN
ejpam-2338	159	6	,	,	PUNCT
ejpam-2338	159	7	8	8	NUM
ejpam-2338	159	8	(	(	PUNCT
ejpam-2338	159	9	2015	2015	NUM
ejpam-2338	159	10	)	)	PUNCT
ejpam-2338	159	11	,	,	PUNCT
ejpam-2338	159	12	294	294	NUM
ejpam-2338	159	13	-	-	SYM
ejpam-2338	159	14	323	323	NUM
ejpam-2338	159	15	302	302	NUM
ejpam-2338	159	16	ehresmann	ehresmann	NOUN
ejpam-2338	159	17	was	be	AUX
ejpam-2338	159	18	probably	probably	ADV
ejpam-2338	159	19	the	the	DET
ejpam-2338	159	20	first	first	ADJ
ejpam-2338	159	21	to	to	PART
ejpam-2338	159	22	recognize	recognize	VERB
ejpam-2338	159	23	the	the	DET
ejpam-2338	159	24	importance	importance	NOUN
ejpam-2338	159	25	of	of	ADP
ejpam-2338	159	26	category	category	NOUN
ejpam-2338	159	27	theory	theory	NOUN
ejpam-2338	159	28	for	for	ADP
ejpam-2338	159	29	differential	differential	ADJ
ejpam-2338	159	30	geometry	geometry	NOUN
ejpam-2338	159	31	.	.	PUNCT
ejpam-2338	160	1	however	however	ADV
ejpam-2338	160	2	,	,	PUNCT
ejpam-2338	160	3	ehresmann	ehresmann	PROPN
ejpam-2338	160	4	’s	’s	PART
ejpam-2338	160	5	‘	'	PUNCT
ejpam-2338	160	6	inductive	inductive	ADJ
ejpam-2338	160	7	’	'	PUNCT
ejpam-2338	160	8	condition	condition	NOUN
ejpam-2338	160	9	was	be	AUX
ejpam-2338	160	10	slightly	slightly	ADV
ejpam-2338	160	11	more	more	ADV
ejpam-2338	160	12	stringent	stringent	ADJ
ejpam-2338	160	13	than	than	ADP
ejpam-2338	160	14	that	that	PRON
ejpam-2338	160	15	given	give	VERB
ejpam-2338	160	16	above	above	ADV
ejpam-2338	160	17	(	(	PUNCT
ejpam-2338	160	18	see	see	VERB
ejpam-2338	160	19	[	[	X
ejpam-2338	160	20	51	51	NUM
ejpam-2338	160	21	,	,	PUNCT
ejpam-2338	160	22	§	§	NOUN
ejpam-2338	160	23	§	§	PROPN
ejpam-2338	160	24	1.6	1.6	NUM
ejpam-2338	160	25	and	and	CCONJ
ejpam-2338	160	26	4.4	4.4	NUM
ejpam-2338	160	27	]	]	PUNCT
ejpam-2338	160	28	for	for	ADP
ejpam-2338	160	29	more	more	ADJ
ejpam-2338	160	30	details	detail	NOUN
ejpam-2338	160	31	on	on	ADP
ejpam-2338	160	32	ehresmann	ehresmann	PROPN
ejpam-2338	160	33	’s	’s	PART
ejpam-2338	160	34	publications	publication	NOUN
ejpam-2338	160	35	)	)	PUNCT
ejpam-2338	160	36	.	.	PUNCT
ejpam-2338	161	1	nevertheless	nevertheless	ADV
ejpam-2338	161	2	,	,	PUNCT
ejpam-2338	161	3	ehresmann	ehresmann	PROPN
ejpam-2338	161	4	achieved	achieve	VERB
ejpam-2338	161	5	an	an	DET
ejpam-2338	161	6	axiomatisation	axiomatisation	NOUN
ejpam-2338	161	7	of	of	ADP
ejpam-2338	161	8	a	a	DET
ejpam-2338	161	9	pseudogroup	pseudogroup	NOUN
ejpam-2338	161	10	of	of	ADP
ejpam-2338	161	11	local	local	ADJ
ejpam-2338	161	12	transformations	transformation	NOUN
ejpam-2338	161	13	and	and	CCONJ
ejpam-2338	161	14	it	it	PRON
ejpam-2338	161	15	is	be	AUX
ejpam-2338	161	16	in	in	ADP
ejpam-2338	161	17	this	this	DET
ejpam-2338	161	18	abstract	abstract	ADJ
ejpam-2338	161	19	form	form	NOUN
ejpam-2338	161	20	that	that	PRON
ejpam-2338	161	21	he	he	PRON
ejpam-2338	161	22	employed	employ	VERB
ejpam-2338	161	23	a	a	DET
ejpam-2338	161	24	pseudogroup	pseudogroup	NOUN
ejpam-2338	161	25	to	to	PART
ejpam-2338	161	26	define	define	VERB
ejpam-2338	161	27	the	the	DET
ejpam-2338	161	28	local	local	ADJ
ejpam-2338	161	29	structures	structure	NOUN
ejpam-2338	161	30	described	describe	VERB
ejpam-2338	161	31	in	in	ADP
ejpam-2338	161	32	section	section	NOUN
ejpam-2338	161	33	3.1	3.1	NUM
ejpam-2338	161	34	.	.	PUNCT
ejpam-2338	162	1	further	further	ADJ
ejpam-2338	162	2	work	work	NOUN
ejpam-2338	162	3	on	on	ADP
ejpam-2338	162	4	the	the	DET
ejpam-2338	162	5	axiomatics	axiomatic	NOUN
ejpam-2338	162	6	of	of	ADP
ejpam-2338	162	7	pseudogroups	pseudogroup	NOUN
ejpam-2338	162	8	was	be	AUX
ejpam-2338	162	9	carried	carry	VERB
ejpam-2338	162	10	out	out	ADP
ejpam-2338	162	11	in	in	ADP
ejpam-2338	162	12	[	[	X
ejpam-2338	162	13	11	11	NUM
ejpam-2338	162	14	,	,	PUNCT
ejpam-2338	162	15	12	12	NUM
ejpam-2338	162	16	,	,	PUNCT
ejpam-2338	162	17	55	55	NUM
ejpam-2338	162	18	]	]	PUNCT
ejpam-2338	162	19	,	,	PUNCT
ejpam-2338	162	20	for	for	ADP
ejpam-2338	162	21	example	example	NOUN
ejpam-2338	162	22	.	.	PUNCT
ejpam-2338	163	1	3.3	3.3	NUM
ejpam-2338	163	2	.	.	PUNCT
ejpam-2338	164	1	the	the	PRON
ejpam-2338	164	2	ehresmann	ehresmann	PROPN
ejpam-2338	164	3	–	–	PUNCT
ejpam-2338	164	4	schein	schein	PROPN
ejpam-2338	164	5	–	–	PUNCT
ejpam-2338	164	6	nambooripad	nambooripad	NOUN
ejpam-2338	164	7	theorem	theorem	VERB
ejpam-2338	164	8	the	the	DET
ejpam-2338	164	9	theories	theory	NOUN
ejpam-2338	164	10	of	of	ADP
ejpam-2338	164	11	inverse	inverse	NOUN
ejpam-2338	164	12	semigroups	semigroup	NOUN
ejpam-2338	164	13	and	and	CCONJ
ejpam-2338	164	14	inductive	inductive	ADJ
ejpam-2338	164	15	groupoids	groupoid	NOUN
ejpam-2338	164	16	developed	develop	VERB
ejpam-2338	164	17	separately	separately	ADV
ejpam-2338	164	18	for	for	ADP
ejpam-2338	164	19	some	some	DET
ejpam-2338	164	20	time	time	NOUN
ejpam-2338	164	21	following	follow	VERB
ejpam-2338	164	22	the	the	DET
ejpam-2338	164	23	definition	definition	NOUN
ejpam-2338	164	24	of	of	ADP
ejpam-2338	164	25	the	the	DET
ejpam-2338	164	26	relevant	relevant	ADJ
ejpam-2338	164	27	concepts	concept	NOUN
ejpam-2338	164	28	.	.	PUNCT
ejpam-2338	165	1	it	it	PRON
ejpam-2338	165	2	seems	seem	VERB
ejpam-2338	165	3	that	that	SCONJ
ejpam-2338	165	4	ehresmann	ehresmann	PROPN
ejpam-2338	165	5	was	be	AUX
ejpam-2338	165	6	aware	aware	ADJ
ejpam-2338	165	7	of	of	ADP
ejpam-2338	165	8	the	the	DET
ejpam-2338	165	9	connection	connection	NOUN
ejpam-2338	165	10	between	between	ADP
ejpam-2338	165	11	his	his	PRON
ejpam-2338	165	12	work	work	NOUN
ejpam-2338	165	13	and	and	CCONJ
ejpam-2338	165	14	that	that	PRON
ejpam-2338	165	15	of	of	ADP
ejpam-2338	165	16	wagner	wagner	PROPN
ejpam-2338	165	17	(	(	PUNCT
ejpam-2338	165	18	see	see	VERB
ejpam-2338	165	19	[	[	X
ejpam-2338	165	20	51	51	NUM
ejpam-2338	165	21	,	,	PUNCT
ejpam-2338	165	22	p.	p.	NOUN
ejpam-2338	165	23	131	131	NUM
ejpam-2338	165	24	]	]	PUNCT
ejpam-2338	165	25	)	)	PUNCT
ejpam-2338	165	26	.	.	PUNCT
ejpam-2338	166	1	however	however	ADV
ejpam-2338	166	2	,	,	PUNCT
ejpam-2338	166	3	it	it	PRON
ejpam-2338	166	4	was	be	AUX
ejpam-2338	166	5	left	leave	VERB
ejpam-2338	166	6	to	to	PART
ejpam-2338	166	7	schein	schein	VERB
ejpam-2338	166	8	to	to	PART
ejpam-2338	166	9	make	make	VERB
ejpam-2338	166	10	the	the	DET
ejpam-2338	166	11	connection	connection	NOUN
ejpam-2338	166	12	explicit	explicit	ADJ
ejpam-2338	166	13	[	[	PUNCT
ejpam-2338	166	14	87	87	NUM
ejpam-2338	166	15	,	,	PUNCT
ejpam-2338	166	16	89	89	NUM
ejpam-2338	166	17	]	]	PUNCT
ejpam-2338	166	18	.	.	PUNCT
ejpam-2338	167	1	by	by	ADP
ejpam-2338	167	2	relaxing	relax	VERB
ejpam-2338	167	3	ehresmann	ehresmann	PROPN
ejpam-2338	167	4	’s	’s	PART
ejpam-2338	167	5	original	original	ADJ
ejpam-2338	167	6	conditions	condition	NOUN
ejpam-2338	167	7	for	for	ADP
ejpam-2338	167	8	‘	'	PUNCT
ejpam-2338	167	9	inductivity	inductivity	NOUN
ejpam-2338	167	10	’	'	PUNCT
ejpam-2338	167	11	,	,	PUNCT
ejpam-2338	167	12	schein	schein	PROPN
ejpam-2338	167	13	proved	prove	VERB
ejpam-2338	167	14	that	that	SCONJ
ejpam-2338	167	15	to	to	ADP
ejpam-2338	167	16	any	any	DET
ejpam-2338	167	17	inverse	inverse	NOUN
ejpam-2338	167	18	semigroup	semigroup	NOUN
ejpam-2338	167	19	there	there	ADV
ejpam-2338	167	20	corresponds	correspond	VERB
ejpam-2338	167	21	an	an	DET
ejpam-2338	167	22	inductive	inductive	ADJ
ejpam-2338	167	23	groupoid	groupoid	NOUN
ejpam-2338	167	24	and	and	CCONJ
ejpam-2338	167	25	vice	vice	ADV
ejpam-2338	167	26	versa	versa	PROPN
ejpam-2338	168	1	[	[	X
ejpam-2338	168	2	89	89	NUM
ejpam-2338	168	3	,	,	PUNCT
ejpam-2338	168	4	p.	p.	NOUN
ejpam-2338	168	5	109	109	NUM
ejpam-2338	169	1	and	and	CCONJ
ejpam-2338	169	2	theorem	theorem	VERB
ejpam-2338	169	3	3.4	3.4	NUM
ejpam-2338	169	4	]	]	PUNCT
ejpam-2338	169	5	.	.	PUNCT
ejpam-2338	170	1	schein	schein	PROPN
ejpam-2338	170	2	’s	’s	PART
ejpam-2338	170	3	name	name	NOUN
ejpam-2338	170	4	for	for	ADP
ejpam-2338	170	5	the	the	DET
ejpam-2338	170	6	groupoids	groupoid	NOUN
ejpam-2338	170	7	obtained	obtain	VERB
ejpam-2338	170	8	from	from	ADP
ejpam-2338	170	9	inverse	inverse	NOUN
ejpam-2338	170	10	semigroups	semigroup	NOUN
ejpam-2338	170	11	was	be	AUX
ejpam-2338	170	12	replenishable	replenishable	ADJ
ejpam-2338	170	13	croisot	croisot	NOUN
ejpam-2338	170	14	groupoids	groupoid	NOUN
ejpam-2338	170	15	.	.	PUNCT
ejpam-2338	171	1	in	in	ADP
ejpam-2338	171	2	essence,†	essence,†	NOUN
ejpam-2338	171	3	the	the	DET
ejpam-2338	171	4	‘	'	PUNCT
ejpam-2338	171	5	replenishable	replenishable	ADJ
ejpam-2338	171	6	’	'	PUNCT
ejpam-2338	171	7	part	part	NOUN
ejpam-2338	171	8	of	of	ADP
ejpam-2338	171	9	the	the	DET
ejpam-2338	171	10	name	name	NOUN
ejpam-2338	171	11	expresses	express	VERB
ejpam-2338	171	12	the	the	DET
ejpam-2338	171	13	inductive	inductive	ADJ
ejpam-2338	171	14	and	and	CCONJ
ejpam-2338	171	15	ordering	order	VERB
ejpam-2338	171	16	conditions	condition	NOUN
ejpam-2338	171	17	;	;	PUNCT
ejpam-2338	171	18	‘	'	PUNCT
ejpam-2338	171	19	croisot	croisot	NOUN
ejpam-2338	171	20	groupoid	groupoid	NOUN
ejpam-2338	171	21	’	'	PUNCT
ejpam-2338	171	22	(	(	PUNCT
ejpam-2338	171	23	in	in	ADP
ejpam-2338	171	24	fact	fact	NOUN
ejpam-2338	171	25	,	,	PUNCT
ejpam-2338	171	26	simply	simply	ADV
ejpam-2338	171	27	a	a	DET
ejpam-2338	171	28	groupoid	groupoid	NOUN
ejpam-2338	171	29	in	in	ADP
ejpam-2338	171	30	our	our	PRON
ejpam-2338	171	31	sense	sense	NOUN
ejpam-2338	171	32	)	)	PUNCT
ejpam-2338	171	33	was	be	AUX
ejpam-2338	171	34	used	use	VERB
ejpam-2338	171	35	for	for	ADP
ejpam-2338	171	36	the	the	DET
ejpam-2338	171	37	underlying	underlying	ADJ
ejpam-2338	171	38	unordered	unordered	ADJ
ejpam-2338	171	39	structure	structure	NOUN
ejpam-2338	171	40	since	since	SCONJ
ejpam-2338	171	41	such	such	ADJ
ejpam-2338	171	42	objects	object	NOUN
ejpam-2338	171	43	had	have	AUX
ejpam-2338	171	44	appeared	appear	VERB
ejpam-2338	171	45	previously	previously	ADV
ejpam-2338	171	46	in	in	ADP
ejpam-2338	171	47	a	a	DET
ejpam-2338	171	48	brief	brief	ADJ
ejpam-2338	171	49	paper	paper	NOUN
ejpam-2338	171	50	by	by	ADP
ejpam-2338	171	51	robert	robert	PROPN
ejpam-2338	171	52	croisot	croisot	PROPN
ejpam-2338	172	1	[	[	X
ejpam-2338	172	2	10	10	NUM
ejpam-2338	172	3	]	]	PUNCT
ejpam-2338	172	4	,	,	PUNCT
ejpam-2338	172	5	whose	whose	DET
ejpam-2338	172	6	own	own	ADJ
ejpam-2338	172	7	name	name	NOUN
ejpam-2338	172	8	for	for	ADP
ejpam-2338	172	9	them	they	PRON
ejpam-2338	172	10	had	have	AUX
ejpam-2338	172	11	been	be	AUX
ejpam-2338	172	12	partial	partial	ADJ
ejpam-2338	172	13	groups	group	NOUN
ejpam-2338	172	14	(	(	PUNCT
ejpam-2338	172	15	groupes	groupe	NOUN
ejpam-2338	172	16	partiels	partiel	NOUN
ejpam-2338	172	17	)	)	PUNCT
ejpam-2338	172	18	.	.	PUNCT
ejpam-2338	173	1	croisot	croisot	PROPN
ejpam-2338	173	2	had	have	AUX
ejpam-2338	173	3	arrived	arrive	VERB
ejpam-2338	173	4	at	at	ADP
ejpam-2338	173	5	these	these	DET
ejpam-2338	173	6	objects	object	NOUN
ejpam-2338	173	7	by	by	ADP
ejpam-2338	173	8	generalising	generalise	VERB
ejpam-2338	173	9	brandt	brandt	PROPN
ejpam-2338	173	10	groupoids	groupoid	NOUN
ejpam-2338	173	11	(	(	PUNCT
ejpam-2338	173	12	on	on	ADP
ejpam-2338	173	13	which	which	PRON
ejpam-2338	173	14	,	,	PUNCT
ejpam-2338	173	15	see	see	VERB
ejpam-2338	173	16	[	[	X
ejpam-2338	173	17	37	37	NUM
ejpam-2338	173	18	,	,	PUNCT
ejpam-2338	173	19	§	§	NOUN
ejpam-2338	173	20	4	4	NUM
ejpam-2338	173	21	]	]	PUNCT
ejpam-2338	173	22	or	or	CCONJ
ejpam-2338	173	23	[	[	X
ejpam-2338	173	24	41	41	NUM
ejpam-2338	173	25	,	,	PUNCT
ejpam-2338	173	26	§	§	NOUN
ejpam-2338	173	27	6.2	6.2	NUM
ejpam-2338	173	28	]	]	PUNCT
ejpam-2338	173	29	)	)	PUNCT
ejpam-2338	173	30	.	.	PUNCT
ejpam-2338	174	1	as	as	SCONJ
ejpam-2338	174	2	schein	schein	PROPN
ejpam-2338	174	3	observed	observe	VERB
ejpam-2338	174	4	,	,	PUNCT
ejpam-2338	174	5	constructing	construct	VERB
ejpam-2338	174	6	an	an	DET
ejpam-2338	174	7	inductive	inductive	ADJ
ejpam-2338	174	8	groupoid	groupoid	NOUN
ejpam-2338	174	9	from	from	ADP
ejpam-2338	174	10	an	an	DET
ejpam-2338	174	11	inverse	inverse	NOUN
ejpam-2338	174	12	semigroup	semigroup	NOUN
ejpam-2338	174	13	is	be	AUX
ejpam-2338	174	14	reasonably	reasonably	ADV
ejpam-2338	174	15	straightforward	straightforward	ADJ
ejpam-2338	174	16	;	;	PUNCT
ejpam-2338	174	17	we	we	PRON
ejpam-2338	174	18	simply	simply	ADV
ejpam-2338	174	19	need	need	VERB
ejpam-2338	174	20	to	to	PART
ejpam-2338	174	21	‘	'	PUNCT
ejpam-2338	174	22	restrict	restrict	VERB
ejpam-2338	174	23	’	'	PUNCT
ejpam-2338	174	24	the	the	DET
ejpam-2338	174	25	semigroup	semigroup	NOUN
ejpam-2338	174	26	’s	’s	PART
ejpam-2338	174	27	multiplication	multiplication	NOUN
ejpam-2338	174	28	in	in	ADP
ejpam-2338	174	29	such	such	DET
ejpam-2338	174	30	a	a	DET
ejpam-2338	174	31	way	way	NOUN
ejpam-2338	174	32	that	that	PRON
ejpam-2338	174	33	we	we	PRON
ejpam-2338	174	34	obtain	obtain	VERB
ejpam-2338	174	35	an	an	DET
ejpam-2338	174	36	inductive	inductive	ADJ
ejpam-2338	174	37	groupoid	groupoid	NOUN
ejpam-2338	174	38	from	from	ADP
ejpam-2338	174	39	the	the	DET
ejpam-2338	174	40	same	same	ADJ
ejpam-2338	174	41	underlying	underlying	ADJ
ejpam-2338	174	42	set	set	NOUN
ejpam-2338	174	43	.	.	PUNCT
ejpam-2338	175	1	the	the	DET
ejpam-2338	175	2	natural	natural	ADJ
ejpam-2338	175	3	partial	partial	ADJ
ejpam-2338	175	4	order	order	NOUN
ejpam-2338	175	5	of	of	ADP
ejpam-2338	175	6	the	the	DET
ejpam-2338	175	7	inverse	inverse	NOUN
ejpam-2338	175	8	semigroup	semigroup	NOUN
ejpam-2338	175	9	(	(	PUNCT
ejpam-2338	175	10	as	as	SCONJ
ejpam-2338	175	11	defined	define	VERB
ejpam-2338	175	12	,	,	PUNCT
ejpam-2338	175	13	for	for	ADP
ejpam-2338	175	14	example	example	NOUN
ejpam-2338	175	15	,	,	PUNCT
ejpam-2338	175	16	in	in	ADP
ejpam-2338	175	17	[	[	X
ejpam-2338	175	18	44	44	NUM
ejpam-2338	175	19	,	,	PUNCT
ejpam-2338	175	20	§	§	NOUN
ejpam-2338	175	21	5.2	5.2	NUM
ejpam-2338	175	22	]	]	PUNCT
ejpam-2338	175	23	)	)	PUNCT
ejpam-2338	175	24	then	then	ADV
ejpam-2338	175	25	serves	serve	VERB
ejpam-2338	175	26	as	as	ADP
ejpam-2338	175	27	the	the	DET
ejpam-2338	175	28	ordering	ordering	NOUN
ejpam-2338	175	29	in	in	ADP
ejpam-2338	175	30	the	the	DET
ejpam-2338	175	31	inductive	inductive	ADJ
ejpam-2338	175	32	groupoid	groupoid	PROPN
ejpam-2338	175	33	.	.	PUNCT
ejpam-2338	176	1	the	the	DET
ejpam-2338	176	2	opposite	opposite	ADJ
ejpam-2338	176	3	construction	construction	NOUN
ejpam-2338	176	4	is	be	AUX
ejpam-2338	176	5	slightly	slightly	ADV
ejpam-2338	176	6	trickier	tricky	ADJ
ejpam-2338	176	7	:	:	PUNCT
ejpam-2338	176	8	we	we	PRON
ejpam-2338	176	9	somehow	somehow	ADV
ejpam-2338	176	10	have	have	VERB
ejpam-2338	176	11	to	to	PART
ejpam-2338	176	12	take	take	VERB
ejpam-2338	176	13	a	a	DET
ejpam-2338	176	14	partial	partial	ADJ
ejpam-2338	176	15	product	product	NOUN
ejpam-2338	176	16	and	and	CCONJ
ejpam-2338	176	17	construct	construct	VERB
ejpam-2338	176	18	a	a	DET
ejpam-2338	176	19	fully	fully	ADV
ejpam-2338	176	20	-	-	PUNCT
ejpam-2338	176	21	defined	define	VERB
ejpam-2338	176	22	one	one	NUM
ejpam-2338	176	23	.	.	PUNCT
ejpam-2338	177	1	the	the	DET
ejpam-2338	177	2	key	key	NOUN
ejpam-2338	177	3	to	to	ADP
ejpam-2338	177	4	this	this	PRON
ejpam-2338	177	5	,	,	PUNCT
ejpam-2338	177	6	however	however	ADV
ejpam-2338	177	7	,	,	PUNCT
ejpam-2338	177	8	had	have	AUX
ejpam-2338	177	9	appeared	appear	VERB
ejpam-2338	177	10	earlier	early	ADV
ejpam-2338	177	11	in	in	ADP
ejpam-2338	177	12	ehresmann	ehresmann	PROPN
ejpam-2338	177	13	’s	’s	PART
ejpam-2338	177	14	work	work	NOUN
ejpam-2338	177	15	,	,	PUNCT
ejpam-2338	177	16	where	where	SCONJ
ejpam-2338	177	17	the	the	DET
ejpam-2338	177	18	partial	partial	ADJ
ejpam-2338	177	19	ordering	ordering	NOUN
ejpam-2338	177	20	in	in	ADP
ejpam-2338	177	21	an	an	DET
ejpam-2338	177	22	inductive	inductive	ADJ
ejpam-2338	177	23	groupoid	groupoid	NOUN
ejpam-2338	177	24	had	have	AUX
ejpam-2338	177	25	always	always	ADV
ejpam-2338	177	26	played	play	VERB
ejpam-2338	177	27	a	a	DET
ejpam-2338	177	28	central	central	ADJ
ejpam-2338	177	29	role	role	NOUN
ejpam-2338	177	30	.	.	PUNCT
ejpam-2338	178	1	indeed	indeed	ADV
ejpam-2338	178	2	,	,	PUNCT
ejpam-2338	178	3	ehresmann	ehresmann	PROPN
ejpam-2338	178	4	observed	observe	VERB
ejpam-2338	178	5	that	that	SCONJ
ejpam-2338	178	6	the	the	DET
ejpam-2338	178	7	partial	partial	ADJ
ejpam-2338	178	8	order	order	NOUN
ejpam-2338	178	9	contains	contain	VERB
ejpam-2338	178	10	the	the	DET
ejpam-2338	178	11	information	information	NOUN
ejpam-2338	178	12	lacking	lack	VERB
ejpam-2338	178	13	in	in	ADP
ejpam-2338	178	14	the	the	DET
ejpam-2338	178	15	partial	partial	ADJ
ejpam-2338	178	16	multiplication	multiplication	NOUN
ejpam-2338	178	17	;	;	PUNCT
ejpam-2338	178	18	together	together	ADV
ejpam-2338	178	19	,	,	PUNCT
ejpam-2338	178	20	they	they	PRON
ejpam-2338	178	21	may	may	AUX
ejpam-2338	178	22	be	be	AUX
ejpam-2338	178	23	used	use	VERB
ejpam-2338	178	24	to	to	PART
ejpam-2338	178	25	construct	construct	VERB
ejpam-2338	178	26	a	a	DET
ejpam-2338	178	27	fully	fully	ADV
ejpam-2338	178	28	-	-	PUNCT
ejpam-2338	178	29	defined	define	VERB
ejpam-2338	178	30	,	,	PUNCT
ejpam-2338	178	31	associative	associative	ADJ
ejpam-2338	178	32	multiplication	multiplication	NOUN
ejpam-2338	178	33	,	,	PUNCT
ejpam-2338	178	34	and	and	CCONJ
ejpam-2338	178	35	thereby	thereby	ADV
ejpam-2338	178	36	construct	construct	VERB
ejpam-2338	178	37	an	an	DET
ejpam-2338	178	38	inverse	inverse	NOUN
ejpam-2338	178	39	semigroup	semigroup	NOUN
ejpam-2338	178	40	from	from	ADP
ejpam-2338	178	41	an	an	DET
ejpam-2338	178	42	inductive	inductive	ADJ
ejpam-2338	178	43	groupoid	groupoid	NOUN
ejpam-2338	178	44	.	.	PUNCT
ejpam-2338	179	1	the	the	DET
ejpam-2338	179	2	results	result	NOUN
ejpam-2338	179	3	of	of	ADP
ejpam-2338	179	4	schein	schein	PROPN
ejpam-2338	179	5	were	be	AUX
ejpam-2338	179	6	subsequently	subsequently	ADV
ejpam-2338	179	7	generalised	generalise	VERB
ejpam-2338	179	8	to	to	ADP
ejpam-2338	179	9	the	the	DET
ejpam-2338	179	10	regular	regular	ADJ
ejpam-2338	179	11	case	case	NOUN
ejpam-2338	179	12	by	by	ADP
ejpam-2338	179	13	k.	k.	PROPN
ejpam-2338	179	14	s.	s.	PROPN
ejpam-2338	179	15	s.	s.	PROPN
ejpam-2338	179	16	nambooripad	nambooripad	PROPN
ejpam-2338	179	17	,	,	PUNCT
ejpam-2338	179	18	whereby	whereby	SCONJ
ejpam-2338	179	19	regular	regular	ADJ
ejpam-2338	179	20	semigroups	semigroup	NOUN
ejpam-2338	179	21	may	may	AUX
ejpam-2338	179	22	be	be	AUX
ejpam-2338	179	23	associated	associate	VERB
ejpam-2338	179	24	with	with	ADP
ejpam-2338	179	25	more	more	ADJ
ejpam-2338	179	26	general	general	ADJ
ejpam-2338	179	27	types	type	NOUN
ejpam-2338	179	28	of	of	ADP
ejpam-2338	179	29	ordered	order	VERB
ejpam-2338	179	30	groupoids	groupoid	NOUN
ejpam-2338	179	31	.	.	PUNCT
ejpam-2338	180	1	nambooripad	nambooripad	PROPN
ejpam-2338	181	1	[	[	X
ejpam-2338	181	2	68	68	NUM
ejpam-2338	181	3	]	]	PUNCT
ejpam-2338	181	4	also	also	ADV
ejpam-2338	181	5	placed	place	VERB
ejpam-2338	181	6	the	the	DET
ejpam-2338	181	7	correspondence	correspondence	NOUN
ejpam-2338	181	8	between	between	ADP
ejpam-2338	181	9	inverse	inverse	NOUN
ejpam-2338	181	10	semigroups	semigroup	NOUN
ejpam-2338	181	11	and	and	CCONJ
ejpam-2338	181	12	inductive	inductive	ADJ
ejpam-2338	181	13	groupoids	groupoid	NOUN
ejpam-2338	181	14	in	in	ADP
ejpam-2338	181	15	a	a	DET
ejpam-2338	181	16	more	more	ADV
ejpam-2338	181	17	technical	technical	ADJ
ejpam-2338	181	18	,	,	PUNCT
ejpam-2338	181	19	category	category	NOUN
ejpam-2338	181	20	-	-	PUNCT
ejpam-2338	181	21	theoretic	theoretic	NOUN
ejpam-2338	181	22	setting	setting	NOUN
ejpam-2338	181	23	.	.	PUNCT
ejpam-2338	182	1	this	this	DET
ejpam-2338	182	2	new	new	ADJ
ejpam-2338	182	3	formulation	formulation	NOUN
ejpam-2338	182	4	,	,	PUNCT
ejpam-2338	182	5	together	together	ADV
ejpam-2338	182	6	with	with	ADP
ejpam-2338	182	7	a	a	DET
ejpam-2338	182	8	subsequent	subsequent	ADJ
ejpam-2338	182	9	extension	extension	NOUN
ejpam-2338	182	10	due	due	ADP
ejpam-2338	182	11	to	to	ADP
ejpam-2338	182	12	nambooripad	nambooripad	NOUN
ejpam-2338	182	13	and	and	CCONJ
ejpam-2338	182	14	veeramony	veeramony	VERB
ejpam-2338	183	1	[	[	X
ejpam-2338	183	2	69	69	NUM
ejpam-2338	183	3	]	]	PUNCT
ejpam-2338	183	4	,	,	PUNCT
ejpam-2338	183	5	were	be	AUX
ejpam-2338	183	6	†i	†i	NOUN
ejpam-2338	183	7	say	say	VERB
ejpam-2338	183	8	‘	'	PUNCT
ejpam-2338	183	9	in	in	ADP
ejpam-2338	183	10	essence	essence	NOUN
ejpam-2338	183	11	’	'	PUNCT
ejpam-2338	183	12	here	here	ADV
ejpam-2338	183	13	because	because	SCONJ
ejpam-2338	183	14	schein	schein	PROPN
ejpam-2338	183	15	did	do	AUX
ejpam-2338	183	16	not	not	PART
ejpam-2338	183	17	define	define	VERB
ejpam-2338	183	18	a	a	DET
ejpam-2338	183	19	replenishable	replenishable	ADJ
ejpam-2338	183	20	croisot	croisot	NOUN
ejpam-2338	183	21	groupoid	groupoid	NOUN
ejpam-2338	183	22	to	to	PART
ejpam-2338	183	23	be	be	AUX
ejpam-2338	183	24	an	an	DET
ejpam-2338	183	25	ordered	order	VERB
ejpam-2338	183	26	object	object	NOUN
ejpam-2338	183	27	.	.	PUNCT
ejpam-2338	184	1	on	on	ADP
ejpam-2338	184	2	the	the	DET
ejpam-2338	184	3	contrary	contrary	NOUN
ejpam-2338	184	4	,	,	PUNCT
ejpam-2338	184	5	he	he	PRON
ejpam-2338	184	6	defined	define	VERB
ejpam-2338	184	7	a	a	DET
ejpam-2338	184	8	replenishable	replenishable	ADJ
ejpam-2338	184	9	croisot	croisot	NOUN
ejpam-2338	184	10	groupoid	groupoid	NOUN
ejpam-2338	184	11	to	to	PART
ejpam-2338	184	12	be	be	AUX
ejpam-2338	184	13	a	a	DET
ejpam-2338	184	14	croisot	croisot	ADJ
ejpam-2338	184	15	groupoid	groupoid	NOUN
ejpam-2338	184	16	which	which	PRON
ejpam-2338	184	17	may	may	AUX
ejpam-2338	184	18	be	be	AUX
ejpam-2338	184	19	obtained	obtain	VERB
ejpam-2338	184	20	from	from	ADP
ejpam-2338	184	21	an	an	DET
ejpam-2338	184	22	inverse	inverse	NOUN
ejpam-2338	184	23	semigroup	semigroup	NOUN
ejpam-2338	184	24	in	in	ADP
ejpam-2338	184	25	a	a	DET
ejpam-2338	184	26	specified	specified	ADJ
ejpam-2338	184	27	way	way	NOUN
ejpam-2338	184	28	(	(	PUNCT
ejpam-2338	184	29	see	see	VERB
ejpam-2338	184	30	[	[	X
ejpam-2338	184	31	40	40	NUM
ejpam-2338	184	32	]	]	PUNCT
ejpam-2338	184	33	)	)	PUNCT
ejpam-2338	184	34	.	.	PUNCT
ejpam-2338	185	1	nevertheless	nevertheless	ADV
ejpam-2338	185	2	,	,	PUNCT
ejpam-2338	185	3	he	he	PRON
ejpam-2338	185	4	then	then	ADV
ejpam-2338	185	5	proved	prove	VERB
ejpam-2338	185	6	that	that	SCONJ
ejpam-2338	185	7	a	a	DET
ejpam-2338	185	8	croisot	croisot	NOUN
ejpam-2338	185	9	groupoid	groupoid	NOUN
ejpam-2338	185	10	is	be	AUX
ejpam-2338	185	11	replenishable	replenishable	ADJ
ejpam-2338	185	12	if	if	SCONJ
ejpam-2338	185	13	and	and	CCONJ
ejpam-2338	185	14	only	only	ADV
ejpam-2338	185	15	if	if	SCONJ
ejpam-2338	185	16	it	it	PRON
ejpam-2338	185	17	can	can	AUX
ejpam-2338	185	18	be	be	AUX
ejpam-2338	185	19	ordered	order	VERB
ejpam-2338	185	20	in	in	ADP
ejpam-2338	185	21	such	such	DET
ejpam-2338	185	22	a	a	DET
ejpam-2338	185	23	way	way	NOUN
ejpam-2338	185	24	as	as	SCONJ
ejpam-2338	185	25	to	to	PART
ejpam-2338	185	26	make	make	VERB
ejpam-2338	185	27	it	it	PRON
ejpam-2338	185	28	inductive	inductive	VERB
ejpam-2338	185	29	.	.	PUNCT
ejpam-2338	186	1	christopher	christopher	PROPN
ejpam-2338	186	2	hollings	hollings	PROPN
ejpam-2338	186	3	/	/	SYM
ejpam-2338	186	4	eur	eur	PROPN
ejpam-2338	186	5	.	.	PUNCT
ejpam-2338	187	1	j.	j.	PROPN
ejpam-2338	187	2	pure	pure	PROPN
ejpam-2338	187	3	appl	appl	PROPN
ejpam-2338	187	4	.	.	PROPN
ejpam-2338	187	5	math	math	PROPN
ejpam-2338	187	6	,	,	PUNCT
ejpam-2338	187	7	8	8	NUM
ejpam-2338	187	8	(	(	PUNCT
ejpam-2338	187	9	2015	2015	NUM
ejpam-2338	187	10	)	)	PUNCT
ejpam-2338	187	11	,	,	PUNCT
ejpam-2338	187	12	294	294	NUM
ejpam-2338	187	13	-	-	SYM
ejpam-2338	187	14	323	323	NUM
ejpam-2338	187	15	303	303	NUM
ejpam-2338	187	16	gathered	gather	VERB
ejpam-2338	187	17	together	together	ADV
ejpam-2338	187	18	into	into	ADP
ejpam-2338	187	19	a	a	DET
ejpam-2338	187	20	single	single	ADJ
ejpam-2338	187	21	theorem	theorem	NOUN
ejpam-2338	187	22	by	by	ADP
ejpam-2338	187	23	lawson	lawson	PROPN
ejpam-2338	187	24	[	[	X
ejpam-2338	187	25	51	51	NUM
ejpam-2338	187	26	,	,	PUNCT
ejpam-2338	187	27	theorem	theorem	VERB
ejpam-2338	187	28	4.1.8	4.1.8	NUM
ejpam-2338	187	29	]	]	PUNCT
ejpam-2338	187	30	,	,	PUNCT
ejpam-2338	187	31	who	who	PRON
ejpam-2338	187	32	named	name	VERB
ejpam-2338	187	33	it	it	PRON
ejpam-2338	187	34	the	the	DET
ejpam-2338	187	35	ehresmann	ehresmann	PROPN
ejpam-2338	187	36	–	–	PUNCT
ejpam-2338	187	37	schein	schein	PROPN
ejpam-2338	187	38	–	–	PUNCT
ejpam-2338	187	39	nambooripad	nambooripad	PROPN
ejpam-2338	187	40	theorem	theorem	VERB
ejpam-2338	187	41	to	to	PART
ejpam-2338	187	42	reflect	reflect	VERB
ejpam-2338	187	43	its	its	PRON
ejpam-2338	187	44	disparate	disparate	ADJ
ejpam-2338	187	45	origins	origin	NOUN
ejpam-2338	187	46	.	.	PUNCT
ejpam-2338	188	1	as	as	SCONJ
ejpam-2338	188	2	noted	note	VERB
ejpam-2338	188	3	in	in	ADP
ejpam-2338	188	4	the	the	DET
ejpam-2338	188	5	introduction	introduction	NOUN
ejpam-2338	188	6	,	,	PUNCT
ejpam-2338	188	7	the	the	DET
ejpam-2338	188	8	ehresmann	ehresmann	PROPN
ejpam-2338	188	9	–	–	PUNCT
ejpam-2338	188	10	schein	schein	PROPN
ejpam-2338	188	11	–	–	PUNCT
ejpam-2338	188	12	nambooripad	nambooripad	NOUN
ejpam-2338	188	13	theorem	theorem	NOUN
ejpam-2338	188	14	,	,	PUNCT
ejpam-2338	188	15	at	at	ADP
ejpam-2338	188	16	its	its	PRON
ejpam-2338	188	17	simplest	simple	ADJ
ejpam-2338	188	18	,	,	PUNCT
ejpam-2338	188	19	states	state	VERB
ejpam-2338	188	20	that	that	SCONJ
ejpam-2338	188	21	we	we	PRON
ejpam-2338	188	22	may	may	AUX
ejpam-2338	188	23	always	always	ADV
ejpam-2338	188	24	construct	construct	VERB
ejpam-2338	188	25	an	an	DET
ejpam-2338	188	26	inverse	inverse	NOUN
ejpam-2338	188	27	semigroup	semigroup	NOUN
ejpam-2338	188	28	from	from	ADP
ejpam-2338	188	29	an	an	DET
ejpam-2338	188	30	inductive	inductive	ADJ
ejpam-2338	188	31	groupoid	groupoid	NOUN
ejpam-2338	188	32	and	and	CCONJ
ejpam-2338	188	33	vice	vice	ADV
ejpam-2338	188	34	versa	versa	ADV
ejpam-2338	188	35	(	(	PUNCT
ejpam-2338	188	36	see	see	VERB
ejpam-2338	188	37	[	[	X
ejpam-2338	188	38	51	51	NUM
ejpam-2338	188	39	]	]	PUNCT
ejpam-2338	188	40	or	or	CCONJ
ejpam-2338	188	41	[	[	X
ejpam-2338	188	42	40	40	NUM
ejpam-2338	188	43	]	]	PUNCT
ejpam-2338	188	44	)	)	PUNCT
ejpam-2338	188	45	.	.	PUNCT
ejpam-2338	189	1	the	the	DET
ejpam-2338	189	2	ehresmann	ehresmann	PROPN
ejpam-2338	189	3	–	–	PUNCT
ejpam-2338	189	4	schein	schein	PROPN
ejpam-2338	189	5	–	–	PUNCT
ejpam-2338	189	6	nambooripad	nambooripad	PROPN
ejpam-2338	189	7	theorem	theorem	NOUN
ejpam-2338	189	8	has	have	AUX
ejpam-2338	189	9	provided	provide	VERB
ejpam-2338	189	10	a	a	DET
ejpam-2338	189	11	useful	useful	ADJ
ejpam-2338	189	12	tool	tool	NOUN
ejpam-2338	189	13	for	for	ADP
ejpam-2338	189	14	inverse	inverse	NOUN
ejpam-2338	189	15	semigroup	semigroup	NOUN
ejpam-2338	189	16	theorists	theorist	NOUN
ejpam-2338	189	17	,	,	PUNCT
ejpam-2338	189	18	who	who	PRON
ejpam-2338	189	19	may	may	AUX
ejpam-2338	189	20	study	study	VERB
ejpam-2338	189	21	inductive	inductive	ADJ
ejpam-2338	189	22	groupoids	groupoid	NOUN
ejpam-2338	189	23	as	as	ADP
ejpam-2338	189	24	a	a	DET
ejpam-2338	189	25	way	way	NOUN
ejpam-2338	189	26	of	of	ADP
ejpam-2338	189	27	informing	inform	VERB
ejpam-2338	189	28	them	they	PRON
ejpam-2338	189	29	about	about	ADP
ejpam-2338	189	30	inverse	inverse	NOUN
ejpam-2338	189	31	semigroups	semigroup	NOUN
ejpam-2338	189	32	:	:	PUNCT
ejpam-2338	189	33	for	for	ADP
ejpam-2338	189	34	example	example	NOUN
ejpam-2338	189	35	,	,	PUNCT
ejpam-2338	189	36	gilbert	gilbert	PROPN
ejpam-2338	190	1	[	[	X
ejpam-2338	190	2	22	22	NUM
ejpam-2338	190	3	]	]	PUNCT
ejpam-2338	190	4	studied	study	VERB
ejpam-2338	190	5	the	the	DET
ejpam-2338	190	6	partial	partial	ADJ
ejpam-2338	190	7	actions	action	NOUN
ejpam-2338	190	8	of	of	ADP
ejpam-2338	190	9	inductive	inductive	ADJ
ejpam-2338	190	10	groupoids	groupoid	NOUN
ejpam-2338	190	11	and	and	CCONJ
ejpam-2338	190	12	linked	link	VERB
ejpam-2338	190	13	these	these	PRON
ejpam-2338	190	14	with	with	ADP
ejpam-2338	190	15	the	the	DET
ejpam-2338	190	16	partial	partial	ADJ
ejpam-2338	190	17	actions	action	NOUN
ejpam-2338	190	18	of	of	ADP
ejpam-2338	190	19	inverse	inverse	NOUN
ejpam-2338	190	20	semigroups	semigroup	NOUN
ejpam-2338	190	21	.	.	PUNCT
ejpam-2338	191	1	the	the	DET
ejpam-2338	191	2	theorem	theorem	NOUN
ejpam-2338	191	3	is	be	AUX
ejpam-2338	191	4	tied	tie	VERB
ejpam-2338	191	5	very	very	ADV
ejpam-2338	191	6	closely	closely	ADV
ejpam-2338	191	7	to	to	ADP
ejpam-2338	191	8	the	the	DET
ejpam-2338	191	9	development	development	NOUN
ejpam-2338	191	10	of	of	ADP
ejpam-2338	191	11	the	the	DET
ejpam-2338	191	12	inverse	inverse	NOUN
ejpam-2338	191	13	semigroup	semigroup	NOUN
ejpam-2338	191	14	concept	concept	NOUN
ejpam-2338	191	15	and	and	CCONJ
ejpam-2338	191	16	gives	give	VERB
ejpam-2338	191	17	a	a	DET
ejpam-2338	191	18	nice	nice	ADJ
ejpam-2338	191	19	expression	expression	NOUN
ejpam-2338	191	20	of	of	ADP
ejpam-2338	191	21	the	the	DET
ejpam-2338	191	22	fact	fact	NOUN
ejpam-2338	191	23	that	that	SCONJ
ejpam-2338	191	24	inverse	inverse	NOUN
ejpam-2338	191	25	semigroups	semigroup	NOUN
ejpam-2338	191	26	and	and	CCONJ
ejpam-2338	191	27	inductive	inductive	ADJ
ejpam-2338	191	28	groupoids	groupoid	NOUN
ejpam-2338	191	29	are	be	AUX
ejpam-2338	191	30	two	two	NUM
ejpam-2338	191	31	distinct	distinct	ADJ
ejpam-2338	191	32	,	,	PUNCT
ejpam-2338	191	33	yet	yet	CCONJ
ejpam-2338	191	34	closely	closely	ADV
ejpam-2338	191	35	related	relate	VERB
ejpam-2338	191	36	,	,	PUNCT
ejpam-2338	191	37	solutions	solution	NOUN
ejpam-2338	191	38	to	to	ADP
ejpam-2338	191	39	the	the	DET
ejpam-2338	191	40	same	same	ADJ
ejpam-2338	191	41	problem	problem	NOUN
ejpam-2338	191	42	.	.	PUNCT
ejpam-2338	192	1	4	4	X
ejpam-2338	192	2	.	.	X
ejpam-2338	192	3	the	the	DET
ejpam-2338	192	4	munn	munn	PROPN
ejpam-2338	192	5	representation	representation	NOUN
ejpam-2338	192	6	in	in	ADP
ejpam-2338	192	7	this	this	DET
ejpam-2338	192	8	section	section	NOUN
ejpam-2338	192	9	,	,	PUNCT
ejpam-2338	192	10	we	we	PRON
ejpam-2338	192	11	turn	turn	VERB
ejpam-2338	192	12	to	to	ADP
ejpam-2338	192	13	the	the	DET
ejpam-2338	192	14	second	second	NOUN
ejpam-2338	192	15	of	of	ADP
ejpam-2338	192	16	the	the	DET
ejpam-2338	192	17	major	major	ADJ
ejpam-2338	192	18	approaches	approach	NOUN
ejpam-2338	192	19	to	to	ADP
ejpam-2338	192	20	the	the	DET
ejpam-2338	192	21	structure	structure	NOUN
ejpam-2338	192	22	of	of	ADP
ejpam-2338	192	23	inverse	inverse	NOUN
ejpam-2338	192	24	semigroups	semigroup	NOUN
ejpam-2338	192	25	:	:	PUNCT
ejpam-2338	192	26	the	the	DET
ejpam-2338	192	27	notion	notion	NOUN
ejpam-2338	192	28	of	of	ADP
ejpam-2338	192	29	a	a	DET
ejpam-2338	192	30	fundamental	fundamental	ADJ
ejpam-2338	192	31	inverse	inverse	NOUN
ejpam-2338	192	32	semigroup	semigroup	NOUN
ejpam-2338	192	33	and	and	CCONJ
ejpam-2338	192	34	the	the	DET
ejpam-2338	192	35	munn	munn	PROPN
ejpam-2338	192	36	representation	representation	NOUN
ejpam-2338	192	37	,	,	PUNCT
ejpam-2338	192	38	both	both	PRON
ejpam-2338	192	39	due	due	ADJ
ejpam-2338	192	40	largely	largely	ADV
ejpam-2338	192	41	to	to	ADP
ejpam-2338	192	42	w.	w.	PROPN
ejpam-2338	192	43	d.	d.	PROPN
ejpam-2338	192	44	munn	munn	PROPN
ejpam-2338	192	45	.	.	PUNCT
ejpam-2338	193	1	fountain	fountain	NOUN
ejpam-2338	193	2	describes	describe	VERB
ejpam-2338	193	3	these	these	PRON
ejpam-2338	193	4	as	as	ADP
ejpam-2338	193	5	munn	munn	PROPN
ejpam-2338	193	6	’s	’s	PART
ejpam-2338	193	7	“	"	PUNCT
ejpam-2338	193	8	most	most	ADV
ejpam-2338	193	9	important	important	ADJ
ejpam-2338	193	10	and	and	CCONJ
ejpam-2338	193	11	influential	influential	ADJ
ejpam-2338	193	12	contributions	contribution	NOUN
ejpam-2338	193	13	to	to	ADP
ejpam-2338	193	14	semigroup	semigroup	PROPN
ejpam-2338	193	15	theory	theory	NOUN
ejpam-2338	193	16	”	"	PUNCT
ejpam-2338	194	1	[	[	X
ejpam-2338	194	2	20	20	NUM
ejpam-2338	194	3	,	,	PUNCT
ejpam-2338	194	4	p.	p.	NOUN
ejpam-2338	194	5	11	11	NUM
ejpam-2338	194	6	]	]	PUNCT
ejpam-2338	194	7	.	.	PUNCT
ejpam-2338	195	1	4.1	4.1	NUM
ejpam-2338	195	2	.	.	PUNCT
ejpam-2338	195	3	separation	separation	NOUN
ejpam-2338	195	4	of	of	ADP
ejpam-2338	195	5	idempotents	idempotent	NOUN
ejpam-2338	195	6	to	to	PART
ejpam-2338	195	7	begin	begin	VERB
ejpam-2338	195	8	,	,	PUNCT
ejpam-2338	195	9	we	we	PRON
ejpam-2338	195	10	need	need	VERB
ejpam-2338	195	11	the	the	DET
ejpam-2338	195	12	notion	notion	NOUN
ejpam-2338	195	13	of	of	ADP
ejpam-2338	195	14	an	an	DET
ejpam-2338	195	15	idempotent	idempotent	NOUN
ejpam-2338	195	16	-	-	PUNCT
ejpam-2338	195	17	separating	separate	VERB
ejpam-2338	195	18	morphism	morphism	NOUN
ejpam-2338	195	19	:	:	PUNCT
ejpam-2338	195	20	a	a	DET
ejpam-2338	195	21	(	(	PUNCT
ejpam-2338	195	22	homo)morphism	homo)morphism	NOUN
ejpam-2338	195	23	which	which	PRON
ejpam-2338	195	24	restricts	restrict	VERB
ejpam-2338	195	25	to	to	ADP
ejpam-2338	195	26	an	an	DET
ejpam-2338	195	27	isomorphism	isomorphism	NOUN
ejpam-2338	195	28	on	on	ADP
ejpam-2338	195	29	idempotents	idempotent	NOUN
ejpam-2338	195	30	,	,	PUNCT
ejpam-2338	195	31	that	that	PRON
ejpam-2338	195	32	is	be	AUX
ejpam-2338	195	33	to	to	PART
ejpam-2338	195	34	say	say	VERB
ejpam-2338	195	35	,	,	PUNCT
ejpam-2338	195	36	it	it	PRON
ejpam-2338	195	37	‘	'	PUNCT
ejpam-2338	195	38	separates	separate	VERB
ejpam-2338	195	39	’	'	PUNCT
ejpam-2338	195	40	idempotents	idempotent	NOUN
ejpam-2338	195	41	.	.	PUNCT
ejpam-2338	196	1	such	such	ADJ
ejpam-2338	196	2	morphisms	morphism	NOUN
ejpam-2338	196	3	made	make	VERB
ejpam-2338	196	4	an	an	DET
ejpam-2338	196	5	early	early	ADJ
ejpam-2338	196	6	appearance	appearance	NOUN
ejpam-2338	196	7	in	in	ADP
ejpam-2338	196	8	preston	preston	PROPN
ejpam-2338	196	9	’s	’s	PART
ejpam-2338	196	10	dphil	dphil	ADJ
ejpam-2338	196	11	thesis	thesis	NOUN
ejpam-2338	196	12	[	[	X
ejpam-2338	196	13	74	74	NUM
ejpam-2338	196	14	]	]	PUNCT
ejpam-2338	196	15	,	,	PUNCT
ejpam-2338	196	16	where	where	SCONJ
ejpam-2338	196	17	they	they	PRON
ejpam-2338	196	18	appeared	appear	VERB
ejpam-2338	196	19	amongst	amongst	ADP
ejpam-2338	196	20	material	material	NOUN
ejpam-2338	196	21	that	that	PRON
ejpam-2338	196	22	was	be	AUX
ejpam-2338	196	23	seemingly	seemingly	ADV
ejpam-2338	196	24	inspired	inspire	VERB
ejpam-2338	196	25	by	by	ADP
ejpam-2338	196	26	group	group	NOUN
ejpam-2338	196	27	-	-	PUNCT
ejpam-2338	196	28	theoretic	theoretic	NOUN
ejpam-2338	196	29	considerations	consideration	NOUN
ejpam-2338	196	30	,	,	PUNCT
ejpam-2338	196	31	such	such	ADJ
ejpam-2338	196	32	as	as	ADP
ejpam-2338	196	33	the	the	DET
ejpam-2338	196	34	notion	notion	NOUN
ejpam-2338	196	35	of	of	ADP
ejpam-2338	196	36	a	a	DET
ejpam-2338	196	37	‘	'	PUNCT
ejpam-2338	196	38	normal	normal	ADJ
ejpam-2338	196	39	’	'	PUNCT
ejpam-2338	196	40	subsemigroup	subsemigroup	NOUN
ejpam-2338	196	41	of	of	ADP
ejpam-2338	196	42	an	an	DET
ejpam-2338	196	43	inverse	inverse	NOUN
ejpam-2338	196	44	semigroup	semigroup	NOUN
ejpam-2338	196	45	(	(	PUNCT
ejpam-2338	196	46	for	for	ADP
ejpam-2338	196	47	further	further	ADJ
ejpam-2338	196	48	comments	comment	NOUN
ejpam-2338	196	49	on	on	ADP
ejpam-2338	196	50	preston	preston	PROPN
ejpam-2338	196	51	’s	’s	PART
ejpam-2338	196	52	thesis	thesis	NOUN
ejpam-2338	196	53	,	,	PUNCT
ejpam-2338	196	54	see	see	VERB
ejpam-2338	196	55	[	[	X
ejpam-2338	196	56	41	41	NUM
ejpam-2338	196	57	,	,	PUNCT
ejpam-2338	196	58	§	§	NOUN
ejpam-2338	196	59	10.6	10.6	NUM
ejpam-2338	196	60	]	]	NUM
ejpam-2338	196	61	)	)	PUNCT
ejpam-2338	196	62	.	.	PUNCT
ejpam-2338	197	1	idempotent	idempotent	NOUN
ejpam-2338	197	2	-	-	PUNCT
ejpam-2338	197	3	separating	separate	VERB
ejpam-2338	197	4	morphisms	morphism	NOUN
ejpam-2338	197	5	went	go	VERB
ejpam-2338	197	6	on	on	ADP
ejpam-2338	197	7	to	to	PART
ejpam-2338	197	8	be	be	AUX
ejpam-2338	197	9	studied	study	VERB
ejpam-2338	197	10	by	by	ADP
ejpam-2338	197	11	other	other	ADJ
ejpam-2338	197	12	authors	author	NOUN
ejpam-2338	197	13	(	(	PUNCT
ejpam-2338	197	14	indeed	indeed	ADV
ejpam-2338	197	15	,	,	PUNCT
ejpam-2338	197	16	see	see	VERB
ejpam-2338	197	17	section	section	NOUN
ejpam-2338	197	18	5	5	NUM
ejpam-2338	197	19	)	)	PUNCT
ejpam-2338	197	20	.	.	PUNCT
ejpam-2338	198	1	allied	ally	VERB
ejpam-2338	198	2	to	to	ADP
ejpam-2338	198	3	the	the	DET
ejpam-2338	198	4	notion	notion	NOUN
ejpam-2338	198	5	of	of	ADP
ejpam-2338	198	6	an	an	DET
ejpam-2338	198	7	idempotent	idempotent	NOUN
ejpam-2338	198	8	-	-	PUNCT
ejpam-2338	198	9	separating	separate	VERB
ejpam-2338	198	10	morphism	morphism	NOUN
ejpam-2338	198	11	is	be	AUX
ejpam-2338	198	12	that	that	PRON
ejpam-2338	198	13	of	of	ADP
ejpam-2338	198	14	an	an	DET
ejpam-2338	198	15	idempotent	idempotent	NOUN
ejpam-2338	198	16	-	-	PUNCT
ejpam-2338	198	17	separating	separate	VERB
ejpam-2338	198	18	congruence	congruence	NOUN
ejpam-2338	198	19	:	:	PUNCT
ejpam-2338	198	20	a	a	DET
ejpam-2338	198	21	congruence	congruence	NOUN
ejpam-2338	198	22	which	which	PRON
ejpam-2338	198	23	has	have	VERB
ejpam-2338	198	24	at	at	ADP
ejpam-2338	198	25	most	most	ADV
ejpam-2338	198	26	one	one	NUM
ejpam-2338	198	27	idempotent	idempotent	NOUN
ejpam-2338	198	28	in	in	ADP
ejpam-2338	198	29	each	each	DET
ejpam-2338	198	30	congruence	congruence	NOUN
ejpam-2338	198	31	class	class	NOUN
ejpam-2338	198	32	.	.	PUNCT
ejpam-2338	199	1	in	in	ADP
ejpam-2338	199	2	particular	particular	ADJ
ejpam-2338	199	3	,	,	PUNCT
ejpam-2338	199	4	howie	howie	PROPN
ejpam-2338	200	1	[	[	X
ejpam-2338	200	2	43	43	NUM
ejpam-2338	200	3	]	]	PUNCT
ejpam-2338	200	4	showed	show	VERB
ejpam-2338	200	5	that	that	SCONJ
ejpam-2338	200	6	any	any	DET
ejpam-2338	200	7	inverse	inverse	NOUN
ejpam-2338	200	8	semigroup	semigroup	NOUN
ejpam-2338	200	9	has	have	VERB
ejpam-2338	200	10	a	a	DET
ejpam-2338	200	11	maximum	maximum	ADJ
ejpam-2338	200	12	idempotent	idempotent	NOUN
ejpam-2338	200	13	-	-	PUNCT
ejpam-2338	200	14	separating	separate	VERB
ejpam-2338	200	15	congruence	congruence	NOUN
ejpam-2338	200	16	:	:	PUNCT
ejpam-2338	200	17	an	an	DET
ejpam-2338	200	18	idempotent	idempotent	NOUN
ejpam-2338	200	19	-	-	PUNCT
ejpam-2338	200	20	separating	separate	VERB
ejpam-2338	200	21	congruence	congruence	NOUN
ejpam-2338	200	22	µ	µ	NOUN
ejpam-2338	200	23	which	which	PRON
ejpam-2338	200	24	contains	contain	VERB
ejpam-2338	200	25	every	every	DET
ejpam-2338	200	26	other	other	ADJ
ejpam-2338	200	27	idempotent	idempotent	NOUN
ejpam-2338	200	28	-	-	PUNCT
ejpam-2338	200	29	separating	separate	VERB
ejpam-2338	200	30	congruence	congruence	NOUN
ejpam-2338	200	31	on	on	ADP
ejpam-2338	200	32	the	the	DET
ejpam-2338	200	33	semigroup	semigroup	NOUN
ejpam-2338	200	34	,	,	PUNCT
ejpam-2338	200	35	that	that	ADV
ejpam-2338	200	36	is	is	ADV
ejpam-2338	200	37	,	,	PUNCT
ejpam-2338	200	38	for	for	ADP
ejpam-2338	200	39	any	any	DET
ejpam-2338	200	40	idempotent	idempotent	NOUN
ejpam-2338	200	41	-	-	PUNCT
ejpam-2338	200	42	separating	separate	VERB
ejpam-2338	200	43	congruence	congruence	NOUN
ejpam-2338	200	44	ρ	ρ	NOUN
ejpam-2338	200	45	,	,	PUNCT
ejpam-2338	200	46	if	if	SCONJ
ejpam-2338	200	47	x	x	PROPN
ejpam-2338	200	48	ρ	ρ	NOUN
ejpam-2338	200	49	y	y	PROPN
ejpam-2338	200	50	,	,	PUNCT
ejpam-2338	200	51	then	then	ADV
ejpam-2338	200	52	x	x	X
ejpam-2338	200	53	µ	µ	PROPN
ejpam-2338	200	54	y	y	NOUN
ejpam-2338	200	55	.	.	PUNCT
ejpam-2338	201	1	howie	howie	PROPN
ejpam-2338	201	2	gave	give	VERB
ejpam-2338	201	3	the	the	DET
ejpam-2338	201	4	following	follow	VERB
ejpam-2338	201	5	characterisation	characterisation	NOUN
ejpam-2338	201	6	of	of	ADP
ejpam-2338	201	7	µ	µ	NOUN
ejpam-2338	201	8	:	:	PUNCT
ejpam-2338	201	9	aµ	aµ	PROPN
ejpam-2338	201	10	b	b	NUM
ejpam-2338	201	11	⇐	⇐	PROPN
ejpam-2338	201	12	⇒	⇒	PROPN
ejpam-2338	201	13	a−1ea	a−1ea	NOUN
ejpam-2338	201	14	=	=	SYM
ejpam-2338	201	15	b−1eb	b−1eb	PROPN
ejpam-2338	201	16	,	,	PUNCT
ejpam-2338	201	17	for	for	ADP
ejpam-2338	201	18	all	all	DET
ejpam-2338	201	19	e	e	PROPN
ejpam-2338	201	20	∈	∈	PROPN
ejpam-2338	201	21	e(s	e(s	PROPN
ejpam-2338	201	22	)	)	PUNCT
ejpam-2338	201	23	.	.	PUNCT
ejpam-2338	202	1	(	(	PUNCT
ejpam-2338	202	2	3	3	X
ejpam-2338	202	3	)	)	PUNCT
ejpam-2338	202	4	there	there	PRON
ejpam-2338	202	5	may	may	AUX
ejpam-2338	202	6	indeed	indeed	ADV
ejpam-2338	202	7	also	also	ADV
ejpam-2338	202	8	have	have	AUX
ejpam-2338	202	9	been	be	AUX
ejpam-2338	202	10	some	some	DET
ejpam-2338	202	11	group	group	NOUN
ejpam-2338	202	12	-	-	PUNCT
ejpam-2338	202	13	theoretic	theoretic	NOUN
ejpam-2338	202	14	inspiration	inspiration	NOUN
ejpam-2338	202	15	behind	behind	ADP
ejpam-2338	202	16	the	the	DET
ejpam-2338	202	17	study	study	NOUN
ejpam-2338	202	18	of	of	ADP
ejpam-2338	202	19	idempotentseparating	idempotentseparate	VERB
ejpam-2338	202	20	congruences	congruence	NOUN
ejpam-2338	202	21	;	;	PUNCT
ejpam-2338	202	22	lawson	lawson	PROPN
ejpam-2338	202	23	[	[	X
ejpam-2338	202	24	51	51	NUM
ejpam-2338	202	25	,	,	PUNCT
ejpam-2338	202	26	p.	p.	NOUN
ejpam-2338	202	27	138	138	NUM
ejpam-2338	203	1	]	]	PUNCT
ejpam-2338	203	2	comments	comment	NOUN
ejpam-2338	203	3	:	:	PUNCT
ejpam-2338	203	4	of	of	ADP
ejpam-2338	203	5	all	all	DET
ejpam-2338	203	6	the	the	DET
ejpam-2338	203	7	types	type	NOUN
ejpam-2338	203	8	of	of	ADP
ejpam-2338	203	9	congruences	congruence	NOUN
ejpam-2338	203	10	on	on	ADP
ejpam-2338	203	11	inverse	inverse	NOUN
ejpam-2338	203	12	semigroups	semigroup	NOUN
ejpam-2338	203	13	,	,	PUNCT
ejpam-2338	203	14	it	it	PRON
ejpam-2338	203	15	is	be	AUX
ejpam-2338	203	16	the	the	DET
ejpam-2338	203	17	idempotent	idempotent	NOUN
ejpam-2338	203	18	-	-	PUNCT
ejpam-2338	203	19	separating	separate	VERB
ejpam-2338	203	20	congruences	congruence	NOUN
ejpam-2338	203	21	which	which	PRON
ejpam-2338	203	22	behave	behave	VERB
ejpam-2338	203	23	most	most	ADV
ejpam-2338	203	24	like	like	ADP
ejpam-2338	203	25	group	group	NOUN
ejpam-2338	203	26	congruences	congruence	NOUN
ejpam-2338	203	27	,	,	PUNCT
ejpam-2338	203	28	in	in	SCONJ
ejpam-2338	203	29	that	that	SCONJ
ejpam-2338	203	30	they	they	PRON
ejpam-2338	203	31	are	be	AUX
ejpam-2338	203	32	entirely	entirely	ADV
ejpam-2338	203	33	determined	determine	VERB
ejpam-2338	203	34	by	by	ADP
ejpam-2338	203	35	their	their	PRON
ejpam-2338	203	36	kernels	kernel	NOUN
ejpam-2338	204	1	[	[	X
ejpam-2338	204	2	sic	sic	ADJ
ejpam-2338	204	3	]	]	X
ejpam-2338	204	4	[	[	X
ejpam-2338	204	5	namely	namely	ADV
ejpam-2338	204	6	,	,	PUNCT
ejpam-2338	204	7	the	the	DET
ejpam-2338	204	8	unions	union	NOUN
ejpam-2338	204	9	of	of	ADP
ejpam-2338	204	10	all	all	DET
ejpam-2338	204	11	congruence	congruence	NOUN
ejpam-2338	204	12	classes	class	NOUN
ejpam-2338	204	13	that	that	PRON
ejpam-2338	204	14	contain	contain	VERB
ejpam-2338	204	15	an	an	DET
ejpam-2338	204	16	idempotent	idempotent	NOUN
ejpam-2338	204	17	]	]	X
ejpam-2338	204	18	.	.	PUNCT
ejpam-2338	205	1	christopher	christopher	PROPN
ejpam-2338	205	2	hollings	hollings	PROPN
ejpam-2338	205	3	/	/	SYM
ejpam-2338	205	4	eur	eur	PROPN
ejpam-2338	205	5	.	.	PUNCT
ejpam-2338	206	1	j.	j.	PROPN
ejpam-2338	206	2	pure	pure	PROPN
ejpam-2338	206	3	appl	appl	PROPN
ejpam-2338	206	4	.	.	PROPN
ejpam-2338	206	5	math	math	PROPN
ejpam-2338	206	6	,	,	PUNCT
ejpam-2338	206	7	8	8	NUM
ejpam-2338	206	8	(	(	PUNCT
ejpam-2338	206	9	2015	2015	NUM
ejpam-2338	206	10	)	)	PUNCT
ejpam-2338	206	11	,	,	PUNCT
ejpam-2338	206	12	294	294	NUM
ejpam-2338	206	13	-	-	SYM
ejpam-2338	206	14	323	323	NUM
ejpam-2338	206	15	304	304	NUM
ejpam-2338	206	16	to	to	PART
ejpam-2338	206	17	return	return	VERB
ejpam-2338	206	18	to	to	ADP
ejpam-2338	206	19	µ	µ	NUM
ejpam-2338	206	20	,	,	PUNCT
ejpam-2338	206	21	we	we	PRON
ejpam-2338	206	22	note	note	VERB
ejpam-2338	206	23	that	that	SCONJ
ejpam-2338	206	24	,	,	PUNCT
ejpam-2338	206	25	as	as	SCONJ
ejpam-2338	206	26	munn	munn	PROPN
ejpam-2338	206	27	[	[	X
ejpam-2338	206	28	63	63	NUM
ejpam-2338	206	29	]	]	PUNCT
ejpam-2338	206	30	showed	show	VERB
ejpam-2338	206	31	,	,	PUNCT
ejpam-2338	206	32	this	this	PRON
ejpam-2338	206	33	is	be	AUX
ejpam-2338	206	34	also	also	ADV
ejpam-2338	206	35	the	the	DET
ejpam-2338	206	36	largest	large	ADJ
ejpam-2338	206	37	congruence	congruence	NOUN
ejpam-2338	206	38	contained	contain	VERB
ejpam-2338	206	39	in	in	ADP
ejpam-2338	206	40	green	green	PROPN
ejpam-2338	206	41	’s	’s	PART
ejpam-2338	206	42	relation	relation	NOUN
ejpam-2338	206	43	h	h	NOUN
ejpam-2338	206	44	.	.	PUNCT
ejpam-2338	207	1	further	far	ADV
ejpam-2338	207	2	early	early	ADJ
ejpam-2338	207	3	results	result	NOUN
ejpam-2338	207	4	on	on	ADP
ejpam-2338	207	5	µ	µ	NOUN
ejpam-2338	207	6	are	be	AUX
ejpam-2338	207	7	due	due	ADJ
ejpam-2338	207	8	to	to	ADP
ejpam-2338	207	9	scheiblich	scheiblich	PROPN
ejpam-2338	207	10	[	[	X
ejpam-2338	207	11	86	86	NUM
ejpam-2338	207	12	]	]	PUNCT
ejpam-2338	207	13	and	and	CCONJ
ejpam-2338	207	14	d.	d.	PROPN
ejpam-2338	207	15	g.	g.	PROPN
ejpam-2338	207	16	green	green	PROPN
ejpam-2338	208	1	[	[	X
ejpam-2338	208	2	31	31	NUM
ejpam-2338	208	3	]	]	PUNCT
ejpam-2338	208	4	.	.	PUNCT
ejpam-2338	209	1	we	we	PRON
ejpam-2338	209	2	observe	observe	VERB
ejpam-2338	209	3	also	also	ADV
ejpam-2338	209	4	that	that	SCONJ
ejpam-2338	209	5	the	the	DET
ejpam-2338	209	6	congruence	congruence	PROPN
ejpam-2338	209	7	µ	µ	X
ejpam-2338	209	8	had	have	AUX
ejpam-2338	209	9	earlier	early	ADV
ejpam-2338	209	10	appeared	appear	VERB
ejpam-2338	209	11	in	in	ADP
ejpam-2338	209	12	work	work	NOUN
ejpam-2338	209	13	of	of	ADP
ejpam-2338	209	14	wagner	wagner	NOUN
ejpam-2338	210	1	[	[	X
ejpam-2338	210	2	99	99	NUM
ejpam-2338	210	3	]	]	PUNCT
ejpam-2338	210	4	,	,	PUNCT
ejpam-2338	210	5	who	who	PRON
ejpam-2338	210	6	had	have	AUX
ejpam-2338	210	7	described	describe	VERB
ejpam-2338	210	8	various	various	ADJ
ejpam-2338	210	9	properties	property	NOUN
ejpam-2338	210	10	of	of	ADP
ejpam-2338	210	11	it	it	PRON
ejpam-2338	210	12	:	:	PUNCT
ejpam-2338	210	13	the	the	DET
ejpam-2338	210	14	‘	'	PUNCT
ejpam-2338	210	15	maximum	maximum	ADJ
ejpam-2338	210	16	idempotent	idempotent	ADJ
ejpam-2338	210	17	-	-	PUNCT
ejpam-2338	210	18	separating	separate	VERB
ejpam-2338	210	19	’	'	PUNCT
ejpam-2338	210	20	property	property	NOUN
ejpam-2338	210	21	,	,	PUNCT
ejpam-2338	210	22	for	for	ADP
ejpam-2338	210	23	example	example	NOUN
ejpam-2338	210	24	,	,	PUNCT
ejpam-2338	210	25	is	be	AUX
ejpam-2338	210	26	implicit	implicit	ADJ
ejpam-2338	210	27	in	in	ADP
ejpam-2338	210	28	wagner	wagner	PROPN
ejpam-2338	210	29	’s	’s	PART
ejpam-2338	210	30	theorem	theorem	PROPN
ejpam-2338	210	31	28	28	NUM
ejpam-2338	210	32	.	.	PUNCT
ejpam-2338	211	1	the	the	DET
ejpam-2338	211	2	characterisation	characterisation	NOUN
ejpam-2338	211	3	(	(	PUNCT
ejpam-2338	211	4	3	3	X
ejpam-2338	211	5	)	)	PUNCT
ejpam-2338	211	6	was	be	AUX
ejpam-2338	211	7	later	later	ADV
ejpam-2338	211	8	obtained	obtain	VERB
ejpam-2338	211	9	independently	independently	ADV
ejpam-2338	211	10	by	by	ADP
ejpam-2338	211	11	shiryaev	shiryaev	PROPN
ejpam-2338	212	1	[	[	X
ejpam-2338	212	2	93	93	NUM
ejpam-2338	212	3	]	]	PUNCT
ejpam-2338	212	4	.	.	PUNCT
ejpam-2338	213	1	4.2	4.2	NUM
ejpam-2338	213	2	.	.	PUNCT
ejpam-2338	214	1	fundamental	fundamental	ADJ
ejpam-2338	214	2	inverse	inverse	NOUN
ejpam-2338	214	3	semigroups	semigroup	NOUN
ejpam-2338	214	4	the	the	DET
ejpam-2338	214	5	congruence	congruence	NOUN
ejpam-2338	214	6	µwent	µwent	NOUN
ejpam-2338	214	7	on	on	ADP
ejpam-2338	214	8	to	to	PART
ejpam-2338	214	9	play	play	VERB
ejpam-2338	214	10	an	an	DET
ejpam-2338	214	11	important	important	ADJ
ejpam-2338	214	12	role	role	NOUN
ejpam-2338	214	13	in	in	ADP
ejpam-2338	214	14	a	a	DET
ejpam-2338	214	15	1970	1970	NUM
ejpam-2338	214	16	paper	paper	NOUN
ejpam-2338	214	17	by	by	ADP
ejpam-2338	214	18	munn	munn	PROPN
ejpam-2338	215	1	[	[	X
ejpam-2338	215	2	65	65	NUM
ejpam-2338	215	3	]	]	PUNCT
ejpam-2338	215	4	.	.	PUNCT
ejpam-2338	216	1	in	in	ADP
ejpam-2338	216	2	this	this	DET
ejpam-2338	216	3	paper	paper	NOUN
ejpam-2338	216	4	,	,	PUNCT
ejpam-2338	216	5	an	an	DET
ejpam-2338	216	6	inverse	inverse	NOUN
ejpam-2338	216	7	semigroup	semigroup	NOUN
ejpam-2338	216	8	s	s	PART
ejpam-2338	216	9	is	be	AUX
ejpam-2338	216	10	said	say	VERB
ejpam-2338	216	11	to	to	PART
ejpam-2338	216	12	be	be	AUX
ejpam-2338	216	13	fundamental	fundamental	ADJ
ejpam-2338	216	14	if	if	SCONJ
ejpam-2338	216	15	µ	µ	ADJ
ejpam-2338	216	16	is	be	AUX
ejpam-2338	216	17	the	the	DET
ejpam-2338	216	18	equality	equality	NOUN
ejpam-2338	216	19	relation	relation	NOUN
ejpam-2338	216	20	,	,	PUNCT
ejpam-2338	216	21	that	that	ADV
ejpam-2338	216	22	is	is	ADV
ejpam-2338	216	23	,	,	PUNCT
ejpam-2338	216	24	sµ	sµ	PROPN
ejpam-2338	216	25	t	t	PROPN
ejpam-2338	217	1	if	if	SCONJ
ejpam-2338	217	2	and	and	CCONJ
ejpam-2338	217	3	only	only	ADV
ejpam-2338	217	4	if	if	SCONJ
ejpam-2338	217	5	s	s	X
ejpam-2338	217	6	=	=	PUNCT
ejpam-2338	217	7	t.	t.	NOUN
ejpam-2338	217	8	since	since	SCONJ
ejpam-2338	217	9	equality	equality	NOUN
ejpam-2338	217	10	is	be	AUX
ejpam-2338	217	11	the	the	DET
ejpam-2338	217	12	smallest	small	ADJ
ejpam-2338	217	13	congruence	congruence	NOUN
ejpam-2338	217	14	on	on	ADP
ejpam-2338	217	15	a	a	DET
ejpam-2338	217	16	semigroup	semigroup	NOUN
ejpam-2338	217	17	(	(	PUNCT
ejpam-2338	217	18	it	it	PRON
ejpam-2338	217	19	is	be	AUX
ejpam-2338	217	20	contained	contain	VERB
ejpam-2338	217	21	in	in	ADP
ejpam-2338	217	22	every	every	DET
ejpam-2338	217	23	other	other	ADJ
ejpam-2338	217	24	congruence	congruence	NOUN
ejpam-2338	217	25	)	)	PUNCT
ejpam-2338	217	26	,	,	PUNCT
ejpam-2338	217	27	and	and	CCONJ
ejpam-2338	217	28	since	since	SCONJ
ejpam-2338	217	29	µ	µ	NOUN
ejpam-2338	217	30	is	be	AUX
ejpam-2338	217	31	the	the	DET
ejpam-2338	217	32	maximum	maximum	ADJ
ejpam-2338	217	33	idempotent	idempotent	NOUN
ejpam-2338	217	34	-	-	PUNCT
ejpam-2338	217	35	separating	separate	VERB
ejpam-2338	217	36	congruence	congruence	NOUN
ejpam-2338	217	37	on	on	ADP
ejpam-2338	217	38	an	an	DET
ejpam-2338	217	39	inverse	inverse	NOUN
ejpam-2338	217	40	semigroup	semigroup	NOUN
ejpam-2338	217	41	,	,	PUNCT
ejpam-2338	217	42	this	this	PRON
ejpam-2338	217	43	means	mean	VERB
ejpam-2338	217	44	that	that	SCONJ
ejpam-2338	217	45	a	a	DET
ejpam-2338	217	46	fundamental	fundamental	ADJ
ejpam-2338	217	47	inverse	inverse	NOUN
ejpam-2338	217	48	semigroup	semigroup	NOUN
ejpam-2338	217	49	has	have	VERB
ejpam-2338	217	50	no	no	DET
ejpam-2338	217	51	idempotentseparating	idempotentseparating	NOUN
ejpam-2338	217	52	congruences	congruence	NOUN
ejpam-2338	217	53	other	other	ADJ
ejpam-2338	217	54	than	than	ADP
ejpam-2338	217	55	equality	equality	NOUN
ejpam-2338	217	56	.	.	PUNCT
ejpam-2338	218	1	thus	thus	ADV
ejpam-2338	218	2	,	,	PUNCT
ejpam-2338	218	3	fundamental	fundamental	ADJ
ejpam-2338	218	4	inverse	inverse	NOUN
ejpam-2338	218	5	semigroups	semigroup	NOUN
ejpam-2338	218	6	represent	represent	VERB
ejpam-2338	218	7	one	one	NUM
ejpam-2338	218	8	extreme	extreme	NOUN
ejpam-2338	218	9	in	in	ADP
ejpam-2338	218	10	the	the	DET
ejpam-2338	218	11	study	study	NOUN
ejpam-2338	218	12	of	of	ADP
ejpam-2338	218	13	idempotent	idempotent	NOUN
ejpam-2338	218	14	-	-	PUNCT
ejpam-2338	218	15	separating	separate	VERB
ejpam-2338	218	16	congruences	congruence	NOUN
ejpam-2338	218	17	.	.	PUNCT
ejpam-2338	219	1	munn	munn	PROPN
ejpam-2338	219	2	’s	’s	PART
ejpam-2338	219	3	goal	goal	NOUN
ejpam-2338	219	4	was	be	AUX
ejpam-2338	219	5	to	to	PART
ejpam-2338	219	6	describe	describe	VERB
ejpam-2338	219	7	the	the	DET
ejpam-2338	219	8	structure	structure	NOUN
ejpam-2338	219	9	of	of	ADP
ejpam-2338	219	10	fundamental	fundamental	ADJ
ejpam-2338	219	11	inverse	inverse	NOUN
ejpam-2338	219	12	semigroups	semigroup	NOUN
ejpam-2338	219	13	.	.	PUNCT
ejpam-2338	220	1	the	the	DET
ejpam-2338	220	2	principal	principal	ADJ
ejpam-2338	220	3	tool	tool	NOUN
ejpam-2338	220	4	for	for	ADP
ejpam-2338	220	5	this	this	PRON
ejpam-2338	220	6	turned	turn	VERB
ejpam-2338	220	7	out	out	ADP
ejpam-2338	220	8	to	to	PART
ejpam-2338	220	9	be	be	AUX
ejpam-2338	220	10	a	a	DET
ejpam-2338	220	11	particular	particular	ADJ
ejpam-2338	220	12	semigroup	semigroup	NOUN
ejpam-2338	220	13	introduced	introduce	VERB
ejpam-2338	220	14	by	by	ADP
ejpam-2338	220	15	munn	munn	PROPN
ejpam-2338	220	16	in	in	ADP
ejpam-2338	220	17	a	a	DET
ejpam-2338	220	18	1966	1966	NUM
ejpam-2338	220	19	paper	paper	NOUN
ejpam-2338	220	20	.	.	PUNCT
ejpam-2338	221	1	let	let	VERB
ejpam-2338	221	2	e	e	PRON
ejpam-2338	221	3	be	be	AUX
ejpam-2338	221	4	a	a	DET
ejpam-2338	221	5	semilattice	semilattice	NOUN
ejpam-2338	221	6	;	;	PUNCT
ejpam-2338	221	7	ie	ie	X
ejpam-2338	221	8	denotes	denote	VERB
ejpam-2338	221	9	the	the	DET
ejpam-2338	221	10	symmetric	symmetric	ADJ
ejpam-2338	221	11	inverse	inverse	NOUN
ejpam-2338	221	12	semigroup	semigroup	NOUN
ejpam-2338	221	13	on	on	ADP
ejpam-2338	221	14	e.	e.	PROPN
ejpam-2338	221	15	we	we	PRON
ejpam-2338	221	16	define	define	VERB
ejpam-2338	221	17	a	a	DET
ejpam-2338	221	18	semigroup	semigroup	NOUN
ejpam-2338	221	19	te	te	PROPN
ejpam-2338	221	20	to	to	PART
ejpam-2338	221	21	be	be	AUX
ejpam-2338	221	22	the	the	DET
ejpam-2338	221	23	inverse	inverse	ADJ
ejpam-2338	221	24	subsemigroup	subsemigroup	NOUN
ejpam-2338	221	25	of	of	ADP
ejpam-2338	221	26	ie	ie	X
ejpam-2338	221	27	consisting	consist	VERB
ejpam-2338	221	28	of	of	ADP
ejpam-2338	221	29	all	all	DET
ejpam-2338	221	30	isomorphisms	isomorphism	NOUN
ejpam-2338	221	31	between	between	ADP
ejpam-2338	221	32	principal	principal	ADJ
ejpam-2338	221	33	ideals	ideal	NOUN
ejpam-2338	221	34	of	of	ADP
ejpam-2338	221	35	e.	e.	PROPN
ejpam-2338	221	36	the	the	DET
ejpam-2338	221	37	semigroup	semigroup	PROPN
ejpam-2338	222	1	te	te	PROPN
ejpam-2338	222	2	is	be	AUX
ejpam-2338	222	3	called	call	VERB
ejpam-2338	222	4	the	the	DET
ejpam-2338	222	5	munn	munn	PROPN
ejpam-2338	222	6	semigroup	semigroup	NOUN
ejpam-2338	222	7	(	(	PUNCT
ejpam-2338	222	8	of	of	ADP
ejpam-2338	222	9	e	e	NOUN
ejpam-2338	222	10	)	)	PUNCT
ejpam-2338	222	11	.	.	PUNCT
ejpam-2338	223	1	it	it	PRON
ejpam-2338	223	2	is	be	AUX
ejpam-2338	223	3	possible	possible	ADJ
ejpam-2338	223	4	to	to	PART
ejpam-2338	223	5	show	show	VERB
ejpam-2338	223	6	that	that	SCONJ
ejpam-2338	223	7	the	the	DET
ejpam-2338	223	8	semilattice	semilattice	NOUN
ejpam-2338	223	9	of	of	ADP
ejpam-2338	223	10	idempotents	idempotent	NOUN
ejpam-2338	223	11	of	of	ADP
ejpam-2338	223	12	te	te	PROPN
ejpam-2338	223	13	is	be	AUX
ejpam-2338	223	14	isomorphic	isomorphic	ADJ
ejpam-2338	223	15	to	to	ADP
ejpam-2338	223	16	e	e	PROPN
ejpam-2338	223	17	(	(	PUNCT
ejpam-2338	223	18	see	see	VERB
ejpam-2338	223	19	,	,	PUNCT
ejpam-2338	223	20	for	for	ADP
ejpam-2338	223	21	example	example	NOUN
ejpam-2338	223	22	,	,	PUNCT
ejpam-2338	223	23	[	[	X
ejpam-2338	223	24	44	44	NUM
ejpam-2338	223	25	,	,	PUNCT
ejpam-2338	223	26	theorem	theorem	VERB
ejpam-2338	223	27	5.4.1	5.4.1	NUM
ejpam-2338	223	28	]	]	PUNCT
ejpam-2338	223	29	)	)	PUNCT
ejpam-2338	223	30	.	.	PUNCT
ejpam-2338	224	1	furthermore	furthermore	ADV
ejpam-2338	224	2	,	,	PUNCT
ejpam-2338	224	3	munn	munn	PROPN
ejpam-2338	224	4	[	[	X
ejpam-2338	224	5	64	64	NUM
ejpam-2338	224	6	]	]	PUNCT
ejpam-2338	224	7	showed	show	VERB
ejpam-2338	224	8	that	that	SCONJ
ejpam-2338	224	9	for	for	ADP
ejpam-2338	224	10	any	any	DET
ejpam-2338	224	11	inverse	inverse	NOUN
ejpam-2338	224	12	semigroup	semigroup	NOUN
ejpam-2338	224	13	s	s	VERB
ejpam-2338	224	14	there	there	PRON
ejpam-2338	224	15	is	be	VERB
ejpam-2338	224	16	a	a	DET
ejpam-2338	224	17	morphism	morphism	NOUN
ejpam-2338	224	18	s	s	PART
ejpam-2338	224	19	→	→	SYM
ejpam-2338	224	20	te(s	te(s	NUM
ejpam-2338	224	21	)	)	PUNCT
ejpam-2338	224	22	which	which	PRON
ejpam-2338	224	23	maps	map	VERB
ejpam-2338	224	24	e(s	e(s	PROPN
ejpam-2338	224	25	)	)	PUNCT
ejpam-2338	224	26	isomorphically	isomorphically	ADV
ejpam-2338	224	27	onto	onto	ADP
ejpam-2338	224	28	e(te(s	e(te(s	NOUN
ejpam-2338	224	29	)	)	PUNCT
ejpam-2338	224	30	)	)	PUNCT
ejpam-2338	224	31	and	and	CCONJ
ejpam-2338	224	32	which	which	PRON
ejpam-2338	224	33	induces	induce	VERB
ejpam-2338	224	34	the	the	DET
ejpam-2338	224	35	maximum	maximum	ADJ
ejpam-2338	224	36	idempotent	idempotent	NOUN
ejpam-2338	224	37	-	-	PUNCT
ejpam-2338	224	38	separating	separate	VERB
ejpam-2338	224	39	congruence	congruence	NOUN
ejpam-2338	224	40	on	on	ADP
ejpam-2338	224	41	s.	s.	PROPN
ejpam-2338	224	42	lawson	lawson	PROPN
ejpam-2338	225	1	[	[	X
ejpam-2338	225	2	51	51	NUM
ejpam-2338	225	3	,	,	PUNCT
ejpam-2338	225	4	p.	p.	NOUN
ejpam-2338	225	5	141	141	NUM
ejpam-2338	225	6	]	]	PUNCT
ejpam-2338	225	7	leaves	leave	VERB
ejpam-2338	225	8	us	we	PRON
ejpam-2338	225	9	in	in	ADP
ejpam-2338	225	10	no	no	DET
ejpam-2338	225	11	doubt	doubt	NOUN
ejpam-2338	225	12	about	about	ADP
ejpam-2338	225	13	the	the	DET
ejpam-2338	225	14	significance	significance	NOUN
ejpam-2338	225	15	of	of	ADP
ejpam-2338	225	16	the	the	DET
ejpam-2338	225	17	munn	munn	PROPN
ejpam-2338	225	18	semigroup	semigroup	PROPN
ejpam-2338	225	19	:	:	PUNCT
ejpam-2338	225	20	this	this	DET
ejpam-2338	225	21	inverse	inverse	NOUN
ejpam-2338	225	22	semigroup	semigroup	NOUN
ejpam-2338	225	23	is	be	AUX
ejpam-2338	225	24	second	second	ADJ
ejpam-2338	225	25	only	only	ADV
ejpam-2338	225	26	to	to	ADP
ejpam-2338	225	27	the	the	DET
ejpam-2338	225	28	symmetric	symmetric	ADJ
ejpam-2338	225	29	inverse	inverse	NOUN
ejpam-2338	225	30	monoid	monoid	NOUN
ejpam-2338	225	31	in	in	ADP
ejpam-2338	225	32	its	its	PRON
ejpam-2338	225	33	importance	importance	NOUN
ejpam-2338	225	34	in	in	ADP
ejpam-2338	225	35	inverse	inverse	NOUN
ejpam-2338	225	36	semigroup	semigroup	PROPN
ejpam-2338	225	37	theory	theory	NOUN
ejpam-2338	225	38	.	.	PUNCT
ejpam-2338	226	1	it	it	PRON
ejpam-2338	226	2	is	be	AUX
ejpam-2338	226	3	particularly	particularly	ADV
ejpam-2338	226	4	useful	useful	ADJ
ejpam-2338	226	5	in	in	ADP
ejpam-2338	226	6	constructing	construct	VERB
ejpam-2338	226	7	examples	example	NOUN
ejpam-2338	226	8	of	of	ADP
ejpam-2338	226	9	inverse	inverse	NOUN
ejpam-2338	226	10	semigroups	semigroup	NOUN
ejpam-2338	226	11	with	with	ADP
ejpam-2338	226	12	a	a	DET
ejpam-2338	226	13	given	give	VERB
ejpam-2338	226	14	semilattice	semilattice	NOUN
ejpam-2338	226	15	of	of	ADP
ejpam-2338	226	16	idempotents	idempotent	NOUN
ejpam-2338	226	17	.	.	PUNCT
ejpam-2338	227	1	the	the	DET
ejpam-2338	227	2	munn	munn	PROPN
ejpam-2338	227	3	semigroup	semigroup	PROPN
ejpam-2338	227	4	plays	play	VERB
ejpam-2338	227	5	a	a	DET
ejpam-2338	227	6	central	central	ADJ
ejpam-2338	227	7	role	role	NOUN
ejpam-2338	227	8	in	in	ADP
ejpam-2338	227	9	munn	munn	PROPN
ejpam-2338	227	10	’s	’s	PART
ejpam-2338	227	11	description	description	NOUN
ejpam-2338	227	12	of	of	ADP
ejpam-2338	227	13	fundamental	fundamental	ADJ
ejpam-2338	227	14	inverse	inverse	NOUN
ejpam-2338	227	15	semigroups	semigroup	NOUN
ejpam-2338	227	16	:	:	PUNCT
ejpam-2338	227	17	the	the	DET
ejpam-2338	227	18	fundamental	fundamental	ADJ
ejpam-2338	227	19	representation	representation	NOUN
ejpam-2338	227	20	,	,	PUNCT
ejpam-2338	227	21	nowadays	nowadays	ADV
ejpam-2338	227	22	termed	term	VERB
ejpam-2338	227	23	the	the	DET
ejpam-2338	227	24	munn	munn	PROPN
ejpam-2338	227	25	representation	representation	NOUN
ejpam-2338	227	26	.	.	PUNCT
ejpam-2338	228	1	this	this	PRON
ejpam-2338	228	2	is	be	AUX
ejpam-2338	228	3	a	a	DET
ejpam-2338	228	4	morphism	morphism	NOUN
ejpam-2338	228	5	α	α	NOUN
ejpam-2338	228	6	:	:	PUNCT
ejpam-2338	228	7	s	s	X
ejpam-2338	228	8	→	→	SYM
ejpam-2338	228	9	ie(s	ie(s	NUM
ejpam-2338	228	10	)	)	PUNCT
ejpam-2338	228	11	,	,	PUNCT
ejpam-2338	228	12	where	where	SCONJ
ejpam-2338	228	13	the	the	DET
ejpam-2338	228	14	partial	partial	ADJ
ejpam-2338	228	15	bijection	bijection	NOUN
ejpam-2338	228	16	aα	aα	NOUN
ejpam-2338	228	17	=	=	NOUN
ejpam-2338	228	18	αa	αa	INTJ
ejpam-2338	228	19	is	be	AUX
ejpam-2338	228	20	given	give	VERB
ejpam-2338	228	21	by	by	ADP
ejpam-2338	228	22	eαa	eαa	NOUN
ejpam-2338	228	23	=	=	SYM
ejpam-2338	228	24	a−1ea	a−1ea	NOUN
ejpam-2338	228	25	on	on	ADP
ejpam-2338	228	26	the	the	DET
ejpam-2338	228	27	domain	domain	NOUN
ejpam-2338	228	28	e(s)aa−1	e(s)aa−1	NOUN
ejpam-2338	228	29	.	.	PUNCT
ejpam-2338	229	1	the	the	DET
ejpam-2338	229	2	munn	munn	PROPN
ejpam-2338	229	3	representation	representation	NOUN
ejpam-2338	229	4	thus	thus	ADV
ejpam-2338	229	5	gives	give	VERB
ejpam-2338	229	6	a	a	DET
ejpam-2338	229	7	rather	rather	ADV
ejpam-2338	229	8	different	different	ADJ
ejpam-2338	229	9	representation	representation	NOUN
ejpam-2338	229	10	of	of	ADP
ejpam-2338	229	11	an	an	DET
ejpam-2338	229	12	inverse	inverse	NOUN
ejpam-2338	229	13	semigroup	semigroup	NOUN
ejpam-2338	229	14	from	from	ADP
ejpam-2338	229	15	that	that	PRON
ejpam-2338	229	16	of	of	ADP
ejpam-2338	229	17	wagner	wagner	NOUN
ejpam-2338	229	18	and	and	CCONJ
ejpam-2338	229	19	preston;‡	preston;‡	ADV
ejpam-2338	229	20	unlike	unlike	ADP
ejpam-2338	229	21	the	the	DET
ejpam-2338	229	22	wagner	wagner	PROPN
ejpam-2338	229	23	–	–	PUNCT
ejpam-2338	229	24	preston	preston	PROPN
ejpam-2338	229	25	representation	representation	NOUN
ejpam-2338	229	26	,	,	PUNCT
ejpam-2338	229	27	the	the	DET
ejpam-2338	229	28	munn	munn	PROPN
ejpam-2338	229	29	representation	representation	NOUN
ejpam-2338	229	30	is	be	AUX
ejpam-2338	229	31	not	not	PART
ejpam-2338	229	32	necessarily	necessarily	ADV
ejpam-2338	229	33	faithful	faithful	ADJ
ejpam-2338	229	34	:	:	PUNCT
ejpam-2338	229	35	it	it	PRON
ejpam-2338	229	36	is	be	AUX
ejpam-2338	229	37	faithful	faithful	ADJ
ejpam-2338	229	38	only	only	ADV
ejpam-2338	229	39	if	if	SCONJ
ejpam-2338	229	40	s	s	NOUN
ejpam-2338	229	41	is	be	AUX
ejpam-2338	229	42	fundamental	fundamental	ADJ
ejpam-2338	229	43	(	(	PUNCT
ejpam-2338	229	44	see	see	VERB
ejpam-2338	229	45	[	[	X
ejpam-2338	229	46	82	82	NUM
ejpam-2338	229	47	]	]	PUNCT
ejpam-2338	229	48	for	for	ADP
ejpam-2338	229	49	efforts	effort	NOUN
ejpam-2338	229	50	to	to	PART
ejpam-2338	229	51	make	make	VERB
ejpam-2338	229	52	the	the	DET
ejpam-2338	229	53	munn	munn	PROPN
ejpam-2338	229	54	representation	representation	NOUN
ejpam-2338	229	55	faithful	faithful	NOUN
ejpam-2338	229	56	for	for	ADP
ejpam-2338	229	57	any	any	DET
ejpam-2338	229	58	s	s	NOUN
ejpam-2338	229	59	)	)	PUNCT
ejpam-2338	229	60	.	.	PUNCT
ejpam-2338	230	1	the	the	DET
ejpam-2338	230	2	munn	munn	PROPN
ejpam-2338	230	3	representation	representation	NOUN
ejpam-2338	230	4	has	have	AUX
ejpam-2338	230	5	also	also	ADV
ejpam-2338	230	6	become	become	VERB
ejpam-2338	230	7	a	a	DET
ejpam-2338	230	8	useful	useful	ADJ
ejpam-2338	230	9	tool	tool	NOUN
ejpam-2338	230	10	in	in	ADP
ejpam-2338	230	11	the	the	DET
ejpam-2338	230	12	study	study	NOUN
ejpam-2338	230	13	of	of	ADP
ejpam-2338	230	14	congruence	congruence	NOUN
ejpam-2338	230	15	-	-	PUNCT
ejpam-2338	230	16	free	free	ADJ
ejpam-2338	230	17	inverse	inverse	NOUN
ejpam-2338	230	18	semigroups	semigroup	NOUN
ejpam-2338	230	19	(	(	PUNCT
ejpam-2338	230	20	inverse	inverse	NOUN
ejpam-2338	230	21	semigroups	semigroup	NOUN
ejpam-2338	230	22	with	with	ADP
ejpam-2338	230	23	no	no	DET
ejpam-2338	230	24	non	non	ADJ
ejpam-2338	230	25	-	-	ADJ
ejpam-2338	230	26	trivial	trivial	ADJ
ejpam-2338	230	27	congruences	congruence	NOUN
ejpam-2338	230	28	)	)	PUNCT
ejpam-2338	230	29	—	—	PUNCT
ejpam-2338	230	30	see	see	VERB
ejpam-2338	230	31	[	[	X
ejpam-2338	230	32	72	72	NUM
ejpam-2338	230	33	,	,	PUNCT
ejpam-2338	230	34	§	§	NOUN
ejpam-2338	230	35	iv.3	iv.3	NOUN
ejpam-2338	230	36	]	]	PUNCT
ejpam-2338	230	37	.	.	PUNCT
ejpam-2338	231	1	‡we	‡we	PROPN
ejpam-2338	231	2	note	note	VERB
ejpam-2338	231	3	that	that	SCONJ
ejpam-2338	231	4	preston	preston	PROPN
ejpam-2338	231	5	had	have	AUX
ejpam-2338	231	6	in	in	ADP
ejpam-2338	231	7	fact	fact	NOUN
ejpam-2338	231	8	carried	carry	VERB
ejpam-2338	231	9	out	out	ADP
ejpam-2338	231	10	some	some	DET
ejpam-2338	231	11	preliminary	preliminary	ADJ
ejpam-2338	231	12	investigations	investigation	NOUN
ejpam-2338	231	13	on	on	ADP
ejpam-2338	231	14	the	the	DET
ejpam-2338	231	15	representation	representation	NOUN
ejpam-2338	231	16	of	of	ADP
ejpam-2338	231	17	inverse	inverse	NOUN
ejpam-2338	231	18	semigroups	semigroup	NOUN
ejpam-2338	231	19	by	by	ADP
ejpam-2338	231	20	partial	partial	ADJ
ejpam-2338	231	21	bijections	bijection	NOUN
ejpam-2338	231	22	of	of	ADP
ejpam-2338	231	23	their	their	PRON
ejpam-2338	231	24	semilattices	semilattice	NOUN
ejpam-2338	231	25	of	of	ADP
ejpam-2338	231	26	idempotents	idempotent	NOUN
ejpam-2338	231	27	in	in	ADP
ejpam-2338	231	28	his	his	PRON
ejpam-2338	231	29	early	early	ADJ
ejpam-2338	231	30	work	work	NOUN
ejpam-2338	231	31	;	;	PUNCT
ejpam-2338	231	32	see	see	VERB
ejpam-2338	231	33	,	,	PUNCT
ejpam-2338	231	34	for	for	ADP
ejpam-2338	231	35	example	example	NOUN
ejpam-2338	231	36	,	,	PUNCT
ejpam-2338	232	1	[	[	X
ejpam-2338	232	2	77	77	NUM
ejpam-2338	232	3	,	,	PUNCT
ejpam-2338	232	4	theorem	theorem	VERB
ejpam-2338	232	5	2	2	NUM
ejpam-2338	232	6	]	]	PUNCT
ejpam-2338	232	7	.	.	PUNCT
ejpam-2338	233	1	christopher	christopher	PROPN
ejpam-2338	233	2	hollings	hollings	PROPN
ejpam-2338	233	3	/	/	SYM
ejpam-2338	233	4	eur	eur	PROPN
ejpam-2338	233	5	.	.	PUNCT
ejpam-2338	234	1	j.	j.	PROPN
ejpam-2338	234	2	pure	pure	PROPN
ejpam-2338	234	3	appl	appl	PROPN
ejpam-2338	234	4	.	.	PROPN
ejpam-2338	234	5	math	math	PROPN
ejpam-2338	234	6	,	,	PUNCT
ejpam-2338	234	7	8	8	NUM
ejpam-2338	234	8	(	(	PUNCT
ejpam-2338	234	9	2015	2015	NUM
ejpam-2338	234	10	)	)	PUNCT
ejpam-2338	234	11	,	,	PUNCT
ejpam-2338	234	12	294	294	NUM
ejpam-2338	234	13	-	-	SYM
ejpam-2338	234	14	323	323	NUM
ejpam-2338	234	15	305	305	NUM
ejpam-2338	234	16	fountain	fountain	NOUN
ejpam-2338	234	17	[	[	X
ejpam-2338	234	18	20	20	NUM
ejpam-2338	234	19	,	,	PUNCT
ejpam-2338	234	20	theorem	theorem	VERB
ejpam-2338	234	21	2.5	2.5	NUM
ejpam-2338	234	22	]	]	PUNCT
ejpam-2338	234	23	presents	present	VERB
ejpam-2338	234	24	the	the	DET
ejpam-2338	234	25	following	follow	VERB
ejpam-2338	234	26	theorem	theorem	VERB
ejpam-2338	234	27	,	,	PUNCT
ejpam-2338	234	28	which	which	PRON
ejpam-2338	234	29	combines	combine	VERB
ejpam-2338	234	30	results	result	NOUN
ejpam-2338	234	31	of	of	ADP
ejpam-2338	234	32	munn	munn	PROPN
ejpam-2338	234	33	’s	’s	PART
ejpam-2338	234	34	1966	1966	NUM
ejpam-2338	234	35	and	and	CCONJ
ejpam-2338	234	36	1970	1970	NUM
ejpam-2338	234	37	papers	paper	NOUN
ejpam-2338	234	38	:	:	PUNCT
ejpam-2338	234	39	theorem	theorem	NOUN
ejpam-2338	234	40	1	1	NUM
ejpam-2338	234	41	.	.	PUNCT
ejpam-2338	235	1	let	let	VERB
ejpam-2338	235	2	s	s	PRON
ejpam-2338	235	3	be	be	AUX
ejpam-2338	235	4	an	an	DET
ejpam-2338	235	5	inverse	inverse	NOUN
ejpam-2338	235	6	semigroup	semigroup	NOUN
ejpam-2338	235	7	with	with	ADP
ejpam-2338	235	8	semilattice	semilattice	NOUN
ejpam-2338	235	9	e	e	PROPN
ejpam-2338	235	10	of	of	ADP
ejpam-2338	235	11	idempotents	idempotent	NOUN
ejpam-2338	235	12	.	.	PUNCT
ejpam-2338	236	1	then	then	ADV
ejpam-2338	236	2	(	(	PUNCT
ejpam-2338	236	3	1	1	X
ejpam-2338	236	4	)	)	PUNCT
ejpam-2338	236	5	te	te	PROPN
ejpam-2338	236	6	is	be	AUX
ejpam-2338	236	7	an	an	DET
ejpam-2338	236	8	inverse	inverse	NOUN
ejpam-2338	236	9	subsemigroup	subsemigroup	NOUN
ejpam-2338	236	10	of	of	ADP
ejpam-2338	236	11	ie	ie	X
ejpam-2338	236	12	;	;	PUNCT
ejpam-2338	236	13	(	(	PUNCT
ejpam-2338	236	14	2	2	X
ejpam-2338	236	15	)	)	PUNCT
ejpam-2338	236	16	if	if	SCONJ
ejpam-2338	236	17	α	α	NOUN
ejpam-2338	236	18	:	:	PUNCT
ejpam-2338	236	19	s→ie(s	s→ie(s	PROPN
ejpam-2338	236	20	)	)	PUNCT
ejpam-2338	236	21	is	be	AUX
ejpam-2338	236	22	the	the	DET
ejpam-2338	236	23	fundamental	fundamental	ADJ
ejpam-2338	236	24	representation	representation	NOUN
ejpam-2338	236	25	,	,	PUNCT
ejpam-2338	236	26	then	then	ADV
ejpam-2338	236	27	imα	imα	VERB
ejpam-2338	236	28	is	be	AUX
ejpam-2338	236	29	a	a	DET
ejpam-2338	236	30	full	full	ADJ
ejpam-2338	236	31	subsemigroup	subsemigroup	NOUN
ejpam-2338	236	32	of	of	ADP
ejpam-2338	236	33	te(s	te(s	NUM
ejpam-2338	236	34	)	)	PUNCT
ejpam-2338	236	35	(	(	PUNCT
ejpam-2338	236	36	that	that	ADV
ejpam-2338	236	37	is	is	ADV
ejpam-2338	236	38	,	,	PUNCT
ejpam-2338	236	39	it	it	PRON
ejpam-2338	236	40	contains	contain	VERB
ejpam-2338	236	41	all	all	DET
ejpam-2338	236	42	the	the	DET
ejpam-2338	236	43	idempotents	idempotent	NOUN
ejpam-2338	236	44	of	of	ADP
ejpam-2338	236	45	te(s	te(s	NUM
ejpam-2338	236	46	)	)	PUNCT
ejpam-2338	236	47	)	)	PUNCT
ejpam-2338	236	48	,	,	PUNCT
ejpam-2338	236	49	imα∼=	imα∼=	PROPN
ejpam-2338	236	50	s/µ	s/µ	NOUN
ejpam-2338	236	51	and	and	CCONJ
ejpam-2338	236	52	imα	imα	NOUN
ejpam-2338	236	53	is	be	AUX
ejpam-2338	236	54	fundamental	fundamental	ADJ
ejpam-2338	236	55	;	;	PUNCT
ejpam-2338	236	56	(	(	PUNCT
ejpam-2338	236	57	3	3	X
ejpam-2338	236	58	)	)	PUNCT
ejpam-2338	236	59	s	s	VERB
ejpam-2338	236	60	is	be	AUX
ejpam-2338	236	61	fundamental	fundamental	ADJ
ejpam-2338	236	62	if	if	SCONJ
ejpam-2338	236	63	and	and	CCONJ
ejpam-2338	236	64	only	only	ADV
ejpam-2338	236	65	if	if	SCONJ
ejpam-2338	236	66	it	it	PRON
ejpam-2338	236	67	is	be	AUX
ejpam-2338	236	68	isomorphic	isomorphic	ADJ
ejpam-2338	236	69	to	to	ADP
ejpam-2338	236	70	a	a	DET
ejpam-2338	236	71	full	full	ADJ
ejpam-2338	236	72	inverse	inverse	NOUN
ejpam-2338	236	73	subsemigroup	subsemigroup	NOUN
ejpam-2338	236	74	of	of	ADP
ejpam-2338	236	75	te(s	te(s	NUM
ejpam-2338	236	76	)	)	PUNCT
ejpam-2338	236	77	.	.	PUNCT
ejpam-2338	237	1	note	note	VERB
ejpam-2338	237	2	,	,	PUNCT
ejpam-2338	237	3	in	in	ADP
ejpam-2338	237	4	particular	particular	ADJ
ejpam-2338	237	5	,	,	PUNCT
ejpam-2338	237	6	that	that	SCONJ
ejpam-2338	237	7	te	te	PROPN
ejpam-2338	237	8	is	be	AUX
ejpam-2338	237	9	itself	itself	PRON
ejpam-2338	237	10	fundamental	fundamental	ADJ
ejpam-2338	237	11	.	.	PUNCT
ejpam-2338	238	1	besides	besides	SCONJ
ejpam-2338	238	2	those	those	DET
ejpam-2338	238	3	results	result	NOUN
ejpam-2338	238	4	listed	list	VERB
ejpam-2338	238	5	above	above	ADV
ejpam-2338	238	6	,	,	PUNCT
ejpam-2338	238	7	munn	munn	PROPN
ejpam-2338	238	8	also	also	ADV
ejpam-2338	238	9	gave	give	VERB
ejpam-2338	238	10	canonical	canonical	ADJ
ejpam-2338	238	11	constructions	construction	NOUN
ejpam-2338	238	12	(	(	PUNCT
ejpam-2338	238	13	by	by	ADP
ejpam-2338	238	14	means	mean	NOUN
ejpam-2338	238	15	of	of	ADP
ejpam-2338	238	16	partial	partial	ADJ
ejpam-2338	238	17	bijections	bijection	NOUN
ejpam-2338	238	18	)	)	PUNCT
ejpam-2338	238	19	for	for	ADP
ejpam-2338	238	20	bisimple	bisimple	ADJ
ejpam-2338	238	21	inverse	inverse	NOUN
ejpam-2338	238	22	semigroups	semigroup	NOUN
ejpam-2338	238	23	,	,	PUNCT
ejpam-2338	238	24	simple	simple	ADJ
ejpam-2338	238	25	inverse	inverse	NOUN
ejpam-2338	238	26	semigroups	semigroup	NOUN
ejpam-2338	238	27	,	,	PUNCT
ejpam-2338	238	28	and	and	CCONJ
ejpam-2338	238	29	inverse	inverse	NOUN
ejpam-2338	238	30	semigroups	semigroup	NOUN
ejpam-2338	238	31	with	with	ADP
ejpam-2338	238	32	no	no	DET
ejpam-2338	238	33	non	non	ADJ
ejpam-2338	238	34	-	-	ADJ
ejpam-2338	238	35	trivial	trivial	ADJ
ejpam-2338	238	36	groups	group	NOUN
ejpam-2338	238	37	as	as	ADP
ejpam-2338	238	38	homomorphic	homomorphic	ADJ
ejpam-2338	238	39	images	image	NOUN
ejpam-2338	238	40	.	.	PUNCT
ejpam-2338	239	1	each	each	PRON
ejpam-2338	239	2	of	of	ADP
ejpam-2338	239	3	these	these	PRON
ejpam-2338	239	4	was	be	AUX
ejpam-2338	239	5	characterised	characterise	VERB
ejpam-2338	239	6	using	use	VERB
ejpam-2338	239	7	a	a	DET
ejpam-2338	239	8	special	special	ADJ
ejpam-2338	239	9	type	type	NOUN
ejpam-2338	239	10	of	of	ADP
ejpam-2338	239	11	subsemigroup	subsemigroup	NOUN
ejpam-2338	239	12	of	of	ADP
ejpam-2338	239	13	te	te	PROPN
ejpam-2338	239	14	.	.	PUNCT
ejpam-2338	240	1	fundamental	fundamental	ADJ
ejpam-2338	240	2	inverse	inverse	NOUN
ejpam-2338	240	3	semigroups	semigroup	NOUN
ejpam-2338	240	4	thus	thus	ADV
ejpam-2338	240	5	live	live	VERB
ejpam-2338	240	6	up	up	ADP
ejpam-2338	240	7	to	to	ADP
ejpam-2338	240	8	their	their	PRON
ejpam-2338	240	9	name	name	NOUN
ejpam-2338	240	10	by	by	ADP
ejpam-2338	240	11	providing	provide	VERB
ejpam-2338	240	12	a	a	DET
ejpam-2338	240	13	foundation	foundation	NOUN
ejpam-2338	240	14	on	on	ADP
ejpam-2338	240	15	which	which	PRON
ejpam-2338	240	16	to	to	PART
ejpam-2338	240	17	construct	construct	VERB
ejpam-2338	240	18	various	various	ADJ
ejpam-2338	240	19	different	different	ADJ
ejpam-2338	240	20	classes	class	NOUN
ejpam-2338	240	21	of	of	ADP
ejpam-2338	240	22	inverse	inverse	NOUN
ejpam-2338	240	23	semigroups	semigroup	NOUN
ejpam-2338	240	24	.	.	PUNCT
ejpam-2338	241	1	although	although	SCONJ
ejpam-2338	241	2	we	we	PRON
ejpam-2338	241	3	have	have	AUX
ejpam-2338	241	4	focused	focus	VERB
ejpam-2338	241	5	on	on	ADP
ejpam-2338	241	6	munn	munn	PROPN
ejpam-2338	241	7	’s	’s	PART
ejpam-2338	241	8	contributions	contribution	NOUN
ejpam-2338	241	9	to	to	ADP
ejpam-2338	241	10	this	this	DET
ejpam-2338	241	11	aspect	aspect	NOUN
ejpam-2338	241	12	of	of	ADP
ejpam-2338	241	13	semigroup	semigroup	PROPN
ejpam-2338	241	14	theory	theory	NOUN
ejpam-2338	241	15	which	which	PRON
ejpam-2338	241	16	bears	bear	VERB
ejpam-2338	241	17	his	his	PRON
ejpam-2338	241	18	name	name	NOUN
ejpam-2338	241	19	,	,	PUNCT
ejpam-2338	241	20	we	we	PRON
ejpam-2338	241	21	note	note	VERB
ejpam-2338	241	22	that	that	SCONJ
ejpam-2338	241	23	he	he	PRON
ejpam-2338	241	24	was	be	AUX
ejpam-2338	241	25	not	not	PART
ejpam-2338	241	26	the	the	DET
ejpam-2338	241	27	only	only	ADJ
ejpam-2338	241	28	person	person	NOUN
ejpam-2338	241	29	to	to	PART
ejpam-2338	241	30	consider	consider	VERB
ejpam-2338	241	31	such	such	ADJ
ejpam-2338	241	32	problems	problem	NOUN
ejpam-2338	241	33	.	.	PUNCT
ejpam-2338	242	1	indeed	indeed	ADV
ejpam-2338	242	2	,	,	PUNCT
ejpam-2338	242	3	wagner	wagner	PROPN
ejpam-2338	243	1	[	[	X
ejpam-2338	243	2	100–102	100–102	NUM
ejpam-2338	243	3	]	]	PUNCT
ejpam-2338	243	4	studied	study	VERB
ejpam-2338	243	5	fundamental	fundamental	ADJ
ejpam-2338	243	6	inverse	inverse	NOUN
ejpam-2338	243	7	semigroups	semigroup	NOUN
ejpam-2338	243	8	independently	independently	ADV
ejpam-2338	243	9	around	around	ADP
ejpam-2338	243	10	the	the	DET
ejpam-2338	243	11	same	same	ADJ
ejpam-2338	243	12	time	time	NOUN
ejpam-2338	243	13	,	,	PUNCT
ejpam-2338	243	14	under	under	ADP
ejpam-2338	243	15	the	the	DET
ejpam-2338	243	16	name	name	NOUN
ejpam-2338	243	17	of	of	ADP
ejpam-2338	243	18	antigroups.§	antigroups.§	NOUN
ejpam-2338	243	19	as	as	ADP
ejpam-2338	243	20	in	in	ADP
ejpam-2338	243	21	his	his	PRON
ejpam-2338	243	22	earlier	early	ADJ
ejpam-2338	243	23	investigation	investigation	NOUN
ejpam-2338	243	24	of	of	ADP
ejpam-2338	243	25	inverse	inverse	NOUN
ejpam-2338	243	26	semigroups	semigroup	NOUN
ejpam-2338	243	27	,	,	PUNCT
ejpam-2338	243	28	wagner	wagner	PROPN
ejpam-2338	243	29	’s	’s	PART
ejpam-2338	243	30	work	work	NOUN
ejpam-2338	243	31	on	on	ADP
ejpam-2338	243	32	fundamental	fundamental	ADJ
ejpam-2338	243	33	inverse	inverse	NOUN
ejpam-2338	243	34	semigroups	semigroup	NOUN
ejpam-2338	243	35	was	be	AUX
ejpam-2338	243	36	based	base	VERB
ejpam-2338	243	37	heavily	heavily	ADV
ejpam-2338	243	38	on	on	ADP
ejpam-2338	243	39	the	the	DET
ejpam-2338	243	40	theory	theory	NOUN
ejpam-2338	243	41	of	of	ADP
ejpam-2338	243	42	binary	binary	ADJ
ejpam-2338	243	43	relations	relation	NOUN
ejpam-2338	243	44	:	:	PUNCT
ejpam-2338	243	45	in	in	ADP
ejpam-2338	243	46	[	[	X
ejpam-2338	243	47	100	100	NUM
ejpam-2338	243	48	]	]	PUNCT
ejpam-2338	243	49	,	,	PUNCT
ejpam-2338	243	50	for	for	ADP
ejpam-2338	243	51	example	example	NOUN
ejpam-2338	243	52	,	,	PUNCT
ejpam-2338	243	53	the	the	DET
ejpam-2338	243	54	majority	majority	NOUN
ejpam-2338	243	55	of	of	ADP
ejpam-2338	243	56	the	the	DET
ejpam-2338	243	57	results	result	NOUN
ejpam-2338	243	58	are	be	AUX
ejpam-2338	243	59	theorems	theorem	NOUN
ejpam-2338	243	60	on	on	ADP
ejpam-2338	243	61	these	these	PRON
ejpam-2338	243	62	,	,	PUNCT
ejpam-2338	243	63	which	which	PRON
ejpam-2338	243	64	are	be	AUX
ejpam-2338	243	65	then	then	ADV
ejpam-2338	243	66	used	use	VERB
ejpam-2338	243	67	to	to	PART
ejpam-2338	243	68	prove	prove	VERB
ejpam-2338	243	69	results	result	NOUN
ejpam-2338	243	70	on	on	ADP
ejpam-2338	243	71	fundamental	fundamental	ADJ
ejpam-2338	243	72	inverse	inverse	NOUN
ejpam-2338	243	73	semigroups	semigroup	NOUN
ejpam-2338	243	74	.	.	PUNCT
ejpam-2338	244	1	the	the	DET
ejpam-2338	244	2	main	main	ADJ
ejpam-2338	244	3	result	result	NOUN
ejpam-2338	244	4	of	of	ADP
ejpam-2338	244	5	this	this	DET
ejpam-2338	244	6	paper	paper	NOUN
ejpam-2338	244	7	is	be	AUX
ejpam-2338	244	8	the	the	DET
ejpam-2338	244	9	following	following	ADJ
ejpam-2338	244	10	extension	extension	NOUN
ejpam-2338	244	11	of	of	ADP
ejpam-2338	244	12	theorem	theorem	ADJ
ejpam-2338	244	13	1	1	NUM
ejpam-2338	244	14	[	[	SYM
ejpam-2338	244	15	100	100	NUM
ejpam-2338	244	16	,	,	PUNCT
ejpam-2338	244	17	theorem	theorem	VERB
ejpam-2338	244	18	11	11	NUM
ejpam-2338	244	19	]	]	NOUN
ejpam-2338	244	20	:	:	PUNCT
ejpam-2338	244	21	theorem	theorem	NOUN
ejpam-2338	244	22	2	2	NUM
ejpam-2338	244	23	.	.	PUNCT
ejpam-2338	244	24	an	an	DET
ejpam-2338	244	25	inverse	inverse	NOUN
ejpam-2338	244	26	semigroup	semigroup	NOUN
ejpam-2338	244	27	s	s	PART
ejpam-2338	244	28	is	be	AUX
ejpam-2338	244	29	fundamental	fundamental	ADJ
ejpam-2338	244	30	if	if	SCONJ
ejpam-2338	244	31	and	and	CCONJ
ejpam-2338	244	32	only	only	ADV
ejpam-2338	244	33	if	if	SCONJ
ejpam-2338	244	34	it	it	PRON
ejpam-2338	244	35	is	be	AUX
ejpam-2338	244	36	isomorphic	isomorphic	ADJ
ejpam-2338	244	37	to	to	ADP
ejpam-2338	244	38	a	a	DET
ejpam-2338	244	39	semigroup	semigroup	NOUN
ejpam-2338	244	40	of	of	ADP
ejpam-2338	244	41	homeomorphisms	homeomorphism	NOUN
ejpam-2338	244	42	between	between	ADP
ejpam-2338	244	43	open	open	ADJ
ejpam-2338	244	44	sets	set	NOUN
ejpam-2338	244	45	of	of	ADP
ejpam-2338	244	46	a	a	DET
ejpam-2338	244	47	t0	t0	PROPN
ejpam-2338	244	48	-	-	ADJ
ejpam-2338	244	49	topological	topological	ADJ
ejpam-2338	244	50	space	space	NOUN
ejpam-2338	244	51	.	.	PUNCT
ejpam-2338	245	1	in	in	ADP
ejpam-2338	245	2	the	the	DET
ejpam-2338	245	3	years	year	NOUN
ejpam-2338	245	4	since	since	SCONJ
ejpam-2338	245	5	its	its	PRON
ejpam-2338	245	6	introduction	introduction	NOUN
ejpam-2338	245	7	,	,	PUNCT
ejpam-2338	245	8	a	a	DET
ejpam-2338	245	9	considerable	considerable	ADJ
ejpam-2338	245	10	theory	theory	NOUN
ejpam-2338	245	11	has	have	AUX
ejpam-2338	245	12	grown	grow	VERB
ejpam-2338	245	13	up	up	ADP
ejpam-2338	245	14	around	around	ADP
ejpam-2338	245	15	the	the	DET
ejpam-2338	245	16	notion	notion	NOUN
ejpam-2338	245	17	of	of	ADP
ejpam-2338	245	18	a	a	DET
ejpam-2338	245	19	fundamental	fundamental	ADJ
ejpam-2338	245	20	inverse	inverse	NOUN
ejpam-2338	245	21	semigroup	semigroup	NOUN
ejpam-2338	245	22	—	—	PUNCT
ejpam-2338	245	23	far	far	ADV
ejpam-2338	245	24	too	too	ADV
ejpam-2338	245	25	much	much	ADJ
ejpam-2338	245	26	to	to	PART
ejpam-2338	245	27	cover	cover	VERB
ejpam-2338	245	28	here	here	ADV
ejpam-2338	245	29	,	,	PUNCT
ejpam-2338	245	30	so	so	ADV
ejpam-2338	245	31	i	i	PRON
ejpam-2338	245	32	refer	refer	VERB
ejpam-2338	245	33	the	the	DET
ejpam-2338	245	34	reader	reader	NOUN
ejpam-2338	245	35	to	to	ADP
ejpam-2338	245	36	the	the	DET
ejpam-2338	245	37	standard	standard	ADJ
ejpam-2338	245	38	texts	text	NOUN
ejpam-2338	245	39	on	on	ADP
ejpam-2338	245	40	inverse	inverse	NOUN
ejpam-2338	245	41	semigroups	semigroup	NOUN
ejpam-2338	245	42	:	:	PUNCT
ejpam-2338	246	1	[	[	X
ejpam-2338	246	2	44	44	NUM
ejpam-2338	246	3	,	,	PUNCT
ejpam-2338	246	4	§	§	NOUN
ejpam-2338	246	5	5.4	5.4	NUM
ejpam-2338	246	6	]	]	PUNCT
ejpam-2338	246	7	,	,	PUNCT
ejpam-2338	246	8	[	[	X
ejpam-2338	246	9	72	72	NUM
ejpam-2338	246	10	,	,	PUNCT
ejpam-2338	246	11	§	§	NOUN
ejpam-2338	246	12	iv.2	iv.2	NOUN
ejpam-2338	246	13	]	]	PUNCT
ejpam-2338	246	14	and	and	CCONJ
ejpam-2338	246	15	[	[	X
ejpam-2338	246	16	51	51	NUM
ejpam-2338	246	17	,	,	PUNCT
ejpam-2338	246	18	§	§	VERB
ejpam-2338	246	19	5.2	5.2	NUM
ejpam-2338	246	20	]	]	PUNCT
ejpam-2338	246	21	.	.	PUNCT
ejpam-2338	247	1	one	one	NUM
ejpam-2338	247	2	appearance	appearance	NOUN
ejpam-2338	247	3	of	of	ADP
ejpam-2338	247	4	fundamental	fundamental	ADJ
ejpam-2338	247	5	inverse	inverse	NOUN
ejpam-2338	247	6	semigroups	semigroup	NOUN
ejpam-2338	247	7	in	in	ADP
ejpam-2338	247	8	the	the	DET
ejpam-2338	247	9	literature	literature	NOUN
ejpam-2338	247	10	that	that	PRON
ejpam-2338	247	11	is	be	AUX
ejpam-2338	247	12	worth	worth	ADJ
ejpam-2338	247	13	noting	note	VERB
ejpam-2338	247	14	,	,	PUNCT
ejpam-2338	247	15	however	however	ADV
ejpam-2338	247	16	,	,	PUNCT
ejpam-2338	247	17	is	be	AUX
ejpam-2338	247	18	mills	mill	NOUN
ejpam-2338	247	19	’	'	PUNCT
ejpam-2338	247	20	use	use	NOUN
ejpam-2338	247	21	of	of	ADP
ejpam-2338	247	22	them	they	PRON
ejpam-2338	247	23	in	in	ADP
ejpam-2338	247	24	the	the	DET
ejpam-2338	247	25	study	study	NOUN
ejpam-2338	247	26	of	of	ADP
ejpam-2338	247	27	partial	partial	ADJ
ejpam-2338	247	28	symmetries	symmetry	NOUN
ejpam-2338	247	29	of	of	ADP
ejpam-2338	247	30	a	a	DET
ejpam-2338	247	31	convex	convex	ADJ
ejpam-2338	247	32	polygon	polygon	NOUN
ejpam-2338	247	33	in	in	ADP
ejpam-2338	247	34	the	the	DET
ejpam-2338	247	35	plane	plane	NOUN
ejpam-2338	247	36	[	[	X
ejpam-2338	247	37	61	61	NUM
ejpam-2338	247	38	]	]	PUNCT
ejpam-2338	247	39	.	.	PUNCT
ejpam-2338	248	1	like	like	ADP
ejpam-2338	248	2	certain	certain	ADJ
ejpam-2338	248	3	earlier	early	ADJ
ejpam-2338	248	4	techniques	technique	NOUN
ejpam-2338	248	5	of	of	ADP
ejpam-2338	248	6	rees	ree	NOUN
ejpam-2338	248	7	and	and	CCONJ
ejpam-2338	248	8	clifford	clifford	PROPN
ejpam-2338	248	9	(	(	PUNCT
ejpam-2338	248	10	discussed	discuss	VERB
ejpam-2338	248	11	in	in	ADP
ejpam-2338	248	12	[	[	X
ejpam-2338	248	13	37	37	NUM
ejpam-2338	248	14	]	]	PUNCT
ejpam-2338	248	15	and	and	CCONJ
ejpam-2338	248	16	[	[	X
ejpam-2338	248	17	41	41	NUM
ejpam-2338	248	18	,	,	PUNCT
ejpam-2338	248	19	chapter	chapter	NOUN
ejpam-2338	248	20	6	6	NUM
ejpam-2338	248	21	]	]	PUNCT
ejpam-2338	248	22	)	)	PUNCT
ejpam-2338	248	23	,	,	PUNCT
ejpam-2338	248	24	munn	munn	PROPN
ejpam-2338	248	25	’s	’s	PART
ejpam-2338	248	26	general	general	ADJ
ejpam-2338	248	27	approach	approach	NOUN
ejpam-2338	248	28	to	to	ADP
ejpam-2338	248	29	the	the	DET
ejpam-2338	248	30	study	study	NOUN
ejpam-2338	248	31	of	of	ADP
ejpam-2338	248	32	fundamental	fundamental	ADJ
ejpam-2338	248	33	inverse	inverse	NOUN
ejpam-2338	248	34	semigroups	semigroup	NOUN
ejpam-2338	248	35	has	have	AUX
ejpam-2338	248	36	provided	provide	VERB
ejpam-2338	248	37	a	a	DET
ejpam-2338	248	38	model	model	NOUN
ejpam-2338	248	39	for	for	ADP
ejpam-2338	248	40	many	many	ADJ
ejpam-2338	248	41	subsequent	subsequent	ADJ
ejpam-2338	248	42	results	result	NOUN
ejpam-2338	248	43	,	,	PUNCT
ejpam-2338	248	44	a	a	DET
ejpam-2338	248	45	flavour	flavour	NOUN
ejpam-2338	248	46	of	of	ADP
ejpam-2338	248	47	which	which	PRON
ejpam-2338	248	48	will	will	AUX
ejpam-2338	248	49	be	be	AUX
ejpam-2338	248	50	given	give	VERB
ejpam-2338	248	51	(	(	PUNCT
ejpam-2338	248	52	in	in	ADP
ejpam-2338	248	53	a	a	DET
ejpam-2338	248	54	specific	specific	ADJ
ejpam-2338	248	55	context	context	NOUN
ejpam-2338	248	56	)	)	PUNCT
ejpam-2338	248	57	in	in	ADP
ejpam-2338	248	58	section	section	NOUN
ejpam-2338	248	59	6.2	6.2	NUM
ejpam-2338	248	60	.	.	PUNCT
ejpam-2338	249	1	5	5	NUM
ejpam-2338	249	2	.	.	X
ejpam-2338	249	3	proper	proper	ADJ
ejpam-2338	249	4	inverse	inverse	NOUN
ejpam-2338	249	5	semigroups	semigroup	NOUN
ejpam-2338	249	6	and	and	CCONJ
ejpam-2338	249	7	the	the	DET
ejpam-2338	249	8	p	p	NOUN
ejpam-2338	249	9	-	-	PUNCT
ejpam-2338	249	10	theorem	theorem	ADJ
ejpam-2338	249	11	our	our	PRON
ejpam-2338	249	12	third	third	ADJ
ejpam-2338	249	13	and	and	CCONJ
ejpam-2338	249	14	final	final	ADJ
ejpam-2338	249	15	approach	approach	NOUN
ejpam-2338	249	16	to	to	ADP
ejpam-2338	249	17	the	the	DET
ejpam-2338	249	18	study	study	NOUN
ejpam-2338	249	19	of	of	ADP
ejpam-2338	249	20	the	the	DET
ejpam-2338	249	21	structure	structure	NOUN
ejpam-2338	249	22	of	of	ADP
ejpam-2338	249	23	inverse	inverse	NOUN
ejpam-2338	249	24	semigroups	semigroup	NOUN
ejpam-2338	249	25	is	be	AUX
ejpam-2338	249	26	derived	derive	VERB
ejpam-2338	249	27	in	in	ADP
ejpam-2338	249	28	large	large	ADJ
ejpam-2338	249	29	part	part	NOUN
ejpam-2338	249	30	from	from	ADP
ejpam-2338	249	31	the	the	DET
ejpam-2338	249	32	work	work	NOUN
ejpam-2338	249	33	of	of	ADP
ejpam-2338	249	34	mcalister	mcalister	NOUN
ejpam-2338	249	35	[	[	X
ejpam-2338	249	36	57	57	NUM
ejpam-2338	249	37	]	]	PUNCT
ejpam-2338	249	38	(	(	PUNCT
ejpam-2338	249	39	though	though	SCONJ
ejpam-2338	249	40	some	some	DET
ejpam-2338	249	41	elements	element	NOUN
ejpam-2338	249	42	were	be	AUX
ejpam-2338	249	43	also	also	ADV
ejpam-2338	249	44	present	present	ADJ
ejpam-2338	249	45	in	in	ADP
ejpam-2338	249	46	a	a	DET
ejpam-2338	249	47	§	§	PROPN
ejpam-2338	249	48	shiryaev	shiryaev	NOUN
ejpam-2338	249	49	[	[	X
ejpam-2338	249	50	93	93	NUM
ejpam-2338	249	51	]	]	PUNCT
ejpam-2338	249	52	called	call	VERB
ejpam-2338	249	53	them	they	PRON
ejpam-2338	249	54	rigid	rigid	ADJ
ejpam-2338	249	55	inverse	inverse	NOUN
ejpam-2338	249	56	semigroups	semigroup	NOUN
ejpam-2338	249	57	,	,	PUNCT
ejpam-2338	249	58	whilst	whilst	SCONJ
ejpam-2338	249	59	petrich	petrich	PROPN
ejpam-2338	249	60	[	[	X
ejpam-2338	249	61	72	72	NUM
ejpam-2338	249	62	,	,	PUNCT
ejpam-2338	249	63	p.	p.	NOUN
ejpam-2338	249	64	135	135	NUM
ejpam-2338	249	65	]	]	PUNCT
ejpam-2338	249	66	suggested	suggest	VERB
ejpam-2338	249	67	the	the	DET
ejpam-2338	249	68	name	name	NOUN
ejpam-2338	249	69	e	e	ADJ
ejpam-2338	249	70	-	-	ADJ
ejpam-2338	249	71	faithful	faithful	ADJ
ejpam-2338	249	72	inverse	inverse	NOUN
ejpam-2338	249	73	semigroup	semigroup	NOUN
ejpam-2338	249	74	,	,	PUNCT
ejpam-2338	249	75	in	in	ADP
ejpam-2338	249	76	view	view	NOUN
ejpam-2338	249	77	of	of	ADP
ejpam-2338	249	78	the	the	DET
ejpam-2338	249	79	fact	fact	NOUN
ejpam-2338	249	80	that	that	SCONJ
ejpam-2338	249	81	the	the	DET
ejpam-2338	249	82	munn	munn	PROPN
ejpam-2338	249	83	representation	representation	NOUN
ejpam-2338	249	84	is	be	AUX
ejpam-2338	249	85	faithful	faithful	ADJ
ejpam-2338	249	86	whenever	whenever	SCONJ
ejpam-2338	249	87	s	s	PROPN
ejpam-2338	249	88	is	be	AUX
ejpam-2338	249	89	fundamental	fundamental	ADJ
ejpam-2338	249	90	.	.	PUNCT
ejpam-2338	250	1	christopher	christopher	PROPN
ejpam-2338	250	2	hollings	hollings	PROPN
ejpam-2338	250	3	/	/	SYM
ejpam-2338	250	4	eur	eur	PROPN
ejpam-2338	250	5	.	.	PUNCT
ejpam-2338	251	1	j.	j.	PROPN
ejpam-2338	251	2	pure	pure	PROPN
ejpam-2338	251	3	appl	appl	PROPN
ejpam-2338	251	4	.	.	PROPN
ejpam-2338	251	5	math	math	PROPN
ejpam-2338	251	6	,	,	PUNCT
ejpam-2338	251	7	8	8	NUM
ejpam-2338	251	8	(	(	PUNCT
ejpam-2338	251	9	2015	2015	NUM
ejpam-2338	251	10	)	)	PUNCT
ejpam-2338	251	11	,	,	PUNCT
ejpam-2338	251	12	294	294	NUM
ejpam-2338	251	13	-	-	SYM
ejpam-2338	251	14	323	323	NUM
ejpam-2338	251	15	306	306	NUM
ejpam-2338	251	16	1939	1939	NUM
ejpam-2338	251	17	paper	paper	NOUN
ejpam-2338	251	18	by	by	ADP
ejpam-2338	251	19	stanisław	stanisław	ADJ
ejpam-2338	251	20	goła̧b	goła̧b	NOUN
ejpam-2338	251	21	,	,	PUNCT
ejpam-2338	251	22	as	as	SCONJ
ejpam-2338	251	23	we	we	PRON
ejpam-2338	251	24	will	will	AUX
ejpam-2338	251	25	see	see	VERB
ejpam-2338	251	26	)	)	PUNCT
ejpam-2338	251	27	.	.	PUNCT
ejpam-2338	252	1	this	this	PRON
ejpam-2338	252	2	is	be	AUX
ejpam-2338	252	3	the	the	DET
ejpam-2338	252	4	study	study	NOUN
ejpam-2338	252	5	of	of	ADP
ejpam-2338	252	6	so	so	ADV
ejpam-2338	252	7	-	-	PUNCT
ejpam-2338	252	8	called	call	VERB
ejpam-2338	252	9	e	e	NOUN
ejpam-2338	252	10	-	-	NOUN
ejpam-2338	252	11	unitary	unitary	ADJ
ejpam-2338	252	12	(	(	PUNCT
ejpam-2338	252	13	or	or	CCONJ
ejpam-2338	252	14	proper	proper	ADJ
ejpam-2338	252	15	)	)	PUNCT
ejpam-2338	252	16	inverse	inverse	NOUN
ejpam-2338	252	17	semigroups	semigroup	NOUN
ejpam-2338	252	18	,	,	PUNCT
ejpam-2338	252	19	culminating	culminate	VERB
ejpam-2338	252	20	in	in	ADP
ejpam-2338	252	21	the	the	DET
ejpam-2338	252	22	celebrated	celebrated	ADJ
ejpam-2338	252	23	p	p	NOUN
ejpam-2338	252	24	-	-	PUNCT
ejpam-2338	252	25	theorem	theorem	ADJ
ejpam-2338	252	26	,	,	PUNCT
ejpam-2338	252	27	which	which	PRON
ejpam-2338	252	28	gave	give	VERB
ejpam-2338	252	29	a	a	DET
ejpam-2338	252	30	complete	complete	ADJ
ejpam-2338	252	31	description	description	NOUN
ejpam-2338	252	32	of	of	ADP
ejpam-2338	252	33	these	these	DET
ejpam-2338	252	34	semigroups	semigroup	NOUN
ejpam-2338	252	35	.	.	PUNCT
ejpam-2338	253	1	5.1	5.1	NUM
ejpam-2338	253	2	.	.	PUNCT
ejpam-2338	254	1	the	the	DET
ejpam-2338	254	2	minimum	minimum	PROPN
ejpam-2338	254	3	group	group	NOUN
ejpam-2338	254	4	congruence	congruence	NOUN
ejpam-2338	254	5	to	to	PART
ejpam-2338	254	6	begin	begin	VERB
ejpam-2338	254	7	,	,	PUNCT
ejpam-2338	254	8	we	we	PRON
ejpam-2338	254	9	should	should	AUX
ejpam-2338	254	10	define	define	VERB
ejpam-2338	254	11	the	the	DET
ejpam-2338	254	12	notion	notion	NOUN
ejpam-2338	254	13	of	of	ADP
ejpam-2338	254	14	a	a	DET
ejpam-2338	254	15	proper	proper	ADJ
ejpam-2338	254	16	inverse	inverse	NOUN
ejpam-2338	254	17	semigroup	semigroup	NOUN
ejpam-2338	254	18	,	,	PUNCT
ejpam-2338	254	19	and	and	CCONJ
ejpam-2338	254	20	in	in	ADP
ejpam-2338	254	21	order	order	NOUN
ejpam-2338	254	22	to	to	PART
ejpam-2338	254	23	do	do	AUX
ejpam-2338	254	24	this	this	PRON
ejpam-2338	254	25	,	,	PUNCT
ejpam-2338	254	26	we	we	PRON
ejpam-2338	254	27	need	need	VERB
ejpam-2338	254	28	that	that	PRON
ejpam-2338	254	29	of	of	ADP
ejpam-2338	254	30	the	the	DET
ejpam-2338	254	31	‘	'	PUNCT
ejpam-2338	254	32	minimum	minimum	ADJ
ejpam-2338	254	33	group	group	NOUN
ejpam-2338	254	34	congruence	congruence	NOUN
ejpam-2338	254	35	’	'	PUNCT
ejpam-2338	254	36	.	.	PUNCT
ejpam-2338	255	1	any	any	DET
ejpam-2338	255	2	congruence	congruence	NOUN
ejpam-2338	255	3	on	on	ADP
ejpam-2338	255	4	a	a	DET
ejpam-2338	255	5	semigroup	semigroup	NOUN
ejpam-2338	255	6	for	for	ADP
ejpam-2338	255	7	which	which	PRON
ejpam-2338	255	8	the	the	DET
ejpam-2338	255	9	corresponding	corresponding	ADJ
ejpam-2338	255	10	factor	factor	NOUN
ejpam-2338	255	11	semigroup	semigroup	NOUN
ejpam-2338	255	12	is	be	AUX
ejpam-2338	255	13	a	a	DET
ejpam-2338	255	14	group	group	NOUN
ejpam-2338	255	15	is	be	AUX
ejpam-2338	255	16	called	call	VERB
ejpam-2338	255	17	a	a	DET
ejpam-2338	255	18	group	group	NOUN
ejpam-2338	255	19	congruence	congruence	NOUN
ejpam-2338	255	20	.	.	PUNCT
ejpam-2338	256	1	munn	munn	PROPN
ejpam-2338	257	1	[	[	X
ejpam-2338	257	2	62	62	NUM
ejpam-2338	257	3	,	,	PUNCT
ejpam-2338	257	4	theorem	theorem	VERB
ejpam-2338	257	5	1	1	NUM
ejpam-2338	257	6	]	]	PUNCT
ejpam-2338	257	7	showed	show	VERB
ejpam-2338	257	8	that	that	SCONJ
ejpam-2338	257	9	if	if	SCONJ
ejpam-2338	257	10	s	s	NOUN
ejpam-2338	257	11	is	be	AUX
ejpam-2338	257	12	an	an	DET
ejpam-2338	257	13	inverse	inverse	NOUN
ejpam-2338	257	14	semigroup	semigroup	NOUN
ejpam-2338	257	15	,	,	PUNCT
ejpam-2338	257	16	then	then	ADV
ejpam-2338	257	17	the	the	DET
ejpam-2338	257	18	congruence	congruence	PROPN
ejpam-2338	257	19	σ	σ	PROPN
ejpam-2338	257	20	on	on	ADP
ejpam-2338	257	21	s	s	AUX
ejpam-2338	257	22	given	give	VERB
ejpam-2338	257	23	by	by	ADP
ejpam-2338	257	24	sσ	sσ	PROPN
ejpam-2338	257	25	t	t	PROPN
ejpam-2338	257	26	⇐	⇐	ADJ
ejpam-2338	257	27	⇒	⇒	PROPN
ejpam-2338	257	28	ea	ea	PROPN
ejpam-2338	257	29	=	=	SYM
ejpam-2338	257	30	eb	eb	PROPN
ejpam-2338	257	31	,	,	PUNCT
ejpam-2338	257	32	for	for	ADP
ejpam-2338	257	33	some	some	DET
ejpam-2338	257	34	e	e	PROPN
ejpam-2338	257	35	∈	∈	PROPN
ejpam-2338	257	36	e(s	e(s	PROPN
ejpam-2338	257	37	)	)	PUNCT
ejpam-2338	257	38	,	,	PUNCT
ejpam-2338	257	39	is	be	AUX
ejpam-2338	257	40	the	the	DET
ejpam-2338	257	41	minimum	minimum	ADJ
ejpam-2338	257	42	group	group	NOUN
ejpam-2338	257	43	congruence	congruence	NOUN
ejpam-2338	257	44	on	on	ADP
ejpam-2338	257	45	s	s	PROPN
ejpam-2338	257	46	(	(	PUNCT
ejpam-2338	257	47	that	that	PRON
ejpam-2338	257	48	is	is	ADV
ejpam-2338	257	49	,	,	PUNCT
ejpam-2338	257	50	a	a	DET
ejpam-2338	257	51	group	group	NOUN
ejpam-2338	257	52	congruence	congruence	NOUN
ejpam-2338	257	53	which	which	PRON
ejpam-2338	257	54	is	be	AUX
ejpam-2338	257	55	contained	contain	VERB
ejpam-2338	257	56	in	in	ADP
ejpam-2338	257	57	every	every	DET
ejpam-2338	257	58	other	other	ADJ
ejpam-2338	257	59	group	group	NOUN
ejpam-2338	257	60	congruence).¶	congruence).¶	NOUN
ejpam-2338	257	61	note	note	VERB
ejpam-2338	257	62	that	that	SCONJ
ejpam-2338	257	63	σ	σ	NOUN
ejpam-2338	257	64	is	be	AUX
ejpam-2338	257	65	necessarily	necessarily	ADV
ejpam-2338	257	66	universal	universal	ADJ
ejpam-2338	257	67	in	in	ADP
ejpam-2338	257	68	any	any	DET
ejpam-2338	257	69	semigroup	semigroup	NOUN
ejpam-2338	257	70	with	with	ADP
ejpam-2338	257	71	a	a	DET
ejpam-2338	257	72	zero	zero	NUM
ejpam-2338	257	73	.	.	PUNCT
ejpam-2338	258	1	since	since	SCONJ
ejpam-2338	258	2	σ	σ	PROPN
ejpam-2338	258	3	is	be	AUX
ejpam-2338	258	4	the	the	DET
ejpam-2338	258	5	smallest	small	ADJ
ejpam-2338	258	6	possible	possible	ADJ
ejpam-2338	258	7	group	group	NOUN
ejpam-2338	258	8	congruence	congruence	NOUN
ejpam-2338	258	9	,	,	PUNCT
ejpam-2338	258	10	the	the	DET
ejpam-2338	258	11	factor	factor	NOUN
ejpam-2338	258	12	semigroup	semigroup	NOUN
ejpam-2338	258	13	s	s	PROPN
ejpam-2338	258	14	/	/	SYM
ejpam-2338	258	15	σ	σ	PROPN
ejpam-2338	258	16	is	be	AUX
ejpam-2338	258	17	the	the	DET
ejpam-2338	258	18	largest	large	ADJ
ejpam-2338	258	19	possible	possible	ADJ
ejpam-2338	258	20	group	group	NOUN
ejpam-2338	258	21	that	that	PRON
ejpam-2338	258	22	can	can	AUX
ejpam-2338	258	23	be	be	AUX
ejpam-2338	258	24	constructed	construct	VERB
ejpam-2338	258	25	in	in	ADP
ejpam-2338	258	26	this	this	DET
ejpam-2338	258	27	way	way	NOUN
ejpam-2338	258	28	;	;	PUNCT
ejpam-2338	258	29	for	for	ADP
ejpam-2338	258	30	this	this	DET
ejpam-2338	258	31	reason	reason	NOUN
ejpam-2338	258	32	,	,	PUNCT
ejpam-2338	258	33	it	it	PRON
ejpam-2338	258	34	is	be	AUX
ejpam-2338	258	35	often	often	ADV
ejpam-2338	258	36	termed	term	VERB
ejpam-2338	258	37	the	the	DET
ejpam-2338	258	38	maximum	maximum	ADJ
ejpam-2338	258	39	group	group	NOUN
ejpam-2338	258	40	image	image	NOUN
ejpam-2338	258	41	of	of	ADP
ejpam-2338	258	42	s.	s.	PROPN
ejpam-2338	258	43	it	it	PRON
ejpam-2338	258	44	is	be	AUX
ejpam-2338	258	45	worth	worth	ADJ
ejpam-2338	258	46	noting	note	VERB
ejpam-2338	258	47	the	the	DET
ejpam-2338	258	48	form	form	NOUN
ejpam-2338	258	49	that	that	PRON
ejpam-2338	258	50	σ	σ	PROPN
ejpam-2338	258	51	takes	take	VERB
ejpam-2338	258	52	when	when	SCONJ
ejpam-2338	258	53	we	we	PRON
ejpam-2338	258	54	move	move	VERB
ejpam-2338	258	55	away	away	ADV
ejpam-2338	258	56	from	from	ADP
ejpam-2338	258	57	the	the	DET
ejpam-2338	258	58	abstract	abstract	ADJ
ejpam-2338	258	59	setting	setting	NOUN
ejpam-2338	258	60	and	and	CCONJ
ejpam-2338	258	61	consider	consider	VERB
ejpam-2338	258	62	partial	partial	ADJ
ejpam-2338	258	63	bijections	bijection	NOUN
ejpam-2338	258	64	.	.	PUNCT
ejpam-2338	259	1	the	the	DET
ejpam-2338	259	2	only	only	ADJ
ejpam-2338	259	3	idempotent	idempotent	ADJ
ejpam-2338	259	4	partial	partial	ADJ
ejpam-2338	259	5	transformations	transformation	NOUN
ejpam-2338	259	6	on	on	ADP
ejpam-2338	259	7	a	a	DET
ejpam-2338	259	8	set	set	NOUN
ejpam-2338	259	9	x	x	VERB
ejpam-2338	259	10	are	be	AUX
ejpam-2338	259	11	the	the	DET
ejpam-2338	259	12	empty	empty	ADJ
ejpam-2338	259	13	transformation	transformation	NOUN
ejpam-2338	259	14	ǫ	ǫ	PRON
ejpam-2338	259	15	and	and	CCONJ
ejpam-2338	259	16	the	the	DET
ejpam-2338	259	17	partial	partial	ADJ
ejpam-2338	259	18	identity	identity	NOUN
ejpam-2338	259	19	transformations	transformation	NOUN
ejpam-2338	259	20	ia	ia	PROPN
ejpam-2338	259	21	,	,	PUNCT
ejpam-2338	259	22	for	for	ADP
ejpam-2338	259	23	a⊆	a⊆	PROPN
ejpam-2338	259	24	x	x	X
ejpam-2338	259	25	.	.	PUNCT
ejpam-2338	260	1	thus	thus	ADV
ejpam-2338	260	2	,	,	PUNCT
ejpam-2338	260	3	for	for	ADP
ejpam-2338	260	4	partial	partial	ADJ
ejpam-2338	260	5	bijections	bijection	NOUN
ejpam-2338	260	6	α	α	PROPN
ejpam-2338	260	7	,	,	PUNCT
ejpam-2338	260	8	β	β	X
ejpam-2338	260	9	on	on	ADP
ejpam-2338	260	10	x	x	SYM
ejpam-2338	260	11	,	,	PUNCT
ejpam-2338	260	12	we	we	PRON
ejpam-2338	260	13	have	have	VERB
ejpam-2338	260	14	ασβ	ασβ	NOUN
ejpam-2338	260	15	⇐	⇐	ADJ
ejpam-2338	260	16	⇒	⇒	NOUN
ejpam-2338	260	17	iaα=	iaα=	PROPN
ejpam-2338	260	18	iaβ	iaβ	ADV
ejpam-2338	260	19	,	,	PUNCT
ejpam-2338	260	20	for	for	ADP
ejpam-2338	260	21	some	some	DET
ejpam-2338	260	22	a⊆	a⊆	NOUN
ejpam-2338	260	23	x	x	X
ejpam-2338	260	24	.	.	PUNCT
ejpam-2338	261	1	but	but	CCONJ
ejpam-2338	261	2	the	the	DET
ejpam-2338	261	3	effect	effect	NOUN
ejpam-2338	261	4	of	of	ADP
ejpam-2338	261	5	composing	compose	VERB
ejpam-2338	261	6	α	α	NOUN
ejpam-2338	261	7	(	(	PUNCT
ejpam-2338	261	8	respectively	respectively	ADV
ejpam-2338	261	9	,	,	PUNCT
ejpam-2338	261	10	β	β	NOUN
ejpam-2338	261	11	)	)	PUNCT
ejpam-2338	261	12	with	with	ADP
ejpam-2338	261	13	ia	ia	PROPN
ejpam-2338	261	14	on	on	ADP
ejpam-2338	261	15	the	the	DET
ejpam-2338	261	16	left	left	NOUN
ejpam-2338	261	17	is	be	AUX
ejpam-2338	261	18	to	to	PART
ejpam-2338	261	19	restrict	restrict	VERB
ejpam-2338	261	20	α	α	PROPN
ejpam-2338	261	21	(	(	PUNCT
ejpam-2338	261	22	respectively	respectively	ADV
ejpam-2338	261	23	,	,	PUNCT
ejpam-2338	261	24	β	β	NOUN
ejpam-2338	261	25	)	)	PUNCT
ejpam-2338	261	26	to	to	ADP
ejpam-2338	261	27	a	a	PRON
ejpam-2338	261	28	;	;	PUNCT
ejpam-2338	261	29	we	we	PRON
ejpam-2338	261	30	can	can	AUX
ejpam-2338	261	31	see	see	VERB
ejpam-2338	261	32	this	this	PRON
ejpam-2338	261	33	by	by	ADP
ejpam-2338	261	34	applying	apply	VERB
ejpam-2338	261	35	(	(	PUNCT
ejpam-2338	261	36	1	1	NUM
ejpam-2338	261	37	)	)	PUNCT
ejpam-2338	261	38	.	.	PUNCT
ejpam-2338	262	1	therefore	therefore	ADV
ejpam-2338	262	2	,	,	PUNCT
ejpam-2338	262	3	the	the	DET
ejpam-2338	262	4	minimum	minimum	NOUN
ejpam-2338	262	5	group	group	NOUN
ejpam-2338	262	6	congruence	congruence	NOUN
ejpam-2338	262	7	takes	take	VERB
ejpam-2338	262	8	the	the	DET
ejpam-2338	262	9	following	follow	VERB
ejpam-2338	262	10	form	form	NOUN
ejpam-2338	262	11	in	in	ADP
ejpam-2338	262	12	any	any	DET
ejpam-2338	262	13	semigroup	semigroup	NOUN
ejpam-2338	262	14	of	of	ADP
ejpam-2338	262	15	partial	partial	ADJ
ejpam-2338	262	16	bijections	bijection	NOUN
ejpam-2338	262	17	:	:	PUNCT
ejpam-2338	262	18	ασβ	ασβ	PROPN
ejpam-2338	262	19	⇐	⇐	PROPN
ejpam-2338	262	20	⇒	⇒	NOUN
ejpam-2338	262	21	α|a	α|a	PUNCT
ejpam-2338	263	1	=	=	X
ejpam-2338	263	2	β	β	NOUN
ejpam-2338	263	3	|a	|a	NOUN
ejpam-2338	263	4	,	,	PUNCT
ejpam-2338	263	5	for	for	ADP
ejpam-2338	263	6	some	some	DET
ejpam-2338	263	7	a⊆	a⊆	NOUN
ejpam-2338	263	8	x	x	X
ejpam-2338	263	9	.	.	PUNCT
ejpam-2338	264	1	(	(	PUNCT
ejpam-2338	264	2	4	4	X
ejpam-2338	264	3	)	)	PUNCT
ejpam-2338	264	4	note	note	NOUN
ejpam-2338	264	5	,	,	PUNCT
ejpam-2338	264	6	however	however	ADV
ejpam-2338	264	7	,	,	PUNCT
ejpam-2338	264	8	that	that	SCONJ
ejpam-2338	264	9	σ	σ	PROPN
ejpam-2338	264	10	is	be	AUX
ejpam-2338	264	11	universal	universal	ADJ
ejpam-2338	264	12	in	in	ADP
ejpam-2338	264	13	ix	ix	PROPN
ejpam-2338	264	14	,	,	PUNCT
ejpam-2338	264	15	indeed	indeed	ADV
ejpam-2338	264	16	in	in	ADP
ejpam-2338	264	17	any	any	DET
ejpam-2338	264	18	semigroup	semigroup	NOUN
ejpam-2338	264	19	of	of	ADP
ejpam-2338	264	20	partial	partial	ADJ
ejpam-2338	264	21	bijections	bijection	NOUN
ejpam-2338	264	22	that	that	PRON
ejpam-2338	264	23	contains	contain	VERB
ejpam-2338	264	24	ǫ	ǫ	PRON
ejpam-2338	264	25	.	.	PUNCT
ejpam-2338	265	1	returning	return	VERB
ejpam-2338	265	2	to	to	ADP
ejpam-2338	265	3	the	the	DET
ejpam-2338	265	4	matter	matter	NOUN
ejpam-2338	265	5	of	of	ADP
ejpam-2338	265	6	proper	proper	ADJ
ejpam-2338	265	7	inverse	inverse	NOUN
ejpam-2338	265	8	semigroups	semigroup	NOUN
ejpam-2338	265	9	,	,	PUNCT
ejpam-2338	265	10	we	we	PRON
ejpam-2338	265	11	are	be	AUX
ejpam-2338	265	12	now	now	ADV
ejpam-2338	265	13	in	in	ADP
ejpam-2338	265	14	a	a	DET
ejpam-2338	265	15	position	position	NOUN
ejpam-2338	265	16	to	to	PART
ejpam-2338	265	17	state	state	VERB
ejpam-2338	265	18	that	that	SCONJ
ejpam-2338	265	19	an	an	DET
ejpam-2338	265	20	inverse	inverse	NOUN
ejpam-2338	265	21	semigroup	semigroup	NOUN
ejpam-2338	265	22	s	s	VERB
ejpam-2338	265	23	is	be	AUX
ejpam-2338	265	24	proper	proper	ADJ
ejpam-2338	265	25	if	if	SCONJ
ejpam-2338	265	26	σ	σ	NOUN
ejpam-2338	265	27	∩	∩	NOUN
ejpam-2338	265	28	r	r	NOUN
ejpam-2338	265	29	is	be	AUX
ejpam-2338	265	30	equality	equality	NOUN
ejpam-2338	265	31	,	,	PUNCT
ejpam-2338	265	32	where	where	SCONJ
ejpam-2338	265	33	r	r	NOUN
ejpam-2338	265	34	denotes	denote	VERB
ejpam-2338	265	35	green	green	PROPN
ejpam-2338	265	36	’s	’s	PART
ejpam-2338	265	37	righthand	righthand	NOUN
ejpam-2338	265	38	relation	relation	PROPN
ejpam-2338	265	39	.	.	PUNCT
ejpam-2338	266	1	in	in	ADP
ejpam-2338	266	2	a	a	DET
ejpam-2338	266	3	less	less	ADV
ejpam-2338	266	4	compact	compact	ADJ
ejpam-2338	266	5	form	form	NOUN
ejpam-2338	266	6	,	,	PUNCT
ejpam-2338	266	7	this	this	PRON
ejpam-2338	266	8	says	say	VERB
ejpam-2338	266	9	that	that	SCONJ
ejpam-2338	266	10	if	if	SCONJ
ejpam-2338	266	11	sσ	sσ	PROPN
ejpam-2338	266	12	t	t	PROPN
ejpam-2338	266	13	and	and	CCONJ
ejpam-2338	266	14	sr	sr	PROPN
ejpam-2338	266	15	t	t	PROPN
ejpam-2338	266	16	,	,	PUNCT
ejpam-2338	266	17	then	then	ADV
ejpam-2338	266	18	s	s	VERB
ejpam-2338	266	19	=	=	PUNCT
ejpam-2338	266	20	t.	t.	X
ejpam-2338	266	21	the	the	DET
ejpam-2338	266	22	first	first	ADJ
ejpam-2338	266	23	appearance	appearance	NOUN
ejpam-2338	266	24	of	of	ADP
ejpam-2338	266	25	proper	proper	ADJ
ejpam-2338	266	26	inverse	inverse	NOUN
ejpam-2338	266	27	semigroups	semigroup	NOUN
ejpam-2338	266	28	in	in	ADP
ejpam-2338	266	29	the	the	DET
ejpam-2338	266	30	literature	literature	NOUN
ejpam-2338	266	31	seems	seem	VERB
ejpam-2338	266	32	to	to	PART
ejpam-2338	266	33	have	have	AUX
ejpam-2338	266	34	been	be	AUX
ejpam-2338	266	35	in	in	ADP
ejpam-2338	266	36	the	the	DET
ejpam-2338	266	37	work	work	NOUN
ejpam-2338	266	38	of	of	ADP
ejpam-2338	266	39	saitô	saitô	PROPN
ejpam-2338	267	1	[	[	X
ejpam-2338	267	2	84	84	NUM
ejpam-2338	267	3	]	]	PUNCT
ejpam-2338	267	4	,	,	PUNCT
ejpam-2338	267	5	who	who	PRON
ejpam-2338	267	6	considered	consider	VERB
ejpam-2338	267	7	them	they	PRON
ejpam-2338	267	8	in	in	ADP
ejpam-2338	267	9	the	the	DET
ejpam-2338	267	10	ordered	order	VERB
ejpam-2338	267	11	case	case	NOUN
ejpam-2338	267	12	and	and	CCONJ
ejpam-2338	267	13	obtained	obtain	VERB
ejpam-2338	267	14	a	a	DET
ejpam-2338	267	15	characterisation	characterisation	NOUN
ejpam-2338	267	16	which	which	PRON
ejpam-2338	267	17	was	be	AUX
ejpam-2338	267	18	subsumed	subsume	VERB
ejpam-2338	267	19	by	by	ADP
ejpam-2338	267	20	that	that	PRON
ejpam-2338	267	21	of	of	ADP
ejpam-2338	267	22	mcalister	mcalister	PROPN
ejpam-2338	267	23	(	(	PUNCT
ejpam-2338	267	24	see	see	VERB
ejpam-2338	267	25	below	below	ADV
ejpam-2338	267	26	)	)	PUNCT
ejpam-2338	267	27	.	.	PUNCT
ejpam-2338	268	1	¶a	¶a	VERB
ejpam-2338	268	2	different	different	ADJ
ejpam-2338	268	3	characterisation	characterisation	NOUN
ejpam-2338	268	4	was	be	AUX
ejpam-2338	268	5	given	give	VERB
ejpam-2338	268	6	by	by	ADP
ejpam-2338	268	7	howie	howie	NOUN
ejpam-2338	269	1	[	[	X
ejpam-2338	269	2	43	43	NUM
ejpam-2338	269	3	]	]	X
ejpam-2338	269	4	;	;	PUNCT
ejpam-2338	269	5	this	this	PRON
ejpam-2338	269	6	may	may	AUX
ejpam-2338	269	7	be	be	AUX
ejpam-2338	269	8	found	find	VERB
ejpam-2338	269	9	in	in	ADP
ejpam-2338	269	10	[	[	X
ejpam-2338	269	11	44	44	NUM
ejpam-2338	269	12	,	,	PUNCT
ejpam-2338	269	13	theorem	theorem	VERB
ejpam-2338	269	14	5.3.5	5.3.5	NOUN
ejpam-2338	269	15	]	]	PUNCT
ejpam-2338	269	16	.	.	PUNCT
ejpam-2338	270	1	although	although	SCONJ
ejpam-2338	270	2	the	the	DET
ejpam-2338	270	3	minimum	minimum	ADJ
ejpam-2338	270	4	group	group	NOUN
ejpam-2338	270	5	congruence	congruence	NOUN
ejpam-2338	270	6	was	be	AUX
ejpam-2338	270	7	exploited	exploit	VERB
ejpam-2338	270	8	more	more	ADV
ejpam-2338	270	9	fully	fully	ADV
ejpam-2338	270	10	by	by	ADP
ejpam-2338	270	11	later	late	ADJ
ejpam-2338	270	12	authors	author	NOUN
ejpam-2338	270	13	,	,	PUNCT
ejpam-2338	270	14	such	such	ADJ
ejpam-2338	270	15	as	as	ADP
ejpam-2338	270	16	munn	munn	PROPN
ejpam-2338	270	17	[	[	X
ejpam-2338	270	18	62	62	NUM
ejpam-2338	270	19	]	]	PUNCT
ejpam-2338	270	20	,	,	PUNCT
ejpam-2338	270	21	it	it	PRON
ejpam-2338	270	22	was	be	AUX
ejpam-2338	270	23	in	in	ADP
ejpam-2338	270	24	fact	fact	NOUN
ejpam-2338	270	25	present	present	ADJ
ejpam-2338	270	26	in	in	ADP
ejpam-2338	270	27	a	a	DET
ejpam-2338	270	28	pair	pair	NOUN
ejpam-2338	270	29	of	of	ADP
ejpam-2338	270	30	earlier	early	ADJ
ejpam-2338	270	31	works	work	NOUN
ejpam-2338	270	32	on	on	ADP
ejpam-2338	270	33	inverse	inverse	NOUN
ejpam-2338	270	34	semigroups	semigroup	NOUN
ejpam-2338	270	35	and	and	CCONJ
ejpam-2338	270	36	related	related	ADJ
ejpam-2338	270	37	topics	topic	NOUN
ejpam-2338	270	38	,	,	PUNCT
ejpam-2338	270	39	namely	namely	ADV
ejpam-2338	270	40	,	,	PUNCT
ejpam-2338	270	41	those	those	PRON
ejpam-2338	270	42	of	of	ADP
ejpam-2338	270	43	goła̧b	goła̧b	PROPN
ejpam-2338	270	44	[	[	X
ejpam-2338	270	45	24	24	NUM
ejpam-2338	270	46	]	]	PUNCT
ejpam-2338	270	47	and	and	CCONJ
ejpam-2338	270	48	rees	ree	VERB
ejpam-2338	271	1	[	[	X
ejpam-2338	271	2	81	81	NUM
ejpam-2338	271	3	]	]	PUNCT
ejpam-2338	271	4	(	(	PUNCT
ejpam-2338	271	5	on	on	ADP
ejpam-2338	271	6	which	which	PRON
ejpam-2338	271	7	,	,	PUNCT
ejpam-2338	271	8	see	see	VERB
ejpam-2338	271	9	§	§	PROPN
ejpam-2338	271	10	10.2	10.2	NUM
ejpam-2338	271	11	and	and	CCONJ
ejpam-2338	271	12	§	§	PROPN
ejpam-2338	271	13	10.6	10.6	NUM
ejpam-2338	271	14	of	of	ADP
ejpam-2338	271	15	[	[	X
ejpam-2338	271	16	41	41	NUM
ejpam-2338	271	17	]	]	PUNCT
ejpam-2338	271	18	,	,	PUNCT
ejpam-2338	271	19	respectively	respectively	ADV
ejpam-2338	271	20	)	)	PUNCT
ejpam-2338	271	21	.	.	PUNCT
ejpam-2338	272	1	both	both	PRON
ejpam-2338	272	2	goła̧b	goła̧b	PROPN
ejpam-2338	272	3	and	and	CCONJ
ejpam-2338	272	4	rees	ree	NOUN
ejpam-2338	272	5	were	be	AUX
ejpam-2338	272	6	working	work	VERB
ejpam-2338	272	7	with	with	ADP
ejpam-2338	272	8	partial	partial	ADJ
ejpam-2338	272	9	bijections	bijection	NOUN
ejpam-2338	272	10	,	,	PUNCT
ejpam-2338	272	11	and	and	CCONJ
ejpam-2338	272	12	thus	thus	ADV
ejpam-2338	272	13	(	(	PUNCT
ejpam-2338	272	14	in	in	ADP
ejpam-2338	272	15	essence	essence	NOUN
ejpam-2338	272	16	)	)	PUNCT
ejpam-2338	272	17	defined	define	VERB
ejpam-2338	272	18	σ	σ	NOUN
ejpam-2338	272	19	in	in	ADP
ejpam-2338	272	20	the	the	DET
ejpam-2338	272	21	form	form	NOUN
ejpam-2338	272	22	given	give	VERB
ejpam-2338	272	23	in	in	ADP
ejpam-2338	272	24	(	(	PUNCT
ejpam-2338	272	25	4	4	NUM
ejpam-2338	272	26	)	)	PUNCT
ejpam-2338	272	27	.	.	PUNCT
ejpam-2338	273	1	we	we	PRON
ejpam-2338	273	2	note	note	VERB
ejpam-2338	273	3	also	also	ADV
ejpam-2338	273	4	that	that	SCONJ
ejpam-2338	273	5	,	,	PUNCT
ejpam-2338	273	6	as	as	ADP
ejpam-2338	273	7	with	with	ADP
ejpam-2338	273	8	so	so	ADV
ejpam-2338	273	9	much	much	ADJ
ejpam-2338	273	10	else	else	ADV
ejpam-2338	273	11	in	in	ADP
ejpam-2338	273	12	the	the	DET
ejpam-2338	273	13	theory	theory	NOUN
ejpam-2338	273	14	of	of	ADP
ejpam-2338	273	15	inverse	inverse	NOUN
ejpam-2338	273	16	semigroups	semigroup	NOUN
ejpam-2338	273	17	,	,	PUNCT
ejpam-2338	273	18	σ	σ	PROPN
ejpam-2338	273	19	put	put	VERB
ejpam-2338	273	20	in	in	ADP
ejpam-2338	273	21	a	a	DET
ejpam-2338	273	22	brief	brief	ADJ
ejpam-2338	273	23	appearance	appearance	NOUN
ejpam-2338	273	24	in	in	ADP
ejpam-2338	273	25	the	the	DET
ejpam-2338	273	26	work	work	NOUN
ejpam-2338	273	27	of	of	ADP
ejpam-2338	273	28	wagner	wagner	NOUN
ejpam-2338	274	1	[	[	X
ejpam-2338	274	2	98	98	NUM
ejpam-2338	274	3	,	,	PUNCT
ejpam-2338	274	4	theorem	theorem	VERB
ejpam-2338	274	5	4.39	4.39	NUM
ejpam-2338	274	6	]	]	PUNCT
ejpam-2338	274	7	.	.	PUNCT
ejpam-2338	275	1	christopher	christopher	PROPN
ejpam-2338	275	2	hollings	hollings	PROPN
ejpam-2338	275	3	/	/	SYM
ejpam-2338	275	4	eur	eur	PROPN
ejpam-2338	275	5	.	.	PUNCT
ejpam-2338	276	1	j.	j.	PROPN
ejpam-2338	276	2	pure	pure	PROPN
ejpam-2338	276	3	appl	appl	PROPN
ejpam-2338	276	4	.	.	PROPN
ejpam-2338	276	5	math	math	PROPN
ejpam-2338	276	6	,	,	PUNCT
ejpam-2338	276	7	8	8	NUM
ejpam-2338	276	8	(	(	PUNCT
ejpam-2338	276	9	2015	2015	NUM
ejpam-2338	276	10	)	)	PUNCT
ejpam-2338	276	11	,	,	PUNCT
ejpam-2338	276	12	294	294	NUM
ejpam-2338	276	13	-	-	SYM
ejpam-2338	276	14	323	323	NUM
ejpam-2338	276	15	307	307	NUM
ejpam-2338	276	16	another	another	DET
ejpam-2338	276	17	special	special	ADJ
ejpam-2338	276	18	property	property	NOUN
ejpam-2338	276	19	of	of	ADP
ejpam-2338	276	20	inverse	inverse	NOUN
ejpam-2338	276	21	semigroups	semigroup	NOUN
ejpam-2338	276	22	that	that	SCONJ
ejpam-2338	276	23	it	it	PRON
ejpam-2338	276	24	is	be	AUX
ejpam-2338	276	25	useful	useful	ADJ
ejpam-2338	276	26	to	to	PART
ejpam-2338	276	27	define	define	VERB
ejpam-2338	276	28	at	at	ADP
ejpam-2338	276	29	this	this	DET
ejpam-2338	276	30	point	point	NOUN
ejpam-2338	276	31	is	be	AUX
ejpam-2338	276	32	the	the	DET
ejpam-2338	276	33	property	property	NOUN
ejpam-2338	276	34	of	of	ADP
ejpam-2338	276	35	being	be	AUX
ejpam-2338	276	36	e	e	NOUN
ejpam-2338	276	37	-	-	NOUN
ejpam-2338	276	38	unitary	unitary	ADJ
ejpam-2338	276	39	.	.	PUNCT
ejpam-2338	277	1	an	an	DET
ejpam-2338	277	2	inverse	inverse	NOUN
ejpam-2338	277	3	semigroup	semigroup	NOUN
ejpam-2338	277	4	s	s	PART
ejpam-2338	277	5	is	be	AUX
ejpam-2338	277	6	said	say	VERB
ejpam-2338	277	7	to	to	PART
ejpam-2338	277	8	be	be	AUX
ejpam-2338	277	9	e	e	NOUN
ejpam-2338	277	10	-	-	NOUN
ejpam-2338	277	11	unitary	unitary	ADJ
ejpam-2338	277	12	if	if	SCONJ
ejpam-2338	277	13	,	,	PUNCT
ejpam-2338	277	14	for	for	ADP
ejpam-2338	277	15	any	any	DET
ejpam-2338	277	16	s	s	X
ejpam-2338	277	17	∈	∈	PROPN
ejpam-2338	277	18	s	s	NOUN
ejpam-2338	277	19	and	and	CCONJ
ejpam-2338	277	20	any	any	DET
ejpam-2338	277	21	e	e	PROPN
ejpam-2338	277	22	∈	∈	PROPN
ejpam-2338	277	23	e(s	e(s	PROPN
ejpam-2338	277	24	)	)	PUNCT
ejpam-2338	277	25	,	,	PUNCT
ejpam-2338	277	26	es	es	X
ejpam-2338	277	27	∈	∈	PROPN
ejpam-2338	277	28	e(s	e(s	PROPN
ejpam-2338	277	29	)	)	PUNCT
ejpam-2338	277	30	implies	imply	VERB
ejpam-2338	277	31	that	that	SCONJ
ejpam-2338	277	32	s	s	VERB
ejpam-2338	277	33	∈	∈	PROPN
ejpam-2338	277	34	e(s	e(s	PROPN
ejpam-2338	277	35	)	)	PUNCT
ejpam-2338	277	36	(	(	PUNCT
ejpam-2338	277	37	that	that	PRON
ejpam-2338	277	38	is	be	AUX
ejpam-2338	277	39	,	,	PUNCT
ejpam-2338	277	40	e(s	e(s	NUM
ejpam-2338	277	41	)	)	PUNCT
ejpam-2338	277	42	forms	form	VERB
ejpam-2338	277	43	a	a	DET
ejpam-2338	277	44	unitary	unitary	ADJ
ejpam-2338	277	45	subset	subset	NOUN
ejpam-2338	277	46	of	of	ADP
ejpam-2338	277	47	s	s	NOUN
ejpam-2338	277	48	)	)	PUNCT
ejpam-2338	277	49	.	.	PUNCT
ejpam-2338	278	1	the	the	DET
ejpam-2338	278	2	reason	reason	NOUN
ejpam-2338	278	3	that	that	SCONJ
ejpam-2338	278	4	this	this	DET
ejpam-2338	278	5	concept	concept	NOUN
ejpam-2338	278	6	is	be	AUX
ejpam-2338	278	7	useful	useful	ADJ
ejpam-2338	278	8	is	be	AUX
ejpam-2338	278	9	that	that	SCONJ
ejpam-2338	278	10	it	it	PRON
ejpam-2338	278	11	does	do	AUX
ejpam-2338	278	12	in	in	ADP
ejpam-2338	278	13	fact	fact	NOUN
ejpam-2338	278	14	give	give	VERB
ejpam-2338	278	15	an	an	DET
ejpam-2338	278	16	alternative	alternative	ADJ
ejpam-2338	278	17	characterisation	characterisation	NOUN
ejpam-2338	278	18	of	of	ADP
ejpam-2338	278	19	proper	proper	ADJ
ejpam-2338	278	20	inverse	inverse	NOUN
ejpam-2338	278	21	semigroups	semigroup	NOUN
ejpam-2338	278	22	:	:	PUNCT
ejpam-2338	278	23	an	an	DET
ejpam-2338	278	24	inverse	inverse	NOUN
ejpam-2338	278	25	semigroup	semigroup	NOUN
ejpam-2338	278	26	is	be	AUX
ejpam-2338	278	27	proper	proper	ADJ
ejpam-2338	278	28	if	if	SCONJ
ejpam-2338	278	29	and	and	CCONJ
ejpam-2338	278	30	only	only	ADV
ejpam-2338	278	31	if	if	SCONJ
ejpam-2338	278	32	it	it	PRON
ejpam-2338	278	33	is	be	AUX
ejpam-2338	278	34	e	e	NOUN
ejpam-2338	278	35	-	-	NOUN
ejpam-2338	278	36	unitary	unitary	ADJ
ejpam-2338	278	37	(	(	PUNCT
ejpam-2338	278	38	see	see	VERB
ejpam-2338	278	39	[	[	X
ejpam-2338	278	40	44	44	NUM
ejpam-2338	278	41	,	,	PUNCT
ejpam-2338	278	42	§	§	NOUN
ejpam-2338	278	43	5.9	5.9	NUM
ejpam-2338	278	44	]	]	PUNCT
ejpam-2338	278	45	)	)	PUNCT
ejpam-2338	278	46	.	.	PUNCT
ejpam-2338	279	1	we	we	PRON
ejpam-2338	279	2	will	will	AUX
ejpam-2338	279	3	use	use	VERB
ejpam-2338	279	4	both	both	DET
ejpam-2338	279	5	characterisations	characterisation	NOUN
ejpam-2338	279	6	(	(	PUNCT
ejpam-2338	279	7	and	and	CCONJ
ejpam-2338	279	8	,	,	PUNCT
ejpam-2338	279	9	indeed	indeed	ADV
ejpam-2338	279	10	,	,	PUNCT
ejpam-2338	279	11	both	both	DET
ejpam-2338	279	12	names	name	NOUN
ejpam-2338	279	13	)	)	PUNCT
ejpam-2338	279	14	throughout	throughout	ADP
ejpam-2338	279	15	this	this	DET
ejpam-2338	279	16	section	section	NOUN
ejpam-2338	279	17	.	.	PUNCT
ejpam-2338	280	1	note	note	VERB
ejpam-2338	280	2	that	that	SCONJ
ejpam-2338	280	3	,	,	PUNCT
ejpam-2338	280	4	rather	rather	ADV
ejpam-2338	280	5	than	than	ADP
ejpam-2338	280	6	‘	'	PUNCT
ejpam-2338	280	7	proper	proper	ADJ
ejpam-2338	280	8	’	'	PUNCT
ejpam-2338	280	9	,	,	PUNCT
ejpam-2338	280	10	o’carroll	o’carroll	PROPN
ejpam-2338	281	1	[	[	X
ejpam-2338	281	2	70	70	NUM
ejpam-2338	281	3	]	]	PUNCT
ejpam-2338	281	4	used	use	VERB
ejpam-2338	281	5	the	the	DET
ejpam-2338	281	6	term	term	NOUN
ejpam-2338	281	7	reduced	reduce	VERB
ejpam-2338	281	8	for	for	ADP
ejpam-2338	281	9	these	these	DET
ejpam-2338	281	10	inverse	inverse	NOUN
ejpam-2338	281	11	semigroups	semigroup	NOUN
ejpam-2338	281	12	.	.	PUNCT
ejpam-2338	282	1	indeed	indeed	ADV
ejpam-2338	282	2	,	,	PUNCT
ejpam-2338	282	3	preston	preston	PROPN
ejpam-2338	282	4	[	[	X
ejpam-2338	282	5	78	78	NUM
ejpam-2338	282	6	]	]	PUNCT
ejpam-2338	282	7	argued	argue	VERB
ejpam-2338	282	8	that	that	SCONJ
ejpam-2338	282	9	this	this	PRON
ejpam-2338	282	10	is	be	AUX
ejpam-2338	282	11	a	a	DET
ejpam-2338	282	12	more	more	ADV
ejpam-2338	282	13	natural	natural	ADJ
ejpam-2338	282	14	term	term	NOUN
ejpam-2338	282	15	,	,	PUNCT
ejpam-2338	282	16	since	since	SCONJ
ejpam-2338	282	17	such	such	DET
ejpam-2338	282	18	a	a	DET
ejpam-2338	282	19	semigroup	semigroup	NOUN
ejpam-2338	282	20	s	s	X
ejpam-2338	282	21	occurs	occur	VERB
ejpam-2338	282	22	when	when	SCONJ
ejpam-2338	282	23	the	the	DET
ejpam-2338	282	24	idempotent	idempotent	NOUN
ejpam-2338	282	25	of	of	ADP
ejpam-2338	282	26	s	s	PROPN
ejpam-2338	282	27	/	/	SYM
ejpam-2338	282	28	σ	σ	PROPN
ejpam-2338	282	29	is	be	AUX
ejpam-2338	282	30	smallest	small	ADJ
ejpam-2338	282	31	:	:	PUNCT
ejpam-2338	282	32	when	when	SCONJ
ejpam-2338	282	33	e(s	e(s	PROPN
ejpam-2338	282	34	)	)	PUNCT
ejpam-2338	282	35	is	be	AUX
ejpam-2338	282	36	a	a	DET
ejpam-2338	282	37	σ	σ	NOUN
ejpam-2338	282	38	-	-	PUNCT
ejpam-2338	282	39	class	class	NOUN
ejpam-2338	282	40	.	.	PUNCT
ejpam-2338	283	1	note	note	VERB
ejpam-2338	283	2	that	that	SCONJ
ejpam-2338	283	3	the	the	DET
ejpam-2338	283	4	‘	'	PUNCT
ejpam-2338	283	5	one	one	NUM
ejpam-2338	283	6	-	-	PUNCT
ejpam-2338	283	7	sidedness	sidedness	NOUN
ejpam-2338	283	8	’	'	PUNCT
ejpam-2338	283	9	in	in	ADP
ejpam-2338	283	10	the	the	DET
ejpam-2338	283	11	definitions	definition	NOUN
ejpam-2338	283	12	of	of	ADP
ejpam-2338	283	13	‘	'	PUNCT
ejpam-2338	283	14	proper	proper	ADJ
ejpam-2338	283	15	’	'	PUNCT
ejpam-2338	283	16	and	and	CCONJ
ejpam-2338	283	17	‘	'	PUNCT
ejpam-2338	283	18	e	e	NOUN
ejpam-2338	283	19	-	-	NOUN
ejpam-2338	283	20	unitary	unitary	ADJ
ejpam-2338	283	21	’	'	PUNCT
ejpam-2338	283	22	is	be	AUX
ejpam-2338	283	23	in	in	ADP
ejpam-2338	283	24	fact	fact	NOUN
ejpam-2338	283	25	only	only	ADV
ejpam-2338	283	26	apparent	apparent	ADJ
ejpam-2338	283	27	:	:	PUNCT
ejpam-2338	283	28	a	a	DET
ejpam-2338	283	29	proper	proper	ADJ
ejpam-2338	283	30	inverse	inverse	NOUN
ejpam-2338	283	31	semigroup	semigroup	NOUN
ejpam-2338	283	32	may	may	AUX
ejpam-2338	283	33	equivalently	equivalently	ADV
ejpam-2338	283	34	be	be	AUX
ejpam-2338	283	35	defined	define	VERB
ejpam-2338	283	36	by	by	ADP
ejpam-2338	283	37	demanding	demand	VERB
ejpam-2338	283	38	that	that	SCONJ
ejpam-2338	283	39	σ	σ	NOUN
ejpam-2338	283	40	∩l	∩l	AUX
ejpam-2338	283	41	be	be	AUX
ejpam-2338	283	42	equality	equality	NOUN
ejpam-2338	283	43	,	,	PUNCT
ejpam-2338	283	44	whilst	whilst	SCONJ
ejpam-2338	283	45	we	we	PRON
ejpam-2338	283	46	may	may	AUX
ejpam-2338	283	47	replace	replace	VERB
ejpam-2338	283	48	‘	'	PUNCT
ejpam-2338	283	49	es	es	NOUN
ejpam-2338	283	50	’	'	PUNCT
ejpam-2338	283	51	by	by	ADP
ejpam-2338	283	52	‘	'	PUNCT
ejpam-2338	283	53	se	se	X
ejpam-2338	283	54	’	'	PUNCT
ejpam-2338	283	55	in	in	ADP
ejpam-2338	283	56	the	the	DET
ejpam-2338	283	57	definition	definition	NOUN
ejpam-2338	283	58	of	of	ADP
ejpam-2338	283	59	an	an	DET
ejpam-2338	283	60	e	e	NOUN
ejpam-2338	283	61	-	-	ADJ
ejpam-2338	283	62	unitary	unitary	ADJ
ejpam-2338	283	63	inverse	inverse	NOUN
ejpam-2338	283	64	semigroup	semigroup	NOUN
ejpam-2338	283	65	(	(	PUNCT
ejpam-2338	283	66	again	again	ADV
ejpam-2338	283	67	,	,	PUNCT
ejpam-2338	283	68	see	see	VERB
ejpam-2338	283	69	[	[	X
ejpam-2338	283	70	44	44	NUM
ejpam-2338	283	71	,	,	PUNCT
ejpam-2338	283	72	§	§	NOUN
ejpam-2338	283	73	5.9	5.9	NUM
ejpam-2338	283	74	]	]	PUNCT
ejpam-2338	283	75	)	)	PUNCT
ejpam-2338	283	76	.	.	PUNCT
ejpam-2338	284	1	5.2	5.2	NUM
ejpam-2338	284	2	.	.	PUNCT
ejpam-2338	285	1	the	the	DET
ejpam-2338	285	2	covering	covering	NOUN
ejpam-2338	285	3	theorem	theorem	VERB
ejpam-2338	285	4	as	as	ADV
ejpam-2338	285	5	well	well	ADV
ejpam-2338	285	6	as	as	ADP
ejpam-2338	285	7	obtaining	obtain	VERB
ejpam-2338	285	8	the	the	DET
ejpam-2338	285	9	p	p	NOUN
ejpam-2338	285	10	-	-	PUNCT
ejpam-2338	285	11	theorem	theorem	ADJ
ejpam-2338	285	12	(	(	PUNCT
ejpam-2338	285	13	to	to	PART
ejpam-2338	285	14	be	be	AUX
ejpam-2338	285	15	stated	state	VERB
ejpam-2338	285	16	below	below	ADV
ejpam-2338	285	17	)	)	PUNCT
ejpam-2338	285	18	in	in	ADP
ejpam-2338	285	19	papers	paper	NOUN
ejpam-2338	285	20	of	of	ADP
ejpam-2338	285	21	1974	1974	NUM
ejpam-2338	285	22	,	,	PUNCT
ejpam-2338	285	23	mcalister	mcalister	PROPN
ejpam-2338	285	24	also	also	ADV
ejpam-2338	285	25	introduced	introduce	VERB
ejpam-2338	285	26	the	the	DET
ejpam-2338	285	27	notion	notion	NOUN
ejpam-2338	285	28	of	of	ADP
ejpam-2338	285	29	an	an	DET
ejpam-2338	285	30	e	e	NOUN
ejpam-2338	285	31	-	-	NOUN
ejpam-2338	285	32	unitary	unitary	ADJ
ejpam-2338	285	33	(	(	PUNCT
ejpam-2338	285	34	or	or	CCONJ
ejpam-2338	285	35	proper	proper	ADJ
ejpam-2338	285	36	)	)	PUNCT
ejpam-2338	285	37	cover	cover	NOUN
ejpam-2338	285	38	for	for	ADP
ejpam-2338	285	39	an	an	DET
ejpam-2338	285	40	inverse	inverse	NOUN
ejpam-2338	285	41	semigroup	semigroup	NOUN
ejpam-2338	285	42	(	(	PUNCT
ejpam-2338	285	43	for	for	ADP
ejpam-2338	285	44	a	a	DET
ejpam-2338	285	45	general	general	ADJ
ejpam-2338	285	46	introduction	introduction	NOUN
ejpam-2338	285	47	to	to	PART
ejpam-2338	285	48	covers	cover	NOUN
ejpam-2338	285	49	for	for	ADP
ejpam-2338	285	50	semigroups	semigroup	NOUN
ejpam-2338	285	51	,	,	PUNCT
ejpam-2338	285	52	see	see	VERB
ejpam-2338	285	53	[	[	X
ejpam-2338	285	54	19	19	NUM
ejpam-2338	285	55	]	]	NUM
ejpam-2338	285	56	)	)	PUNCT
ejpam-2338	285	57	.	.	PUNCT
ejpam-2338	286	1	such	such	DET
ejpam-2338	286	2	a	a	DET
ejpam-2338	286	3	notion	notion	NOUN
ejpam-2338	286	4	contrasts	contrast	VERB
ejpam-2338	286	5	with	with	ADP
ejpam-2338	286	6	that	that	PRON
ejpam-2338	286	7	of	of	ADP
ejpam-2338	286	8	the	the	DET
ejpam-2338	286	9	much	much	ADV
ejpam-2338	286	10	-	-	PUNCT
ejpam-2338	286	11	studied	study	VERB
ejpam-2338	286	12	‘	'	PUNCT
ejpam-2338	286	13	embedding	embed	VERB
ejpam-2338	286	14	problems	problem	NOUN
ejpam-2338	286	15	’	'	PUNCT
ejpam-2338	286	16	for	for	ADP
ejpam-2338	286	17	semigroups	semigroup	NOUN
ejpam-2338	286	18	:	:	PUNCT
ejpam-2338	286	19	the	the	DET
ejpam-2338	286	20	question	question	NOUN
ejpam-2338	286	21	of	of	ADP
ejpam-2338	286	22	whether	whether	SCONJ
ejpam-2338	286	23	a	a	DET
ejpam-2338	286	24	given	give	VERB
ejpam-2338	286	25	semigroup	semigroup	NOUN
ejpam-2338	286	26	can	can	AUX
ejpam-2338	286	27	be	be	AUX
ejpam-2338	286	28	embedded	embed	VERB
ejpam-2338	286	29	in	in	ADP
ejpam-2338	286	30	another	another	DET
ejpam-2338	286	31	semigroup	semigroup	NOUN
ejpam-2338	286	32	with	with	ADP
ejpam-2338	286	33	‘	'	PUNCT
ejpam-2338	286	34	nice	nice	ADJ
ejpam-2338	286	35	’	'	PUNCT
ejpam-2338	286	36	properties	property	NOUN
ejpam-2338	286	37	,	,	PUNCT
ejpam-2338	286	38	for	for	ADP
ejpam-2338	286	39	example	example	NOUN
ejpam-2338	286	40	,	,	PUNCT
ejpam-2338	286	41	a	a	DET
ejpam-2338	286	42	group	group	NOUN
ejpam-2338	286	43	(	(	PUNCT
ejpam-2338	286	44	see	see	VERB
ejpam-2338	286	45	[	[	X
ejpam-2338	286	46	41	41	NUM
ejpam-2338	286	47	,	,	PUNCT
ejpam-2338	286	48	chapter	chapter	NOUN
ejpam-2338	286	49	5	5	NUM
ejpam-2338	286	50	]	]	PUNCT
ejpam-2338	286	51	and	and	CCONJ
ejpam-2338	286	52	[	[	X
ejpam-2338	286	53	42	42	NUM
ejpam-2338	286	54	]	]	PUNCT
ejpam-2338	286	55	)	)	PUNCT
ejpam-2338	286	56	.	.	PUNCT
ejpam-2338	287	1	the	the	DET
ejpam-2338	287	2	problem	problem	NOUN
ejpam-2338	287	3	of	of	ADP
ejpam-2338	287	4	finding	find	VERB
ejpam-2338	287	5	covers	cover	NOUN
ejpam-2338	287	6	for	for	ADP
ejpam-2338	287	7	semigroups	semigroup	NOUN
ejpam-2338	287	8	is	be	AUX
ejpam-2338	287	9	in	in	ADP
ejpam-2338	287	10	some	some	DET
ejpam-2338	287	11	sense	sense	NOUN
ejpam-2338	287	12	the	the	DET
ejpam-2338	287	13	‘	'	PUNCT
ejpam-2338	287	14	opposite	opposite	ADJ
ejpam-2338	287	15	’	'	PUNCT
ejpam-2338	287	16	problem	problem	NOUN
ejpam-2338	287	17	:	:	PUNCT
ejpam-2338	287	18	whereas	whereas	SCONJ
ejpam-2338	287	19	the	the	DET
ejpam-2338	287	20	embedding	embed	VERB
ejpam-2338	287	21	problem	problem	NOUN
ejpam-2338	287	22	takes	take	VERB
ejpam-2338	287	23	a	a	DET
ejpam-2338	287	24	semigroup	semigroup	NOUN
ejpam-2338	287	25	s	s	NOUN
ejpam-2338	287	26	and	and	CCONJ
ejpam-2338	287	27	seeks	seek	VERB
ejpam-2338	287	28	an	an	DET
ejpam-2338	287	29	injective	injective	ADJ
ejpam-2338	287	30	morphism	morphism	NOUN
ejpam-2338	287	31	from	from	ADP
ejpam-2338	287	32	s	s	PRON
ejpam-2338	287	33	into	into	ADP
ejpam-2338	287	34	some	some	DET
ejpam-2338	287	35	other	other	ADJ
ejpam-2338	287	36	semigroup	semigroup	PROPN
ejpam-2338	287	37	t	t	PROPN
ejpam-2338	287	38	with	with	ADP
ejpam-2338	287	39	particular	particular	ADJ
ejpam-2338	287	40	properties	property	NOUN
ejpam-2338	287	41	,	,	PUNCT
ejpam-2338	287	42	the	the	DET
ejpam-2338	287	43	‘	'	PUNCT
ejpam-2338	287	44	covering	covering	NOUN
ejpam-2338	287	45	problem	problem	NOUN
ejpam-2338	287	46	’	'	PUNCT
ejpam-2338	287	47	seeks	seek	VERB
ejpam-2338	287	48	a	a	DET
ejpam-2338	287	49	surjective	surjective	ADJ
ejpam-2338	287	50	morphism	morphism	NOUN
ejpam-2338	287	51	from	from	ADP
ejpam-2338	287	52	t	t	PROPN
ejpam-2338	287	53	onto	onto	ADP
ejpam-2338	287	54	s.	s.	PROPN
ejpam-2338	287	55	in	in	ADP
ejpam-2338	287	56	particular	particular	ADJ
ejpam-2338	287	57	,	,	PUNCT
ejpam-2338	287	58	as	as	SCONJ
ejpam-2338	287	59	noted	note	VERB
ejpam-2338	287	60	above	above	ADV
ejpam-2338	287	61	,	,	PUNCT
ejpam-2338	287	62	mcalister	mcalister	PROPN
ejpam-2338	287	63	sought	seek	VERB
ejpam-2338	287	64	an	an	DET
ejpam-2338	287	65	e	e	NOUN
ejpam-2338	287	66	-	-	ADJ
ejpam-2338	287	67	unitary	unitary	ADJ
ejpam-2338	287	68	cover	cover	NOUN
ejpam-2338	287	69	for	for	ADP
ejpam-2338	287	70	an	an	DET
ejpam-2338	287	71	arbitrary	arbitrary	ADJ
ejpam-2338	287	72	inverse	inverse	NOUN
ejpam-2338	287	73	semigroup	semigroup	NOUN
ejpam-2338	287	74	s	s	PART
ejpam-2338	287	75	:	:	PUNCT
ejpam-2338	287	76	an	an	DET
ejpam-2338	287	77	e	e	NOUN
ejpam-2338	287	78	-	-	NOUN
ejpam-2338	287	79	unitary	unitary	ADJ
ejpam-2338	287	80	semigroup	semigroup	PROPN
ejpam-2338	287	81	t	t	PROPN
ejpam-2338	287	82	and	and	CCONJ
ejpam-2338	287	83	a	a	DET
ejpam-2338	287	84	surjective	surjective	ADJ
ejpam-2338	287	85	morphism	morphism	NOUN
ejpam-2338	287	86	φ	φ	PROPN
ejpam-2338	287	87	such	such	ADJ
ejpam-2338	287	88	that	that	SCONJ
ejpam-2338	287	89	s	s	PART
ejpam-2338	287	90	is	be	AUX
ejpam-2338	287	91	the	the	DET
ejpam-2338	287	92	homomorphic	homomorphic	ADJ
ejpam-2338	287	93	image	image	NOUN
ejpam-2338	287	94	of	of	ADP
ejpam-2338	287	95	t	t	PROPN
ejpam-2338	287	96	under	under	ADP
ejpam-2338	287	97	φ	φ	NUM
ejpam-2338	287	98	.	.	PUNCT
ejpam-2338	288	1	in	in	ADP
ejpam-2338	288	2	fact	fact	NOUN
ejpam-2338	288	3	,	,	PUNCT
ejpam-2338	288	4	mcalister	mcalister	PROPN
ejpam-2338	288	5	went	go	VERB
ejpam-2338	288	6	further	far	ADV
ejpam-2338	288	7	;	;	PUNCT
ejpam-2338	288	8	he	he	PRON
ejpam-2338	288	9	showed	show	VERB
ejpam-2338	288	10	that	that	SCONJ
ejpam-2338	288	11	such	such	DET
ejpam-2338	288	12	a	a	DET
ejpam-2338	288	13	cover	cover	NOUN
ejpam-2338	288	14	exists	exist	VERB
ejpam-2338	288	15	for	for	ADP
ejpam-2338	288	16	any	any	DET
ejpam-2338	288	17	inverse	inverse	NOUN
ejpam-2338	288	18	semigroup	semigroup	NOUN
ejpam-2338	288	19	via	via	ADP
ejpam-2338	288	20	an	an	DET
ejpam-2338	288	21	idempotent	idempotent	NOUN
ejpam-2338	288	22	-	-	PUNCT
ejpam-2338	288	23	separating	separate	VERB
ejpam-2338	288	24	morphism	morphism	NOUN
ejpam-2338	288	25	(	(	PUNCT
ejpam-2338	288	26	which	which	PRON
ejpam-2338	288	27	,	,	PUNCT
ejpam-2338	288	28	intuitively	intuitively	ADV
ejpam-2338	288	29	,	,	PUNCT
ejpam-2338	288	30	has	have	VERB
ejpam-2338	288	31	the	the	DET
ejpam-2338	288	32	effect	effect	NOUN
ejpam-2338	288	33	of	of	ADP
ejpam-2338	288	34	making	make	VERB
ejpam-2338	288	35	the	the	DET
ejpam-2338	288	36	cover	cover	NOUN
ejpam-2338	288	37	‘	'	PUNCT
ejpam-2338	288	38	tighter	tight	ADJ
ejpam-2338	288	39	’	'	PUNCT
ejpam-2338	288	40	)	)	PUNCT
ejpam-2338	288	41	—	—	PUNCT
ejpam-2338	288	42	the	the	DET
ejpam-2338	288	43	so	so	ADV
ejpam-2338	288	44	-	-	PUNCT
ejpam-2338	288	45	called	call	VERB
ejpam-2338	288	46	covering	covering	NOUN
ejpam-2338	288	47	theorem	theorem	NOUN
ejpam-2338	288	48	:	:	PUNCT
ejpam-2338	288	49	theorem	theorem	ADJ
ejpam-2338	288	50	3	3	NUM
ejpam-2338	288	51	(	(	PUNCT
ejpam-2338	288	52	[	[	X
ejpam-2338	288	53	51	51	NUM
ejpam-2338	288	54	,	,	PUNCT
ejpam-2338	288	55	theorem	theorem	VERB
ejpam-2338	288	56	2.2.4	2.2.4	NUM
ejpam-2338	288	57	]	]	NUM
ejpam-2338	288	58	)	)	PUNCT
ejpam-2338	288	59	.	.	PUNCT
ejpam-2338	289	1	every	every	DET
ejpam-2338	289	2	inverse	inverse	NOUN
ejpam-2338	289	3	semigroup	semigroup	NOUN
ejpam-2338	289	4	is	be	AUX
ejpam-2338	289	5	the	the	DET
ejpam-2338	289	6	image	image	NOUN
ejpam-2338	289	7	of	of	ADP
ejpam-2338	289	8	a	a	DET
ejpam-2338	289	9	proper	proper	ADJ
ejpam-2338	289	10	inverse	inverse	NOUN
ejpam-2338	289	11	semigroup	semigroup	NOUN
ejpam-2338	289	12	under	under	ADP
ejpam-2338	289	13	an	an	DET
ejpam-2338	289	14	idempotent	idempotent	NOUN
ejpam-2338	289	15	-	-	PUNCT
ejpam-2338	289	16	separating	separate	VERB
ejpam-2338	289	17	morphism	morphism	NOUN
ejpam-2338	289	18	.	.	PUNCT
ejpam-2338	290	1	lawson	lawson	PROPN
ejpam-2338	291	1	[	[	X
ejpam-2338	291	2	50	50	NUM
ejpam-2338	291	3	,	,	PUNCT
ejpam-2338	291	4	p.	p.	NOUN
ejpam-2338	291	5	73	73	NUM
ejpam-2338	291	6	]	]	PUNCT
ejpam-2338	291	7	observes	observe	VERB
ejpam-2338	291	8	that	that	SCONJ
ejpam-2338	291	9	gérard	gérard	PROPN
ejpam-2338	291	10	joubert	joubert	PROPN
ejpam-2338	291	11	,	,	PUNCT
ejpam-2338	291	12	a	a	DET
ejpam-2338	291	13	student	student	NOUN
ejpam-2338	291	14	of	of	ADP
ejpam-2338	291	15	ehresmann	ehresmann	PROPN
ejpam-2338	291	16	,	,	PUNCT
ejpam-2338	291	17	had	have	AUX
ejpam-2338	291	18	earlier	early	ADV
ejpam-2338	291	19	proved	prove	VERB
ejpam-2338	291	20	a	a	DET
ejpam-2338	291	21	result	result	NOUN
ejpam-2338	291	22	which	which	PRON
ejpam-2338	291	23	is	be	AUX
ejpam-2338	291	24	equivalent	equivalent	ADJ
ejpam-2338	291	25	to	to	ADP
ejpam-2338	291	26	the	the	DET
ejpam-2338	291	27	covering	covering	NOUN
ejpam-2338	291	28	theorem	theorem	NOUN
ejpam-2338	291	29	[	[	X
ejpam-2338	291	30	46	46	NUM
ejpam-2338	291	31	]	]	PUNCT
ejpam-2338	291	32	.	.	PUNCT
ejpam-2338	292	1	we	we	PRON
ejpam-2338	292	2	will	will	AUX
ejpam-2338	292	3	link	link	VERB
ejpam-2338	292	4	e	e	NOUN
ejpam-2338	292	5	-	-	NOUN
ejpam-2338	292	6	unitary	unitary	ADJ
ejpam-2338	292	7	covers	cover	NOUN
ejpam-2338	292	8	with	with	ADP
ejpam-2338	292	9	the	the	DET
ejpam-2338	292	10	p	p	NOUN
ejpam-2338	292	11	-	-	PUNCT
ejpam-2338	292	12	theorem	theorem	ADJ
ejpam-2338	292	13	below	below	ADV
ejpam-2338	292	14	,	,	PUNCT
ejpam-2338	292	15	but	but	CCONJ
ejpam-2338	292	16	we	we	PRON
ejpam-2338	292	17	must	must	AUX
ejpam-2338	292	18	first	first	ADV
ejpam-2338	292	19	define	define	VERB
ejpam-2338	292	20	the	the	DET
ejpam-2338	292	21	notion	notion	NOUN
ejpam-2338	292	22	of	of	ADP
ejpam-2338	292	23	a	a	DET
ejpam-2338	292	24	p	p	NOUN
ejpam-2338	292	25	-	-	PUNCT
ejpam-2338	292	26	semigroup	semigroup	NOUN
ejpam-2338	292	27	.	.	PUNCT
ejpam-2338	293	1	5.3	5.3	NUM
ejpam-2338	293	2	.	.	PUNCT
ejpam-2338	294	1	p	p	X
ejpam-2338	294	2	-	-	PUNCT
ejpam-2338	294	3	semigroups	semigroup	NOUN
ejpam-2338	294	4	as	as	SCONJ
ejpam-2338	294	5	already	already	ADV
ejpam-2338	294	6	commented	comment	VERB
ejpam-2338	294	7	,	,	PUNCT
ejpam-2338	294	8	mcalister	mcalister	PROPN
ejpam-2338	294	9	’s	’s	PART
ejpam-2338	294	10	p	p	NOUN
ejpam-2338	294	11	-	-	PUNCT
ejpam-2338	294	12	theorem	theorem	NOUN
ejpam-2338	294	13	gives	give	VERB
ejpam-2338	294	14	a	a	DET
ejpam-2338	294	15	complete	complete	ADJ
ejpam-2338	294	16	characterisation	characterisation	NOUN
ejpam-2338	294	17	of	of	ADP
ejpam-2338	294	18	the	the	DET
ejpam-2338	294	19	structure	structure	NOUN
ejpam-2338	294	20	of	of	ADP
ejpam-2338	294	21	proper	proper	ADJ
ejpam-2338	294	22	inverse	inverse	NOUN
ejpam-2338	294	23	semigroups	semigroup	NOUN
ejpam-2338	294	24	.	.	PUNCT
ejpam-2338	295	1	the	the	DET
ejpam-2338	295	2	central	central	ADJ
ejpam-2338	295	3	concept	concept	NOUN
ejpam-2338	295	4	in	in	ADP
ejpam-2338	295	5	the	the	DET
ejpam-2338	295	6	p	p	NOUN
ejpam-2338	295	7	-	-	PUNCT
ejpam-2338	295	8	theorem	theorem	ADJ
ejpam-2338	295	9	is	be	AUX
ejpam-2338	295	10	that	that	PRON
ejpam-2338	295	11	of	of	ADP
ejpam-2338	295	12	a	a	DET
ejpam-2338	295	13	psemigroup	psemigroup	NOUN
ejpam-2338	295	14	,	,	PUNCT
ejpam-2338	295	15	a	a	DET
ejpam-2338	295	16	semigroup	semigroup	NOUN
ejpam-2338	295	17	constructed	construct	VERB
ejpam-2338	295	18	according	accord	VERB
ejpam-2338	295	19	to	to	ADP
ejpam-2338	295	20	a	a	DET
ejpam-2338	295	21	particular	particular	ADJ
ejpam-2338	295	22	recipe	recipe	NOUN
ejpam-2338	295	23	,	,	PUNCT
ejpam-2338	295	24	which	which	PRON
ejpam-2338	295	25	we	we	PRON
ejpam-2338	295	26	now	now	ADV
ejpam-2338	295	27	describe	describe	VERB
ejpam-2338	295	28	,	,	PUNCT
ejpam-2338	295	29	christopher	christopher	PROPN
ejpam-2338	295	30	hollings	hollings	PROPN
ejpam-2338	295	31	/	/	SYM
ejpam-2338	295	32	eur	eur	PROPN
ejpam-2338	295	33	.	.	PUNCT
ejpam-2338	296	1	j.	j.	PROPN
ejpam-2338	296	2	pure	pure	PROPN
ejpam-2338	296	3	appl	appl	PROPN
ejpam-2338	296	4	.	.	PROPN
ejpam-2338	296	5	math	math	PROPN
ejpam-2338	296	6	,	,	PUNCT
ejpam-2338	296	7	8	8	NUM
ejpam-2338	296	8	(	(	PUNCT
ejpam-2338	296	9	2015	2015	NUM
ejpam-2338	296	10	)	)	PUNCT
ejpam-2338	296	11	,	,	PUNCT
ejpam-2338	296	12	294	294	NUM
ejpam-2338	296	13	-	-	SYM
ejpam-2338	296	14	323	323	NUM
ejpam-2338	296	15	308	308	NUM
ejpam-2338	296	16	following	follow	VERB
ejpam-2338	296	17	the	the	DET
ejpam-2338	296	18	account	account	NOUN
ejpam-2338	296	19	of	of	ADP
ejpam-2338	296	20	howie	howie	NOUN
ejpam-2338	296	21	[	[	X
ejpam-2338	296	22	44	44	NUM
ejpam-2338	296	23	,	,	PUNCT
ejpam-2338	296	24	§	§	PROPN
ejpam-2338	296	25	5.9	5.9	NUM
ejpam-2338	296	26	]	]	PUNCT
ejpam-2338	296	27	.	.	PUNCT
ejpam-2338	297	1	letx	letx	PROPN
ejpam-2338	297	2	be	be	AUX
ejpam-2338	297	3	a	a	DET
ejpam-2338	297	4	partially	partially	ADV
ejpam-2338	297	5	ordered	order	VERB
ejpam-2338	297	6	set	set	NOUN
ejpam-2338	297	7	(	(	PUNCT
ejpam-2338	297	8	with	with	ADP
ejpam-2338	297	9	partial	partial	ADJ
ejpam-2338	297	10	order	order	NOUN
ejpam-2338	297	11	≤	≤	NUM
ejpam-2338	297	12	)	)	PUNCT
ejpam-2338	297	13	,	,	PUNCT
ejpam-2338	297	14	and	and	CCONJ
ejpam-2338	297	15	let	let	VERB
ejpam-2338	297	16	y	y	PRON
ejpam-2338	297	17	be	be	AUX
ejpam-2338	297	18	a	a	DET
ejpam-2338	297	19	subset	subset	NOUN
ejpam-2338	297	20	of	of	ADP
ejpam-2338	297	21	x	x	X
ejpam-2338	297	22	.	.	PUNCT
ejpam-2338	298	1	we	we	PRON
ejpam-2338	298	2	assume	assume	VERB
ejpam-2338	298	3	the	the	DET
ejpam-2338	298	4	following	follow	VERB
ejpam-2338	298	5	properties	property	NOUN
ejpam-2338	298	6	of	of	ADP
ejpam-2338	298	7	y	y	PROPN
ejpam-2338	298	8	:	:	PUNCT
ejpam-2338	298	9	(	(	PUNCT
ejpam-2338	298	10	1	1	X
ejpam-2338	298	11	)	)	PUNCT
ejpam-2338	298	12	y	y	PROPN
ejpam-2338	298	13	is	be	AUX
ejpam-2338	298	14	a	a	DET
ejpam-2338	298	15	∧-semilattice	∧-semilattice	NOUN
ejpam-2338	298	16	,	,	PUNCT
ejpam-2338	298	17	that	that	ADV
ejpam-2338	298	18	is	is	ADV
ejpam-2338	298	19	,	,	PUNCT
ejpam-2338	298	20	every	every	DET
ejpam-2338	298	21	pair	pair	NOUN
ejpam-2338	298	22	of	of	ADP
ejpam-2338	298	23	elements	element	NOUN
ejpam-2338	298	24	a	a	PRON
ejpam-2338	298	25	,	,	PUNCT
ejpam-2338	298	26	b	b	X
ejpam-2338	298	27	∈	∈	PROPN
ejpam-2338	298	28	y	y	PROPN
ejpam-2338	298	29	has	have	VERB
ejpam-2338	298	30	a	a	DET
ejpam-2338	298	31	greatest	greatest	ADV
ejpam-2338	298	32	lower	low	ADJ
ejpam-2338	298	33	bound	bind	VERB
ejpam-2338	298	34	a	a	DET
ejpam-2338	298	35	∧	∧	PROPN
ejpam-2338	298	36	b	b	PROPN
ejpam-2338	298	37	∈	∈	PROPN
ejpam-2338	298	38	y	y	PROPN
ejpam-2338	298	39	with	with	ADP
ejpam-2338	298	40	respect	respect	NOUN
ejpam-2338	298	41	to	to	ADP
ejpam-2338	298	42	≤	≤	NUM
ejpam-2338	298	43	;	;	PUNCT
ejpam-2338	298	44	(	(	PUNCT
ejpam-2338	298	45	2	2	X
ejpam-2338	298	46	)	)	PUNCT
ejpam-2338	298	47	y	y	PROPN
ejpam-2338	298	48	is	be	AUX
ejpam-2338	298	49	an	an	DET
ejpam-2338	298	50	order	order	NOUN
ejpam-2338	298	51	ideal	ideal	NOUN
ejpam-2338	298	52	of	of	ADP
ejpam-2338	298	53	x	x	SYM
ejpam-2338	298	54	,	,	PUNCT
ejpam-2338	298	55	that	that	ADV
ejpam-2338	298	56	is	is	ADV
ejpam-2338	298	57	,	,	PUNCT
ejpam-2338	299	1	if	if	SCONJ
ejpam-2338	299	2	a	a	DET
ejpam-2338	299	3	∈	∈	PROPN
ejpam-2338	299	4	y	y	PROPN
ejpam-2338	299	5	and	and	CCONJ
ejpam-2338	299	6	b	b	PROPN
ejpam-2338	299	7	≤	≤	NOUN
ejpam-2338	299	8	a	a	PRON
ejpam-2338	299	9	,	,	PUNCT
ejpam-2338	299	10	for	for	ADP
ejpam-2338	299	11	any	any	DET
ejpam-2338	299	12	b	b	NOUN
ejpam-2338	299	13	∈	∈	PROPN
ejpam-2338	299	14	x	x	X
ejpam-2338	299	15	,	,	PUNCT
ejpam-2338	299	16	then	then	ADV
ejpam-2338	299	17	b	b	X
ejpam-2338	299	18	∈	∈	PROPN
ejpam-2338	299	19	y	y	PROPN
ejpam-2338	299	20	.	.	PUNCT
ejpam-2338	300	1	now	now	ADV
ejpam-2338	300	2	suppose	suppose	VERB
ejpam-2338	300	3	that	that	SCONJ
ejpam-2338	300	4	g	g	PROPN
ejpam-2338	300	5	is	be	AUX
ejpam-2338	300	6	a	a	DET
ejpam-2338	300	7	group	group	NOUN
ejpam-2338	300	8	(	(	PUNCT
ejpam-2338	300	9	with	with	ADP
ejpam-2338	300	10	identity	identity	NOUN
ejpam-2338	300	11	e	e	NOUN
ejpam-2338	300	12	)	)	PUNCT
ejpam-2338	300	13	that	that	PRON
ejpam-2338	300	14	acts	act	VERB
ejpam-2338	300	15	on	on	ADP
ejpam-2338	300	16	x	x	PUNCT
ejpam-2338	300	17	on	on	ADP
ejpam-2338	300	18	the	the	DET
ejpam-2338	300	19	left	left	NOUN
ejpam-2338	300	20	by	by	ADP
ejpam-2338	300	21	order	order	NOUN
ejpam-2338	300	22	automorphisms	automorphism	NOUN
ejpam-2338	300	23	(	(	PUNCT
ejpam-2338	300	24	with	with	ADP
ejpam-2338	300	25	the	the	DET
ejpam-2338	300	26	action	action	NOUN
ejpam-2338	300	27	denoted	denote	VERB
ejpam-2338	300	28	by	by	ADP
ejpam-2338	300	29	·	·	PUNCT
ejpam-2338	300	30	)	)	PUNCT
ejpam-2338	300	31	.	.	PUNCT
ejpam-2338	301	1	we	we	PRON
ejpam-2338	301	2	may	may	AUX
ejpam-2338	301	3	express	express	VERB
ejpam-2338	301	4	this	this	PRON
ejpam-2338	301	5	as	as	SCONJ
ejpam-2338	301	6	follows	follow	VERB
ejpam-2338	301	7	:	:	PUNCT
ejpam-2338	301	8	(	(	PUNCT
ejpam-2338	301	9	3	3	X
ejpam-2338	301	10	)	)	PUNCT
ejpam-2338	301	11	for	for	ADP
ejpam-2338	301	12	all	all	DET
ejpam-2338	301	13	a	a	DET
ejpam-2338	301	14	∈	∈	NOUN
ejpam-2338	301	15	x	x	X
ejpam-2338	301	16	,	,	PUNCT
ejpam-2338	301	17	e	e	X
ejpam-2338	301	18	·	·	PUNCT
ejpam-2338	301	19	a	a	X
ejpam-2338	301	20	=	=	X
ejpam-2338	301	21	a	a	NOUN
ejpam-2338	301	22	;	;	PUNCT
ejpam-2338	301	23	(	(	PUNCT
ejpam-2338	301	24	4	4	X
ejpam-2338	301	25	)	)	PUNCT
ejpam-2338	301	26	for	for	ADP
ejpam-2338	301	27	all	all	PRON
ejpam-2338	301	28	g	g	PROPN
ejpam-2338	301	29	∈	∈	PROPN
ejpam-2338	301	30	g	g	NOUN
ejpam-2338	301	31	and	and	CCONJ
ejpam-2338	301	32	all	all	DET
ejpam-2338	301	33	a	a	PRON
ejpam-2338	301	34	,	,	PUNCT
ejpam-2338	301	35	b	b	X
ejpam-2338	301	36	∈	∈	PROPN
ejpam-2338	301	37	x	x	X
ejpam-2338	301	38	,	,	PUNCT
ejpam-2338	301	39	a	a	DET
ejpam-2338	301	40	≤	≤	NUM
ejpam-2338	301	41	b	b	NOUN
ejpam-2338	301	42	if	if	SCONJ
ejpam-2338	302	1	and	and	CCONJ
ejpam-2338	302	2	only	only	ADV
ejpam-2338	302	3	if	if	SCONJ
ejpam-2338	302	4	g	g	PROPN
ejpam-2338	302	5	·	·	PUNCT
ejpam-2338	302	6	a	a	DET
ejpam-2338	302	7	≤	≤	ADV
ejpam-2338	302	8	g	g	NOUN
ejpam-2338	302	9	·	·	PUNCT
ejpam-2338	302	10	b	b	NOUN
ejpam-2338	302	11	;	;	PUNCT
ejpam-2338	302	12	(	(	PUNCT
ejpam-2338	302	13	5	5	X
ejpam-2338	302	14	)	)	PUNCT
ejpam-2338	302	15	for	for	ADP
ejpam-2338	302	16	all	all	DET
ejpam-2338	302	17	g	g	NOUN
ejpam-2338	302	18	,	,	PUNCT
ejpam-2338	302	19	h	h	NOUN
ejpam-2338	302	20	∈	∈	PROPN
ejpam-2338	302	21	g	g	PROPN
ejpam-2338	302	22	and	and	CCONJ
ejpam-2338	302	23	all	all	DET
ejpam-2338	302	24	a	a	DET
ejpam-2338	302	25	∈	∈	NOUN
ejpam-2338	302	26	x	x	X
ejpam-2338	302	27	,	,	PUNCT
ejpam-2338	302	28	g	g	PROPN
ejpam-2338	302	29	·	·	PUNCT
ejpam-2338	302	30	(	(	PUNCT
ejpam-2338	302	31	h	h	NOUN
ejpam-2338	302	32	·	·	PUNCT
ejpam-2338	303	1	a	a	X
ejpam-2338	303	2	)	)	PUNCT
ejpam-2338	303	3	=	=	SYM
ejpam-2338	303	4	(	(	PUNCT
ejpam-2338	303	5	gh	gh	PROPN
ejpam-2338	303	6	)	)	PUNCT
ejpam-2338	303	7	·	·	PUNCT
ejpam-2338	303	8	a.	a.	NOUN
ejpam-2338	303	9	note	note	VERB
ejpam-2338	303	10	that	that	SCONJ
ejpam-2338	303	11	condition	condition	NOUN
ejpam-2338	303	12	(	(	PUNCT
ejpam-2338	303	13	4	4	X
ejpam-2338	303	14	)	)	PUNCT
ejpam-2338	303	15	gives	give	VERB
ejpam-2338	303	16	order	order	NOUN
ejpam-2338	303	17	-	-	PUNCT
ejpam-2338	303	18	preservation	preservation	NOUN
ejpam-2338	303	19	,	,	PUNCT
ejpam-2338	303	20	and	and	CCONJ
ejpam-2338	303	21	(	(	PUNCT
ejpam-2338	303	22	5	5	X
ejpam-2338	303	23	)	)	PUNCT
ejpam-2338	303	24	gives	give	VERB
ejpam-2338	303	25	the	the	DET
ejpam-2338	303	26	‘	'	PUNCT
ejpam-2338	303	27	morphism	morphism	NOUN
ejpam-2338	303	28	’	'	PUNCT
ejpam-2338	303	29	property	property	NOUN
ejpam-2338	303	30	;	;	PUNCT
ejpam-2338	303	31	conditions	condition	NOUN
ejpam-2338	303	32	(	(	PUNCT
ejpam-2338	303	33	3	3	NUM
ejpam-2338	303	34	)	)	PUNCT
ejpam-2338	303	35	and	and	CCONJ
ejpam-2338	303	36	(	(	PUNCT
ejpam-2338	303	37	5	5	X
ejpam-2338	303	38	)	)	PUNCT
ejpam-2338	303	39	imply	imply	VERB
ejpam-2338	303	40	that	that	SCONJ
ejpam-2338	303	41	the	the	DET
ejpam-2338	303	42	action	action	NOUN
ejpam-2338	303	43	is	be	AUX
ejpam-2338	303	44	by	by	ADP
ejpam-2338	303	45	bijections	bijection	NOUN
ejpam-2338	303	46	.	.	PUNCT
ejpam-2338	304	1	going	go	VERB
ejpam-2338	304	2	further	far	ADV
ejpam-2338	304	3	,	,	PUNCT
ejpam-2338	304	4	the	the	DET
ejpam-2338	304	5	triple	triple	ADJ
ejpam-2338	304	6	(	(	PUNCT
ejpam-2338	304	7	g	g	NOUN
ejpam-2338	304	8	,	,	PUNCT
ejpam-2338	304	9	x	x	X
ejpam-2338	304	10	,	,	PUNCT
ejpam-2338	304	11	y	y	PROPN
ejpam-2338	304	12	)	)	PUNCT
ejpam-2338	304	13	is	be	AUX
ejpam-2338	304	14	called	call	VERB
ejpam-2338	304	15	a	a	DET
ejpam-2338	304	16	mcalister	mcalister	NOUN
ejpam-2338	304	17	triple	triple	ADV
ejpam-2338	304	18	if	if	SCONJ
ejpam-2338	304	19	it	it	PRON
ejpam-2338	304	20	satisfies	satisfy	VERB
ejpam-2338	304	21	the	the	DET
ejpam-2338	304	22	following	follow	VERB
ejpam-2338	304	23	extra	extra	ADJ
ejpam-2338	304	24	conditions	condition	NOUN
ejpam-2338	304	25	:	:	PUNCT
ejpam-2338	304	26	(	(	PUNCT
ejpam-2338	304	27	6	6	NUM
ejpam-2338	304	28	)	)	PUNCT
ejpam-2338	304	29	for	for	ADP
ejpam-2338	304	30	each	each	DET
ejpam-2338	304	31	b	b	PROPN
ejpam-2338	304	32	∈	∈	PROPN
ejpam-2338	304	33	x	x	X
ejpam-2338	304	34	,	,	PUNCT
ejpam-2338	304	35	there	there	PRON
ejpam-2338	304	36	exist	exist	VERB
ejpam-2338	304	37	g	g	PROPN
ejpam-2338	304	38	∈	∈	PROPN
ejpam-2338	304	39	g	g	PROPN
ejpam-2338	304	40	and	and	CCONJ
ejpam-2338	304	41	a	a	DET
ejpam-2338	304	42	∈	∈	NOUN
ejpam-2338	304	43	y	y	NOUN
ejpam-2338	305	1	such	such	ADJ
ejpam-2338	305	2	that	that	SCONJ
ejpam-2338	305	3	g	g	NOUN
ejpam-2338	305	4	·	·	PUNCT
ejpam-2338	305	5	a	a	DET
ejpam-2338	305	6	=	=	SYM
ejpam-2338	305	7	b	b	NOUN
ejpam-2338	305	8	;	;	PUNCT
ejpam-2338	305	9	(	(	PUNCT
ejpam-2338	305	10	7	7	X
ejpam-2338	305	11	)	)	PUNCT
ejpam-2338	305	12	for	for	ADP
ejpam-2338	305	13	all	all	PRON
ejpam-2338	305	14	g	g	PROPN
ejpam-2338	305	15	∈	∈	PROPN
ejpam-2338	305	16	g	g	PROPN
ejpam-2338	305	17	,	,	PUNCT
ejpam-2338	305	18	y	y	PROPN
ejpam-2338	305	19	∩	∩	PROPN
ejpam-2338	305	20	g	g	PROPN
ejpam-2338	305	21	·	·	PUNCT
ejpam-2338	305	22	y	y	PROPN
ejpam-2338	305	23	6=	6=	NUM
ejpam-2338	305	24	;	;	PUNCT
ejpam-2338	305	25	.	.	PUNCT
ejpam-2338	306	1	using	use	VERB
ejpam-2338	306	2	a	a	DET
ejpam-2338	306	3	mcalister	mcalister	NOUN
ejpam-2338	306	4	triple	triple	NOUN
ejpam-2338	306	5	we	we	PRON
ejpam-2338	306	6	define	define	VERB
ejpam-2338	306	7	a	a	DET
ejpam-2338	306	8	semigroup	semigroup	PROPN
ejpam-2338	306	9	p(g	p(g	NOUN
ejpam-2338	306	10	,	,	PUNCT
ejpam-2338	306	11	x	x	X
ejpam-2338	306	12	,	,	PUNCT
ejpam-2338	306	13	y	y	PROPN
ejpam-2338	306	14	)	)	PUNCT
ejpam-2338	306	15	to	to	PART
ejpam-2338	306	16	have	have	VERB
ejpam-2338	306	17	underlying	underlie	VERB
ejpam-2338	306	18	set	set	NOUN
ejpam-2338	306	19	{	{	PUNCT
ejpam-2338	306	20	(	(	PUNCT
ejpam-2338	306	21	a	a	PRON
ejpam-2338	306	22	,	,	PUNCT
ejpam-2338	306	23	g	g	NOUN
ejpam-2338	306	24	)	)	PUNCT
ejpam-2338	306	25	∈	∈	PROPN
ejpam-2338	307	1	y	y	NOUN
ejpam-2338	307	2	×	×	NOUN
ejpam-2338	307	3	g	g	NOUN
ejpam-2338	307	4	:	:	PUNCT
ejpam-2338	307	5	g−1	g−1	PROPN
ejpam-2338	307	6	·	·	PUNCT
ejpam-2338	307	7	a	a	DET
ejpam-2338	307	8	∈	∈	PROPN
ejpam-2338	307	9	y	y	PROPN
ejpam-2338	307	10	}	}	PUNCT
ejpam-2338	307	11	(	(	PUNCT
ejpam-2338	307	12	5	5	NUM
ejpam-2338	307	13	)	)	PUNCT
ejpam-2338	307	14	and	and	CCONJ
ejpam-2338	307	15	multiplication	multiplication	NOUN
ejpam-2338	307	16	(	(	PUNCT
ejpam-2338	307	17	a	a	DET
ejpam-2338	307	18	,	,	PUNCT
ejpam-2338	307	19	g)(b	g)(b	ADJ
ejpam-2338	307	20	,	,	PUNCT
ejpam-2338	307	21	h	h	NOUN
ejpam-2338	307	22	)	)	PUNCT
ejpam-2338	307	23	=	=	SYM
ejpam-2338	307	24	(	(	PUNCT
ejpam-2338	307	25	a	a	DET
ejpam-2338	307	26	∧	∧	PROPN
ejpam-2338	307	27	g	g	PROPN
ejpam-2338	307	28	·	·	SYM
ejpam-2338	307	29	b	b	X
ejpam-2338	307	30	,	,	PUNCT
ejpam-2338	307	31	gh	gh	PROPN
ejpam-2338	307	32	)	)	PUNCT
ejpam-2338	307	33	.	.	PUNCT
ejpam-2338	308	1	as	as	SCONJ
ejpam-2338	308	2	mcalister	mcalister	PROPN
ejpam-2338	308	3	showed	show	VERB
ejpam-2338	308	4	,	,	PUNCT
ejpam-2338	308	5	any	any	DET
ejpam-2338	308	6	semigroup	semigroup	NOUN
ejpam-2338	308	7	constructed	construct	VERB
ejpam-2338	308	8	in	in	ADP
ejpam-2338	308	9	this	this	DET
ejpam-2338	308	10	way	way	NOUN
ejpam-2338	308	11	is	be	AUX
ejpam-2338	308	12	an	an	DET
ejpam-2338	308	13	inverse	inverse	NOUN
ejpam-2338	308	14	semigroup	semigroup	NOUN
ejpam-2338	308	15	with	with	ADP
ejpam-2338	308	16	(	(	PUNCT
ejpam-2338	308	17	a	a	PRON
ejpam-2338	308	18	,	,	PUNCT
ejpam-2338	308	19	g)−1	g)−1	NOUN
ejpam-2338	308	20	=	=	SYM
ejpam-2338	308	21	(	(	PUNCT
ejpam-2338	308	22	g−1a	g−1a	PROPN
ejpam-2338	308	23	,	,	PUNCT
ejpam-2338	308	24	g−1	g−1	PROPN
ejpam-2338	308	25	)	)	PUNCT
ejpam-2338	308	26	,	,	PUNCT
ejpam-2338	308	27	and	and	CCONJ
ejpam-2338	308	28	,	,	PUNCT
ejpam-2338	308	29	moreover	moreover	ADV
ejpam-2338	308	30	,	,	PUNCT
ejpam-2338	308	31	it	it	PRON
ejpam-2338	308	32	is	be	AUX
ejpam-2338	308	33	proper	proper	ADJ
ejpam-2338	308	34	.	.	PUNCT
ejpam-2338	309	1	such	such	DET
ejpam-2338	309	2	a	a	DET
ejpam-2338	309	3	semigroup	semigroup	NOUN
ejpam-2338	309	4	is	be	AUX
ejpam-2338	309	5	termed	term	VERB
ejpam-2338	309	6	a	a	DET
ejpam-2338	309	7	p	p	NOUN
ejpam-2338	309	8	-	-	PUNCT
ejpam-2338	309	9	semigroup	semigroup	NOUN
ejpam-2338	309	10	.	.	PUNCT
ejpam-2338	310	1	the	the	DET
ejpam-2338	310	2	p	p	NOUN
ejpam-2338	310	3	-	-	PUNCT
ejpam-2338	310	4	theorem	theorem	ADJ
ejpam-2338	310	5	runs	run	NOUN
ejpam-2338	310	6	as	as	SCONJ
ejpam-2338	310	7	follows	follow	VERB
ejpam-2338	310	8	(	(	PUNCT
ejpam-2338	310	9	see	see	VERB
ejpam-2338	310	10	,	,	PUNCT
ejpam-2338	310	11	for	for	ADP
ejpam-2338	310	12	example	example	NOUN
ejpam-2338	310	13	,	,	PUNCT
ejpam-2338	310	14	[	[	X
ejpam-2338	310	15	51	51	NUM
ejpam-2338	310	16	,	,	PUNCT
ejpam-2338	310	17	theorem	theorem	VERB
ejpam-2338	310	18	7.2.15	7.2.15	NUM
ejpam-2338	310	19	]	]	PUNCT
ejpam-2338	310	20	):	):	PUNCT
ejpam-2338	310	21	theorem	theorem	ADJ
ejpam-2338	310	22	4	4	NUM
ejpam-2338	310	23	.	.	PUNCT
ejpam-2338	311	1	every	every	DET
ejpam-2338	311	2	proper	proper	ADJ
ejpam-2338	311	3	inverse	inverse	NOUN
ejpam-2338	311	4	semigroup	semigroup	NOUN
ejpam-2338	311	5	is	be	AUX
ejpam-2338	311	6	isomorphic	isomorphic	ADJ
ejpam-2338	311	7	to	to	ADP
ejpam-2338	311	8	a	a	DET
ejpam-2338	311	9	p	p	NOUN
ejpam-2338	311	10	-	-	PUNCT
ejpam-2338	311	11	semigroup	semigroup	NOUN
ejpam-2338	311	12	.	.	PUNCT
ejpam-2338	312	1	in	in	ADP
ejpam-2338	312	2	this	this	DET
ejpam-2338	312	3	way	way	NOUN
ejpam-2338	312	4	,	,	PUNCT
ejpam-2338	312	5	e	e	NOUN
ejpam-2338	312	6	-	-	ADJ
ejpam-2338	312	7	unitary	unitary	ADJ
ejpam-2338	312	8	inverse	inverse	NOUN
ejpam-2338	312	9	semigroups	semigroup	NOUN
ejpam-2338	312	10	were	be	AUX
ejpam-2338	312	11	described	describe	VERB
ejpam-2338	312	12	in	in	ADP
ejpam-2338	312	13	a	a	DET
ejpam-2338	312	14	similar	similar	ADJ
ejpam-2338	312	15	spirit	spirit	NOUN
ejpam-2338	312	16	to	to	ADP
ejpam-2338	312	17	rees	ree	NOUN
ejpam-2338	312	18	’	'	PUNCT
ejpam-2338	312	19	characterisation	characterisation	NOUN
ejpam-2338	312	20	of	of	ADP
ejpam-2338	312	21	completely	completely	ADV
ejpam-2338	312	22	0	0	NUM
ejpam-2338	312	23	-	-	PUNCT
ejpam-2338	312	24	simple	simple	ADJ
ejpam-2338	312	25	semigroups	semigroup	NOUN
ejpam-2338	312	26	[	[	X
ejpam-2338	312	27	80	80	NUM
ejpam-2338	312	28	]	]	PUNCT
ejpam-2338	312	29	.	.	PUNCT
ejpam-2338	313	1	mcalister	mcalister	PROPN
ejpam-2338	313	2	’s	’s	PART
ejpam-2338	313	3	original	original	ADJ
ejpam-2338	313	4	proof	proof	NOUN
ejpam-2338	313	5	of	of	ADP
ejpam-2338	313	6	this	this	DET
ejpam-2338	313	7	theorem	theorem	NOUN
ejpam-2338	313	8	was	be	AUX
ejpam-2338	313	9	somewhat	somewhat	ADV
ejpam-2338	313	10	involved	involve	VERB
ejpam-2338	313	11	,	,	PUNCT
ejpam-2338	313	12	but	but	CCONJ
ejpam-2338	313	13	it	it	PRON
ejpam-2338	313	14	was	be	AUX
ejpam-2338	313	15	n’t	not	PART
ejpam-2338	313	16	long	long	ADV
ejpam-2338	313	17	before	before	ADP
ejpam-2338	313	18	schein	schein	PROPN
ejpam-2338	313	19	[	[	X
ejpam-2338	313	20	88	88	NUM
ejpam-2338	313	21	]	]	PUNCT
ejpam-2338	313	22	and	and	CCONJ
ejpam-2338	313	23	munn	munn	PROPN
ejpam-2338	314	1	[	[	X
ejpam-2338	314	2	66	66	NUM
ejpam-2338	314	3	]	]	PUNCT
ejpam-2338	314	4	provided	provide	VERB
ejpam-2338	314	5	shorter	short	ADJ
ejpam-2338	314	6	ones	one	NOUN
ejpam-2338	314	7	.	.	PUNCT
ejpam-2338	315	1	indeed	indeed	ADV
ejpam-2338	315	2	,	,	PUNCT
ejpam-2338	315	3	the	the	DET
ejpam-2338	315	4	p	p	NOUN
ejpam-2338	315	5	-	-	PUNCT
ejpam-2338	315	6	theorem	theorem	ADJ
ejpam-2338	315	7	seems	seem	VERB
ejpam-2338	315	8	to	to	PART
ejpam-2338	315	9	exert	exert	VERB
ejpam-2338	315	10	a	a	DET
ejpam-2338	315	11	certain	certain	ADJ
ejpam-2338	315	12	fascination	fascination	NOUN
ejpam-2338	315	13	amongst	amongst	ADP
ejpam-2338	315	14	semigroup	semigroup	ADJ
ejpam-2338	315	15	theorists	theorist	NOUN
ejpam-2338	315	16	,	,	PUNCT
ejpam-2338	315	17	as	as	SCONJ
ejpam-2338	315	18	several	several	ADJ
ejpam-2338	315	19	distinct	distinct	ADJ
ejpam-2338	315	20	proofs	proof	NOUN
ejpam-2338	315	21	have	have	AUX
ejpam-2338	315	22	been	be	AUX
ejpam-2338	315	23	provided	provide	VERB
ejpam-2338	315	24	over	over	ADP
ejpam-2338	315	25	the	the	DET
ejpam-2338	315	26	years	year	NOUN
ejpam-2338	315	27	:	:	PUNCT
ejpam-2338	315	28	besides	besides	SCONJ
ejpam-2338	315	29	those	those	PRON
ejpam-2338	315	30	of	of	ADP
ejpam-2338	315	31	schein	schein	PROPN
ejpam-2338	315	32	(	(	PUNCT
ejpam-2338	315	33	to	to	PART
ejpam-2338	315	34	be	be	AUX
ejpam-2338	315	35	dealt	deal	VERB
ejpam-2338	315	36	with	with	ADP
ejpam-2338	315	37	shortly	shortly	ADV
ejpam-2338	315	38	)	)	PUNCT
ejpam-2338	315	39	and	and	CCONJ
ejpam-2338	315	40	munn	munn	PROPN
ejpam-2338	315	41	(	(	PUNCT
ejpam-2338	315	42	described	describe	VERB
ejpam-2338	315	43	by	by	ADP
ejpam-2338	315	44	mcalister	mcalister	PROPN
ejpam-2338	315	45	[	[	X
ejpam-2338	315	46	59	59	NUM
ejpam-2338	315	47	,	,	PUNCT
ejpam-2338	315	48	p.	p.	NOUN
ejpam-2338	315	49	138	138	NUM
ejpam-2338	315	50	]	]	PUNCT
ejpam-2338	315	51	as	as	ADP
ejpam-2338	315	52	a	a	DET
ejpam-2338	315	53	“	"	PUNCT
ejpam-2338	315	54	gem	gem	NOUN
ejpam-2338	315	55	”	"	PUNCT
ejpam-2338	315	56	)	)	PUNCT
ejpam-2338	315	57	,	,	PUNCT
ejpam-2338	315	58	there	there	PRON
ejpam-2338	315	59	are	be	VERB
ejpam-2338	315	60	proofs	proof	NOUN
ejpam-2338	315	61	by	by	ADP
ejpam-2338	315	62	reilly	reilly	PROPN
ejpam-2338	315	63	and	and	CCONJ
ejpam-2338	315	64	munn	munn	PROPN
ejpam-2338	316	1	[	[	X
ejpam-2338	316	2	83	83	NUM
ejpam-2338	316	3	]	]	PUNCT
ejpam-2338	316	4	,	,	PUNCT
ejpam-2338	316	5	petrich	petrich	NOUN
ejpam-2338	316	6	and	and	CCONJ
ejpam-2338	316	7	reilly	reilly	ADV
ejpam-2338	317	1	[	[	X
ejpam-2338	317	2	73	73	NUM
ejpam-2338	317	3	]	]	PUNCT
ejpam-2338	317	4	,	,	PUNCT
ejpam-2338	317	5	and	and	CCONJ
ejpam-2338	317	6	wilkinson	wilkinson	PROPN
ejpam-2338	318	1	[	[	X
ejpam-2338	318	2	103	103	NUM
ejpam-2338	318	3	]	]	PUNCT
ejpam-2338	318	4	,	,	PUNCT
ejpam-2338	318	5	for	for	ADP
ejpam-2338	318	6	example	example	NOUN
ejpam-2338	318	7	.	.	PUNCT
ejpam-2338	319	1	a	a	DET
ejpam-2338	319	2	homological	homological	ADJ
ejpam-2338	319	3	proof	proof	NOUN
ejpam-2338	319	4	was	be	AUX
ejpam-2338	319	5	given	give	VERB
ejpam-2338	319	6	by	by	ADP
ejpam-2338	319	7	loganathan	loganathan	PROPN
ejpam-2338	319	8	[	[	X
ejpam-2338	319	9	54	54	NUM
ejpam-2338	319	10	]	]	PUNCT
ejpam-2338	319	11	,	,	PUNCT
ejpam-2338	319	12	whilst	whilst	SCONJ
ejpam-2338	319	13	margolis	margolis	PROPN
ejpam-2338	319	14	and	and	CCONJ
ejpam-2338	319	15	pin	pin	NOUN
ejpam-2338	319	16	[	[	X
ejpam-2338	319	17	56	56	NUM
ejpam-2338	319	18	]	]	PUNCT
ejpam-2338	319	19	proved	prove	VERB
ejpam-2338	319	20	the	the	DET
ejpam-2338	319	21	theorem	theorem	NOUN
ejpam-2338	319	22	using	use	VERB
ejpam-2338	319	23	the	the	DET
ejpam-2338	319	24	grothendieck	grothendieck	NOUN
ejpam-2338	319	25	construction	construction	NOUN
ejpam-2338	319	26	.	.	PUNCT
ejpam-2338	320	1	perhaps	perhaps	ADV
ejpam-2338	320	2	the	the	DET
ejpam-2338	320	3	most	most	ADV
ejpam-2338	320	4	recent	recent	ADJ
ejpam-2338	320	5	proof	proof	NOUN
ejpam-2338	320	6	is	be	AUX
ejpam-2338	320	7	that	that	PRON
ejpam-2338	320	8	of	of	ADP
ejpam-2338	320	9	kellendonk	kellendonk	PROPN
ejpam-2338	320	10	and	and	CCONJ
ejpam-2338	320	11	lawson	lawson	PROPN
ejpam-2338	321	1	[	[	X
ejpam-2338	321	2	47	47	NUM
ejpam-2338	321	3	]	]	PUNCT
ejpam-2338	321	4	in	in	ADP
ejpam-2338	321	5	the	the	DET
ejpam-2338	321	6	context	context	NOUN
ejpam-2338	321	7	of	of	ADP
ejpam-2338	321	8	partial	partial	ADJ
ejpam-2338	321	9	group	group	NOUN
ejpam-2338	321	10	actions	action	NOUN
ejpam-2338	321	11	;	;	PUNCT
ejpam-2338	321	12	indeed	indeed	ADV
ejpam-2338	321	13	,	,	PUNCT
ejpam-2338	321	14	petrich	petrich	PROPN
ejpam-2338	321	15	and	and	CCONJ
ejpam-2338	321	16	reilly	reilly	PROPN
ejpam-2338	321	17	’s	’s	PART
ejpam-2338	321	18	previous	previous	ADJ
ejpam-2338	321	19	approach	approach	NOUN
ejpam-2338	321	20	to	to	ADP
ejpam-2338	321	21	proper	proper	ADJ
ejpam-2338	321	22	inverse	inverse	NOUN
ejpam-2338	321	23	semigroups	semigroup	NOUN
ejpam-2338	321	24	had	have	AUX
ejpam-2338	321	25	also	also	ADV
ejpam-2338	321	26	been	be	AUX
ejpam-2338	321	27	by	by	ADP
ejpam-2338	321	28	partial	partial	ADJ
ejpam-2338	321	29	actions	action	NOUN
ejpam-2338	321	30	—	—	PUNCT
ejpam-2338	321	31	using	use	VERB
ejpam-2338	321	32	these	these	PRON
ejpam-2338	321	33	,	,	PUNCT
ejpam-2338	321	34	it	it	PRON
ejpam-2338	321	35	is	be	AUX
ejpam-2338	321	36	christopher	christopher	PROPN
ejpam-2338	321	37	hollings	hollings	PROPN
ejpam-2338	321	38	/	/	SYM
ejpam-2338	321	39	eur	eur	PROPN
ejpam-2338	321	40	.	.	PUNCT
ejpam-2338	322	1	j.	j.	PROPN
ejpam-2338	322	2	pure	pure	PROPN
ejpam-2338	322	3	appl	appl	PROPN
ejpam-2338	322	4	.	.	PROPN
ejpam-2338	322	5	math	math	PROPN
ejpam-2338	322	6	,	,	PUNCT
ejpam-2338	322	7	8	8	NUM
ejpam-2338	322	8	(	(	PUNCT
ejpam-2338	322	9	2015	2015	NUM
ejpam-2338	322	10	)	)	PUNCT
ejpam-2338	322	11	,	,	PUNCT
ejpam-2338	322	12	294	294	NUM
ejpam-2338	322	13	-	-	SYM
ejpam-2338	322	14	323	323	NUM
ejpam-2338	322	15	309	309	NUM
ejpam-2338	322	16	possible	possible	ADJ
ejpam-2338	322	17	to	to	PART
ejpam-2338	322	18	avoid	avoid	VERB
ejpam-2338	322	19	the	the	DET
ejpam-2338	322	20	need	need	NOUN
ejpam-2338	322	21	for	for	ADP
ejpam-2338	322	22	y	y	PROPN
ejpam-2338	322	23	in	in	ADP
ejpam-2338	322	24	the	the	DET
ejpam-2338	322	25	construction	construction	NOUN
ejpam-2338	322	26	,	,	PUNCT
ejpam-2338	322	27	which	which	PRON
ejpam-2338	322	28	means	mean	VERB
ejpam-2338	322	29	furthermore	furthermore	ADV
ejpam-2338	322	30	that	that	SCONJ
ejpam-2338	322	31	this	this	DET
ejpam-2338	322	32	technique	technique	NOUN
ejpam-2338	322	33	may	may	AUX
ejpam-2338	322	34	be	be	AUX
ejpam-2338	322	35	adapted	adapt	VERB
ejpam-2338	322	36	to	to	ADP
ejpam-2338	322	37	some	some	PRON
ejpam-2338	322	38	of	of	ADP
ejpam-2338	322	39	the	the	DET
ejpam-2338	322	40	generalisations	generalisation	NOUN
ejpam-2338	322	41	of	of	ADP
ejpam-2338	322	42	inverse	inverse	NOUN
ejpam-2338	322	43	semigroups	semigroup	NOUN
ejpam-2338	322	44	that	that	PRON
ejpam-2338	322	45	we	we	PRON
ejpam-2338	322	46	deal	deal	VERB
ejpam-2338	322	47	with	with	ADP
ejpam-2338	322	48	in	in	ADP
ejpam-2338	322	49	section	section	NOUN
ejpam-2338	322	50	6	6	NUM
ejpam-2338	322	51	,	,	PUNCT
ejpam-2338	322	52	for	for	ADP
ejpam-2338	322	53	which	which	PRON
ejpam-2338	322	54	the	the	DET
ejpam-2338	322	55	approach	approach	NOUN
ejpam-2338	322	56	involving	involve	VERB
ejpam-2338	322	57	total	total	ADJ
ejpam-2338	322	58	actions	action	NOUN
ejpam-2338	322	59	does	do	AUX
ejpam-2338	322	60	not	not	PART
ejpam-2338	322	61	work	work	VERB
ejpam-2338	322	62	.	.	PUNCT
ejpam-2338	323	1	see	see	VERB
ejpam-2338	323	2	[	[	X
ejpam-2338	323	3	52	52	NUM
ejpam-2338	323	4	]	]	PUNCT
ejpam-2338	323	5	for	for	ADP
ejpam-2338	323	6	a	a	DET
ejpam-2338	323	7	list	list	NOUN
ejpam-2338	323	8	of	of	ADP
ejpam-2338	323	9	proofs	proof	NOUN
ejpam-2338	323	10	of	of	ADP
ejpam-2338	323	11	the	the	DET
ejpam-2338	323	12	p	p	NOUN
ejpam-2338	323	13	-	-	PUNCT
ejpam-2338	323	14	theorem	theorem	ADJ
ejpam-2338	323	15	,	,	PUNCT
ejpam-2338	323	16	as	as	ADV
ejpam-2338	323	17	well	well	ADV
ejpam-2338	323	18	as	as	ADP
ejpam-2338	323	19	for	for	ADP
ejpam-2338	323	20	examples	example	NOUN
ejpam-2338	323	21	of	of	ADP
ejpam-2338	323	22	e	e	NOUN
ejpam-2338	323	23	-	-	ADJ
ejpam-2338	323	24	unitary	unitary	ADJ
ejpam-2338	323	25	inverse	inverse	NOUN
ejpam-2338	323	26	semigroups	semigroup	NOUN
ejpam-2338	323	27	.	.	PUNCT
ejpam-2338	324	1	5.4	5.4	NUM
ejpam-2338	324	2	.	.	PUNCT
ejpam-2338	324	3	background	background	NOUN
ejpam-2338	324	4	to	to	ADP
ejpam-2338	324	5	the	the	DET
ejpam-2338	324	6	covering	covering	NOUN
ejpam-2338	324	7	and	and	CCONJ
ejpam-2338	324	8	p	p	NOUN
ejpam-2338	324	9	-	-	PUNCT
ejpam-2338	324	10	theorems	theorems	PROPN
ejpam-2338	324	11	mcalister	mcalister	NOUN
ejpam-2338	324	12	linked	link	VERB
ejpam-2338	324	13	e	e	ADJ
ejpam-2338	324	14	-	-	ADJ
ejpam-2338	324	15	unitary	unitary	ADJ
ejpam-2338	324	16	covers	cover	NOUN
ejpam-2338	324	17	for	for	ADP
ejpam-2338	324	18	semigroups	semigroup	NOUN
ejpam-2338	324	19	with	with	ADP
ejpam-2338	324	20	isomorphism	isomorphism	NOUN
ejpam-2338	324	21	extension	extension	NOUN
ejpam-2338	324	22	theorems	theorem	NOUN
ejpam-2338	324	23	for	for	ADP
ejpam-2338	324	24	groups	group	NOUN
ejpam-2338	324	25	.	.	PUNCT
ejpam-2338	325	1	he	he	PRON
ejpam-2338	325	2	noted	note	VERB
ejpam-2338	325	3	[	[	X
ejpam-2338	325	4	58	58	NUM
ejpam-2338	325	5	,	,	PUNCT
ejpam-2338	325	6	p.	p.	NOUN
ejpam-2338	325	7	9	9	NUM
ejpam-2338	325	8	]	]	PUNCT
ejpam-2338	325	9	that	that	DET
ejpam-2338	325	10	higman	higman	PROPN
ejpam-2338	325	11	,	,	PUNCT
ejpam-2338	325	12	neumann	neumann	PROPN
ejpam-2338	325	13	and	and	CCONJ
ejpam-2338	325	14	neumann	neumann	PROPN
ejpam-2338	326	1	[	[	X
ejpam-2338	326	2	35	35	NUM
ejpam-2338	326	3	]	]	PUNCT
ejpam-2338	326	4	had	have	AUX
ejpam-2338	326	5	shown	show	VERB
ejpam-2338	326	6	that	that	SCONJ
ejpam-2338	326	7	any	any	DET
ejpam-2338	326	8	group	group	NOUN
ejpam-2338	326	9	g	g	PROPN
ejpam-2338	326	10	may	may	AUX
ejpam-2338	326	11	be	be	AUX
ejpam-2338	326	12	embedded	embed	VERB
ejpam-2338	326	13	in	in	ADP
ejpam-2338	326	14	a	a	DET
ejpam-2338	326	15	group	group	NOUN
ejpam-2338	326	16	h	h	NOUN
ejpam-2338	326	17	in	in	ADP
ejpam-2338	326	18	such	such	DET
ejpam-2338	326	19	a	a	DET
ejpam-2338	326	20	way	way	NOUN
ejpam-2338	326	21	that	that	PRON
ejpam-2338	326	22	every	every	DET
ejpam-2338	326	23	isomorphism	isomorphism	NOUN
ejpam-2338	326	24	between	between	ADP
ejpam-2338	326	25	subgroups	subgroup	NOUN
ejpam-2338	326	26	of	of	ADP
ejpam-2338	326	27	g	g	PROPN
ejpam-2338	326	28	is	be	AUX
ejpam-2338	326	29	induced	induce	VERB
ejpam-2338	326	30	by	by	ADP
ejpam-2338	326	31	conjugation	conjugation	NOUN
ejpam-2338	326	32	by	by	ADP
ejpam-2338	326	33	an	an	DET
ejpam-2338	326	34	element	element	NOUN
ejpam-2338	326	35	of	of	ADP
ejpam-2338	326	36	h.	h.	PROPN
ejpam-2338	326	37	mcalister	mcalister	PROPN
ejpam-2338	326	38	observed	observe	VERB
ejpam-2338	326	39	that	that	SCONJ
ejpam-2338	326	40	a	a	DET
ejpam-2338	326	41	psemigroup	psemigroup	NOUN
ejpam-2338	326	42	is	be	AUX
ejpam-2338	326	43	easily	easily	ADV
ejpam-2338	326	44	obtained	obtain	VERB
ejpam-2338	326	45	from	from	ADP
ejpam-2338	326	46	this	this	DET
ejpam-2338	326	47	set	set	NOUN
ejpam-2338	326	48	-	-	PUNCT
ejpam-2338	326	49	up	up	NOUN
ejpam-2338	326	50	.	.	PUNCT
ejpam-2338	327	1	let	let	VERB
ejpam-2338	327	2	lg	lg	NOUN
ejpam-2338	327	3	denote	denote	VERB
ejpam-2338	327	4	the	the	DET
ejpam-2338	327	5	∧-semilattice	∧-semilattice	NOUN
ejpam-2338	327	6	of	of	ADP
ejpam-2338	327	7	subgroups	subgroup	NOUN
ejpam-2338	327	8	of	of	ADP
ejpam-2338	327	9	g	g	NOUN
ejpam-2338	327	10	,	,	PUNCT
ejpam-2338	327	11	and	and	CCONJ
ejpam-2338	327	12	let	let	VERB
ejpam-2338	327	13	lh	lh	PROPN
ejpam-2338	327	14	denote	denote	VERB
ejpam-2338	327	15	that	that	PRON
ejpam-2338	327	16	of	of	ADP
ejpam-2338	327	17	h.	h.	PROPN
ejpam-2338	327	18	then	then	ADV
ejpam-2338	327	19	h	h	PROPN
ejpam-2338	327	20	acts	act	VERB
ejpam-2338	327	21	on	on	ADP
ejpam-2338	327	22	lh	lh	PROPN
ejpam-2338	327	23	,	,	PUNCT
ejpam-2338	327	24	and	and	CCONJ
ejpam-2338	327	25	lg	lg	NOUN
ejpam-2338	327	26	is	be	AUX
ejpam-2338	327	27	an	an	DET
ejpam-2338	327	28	ideal	ideal	NOUN
ejpam-2338	327	29	of	of	ADP
ejpam-2338	327	30	lh	lh	PROPN
ejpam-2338	327	31	,	,	PUNCT
ejpam-2338	327	32	which	which	PRON
ejpam-2338	327	33	means	mean	VERB
ejpam-2338	327	34	that	that	SCONJ
ejpam-2338	327	35	we	we	PRON
ejpam-2338	327	36	can	can	AUX
ejpam-2338	327	37	construct	construct	VERB
ejpam-2338	327	38	the	the	DET
ejpam-2338	327	39	p	p	NOUN
ejpam-2338	327	40	-	-	PUNCT
ejpam-2338	327	41	semigroup	semigroup	NOUN
ejpam-2338	327	42	p(h	p(h	PROPN
ejpam-2338	327	43	,	,	PUNCT
ejpam-2338	327	44	lh	lh	PROPN
ejpam-2338	327	45	,	,	PUNCT
ejpam-2338	327	46	lg	lg	PROPN
ejpam-2338	327	47	)	)	PUNCT
ejpam-2338	327	48	.	.	PUNCT
ejpam-2338	328	1	for	for	ADP
ejpam-2338	328	2	any	any	DET
ejpam-2338	328	3	subgroup	subgroup	NOUN
ejpam-2338	328	4	a	a	PRON
ejpam-2338	328	5	of	of	ADP
ejpam-2338	328	6	h	h	NOUN
ejpam-2338	328	7	,	,	PUNCT
ejpam-2338	328	8	let	let	VERB
ejpam-2338	328	9	ig	ig	PRON
ejpam-2338	328	10	|a	|a	NOUN
ejpam-2338	328	11	denote	denote	VERB
ejpam-2338	328	12	the	the	DET
ejpam-2338	328	13	isomorphism	isomorphism	NOUN
ejpam-2338	328	14	of	of	ADP
ejpam-2338	328	15	a	a	PRON
ejpam-2338	328	16	onto	onto	ADP
ejpam-2338	328	17	g−1ag	g−1ag	NOUN
ejpam-2338	328	18	,	,	PUNCT
ejpam-2338	328	19	induced	induce	VERB
ejpam-2338	328	20	by	by	ADP
ejpam-2338	328	21	conjugation	conjugation	NOUN
ejpam-2338	328	22	by	by	ADP
ejpam-2338	328	23	g	g	PROPN
ejpam-2338	328	24	∈	∈	PROPN
ejpam-2338	328	25	h.	h.	PROPN
ejpam-2338	328	26	let	let	VERB
ejpam-2338	328	27	ag	ag	PROPN
ejpam-2338	328	28	be	be	AUX
ejpam-2338	328	29	the	the	DET
ejpam-2338	328	30	inverse	inverse	NOUN
ejpam-2338	328	31	semigroup	semigroup	NOUN
ejpam-2338	328	32	of	of	ADP
ejpam-2338	328	33	isomorphisms	isomorphism	NOUN
ejpam-2338	328	34	between	between	ADP
ejpam-2338	328	35	subgroups	subgroup	NOUN
ejpam-2338	328	36	of	of	ADP
ejpam-2338	328	37	g.	g.	PROPN
ejpam-2338	328	38	then	then	ADV
ejpam-2338	328	39	the	the	DET
ejpam-2338	328	40	map	map	NOUN
ejpam-2338	328	41	which	which	PRON
ejpam-2338	328	42	sends	send	VERB
ejpam-2338	328	43	(	(	PUNCT
ejpam-2338	328	44	a	a	PRON
ejpam-2338	328	45	,	,	PUNCT
ejpam-2338	328	46	g	g	NOUN
ejpam-2338	328	47	)	)	PUNCT
ejpam-2338	328	48	∈	∈	NOUN
ejpam-2338	328	49	p(h	p(h	PROPN
ejpam-2338	328	50	,	,	PUNCT
ejpam-2338	328	51	lh	lh	PROPN
ejpam-2338	328	52	,	,	PUNCT
ejpam-2338	328	53	lg	lg	NOUN
ejpam-2338	328	54	)	)	PUNCT
ejpam-2338	328	55	to	to	ADP
ejpam-2338	328	56	ig	ig	PROPN
ejpam-2338	328	57	|a	|a	VERB
ejpam-2338	328	58	is	be	AUX
ejpam-2338	328	59	an	an	DET
ejpam-2338	328	60	idempotent	idempotent	NOUN
ejpam-2338	328	61	-	-	PUNCT
ejpam-2338	328	62	separating	separate	VERB
ejpam-2338	328	63	morphism	morphism	NOUN
ejpam-2338	328	64	onto	onto	ADP
ejpam-2338	328	65	ag	ag	PROPN
ejpam-2338	328	66	,	,	PUNCT
ejpam-2338	328	67	that	that	ADV
ejpam-2338	328	68	is	is	ADV
ejpam-2338	328	69	,	,	PUNCT
ejpam-2338	328	70	an	an	DET
ejpam-2338	328	71	eunitary	eunitary	ADJ
ejpam-2338	328	72	cover	cover	NOUN
ejpam-2338	328	73	for	for	ADP
ejpam-2338	328	74	ag	ag	PROPN
ejpam-2338	328	75	.	.	PUNCT
ejpam-2338	329	1	mcalister	mcalister	PROPN
ejpam-2338	330	1	[	[	X
ejpam-2338	330	2	58	58	NUM
ejpam-2338	330	3	,	,	PUNCT
ejpam-2338	330	4	p.	p.	NOUN
ejpam-2338	330	5	9	9	NUM
ejpam-2338	330	6	]	]	PUNCT
ejpam-2338	330	7	commented	comment	VERB
ejpam-2338	330	8	:	:	PUNCT
ejpam-2338	330	9	what	what	PRON
ejpam-2338	330	10	this	this	DET
ejpam-2338	330	11	example	example	NOUN
ejpam-2338	330	12	points	point	VERB
ejpam-2338	330	13	out	out	ADP
ejpam-2338	330	14	,	,	PUNCT
ejpam-2338	330	15	i	i	PRON
ejpam-2338	330	16	think	think	VERB
ejpam-2338	330	17	,	,	PUNCT
ejpam-2338	330	18	is	be	AUX
ejpam-2338	330	19	that	that	SCONJ
ejpam-2338	330	20	the	the	DET
ejpam-2338	330	21	search	search	NOUN
ejpam-2338	330	22	for	for	ADP
ejpam-2338	330	23	e	e	NOUN
ejpam-2338	330	24	-	-	NOUN
ejpam-2338	330	25	unitary	unitary	ADJ
ejpam-2338	330	26	covers	cover	NOUN
ejpam-2338	330	27	for	for	ADP
ejpam-2338	330	28	inverse	inverse	NOUN
ejpam-2338	330	29	semigroups	semigroup	NOUN
ejpam-2338	330	30	has	have	VERB
ejpam-2338	330	31	a	a	DET
ejpam-2338	330	32	natural	natural	ADJ
ejpam-2338	330	33	interpretation	interpretation	NOUN
ejpam-2338	330	34	.	.	PUNCT
ejpam-2338	331	1	it	it	PRON
ejpam-2338	331	2	fits	fit	VERB
ejpam-2338	331	3	into	into	ADP
ejpam-2338	331	4	the	the	DET
ejpam-2338	331	5	framework	framework	NOUN
ejpam-2338	331	6	of	of	ADP
ejpam-2338	331	7	isomorphism	isomorphism	NOUN
ejpam-2338	331	8	extension	extension	NOUN
ejpam-2338	331	9	theorems	theorem	NOUN
ejpam-2338	331	10	like	like	ADP
ejpam-2338	331	11	that	that	PRON
ejpam-2338	331	12	of	of	ADP
ejpam-2338	331	13	higman	higman	NOUN
ejpam-2338	331	14	and	and	CCONJ
ejpam-2338	331	15	the	the	DET
ejpam-2338	331	16	neumanns	neumann	NOUN
ejpam-2338	331	17	and	and	CCONJ
ejpam-2338	331	18	thus	thus	ADV
ejpam-2338	331	19	,	,	PUNCT
ejpam-2338	331	20	in	in	ADP
ejpam-2338	331	21	turn	turn	NOUN
ejpam-2338	331	22	,	,	PUNCT
ejpam-2338	331	23	is	be	AUX
ejpam-2338	331	24	related	relate	VERB
ejpam-2338	331	25	to	to	ADP
ejpam-2338	331	26	questions	question	NOUN
ejpam-2338	331	27	about	about	ADP
ejpam-2338	331	28	amalgamations	amalgamation	NOUN
ejpam-2338	331	29	.	.	PUNCT
ejpam-2338	332	1	in	in	ADP
ejpam-2338	332	2	[	[	X
ejpam-2338	332	3	59	59	NUM
ejpam-2338	332	4	]	]	PUNCT
ejpam-2338	332	5	,	,	PUNCT
ejpam-2338	332	6	mcalister	mcalister	PROPN
ejpam-2338	332	7	described	describe	VERB
ejpam-2338	332	8	the	the	DET
ejpam-2338	332	9	background	background	NOUN
ejpam-2338	332	10	to	to	ADP
ejpam-2338	332	11	his	his	PRON
ejpam-2338	332	12	construction	construction	NOUN
ejpam-2338	332	13	of	of	ADP
ejpam-2338	332	14	p	p	NOUN
ejpam-2338	332	15	-	-	PUNCT
ejpam-2338	332	16	semigroups	semigroup	NOUN
ejpam-2338	332	17	and	and	CCONJ
ejpam-2338	332	18	his	his	PRON
ejpam-2338	332	19	proof	proof	NOUN
ejpam-2338	332	20	of	of	ADP
ejpam-2338	332	21	the	the	DET
ejpam-2338	332	22	p	p	NOUN
ejpam-2338	332	23	-	-	PUNCT
ejpam-2338	332	24	theorem	theorem	ADJ
ejpam-2338	332	25	.	.	PUNCT
ejpam-2338	333	1	he	he	PRON
ejpam-2338	333	2	commented	comment	VERB
ejpam-2338	333	3	that	that	SCONJ
ejpam-2338	333	4	during	during	ADP
ejpam-2338	333	5	the	the	DET
ejpam-2338	333	6	1960s	1960	NOUN
ejpam-2338	333	7	,	,	PUNCT
ejpam-2338	333	8	much	much	ADJ
ejpam-2338	333	9	work	work	NOUN
ejpam-2338	333	10	had	have	AUX
ejpam-2338	333	11	been	be	AUX
ejpam-2338	333	12	done	do	VERB
ejpam-2338	333	13	on	on	ADP
ejpam-2338	333	14	the	the	DET
ejpam-2338	333	15	structure	structure	NOUN
ejpam-2338	333	16	of	of	ADP
ejpam-2338	333	17	inverse	inverse	NOUN
ejpam-2338	333	18	semigroups	semigroup	NOUN
ejpam-2338	333	19	.	.	PUNCT
ejpam-2338	334	1	there	there	PRON
ejpam-2338	334	2	existed	exist	VERB
ejpam-2338	334	3	various	various	ADJ
ejpam-2338	334	4	decompositions	decomposition	NOUN
ejpam-2338	334	5	whereby	whereby	SCONJ
ejpam-2338	334	6	inverse	inverse	NOUN
ejpam-2338	334	7	semigroups	semigroup	NOUN
ejpam-2338	334	8	could	could	AUX
ejpam-2338	334	9	be	be	AUX
ejpam-2338	334	10	studied	study	VERB
ejpam-2338	334	11	in	in	ADP
ejpam-2338	334	12	terms	term	NOUN
ejpam-2338	334	13	of	of	ADP
ejpam-2338	334	14	‘	'	PUNCT
ejpam-2338	334	15	simpler	simple	ADJ
ejpam-2338	334	16	’	'	PUNCT
ejpam-2338	334	17	components	component	NOUN
ejpam-2338	334	18	,	,	PUNCT
ejpam-2338	334	19	such	such	ADJ
ejpam-2338	334	20	as	as	ADP
ejpam-2338	334	21	groups	group	NOUN
ejpam-2338	334	22	and	and	CCONJ
ejpam-2338	334	23	semilattices	semilattice	NOUN
ejpam-2338	334	24	(	(	PUNCT
ejpam-2338	334	25	for	for	ADP
ejpam-2338	334	26	a	a	DET
ejpam-2338	334	27	survey	survey	NOUN
ejpam-2338	334	28	of	of	ADP
ejpam-2338	334	29	these	these	DET
ejpam-2338	334	30	various	various	ADJ
ejpam-2338	334	31	approaches	approach	NOUN
ejpam-2338	334	32	,	,	PUNCT
ejpam-2338	334	33	see	see	VERB
ejpam-2338	334	34	[	[	X
ejpam-2338	334	35	78	78	NUM
ejpam-2338	334	36	]	]	PUNCT
ejpam-2338	334	37	)	)	PUNCT
ejpam-2338	334	38	.	.	PUNCT
ejpam-2338	335	1	however	however	ADV
ejpam-2338	335	2	,	,	PUNCT
ejpam-2338	335	3	there	there	PRON
ejpam-2338	335	4	was	be	VERB
ejpam-2338	335	5	a	a	DET
ejpam-2338	335	6	problem	problem	NOUN
ejpam-2338	335	7	with	with	ADP
ejpam-2338	335	8	these	these	DET
ejpam-2338	335	9	structure	structure	NOUN
ejpam-2338	335	10	theorems	theorem	VERB
ejpam-2338	335	11	:	:	PUNCT
ejpam-2338	335	12	the	the	DET
ejpam-2338	335	13	building	building	NOUN
ejpam-2338	335	14	blocks	block	NOUN
ejpam-2338	335	15	.	.	PUNCT
ejpam-2338	335	16	.	.	PUNCT
ejpam-2338	336	1	.	.	PUNCT
ejpam-2338	337	1	were	be	AUX
ejpam-2338	337	2	simple	simple	ADJ
ejpam-2338	337	3	and	and	CCONJ
ejpam-2338	337	4	natural	natural	ADJ
ejpam-2338	337	5	.	.	PUNCT
ejpam-2338	338	1	the	the	DET
ejpam-2338	338	2	interrelations	interrelation	NOUN
ejpam-2338	338	3	between	between	ADP
ejpam-2338	338	4	the	the	DET
ejpam-2338	338	5	building	building	NOUN
ejpam-2338	338	6	blocks	block	NOUN
ejpam-2338	338	7	were	be	AUX
ejpam-2338	338	8	not	not	PART
ejpam-2338	338	9	.	.	PUNCT
ejpam-2338	339	1	[	[	X
ejpam-2338	339	2	59	59	NUM
ejpam-2338	339	3	,	,	PUNCT
ejpam-2338	339	4	p.	p.	NOUN
ejpam-2338	339	5	134	134	NUM
ejpam-2338	339	6	]	]	PUNCT
ejpam-2338	339	7	in	in	ADP
ejpam-2338	339	8	many	many	ADJ
ejpam-2338	339	9	cases	case	NOUN
ejpam-2338	339	10	,	,	PUNCT
ejpam-2338	339	11	these	these	DET
ejpam-2338	339	12	interrelations	interrelation	NOUN
ejpam-2338	339	13	were	be	AUX
ejpam-2338	339	14	complicated	complicated	ADJ
ejpam-2338	339	15	and	and	CCONJ
ejpam-2338	339	16	considerably	considerably	ADV
ejpam-2338	339	17	less	less	ADJ
ejpam-2338	339	18	than	than	ADP
ejpam-2338	339	19	transparent	transparent	ADJ
ejpam-2338	339	20	.	.	PUNCT
ejpam-2338	340	1	mcalister	mcalister	PROPN
ejpam-2338	340	2	commented	comment	VERB
ejpam-2338	340	3	:	:	PUNCT
ejpam-2338	340	4	frankly	frankly	ADV
ejpam-2338	340	5	,	,	PUNCT
ejpam-2338	340	6	the	the	DET
ejpam-2338	340	7	structure	structure	NOUN
ejpam-2338	340	8	theory	theory	NOUN
ejpam-2338	340	9	of	of	ADP
ejpam-2338	340	10	inverse	inverse	NOUN
ejpam-2338	340	11	semigroups	semigroup	NOUN
ejpam-2338	340	12	had	have	AUX
ejpam-2338	340	13	reached	reach	VERB
ejpam-2338	340	14	the	the	DET
ejpam-2338	340	15	point	point	NOUN
ejpam-2338	340	16	of	of	ADP
ejpam-2338	340	17	diminishing	diminish	VERB
ejpam-2338	340	18	returns	return	NOUN
ejpam-2338	340	19	.	.	PUNCT
ejpam-2338	341	1	one	one	PRON
ejpam-2338	341	2	could	could	AUX
ejpam-2338	341	3	reasonably	reasonably	ADV
ejpam-2338	341	4	say	say	VERB
ejpam-2338	341	5	that	that	SCONJ
ejpam-2338	341	6	each	each	DET
ejpam-2338	341	7	new	new	ADJ
ejpam-2338	341	8	theorem	theorem	NOUN
ejpam-2338	341	9	resulted	result	VERB
ejpam-2338	341	10	in	in	ADP
ejpam-2338	341	11	a	a	DET
ejpam-2338	341	12	gain	gain	NOUN
ejpam-2338	341	13	of	of	ADP
ejpam-2338	341	14	information	information	NOUN
ejpam-2338	341	15	but	but	CCONJ
ejpam-2338	341	16	a	a	DET
ejpam-2338	341	17	loss	loss	NOUN
ejpam-2338	341	18	of	of	ADP
ejpam-2338	341	19	insight	insight	NOUN
ejpam-2338	341	20	.	.	PUNCT
ejpam-2338	342	1	[	[	X
ejpam-2338	342	2	59	59	NUM
ejpam-2338	342	3	,	,	PUNCT
ejpam-2338	342	4	p.	p.	NOUN
ejpam-2338	342	5	134	134	NUM
ejpam-2338	342	6	]	]	PUNCT
ejpam-2338	342	7	a	a	DET
ejpam-2338	342	8	new	new	ADJ
ejpam-2338	342	9	approach	approach	NOUN
ejpam-2338	342	10	was	be	AUX
ejpam-2338	342	11	therefore	therefore	ADV
ejpam-2338	342	12	needed	need	VERB
ejpam-2338	342	13	.	.	PUNCT
ejpam-2338	343	1	this	this	PRON
ejpam-2338	343	2	was	be	AUX
ejpam-2338	343	3	provided	provide	VERB
ejpam-2338	343	4	by	by	ADP
ejpam-2338	343	5	scheiblich	scheiblich	PROPN
ejpam-2338	343	6	’s	’s	PART
ejpam-2338	343	7	construction	construction	NOUN
ejpam-2338	343	8	of	of	ADP
ejpam-2338	343	9	the	the	DET
ejpam-2338	343	10	free	free	ADJ
ejpam-2338	343	11	inverse	inverse	NOUN
ejpam-2338	343	12	semigroup	semigroup	NOUN
ejpam-2338	343	13	(	(	PUNCT
ejpam-2338	343	14	which	which	PRON
ejpam-2338	343	15	is	be	AUX
ejpam-2338	343	16	proper	proper	ADJ
ejpam-2338	343	17	—	—	PUNCT
ejpam-2338	343	18	see	see	VERB
ejpam-2338	343	19	[	[	X
ejpam-2338	343	20	44	44	NUM
ejpam-2338	343	21	,	,	PUNCT
ejpam-2338	343	22	§	§	NOUN
ejpam-2338	343	23	5.10	5.10	NUM
ejpam-2338	343	24	]	]	PUNCT
ejpam-2338	343	25	)	)	PUNCT
ejpam-2338	343	26	,	,	PUNCT
ejpam-2338	343	27	in	in	ADP
ejpam-2338	343	28	which	which	PRON
ejpam-2338	343	29	it	it	PRON
ejpam-2338	343	30	is	be	AUX
ejpam-2338	343	31	possible	possible	ADJ
ejpam-2338	343	32	to	to	PART
ejpam-2338	343	33	see	see	VERB
ejpam-2338	343	34	many	many	ADJ
ejpam-2338	343	35	similarities	similarity	NOUN
ejpam-2338	343	36	with	with	ADP
ejpam-2338	343	37	the	the	DET
ejpam-2338	343	38	construction	construction	NOUN
ejpam-2338	343	39	of	of	ADP
ejpam-2338	343	40	a	a	DET
ejpam-2338	343	41	p	p	NOUN
ejpam-2338	343	42	-	-	PUNCT
ejpam-2338	343	43	semigroup	semigroup	NOUN
ejpam-2338	343	44	(	(	PUNCT
ejpam-2338	343	45	[	[	X
ejpam-2338	343	46	85	85	NUM
ejpam-2338	343	47	]	]	PUNCT
ejpam-2338	343	48	;	;	PUNCT
ejpam-2338	343	49	see	see	VERB
ejpam-2338	343	50	also	also	ADV
ejpam-2338	343	51	[	[	X
ejpam-2338	343	52	59	59	NUM
ejpam-2338	343	53	,	,	PUNCT
ejpam-2338	343	54	pp	pp	ADJ
ejpam-2338	343	55	.	.	PUNCT
ejpam-2338	344	1	134–135	134–135	NUM
ejpam-2338	344	2	]	]	NUM
ejpam-2338	344	3	)	)	PUNCT
ejpam-2338	344	4	.	.	PUNCT
ejpam-2338	345	1	working	work	VERB
ejpam-2338	345	2	on	on	ADP
ejpam-2338	345	3	the	the	DET
ejpam-2338	345	4	principle	principle	NOUN
ejpam-2338	345	5	that	that	SCONJ
ejpam-2338	345	6	“	"	PUNCT
ejpam-2338	345	7	if	if	SCONJ
ejpam-2338	345	8	an	an	DET
ejpam-2338	345	9	object	object	NOUN
ejpam-2338	345	10	is	be	AUX
ejpam-2338	345	11	simple	simple	ADJ
ejpam-2338	345	12	[	[	X
ejpam-2338	345	13	then	then	ADV
ejpam-2338	345	14	]	]	X
ejpam-2338	345	15	so	so	CCONJ
ejpam-2338	345	16	are	be	AUX
ejpam-2338	345	17	its	its	PRON
ejpam-2338	345	18	homomorphic	homomorphic	ADJ
ejpam-2338	345	19	images	image	NOUN
ejpam-2338	345	20	”	"	PUNCT
ejpam-2338	345	21	[	[	X
ejpam-2338	345	22	59	59	NUM
ejpam-2338	345	23	,	,	PUNCT
ejpam-2338	345	24	p.	p.	NOUN
ejpam-2338	345	25	135	135	NUM
ejpam-2338	345	26	]	]	PUNCT
ejpam-2338	345	27	,	,	PUNCT
ejpam-2338	345	28	mcalister	mcalister	PROPN
ejpam-2338	345	29	set	set	VERB
ejpam-2338	345	30	out	out	ADP
ejpam-2338	345	31	to	to	ADP
ejpam-2338	345	32	christopher	christopher	PROPN
ejpam-2338	345	33	hollings	hollings	PROPN
ejpam-2338	345	34	/	/	SYM
ejpam-2338	345	35	eur	eur	PROPN
ejpam-2338	345	36	.	.	PUNCT
ejpam-2338	346	1	j.	j.	PROPN
ejpam-2338	346	2	pure	pure	PROPN
ejpam-2338	346	3	appl	appl	PROPN
ejpam-2338	346	4	.	.	PROPN
ejpam-2338	346	5	math	math	PROPN
ejpam-2338	346	6	,	,	PUNCT
ejpam-2338	346	7	8	8	NUM
ejpam-2338	346	8	(	(	PUNCT
ejpam-2338	346	9	2015	2015	NUM
ejpam-2338	346	10	)	)	PUNCT
ejpam-2338	346	11	,	,	PUNCT
ejpam-2338	346	12	294	294	NUM
ejpam-2338	346	13	-	-	SYM
ejpam-2338	346	14	323	323	NUM
ejpam-2338	346	15	310	310	NUM
ejpam-2338	346	16	construct	construct	VERB
ejpam-2338	346	17	a	a	DET
ejpam-2338	346	18	family	family	NOUN
ejpam-2338	346	19	of	of	ADP
ejpam-2338	346	20	inverse	inverse	NOUN
ejpam-2338	346	21	semigroups	semigroup	NOUN
ejpam-2338	346	22	from	from	ADP
ejpam-2338	346	23	simple	simple	ADJ
ejpam-2338	346	24	,	,	PUNCT
ejpam-2338	346	25	familiar	familiar	ADJ
ejpam-2338	346	26	,	,	PUNCT
ejpam-2338	346	27	naturally	naturally	ADV
ejpam-2338	346	28	related	relate	VERB
ejpam-2338	346	29	objects	object	NOUN
ejpam-2338	346	30	in	in	ADP
ejpam-2338	346	31	such	such	DET
ejpam-2338	346	32	a	a	DET
ejpam-2338	346	33	way	way	NOUN
ejpam-2338	346	34	that	that	PRON
ejpam-2338	346	35	every	every	DET
ejpam-2338	346	36	inverse	inverse	NOUN
ejpam-2338	346	37	semigroup	semigroup	NOUN
ejpam-2338	346	38	is	be	AUX
ejpam-2338	346	39	a	a	DET
ejpam-2338	346	40	nice	nice	ADJ
ejpam-2338	346	41	homomorphic	homomorphic	ADJ
ejpam-2338	346	42	image	image	NOUN
ejpam-2338	346	43	of	of	ADP
ejpam-2338	346	44	a	a	DET
ejpam-2338	346	45	member	member	NOUN
ejpam-2338	346	46	of	of	ADP
ejpam-2338	346	47	the	the	DET
ejpam-2338	346	48	family	family	NOUN
ejpam-2338	346	49	.	.	PUNCT
ejpam-2338	347	1	[	[	X
ejpam-2338	347	2	59	59	NUM
ejpam-2338	347	3	,	,	PUNCT
ejpam-2338	347	4	p.	p.	NOUN
ejpam-2338	347	5	136	136	NUM
ejpam-2338	347	6	]	]	PUNCT
ejpam-2338	347	7	scheiblich	scheiblich	PROPN
ejpam-2338	347	8	’s	’s	PART
ejpam-2338	347	9	construction	construction	NOUN
ejpam-2338	347	10	provided	provide	VERB
ejpam-2338	347	11	a	a	DET
ejpam-2338	347	12	guide	guide	NOUN
ejpam-2338	347	13	and	and	CCONJ
ejpam-2338	347	14	the	the	DET
ejpam-2338	347	15	result	result	NOUN
ejpam-2338	347	16	was	be	AUX
ejpam-2338	347	17	the	the	DET
ejpam-2338	347	18	notion	notion	NOUN
ejpam-2338	347	19	of	of	ADP
ejpam-2338	347	20	a	a	DET
ejpam-2338	347	21	proper	proper	ADJ
ejpam-2338	347	22	inverse	inverse	NOUN
ejpam-2338	347	23	semigroup	semigroup	NOUN
ejpam-2338	347	24	,	,	PUNCT
ejpam-2338	347	25	via	via	ADP
ejpam-2338	347	26	that	that	PRON
ejpam-2338	347	27	of	of	ADP
ejpam-2338	347	28	an	an	DET
ejpam-2338	347	29	e	e	NOUN
ejpam-2338	347	30	-	-	ADJ
ejpam-2338	347	31	unitary	unitary	ADJ
ejpam-2338	347	32	cover	cover	NOUN
ejpam-2338	347	33	.	.	PUNCT
ejpam-2338	348	1	as	as	SCONJ
ejpam-2338	348	2	we	we	PRON
ejpam-2338	348	3	have	have	AUX
ejpam-2338	348	4	seen	see	VERB
ejpam-2338	348	5	,	,	PUNCT
ejpam-2338	348	6	the	the	DET
ejpam-2338	348	7	“	"	PUNCT
ejpam-2338	348	8	simple	simple	ADJ
ejpam-2338	348	9	,	,	PUNCT
ejpam-2338	348	10	familiar	familiar	ADJ
ejpam-2338	348	11	,	,	PUNCT
ejpam-2338	348	12	naturally	naturally	ADV
ejpam-2338	348	13	related	relate	VERB
ejpam-2338	348	14	objects	object	NOUN
ejpam-2338	348	15	”	"	PUNCT
ejpam-2338	348	16	are	be	AUX
ejpam-2338	348	17	partially	partially	ADV
ejpam-2338	348	18	ordered	order	VERB
ejpam-2338	348	19	sets	set	NOUN
ejpam-2338	348	20	,	,	PUNCT
ejpam-2338	348	21	semilattices	semilattice	NOUN
ejpam-2338	348	22	and	and	CCONJ
ejpam-2338	348	23	groups	group	NOUN
ejpam-2338	348	24	;	;	PUNCT
ejpam-2338	348	25	“	"	PUNCT
ejpam-2338	348	26	nice	nice	ADJ
ejpam-2338	348	27	”	"	PUNCT
ejpam-2338	348	28	in	in	ADP
ejpam-2338	348	29	this	this	DET
ejpam-2338	348	30	context	context	NOUN
ejpam-2338	348	31	means	mean	VERB
ejpam-2338	348	32	‘	'	PUNCT
ejpam-2338	348	33	idempotent	idempotent	ADJ
ejpam-2338	348	34	-	-	PUNCT
ejpam-2338	348	35	separating	separate	VERB
ejpam-2338	348	36	’	'	PUNCT
ejpam-2338	348	37	.	.	PUNCT
ejpam-2338	349	1	mcalister	mcalister	PROPN
ejpam-2338	349	2	’s	’s	PART
ejpam-2338	349	3	covering	covering	NOUN
ejpam-2338	349	4	and	and	CCONJ
ejpam-2338	349	5	p	p	NOUN
ejpam-2338	349	6	-	-	PUNCT
ejpam-2338	349	7	theorems	theorem	NOUN
ejpam-2338	349	8	were	be	AUX
ejpam-2338	349	9	very	very	ADV
ejpam-2338	349	10	much	much	ADV
ejpam-2338	349	11	simpler	simple	ADJ
ejpam-2338	349	12	than	than	ADP
ejpam-2338	349	13	many	many	ADJ
ejpam-2338	349	14	of	of	ADP
ejpam-2338	349	15	the	the	DET
ejpam-2338	349	16	other	other	ADJ
ejpam-2338	349	17	pre	pre	ADJ
ejpam-2338	349	18	-	-	ADJ
ejpam-2338	349	19	existing	exist	VERB
ejpam-2338	349	20	structure	structure	NOUN
ejpam-2338	349	21	theorems	theorem	NOUN
ejpam-2338	349	22	for	for	ADP
ejpam-2338	349	23	inverse	inverse	NOUN
ejpam-2338	349	24	semigroups	semigroup	NOUN
ejpam-2338	349	25	,	,	PUNCT
ejpam-2338	349	26	so	so	ADV
ejpam-2338	349	27	much	much	ADV
ejpam-2338	349	28	so	so	SCONJ
ejpam-2338	349	29	that	that	SCONJ
ejpam-2338	349	30	a.	a.	PROPN
ejpam-2338	349	31	h.	h.	PROPN
ejpam-2338	349	32	clifford	clifford	PROPN
ejpam-2338	349	33	’s	’s	PART
ejpam-2338	349	34	initial	initial	ADJ
ejpam-2338	349	35	reaction	reaction	NOUN
ejpam-2338	349	36	to	to	ADP
ejpam-2338	349	37	these	these	DET
ejpam-2338	349	38	theorems	theorem	NOUN
ejpam-2338	349	39	was	be	AUX
ejpam-2338	349	40	to	to	PART
ejpam-2338	349	41	say	say	VERB
ejpam-2338	349	42	“	"	PUNCT
ejpam-2338	349	43	that	that	PRON
ejpam-2338	349	44	ca	can	AUX
ejpam-2338	349	45	n’t	not	PART
ejpam-2338	349	46	possibly	possibly	ADV
ejpam-2338	349	47	be	be	AUX
ejpam-2338	349	48	true	true	ADJ
ejpam-2338	349	49	”	"	PUNCT
ejpam-2338	350	1	[	[	X
ejpam-2338	350	2	59	59	NUM
ejpam-2338	350	3	,	,	PUNCT
ejpam-2338	350	4	p.	p.	NOUN
ejpam-2338	350	5	137	137	NUM
ejpam-2338	350	6	]	]	PUNCT
ejpam-2338	350	7	.	.	PUNCT
ejpam-2338	351	1	5.5	5.5	NUM
ejpam-2338	351	2	.	.	PUNCT
ejpam-2338	352	1	a	a	DET
ejpam-2338	352	2	naive	naive	ADJ
ejpam-2338	352	3	approach	approach	NOUN
ejpam-2338	352	4	i	i	PRON
ejpam-2338	352	5	have	have	AUX
ejpam-2338	352	6	glossed	gloss	VERB
ejpam-2338	352	7	over	over	ADP
ejpam-2338	352	8	much	much	ADJ
ejpam-2338	352	9	of	of	ADP
ejpam-2338	352	10	the	the	DET
ejpam-2338	352	11	technical	technical	ADJ
ejpam-2338	352	12	development	development	NOUN
ejpam-2338	352	13	of	of	ADP
ejpam-2338	352	14	proper	proper	ADJ
ejpam-2338	352	15	inverse	inverse	NOUN
ejpam-2338	352	16	semigroups	semigroup	NOUN
ejpam-2338	352	17	.	.	PUNCT
ejpam-2338	353	1	as	as	ADP
ejpam-2338	353	2	in	in	ADP
ejpam-2338	353	3	previous	previous	ADJ
ejpam-2338	353	4	sections	section	NOUN
ejpam-2338	353	5	,	,	PUNCT
ejpam-2338	353	6	my	my	PRON
ejpam-2338	353	7	aim	aim	NOUN
ejpam-2338	353	8	is	be	AUX
ejpam-2338	353	9	to	to	PART
ejpam-2338	353	10	provide	provide	VERB
ejpam-2338	353	11	an	an	DET
ejpam-2338	353	12	intuitive	intuitive	ADJ
ejpam-2338	353	13	understanding	understanding	NOUN
ejpam-2338	353	14	.	.	PUNCT
ejpam-2338	354	1	to	to	ADP
ejpam-2338	354	2	this	this	DET
ejpam-2338	354	3	end	end	NOUN
ejpam-2338	354	4	,	,	PUNCT
ejpam-2338	354	5	we	we	PRON
ejpam-2338	354	6	now	now	ADV
ejpam-2338	354	7	turn	turn	VERB
ejpam-2338	354	8	to	to	ADP
ejpam-2338	354	9	an	an	DET
ejpam-2338	354	10	article	article	NOUN
ejpam-2338	354	11	of	of	ADP
ejpam-2338	354	12	1980	1980	NUM
ejpam-2338	354	13	,	,	PUNCT
ejpam-2338	354	14	in	in	ADP
ejpam-2338	354	15	which	which	PRON
ejpam-2338	354	16	mcalister	mcalister	NOUN
ejpam-2338	354	17	provided	provide	VERB
ejpam-2338	354	18	a	a	DET
ejpam-2338	354	19	naive	naive	ADJ
ejpam-2338	354	20	approach	approach	NOUN
ejpam-2338	354	21	to	to	ADP
ejpam-2338	354	22	the	the	DET
ejpam-2338	354	23	structure	structure	NOUN
ejpam-2338	354	24	of	of	ADP
ejpam-2338	354	25	inverse	inverse	NOUN
ejpam-2338	354	26	semigroups	semigroup	NOUN
ejpam-2338	354	27	to	to	PART
ejpam-2338	354	28	motivate	motivate	VERB
ejpam-2338	354	29	the	the	DET
ejpam-2338	354	30	introduction	introduction	NOUN
ejpam-2338	354	31	of	of	ADP
ejpam-2338	354	32	p	p	NOUN
ejpam-2338	354	33	-	-	PUNCT
ejpam-2338	354	34	semigroups	semigroup	NOUN
ejpam-2338	354	35	and	and	CCONJ
ejpam-2338	354	36	e	e	NOUN
ejpam-2338	354	37	-	-	ADJ
ejpam-2338	354	38	unitary	unitary	ADJ
ejpam-2338	354	39	inverse	inverse	NOUN
ejpam-2338	354	40	semigroups	semigroup	NOUN
ejpam-2338	354	41	.	.	PUNCT
ejpam-2338	355	1	[	[	X
ejpam-2338	355	2	58	58	NUM
ejpam-2338	355	3	,	,	PUNCT
ejpam-2338	355	4	p.	p.	NOUN
ejpam-2338	355	5	1	1	NUM
ejpam-2338	355	6	]	]	PUNCT
ejpam-2338	355	7	although	although	SCONJ
ejpam-2338	355	8	this	this	PRON
ejpam-2338	355	9	is	be	AUX
ejpam-2338	355	10	not	not	PART
ejpam-2338	355	11	the	the	DET
ejpam-2338	355	12	way	way	NOUN
ejpam-2338	355	13	in	in	ADP
ejpam-2338	355	14	which	which	PRON
ejpam-2338	355	15	the	the	DET
ejpam-2338	355	16	notion	notion	NOUN
ejpam-2338	355	17	of	of	ADP
ejpam-2338	355	18	an	an	DET
ejpam-2338	355	19	e	e	NOUN
ejpam-2338	355	20	-	-	ADJ
ejpam-2338	355	21	unitary	unitary	ADJ
ejpam-2338	355	22	inverse	inverse	NOUN
ejpam-2338	355	23	semigroup	semigroup	NOUN
ejpam-2338	355	24	emerged	emerge	VERB
ejpam-2338	355	25	,	,	PUNCT
ejpam-2338	355	26	it	it	PRON
ejpam-2338	355	27	is	be	AUX
ejpam-2338	355	28	instructive	instructive	ADJ
ejpam-2338	355	29	to	to	PART
ejpam-2338	355	30	consider	consider	VERB
ejpam-2338	355	31	this	this	DET
ejpam-2338	355	32	“	"	PUNCT
ejpam-2338	355	33	naive	naive	ADJ
ejpam-2338	355	34	approach	approach	NOUN
ejpam-2338	355	35	”	"	PUNCT
ejpam-2338	355	36	.	.	PUNCT
ejpam-2338	356	1	mcalister	mcalister	PROPN
ejpam-2338	356	2	began	begin	VERB
ejpam-2338	356	3	by	by	ADP
ejpam-2338	356	4	recalling	recall	VERB
ejpam-2338	356	5	the	the	DET
ejpam-2338	356	6	easy	easy	ADJ
ejpam-2338	356	7	observation	observation	NOUN
ejpam-2338	356	8	that	that	SCONJ
ejpam-2338	356	9	in	in	ADP
ejpam-2338	356	10	any	any	DET
ejpam-2338	356	11	inverse	inverse	NOUN
ejpam-2338	356	12	semigroup	semigroup	NOUN
ejpam-2338	356	13	s	s	PART
ejpam-2338	356	14	,	,	PUNCT
ejpam-2338	356	15	there	there	PRON
ejpam-2338	356	16	is	be	VERB
ejpam-2338	356	17	a	a	DET
ejpam-2338	356	18	group	group	NOUN
ejpam-2338	356	19	he	he	PRON
ejpam-2338	356	20	around	around	ADP
ejpam-2338	356	21	each	each	DET
ejpam-2338	356	22	idempotent	idempotent	ADJ
ejpam-2338	356	23	e	e	NOUN
ejpam-2338	356	24	,	,	PUNCT
ejpam-2338	356	25	consisting	consist	VERB
ejpam-2338	356	26	of	of	ADP
ejpam-2338	356	27	those	those	DET
ejpam-2338	356	28	elements	element	NOUN
ejpam-2338	356	29	which	which	PRON
ejpam-2338	356	30	have	have	VERB
ejpam-2338	356	31	e	e	NOUN
ejpam-2338	356	32	as	as	ADV
ejpam-2338	356	33	both	both	CCONJ
ejpam-2338	356	34	a	a	DET
ejpam-2338	356	35	left	left	NOUN
ejpam-2338	356	36	and	and	CCONJ
ejpam-2338	356	37	a	a	DET
ejpam-2338	356	38	right	right	ADJ
ejpam-2338	356	39	identity	identity	NOUN
ejpam-2338	356	40	.	.	PUNCT
ejpam-2338	357	1	however	however	ADV
ejpam-2338	357	2	,	,	PUNCT
ejpam-2338	357	3	these	these	DET
ejpam-2338	357	4	groups	group	NOUN
ejpam-2338	357	5	do	do	AUX
ejpam-2338	357	6	not	not	PART
ejpam-2338	357	7	necessarily	necessarily	ADV
ejpam-2338	357	8	exhaust	exhaust	VERB
ejpam-2338	357	9	s	s	NOUN
ejpam-2338	358	1	and	and	CCONJ
ejpam-2338	358	2	it	it	PRON
ejpam-2338	358	3	need	need	AUX
ejpam-2338	358	4	not	not	PART
ejpam-2338	358	5	be	be	AUX
ejpam-2338	358	6	the	the	DET
ejpam-2338	358	7	case	case	NOUN
ejpam-2338	359	1	that	that	SCONJ
ejpam-2338	359	2	heh	heh	INTJ
ejpam-2338	359	3	f	f	PROPN
ejpam-2338	360	1	⊆	⊆	NUM
ejpam-2338	360	2	he	he	PRON
ejpam-2338	360	3	f	f	PROPN
ejpam-2338	360	4	.	.	PUNCT
ejpam-2338	361	1	as	as	SCONJ
ejpam-2338	361	2	i	i	PRON
ejpam-2338	361	3	have	have	AUX
ejpam-2338	361	4	described	describe	VERB
ejpam-2338	361	5	elsewhere	elsewhere	ADV
ejpam-2338	361	6	(	(	PUNCT
ejpam-2338	361	7	[	[	X
ejpam-2338	361	8	37	37	NUM
ejpam-2338	361	9	,	,	PUNCT
ejpam-2338	361	10	§	§	NOUN
ejpam-2338	361	11	7	7	NUM
ejpam-2338	361	12	]	]	PUNCT
ejpam-2338	361	13	and	and	CCONJ
ejpam-2338	361	14	[	[	X
ejpam-2338	361	15	41	41	NUM
ejpam-2338	361	16	,	,	PUNCT
ejpam-2338	361	17	§	§	VERB
ejpam-2338	361	18	6.6	6.6	NUM
ejpam-2338	361	19	]	]	NUM
ejpam-2338	361	20	)	)	PUNCT
ejpam-2338	361	21	,	,	PUNCT
ejpam-2338	361	22	clifford	clifford	PROPN
ejpam-2338	361	23	had	have	AUX
ejpam-2338	361	24	faced	face	VERB
ejpam-2338	361	25	this	this	DET
ejpam-2338	361	26	very	very	ADJ
ejpam-2338	361	27	problem	problem	NOUN
ejpam-2338	361	28	,	,	PUNCT
ejpam-2338	361	29	but	but	CCONJ
ejpam-2338	361	30	,	,	PUNCT
ejpam-2338	361	31	in	in	ADP
ejpam-2338	361	32	a	a	DET
ejpam-2338	361	33	paper	paper	NOUN
ejpam-2338	361	34	of	of	ADP
ejpam-2338	361	35	1941	1941	NUM
ejpam-2338	361	36	,	,	PUNCT
ejpam-2338	361	37	had	have	AUX
ejpam-2338	361	38	shown	show	VERB
ejpam-2338	361	39	that	that	SCONJ
ejpam-2338	361	40	if	if	SCONJ
ejpam-2338	361	41	the	the	DET
ejpam-2338	361	42	idempotents	idempotent	NOUN
ejpam-2338	361	43	of	of	ADP
ejpam-2338	361	44	s	s	NOUN
ejpam-2338	361	45	are	be	AUX
ejpam-2338	361	46	central	central	ADJ
ejpam-2338	361	47	,	,	PUNCT
ejpam-2338	361	48	then	then	ADV
ejpam-2338	361	49	not	not	PART
ejpam-2338	361	50	only	only	ADV
ejpam-2338	361	51	is	be	AUX
ejpam-2338	361	52	s	s	PRON
ejpam-2338	361	53	the	the	DET
ejpam-2338	361	54	(	(	PUNCT
ejpam-2338	361	55	disjoint	disjoint	PROPN
ejpam-2338	361	56	)	)	PUNCT
ejpam-2338	361	57	union	union	NOUN
ejpam-2338	361	58	of	of	ADP
ejpam-2338	361	59	the	the	DET
ejpam-2338	361	60	groups	group	NOUN
ejpam-2338	361	61	he	he	PRON
ejpam-2338	361	62	,	,	PUNCT
ejpam-2338	361	63	but	but	CCONJ
ejpam-2338	361	64	also	also	ADV
ejpam-2338	361	65	heh	heh	INTJ
ejpam-2338	361	66	f	f	PROPN
ejpam-2338	362	1	⊆	⊆	NUM
ejpam-2338	362	2	he	he	PRON
ejpam-2338	362	3	f	f	PROPN
ejpam-2338	362	4	.	.	PUNCT
ejpam-2338	363	1	he	he	PRON
ejpam-2338	363	2	had	have	AUX
ejpam-2338	363	3	shown	show	VERB
ejpam-2338	363	4	further	far	ADV
ejpam-2338	363	5	that	that	SCONJ
ejpam-2338	363	6	the	the	DET
ejpam-2338	363	7	multiplication	multiplication	NOUN
ejpam-2338	363	8	in	in	ADP
ejpam-2338	363	9	s	s	PROPN
ejpam-2338	363	10	is	be	AUX
ejpam-2338	363	11	determined	determine	VERB
ejpam-2338	363	12	by	by	ADP
ejpam-2338	363	13	a	a	DET
ejpam-2338	363	14	family	family	NOUN
ejpam-2338	363	15	of	of	ADP
ejpam-2338	363	16	morphisms	morphism	NOUN
ejpam-2338	363	17	φe	φe	INTJ
ejpam-2338	363	18	,	,	PUNCT
ejpam-2338	363	19	f	f	PROPN
ejpam-2338	363	20	:	:	PUNCT
ejpam-2338	363	21	he	he	PRON
ejpam-2338	363	22	→	→	PUNCT
ejpam-2338	363	23	h	h	PROPN
ejpam-2338	363	24	f	f	PROPN
ejpam-2338	363	25	for	for	ADP
ejpam-2338	363	26	e	e	PROPN
ejpam-2338	363	27	≥	≥	X
ejpam-2338	363	28	f	f	X
ejpam-2338	363	29	.	.	PUNCT
ejpam-2338	364	1	we	we	PRON
ejpam-2338	364	2	see	see	VERB
ejpam-2338	364	3	that	that	SCONJ
ejpam-2338	364	4	in	in	ADP
ejpam-2338	364	5	this	this	DET
ejpam-2338	364	6	case	case	NOUN
ejpam-2338	364	7	s	s	VERB
ejpam-2338	364	8	is	be	AUX
ejpam-2338	364	9	completely	completely	ADV
ejpam-2338	364	10	determined	determine	VERB
ejpam-2338	364	11	by	by	ADP
ejpam-2338	364	12	the	the	DET
ejpam-2338	364	13	groups	group	NOUN
ejpam-2338	364	14	he	he	PRON
ejpam-2338	364	15	and	and	CCONJ
ejpam-2338	364	16	its	its	PRON
ejpam-2338	364	17	semilattice	semilattice	NOUN
ejpam-2338	364	18	of	of	ADP
ejpam-2338	364	19	idempotents	idempotent	NOUN
ejpam-2338	364	20	.	.	PUNCT
ejpam-2338	365	1	as	as	SCONJ
ejpam-2338	365	2	mcalister	mcalister	PROPN
ejpam-2338	365	3	[	[	X
ejpam-2338	365	4	58	58	NUM
ejpam-2338	365	5	,	,	PUNCT
ejpam-2338	365	6	p.	p.	NOUN
ejpam-2338	365	7	2	2	NUM
ejpam-2338	365	8	]	]	PUNCT
ejpam-2338	365	9	commented	comment	VERB
ejpam-2338	365	10	:	:	PUNCT
ejpam-2338	365	11	in	in	ADP
ejpam-2338	365	12	view	view	NOUN
ejpam-2338	365	13	of	of	ADP
ejpam-2338	365	14	this	this	PRON
ejpam-2338	365	15	,	,	PUNCT
ejpam-2338	365	16	it	it	PRON
ejpam-2338	365	17	is	be	AUX
ejpam-2338	365	18	natural	natural	ADJ
ejpam-2338	365	19	to	to	PART
ejpam-2338	365	20	wonder	wonder	VERB
ejpam-2338	365	21	to	to	ADP
ejpam-2338	365	22	what	what	DET
ejpam-2338	365	23	extent	extent	NOUN
ejpam-2338	365	24	inverse	inverse	NOUN
ejpam-2338	365	25	semigroups	semigroup	NOUN
ejpam-2338	365	26	can	can	AUX
ejpam-2338	365	27	be	be	AUX
ejpam-2338	365	28	constructed	construct	VERB
ejpam-2338	365	29	from	from	ADP
ejpam-2338	365	30	groups	group	NOUN
ejpam-2338	365	31	and	and	CCONJ
ejpam-2338	365	32	semilattices	semilattice	NOUN
ejpam-2338	365	33	.	.	PUNCT
ejpam-2338	366	1	indeed	indeed	ADV
ejpam-2338	366	2	much	much	ADJ
ejpam-2338	366	3	of	of	ADP
ejpam-2338	366	4	the	the	DET
ejpam-2338	366	5	structure	structure	NOUN
ejpam-2338	366	6	theory	theory	NOUN
ejpam-2338	366	7	of	of	ADP
ejpam-2338	366	8	inverse	inverse	NOUN
ejpam-2338	366	9	semigroups	semigroup	NOUN
ejpam-2338	366	10	has	have	AUX
ejpam-2338	366	11	been	be	AUX
ejpam-2338	366	12	concerned	concern	VERB
ejpam-2338	366	13	with	with	ADP
ejpam-2338	366	14	this	this	DET
ejpam-2338	366	15	problem	problem	NOUN
ejpam-2338	366	16	.	.	PUNCT
ejpam-2338	367	1	the	the	DET
ejpam-2338	367	2	most	most	ADV
ejpam-2338	367	3	naive	naive	ADJ
ejpam-2338	367	4	way	way	NOUN
ejpam-2338	367	5	to	to	PART
ejpam-2338	367	6	combine	combine	VERB
ejpam-2338	367	7	a	a	DET
ejpam-2338	367	8	group	group	NOUN
ejpam-2338	367	9	and	and	CCONJ
ejpam-2338	367	10	a	a	DET
ejpam-2338	367	11	semilattice	semilattice	NOUN
ejpam-2338	367	12	is	be	AUX
ejpam-2338	367	13	simply	simply	ADV
ejpam-2338	367	14	to	to	PART
ejpam-2338	367	15	take	take	VERB
ejpam-2338	367	16	their	their	PRON
ejpam-2338	367	17	direct	direct	ADJ
ejpam-2338	367	18	product	product	NOUN
ejpam-2338	367	19	.	.	PUNCT
ejpam-2338	368	1	if	if	SCONJ
ejpam-2338	368	2	we	we	PRON
ejpam-2338	368	3	do	do	VERB
ejpam-2338	368	4	this	this	PRON
ejpam-2338	368	5	,	,	PUNCT
ejpam-2338	368	6	the	the	DET
ejpam-2338	368	7	result	result	NOUN
ejpam-2338	368	8	is	be	AUX
ejpam-2338	368	9	certainly	certainly	ADV
ejpam-2338	368	10	an	an	DET
ejpam-2338	368	11	inverse	inverse	NOUN
ejpam-2338	368	12	semigroup	semigroup	NOUN
ejpam-2338	368	13	,	,	PUNCT
ejpam-2338	368	14	but	but	CCONJ
ejpam-2338	368	15	it	it	PRON
ejpam-2338	368	16	is	be	AUX
ejpam-2338	368	17	an	an	DET
ejpam-2338	368	18	inverse	inverse	NOUN
ejpam-2338	368	19	semigroup	semigroup	NOUN
ejpam-2338	368	20	with	with	ADP
ejpam-2338	368	21	central	central	ADJ
ejpam-2338	368	22	idempotents	idempotent	NOUN
ejpam-2338	368	23	,	,	PUNCT
ejpam-2338	368	24	so	so	SCONJ
ejpam-2338	368	25	we	we	PRON
ejpam-2338	368	26	can	can	AUX
ejpam-2338	368	27	not	not	PART
ejpam-2338	368	28	construct	construct	VERB
ejpam-2338	368	29	every	every	DET
ejpam-2338	368	30	inverse	inverse	NOUN
ejpam-2338	368	31	semigroup	semigroup	NOUN
ejpam-2338	368	32	in	in	ADP
ejpam-2338	368	33	this	this	DET
ejpam-2338	368	34	way	way	NOUN
ejpam-2338	368	35	.	.	PUNCT
ejpam-2338	369	1	as	as	SCONJ
ejpam-2338	369	2	mcalister	mcalister	PROPN
ejpam-2338	369	3	[	[	X
ejpam-2338	369	4	58	58	NUM
ejpam-2338	369	5	,	,	PUNCT
ejpam-2338	369	6	p.	p.	NOUN
ejpam-2338	369	7	2	2	NUM
ejpam-2338	369	8	]	]	PUNCT
ejpam-2338	369	9	noted	note	VERB
ejpam-2338	369	10	,	,	PUNCT
ejpam-2338	369	11	“	"	PUNCT
ejpam-2338	369	12	[	[	X
ejpam-2338	369	13	o]ne	o]ne	NOUN
ejpam-2338	369	14	needs	need	VERB
ejpam-2338	369	15	a	a	DET
ejpam-2338	369	16	mechanism	mechanism	NOUN
ejpam-2338	369	17	to	to	PART
ejpam-2338	369	18	account	account	VERB
ejpam-2338	369	19	for	for	ADP
ejpam-2338	369	20	the	the	DET
ejpam-2338	369	21	non	non	NOUN
ejpam-2338	369	22	-	-	NOUN
ejpam-2338	369	23	centrality	centrality	NOUN
ejpam-2338	369	24	of	of	ADP
ejpam-2338	369	25	idempotents	idempotent	NOUN
ejpam-2338	369	26	”	"	PUNCT
ejpam-2338	369	27	.	.	PUNCT
ejpam-2338	370	1	he	he	PRON
ejpam-2338	370	2	suggested	suggest	VERB
ejpam-2338	370	3	that	that	SCONJ
ejpam-2338	370	4	such	such	DET
ejpam-2338	370	5	a	a	DET
ejpam-2338	370	6	mechanism	mechanism	NOUN
ejpam-2338	370	7	may	may	AUX
ejpam-2338	370	8	be	be	AUX
ejpam-2338	370	9	found	find	VERB
ejpam-2338	370	10	in	in	ADP
ejpam-2338	370	11	the	the	DET
ejpam-2338	370	12	semidirect	semidirect	NOUN
ejpam-2338	370	13	product	product	NOUN
ejpam-2338	370	14	construction	construction	NOUN
ejpam-2338	370	15	:	:	PUNCT
ejpam-2338	370	16	suppose	suppose	VERB
ejpam-2338	370	17	that	that	SCONJ
ejpam-2338	370	18	a	a	DET
ejpam-2338	370	19	group	group	NOUN
ejpam-2338	370	20	g	g	NOUN
ejpam-2338	370	21	acts	act	VERB
ejpam-2338	370	22	on	on	ADP
ejpam-2338	370	23	the	the	DET
ejpam-2338	370	24	left	left	NOUN
ejpam-2338	370	25	of	of	ADP
ejpam-2338	370	26	a	a	DET
ejpam-2338	370	27	semilattice	semilattice	NOUN
ejpam-2338	370	28	e	e	NOUN
ejpam-2338	370	29	by	by	ADP
ejpam-2338	370	30	automorphisms	automorphism	NOUN
ejpam-2338	370	31	—	—	PUNCT
ejpam-2338	370	32	the	the	DET
ejpam-2338	370	33	semidirect	semidirect	NOUN
ejpam-2338	370	34	product	product	NOUN
ejpam-2338	370	35	of	of	ADP
ejpam-2338	370	36	e	e	NOUN
ejpam-2338	370	37	by	by	ADP
ejpam-2338	370	38	g	g	PROPN
ejpam-2338	370	39	is	be	AUX
ejpam-2338	370	40	the	the	DET
ejpam-2338	370	41	set	set	NOUN
ejpam-2338	370	42	of	of	ADP
ejpam-2338	370	43	all	all	DET
ejpam-2338	370	44	pairs	pair	NOUN
ejpam-2338	370	45	(	(	PUNCT
ejpam-2338	370	46	e	e	NOUN
ejpam-2338	370	47	,	,	PUNCT
ejpam-2338	370	48	g	g	NOUN
ejpam-2338	370	49	)	)	PUNCT
ejpam-2338	370	50	∈	∈	PROPN
ejpam-2338	370	51	e	e	X
ejpam-2338	370	52	×	×	NOUN
ejpam-2338	370	53	g	g	PROPN
ejpam-2338	370	54	,	,	PUNCT
ejpam-2338	370	55	under	under	ADP
ejpam-2338	370	56	the	the	DET
ejpam-2338	370	57	multiplication	multiplication	NOUN
ejpam-2338	370	58	(	(	PUNCT
ejpam-2338	370	59	e	e	NOUN
ejpam-2338	370	60	,	,	PUNCT
ejpam-2338	370	61	g	g	NOUN
ejpam-2338	370	62	)	)	PUNCT
ejpam-2338	370	63	(	(	PUNCT
ejpam-2338	370	64	f	f	X
ejpam-2338	370	65	,	,	PUNCT
ejpam-2338	370	66	h	h	NOUN
ejpam-2338	370	67	)	)	PUNCT
ejpam-2338	370	68	=	=	SYM
ejpam-2338	370	69	(	(	PUNCT
ejpam-2338	370	70	e(g	e(g	PROPN
ejpam-2338	370	71	·	·	PUNCT
ejpam-2338	370	72	f	f	X
ejpam-2338	370	73	)	)	PUNCT
ejpam-2338	370	74	,	,	PUNCT
ejpam-2338	370	75	gh	gh	PROPN
ejpam-2338	370	76	)	)	PUNCT
ejpam-2338	370	77	.	.	PUNCT
ejpam-2338	371	1	christopher	christopher	PROPN
ejpam-2338	371	2	hollings	hollings	PROPN
ejpam-2338	371	3	/	/	SYM
ejpam-2338	371	4	eur	eur	PROPN
ejpam-2338	371	5	.	.	PUNCT
ejpam-2338	372	1	j.	j.	PROPN
ejpam-2338	372	2	pure	pure	PROPN
ejpam-2338	372	3	appl	appl	PROPN
ejpam-2338	372	4	.	.	PROPN
ejpam-2338	372	5	math	math	PROPN
ejpam-2338	372	6	,	,	PUNCT
ejpam-2338	372	7	8	8	NUM
ejpam-2338	372	8	(	(	PUNCT
ejpam-2338	372	9	2015	2015	NUM
ejpam-2338	372	10	)	)	PUNCT
ejpam-2338	372	11	,	,	PUNCT
ejpam-2338	372	12	294	294	NUM
ejpam-2338	372	13	-	-	SYM
ejpam-2338	372	14	323	323	NUM
ejpam-2338	372	15	311	311	NUM
ejpam-2338	372	16	such	such	DET
ejpam-2338	372	17	a	a	DET
ejpam-2338	372	18	semidirect	semidirect	NOUN
ejpam-2338	372	19	product	product	NOUN
ejpam-2338	372	20	,	,	PUNCT
ejpam-2338	372	21	p(g	p(g	PROPN
ejpam-2338	372	22	,	,	PUNCT
ejpam-2338	372	23	e	e	NOUN
ejpam-2338	372	24	,	,	PUNCT
ejpam-2338	372	25	e	e	NOUN
ejpam-2338	372	26	)	)	PUNCT
ejpam-2338	372	27	,	,	PUNCT
ejpam-2338	372	28	is	be	AUX
ejpam-2338	372	29	an	an	DET
ejpam-2338	372	30	inverse	inverse	NOUN
ejpam-2338	372	31	semigroup	semigroup	NOUN
ejpam-2338	372	32	and	and	CCONJ
ejpam-2338	372	33	,	,	PUNCT
ejpam-2338	372	34	moreover	moreover	ADV
ejpam-2338	372	35	,	,	PUNCT
ejpam-2338	372	36	it	it	PRON
ejpam-2338	372	37	is	be	AUX
ejpam-2338	372	38	an	an	DET
ejpam-2338	372	39	inverse	inverse	NOUN
ejpam-2338	372	40	semigroup	semigroup	NOUN
ejpam-2338	372	41	with	with	ADP
ejpam-2338	372	42	non	non	ADJ
ejpam-2338	372	43	-	-	ADJ
ejpam-2338	372	44	central	central	ADJ
ejpam-2338	372	45	idempotents	idempotent	NOUN
ejpam-2338	372	46	.	.	PUNCT
ejpam-2338	373	1	however	however	ADV
ejpam-2338	373	2	,	,	PUNCT
ejpam-2338	373	3	once	once	ADV
ejpam-2338	373	4	again	again	ADV
ejpam-2338	373	5	,	,	PUNCT
ejpam-2338	373	6	this	this	DET
ejpam-2338	373	7	construction	construction	NOUN
ejpam-2338	373	8	will	will	AUX
ejpam-2338	373	9	not	not	PART
ejpam-2338	373	10	serve	serve	VERB
ejpam-2338	373	11	to	to	PART
ejpam-2338	373	12	describe	describe	VERB
ejpam-2338	373	13	all	all	DET
ejpam-2338	373	14	inverse	inverse	NOUN
ejpam-2338	373	15	semigroups	semigroup	NOUN
ejpam-2338	373	16	,	,	PUNCT
ejpam-2338	373	17	this	this	DET
ejpam-2338	373	18	time	time	NOUN
ejpam-2338	373	19	because	because	SCONJ
ejpam-2338	373	20	it	it	PRON
ejpam-2338	373	21	can	can	AUX
ejpam-2338	373	22	not	not	PART
ejpam-2338	373	23	have	have	VERB
ejpam-2338	373	24	a	a	DET
ejpam-2338	373	25	zero	zero	NUM
ejpam-2338	373	26	element	element	NOUN
ejpam-2338	373	27	.	.	PUNCT
ejpam-2338	374	1	nevertheless	nevertheless	ADV
ejpam-2338	374	2	,	,	PUNCT
ejpam-2338	374	3	such	such	DET
ejpam-2338	374	4	a	a	DET
ejpam-2338	374	5	semidirect	semidirect	NOUN
ejpam-2338	374	6	product	product	NOUN
ejpam-2338	374	7	can	can	AUX
ejpam-2338	374	8	be	be	AUX
ejpam-2338	374	9	connected	connect	VERB
ejpam-2338	374	10	with	with	ADP
ejpam-2338	374	11	a	a	DET
ejpam-2338	374	12	geometric	geometric	ADJ
ejpam-2338	374	13	example	example	NOUN
ejpam-2338	374	14	[	[	X
ejpam-2338	374	15	58	58	NUM
ejpam-2338	374	16	,	,	PUNCT
ejpam-2338	374	17	example	example	NOUN
ejpam-2338	374	18	1.3	1.3	NUM
ejpam-2338	374	19	]	]	PUNCT
ejpam-2338	374	20	.	.	PUNCT
ejpam-2338	375	1	let	let	VERB
ejpam-2338	375	2	an	an	DET
ejpam-2338	375	3	denote	denote	NOUN
ejpam-2338	375	4	n	n	CCONJ
ejpam-2338	375	5	-	-	PUNCT
ejpam-2338	375	6	dimensional	dimensional	ADJ
ejpam-2338	375	7	real	real	ADJ
ejpam-2338	375	8	affine	affine	NOUN
ejpam-2338	375	9	space	space	NOUN
ejpam-2338	375	10	;	;	PUNCT
ejpam-2338	375	11	a	a	DET
ejpam-2338	375	12	geometric	geometric	ADJ
ejpam-2338	375	13	figure	figure	NOUN
ejpam-2338	375	14	is	be	AUX
ejpam-2338	375	15	a	a	DET
ejpam-2338	375	16	compact	compact	ADJ
ejpam-2338	375	17	connected	connect	VERB
ejpam-2338	375	18	subset	subset	NOUN
ejpam-2338	375	19	of	of	ADP
ejpam-2338	375	20	an	an	PRON
ejpam-2338	375	21	.	.	PUNCT
ejpam-2338	376	1	the	the	DET
ejpam-2338	376	2	set	set	ADJ
ejpam-2338	376	3	f	f	PROPN
ejpam-2338	376	4	of	of	ADP
ejpam-2338	376	5	geometric	geometric	ADJ
ejpam-2338	376	6	figures	figure	NOUN
ejpam-2338	376	7	forms	form	VERB
ejpam-2338	376	8	a	a	DET
ejpam-2338	376	9	semilattice	semilattice	NOUN
ejpam-2338	376	10	under	under	ADP
ejpam-2338	376	11	convex	convex	NOUN
ejpam-2338	376	12	join	join	NOUN
ejpam-2338	376	13	,	,	PUNCT
ejpam-2338	376	14	and	and	CCONJ
ejpam-2338	376	15	the	the	DET
ejpam-2338	376	16	n	n	CCONJ
ejpam-2338	376	17	-	-	PUNCT
ejpam-2338	376	18	dimensional	dimensional	ADJ
ejpam-2338	376	19	affine	affine	NOUN
ejpam-2338	376	20	group	group	NOUN
ejpam-2338	376	21	g	g	PROPN
ejpam-2338	376	22	acts	act	VERB
ejpam-2338	376	23	on	on	ADP
ejpam-2338	376	24	f	f	PROPN
ejpam-2338	376	25	via	via	ADP
ejpam-2338	376	26	g	g	PROPN
ejpam-2338	376	27	·	·	PUNCT
ejpam-2338	376	28	a	a	DET
ejpam-2338	376	29	=	=	X
ejpam-2338	376	30	ag−1	ag−1	PROPN
ejpam-2338	376	31	,	,	PUNCT
ejpam-2338	376	32	for	for	ADP
ejpam-2338	376	33	a	a	DET
ejpam-2338	376	34	∈	∈	PROPN
ejpam-2338	376	35	f	f	NOUN
ejpam-2338	376	36	and	and	CCONJ
ejpam-2338	376	37	g	g	PROPN
ejpam-2338	376	38	∈	∈	PROPN
ejpam-2338	376	39	g	g	PROPN
ejpam-2338	376	40	,	,	PUNCT
ejpam-2338	376	41	where	where	SCONJ
ejpam-2338	376	42	ag−1	ag−1	PROPN
ejpam-2338	376	43	denotes	denote	VERB
ejpam-2338	376	44	the	the	DET
ejpam-2338	376	45	result	result	NOUN
ejpam-2338	376	46	of	of	ADP
ejpam-2338	376	47	applying	apply	VERB
ejpam-2338	376	48	the	the	DET
ejpam-2338	376	49	transformation	transformation	NOUN
ejpam-2338	376	50	g−1	g−1	VERB
ejpam-2338	376	51	to	to	ADP
ejpam-2338	376	52	the	the	DET
ejpam-2338	376	53	figure	figure	NOUN
ejpam-2338	376	54	a.	a.	NOUN
ejpam-2338	376	55	we	we	PRON
ejpam-2338	376	56	may	may	AUX
ejpam-2338	376	57	of	of	ADP
ejpam-2338	376	58	course	course	NOUN
ejpam-2338	376	59	associate	associate	VERB
ejpam-2338	376	60	a	a	DET
ejpam-2338	376	61	semidirect	semidirect	NOUN
ejpam-2338	376	62	product	product	NOUN
ejpam-2338	376	63	p(g	p(g	PROPN
ejpam-2338	376	64	,	,	PUNCT
ejpam-2338	376	65	f	f	PROPN
ejpam-2338	376	66	,	,	PUNCT
ejpam-2338	376	67	f	f	X
ejpam-2338	376	68	)	)	PUNCT
ejpam-2338	376	69	with	with	ADP
ejpam-2338	376	70	this	this	DET
ejpam-2338	376	71	action	action	NOUN
ejpam-2338	376	72	.	.	PUNCT
ejpam-2338	377	1	mcalister	mcalister	PROPN
ejpam-2338	378	1	[	[	X
ejpam-2338	378	2	58	58	NUM
ejpam-2338	378	3	,	,	PUNCT
ejpam-2338	378	4	p.	p.	NOUN
ejpam-2338	378	5	4	4	NUM
ejpam-2338	378	6	]	]	PUNCT
ejpam-2338	378	7	observed	observe	VERB
ejpam-2338	378	8	that	that	SCONJ
ejpam-2338	378	9	p(g	p(g	PROPN
ejpam-2338	378	10	,	,	PUNCT
ejpam-2338	378	11	f	f	PROPN
ejpam-2338	378	12	,	,	PUNCT
ejpam-2338	378	13	f	f	X
ejpam-2338	378	14	)	)	PUNCT
ejpam-2338	378	15	has	have	VERB
ejpam-2338	378	16	a	a	DET
ejpam-2338	378	17	particularly	particularly	ADV
ejpam-2338	378	18	interesting	interesting	ADJ
ejpam-2338	378	19	ideal	ideal	ADJ
ejpam-2338	378	20	structure	structure	NOUN
ejpam-2338	378	21	,	,	PUNCT
ejpam-2338	378	22	but	but	CCONJ
ejpam-2338	378	23	that	that	SCONJ
ejpam-2338	378	24	it	it	PRON
ejpam-2338	378	25	is	be	AUX
ejpam-2338	378	26	“	"	PUNCT
ejpam-2338	378	27	not	not	PART
ejpam-2338	378	28	quite	quite	ADV
ejpam-2338	378	29	so	so	ADV
ejpam-2338	378	30	satisfying	satisfying	ADJ
ejpam-2338	378	31	”	"	PUNCT
ejpam-2338	378	32	from	from	ADP
ejpam-2338	378	33	the	the	DET
ejpam-2338	378	34	geometric	geometric	ADJ
ejpam-2338	378	35	viewpoint	viewpoint	NOUN
ejpam-2338	378	36	.	.	PUNCT
ejpam-2338	379	1	the	the	DET
ejpam-2338	379	2	problem	problem	NOUN
ejpam-2338	379	3	is	be	AUX
ejpam-2338	379	4	that	that	SCONJ
ejpam-2338	379	5	the	the	DET
ejpam-2338	379	6	set	set	NOUN
ejpam-2338	379	7	of	of	ADP
ejpam-2338	379	8	all	all	DET
ejpam-2338	379	9	geometric	geometric	ADJ
ejpam-2338	379	10	figures	figure	NOUN
ejpam-2338	379	11	is	be	AUX
ejpam-2338	379	12	rather	rather	ADV
ejpam-2338	379	13	too	too	ADV
ejpam-2338	379	14	large	large	ADJ
ejpam-2338	379	15	to	to	PART
ejpam-2338	379	16	handle	handle	VERB
ejpam-2338	379	17	;	;	PUNCT
ejpam-2338	379	18	we	we	PRON
ejpam-2338	379	19	should	should	AUX
ejpam-2338	379	20	‘	'	PUNCT
ejpam-2338	379	21	localise	localise	VERB
ejpam-2338	379	22	’	'	PUNCT
ejpam-2338	379	23	them	they	PRON
ejpam-2338	379	24	in	in	ADP
ejpam-2338	379	25	some	some	DET
ejpam-2338	379	26	way	way	NOUN
ejpam-2338	379	27	.	.	PUNCT
ejpam-2338	380	1	we	we	PRON
ejpam-2338	380	2	do	do	VERB
ejpam-2338	380	3	this	this	PRON
ejpam-2338	380	4	by	by	ADP
ejpam-2338	380	5	restricting	restrict	VERB
ejpam-2338	380	6	our	our	PRON
ejpam-2338	380	7	attention	attention	NOUN
ejpam-2338	380	8	to	to	ADP
ejpam-2338	380	9	those	those	DET
ejpam-2338	380	10	geometric	geometric	ADJ
ejpam-2338	380	11	figures	figure	NOUN
ejpam-2338	380	12	which	which	PRON
ejpam-2338	380	13	contain	contain	VERB
ejpam-2338	380	14	the	the	DET
ejpam-2338	380	15	origin	origin	NOUN
ejpam-2338	380	16	;	;	PUNCT
ejpam-2338	380	17	let	let	VERB
ejpam-2338	380	18	the	the	DET
ejpam-2338	380	19	set	set	NOUN
ejpam-2338	380	20	of	of	ADP
ejpam-2338	380	21	all	all	DET
ejpam-2338	380	22	such	such	ADJ
ejpam-2338	380	23	be	be	AUX
ejpam-2338	380	24	denoted	denote	VERB
ejpam-2338	380	25	by	by	ADP
ejpam-2338	380	26	e.	e.	PROPN
ejpam-2338	380	27	however	however	ADV
ejpam-2338	380	28	,	,	PUNCT
ejpam-2338	380	29	this	this	PRON
ejpam-2338	380	30	causes	cause	VERB
ejpam-2338	380	31	a	a	DET
ejpam-2338	380	32	new	new	ADJ
ejpam-2338	380	33	problem	problem	NOUN
ejpam-2338	380	34	:	:	PUNCT
ejpam-2338	380	35	g	g	PROPN
ejpam-2338	380	36	may	may	AUX
ejpam-2338	380	37	translate	translate	VERB
ejpam-2338	380	38	elements	element	NOUN
ejpam-2338	380	39	of	of	ADP
ejpam-2338	380	40	e	e	PROPN
ejpam-2338	380	41	out	out	ADP
ejpam-2338	380	42	of	of	ADP
ejpam-2338	380	43	e	e	NOUN
ejpam-2338	380	44	,	,	PUNCT
ejpam-2338	380	45	and	and	CCONJ
ejpam-2338	380	46	so	so	ADV
ejpam-2338	380	47	we	we	PRON
ejpam-2338	380	48	can	can	AUX
ejpam-2338	380	49	not	not	PART
ejpam-2338	380	50	construct	construct	VERB
ejpam-2338	380	51	the	the	DET
ejpam-2338	380	52	semidirect	semidirect	NOUN
ejpam-2338	380	53	product	product	NOUN
ejpam-2338	380	54	of	of	ADP
ejpam-2338	380	55	e	e	PROPN
ejpam-2338	380	56	by	by	ADP
ejpam-2338	380	57	g.	g.	PROPN
ejpam-2338	380	58	instead	instead	ADV
ejpam-2338	380	59	,	,	PUNCT
ejpam-2338	380	60	we	we	PRON
ejpam-2338	380	61	limit	limit	VERB
ejpam-2338	380	62	ourselves	ourselves	PRON
ejpam-2338	380	63	to	to	ADP
ejpam-2338	380	64	those	those	DET
ejpam-2338	380	65	pairs	pair	NOUN
ejpam-2338	380	66	(	(	PUNCT
ejpam-2338	380	67	a	a	PRON
ejpam-2338	380	68	,	,	PUNCT
ejpam-2338	380	69	g	g	NOUN
ejpam-2338	380	70	)	)	PUNCT
ejpam-2338	380	71	∈	∈	PROPN
ejpam-2338	381	1	e	e	NOUN
ejpam-2338	381	2	×	×	NOUN
ejpam-2338	381	3	g	g	NOUN
ejpam-2338	381	4	for	for	ADP
ejpam-2338	381	5	which	which	PRON
ejpam-2338	381	6	g−1	g−1	PROPN
ejpam-2338	381	7	·	·	PUNCT
ejpam-2338	381	8	a	a	DET
ejpam-2338	381	9	=	=	NOUN
ejpam-2338	381	10	ag	ag	PROPN
ejpam-2338	381	11	also	also	ADV
ejpam-2338	381	12	lies	lie	VERB
ejpam-2338	381	13	in	in	ADP
ejpam-2338	381	14	e.	e.	PROPN
ejpam-2338	381	15	that	that	PRON
ejpam-2338	381	16	is	be	AUX
ejpam-2338	381	17	,	,	PUNCT
ejpam-2338	381	18	we	we	PRON
ejpam-2338	381	19	confine	confine	VERB
ejpam-2338	381	20	our	our	PRON
ejpam-2338	381	21	attention	attention	NOUN
ejpam-2338	381	22	to	to	ADP
ejpam-2338	381	23	the	the	DET
ejpam-2338	381	24	set	set	NOUN
ejpam-2338	381	25	{	{	PUNCT
ejpam-2338	381	26	(	(	PUNCT
ejpam-2338	381	27	a	a	PRON
ejpam-2338	381	28	,	,	PUNCT
ejpam-2338	381	29	g	g	NOUN
ejpam-2338	381	30	)	)	PUNCT
ejpam-2338	381	31	∈	∈	PROPN
ejpam-2338	382	1	e	e	NOUN
ejpam-2338	382	2	×	×	NOUN
ejpam-2338	382	3	g	g	NOUN
ejpam-2338	382	4	:	:	PUNCT
ejpam-2338	382	5	g−1	g−1	PROPN
ejpam-2338	382	6	·	·	PUNCT
ejpam-2338	382	7	a	a	DET
ejpam-2338	382	8	∈	∈	NOUN
ejpam-2338	382	9	e	e	NOUN
ejpam-2338	382	10	}	}	PUNCT
ejpam-2338	382	11	,	,	PUNCT
ejpam-2338	382	12	but	but	CCONJ
ejpam-2338	382	13	we	we	PRON
ejpam-2338	382	14	retain	retain	VERB
ejpam-2338	382	15	the	the	DET
ejpam-2338	382	16	semidirect	semidirect	NOUN
ejpam-2338	382	17	product	product	NOUN
ejpam-2338	382	18	multiplication	multiplication	NOUN
ejpam-2338	382	19	.	.	PUNCT
ejpam-2338	383	1	we	we	PRON
ejpam-2338	383	2	denote	denote	VERB
ejpam-2338	383	3	this	this	DET
ejpam-2338	383	4	new	new	ADJ
ejpam-2338	383	5	construction	construction	NOUN
ejpam-2338	383	6	by	by	ADP
ejpam-2338	383	7	p(g	p(g	PROPN
ejpam-2338	383	8	,	,	PUNCT
ejpam-2338	383	9	f	f	X
ejpam-2338	383	10	,	,	PUNCT
ejpam-2338	383	11	e	e	NOUN
ejpam-2338	383	12	)	)	PUNCT
ejpam-2338	383	13	and	and	CCONJ
ejpam-2338	383	14	observe	observe	VERB
ejpam-2338	383	15	that	that	SCONJ
ejpam-2338	383	16	it	it	PRON
ejpam-2338	383	17	is	be	AUX
ejpam-2338	383	18	an	an	DET
ejpam-2338	383	19	inverse	inverse	NOUN
ejpam-2338	383	20	subsemigroup	subsemigroup	NOUN
ejpam-2338	383	21	of	of	ADP
ejpam-2338	383	22	p(g	p(g	PROPN
ejpam-2338	383	23	,	,	PUNCT
ejpam-2338	383	24	f	f	PROPN
ejpam-2338	383	25	,	,	PUNCT
ejpam-2338	383	26	f	f	PROPN
ejpam-2338	383	27	)	)	PUNCT
ejpam-2338	383	28	.	.	PUNCT
ejpam-2338	384	1	comparing	compare	VERB
ejpam-2338	384	2	it	it	PRON
ejpam-2338	384	3	also	also	ADV
ejpam-2338	384	4	with	with	ADP
ejpam-2338	384	5	(	(	PUNCT
ejpam-2338	384	6	5	5	NUM
ejpam-2338	384	7	)	)	PUNCT
ejpam-2338	384	8	,	,	PUNCT
ejpam-2338	384	9	we	we	PRON
ejpam-2338	384	10	see	see	VERB
ejpam-2338	384	11	that	that	SCONJ
ejpam-2338	384	12	,	,	PUNCT
ejpam-2338	384	13	as	as	SCONJ
ejpam-2338	384	14	the	the	DET
ejpam-2338	384	15	notation	notation	NOUN
ejpam-2338	384	16	suggests	suggest	VERB
ejpam-2338	384	17	,	,	PUNCT
ejpam-2338	384	18	p(g	p(g	PROPN
ejpam-2338	384	19	,	,	PUNCT
ejpam-2338	384	20	f	f	X
ejpam-2338	384	21	,	,	PUNCT
ejpam-2338	384	22	e	e	NOUN
ejpam-2338	384	23	)	)	PUNCT
ejpam-2338	384	24	is	be	AUX
ejpam-2338	384	25	a	a	DET
ejpam-2338	384	26	special	special	ADJ
ejpam-2338	384	27	case	case	NOUN
ejpam-2338	384	28	of	of	ADP
ejpam-2338	384	29	a	a	DET
ejpam-2338	384	30	p	p	NOUN
ejpam-2338	384	31	-	-	PUNCT
ejpam-2338	384	32	semigroup	semigroup	NOUN
ejpam-2338	384	33	.	.	PUNCT
ejpam-2338	385	1	mcalister	mcalister	PROPN
ejpam-2338	385	2	noted	note	VERB
ejpam-2338	385	3	that	that	SCONJ
ejpam-2338	385	4	,	,	PUNCT
ejpam-2338	385	5	just	just	ADV
ejpam-2338	385	6	like	like	ADP
ejpam-2338	385	7	semidirect	semidirect	NOUN
ejpam-2338	385	8	products	product	NOUN
ejpam-2338	385	9	,	,	PUNCT
ejpam-2338	385	10	p	p	NOUN
ejpam-2338	385	11	-	-	PUNCT
ejpam-2338	385	12	semigroups	semigroup	NOUN
ejpam-2338	385	13	in	in	ADP
ejpam-2338	385	14	which	which	PRON
ejpam-2338	385	15	the	the	DET
ejpam-2338	385	16	group	group	NOUN
ejpam-2338	385	17	is	be	AUX
ejpam-2338	385	18	non	non	ADJ
ejpam-2338	385	19	-	-	ADJ
ejpam-2338	385	20	trivial	trivial	ADJ
ejpam-2338	385	21	can	can	AUX
ejpam-2338	385	22	not	not	PART
ejpam-2338	385	23	have	have	VERB
ejpam-2338	385	24	a	a	DET
ejpam-2338	385	25	zero	zero	NUM
ejpam-2338	385	26	element	element	NOUN
ejpam-2338	385	27	,	,	PUNCT
ejpam-2338	385	28	and	and	CCONJ
ejpam-2338	385	29	so	so	ADV
ejpam-2338	385	30	not	not	PART
ejpam-2338	385	31	all	all	DET
ejpam-2338	385	32	inverse	inverse	NOUN
ejpam-2338	385	33	semigroups	semigroup	NOUN
ejpam-2338	385	34	can	can	AUX
ejpam-2338	385	35	be	be	AUX
ejpam-2338	385	36	realised	realise	VERB
ejpam-2338	385	37	as	as	ADP
ejpam-2338	385	38	p	p	NOUN
ejpam-2338	385	39	-	-	PUNCT
ejpam-2338	385	40	semigroups	semigroup	NOUN
ejpam-2338	385	41	.	.	PUNCT
ejpam-2338	386	1	thus	thus	ADV
ejpam-2338	386	2	,	,	PUNCT
ejpam-2338	386	3	the	the	DET
ejpam-2338	386	4	‘	'	PUNCT
ejpam-2338	386	5	goal	goal	NOUN
ejpam-2338	386	6	’	'	PUNCT
ejpam-2338	386	7	of	of	ADP
ejpam-2338	386	8	these	these	DET
ejpam-2338	386	9	considerations	consideration	NOUN
ejpam-2338	386	10	has	have	AUX
ejpam-2338	386	11	not	not	PART
ejpam-2338	386	12	been	be	AUX
ejpam-2338	386	13	reached	reach	VERB
ejpam-2338	386	14	—	—	PUNCT
ejpam-2338	386	15	we	we	PRON
ejpam-2338	386	16	have	have	AUX
ejpam-2338	386	17	not	not	PART
ejpam-2338	386	18	managed	manage	VERB
ejpam-2338	386	19	to	to	PART
ejpam-2338	386	20	give	give	VERB
ejpam-2338	386	21	a	a	DET
ejpam-2338	386	22	complete	complete	ADJ
ejpam-2338	386	23	description	description	NOUN
ejpam-2338	386	24	of	of	ADP
ejpam-2338	386	25	inverse	inverse	NOUN
ejpam-2338	386	26	semigroups	semigroup	NOUN
ejpam-2338	386	27	in	in	ADP
ejpam-2338	386	28	terms	term	NOUN
ejpam-2338	386	29	of	of	ADP
ejpam-2338	386	30	groups	group	NOUN
ejpam-2338	386	31	and	and	CCONJ
ejpam-2338	386	32	semilattices	semilattice	NOUN
ejpam-2338	386	33	—	—	PUNCT
ejpam-2338	386	34	but	but	CCONJ
ejpam-2338	386	35	we	we	PRON
ejpam-2338	386	36	have	have	AUX
ejpam-2338	386	37	derived	derive	VERB
ejpam-2338	386	38	an	an	DET
ejpam-2338	386	39	interesting	interesting	ADJ
ejpam-2338	386	40	class	class	NOUN
ejpam-2338	386	41	of	of	ADP
ejpam-2338	386	42	inverse	inverse	NOUN
ejpam-2338	386	43	semigroups	semigroup	NOUN
ejpam-2338	386	44	to	to	PART
ejpam-2338	386	45	study	study	VERB
ejpam-2338	386	46	.	.	PUNCT
ejpam-2338	387	1	in	in	ADP
ejpam-2338	387	2	order	order	NOUN
ejpam-2338	387	3	to	to	PART
ejpam-2338	387	4	study	study	VERB
ejpam-2338	387	5	inverse	inverse	NOUN
ejpam-2338	387	6	semigroups	semigroup	NOUN
ejpam-2338	387	7	with	with	ADP
ejpam-2338	387	8	zero	zero	NUM
ejpam-2338	387	9	which	which	PRON
ejpam-2338	387	10	satisfy	satisfy	VERB
ejpam-2338	387	11	something	something	PRON
ejpam-2338	387	12	like	like	ADP
ejpam-2338	387	13	the	the	DET
ejpam-2338	387	14	e	e	NOUN
ejpam-2338	387	15	-	-	NOUN
ejpam-2338	387	16	unitary	unitary	ADJ
ejpam-2338	387	17	property	property	NOUN
ejpam-2338	387	18	,	,	PUNCT
ejpam-2338	387	19	we	we	PRON
ejpam-2338	387	20	must	must	AUX
ejpam-2338	387	21	instead	instead	ADV
ejpam-2338	387	22	consider	consider	VERB
ejpam-2338	387	23	so	so	ADV
ejpam-2338	387	24	-	-	PUNCT
ejpam-2338	387	25	called	call	VERB
ejpam-2338	387	26	0	0	NUM
ejpam-2338	387	27	-	-	PUNCT
ejpam-2338	387	28	e	e	NOUN
ejpam-2338	387	29	-	-	ADJ
ejpam-2338	387	30	unitary	unitary	ADJ
ejpam-2338	387	31	inverse	inverse	NOUN
ejpam-2338	387	32	semigroups	semigroup	NOUN
ejpam-2338	387	33	:	:	PUNCT
ejpam-2338	387	34	an	an	DET
ejpam-2338	387	35	inverse	inverse	NOUN
ejpam-2338	387	36	semigroup	semigroup	NOUN
ejpam-2338	387	37	with	with	ADP
ejpam-2338	387	38	zero	zero	NUM
ejpam-2338	387	39	is	be	AUX
ejpam-2338	387	40	0	0	NUM
ejpam-2338	387	41	-	-	PUNCT
ejpam-2338	387	42	e	e	NOUN
ejpam-2338	387	43	-	-	NOUN
ejpam-2338	387	44	unitary	unitary	ADJ
ejpam-2338	387	45	whenever	whenever	ADV
ejpam-2338	387	46	,	,	PUNCT
ejpam-2338	387	47	for	for	ADP
ejpam-2338	387	48	any	any	DET
ejpam-2338	387	49	non	non	ADJ
ejpam-2338	387	50	-	-	ADJ
ejpam-2338	387	51	zero	zero	ADJ
ejpam-2338	387	52	idempotent	idempotent	ADJ
ejpam-2338	387	53	e	e	NOUN
ejpam-2338	387	54	,	,	PUNCT
ejpam-2338	387	55	e	e	PROPN
ejpam-2338	387	56	≤	≤	PROPN
ejpam-2338	387	57	s	s	VERB
ejpam-2338	387	58	implies	imply	VERB
ejpam-2338	387	59	that	that	SCONJ
ejpam-2338	387	60	s	s	VERB
ejpam-2338	387	61	is	be	AUX
ejpam-2338	387	62	idempotent	idempotent	ADJ
ejpam-2338	387	63	.	.	PUNCT
ejpam-2338	388	1	for	for	ADP
ejpam-2338	388	2	more	more	ADJ
ejpam-2338	388	3	details	detail	NOUN
ejpam-2338	388	4	on	on	ADP
ejpam-2338	388	5	these	these	DET
ejpam-2338	388	6	semigroups	semigroup	NOUN
ejpam-2338	388	7	,	,	PUNCT
ejpam-2338	388	8	see	see	VERB
ejpam-2338	388	9	[	[	X
ejpam-2338	388	10	51	51	NUM
ejpam-2338	388	11	,	,	PUNCT
ejpam-2338	388	12	chapter	chapter	NOUN
ejpam-2338	388	13	9	9	NUM
ejpam-2338	388	14	]	]	PUNCT
ejpam-2338	388	15	.	.	PUNCT
ejpam-2338	389	1	5.6	5.6	NUM
ejpam-2338	389	2	.	.	PUNCT
ejpam-2338	390	1	goła̧b	goła̧b	VERB
ejpam-2338	390	2	’s	’s	PART
ejpam-2338	390	3	approach	approach	NOUN
ejpam-2338	390	4	earlier	early	ADV
ejpam-2338	390	5	on	on	ADV
ejpam-2338	390	6	,	,	PUNCT
ejpam-2338	390	7	i	i	PRON
ejpam-2338	390	8	indicated	indicate	VERB
ejpam-2338	390	9	that	that	SCONJ
ejpam-2338	390	10	the	the	DET
ejpam-2338	390	11	1939	1939	NUM
ejpam-2338	390	12	work	work	NOUN
ejpam-2338	390	13	of	of	ADP
ejpam-2338	390	14	goła̧b	goła̧b	PRON
ejpam-2338	390	15	contained	contain	VERB
ejpam-2338	390	16	the	the	DET
ejpam-2338	390	17	ingredients	ingredient	NOUN
ejpam-2338	390	18	for	for	ADP
ejpam-2338	390	19	the	the	DET
ejpam-2338	390	20	proof	proof	NOUN
ejpam-2338	390	21	of	of	ADP
ejpam-2338	390	22	the	the	DET
ejpam-2338	390	23	p	p	NOUN
ejpam-2338	390	24	-	-	PUNCT
ejpam-2338	390	25	theorem	theorem	ADJ
ejpam-2338	390	26	(	(	PUNCT
ejpam-2338	390	27	to	to	PART
ejpam-2338	390	28	quote	quote	VERB
ejpam-2338	390	29	[	[	X
ejpam-2338	390	30	92	92	NUM
ejpam-2338	390	31	,	,	PUNCT
ejpam-2338	390	32	p.	p.	NOUN
ejpam-2338	390	33	152	152	NUM
ejpam-2338	390	34	]	]	PUNCT
ejpam-2338	390	35	,	,	PUNCT
ejpam-2338	390	36	it	it	PRON
ejpam-2338	390	37	contained	contain	VERB
ejpam-2338	390	38	the	the	DET
ejpam-2338	390	39	“	"	PUNCT
ejpam-2338	390	40	key	key	ADJ
ejpam-2338	390	41	idea	idea	NOUN
ejpam-2338	390	42	”	"	PUNCT
ejpam-2338	390	43	)	)	PUNCT
ejpam-2338	390	44	.	.	PUNCT
ejpam-2338	391	1	in	in	ADP
ejpam-2338	391	2	order	order	NOUN
ejpam-2338	391	3	to	to	PART
ejpam-2338	391	4	explain	explain	VERB
ejpam-2338	391	5	this	this	PRON
ejpam-2338	391	6	,	,	PUNCT
ejpam-2338	391	7	we	we	PRON
ejpam-2338	391	8	need	need	VERB
ejpam-2338	391	9	to	to	PART
ejpam-2338	391	10	recall	recall	VERB
ejpam-2338	391	11	the	the	DET
ejpam-2338	391	12	compatibility	compatibility	NOUN
ejpam-2338	391	13	relation	relation	NOUN
ejpam-2338	391	14	from	from	ADP
ejpam-2338	391	15	section	section	NOUN
ejpam-2338	391	16	3	3	NUM
ejpam-2338	391	17	.	.	PUNCT
ejpam-2338	392	1	this	this	PRON
ejpam-2338	392	2	was	be	AUX
ejpam-2338	392	3	a	a	DET
ejpam-2338	392	4	relation	relation	NOUN
ejpam-2338	392	5	∼	∼	NOUN
ejpam-2338	392	6	that	that	PRON
ejpam-2338	392	7	we	we	PRON
ejpam-2338	392	8	defined	define	VERB
ejpam-2338	392	9	on	on	ADP
ejpam-2338	392	10	partial	partial	ADJ
ejpam-2338	392	11	bijections	bijection	NOUN
ejpam-2338	392	12	f	f	NOUN
ejpam-2338	392	13	,	,	PUNCT
ejpam-2338	392	14	g	g	PROPN
ejpam-2338	392	15	by	by	ADP
ejpam-2338	392	16	the	the	DET
ejpam-2338	392	17	rule	rule	NOUN
ejpam-2338	392	18	that	that	SCONJ
ejpam-2338	392	19	f	f	PROPN
ejpam-2338	392	20	∼	∼	VERB
ejpam-2338	392	21	g	g	NOUN
ejpam-2338	392	22	if	if	SCONJ
ejpam-2338	392	23	and	and	CCONJ
ejpam-2338	392	24	only	only	ADV
ejpam-2338	392	25	if	if	SCONJ
ejpam-2338	392	26	f	f	PROPN
ejpam-2338	392	27	∪	∪	VERB
ejpam-2338	392	28	g	g	PROPN
ejpam-2338	392	29	is	be	AUX
ejpam-2338	392	30	also	also	ADV
ejpam-2338	392	31	a	a	DET
ejpam-2338	392	32	partial	partial	ADJ
ejpam-2338	392	33	bijection	bijection	NOUN
ejpam-2338	392	34	.	.	PUNCT
ejpam-2338	393	1	lawson	lawson	PROPN
ejpam-2338	394	1	[	[	X
ejpam-2338	394	2	51	51	NUM
ejpam-2338	394	3	,	,	PUNCT
ejpam-2338	394	4	proposition	proposition	NOUN
ejpam-2338	394	5	1.2.1	1.2.1	NUM
ejpam-2338	394	6	]	]	PUNCT
ejpam-2338	394	7	demonstrates	demonstrate	VERB
ejpam-2338	394	8	that	that	SCONJ
ejpam-2338	394	9	f	f	PROPN
ejpam-2338	394	10	∼	∼	NOUN
ejpam-2338	394	11	g	g	NOUN
ejpam-2338	394	12	precisely	precisely	ADV
ejpam-2338	394	13	when	when	SCONJ
ejpam-2338	394	14	f	f	PROPN
ejpam-2338	394	15	g−1	g−1	PROPN
ejpam-2338	394	16	and	and	CCONJ
ejpam-2338	394	17	f	f	PROPN
ejpam-2338	394	18	−1	−1	NOUN
ejpam-2338	394	19	g	g	PROPN
ejpam-2338	394	20	are	be	AUX
ejpam-2338	394	21	partial	partial	ADJ
ejpam-2338	394	22	identity	identity	NOUN
ejpam-2338	394	23	transformations	transformation	NOUN
ejpam-2338	394	24	.	.	PUNCT
ejpam-2338	395	1	thus	thus	ADV
ejpam-2338	395	2	,	,	PUNCT
ejpam-2338	395	3	when	when	SCONJ
ejpam-2338	395	4	we	we	PRON
ejpam-2338	395	5	pass	pass	VERB
ejpam-2338	395	6	from	from	ADP
ejpam-2338	395	7	partial	partial	ADJ
ejpam-2338	395	8	bijections	bijection	NOUN
ejpam-2338	395	9	to	to	ADP
ejpam-2338	395	10	the	the	DET
ejpam-2338	395	11	christopher	christopher	PROPN
ejpam-2338	395	12	hollings	hollings	PROPN
ejpam-2338	395	13	/	/	SYM
ejpam-2338	395	14	eur	eur	PROPN
ejpam-2338	395	15	.	.	PUNCT
ejpam-2338	396	1	j.	j.	PROPN
ejpam-2338	396	2	pure	pure	PROPN
ejpam-2338	396	3	appl	appl	PROPN
ejpam-2338	396	4	.	.	PROPN
ejpam-2338	396	5	math	math	PROPN
ejpam-2338	396	6	,	,	PUNCT
ejpam-2338	396	7	8	8	NUM
ejpam-2338	396	8	(	(	PUNCT
ejpam-2338	396	9	2015	2015	NUM
ejpam-2338	396	10	)	)	PUNCT
ejpam-2338	396	11	,	,	PUNCT
ejpam-2338	396	12	294	294	NUM
ejpam-2338	396	13	-	-	SYM
ejpam-2338	396	14	323	323	NUM
ejpam-2338	396	15	312	312	NUM
ejpam-2338	396	16	abstract	abstract	ADJ
ejpam-2338	396	17	setting	setting	NOUN
ejpam-2338	396	18	,	,	PUNCT
ejpam-2338	396	19	the	the	DET
ejpam-2338	396	20	compatibility	compatibility	NOUN
ejpam-2338	396	21	relation	relation	NOUN
ejpam-2338	396	22	on	on	ADP
ejpam-2338	396	23	an	an	DET
ejpam-2338	396	24	inverse	inverse	NOUN
ejpam-2338	396	25	semigroup	semigroup	NOUN
ejpam-2338	396	26	s	s	PART
ejpam-2338	396	27	is	be	AUX
ejpam-2338	396	28	defined	define	VERB
ejpam-2338	396	29	as	as	SCONJ
ejpam-2338	396	30	follows	follow	VERB
ejpam-2338	396	31	:	:	PUNCT
ejpam-2338	396	32	s	s	AUX
ejpam-2338	396	33	∼	∼	NOUN
ejpam-2338	396	34	t	t	NOUN
ejpam-2338	396	35	⇐	⇐	PROPN
ejpam-2338	396	36	⇒	⇒	PROPN
ejpam-2338	396	37	st−1	st−1	PROPN
ejpam-2338	396	38	,	,	PUNCT
ejpam-2338	396	39	s−1	s−1	PROPN
ejpam-2338	396	40	t	t	NOUN
ejpam-2338	396	41	∈	∈	PROPN
ejpam-2338	396	42	e(s	e(s	PROPN
ejpam-2338	396	43	)	)	PUNCT
ejpam-2338	396	44	.	.	PUNCT
ejpam-2338	397	1	the	the	DET
ejpam-2338	397	2	relation∼	relation∼	NOUN
ejpam-2338	397	3	is	be	AUX
ejpam-2338	397	4	not	not	PART
ejpam-2338	397	5	an	an	DET
ejpam-2338	397	6	equivalence	equivalence	NOUN
ejpam-2338	397	7	relation	relation	NOUN
ejpam-2338	397	8	,	,	PUNCT
ejpam-2338	397	9	since	since	SCONJ
ejpam-2338	397	10	it	it	PRON
ejpam-2338	397	11	fails	fail	VERB
ejpam-2338	397	12	to	to	PART
ejpam-2338	397	13	be	be	AUX
ejpam-2338	397	14	transitive	transitive	ADJ
ejpam-2338	397	15	in	in	ADP
ejpam-2338	397	16	general	general	ADJ
ejpam-2338	397	17	.	.	PUNCT
ejpam-2338	398	1	this	this	PRON
ejpam-2338	398	2	begs	beg	VERB
ejpam-2338	398	3	the	the	DET
ejpam-2338	398	4	question	question	NOUN
ejpam-2338	398	5	:	:	PUNCT
ejpam-2338	398	6	for	for	ADP
ejpam-2338	398	7	which	which	PRON
ejpam-2338	398	8	inverse	inverse	NOUN
ejpam-2338	398	9	semigroups	semigroup	NOUN
ejpam-2338	398	10	is	be	AUX
ejpam-2338	398	11	∼	∼	NOUN
ejpam-2338	398	12	transitive	transitive	ADJ
ejpam-2338	398	13	?	?	PUNCT
ejpam-2338	399	1	the	the	DET
ejpam-2338	399	2	answer	answer	NOUN
ejpam-2338	399	3	:	:	PUNCT
ejpam-2338	399	4	∼	∼	NOUN
ejpam-2338	399	5	is	be	AUX
ejpam-2338	399	6	transitive	transitive	ADJ
ejpam-2338	399	7	on	on	ADP
ejpam-2338	399	8	an	an	DET
ejpam-2338	399	9	inverse	inverse	NOUN
ejpam-2338	399	10	semigroup	semigroup	NOUN
ejpam-2338	399	11	s	s	X
ejpam-2338	399	12	if	if	SCONJ
ejpam-2338	400	1	and	and	CCONJ
ejpam-2338	400	2	only	only	ADV
ejpam-2338	400	3	if	if	SCONJ
ejpam-2338	400	4	s	s	NOUN
ejpam-2338	400	5	is	be	AUX
ejpam-2338	400	6	e	e	NOUN
ejpam-2338	400	7	-	-	NOUN
ejpam-2338	400	8	unitary	unitary	ADJ
ejpam-2338	400	9	.	.	PUNCT
ejpam-2338	401	1	moreover	moreover	ADV
ejpam-2338	401	2	,	,	PUNCT
ejpam-2338	401	3	in	in	ADP
ejpam-2338	401	4	an	an	DET
ejpam-2338	401	5	e	e	NOUN
ejpam-2338	401	6	-	-	ADJ
ejpam-2338	401	7	unitary	unitary	ADJ
ejpam-2338	401	8	inverse	inverse	NOUN
ejpam-2338	401	9	semigroup	semigroup	NOUN
ejpam-2338	401	10	,	,	PUNCT
ejpam-2338	401	11	∼	∼	NOUN
ejpam-2338	401	12	coincides	coincide	NOUN
ejpam-2338	401	13	with	with	ADP
ejpam-2338	401	14	the	the	DET
ejpam-2338	401	15	minimum	minimum	ADJ
ejpam-2338	401	16	group	group	NOUN
ejpam-2338	401	17	congruence	congruence	PROPN
ejpam-2338	401	18	σ	σ	PROPN
ejpam-2338	402	1	[	[	X
ejpam-2338	402	2	51	51	NUM
ejpam-2338	402	3	,	,	PUNCT
ejpam-2338	402	4	theorem	theorem	VERB
ejpam-2338	402	5	2.4.6	2.4.6	NUM
ejpam-2338	402	6	]	]	PUNCT
ejpam-2338	402	7	.	.	PUNCT
ejpam-2338	403	1	the	the	DET
ejpam-2338	403	2	transitivity	transitivity	NOUN
ejpam-2338	403	3	of	of	ADP
ejpam-2338	403	4	the	the	DET
ejpam-2338	403	5	compatibility	compatibility	NOUN
ejpam-2338	403	6	relation	relation	NOUN
ejpam-2338	403	7	means	mean	VERB
ejpam-2338	403	8	that	that	SCONJ
ejpam-2338	403	9	an	an	DET
ejpam-2338	403	10	e	e	NOUN
ejpam-2338	403	11	-	-	ADJ
ejpam-2338	403	12	unitary	unitary	ADJ
ejpam-2338	403	13	inverse	inverse	NOUN
ejpam-2338	403	14	semigroup	semigroup	NOUN
ejpam-2338	403	15	s	s	PROPN
ejpam-2338	403	16	of	of	ADP
ejpam-2338	403	17	partial	partial	ADJ
ejpam-2338	403	18	bijections	bijection	NOUN
ejpam-2338	403	19	has	have	VERB
ejpam-2338	403	20	the	the	DET
ejpam-2338	403	21	‘	'	PUNCT
ejpam-2338	403	22	unique	unique	ADJ
ejpam-2338	403	23	extension	extension	NOUN
ejpam-2338	403	24	’	'	PUNCT
ejpam-2338	403	25	property	property	NOUN
ejpam-2338	403	26	(	(	PUNCT
ejpam-2338	403	27	as	as	SCONJ
ejpam-2338	403	28	used	use	VERB
ejpam-2338	403	29	by	by	ADP
ejpam-2338	403	30	goła̧b	goła̧b	PROPN
ejpam-2338	403	31	—	—	PUNCT
ejpam-2338	403	32	see	see	VERB
ejpam-2338	403	33	[	[	X
ejpam-2338	403	34	41	41	NUM
ejpam-2338	403	35	,	,	PUNCT
ejpam-2338	403	36	p.	p.	NOUN
ejpam-2338	403	37	257	257	NUM
ejpam-2338	403	38	]	]	PUNCT
ejpam-2338	403	39	):	):	PUNCT
ejpam-2338	403	40	any	any	DET
ejpam-2338	403	41	α	α	PROPN
ejpam-2338	403	42	∈	∈	NOUN
ejpam-2338	403	43	s	s	PART
ejpam-2338	403	44	may	may	AUX
ejpam-2338	403	45	be	be	AUX
ejpam-2338	403	46	extended	extend	VERB
ejpam-2338	403	47	to	to	ADP
ejpam-2338	403	48	at	at	ADP
ejpam-2338	403	49	most	most	ADV
ejpam-2338	403	50	one	one	NUM
ejpam-2338	403	51	partial	partial	ADJ
ejpam-2338	403	52	bijection	bijection	NOUN
ejpam-2338	403	53	on	on	ADP
ejpam-2338	403	54	a	a	DET
ejpam-2338	403	55	set	set	ADJ
ejpam-2338	403	56	a⊇	a⊇	PROPN
ejpam-2338	403	57	domα	domα	NOUN
ejpam-2338	403	58	.	.	PUNCT
ejpam-2338	404	1	in	in	ADP
ejpam-2338	404	2	explaining	explain	VERB
ejpam-2338	404	3	goła̧b	goła̧b	NOUN
ejpam-2338	404	4	’s	’s	PART
ejpam-2338	404	5	approach	approach	NOUN
ejpam-2338	404	6	to	to	ADP
ejpam-2338	404	7	the	the	DET
ejpam-2338	404	8	p	p	NOUN
ejpam-2338	404	9	-	-	PUNCT
ejpam-2338	404	10	theorem	theorem	ADJ
ejpam-2338	404	11	,	,	PUNCT
ejpam-2338	404	12	we	we	PRON
ejpam-2338	404	13	follow	follow	VERB
ejpam-2338	404	14	schein	schein	NOUN
ejpam-2338	405	1	[	[	X
ejpam-2338	405	2	91	91	NUM
ejpam-2338	405	3	]	]	PUNCT
ejpam-2338	405	4	.	.	PUNCT
ejpam-2338	406	1	let	let	VERB
ejpam-2338	406	2	σ	σ	NOUN
ejpam-2338	406	3	be	be	AUX
ejpam-2338	406	4	any	any	DET
ejpam-2338	406	5	inverse	inverse	NOUN
ejpam-2338	406	6	semigroup	semigroup	NOUN
ejpam-2338	406	7	of	of	ADP
ejpam-2338	406	8	partial	partial	ADJ
ejpam-2338	406	9	bijections	bijection	NOUN
ejpam-2338	406	10	in	in	ADP
ejpam-2338	406	11	which	which	PRON
ejpam-2338	406	12	the	the	DET
ejpam-2338	406	13	compatibility	compatibility	NOUN
ejpam-2338	406	14	relation	relation	NOUN
ejpam-2338	406	15	is	be	AUX
ejpam-2338	406	16	transitive	transitive	ADJ
ejpam-2338	406	17	.	.	PUNCT
ejpam-2338	407	1	thus	thus	ADV
ejpam-2338	407	2	,	,	PUNCT
ejpam-2338	407	3	the	the	DET
ejpam-2338	407	4	union	union	NOUN
ejpam-2338	407	5	(	(	PUNCT
ejpam-2338	407	6	as	as	ADP
ejpam-2338	407	7	partial	partial	ADJ
ejpam-2338	407	8	mappings	mapping	NOUN
ejpam-2338	407	9	,	,	PUNCT
ejpam-2338	407	10	in	in	ADP
ejpam-2338	407	11	the	the	DET
ejpam-2338	407	12	sense	sense	NOUN
ejpam-2338	407	13	of	of	ADP
ejpam-2338	407	14	p.	p.	NOUN
ejpam-2338	407	15	298	298	NUM
ejpam-2338	407	16	)	)	PUNCT
ejpam-2338	407	17	of	of	ADP
ejpam-2338	407	18	any	any	DET
ejpam-2338	407	19	collection	collection	NOUN
ejpam-2338	407	20	of	of	ADP
ejpam-2338	407	21	elements	element	NOUN
ejpam-2338	407	22	from	from	ADP
ejpam-2338	407	23	σ	σ	PROPN
ejpam-2338	407	24	is	be	AUX
ejpam-2338	407	25	also	also	ADV
ejpam-2338	407	26	a	a	DET
ejpam-2338	407	27	partial	partial	ADJ
ejpam-2338	407	28	bijection	bijection	NOUN
ejpam-2338	407	29	.	.	PUNCT
ejpam-2338	408	1	since	since	SCONJ
ejpam-2338	408	2	∼	∼	NOUN
ejpam-2338	408	3	and	and	CCONJ
ejpam-2338	408	4	σ	σ	NOUN
ejpam-2338	408	5	coincide	coincide	NOUN
ejpam-2338	408	6	in	in	ADP
ejpam-2338	408	7	such	such	DET
ejpam-2338	408	8	a	a	DET
ejpam-2338	408	9	semigroup	semigroup	NOUN
ejpam-2338	408	10	,	,	PUNCT
ejpam-2338	408	11	any	any	DET
ejpam-2338	408	12	σ	σ	NOUN
ejpam-2338	408	13	-	-	PUNCT
ejpam-2338	408	14	class	class	NOUN
ejpam-2338	408	15	in	in	ADP
ejpam-2338	408	16	σ	σ	PROPN
ejpam-2338	408	17	is	be	AUX
ejpam-2338	408	18	a	a	DET
ejpam-2338	408	19	compatible	compatible	ADJ
ejpam-2338	408	20	subset	subset	NOUN
ejpam-2338	408	21	(	(	PUNCT
ejpam-2338	408	22	p.	p.	NOUN
ejpam-2338	408	23	298	298	NUM
ejpam-2338	408	24	)	)	PUNCT
ejpam-2338	408	25	.	.	PUNCT
ejpam-2338	409	1	for	for	ADP
ejpam-2338	409	2	any	any	DET
ejpam-2338	409	3	α	α	PROPN
ejpam-2338	409	4	∈	∈	PROPN
ejpam-2338	409	5	σ	σ	PROPN
ejpam-2338	409	6	,	,	PUNCT
ejpam-2338	409	7	let	let	VERB
ejpam-2338	409	8	α	α	PRON
ejpam-2338	409	9	denote	denote	VERB
ejpam-2338	409	10	the	the	DET
ejpam-2338	409	11	partial	partial	ADJ
ejpam-2338	409	12	bijection	bijection	NOUN
ejpam-2338	409	13	formed	form	VERB
ejpam-2338	409	14	as	as	ADP
ejpam-2338	409	15	the	the	DET
ejpam-2338	409	16	union	union	NOUN
ejpam-2338	409	17	of	of	ADP
ejpam-2338	409	18	all	all	DET
ejpam-2338	409	19	elements	element	NOUN
ejpam-2338	409	20	of	of	ADP
ejpam-2338	409	21	the	the	DET
ejpam-2338	409	22	σ	σ	NOUN
ejpam-2338	409	23	-	-	PUNCT
ejpam-2338	409	24	class	class	NOUN
ejpam-2338	409	25	of	of	ADP
ejpam-2338	409	26	α	α	NOUN
ejpam-2338	409	27	.	.	PUNCT
ejpam-2338	410	1	it	it	PRON
ejpam-2338	410	2	is	be	AUX
ejpam-2338	410	3	reasonably	reasonably	ADV
ejpam-2338	410	4	clear	clear	ADJ
ejpam-2338	410	5	that	that	SCONJ
ejpam-2338	410	6	α	α	PRON
ejpam-2338	410	7	=	=	VERB
ejpam-2338	410	8	α|domα	α|domα	NOUN
ejpam-2338	410	9	and	and	CCONJ
ejpam-2338	410	10	also	also	ADV
ejpam-2338	410	11	that	that	SCONJ
ejpam-2338	410	12	such	such	ADJ
ejpam-2338	410	13	partial	partial	ADJ
ejpam-2338	410	14	bijections	bijection	NOUN
ejpam-2338	410	15	α	α	PRON
ejpam-2338	410	16	are	be	AUX
ejpam-2338	410	17	in	in	ADP
ejpam-2338	410	18	a	a	DET
ejpam-2338	410	19	one	one	NUM
ejpam-2338	410	20	-	-	PUNCT
ejpam-2338	410	21	one	one	NUM
ejpam-2338	410	22	correspondence	correspondence	NOUN
ejpam-2338	410	23	with	with	ADP
ejpam-2338	410	24	the	the	DET
ejpam-2338	410	25	σ	σ	NOUN
ejpam-2338	410	26	-	-	PUNCT
ejpam-2338	410	27	classes	class	NOUN
ejpam-2338	410	28	of	of	ADP
ejpam-2338	410	29	σ	σ	PROPN
ejpam-2338	410	30	.	.	PUNCT
ejpam-2338	411	1	let	let	VERB
ejpam-2338	411	2	g	g	NOUN
ejpam-2338	411	3	=	=	PRON
ejpam-2338	411	4	{	{	PUNCT
ejpam-2338	411	5	α	α	NOUN
ejpam-2338	411	6	:	:	PUNCT
ejpam-2338	411	7	α	α	PROPN
ejpam-2338	411	8	∈	∈	PROPN
ejpam-2338	411	9	σ	σ	PROPN
ejpam-2338	411	10	}	}	PUNCT
ejpam-2338	411	11	.	.	PUNCT
ejpam-2338	412	1	defining	define	VERB
ejpam-2338	412	2	an	an	DET
ejpam-2338	412	3	operation	operation	NOUN
ejpam-2338	412	4	α	α	NOUN
ejpam-2338	412	5	◦	◦	NOUN
ejpam-2338	412	6	β	β	X
ejpam-2338	412	7	=	=	SYM
ejpam-2338	412	8	αβ	αβ	INTJ
ejpam-2338	412	9	in	in	ADP
ejpam-2338	412	10	g	g	NOUN
ejpam-2338	412	11	,	,	PUNCT
ejpam-2338	412	12	we	we	PRON
ejpam-2338	412	13	obtain	obtain	VERB
ejpam-2338	412	14	a	a	DET
ejpam-2338	412	15	group	group	NOUN
ejpam-2338	412	16	(	(	PUNCT
ejpam-2338	412	17	g	g	NOUN
ejpam-2338	412	18	,	,	PUNCT
ejpam-2338	412	19	◦	◦	NOUN
ejpam-2338	412	20	)	)	PUNCT
ejpam-2338	412	21	which	which	PRON
ejpam-2338	412	22	is	be	AUX
ejpam-2338	412	23	isomorphic	isomorphic	ADJ
ejpam-2338	412	24	toς	toς	PROPN
ejpam-2338	412	25	/	/	SYM
ejpam-2338	412	26	σ	σ	PROPN
ejpam-2338	412	27	.	.	PUNCT
ejpam-2338	413	1	next	next	ADV
ejpam-2338	413	2	,	,	PUNCT
ejpam-2338	413	3	we	we	PRON
ejpam-2338	413	4	observe	observe	VERB
ejpam-2338	413	5	that	that	SCONJ
ejpam-2338	413	6	the	the	DET
ejpam-2338	413	7	elements	element	NOUN
ejpam-2338	413	8	α	α	X
ejpam-2338	413	9	∈	∈	PROPN
ejpam-2338	413	10	σ	σ	NOUN
ejpam-2338	413	11	are	be	AUX
ejpam-2338	413	12	in	in	ADP
ejpam-2338	413	13	a	a	DET
ejpam-2338	413	14	one	one	NUM
ejpam-2338	413	15	-	-	PUNCT
ejpam-2338	413	16	one	one	NUM
ejpam-2338	413	17	correspondence	correspondence	NOUN
ejpam-2338	413	18	with	with	ADP
ejpam-2338	413	19	pairs	pair	NOUN
ejpam-2338	413	20	of	of	ADP
ejpam-2338	413	21	the	the	DET
ejpam-2338	413	22	form	form	NOUN
ejpam-2338	413	23	(	(	PUNCT
ejpam-2338	413	24	domα	domα	NOUN
ejpam-2338	413	25	,	,	PUNCT
ejpam-2338	413	26	α	α	NOUN
ejpam-2338	413	27	)	)	PUNCT
ejpam-2338	413	28	.	.	PUNCT
ejpam-2338	414	1	this	this	PRON
ejpam-2338	414	2	becomes	become	VERB
ejpam-2338	414	3	an	an	DET
ejpam-2338	414	4	isomorphism	isomorphism	NOUN
ejpam-2338	414	5	if	if	SCONJ
ejpam-2338	414	6	we	we	PRON
ejpam-2338	414	7	define	define	VERB
ejpam-2338	414	8	the	the	DET
ejpam-2338	414	9	following	follow	VERB
ejpam-2338	414	10	operation	operation	NOUN
ejpam-2338	414	11	on	on	ADP
ejpam-2338	414	12	the	the	DET
ejpam-2338	414	13	pairs	pair	NOUN
ejpam-2338	414	14	(	(	PUNCT
ejpam-2338	414	15	domα	domα	NOUN
ejpam-2338	414	16	,	,	PUNCT
ejpam-2338	414	17	α	α	X
ejpam-2338	414	18	):	):	PUNCT
ejpam-2338	414	19	(	(	PUNCT
ejpam-2338	414	20	domα	domα	NOUN
ejpam-2338	414	21	,	,	PUNCT
ejpam-2338	414	22	α)(domβ	α)(domβ	PROPN
ejpam-2338	414	23	,	,	PUNCT
ejpam-2338	414	24	β	β	X
ejpam-2338	414	25	)	)	PUNCT
ejpam-2338	414	26	=	=	SYM
ejpam-2338	414	27	(	(	PUNCT
ejpam-2338	414	28	(	(	PUNCT
ejpam-2338	414	29	domβ)α−1,α	domβ)α−1,α	ADP
ejpam-2338	414	30	◦	◦	NOUN
ejpam-2338	414	31	β	β	NOUN
ejpam-2338	414	32	)	)	PUNCT
ejpam-2338	414	33	.	.	PUNCT
ejpam-2338	415	1	we	we	PRON
ejpam-2338	415	2	note	note	VERB
ejpam-2338	415	3	that	that	SCONJ
ejpam-2338	415	4	y	y	PROPN
ejpam-2338	415	5	=	=	PRON
ejpam-2338	415	6	{	{	PUNCT
ejpam-2338	415	7	domα	domα	NOUN
ejpam-2338	415	8	:	:	PUNCT
ejpam-2338	415	9	α	α	PROPN
ejpam-2338	415	10	∈	∈	PROPN
ejpam-2338	415	11	σ	σ	PROPN
ejpam-2338	415	12	}	}	PUNCT
ejpam-2338	415	13	is	be	AUX
ejpam-2338	415	14	a	a	DET
ejpam-2338	415	15	semilattice	semilattice	NOUN
ejpam-2338	415	16	isomorphic	isomorphic	ADJ
ejpam-2338	415	17	to	to	ADP
ejpam-2338	415	18	e(σ	e(σ	PROPN
ejpam-2338	415	19	)	)	PUNCT
ejpam-2338	415	20	,	,	PUNCT
ejpam-2338	415	21	and	and	CCONJ
ejpam-2338	415	22	,	,	PUNCT
ejpam-2338	415	23	moreover	moreover	ADV
ejpam-2338	415	24	,	,	PUNCT
ejpam-2338	415	25	that	that	SCONJ
ejpam-2338	415	26	y	y	PROPN
ejpam-2338	415	27	is	be	AUX
ejpam-2338	415	28	contained	contain	VERB
ejpam-2338	415	29	in	in	ADP
ejpam-2338	415	30	x	x	X
ejpam-2338	415	31	,	,	PUNCT
ejpam-2338	415	32	the	the	DET
ejpam-2338	415	33	inclusion	inclusion	NOUN
ejpam-2338	415	34	-	-	PUNCT
ejpam-2338	415	35	ordered	order	VERB
ejpam-2338	415	36	set	set	NOUN
ejpam-2338	415	37	of	of	ADP
ejpam-2338	415	38	sets	set	NOUN
ejpam-2338	415	39	of	of	ADP
ejpam-2338	415	40	the	the	DET
ejpam-2338	415	41	form	form	NOUN
ejpam-2338	415	42	(	(	PUNCT
ejpam-2338	415	43	domβ)α−1	domβ)α−1	PROPN
ejpam-2338	415	44	,	,	PUNCT
ejpam-2338	415	45	for	for	ADP
ejpam-2338	415	46	α	α	NOUN
ejpam-2338	415	47	,	,	PUNCT
ejpam-2338	415	48	β	β	PROPN
ejpam-2338	415	49	∈	∈	PROPN
ejpam-2338	415	50	σ	σ	PROPN
ejpam-2338	415	51	.	.	PUNCT
ejpam-2338	416	1	finally	finally	ADV
ejpam-2338	416	2	,	,	PUNCT
ejpam-2338	416	3	we	we	PRON
ejpam-2338	416	4	observe	observe	VERB
ejpam-2338	416	5	that	that	SCONJ
ejpam-2338	416	6	g	g	PROPN
ejpam-2338	416	7	acts	act	VERB
ejpam-2338	416	8	on	on	ADP
ejpam-2338	416	9	x	x	X
ejpam-2338	416	10	:	:	PUNCT
ejpam-2338	416	11	α	α	X
ejpam-2338	416	12	·	·	PUNCT
ejpam-2338	416	13	domβ	domβ	X
ejpam-2338	416	14	=	=	SYM
ejpam-2338	416	15	(	(	PUNCT
ejpam-2338	416	16	domβ)α−1	domβ)α−1	PROPN
ejpam-2338	416	17	.	.	PUNCT
ejpam-2338	417	1	in	in	ADP
ejpam-2338	417	2	this	this	DET
ejpam-2338	417	3	way	way	NOUN
ejpam-2338	417	4	,	,	PUNCT
ejpam-2338	417	5	the	the	DET
ejpam-2338	417	6	g	g	NOUN
ejpam-2338	417	7	,	,	PUNCT
ejpam-2338	417	8	x	x	PUNCT
ejpam-2338	417	9	and	and	CCONJ
ejpam-2338	417	10	y	y	PROPN
ejpam-2338	417	11	that	that	PRON
ejpam-2338	417	12	we	we	PRON
ejpam-2338	417	13	have	have	AUX
ejpam-2338	417	14	just	just	ADV
ejpam-2338	417	15	constructed	construct	VERB
ejpam-2338	417	16	serve	serve	VERB
ejpam-2338	417	17	as	as	ADP
ejpam-2338	417	18	the	the	DET
ejpam-2338	417	19	ingredients	ingredient	NOUN
ejpam-2338	417	20	for	for	ADP
ejpam-2338	417	21	the	the	DET
ejpam-2338	417	22	representation	representation	NOUN
ejpam-2338	417	23	of	of	ADP
ejpam-2338	417	24	σ	σ	PROPN
ejpam-2338	417	25	as	as	ADP
ejpam-2338	417	26	a	a	DET
ejpam-2338	417	27	p	p	ADJ
ejpam-2338	417	28	-	-	PUNCT
ejpam-2338	417	29	semigroup	semigroup	NOUN
ejpam-2338	417	30	p(g	p(g	PROPN
ejpam-2338	417	31	,	,	PUNCT
ejpam-2338	417	32	x	x	X
ejpam-2338	417	33	,	,	PUNCT
ejpam-2338	417	34	y	y	PROPN
ejpam-2338	417	35	)	)	PUNCT
ejpam-2338	417	36	.	.	PUNCT
ejpam-2338	418	1	an	an	DET
ejpam-2338	418	2	abstract	abstract	ADJ
ejpam-2338	418	3	version	version	NOUN
ejpam-2338	418	4	of	of	ADP
ejpam-2338	418	5	this	this	DET
ejpam-2338	418	6	proof	proof	NOUN
ejpam-2338	418	7	was	be	AUX
ejpam-2338	418	8	given	give	VERB
ejpam-2338	418	9	by	by	ADP
ejpam-2338	418	10	schein	schein	PROPN
ejpam-2338	418	11	in	in	ADP
ejpam-2338	418	12	1975	1975	NUM
ejpam-2338	418	13	as	as	ADP
ejpam-2338	418	14	his	his	PRON
ejpam-2338	418	15	new	new	ADJ
ejpam-2338	418	16	proof	proof	NOUN
ejpam-2338	418	17	of	of	ADP
ejpam-2338	418	18	the	the	DET
ejpam-2338	418	19	p	p	NOUN
ejpam-2338	418	20	-	-	PUNCT
ejpam-2338	418	21	theorem	theorem	ADJ
ejpam-2338	418	22	.	.	PUNCT
ejpam-2338	419	1	he	he	PRON
ejpam-2338	419	2	commented	comment	VERB
ejpam-2338	419	3	,	,	PUNCT
ejpam-2338	419	4	however	however	ADV
ejpam-2338	419	5	,	,	PUNCT
ejpam-2338	419	6	that	that	SCONJ
ejpam-2338	419	7	what	what	PRON
ejpam-2338	419	8	is	be	AUX
ejpam-2338	419	9	remarkable	remarkable	ADJ
ejpam-2338	419	10	is	be	AUX
ejpam-2338	419	11	that	that	SCONJ
ejpam-2338	419	12	after	after	SCONJ
ejpam-2338	419	13	[	[	X
ejpam-2338	419	14	this	this	PRON
ejpam-2338	419	15	]	]	PUNCT
ejpam-2338	419	16	was	be	AUX
ejpam-2338	419	17	published	publish	VERB
ejpam-2338	419	18	,	,	PUNCT
ejpam-2338	419	19	i	i	PRON
ejpam-2338	419	20	discovered	discover	VERB
ejpam-2338	419	21	that	that	SCONJ
ejpam-2338	419	22	something	something	PRON
ejpam-2338	419	23	like	like	ADP
ejpam-2338	419	24	the	the	DET
ejpam-2338	419	25	argument	argument	NOUN
ejpam-2338	419	26	leading	lead	VERB
ejpam-2338	419	27	to	to	ADP
ejpam-2338	419	28	this	this	DET
ejpam-2338	419	29	result	result	NOUN
ejpam-2338	419	30	was	be	AUX
ejpam-2338	419	31	made	make	VERB
ejpam-2338	419	32	as	as	ADV
ejpam-2338	419	33	early	early	ADV
ejpam-2338	419	34	as	as	ADP
ejpam-2338	419	35	in	in	ADP
ejpam-2338	419	36	1939	1939	NUM
ejpam-2338	419	37	by	by	ADP
ejpam-2338	419	38	goła̧b	goła̧b	PRON
ejpam-2338	419	39	.	.	PUNCT
ejpam-2338	419	40	.	.	PUNCT
ejpam-2338	419	41	.	.	PUNCT
ejpam-2338	420	1	[	[	X
ejpam-2338	420	2	91	91	NUM
ejpam-2338	420	3	]	]	PUNCT
ejpam-2338	420	4	indeed	indeed	ADV
ejpam-2338	420	5	,	,	PUNCT
ejpam-2338	420	6	analogues	analogue	NOUN
ejpam-2338	420	7	of	of	ADP
ejpam-2338	420	8	α	α	NOUN
ejpam-2338	420	9	,	,	PUNCT
ejpam-2338	420	10	and	and	CCONJ
ejpam-2338	420	11	also	also	ADV
ejpam-2338	420	12	the	the	DET
ejpam-2338	420	13	composition	composition	NOUN
ejpam-2338	420	14	◦	◦	NOUN
ejpam-2338	420	15	,	,	PUNCT
ejpam-2338	420	16	appear	appear	VERB
ejpam-2338	420	17	in	in	ADP
ejpam-2338	420	18	goła̧b	goła̧b	NOUN
ejpam-2338	420	19	’s	’s	PART
ejpam-2338	420	20	work	work	NOUN
ejpam-2338	420	21	.	.	PUNCT
ejpam-2338	421	1	the	the	DET
ejpam-2338	421	2	fact	fact	NOUN
ejpam-2338	421	3	that	that	SCONJ
ejpam-2338	421	4	he	he	PRON
ejpam-2338	421	5	was	be	AUX
ejpam-2338	421	6	not	not	PART
ejpam-2338	421	7	working	work	VERB
ejpam-2338	421	8	with	with	ADP
ejpam-2338	421	9	the	the	DET
ejpam-2338	421	10	full	full	ADJ
ejpam-2338	421	11	composition	composition	NOUN
ejpam-2338	421	12	of	of	ADP
ejpam-2338	421	13	(	(	PUNCT
ejpam-2338	421	14	1	1	NUM
ejpam-2338	421	15	)	)	PUNCT
ejpam-2338	421	16	(	(	PUNCT
ejpam-2338	421	17	see	see	VERB
ejpam-2338	421	18	[	[	X
ejpam-2338	421	19	41	41	NUM
ejpam-2338	421	20	,	,	PUNCT
ejpam-2338	421	21	§	§	PROPN
ejpam-2338	421	22	10.2	10.2	NUM
ejpam-2338	421	23	]	]	PUNCT
ejpam-2338	421	24	)	)	PUNCT
ejpam-2338	421	25	does	do	AUX
ejpam-2338	421	26	not	not	PART
ejpam-2338	421	27	seem	seem	VERB
ejpam-2338	421	28	to	to	PART
ejpam-2338	421	29	have	have	AUX
ejpam-2338	421	30	hampered	hamper	VERB
ejpam-2338	421	31	him	he	PRON
ejpam-2338	421	32	.	.	PUNCT
ejpam-2338	422	1	in	in	ADP
ejpam-2338	422	2	fact	fact	NOUN
ejpam-2338	422	3	,	,	PUNCT
ejpam-2338	422	4	schein	schein	PROPN
ejpam-2338	422	5	noted	note	VERB
ejpam-2338	422	6	:	:	PUNCT
ejpam-2338	422	7	ifς	ifς	NOUN
ejpam-2338	422	8	does	do	AUX
ejpam-2338	422	9	contain	contain	VERB
ejpam-2338	422	10	the	the	DET
ejpam-2338	422	11	empty	empty	ADJ
ejpam-2338	422	12	transformation	transformation	NOUN
ejpam-2338	422	13	[	[	X
ejpam-2338	422	14	which	which	DET
ejpam-2338	422	15	schein	schein	NOUN
ejpam-2338	422	16	denoted	denote	VERB
ejpam-2338	422	17	here	here	ADV
ejpam-2338	422	18	by	by	ADP
ejpam-2338	422	19	;	;	PUNCT
ejpam-2338	422	20	]	]	PUNCT
ejpam-2338	422	21	,	,	PUNCT
ejpam-2338	422	22	then	then	ADV
ejpam-2338	422	23	any	any	DET
ejpam-2338	422	24	two	two	NUM
ejpam-2338	422	25	elements	element	NOUN
ejpam-2338	422	26	of	of	ADP
ejpam-2338	422	27	σ	σ	NOUN
ejpam-2338	422	28	are	be	AUX
ejpam-2338	422	29	compatible	compatible	ADJ
ejpam-2338	422	30	(	(	PUNCT
ejpam-2338	422	31	because	because	SCONJ
ejpam-2338	422	32	each	each	DET
ejpam-2338	422	33	one	one	NOUN
ejpam-2338	422	34	is	be	AUX
ejpam-2338	422	35	compatible	compatible	ADJ
ejpam-2338	422	36	with	with	ADP
ejpam-2338	422	37	;	;	PUNCT
ejpam-2338	422	38	and	and	CCONJ
ejpam-2338	422	39	the	the	DET
ejpam-2338	422	40	compatibility	compatibility	NOUN
ejpam-2338	422	41	relation	relation	NOUN
ejpam-2338	422	42	was	be	AUX
ejpam-2338	422	43	supposed	suppose	VERB
ejpam-2338	422	44	to	to	PART
ejpam-2338	422	45	be	be	AUX
ejpam-2338	422	46	transitive	transitive	ADJ
ejpam-2338	422	47	)	)	PUNCT
ejpam-2338	422	48	,	,	PUNCT
ejpam-2338	422	49	so	so	ADV
ejpam-2338	422	50	σ	σ	PROPN
ejpam-2338	422	51	is	be	AUX
ejpam-2338	422	52	a	a	DET
ejpam-2338	422	53	semilattice	semilattice	NOUN
ejpam-2338	422	54	,	,	PUNCT
ejpam-2338	422	55	and	and	CCONJ
ejpam-2338	422	56	the	the	DET
ejpam-2338	422	57	whole	whole	ADJ
ejpam-2338	422	58	theorem	theorem	ADJ
ejpam-2338	422	59	degenerates	degenerate	NOUN
ejpam-2338	422	60	.	.	PUNCT
ejpam-2338	423	1	thus	thus	ADV
ejpam-2338	423	2	we	we	PRON
ejpam-2338	423	3	may	may	AUX
ejpam-2338	423	4	as	as	ADV
ejpam-2338	423	5	well	well	ADV
ejpam-2338	423	6	consider	consider	VERB
ejpam-2338	423	7	the	the	DET
ejpam-2338	423	8	case	case	NOUN
ejpam-2338	423	9	when	when	SCONJ
ejpam-2338	423	10	;	;	PUNCT
ejpam-2338	423	11	/∈	/∈	PROPN
ejpam-2338	423	12	σ	σ	PROPN
ejpam-2338	423	13	.	.	PROPN
ejpam-2338	423	14	christopher	christopher	PROPN
ejpam-2338	423	15	hollings	hollings	PROPN
ejpam-2338	423	16	/	/	SYM
ejpam-2338	423	17	eur	eur	PROPN
ejpam-2338	423	18	.	.	PUNCT
ejpam-2338	424	1	j.	j.	PROPN
ejpam-2338	424	2	pure	pure	PROPN
ejpam-2338	424	3	appl	appl	PROPN
ejpam-2338	424	4	.	.	PROPN
ejpam-2338	424	5	math	math	PROPN
ejpam-2338	424	6	,	,	PUNCT
ejpam-2338	424	7	8	8	NUM
ejpam-2338	424	8	(	(	PUNCT
ejpam-2338	424	9	2015	2015	NUM
ejpam-2338	424	10	)	)	PUNCT
ejpam-2338	424	11	,	,	PUNCT
ejpam-2338	424	12	294	294	NUM
ejpam-2338	424	13	-	-	SYM
ejpam-2338	424	14	323	323	NUM
ejpam-2338	424	15	313	313	NUM
ejpam-2338	424	16	allowing	allow	VERB
ejpam-2338	424	17	for	for	ADP
ejpam-2338	424	18	the	the	DET
ejpam-2338	424	19	lack	lack	NOUN
ejpam-2338	424	20	of	of	ADP
ejpam-2338	424	21	;	;	PUNCT
ejpam-2338	424	22	,	,	PUNCT
ejpam-2338	424	23	the	the	DET
ejpam-2338	424	24	objects	object	NOUN
ejpam-2338	424	25	studied	study	VERB
ejpam-2338	424	26	by	by	ADP
ejpam-2338	424	27	goła̧b	goła̧b	PROPN
ejpam-2338	424	28	(	(	PUNCT
ejpam-2338	424	29	specifically	specifically	ADV
ejpam-2338	424	30	,	,	PUNCT
ejpam-2338	424	31	his	his	PRON
ejpam-2338	424	32	‘	'	PUNCT
ejpam-2338	424	33	pseudogroups	pseudogroup	NOUN
ejpam-2338	424	34	in	in	ADP
ejpam-2338	424	35	the	the	DET
ejpam-2338	424	36	narrower	narrow	ADJ
ejpam-2338	424	37	sense	sense	NOUN
ejpam-2338	424	38	’	'	PUNCT
ejpam-2338	424	39	—	—	PUNCT
ejpam-2338	424	40	see	see	VERB
ejpam-2338	424	41	[	[	X
ejpam-2338	424	42	41	41	NUM
ejpam-2338	424	43	,	,	PUNCT
ejpam-2338	424	44	p.	p.	NOUN
ejpam-2338	424	45	257	257	NUM
ejpam-2338	424	46	]	]	PUNCT
ejpam-2338	424	47	)	)	PUNCT
ejpam-2338	424	48	were	be	AUX
ejpam-2338	424	49	in	in	ADP
ejpam-2338	424	50	fact	fact	NOUN
ejpam-2338	424	51	e	e	NOUN
ejpam-2338	424	52	-	-	ADJ
ejpam-2338	424	53	unitary	unitary	ADJ
ejpam-2338	424	54	inverse	inverse	NOUN
ejpam-2338	424	55	semigroups	semigroup	NOUN
ejpam-2338	424	56	.	.	PUNCT
ejpam-2338	425	1	the	the	DET
ejpam-2338	425	2	avoidance	avoidance	NOUN
ejpam-2338	425	3	of	of	ADP
ejpam-2338	425	4	the	the	DET
ejpam-2338	425	5	empty	empty	ADJ
ejpam-2338	425	6	transformation	transformation	NOUN
ejpam-2338	425	7	may	may	AUX
ejpam-2338	425	8	not	not	PART
ejpam-2338	425	9	have	have	AUX
ejpam-2338	425	10	caused	cause	VERB
ejpam-2338	425	11	such	such	DET
ejpam-2338	425	12	a	a	DET
ejpam-2338	425	13	great	great	ADJ
ejpam-2338	425	14	difficulty	difficulty	NOUN
ejpam-2338	425	15	after	after	ADV
ejpam-2338	425	16	all	all	ADV
ejpam-2338	425	17	.	.	PUNCT
ejpam-2338	426	1	by	by	ADP
ejpam-2338	426	2	way	way	NOUN
ejpam-2338	426	3	of	of	ADP
ejpam-2338	426	4	concluding	conclude	VERB
ejpam-2338	426	5	this	this	DET
ejpam-2338	426	6	section	section	NOUN
ejpam-2338	426	7	,	,	PUNCT
ejpam-2338	426	8	we	we	PRON
ejpam-2338	426	9	comment	comment	VERB
ejpam-2338	426	10	upon	upon	SCONJ
ejpam-2338	426	11	the	the	DET
ejpam-2338	426	12	legacy	legacy	NOUN
ejpam-2338	426	13	of	of	ADP
ejpam-2338	426	14	mcalister	mcalister	PROPN
ejpam-2338	426	15	’s	’s	PART
ejpam-2338	426	16	work	work	NOUN
ejpam-2338	426	17	.	.	PUNCT
ejpam-2338	427	1	just	just	ADV
ejpam-2338	427	2	like	like	ADP
ejpam-2338	427	3	the	the	DET
ejpam-2338	427	4	constructions	construction	NOUN
ejpam-2338	427	5	described	describe	VERB
ejpam-2338	427	6	in	in	ADP
ejpam-2338	427	7	section	section	NOUN
ejpam-2338	427	8	4	4	NUM
ejpam-2338	427	9	,	,	PUNCT
ejpam-2338	427	10	as	as	ADV
ejpam-2338	427	11	well	well	ADV
ejpam-2338	427	12	as	as	ADP
ejpam-2338	427	13	those	those	PRON
ejpam-2338	427	14	of	of	ADP
ejpam-2338	427	15	rees	ree	NOUN
ejpam-2338	427	16	and	and	CCONJ
ejpam-2338	427	17	clifford	clifford	PROPN
ejpam-2338	427	18	(	(	PUNCT
ejpam-2338	427	19	see	see	VERB
ejpam-2338	427	20	the	the	DET
ejpam-2338	427	21	comments	comment	NOUN
ejpam-2338	427	22	in	in	ADP
ejpam-2338	427	23	[	[	X
ejpam-2338	427	24	37	37	NUM
ejpam-2338	427	25	]	]	PUNCT
ejpam-2338	427	26	and	and	CCONJ
ejpam-2338	427	27	[	[	X
ejpam-2338	427	28	41	41	NUM
ejpam-2338	427	29	,	,	PUNCT
ejpam-2338	427	30	chapter	chapter	NOUN
ejpam-2338	427	31	6	6	NUM
ejpam-2338	427	32	]	]	PUNCT
ejpam-2338	427	33	)	)	PUNCT
ejpam-2338	427	34	,	,	PUNCT
ejpam-2338	427	35	mcalister	mcalister	PROPN
ejpam-2338	427	36	’s	’s	PART
ejpam-2338	427	37	covering	covering	NOUN
ejpam-2338	427	38	and	and	CCONJ
ejpam-2338	427	39	p	p	NOUN
ejpam-2338	427	40	-	-	PUNCT
ejpam-2338	427	41	theorems	theorem	NOUN
ejpam-2338	427	42	have	have	AUX
ejpam-2338	427	43	provided	provide	VERB
ejpam-2338	427	44	models	model	NOUN
ejpam-2338	427	45	for	for	ADP
ejpam-2338	427	46	the	the	DET
ejpam-2338	427	47	research	research	NOUN
ejpam-2338	427	48	of	of	ADP
ejpam-2338	427	49	subsequent	subsequent	ADJ
ejpam-2338	427	50	semigroup	semigroup	NOUN
ejpam-2338	427	51	theorists	theorist	NOUN
ejpam-2338	427	52	.	.	PUNCT
ejpam-2338	428	1	we	we	PRON
ejpam-2338	428	2	mention	mention	VERB
ejpam-2338	428	3	,	,	PUNCT
ejpam-2338	428	4	in	in	ADP
ejpam-2338	428	5	particular	particular	ADJ
ejpam-2338	428	6	,	,	PUNCT
ejpam-2338	428	7	o’carroll	o’carroll	PROPN
ejpam-2338	428	8	’s	’s	PART
ejpam-2338	428	9	embedding	embed	VERB
ejpam-2338	428	10	theorem	theorem	NOUN
ejpam-2338	428	11	(	(	PUNCT
ejpam-2338	428	12	[	[	X
ejpam-2338	428	13	71	71	NUM
ejpam-2338	428	14	]	]	PUNCT
ejpam-2338	428	15	;	;	PUNCT
ejpam-2338	428	16	see	see	VERB
ejpam-2338	428	17	also	also	ADV
ejpam-2338	428	18	[	[	X
ejpam-2338	428	19	51	51	NUM
ejpam-2338	428	20	,	,	PUNCT
ejpam-2338	428	21	theorem	theorem	VERB
ejpam-2338	428	22	7.1.5	7.1.5	NOUN
ejpam-2338	428	23	]	]	X
ejpam-2338	428	24	)	)	PUNCT
ejpam-2338	428	25	,	,	PUNCT
ejpam-2338	428	26	which	which	PRON
ejpam-2338	428	27	was	be	AUX
ejpam-2338	428	28	proved	prove	VERB
ejpam-2338	428	29	on	on	ADP
ejpam-2338	428	30	the	the	DET
ejpam-2338	428	31	basis	basis	NOUN
ejpam-2338	428	32	of	of	ADP
ejpam-2338	428	33	the	the	DET
ejpam-2338	428	34	p	p	NOUN
ejpam-2338	428	35	-	-	PUNCT
ejpam-2338	428	36	theorem	theorem	ADJ
ejpam-2338	428	37	,	,	PUNCT
ejpam-2338	428	38	and	and	CCONJ
ejpam-2338	428	39	provides	provide	VERB
ejpam-2338	428	40	a	a	DET
ejpam-2338	428	41	useful	useful	ADJ
ejpam-2338	428	42	characterisation	characterisation	NOUN
ejpam-2338	428	43	of	of	ADP
ejpam-2338	428	44	proper	proper	ADJ
ejpam-2338	428	45	inverse	inverse	NOUN
ejpam-2338	428	46	semigroups	semigroup	NOUN
ejpam-2338	428	47	:	:	PUNCT
ejpam-2338	428	48	theorem	theorem	NOUN
ejpam-2338	428	49	5	5	NUM
ejpam-2338	428	50	.	.	PUNCT
ejpam-2338	429	1	an	an	DET
ejpam-2338	429	2	inverse	inverse	NOUN
ejpam-2338	429	3	semigroup	semigroup	NOUN
ejpam-2338	429	4	is	be	AUX
ejpam-2338	429	5	proper	proper	ADJ
ejpam-2338	429	6	if	if	SCONJ
ejpam-2338	429	7	and	and	CCONJ
ejpam-2338	429	8	only	only	ADV
ejpam-2338	429	9	if	if	SCONJ
ejpam-2338	429	10	it	it	PRON
ejpam-2338	429	11	can	can	AUX
ejpam-2338	429	12	be	be	AUX
ejpam-2338	429	13	embedded	embed	VERB
ejpam-2338	429	14	in	in	ADP
ejpam-2338	429	15	the	the	DET
ejpam-2338	429	16	semidirect	semidirect	NOUN
ejpam-2338	429	17	product	product	NOUN
ejpam-2338	429	18	of	of	ADP
ejpam-2338	429	19	a	a	DET
ejpam-2338	429	20	semilattice	semilattice	NOUN
ejpam-2338	429	21	by	by	ADP
ejpam-2338	429	22	a	a	DET
ejpam-2338	429	23	group	group	NOUN
ejpam-2338	429	24	.	.	PUNCT
ejpam-2338	430	1	moreover	moreover	ADV
ejpam-2338	430	2	,	,	PUNCT
ejpam-2338	430	3	there	there	PRON
ejpam-2338	430	4	are	be	VERB
ejpam-2338	430	5	several	several	ADJ
ejpam-2338	430	6	analogues	analogue	NOUN
ejpam-2338	430	7	of	of	ADP
ejpam-2338	430	8	the	the	DET
ejpam-2338	430	9	p	p	NOUN
ejpam-2338	430	10	-	-	PUNCT
ejpam-2338	430	11	theorem	theorem	NOUN
ejpam-2338	430	12	in	in	ADP
ejpam-2338	430	13	the	the	DET
ejpam-2338	430	14	literature	literature	NOUN
ejpam-2338	430	15	for	for	ADP
ejpam-2338	430	16	various	various	ADJ
ejpam-2338	430	17	generalisations	generalisation	NOUN
ejpam-2338	430	18	of	of	ADP
ejpam-2338	430	19	inverse	inverse	NOUN
ejpam-2338	430	20	semigroups	semigroup	NOUN
ejpam-2338	430	21	:	:	PUNCT
ejpam-2338	430	22	see	see	VERB
ejpam-2338	430	23	the	the	DET
ejpam-2338	430	24	next	next	ADJ
ejpam-2338	430	25	section	section	NOUN
ejpam-2338	430	26	.	.	PUNCT
ejpam-2338	431	1	mcalister	mcalister	PROPN
ejpam-2338	431	2	’s	’s	PART
ejpam-2338	431	3	goal	goal	NOUN
ejpam-2338	431	4	of	of	ADP
ejpam-2338	431	5	constructing	construct	VERB
ejpam-2338	431	6	a	a	DET
ejpam-2338	431	7	family	family	NOUN
ejpam-2338	431	8	of	of	ADP
ejpam-2338	431	9	inverse	inverse	NOUN
ejpam-2338	431	10	semigroups	semigroup	NOUN
ejpam-2338	431	11	from	from	ADP
ejpam-2338	431	12	“	"	PUNCT
ejpam-2338	431	13	simple	simple	ADJ
ejpam-2338	431	14	,	,	PUNCT
ejpam-2338	431	15	familiar	familiar	ADJ
ejpam-2338	431	16	,	,	PUNCT
ejpam-2338	431	17	naturally	naturally	ADV
ejpam-2338	431	18	related	relate	VERB
ejpam-2338	431	19	objects	object	NOUN
ejpam-2338	431	20	”	"	PUNCT
ejpam-2338	431	21	(	(	PUNCT
ejpam-2338	431	22	see	see	VERB
ejpam-2338	431	23	p.	p.	NOUN
ejpam-2338	431	24	310	310	NUM
ejpam-2338	431	25	)	)	PUNCT
ejpam-2338	431	26	was	be	AUX
ejpam-2338	431	27	certainly	certainly	ADV
ejpam-2338	431	28	achieved	achieve	VERB
ejpam-2338	431	29	.	.	PUNCT
ejpam-2338	432	1	6	6	X
ejpam-2338	432	2	.	.	X
ejpam-2338	433	1	some	some	DET
ejpam-2338	433	2	generalisations	generalisation	NOUN
ejpam-2338	433	3	i	i	PRON
ejpam-2338	433	4	give	give	VERB
ejpam-2338	433	5	here	here	ADV
ejpam-2338	433	6	a	a	DET
ejpam-2338	433	7	brief	brief	ADJ
ejpam-2338	433	8	indication	indication	NOUN
ejpam-2338	433	9	(	(	PUNCT
ejpam-2338	433	10	with	with	ADP
ejpam-2338	433	11	just	just	ADV
ejpam-2338	433	12	one	one	NUM
ejpam-2338	433	13	or	or	CCONJ
ejpam-2338	433	14	two	two	NUM
ejpam-2338	433	15	sample	sample	NOUN
ejpam-2338	433	16	results	result	NOUN
ejpam-2338	433	17	)	)	PUNCT
ejpam-2338	433	18	of	of	ADP
ejpam-2338	433	19	some	some	PRON
ejpam-2338	433	20	of	of	ADP
ejpam-2338	433	21	the	the	DET
ejpam-2338	433	22	ways	way	NOUN
ejpam-2338	433	23	in	in	ADP
ejpam-2338	433	24	which	which	PRON
ejpam-2338	433	25	the	the	DET
ejpam-2338	433	26	constructions	construction	NOUN
ejpam-2338	433	27	and	and	CCONJ
ejpam-2338	433	28	notions	notion	NOUN
ejpam-2338	433	29	of	of	ADP
ejpam-2338	433	30	the	the	DET
ejpam-2338	433	31	foregoing	forego	VERB
ejpam-2338	433	32	sections	section	NOUN
ejpam-2338	433	33	have	have	AUX
ejpam-2338	433	34	been	be	AUX
ejpam-2338	433	35	extended	extend	VERB
ejpam-2338	433	36	to	to	ADP
ejpam-2338	433	37	more	more	ADJ
ejpam-2338	433	38	general	general	ADJ
ejpam-2338	433	39	classes	class	NOUN
ejpam-2338	433	40	of	of	ADP
ejpam-2338	433	41	semigroups	semigroup	NOUN
ejpam-2338	433	42	.	.	PUNCT
ejpam-2338	434	1	in	in	ADP
ejpam-2338	434	2	the	the	DET
ejpam-2338	434	3	interests	interest	NOUN
ejpam-2338	434	4	of	of	ADP
ejpam-2338	434	5	saving	save	VERB
ejpam-2338	434	6	space	space	NOUN
ejpam-2338	434	7	,	,	PUNCT
ejpam-2338	434	8	i	i	PRON
ejpam-2338	434	9	confine	confine	VERB
ejpam-2338	434	10	my	my	PRON
ejpam-2338	434	11	attention	attention	NOUN
ejpam-2338	434	12	mostly	mostly	ADV
ejpam-2338	434	13	to	to	ADP
ejpam-2338	434	14	non	non	ADJ
ejpam-2338	434	15	-	-	ADJ
ejpam-2338	434	16	regular	regular	ADJ
ejpam-2338	434	17	generalisations	generalisation	NOUN
ejpam-2338	434	18	of	of	ADP
ejpam-2338	434	19	inverse	inverse	NOUN
ejpam-2338	434	20	semigroups	semigroup	NOUN
ejpam-2338	434	21	(	(	PUNCT
ejpam-2338	434	22	specifically	specifically	ADV
ejpam-2338	434	23	,	,	PUNCT
ejpam-2338	434	24	those	those	PRON
ejpam-2338	434	25	discussed	discuss	VERB
ejpam-2338	434	26	in	in	ADP
ejpam-2338	434	27	[	[	X
ejpam-2338	434	28	36	36	NUM
ejpam-2338	434	29	]	]	NUM
ejpam-2338	434	30	)	)	PUNCT
ejpam-2338	434	31	.	.	PUNCT
ejpam-2338	435	1	moreover	moreover	ADV
ejpam-2338	435	2	,	,	PUNCT
ejpam-2338	435	3	i	i	PRON
ejpam-2338	435	4	do	do	AUX
ejpam-2338	435	5	not	not	PART
ejpam-2338	435	6	define	define	VERB
ejpam-2338	435	7	any	any	PRON
ejpam-2338	435	8	of	of	ADP
ejpam-2338	435	9	these	these	DET
ejpam-2338	435	10	semigroups	semigroup	NOUN
ejpam-2338	435	11	here	here	ADV
ejpam-2338	435	12	—	—	PUNCT
ejpam-2338	435	13	i	i	PRON
ejpam-2338	435	14	instead	instead	ADV
ejpam-2338	435	15	refer	refer	VERB
ejpam-2338	435	16	the	the	DET
ejpam-2338	435	17	reader	reader	NOUN
ejpam-2338	435	18	to	to	ADP
ejpam-2338	435	19	the	the	DET
ejpam-2338	435	20	sources	source	NOUN
ejpam-2338	435	21	cited	cite	VERB
ejpam-2338	435	22	.	.	PUNCT
ejpam-2338	436	1	a	a	DET
ejpam-2338	436	2	more	more	ADV
ejpam-2338	436	3	detailed	detailed	ADJ
ejpam-2338	436	4	survey	survey	NOUN
ejpam-2338	436	5	of	of	ADP
ejpam-2338	436	6	the	the	DET
ejpam-2338	436	7	use	use	NOUN
ejpam-2338	436	8	of	of	ADP
ejpam-2338	436	9	these	these	DET
ejpam-2338	436	10	methods	method	NOUN
ejpam-2338	436	11	in	in	ADP
ejpam-2338	436	12	the	the	DET
ejpam-2338	436	13	non	non	ADJ
ejpam-2338	436	14	-	-	ADJ
ejpam-2338	436	15	regular	regular	ADJ
ejpam-2338	436	16	setting	setting	NOUN
ejpam-2338	436	17	may	may	AUX
ejpam-2338	436	18	be	be	AUX
ejpam-2338	436	19	found	find	VERB
ejpam-2338	436	20	in	in	ADP
ejpam-2338	436	21	[	[	X
ejpam-2338	436	22	29	29	NUM
ejpam-2338	436	23	]	]	PUNCT
ejpam-2338	436	24	.	.	PUNCT
ejpam-2338	437	1	6.1	6.1	NUM
ejpam-2338	437	2	.	.	NUM
ejpam-2338	437	3	inductive	inductive	ADJ
ejpam-2338	437	4	categories	category	NOUN
ejpam-2338	437	5	the	the	DET
ejpam-2338	437	6	connection	connection	NOUN
ejpam-2338	437	7	between	between	ADP
ejpam-2338	437	8	inverse	inverse	NOUN
ejpam-2338	437	9	semigroups	semigroup	NOUN
ejpam-2338	437	10	and	and	CCONJ
ejpam-2338	437	11	inductive	inductive	ADJ
ejpam-2338	437	12	groupoids	groupoid	NOUN
ejpam-2338	437	13	was	be	AUX
ejpam-2338	437	14	first	first	ADV
ejpam-2338	437	15	generalised	generalise	VERB
ejpam-2338	437	16	to	to	ADP
ejpam-2338	437	17	the	the	DET
ejpam-2338	437	18	ample	ample	ADJ
ejpam-2338	437	19	semigroups	semigroup	NOUN
ejpam-2338	437	20	of	of	ADP
ejpam-2338	437	21	fountain	fountain	NOUN
ejpam-2338	437	22	[	[	X
ejpam-2338	437	23	17	17	NUM
ejpam-2338	437	24	,	,	PUNCT
ejpam-2338	437	25	18	18	NUM
ejpam-2338	437	26	]	]	PUNCT
ejpam-2338	437	27	by	by	ADP
ejpam-2338	437	28	armstrong	armstrong	PROPN
ejpam-2338	438	1	[	[	X
ejpam-2338	438	2	1	1	NUM
ejpam-2338	438	3	]	]	PUNCT
ejpam-2338	438	4	,	,	PUNCT
ejpam-2338	438	5	where	where	SCONJ
ejpam-2338	438	6	the	the	DET
ejpam-2338	438	7	object	object	NOUN
ejpam-2338	438	8	to	to	PART
ejpam-2338	438	9	which	which	PRON
ejpam-2338	438	10	an	an	DET
ejpam-2338	438	11	ample	ample	ADJ
ejpam-2338	438	12	semigroup	semigroup	NOUN
ejpam-2338	438	13	corresponds	correspond	NOUN
ejpam-2338	438	14	is	be	AUX
ejpam-2338	438	15	an	an	DET
ejpam-2338	438	16	inductive	inductive	ADJ
ejpam-2338	438	17	cancellative	cancellative	ADJ
ejpam-2338	438	18	category	category	NOUN
ejpam-2338	438	19	.	.	PUNCT
ejpam-2338	439	1	the	the	DET
ejpam-2338	439	2	latter	latter	ADJ
ejpam-2338	439	3	is	be	AUX
ejpam-2338	439	4	obtained	obtain	VERB
ejpam-2338	439	5	from	from	ADP
ejpam-2338	439	6	an	an	DET
ejpam-2338	439	7	inductive	inductive	ADJ
ejpam-2338	439	8	groupoid	groupoid	NOUN
ejpam-2338	439	9	by	by	ADP
ejpam-2338	439	10	dropping	drop	VERB
ejpam-2338	439	11	the	the	DET
ejpam-2338	439	12	requirement	requirement	NOUN
ejpam-2338	439	13	that	that	SCONJ
ejpam-2338	439	14	all	all	DET
ejpam-2338	439	15	arrows	arrow	NOUN
ejpam-2338	439	16	be	be	VERB
ejpam-2338	439	17	invertible	invertible	ADJ
ejpam-2338	439	18	(	(	PUNCT
ejpam-2338	439	19	modifying	modify	VERB
ejpam-2338	439	20	the	the	DET
ejpam-2338	439	21	statements	statement	NOUN
ejpam-2338	439	22	of	of	ADP
ejpam-2338	439	23	certain	certain	ADJ
ejpam-2338	439	24	of	of	ADP
ejpam-2338	439	25	the	the	DET
ejpam-2338	439	26	defining	define	VERB
ejpam-2338	439	27	axioms	axiom	NOUN
ejpam-2338	439	28	in	in	ADP
ejpam-2338	439	29	order	order	NOUN
ejpam-2338	439	30	to	to	PART
ejpam-2338	439	31	take	take	VERB
ejpam-2338	439	32	account	account	NOUN
ejpam-2338	439	33	of	of	ADP
ejpam-2338	439	34	the	the	DET
ejpam-2338	439	35	lack	lack	NOUN
ejpam-2338	439	36	of	of	ADP
ejpam-2338	439	37	inverses	inverse	NOUN
ejpam-2338	439	38	)	)	PUNCT
ejpam-2338	439	39	,	,	PUNCT
ejpam-2338	439	40	but	but	CCONJ
ejpam-2338	439	41	nevertheless	nevertheless	ADV
ejpam-2338	439	42	insisting	insist	VERB
ejpam-2338	439	43	that	that	SCONJ
ejpam-2338	439	44	their	their	PRON
ejpam-2338	439	45	composition	composition	NOUN
ejpam-2338	439	46	be	be	AUX
ejpam-2338	439	47	‘	'	PUNCT
ejpam-2338	439	48	cancellative	cancellative	ADJ
ejpam-2338	439	49	’	'	PUNCT
ejpam-2338	439	50	in	in	ADP
ejpam-2338	439	51	an	an	DET
ejpam-2338	439	52	appropriate	appropriate	ADJ
ejpam-2338	439	53	sense	sense	NOUN
ejpam-2338	439	54	.	.	PUNCT
ejpam-2338	440	1	successive	successive	ADJ
ejpam-2338	440	2	generalisations	generalisation	NOUN
ejpam-2338	440	3	of	of	ADP
ejpam-2338	440	4	armstrong	armstrong	PROPN
ejpam-2338	440	5	’s	’s	PART
ejpam-2338	440	6	result	result	NOUN
ejpam-2338	440	7	were	be	AUX
ejpam-2338	440	8	given	give	VERB
ejpam-2338	440	9	by	by	ADP
ejpam-2338	440	10	lawson	lawson	PROPN
ejpam-2338	440	11	,	,	PUNCT
ejpam-2338	440	12	first	first	ADV
ejpam-2338	440	13	for	for	ADP
ejpam-2338	440	14	what	what	PRON
ejpam-2338	440	15	are	be	AUX
ejpam-2338	440	16	now	now	ADV
ejpam-2338	440	17	termed	term	VERB
ejpam-2338	440	18	full	full	ADJ
ejpam-2338	440	19	restriction	restriction	NOUN
ejpam-2338	440	20	semigroups	semigroup	NOUN
ejpam-2338	440	21	and	and	CCONJ
ejpam-2338	440	22	inductive	inductive	ADJ
ejpam-2338	440	23	unipotent	unipotent	ADJ
ejpam-2338	440	24	categories	category	NOUN
ejpam-2338	440	25	,	,	PUNCT
ejpam-2338	440	26	and	and	CCONJ
ejpam-2338	440	27	then	then	ADV
ejpam-2338	440	28	for	for	ADP
ejpam-2338	440	29	arbitrary	arbitrary	ADJ
ejpam-2338	440	30	restriction	restriction	NOUN
ejpam-2338	440	31	semigroups	semigroup	NOUN
ejpam-2338	440	32	and	and	CCONJ
ejpam-2338	440	33	arbitrary	arbitrary	ADJ
ejpam-2338	440	34	inductive	inductive	ADJ
ejpam-2338	440	35	categories	category	NOUN
ejpam-2338	440	36	.	.	PUNCT
ejpam-2338	441	1	in	in	ADP
ejpam-2338	441	2	addition	addition	NOUN
ejpam-2338	441	3	,	,	PUNCT
ejpam-2338	441	4	lawson	lawson	PROPN
ejpam-2338	441	5	provided	provide	VERB
ejpam-2338	441	6	a	a	DET
ejpam-2338	441	7	category	category	NOUN
ejpam-2338	441	8	-	-	PUNCT
ejpam-2338	441	9	theoretic	theoretic	NOUN
ejpam-2338	441	10	formulation	formulation	NOUN
ejpam-2338	441	11	of	of	ADP
ejpam-2338	441	12	these	these	DET
ejpam-2338	441	13	results	result	NOUN
ejpam-2338	441	14	,	,	PUNCT
ejpam-2338	441	15	in	in	ADP
ejpam-2338	441	16	which	which	PRON
ejpam-2338	441	17	terms	term	NOUN
ejpam-2338	441	18	the	the	DET
ejpam-2338	441	19	original	original	ADJ
ejpam-2338	441	20	ehresmann	ehresmann	NOUN
ejpam-2338	441	21	–	–	PUNCT
ejpam-2338	441	22	schein	schein	PROPN
ejpam-2338	441	23	–	–	PUNCT
ejpam-2338	441	24	nambooripad	nambooripad	PROPN
ejpam-2338	441	25	theorem	theorem	NOUN
ejpam-2338	441	26	may	may	AUX
ejpam-2338	441	27	also	also	ADV
ejpam-2338	441	28	be	be	AUX
ejpam-2338	441	29	expressed	express	VERB
ejpam-2338	441	30	(	(	PUNCT
ejpam-2338	441	31	see	see	VERB
ejpam-2338	441	32	[	[	X
ejpam-2338	441	33	51	51	NUM
ejpam-2338	441	34	,	,	PUNCT
ejpam-2338	441	35	theorem	theorem	VERB
ejpam-2338	441	36	4.1.8	4.1.8	NUM
ejpam-2338	441	37	]	]	PUNCT
ejpam-2338	441	38	)	)	PUNCT
ejpam-2338	441	39	,	,	PUNCT
ejpam-2338	441	40	although	although	SCONJ
ejpam-2338	441	41	this	this	DET
ejpam-2338	441	42	language	language	NOUN
ejpam-2338	441	43	was	be	AUX
ejpam-2338	441	44	not	not	PART
ejpam-2338	441	45	employed	employ	VERB
ejpam-2338	441	46	by	by	ADP
ejpam-2338	441	47	armstrong	armstrong	PROPN
ejpam-2338	441	48	.	.	PUNCT
ejpam-2338	442	1	further	further	PROPN
ejpam-2338	442	2	technical	technical	ADJ
ejpam-2338	442	3	details	detail	NOUN
ejpam-2338	442	4	were	be	AUX
ejpam-2338	442	5	added	add	VERB
ejpam-2338	442	6	to	to	ADP
ejpam-2338	442	7	the	the	DET
ejpam-2338	442	8	general	general	ADJ
ejpam-2338	442	9	case	case	NOUN
ejpam-2338	442	10	in	in	ADP
ejpam-2338	442	11	[	[	X
ejpam-2338	442	12	38	38	NUM
ejpam-2338	442	13	]	]	PUNCT
ejpam-2338	442	14	.	.	PUNCT
ejpam-2338	443	1	the	the	DET
ejpam-2338	443	2	historical	historical	ADJ
ejpam-2338	443	3	development	development	NOUN
ejpam-2338	443	4	of	of	ADP
ejpam-2338	443	5	these	these	DET
ejpam-2338	443	6	generalisations	generalisation	NOUN
ejpam-2338	443	7	is	be	AUX
ejpam-2338	443	8	dealt	deal	VERB
ejpam-2338	443	9	with	with	ADP
ejpam-2338	443	10	in	in	ADP
ejpam-2338	443	11	more	more	ADJ
ejpam-2338	443	12	detail	detail	NOUN
ejpam-2338	443	13	in	in	ADP
ejpam-2338	443	14	[	[	X
ejpam-2338	443	15	40	40	NUM
ejpam-2338	443	16	]	]	PUNCT
ejpam-2338	443	17	,	,	PUNCT
ejpam-2338	443	18	where	where	SCONJ
ejpam-2338	443	19	their	their	PRON
ejpam-2338	443	20	precise	precise	ADJ
ejpam-2338	443	21	formulations	formulation	NOUN
ejpam-2338	443	22	may	may	AUX
ejpam-2338	443	23	also	also	ADV
ejpam-2338	443	24	be	be	AUX
ejpam-2338	443	25	found	find	VERB
ejpam-2338	443	26	.	.	PUNCT
ejpam-2338	444	1	christopher	christopher	PROPN
ejpam-2338	444	2	hollings	hollings	PROPN
ejpam-2338	444	3	/	/	SYM
ejpam-2338	444	4	eur	eur	PROPN
ejpam-2338	444	5	.	.	PUNCT
ejpam-2338	445	1	j.	j.	PROPN
ejpam-2338	445	2	pure	pure	PROPN
ejpam-2338	445	3	appl	appl	PROPN
ejpam-2338	445	4	.	.	PROPN
ejpam-2338	445	5	math	math	PROPN
ejpam-2338	445	6	,	,	PUNCT
ejpam-2338	445	7	8	8	NUM
ejpam-2338	445	8	(	(	PUNCT
ejpam-2338	445	9	2015	2015	NUM
ejpam-2338	445	10	)	)	PUNCT
ejpam-2338	445	11	,	,	PUNCT
ejpam-2338	445	12	294	294	NUM
ejpam-2338	445	13	-	-	SYM
ejpam-2338	445	14	323	323	NUM
ejpam-2338	445	15	314	314	NUM
ejpam-2338	445	16	we	we	PRON
ejpam-2338	445	17	note	note	VERB
ejpam-2338	445	18	that	that	SCONJ
ejpam-2338	445	19	inverse	inverse	NOUN
ejpam-2338	445	20	,	,	PUNCT
ejpam-2338	445	21	ample	ample	ADJ
ejpam-2338	445	22	and	and	CCONJ
ejpam-2338	445	23	restriction	restriction	NOUN
ejpam-2338	445	24	semigroups	semigroup	NOUN
ejpam-2338	445	25	are	be	AUX
ejpam-2338	445	26	all	all	PRON
ejpam-2338	445	27	inherently	inherently	ADV
ejpam-2338	445	28	‘	'	PUNCT
ejpam-2338	445	29	two	two	NUM
ejpam-2338	445	30	-	-	PUNCT
ejpam-2338	445	31	sided	sided	ADJ
ejpam-2338	445	32	’	'	PUNCT
ejpam-2338	445	33	:	:	PUNCT
ejpam-2338	445	34	elements	element	NOUN
ejpam-2338	445	35	of	of	ADP
ejpam-2338	445	36	inverse	inverse	NOUN
ejpam-2338	445	37	semigroups	semigroup	NOUN
ejpam-2338	445	38	have	have	VERB
ejpam-2338	445	39	two	two	NUM
ejpam-2338	445	40	-	-	PUNCT
ejpam-2338	445	41	sided	sided	ADJ
ejpam-2338	445	42	inverses	inverse	NOUN
ejpam-2338	445	43	,	,	PUNCT
ejpam-2338	445	44	whilst	whilst	SCONJ
ejpam-2338	445	45	members	member	NOUN
ejpam-2338	445	46	of	of	ADP
ejpam-2338	445	47	the	the	DET
ejpam-2338	445	48	latter	latter	ADJ
ejpam-2338	445	49	two	two	NUM
ejpam-2338	445	50	classes	class	NOUN
ejpam-2338	445	51	of	of	ADP
ejpam-2338	445	52	semigroups	semigroup	NOUN
ejpam-2338	445	53	come	come	VERB
ejpam-2338	445	54	equipped	equip	VERB
ejpam-2338	445	55	with	with	ADP
ejpam-2338	445	56	two	two	NUM
ejpam-2338	445	57	unary	unary	ADJ
ejpam-2338	445	58	operations	operation	NOUN
ejpam-2338	445	59	.	.	PUNCT
ejpam-2338	446	1	the	the	DET
ejpam-2338	446	2	connection	connection	NOUN
ejpam-2338	446	3	between	between	ADP
ejpam-2338	446	4	ample	ample	ADJ
ejpam-2338	446	5	and	and	CCONJ
ejpam-2338	446	6	restriction	restriction	NOUN
ejpam-2338	446	7	semigroups	semigroup	NOUN
ejpam-2338	446	8	and	and	CCONJ
ejpam-2338	446	9	the	the	DET
ejpam-2338	446	10	appropriate	appropriate	ADJ
ejpam-2338	446	11	classes	class	NOUN
ejpam-2338	446	12	of	of	ADP
ejpam-2338	446	13	inductive	inductive	ADJ
ejpam-2338	446	14	categories	category	NOUN
ejpam-2338	446	15	therefore	therefore	ADV
ejpam-2338	446	16	emerges	emerge	VERB
ejpam-2338	446	17	as	as	ADP
ejpam-2338	446	18	being	be	AUX
ejpam-2338	446	19	quite	quite	ADV
ejpam-2338	446	20	natural	natural	ADJ
ejpam-2338	446	21	:	:	PUNCT
ejpam-2338	446	22	the	the	DET
ejpam-2338	446	23	unary	unary	ADJ
ejpam-2338	446	24	operations	operation	NOUN
ejpam-2338	446	25	become	become	VERB
ejpam-2338	446	26	the	the	DET
ejpam-2338	446	27	domain	domain	NOUN
ejpam-2338	446	28	and	and	CCONJ
ejpam-2338	446	29	range	range	NOUN
ejpam-2338	446	30	operations	operation	NOUN
ejpam-2338	446	31	.	.	PUNCT
ejpam-2338	447	1	nevertheless	nevertheless	ADV
ejpam-2338	447	2	,	,	PUNCT
ejpam-2338	447	3	it	it	PRON
ejpam-2338	447	4	is	be	AUX
ejpam-2338	447	5	also	also	ADV
ejpam-2338	447	6	possible	possible	ADJ
ejpam-2338	447	7	to	to	PART
ejpam-2338	447	8	extend	extend	VERB
ejpam-2338	447	9	the	the	DET
ejpam-2338	447	10	‘	'	PUNCT
ejpam-2338	447	11	ehresmann	ehresmann	PROPN
ejpam-2338	447	12	–	–	PUNCT
ejpam-2338	447	13	schein	schein	PROPN
ejpam-2338	447	14	–	–	PUNCT
ejpam-2338	447	15	nambooripad	nambooripad	NOUN
ejpam-2338	447	16	’	'	PUNCT
ejpam-2338	447	17	approach	approach	NOUN
ejpam-2338	447	18	to	to	ADP
ejpam-2338	447	19	one	one	NUM
ejpam-2338	447	20	-	-	PUNCT
ejpam-2338	447	21	sided	side	VERB
ejpam-2338	447	22	restriction	restriction	NOUN
ejpam-2338	447	23	semigroups	semigroup	NOUN
ejpam-2338	447	24	(	(	PUNCT
ejpam-2338	447	25	in	in	ADP
ejpam-2338	447	26	which	which	PRON
ejpam-2338	447	27	only	only	ADV
ejpam-2338	447	28	one	one	NUM
ejpam-2338	447	29	unary	unary	ADJ
ejpam-2338	447	30	operation	operation	NOUN
ejpam-2338	447	31	is	be	AUX
ejpam-2338	447	32	present	present	ADJ
ejpam-2338	447	33	)	)	PUNCT
ejpam-2338	447	34	.	.	PUNCT
ejpam-2338	448	1	in	in	ADP
ejpam-2338	448	2	this	this	DET
ejpam-2338	448	3	case	case	NOUN
ejpam-2338	448	4	,	,	PUNCT
ejpam-2338	448	5	however	however	ADV
ejpam-2338	448	6	,	,	PUNCT
ejpam-2338	448	7	we	we	PRON
ejpam-2338	448	8	do	do	AUX
ejpam-2338	448	9	not	not	PART
ejpam-2338	448	10	employ	employ	VERB
ejpam-2338	448	11	inductive	inductive	ADJ
ejpam-2338	448	12	categories	category	NOUN
ejpam-2338	448	13	,	,	PUNCT
ejpam-2338	448	14	but	but	CCONJ
ejpam-2338	448	15	objects	object	NOUN
ejpam-2338	448	16	that	that	PRON
ejpam-2338	448	17	have	have	AUX
ejpam-2338	448	18	been	be	AUX
ejpam-2338	448	19	dubbed	dub	VERB
ejpam-2338	448	20	inductive	inductive	ADJ
ejpam-2338	448	21	constellations	constellation	NOUN
ejpam-2338	448	22	.	.	PUNCT
ejpam-2338	449	1	these	these	PRON
ejpam-2338	449	2	are	be	AUX
ejpam-2338	449	3	‘	'	PUNCT
ejpam-2338	449	4	one	one	NUM
ejpam-2338	449	5	-	-	PUNCT
ejpam-2338	449	6	sided	sided	ADJ
ejpam-2338	449	7	’	'	PUNCT
ejpam-2338	449	8	analogues	analogue	NOUN
ejpam-2338	449	9	of	of	ADP
ejpam-2338	449	10	inductive	inductive	ADJ
ejpam-2338	449	11	categories	category	NOUN
ejpam-2338	449	12	,	,	PUNCT
ejpam-2338	449	13	in	in	ADP
ejpam-2338	449	14	which	which	PRON
ejpam-2338	449	15	we	we	PRON
ejpam-2338	449	16	have	have	VERB
ejpam-2338	449	17	a	a	DET
ejpam-2338	449	18	notion	notion	NOUN
ejpam-2338	449	19	corresponding	correspond	VERB
ejpam-2338	449	20	to	to	ADP
ejpam-2338	449	21	‘	'	PUNCT
ejpam-2338	449	22	domain	domain	VERB
ejpam-2338	449	23	’	'	PUNCT
ejpam-2338	449	24	,	,	PUNCT
ejpam-2338	449	25	but	but	CCONJ
ejpam-2338	449	26	no	no	DET
ejpam-2338	449	27	concept	concept	NOUN
ejpam-2338	449	28	of	of	ADP
ejpam-2338	449	29	‘	'	PUNCT
ejpam-2338	449	30	range	range	NOUN
ejpam-2338	449	31	’	'	PUNCT
ejpam-2338	449	32	.	.	PUNCT
ejpam-2338	450	1	the	the	DET
ejpam-2338	450	2	definition	definition	NOUN
ejpam-2338	450	3	of	of	ADP
ejpam-2338	450	4	these	these	DET
ejpam-2338	450	5	objects	object	NOUN
ejpam-2338	450	6	,	,	PUNCT
ejpam-2338	450	7	together	together	ADV
ejpam-2338	450	8	with	with	ADP
ejpam-2338	450	9	the	the	DET
ejpam-2338	450	10	formulation	formulation	NOUN
ejpam-2338	450	11	of	of	ADP
ejpam-2338	450	12	an	an	DET
ejpam-2338	450	13	ehresmann	ehresmann	PROPN
ejpam-2338	450	14	–	–	PUNCT
ejpam-2338	450	15	schein	schein	PROPN
ejpam-2338	450	16	–	–	PUNCT
ejpam-2338	450	17	nambooripad	nambooripad	NOUN
ejpam-2338	450	18	-	-	PUNCT
ejpam-2338	450	19	type	type	NOUN
ejpam-2338	450	20	theorem	theorem	NOUN
ejpam-2338	450	21	for	for	ADP
ejpam-2338	450	22	these	these	PRON
ejpam-2338	450	23	and	and	CCONJ
ejpam-2338	450	24	left	leave	VERB
ejpam-2338	450	25	restriction	restriction	NOUN
ejpam-2338	450	26	semigroups	semigroup	NOUN
ejpam-2338	450	27	,	,	PUNCT
ejpam-2338	450	28	may	may	AUX
ejpam-2338	450	29	be	be	AUX
ejpam-2338	450	30	found	find	VERB
ejpam-2338	450	31	in	in	ADP
ejpam-2338	450	32	[	[	X
ejpam-2338	450	33	30	30	NUM
ejpam-2338	450	34	,	,	PUNCT
ejpam-2338	450	35	39	39	NUM
ejpam-2338	450	36	]	]	PUNCT
ejpam-2338	450	37	.	.	PUNCT
ejpam-2338	451	1	6.2	6.2	NUM
ejpam-2338	451	2	.	.	PUNCT
ejpam-2338	452	1	munn	munn	NOUN
ejpam-2338	452	2	-	-	PUNCT
ejpam-2338	452	3	type	type	NOUN
ejpam-2338	452	4	representations	representation	VERB
ejpam-2338	452	5	the	the	DET
ejpam-2338	452	6	first	first	ADJ
ejpam-2338	452	7	generalisation	generalisation	NOUN
ejpam-2338	452	8	of	of	ADP
ejpam-2338	452	9	munn	munn	PROPN
ejpam-2338	452	10	’s	’s	PART
ejpam-2338	452	11	major	major	ADJ
ejpam-2338	452	12	result	result	NOUN
ejpam-2338	452	13	(	(	PUNCT
ejpam-2338	452	14	theorem	theorem	NOUN
ejpam-2338	452	15	1	1	NUM
ejpam-2338	452	16	)	)	PUNCT
ejpam-2338	452	17	was	be	AUX
ejpam-2338	452	18	derived	derive	VERB
ejpam-2338	452	19	by	by	ADP
ejpam-2338	452	20	fountain	fountain	NOUN
ejpam-2338	452	21	[	[	X
ejpam-2338	452	22	18	18	NUM
ejpam-2338	452	23	]	]	PUNCT
ejpam-2338	452	24	for	for	ADP
ejpam-2338	452	25	a	a	DET
ejpam-2338	452	26	particular	particular	ADJ
ejpam-2338	452	27	class	class	NOUN
ejpam-2338	452	28	of	of	ADP
ejpam-2338	452	29	so	so	ADV
ejpam-2338	452	30	-	-	PUNCT
ejpam-2338	452	31	called	call	VERB
ejpam-2338	452	32	adequate	adequate	ADJ
ejpam-2338	452	33	semigroups	semigroup	NOUN
ejpam-2338	452	34	,	,	PUNCT
ejpam-2338	452	35	which	which	PRON
ejpam-2338	452	36	,	,	PUNCT
ejpam-2338	452	37	in	in	ADP
ejpam-2338	452	38	common	common	ADJ
ejpam-2338	452	39	with	with	ADP
ejpam-2338	452	40	several	several	ADJ
ejpam-2338	452	41	of	of	ADP
ejpam-2338	452	42	the	the	DET
ejpam-2338	452	43	other	other	ADJ
ejpam-2338	452	44	classes	class	NOUN
ejpam-2338	452	45	of	of	ADP
ejpam-2338	452	46	non	non	ADJ
ejpam-2338	452	47	-	-	ADJ
ejpam-2338	452	48	regular	regular	ADJ
ejpam-2338	452	49	semigroups	semigroup	NOUN
ejpam-2338	452	50	dealt	deal	VERB
ejpam-2338	452	51	with	with	ADP
ejpam-2338	452	52	here	here	ADV
ejpam-2338	452	53	,	,	PUNCT
ejpam-2338	452	54	may	may	AUX
ejpam-2338	452	55	be	be	AUX
ejpam-2338	452	56	defined	define	VERB
ejpam-2338	452	57	in	in	ADP
ejpam-2338	452	58	terms	term	NOUN
ejpam-2338	452	59	of	of	ADP
ejpam-2338	452	60	the	the	DET
ejpam-2338	452	61	‘	'	PUNCT
ejpam-2338	452	62	starred	starred	ADJ
ejpam-2338	452	63	’	'	PUNCT
ejpam-2338	452	64	generalisations	generalisation	NOUN
ejpam-2338	452	65	of	of	ADP
ejpam-2338	452	66	green	green	PROPN
ejpam-2338	452	67	’s	’s	PART
ejpam-2338	452	68	relations	relation	NOUN
ejpam-2338	452	69	.	.	PUNCT
ejpam-2338	453	1	fountain	fountain	NOUN
ejpam-2338	453	2	observed	observe	VERB
ejpam-2338	453	3	,	,	PUNCT
ejpam-2338	453	4	however	however	ADV
ejpam-2338	453	5	,	,	PUNCT
ejpam-2338	453	6	that	that	SCONJ
ejpam-2338	453	7	,	,	PUNCT
ejpam-2338	453	8	unlike	unlike	ADP
ejpam-2338	453	9	an	an	DET
ejpam-2338	453	10	inverse	inverse	NOUN
ejpam-2338	453	11	semigroup	semigroup	NOUN
ejpam-2338	453	12	,	,	PUNCT
ejpam-2338	453	13	an	an	DET
ejpam-2338	453	14	adequate	adequate	ADJ
ejpam-2338	453	15	semigroup	semigroup	NOUN
ejpam-2338	453	16	need	need	AUX
ejpam-2338	453	17	not	not	PART
ejpam-2338	453	18	have	have	VERB
ejpam-2338	453	19	a	a	DET
ejpam-2338	453	20	maximum	maximum	ADJ
ejpam-2338	453	21	idempotent	idempotent	NOUN
ejpam-2338	453	22	-	-	PUNCT
ejpam-2338	453	23	separating	separate	VERB
ejpam-2338	453	24	congruence	congruence	NOUN
ejpam-2338	453	25	.	.	PUNCT
ejpam-2338	454	1	recall	recall	PROPN
ejpam-2338	454	2	,	,	PUNCT
ejpam-2338	454	3	however	however	ADV
ejpam-2338	454	4	,	,	PUNCT
ejpam-2338	454	5	that	that	SCONJ
ejpam-2338	454	6	munn	munn	PROPN
ejpam-2338	455	1	[	[	X
ejpam-2338	455	2	63	63	NUM
ejpam-2338	455	3	]	]	PUNCT
ejpam-2338	455	4	had	have	AUX
ejpam-2338	455	5	observed	observe	VERB
ejpam-2338	455	6	that	that	SCONJ
ejpam-2338	455	7	the	the	DET
ejpam-2338	455	8	maximum	maximum	ADJ
ejpam-2338	455	9	idempotent	idempotent	NOUN
ejpam-2338	455	10	-	-	PUNCT
ejpam-2338	455	11	separating	separate	VERB
ejpam-2338	455	12	congruence	congruence	NOUN
ejpam-2338	455	13	on	on	ADP
ejpam-2338	455	14	an	an	DET
ejpam-2338	455	15	inverse	inverse	NOUN
ejpam-2338	455	16	semigroup	semigroup	NOUN
ejpam-2338	455	17	is	be	AUX
ejpam-2338	455	18	the	the	DET
ejpam-2338	455	19	largest	large	ADJ
ejpam-2338	455	20	congruence	congruence	NOUN
ejpam-2338	455	21	contained	contain	VERB
ejpam-2338	455	22	in	in	ADP
ejpam-2338	455	23	green	green	PROPN
ejpam-2338	455	24	’s	’s	PART
ejpam-2338	455	25	relation	relation	NOUN
ejpam-2338	455	26	h	h	PROPN
ejpam-2338	455	27	.	.	PUNCT
ejpam-2338	456	1	taking	take	VERB
ejpam-2338	456	2	inspiration	inspiration	NOUN
ejpam-2338	456	3	from	from	ADP
ejpam-2338	456	4	this	this	PRON
ejpam-2338	456	5	,	,	PUNCT
ejpam-2338	456	6	fountain	fountain	NOUN
ejpam-2338	456	7	therefore	therefore	ADV
ejpam-2338	456	8	pursued	pursue	VERB
ejpam-2338	456	9	a	a	DET
ejpam-2338	456	10	different	different	ADJ
ejpam-2338	456	11	line	line	NOUN
ejpam-2338	456	12	of	of	ADP
ejpam-2338	456	13	enquiry	enquiry	NOUN
ejpam-2338	456	14	by	by	ADP
ejpam-2338	456	15	investigating	investigate	VERB
ejpam-2338	456	16	the	the	DET
ejpam-2338	456	17	largest	large	ADJ
ejpam-2338	456	18	congruence	congruence	NOUN
ejpam-2338	456	19	contained	contain	VERB
ejpam-2338	456	20	in	in	ADP
ejpam-2338	456	21	the	the	DET
ejpam-2338	456	22	starred	star	VERB
ejpam-2338	456	23	green	green	NOUN
ejpam-2338	456	24	’s	’s	PART
ejpam-2338	456	25	relationh	relationh	PROPN
ejpam-2338	456	26	∗	∗	NOUN
ejpam-2338	456	27	;	;	PUNCT
ejpam-2338	456	28	any	any	DET
ejpam-2338	456	29	congruence	congruence	NOUN
ejpam-2338	456	30	contained	contain	VERB
ejpam-2338	456	31	in	in	ADP
ejpam-2338	456	32	h	h	PROPN
ejpam-2338	456	33	∗	∗	NOUN
ejpam-2338	456	34	is	be	AUX
ejpam-2338	456	35	idempotent	idempotent	ADJ
ejpam-2338	456	36	-	-	PUNCT
ejpam-2338	456	37	separating	separate	VERB
ejpam-2338	456	38	,	,	PUNCT
ejpam-2338	456	39	but	but	CCONJ
ejpam-2338	456	40	the	the	DET
ejpam-2338	456	41	converse	converse	NOUN
ejpam-2338	456	42	does	do	AUX
ejpam-2338	456	43	not	not	PART
ejpam-2338	456	44	necessarily	necessarily	ADV
ejpam-2338	456	45	hold	hold	VERB
ejpam-2338	456	46	.	.	PUNCT
ejpam-2338	457	1	furthermore	furthermore	ADV
ejpam-2338	457	2	,	,	PUNCT
ejpam-2338	457	3	as	as	ADP
ejpam-2338	457	4	in	in	ADP
ejpam-2338	457	5	other	other	ADJ
ejpam-2338	457	6	situations	situation	NOUN
ejpam-2338	457	7	in	in	ADP
ejpam-2338	457	8	the	the	DET
ejpam-2338	457	9	study	study	NOUN
ejpam-2338	457	10	of	of	ADP
ejpam-2338	457	11	adequate	adequate	ADJ
ejpam-2338	457	12	semigroups	semigroup	NOUN
ejpam-2338	457	13	,	,	PUNCT
ejpam-2338	457	14	it	it	PRON
ejpam-2338	457	15	transpired	transpire	VERB
ejpam-2338	457	16	that	that	SCONJ
ejpam-2338	457	17	in	in	ADP
ejpam-2338	457	18	order	order	NOUN
ejpam-2338	457	19	to	to	PART
ejpam-2338	457	20	develop	develop	VERB
ejpam-2338	457	21	a	a	DET
ejpam-2338	457	22	suitable	suitable	ADJ
ejpam-2338	457	23	analogue	analogue	NOUN
ejpam-2338	457	24	of	of	ADP
ejpam-2338	457	25	theorem	theorem	NOUN
ejpam-2338	457	26	1	1	NUM
ejpam-2338	457	27	(	(	PUNCT
ejpam-2338	457	28	using	use	VERB
ejpam-2338	457	29	the	the	DET
ejpam-2338	457	30	same	same	ADJ
ejpam-2338	457	31	notion	notion	NOUN
ejpam-2338	457	32	of	of	ADP
ejpam-2338	457	33	munn	munn	PROPN
ejpam-2338	457	34	semigroup	semigroup	PROPN
ejpam-2338	457	35	as	as	ADP
ejpam-2338	457	36	in	in	ADP
ejpam-2338	457	37	section	section	NOUN
ejpam-2338	457	38	4	4	NUM
ejpam-2338	457	39	)	)	PUNCT
ejpam-2338	457	40	,	,	PUNCT
ejpam-2338	457	41	it	it	PRON
ejpam-2338	457	42	was	be	AUX
ejpam-2338	457	43	necessary	necessary	ADJ
ejpam-2338	457	44	to	to	PART
ejpam-2338	457	45	deal	deal	VERB
ejpam-2338	457	46	with	with	ADP
ejpam-2338	457	47	a	a	DET
ejpam-2338	457	48	special	special	ADJ
ejpam-2338	457	49	class	class	NOUN
ejpam-2338	457	50	of	of	ADP
ejpam-2338	457	51	adequate	adequate	ADJ
ejpam-2338	457	52	semigroups	semigroup	NOUN
ejpam-2338	457	53	,	,	PUNCT
ejpam-2338	457	54	namely	namely	ADV
ejpam-2338	457	55	ample	ample	ADJ
ejpam-2338	457	56	semigroups	semigroup	NOUN
ejpam-2338	457	57	:	:	PUNCT
ejpam-2338	457	58	theorem	theorem	NOUN
ejpam-2338	457	59	6	6	NUM
ejpam-2338	457	60	(	(	PUNCT
ejpam-2338	457	61	[	[	X
ejpam-2338	457	62	18	18	NUM
ejpam-2338	457	63	,	,	PUNCT
ejpam-2338	457	64	proposition	proposition	NOUN
ejpam-2338	457	65	4.5	4.5	NUM
ejpam-2338	457	66	]	]	PUNCT
ejpam-2338	457	67	)	)	PUNCT
ejpam-2338	457	68	.	.	PUNCT
ejpam-2338	458	1	for	for	ADP
ejpam-2338	458	2	any	any	DET
ejpam-2338	458	3	ample	ample	ADJ
ejpam-2338	458	4	semigroup	semigroup	NOUN
ejpam-2338	458	5	s	s	PROPN
ejpam-2338	458	6	,	,	PUNCT
ejpam-2338	458	7	there	there	PRON
ejpam-2338	458	8	is	be	VERB
ejpam-2338	458	9	a	a	DET
ejpam-2338	458	10	morphism	morphism	NOUN
ejpam-2338	458	11	s→	s→	X
ejpam-2338	458	12	te(s	te(s	PUNCT
ejpam-2338	458	13	)	)	PUNCT
ejpam-2338	458	14	which	which	PRON
ejpam-2338	458	15	maps	map	VERB
ejpam-2338	458	16	e(s	e(s	PROPN
ejpam-2338	458	17	)	)	PUNCT
ejpam-2338	458	18	isomorphically	isomorphically	ADV
ejpam-2338	458	19	onto	onto	ADP
ejpam-2338	458	20	e(te(s	e(te(s	NOUN
ejpam-2338	458	21	)	)	PUNCT
ejpam-2338	458	22	)	)	PUNCT
ejpam-2338	458	23	and	and	CCONJ
ejpam-2338	458	24	which	which	PRON
ejpam-2338	458	25	induces	induce	VERB
ejpam-2338	458	26	the	the	DET
ejpam-2338	458	27	largest	large	ADJ
ejpam-2338	458	28	congruence	congruence	NOUN
ejpam-2338	458	29	contained	contain	VERB
ejpam-2338	458	30	inh	inh	PROPN
ejpam-2338	458	31	∗.	∗.	PROPN
ejpam-2338	458	32	further	further	ADJ
ejpam-2338	458	33	generalisations	generalisation	NOUN
ejpam-2338	458	34	of	of	ADP
ejpam-2338	458	35	the	the	DET
ejpam-2338	458	36	notions	notion	NOUN
ejpam-2338	458	37	of	of	ADP
ejpam-2338	458	38	a	a	DET
ejpam-2338	458	39	munn	munn	PROPN
ejpam-2338	458	40	semigroup	semigroup	NOUN
ejpam-2338	458	41	and	and	CCONJ
ejpam-2338	458	42	of	of	ADP
ejpam-2338	458	43	a	a	DET
ejpam-2338	458	44	fundamental	fundamental	ADJ
ejpam-2338	458	45	inverse	inverse	NOUN
ejpam-2338	458	46	semigroup	semigroup	NOUN
ejpam-2338	458	47	to	to	ADP
ejpam-2338	458	48	other	other	ADJ
ejpam-2338	458	49	non	non	ADJ
ejpam-2338	458	50	-	-	ADJ
ejpam-2338	458	51	regular	regular	ADJ
ejpam-2338	458	52	cases	case	NOUN
ejpam-2338	458	53	were	be	AUX
ejpam-2338	458	54	later	later	ADV
ejpam-2338	458	55	obtained	obtain	VERB
ejpam-2338	458	56	in	in	ADP
ejpam-2338	458	57	[	[	X
ejpam-2338	458	58	15	15	NUM
ejpam-2338	458	59	,	,	PUNCT
ejpam-2338	458	60	16	16	NUM
ejpam-2338	458	61	,	,	PUNCT
ejpam-2338	458	62	21	21	NUM
ejpam-2338	458	63	,	,	PUNCT
ejpam-2338	458	64	27	27	NUM
ejpam-2338	458	65	,	,	PUNCT
ejpam-2338	458	66	48	48	NUM
ejpam-2338	458	67	]	]	PUNCT
ejpam-2338	458	68	.	.	PUNCT
ejpam-2338	459	1	generalisations	generalisation	NOUN
ejpam-2338	459	2	of	of	ADP
ejpam-2338	459	3	munn	munn	PROPN
ejpam-2338	459	4	’s	’s	PART
ejpam-2338	459	5	methods	method	NOUN
ejpam-2338	459	6	to	to	ADP
ejpam-2338	459	7	the	the	DET
ejpam-2338	459	8	regular	regular	ADJ
ejpam-2338	459	9	case	case	NOUN
ejpam-2338	459	10	were	be	AUX
ejpam-2338	459	11	considered	consider	VERB
ejpam-2338	459	12	in	in	ADP
ejpam-2338	459	13	[	[	X
ejpam-2338	459	14	32	32	NUM
ejpam-2338	459	15	,	,	PUNCT
ejpam-2338	459	16	33	33	NUM
ejpam-2338	459	17	,	,	PUNCT
ejpam-2338	459	18	67	67	NUM
ejpam-2338	459	19	]	]	PUNCT
ejpam-2338	459	20	.	.	PUNCT
ejpam-2338	460	1	it	it	PRON
ejpam-2338	460	2	is	be	AUX
ejpam-2338	460	3	interesting	interesting	ADJ
ejpam-2338	460	4	to	to	PART
ejpam-2338	460	5	note	note	VERB
ejpam-2338	460	6	also	also	ADV
ejpam-2338	460	7	that	that	SCONJ
ejpam-2338	460	8	zhitomirskii	zhitomirskii	PROPN
ejpam-2338	461	1	[	[	X
ejpam-2338	461	2	104	104	NUM
ejpam-2338	461	3	]	]	PUNCT
ejpam-2338	461	4	even	even	ADV
ejpam-2338	461	5	extended	extend	VERB
ejpam-2338	461	6	the	the	DET
ejpam-2338	461	7	munn	munn	PROPN
ejpam-2338	461	8	representation	representation	NOUN
ejpam-2338	461	9	to	to	ADP
ejpam-2338	461	10	wagner	wagner	PROPN
ejpam-2338	461	11	’s	’s	PART
ejpam-2338	461	12	generalised	generalise	VERB
ejpam-2338	461	13	heaps	heap	NOUN
ejpam-2338	461	14	(	(	PUNCT
ejpam-2338	461	15	on	on	ADP
ejpam-2338	461	16	which	which	PRON
ejpam-2338	461	17	,	,	PUNCT
ejpam-2338	461	18	see	see	VERB
ejpam-2338	461	19	[	[	X
ejpam-2338	461	20	41	41	NUM
ejpam-2338	461	21	,	,	PUNCT
ejpam-2338	461	22	§	§	PROPN
ejpam-2338	461	23	10.4	10.4	NUM
ejpam-2338	461	24	]	]	PUNCT
ejpam-2338	461	25	)	)	PUNCT
ejpam-2338	461	26	.	.	PUNCT
ejpam-2338	462	1	6.3	6.3	NUM
ejpam-2338	462	2	.	.	PUNCT
ejpam-2338	462	3	proper	proper	ADJ
ejpam-2338	462	4	semigroups	semigroup	NOUN
ejpam-2338	462	5	of	of	ADP
ejpam-2338	462	6	other	other	ADJ
ejpam-2338	462	7	types	type	NOUN
ejpam-2338	462	8	recall	recall	VERB
ejpam-2338	462	9	the	the	DET
ejpam-2338	462	10	observation	observation	NOUN
ejpam-2338	462	11	in	in	ADP
ejpam-2338	462	12	section	section	NOUN
ejpam-2338	462	13	5	5	NUM
ejpam-2338	462	14	that	that	PRON
ejpam-2338	462	15	,	,	PUNCT
ejpam-2338	462	16	although	although	SCONJ
ejpam-2338	462	17	defined	define	VERB
ejpam-2338	462	18	separately	separately	ADV
ejpam-2338	462	19	,	,	PUNCT
ejpam-2338	462	20	the	the	DET
ejpam-2338	462	21	notions	notion	NOUN
ejpam-2338	462	22	of	of	ADP
ejpam-2338	462	23	‘	'	PUNCT
ejpam-2338	462	24	proper	proper	ADJ
ejpam-2338	462	25	’	'	PUNCT
ejpam-2338	462	26	and	and	CCONJ
ejpam-2338	462	27	‘	'	PUNCT
ejpam-2338	462	28	e	e	NOUN
ejpam-2338	462	29	-	-	ADJ
ejpam-2338	462	30	unitary	unitary	ADJ
ejpam-2338	462	31	’	'	PUNCT
ejpam-2338	462	32	coincide	coincide	NOUN
ejpam-2338	462	33	for	for	ADP
ejpam-2338	462	34	inverse	inverse	NOUN
ejpam-2338	462	35	semigroups	semigroup	NOUN
ejpam-2338	462	36	.	.	PUNCT
ejpam-2338	463	1	this	this	PRON
ejpam-2338	463	2	,	,	PUNCT
ejpam-2338	463	3	however	however	ADV
ejpam-2338	463	4	,	,	PUNCT
ejpam-2338	463	5	is	be	AUX
ejpam-2338	463	6	not	not	PART
ejpam-2338	463	7	the	the	DET
ejpam-2338	463	8	case	case	NOUN
ejpam-2338	463	9	for	for	ADP
ejpam-2338	463	10	the	the	DET
ejpam-2338	463	11	nonregular	nonregular	ADJ
ejpam-2338	463	12	generalisations	generalisation	NOUN
ejpam-2338	463	13	of	of	ADP
ejpam-2338	463	14	inverse	inverse	NOUN
ejpam-2338	463	15	semigroups	semigroup	NOUN
ejpam-2338	463	16	that	that	PRON
ejpam-2338	463	17	we	we	PRON
ejpam-2338	463	18	deal	deal	VERB
ejpam-2338	463	19	with	with	ADP
ejpam-2338	463	20	here	here	ADV
ejpam-2338	463	21	,	,	PUNCT
ejpam-2338	463	22	an	an	DET
ejpam-2338	463	23	observation	observation	NOUN
ejpam-2338	463	24	first	first	ADV
ejpam-2338	463	25	made	make	VERB
ejpam-2338	463	26	references	reference	NOUN
ejpam-2338	463	27	315	315	NUM
ejpam-2338	463	28	by	by	ADP
ejpam-2338	463	29	fountain	fountain	NOUN
ejpam-2338	463	30	[	[	X
ejpam-2338	463	31	17	17	NUM
ejpam-2338	463	32	,	,	PUNCT
ejpam-2338	463	33	example	example	NOUN
ejpam-2338	463	34	3	3	NUM
ejpam-2338	463	35	]	]	PUNCT
ejpam-2338	463	36	.	.	PUNCT
ejpam-2338	464	1	efforts	effort	NOUN
ejpam-2338	464	2	to	to	PART
ejpam-2338	464	3	generalise	generalise	VERB
ejpam-2338	464	4	mcalister	mcalister	PROPN
ejpam-2338	464	5	’s	’s	PART
ejpam-2338	464	6	notions	notion	NOUN
ejpam-2338	464	7	to	to	ADP
ejpam-2338	464	8	the	the	DET
ejpam-2338	464	9	non	non	ADJ
ejpam-2338	464	10	-	-	ADJ
ejpam-2338	464	11	regular	regular	ADJ
ejpam-2338	464	12	case	case	NOUN
ejpam-2338	464	13	appear	appear	VERB
ejpam-2338	464	14	therefore	therefore	ADV
ejpam-2338	464	15	to	to	PART
ejpam-2338	464	16	have	have	AUX
ejpam-2338	464	17	focused	focus	VERB
ejpam-2338	464	18	on	on	ADP
ejpam-2338	464	19	the	the	DET
ejpam-2338	464	20	semigroups	semigroup	NOUN
ejpam-2338	464	21	which	which	PRON
ejpam-2338	464	22	are	be	AUX
ejpam-2338	464	23	‘	'	PUNCT
ejpam-2338	464	24	proper	proper	ADJ
ejpam-2338	464	25	’	'	PUNCT
ejpam-2338	464	26	in	in	ADP
ejpam-2338	464	27	a	a	DET
ejpam-2338	464	28	suitable	suitable	ADJ
ejpam-2338	464	29	sense	sense	NOUN
ejpam-2338	464	30	(	(	PUNCT
ejpam-2338	464	31	obtained	obtain	VERB
ejpam-2338	464	32	from	from	ADP
ejpam-2338	464	33	the	the	DET
ejpam-2338	464	34	original	original	ADJ
ejpam-2338	464	35	definition	definition	NOUN
ejpam-2338	464	36	by	by	ADP
ejpam-2338	464	37	replacement	replacement	NOUN
ejpam-2338	464	38	of	of	ADP
ejpam-2338	464	39	green	green	PROPN
ejpam-2338	464	40	’s	’s	PART
ejpam-2338	464	41	relations	relation	NOUN
ejpam-2338	464	42	with	with	ADP
ejpam-2338	464	43	their	their	PRON
ejpam-2338	464	44	appropriate	appropriate	ADJ
ejpam-2338	464	45	generalisations	generalisation	NOUN
ejpam-2338	464	46	)	)	PUNCT
ejpam-2338	464	47	.	.	PUNCT
ejpam-2338	465	1	we	we	PRON
ejpam-2338	465	2	have	have	AUX
ejpam-2338	465	3	,	,	PUNCT
ejpam-2338	465	4	for	for	ADP
ejpam-2338	465	5	example	example	NOUN
ejpam-2338	465	6	,	,	PUNCT
ejpam-2338	465	7	the	the	DET
ejpam-2338	465	8	following	follow	VERB
ejpam-2338	465	9	right	right	ADJ
ejpam-2338	465	10	ample	ample	ADJ
ejpam-2338	465	11	(	(	PUNCT
ejpam-2338	465	12	monoid	monoid	NOUN
ejpam-2338	465	13	)	)	PUNCT
ejpam-2338	465	14	version	version	NOUN
ejpam-2338	465	15	of	of	ADP
ejpam-2338	465	16	theorem	theorem	ADJ
ejpam-2338	465	17	3	3	NUM
ejpam-2338	465	18	(	(	PUNCT
ejpam-2338	465	19	mcalister	mcalister	PROPN
ejpam-2338	465	20	’s	’s	PART
ejpam-2338	465	21	covering	covering	NOUN
ejpam-2338	465	22	theorem	theorem	NOUN
ejpam-2338	465	23	):	):	PUNCT
ejpam-2338	465	24	theorem	theorem	ADJ
ejpam-2338	465	25	7	7	NUM
ejpam-2338	465	26	(	(	PUNCT
ejpam-2338	465	27	[	[	X
ejpam-2338	465	28	17	17	NUM
ejpam-2338	465	29	,	,	PUNCT
ejpam-2338	465	30	theorem	theorem	VERB
ejpam-2338	465	31	3.3	3.3	NUM
ejpam-2338	465	32	]	]	PUNCT
ejpam-2338	465	33	)	)	PUNCT
ejpam-2338	465	34	.	.	PUNCT
ejpam-2338	466	1	every	every	DET
ejpam-2338	466	2	right	right	ADJ
ejpam-2338	466	3	ample	ample	ADJ
ejpam-2338	466	4	monoid	monoid	NOUN
ejpam-2338	466	5	is	be	AUX
ejpam-2338	466	6	the	the	DET
ejpam-2338	466	7	image	image	NOUN
ejpam-2338	466	8	of	of	ADP
ejpam-2338	466	9	a	a	DET
ejpam-2338	466	10	proper	proper	ADJ
ejpam-2338	466	11	right	right	ADJ
ejpam-2338	466	12	ample	ample	ADJ
ejpam-2338	466	13	monoid	monoid	NOUN
ejpam-2338	466	14	under	under	ADP
ejpam-2338	466	15	an	an	DET
ejpam-2338	466	16	l	l	NOUN
ejpam-2338	466	17	∗-morphism	∗-morphism	NOUN
ejpam-2338	466	18	,	,	PUNCT
ejpam-2338	466	19	where	where	SCONJ
ejpam-2338	466	20	an	an	DET
ejpam-2338	466	21	l	l	NOUN
ejpam-2338	466	22	∗-morphism	∗-morphism	NOUN
ejpam-2338	466	23	is	be	AUX
ejpam-2338	466	24	a	a	DET
ejpam-2338	466	25	morphism	morphism	ADJ
ejpam-2338	466	26	θ	θ	PROPN
ejpam-2338	466	27	for	for	ADP
ejpam-2338	466	28	which	which	PRON
ejpam-2338	466	29	sl	sl	NOUN
ejpam-2338	466	30	∗	∗	NOUN
ejpam-2338	466	31	t	t	NOUN
ejpam-2338	466	32	whenever	whenever	SCONJ
ejpam-2338	466	33	sθ	sθ	ADP
ejpam-2338	466	34	=	=	NOUN
ejpam-2338	466	35	tθ	tθ	NOUN
ejpam-2338	466	36	.	.	PUNCT
ejpam-2338	467	1	note	note	VERB
ejpam-2338	467	2	that	that	SCONJ
ejpam-2338	467	3	such	such	DET
ejpam-2338	467	4	an	an	DET
ejpam-2338	467	5	l	l	NOUN
ejpam-2338	467	6	∗-morphism	∗-morphism	NOUN
ejpam-2338	467	7	is	be	AUX
ejpam-2338	467	8	idempotent	idempotent	ADJ
ejpam-2338	467	9	-	-	PUNCT
ejpam-2338	467	10	separating	separate	VERB
ejpam-2338	467	11	.	.	PUNCT
ejpam-2338	468	1	fountain	fountain	NOUN
ejpam-2338	468	2	subsequently	subsequently	ADV
ejpam-2338	468	3	described	describe	VERB
ejpam-2338	468	4	a	a	DET
ejpam-2338	468	5	generalisation	generalisation	NOUN
ejpam-2338	468	6	of	of	ADP
ejpam-2338	468	7	mcalister	mcalister	PROPN
ejpam-2338	468	8	’s	’s	PART
ejpam-2338	468	9	p	p	NOUN
ejpam-2338	468	10	-	-	PUNCT
ejpam-2338	468	11	semigroups	semigroup	NOUN
ejpam-2338	468	12	,	,	PUNCT
ejpam-2338	468	13	which	which	PRON
ejpam-2338	468	14	he	he	PRON
ejpam-2338	468	15	termed	term	VERB
ejpam-2338	468	16	mcalister	mcalister	PROPN
ejpam-2338	468	17	monoids	monoids	PROPN
ejpam-2338	468	18	,	,	PUNCT
ejpam-2338	468	19	and	and	CCONJ
ejpam-2338	468	20	used	use	VERB
ejpam-2338	468	21	these	these	PRON
ejpam-2338	468	22	to	to	PART
ejpam-2338	468	23	derive	derive	VERB
ejpam-2338	468	24	the	the	DET
ejpam-2338	468	25	following	follow	VERB
ejpam-2338	468	26	generalised	generalise	VERB
ejpam-2338	468	27	p	p	NOUN
ejpam-2338	468	28	-	-	PUNCT
ejpam-2338	468	29	theorem	theorem	ADJ
ejpam-2338	468	30	:	:	PUNCT
ejpam-2338	468	31	theorem	theorem	ADJ
ejpam-2338	468	32	8	8	NUM
ejpam-2338	468	33	(	(	PUNCT
ejpam-2338	468	34	[	[	X
ejpam-2338	468	35	17	17	NUM
ejpam-2338	468	36	,	,	PUNCT
ejpam-2338	468	37	theorem	theorem	VERB
ejpam-2338	468	38	4.3	4.3	NUM
ejpam-2338	468	39	]	]	PUNCT
ejpam-2338	468	40	)	)	PUNCT
ejpam-2338	468	41	.	.	PUNCT
ejpam-2338	469	1	every	every	DET
ejpam-2338	469	2	proper	proper	ADJ
ejpam-2338	469	3	right	right	ADJ
ejpam-2338	469	4	ample	ample	ADJ
ejpam-2338	469	5	monoid	monoid	NOUN
ejpam-2338	469	6	is	be	AUX
ejpam-2338	469	7	isomorphic	isomorphic	ADJ
ejpam-2338	469	8	to	to	ADP
ejpam-2338	469	9	a	a	DET
ejpam-2338	469	10	mcalister	mcalister	PROPN
ejpam-2338	469	11	monoid	monoid	PROPN
ejpam-2338	469	12	.	.	PUNCT
ejpam-2338	470	1	these	these	DET
ejpam-2338	470	2	theorems	theorem	NOUN
ejpam-2338	470	3	are	be	AUX
ejpam-2338	470	4	easily	easily	ADV
ejpam-2338	470	5	adapted	adapt	VERB
ejpam-2338	470	6	to	to	ADP
ejpam-2338	470	7	the	the	DET
ejpam-2338	470	8	semigroup	semigroup	PROPN
ejpam-2338	470	9	case	case	NOUN
ejpam-2338	470	10	.	.	PUNCT
ejpam-2338	471	1	versions	version	NOUN
ejpam-2338	471	2	for	for	ADP
ejpam-2338	471	3	two	two	NUM
ejpam-2338	471	4	-	-	PUNCT
ejpam-2338	471	5	sided	sided	ADJ
ejpam-2338	471	6	ample	ample	ADJ
ejpam-2338	471	7	semigroups	semigroup	NOUN
ejpam-2338	471	8	appear	appear	VERB
ejpam-2338	471	9	in	in	ADP
ejpam-2338	471	10	[	[	X
ejpam-2338	471	11	49	49	NUM
ejpam-2338	471	12	]	]	PUNCT
ejpam-2338	471	13	as	as	ADP
ejpam-2338	471	14	theorems	theorem	NOUN
ejpam-2338	471	15	3.8	3.8	NUM
ejpam-2338	471	16	and	and	CCONJ
ejpam-2338	471	17	2.11	2.11	NUM
ejpam-2338	471	18	,	,	PUNCT
ejpam-2338	471	19	respectively	respectively	ADV
ejpam-2338	471	20	.	.	PUNCT
ejpam-2338	472	1	further	further	ADJ
ejpam-2338	472	2	generalisations	generalisation	NOUN
ejpam-2338	472	3	of	of	ADP
ejpam-2338	472	4	mcalister	mcalister	PROPN
ejpam-2338	472	5	’s	’s	PART
ejpam-2338	472	6	notions	notion	NOUN
ejpam-2338	472	7	in	in	ADP
ejpam-2338	472	8	certain	certain	ADJ
ejpam-2338	472	9	one	one	NUM
ejpam-2338	472	10	-	-	PUNCT
ejpam-2338	472	11	sided	sided	ADJ
ejpam-2338	472	12	non	non	ADJ
ejpam-2338	472	13	-	-	ADJ
ejpam-2338	472	14	regular	regular	ADJ
ejpam-2338	472	15	cases	case	NOUN
ejpam-2338	472	16	appeared	appear	VERB
ejpam-2338	472	17	in	in	ADP
ejpam-2338	472	18	[	[	X
ejpam-2338	472	19	25	25	NUM
ejpam-2338	472	20	,	,	PUNCT
ejpam-2338	472	21	26	26	NUM
ejpam-2338	472	22	,	,	PUNCT
ejpam-2338	472	23	28	28	NUM
ejpam-2338	472	24	]	]	PUNCT
ejpam-2338	472	25	.	.	PUNCT
ejpam-2338	473	1	results	result	NOUN
ejpam-2338	473	2	for	for	ADP
ejpam-2338	473	3	two	two	NUM
ejpam-2338	473	4	-	-	PUNCT
ejpam-2338	473	5	sided	side	VERB
ejpam-2338	473	6	restriction	restriction	NOUN
ejpam-2338	473	7	semigroups	semigroup	NOUN
ejpam-2338	473	8	took	take	VERB
ejpam-2338	473	9	a	a	DET
ejpam-2338	473	10	little	little	ADJ
ejpam-2338	473	11	longer	long	ADJ
ejpam-2338	473	12	to	to	PART
ejpam-2338	473	13	develop	develop	VERB
ejpam-2338	473	14	,	,	PUNCT
ejpam-2338	473	15	but	but	CCONJ
ejpam-2338	473	16	may	may	AUX
ejpam-2338	473	17	be	be	AUX
ejpam-2338	473	18	found	find	VERB
ejpam-2338	473	19	in	in	ADP
ejpam-2338	473	20	[	[	X
ejpam-2338	473	21	8	8	NUM
ejpam-2338	473	22	,	,	PUNCT
ejpam-2338	473	23	9	9	NUM
ejpam-2338	473	24	]	]	PUNCT
ejpam-2338	473	25	.	.	PUNCT
ejpam-2338	474	1	we	we	PRON
ejpam-2338	474	2	note	note	VERB
ejpam-2338	474	3	that	that	SCONJ
ejpam-2338	474	4	the	the	DET
ejpam-2338	474	5	generalisation	generalisation	NOUN
ejpam-2338	474	6	to	to	ADP
ejpam-2338	474	7	the	the	DET
ejpam-2338	474	8	two	two	NUM
ejpam-2338	474	9	-	-	PUNCT
ejpam-2338	474	10	sided	sided	ADJ
ejpam-2338	474	11	cases	case	NOUN
ejpam-2338	474	12	here	here	ADV
ejpam-2338	474	13	are	be	AUX
ejpam-2338	474	14	rather	rather	ADV
ejpam-2338	474	15	harder	hard	ADJ
ejpam-2338	474	16	than	than	ADP
ejpam-2338	474	17	to	to	ADP
ejpam-2338	474	18	the	the	DET
ejpam-2338	474	19	onesided	onesided	ADJ
ejpam-2338	474	20	,	,	PUNCT
ejpam-2338	474	21	and	and	CCONJ
ejpam-2338	474	22	,	,	PUNCT
ejpam-2338	474	23	to	to	PART
ejpam-2338	474	24	pick	pick	VERB
ejpam-2338	474	25	up	up	ADP
ejpam-2338	474	26	on	on	ADP
ejpam-2338	474	27	the	the	DET
ejpam-2338	474	28	comments	comment	NOUN
ejpam-2338	474	29	at	at	ADP
ejpam-2338	474	30	the	the	DET
ejpam-2338	474	31	end	end	NOUN
ejpam-2338	474	32	of	of	ADP
ejpam-2338	474	33	section	section	NOUN
ejpam-2338	474	34	5.3	5.3	NUM
ejpam-2338	474	35	,	,	PUNCT
ejpam-2338	474	36	are	be	AUX
ejpam-2338	474	37	achieved	achieve	VERB
ejpam-2338	474	38	through	through	ADP
ejpam-2338	474	39	the	the	DET
ejpam-2338	474	40	use	use	NOUN
ejpam-2338	474	41	of	of	ADP
ejpam-2338	474	42	partial	partial	ADJ
ejpam-2338	474	43	actions	action	NOUN
ejpam-2338	474	44	.	.	PUNCT
ejpam-2338	475	1	regular	regular	ADJ
ejpam-2338	475	2	generalisations	generalisation	NOUN
ejpam-2338	475	3	of	of	ADP
ejpam-2338	475	4	the	the	DET
ejpam-2338	475	5	p	p	NOUN
ejpam-2338	475	6	-	-	PUNCT
ejpam-2338	475	7	theorem	theorem	ADJ
ejpam-2338	475	8	are	be	AUX
ejpam-2338	475	9	discussed	discuss	VERB
ejpam-2338	475	10	in	in	ADP
ejpam-2338	475	11	[	[	X
ejpam-2338	475	12	94	94	NUM
ejpam-2338	475	13	]	]	PUNCT
ejpam-2338	475	14	,	,	PUNCT
ejpam-2338	475	15	whilst	whilst	SCONJ
ejpam-2338	475	16	versions	version	NOUN
ejpam-2338	475	17	for	for	ADP
ejpam-2338	475	18	inductive	inductive	ADJ
ejpam-2338	475	19	groupoids	groupoid	NOUN
ejpam-2338	475	20	feature	feature	VERB
ejpam-2338	475	21	in	in	ADP
ejpam-2338	475	22	[	[	X
ejpam-2338	475	23	23	23	NUM
ejpam-2338	475	24	,	,	PUNCT
ejpam-2338	475	25	60	60	NUM
ejpam-2338	475	26	]	]	PUNCT
ejpam-2338	475	27	;	;	PUNCT
ejpam-2338	475	28	the	the	DET
ejpam-2338	475	29	inductive	inductive	ADJ
ejpam-2338	475	30	groupoids	groupoid	NOUN
ejpam-2338	475	31	to	to	ADP
ejpam-2338	475	32	which	which	PRON
ejpam-2338	475	33	e	e	NOUN
ejpam-2338	475	34	-	-	NOUN
ejpam-2338	475	35	unitary	unitary	ADJ
ejpam-2338	475	36	inverse	inverse	NOUN
ejpam-2338	475	37	semigroups	semigroup	NOUN
ejpam-2338	475	38	correspond	correspond	VERB
ejpam-2338	475	39	under	under	ADP
ejpam-2338	475	40	the	the	DET
ejpam-2338	475	41	ehresmann	ehresmann	PROPN
ejpam-2338	475	42	–	–	PUNCT
ejpam-2338	475	43	schein	schein	PROPN
ejpam-2338	475	44	–	–	PUNCT
ejpam-2338	475	45	nambooripad	nambooripad	PROPN
ejpam-2338	475	46	theorem	theorem	NOUN
ejpam-2338	475	47	are	be	AUX
ejpam-2338	475	48	termed	term	VERB
ejpam-2338	475	49	incompressible	incompressible	ADJ
ejpam-2338	475	50	inductive	inductive	ADJ
ejpam-2338	475	51	groupoids	groupoid	NOUN
ejpam-2338	475	52	.	.	PUNCT
ejpam-2338	476	1	acknowledgements	acknowledgement	NOUN
ejpam-2338	476	2	this	this	DET
ejpam-2338	476	3	article	article	NOUN
ejpam-2338	476	4	represents	represent	VERB
ejpam-2338	476	5	an	an	DET
ejpam-2338	476	6	addendum	addendum	NOUN
ejpam-2338	476	7	to	to	ADP
ejpam-2338	476	8	[	[	X
ejpam-2338	476	9	41	41	NUM
ejpam-2338	476	10	,	,	PUNCT
ejpam-2338	476	11	chapter	chapter	NOUN
ejpam-2338	476	12	10	10	NUM
ejpam-2338	476	13	]	]	PUNCT
ejpam-2338	476	14	and	and	CCONJ
ejpam-2338	476	15	,	,	PUNCT
ejpam-2338	476	16	as	as	ADP
ejpam-2338	476	17	such	such	ADJ
ejpam-2338	476	18	,	,	PUNCT
ejpam-2338	476	19	contains	contain	VERB
ejpam-2338	476	20	research	research	NOUN
ejpam-2338	476	21	that	that	PRON
ejpam-2338	476	22	was	be	AUX
ejpam-2338	476	23	carried	carry	VERB
ejpam-2338	476	24	out	out	ADP
ejpam-2338	476	25	at	at	ADP
ejpam-2338	476	26	the	the	DET
ejpam-2338	476	27	mathematical	mathematical	ADJ
ejpam-2338	476	28	institute	institute	NOUN
ejpam-2338	476	29	of	of	ADP
ejpam-2338	476	30	the	the	DET
ejpam-2338	476	31	university	university	NOUN
ejpam-2338	476	32	of	of	ADP
ejpam-2338	476	33	oxford	oxford	PROPN
ejpam-2338	476	34	under	under	ADP
ejpam-2338	476	35	the	the	DET
ejpam-2338	476	36	auspices	auspex	NOUN
ejpam-2338	476	37	of	of	ADP
ejpam-2338	476	38	research	research	NOUN
ejpam-2338	476	39	project	project	NOUN
ejpam-2338	476	40	grant	grant	VERB
ejpam-2338	476	41	f/08	f/08	ADJ
ejpam-2338	476	42	772	772	NUM
ejpam-2338	476	43	/	/	SYM
ejpam-2338	476	44	f	f	NOUN
ejpam-2338	476	45	from	from	ADP
ejpam-2338	476	46	the	the	DET
ejpam-2338	476	47	leverhulme	leverhulme	PROPN
ejpam-2338	476	48	trust	trust	NOUN
ejpam-2338	476	49	.	.	PUNCT
ejpam-2338	477	1	i	i	PRON
ejpam-2338	477	2	am	be	AUX
ejpam-2338	477	3	grateful	grateful	ADJ
ejpam-2338	477	4	to	to	ADP
ejpam-2338	477	5	peter	peter	PROPN
ejpam-2338	477	6	m.	m.	PROPN
ejpam-2338	477	7	neumann	neumann	PROPN
ejpam-2338	477	8	for	for	ADP
ejpam-2338	477	9	his	his	PRON
ejpam-2338	477	10	critical	critical	ADJ
ejpam-2338	477	11	comments	comment	NOUN
ejpam-2338	477	12	on	on	ADP
ejpam-2338	477	13	an	an	DET
ejpam-2338	477	14	earlier	early	ADJ
ejpam-2338	477	15	draft	draft	NOUN
ejpam-2338	477	16	of	of	ADP
ejpam-2338	477	17	this	this	DET
ejpam-2338	477	18	article	article	NOUN
ejpam-2338	477	19	,	,	PUNCT
ejpam-2338	477	20	and	and	CCONJ
ejpam-2338	477	21	also	also	ADV
ejpam-2338	477	22	to	to	ADP
ejpam-2338	477	23	the	the	DET
ejpam-2338	477	24	anonymous	anonymous	ADJ
ejpam-2338	477	25	referee	referee	NOUN
ejpam-2338	477	26	for	for	ADP
ejpam-2338	477	27	a	a	DET
ejpam-2338	477	28	very	very	ADV
ejpam-2338	477	29	detailed	detailed	ADJ
ejpam-2338	477	30	list	list	NOUN
ejpam-2338	477	31	of	of	ADP
ejpam-2338	477	32	suggestions	suggestion	NOUN
ejpam-2338	477	33	which	which	PRON
ejpam-2338	477	34	have	have	AUX
ejpam-2338	477	35	improved	improve	VERB
ejpam-2338	477	36	the	the	DET
ejpam-2338	477	37	article	article	NOUN
ejpam-2338	477	38	considerably	considerably	ADV
ejpam-2338	477	39	.	.	PUNCT
ejpam-2338	478	1	references	reference	NOUN
ejpam-2338	478	2	[	[	X
ejpam-2338	478	3	1	1	X
ejpam-2338	478	4	]	]	PUNCT
ejpam-2338	478	5	s.	s.	PROPN
ejpam-2338	478	6	armstrong	armstrong	PROPN
ejpam-2338	478	7	.	.	PUNCT
ejpam-2338	479	1	the	the	DET
ejpam-2338	479	2	structure	structure	NOUN
ejpam-2338	479	3	of	of	ADP
ejpam-2338	479	4	type	type	NOUN
ejpam-2338	479	5	a	a	DET
ejpam-2338	479	6	semigroups	semigroup	NOUN
ejpam-2338	479	7	,	,	PUNCT
ejpam-2338	479	8	semigroup	semigroup	PROPN
ejpam-2338	479	9	forum	forum	PROPN
ejpam-2338	479	10	29	29	NUM
ejpam-2338	479	11	,	,	PUNCT
ejpam-2338	479	12	319–336	319–336	NUM
ejpam-2338	479	13	.	.	PUNCT
ejpam-2338	479	14	1984	1984	NUM
ejpam-2338	479	15	.	.	PUNCT
ejpam-2338	480	1	http://dx.doi.org/10.1007/bf02573337	http://dx.doi.org/10.1007/bf02573337	PROPN
ejpam-2338	481	1	[	[	X
ejpam-2338	481	2	2	2	NUM
ejpam-2338	481	3	]	]	X
ejpam-2338	481	4	g.	g.	NOUN
ejpam-2338	481	5	birkhoff	birkhoff	NOUN
ejpam-2338	481	6	and	and	CCONJ
ejpam-2338	481	7	m.	m.	PROPN
ejpam-2338	481	8	k.	k.	PROPN
ejpam-2338	481	9	bennett	bennett	PROPN
ejpam-2338	481	10	.	.	PUNCT
ejpam-2338	482	1	felix	felix	PROPN
ejpam-2338	482	2	klein	klein	PROPN
ejpam-2338	482	3	and	and	CCONJ
ejpam-2338	482	4	his	his	PRON
ejpam-2338	482	5	“	"	PUNCT
ejpam-2338	482	6	erlanger	erlanger	PROPN
ejpam-2338	482	7	programm	programm	PROPN
ejpam-2338	482	8	”	"	PUNCT
ejpam-2338	482	9	,	,	PUNCT
ejpam-2338	482	10	in	in	ADP
ejpam-2338	482	11	:	:	PUNCT
ejpam-2338	482	12	w.	w.	PROPN
ejpam-2338	482	13	aspray	aspray	PROPN
ejpam-2338	482	14	and	and	CCONJ
ejpam-2338	482	15	p.	p.	PROPN
ejpam-2338	482	16	kitcher	kitcher	PROPN
ejpam-2338	482	17	(	(	PUNCT
ejpam-2338	482	18	eds	ed	NOUN
ejpam-2338	482	19	.	.	PUNCT
ejpam-2338	482	20	)	)	PUNCT
ejpam-2338	482	21	.	.	PUNCT
ejpam-2338	483	1	history	history	NOUN
ejpam-2338	483	2	and	and	CCONJ
ejpam-2338	483	3	philosophy	philosophy	NOUN
ejpam-2338	483	4	of	of	ADP
ejpam-2338	483	5	modern	modern	ADJ
ejpam-2338	483	6	mathematics	mathematic	NOUN
ejpam-2338	483	7	,	,	PUNCT
ejpam-2338	483	8	minnesota	minnesota	PROPN
ejpam-2338	483	9	studies	study	NOUN
ejpam-2338	483	10	in	in	ADP
ejpam-2338	483	11	the	the	DET
ejpam-2338	483	12	philosophy	philosophy	NOUN
ejpam-2338	483	13	of	of	ADP
ejpam-2338	483	14	science	science	NOUN
ejpam-2338	483	15	,	,	PUNCT
ejpam-2338	483	16	vol	vol	NOUN
ejpam-2338	483	17	.	.	PUNCT
ejpam-2338	484	1	xi	xi	PROPN
ejpam-2338	484	2	,	,	PUNCT
ejpam-2338	484	3	university	university	PROPN
ejpam-2338	484	4	of	of	ADP
ejpam-2338	484	5	minnesota	minnesota	PROPN
ejpam-2338	484	6	press	press	PROPN
ejpam-2338	484	7	,	,	PUNCT
ejpam-2338	484	8	minneapolis	minneapolis	PROPN
ejpam-2338	484	9	,	,	PUNCT
ejpam-2338	484	10	pp	pp	ADP
ejpam-2338	484	11	.	.	PUNCT
ejpam-2338	485	1	145–176	145–176	NUM
ejpam-2338	485	2	.	.	PUNCT
ejpam-2338	485	3	1988	1988	NUM
ejpam-2338	485	4	.	.	PUNCT
ejpam-2338	486	1	references	reference	NOUN
ejpam-2338	486	2	316	316	NUM
ejpam-2338	486	3	[	[	X
ejpam-2338	486	4	3	3	NUM
ejpam-2338	486	5	]	]	X
ejpam-2338	486	6	r.	r.	PROPN
ejpam-2338	486	7	brown	brown	PROPN
ejpam-2338	486	8	.	.	PUNCT
ejpam-2338	487	1	from	from	ADP
ejpam-2338	487	2	groups	group	NOUN
ejpam-2338	487	3	to	to	ADP
ejpam-2338	487	4	groupoids	groupoid	NOUN
ejpam-2338	487	5	:	:	PUNCT
ejpam-2338	487	6	a	a	DET
ejpam-2338	487	7	brief	brief	ADJ
ejpam-2338	487	8	survey	survey	NOUN
ejpam-2338	487	9	,	,	PUNCT
ejpam-2338	487	10	bulletin	bulletin	NOUN
ejpam-2338	487	11	of	of	ADP
ejpam-2338	487	12	the	the	DET
ejpam-2338	487	13	london	london	PROPN
ejpam-2338	487	14	mathematical	mathematical	ADJ
ejpam-2338	487	15	society	society	NOUN
ejpam-2338	487	16	19	19	NUM
ejpam-2338	487	17	,	,	PUNCT
ejpam-2338	487	18	113–134	113–134	NUM
ejpam-2338	487	19	.	.	PUNCT
ejpam-2338	487	20	1987	1987	NUM
ejpam-2338	487	21	.	.	PUNCT
ejpam-2338	488	1	http://dx.doi.org/10.1112/blms/19.2.113	http://dx.doi.org/10.1112/blms/19.2.113	NOUN
ejpam-2338	489	1	[	[	X
ejpam-2338	489	2	4	4	NUM
ejpam-2338	489	3	]	]	X
ejpam-2338	489	4	r.	r.	PROPN
ejpam-2338	489	5	brown	brown	PROPN
ejpam-2338	489	6	.	.	PUNCT
ejpam-2338	490	1	groupoids	groupoid	NOUN
ejpam-2338	490	2	and	and	CCONJ
ejpam-2338	490	3	crossed	cross	VERB
ejpam-2338	490	4	objects	object	NOUN
ejpam-2338	490	5	in	in	ADP
ejpam-2338	490	6	algebraic	algebraic	ADJ
ejpam-2338	490	7	topology	topology	NOUN
ejpam-2338	490	8	,	,	PUNCT
ejpam-2338	490	9	homology	homology	NOUN
ejpam-2338	490	10	,	,	PUNCT
ejpam-2338	490	11	homotopy	homotopy	NOUN
ejpam-2338	490	12	and	and	CCONJ
ejpam-2338	490	13	applications	application	NOUN
ejpam-2338	490	14	1(1	1(1	NUM
ejpam-2338	490	15	)	)	PUNCT
ejpam-2338	490	16	,	,	PUNCT
ejpam-2338	490	17	1–78	1–78	PROPN
ejpam-2338	490	18	.	.	PUNCT
ejpam-2338	490	19	1999	1999	NUM
ejpam-2338	490	20	.	.	PUNCT
ejpam-2338	491	1	http://dx.doi.org/10.4310/hha.1999.v1	http://dx.doi.org/10.4310/hha.1999.v1	PROPN
ejpam-2338	491	2	.	.	PUNCT
ejpam-2338	492	1	n1.a1	n1.a1	PUNCT
ejpam-2338	493	1	[	[	X
ejpam-2338	493	2	5	5	X
ejpam-2338	493	3	]	]	PUNCT
ejpam-2338	493	4	r.	r.	PROPN
ejpam-2338	493	5	brown	brown	PROPN
ejpam-2338	493	6	.	.	PUNCT
ejpam-2338	494	1	three	three	NUM
ejpam-2338	494	2	themes	theme	NOUN
ejpam-2338	494	3	in	in	ADP
ejpam-2338	494	4	the	the	DET
ejpam-2338	494	5	work	work	NOUN
ejpam-2338	494	6	of	of	ADP
ejpam-2338	494	7	charles	charles	PROPN
ejpam-2338	494	8	ehresmann	ehresmann	PROPN
ejpam-2338	494	9	:	:	PUNCT
ejpam-2338	494	10	local	local	ADJ
ejpam-2338	494	11	-	-	PUNCT
ejpam-2338	494	12	to	to	ADP
ejpam-2338	494	13	-	-	PUNCT
ejpam-2338	494	14	global	global	ADJ
ejpam-2338	494	15	;	;	PUNCT
ejpam-2338	494	16	groupoids	groupoid	NOUN
ejpam-2338	494	17	;	;	PUNCT
ejpam-2338	494	18	higher	high	ADJ
ejpam-2338	494	19	dimensions	dimension	NOUN
ejpam-2338	494	20	,	,	PUNCT
ejpam-2338	494	21	in	in	ADP
ejpam-2338	494	22	:	:	PUNCT
ejpam-2338	494	23	jan	jan	PROPN
ejpam-2338	494	24	kubarski	kubarski	PROPN
ejpam-2338	494	25	,	,	PUNCT
ejpam-2338	494	26	jean	jean	PROPN
ejpam-2338	494	27	pradines	pradine	NOUN
ejpam-2338	494	28	,	,	PUNCT
ejpam-2338	494	29	tomasz	tomasz	PROPN
ejpam-2338	494	30	rybicki	rybicki	PROPN
ejpam-2338	494	31	,	,	PUNCT
ejpam-2338	494	32	and	and	CCONJ
ejpam-2338	494	33	robert	robert	PROPN
ejpam-2338	494	34	wolak	wolak	PROPN
ejpam-2338	494	35	(	(	PUNCT
ejpam-2338	494	36	eds	ed	NOUN
ejpam-2338	494	37	.	.	PUNCT
ejpam-2338	494	38	)	)	PUNCT
ejpam-2338	494	39	.	.	PUNCT
ejpam-2338	495	1	geometry	geometry	NOUN
ejpam-2338	495	2	and	and	CCONJ
ejpam-2338	495	3	topology	topology	NOUN
ejpam-2338	495	4	of	of	ADP
ejpam-2338	495	5	manifolds	manifold	NOUN
ejpam-2338	495	6	,	,	PUNCT
ejpam-2338	495	7	banach	banach	NOUN
ejpam-2338	495	8	center	center	NOUN
ejpam-2338	495	9	publications	publication	NOUN
ejpam-2338	495	10	,	,	PUNCT
ejpam-2338	495	11	vol	vol	NOUN
ejpam-2338	495	12	.	.	PROPN
ejpam-2338	495	13	76	76	NUM
ejpam-2338	495	14	,	,	PUNCT
ejpam-2338	495	15	polish	polish	PROPN
ejpam-2338	495	16	academy	academy	PROPN
ejpam-2338	495	17	sciences	sciences	PROPN
ejpam-2338	495	18	,	,	PUNCT
ejpam-2338	495	19	warsaw	warsaw	PROPN
ejpam-2338	495	20	,	,	PUNCT
ejpam-2338	495	21	pp	pp	X
ejpam-2338	495	22	.	.	PUNCT
ejpam-2338	496	1	51–63	51–63	NUM
ejpam-2338	496	2	.	.	NOUN
ejpam-2338	496	3	2007	2007	NUM
ejpam-2338	496	4	.	.	PUNCT
ejpam-2338	497	1	[	[	X
ejpam-2338	497	2	6	6	NUM
ejpam-2338	497	3	]	]	PUNCT
ejpam-2338	497	4	a.	a.	NOUN
ejpam-2338	497	5	h.	h.	PROPN
ejpam-2338	497	6	clifford	clifford	PROPN
ejpam-2338	497	7	.	.	PUNCT
ejpam-2338	498	1	semigroups	semigroup	NOUN
ejpam-2338	498	2	admitting	admit	VERB
ejpam-2338	498	3	relative	relative	ADJ
ejpam-2338	498	4	inverses	inverse	NOUN
ejpam-2338	498	5	,	,	PUNCT
ejpam-2338	498	6	ann	ann	PROPN
ejpam-2338	498	7	.	.	PROPN
ejpam-2338	498	8	math	math	PROPN
ejpam-2338	498	9	.	.	PUNCT
ejpam-2338	499	1	(	(	PUNCT
ejpam-2338	499	2	2	2	X
ejpam-2338	499	3	)	)	PUNCT
ejpam-2338	499	4	42	42	NUM
ejpam-2338	499	5	,	,	PUNCT
ejpam-2338	499	6	1037–1049	1037–1049	NUM
ejpam-2338	499	7	.	.	PUNCT
ejpam-2338	500	1	1941	1941	NUM
ejpam-2338	500	2	.	.	PUNCT
ejpam-2338	501	1	http://www.jstor.org/stable/1968781	http://www.jstor.org/stable/1968781	X
ejpam-2338	502	1	[	[	X
ejpam-2338	502	2	7	7	NUM
ejpam-2338	502	3	]	]	PUNCT
ejpam-2338	502	4	a.	a.	NOUN
ejpam-2338	502	5	cogliati	cogliati	NOUN
ejpam-2338	502	6	.	.	PUNCT
ejpam-2338	503	1	early	early	ADJ
ejpam-2338	503	2	history	history	NOUN
ejpam-2338	503	3	of	of	ADP
ejpam-2338	503	4	infinite	infinite	ADJ
ejpam-2338	503	5	continuous	continuous	ADJ
ejpam-2338	503	6	groups	group	NOUN
ejpam-2338	503	7	,	,	PUNCT
ejpam-2338	503	8	1883–1898	1883–1898	NUM
ejpam-2338	503	9	,	,	PUNCT
ejpam-2338	503	10	historia	historia	PROPN
ejpam-2338	503	11	mathematica	mathematica	PROPN
ejpam-2338	503	12	41(3	41(3	NUM
ejpam-2338	503	13	)	)	PUNCT
ejpam-2338	503	14	291–332	291–332	NUM
ejpam-2338	503	15	.	.	NOUN
ejpam-2338	503	16	2014	2014	NUM
ejpam-2338	503	17	.	.	PUNCT
ejpam-2338	504	1	http://dx.doi.org/10.1016/j.hm.2014.03.002	http://dx.doi.org/10.1016/j.hm.2014.03.002	NOUN
ejpam-2338	504	2	.	.	PUNCT
ejpam-2338	505	1	[	[	X
ejpam-2338	505	2	8	8	NUM
ejpam-2338	505	3	]	]	X
ejpam-2338	505	4	c.	c.	NOUN
ejpam-2338	505	5	cornock	cornock	NOUN
ejpam-2338	505	6	.	.	PUNCT
ejpam-2338	506	1	restriction	restriction	NOUN
ejpam-2338	506	2	semigroups	semigroup	VERB
ejpam-2338	506	3	:	:	PUNCT
ejpam-2338	506	4	structure	structure	NOUN
ejpam-2338	506	5	,	,	PUNCT
ejpam-2338	506	6	varieties	variety	NOUN
ejpam-2338	506	7	and	and	CCONJ
ejpam-2338	506	8	presentations	presentation	NOUN
ejpam-2338	506	9	,	,	PUNCT
ejpam-2338	506	10	phd	phd	NOUN
ejpam-2338	506	11	thesis	thesis	NOUN
ejpam-2338	506	12	,	,	PUNCT
ejpam-2338	506	13	university	university	PROPN
ejpam-2338	506	14	of	of	ADP
ejpam-2338	506	15	york	york	PROPN
ejpam-2338	506	16	,	,	PUNCT
ejpam-2338	506	17	2011	2011	NUM
ejpam-2338	506	18	.	.	PUNCT
ejpam-2338	507	1	[	[	X
ejpam-2338	507	2	9	9	NUM
ejpam-2338	507	3	]	]	PUNCT
ejpam-2338	507	4	c.	c.	NOUN
ejpam-2338	507	5	cornock	cornock	NOUN
ejpam-2338	507	6	and	and	CCONJ
ejpam-2338	507	7	v.	v.	ADP
ejpam-2338	507	8	gould	gould	PROPN
ejpam-2338	507	9	.	.	PUNCT
ejpam-2338	508	1	proper	proper	ADJ
ejpam-2338	508	2	two	two	NUM
ejpam-2338	508	3	-	-	PUNCT
ejpam-2338	508	4	sided	sided	ADJ
ejpam-2338	508	5	restriction	restriction	NOUN
ejpam-2338	508	6	semigroups	semigroup	NOUN
ejpam-2338	508	7	and	and	CCONJ
ejpam-2338	508	8	partial	partial	ADJ
ejpam-2338	508	9	actions	action	NOUN
ejpam-2338	508	10	,	,	PUNCT
ejpam-2338	508	11	journal	journal	NOUN
ejpam-2338	508	12	of	of	ADP
ejpam-2338	508	13	pure	pure	ADJ
ejpam-2338	508	14	and	and	CCONJ
ejpam-2338	508	15	applied	apply	VERB
ejpam-2338	508	16	algebra	algebra	NOUN
ejpam-2338	508	17	216(4	216(4	NUM
ejpam-2338	508	18	)	)	PUNCT
ejpam-2338	508	19	935–949	935–949	NUM
ejpam-2338	508	20	.	.	PUNCT
ejpam-2338	508	21	2012	2012	NUM
ejpam-2338	508	22	.	.	PUNCT
ejpam-2338	509	1	http://dx.doi.org/	http://dx.doi.org/	PRON
ejpam-2338	509	2	10.1016	10.1016	NUM
ejpam-2338	509	3	/	/	SYM
ejpam-2338	509	4	j.jpaa.2011.10.015	j.jpaa.2011.10.015	PROPN
ejpam-2338	510	1	[	[	X
ejpam-2338	510	2	10	10	NUM
ejpam-2338	510	3	]	]	X
ejpam-2338	510	4	r.	r.	PROPN
ejpam-2338	510	5	croisot	croisot	PROPN
ejpam-2338	510	6	.	.	PUNCT
ejpam-2338	511	1	une	une	PROPN
ejpam-2338	511	2	interprétation	interprétation	PROPN
ejpam-2338	511	3	des	des	PROPN
ejpam-2338	511	4	relations	relation	NOUN
ejpam-2338	511	5	d’équivalence	d’équivalence	NOUN
ejpam-2338	511	6	dans	dan	NOUN
ejpam-2338	511	7	un	un	PROPN
ejpam-2338	511	8	ensemble	ensemble	PROPN
ejpam-2338	511	9	,	,	PUNCT
ejpam-2338	511	10	comptes	compte	VERB
ejpam-2338	511	11	rendus	rendus	PROPN
ejpam-2338	511	12	hebdomadaires	hebdomadaires	PROPN
ejpam-2338	511	13	des	des	PROPN
ejpam-2338	511	14	séances	séances	PROPN
ejpam-2338	511	15	de	de	X
ejpam-2338	511	16	l’académie	l’académie	PROPN
ejpam-2338	511	17	des	des	PROPN
ejpam-2338	511	18	sciences	sciences	PROPN
ejpam-2338	511	19	de	de	PROPN
ejpam-2338	511	20	paris	paris	PROPN
ejpam-2338	511	21	226	226	NUM
ejpam-2338	511	22	616–617	616–617	NUM
ejpam-2338	511	23	.	.	PUNCT
ejpam-2338	512	1	1948	1948	NUM
ejpam-2338	513	1	[	[	X
ejpam-2338	513	2	11	11	NUM
ejpam-2338	513	3	]	]	PUNCT
ejpam-2338	513	4	l.	l.	PROPN
ejpam-2338	513	5	dubikajtis	dubikajtis	PROPN
ejpam-2338	513	6	.	.	PUNCT
ejpam-2338	514	1	certaines	certaines	PROPN
ejpam-2338	514	2	extensions	extension	NOUN
ejpam-2338	514	3	de	de	X
ejpam-2338	514	4	la	la	X
ejpam-2338	514	5	notion	notion	NOUN
ejpam-2338	514	6	de	de	X
ejpam-2338	514	7	groupoide	groupoide	PROPN
ejpam-2338	514	8	inductif	inductif	PROPN
ejpam-2338	514	9	et	et	PROPN
ejpam-2338	514	10	de	de	X
ejpam-2338	514	11	celle	celle	X
ejpam-2338	514	12	de	de	X
ejpam-2338	514	13	pseudogroupe	pseudogroupe	PROPN
ejpam-2338	514	14	,	,	PUNCT
ejpam-2338	514	15	colloquium	colloquium	NOUN
ejpam-2338	514	16	mathematicum	mathematicum	NOUN
ejpam-2338	514	17	12(2	12(2	NUM
ejpam-2338	514	18	)	)	PUNCT
ejpam-2338	514	19	163–185	163–185	NUM
ejpam-2338	514	20	.	.	PUNCT
ejpam-2338	514	21	1964	1964	NUM
ejpam-2338	514	22	.	.	PUNCT
ejpam-2338	515	1	http://pldml.icm.edu.pl/pldml/element/bwmeta1.element	http://pldml.icm.edu.pl/pldml/element/bwmeta1.element	NOUN
ejpam-2338	515	2	.	.	PUNCT
ejpam-2338	516	1	bwnjournal	bwnjournal	ADJ
ejpam-2338	516	2	-	-	PUNCT
ejpam-2338	516	3	article	article	NOUN
ejpam-2338	516	4	-	-	PUNCT
ejpam-2338	516	5	cmv12i2p163bwm	cmv12i2p163bwm	PROPN
ejpam-2338	516	6	[	[	X
ejpam-2338	516	7	12	12	NUM
ejpam-2338	516	8	]	]	PUNCT
ejpam-2338	516	9	l.	l.	PROPN
ejpam-2338	516	10	dubikajtis	dubikajtis	PROPN
ejpam-2338	516	11	and	and	CCONJ
ejpam-2338	516	12	p.	p.	PROPN
ejpam-2338	516	13	jarek	jarek	PROPN
ejpam-2338	516	14	.	.	PUNCT
ejpam-2338	517	1	pseudogroupe	pseudogroupe	PROPN
ejpam-2338	517	2	élémentaire	élémentaire	VERB
ejpam-2338	517	3	commutatif	commutatif	PROPN
ejpam-2338	517	4	et	et	NOUN
ejpam-2338	517	5	semi	semi	ADJ
ejpam-2338	517	6	-	-	ADJ
ejpam-2338	517	7	groupe	groupe	ADJ
ejpam-2338	517	8	régulier	régulier	NOUN
ejpam-2338	517	9	commutatif	commutatif	NOUN
ejpam-2338	517	10	,	,	PUNCT
ejpam-2338	517	11	colloquium	colloquium	NOUN
ejpam-2338	517	12	mathematicum	mathematicum	NOUN
ejpam-2338	517	13	12(2	12(2	NUM
ejpam-2338	517	14	)	)	PUNCT
ejpam-2338	518	1	187–193	187–193	NUM
ejpam-2338	518	2	.	.	PUNCT
ejpam-2338	518	3	1964	1964	NUM
ejpam-2338	518	4	.	.	PUNCT
ejpam-2338	519	1	http://pldml.icm.edu.pl/pldml/element/	http://pldml.icm.edu.pl/pldml/element/	X
ejpam-2338	519	2	bwmeta1.element.bwnjournal	bwmeta1.element.bwnjournal	ADJ
ejpam-2338	519	3	-	-	PUNCT
ejpam-2338	519	4	article	article	NOUN
ejpam-2338	519	5	-	-	PUNCT
ejpam-2338	519	6	cmv12i2p187bwm?q=	cmv12i2p187bwm?q=	X
ejpam-2338	519	7	051344f6	051344f6	NUM
ejpam-2338	519	8	-	-	PUNCT
ejpam-2338	519	9	7d2c-4487	7d2c-4487	NUM
ejpam-2338	519	10	-	-	PUNCT
ejpam-2338	519	11	be5d-5a5420f9c761$1&qt	be5d-5a5420f9c761$1&qt	NOUN
ejpam-2338	519	12	=	=	NOUN
ejpam-2338	519	13	in_page	in_page	NOUN
ejpam-2338	519	14	[	[	PUNCT
ejpam-2338	519	15	13	13	NUM
ejpam-2338	519	16	]	]	X
ejpam-2338	519	17	ch	ch	NOUN
ejpam-2338	519	18	.	.	PROPN
ejpam-2338	519	19	ehresmann	ehresmann	PROPN
ejpam-2338	519	20	.	.	PUNCT
ejpam-2338	520	1	gattungen	gattungen	PROPN
ejpam-2338	520	2	von	von	PROPN
ejpam-2338	520	3	lokalen	lokalen	PROPN
ejpam-2338	520	4	strukturen	strukturen	PROPN
ejpam-2338	520	5	,	,	PUNCT
ejpam-2338	520	6	jahresbericht	jahresbericht	PROPN
ejpam-2338	520	7	der	der	PROPN
ejpam-2338	520	8	deutschen	deutschen	PROPN
ejpam-2338	520	9	mathematiker	mathematiker	PROPN
ejpam-2338	520	10	-	-	PUNCT
ejpam-2338	520	11	vereinigung	vereinigung	PROPN
ejpam-2338	520	12	60	60	NUM
ejpam-2338	520	13	49–77	49–77	NUM
ejpam-2338	520	14	.	.	PUNCT
ejpam-2338	521	1	1957	1957	NUM
ejpam-2338	521	2	.	.	PUNCT
ejpam-2338	522	1	http://gdz.sub.uni-goettingen.de/	http://gdz.sub.uni-goettingen.de/	PROPN
ejpam-2338	522	2	dms	dms	NOUN
ejpam-2338	522	3	/	/	SYM
ejpam-2338	522	4	load	load	NOUN
ejpam-2338	522	5	/	/	SYM
ejpam-2338	522	6	img/?ppn	img/?ppn	NOUN
ejpam-2338	522	7	=	=	NOUN
ejpam-2338	522	8	gdzppn002134942&iddoc=248455	gdzppn002134942&iddoc=248455	NOUN
ejpam-2338	523	1	[	[	X
ejpam-2338	523	2	14	14	NUM
ejpam-2338	523	3	]	]	X
ejpam-2338	523	4	ch	ch	NOUN
ejpam-2338	523	5	.	.	PUNCT
ejpam-2338	523	6	ehresmann	ehresmann	PROPN
ejpam-2338	523	7	.	.	PUNCT
ejpam-2338	524	1	oeuvres	oeuvre	NOUN
ejpam-2338	524	2	complètes	complète	NOUN
ejpam-2338	524	3	et	et	PROPN
ejpam-2338	524	4	commentées	commentées	PROPN
ejpam-2338	524	5	,	,	PUNCT
ejpam-2338	524	6	supplements	supplement	NOUN
ejpam-2338	524	7	to	to	ADP
ejpam-2338	524	8	cahiers	cahier	NOUN
ejpam-2338	524	9	de	de	X
ejpam-2338	524	10	topologie	topologie	PROPN
ejpam-2338	524	11	et	et	PROPN
ejpam-2338	524	12	géométrie	géométrie	VERB
ejpam-2338	524	13	différentielle	différentielle	PROPN
ejpam-2338	524	14	(	(	PUNCT
ejpam-2338	524	15	a.	a.	PROPN
ejpam-2338	524	16	c.	c.	PROPN
ejpam-2338	524	17	ehresmann	ehresmann	PROPN
ejpam-2338	524	18	,	,	PUNCT
ejpam-2338	524	19	ed	ed	NOUN
ejpam-2338	524	20	.	.	PUNCT
ejpam-2338	524	21	)	)	PUNCT
ejpam-2338	524	22	,	,	PUNCT
ejpam-2338	524	23	amiens	amien	NOUN
ejpam-2338	524	24	,	,	PUNCT
ejpam-2338	524	25	1980–83	1980–83	NUM
ejpam-2338	524	26	.	.	PUNCT
ejpam-2338	525	1	references	reference	NOUN
ejpam-2338	525	2	317	317	NUM
ejpam-2338	525	3	[	[	X
ejpam-2338	525	4	15	15	NUM
ejpam-2338	525	5	]	]	X
ejpam-2338	525	6	a.	a.	PROPN
ejpam-2338	525	7	el	el	PROPN
ejpam-2338	525	8	-	-	PUNCT
ejpam-2338	525	9	qallali	qallali	PROPN
ejpam-2338	525	10	.	.	PUNCT
ejpam-2338	525	11	structure	structure	NOUN
ejpam-2338	525	12	theory	theory	NOUN
ejpam-2338	525	13	for	for	ADP
ejpam-2338	525	14	abundant	abundant	ADJ
ejpam-2338	525	15	and	and	CCONJ
ejpam-2338	525	16	related	related	ADJ
ejpam-2338	525	17	semigroups	semigroup	NOUN
ejpam-2338	525	18	,	,	PUNCT
ejpam-2338	525	19	dphil	dphil	ADJ
ejpam-2338	525	20	thesis	thesis	NOUN
ejpam-2338	525	21	,	,	PUNCT
ejpam-2338	525	22	university	university	PROPN
ejpam-2338	525	23	of	of	ADP
ejpam-2338	525	24	york	york	PROPN
ejpam-2338	525	25	,	,	PUNCT
ejpam-2338	525	26	1980	1980	NUM
ejpam-2338	525	27	.	.	PUNCT
ejpam-2338	526	1	[	[	X
ejpam-2338	526	2	16	16	NUM
ejpam-2338	526	3	]	]	X
ejpam-2338	526	4	a.	a.	PROPN
ejpam-2338	526	5	el	el	PROPN
ejpam-2338	526	6	-	-	PUNCT
ejpam-2338	526	7	qallali	qallali	PROPN
ejpam-2338	526	8	,	,	PUNCT
ejpam-2338	526	9	j.	j.	PROPN
ejpam-2338	526	10	fountain	fountain	PROPN
ejpam-2338	526	11	,	,	PUNCT
ejpam-2338	526	12	and	and	CCONJ
ejpam-2338	526	13	v.	v.	ADP
ejpam-2338	526	14	gould	gould	PROPN
ejpam-2338	526	15	.	.	PUNCT
ejpam-2338	527	1	fundamental	fundamental	ADJ
ejpam-2338	527	2	representations	representation	NOUN
ejpam-2338	527	3	for	for	ADP
ejpam-2338	527	4	classes	class	NOUN
ejpam-2338	527	5	of	of	ADP
ejpam-2338	527	6	semigroups	semigroup	NOUN
ejpam-2338	527	7	containing	contain	VERB
ejpam-2338	527	8	a	a	DET
ejpam-2338	527	9	band	band	NOUN
ejpam-2338	527	10	of	of	ADP
ejpam-2338	527	11	idempotents	idempotent	NOUN
ejpam-2338	527	12	,	,	PUNCT
ejpam-2338	527	13	communications	communication	NOUN
ejpam-2338	527	14	in	in	ADP
ejpam-2338	527	15	algebra	algebra	NOUN
ejpam-2338	527	16	36	36	NUM
ejpam-2338	527	17	2998–3031	2998–3031	NUM
ejpam-2338	527	18	.	.	PUNCT
ejpam-2338	528	1	2008	2008	NUM
ejpam-2338	528	2	.	.	PUNCT
ejpam-2338	529	1	http://dx.doi.org/10.1080/00927870802110649	http://dx.doi.org/10.1080/00927870802110649	NOUN
ejpam-2338	530	1	[	[	X
ejpam-2338	530	2	17	17	NUM
ejpam-2338	530	3	]	]	X
ejpam-2338	530	4	j.	j.	PROPN
ejpam-2338	530	5	fountain	fountain	PROPN
ejpam-2338	530	6	.	.	PUNCT
ejpam-2338	531	1	a	a	DET
ejpam-2338	531	2	class	class	NOUN
ejpam-2338	531	3	of	of	ADP
ejpam-2338	531	4	right	right	ADJ
ejpam-2338	531	5	pp	pp	ADP
ejpam-2338	531	6	monoids	monoid	NOUN
ejpam-2338	531	7	,	,	PUNCT
ejpam-2338	531	8	quarterly	quarterly	ADJ
ejpam-2338	531	9	journal	journal	NOUN
ejpam-2338	531	10	of	of	ADP
ejpam-2338	531	11	mathematics	mathematic	NOUN
ejpam-2338	531	12	,	,	PUNCT
ejpam-2338	531	13	oxford	oxford	PROPN
ejpam-2338	531	14	(	(	PUNCT
ejpam-2338	531	15	2	2	NUM
ejpam-2338	531	16	)	)	PUNCT
ejpam-2338	531	17	28	28	NUM
ejpam-2338	531	18	285–300	285–300	NUM
ejpam-2338	531	19	.	.	PUNCT
ejpam-2338	531	20	1977	1977	NUM
ejpam-2338	531	21	.	.	PUNCT
ejpam-2338	532	1	http://dx.doi.org/10.1093/qmath/28.3.285	http://dx.doi.org/10.1093/qmath/28.3.285	PROPN
ejpam-2338	532	2	[	[	X
ejpam-2338	532	3	18	18	NUM
ejpam-2338	532	4	]	]	X
ejpam-2338	532	5	j.	j.	PROPN
ejpam-2338	532	6	fountain	fountain	PROPN
ejpam-2338	532	7	.	.	PUNCT
ejpam-2338	533	1	adequate	adequate	ADJ
ejpam-2338	533	2	semigroups	semigroup	NOUN
ejpam-2338	533	3	,	,	PUNCT
ejpam-2338	533	4	proceedings	proceeding	NOUN
ejpam-2338	533	5	of	of	ADP
ejpam-2338	533	6	the	the	DET
ejpam-2338	533	7	edinburgh	edinburgh	PROPN
ejpam-2338	533	8	mathematical	mathematical	PROPN
ejpam-2338	533	9	society	society	NOUN
ejpam-2338	533	10	(	(	PUNCT
ejpam-2338	533	11	2	2	NUM
ejpam-2338	533	12	)	)	PUNCT
ejpam-2338	533	13	22	22	NUM
ejpam-2338	533	14	113–125	113–125	NUM
ejpam-2338	533	15	.	.	PUNCT
ejpam-2338	533	16	1979	1979	NUM
ejpam-2338	533	17	.	.	PUNCT
ejpam-2338	534	1	http://dx.doi.org/10.1017/s0013091500016230	http://dx.doi.org/10.1017/s0013091500016230	X
ejpam-2338	535	1	[	[	X
ejpam-2338	535	2	19	19	NUM
ejpam-2338	535	3	]	]	PUNCT
ejpam-2338	535	4	j.	j.	PROPN
ejpam-2338	535	5	fountain	fountain	PROPN
ejpam-2338	535	6	.	.	PUNCT
ejpam-2338	536	1	an	an	DET
ejpam-2338	536	2	introduction	introduction	NOUN
ejpam-2338	536	3	to	to	ADP
ejpam-2338	536	4	covers	cover	NOUN
ejpam-2338	536	5	for	for	ADP
ejpam-2338	536	6	semigroups	semigroup	NOUN
ejpam-2338	536	7	,	,	PUNCT
ejpam-2338	536	8	in	in	ADP
ejpam-2338	536	9	:	:	PUNCT
ejpam-2338	536	10	gracinda	gracinda	PROPN
ejpam-2338	536	11	m.	m.	PROPN
ejpam-2338	536	12	s.	s.	PROPN
ejpam-2338	536	13	gomes	gomes	PROPN
ejpam-2338	536	14	,	,	PUNCT
ejpam-2338	536	15	jean	jean	PROPN
ejpam-2338	536	16	éric	éric	PROPN
ejpam-2338	536	17	pin	pin	PROPN
ejpam-2338	536	18	,	,	PUNCT
ejpam-2338	536	19	and	and	CCONJ
ejpam-2338	536	20	pedro	pedro	PROPN
ejpam-2338	536	21	v.	v.	ADP
ejpam-2338	536	22	silva	silva	PROPN
ejpam-2338	536	23	(	(	PUNCT
ejpam-2338	536	24	eds	eds	PROPN
ejpam-2338	536	25	.	.	PUNCT
ejpam-2338	536	26	)	)	PUNCT
ejpam-2338	536	27	.	.	PUNCT
ejpam-2338	537	1	semigroups	semigroup	NOUN
ejpam-2338	537	2	,	,	PUNCT
ejpam-2338	537	3	algorithms	algorithm	NOUN
ejpam-2338	537	4	,	,	PUNCT
ejpam-2338	537	5	automata	automata	NOUN
ejpam-2338	537	6	and	and	CCONJ
ejpam-2338	537	7	languages	language	NOUN
ejpam-2338	537	8	(	(	PUNCT
ejpam-2338	537	9	coimbra	coimbra	NOUN
ejpam-2338	537	10	,	,	PUNCT
ejpam-2338	537	11	2001	2001	NUM
ejpam-2338	537	12	)	)	PUNCT
ejpam-2338	537	13	,	,	PUNCT
ejpam-2338	537	14	world	world	NOUN
ejpam-2338	537	15	scientific	scientific	ADJ
ejpam-2338	537	16	publications	publication	NOUN
ejpam-2338	537	17	,	,	PUNCT
ejpam-2338	537	18	river	river	NOUN
ejpam-2338	537	19	edge	edge	NOUN
ejpam-2338	537	20	,	,	PUNCT
ejpam-2338	537	21	nj	nj	PROPN
ejpam-2338	537	22	,	,	PUNCT
ejpam-2338	537	23	pp	pp	ADP
ejpam-2338	537	24	.	.	PUNCT
ejpam-2338	538	1	155–194	155–194	NUM
ejpam-2338	538	2	.	.	PUNCT
ejpam-2338	539	1	2002	2002	NUM
ejpam-2338	539	2	.	.	PUNCT
ejpam-2338	540	1	[	[	X
ejpam-2338	540	2	20	20	NUM
ejpam-2338	540	3	]	]	PUNCT
ejpam-2338	540	4	j.	j.	PROPN
ejpam-2338	540	5	fountain	fountain	PROPN
ejpam-2338	540	6	.	.	PUNCT
ejpam-2338	541	1	the	the	DET
ejpam-2338	541	2	work	work	NOUN
ejpam-2338	541	3	of	of	ADP
ejpam-2338	541	4	douglas	douglas	PROPN
ejpam-2338	541	5	munn	munn	PROPN
ejpam-2338	541	6	and	and	CCONJ
ejpam-2338	541	7	its	its	PRON
ejpam-2338	541	8	legacy	legacy	NOUN
ejpam-2338	541	9	,	,	PUNCT
ejpam-2338	541	10	semigroup	semigroup	PROPN
ejpam-2338	541	11	forum	forum	PROPN
ejpam-2338	541	12	81(1	81(1	NUM
ejpam-2338	541	13	)	)	PUNCT
ejpam-2338	541	14	2–25	2–25	NOUN
ejpam-2338	541	15	.	.	PUNCT
ejpam-2338	541	16	2010	2010	NUM
ejpam-2338	541	17	;	;	PUNCT
ejpam-2338	541	18	erratum	erratum	PROPN
ejpam-2338	541	19	:	:	PUNCT
ejpam-2338	541	20	ibid	ibid	NOUN
ejpam-2338	541	21	.	.	PUNCT
ejpam-2338	542	1	82(1	82(1	NOUN
ejpam-2338	542	2	)	)	PUNCT
ejpam-2338	542	3	197	197	NUM
ejpam-2338	542	4	.	.	PUNCT
ejpam-2338	543	1	2011	2011	NUM
ejpam-2338	543	2	.	.	PUNCT
ejpam-2338	544	1	http://dx.doi.org/10.1007/	http://dx.doi.org/10.1007/	NOUN
ejpam-2338	544	2	s00233	s00233	NOUN
ejpam-2338	544	3	-	-	PUNCT
ejpam-2338	544	4	010	010	NUM
ejpam-2338	544	5	-	-	PUNCT
ejpam-2338	544	6	9240	9240	NUM
ejpam-2338	544	7	-	-	SYM
ejpam-2338	544	8	3	3	NUM
ejpam-2338	544	9	,	,	PUNCT
ejpam-2338	544	10	http://dx.doi.org/10.1007/s00233-010-9277-3	http://dx.doi.org/10.1007/s00233-010-9277-3	PUNCT
ejpam-2338	545	1	[	[	X
ejpam-2338	545	2	21	21	NUM
ejpam-2338	545	3	]	]	X
ejpam-2338	545	4	j.	j.	PROPN
ejpam-2338	545	5	fountain	fountain	PROPN
ejpam-2338	545	6	,	,	PUNCT
ejpam-2338	545	7	g.	g.	PROPN
ejpam-2338	545	8	gomes	gomes	PROPN
ejpam-2338	545	9	,	,	PUNCT
ejpam-2338	545	10	and	and	CCONJ
ejpam-2338	545	11	v.	v.	ADP
ejpam-2338	545	12	gould	gould	PROPN
ejpam-2338	545	13	.	.	PUNCT
ejpam-2338	546	1	a	a	DET
ejpam-2338	546	2	munn	munn	NOUN
ejpam-2338	546	3	-	-	PUNCT
ejpam-2338	546	4	type	type	NOUN
ejpam-2338	546	5	representation	representation	NOUN
ejpam-2338	546	6	for	for	ADP
ejpam-2338	546	7	a	a	DET
ejpam-2338	546	8	class	class	NOUN
ejpam-2338	546	9	of	of	ADP
ejpam-2338	546	10	esemiadequate	esemiadequate	NOUN
ejpam-2338	546	11	semigroups	semigroup	NOUN
ejpam-2338	546	12	,	,	PUNCT
ejpam-2338	546	13	journal	journal	NOUN
ejpam-2338	546	14	of	of	ADP
ejpam-2338	546	15	algebra	algebra	NOUN
ejpam-2338	546	16	218	218	NUM
ejpam-2338	546	17	693–714	693–714	NUM
ejpam-2338	546	18	.	.	PUNCT
ejpam-2338	546	19	1999	1999	NUM
ejpam-2338	546	20	.	.	PUNCT
ejpam-2338	547	1	http://dx.doi	http://dx.doi	NOUN
ejpam-2338	547	2	.	.	PUNCT
ejpam-2338	548	1	org/10.1006	org/10.1006	PROPN
ejpam-2338	548	2	/	/	SYM
ejpam-2338	548	3	jabr.1999.7871	jabr.1999.7871	PROPN
ejpam-2338	549	1	[	[	X
ejpam-2338	549	2	22	22	NUM
ejpam-2338	549	3	]	]	X
ejpam-2338	549	4	n.	n.	PROPN
ejpam-2338	549	5	d.	d.	PROPN
ejpam-2338	549	6	gilbert	gilbert	PROPN
ejpam-2338	549	7	.	.	PUNCT
ejpam-2338	550	1	actions	action	NOUN
ejpam-2338	550	2	and	and	CCONJ
ejpam-2338	550	3	expansions	expansion	NOUN
ejpam-2338	550	4	of	of	ADP
ejpam-2338	550	5	ordered	order	VERB
ejpam-2338	550	6	groupoids	groupoid	NOUN
ejpam-2338	550	7	,	,	PUNCT
ejpam-2338	550	8	journal	journal	NOUN
ejpam-2338	550	9	of	of	ADP
ejpam-2338	550	10	pure	pure	ADJ
ejpam-2338	550	11	and	and	CCONJ
ejpam-2338	550	12	applied	applied	ADJ
ejpam-2338	550	13	algebra	algebra	NOUN
ejpam-2338	550	14	198	198	NUM
ejpam-2338	550	15	175–195	175–195	NUM
ejpam-2338	550	16	.	.	PROPN
ejpam-2338	550	17	2005	2005	NUM
ejpam-2338	550	18	.	.	PUNCT
ejpam-2338	551	1	http://dx.doi.org/10.1016/j.jpaa.2004.11.006	http://dx.doi.org/10.1016/j.jpaa.2004.11.006	NUM
ejpam-2338	551	2	[	[	X
ejpam-2338	551	3	23	23	NUM
ejpam-2338	551	4	]	]	X
ejpam-2338	551	5	n.	n.	PROPN
ejpam-2338	551	6	d.	d.	PROPN
ejpam-2338	551	7	gilbert	gilbert	PROPN
ejpam-2338	551	8	.	.	PUNCT
ejpam-2338	552	1	a	a	DET
ejpam-2338	552	2	p	p	NOUN
ejpam-2338	552	3	-	-	PUNCT
ejpam-2338	552	4	theorem	theorem	NOUN
ejpam-2338	552	5	for	for	ADP
ejpam-2338	552	6	ordered	order	VERB
ejpam-2338	552	7	groupoids	groupoid	NOUN
ejpam-2338	552	8	,	,	PUNCT
ejpam-2338	552	9	in	in	ADP
ejpam-2338	552	10	:	:	PUNCT
ejpam-2338	552	11	j.	j.	PROPN
ejpam-2338	552	12	m.	m.	PROPN
ejpam-2338	552	13	andré	andré	PROPN
ejpam-2338	552	14	,	,	PUNCT
ejpam-2338	552	15	m.	m.	PROPN
ejpam-2338	552	16	j.	j.	PROPN
ejpam-2338	552	17	j.	j.	PROPN
ejpam-2338	552	18	branco	branco	PROPN
ejpam-2338	552	19	,	,	PUNCT
ejpam-2338	552	20	v.	v.	PROPN
ejpam-2338	552	21	h.	h.	PROPN
ejpam-2338	552	22	fernandes	fernandes	PROPN
ejpam-2338	552	23	,	,	PUNCT
ejpam-2338	552	24	j.	j.	PROPN
ejpam-2338	552	25	fountain	fountain	PROPN
ejpam-2338	552	26	,	,	PUNCT
ejpam-2338	552	27	g.	g.	PROPN
ejpam-2338	552	28	m.	m.	PROPN
ejpam-2338	552	29	s.	s.	PROPN
ejpam-2338	552	30	gomes	gomes	PROPN
ejpam-2338	552	31	,	,	PUNCT
ejpam-2338	552	32	and	and	CCONJ
ejpam-2338	552	33	j.	j.	PROPN
ejpam-2338	552	34	c.	c.	PROPN
ejpam-2338	552	35	meakin	meakin	PROPN
ejpam-2338	552	36	(	(	PUNCT
ejpam-2338	552	37	eds	ed	NOUN
ejpam-2338	552	38	.	.	PUNCT
ejpam-2338	552	39	)	)	PUNCT
ejpam-2338	552	40	.	.	PUNCT
ejpam-2338	553	1	proceedings	proceeding	NOUN
ejpam-2338	553	2	of	of	ADP
ejpam-2338	553	3	the	the	DET
ejpam-2338	553	4	international	international	ADJ
ejpam-2338	553	5	conference	conference	NOUN
ejpam-2338	553	6	“	"	PUNCT
ejpam-2338	553	7	semigroups	semigroup	NOUN
ejpam-2338	553	8	and	and	CCONJ
ejpam-2338	553	9	formal	formal	ADJ
ejpam-2338	553	10	languages	language	NOUN
ejpam-2338	553	11	”	"	PUNCT
ejpam-2338	553	12	in	in	ADP
ejpam-2338	553	13	honour	honour	NOUN
ejpam-2338	553	14	of	of	ADP
ejpam-2338	553	15	the	the	DET
ejpam-2338	553	16	65th	65th	ADJ
ejpam-2338	553	17	birthday	birthday	NOUN
ejpam-2338	553	18	of	of	ADP
ejpam-2338	553	19	donald	donald	PROPN
ejpam-2338	553	20	b.	b.	PROPN
ejpam-2338	553	21	mcalister	mcalister	PROPN
ejpam-2338	553	22	,	,	PUNCT
ejpam-2338	553	23	world	world	NOUN
ejpam-2338	553	24	scientific	scientific	ADJ
ejpam-2338	553	25	publications	publication	NOUN
ejpam-2338	553	26	,	,	PUNCT
ejpam-2338	553	27	hackensack	hackensack	PROPN
ejpam-2338	553	28	,	,	PUNCT
ejpam-2338	553	29	nj	nj	PROPN
ejpam-2338	553	30	,	,	PUNCT
ejpam-2338	553	31	pp	pp	ADJ
ejpam-2338	553	32	.	.	PUNCT
ejpam-2338	554	1	84	84	NUM
ejpam-2338	554	2	–	–	PUNCT
ejpam-2338	554	3	100	100	NUM
ejpam-2338	554	4	.	.	PUNCT
ejpam-2338	554	5	2007	2007	NUM
ejpam-2338	554	6	.	.	PUNCT
ejpam-2338	555	1	[	[	X
ejpam-2338	555	2	24	24	NUM
ejpam-2338	555	3	]	]	X
ejpam-2338	555	4	s.	s.	PROPN
ejpam-2338	555	5	goła̧b	goła̧b	PROPN
ejpam-2338	555	6	.	.	PUNCT
ejpam-2338	556	1	über	über	PROPN
ejpam-2338	556	2	den	den	PROPN
ejpam-2338	556	3	begriff	begriff	PROPN
ejpam-2338	556	4	der	der	NOUN
ejpam-2338	556	5	‘	'	PUNCT
ejpam-2338	556	6	pseudogruppe	pseudogruppe	PROPN
ejpam-2338	556	7	von	von	PROPN
ejpam-2338	556	8	transformationen	transformationen	PROPN
ejpam-2338	556	9	’	'	PUNCT
ejpam-2338	556	10	,	,	PUNCT
ejpam-2338	556	11	mathematische	mathematische	NOUN
ejpam-2338	556	12	annalen	annalen	VERB
ejpam-2338	556	13	116	116	NUM
ejpam-2338	556	14	768–780	768–780	NUM
ejpam-2338	556	15	.	.	PUNCT
ejpam-2338	556	16	1939	1939	NUM
ejpam-2338	556	17	.	.	PUNCT
ejpam-2338	557	1	http://dx.doi.org/10.1007/bf01597390	http://dx.doi.org/10.1007/bf01597390	X
ejpam-2338	558	1	[	[	X
ejpam-2338	558	2	25	25	NUM
ejpam-2338	558	3	]	]	X
ejpam-2338	558	4	g.	g.	PROPN
ejpam-2338	558	5	m.	m.	PROPN
ejpam-2338	558	6	s.	s.	PROPN
ejpam-2338	558	7	gomes	gomes	PROPN
ejpam-2338	558	8	and	and	CCONJ
ejpam-2338	558	9	v.	v.	ADP
ejpam-2338	558	10	gould	gould	PROPN
ejpam-2338	558	11	.	.	PUNCT
ejpam-2338	559	1	proper	proper	ADJ
ejpam-2338	559	2	weakly	weakly	ADJ
ejpam-2338	559	3	left	left	ADJ
ejpam-2338	559	4	ample	ample	ADJ
ejpam-2338	559	5	semigroups	semigroup	NOUN
ejpam-2338	559	6	,	,	PUNCT
ejpam-2338	559	7	international	international	ADJ
ejpam-2338	559	8	journal	journal	NOUN
ejpam-2338	559	9	of	of	ADP
ejpam-2338	559	10	algebra	algebra	NOUN
ejpam-2338	559	11	and	and	CCONJ
ejpam-2338	559	12	computation	computation	NOUN
ejpam-2338	559	13	9	9	NUM
ejpam-2338	559	14	721–739	721–739	NUM
ejpam-2338	559	15	.	.	PUNCT
ejpam-2338	559	16	1999	1999	NUM
ejpam-2338	559	17	.	.	PUNCT
ejpam-2338	560	1	http://dx.doi.org/10.1142/	http://dx.doi.org/10.1142/	PUNCT
ejpam-2338	561	1	s0218196799000412	s0218196799000412	INTJ
ejpam-2338	561	2	[	[	X
ejpam-2338	561	3	26	26	NUM
ejpam-2338	561	4	]	]	X
ejpam-2338	561	5	g.	g.	PROPN
ejpam-2338	561	6	m.	m.	PROPN
ejpam-2338	561	7	s.	s.	PROPN
ejpam-2338	561	8	gomes	gomes	PROPN
ejpam-2338	561	9	and	and	CCONJ
ejpam-2338	561	10	v.	v.	ADP
ejpam-2338	561	11	gould	gould	PROPN
ejpam-2338	561	12	.	.	PUNCT
ejpam-2338	562	1	graph	graph	NOUN
ejpam-2338	562	2	expansions	expansion	NOUN
ejpam-2338	562	3	of	of	ADP
ejpam-2338	562	4	unipotent	unipotent	ADJ
ejpam-2338	562	5	monoids	monoid	NOUN
ejpam-2338	562	6	,	,	PUNCT
ejpam-2338	562	7	communications	communication	NOUN
ejpam-2338	562	8	in	in	ADP
ejpam-2338	562	9	algebra	algebra	NOUN
ejpam-2338	562	10	28	28	NUM
ejpam-2338	562	11	447–463	447–463	NUM
ejpam-2338	562	12	.	.	PROPN
ejpam-2338	562	13	2000	2000	NUM
ejpam-2338	562	14	.	.	PUNCT
ejpam-2338	563	1	http://dx.doi.org/10.1080/00927870008841083	http://dx.doi.org/10.1080/00927870008841083	PROPN
ejpam-2338	564	1	[	[	X
ejpam-2338	564	2	27	27	NUM
ejpam-2338	564	3	]	]	X
ejpam-2338	564	4	g.	g.	PROPN
ejpam-2338	564	5	m.	m.	PROPN
ejpam-2338	564	6	s.	s.	PROPN
ejpam-2338	564	7	gomes	gomes	PROPN
ejpam-2338	564	8	and	and	CCONJ
ejpam-2338	564	9	v.	v.	ADP
ejpam-2338	564	10	gould	gould	PROPN
ejpam-2338	564	11	.	.	PUNCT
ejpam-2338	565	1	fundamental	fundamental	ADJ
ejpam-2338	565	2	ehresmann	ehresmann	PROPN
ejpam-2338	565	3	semigroups	semigroup	NOUN
ejpam-2338	565	4	,	,	PUNCT
ejpam-2338	565	5	semigroup	semigroup	PROPN
ejpam-2338	565	6	forum	forum	PROPN
ejpam-2338	565	7	63	63	NUM
ejpam-2338	565	8	11–33	11–33	NUM
ejpam-2338	565	9	.	.	PUNCT
ejpam-2338	566	1	2001	2001	NUM
ejpam-2338	566	2	.	.	PUNCT
ejpam-2338	567	1	http://dx.doi.org/10.1007/s002330010054	http://dx.doi.org/10.1007/s002330010054	PROPN
ejpam-2338	567	2	references	reference	NOUN
ejpam-2338	567	3	318	318	NUM
ejpam-2338	567	4	[	[	X
ejpam-2338	567	5	28	28	NUM
ejpam-2338	567	6	]	]	X
ejpam-2338	567	7	g.	g.	PROPN
ejpam-2338	567	8	m.	m.	PROPN
ejpam-2338	567	9	s.	s.	PROPN
ejpam-2338	567	10	gomes	gomes	PROPN
ejpam-2338	567	11	and	and	CCONJ
ejpam-2338	567	12	v.	v.	PROPN
ejpam-2338	567	13	gould	gould	PROPN
ejpam-2338	567	14	.	.	PUNCT
ejpam-2338	568	1	finite	finite	VERB
ejpam-2338	568	2	proper	proper	ADJ
ejpam-2338	568	3	covers	cover	NOUN
ejpam-2338	568	4	in	in	ADP
ejpam-2338	568	5	a	a	DET
ejpam-2338	568	6	class	class	NOUN
ejpam-2338	568	7	of	of	ADP
ejpam-2338	568	8	finite	finite	ADJ
ejpam-2338	568	9	semigroups	semigroup	NOUN
ejpam-2338	568	10	with	with	ADP
ejpam-2338	568	11	commuting	commuting	NOUN
ejpam-2338	568	12	idempotents	idempotent	NOUN
ejpam-2338	568	13	,	,	PUNCT
ejpam-2338	568	14	semigroup	semigroup	PROPN
ejpam-2338	568	15	forum	forum	PROPN
ejpam-2338	568	16	66	66	NUM
ejpam-2338	568	17	433–454	433–454	NUM
ejpam-2338	568	18	.	.	PUNCT
ejpam-2338	568	19	2003	2003	NUM
ejpam-2338	568	20	.	.	PUNCT
ejpam-2338	569	1	http://dx.doi.org/	http://dx.doi.org/	X
ejpam-2338	569	2	10.1007	10.1007	NUM
ejpam-2338	569	3	/	/	SYM
ejpam-2338	569	4	s002330010144	s002330010144	PROPN
ejpam-2338	569	5	[	[	X
ejpam-2338	569	6	29	29	NUM
ejpam-2338	569	7	]	]	X
ejpam-2338	569	8	v.	v.	PROPN
ejpam-2338	569	9	gould	gould	PROPN
ejpam-2338	569	10	.	.	PUNCT
ejpam-2338	570	1	restriction	restriction	NOUN
ejpam-2338	570	2	and	and	CCONJ
ejpam-2338	570	3	ehresmann	ehresmann	PROPN
ejpam-2338	570	4	semigroups	semigroup	NOUN
ejpam-2338	570	5	,	,	PUNCT
ejpam-2338	570	6	in	in	ADP
ejpam-2338	570	7	wanida	wanida	PROPN
ejpam-2338	570	8	hemakul	hemakul	PROPN
ejpam-2338	570	9	,	,	PUNCT
ejpam-2338	570	10	sri	sri	PROPN
ejpam-2338	570	11	wahyuni	wahyuni	PROPN
ejpam-2338	570	12	,	,	PUNCT
ejpam-2338	570	13	and	and	CCONJ
ejpam-2338	570	14	polly	polly	PROPN
ejpam-2338	570	15	w.	w.	PROPN
ejpam-2338	570	16	sy	sy	PROPN
ejpam-2338	570	17	(	(	PUNCT
ejpam-2338	570	18	eds	ed	NOUN
ejpam-2338	570	19	.	.	PUNCT
ejpam-2338	570	20	)	)	PUNCT
ejpam-2338	570	21	.	.	PUNCT
ejpam-2338	571	1	proceedings	proceeding	NOUN
ejpam-2338	571	2	of	of	ADP
ejpam-2338	571	3	the	the	DET
ejpam-2338	571	4	international	international	ADJ
ejpam-2338	571	5	conference	conference	NOUN
ejpam-2338	571	6	on	on	ADP
ejpam-2338	571	7	algebra	algebra	PROPN
ejpam-2338	571	8	2010	2010	NUM
ejpam-2338	571	9	,	,	PUNCT
ejpam-2338	571	10	advances	advance	NOUN
ejpam-2338	571	11	in	in	ADP
ejpam-2338	571	12	algebraic	algebraic	ADJ
ejpam-2338	571	13	structures	structure	NOUN
ejpam-2338	571	14	,	,	PUNCT
ejpam-2338	571	15	world	world	NOUN
ejpam-2338	571	16	scientific	scientific	ADJ
ejpam-2338	571	17	,	,	PUNCT
ejpam-2338	571	18	pp	pp	ADJ
ejpam-2338	571	19	.	.	PUNCT
ejpam-2338	572	1	265–288	265–288	NUM
ejpam-2338	572	2	.	.	NOUN
ejpam-2338	572	3	2012	2012	NUM
ejpam-2338	572	4	.	.	PUNCT
ejpam-2338	573	1	[	[	X
ejpam-2338	573	2	30	30	NUM
ejpam-2338	573	3	]	]	X
ejpam-2338	573	4	v.	v.	PROPN
ejpam-2338	573	5	gould	gould	PROPN
ejpam-2338	573	6	and	and	CCONJ
ejpam-2338	573	7	c.	c.	PROPN
ejpam-2338	573	8	hollings	holling	NOUN
ejpam-2338	573	9	,	,	PUNCT
ejpam-2338	573	10	restriction	restriction	NOUN
ejpam-2338	573	11	semigroups	semigroup	NOUN
ejpam-2338	573	12	and	and	CCONJ
ejpam-2338	573	13	inductive	inductive	ADJ
ejpam-2338	573	14	constellations	constellation	NOUN
ejpam-2338	573	15	,	,	PUNCT
ejpam-2338	573	16	communications	communication	NOUN
ejpam-2338	573	17	in	in	ADP
ejpam-2338	573	18	algebra	algebra	PROPN
ejpam-2338	573	19	38(1	38(1	NUM
ejpam-2338	573	20	)	)	PUNCT
ejpam-2338	573	21	261–287	261–287	NUM
ejpam-2338	573	22	.	.	PUNCT
ejpam-2338	574	1	2010	2010	NUM
ejpam-2338	574	2	.	.	PUNCT
ejpam-2338	575	1	http://dx.doi.org/10.1080/	http://dx.doi.org/10.1080/	NOUN
ejpam-2338	575	2	00927870902887096	00927870902887096	NUM
ejpam-2338	576	1	[	[	X
ejpam-2338	576	2	31	31	NUM
ejpam-2338	576	3	]	]	X
ejpam-2338	576	4	d.	d.	PROPN
ejpam-2338	576	5	g.	g.	PROPN
ejpam-2338	576	6	green	green	PROPN
ejpam-2338	576	7	.	.	PUNCT
ejpam-2338	577	1	the	the	DET
ejpam-2338	577	2	lattice	lattice	NOUN
ejpam-2338	577	3	of	of	ADP
ejpam-2338	577	4	congruences	congruence	NOUN
ejpam-2338	577	5	on	on	ADP
ejpam-2338	577	6	an	an	DET
ejpam-2338	577	7	inverse	inverse	NOUN
ejpam-2338	577	8	semigroup	semigroup	NOUN
ejpam-2338	577	9	,	,	PUNCT
ejpam-2338	577	10	pacific	pacific	PROPN
ejpam-2338	577	11	journal	journal	NOUN
ejpam-2338	577	12	of	of	ADP
ejpam-2338	577	13	mathematics	mathematic	NOUN
ejpam-2338	577	14	57	57	NUM
ejpam-2338	577	15	141–152	141–152	NUM
ejpam-2338	577	16	.	.	PUNCT
ejpam-2338	577	17	1975	1975	NUM
ejpam-2338	577	18	.	.	PUNCT
ejpam-2338	578	1	http://projecteuclid.org/euclid.pjm/	http://projecteuclid.org/euclid.pjm/	X
ejpam-2338	578	2	1102906180	1102906180	NUM
ejpam-2338	579	1	[	[	X
ejpam-2338	579	2	32	32	NUM
ejpam-2338	579	3	]	]	PUNCT
ejpam-2338	579	4	t.	t.	PROPN
ejpam-2338	579	5	e.	e.	PROPN
ejpam-2338	579	6	hall	hall	PROPN
ejpam-2338	579	7	.	.	PUNCT
ejpam-2338	580	1	on	on	ADP
ejpam-2338	580	2	orthodox	orthodox	ADJ
ejpam-2338	580	3	semigroups	semigroup	NOUN
ejpam-2338	580	4	and	and	CCONJ
ejpam-2338	580	5	uniform	uniform	NOUN
ejpam-2338	580	6	and	and	CCONJ
ejpam-2338	580	7	anti	anti	ADJ
ejpam-2338	580	8	-	-	ADJ
ejpam-2338	580	9	uniform	uniform	ADJ
ejpam-2338	580	10	bands	band	NOUN
ejpam-2338	580	11	,	,	PUNCT
ejpam-2338	580	12	journal	journal	NOUN
ejpam-2338	580	13	of	of	ADP
ejpam-2338	580	14	algebra	algebra	NOUN
ejpam-2338	580	15	16	16	NUM
ejpam-2338	580	16	204–217	204–217	NUM
ejpam-2338	580	17	.	.	PUNCT
ejpam-2338	580	18	1970	1970	NUM
ejpam-2338	580	19	.	.	PUNCT
ejpam-2338	580	20	http://dx.doi.org/10.1016/0021-8693(70)90025-6	http://dx.doi.org/10.1016/0021-8693(70)90025-6	PROPN
ejpam-2338	581	1	[	[	X
ejpam-2338	581	2	33	33	NUM
ejpam-2338	581	3	]	]	PUNCT
ejpam-2338	581	4	t.	t.	PROPN
ejpam-2338	581	5	e.	e.	PROPN
ejpam-2338	581	6	hall	hall	PROPN
ejpam-2338	581	7	.	.	PUNCT
ejpam-2338	582	1	on	on	ADP
ejpam-2338	582	2	regular	regular	ADJ
ejpam-2338	582	3	semigroups	semigroup	NOUN
ejpam-2338	582	4	,	,	PUNCT
ejpam-2338	582	5	journal	journal	NOUN
ejpam-2338	582	6	of	of	ADP
ejpam-2338	582	7	algebra	algebra	PROPN
ejpam-2338	582	8	24	24	NUM
ejpam-2338	582	9	1–24	1–24	PROPN
ejpam-2338	582	10	.	.	PUNCT
ejpam-2338	583	1	1973	1973	NUM
ejpam-2338	583	2	.	.	PUNCT
ejpam-2338	584	1	http://dx.doi	http://dx.doi	NOUN
ejpam-2338	584	2	.	.	PUNCT
ejpam-2338	585	1	org/10.1016/0021	org/10.1016/0021	ADV
ejpam-2338	585	2	-	-	PUNCT
ejpam-2338	585	3	8693(73)90150	8693(73)90150	NUM
ejpam-2338	585	4	-	-	SYM
ejpam-2338	585	5	6	6	NUM
ejpam-2338	586	1	[	[	SYM
ejpam-2338	586	2	34	34	NUM
ejpam-2338	586	3	]	]	PUNCT
ejpam-2338	586	4	t.	t.	PROPN
ejpam-2338	586	5	hawkins	hawkins	PROPN
ejpam-2338	586	6	.	.	PUNCT
ejpam-2338	587	1	the	the	DET
ejpam-2338	587	2	erlanger	erlanger	PROPN
ejpam-2338	587	3	programm	programm	PROPN
ejpam-2338	587	4	of	of	ADP
ejpam-2338	587	5	felix	felix	PROPN
ejpam-2338	587	6	klein	klein	PROPN
ejpam-2338	587	7	:	:	PUNCT
ejpam-2338	587	8	reflections	reflection	NOUN
ejpam-2338	587	9	on	on	ADP
ejpam-2338	587	10	its	its	PRON
ejpam-2338	587	11	place	place	NOUN
ejpam-2338	587	12	in	in	ADP
ejpam-2338	587	13	the	the	DET
ejpam-2338	587	14	history	history	NOUN
ejpam-2338	587	15	of	of	ADP
ejpam-2338	587	16	mathematics	mathematic	NOUN
ejpam-2338	587	17	,	,	PUNCT
ejpam-2338	587	18	historia	historia	PROPN
ejpam-2338	587	19	mathematica	mathematica	PROPN
ejpam-2338	587	20	11	11	NUM
ejpam-2338	587	21	442–470	442–470	NUM
ejpam-2338	587	22	.	.	PUNCT
ejpam-2338	587	23	1984	1984	NUM
ejpam-2338	587	24	.	.	PUNCT
ejpam-2338	588	1	http://dx.doi.org/10	http://dx.doi.org/10	ADJ
ejpam-2338	588	2	.	.	PUNCT
ejpam-2338	589	1	1016/0315	1016/0315	NUM
ejpam-2338	589	2	-	-	PUNCT
ejpam-2338	589	3	0860(84)90028	0860(84)90028	ADP
ejpam-2338	589	4	-	-	PUNCT
ejpam-2338	589	5	4	4	NUM
ejpam-2338	589	6	[	[	SYM
ejpam-2338	589	7	35	35	NUM
ejpam-2338	589	8	]	]	X
ejpam-2338	589	9	g.	g.	PROPN
ejpam-2338	589	10	higman	higman	PROPN
ejpam-2338	589	11	,	,	PUNCT
ejpam-2338	589	12	b.	b.	PROPN
ejpam-2338	589	13	h.	h.	PROPN
ejpam-2338	589	14	neumann	neumann	PROPN
ejpam-2338	589	15	,	,	PUNCT
ejpam-2338	589	16	and	and	CCONJ
ejpam-2338	589	17	h.	h.	PROPN
ejpam-2338	589	18	neumann	neumann	PROPN
ejpam-2338	589	19	.	.	PUNCT
ejpam-2338	590	1	embedding	embed	VERB
ejpam-2338	590	2	theorems	theorem	NOUN
ejpam-2338	590	3	for	for	ADP
ejpam-2338	590	4	groups	group	NOUN
ejpam-2338	590	5	,	,	PUNCT
ejpam-2338	590	6	journal	journal	NOUN
ejpam-2338	590	7	of	of	ADP
ejpam-2338	590	8	the	the	DET
ejpam-2338	590	9	london	london	PROPN
ejpam-2338	590	10	mathematical	mathematical	ADJ
ejpam-2338	590	11	society	society	NOUN
ejpam-2338	590	12	24	24	NUM
ejpam-2338	590	13	247–254	247–254	NUM
ejpam-2338	590	14	.	.	PUNCT
ejpam-2338	591	1	1949	1949	NUM
ejpam-2338	591	2	.	.	PUNCT
ejpam-2338	592	1	http://dx.doi.org/10	http://dx.doi.org/10	ADJ
ejpam-2338	592	2	.	.	PUNCT
ejpam-2338	593	1	1112	1112	NUM
ejpam-2338	593	2	/	/	SYM
ejpam-2338	593	3	jlms	jlm	NOUN
ejpam-2338	593	4	/	/	SYM
ejpam-2338	593	5	s1	s1	PROPN
ejpam-2338	593	6	-	-	PUNCT
ejpam-2338	593	7	24.4.247	24.4.247	PROPN
ejpam-2338	593	8	[	[	X
ejpam-2338	593	9	36	36	NUM
ejpam-2338	593	10	]	]	X
ejpam-2338	593	11	c.	c.	PROPN
ejpam-2338	593	12	hollings	holling	NOUN
ejpam-2338	593	13	.	.	PUNCT
ejpam-2338	594	1	from	from	ADP
ejpam-2338	594	2	right	right	ADJ
ejpam-2338	594	3	pp	pp	ADV
ejpam-2338	594	4	monoids	monoid	NOUN
ejpam-2338	594	5	to	to	ADP
ejpam-2338	594	6	restriction	restriction	NOUN
ejpam-2338	594	7	semigroups	semigroup	NOUN
ejpam-2338	594	8	:	:	PUNCT
ejpam-2338	594	9	a	a	DET
ejpam-2338	594	10	survey	survey	NOUN
ejpam-2338	594	11	,	,	PUNCT
ejpam-2338	594	12	european	european	PROPN
ejpam-2338	594	13	journal	journal	PROPN
ejpam-2338	594	14	of	of	ADP
ejpam-2338	594	15	pure	pure	ADJ
ejpam-2338	594	16	and	and	CCONJ
ejpam-2338	594	17	applied	applied	ADJ
ejpam-2338	594	18	mathematics	mathematic	NOUN
ejpam-2338	594	19	2(1	2(1	NUM
ejpam-2338	594	20	)	)	PUNCT
ejpam-2338	594	21	21–37	21–37	NUM
ejpam-2338	594	22	.	.	PUNCT
ejpam-2338	594	23	2009	2009	NUM
ejpam-2338	594	24	.	.	PUNCT
ejpam-2338	595	1	http://www.ejpam.com/index	http://www.ejpam.com/index	PROPN
ejpam-2338	595	2	.	.	PUNCT
ejpam-2338	596	1	php	php	PROPN
ejpam-2338	596	2	/	/	SYM
ejpam-2338	596	3	ejpam	ejpam	NOUN
ejpam-2338	596	4	/	/	SYM
ejpam-2338	596	5	article	article	NOUN
ejpam-2338	596	6	/	/	SYM
ejpam-2338	596	7	view/221/43	view/221/43	PROPN
ejpam-2338	597	1	[	[	X
ejpam-2338	597	2	37	37	NUM
ejpam-2338	597	3	]	]	X
ejpam-2338	597	4	c.	c.	PROPN
ejpam-2338	597	5	hollings	holling	NOUN
ejpam-2338	597	6	.	.	PUNCT
ejpam-2338	598	1	the	the	DET
ejpam-2338	598	2	early	early	ADJ
ejpam-2338	598	3	development	development	NOUN
ejpam-2338	598	4	of	of	ADP
ejpam-2338	598	5	the	the	DET
ejpam-2338	598	6	algebraic	algebraic	ADJ
ejpam-2338	598	7	theory	theory	NOUN
ejpam-2338	598	8	of	of	ADP
ejpam-2338	598	9	semigroups	semigroup	NOUN
ejpam-2338	598	10	,	,	PUNCT
ejpam-2338	598	11	archive	archive	NOUN
ejpam-2338	598	12	for	for	ADP
ejpam-2338	598	13	history	history	NOUN
ejpam-2338	598	14	of	of	ADP
ejpam-2338	598	15	exact	exact	ADJ
ejpam-2338	598	16	sciences	science	NOUN
ejpam-2338	598	17	63(5	63(5	NOUN
ejpam-2338	598	18	)	)	PUNCT
ejpam-2338	598	19	497–536	497–536	NUM
ejpam-2338	598	20	.	.	PUNCT
ejpam-2338	598	21	2009	2009	NUM
ejpam-2338	598	22	.	.	PUNCT
ejpam-2338	599	1	http://dx.doi.org/10.1007/	http://dx.doi.org/10.1007/	PROPN
ejpam-2338	599	2	s00407	s00407	PROPN
ejpam-2338	599	3	-	-	PUNCT
ejpam-2338	599	4	009	009	NUM
ejpam-2338	599	5	-	-	PUNCT
ejpam-2338	599	6	0044	0044	NUM
ejpam-2338	599	7	-	-	SYM
ejpam-2338	599	8	3	3	NUM
ejpam-2338	599	9	[	[	X
ejpam-2338	599	10	38	38	NUM
ejpam-2338	599	11	]	]	PUNCT
ejpam-2338	599	12	c.	c.	PROPN
ejpam-2338	599	13	hollings	holling	NOUN
ejpam-2338	599	14	.	.	PUNCT
ejpam-2338	600	1	extending	extend	VERB
ejpam-2338	600	2	the	the	DET
ejpam-2338	600	3	ehresmann	ehresmann	PROPN
ejpam-2338	600	4	–	–	PUNCT
ejpam-2338	600	5	schein	schein	PROPN
ejpam-2338	600	6	–	–	PUNCT
ejpam-2338	600	7	nambooripad	nambooripad	NOUN
ejpam-2338	600	8	theorem	theorem	NOUN
ejpam-2338	600	9	,	,	PUNCT
ejpam-2338	600	10	semigroup	semigroup	PROPN
ejpam-2338	600	11	forum	forum	PROPN
ejpam-2338	600	12	80(3	80(3	NUM
ejpam-2338	600	13	)	)	PUNCT
ejpam-2338	600	14	453–476	453–476	NUM
ejpam-2338	600	15	.	.	PUNCT
ejpam-2338	600	16	2010	2010	NUM
ejpam-2338	600	17	.	.	PUNCT
ejpam-2338	601	1	http://dx.doi.org/10.1007/s00233-010-9215-4	http://dx.doi.org/10.1007/s00233-010-9215-4	PUNCT
ejpam-2338	602	1	[	[	X
ejpam-2338	602	2	39	39	NUM
ejpam-2338	602	3	]	]	PUNCT
ejpam-2338	602	4	c.	c.	PROPN
ejpam-2338	602	5	hollings	holling	NOUN
ejpam-2338	602	6	.	.	PUNCT
ejpam-2338	603	1	on	on	ADP
ejpam-2338	603	2	conditions	condition	NOUN
ejpam-2338	603	3	for	for	ADP
ejpam-2338	603	4	constellations	constellation	NOUN
ejpam-2338	603	5	,	,	PUNCT
ejpam-2338	603	6	international	international	ADJ
ejpam-2338	603	7	electronic	electronic	ADJ
ejpam-2338	603	8	journal	journal	NOUN
ejpam-2338	603	9	of	of	ADP
ejpam-2338	603	10	algebra	algebra	PROPN
ejpam-2338	603	11	10	10	NUM
ejpam-2338	603	12	1–24	1–24	NOUN
ejpam-2338	603	13	.	.	PUNCT
ejpam-2338	604	1	2011	2011	NUM
ejpam-2338	604	2	.	.	PUNCT
ejpam-2338	605	1	http://www.ieja.net/files/papers/volume-10/	http://www.ieja.net/files/papers/volume-10/	PROPN
ejpam-2338	606	1	volume-9	volume-9	NOUN
ejpam-2338	606	2	-	-	ADJ
ejpam-2338	606	3	-2011/1	-2011/1	NUM
ejpam-2338	606	4	-	-	PUNCT
ejpam-2338	606	5	v10	v10	NOUN
ejpam-2338	606	6	-	-	NOUN
ejpam-2338	606	7	2011.pdf	2011.pdf	NOUN
ejpam-2338	606	8	[	[	X
ejpam-2338	606	9	40	40	NUM
ejpam-2338	606	10	]	]	PUNCT
ejpam-2338	606	11	c.	c.	PROPN
ejpam-2338	606	12	hollings	holling	NOUN
ejpam-2338	606	13	.	.	PUNCT
ejpam-2338	607	1	the	the	DET
ejpam-2338	607	2	ehresmann	ehresmann	PROPN
ejpam-2338	607	3	–	–	PUNCT
ejpam-2338	607	4	schein	schein	PROPN
ejpam-2338	607	5	–	–	PUNCT
ejpam-2338	607	6	nambooripad	nambooripad	NOUN
ejpam-2338	607	7	theorem	theorem	NOUN
ejpam-2338	607	8	and	and	CCONJ
ejpam-2338	607	9	its	its	PRON
ejpam-2338	607	10	successors	successor	NOUN
ejpam-2338	607	11	,	,	PUNCT
ejpam-2338	607	12	european	european	ADJ
ejpam-2338	607	13	journal	journal	PROPN
ejpam-2338	607	14	of	of	ADP
ejpam-2338	607	15	pure	pure	ADJ
ejpam-2338	607	16	and	and	CCONJ
ejpam-2338	607	17	applied	apply	VERB
ejpam-2338	607	18	mathematics	mathematic	NOUN
ejpam-2338	607	19	5(4	5(4	NOUN
ejpam-2338	607	20	)	)	PUNCT
ejpam-2338	607	21	414–450	414–450	NUM
ejpam-2338	607	22	.	.	PUNCT
ejpam-2338	607	23	2012	2012	NUM
ejpam-2338	607	24	.	.	PUNCT
ejpam-2338	608	1	http://www	http://www	PROPN
ejpam-2338	608	2	.	.	PUNCT
ejpam-2338	609	1	ejpam.com/index.php/ejpam/article/view/1535/268	ejpam.com/index.php/ejpam/article/view/1535/268	PRON
ejpam-2338	609	2	references	reference	NOUN
ejpam-2338	609	3	319	319	NUM
ejpam-2338	610	1	[	[	X
ejpam-2338	610	2	41	41	NUM
ejpam-2338	610	3	]	]	X
ejpam-2338	610	4	c.	c.	PROPN
ejpam-2338	610	5	hollings	holling	NOUN
ejpam-2338	610	6	.	.	PUNCT
ejpam-2338	611	1	mathematics	mathematic	NOUN
ejpam-2338	611	2	across	across	ADP
ejpam-2338	611	3	the	the	DET
ejpam-2338	611	4	iron	iron	NOUN
ejpam-2338	611	5	curtain	curtain	NOUN
ejpam-2338	611	6	:	:	PUNCT
ejpam-2338	611	7	a	a	DET
ejpam-2338	611	8	history	history	NOUN
ejpam-2338	611	9	of	of	ADP
ejpam-2338	611	10	the	the	DET
ejpam-2338	611	11	algebraic	algebraic	ADJ
ejpam-2338	611	12	theory	theory	NOUN
ejpam-2338	611	13	of	of	ADP
ejpam-2338	611	14	semigroups	semigroup	NOUN
ejpam-2338	611	15	,	,	PUNCT
ejpam-2338	611	16	history	history	NOUN
ejpam-2338	611	17	of	of	ADP
ejpam-2338	611	18	mathematics	mathematic	NOUN
ejpam-2338	611	19	,	,	PUNCT
ejpam-2338	611	20	volume	volume	NOUN
ejpam-2338	611	21	41	41	NUM
ejpam-2338	611	22	,	,	PUNCT
ejpam-2338	611	23	american	american	PROPN
ejpam-2338	611	24	mathematical	mathematical	ADJ
ejpam-2338	611	25	society	society	NOUN
ejpam-2338	611	26	,	,	PUNCT
ejpam-2338	611	27	providence	providence	NOUN
ejpam-2338	611	28	,	,	PUNCT
ejpam-2338	611	29	ri	ri	NOUN
ejpam-2338	611	30	,	,	PUNCT
ejpam-2338	611	31	2014	2014	NUM
ejpam-2338	611	32	.	.	PUNCT
ejpam-2338	612	1	[	[	X
ejpam-2338	612	2	42	42	NUM
ejpam-2338	612	3	]	]	X
ejpam-2338	612	4	c.	c.	PROPN
ejpam-2338	612	5	hollings	holling	NOUN
ejpam-2338	612	6	.	.	PUNCT
ejpam-2338	613	1	embedding	embed	VERB
ejpam-2338	613	2	semigroups	semigroup	NOUN
ejpam-2338	613	3	in	in	ADP
ejpam-2338	613	4	groups	group	NOUN
ejpam-2338	613	5	:	:	PUNCT
ejpam-2338	613	6	not	not	PART
ejpam-2338	613	7	as	as	ADV
ejpam-2338	613	8	simple	simple	ADJ
ejpam-2338	613	9	as	as	SCONJ
ejpam-2338	613	10	it	it	PRON
ejpam-2338	613	11	might	might	AUX
ejpam-2338	613	12	seem	seem	VERB
ejpam-2338	613	13	,	,	PUNCT
ejpam-2338	613	14	archive	archive	NOUN
ejpam-2338	613	15	for	for	ADP
ejpam-2338	613	16	history	history	NOUN
ejpam-2338	613	17	of	of	ADP
ejpam-2338	613	18	exact	exact	ADJ
ejpam-2338	613	19	sciences	science	NOUN
ejpam-2338	613	20	68(5	68(5	NUM
ejpam-2338	613	21	)	)	PUNCT
ejpam-2338	613	22	641–692	641–692	NUM
ejpam-2338	613	23	.	.	PUNCT
ejpam-2338	613	24	2014	2014	NUM
ejpam-2338	613	25	.	.	PUNCT
ejpam-2338	614	1	http://dx.doi.org/10.1007/	http://dx.doi.org/10.1007/	PROPN
ejpam-2338	614	2	s00407	s00407	PROPN
ejpam-2338	614	3	-	-	PUNCT
ejpam-2338	614	4	014	014	NUM
ejpam-2338	614	5	-	-	PUNCT
ejpam-2338	614	6	0138	0138	NUM
ejpam-2338	614	7	-	-	SYM
ejpam-2338	614	8	4	4	NUM
ejpam-2338	614	9	[	[	SYM
ejpam-2338	614	10	43	43	NUM
ejpam-2338	614	11	]	]	X
ejpam-2338	614	12	j.	j.	PROPN
ejpam-2338	614	13	m.	m.	PROPN
ejpam-2338	614	14	howie	howie	PROPN
ejpam-2338	614	15	.	.	PUNCT
ejpam-2338	615	1	the	the	DET
ejpam-2338	615	2	maximum	maximum	ADJ
ejpam-2338	615	3	idempotent	idempotent	NOUN
ejpam-2338	615	4	-	-	PUNCT
ejpam-2338	615	5	separating	separate	VERB
ejpam-2338	615	6	congruence	congruence	NOUN
ejpam-2338	615	7	on	on	ADP
ejpam-2338	615	8	an	an	DET
ejpam-2338	615	9	inverse	inverse	NOUN
ejpam-2338	615	10	semigroup	semigroup	NOUN
ejpam-2338	615	11	,	,	PUNCT
ejpam-2338	615	12	proceedings	proceeding	NOUN
ejpam-2338	615	13	of	of	ADP
ejpam-2338	615	14	the	the	DET
ejpam-2338	615	15	edinburgh	edinburgh	PROPN
ejpam-2338	615	16	mathematical	mathematical	PROPN
ejpam-2338	615	17	society	society	NOUN
ejpam-2338	615	18	14	14	NUM
ejpam-2338	615	19	71–79	71–79	ADV
ejpam-2338	615	20	.	.	PUNCT
ejpam-2338	616	1	1964	1964	NUM
ejpam-2338	616	2	.	.	PUNCT
ejpam-2338	617	1	http://dx.doi	http://dx.doi	NOUN
ejpam-2338	617	2	.	.	PUNCT
ejpam-2338	618	1	org/10.1017	org/10.1017	CCONJ
ejpam-2338	618	2	/	/	SYM
ejpam-2338	618	3	s0013091500011251	s0013091500011251	PROPN
ejpam-2338	619	1	[	[	X
ejpam-2338	619	2	44	44	NUM
ejpam-2338	619	3	]	]	PUNCT
ejpam-2338	619	4	j.	j.	PROPN
ejpam-2338	619	5	m.	m.	PROPN
ejpam-2338	619	6	howie	howie	PROPN
ejpam-2338	619	7	.	.	PUNCT
ejpam-2338	620	1	fundamentals	fundamental	NOUN
ejpam-2338	620	2	of	of	ADP
ejpam-2338	620	3	semigroup	semigroup	PROPN
ejpam-2338	620	4	theory	theory	NOUN
ejpam-2338	620	5	,	,	PUNCT
ejpam-2338	620	6	lms	lms	NOUN
ejpam-2338	620	7	monographs	monograph	NOUN
ejpam-2338	620	8	,	,	PUNCT
ejpam-2338	620	9	new	new	ADJ
ejpam-2338	620	10	series	series	NOUN
ejpam-2338	620	11	,	,	PUNCT
ejpam-2338	620	12	no	no	INTJ
ejpam-2338	620	13	.	.	PROPN
ejpam-2338	620	14	12	12	NUM
ejpam-2338	620	15	,	,	PUNCT
ejpam-2338	620	16	clarendon	clarendon	PROPN
ejpam-2338	620	17	press	press	NOUN
ejpam-2338	620	18	,	,	PUNCT
ejpam-2338	620	19	oxford	oxford	NOUN
ejpam-2338	620	20	,	,	PUNCT
ejpam-2338	620	21	1995	1995	NUM
ejpam-2338	620	22	.	.	PUNCT
ejpam-2338	621	1	[	[	X
ejpam-2338	621	2	45	45	NUM
ejpam-2338	621	3	]	]	X
ejpam-2338	621	4	n.	n.	PROPN
ejpam-2338	621	5	jacobson	jacobson	PROPN
ejpam-2338	621	6	.	.	PUNCT
ejpam-2338	621	7	basic	basic	ADJ
ejpam-2338	621	8	algebra	algebra	PROPN
ejpam-2338	621	9	,	,	PUNCT
ejpam-2338	621	10	vol	vol	NOUN
ejpam-2338	621	11	.	.	PROPN
ejpam-2338	621	12	2	2	NUM
ejpam-2338	621	13	,	,	PUNCT
ejpam-2338	621	14	w.	w.	PROPN
ejpam-2338	621	15	h.	h.	PROPN
ejpam-2338	621	16	freeman	freeman	PROPN
ejpam-2338	621	17	and	and	CCONJ
ejpam-2338	621	18	co.	co.	PROPN
ejpam-2338	621	19	,	,	PUNCT
ejpam-2338	621	20	san	san	PROPN
ejpam-2338	621	21	francisco	francisco	PROPN
ejpam-2338	621	22	,	,	PUNCT
ejpam-2338	621	23	1980	1980	NUM
ejpam-2338	621	24	.	.	PUNCT
ejpam-2338	622	1	[	[	X
ejpam-2338	622	2	46	46	NUM
ejpam-2338	622	3	]	]	X
ejpam-2338	622	4	g.	g.	PROPN
ejpam-2338	622	5	joubert	joubert	PROPN
ejpam-2338	622	6	.	.	PUNCT
ejpam-2338	623	1	contribution	contribution	PROPN
ejpam-2338	623	2	à	à	X
ejpam-2338	623	3	l’étude	l’étude	X
ejpam-2338	623	4	des	des	X
ejpam-2338	623	5	catégories	catégories	PROPN
ejpam-2338	623	6	ordonnées	ordonnées	PROPN
ejpam-2338	623	7	,	,	PUNCT
ejpam-2338	623	8	applications	application	NOUN
ejpam-2338	623	9	aux	aux	PROPN
ejpam-2338	623	10	structures	structure	NOUN
ejpam-2338	623	11	feuilletées	feuilletées	PROPN
ejpam-2338	623	12	,	,	PUNCT
ejpam-2338	623	13	cahiers	cahier	NOUN
ejpam-2338	623	14	de	de	ADP
ejpam-2338	623	15	topologie	topologie	PROPN
ejpam-2338	623	16	et	et	PROPN
ejpam-2338	623	17	géométrie	géométrie	VERB
ejpam-2338	623	18	différentielle	différentielle	PROPN
ejpam-2338	623	19	catégoriques	catégorique	NOUN
ejpam-2338	623	20	8	8	NUM
ejpam-2338	623	21	1–117	1–117	NUM
ejpam-2338	623	22	.	.	NOUN
ejpam-2338	623	23	1966	1966	NUM
ejpam-2338	623	24	.	.	PUNCT
ejpam-2338	624	1	[	[	X
ejpam-2338	624	2	47	47	NUM
ejpam-2338	624	3	]	]	PUNCT
ejpam-2338	624	4	j.	j.	PROPN
ejpam-2338	624	5	kellendonk	kellendonk	PROPN
ejpam-2338	624	6	and	and	CCONJ
ejpam-2338	624	7	mark	mark	PROPN
ejpam-2338	624	8	v.	v.	PROPN
ejpam-2338	624	9	lawson	lawson	PROPN
ejpam-2338	624	10	.	.	PUNCT
ejpam-2338	625	1	partial	partial	ADJ
ejpam-2338	625	2	actions	action	NOUN
ejpam-2338	625	3	of	of	ADP
ejpam-2338	625	4	groups	group	NOUN
ejpam-2338	625	5	,	,	PUNCT
ejpam-2338	625	6	international	international	ADJ
ejpam-2338	625	7	journal	journal	NOUN
ejpam-2338	625	8	of	of	ADP
ejpam-2338	625	9	algebra	algebra	NOUN
ejpam-2338	625	10	and	and	CCONJ
ejpam-2338	625	11	computation	computation	NOUN
ejpam-2338	625	12	14	14	NUM
ejpam-2338	625	13	87–114	87–114	NUM
ejpam-2338	625	14	.	.	PUNCT
ejpam-2338	625	15	2004	2004	NUM
ejpam-2338	625	16	.	.	PUNCT
ejpam-2338	626	1	http://dx.doi.org/10.1142/	http://dx.doi.org/10.1142/	PROPN
ejpam-2338	627	1	s0218196704001657	s0218196704001657	PRON
ejpam-2338	628	1	[	[	X
ejpam-2338	628	2	48	48	NUM
ejpam-2338	628	3	]	]	PUNCT
ejpam-2338	628	4	m.	m.	NOUN
ejpam-2338	628	5	v.	v.	ADP
ejpam-2338	628	6	lawson	lawson	PROPN
ejpam-2338	628	7	.	.	PUNCT
ejpam-2338	629	1	the	the	DET
ejpam-2338	629	2	structure	structure	NOUN
ejpam-2338	629	3	theory	theory	NOUN
ejpam-2338	629	4	of	of	ADP
ejpam-2338	629	5	abundant	abundant	ADJ
ejpam-2338	629	6	semigroups	semigroup	NOUN
ejpam-2338	629	7	,	,	PUNCT
ejpam-2338	629	8	dphil	dphil	ADJ
ejpam-2338	629	9	thesis	thesis	NOUN
ejpam-2338	629	10	,	,	PUNCT
ejpam-2338	629	11	university	university	PROPN
ejpam-2338	629	12	of	of	ADP
ejpam-2338	629	13	york	york	PROPN
ejpam-2338	629	14	,	,	PUNCT
ejpam-2338	629	15	1985	1985	NUM
ejpam-2338	629	16	.	.	PUNCT
ejpam-2338	630	1	[	[	X
ejpam-2338	630	2	49	49	NUM
ejpam-2338	630	3	]	]	PUNCT
ejpam-2338	630	4	m.	m.	NOUN
ejpam-2338	630	5	v.	v.	ADP
ejpam-2338	630	6	lawson	lawson	PROPN
ejpam-2338	630	7	.	.	PUNCT
ejpam-2338	631	1	the	the	DET
ejpam-2338	631	2	structure	structure	NOUN
ejpam-2338	631	3	of	of	ADP
ejpam-2338	631	4	type	type	NOUN
ejpam-2338	631	5	a	a	DET
ejpam-2338	631	6	semigroups	semigroup	NOUN
ejpam-2338	631	7	,	,	PUNCT
ejpam-2338	631	8	quarterly	quarterly	ADJ
ejpam-2338	631	9	journal	journal	NOUN
ejpam-2338	631	10	of	of	ADP
ejpam-2338	631	11	mathematics	mathematic	NOUN
ejpam-2338	631	12	,	,	PUNCT
ejpam-2338	631	13	oxford	oxford	PROPN
ejpam-2338	631	14	(	(	PUNCT
ejpam-2338	631	15	2	2	NUM
ejpam-2338	631	16	)	)	PUNCT
ejpam-2338	631	17	37	37	NUM
ejpam-2338	631	18	279–298	279–298	NUM
ejpam-2338	631	19	.	.	PUNCT
ejpam-2338	632	1	1986	1986	NUM
ejpam-2338	632	2	.	.	PUNCT
ejpam-2338	633	1	http://dx.doi.org/10.1093/qmath/37.3.279	http://dx.doi.org/10.1093/qmath/37.3.279	NOUN
ejpam-2338	633	2	[	[	X
ejpam-2338	633	3	50	50	NUM
ejpam-2338	633	4	]	]	PUNCT
ejpam-2338	633	5	m.	m.	NOUN
ejpam-2338	633	6	v.	v.	ADP
ejpam-2338	633	7	lawson	lawson	PROPN
ejpam-2338	633	8	.	.	PUNCT
ejpam-2338	634	1	a	a	DET
ejpam-2338	634	2	note	note	NOUN
ejpam-2338	634	3	on	on	ADP
ejpam-2338	634	4	a	a	DET
ejpam-2338	634	5	paper	paper	NOUN
ejpam-2338	634	6	of	of	ADP
ejpam-2338	634	7	joubert	joubert	PROPN
ejpam-2338	634	8	,	,	PUNCT
ejpam-2338	634	9	semigroup	semigroup	PROPN
ejpam-2338	634	10	forum	forum	PROPN
ejpam-2338	634	11	47	47	NUM
ejpam-2338	634	12	389–392	389–392	NUM
ejpam-2338	634	13	.	.	PROPN
ejpam-2338	634	14	1993	1993	NUM
ejpam-2338	634	15	.	.	PUNCT
ejpam-2338	635	1	http	http	ADJ
ejpam-2338	635	2	:	:	PUNCT
ejpam-2338	636	1	dx.doi.org/10.1007/bf02573776	dx.doi.org/10.1007/bf02573776	PROPN
ejpam-2338	636	2	[	[	X
ejpam-2338	636	3	51	51	NUM
ejpam-2338	636	4	]	]	PUNCT
ejpam-2338	636	5	m.	m.	NOUN
ejpam-2338	636	6	v.	v.	ADP
ejpam-2338	636	7	lawson	lawson	PROPN
ejpam-2338	636	8	.	.	PUNCT
ejpam-2338	637	1	inverse	inverse	PROPN
ejpam-2338	637	2	semigroups	semigroup	NOUN
ejpam-2338	637	3	:	:	PUNCT
ejpam-2338	637	4	the	the	DET
ejpam-2338	637	5	theory	theory	NOUN
ejpam-2338	637	6	of	of	ADP
ejpam-2338	637	7	partial	partial	ADJ
ejpam-2338	637	8	symmetries	symmetry	NOUN
ejpam-2338	637	9	,	,	PUNCT
ejpam-2338	637	10	world	world	NOUN
ejpam-2338	637	11	scientific	scientific	ADJ
ejpam-2338	637	12	,	,	PUNCT
ejpam-2338	637	13	1998	1998	NUM
ejpam-2338	637	14	.	.	PUNCT
ejpam-2338	638	1	[	[	X
ejpam-2338	638	2	52	52	NUM
ejpam-2338	638	3	]	]	PUNCT
ejpam-2338	638	4	m.	m.	NOUN
ejpam-2338	638	5	v.	v.	ADP
ejpam-2338	638	6	lawson	lawson	PROPN
ejpam-2338	638	7	and	and	CCONJ
ejpam-2338	638	8	stuart	stuart	PROPN
ejpam-2338	638	9	w.	w.	PROPN
ejpam-2338	638	10	margolis	margolis	PROPN
ejpam-2338	638	11	.	.	PROPN
ejpam-2338	639	1	in	in	ADP
ejpam-2338	639	2	mcalister	mcalister	PROPN
ejpam-2338	639	3	’s	’s	PART
ejpam-2338	639	4	footsteps	footstep	NOUN
ejpam-2338	639	5	:	:	PUNCT
ejpam-2338	639	6	a	a	DET
ejpam-2338	639	7	random	random	ADJ
ejpam-2338	639	8	ramble	ramble	NOUN
ejpam-2338	639	9	around	around	ADP
ejpam-2338	639	10	the	the	DET
ejpam-2338	639	11	p	p	NOUN
ejpam-2338	639	12	-	-	PUNCT
ejpam-2338	639	13	theorem	theorem	ADJ
ejpam-2338	639	14	,	,	PUNCT
ejpam-2338	639	15	in	in	ADP
ejpam-2338	639	16	:	:	PUNCT
ejpam-2338	639	17	j.	j.	PROPN
ejpam-2338	639	18	m.	m.	PROPN
ejpam-2338	639	19	andré	andré	PROPN
ejpam-2338	639	20	,	,	PUNCT
ejpam-2338	639	21	m.	m.	PROPN
ejpam-2338	639	22	j.	j.	PROPN
ejpam-2338	639	23	j.	j.	PROPN
ejpam-2338	639	24	branco	branco	PROPN
ejpam-2338	639	25	,	,	PUNCT
ejpam-2338	639	26	v.	v.	PROPN
ejpam-2338	639	27	h.	h.	PROPN
ejpam-2338	639	28	fernandes	fernandes	PROPN
ejpam-2338	639	29	,	,	PUNCT
ejpam-2338	639	30	j.	j.	PROPN
ejpam-2338	639	31	fountain	fountain	PROPN
ejpam-2338	639	32	,	,	PUNCT
ejpam-2338	639	33	g.	g.	PROPN
ejpam-2338	639	34	m.	m.	PROPN
ejpam-2338	639	35	s.	s.	PROPN
ejpam-2338	639	36	gomes	gomes	PROPN
ejpam-2338	639	37	,	,	PUNCT
ejpam-2338	639	38	and	and	CCONJ
ejpam-2338	639	39	j.	j.	PROPN
ejpam-2338	639	40	c.	c.	PROPN
ejpam-2338	639	41	meakin	meakin	PROPN
ejpam-2338	639	42	(	(	PUNCT
ejpam-2338	639	43	eds	ed	NOUN
ejpam-2338	639	44	.	.	PUNCT
ejpam-2338	639	45	)	)	PUNCT
ejpam-2338	639	46	.	.	PUNCT
ejpam-2338	640	1	proceedings	proceeding	NOUN
ejpam-2338	640	2	of	of	ADP
ejpam-2338	640	3	the	the	DET
ejpam-2338	640	4	international	international	ADJ
ejpam-2338	640	5	conference	conference	NOUN
ejpam-2338	640	6	“	"	PUNCT
ejpam-2338	640	7	semigroups	semigroup	NOUN
ejpam-2338	640	8	and	and	CCONJ
ejpam-2338	640	9	formal	formal	ADJ
ejpam-2338	640	10	languages	language	NOUN
ejpam-2338	640	11	”	"	PUNCT
ejpam-2338	640	12	in	in	ADP
ejpam-2338	640	13	honour	honour	NOUN
ejpam-2338	640	14	of	of	ADP
ejpam-2338	640	15	the	the	DET
ejpam-2338	640	16	65th	65th	ADJ
ejpam-2338	640	17	birthday	birthday	NOUN
ejpam-2338	640	18	of	of	ADP
ejpam-2338	640	19	donald	donald	PROPN
ejpam-2338	640	20	b.	b.	PROPN
ejpam-2338	640	21	mcalister	mcalister	PROPN
ejpam-2338	640	22	,	,	PUNCT
ejpam-2338	640	23	world	world	NOUN
ejpam-2338	640	24	scientific	scientific	ADJ
ejpam-2338	640	25	publications	publication	NOUN
ejpam-2338	640	26	,	,	PUNCT
ejpam-2338	640	27	hackensack	hackensack	PROPN
ejpam-2338	640	28	,	,	PUNCT
ejpam-2338	640	29	nj	nj	PROPN
ejpam-2338	640	30	,	,	PUNCT
ejpam-2338	640	31	pp	pp	ADP
ejpam-2338	640	32	.	.	PUNCT
ejpam-2338	641	1	145–163	145–163	NUM
ejpam-2338	641	2	.	.	NOUN
ejpam-2338	641	3	2007	2007	NUM
ejpam-2338	641	4	.	.	PUNCT
ejpam-2338	642	1	[	[	X
ejpam-2338	642	2	53	53	NUM
ejpam-2338	642	3	]	]	PUNCT
ejpam-2338	642	4	s.	s.	PROPN
ejpam-2338	642	5	lie	lie	PROPN
ejpam-2338	642	6	,	,	PUNCT
ejpam-2338	642	7	die	die	VERB
ejpam-2338	642	8	grundlagen	grundlagen	PROPN
ejpam-2338	642	9	für	für	PROPN
ejpam-2338	642	10	die	die	VERB
ejpam-2338	642	11	theorie	theorie	PROPN
ejpam-2338	642	12	der	der	PROPN
ejpam-2338	642	13	unendlichen	unendlichen	SCONJ
ejpam-2338	642	14	kontinuierlichen	kontinuierlichen	PROPN
ejpam-2338	642	15	transformationsgruppen	transformationsgruppen	PROPN
ejpam-2338	642	16	i	i	PROPN
ejpam-2338	642	17	,	,	PUNCT
ejpam-2338	642	18	leipzig	leipzig	PROPN
ejpam-2338	642	19	,	,	PUNCT
ejpam-2338	642	20	berichte	berichte	VERB
ejpam-2338	642	21	3	3	NUM
ejpam-2338	642	22	316–352	316–352	NUM
ejpam-2338	642	23	;	;	PUNCT
ejpam-2338	642	24	ii	ii	NOUN
ejpam-2338	642	25	,	,	PUNCT
ejpam-2338	642	26	ibid	ibid	NOUN
ejpam-2338	642	27	.	.	PUNCT
ejpam-2338	643	1	353–393	353–393	NUM
ejpam-2338	643	2	.	.	PUNCT
ejpam-2338	643	3	1891	1891	NUM
ejpam-2338	643	4	.	.	PUNCT
ejpam-2338	644	1	[	[	X
ejpam-2338	644	2	54	54	NUM
ejpam-2338	644	3	]	]	PUNCT
ejpam-2338	644	4	m.	m.	NOUN
ejpam-2338	644	5	loganathan	loganathan	PROPN
ejpam-2338	644	6	.	.	PUNCT
ejpam-2338	645	1	cohomology	cohomology	NOUN
ejpam-2338	645	2	of	of	ADP
ejpam-2338	645	3	inverse	inverse	NOUN
ejpam-2338	645	4	semigroups	semigroup	NOUN
ejpam-2338	645	5	,	,	PUNCT
ejpam-2338	645	6	journal	journal	NOUN
ejpam-2338	645	7	of	of	ADP
ejpam-2338	645	8	algebra	algebra	NOUN
ejpam-2338	645	9	70	70	NUM
ejpam-2338	645	10	375–393	375–393	NUM
ejpam-2338	645	11	.	.	PUNCT
ejpam-2338	646	1	1981	1981	NUM
ejpam-2338	646	2	.	.	PUNCT
ejpam-2338	647	1	http://dx.doi.org/10.1016/0021-8693(81)90225-8	http://dx.doi.org/10.1016/0021-8693(81)90225-8	PROPN
ejpam-2338	647	2	references	reference	VERB
ejpam-2338	647	3	320	320	NUM
ejpam-2338	647	4	[	[	SYM
ejpam-2338	647	5	55	55	NUM
ejpam-2338	647	6	]	]	PUNCT
ejpam-2338	647	7	f.	f.	PROPN
ejpam-2338	647	8	maniakowski	maniakowski	PROPN
ejpam-2338	647	9	.	.	PUNCT
ejpam-2338	648	1	sur	sur	PROPN
ejpam-2338	648	2	les	les	PROPN
ejpam-2338	648	3	axiomes	axiomes	PROPN
ejpam-2338	648	4	du	du	PROPN
ejpam-2338	648	5	pseudogroupe	pseudogroupe	PROPN
ejpam-2338	648	6	,	,	PUNCT
ejpam-2338	648	7	bulletin	bulletin	NOUN
ejpam-2338	648	8	de	de	X
ejpam-2338	648	9	l’académie	l’académie	PROPN
ejpam-2338	648	10	polonaise	polonaise	PROPN
ejpam-2338	648	11	des	des	PROPN
ejpam-2338	648	12	sciences	sciences	PROPN
ejpam-2338	648	13	.	.	PUNCT
ejpam-2338	649	1	série	série	PROPN
ejpam-2338	649	2	des	des	PROPN
ejpam-2338	649	3	sciences	sciences	PROPN
ejpam-2338	649	4	mathématiques	mathématique	NOUN
ejpam-2338	649	5	,	,	PUNCT
ejpam-2338	649	6	astronomiques	astronomique	VERB
ejpam-2338	649	7	et	et	NOUN
ejpam-2338	649	8	physiques	physique	NOUN
ejpam-2338	649	9	12(4	12(4	NUM
ejpam-2338	649	10	)	)	PUNCT
ejpam-2338	649	11	197–201	197–201	NUM
ejpam-2338	649	12	.	.	PUNCT
ejpam-2338	649	13	1964	1964	NUM
ejpam-2338	649	14	.	.	PUNCT
ejpam-2338	650	1	[	[	X
ejpam-2338	650	2	56	56	NUM
ejpam-2338	650	3	]	]	PUNCT
ejpam-2338	650	4	s.	s.	PROPN
ejpam-2338	650	5	w.	w.	PROPN
ejpam-2338	650	6	margolis	margolis	PROPN
ejpam-2338	650	7	and	and	CCONJ
ejpam-2338	650	8	j.-e	j.-e	PROPN
ejpam-2338	650	9	.	.	PUNCT
ejpam-2338	651	1	pin	pin	NOUN
ejpam-2338	651	2	.	.	PUNCT
ejpam-2338	652	1	inverse	inverse	NOUN
ejpam-2338	652	2	semigroups	semigroup	NOUN
ejpam-2338	652	3	and	and	CCONJ
ejpam-2338	652	4	extensions	extension	NOUN
ejpam-2338	652	5	of	of	ADP
ejpam-2338	652	6	groups	group	NOUN
ejpam-2338	652	7	by	by	ADP
ejpam-2338	652	8	semilattices	semilattice	NOUN
ejpam-2338	652	9	,	,	PUNCT
ejpam-2338	652	10	journal	journal	NOUN
ejpam-2338	652	11	of	of	ADP
ejpam-2338	652	12	algebra	algebra	NOUN
ejpam-2338	652	13	110	110	NUM
ejpam-2338	652	14	277–297	277–297	NUM
ejpam-2338	652	15	.	.	PUNCT
ejpam-2338	652	16	1987	1987	NUM
ejpam-2338	652	17	.	.	PUNCT
ejpam-2338	653	1	http://dx.doi.org/10.1016/	http://dx.doi.org/10.1016/	NOUN
ejpam-2338	653	2	0021	0021	NUM
ejpam-2338	653	3	-	-	PUNCT
ejpam-2338	653	4	8693(87)90046	8693(87)90046	NUM
ejpam-2338	653	5	-	-	SYM
ejpam-2338	653	6	9	9	NUM
ejpam-2338	653	7	[	[	SYM
ejpam-2338	653	8	57	57	NUM
ejpam-2338	653	9	]	]	X
ejpam-2338	653	10	d.	d.	PROPN
ejpam-2338	653	11	b.	b.	PROPN
ejpam-2338	653	12	mcalister	mcalister	PROPN
ejpam-2338	653	13	.	.	PUNCT
ejpam-2338	654	1	groups	group	NOUN
ejpam-2338	654	2	,	,	PUNCT
ejpam-2338	654	3	semilattices	semilattice	NOUN
ejpam-2338	654	4	and	and	CCONJ
ejpam-2338	654	5	inverse	inverse	NOUN
ejpam-2338	654	6	semigroups	semigroup	NOUN
ejpam-2338	654	7	,	,	PUNCT
ejpam-2338	654	8	transactions	transaction	NOUN
ejpam-2338	654	9	of	of	ADP
ejpam-2338	654	10	the	the	DET
ejpam-2338	654	11	american	american	PROPN
ejpam-2338	654	12	mathematical	mathematical	PROPN
ejpam-2338	654	13	society	society	NOUN
ejpam-2338	654	14	192	192	NUM
ejpam-2338	654	15	227–244	227–244	NUM
ejpam-2338	654	16	.	.	PUNCT
ejpam-2338	654	17	1974	1974	NUM
ejpam-2338	654	18	.	.	PUNCT
ejpam-2338	655	1	http://www.jstor.org/stable/	http://www.jstor.org/stable/	NOUN
ejpam-2338	655	2	1996831	1996831	NUM
ejpam-2338	656	1	[	[	X
ejpam-2338	656	2	58	58	NUM
ejpam-2338	656	3	]	]	PUNCT
ejpam-2338	656	4	d.	d.	PROPN
ejpam-2338	656	5	b.	b.	PROPN
ejpam-2338	656	6	mcalister	mcalister	PROPN
ejpam-2338	656	7	.	.	PUNCT
ejpam-2338	657	1	a	a	DET
ejpam-2338	657	2	random	random	ADJ
ejpam-2338	657	3	ramble	ramble	NOUN
ejpam-2338	657	4	through	through	ADP
ejpam-2338	657	5	inverse	inverse	NOUN
ejpam-2338	657	6	semigroups	semigroup	NOUN
ejpam-2338	657	7	,	,	PUNCT
ejpam-2338	657	8	in	in	ADP
ejpam-2338	657	9	:	:	PUNCT
ejpam-2338	657	10	t.	t.	PROPN
ejpam-2338	657	11	e.	e.	PROPN
ejpam-2338	657	12	hall	hall	PROPN
ejpam-2338	657	13	,	,	PUNCT
ejpam-2338	657	14	p.	p.	PROPN
ejpam-2338	657	15	r.	r.	PROPN
ejpam-2338	657	16	jones	jones	PROPN
ejpam-2338	657	17	,	,	PUNCT
ejpam-2338	657	18	and	and	CCONJ
ejpam-2338	657	19	g.	g.	PROPN
ejpam-2338	657	20	b.	b.	PROPN
ejpam-2338	657	21	preston	preston	PROPN
ejpam-2338	657	22	(	(	PUNCT
ejpam-2338	657	23	eds	eds	PROPN
ejpam-2338	657	24	.	.	PUNCT
ejpam-2338	657	25	)	)	PUNCT
ejpam-2338	657	26	.	.	PUNCT
ejpam-2338	658	1	semigroups	semigroup	NOUN
ejpam-2338	658	2	(	(	PUNCT
ejpam-2338	658	3	monash	monash	PROPN
ejpam-2338	658	4	university	university	PROPN
ejpam-2338	658	5	conference	conference	NOUN
ejpam-2338	658	6	on	on	ADP
ejpam-2338	658	7	semigroups	semigroup	NOUN
ejpam-2338	658	8	,	,	PUNCT
ejpam-2338	658	9	1979	1979	NUM
ejpam-2338	658	10	)	)	PUNCT
ejpam-2338	658	11	,	,	PUNCT
ejpam-2338	658	12	academic	academic	ADJ
ejpam-2338	658	13	press	press	NOUN
ejpam-2338	658	14	,	,	PUNCT
ejpam-2338	658	15	ny	ny	PROPN
ejpam-2338	658	16	,	,	PUNCT
ejpam-2338	658	17	pp	pp	PROPN
ejpam-2338	658	18	.	.	PUNCT
ejpam-2338	659	1	1–20	1–20	NUM
ejpam-2338	659	2	.	.	PUNCT
ejpam-2338	659	3	1980	1980	NUM
ejpam-2338	659	4	.	.	PUNCT
ejpam-2338	660	1	[	[	X
ejpam-2338	660	2	59	59	NUM
ejpam-2338	660	3	]	]	PUNCT
ejpam-2338	660	4	d.	d.	PROPN
ejpam-2338	660	5	b.	b.	PROPN
ejpam-2338	660	6	mcalister	mcalister	PROPN
ejpam-2338	660	7	.	.	PUNCT
ejpam-2338	661	1	an	an	DET
ejpam-2338	661	2	introduction	introduction	NOUN
ejpam-2338	661	3	to	to	ADP
ejpam-2338	661	4	e∗-unitary	e∗-unitary	ADJ
ejpam-2338	661	5	inverse	inverse	NOUN
ejpam-2338	661	6	semigroups	semigroup	NOUN
ejpam-2338	661	7	—	—	PUNCT
ejpam-2338	661	8	from	from	ADP
ejpam-2338	661	9	an	an	DET
ejpam-2338	661	10	old	old	ADJ
ejpam-2338	661	11	fashioned	fashioned	ADJ
ejpam-2338	661	12	perspective	perspective	NOUN
ejpam-2338	661	13	,	,	PUNCT
ejpam-2338	661	14	in	in	ADP
ejpam-2338	661	15	:	:	PUNCT
ejpam-2338	661	16	i.	i.	PROPN
ejpam-2338	661	17	m.	m.	PROPN
ejpam-2338	661	18	araújo	araújo	PROPN
ejpam-2338	661	19	,	,	PUNCT
ejpam-2338	661	20	m.	m.	PROPN
ejpam-2338	661	21	j.	j.	PROPN
ejpam-2338	661	22	j.	j.	PROPN
ejpam-2338	661	23	branco	branco	PROPN
ejpam-2338	661	24	,	,	PUNCT
ejpam-2338	661	25	v.	v.	PROPN
ejpam-2338	661	26	h.	h.	PROPN
ejpam-2338	661	27	fernandes	fernandes	PROPN
ejpam-2338	661	28	,	,	PUNCT
ejpam-2338	661	29	and	and	CCONJ
ejpam-2338	661	30	g.	g.	PROPN
ejpam-2338	661	31	m.	m.	PROPN
ejpam-2338	661	32	s.	s.	PROPN
ejpam-2338	661	33	gomes	gomes	PROPN
ejpam-2338	661	34	(	(	PUNCT
ejpam-2338	661	35	eds	ed	NOUN
ejpam-2338	661	36	.	.	PUNCT
ejpam-2338	661	37	)	)	PUNCT
ejpam-2338	661	38	.	.	PUNCT
ejpam-2338	662	1	proceedings	proceeding	NOUN
ejpam-2338	662	2	of	of	ADP
ejpam-2338	662	3	the	the	DET
ejpam-2338	662	4	workshop	workshop	NOUN
ejpam-2338	662	5	“	"	PUNCT
ejpam-2338	662	6	semigroups	semigroup	NOUN
ejpam-2338	662	7	and	and	CCONJ
ejpam-2338	662	8	languages	language	NOUN
ejpam-2338	662	9	”	"	PUNCT
ejpam-2338	662	10	(	(	PUNCT
ejpam-2338	662	11	lisbon	lisbon	PROPN
ejpam-2338	662	12	,	,	PUNCT
ejpam-2338	662	13	portugal	portugal	PROPN
ejpam-2338	662	14	,	,	PUNCT
ejpam-2338	662	15	27	27	NUM
ejpam-2338	662	16	–	–	PUNCT
ejpam-2338	662	17	29	29	NUM
ejpam-2338	662	18	november	november	PROPN
ejpam-2338	662	19	2002	2002	NUM
ejpam-2338	662	20	)	)	PUNCT
ejpam-2338	662	21	,	,	PUNCT
ejpam-2338	662	22	world	world	NOUN
ejpam-2338	662	23	scientific	scientific	ADJ
ejpam-2338	662	24	publications	publication	NOUN
ejpam-2338	662	25	,	,	PUNCT
ejpam-2338	662	26	river	river	NOUN
ejpam-2338	662	27	edge	edge	NOUN
ejpam-2338	662	28	,	,	PUNCT
ejpam-2338	662	29	nj	nj	PROPN
ejpam-2338	662	30	,	,	PUNCT
ejpam-2338	662	31	pp	pp	ADJ
ejpam-2338	662	32	.	.	PUNCT
ejpam-2338	663	1	133–150	133–150	NUM
ejpam-2338	663	2	.	.	PUNCT
ejpam-2338	663	3	2004	2004	NUM
ejpam-2338	663	4	.	.	PUNCT
ejpam-2338	664	1	[	[	X
ejpam-2338	664	2	60	60	NUM
ejpam-2338	664	3	]	]	X
ejpam-2338	664	4	e.	e.	PROPN
ejpam-2338	664	5	c.	c.	PROPN
ejpam-2338	664	6	miller	miller	PROPN
ejpam-2338	664	7	.	.	PUNCT
ejpam-2338	665	1	structure	structure	NOUN
ejpam-2338	665	2	theorems	theorem	NOUN
ejpam-2338	665	3	for	for	ADP
ejpam-2338	665	4	ordered	order	VERB
ejpam-2338	665	5	groupoids	groupoid	NOUN
ejpam-2338	665	6	,	,	PUNCT
ejpam-2338	665	7	phd	phd	NOUN
ejpam-2338	665	8	thesis	thesis	NOUN
ejpam-2338	665	9	,	,	PUNCT
ejpam-2338	665	10	heriot	heriot	NOUN
ejpam-2338	665	11	-	-	PUNCT
ejpam-2338	665	12	watt	watt	NOUN
ejpam-2338	665	13	university	university	NOUN
ejpam-2338	665	14	,	,	PUNCT
ejpam-2338	665	15	2009	2009	NUM
ejpam-2338	665	16	.	.	PUNCT
ejpam-2338	666	1	[	[	X
ejpam-2338	666	2	61	61	NUM
ejpam-2338	666	3	]	]	PUNCT
ejpam-2338	666	4	j.	j.	PROPN
ejpam-2338	666	5	e.	e.	PROPN
ejpam-2338	666	6	mills	mills	PROPN
ejpam-2338	666	7	.	.	PUNCT
ejpam-2338	667	1	the	the	DET
ejpam-2338	667	2	inverse	inverse	NOUN
ejpam-2338	667	3	semigroup	semigroup	NOUN
ejpam-2338	667	4	of	of	ADP
ejpam-2338	667	5	partial	partial	ADJ
ejpam-2338	667	6	symmetries	symmetry	NOUN
ejpam-2338	667	7	of	of	ADP
ejpam-2338	667	8	a	a	DET
ejpam-2338	667	9	convex	convex	ADJ
ejpam-2338	667	10	polygon	polygon	NOUN
ejpam-2338	667	11	,	,	PUNCT
ejpam-2338	667	12	semigroup	semigroup	PROPN
ejpam-2338	667	13	forum	forum	PROPN
ejpam-2338	667	14	41(2	41(2	NUM
ejpam-2338	667	15	)	)	PUNCT
ejpam-2338	667	16	127–143	127–143	NUM
ejpam-2338	667	17	.	.	PUNCT
ejpam-2338	667	18	1990	1990	NUM
ejpam-2338	667	19	.	.	PUNCT
ejpam-2338	668	1	http://dx.doi.org/10.1007/bf02573384	http://dx.doi.org/10.1007/bf02573384	PROPN
ejpam-2338	668	2	[	[	X
ejpam-2338	668	3	62	62	NUM
ejpam-2338	668	4	]	]	PUNCT
ejpam-2338	668	5	w.	w.	PROPN
ejpam-2338	668	6	d.	d.	PROPN
ejpam-2338	668	7	munn	munn	PROPN
ejpam-2338	668	8	.	.	PUNCT
ejpam-2338	669	1	a	a	DET
ejpam-2338	669	2	class	class	NOUN
ejpam-2338	669	3	of	of	ADP
ejpam-2338	669	4	irreducible	irreducible	ADJ
ejpam-2338	669	5	matrix	matrix	NOUN
ejpam-2338	669	6	representations	representation	NOUN
ejpam-2338	669	7	of	of	ADP
ejpam-2338	669	8	an	an	DET
ejpam-2338	669	9	arbitrary	arbitrary	ADJ
ejpam-2338	669	10	inverse	inverse	NOUN
ejpam-2338	669	11	semigroup	semigroup	NOUN
ejpam-2338	669	12	,	,	PUNCT
ejpam-2338	669	13	proceedings	proceeding	NOUN
ejpam-2338	669	14	of	of	ADP
ejpam-2338	669	15	the	the	DET
ejpam-2338	669	16	glasgow	glasgow	PROPN
ejpam-2338	669	17	mathematical	mathematical	PROPN
ejpam-2338	669	18	association	association	PROPN
ejpam-2338	669	19	5	5	NUM
ejpam-2338	669	20	41–48	41–48	NUM
ejpam-2338	669	21	.	.	PUNCT
ejpam-2338	669	22	1971	1971	NUM
ejpam-2338	669	23	.	.	PUNCT
ejpam-2338	670	1	http	http	ADJ
ejpam-2338	670	2	:	:	PUNCT
ejpam-2338	670	3	//dx.doi.org/10.1017	//dx.doi.org/10.1017	X
ejpam-2338	670	4	/	/	SYM
ejpam-2338	670	5	s2040618500034286	s2040618500034286	ADJ
ejpam-2338	670	6	[	[	PUNCT
ejpam-2338	670	7	63	63	NUM
ejpam-2338	670	8	]	]	PUNCT
ejpam-2338	670	9	w.	w.	PROPN
ejpam-2338	670	10	d.	d.	PROPN
ejpam-2338	670	11	munn	munn	PROPN
ejpam-2338	670	12	.	.	PUNCT
ejpam-2338	671	1	a	a	DET
ejpam-2338	671	2	certain	certain	ADJ
ejpam-2338	671	3	sublattice	sublattice	NOUN
ejpam-2338	671	4	of	of	ADP
ejpam-2338	671	5	the	the	DET
ejpam-2338	671	6	lattice	lattice	NOUN
ejpam-2338	671	7	of	of	ADP
ejpam-2338	671	8	congruences	congruence	NOUN
ejpam-2338	671	9	on	on	ADP
ejpam-2338	671	10	a	a	DET
ejpam-2338	671	11	regular	regular	ADJ
ejpam-2338	671	12	semigroup	semigroup	NOUN
ejpam-2338	671	13	,	,	PUNCT
ejpam-2338	671	14	proceedings	proceeding	NOUN
ejpam-2338	671	15	of	of	ADP
ejpam-2338	671	16	the	the	DET
ejpam-2338	671	17	cambridge	cambridge	PROPN
ejpam-2338	671	18	philosophical	philosophical	ADJ
ejpam-2338	671	19	society	society	NOUN
ejpam-2338	671	20	60	60	NUM
ejpam-2338	671	21	385–391	385–391	NUM
ejpam-2338	671	22	.	.	PUNCT
ejpam-2338	671	23	1964	1964	NUM
ejpam-2338	671	24	.	.	PUNCT
ejpam-2338	672	1	http://dx	http://dx	NOUN
ejpam-2338	672	2	.	.	PUNCT
ejpam-2338	673	1	doi.org/10.1017/s0305004100037890	doi.org/10.1017/s0305004100037890	VERB
ejpam-2338	674	1	[	[	X
ejpam-2338	674	2	64	64	NUM
ejpam-2338	674	3	]	]	PUNCT
ejpam-2338	674	4	w.	w.	PROPN
ejpam-2338	674	5	d.	d.	PROPN
ejpam-2338	674	6	munn	munn	PROPN
ejpam-2338	674	7	.	.	PUNCT
ejpam-2338	675	1	uniform	uniform	PROPN
ejpam-2338	675	2	semilattices	semilattice	NOUN
ejpam-2338	675	3	and	and	CCONJ
ejpam-2338	675	4	bisimple	bisimple	ADJ
ejpam-2338	675	5	inverse	inverse	NOUN
ejpam-2338	675	6	semigroups	semigroup	NOUN
ejpam-2338	675	7	,	,	PUNCT
ejpam-2338	675	8	quarterly	quarterly	ADJ
ejpam-2338	675	9	journal	journal	NOUN
ejpam-2338	675	10	of	of	ADP
ejpam-2338	675	11	mathematics	mathematic	NOUN
ejpam-2338	675	12	,	,	PUNCT
ejpam-2338	675	13	oxford	oxford	PROPN
ejpam-2338	675	14	(	(	PUNCT
ejpam-2338	675	15	2	2	NUM
ejpam-2338	675	16	)	)	PUNCT
ejpam-2338	675	17	17	17	NUM
ejpam-2338	675	18	151–159	151–159	NUM
ejpam-2338	675	19	.	.	PUNCT
ejpam-2338	675	20	1966	1966	NUM
ejpam-2338	675	21	.	.	PUNCT
ejpam-2338	676	1	http://dx.doi.org/10.1093/qmath/	http://dx.doi.org/10.1093/qmath/	NOUN
ejpam-2338	677	1	17.1.151	17.1.151	NUM
ejpam-2338	677	2	[	[	X
ejpam-2338	677	3	65	65	NUM
ejpam-2338	677	4	]	]	X
ejpam-2338	677	5	w.	w.	PROPN
ejpam-2338	677	6	d.	d.	PROPN
ejpam-2338	677	7	munn	munn	PROPN
ejpam-2338	677	8	.	.	PUNCT
ejpam-2338	678	1	fundamental	fundamental	ADJ
ejpam-2338	678	2	inverse	inverse	NOUN
ejpam-2338	678	3	semigroups	semigroup	NOUN
ejpam-2338	678	4	,	,	PUNCT
ejpam-2338	678	5	quarterly	quarterly	ADJ
ejpam-2338	678	6	journal	journal	NOUN
ejpam-2338	678	7	of	of	ADP
ejpam-2338	678	8	mathematics	mathematic	NOUN
ejpam-2338	678	9	,	,	PUNCT
ejpam-2338	678	10	oxford	oxford	PROPN
ejpam-2338	678	11	(	(	PUNCT
ejpam-2338	678	12	2	2	NUM
ejpam-2338	678	13	)	)	PUNCT
ejpam-2338	678	14	21	21	NUM
ejpam-2338	678	15	157–170	157–170	NUM
ejpam-2338	678	16	.	.	PUNCT
ejpam-2338	679	1	1970	1970	NUM
ejpam-2338	679	2	.	.	PUNCT
ejpam-2338	680	1	http://dx.doi.org/10.1093/qmath/21.2.157	http://dx.doi.org/10.1093/qmath/21.2.157	NOUN
ejpam-2338	681	1	[	[	X
ejpam-2338	681	2	66	66	NUM
ejpam-2338	681	3	]	]	PUNCT
ejpam-2338	681	4	w.	w.	PROPN
ejpam-2338	681	5	d.	d.	PROPN
ejpam-2338	681	6	munn	munn	PROPN
ejpam-2338	681	7	.	.	PUNCT
ejpam-2338	682	1	a	a	DET
ejpam-2338	682	2	note	note	NOUN
ejpam-2338	682	3	on	on	ADP
ejpam-2338	682	4	e	e	NOUN
ejpam-2338	682	5	-	-	ADJ
ejpam-2338	682	6	unitary	unitary	ADJ
ejpam-2338	682	7	inverse	inverse	NOUN
ejpam-2338	682	8	semigroups	semigroup	NOUN
ejpam-2338	682	9	,	,	PUNCT
ejpam-2338	682	10	bulletin	bulletin	NOUN
ejpam-2338	682	11	of	of	ADP
ejpam-2338	682	12	the	the	DET
ejpam-2338	682	13	london	london	PROPN
ejpam-2338	682	14	mathematical	mathematical	ADJ
ejpam-2338	682	15	society	society	NOUN
ejpam-2338	682	16	8	8	NUM
ejpam-2338	682	17	71–76	71–76	NUM
ejpam-2338	682	18	.	.	PUNCT
ejpam-2338	682	19	1976	1976	NUM
ejpam-2338	682	20	.	.	PUNCT
ejpam-2338	683	1	http://dx.doi.org/10.1112/blms/8.1.71	http://dx.doi.org/10.1112/blms/8.1.71	PROPN
ejpam-2338	683	2	[	[	X
ejpam-2338	683	3	67	67	NUM
ejpam-2338	683	4	]	]	PUNCT
ejpam-2338	683	5	k.	k.	PROPN
ejpam-2338	683	6	s.	s.	PROPN
ejpam-2338	683	7	s.	s.	PROPN
ejpam-2338	683	8	nambooripad	nambooripad	PROPN
ejpam-2338	683	9	.	.	PUNCT
ejpam-2338	684	1	structure	structure	NOUN
ejpam-2338	684	2	of	of	ADP
ejpam-2338	684	3	regular	regular	ADJ
ejpam-2338	684	4	semigroups	semigroup	NOUN
ejpam-2338	684	5	i.	i.	PROPN
ejpam-2338	684	6	fundamental	fundamental	PROPN
ejpam-2338	684	7	regular	regular	ADJ
ejpam-2338	684	8	semigroups	semigroup	NOUN
ejpam-2338	684	9	,	,	PUNCT
ejpam-2338	684	10	semigroup	semigroup	PROPN
ejpam-2338	684	11	forum	forum	NOUN
ejpam-2338	684	12	9	9	NUM
ejpam-2338	684	13	354–363	354–363	NUM
ejpam-2338	684	14	.	.	PUNCT
ejpam-2338	685	1	1974/1975	1974/1975	NUM
ejpam-2338	685	2	;	;	PUNCT
ejpam-2338	685	3	ii	ii	X
ejpam-2338	685	4	.	.	PUNCT
ejpam-2338	686	1	the	the	DET
ejpam-2338	686	2	general	general	ADJ
ejpam-2338	686	3	case	case	NOUN
ejpam-2338	686	4	,	,	PUNCT
ejpam-2338	686	5	ibid	ibid	NOUN
ejpam-2338	686	6	.	.	PUNCT
ejpam-2338	686	7	references	reference	NOUN
ejpam-2338	686	8	321	321	NUM
ejpam-2338	686	9	364–371	364–371	NUM
ejpam-2338	686	10	.	.	PUNCT
ejpam-2338	687	1	http://dx.doi.org/10.1007/bf02194864	http://dx.doi.org/10.1007/bf02194864	PROPN
ejpam-2338	687	2	,	,	PUNCT
ejpam-2338	687	3	http://dx.doi.org/10	http://dx.doi.org/10	PROPN
ejpam-2338	687	4	.	.	PUNCT
ejpam-2338	688	1	1007	1007	NUM
ejpam-2338	688	2	/	/	SYM
ejpam-2338	688	3	bf02194865	bf02194865	ADJ
ejpam-2338	688	4	[	[	X
ejpam-2338	688	5	68	68	NUM
ejpam-2338	688	6	]	]	PUNCT
ejpam-2338	688	7	k.	k.	PROPN
ejpam-2338	688	8	s.	s.	PROPN
ejpam-2338	688	9	s.	s.	PROPN
ejpam-2338	688	10	nambooripad	nambooripad	PROPN
ejpam-2338	688	11	.	.	PUNCT
ejpam-2338	689	1	structure	structure	NOUN
ejpam-2338	689	2	of	of	ADP
ejpam-2338	689	3	regular	regular	ADJ
ejpam-2338	689	4	semigroups	semigroup	NOUN
ejpam-2338	689	5	i	i	PRON
ejpam-2338	689	6	,	,	PUNCT
ejpam-2338	689	7	memoirs	memoir	NOUN
ejpam-2338	689	8	of	of	ADP
ejpam-2338	689	9	the	the	DET
ejpam-2338	689	10	american	american	PROPN
ejpam-2338	689	11	mathematical	mathematical	PROPN
ejpam-2338	689	12	society	society	NOUN
ejpam-2338	689	13	22	22	NUM
ejpam-2338	689	14	,	,	PUNCT
ejpam-2338	689	15	no	no	INTJ
ejpam-2338	689	16	.	.	NOUN
ejpam-2338	689	17	224	224	NUM
ejpam-2338	689	18	.	.	PUNCT
ejpam-2338	690	1	1979	1979	NUM
ejpam-2338	690	2	.	.	PUNCT
ejpam-2338	691	1	[	[	X
ejpam-2338	691	2	69	69	NUM
ejpam-2338	691	3	]	]	PUNCT
ejpam-2338	691	4	k.	k.	PROPN
ejpam-2338	691	5	s.	s.	PROPN
ejpam-2338	691	6	s.	s.	PROPN
ejpam-2338	691	7	nambooripad	nambooripad	PROPN
ejpam-2338	691	8	and	and	CCONJ
ejpam-2338	691	9	r.	r.	PROPN
ejpam-2338	691	10	veeramony	veeramony	PROPN
ejpam-2338	691	11	.	.	PUNCT
ejpam-2338	692	1	subdirect	subdirect	NOUN
ejpam-2338	692	2	products	product	NOUN
ejpam-2338	692	3	of	of	ADP
ejpam-2338	692	4	regular	regular	ADJ
ejpam-2338	692	5	semigroups	semigroup	NOUN
ejpam-2338	692	6	,	,	PUNCT
ejpam-2338	692	7	semigroup	semigroup	PROPN
ejpam-2338	692	8	forum	forum	PROPN
ejpam-2338	692	9	27(1–4	27(1–4	NOUN
ejpam-2338	692	10	)	)	PUNCT
ejpam-2338	692	11	265–307	265–307	NUM
ejpam-2338	692	12	.	.	PUNCT
ejpam-2338	692	13	1983	1983	NUM
ejpam-2338	692	14	.	.	PUNCT
ejpam-2338	693	1	http://dx.doi.org/10.1007/bf02572743	http://dx.doi.org/10.1007/bf02572743	X
ejpam-2338	694	1	[	[	X
ejpam-2338	694	2	70	70	NUM
ejpam-2338	694	3	]	]	PUNCT
ejpam-2338	694	4	l.	l.	PROPN
ejpam-2338	694	5	o’carroll	o’carroll	PROPN
ejpam-2338	694	6	.	.	PUNCT
ejpam-2338	695	1	reduced	reduce	VERB
ejpam-2338	695	2	inverse	inverse	NOUN
ejpam-2338	695	3	semigroups	semigroup	NOUN
ejpam-2338	695	4	,	,	PUNCT
ejpam-2338	695	5	semigroup	semigroup	PROPN
ejpam-2338	695	6	forum	forum	PROPN
ejpam-2338	695	7	8(3	8(3	NUM
ejpam-2338	695	8	)	)	PUNCT
ejpam-2338	696	1	270–276	270–276	NUM
ejpam-2338	696	2	.	.	PUNCT
ejpam-2338	696	3	1974	1974	NUM
ejpam-2338	696	4	.	.	PUNCT
ejpam-2338	697	1	http	http	ADJ
ejpam-2338	697	2	:	:	PUNCT
ejpam-2338	697	3	//dx.doi.org/10.1007	//dx.doi.org/10.1007	ADJ
ejpam-2338	697	4	/	/	SYM
ejpam-2338	697	5	bf02194769	bf02194769	NOUN
ejpam-2338	698	1	[	[	X
ejpam-2338	698	2	71	71	NUM
ejpam-2338	698	3	]	]	PUNCT
ejpam-2338	698	4	l.	l.	PROPN
ejpam-2338	698	5	o’carroll	o’carroll	PROPN
ejpam-2338	698	6	.	.	PUNCT
ejpam-2338	699	1	embedding	embed	VERB
ejpam-2338	699	2	theorems	theorem	NOUN
ejpam-2338	699	3	for	for	ADP
ejpam-2338	699	4	proper	proper	ADJ
ejpam-2338	699	5	inverse	inverse	NOUN
ejpam-2338	699	6	semigroups	semigroup	NOUN
ejpam-2338	699	7	,	,	PUNCT
ejpam-2338	699	8	journal	journal	NOUN
ejpam-2338	699	9	of	of	ADP
ejpam-2338	699	10	algebra	algebra	PROPN
ejpam-2338	699	11	42(1	42(1	NOUN
ejpam-2338	699	12	)	)	PUNCT
ejpam-2338	699	13	26–40	26–40	NUM
ejpam-2338	699	14	.	.	PUNCT
ejpam-2338	699	15	1976	1976	NUM
ejpam-2338	699	16	.	.	PUNCT
ejpam-2338	700	1	http://dx.doi.org/doi:10.1016/0021-8693(76)90023-5	http://dx.doi.org/doi:10.1016/0021-8693(76)90023-5	NOUN
ejpam-2338	701	1	[	[	X
ejpam-2338	701	2	72	72	NUM
ejpam-2338	701	3	]	]	PUNCT
ejpam-2338	701	4	m.	m.	NOUN
ejpam-2338	701	5	petrich	petrich	PROPN
ejpam-2338	701	6	.	.	PUNCT
ejpam-2338	702	1	inverse	inverse	NOUN
ejpam-2338	702	2	semigroups	semigroup	NOUN
ejpam-2338	702	3	,	,	PUNCT
ejpam-2338	702	4	john	john	PROPN
ejpam-2338	702	5	wiley	wiley	PROPN
ejpam-2338	702	6	and	and	CCONJ
ejpam-2338	702	7	sons	son	NOUN
ejpam-2338	702	8	,	,	PUNCT
ejpam-2338	702	9	1984	1984	NUM
ejpam-2338	702	10	.	.	PUNCT
ejpam-2338	703	1	[	[	X
ejpam-2338	703	2	73	73	NUM
ejpam-2338	703	3	]	]	PUNCT
ejpam-2338	703	4	m.	m.	NOUN
ejpam-2338	703	5	petrich	petrich	PROPN
ejpam-2338	703	6	and	and	CCONJ
ejpam-2338	703	7	n.	n.	PROPN
ejpam-2338	703	8	r.	r.	PROPN
ejpam-2338	703	9	reilly	reilly	PROPN
ejpam-2338	703	10	.	.	PUNCT
ejpam-2338	704	1	a	a	DET
ejpam-2338	704	2	representation	representation	NOUN
ejpam-2338	704	3	of	of	ADP
ejpam-2338	704	4	e	e	NOUN
ejpam-2338	704	5	-	-	ADJ
ejpam-2338	704	6	unitary	unitary	ADJ
ejpam-2338	704	7	semigroups	semigroup	NOUN
ejpam-2338	704	8	,	,	PUNCT
ejpam-2338	704	9	quarterly	quarterly	ADJ
ejpam-2338	704	10	journal	journal	NOUN
ejpam-2338	704	11	of	of	ADP
ejpam-2338	704	12	mathematics	mathematic	NOUN
ejpam-2338	704	13	,	,	PUNCT
ejpam-2338	704	14	oxford	oxford	PROPN
ejpam-2338	704	15	(	(	PUNCT
ejpam-2338	704	16	2	2	NUM
ejpam-2338	704	17	)	)	PUNCT
ejpam-2338	704	18	30	30	NUM
ejpam-2338	704	19	339–350	339–350	NUM
ejpam-2338	704	20	.	.	PUNCT
ejpam-2338	704	21	1979	1979	NUM
ejpam-2338	704	22	.	.	PUNCT
ejpam-2338	705	1	http://dx.doi.org/10.1093/	http://dx.doi.org/10.1093/	X
ejpam-2338	705	2	qmath/30.3.339	qmath/30.3.339	PUNCT
ejpam-2338	706	1	[	[	X
ejpam-2338	706	2	74	74	NUM
ejpam-2338	706	3	]	]	PUNCT
ejpam-2338	706	4	g.	g.	PROPN
ejpam-2338	706	5	b.	b.	PROPN
ejpam-2338	706	6	preston	preston	PROPN
ejpam-2338	706	7	.	.	PUNCT
ejpam-2338	707	1	some	some	DET
ejpam-2338	707	2	problems	problem	NOUN
ejpam-2338	707	3	in	in	ADP
ejpam-2338	707	4	the	the	DET
ejpam-2338	707	5	theory	theory	NOUN
ejpam-2338	707	6	of	of	ADP
ejpam-2338	707	7	ideals	ideal	NOUN
ejpam-2338	707	8	,	,	PUNCT
ejpam-2338	707	9	dphil	dphil	ADJ
ejpam-2338	707	10	thesis	thesis	NOUN
ejpam-2338	707	11	,	,	PUNCT
ejpam-2338	707	12	university	university	NOUN
ejpam-2338	707	13	of	of	ADP
ejpam-2338	707	14	oxford	oxford	PROPN
ejpam-2338	707	15	,	,	PUNCT
ejpam-2338	707	16	1953	1953	NUM
ejpam-2338	707	17	.	.	PUNCT
ejpam-2338	708	1	[	[	X
ejpam-2338	708	2	75	75	NUM
ejpam-2338	708	3	]	]	X
ejpam-2338	708	4	g.	g.	PROPN
ejpam-2338	708	5	b.	b.	PROPN
ejpam-2338	708	6	preston	preston	PROPN
ejpam-2338	708	7	.	.	PUNCT
ejpam-2338	709	1	inverse	inverse	PROPN
ejpam-2338	709	2	semi	semi	NOUN
ejpam-2338	709	3	-	-	NOUN
ejpam-2338	709	4	groups	group	NOUN
ejpam-2338	709	5	,	,	PUNCT
ejpam-2338	709	6	journal	journal	NOUN
ejpam-2338	709	7	of	of	ADP
ejpam-2338	709	8	the	the	DET
ejpam-2338	709	9	london	london	PROPN
ejpam-2338	709	10	mathematical	mathematical	ADJ
ejpam-2338	709	11	society	society	NOUN
ejpam-2338	709	12	29	29	NUM
ejpam-2338	709	13	396	396	NUM
ejpam-2338	709	14	–	–	PUNCT
ejpam-2338	709	15	403	403	NUM
ejpam-2338	709	16	.	.	PUNCT
ejpam-2338	710	1	1954	1954	NUM
ejpam-2338	710	2	.	.	PUNCT
ejpam-2338	711	1	http://dx.doi.org/doi:10.1112/jlms/s1-29.4.396	http://dx.doi.org/doi:10.1112/jlms/s1-29.4.396	PROPN
ejpam-2338	712	1	[	[	X
ejpam-2338	712	2	76	76	NUM
ejpam-2338	712	3	]	]	X
ejpam-2338	712	4	g.	g.	PROPN
ejpam-2338	712	5	b.	b.	PROPN
ejpam-2338	712	6	preston	preston	PROPN
ejpam-2338	712	7	.	.	PUNCT
ejpam-2338	713	1	inverse	inverse	PROPN
ejpam-2338	713	2	semi	semi	NOUN
ejpam-2338	713	3	-	-	NOUN
ejpam-2338	713	4	groups	group	NOUN
ejpam-2338	713	5	with	with	ADP
ejpam-2338	713	6	minimal	minimal	ADJ
ejpam-2338	713	7	right	right	ADJ
ejpam-2338	713	8	ideals	ideal	NOUN
ejpam-2338	713	9	,	,	PUNCT
ejpam-2338	713	10	journal	journal	NOUN
ejpam-2338	713	11	of	of	ADP
ejpam-2338	713	12	the	the	DET
ejpam-2338	713	13	london	london	PROPN
ejpam-2338	713	14	mathematical	mathematical	ADJ
ejpam-2338	713	15	society	society	NOUN
ejpam-2338	713	16	29	29	NUM
ejpam-2338	713	17	404–411	404–411	NUM
ejpam-2338	713	18	.	.	PUNCT
ejpam-2338	714	1	1954	1954	NUM
ejpam-2338	714	2	.	.	PUNCT
ejpam-2338	715	1	http://dx.doi.org/doi:10.1112/jlms/	http://dx.doi.org/doi:10.1112/jlms/	NUM
ejpam-2338	715	2	s1	s1	NOUN
ejpam-2338	715	3	-	-	PUNCT
ejpam-2338	715	4	29.4.404	29.4.404	NOUN
ejpam-2338	716	1	[	[	X
ejpam-2338	716	2	77	77	NUM
ejpam-2338	716	3	]	]	X
ejpam-2338	716	4	g.	g.	PROPN
ejpam-2338	716	5	b.	b.	PROPN
ejpam-2338	716	6	preston	preston	PROPN
ejpam-2338	716	7	representations	representation	NOUN
ejpam-2338	716	8	of	of	ADP
ejpam-2338	716	9	inverse	inverse	NOUN
ejpam-2338	716	10	semi	semi	NOUN
ejpam-2338	716	11	-	-	NOUN
ejpam-2338	716	12	groups	group	NOUN
ejpam-2338	716	13	,	,	PUNCT
ejpam-2338	716	14	journal	journal	NOUN
ejpam-2338	716	15	of	of	ADP
ejpam-2338	716	16	the	the	DET
ejpam-2338	716	17	london	london	PROPN
ejpam-2338	716	18	mathematical	mathematical	ADJ
ejpam-2338	716	19	society	society	NOUN
ejpam-2338	716	20	29	29	NUM
ejpam-2338	716	21	411–419	411–419	NUM
ejpam-2338	716	22	.	.	PUNCT
ejpam-2338	717	1	1954	1954	NUM
ejpam-2338	717	2	.	.	PUNCT
ejpam-2338	718	1	http://dx.doi.org/doi:10.1112/jlms/s1-29.4	http://dx.doi.org/doi:10.1112/jlms/s1-29.4	PROPN
ejpam-2338	718	2	.	.	PUNCT
ejpam-2338	719	1	411	411	NUM
ejpam-2338	720	1	[	[	X
ejpam-2338	720	2	78	78	NUM
ejpam-2338	720	3	]	]	PUNCT
ejpam-2338	720	4	g.	g.	PROPN
ejpam-2338	720	5	b.	b.	PROPN
ejpam-2338	720	6	preston	preston	PROPN
ejpam-2338	720	7	.	.	PUNCT
ejpam-2338	721	1	the	the	DET
ejpam-2338	721	2	construction	construction	NOUN
ejpam-2338	721	3	of	of	ADP
ejpam-2338	721	4	semigroups	semigroup	NOUN
ejpam-2338	721	5	from	from	ADP
ejpam-2338	721	6	groups	group	NOUN
ejpam-2338	721	7	and	and	CCONJ
ejpam-2338	721	8	semilattices	semilattice	NOUN
ejpam-2338	721	9	,	,	PUNCT
ejpam-2338	721	10	in	in	ADP
ejpam-2338	721	11	:	:	PUNCT
ejpam-2338	721	12	mariepaule	mariepaule	ADJ
ejpam-2338	721	13	malliavin	malliavin	NOUN
ejpam-2338	721	14	(	(	PUNCT
ejpam-2338	721	15	ed	ed	NOUN
ejpam-2338	721	16	.	.	PUNCT
ejpam-2338	721	17	)	)	PUNCT
ejpam-2338	721	18	.	.	PUNCT
ejpam-2338	722	1	groupe	groupe	PROPN
ejpam-2338	722	2	d’étude	d’étude	ADJ
ejpam-2338	722	3	d’algèbre	d’algèbre	PROPN
ejpam-2338	722	4	,	,	PUNCT
ejpam-2338	722	5	1re	1re	ADJ
ejpam-2338	722	6	année	année	NOUN
ejpam-2338	722	7	(	(	PUNCT
ejpam-2338	722	8	1975/76	1975/76	NUM
ejpam-2338	722	9	)	)	PUNCT
ejpam-2338	722	10	,	,	PUNCT
ejpam-2338	722	11	secrétariat	secrétariat	NOUN
ejpam-2338	722	12	mathematique	mathematique	NOUN
ejpam-2338	722	13	,	,	PUNCT
ejpam-2338	722	14	paris	paris	PROPN
ejpam-2338	722	15	,	,	PUNCT
ejpam-2338	722	16	10pp	10pp	NOUN
ejpam-2338	722	17	.	.	PUNCT
ejpam-2338	722	18	1978	1978	NUM
ejpam-2338	722	19	.	.	PUNCT
ejpam-2338	723	1	[	[	X
ejpam-2338	723	2	79	79	NUM
ejpam-2338	723	3	]	]	X
ejpam-2338	723	4	g.	g.	PROPN
ejpam-2338	723	5	b.	b.	PROPN
ejpam-2338	723	6	preston	preston	PROPN
ejpam-2338	723	7	.	.	PUNCT
ejpam-2338	724	1	personal	personal	ADJ
ejpam-2338	724	2	reminiscences	reminiscence	NOUN
ejpam-2338	724	3	of	of	ADP
ejpam-2338	724	4	the	the	DET
ejpam-2338	724	5	early	early	ADJ
ejpam-2338	724	6	history	history	NOUN
ejpam-2338	724	7	of	of	ADP
ejpam-2338	724	8	semigroups	semigroup	NOUN
ejpam-2338	724	9	,	,	PUNCT
ejpam-2338	724	10	in	in	ADP
ejpam-2338	724	11	:	:	PUNCT
ejpam-2338	724	12	t.	t.	PROPN
ejpam-2338	724	13	e.	e.	PROPN
ejpam-2338	724	14	hall	hall	PROPN
ejpam-2338	724	15	,	,	PUNCT
ejpam-2338	724	16	p.	p.	PROPN
ejpam-2338	724	17	r.	r.	PROPN
ejpam-2338	724	18	jones	jones	PROPN
ejpam-2338	724	19	,	,	PUNCT
ejpam-2338	724	20	and	and	CCONJ
ejpam-2338	724	21	j.	j.	PROPN
ejpam-2338	724	22	c.	c.	PROPN
ejpam-2338	724	23	meakin	meakin	PROPN
ejpam-2338	724	24	(	(	PUNCT
ejpam-2338	724	25	eds	ed	NOUN
ejpam-2338	724	26	.	.	PUNCT
ejpam-2338	724	27	)	)	PUNCT
ejpam-2338	724	28	.	.	PUNCT
ejpam-2338	725	1	monash	monash	PROPN
ejpam-2338	725	2	conference	conference	PROPN
ejpam-2338	725	3	on	on	ADP
ejpam-2338	725	4	semigroup	semigroup	PROPN
ejpam-2338	725	5	theory	theory	NOUN
ejpam-2338	725	6	,	,	PUNCT
ejpam-2338	725	7	melbourne	melbourne	PROPN
ejpam-2338	725	8	1990	1990	NUM
ejpam-2338	725	9	,	,	PUNCT
ejpam-2338	725	10	world	world	NOUN
ejpam-2338	725	11	scientific	scientific	ADJ
ejpam-2338	725	12	,	,	PUNCT
ejpam-2338	725	13	river	river	NOUN
ejpam-2338	725	14	edge	edge	NOUN
ejpam-2338	725	15	,	,	PUNCT
ejpam-2338	725	16	nj	nj	PROPN
ejpam-2338	725	17	,	,	PUNCT
ejpam-2338	725	18	pp	pp	ADJ
ejpam-2338	725	19	.	.	PUNCT
ejpam-2338	726	1	16–30	16–30	NUM
ejpam-2338	726	2	.	.	PUNCT
ejpam-2338	726	3	1991	1991	NUM
ejpam-2338	726	4	.	.	PUNCT
ejpam-2338	727	1	[	[	X
ejpam-2338	727	2	80	80	NUM
ejpam-2338	727	3	]	]	X
ejpam-2338	727	4	d.	d.	PROPN
ejpam-2338	727	5	rees	rees	PROPN
ejpam-2338	727	6	.	.	PUNCT
ejpam-2338	728	1	on	on	ADP
ejpam-2338	728	2	semi	semi	NOUN
ejpam-2338	728	3	-	-	NOUN
ejpam-2338	728	4	groups	group	NOUN
ejpam-2338	728	5	,	,	PUNCT
ejpam-2338	728	6	proceedings	proceeding	NOUN
ejpam-2338	728	7	of	of	ADP
ejpam-2338	728	8	the	the	DET
ejpam-2338	728	9	cambridge	cambridge	PROPN
ejpam-2338	728	10	philosophical	philosophical	PROPN
ejpam-2338	728	11	society	society	NOUN
ejpam-2338	728	12	36	36	NUM
ejpam-2338	728	13	387	387	NUM
ejpam-2338	728	14	–	–	PUNCT
ejpam-2338	728	15	400	400	NUM
ejpam-2338	728	16	.	.	PUNCT
ejpam-2338	728	17	1940	1940	NUM
ejpam-2338	728	18	.	.	PUNCT
ejpam-2338	729	1	http://dx.doi.org/10.1017/s0305004100017436	http://dx.doi.org/10.1017/s0305004100017436	X
ejpam-2338	730	1	[	[	X
ejpam-2338	730	2	81	81	NUM
ejpam-2338	730	3	]	]	PUNCT
ejpam-2338	730	4	d.	d.	PROPN
ejpam-2338	730	5	rees	rees	PROPN
ejpam-2338	730	6	.	.	PUNCT
ejpam-2338	731	1	on	on	ADP
ejpam-2338	731	2	the	the	DET
ejpam-2338	731	3	group	group	NOUN
ejpam-2338	731	4	of	of	ADP
ejpam-2338	731	5	a	a	DET
ejpam-2338	731	6	set	set	NOUN
ejpam-2338	731	7	of	of	ADP
ejpam-2338	731	8	partial	partial	ADJ
ejpam-2338	731	9	transformations	transformation	NOUN
ejpam-2338	731	10	,	,	PUNCT
ejpam-2338	731	11	journal	journal	NOUN
ejpam-2338	731	12	of	of	ADP
ejpam-2338	731	13	the	the	DET
ejpam-2338	731	14	london	london	PROPN
ejpam-2338	731	15	mathematical	mathematical	ADJ
ejpam-2338	731	16	society	society	NOUN
ejpam-2338	731	17	22	22	NUM
ejpam-2338	731	18	281–284	281–284	NUM
ejpam-2338	731	19	.	.	PUNCT
ejpam-2338	731	20	1947	1947	NUM
ejpam-2338	731	21	.	.	PUNCT
ejpam-2338	732	1	http://dx.doi.org/doi:10.1112/jlms/	http://dx.doi.org/doi:10.1112/jlms/	NUM
ejpam-2338	732	2	s1	s1	NOUN
ejpam-2338	732	3	-	-	PUNCT
ejpam-2338	732	4	22.4.281	22.4.281	NUM
ejpam-2338	732	5	references	reference	NOUN
ejpam-2338	732	6	322	322	NUM
ejpam-2338	732	7	[	[	X
ejpam-2338	732	8	82	82	NUM
ejpam-2338	732	9	]	]	X
ejpam-2338	732	10	n.	n.	PROPN
ejpam-2338	732	11	r.	r.	PROPN
ejpam-2338	732	12	reilly	reilly	PROPN
ejpam-2338	732	13	.	.	PUNCT
ejpam-2338	733	1	enlarging	enlarge	VERB
ejpam-2338	733	2	the	the	DET
ejpam-2338	733	3	munn	munn	PROPN
ejpam-2338	733	4	representation	representation	NOUN
ejpam-2338	733	5	of	of	ADP
ejpam-2338	733	6	inverse	inverse	NOUN
ejpam-2338	733	7	semigroups	semigroup	NOUN
ejpam-2338	733	8	,	,	PUNCT
ejpam-2338	733	9	journal	journal	NOUN
ejpam-2338	733	10	of	of	ADP
ejpam-2338	733	11	the	the	DET
ejpam-2338	733	12	australian	australian	ADJ
ejpam-2338	733	13	mathematical	mathematical	ADJ
ejpam-2338	733	14	society	society	NOUN
ejpam-2338	733	15	.	.	PUNCT
ejpam-2338	734	1	series	series	PROPN
ejpam-2338	734	2	a	a	DET
ejpam-2338	734	3	23(1	23(1	NOUN
ejpam-2338	734	4	)	)	PUNCT
ejpam-2338	734	5	28–41	28–41	NUM
ejpam-2338	734	6	.	.	PUNCT
ejpam-2338	735	1	1977	1977	NUM
ejpam-2338	735	2	.	.	PUNCT
ejpam-2338	736	1	http://dx.doi.org/	http://dx.doi.org/	PRON
ejpam-2338	736	2	10.1017	10.1017	NUM
ejpam-2338	736	3	/	/	SYM
ejpam-2338	736	4	s1446788700017316	s1446788700017316	PROPN
ejpam-2338	737	1	[	[	X
ejpam-2338	737	2	83	83	NUM
ejpam-2338	737	3	]	]	X
ejpam-2338	737	4	n.	n.	PROPN
ejpam-2338	737	5	r.	r.	PROPN
ejpam-2338	737	6	reilly	reilly	PROPN
ejpam-2338	737	7	and	and	CCONJ
ejpam-2338	737	8	w.	w.	PROPN
ejpam-2338	737	9	d.	d.	PROPN
ejpam-2338	737	10	munn	munn	PROPN
ejpam-2338	737	11	.	.	PUNCT
ejpam-2338	738	1	e	e	X
ejpam-2338	738	2	-	-	ADJ
ejpam-2338	738	3	unitary	unitary	ADJ
ejpam-2338	738	4	congruences	congruence	NOUN
ejpam-2338	738	5	on	on	ADP
ejpam-2338	738	6	inverse	inverse	NOUN
ejpam-2338	738	7	semigroups	semigroup	NOUN
ejpam-2338	738	8	,	,	PUNCT
ejpam-2338	738	9	glasgow	glasgow	PROPN
ejpam-2338	738	10	mathematical	mathematical	ADJ
ejpam-2338	738	11	journal	journal	PROPN
ejpam-2338	738	12	17	17	NUM
ejpam-2338	738	13	57–75	57–75	NUM
ejpam-2338	738	14	.	.	PUNCT
ejpam-2338	738	15	1976	1976	NUM
ejpam-2338	738	16	.	.	PUNCT
ejpam-2338	739	1	http://journals.cambridge.org/	http://journals.cambridge.org/	PRON
ejpam-2338	739	2	article_s0017089500002731	article_s0017089500002731	PROPN
ejpam-2338	740	1	[	[	X
ejpam-2338	740	2	84	84	NUM
ejpam-2338	740	3	]	]	PUNCT
ejpam-2338	740	4	t.	t.	PROPN
ejpam-2338	740	5	saitô	saitô	PROPN
ejpam-2338	740	6	.	.	PUNCT
ejpam-2338	741	1	proper	proper	ADJ
ejpam-2338	741	2	ordered	order	VERB
ejpam-2338	741	3	inverse	inverse	NOUN
ejpam-2338	741	4	semigroups	semigroup	NOUN
ejpam-2338	741	5	,	,	PUNCT
ejpam-2338	741	6	pacific	pacific	PROPN
ejpam-2338	741	7	journal	journal	NOUN
ejpam-2338	741	8	of	of	ADP
ejpam-2338	741	9	mathematics	mathematics	PROPN
ejpam-2338	741	10	15	15	NUM
ejpam-2338	741	11	649–666	649–666	NUM
ejpam-2338	741	12	.	.	PUNCT
ejpam-2338	741	13	1965	1965	NUM
ejpam-2338	741	14	.	.	PUNCT
ejpam-2338	742	1	http://projecteuclid.org/euclid.pjm/1102995815	http://projecteuclid.org/euclid.pjm/1102995815	NOUN
ejpam-2338	743	1	[	[	X
ejpam-2338	743	2	85	85	NUM
ejpam-2338	743	3	]	]	PUNCT
ejpam-2338	743	4	h.	h.	PROPN
ejpam-2338	743	5	e.	e.	PROPN
ejpam-2338	743	6	scheiblich	scheiblich	PROPN
ejpam-2338	743	7	.	.	PUNCT
ejpam-2338	744	1	free	free	ADJ
ejpam-2338	744	2	inverse	inverse	NOUN
ejpam-2338	744	3	semigroups	semigroup	NOUN
ejpam-2338	744	4	,	,	PUNCT
ejpam-2338	744	5	semigroup	semigroup	PROPN
ejpam-2338	744	6	forum	forum	PROPN
ejpam-2338	744	7	4	4	NUM
ejpam-2338	744	8	351–359	351–359	NUM
ejpam-2338	744	9	.	.	PUNCT
ejpam-2338	745	1	1972	1972	NUM
ejpam-2338	745	2	.	.	PUNCT
ejpam-2338	746	1	http	http	ADJ
ejpam-2338	746	2	:	:	PUNCT
ejpam-2338	746	3	//dx.doi.org/10.1007	//dx.doi.org/10.1007	PUNCT
ejpam-2338	746	4	/	/	SYM
ejpam-2338	746	5	bf02570809	bf02570809	PROPN
ejpam-2338	747	1	[	[	X
ejpam-2338	747	2	86	86	NUM
ejpam-2338	747	3	]	]	X
ejpam-2338	747	4	h.	h.	PROPN
ejpam-2338	747	5	e.	e.	PROPN
ejpam-2338	747	6	scheiblich	scheiblich	PROPN
ejpam-2338	747	7	.	.	PUNCT
ejpam-2338	748	1	kernels	kernel	NOUN
ejpam-2338	748	2	of	of	ADP
ejpam-2338	748	3	inverse	inverse	NOUN
ejpam-2338	748	4	semigroup	semigroup	PROPN
ejpam-2338	748	5	homomorphisms	homomorphism	NOUN
ejpam-2338	748	6	,	,	PUNCT
ejpam-2338	748	7	journal	journal	NOUN
ejpam-2338	748	8	of	of	ADP
ejpam-2338	748	9	the	the	DET
ejpam-2338	748	10	australian	australian	ADJ
ejpam-2338	748	11	mathematical	mathematical	ADJ
ejpam-2338	748	12	society	society	NOUN
ejpam-2338	748	13	18	18	NUM
ejpam-2338	748	14	289–292	289–292	NUM
ejpam-2338	748	15	.	.	PUNCT
ejpam-2338	748	16	1974	1974	NUM
ejpam-2338	748	17	.	.	PUNCT
ejpam-2338	749	1	http://dx.doi.org/10.1017/	http://dx.doi.org/10.1017/	CCONJ
ejpam-2338	750	1	s1446788700022862	s1446788700022862	NOUN
ejpam-2338	750	2	[	[	NOUN
ejpam-2338	750	3	87	87	NUM
ejpam-2338	750	4	]	]	PUNCT
ejpam-2338	750	5	b.	b.	PROPN
ejpam-2338	750	6	m.	m.	PROPN
ejpam-2338	750	7	schein	schein	PROPN
ejpam-2338	750	8	.	.	PUNCT
ejpam-2338	751	1	on	on	ADP
ejpam-2338	751	2	the	the	DET
ejpam-2338	751	3	theory	theory	NOUN
ejpam-2338	751	4	of	of	ADP
ejpam-2338	751	5	generalised	generalised	ADJ
ejpam-2338	751	6	heaps	heap	NOUN
ejpam-2338	751	7	and	and	CCONJ
ejpam-2338	751	8	generalised	generalised	ADJ
ejpam-2338	751	9	groups	group	NOUN
ejpam-2338	751	10	,	,	PUNCT
ejpam-2338	751	11	in	in	ADP
ejpam-2338	751	12	:	:	PUNCT
ejpam-2338	751	13	v.	v.	PROPN
ejpam-2338	751	14	v.	v.	ADP
ejpam-2338	751	15	wagner	wagner	PROPN
ejpam-2338	751	16	(	(	PUNCT
ejpam-2338	751	17	ed	ed	NOUN
ejpam-2338	751	18	.	.	PUNCT
ejpam-2338	751	19	)	)	PUNCT
ejpam-2338	751	20	.	.	PUNCT
ejpam-2338	752	1	theory	theory	NOUN
ejpam-2338	752	2	of	of	ADP
ejpam-2338	752	3	semigroups	semigroup	NOUN
ejpam-2338	752	4	and	and	CCONJ
ejpam-2338	752	5	its	its	PRON
ejpam-2338	752	6	applications	application	NOUN
ejpam-2338	752	7	,	,	PUNCT
ejpam-2338	752	8	vol	vol	NOUN
ejpam-2338	752	9	.	.	PROPN
ejpam-2338	752	10	1	1	NUM
ejpam-2338	752	11	,	,	PUNCT
ejpam-2338	752	12	izdat	izdat	NOUN
ejpam-2338	752	13	.	.	PUNCT
ejpam-2338	753	1	saratov	saratov	PROPN
ejpam-2338	753	2	.	.	PUNCT
ejpam-2338	754	1	univ	univ	PROPN
ejpam-2338	754	2	.	.	PROPN
ejpam-2338	754	3	,	,	PUNCT
ejpam-2338	754	4	saratov	saratov	PROPN
ejpam-2338	754	5	,	,	PUNCT
ejpam-2338	754	6	pp	pp	X
ejpam-2338	754	7	.	.	PUNCT
ejpam-2338	755	1	286–324	286–324	NUM
ejpam-2338	755	2	(	(	PUNCT
ejpam-2338	755	3	in	in	ADP
ejpam-2338	755	4	russian	russian	NOUN
ejpam-2338	755	5	)	)	PUNCT
ejpam-2338	755	6	.	.	PUNCT
ejpam-2338	756	1	1965	1965	NUM
ejpam-2338	756	2	.	.	PUNCT
ejpam-2338	757	1	[	[	X
ejpam-2338	757	2	88	88	NUM
ejpam-2338	757	3	]	]	X
ejpam-2338	757	4	b.	b.	PROPN
ejpam-2338	757	5	m.	m.	PROPN
ejpam-2338	757	6	schein	schein	PROPN
ejpam-2338	757	7	.	.	PUNCT
ejpam-2338	758	1	a	a	DET
ejpam-2338	758	2	new	new	ADJ
ejpam-2338	758	3	proof	proof	NOUN
ejpam-2338	758	4	for	for	ADP
ejpam-2338	758	5	the	the	DET
ejpam-2338	758	6	mcalister	mcalister	NOUN
ejpam-2338	758	7	“	"	PUNCT
ejpam-2338	758	8	p	p	PROPN
ejpam-2338	758	9	-	-	PUNCT
ejpam-2338	758	10	theorem	theorem	ADJ
ejpam-2338	758	11	”	"	PUNCT
ejpam-2338	758	12	,	,	PUNCT
ejpam-2338	758	13	semigroup	semigroup	PROPN
ejpam-2338	758	14	forum	forum	PROPN
ejpam-2338	758	15	10	10	NUM
ejpam-2338	758	16	185–188	185–188	NUM
ejpam-2338	758	17	.	.	PUNCT
ejpam-2338	758	18	1975	1975	NUM
ejpam-2338	758	19	.	.	PUNCT
ejpam-2338	759	1	http://dx.doi.org/10.1007/bf02194884	http://dx.doi.org/10.1007/bf02194884	PROPN
ejpam-2338	760	1	[	[	X
ejpam-2338	760	2	89	89	NUM
ejpam-2338	760	3	]	]	X
ejpam-2338	760	4	b.	b.	PROPN
ejpam-2338	760	5	m.	m.	PROPN
ejpam-2338	760	6	schein	schein	PROPN
ejpam-2338	760	7	.	.	PUNCT
ejpam-2338	761	1	on	on	ADP
ejpam-2338	761	2	the	the	DET
ejpam-2338	761	3	theory	theory	NOUN
ejpam-2338	761	4	of	of	ADP
ejpam-2338	761	5	inverse	inverse	NOUN
ejpam-2338	761	6	semigroups	semigroup	NOUN
ejpam-2338	761	7	and	and	CCONJ
ejpam-2338	761	8	generalised	generalised	ADJ
ejpam-2338	761	9	grouds	groud	NOUN
ejpam-2338	761	10	,	,	PUNCT
ejpam-2338	761	11	american	american	PROPN
ejpam-2338	761	12	mathematical	mathematical	ADJ
ejpam-2338	761	13	society	society	NOUN
ejpam-2338	761	14	translations	translation	NOUN
ejpam-2338	761	15	(	(	PUNCT
ejpam-2338	761	16	2	2	NUM
ejpam-2338	761	17	)	)	PUNCT
ejpam-2338	761	18	113	113	NUM
ejpam-2338	761	19	89–122	89–122	NUM
ejpam-2338	761	20	;	;	PUNCT
ejpam-2338	761	21	expanded	expand	VERB
ejpam-2338	761	22	english	english	ADJ
ejpam-2338	761	23	translation	translation	NOUN
ejpam-2338	761	24	of	of	ADP
ejpam-2338	761	25	[	[	X
ejpam-2338	761	26	87	87	NUM
ejpam-2338	761	27	]	]	PUNCT
ejpam-2338	761	28	.	.	PUNCT
ejpam-2338	762	1	1979	1979	NUM
ejpam-2338	762	2	.	.	PUNCT
ejpam-2338	763	1	[	[	X
ejpam-2338	763	2	90	90	NUM
ejpam-2338	763	3	]	]	PUNCT
ejpam-2338	763	4	b.	b.	PROPN
ejpam-2338	763	5	m.	m.	PROPN
ejpam-2338	763	6	schein	schein	PROPN
ejpam-2338	763	7	.	.	PUNCT
ejpam-2338	764	1	obituary	obituary	PROPN
ejpam-2338	764	2	:	:	PUNCT
ejpam-2338	765	1	victor	victor	PROPN
ejpam-2338	765	2	vladimirovich	vladimirovich	PROPN
ejpam-2338	765	3	vagner	vagner	NOUN
ejpam-2338	765	4	(	(	PUNCT
ejpam-2338	765	5	1908–1981	1908–1981	NUM
ejpam-2338	765	6	)	)	PUNCT
ejpam-2338	765	7	,	,	PUNCT
ejpam-2338	765	8	semigroup	semigroup	PROPN
ejpam-2338	765	9	forum	forum	PROPN
ejpam-2338	765	10	23	23	NUM
ejpam-2338	765	11	189–200	189–200	NUM
ejpam-2338	765	12	.	.	PUNCT
ejpam-2338	765	13	1981	1981	NUM
ejpam-2338	765	14	.	.	PUNCT
ejpam-2338	766	1	http://dx.doi.org/10.1007/bf02676643	http://dx.doi.org/10.1007/bf02676643	NOUN
ejpam-2338	767	1	[	[	X
ejpam-2338	767	2	91	91	NUM
ejpam-2338	767	3	]	]	X
ejpam-2338	767	4	b.	b.	PROPN
ejpam-2338	767	5	m.	m.	PROPN
ejpam-2338	767	6	schein	schein	PROPN
ejpam-2338	767	7	.	.	PUNCT
ejpam-2338	768	1	prehistory	prehistory	NOUN
ejpam-2338	768	2	of	of	ADP
ejpam-2338	768	3	the	the	DET
ejpam-2338	768	4	theory	theory	NOUN
ejpam-2338	768	5	of	of	ADP
ejpam-2338	768	6	inverse	inverse	NOUN
ejpam-2338	768	7	semigroups	semigroup	NOUN
ejpam-2338	768	8	,	,	PUNCT
ejpam-2338	768	9	in	in	ADP
ejpam-2338	768	10	:	:	PUNCT
ejpam-2338	768	11	robert	robert	PROPN
ejpam-2338	768	12	j.	j.	PROPN
ejpam-2338	768	13	koch	koch	PROPN
ejpam-2338	768	14	and	and	CCONJ
ejpam-2338	768	15	john	john	PROPN
ejpam-2338	768	16	a.	a.	PROPN
ejpam-2338	768	17	hildebrandt	hildebrandt	PROPN
ejpam-2338	768	18	(	(	PUNCT
ejpam-2338	768	19	eds	ed	NOUN
ejpam-2338	768	20	.	.	PUNCT
ejpam-2338	768	21	)	)	PUNCT
ejpam-2338	768	22	.	.	PUNCT
ejpam-2338	769	1	proceedings	proceeding	NOUN
ejpam-2338	769	2	of	of	ADP
ejpam-2338	769	3	the	the	DET
ejpam-2338	769	4	1986	1986	NUM
ejpam-2338	769	5	lsu	lsu	NOUN
ejpam-2338	769	6	semigroup	semigroup	PROPN
ejpam-2338	769	7	conference	conference	NOUN
ejpam-2338	769	8	:	:	PUNCT
ejpam-2338	769	9	kochfest	kochf	ADJ
ejpam-2338	769	10	60	60	NUM
ejpam-2338	769	11	,	,	PUNCT
ejpam-2338	769	12	louisiana	louisiana	PROPN
ejpam-2338	769	13	state	state	PROPN
ejpam-2338	769	14	univ	univ	PROPN
ejpam-2338	769	15	.	.	PROPN
ejpam-2338	769	16	,	,	PUNCT
ejpam-2338	769	17	baton	baton	PROPN
ejpam-2338	769	18	rouge	rouge	NOUN
ejpam-2338	769	19	,	,	PUNCT
ejpam-2338	769	20	la	la	PROPN
ejpam-2338	769	21	.	.	PROPN
ejpam-2338	769	22	,	,	PUNCT
ejpam-2338	769	23	pp	pp	ADJ
ejpam-2338	769	24	.	.	PUNCT
ejpam-2338	770	1	72–76	72–76	NUM
ejpam-2338	770	2	.	.	PUNCT
ejpam-2338	770	3	1989	1989	NUM
ejpam-2338	770	4	.	.	PUNCT
ejpam-2338	771	1	[	[	X
ejpam-2338	771	2	92	92	NUM
ejpam-2338	771	3	]	]	X
ejpam-2338	771	4	b.	b.	PROPN
ejpam-2338	771	5	m.	m.	PROPN
ejpam-2338	771	6	schein	schein	PROPN
ejpam-2338	771	7	.	.	PROPN
ejpam-2338	771	8	book	book	PROPN
ejpam-2338	771	9	review	review	PROPN
ejpam-2338	771	10	:	:	PUNCT
ejpam-2338	771	11	‘	'	PUNCT
ejpam-2338	771	12	inverse	inverse	ADJ
ejpam-2338	771	13	semigroups	semigroup	NOUN
ejpam-2338	771	14	:	:	PUNCT
ejpam-2338	771	15	the	the	DET
ejpam-2338	771	16	theory	theory	NOUN
ejpam-2338	771	17	of	of	ADP
ejpam-2338	771	18	partial	partial	ADJ
ejpam-2338	771	19	symmetries	symmetry	NOUN
ejpam-2338	771	20	’	'	PUNCT
ejpam-2338	771	21	by	by	ADP
ejpam-2338	771	22	mark	mark	PROPN
ejpam-2338	771	23	v.	v.	PROPN
ejpam-2338	771	24	lawson	lawson	PROPN
ejpam-2338	771	25	,	,	PUNCT
ejpam-2338	771	26	semigroup	semigroup	PROPN
ejpam-2338	771	27	forum	forum	PROPN
ejpam-2338	771	28	65(1	65(1	NOUN
ejpam-2338	771	29	)	)	PUNCT
ejpam-2338	771	30	149–158	149–158	NUM
ejpam-2338	771	31	.	.	PUNCT
ejpam-2338	771	32	2002	2002	NUM
ejpam-2338	771	33	.	.	PUNCT
ejpam-2338	772	1	http://dx.doi.org/10	http://dx.doi.org/10	ADJ
ejpam-2338	772	2	.	.	PUNCT
ejpam-2338	773	1	1007	1007	NUM
ejpam-2338	773	2	/	/	SYM
ejpam-2338	773	3	s002330010132	s002330010132	NOUN
ejpam-2338	774	1	[	[	X
ejpam-2338	774	2	93	93	X
ejpam-2338	774	3	]	]	PUNCT
ejpam-2338	774	4	v.	v.	ADP
ejpam-2338	774	5	m.	m.	NOUN
ejpam-2338	774	6	shiryae	shiryae	PROPN
ejpam-2338	774	7	.	.	PUNCT
ejpam-2338	775	1	on	on	ADP
ejpam-2338	775	2	a	a	DET
ejpam-2338	775	3	class	class	NOUN
ejpam-2338	775	4	of	of	ADP
ejpam-2338	775	5	inverse	inverse	NOUN
ejpam-2338	775	6	semigroups	semigroup	NOUN
ejpam-2338	775	7	,	,	PUNCT
ejpam-2338	775	8	vestnik	vestnik	PROPN
ejpam-2338	775	9	belorus	belorus	PROPN
ejpam-2338	775	10	.	.	PUNCT
ejpam-2338	776	1	univ	univ	PROPN
ejpam-2338	776	2	.	.	PUNCT
ejpam-2338	776	3	ser	ser	PROPN
ejpam-2338	776	4	.	.	PUNCT
ejpam-2338	777	1	i	i	PRON
ejpam-2338	777	2	,	,	PUNCT
ejpam-2338	777	3	no	no	INTJ
ejpam-2338	777	4	.	.	NOUN
ejpam-2338	777	5	2	2	NUM
ejpam-2338	777	6	,	,	PUNCT
ejpam-2338	777	7	10–13	10–13	NUM
ejpam-2338	777	8	.	.	NOUN
ejpam-2338	777	9	1970	1970	NUM
ejpam-2338	777	10	.	.	PUNCT
ejpam-2338	778	1	[	[	X
ejpam-2338	778	2	94	94	NUM
ejpam-2338	778	3	]	]	X
ejpam-2338	778	4	m.	m.	PROPN
ejpam-2338	778	5	b.	b.	PROPN
ejpam-2338	778	6	szendrei	szendrei	PROPN
ejpam-2338	778	7	.	.	PUNCT
ejpam-2338	779	1	some	some	DET
ejpam-2338	779	2	open	open	ADJ
ejpam-2338	779	3	problems	problem	NOUN
ejpam-2338	779	4	in	in	ADP
ejpam-2338	779	5	the	the	DET
ejpam-2338	779	6	structure	structure	NOUN
ejpam-2338	779	7	theory	theory	NOUN
ejpam-2338	779	8	of	of	ADP
ejpam-2338	779	9	regular	regular	ADJ
ejpam-2338	779	10	semigroups	semigroup	NOUN
ejpam-2338	779	11	,	,	PUNCT
ejpam-2338	779	12	semigroup	semigroup	PROPN
ejpam-2338	779	13	forum	forum	PROPN
ejpam-2338	779	14	64(2	64(2	NUM
ejpam-2338	779	15	)	)	PUNCT
ejpam-2338	780	1	213–223	213–223	NUM
ejpam-2338	780	2	.	.	PUNCT
ejpam-2338	781	1	2002	2002	NUM
ejpam-2338	781	2	.	.	PUNCT
ejpam-2338	782	1	http://dx.doi.org/10.1007/s002330010100	http://dx.doi.org/10.1007/s002330010100	X
ejpam-2338	783	1	[	[	X
ejpam-2338	783	2	95	95	NUM
ejpam-2338	783	3	]	]	X
ejpam-2338	783	4	o.	o.	PROPN
ejpam-2338	783	5	veblen	veblen	PROPN
ejpam-2338	783	6	and	and	CCONJ
ejpam-2338	783	7	j.	j.	PROPN
ejpam-2338	783	8	h.	h.	PROPN
ejpam-2338	783	9	c.	c.	PROPN
ejpam-2338	783	10	whitehead	whitehead	PROPN
ejpam-2338	783	11	.	.	PUNCT
ejpam-2338	784	1	the	the	DET
ejpam-2338	784	2	foundations	foundation	NOUN
ejpam-2338	784	3	of	of	ADP
ejpam-2338	784	4	differential	differential	ADJ
ejpam-2338	784	5	geometry	geometry	NOUN
ejpam-2338	784	6	,	,	PUNCT
ejpam-2338	784	7	cambridge	cambridge	PROPN
ejpam-2338	784	8	tract	tract	NOUN
ejpam-2338	784	9	no	no	INTJ
ejpam-2338	784	10	.	.	PROPN
ejpam-2338	784	11	24	24	NUM
ejpam-2338	784	12	,	,	PUNCT
ejpam-2338	784	13	cambridge	cambridge	PROPN
ejpam-2338	784	14	university	university	PROPN
ejpam-2338	784	15	press	press	PROPN
ejpam-2338	784	16	,	,	PUNCT
ejpam-2338	784	17	cambridge	cambridge	PROPN
ejpam-2338	784	18	,	,	PUNCT
ejpam-2338	784	19	1932	1932	NUM
ejpam-2338	784	20	.	.	PUNCT
ejpam-2338	784	21	references	reference	NOUN
ejpam-2338	784	22	323	323	NUM
ejpam-2338	785	1	[	[	X
ejpam-2338	785	2	96	96	NUM
ejpam-2338	785	3	]	]	X
ejpam-2338	785	4	v.	v.	PROPN
ejpam-2338	785	5	v.	v.	PROPN
ejpam-2338	785	6	wagner	wagner	PROPN
ejpam-2338	785	7	.	.	PUNCT
ejpam-2338	786	1	on	on	ADP
ejpam-2338	786	2	the	the	DET
ejpam-2338	786	3	theory	theory	NOUN
ejpam-2338	786	4	of	of	ADP
ejpam-2338	786	5	partial	partial	ADJ
ejpam-2338	786	6	transformations	transformation	NOUN
ejpam-2338	786	7	,	,	PUNCT
ejpam-2338	786	8	doklady	doklady	NOUN
ejpam-2338	786	9	akademii	akademii	NOUN
ejpam-2338	786	10	nauk	nauk	NOUN
ejpam-2338	786	11	sssr	sssr	NOUN
ejpam-2338	786	12	84	84	NUM
ejpam-2338	787	1	653–656	653–656	NUM
ejpam-2338	787	2	(	(	PUNCT
ejpam-2338	787	3	in	in	ADP
ejpam-2338	787	4	russian	russian	NOUN
ejpam-2338	787	5	)	)	PUNCT
ejpam-2338	787	6	.	.	PUNCT
ejpam-2338	788	1	1952	1952	NUM
ejpam-2338	788	2	.	.	PUNCT
ejpam-2338	789	1	[	[	X
ejpam-2338	789	2	97	97	NUM
ejpam-2338	789	3	]	]	X
ejpam-2338	789	4	v.	v.	PROPN
ejpam-2338	789	5	v.	v.	PROPN
ejpam-2338	789	6	wagner	wagner	PROPN
ejpam-2338	789	7	.	.	PUNCT
ejpam-2338	790	1	generalised	generalise	VERB
ejpam-2338	790	2	groups	group	NOUN
ejpam-2338	790	3	,	,	PUNCT
ejpam-2338	790	4	doklady	doklady	NOUN
ejpam-2338	790	5	akademii	akademii	NOUN
ejpam-2338	790	6	nauk	nauk	NOUN
ejpam-2338	790	7	sssr	sssr	NOUN
ejpam-2338	790	8	84	84	NUM
ejpam-2338	790	9	1119–1122	1119–1122	NUM
ejpam-2338	790	10	(	(	PUNCT
ejpam-2338	790	11	in	in	ADP
ejpam-2338	790	12	russian	russian	NOUN
ejpam-2338	790	13	)	)	PUNCT
ejpam-2338	790	14	.	.	PUNCT
ejpam-2338	791	1	1952	1952	NUM
ejpam-2338	791	2	.	.	PUNCT
ejpam-2338	792	1	[	[	X
ejpam-2338	792	2	98	98	NUM
ejpam-2338	792	3	]	]	X
ejpam-2338	792	4	v.	v.	PROPN
ejpam-2338	792	5	v.	v.	PROPN
ejpam-2338	792	6	wagner	wagner	PROPN
ejpam-2338	792	7	.	.	PUNCT
ejpam-2338	793	1	the	the	DET
ejpam-2338	793	2	theory	theory	NOUN
ejpam-2338	793	3	of	of	ADP
ejpam-2338	793	4	generalised	generalised	ADJ
ejpam-2338	793	5	heaps	heap	NOUN
ejpam-2338	793	6	and	and	CCONJ
ejpam-2338	793	7	generalised	generalised	ADJ
ejpam-2338	793	8	groups	group	NOUN
ejpam-2338	793	9	,	,	PUNCT
ejpam-2338	793	10	matematicheskii	matematicheskii	NOUN
ejpam-2338	793	11	sbornik	sbornik	VERB
ejpam-2338	793	12	32	32	NUM
ejpam-2338	793	13	545–632	545–632	NUM
ejpam-2338	793	14	(	(	PUNCT
ejpam-2338	793	15	in	in	ADP
ejpam-2338	793	16	russian	russian	NOUN
ejpam-2338	793	17	)	)	PUNCT
ejpam-2338	793	18	.	.	PUNCT
ejpam-2338	794	1	1953	1953	NUM
ejpam-2338	794	2	.	.	PUNCT
ejpam-2338	795	1	http://mi.mathnet.ru/eng/msb5322	http://mi.mathnet.ru/eng/msb5322	PUNCT
ejpam-2338	796	1	[	[	X
ejpam-2338	796	2	99	99	NUM
ejpam-2338	796	3	]	]	X
ejpam-2338	796	4	v.	v.	PROPN
ejpam-2338	796	5	v.	v.	PROPN
ejpam-2338	796	6	wagner	wagner	PROPN
ejpam-2338	796	7	.	.	PUNCT
ejpam-2338	796	8	semigroups	semigroups	PROPN
ejpam-2338	796	9	associated	associate	VERB
ejpam-2338	796	10	with	with	ADP
ejpam-2338	796	11	generalised	generalised	ADJ
ejpam-2338	796	12	heaps	heap	NOUN
ejpam-2338	796	13	,	,	PUNCT
ejpam-2338	796	14	matematicheskii	matematicheskii	NOUN
ejpam-2338	796	15	sbornik	sbornik	VERB
ejpam-2338	796	16	52	52	NUM
ejpam-2338	796	17	597–628	597–628	NUM
ejpam-2338	796	18	(	(	PUNCT
ejpam-2338	796	19	in	in	ADP
ejpam-2338	796	20	russian	russian	NOUN
ejpam-2338	796	21	)	)	PUNCT
ejpam-2338	796	22	.	.	PUNCT
ejpam-2338	797	1	1960	1960	NUM
ejpam-2338	797	2	.	.	PUNCT
ejpam-2338	798	1	http://mi.mathnet.ru/eng/msb4833	http://mi.mathnet.ru/eng/msb4833	X
ejpam-2338	799	1	[	[	X
ejpam-2338	799	2	100	100	NUM
ejpam-2338	799	3	]	]	PUNCT
ejpam-2338	799	4	v.	v.	PROPN
ejpam-2338	799	5	v.	v.	PROPN
ejpam-2338	799	6	wagner	wagner	PROPN
ejpam-2338	799	7	.	.	PUNCT
ejpam-2338	800	1	on	on	ADP
ejpam-2338	800	2	the	the	DET
ejpam-2338	800	3	theory	theory	NOUN
ejpam-2338	800	4	of	of	ADP
ejpam-2338	800	5	antigroups	antigroup	NOUN
ejpam-2338	800	6	,	,	PUNCT
ejpam-2338	800	7	izvestiya	izvestiya	PROPN
ejpam-2338	800	8	vysshikh	vysshikh	PROPN
ejpam-2338	800	9	uchebnykh	uchebnykh	ADJ
ejpam-2338	800	10	zavedenii	zavedenii	NOUN
ejpam-2338	800	11	.	.	PUNCT
ejpam-2338	801	1	matematika	matematika	PROPN
ejpam-2338	801	2	,	,	PUNCT
ejpam-2338	801	3	no	no	INTJ
ejpam-2338	801	4	.	.	NOUN
ejpam-2338	801	5	4	4	NUM
ejpam-2338	801	6	,	,	PUNCT
ejpam-2338	801	7	3–15	3–15	PROPN
ejpam-2338	801	8	(	(	PUNCT
ejpam-2338	801	9	in	in	ADP
ejpam-2338	801	10	russian	russian	NOUN
ejpam-2338	801	11	)	)	PUNCT
ejpam-2338	801	12	.	.	PUNCT
ejpam-2338	802	1	1971	1971	NUM
ejpam-2338	802	2	.	.	PUNCT
ejpam-2338	802	3	http://mi.mathnet.ru/eng/ivm3975	http://mi.mathnet.ru/eng/ivm3975	PROPN
ejpam-2338	803	1	[	[	X
ejpam-2338	803	2	101	101	X
ejpam-2338	803	3	]	]	PUNCT
ejpam-2338	803	4	v.	v.	PROPN
ejpam-2338	803	5	v.	v.	PROPN
ejpam-2338	803	6	wagner	wagner	PROPN
ejpam-2338	803	7	.	.	PUNCT
ejpam-2338	804	1	t	t	PROPN
ejpam-2338	804	2	-	-	PUNCT
ejpam-2338	804	3	simple	simple	ADJ
ejpam-2338	804	4	representations	representation	NOUN
ejpam-2338	804	5	of	of	ADP
ejpam-2338	804	6	antigroups	antigroup	NOUN
ejpam-2338	804	7	,	,	PUNCT
ejpam-2338	804	8	izvestiya	izvestiya	PROPN
ejpam-2338	804	9	vysshikh	vysshikh	PROPN
ejpam-2338	804	10	uchebnykh	uchebnykh	ADJ
ejpam-2338	804	11	zavedenii	zavedenii	NOUN
ejpam-2338	804	12	.	.	PUNCT
ejpam-2338	805	1	matematika	matematika	PROPN
ejpam-2338	805	2	,	,	PUNCT
ejpam-2338	805	3	no	no	INTJ
ejpam-2338	805	4	.	.	NOUN
ejpam-2338	805	5	9	9	NUM
ejpam-2338	805	6	,	,	PUNCT
ejpam-2338	805	7	18–29	18–29	NUM
ejpam-2338	805	8	(	(	PUNCT
ejpam-2338	805	9	in	in	ADP
ejpam-2338	805	10	russian	russian	NOUN
ejpam-2338	805	11	)	)	PUNCT
ejpam-2338	805	12	.	.	PUNCT
ejpam-2338	806	1	1971	1971	NUM
ejpam-2338	806	2	.	.	PUNCT
ejpam-2338	807	1	http://mi.mathnet.ru/eng/	http://mi.mathnet.ru/eng/	ADJ
ejpam-2338	807	2	ivm3922	ivm3922	NOUN
ejpam-2338	807	3	[	[	X
ejpam-2338	807	4	102	102	NUM
ejpam-2338	807	5	]	]	X
ejpam-2338	807	6	v.	v.	PROPN
ejpam-2338	807	7	v.	v.	PROPN
ejpam-2338	807	8	wagner	wagner	PROPN
ejpam-2338	807	9	.	.	PUNCT
ejpam-2338	808	1	on	on	ADP
ejpam-2338	808	2	the	the	DET
ejpam-2338	808	3	theory	theory	NOUN
ejpam-2338	808	4	of	of	ADP
ejpam-2338	808	5	involuted	involute	VERB
ejpam-2338	808	6	semigroups	semigroup	NOUN
ejpam-2338	808	7	,	,	PUNCT
ejpam-2338	808	8	izvestiya	izvestiya	PROPN
ejpam-2338	808	9	vysshikh	vysshikh	PROPN
ejpam-2338	808	10	uchebnykh	uchebnykh	ADJ
ejpam-2338	808	11	zavedenii	zavedenii	NOUN
ejpam-2338	808	12	.	.	PUNCT
ejpam-2338	809	1	matematika	matematika	PROPN
ejpam-2338	809	2	,	,	PUNCT
ejpam-2338	809	3	no	no	INTJ
ejpam-2338	809	4	.	.	NOUN
ejpam-2338	809	5	10	10	NUM
ejpam-2338	809	6	,	,	PUNCT
ejpam-2338	809	7	24–35	24–35	NUM
ejpam-2338	809	8	(	(	PUNCT
ejpam-2338	809	9	in	in	ADP
ejpam-2338	809	10	russian	russian	NOUN
ejpam-2338	809	11	)	)	PUNCT
ejpam-2338	809	12	.	.	PUNCT
ejpam-2338	810	1	1971	1971	NUM
ejpam-2338	810	2	.	.	PUNCT
ejpam-2338	811	1	http://mi.mathnet.ru/eng/	http://mi.mathnet.ru/eng/	ADJ
ejpam-2338	811	2	ivm3936	ivm3936	NOUN
ejpam-2338	811	3	[	[	X
ejpam-2338	811	4	103	103	NUM
ejpam-2338	811	5	]	]	X
ejpam-2338	811	6	r.	r.	PROPN
ejpam-2338	811	7	wilkinson	wilkinson	PROPN
ejpam-2338	811	8	.	.	PUNCT
ejpam-2338	812	1	a	a	DET
ejpam-2338	812	2	description	description	NOUN
ejpam-2338	812	3	of	of	ADP
ejpam-2338	812	4	e	e	NOUN
ejpam-2338	812	5	-	-	ADJ
ejpam-2338	812	6	unitary	unitary	ADJ
ejpam-2338	812	7	inverse	inverse	NOUN
ejpam-2338	812	8	semigroups	semigroup	NOUN
ejpam-2338	812	9	,	,	PUNCT
ejpam-2338	812	10	proceedings	proceeding	NOUN
ejpam-2338	812	11	of	of	ADP
ejpam-2338	812	12	the	the	DET
ejpam-2338	812	13	royal	royal	ADJ
ejpam-2338	812	14	society	society	NOUN
ejpam-2338	812	15	of	of	ADP
ejpam-2338	812	16	edinburgh	edinburgh	PROPN
ejpam-2338	812	17	.	.	PROPN
ejpam-2338	813	1	section	section	PROPN
ejpam-2338	813	2	a	a	DET
ejpam-2338	813	3	95	95	NUM
ejpam-2338	813	4	239–242	239–242	NUM
ejpam-2338	813	5	.	.	PUNCT
ejpam-2338	814	1	1983	1983	NUM
ejpam-2338	814	2	.	.	PUNCT
ejpam-2338	815	1	[	[	X
ejpam-2338	815	2	104	104	X
ejpam-2338	815	3	]	]	X
ejpam-2338	815	4	g.	g.	PROPN
ejpam-2338	815	5	i.	i.	PROPN
ejpam-2338	815	6	zhitomirskii	zhitomirskii	PROPN
ejpam-2338	815	7	.	.	PUNCT
ejpam-2338	816	1	bisimple	bisimple	VERB
ejpam-2338	816	2	generalized	generalized	ADJ
ejpam-2338	816	3	heaps	heap	NOUN
ejpam-2338	816	4	,	,	PUNCT
ejpam-2338	816	5	in	in	ADP
ejpam-2338	816	6	:	:	PUNCT
ejpam-2338	816	7	theory	theory	NOUN
ejpam-2338	816	8	of	of	ADP
ejpam-2338	816	9	semigroups	semigroup	NOUN
ejpam-2338	816	10	and	and	CCONJ
ejpam-2338	816	11	its	its	PRON
ejpam-2338	816	12	applications	application	NOUN
ejpam-2338	816	13	,	,	PUNCT
ejpam-2338	816	14	vol	vol	NOUN
ejpam-2338	816	15	.	.	PROPN
ejpam-2338	817	1	3	3	NUM
ejpam-2338	817	2	,	,	PUNCT
ejpam-2338	817	3	izdat	izdat	NOUN
ejpam-2338	817	4	.	.	PUNCT
ejpam-2338	818	1	saratov	saratov	PROPN
ejpam-2338	818	2	.	.	PUNCT
ejpam-2338	819	1	univ	univ	PROPN
ejpam-2338	819	2	.	.	PROPN
ejpam-2338	819	3	,	,	PUNCT
ejpam-2338	819	4	saratov	saratov	PROPN
ejpam-2338	819	5	,	,	PUNCT
ejpam-2338	819	6	pp	pp	PROPN
ejpam-2338	819	7	.	.	PUNCT
ejpam-2338	820	1	24–30	24–30	NUM
ejpam-2338	820	2	,	,	PUNCT
ejpam-2338	820	3	151	151	NUM
ejpam-2338	820	4	(	(	PUNCT
ejpam-2338	820	5	in	in	ADP
ejpam-2338	820	6	russian	russian	NOUN
ejpam-2338	820	7	)	)	PUNCT
ejpam-2338	820	8	.	.	PUNCT
ejpam-2338	821	1	1974	1974	NUM
ejpam-2338	821	2	.	.	PUNCT