id	sid	tid	token	lemma	pos
ejpam-221	1	1	2_hollings.dvi	2_hollings.dvi	NUM
ejpam-221	1	2	european	european	ADJ
ejpam-221	1	3	journal	journal	NOUN
ejpam-221	1	4	of	of	ADP
ejpam-221	1	5	pure	pure	ADJ
ejpam-221	1	6	and	and	CCONJ
ejpam-221	1	7	applied	apply	VERB
ejpam-221	1	8	mathematics	mathematic	NOUN
ejpam-221	1	9	vol	vol	NOUN
ejpam-221	1	10	.	.	PROPN
ejpam-221	2	1	2	2	NUM
ejpam-221	2	2	,	,	PUNCT
ejpam-221	2	3	no	no	INTJ
ejpam-221	2	4	.	.	NOUN
ejpam-221	2	5	1	1	NUM
ejpam-221	2	6	,	,	PUNCT
ejpam-221	2	7	2009	2009	NUM
ejpam-221	2	8	,	,	PUNCT
ejpam-221	2	9	(	(	PUNCT
ejpam-221	2	10	21	21	NUM
ejpam-221	2	11	-	-	SYM
ejpam-221	2	12	57	57	NUM
ejpam-221	2	13	)	)	PUNCT
ejpam-221	2	14	issn	issn	PROPN
ejpam-221	2	15	1307	1307	NUM
ejpam-221	2	16	-	-	SYM
ejpam-221	2	17	5543	5543	NUM
ejpam-221	2	18	–	–	PUNCT
ejpam-221	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-221	2	20	from	from	ADP
ejpam-221	2	21	right	right	ADJ
ejpam-221	3	1	pp	pp	ADV
ejpam-221	3	2	monoids	monoid	NOUN
ejpam-221	3	3	to	to	ADP
ejpam-221	3	4	restriction	restriction	NOUN
ejpam-221	3	5	semigroups	semigroup	NOUN
ejpam-221	3	6	:	:	PUNCT
ejpam-221	3	7	a	a	DET
ejpam-221	3	8	survey	survey	NOUN
ejpam-221	3	9	christopher	christopher	PROPN
ejpam-221	3	10	hollings∗	hollings∗	PROPN
ejpam-221	3	11	centro	centro	PROPN
ejpam-221	3	12	de	de	PROPN
ejpam-221	3	13	álgebra	álgebra	PROPN
ejpam-221	3	14	da	da	PROPN
ejpam-221	3	15	universidade	universidade	PROPN
ejpam-221	3	16	de	de	PROPN
ejpam-221	3	17	lisboa	lisboa	PROPN
ejpam-221	3	18	av	av	PROPN
ejpam-221	3	19	.	.	PROPN
ejpam-221	3	20	prof	prof	PROPN
ejpam-221	3	21	.	.	PROPN
ejpam-221	3	22	gama	gama	PROPN
ejpam-221	3	23	pinto	pinto	NOUN
ejpam-221	3	24	2	2	NUM
ejpam-221	3	25	1649	1649	NUM
ejpam-221	3	26	-	-	SYM
ejpam-221	3	27	003	003	NUM
ejpam-221	3	28	lisboa	lisboa	PROPN
ejpam-221	3	29	portugal	portugal	PROPN
ejpam-221	3	30	abstract	abstract	NOUN
ejpam-221	3	31	.	.	PUNCT
ejpam-221	4	1	left	leave	VERB
ejpam-221	4	2	restriction	restriction	NOUN
ejpam-221	4	3	semigroups	semigroup	NOUN
ejpam-221	4	4	are	be	AUX
ejpam-221	4	5	a	a	DET
ejpam-221	4	6	class	class	NOUN
ejpam-221	4	7	of	of	ADP
ejpam-221	4	8	semigroups	semigroup	NOUN
ejpam-221	4	9	which	which	PRON
ejpam-221	4	10	generalise	generalise	VERB
ejpam-221	4	11	inverse	inverse	NOUN
ejpam-221	4	12	semigroups	semigroup	NOUN
ejpam-221	4	13	and	and	CCONJ
ejpam-221	4	14	which	which	PRON
ejpam-221	4	15	emerge	emerge	VERB
ejpam-221	4	16	very	very	ADV
ejpam-221	4	17	naturally	naturally	ADV
ejpam-221	4	18	from	from	ADP
ejpam-221	4	19	the	the	DET
ejpam-221	4	20	study	study	NOUN
ejpam-221	4	21	of	of	ADP
ejpam-221	4	22	partial	partial	ADJ
ejpam-221	4	23	transformations	transformation	NOUN
ejpam-221	4	24	of	of	ADP
ejpam-221	4	25	a	a	DET
ejpam-221	4	26	set	set	NOUN
ejpam-221	4	27	.	.	PUNCT
ejpam-221	5	1	consequently	consequently	ADV
ejpam-221	5	2	,	,	PUNCT
ejpam-221	5	3	they	they	PRON
ejpam-221	5	4	have	have	AUX
ejpam-221	5	5	arisen	arise	VERB
ejpam-221	5	6	in	in	ADP
ejpam-221	5	7	a	a	DET
ejpam-221	5	8	variety	variety	NOUN
ejpam-221	5	9	of	of	ADP
ejpam-221	5	10	different	different	ADJ
ejpam-221	5	11	contexts	contexts	NOUN
ejpam-221	5	12	,	,	PUNCT
ejpam-221	5	13	under	under	ADP
ejpam-221	5	14	a	a	DET
ejpam-221	5	15	range	range	NOUN
ejpam-221	5	16	of	of	ADP
ejpam-221	5	17	names	name	NOUN
ejpam-221	5	18	.	.	PUNCT
ejpam-221	6	1	one	one	NUM
ejpam-221	6	2	of	of	ADP
ejpam-221	6	3	the	the	DET
ejpam-221	6	4	various	various	ADJ
ejpam-221	6	5	guises	guise	NOUN
ejpam-221	6	6	under	under	ADP
ejpam-221	6	7	which	which	PRON
ejpam-221	6	8	left	leave	VERB
ejpam-221	6	9	restriction	restriction	NOUN
ejpam-221	6	10	semigroups	semigroup	NOUN
ejpam-221	6	11	have	have	AUX
ejpam-221	6	12	appeared	appear	VERB
ejpam-221	6	13	is	be	AUX
ejpam-221	6	14	that	that	PRON
ejpam-221	6	15	of	of	ADP
ejpam-221	6	16	weakly	weakly	ADJ
ejpam-221	6	17	left	left	ADJ
ejpam-221	6	18	e	e	NOUN
ejpam-221	6	19	-	-	ADJ
ejpam-221	6	20	ample	ample	ADJ
ejpam-221	6	21	semigroups	semigroup	NOUN
ejpam-221	6	22	,	,	PUNCT
ejpam-221	6	23	as	as	SCONJ
ejpam-221	6	24	studied	study	VERB
ejpam-221	6	25	by	by	ADP
ejpam-221	6	26	fountain	fountain	NOUN
ejpam-221	6	27	,	,	PUNCT
ejpam-221	6	28	gomes	gome	NOUN
ejpam-221	6	29	,	,	PUNCT
ejpam-221	6	30	gould	gould	PROPN
ejpam-221	6	31	and	and	CCONJ
ejpam-221	6	32	lawson	lawson	PROPN
ejpam-221	6	33	,	,	PUNCT
ejpam-221	6	34	amongst	amongst	ADP
ejpam-221	6	35	others	other	NOUN
ejpam-221	6	36	.	.	PUNCT
ejpam-221	7	1	in	in	ADP
ejpam-221	7	2	the	the	DET
ejpam-221	7	3	present	present	ADJ
ejpam-221	7	4	article	article	NOUN
ejpam-221	7	5	,	,	PUNCT
ejpam-221	7	6	we	we	PRON
ejpam-221	7	7	will	will	AUX
ejpam-221	7	8	survey	survey	VERB
ejpam-221	7	9	the	the	DET
ejpam-221	7	10	historical	historical	ADJ
ejpam-221	7	11	development	development	NOUN
ejpam-221	7	12	of	of	ADP
ejpam-221	7	13	the	the	DET
ejpam-221	7	14	study	study	NOUN
ejpam-221	7	15	of	of	ADP
ejpam-221	7	16	left	left	ADJ
ejpam-221	7	17	restriction	restriction	NOUN
ejpam-221	7	18	semigroups	semigroup	NOUN
ejpam-221	7	19	,	,	PUNCT
ejpam-221	7	20	from	from	ADP
ejpam-221	7	21	the	the	DET
ejpam-221	7	22	‘	'	PUNCT
ejpam-221	7	23	weakly	weakly	ADJ
ejpam-221	7	24	left	left	ADJ
ejpam-221	7	25	e	e	NOUN
ejpam-221	7	26	-	-	ADJ
ejpam-221	7	27	ample	ample	ADJ
ejpam-221	7	28	’	'	PUNCT
ejpam-221	7	29	perspective	perspective	NOUN
ejpam-221	7	30	,	,	PUNCT
ejpam-221	7	31	and	and	CCONJ
ejpam-221	7	32	sketch	sketch	VERB
ejpam-221	7	33	out	out	ADP
ejpam-221	7	34	the	the	DET
ejpam-221	7	35	basic	basic	ADJ
ejpam-221	7	36	aspects	aspect	NOUN
ejpam-221	7	37	of	of	ADP
ejpam-221	7	38	their	their	PRON
ejpam-221	7	39	theory	theory	NOUN
ejpam-221	7	40	.	.	PUNCT
ejpam-221	8	1	ams	am	NOUN
ejpam-221	8	2	subject	subject	ADJ
ejpam-221	8	3	classifications	classification	NOUN
ejpam-221	8	4	:	:	PUNCT
ejpam-221	8	5	01	01	NUM
ejpam-221	8	6	a	a	DET
ejpam-221	8	7	60	60	NUM
ejpam-221	8	8	,	,	PUNCT
ejpam-221	8	9	20	20	NUM
ejpam-221	8	10	-	-	SYM
ejpam-221	8	11	03	03	NUM
ejpam-221	8	12	,	,	PUNCT
ejpam-221	9	1	20	20	NUM
ejpam-221	9	2	m	m	NOUN
ejpam-221	9	3	20	20	NUM
ejpam-221	9	4	.	.	PUNCT
ejpam-221	10	1	key	key	ADJ
ejpam-221	10	2	words	word	NOUN
ejpam-221	10	3	:	:	PUNCT
ejpam-221	10	4	right	right	ADV
ejpam-221	10	5	pp	pp	ADV
ejpam-221	10	6	monoid	monoid	PROPN
ejpam-221	10	7	,	,	PUNCT
ejpam-221	10	8	left	leave	VERB
ejpam-221	10	9	ample	ample	ADJ
ejpam-221	10	10	semigroup	semigroup	NOUN
ejpam-221	10	11	,	,	PUNCT
ejpam-221	10	12	weakly	weakly	ADV
ejpam-221	10	13	left	left	ADJ
ejpam-221	10	14	e	e	NOUN
ejpam-221	10	15	-	-	ADJ
ejpam-221	10	16	ample	ample	ADJ
ejpam-221	10	17	semigroup	semigroup	NOUN
ejpam-221	10	18	,	,	PUNCT
ejpam-221	10	19	restriction	restriction	NOUN
ejpam-221	10	20	semigroup	semigroup	NOUN
ejpam-221	10	21	,	,	PUNCT
ejpam-221	10	22	partial	partial	ADJ
ejpam-221	10	23	transformation	transformation	NOUN
ejpam-221	10	24	.	.	PUNCT
ejpam-221	11	1	introduction	introduction	NOUN
ejpam-221	11	2	in	in	ADP
ejpam-221	11	3	the	the	DET
ejpam-221	11	4	mid	mid	ADJ
ejpam-221	11	5	-	-	ADJ
ejpam-221	11	6	twentieth	twentieth	ADJ
ejpam-221	11	7	century	century	NOUN
ejpam-221	11	8	,	,	PUNCT
ejpam-221	11	9	the	the	DET
ejpam-221	11	10	study	study	NOUN
ejpam-221	11	11	of	of	ADP
ejpam-221	11	12	systems	system	NOUN
ejpam-221	11	13	of	of	ADP
ejpam-221	11	14	partial	partial	ADJ
ejpam-221	11	15	one	one	NUM
ejpam-221	11	16	-	-	PUNCT
ejpam-221	11	17	one	one	NUM
ejpam-221	11	18	mappings	mapping	NOUN
ejpam-221	11	19	(	(	PUNCT
ejpam-221	11	20	partial	partial	ADJ
ejpam-221	11	21	bijections	bijection	NOUN
ejpam-221	11	22	)	)	PUNCT
ejpam-221	11	23	of	of	ADP
ejpam-221	11	24	a	a	DET
ejpam-221	11	25	set	set	NOUN
ejpam-221	11	26	yielded	yield	VERB
ejpam-221	11	27	the	the	DET
ejpam-221	11	28	abstract	abstract	ADJ
ejpam-221	11	29	notion	notion	NOUN
ejpam-221	11	30	of	of	ADP
ejpam-221	11	31	an	an	DET
ejpam-221	11	32	inverse	inverse	NOUN
ejpam-221	11	33	semigroup	semigroup	NOUN
ejpam-221	11	34	,	,	PUNCT
ejpam-221	11	35	as	as	SCONJ
ejpam-221	11	36	introduced	introduce	VERB
ejpam-221	11	37	(	(	PUNCT
ejpam-221	11	38	independently	independently	ADV
ejpam-221	11	39	)	)	PUNCT
ejpam-221	11	40	by	by	ADP
ejpam-221	11	41	wagner	wagner	PROPN
ejpam-221	12	1	[	[	X
ejpam-221	12	2	78	78	NUM
ejpam-221	12	3	,	,	PUNCT
ejpam-221	12	4	79	79	NUM
ejpam-221	12	5	]	]	PUNCT
ejpam-221	12	6	and	and	CCONJ
ejpam-221	12	7	preston	preston	PROPN
ejpam-221	12	8	[	[	X
ejpam-221	12	9	60–62	60–62	NOUN
ejpam-221	12	10	]	]	PUNCT
ejpam-221	12	11	.	.	PUNCT
ejpam-221	13	1	let	let	VERB
ejpam-221	13	2	x	x	PRON
ejpam-221	13	3	be	be	AUX
ejpam-221	13	4	a	a	DET
ejpam-221	13	5	nonempty	nonempty	ADV
ejpam-221	13	6	set	set	VERB
ejpam-221	13	7	and	and	CCONJ
ejpam-221	13	8	let	let	VERB
ejpam-221	13	9	ix	ix	PRON
ejpam-221	13	10	∗corresponding	∗corresponde	VERB
ejpam-221	13	11	author	author	NOUN
ejpam-221	13	12	.	.	PUNCT
ejpam-221	14	1	email	email	NOUN
ejpam-221	14	2	address	address	NOUN
ejpam-221	14	3	:	:	PUNCT
ejpam-221	14	4	dh500	dh500	ADJ
ejpam-221	14	5	�	�	NOUN
ejpam-221	14	6	ii.f	ii.f	NOUN
ejpam-221	14	7	.ul.pt	.ul.pt	PROPN
ejpam-221	14	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-221	14	9	21	21	NUM
ejpam-221	15	1	c	c	X
ejpam-221	15	2	©	©	PROPN
ejpam-221	15	3	2009	2009	NUM
ejpam-221	15	4	ejpam	ejpam	NOUN
ejpam-221	15	5	all	all	DET
ejpam-221	15	6	rights	right	NOUN
ejpam-221	15	7	reserved	reserve	VERB
ejpam-221	15	8	.	.	PUNCT
ejpam-221	16	1	c.	c.	PROPN
ejpam-221	16	2	hollings	holling	NOUN
ejpam-221	16	3	/	/	SYM
ejpam-221	16	4	eur	eur	PROPN
ejpam-221	16	5	.	.	PUNCT
ejpam-221	17	1	j.	j.	PROPN
ejpam-221	17	2	pure	pure	PROPN
ejpam-221	17	3	appl	appl	PROPN
ejpam-221	17	4	.	.	PROPN
ejpam-221	17	5	math	math	PROPN
ejpam-221	17	6	,	,	PUNCT
ejpam-221	17	7	2	2	NUM
ejpam-221	17	8	(	(	PUNCT
ejpam-221	17	9	2009	2009	NUM
ejpam-221	17	10	)	)	PUNCT
ejpam-221	17	11	,	,	PUNCT
ejpam-221	17	12	(	(	PUNCT
ejpam-221	17	13	21	21	NUM
ejpam-221	17	14	-	-	SYM
ejpam-221	17	15	57	57	NUM
ejpam-221	17	16	)	)	PUNCT
ejpam-221	17	17	22	22	NUM
ejpam-221	17	18	denote	denote	VERB
ejpam-221	17	19	the	the	DET
ejpam-221	17	20	collection	collection	NOUN
ejpam-221	17	21	of	of	ADP
ejpam-221	17	22	all	all	DET
ejpam-221	17	23	partial	partial	ADJ
ejpam-221	17	24	bijections	bijection	NOUN
ejpam-221	17	25	of	of	ADP
ejpam-221	17	26	x	x	X
ejpam-221	17	27	.	.	PUNCT
ejpam-221	18	1	then	then	ADV
ejpam-221	18	2	ix	ix	PROPN
ejpam-221	18	3	forms	form	VERB
ejpam-221	18	4	a	a	DET
ejpam-221	18	5	monoid	monoid	NOUN
ejpam-221	18	6	,	,	PUNCT
ejpam-221	18	7	termed	term	VERB
ejpam-221	18	8	a	a	DET
ejpam-221	18	9	symmetric	symmetric	ADJ
ejpam-221	18	10	inverse	inverse	NOUN
ejpam-221	18	11	monoid	monoid	NOUN
ejpam-221	18	12	,	,	PUNCT
ejpam-221	18	13	under	under	ADP
ejpam-221	18	14	the	the	DET
ejpam-221	18	15	following	follow	VERB
ejpam-221	18	16	composition	composition	NOUN
ejpam-221	18	17	(	(	PUNCT
ejpam-221	18	18	performed	perform	VERB
ejpam-221	18	19	from	from	ADP
ejpam-221	18	20	left	leave	VERB
ejpam-221	18	21	to	to	ADP
ejpam-221	18	22	right†	right†	VERB
ejpam-221	18	23	):	):	PUNCT
ejpam-221	18	24	for	for	ADP
ejpam-221	18	25	α	α	NOUN
ejpam-221	18	26	,	,	PUNCT
ejpam-221	18	27	β	β	X
ejpam-221	18	28	∈	∈	PROPN
ejpam-221	18	29	ix	ix	ADV
ejpam-221	18	30	,	,	PUNCT
ejpam-221	18	31	domαβ	domαβ	NOUN
ejpam-221	18	32	=	=	SYM
ejpam-221	18	33	(	(	PUNCT
ejpam-221	18	34	imα∩	imα∩	NOUN
ejpam-221	18	35	domβ)α−1	domβ)α−1	NUM
ejpam-221	18	36	(	(	PUNCT
ejpam-221	18	37	∗	∗	NOUN
ejpam-221	18	38	)	)	PUNCT
ejpam-221	18	39	where	where	SCONJ
ejpam-221	18	40	α−1	α−1	PROPN
ejpam-221	18	41	denotes	denote	VERB
ejpam-221	18	42	the	the	DET
ejpam-221	18	43	preimage	preimage	NOUN
ejpam-221	18	44	under	under	ADP
ejpam-221	18	45	α	α	NOUN
ejpam-221	18	46	,	,	PUNCT
ejpam-221	18	47	and	and	CCONJ
ejpam-221	18	48	,	,	PUNCT
ejpam-221	18	49	for	for	ADP
ejpam-221	18	50	x	x	PUNCT
ejpam-221	18	51	in	in	ADP
ejpam-221	18	52	this	this	DET
ejpam-221	18	53	domain	domain	NOUN
ejpam-221	18	54	,	,	PUNCT
ejpam-221	18	55	x(αβ	x(αβ	NUM
ejpam-221	18	56	)	)	PUNCT
ejpam-221	18	57	=	=	PUNCT
ejpam-221	19	1	(	(	PUNCT
ejpam-221	19	2	xα)β	xα)β	PROPN
ejpam-221	19	3	.	.	PUNCT
ejpam-221	20	1	it	it	PRON
ejpam-221	20	2	is	be	AUX
ejpam-221	20	3	clear	clear	ADJ
ejpam-221	20	4	that	that	SCONJ
ejpam-221	20	5	any	any	DET
ejpam-221	20	6	partial	partial	ADJ
ejpam-221	20	7	bijection	bijection	NOUN
ejpam-221	20	8	α	α	NOUN
ejpam-221	20	9	is	be	AUX
ejpam-221	20	10	invertible	invertible	ADJ
ejpam-221	20	11	on	on	ADP
ejpam-221	20	12	its	its	PRON
ejpam-221	20	13	image	image	NOUN
ejpam-221	20	14	,	,	PUNCT
ejpam-221	20	15	with	with	ADP
ejpam-221	20	16	inverse	inverse	NOUN
ejpam-221	20	17	α−1	α−1	PROPN
ejpam-221	20	18	:	:	PUNCT
ejpam-221	20	19	imα→	imα→	PROPN
ejpam-221	20	20	domα	domα	NOUN
ejpam-221	20	21	.	.	PUNCT
ejpam-221	21	1	any	any	DET
ejpam-221	21	2	inverse	inverse	NOUN
ejpam-221	21	3	semigroup	semigroup	NOUN
ejpam-221	21	4	may	may	AUX
ejpam-221	21	5	be	be	AUX
ejpam-221	21	6	regarded	regard	VERB
ejpam-221	21	7	as	as	ADP
ejpam-221	21	8	a	a	DET
ejpam-221	21	9	subsemigroup	subsemigroup	NOUN
ejpam-221	21	10	of	of	ADP
ejpam-221	21	11	some	some	PRON
ejpam-221	21	12	ix	ix	ADP
ejpam-221	21	13	that	that	PRON
ejpam-221	21	14	is	be	AUX
ejpam-221	21	15	closed	close	VERB
ejpam-221	21	16	under	under	ADP
ejpam-221	21	17	the	the	DET
ejpam-221	21	18	unary	unary	ADJ
ejpam-221	21	19	operation	operation	NOUN
ejpam-221	21	20	−1	−1	NOUN
ejpam-221	21	21	.	.	PUNCT
ejpam-221	22	1	there	there	PRON
ejpam-221	22	2	are	be	VERB
ejpam-221	22	3	a	a	DET
ejpam-221	22	4	number	number	NOUN
ejpam-221	22	5	of	of	ADP
ejpam-221	22	6	different	different	ADJ
ejpam-221	22	7	approaches	approach	NOUN
ejpam-221	22	8	to	to	ADP
ejpam-221	22	9	the	the	DET
ejpam-221	22	10	study	study	NOUN
ejpam-221	22	11	of	of	ADP
ejpam-221	22	12	inverse	inverse	NOUN
ejpam-221	22	13	semigroups	semigroup	NOUN
ejpam-221	22	14	,	,	PUNCT
ejpam-221	22	15	and	and	CCONJ
ejpam-221	22	16	these	these	PRON
ejpam-221	22	17	may	may	AUX
ejpam-221	22	18	be	be	AUX
ejpam-221	22	19	embodied	embody	VERB
ejpam-221	22	20	in	in	ADP
ejpam-221	22	21	a	a	DET
ejpam-221	22	22	sequence	sequence	NOUN
ejpam-221	22	23	of	of	ADP
ejpam-221	22	24	structure	structure	NOUN
ejpam-221	22	25	theorems	theorem	NOUN
ejpam-221	22	26	(	(	PUNCT
ejpam-221	22	27	for	for	ADP
ejpam-221	22	28	example	example	NOUN
ejpam-221	22	29	,	,	PUNCT
ejpam-221	22	30	theorems	theorem	NOUN
ejpam-221	22	31	1.12	1.12	NUM
ejpam-221	22	32	,	,	PUNCT
ejpam-221	22	33	1.13	1.13	NUM
ejpam-221	22	34	,	,	PUNCT
ejpam-221	22	35	1.17	1.17	NUM
ejpam-221	22	36	and	and	CCONJ
ejpam-221	22	37	1.19	1.19	NUM
ejpam-221	22	38	)	)	PUNCT
ejpam-221	22	39	.	.	PUNCT
ejpam-221	23	1	more	more	ADV
ejpam-221	23	2	generally	generally	ADV
ejpam-221	23	3	,	,	PUNCT
ejpam-221	23	4	we	we	PRON
ejpam-221	23	5	can	can	AUX
ejpam-221	23	6	study	study	VERB
ejpam-221	23	7	systems	system	NOUN
ejpam-221	23	8	of	of	ADP
ejpam-221	23	9	arbitrary	arbitrary	ADJ
ejpam-221	23	10	partial	partial	ADJ
ejpam-221	23	11	transformations	transformation	NOUN
ejpam-221	23	12	of	of	ADP
ejpam-221	23	13	a	a	DET
ejpam-221	23	14	set	set	NOUN
ejpam-221	23	15	,	,	PUNCT
ejpam-221	23	16	not	not	PART
ejpam-221	23	17	just	just	ADV
ejpam-221	23	18	the	the	DET
ejpam-221	23	19	injective	injective	ADJ
ejpam-221	23	20	ones	one	NOUN
ejpam-221	23	21	.	.	PUNCT
ejpam-221	24	1	at	at	ADP
ejpam-221	24	2	least	least	ADV
ejpam-221	24	3	initially	initially	ADV
ejpam-221	24	4	,	,	PUNCT
ejpam-221	24	5	the	the	DET
ejpam-221	24	6	study	study	NOUN
ejpam-221	24	7	of	of	ADP
ejpam-221	24	8	such	such	ADJ
ejpam-221	24	9	systems	system	NOUN
ejpam-221	24	10	was	be	AUX
ejpam-221	24	11	guided	guide	VERB
ejpam-221	24	12	by	by	ADP
ejpam-221	24	13	analogy	analogy	NOUN
ejpam-221	24	14	with	with	ADP
ejpam-221	24	15	the	the	DET
ejpam-221	24	16	above	above	ADJ
ejpam-221	24	17	case	case	NOUN
ejpam-221	24	18	of	of	ADP
ejpam-221	24	19	partial	partial	ADJ
ejpam-221	24	20	bijections	bijection	NOUN
ejpam-221	24	21	.	.	PUNCT
ejpam-221	25	1	it	it	PRON
ejpam-221	25	2	was	be	AUX
ejpam-221	25	3	discovered	discover	VERB
ejpam-221	25	4	that	that	SCONJ
ejpam-221	25	5	if	if	SCONJ
ejpam-221	25	6	we	we	PRON
ejpam-221	25	7	are	be	AUX
ejpam-221	25	8	to	to	PART
ejpam-221	25	9	obtain	obtain	VERB
ejpam-221	25	10	satisfactory	satisfactory	ADJ
ejpam-221	25	11	analogues	analogue	NOUN
ejpam-221	25	12	of	of	ADP
ejpam-221	25	13	various	various	ADJ
ejpam-221	25	14	results	result	NOUN
ejpam-221	25	15	for	for	ADP
ejpam-221	25	16	inverse	inverse	NOUN
ejpam-221	25	17	semigroups	semigroup	NOUN
ejpam-221	25	18	,	,	PUNCT
ejpam-221	25	19	then	then	ADV
ejpam-221	25	20	we	we	PRON
ejpam-221	25	21	must	must	AUX
ejpam-221	25	22	consider	consider	VERB
ejpam-221	25	23	so	so	ADV
ejpam-221	25	24	-	-	PUNCT
ejpam-221	25	25	called	call	VERB
ejpam-221	25	26	left	left	ADJ
ejpam-221	25	27	restriction	restriction	NOUN
ejpam-221	25	28	semigroups	semigroup	NOUN
ejpam-221	25	29	.	.	PUNCT
ejpam-221	26	1	if	if	SCONJ
ejpam-221	26	2	we	we	PRON
ejpam-221	26	3	denote	denote	VERB
ejpam-221	26	4	by	by	ADP
ejpam-221	26	5	p	p	PROPN
ejpam-221	26	6	t	t	PROPN
ejpam-221	26	7	x	x	PUNCT
ejpam-221	26	8	the	the	DET
ejpam-221	26	9	partial	partial	ADJ
ejpam-221	26	10	transformation	transformation	NOUN
ejpam-221	26	11	monoid	monoid	NOUN
ejpam-221	26	12	of	of	ADP
ejpam-221	26	13	a	a	DET
ejpam-221	26	14	set	set	NOUN
ejpam-221	26	15	x	x	SYM
ejpam-221	26	16	,	,	PUNCT
ejpam-221	26	17	i.e.	i.e.	X
ejpam-221	26	18	,	,	PUNCT
ejpam-221	26	19	the	the	DET
ejpam-221	26	20	collection	collection	NOUN
ejpam-221	26	21	of	of	ADP
ejpam-221	26	22	all	all	DET
ejpam-221	26	23	partial	partial	ADJ
ejpam-221	26	24	transformations	transformation	NOUN
ejpam-221	26	25	of	of	ADP
ejpam-221	26	26	x	x	PUNCT
ejpam-221	26	27	,	,	PUNCT
ejpam-221	26	28	under	under	ADP
ejpam-221	26	29	the	the	DET
ejpam-221	26	30	(	(	PUNCT
ejpam-221	26	31	left	leave	VERB
ejpam-221	26	32	-	-	PUNCT
ejpam-221	26	33	to	to	ADP
ejpam-221	26	34	-	-	PUNCT
ejpam-221	26	35	right	right	ADJ
ejpam-221	26	36	)	)	PUNCT
ejpam-221	26	37	composition	composition	NOUN
ejpam-221	26	38	(	(	PUNCT
ejpam-221	26	39	∗	∗	NOUN
ejpam-221	26	40	)	)	PUNCT
ejpam-221	26	41	,	,	PUNCT
ejpam-221	26	42	then	then	ADV
ejpam-221	26	43	a	a	DET
ejpam-221	26	44	left	left	ADJ
ejpam-221	26	45	restriction	restriction	NOUN
ejpam-221	26	46	semigroup	semigroup	NOUN
ejpam-221	26	47	may	may	AUX
ejpam-221	26	48	be	be	AUX
ejpam-221	26	49	characterised	characterise	VERB
ejpam-221	26	50	as	as	ADP
ejpam-221	26	51	a	a	DET
ejpam-221	26	52	subsemigroup	subsemigroup	NOUN
ejpam-221	26	53	of	of	ADP
ejpam-221	26	54	some	some	DET
ejpam-221	26	55	p	p	NOUN
ejpam-221	26	56	t	t	NOUN
ejpam-221	26	57	x	x	PUNCT
ejpam-221	26	58	that	that	PRON
ejpam-221	26	59	is	be	AUX
ejpam-221	26	60	closed	close	VERB
ejpam-221	26	61	under	under	ADP
ejpam-221	26	62	the	the	DET
ejpam-221	26	63	unary	unary	ADJ
ejpam-221	26	64	operation	operation	NOUN
ejpam-221	26	65	α	α	PROPN
ejpam-221	26	66	7→	7→	NUM
ejpam-221	26	67	idomα	idomα	NOUN
ejpam-221	26	68	,	,	PUNCT
ejpam-221	26	69	where	where	SCONJ
ejpam-221	26	70	idomα	idomα	NOUN
ejpam-221	26	71	denotes	denote	VERB
ejpam-221	26	72	the	the	DET
ejpam-221	26	73	identity	identity	NOUN
ejpam-221	26	74	mapping	mapping	NOUN
ejpam-221	26	75	on	on	ADP
ejpam-221	26	76	the	the	DET
ejpam-221	26	77	domain	domain	NOUN
ejpam-221	26	78	of	of	ADP
ejpam-221	26	79	α	α	NOUN
ejpam-221	26	80	.	.	PUNCT
ejpam-221	27	1	on	on	ADP
ejpam-221	27	2	the	the	DET
ejpam-221	27	3	other	other	ADJ
ejpam-221	27	4	hand	hand	NOUN
ejpam-221	27	5	,	,	PUNCT
ejpam-221	27	6	let	let	VERB
ejpam-221	27	7	p	p	PRON
ejpam-221	27	8	t	t	PROPN
ejpam-221	27	9	∗x	∗x	PROPN
ejpam-221	27	10	denote	denote	VERB
ejpam-221	27	11	the	the	DET
ejpam-221	27	12	dual	dual	ADJ
ejpam-221	27	13	partial	partial	ADJ
ejpam-221	27	14	transformation	transformation	NOUN
ejpam-221	27	15	monoid	monoid	NOUN
ejpam-221	27	16	of	of	ADP
ejpam-221	27	17	x	x	X
ejpam-221	27	18	:	:	PUNCT
ejpam-221	27	19	the	the	DET
ejpam-221	27	20	collection	collection	NOUN
ejpam-221	27	21	of	of	ADP
ejpam-221	27	22	all	all	DET
ejpam-221	27	23	partial	partial	ADJ
ejpam-221	27	24	transformations	transformation	NOUN
ejpam-221	27	25	of	of	ADP
ejpam-221	27	26	x	x	SYM
ejpam-221	27	27	,	,	PUNCT
ejpam-221	27	28	composed	compose	VERB
ejpam-221	27	29	from	from	ADP
ejpam-221	27	30	right	right	ADJ
ejpam-221	27	31	to	to	PART
ejpam-221	27	32	left	left	VERB
ejpam-221	27	33	.	.	PUNCT
ejpam-221	28	1	a	a	DET
ejpam-221	28	2	right	right	ADJ
ejpam-221	28	3	restriction	restriction	NOUN
ejpam-221	28	4	semigroup	semigroup	NOUN
ejpam-221	28	5	is	be	AUX
ejpam-221	28	6	a	a	DET
ejpam-221	28	7	subsemigroup	subsemigroup	NOUN
ejpam-221	28	8	of	of	ADP
ejpam-221	28	9	some	some	DET
ejpam-221	28	10	p	p	X
ejpam-221	28	11	t	t	NOUN
ejpam-221	28	12	∗x	∗x	NOUN
ejpam-221	28	13	that	that	PRON
ejpam-221	28	14	is	be	AUX
ejpam-221	28	15	closed	close	VERB
ejpam-221	28	16	under	under	ADP
ejpam-221	28	17	the	the	DET
ejpam-221	28	18	unary	unary	ADJ
ejpam-221	28	19	operation	operation	NOUN
ejpam-221	28	20	α	α	PROPN
ejpam-221	28	21	7→	7→	NUM
ejpam-221	28	22	idomα	idomα	NOUN
ejpam-221	28	23	.	.	PUNCT
ejpam-221	29	1	a	a	DET
ejpam-221	29	2	semigroup	semigroup	NOUN
ejpam-221	29	3	that	that	PRON
ejpam-221	29	4	is	be	AUX
ejpam-221	29	5	both	both	CCONJ
ejpam-221	29	6	a	a	DET
ejpam-221	29	7	left	left	NOUN
ejpam-221	29	8	and	and	CCONJ
ejpam-221	29	9	a	a	DET
ejpam-221	29	10	right	right	ADJ
ejpam-221	29	11	restriction	restriction	NOUN
ejpam-221	29	12	semigroup	semigroup	NOUN
ejpam-221	29	13	,	,	PUNCT
ejpam-221	29	14	with	with	ADP
ejpam-221	29	15	respect	respect	NOUN
ejpam-221	29	16	to	to	ADP
ejpam-221	29	17	the	the	DET
ejpam-221	29	18	same	same	ADJ
ejpam-221	29	19	semilattice	semilattice	NOUN
ejpam-221	29	20	(	(	PUNCT
ejpam-221	29	21	see	see	VERB
ejpam-221	29	22	section	section	NOUN
ejpam-221	29	23	3	3	NUM
ejpam-221	29	24	)	)	PUNCT
ejpam-221	29	25	,	,	PUNCT
ejpam-221	29	26	is	be	AUX
ejpam-221	29	27	called	call	VERB
ejpam-221	29	28	a	a	DET
ejpam-221	29	29	two	two	NUM
ejpam-221	29	30	-	-	PUNCT
ejpam-221	29	31	sided	side	VERB
ejpam-221	29	32	restriction	restriction	NOUN
ejpam-221	29	33	semigroup	semigroup	NOUN
ejpam-221	29	34	.	.	PUNCT
ejpam-221	30	1	so	so	ADV
ejpam-221	30	2	natural	natural	ADJ
ejpam-221	30	3	is	be	AUX
ejpam-221	30	4	the	the	DET
ejpam-221	30	5	notion	notion	NOUN
ejpam-221	30	6	of	of	ADP
ejpam-221	30	7	a	a	DET
ejpam-221	30	8	left	left	ADJ
ejpam-221	30	9	restriction	restriction	NOUN
ejpam-221	30	10	semigroup	semigroup	NOUN
ejpam-221	30	11	that	that	SCONJ
ejpam-221	30	12	it	it	PRON
ejpam-221	30	13	has	have	AUX
ejpam-221	30	14	appeared	appear	VERB
ejpam-221	30	15	in	in	ADP
ejpam-221	30	16	a	a	DET
ejpam-221	30	17	variety	variety	NOUN
ejpam-221	30	18	of	of	ADP
ejpam-221	30	19	different	different	ADJ
ejpam-221	30	20	contexts	contexts	NOUN
ejpam-221	30	21	,	,	PUNCT
ejpam-221	30	22	under	under	ADP
ejpam-221	30	23	a	a	DET
ejpam-221	30	24	range	range	NOUN
ejpam-221	30	25	of	of	ADP
ejpam-221	30	26	different	different	ADJ
ejpam-221	30	27	names	name	NOUN
ejpam-221	30	28	,	,	PUNCT
ejpam-221	30	29	to	to	ADP
ejpam-221	30	30	wit	wit	NOUN
ejpam-221	30	31	:	:	PUNCT
ejpam-221	30	32	(	(	PUNCT
ejpam-221	30	33	1973	1973	NUM
ejpam-221	30	34	)	)	PUNCT
ejpam-221	30	35	in	in	ADP
ejpam-221	30	36	the	the	DET
ejpam-221	30	37	work	work	NOUN
ejpam-221	30	38	of	of	ADP
ejpam-221	30	39	trokhimenko	trokhimenko	ADJ
ejpam-221	30	40	[	[	X
ejpam-221	30	41	76	76	NUM
ejpam-221	30	42	]	]	X
ejpam-221	30	43	,	,	PUNCT
ejpam-221	30	44	as	as	SCONJ
ejpam-221	30	45	a	a	DET
ejpam-221	30	46	special	special	ADJ
ejpam-221	30	47	case	case	NOUN
ejpam-221	30	48	of	of	ADP
ejpam-221	30	49	the	the	DET
ejpam-221	30	50	menger	menger	PROPN
ejpam-221	30	51	function	function	NOUN
ejpam-221	30	52	systems	system	NOUN
ejpam-221	30	53	studied	study	VERB
ejpam-221	30	54	†we	†we	NUM
ejpam-221	30	55	sound	sound	NOUN
ejpam-221	30	56	a	a	DET
ejpam-221	30	57	note	note	NOUN
ejpam-221	30	58	of	of	ADP
ejpam-221	30	59	caution	caution	NOUN
ejpam-221	30	60	:	:	PUNCT
ejpam-221	30	61	the	the	DET
ejpam-221	30	62	convention	convention	NOUN
ejpam-221	30	63	in	in	ADP
ejpam-221	30	64	this	this	DET
ejpam-221	30	65	article	article	NOUN
ejpam-221	30	66	will	will	AUX
ejpam-221	30	67	be	be	AUX
ejpam-221	30	68	to	to	PART
ejpam-221	30	69	compose	compose	VERB
ejpam-221	30	70	functions	function	NOUN
ejpam-221	30	71	from	from	ADP
ejpam-221	30	72	left	left	ADJ
ejpam-221	30	73	to	to	ADP
ejpam-221	30	74	right	right	NOUN
ejpam-221	30	75	.	.	PUNCT
ejpam-221	31	1	however	however	ADV
ejpam-221	31	2	,	,	PUNCT
ejpam-221	31	3	we	we	PRON
ejpam-221	31	4	will	will	AUX
ejpam-221	31	5	also	also	ADV
ejpam-221	31	6	have	have	VERB
ejpam-221	31	7	occasion	occasion	NOUN
ejpam-221	31	8	to	to	PART
ejpam-221	31	9	make	make	VERB
ejpam-221	31	10	brief	brief	ADJ
ejpam-221	31	11	comments	comment	NOUN
ejpam-221	31	12	on	on	ADP
ejpam-221	31	13	right	right	NOUN
ejpam-221	31	14	-	-	PUNCT
ejpam-221	31	15	to	to	ADP
ejpam-221	31	16	-	-	PUNCT
ejpam-221	31	17	left	leave	VERB
ejpam-221	31	18	composition	composition	NOUN
ejpam-221	31	19	.	.	PUNCT
ejpam-221	32	1	c.	c.	PROPN
ejpam-221	32	2	hollings	holling	NOUN
ejpam-221	32	3	/	/	SYM
ejpam-221	32	4	eur	eur	PROPN
ejpam-221	32	5	.	.	PUNCT
ejpam-221	33	1	j.	j.	PROPN
ejpam-221	33	2	pure	pure	PROPN
ejpam-221	33	3	appl	appl	PROPN
ejpam-221	33	4	.	.	PROPN
ejpam-221	33	5	math	math	PROPN
ejpam-221	33	6	,	,	PUNCT
ejpam-221	33	7	2	2	NUM
ejpam-221	33	8	(	(	PUNCT
ejpam-221	33	9	2009	2009	NUM
ejpam-221	33	10	)	)	PUNCT
ejpam-221	33	11	,	,	PUNCT
ejpam-221	33	12	(	(	PUNCT
ejpam-221	33	13	21	21	NUM
ejpam-221	33	14	-	-	SYM
ejpam-221	33	15	57	57	NUM
ejpam-221	33	16	)	)	PUNCT
ejpam-221	33	17	23	23	NUM
ejpam-221	33	18	by	by	ADP
ejpam-221	33	19	schweizer	schweizer	PROPN
ejpam-221	33	20	and	and	CCONJ
ejpam-221	33	21	sklar	sklar	ADJ
ejpam-221	34	1	[	[	X
ejpam-221	34	2	66–69	66–69	NOUN
ejpam-221	34	3	]	]	PUNCT
ejpam-221	34	4	,	,	PUNCT
ejpam-221	34	5	which	which	PRON
ejpam-221	34	6	arose	arise	VERB
ejpam-221	34	7	from	from	ADP
ejpam-221	34	8	attempts	attempt	NOUN
ejpam-221	34	9	to	to	PART
ejpam-221	34	10	axiomatise	axiomatise	VERB
ejpam-221	34	11	semigroups	semigroup	NOUN
ejpam-221	34	12	with	with	ADP
ejpam-221	34	13	additional	additional	ADJ
ejpam-221	34	14	operations	operation	NOUN
ejpam-221	34	15	embedded	embed	VERB
ejpam-221	34	16	in	in	ADP
ejpam-221	34	17	some	some	DET
ejpam-221	34	18	p	p	NOUN
ejpam-221	34	19	t	t	NOUN
ejpam-221	34	20	x	x	PUNCT
ejpam-221	34	21	(	(	PUNCT
ejpam-221	34	22	see	see	VERB
ejpam-221	34	23	[	[	X
ejpam-221	34	24	40,64	40,64	NUM
ejpam-221	34	25	]	]	X
ejpam-221	34	26	)	)	PUNCT
ejpam-221	34	27	;	;	PUNCT
ejpam-221	34	28	(	(	PUNCT
ejpam-221	34	29	1981	1981	NUM
ejpam-221	34	30	)	)	PUNCT
ejpam-221	34	31	as	as	ADP
ejpam-221	34	32	the	the	DET
ejpam-221	34	33	type	type	NOUN
ejpam-221	34	34	sl2	sl2	PROPN
ejpam-221	34	35	γ	γ	PROPN
ejpam-221	34	36	-	-	PUNCT
ejpam-221	34	37	semigroups	semigroup	NOUN
ejpam-221	34	38	of	of	ADP
ejpam-221	34	39	batbedat	batbedat	NOUN
ejpam-221	34	40	[	[	X
ejpam-221	34	41	2	2	NUM
ejpam-221	34	42	,	,	PUNCT
ejpam-221	34	43	3	3	NUM
ejpam-221	34	44	]	]	PUNCT
ejpam-221	34	45	,	,	PUNCT
ejpam-221	34	46	which	which	PRON
ejpam-221	34	47	arose	arise	VERB
ejpam-221	34	48	as	as	ADP
ejpam-221	34	49	a	a	DET
ejpam-221	34	50	generalisation	generalisation	NOUN
ejpam-221	34	51	of	of	ADP
ejpam-221	34	52	inverse	inverse	NOUN
ejpam-221	34	53	semigroups	semigroup	NOUN
ejpam-221	34	54	whereby	whereby	SCONJ
ejpam-221	34	55	the	the	DET
ejpam-221	34	56	unary	unary	ADJ
ejpam-221	34	57	operation	operation	NOUN
ejpam-221	34	58	x	x	SYM
ejpam-221	34	59	7→	7→	NUM
ejpam-221	34	60	x	x	SYM
ejpam-221	34	61	x−1	x−1	PROPN
ejpam-221	34	62	was	be	AUX
ejpam-221	34	63	formally	formally	ADV
ejpam-221	34	64	replaced	replace	VERB
ejpam-221	34	65	by	by	ADP
ejpam-221	34	66	a	a	DET
ejpam-221	34	67	function	function	NOUN
ejpam-221	34	68	γ	γ	NOUN
ejpam-221	34	69	:	:	PUNCT
ejpam-221	34	70	s→	s→	X
ejpam-221	34	71	e(s	e(s	PROPN
ejpam-221	34	72	)	)	PUNCT
ejpam-221	34	73	;	;	PUNCT
ejpam-221	34	74	(	(	PUNCT
ejpam-221	34	75	1991	1991	NUM
ejpam-221	34	76	)	)	PUNCT
ejpam-221	34	77	as	as	ADP
ejpam-221	34	78	the	the	DET
ejpam-221	34	79	idempotent	idempotent	NOUN
ejpam-221	34	80	-	-	PUNCT
ejpam-221	34	81	connected	connect	VERB
ejpam-221	34	82	ehresmann	ehresmann	NOUN
ejpam-221	34	83	semigroups	semigroup	NOUN
ejpam-221	34	84	of	of	ADP
ejpam-221	34	85	lawson	lawson	PROPN
ejpam-221	35	1	[	[	X
ejpam-221	35	2	47	47	NUM
ejpam-221	35	3	]	]	PUNCT
ejpam-221	35	4	,	,	PUNCT
ejpam-221	35	5	who	who	PRON
ejpam-221	35	6	was	be	AUX
ejpam-221	35	7	drawing	draw	VERB
ejpam-221	35	8	connections	connection	NOUN
ejpam-221	35	9	between	between	ADP
ejpam-221	35	10	semigroup	semigroup	PROPN
ejpam-221	35	11	theory	theory	NOUN
ejpam-221	35	12	and	and	CCONJ
ejpam-221	35	13	the	the	DET
ejpam-221	35	14	category	category	NOUN
ejpam-221	35	15	-	-	PUNCT
ejpam-221	35	16	theoretic	theoretic	NOUN
ejpam-221	35	17	work	work	NOUN
ejpam-221	35	18	of	of	ADP
ejpam-221	35	19	ehresmann	ehresmann	PROPN
ejpam-221	36	1	[	[	X
ejpam-221	36	2	14	14	NUM
ejpam-221	36	3	]	]	PUNCT
ejpam-221	36	4	,	,	PUNCT
ejpam-221	36	5	with	with	ADP
ejpam-221	36	6	the	the	DET
ejpam-221	36	7	goal	goal	NOUN
ejpam-221	36	8	of	of	ADP
ejpam-221	36	9	applying	apply	VERB
ejpam-221	36	10	techniques	technique	NOUN
ejpam-221	36	11	from	from	ADP
ejpam-221	36	12	category	category	NOUN
ejpam-221	36	13	theory	theory	NOUN
ejpam-221	36	14	to	to	ADP
ejpam-221	36	15	semigroup	semigroup	PROPN
ejpam-221	36	16	theory	theory	NOUN
ejpam-221	36	17	;	;	PUNCT
ejpam-221	36	18	(	(	PUNCT
ejpam-221	36	19	2001	2001	NUM
ejpam-221	36	20	)	)	PUNCT
ejpam-221	36	21	as	as	ADP
ejpam-221	36	22	the	the	DET
ejpam-221	36	23	twisted	twisted	ADJ
ejpam-221	36	24	lc	lc	NOUN
ejpam-221	36	25	-	-	PUNCT
ejpam-221	36	26	semigroups	semigroup	NOUN
ejpam-221	36	27	of	of	ADP
ejpam-221	36	28	jackson	jackson	PROPN
ejpam-221	36	29	and	and	CCONJ
ejpam-221	36	30	stokes	stoke	VERB
ejpam-221	36	31	[	[	X
ejpam-221	36	32	39	39	NUM
ejpam-221	36	33	]	]	PUNCT
ejpam-221	36	34	,	,	PUNCT
ejpam-221	36	35	which	which	PRON
ejpam-221	36	36	arose	arise	VERB
ejpam-221	36	37	from	from	ADP
ejpam-221	36	38	considerations	consideration	NOUN
ejpam-221	36	39	of	of	ADP
ejpam-221	36	40	closure	closure	NOUN
ejpam-221	36	41	operators	operator	NOUN
ejpam-221	36	42	;	;	PUNCT
ejpam-221	36	43	(	(	PUNCT
ejpam-221	36	44	2006	2006	NUM
ejpam-221	36	45	)	)	PUNCT
ejpam-221	36	46	as	as	ADP
ejpam-221	36	47	the	the	DET
ejpam-221	36	48	guarded	guard	VERB
ejpam-221	36	49	semigroups	semigroup	NOUN
ejpam-221	36	50	of	of	ADP
ejpam-221	36	51	manes	mane	NOUN
ejpam-221	36	52	[	[	X
ejpam-221	36	53	51	51	NUM
ejpam-221	36	54	]	]	PUNCT
ejpam-221	36	55	,	,	PUNCT
ejpam-221	36	56	which	which	PRON
ejpam-221	36	57	arose	arise	VERB
ejpam-221	36	58	via	via	ADP
ejpam-221	36	59	theoretical	theoretical	ADJ
ejpam-221	36	60	computer	computer	NOUN
ejpam-221	36	61	science	science	NOUN
ejpam-221	36	62	from	from	ADP
ejpam-221	36	63	the	the	DET
ejpam-221	36	64	restriction	restriction	NOUN
ejpam-221	36	65	categories	category	NOUN
ejpam-221	36	66	of	of	ADP
ejpam-221	36	67	cockett	cockett	NOUN
ejpam-221	36	68	and	and	CCONJ
ejpam-221	36	69	lack	lack	VERB
ejpam-221	36	70	[	[	X
ejpam-221	36	71	6	6	NUM
ejpam-221	36	72	]	]	PUNCT
ejpam-221	36	73	.	.	PUNCT
ejpam-221	37	1	the	the	DET
ejpam-221	37	2	term	term	NOUN
ejpam-221	37	3	restriction	restriction	NOUN
ejpam-221	37	4	semigroup	semigroup	NOUN
ejpam-221	37	5	,	,	PUNCT
ejpam-221	37	6	inspired	inspire	VERB
ejpam-221	37	7	by	by	ADP
ejpam-221	37	8	the	the	DET
ejpam-221	37	9	nomenclature	nomenclature	NOUN
ejpam-221	37	10	of	of	ADP
ejpam-221	37	11	cockett	cockett	NOUN
ejpam-221	37	12	and	and	CCONJ
ejpam-221	37	13	lack	lack	NOUN
ejpam-221	37	14	for	for	ADP
ejpam-221	37	15	categories	category	NOUN
ejpam-221	37	16	,	,	PUNCT
ejpam-221	37	17	is	be	AUX
ejpam-221	37	18	a	a	DET
ejpam-221	37	19	recent	recent	ADJ
ejpam-221	37	20	attempt	attempt	NOUN
ejpam-221	37	21	to	to	PART
ejpam-221	37	22	streamline	streamline	VERB
ejpam-221	37	23	and	and	CCONJ
ejpam-221	37	24	harmonise	harmonise	VERB
ejpam-221	37	25	the	the	DET
ejpam-221	37	26	terminology	terminology	NOUN
ejpam-221	37	27	,	,	PUNCT
ejpam-221	37	28	and	and	CCONJ
ejpam-221	37	29	was	be	AUX
ejpam-221	37	30	first	first	ADV
ejpam-221	37	31	used	use	VERB
ejpam-221	37	32	in	in	ADP
ejpam-221	37	33	[	[	X
ejpam-221	37	34	7	7	NUM
ejpam-221	37	35	]	]	PUNCT
ejpam-221	37	36	.	.	PUNCT
ejpam-221	38	1	the	the	DET
ejpam-221	38	2	idempotent	idempotent	NOUN
ejpam-221	38	3	-	-	PUNCT
ejpam-221	38	4	connected	connect	VERB
ejpam-221	38	5	ehresmann	ehresmann	NOUN
ejpam-221	38	6	semigroups	semigroup	NOUN
ejpam-221	38	7	of	of	ADP
ejpam-221	38	8	lawson	lawson	PROPN
ejpam-221	38	9	[	[	X
ejpam-221	38	10	47	47	NUM
ejpam-221	38	11	]	]	PUNCT
ejpam-221	38	12	are	be	AUX
ejpam-221	38	13	in	in	ADP
ejpam-221	38	14	fact	fact	NOUN
ejpam-221	38	15	two	two	NUM
ejpam-221	38	16	-	-	PUNCT
ejpam-221	38	17	sided	sided	ADJ
ejpam-221	38	18	restriction	restriction	NOUN
ejpam-221	38	19	semigroups	semigroup	NOUN
ejpam-221	38	20	and	and	CCONJ
ejpam-221	38	21	generalise	generalise	VERB
ejpam-221	38	22	the	the	DET
ejpam-221	38	23	ample	ample	ADJ
ejpam-221	38	24	semigroups	semigroup	NOUN
ejpam-221	38	25	of	of	ADP
ejpam-221	38	26	fountain	fountain	NOUN
ejpam-221	38	27	[	[	X
ejpam-221	38	28	22	22	NUM
ejpam-221	38	29	,	,	PUNCT
ejpam-221	38	30	24	24	NUM
ejpam-221	38	31	]	]	PUNCT
ejpam-221	38	32	.	.	PUNCT
ejpam-221	39	1	for	for	ADP
ejpam-221	39	2	this	this	DET
ejpam-221	39	3	reason	reason	NOUN
ejpam-221	39	4	,	,	PUNCT
ejpam-221	39	5	they	they	PRON
ejpam-221	39	6	were	be	AUX
ejpam-221	39	7	subsequently	subsequently	ADV
ejpam-221	39	8	known	know	VERB
ejpam-221	39	9	as	as	ADP
ejpam-221	39	10	weakly	weakly	ADJ
ejpam-221	39	11	e	e	NOUN
ejpam-221	39	12	-	-	ADJ
ejpam-221	39	13	ample	ample	ADJ
ejpam-221	39	14	semigroups	semigroup	NOUN
ejpam-221	39	15	;	;	PUNCT
ejpam-221	39	16	the	the	DET
ejpam-221	39	17	‘	'	PUNCT
ejpam-221	39	18	e	e	NOUN
ejpam-221	39	19	’	'	PUNCT
ejpam-221	39	20	reflects	reflect	VERB
ejpam-221	39	21	the	the	DET
ejpam-221	39	22	fact	fact	NOUN
ejpam-221	39	23	that	that	SCONJ
ejpam-221	39	24	these	these	DET
ejpam-221	39	25	semigroups	semigroup	NOUN
ejpam-221	39	26	may	may	AUX
ejpam-221	39	27	be	be	AUX
ejpam-221	39	28	defined	define	VERB
ejpam-221	39	29	in	in	ADP
ejpam-221	39	30	terms	term	NOUN
ejpam-221	39	31	of	of	ADP
ejpam-221	39	32	a	a	DET
ejpam-221	39	33	distinguished	distinguished	ADJ
ejpam-221	39	34	subsemilattice	subsemilattice	NOUN
ejpam-221	39	35	e	e	NOUN
ejpam-221	39	36	⊆	⊆	NUM
ejpam-221	39	37	e(s	e(s	PROPN
ejpam-221	39	38	)	)	PUNCT
ejpam-221	39	39	,	,	PUNCT
ejpam-221	39	40	whereas	whereas	SCONJ
ejpam-221	39	41	ample	ample	ADJ
ejpam-221	39	42	semigroups	semigroup	NOUN
ejpam-221	39	43	are	be	AUX
ejpam-221	39	44	defined	define	VERB
ejpam-221	39	45	with	with	ADP
ejpam-221	39	46	respect	respect	NOUN
ejpam-221	39	47	to	to	ADP
ejpam-221	39	48	the	the	DET
ejpam-221	39	49	whole	whole	NOUN
ejpam-221	39	50	of	of	ADP
ejpam-221	39	51	e(s	e(s	PROPN
ejpam-221	39	52	)	)	PUNCT
ejpam-221	39	53	.	.	PUNCT
ejpam-221	40	1	in	in	ADP
ejpam-221	40	2	the	the	DET
ejpam-221	40	3	one	one	NUM
ejpam-221	40	4	-	-	PUNCT
ejpam-221	40	5	sided	side	VERB
ejpam-221	40	6	case	case	NOUN
ejpam-221	40	7	,	,	PUNCT
ejpam-221	40	8	weakly	weakly	ADV
ejpam-221	40	9	left	left	ADJ
ejpam-221	40	10	/	/	SYM
ejpam-221	40	11	right	right	ADJ
ejpam-221	40	12	e	e	NOUN
ejpam-221	40	13	-	-	ADJ
ejpam-221	40	14	ample	ample	ADJ
ejpam-221	40	15	semigroups	semigroup	NOUN
ejpam-221	40	16	are	be	AUX
ejpam-221	40	17	simply	simply	ADV
ejpam-221	40	18	left	leave	VERB
ejpam-221	40	19	/	/	SYM
ejpam-221	40	20	right	right	ADJ
ejpam-221	40	21	restriction	restriction	NOUN
ejpam-221	40	22	semigroups	semigroup	NOUN
ejpam-221	40	23	;	;	PUNCT
ejpam-221	40	24	these	these	PRON
ejpam-221	40	25	have	have	AUX
ejpam-221	40	26	been	be	AUX
ejpam-221	40	27	studied	study	VERB
ejpam-221	40	28	by	by	ADP
ejpam-221	40	29	gomes	gome	NOUN
ejpam-221	40	30	,	,	PUNCT
ejpam-221	40	31	gould	gould	PROPN
ejpam-221	40	32	,	,	PUNCT
ejpam-221	40	33	and	and	CCONJ
ejpam-221	40	34	others	other	NOUN
ejpam-221	40	35	of	of	ADP
ejpam-221	40	36	the	the	DET
ejpam-221	40	37	‘	'	PUNCT
ejpam-221	40	38	york	york	NOUN
ejpam-221	40	39	-	-	PUNCT
ejpam-221	40	40	inspired	inspire	VERB
ejpam-221	40	41	’	'	PUNCT
ejpam-221	40	42	school	school	NOUN
ejpam-221	40	43	.	.	PUNCT
ejpam-221	41	1	in	in	ADP
ejpam-221	41	2	the	the	DET
ejpam-221	41	3	present	present	ADJ
ejpam-221	41	4	article	article	NOUN
ejpam-221	41	5	,	,	PUNCT
ejpam-221	41	6	we	we	PRON
ejpam-221	41	7	will	will	AUX
ejpam-221	41	8	survey	survey	VERB
ejpam-221	41	9	the	the	DET
ejpam-221	41	10	development	development	NOUN
ejpam-221	41	11	of	of	ADP
ejpam-221	41	12	restriction	restriction	NOUN
ejpam-221	41	13	semigroups	semigroup	NOUN
ejpam-221	41	14	from	from	ADP
ejpam-221	41	15	the	the	DET
ejpam-221	41	16	‘	'	PUNCT
ejpam-221	41	17	york	york	NOUN
ejpam-221	41	18	’	'	PUNCT
ejpam-221	41	19	perspective	perspective	NOUN
ejpam-221	41	20	.	.	PUNCT
ejpam-221	42	1	we	we	PRON
ejpam-221	42	2	will	will	AUX
ejpam-221	42	3	begin	begin	VERB
ejpam-221	42	4	with	with	ADP
ejpam-221	42	5	notions	notion	NOUN
ejpam-221	42	6	from	from	ADP
ejpam-221	42	7	the	the	DET
ejpam-221	42	8	homological	homological	ADJ
ejpam-221	42	9	classification	classification	NOUN
ejpam-221	42	10	of	of	ADP
ejpam-221	42	11	monoids	monoid	NOUN
ejpam-221	42	12	,	,	PUNCT
ejpam-221	42	13	such	such	ADJ
ejpam-221	42	14	as	as	ADP
ejpam-221	42	15	that	that	PRON
ejpam-221	42	16	of	of	ADP
ejpam-221	42	17	a	a	DET
ejpam-221	42	18	right	right	NOUN
ejpam-221	42	19	pp	pp	ADP
ejpam-221	42	20	monoid	monoid	NOUN
ejpam-221	42	21	,	,	PUNCT
ejpam-221	42	22	which	which	PRON
ejpam-221	42	23	led	lead	VERB
ejpam-221	42	24	to	to	ADP
ejpam-221	42	25	the	the	DET
ejpam-221	42	26	initial	initial	ADJ
ejpam-221	42	27	definition	definition	NOUN
ejpam-221	42	28	of	of	ADP
ejpam-221	42	29	a	a	DET
ejpam-221	42	30	left	left	ADJ
ejpam-221	42	31	ample	ample	ADJ
ejpam-221	42	32	semigroup	semigroup	NOUN
ejpam-221	42	33	,	,	PUNCT
ejpam-221	42	34	before	before	ADP
ejpam-221	42	35	moving	move	VERB
ejpam-221	42	36	through	through	ADP
ejpam-221	42	37	successive	successive	ADJ
ejpam-221	42	38	generalisations	generalisation	NOUN
ejpam-221	42	39	to	to	PART
ejpam-221	42	40	arrive	arrive	VERB
ejpam-221	42	41	at	at	ADP
ejpam-221	42	42	weakly	weakly	ADJ
ejpam-221	42	43	left	left	ADJ
ejpam-221	42	44	e	e	NOUN
ejpam-221	42	45	-	-	ADJ
ejpam-221	42	46	ample	ample	ADJ
ejpam-221	42	47	semigroups	semigroup	NOUN
ejpam-221	42	48	,	,	PUNCT
ejpam-221	42	49	i.e.	i.e.	X
ejpam-221	42	50	,	,	PUNCT
ejpam-221	42	51	left	leave	VERB
ejpam-221	42	52	c.	c.	PROPN
ejpam-221	42	53	hollings	holling	NOUN
ejpam-221	42	54	/	/	SYM
ejpam-221	42	55	eur	eur	PROPN
ejpam-221	42	56	.	.	PUNCT
ejpam-221	43	1	j.	j.	PROPN
ejpam-221	43	2	pure	pure	PROPN
ejpam-221	43	3	appl	appl	PROPN
ejpam-221	43	4	.	.	PROPN
ejpam-221	43	5	math	math	PROPN
ejpam-221	43	6	,	,	PUNCT
ejpam-221	43	7	2	2	NUM
ejpam-221	43	8	(	(	PUNCT
ejpam-221	43	9	2009	2009	NUM
ejpam-221	43	10	)	)	PUNCT
ejpam-221	43	11	,	,	PUNCT
ejpam-221	43	12	(	(	PUNCT
ejpam-221	43	13	21	21	NUM
ejpam-221	43	14	-	-	SYM
ejpam-221	43	15	57	57	NUM
ejpam-221	43	16	)	)	PUNCT
ejpam-221	44	1	24	24	NUM
ejpam-221	44	2	restriction	restriction	NOUN
ejpam-221	44	3	semigroups	semigroup	NOUN
ejpam-221	44	4	.	.	PUNCT
ejpam-221	45	1	the	the	DET
ejpam-221	45	2	structure	structure	NOUN
ejpam-221	45	3	of	of	ADP
ejpam-221	45	4	the	the	DET
ejpam-221	45	5	article	article	NOUN
ejpam-221	45	6	is	be	AUX
ejpam-221	45	7	as	as	SCONJ
ejpam-221	45	8	follows	follow	VERB
ejpam-221	45	9	.	.	PUNCT
ejpam-221	46	1	we	we	PRON
ejpam-221	46	2	begin	begin	VERB
ejpam-221	46	3	with	with	ADP
ejpam-221	46	4	an	an	DET
ejpam-221	46	5	historical	historical	ADJ
ejpam-221	46	6	survey	survey	NOUN
ejpam-221	46	7	of	of	ADP
ejpam-221	46	8	the	the	DET
ejpam-221	46	9	development	development	NOUN
ejpam-221	46	10	of	of	ADP
ejpam-221	46	11	these	these	DET
ejpam-221	46	12	semigroups	semigroup	NOUN
ejpam-221	46	13	;	;	PUNCT
ejpam-221	46	14	since	since	SCONJ
ejpam-221	46	15	this	this	DET
ejpam-221	46	16	survey	survey	NOUN
ejpam-221	46	17	is	be	AUX
ejpam-221	46	18	quite	quite	ADV
ejpam-221	46	19	lengthy	lengthy	ADJ
ejpam-221	46	20	,	,	PUNCT
ejpam-221	46	21	we	we	PRON
ejpam-221	46	22	break	break	VERB
ejpam-221	46	23	it	it	PRON
ejpam-221	46	24	down	down	ADP
ejpam-221	46	25	into	into	ADP
ejpam-221	46	26	two	two	NUM
ejpam-221	46	27	parts	part	NOUN
ejpam-221	46	28	:	:	PUNCT
ejpam-221	46	29	section	section	NOUN
ejpam-221	46	30	1	1	NUM
ejpam-221	46	31	deals	deal	NOUN
ejpam-221	46	32	with	with	ADP
ejpam-221	46	33	left	left	ADJ
ejpam-221	46	34	ample	ample	ADJ
ejpam-221	46	35	semigroups	semigroup	NOUN
ejpam-221	46	36	,	,	PUNCT
ejpam-221	46	37	via	via	ADP
ejpam-221	46	38	right	right	ADJ
ejpam-221	46	39	pp	pp	ADP
ejpam-221	46	40	monoids	monoid	NOUN
ejpam-221	46	41	,	,	PUNCT
ejpam-221	46	42	whilst	whilst	SCONJ
ejpam-221	46	43	section	section	NOUN
ejpam-221	46	44	2	2	NUM
ejpam-221	46	45	completes	complete	VERB
ejpam-221	46	46	the	the	DET
ejpam-221	46	47	story	story	NOUN
ejpam-221	46	48	by	by	ADP
ejpam-221	46	49	describing	describe	VERB
ejpam-221	46	50	the	the	DET
ejpam-221	46	51	work	work	NOUN
ejpam-221	46	52	leading	lead	VERB
ejpam-221	46	53	to	to	ADP
ejpam-221	46	54	the	the	DET
ejpam-221	46	55	eventual	eventual	ADJ
ejpam-221	46	56	definition	definition	NOUN
ejpam-221	46	57	of	of	ADP
ejpam-221	46	58	weakly	weakly	ADJ
ejpam-221	46	59	left	left	ADJ
ejpam-221	46	60	e	e	NOUN
ejpam-221	46	61	-	-	ADJ
ejpam-221	46	62	ample	ample	ADJ
ejpam-221	46	63	semigroups	semigroup	NOUN
ejpam-221	46	64	.	.	PUNCT
ejpam-221	47	1	sections	section	NOUN
ejpam-221	48	1	3–5	3–5	NUM
ejpam-221	48	2	collate	collate	VERB
ejpam-221	48	3	the	the	DET
ejpam-221	48	4	work	work	NOUN
ejpam-221	48	5	of	of	ADP
ejpam-221	48	6	a	a	DET
ejpam-221	48	7	number	number	NOUN
ejpam-221	48	8	of	of	ADP
ejpam-221	48	9	authors	author	NOUN
ejpam-221	48	10	,	,	PUNCT
ejpam-221	48	11	but	but	CCONJ
ejpam-221	48	12	of	of	ADP
ejpam-221	48	13	el	el	PROPN
ejpam-221	48	14	-	-	PUNCT
ejpam-221	48	15	qallali	qallali	PROPN
ejpam-221	49	1	[	[	X
ejpam-221	49	2	15	15	NUM
ejpam-221	49	3	]	]	PUNCT
ejpam-221	49	4	,	,	PUNCT
ejpam-221	49	5	fountain	fountain	NOUN
ejpam-221	49	6	[	[	X
ejpam-221	49	7	22	22	NUM
ejpam-221	49	8	,	,	PUNCT
ejpam-221	49	9	24	24	NUM
ejpam-221	49	10	]	]	PUNCT
ejpam-221	49	11	and	and	CCONJ
ejpam-221	49	12	lawson	lawson	PROPN
ejpam-221	50	1	[	[	X
ejpam-221	50	2	43	43	NUM
ejpam-221	50	3	,	,	PUNCT
ejpam-221	50	4	47	47	NUM
ejpam-221	50	5	]	]	PUNCT
ejpam-221	50	6	in	in	ADP
ejpam-221	50	7	particular	particular	ADJ
ejpam-221	50	8	.	.	PUNCT
ejpam-221	51	1	much	much	ADJ
ejpam-221	51	2	of	of	ADP
ejpam-221	51	3	this	this	DET
ejpam-221	51	4	material	material	NOUN
ejpam-221	51	5	is	be	AUX
ejpam-221	51	6	‘	'	PUNCT
ejpam-221	51	7	folklore	folklore	NOUN
ejpam-221	51	8	’	'	PUNCT
ejpam-221	51	9	,	,	PUNCT
ejpam-221	51	10	in	in	SCONJ
ejpam-221	51	11	that	that	SCONJ
ejpam-221	51	12	it	it	PRON
ejpam-221	51	13	is	be	AUX
ejpam-221	51	14	difficult	difficult	ADJ
ejpam-221	51	15	to	to	PART
ejpam-221	51	16	determine	determine	VERB
ejpam-221	51	17	where	where	SCONJ
ejpam-221	51	18	and	and	CCONJ
ejpam-221	51	19	when	when	SCONJ
ejpam-221	51	20	it	it	PRON
ejpam-221	51	21	first	first	ADV
ejpam-221	51	22	appeared	appear	VERB
ejpam-221	51	23	in	in	ADP
ejpam-221	51	24	print	print	NOUN
ejpam-221	51	25	;	;	PUNCT
ejpam-221	51	26	we	we	PRON
ejpam-221	51	27	have	have	AUX
ejpam-221	51	28	drawn	draw	VERB
ejpam-221	51	29	heavily	heavily	ADV
ejpam-221	51	30	on	on	ADP
ejpam-221	51	31	the	the	DET
ejpam-221	51	32	notes	note	NOUN
ejpam-221	51	33	of	of	ADP
ejpam-221	51	34	gould	gould	PROPN
ejpam-221	51	35	[	[	X
ejpam-221	51	36	30	30	NUM
ejpam-221	51	37	]	]	PUNCT
ejpam-221	51	38	.	.	PUNCT
ejpam-221	52	1	in	in	ADP
ejpam-221	52	2	section	section	NOUN
ejpam-221	52	3	3	3	NUM
ejpam-221	52	4	,	,	PUNCT
ejpam-221	52	5	we	we	PRON
ejpam-221	52	6	expand	expand	VERB
ejpam-221	52	7	upon	upon	SCONJ
ejpam-221	52	8	the	the	DET
ejpam-221	52	9	comments	comment	NOUN
ejpam-221	52	10	made	make	VERB
ejpam-221	52	11	at	at	ADP
ejpam-221	52	12	the	the	DET
ejpam-221	52	13	beginning	beginning	NOUN
ejpam-221	52	14	of	of	ADP
ejpam-221	52	15	this	this	DET
ejpam-221	52	16	introduction	introduction	NOUN
ejpam-221	52	17	by	by	ADP
ejpam-221	52	18	defining	define	VERB
ejpam-221	52	19	restriction	restriction	NOUN
ejpam-221	52	20	semigroups	semigroup	NOUN
ejpam-221	52	21	by	by	ADP
ejpam-221	52	22	means	mean	NOUN
ejpam-221	52	23	of	of	ADP
ejpam-221	52	24	partial	partial	ADJ
ejpam-221	52	25	transformations	transformation	NOUN
ejpam-221	52	26	.	.	PUNCT
ejpam-221	53	1	we	we	PRON
ejpam-221	53	2	will	will	AUX
ejpam-221	53	3	focus	focus	VERB
ejpam-221	53	4	our	our	PRON
ejpam-221	53	5	attention	attention	NOUN
ejpam-221	53	6	on	on	ADP
ejpam-221	53	7	left	left	ADJ
ejpam-221	53	8	restriction	restriction	NOUN
ejpam-221	53	9	semigroups	semigroup	NOUN
ejpam-221	53	10	;	;	PUNCT
ejpam-221	53	11	the	the	DET
ejpam-221	53	12	right	right	ADJ
ejpam-221	53	13	-	-	PUNCT
ejpam-221	53	14	hand	hand	NOUN
ejpam-221	53	15	version	version	NOUN
ejpam-221	53	16	may	may	AUX
ejpam-221	53	17	be	be	AUX
ejpam-221	53	18	defined	define	VERB
ejpam-221	53	19	dually	dually	ADV
ejpam-221	53	20	.	.	PUNCT
ejpam-221	54	1	in	in	ADP
ejpam-221	54	2	section	section	NOUN
ejpam-221	54	3	4	4	NUM
ejpam-221	54	4	we	we	PRON
ejpam-221	54	5	present	present	VERB
ejpam-221	54	6	the	the	DET
ejpam-221	54	7	abstract	abstract	ADJ
ejpam-221	54	8	definition	definition	NOUN
ejpam-221	54	9	of	of	ADP
ejpam-221	54	10	a	a	DET
ejpam-221	54	11	weakly	weakly	ADJ
ejpam-221	54	12	left	left	ADJ
ejpam-221	54	13	eample	eample	NOUN
ejpam-221	54	14	semigroup	semigroup	NOUN
ejpam-221	54	15	and	and	CCONJ
ejpam-221	54	16	prove	prove	VERB
ejpam-221	54	17	that	that	SCONJ
ejpam-221	54	18	this	this	PRON
ejpam-221	54	19	is	be	AUX
ejpam-221	54	20	in	in	ADP
ejpam-221	54	21	fact	fact	NOUN
ejpam-221	54	22	equivalent	equivalent	ADJ
ejpam-221	54	23	to	to	ADP
ejpam-221	54	24	the	the	DET
ejpam-221	54	25	concrete	concrete	ADJ
ejpam-221	54	26	description	description	NOUN
ejpam-221	54	27	of	of	ADP
ejpam-221	54	28	a	a	DET
ejpam-221	54	29	left	left	ADJ
ejpam-221	54	30	restriction	restriction	NOUN
ejpam-221	54	31	semigroup	semigroup	NOUN
ejpam-221	54	32	,	,	PUNCT
ejpam-221	54	33	as	as	SCONJ
ejpam-221	54	34	given	give	VERB
ejpam-221	54	35	in	in	ADP
ejpam-221	54	36	section	section	NOUN
ejpam-221	54	37	3	3	NUM
ejpam-221	54	38	.	.	PUNCT
ejpam-221	55	1	we	we	PRON
ejpam-221	55	2	record	record	VERB
ejpam-221	55	3	some	some	PRON
ejpam-221	55	4	of	of	ADP
ejpam-221	55	5	the	the	DET
ejpam-221	55	6	basic	basic	ADJ
ejpam-221	55	7	results	result	NOUN
ejpam-221	55	8	in	in	ADP
ejpam-221	55	9	the	the	DET
ejpam-221	55	10	theory	theory	NOUN
ejpam-221	55	11	of	of	ADP
ejpam-221	55	12	left	left	ADJ
ejpam-221	55	13	restriction	restriction	NOUN
ejpam-221	55	14	semigroups	semigroup	NOUN
ejpam-221	55	15	,	,	PUNCT
ejpam-221	55	16	before	before	ADP
ejpam-221	55	17	moving	move	VERB
ejpam-221	55	18	on	on	ADP
ejpam-221	55	19	to	to	ADP
ejpam-221	55	20	section	section	NOUN
ejpam-221	55	21	5	5	NUM
ejpam-221	55	22	,	,	PUNCT
ejpam-221	55	23	where	where	SCONJ
ejpam-221	55	24	we	we	PRON
ejpam-221	55	25	consider	consider	VERB
ejpam-221	55	26	the	the	DET
ejpam-221	55	27	special	special	ADJ
ejpam-221	55	28	case	case	NOUN
ejpam-221	55	29	of	of	ADP
ejpam-221	55	30	left	left	ADJ
ejpam-221	55	31	ample	ample	ADJ
ejpam-221	55	32	semigroups	semigroup	NOUN
ejpam-221	55	33	.	.	PUNCT
ejpam-221	56	1	since	since	SCONJ
ejpam-221	56	2	the	the	DET
ejpam-221	56	3	nomenclature	nomenclature	NOUN
ejpam-221	56	4	which	which	PRON
ejpam-221	56	5	we	we	PRON
ejpam-221	56	6	will	will	AUX
ejpam-221	56	7	have	have	VERB
ejpam-221	56	8	occasion	occasion	NOUN
ejpam-221	56	9	to	to	PART
ejpam-221	56	10	wade	wade	VERB
ejpam-221	56	11	through	through	ADP
ejpam-221	56	12	in	in	ADP
ejpam-221	56	13	sections	section	NOUN
ejpam-221	56	14	1	1	NUM
ejpam-221	56	15	and	and	CCONJ
ejpam-221	56	16	2	2	NUM
ejpam-221	56	17	can	can	AUX
ejpam-221	56	18	be	be	AUX
ejpam-221	56	19	somewhat	somewhat	ADV
ejpam-221	56	20	torturous	torturous	ADJ
ejpam-221	56	21	,	,	PUNCT
ejpam-221	56	22	we	we	PRON
ejpam-221	56	23	conclude	conclude	VERB
ejpam-221	56	24	the	the	DET
ejpam-221	56	25	article	article	NOUN
ejpam-221	56	26	by	by	ADP
ejpam-221	56	27	providing	provide	VERB
ejpam-221	56	28	the	the	DET
ejpam-221	56	29	reader	reader	NOUN
ejpam-221	56	30	with	with	ADP
ejpam-221	56	31	an	an	DET
ejpam-221	56	32	appendix	appendix	NOUN
ejpam-221	56	33	summarising	summarise	VERB
ejpam-221	56	34	this	this	DET
ejpam-221	56	35	terminology	terminology	NOUN
ejpam-221	56	36	.	.	PUNCT
ejpam-221	57	1	we	we	PRON
ejpam-221	57	2	note	note	VERB
ejpam-221	57	3	that	that	SCONJ
ejpam-221	57	4	left	leave	VERB
ejpam-221	57	5	restriction	restriction	NOUN
ejpam-221	57	6	semigroups	semigroup	NOUN
ejpam-221	57	7	form	form	VERB
ejpam-221	57	8	a	a	DET
ejpam-221	57	9	variety	variety	NOUN
ejpam-221	57	10	of	of	ADP
ejpam-221	57	11	algebras	algebra	NOUN
ejpam-221	57	12	of	of	ADP
ejpam-221	57	13	type	type	NOUN
ejpam-221	57	14	(	(	PUNCT
ejpam-221	57	15	2,1	2,1	NUM
ejpam-221	57	16	)	)	PUNCT
ejpam-221	57	17	and	and	CCONJ
ejpam-221	57	18	can	can	AUX
ejpam-221	57	19	therefore	therefore	ADV
ejpam-221	57	20	be	be	AUX
ejpam-221	57	21	defined	define	VERB
ejpam-221	57	22	by	by	ADP
ejpam-221	57	23	a	a	DET
ejpam-221	57	24	system	system	NOUN
ejpam-221	57	25	of	of	ADP
ejpam-221	57	26	identities	identity	NOUN
ejpam-221	57	27	first	first	ADV
ejpam-221	57	28	presented	present	VERB
ejpam-221	57	29	in	in	ADP
ejpam-221	57	30	[	[	X
ejpam-221	57	31	39	39	NUM
ejpam-221	57	32	]	]	PUNCT
ejpam-221	57	33	;	;	PUNCT
ejpam-221	57	34	full	full	ADJ
ejpam-221	57	35	left	left	ADJ
ejpam-221	57	36	restriction	restriction	NOUN
ejpam-221	57	37	(	(	PUNCT
ejpam-221	57	38	see	see	VERB
ejpam-221	57	39	section	section	NOUN
ejpam-221	57	40	3	3	NUM
ejpam-221	57	41	)	)	PUNCT
ejpam-221	57	42	and	and	CCONJ
ejpam-221	57	43	left	leave	VERB
ejpam-221	57	44	ample	ample	ADJ
ejpam-221	57	45	semigroups	semigroup	NOUN
ejpam-221	57	46	form	form	VERB
ejpam-221	57	47	quasi	quasi	NOUN
ejpam-221	57	48	-	-	NOUN
ejpam-221	57	49	varieties	variety	NOUN
ejpam-221	57	50	of	of	ADP
ejpam-221	57	51	type	type	NOUN
ejpam-221	57	52	(	(	PUNCT
ejpam-221	57	53	2,1	2,1	NUM
ejpam-221	57	54	)	)	PUNCT
ejpam-221	57	55	.	.	PUNCT
ejpam-221	58	1	however	however	ADV
ejpam-221	58	2	,	,	PUNCT
ejpam-221	58	3	this	this	PRON
ejpam-221	58	4	is	be	AUX
ejpam-221	58	5	not	not	PART
ejpam-221	58	6	an	an	DET
ejpam-221	58	7	approach	approach	NOUN
ejpam-221	58	8	we	we	PRON
ejpam-221	58	9	will	will	AUX
ejpam-221	58	10	take	take	VERB
ejpam-221	58	11	in	in	ADP
ejpam-221	58	12	the	the	DET
ejpam-221	58	13	present	present	ADJ
ejpam-221	58	14	article	article	NOUN
ejpam-221	58	15	;	;	PUNCT
ejpam-221	58	16	we	we	PRON
ejpam-221	58	17	hope	hope	VERB
ejpam-221	58	18	to	to	PART
ejpam-221	58	19	do	do	VERB
ejpam-221	58	20	so	so	ADV
ejpam-221	58	21	in	in	ADP
ejpam-221	58	22	a	a	DET
ejpam-221	58	23	future	future	ADJ
ejpam-221	58	24	article	article	NOUN
ejpam-221	58	25	,	,	PUNCT
ejpam-221	58	26	as	as	ADV
ejpam-221	58	27	well	well	ADV
ejpam-221	58	28	as	as	ADP
ejpam-221	58	29	drawing	draw	VERB
ejpam-221	58	30	further	further	ADJ
ejpam-221	58	31	connections	connection	NOUN
ejpam-221	58	32	with	with	ADP
ejpam-221	58	33	left	left	ADJ
ejpam-221	58	34	restriction	restriction	NOUN
ejpam-221	58	35	semigroups	semigroup	NOUN
ejpam-221	58	36	in	in	ADP
ejpam-221	58	37	their	their	PRON
ejpam-221	58	38	various	various	ADJ
ejpam-221	58	39	other	other	ADJ
ejpam-221	58	40	guises	guise	NOUN
ejpam-221	58	41	.	.	PUNCT
ejpam-221	59	1	for	for	ADP
ejpam-221	59	2	the	the	DET
ejpam-221	59	3	present	present	NOUN
ejpam-221	59	4	,	,	PUNCT
ejpam-221	59	5	we	we	PRON
ejpam-221	59	6	note	note	VERB
ejpam-221	59	7	that	that	SCONJ
ejpam-221	59	8	the	the	DET
ejpam-221	59	9	equivalence	equivalence	NOUN
ejpam-221	59	10	of	of	ADP
ejpam-221	59	11	the	the	DET
ejpam-221	59	12	classes	class	NOUN
ejpam-221	59	13	of	of	ADP
ejpam-221	59	14	type	type	NOUN
ejpam-221	59	15	sl2	sl2	PROPN
ejpam-221	59	16	γ-	γ-	PROPN
ejpam-221	59	17	,	,	PUNCT
ejpam-221	59	18	weakly	weakly	ADV
ejpam-221	59	19	left	left	ADJ
ejpam-221	59	20	e	e	NOUN
ejpam-221	59	21	-	-	ADJ
ejpam-221	59	22	ample	ample	ADJ
ejpam-221	59	23	,	,	PUNCT
ejpam-221	59	24	left	leave	VERB
ejpam-221	59	25	lc-	lc-	PROPN
ejpam-221	59	26	,	,	PUNCT
ejpam-221	59	27	and	and	CCONJ
ejpam-221	59	28	guarded	guard	VERB
ejpam-221	59	29	semigroups	semigroup	NOUN
ejpam-221	59	30	is	be	AUX
ejpam-221	59	31	demonstrated	demonstrate	VERB
ejpam-221	59	32	in	in	ADP
ejpam-221	59	33	[	[	X
ejpam-221	59	34	35	35	NUM
ejpam-221	59	35	,	,	PUNCT
ejpam-221	59	36	§	§	NOUN
ejpam-221	59	37	2.6	2.6	NUM
ejpam-221	59	38	]	]	PUNCT
ejpam-221	59	39	.	.	PUNCT
ejpam-221	60	1	in	in	ADP
ejpam-221	60	2	[	[	X
ejpam-221	60	3	32	32	NUM
ejpam-221	60	4	]	]	PUNCT
ejpam-221	60	5	,	,	PUNCT
ejpam-221	60	6	the	the	DET
ejpam-221	60	7	adjective	adjective	ADJ
ejpam-221	60	8	‘	'	PUNCT
ejpam-221	60	9	left	leave	VERB
ejpam-221	60	10	’	'	PUNCT
ejpam-221	60	11	is	be	AUX
ejpam-221	60	12	dropped	drop	VERB
ejpam-221	60	13	and	and	CCONJ
ejpam-221	60	14	left	leave	VERB
ejpam-221	60	15	restriction	restriction	NOUN
ejpam-221	60	16	semigroups	semigroup	NOUN
ejpam-221	60	17	are	be	AUX
ejpam-221	60	18	termed	term	VERB
ejpam-221	60	19	simply	simply	ADV
ejpam-221	60	20	‘	'	PUNCT
ejpam-221	60	21	restriction	restriction	NOUN
ejpam-221	60	22	semigroups	semigroup	NOUN
ejpam-221	60	23	’	'	PUNCT
ejpam-221	60	24	,	,	PUNCT
ejpam-221	60	25	since	since	SCONJ
ejpam-221	60	26	these	these	PRON
ejpam-221	60	27	are	be	AUX
ejpam-221	60	28	the	the	DET
ejpam-221	60	29	objects	object	NOUN
ejpam-221	60	30	of	of	ADP
ejpam-221	60	31	interest	interest	NOUN
ejpam-221	60	32	in	in	ADP
ejpam-221	60	33	that	that	DET
ejpam-221	60	34	paper	paper	NOUN
ejpam-221	60	35	;	;	PUNCT
ejpam-221	60	36	in	in	ADP
ejpam-221	60	37	[	[	X
ejpam-221	60	38	36	36	NUM
ejpam-221	60	39	]	]	PUNCT
ejpam-221	60	40	,	,	PUNCT
ejpam-221	60	41	on	on	ADP
ejpam-221	60	42	the	the	DET
ejpam-221	60	43	other	other	ADJ
ejpam-221	60	44	hand	hand	NOUN
ejpam-221	60	45	,	,	PUNCT
ejpam-221	60	46	the	the	DET
ejpam-221	60	47	term	term	NOUN
ejpam-221	60	48	‘	'	PUNCT
ejpam-221	60	49	restriction	restriction	NOUN
ejpam-221	60	50	semigroup	semigroup	NOUN
ejpam-221	60	51	’	'	PUNCT
ejpam-221	60	52	is	be	AUX
ejpam-221	60	53	used	use	VERB
ejpam-221	60	54	to	to	PART
ejpam-221	60	55	refer	refer	VERB
ejpam-221	60	56	to	to	ADP
ejpam-221	60	57	the	the	DET
ejpam-221	60	58	two	two	NUM
ejpam-221	60	59	-	-	PUNCT
ejpam-221	60	60	sided	side	VERB
ejpam-221	60	61	case	case	NOUN
ejpam-221	60	62	for	for	ADP
ejpam-221	60	63	similar	similar	ADJ
ejpam-221	60	64	reasons	reason	NOUN
ejpam-221	60	65	.	.	PUNCT
ejpam-221	61	1	in	in	ADP
ejpam-221	61	2	the	the	DET
ejpam-221	61	3	present	present	ADJ
ejpam-221	61	4	article	article	NOUN
ejpam-221	61	5	,	,	PUNCT
ejpam-221	61	6	in	in	ADP
ejpam-221	61	7	the	the	DET
ejpam-221	61	8	interests	interest	NOUN
ejpam-221	61	9	of	of	ADP
ejpam-221	61	10	clarity	clarity	NOUN
ejpam-221	61	11	,	,	PUNCT
ejpam-221	61	12	we	we	PRON
ejpam-221	61	13	will	will	AUX
ejpam-221	61	14	only	only	ADV
ejpam-221	61	15	drop	drop	VERB
ejpam-221	61	16	these	these	DET
ejpam-221	61	17	qualifiers	qualifier	NOUN
ejpam-221	61	18	c.	c.	PROPN
ejpam-221	61	19	hollings	hollings	PROPN
ejpam-221	61	20	/	/	SYM
ejpam-221	61	21	eur	eur	PROPN
ejpam-221	61	22	.	.	PUNCT
ejpam-221	62	1	j.	j.	PROPN
ejpam-221	62	2	pure	pure	PROPN
ejpam-221	62	3	appl	appl	PROPN
ejpam-221	62	4	.	.	PROPN
ejpam-221	62	5	math	math	PROPN
ejpam-221	62	6	,	,	PUNCT
ejpam-221	62	7	2	2	NUM
ejpam-221	62	8	(	(	PUNCT
ejpam-221	62	9	2009	2009	NUM
ejpam-221	62	10	)	)	PUNCT
ejpam-221	62	11	,	,	PUNCT
ejpam-221	62	12	(	(	PUNCT
ejpam-221	62	13	21	21	NUM
ejpam-221	62	14	-	-	SYM
ejpam-221	62	15	57	57	NUM
ejpam-221	62	16	)	)	PUNCT
ejpam-221	62	17	25	25	NUM
ejpam-221	62	18	when	when	SCONJ
ejpam-221	62	19	making	make	VERB
ejpam-221	62	20	a	a	DET
ejpam-221	62	21	statement	statement	NOUN
ejpam-221	62	22	which	which	PRON
ejpam-221	62	23	applies	apply	VERB
ejpam-221	62	24	equally	equally	ADV
ejpam-221	62	25	well	well	ADV
ejpam-221	62	26	to	to	PART
ejpam-221	62	27	left	left	VERB
ejpam-221	62	28	,	,	PUNCT
ejpam-221	62	29	right	right	ADJ
ejpam-221	62	30	and	and	CCONJ
ejpam-221	62	31	two	two	NUM
ejpam-221	62	32	-	-	PUNCT
ejpam-221	62	33	sided	sided	ADJ
ejpam-221	62	34	restriction	restriction	NOUN
ejpam-221	62	35	semigroups	semigroup	NOUN
ejpam-221	62	36	.	.	PUNCT
ejpam-221	63	1	for	for	ADP
ejpam-221	63	2	later	later	ADJ
ejpam-221	63	3	use	use	NOUN
ejpam-221	63	4	,	,	PUNCT
ejpam-221	63	5	the	the	DET
ejpam-221	63	6	uninitiated	uninitiated	ADJ
ejpam-221	63	7	reader	reader	NOUN
ejpam-221	63	8	should	should	AUX
ejpam-221	63	9	bear	bear	VERB
ejpam-221	63	10	in	in	ADP
ejpam-221	63	11	mind	mind	NOUN
ejpam-221	63	12	the	the	DET
ejpam-221	63	13	definition	definition	NOUN
ejpam-221	63	14	of	of	ADP
ejpam-221	63	15	green	green	PROPN
ejpam-221	63	16	’s	’s	PART
ejpam-221	63	17	(	(	PUNCT
ejpam-221	63	18	equivalence	equivalence	NOUN
ejpam-221	63	19	)	)	PUNCT
ejpam-221	63	20	relation	relation	NOUN
ejpam-221	63	21	r	r	NOUN
ejpam-221	63	22	in	in	ADP
ejpam-221	63	23	a	a	DET
ejpam-221	63	24	semigroup	semigroup	NOUN
ejpam-221	63	25	s	s	NOUN
ejpam-221	63	26	:	:	PUNCT
ejpam-221	63	27	two	two	NUM
ejpam-221	63	28	elements	element	NOUN
ejpam-221	63	29	a	a	PRON
ejpam-221	63	30	,	,	PUNCT
ejpam-221	63	31	b	b	X
ejpam-221	63	32	∈	∈	NOUN
ejpam-221	63	33	s	s	AUX
ejpam-221	63	34	are	be	AUX
ejpam-221	63	35	r	r	NOUN
ejpam-221	63	36	-	-	PUNCT
ejpam-221	63	37	related	relate	VERB
ejpam-221	63	38	if	if	SCONJ
ejpam-221	63	39	they	they	PRON
ejpam-221	63	40	generate	generate	VERB
ejpam-221	63	41	the	the	DET
ejpam-221	63	42	same	same	ADJ
ejpam-221	63	43	principal	principal	NOUN
ejpam-221	63	44	right	right	ADJ
ejpam-221	63	45	ideal	ideal	NOUN
ejpam-221	63	46	.	.	PUNCT
ejpam-221	64	1	any	any	DET
ejpam-221	64	2	idempotent	idempotent	NOUN
ejpam-221	64	3	is	be	AUX
ejpam-221	64	4	a	a	DET
ejpam-221	64	5	left	left	ADJ
ejpam-221	64	6	identity	identity	NOUN
ejpam-221	64	7	for	for	ADP
ejpam-221	64	8	its	its	PRON
ejpam-221	64	9	r	r	NOUN
ejpam-221	64	10	-	-	PUNCT
ejpam-221	64	11	class	class	NOUN
ejpam-221	64	12	.	.	PUNCT
ejpam-221	65	1	green	green	PROPN
ejpam-221	65	2	’s	’s	PART
ejpam-221	65	3	relation	relation	NOUN
ejpam-221	65	4	l	l	NOUN
ejpam-221	65	5	may	may	AUX
ejpam-221	65	6	be	be	AUX
ejpam-221	65	7	defined	define	VERB
ejpam-221	65	8	as	as	ADP
ejpam-221	65	9	the	the	DET
ejpam-221	65	10	left	left	ADJ
ejpam-221	65	11	-	-	PUNCT
ejpam-221	65	12	right	right	NOUN
ejpam-221	65	13	dual	dual	ADV
ejpam-221	65	14	of	of	ADP
ejpam-221	65	15	r	r	NOUN
ejpam-221	65	16	;	;	PUNCT
ejpam-221	65	17	the	the	DET
ejpam-221	65	18	relation	relation	NOUN
ejpam-221	65	19	h	h	NOUN
ejpam-221	65	20	is	be	AUX
ejpam-221	65	21	defined	define	VERB
ejpam-221	65	22	byh	byh	ADP
ejpam-221	65	23	=	=	NOUN
ejpam-221	65	24	r	r	NOUN
ejpam-221	65	25	∩l	∩l	NOUN
ejpam-221	65	26	.	.	PUNCT
ejpam-221	66	1	any	any	DET
ejpam-221	66	2	other	other	ADJ
ejpam-221	66	3	unexplained	unexplained	ADJ
ejpam-221	66	4	semigroup	semigroup	NOUN
ejpam-221	66	5	-	-	PUNCT
ejpam-221	66	6	theoretic	theoretic	NOUN
ejpam-221	66	7	terminology	terminology	NOUN
ejpam-221	66	8	or	or	CCONJ
ejpam-221	66	9	notation	notation	NOUN
ejpam-221	66	10	may	may	AUX
ejpam-221	66	11	be	be	AUX
ejpam-221	66	12	found	find	VERB
ejpam-221	66	13	in	in	ADP
ejpam-221	66	14	[	[	X
ejpam-221	66	15	37	37	NUM
ejpam-221	66	16	]	]	SYM
ejpam-221	66	17	.	.	PUNCT
ejpam-221	67	1	1	1	X
ejpam-221	67	2	.	.	X
ejpam-221	67	3	historical	historical	ADJ
ejpam-221	67	4	development	development	NOUN
ejpam-221	68	1	i	i	PRON
ejpam-221	68	2	:	:	PUNCT
ejpam-221	68	3	left	leave	VERB
ejpam-221	68	4	ample	ample	ADJ
ejpam-221	68	5	semigroups	semigroup	NOUN
ejpam-221	68	6	we	we	PRON
ejpam-221	68	7	begin	begin	VERB
ejpam-221	68	8	by	by	ADP
ejpam-221	68	9	giving	give	VERB
ejpam-221	68	10	a	a	DET
ejpam-221	68	11	two	two	NUM
ejpam-221	68	12	-	-	PUNCT
ejpam-221	68	13	part	part	NOUN
ejpam-221	68	14	historical	historical	ADJ
ejpam-221	68	15	survey	survey	NOUN
ejpam-221	68	16	of	of	ADP
ejpam-221	68	17	the	the	DET
ejpam-221	68	18	origins	origin	NOUN
ejpam-221	68	19	of	of	ADP
ejpam-221	68	20	restriction	restriction	NOUN
ejpam-221	68	21	semigroups	semigroup	NOUN
ejpam-221	68	22	,	,	PUNCT
ejpam-221	68	23	from	from	ADP
ejpam-221	68	24	the	the	DET
ejpam-221	68	25	point	point	NOUN
ejpam-221	68	26	of	of	ADP
ejpam-221	68	27	view	view	NOUN
ejpam-221	68	28	of	of	ADP
ejpam-221	68	29	the	the	DET
ejpam-221	68	30	‘	'	PUNCT
ejpam-221	68	31	york	york	NOUN
ejpam-221	68	32	’	'	PUNCT
ejpam-221	68	33	school	school	NOUN
ejpam-221	68	34	.	.	PUNCT
ejpam-221	69	1	in	in	ADP
ejpam-221	69	2	this	this	DET
ejpam-221	69	3	section	section	NOUN
ejpam-221	69	4	,	,	PUNCT
ejpam-221	69	5	we	we	PRON
ejpam-221	69	6	deal	deal	VERB
ejpam-221	69	7	with	with	ADP
ejpam-221	69	8	left	left	ADJ
ejpam-221	69	9	ample	ample	ADJ
ejpam-221	69	10	semigroups	semigroup	NOUN
ejpam-221	69	11	;	;	PUNCT
ejpam-221	69	12	weakly	weakly	ADV
ejpam-221	69	13	left	leave	VERB
ejpam-221	69	14	e	e	NOUN
ejpam-221	69	15	-	-	ADJ
ejpam-221	69	16	ample	ample	ADJ
ejpam-221	69	17	semigroups	semigroup	NOUN
ejpam-221	69	18	follow	follow	VERB
ejpam-221	69	19	in	in	ADP
ejpam-221	69	20	section	section	NOUN
ejpam-221	69	21	2	2	NUM
ejpam-221	69	22	.	.	PUNCT
ejpam-221	70	1	the	the	DET
ejpam-221	70	2	present	present	ADJ
ejpam-221	70	3	section	section	NOUN
ejpam-221	70	4	is	be	AUX
ejpam-221	70	5	based	base	VERB
ejpam-221	70	6	upon	upon	SCONJ
ejpam-221	70	7	the	the	DET
ejpam-221	70	8	similar	similar	ADJ
ejpam-221	70	9	introductory	introductory	ADJ
ejpam-221	70	10	chapters	chapter	NOUN
ejpam-221	70	11	of	of	ADP
ejpam-221	70	12	the	the	DET
ejpam-221	70	13	d.phil	d.phil	PROPN
ejpam-221	70	14	.	.	PUNCT
ejpam-221	71	1	theses	thesis	NOUN
ejpam-221	71	2	of	of	ADP
ejpam-221	71	3	el	el	PROPN
ejpam-221	71	4	-	-	PROPN
ejpam-221	71	5	qallali	qallali	PROPN
ejpam-221	72	1	[	[	X
ejpam-221	72	2	15	15	NUM
ejpam-221	72	3	]	]	PUNCT
ejpam-221	72	4	and	and	CCONJ
ejpam-221	72	5	lawson	lawson	PROPN
ejpam-221	73	1	[	[	X
ejpam-221	73	2	43	43	NUM
ejpam-221	73	3	]	]	PUNCT
ejpam-221	73	4	.	.	PUNCT
ejpam-221	74	1	another	another	DET
ejpam-221	74	2	invaluable	invaluable	ADJ
ejpam-221	74	3	source	source	NOUN
ejpam-221	74	4	,	,	PUNCT
ejpam-221	74	5	both	both	PRON
ejpam-221	74	6	for	for	ADP
ejpam-221	74	7	this	this	DET
ejpam-221	74	8	section	section	NOUN
ejpam-221	74	9	and	and	CCONJ
ejpam-221	74	10	the	the	DET
ejpam-221	74	11	next	next	ADJ
ejpam-221	74	12	,	,	PUNCT
ejpam-221	74	13	was	be	AUX
ejpam-221	74	14	ample	ample	ADJ
ejpam-221	74	15	and	and	CCONJ
ejpam-221	74	16	left	leave	VERB
ejpam-221	74	17	ample	ample	ADJ
ejpam-221	74	18	semigroups	semigroup	NOUN
ejpam-221	75	1	[	[	X
ejpam-221	75	2	26	26	NUM
ejpam-221	75	3	]	]	PUNCT
ejpam-221	75	4	,	,	PUNCT
ejpam-221	75	5	the	the	DET
ejpam-221	75	6	extended	extended	ADJ
ejpam-221	75	7	abstract	abstract	NOUN
ejpam-221	75	8	of	of	ADP
ejpam-221	75	9	a	a	DET
ejpam-221	75	10	survey	survey	NOUN
ejpam-221	75	11	talk	talk	NOUN
ejpam-221	75	12	given	give	VERB
ejpam-221	75	13	by	by	ADP
ejpam-221	75	14	john	john	PROPN
ejpam-221	75	15	fountain	fountain	PROPN
ejpam-221	75	16	in	in	ADP
ejpam-221	75	17	calgary	calgary	PROPN
ejpam-221	75	18	in	in	ADP
ejpam-221	75	19	june	june	PROPN
ejpam-221	75	20	2006	2006	NUM
ejpam-221	75	21	.	.	PUNCT
ejpam-221	76	1	as	as	SCONJ
ejpam-221	76	2	indicated	indicate	VERB
ejpam-221	76	3	in	in	ADP
ejpam-221	76	4	the	the	DET
ejpam-221	76	5	introduction	introduction	NOUN
ejpam-221	76	6	,	,	PUNCT
ejpam-221	76	7	the	the	DET
ejpam-221	76	8	most	most	ADV
ejpam-221	76	9	natural	natural	ADJ
ejpam-221	76	10	way	way	NOUN
ejpam-221	76	11	to	to	PART
ejpam-221	76	12	introduce	introduce	VERB
ejpam-221	76	13	restriction	restriction	NOUN
ejpam-221	76	14	semigroups	semigroup	NOUN
ejpam-221	76	15	is	be	AUX
ejpam-221	76	16	via	via	ADP
ejpam-221	76	17	the	the	DET
ejpam-221	76	18	partial	partial	ADJ
ejpam-221	76	19	transformations	transformation	NOUN
ejpam-221	76	20	of	of	ADP
ejpam-221	76	21	a	a	DET
ejpam-221	76	22	set	set	NOUN
ejpam-221	76	23	.	.	PUNCT
ejpam-221	77	1	indeed	indeed	ADV
ejpam-221	77	2	,	,	PUNCT
ejpam-221	77	3	this	this	PRON
ejpam-221	77	4	is	be	AUX
ejpam-221	77	5	what	what	PRON
ejpam-221	77	6	we	we	PRON
ejpam-221	77	7	will	will	AUX
ejpam-221	77	8	do	do	VERB
ejpam-221	77	9	in	in	ADP
ejpam-221	77	10	section	section	NOUN
ejpam-221	77	11	3	3	NUM
ejpam-221	77	12	.	.	PUNCT
ejpam-221	78	1	however	however	ADV
ejpam-221	78	2	,	,	PUNCT
ejpam-221	78	3	our	our	PRON
ejpam-221	78	4	historical	historical	ADJ
ejpam-221	78	5	summary	summary	NOUN
ejpam-221	78	6	begins	begin	VERB
ejpam-221	78	7	in	in	ADP
ejpam-221	78	8	a	a	DET
ejpam-221	78	9	rather	rather	ADV
ejpam-221	78	10	different	different	ADJ
ejpam-221	78	11	place	place	NOUN
ejpam-221	78	12	,	,	PUNCT
ejpam-221	78	13	with	with	ADP
ejpam-221	78	14	the	the	DET
ejpam-221	78	15	homological	homological	ADJ
ejpam-221	78	16	classification	classification	NOUN
ejpam-221	78	17	of	of	ADP
ejpam-221	78	18	monoids	monoid	NOUN
ejpam-221	78	19	.	.	PUNCT
ejpam-221	79	1	we	we	PRON
ejpam-221	79	2	first	first	ADV
ejpam-221	79	3	require	require	VERB
ejpam-221	79	4	the	the	DET
ejpam-221	79	5	definitions	definition	NOUN
ejpam-221	79	6	of	of	ADP
ejpam-221	79	7	both	both	DET
ejpam-221	79	8	s	s	NOUN
ejpam-221	79	9	-	-	NOUN
ejpam-221	79	10	acts	act	NOUN
ejpam-221	79	11	and	and	CCONJ
ejpam-221	79	12	s	s	NOUN
ejpam-221	79	13	-	-	NOUN
ejpam-221	79	14	morphisms	morphisms	ADJ
ejpam-221	79	15	:	:	PUNCT
ejpam-221	79	16	definition	definition	NOUN
ejpam-221	79	17	1.1	1.1	NUM
ejpam-221	79	18	.	.	PUNCT
ejpam-221	80	1	[	[	X
ejpam-221	80	2	37	37	NUM
ejpam-221	80	3	,	,	PUNCT
ejpam-221	80	4	§	§	NOUN
ejpam-221	80	5	8.1	8.1	NUM
ejpam-221	80	6	]	]	PUNCT
ejpam-221	80	7	let	let	VERB
ejpam-221	80	8	s	s	PRON
ejpam-221	80	9	be	be	AUX
ejpam-221	80	10	a	a	DET
ejpam-221	80	11	monoid	monoid	NOUN
ejpam-221	80	12	.	.	PUNCT
ejpam-221	81	1	a	a	DET
ejpam-221	81	2	set	set	NOUN
ejpam-221	81	3	x	x	PUNCT
ejpam-221	81	4	is	be	AUX
ejpam-221	81	5	called	call	VERB
ejpam-221	81	6	a	a	DET
ejpam-221	81	7	right	right	ADJ
ejpam-221	81	8	s	s	NOUN
ejpam-221	81	9	-	-	NOUN
ejpam-221	81	10	act	act	NOUN
ejpam-221	81	11	(	(	PUNCT
ejpam-221	81	12	or	or	CCONJ
ejpam-221	81	13	s	s	VERB
ejpam-221	81	14	-	-	PUNCT
ejpam-221	81	15	set	set	VERB
ejpam-221	81	16	or	or	CCONJ
ejpam-221	81	17	s	s	NOUN
ejpam-221	81	18	-	-	NOUN
ejpam-221	81	19	system	system	NOUN
ejpam-221	81	20	)	)	PUNCT
ejpam-221	81	21	if	if	SCONJ
ejpam-221	81	22	s	s	PRON
ejpam-221	81	23	acts	act	VERB
ejpam-221	81	24	on	on	ADP
ejpam-221	81	25	x	x	PUNCT
ejpam-221	81	26	on	on	ADP
ejpam-221	81	27	the	the	DET
ejpam-221	81	28	right	right	NOUN
ejpam-221	81	29	,	,	PUNCT
ejpam-221	81	30	i.e.	i.e.	X
ejpam-221	81	31	,	,	PUNCT
ejpam-221	81	32	if	if	SCONJ
ejpam-221	81	33	there	there	PRON
ejpam-221	81	34	is	be	VERB
ejpam-221	81	35	a	a	DET
ejpam-221	81	36	mapping	mapping	NOUN
ejpam-221	81	37	x	x	SYM
ejpam-221	81	38	×s→	×s→	PROPN
ejpam-221	81	39	x	x	X
ejpam-221	81	40	,	,	PUNCT
ejpam-221	81	41	written	write	VERB
ejpam-221	81	42	(	(	PUNCT
ejpam-221	81	43	x	x	X
ejpam-221	81	44	,	,	PUNCT
ejpam-221	81	45	s	s	PROPN
ejpam-221	81	46	)	)	PUNCT
ejpam-221	81	47	7→	7→	NUM
ejpam-221	81	48	x	x	PUNCT
ejpam-221	81	49	·	·	SYM
ejpam-221	81	50	s	s	X
ejpam-221	81	51	and	and	CCONJ
ejpam-221	81	52	such	such	ADJ
ejpam-221	81	53	that	that	PRON
ejpam-221	81	54	(	(	PUNCT
ejpam-221	81	55	x	x	X
ejpam-221	81	56	·	·	PUNCT
ejpam-221	81	57	s	s	X
ejpam-221	81	58	)	)	PUNCT
ejpam-221	81	59	·	·	PUNCT
ejpam-221	81	60	t	t	X
ejpam-221	81	61	=	=	PUNCT
ejpam-221	81	62	x	x	SYM
ejpam-221	81	63	·	·	PUNCT
ejpam-221	81	64	st	st	PROPN
ejpam-221	81	65	,	,	PUNCT
ejpam-221	81	66	for	for	ADP
ejpam-221	81	67	all	all	DET
ejpam-221	81	68	x	x	SYM
ejpam-221	81	69	∈	∈	PROPN
ejpam-221	81	70	x	x	X
ejpam-221	81	71	and	and	CCONJ
ejpam-221	81	72	s	s	PROPN
ejpam-221	81	73	,	,	PUNCT
ejpam-221	81	74	t	t	PROPN
ejpam-221	81	75	∈	∈	PROPN
ejpam-221	81	76	s	s	X
ejpam-221	81	77	,	,	PUNCT
ejpam-221	81	78	and	and	CCONJ
ejpam-221	81	79	x	x	X
ejpam-221	81	80	·	·	PUNCT
ejpam-221	81	81	1	1	NUM
ejpam-221	81	82	=	=	SYM
ejpam-221	81	83	x	x	X
ejpam-221	81	84	,	,	PUNCT
ejpam-221	81	85	for	for	ADP
ejpam-221	81	86	all	all	DET
ejpam-221	81	87	x	x	SYM
ejpam-221	81	88	∈	∈	NOUN
ejpam-221	81	89	x	x	X
ejpam-221	81	90	.	.	PUNCT
ejpam-221	82	1	(	(	PUNCT
ejpam-221	82	2	left	leave	VERB
ejpam-221	82	3	s	s	NOUN
ejpam-221	82	4	-	-	PUNCT
ejpam-221	82	5	acts	act	NOUN
ejpam-221	82	6	are	be	AUX
ejpam-221	82	7	defined	define	VERB
ejpam-221	82	8	dually	dually	ADV
ejpam-221	82	9	.	.	PUNCT
ejpam-221	82	10	)	)	PUNCT
ejpam-221	83	1	let	let	VERB
ejpam-221	83	2	x	x	PRON
ejpam-221	83	3	and	and	CCONJ
ejpam-221	83	4	y	y	PROPN
ejpam-221	83	5	be	be	AUX
ejpam-221	83	6	two	two	NUM
ejpam-221	83	7	right	right	ADJ
ejpam-221	83	8	s	s	NOUN
ejpam-221	83	9	-	-	PUNCT
ejpam-221	83	10	acts	act	NOUN
ejpam-221	83	11	.	.	PUNCT
ejpam-221	84	1	a	a	DET
ejpam-221	84	2	function	function	NOUN
ejpam-221	84	3	ϕ	ϕ	NOUN
ejpam-221	84	4	:	:	PUNCT
ejpam-221	84	5	x	x	SYM
ejpam-221	84	6	→	→	SYM
ejpam-221	84	7	y	y	PROPN
ejpam-221	84	8	is	be	AUX
ejpam-221	84	9	called	call	VERB
ejpam-221	84	10	an	an	DET
ejpam-221	84	11	s	s	NOUN
ejpam-221	84	12	-	-	NOUN
ejpam-221	84	13	morphism	morphism	NOUN
ejpam-221	84	14	if	if	SCONJ
ejpam-221	84	15	(	(	PUNCT
ejpam-221	84	16	x	x	X
ejpam-221	84	17	·	·	PUNCT
ejpam-221	84	18	s)ϕ	s)ϕ	NOUN
ejpam-221	84	19	=	=	PUNCT
ejpam-221	84	20	xϕ	xϕ	X
ejpam-221	84	21	·	·	PUNCT
ejpam-221	85	1	s	s	X
ejpam-221	85	2	,	,	PUNCT
ejpam-221	85	3	for	for	ADP
ejpam-221	85	4	all	all	DET
ejpam-221	85	5	x	x	SYM
ejpam-221	85	6	∈	∈	PROPN
ejpam-221	85	7	x	x	X
ejpam-221	85	8	and	and	CCONJ
ejpam-221	85	9	s	s	PROPN
ejpam-221	85	10	∈	∈	PROPN
ejpam-221	85	11	s.	s.	PROPN
ejpam-221	85	12	if	if	SCONJ
ejpam-221	85	13	s	s	PROPN
ejpam-221	85	14	is	be	AUX
ejpam-221	85	15	a	a	DET
ejpam-221	85	16	monoid	monoid	NOUN
ejpam-221	85	17	,	,	PUNCT
ejpam-221	85	18	then	then	ADV
ejpam-221	85	19	any	any	DET
ejpam-221	85	20	right	right	ADJ
ejpam-221	85	21	ideal	ideal	NOUN
ejpam-221	85	22	of	of	ADP
ejpam-221	85	23	s	s	PRON
ejpam-221	85	24	may	may	AUX
ejpam-221	85	25	be	be	AUX
ejpam-221	85	26	regarded	regard	VERB
ejpam-221	85	27	as	as	ADP
ejpam-221	85	28	a	a	DET
ejpam-221	85	29	right	right	ADJ
ejpam-221	85	30	s	s	NOUN
ejpam-221	85	31	-	-	NOUN
ejpam-221	85	32	act	act	NOUN
ejpam-221	85	33	,	,	PUNCT
ejpam-221	85	34	where	where	SCONJ
ejpam-221	85	35	the	the	DET
ejpam-221	85	36	action	action	NOUN
ejpam-221	85	37	in	in	ADP
ejpam-221	85	38	question	question	NOUN
ejpam-221	85	39	is	be	AUX
ejpam-221	85	40	that	that	SCONJ
ejpam-221	85	41	by	by	ADP
ejpam-221	85	42	right	right	ADJ
ejpam-221	85	43	multiplication	multiplication	NOUN
ejpam-221	85	44	.	.	PUNCT
ejpam-221	86	1	similarly	similarly	ADV
ejpam-221	86	2	,	,	PUNCT
ejpam-221	86	3	any	any	DET
ejpam-221	86	4	left	left	ADJ
ejpam-221	86	5	ideal	ideal	NOUN
ejpam-221	86	6	is	be	AUX
ejpam-221	86	7	a	a	DET
ejpam-221	86	8	left	left	ADJ
ejpam-221	86	9	s	s	NOUN
ejpam-221	86	10	-	-	NOUN
ejpam-221	86	11	act	act	NOUN
ejpam-221	86	12	.	.	PUNCT
ejpam-221	87	1	c.	c.	PROPN
ejpam-221	87	2	hollings	holling	NOUN
ejpam-221	87	3	/	/	SYM
ejpam-221	87	4	eur	eur	PROPN
ejpam-221	87	5	.	.	PUNCT
ejpam-221	88	1	j.	j.	PROPN
ejpam-221	88	2	pure	pure	PROPN
ejpam-221	88	3	appl	appl	PROPN
ejpam-221	88	4	.	.	PROPN
ejpam-221	88	5	math	math	PROPN
ejpam-221	88	6	,	,	PUNCT
ejpam-221	88	7	2	2	NUM
ejpam-221	88	8	(	(	PUNCT
ejpam-221	88	9	2009	2009	NUM
ejpam-221	88	10	)	)	PUNCT
ejpam-221	88	11	,	,	PUNCT
ejpam-221	88	12	(	(	PUNCT
ejpam-221	88	13	21	21	NUM
ejpam-221	88	14	-	-	SYM
ejpam-221	88	15	57	57	NUM
ejpam-221	88	16	)	)	PUNCT
ejpam-221	88	17	26	26	NUM
ejpam-221	88	18	just	just	ADV
ejpam-221	88	19	as	as	SCONJ
ejpam-221	88	20	rings	ring	NOUN
ejpam-221	88	21	may	may	AUX
ejpam-221	88	22	be	be	AUX
ejpam-221	88	23	studied	study	VERB
ejpam-221	88	24	via	via	ADP
ejpam-221	88	25	their	their	PRON
ejpam-221	88	26	actions	action	NOUN
ejpam-221	88	27	on	on	ADP
ejpam-221	88	28	modules	module	NOUN
ejpam-221	88	29	[	[	X
ejpam-221	88	30	33	33	NUM
ejpam-221	88	31	]	]	PUNCT
ejpam-221	88	32	,	,	PUNCT
ejpam-221	88	33	so	so	ADV
ejpam-221	88	34	too	too	ADV
ejpam-221	88	35	can	can	AUX
ejpam-221	88	36	monoids	monoid	NOUN
ejpam-221	88	37	be	be	AUX
ejpam-221	88	38	studied	study	VERB
ejpam-221	88	39	via	via	ADP
ejpam-221	88	40	their	their	PRON
ejpam-221	88	41	s	s	NOUN
ejpam-221	88	42	-	-	NOUN
ejpam-221	88	43	acts	act	NOUN
ejpam-221	88	44	,	,	PUNCT
ejpam-221	88	45	a	a	DET
ejpam-221	88	46	study	study	NOUN
ejpam-221	88	47	taken	take	VERB
ejpam-221	88	48	up	up	ADP
ejpam-221	88	49	in	in	ADP
ejpam-221	88	50	[	[	X
ejpam-221	88	51	71	71	NUM
ejpam-221	88	52	]	]	PUNCT
ejpam-221	88	53	,	,	PUNCT
ejpam-221	88	54	for	for	ADP
ejpam-221	88	55	example	example	NOUN
ejpam-221	88	56	.	.	PUNCT
ejpam-221	89	1	in	in	ADP
ejpam-221	89	2	the	the	DET
ejpam-221	89	3	case	case	NOUN
ejpam-221	89	4	of	of	ADP
ejpam-221	89	5	rings	ring	NOUN
ejpam-221	89	6	,	,	PUNCT
ejpam-221	89	7	two	two	NUM
ejpam-221	89	8	properties	property	NOUN
ejpam-221	89	9	which	which	PRON
ejpam-221	89	10	prove	prove	VERB
ejpam-221	89	11	useful	useful	ADJ
ejpam-221	89	12	are	be	AUX
ejpam-221	89	13	the	the	DET
ejpam-221	89	14	categorically	categorically	ADV
ejpam-221	89	15	defined	define	VERB
ejpam-221	89	16	injectivity	injectivity	NOUN
ejpam-221	89	17	and	and	CCONJ
ejpam-221	89	18	projectivity	projectivity	NOUN
ejpam-221	89	19	(	(	PUNCT
ejpam-221	89	20	see	see	VERB
ejpam-221	89	21	[	[	X
ejpam-221	89	22	41	41	NUM
ejpam-221	89	23	,	,	PUNCT
ejpam-221	89	24	pp	pp	ADJ
ejpam-221	89	25	.	.	PUNCT
ejpam-221	90	1	7	7	NUM
ejpam-221	90	2	,	,	PUNCT
ejpam-221	90	3	10	10	NUM
ejpam-221	90	4	]	]	NUM
ejpam-221	90	5	)	)	PUNCT
ejpam-221	90	6	.	.	PUNCT
ejpam-221	91	1	we	we	PRON
ejpam-221	91	2	define	define	VERB
ejpam-221	91	3	the	the	DET
ejpam-221	91	4	‘s	‘s	NOUN
ejpam-221	91	5	-	-	PUNCT
ejpam-221	91	6	act	act	NOUN
ejpam-221	91	7	’	'	PUNCT
ejpam-221	91	8	versions	version	NOUN
ejpam-221	91	9	of	of	ADP
ejpam-221	91	10	these	these	DET
ejpam-221	91	11	properties	property	NOUN
ejpam-221	91	12	,	,	PUNCT
ejpam-221	91	13	bearing	bear	VERB
ejpam-221	91	14	in	in	ADP
ejpam-221	91	15	mind	mind	NOUN
ejpam-221	91	16	that	that	SCONJ
ejpam-221	91	17	in	in	ADP
ejpam-221	91	18	the	the	DET
ejpam-221	91	19	category	category	NOUN
ejpam-221	91	20	of	of	ADP
ejpam-221	91	21	s	s	NOUN
ejpam-221	91	22	-	-	PUNCT
ejpam-221	91	23	acts	act	NOUN
ejpam-221	91	24	and	and	CCONJ
ejpam-221	91	25	s	s	NOUN
ejpam-221	91	26	-	-	NOUN
ejpam-221	91	27	morphisms	morphism	NOUN
ejpam-221	91	28	,	,	PUNCT
ejpam-221	91	29	s	s	NOUN
ejpam-221	91	30	-	-	PUNCT
ejpam-221	91	31	epimorphisms	epimorphism	NOUN
ejpam-221	91	32	are	be	AUX
ejpam-221	91	33	onto	onto	ADP
ejpam-221	91	34	and	and	CCONJ
ejpam-221	91	35	s	s	NOUN
ejpam-221	91	36	-	-	PUNCT
ejpam-221	91	37	monomorphisms	monomorphism	NOUN
ejpam-221	91	38	are	be	AUX
ejpam-221	91	39	one	one	NUM
ejpam-221	91	40	-	-	PUNCT
ejpam-221	91	41	one	one	NUM
ejpam-221	91	42	:	:	PUNCT
ejpam-221	91	43	definition	definition	NOUN
ejpam-221	91	44	1.2	1.2	NUM
ejpam-221	91	45	.	.	PUNCT
ejpam-221	92	1	[	[	X
ejpam-221	92	2	21	21	NUM
ejpam-221	92	3	]	]	X
ejpam-221	92	4	let	let	VERB
ejpam-221	92	5	s	s	PRON
ejpam-221	92	6	be	be	AUX
ejpam-221	92	7	a	a	DET
ejpam-221	92	8	monoid	monoid	NOUN
ejpam-221	92	9	and	and	CCONJ
ejpam-221	92	10	let	let	VERB
ejpam-221	92	11	x	x	PRON
ejpam-221	92	12	be	be	AUX
ejpam-221	92	13	an	an	DET
ejpam-221	92	14	s	s	NOUN
ejpam-221	92	15	-	-	NOUN
ejpam-221	92	16	act	act	NOUN
ejpam-221	92	17	.	.	PUNCT
ejpam-221	93	1	we	we	PRON
ejpam-221	93	2	say	say	VERB
ejpam-221	93	3	that	that	SCONJ
ejpam-221	93	4	x	x	PRON
ejpam-221	93	5	is	be	AUX
ejpam-221	93	6	injective	injective	ADJ
ejpam-221	93	7	if	if	SCONJ
ejpam-221	93	8	,	,	PUNCT
ejpam-221	93	9	for	for	ADP
ejpam-221	93	10	any	any	DET
ejpam-221	93	11	s	s	NOUN
ejpam-221	93	12	-	-	PUNCT
ejpam-221	93	13	acts	acts	NOUN
ejpam-221	93	14	y	y	PROPN
ejpam-221	93	15	and	and	CCONJ
ejpam-221	93	16	z	z	PROPN
ejpam-221	93	17	with	with	ADP
ejpam-221	93	18	z	z	PROPN
ejpam-221	93	19	⊆	⊆	NUM
ejpam-221	93	20	y	y	PROPN
ejpam-221	93	21	,	,	PUNCT
ejpam-221	93	22	any	any	DET
ejpam-221	93	23	s	s	NOUN
ejpam-221	93	24	-	-	PUNCT
ejpam-221	93	25	morphism	morphism	ADJ
ejpam-221	93	26	ϕ	ϕ	NOUN
ejpam-221	93	27	:	:	PUNCT
ejpam-221	93	28	z	z	NOUN
ejpam-221	93	29	→	→	PUNCT
ejpam-221	93	30	x	x	X
ejpam-221	93	31	may	may	AUX
ejpam-221	93	32	be	be	AUX
ejpam-221	93	33	extended	extend	VERB
ejpam-221	93	34	to	to	ADP
ejpam-221	93	35	an	an	DET
ejpam-221	93	36	s	s	NOUN
ejpam-221	93	37	-	-	NOUN
ejpam-221	93	38	morphism	morphism	NOUN
ejpam-221	93	39	ϕ′	ϕ′	PROPN
ejpam-221	93	40	:	:	PUNCT
ejpam-221	93	41	y	y	X
ejpam-221	93	42	→	→	PUNCT
ejpam-221	93	43	x	x	X
ejpam-221	93	44	such	such	ADJ
ejpam-221	93	45	that	that	SCONJ
ejpam-221	93	46	the	the	DET
ejpam-221	93	47	following	follow	VERB
ejpam-221	93	48	diagram	diagram	NOUN
ejpam-221	93	49	commutes	commute	NOUN
ejpam-221	93	50	:	:	PUNCT
ejpam-221	93	51	y	y	PROPN
ejpam-221	93	52	z	z	PROPN
ejpam-221	93	53	i	i	PRON
ejpam-221	93	54	6	6	NUM
ejpam-221	93	55	ϕ	ϕ	NOUN
ejpam-221	93	56	x	x	X
ejpam-221	93	57	ϕ′	ϕ′	X
ejpam-221	93	58	where	where	SCONJ
ejpam-221	93	59	i	i	PRON
ejpam-221	93	60	:	:	PUNCT
ejpam-221	93	61	z	z	X
ejpam-221	93	62	→	→	SYM
ejpam-221	93	63	y	y	PROPN
ejpam-221	93	64	is	be	AUX
ejpam-221	93	65	inclusion	inclusion	NOUN
ejpam-221	93	66	.	.	PUNCT
ejpam-221	94	1	definition	definition	NOUN
ejpam-221	94	2	1.3	1.3	NUM
ejpam-221	94	3	.	.	PUNCT
ejpam-221	95	1	[	[	X
ejpam-221	95	2	22	22	NUM
ejpam-221	95	3	,	,	PUNCT
ejpam-221	95	4	p.	p.	NOUN
ejpam-221	95	5	285	285	NUM
ejpam-221	95	6	]	]	PUNCT
ejpam-221	95	7	let	let	VERB
ejpam-221	95	8	s	s	PRON
ejpam-221	95	9	be	be	AUX
ejpam-221	95	10	a	a	DET
ejpam-221	95	11	monoid	monoid	NOUN
ejpam-221	95	12	and	and	CCONJ
ejpam-221	95	13	let	let	VERB
ejpam-221	95	14	x	x	PRON
ejpam-221	95	15	be	be	AUX
ejpam-221	95	16	an	an	DET
ejpam-221	95	17	s	s	NOUN
ejpam-221	95	18	-	-	NOUN
ejpam-221	95	19	act	act	NOUN
ejpam-221	95	20	.	.	PUNCT
ejpam-221	96	1	we	we	PRON
ejpam-221	96	2	say	say	VERB
ejpam-221	96	3	that	that	SCONJ
ejpam-221	96	4	x	x	PRON
ejpam-221	96	5	is	be	AUX
ejpam-221	96	6	projective	projective	ADJ
ejpam-221	96	7	if	if	SCONJ
ejpam-221	96	8	,	,	PUNCT
ejpam-221	96	9	for	for	ADP
ejpam-221	96	10	any	any	DET
ejpam-221	96	11	pair	pair	NOUN
ejpam-221	96	12	of	of	ADP
ejpam-221	96	13	s	s	NOUN
ejpam-221	96	14	-	-	PUNCT
ejpam-221	96	15	acts	acts	NOUN
ejpam-221	96	16	y	y	PROPN
ejpam-221	96	17	and	and	CCONJ
ejpam-221	96	18	z	z	PROPN
ejpam-221	96	19	,	,	PUNCT
ejpam-221	96	20	any	any	DET
ejpam-221	96	21	s	s	NOUN
ejpam-221	96	22	-	-	PUNCT
ejpam-221	96	23	epimorphism	epimorphism	NOUN
ejpam-221	96	24	ψ	ψ	X
ejpam-221	96	25	:	:	PUNCT
ejpam-221	96	26	y	y	PROPN
ejpam-221	96	27	→	→	SYM
ejpam-221	96	28	z	z	PROPN
ejpam-221	96	29	and	and	CCONJ
ejpam-221	96	30	any	any	DET
ejpam-221	96	31	smorphism	smorphism	NOUN
ejpam-221	96	32	ϕ	ϕ	X
ejpam-221	96	33	:	:	PUNCT
ejpam-221	96	34	x	x	SYM
ejpam-221	96	35	→	→	SYM
ejpam-221	96	36	z	z	NOUN
ejpam-221	96	37	,	,	PUNCT
ejpam-221	96	38	there	there	PRON
ejpam-221	96	39	exists	exist	VERB
ejpam-221	96	40	an	an	DET
ejpam-221	96	41	s	s	NOUN
ejpam-221	96	42	-	-	PUNCT
ejpam-221	96	43	morphism	morphism	ADJ
ejpam-221	96	44	π	π	NOUN
ejpam-221	96	45	:	:	PUNCT
ejpam-221	96	46	x	x	X
ejpam-221	96	47	→	→	SYM
ejpam-221	96	48	y	y	PROPN
ejpam-221	96	49	such	such	ADJ
ejpam-221	96	50	that	that	SCONJ
ejpam-221	96	51	the	the	DET
ejpam-221	96	52	following	follow	VERB
ejpam-221	96	53	diagram	diagram	NOUN
ejpam-221	96	54	commutes	commute	NOUN
ejpam-221	96	55	:	:	PUNCT
ejpam-221	96	56	y	y	PROPN
ejpam-221	96	57	z	z	PROPN
ejpam-221	96	58	ψ	ψ	NOUN
ejpam-221	96	59	?	?	PUNCT
ejpam-221	97	1	�	�	PROPN
ejpam-221	97	2	ϕ	ϕ	NOUN
ejpam-221	97	3	x	x	X
ejpam-221	97	4	π	π	PROPN
ejpam-221	97	5	�	�	PROPN
ejpam-221	97	6	a	a	DET
ejpam-221	97	7	monoid	monoid	NOUN
ejpam-221	97	8	for	for	ADP
ejpam-221	97	9	which	which	PRON
ejpam-221	97	10	every	every	DET
ejpam-221	97	11	right	right	NOUN
ejpam-221	97	12	s	s	NOUN
ejpam-221	97	13	-	-	NOUN
ejpam-221	97	14	act	act	NOUN
ejpam-221	97	15	is	be	AUX
ejpam-221	97	16	injective	injective	ADJ
ejpam-221	97	17	is	be	AUX
ejpam-221	97	18	called	call	VERB
ejpam-221	97	19	a	a	DET
ejpam-221	97	20	completely	completely	ADV
ejpam-221	97	21	right	right	ADJ
ejpam-221	97	22	injective	injective	ADJ
ejpam-221	97	23	monoid	monoid	NOUN
ejpam-221	97	24	.	.	PUNCT
ejpam-221	98	1	if	if	SCONJ
ejpam-221	98	2	,	,	PUNCT
ejpam-221	98	3	in	in	ADP
ejpam-221	98	4	addition	addition	NOUN
ejpam-221	98	5	,	,	PUNCT
ejpam-221	98	6	every	every	DET
ejpam-221	98	7	left	left	ADJ
ejpam-221	98	8	s	s	NOUN
ejpam-221	98	9	-	-	PUNCT
ejpam-221	98	10	act	act	NOUN
ejpam-221	98	11	is	be	AUX
ejpam-221	98	12	injective	injective	ADJ
ejpam-221	98	13	,	,	PUNCT
ejpam-221	98	14	then	then	ADV
ejpam-221	98	15	the	the	DET
ejpam-221	98	16	monoid	monoid	NOUN
ejpam-221	98	17	is	be	AUX
ejpam-221	98	18	said	say	VERB
ejpam-221	98	19	to	to	PART
ejpam-221	98	20	be	be	AUX
ejpam-221	98	21	completely	completely	ADV
ejpam-221	98	22	injective	injective	ADJ
ejpam-221	98	23	.	.	PUNCT
ejpam-221	99	1	the	the	DET
ejpam-221	99	2	study	study	NOUN
ejpam-221	99	3	of	of	ADP
ejpam-221	99	4	such	such	ADJ
ejpam-221	99	5	monoids	monoid	NOUN
ejpam-221	99	6	was	be	AUX
ejpam-221	99	7	initiated	initiate	VERB
ejpam-221	99	8	by	by	ADP
ejpam-221	99	9	feller	feller	NOUN
ejpam-221	99	10	and	and	CCONJ
ejpam-221	99	11	gantos	gantos	NOUN
ejpam-221	99	12	[	[	X
ejpam-221	99	13	18–20	18–20	NUM
ejpam-221	99	14	]	]	PUNCT
ejpam-221	99	15	,	,	PUNCT
ejpam-221	99	16	who	who	PRON
ejpam-221	99	17	obtained	obtain	VERB
ejpam-221	99	18	characterisations	characterisation	NOUN
ejpam-221	99	19	of	of	ADP
ejpam-221	99	20	those	those	DET
ejpam-221	99	21	completely	completely	ADV
ejpam-221	99	22	injective	injective	ADJ
ejpam-221	99	23	monoids	monoid	NOUN
ejpam-221	99	24	which	which	PRON
ejpam-221	99	25	are	be	AUX
ejpam-221	99	26	unions	union	NOUN
ejpam-221	99	27	of	of	ADP
ejpam-221	99	28	groups	group	NOUN
ejpam-221	99	29	,	,	PUNCT
ejpam-221	99	30	inverse	inverse	NOUN
ejpam-221	99	31	semigroups	semigroup	NOUN
ejpam-221	99	32	,	,	PUNCT
ejpam-221	99	33	or	or	CCONJ
ejpam-221	99	34	both	both	PRON
ejpam-221	99	35	.	.	PUNCT
ejpam-221	100	1	a	a	DET
ejpam-221	100	2	description	description	NOUN
ejpam-221	100	3	for	for	ADP
ejpam-221	100	4	the	the	DET
ejpam-221	100	5	general	general	ADJ
ejpam-221	100	6	case	case	NOUN
ejpam-221	100	7	was	be	AUX
ejpam-221	100	8	obtained	obtain	VERB
ejpam-221	100	9	by	by	ADP
ejpam-221	100	10	fountain	fountain	NOUN
ejpam-221	100	11	[	[	X
ejpam-221	100	12	21	21	NUM
ejpam-221	100	13	]	]	PUNCT
ejpam-221	100	14	.	.	PUNCT
ejpam-221	101	1	furc	furc	NOUN
ejpam-221	101	2	.	.	PUNCT
ejpam-221	102	1	hollings	holling	NOUN
ejpam-221	102	2	/	/	SYM
ejpam-221	102	3	eur	eur	PROPN
ejpam-221	102	4	.	.	PUNCT
ejpam-221	103	1	j.	j.	PROPN
ejpam-221	103	2	pure	pure	PROPN
ejpam-221	103	3	appl	appl	PROPN
ejpam-221	103	4	.	.	PROPN
ejpam-221	103	5	math	math	PROPN
ejpam-221	103	6	,	,	PUNCT
ejpam-221	103	7	2	2	NUM
ejpam-221	103	8	(	(	PUNCT
ejpam-221	103	9	2009	2009	NUM
ejpam-221	103	10	)	)	PUNCT
ejpam-221	103	11	,	,	PUNCT
ejpam-221	103	12	(	(	PUNCT
ejpam-221	103	13	21	21	NUM
ejpam-221	103	14	-	-	SYM
ejpam-221	103	15	57	57	NUM
ejpam-221	103	16	)	)	PUNCT
ejpam-221	103	17	27	27	NUM
ejpam-221	103	18	ther	ther	ADV
ejpam-221	103	19	necessary	necessary	ADJ
ejpam-221	103	20	and	and	CCONJ
ejpam-221	103	21	sufficient	sufficient	ADJ
ejpam-221	103	22	conditions	condition	NOUN
ejpam-221	103	23	for	for	SCONJ
ejpam-221	103	24	a	a	DET
ejpam-221	103	25	monoid	monoid	NOUN
ejpam-221	103	26	to	to	PART
ejpam-221	103	27	be	be	AUX
ejpam-221	103	28	completely	completely	ADV
ejpam-221	103	29	right	right	ADJ
ejpam-221	103	30	injective	injective	ADJ
ejpam-221	103	31	were	be	AUX
ejpam-221	103	32	obtained	obtain	VERB
ejpam-221	103	33	by	by	ADP
ejpam-221	103	34	shoji	shoji	NOUN
ejpam-221	103	35	[	[	X
ejpam-221	103	36	70	70	NUM
ejpam-221	103	37	]	]	PUNCT
ejpam-221	103	38	.	.	PUNCT
ejpam-221	104	1	the	the	DET
ejpam-221	104	2	study	study	NOUN
ejpam-221	104	3	of	of	ADP
ejpam-221	104	4	monoids	monoid	NOUN
ejpam-221	104	5	whose	whose	DET
ejpam-221	104	6	every	every	DET
ejpam-221	104	7	s	s	NOUN
ejpam-221	104	8	-	-	PUNCT
ejpam-221	104	9	act	act	NOUN
ejpam-221	104	10	is	be	AUX
ejpam-221	104	11	projective	projective	ADJ
ejpam-221	104	12	,	,	PUNCT
ejpam-221	104	13	on	on	ADP
ejpam-221	104	14	the	the	DET
ejpam-221	104	15	other	other	ADJ
ejpam-221	104	16	hand	hand	NOUN
ejpam-221	104	17	,	,	PUNCT
ejpam-221	104	18	is	be	AUX
ejpam-221	104	19	far	far	ADV
ejpam-221	104	20	less	less	ADV
ejpam-221	104	21	fruitful	fruitful	ADJ
ejpam-221	104	22	;	;	PUNCT
ejpam-221	104	23	isbell	isbell	PROPN
ejpam-221	105	1	[	[	X
ejpam-221	105	2	38	38	NUM
ejpam-221	105	3	]	]	PUNCT
ejpam-221	105	4	showed	show	VERB
ejpam-221	105	5	that	that	SCONJ
ejpam-221	105	6	the	the	DET
ejpam-221	105	7	only	only	ADJ
ejpam-221	105	8	such	such	ADJ
ejpam-221	105	9	monoid	monoid	NOUN
ejpam-221	105	10	is	be	AUX
ejpam-221	105	11	trivial	trivial	ADJ
ejpam-221	105	12	.	.	PUNCT
ejpam-221	106	1	if	if	SCONJ
ejpam-221	106	2	one	one	PRON
ejpam-221	106	3	is	be	AUX
ejpam-221	106	4	to	to	PART
ejpam-221	106	5	study	study	VERB
ejpam-221	106	6	monoids	monoid	NOUN
ejpam-221	106	7	with	with	ADP
ejpam-221	106	8	projective	projective	ADJ
ejpam-221	106	9	s	s	NOUN
ejpam-221	106	10	-	-	PUNCT
ejpam-221	106	11	acts	act	NOUN
ejpam-221	106	12	,	,	PUNCT
ejpam-221	106	13	then	then	ADV
ejpam-221	106	14	one	one	PRON
ejpam-221	106	15	must	must	AUX
ejpam-221	106	16	relax	relax	VERB
ejpam-221	106	17	the	the	DET
ejpam-221	106	18	conditions	condition	NOUN
ejpam-221	106	19	somewhat	somewhat	ADV
ejpam-221	106	20	.	.	PUNCT
ejpam-221	107	1	for	for	ADP
ejpam-221	107	2	example	example	NOUN
ejpam-221	107	3	,	,	PUNCT
ejpam-221	107	4	one	one	PRON
ejpam-221	107	5	can	can	AUX
ejpam-221	107	6	consider	consider	VERB
ejpam-221	107	7	monoids	monoid	NOUN
ejpam-221	107	8	in	in	ADP
ejpam-221	107	9	which	which	PRON
ejpam-221	107	10	all	all	DET
ejpam-221	107	11	right	right	ADJ
ejpam-221	107	12	ideals	ideal	NOUN
ejpam-221	107	13	(	(	PUNCT
ejpam-221	107	14	regarded	regard	VERB
ejpam-221	107	15	as	as	ADP
ejpam-221	107	16	right	right	ADJ
ejpam-221	107	17	s	s	NOUN
ejpam-221	107	18	-	-	PUNCT
ejpam-221	107	19	acts	act	NOUN
ejpam-221	107	20	)	)	PUNCT
ejpam-221	107	21	are	be	AUX
ejpam-221	107	22	required	require	VERB
ejpam-221	107	23	to	to	PART
ejpam-221	107	24	be	be	AUX
ejpam-221	107	25	projective	projective	ADJ
ejpam-221	107	26	;	;	PUNCT
ejpam-221	107	27	these	these	DET
ejpam-221	107	28	monoids	monoid	NOUN
ejpam-221	107	29	are	be	AUX
ejpam-221	107	30	termed	term	VERB
ejpam-221	107	31	right	right	ADJ
ejpam-221	107	32	hereditary	hereditary	ADJ
ejpam-221	107	33	monoids	monoid	NOUN
ejpam-221	107	34	and	and	CCONJ
ejpam-221	107	35	were	be	AUX
ejpam-221	107	36	studied	study	VERB
ejpam-221	107	37	by	by	ADP
ejpam-221	107	38	dorofeeva	dorofeeva	NOUN
ejpam-221	108	1	[	[	X
ejpam-221	108	2	10	10	NUM
ejpam-221	108	3	]	]	PUNCT
ejpam-221	108	4	.	.	PUNCT
ejpam-221	109	1	if	if	SCONJ
ejpam-221	109	2	we	we	PRON
ejpam-221	109	3	relax	relax	VERB
ejpam-221	109	4	the	the	DET
ejpam-221	109	5	conditions	condition	NOUN
ejpam-221	109	6	even	even	ADV
ejpam-221	109	7	further	far	ADV
ejpam-221	109	8	and	and	CCONJ
ejpam-221	109	9	consider	consider	VERB
ejpam-221	109	10	those	those	DET
ejpam-221	109	11	monoids	monoid	NOUN
ejpam-221	109	12	for	for	ADP
ejpam-221	109	13	which	which	PRON
ejpam-221	109	14	only	only	ADV
ejpam-221	109	15	the	the	DET
ejpam-221	109	16	principal	principal	ADJ
ejpam-221	109	17	right	right	ADJ
ejpam-221	109	18	ideals	ideal	NOUN
ejpam-221	109	19	are	be	AUX
ejpam-221	109	20	projective	projective	ADJ
ejpam-221	109	21	as	as	ADP
ejpam-221	109	22	right	right	ADJ
ejpam-221	109	23	s	s	NOUN
ejpam-221	109	24	-	-	PUNCT
ejpam-221	109	25	acts	act	VERB
ejpam-221	109	26	,	,	PUNCT
ejpam-221	109	27	then	then	ADV
ejpam-221	109	28	we	we	PRON
ejpam-221	109	29	obtain	obtain	VERB
ejpam-221	109	30	so	so	ADV
ejpam-221	109	31	-	-	PUNCT
ejpam-221	109	32	called	call	VERB
ejpam-221	109	33	right	right	ADV
ejpam-221	109	34	principally	principally	ADV
ejpam-221	109	35	projective	projective	ADJ
ejpam-221	109	36	(	(	PUNCT
ejpam-221	109	37	or	or	CCONJ
ejpam-221	109	38	right	right	ADJ
ejpam-221	109	39	pp	pp	ADJ
ejpam-221	109	40	)	)	PUNCT
ejpam-221	109	41	monoids	monoid	NOUN
ejpam-221	109	42	.	.	PUNCT
ejpam-221	110	1	left	leave	VERB
ejpam-221	110	2	pp	pp	PROPN
ejpam-221	110	3	monoids	monoid	NOUN
ejpam-221	110	4	are	be	AUX
ejpam-221	110	5	defined	define	VERB
ejpam-221	110	6	dually	dually	ADV
ejpam-221	110	7	;	;	PUNCT
ejpam-221	110	8	a	a	DET
ejpam-221	110	9	monoid	monoid	NOUN
ejpam-221	110	10	which	which	PRON
ejpam-221	110	11	is	be	AUX
ejpam-221	110	12	both	both	ADV
ejpam-221	110	13	right	right	ADJ
ejpam-221	110	14	and	and	CCONJ
ejpam-221	110	15	left	leave	VERB
ejpam-221	110	16	pp	pp	ADV
ejpam-221	110	17	is	be	AUX
ejpam-221	110	18	called	call	VERB
ejpam-221	110	19	simply	simply	ADV
ejpam-221	110	20	pp	pp	ADV
ejpam-221	110	21	.	.	PUNCT
ejpam-221	111	1	any	any	DET
ejpam-221	111	2	regular	regular	ADJ
ejpam-221	111	3	monoid	monoid	NOUN
ejpam-221	111	4	is	be	AUX
ejpam-221	111	5	necessarily	necessarily	ADV
ejpam-221	111	6	pp	pp	ADJ
ejpam-221	111	7	,	,	PUNCT
ejpam-221	111	8	as	as	SCONJ
ejpam-221	111	9	we	we	PRON
ejpam-221	111	10	will	will	AUX
ejpam-221	111	11	see	see	VERB
ejpam-221	111	12	shortly	shortly	ADV
ejpam-221	111	13	.	.	PUNCT
ejpam-221	112	1	the	the	DET
ejpam-221	112	2	study	study	NOUN
ejpam-221	112	3	of	of	ADP
ejpam-221	112	4	pp	pp	PROPN
ejpam-221	112	5	monoids	monoid	NOUN
ejpam-221	112	6	was	be	AUX
ejpam-221	112	7	intiated	intiate	VERB
ejpam-221	112	8	by	by	ADP
ejpam-221	112	9	kilp	kilp	NOUN
ejpam-221	112	10	in	in	ADP
ejpam-221	112	11	[	[	X
ejpam-221	112	12	42	42	NUM
ejpam-221	112	13	]	]	PUNCT
ejpam-221	112	14	,	,	PUNCT
ejpam-221	112	15	where	where	SCONJ
ejpam-221	112	16	the	the	DET
ejpam-221	112	17	commutative	commutative	ADJ
ejpam-221	112	18	case	case	NOUN
ejpam-221	112	19	was	be	AUX
ejpam-221	112	20	considered	consider	VERB
ejpam-221	112	21	;	;	PUNCT
ejpam-221	112	22	kilp	kilp	PROPN
ejpam-221	112	23	obtained	obtain	VERB
ejpam-221	112	24	a	a	DET
ejpam-221	112	25	characterisation	characterisation	NOUN
ejpam-221	112	26	of	of	ADP
ejpam-221	112	27	commutative	commutative	ADJ
ejpam-221	112	28	pp	pp	PROPN
ejpam-221	112	29	monoids	monoid	NOUN
ejpam-221	112	30	as	as	ADP
ejpam-221	112	31	strong	strong	ADJ
ejpam-221	112	32	semilattices‡	semilattices‡	NOUN
ejpam-221	112	33	of	of	ADP
ejpam-221	112	34	commutative	commutative	ADJ
ejpam-221	112	35	cancellative	cancellative	ADJ
ejpam-221	112	36	monoids	monoid	NOUN
ejpam-221	112	37	.	.	PUNCT
ejpam-221	113	1	this	this	DET
ejpam-221	113	2	result	result	NOUN
ejpam-221	113	3	was	be	AUX
ejpam-221	113	4	generalised	generalise	VERB
ejpam-221	113	5	to	to	ADP
ejpam-221	113	6	the	the	DET
ejpam-221	113	7	case	case	NOUN
ejpam-221	113	8	of	of	ADP
ejpam-221	113	9	right	right	ADV
ejpam-221	113	10	pp	pp	ADV
ejpam-221	113	11	monoids	monoid	NOUN
ejpam-221	113	12	with	with	ADP
ejpam-221	113	13	central	central	ADJ
ejpam-221	113	14	idempotents	idempotent	NOUN
ejpam-221	113	15	by	by	ADP
ejpam-221	113	16	fountain	fountain	NOUN
ejpam-221	113	17	[	[	X
ejpam-221	113	18	23	23	NUM
ejpam-221	113	19	]	]	X
ejpam-221	113	20	;	;	PUNCT
ejpam-221	113	21	such	such	DET
ejpam-221	113	22	a	a	DET
ejpam-221	113	23	monoid	monoid	NOUN
ejpam-221	113	24	is	be	AUX
ejpam-221	113	25	exactly	exactly	ADV
ejpam-221	113	26	a	a	DET
ejpam-221	113	27	strong	strong	ADJ
ejpam-221	113	28	semilattice	semilattice	NOUN
ejpam-221	113	29	of	of	ADP
ejpam-221	113	30	left	left	ADJ
ejpam-221	113	31	cancellative	cancellative	ADJ
ejpam-221	113	32	monoids	monoid	NOUN
ejpam-221	113	33	.	.	PUNCT
ejpam-221	114	1	a	a	DET
ejpam-221	114	2	left	left	ADJ
ejpam-221	114	3	cancellative	cancellative	ADJ
ejpam-221	114	4	monoid	monoid	NOUN
ejpam-221	114	5	is	be	AUX
ejpam-221	114	6	therefore	therefore	ADV
ejpam-221	114	7	right	right	ADV
ejpam-221	114	8	pp	pp	ADV
ejpam-221	114	9	.	.	PUNCT
ejpam-221	115	1	it	it	PRON
ejpam-221	115	2	is	be	AUX
ejpam-221	115	3	in	in	ADP
ejpam-221	115	4	fact	fact	NOUN
ejpam-221	115	5	possible	possible	ADJ
ejpam-221	115	6	to	to	PART
ejpam-221	115	7	give	give	VERB
ejpam-221	115	8	a	a	DET
ejpam-221	115	9	characterisation	characterisation	NOUN
ejpam-221	115	10	of	of	ADP
ejpam-221	115	11	right	right	ADJ
ejpam-221	115	12	pp	pp	ADV
ejpam-221	115	13	monoids	monoid	NOUN
ejpam-221	115	14	which	which	PRON
ejpam-221	115	15	makes	make	VERB
ejpam-221	115	16	no	no	DET
ejpam-221	115	17	reference	reference	NOUN
ejpam-221	115	18	to	to	ADP
ejpam-221	115	19	s	s	NOUN
ejpam-221	115	20	-	-	PUNCT
ejpam-221	115	21	acts	act	NOUN
ejpam-221	115	22	.	.	PUNCT
ejpam-221	116	1	for	for	ADP
ejpam-221	116	2	this	this	PRON
ejpam-221	116	3	,	,	PUNCT
ejpam-221	116	4	we	we	PRON
ejpam-221	116	5	need	need	VERB
ejpam-221	116	6	a	a	DET
ejpam-221	116	7	notion	notion	NOUN
ejpam-221	116	8	introduced	introduce	VERB
ejpam-221	116	9	by	by	ADP
ejpam-221	116	10	skornjakov	skornjakov	NOUN
ejpam-221	116	11	[	[	X
ejpam-221	116	12	71	71	NUM
ejpam-221	116	13	]	]	PUNCT
ejpam-221	116	14	and	and	CCONJ
ejpam-221	116	15	dorofeeva	dorofeeva	X
ejpam-221	117	1	[	[	X
ejpam-221	117	2	10	10	NUM
ejpam-221	117	3	]	]	PUNCT
ejpam-221	117	4	:	:	PUNCT
ejpam-221	117	5	definition	definition	NOUN
ejpam-221	117	6	1.4	1.4	NUM
ejpam-221	117	7	.	.	PUNCT
ejpam-221	118	1	let	let	VERB
ejpam-221	118	2	s	s	PRON
ejpam-221	118	3	be	be	AUX
ejpam-221	118	4	a	a	DET
ejpam-221	118	5	monoid	monoid	NOUN
ejpam-221	118	6	and	and	CCONJ
ejpam-221	118	7	let	let	VERB
ejpam-221	118	8	e	e	X
ejpam-221	118	9	∈	∈	PROPN
ejpam-221	118	10	e(s	e(s	PROPN
ejpam-221	118	11	)	)	PUNCT
ejpam-221	118	12	.	.	PUNCT
ejpam-221	119	1	an	an	DET
ejpam-221	119	2	element	element	NOUN
ejpam-221	119	3	a	a	DET
ejpam-221	119	4	∈	∈	NOUN
ejpam-221	119	5	s	s	NOUN
ejpam-221	119	6	is	be	AUX
ejpam-221	119	7	said	say	VERB
ejpam-221	119	8	to	to	PART
ejpam-221	119	9	be	be	AUX
ejpam-221	119	10	left	leave	VERB
ejpam-221	119	11	e	e	NOUN
ejpam-221	119	12	-	-	NOUN
ejpam-221	119	13	cancellable	cancellable	ADJ
ejpam-221	119	14	if	if	SCONJ
ejpam-221	119	15	e	e	NOUN
ejpam-221	119	16	is	be	AUX
ejpam-221	119	17	a	a	DET
ejpam-221	119	18	right	right	ADJ
ejpam-221	119	19	identity	identity	NOUN
ejpam-221	119	20	for	for	ADP
ejpam-221	119	21	a	a	PRON
ejpam-221	119	22	and	and	CCONJ
ejpam-221	119	23	ax	ax	NOUN
ejpam-221	119	24	=	=	PUNCT
ejpam-221	119	25	a	a	DET
ejpam-221	119	26	y	y	PROPN
ejpam-221	119	27	=	=	NOUN
ejpam-221	119	28	⇒	⇒	VERB
ejpam-221	119	29	ex	ex	X
ejpam-221	119	30	=	=	PUNCT
ejpam-221	119	31	e	e	SYM
ejpam-221	119	32	y	y	PROPN
ejpam-221	119	33	,	,	PUNCT
ejpam-221	119	34	for	for	ADP
ejpam-221	119	35	all	all	DET
ejpam-221	119	36	x	x	SYM
ejpam-221	119	37	,	,	PUNCT
ejpam-221	119	38	y	y	PROPN
ejpam-221	119	39	∈	∈	PROPN
ejpam-221	119	40	s.	s.	PROPN
ejpam-221	119	41	then	then	ADV
ejpam-221	119	42	,	,	PUNCT
ejpam-221	119	43	from	from	ADP
ejpam-221	119	44	[	[	X
ejpam-221	119	45	42	42	NUM
ejpam-221	119	46	]	]	PUNCT
ejpam-221	119	47	,	,	PUNCT
ejpam-221	119	48	we	we	PRON
ejpam-221	119	49	have	have	AUX
ejpam-221	119	50	:	:	PUNCT
ejpam-221	119	51	proposition	proposition	VERB
ejpam-221	119	52	1.5	1.5	NUM
ejpam-221	119	53	.	.	PUNCT
ejpam-221	120	1	a	a	DET
ejpam-221	120	2	monoid	monoid	NOUN
ejpam-221	120	3	s	s	X
ejpam-221	120	4	is	be	AUX
ejpam-221	120	5	right	right	ADJ
ejpam-221	120	6	pp	pp	ADV
ejpam-221	120	7	if	if	SCONJ
ejpam-221	120	8	,	,	PUNCT
ejpam-221	120	9	and	and	CCONJ
ejpam-221	120	10	only	only	ADV
ejpam-221	120	11	if	if	SCONJ
ejpam-221	120	12	,	,	PUNCT
ejpam-221	120	13	for	for	ADP
ejpam-221	120	14	each	each	DET
ejpam-221	120	15	element	element	NOUN
ejpam-221	120	16	a	a	DET
ejpam-221	120	17	∈	∈	ADJ
ejpam-221	120	18	s	s	NOUN
ejpam-221	120	19	,	,	PUNCT
ejpam-221	120	20	there	there	PRON
ejpam-221	120	21	is	be	VERB
ejpam-221	120	22	an	an	DET
ejpam-221	120	23	ea	ea	NOUN
ejpam-221	120	24	∈	∈	PROPN
ejpam-221	120	25	e(s	e(s	PROPN
ejpam-221	120	26	)	)	PUNCT
ejpam-221	120	27	such	such	ADJ
ejpam-221	120	28	that	that	SCONJ
ejpam-221	120	29	a	a	PRON
ejpam-221	120	30	is	be	AUX
ejpam-221	120	31	left	leave	VERB
ejpam-221	120	32	ea	ea	NOUN
ejpam-221	120	33	-	-	NOUN
ejpam-221	120	34	cancellable	cancellable	ADJ
ejpam-221	120	35	.	.	PUNCT
ejpam-221	121	1	‡for	‡for	ADP
ejpam-221	121	2	the	the	DET
ejpam-221	121	3	notion	notion	NOUN
ejpam-221	121	4	of	of	ADP
ejpam-221	121	5	a	a	DET
ejpam-221	121	6	semilattice	semilattice	NOUN
ejpam-221	121	7	of	of	ADP
ejpam-221	121	8	semigroups	semigroup	NOUN
ejpam-221	121	9	,	,	PUNCT
ejpam-221	121	10	see	see	VERB
ejpam-221	121	11	[	[	X
ejpam-221	121	12	5	5	NUM
ejpam-221	121	13	,	,	PUNCT
ejpam-221	121	14	§	§	NOUN
ejpam-221	121	15	1.8	1.8	NUM
ejpam-221	121	16	]	]	PUNCT
ejpam-221	121	17	.	.	PUNCT
ejpam-221	122	1	c.	c.	PROPN
ejpam-221	122	2	hollings	holling	NOUN
ejpam-221	122	3	/	/	SYM
ejpam-221	122	4	eur	eur	PROPN
ejpam-221	122	5	.	.	PUNCT
ejpam-221	123	1	j.	j.	PROPN
ejpam-221	123	2	pure	pure	PROPN
ejpam-221	123	3	appl	appl	PROPN
ejpam-221	123	4	.	.	PROPN
ejpam-221	123	5	math	math	PROPN
ejpam-221	123	6	,	,	PUNCT
ejpam-221	123	7	2	2	NUM
ejpam-221	123	8	(	(	PUNCT
ejpam-221	123	9	2009	2009	NUM
ejpam-221	123	10	)	)	PUNCT
ejpam-221	123	11	,	,	PUNCT
ejpam-221	123	12	(	(	PUNCT
ejpam-221	123	13	21	21	NUM
ejpam-221	123	14	-	-	SYM
ejpam-221	123	15	57	57	NUM
ejpam-221	123	16	)	)	PUNCT
ejpam-221	123	17	28	28	NUM
ejpam-221	123	18	the	the	DET
ejpam-221	123	19	notion	notion	NOUN
ejpam-221	123	20	of	of	ADP
ejpam-221	123	21	left	left	ADJ
ejpam-221	123	22	e	e	NOUN
ejpam-221	123	23	-	-	NOUN
ejpam-221	123	24	cancellability	cancellability	ADJ
ejpam-221	123	25	,	,	PUNCT
ejpam-221	123	26	and	and	CCONJ
ejpam-221	123	27	hence	hence	ADV
ejpam-221	123	28	the	the	DET
ejpam-221	123	29	definition	definition	NOUN
ejpam-221	123	30	of	of	ADP
ejpam-221	123	31	a	a	DET
ejpam-221	123	32	right	right	NOUN
ejpam-221	123	33	pp	pp	ADP
ejpam-221	123	34	monoid	monoid	NOUN
ejpam-221	123	35	,	,	PUNCT
ejpam-221	123	36	were	be	AUX
ejpam-221	123	37	recast	recast	VERB
ejpam-221	123	38	once	once	ADV
ejpam-221	123	39	more	more	ADJ
ejpam-221	123	40	by	by	ADP
ejpam-221	123	41	fountain	fountain	NOUN
ejpam-221	123	42	[	[	X
ejpam-221	123	43	22	22	NUM
ejpam-221	123	44	]	]	PUNCT
ejpam-221	123	45	.	.	PUNCT
ejpam-221	124	1	before	before	SCONJ
ejpam-221	124	2	we	we	PRON
ejpam-221	124	3	describe	describe	VERB
ejpam-221	124	4	this	this	DET
ejpam-221	124	5	important	important	ADJ
ejpam-221	124	6	development	development	NOUN
ejpam-221	124	7	,	,	PUNCT
ejpam-221	124	8	however	however	ADV
ejpam-221	124	9	,	,	PUNCT
ejpam-221	124	10	let	let	VERB
ejpam-221	124	11	us	we	PRON
ejpam-221	124	12	take	take	VERB
ejpam-221	124	13	a	a	DET
ejpam-221	124	14	step	step	NOUN
ejpam-221	124	15	back	back	ADV
ejpam-221	124	16	and	and	CCONJ
ejpam-221	124	17	consider	consider	VERB
ejpam-221	124	18	a	a	DET
ejpam-221	124	19	definition	definition	NOUN
ejpam-221	124	20	of	of	ADP
ejpam-221	124	21	lyapin	lyapin	NOUN
ejpam-221	125	1	[	[	X
ejpam-221	125	2	50	50	NUM
ejpam-221	125	3	]	]	NUM
ejpam-221	125	4	:	:	PUNCT
ejpam-221	125	5	definition	definition	NOUN
ejpam-221	125	6	1.6	1.6	NUM
ejpam-221	125	7	.	.	PUNCT
ejpam-221	126	1	[	[	X
ejpam-221	126	2	50	50	NUM
ejpam-221	126	3	,	,	PUNCT
ejpam-221	126	4	chapter	chapter	NOUN
ejpam-221	126	5	x	x	NOUN
ejpam-221	126	6	,	,	PUNCT
ejpam-221	126	7	§	§	NOUN
ejpam-221	126	8	4.2	4.2	NUM
ejpam-221	126	9	]	]	PUNCT
ejpam-221	126	10	let	let	VERB
ejpam-221	126	11	s	s	PRON
ejpam-221	126	12	be	be	AUX
ejpam-221	126	13	a	a	DET
ejpam-221	126	14	semigroup	semigroup	NOUN
ejpam-221	126	15	.	.	PUNCT
ejpam-221	127	1	a	a	DET
ejpam-221	127	2	potential	potential	ADJ
ejpam-221	127	3	property	property	NOUN
ejpam-221	127	4	in	in	ADP
ejpam-221	127	5	s	s	PROPN
ejpam-221	127	6	is	be	AUX
ejpam-221	127	7	a	a	DET
ejpam-221	127	8	property	property	NOUN
ejpam-221	127	9	which	which	PRON
ejpam-221	127	10	holds	hold	VERB
ejpam-221	127	11	in	in	ADP
ejpam-221	127	12	some	some	DET
ejpam-221	127	13	oversemigroup	oversemigroup	ADJ
ejpam-221	127	14	t	t	PROPN
ejpam-221	127	15	of	of	ADP
ejpam-221	127	16	s.	s.	PROPN
ejpam-221	127	17	for	for	ADP
ejpam-221	127	18	example	example	NOUN
ejpam-221	127	19	,	,	PUNCT
ejpam-221	127	20	in	in	ADP
ejpam-221	127	21	[	[	PUNCT
ejpam-221	127	22	50	50	NUM
ejpam-221	127	23	]	]	PUNCT
ejpam-221	127	24	,	,	PUNCT
ejpam-221	127	25	lyapin	lyapin	PROPN
ejpam-221	127	26	considered	consider	VERB
ejpam-221	127	27	potential	potential	ADJ
ejpam-221	127	28	invertibility	invertibility	NOUN
ejpam-221	127	29	of	of	ADP
ejpam-221	127	30	elements	element	NOUN
ejpam-221	127	31	in	in	ADP
ejpam-221	127	32	semigroups	semigroup	NOUN
ejpam-221	127	33	.	.	PUNCT
ejpam-221	128	1	a	a	DET
ejpam-221	128	2	range	range	NOUN
ejpam-221	128	3	of	of	ADP
ejpam-221	128	4	other	other	ADJ
ejpam-221	128	5	potential	potential	ADJ
ejpam-221	128	6	properties	property	NOUN
ejpam-221	128	7	were	be	AUX
ejpam-221	128	8	studied	study	VERB
ejpam-221	128	9	by	by	ADP
ejpam-221	128	10	šutov	šutov	NOUN
ejpam-221	128	11	in	in	ADP
ejpam-221	128	12	[	[	X
ejpam-221	128	13	72–75	72–75	NOUN
ejpam-221	128	14	]	]	PUNCT
ejpam-221	128	15	.	.	PUNCT
ejpam-221	129	1	in	in	ADP
ejpam-221	129	2	particular	particular	ADJ
ejpam-221	129	3	,	,	PUNCT
ejpam-221	129	4	šutov	šutov	NOUN
ejpam-221	129	5	investigated	investigate	VERB
ejpam-221	129	6	the	the	DET
ejpam-221	129	7	notion	notion	NOUN
ejpam-221	129	8	of	of	ADP
ejpam-221	129	9	potential	potential	ADJ
ejpam-221	129	10	divisibility	divisibility	NOUN
ejpam-221	129	11	of	of	ADP
ejpam-221	129	12	elements	element	NOUN
ejpam-221	129	13	[	[	X
ejpam-221	129	14	73	73	NUM
ejpam-221	129	15	]	]	X
ejpam-221	129	16	:	:	PUNCT
ejpam-221	129	17	elements	element	NOUN
ejpam-221	129	18	a	a	DET
ejpam-221	129	19	,	,	PUNCT
ejpam-221	129	20	b	b	PROPN
ejpam-221	129	21	of	of	ADP
ejpam-221	129	22	a	a	DET
ejpam-221	129	23	semigroup	semigroup	NOUN
ejpam-221	129	24	s	s	PART
ejpam-221	129	25	potentially	potentially	ADV
ejpam-221	129	26	divide	divide	VERB
ejpam-221	129	27	each	each	DET
ejpam-221	129	28	other	other	ADJ
ejpam-221	129	29	(	(	PUNCT
ejpam-221	129	30	on	on	ADP
ejpam-221	129	31	the	the	DET
ejpam-221	129	32	right	right	NOUN
ejpam-221	129	33	)	)	PUNCT
ejpam-221	129	34	if	if	SCONJ
ejpam-221	129	35	,	,	PUNCT
ejpam-221	129	36	and	and	CCONJ
ejpam-221	129	37	only	only	ADV
ejpam-221	129	38	if	if	SCONJ
ejpam-221	129	39	,	,	PUNCT
ejpam-221	129	40	there	there	PRON
ejpam-221	129	41	exist	exist	VERB
ejpam-221	129	42	an	an	DET
ejpam-221	129	43	oversemigroup	oversemigroup	ADJ
ejpam-221	129	44	t	t	NOUN
ejpam-221	129	45	of	of	ADP
ejpam-221	129	46	s	s	NOUN
ejpam-221	129	47	and	and	CCONJ
ejpam-221	129	48	elements	element	NOUN
ejpam-221	129	49	s	s	PART
ejpam-221	129	50	,	,	PUNCT
ejpam-221	129	51	t	t	PROPN
ejpam-221	129	52	∈	∈	PROPN
ejpam-221	129	53	t	t	NOUN
ejpam-221	129	54	such	such	ADJ
ejpam-221	129	55	that	that	PRON
ejpam-221	129	56	as	as	ADP
ejpam-221	129	57	=	=	PROPN
ejpam-221	129	58	b	b	PROPN
ejpam-221	129	59	and	and	CCONJ
ejpam-221	129	60	bt	bt	NOUN
ejpam-221	129	61	=	=	PUNCT
ejpam-221	129	62	a	a	PRON
ejpam-221	129	63	in	in	ADP
ejpam-221	129	64	t	t	PROPN
ejpam-221	129	65	.	.	PUNCT
ejpam-221	130	1	in	in	ADP
ejpam-221	130	2	other	other	ADJ
ejpam-221	130	3	words	word	NOUN
ejpam-221	130	4	,	,	PUNCT
ejpam-221	130	5	a	a	PRON
ejpam-221	130	6	and	and	CCONJ
ejpam-221	130	7	b	b	NOUN
ejpam-221	130	8	potentially	potentially	ADV
ejpam-221	130	9	divide	divide	VERB
ejpam-221	130	10	eachother	eachother	ADJ
ejpam-221	130	11	if	if	SCONJ
ejpam-221	130	12	,	,	PUNCT
ejpam-221	130	13	and	and	CCONJ
ejpam-221	130	14	only	only	ADV
ejpam-221	130	15	if	if	SCONJ
ejpam-221	130	16	,	,	PUNCT
ejpam-221	130	17	they	they	PRON
ejpam-221	130	18	are	be	AUX
ejpam-221	130	19	r	r	NOUN
ejpam-221	130	20	-	-	PUNCT
ejpam-221	130	21	related	relate	VERB
ejpam-221	130	22	in	in	ADP
ejpam-221	130	23	some	some	DET
ejpam-221	130	24	oversemigroup	oversemigroup	NOUN
ejpam-221	130	25	.	.	PUNCT
ejpam-221	131	1	dually	dually	ADV
ejpam-221	131	2	for	for	ADP
ejpam-221	131	3	potential	potential	ADJ
ejpam-221	131	4	left	leave	VERB
ejpam-221	131	5	division	division	NOUN
ejpam-221	131	6	.	.	PUNCT
ejpam-221	132	1	the	the	DET
ejpam-221	132	2	notion	notion	NOUN
ejpam-221	132	3	of	of	ADP
ejpam-221	132	4	potential	potential	ADJ
ejpam-221	132	5	divisibility	divisibility	NOUN
ejpam-221	132	6	arose	arise	VERB
ejpam-221	132	7	again	again	ADV
ejpam-221	132	8	in	in	ADP
ejpam-221	132	9	work	work	NOUN
ejpam-221	132	10	of	of	ADP
ejpam-221	132	11	both	both	DET
ejpam-221	132	12	pastijn	pastijn	NOUN
ejpam-221	133	1	[	[	X
ejpam-221	133	2	59	59	NUM
ejpam-221	133	3	]	]	PUNCT
ejpam-221	133	4	and	and	CCONJ
ejpam-221	133	5	mcalister	mcalister	NOUN
ejpam-221	134	1	[	[	X
ejpam-221	134	2	54	54	NUM
ejpam-221	134	3	]	]	PUNCT
ejpam-221	134	4	,	,	PUNCT
ejpam-221	134	5	though	though	SCONJ
ejpam-221	134	6	not	not	PART
ejpam-221	134	7	under	under	ADP
ejpam-221	134	8	that	that	DET
ejpam-221	134	9	name	name	NOUN
ejpam-221	134	10	.	.	PUNCT
ejpam-221	135	1	in	in	ADP
ejpam-221	135	2	[	[	X
ejpam-221	135	3	54	54	NUM
ejpam-221	135	4	]	]	PUNCT
ejpam-221	135	5	,	,	PUNCT
ejpam-221	135	6	mcalister	mcalister	PROPN
ejpam-221	135	7	arrived	arrive	VERB
ejpam-221	135	8	at	at	ADP
ejpam-221	135	9	the	the	DET
ejpam-221	135	10	following	following	ADJ
ejpam-221	135	11	definition	definition	NOUN
ejpam-221	135	12	of	of	ADP
ejpam-221	135	13	a	a	DET
ejpam-221	135	14	potential	potential	ADJ
ejpam-221	135	15	property	property	NOUN
ejpam-221	135	16	via	via	ADP
ejpam-221	135	17	the	the	DET
ejpam-221	135	18	study	study	NOUN
ejpam-221	135	19	of	of	ADP
ejpam-221	135	20	partial	partial	ADJ
ejpam-221	135	21	right	right	ADJ
ejpam-221	135	22	translations	translation	NOUN
ejpam-221	135	23	:	:	PUNCT
ejpam-221	135	24	definition	definition	NOUN
ejpam-221	135	25	1.7	1.7	NUM
ejpam-221	135	26	.	.	PUNCT
ejpam-221	136	1	[	[	X
ejpam-221	136	2	54	54	NUM
ejpam-221	136	3	,	,	PUNCT
ejpam-221	136	4	definition	definition	NOUN
ejpam-221	136	5	1.6	1.6	NUM
ejpam-221	136	6	]	]	PUNCT
ejpam-221	136	7	let	let	VERB
ejpam-221	136	8	s	s	PRON
ejpam-221	136	9	be	be	AUX
ejpam-221	136	10	a	a	DET
ejpam-221	136	11	semigroup	semigroup	NOUN
ejpam-221	136	12	and	and	CCONJ
ejpam-221	136	13	let	let	VERB
ejpam-221	136	14	a	a	DET
ejpam-221	136	15	,	,	PUNCT
ejpam-221	136	16	b	b	X
ejpam-221	136	17	∈	∈	PROPN
ejpam-221	136	18	s.	s.	PROPN
ejpam-221	136	19	we	we	PRON
ejpam-221	136	20	define	define	VERB
ejpam-221	136	21	the	the	DET
ejpam-221	136	22	equivalence	equivalence	NOUN
ejpam-221	136	23	relation	relation	NOUN
ejpam-221	136	24	r∗	r∗	VERB
ejpam-221	136	25	on	on	ADP
ejpam-221	136	26	s	s	PRON
ejpam-221	136	27	by	by	ADP
ejpam-221	136	28	saying	say	VERB
ejpam-221	137	1	that	that	SCONJ
ejpam-221	137	2	ar∗	ar∗	PROPN
ejpam-221	137	3	b	b	NOUN
ejpam-221	137	4	if	if	SCONJ
ejpam-221	137	5	,	,	PUNCT
ejpam-221	137	6	and	and	CCONJ
ejpam-221	137	7	only	only	ADV
ejpam-221	137	8	if	if	SCONJ
ejpam-221	137	9	,	,	PUNCT
ejpam-221	137	10	a	a	PRON
ejpam-221	137	11	and	and	CCONJ
ejpam-221	137	12	b	b	NOUN
ejpam-221	137	13	are	be	AUX
ejpam-221	137	14	r	r	NOUN
ejpam-221	137	15	-	-	PUNCT
ejpam-221	137	16	related	relate	VERB
ejpam-221	137	17	in	in	ADP
ejpam-221	137	18	some	some	DET
ejpam-221	137	19	oversemigroup	oversemigroup	ADJ
ejpam-221	137	20	t	t	PROPN
ejpam-221	137	21	of	of	ADP
ejpam-221	137	22	s.	s.	PROPN
ejpam-221	137	23	through	through	ADP
ejpam-221	137	24	a	a	DET
ejpam-221	137	25	generalisation	generalisation	NOUN
ejpam-221	137	26	of	of	ADP
ejpam-221	137	27	a	a	DET
ejpam-221	137	28	construction	construction	NOUN
ejpam-221	137	29	of	of	ADP
ejpam-221	137	30	schützenberger	schützenberger	NOUN
ejpam-221	137	31	,	,	PUNCT
ejpam-221	137	32	pastijn	pastijn	NOUN
ejpam-221	137	33	arrived	arrive	VERB
ejpam-221	137	34	at	at	ADP
ejpam-221	137	35	the	the	DET
ejpam-221	137	36	definition	definition	NOUN
ejpam-221	137	37	of	of	ADP
ejpam-221	137	38	the	the	DET
ejpam-221	137	39	dual	dual	ADJ
ejpam-221	137	40	relation	relation	NOUN
ejpam-221	137	41	l	l	NOUN
ejpam-221	137	42	∗	∗	NOUN
ejpam-221	137	43	[	[	X
ejpam-221	137	44	59	59	NUM
ejpam-221	137	45	,	,	PUNCT
ejpam-221	137	46	p.	p.	NOUN
ejpam-221	137	47	239].§	239].§	NUM
ejpam-221	138	1	the	the	DET
ejpam-221	138	2	relations	relation	NOUN
ejpam-221	138	3	r∗	r∗	VERB
ejpam-221	138	4	and	and	CCONJ
ejpam-221	138	5	l	l	NOUN
ejpam-221	138	6	∗	∗	NOUN
ejpam-221	138	7	may	may	AUX
ejpam-221	138	8	be	be	AUX
ejpam-221	138	9	regarded	regard	VERB
ejpam-221	138	10	as	as	ADP
ejpam-221	138	11	generalisations	generalisation	NOUN
ejpam-221	138	12	of	of	ADP
ejpam-221	138	13	green	green	PROPN
ejpam-221	138	14	’s	’s	PART
ejpam-221	138	15	relations	relation	NOUN
ejpam-221	138	16	r	r	NOUN
ejpam-221	138	17	and	and	CCONJ
ejpam-221	138	18	l	l	NOUN
ejpam-221	138	19	;	;	PUNCT
ejpam-221	138	20	it	it	PRON
ejpam-221	138	21	is	be	AUX
ejpam-221	138	22	clear	clear	ADJ
ejpam-221	138	23	that	that	SCONJ
ejpam-221	138	24	r	r	NOUN
ejpam-221	138	25	⊆r∗	⊆r∗	NOUN
ejpam-221	138	26	and	and	CCONJ
ejpam-221	138	27	l	l	PROPN
ejpam-221	138	28	⊆l	⊆l	NOUN
ejpam-221	138	29	∗.	∗.	PROPN
ejpam-221	138	30	we	we	PRON
ejpam-221	138	31	note	note	VERB
ejpam-221	138	32	that	that	SCONJ
ejpam-221	138	33	the	the	DET
ejpam-221	138	34	formulation	formulation	NOUN
ejpam-221	138	35	of	of	ADP
ejpam-221	138	36	r∗	r∗	PROPN
ejpam-221	138	37	which	which	PRON
ejpam-221	138	38	will	will	AUX
ejpam-221	138	39	appear	appear	VERB
ejpam-221	138	40	later	later	ADV
ejpam-221	138	41	as	as	ADP
ejpam-221	138	42	our	our	PRON
ejpam-221	138	43	equation	equation	NOUN
ejpam-221	138	44	(	(	PUNCT
ejpam-221	138	45	5.1	5.1	NUM
ejpam-221	138	46	)	)	PUNCT
ejpam-221	138	47	,	,	PUNCT
ejpam-221	138	48	namely	namely	ADV
ejpam-221	138	49	,	,	PUNCT
ejpam-221	138	50	ar∗	ar∗	PROPN
ejpam-221	138	51	b	b	NUM
ejpam-221	138	52	⇐	⇐	PROPN
ejpam-221	138	53	⇒∀x	⇒∀x	NOUN
ejpam-221	138	54	,	,	PUNCT
ejpam-221	138	55	y	y	PROPN
ejpam-221	138	56	∈	∈	PROPN
ejpam-221	138	57	s1[xa	s1[xa	NOUN
ejpam-221	138	58	=	=	PUNCT
ejpam-221	138	59	ya⇔	ya⇔	NOUN
ejpam-221	138	60	x	x	X
ejpam-221	138	61	b	b	X
ejpam-221	138	62	=	=	SYM
ejpam-221	138	63	y	y	PROPN
ejpam-221	138	64	b	b	PROPN
ejpam-221	138	65	]	]	X
ejpam-221	138	66	,	,	PUNCT
ejpam-221	138	67	(	(	PUNCT
ejpam-221	138	68	1.1	1.1	NUM
ejpam-221	138	69	)	)	PUNCT
ejpam-221	138	70	is	be	AUX
ejpam-221	138	71	implicit	implicit	ADJ
ejpam-221	138	72	both	both	CCONJ
ejpam-221	138	73	in	in	ADP
ejpam-221	138	74	[	[	X
ejpam-221	138	75	8	8	NUM
ejpam-221	138	76	]	]	PUNCT
ejpam-221	138	77	and	and	CCONJ
ejpam-221	138	78	in	in	ADP
ejpam-221	138	79	[	[	X
ejpam-221	138	80	50	50	NUM
ejpam-221	138	81	,	,	PUNCT
ejpam-221	138	82	chapter	chapter	NOUN
ejpam-221	138	83	x	x	NOUN
ejpam-221	138	84	,	,	PUNCT
ejpam-221	138	85	§	§	VERB
ejpam-221	138	86	1.6	1.6	NUM
ejpam-221	138	87	]	]	PUNCT
ejpam-221	138	88	.	.	PUNCT
ejpam-221	139	1	returning	return	VERB
ejpam-221	139	2	to	to	ADP
ejpam-221	139	3	right	right	ADJ
ejpam-221	139	4	pp	pp	ADP
ejpam-221	139	5	monoids	monoid	NOUN
ejpam-221	139	6	,	,	PUNCT
ejpam-221	139	7	we	we	PRON
ejpam-221	139	8	first	first	ADV
ejpam-221	139	9	have	have	VERB
ejpam-221	139	10	the	the	DET
ejpam-221	139	11	following	following	NOUN
ejpam-221	139	12	,	,	PUNCT
ejpam-221	139	13	from	from	ADP
ejpam-221	139	14	[	[	X
ejpam-221	139	15	22	22	NUM
ejpam-221	139	16	]	]	X
ejpam-221	139	17	:	:	PUNCT
ejpam-221	139	18	§	§	VERB
ejpam-221	139	19	pastijn	pastijn	NOUN
ejpam-221	139	20	denoted	denote	VERB
ejpam-221	139	21	l	l	NOUN
ejpam-221	139	22	∗	∗	NOUN
ejpam-221	139	23	by	by	ADP
ejpam-221	139	24	fl	fl	PROPN
ejpam-221	139	25	—	—	PUNCT
ejpam-221	139	26	this	this	PRON
ejpam-221	139	27	should	should	AUX
ejpam-221	139	28	not	not	PART
ejpam-221	139	29	to	to	PART
ejpam-221	139	30	be	be	AUX
ejpam-221	139	31	confused	confuse	VERB
ejpam-221	139	32	with	with	ADP
ejpam-221	139	33	the	the	DET
ejpam-221	139	34	fl	fl	NOUN
ejpam-221	139	35	of	of	ADP
ejpam-221	139	36	the	the	DET
ejpam-221	139	37	subsequent	subsequent	ADJ
ejpam-221	139	38	theory	theory	NOUN
ejpam-221	139	39	of	of	ADP
ejpam-221	139	40	weakly	weakly	ADJ
ejpam-221	139	41	right	right	ADJ
ejpam-221	139	42	ample	ample	ADJ
ejpam-221	139	43	semigroups	semigroup	NOUN
ejpam-221	139	44	!	!	PUNCT
ejpam-221	140	1	c.	c.	NOUN
ejpam-221	140	2	hollings	holling	NOUN
ejpam-221	140	3	/	/	SYM
ejpam-221	140	4	eur	eur	PROPN
ejpam-221	140	5	.	.	PUNCT
ejpam-221	141	1	j.	j.	PROPN
ejpam-221	141	2	pure	pure	PROPN
ejpam-221	141	3	appl	appl	PROPN
ejpam-221	141	4	.	.	PROPN
ejpam-221	141	5	math	math	PROPN
ejpam-221	141	6	,	,	PUNCT
ejpam-221	141	7	2	2	NUM
ejpam-221	141	8	(	(	PUNCT
ejpam-221	141	9	2009	2009	NUM
ejpam-221	141	10	)	)	PUNCT
ejpam-221	141	11	,	,	PUNCT
ejpam-221	141	12	(	(	PUNCT
ejpam-221	141	13	21	21	NUM
ejpam-221	141	14	-	-	SYM
ejpam-221	141	15	57	57	NUM
ejpam-221	141	16	)	)	PUNCT
ejpam-221	141	17	29	29	NUM
ejpam-221	142	1	lemma	lemma	PROPN
ejpam-221	142	2	1.8	1.8	NUM
ejpam-221	142	3	.	.	PUNCT
ejpam-221	143	1	[	[	X
ejpam-221	143	2	22	22	NUM
ejpam-221	143	3	,	,	PUNCT
ejpam-221	143	4	p.	p.	NOUN
ejpam-221	143	5	286	286	NUM
ejpam-221	143	6	]	]	PUNCT
ejpam-221	143	7	let	let	VERB
ejpam-221	143	8	s	s	PRON
ejpam-221	143	9	be	be	AUX
ejpam-221	143	10	a	a	DET
ejpam-221	143	11	semigroup	semigroup	NOUN
ejpam-221	143	12	and	and	CCONJ
ejpam-221	143	13	let	let	VERB
ejpam-221	143	14	a	a	DET
ejpam-221	143	15	,	,	PUNCT
ejpam-221	143	16	b	b	X
ejpam-221	143	17	∈	∈	PROPN
ejpam-221	143	18	s.	s.	PROPN
ejpam-221	143	19	then	then	ADV
ejpam-221	143	20	al	al	PROPN
ejpam-221	143	21	∗	∗	PROPN
ejpam-221	143	22	b	b	PROPN
ejpam-221	143	23	if	if	SCONJ
ejpam-221	143	24	,	,	PUNCT
ejpam-221	143	25	and	and	CCONJ
ejpam-221	143	26	only	only	ADV
ejpam-221	143	27	if	if	SCONJ
ejpam-221	143	28	,	,	PUNCT
ejpam-221	143	29	there	there	PRON
ejpam-221	143	30	is	be	VERB
ejpam-221	143	31	an	an	DET
ejpam-221	143	32	e	e	PROPN
ejpam-221	143	33	∈	∈	PROPN
ejpam-221	143	34	e(s	e(s	PROPN
ejpam-221	143	35	)	)	PUNCT
ejpam-221	143	36	such	such	ADJ
ejpam-221	143	37	that	that	SCONJ
ejpam-221	143	38	a	a	PRON
ejpam-221	143	39	and	and	CCONJ
ejpam-221	143	40	b	b	NOUN
ejpam-221	143	41	are	be	AUX
ejpam-221	143	42	both	both	PRON
ejpam-221	143	43	left	leave	VERB
ejpam-221	143	44	e	e	NOUN
ejpam-221	143	45	-	-	NOUN
ejpam-221	143	46	cancellable	cancellable	ADJ
ejpam-221	143	47	.	.	PUNCT
ejpam-221	144	1	consequently	consequently	ADV
ejpam-221	144	2	:	:	PUNCT
ejpam-221	144	3	proposition	proposition	NOUN
ejpam-221	144	4	1.9	1.9	NUM
ejpam-221	144	5	.	.	PUNCT
ejpam-221	145	1	[	[	X
ejpam-221	145	2	22	22	NUM
ejpam-221	145	3	,	,	PUNCT
ejpam-221	145	4	p.	p.	NOUN
ejpam-221	145	5	286	286	NUM
ejpam-221	145	6	]	]	PUNCT
ejpam-221	145	7	a	a	DET
ejpam-221	145	8	monoid	monoid	NOUN
ejpam-221	145	9	s	s	X
ejpam-221	145	10	is	be	AUX
ejpam-221	145	11	right	right	ADJ
ejpam-221	145	12	pp	pp	ADV
ejpam-221	145	13	if	if	SCONJ
ejpam-221	145	14	,	,	PUNCT
ejpam-221	145	15	and	and	CCONJ
ejpam-221	145	16	only	only	ADV
ejpam-221	145	17	if	if	SCONJ
ejpam-221	145	18	,	,	PUNCT
ejpam-221	145	19	every	every	DET
ejpam-221	145	20	element	element	NOUN
ejpam-221	145	21	isl	isl	PROPN
ejpam-221	145	22	∗-related	∗-relate	VERB
ejpam-221	145	23	to	to	ADP
ejpam-221	145	24	an	an	DET
ejpam-221	145	25	idempotent	idempotent	NOUN
ejpam-221	145	26	.	.	PUNCT
ejpam-221	146	1	one	one	NUM
ejpam-221	146	2	thing	thing	NOUN
ejpam-221	146	3	which	which	PRON
ejpam-221	146	4	is	be	AUX
ejpam-221	146	5	immediately	immediately	ADV
ejpam-221	146	6	apparent	apparent	ADJ
ejpam-221	146	7	from	from	ADP
ejpam-221	146	8	this	this	DET
ejpam-221	146	9	characterisation	characterisation	NOUN
ejpam-221	146	10	of	of	ADP
ejpam-221	146	11	right	right	ADJ
ejpam-221	146	12	pp	pp	ADV
ejpam-221	146	13	monoids	monoid	VERB
ejpam-221	146	14	(	(	PUNCT
ejpam-221	146	15	and	and	CCONJ
ejpam-221	146	16	,	,	PUNCT
ejpam-221	146	17	indeed	indeed	ADV
ejpam-221	146	18	,	,	PUNCT
ejpam-221	146	19	from	from	ADP
ejpam-221	146	20	that	that	PRON
ejpam-221	146	21	in	in	ADP
ejpam-221	146	22	proposition	proposition	NOUN
ejpam-221	146	23	1.5	1.5	NUM
ejpam-221	146	24	)	)	PUNCT
ejpam-221	146	25	is	be	AUX
ejpam-221	146	26	the	the	DET
ejpam-221	146	27	fact	fact	NOUN
ejpam-221	146	28	that	that	SCONJ
ejpam-221	146	29	the	the	DET
ejpam-221	146	30	presence	presence	NOUN
ejpam-221	146	31	of	of	ADP
ejpam-221	146	32	an	an	DET
ejpam-221	146	33	identity	identity	NOUN
ejpam-221	146	34	is	be	AUX
ejpam-221	146	35	no	no	ADV
ejpam-221	146	36	longer	long	ADV
ejpam-221	146	37	required	require	VERB
ejpam-221	146	38	.	.	PUNCT
ejpam-221	147	1	we	we	PRON
ejpam-221	147	2	can	can	AUX
ejpam-221	147	3	therefore	therefore	ADV
ejpam-221	147	4	define	define	VERB
ejpam-221	147	5	right	right	ADV
ejpam-221	147	6	pp	pp	ADP
ejpam-221	147	7	semigroups	semigroup	NOUN
ejpam-221	147	8	.	.	PUNCT
ejpam-221	148	1	notice	notice	NOUN
ejpam-221	148	2	also	also	ADV
ejpam-221	148	3	that	that	SCONJ
ejpam-221	148	4	there	there	PRON
ejpam-221	148	5	is	be	VERB
ejpam-221	148	6	no	no	PRON
ejpam-221	148	7	longer	long	ADV
ejpam-221	148	8	any	any	DET
ejpam-221	148	9	reference	reference	NOUN
ejpam-221	148	10	to	to	ADP
ejpam-221	148	11	s	s	NOUN
ejpam-221	148	12	-	-	PUNCT
ejpam-221	148	13	acts	act	NOUN
ejpam-221	148	14	or	or	CCONJ
ejpam-221	148	15	projectivity	projectivity	NOUN
ejpam-221	148	16	.	.	PUNCT
ejpam-221	149	1	for	for	ADP
ejpam-221	149	2	this	this	DET
ejpam-221	149	3	reason	reason	NOUN
ejpam-221	149	4	,	,	PUNCT
ejpam-221	149	5	right	right	ADV
ejpam-221	149	6	pp	pp	ADP
ejpam-221	149	7	semigroups	semigroup	NOUN
ejpam-221	149	8	were	be	AUX
ejpam-221	149	9	renamed	rename	VERB
ejpam-221	149	10	right	right	ADJ
ejpam-221	149	11	abundant	abundant	ADJ
ejpam-221	149	12	semigroups	semigroup	NOUN
ejpam-221	149	13	,	,	PUNCT
ejpam-221	149	14	since	since	SCONJ
ejpam-221	149	15	“	"	PUNCT
ejpam-221	149	16	such	such	DET
ejpam-221	149	17	a	a	DET
ejpam-221	149	18	semigroup	semigroup	NOUN
ejpam-221	149	19	has	have	VERB
ejpam-221	149	20	a	a	DET
ejpam-221	149	21	plentiful	plentiful	ADJ
ejpam-221	149	22	supply	supply	NOUN
ejpam-221	149	23	of	of	ADP
ejpam-221	149	24	idempotents	idempotent	NOUN
ejpam-221	149	25	”	"	PUNCT
ejpam-221	150	1	[	[	X
ejpam-221	150	2	25	25	NUM
ejpam-221	150	3	,	,	PUNCT
ejpam-221	150	4	p.	p.	NOUN
ejpam-221	150	5	103	103	NUM
ejpam-221	150	6	]	]	PUNCT
ejpam-221	150	7	.	.	PUNCT
ejpam-221	151	1	similarly	similarly	ADV
ejpam-221	151	2	,	,	PUNCT
ejpam-221	151	3	left	leave	VERB
ejpam-221	151	4	pp	pp	ADP
ejpam-221	151	5	semigroups	semigroup	NOUN
ejpam-221	151	6	(	(	PUNCT
ejpam-221	151	7	in	in	ADP
ejpam-221	151	8	which	which	PRON
ejpam-221	151	9	every	every	DET
ejpam-221	151	10	element	element	NOUN
ejpam-221	151	11	is	be	AUX
ejpam-221	151	12	r∗related	r∗relate	VERB
ejpam-221	151	13	to	to	ADP
ejpam-221	151	14	an	an	DET
ejpam-221	151	15	idempotent	idempotent	NOUN
ejpam-221	151	16	)	)	PUNCT
ejpam-221	151	17	became	became	AUX
ejpam-221	151	18	left	leave	VERB
ejpam-221	151	19	abundant	abundant	ADJ
ejpam-221	151	20	semigroups	semigroup	NOUN
ejpam-221	151	21	;	;	PUNCT
ejpam-221	151	22	a	a	DET
ejpam-221	151	23	semigroup	semigroup	NOUN
ejpam-221	151	24	which	which	PRON
ejpam-221	151	25	is	be	AUX
ejpam-221	151	26	both	both	PRON
ejpam-221	151	27	left	leave	VERB
ejpam-221	151	28	and	and	CCONJ
ejpam-221	151	29	right	right	ADJ
ejpam-221	151	30	abundant	abundant	ADJ
ejpam-221	151	31	is	be	AUX
ejpam-221	151	32	called	call	VERB
ejpam-221	151	33	simply	simply	ADV
ejpam-221	151	34	abundant	abundant	ADJ
ejpam-221	151	35	.	.	PUNCT
ejpam-221	152	1	such	such	ADJ
ejpam-221	152	2	semigroups	semigroup	NOUN
ejpam-221	152	3	were	be	AUX
ejpam-221	152	4	studied	study	VERB
ejpam-221	152	5	extensively	extensively	ADV
ejpam-221	152	6	in	in	ADP
ejpam-221	152	7	[	[	X
ejpam-221	152	8	15	15	NUM
ejpam-221	152	9	]	]	PUNCT
ejpam-221	152	10	and	and	CCONJ
ejpam-221	152	11	[	[	X
ejpam-221	152	12	25	25	NUM
ejpam-221	152	13	]	]	PUNCT
ejpam-221	152	14	.	.	PUNCT
ejpam-221	153	1	we	we	PRON
ejpam-221	153	2	have	have	AUX
ejpam-221	153	3	already	already	ADV
ejpam-221	153	4	commented	comment	VERB
ejpam-221	153	5	that	that	SCONJ
ejpam-221	153	6	every	every	DET
ejpam-221	153	7	regular	regular	ADJ
ejpam-221	153	8	semigroup	semigroup	NOUN
ejpam-221	153	9	is	be	AUX
ejpam-221	153	10	abundant	abundant	ADJ
ejpam-221	153	11	.	.	PUNCT
ejpam-221	154	1	to	to	PART
ejpam-221	154	2	see	see	VERB
ejpam-221	154	3	this	this	PRON
ejpam-221	154	4	,	,	PUNCT
ejpam-221	154	5	we	we	PRON
ejpam-221	154	6	recall	recall	VERB
ejpam-221	154	7	that	that	SCONJ
ejpam-221	154	8	r	r	NOUN
ejpam-221	154	9	⊆	⊆	NUM
ejpam-221	154	10	r∗	r∗	NOUN
ejpam-221	154	11	and	and	CCONJ
ejpam-221	154	12	l	l	NOUN
ejpam-221	154	13	⊆	⊆	NUM
ejpam-221	154	14	l	l	NOUN
ejpam-221	154	15	∗	∗	NOUN
ejpam-221	154	16	,	,	PUNCT
ejpam-221	154	17	and	and	CCONJ
ejpam-221	154	18	note	note	VERB
ejpam-221	154	19	the	the	DET
ejpam-221	154	20	following	follow	VERB
ejpam-221	154	21	characterisation	characterisation	NOUN
ejpam-221	154	22	of	of	ADP
ejpam-221	154	23	a	a	DET
ejpam-221	154	24	regular	regular	ADJ
ejpam-221	154	25	semigroup	semigroup	NOUN
ejpam-221	154	26	:	:	PUNCT
ejpam-221	154	27	proposition	proposition	NOUN
ejpam-221	154	28	1.10	1.10	NUM
ejpam-221	154	29	.	.	PUNCT
ejpam-221	155	1	[	[	X
ejpam-221	155	2	37	37	NUM
ejpam-221	155	3	,	,	PUNCT
ejpam-221	155	4	proposition	proposition	NOUN
ejpam-221	155	5	2.3.2	2.3.2	NUM
ejpam-221	155	6	]	]	PUNCT
ejpam-221	155	7	a	a	DET
ejpam-221	155	8	semigroup	semigroup	NOUN
ejpam-221	155	9	s	s	VERB
ejpam-221	155	10	is	be	AUX
ejpam-221	155	11	regular	regular	ADJ
ejpam-221	155	12	if	if	SCONJ
ejpam-221	155	13	,	,	PUNCT
ejpam-221	155	14	and	and	CCONJ
ejpam-221	155	15	only	only	ADV
ejpam-221	155	16	if	if	SCONJ
ejpam-221	155	17	:	:	PUNCT
ejpam-221	155	18	(	(	PUNCT
ejpam-221	155	19	i	i	NOUN
ejpam-221	155	20	)	)	PUNCT
ejpam-221	155	21	every	every	DET
ejpam-221	155	22	r	r	NOUN
ejpam-221	155	23	-	-	PUNCT
ejpam-221	155	24	class	class	NOUN
ejpam-221	155	25	contains	contain	VERB
ejpam-221	155	26	an	an	DET
ejpam-221	155	27	idempotent	idempotent	NOUN
ejpam-221	155	28	;	;	PUNCT
ejpam-221	155	29	(	(	PUNCT
ejpam-221	155	30	ii	ii	NOUN
ejpam-221	155	31	)	)	PUNCT
ejpam-221	155	32	every	every	DET
ejpam-221	155	33	l	l	NOUN
ejpam-221	155	34	-class	-class	PROPN
ejpam-221	155	35	contains	contain	VERB
ejpam-221	155	36	an	an	DET
ejpam-221	155	37	idempotent	idempotent	NOUN
ejpam-221	155	38	.	.	PUNCT
ejpam-221	156	1	we	we	PRON
ejpam-221	156	2	see	see	VERB
ejpam-221	156	3	then	then	ADV
ejpam-221	156	4	that	that	SCONJ
ejpam-221	156	5	every	every	DET
ejpam-221	156	6	r∗-class	r∗-class	NOUN
ejpam-221	156	7	and	and	CCONJ
ejpam-221	156	8	every	every	DET
ejpam-221	156	9	l	l	NOUN
ejpam-221	156	10	∗-class	∗-class	NOUN
ejpam-221	156	11	of	of	ADP
ejpam-221	156	12	a	a	DET
ejpam-221	156	13	regular	regular	ADJ
ejpam-221	156	14	semigroup	semigroup	NOUN
ejpam-221	156	15	s	s	NOUN
ejpam-221	156	16	contains	contain	VERB
ejpam-221	156	17	an	an	DET
ejpam-221	156	18	idempotent	idempotent	NOUN
ejpam-221	156	19	;	;	PUNCT
ejpam-221	156	20	s	s	X
ejpam-221	156	21	is	be	AUX
ejpam-221	156	22	therefore	therefore	ADV
ejpam-221	156	23	abundant	abundant	ADJ
ejpam-221	156	24	.	.	PUNCT
ejpam-221	157	1	indeed	indeed	ADV
ejpam-221	157	2	,	,	PUNCT
ejpam-221	157	3	in	in	ADP
ejpam-221	157	4	a	a	DET
ejpam-221	157	5	regular	regular	ADJ
ejpam-221	157	6	semigroup	semigroup	NOUN
ejpam-221	157	7	,	,	PUNCT
ejpam-221	157	8	we	we	PRON
ejpam-221	157	9	have	have	AUX
ejpam-221	157	10	r∗	r∗	VERB
ejpam-221	157	11	=	=	PUNCT
ejpam-221	157	12	r	r	NOUN
ejpam-221	157	13	and	and	CCONJ
ejpam-221	157	14	l	l	NOUN
ejpam-221	157	15	∗	∗	NOUN
ejpam-221	157	16	=	=	SYM
ejpam-221	157	17	l	l	NOUN
ejpam-221	157	18	;	;	PUNCT
ejpam-221	157	19	we	we	PRON
ejpam-221	157	20	will	will	AUX
ejpam-221	157	21	provide	provide	VERB
ejpam-221	157	22	a	a	DET
ejpam-221	157	23	proof	proof	NOUN
ejpam-221	157	24	of	of	ADP
ejpam-221	157	25	this	this	PRON
ejpam-221	157	26	in	in	ADP
ejpam-221	157	27	section	section	NOUN
ejpam-221	157	28	4	4	NUM
ejpam-221	157	29	(	(	PUNCT
ejpam-221	157	30	lemmas	lemmas	PROPN
ejpam-221	157	31	4.1	4.1	NUM
ejpam-221	157	32	and	and	CCONJ
ejpam-221	157	33	4.14	4.14	NUM
ejpam-221	157	34	)	)	PUNCT
ejpam-221	157	35	.	.	PUNCT
ejpam-221	158	1	we	we	PRON
ejpam-221	158	2	now	now	ADV
ejpam-221	158	3	recall	recall	VERB
ejpam-221	158	4	the	the	DET
ejpam-221	158	5	definition	definition	NOUN
ejpam-221	158	6	of	of	ADP
ejpam-221	158	7	a	a	DET
ejpam-221	158	8	clifford	clifford	PROPN
ejpam-221	158	9	semigroup	semigroup	NOUN
ejpam-221	158	10	[	[	X
ejpam-221	158	11	37	37	NUM
ejpam-221	158	12	,	,	PUNCT
ejpam-221	158	13	§	§	NOUN
ejpam-221	158	14	4.2	4.2	NUM
ejpam-221	158	15	]	]	PUNCT
ejpam-221	158	16	as	as	ADP
ejpam-221	158	17	a	a	DET
ejpam-221	158	18	regular	regular	ADJ
ejpam-221	158	19	semigroup	semigroup	NOUN
ejpam-221	158	20	with	with	ADP
ejpam-221	158	21	central	central	ADJ
ejpam-221	158	22	idempotents	idempotent	NOUN
ejpam-221	158	23	.	.	PUNCT
ejpam-221	159	1	we	we	PRON
ejpam-221	159	2	recall	recall	VERB
ejpam-221	159	3	also	also	ADV
ejpam-221	159	4	the	the	DET
ejpam-221	159	5	following	following	ADJ
ejpam-221	159	6	result	result	NOUN
ejpam-221	159	7	,	,	PUNCT
ejpam-221	159	8	originally	originally	ADV
ejpam-221	159	9	due	due	ADP
ejpam-221	159	10	to	to	ADP
ejpam-221	159	11	clifford	clifford	PROPN
ejpam-221	159	12	[	[	X
ejpam-221	159	13	4	4	NUM
ejpam-221	159	14	]	]	PUNCT
ejpam-221	159	15	,	,	PUNCT
ejpam-221	159	16	and	and	CCONJ
ejpam-221	159	17	presented	present	VERB
ejpam-221	159	18	in	in	ADP
ejpam-221	159	19	[	[	X
ejpam-221	159	20	37	37	NUM
ejpam-221	159	21	,	,	PUNCT
ejpam-221	159	22	theorem	theorem	VERB
ejpam-221	159	23	4.2.1	4.2.1	NUM
ejpam-221	159	24	]	]	X
ejpam-221	159	25	:	:	PUNCT
ejpam-221	159	26	c.	c.	PROPN
ejpam-221	159	27	hollings	hollings	PROPN
ejpam-221	159	28	/	/	SYM
ejpam-221	159	29	eur	eur	PROPN
ejpam-221	159	30	.	.	PUNCT
ejpam-221	160	1	j.	j.	PROPN
ejpam-221	160	2	pure	pure	PROPN
ejpam-221	160	3	appl	appl	PROPN
ejpam-221	160	4	.	.	PROPN
ejpam-221	160	5	math	math	PROPN
ejpam-221	160	6	,	,	PUNCT
ejpam-221	160	7	2	2	NUM
ejpam-221	160	8	(	(	PUNCT
ejpam-221	160	9	2009	2009	NUM
ejpam-221	160	10	)	)	PUNCT
ejpam-221	160	11	,	,	PUNCT
ejpam-221	160	12	(	(	PUNCT
ejpam-221	160	13	21	21	NUM
ejpam-221	160	14	-	-	SYM
ejpam-221	160	15	57	57	NUM
ejpam-221	160	16	)	)	PUNCT
ejpam-221	160	17	30	30	NUM
ejpam-221	160	18	theorem	theorem	VERB
ejpam-221	160	19	1.11	1.11	NUM
ejpam-221	160	20	.	.	PUNCT
ejpam-221	161	1	a	a	DET
ejpam-221	161	2	semigroup	semigroup	NOUN
ejpam-221	161	3	s	s	VERB
ejpam-221	161	4	is	be	AUX
ejpam-221	161	5	a	a	DET
ejpam-221	161	6	clifford	clifford	PROPN
ejpam-221	161	7	semigroup	semigroup	NOUN
ejpam-221	161	8	if	if	SCONJ
ejpam-221	161	9	,	,	PUNCT
ejpam-221	161	10	and	and	CCONJ
ejpam-221	161	11	only	only	ADV
ejpam-221	161	12	if	if	SCONJ
ejpam-221	161	13	,	,	PUNCT
ejpam-221	161	14	it	it	PRON
ejpam-221	161	15	is	be	AUX
ejpam-221	161	16	a	a	DET
ejpam-221	161	17	strong	strong	ADJ
ejpam-221	161	18	semilattice	semilattice	NOUN
ejpam-221	161	19	of	of	ADP
ejpam-221	161	20	groups	group	NOUN
ejpam-221	161	21	.	.	PUNCT
ejpam-221	162	1	we	we	PRON
ejpam-221	162	2	see	see	VERB
ejpam-221	162	3	then	then	ADV
ejpam-221	162	4	that	that	SCONJ
ejpam-221	162	5	the	the	DET
ejpam-221	162	6	result	result	NOUN
ejpam-221	162	7	of	of	ADP
ejpam-221	162	8	fountain	fountain	NOUN
ejpam-221	162	9	[	[	X
ejpam-221	162	10	23	23	NUM
ejpam-221	162	11	]	]	PUNCT
ejpam-221	162	12	which	which	PRON
ejpam-221	162	13	states	state	VERB
ejpam-221	162	14	that	that	SCONJ
ejpam-221	162	15	every	every	PRON
ejpam-221	162	16	right	right	ADJ
ejpam-221	162	17	abundant	abundant	ADJ
ejpam-221	162	18	monoid	monoid	NOUN
ejpam-221	162	19	with	with	ADP
ejpam-221	162	20	central	central	ADJ
ejpam-221	162	21	idempotents	idempotent	NOUN
ejpam-221	162	22	is	be	AUX
ejpam-221	162	23	a	a	DET
ejpam-221	162	24	strong	strong	ADJ
ejpam-221	162	25	semilattice	semilattice	NOUN
ejpam-221	162	26	of	of	ADP
ejpam-221	162	27	left	left	ADJ
ejpam-221	162	28	cancellative	cancellative	ADJ
ejpam-221	162	29	monoids	monoid	NOUN
ejpam-221	162	30	provides	provide	VERB
ejpam-221	162	31	a	a	DET
ejpam-221	162	32	one	one	NUM
ejpam-221	162	33	-	-	PUNCT
ejpam-221	162	34	sided	sided	ADJ
ejpam-221	162	35	analogue	analogue	NOUN
ejpam-221	162	36	of	of	ADP
ejpam-221	162	37	this	this	DET
ejpam-221	162	38	last	last	ADJ
ejpam-221	162	39	theorem	theorem	NOUN
ejpam-221	162	40	.	.	PUNCT
ejpam-221	163	1	furthermore	furthermore	ADV
ejpam-221	163	2	,	,	PUNCT
ejpam-221	163	3	in	in	ADP
ejpam-221	163	4	the	the	DET
ejpam-221	163	5	two	two	NUM
ejpam-221	163	6	-	-	PUNCT
ejpam-221	163	7	sided	side	VERB
ejpam-221	163	8	case	case	NOUN
ejpam-221	163	9	,	,	PUNCT
ejpam-221	163	10	abundant	abundant	ADJ
ejpam-221	163	11	semigroups	semigroup	NOUN
ejpam-221	163	12	with	with	ADP
ejpam-221	163	13	central	central	ADJ
ejpam-221	163	14	idempotents	idempotent	NOUN
ejpam-221	163	15	are	be	AUX
ejpam-221	163	16	strong	strong	ADJ
ejpam-221	163	17	semilattices	semilattice	NOUN
ejpam-221	163	18	of	of	ADP
ejpam-221	163	19	cancellative	cancellative	ADJ
ejpam-221	163	20	monoids	monoid	NOUN
ejpam-221	163	21	;	;	PUNCT
ejpam-221	163	22	abundant	abundant	ADJ
ejpam-221	163	23	semigroups	semigroup	NOUN
ejpam-221	163	24	with	with	ADP
ejpam-221	163	25	central	central	ADJ
ejpam-221	163	26	idempotents	idempotent	NOUN
ejpam-221	163	27	may	may	AUX
ejpam-221	163	28	therefore	therefore	ADV
ejpam-221	163	29	be	be	AUX
ejpam-221	163	30	regarded	regard	VERB
ejpam-221	163	31	as	as	ADP
ejpam-221	163	32	analogues	analogue	NOUN
ejpam-221	163	33	of	of	ADP
ejpam-221	163	34	clifford	clifford	PROPN
ejpam-221	163	35	semigroups	semigroup	NOUN
ejpam-221	163	36	.	.	PUNCT
ejpam-221	164	1	more	more	ADV
ejpam-221	164	2	generally	generally	ADV
ejpam-221	164	3	,	,	PUNCT
ejpam-221	164	4	abundant	abundant	ADJ
ejpam-221	164	5	semigroups	semigroup	NOUN
ejpam-221	164	6	are	be	AUX
ejpam-221	164	7	analogous	analogous	ADJ
ejpam-221	164	8	to	to	ADP
ejpam-221	164	9	regular	regular	ADJ
ejpam-221	164	10	semigroups	semigroup	NOUN
ejpam-221	164	11	.	.	PUNCT
ejpam-221	165	1	the	the	DET
ejpam-221	165	2	validity	validity	NOUN
ejpam-221	165	3	of	of	ADP
ejpam-221	165	4	this	this	DET
ejpam-221	165	5	analogy	analogy	NOUN
ejpam-221	165	6	is	be	AUX
ejpam-221	165	7	demonstrated	demonstrate	VERB
ejpam-221	165	8	if	if	SCONJ
ejpam-221	165	9	we	we	PRON
ejpam-221	165	10	compare	compare	VERB
ejpam-221	165	11	proposition	proposition	NOUN
ejpam-221	165	12	1.9	1.9	NUM
ejpam-221	165	13	with	with	ADP
ejpam-221	165	14	proposition	proposition	NOUN
ejpam-221	165	15	1.10	1.10	NUM
ejpam-221	165	16	.	.	PUNCT
ejpam-221	166	1	the	the	DET
ejpam-221	166	2	initial	initial	ADJ
ejpam-221	166	3	study	study	NOUN
ejpam-221	166	4	of	of	ADP
ejpam-221	166	5	abundant	abundant	ADJ
ejpam-221	166	6	semigroups	semigroup	NOUN
ejpam-221	166	7	was	be	AUX
ejpam-221	166	8	therefore	therefore	ADV
ejpam-221	166	9	guided	guide	VERB
ejpam-221	166	10	by	by	ADP
ejpam-221	166	11	the	the	DET
ejpam-221	166	12	existing	exist	VERB
ejpam-221	166	13	results	result	NOUN
ejpam-221	166	14	for	for	ADP
ejpam-221	166	15	regular	regular	ADJ
ejpam-221	166	16	semgroups	semgroup	NOUN
ejpam-221	166	17	.	.	PUNCT
ejpam-221	167	1	one	one	NUM
ejpam-221	167	2	important	important	ADJ
ejpam-221	167	3	point	point	NOUN
ejpam-221	167	4	to	to	PART
ejpam-221	167	5	note	note	VERB
ejpam-221	167	6	at	at	ADP
ejpam-221	167	7	this	this	DET
ejpam-221	167	8	stage	stage	NOUN
ejpam-221	167	9	is	be	AUX
ejpam-221	167	10	that	that	SCONJ
ejpam-221	167	11	for	for	ADP
ejpam-221	167	12	regular	regular	ADJ
ejpam-221	167	13	semigroups	semigroup	NOUN
ejpam-221	167	14	,	,	PUNCT
ejpam-221	167	15	each	each	PRON
ejpam-221	167	16	of	of	ADP
ejpam-221	167	17	conditions	condition	NOUN
ejpam-221	167	18	(	(	PUNCT
ejpam-221	167	19	i	i	NOUN
ejpam-221	167	20	)	)	PUNCT
ejpam-221	167	21	and	and	CCONJ
ejpam-221	167	22	(	(	PUNCT
ejpam-221	167	23	ii	ii	NOUN
ejpam-221	167	24	)	)	PUNCT
ejpam-221	167	25	in	in	ADP
ejpam-221	167	26	proposition	proposition	NOUN
ejpam-221	167	27	1.10	1.10	NUM
ejpam-221	167	28	implies	imply	VERB
ejpam-221	167	29	the	the	DET
ejpam-221	167	30	other	other	ADJ
ejpam-221	167	31	.	.	PUNCT
ejpam-221	168	1	the	the	DET
ejpam-221	168	2	‘	'	PUNCT
ejpam-221	168	3	starred	starred	ADJ
ejpam-221	168	4	’	'	PUNCT
ejpam-221	168	5	versions	version	NOUN
ejpam-221	168	6	of	of	ADP
ejpam-221	168	7	these	these	DET
ejpam-221	168	8	conditions	condition	NOUN
ejpam-221	168	9	,	,	PUNCT
ejpam-221	168	10	however	however	ADV
ejpam-221	168	11	,	,	PUNCT
ejpam-221	168	12	are	be	AUX
ejpam-221	168	13	completely	completely	ADV
ejpam-221	168	14	independent	independent	ADJ
ejpam-221	168	15	.	.	PUNCT
ejpam-221	169	1	this	this	PRON
ejpam-221	169	2	is	be	AUX
ejpam-221	169	3	why	why	SCONJ
ejpam-221	169	4	we	we	PRON
ejpam-221	169	5	have	have	VERB
ejpam-221	169	6	one	one	NUM
ejpam-221	169	7	-	-	PUNCT
ejpam-221	169	8	sided	side	VERB
ejpam-221	169	9	as	as	ADV
ejpam-221	169	10	well	well	ADV
ejpam-221	169	11	as	as	ADP
ejpam-221	169	12	two	two	NUM
ejpam-221	169	13	-	-	PUNCT
ejpam-221	169	14	sided	sided	ADJ
ejpam-221	169	15	analogues	analogue	NOUN
ejpam-221	169	16	of	of	ADP
ejpam-221	169	17	regular	regular	ADJ
ejpam-221	169	18	semigroups	semigroup	NOUN
ejpam-221	169	19	.	.	PUNCT
ejpam-221	170	1	a	a	DET
ejpam-221	170	2	left	left	ADJ
ejpam-221	170	3	cancellative	cancellative	ADJ
ejpam-221	170	4	semigroup	semigroup	NOUN
ejpam-221	170	5	which	which	PRON
ejpam-221	170	6	is	be	AUX
ejpam-221	170	7	not	not	PART
ejpam-221	170	8	right	right	ADJ
ejpam-221	170	9	cancellative	cancellative	ADJ
ejpam-221	170	10	is	be	AUX
ejpam-221	170	11	an	an	DET
ejpam-221	170	12	example	example	NOUN
ejpam-221	170	13	of	of	ADP
ejpam-221	170	14	a	a	DET
ejpam-221	170	15	right	right	ADJ
ejpam-221	170	16	abundant	abundant	ADJ
ejpam-221	170	17	semigroup	semigroup	NOUN
ejpam-221	170	18	which	which	PRON
ejpam-221	170	19	is	be	AUX
ejpam-221	170	20	not	not	PART
ejpam-221	170	21	left	leave	VERB
ejpam-221	170	22	abundant	abundant	ADJ
ejpam-221	170	23	.	.	PUNCT
ejpam-221	171	1	two	two	NUM
ejpam-221	171	2	special	special	ADJ
ejpam-221	171	3	classes	class	NOUN
ejpam-221	171	4	of	of	ADP
ejpam-221	171	5	regular	regular	ADJ
ejpam-221	171	6	semigroups	semigroup	NOUN
ejpam-221	171	7	which	which	PRON
ejpam-221	171	8	have	have	AUX
ejpam-221	171	9	seen	see	VERB
ejpam-221	171	10	extensive	extensive	ADJ
ejpam-221	171	11	study	study	NOUN
ejpam-221	171	12	are	be	AUX
ejpam-221	171	13	so	so	ADV
ejpam-221	171	14	-	-	PUNCT
ejpam-221	171	15	called	call	VERB
ejpam-221	171	16	orthodox	orthodox	NOUN
ejpam-221	171	17	semigroups	semigroup	NOUN
ejpam-221	172	1	[	[	X
ejpam-221	172	2	37	37	NUM
ejpam-221	172	3	,	,	PUNCT
ejpam-221	172	4	§	§	NOUN
ejpam-221	172	5	6.2	6.2	NUM
ejpam-221	172	6	]	]	PUNCT
ejpam-221	172	7	,	,	PUNCT
ejpam-221	172	8	in	in	ADP
ejpam-221	172	9	which	which	PRON
ejpam-221	172	10	the	the	DET
ejpam-221	172	11	idempotents	idempotent	NOUN
ejpam-221	172	12	form	form	VERB
ejpam-221	172	13	a	a	DET
ejpam-221	172	14	subsemigroup	subsemigroup	NOUN
ejpam-221	172	15	,	,	PUNCT
ejpam-221	172	16	and	and	CCONJ
ejpam-221	172	17	,	,	PUNCT
ejpam-221	172	18	of	of	ADP
ejpam-221	172	19	course	course	NOUN
ejpam-221	172	20	,	,	PUNCT
ejpam-221	172	21	inverse	inverse	NOUN
ejpam-221	172	22	semigroups	semigroup	NOUN
ejpam-221	172	23	,	,	PUNCT
ejpam-221	172	24	in	in	ADP
ejpam-221	172	25	which	which	PRON
ejpam-221	172	26	the	the	DET
ejpam-221	172	27	idempotents	idempotent	NOUN
ejpam-221	172	28	form	form	VERB
ejpam-221	172	29	a	a	DET
ejpam-221	172	30	semilattice	semilattice	NOUN
ejpam-221	172	31	.	.	PUNCT
ejpam-221	173	1	this	this	DET
ejpam-221	173	2	hints	hint	VERB
ejpam-221	173	3	at	at	ADP
ejpam-221	173	4	two	two	NUM
ejpam-221	173	5	special	special	ADJ
ejpam-221	173	6	classes	class	NOUN
ejpam-221	173	7	of	of	ADP
ejpam-221	173	8	abundant	abundant	ADJ
ejpam-221	173	9	semigroups	semigroup	NOUN
ejpam-221	173	10	whose	whose	DET
ejpam-221	173	11	study	study	NOUN
ejpam-221	173	12	may	may	AUX
ejpam-221	173	13	be	be	AUX
ejpam-221	173	14	fruitful	fruitful	ADJ
ejpam-221	173	15	.	.	PUNCT
ejpam-221	174	1	abundant	abundant	ADJ
ejpam-221	174	2	semigroups	semigroup	NOUN
ejpam-221	174	3	in	in	ADP
ejpam-221	174	4	which	which	PRON
ejpam-221	174	5	the	the	DET
ejpam-221	174	6	idempotents	idempotent	NOUN
ejpam-221	174	7	form	form	VERB
ejpam-221	174	8	a	a	DET
ejpam-221	174	9	subsemigroup	subsemigroup	NOUN
ejpam-221	174	10	have	have	AUX
ejpam-221	174	11	been	be	AUX
ejpam-221	174	12	studied	study	VERB
ejpam-221	174	13	under	under	ADP
ejpam-221	174	14	the	the	DET
ejpam-221	174	15	name	name	NOUN
ejpam-221	174	16	of	of	ADP
ejpam-221	174	17	quasiadequate	quasiadequate	NOUN
ejpam-221	174	18	semigroups	semigroup	NOUN
ejpam-221	174	19	[	[	X
ejpam-221	174	20	15–17	15–17	NUM
ejpam-221	174	21	]	]	PUNCT
ejpam-221	174	22	,	,	PUNCT
ejpam-221	174	23	and	and	CCONJ
ejpam-221	174	24	a	a	DET
ejpam-221	174	25	theory	theory	NOUN
ejpam-221	174	26	has	have	AUX
ejpam-221	174	27	been	be	AUX
ejpam-221	174	28	developed	develop	VERB
ejpam-221	174	29	for	for	ADP
ejpam-221	174	30	these	these	PRON
ejpam-221	174	31	which	which	PRON
ejpam-221	174	32	mirrors	mirror	VERB
ejpam-221	174	33	that	that	PRON
ejpam-221	174	34	of	of	ADP
ejpam-221	174	35	hall	hall	NOUN
ejpam-221	175	1	[	[	X
ejpam-221	175	2	34	34	NUM
ejpam-221	175	3	]	]	PUNCT
ejpam-221	175	4	for	for	ADP
ejpam-221	175	5	orthodox	orthodox	ADJ
ejpam-221	175	6	semigroups	semigroup	NOUN
ejpam-221	175	7	.	.	PUNCT
ejpam-221	176	1	an	an	DET
ejpam-221	176	2	abundant	abundant	ADJ
ejpam-221	176	3	semigroup	semigroup	NOUN
ejpam-221	176	4	in	in	ADP
ejpam-221	176	5	which	which	PRON
ejpam-221	176	6	the	the	DET
ejpam-221	176	7	idempotents	idempotent	NOUN
ejpam-221	176	8	form	form	VERB
ejpam-221	176	9	a	a	DET
ejpam-221	176	10	subsemilattice	subsemilattice	NOUN
ejpam-221	176	11	is	be	AUX
ejpam-221	176	12	termed	term	VERB
ejpam-221	176	13	an	an	DET
ejpam-221	176	14	adequate	adequate	ADJ
ejpam-221	176	15	semigroup	semigroup	NOUN
ejpam-221	176	16	,	,	PUNCT
ejpam-221	176	17	“	"	PUNCT
ejpam-221	176	18	since	since	SCONJ
ejpam-221	176	19	it	it	PRON
ejpam-221	176	20	contains	contain	VERB
ejpam-221	176	21	a	a	DET
ejpam-221	176	22	sufficient	sufficient	ADJ
ejpam-221	176	23	supply	supply	NOUN
ejpam-221	176	24	of	of	ADP
ejpam-221	176	25	suitable	suitable	ADJ
ejpam-221	176	26	idempotents	idempotent	NOUN
ejpam-221	176	27	”	"	PUNCT
ejpam-221	177	1	[	[	X
ejpam-221	177	2	24	24	NUM
ejpam-221	177	3	,	,	PUNCT
ejpam-221	177	4	p.	p.	NOUN
ejpam-221	177	5	113	113	NUM
ejpam-221	177	6	]	]	PUNCT
ejpam-221	177	7	.	.	PUNCT
ejpam-221	178	1	left	leave	VERB
ejpam-221	178	2	adequate	adequate	ADJ
ejpam-221	178	3	and	and	CCONJ
ejpam-221	178	4	right	right	ADJ
ejpam-221	178	5	adequate	adequate	ADJ
ejpam-221	178	6	semigroups	semigroup	NOUN
ejpam-221	178	7	are	be	AUX
ejpam-221	178	8	also	also	ADV
ejpam-221	178	9	easily	easily	ADV
ejpam-221	178	10	defined	define	VERB
ejpam-221	178	11	.	.	PUNCT
ejpam-221	179	1	the	the	DET
ejpam-221	179	2	study	study	NOUN
ejpam-221	179	3	of	of	ADP
ejpam-221	179	4	right	right	ADJ
ejpam-221	179	5	adequate	adequate	ADJ
ejpam-221	179	6	semigroups	semigroup	NOUN
ejpam-221	179	7	was	be	AUX
ejpam-221	179	8	initiated	initiate	VERB
ejpam-221	179	9	in	in	ADP
ejpam-221	179	10	[	[	X
ejpam-221	179	11	22	22	NUM
ejpam-221	179	12	]	]	PUNCT
ejpam-221	179	13	;	;	PUNCT
ejpam-221	179	14	the	the	DET
ejpam-221	179	15	two	two	NUM
ejpam-221	179	16	-	-	PUNCT
ejpam-221	179	17	sided	side	VERB
ejpam-221	179	18	case	case	NOUN
ejpam-221	179	19	was	be	AUX
ejpam-221	179	20	considered	consider	VERB
ejpam-221	179	21	in	in	ADP
ejpam-221	179	22	[	[	X
ejpam-221	179	23	24	24	NUM
ejpam-221	179	24	]	]	PUNCT
ejpam-221	179	25	.	.	PUNCT
ejpam-221	180	1	the	the	DET
ejpam-221	180	2	early	early	ADJ
ejpam-221	180	3	study	study	NOUN
ejpam-221	180	4	of	of	ADP
ejpam-221	180	5	(	(	PUNCT
ejpam-221	180	6	left	left	ADJ
ejpam-221	180	7	/	/	SYM
ejpam-221	180	8	right	right	ADJ
ejpam-221	180	9	)	)	PUNCT
ejpam-221	180	10	adequate	adequate	ADJ
ejpam-221	180	11	semigroups	semigroup	NOUN
ejpam-221	180	12	was	be	AUX
ejpam-221	180	13	guided	guide	VERB
ejpam-221	180	14	by	by	ADP
ejpam-221	180	15	the	the	DET
ejpam-221	180	16	analogy	analogy	NOUN
ejpam-221	180	17	with	with	ADP
ejpam-221	180	18	inverse	inverse	NOUN
ejpam-221	180	19	semigroups	semigroup	NOUN
ejpam-221	180	20	.	.	PUNCT
ejpam-221	181	1	in	in	ADP
ejpam-221	181	2	[	[	X
ejpam-221	181	3	22	22	NUM
ejpam-221	181	4	]	]	PUNCT
ejpam-221	181	5	,	,	PUNCT
ejpam-221	181	6	fountain	fountain	NOUN
ejpam-221	181	7	(	(	PUNCT
ejpam-221	181	8	who	who	PRON
ejpam-221	181	9	,	,	PUNCT
ejpam-221	181	10	at	at	ADP
ejpam-221	181	11	this	this	DET
ejpam-221	181	12	stage	stage	NOUN
ejpam-221	181	13	,	,	PUNCT
ejpam-221	181	14	was	be	AUX
ejpam-221	181	15	still	still	ADV
ejpam-221	181	16	working	work	VERB
ejpam-221	181	17	in	in	ADP
ejpam-221	181	18	the	the	DET
ejpam-221	181	19	monoid	monoid	NOUN
ejpam-221	181	20	case	case	NOUN
ejpam-221	181	21	)	)	PUNCT
ejpam-221	181	22	sought	seek	VERB
ejpam-221	181	23	an	an	DET
ejpam-221	181	24	analogue	analogue	NOUN
ejpam-221	181	25	for	for	ADP
ejpam-221	181	26	right	right	ADJ
ejpam-221	181	27	adequate	adequate	ADJ
ejpam-221	181	28	semigroups	semigroup	NOUN
ejpam-221	181	29	of	of	ADP
ejpam-221	181	30	two	two	NUM
ejpam-221	181	31	results	result	NOUN
ejpam-221	181	32	of	of	ADP
ejpam-221	181	33	mcalister	mcalister	NOUN
ejpam-221	181	34	[	[	X
ejpam-221	181	35	52	52	NUM
ejpam-221	181	36	,	,	PUNCT
ejpam-221	181	37	53	53	NUM
ejpam-221	181	38	]	]	PUNCT
ejpam-221	181	39	for	for	ADP
ejpam-221	181	40	c.	c.	PROPN
ejpam-221	181	41	hollings	holling	NOUN
ejpam-221	181	42	/	/	SYM
ejpam-221	181	43	eur	eur	PROPN
ejpam-221	181	44	.	.	PUNCT
ejpam-221	182	1	j.	j.	PROPN
ejpam-221	182	2	pure	pure	PROPN
ejpam-221	182	3	appl	appl	PROPN
ejpam-221	182	4	.	.	PROPN
ejpam-221	182	5	math	math	PROPN
ejpam-221	182	6	,	,	PUNCT
ejpam-221	182	7	2	2	NUM
ejpam-221	182	8	(	(	PUNCT
ejpam-221	182	9	2009	2009	NUM
ejpam-221	182	10	)	)	PUNCT
ejpam-221	182	11	,	,	PUNCT
ejpam-221	182	12	(	(	PUNCT
ejpam-221	182	13	21	21	NUM
ejpam-221	182	14	-	-	SYM
ejpam-221	182	15	57	57	NUM
ejpam-221	182	16	)	)	PUNCT
ejpam-221	182	17	31	31	NUM
ejpam-221	182	18	inverse	inverse	NOUN
ejpam-221	182	19	semigroups	semigroup	NOUN
ejpam-221	182	20	:	:	PUNCT
ejpam-221	182	21	theorem	theorem	VERB
ejpam-221	182	22	1.12	1.12	NUM
ejpam-221	182	23	(	(	PUNCT
ejpam-221	182	24	mcalister	mcalister	PROPN
ejpam-221	182	25	’s	’s	PART
ejpam-221	182	26	covering	covering	NOUN
ejpam-221	182	27	theorem	theorem	NOUN
ejpam-221	182	28	)	)	PUNCT
ejpam-221	182	29	.	.	PUNCT
ejpam-221	183	1	[	[	X
ejpam-221	183	2	49	49	NUM
ejpam-221	183	3	,	,	PUNCT
ejpam-221	183	4	theorem	theorem	VERB
ejpam-221	183	5	2.2.4	2.2.4	NUM
ejpam-221	183	6	]	]	PUNCT
ejpam-221	183	7	every	every	DET
ejpam-221	183	8	inverse	inverse	NOUN
ejpam-221	183	9	semigroup	semigroup	NOUN
ejpam-221	183	10	is	be	AUX
ejpam-221	183	11	the	the	DET
ejpam-221	183	12	image	image	NOUN
ejpam-221	183	13	of	of	ADP
ejpam-221	183	14	a	a	DET
ejpam-221	183	15	proper	proper	ADJ
ejpam-221	183	16	inverse	inverse	NOUN
ejpam-221	183	17	semigroup	semigroup	NOUN
ejpam-221	183	18	under	under	ADP
ejpam-221	183	19	an	an	DET
ejpam-221	183	20	idempotent	idempotent	NOUN
ejpam-221	183	21	-	-	PUNCT
ejpam-221	183	22	separating	separate	VERB
ejpam-221	183	23	morphism	morphism	NOUN
ejpam-221	183	24	.	.	PUNCT
ejpam-221	184	1	theorem	theorem	ADJ
ejpam-221	184	2	1.13	1.13	NUM
ejpam-221	184	3	(	(	PUNCT
ejpam-221	184	4	mcalister	mcalister	PROPN
ejpam-221	184	5	’s	’s	PART
ejpam-221	184	6	p	p	NOUN
ejpam-221	184	7	-	-	PUNCT
ejpam-221	184	8	theorem	theorem	ADJ
ejpam-221	184	9	)	)	PUNCT
ejpam-221	184	10	.	.	PUNCT
ejpam-221	185	1	[	[	X
ejpam-221	185	2	49	49	NUM
ejpam-221	185	3	,	,	PUNCT
ejpam-221	185	4	theorem	theorem	VERB
ejpam-221	185	5	7.2.15	7.2.15	NUM
ejpam-221	185	6	]	]	PUNCT
ejpam-221	185	7	every	every	DET
ejpam-221	185	8	e	e	NOUN
ejpam-221	185	9	-	-	ADJ
ejpam-221	185	10	unitary	unitary	ADJ
ejpam-221	185	11	inverse	inverse	NOUN
ejpam-221	185	12	semigroup	semigroup	NOUN
ejpam-221	185	13	is	be	AUX
ejpam-221	185	14	isomorphic	isomorphic	ADJ
ejpam-221	185	15	to	to	ADP
ejpam-221	185	16	a	a	DET
ejpam-221	185	17	‘	'	PUNCT
ejpam-221	185	18	p	p	NOUN
ejpam-221	185	19	-	-	PUNCT
ejpam-221	185	20	semigroup	semigroup	NOUN
ejpam-221	185	21	’	'	PUNCT
ejpam-221	185	22	,	,	PUNCT
ejpam-221	185	23	constructed	construct	VERB
ejpam-221	185	24	from	from	ADP
ejpam-221	185	25	a	a	DET
ejpam-221	185	26	group	group	NOUN
ejpam-221	185	27	,	,	PUNCT
ejpam-221	185	28	a	a	DET
ejpam-221	185	29	poset	poset	NOUN
ejpam-221	185	30	and	and	CCONJ
ejpam-221	185	31	a	a	DET
ejpam-221	185	32	semilattice	semilattice	NOUN
ejpam-221	185	33	.	.	PUNCT
ejpam-221	186	1	fountain	fountain	NOUN
ejpam-221	186	2	determined	determine	VERB
ejpam-221	186	3	that	that	SCONJ
ejpam-221	186	4	if	if	SCONJ
ejpam-221	186	5	right	right	ADV
ejpam-221	186	6	adequate	adequate	ADJ
ejpam-221	186	7	analogues	analogue	NOUN
ejpam-221	186	8	are	be	AUX
ejpam-221	186	9	to	to	PART
ejpam-221	186	10	be	be	AUX
ejpam-221	186	11	developed	develop	VERB
ejpam-221	186	12	for	for	ADP
ejpam-221	186	13	these	these	DET
ejpam-221	186	14	theorems	theorem	NOUN
ejpam-221	186	15	,	,	PUNCT
ejpam-221	186	16	then	then	ADV
ejpam-221	186	17	we	we	PRON
ejpam-221	186	18	must	must	AUX
ejpam-221	186	19	restrict	restrict	VERB
ejpam-221	186	20	our	our	PRON
ejpam-221	186	21	attention	attention	NOUN
ejpam-221	186	22	to	to	ADP
ejpam-221	186	23	a	a	DET
ejpam-221	186	24	particular	particular	ADJ
ejpam-221	186	25	subclass	subclass	NOUN
ejpam-221	186	26	of	of	ADP
ejpam-221	186	27	right	right	ADJ
ejpam-221	186	28	adequate	adequate	ADJ
ejpam-221	186	29	monoids	monoid	NOUN
ejpam-221	186	30	,	,	PUNCT
ejpam-221	186	31	which	which	PRON
ejpam-221	186	32	he	he	PRON
ejpam-221	186	33	termed	term	VERB
ejpam-221	186	34	right	right	ADJ
ejpam-221	186	35	type	type	NOUN
ejpam-221	186	36	a	a	DET
ejpam-221	186	37	monoids	monoid	NOUN
ejpam-221	186	38	.	.	PUNCT
ejpam-221	187	1	a	a	DET
ejpam-221	187	2	right	right	ADV
ejpam-221	187	3	adequate	adequate	ADJ
ejpam-221	187	4	monoid	monoid	PROPN
ejpam-221	187	5	s	s	X
ejpam-221	187	6	is	be	AUX
ejpam-221	187	7	right	right	ADJ
ejpam-221	187	8	type	type	NOUN
ejpam-221	187	9	a	a	DET
ejpam-221	187	10	if	if	NOUN
ejpam-221	187	11	,	,	PUNCT
ejpam-221	187	12	and	and	CCONJ
ejpam-221	187	13	only	only	ADV
ejpam-221	187	14	if	if	SCONJ
ejpam-221	187	15	,	,	PUNCT
ejpam-221	187	16	es	es	ADP
ejpam-221	187	17	∩	∩	NOUN
ejpam-221	187	18	as	as	ADP
ejpam-221	187	19	=	=	PROPN
ejpam-221	187	20	eas	ea	NOUN
ejpam-221	187	21	,	,	PUNCT
ejpam-221	187	22	for	for	ADP
ejpam-221	187	23	a	a	DET
ejpam-221	187	24	∈	∈	PROPN
ejpam-221	187	25	s	s	PART
ejpam-221	187	26	and	and	CCONJ
ejpam-221	187	27	e	e	PROPN
ejpam-221	187	28	∈	∈	PROPN
ejpam-221	187	29	e(s	e(s	PROPN
ejpam-221	187	30	)	)	PUNCT
ejpam-221	187	31	.	.	PUNCT
ejpam-221	188	1	(	(	PUNCT
ejpam-221	188	2	1.2	1.2	NUM
ejpam-221	188	3	)	)	PUNCT
ejpam-221	188	4	similarly	similarly	ADV
ejpam-221	188	5	,	,	PUNCT
ejpam-221	188	6	a	a	DET
ejpam-221	188	7	left	left	ADJ
ejpam-221	188	8	adequate	adequate	ADJ
ejpam-221	188	9	monoid	monoid	PROPN
ejpam-221	188	10	s	s	X
ejpam-221	188	11	is	be	AUX
ejpam-221	188	12	left	leave	VERB
ejpam-221	188	13	type	type	NOUN
ejpam-221	188	14	a	a	DET
ejpam-221	188	15	if	if	NOUN
ejpam-221	188	16	,	,	PUNCT
ejpam-221	188	17	and	and	CCONJ
ejpam-221	188	18	only	only	ADV
ejpam-221	188	19	if	if	SCONJ
ejpam-221	188	20	,	,	PUNCT
ejpam-221	188	21	se	se	PROPN
ejpam-221	188	22	∩	∩	PROPN
ejpam-221	188	23	sa	sa	PROPN
ejpam-221	188	24	=	=	SYM
ejpam-221	188	25	sea	sea	PROPN
ejpam-221	188	26	,	,	PUNCT
ejpam-221	188	27	for	for	ADP
ejpam-221	188	28	a	a	DET
ejpam-221	188	29	∈	∈	PROPN
ejpam-221	188	30	s	s	PART
ejpam-221	188	31	and	and	CCONJ
ejpam-221	188	32	e	e	PROPN
ejpam-221	188	33	∈	∈	PROPN
ejpam-221	188	34	e(s	e(s	PROPN
ejpam-221	188	35	)	)	PUNCT
ejpam-221	188	36	;	;	PUNCT
ejpam-221	188	37	(	(	PUNCT
ejpam-221	188	38	1.3	1.3	NUM
ejpam-221	188	39	)	)	PUNCT
ejpam-221	188	40	a	a	DET
ejpam-221	188	41	monoid	monoid	NOUN
ejpam-221	188	42	which	which	PRON
ejpam-221	188	43	is	be	AUX
ejpam-221	188	44	both	both	PRON
ejpam-221	188	45	left	leave	VERB
ejpam-221	188	46	and	and	CCONJ
ejpam-221	188	47	right	right	ADJ
ejpam-221	188	48	type	type	NOUN
ejpam-221	188	49	a	a	PRON
ejpam-221	188	50	is	be	AUX
ejpam-221	188	51	called	call	VERB
ejpam-221	188	52	simply	simply	ADV
ejpam-221	188	53	type	type	NOUN
ejpam-221	188	54	a.¶	a.¶	NOUN
ejpam-221	188	55	we	we	PRON
ejpam-221	188	56	note	note	VERB
ejpam-221	188	57	that	that	SCONJ
ejpam-221	188	58	every	every	DET
ejpam-221	188	59	inverse	inverse	NOUN
ejpam-221	188	60	semigroup	semigroup	NOUN
ejpam-221	188	61	is	be	AUX
ejpam-221	188	62	(	(	PUNCT
ejpam-221	188	63	left	left	ADJ
ejpam-221	188	64	/	/	SYM
ejpam-221	188	65	right	right	ADJ
ejpam-221	188	66	)	)	PUNCT
ejpam-221	188	67	type	type	NOUN
ejpam-221	188	68	a	a	DET
ejpam-221	188	69	(	(	PUNCT
ejpam-221	188	70	see	see	NOUN
ejpam-221	188	71	section	section	NOUN
ejpam-221	188	72	5	5	NUM
ejpam-221	188	73	)	)	PUNCT
ejpam-221	188	74	.	.	PUNCT
ejpam-221	189	1	the	the	DET
ejpam-221	189	2	terminology	terminology	NOUN
ejpam-221	189	3	‘	'	PUNCT
ejpam-221	189	4	type	type	NOUN
ejpam-221	189	5	a	a	PRON
ejpam-221	189	6	’	'	PUNCT
ejpam-221	189	7	was	be	AUX
ejpam-221	189	8	subsequently	subsequently	ADV
ejpam-221	189	9	replaced	replace	VERB
ejpam-221	189	10	by	by	ADP
ejpam-221	189	11	the	the	DET
ejpam-221	189	12	term	term	NOUN
ejpam-221	189	13	‘	'	PUNCT
ejpam-221	189	14	ample	ample	ADJ
ejpam-221	189	15	’	'	PUNCT
ejpam-221	189	16	,	,	PUNCT
ejpam-221	189	17	as	as	SCONJ
ejpam-221	189	18	we	we	PRON
ejpam-221	189	19	will	will	AUX
ejpam-221	189	20	see	see	VERB
ejpam-221	189	21	.	.	PUNCT
ejpam-221	190	1	we	we	PRON
ejpam-221	190	2	have	have	VERB
ejpam-221	190	3	the	the	DET
ejpam-221	190	4	following	follow	VERB
ejpam-221	190	5	analogue	analogue	NOUN
ejpam-221	190	6	of	of	ADP
ejpam-221	190	7	mcalister	mcalister	PROPN
ejpam-221	190	8	’s	’s	PART
ejpam-221	190	9	covering	covering	NOUN
ejpam-221	190	10	theorem	theorem	NOUN
ejpam-221	190	11	:	:	PUNCT
ejpam-221	190	12	theorem	theorem	NOUN
ejpam-221	190	13	1.14	1.14	NUM
ejpam-221	190	14	.	.	PUNCT
ejpam-221	191	1	[	[	X
ejpam-221	191	2	22	22	NUM
ejpam-221	191	3	,	,	PUNCT
ejpam-221	191	4	theorem	theorem	VERB
ejpam-221	191	5	3.3	3.3	NUM
ejpam-221	191	6	]	]	PUNCT
ejpam-221	191	7	every	every	DET
ejpam-221	191	8	right	right	ADJ
ejpam-221	191	9	type	type	NOUN
ejpam-221	191	10	a	a	DET
ejpam-221	191	11	monoid	monoid	NOUN
ejpam-221	191	12	is	be	AUX
ejpam-221	191	13	the	the	DET
ejpam-221	191	14	image	image	NOUN
ejpam-221	191	15	of	of	ADP
ejpam-221	191	16	a	a	DET
ejpam-221	191	17	proper	proper	ADJ
ejpam-221	191	18	right	right	ADJ
ejpam-221	191	19	type	type	NOUN
ejpam-221	191	20	a	a	DET
ejpam-221	191	21	monoid	monoid	NOUN
ejpam-221	191	22	under	under	ADP
ejpam-221	191	23	an	an	DET
ejpam-221	191	24	l	l	NOUN
ejpam-221	191	25	∗-morphism	∗-morphism	NOUN
ejpam-221	191	26	,	,	PUNCT
ejpam-221	191	27	where	where	SCONJ
ejpam-221	191	28	an	an	DET
ejpam-221	191	29	l	l	NOUN
ejpam-221	191	30	∗-morphism	∗-morphism	NOUN
ejpam-221	191	31	is	be	AUX
ejpam-221	191	32	a	a	DET
ejpam-221	191	33	morphism	morphism	ADJ
ejpam-221	191	34	θ	θ	PROPN
ejpam-221	191	35	for	for	ADP
ejpam-221	191	36	which	which	PRON
ejpam-221	191	37	sθ	sθ	ADP
ejpam-221	191	38	=	=	NOUN
ejpam-221	191	39	tθ	tθ	NOUN
ejpam-221	191	40	=	=	NOUN
ejpam-221	191	41	⇒	⇒	NOUN
ejpam-221	191	42	sl	sl	NOUN
ejpam-221	191	43	∗	∗	NOUN
ejpam-221	191	44	t.	t.	NOUN
ejpam-221	191	45	recall	recall	NOUN
ejpam-221	191	46	that	that	SCONJ
ejpam-221	191	47	an	an	DET
ejpam-221	191	48	inverse	inverse	NOUN
ejpam-221	191	49	semigroup	semigroup	NOUN
ejpam-221	191	50	s	s	VERB
ejpam-221	191	51	is	be	AUX
ejpam-221	191	52	e	e	NOUN
ejpam-221	191	53	-	-	NOUN
ejpam-221	191	54	unitary	unitary	ADJ
ejpam-221	191	55	if	if	NOUN
ejpam-221	191	56	,	,	PUNCT
ejpam-221	191	57	and	and	CCONJ
ejpam-221	191	58	only	only	ADV
ejpam-221	191	59	if	if	SCONJ
ejpam-221	191	60	,	,	PUNCT
ejpam-221	191	61	it	it	PRON
ejpam-221	191	62	is	be	AUX
ejpam-221	191	63	proper	proper	ADJ
ejpam-221	191	64	[	[	X
ejpam-221	191	65	37	37	NUM
ejpam-221	191	66	,	,	PUNCT
ejpam-221	191	67	proposition	proposition	NOUN
ejpam-221	191	68	5.9.1	5.9.1	NUM
ejpam-221	191	69	]	]	PUNCT
ejpam-221	191	70	.	.	PUNCT
ejpam-221	192	1	however	however	ADV
ejpam-221	192	2	,	,	PUNCT
ejpam-221	192	3	after	after	ADP
ejpam-221	192	4	defining	define	VERB
ejpam-221	192	5	an	an	DET
ejpam-221	192	6	appropriate	appropriate	ADJ
ejpam-221	192	7	notion	notion	NOUN
ejpam-221	192	8	of	of	ADP
ejpam-221	192	9	‘	'	PUNCT
ejpam-221	192	10	proper	proper	ADJ
ejpam-221	192	11	’	'	PUNCT
ejpam-221	192	12	,	,	PUNCT
ejpam-221	192	13	fountain	fountain	NOUN
ejpam-221	192	14	observed	observe	VERB
ejpam-221	192	15	that	that	SCONJ
ejpam-221	192	16	an	an	DET
ejpam-221	192	17	e	e	NOUN
ejpam-221	192	18	-	-	NOUN
ejpam-221	192	19	unitary	unitary	ADJ
ejpam-221	192	20	right	right	ADJ
ejpam-221	192	21	type	type	NOUN
ejpam-221	192	22	a	a	DET
ejpam-221	192	23	monoid	monoid	NOUN
ejpam-221	192	24	need	need	AUX
ejpam-221	192	25	not	not	PART
ejpam-221	192	26	be	be	AUX
ejpam-221	192	27	proper	proper	ADJ
ejpam-221	192	28	in	in	ADP
ejpam-221	192	29	this	this	DET
ejpam-221	192	30	sense	sense	NOUN
ejpam-221	192	31	—	—	PUNCT
ejpam-221	192	32	see	see	VERB
ejpam-221	192	33	[	[	X
ejpam-221	192	34	22	22	NUM
ejpam-221	192	35	,	,	PUNCT
ejpam-221	192	36	example	example	NOUN
ejpam-221	192	37	3	3	NUM
ejpam-221	192	38	]	]	PUNCT
ejpam-221	192	39	.	.	PUNCT
ejpam-221	193	1	fountain	fountain	NOUN
ejpam-221	193	2	went	go	VERB
ejpam-221	193	3	on	on	ADP
ejpam-221	193	4	to	to	PART
ejpam-221	193	5	construct	construct	VERB
ejpam-221	193	6	a	a	DET
ejpam-221	193	7	generalisation	generalisation	NOUN
ejpam-221	193	8	of	of	ADP
ejpam-221	193	9	mcalister	mcalister	PROPN
ejpam-221	193	10	’s	’s	PART
ejpam-221	193	11	p	p	NOUN
ejpam-221	193	12	-	-	PUNCT
ejpam-221	193	13	semigroups	semigroup	NOUN
ejpam-221	193	14	,	,	PUNCT
ejpam-221	193	15	which	which	PRON
ejpam-221	193	16	he	he	PRON
ejpam-221	193	17	termed	term	VERB
ejpam-221	193	18	mcalister	mcalister	PROPN
ejpam-221	193	19	monoids	monoid	NOUN
ejpam-221	193	20	.	.	PUNCT
ejpam-221	194	1	using	use	VERB
ejpam-221	194	2	these	these	PRON
ejpam-221	194	3	,	,	PUNCT
ejpam-221	194	4	we	we	PRON
ejpam-221	194	5	have	have	VERB
ejpam-221	194	6	the	the	DET
ejpam-221	194	7	following	follow	VERB
ejpam-221	194	8	analogue	analogue	NOUN
ejpam-221	194	9	of	of	ADP
ejpam-221	194	10	the	the	DET
ejpam-221	194	11	p	p	NOUN
ejpam-221	194	12	-	-	PUNCT
ejpam-221	194	13	theorem	theorem	ADJ
ejpam-221	194	14	:	:	PUNCT
ejpam-221	194	15	¶in	¶in	PROPN
ejpam-221	194	16	[	[	NOUN
ejpam-221	194	17	22	22	NUM
ejpam-221	194	18	]	]	PUNCT
ejpam-221	194	19	,	,	PUNCT
ejpam-221	194	20	fountain	fountain	NOUN
ejpam-221	194	21	used	use	VERB
ejpam-221	194	22	the	the	DET
ejpam-221	194	23	term	term	NOUN
ejpam-221	194	24	‘	'	PUNCT
ejpam-221	194	25	type	type	NOUN
ejpam-221	194	26	a	a	PRON
ejpam-221	194	27	’	'	PUNCT
ejpam-221	194	28	to	to	PART
ejpam-221	194	29	mean	mean	VERB
ejpam-221	194	30	‘	'	PUNCT
ejpam-221	194	31	right	right	ADJ
ejpam-221	194	32	type	type	NOUN
ejpam-221	194	33	a	a	PRON
ejpam-221	194	34	’	'	PUNCT
ejpam-221	194	35	.	.	PUNCT
ejpam-221	195	1	c.	c.	PROPN
ejpam-221	195	2	hollings	holling	NOUN
ejpam-221	195	3	/	/	SYM
ejpam-221	195	4	eur	eur	PROPN
ejpam-221	195	5	.	.	PUNCT
ejpam-221	196	1	j.	j.	PROPN
ejpam-221	196	2	pure	pure	PROPN
ejpam-221	196	3	appl	appl	PROPN
ejpam-221	196	4	.	.	PROPN
ejpam-221	196	5	math	math	PROPN
ejpam-221	196	6	,	,	PUNCT
ejpam-221	196	7	2	2	NUM
ejpam-221	196	8	(	(	PUNCT
ejpam-221	196	9	2009	2009	NUM
ejpam-221	196	10	)	)	PUNCT
ejpam-221	196	11	,	,	PUNCT
ejpam-221	196	12	(	(	PUNCT
ejpam-221	196	13	21	21	NUM
ejpam-221	196	14	-	-	SYM
ejpam-221	196	15	57	57	NUM
ejpam-221	196	16	)	)	PUNCT
ejpam-221	196	17	32	32	NUM
ejpam-221	196	18	theorem	theorem	VERB
ejpam-221	196	19	1.15	1.15	NUM
ejpam-221	196	20	.	.	PUNCT
ejpam-221	197	1	[	[	X
ejpam-221	197	2	22	22	NUM
ejpam-221	197	3	,	,	PUNCT
ejpam-221	197	4	theorem	theorem	VERB
ejpam-221	197	5	4.3	4.3	NUM
ejpam-221	197	6	]	]	PUNCT
ejpam-221	197	7	every	every	DET
ejpam-221	197	8	proper	proper	ADJ
ejpam-221	197	9	right	right	ADJ
ejpam-221	197	10	type	type	NOUN
ejpam-221	197	11	a	a	DET
ejpam-221	197	12	monoid	monoid	NOUN
ejpam-221	197	13	is	be	AUX
ejpam-221	197	14	isomorphic	isomorphic	ADJ
ejpam-221	197	15	to	to	ADP
ejpam-221	197	16	a	a	DET
ejpam-221	197	17	mcalister	mcalister	PROPN
ejpam-221	197	18	monoid	monoid	PROPN
ejpam-221	197	19	.	.	PUNCT
ejpam-221	198	1	these	these	DET
ejpam-221	198	2	theorems	theorem	NOUN
ejpam-221	198	3	are	be	AUX
ejpam-221	198	4	easily	easily	ADV
ejpam-221	198	5	adapted	adapt	VERB
ejpam-221	198	6	to	to	ADP
ejpam-221	198	7	the	the	DET
ejpam-221	198	8	semigroup	semigroup	PROPN
ejpam-221	198	9	case	case	NOUN
ejpam-221	198	10	.	.	PUNCT
ejpam-221	199	1	two	two	NUM
ejpam-221	199	2	-	-	PUNCT
ejpam-221	199	3	sided	sided	ADJ
ejpam-221	199	4	versions	version	NOUN
ejpam-221	199	5	appear	appear	VERB
ejpam-221	199	6	in	in	ADP
ejpam-221	199	7	[	[	X
ejpam-221	199	8	44	44	NUM
ejpam-221	199	9	]	]	PUNCT
ejpam-221	199	10	as	as	ADP
ejpam-221	199	11	theorems	theorem	NOUN
ejpam-221	199	12	3.8	3.8	NUM
ejpam-221	199	13	and	and	CCONJ
ejpam-221	199	14	2.11	2.11	NUM
ejpam-221	199	15	,	,	PUNCT
ejpam-221	199	16	respectively	respectively	ADV
ejpam-221	199	17	.	.	PUNCT
ejpam-221	200	1	there	there	PRON
ejpam-221	200	2	are	be	VERB
ejpam-221	200	3	two	two	NUM
ejpam-221	200	4	other	other	ADJ
ejpam-221	200	5	major	major	ADJ
ejpam-221	200	6	approaches	approach	NOUN
ejpam-221	200	7	to	to	ADP
ejpam-221	200	8	the	the	DET
ejpam-221	200	9	study	study	NOUN
ejpam-221	200	10	of	of	ADP
ejpam-221	200	11	inverse	inverse	NOUN
ejpam-221	200	12	semigroups	semigroup	NOUN
ejpam-221	200	13	:	:	PUNCT
ejpam-221	200	14	that	that	SCONJ
ejpam-221	200	15	which	which	PRON
ejpam-221	200	16	connects	connect	VERB
ejpam-221	200	17	inverse	inverse	NOUN
ejpam-221	200	18	semigroups	semigroup	NOUN
ejpam-221	200	19	with	with	ADP
ejpam-221	200	20	inductive	inductive	ADJ
ejpam-221	200	21	groupoids	groupoid	NOUN
ejpam-221	200	22	,	,	PUNCT
ejpam-221	200	23	and	and	CCONJ
ejpam-221	200	24	that	that	PRON
ejpam-221	200	25	via	via	ADP
ejpam-221	200	26	the	the	DET
ejpam-221	200	27	notion	notion	NOUN
ejpam-221	200	28	of	of	ADP
ejpam-221	200	29	a	a	DET
ejpam-221	200	30	munn	munn	PROPN
ejpam-221	200	31	semigroup	semigroup	PROPN
ejpam-221	200	32	.	.	PUNCT
ejpam-221	201	1	each	each	PRON
ejpam-221	201	2	of	of	ADP
ejpam-221	201	3	these	these	DET
ejpam-221	201	4	methods	method	NOUN
ejpam-221	201	5	may	may	AUX
ejpam-221	201	6	be	be	AUX
ejpam-221	201	7	extended	extend	VERB
ejpam-221	201	8	to	to	ADP
ejpam-221	201	9	the	the	DET
ejpam-221	201	10	study	study	NOUN
ejpam-221	201	11	of	of	ADP
ejpam-221	201	12	type	type	NOUN
ejpam-221	201	13	a	a	DET
ejpam-221	201	14	semigroups	semigroup	NOUN
ejpam-221	201	15	.	.	PUNCT
ejpam-221	202	1	we	we	PRON
ejpam-221	202	2	first	first	ADV
ejpam-221	202	3	consider	consider	VERB
ejpam-221	202	4	the	the	DET
ejpam-221	202	5	analogue	analogue	NOUN
ejpam-221	202	6	of	of	ADP
ejpam-221	202	7	munn	munn	PROPN
ejpam-221	202	8	’s	’s	PART
ejpam-221	202	9	work	work	NOUN
ejpam-221	202	10	[	[	X
ejpam-221	202	11	57	57	NUM
ejpam-221	202	12	]	]	PUNCT
ejpam-221	202	13	.	.	PUNCT
ejpam-221	203	1	definition	definition	NOUN
ejpam-221	203	2	1.16	1.16	NUM
ejpam-221	203	3	.	.	PUNCT
ejpam-221	204	1	[	[	X
ejpam-221	204	2	37	37	NUM
ejpam-221	204	3	,	,	PUNCT
ejpam-221	204	4	p.	p.	NOUN
ejpam-221	204	5	162	162	NUM
ejpam-221	204	6	]	]	PUNCT
ejpam-221	204	7	let	let	VERB
ejpam-221	204	8	e	e	PRON
ejpam-221	204	9	be	be	AUX
ejpam-221	204	10	a	a	DET
ejpam-221	204	11	semilattice	semilattice	NOUN
ejpam-221	204	12	.	.	PUNCT
ejpam-221	205	1	the	the	DET
ejpam-221	205	2	munn	munn	PROPN
ejpam-221	205	3	semigroup	semigroup	PROPN
ejpam-221	205	4	te	te	PROPN
ejpam-221	205	5	of	of	ADP
ejpam-221	205	6	e	e	PROPN
ejpam-221	205	7	is	be	AUX
ejpam-221	205	8	the	the	DET
ejpam-221	205	9	inverse	inverse	ADJ
ejpam-221	205	10	subsemigroup	subsemigroup	NOUN
ejpam-221	205	11	of	of	ADP
ejpam-221	205	12	ie	ie	PRON
ejpam-221	205	13	which	which	PRON
ejpam-221	205	14	consists	consist	VERB
ejpam-221	205	15	of	of	ADP
ejpam-221	205	16	all	all	DET
ejpam-221	205	17	isomorphisms	isomorphism	NOUN
ejpam-221	205	18	between	between	ADP
ejpam-221	205	19	principal	principal	ADJ
ejpam-221	205	20	ideals	ideal	NOUN
ejpam-221	205	21	of	of	ADP
ejpam-221	205	22	e.	e.	PROPN
ejpam-221	205	23	we	we	PRON
ejpam-221	205	24	note	note	VERB
ejpam-221	205	25	that	that	SCONJ
ejpam-221	205	26	e(te	e(te	PROPN
ejpam-221	205	27	)	)	PUNCT
ejpam-221	205	28	is	be	AUX
ejpam-221	205	29	isomorphic	isomorphic	ADJ
ejpam-221	205	30	to	to	ADP
ejpam-221	205	31	e	e	PROPN
ejpam-221	205	32	[	[	X
ejpam-221	205	33	37	37	NUM
ejpam-221	205	34	,	,	PUNCT
ejpam-221	205	35	theorem	theorem	VERB
ejpam-221	205	36	5.4.1	5.4.1	NUM
ejpam-221	205	37	]	]	PUNCT
ejpam-221	205	38	.	.	PUNCT
ejpam-221	206	1	munn	munn	PROPN
ejpam-221	206	2	’s	’s	PART
ejpam-221	206	3	major	major	ADJ
ejpam-221	206	4	result	result	NOUN
ejpam-221	206	5	was	be	AUX
ejpam-221	206	6	the	the	DET
ejpam-221	206	7	following	following	NOUN
ejpam-221	206	8	:	:	PUNCT
ejpam-221	206	9	theorem	theorem	VERB
ejpam-221	206	10	1.17	1.17	NUM
ejpam-221	206	11	.	.	PUNCT
ejpam-221	207	1	[	[	X
ejpam-221	207	2	37	37	NUM
ejpam-221	207	3	,	,	PUNCT
ejpam-221	207	4	theorem	theorem	VERB
ejpam-221	207	5	5.4.4	5.4.4	NUM
ejpam-221	207	6	]	]	PUNCT
ejpam-221	207	7	for	for	ADP
ejpam-221	207	8	any	any	DET
ejpam-221	207	9	inverse	inverse	NOUN
ejpam-221	207	10	semigroup	semigroup	NOUN
ejpam-221	207	11	s	s	PART
ejpam-221	207	12	,	,	PUNCT
ejpam-221	207	13	there	there	PRON
ejpam-221	207	14	is	be	VERB
ejpam-221	207	15	a	a	DET
ejpam-221	207	16	morphism	morphism	NOUN
ejpam-221	207	17	s	s	PART
ejpam-221	207	18	→	→	SYM
ejpam-221	207	19	te(s	te(s	NUM
ejpam-221	207	20	)	)	PUNCT
ejpam-221	207	21	which	which	PRON
ejpam-221	207	22	maps	map	VERB
ejpam-221	207	23	e(s	e(s	PROPN
ejpam-221	207	24	)	)	PUNCT
ejpam-221	207	25	isomorphically	isomorphically	ADV
ejpam-221	207	26	onto	onto	ADP
ejpam-221	207	27	e(te(s	e(te(s	NOUN
ejpam-221	207	28	)	)	PUNCT
ejpam-221	207	29	)	)	PUNCT
ejpam-221	207	30	and	and	CCONJ
ejpam-221	207	31	which	which	PRON
ejpam-221	207	32	induces	induce	VERB
ejpam-221	207	33	the	the	DET
ejpam-221	207	34	maximum	maximum	ADJ
ejpam-221	207	35	idempotentseparating	idempotentseparate	VERB
ejpam-221	207	36	congruence	congruence	NOUN
ejpam-221	207	37	on	on	ADP
ejpam-221	207	38	s.	s.	PROPN
ejpam-221	207	39	in	in	ADP
ejpam-221	207	40	[	[	X
ejpam-221	207	41	24	24	NUM
ejpam-221	207	42	]	]	PUNCT
ejpam-221	207	43	,	,	PUNCT
ejpam-221	207	44	fountain	fountain	NOUN
ejpam-221	207	45	investigated	investigate	VERB
ejpam-221	207	46	the	the	DET
ejpam-221	207	47	generalisation	generalisation	NOUN
ejpam-221	207	48	of	of	ADP
ejpam-221	207	49	this	this	DET
ejpam-221	207	50	result	result	NOUN
ejpam-221	207	51	to	to	ADP
ejpam-221	207	52	the	the	DET
ejpam-221	207	53	case	case	NOUN
ejpam-221	207	54	of	of	ADP
ejpam-221	207	55	adequate	adequate	ADJ
ejpam-221	207	56	semigroups	semigroup	NOUN
ejpam-221	207	57	.	.	PUNCT
ejpam-221	208	1	he	he	PRON
ejpam-221	208	2	observed	observe	VERB
ejpam-221	208	3	,	,	PUNCT
ejpam-221	208	4	however	however	ADV
ejpam-221	208	5	,	,	PUNCT
ejpam-221	208	6	that	that	SCONJ
ejpam-221	208	7	an	an	DET
ejpam-221	208	8	adequate	adequate	ADJ
ejpam-221	208	9	semigroup	semigroup	NOUN
ejpam-221	208	10	need	need	AUX
ejpam-221	208	11	not	not	PART
ejpam-221	208	12	have	have	VERB
ejpam-221	208	13	a	a	DET
ejpam-221	208	14	largest	large	ADJ
ejpam-221	208	15	idempotent	idempotent	ADJ
ejpam-221	208	16	-	-	PUNCT
ejpam-221	208	17	separting	separte	VERB
ejpam-221	208	18	congruence	congruence	NOUN
ejpam-221	208	19	.	.	PUNCT
ejpam-221	209	1	it	it	PRON
ejpam-221	209	2	was	be	AUX
ejpam-221	209	3	therefore	therefore	ADV
ejpam-221	209	4	necessary	necessary	ADJ
ejpam-221	209	5	to	to	PART
ejpam-221	209	6	pursue	pursue	VERB
ejpam-221	209	7	the	the	DET
ejpam-221	209	8	generalisation	generalisation	NOUN
ejpam-221	209	9	down	down	ADP
ejpam-221	209	10	a	a	DET
ejpam-221	209	11	slightly	slightly	ADV
ejpam-221	209	12	different	different	ADJ
ejpam-221	209	13	path	path	NOUN
ejpam-221	209	14	.	.	PUNCT
ejpam-221	210	1	as	as	SCONJ
ejpam-221	210	2	determined	determine	VERB
ejpam-221	210	3	by	by	ADP
ejpam-221	210	4	munn	munn	PROPN
ejpam-221	211	1	[	[	X
ejpam-221	211	2	56	56	NUM
ejpam-221	211	3	]	]	PUNCT
ejpam-221	211	4	,	,	PUNCT
ejpam-221	211	5	the	the	DET
ejpam-221	211	6	maximum	maximum	ADJ
ejpam-221	211	7	idempotentseparating	idempotentseparate	VERB
ejpam-221	211	8	congruence	congruence	NOUN
ejpam-221	211	9	on	on	ADP
ejpam-221	211	10	an	an	DET
ejpam-221	211	11	inverse	inverse	NOUN
ejpam-221	211	12	semigroup	semigroup	NOUN
ejpam-221	211	13	is	be	AUX
ejpam-221	211	14	the	the	DET
ejpam-221	211	15	largest	large	ADJ
ejpam-221	211	16	congruence	congruence	NOUN
ejpam-221	211	17	contained	contain	VERB
ejpam-221	211	18	in	in	ADP
ejpam-221	211	19	green	green	PROPN
ejpam-221	211	20	’s	’s	PART
ejpam-221	211	21	relation	relation	NOUN
ejpam-221	211	22	h	h	NOUN
ejpam-221	211	23	.	.	PUNCT
ejpam-221	212	1	fountain	fountain	NOUN
ejpam-221	212	2	therefore	therefore	ADV
ejpam-221	212	3	investigated	investigate	VERB
ejpam-221	212	4	the	the	DET
ejpam-221	212	5	largest	large	ADJ
ejpam-221	212	6	congruence	congruence	NOUN
ejpam-221	212	7	contained	contain	VERB
ejpam-221	212	8	in	in	ADP
ejpam-221	212	9	h	h	NOUN
ejpam-221	212	10	∗	∗	NOUN
ejpam-221	212	11	=	=	PUNCT
ejpam-221	212	12	r∗	r∗	PROPN
ejpam-221	212	13	∩	∩	NOUN
ejpam-221	212	14	l	l	NOUN
ejpam-221	212	15	∗	∗	NOUN
ejpam-221	212	16	;	;	PUNCT
ejpam-221	212	17	any	any	DET
ejpam-221	212	18	congruence	congruence	NOUN
ejpam-221	212	19	contained	contain	VERB
ejpam-221	212	20	in	in	ADP
ejpam-221	212	21	h	h	PROPN
ejpam-221	212	22	∗	∗	NOUN
ejpam-221	212	23	is	be	AUX
ejpam-221	212	24	idempotent	idempotent	ADJ
ejpam-221	212	25	-	-	PUNCT
ejpam-221	212	26	separating	separate	VERB
ejpam-221	212	27	,	,	PUNCT
ejpam-221	212	28	but	but	CCONJ
ejpam-221	212	29	the	the	DET
ejpam-221	212	30	converse	converse	NOUN
ejpam-221	212	31	is	be	AUX
ejpam-221	212	32	not	not	PART
ejpam-221	212	33	necessarily	necessarily	ADV
ejpam-221	212	34	true	true	ADJ
ejpam-221	212	35	.	.	PUNCT
ejpam-221	213	1	moreover	moreover	ADV
ejpam-221	213	2	,	,	PUNCT
ejpam-221	213	3	it	it	PRON
ejpam-221	213	4	once	once	ADV
ejpam-221	213	5	again	again	ADV
ejpam-221	213	6	transpired	transpire	VERB
ejpam-221	213	7	that	that	SCONJ
ejpam-221	213	8	if	if	SCONJ
ejpam-221	213	9	one	one	PRON
ejpam-221	213	10	is	be	AUX
ejpam-221	213	11	to	to	PART
ejpam-221	213	12	develop	develop	VERB
ejpam-221	213	13	a	a	DET
ejpam-221	213	14	suitable	suitable	ADJ
ejpam-221	213	15	analogue	analogue	NOUN
ejpam-221	213	16	of	of	ADP
ejpam-221	213	17	theorem	theorem	NOUN
ejpam-221	213	18	1.17	1.17	NUM
ejpam-221	213	19	,	,	PUNCT
ejpam-221	213	20	then	then	ADV
ejpam-221	213	21	one	one	PRON
ejpam-221	213	22	must	must	AUX
ejpam-221	213	23	once	once	ADV
ejpam-221	213	24	again	again	ADV
ejpam-221	213	25	restrict	restrict	VERB
ejpam-221	213	26	one	one	NUM
ejpam-221	213	27	’s	’s	PART
ejpam-221	213	28	attention	attention	NOUN
ejpam-221	213	29	to	to	PART
ejpam-221	213	30	type	type	VERB
ejpam-221	213	31	a	a	DET
ejpam-221	213	32	semigroups	semigroup	NOUN
ejpam-221	213	33	:	:	PUNCT
ejpam-221	213	34	theorem	theorem	NOUN
ejpam-221	213	35	1.18	1.18	NUM
ejpam-221	213	36	.	.	PUNCT
ejpam-221	214	1	[	[	X
ejpam-221	214	2	24	24	NUM
ejpam-221	214	3	,	,	PUNCT
ejpam-221	214	4	proposition	proposition	NOUN
ejpam-221	214	5	4.5	4.5	NUM
ejpam-221	214	6	]	]	PUNCT
ejpam-221	214	7	for	for	ADP
ejpam-221	214	8	any	any	DET
ejpam-221	214	9	type	type	NOUN
ejpam-221	214	10	a	a	DET
ejpam-221	214	11	semigroup	semigroup	NOUN
ejpam-221	214	12	s	s	NOUN
ejpam-221	214	13	,	,	PUNCT
ejpam-221	214	14	there	there	PRON
ejpam-221	214	15	is	be	VERB
ejpam-221	214	16	a	a	DET
ejpam-221	214	17	morphism	morphism	NOUN
ejpam-221	214	18	s	s	PART
ejpam-221	214	19	→	→	SYM
ejpam-221	214	20	te(s	te(s	NUM
ejpam-221	214	21	)	)	PUNCT
ejpam-221	214	22	which	which	PRON
ejpam-221	214	23	maps	map	VERB
ejpam-221	214	24	e(s	e(s	PROPN
ejpam-221	214	25	)	)	PUNCT
ejpam-221	214	26	isomorphically	isomorphically	ADV
ejpam-221	214	27	onto	onto	ADP
ejpam-221	214	28	e(te(s	e(te(s	NOUN
ejpam-221	214	29	)	)	PUNCT
ejpam-221	214	30	)	)	PUNCT
ejpam-221	214	31	and	and	CCONJ
ejpam-221	214	32	which	which	PRON
ejpam-221	214	33	induces	induce	VERB
ejpam-221	214	34	the	the	DET
ejpam-221	214	35	largest	large	ADJ
ejpam-221	214	36	congruence	congruence	NOUN
ejpam-221	214	37	contained	contain	VERB
ejpam-221	214	38	inh	inh	PROPN
ejpam-221	214	39	∗.	∗.	PROPN
ejpam-221	214	40	c.	c.	PROPN
ejpam-221	214	41	hollings	holling	NOUN
ejpam-221	214	42	/	/	SYM
ejpam-221	214	43	eur	eur	PROPN
ejpam-221	214	44	.	.	PUNCT
ejpam-221	215	1	j.	j.	PROPN
ejpam-221	215	2	pure	pure	PROPN
ejpam-221	215	3	appl	appl	PROPN
ejpam-221	215	4	.	.	PROPN
ejpam-221	215	5	math	math	PROPN
ejpam-221	215	6	,	,	PUNCT
ejpam-221	215	7	2	2	NUM
ejpam-221	215	8	(	(	PUNCT
ejpam-221	215	9	2009	2009	NUM
ejpam-221	215	10	)	)	PUNCT
ejpam-221	215	11	,	,	PUNCT
ejpam-221	215	12	(	(	PUNCT
ejpam-221	215	13	21	21	NUM
ejpam-221	215	14	-	-	SYM
ejpam-221	215	15	57	57	NUM
ejpam-221	215	16	)	)	PUNCT
ejpam-221	215	17	33	33	NUM
ejpam-221	215	18	as	as	SCONJ
ejpam-221	215	19	commented	comment	VERB
ejpam-221	215	20	above	above	ADV
ejpam-221	215	21	,	,	PUNCT
ejpam-221	215	22	another	another	DET
ejpam-221	215	23	major	major	ADJ
ejpam-221	215	24	approach	approach	NOUN
ejpam-221	215	25	to	to	ADP
ejpam-221	215	26	the	the	DET
ejpam-221	215	27	study	study	NOUN
ejpam-221	215	28	of	of	ADP
ejpam-221	215	29	the	the	DET
ejpam-221	215	30	structure	structure	NOUN
ejpam-221	215	31	of	of	ADP
ejpam-221	215	32	inverse	inverse	NOUN
ejpam-221	215	33	semigroups	semigroup	NOUN
ejpam-221	215	34	is	be	AUX
ejpam-221	215	35	that	that	SCONJ
ejpam-221	215	36	via	via	ADP
ejpam-221	215	37	the	the	DET
ejpam-221	215	38	notion	notion	NOUN
ejpam-221	215	39	of	of	ADP
ejpam-221	215	40	an	an	DET
ejpam-221	215	41	inductive	inductive	ADJ
ejpam-221	215	42	groupoid	groupoid	NOUN
ejpam-221	215	43	:	:	PUNCT
ejpam-221	215	44	a	a	DET
ejpam-221	215	45	type	type	NOUN
ejpam-221	215	46	of	of	ADP
ejpam-221	215	47	small	small	ADJ
ejpam-221	215	48	,	,	PUNCT
ejpam-221	215	49	ordered	order	VERB
ejpam-221	215	50	category	category	NOUN
ejpam-221	215	51	in	in	ADP
ejpam-221	215	52	which	which	PRON
ejpam-221	215	53	all	all	DET
ejpam-221	215	54	arrows	arrow	NOUN
ejpam-221	215	55	are	be	AUX
ejpam-221	215	56	invertible	invertible	ADJ
ejpam-221	215	57	.	.	PUNCT
ejpam-221	216	1	inverse	inverse	NOUN
ejpam-221	216	2	semigroups	semigroup	NOUN
ejpam-221	216	3	and	and	CCONJ
ejpam-221	216	4	inductive	inductive	ADJ
ejpam-221	216	5	groupoids	groupoid	NOUN
ejpam-221	216	6	are	be	AUX
ejpam-221	216	7	two	two	NUM
ejpam-221	216	8	solutions	solution	NOUN
ejpam-221	216	9	to	to	ADP
ejpam-221	216	10	the	the	DET
ejpam-221	216	11	problem	problem	NOUN
ejpam-221	216	12	of	of	ADP
ejpam-221	216	13	finding	find	VERB
ejpam-221	216	14	an	an	DET
ejpam-221	216	15	abstract	abstract	ADJ
ejpam-221	216	16	version	version	NOUN
ejpam-221	216	17	of	of	ADP
ejpam-221	216	18	the	the	DET
ejpam-221	216	19	pseudogroups	pseudogroup	NOUN
ejpam-221	216	20	of	of	ADP
ejpam-221	216	21	veblen	veblen	PROPN
ejpam-221	216	22	and	and	CCONJ
ejpam-221	216	23	whitehead	whitehead	PROPN
ejpam-221	217	1	[	[	X
ejpam-221	217	2	77	77	NUM
ejpam-221	217	3	,	,	PUNCT
ejpam-221	217	4	p.	p.	NOUN
ejpam-221	217	5	38	38	NUM
ejpam-221	217	6	]	]	PUNCT
ejpam-221	217	7	.	.	PUNCT
ejpam-221	218	1	the	the	DET
ejpam-221	218	2	inductive	inductive	ADJ
ejpam-221	218	3	groupoid	groupoid	PROPN
ejpam-221	218	4	approach	approach	NOUN
ejpam-221	218	5	was	be	AUX
ejpam-221	218	6	pioneered	pioneer	VERB
ejpam-221	218	7	by	by	ADP
ejpam-221	218	8	ehresmann	ehresmann	PROPN
ejpam-221	219	1	[	[	X
ejpam-221	219	2	11	11	NUM
ejpam-221	219	3	,	,	PUNCT
ejpam-221	219	4	13	13	NUM
ejpam-221	219	5	]	]	PUNCT
ejpam-221	219	6	,	,	PUNCT
ejpam-221	219	7	whilst	whilst	SCONJ
ejpam-221	219	8	inverse	inverse	NOUN
ejpam-221	219	9	semigroups	semigroup	NOUN
ejpam-221	219	10	were	be	AUX
ejpam-221	219	11	introduced	introduce	VERB
ejpam-221	219	12	independently	independently	ADV
ejpam-221	219	13	by	by	ADP
ejpam-221	219	14	wagner	wagner	PROPN
ejpam-221	219	15	and	and	CCONJ
ejpam-221	219	16	preston	preston	PROPN
ejpam-221	219	17	,	,	PUNCT
ejpam-221	219	18	as	as	SCONJ
ejpam-221	219	19	we	we	PRON
ejpam-221	219	20	have	have	AUX
ejpam-221	219	21	seen	see	VERB
ejpam-221	219	22	.	.	PUNCT
ejpam-221	220	1	thus	thus	ADV
ejpam-221	220	2	,	,	PUNCT
ejpam-221	220	3	given	give	VERB
ejpam-221	220	4	that	that	DET
ejpam-221	220	5	inverse	inverse	NOUN
ejpam-221	220	6	semigroups	semigroup	NOUN
ejpam-221	220	7	and	and	CCONJ
ejpam-221	220	8	inductive	inductive	ADJ
ejpam-221	220	9	groupoids	groupoid	NOUN
ejpam-221	220	10	share	share	VERB
ejpam-221	220	11	a	a	DET
ejpam-221	220	12	common	common	ADJ
ejpam-221	220	13	origin	origin	NOUN
ejpam-221	220	14	,	,	PUNCT
ejpam-221	220	15	it	it	PRON
ejpam-221	220	16	is	be	AUX
ejpam-221	220	17	not	not	PART
ejpam-221	220	18	surprising	surprising	ADJ
ejpam-221	220	19	that	that	SCONJ
ejpam-221	220	20	their	their	PRON
ejpam-221	220	21	respective	respective	ADJ
ejpam-221	220	22	theories	theory	NOUN
ejpam-221	220	23	can	can	AUX
ejpam-221	220	24	be	be	AUX
ejpam-221	220	25	connected	connect	VERB
ejpam-221	220	26	in	in	ADP
ejpam-221	220	27	an	an	DET
ejpam-221	220	28	extremely	extremely	ADV
ejpam-221	220	29	natural	natural	ADJ
ejpam-221	220	30	way	way	NOUN
ejpam-221	220	31	.	.	PUNCT
ejpam-221	221	1	this	this	DET
ejpam-221	221	2	linking	linking	NOUN
ejpam-221	221	3	of	of	ADP
ejpam-221	221	4	theories	theory	NOUN
ejpam-221	221	5	was	be	AUX
ejpam-221	221	6	pieced	piece	VERB
ejpam-221	221	7	together	together	ADV
ejpam-221	221	8	by	by	ADP
ejpam-221	221	9	a	a	DET
ejpam-221	221	10	number	number	NOUN
ejpam-221	221	11	of	of	ADP
ejpam-221	221	12	authors	author	NOUN
ejpam-221	221	13	[	[	X
ejpam-221	221	14	11	11	NUM
ejpam-221	221	15	,	,	PUNCT
ejpam-221	221	16	12	12	NUM
ejpam-221	221	17	,	,	PUNCT
ejpam-221	221	18	58	58	NUM
ejpam-221	221	19	,	,	PUNCT
ejpam-221	221	20	63	63	NUM
ejpam-221	221	21	,	,	PUNCT
ejpam-221	221	22	65	65	NUM
ejpam-221	221	23	]	]	PUNCT
ejpam-221	221	24	and	and	CCONJ
ejpam-221	221	25	is	be	AUX
ejpam-221	221	26	enshrined	enshrine	VERB
ejpam-221	221	27	in	in	ADP
ejpam-221	221	28	the	the	DET
ejpam-221	221	29	following	following	ADJ
ejpam-221	221	30	result	result	NOUN
ejpam-221	221	31	,	,	PUNCT
ejpam-221	221	32	named	name	VERB
ejpam-221	221	33	the	the	DET
ejpam-221	221	34	ehresmann	ehresmann	PROPN
ejpam-221	221	35	-	-	PUNCT
ejpam-221	221	36	schein	schein	PROPN
ejpam-221	221	37	-	-	PUNCT
ejpam-221	221	38	nambooripad	nambooripad	NOUN
ejpam-221	221	39	theorem	theorem	NOUN
ejpam-221	221	40	to	to	PART
ejpam-221	221	41	reflect	reflect	VERB
ejpam-221	221	42	its	its	PRON
ejpam-221	221	43	disparate	disparate	ADJ
ejpam-221	221	44	origins	origin	NOUN
ejpam-221	221	45	:	:	PUNCT
ejpam-221	221	46	theorem	theorem	VERB
ejpam-221	221	47	1.19	1.19	NUM
ejpam-221	221	48	.	.	PUNCT
ejpam-221	222	1	[	[	X
ejpam-221	222	2	49	49	NUM
ejpam-221	222	3	,	,	PUNCT
ejpam-221	222	4	theorem	theorem	VERB
ejpam-221	222	5	4.1.8	4.1.8	NUM
ejpam-221	222	6	]	]	X
ejpam-221	222	7	the	the	DET
ejpam-221	222	8	category	category	NOUN
ejpam-221	222	9	of	of	ADP
ejpam-221	222	10	inverse	inverse	NOUN
ejpam-221	222	11	semigroups	semigroup	NOUN
ejpam-221	222	12	and	and	CCONJ
ejpam-221	222	13	∨-premorphisms	∨-premorphism	NOUN
ejpam-221	222	14	is	be	AUX
ejpam-221	222	15	isomorphic	isomorphic	ADJ
ejpam-221	222	16	to	to	ADP
ejpam-221	222	17	the	the	DET
ejpam-221	222	18	category	category	NOUN
ejpam-221	222	19	of	of	ADP
ejpam-221	222	20	inductive	inductive	ADJ
ejpam-221	222	21	groupoids	groupoid	NOUN
ejpam-221	222	22	and	and	CCONJ
ejpam-221	222	23	ordered	order	VERB
ejpam-221	222	24	functors	functor	NOUN
ejpam-221	222	25	;	;	PUNCT
ejpam-221	222	26	the	the	DET
ejpam-221	222	27	category	category	NOUN
ejpam-221	222	28	of	of	ADP
ejpam-221	222	29	inverse	inverse	NOUN
ejpam-221	222	30	semigroups	semigroup	NOUN
ejpam-221	222	31	and	and	CCONJ
ejpam-221	222	32	morphisms	morphism	NOUN
ejpam-221	222	33	is	be	AUX
ejpam-221	222	34	isomorphic	isomorphic	ADJ
ejpam-221	222	35	to	to	ADP
ejpam-221	222	36	the	the	DET
ejpam-221	222	37	category	category	NOUN
ejpam-221	222	38	of	of	ADP
ejpam-221	222	39	inductive	inductive	ADJ
ejpam-221	222	40	groupoids	groupoid	NOUN
ejpam-221	222	41	and	and	CCONJ
ejpam-221	222	42	inductive	inductive	ADJ
ejpam-221	222	43	functors	functor	NOUN
ejpam-221	222	44	.	.	PUNCT
ejpam-221	223	1	(	(	PUNCT
ejpam-221	223	2	an	an	DET
ejpam-221	223	3	ordered	order	VERB
ejpam-221	223	4	functor	functor	NOUN
ejpam-221	223	5	is	be	AUX
ejpam-221	223	6	simply	simply	ADV
ejpam-221	223	7	an	an	DET
ejpam-221	223	8	order	order	NOUN
ejpam-221	223	9	-	-	PUNCT
ejpam-221	223	10	preserving	preserve	VERB
ejpam-221	223	11	functor	functor	NOUN
ejpam-221	223	12	;	;	PUNCT
ejpam-221	223	13	an	an	DET
ejpam-221	223	14	inductive	inductive	ADJ
ejpam-221	223	15	functor	functor	PROPN
ejpam-221	223	16	is	be	AUX
ejpam-221	223	17	a	a	DET
ejpam-221	223	18	special	special	ADJ
ejpam-221	223	19	type	type	NOUN
ejpam-221	223	20	of	of	ADP
ejpam-221	223	21	ordered	order	VERB
ejpam-221	223	22	functor	functor	PROPN
ejpam-221	223	23	.	.	PUNCT
ejpam-221	224	1	a	a	DET
ejpam-221	224	2	∨-premorphism	∨-premorphism	NOUN
ejpam-221	224	3	is	be	AUX
ejpam-221	224	4	a	a	DET
ejpam-221	224	5	function	function	NOUN
ejpam-221	224	6	θ	θ	NOUN
ejpam-221	224	7	:	:	PUNCT
ejpam-221	224	8	s→	s→	PROPN
ejpam-221	224	9	t	t	NOUN
ejpam-221	224	10	between	between	ADP
ejpam-221	224	11	inverse	inverse	NOUN
ejpam-221	224	12	semigroups	semigroup	NOUN
ejpam-221	224	13	such	such	ADJ
ejpam-221	224	14	that	that	SCONJ
ejpam-221	224	15	(	(	PUNCT
ejpam-221	224	16	st)θ	st)θ	PROPN
ejpam-221	224	17	≤	≤	NOUN
ejpam-221	224	18	(	(	PUNCT
ejpam-221	224	19	sθ)(tθ	sθ)(tθ	PROPN
ejpam-221	224	20	)	)	PUNCT
ejpam-221	224	21	.	.	PUNCT
ejpam-221	224	22	)	)	PUNCT
ejpam-221	225	1	further	further	ADJ
ejpam-221	225	2	details	detail	NOUN
ejpam-221	225	3	on	on	ADP
ejpam-221	225	4	the	the	DET
ejpam-221	225	5	ehresmann	ehresmann	PROPN
ejpam-221	225	6	-	-	PUNCT
ejpam-221	225	7	schein	schein	PROPN
ejpam-221	225	8	-	-	PUNCT
ejpam-221	225	9	nambooripad	nambooripad	PROPN
ejpam-221	225	10	theorem	theorem	NOUN
ejpam-221	225	11	can	can	AUX
ejpam-221	225	12	be	be	AUX
ejpam-221	225	13	found	find	VERB
ejpam-221	225	14	in	in	ADP
ejpam-221	225	15	[	[	X
ejpam-221	225	16	49	49	NUM
ejpam-221	225	17	]	]	PUNCT
ejpam-221	225	18	,	,	PUNCT
ejpam-221	225	19	for	for	ADP
ejpam-221	225	20	which	which	DET
ejpam-221	225	21	book	book	NOUN
ejpam-221	225	22	it	it	PRON
ejpam-221	225	23	provides	provide	VERB
ejpam-221	225	24	the	the	DET
ejpam-221	225	25	main	main	ADJ
ejpam-221	225	26	focus	focus	NOUN
ejpam-221	225	27	.	.	PUNCT
ejpam-221	226	1	with	with	SCONJ
ejpam-221	226	2	this	this	DET
ejpam-221	226	3	connection	connection	NOUN
ejpam-221	226	4	between	between	ADP
ejpam-221	226	5	inverse	inverse	NOUN
ejpam-221	226	6	semigroups	semigroup	NOUN
ejpam-221	226	7	and	and	CCONJ
ejpam-221	226	8	inductive	inductive	ADJ
ejpam-221	226	9	groupoids	groupoid	NOUN
ejpam-221	226	10	established	establish	VERB
ejpam-221	226	11	,	,	PUNCT
ejpam-221	226	12	it	it	PRON
ejpam-221	226	13	was	be	AUX
ejpam-221	226	14	natural	natural	ADJ
ejpam-221	226	15	to	to	PART
ejpam-221	226	16	seek	seek	VERB
ejpam-221	226	17	generalisations	generalisation	NOUN
ejpam-221	226	18	.	.	PUNCT
ejpam-221	227	1	the	the	DET
ejpam-221	227	2	regular	regular	ADJ
ejpam-221	227	3	case	case	NOUN
ejpam-221	227	4	,	,	PUNCT
ejpam-221	227	5	for	for	ADP
ejpam-221	227	6	example	example	NOUN
ejpam-221	227	7	,	,	PUNCT
ejpam-221	227	8	was	be	AUX
ejpam-221	227	9	considered	consider	VERB
ejpam-221	227	10	by	by	ADP
ejpam-221	227	11	nambooripad	nambooripad	NOUN
ejpam-221	227	12	[	[	X
ejpam-221	227	13	58	58	NUM
ejpam-221	227	14	]	]	PUNCT
ejpam-221	227	15	.	.	PUNCT
ejpam-221	228	1	but	but	CCONJ
ejpam-221	228	2	what	what	PRON
ejpam-221	228	3	of	of	ADP
ejpam-221	228	4	the	the	DET
ejpam-221	228	5	non	non	ADJ
ejpam-221	228	6	-	-	ADJ
ejpam-221	228	7	regular	regular	ADJ
ejpam-221	228	8	generalisations	generalisation	NOUN
ejpam-221	228	9	of	of	ADP
ejpam-221	228	10	inverse	inverse	NOUN
ejpam-221	228	11	semigroups	semigroup	NOUN
ejpam-221	228	12	,	,	PUNCT
ejpam-221	228	13	such	such	ADJ
ejpam-221	228	14	as	as	ADP
ejpam-221	228	15	type	type	NOUN
ejpam-221	228	16	a	a	DET
ejpam-221	228	17	semigroups	semigroup	NOUN
ejpam-221	228	18	?	?	PUNCT
ejpam-221	229	1	furthermore	furthermore	ADV
ejpam-221	229	2	,	,	PUNCT
ejpam-221	229	3	since	since	SCONJ
ejpam-221	229	4	a	a	DET
ejpam-221	229	5	groupoid	groupoid	NOUN
ejpam-221	229	6	is	be	AUX
ejpam-221	229	7	a	a	DET
ejpam-221	229	8	very	very	ADV
ejpam-221	229	9	specialised	specialised	ADJ
ejpam-221	229	10	type	type	NOUN
ejpam-221	229	11	of	of	ADP
ejpam-221	229	12	category	category	NOUN
ejpam-221	229	13	,	,	PUNCT
ejpam-221	229	14	we	we	PRON
ejpam-221	229	15	might	might	AUX
ejpam-221	229	16	ask	ask	VERB
ejpam-221	229	17	what	what	DET
ejpam-221	229	18	type	type	NOUN
ejpam-221	229	19	of	of	ADP
ejpam-221	229	20	semigroup	semigroup	NOUN
ejpam-221	229	21	may	may	AUX
ejpam-221	229	22	be	be	AUX
ejpam-221	229	23	associated	associate	VERB
ejpam-221	229	24	with	with	ADP
ejpam-221	229	25	a	a	DET
ejpam-221	229	26	more	more	ADV
ejpam-221	229	27	general	general	ADJ
ejpam-221	229	28	category	category	NOUN
ejpam-221	229	29	,	,	PUNCT
ejpam-221	229	30	or	or	CCONJ
ejpam-221	229	31	even	even	ADV
ejpam-221	229	32	with	with	ADP
ejpam-221	229	33	an	an	DET
ejpam-221	229	34	arbitrary	arbitrary	ADJ
ejpam-221	229	35	category	category	NOUN
ejpam-221	229	36	.	.	PUNCT
ejpam-221	230	1	this	this	DET
ejpam-221	230	2	question	question	NOUN
ejpam-221	230	3	has	have	AUX
ejpam-221	230	4	indeed	indeed	ADV
ejpam-221	230	5	been	be	AUX
ejpam-221	230	6	answered	answer	VERB
ejpam-221	230	7	,	,	PUNCT
ejpam-221	230	8	via	via	ADP
ejpam-221	230	9	a	a	DET
ejpam-221	230	10	succession	succession	NOUN
ejpam-221	230	11	of	of	ADP
ejpam-221	230	12	generalisations	generalisation	NOUN
ejpam-221	230	13	of	of	ADP
ejpam-221	230	14	the	the	DET
ejpam-221	230	15	ehresmann	ehresmann	PROPN
ejpam-221	230	16	-	-	PUNCT
ejpam-221	230	17	schein	schein	PROPN
ejpam-221	230	18	-	-	PUNCT
ejpam-221	230	19	nambooripad	nambooripad	NOUN
ejpam-221	230	20	theorem	theorem	NOUN
ejpam-221	230	21	.	.	PUNCT
ejpam-221	231	1	we	we	PRON
ejpam-221	231	2	note	note	VERB
ejpam-221	231	3	here	here	ADV
ejpam-221	231	4	that	that	SCONJ
ejpam-221	231	5	since	since	SCONJ
ejpam-221	231	6	a	a	DET
ejpam-221	231	7	category	category	NOUN
ejpam-221	231	8	is	be	AUX
ejpam-221	231	9	an	an	DET
ejpam-221	231	10	inherently	inherently	ADV
ejpam-221	231	11	‘	'	PUNCT
ejpam-221	231	12	two	two	NUM
ejpam-221	231	13	-	-	PUNCT
ejpam-221	231	14	sided	sided	ADJ
ejpam-221	231	15	’	'	PUNCT
ejpam-221	231	16	object	object	NOUN
ejpam-221	231	17	(	(	PUNCT
ejpam-221	231	18	every	every	DET
ejpam-221	231	19	object	object	NOUN
ejpam-221	231	20	has	have	VERB
ejpam-221	231	21	a	a	DET
ejpam-221	231	22	domain	domain	NOUN
ejpam-221	231	23	and	and	CCONJ
ejpam-221	231	24	a	a	DET
ejpam-221	231	25	range	range	NOUN
ejpam-221	231	26	)	)	PUNCT
ejpam-221	231	27	,	,	PUNCT
ejpam-221	231	28	then	then	ADV
ejpam-221	231	29	it	it	PRON
ejpam-221	231	30	is	be	AUX
ejpam-221	231	31	c.	c.	PROPN
ejpam-221	231	32	hollings	hollings	PROPN
ejpam-221	231	33	/	/	SYM
ejpam-221	231	34	eur	eur	PROPN
ejpam-221	231	35	.	.	PUNCT
ejpam-221	232	1	j.	j.	PROPN
ejpam-221	232	2	pure	pure	PROPN
ejpam-221	232	3	appl	appl	PROPN
ejpam-221	232	4	.	.	PROPN
ejpam-221	232	5	math	math	PROPN
ejpam-221	232	6	,	,	PUNCT
ejpam-221	232	7	2	2	NUM
ejpam-221	232	8	(	(	PUNCT
ejpam-221	232	9	2009	2009	NUM
ejpam-221	232	10	)	)	PUNCT
ejpam-221	232	11	,	,	PUNCT
ejpam-221	232	12	(	(	PUNCT
ejpam-221	232	13	21	21	NUM
ejpam-221	232	14	-	-	SYM
ejpam-221	232	15	57	57	NUM
ejpam-221	232	16	)	)	PUNCT
ejpam-221	232	17	34	34	NUM
ejpam-221	232	18	two	two	NUM
ejpam-221	232	19	-	-	PUNCT
ejpam-221	232	20	sided	sided	ADJ
ejpam-221	232	21	type	type	NOUN
ejpam-221	232	22	a	a	DET
ejpam-221	232	23	semigroups	semigroup	NOUN
ejpam-221	232	24	which	which	PRON
ejpam-221	232	25	must	must	AUX
ejpam-221	232	26	be	be	AUX
ejpam-221	232	27	studied	study	VERB
ejpam-221	232	28	in	in	ADP
ejpam-221	232	29	this	this	DET
ejpam-221	232	30	context	context	NOUN
ejpam-221	232	31	.	.	PUNCT
ejpam-221	233	1	the	the	DET
ejpam-221	233	2	first	first	ADJ
ejpam-221	233	3	of	of	ADP
ejpam-221	233	4	the	the	DET
ejpam-221	233	5	generalisations	generalisation	NOUN
ejpam-221	233	6	of	of	ADP
ejpam-221	233	7	theorem	theorem	NOUN
ejpam-221	233	8	1.19	1.19	NUM
ejpam-221	233	9	is	be	AUX
ejpam-221	233	10	due	due	ADJ
ejpam-221	233	11	to	to	ADP
ejpam-221	233	12	armstrong	armstrong	PROPN
ejpam-221	234	1	[	[	X
ejpam-221	234	2	1	1	NUM
ejpam-221	234	3	]	]	PUNCT
ejpam-221	234	4	and	and	CCONJ
ejpam-221	234	5	is	be	AUX
ejpam-221	234	6	rooted	root	VERB
ejpam-221	234	7	firmly	firmly	ADV
ejpam-221	234	8	in	in	ADP
ejpam-221	234	9	the	the	DET
ejpam-221	234	10	work	work	NOUN
ejpam-221	234	11	of	of	ADP
ejpam-221	234	12	meakin	meakin	NOUN
ejpam-221	234	13	[	[	X
ejpam-221	234	14	55	55	NUM
ejpam-221	234	15	]	]	PUNCT
ejpam-221	234	16	.	.	PUNCT
ejpam-221	235	1	meakin	meakin	PROPN
ejpam-221	235	2	had	have	AUX
ejpam-221	235	3	studied	study	VERB
ejpam-221	235	4	the	the	DET
ejpam-221	235	5	structure	structure	NOUN
ejpam-221	235	6	of	of	ADP
ejpam-221	235	7	an	an	DET
ejpam-221	235	8	inverse	inverse	NOUN
ejpam-221	235	9	semigroup	semigroup	NOUN
ejpam-221	235	10	s	s	X
ejpam-221	235	11	by	by	ADP
ejpam-221	235	12	means	mean	NOUN
ejpam-221	235	13	of	of	ADP
ejpam-221	235	14	so	so	ADV
ejpam-221	235	15	-	-	PUNCT
ejpam-221	235	16	called	call	VERB
ejpam-221	235	17	‘	'	PUNCT
ejpam-221	235	18	structure	structure	NOUN
ejpam-221	235	19	mappings	mapping	NOUN
ejpam-221	235	20	’	'	PUNCT
ejpam-221	235	21	,	,	PUNCT
ejpam-221	235	22	that	that	ADV
ejpam-221	235	23	is	is	ADV
ejpam-221	235	24	,	,	PUNCT
ejpam-221	235	25	mappings	mapping	NOUN
ejpam-221	235	26	betweenr	betweenr	NOUN
ejpam-221	235	27	-	-	PUNCT
ejpam-221	235	28	classes	class	NOUN
ejpam-221	235	29	of	of	ADP
ejpam-221	235	30	s.	s.	PROPN
ejpam-221	235	31	armstrong	armstrong	PROPN
ejpam-221	235	32	generalised	generalise	VERB
ejpam-221	235	33	this	this	DET
ejpam-221	235	34	approach	approach	NOUN
ejpam-221	235	35	to	to	ADP
ejpam-221	235	36	the	the	DET
ejpam-221	235	37	study	study	NOUN
ejpam-221	235	38	of	of	ADP
ejpam-221	235	39	type	type	NOUN
ejpam-221	235	40	a	a	DET
ejpam-221	235	41	semigroups	semigroup	NOUN
ejpam-221	235	42	by	by	ADP
ejpam-221	235	43	considering	consider	VERB
ejpam-221	235	44	mappings	mapping	NOUN
ejpam-221	235	45	betweenr∗andl	betweenr∗andl	ADJ
ejpam-221	235	46	∗-classes	∗-classe	NOUN
ejpam-221	235	47	.	.	PUNCT
ejpam-221	236	1	in	in	ADP
ejpam-221	236	2	her	she	PRON
ejpam-221	236	3	theorem	theorem	ADJ
ejpam-221	236	4	3.9	3.9	NUM
ejpam-221	236	5	,	,	PUNCT
ejpam-221	236	6	armstrong	armstrong	PROPN
ejpam-221	236	7	extended	extend	VERB
ejpam-221	236	8	the	the	DET
ejpam-221	236	9	ehresmannschein	ehresmannschein	PROPN
ejpam-221	236	10	-	-	PUNCT
ejpam-221	236	11	nambooripad	nambooripad	NOUN
ejpam-221	236	12	theorem	theorem	NOUN
ejpam-221	236	13	to	to	ADP
ejpam-221	236	14	the	the	DET
ejpam-221	236	15	case	case	NOUN
ejpam-221	236	16	of	of	ADP
ejpam-221	236	17	type	type	NOUN
ejpam-221	236	18	a	a	DET
ejpam-221	236	19	semigroups	semigroup	NOUN
ejpam-221	236	20	and	and	CCONJ
ejpam-221	236	21	inductive	inductive	ADJ
ejpam-221	236	22	cancellative	cancellative	ADJ
ejpam-221	236	23	categories	category	NOUN
ejpam-221	236	24	:	:	PUNCT
ejpam-221	236	25	theorem	theorem	VERB
ejpam-221	236	26	1.20	1.20	NUM
ejpam-221	236	27	.	.	PUNCT
ejpam-221	237	1	[	[	X
ejpam-221	237	2	1	1	X
ejpam-221	237	3	]	]	PUNCT
ejpam-221	237	4	the	the	DET
ejpam-221	237	5	category	category	NOUN
ejpam-221	237	6	of	of	ADP
ejpam-221	237	7	type	type	NOUN
ejpam-221	237	8	a	a	DET
ejpam-221	237	9	semigroups	semigroup	NOUN
ejpam-221	237	10	and	and	CCONJ
ejpam-221	237	11	(	(	PUNCT
ejpam-221	237	12	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-221	237	13	is	be	AUX
ejpam-221	237	14	isomorphic	isomorphic	ADJ
ejpam-221	237	15	to	to	ADP
ejpam-221	237	16	the	the	DET
ejpam-221	237	17	category	category	NOUN
ejpam-221	237	18	of	of	ADP
ejpam-221	237	19	inductive	inductive	ADJ
ejpam-221	237	20	cancellative	cancellative	ADJ
ejpam-221	237	21	categories	category	NOUN
ejpam-221	237	22	and	and	CCONJ
ejpam-221	237	23	inductive	inductive	ADJ
ejpam-221	237	24	functors	functor	NOUN
ejpam-221	237	25	.	.	PUNCT
ejpam-221	238	1	note	note	NOUN
ejpam-221	238	2	,	,	PUNCT
ejpam-221	238	3	however	however	ADV
ejpam-221	238	4	,	,	PUNCT
ejpam-221	238	5	that	that	SCONJ
ejpam-221	238	6	armstrong	armstrong	PROPN
ejpam-221	238	7	did	do	AUX
ejpam-221	238	8	not	not	PART
ejpam-221	238	9	give	give	VERB
ejpam-221	238	10	such	such	DET
ejpam-221	238	11	a	a	DET
ejpam-221	238	12	category	category	NOUN
ejpam-221	238	13	-	-	PUNCT
ejpam-221	238	14	theoretic	theoretic	NOUN
ejpam-221	238	15	formulation	formulation	NOUN
ejpam-221	238	16	.	.	PUNCT
ejpam-221	239	1	since	since	SCONJ
ejpam-221	239	2	the	the	DET
ejpam-221	239	3	definition	definition	NOUN
ejpam-221	239	4	of	of	ADP
ejpam-221	239	5	an	an	DET
ejpam-221	239	6	inductive	inductive	ADJ
ejpam-221	239	7	cancellative	cancellative	ADJ
ejpam-221	239	8	category	category	NOUN
ejpam-221	239	9	is	be	AUX
ejpam-221	239	10	somewhat	somewhat	ADV
ejpam-221	239	11	complicated	complicated	ADJ
ejpam-221	239	12	,	,	PUNCT
ejpam-221	239	13	we	we	PRON
ejpam-221	239	14	will	will	AUX
ejpam-221	239	15	not	not	PART
ejpam-221	239	16	go	go	VERB
ejpam-221	239	17	into	into	ADP
ejpam-221	239	18	further	further	ADJ
ejpam-221	239	19	detail	detail	NOUN
ejpam-221	239	20	here	here	ADV
ejpam-221	239	21	;	;	PUNCT
ejpam-221	239	22	a	a	DET
ejpam-221	239	23	summary	summary	NOUN
ejpam-221	239	24	appears	appear	VERB
ejpam-221	239	25	in	in	ADP
ejpam-221	239	26	[	[	X
ejpam-221	239	27	35	35	NUM
ejpam-221	239	28	,	,	PUNCT
ejpam-221	239	29	chapter	chapter	NOUN
ejpam-221	239	30	7	7	NUM
ejpam-221	239	31	]	]	PUNCT
ejpam-221	239	32	.	.	PUNCT
ejpam-221	240	1	in	in	ADP
ejpam-221	240	2	[	[	X
ejpam-221	240	3	24	24	NUM
ejpam-221	240	4	,	,	PUNCT
ejpam-221	240	5	p.	p.	NOUN
ejpam-221	240	6	115	115	NUM
ejpam-221	240	7	]	]	PUNCT
ejpam-221	240	8	,	,	PUNCT
ejpam-221	240	9	fountain	fountain	NOUN
ejpam-221	240	10	gave	give	VERB
ejpam-221	240	11	an	an	DET
ejpam-221	240	12	alternative	alternative	ADJ
ejpam-221	240	13	characterisation	characterisation	NOUN
ejpam-221	240	14	of	of	ADP
ejpam-221	240	15	(	(	PUNCT
ejpam-221	240	16	left	left	ADJ
ejpam-221	240	17	/	/	SYM
ejpam-221	240	18	right	right	ADJ
ejpam-221	240	19	)	)	PUNCT
ejpam-221	240	20	type	type	NOUN
ejpam-221	240	21	a	a	DET
ejpam-221	240	22	semigroups	semigroup	NOUN
ejpam-221	240	23	;	;	PUNCT
ejpam-221	240	24	this	this	PRON
ejpam-221	240	25	is	be	AUX
ejpam-221	240	26	the	the	DET
ejpam-221	240	27	definition	definition	NOUN
ejpam-221	240	28	which	which	PRON
ejpam-221	240	29	is	be	AUX
ejpam-221	240	30	most	most	ADV
ejpam-221	240	31	often	often	ADV
ejpam-221	240	32	used	use	VERB
ejpam-221	240	33	in	in	ADP
ejpam-221	240	34	current	current	ADJ
ejpam-221	240	35	papers	paper	NOUN
ejpam-221	240	36	(	(	PUNCT
ejpam-221	240	37	and	and	CCONJ
ejpam-221	240	38	which	which	PRON
ejpam-221	240	39	will	will	AUX
ejpam-221	240	40	appear	appear	VERB
ejpam-221	240	41	in	in	ADP
ejpam-221	240	42	section	section	NOUN
ejpam-221	240	43	5	5	NUM
ejpam-221	240	44	)	)	PUNCT
ejpam-221	240	45	.	.	PUNCT
ejpam-221	241	1	it	it	PRON
ejpam-221	241	2	should	should	AUX
ejpam-221	241	3	also	also	ADV
ejpam-221	241	4	be	be	AUX
ejpam-221	241	5	noted	note	VERB
ejpam-221	241	6	that	that	SCONJ
ejpam-221	241	7	type	type	NOUN
ejpam-221	241	8	a	a	DET
ejpam-221	241	9	semigroups	semigroup	NOUN
ejpam-221	241	10	are	be	AUX
ejpam-221	241	11	now	now	ADV
ejpam-221	241	12	known	know	VERB
ejpam-221	241	13	as	as	ADP
ejpam-221	241	14	ample	ample	ADJ
ejpam-221	241	15	semigroups	semigroup	NOUN
ejpam-221	241	16	,	,	PUNCT
ejpam-221	241	17	a	a	DET
ejpam-221	241	18	term	term	NOUN
ejpam-221	241	19	which	which	PRON
ejpam-221	241	20	was	be	AUX
ejpam-221	241	21	introduced	introduce	VERB
ejpam-221	241	22	in	in	ADP
ejpam-221	241	23	[	[	X
ejpam-221	241	24	31	31	NUM
ejpam-221	241	25	]	]	PUNCT
ejpam-221	241	26	;	;	PUNCT
ejpam-221	241	27	as	as	SCONJ
ejpam-221	241	28	interest	interest	NOUN
ejpam-221	241	29	in	in	ADP
ejpam-221	241	30	these	these	DET
ejpam-221	241	31	semigroups	semigroup	NOUN
ejpam-221	241	32	grew	grow	VERB
ejpam-221	241	33	,	,	PUNCT
ejpam-221	241	34	it	it	PRON
ejpam-221	241	35	was	be	AUX
ejpam-221	241	36	decided	decide	VERB
ejpam-221	241	37	that	that	SCONJ
ejpam-221	241	38	they	they	PRON
ejpam-221	241	39	needed	need	VERB
ejpam-221	241	40	a	a	DET
ejpam-221	241	41	more	more	ADV
ejpam-221	241	42	exciting	exciting	ADJ
ejpam-221	241	43	name	name	NOUN
ejpam-221	241	44	—	—	PUNCT
ejpam-221	241	45	the	the	DET
ejpam-221	241	46	name	name	NOUN
ejpam-221	241	47	‘	'	PUNCT
ejpam-221	241	48	ample	ample	ADJ
ejpam-221	241	49	’	'	PUNCT
ejpam-221	241	50	was	be	AUX
ejpam-221	241	51	chosen	choose	VERB
ejpam-221	241	52	not	not	PART
ejpam-221	241	53	only	only	ADV
ejpam-221	241	54	for	for	ADP
ejpam-221	241	55	its	its	PRON
ejpam-221	241	56	alliterational	alliterational	ADJ
ejpam-221	241	57	value	value	NOUN
ejpam-221	241	58	,	,	PUNCT
ejpam-221	241	59	but	but	CCONJ
ejpam-221	241	60	also	also	ADV
ejpam-221	241	61	because	because	SCONJ
ejpam-221	241	62	such	such	ADJ
ejpam-221	241	63	semigroups	semigroup	NOUN
ejpam-221	241	64	contain	contain	VERB
ejpam-221	241	65	an	an	DET
ejpam-221	241	66	‘	'	PUNCT
ejpam-221	241	67	ample	ample	ADJ
ejpam-221	241	68	’	'	PUNCT
ejpam-221	241	69	supply	supply	NOUN
ejpam-221	241	70	of	of	ADP
ejpam-221	241	71	idempotents	idempotent	NOUN
ejpam-221	241	72	.	.	PUNCT
ejpam-221	242	1	we	we	PRON
ejpam-221	242	2	will	will	AUX
ejpam-221	242	3	consider	consider	VERB
ejpam-221	242	4	left	leave	VERB
ejpam-221	242	5	ample	ample	ADJ
ejpam-221	242	6	semigroups	semigroup	NOUN
ejpam-221	242	7	in	in	ADP
ejpam-221	242	8	more	more	ADJ
ejpam-221	242	9	detail	detail	NOUN
ejpam-221	242	10	in	in	ADP
ejpam-221	242	11	section	section	NOUN
ejpam-221	242	12	5	5	NUM
ejpam-221	242	13	.	.	NOUN
ejpam-221	243	1	2	2	NUM
ejpam-221	243	2	.	.	NOUN
ejpam-221	243	3	historical	historical	PROPN
ejpam-221	243	4	development	development	PROPN
ejpam-221	243	5	ii	ii	PROPN
ejpam-221	243	6	:	:	PUNCT
ejpam-221	243	7	weakly	weakly	ADV
ejpam-221	243	8	left	leave	VERB
ejpam-221	243	9	e	e	NOUN
ejpam-221	243	10	-	-	ADJ
ejpam-221	243	11	ample	ample	ADJ
ejpam-221	243	12	semigroups	semigroup	NOUN
ejpam-221	243	13	we	we	PRON
ejpam-221	243	14	continue	continue	VERB
ejpam-221	243	15	our	our	PRON
ejpam-221	243	16	journey	journey	NOUN
ejpam-221	243	17	through	through	ADP
ejpam-221	243	18	the	the	DET
ejpam-221	243	19	historical	historical	ADJ
ejpam-221	243	20	development	development	NOUN
ejpam-221	243	21	of	of	ADP
ejpam-221	243	22	restriction	restriction	NOUN
ejpam-221	243	23	semigroups	semigroup	NOUN
ejpam-221	243	24	by	by	ADP
ejpam-221	243	25	considering	consider	VERB
ejpam-221	243	26	a	a	DET
ejpam-221	243	27	generalisation	generalisation	NOUN
ejpam-221	243	28	of	of	ADP
ejpam-221	243	29	ample	ample	ADJ
ejpam-221	243	30	semigroups	semigroup	NOUN
ejpam-221	243	31	whose	whose	DET
ejpam-221	243	32	study	study	NOUN
ejpam-221	243	33	(	(	PUNCT
ejpam-221	243	34	within	within	ADP
ejpam-221	243	35	the	the	DET
ejpam-221	243	36	‘	'	PUNCT
ejpam-221	243	37	york	york	NOUN
ejpam-221	243	38	’	'	PUNCT
ejpam-221	243	39	school	school	NOUN
ejpam-221	243	40	)	)	PUNCT
ejpam-221	243	41	was	be	AUX
ejpam-221	243	42	initiated	initiate	VERB
ejpam-221	243	43	by	by	ADP
ejpam-221	243	44	el	el	PROPN
ejpam-221	243	45	-	-	PROPN
ejpam-221	243	46	qallali	qallali	PROPN
ejpam-221	244	1	[	[	X
ejpam-221	244	2	15	15	NUM
ejpam-221	244	3	]	]	PUNCT
ejpam-221	244	4	.	.	PUNCT
ejpam-221	245	1	el	el	PROPN
ejpam-221	245	2	-	-	PUNCT
ejpam-221	245	3	qallali	qallali	PROPN
ejpam-221	245	4	began	begin	VERB
ejpam-221	245	5	the	the	DET
ejpam-221	245	6	final	final	ADJ
ejpam-221	245	7	chapter	chapter	NOUN
ejpam-221	245	8	of	of	ADP
ejpam-221	245	9	his	his	PRON
ejpam-221	245	10	thesis	thesis	NOUN
ejpam-221	245	11	by	by	ADP
ejpam-221	245	12	recalling	recall	VERB
ejpam-221	245	13	an	an	DET
ejpam-221	245	14	alternative	alternative	ADJ
ejpam-221	245	15	characterisation	characterisation	NOUN
ejpam-221	245	16	of	of	ADP
ejpam-221	245	17	l	l	NOUN
ejpam-221	245	18	∗	∗	NOUN
ejpam-221	245	19	and	and	CCONJ
ejpam-221	245	20	r∗	r∗	NOUN
ejpam-221	245	21	which	which	PRON
ejpam-221	245	22	appears	appear	VERB
ejpam-221	245	23	in	in	ADP
ejpam-221	245	24	[	[	X
ejpam-221	245	25	25	25	NUM
ejpam-221	245	26	]	]	PUNCT
ejpam-221	245	27	for	for	ADP
ejpam-221	245	28	abundant	abundant	ADJ
ejpam-221	245	29	semigroups	semigroup	NOUN
ejpam-221	245	30	:	:	PUNCT
ejpam-221	245	31	proposition	proposition	NOUN
ejpam-221	245	32	2.1	2.1	NUM
ejpam-221	245	33	.	.	PUNCT
ejpam-221	246	1	[	[	X
ejpam-221	246	2	25	25	NUM
ejpam-221	246	3	,	,	PUNCT
ejpam-221	246	4	corollary	corollary	ADJ
ejpam-221	246	5	1.10	1.10	NUM
ejpam-221	246	6	]	]	PUNCT
ejpam-221	246	7	let	let	VERB
ejpam-221	246	8	s	s	PRON
ejpam-221	246	9	be	be	AUX
ejpam-221	246	10	an	an	DET
ejpam-221	246	11	abundant	abundant	ADJ
ejpam-221	246	12	semigroup	semigroup	NOUN
ejpam-221	246	13	.	.	PUNCT
ejpam-221	247	1	then	then	ADV
ejpam-221	247	2	,	,	PUNCT
ejpam-221	247	3	for	for	ADP
ejpam-221	247	4	any	any	DET
ejpam-221	247	5	e	e	PROPN
ejpam-221	247	6	∈	∈	PROPN
ejpam-221	247	7	e(s	e(s	PROPN
ejpam-221	247	8	)	)	PUNCT
ejpam-221	247	9	,	,	PUNCT
ejpam-221	247	10	c.	c.	PROPN
ejpam-221	247	11	hollings	holling	NOUN
ejpam-221	247	12	/	/	SYM
ejpam-221	247	13	eur	eur	PROPN
ejpam-221	247	14	.	.	PUNCT
ejpam-221	248	1	j.	j.	PROPN
ejpam-221	248	2	pure	pure	PROPN
ejpam-221	248	3	appl	appl	PROPN
ejpam-221	248	4	.	.	PROPN
ejpam-221	248	5	math	math	PROPN
ejpam-221	248	6	,	,	PUNCT
ejpam-221	248	7	2	2	NUM
ejpam-221	248	8	(	(	PUNCT
ejpam-221	248	9	2009	2009	NUM
ejpam-221	248	10	)	)	PUNCT
ejpam-221	248	11	,	,	PUNCT
ejpam-221	248	12	(	(	PUNCT
ejpam-221	248	13	21	21	NUM
ejpam-221	248	14	-	-	SYM
ejpam-221	248	15	57	57	NUM
ejpam-221	248	16	)	)	PUNCT
ejpam-221	248	17	35	35	NUM
ejpam-221	248	18	al	al	PROPN
ejpam-221	248	19	∗	∗	X
ejpam-221	248	20	e	e	PROPN
ejpam-221	248	21	(	(	PUNCT
ejpam-221	248	22	ar∗	ar∗	PROPN
ejpam-221	248	23	e	e	NOUN
ejpam-221	248	24	)	)	PUNCT
ejpam-221	249	1	if	if	SCONJ
ejpam-221	249	2	,	,	PUNCT
ejpam-221	249	3	and	and	CCONJ
ejpam-221	249	4	only	only	ADV
ejpam-221	249	5	if	if	SCONJ
ejpam-221	249	6	,	,	PUNCT
ejpam-221	249	7	a	a	DET
ejpam-221	249	8	∈	∈	PROPN
ejpam-221	249	9	se	se	X
ejpam-221	249	10	(	(	PUNCT
ejpam-221	249	11	a	a	DET
ejpam-221	249	12	∈	∈	PROPN
ejpam-221	249	13	es	es	NOUN
ejpam-221	249	14	)	)	PUNCT
ejpam-221	249	15	and	and	CCONJ
ejpam-221	249	16	se	se	X
ejpam-221	249	17	(	(	PUNCT
ejpam-221	249	18	es	es	NOUN
ejpam-221	249	19	)	)	PUNCT
ejpam-221	249	20	is	be	AUX
ejpam-221	249	21	contained	contain	VERB
ejpam-221	249	22	in	in	ADP
ejpam-221	249	23	every	every	DET
ejpam-221	249	24	idempotentgenerated	idempotentgenerate	VERB
ejpam-221	249	25	left	leave	VERB
ejpam-221	249	26	(	(	PUNCT
ejpam-221	249	27	right	right	ADJ
ejpam-221	249	28	)	)	PUNCT
ejpam-221	249	29	ideal	ideal	NOUN
ejpam-221	249	30	which	which	PRON
ejpam-221	249	31	contains	contain	VERB
ejpam-221	249	32	a.	a.	NOUN
ejpam-221	249	33	inspired	inspire	VERB
ejpam-221	249	34	by	by	ADP
ejpam-221	249	35	this	this	DET
ejpam-221	249	36	last	last	ADJ
ejpam-221	249	37	result	result	NOUN
ejpam-221	249	38	,	,	PUNCT
ejpam-221	249	39	el	el	PROPN
ejpam-221	249	40	-	-	PUNCT
ejpam-221	249	41	qallali	qallali	PROPN
ejpam-221	249	42	investigated	investigate	VERB
ejpam-221	249	43	a	a	DET
ejpam-221	249	44	more	more	ADV
ejpam-221	249	45	general	general	ADJ
ejpam-221	249	46	class	class	NOUN
ejpam-221	249	47	of	of	ADP
ejpam-221	249	48	semigroups	semigroup	NOUN
ejpam-221	249	49	in	in	ADP
ejpam-221	249	50	which	which	PRON
ejpam-221	249	51	every	every	DET
ejpam-221	249	52	element	element	NOUN
ejpam-221	249	53	is	be	AUX
ejpam-221	249	54	contained	contain	VERB
ejpam-221	249	55	in	in	ADP
ejpam-221	249	56	a	a	DET
ejpam-221	249	57	minimum	minimum	ADJ
ejpam-221	249	58	idempotent	idempotent	NOUN
ejpam-221	249	59	-	-	PUNCT
ejpam-221	249	60	generated	generate	VERB
ejpam-221	249	61	left	left	NOUN
ejpam-221	249	62	(	(	PUNCT
ejpam-221	249	63	right	right	ADJ
ejpam-221	249	64	)	)	PUNCT
ejpam-221	249	65	ideal	ideal	NOUN
ejpam-221	249	66	.	.	PUNCT
ejpam-221	250	1	such	such	ADJ
ejpam-221	250	2	semigroups	semigroup	NOUN
ejpam-221	250	3	are	be	AUX
ejpam-221	250	4	termed	term	VERB
ejpam-221	250	5	semiabundant	semiabundant	ADJ
ejpam-221	250	6	semigroups	semigroup	NOUN
ejpam-221	250	7	.	.	PUNCT
ejpam-221	251	1	el	el	PROPN
ejpam-221	251	2	-	-	PUNCT
ejpam-221	251	3	qallali	qallali	ADJ
ejpam-221	251	4	introduced	introduce	VERB
ejpam-221	251	5	equivalence	equivalence	NOUN
ejpam-221	251	6	relations	relation	NOUN
ejpam-221	251	7	fl	fl	NOUN
ejpam-221	251	8	and	and	CCONJ
ejpam-221	251	9	er	er	INTJ
ejpam-221	251	10	with	with	ADP
ejpam-221	251	11	l	l	NOUN
ejpam-221	251	12	∗	∗	NOUN
ejpam-221	251	13	⊆	⊆	NUM
ejpam-221	251	14	fl	fl	NOUN
ejpam-221	251	15	and	and	CCONJ
ejpam-221	251	16	r∗	r∗	VERB
ejpam-221	251	17	⊆	⊆	NUM
ejpam-221	251	18	er	er	INTJ
ejpam-221	251	19	,	,	PUNCT
ejpam-221	251	20	and	and	CCONJ
ejpam-221	251	21	demonstrated	demonstrate	VERB
ejpam-221	251	22	that	that	SCONJ
ejpam-221	251	23	a	a	DET
ejpam-221	251	24	semigroup	semigroup	NOUN
ejpam-221	251	25	is	be	AUX
ejpam-221	251	26	semiabundant	semiabundant	ADJ
ejpam-221	251	27	if	if	SCONJ
ejpam-221	251	28	,	,	PUNCT
ejpam-221	251	29	and	and	CCONJ
ejpam-221	251	30	only	only	ADV
ejpam-221	251	31	if	if	SCONJ
ejpam-221	251	32	,	,	PUNCT
ejpam-221	251	33	each	each	DET
ejpam-221	251	34	element	element	NOUN
ejpam-221	251	35	is	be	AUX
ejpam-221	251	36	both	both	PRON
ejpam-221	251	37	fl	fl	PROPN
ejpam-221	251	38	and	and	CCONJ
ejpam-221	251	39	er	er	ADV
ejpam-221	251	40	-	-	PUNCT
ejpam-221	251	41	related	relate	VERB
ejpam-221	251	42	to	to	ADP
ejpam-221	251	43	an	an	DET
ejpam-221	251	44	idempotent	idempotent	NOUN
ejpam-221	251	45	.	.	PUNCT
ejpam-221	252	1	it	it	PRON
ejpam-221	252	2	is	be	AUX
ejpam-221	252	3	therefore	therefore	ADV
ejpam-221	252	4	clear	clear	ADJ
ejpam-221	252	5	that	that	SCONJ
ejpam-221	252	6	any	any	DET
ejpam-221	252	7	abundant	abundant	ADJ
ejpam-221	252	8	semigroup	semigroup	NOUN
ejpam-221	252	9	is	be	AUX
ejpam-221	252	10	semiabundant	semiabundant	NOUN
ejpam-221	252	11	.	.	PUNCT
ejpam-221	253	1	left	leave	VERB
ejpam-221	253	2	semiabundant	semiabundant	NOUN
ejpam-221	253	3	semigroups	semigroup	NOUN
ejpam-221	253	4	are	be	AUX
ejpam-221	253	5	easily	easily	ADV
ejpam-221	253	6	defined	define	VERB
ejpam-221	253	7	as	as	ADP
ejpam-221	253	8	semigroups	semigroup	NOUN
ejpam-221	253	9	in	in	ADP
ejpam-221	253	10	which	which	PRON
ejpam-221	253	11	every	every	DET
ejpam-221	253	12	element	element	NOUN
ejpam-221	253	13	is	be	AUX
ejpam-221	253	14	er	er	ADV
ejpam-221	253	15	-	-	PUNCT
ejpam-221	253	16	related	relate	VERB
ejpam-221	253	17	to	to	ADP
ejpam-221	253	18	an	an	DET
ejpam-221	253	19	idempotent	idempotent	NOUN
ejpam-221	253	20	.	.	PUNCT
ejpam-221	254	1	dually	dually	ADV
ejpam-221	254	2	for	for	ADP
ejpam-221	254	3	right	right	ADJ
ejpam-221	254	4	semiabundant	semiabundant	PROPN
ejpam-221	254	5	semigroups	semigroup	NOUN
ejpam-221	254	6	.	.	PUNCT
ejpam-221	255	1	by	by	ADP
ejpam-221	255	2	analogy	analogy	NOUN
ejpam-221	255	3	with	with	ADP
ejpam-221	255	4	abundant	abundant	ADJ
ejpam-221	255	5	semigroups	semigroup	NOUN
ejpam-221	255	6	,	,	PUNCT
ejpam-221	255	7	el	el	PROPN
ejpam-221	255	8	-	-	NOUN
ejpam-221	255	9	qallali	qallali	PROPN
ejpam-221	256	1	[	[	X
ejpam-221	256	2	15	15	NUM
ejpam-221	256	3	]	]	PUNCT
ejpam-221	256	4	investigated	investigate	VERB
ejpam-221	256	5	semiabundant	semiabundant	NOUN
ejpam-221	256	6	semigroups	semigroup	NOUN
ejpam-221	256	7	in	in	ADP
ejpam-221	256	8	which	which	PRON
ejpam-221	256	9	the	the	DET
ejpam-221	256	10	idempotents	idempotent	NOUN
ejpam-221	256	11	form	form	VERB
ejpam-221	256	12	a	a	DET
ejpam-221	256	13	subsemigroup	subsemigroup	NOUN
ejpam-221	256	14	(	(	PUNCT
ejpam-221	256	15	q	q	NOUN
ejpam-221	256	16	-	-	PUNCT
ejpam-221	256	17	semigroups	semigroup	NOUN
ejpam-221	256	18	)	)	PUNCT
ejpam-221	256	19	,	,	PUNCT
ejpam-221	256	20	and	and	CCONJ
ejpam-221	256	21	in	in	ADP
ejpam-221	256	22	which	which	PRON
ejpam-221	256	23	the	the	DET
ejpam-221	256	24	idempotents	idempotent	NOUN
ejpam-221	256	25	form	form	VERB
ejpam-221	256	26	a	a	DET
ejpam-221	256	27	subsemilattice	subsemilattice	NOUN
ejpam-221	256	28	(	(	PUNCT
ejpam-221	256	29	semiadequate	semiadequate	NOUN
ejpam-221	256	30	semigroups	semigroup	NOUN
ejpam-221	256	31	)	)	PUNCT
ejpam-221	256	32	.	.	PUNCT
ejpam-221	257	1	pursuing	pursue	VERB
ejpam-221	257	2	the	the	DET
ejpam-221	257	3	analogy	analogy	NOUN
ejpam-221	257	4	further	far	ADV
ejpam-221	257	5	,	,	PUNCT
ejpam-221	257	6	el	el	PROPN
ejpam-221	257	7	-	-	PUNCT
ejpam-221	257	8	qallali	qallali	PROPN
ejpam-221	257	9	realised	realise	VERB
ejpam-221	257	10	that	that	SCONJ
ejpam-221	257	11	whilst	whilst	SCONJ
ejpam-221	257	12	l	l	NOUN
ejpam-221	257	13	∗	∗	NOUN
ejpam-221	257	14	is	be	AUX
ejpam-221	257	15	always	always	ADV
ejpam-221	257	16	a	a	DET
ejpam-221	257	17	right	right	ADJ
ejpam-221	257	18	congruence	congruence	NOUN
ejpam-221	257	19	andr∗	andr∗	PROPN
ejpam-221	257	20	is	be	AUX
ejpam-221	257	21	always	always	ADV
ejpam-221	257	22	a	a	DET
ejpam-221	257	23	left	left	ADJ
ejpam-221	257	24	congruence	congruence	NOUN
ejpam-221	257	25	,	,	PUNCT
ejpam-221	258	1	fl	fl	PROPN
ejpam-221	258	2	and	and	CCONJ
ejpam-221	258	3	er	er	INTJ
ejpam-221	258	4	need	need	AUX
ejpam-221	258	5	not	not	PART
ejpam-221	258	6	be	be	AUX
ejpam-221	258	7	right	right	ADJ
ejpam-221	258	8	and	and	CCONJ
ejpam-221	258	9	left	left	ADJ
ejpam-221	258	10	congruences	congruence	NOUN
ejpam-221	258	11	,	,	PUNCT
ejpam-221	258	12	respectively	respectively	ADV
ejpam-221	258	13	.	.	PUNCT
ejpam-221	259	1	since	since	SCONJ
ejpam-221	259	2	these	these	PRON
ejpam-221	259	3	are	be	AUX
ejpam-221	259	4	particularly	particularly	ADV
ejpam-221	259	5	useful	useful	ADJ
ejpam-221	259	6	properties	property	NOUN
ejpam-221	259	7	to	to	PART
ejpam-221	259	8	have	have	VERB
ejpam-221	259	9	,	,	PUNCT
ejpam-221	259	10	el	el	PROPN
ejpam-221	259	11	-	-	PUNCT
ejpam-221	259	12	qallali	qallali	PROPN
ejpam-221	259	13	restricted	restrict	VERB
ejpam-221	259	14	his	his	PRON
ejpam-221	259	15	attention	attention	NOUN
ejpam-221	259	16	to	to	ADP
ejpam-221	259	17	those	those	DET
ejpam-221	259	18	qand	qand	PROPN
ejpam-221	259	19	semiadequate	semiadequate	NOUN
ejpam-221	259	20	semigroups	semigroup	NOUN
ejpam-221	259	21	in	in	ADP
ejpam-221	259	22	which	which	PRON
ejpam-221	259	23	(	(	PUNCT
ejpam-221	259	24	cl	cl	NOUN
ejpam-221	259	25	)	)	PUNCT
ejpam-221	259	26	er	er	INTJ
ejpam-221	259	27	is	be	AUX
ejpam-221	259	28	a	a	DET
ejpam-221	259	29	left	left	ADJ
ejpam-221	259	30	congruence	congruence	NOUN
ejpam-221	259	31	,	,	PUNCT
ejpam-221	259	32	and	and	CCONJ
ejpam-221	259	33	(	(	PUNCT
ejpam-221	259	34	cr	cr	NOUN
ejpam-221	259	35	)	)	PUNCT
ejpam-221	259	36	fl	fl	PROPN
ejpam-221	259	37	is	be	AUX
ejpam-221	259	38	a	a	DET
ejpam-221	259	39	right	right	ADJ
ejpam-221	259	40	congruence	congruence	NOUN
ejpam-221	259	41	.	.	PUNCT
ejpam-221	260	1	in	in	ADP
ejpam-221	260	2	chapter	chapter	NOUN
ejpam-221	260	3	viii	viii	NOUN
ejpam-221	260	4	of	of	ADP
ejpam-221	260	5	[	[	X
ejpam-221	260	6	15	15	NUM
ejpam-221	260	7	]	]	X
ejpam-221	260	8	,	,	PUNCT
ejpam-221	260	9	a	a	DET
ejpam-221	260	10	structure	structure	NOUN
ejpam-221	260	11	theory	theory	NOUN
ejpam-221	260	12	was	be	AUX
ejpam-221	260	13	obtained	obtain	VERB
ejpam-221	260	14	for	for	ADP
ejpam-221	260	15	q	q	NOUN
ejpam-221	260	16	-	-	PUNCT
ejpam-221	260	17	semigroups	semigroup	NOUN
ejpam-221	260	18	which	which	PRON
ejpam-221	260	19	mirrored	mirror	VERB
ejpam-221	260	20	that	that	SCONJ
ejpam-221	260	21	already	already	ADV
ejpam-221	260	22	obtained	obtain	VERB
ejpam-221	260	23	for	for	ADP
ejpam-221	260	24	quasi	quasi	ADJ
ejpam-221	260	25	-	-	ADJ
ejpam-221	260	26	adequate	adequate	ADJ
ejpam-221	260	27	semigroups	semigroup	NOUN
ejpam-221	260	28	in	in	ADP
ejpam-221	260	29	chapter	chapter	NOUN
ejpam-221	260	30	v.	v.	INTJ
ejpam-221	260	31	towards	towards	ADP
ejpam-221	260	32	the	the	DET
ejpam-221	260	33	end	end	NOUN
ejpam-221	260	34	of	of	ADP
ejpam-221	260	35	the	the	DET
ejpam-221	260	36	thesis	thesis	NOUN
ejpam-221	260	37	,	,	PUNCT
ejpam-221	260	38	el	el	PROPN
ejpam-221	260	39	-	-	PUNCT
ejpam-221	260	40	qallali	qallali	PROPN
ejpam-221	260	41	obtained	obtain	VERB
ejpam-221	260	42	structural	structural	ADJ
ejpam-221	260	43	results	result	NOUN
ejpam-221	260	44	for	for	ADP
ejpam-221	260	45	so	so	ADV
ejpam-221	260	46	-	-	PUNCT
ejpam-221	260	47	called	call	VERB
ejpam-221	260	48	idempotent	idempotent	NOUN
ejpam-221	260	49	-	-	PUNCT
ejpam-221	260	50	connected	connect	VERB
ejpam-221	260	51	semiadequate	semiadequate	NOUN
ejpam-221	260	52	semigroups	semigroup	NOUN
ejpam-221	260	53	with	with	ADP
ejpam-221	260	54	(	(	PUNCT
ejpam-221	260	55	cl	cl	NOUN
ejpam-221	260	56	)	)	PUNCT
ejpam-221	260	57	and	and	CCONJ
ejpam-221	260	58	(	(	PUNCT
ejpam-221	260	59	cr	cr	NOUN
ejpam-221	260	60	)	)	PUNCT
ejpam-221	260	61	,	,	PUNCT
ejpam-221	260	62	or	or	CCONJ
ejpam-221	260	63	type	type	NOUN
ejpam-221	260	64	t	t	NOUN
ejpam-221	260	65	semigroups	semigroup	NOUN
ejpam-221	260	66	,	,	PUNCT
ejpam-221	260	67	as	as	SCONJ
ejpam-221	260	68	he	he	PRON
ejpam-221	260	69	called	call	VERB
ejpam-221	260	70	them	they	PRON
ejpam-221	260	71	.	.	PUNCT
ejpam-221	261	1	the	the	DET
ejpam-221	261	2	‘	'	PUNCT
ejpam-221	261	3	idempotentconnected	idempotentconnected	ADJ
ejpam-221	261	4	’	'	PUNCT
ejpam-221	261	5	conditions	condition	NOUN
ejpam-221	261	6	are	be	AUX
ejpam-221	261	7	equivalent	equivalent	ADJ
ejpam-221	261	8	to	to	ADP
ejpam-221	261	9	the	the	DET
ejpam-221	261	10	conditions	condition	NOUN
ejpam-221	261	11	(	(	PUNCT
ejpam-221	261	12	1.2	1.2	NUM
ejpam-221	261	13	)	)	PUNCT
ejpam-221	261	14	and	and	CCONJ
ejpam-221	261	15	(	(	PUNCT
ejpam-221	261	16	1.3	1.3	NUM
ejpam-221	261	17	)	)	PUNCT
ejpam-221	261	18	previously	previously	ADV
ejpam-221	261	19	imposed	impose	VERB
ejpam-221	261	20	on	on	ADP
ejpam-221	261	21	an	an	DET
ejpam-221	261	22	adequate	adequate	ADJ
ejpam-221	261	23	semigroup	semigroup	NOUN
ejpam-221	261	24	in	in	ADP
ejpam-221	261	25	order	order	NOUN
ejpam-221	261	26	to	to	PART
ejpam-221	261	27	make	make	VERB
ejpam-221	261	28	it	it	PRON
ejpam-221	261	29	type	type	VERB
ejpam-221	261	30	a.	a.	NOUN
ejpam-221	261	31	thus	thus	ADV
ejpam-221	261	32	type	type	NOUN
ejpam-221	261	33	t	t	PROPN
ejpam-221	261	34	semigroups	semigroup	NOUN
ejpam-221	261	35	generalise	generalise	AUX
ejpam-221	261	36	type	type	VERB
ejpam-221	261	37	a	a	DET
ejpam-221	261	38	semigroups	semigroup	NOUN
ejpam-221	261	39	.	.	PUNCT
ejpam-221	262	1	el	el	PROPN
ejpam-221	262	2	-	-	PUNCT
ejpam-221	262	3	qallali	qallali	PROPN
ejpam-221	262	4	proved	prove	VERB
ejpam-221	262	5	an	an	DET
ejpam-221	262	6	analogue	analogue	NOUN
ejpam-221	262	7	of	of	ADP
ejpam-221	262	8	theorem	theorem	NOUN
ejpam-221	262	9	1.18	1.18	NUM
ejpam-221	262	10	for	for	ADP
ejpam-221	262	11	type	type	NOUN
ejpam-221	262	12	t	t	NOUN
ejpam-221	262	13	semigroups	semigroups	X
ejpam-221	262	14	[	[	X
ejpam-221	262	15	15	15	NUM
ejpam-221	262	16	]	]	PUNCT
ejpam-221	262	17	.	.	PUNCT
ejpam-221	263	1	given	give	VERB
ejpam-221	263	2	a	a	DET
ejpam-221	263	3	left	left	ADJ
ejpam-221	263	4	semiadequate	semiadequate	NOUN
ejpam-221	263	5	semigroup	semigroup	NOUN
ejpam-221	263	6	,	,	PUNCT
ejpam-221	263	7	it	it	PRON
ejpam-221	263	8	is	be	AUX
ejpam-221	263	9	possible	possible	ADJ
ejpam-221	263	10	to	to	PART
ejpam-221	263	11	define	define	VERB
ejpam-221	263	12	a	a	DET
ejpam-221	263	13	left	left	ADJ
ejpam-221	263	14	type	type	NOUN
ejpam-221	263	15	t	t	PROPN
ejpam-221	263	16	semigroup	semigroup	NOUN
ejpam-221	263	17	by	by	ADP
ejpam-221	263	18	imposing	impose	VERB
ejpam-221	263	19	an	an	DET
ejpam-221	263	20	appropriate	appropriate	ADJ
ejpam-221	263	21	one	one	NUM
ejpam-221	263	22	-	-	PUNCT
ejpam-221	263	23	sided	sided	ADJ
ejpam-221	263	24	version	version	NOUN
ejpam-221	263	25	of	of	ADP
ejpam-221	263	26	the	the	DET
ejpam-221	263	27	idempotent	idempotent	ADV
ejpam-221	263	28	-	-	PUNCT
ejpam-221	263	29	connected	connect	VERB
ejpam-221	263	30	condition	condition	NOUN
ejpam-221	263	31	(	(	PUNCT
ejpam-221	263	32	equivalent	equivalent	ADJ
ejpam-221	263	33	c.	c.	PROPN
ejpam-221	263	34	hollings	holling	NOUN
ejpam-221	263	35	/	/	SYM
ejpam-221	263	36	eur	eur	PROPN
ejpam-221	263	37	.	.	PUNCT
ejpam-221	264	1	j.	j.	PROPN
ejpam-221	264	2	pure	pure	PROPN
ejpam-221	264	3	appl	appl	PROPN
ejpam-221	264	4	.	.	PROPN
ejpam-221	264	5	math	math	PROPN
ejpam-221	264	6	,	,	PUNCT
ejpam-221	264	7	2	2	NUM
ejpam-221	264	8	(	(	PUNCT
ejpam-221	264	9	2009	2009	NUM
ejpam-221	264	10	)	)	PUNCT
ejpam-221	264	11	,	,	PUNCT
ejpam-221	264	12	(	(	PUNCT
ejpam-221	264	13	21	21	NUM
ejpam-221	264	14	-	-	SYM
ejpam-221	264	15	57	57	NUM
ejpam-221	264	16	)	)	PUNCT
ejpam-221	264	17	36	36	NUM
ejpam-221	264	18	to	to	PART
ejpam-221	264	19	(	(	PUNCT
ejpam-221	264	20	1.3	1.3	NUM
ejpam-221	264	21	)	)	PUNCT
ejpam-221	264	22	)	)	PUNCT
ejpam-221	264	23	,	,	PUNCT
ejpam-221	264	24	and	and	CCONJ
ejpam-221	264	25	by	by	ADP
ejpam-221	264	26	only	only	ADV
ejpam-221	264	27	insisting	insist	VERB
ejpam-221	264	28	that	that	SCONJ
ejpam-221	264	29	(	(	PUNCT
ejpam-221	264	30	cl	cl	NOUN
ejpam-221	264	31	)	)	PUNCT
ejpam-221	264	32	hold	hold	NOUN
ejpam-221	264	33	.	.	PUNCT
ejpam-221	265	1	dually	dually	ADV
ejpam-221	265	2	for	for	ADP
ejpam-221	265	3	right	right	ADJ
ejpam-221	265	4	type	type	NOUN
ejpam-221	265	5	t	t	PROPN
ejpam-221	265	6	semigroups	semigroup	NOUN
ejpam-221	265	7	.	.	PUNCT
ejpam-221	266	1	(	(	PUNCT
ejpam-221	266	2	left	leave	VERB
ejpam-221	266	3	/	/	SYM
ejpam-221	266	4	right	right	ADJ
ejpam-221	266	5	)	)	PUNCT
ejpam-221	266	6	type	type	NOUN
ejpam-221	266	7	t	t	NOUN
ejpam-221	266	8	semigroups	semigroup	NOUN
ejpam-221	266	9	came	come	VERB
ejpam-221	266	10	to	to	PART
ejpam-221	266	11	be	be	AUX
ejpam-221	266	12	known	know	VERB
ejpam-221	266	13	as	as	ADP
ejpam-221	266	14	weakly	weakly	ADJ
ejpam-221	266	15	(	(	PUNCT
ejpam-221	266	16	left	left	ADJ
ejpam-221	266	17	/	/	SYM
ejpam-221	266	18	right	right	ADJ
ejpam-221	266	19	)	)	PUNCT
ejpam-221	266	20	ample	ample	ADJ
ejpam-221	266	21	semigroups	semigroup	NOUN
ejpam-221	266	22	,	,	PUNCT
ejpam-221	266	23	owing	owe	VERB
ejpam-221	266	24	to	to	ADP
ejpam-221	266	25	their	their	PRON
ejpam-221	266	26	being	be	AUX
ejpam-221	266	27	a	a	DET
ejpam-221	266	28	generalisation	generalisation	NOUN
ejpam-221	266	29	of	of	ADP
ejpam-221	266	30	ample	ample	ADJ
ejpam-221	266	31	semigroups	semigroup	NOUN
ejpam-221	266	32	.	.	PUNCT
ejpam-221	267	1	weakly	weakly	ADV
ejpam-221	267	2	left	leave	VERB
ejpam-221	267	3	ample	ample	ADJ
ejpam-221	267	4	analogues	analogue	NOUN
ejpam-221	267	5	of	of	ADP
ejpam-221	267	6	mcalister	mcalister	PROPN
ejpam-221	267	7	’s	’s	PART
ejpam-221	267	8	covering	covering	NOUN
ejpam-221	267	9	and	and	CCONJ
ejpam-221	267	10	p	p	NOUN
ejpam-221	267	11	-	-	PUNCT
ejpam-221	267	12	theorems	theorem	NOUN
ejpam-221	267	13	were	be	AUX
ejpam-221	267	14	developed	develop	VERB
ejpam-221	267	15	in	in	ADP
ejpam-221	267	16	[	[	X
ejpam-221	267	17	27–29	27–29	NOUN
ejpam-221	267	18	]	]	X
ejpam-221	267	19	,	,	PUNCT
ejpam-221	267	20	whilst	whilst	SCONJ
ejpam-221	267	21	lawson	lawson	PROPN
ejpam-221	268	1	[	[	X
ejpam-221	268	2	43	43	NUM
ejpam-221	268	3	]	]	PUNCT
ejpam-221	268	4	obtained	obtain	VERB
ejpam-221	268	5	the	the	DET
ejpam-221	268	6	following	following	ADJ
ejpam-221	268	7	generalisation	generalisation	NOUN
ejpam-221	268	8	of	of	ADP
ejpam-221	268	9	theorem	theorem	ADJ
ejpam-221	268	10	1.20	1.20	NUM
ejpam-221	268	11	:	:	PUNCT
ejpam-221	268	12	theorem	theorem	VERB
ejpam-221	268	13	2.2	2.2	NUM
ejpam-221	268	14	.	.	PUNCT
ejpam-221	269	1	[	[	X
ejpam-221	269	2	43	43	NUM
ejpam-221	269	3	]	]	PUNCT
ejpam-221	269	4	the	the	DET
ejpam-221	269	5	category	category	NOUN
ejpam-221	269	6	of	of	ADP
ejpam-221	269	7	weakly	weakly	ADJ
ejpam-221	269	8	ample	ample	ADJ
ejpam-221	269	9	semigroups	semigroup	NOUN
ejpam-221	269	10	and	and	CCONJ
ejpam-221	269	11	(	(	PUNCT
ejpam-221	269	12	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-221	269	13	is	be	AUX
ejpam-221	269	14	isomorphic	isomorphic	ADJ
ejpam-221	269	15	to	to	ADP
ejpam-221	269	16	the	the	DET
ejpam-221	269	17	category	category	NOUN
ejpam-221	269	18	of	of	ADP
ejpam-221	269	19	inductive	inductive	ADJ
ejpam-221	269	20	unipotent	unipotent	ADJ
ejpam-221	269	21	categories	category	NOUN
ejpam-221	269	22	and	and	CCONJ
ejpam-221	269	23	inductive	inductive	ADJ
ejpam-221	269	24	functors	functor	NOUN
ejpam-221	269	25	.	.	PUNCT
ejpam-221	270	1	(	(	PUNCT
ejpam-221	270	2	a	a	DET
ejpam-221	270	3	unipotent	unipotent	ADJ
ejpam-221	270	4	category	category	NOUN
ejpam-221	270	5	is	be	AUX
ejpam-221	270	6	a	a	DET
ejpam-221	270	7	category	category	NOUN
ejpam-221	270	8	whose	whose	DET
ejpam-221	270	9	only	only	ADJ
ejpam-221	270	10	idempotents	idempotent	NOUN
ejpam-221	270	11	are	be	AUX
ejpam-221	270	12	its	its	PRON
ejpam-221	270	13	identities	identity	NOUN
ejpam-221	270	14	.	.	PUNCT
ejpam-221	270	15	)	)	PUNCT
ejpam-221	271	1	note	note	VERB
ejpam-221	271	2	that	that	SCONJ
ejpam-221	271	3	,	,	PUNCT
ejpam-221	271	4	just	just	ADV
ejpam-221	271	5	like	like	ADP
ejpam-221	271	6	armstrong	armstrong	PROPN
ejpam-221	271	7	,	,	PUNCT
ejpam-221	271	8	lawson	lawson	PROPN
ejpam-221	271	9	did	do	AUX
ejpam-221	271	10	not	not	PART
ejpam-221	271	11	formulate	formulate	VERB
ejpam-221	271	12	the	the	DET
ejpam-221	271	13	above	above	ADJ
ejpam-221	271	14	theorem	theorem	NOUN
ejpam-221	271	15	in	in	ADP
ejpam-221	271	16	categorytheoretic	categorytheoretic	ADJ
ejpam-221	271	17	terms	term	NOUN
ejpam-221	271	18	.	.	PUNCT
ejpam-221	272	1	in	in	ADP
ejpam-221	272	2	[	[	X
ejpam-221	272	3	47	47	NUM
ejpam-221	272	4	]	]	PUNCT
ejpam-221	272	5	,	,	PUNCT
ejpam-221	272	6	lawson	lawson	PROPN
ejpam-221	272	7	began	begin	VERB
ejpam-221	272	8	to	to	PART
ejpam-221	272	9	follow	follow	VERB
ejpam-221	272	10	up	up	ADP
ejpam-221	272	11	on	on	ADP
ejpam-221	272	12	the	the	DET
ejpam-221	272	13	earlier	early	ADJ
ejpam-221	272	14	work	work	NOUN
ejpam-221	272	15	in	in	ADP
ejpam-221	272	16	his	his	PRON
ejpam-221	272	17	thesis	thesis	NOUN
ejpam-221	273	1	[	[	X
ejpam-221	273	2	43	43	NUM
ejpam-221	273	3	]	]	PUNCT
ejpam-221	273	4	by	by	ADP
ejpam-221	273	5	drawing	draw	VERB
ejpam-221	273	6	connections	connection	NOUN
ejpam-221	273	7	between	between	ADP
ejpam-221	273	8	the	the	DET
ejpam-221	273	9	study	study	NOUN
ejpam-221	273	10	of	of	ADP
ejpam-221	273	11	semiabundant	semiabundant	PROPN
ejpam-221	273	12	semigroups	semigroup	NOUN
ejpam-221	273	13	and	and	CCONJ
ejpam-221	273	14	the	the	DET
ejpam-221	273	15	category	category	NOUN
ejpam-221	273	16	-	-	PUNCT
ejpam-221	273	17	theoretic	theoretic	NOUN
ejpam-221	273	18	work	work	NOUN
ejpam-221	273	19	of	of	ADP
ejpam-221	273	20	ehresmann	ehresmann	PROPN
ejpam-221	274	1	[	[	X
ejpam-221	274	2	14	14	NUM
ejpam-221	274	3	]	]	PUNCT
ejpam-221	274	4	.	.	PUNCT
ejpam-221	275	1	the	the	DET
ejpam-221	275	2	goal	goal	NOUN
ejpam-221	275	3	of	of	ADP
ejpam-221	275	4	this	this	DET
ejpam-221	275	5	linking	linking	NOUN
ejpam-221	275	6	of	of	ADP
ejpam-221	275	7	theories	theory	NOUN
ejpam-221	275	8	was	be	AUX
ejpam-221	275	9	the	the	DET
ejpam-221	275	10	application	application	NOUN
ejpam-221	275	11	of	of	ADP
ejpam-221	275	12	techniques	technique	NOUN
ejpam-221	275	13	from	from	ADP
ejpam-221	275	14	category	category	NOUN
ejpam-221	275	15	theory	theory	NOUN
ejpam-221	275	16	to	to	ADP
ejpam-221	275	17	semigroup	semigroup	PROPN
ejpam-221	275	18	theory	theory	NOUN
ejpam-221	275	19	;	;	PUNCT
ejpam-221	275	20	lawson	lawson	PROPN
ejpam-221	275	21	gave	give	VERB
ejpam-221	275	22	such	such	DET
ejpam-221	275	23	an	an	DET
ejpam-221	275	24	approach	approach	NOUN
ejpam-221	275	25	for	for	ADP
ejpam-221	275	26	inverse	inverse	NOUN
ejpam-221	275	27	semigroups	semigroup	NOUN
ejpam-221	275	28	in	in	ADP
ejpam-221	275	29	[	[	X
ejpam-221	275	30	45	45	NUM
ejpam-221	275	31	,	,	PUNCT
ejpam-221	275	32	48	48	NUM
ejpam-221	275	33	]	]	PUNCT
ejpam-221	275	34	.	.	PUNCT
ejpam-221	276	1	a	a	DET
ejpam-221	276	2	significant	significant	ADJ
ejpam-221	276	3	innovation	innovation	NOUN
ejpam-221	276	4	introduced	introduce	VERB
ejpam-221	276	5	by	by	ADP
ejpam-221	276	6	lawson	lawson	PROPN
ejpam-221	276	7	was	be	AUX
ejpam-221	276	8	the	the	DET
ejpam-221	276	9	realisation	realisation	NOUN
ejpam-221	276	10	that	that	SCONJ
ejpam-221	276	11	the	the	DET
ejpam-221	276	12	relations	relation	NOUN
ejpam-221	276	13	fl	fl	NOUN
ejpam-221	276	14	and	and	CCONJ
ejpam-221	276	15	er	er	INTJ
ejpam-221	276	16	need	need	AUX
ejpam-221	276	17	not	not	PART
ejpam-221	276	18	be	be	AUX
ejpam-221	276	19	defined	define	VERB
ejpam-221	276	20	with	with	ADP
ejpam-221	276	21	respect	respect	NOUN
ejpam-221	276	22	to	to	ADP
ejpam-221	276	23	the	the	DET
ejpam-221	276	24	whole	whole	ADJ
ejpam-221	276	25	set	set	NOUN
ejpam-221	276	26	of	of	ADP
ejpam-221	276	27	idempotents	idempotent	NOUN
ejpam-221	276	28	of	of	ADP
ejpam-221	276	29	a	a	DET
ejpam-221	276	30	semigroup	semigroup	NOUN
ejpam-221	276	31	.	.	PUNCT
ejpam-221	277	1	recall	recall	VERB
ejpam-221	277	2	that	that	SCONJ
ejpam-221	277	3	el	el	PROPN
ejpam-221	277	4	-	-	PUNCT
ejpam-221	277	5	qallali	qallali	PROPN
ejpam-221	277	6	defined	define	VERB
ejpam-221	277	7	a	a	DET
ejpam-221	277	8	semigroup	semigroup	NOUN
ejpam-221	277	9	to	to	PART
ejpam-221	277	10	be	be	AUX
ejpam-221	277	11	semiabundant	semiabundant	ADJ
ejpam-221	277	12	if	if	SCONJ
ejpam-221	277	13	every	every	DET
ejpam-221	277	14	element	element	NOUN
ejpam-221	277	15	is	be	AUX
ejpam-221	277	16	contained	contain	VERB
ejpam-221	277	17	in	in	ADP
ejpam-221	277	18	a	a	DET
ejpam-221	277	19	minimum	minimum	ADJ
ejpam-221	277	20	idempotent	idempotent	NOUN
ejpam-221	277	21	-	-	PUNCT
ejpam-221	277	22	generated	generate	VERB
ejpam-221	277	23	left	left	NOUN
ejpam-221	277	24	(	(	PUNCT
ejpam-221	277	25	right	right	ADJ
ejpam-221	277	26	)	)	PUNCT
ejpam-221	277	27	ideal	ideal	NOUN
ejpam-221	277	28	;	;	PUNCT
ejpam-221	277	29	lawson	lawson	PROPN
ejpam-221	277	30	,	,	PUNCT
ejpam-221	277	31	inspired	inspire	VERB
ejpam-221	277	32	by	by	ADP
ejpam-221	277	33	some	some	DET
ejpam-221	277	34	work	work	NOUN
ejpam-221	277	35	of	of	ADP
ejpam-221	277	36	de	de	X
ejpam-221	277	37	barros	barros	X
ejpam-221	278	1	[	[	X
ejpam-221	278	2	9	9	NUM
ejpam-221	278	3	]	]	PUNCT
ejpam-221	278	4	,	,	PUNCT
ejpam-221	278	5	extended	extend	VERB
ejpam-221	278	6	this	this	DET
ejpam-221	278	7	definition	definition	NOUN
ejpam-221	278	8	by	by	ADP
ejpam-221	278	9	insisting	insist	VERB
ejpam-221	278	10	that	that	SCONJ
ejpam-221	278	11	every	every	DET
ejpam-221	278	12	element	element	NOUN
ejpam-221	278	13	be	be	AUX
ejpam-221	278	14	contained	contain	VERB
ejpam-221	278	15	in	in	ADP
ejpam-221	278	16	a	a	DET
ejpam-221	278	17	minimum	minimum	ADJ
ejpam-221	278	18	left	left	NOUN
ejpam-221	278	19	(	(	PUNCT
ejpam-221	278	20	right	right	ADJ
ejpam-221	278	21	)	)	PUNCT
ejpam-221	278	22	ideal	ideal	NOUN
ejpam-221	278	23	generated	generate	VERB
ejpam-221	278	24	not	not	PART
ejpam-221	278	25	by	by	ADP
ejpam-221	278	26	an	an	DET
ejpam-221	278	27	arbitrary	arbitrary	ADJ
ejpam-221	278	28	idempotent	idempotent	NOUN
ejpam-221	278	29	,	,	PUNCT
ejpam-221	278	30	but	but	CCONJ
ejpam-221	278	31	by	by	ADP
ejpam-221	278	32	an	an	DET
ejpam-221	278	33	idempotent	idempotent	NOUN
ejpam-221	278	34	from	from	ADP
ejpam-221	278	35	some	some	DET
ejpam-221	278	36	distinguished	distinguished	ADJ
ejpam-221	278	37	subset	subset	VERB
ejpam-221	278	38	u	u	NOUN
ejpam-221	278	39	⊆	⊆	NUM
ejpam-221	278	40	e(s	e(s	PROPN
ejpam-221	278	41	)	)	PUNCT
ejpam-221	278	42	.	.	PUNCT
ejpam-221	279	1	such	such	DET
ejpam-221	279	2	a	a	DET
ejpam-221	279	3	semigroup	semigroup	NOUN
ejpam-221	279	4	was	be	AUX
ejpam-221	279	5	termed	term	VERB
ejpam-221	279	6	a	a	DET
ejpam-221	279	7	u	u	ADJ
ejpam-221	279	8	-	-	NOUN
ejpam-221	279	9	semiabundant	semiabundant	ADJ
ejpam-221	279	10	semigroup	semigroup	NOUN
ejpam-221	280	1	[	[	X
ejpam-221	280	2	47	47	NUM
ejpam-221	280	3	,	,	PUNCT
ejpam-221	280	4	p.	p.	NOUN
ejpam-221	280	5	425	425	NUM
ejpam-221	280	6	]	]	PUNCT
ejpam-221	280	7	.	.	PUNCT
ejpam-221	281	1	these	these	DET
ejpam-221	281	2	semigroups	semigroup	NOUN
ejpam-221	281	3	first	first	ADV
ejpam-221	281	4	appeared	appear	VERB
ejpam-221	281	5	in	in	ADP
ejpam-221	281	6	[	[	X
ejpam-221	281	7	46	46	NUM
ejpam-221	281	8	]	]	PUNCT
ejpam-221	281	9	,	,	PUNCT
ejpam-221	281	10	in	in	ADP
ejpam-221	281	11	which	which	PRON
ejpam-221	281	12	a	a	DET
ejpam-221	281	13	certain	certain	ADJ
ejpam-221	281	14	special	special	ADJ
ejpam-221	281	15	class	class	NOUN
ejpam-221	281	16	of	of	ADP
ejpam-221	281	17	u	u	NOUN
ejpam-221	281	18	-	-	ADJ
ejpam-221	281	19	semiabundant	semiabundant	ADJ
ejpam-221	281	20	semigroups	semigroup	NOUN
ejpam-221	281	21	,	,	PUNCT
ejpam-221	281	22	called	call	VERB
ejpam-221	281	23	rees	rees	PROPN
ejpam-221	281	24	semigroups	semigroup	NOUN
ejpam-221	281	25	,	,	PUNCT
ejpam-221	281	26	provided	provide	VERB
ejpam-221	281	27	an	an	DET
ejpam-221	281	28	abstract	abstract	ADJ
ejpam-221	281	29	model	model	NOUN
ejpam-221	281	30	for	for	ADP
ejpam-221	281	31	rees	ree	NOUN
ejpam-221	281	32	matrix	matrix	NOUN
ejpam-221	281	33	semigroups	semigroup	NOUN
ejpam-221	281	34	over	over	ADP
ejpam-221	281	35	an	an	DET
ejpam-221	281	36	arbitrary	arbitrary	ADJ
ejpam-221	281	37	monoid	monoid	NOUN
ejpam-221	281	38	.	.	PUNCT
ejpam-221	282	1	it	it	PRON
ejpam-221	282	2	is	be	AUX
ejpam-221	282	3	clear	clear	ADJ
ejpam-221	282	4	that	that	SCONJ
ejpam-221	282	5	a	a	DET
ejpam-221	282	6	u	u	NOUN
ejpam-221	282	7	-	-	NOUN
ejpam-221	282	8	semiabundant	semiabundant	ADJ
ejpam-221	282	9	semigroup	semigroup	NOUN
ejpam-221	282	10	with	with	ADP
ejpam-221	282	11	u	u	NOUN
ejpam-221	282	12	=	=	SYM
ejpam-221	282	13	e(s	e(s	PROPN
ejpam-221	282	14	)	)	PUNCT
ejpam-221	282	15	is	be	AUX
ejpam-221	282	16	semiabundant	semiabundant	PROPN
ejpam-221	282	17	.	.	PUNCT
ejpam-221	283	1	lawson	lawson	PROPN
ejpam-221	283	2	wrote	write	VERB
ejpam-221	283	3	down	down	ADP
ejpam-221	283	4	new	new	ADJ
ejpam-221	283	5	versions	version	NOUN
ejpam-221	283	6	of	of	ADP
ejpam-221	283	7	the	the	DET
ejpam-221	283	8	relations	relation	NOUN
ejpam-221	283	9	of	of	ADP
ejpam-221	283	10	fl	fl	PRON
ejpam-221	283	11	and	and	CCONJ
ejpam-221	283	12	er	er	INTJ
ejpam-221	283	13	,	,	PUNCT
ejpam-221	283	14	which	which	PRON
ejpam-221	283	15	were	be	AUX
ejpam-221	283	16	defined	define	VERB
ejpam-221	283	17	in	in	ADP
ejpam-221	283	18	terms	term	NOUN
ejpam-221	283	19	of	of	ADP
ejpam-221	283	20	u	u	NOUN
ejpam-221	283	21	;	;	PUNCT
ejpam-221	283	22	we	we	PRON
ejpam-221	283	23	will	will	AUX
ejpam-221	283	24	denote	denote	VERB
ejpam-221	283	25	these	these	PRON
ejpam-221	283	26	by	by	ADP
ejpam-221	283	27	flu	flu	NOUN
ejpam-221	283	28	and	and	CCONJ
ejpam-221	283	29	eru	eru	PROPN
ejpam-221	283	30	.	.	PUNCT
ejpam-221	284	1	thus	thus	ADV
ejpam-221	284	2	a	a	DET
ejpam-221	284	3	semigroup	semigroup	NOUN
ejpam-221	284	4	is	be	AUX
ejpam-221	284	5	u	u	NOUN
ejpam-221	284	6	-	-	NOUN
ejpam-221	284	7	semiabundant	semiabundant	ADJ
ejpam-221	284	8	if	if	SCONJ
ejpam-221	284	9	every	every	DET
ejpam-221	284	10	element	element	NOUN
ejpam-221	284	11	is	be	AUX
ejpam-221	284	12	both	both	PRON
ejpam-221	284	13	flu	flu	NOUN
ejpam-221	284	14	and	and	CCONJ
ejpam-221	284	15	eru	eru	PROPN
ejpam-221	284	16	-related	-relate	VERB
ejpam-221	284	17	to	to	ADP
ejpam-221	284	18	an	an	DET
ejpam-221	284	19	idempotent	idempotent	NOUN
ejpam-221	284	20	in	in	ADP
ejpam-221	284	21	u	u	PROPN
ejpam-221	284	22	.	.	PUNCT
ejpam-221	285	1	as	as	SCONJ
ejpam-221	285	2	one	one	PRON
ejpam-221	285	3	might	might	AUX
ejpam-221	285	4	expect	expect	VERB
ejpam-221	285	5	,	,	PUNCT
ejpam-221	285	6	given	give	VERB
ejpam-221	285	7	all	all	DET
ejpam-221	285	8	the	the	DET
ejpam-221	285	9	terminology	terminology	NOUN
ejpam-221	285	10	thus	thus	ADV
ejpam-221	285	11	far	far	ADV
ejpam-221	285	12	,	,	PUNCT
ejpam-221	285	13	u	u	NOUN
ejpam-221	285	14	-	-	NOUN
ejpam-221	285	15	semiabundant	semiabundant	ADJ
ejpam-221	285	16	semigroups	semigroup	NOUN
ejpam-221	285	17	in	in	ADP
ejpam-221	285	18	c.	c.	PROPN
ejpam-221	285	19	hollings	holling	NOUN
ejpam-221	285	20	/	/	SYM
ejpam-221	285	21	eur	eur	PROPN
ejpam-221	285	22	.	.	PUNCT
ejpam-221	286	1	j.	j.	PROPN
ejpam-221	286	2	pure	pure	PROPN
ejpam-221	286	3	appl	appl	PROPN
ejpam-221	286	4	.	.	PROPN
ejpam-221	286	5	math	math	PROPN
ejpam-221	286	6	,	,	PUNCT
ejpam-221	286	7	2	2	NUM
ejpam-221	286	8	(	(	PUNCT
ejpam-221	286	9	2009	2009	NUM
ejpam-221	286	10	)	)	PUNCT
ejpam-221	286	11	,	,	PUNCT
ejpam-221	286	12	(	(	PUNCT
ejpam-221	286	13	21	21	NUM
ejpam-221	286	14	-	-	SYM
ejpam-221	286	15	57	57	NUM
ejpam-221	286	16	)	)	PUNCT
ejpam-221	286	17	37	37	NUM
ejpam-221	286	18	which	which	PRON
ejpam-221	286	19	u	u	PRON
ejpam-221	286	20	forms	form	VERB
ejpam-221	286	21	a	a	DET
ejpam-221	286	22	subsemilattice	subsemilattice	NOUN
ejpam-221	286	23	were	be	AUX
ejpam-221	286	24	called	call	VERB
ejpam-221	286	25	u	u	NOUN
ejpam-221	286	26	-	-	NOUN
ejpam-221	286	27	semiadequate	semiadequate	NOUN
ejpam-221	286	28	[	[	X
ejpam-221	286	29	47	47	NUM
ejpam-221	286	30	,	,	PUNCT
ejpam-221	286	31	p.	p.	NOUN
ejpam-221	286	32	434	434	NUM
ejpam-221	286	33	]	]	PUNCT
ejpam-221	286	34	.	.	PUNCT
ejpam-221	287	1	as	as	SCONJ
ejpam-221	287	2	has	have	AUX
ejpam-221	287	3	been	be	AUX
ejpam-221	287	4	observed	observe	VERB
ejpam-221	287	5	,	,	PUNCT
ejpam-221	287	6	lawson	lawson	PROPN
ejpam-221	287	7	’s	’s	PART
ejpam-221	287	8	goal	goal	NOUN
ejpam-221	287	9	was	be	AUX
ejpam-221	287	10	to	to	PART
ejpam-221	287	11	draw	draw	VERB
ejpam-221	287	12	connections	connection	NOUN
ejpam-221	287	13	between	between	ADP
ejpam-221	287	14	particular	particular	ADJ
ejpam-221	287	15	classes	class	NOUN
ejpam-221	287	16	of	of	ADP
ejpam-221	287	17	semigroups	semigroup	NOUN
ejpam-221	287	18	and	and	CCONJ
ejpam-221	287	19	small	small	ADJ
ejpam-221	287	20	ordered	order	VERB
ejpam-221	287	21	categories	category	NOUN
ejpam-221	287	22	.	.	PUNCT
ejpam-221	288	1	to	to	ADP
ejpam-221	288	2	this	this	DET
ejpam-221	288	3	end	end	NOUN
ejpam-221	288	4	,	,	PUNCT
ejpam-221	288	5	he	he	PRON
ejpam-221	288	6	defined	define	VERB
ejpam-221	288	7	an	an	DET
ejpam-221	288	8	ehresmann	ehresmann	NOUN
ejpam-221	288	9	category	category	NOUN
ejpam-221	288	10	to	to	PART
ejpam-221	288	11	be	be	AUX
ejpam-221	288	12	a	a	DET
ejpam-221	288	13	small	small	ADJ
ejpam-221	288	14	category	category	NOUN
ejpam-221	288	15	equipped	equip	VERB
ejpam-221	288	16	with	with	ADP
ejpam-221	288	17	two	two	NUM
ejpam-221	288	18	partial	partial	ADJ
ejpam-221	288	19	order	order	NOUN
ejpam-221	288	20	relations	relation	NOUN
ejpam-221	288	21	,	,	PUNCT
ejpam-221	288	22	satisfying	satisfy	VERB
ejpam-221	288	23	certain	certain	ADJ
ejpam-221	288	24	conditions	condition	NOUN
ejpam-221	288	25	.	.	PUNCT
ejpam-221	289	1	he	he	PRON
ejpam-221	289	2	then	then	ADV
ejpam-221	289	3	showed	show	VERB
ejpam-221	289	4	that	that	SCONJ
ejpam-221	289	5	every	every	DET
ejpam-221	289	6	such	such	ADJ
ejpam-221	289	7	category	category	NOUN
ejpam-221	289	8	gives	give	VERB
ejpam-221	289	9	rise	rise	NOUN
ejpam-221	289	10	to	to	ADP
ejpam-221	289	11	a	a	DET
ejpam-221	289	12	particular	particular	ADJ
ejpam-221	289	13	type	type	NOUN
ejpam-221	289	14	of	of	ADP
ejpam-221	289	15	semigroup	semigroup	NOUN
ejpam-221	289	16	,	,	PUNCT
ejpam-221	289	17	which	which	PRON
ejpam-221	289	18	was	be	AUX
ejpam-221	289	19	given	give	VERB
ejpam-221	289	20	the	the	DET
ejpam-221	289	21	appropriate	appropriate	ADJ
ejpam-221	289	22	name	name	NOUN
ejpam-221	289	23	of	of	ADP
ejpam-221	289	24	ehresmann	ehresmann	PROPN
ejpam-221	289	25	semigroup	semigroup	PROPN
ejpam-221	289	26	.	.	PUNCT
ejpam-221	290	1	furthermore	furthermore	ADV
ejpam-221	290	2	,	,	PUNCT
ejpam-221	290	3	he	he	PRON
ejpam-221	290	4	demonstrated	demonstrate	VERB
ejpam-221	290	5	the	the	DET
ejpam-221	290	6	converse	converse	NOUN
ejpam-221	290	7	:	:	PUNCT
ejpam-221	290	8	that	that	SCONJ
ejpam-221	290	9	to	to	ADP
ejpam-221	290	10	every	every	DET
ejpam-221	290	11	ehresmann	ehresmann	PROPN
ejpam-221	290	12	semigroup	semigroup	NOUN
ejpam-221	290	13	there	there	PRON
ejpam-221	290	14	is	be	VERB
ejpam-221	290	15	associated	associate	VERB
ejpam-221	290	16	an	an	DET
ejpam-221	290	17	ehresmann	ehresmann	NOUN
ejpam-221	290	18	category	category	NOUN
ejpam-221	290	19	[	[	X
ejpam-221	290	20	47	47	NUM
ejpam-221	290	21	,	,	PUNCT
ejpam-221	290	22	§	§	NOUN
ejpam-221	290	23	4	4	NUM
ejpam-221	290	24	]	]	PUNCT
ejpam-221	290	25	.	.	PUNCT
ejpam-221	291	1	ehresmann	ehresmann	PROPN
ejpam-221	291	2	semigroups	semigroup	NOUN
ejpam-221	291	3	are	be	AUX
ejpam-221	291	4	,	,	PUNCT
ejpam-221	291	5	in	in	ADP
ejpam-221	291	6	fact	fact	NOUN
ejpam-221	291	7	,	,	PUNCT
ejpam-221	291	8	precisely	precisely	ADV
ejpam-221	291	9	those	those	DET
ejpam-221	291	10	u	u	ADJ
ejpam-221	291	11	-	-	ADJ
ejpam-221	291	12	semiadequate	semiadequate	ADJ
ejpam-221	291	13	semigroups	semigroup	NOUN
ejpam-221	291	14	in	in	ADP
ejpam-221	291	15	which	which	PRON
ejpam-221	291	16	(	(	PUNCT
ejpam-221	291	17	cl	cl	NOUN
ejpam-221	291	18	)	)	PUNCT
ejpam-221	291	19	and	and	CCONJ
ejpam-221	291	20	(	(	PUNCT
ejpam-221	291	21	cr	cr	NOUN
ejpam-221	291	22	)	)	PUNCT
ejpam-221	291	23	hold	hold	NOUN
ejpam-221	291	24	.	.	PUNCT
ejpam-221	292	1	lawson	lawson	PROPN
ejpam-221	292	2	generalised	generalise	VERB
ejpam-221	292	3	the	the	DET
ejpam-221	292	4	‘	'	PUNCT
ejpam-221	292	5	morphisms	morphism	NOUN
ejpam-221	292	6	’	'	PUNCT
ejpam-221	292	7	part	part	NOUN
ejpam-221	292	8	of	of	ADP
ejpam-221	292	9	theorem	theorem	ADJ
ejpam-221	292	10	1.19	1.19	NUM
ejpam-221	292	11	to	to	PART
ejpam-221	292	12	give	give	VERB
ejpam-221	292	13	an	an	DET
ejpam-221	292	14	isomorphism	isomorphism	NOUN
ejpam-221	292	15	between	between	ADP
ejpam-221	292	16	the	the	DET
ejpam-221	292	17	category	category	NOUN
ejpam-221	292	18	of	of	ADP
ejpam-221	292	19	ehresmann	ehresmann	PROPN
ejpam-221	292	20	semigroups	semigroup	NOUN
ejpam-221	292	21	and	and	CCONJ
ejpam-221	292	22	certain	certain	ADJ
ejpam-221	292	23	morphisms	morphism	NOUN
ejpam-221	292	24	,	,	PUNCT
ejpam-221	292	25	and	and	CCONJ
ejpam-221	292	26	the	the	DET
ejpam-221	292	27	category	category	NOUN
ejpam-221	292	28	of	of	ADP
ejpam-221	292	29	ehresmann	ehresmann	PROPN
ejpam-221	292	30	categories	category	NOUN
ejpam-221	292	31	and	and	CCONJ
ejpam-221	292	32	certain	certain	ADJ
ejpam-221	292	33	functors	functor	NOUN
ejpam-221	292	34	.	.	PUNCT
ejpam-221	293	1	in	in	ADP
ejpam-221	293	2	the	the	DET
ejpam-221	293	3	final	final	ADJ
ejpam-221	293	4	section	section	NOUN
ejpam-221	293	5	of	of	ADP
ejpam-221	293	6	[	[	X
ejpam-221	293	7	47	47	NUM
ejpam-221	293	8	]	]	PUNCT
ejpam-221	293	9	,	,	PUNCT
ejpam-221	293	10	lawson	lawson	PROPN
ejpam-221	293	11	considered	consider	VERB
ejpam-221	293	12	a	a	DET
ejpam-221	293	13	number	number	NOUN
ejpam-221	293	14	of	of	ADP
ejpam-221	293	15	special	special	ADJ
ejpam-221	293	16	cases	case	NOUN
ejpam-221	293	17	of	of	ADP
ejpam-221	293	18	ehresmann	ehresmann	PROPN
ejpam-221	293	19	semigroups	semigroup	NOUN
ejpam-221	293	20	.	.	PUNCT
ejpam-221	294	1	amongst	amongst	ADP
ejpam-221	294	2	these	these	PRON
ejpam-221	294	3	were	be	AUX
ejpam-221	294	4	idempotent	idempotent	ADJ
ejpam-221	294	5	-	-	PUNCT
ejpam-221	294	6	connected	connect	VERB
ejpam-221	294	7	ehresmann	ehresmann	NOUN
ejpam-221	294	8	semigroups	semigroup	NOUN
ejpam-221	294	9	;	;	PUNCT
ejpam-221	294	10	these	these	PRON
ejpam-221	294	11	,	,	PUNCT
ejpam-221	294	12	in	in	ADP
ejpam-221	294	13	fact	fact	NOUN
ejpam-221	294	14	,	,	PUNCT
ejpam-221	294	15	were	be	AUX
ejpam-221	294	16	none	none	NOUN
ejpam-221	294	17	other	other	ADJ
ejpam-221	294	18	than	than	ADP
ejpam-221	294	19	(	(	PUNCT
ejpam-221	294	20	two	two	NUM
ejpam-221	294	21	-	-	PUNCT
ejpam-221	294	22	sided	sided	ADJ
ejpam-221	294	23	)	)	PUNCT
ejpam-221	294	24	weakly	weakly	ADJ
ejpam-221	294	25	e	e	NOUN
ejpam-221	294	26	-	-	ADJ
ejpam-221	294	27	ample	ample	ADJ
ejpam-221	294	28	semigroups	semigroup	NOUN
ejpam-221	294	29	,	,	PUNCT
ejpam-221	294	30	where	where	SCONJ
ejpam-221	294	31	we	we	PRON
ejpam-221	294	32	have	have	AUX
ejpam-221	294	33	exchanged	exchange	VERB
ejpam-221	294	34	lawson	lawson	PROPN
ejpam-221	294	35	’s	’s	PART
ejpam-221	294	36	‘	'	PUNCT
ejpam-221	294	37	u	u	NOUN
ejpam-221	294	38	’	'	PUNCT
ejpam-221	294	39	for	for	ADP
ejpam-221	294	40	the	the	DET
ejpam-221	294	41	subsequently	subsequently	ADV
ejpam-221	294	42	more	more	ADV
ejpam-221	294	43	usual	usual	ADJ
ejpam-221	294	44	‘	'	PUNCT
ejpam-221	294	45	e	e	NOUN
ejpam-221	294	46	’	'	PUNCT
ejpam-221	294	47	.	.	PUNCT
ejpam-221	295	1	it	it	PRON
ejpam-221	295	2	is	be	AUX
ejpam-221	295	3	very	very	ADV
ejpam-221	295	4	easy	easy	ADJ
ejpam-221	295	5	to	to	PART
ejpam-221	295	6	write	write	VERB
ejpam-221	295	7	down	down	ADP
ejpam-221	295	8	the	the	DET
ejpam-221	295	9	one	one	NUM
ejpam-221	295	10	-	-	PUNCT
ejpam-221	295	11	sided	sided	ADJ
ejpam-221	295	12	definitions	definition	NOUN
ejpam-221	295	13	for	for	ADP
ejpam-221	295	14	weakly	weakly	ADJ
ejpam-221	295	15	left	left	ADJ
ejpam-221	295	16	e	e	NOUN
ejpam-221	295	17	-	-	NOUN
ejpam-221	295	18	ample	ample	ADJ
ejpam-221	295	19	(	(	PUNCT
ejpam-221	295	20	left	leave	VERB
ejpam-221	295	21	restriction	restriction	NOUN
ejpam-221	295	22	)	)	PUNCT
ejpam-221	295	23	and	and	CCONJ
ejpam-221	296	1	weakly	weakly	ADJ
ejpam-221	296	2	right	right	ADJ
ejpam-221	296	3	e	e	NOUN
ejpam-221	296	4	-	-	NOUN
ejpam-221	296	5	ample	ample	ADJ
ejpam-221	296	6	(	(	PUNCT
ejpam-221	296	7	right	right	ADJ
ejpam-221	296	8	restriction	restriction	NOUN
ejpam-221	296	9	)	)	PUNCT
ejpam-221	296	10	semigroups	semigroup	NOUN
ejpam-221	296	11	.	.	PUNCT
ejpam-221	297	1	lawson	lawson	PROPN
ejpam-221	297	2	specialised	specialise	VERB
ejpam-221	297	3	the	the	DET
ejpam-221	297	4	above	above	ADJ
ejpam-221	297	5	isomorphism	isomorphism	NOUN
ejpam-221	297	6	of	of	ADP
ejpam-221	297	7	categories	category	NOUN
ejpam-221	297	8	(	(	PUNCT
ejpam-221	297	9	for	for	ADP
ejpam-221	297	10	ehresmann	ehresmann	PROPN
ejpam-221	297	11	semigroups	semigroup	NOUN
ejpam-221	297	12	)	)	PUNCT
ejpam-221	297	13	to	to	ADP
ejpam-221	297	14	this	this	DET
ejpam-221	297	15	special	special	ADJ
ejpam-221	297	16	case	case	NOUN
ejpam-221	297	17	,	,	PUNCT
ejpam-221	297	18	thereby	thereby	ADV
ejpam-221	297	19	providing	provide	VERB
ejpam-221	297	20	the	the	DET
ejpam-221	297	21	following	follow	VERB
ejpam-221	297	22	generalisation	generalisation	NOUN
ejpam-221	297	23	of	of	ADP
ejpam-221	297	24	theorem	theorem	NOUN
ejpam-221	297	25	1.20	1.20	NUM
ejpam-221	297	26	,	,	PUNCT
ejpam-221	297	27	a	a	DET
ejpam-221	297	28	‘	'	PUNCT
ejpam-221	297	29	weakly	weakly	ADJ
ejpam-221	297	30	e	e	ADJ
ejpam-221	297	31	-	-	ADJ
ejpam-221	297	32	ample	ample	ADJ
ejpam-221	297	33	’	'	PUNCT
ejpam-221	297	34	version	version	NOUN
ejpam-221	297	35	of	of	ADP
ejpam-221	297	36	the	the	DET
ejpam-221	297	37	‘	'	PUNCT
ejpam-221	297	38	morphisms	morphism	NOUN
ejpam-221	297	39	’	'	PUNCT
ejpam-221	297	40	part	part	NOUN
ejpam-221	297	41	of	of	ADP
ejpam-221	297	42	theorem	theorem	ADJ
ejpam-221	297	43	1.19:‖	1.19:‖	PROPN
ejpam-221	297	44	theorem	theorem	VERB
ejpam-221	297	45	2.3	2.3	NUM
ejpam-221	297	46	.	.	PUNCT
ejpam-221	298	1	[	[	X
ejpam-221	298	2	47	47	NUM
ejpam-221	298	3	]	]	PUNCT
ejpam-221	298	4	the	the	DET
ejpam-221	298	5	category	category	NOUN
ejpam-221	298	6	of	of	ADP
ejpam-221	298	7	weakly	weakly	ADJ
ejpam-221	298	8	e	e	NOUN
ejpam-221	298	9	-	-	ADJ
ejpam-221	298	10	ample	ample	ADJ
ejpam-221	298	11	semigroups	semigroup	NOUN
ejpam-221	298	12	and	and	CCONJ
ejpam-221	298	13	(	(	PUNCT
ejpam-221	298	14	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-221	298	15	is	be	AUX
ejpam-221	298	16	isomorphic	isomorphic	ADJ
ejpam-221	298	17	to	to	ADP
ejpam-221	298	18	the	the	DET
ejpam-221	298	19	category	category	NOUN
ejpam-221	298	20	of	of	ADP
ejpam-221	298	21	inductive	inductive	ADJ
ejpam-221	298	22	categories	category	NOUN
ejpam-221	298	23	and	and	CCONJ
ejpam-221	298	24	inductive	inductive	ADJ
ejpam-221	298	25	functors	functor	NOUN
ejpam-221	298	26	.	.	PUNCT
ejpam-221	299	1	in	in	ADP
ejpam-221	299	2	[	[	X
ejpam-221	299	3	47	47	NUM
ejpam-221	299	4	,	,	PUNCT
ejpam-221	299	5	example	example	NOUN
ejpam-221	299	6	3.21	3.21	NUM
ejpam-221	299	7	]	]	PUNCT
ejpam-221	299	8	,	,	PUNCT
ejpam-221	299	9	lawson	lawson	PROPN
ejpam-221	299	10	presented	present	VERB
ejpam-221	299	11	a	a	DET
ejpam-221	299	12	number	number	NOUN
ejpam-221	299	13	of	of	ADP
ejpam-221	299	14	examples	example	NOUN
ejpam-221	299	15	of	of	ADP
ejpam-221	299	16	the	the	DET
ejpam-221	299	17	various	various	ADJ
ejpam-221	299	18	classes	class	NOUN
ejpam-221	299	19	of	of	ADP
ejpam-221	299	20	u	u	NOUN
ejpam-221	299	21	-	-	ADJ
ejpam-221	299	22	semiabundant	semiabundant	ADJ
ejpam-221	299	23	semigroups	semigroup	NOUN
ejpam-221	299	24	.	.	PUNCT
ejpam-221	300	1	amongst	amongst	ADP
ejpam-221	300	2	these	these	PRON
ejpam-221	300	3	appeared	appear	VERB
ejpam-221	300	4	the	the	DET
ejpam-221	300	5	example	example	NOUN
ejpam-221	300	6	of	of	ADP
ejpam-221	300	7	the	the	DET
ejpam-221	300	8	partial	partial	ADJ
ejpam-221	300	9	transformation	transformation	NOUN
ejpam-221	300	10	monoid	monoid	PROPN
ejpam-221	300	11	p	p	PROPN
ejpam-221	300	12	t	t	PROPN
ejpam-221	300	13	x	x	PUNCT
ejpam-221	300	14	on	on	ADP
ejpam-221	300	15	a	a	DET
ejpam-221	300	16	set	set	NOUN
ejpam-221	300	17	x	x	SYM
ejpam-221	300	18	,	,	PUNCT
ejpam-221	300	19	which	which	PRON
ejpam-221	300	20	,	,	PUNCT
ejpam-221	300	21	as	as	SCONJ
ejpam-221	300	22	we	we	PRON
ejpam-221	300	23	have	have	AUX
ejpam-221	300	24	seen	see	VERB
ejpam-221	300	25	,	,	PUNCT
ejpam-221	300	26	is	be	AUX
ejpam-221	300	27	a	a	DET
ejpam-221	300	28	left	left	ADJ
ejpam-221	300	29	restriction	restriction	NOUN
ejpam-221	300	30	semigroup	semigroup	NOUN
ejpam-221	300	31	.	.	PUNCT
ejpam-221	301	1	in	in	ADP
ejpam-221	301	2	fact	fact	NOUN
ejpam-221	301	3	,	,	PUNCT
ejpam-221	301	4	as	as	SCONJ
ejpam-221	301	5	we	we	PRON
ejpam-221	301	6	have	have	AUX
ejpam-221	301	7	also	also	ADV
ejpam-221	301	8	seen	see	VERB
ejpam-221	301	9	,	,	PUNCT
ejpam-221	301	10	any	any	DET
ejpam-221	301	11	left	left	ADJ
ejpam-221	301	12	restriction	restriction	NOUN
ejpam-221	301	13	semigroup	semigroup	NOUN
ejpam-221	301	14	arises	arise	VERB
ejpam-221	301	15	in	in	ADP
ejpam-221	301	16	an	an	DET
ejpam-221	301	17	extremely	extremely	ADV
ejpam-221	301	18	natural	natural	ADJ
ejpam-221	301	19	way	way	NOUN
ejpam-221	301	20	as	as	ADP
ejpam-221	301	21	a	a	DET
ejpam-221	301	22	(	(	PUNCT
ejpam-221	301	23	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	301	24	of	of	ADP
ejpam-221	301	25	some	some	DET
ejpam-221	301	26	p	p	NOUN
ejpam-221	301	27	t	t	NOUN
ejpam-221	301	28	x	x	X
ejpam-221	301	29	;	;	PUNCT
ejpam-221	301	30	in	in	ADP
ejpam-221	301	31	the	the	DET
ejpam-221	301	32	following	follow	VERB
ejpam-221	301	33	section	section	NOUN
ejpam-221	301	34	,	,	PUNCT
ejpam-221	301	35	we	we	PRON
ejpam-221	301	36	will	will	AUX
ejpam-221	301	37	introduce	introduce	VERB
ejpam-221	301	38	the	the	DET
ejpam-221	301	39	specifics	specific	NOUN
ejpam-221	301	40	of	of	ADP
ejpam-221	301	41	the	the	DET
ejpam-221	301	42	theory	theory	NOUN
ejpam-221	301	43	of	of	ADP
ejpam-221	301	44	left	left	ADJ
ejpam-221	301	45	restriction	restriction	NOUN
ejpam-221	301	46	semigroups	semigroup	NOUN
ejpam-221	301	47	via	via	ADP
ejpam-221	301	48	partial	partial	ADJ
ejpam-221	301	49	transformation	transformation	NOUN
ejpam-221	301	50	monoids	monoid	NOUN
ejpam-221	301	51	.	.	PUNCT
ejpam-221	302	1	‖a	‖a	NOUN
ejpam-221	302	2	‘	'	PUNCT
ejpam-221	302	3	weakly	weakly	ADJ
ejpam-221	302	4	e	e	ADJ
ejpam-221	302	5	-	-	ADJ
ejpam-221	302	6	ample	ample	ADJ
ejpam-221	302	7	’	'	PUNCT
ejpam-221	302	8	generalisation	generalisation	NOUN
ejpam-221	302	9	of	of	ADP
ejpam-221	302	10	the	the	DET
ejpam-221	302	11	‘	'	PUNCT
ejpam-221	302	12	∨-premorphisms	∨-premorphism	NOUN
ejpam-221	302	13	’	'	PUNCT
ejpam-221	302	14	part	part	NOUN
ejpam-221	302	15	can	can	AUX
ejpam-221	302	16	be	be	AUX
ejpam-221	302	17	found	find	VERB
ejpam-221	302	18	in	in	ADP
ejpam-221	302	19	[	[	X
ejpam-221	302	20	36	36	NUM
ejpam-221	302	21	]	]	PUNCT
ejpam-221	302	22	.	.	PUNCT
ejpam-221	303	1	c.	c.	PROPN
ejpam-221	303	2	hollings	holling	NOUN
ejpam-221	303	3	/	/	SYM
ejpam-221	303	4	eur	eur	PROPN
ejpam-221	303	5	.	.	PUNCT
ejpam-221	304	1	j.	j.	PROPN
ejpam-221	304	2	pure	pure	PROPN
ejpam-221	304	3	appl	appl	PROPN
ejpam-221	304	4	.	.	PROPN
ejpam-221	304	5	math	math	PROPN
ejpam-221	304	6	,	,	PUNCT
ejpam-221	304	7	2	2	NUM
ejpam-221	304	8	(	(	PUNCT
ejpam-221	304	9	2009	2009	NUM
ejpam-221	304	10	)	)	PUNCT
ejpam-221	304	11	,	,	PUNCT
ejpam-221	304	12	(	(	PUNCT
ejpam-221	304	13	21	21	NUM
ejpam-221	304	14	-	-	SYM
ejpam-221	304	15	57	57	NUM
ejpam-221	304	16	)	)	PUNCT
ejpam-221	304	17	38	38	NUM
ejpam-221	304	18	3	3	NUM
ejpam-221	304	19	.	.	PUNCT
ejpam-221	304	20	partial	partial	ADJ
ejpam-221	304	21	transformations	transformation	NOUN
ejpam-221	304	22	restriction	restriction	NOUN
ejpam-221	304	23	semigroups	semigroup	NOUN
ejpam-221	304	24	arise	arise	VERB
ejpam-221	304	25	very	very	ADV
ejpam-221	304	26	naturally	naturally	ADV
ejpam-221	304	27	from	from	ADP
ejpam-221	304	28	partial	partial	ADJ
ejpam-221	304	29	transformation	transformation	NOUN
ejpam-221	304	30	monoids	monoid	NOUN
ejpam-221	304	31	in	in	ADP
ejpam-221	304	32	much	much	ADV
ejpam-221	304	33	the	the	DET
ejpam-221	304	34	same	same	ADJ
ejpam-221	304	35	way	way	NOUN
ejpam-221	304	36	that	that	PRON
ejpam-221	304	37	inverse	inverse	NOUN
ejpam-221	304	38	semigroups	semigroup	NOUN
ejpam-221	304	39	arise	arise	VERB
ejpam-221	304	40	from	from	ADP
ejpam-221	304	41	symmetric	symmetric	ADJ
ejpam-221	304	42	inverse	inverse	NOUN
ejpam-221	304	43	monoids	monoid	NOUN
ejpam-221	304	44	.	.	PUNCT
ejpam-221	305	1	we	we	PRON
ejpam-221	305	2	therefore	therefore	ADV
ejpam-221	305	3	begin	begin	VERB
ejpam-221	305	4	by	by	ADP
ejpam-221	305	5	expanding	expand	VERB
ejpam-221	305	6	upon	upon	SCONJ
ejpam-221	305	7	our	our	PRON
ejpam-221	305	8	comments	comment	NOUN
ejpam-221	305	9	on	on	ADP
ejpam-221	305	10	partial	partial	ADJ
ejpam-221	305	11	transformations	transformation	NOUN
ejpam-221	305	12	in	in	ADP
ejpam-221	305	13	the	the	DET
ejpam-221	305	14	introduction	introduction	NOUN
ejpam-221	305	15	.	.	PUNCT
ejpam-221	306	1	a	a	DET
ejpam-221	306	2	partial	partial	ADJ
ejpam-221	306	3	transformation	transformation	NOUN
ejpam-221	306	4	of	of	ADP
ejpam-221	306	5	a	a	DET
ejpam-221	306	6	set	set	NOUN
ejpam-221	306	7	x	x	PUNCT
ejpam-221	306	8	is	be	AUX
ejpam-221	306	9	a	a	DET
ejpam-221	306	10	function	function	NOUN
ejpam-221	306	11	a→	a→	PUNCT
ejpam-221	306	12	b	b	NOUN
ejpam-221	306	13	,	,	PUNCT
ejpam-221	306	14	where	where	SCONJ
ejpam-221	306	15	a	a	DET
ejpam-221	306	16	,	,	PUNCT
ejpam-221	306	17	b	b	NOUN
ejpam-221	306	18	⊆	⊆	NUM
ejpam-221	306	19	x	x	X
ejpam-221	306	20	.	.	PUNCT
ejpam-221	307	1	the	the	DET
ejpam-221	307	2	collection	collection	NOUN
ejpam-221	307	3	of	of	ADP
ejpam-221	307	4	all	all	DET
ejpam-221	307	5	partial	partial	ADJ
ejpam-221	307	6	transformations	transformation	NOUN
ejpam-221	307	7	of	of	ADP
ejpam-221	307	8	x	x	SYM
ejpam-221	307	9	is	be	AUX
ejpam-221	307	10	denoted	denote	VERB
ejpam-221	307	11	p	p	PROPN
ejpam-221	307	12	t	t	NOUN
ejpam-221	307	13	x	x	X
ejpam-221	307	14	.	.	PUNCT
ejpam-221	308	1	under	under	ADP
ejpam-221	308	2	the	the	DET
ejpam-221	308	3	(	(	PUNCT
ejpam-221	308	4	left	leave	VERB
ejpam-221	308	5	-	-	PUNCT
ejpam-221	308	6	to	to	ADP
ejpam-221	308	7	-	-	PUNCT
ejpam-221	308	8	right	right	ADJ
ejpam-221	308	9	)	)	PUNCT
ejpam-221	308	10	composition	composition	NOUN
ejpam-221	308	11	(	(	PUNCT
ejpam-221	308	12	∗	∗	NOUN
ejpam-221	308	13	)	)	PUNCT
ejpam-221	308	14	from	from	ADP
ejpam-221	308	15	the	the	DET
ejpam-221	308	16	introduction	introduction	NOUN
ejpam-221	308	17	,	,	PUNCT
ejpam-221	308	18	p	p	PROPN
ejpam-221	308	19	t	t	NOUN
ejpam-221	308	20	x	x	PUNCT
ejpam-221	308	21	forms	form	VERB
ejpam-221	308	22	a	a	DET
ejpam-221	308	23	monoid	monoid	NOUN
ejpam-221	308	24	—	—	PUNCT
ejpam-221	308	25	the	the	DET
ejpam-221	308	26	partial	partial	ADJ
ejpam-221	308	27	transformation	transformation	NOUN
ejpam-221	308	28	monoid	monoid	NOUN
ejpam-221	308	29	on	on	ADP
ejpam-221	308	30	x	x	X
ejpam-221	308	31	.	.	PUNCT
ejpam-221	309	1	the	the	DET
ejpam-221	309	2	partial	partial	ADJ
ejpam-221	309	3	mapping	mapping	NOUN
ejpam-221	309	4	with	with	ADP
ejpam-221	309	5	domain	domain	NOUN
ejpam-221	309	6	;	;	PUNCT
ejpam-221	309	7	,	,	PUNCT
ejpam-221	309	8	called	call	VERB
ejpam-221	309	9	the	the	DET
ejpam-221	309	10	empty	empty	ADJ
ejpam-221	309	11	transformation	transformation	NOUN
ejpam-221	309	12	,	,	PUNCT
ejpam-221	309	13	is	be	AUX
ejpam-221	309	14	denoted	denote	VERB
ejpam-221	309	15	by	by	ADP
ejpam-221	309	16	ǫ	ǫ	PRON
ejpam-221	309	17	.	.	PUNCT
ejpam-221	310	1	it	it	PRON
ejpam-221	310	2	is	be	AUX
ejpam-221	310	3	clear	clear	ADJ
ejpam-221	310	4	that	that	SCONJ
ejpam-221	310	5	ix	ix	ADV
ejpam-221	310	6	,	,	PUNCT
ejpam-221	310	7	the	the	DET
ejpam-221	310	8	symmetric	symmetric	ADJ
ejpam-221	310	9	inverse	inverse	NOUN
ejpam-221	310	10	monoid	monoid	NOUN
ejpam-221	310	11	on	on	ADP
ejpam-221	310	12	x	x	X
ejpam-221	310	13	,	,	PUNCT
ejpam-221	310	14	is	be	AUX
ejpam-221	310	15	an	an	DET
ejpam-221	310	16	inverse	inverse	ADJ
ejpam-221	310	17	submonoid	submonoid	NOUN
ejpam-221	310	18	of	of	ADP
ejpam-221	310	19	p	p	PROPN
ejpam-221	310	20	t	t	PROPN
ejpam-221	310	21	x	x	X
ejpam-221	310	22	.	.	PUNCT
ejpam-221	311	1	the	the	DET
ejpam-221	311	2	full	full	ADJ
ejpam-221	311	3	transformation	transformation	NOUN
ejpam-221	311	4	monoid	monoid	PROPN
ejpam-221	311	5	tx	tx	PROPN
ejpam-221	311	6	is	be	AUX
ejpam-221	311	7	also	also	ADV
ejpam-221	311	8	a	a	DET
ejpam-221	311	9	submonoid	submonoid	NOUN
ejpam-221	311	10	of	of	ADP
ejpam-221	311	11	p	p	PROPN
ejpam-221	311	12	t	t	PROPN
ejpam-221	311	13	x	x	X
ejpam-221	311	14	,	,	PUNCT
ejpam-221	311	15	since	since	SCONJ
ejpam-221	311	16	any	any	DET
ejpam-221	311	17	mapping	mapping	NOUN
ejpam-221	311	18	x	x	PUNCT
ejpam-221	311	19	→	→	SYM
ejpam-221	311	20	x	x	SYM
ejpam-221	311	21	qualifies	qualifie	NOUN
ejpam-221	311	22	as	as	ADP
ejpam-221	311	23	a	a	DET
ejpam-221	311	24	‘	'	PUNCT
ejpam-221	311	25	partial	partial	ADJ
ejpam-221	311	26	transformation	transformation	NOUN
ejpam-221	311	27	’	'	PUNCT
ejpam-221	311	28	of	of	ADP
ejpam-221	311	29	x	x	SYM
ejpam-221	311	30	.	.	PUNCT
ejpam-221	312	1	amongst	amongst	ADP
ejpam-221	312	2	the	the	DET
ejpam-221	312	3	elements	element	NOUN
ejpam-221	312	4	of	of	ADP
ejpam-221	312	5	p	p	PROPN
ejpam-221	312	6	t	t	PROPN
ejpam-221	312	7	x	x	INTJ
ejpam-221	312	8	,	,	PUNCT
ejpam-221	312	9	there	there	PRON
ejpam-221	312	10	are	be	VERB
ejpam-221	312	11	certain	certain	ADJ
ejpam-221	312	12	idempotents	idempotent	NOUN
ejpam-221	312	13	which	which	PRON
ejpam-221	312	14	will	will	AUX
ejpam-221	312	15	be	be	AUX
ejpam-221	312	16	vital	vital	ADJ
ejpam-221	312	17	to	to	ADP
ejpam-221	312	18	our	our	PRON
ejpam-221	312	19	definition	definition	NOUN
ejpam-221	312	20	of	of	ADP
ejpam-221	312	21	restriction	restriction	NOUN
ejpam-221	312	22	semigroups	semigroup	NOUN
ejpam-221	312	23	.	.	PUNCT
ejpam-221	313	1	these	these	PRON
ejpam-221	313	2	are	be	AUX
ejpam-221	313	3	the	the	DET
ejpam-221	313	4	idempotents	idempotent	NOUN
ejpam-221	313	5	of	of	ADP
ejpam-221	313	6	the	the	DET
ejpam-221	313	7	form	form	NOUN
ejpam-221	313	8	iz	iz	INTJ
ejpam-221	313	9	,	,	PUNCT
ejpam-221	313	10	for	for	ADP
ejpam-221	313	11	z	z	PROPN
ejpam-221	313	12	⊆	⊆	NUM
ejpam-221	313	13	x	x	SYM
ejpam-221	313	14	,	,	PUNCT
ejpam-221	313	15	i.e.	i.e.	X
ejpam-221	313	16	,	,	PUNCT
ejpam-221	313	17	those	those	DET
ejpam-221	313	18	idempotents	idempotent	NOUN
ejpam-221	313	19	which	which	PRON
ejpam-221	313	20	are	be	AUX
ejpam-221	313	21	identities	identity	NOUN
ejpam-221	313	22	on	on	ADP
ejpam-221	313	23	their	their	PRON
ejpam-221	313	24	domains	domain	NOUN
ejpam-221	313	25	.	.	PUNCT
ejpam-221	314	1	we	we	PRON
ejpam-221	314	2	will	will	AUX
ejpam-221	314	3	refer	refer	VERB
ejpam-221	314	4	to	to	ADP
ejpam-221	314	5	such	such	ADJ
ejpam-221	314	6	idempotents	idempotent	NOUN
ejpam-221	314	7	as	as	ADP
ejpam-221	314	8	partial	partial	ADJ
ejpam-221	314	9	identities	identity	NOUN
ejpam-221	314	10	.	.	PUNCT
ejpam-221	315	1	let	let	VERB
ejpam-221	315	2	ex	ex	PRON
ejpam-221	315	3	⊆	⊆	NUM
ejpam-221	315	4	e(p	e(p	PROPN
ejpam-221	315	5	t	t	PROPN
ejpam-221	315	6	x	x	PUNCT
ejpam-221	315	7	)	)	PUNCT
ejpam-221	315	8	be	be	AUX
ejpam-221	315	9	the	the	DET
ejpam-221	315	10	set	set	NOUN
ejpam-221	315	11	of	of	ADP
ejpam-221	315	12	partial	partial	ADJ
ejpam-221	315	13	identities	identity	NOUN
ejpam-221	315	14	of	of	ADP
ejpam-221	315	15	p	p	PROPN
ejpam-221	315	16	t	t	PROPN
ejpam-221	315	17	x	x	X
ejpam-221	315	18	.	.	PUNCT
ejpam-221	316	1	we	we	PRON
ejpam-221	316	2	note	note	VERB
ejpam-221	316	3	that	that	SCONJ
ejpam-221	316	4	e(ix	e(ix	PROPN
ejpam-221	316	5	)	)	PUNCT
ejpam-221	316	6	=	=	SYM
ejpam-221	317	1	ex	ex	X
ejpam-221	317	2	.	.	PUNCT
ejpam-221	318	1	we	we	PRON
ejpam-221	318	2	stress	stress	VERB
ejpam-221	318	3	,	,	PUNCT
ejpam-221	318	4	however	however	ADV
ejpam-221	318	5	,	,	PUNCT
ejpam-221	318	6	that	that	SCONJ
ejpam-221	318	7	,	,	PUNCT
ejpam-221	318	8	in	in	ADP
ejpam-221	318	9	general	general	ADJ
ejpam-221	318	10	,	,	PUNCT
ejpam-221	318	11	p	p	PROPN
ejpam-221	318	12	t	t	PROPN
ejpam-221	318	13	x	x	AUX
ejpam-221	318	14	will	will	AUX
ejpam-221	318	15	have	have	VERB
ejpam-221	318	16	idempotents	idempotent	NOUN
ejpam-221	318	17	other	other	ADJ
ejpam-221	318	18	than	than	ADP
ejpam-221	318	19	those	those	PRON
ejpam-221	318	20	in	in	ADP
ejpam-221	318	21	ex	ex	PRON
ejpam-221	318	22	.	.	PUNCT
ejpam-221	319	1	for	for	ADP
ejpam-221	319	2	example	example	NOUN
ejpam-221	319	3	,	,	PUNCT
ejpam-221	319	4	for	for	ADP
ejpam-221	319	5	any	any	DET
ejpam-221	319	6	fixed	fix	VERB
ejpam-221	319	7	element	element	NOUN
ejpam-221	319	8	x	x	SYM
ejpam-221	319	9	∈	∈	PROPN
ejpam-221	319	10	x	x	X
ejpam-221	319	11	,	,	PUNCT
ejpam-221	319	12	the	the	DET
ejpam-221	319	13	constant	constant	ADJ
ejpam-221	319	14	mapping	mapping	NOUN
ejpam-221	319	15	cx	cx	NOUN
ejpam-221	319	16	:	:	PUNCT
ejpam-221	319	17	x	x	X
ejpam-221	319	18	→	→	SYM
ejpam-221	319	19	x	x	X
ejpam-221	319	20	which	which	PRON
ejpam-221	319	21	sends	send	VERB
ejpam-221	319	22	every	every	DET
ejpam-221	319	23	element	element	NOUN
ejpam-221	319	24	of	of	ADP
ejpam-221	319	25	x	x	PUNCT
ejpam-221	319	26	to	to	ADP
ejpam-221	319	27	x	x	PRON
ejpam-221	319	28	,	,	PUNCT
ejpam-221	319	29	is	be	AUX
ejpam-221	319	30	an	an	DET
ejpam-221	319	31	idempotent	idempotent	NOUN
ejpam-221	319	32	of	of	ADP
ejpam-221	319	33	p	p	PROPN
ejpam-221	319	34	t	t	PROPN
ejpam-221	319	35	x	x	PUNCT
ejpam-221	319	36	which	which	PRON
ejpam-221	319	37	is	be	AUX
ejpam-221	319	38	not	not	PART
ejpam-221	319	39	a	a	DET
ejpam-221	319	40	partial	partial	ADJ
ejpam-221	319	41	identity	identity	NOUN
ejpam-221	319	42	.	.	PUNCT
ejpam-221	320	1	we	we	PRON
ejpam-221	320	2	consider	consider	VERB
ejpam-221	320	3	the	the	DET
ejpam-221	320	4	following	follow	VERB
ejpam-221	320	5	unary	unary	ADJ
ejpam-221	320	6	operation	operation	NOUN
ejpam-221	320	7	on	on	ADP
ejpam-221	320	8	partial	partial	ADJ
ejpam-221	320	9	transformations	transformation	NOUN
ejpam-221	320	10	:	:	PUNCT
ejpam-221	320	11	α	α	PROPN
ejpam-221	320	12	7→	7→	NUM
ejpam-221	320	13	idomα	idomα	NOUN
ejpam-221	320	14	.	.	PUNCT
ejpam-221	321	1	in	in	ADP
ejpam-221	321	2	p	p	PROPN
ejpam-221	321	3	t	t	PROPN
ejpam-221	321	4	x	x	PUNCT
ejpam-221	321	5	,	,	PUNCT
ejpam-221	321	6	we	we	PRON
ejpam-221	321	7	will	will	AUX
ejpam-221	321	8	denote	denote	VERB
ejpam-221	321	9	this	this	DET
ejpam-221	321	10	operation	operation	NOUN
ejpam-221	321	11	by	by	ADP
ejpam-221	321	12	+	+	PROPN
ejpam-221	321	13	,	,	PUNCT
ejpam-221	321	14	whilst	whilst	SCONJ
ejpam-221	321	15	in	in	ADP
ejpam-221	321	16	p	p	PROPN
ejpam-221	321	17	t	t	NOUN
ejpam-221	321	18	∗x	∗x	PUNCT
ejpam-221	321	19	,	,	PUNCT
ejpam-221	321	20	it	it	PRON
ejpam-221	321	21	will	will	AUX
ejpam-221	321	22	be	be	AUX
ejpam-221	321	23	denoted	denote	VERB
ejpam-221	321	24	by	by	ADP
ejpam-221	321	25	∗.	∗.	PROPN
ejpam-221	321	26	let	let	VERB
ejpam-221	321	27	s	s	PRON
ejpam-221	321	28	be	be	AUX
ejpam-221	321	29	a	a	DET
ejpam-221	321	30	subsemigroup	subsemigroup	NOUN
ejpam-221	321	31	of	of	ADP
ejpam-221	321	32	p	p	PROPN
ejpam-221	321	33	t	t	PROPN
ejpam-221	321	34	x	x	X
ejpam-221	321	35	.	.	PUNCT
ejpam-221	322	1	we	we	PRON
ejpam-221	322	2	put	put	VERB
ejpam-221	322	3	s+	s+	PUNCT
ejpam-221	322	4	=	=	PUNCT
ejpam-221	322	5	{	{	PUNCT
ejpam-221	322	6	α+	α+	X
ejpam-221	322	7	:	:	PUNCT
ejpam-221	322	8	α	α	PROPN
ejpam-221	322	9	∈	∈	PROPN
ejpam-221	322	10	s	s	PART
ejpam-221	322	11	}	}	PUNCT
ejpam-221	322	12	⊆	⊆	NUM
ejpam-221	322	13	e(s	e(s	NUM
ejpam-221	322	14	)	)	PUNCT
ejpam-221	322	15	.	.	PUNCT
ejpam-221	323	1	definition	definition	NOUN
ejpam-221	323	2	3.1	3.1	NUM
ejpam-221	323	3	.	.	PUNCT
ejpam-221	324	1	let	let	VERB
ejpam-221	324	2	s	s	PRON
ejpam-221	324	3	be	be	AUX
ejpam-221	324	4	a	a	DET
ejpam-221	324	5	subsemigroup	subsemigroup	NOUN
ejpam-221	324	6	of	of	ADP
ejpam-221	324	7	some	some	DET
ejpam-221	324	8	p	p	NOUN
ejpam-221	324	9	t	t	NOUN
ejpam-221	324	10	x	x	INTJ
ejpam-221	324	11	.	.	PUNCT
ejpam-221	325	1	if	if	SCONJ
ejpam-221	325	2	s	s	NOUN
ejpam-221	325	3	is	be	AUX
ejpam-221	325	4	closed	close	VERB
ejpam-221	325	5	under	under	ADP
ejpam-221	325	6	+	+	ADJ
ejpam-221	325	7	,	,	PUNCT
ejpam-221	325	8	i.e.	i.e.	X
ejpam-221	325	9	,	,	PUNCT
ejpam-221	325	10	if	if	SCONJ
ejpam-221	325	11	s+	s+	ADV
ejpam-221	325	12	⊆	⊆	NUM
ejpam-221	325	13	s	s	NOUN
ejpam-221	325	14	,	,	PUNCT
ejpam-221	325	15	then	then	ADV
ejpam-221	325	16	we	we	PRON
ejpam-221	325	17	call	call	VERB
ejpam-221	325	18	s	s	PRON
ejpam-221	325	19	a	a	DET
ejpam-221	325	20	left	left	ADJ
ejpam-221	325	21	restriction	restriction	NOUN
ejpam-221	325	22	semigroup	semigroup	NOUN
ejpam-221	325	23	with	with	ADP
ejpam-221	325	24	respect	respect	NOUN
ejpam-221	325	25	to	to	ADP
ejpam-221	325	26	s+	s+	PUNCT
ejpam-221	325	27	.	.	PUNCT
ejpam-221	326	1	now	now	ADV
ejpam-221	326	2	let	let	VERB
ejpam-221	326	3	t	t	NOUN
ejpam-221	326	4	be	be	AUX
ejpam-221	326	5	a	a	DET
ejpam-221	326	6	subsemigroup	subsemigroup	NOUN
ejpam-221	326	7	of	of	ADP
ejpam-221	326	8	some	some	DET
ejpam-221	326	9	p	p	NOUN
ejpam-221	326	10	t	t	NOUN
ejpam-221	326	11	∗x	∗x	NOUN
ejpam-221	326	12	.	.	PUNCT
ejpam-221	327	1	we	we	PRON
ejpam-221	327	2	put	put	VERB
ejpam-221	327	3	t	t	PROPN
ejpam-221	327	4	∗	∗	NOUN
ejpam-221	327	5	=	=	PUNCT
ejpam-221	327	6	{	{	PUNCT
ejpam-221	327	7	α∗	α∗	NOUN
ejpam-221	327	8	:	:	PUNCT
ejpam-221	328	1	α	α	PROPN
ejpam-221	328	2	∈	∈	PROPN
ejpam-221	328	3	t	t	PROPN
ejpam-221	328	4	}	}	PUNCT
ejpam-221	328	5	⊆	⊆	NUM
ejpam-221	328	6	e(t	e(t	NOUN
ejpam-221	328	7	)	)	PUNCT
ejpam-221	328	8	.	.	PUNCT
ejpam-221	329	1	c.	c.	PROPN
ejpam-221	329	2	hollings	holling	NOUN
ejpam-221	329	3	/	/	SYM
ejpam-221	329	4	eur	eur	PROPN
ejpam-221	329	5	.	.	PUNCT
ejpam-221	330	1	j.	j.	PROPN
ejpam-221	330	2	pure	pure	PROPN
ejpam-221	330	3	appl	appl	PROPN
ejpam-221	330	4	.	.	PROPN
ejpam-221	330	5	math	math	PROPN
ejpam-221	330	6	,	,	PUNCT
ejpam-221	330	7	2	2	NUM
ejpam-221	330	8	(	(	PUNCT
ejpam-221	330	9	2009	2009	NUM
ejpam-221	330	10	)	)	PUNCT
ejpam-221	330	11	,	,	PUNCT
ejpam-221	330	12	(	(	PUNCT
ejpam-221	330	13	21	21	NUM
ejpam-221	330	14	-	-	SYM
ejpam-221	330	15	57	57	NUM
ejpam-221	330	16	)	)	PUNCT
ejpam-221	330	17	39	39	NUM
ejpam-221	330	18	definition	definition	NOUN
ejpam-221	330	19	3.2	3.2	NUM
ejpam-221	330	20	.	.	PUNCT
ejpam-221	331	1	let	let	VERB
ejpam-221	331	2	t	t	NOUN
ejpam-221	331	3	be	be	AUX
ejpam-221	331	4	a	a	DET
ejpam-221	331	5	subsemigroup	subsemigroup	NOUN
ejpam-221	331	6	of	of	ADP
ejpam-221	331	7	some	some	DET
ejpam-221	331	8	p	p	NOUN
ejpam-221	331	9	t	t	NOUN
ejpam-221	331	10	∗x	∗x	NOUN
ejpam-221	331	11	.	.	PUNCT
ejpam-221	332	1	if	if	SCONJ
ejpam-221	332	2	t	t	PROPN
ejpam-221	332	3	is	be	AUX
ejpam-221	332	4	closed	close	VERB
ejpam-221	332	5	under	under	ADP
ejpam-221	332	6	∗	∗	NOUN
ejpam-221	332	7	,	,	PUNCT
ejpam-221	332	8	i.e.	i.e.	X
ejpam-221	332	9	,	,	PUNCT
ejpam-221	332	10	if	if	SCONJ
ejpam-221	332	11	t	t	PROPN
ejpam-221	332	12	∗	∗	VERB
ejpam-221	332	13	⊆	⊆	NUM
ejpam-221	332	14	t	t	NOUN
ejpam-221	332	15	,	,	PUNCT
ejpam-221	332	16	then	then	ADV
ejpam-221	332	17	we	we	PRON
ejpam-221	332	18	call	call	VERB
ejpam-221	332	19	t	t	PROPN
ejpam-221	332	20	a	a	DET
ejpam-221	332	21	right	right	ADJ
ejpam-221	332	22	restriction	restriction	NOUN
ejpam-221	332	23	semigroup	semigroup	NOUN
ejpam-221	332	24	with	with	ADP
ejpam-221	332	25	respect	respect	NOUN
ejpam-221	332	26	to	to	ADP
ejpam-221	332	27	t	t	PROPN
ejpam-221	332	28	∗.	∗.	PROPN
ejpam-221	332	29	definition	definition	NOUN
ejpam-221	332	30	3.3	3.3	NUM
ejpam-221	332	31	.	.	PUNCT
ejpam-221	333	1	let	let	VERB
ejpam-221	333	2	s	s	PRON
ejpam-221	333	3	be	be	AUX
ejpam-221	333	4	a	a	DET
ejpam-221	333	5	semigroup	semigroup	NOUN
ejpam-221	333	6	.	.	PUNCT
ejpam-221	334	1	if	if	SCONJ
ejpam-221	334	2	s	s	NOUN
ejpam-221	334	3	is	be	AUX
ejpam-221	334	4	simultaneously	simultaneously	ADV
ejpam-221	334	5	isomorphic	isomorphic	ADJ
ejpam-221	334	6	to	to	ADP
ejpam-221	334	7	a	a	DET
ejpam-221	334	8	subsemigroup	subsemigroup	NOUN
ejpam-221	334	9	of	of	ADP
ejpam-221	334	10	some	some	DET
ejpam-221	334	11	p	p	NOUN
ejpam-221	334	12	t	t	NOUN
ejpam-221	334	13	x	x	PUNCT
ejpam-221	334	14	that	that	PRON
ejpam-221	334	15	is	be	AUX
ejpam-221	334	16	closed	close	VERB
ejpam-221	334	17	under	under	ADP
ejpam-221	334	18	+	+	ADV
ejpam-221	334	19	,	,	PUNCT
ejpam-221	334	20	and	and	CCONJ
ejpam-221	334	21	to	to	ADP
ejpam-221	334	22	a	a	DET
ejpam-221	334	23	subsemigroup	subsemigroup	NOUN
ejpam-221	334	24	of	of	ADP
ejpam-221	334	25	some	some	PRON
ejpam-221	334	26	p	p	NOUN
ejpam-221	334	27	t	t	X
ejpam-221	335	1	∗y	∗y	PROPN
ejpam-221	336	1	that	that	PRON
ejpam-221	336	2	is	be	AUX
ejpam-221	336	3	closed	close	VERB
ejpam-221	336	4	under	under	ADP
ejpam-221	336	5	∗	∗	NOUN
ejpam-221	336	6	,	,	PUNCT
ejpam-221	336	7	and	and	CCONJ
ejpam-221	336	8	if	if	SCONJ
ejpam-221	336	9	,	,	PUNCT
ejpam-221	336	10	in	in	ADP
ejpam-221	336	11	addition	addition	NOUN
ejpam-221	336	12	,	,	PUNCT
ejpam-221	336	13	the	the	DET
ejpam-221	336	14	(	(	PUNCT
ejpam-221	336	15	images	image	NOUN
ejpam-221	336	16	of	of	ADP
ejpam-221	336	17	the	the	DET
ejpam-221	336	18	)	)	PUNCT
ejpam-221	336	19	semilattices	semilattice	NOUN
ejpam-221	336	20	s+	s+	PUNCT
ejpam-221	336	21	and	and	CCONJ
ejpam-221	336	22	s∗	s∗	PROPN
ejpam-221	336	23	coincide	coincide	NOUN
ejpam-221	336	24	,	,	PUNCT
ejpam-221	336	25	then	then	ADV
ejpam-221	336	26	we	we	PRON
ejpam-221	336	27	call	call	VERB
ejpam-221	336	28	s	s	VERB
ejpam-221	336	29	a	a	DET
ejpam-221	336	30	two	two	NUM
ejpam-221	336	31	-	-	PUNCT
ejpam-221	336	32	sided	side	VERB
ejpam-221	336	33	restriction	restriction	NOUN
ejpam-221	336	34	semigroup	semigroup	NOUN
ejpam-221	336	35	with	with	ADP
ejpam-221	336	36	respect	respect	NOUN
ejpam-221	336	37	to	to	ADP
ejpam-221	336	38	s+	s+	NOUN
ejpam-221	336	39	=	=	PUNCT
ejpam-221	336	40	s∗.	s∗.	ADJ
ejpam-221	336	41	a	a	DET
ejpam-221	336	42	semigroup	semigroup	NOUN
ejpam-221	336	43	s	s	PRON
ejpam-221	336	44	that	that	PRON
ejpam-221	336	45	forms	form	VERB
ejpam-221	336	46	a	a	DET
ejpam-221	336	47	left	left	ADJ
ejpam-221	336	48	/	/	SYM
ejpam-221	336	49	right	right	ADJ
ejpam-221	336	50	/	/	SYM
ejpam-221	336	51	two	two	NUM
ejpam-221	336	52	-	-	PUNCT
ejpam-221	336	53	sided	side	VERB
ejpam-221	336	54	restriction	restriction	NOUN
ejpam-221	336	55	semigroup	semigroup	NOUN
ejpam-221	336	56	with	with	ADP
ejpam-221	336	57	respect	respect	NOUN
ejpam-221	336	58	to	to	ADP
ejpam-221	336	59	the	the	DET
ejpam-221	336	60	whole	whole	NOUN
ejpam-221	336	61	of	of	ADP
ejpam-221	336	62	e(s	e(s	PROPN
ejpam-221	336	63	)	)	PUNCT
ejpam-221	336	64	will	will	AUX
ejpam-221	336	65	be	be	AUX
ejpam-221	336	66	termed	term	VERB
ejpam-221	336	67	a	a	DET
ejpam-221	336	68	full	full	ADJ
ejpam-221	336	69	left	left	ADJ
ejpam-221	336	70	/	/	SYM
ejpam-221	336	71	right	right	ADJ
ejpam-221	336	72	/	/	SYM
ejpam-221	336	73	two	two	NUM
ejpam-221	336	74	-	-	PUNCT
ejpam-221	336	75	sided	side	VERB
ejpam-221	336	76	restriction	restriction	NOUN
ejpam-221	336	77	semigroup	semigroup	NOUN
ejpam-221	336	78	.	.	PUNCT
ejpam-221	337	1	it	it	PRON
ejpam-221	337	2	is	be	AUX
ejpam-221	337	3	clear	clear	ADJ
ejpam-221	337	4	that	that	SCONJ
ejpam-221	337	5	p	p	PROPN
ejpam-221	337	6	t	t	PROPN
ejpam-221	337	7	x	x	VERB
ejpam-221	337	8	is	be	AUX
ejpam-221	337	9	a	a	DET
ejpam-221	337	10	left	left	ADJ
ejpam-221	337	11	restriction	restriction	NOUN
ejpam-221	337	12	semigroup	semigroup	NOUN
ejpam-221	337	13	.	.	PUNCT
ejpam-221	338	1	furthermore	furthermore	ADV
ejpam-221	338	2	,	,	PUNCT
ejpam-221	338	3	a	a	DET
ejpam-221	338	4	left	left	ADJ
ejpam-221	338	5	restriction	restriction	NOUN
ejpam-221	338	6	semigroup	semigroup	NOUN
ejpam-221	338	7	may	may	AUX
ejpam-221	338	8	be	be	AUX
ejpam-221	338	9	regarded	regard	VERB
ejpam-221	338	10	as	as	ADP
ejpam-221	338	11	a	a	DET
ejpam-221	338	12	(	(	PUNCT
ejpam-221	338	13	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	338	14	of	of	ADP
ejpam-221	338	15	p	p	PROPN
ejpam-221	338	16	t	t	PROPN
ejpam-221	338	17	x	x	PUNCT
ejpam-221	338	18	.	.	PUNCT
ejpam-221	339	1	observe	observe	VERB
ejpam-221	339	2	that	that	SCONJ
ejpam-221	339	3	in	in	ADP
ejpam-221	339	4	any	any	PRON
ejpam-221	339	5	ix	ix	ADV
ejpam-221	339	6	,	,	PUNCT
ejpam-221	339	7	+	+	CCONJ
ejpam-221	339	8	can	can	AUX
ejpam-221	339	9	be	be	AUX
ejpam-221	339	10	expressed	express	VERB
ejpam-221	339	11	as	as	SCONJ
ejpam-221	339	12	follows	follow	VERB
ejpam-221	339	13	,	,	PUNCT
ejpam-221	339	14	for	for	ADP
ejpam-221	339	15	α	α	PRON
ejpam-221	339	16	∈	∈	PROPN
ejpam-221	339	17	ix	ix	X
ejpam-221	339	18	:	:	PUNCT
ejpam-221	339	19	α+	α+	X
ejpam-221	339	20	=	=	SYM
ejpam-221	339	21	αα−1	αα−1	NOUN
ejpam-221	339	22	.	.	PUNCT
ejpam-221	340	1	(	(	PUNCT
ejpam-221	340	2	3.1	3.1	NUM
ejpam-221	340	3	)	)	PUNCT
ejpam-221	340	4	therefore	therefore	ADV
ejpam-221	340	5	,	,	PUNCT
ejpam-221	340	6	the	the	DET
ejpam-221	340	7	fact	fact	NOUN
ejpam-221	340	8	that	that	SCONJ
ejpam-221	340	9	ix	ix	ADV
ejpam-221	340	10	is	be	AUX
ejpam-221	340	11	closed	close	VERB
ejpam-221	340	12	under	under	ADP
ejpam-221	340	13	composition	composition	NOUN
ejpam-221	340	14	and	and	CCONJ
ejpam-221	340	15	inverses	inverse	NOUN
ejpam-221	340	16	ensures	ensure	VERB
ejpam-221	340	17	that	that	SCONJ
ejpam-221	340	18	it	it	PRON
ejpam-221	340	19	is	be	AUX
ejpam-221	340	20	closed	close	VERB
ejpam-221	340	21	under	under	ADP
ejpam-221	340	22	+	+	PROPN
ejpam-221	340	23	.	.	PUNCT
ejpam-221	341	1	furthermore	furthermore	ADV
ejpam-221	341	2	,	,	PUNCT
ejpam-221	341	3	(	(	PUNCT
ejpam-221	341	4	ix	ix	ADV
ejpam-221	341	5	)	)	PUNCT
ejpam-221	341	6	+	+	PUNCT
ejpam-221	342	1	=	=	SYM
ejpam-221	342	2	ex	ex	X
ejpam-221	342	3	.	.	PUNCT
ejpam-221	343	1	thus	thus	ADV
ejpam-221	343	2	,	,	PUNCT
ejpam-221	343	3	ix	ix	ADV
ejpam-221	343	4	is	be	AUX
ejpam-221	343	5	a	a	DET
ejpam-221	343	6	full	full	ADJ
ejpam-221	343	7	left	left	NOUN
ejpam-221	343	8	restriction	restriction	NOUN
ejpam-221	343	9	semigroup	semigroup	NOUN
ejpam-221	343	10	.	.	PUNCT
ejpam-221	344	1	moreover	moreover	ADV
ejpam-221	344	2	,	,	PUNCT
ejpam-221	344	3	by	by	ADP
ejpam-221	344	4	the	the	DET
ejpam-221	344	5	wagner	wagner	PROPN
ejpam-221	344	6	-	-	PUNCT
ejpam-221	344	7	preston	preston	PROPN
ejpam-221	344	8	representation	representation	NOUN
ejpam-221	344	9	theorem	theorem	VERB
ejpam-221	344	10	[	[	X
ejpam-221	344	11	49	49	NUM
ejpam-221	344	12	,	,	PUNCT
ejpam-221	344	13	theorem	theorem	VERB
ejpam-221	344	14	1.5.1	1.5.1	NUM
ejpam-221	344	15	]	]	X
ejpam-221	344	16	,	,	PUNCT
ejpam-221	344	17	any	any	DET
ejpam-221	344	18	inverse	inverse	NOUN
ejpam-221	344	19	semigroup	semigroup	NOUN
ejpam-221	344	20	is	be	AUX
ejpam-221	344	21	a	a	DET
ejpam-221	344	22	full	full	ADJ
ejpam-221	344	23	left	left	NOUN
ejpam-221	344	24	restriction	restriction	NOUN
ejpam-221	344	25	semigroup	semigroup	NOUN
ejpam-221	344	26	.	.	PUNCT
ejpam-221	345	1	in	in	ADP
ejpam-221	345	2	the	the	DET
ejpam-221	345	3	following	following	ADJ
ejpam-221	345	4	section	section	NOUN
ejpam-221	345	5	,	,	PUNCT
ejpam-221	345	6	we	we	PRON
ejpam-221	345	7	will	will	AUX
ejpam-221	345	8	prove	prove	VERB
ejpam-221	345	9	this	this	PRON
ejpam-221	345	10	explicitly	explicitly	ADV
ejpam-221	345	11	in	in	ADP
ejpam-221	345	12	an	an	DET
ejpam-221	345	13	abstract	abstract	ADJ
ejpam-221	345	14	setting	setting	NOUN
ejpam-221	345	15	.	.	PUNCT
ejpam-221	346	1	note	note	VERB
ejpam-221	346	2	that	that	SCONJ
ejpam-221	346	3	ix	ix	ADV
ejpam-221	346	4	is	be	AUX
ejpam-221	346	5	left	leave	VERB
ejpam-221	346	6	-	-	PUNCT
ejpam-221	346	7	right	right	NOUN
ejpam-221	346	8	dual	dual	ADJ
ejpam-221	346	9	and	and	CCONJ
ejpam-221	346	10	must	must	AUX
ejpam-221	346	11	therefore	therefore	ADV
ejpam-221	346	12	also	also	ADV
ejpam-221	346	13	be	be	AUX
ejpam-221	346	14	a	a	DET
ejpam-221	346	15	full	full	ADJ
ejpam-221	346	16	right	right	ADJ
ejpam-221	346	17	restriction	restriction	NOUN
ejpam-221	346	18	semigroup	semigroup	NOUN
ejpam-221	346	19	,	,	PUNCT
ejpam-221	346	20	hence	hence	ADV
ejpam-221	346	21	a	a	DET
ejpam-221	346	22	full	full	ADJ
ejpam-221	346	23	two	two	NUM
ejpam-221	346	24	-	-	PUNCT
ejpam-221	346	25	sided	sided	ADJ
ejpam-221	346	26	restriction	restriction	NOUN
ejpam-221	346	27	semigroup	semigroup	NOUN
ejpam-221	346	28	.	.	PUNCT
ejpam-221	347	1	in	in	ADP
ejpam-221	347	2	ix	ix	ADV
ejpam-221	347	3	,	,	PUNCT
ejpam-221	347	4	the	the	DET
ejpam-221	347	5	unary	unary	ADJ
ejpam-221	347	6	operation	operation	NOUN
ejpam-221	347	7	∗	∗	NOUN
ejpam-221	347	8	can	can	AUX
ejpam-221	347	9	be	be	AUX
ejpam-221	347	10	written	write	VERB
ejpam-221	347	11	as	as	ADP
ejpam-221	347	12	α∗	α∗	NOUN
ejpam-221	347	13	=	=	SYM
ejpam-221	347	14	α−1α	α−1α	NOUN
ejpam-221	347	15	.	.	PUNCT
ejpam-221	348	1	(	(	PUNCT
ejpam-221	348	2	3.2	3.2	NUM
ejpam-221	348	3	)	)	PUNCT
ejpam-221	348	4	by	by	ADP
ejpam-221	348	5	way	way	NOUN
ejpam-221	348	6	of	of	ADP
ejpam-221	348	7	concluding	conclude	VERB
ejpam-221	348	8	this	this	DET
ejpam-221	348	9	section	section	NOUN
ejpam-221	348	10	,	,	PUNCT
ejpam-221	348	11	we	we	PRON
ejpam-221	348	12	note	note	VERB
ejpam-221	348	13	that	that	SCONJ
ejpam-221	348	14	a	a	DET
ejpam-221	348	15	partial	partial	ADJ
ejpam-221	348	16	transformation	transformation	NOUN
ejpam-221	348	17	monoid	monoid	NOUN
ejpam-221	348	18	possesses	possess	VERB
ejpam-221	348	19	an	an	DET
ejpam-221	348	20	obvious	obvious	ADJ
ejpam-221	348	21	partial	partial	ADJ
ejpam-221	348	22	order	order	NOUN
ejpam-221	348	23	:	:	PUNCT
ejpam-221	349	1	α≤	α≤	PROPN
ejpam-221	349	2	β	β	X
ejpam-221	349	3	⇐	⇐	ADJ
ejpam-221	349	4	⇒	⇒	PROPN
ejpam-221	349	5	α	α	NOUN
ejpam-221	349	6	=	=	X
ejpam-221	349	7	β	β	NOUN
ejpam-221	349	8	|domα	|domα	NOUN
ejpam-221	349	9	.	.	PUNCT
ejpam-221	350	1	(	(	PUNCT
ejpam-221	350	2	3.3	3.3	NUM
ejpam-221	350	3	)	)	PUNCT
ejpam-221	350	4	this	this	DET
ejpam-221	350	5	partial	partial	ADJ
ejpam-221	350	6	order	order	NOUN
ejpam-221	350	7	is	be	AUX
ejpam-221	350	8	natural	natural	ADJ
ejpam-221	350	9	,	,	PUNCT
ejpam-221	350	10	in	in	ADP
ejpam-221	350	11	the	the	DET
ejpam-221	350	12	sense	sense	NOUN
ejpam-221	350	13	that	that	SCONJ
ejpam-221	350	14	it	it	PRON
ejpam-221	350	15	is	be	AUX
ejpam-221	350	16	compatible	compatible	ADJ
ejpam-221	350	17	with	with	ADP
ejpam-221	350	18	composition	composition	NOUN
ejpam-221	350	19	and	and	CCONJ
ejpam-221	350	20	restricts	restrict	VERB
ejpam-221	350	21	to	to	ADP
ejpam-221	350	22	the	the	DET
ejpam-221	350	23	usual	usual	ADJ
ejpam-221	350	24	partial	partial	ADJ
ejpam-221	350	25	order	order	NOUN
ejpam-221	350	26	on	on	ADP
ejpam-221	350	27	ex	ex	PRON
ejpam-221	350	28	.	.	PUNCT
ejpam-221	351	1	in	in	ADP
ejpam-221	351	2	tx	tx	PROPN
ejpam-221	351	3	,	,	PUNCT
ejpam-221	351	4	the	the	DET
ejpam-221	351	5	ordering	ordering	NOUN
ejpam-221	351	6	of	of	ADP
ejpam-221	351	7	(	(	PUNCT
ejpam-221	351	8	3.3	3.3	NUM
ejpam-221	351	9	)	)	PUNCT
ejpam-221	351	10	becomes	become	VERB
ejpam-221	351	11	trivial	trivial	ADJ
ejpam-221	351	12	.	.	PUNCT
ejpam-221	352	1	note	note	VERB
ejpam-221	352	2	also	also	ADV
ejpam-221	352	3	that	that	SCONJ
ejpam-221	352	4	when	when	SCONJ
ejpam-221	352	5	this	this	DET
ejpam-221	352	6	ordering	ordering	NOUN
ejpam-221	352	7	is	be	AUX
ejpam-221	352	8	applied	apply	VERB
ejpam-221	352	9	in	in	ADP
ejpam-221	352	10	the	the	DET
ejpam-221	352	11	inverse	inverse	NOUN
ejpam-221	352	12	case	case	NOUN
ejpam-221	352	13	,	,	PUNCT
ejpam-221	352	14	it	it	PRON
ejpam-221	352	15	yields	yield	VERB
ejpam-221	352	16	,	,	PUNCT
ejpam-221	352	17	for	for	ADP
ejpam-221	352	18	example	example	NOUN
ejpam-221	352	19	,	,	PUNCT
ejpam-221	352	20	the	the	DET
ejpam-221	352	21	ordering	ordering	NOUN
ejpam-221	352	22	in	in	ADP
ejpam-221	352	23	an	an	DET
ejpam-221	352	24	inductive	inductive	ADJ
ejpam-221	352	25	groupoid	groupoid	NOUN
ejpam-221	352	26	,	,	PUNCT
ejpam-221	352	27	as	as	ADP
ejpam-221	352	28	per	per	ADP
ejpam-221	352	29	theorem	theorem	NOUN
ejpam-221	352	30	1.19	1.19	NUM
ejpam-221	352	31	.	.	PUNCT
ejpam-221	353	1	c.	c.	NOUN
ejpam-221	353	2	hollings	holling	NOUN
ejpam-221	353	3	/	/	SYM
ejpam-221	353	4	eur	eur	PROPN
ejpam-221	353	5	.	.	PUNCT
ejpam-221	354	1	j.	j.	PROPN
ejpam-221	354	2	pure	pure	PROPN
ejpam-221	354	3	appl	appl	PROPN
ejpam-221	354	4	.	.	PROPN
ejpam-221	354	5	math	math	PROPN
ejpam-221	354	6	,	,	PUNCT
ejpam-221	354	7	2	2	NUM
ejpam-221	354	8	(	(	PUNCT
ejpam-221	354	9	2009	2009	NUM
ejpam-221	354	10	)	)	PUNCT
ejpam-221	354	11	,	,	PUNCT
ejpam-221	354	12	(	(	PUNCT
ejpam-221	354	13	21	21	NUM
ejpam-221	354	14	-	-	SYM
ejpam-221	354	15	57	57	NUM
ejpam-221	354	16	)	)	PUNCT
ejpam-221	354	17	40	40	NUM
ejpam-221	354	18	4	4	NUM
ejpam-221	354	19	.	.	PUNCT
ejpam-221	355	1	the	the	DET
ejpam-221	355	2	abstract	abstract	ADJ
ejpam-221	355	3	characterisation	characterisation	NOUN
ejpam-221	355	4	we	we	PRON
ejpam-221	355	5	have	have	AUX
ejpam-221	355	6	seen	see	VERB
ejpam-221	355	7	that	that	SCONJ
ejpam-221	355	8	restriction	restriction	NOUN
ejpam-221	355	9	semigroups	semigroup	NOUN
ejpam-221	355	10	arise	arise	VERB
ejpam-221	355	11	very	very	ADV
ejpam-221	355	12	naturally	naturally	ADV
ejpam-221	355	13	from	from	ADP
ejpam-221	355	14	partial	partial	ADJ
ejpam-221	355	15	transformation	transformation	NOUN
ejpam-221	355	16	monoids	monoid	NOUN
ejpam-221	355	17	;	;	PUNCT
ejpam-221	355	18	they	they	PRON
ejpam-221	355	19	also	also	ADV
ejpam-221	355	20	have	have	VERB
ejpam-221	355	21	a	a	DET
ejpam-221	355	22	useful	useful	ADJ
ejpam-221	355	23	abstract	abstract	ADJ
ejpam-221	355	24	characterisation	characterisation	NOUN
ejpam-221	355	25	.	.	PUNCT
ejpam-221	356	1	harking	hark	VERB
ejpam-221	356	2	back	back	ADV
ejpam-221	356	3	to	to	ADP
ejpam-221	356	4	the	the	DET
ejpam-221	356	5	terminology	terminology	NOUN
ejpam-221	356	6	we	we	PRON
ejpam-221	356	7	saw	see	VERB
ejpam-221	356	8	unfold	unfold	NOUN
ejpam-221	356	9	in	in	ADP
ejpam-221	356	10	section	section	NOUN
ejpam-221	356	11	2	2	NUM
ejpam-221	356	12	,	,	PUNCT
ejpam-221	356	13	we	we	PRON
ejpam-221	356	14	will	will	AUX
ejpam-221	356	15	introduce	introduce	VERB
ejpam-221	356	16	the	the	DET
ejpam-221	356	17	abstract	abstract	ADJ
ejpam-221	356	18	definition	definition	NOUN
ejpam-221	356	19	under	under	ADP
ejpam-221	356	20	the	the	DET
ejpam-221	356	21	name	name	NOUN
ejpam-221	356	22	weakly	weakly	ADV
ejpam-221	356	23	left	leave	VERB
ejpam-221	356	24	e	e	NOUN
ejpam-221	356	25	-	-	ADJ
ejpam-221	356	26	ample	ample	ADJ
ejpam-221	356	27	semigroup	semigroup	NOUN
ejpam-221	356	28	and	and	CCONJ
ejpam-221	356	29	then	then	ADV
ejpam-221	356	30	prove	prove	VERB
ejpam-221	356	31	that	that	SCONJ
ejpam-221	356	32	these	these	PRON
ejpam-221	356	33	are	be	AUX
ejpam-221	356	34	in	in	ADP
ejpam-221	356	35	fact	fact	NOUN
ejpam-221	356	36	precisely	precisely	ADV
ejpam-221	356	37	the	the	DET
ejpam-221	356	38	left	left	ADJ
ejpam-221	356	39	restriction	restriction	NOUN
ejpam-221	356	40	semigroups	semigroup	VERB
ejpam-221	356	41	that	that	SCONJ
ejpam-221	356	42	we	we	PRON
ejpam-221	356	43	defined	define	VERB
ejpam-221	356	44	via	via	ADP
ejpam-221	356	45	partial	partial	ADJ
ejpam-221	356	46	transformations	transformation	NOUN
ejpam-221	356	47	in	in	ADP
ejpam-221	356	48	the	the	DET
ejpam-221	356	49	previous	previous	ADJ
ejpam-221	356	50	section	section	NOUN
ejpam-221	356	51	.	.	PUNCT
ejpam-221	357	1	note	note	VERB
ejpam-221	357	2	that	that	SCONJ
ejpam-221	357	3	we	we	PRON
ejpam-221	357	4	will	will	AUX
ejpam-221	357	5	focus	focus	VERB
ejpam-221	357	6	our	our	PRON
ejpam-221	357	7	attention	attention	NOUN
ejpam-221	357	8	on	on	ADP
ejpam-221	357	9	the	the	DET
ejpam-221	357	10	left	left	ADJ
ejpam-221	357	11	-	-	PUNCT
ejpam-221	357	12	hand	hand	NOUN
ejpam-221	357	13	versions	version	NOUN
ejpam-221	357	14	of	of	ADP
ejpam-221	357	15	these	these	DET
ejpam-221	357	16	semigroups	semigroup	NOUN
ejpam-221	357	17	;	;	PUNCT
ejpam-221	357	18	the	the	DET
ejpam-221	357	19	right	right	ADJ
ejpam-221	357	20	-	-	PUNCT
ejpam-221	357	21	hand	hand	NOUN
ejpam-221	357	22	version	version	NOUN
ejpam-221	357	23	is	be	AUX
ejpam-221	357	24	dual	dual	ADJ
ejpam-221	357	25	.	.	PUNCT
ejpam-221	358	1	let	let	VERB
ejpam-221	358	2	s	s	PRON
ejpam-221	358	3	be	be	AUX
ejpam-221	358	4	a	a	DET
ejpam-221	358	5	semigroup	semigroup	NOUN
ejpam-221	358	6	and	and	CCONJ
ejpam-221	358	7	let	let	VERB
ejpam-221	358	8	e	e	NOUN
ejpam-221	358	9	⊆	⊆	NUM
ejpam-221	358	10	e(s	e(s	PROPN
ejpam-221	358	11	)	)	PUNCT
ejpam-221	358	12	be	be	AUX
ejpam-221	358	13	a	a	DET
ejpam-221	358	14	distinguished	distinguished	ADJ
ejpam-221	358	15	subset	subset	NOUN
ejpam-221	358	16	of	of	ADP
ejpam-221	358	17	idempotents	idempotent	NOUN
ejpam-221	358	18	of	of	ADP
ejpam-221	358	19	s.	s.	PROPN
ejpam-221	358	20	we	we	PRON
ejpam-221	358	21	define	define	VERB
ejpam-221	358	22	the	the	DET
ejpam-221	358	23	relation	relation	NOUN
ejpam-221	358	24	ere	ere	NOUN
ejpam-221	358	25	on	on	ADP
ejpam-221	358	26	s	s	PRON
ejpam-221	358	27	by	by	ADP
ejpam-221	358	28	the	the	DET
ejpam-221	358	29	rule	rule	NOUN
ejpam-221	358	30	that	that	SCONJ
ejpam-221	358	31	a	a	DET
ejpam-221	358	32	ere	ere	PROPN
ejpam-221	358	33	b	b	PROPN
ejpam-221	358	34	⇐	⇐	PROPN
ejpam-221	358	35	⇒∀e	⇒∀e	PROPN
ejpam-221	358	36	∈	∈	PROPN
ejpam-221	358	37	e[ea	e[ea	PROPN
ejpam-221	358	38	=	=	PUNCT
ejpam-221	358	39	a⇔	a⇔	PROPN
ejpam-221	358	40	eb	eb	PROPN
ejpam-221	358	41	=	=	SYM
ejpam-221	358	42	b	b	PROPN
ejpam-221	358	43	]	]	X
ejpam-221	358	44	,	,	PUNCT
ejpam-221	358	45	(	(	PUNCT
ejpam-221	358	46	4.1	4.1	NUM
ejpam-221	358	47	)	)	PUNCT
ejpam-221	358	48	for	for	ADP
ejpam-221	358	49	a	a	DET
ejpam-221	358	50	,	,	PUNCT
ejpam-221	358	51	b	b	PROPN
ejpam-221	358	52	∈	∈	PROPN
ejpam-221	358	53	s.	s.	PROPN
ejpam-221	358	54	thus	thus	ADV
ejpam-221	358	55	,	,	PUNCT
ejpam-221	358	56	two	two	NUM
ejpam-221	358	57	elements	element	NOUN
ejpam-221	358	58	a	a	PRON
ejpam-221	358	59	,	,	PUNCT
ejpam-221	358	60	b	b	PROPN
ejpam-221	358	61	are	be	AUX
ejpam-221	358	62	ere	ere	PROPN
ejpam-221	358	63	-related	-relate	VERB
ejpam-221	358	64	if	if	SCONJ
ejpam-221	358	65	,	,	PUNCT
ejpam-221	358	66	and	and	CCONJ
ejpam-221	358	67	only	only	ADV
ejpam-221	358	68	if	if	SCONJ
ejpam-221	358	69	,	,	PUNCT
ejpam-221	358	70	they	they	PRON
ejpam-221	358	71	have	have	VERB
ejpam-221	358	72	the	the	DET
ejpam-221	358	73	same	same	ADJ
ejpam-221	358	74	left	leave	VERB
ejpam-221	358	75	identities	identity	NOUN
ejpam-221	358	76	in	in	ADP
ejpam-221	358	77	e.	e.	PROPN
ejpam-221	358	78	it	it	PRON
ejpam-221	358	79	is	be	AUX
ejpam-221	358	80	easy	easy	ADJ
ejpam-221	358	81	to	to	PART
ejpam-221	358	82	see	see	VERB
ejpam-221	358	83	that	that	SCONJ
ejpam-221	358	84	ere	ere	PROPN
ejpam-221	358	85	is	be	AUX
ejpam-221	358	86	an	an	DET
ejpam-221	358	87	equivalence	equivalence	NOUN
ejpam-221	358	88	relation	relation	NOUN
ejpam-221	358	89	.	.	PUNCT
ejpam-221	359	1	if	if	SCONJ
ejpam-221	359	2	e	e	PROPN
ejpam-221	359	3	=	=	SYM
ejpam-221	359	4	e(s	e(s	PROPN
ejpam-221	359	5	)	)	PUNCT
ejpam-221	359	6	,	,	PUNCT
ejpam-221	359	7	then	then	ADV
ejpam-221	359	8	we	we	PRON
ejpam-221	359	9	denote	denote	VERB
ejpam-221	359	10	ere	ere	NOUN
ejpam-221	359	11	by	by	ADP
ejpam-221	359	12	er	er	INTJ
ejpam-221	359	13	.	.	PUNCT
ejpam-221	360	1	note	note	VERB
ejpam-221	360	2	that	that	SCONJ
ejpam-221	360	3	er	er	INTJ
ejpam-221	360	4	⊆	⊆	NUM
ejpam-221	360	5	ere	ere	NOUN
ejpam-221	360	6	,	,	PUNCT
ejpam-221	360	7	for	for	ADP
ejpam-221	360	8	any	any	DET
ejpam-221	360	9	e.	e.	PROPN
ejpam-221	360	10	as	as	SCONJ
ejpam-221	360	11	indicated	indicate	VERB
ejpam-221	360	12	in	in	ADP
ejpam-221	360	13	section	section	NOUN
ejpam-221	360	14	2	2	NUM
ejpam-221	360	15	,	,	PUNCT
ejpam-221	360	16	the	the	DET
ejpam-221	360	17	relation	relation	NOUN
ejpam-221	360	18	ere	ere	PROPN
ejpam-221	360	19	is	be	AUX
ejpam-221	360	20	a	a	DET
ejpam-221	360	21	generalisation	generalisation	NOUN
ejpam-221	360	22	of	of	ADP
ejpam-221	360	23	green	green	PROPN
ejpam-221	360	24	’s	’s	PART
ejpam-221	360	25	relation	relation	NOUN
ejpam-221	360	26	r	r	NOUN
ejpam-221	360	27	;	;	PUNCT
ejpam-221	360	28	we	we	PRON
ejpam-221	360	29	now	now	ADV
ejpam-221	360	30	prove	prove	VERB
ejpam-221	360	31	that	that	SCONJ
ejpam-221	360	32	this	this	PRON
ejpam-221	360	33	is	be	AUX
ejpam-221	360	34	the	the	DET
ejpam-221	360	35	case	case	NOUN
ejpam-221	360	36	.	.	PUNCT
ejpam-221	361	1	we	we	PRON
ejpam-221	361	2	also	also	ADV
ejpam-221	361	3	take	take	VERB
ejpam-221	361	4	this	this	DET
ejpam-221	361	5	opportunity	opportunity	NOUN
ejpam-221	361	6	to	to	PART
ejpam-221	361	7	make	make	VERB
ejpam-221	361	8	the	the	DET
ejpam-221	361	9	connection	connection	NOUN
ejpam-221	361	10	between	between	ADP
ejpam-221	361	11	ere	ere	PROPN
ejpam-221	361	12	and	and	CCONJ
ejpam-221	361	13	the	the	DET
ejpam-221	361	14	relation	relation	NOUN
ejpam-221	361	15	r∗	r∗	NOUN
ejpam-221	361	16	which	which	PRON
ejpam-221	361	17	we	we	PRON
ejpam-221	361	18	saw	see	VERB
ejpam-221	361	19	in	in	ADP
ejpam-221	361	20	section	section	NOUN
ejpam-221	361	21	1	1	NUM
ejpam-221	361	22	(	(	PUNCT
ejpam-221	361	23	as	as	ADP
ejpam-221	361	24	equation	equation	NOUN
ejpam-221	361	25	(	(	PUNCT
ejpam-221	361	26	1.1	1.1	NUM
ejpam-221	361	27	)	)	PUNCT
ejpam-221	361	28	)	)	PUNCT
ejpam-221	361	29	and	and	CCONJ
ejpam-221	361	30	will	will	AUX
ejpam-221	361	31	see	see	VERB
ejpam-221	361	32	again	again	ADV
ejpam-221	361	33	in	in	ADP
ejpam-221	361	34	the	the	DET
ejpam-221	361	35	following	follow	VERB
ejpam-221	361	36	section	section	NOUN
ejpam-221	361	37	.	.	PUNCT
ejpam-221	362	1	lemma	lemma	PROPN
ejpam-221	362	2	4.1	4.1	NUM
ejpam-221	362	3	.	.	PUNCT
ejpam-221	363	1	if	if	SCONJ
ejpam-221	363	2	s	s	PROPN
ejpam-221	363	3	is	be	AUX
ejpam-221	363	4	a	a	DET
ejpam-221	363	5	semigroup	semigroup	NOUN
ejpam-221	363	6	with	with	ADP
ejpam-221	363	7	subset	subset	NOUN
ejpam-221	363	8	e	e	PROPN
ejpam-221	363	9	⊆	⊆	NUM
ejpam-221	363	10	e(s	e(s	PROPN
ejpam-221	363	11	)	)	PUNCT
ejpam-221	363	12	,	,	PUNCT
ejpam-221	363	13	then	then	ADV
ejpam-221	363	14	r	r	NOUN
ejpam-221	363	15	⊆r∗	⊆r∗	PUNCT
ejpam-221	363	16	⊆	⊆	NUM
ejpam-221	363	17	er	er	SYM
ejpam-221	363	18	⊆	⊆	NUM
ejpam-221	363	19	ere	ere	NOUN
ejpam-221	363	20	in	in	ADP
ejpam-221	363	21	s.	s.	PROPN
ejpam-221	363	22	proof	proof	PROPN
ejpam-221	363	23	.	.	PUNCT
ejpam-221	364	1	suppose	suppose	VERB
ejpam-221	364	2	that	that	SCONJ
ejpam-221	364	3	ar	ar	PROPN
ejpam-221	364	4	b	b	PROPN
ejpam-221	364	5	in	in	ADP
ejpam-221	364	6	s1	s1	NOUN
ejpam-221	364	7	.	.	PUNCT
ejpam-221	365	1	then	then	ADV
ejpam-221	365	2	there	there	PRON
ejpam-221	365	3	exist	exist	VERB
ejpam-221	365	4	c	c	NOUN
ejpam-221	365	5	,	,	PUNCT
ejpam-221	365	6	d	d	PROPN
ejpam-221	365	7	∈	∈	PROPN
ejpam-221	365	8	s	s	VERB
ejpam-221	365	9	with	with	ADP
ejpam-221	365	10	a	a	DET
ejpam-221	365	11	=	=	SYM
ejpam-221	365	12	bc	bc	PROPN
ejpam-221	365	13	and	and	CCONJ
ejpam-221	365	14	b	b	X
ejpam-221	365	15	=	=	SYM
ejpam-221	365	16	ad	ad	NOUN
ejpam-221	365	17	.	.	PUNCT
ejpam-221	366	1	for	for	ADP
ejpam-221	366	2	any	any	DET
ejpam-221	366	3	x	x	SYM
ejpam-221	366	4	,	,	PUNCT
ejpam-221	366	5	y	y	PROPN
ejpam-221	366	6	∈	∈	PROPN
ejpam-221	366	7	s1	s1	NOUN
ejpam-221	366	8	,	,	PUNCT
ejpam-221	366	9	it	it	PRON
ejpam-221	366	10	is	be	AUX
ejpam-221	366	11	clear	clear	ADJ
ejpam-221	366	12	that	that	SCONJ
ejpam-221	366	13	if	if	SCONJ
ejpam-221	366	14	xa	xa	PROPN
ejpam-221	366	15	=	=	PROPN
ejpam-221	366	16	ya	ya	PROPN
ejpam-221	366	17	,	,	PUNCT
ejpam-221	366	18	then	then	ADV
ejpam-221	366	19	xad	xad	PROPN
ejpam-221	366	20	=	=	PROPN
ejpam-221	366	21	yad	yad	PROPN
ejpam-221	366	22	,	,	PUNCT
ejpam-221	366	23	whence	whence	NOUN
ejpam-221	366	24	x	x	SYM
ejpam-221	366	25	b	b	X
ejpam-221	366	26	=	=	SYM
ejpam-221	366	27	y	y	PROPN
ejpam-221	366	28	b.	b.	PROPN
ejpam-221	366	29	similarly	similarly	ADV
ejpam-221	366	30	,	,	PUNCT
ejpam-221	366	31	the	the	DET
ejpam-221	366	32	converse	converse	NOUN
ejpam-221	366	33	,	,	PUNCT
ejpam-221	366	34	hence	hence	ADV
ejpam-221	366	35	ar∗	ar∗	PROPN
ejpam-221	366	36	b.	b.	PROPN
ejpam-221	366	37	now	now	ADV
ejpam-221	366	38	suppose	suppose	VERB
ejpam-221	366	39	that	that	SCONJ
ejpam-221	366	40	ar∗	ar∗	PROPN
ejpam-221	366	41	b.	b.	PROPN
ejpam-221	366	42	we	we	PRON
ejpam-221	366	43	can	can	AUX
ejpam-221	366	44	set	set	VERB
ejpam-221	366	45	y	y	PROPN
ejpam-221	366	46	=	=	SYM
ejpam-221	366	47	1	1	NUM
ejpam-221	366	48	and	and	CCONJ
ejpam-221	366	49	x	x	SYM
ejpam-221	366	50	=	=	SYM
ejpam-221	366	51	e	e	X
ejpam-221	366	52	in	in	ADP
ejpam-221	366	53	(	(	PUNCT
ejpam-221	366	54	1.1	1.1	NUM
ejpam-221	366	55	)	)	PUNCT
ejpam-221	366	56	,	,	PUNCT
ejpam-221	366	57	for	for	ADP
ejpam-221	366	58	any	any	DET
ejpam-221	366	59	e	e	PROPN
ejpam-221	366	60	∈	∈	PROPN
ejpam-221	366	61	e(s	e(s	PROPN
ejpam-221	366	62	)	)	PUNCT
ejpam-221	366	63	,	,	PUNCT
ejpam-221	366	64	to	to	PART
ejpam-221	366	65	obtain	obtain	VERB
ejpam-221	366	66	ea	ea	NOUN
ejpam-221	366	67	=	=	PUNCT
ejpam-221	366	68	a⇔	a⇔	PROPN
ejpam-221	366	69	eb	eb	PROPN
ejpam-221	366	70	=	=	PROPN
ejpam-221	366	71	b.	b.	PROPN
ejpam-221	366	72	hence	hence	ADV
ejpam-221	366	73	r∗	r∗	VERB
ejpam-221	366	74	⊆	⊆	NUM
ejpam-221	366	75	er	er	INTJ
ejpam-221	366	76	.	.	PUNCT
ejpam-221	367	1	we	we	PRON
ejpam-221	367	2	observed	observe	VERB
ejpam-221	367	3	above	above	ADP
ejpam-221	367	4	that	that	SCONJ
ejpam-221	367	5	er	er	INTJ
ejpam-221	367	6	⊆	⊆	NUM
ejpam-221	367	7	ere	ere	NOUN
ejpam-221	367	8	.	.	PUNCT
ejpam-221	368	1	c.	c.	PROPN
ejpam-221	368	2	hollings	holling	NOUN
ejpam-221	368	3	/	/	SYM
ejpam-221	368	4	eur	eur	PROPN
ejpam-221	368	5	.	.	PUNCT
ejpam-221	369	1	j.	j.	PROPN
ejpam-221	369	2	pure	pure	PROPN
ejpam-221	369	3	appl	appl	PROPN
ejpam-221	369	4	.	.	PROPN
ejpam-221	369	5	math	math	PROPN
ejpam-221	369	6	,	,	PUNCT
ejpam-221	369	7	2	2	NUM
ejpam-221	369	8	(	(	PUNCT
ejpam-221	369	9	2009	2009	NUM
ejpam-221	369	10	)	)	PUNCT
ejpam-221	369	11	,	,	PUNCT
ejpam-221	369	12	(	(	PUNCT
ejpam-221	369	13	21	21	NUM
ejpam-221	369	14	-	-	SYM
ejpam-221	369	15	57	57	NUM
ejpam-221	369	16	)	)	PUNCT
ejpam-221	369	17	41	41	NUM
ejpam-221	370	1	we	we	PRON
ejpam-221	370	2	note	note	VERB
ejpam-221	370	3	the	the	DET
ejpam-221	370	4	following	follow	VERB
ejpam-221	370	5	simpler	simple	ADJ
ejpam-221	370	6	condition	condition	NOUN
ejpam-221	370	7	for	for	ADP
ejpam-221	370	8	an	an	DET
ejpam-221	370	9	element	element	NOUN
ejpam-221	370	10	a	a	DET
ejpam-221	370	11	∈	∈	NOUN
ejpam-221	370	12	s	s	VERB
ejpam-221	370	13	to	to	PART
ejpam-221	370	14	be	be	AUX
ejpam-221	370	15	ere	ere	NOUN
ejpam-221	370	16	-	-	PUNCT
ejpam-221	370	17	related	relate	VERB
ejpam-221	370	18	to	to	ADP
ejpam-221	370	19	an	an	DET
ejpam-221	370	20	idempotent	idempotent	NOUN
ejpam-221	370	21	e	e	NOUN
ejpam-221	370	22	∈	∈	PROPN
ejpam-221	370	23	e	e	NOUN
ejpam-221	370	24	:	:	PUNCT
ejpam-221	370	25	a	a	DET
ejpam-221	370	26	ere	ere	PROPN
ejpam-221	370	27	e	e	NOUN
ejpam-221	370	28	⇐	⇐	ADJ
ejpam-221	370	29	⇒	⇒	NOUN
ejpam-221	370	30	ea	ea	PUNCT
ejpam-221	371	1	=	=	PUNCT
ejpam-221	371	2	a	a	PRON
ejpam-221	371	3	and	and	CCONJ
ejpam-221	371	4	∀g	∀g	NOUN
ejpam-221	371	5	∈	∈	NOUN
ejpam-221	371	6	e[ga	e[ga	X
ejpam-221	372	1	=	=	PUNCT
ejpam-221	372	2	a⇒	a⇒	PROPN
ejpam-221	372	3	ge	ge	PROPN
ejpam-221	372	4	=	=	PUNCT
ejpam-221	372	5	e	e	X
ejpam-221	372	6	]	]	X
ejpam-221	372	7	.	.	PUNCT
ejpam-221	373	1	(	(	PUNCT
ejpam-221	373	2	4.2	4.2	NUM
ejpam-221	373	3	)	)	PUNCT
ejpam-221	373	4	harking	hark	VERB
ejpam-221	373	5	back	back	ADV
ejpam-221	373	6	to	to	ADP
ejpam-221	373	7	the	the	DET
ejpam-221	373	8	discussion	discussion	NOUN
ejpam-221	373	9	of	of	ADP
ejpam-221	373	10	minimal	minimal	ADJ
ejpam-221	373	11	idempotent	idempotent	NOUN
ejpam-221	373	12	-	-	PUNCT
ejpam-221	373	13	generated	generate	VERB
ejpam-221	373	14	ideals	ideal	NOUN
ejpam-221	373	15	in	in	ADP
ejpam-221	373	16	section	section	NOUN
ejpam-221	373	17	2	2	NUM
ejpam-221	373	18	,	,	PUNCT
ejpam-221	373	19	we	we	PRON
ejpam-221	373	20	note	note	VERB
ejpam-221	373	21	that	that	SCONJ
ejpam-221	373	22	(	(	PUNCT
ejpam-221	373	23	4.2	4.2	NUM
ejpam-221	373	24	)	)	PUNCT
ejpam-221	373	25	tells	tell	VERB
ejpam-221	373	26	us	we	PRON
ejpam-221	373	27	that	that	SCONJ
ejpam-221	373	28	a	a	DET
ejpam-221	373	29	ere	ere	NOUN
ejpam-221	373	30	e	e	NOUN
ejpam-221	373	31	if	if	SCONJ
ejpam-221	373	32	,	,	PUNCT
ejpam-221	373	33	and	and	CCONJ
ejpam-221	373	34	only	only	ADV
ejpam-221	373	35	if	if	SCONJ
ejpam-221	373	36	,	,	PUNCT
ejpam-221	373	37	as1	as1	PROPN
ejpam-221	373	38	⊆	⊆	PROPN
ejpam-221	373	39	es1	es1	PROPN
ejpam-221	373	40	,	,	PUNCT
ejpam-221	373	41	where	where	SCONJ
ejpam-221	373	42	es1	es1	PROPN
ejpam-221	373	43	is	be	AUX
ejpam-221	373	44	the	the	DET
ejpam-221	373	45	smallest	small	ADJ
ejpam-221	373	46	principal	principal	ADJ
ejpam-221	373	47	right	right	ADJ
ejpam-221	373	48	ideal	ideal	NOUN
ejpam-221	373	49	to	to	PART
ejpam-221	373	50	be	be	AUX
ejpam-221	373	51	generated	generate	VERB
ejpam-221	373	52	by	by	ADP
ejpam-221	373	53	an	an	DET
ejpam-221	373	54	idempotent	idempotent	NOUN
ejpam-221	373	55	from	from	ADP
ejpam-221	373	56	e	e	NOUN
ejpam-221	373	57	and	and	CCONJ
ejpam-221	373	58	to	to	PART
ejpam-221	373	59	contain	contain	VERB
ejpam-221	373	60	as1	as1	NOUN
ejpam-221	373	61	.	.	PUNCT
ejpam-221	373	62	lemma	lemma	PROPN
ejpam-221	373	63	4.2	4.2	NUM
ejpam-221	373	64	.	.	PUNCT
ejpam-221	374	1	let	let	VERB
ejpam-221	374	2	s	s	PRON
ejpam-221	374	3	be	be	AUX
ejpam-221	374	4	a	a	DET
ejpam-221	374	5	semigroup	semigroup	NOUN
ejpam-221	374	6	with	with	ADP
ejpam-221	374	7	subset	subset	NOUN
ejpam-221	374	8	e	e	PROPN
ejpam-221	374	9	⊆	⊆	NUM
ejpam-221	374	10	e(s	e(s	PROPN
ejpam-221	374	11	)	)	PUNCT
ejpam-221	374	12	.	.	PUNCT
ejpam-221	375	1	then	then	ADV
ejpam-221	375	2	e	e	PROPN
ejpam-221	375	3	ere	ere	PROPN
ejpam-221	375	4	f	f	PROPN
ejpam-221	375	5	if	if	SCONJ
ejpam-221	375	6	,	,	PUNCT
ejpam-221	375	7	and	and	CCONJ
ejpam-221	375	8	only	only	ADV
ejpam-221	375	9	if	if	SCONJ
ejpam-221	375	10	,	,	PUNCT
ejpam-221	375	11	er	er	INTJ
ejpam-221	375	12	f	f	X
ejpam-221	375	13	.	.	PUNCT
ejpam-221	376	1	proof	proof	NOUN
ejpam-221	376	2	.	.	PUNCT
ejpam-221	377	1	let	let	VERB
ejpam-221	377	2	e	e	X
ejpam-221	377	3	,	,	PUNCT
ejpam-221	377	4	f	f	PROPN
ejpam-221	377	5	∈	∈	PROPN
ejpam-221	377	6	s	s	PART
ejpam-221	377	7	and	and	CCONJ
ejpam-221	377	8	suppose	suppose	VERB
ejpam-221	377	9	that	that	SCONJ
ejpam-221	377	10	e	e	PROPN
ejpam-221	377	11	ere	ere	PROPN
ejpam-221	377	12	f	f	PROPN
ejpam-221	377	13	.	.	PUNCT
ejpam-221	378	1	then	then	ADV
ejpam-221	378	2	,	,	PUNCT
ejpam-221	378	3	by	by	ADP
ejpam-221	378	4	(	(	PUNCT
ejpam-221	378	5	4.2	4.2	NUM
ejpam-221	378	6	)	)	PUNCT
ejpam-221	378	7	,	,	PUNCT
ejpam-221	378	8	e	e	PROPN
ejpam-221	378	9	f	f	PROPN
ejpam-221	378	10	=	=	SYM
ejpam-221	378	11	f	f	PROPN
ejpam-221	378	12	and	and	CCONJ
ejpam-221	378	13	f	f	PROPN
ejpam-221	378	14	e	e	PROPN
ejpam-221	378	15	=	=	SYM
ejpam-221	378	16	e	e	NOUN
ejpam-221	378	17	,	,	PUNCT
ejpam-221	378	18	hence	hence	ADV
ejpam-221	378	19	er	er	INTJ
ejpam-221	378	20	f	f	X
ejpam-221	378	21	.	.	PUNCT
ejpam-221	379	1	the	the	DET
ejpam-221	379	2	converse	converse	NOUN
ejpam-221	379	3	follows	follow	VERB
ejpam-221	379	4	from	from	ADP
ejpam-221	379	5	lemma	lemma	PROPN
ejpam-221	379	6	4.1	4.1	NUM
ejpam-221	379	7	.	.	PUNCT
ejpam-221	380	1	in	in	ADP
ejpam-221	380	2	the	the	DET
ejpam-221	380	3	special	special	ADJ
ejpam-221	380	4	case	case	NOUN
ejpam-221	380	5	where	where	SCONJ
ejpam-221	380	6	e	e	NOUN
ejpam-221	380	7	is	be	AUX
ejpam-221	380	8	a	a	DET
ejpam-221	380	9	semilattice	semilattice	NOUN
ejpam-221	380	10	,	,	PUNCT
ejpam-221	380	11	we	we	PRON
ejpam-221	380	12	have	have	VERB
ejpam-221	380	13	the	the	DET
ejpam-221	380	14	following	follow	VERB
ejpam-221	380	15	easy	easy	ADJ
ejpam-221	380	16	consequence	consequence	NOUN
ejpam-221	380	17	of	of	ADP
ejpam-221	380	18	lemma	lemma	PROPN
ejpam-221	380	19	4.2	4.2	NUM
ejpam-221	380	20	:	:	PUNCT
ejpam-221	380	21	lemma	lemma	PROPN
ejpam-221	380	22	4.3	4.3	NUM
ejpam-221	380	23	.	.	PUNCT
ejpam-221	381	1	let	let	VERB
ejpam-221	381	2	s	s	PRON
ejpam-221	381	3	be	be	AUX
ejpam-221	381	4	a	a	DET
ejpam-221	381	5	semigroup	semigroup	NOUN
ejpam-221	381	6	with	with	ADP
ejpam-221	381	7	subsemilattice	subsemilattice	NOUN
ejpam-221	381	8	e	e	NOUN
ejpam-221	381	9	⊆	⊆	NUM
ejpam-221	381	10	e(s	e(s	PROPN
ejpam-221	381	11	)	)	PUNCT
ejpam-221	381	12	.	.	PUNCT
ejpam-221	382	1	each	each	DET
ejpam-221	382	2	element	element	NOUN
ejpam-221	382	3	of	of	ADP
ejpam-221	382	4	s	s	PROPN
ejpam-221	382	5	is	be	AUX
ejpam-221	382	6	ere	ere	NOUN
ejpam-221	382	7	-	-	PUNCT
ejpam-221	382	8	related	relate	VERB
ejpam-221	382	9	to	to	ADP
ejpam-221	382	10	at	at	ADP
ejpam-221	382	11	most	most	ADV
ejpam-221	382	12	one	one	NUM
ejpam-221	382	13	idempotent	idempotent	NOUN
ejpam-221	382	14	from	from	ADP
ejpam-221	382	15	e.	e.	PROPN
ejpam-221	382	16	indeed	indeed	ADV
ejpam-221	382	17	,	,	PUNCT
ejpam-221	382	18	we	we	PRON
ejpam-221	382	19	are	be	AUX
ejpam-221	382	20	most	most	ADV
ejpam-221	382	21	interested	interested	ADJ
ejpam-221	382	22	in	in	ADP
ejpam-221	382	23	the	the	DET
ejpam-221	382	24	case	case	NOUN
ejpam-221	382	25	when	when	SCONJ
ejpam-221	382	26	e	e	PROPN
ejpam-221	382	27	is	be	AUX
ejpam-221	382	28	a	a	DET
ejpam-221	382	29	semilattice	semilattice	NOUN
ejpam-221	382	30	.	.	PUNCT
ejpam-221	383	1	we	we	PRON
ejpam-221	383	2	now	now	ADV
ejpam-221	383	3	give	give	VERB
ejpam-221	383	4	an	an	DET
ejpam-221	383	5	abstract	abstract	ADJ
ejpam-221	383	6	definition	definition	NOUN
ejpam-221	383	7	for	for	ADP
ejpam-221	383	8	a	a	DET
ejpam-221	383	9	weakly	weakly	ADJ
ejpam-221	383	10	left	left	ADJ
ejpam-221	383	11	e	e	NOUN
ejpam-221	383	12	-	-	ADJ
ejpam-221	383	13	ample	ample	ADJ
ejpam-221	383	14	semigroup	semigroup	NOUN
ejpam-221	383	15	;	;	PUNCT
ejpam-221	383	16	we	we	PRON
ejpam-221	383	17	will	will	AUX
ejpam-221	383	18	ultimately	ultimately	ADV
ejpam-221	383	19	prove	prove	VERB
ejpam-221	383	20	that	that	SCONJ
ejpam-221	383	21	this	this	PRON
ejpam-221	383	22	is	be	AUX
ejpam-221	383	23	equivalent	equivalent	ADJ
ejpam-221	383	24	to	to	ADP
ejpam-221	383	25	a	a	DET
ejpam-221	383	26	left	left	ADJ
ejpam-221	383	27	restriction	restriction	NOUN
ejpam-221	383	28	semigroup	semigroup	NOUN
ejpam-221	383	29	.	.	PUNCT
ejpam-221	384	1	definition	definition	NOUN
ejpam-221	384	2	4.4	4.4	NUM
ejpam-221	384	3	.	.	PUNCT
ejpam-221	385	1	a	a	DET
ejpam-221	385	2	semigroup	semigroup	NOUN
ejpam-221	385	3	s	s	X
ejpam-221	385	4	with	with	ADP
ejpam-221	385	5	subsemilattice	subsemilattice	NOUN
ejpam-221	385	6	e	e	NOUN
ejpam-221	385	7	⊆	⊆	NUM
ejpam-221	385	8	e(s	e(s	PROPN
ejpam-221	385	9	)	)	PUNCT
ejpam-221	385	10	is	be	AUX
ejpam-221	385	11	called	call	VERB
ejpam-221	385	12	a	a	DET
ejpam-221	385	13	weakly	weakly	ADJ
ejpam-221	385	14	left	left	ADJ
ejpam-221	385	15	e	e	NOUN
ejpam-221	385	16	-	-	ADJ
ejpam-221	385	17	ample	ample	ADJ
ejpam-221	385	18	semigroup	semigroup	NOUN
ejpam-221	385	19	if	if	SCONJ
ejpam-221	385	20	1	1	NUM
ejpam-221	385	21	.	.	PUNCT
ejpam-221	386	1	every	every	DET
ejpam-221	386	2	element	element	NOUN
ejpam-221	386	3	a	a	PRON
ejpam-221	386	4	is	be	AUX
ejpam-221	386	5	ere	ere	NOUN
ejpam-221	386	6	-	-	PUNCT
ejpam-221	386	7	related	relate	VERB
ejpam-221	386	8	to	to	ADP
ejpam-221	386	9	an	an	DET
ejpam-221	386	10	idempotent	idempotent	NOUN
ejpam-221	386	11	a+	a+	PUNCT
ejpam-221	386	12	∈	∈	PROPN
ejpam-221	386	13	e	e	NOUN
ejpam-221	386	14	;	;	PUNCT
ejpam-221	386	15	2	2	X
ejpam-221	386	16	.	.	X
ejpam-221	386	17	ere	ere	PROPN
ejpam-221	386	18	is	be	AUX
ejpam-221	386	19	a	a	DET
ejpam-221	386	20	left	left	ADJ
ejpam-221	386	21	congruence	congruence	NOUN
ejpam-221	386	22	;	;	PUNCT
ejpam-221	386	23	3	3	X
ejpam-221	386	24	.	.	X
ejpam-221	387	1	for	for	ADP
ejpam-221	387	2	all	all	DET
ejpam-221	387	3	a	a	DET
ejpam-221	387	4	∈	∈	NOUN
ejpam-221	387	5	s	s	PART
ejpam-221	387	6	and	and	CCONJ
ejpam-221	387	7	all	all	DET
ejpam-221	387	8	e	e	X
ejpam-221	387	9	∈	∈	PROPN
ejpam-221	387	10	e	e	NOUN
ejpam-221	387	11	,	,	PUNCT
ejpam-221	387	12	ae	ae	PROPN
ejpam-221	387	13	=	=	SYM
ejpam-221	387	14	(	(	PUNCT
ejpam-221	387	15	ae)+a	ae)+a	PROPN
ejpam-221	387	16	.	.	PUNCT
ejpam-221	388	1	a	a	DET
ejpam-221	388	2	weakly	weakly	ADJ
ejpam-221	388	3	left	left	ADJ
ejpam-221	388	4	e	e	NOUN
ejpam-221	388	5	-	-	ADJ
ejpam-221	388	6	ample	ample	ADJ
ejpam-221	388	7	monoid	monoid	NOUN
ejpam-221	388	8	is	be	AUX
ejpam-221	388	9	defined	define	VERB
ejpam-221	388	10	analogously	analogously	ADV
ejpam-221	388	11	;	;	PUNCT
ejpam-221	388	12	in	in	ADP
ejpam-221	388	13	this	this	DET
ejpam-221	388	14	instance	instance	NOUN
ejpam-221	388	15	,	,	PUNCT
ejpam-221	388	16	we	we	PRON
ejpam-221	388	17	require	require	VERB
ejpam-221	388	18	1	1	NUM
ejpam-221	388	19	∈	∈	PROPN
ejpam-221	388	20	e.	e.	PROPN
ejpam-221	388	21	c.	c.	PROPN
ejpam-221	388	22	hollings	hollings	PROPN
ejpam-221	388	23	/	/	SYM
ejpam-221	388	24	eur	eur	PROPN
ejpam-221	388	25	.	.	PUNCT
ejpam-221	389	1	j.	j.	PROPN
ejpam-221	389	2	pure	pure	PROPN
ejpam-221	389	3	appl	appl	PROPN
ejpam-221	389	4	.	.	PROPN
ejpam-221	389	5	math	math	PROPN
ejpam-221	389	6	,	,	PUNCT
ejpam-221	389	7	2	2	NUM
ejpam-221	389	8	(	(	PUNCT
ejpam-221	389	9	2009	2009	NUM
ejpam-221	389	10	)	)	PUNCT
ejpam-221	389	11	,	,	PUNCT
ejpam-221	389	12	(	(	PUNCT
ejpam-221	389	13	21	21	NUM
ejpam-221	389	14	-	-	SYM
ejpam-221	389	15	57	57	NUM
ejpam-221	389	16	)	)	PUNCT
ejpam-221	389	17	42	42	NUM
ejpam-221	389	18	thus	thus	ADV
ejpam-221	389	19	,	,	PUNCT
ejpam-221	389	20	in	in	ADP
ejpam-221	389	21	a	a	DET
ejpam-221	389	22	weakly	weakly	ADJ
ejpam-221	389	23	left	left	ADJ
ejpam-221	389	24	e	e	NOUN
ejpam-221	389	25	-	-	ADJ
ejpam-221	389	26	ample	ample	ADJ
ejpam-221	389	27	semigroup	semigroup	NOUN
ejpam-221	389	28	,	,	PUNCT
ejpam-221	390	1	a	a	DET
ejpam-221	390	2	ere	ere	PROPN
ejpam-221	390	3	b	b	PROPN
ejpam-221	390	4	if	if	SCONJ
ejpam-221	390	5	,	,	PUNCT
ejpam-221	390	6	and	and	CCONJ
ejpam-221	390	7	only	only	ADV
ejpam-221	390	8	if	if	SCONJ
ejpam-221	390	9	,	,	PUNCT
ejpam-221	390	10	a+	a+	PUNCT
ejpam-221	390	11	=	=	NUM
ejpam-221	390	12	b+	b+	X
ejpam-221	390	13	.	.	PUNCT
ejpam-221	391	1	the	the	DET
ejpam-221	391	2	idempotent	idempotent	NOUN
ejpam-221	391	3	a+	a+	PUNCT
ejpam-221	391	4	is	be	AUX
ejpam-221	391	5	well	well	ADV
ejpam-221	391	6	-	-	PUNCT
ejpam-221	391	7	defined	define	VERB
ejpam-221	391	8	,	,	PUNCT
ejpam-221	391	9	thanks	thank	NOUN
ejpam-221	391	10	to	to	ADP
ejpam-221	391	11	lemma	lemma	PROPN
ejpam-221	391	12	4.3	4.3	NUM
ejpam-221	391	13	,	,	PUNCT
ejpam-221	391	14	and	and	CCONJ
ejpam-221	391	15	is	be	AUX
ejpam-221	391	16	a	a	DET
ejpam-221	391	17	left	left	ADJ
ejpam-221	391	18	identity	identity	NOUN
ejpam-221	391	19	for	for	ADP
ejpam-221	391	20	a.	a.	NOUN
ejpam-221	391	21	it	it	PRON
ejpam-221	391	22	is	be	AUX
ejpam-221	391	23	also	also	ADV
ejpam-221	391	24	clear	clear	ADJ
ejpam-221	391	25	that	that	SCONJ
ejpam-221	391	26	e+	e+	VERB
ejpam-221	391	27	=	=	SYM
ejpam-221	391	28	e	e	X
ejpam-221	391	29	and	and	CCONJ
ejpam-221	391	30	(	(	PUNCT
ejpam-221	391	31	a+)+	a+)+	NOUN
ejpam-221	391	32	=	=	SYM
ejpam-221	391	33	a+	a+	X
ejpam-221	391	34	,	,	PUNCT
ejpam-221	391	35	for	for	ADP
ejpam-221	391	36	any	any	DET
ejpam-221	391	37	e	e	NOUN
ejpam-221	391	38	∈	∈	PROPN
ejpam-221	391	39	e	e	NOUN
ejpam-221	391	40	and	and	CCONJ
ejpam-221	391	41	any	any	DET
ejpam-221	391	42	a	a	DET
ejpam-221	391	43	∈	∈	PROPN
ejpam-221	391	44	s.	s.	PROPN
ejpam-221	391	45	a	a	DET
ejpam-221	391	46	weakly	weakly	ADJ
ejpam-221	391	47	left	left	ADJ
ejpam-221	391	48	e	e	NOUN
ejpam-221	391	49	-	-	ADJ
ejpam-221	391	50	ample	ample	ADJ
ejpam-221	391	51	semigroup	semigroup	NOUN
ejpam-221	391	52	may	may	AUX
ejpam-221	391	53	be	be	AUX
ejpam-221	391	54	regarded	regard	VERB
ejpam-221	391	55	(	(	PUNCT
ejpam-221	391	56	and	and	CCONJ
ejpam-221	391	57	,	,	PUNCT
ejpam-221	391	58	indeed	indeed	ADV
ejpam-221	391	59	,	,	PUNCT
ejpam-221	391	60	defined	define	VERB
ejpam-221	391	61	[	[	PUNCT
ejpam-221	391	62	32	32	NUM
ejpam-221	391	63	]	]	PUNCT
ejpam-221	391	64	)	)	PUNCT
ejpam-221	391	65	as	as	ADP
ejpam-221	391	66	an	an	DET
ejpam-221	391	67	algebra	algebra	NOUN
ejpam-221	391	68	of	of	ADP
ejpam-221	391	69	type	type	NOUN
ejpam-221	391	70	(	(	PUNCT
ejpam-221	391	71	2,1	2,1	NUM
ejpam-221	391	72	)	)	PUNCT
ejpam-221	391	73	.	.	PUNCT
ejpam-221	392	1	the	the	DET
ejpam-221	392	2	identity	identity	NOUN
ejpam-221	392	3	in	in	ADP
ejpam-221	392	4	condition	condition	NOUN
ejpam-221	392	5	(	(	PUNCT
ejpam-221	392	6	3	3	NUM
ejpam-221	392	7	)	)	PUNCT
ejpam-221	392	8	of	of	ADP
ejpam-221	392	9	definition	definition	NOUN
ejpam-221	392	10	4.4	4.4	NUM
ejpam-221	392	11	will	will	AUX
ejpam-221	392	12	be	be	AUX
ejpam-221	392	13	referred	refer	VERB
ejpam-221	392	14	to	to	ADP
ejpam-221	392	15	throughout	throughout	ADP
ejpam-221	392	16	as	as	ADP
ejpam-221	392	17	the	the	DET
ejpam-221	392	18	‘	'	PUNCT
ejpam-221	392	19	left	leave	VERB
ejpam-221	392	20	ample	ample	ADJ
ejpam-221	392	21	identity	identity	NOUN
ejpam-221	392	22	’	'	PUNCT
ejpam-221	392	23	.	.	PUNCT
ejpam-221	393	1	this	this	DET
ejpam-221	393	2	identity	identity	NOUN
ejpam-221	393	3	is	be	AUX
ejpam-221	393	4	equivalent	equivalent	ADJ
ejpam-221	393	5	to	to	ADP
ejpam-221	393	6	the	the	DET
ejpam-221	393	7	‘	'	PUNCT
ejpam-221	393	8	idempotent	idempotent	ADJ
ejpam-221	393	9	connected	connect	VERB
ejpam-221	393	10	’	'	PUNCT
ejpam-221	393	11	condition	condition	NOUN
ejpam-221	393	12	of	of	ADP
ejpam-221	393	13	(	(	PUNCT
ejpam-221	393	14	1.3	1.3	NUM
ejpam-221	393	15	)	)	PUNCT
ejpam-221	393	16	.	.	PUNCT
ejpam-221	394	1	with	with	ADP
ejpam-221	394	2	regard	regard	NOUN
ejpam-221	394	3	to	to	ADP
ejpam-221	394	4	the	the	DET
ejpam-221	394	5	last	last	ADJ
ejpam-221	394	6	part	part	NOUN
ejpam-221	394	7	of	of	ADP
ejpam-221	394	8	definition	definition	NOUN
ejpam-221	394	9	4.4	4.4	NUM
ejpam-221	394	10	,	,	PUNCT
ejpam-221	394	11	we	we	PRON
ejpam-221	394	12	note	note	VERB
ejpam-221	394	13	that	that	SCONJ
ejpam-221	394	14	if	if	SCONJ
ejpam-221	394	15	s	s	NOUN
ejpam-221	394	16	is	be	AUX
ejpam-221	394	17	a	a	DET
ejpam-221	394	18	weakly	weakly	ADJ
ejpam-221	394	19	left	left	ADJ
ejpam-221	394	20	e	e	NOUN
ejpam-221	394	21	-	-	ADJ
ejpam-221	394	22	ample	ample	ADJ
ejpam-221	394	23	semigroup	semigroup	NOUN
ejpam-221	395	1	and	and	CCONJ
ejpam-221	395	2	we	we	PRON
ejpam-221	395	3	adjoin	adjoin	VERB
ejpam-221	395	4	an	an	DET
ejpam-221	395	5	identity	identity	NOUN
ejpam-221	395	6	1	1	NUM
ejpam-221	395	7	to	to	ADP
ejpam-221	395	8	s	s	PRON
ejpam-221	395	9	,	,	PUNCT
ejpam-221	395	10	then	then	ADV
ejpam-221	395	11	s1	s1	NOUN
ejpam-221	395	12	is	be	AUX
ejpam-221	395	13	a	a	DET
ejpam-221	395	14	weakly	weakly	ADJ
ejpam-221	395	15	left	leave	VERB
ejpam-221	395	16	e1	e1	NOUN
ejpam-221	395	17	-	-	PUNCT
ejpam-221	395	18	ample	ample	ADJ
ejpam-221	395	19	monoid	monoid	NOUN
ejpam-221	395	20	.	.	PUNCT
ejpam-221	396	1	a	a	DET
ejpam-221	396	2	semigroup	semigroup	NOUN
ejpam-221	396	3	s	s	X
ejpam-221	396	4	which	which	PRON
ejpam-221	396	5	is	be	AUX
ejpam-221	396	6	weakly	weakly	ADV
ejpam-221	396	7	left	left	ADJ
ejpam-221	396	8	e	e	NOUN
ejpam-221	396	9	-	-	NOUN
ejpam-221	396	10	ample	ample	ADJ
ejpam-221	396	11	for	for	ADP
ejpam-221	396	12	e	e	NOUN
ejpam-221	396	13	=	=	SYM
ejpam-221	396	14	e(s	e(s	PROPN
ejpam-221	396	15	)	)	PUNCT
ejpam-221	396	16	is	be	AUX
ejpam-221	396	17	called	call	VERB
ejpam-221	396	18	simply	simply	ADV
ejpam-221	396	19	a	a	DET
ejpam-221	396	20	weakly	weakly	ADJ
ejpam-221	396	21	left	left	ADJ
ejpam-221	396	22	ample	ample	ADJ
ejpam-221	396	23	semigroup	semigroup	NOUN
ejpam-221	396	24	;	;	PUNCT
ejpam-221	396	25	in	in	ADP
ejpam-221	396	26	this	this	DET
ejpam-221	396	27	instance	instance	NOUN
ejpam-221	396	28	,	,	PUNCT
ejpam-221	396	29	definition	definition	NOUN
ejpam-221	396	30	4.4	4.4	NUM
ejpam-221	396	31	can	can	AUX
ejpam-221	396	32	of	of	ADP
ejpam-221	396	33	course	course	NOUN
ejpam-221	396	34	be	be	AUX
ejpam-221	396	35	rewritten	rewrite	VERB
ejpam-221	396	36	in	in	ADP
ejpam-221	396	37	terms	term	NOUN
ejpam-221	396	38	of	of	ADP
ejpam-221	396	39	er	er	INTJ
ejpam-221	396	40	.	.	PUNCT
ejpam-221	397	1	once	once	SCONJ
ejpam-221	397	2	we	we	PRON
ejpam-221	397	3	have	have	AUX
ejpam-221	397	4	completed	complete	VERB
ejpam-221	397	5	the	the	DET
ejpam-221	397	6	proof	proof	NOUN
ejpam-221	397	7	that	that	SCONJ
ejpam-221	397	8	weakly	weakly	ADV
ejpam-221	397	9	left	leave	VERB
ejpam-221	397	10	e	e	NOUN
ejpam-221	397	11	-	-	ADJ
ejpam-221	397	12	ample	ample	ADJ
ejpam-221	397	13	semigroups	semigroup	NOUN
ejpam-221	397	14	are	be	AUX
ejpam-221	397	15	precisely	precisely	ADV
ejpam-221	397	16	left	leave	VERB
ejpam-221	397	17	restriction	restriction	NOUN
ejpam-221	397	18	semigroups	semigroup	NOUN
ejpam-221	397	19	,	,	PUNCT
ejpam-221	397	20	we	we	PRON
ejpam-221	397	21	will	will	AUX
ejpam-221	397	22	see	see	VERB
ejpam-221	397	23	as	as	ADP
ejpam-221	397	24	an	an	DET
ejpam-221	397	25	easy	easy	ADJ
ejpam-221	397	26	corollary	corollary	NOUN
ejpam-221	397	27	that	that	SCONJ
ejpam-221	397	28	weakly	weakly	ADJ
ejpam-221	397	29	left	leave	VERB
ejpam-221	397	30	ample	ample	ADJ
ejpam-221	397	31	semigroups	semigroup	NOUN
ejpam-221	397	32	are	be	AUX
ejpam-221	397	33	precisely	precisely	ADV
ejpam-221	397	34	full	full	ADJ
ejpam-221	397	35	left	left	ADJ
ejpam-221	397	36	restriction	restriction	NOUN
ejpam-221	397	37	semigroups	semigroup	NOUN
ejpam-221	397	38	.	.	PUNCT
ejpam-221	398	1	our	our	PRON
ejpam-221	398	2	first	first	ADJ
ejpam-221	398	3	step	step	NOUN
ejpam-221	398	4	towards	towards	ADP
ejpam-221	398	5	proving	prove	VERB
ejpam-221	398	6	that	that	SCONJ
ejpam-221	398	7	definitions	definition	NOUN
ejpam-221	398	8	3.1	3.1	NUM
ejpam-221	398	9	and	and	CCONJ
ejpam-221	398	10	4.4	4.4	NUM
ejpam-221	398	11	are	be	AUX
ejpam-221	398	12	equivalent	equivalent	ADJ
ejpam-221	398	13	is	be	AUX
ejpam-221	398	14	the	the	DET
ejpam-221	398	15	following	following	NOUN
ejpam-221	398	16	:	:	PUNCT
ejpam-221	398	17	proposition	proposition	NOUN
ejpam-221	398	18	4.5	4.5	NUM
ejpam-221	398	19	.	.	PUNCT
ejpam-221	399	1	a	a	DET
ejpam-221	399	2	partial	partial	ADJ
ejpam-221	399	3	transformation	transformation	NOUN
ejpam-221	399	4	monoid	monoid	NOUN
ejpam-221	399	5	p	p	PROPN
ejpam-221	399	6	t	t	PROPN
ejpam-221	399	7	x	x	VERB
ejpam-221	399	8	is	be	AUX
ejpam-221	399	9	weakly	weakly	ADV
ejpam-221	399	10	left	leave	VERB
ejpam-221	399	11	ex	ex	PRON
ejpam-221	399	12	-ample	-ample	NOUN
ejpam-221	399	13	.	.	PUNCT
ejpam-221	400	1	we	we	PRON
ejpam-221	400	2	first	first	ADV
ejpam-221	400	3	note	note	VERB
ejpam-221	400	4	the	the	DET
ejpam-221	400	5	following	follow	VERB
ejpam-221	400	6	lemma	lemma	PROPN
ejpam-221	400	7	:	:	PUNCT
ejpam-221	400	8	lemma	lemma	PROPN
ejpam-221	400	9	4.6	4.6	NUM
ejpam-221	400	10	.	.	PUNCT
ejpam-221	401	1	for	for	ADP
ejpam-221	401	2	α	α	NOUN
ejpam-221	401	3	,	,	PUNCT
ejpam-221	401	4	β	β	X
ejpam-221	401	5	∈	∈	PROPN
ejpam-221	401	6	p	p	X
ejpam-221	401	7	t	t	PROPN
ejpam-221	401	8	x	x	X
ejpam-221	401	9	,	,	PUNCT
ejpam-221	401	10	α	α	PROPN
ejpam-221	401	11	erex	erex	PROPN
ejpam-221	401	12	β	β	X
ejpam-221	401	13	⇐	⇐	ADJ
ejpam-221	401	14	⇒	⇒	PROPN
ejpam-221	401	15	domα	domα	NOUN
ejpam-221	401	16	=	=	PUNCT
ejpam-221	401	17	domβ	domβ	PROPN
ejpam-221	401	18	.	.	PUNCT
ejpam-221	402	1	(	(	PUNCT
ejpam-221	402	2	4.3	4.3	NUM
ejpam-221	402	3	)	)	PUNCT
ejpam-221	402	4	proof	proof	NOUN
ejpam-221	402	5	.	.	PUNCT
ejpam-221	403	1	from	from	ADP
ejpam-221	403	2	(	(	PUNCT
ejpam-221	403	3	4.1	4.1	NUM
ejpam-221	403	4	)	)	PUNCT
ejpam-221	403	5	,	,	PUNCT
ejpam-221	403	6	we	we	PRON
ejpam-221	403	7	have	have	VERB
ejpam-221	403	8	α	α	PRON
ejpam-221	403	9	erex	erex	PROPN
ejpam-221	403	10	β	β	X
ejpam-221	403	11	⇐	⇐	PROPN
ejpam-221	403	12	⇒∀iy	⇒∀iy	PROPN
ejpam-221	403	13	∈	∈	PROPN
ejpam-221	403	14	ex	ex	X
ejpam-221	404	1	[	[	X
ejpam-221	404	2	iyα=	iyα=	PROPN
ejpam-221	404	3	α⇔	α⇔	NOUN
ejpam-221	404	4	iyβ	iyβ	VERB
ejpam-221	404	5	=	=	SYM
ejpam-221	404	6	β	β	X
ejpam-221	404	7	]	]	X
ejpam-221	404	8	.	.	PUNCT
ejpam-221	405	1	we	we	PRON
ejpam-221	405	2	observe	observe	VERB
ejpam-221	405	3	that	that	DET
ejpam-221	405	4	dom	dom	NOUN
ejpam-221	405	5	iyα=	iyα=	PROPN
ejpam-221	405	6	y	y	PROPN
ejpam-221	405	7	∩	∩	NOUN
ejpam-221	405	8	domα	domα	NOUN
ejpam-221	405	9	,	,	PUNCT
ejpam-221	405	10	so	so	SCONJ
ejpam-221	405	11	that	that	SCONJ
ejpam-221	405	12	α	α	PRON
ejpam-221	405	13	erex	erex	NOUN
ejpam-221	405	14	β	β	X
ejpam-221	405	15	⇐	⇐	ADJ
ejpam-221	405	16	⇒∀y	⇒∀y	PROPN
ejpam-221	405	17	⊆	⊆	NUM
ejpam-221	405	18	x	x	SYM
ejpam-221	406	1	[	[	X
ejpam-221	406	2	domα⊆	domα⊆	PROPN
ejpam-221	406	3	y	y	PROPN
ejpam-221	406	4	⇔	⇔	PROPN
ejpam-221	406	5	domβ	domβ	PROPN
ejpam-221	406	6	⊆	⊆	NUM
ejpam-221	406	7	y	y	PROPN
ejpam-221	406	8	]	]	PUNCT
ejpam-221	406	9	.	.	PUNCT
ejpam-221	407	1	the	the	DET
ejpam-221	407	2	result	result	NOUN
ejpam-221	407	3	now	now	ADV
ejpam-221	407	4	follows	follow	VERB
ejpam-221	407	5	.	.	PUNCT
ejpam-221	408	1	we	we	PRON
ejpam-221	408	2	can	can	AUX
ejpam-221	408	3	now	now	ADV
ejpam-221	408	4	proceed	proceed	VERB
ejpam-221	408	5	with	with	ADP
ejpam-221	408	6	the	the	DET
ejpam-221	408	7	following	follow	VERB
ejpam-221	408	8	proof	proof	NOUN
ejpam-221	408	9	:	:	PUNCT
ejpam-221	408	10	c.	c.	PROPN
ejpam-221	408	11	hollings	holling	NOUN
ejpam-221	408	12	/	/	SYM
ejpam-221	408	13	eur	eur	PROPN
ejpam-221	408	14	.	.	PUNCT
ejpam-221	409	1	j.	j.	PROPN
ejpam-221	409	2	pure	pure	PROPN
ejpam-221	409	3	appl	appl	PROPN
ejpam-221	409	4	.	.	PROPN
ejpam-221	409	5	math	math	PROPN
ejpam-221	409	6	,	,	PUNCT
ejpam-221	409	7	2	2	NUM
ejpam-221	409	8	(	(	PUNCT
ejpam-221	409	9	2009	2009	NUM
ejpam-221	409	10	)	)	PUNCT
ejpam-221	409	11	,	,	PUNCT
ejpam-221	409	12	(	(	PUNCT
ejpam-221	409	13	21	21	NUM
ejpam-221	409	14	-	-	SYM
ejpam-221	409	15	57	57	NUM
ejpam-221	409	16	)	)	PUNCT
ejpam-221	409	17	43	43	NUM
ejpam-221	409	18	proof	proof	NOUN
ejpam-221	409	19	.	.	PUNCT
ejpam-221	410	1	[	[	X
ejpam-221	410	2	proof	proof	NOUN
ejpam-221	410	3	of	of	ADP
ejpam-221	410	4	proposition	proposition	NOUN
ejpam-221	410	5	4.5	4.5	NUM
ejpam-221	410	6	]	]	PUNCT
ejpam-221	410	7	let	let	VERB
ejpam-221	410	8	α	α	NOUN
ejpam-221	410	9	∈	∈	PROPN
ejpam-221	410	10	p	p	X
ejpam-221	410	11	t	t	PROPN
ejpam-221	410	12	x	x	X
ejpam-221	410	13	.	.	PUNCT
ejpam-221	411	1	it	it	PRON
ejpam-221	411	2	follows	follow	VERB
ejpam-221	411	3	immediately	immediately	ADV
ejpam-221	411	4	from	from	ADP
ejpam-221	411	5	lemma	lemma	PROPN
ejpam-221	411	6	4.6	4.6	NUM
ejpam-221	411	7	that	that	PRON
ejpam-221	411	8	α	α	PROPN
ejpam-221	411	9	erex	erex	PROPN
ejpam-221	411	10	idomα	idomα	PROPN
ejpam-221	411	11	.	.	PUNCT
ejpam-221	412	1	by	by	ADP
ejpam-221	412	2	lemma	lemma	PROPN
ejpam-221	412	3	4.3	4.3	NUM
ejpam-221	412	4	,	,	PUNCT
ejpam-221	412	5	idomα	idomα	NOUN
ejpam-221	412	6	is	be	AUX
ejpam-221	412	7	the	the	DET
ejpam-221	412	8	only	only	ADJ
ejpam-221	412	9	idempotent	idempotent	NOUN
ejpam-221	412	10	in	in	ADP
ejpam-221	412	11	ex	ex	PRON
ejpam-221	412	12	to	to	PART
ejpam-221	412	13	which	which	PRON
ejpam-221	412	14	α	α	PRON
ejpam-221	412	15	is	be	AUX
ejpam-221	412	16	erex	erex	PROPN
ejpam-221	412	17	-related	-relate	VERB
ejpam-221	412	18	.	.	PUNCT
ejpam-221	413	1	the	the	DET
ejpam-221	413	2	‘	'	PUNCT
ejpam-221	413	3	weakly	weakly	ADJ
ejpam-221	413	4	left	left	ADJ
ejpam-221	413	5	e	e	NOUN
ejpam-221	413	6	-	-	ADJ
ejpam-221	413	7	ample	ample	ADJ
ejpam-221	413	8	’	'	PUNCT
ejpam-221	413	9	+	+	NUM
ejpam-221	413	10	of	of	ADP
ejpam-221	413	11	defintion	defintion	NOUN
ejpam-221	413	12	4.4	4.4	NUM
ejpam-221	413	13	therefore	therefore	ADV
ejpam-221	413	14	coincides	coincide	VERB
ejpam-221	413	15	with	with	ADP
ejpam-221	413	16	the	the	DET
ejpam-221	413	17	‘	'	PUNCT
ejpam-221	413	18	left	left	ADJ
ejpam-221	413	19	restriction	restriction	NOUN
ejpam-221	413	20	’	'	PUNCT
ejpam-221	414	1	+	+	NUM
ejpam-221	414	2	of	of	ADP
ejpam-221	414	3	definition	definition	NOUN
ejpam-221	414	4	3.1	3.1	NUM
ejpam-221	414	5	.	.	PUNCT
ejpam-221	415	1	now	now	ADV
ejpam-221	415	2	suppose	suppose	VERB
ejpam-221	415	3	that	that	SCONJ
ejpam-221	415	4	α	α	PROPN
ejpam-221	415	5	erex	erex	PROPN
ejpam-221	415	6	β	β	PROPN
ejpam-221	415	7	,	,	PUNCT
ejpam-221	415	8	i.e.	i.e.	X
ejpam-221	415	9	,	,	PUNCT
ejpam-221	415	10	domα	domα	NOUN
ejpam-221	415	11	=	=	SYM
ejpam-221	415	12	domβ	domβ	NOUN
ejpam-221	415	13	,	,	PUNCT
ejpam-221	415	14	and	and	CCONJ
ejpam-221	415	15	let	let	VERB
ejpam-221	415	16	γ	γ	X
ejpam-221	415	17	∈	∈	PROPN
ejpam-221	415	18	p	p	PROPN
ejpam-221	415	19	t	t	PROPN
ejpam-221	415	20	x	x	X
ejpam-221	415	21	.	.	PUNCT
ejpam-221	416	1	we	we	PRON
ejpam-221	416	2	will	will	AUX
ejpam-221	416	3	show	show	VERB
ejpam-221	416	4	that	that	SCONJ
ejpam-221	416	5	γα	γα	VERB
ejpam-221	416	6	erex	erex	NOUN
ejpam-221	416	7	γβ	γβ	PRON
ejpam-221	416	8	by	by	ADP
ejpam-221	416	9	using	use	VERB
ejpam-221	416	10	(	(	PUNCT
ejpam-221	416	11	4.3	4.3	NUM
ejpam-221	416	12	)	)	PUNCT
ejpam-221	416	13	.	.	PUNCT
ejpam-221	417	1	we	we	PRON
ejpam-221	417	2	have	have	VERB
ejpam-221	417	3	domγα=	domγα=	PROPN
ejpam-221	417	4	(	(	PUNCT
ejpam-221	417	5	imγ∩	imγ∩	NOUN
ejpam-221	417	6	domα)γ−1	domα)γ−1	PROPN
ejpam-221	417	7	=	=	SYM
ejpam-221	417	8	(	(	PUNCT
ejpam-221	417	9	imγ∩	imγ∩	NOUN
ejpam-221	417	10	domβ)γ−1	domβ)γ−1	NUM
ejpam-221	417	11	=	=	SYM
ejpam-221	417	12	domγβ	domγβ	NOUN
ejpam-221	417	13	.	.	PUNCT
ejpam-221	418	1	thus	thus	ADV
ejpam-221	418	2	erex	erex	PROPN
ejpam-221	418	3	is	be	AUX
ejpam-221	418	4	a	a	DET
ejpam-221	418	5	left	left	ADJ
ejpam-221	418	6	congruence	congruence	NOUN
ejpam-221	418	7	.	.	PUNCT
ejpam-221	419	1	it	it	PRON
ejpam-221	419	2	only	only	ADV
ejpam-221	419	3	remains	remain	VERB
ejpam-221	419	4	to	to	PART
ejpam-221	419	5	verify	verify	VERB
ejpam-221	419	6	that	that	SCONJ
ejpam-221	419	7	the	the	DET
ejpam-221	419	8	left	left	ADJ
ejpam-221	419	9	ample	ample	ADJ
ejpam-221	419	10	identity	identity	NOUN
ejpam-221	419	11	holds	hold	NOUN
ejpam-221	419	12	.	.	PUNCT
ejpam-221	420	1	let	let	VERB
ejpam-221	420	2	α	α	PRON
ejpam-221	420	3	∈	∈	PROPN
ejpam-221	420	4	p	p	X
ejpam-221	420	5	t	t	PROPN
ejpam-221	420	6	x	x	X
ejpam-221	420	7	and	and	CCONJ
ejpam-221	420	8	ia	ia	PROPN
ejpam-221	420	9	∈	∈	PROPN
ejpam-221	421	1	ex	ex	X
ejpam-221	421	2	.	.	PUNCT
ejpam-221	422	1	then	then	ADV
ejpam-221	422	2	domαia	domαia	VERB
ejpam-221	422	3	=	=	PUNCT
ejpam-221	422	4	(	(	PUNCT
ejpam-221	422	5	imα∩	imα∩	NOUN
ejpam-221	422	6	dom	dom	PROPN
ejpam-221	422	7	ia)α	ia)α	PROPN
ejpam-221	422	8	−1	−1	NOUN
ejpam-221	422	9	=	=	SYM
ejpam-221	422	10	(	(	PUNCT
ejpam-221	422	11	imα∩	imα∩	NOUN
ejpam-221	422	12	a)α−1	a)α−1	VERB
ejpam-221	422	13	⊆	⊆	NUM
ejpam-221	422	14	domα	domα	NOUN
ejpam-221	422	15	.	.	PUNCT
ejpam-221	423	1	note	note	VERB
ejpam-221	423	2	also	also	ADV
ejpam-221	423	3	that	that	PRON
ejpam-221	423	4	im(αia	im(αia	ADV
ejpam-221	423	5	)	)	PUNCT
ejpam-221	424	1	+	+	CCONJ
ejpam-221	424	2	=	=	SYM
ejpam-221	424	3	dom(αia	dom(αia	NOUN
ejpam-221	424	4	)	)	PUNCT
ejpam-221	425	1	+	+	CCONJ
ejpam-221	425	2	=	=	SYM
ejpam-221	425	3	domαia	domαia	NOUN
ejpam-221	425	4	.	.	PUNCT
ejpam-221	426	1	we	we	PRON
ejpam-221	426	2	have	have	AUX
ejpam-221	426	3	dom(αia	dom(αia	VERB
ejpam-221	426	4	)	)	PUNCT
ejpam-221	427	1	+	+	NOUN
ejpam-221	427	2	α	α	NOUN
ejpam-221	427	3	=	=	SYM
ejpam-221	427	4	�	�	PROPN
ejpam-221	427	5	im(αia	im(αia	NUM
ejpam-221	427	6	)	)	PUNCT
ejpam-221	427	7	+	+	NUM
ejpam-221	427	8	∩	∩	ADJ
ejpam-221	427	9	domα	domα	NOUN
ejpam-221	427	10	�	�	PROPN
ejpam-221	427	11	�	�	PROPN
ejpam-221	427	12	(	(	PUNCT
ejpam-221	427	13	αia	αia	NOUN
ejpam-221	427	14	)	)	PUNCT
ejpam-221	428	1	+	+	CCONJ
ejpam-221	428	2	�	�	NOUN
ejpam-221	428	3	−1	−1	NOUN
ejpam-221	428	4	=	=	SYM
ejpam-221	428	5	domαia∩	domαia∩	NOUN
ejpam-221	428	6	domα=	domα=	NUM
ejpam-221	428	7	domαia	domαia	NOUN
ejpam-221	428	8	,	,	PUNCT
ejpam-221	428	9	as	as	SCONJ
ejpam-221	428	10	required	require	VERB
ejpam-221	428	11	.	.	PUNCT
ejpam-221	429	1	for	for	ADP
ejpam-221	429	2	any	any	DET
ejpam-221	429	3	x	x	NOUN
ejpam-221	429	4	in	in	ADP
ejpam-221	429	5	this	this	DET
ejpam-221	429	6	domain	domain	NOUN
ejpam-221	429	7	:	:	PUNCT
ejpam-221	429	8	x(αia	x(αia	X
ejpam-221	429	9	)	)	PUNCT
ejpam-221	430	1	+	+	NOUN
ejpam-221	430	2	α	α	NOUN
ejpam-221	430	3	=	=	SYM
ejpam-221	430	4	xα=	xα=	PROPN
ejpam-221	430	5	xαia	xαia	PROPN
ejpam-221	430	6	.	.	PUNCT
ejpam-221	431	1	it	it	PRON
ejpam-221	431	2	is	be	AUX
ejpam-221	431	3	clear	clear	ADJ
ejpam-221	431	4	that	that	SCONJ
ejpam-221	431	5	the	the	DET
ejpam-221	431	6	details	detail	NOUN
ejpam-221	431	7	of	of	ADP
ejpam-221	431	8	the	the	DET
ejpam-221	431	9	proof	proof	NOUN
ejpam-221	431	10	of	of	ADP
ejpam-221	431	11	proposition	proposition	NOUN
ejpam-221	431	12	4.5	4.5	NUM
ejpam-221	431	13	apply	apply	VERB
ejpam-221	431	14	equally	equally	ADV
ejpam-221	431	15	well	well	ADV
ejpam-221	431	16	to	to	ADP
ejpam-221	431	17	any	any	DET
ejpam-221	431	18	subsemigroup	subsemigroup	NOUN
ejpam-221	431	19	of	of	ADP
ejpam-221	431	20	p	p	PROPN
ejpam-221	431	21	t	t	PROPN
ejpam-221	431	22	x	x	PUNCT
ejpam-221	431	23	that	that	PRON
ejpam-221	431	24	is	be	AUX
ejpam-221	431	25	closed	close	VERB
ejpam-221	431	26	under	under	ADP
ejpam-221	431	27	+	+	ADJ
ejpam-221	431	28	,	,	PUNCT
ejpam-221	431	29	i.e.	i.e.	X
ejpam-221	431	30	,	,	PUNCT
ejpam-221	431	31	to	to	ADP
ejpam-221	431	32	any	any	DET
ejpam-221	431	33	left	left	ADJ
ejpam-221	431	34	restriction	restriction	NOUN
ejpam-221	431	35	semigroup	semigroup	NOUN
ejpam-221	431	36	.	.	PUNCT
ejpam-221	432	1	corollary	corollary	ADJ
ejpam-221	432	2	4.7	4.7	NUM
ejpam-221	432	3	.	.	PUNCT
ejpam-221	433	1	let	let	VERB
ejpam-221	433	2	s	s	PRON
ejpam-221	433	3	be	be	AUX
ejpam-221	433	4	a	a	DET
ejpam-221	433	5	left	left	ADJ
ejpam-221	433	6	restriction	restriction	NOUN
ejpam-221	433	7	semigroup	semigroup	NOUN
ejpam-221	433	8	with	with	ADP
ejpam-221	433	9	respect	respect	NOUN
ejpam-221	433	10	to	to	ADP
ejpam-221	433	11	a	a	DET
ejpam-221	433	12	subsemilattice	subsemilattice	NOUN
ejpam-221	433	13	e	e	NOUN
ejpam-221	433	14	⊆	⊆	NUM
ejpam-221	433	15	e(s	e(s	PROPN
ejpam-221	433	16	)	)	PUNCT
ejpam-221	433	17	.	.	PUNCT
ejpam-221	434	1	then	then	ADV
ejpam-221	434	2	s	s	VERB
ejpam-221	434	3	is	be	AUX
ejpam-221	434	4	weakly	weakly	ADV
ejpam-221	434	5	left	left	ADJ
ejpam-221	434	6	e	e	NOUN
ejpam-221	434	7	-	-	NOUN
ejpam-221	434	8	ample	ample	ADJ
ejpam-221	434	9	.	.	PUNCT
ejpam-221	435	1	it	it	PRON
ejpam-221	435	2	remains	remain	VERB
ejpam-221	435	3	to	to	PART
ejpam-221	435	4	show	show	VERB
ejpam-221	435	5	that	that	SCONJ
ejpam-221	435	6	a	a	DET
ejpam-221	435	7	given	give	VERB
ejpam-221	435	8	weakly	weakly	ADJ
ejpam-221	435	9	left	left	ADJ
ejpam-221	435	10	e	e	NOUN
ejpam-221	435	11	-	-	ADJ
ejpam-221	435	12	ample	ample	ADJ
ejpam-221	435	13	semigroup	semigroup	NOUN
ejpam-221	435	14	s	s	PART
ejpam-221	435	15	is	be	AUX
ejpam-221	435	16	a	a	DET
ejpam-221	435	17	left	left	ADJ
ejpam-221	435	18	restriction	restriction	NOUN
ejpam-221	435	19	semigroup	semigroup	NOUN
ejpam-221	435	20	with	with	ADP
ejpam-221	435	21	respect	respect	NOUN
ejpam-221	435	22	to	to	ADP
ejpam-221	435	23	e.	e.	PROPN
ejpam-221	435	24	before	before	SCONJ
ejpam-221	435	25	we	we	PRON
ejpam-221	435	26	do	do	VERB
ejpam-221	435	27	so	so	ADV
ejpam-221	435	28	,	,	PUNCT
ejpam-221	435	29	however	however	ADV
ejpam-221	435	30	,	,	PUNCT
ejpam-221	435	31	we	we	PRON
ejpam-221	435	32	first	first	ADV
ejpam-221	435	33	record	record	VERB
ejpam-221	435	34	some	some	DET
ejpam-221	435	35	additional	additional	ADJ
ejpam-221	435	36	properties	property	NOUN
ejpam-221	435	37	of	of	ADP
ejpam-221	435	38	weakly	weakly	ADJ
ejpam-221	435	39	left	left	ADJ
ejpam-221	435	40	e	e	NOUN
ejpam-221	435	41	-	-	ADJ
ejpam-221	435	42	ample	ample	ADJ
ejpam-221	435	43	semigroups	semigroup	NOUN
ejpam-221	435	44	,	,	PUNCT
ejpam-221	435	45	including	include	VERB
ejpam-221	435	46	the	the	DET
ejpam-221	435	47	following	follow	VERB
ejpam-221	435	48	useful	useful	ADJ
ejpam-221	435	49	characterisation	characterisation	NOUN
ejpam-221	435	50	of	of	ADP
ejpam-221	435	51	condition	condition	NOUN
ejpam-221	435	52	(	(	PUNCT
ejpam-221	435	53	2	2	NUM
ejpam-221	435	54	)	)	PUNCT
ejpam-221	435	55	of	of	ADP
ejpam-221	435	56	definition	definition	NOUN
ejpam-221	435	57	4.4	4.4	NUM
ejpam-221	435	58	:	:	PUNCT
ejpam-221	435	59	lemma	lemma	PROPN
ejpam-221	435	60	4.8	4.8	NUM
ejpam-221	435	61	.	.	PUNCT
ejpam-221	436	1	let	let	VERB
ejpam-221	436	2	s	s	PRON
ejpam-221	436	3	be	be	AUX
ejpam-221	436	4	a	a	DET
ejpam-221	436	5	semigroup	semigroup	NOUN
ejpam-221	436	6	in	in	ADP
ejpam-221	436	7	which	which	PRON
ejpam-221	436	8	every	every	DET
ejpam-221	436	9	element	element	NOUN
ejpam-221	436	10	a	a	PRON
ejpam-221	436	11	is	be	AUX
ejpam-221	436	12	ere	ere	NOUN
ejpam-221	436	13	-	-	PUNCT
ejpam-221	436	14	related	relate	VERB
ejpam-221	436	15	to	to	ADP
ejpam-221	436	16	an	an	DET
ejpam-221	436	17	idempotent	idempotent	NOUN
ejpam-221	436	18	a+	a+	PUNCT
ejpam-221	436	19	∈	∈	PROPN
ejpam-221	436	20	e	e	NOUN
ejpam-221	436	21	,	,	PUNCT
ejpam-221	436	22	for	for	ADP
ejpam-221	436	23	some	some	DET
ejpam-221	436	24	subsemilattice	subsemilattice	NOUN
ejpam-221	436	25	e	e	NOUN
ejpam-221	436	26	⊆	⊆	NUM
ejpam-221	436	27	e(s	e(s	PROPN
ejpam-221	436	28	)	)	PUNCT
ejpam-221	436	29	.	.	PUNCT
ejpam-221	437	1	then	then	ADV
ejpam-221	437	2	ere	ere	PROPN
ejpam-221	437	3	is	be	AUX
ejpam-221	437	4	a	a	DET
ejpam-221	437	5	left	left	ADJ
ejpam-221	437	6	congruence	congruence	NOUN
ejpam-221	437	7	if	if	SCONJ
ejpam-221	437	8	,	,	PUNCT
ejpam-221	437	9	and	and	CCONJ
ejpam-221	437	10	only	only	ADV
ejpam-221	437	11	if	if	SCONJ
ejpam-221	437	12	,	,	PUNCT
ejpam-221	437	13	(	(	PUNCT
ejpam-221	437	14	st)+	st)+	NOUN
ejpam-221	437	15	=	=	SYM
ejpam-221	437	16	(	(	PUNCT
ejpam-221	437	17	st+)+	st+)+	ADJ
ejpam-221	437	18	,	,	PUNCT
ejpam-221	437	19	for	for	ADP
ejpam-221	437	20	all	all	DET
ejpam-221	437	21	s	s	PROPN
ejpam-221	437	22	,	,	PUNCT
ejpam-221	437	23	t	t	PROPN
ejpam-221	437	24	∈	∈	PROPN
ejpam-221	437	25	s.	s.	PROPN
ejpam-221	437	26	c.	c.	PROPN
ejpam-221	437	27	hollings	hollings	PROPN
ejpam-221	437	28	/	/	SYM
ejpam-221	437	29	eur	eur	PROPN
ejpam-221	437	30	.	.	PUNCT
ejpam-221	438	1	j.	j.	PROPN
ejpam-221	438	2	pure	pure	PROPN
ejpam-221	438	3	appl	appl	PROPN
ejpam-221	438	4	.	.	PROPN
ejpam-221	438	5	math	math	PROPN
ejpam-221	438	6	,	,	PUNCT
ejpam-221	438	7	2	2	NUM
ejpam-221	438	8	(	(	PUNCT
ejpam-221	438	9	2009	2009	NUM
ejpam-221	438	10	)	)	PUNCT
ejpam-221	438	11	,	,	PUNCT
ejpam-221	438	12	(	(	PUNCT
ejpam-221	438	13	21	21	NUM
ejpam-221	438	14	-	-	SYM
ejpam-221	438	15	57	57	NUM
ejpam-221	438	16	)	)	PUNCT
ejpam-221	438	17	44	44	NUM
ejpam-221	438	18	proof	proof	NOUN
ejpam-221	438	19	.	.	PUNCT
ejpam-221	438	20	suppose	suppose	VERB
ejpam-221	438	21	that	that	SCONJ
ejpam-221	438	22	ere	ere	PROPN
ejpam-221	438	23	is	be	AUX
ejpam-221	438	24	a	a	DET
ejpam-221	438	25	left	left	ADJ
ejpam-221	438	26	congruence	congruence	NOUN
ejpam-221	438	27	.	.	PUNCT
ejpam-221	439	1	it	it	PRON
ejpam-221	439	2	then	then	ADV
ejpam-221	439	3	follows	follow	VERB
ejpam-221	439	4	immediately	immediately	ADV
ejpam-221	439	5	from	from	ADP
ejpam-221	439	6	t	t	PROPN
ejpam-221	439	7	ere	ere	PROPN
ejpam-221	439	8	t+	t+	PUNCT
ejpam-221	439	9	that	that	PRON
ejpam-221	439	10	st	st	PROPN
ejpam-221	439	11	ere	ere	PROPN
ejpam-221	439	12	st+	st+	PROPN
ejpam-221	439	13	,	,	PUNCT
ejpam-221	439	14	i.e.	i.e.	X
ejpam-221	439	15	,	,	PUNCT
ejpam-221	439	16	(	(	PUNCT
ejpam-221	439	17	st)+	st)+	NOUN
ejpam-221	439	18	=	=	SYM
ejpam-221	439	19	(	(	PUNCT
ejpam-221	439	20	st+)+	st+)+	ADJ
ejpam-221	439	21	.	.	PUNCT
ejpam-221	440	1	conversely	conversely	ADV
ejpam-221	440	2	,	,	PUNCT
ejpam-221	440	3	suppose	suppose	VERB
ejpam-221	440	4	that	that	SCONJ
ejpam-221	440	5	(	(	PUNCT
ejpam-221	440	6	st)+	st)+	NOUN
ejpam-221	440	7	=	=	SYM
ejpam-221	440	8	(	(	PUNCT
ejpam-221	440	9	st+)+	st+)+	ADJ
ejpam-221	440	10	,	,	PUNCT
ejpam-221	440	11	for	for	ADP
ejpam-221	440	12	all	all	DET
ejpam-221	440	13	s	s	PROPN
ejpam-221	440	14	,	,	PUNCT
ejpam-221	440	15	t	t	PROPN
ejpam-221	440	16	∈	∈	PROPN
ejpam-221	440	17	s.	s.	PROPN
ejpam-221	440	18	then	then	ADV
ejpam-221	440	19	st	st	PROPN
ejpam-221	440	20	ere	ere	PROPN
ejpam-221	440	21	st+	st+	PROPN
ejpam-221	440	22	.	.	PROPN
ejpam-221	441	1	for	for	ADP
ejpam-221	441	2	any	any	DET
ejpam-221	441	3	u	u	PROPN
ejpam-221	441	4	∈	∈	PROPN
ejpam-221	441	5	s	s	VERB
ejpam-221	441	6	with	with	ADP
ejpam-221	441	7	u	u	PROPN
ejpam-221	441	8	ere	ere	PROPN
ejpam-221	441	9	t	t	PROPN
ejpam-221	441	10	,	,	PUNCT
ejpam-221	441	11	we	we	PRON
ejpam-221	441	12	have	have	AUX
ejpam-221	441	13	(	(	PUNCT
ejpam-221	441	14	st+)+	st+)+	ADJ
ejpam-221	441	15	=	=	SYM
ejpam-221	441	16	(	(	PUNCT
ejpam-221	441	17	su+)+	su+)+	ADJ
ejpam-221	441	18	=	=	SYM
ejpam-221	441	19	(	(	PUNCT
ejpam-221	441	20	su)+	su)+	PROPN
ejpam-221	441	21	,	,	PUNCT
ejpam-221	441	22	hence	hence	ADV
ejpam-221	441	23	st	st	PROPN
ejpam-221	441	24	ere	ere	PROPN
ejpam-221	441	25	st+	st+	PROPN
ejpam-221	441	26	ere	ere	PROPN
ejpam-221	441	27	su+	su+	PROPN
ejpam-221	441	28	ere	ere	PROPN
ejpam-221	441	29	su	su	PROPN
ejpam-221	441	30	.	.	PUNCT
ejpam-221	442	1	thus	thus	ADV
ejpam-221	442	2	ere	ere	PROPN
ejpam-221	442	3	is	be	AUX
ejpam-221	442	4	a	a	DET
ejpam-221	442	5	left	left	ADJ
ejpam-221	442	6	congruence	congruence	NOUN
ejpam-221	442	7	.	.	PUNCT
ejpam-221	443	1	a	a	DET
ejpam-221	443	2	weakly	weakly	ADJ
ejpam-221	443	3	left	left	ADJ
ejpam-221	443	4	e	e	NOUN
ejpam-221	443	5	-	-	ADJ
ejpam-221	443	6	ample	ample	ADJ
ejpam-221	443	7	semigroup	semigroup	NOUN
ejpam-221	443	8	possesses	possess	VERB
ejpam-221	443	9	a	a	DET
ejpam-221	443	10	(	(	PUNCT
ejpam-221	443	11	natural	natural	ADJ
ejpam-221	443	12	)	)	PUNCT
ejpam-221	443	13	partial	partial	ADJ
ejpam-221	443	14	order	order	NOUN
ejpam-221	443	15	analogous	analogous	ADJ
ejpam-221	443	16	to	to	ADP
ejpam-221	443	17	that	that	PRON
ejpam-221	443	18	in	in	ADP
ejpam-221	443	19	an	an	DET
ejpam-221	443	20	inverse	inverse	NOUN
ejpam-221	443	21	semigroup	semigroup	NOUN
ejpam-221	443	22	;	;	PUNCT
ejpam-221	443	23	this	this	PRON
ejpam-221	443	24	is	be	AUX
ejpam-221	443	25	,	,	PUNCT
ejpam-221	443	26	of	of	ADP
ejpam-221	443	27	course	course	NOUN
ejpam-221	443	28	,	,	PUNCT
ejpam-221	443	29	an	an	DET
ejpam-221	443	30	abstract	abstract	ADJ
ejpam-221	443	31	version	version	NOUN
ejpam-221	443	32	of	of	ADP
ejpam-221	443	33	the	the	DET
ejpam-221	443	34	ordering	ordering	NOUN
ejpam-221	443	35	of	of	ADP
ejpam-221	443	36	(	(	PUNCT
ejpam-221	443	37	3.3	3.3	NUM
ejpam-221	443	38	):	):	PUNCT
ejpam-221	443	39	a	a	DET
ejpam-221	443	40	≤	≤	NUM
ejpam-221	443	41	b	b	NUM
ejpam-221	443	42	⇐	⇐	ADJ
ejpam-221	443	43	⇒	⇒	NOUN
ejpam-221	443	44	a	a	DET
ejpam-221	443	45	=	=	SYM
ejpam-221	443	46	eb	eb	PROPN
ejpam-221	443	47	,	,	PUNCT
ejpam-221	443	48	(	(	PUNCT
ejpam-221	443	49	4.4	4.4	NUM
ejpam-221	443	50	)	)	PUNCT
ejpam-221	443	51	for	for	ADP
ejpam-221	443	52	some	some	DET
ejpam-221	443	53	e	e	PROPN
ejpam-221	443	54	∈	∈	PROPN
ejpam-221	443	55	e.	e.	PROPN
ejpam-221	443	56	equivalently	equivalently	PROPN
ejpam-221	443	57	,	,	PUNCT
ejpam-221	443	58	a	a	DET
ejpam-221	443	59	≤	≤	NUM
ejpam-221	443	60	b	b	NUM
ejpam-221	443	61	⇐	⇐	ADJ
ejpam-221	443	62	⇒	⇒	NOUN
ejpam-221	443	63	a	a	DET
ejpam-221	443	64	=	=	NOUN
ejpam-221	443	65	a+b	a+b	PROPN
ejpam-221	443	66	.	.	PUNCT
ejpam-221	444	1	to	to	PART
ejpam-221	444	2	see	see	VERB
ejpam-221	444	3	this	this	DET
ejpam-221	444	4	equivalence	equivalence	NOUN
ejpam-221	444	5	,	,	PUNCT
ejpam-221	444	6	we	we	PRON
ejpam-221	444	7	start	start	VERB
ejpam-221	444	8	with	with	ADP
ejpam-221	444	9	a	a	DET
ejpam-221	444	10	=	=	SYM
ejpam-221	444	11	eb	eb	PROPN
ejpam-221	444	12	and	and	CCONJ
ejpam-221	444	13	use	use	VERB
ejpam-221	444	14	lemma	lemma	PROPN
ejpam-221	444	15	4.8	4.8	NUM
ejpam-221	444	16	to	to	PART
ejpam-221	444	17	obtain	obtain	VERB
ejpam-221	444	18	a+	a+	PRON
ejpam-221	444	19	=	=	SYM
ejpam-221	444	20	(	(	PUNCT
ejpam-221	444	21	eb)+	eb)+	NOUN
ejpam-221	444	22	=	=	SYM
ejpam-221	444	23	(	(	PUNCT
ejpam-221	444	24	eb+)+	eb+)+	ADJ
ejpam-221	444	25	=	=	SYM
ejpam-221	444	26	eb+	eb+	NOUN
ejpam-221	444	27	,	,	PUNCT
ejpam-221	444	28	so	so	SCONJ
ejpam-221	444	29	that	that	SCONJ
ejpam-221	444	30	a	a	DET
ejpam-221	444	31	=	=	X
ejpam-221	444	32	eb	eb	PROPN
ejpam-221	444	33	=	=	SYM
ejpam-221	444	34	eb+b	eb+b	PROPN
ejpam-221	444	35	=	=	SYM
ejpam-221	444	36	a+b	a+b	PROPN
ejpam-221	444	37	,	,	PUNCT
ejpam-221	444	38	as	as	SCONJ
ejpam-221	444	39	required	require	VERB
ejpam-221	444	40	.	.	PUNCT
ejpam-221	445	1	the	the	DET
ejpam-221	445	2	converse	converse	NOUN
ejpam-221	445	3	is	be	AUX
ejpam-221	445	4	clear	clear	ADJ
ejpam-221	445	5	.	.	PUNCT
ejpam-221	446	1	the	the	DET
ejpam-221	446	2	partial	partial	ADJ
ejpam-221	446	3	order	order	NOUN
ejpam-221	446	4	in	in	ADP
ejpam-221	446	5	a	a	DET
ejpam-221	446	6	weakly	weakly	ADJ
ejpam-221	446	7	left	left	ADJ
ejpam-221	446	8	e	e	NOUN
ejpam-221	446	9	-	-	ADJ
ejpam-221	446	10	ample	ample	ADJ
ejpam-221	446	11	semigroup	semigroup	NOUN
ejpam-221	446	12	is	be	AUX
ejpam-221	446	13	compatible	compatible	ADJ
ejpam-221	446	14	with	with	ADP
ejpam-221	446	15	multiplication	multiplication	NOUN
ejpam-221	446	16	(	(	PUNCT
ejpam-221	446	17	thanks	thank	NOUN
ejpam-221	446	18	to	to	ADP
ejpam-221	446	19	the	the	DET
ejpam-221	446	20	left	left	ADJ
ejpam-221	446	21	ample	ample	ADJ
ejpam-221	446	22	identity	identity	NOUN
ejpam-221	446	23	)	)	PUNCT
ejpam-221	446	24	and	and	CCONJ
ejpam-221	446	25	,	,	PUNCT
ejpam-221	446	26	in	in	ADP
ejpam-221	446	27	e	e	NOUN
ejpam-221	446	28	,	,	PUNCT
ejpam-221	446	29	restricts	restrict	VERB
ejpam-221	446	30	to	to	ADP
ejpam-221	446	31	the	the	DET
ejpam-221	446	32	‘	'	PUNCT
ejpam-221	446	33	usual	usual	ADJ
ejpam-221	446	34	’	'	PUNCT
ejpam-221	446	35	ordering	ordering	NOUN
ejpam-221	446	36	of	of	ADP
ejpam-221	446	37	idempotents	idempotent	NOUN
ejpam-221	446	38	:	:	PUNCT
ejpam-221	446	39	e	e	X
ejpam-221	446	40	≤	≤	NUM
ejpam-221	446	41	f	f	NOUN
ejpam-221	447	1	if	if	SCONJ
ejpam-221	447	2	,	,	PUNCT
ejpam-221	447	3	and	and	CCONJ
ejpam-221	447	4	only	only	ADV
ejpam-221	447	5	if	if	SCONJ
ejpam-221	447	6	,	,	PUNCT
ejpam-221	447	7	e	e	PROPN
ejpam-221	447	8	=	=	SYM
ejpam-221	447	9	e	e	PROPN
ejpam-221	447	10	f	f	PROPN
ejpam-221	447	11	.	.	PUNCT
ejpam-221	448	1	lemma	lemma	PROPN
ejpam-221	448	2	4.9	4.9	NUM
ejpam-221	448	3	.	.	PUNCT
ejpam-221	449	1	let	let	VERB
ejpam-221	449	2	s	s	PRON
ejpam-221	449	3	be	be	AUX
ejpam-221	449	4	a	a	DET
ejpam-221	449	5	weakly	weakly	ADJ
ejpam-221	449	6	left	left	ADJ
ejpam-221	449	7	e	e	NOUN
ejpam-221	449	8	-	-	ADJ
ejpam-221	449	9	ample	ample	ADJ
ejpam-221	449	10	semigroup	semigroup	NOUN
ejpam-221	449	11	with	with	ADP
ejpam-221	449	12	partial	partial	ADJ
ejpam-221	449	13	order	order	NOUN
ejpam-221	449	14	≤.	≤.	NOUN
ejpam-221	449	15	if	if	SCONJ
ejpam-221	449	16	s	s	VERB
ejpam-221	449	17	∈	∈	PROPN
ejpam-221	449	18	s	s	PART
ejpam-221	449	19	and	and	CCONJ
ejpam-221	449	20	e	e	PROPN
ejpam-221	449	21	∈	∈	PROPN
ejpam-221	449	22	e	e	NOUN
ejpam-221	449	23	,	,	PUNCT
ejpam-221	449	24	then	then	ADV
ejpam-221	449	25	se	se	X
ejpam-221	449	26	≤	≤	ADJ
ejpam-221	449	27	s.	s.	PROPN
ejpam-221	449	28	proof	proof	PROPN
ejpam-221	449	29	.	.	PUNCT
ejpam-221	450	1	if	if	SCONJ
ejpam-221	450	2	we	we	PRON
ejpam-221	450	3	apply	apply	VERB
ejpam-221	450	4	the	the	DET
ejpam-221	450	5	left	left	ADJ
ejpam-221	450	6	ample	ample	ADJ
ejpam-221	450	7	identity	identity	NOUN
ejpam-221	450	8	,	,	PUNCT
ejpam-221	450	9	then	then	ADV
ejpam-221	450	10	we	we	PRON
ejpam-221	450	11	have	have	VERB
ejpam-221	450	12	se	se	X
ejpam-221	450	13	=	=	SYM
ejpam-221	450	14	(	(	PUNCT
ejpam-221	450	15	se)+s	se)+s	NOUN
ejpam-221	450	16	≤	≤	PROPN
ejpam-221	450	17	s	s	PART
ejpam-221	450	18	,	,	PUNCT
ejpam-221	450	19	by	by	ADP
ejpam-221	450	20	(	(	PUNCT
ejpam-221	450	21	4.4	4.4	NUM
ejpam-221	450	22	)	)	PUNCT
ejpam-221	450	23	.	.	PUNCT
ejpam-221	451	1	we	we	PRON
ejpam-221	451	2	observed	observe	VERB
ejpam-221	451	3	earlier	early	ADV
ejpam-221	451	4	that	that	SCONJ
ejpam-221	451	5	a+	a+	PUNCT
ejpam-221	451	6	is	be	AUX
ejpam-221	451	7	a	a	DET
ejpam-221	451	8	left	left	ADJ
ejpam-221	451	9	identity	identity	NOUN
ejpam-221	451	10	for	for	ADP
ejpam-221	451	11	a	a	PRON
ejpam-221	451	12	in	in	ADP
ejpam-221	451	13	a	a	DET
ejpam-221	451	14	weakly	weakly	ADJ
ejpam-221	451	15	left	left	ADJ
ejpam-221	451	16	e	e	NOUN
ejpam-221	451	17	-	-	ADJ
ejpam-221	451	18	ample	ample	ADJ
ejpam-221	451	19	semigroup	semigroup	NOUN
ejpam-221	451	20	;	;	PUNCT
ejpam-221	451	21	we	we	PRON
ejpam-221	451	22	can	can	AUX
ejpam-221	451	23	now	now	ADV
ejpam-221	451	24	say	say	VERB
ejpam-221	451	25	a	a	DET
ejpam-221	451	26	little	little	ADJ
ejpam-221	451	27	more	more	ADJ
ejpam-221	451	28	:	:	PUNCT
ejpam-221	451	29	lemma	lemma	PROPN
ejpam-221	451	30	4.10	4.10	NUM
ejpam-221	451	31	.	.	PUNCT
ejpam-221	452	1	with	with	ADP
ejpam-221	452	2	respect	respect	NOUN
ejpam-221	452	3	to	to	ADP
ejpam-221	452	4	≤	≤	NUM
ejpam-221	452	5	,	,	PUNCT
ejpam-221	452	6	a+	a+	PUNCT
ejpam-221	452	7	is	be	AUX
ejpam-221	452	8	the	the	DET
ejpam-221	452	9	least	least	ADJ
ejpam-221	452	10	left	left	ADJ
ejpam-221	452	11	identity	identity	NOUN
ejpam-221	452	12	for	for	ADP
ejpam-221	452	13	a.	a.	NOUN
ejpam-221	452	14	c.	c.	PROPN
ejpam-221	452	15	hollings	hollings	PROPN
ejpam-221	452	16	/	/	SYM
ejpam-221	452	17	eur	eur	PROPN
ejpam-221	452	18	.	.	PUNCT
ejpam-221	453	1	j.	j.	PROPN
ejpam-221	453	2	pure	pure	PROPN
ejpam-221	453	3	appl	appl	PROPN
ejpam-221	453	4	.	.	PROPN
ejpam-221	453	5	math	math	PROPN
ejpam-221	453	6	,	,	PUNCT
ejpam-221	453	7	2	2	NUM
ejpam-221	453	8	(	(	PUNCT
ejpam-221	453	9	2009	2009	NUM
ejpam-221	453	10	)	)	PUNCT
ejpam-221	453	11	,	,	PUNCT
ejpam-221	453	12	(	(	PUNCT
ejpam-221	453	13	21	21	NUM
ejpam-221	453	14	-	-	SYM
ejpam-221	453	15	57	57	NUM
ejpam-221	453	16	)	)	PUNCT
ejpam-221	453	17	45	45	NUM
ejpam-221	453	18	proof	proof	NOUN
ejpam-221	453	19	.	.	PUNCT
ejpam-221	454	1	this	this	PRON
ejpam-221	454	2	follows	follow	VERB
ejpam-221	454	3	from	from	ADP
ejpam-221	454	4	(	(	PUNCT
ejpam-221	454	5	4.2	4.2	NUM
ejpam-221	454	6	)	)	PUNCT
ejpam-221	454	7	.	.	PUNCT
ejpam-221	455	1	lemma	lemma	PROPN
ejpam-221	455	2	4.11	4.11	NUM
ejpam-221	455	3	.	.	PUNCT
ejpam-221	456	1	[	[	X
ejpam-221	456	2	24	24	NUM
ejpam-221	456	3	,	,	PUNCT
ejpam-221	456	4	proposition	proposition	NOUN
ejpam-221	456	5	1.6	1.6	NUM
ejpam-221	456	6	]	]	PUNCT
ejpam-221	456	7	let	let	VERB
ejpam-221	456	8	s	s	PRON
ejpam-221	456	9	be	be	AUX
ejpam-221	456	10	a	a	DET
ejpam-221	456	11	weakly	weakly	ADJ
ejpam-221	456	12	left	left	ADJ
ejpam-221	456	13	e	e	NOUN
ejpam-221	456	14	-	-	ADJ
ejpam-221	456	15	ample	ample	ADJ
ejpam-221	456	16	semigroup	semigroup	NOUN
ejpam-221	456	17	with	with	ADP
ejpam-221	456	18	partial	partial	ADJ
ejpam-221	456	19	order	order	NOUN
ejpam-221	456	20	≤	≤	NOUN
ejpam-221	456	21	,	,	PUNCT
ejpam-221	456	22	and	and	CCONJ
ejpam-221	456	23	let	let	VERB
ejpam-221	456	24	s	s	NOUN
ejpam-221	456	25	,	,	PUNCT
ejpam-221	456	26	t	t	PROPN
ejpam-221	456	27	∈	∈	PROPN
ejpam-221	456	28	s.	s.	PROPN
ejpam-221	456	29	then	then	ADV
ejpam-221	456	30	(	(	PUNCT
ejpam-221	456	31	st)+	st)+	NOUN
ejpam-221	456	32	≤	≤	NOUN
ejpam-221	456	33	s+	s+	ADV
ejpam-221	456	34	.	.	PUNCT
ejpam-221	457	1	proof	proof	NOUN
ejpam-221	457	2	.	.	PUNCT
ejpam-221	458	1	we	we	PRON
ejpam-221	458	2	make	make	VERB
ejpam-221	458	3	the	the	DET
ejpam-221	458	4	easy	easy	ADJ
ejpam-221	458	5	observation	observation	NOUN
ejpam-221	458	6	that	that	SCONJ
ejpam-221	458	7	s+	s+	ADV
ejpam-221	458	8	is	be	AUX
ejpam-221	458	9	a	a	DET
ejpam-221	458	10	left	left	ADJ
ejpam-221	458	11	identity	identity	NOUN
ejpam-221	458	12	for	for	ADP
ejpam-221	458	13	st	st	PROPN
ejpam-221	458	14	.	.	PROPN
ejpam-221	458	15	the	the	DET
ejpam-221	458	16	result	result	NOUN
ejpam-221	458	17	then	then	ADV
ejpam-221	458	18	follows	follow	VERB
ejpam-221	458	19	from	from	ADP
ejpam-221	458	20	lemma	lemma	PROPN
ejpam-221	458	21	4.10	4.10	NUM
ejpam-221	458	22	.	.	PUNCT
ejpam-221	459	1	the	the	DET
ejpam-221	459	2	following	follow	VERB
ejpam-221	459	3	representation	representation	NOUN
ejpam-221	459	4	theorem	theorem	VERB
ejpam-221	459	5	,	,	PUNCT
ejpam-221	459	6	which	which	PRON
ejpam-221	459	7	first	first	ADV
ejpam-221	459	8	appeared	appear	VERB
ejpam-221	459	9	in	in	ADP
ejpam-221	459	10	[	[	X
ejpam-221	459	11	76	76	NUM
ejpam-221	459	12	]	]	PUNCT
ejpam-221	459	13	,	,	PUNCT
ejpam-221	459	14	completes	complete	VERB
ejpam-221	459	15	the	the	DET
ejpam-221	459	16	proof	proof	NOUN
ejpam-221	459	17	that	that	PRON
ejpam-221	459	18	left	leave	VERB
ejpam-221	459	19	restriction	restriction	NOUN
ejpam-221	459	20	and	and	CCONJ
ejpam-221	459	21	weakly	weakly	ADJ
ejpam-221	459	22	left	left	ADJ
ejpam-221	459	23	e	e	NOUN
ejpam-221	459	24	-	-	ADJ
ejpam-221	459	25	ample	ample	ADJ
ejpam-221	459	26	semigroups	semigroup	NOUN
ejpam-221	459	27	are	be	AUX
ejpam-221	459	28	indeed	indeed	ADV
ejpam-221	459	29	one	one	NUM
ejpam-221	459	30	and	and	CCONJ
ejpam-221	459	31	the	the	DET
ejpam-221	459	32	same	same	ADJ
ejpam-221	459	33	by	by	ADP
ejpam-221	459	34	providing	provide	VERB
ejpam-221	459	35	a	a	DET
ejpam-221	459	36	representation	representation	NOUN
ejpam-221	459	37	of	of	ADP
ejpam-221	459	38	a	a	DET
ejpam-221	459	39	given	give	VERB
ejpam-221	459	40	weakly	weakly	ADJ
ejpam-221	459	41	left	left	ADJ
ejpam-221	459	42	e	e	NOUN
ejpam-221	459	43	-	-	ADJ
ejpam-221	459	44	ample	ample	ADJ
ejpam-221	459	45	semigroup	semigroup	NOUN
ejpam-221	459	46	as	as	ADP
ejpam-221	459	47	a	a	DET
ejpam-221	459	48	(	(	PUNCT
ejpam-221	459	49	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	459	50	of	of	ADP
ejpam-221	459	51	a	a	DET
ejpam-221	459	52	partial	partial	ADJ
ejpam-221	459	53	transformation	transformation	NOUN
ejpam-221	459	54	monoid	monoid	NOUN
ejpam-221	459	55	.	.	PUNCT
ejpam-221	460	1	we	we	PRON
ejpam-221	460	2	note	note	VERB
ejpam-221	460	3	that	that	SCONJ
ejpam-221	460	4	if	if	SCONJ
ejpam-221	460	5	we	we	PRON
ejpam-221	460	6	regard	regard	VERB
ejpam-221	460	7	a	a	DET
ejpam-221	460	8	weakly	weakly	ADJ
ejpam-221	460	9	left	left	ADJ
ejpam-221	460	10	e	e	NOUN
ejpam-221	460	11	-	-	ADJ
ejpam-221	460	12	ample	ample	ADJ
ejpam-221	460	13	semigroup	semigroup	NOUN
ejpam-221	460	14	as	as	ADP
ejpam-221	460	15	a	a	DET
ejpam-221	460	16	subsemigroup	subsemigroup	NOUN
ejpam-221	460	17	of	of	ADP
ejpam-221	460	18	p	p	PROPN
ejpam-221	460	19	t	t	PROPN
ejpam-221	460	20	x	x	X
ejpam-221	460	21	,	,	PUNCT
ejpam-221	460	22	as	as	ADP
ejpam-221	460	23	per	per	ADP
ejpam-221	460	24	the	the	DET
ejpam-221	460	25	following	following	NOUN
ejpam-221	460	26	theorem	theorem	NOUN
ejpam-221	460	27	,	,	PUNCT
ejpam-221	460	28	then	then	ADV
ejpam-221	460	29	lemmas	lemmas	PROPN
ejpam-221	460	30	4.9–4.11	4.9–4.11	PROPN
ejpam-221	460	31	follow	follow	VERB
ejpam-221	460	32	easily	easily	ADV
ejpam-221	460	33	from	from	ADP
ejpam-221	460	34	(	(	PUNCT
ejpam-221	460	35	3.3	3.3	NUM
ejpam-221	460	36	)	)	PUNCT
ejpam-221	460	37	.	.	PUNCT
ejpam-221	461	1	theorem	theorem	VERB
ejpam-221	461	2	4.12	4.12	NUM
ejpam-221	461	3	.	.	PUNCT
ejpam-221	462	1	let	let	VERB
ejpam-221	462	2	s	s	PRON
ejpam-221	462	3	be	be	AUX
ejpam-221	462	4	a	a	DET
ejpam-221	462	5	weakly	weakly	ADJ
ejpam-221	462	6	left	left	ADJ
ejpam-221	462	7	e	e	NOUN
ejpam-221	462	8	-	-	ADJ
ejpam-221	462	9	ample	ample	ADJ
ejpam-221	462	10	semigroup	semigroup	NOUN
ejpam-221	462	11	,	,	PUNCT
ejpam-221	462	12	regarded	regard	VERB
ejpam-221	462	13	as	as	ADP
ejpam-221	462	14	an	an	DET
ejpam-221	462	15	algebra	algebra	NOUN
ejpam-221	462	16	of	of	ADP
ejpam-221	462	17	type	type	NOUN
ejpam-221	462	18	(	(	PUNCT
ejpam-221	462	19	2,1	2,1	NUM
ejpam-221	462	20	)	)	PUNCT
ejpam-221	462	21	.	.	PUNCT
ejpam-221	463	1	then	then	ADV
ejpam-221	463	2	the	the	DET
ejpam-221	463	3	mapping	mapping	NOUN
ejpam-221	463	4	φ	φ	NOUN
ejpam-221	463	5	:	:	PUNCT
ejpam-221	463	6	s→p	s→p	PROPN
ejpam-221	463	7	t	t	NOUN
ejpam-221	463	8	s	s	AUX
ejpam-221	463	9	given	give	VERB
ejpam-221	463	10	by	by	ADP
ejpam-221	463	11	dom	dom	NOUN
ejpam-221	463	12	sφ	sφ	PROPN
ejpam-221	463	13	=	=	PROPN
ejpam-221	463	14	ss+	ss+	PROPN
ejpam-221	463	15	and	and	CCONJ
ejpam-221	463	16	x(sφ	x(sφ	NOUN
ejpam-221	463	17	)	)	PUNCT
ejpam-221	463	18	=	=	SYM
ejpam-221	463	19	xs	xs	PROPN
ejpam-221	463	20	,	,	PUNCT
ejpam-221	463	21	∀x	∀x	X
ejpam-221	463	22	∈	∈	PROPN
ejpam-221	463	23	dom	dom	NOUN
ejpam-221	463	24	sφ	sφ	PROPN
ejpam-221	463	25	,	,	PUNCT
ejpam-221	463	26	is	be	AUX
ejpam-221	463	27	a	a	DET
ejpam-221	463	28	representation	representation	NOUN
ejpam-221	463	29	of	of	ADP
ejpam-221	463	30	s	s	PRON
ejpam-221	463	31	as	as	ADP
ejpam-221	463	32	a	a	DET
ejpam-221	463	33	(	(	PUNCT
ejpam-221	463	34	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	463	35	of	of	ADP
ejpam-221	463	36	p	p	PROPN
ejpam-221	463	37	t	t	PROPN
ejpam-221	463	38	s	s	PART
ejpam-221	463	39	.	.	PUNCT
ejpam-221	464	1	proof	proof	NOUN
ejpam-221	464	2	.	.	PUNCT
ejpam-221	465	1	we	we	PRON
ejpam-221	465	2	must	must	AUX
ejpam-221	465	3	show	show	VERB
ejpam-221	465	4	that	that	SCONJ
ejpam-221	465	5	φ	φ	PROPN
ejpam-221	465	6	is	be	AUX
ejpam-221	465	7	an	an	DET
ejpam-221	465	8	injective	injective	ADJ
ejpam-221	465	9	(	(	PUNCT
ejpam-221	465	10	2,1)-morphism	2,1)-morphism	NUM
ejpam-221	465	11	.	.	PUNCT
ejpam-221	466	1	note	note	VERB
ejpam-221	466	2	that	that	SCONJ
ejpam-221	466	3	the	the	DET
ejpam-221	466	4	‘	'	PUNCT
ejpam-221	466	5	1	1	NUM
ejpam-221	466	6	’	'	PUNCT
ejpam-221	466	7	part	part	NOUN
ejpam-221	466	8	of	of	ADP
ejpam-221	466	9	‘	'	PUNCT
ejpam-221	466	10	(	(	PUNCT
ejpam-221	466	11	2,1)morphism	2,1)morphism	NUM
ejpam-221	466	12	’	'	PUNCT
ejpam-221	466	13	indicates	indicate	VERB
ejpam-221	466	14	that	that	SCONJ
ejpam-221	466	15	φ	φ	PROPN
ejpam-221	466	16	should	should	AUX
ejpam-221	466	17	send	send	VERB
ejpam-221	466	18	the	the	DET
ejpam-221	466	19	‘	'	PUNCT
ejpam-221	466	20	weakly	weakly	ADJ
ejpam-221	466	21	left	left	ADJ
ejpam-221	466	22	e	e	NOUN
ejpam-221	466	23	-	-	ADJ
ejpam-221	466	24	ample	ample	ADJ
ejpam-221	466	25	’	'	PUNCT
ejpam-221	466	26	+	+	CCONJ
ejpam-221	466	27	to	to	ADP
ejpam-221	466	28	the	the	DET
ejpam-221	466	29	‘	'	PUNCT
ejpam-221	466	30	left	left	ADJ
ejpam-221	466	31	restriction	restriction	NOUN
ejpam-221	466	32	’	'	PUNCT
ejpam-221	467	1	+	+	PROPN
ejpam-221	467	2	.	.	PUNCT
ejpam-221	467	3	we	we	PRON
ejpam-221	467	4	first	first	ADV
ejpam-221	467	5	show	show	VERB
ejpam-221	467	6	that	that	SCONJ
ejpam-221	467	7	φ	φ	PROPN
ejpam-221	467	8	respects	respect	VERB
ejpam-221	467	9	+	+	CCONJ
ejpam-221	467	10	in	in	ADP
ejpam-221	467	11	this	this	DET
ejpam-221	467	12	way	way	NOUN
ejpam-221	467	13	.	.	PUNCT
ejpam-221	468	1	for	for	ADP
ejpam-221	468	2	s	s	PROPN
ejpam-221	468	3	∈	∈	PROPN
ejpam-221	468	4	s	s	PART
ejpam-221	468	5	,	,	PUNCT
ejpam-221	468	6	we	we	PRON
ejpam-221	468	7	have	have	VERB
ejpam-221	468	8	(	(	PUNCT
ejpam-221	468	9	sφ)+	sφ)+	NOUN
ejpam-221	468	10	=	=	NOUN
ejpam-221	468	11	idom	idom	PROPN
ejpam-221	469	1	sφ	sφ	PRON
ejpam-221	469	2	,	,	PUNCT
ejpam-221	469	3	so	so	ADV
ejpam-221	469	4	dom(sφ)+	dom(sφ)+	PROPN
ejpam-221	469	5	=	=	PUNCT
ejpam-221	469	6	dom	dom	NOUN
ejpam-221	469	7	sφ	sφ	NOUN
ejpam-221	469	8	=	=	PUNCT
ejpam-221	469	9	ss+	ss+	NOUN
ejpam-221	469	10	=	=	SYM
ejpam-221	469	11	s(s+)+	s(s+)+	ADJ
ejpam-221	469	12	=	=	SYM
ejpam-221	469	13	dom	dom	NOUN
ejpam-221	469	14	s+φ	s+φ	PROPN
ejpam-221	469	15	.	.	PUNCT
ejpam-221	470	1	let	let	VERB
ejpam-221	470	2	x	x	PRON
ejpam-221	470	3	belong	belong	VERB
ejpam-221	470	4	to	to	ADP
ejpam-221	470	5	this	this	DET
ejpam-221	470	6	domain	domain	NOUN
ejpam-221	470	7	.	.	PUNCT
ejpam-221	471	1	then	then	ADV
ejpam-221	471	2	x	x	X
ejpam-221	471	3	=	=	SYM
ejpam-221	471	4	ys+	ys+	PROPN
ejpam-221	471	5	,	,	PUNCT
ejpam-221	471	6	for	for	ADP
ejpam-221	471	7	some	some	DET
ejpam-221	471	8	y	y	PROPN
ejpam-221	471	9	∈	∈	PROPN
ejpam-221	471	10	s	s	NOUN
ejpam-221	471	11	,	,	PUNCT
ejpam-221	471	12	so	so	ADV
ejpam-221	471	13	x(s+φ	x(s+φ	NOUN
ejpam-221	471	14	)	)	PUNCT
ejpam-221	472	1	=	=	SYM
ejpam-221	472	2	xs+	xs+	NOUN
ejpam-221	473	1	=	=	SYM
ejpam-221	473	2	ys+s+	ys+s+	PROPN
ejpam-221	473	3	=	=	PUNCT
ejpam-221	473	4	ys+	ys+	PROPN
ejpam-221	473	5	=	=	PUNCT
ejpam-221	473	6	x	x	PUNCT
ejpam-221	474	1	=	=	PUNCT
ejpam-221	474	2	x(sφ)+	x(sφ)+	PROPN
ejpam-221	474	3	.	.	PUNCT
ejpam-221	475	1	we	we	PRON
ejpam-221	475	2	now	now	ADV
ejpam-221	475	3	show	show	VERB
ejpam-221	475	4	that	that	SCONJ
ejpam-221	475	5	φ	φ	PROPN
ejpam-221	475	6	respects	respect	VERB
ejpam-221	475	7	multiplication	multiplication	NOUN
ejpam-221	475	8	.	.	PUNCT
ejpam-221	476	1	let	let	VERB
ejpam-221	476	2	s	s	NOUN
ejpam-221	476	3	,	,	PUNCT
ejpam-221	476	4	t	t	PROPN
ejpam-221	476	5	∈	∈	PROPN
ejpam-221	476	6	s.	s.	PROPN
ejpam-221	476	7	then	then	ADV
ejpam-221	476	8	dom(sφ)(tφ	dom(sφ)(tφ	AUX
ejpam-221	476	9	)	)	PUNCT
ejpam-221	476	10	is	be	AUX
ejpam-221	476	11	the	the	DET
ejpam-221	476	12	set	set	NOUN
ejpam-221	476	13	of	of	ADP
ejpam-221	476	14	all	all	DET
ejpam-221	476	15	those	those	DET
ejpam-221	476	16	elements	element	NOUN
ejpam-221	476	17	x	x	SYM
ejpam-221	476	18	∈	∈	NOUN
ejpam-221	476	19	dom	dom	NOUN
ejpam-221	477	1	sφ	sφ	PRON
ejpam-221	477	2	such	such	ADJ
ejpam-221	477	3	that	that	SCONJ
ejpam-221	477	4	x(sφ	x(sφ	NOUN
ejpam-221	477	5	)	)	PUNCT
ejpam-221	477	6	=	=	PUNCT
ejpam-221	477	7	xs	xs	PROPN
ejpam-221	477	8	∈	∈	PROPN
ejpam-221	477	9	dom	dom	PROPN
ejpam-221	477	10	tφ	tφ	PROPN
ejpam-221	477	11	:	:	PUNCT
ejpam-221	477	12	dom(sφ)(tφ	dom(sφ)(tφ	X
ejpam-221	477	13	)	)	PUNCT
ejpam-221	477	14	=	=	PRON
ejpam-221	477	15	{	{	PUNCT
ejpam-221	477	16	x	x	PUNCT
ejpam-221	477	17	∈	∈	PROPN
ejpam-221	477	18	ss+	ss+	NOUN
ejpam-221	477	19	:	:	PUNCT
ejpam-221	477	20	xs	xs	PROPN
ejpam-221	477	21	∈	∈	PROPN
ejpam-221	477	22	st+	st+	PROPN
ejpam-221	477	23	}	}	PUNCT
ejpam-221	477	24	.	.	PUNCT
ejpam-221	478	1	(	(	PUNCT
ejpam-221	478	2	4.5	4.5	NUM
ejpam-221	478	3	)	)	PUNCT
ejpam-221	478	4	c.	c.	PROPN
ejpam-221	478	5	hollings	holling	NOUN
ejpam-221	478	6	/	/	SYM
ejpam-221	478	7	eur	eur	PROPN
ejpam-221	478	8	.	.	PUNCT
ejpam-221	479	1	j.	j.	PROPN
ejpam-221	479	2	pure	pure	PROPN
ejpam-221	479	3	appl	appl	PROPN
ejpam-221	479	4	.	.	PROPN
ejpam-221	479	5	math	math	PROPN
ejpam-221	479	6	,	,	PUNCT
ejpam-221	479	7	2	2	NUM
ejpam-221	479	8	(	(	PUNCT
ejpam-221	479	9	2009	2009	NUM
ejpam-221	479	10	)	)	PUNCT
ejpam-221	479	11	,	,	PUNCT
ejpam-221	479	12	(	(	PUNCT
ejpam-221	479	13	21	21	NUM
ejpam-221	479	14	-	-	SYM
ejpam-221	479	15	57	57	NUM
ejpam-221	479	16	)	)	PUNCT
ejpam-221	479	17	46	46	NUM
ejpam-221	479	18	let	let	VERB
ejpam-221	479	19	x	x	X
ejpam-221	479	20	∈	∈	VERB
ejpam-221	479	21	dom(sφ)(tφ	dom(sφ)(tφ	NOUN
ejpam-221	479	22	)	)	PUNCT
ejpam-221	479	23	.	.	PUNCT
ejpam-221	480	1	we	we	PRON
ejpam-221	480	2	deduce	deduce	VERB
ejpam-221	480	3	from	from	ADP
ejpam-221	480	4	(	(	PUNCT
ejpam-221	480	5	4.5	4.5	NUM
ejpam-221	480	6	)	)	PUNCT
ejpam-221	480	7	that	that	PRON
ejpam-221	480	8	xs+	xs+	VERB
ejpam-221	481	1	=	=	PUNCT
ejpam-221	481	2	x	x	X
ejpam-221	481	3	;	;	PUNCT
ejpam-221	481	4	(	(	PUNCT
ejpam-221	481	5	4.6	4.6	NUM
ejpam-221	481	6	)	)	PUNCT
ejpam-221	481	7	xst+	xst+	PUNCT
ejpam-221	482	1	=	=	PROPN
ejpam-221	482	2	xs	xs	PROPN
ejpam-221	482	3	.	.	PUNCT
ejpam-221	483	1	(	(	PUNCT
ejpam-221	483	2	4.7	4.7	NUM
ejpam-221	483	3	)	)	PUNCT
ejpam-221	483	4	then	then	ADV
ejpam-221	483	5	x	x	X
ejpam-221	483	6	=	=	PUNCT
ejpam-221	483	7	xs+	xs+	NOUN
ejpam-221	483	8	,	,	PUNCT
ejpam-221	483	9	by	by	ADP
ejpam-221	483	10	(	(	PUNCT
ejpam-221	483	11	4.6	4.6	NUM
ejpam-221	483	12	)	)	PUNCT
ejpam-221	483	13	=	=	SYM
ejpam-221	483	14	(	(	PUNCT
ejpam-221	483	15	xs+)+x	xs+)+x	ADV
ejpam-221	483	16	,	,	PUNCT
ejpam-221	483	17	by	by	ADP
ejpam-221	483	18	the	the	DET
ejpam-221	483	19	left	left	ADJ
ejpam-221	483	20	ample	ample	ADJ
ejpam-221	483	21	identity	identity	NOUN
ejpam-221	483	22	=	=	SYM
ejpam-221	483	23	(	(	PUNCT
ejpam-221	483	24	xs)+x	xs)+x	NOUN
ejpam-221	483	25	,	,	PUNCT
ejpam-221	483	26	by	by	ADP
ejpam-221	483	27	lemma	lemma	PROPN
ejpam-221	483	28	4.8	4.8	NUM
ejpam-221	483	29	=	=	SYM
ejpam-221	483	30	(	(	PUNCT
ejpam-221	483	31	xst+)+x	xst+)+x	PROPN
ejpam-221	483	32	,	,	PUNCT
ejpam-221	483	33	by	by	ADP
ejpam-221	483	34	(	(	PUNCT
ejpam-221	483	35	4.7	4.7	NUM
ejpam-221	483	36	)	)	PUNCT
ejpam-221	483	37	=	=	SYM
ejpam-221	483	38	(	(	PUNCT
ejpam-221	483	39	xst)+x	xst)+x	PROPN
ejpam-221	483	40	,	,	PUNCT
ejpam-221	483	41	by	by	ADP
ejpam-221	483	42	lemma	lemma	PROPN
ejpam-221	483	43	4.8	4.8	NUM
ejpam-221	483	44	=	=	SYM
ejpam-221	483	45	(	(	PUNCT
ejpam-221	483	46	x(st)+)+x	x(st)+)+x	INTJ
ejpam-221	483	47	,	,	PUNCT
ejpam-221	483	48	by	by	ADP
ejpam-221	483	49	lemma	lemma	PROPN
ejpam-221	483	50	4.8	4.8	NUM
ejpam-221	483	51	=	=	SYM
ejpam-221	483	52	x(st)+	x(st)+	PROPN
ejpam-221	483	53	,	,	PUNCT
ejpam-221	483	54	by	by	ADP
ejpam-221	483	55	the	the	DET
ejpam-221	483	56	left	left	ADJ
ejpam-221	483	57	ample	ample	ADJ
ejpam-221	483	58	identity	identity	NOUN
ejpam-221	483	59	.	.	PUNCT
ejpam-221	484	1	hence	hence	ADV
ejpam-221	484	2	x	x	PUNCT
ejpam-221	484	3	∈	∈	PROPN
ejpam-221	484	4	s(st)+	s(st)+	PROPN
ejpam-221	484	5	=	=	SYM
ejpam-221	484	6	dom(st)φ	dom(st)φ	PROPN
ejpam-221	484	7	.	.	PUNCT
ejpam-221	484	8	conversely	conversely	ADV
ejpam-221	484	9	,	,	PUNCT
ejpam-221	484	10	suppose	suppose	VERB
ejpam-221	484	11	that	that	SCONJ
ejpam-221	484	12	x	x	PUNCT
ejpam-221	484	13	∈	∈	PROPN
ejpam-221	484	14	dom(st)φ	dom(st)φ	PROPN
ejpam-221	485	1	=	=	SYM
ejpam-221	485	2	s(st)+	s(st)+	PROPN
ejpam-221	485	3	.	.	PUNCT
ejpam-221	486	1	then	then	ADV
ejpam-221	486	2	x(st)+	x(st)+	PROPN
ejpam-221	487	1	=	=	PUNCT
ejpam-221	487	2	x	x	SYM
ejpam-221	487	3	,	,	PUNCT
ejpam-221	487	4	(	(	PUNCT
ejpam-221	487	5	4.8	4.8	NUM
ejpam-221	487	6	)	)	PUNCT
ejpam-221	487	7	so	so	ADV
ejpam-221	487	8	xs+	xs+	VERB
ejpam-221	487	9	=	=	PUNCT
ejpam-221	487	10	x(st)+s+	x(st)+s+	PROPN
ejpam-221	488	1	=	=	SYM
ejpam-221	488	2	x(st)+	x(st)+	PROPN
ejpam-221	488	3	,	,	PUNCT
ejpam-221	488	4	by	by	ADP
ejpam-221	488	5	lemma	lemma	PROPN
ejpam-221	488	6	4.11	4.11	NUM
ejpam-221	488	7	=	=	SYM
ejpam-221	488	8	x	x	X
ejpam-221	488	9	,	,	PUNCT
ejpam-221	488	10	in	in	ADP
ejpam-221	488	11	which	which	DET
ejpam-221	488	12	case	case	NOUN
ejpam-221	488	13	,	,	PUNCT
ejpam-221	488	14	x	x	SYM
ejpam-221	488	15	∈	∈	NOUN
ejpam-221	488	16	ss+	ss+	NOUN
ejpam-221	488	17	=	=	SYM
ejpam-221	488	18	dom	dom	NOUN
ejpam-221	488	19	sφ	sφ	PROPN
ejpam-221	488	20	.	.	PROPN
ejpam-221	488	21	next	next	ADJ
ejpam-221	488	22	,	,	PUNCT
ejpam-221	488	23	x(sφ	x(sφ	NUM
ejpam-221	488	24	)	)	PUNCT
ejpam-221	489	1	=	=	SYM
ejpam-221	489	2	xs	xs	NOUN
ejpam-221	489	3	=	=	PUNCT
ejpam-221	490	1	x(st)+s	x(st)+s	ADJ
ejpam-221	490	2	,	,	PUNCT
ejpam-221	490	3	by	by	ADP
ejpam-221	490	4	(	(	PUNCT
ejpam-221	490	5	4.8	4.8	NUM
ejpam-221	490	6	)	)	PUNCT
ejpam-221	490	7	=	=	PUNCT
ejpam-221	491	1	x(st+)+s	x(st+)+s	PROPN
ejpam-221	491	2	,	,	PUNCT
ejpam-221	491	3	by	by	ADP
ejpam-221	491	4	lemma	lemma	PROPN
ejpam-221	491	5	4.8	4.8	NUM
ejpam-221	491	6	=	=	SYM
ejpam-221	491	7	xst+	xst+	PROPN
ejpam-221	491	8	,	,	PUNCT
ejpam-221	491	9	by	by	ADP
ejpam-221	491	10	the	the	DET
ejpam-221	491	11	left	left	ADJ
ejpam-221	491	12	ample	ample	ADJ
ejpam-221	491	13	identity	identity	NOUN
ejpam-221	491	14	.	.	PUNCT
ejpam-221	492	1	thus	thus	ADV
ejpam-221	492	2	x(sφ	x(sφ	NUM
ejpam-221	492	3	)	)	PUNCT
ejpam-221	492	4	∈	∈	PROPN
ejpam-221	492	5	st+	st+	NOUN
ejpam-221	492	6	=	=	NOUN
ejpam-221	492	7	dom	dom	PROPN
ejpam-221	492	8	tφ	tφ	PROPN
ejpam-221	492	9	.	.	PUNCT
ejpam-221	493	1	we	we	PRON
ejpam-221	493	2	conclude	conclude	VERB
ejpam-221	493	3	that	that	SCONJ
ejpam-221	493	4	x	x	PUNCT
ejpam-221	493	5	∈	∈	PROPN
ejpam-221	493	6	dom(sφ)(tφ	dom(sφ)(tφ	NOUN
ejpam-221	493	7	)	)	PUNCT
ejpam-221	493	8	.	.	PUNCT
ejpam-221	494	1	therefore	therefore	ADV
ejpam-221	494	2	,	,	PUNCT
ejpam-221	494	3	dom(sφ)(tφ	dom(sφ)(tφ	X
ejpam-221	494	4	)	)	PUNCT
ejpam-221	494	5	=	=	SYM
ejpam-221	494	6	dom(st)φ	dom(st)φ	PROPN
ejpam-221	494	7	.	.	PUNCT
ejpam-221	495	1	it	it	PRON
ejpam-221	495	2	is	be	AUX
ejpam-221	495	3	clear	clear	ADJ
ejpam-221	495	4	that	that	SCONJ
ejpam-221	495	5	x(sφ)(tφ	x(sφ)(tφ	PROPN
ejpam-221	495	6	)	)	PUNCT
ejpam-221	495	7	=	=	SYM
ejpam-221	496	1	x(st)φ	x(st)φ	PROPN
ejpam-221	496	2	,	,	PUNCT
ejpam-221	496	3	for	for	ADP
ejpam-221	496	4	x	x	PUNCT
ejpam-221	496	5	in	in	ADP
ejpam-221	496	6	this	this	DET
ejpam-221	496	7	domain	domain	NOUN
ejpam-221	496	8	,	,	PUNCT
ejpam-221	496	9	hence	hence	ADV
ejpam-221	496	10	(	(	PUNCT
ejpam-221	496	11	sφ)(tφ	sφ)(tφ	X
ejpam-221	496	12	)	)	PUNCT
ejpam-221	496	13	=	=	SYM
ejpam-221	496	14	(	(	PUNCT
ejpam-221	496	15	st)φ	st)φ	PROPN
ejpam-221	496	16	.	.	PUNCT
ejpam-221	497	1	finally	finally	ADV
ejpam-221	497	2	,	,	PUNCT
ejpam-221	497	3	we	we	PRON
ejpam-221	497	4	must	must	AUX
ejpam-221	497	5	show	show	VERB
ejpam-221	497	6	that	that	SCONJ
ejpam-221	497	7	φ	φ	PROPN
ejpam-221	497	8	is	be	AUX
ejpam-221	497	9	one	one	NUM
ejpam-221	497	10	-	-	PUNCT
ejpam-221	497	11	one	one	NUM
ejpam-221	497	12	.	.	PUNCT
ejpam-221	497	13	suppose	suppose	VERB
ejpam-221	497	14	that	that	SCONJ
ejpam-221	497	15	sφ	sφ	PROPN
ejpam-221	497	16	=	=	SYM
ejpam-221	497	17	tφ	tφ	PROPN
ejpam-221	497	18	,	,	PUNCT
ejpam-221	497	19	for	for	ADP
ejpam-221	497	20	some	some	DET
ejpam-221	497	21	s	s	NOUN
ejpam-221	497	22	,	,	PUNCT
ejpam-221	497	23	t	t	PROPN
ejpam-221	497	24	∈	∈	PROPN
ejpam-221	497	25	s.	s.	PROPN
ejpam-221	497	26	then	then	ADV
ejpam-221	497	27	ss+	ss+	PROPN
ejpam-221	497	28	=	=	SYM
ejpam-221	497	29	dom	dom	NOUN
ejpam-221	497	30	sφ	sφ	NOUN
ejpam-221	497	31	=	=	PUNCT
ejpam-221	497	32	dom	dom	NOUN
ejpam-221	497	33	tφ	tφ	PROPN
ejpam-221	497	34	=	=	PROPN
ejpam-221	497	35	st+	st+	PROPN
ejpam-221	497	36	,	,	PUNCT
ejpam-221	497	37	whence	whence	NOUN
ejpam-221	497	38	s+	s+	ADV
ejpam-221	497	39	=	=	PUNCT
ejpam-221	497	40	ut+	ut+	ADJ
ejpam-221	497	41	and	and	CCONJ
ejpam-221	497	42	t+	t+	NOUN
ejpam-221	497	43	=	=	NOUN
ejpam-221	497	44	vs+	vs+	NOUN
ejpam-221	497	45	,	,	PUNCT
ejpam-221	497	46	for	for	ADP
ejpam-221	497	47	some	some	DET
ejpam-221	497	48	u	u	NOUN
ejpam-221	497	49	,	,	PUNCT
ejpam-221	497	50	v	v	ADP
ejpam-221	497	51	∈	∈	PROPN
ejpam-221	497	52	s	s	NOUN
ejpam-221	497	53	,	,	PUNCT
ejpam-221	497	54	i.e.	i.e.	X
ejpam-221	497	55	,	,	PUNCT
ejpam-221	497	56	c.	c.	PROPN
ejpam-221	497	57	hollings	holling	NOUN
ejpam-221	497	58	/	/	SYM
ejpam-221	497	59	eur	eur	PROPN
ejpam-221	497	60	.	.	PUNCT
ejpam-221	498	1	j.	j.	PROPN
ejpam-221	498	2	pure	pure	PROPN
ejpam-221	498	3	appl	appl	PROPN
ejpam-221	498	4	.	.	PROPN
ejpam-221	498	5	math	math	PROPN
ejpam-221	498	6	,	,	PUNCT
ejpam-221	498	7	2	2	NUM
ejpam-221	498	8	(	(	PUNCT
ejpam-221	498	9	2009	2009	NUM
ejpam-221	498	10	)	)	PUNCT
ejpam-221	498	11	,	,	PUNCT
ejpam-221	498	12	(	(	PUNCT
ejpam-221	498	13	21	21	NUM
ejpam-221	498	14	-	-	SYM
ejpam-221	498	15	57	57	NUM
ejpam-221	498	16	)	)	PUNCT
ejpam-221	498	17	47	47	NUM
ejpam-221	498	18	s+l	s+l	NUM
ejpam-221	498	19	t+	t+	PUNCT
ejpam-221	498	20	.	.	PUNCT
ejpam-221	499	1	it	it	PRON
ejpam-221	499	2	follows	follow	VERB
ejpam-221	499	3	that	that	SCONJ
ejpam-221	499	4	s+	s+	ADV
ejpam-221	499	5	=	=	PUNCT
ejpam-221	499	6	t+	t+	PROPN
ejpam-221	499	7	.	.	PUNCT
ejpam-221	500	1	finally	finally	ADV
ejpam-221	500	2	,	,	PUNCT
ejpam-221	500	3	we	we	PRON
ejpam-221	500	4	have	have	VERB
ejpam-221	500	5	s+	s+	ADV
ejpam-221	500	6	=	=	SYM
ejpam-221	500	7	t+	t+	PUNCT
ejpam-221	500	8	∈	∈	PROPN
ejpam-221	500	9	dom	dom	NOUN
ejpam-221	500	10	sφ	sφ	NOUN
ejpam-221	500	11	=	=	PUNCT
ejpam-221	500	12	dom	dom	PROPN
ejpam-221	500	13	tφ	tφ	PROPN
ejpam-221	500	14	,	,	PUNCT
ejpam-221	500	15	so	so	SCONJ
ejpam-221	500	16	s+(sφ	s+(sφ	NOUN
ejpam-221	500	17	)	)	PUNCT
ejpam-221	500	18	=	=	PUNCT
ejpam-221	500	19	t+(tφ)⇒	t+(tφ)⇒	ADP
ejpam-221	500	20	s+s	s+s	PROPN
ejpam-221	500	21	=	=	PUNCT
ejpam-221	500	22	t+	t+	PUNCT
ejpam-221	500	23	t	t	PROPN
ejpam-221	500	24	⇒	⇒	NOUN
ejpam-221	500	25	s	s	PART
ejpam-221	500	26	=	=	SYM
ejpam-221	500	27	t	t	PROPN
ejpam-221	500	28	,	,	PUNCT
ejpam-221	500	29	as	as	SCONJ
ejpam-221	500	30	required	require	VERB
ejpam-221	500	31	.	.	PUNCT
ejpam-221	501	1	thus	thus	ADV
ejpam-221	501	2	:	:	PUNCT
ejpam-221	501	3	theorem	theorem	VERB
ejpam-221	501	4	4.13	4.13	NUM
ejpam-221	501	5	.	.	PUNCT
ejpam-221	502	1	weakly	weakly	ADV
ejpam-221	502	2	left	leave	VERB
ejpam-221	502	3	e	e	NOUN
ejpam-221	502	4	-	-	ADJ
ejpam-221	502	5	ample	ample	ADJ
ejpam-221	502	6	semigroups	semigroup	NOUN
ejpam-221	502	7	are	be	AUX
ejpam-221	502	8	precisely	precisely	ADV
ejpam-221	502	9	left	leave	VERB
ejpam-221	502	10	restriction	restriction	NOUN
ejpam-221	502	11	semigroups	semigroup	NOUN
ejpam-221	502	12	;	;	PUNCT
ejpam-221	502	13	weakly	weakly	ADV
ejpam-221	502	14	left	leave	VERB
ejpam-221	502	15	ample	ample	ADJ
ejpam-221	502	16	semigroups	semigroup	NOUN
ejpam-221	502	17	are	be	AUX
ejpam-221	502	18	precisely	precisely	ADV
ejpam-221	502	19	full	full	ADJ
ejpam-221	502	20	left	left	ADJ
ejpam-221	502	21	restriction	restriction	NOUN
ejpam-221	502	22	semigroups	semigroup	NOUN
ejpam-221	502	23	.	.	PUNCT
ejpam-221	503	1	from	from	ADP
ejpam-221	503	2	here	here	ADV
ejpam-221	503	3	on	on	ADV
ejpam-221	503	4	,	,	PUNCT
ejpam-221	503	5	we	we	PRON
ejpam-221	503	6	will	will	AUX
ejpam-221	503	7	use	use	VERB
ejpam-221	503	8	the	the	DET
ejpam-221	503	9	term	term	NOUN
ejpam-221	503	10	‘	'	PUNCT
ejpam-221	503	11	left	leave	VERB
ejpam-221	503	12	restriction	restriction	NOUN
ejpam-221	503	13	semigroup	semigroup	NOUN
ejpam-221	503	14	’	'	PUNCT
ejpam-221	503	15	.	.	PUNCT
ejpam-221	504	1	in	in	ADP
ejpam-221	504	2	the	the	DET
ejpam-221	504	3	previous	previous	ADJ
ejpam-221	504	4	section	section	NOUN
ejpam-221	504	5	,	,	PUNCT
ejpam-221	504	6	we	we	PRON
ejpam-221	504	7	observed	observe	VERB
ejpam-221	504	8	that	that	SCONJ
ejpam-221	504	9	left	leave	VERB
ejpam-221	504	10	restriction	restriction	NOUN
ejpam-221	504	11	semigroups	semigroup	NOUN
ejpam-221	504	12	generalise	generalise	VERB
ejpam-221	504	13	inverse	inverse	NOUN
ejpam-221	504	14	semigroups	semigroup	NOUN
ejpam-221	504	15	.	.	PUNCT
ejpam-221	505	1	we	we	PRON
ejpam-221	505	2	now	now	ADV
ejpam-221	505	3	prove	prove	VERB
ejpam-221	505	4	this	this	PRON
ejpam-221	505	5	explicitly	explicitly	ADV
ejpam-221	505	6	in	in	ADP
ejpam-221	505	7	the	the	DET
ejpam-221	505	8	abstract	abstract	ADJ
ejpam-221	505	9	setting	setting	NOUN
ejpam-221	505	10	.	.	PUNCT
ejpam-221	506	1	first	first	ADV
ejpam-221	506	2	note	note	VERB
ejpam-221	506	3	the	the	DET
ejpam-221	506	4	following	following	NOUN
ejpam-221	506	5	:	:	PUNCT
ejpam-221	506	6	lemma	lemma	PROPN
ejpam-221	506	7	4.14	4.14	NUM
ejpam-221	506	8	.	.	PUNCT
ejpam-221	507	1	in	in	ADP
ejpam-221	507	2	a	a	DET
ejpam-221	507	3	regular	regular	ADJ
ejpam-221	507	4	semigroup	semigroup	NOUN
ejpam-221	507	5	,	,	PUNCT
ejpam-221	507	6	r	r	NOUN
ejpam-221	507	7	=	=	SYM
ejpam-221	507	8	er	er	INTJ
ejpam-221	507	9	.	.	PUNCT
ejpam-221	507	10	proof	proof	NOUN
ejpam-221	507	11	.	.	PUNCT
ejpam-221	508	1	let	let	VERB
ejpam-221	508	2	s	s	PRON
ejpam-221	508	3	be	be	AUX
ejpam-221	508	4	a	a	DET
ejpam-221	508	5	regular	regular	ADJ
ejpam-221	508	6	semigroup	semigroup	NOUN
ejpam-221	508	7	.	.	PUNCT
ejpam-221	509	1	we	we	PRON
ejpam-221	509	2	know	know	VERB
ejpam-221	509	3	from	from	ADP
ejpam-221	509	4	lemma	lemma	PROPN
ejpam-221	509	5	4.1	4.1	NUM
ejpam-221	509	6	that	that	PRON
ejpam-221	509	7	r	r	NOUN
ejpam-221	509	8	⊆	⊆	NUM
ejpam-221	509	9	er	er	INTJ
ejpam-221	509	10	.	.	PUNCT
ejpam-221	510	1	it	it	PRON
ejpam-221	510	2	remains	remain	VERB
ejpam-221	510	3	to	to	PART
ejpam-221	510	4	show	show	VERB
ejpam-221	510	5	the	the	DET
ejpam-221	510	6	reverse	reverse	ADJ
ejpam-221	510	7	inclusion	inclusion	NOUN
ejpam-221	510	8	.	.	PUNCT
ejpam-221	511	1	let	let	VERB
ejpam-221	511	2	a	a	DET
ejpam-221	511	3	,	,	PUNCT
ejpam-221	511	4	b	b	PROPN
ejpam-221	511	5	∈	∈	NOUN
ejpam-221	511	6	s	s	PART
ejpam-221	511	7	and	and	CCONJ
ejpam-221	511	8	suppose	suppose	VERB
ejpam-221	511	9	that	that	SCONJ
ejpam-221	511	10	a	a	DET
ejpam-221	511	11	er	er	INTJ
ejpam-221	511	12	b.	b.	NOUN
ejpam-221	511	13	since	since	SCONJ
ejpam-221	511	14	s	s	PROPN
ejpam-221	511	15	is	be	AUX
ejpam-221	511	16	regular	regular	ADJ
ejpam-221	511	17	,	,	PUNCT
ejpam-221	511	18	there	there	PRON
ejpam-221	511	19	exists	exist	VERB
ejpam-221	511	20	a′	a′	PROPN
ejpam-221	511	21	∈	∈	PROPN
ejpam-221	511	22	s	s	PART
ejpam-221	511	23	with	with	ADP
ejpam-221	511	24	aa′a	aa′a	PROPN
ejpam-221	511	25	=	=	SYM
ejpam-221	511	26	a	a	NOUN
ejpam-221	511	27	,	,	PUNCT
ejpam-221	511	28	so	so	SCONJ
ejpam-221	511	29	that	that	SCONJ
ejpam-221	511	30	aa′	aa′	ADJ
ejpam-221	511	31	is	be	AUX
ejpam-221	511	32	a	a	DET
ejpam-221	511	33	left	left	ADJ
ejpam-221	511	34	identity	identity	NOUN
ejpam-221	511	35	for	for	ADP
ejpam-221	511	36	a.	a.	NOUN
ejpam-221	511	37	consequently	consequently	ADV
ejpam-221	511	38	,	,	PUNCT
ejpam-221	511	39	aa′	aa′	X
ejpam-221	511	40	is	be	AUX
ejpam-221	511	41	a	a	DET
ejpam-221	511	42	left	left	ADJ
ejpam-221	511	43	identity	identity	NOUN
ejpam-221	511	44	for	for	ADP
ejpam-221	511	45	b	b	NOUN
ejpam-221	511	46	also	also	ADV
ejpam-221	511	47	:	:	PUNCT
ejpam-221	511	48	aa′b	aa′b	PROPN
ejpam-221	511	49	=	=	SYM
ejpam-221	511	50	b	b	PROPN
ejpam-221	511	51	,	,	PUNCT
ejpam-221	511	52	whence	whence	PROPN
ejpam-221	511	53	b	b	PROPN
ejpam-221	511	54	≤r	≤r	VERB
ejpam-221	511	55	a.	a.	NOUN
ejpam-221	511	56	similarly	similarly	ADV
ejpam-221	511	57	,	,	PUNCT
ejpam-221	511	58	there	there	PRON
ejpam-221	511	59	exists	exist	VERB
ejpam-221	511	60	a	a	DET
ejpam-221	511	61	b′	b′	NUM
ejpam-221	511	62	∈	∈	NOUN
ejpam-221	511	63	s	s	NOUN
ejpam-221	511	64	with	with	ADP
ejpam-221	511	65	bb′a	bb′a	NOUN
ejpam-221	511	66	=	=	NOUN
ejpam-221	511	67	a.	a.	NOUN
ejpam-221	511	68	we	we	PRON
ejpam-221	511	69	conclude	conclude	VERB
ejpam-221	511	70	that	that	SCONJ
ejpam-221	511	71	ar	ar	PROPN
ejpam-221	511	72	b.	b.	PROPN
ejpam-221	511	73	lemma	lemma	PROPN
ejpam-221	511	74	4.15	4.15	NUM
ejpam-221	511	75	.	.	PUNCT
ejpam-221	512	1	every	every	DET
ejpam-221	512	2	inverse	inverse	NOUN
ejpam-221	512	3	semigroup	semigroup	NOUN
ejpam-221	512	4	is	be	AUX
ejpam-221	512	5	a	a	DET
ejpam-221	512	6	full	full	ADJ
ejpam-221	512	7	two	two	NUM
ejpam-221	512	8	-	-	PUNCT
ejpam-221	512	9	sided	sided	ADJ
ejpam-221	512	10	restriction	restriction	NOUN
ejpam-221	512	11	semigroup	semigroup	VERB
ejpam-221	512	12	with	with	ADP
ejpam-221	512	13	a+	a+	PRON
ejpam-221	512	14	=	=	SYM
ejpam-221	512	15	aa−1	aa−1	PROPN
ejpam-221	512	16	and	and	CCONJ
ejpam-221	512	17	a∗	a∗	PROPN
ejpam-221	512	18	=	=	SYM
ejpam-221	512	19	a−1a	a−1a	PROPN
ejpam-221	512	20	,	,	PUNCT
ejpam-221	512	21	for	for	ADP
ejpam-221	512	22	each	each	DET
ejpam-221	512	23	a	a	DET
ejpam-221	512	24	∈	∈	PROPN
ejpam-221	512	25	s.	s.	PROPN
ejpam-221	512	26	proof	proof	NOUN
ejpam-221	512	27	.	.	PUNCT
ejpam-221	513	1	let	let	VERB
ejpam-221	513	2	s	s	PRON
ejpam-221	513	3	be	be	AUX
ejpam-221	513	4	an	an	DET
ejpam-221	513	5	inverse	inverse	NOUN
ejpam-221	513	6	semigroup	semigroup	NOUN
ejpam-221	513	7	.	.	PUNCT
ejpam-221	514	1	we	we	PRON
ejpam-221	514	2	will	will	AUX
ejpam-221	514	3	show	show	VERB
ejpam-221	514	4	that	that	SCONJ
ejpam-221	514	5	s	s	VERB
ejpam-221	514	6	is	be	AUX
ejpam-221	514	7	a	a	DET
ejpam-221	514	8	left	left	ADJ
ejpam-221	514	9	restriction	restriction	NOUN
ejpam-221	514	10	semigroup	semigroup	NOUN
ejpam-221	514	11	;	;	PUNCT
ejpam-221	514	12	the	the	DET
ejpam-221	514	13	proof	proof	NOUN
ejpam-221	514	14	that	that	PRON
ejpam-221	514	15	s	s	VERB
ejpam-221	514	16	is	be	AUX
ejpam-221	514	17	a	a	DET
ejpam-221	514	18	right	right	ADJ
ejpam-221	514	19	restriction	restriction	NOUN
ejpam-221	514	20	semigroup	semigroup	NOUN
ejpam-221	514	21	(	(	PUNCT
ejpam-221	514	22	as	as	ADP
ejpam-221	514	23	per	per	ADP
ejpam-221	514	24	the	the	DET
ejpam-221	514	25	abstract	abstract	ADJ
ejpam-221	514	26	description	description	NOUN
ejpam-221	514	27	in	in	ADP
ejpam-221	514	28	definition	definition	NOUN
ejpam-221	514	29	4.16	4.16	NUM
ejpam-221	514	30	below	below	ADV
ejpam-221	514	31	,	,	PUNCT
ejpam-221	514	32	where	where	SCONJ
ejpam-221	514	33	,	,	PUNCT
ejpam-221	514	34	moreover	moreover	ADV
ejpam-221	514	35	,	,	PUNCT
ejpam-221	514	36	∗	∗	NOUN
ejpam-221	514	37	is	be	AUX
ejpam-221	514	38	defined	define	VERB
ejpam-221	514	39	)	)	PUNCT
ejpam-221	514	40	is	be	AUX
ejpam-221	514	41	dual	dual	ADJ
ejpam-221	514	42	.	.	PUNCT
ejpam-221	515	1	we	we	PRON
ejpam-221	515	2	know	know	VERB
ejpam-221	515	3	that	that	SCONJ
ejpam-221	515	4	e(s	e(s	PROPN
ejpam-221	515	5	)	)	PUNCT
ejpam-221	515	6	forms	form	VERB
ejpam-221	515	7	a	a	DET
ejpam-221	515	8	semilattice	semilattice	NOUN
ejpam-221	515	9	and	and	CCONJ
ejpam-221	515	10	that	that	SCONJ
ejpam-221	515	11	ar	ar	VERB
ejpam-221	515	12	aa−1	aa−1	PROPN
ejpam-221	515	13	.	.	PUNCT
ejpam-221	516	1	it	it	PRON
ejpam-221	516	2	therefore	therefore	ADV
ejpam-221	516	3	follows	follow	VERB
ejpam-221	516	4	from	from	ADP
ejpam-221	516	5	lemma	lemma	PROPN
ejpam-221	516	6	4.14	4.14	NUM
ejpam-221	516	7	that	that	PRON
ejpam-221	516	8	every	every	DET
ejpam-221	516	9	element	element	NOUN
ejpam-221	516	10	a	a	PRON
ejpam-221	516	11	of	of	ADP
ejpam-221	516	12	s	s	NOUN
ejpam-221	516	13	is	be	AUX
ejpam-221	516	14	er	er	INTJ
ejpam-221	516	15	-	-	PUNCT
ejpam-221	516	16	related	relate	VERB
ejpam-221	516	17	to	to	ADP
ejpam-221	516	18	an	an	DET
ejpam-221	516	19	idempotent	idempotent	ADJ
ejpam-221	516	20	,	,	PUNCT
ejpam-221	516	21	namely	namely	ADV
ejpam-221	516	22	aa−1	aa−1	NOUN
ejpam-221	516	23	.	.	PUNCT
ejpam-221	517	1	we	we	PRON
ejpam-221	517	2	also	also	ADV
ejpam-221	517	3	know	know	VERB
ejpam-221	517	4	that	that	SCONJ
ejpam-221	517	5	r	r	NOUN
ejpam-221	517	6	is	be	AUX
ejpam-221	517	7	a	a	DET
ejpam-221	517	8	left	left	ADJ
ejpam-221	517	9	congruence	congruence	NOUN
ejpam-221	517	10	.	.	PUNCT
ejpam-221	518	1	it	it	PRON
ejpam-221	518	2	therefore	therefore	ADV
ejpam-221	518	3	only	only	ADV
ejpam-221	518	4	remains	remain	VERB
ejpam-221	518	5	to	to	PART
ejpam-221	518	6	show	show	VERB
ejpam-221	518	7	that	that	SCONJ
ejpam-221	518	8	the	the	DET
ejpam-221	518	9	left	left	ADJ
ejpam-221	518	10	ample	ample	ADJ
ejpam-221	518	11	identity	identity	NOUN
ejpam-221	518	12	holds	hold	VERB
ejpam-221	518	13	:	:	PUNCT
ejpam-221	518	14	(	(	PUNCT
ejpam-221	518	15	ae)+a	ae)+a	X
ejpam-221	518	16	=	=	SYM
ejpam-221	518	17	(	(	PUNCT
ejpam-221	518	18	ae)(ae)−1a	ae)(ae)−1a	NOUN
ejpam-221	518	19	=	=	PUNCT
ejpam-221	518	20	aeea−1a	aeea−1a	PROPN
ejpam-221	518	21	=	=	SYM
ejpam-221	518	22	aea−1a	aea−1a	NOUN
ejpam-221	519	1	=	=	PUNCT
ejpam-221	519	2	aa−1ae	aa−1ae	NUM
ejpam-221	519	3	=	=	SYM
ejpam-221	519	4	ae	ae	PROPN
ejpam-221	519	5	,	,	PUNCT
ejpam-221	519	6	c.	c.	PROPN
ejpam-221	519	7	hollings	holling	NOUN
ejpam-221	519	8	/	/	SYM
ejpam-221	519	9	eur	eur	PROPN
ejpam-221	519	10	.	.	PUNCT
ejpam-221	520	1	j.	j.	PROPN
ejpam-221	520	2	pure	pure	PROPN
ejpam-221	520	3	appl	appl	PROPN
ejpam-221	520	4	.	.	PROPN
ejpam-221	520	5	math	math	PROPN
ejpam-221	520	6	,	,	PUNCT
ejpam-221	520	7	2	2	NUM
ejpam-221	520	8	(	(	PUNCT
ejpam-221	520	9	2009	2009	NUM
ejpam-221	520	10	)	)	PUNCT
ejpam-221	520	11	,	,	PUNCT
ejpam-221	520	12	(	(	PUNCT
ejpam-221	520	13	21	21	NUM
ejpam-221	520	14	-	-	SYM
ejpam-221	520	15	57	57	NUM
ejpam-221	520	16	)	)	PUNCT
ejpam-221	520	17	48	48	NUM
ejpam-221	520	18	as	as	SCONJ
ejpam-221	520	19	required	require	VERB
ejpam-221	520	20	.	.	PUNCT
ejpam-221	521	1	note	note	VERB
ejpam-221	521	2	that	that	SCONJ
ejpam-221	521	3	any	any	DET
ejpam-221	521	4	monoid	monoid	NOUN
ejpam-221	521	5	can	can	AUX
ejpam-221	521	6	be	be	AUX
ejpam-221	521	7	regarded	regard	VERB
ejpam-221	521	8	as	as	ADP
ejpam-221	521	9	a	a	DET
ejpam-221	521	10	left	left	ADJ
ejpam-221	521	11	restriction	restriction	NOUN
ejpam-221	521	12	monoid	monoid	NOUN
ejpam-221	521	13	with	with	ADP
ejpam-221	521	14	respect	respect	NOUN
ejpam-221	521	15	to	to	ADP
ejpam-221	521	16	{	{	PUNCT
ejpam-221	521	17	1	1	NUM
ejpam-221	521	18	}	}	PUNCT
ejpam-221	521	19	,	,	PUNCT
ejpam-221	521	20	with	with	ADP
ejpam-221	521	21	a+	a+	PUNCT
ejpam-221	521	22	=	=	NOUN
ejpam-221	521	23	1	1	NUM
ejpam-221	521	24	,	,	PUNCT
ejpam-221	521	25	for	for	SCONJ
ejpam-221	521	26	all	all	DET
ejpam-221	521	27	elements	element	NOUN
ejpam-221	521	28	a.	a.	NOUN
ejpam-221	521	29	a	a	DET
ejpam-221	521	30	unipotent	unipotent	ADJ
ejpam-221	521	31	monoid	monoid	NOUN
ejpam-221	521	32	(	(	PUNCT
ejpam-221	521	33	i.e.	i.e.	X
ejpam-221	521	34	,	,	PUNCT
ejpam-221	521	35	a	a	DET
ejpam-221	521	36	monoid	monoid	NOUN
ejpam-221	521	37	whose	whose	DET
ejpam-221	521	38	only	only	ADJ
ejpam-221	521	39	idempotent	idempotent	NOUN
ejpam-221	521	40	is	be	AUX
ejpam-221	521	41	its	its	PRON
ejpam-221	521	42	identity	identity	NOUN
ejpam-221	521	43	)	)	PUNCT
ejpam-221	521	44	is	be	AUX
ejpam-221	521	45	therefore	therefore	ADV
ejpam-221	521	46	a	a	DET
ejpam-221	521	47	full	full	ADJ
ejpam-221	521	48	left	left	ADJ
ejpam-221	521	49	restriction	restriction	NOUN
ejpam-221	521	50	monoid	monoid	NOUN
ejpam-221	521	51	.	.	PUNCT
ejpam-221	522	1	by	by	ADP
ejpam-221	522	2	way	way	NOUN
ejpam-221	522	3	of	of	ADP
ejpam-221	522	4	concluding	conclude	VERB
ejpam-221	522	5	this	this	DET
ejpam-221	522	6	section	section	NOUN
ejpam-221	522	7	,	,	PUNCT
ejpam-221	522	8	and	and	CCONJ
ejpam-221	522	9	for	for	ADP
ejpam-221	522	10	completeness	completeness	NOUN
ejpam-221	522	11	,	,	PUNCT
ejpam-221	522	12	we	we	PRON
ejpam-221	522	13	record	record	VERB
ejpam-221	522	14	the	the	DET
ejpam-221	522	15	definition	definition	NOUN
ejpam-221	522	16	of	of	ADP
ejpam-221	522	17	the	the	DET
ejpam-221	522	18	dual	dual	ADJ
ejpam-221	522	19	equivalence	equivalence	NOUN
ejpam-221	522	20	relation	relation	NOUN
ejpam-221	522	21	fle	fle	NOUN
ejpam-221	522	22	and	and	CCONJ
ejpam-221	522	23	,	,	PUNCT
ejpam-221	522	24	consequently	consequently	ADV
ejpam-221	522	25	,	,	PUNCT
ejpam-221	522	26	that	that	PRON
ejpam-221	522	27	of	of	ADP
ejpam-221	522	28	a	a	DET
ejpam-221	522	29	right	right	ADJ
ejpam-221	522	30	restriction	restriction	NOUN
ejpam-221	522	31	semigroup	semigroup	NOUN
ejpam-221	522	32	(	(	PUNCT
ejpam-221	522	33	weakly	weakly	ADV
ejpam-221	522	34	right	right	ADJ
ejpam-221	522	35	e	e	NOUN
ejpam-221	522	36	-	-	ADJ
ejpam-221	522	37	ample	ample	ADJ
ejpam-221	522	38	semigroup	semigroup	NOUN
ejpam-221	522	39	)	)	PUNCT
ejpam-221	522	40	.	.	PUNCT
ejpam-221	523	1	definition	definition	NOUN
ejpam-221	523	2	4.16	4.16	NUM
ejpam-221	523	3	.	.	PUNCT
ejpam-221	524	1	let	let	VERB
ejpam-221	524	2	s	s	PRON
ejpam-221	524	3	be	be	AUX
ejpam-221	524	4	a	a	DET
ejpam-221	524	5	semigroup	semigroup	NOUN
ejpam-221	524	6	and	and	CCONJ
ejpam-221	524	7	let	let	VERB
ejpam-221	524	8	e	e	NOUN
ejpam-221	524	9	⊆	⊆	NUM
ejpam-221	524	10	e(s	e(s	PROPN
ejpam-221	524	11	)	)	PUNCT
ejpam-221	524	12	be	be	AUX
ejpam-221	524	13	a	a	DET
ejpam-221	524	14	distinguished	distinguished	ADJ
ejpam-221	524	15	subsemilattice	subsemilattice	NOUN
ejpam-221	524	16	of	of	ADP
ejpam-221	524	17	s.	s.	PROPN
ejpam-221	524	18	we	we	PRON
ejpam-221	524	19	define	define	VERB
ejpam-221	524	20	the	the	DET
ejpam-221	524	21	relation	relation	NOUN
ejpam-221	524	22	fle	fle	NOUN
ejpam-221	524	23	on	on	ADP
ejpam-221	524	24	s	s	PRON
ejpam-221	524	25	by	by	ADP
ejpam-221	524	26	the	the	DET
ejpam-221	524	27	rule	rule	NOUN
ejpam-221	524	28	that	that	SCONJ
ejpam-221	524	29	a	a	DET
ejpam-221	524	30	fle	fle	NOUN
ejpam-221	524	31	b	b	SYM
ejpam-221	524	32	⇐	⇐	PROPN
ejpam-221	524	33	⇒∀e	⇒∀e	PROPN
ejpam-221	524	34	∈	∈	PROPN
ejpam-221	524	35	e[ae	e[ae	PROPN
ejpam-221	524	36	=	=	NOUN
ejpam-221	524	37	a⇔	a⇔	NOUN
ejpam-221	524	38	be	be	AUX
ejpam-221	524	39	=	=	PUNCT
ejpam-221	524	40	b	b	NOUN
ejpam-221	524	41	]	]	X
ejpam-221	524	42	,	,	PUNCT
ejpam-221	524	43	for	for	ADP
ejpam-221	524	44	a	a	DET
ejpam-221	524	45	,	,	PUNCT
ejpam-221	524	46	b	b	PROPN
ejpam-221	524	47	∈	∈	PROPN
ejpam-221	524	48	s.	s.	PROPN
ejpam-221	524	49	we	we	PRON
ejpam-221	524	50	call	call	VERB
ejpam-221	524	51	s	s	PRON
ejpam-221	524	52	a	a	DET
ejpam-221	524	53	right	right	ADJ
ejpam-221	524	54	restriction	restriction	NOUN
ejpam-221	524	55	semigroup	semigroup	NOUN
ejpam-221	524	56	with	with	ADP
ejpam-221	524	57	respect	respect	NOUN
ejpam-221	524	58	to	to	ADP
ejpam-221	524	59	e	e	NOUN
ejpam-221	524	60	if	if	SCONJ
ejpam-221	524	61	1	1	NUM
ejpam-221	524	62	.	.	PUNCT
ejpam-221	525	1	every	every	DET
ejpam-221	525	2	element	element	NOUN
ejpam-221	525	3	a	a	PRON
ejpam-221	525	4	is	be	AUX
ejpam-221	525	5	fle	fle	NOUN
ejpam-221	525	6	-	-	PUNCT
ejpam-221	525	7	related	relate	VERB
ejpam-221	525	8	to	to	ADP
ejpam-221	525	9	an	an	DET
ejpam-221	525	10	idempotent	idempotent	ADJ
ejpam-221	525	11	a∗	a∗	PROPN
ejpam-221	525	12	∈	∈	PROPN
ejpam-221	525	13	e	e	NOUN
ejpam-221	525	14	;	;	PUNCT
ejpam-221	525	15	2	2	X
ejpam-221	525	16	.	.	X
ejpam-221	525	17	fle	fle	NOUN
ejpam-221	525	18	is	be	AUX
ejpam-221	525	19	a	a	DET
ejpam-221	525	20	right	right	ADJ
ejpam-221	525	21	congruence	congruence	NOUN
ejpam-221	525	22	;	;	PUNCT
ejpam-221	525	23	3	3	X
ejpam-221	525	24	.	.	X
ejpam-221	526	1	for	for	ADP
ejpam-221	526	2	all	all	DET
ejpam-221	526	3	a	a	DET
ejpam-221	526	4	∈	∈	NOUN
ejpam-221	526	5	s	s	PART
ejpam-221	526	6	and	and	CCONJ
ejpam-221	526	7	all	all	DET
ejpam-221	526	8	e	e	X
ejpam-221	526	9	∈	∈	PROPN
ejpam-221	526	10	e	e	NOUN
ejpam-221	526	11	,	,	PUNCT
ejpam-221	526	12	ea	ea	X
ejpam-221	526	13	=	=	SYM
ejpam-221	526	14	a(ea)∗.	a(ea)∗.	PROPN
ejpam-221	526	15	all	all	DET
ejpam-221	526	16	the	the	DET
ejpam-221	526	17	results	result	NOUN
ejpam-221	526	18	of	of	ADP
ejpam-221	526	19	this	this	DET
ejpam-221	526	20	section	section	NOUN
ejpam-221	526	21	have	have	VERB
ejpam-221	526	22	right	right	ADJ
ejpam-221	526	23	-	-	PUNCT
ejpam-221	526	24	hand	hand	NOUN
ejpam-221	526	25	analogues	analogue	NOUN
ejpam-221	526	26	in	in	ADP
ejpam-221	526	27	terms	term	NOUN
ejpam-221	526	28	of	of	ADP
ejpam-221	526	29	fle	fle	NOUN
ejpam-221	526	30	and	and	CCONJ
ejpam-221	526	31	∗.	∗.	PROPN
ejpam-221	526	32	5	5	NUM
ejpam-221	526	33	.	.	PUNCT
ejpam-221	526	34	left	leave	VERB
ejpam-221	526	35	ample	ample	ADJ
ejpam-221	526	36	semigroups	semigroup	NOUN
ejpam-221	526	37	as	as	SCONJ
ejpam-221	526	38	we	we	PRON
ejpam-221	526	39	saw	see	VERB
ejpam-221	526	40	in	in	ADP
ejpam-221	526	41	sections	section	NOUN
ejpam-221	526	42	1	1	NUM
ejpam-221	526	43	and	and	CCONJ
ejpam-221	526	44	2	2	NUM
ejpam-221	526	45	,	,	PUNCT
ejpam-221	526	46	left	leave	VERB
ejpam-221	526	47	restriction	restriction	NOUN
ejpam-221	526	48	semigroups	semigroup	NOUN
ejpam-221	526	49	generalise	generalise	VERB
ejpam-221	526	50	the	the	DET
ejpam-221	526	51	left	left	ADJ
ejpam-221	526	52	ample	ample	ADJ
ejpam-221	526	53	semigroups	semigroup	NOUN
ejpam-221	526	54	of	of	ADP
ejpam-221	526	55	fountain	fountain	NOUN
ejpam-221	526	56	[	[	X
ejpam-221	526	57	22,24	22,24	X
ejpam-221	526	58	]	]	X
ejpam-221	526	59	.	.	PUNCT
ejpam-221	527	1	as	as	ADP
ejpam-221	527	2	in	in	ADP
ejpam-221	527	3	the	the	DET
ejpam-221	527	4	more	more	ADV
ejpam-221	527	5	general	general	ADJ
ejpam-221	527	6	case	case	NOUN
ejpam-221	527	7	,	,	PUNCT
ejpam-221	527	8	left	leave	VERB
ejpam-221	527	9	ample	ample	ADJ
ejpam-221	527	10	semigroups	semigroup	NOUN
ejpam-221	527	11	have	have	VERB
ejpam-221	527	12	both	both	CCONJ
ejpam-221	527	13	a	a	DET
ejpam-221	527	14	characterisation	characterisation	NOUN
ejpam-221	527	15	as	as	ADP
ejpam-221	527	16	semigroups	semigroup	NOUN
ejpam-221	527	17	of	of	ADP
ejpam-221	527	18	partial	partial	ADJ
ejpam-221	527	19	transformations	transformation	NOUN
ejpam-221	527	20	(	(	PUNCT
ejpam-221	527	21	this	this	DET
ejpam-221	527	22	time	time	NOUN
ejpam-221	527	23	,	,	PUNCT
ejpam-221	527	24	one	one	NUM
ejpam-221	527	25	-	-	PUNCT
ejpam-221	527	26	one	one	NUM
ejpam-221	527	27	partial	partial	ADJ
ejpam-221	527	28	transformations	transformation	NOUN
ejpam-221	527	29	)	)	PUNCT
ejpam-221	527	30	,	,	PUNCT
ejpam-221	527	31	and	and	CCONJ
ejpam-221	527	32	also	also	ADV
ejpam-221	527	33	an	an	DET
ejpam-221	527	34	abstract	abstract	ADJ
ejpam-221	527	35	description	description	NOUN
ejpam-221	527	36	.	.	PUNCT
ejpam-221	528	1	we	we	PRON
ejpam-221	528	2	present	present	VERB
ejpam-221	528	3	both	both	DET
ejpam-221	528	4	points	point	NOUN
ejpam-221	528	5	of	of	ADP
ejpam-221	528	6	view	view	NOUN
ejpam-221	528	7	here	here	ADV
ejpam-221	528	8	,	,	PUNCT
ejpam-221	528	9	but	but	CCONJ
ejpam-221	528	10	we	we	PRON
ejpam-221	528	11	do	do	AUX
ejpam-221	528	12	not	not	PART
ejpam-221	528	13	prove	prove	VERB
ejpam-221	528	14	their	their	PRON
ejpam-221	528	15	equivalence	equivalence	NOUN
ejpam-221	528	16	;	;	PUNCT
ejpam-221	528	17	the	the	DET
ejpam-221	528	18	proof	proof	NOUN
ejpam-221	528	19	is	be	AUX
ejpam-221	528	20	easily	easily	ADV
ejpam-221	528	21	achieved	achieve	VERB
ejpam-221	528	22	by	by	ADP
ejpam-221	528	23	adapting	adapt	VERB
ejpam-221	528	24	those	those	PRON
ejpam-221	528	25	of	of	ADP
ejpam-221	528	26	corollary	corollary	ADJ
ejpam-221	528	27	4.7	4.7	NUM
ejpam-221	528	28	and	and	CCONJ
ejpam-221	528	29	theorem	theorem	VERB
ejpam-221	528	30	4.12	4.12	NUM
ejpam-221	528	31	.	.	PUNCT
ejpam-221	529	1	let	let	VERB
ejpam-221	529	2	ix	ix	PRON
ejpam-221	529	3	be	be	AUX
ejpam-221	529	4	the	the	DET
ejpam-221	529	5	symmetric	symmetric	ADJ
ejpam-221	529	6	inverse	inverse	NOUN
ejpam-221	529	7	monoid	monoid	NOUN
ejpam-221	529	8	on	on	ADP
ejpam-221	529	9	a	a	DET
ejpam-221	529	10	set	set	NOUN
ejpam-221	529	11	x	x	X
ejpam-221	529	12	.	.	PUNCT
ejpam-221	530	1	there	there	PRON
ejpam-221	530	2	are	be	VERB
ejpam-221	530	3	three	three	NUM
ejpam-221	530	4	natural	natural	ADJ
ejpam-221	530	5	unary	unary	ADJ
ejpam-221	530	6	operations	operation	NOUN
ejpam-221	530	7	which	which	PRON
ejpam-221	530	8	we	we	PRON
ejpam-221	530	9	can	can	AUX
ejpam-221	530	10	consider	consider	VERB
ejpam-221	530	11	on	on	ADP
ejpam-221	530	12	ix	ix	X
ejpam-221	530	13	:	:	PUNCT
ejpam-221	530	14	the	the	DET
ejpam-221	530	15	operations	operation	NOUN
ejpam-221	530	16	+	+	CCONJ
ejpam-221	530	17	and	and	CCONJ
ejpam-221	530	18	∗	∗	NOUN
ejpam-221	530	19	,	,	PUNCT
ejpam-221	530	20	given	give	VERB
ejpam-221	530	21	in	in	ADP
ejpam-221	530	22	(	(	PUNCT
ejpam-221	530	23	3.1	3.1	NUM
ejpam-221	530	24	)	)	PUNCT
ejpam-221	530	25	and	and	CCONJ
ejpam-221	530	26	(	(	PUNCT
ejpam-221	530	27	3.2	3.2	NUM
ejpam-221	530	28	)	)	PUNCT
ejpam-221	530	29	,	,	PUNCT
ejpam-221	530	30	and	and	CCONJ
ejpam-221	530	31	c.	c.	PROPN
ejpam-221	530	32	hollings	holling	NOUN
ejpam-221	530	33	/	/	SYM
ejpam-221	530	34	eur	eur	PROPN
ejpam-221	530	35	.	.	PUNCT
ejpam-221	531	1	j.	j.	PROPN
ejpam-221	531	2	pure	pure	PROPN
ejpam-221	531	3	appl	appl	PROPN
ejpam-221	531	4	.	.	PROPN
ejpam-221	531	5	math	math	PROPN
ejpam-221	531	6	,	,	PUNCT
ejpam-221	531	7	2	2	NUM
ejpam-221	531	8	(	(	PUNCT
ejpam-221	531	9	2009	2009	NUM
ejpam-221	531	10	)	)	PUNCT
ejpam-221	531	11	,	,	PUNCT
ejpam-221	531	12	(	(	PUNCT
ejpam-221	531	13	21	21	NUM
ejpam-221	531	14	-	-	SYM
ejpam-221	531	15	57	57	NUM
ejpam-221	531	16	)	)	PUNCT
ejpam-221	531	17	49	49	NUM
ejpam-221	531	18	inversion	inversion	NOUN
ejpam-221	531	19	α	α	NOUN
ejpam-221	531	20	7→	7→	PROPN
ejpam-221	532	1	α−1	α−1	NOUN
ejpam-221	532	2	.	.	PUNCT
ejpam-221	533	1	let	let	VERB
ejpam-221	533	2	s	s	PRON
ejpam-221	533	3	be	be	AUX
ejpam-221	533	4	a	a	DET
ejpam-221	533	5	subsemigroup	subsemigroup	NOUN
ejpam-221	533	6	of	of	ADP
ejpam-221	533	7	ix	ix	PROPN
ejpam-221	533	8	.	.	PUNCT
ejpam-221	534	1	we	we	PRON
ejpam-221	534	2	know	know	VERB
ejpam-221	534	3	that	that	SCONJ
ejpam-221	534	4	if	if	SCONJ
ejpam-221	534	5	s	s	NOUN
ejpam-221	534	6	is	be	AUX
ejpam-221	534	7	closed	close	VERB
ejpam-221	534	8	under	under	ADP
ejpam-221	534	9	−1	−1	NOUN
ejpam-221	534	10	,	,	PUNCT
ejpam-221	534	11	then	then	ADV
ejpam-221	534	12	s	s	VERB
ejpam-221	534	13	is	be	AUX
ejpam-221	534	14	an	an	DET
ejpam-221	534	15	inverse	inverse	NOUN
ejpam-221	534	16	semigroup	semigroup	NOUN
ejpam-221	534	17	,	,	PUNCT
ejpam-221	534	18	which	which	PRON
ejpam-221	534	19	may	may	AUX
ejpam-221	534	20	be	be	AUX
ejpam-221	534	21	regarded	regard	VERB
ejpam-221	534	22	as	as	ADP
ejpam-221	534	23	a	a	DET
ejpam-221	534	24	(	(	PUNCT
ejpam-221	534	25	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	534	26	of	of	ADP
ejpam-221	534	27	ix	ix	PROPN
ejpam-221	534	28	,	,	PUNCT
ejpam-221	534	29	with	with	ADP
ejpam-221	534	30	unary	unary	ADJ
ejpam-221	534	31	operation	operation	NOUN
ejpam-221	534	32	−1	−1	NOUN
ejpam-221	534	33	.	.	PUNCT
ejpam-221	535	1	in	in	ADP
ejpam-221	535	2	contrast	contrast	NOUN
ejpam-221	535	3	,	,	PUNCT
ejpam-221	535	4	if	if	SCONJ
ejpam-221	535	5	s	s	NOUN
ejpam-221	535	6	is	be	AUX
ejpam-221	535	7	closed	close	VERB
ejpam-221	535	8	under	under	ADP
ejpam-221	535	9	+	+	PROPN
ejpam-221	535	10	,	,	PUNCT
ejpam-221	535	11	say	say	INTJ
ejpam-221	535	12	,	,	PUNCT
ejpam-221	535	13	then	then	ADV
ejpam-221	535	14	we	we	PRON
ejpam-221	535	15	call	call	VERB
ejpam-221	535	16	s	s	PRON
ejpam-221	535	17	a	a	DET
ejpam-221	535	18	left	left	ADJ
ejpam-221	535	19	ample	ample	ADJ
ejpam-221	535	20	semigroup	semigroup	NOUN
ejpam-221	535	21	.	.	PUNCT
ejpam-221	536	1	it	it	PRON
ejpam-221	536	2	is	be	AUX
ejpam-221	536	3	clear	clear	ADJ
ejpam-221	536	4	that	that	SCONJ
ejpam-221	536	5	such	such	DET
ejpam-221	536	6	an	an	DET
ejpam-221	536	7	s	s	NOUN
ejpam-221	536	8	is	be	AUX
ejpam-221	536	9	also	also	ADV
ejpam-221	536	10	a	a	DET
ejpam-221	536	11	(	(	PUNCT
ejpam-221	536	12	2,1)-subalgebra	2,1)-subalgebra	NUM
ejpam-221	536	13	of	of	ADP
ejpam-221	536	14	ix	ix	PROPN
ejpam-221	536	15	,	,	PUNCT
ejpam-221	536	16	this	this	DET
ejpam-221	536	17	time	time	NOUN
ejpam-221	536	18	with	with	ADP
ejpam-221	536	19	unary	unary	ADJ
ejpam-221	536	20	operation	operation	NOUN
ejpam-221	537	1	+	+	PROPN
ejpam-221	537	2	.	.	PUNCT
ejpam-221	538	1	since	since	SCONJ
ejpam-221	538	2	ix	ix	ADP
ejpam-221	538	3	⊆	⊆	NUM
ejpam-221	538	4	p	p	X
ejpam-221	538	5	t	t	PROPN
ejpam-221	538	6	x	x	INTJ
ejpam-221	538	7	,	,	PUNCT
ejpam-221	538	8	it	it	PRON
ejpam-221	538	9	is	be	AUX
ejpam-221	538	10	immediate	immediate	ADJ
ejpam-221	538	11	that	that	SCONJ
ejpam-221	538	12	a	a	DET
ejpam-221	538	13	left	left	ADJ
ejpam-221	538	14	ample	ample	ADJ
ejpam-221	538	15	semigroup	semigroup	NOUN
ejpam-221	538	16	is	be	AUX
ejpam-221	538	17	a	a	DET
ejpam-221	538	18	full	full	ADJ
ejpam-221	538	19	left	left	NOUN
ejpam-221	538	20	restriction	restriction	NOUN
ejpam-221	538	21	semigroup	semigroup	NOUN
ejpam-221	538	22	.	.	PUNCT
ejpam-221	539	1	right	right	ADJ
ejpam-221	539	2	ample	ample	ADJ
ejpam-221	539	3	semigroups	semigroup	NOUN
ejpam-221	539	4	may	may	AUX
ejpam-221	539	5	be	be	AUX
ejpam-221	539	6	defined	define	VERB
ejpam-221	539	7	in	in	ADP
ejpam-221	539	8	a	a	DET
ejpam-221	539	9	similar	similar	ADJ
ejpam-221	539	10	way	way	NOUN
ejpam-221	539	11	by	by	ADP
ejpam-221	539	12	considering	consider	VERB
ejpam-221	539	13	closure	closure	NOUN
ejpam-221	539	14	under	under	ADP
ejpam-221	539	15	∗.	∗.	PROPN
ejpam-221	539	16	note	note	NOUN
ejpam-221	539	17	that	that	SCONJ
ejpam-221	539	18	there	there	PRON
ejpam-221	539	19	is	be	VERB
ejpam-221	539	20	no	no	DET
ejpam-221	539	21	need	need	NOUN
ejpam-221	539	22	to	to	PART
ejpam-221	539	23	introduce	introduce	VERB
ejpam-221	539	24	the	the	DET
ejpam-221	539	25	intermediate	intermediate	ADJ
ejpam-221	539	26	notion	notion	NOUN
ejpam-221	539	27	of	of	ADP
ejpam-221	539	28	a	a	DET
ejpam-221	539	29	‘	'	PUNCT
ejpam-221	539	30	left	left	ADJ
ejpam-221	539	31	e	e	NOUN
ejpam-221	539	32	-	-	ADJ
ejpam-221	539	33	ample	ample	ADJ
ejpam-221	539	34	’	'	PUNCT
ejpam-221	539	35	semigroup	semigroup	NOUN
ejpam-221	539	36	’	'	PUNCT
ejpam-221	539	37	:	:	PUNCT
ejpam-221	539	38	such	such	DET
ejpam-221	539	39	a	a	DET
ejpam-221	539	40	semigroup	semigroup	NOUN
ejpam-221	539	41	is	be	AUX
ejpam-221	539	42	necessarily	necessarily	ADV
ejpam-221	539	43	left	leave	VERB
ejpam-221	539	44	ample	ample	ADJ
ejpam-221	539	45	,	,	PUNCT
ejpam-221	539	46	since	since	SCONJ
ejpam-221	539	47	it	it	PRON
ejpam-221	539	48	can	can	AUX
ejpam-221	539	49	contain	contain	VERB
ejpam-221	539	50	idempotents	idempotent	NOUN
ejpam-221	539	51	only	only	ADV
ejpam-221	539	52	from	from	ADP
ejpam-221	539	53	ex	ex	PRON
ejpam-221	539	54	.	.	PUNCT
ejpam-221	540	1	just	just	ADV
ejpam-221	540	2	as	as	SCONJ
ejpam-221	540	3	we	we	PRON
ejpam-221	540	4	did	do	VERB
ejpam-221	540	5	for	for	ADP
ejpam-221	540	6	left	left	ADJ
ejpam-221	540	7	restriction	restriction	NOUN
ejpam-221	540	8	semigroups	semigroup	NOUN
ejpam-221	540	9	,	,	PUNCT
ejpam-221	540	10	we	we	PRON
ejpam-221	540	11	now	now	ADV
ejpam-221	540	12	provide	provide	VERB
ejpam-221	540	13	an	an	DET
ejpam-221	540	14	abstract	abstract	ADJ
ejpam-221	540	15	characterisation	characterisation	NOUN
ejpam-221	540	16	of	of	ADP
ejpam-221	540	17	left	left	ADJ
ejpam-221	540	18	ample	ample	ADJ
ejpam-221	540	19	semigroups	semigroup	NOUN
ejpam-221	540	20	.	.	PUNCT
ejpam-221	541	1	recall	recall	NOUN
ejpam-221	541	2	from	from	ADP
ejpam-221	541	3	section	section	NOUN
ejpam-221	541	4	1	1	NUM
ejpam-221	541	5	that	that	SCONJ
ejpam-221	541	6	the	the	DET
ejpam-221	541	7	equivalence	equivalence	NOUN
ejpam-221	541	8	relation	relation	NOUN
ejpam-221	541	9	r∗	r∗	NOUN
ejpam-221	541	10	is	be	AUX
ejpam-221	541	11	defined	define	VERB
ejpam-221	541	12	on	on	ADP
ejpam-221	541	13	a	a	DET
ejpam-221	541	14	semigroup	semigroup	NOUN
ejpam-221	541	15	s	s	NOUN
ejpam-221	541	16	by	by	ADP
ejpam-221	541	17	saying	say	VERB
ejpam-221	541	18	that	that	SCONJ
ejpam-221	541	19	ar∗	ar∗	PROPN
ejpam-221	541	20	b	b	NOUN
ejpam-221	541	21	if	if	SCONJ
ejpam-221	541	22	,	,	PUNCT
ejpam-221	541	23	and	and	CCONJ
ejpam-221	541	24	only	only	ADV
ejpam-221	541	25	if	if	SCONJ
ejpam-221	541	26	,	,	PUNCT
ejpam-221	541	27	ar	ar	PROPN
ejpam-221	541	28	b	b	PROPN
ejpam-221	541	29	in	in	ADP
ejpam-221	541	30	some	some	DET
ejpam-221	541	31	oversemigroup	oversemigroup	NOUN
ejpam-221	541	32	t	t	NOUN
ejpam-221	541	33	.	.	PUNCT
ejpam-221	542	1	consequently	consequently	ADV
ejpam-221	542	2	,	,	PUNCT
ejpam-221	542	3	r	r	NOUN
ejpam-221	542	4	⊆	⊆	NUM
ejpam-221	542	5	r∗.	r∗.	NOUN
ejpam-221	542	6	fountain	fountain	NOUN
ejpam-221	542	7	[	[	X
ejpam-221	542	8	24	24	NUM
ejpam-221	542	9	,	,	PUNCT
ejpam-221	542	10	lemma	lemma	PROPN
ejpam-221	542	11	1.1	1.1	NUM
ejpam-221	542	12	]	]	PUNCT
ejpam-221	542	13	proved	prove	VERB
ejpam-221	542	14	that	that	SCONJ
ejpam-221	542	15	r∗	r∗	PROPN
ejpam-221	542	16	has	have	VERB
ejpam-221	542	17	the	the	DET
ejpam-221	542	18	following	follow	VERB
ejpam-221	542	19	equivalent	equivalent	ADJ
ejpam-221	542	20	description	description	NOUN
ejpam-221	542	21	:	:	PUNCT
ejpam-221	542	22	ar∗	ar∗	PROPN
ejpam-221	542	23	b	b	NUM
ejpam-221	542	24	⇐	⇐	PROPN
ejpam-221	542	25	⇒∀x	⇒∀x	NOUN
ejpam-221	542	26	,	,	PUNCT
ejpam-221	542	27	y	y	PROPN
ejpam-221	542	28	∈	∈	PROPN
ejpam-221	542	29	s1[xa	s1[xa	NOUN
ejpam-221	542	30	=	=	PUNCT
ejpam-221	542	31	ya⇔	ya⇔	NOUN
ejpam-221	542	32	x	x	X
ejpam-221	542	33	b	b	X
ejpam-221	542	34	=	=	SYM
ejpam-221	542	35	y	y	PROPN
ejpam-221	542	36	b	b	PROPN
ejpam-221	542	37	]	]	X
ejpam-221	542	38	.	.	PUNCT
ejpam-221	543	1	(	(	PUNCT
ejpam-221	543	2	5.1	5.1	NUM
ejpam-221	543	3	)	)	PUNCT
ejpam-221	543	4	it	it	PRON
ejpam-221	543	5	is	be	AUX
ejpam-221	543	6	clear	clear	ADJ
ejpam-221	543	7	thatr∗	thatr∗	NOUN
ejpam-221	543	8	is	be	AUX
ejpam-221	543	9	a	a	DET
ejpam-221	543	10	left	left	ADJ
ejpam-221	543	11	congruence	congruence	NOUN
ejpam-221	543	12	.	.	PUNCT
ejpam-221	544	1	as	as	ADP
ejpam-221	544	2	with	with	ADP
ejpam-221	544	3	ere	ere	NOUN
ejpam-221	544	4	,	,	PUNCT
ejpam-221	544	5	we	we	PRON
ejpam-221	544	6	have	have	VERB
ejpam-221	544	7	a	a	DET
ejpam-221	544	8	simpler	simple	ADJ
ejpam-221	544	9	condition	condition	NOUN
ejpam-221	544	10	for	for	ADP
ejpam-221	544	11	an	an	DET
ejpam-221	544	12	element	element	NOUN
ejpam-221	544	13	a	a	PRON
ejpam-221	544	14	of	of	ADP
ejpam-221	544	15	a	a	DET
ejpam-221	544	16	semigroup	semigroup	NOUN
ejpam-221	544	17	s	s	VERB
ejpam-221	544	18	to	to	PART
ejpam-221	544	19	be	be	AUX
ejpam-221	544	20	r∗-related	r∗-relate	VERB
ejpam-221	544	21	to	to	ADP
ejpam-221	544	22	an	an	DET
ejpam-221	544	23	idempotent	idempotent	NOUN
ejpam-221	544	24	e	e	NOUN
ejpam-221	544	25	∈	∈	PROPN
ejpam-221	544	26	e(s	e(s	PROPN
ejpam-221	544	27	):	):	PUNCT
ejpam-221	544	28	ar∗	ar∗	NOUN
ejpam-221	544	29	e	e	X
ejpam-221	544	30	⇐	⇐	ADJ
ejpam-221	544	31	⇒	⇒	NOUN
ejpam-221	544	32	ea	ea	PUNCT
ejpam-221	545	1	=	=	PUNCT
ejpam-221	545	2	a	a	PROPN
ejpam-221	545	3	and	and	CCONJ
ejpam-221	545	4	∀x	∀x	NUM
ejpam-221	545	5	,	,	PUNCT
ejpam-221	545	6	y	y	PROPN
ejpam-221	545	7	∈	∈	PROPN
ejpam-221	545	8	s1[xa	s1[xa	NOUN
ejpam-221	545	9	=	=	SYM
ejpam-221	545	10	ya⇒	ya⇒	PROPN
ejpam-221	545	11	xe	xe	PROPN
ejpam-221	545	12	=	=	PROPN
ejpam-221	545	13	ye	ye	PROPN
ejpam-221	545	14	]	]	X
ejpam-221	545	15	.	.	PUNCT
ejpam-221	546	1	(	(	PUNCT
ejpam-221	546	2	cf	cf	NOUN
ejpam-221	546	3	.	.	PUNCT
ejpam-221	547	1	definition	definition	NOUN
ejpam-221	547	2	1.4	1.4	NUM
ejpam-221	547	3	.	.	PUNCT
ejpam-221	547	4	)	)	PUNCT
ejpam-221	548	1	lemma	lemma	PROPN
ejpam-221	548	2	5.1	5.1	NUM
ejpam-221	548	3	.	.	PUNCT
ejpam-221	549	1	let	let	VERB
ejpam-221	549	2	s	s	PRON
ejpam-221	549	3	be	be	AUX
ejpam-221	549	4	an	an	DET
ejpam-221	549	5	arbitrary	arbitrary	ADJ
ejpam-221	549	6	semigroup	semigroup	NOUN
ejpam-221	549	7	.	.	PUNCT
ejpam-221	550	1	for	for	ADP
ejpam-221	550	2	e	e	PROPN
ejpam-221	550	3	,	,	PUNCT
ejpam-221	550	4	f	f	PROPN
ejpam-221	550	5	∈	∈	PROPN
ejpam-221	550	6	e(s	e(s	PROPN
ejpam-221	550	7	)	)	PUNCT
ejpam-221	550	8	,	,	PUNCT
ejpam-221	550	9	er∗	er∗	VERB
ejpam-221	550	10	f	f	PROPN
ejpam-221	550	11	if	if	SCONJ
ejpam-221	550	12	,	,	PUNCT
ejpam-221	550	13	and	and	CCONJ
ejpam-221	550	14	only	only	ADV
ejpam-221	550	15	if	if	SCONJ
ejpam-221	550	16	,	,	PUNCT
ejpam-221	550	17	er	er	INTJ
ejpam-221	550	18	f	f	X
ejpam-221	550	19	.	.	PUNCT
ejpam-221	551	1	proof	proof	NOUN
ejpam-221	551	2	.	.	PUNCT
ejpam-221	552	1	similar	similar	ADJ
ejpam-221	552	2	to	to	ADP
ejpam-221	552	3	lemma	lemma	PROPN
ejpam-221	552	4	4.2	4.2	NUM
ejpam-221	552	5	.	.	PUNCT
ejpam-221	553	1	the	the	DET
ejpam-221	553	2	following	follow	VERB
ejpam-221	553	3	is	be	AUX
ejpam-221	553	4	an	an	DET
ejpam-221	553	5	immediate	immediate	ADJ
ejpam-221	553	6	consequence	consequence	NOUN
ejpam-221	553	7	of	of	ADP
ejpam-221	553	8	lemma	lemma	PROPN
ejpam-221	553	9	5.1	5.1	NUM
ejpam-221	553	10	:	:	PUNCT
ejpam-221	553	11	lemma	lemma	PROPN
ejpam-221	553	12	5.2	5.2	NUM
ejpam-221	553	13	.	.	PUNCT
ejpam-221	554	1	let	let	VERB
ejpam-221	554	2	s	s	PRON
ejpam-221	554	3	be	be	AUX
ejpam-221	554	4	a	a	DET
ejpam-221	554	5	semigroup	semigroup	NOUN
ejpam-221	554	6	whose	whose	DET
ejpam-221	554	7	idempotents	idempotent	NOUN
ejpam-221	554	8	form	form	VERB
ejpam-221	554	9	a	a	DET
ejpam-221	554	10	subsemilattice	subsemilattice	NOUN
ejpam-221	554	11	e(s	e(s	PROPN
ejpam-221	554	12	)	)	PUNCT
ejpam-221	554	13	.	.	PUNCT
ejpam-221	555	1	each	each	DET
ejpam-221	555	2	element	element	NOUN
ejpam-221	555	3	of	of	ADP
ejpam-221	555	4	s	s	PROPN
ejpam-221	555	5	is	be	AUX
ejpam-221	555	6	r∗-related	r∗-relate	VERB
ejpam-221	555	7	to	to	ADP
ejpam-221	555	8	at	at	ADP
ejpam-221	555	9	most	most	ADV
ejpam-221	555	10	one	one	NUM
ejpam-221	555	11	idempotent	idempotent	NOUN
ejpam-221	555	12	.	.	PUNCT
ejpam-221	556	1	left	leave	VERB
ejpam-221	556	2	ample	ample	ADJ
ejpam-221	556	3	semigroups	semigroup	NOUN
ejpam-221	556	4	have	have	VERB
ejpam-221	556	5	the	the	DET
ejpam-221	556	6	following	follow	VERB
ejpam-221	556	7	abstract	abstract	ADJ
ejpam-221	556	8	description	description	NOUN
ejpam-221	556	9	:	:	PUNCT
ejpam-221	556	10	definition	definition	NOUN
ejpam-221	556	11	5.3	5.3	NUM
ejpam-221	556	12	.	.	PUNCT
ejpam-221	557	1	a	a	DET
ejpam-221	557	2	semigroup	semigroup	NOUN
ejpam-221	557	3	s	s	PART
ejpam-221	557	4	is	be	AUX
ejpam-221	557	5	left	leave	VERB
ejpam-221	557	6	ample	ample	ADJ
ejpam-221	557	7	if	if	SCONJ
ejpam-221	557	8	c.	c.	PROPN
ejpam-221	557	9	hollings	hollings	PROPN
ejpam-221	557	10	/	/	SYM
ejpam-221	557	11	eur	eur	PROPN
ejpam-221	557	12	.	.	PUNCT
ejpam-221	558	1	j.	j.	PROPN
ejpam-221	558	2	pure	pure	PROPN
ejpam-221	558	3	appl	appl	PROPN
ejpam-221	558	4	.	.	PROPN
ejpam-221	558	5	math	math	PROPN
ejpam-221	558	6	,	,	PUNCT
ejpam-221	558	7	2	2	NUM
ejpam-221	558	8	(	(	PUNCT
ejpam-221	558	9	2009	2009	NUM
ejpam-221	558	10	)	)	PUNCT
ejpam-221	558	11	,	,	PUNCT
ejpam-221	558	12	(	(	PUNCT
ejpam-221	558	13	21	21	NUM
ejpam-221	558	14	-	-	SYM
ejpam-221	558	15	57	57	NUM
ejpam-221	558	16	)	)	PUNCT
ejpam-221	558	17	50	50	NUM
ejpam-221	558	18	1	1	NUM
ejpam-221	558	19	.	.	PUNCT
ejpam-221	559	1	every	every	DET
ejpam-221	559	2	element	element	NOUN
ejpam-221	559	3	a	a	NOUN
ejpam-221	559	4	is	be	AUX
ejpam-221	559	5	r∗-related	r∗-relate	VERB
ejpam-221	559	6	to	to	ADP
ejpam-221	559	7	an	an	DET
ejpam-221	559	8	idempotent	idempotent	NOUN
ejpam-221	559	9	,	,	PUNCT
ejpam-221	559	10	denoted	denote	VERB
ejpam-221	559	11	by	by	ADP
ejpam-221	559	12	a†	a†	NOUN
ejpam-221	559	13	;	;	PUNCT
ejpam-221	559	14	2	2	NUM
ejpam-221	559	15	.	.	X
ejpam-221	560	1	for	for	ADP
ejpam-221	560	2	all	all	DET
ejpam-221	560	3	a	a	DET
ejpam-221	560	4	∈	∈	NOUN
ejpam-221	560	5	s	s	PART
ejpam-221	560	6	and	and	CCONJ
ejpam-221	560	7	all	all	DET
ejpam-221	560	8	e	e	PROPN
ejpam-221	560	9	∈	∈	PROPN
ejpam-221	560	10	e(s	e(s	PROPN
ejpam-221	560	11	)	)	PUNCT
ejpam-221	560	12	,	,	PUNCT
ejpam-221	560	13	ae	ae	PROPN
ejpam-221	560	14	=	=	PUNCT
ejpam-221	560	15	(	(	PUNCT
ejpam-221	560	16	ae)†a	ae)†a	NOUN
ejpam-221	560	17	.	.	PUNCT
ejpam-221	561	1	by	by	ADP
ejpam-221	561	2	lemma	lemma	PROPN
ejpam-221	561	3	4.1	4.1	NUM
ejpam-221	561	4	and	and	CCONJ
ejpam-221	561	5	the	the	DET
ejpam-221	561	6	fact	fact	NOUN
ejpam-221	561	7	that	that	SCONJ
ejpam-221	561	8	r∗	r∗	PROPN
ejpam-221	561	9	is	be	AUX
ejpam-221	561	10	a	a	DET
ejpam-221	561	11	left	left	ADJ
ejpam-221	561	12	congruence	congruence	NOUN
ejpam-221	561	13	,	,	PUNCT
ejpam-221	561	14	it	it	PRON
ejpam-221	561	15	is	be	AUX
ejpam-221	561	16	easy	easy	ADJ
ejpam-221	561	17	to	to	PART
ejpam-221	561	18	see	see	VERB
ejpam-221	561	19	that	that	SCONJ
ejpam-221	561	20	every	every	PRON
ejpam-221	561	21	left	leave	VERB
ejpam-221	561	22	ample	ample	ADJ
ejpam-221	561	23	semigroup	semigroup	NOUN
ejpam-221	561	24	is	be	AUX
ejpam-221	561	25	a	a	DET
ejpam-221	561	26	full	full	ADJ
ejpam-221	561	27	left	left	ADJ
ejpam-221	561	28	restriction	restriction	NOUN
ejpam-221	561	29	.	.	PUNCT
ejpam-221	562	1	indeed	indeed	ADV
ejpam-221	562	2	,	,	PUNCT
ejpam-221	562	3	we	we	PRON
ejpam-221	562	4	have	have	VERB
ejpam-221	562	5	the	the	DET
ejpam-221	562	6	following	following	NOUN
ejpam-221	562	7	:	:	PUNCT
ejpam-221	562	8	lemma	lemma	PROPN
ejpam-221	562	9	5.4	5.4	NUM
ejpam-221	562	10	.	.	PUNCT
ejpam-221	563	1	in	in	ADP
ejpam-221	563	2	a	a	DET
ejpam-221	563	3	left	left	ADJ
ejpam-221	563	4	ample	ample	ADJ
ejpam-221	563	5	semigroup	semigroup	NOUN
ejpam-221	563	6	,	,	PUNCT
ejpam-221	563	7	a†	a†	NOUN
ejpam-221	563	8	=	=	SYM
ejpam-221	563	9	a+	a+	X
ejpam-221	563	10	,	,	PUNCT
ejpam-221	563	11	for	for	ADP
ejpam-221	563	12	all	all	DET
ejpam-221	563	13	elements	element	NOUN
ejpam-221	563	14	a.	a.	NOUN
ejpam-221	563	15	proof	proof	NOUN
ejpam-221	563	16	.	.	PUNCT
ejpam-221	564	1	observe	observe	VERB
ejpam-221	564	2	that	that	SCONJ
ejpam-221	564	3	if	if	SCONJ
ejpam-221	564	4	ar∗	ar∗	PROPN
ejpam-221	564	5	e	e	PROPN
ejpam-221	564	6	∈	∈	PROPN
ejpam-221	564	7	e(s	e(s	PROPN
ejpam-221	564	8	)	)	PUNCT
ejpam-221	564	9	,	,	PUNCT
ejpam-221	564	10	then	then	ADV
ejpam-221	564	11	a	a	DET
ejpam-221	564	12	er	er	INTJ
ejpam-221	564	13	e	e	NOUN
ejpam-221	564	14	,	,	PUNCT
ejpam-221	564	15	by	by	ADP
ejpam-221	564	16	lemma	lemma	PROPN
ejpam-221	564	17	4.1	4.1	NUM
ejpam-221	564	18	.	.	PUNCT
ejpam-221	565	1	it	it	PRON
ejpam-221	565	2	follows	follow	VERB
ejpam-221	565	3	that	that	SCONJ
ejpam-221	565	4	a†	a†	NOUN
ejpam-221	565	5	=	=	SYM
ejpam-221	565	6	a+	a+	PROPN
ejpam-221	565	7	.	.	NOUN
ejpam-221	565	8	from	from	ADP
ejpam-221	565	9	here	here	ADV
ejpam-221	565	10	on	on	ADV
ejpam-221	565	11	,	,	PUNCT
ejpam-221	565	12	we	we	PRON
ejpam-221	565	13	will	will	AUX
ejpam-221	565	14	drop	drop	VERB
ejpam-221	565	15	the	the	DET
ejpam-221	565	16	notation	notation	NOUN
ejpam-221	565	17	‘	'	PUNCT
ejpam-221	565	18	a†	a†	NOUN
ejpam-221	565	19	’	'	PUNCT
ejpam-221	565	20	in	in	ADP
ejpam-221	565	21	favour	favour	NOUN
ejpam-221	565	22	of	of	ADP
ejpam-221	565	23	‘	'	PUNCT
ejpam-221	565	24	a+	a+	NOUN
ejpam-221	565	25	’	'	PUNCT
ejpam-221	565	26	.	.	PUNCT
ejpam-221	566	1	lemma	lemma	PROPN
ejpam-221	566	2	5.5	5.5	NUM
ejpam-221	566	3	.	.	PUNCT
ejpam-221	567	1	let	let	VERB
ejpam-221	567	2	s	s	PRON
ejpam-221	567	3	be	be	AUX
ejpam-221	567	4	a	a	DET
ejpam-221	567	5	left	left	ADJ
ejpam-221	567	6	restriction	restriction	NOUN
ejpam-221	567	7	semigroup	semigroup	NOUN
ejpam-221	567	8	with	with	ADP
ejpam-221	567	9	respect	respect	NOUN
ejpam-221	567	10	to	to	ADP
ejpam-221	567	11	some	some	DET
ejpam-221	567	12	e	e	NOUN
ejpam-221	567	13	⊆	⊆	NUM
ejpam-221	567	14	e(s	e(s	PROPN
ejpam-221	567	15	)	)	PUNCT
ejpam-221	567	16	.	.	PUNCT
ejpam-221	568	1	then	then	ADV
ejpam-221	568	2	s	s	VERB
ejpam-221	568	3	is	be	AUX
ejpam-221	568	4	left	leave	VERB
ejpam-221	568	5	ample	ample	ADJ
ejpam-221	568	6	if	if	SCONJ
ejpam-221	568	7	,	,	PUNCT
ejpam-221	568	8	and	and	CCONJ
ejpam-221	568	9	only	only	ADV
ejpam-221	568	10	if	if	SCONJ
ejpam-221	568	11	,	,	PUNCT
ejpam-221	568	12	r∗	r∗	PROPN
ejpam-221	568	13	=	=	PROPN
ejpam-221	568	14	ere	ere	PROPN
ejpam-221	568	15	.	.	PUNCT
ejpam-221	569	1	proof	proof	NOUN
ejpam-221	569	2	.	.	PUNCT
ejpam-221	570	1	let	let	VERB
ejpam-221	570	2	s	s	PRON
ejpam-221	570	3	be	be	AUX
ejpam-221	570	4	a	a	DET
ejpam-221	570	5	left	left	ADJ
ejpam-221	570	6	ample	ample	ADJ
ejpam-221	570	7	semigroup	semigroup	NOUN
ejpam-221	570	8	.	.	PUNCT
ejpam-221	571	1	we	we	PRON
ejpam-221	571	2	know	know	VERB
ejpam-221	571	3	that	that	PRON
ejpam-221	571	4	r∗	r∗	VERB
ejpam-221	571	5	⊆	⊆	NUM
ejpam-221	571	6	ere	ere	NOUN
ejpam-221	571	7	,	,	PUNCT
ejpam-221	571	8	so	so	ADV
ejpam-221	571	9	we	we	PRON
ejpam-221	571	10	prove	prove	VERB
ejpam-221	571	11	the	the	DET
ejpam-221	571	12	reverse	reverse	ADJ
ejpam-221	571	13	inclusion	inclusion	NOUN
ejpam-221	571	14	.	.	PUNCT
ejpam-221	572	1	let	let	VERB
ejpam-221	572	2	a	a	DET
ejpam-221	572	3	ere	ere	PROPN
ejpam-221	572	4	b	b	PROPN
ejpam-221	572	5	,	,	PUNCT
ejpam-221	572	6	for	for	ADP
ejpam-221	572	7	a	a	DET
ejpam-221	572	8	,	,	PUNCT
ejpam-221	572	9	b	b	PROPN
ejpam-221	572	10	∈	∈	PROPN
ejpam-221	572	11	s.	s.	PROPN
ejpam-221	572	12	then	then	ADV
ejpam-221	572	13	a+	a+	PUNCT
ejpam-221	572	14	=	=	PUNCT
ejpam-221	572	15	b+	b+	X
ejpam-221	572	16	.	.	PUNCT
ejpam-221	573	1	hence	hence	ADV
ejpam-221	573	2	ar∗	ar∗	NOUN
ejpam-221	573	3	a+	a+	PUNCT
ejpam-221	573	4	=	=	SYM
ejpam-221	573	5	b+r∗	b+r∗	NUM
ejpam-221	573	6	b.	b.	NOUN
ejpam-221	573	7	conversely	conversely	ADV
ejpam-221	573	8	,	,	PUNCT
ejpam-221	573	9	suppose	suppose	VERB
ejpam-221	573	10	that	that	SCONJ
ejpam-221	573	11	r∗	r∗	PROPN
ejpam-221	573	12	=	=	PUNCT
ejpam-221	573	13	ere	ere	PROPN
ejpam-221	573	14	.	.	PUNCT
ejpam-221	574	1	then	then	ADV
ejpam-221	574	2	s	s	VERB
ejpam-221	574	3	is	be	AUX
ejpam-221	574	4	clearly	clearly	ADV
ejpam-221	574	5	left	leave	VERB
ejpam-221	574	6	ample	ample	ADJ
ejpam-221	574	7	.	.	PUNCT
ejpam-221	575	1	lemma	lemma	PROPN
ejpam-221	575	2	5.6	5.6	NUM
ejpam-221	575	3	.	.	PUNCT
ejpam-221	576	1	let	let	VERB
ejpam-221	576	2	s	s	PRON
ejpam-221	576	3	be	be	AUX
ejpam-221	576	4	a	a	DET
ejpam-221	576	5	left	left	ADJ
ejpam-221	576	6	restriction	restriction	NOUN
ejpam-221	576	7	semigroup	semigroup	NOUN
ejpam-221	576	8	with	with	ADP
ejpam-221	576	9	respect	respect	NOUN
ejpam-221	576	10	to	to	ADP
ejpam-221	576	11	some	some	DET
ejpam-221	576	12	e	e	NOUN
ejpam-221	576	13	⊆	⊆	NUM
ejpam-221	576	14	e(s	e(s	PROPN
ejpam-221	576	15	)	)	PUNCT
ejpam-221	576	16	,	,	PUNCT
ejpam-221	576	17	and	and	CCONJ
ejpam-221	576	18	let	let	VERB
ejpam-221	576	19	φ	φ	PROPN
ejpam-221	576	20	be	be	AUX
ejpam-221	576	21	the	the	DET
ejpam-221	576	22	function	function	NOUN
ejpam-221	576	23	of	of	ADP
ejpam-221	576	24	theorem	theorem	ADJ
ejpam-221	576	25	4.12	4.12	NUM
ejpam-221	576	26	.	.	PUNCT
ejpam-221	577	1	then	then	ADV
ejpam-221	577	2	s	s	VERB
ejpam-221	577	3	is	be	AUX
ejpam-221	577	4	left	leave	VERB
ejpam-221	577	5	ample	ample	ADJ
ejpam-221	577	6	if	if	SCONJ
ejpam-221	577	7	,	,	PUNCT
ejpam-221	577	8	and	and	CCONJ
ejpam-221	577	9	only	only	ADV
ejpam-221	577	10	if	if	SCONJ
ejpam-221	577	11	,	,	PUNCT
ejpam-221	577	12	imφ	imφ	VERB
ejpam-221	577	13	⊆	⊆	NUM
ejpam-221	577	14	is	be	AUX
ejpam-221	577	15	.	.	PUNCT
ejpam-221	578	1	proof	proof	NOUN
ejpam-221	578	2	.	.	PUNCT
ejpam-221	579	1	let	let	VERB
ejpam-221	579	2	s	s	PRON
ejpam-221	579	3	be	be	AUX
ejpam-221	579	4	a	a	DET
ejpam-221	579	5	left	left	ADJ
ejpam-221	579	6	ample	ample	ADJ
ejpam-221	579	7	semigroup	semigroup	NOUN
ejpam-221	579	8	.	.	PUNCT
ejpam-221	580	1	let	let	VERB
ejpam-221	580	2	x	x	PRON
ejpam-221	580	3	,	,	PUNCT
ejpam-221	580	4	y	y	PROPN
ejpam-221	580	5	∈	∈	PROPN
ejpam-221	580	6	dom	dom	NOUN
ejpam-221	580	7	sφ	sφ	PROPN
ejpam-221	580	8	,	,	PUNCT
ejpam-221	580	9	for	for	ADP
ejpam-221	580	10	some	some	DET
ejpam-221	580	11	s	s	NOUN
ejpam-221	580	12	∈	∈	NOUN
ejpam-221	580	13	s	s	NOUN
ejpam-221	580	14	,	,	PUNCT
ejpam-221	580	15	and	and	CCONJ
ejpam-221	580	16	suppose	suppose	VERB
ejpam-221	580	17	that	that	SCONJ
ejpam-221	580	18	x(sφ	x(sφ	NOUN
ejpam-221	580	19	)	)	PUNCT
ejpam-221	580	20	=	=	SYM
ejpam-221	580	21	y(sφ	y(sφ	NOUN
ejpam-221	580	22	)	)	PUNCT
ejpam-221	580	23	,	,	PUNCT
ejpam-221	581	1	i.e.	i.e.	X
ejpam-221	581	2	,	,	PUNCT
ejpam-221	581	3	xs	xs	PROPN
ejpam-221	581	4	=	=	PUNCT
ejpam-221	581	5	ys	ys	PROPN
ejpam-221	581	6	.	.	PUNCT
ejpam-221	582	1	by	by	ADP
ejpam-221	582	2	lemma	lemma	PROPN
ejpam-221	582	3	5.5	5.5	NUM
ejpam-221	582	4	,	,	PUNCT
ejpam-221	582	5	r∗	r∗	PROPN
ejpam-221	582	6	=	=	PUNCT
ejpam-221	582	7	ere	ere	PROPN
ejpam-221	582	8	,	,	PUNCT
ejpam-221	582	9	so	so	ADV
ejpam-221	582	10	xs+	xs+	PROPN
ejpam-221	582	11	=	=	PROPN
ejpam-221	582	12	ys+	ys+	PROPN
ejpam-221	582	13	,	,	PUNCT
ejpam-221	582	14	since	since	SCONJ
ejpam-221	582	15	sr∗	sr∗	ADV
ejpam-221	582	16	s+	s+	ADV
ejpam-221	582	17	.	.	PUNCT
ejpam-221	583	1	then	then	ADV
ejpam-221	583	2	xs+	xs+	VERB
ejpam-221	583	3	=	=	PUNCT
ejpam-221	583	4	ys+⇔	ys+⇔	NOUN
ejpam-221	583	5	x(s+φ	x(s+φ	NOUN
ejpam-221	583	6	)	)	PUNCT
ejpam-221	584	1	=	=	SYM
ejpam-221	584	2	y(s+φ)⇔	y(s+φ)⇔	PROPN
ejpam-221	584	3	x(sφ)+	x(sφ)+	PUNCT
ejpam-221	585	1	=	=	PUNCT
ejpam-221	585	2	y(sφ)+⇔	y(sφ)+⇔	PROPN
ejpam-221	585	3	x	x	X
ejpam-221	586	1	=	=	PUNCT
ejpam-221	586	2	y.	y.	PROPN
ejpam-221	586	3	therefore	therefore	ADV
ejpam-221	586	4	sφ	sφ	PROPN
ejpam-221	586	5	is	be	AUX
ejpam-221	586	6	one	one	NUM
ejpam-221	586	7	-	-	PUNCT
ejpam-221	586	8	one	one	NUM
ejpam-221	586	9	,	,	PUNCT
ejpam-221	586	10	i.e.	i.e.	X
ejpam-221	586	11	,	,	PUNCT
ejpam-221	586	12	sφ	sφ	ADP
ejpam-221	586	13	∈	∈	PROPN
ejpam-221	586	14	is	be	AUX
ejpam-221	586	15	.	.	PUNCT
ejpam-221	587	1	conversely	conversely	ADV
ejpam-221	587	2	,	,	PUNCT
ejpam-221	587	3	suppose	suppose	VERB
ejpam-221	587	4	that	that	SCONJ
ejpam-221	587	5	imφ	imφ	NOUN
ejpam-221	587	6	⊆	⊆	NUM
ejpam-221	587	7	is	be	AUX
ejpam-221	587	8	.	.	PUNCT
ejpam-221	588	1	then	then	ADV
ejpam-221	588	2	,	,	PUNCT
ejpam-221	588	3	since	since	SCONJ
ejpam-221	588	4	φ	φ	PROPN
ejpam-221	588	5	is	be	AUX
ejpam-221	588	6	a	a	DET
ejpam-221	588	7	(	(	PUNCT
ejpam-221	588	8	2,1)-morphism	2,1)-morphism	NUM
ejpam-221	588	9	,	,	PUNCT
ejpam-221	588	10	imφ	imφ	NOUN
ejpam-221	588	11	is	be	AUX
ejpam-221	588	12	a	a	DET
ejpam-221	588	13	(	(	PUNCT
ejpam-221	588	14	2,1)subalgebra	2,1)subalgebra	NUM
ejpam-221	588	15	of	of	ADP
ejpam-221	588	16	is	be	AUX
ejpam-221	588	17	.	.	PUNCT
ejpam-221	589	1	by	by	ADP
ejpam-221	589	2	the	the	DET
ejpam-221	589	3	remarks	remark	NOUN
ejpam-221	589	4	in	in	ADP
ejpam-221	589	5	the	the	DET
ejpam-221	589	6	opening	opening	NOUN
ejpam-221	589	7	paragraphs	paragraph	NOUN
ejpam-221	589	8	of	of	ADP
ejpam-221	589	9	this	this	DET
ejpam-221	589	10	section	section	NOUN
ejpam-221	589	11	,	,	PUNCT
ejpam-221	589	12	s	s	PART
ejpam-221	589	13	is	be	AUX
ejpam-221	589	14	left	leave	VERB
ejpam-221	589	15	ample	ample	ADJ
ejpam-221	589	16	.	.	PUNCT
ejpam-221	590	1	we	we	PRON
ejpam-221	590	2	see	see	VERB
ejpam-221	590	3	from	from	ADP
ejpam-221	590	4	lemmas	lemmas	PROPN
ejpam-221	590	5	4.1	4.1	NUM
ejpam-221	590	6	and	and	CCONJ
ejpam-221	590	7	4.14	4.14	NUM
ejpam-221	590	8	that	that	PRON
ejpam-221	590	9	r	r	NOUN
ejpam-221	590	10	=	=	PUNCT
ejpam-221	590	11	r∗	r∗	NOUN
ejpam-221	590	12	=	=	SYM
ejpam-221	590	13	er	er	INTJ
ejpam-221	590	14	in	in	ADP
ejpam-221	590	15	a	a	DET
ejpam-221	590	16	regular	regular	ADJ
ejpam-221	590	17	semigroup	semigroup	NOUN
ejpam-221	590	18	.	.	PUNCT
ejpam-221	591	1	it	it	PRON
ejpam-221	591	2	is	be	AUX
ejpam-221	591	3	clear	clear	ADJ
ejpam-221	591	4	from	from	ADP
ejpam-221	591	5	lemmas	lemmas	PROPN
ejpam-221	591	6	4.15	4.15	NUM
ejpam-221	591	7	and	and	CCONJ
ejpam-221	591	8	5.6	5.6	NUM
ejpam-221	591	9	that	that	PRON
ejpam-221	591	10	every	every	DET
ejpam-221	591	11	inverse	inverse	NOUN
ejpam-221	591	12	semigroup	semigroup	NOUN
ejpam-221	591	13	is	be	AUX
ejpam-221	591	14	left	leave	VERB
ejpam-221	591	15	ample	ample	ADJ
ejpam-221	591	16	.	.	PUNCT
ejpam-221	592	1	it	it	PRON
ejpam-221	592	2	is	be	AUX
ejpam-221	592	3	also	also	ADV
ejpam-221	592	4	clear	clear	ADJ
ejpam-221	592	5	that	that	SCONJ
ejpam-221	592	6	a	a	DET
ejpam-221	592	7	right	right	ADJ
ejpam-221	592	8	cancellative	cancellative	ADJ
ejpam-221	592	9	semigroup	semigroup	NOUN
ejpam-221	592	10	is	be	AUX
ejpam-221	592	11	left	leave	VERB
ejpam-221	592	12	ample	ample	ADJ
ejpam-221	592	13	.	.	PUNCT
ejpam-221	593	1	once	once	ADV
ejpam-221	593	2	again	again	ADV
ejpam-221	593	3	,	,	PUNCT
ejpam-221	593	4	for	for	ADP
ejpam-221	593	5	completeness	completeness	NOUN
ejpam-221	593	6	,	,	PUNCT
ejpam-221	593	7	we	we	PRON
ejpam-221	593	8	conclude	conclude	VERB
ejpam-221	593	9	this	this	DET
ejpam-221	593	10	section	section	NOUN
ejpam-221	593	11	by	by	ADP
ejpam-221	593	12	recording	record	VERB
ejpam-221	593	13	the	the	DET
ejpam-221	593	14	definition	definition	NOUN
ejpam-221	593	15	of	of	ADP
ejpam-221	593	16	the	the	DET
ejpam-221	593	17	dual	dual	ADJ
ejpam-221	593	18	equivalence	equivalence	NOUN
ejpam-221	593	19	relation	relation	NOUN
ejpam-221	593	20	l	l	NOUN
ejpam-221	593	21	∗	∗	NOUN
ejpam-221	593	22	and	and	CCONJ
ejpam-221	593	23	,	,	PUNCT
ejpam-221	593	24	consequently	consequently	ADV
ejpam-221	593	25	,	,	PUNCT
ejpam-221	593	26	that	that	PRON
ejpam-221	593	27	of	of	ADP
ejpam-221	593	28	a	a	DET
ejpam-221	593	29	right	right	ADJ
ejpam-221	593	30	ample	ample	ADJ
ejpam-221	593	31	semigroup	semigroup	NOUN
ejpam-221	593	32	.	.	PUNCT
ejpam-221	594	1	c.	c.	PROPN
ejpam-221	594	2	hollings	hollings	PROPN
ejpam-221	594	3	/	/	SYM
ejpam-221	594	4	eur	eur	PROPN
ejpam-221	594	5	.	.	PUNCT
ejpam-221	595	1	j.	j.	PROPN
ejpam-221	595	2	pure	pure	PROPN
ejpam-221	595	3	appl	appl	PROPN
ejpam-221	595	4	.	.	PROPN
ejpam-221	595	5	math	math	PROPN
ejpam-221	595	6	,	,	PUNCT
ejpam-221	595	7	2	2	NUM
ejpam-221	595	8	(	(	PUNCT
ejpam-221	595	9	2009	2009	NUM
ejpam-221	595	10	)	)	PUNCT
ejpam-221	595	11	,	,	PUNCT
ejpam-221	595	12	(	(	PUNCT
ejpam-221	595	13	21	21	NUM
ejpam-221	595	14	-	-	SYM
ejpam-221	595	15	57	57	NUM
ejpam-221	595	16	)	)	PUNCT
ejpam-221	595	17	51	51	NUM
ejpam-221	595	18	definition	definition	NOUN
ejpam-221	595	19	5.7	5.7	NUM
ejpam-221	595	20	.	.	PUNCT
ejpam-221	596	1	we	we	PRON
ejpam-221	596	2	define	define	VERB
ejpam-221	596	3	the	the	DET
ejpam-221	596	4	equivalence	equivalence	NOUN
ejpam-221	596	5	relation	relation	NOUN
ejpam-221	596	6	l	l	NOUN
ejpam-221	596	7	∗	∗	NOUN
ejpam-221	596	8	on	on	ADP
ejpam-221	596	9	a	a	DET
ejpam-221	596	10	semigroup	semigroup	NOUN
ejpam-221	596	11	s	s	NOUN
ejpam-221	596	12	by	by	ADP
ejpam-221	596	13	the	the	DET
ejpam-221	596	14	rule	rule	NOUN
ejpam-221	596	15	that	that	PRON
ejpam-221	596	16	al	al	PROPN
ejpam-221	596	17	∗	∗	PROPN
ejpam-221	596	18	b	b	PROPN
ejpam-221	596	19	⇐	⇐	PROPN
ejpam-221	596	20	⇒∀x	⇒∀x	NOUN
ejpam-221	596	21	,	,	PUNCT
ejpam-221	596	22	y	y	PROPN
ejpam-221	596	23	∈	∈	PROPN
ejpam-221	596	24	s1[ax	s1[ax	NOUN
ejpam-221	596	25	=	=	PRON
ejpam-221	596	26	a	a	DET
ejpam-221	596	27	y⇔	y⇔	NOUN
ejpam-221	596	28	bx	bx	NOUN
ejpam-221	596	29	=	=	SYM
ejpam-221	596	30	b	b	PROPN
ejpam-221	596	31	y	y	PROPN
ejpam-221	596	32	]	]	X
ejpam-221	596	33	,	,	PUNCT
ejpam-221	596	34	for	for	ADP
ejpam-221	596	35	a	a	DET
ejpam-221	596	36	,	,	PUNCT
ejpam-221	596	37	b	b	PROPN
ejpam-221	596	38	∈	∈	PROPN
ejpam-221	596	39	s.	s.	PROPN
ejpam-221	596	40	we	we	PRON
ejpam-221	596	41	call	call	VERB
ejpam-221	596	42	s	s	VERB
ejpam-221	596	43	right	right	ADJ
ejpam-221	596	44	ample	ample	ADJ
ejpam-221	596	45	if	if	SCONJ
ejpam-221	596	46	1	1	NUM
ejpam-221	596	47	.	.	X
ejpam-221	597	1	every	every	DET
ejpam-221	597	2	element	element	NOUN
ejpam-221	597	3	a	a	PRON
ejpam-221	597	4	is	be	AUX
ejpam-221	597	5	l	l	NOUN
ejpam-221	597	6	∗-related	∗-relate	VERB
ejpam-221	597	7	to	to	ADP
ejpam-221	597	8	an	an	DET
ejpam-221	597	9	idempotent	idempotent	NOUN
ejpam-221	597	10	,	,	PUNCT
ejpam-221	597	11	denoted	denote	VERB
ejpam-221	597	12	by	by	ADP
ejpam-221	597	13	a∗	a∗	NOUN
ejpam-221	597	14	;	;	PUNCT
ejpam-221	597	15	2	2	X
ejpam-221	597	16	.	.	X
ejpam-221	597	17	for	for	ADP
ejpam-221	597	18	all	all	DET
ejpam-221	597	19	a	a	DET
ejpam-221	597	20	∈	∈	NOUN
ejpam-221	597	21	s	s	PART
ejpam-221	597	22	and	and	CCONJ
ejpam-221	597	23	all	all	PRON
ejpam-221	597	24	e	e	PROPN
ejpam-221	597	25	∈	∈	PROPN
ejpam-221	597	26	e(s	e(s	PROPN
ejpam-221	597	27	)	)	PUNCT
ejpam-221	597	28	,	,	PUNCT
ejpam-221	597	29	ea	ea	X
ejpam-221	598	1	=	=	SYM
ejpam-221	599	1	a(ea)∗.	a(ea)∗.	PROPN
ejpam-221	600	1	all	all	DET
ejpam-221	600	2	the	the	DET
ejpam-221	600	3	results	result	NOUN
ejpam-221	600	4	of	of	ADP
ejpam-221	600	5	this	this	DET
ejpam-221	600	6	section	section	NOUN
ejpam-221	600	7	have	have	VERB
ejpam-221	600	8	right	right	ADJ
ejpam-221	600	9	-	-	PUNCT
ejpam-221	600	10	hand	hand	NOUN
ejpam-221	600	11	analogues	analogue	NOUN
ejpam-221	600	12	in	in	ADP
ejpam-221	600	13	terms	term	NOUN
ejpam-221	600	14	of	of	ADP
ejpam-221	600	15	l	l	NOUN
ejpam-221	600	16	∗	∗	NOUN
ejpam-221	600	17	and	and	CCONJ
ejpam-221	600	18	∗.	∗.	NOUN
ejpam-221	600	19	appendix	appendix	NOUN
ejpam-221	600	20	:	:	PUNCT
ejpam-221	600	21	summary	summary	NOUN
ejpam-221	600	22	of	of	ADP
ejpam-221	600	23	terminology	terminology	NOUN
ejpam-221	600	24	as	as	SCONJ
ejpam-221	600	25	we	we	PRON
ejpam-221	600	26	saw	see	VERB
ejpam-221	600	27	in	in	ADP
ejpam-221	600	28	sections	section	NOUN
ejpam-221	600	29	1	1	NUM
ejpam-221	600	30	and	and	CCONJ
ejpam-221	600	31	2	2	NUM
ejpam-221	600	32	,	,	PUNCT
ejpam-221	600	33	when	when	SCONJ
ejpam-221	600	34	approached	approach	VERB
ejpam-221	600	35	from	from	ADP
ejpam-221	600	36	the	the	DET
ejpam-221	600	37	point	point	NOUN
ejpam-221	600	38	of	of	ADP
ejpam-221	600	39	view	view	NOUN
ejpam-221	600	40	of	of	ADP
ejpam-221	600	41	s	s	NOUN
ejpam-221	600	42	-	-	PUNCT
ejpam-221	600	43	acts	act	NOUN
ejpam-221	600	44	,	,	PUNCT
ejpam-221	600	45	the	the	DET
ejpam-221	600	46	terminology	terminology	NOUN
ejpam-221	600	47	associated	associate	VERB
ejpam-221	600	48	with	with	ADP
ejpam-221	600	49	the	the	DET
ejpam-221	600	50	class	class	NOUN
ejpam-221	600	51	of	of	ADP
ejpam-221	600	52	semigroups	semigroup	NOUN
ejpam-221	600	53	which	which	PRON
ejpam-221	600	54	we	we	PRON
ejpam-221	600	55	are	be	AUX
ejpam-221	600	56	now	now	ADV
ejpam-221	600	57	calling	call	VERB
ejpam-221	600	58	‘	'	PUNCT
ejpam-221	600	59	left	leave	VERB
ejpam-221	600	60	restriction	restriction	NOUN
ejpam-221	600	61	semigroups	semigroup	NOUN
ejpam-221	600	62	’	'	PUNCT
ejpam-221	600	63	has	have	AUX
ejpam-221	600	64	had	have	VERB
ejpam-221	600	65	a	a	DET
ejpam-221	600	66	somewhat	somewhat	ADV
ejpam-221	600	67	torturous	torturous	ADJ
ejpam-221	600	68	history	history	NOUN
ejpam-221	600	69	,	,	PUNCT
ejpam-221	600	70	with	with	ADP
ejpam-221	600	71	a	a	DET
ejpam-221	600	72	number	number	NOUN
ejpam-221	600	73	of	of	ADP
ejpam-221	600	74	changes	change	NOUN
ejpam-221	600	75	along	along	ADP
ejpam-221	600	76	the	the	DET
ejpam-221	600	77	way	way	NOUN
ejpam-221	600	78	.	.	PUNCT
ejpam-221	601	1	unfortunately	unfortunately	ADV
ejpam-221	601	2	,	,	PUNCT
ejpam-221	601	3	if	if	SCONJ
ejpam-221	601	4	one	one	PRON
ejpam-221	601	5	is	be	AUX
ejpam-221	601	6	to	to	PART
ejpam-221	601	7	study	study	VERB
ejpam-221	601	8	the	the	DET
ejpam-221	601	9	earlier	early	ADJ
ejpam-221	601	10	papers	paper	NOUN
ejpam-221	601	11	on	on	ADP
ejpam-221	601	12	this	this	DET
ejpam-221	601	13	subject	subject	NOUN
ejpam-221	601	14	,	,	PUNCT
ejpam-221	601	15	then	then	ADV
ejpam-221	601	16	one	one	PRON
ejpam-221	601	17	must	must	AUX
ejpam-221	601	18	be	be	AUX
ejpam-221	601	19	familiar	familiar	ADJ
ejpam-221	601	20	with	with	ADP
ejpam-221	601	21	all	all	PRON
ejpam-221	601	22	of	of	ADP
ejpam-221	601	23	the	the	DET
ejpam-221	601	24	former	former	ADJ
ejpam-221	601	25	names	name	NOUN
ejpam-221	601	26	of	of	ADP
ejpam-221	601	27	these	these	DET
ejpam-221	601	28	semigroups	semigroup	NOUN
ejpam-221	601	29	.	.	PUNCT
ejpam-221	602	1	we	we	PRON
ejpam-221	602	2	therefore	therefore	ADV
ejpam-221	602	3	provide	provide	VERB
ejpam-221	602	4	a	a	DET
ejpam-221	602	5	short	short	ADJ
ejpam-221	602	6	summary	summary	NOUN
ejpam-221	602	7	of	of	ADP
ejpam-221	602	8	the	the	DET
ejpam-221	602	9	various	various	ADJ
ejpam-221	602	10	terms	term	NOUN
ejpam-221	602	11	found	find	VERB
ejpam-221	602	12	in	in	ADP
ejpam-221	602	13	this	this	DET
ejpam-221	602	14	area	area	NOUN
ejpam-221	602	15	of	of	ADP
ejpam-221	602	16	study	study	NOUN
ejpam-221	602	17	.	.	PUNCT
ejpam-221	603	1	we	we	PRON
ejpam-221	603	2	will	will	AUX
ejpam-221	603	3	restrict	restrict	VERB
ejpam-221	603	4	our	our	PRON
ejpam-221	603	5	attention	attention	NOUN
ejpam-221	603	6	to	to	ADP
ejpam-221	603	7	the	the	DET
ejpam-221	603	8	left	left	ADJ
ejpam-221	603	9	-	-	PUNCT
ejpam-221	603	10	hand	hand	NOUN
ejpam-221	603	11	versions	version	NOUN
ejpam-221	603	12	of	of	ADP
ejpam-221	603	13	these	these	DET
ejpam-221	603	14	various	various	ADJ
ejpam-221	603	15	classes	class	NOUN
ejpam-221	603	16	of	of	ADP
ejpam-221	603	17	semigroups	semigroup	NOUN
ejpam-221	603	18	;	;	PUNCT
ejpam-221	603	19	the	the	DET
ejpam-221	603	20	right	right	ADJ
ejpam-221	603	21	-	-	PUNCT
ejpam-221	603	22	hand	hand	NOUN
ejpam-221	603	23	version	version	NOUN
ejpam-221	603	24	may	may	AUX
ejpam-221	603	25	be	be	AUX
ejpam-221	603	26	defined	define	VERB
ejpam-221	603	27	dually	dually	ADV
ejpam-221	603	28	.	.	PUNCT
ejpam-221	604	1	let	let	VERB
ejpam-221	604	2	s	s	PRON
ejpam-221	604	3	be	be	AUX
ejpam-221	604	4	a	a	DET
ejpam-221	604	5	semigroup	semigroup	NOUN
ejpam-221	604	6	with	with	ADP
ejpam-221	604	7	a	a	DET
ejpam-221	604	8	distinguished	distinguished	ADJ
ejpam-221	604	9	subset	subset	NOUN
ejpam-221	604	10	e	e	NOUN
ejpam-221	604	11	⊆	⊆	NUM
ejpam-221	604	12	e(s	e(s	PROPN
ejpam-221	604	13	)	)	PUNCT
ejpam-221	604	14	.	.	PUNCT
ejpam-221	605	1	we	we	PRON
ejpam-221	605	2	will	will	AUX
ejpam-221	605	3	call	call	VERB
ejpam-221	605	4	s	s	PRON
ejpam-221	605	5	•	•	NOUN
ejpam-221	605	6	left	leave	VERB
ejpam-221	605	7	e	e	NOUN
ejpam-221	605	8	-	-	NOUN
ejpam-221	605	9	semiabundant	semiabundant	ADJ
ejpam-221	605	10	if	if	SCONJ
ejpam-221	605	11	every	every	DET
ejpam-221	605	12	element	element	NOUN
ejpam-221	605	13	is	be	AUX
ejpam-221	605	14	ere	ere	NOUN
ejpam-221	605	15	-	-	PUNCT
ejpam-221	605	16	related	relate	VERB
ejpam-221	605	17	to	to	ADP
ejpam-221	605	18	an	an	DET
ejpam-221	605	19	idempotent	idempotent	NOUN
ejpam-221	605	20	from	from	ADP
ejpam-221	605	21	e	e	NOUN
ejpam-221	605	22	,	,	PUNCT
ejpam-221	605	23	and	and	CCONJ
ejpam-221	605	24	•	•	ADV
ejpam-221	605	25	left	leave	VERB
ejpam-221	605	26	e	e	NOUN
ejpam-221	605	27	-	-	NOUN
ejpam-221	605	28	abundant	abundant	ADJ
ejpam-221	605	29	if	if	SCONJ
ejpam-221	605	30	every	every	DET
ejpam-221	605	31	element	element	NOUN
ejpam-221	605	32	is	be	AUX
ejpam-221	605	33	r∗-related	r∗-relate	VERB
ejpam-221	605	34	to	to	ADP
ejpam-221	605	35	an	an	DET
ejpam-221	605	36	idempotent	idempotent	NOUN
ejpam-221	605	37	from	from	ADP
ejpam-221	605	38	e.	e.	PROPN
ejpam-221	605	39	in	in	ADP
ejpam-221	605	40	either	either	DET
ejpam-221	605	41	case	case	NOUN
ejpam-221	605	42	,	,	PUNCT
ejpam-221	605	43	if	if	SCONJ
ejpam-221	605	44	e	e	NOUN
ejpam-221	605	45	=	=	SYM
ejpam-221	605	46	e(s	e(s	PROPN
ejpam-221	605	47	)	)	PUNCT
ejpam-221	605	48	,	,	PUNCT
ejpam-221	605	49	then	then	ADV
ejpam-221	605	50	we	we	PRON
ejpam-221	605	51	will	will	AUX
ejpam-221	605	52	omit	omit	VERB
ejpam-221	605	53	the	the	DET
ejpam-221	605	54	‘	'	PUNCT
ejpam-221	605	55	e	e	NOUN
ejpam-221	605	56	’	'	PUNCT
ejpam-221	605	57	.	.	PUNCT
ejpam-221	606	1	these	these	DET
ejpam-221	606	2	terms	term	NOUN
ejpam-221	606	3	will	will	AUX
ejpam-221	606	4	serve	serve	VERB
ejpam-221	606	5	as	as	ADP
ejpam-221	606	6	our	our	PRON
ejpam-221	606	7	basic	basic	ADJ
ejpam-221	606	8	terminology	terminology	NOUN
ejpam-221	606	9	:	:	PUNCT
ejpam-221	606	10	everything	everything	PRON
ejpam-221	606	11	else	else	ADV
ejpam-221	606	12	will	will	AUX
ejpam-221	606	13	be	be	AUX
ejpam-221	606	14	defined	define	VERB
ejpam-221	606	15	in	in	ADP
ejpam-221	606	16	terms	term	NOUN
ejpam-221	606	17	of	of	ADP
ejpam-221	606	18	these	these	PRON
ejpam-221	606	19	.	.	PUNCT
ejpam-221	607	1	let	let	AUX
ejpam-221	607	2	(	(	PUNCT
ejpam-221	607	3	cl	cl	NOUN
ejpam-221	607	4	)	)	PUNCT
ejpam-221	607	5	denote	denote	VERB
ejpam-221	607	6	the	the	DET
ejpam-221	607	7	condition	condition	NOUN
ejpam-221	607	8	that	that	SCONJ
ejpam-221	607	9	ere	ere	PROPN
ejpam-221	607	10	be	be	AUX
ejpam-221	607	11	a	a	DET
ejpam-221	607	12	left	left	ADJ
ejpam-221	607	13	congruence	congruence	NOUN
ejpam-221	607	14	,	,	PUNCT
ejpam-221	607	15	and	and	CCONJ
ejpam-221	607	16	(	(	PUNCT
ejpam-221	607	17	la	la	NOUN
ejpam-221	607	18	)	)	PUNCT
ejpam-221	607	19	denote	denote	VERB
ejpam-221	607	20	the	the	DET
ejpam-221	607	21	left	left	ADJ
ejpam-221	607	22	ample	ample	ADJ
ejpam-221	607	23	identity	identity	NOUN
ejpam-221	607	24	:	:	PUNCT
ejpam-221	607	25	ae	ae	PROPN
ejpam-221	607	26	=	=	SYM
ejpam-221	607	27	(	(	PUNCT
ejpam-221	607	28	ae)+a	ae)+a	PROPN
ejpam-221	607	29	,	,	PUNCT
ejpam-221	607	30	for	for	ADP
ejpam-221	607	31	all	all	DET
ejpam-221	607	32	a	a	DET
ejpam-221	607	33	∈	∈	NOUN
ejpam-221	607	34	s	s	PART
ejpam-221	607	35	and	and	CCONJ
ejpam-221	607	36	all	all	DET
ejpam-221	607	37	e	e	PROPN
ejpam-221	607	38	∈	∈	PROPN
ejpam-221	607	39	e.	e.	PROPN
ejpam-221	607	40	table	table	PROPN
ejpam-221	607	41	1	1	NUM
ejpam-221	607	42	summarises	summarise	VERB
ejpam-221	607	43	the	the	DET
ejpam-221	607	44	various	various	ADJ
ejpam-221	607	45	classes	class	NOUN
ejpam-221	607	46	of	of	ADP
ejpam-221	607	47	semigroups	semigroup	NOUN
ejpam-221	607	48	mentioned	mention	VERB
ejpam-221	607	49	in	in	ADP
ejpam-221	607	50	sections	section	NOUN
ejpam-221	607	51	1	1	NUM
ejpam-221	607	52	and	and	CCONJ
ejpam-221	607	53	2	2	NUM
ejpam-221	607	54	.	.	X
ejpam-221	607	55	observe	observe	VERB
ejpam-221	607	56	that	that	SCONJ
ejpam-221	607	57	there	there	PRON
ejpam-221	607	58	have	have	AUX
ejpam-221	607	59	been	be	AUX
ejpam-221	607	60	two	two	NUM
ejpam-221	607	61	conventions	convention	NOUN
ejpam-221	607	62	for	for	ADP
ejpam-221	607	63	the	the	DET
ejpam-221	607	64	naming	naming	NOUN
ejpam-221	607	65	of	of	ADP
ejpam-221	607	66	these	these	DET
ejpam-221	607	67	semigroups	semigroup	NOUN
ejpam-221	607	68	:	:	PUNCT
ejpam-221	607	69	in	in	ADP
ejpam-221	607	70	most	most	ADJ
ejpam-221	607	71	cases	case	NOUN
ejpam-221	607	72	,	,	PUNCT
ejpam-221	607	73	the	the	DET
ejpam-221	607	74	switch	switch	NOUN
ejpam-221	607	75	from	from	ADP
ejpam-221	607	76	semigroups	semigroup	NOUN
ejpam-221	607	77	defined	define	VERB
ejpam-221	607	78	in	in	ADP
ejpam-221	607	79	terms	term	NOUN
ejpam-221	607	80	ofr∗	ofr∗	ADJ
ejpam-221	607	81	to	to	ADP
ejpam-221	607	82	those	those	PRON
ejpam-221	607	83	defined	define	VERB
ejpam-221	607	84	in	in	ADP
ejpam-221	607	85	terms	term	NOUN
ejpam-221	607	86	of	of	ADP
ejpam-221	607	87	ere	ere	PROPN
ejpam-221	607	88	has	have	AUX
ejpam-221	607	89	been	be	AUX
ejpam-221	607	90	denoted	denote	VERB
ejpam-221	607	91	by	by	ADP
ejpam-221	607	92	the	the	DET
ejpam-221	607	93	addition	addition	NOUN
ejpam-221	607	94	of	of	ADP
ejpam-221	607	95	the	the	DET
ejpam-221	607	96	prefix	prefix	NOUN
ejpam-221	607	97	‘	'	PUNCT
ejpam-221	607	98	semi-	semi-	ADJ
ejpam-221	607	99	’	'	PUNCT
ejpam-221	607	100	,	,	PUNCT
ejpam-221	607	101	whilst	whilst	SCONJ
ejpam-221	607	102	in	in	ADP
ejpam-221	607	103	one	one	NUM
ejpam-221	607	104	case	case	NOUN
ejpam-221	607	105	,	,	PUNCT
ejpam-221	607	106	it	it	PRON
ejpam-221	607	107	has	have	VERB
ejpam-221	607	108	c.	c.	PROPN
ejpam-221	607	109	hollings	holling	NOUN
ejpam-221	607	110	/	/	SYM
ejpam-221	607	111	eur	eur	PROPN
ejpam-221	607	112	.	.	PUNCT
ejpam-221	608	1	j.	j.	PROPN
ejpam-221	608	2	pure	pure	PROPN
ejpam-221	608	3	appl	appl	PROPN
ejpam-221	608	4	.	.	PROPN
ejpam-221	608	5	math	math	PROPN
ejpam-221	608	6	,	,	PUNCT
ejpam-221	608	7	2	2	NUM
ejpam-221	608	8	(	(	PUNCT
ejpam-221	608	9	2009	2009	NUM
ejpam-221	608	10	)	)	PUNCT
ejpam-221	608	11	,	,	PUNCT
ejpam-221	608	12	(	(	PUNCT
ejpam-221	608	13	21	21	NUM
ejpam-221	608	14	-	-	SYM
ejpam-221	608	15	57	57	NUM
ejpam-221	608	16	)	)	PUNCT
ejpam-221	608	17	52	52	NUM
ejpam-221	608	18	been	be	AUX
ejpam-221	608	19	signified	signify	VERB
ejpam-221	608	20	by	by	ADP
ejpam-221	608	21	the	the	DET
ejpam-221	608	22	inclusion	inclusion	NOUN
ejpam-221	608	23	of	of	ADP
ejpam-221	608	24	the	the	DET
ejpam-221	608	25	word	word	NOUN
ejpam-221	608	26	‘	'	PUNCT
ejpam-221	608	27	weakly	weakly	ADJ
ejpam-221	608	28	’	'	PUNCT
ejpam-221	608	29	.	.	PUNCT
ejpam-221	609	1	the	the	DET
ejpam-221	609	2	latter	latter	ADJ
ejpam-221	609	3	convention	convention	NOUN
ejpam-221	609	4	is	be	AUX
ejpam-221	609	5	the	the	DET
ejpam-221	609	6	more	more	ADV
ejpam-221	609	7	recent	recent	ADJ
ejpam-221	609	8	.	.	PUNCT
ejpam-221	610	1	at	at	ADP
ejpam-221	610	2	the	the	DET
ejpam-221	610	3	risk	risk	NOUN
ejpam-221	610	4	of	of	ADP
ejpam-221	610	5	causing	cause	VERB
ejpam-221	610	6	further	further	ADJ
ejpam-221	610	7	confusion	confusion	NOUN
ejpam-221	610	8	,	,	PUNCT
ejpam-221	610	9	left	leave	VERB
ejpam-221	610	10	e	e	NOUN
ejpam-221	610	11	-	-	NOUN
ejpam-221	610	12	semiabundant	semiabundant	ADJ
ejpam-221	610	13	semigroups	semigroup	NOUN
ejpam-221	610	14	,	,	PUNCT
ejpam-221	610	15	for	for	ADP
ejpam-221	610	16	example	example	NOUN
ejpam-221	610	17	,	,	PUNCT
ejpam-221	610	18	would	would	AUX
ejpam-221	610	19	probably	probably	ADV
ejpam-221	610	20	now	now	ADV
ejpam-221	610	21	be	be	AUX
ejpam-221	610	22	called	call	VERB
ejpam-221	610	23	‘	'	PUNCT
ejpam-221	610	24	weakly	weakly	ADV
ejpam-221	610	25	left	left	ADJ
ejpam-221	610	26	e	e	ADJ
ejpam-221	610	27	-	-	ADJ
ejpam-221	610	28	abundant	abundant	ADJ
ejpam-221	610	29	semigroups	semigroup	NOUN
ejpam-221	610	30	’	'	PUNCT
ejpam-221	610	31	!	!	PUNCT
ejpam-221	611	1	as	as	ADP
ejpam-221	611	2	a	a	DET
ejpam-221	611	3	final	final	ADJ
ejpam-221	611	4	comment	comment	NOUN
ejpam-221	611	5	,	,	PUNCT
ejpam-221	611	6	we	we	PRON
ejpam-221	611	7	note	note	VERB
ejpam-221	611	8	that	that	SCONJ
ejpam-221	611	9	lawson	lawson	PROPN
ejpam-221	611	10	’s	’s	PART
ejpam-221	611	11	ehresmann	ehresmann	PROPN
ejpam-221	611	12	semigroups	semigroup	NOUN
ejpam-221	611	13	appear	appear	VERB
ejpam-221	611	14	only	only	ADV
ejpam-221	611	15	in	in	ADP
ejpam-221	611	16	their	their	PRON
ejpam-221	611	17	two	two	NUM
ejpam-221	611	18	-	-	PUNCT
ejpam-221	611	19	sided	sided	ADJ
ejpam-221	611	20	form	form	NOUN
ejpam-221	611	21	in	in	ADP
ejpam-221	611	22	[	[	X
ejpam-221	611	23	47	47	NUM
ejpam-221	611	24	]	]	PUNCT
ejpam-221	611	25	but	but	CCONJ
ejpam-221	611	26	it	it	PRON
ejpam-221	611	27	is	be	AUX
ejpam-221	611	28	easy	easy	ADJ
ejpam-221	611	29	to	to	PART
ejpam-221	611	30	see	see	VERB
ejpam-221	611	31	that	that	SCONJ
ejpam-221	611	32	we	we	PRON
ejpam-221	611	33	can	can	AUX
ejpam-221	611	34	write	write	VERB
ejpam-221	611	35	down	down	ADP
ejpam-221	611	36	one	one	NUM
ejpam-221	611	37	-	-	PUNCT
ejpam-221	611	38	sided	sided	ADJ
ejpam-221	611	39	versions	version	NOUN
ejpam-221	611	40	also	also	ADV
ejpam-221	611	41	.	.	PUNCT
ejpam-221	612	1	we	we	PRON
ejpam-221	612	2	have	have	AUX
ejpam-221	612	3	omitted	omit	VERB
ejpam-221	612	4	lawson	lawson	PROPN
ejpam-221	612	5	’s	’s	PART
ejpam-221	612	6	rees	rees	PROPN
ejpam-221	612	7	semigroups	semigroup	VERB
ejpam-221	613	1	[	[	X
ejpam-221	613	2	46	46	NUM
ejpam-221	613	3	]	]	PUNCT
ejpam-221	613	4	from	from	ADP
ejpam-221	613	5	table	table	NOUN
ejpam-221	613	6	1	1	NUM
ejpam-221	613	7	,	,	PUNCT
ejpam-221	613	8	as	as	SCONJ
ejpam-221	613	9	they	they	PRON
ejpam-221	613	10	can	can	AUX
ejpam-221	613	11	not	not	PART
ejpam-221	613	12	be	be	AUX
ejpam-221	613	13	defined	define	VERB
ejpam-221	613	14	in	in	ADP
ejpam-221	613	15	a	a	DET
ejpam-221	613	16	single	single	ADJ
ejpam-221	613	17	line	line	NOUN
ejpam-221	613	18	;	;	PUNCT
ejpam-221	613	19	suffice	suffice	VERB
ejpam-221	613	20	it	it	PRON
ejpam-221	613	21	to	to	PART
ejpam-221	613	22	say	say	VERB
ejpam-221	613	23	that	that	SCONJ
ejpam-221	613	24	they	they	PRON
ejpam-221	613	25	are	be	AUX
ejpam-221	613	26	a	a	DET
ejpam-221	613	27	special	special	ADJ
ejpam-221	613	28	class	class	NOUN
ejpam-221	613	29	of	of	ADP
ejpam-221	613	30	(	(	PUNCT
ejpam-221	613	31	two	two	NUM
ejpam-221	613	32	-	-	PUNCT
ejpam-221	613	33	sided	sided	ADJ
ejpam-221	613	34	)	)	PUNCT
ejpam-221	613	35	e	e	X
ejpam-221	613	36	-	-	NOUN
ejpam-221	613	37	semiabundant	semiabundant	ADJ
ejpam-221	613	38	semigroups	semigroup	NOUN
ejpam-221	613	39	.	.	PUNCT
ejpam-221	614	1	name	name	NOUN
ejpam-221	614	2	definition	definition	NOUN
ejpam-221	614	3	left	leave	VERB
ejpam-221	614	4	ehresmann	ehresmann	PROPN
ejpam-221	614	5	left	leave	VERB
ejpam-221	614	6	e	e	NOUN
ejpam-221	614	7	-	-	NOUN
ejpam-221	614	8	semiadequate	semiadequate	ADJ
ejpam-221	614	9	with	with	ADP
ejpam-221	614	10	(	(	PUNCT
ejpam-221	614	11	cl	cl	NOUN
ejpam-221	614	12	)	)	PUNCT
ejpam-221	614	13	left	leave	VERB
ejpam-221	614	14	idempotent	idempotent	NOUN
ejpam-221	614	15	-	-	PUNCT
ejpam-221	614	16	connected	connect	VERB
ejpam-221	614	17	ehresmann	ehresmann	NOUN
ejpam-221	614	18	=	=	SYM
ejpam-221	614	19	weakly	weakly	ADV
ejpam-221	614	20	left	leave	VERB
ejpam-221	614	21	e	e	NOUN
ejpam-221	614	22	-	-	ADJ
ejpam-221	614	23	ample	ample	ADJ
ejpam-221	614	24	left	leave	VERB
ejpam-221	614	25	adequate	adequate	ADV
ejpam-221	614	26	left	leave	VERB
ejpam-221	614	27	abundant	abundant	ADJ
ejpam-221	614	28	with	with	ADP
ejpam-221	614	29	e(s	e(s	PROPN
ejpam-221	614	30	)	)	PUNCT
ejpam-221	614	31	a	a	DET
ejpam-221	614	32	semilattice	semilattice	NOUN
ejpam-221	614	33	left	leave	VERB
ejpam-221	614	34	e	e	NOUN
ejpam-221	614	35	-	-	ADJ
ejpam-221	614	36	adequate	adequate	ADJ
ejpam-221	614	37	left	leave	VERB
ejpam-221	614	38	e	e	NOUN
ejpam-221	614	39	-	-	NOUN
ejpam-221	614	40	abundant	abundant	ADJ
ejpam-221	614	41	with	with	ADP
ejpam-221	614	42	e	e	NOUN
ejpam-221	614	43	a	a	DET
ejpam-221	614	44	semilattice	semilattice	NOUN
ejpam-221	614	45	left	leave	VERB
ejpam-221	614	46	ample	ample	ADJ
ejpam-221	614	47	left	leave	VERB
ejpam-221	614	48	adequate	adequate	ADJ
ejpam-221	614	49	with	with	ADP
ejpam-221	614	50	(	(	PUNCT
ejpam-221	614	51	la	la	ADJ
ejpam-221	614	52	)	)	PUNCT
ejpam-221	614	53	left	leave	VERB
ejpam-221	614	54	e	e	NOUN
ejpam-221	614	55	-	-	NOUN
ejpam-221	614	56	semiadequate	semiadequate	ADJ
ejpam-221	614	57	left	left	ADJ
ejpam-221	614	58	e	e	NOUN
ejpam-221	614	59	-	-	NOUN
ejpam-221	614	60	semiabundant	semiabundant	ADJ
ejpam-221	614	61	with	with	ADP
ejpam-221	614	62	e	e	PROPN
ejpam-221	614	63	a	a	DET
ejpam-221	614	64	semilattice	semilattice	NOUN
ejpam-221	614	65	left	leave	VERB
ejpam-221	614	66	pp	pp	ADP
ejpam-221	614	67	=	=	PUNCT
ejpam-221	614	68	left	leave	VERB
ejpam-221	614	69	abundant	abundant	ADJ
ejpam-221	614	70	left	left	ADJ
ejpam-221	614	71	qleft	qleft	ADJ
ejpam-221	614	72	semiabundant	semiabundant	NOUN
ejpam-221	614	73	with	with	ADP
ejpam-221	614	74	e(s	e(s	PROPN
ejpam-221	614	75	)	)	PUNCT
ejpam-221	614	76	a	a	DET
ejpam-221	614	77	band	band	NOUN
ejpam-221	614	78	left	leave	VERB
ejpam-221	614	79	quasi	quasi	ADJ
ejpam-221	614	80	-	-	ADJ
ejpam-221	614	81	adequate	adequate	ADJ
ejpam-221	614	82	left	leave	VERB
ejpam-221	614	83	abundant	abundant	ADJ
ejpam-221	614	84	with	with	ADP
ejpam-221	614	85	e(s	e(s	PROPN
ejpam-221	614	86	)	)	PUNCT
ejpam-221	614	87	a	a	DET
ejpam-221	614	88	band	band	NOUN
ejpam-221	614	89	left	leave	VERB
ejpam-221	614	90	restriction	restriction	NOUN
ejpam-221	614	91	=	=	SYM
ejpam-221	614	92	weakly	weakly	ADV
ejpam-221	614	93	left	leave	VERB
ejpam-221	614	94	e	e	NOUN
ejpam-221	614	95	-	-	ADJ
ejpam-221	614	96	ample	ample	ADJ
ejpam-221	614	97	left	left	ADJ
ejpam-221	614	98	semiadequate	semiadequate	NOUN
ejpam-221	614	99	left	leave	VERB
ejpam-221	614	100	semiabundant	semiabundant	NOUN
ejpam-221	614	101	with	with	ADP
ejpam-221	614	102	e(s	e(s	PROPN
ejpam-221	614	103	)	)	PUNCT
ejpam-221	614	104	a	a	DET
ejpam-221	614	105	semilattice	semilattice	NOUN
ejpam-221	614	106	left	leave	VERB
ejpam-221	614	107	type	type	NOUN
ejpam-221	614	108	a	a	PRON
ejpam-221	614	109	=	=	PUNCT
ejpam-221	614	110	left	leave	VERB
ejpam-221	614	111	ample	ample	ADJ
ejpam-221	614	112	left	left	ADJ
ejpam-221	614	113	type	type	NOUN
ejpam-221	614	114	t	t	NOUN
ejpam-221	614	115	=	=	PUNCT
ejpam-221	614	116	weakly	weakly	ADV
ejpam-221	614	117	left	leave	VERB
ejpam-221	614	118	ample	ample	ADJ
ejpam-221	614	119	weakly	weakly	ADJ
ejpam-221	614	120	left	left	ADJ
ejpam-221	614	121	ample	ample	ADJ
ejpam-221	614	122	left	left	ADJ
ejpam-221	614	123	semiadequate	semiadequate	NOUN
ejpam-221	614	124	with	with	ADP
ejpam-221	614	125	(	(	PUNCT
ejpam-221	614	126	cl	cl	NOUN
ejpam-221	614	127	)	)	PUNCT
ejpam-221	614	128	and	and	CCONJ
ejpam-221	614	129	(	(	PUNCT
ejpam-221	614	130	la	la	ADJ
ejpam-221	614	131	)	)	PUNCT
ejpam-221	614	132	weakly	weakly	ADV
ejpam-221	614	133	left	leave	VERB
ejpam-221	614	134	e	e	NOUN
ejpam-221	614	135	-	-	ADJ
ejpam-221	614	136	ample	ample	ADJ
ejpam-221	614	137	left	leave	VERB
ejpam-221	614	138	ehresmann	ehresmann	PROPN
ejpam-221	614	139	with	with	ADP
ejpam-221	614	140	(	(	PUNCT
ejpam-221	614	141	la)table	la)table	ADJ
ejpam-221	614	142	1	1	NUM
ejpam-221	614	143	:	:	PUNCT
ejpam-221	614	144	guide	guide	VERB
ejpam-221	614	145	to	to	ADP
ejpam-221	614	146	the	the	DET
ejpam-221	614	147	terminology	terminology	NOUN
ejpam-221	614	148	of	of	ADP
ejpam-221	614	149	se	se	PROPN
ejpam-221	614	150	tions	tion	NOUN
ejpam-221	614	151	1	1	NUM
ejpam-221	614	152	and	and	CCONJ
ejpam-221	614	153	2	2	NUM
ejpam-221	614	154	references	reference	NOUN
ejpam-221	614	155	53	53	NUM
ejpam-221	614	156	acknowledgements	acknowledgement	NOUN
ejpam-221	614	157	.	.	PUNCT
ejpam-221	615	1	this	this	DET
ejpam-221	615	2	article	article	NOUN
ejpam-221	615	3	was	be	AUX
ejpam-221	615	4	completed	complete	VERB
ejpam-221	615	5	at	at	ADP
ejpam-221	615	6	caul	caul	NOUN
ejpam-221	615	7	under	under	ADP
ejpam-221	615	8	fct	fct	ADJ
ejpam-221	615	9	post	post	ADJ
ejpam-221	615	10	-	-	ADJ
ejpam-221	615	11	doctoral	doctoral	ADJ
ejpam-221	615	12	research	research	NOUN
ejpam-221	615	13	grant	grant	NOUN
ejpam-221	615	14	sfrh	sfrh	NOUN
ejpam-221	615	15	/	/	SYM
ejpam-221	615	16	bpd/34698/2007	bpd/34698/2007	ADJ
ejpam-221	615	17	.	.	PUNCT
ejpam-221	616	1	my	my	PRON
ejpam-221	616	2	thanks	thank	NOUN
ejpam-221	616	3	are	be	AUX
ejpam-221	616	4	due	due	ADJ
ejpam-221	616	5	to	to	ADP
ejpam-221	616	6	victoria	victoria	PROPN
ejpam-221	616	7	gould	gould	PROPN
ejpam-221	616	8	for	for	ADP
ejpam-221	616	9	many	many	ADJ
ejpam-221	616	10	useful	useful	ADJ
ejpam-221	616	11	comments	comment	NOUN
ejpam-221	616	12	.	.	PUNCT
ejpam-221	617	1	references	reference	NOUN
ejpam-221	617	2	[	[	X
ejpam-221	617	3	1	1	X
ejpam-221	617	4	]	]	PUNCT
ejpam-221	617	5	s.	s.	PROPN
ejpam-221	617	6	armstrong	armstrong	PROPN
ejpam-221	617	7	.	.	PUNCT
ejpam-221	618	1	the	the	DET
ejpam-221	618	2	structure	structure	NOUN
ejpam-221	618	3	of	of	ADP
ejpam-221	618	4	type	type	NOUN
ejpam-221	618	5	a	a	DET
ejpam-221	618	6	semigroups	semigroup	NOUN
ejpam-221	618	7	.	.	PUNCT
ejpam-221	619	1	semigroup	semigroup	PROPN
ejpam-221	619	2	forum	forum	PROPN
ejpam-221	619	3	,	,	PUNCT
ejpam-221	619	4	29:319–336	29:319–336	PROPN
ejpam-221	619	5	,	,	PUNCT
ejpam-221	619	6	1984	1984	NUM
ejpam-221	619	7	.	.	PUNCT
ejpam-221	620	1	[	[	X
ejpam-221	620	2	2	2	NUM
ejpam-221	620	3	]	]	PUNCT
ejpam-221	620	4	a.	a.	NOUN
ejpam-221	620	5	batbedat	batbedat	NOUN
ejpam-221	620	6	.	.	PUNCT
ejpam-221	621	1	γ	γ	PROPN
ejpam-221	621	2	-	-	PUNCT
ejpam-221	621	3	demi	demi	NOUN
ejpam-221	621	4	-	-	PUNCT
ejpam-221	621	5	groupes	groupe	NOUN
ejpam-221	621	6	,	,	PUNCT
ejpam-221	621	7	demi	demi	NOUN
ejpam-221	621	8	-	-	PUNCT
ejpam-221	621	9	modules	module	NOUN
ejpam-221	621	10	,	,	PUNCT
ejpam-221	621	11	produit	produit	NOUN
ejpam-221	621	12	demi	demi	NOUN
ejpam-221	621	13	-	-	PUNCT
ejpam-221	621	14	direct	direct	ADJ
ejpam-221	621	15	.	.	PUNCT
ejpam-221	622	1	in	in	ADP
ejpam-221	622	2	semigroups	semigroups	PROPN
ejpam-221	622	3	proceedings	proceeding	NOUN
ejpam-221	622	4	:	:	PUNCT
ejpam-221	622	5	oberwolfach	oberwolfach	ADV
ejpam-221	622	6	1979	1979	NUM
ejpam-221	622	7	,	,	PUNCT
ejpam-221	622	8	lecture	lecture	NOUN
ejpam-221	622	9	notes	note	NOUN
ejpam-221	622	10	in	in	ADP
ejpam-221	622	11	mathematics	mathematic	NOUN
ejpam-221	622	12	855	855	NUM
ejpam-221	622	13	,	,	PUNCT
ejpam-221	622	14	pages	page	NOUN
ejpam-221	622	15	1–18	1–18	PROPN
ejpam-221	622	16	.	.	PUNCT
ejpam-221	622	17	springer	springer	NOUN
ejpam-221	622	18	-	-	PUNCT
ejpam-221	622	19	verlag	verlag	PROPN
ejpam-221	622	20	,	,	PUNCT
ejpam-221	622	21	1981	1981	NUM
ejpam-221	622	22	.	.	PUNCT
ejpam-221	623	1	[	[	X
ejpam-221	623	2	3	3	NUM
ejpam-221	623	3	]	]	PUNCT
ejpam-221	623	4	a.	a.	NOUN
ejpam-221	623	5	batbedat	batbedat	NOUN
ejpam-221	623	6	and	and	CCONJ
ejpam-221	623	7	j.	j.	PROPN
ejpam-221	623	8	b.	b.	PROPN
ejpam-221	623	9	fountain	fountain	PROPN
ejpam-221	623	10	.	.	PUNCT
ejpam-221	624	1	connections	connection	NOUN
ejpam-221	624	2	between	between	ADP
ejpam-221	624	3	left	leave	VERB
ejpam-221	624	4	adequate	adequate	ADJ
ejpam-221	624	5	semigroups	semigroup	NOUN
ejpam-221	624	6	and	and	CCONJ
ejpam-221	624	7	γsemigroups	γsemigroup	NOUN
ejpam-221	624	8	.	.	PUNCT
ejpam-221	625	1	semigroup	semigroup	PROPN
ejpam-221	625	2	forum	forum	PROPN
ejpam-221	625	3	,	,	PUNCT
ejpam-221	625	4	22:59–65	22:59–65	NUM
ejpam-221	625	5	,	,	PUNCT
ejpam-221	625	6	1981	1981	NUM
ejpam-221	625	7	.	.	PUNCT
ejpam-221	626	1	[	[	X
ejpam-221	626	2	4	4	NUM
ejpam-221	626	3	]	]	PUNCT
ejpam-221	626	4	a.	a.	NOUN
ejpam-221	626	5	h.	h.	PROPN
ejpam-221	626	6	clifford	clifford	PROPN
ejpam-221	626	7	.	.	PUNCT
ejpam-221	627	1	semigroups	semigroup	NOUN
ejpam-221	627	2	admitting	admit	VERB
ejpam-221	627	3	relative	relative	ADJ
ejpam-221	627	4	inverses	inverse	NOUN
ejpam-221	627	5	.	.	PUNCT
ejpam-221	628	1	ann	ann	PROPN
ejpam-221	628	2	.	.	PUNCT
ejpam-221	628	3	math	math	PROPN
ejpam-221	628	4	.	.	PUNCT
ejpam-221	629	1	(	(	PUNCT
ejpam-221	629	2	2	2	NUM
ejpam-221	629	3	)	)	PUNCT
ejpam-221	629	4	,	,	PUNCT
ejpam-221	629	5	42:1037–1049	42:1037–1049	NUM
ejpam-221	629	6	,	,	PUNCT
ejpam-221	629	7	1941	1941	NUM
ejpam-221	629	8	.	.	PUNCT
ejpam-221	630	1	[	[	X
ejpam-221	630	2	5	5	NUM
ejpam-221	630	3	]	]	PUNCT
ejpam-221	630	4	a.	a.	NOUN
ejpam-221	630	5	h.	h.	PROPN
ejpam-221	630	6	clifford	clifford	PROPN
ejpam-221	630	7	and	and	CCONJ
ejpam-221	630	8	g.	g.	PROPN
ejpam-221	630	9	b.	b.	PROPN
ejpam-221	630	10	preston	preston	PROPN
ejpam-221	630	11	.	.	PUNCT
ejpam-221	631	1	the	the	DET
ejpam-221	631	2	algebraic	algebraic	PROPN
ejpam-221	631	3	theory	theory	NOUN
ejpam-221	631	4	of	of	ADP
ejpam-221	631	5	semigroups	semigroup	NOUN
ejpam-221	631	6	,	,	PUNCT
ejpam-221	631	7	volume	volume	NOUN
ejpam-221	631	8	1	1	NUM
ejpam-221	631	9	of	of	ADP
ejpam-221	631	10	mathematical	mathematical	ADJ
ejpam-221	631	11	surveys	survey	NOUN
ejpam-221	631	12	,	,	PUNCT
ejpam-221	631	13	no	no	INTJ
ejpam-221	631	14	.	.	NOUN
ejpam-221	631	15	7	7	X
ejpam-221	631	16	.	.	X
ejpam-221	631	17	american	american	PROPN
ejpam-221	631	18	mathematical	mathematical	PROPN
ejpam-221	631	19	society	society	NOUN
ejpam-221	631	20	,	,	PUNCT
ejpam-221	631	21	providence	providence	NOUN
ejpam-221	631	22	,	,	PUNCT
ejpam-221	631	23	ri	ri	PROPN
ejpam-221	631	24	,	,	PUNCT
ejpam-221	631	25	1961	1961	NUM
ejpam-221	631	26	.	.	PUNCT
ejpam-221	632	1	[	[	X
ejpam-221	632	2	6	6	NUM
ejpam-221	632	3	]	]	PUNCT
ejpam-221	632	4	j.	j.	PROPN
ejpam-221	632	5	r.	r.	PROPN
ejpam-221	632	6	b.	b.	PROPN
ejpam-221	632	7	cockett	cockett	PROPN
ejpam-221	632	8	and	and	CCONJ
ejpam-221	632	9	s.	s.	PROPN
ejpam-221	632	10	lack	lack	PROPN
ejpam-221	632	11	.	.	PUNCT
ejpam-221	633	1	restriction	restriction	NOUN
ejpam-221	633	2	categories	category	NOUN
ejpam-221	634	1	i	i	PRON
ejpam-221	634	2	:	:	PUNCT
ejpam-221	634	3	categories	category	NOUN
ejpam-221	634	4	of	of	ADP
ejpam-221	634	5	partial	partial	ADJ
ejpam-221	634	6	maps	map	NOUN
ejpam-221	634	7	.	.	PUNCT
ejpam-221	635	1	theoret	theoret	VERB
ejpam-221	635	2	.	.	PUNCT
ejpam-221	636	1	comput	comput	NOUN
ejpam-221	636	2	.	.	PUNCT
ejpam-221	637	1	sci	sci	PROPN
ejpam-221	637	2	.	.	PROPN
ejpam-221	637	3	,	,	PUNCT
ejpam-221	637	4	270:223–259	270:223–259	NUM
ejpam-221	637	5	,	,	PUNCT
ejpam-221	637	6	2002	2002	NUM
ejpam-221	637	7	.	.	PUNCT
ejpam-221	638	1	[	[	X
ejpam-221	638	2	7	7	X
ejpam-221	638	3	]	]	X
ejpam-221	638	4	j.	j.	PROPN
ejpam-221	638	5	r.	r.	PROPN
ejpam-221	638	6	b.	b.	PROPN
ejpam-221	638	7	cockett	cockett	PROPN
ejpam-221	638	8	and	and	CCONJ
ejpam-221	638	9	e.	e.	PROPN
ejpam-221	638	10	manes	mane	NOUN
ejpam-221	638	11	.	.	PUNCT
ejpam-221	639	1	boolean	boolean	ADJ
ejpam-221	639	2	and	and	CCONJ
ejpam-221	639	3	classical	classical	ADJ
ejpam-221	639	4	restriction	restriction	NOUN
ejpam-221	639	5	categories	category	NOUN
ejpam-221	639	6	.	.	PUNCT
ejpam-221	640	1	submitted	submit	VERB
ejpam-221	640	2	.	.	PUNCT
ejpam-221	641	1	[	[	X
ejpam-221	641	2	8	8	NUM
ejpam-221	641	3	]	]	X
ejpam-221	642	1	p.	p.	NOUN
ejpam-221	642	2	m.	m.	NOUN
ejpam-221	642	3	cohn	cohn	PROPN
ejpam-221	642	4	.	.	PUNCT
ejpam-221	642	5	embeddings	embedding	NOUN
ejpam-221	642	6	in	in	ADP
ejpam-221	642	7	semigroups	semigroup	NOUN
ejpam-221	642	8	with	with	ADP
ejpam-221	642	9	one	one	NUM
ejpam-221	642	10	-	-	PUNCT
ejpam-221	642	11	sided	sided	ADJ
ejpam-221	642	12	division	division	NOUN
ejpam-221	642	13	.	.	PUNCT
ejpam-221	643	1	j.	j.	PROPN
ejpam-221	643	2	london	london	PROPN
ejpam-221	643	3	math	math	PROPN
ejpam-221	643	4	.	.	PUNCT
ejpam-221	644	1	soc	soc	PROPN
ejpam-221	644	2	.	.	PUNCT
ejpam-221	644	3	,	,	PUNCT
ejpam-221	644	4	31:169	31:169	NUM
ejpam-221	644	5	–	–	PUNCT
ejpam-221	644	6	181	181	NUM
ejpam-221	644	7	,	,	PUNCT
ejpam-221	644	8	1956	1956	NUM
ejpam-221	644	9	.	.	PUNCT
ejpam-221	645	1	[	[	X
ejpam-221	645	2	9	9	NUM
ejpam-221	645	3	]	]	PUNCT
ejpam-221	645	4	c.	c.	PROPN
ejpam-221	645	5	m.	m.	PROPN
ejpam-221	645	6	de	de	PROPN
ejpam-221	645	7	barros	barros	PROPN
ejpam-221	645	8	.	.	PUNCT
ejpam-221	646	1	sur	sur	PROPN
ejpam-221	646	2	les	les	PROPN
ejpam-221	646	3	catégories	catégories	PROPN
ejpam-221	646	4	ordonnées	ordonnées	PROPN
ejpam-221	646	5	régulières	régulière	NOUN
ejpam-221	646	6	.	.	PUNCT
ejpam-221	647	1	cah	cah	PROPN
ejpam-221	647	2	.	.	PUNCT
ejpam-221	648	1	topol	topol	PROPN
ejpam-221	648	2	.	.	PUNCT
ejpam-221	649	1	géom	géom	PROPN
ejpam-221	649	2	.	.	PUNCT
ejpam-221	650	1	différ	différ	PROPN
ejpam-221	650	2	.	.	PUNCT
ejpam-221	651	1	catég	catég	PROPN
ejpam-221	651	2	.	.	PUNCT
ejpam-221	652	1	,	,	PUNCT
ejpam-221	652	2	11:23	11:23	NUM
ejpam-221	652	3	–	–	PUNCT
ejpam-221	652	4	55	55	NUM
ejpam-221	652	5	,	,	PUNCT
ejpam-221	652	6	1969	1969	NUM
ejpam-221	652	7	.	.	PUNCT
ejpam-221	653	1	[	[	X
ejpam-221	653	2	10	10	NUM
ejpam-221	653	3	]	]	PUNCT
ejpam-221	653	4	m.	m.	NOUN
ejpam-221	653	5	p.	p.	PROPN
ejpam-221	653	6	dorofeeva	dorofeeva	PROPN
ejpam-221	653	7	.	.	PUNCT
ejpam-221	654	1	hereditary	hereditary	ADJ
ejpam-221	654	2	and	and	CCONJ
ejpam-221	654	3	semi	semi	ADJ
ejpam-221	654	4	-	-	ADJ
ejpam-221	654	5	hereditary	hereditary	ADJ
ejpam-221	654	6	monoids	monoid	NOUN
ejpam-221	654	7	.	.	PUNCT
ejpam-221	655	1	semigroup	semigroup	PROPN
ejpam-221	655	2	forum	forum	PROPN
ejpam-221	655	3	,	,	PUNCT
ejpam-221	655	4	4:301–311	4:301–311	NOUN
ejpam-221	655	5	,	,	PUNCT
ejpam-221	655	6	1972	1972	NUM
ejpam-221	655	7	.	.	PUNCT
ejpam-221	656	1	[	[	X
ejpam-221	656	2	11	11	NUM
ejpam-221	656	3	]	]	X
ejpam-221	656	4	c.	c.	PROPN
ejpam-221	656	5	ehresmann	ehresmann	PROPN
ejpam-221	656	6	.	.	PUNCT
ejpam-221	657	1	gattungen	gattungen	PROPN
ejpam-221	657	2	von	von	PROPN
ejpam-221	657	3	lokalen	lokalen	PROPN
ejpam-221	657	4	strukturen	strukturen	PROPN
ejpam-221	657	5	.	.	PUNCT
ejpam-221	658	1	jahresbericht	jahresbericht	PROPN
ejpam-221	658	2	der	der	PROPN
ejpam-221	658	3	deutschen	deutschen	PROPN
ejpam-221	658	4	mathematikervereinigung	mathematikervereinigung	PROPN
ejpam-221	658	5	,	,	PUNCT
ejpam-221	658	6	60:49–77	60:49–77	NUM
ejpam-221	658	7	,	,	PUNCT
ejpam-221	658	8	1957	1957	NUM
ejpam-221	658	9	.	.	PUNCT
ejpam-221	659	1	[	[	X
ejpam-221	659	2	12	12	NUM
ejpam-221	659	3	]	]	X
ejpam-221	659	4	c.	c.	PROPN
ejpam-221	659	5	ehresmann	ehresmann	PROPN
ejpam-221	659	6	.	.	PUNCT
ejpam-221	660	1	catégories	catégorie	NOUN
ejpam-221	660	2	inductives	inductive	VERB
ejpam-221	660	3	et	et	PROPN
ejpam-221	660	4	pseudogroupes	pseudogroupe	NOUN
ejpam-221	660	5	.	.	PUNCT
ejpam-221	661	1	annales	annales	PROPN
ejpam-221	661	2	de	de	PROPN
ejpam-221	661	3	l’institut	l’institut	PROPN
ejpam-221	661	4	fourier	fourier	NOUN
ejpam-221	661	5	,	,	PUNCT
ejpam-221	661	6	grenoble	grenoble	ADJ
ejpam-221	661	7	,	,	PUNCT
ejpam-221	661	8	10:307–336	10:307–336	PROPN
ejpam-221	661	9	,	,	PUNCT
ejpam-221	661	10	1960	1960	NUM
ejpam-221	661	11	.	.	PUNCT
ejpam-221	662	1	[	[	X
ejpam-221	662	2	13	13	NUM
ejpam-221	662	3	]	]	X
ejpam-221	662	4	c.	c.	PROPN
ejpam-221	662	5	ehresmann	ehresmann	PROPN
ejpam-221	662	6	.	.	PUNCT
ejpam-221	663	1	catégories	catégorie	NOUN
ejpam-221	663	2	et	et	NOUN
ejpam-221	663	3	structures	structure	NOUN
ejpam-221	663	4	.	.	PUNCT
ejpam-221	664	1	dunod	dunod	PROPN
ejpam-221	664	2	,	,	PUNCT
ejpam-221	664	3	paris	paris	PROPN
ejpam-221	664	4	,	,	PUNCT
ejpam-221	664	5	1965	1965	NUM
ejpam-221	664	6	.	.	PUNCT
ejpam-221	665	1	[	[	X
ejpam-221	665	2	14	14	NUM
ejpam-221	665	3	]	]	X
ejpam-221	665	4	c.	c.	PROPN
ejpam-221	665	5	ehresmann	ehresmann	PROPN
ejpam-221	665	6	.	.	PUNCT
ejpam-221	666	1	oeuvres	oeuvre	NOUN
ejpam-221	666	2	complètes	complète	NOUN
ejpam-221	666	3	et	et	NOUN
ejpam-221	666	4	commentèes	commentèe	NOUN
ejpam-221	666	5	.	.	PUNCT
ejpam-221	667	1	in	in	ADP
ejpam-221	667	2	a.	a.	PROPN
ejpam-221	667	3	c.	c.	PROPN
ejpam-221	667	4	ehresmann	ehresmann	PROPN
ejpam-221	667	5	,	,	PUNCT
ejpam-221	667	6	editor	editor	NOUN
ejpam-221	667	7	,	,	PUNCT
ejpam-221	667	8	supplements	supplement	NOUN
ejpam-221	667	9	to	to	ADP
ejpam-221	667	10	cahiers	cahier	NOUN
ejpam-221	667	11	de	de	ADP
ejpam-221	667	12	topolgie	topolgie	X
ejpam-221	667	13	et	et	PROPN
ejpam-221	667	14	géométrie	géométrie	VERB
ejpam-221	667	15	différentielle	différentielle	PROPN
ejpam-221	667	16	.	.	PUNCT
ejpam-221	668	1	amiens	amien	NOUN
ejpam-221	668	2	,	,	PUNCT
ejpam-221	668	3	1980	1980	NUM
ejpam-221	668	4	-	-	SYM
ejpam-221	668	5	83	83	NUM
ejpam-221	668	6	.	.	PUNCT
ejpam-221	669	1	[	[	X
ejpam-221	669	2	15	15	NUM
ejpam-221	669	3	]	]	X
ejpam-221	669	4	a.	a.	PROPN
ejpam-221	669	5	el	el	PROPN
ejpam-221	669	6	-	-	PUNCT
ejpam-221	669	7	qallali	qallali	PROPN
ejpam-221	669	8	.	.	PUNCT
ejpam-221	670	1	structure	structure	NOUN
ejpam-221	670	2	theory	theory	NOUN
ejpam-221	670	3	for	for	ADP
ejpam-221	670	4	abundant	abundant	ADJ
ejpam-221	670	5	and	and	CCONJ
ejpam-221	670	6	related	related	ADJ
ejpam-221	670	7	semigroups	semigroup	NOUN
ejpam-221	670	8	.	.	PUNCT
ejpam-221	671	1	phd	phd	NOUN
ejpam-221	671	2	thesis	thesis	NOUN
ejpam-221	671	3	,	,	PUNCT
ejpam-221	671	4	university	university	PROPN
ejpam-221	671	5	of	of	ADP
ejpam-221	671	6	york	york	PROPN
ejpam-221	671	7	,	,	PUNCT
ejpam-221	671	8	1980	1980	NUM
ejpam-221	671	9	.	.	PUNCT
ejpam-221	672	1	[	[	X
ejpam-221	672	2	16	16	NUM
ejpam-221	672	3	]	]	X
ejpam-221	672	4	a.	a.	PROPN
ejpam-221	672	5	el	el	PROPN
ejpam-221	672	6	-	-	PUNCT
ejpam-221	672	7	qallali	qallali	PROPN
ejpam-221	672	8	.	.	PUNCT
ejpam-221	673	1	quasi	quasi	ADJ
ejpam-221	673	2	-	-	ADJ
ejpam-221	673	3	adequate	adequate	ADJ
ejpam-221	673	4	semigroups	semigroups	PROPN
ejpam-221	673	5	ii	ii	PROPN
ejpam-221	673	6	.	.	PUNCT
ejpam-221	673	7	semigroup	semigroup	PROPN
ejpam-221	673	8	forum	forum	PROPN
ejpam-221	673	9	,	,	PUNCT
ejpam-221	673	10	44:273–282	44:273–282	PROPN
ejpam-221	673	11	,	,	PUNCT
ejpam-221	673	12	1992	1992	NUM
ejpam-221	673	13	.	.	PUNCT
ejpam-221	674	1	references	reference	NOUN
ejpam-221	674	2	54	54	NUM
ejpam-221	674	3	[	[	X
ejpam-221	674	4	17	17	NUM
ejpam-221	674	5	]	]	X
ejpam-221	674	6	a.	a.	PROPN
ejpam-221	674	7	el	el	PROPN
ejpam-221	674	8	-	-	PROPN
ejpam-221	674	9	qallali	qallali	PROPN
ejpam-221	674	10	and	and	CCONJ
ejpam-221	674	11	j.	j.	PROPN
ejpam-221	674	12	b.	b.	PROPN
ejpam-221	674	13	fountain	fountain	PROPN
ejpam-221	674	14	.	.	PUNCT
ejpam-221	675	1	quasi	quasi	ADJ
ejpam-221	675	2	-	-	ADJ
ejpam-221	675	3	adequate	adequate	ADJ
ejpam-221	675	4	semigroups	semigroup	NOUN
ejpam-221	675	5	.	.	PUNCT
ejpam-221	676	1	proc	proc	PROPN
ejpam-221	676	2	.	.	PUNCT
ejpam-221	677	1	roy	roy	PROPN
ejpam-221	677	2	.	.	PROPN
ejpam-221	677	3	soc	soc	PROPN
ejpam-221	677	4	.	.	PUNCT
ejpam-221	678	1	edinburgh	edinburgh	PROPN
ejpam-221	678	2	sect	sect	PROPN
ejpam-221	678	3	.	.	PUNCT
ejpam-221	679	1	a	a	DET
ejpam-221	679	2	,	,	PUNCT
ejpam-221	679	3	91:91–99	91:91–99	NUM
ejpam-221	679	4	,	,	PUNCT
ejpam-221	679	5	1981	1981	NUM
ejpam-221	679	6	.	.	PUNCT
ejpam-221	680	1	[	[	X
ejpam-221	680	2	18	18	NUM
ejpam-221	680	3	]	]	X
ejpam-221	680	4	e.	e.	PROPN
ejpam-221	680	5	h.	h.	PROPN
ejpam-221	680	6	feller	feller	PROPN
ejpam-221	680	7	and	and	CCONJ
ejpam-221	680	8	r.	r.	PROPN
ejpam-221	680	9	l.	l.	PROPN
ejpam-221	680	10	gantos	gantos	PROPN
ejpam-221	680	11	.	.	PUNCT
ejpam-221	681	1	completely	completely	ADV
ejpam-221	681	2	injective	injective	ADJ
ejpam-221	681	3	semigroups	semigroup	NOUN
ejpam-221	681	4	.	.	PUNCT
ejpam-221	682	1	pacific	pacific	PROPN
ejpam-221	682	2	j.	j.	PROPN
ejpam-221	682	3	math	math	PROPN
ejpam-221	682	4	.	.	PUNCT
ejpam-221	682	5	,	,	PUNCT
ejpam-221	683	1	31:359–366	31:359–366	PROPN
ejpam-221	683	2	,	,	PUNCT
ejpam-221	683	3	1969	1969	NUM
ejpam-221	683	4	.	.	PUNCT
ejpam-221	684	1	[	[	X
ejpam-221	684	2	19	19	NUM
ejpam-221	684	3	]	]	X
ejpam-221	684	4	e.	e.	PROPN
ejpam-221	684	5	h.	h.	PROPN
ejpam-221	684	6	feller	feller	PROPN
ejpam-221	684	7	and	and	CCONJ
ejpam-221	684	8	r.	r.	PROPN
ejpam-221	684	9	l.	l.	PROPN
ejpam-221	684	10	gantos	gantos	PROPN
ejpam-221	684	11	.	.	PUNCT
ejpam-221	685	1	completely	completely	ADV
ejpam-221	685	2	injective	injective	ADJ
ejpam-221	685	3	semigroups	semigroup	NOUN
ejpam-221	685	4	with	with	ADP
ejpam-221	685	5	central	central	ADJ
ejpam-221	685	6	idempotents	idempotent	NOUN
ejpam-221	685	7	.	.	PUNCT
ejpam-221	686	1	glasgow	glasgow	PROPN
ejpam-221	686	2	math	math	NOUN
ejpam-221	686	3	.	.	PUNCT
ejpam-221	687	1	j.	j.	PROPN
ejpam-221	687	2	,	,	PUNCT
ejpam-221	687	3	10:16–20	10:16–20	PROPN
ejpam-221	687	4	,	,	PUNCT
ejpam-221	687	5	1969	1969	NUM
ejpam-221	687	6	.	.	PUNCT
ejpam-221	688	1	[	[	X
ejpam-221	688	2	20	20	NUM
ejpam-221	688	3	]	]	PUNCT
ejpam-221	688	4	e.	e.	PROPN
ejpam-221	688	5	h.	h.	PROPN
ejpam-221	688	6	feller	feller	PROPN
ejpam-221	688	7	and	and	CCONJ
ejpam-221	688	8	r.	r.	PROPN
ejpam-221	688	9	l.	l.	PROPN
ejpam-221	688	10	gantos	gantos	PROPN
ejpam-221	688	11	.	.	PUNCT
ejpam-221	689	1	completely	completely	ADV
ejpam-221	689	2	right	right	ADJ
ejpam-221	689	3	injective	injective	ADJ
ejpam-221	689	4	semigroups	semigroup	NOUN
ejpam-221	689	5	that	that	PRON
ejpam-221	689	6	are	be	AUX
ejpam-221	689	7	unions	union	NOUN
ejpam-221	689	8	of	of	ADP
ejpam-221	689	9	groups	group	NOUN
ejpam-221	689	10	.	.	PUNCT
ejpam-221	690	1	glasgow	glasgow	PROPN
ejpam-221	690	2	math	math	PROPN
ejpam-221	690	3	.	.	PUNCT
ejpam-221	691	1	j.	j.	PROPN
ejpam-221	691	2	,	,	PUNCT
ejpam-221	691	3	12:43–49	12:43–49	NUM
ejpam-221	691	4	,	,	PUNCT
ejpam-221	691	5	1971	1971	NUM
ejpam-221	691	6	.	.	PUNCT
ejpam-221	692	1	[	[	X
ejpam-221	692	2	21	21	NUM
ejpam-221	692	3	]	]	X
ejpam-221	692	4	j.	j.	PROPN
ejpam-221	692	5	fountain	fountain	PROPN
ejpam-221	692	6	.	.	PUNCT
ejpam-221	693	1	completely	completely	ADV
ejpam-221	693	2	right	right	ADJ
ejpam-221	693	3	injective	injective	ADJ
ejpam-221	693	4	semigroups	semigroup	NOUN
ejpam-221	693	5	.	.	PUNCT
ejpam-221	694	1	proc	proc	PROPN
ejpam-221	694	2	.	.	PUNCT
ejpam-221	695	1	london	london	PROPN
ejpam-221	695	2	math	math	PROPN
ejpam-221	695	3	.	.	PUNCT
ejpam-221	696	1	soc	soc	PROPN
ejpam-221	696	2	.	.	PUNCT
ejpam-221	697	1	(	(	PUNCT
ejpam-221	697	2	3	3	NUM
ejpam-221	697	3	)	)	PUNCT
ejpam-221	697	4	,	,	PUNCT
ejpam-221	697	5	28:28–44	28:28–44	NUM
ejpam-221	697	6	,	,	PUNCT
ejpam-221	697	7	1974	1974	NUM
ejpam-221	697	8	.	.	PUNCT
ejpam-221	698	1	[	[	X
ejpam-221	698	2	22	22	NUM
ejpam-221	698	3	]	]	X
ejpam-221	698	4	j.	j.	PROPN
ejpam-221	698	5	fountain	fountain	PROPN
ejpam-221	698	6	.	.	PUNCT
ejpam-221	699	1	a	a	DET
ejpam-221	699	2	class	class	NOUN
ejpam-221	699	3	of	of	ADP
ejpam-221	699	4	right	right	ADJ
ejpam-221	699	5	pp	pp	ADP
ejpam-221	699	6	monoids	monoid	NOUN
ejpam-221	699	7	.	.	PUNCT
ejpam-221	700	1	quart	quart	NOUN
ejpam-221	700	2	.	.	PUNCT
ejpam-221	701	1	j.	j.	PROPN
ejpam-221	701	2	math	math	PROPN
ejpam-221	701	3	.	.	PUNCT
ejpam-221	701	4	,	,	PUNCT
ejpam-221	701	5	oxford	oxford	PROPN
ejpam-221	701	6	(	(	PUNCT
ejpam-221	701	7	2	2	NUM
ejpam-221	701	8	)	)	PUNCT
ejpam-221	701	9	,	,	PUNCT
ejpam-221	701	10	28:285–300	28:285–300	PROPN
ejpam-221	701	11	,	,	PUNCT
ejpam-221	701	12	1977	1977	NUM
ejpam-221	701	13	.	.	PUNCT
ejpam-221	702	1	[	[	X
ejpam-221	702	2	23	23	NUM
ejpam-221	702	3	]	]	PUNCT
ejpam-221	702	4	j.	j.	PROPN
ejpam-221	702	5	fountain	fountain	PROPN
ejpam-221	702	6	.	.	PUNCT
ejpam-221	703	1	right	right	INTJ
ejpam-221	703	2	pp	pp	ADV
ejpam-221	703	3	monoids	monoid	NOUN
ejpam-221	703	4	with	with	ADP
ejpam-221	703	5	central	central	ADJ
ejpam-221	703	6	idempotents	idempotent	NOUN
ejpam-221	703	7	.	.	PUNCT
ejpam-221	704	1	semigroup	semigroup	PROPN
ejpam-221	704	2	forum	forum	PROPN
ejpam-221	704	3	,	,	PUNCT
ejpam-221	704	4	13:229–237	13:229–237	NUM
ejpam-221	704	5	,	,	PUNCT
ejpam-221	704	6	1977	1977	NUM
ejpam-221	704	7	.	.	PUNCT
ejpam-221	705	1	[	[	X
ejpam-221	705	2	24	24	NUM
ejpam-221	705	3	]	]	PUNCT
ejpam-221	705	4	j.	j.	PROPN
ejpam-221	705	5	fountain	fountain	PROPN
ejpam-221	705	6	.	.	PUNCT
ejpam-221	706	1	adequate	adequate	ADJ
ejpam-221	706	2	semigroups	semigroup	NOUN
ejpam-221	706	3	.	.	PUNCT
ejpam-221	707	1	proc	proc	PROPN
ejpam-221	707	2	.	.	PUNCT
ejpam-221	708	1	edinburgh	edinburgh	PROPN
ejpam-221	708	2	math	math	PROPN
ejpam-221	708	3	.	.	PUNCT
ejpam-221	709	1	soc	soc	PROPN
ejpam-221	709	2	.	.	PUNCT
ejpam-221	710	1	(	(	PUNCT
ejpam-221	710	2	2	2	NUM
ejpam-221	710	3	)	)	PUNCT
ejpam-221	710	4	,	,	PUNCT
ejpam-221	710	5	22:113–125	22:113–125	NUM
ejpam-221	710	6	,	,	PUNCT
ejpam-221	710	7	1979	1979	NUM
ejpam-221	710	8	.	.	PUNCT
ejpam-221	711	1	[	[	X
ejpam-221	711	2	25	25	NUM
ejpam-221	711	3	]	]	PUNCT
ejpam-221	711	4	j.	j.	PROPN
ejpam-221	711	5	fountain	fountain	PROPN
ejpam-221	711	6	.	.	PUNCT
ejpam-221	712	1	abundant	abundant	ADJ
ejpam-221	712	2	semigroups	semigroup	NOUN
ejpam-221	712	3	.	.	PUNCT
ejpam-221	713	1	proc	proc	NOUN
ejpam-221	713	2	.	.	PUNCT
ejpam-221	714	1	london	london	PROPN
ejpam-221	714	2	math	math	PROPN
ejpam-221	714	3	.	.	PUNCT
ejpam-221	715	1	soc	soc	PROPN
ejpam-221	715	2	.	.	PUNCT
ejpam-221	716	1	(	(	PUNCT
ejpam-221	716	2	3	3	NUM
ejpam-221	716	3	)	)	PUNCT
ejpam-221	716	4	,	,	PUNCT
ejpam-221	716	5	44:103–129	44:103–129	PROPN
ejpam-221	716	6	,	,	PUNCT
ejpam-221	716	7	1982	1982	NUM
ejpam-221	716	8	.	.	PUNCT
ejpam-221	717	1	[	[	X
ejpam-221	717	2	26	26	NUM
ejpam-221	717	3	]	]	X
ejpam-221	717	4	j.	j.	PROPN
ejpam-221	717	5	fountain	fountain	PROPN
ejpam-221	717	6	.	.	PUNCT
ejpam-221	718	1	ample	ample	ADJ
ejpam-221	718	2	and	and	CCONJ
ejpam-221	718	3	left	leave	VERB
ejpam-221	718	4	ample	ample	ADJ
ejpam-221	718	5	semigroups	semigroup	NOUN
ejpam-221	718	6	:	:	PUNCT
ejpam-221	718	7	extended	extended	ADJ
ejpam-221	718	8	abstract	abstract	NOUN
ejpam-221	718	9	.	.	PUNCT
ejpam-221	719	1	categories	category	NOUN
ejpam-221	719	2	and	and	CCONJ
ejpam-221	719	3	semigroups	semigroup	NOUN
ejpam-221	719	4	workshop	workshop	NOUN
ejpam-221	719	5	,	,	PUNCT
ejpam-221	719	6	calgary	calgary	PROPN
ejpam-221	719	7	,	,	PUNCT
ejpam-221	719	8	june	june	PROPN
ejpam-221	719	9	2nd	2nd	PROPN
ejpam-221	719	10	2006	2006	NUM
ejpam-221	719	11	.	.	PUNCT
ejpam-221	720	1	http://pages.cpsc.ucalgary.ca/∼robin/fmcs/fmcs_06/amplesurvey2.pdf	http://pages.cpsc.ucalgary.ca/∼robin/fmcs/fmcs_06/amplesurvey2.pdf	NOUN
ejpam-221	720	2	.	.	PUNCT
ejpam-221	721	1	[	[	X
ejpam-221	721	2	27	27	NUM
ejpam-221	721	3	]	]	X
ejpam-221	721	4	g.	g.	PROPN
ejpam-221	721	5	m.	m.	PROPN
ejpam-221	721	6	s.	s.	PROPN
ejpam-221	721	7	gomes	gomes	PROPN
ejpam-221	721	8	and	and	CCONJ
ejpam-221	721	9	v.	v.	ADP
ejpam-221	721	10	gould	gould	PROPN
ejpam-221	721	11	.	.	PUNCT
ejpam-221	722	1	proper	proper	ADJ
ejpam-221	722	2	weakly	weakly	ADJ
ejpam-221	722	3	left	leave	VERB
ejpam-221	722	4	ample	ample	ADJ
ejpam-221	722	5	semigroups	semigroup	NOUN
ejpam-221	722	6	.	.	PUNCT
ejpam-221	723	1	internat	internat	PROPN
ejpam-221	723	2	.	.	PUNCT
ejpam-221	724	1	j.	j.	PROPN
ejpam-221	724	2	algebra	algebra	PROPN
ejpam-221	724	3	comput	comput	PROPN
ejpam-221	724	4	.	.	PUNCT
ejpam-221	724	5	,	,	PUNCT
ejpam-221	724	6	9:721–739	9:721–739	NOUN
ejpam-221	724	7	,	,	PUNCT
ejpam-221	724	8	1999	1999	NUM
ejpam-221	724	9	.	.	PUNCT
ejpam-221	725	1	[	[	X
ejpam-221	725	2	28	28	NUM
ejpam-221	725	3	]	]	X
ejpam-221	725	4	g.	g.	PROPN
ejpam-221	725	5	m.	m.	PROPN
ejpam-221	725	6	s.	s.	PROPN
ejpam-221	725	7	gomes	gomes	PROPN
ejpam-221	725	8	and	and	CCONJ
ejpam-221	725	9	v.	v.	ADP
ejpam-221	725	10	gould	gould	PROPN
ejpam-221	725	11	.	.	PUNCT
ejpam-221	726	1	graph	graph	NOUN
ejpam-221	726	2	expansions	expansion	NOUN
ejpam-221	726	3	of	of	ADP
ejpam-221	726	4	unipotent	unipotent	ADJ
ejpam-221	726	5	monoids	monoid	NOUN
ejpam-221	726	6	.	.	PUNCT
ejpam-221	727	1	comm	comm	NOUN
ejpam-221	727	2	.	.	PUNCT
ejpam-221	728	1	algebra	algebra	PROPN
ejpam-221	728	2	,	,	PUNCT
ejpam-221	728	3	28:447	28:447	NUM
ejpam-221	728	4	–	–	PUNCT
ejpam-221	728	5	463	463	NUM
ejpam-221	728	6	,	,	PUNCT
ejpam-221	728	7	2000	2000	NUM
ejpam-221	728	8	.	.	PUNCT
ejpam-221	729	1	[	[	X
ejpam-221	729	2	29	29	NUM
ejpam-221	729	3	]	]	X
ejpam-221	729	4	g.	g.	PROPN
ejpam-221	729	5	m.	m.	PROPN
ejpam-221	729	6	s.	s.	PROPN
ejpam-221	729	7	gomes	gomes	PROPN
ejpam-221	729	8	and	and	CCONJ
ejpam-221	729	9	v.	v.	PROPN
ejpam-221	729	10	gould	gould	PROPN
ejpam-221	729	11	.	.	PUNCT
ejpam-221	730	1	finite	finite	VERB
ejpam-221	730	2	proper	proper	ADJ
ejpam-221	730	3	covers	cover	NOUN
ejpam-221	730	4	in	in	ADP
ejpam-221	730	5	a	a	DET
ejpam-221	730	6	class	class	NOUN
ejpam-221	730	7	of	of	ADP
ejpam-221	730	8	finite	finite	ADJ
ejpam-221	730	9	semigroups	semigroup	NOUN
ejpam-221	730	10	with	with	ADP
ejpam-221	730	11	commuting	commute	VERB
ejpam-221	730	12	idempotents	idempotent	NOUN
ejpam-221	730	13	.	.	PUNCT
ejpam-221	731	1	semigroup	semigroup	PROPN
ejpam-221	731	2	forum	forum	PROPN
ejpam-221	731	3	,	,	PUNCT
ejpam-221	731	4	66:433–454	66:433–454	PROPN
ejpam-221	731	5	,	,	PUNCT
ejpam-221	731	6	2003	2003	NUM
ejpam-221	731	7	.	.	PUNCT
ejpam-221	732	1	[	[	X
ejpam-221	732	2	30	30	NUM
ejpam-221	732	3	]	]	X
ejpam-221	732	4	v.	v.	PROPN
ejpam-221	732	5	gould	gould	PROPN
ejpam-221	732	6	.	.	PUNCT
ejpam-221	733	1	(	(	PUNCT
ejpam-221	733	2	weakly	weakly	ADV
ejpam-221	733	3	)	)	PUNCT
ejpam-221	733	4	left	leave	VERB
ejpam-221	733	5	e	e	NOUN
ejpam-221	733	6	-	-	ADJ
ejpam-221	733	7	ample	ample	ADJ
ejpam-221	733	8	semigroups	semigroup	NOUN
ejpam-221	733	9	.	.	PUNCT
ejpam-221	734	1	http://www-users.york.ac.uk/∼varg1/finitela.ps	http://www-users.york.ac.uk/∼varg1/finitela.ps	PROPN
ejpam-221	734	2	.	.	PUNCT
ejpam-221	735	1	[	[	X
ejpam-221	735	2	31	31	NUM
ejpam-221	735	3	]	]	PUNCT
ejpam-221	735	4	v.	v.	PROPN
ejpam-221	735	5	gould	gould	PROPN
ejpam-221	735	6	.	.	PUNCT
ejpam-221	736	1	graph	graph	NOUN
ejpam-221	736	2	expansions	expansion	NOUN
ejpam-221	736	3	of	of	ADP
ejpam-221	736	4	right	right	ADJ
ejpam-221	736	5	cancellative	cancellative	ADJ
ejpam-221	736	6	monoids	monoid	NOUN
ejpam-221	736	7	.	.	PUNCT
ejpam-221	737	1	internat	internat	PROPN
ejpam-221	737	2	.	.	PUNCT
ejpam-221	738	1	j.	j.	PROPN
ejpam-221	738	2	algebra	algebra	PROPN
ejpam-221	738	3	comput	comput	PROPN
ejpam-221	738	4	.	.	PUNCT
ejpam-221	738	5	,	,	PUNCT
ejpam-221	738	6	6:713	6:713	X
ejpam-221	738	7	–	–	PUNCT
ejpam-221	738	8	733	733	NUM
ejpam-221	738	9	,	,	PUNCT
ejpam-221	738	10	1996	1996	NUM
ejpam-221	738	11	.	.	PUNCT
ejpam-221	739	1	[	[	X
ejpam-221	739	2	32	32	NUM
ejpam-221	739	3	]	]	PUNCT
ejpam-221	739	4	v.	v.	PROPN
ejpam-221	739	5	gould	gould	PROPN
ejpam-221	739	6	and	and	CCONJ
ejpam-221	739	7	c.	c.	PROPN
ejpam-221	739	8	hollings	holling	NOUN
ejpam-221	739	9	.	.	PUNCT
ejpam-221	740	1	restriction	restriction	NOUN
ejpam-221	740	2	semigroups	semigroup	NOUN
ejpam-221	740	3	and	and	CCONJ
ejpam-221	740	4	inductive	inductive	ADJ
ejpam-221	740	5	constellations	constellation	NOUN
ejpam-221	740	6	.	.	PUNCT
ejpam-221	741	1	submitted	submit	VERB
ejpam-221	741	2	.	.	PUNCT
ejpam-221	742	1	[	[	X
ejpam-221	742	2	33	33	NUM
ejpam-221	742	3	]	]	PUNCT
ejpam-221	742	4	w.	w.	PROPN
ejpam-221	742	5	h.	h.	PROPN
ejpam-221	742	6	gustafson	gustafson	PROPN
ejpam-221	742	7	.	.	PUNCT
ejpam-221	743	1	the	the	DET
ejpam-221	743	2	history	history	NOUN
ejpam-221	743	3	of	of	ADP
ejpam-221	743	4	algebras	algebra	NOUN
ejpam-221	743	5	and	and	CCONJ
ejpam-221	743	6	their	their	PRON
ejpam-221	743	7	representations	representation	NOUN
ejpam-221	743	8	.	.	PUNCT
ejpam-221	744	1	in	in	ADP
ejpam-221	744	2	representations	representation	NOUN
ejpam-221	744	3	of	of	ADP
ejpam-221	744	4	algebras	algebra	NOUN
ejpam-221	744	5	,	,	PUNCT
ejpam-221	744	6	lecture	lecture	NOUN
ejpam-221	744	7	notes	note	NOUN
ejpam-221	744	8	in	in	ADP
ejpam-221	744	9	mathematics	mathematics	PROPN
ejpam-221	744	10	944	944	NUM
ejpam-221	744	11	,	,	PUNCT
ejpam-221	744	12	pages	page	NOUN
ejpam-221	744	13	1–28	1–28	PROPN
ejpam-221	744	14	.	.	PUNCT
ejpam-221	744	15	springer	springer	NOUN
ejpam-221	744	16	,	,	PUNCT
ejpam-221	744	17	1982	1982	NUM
ejpam-221	744	18	.	.	PUNCT
ejpam-221	745	1	[	[	X
ejpam-221	745	2	34	34	NUM
ejpam-221	745	3	]	]	PUNCT
ejpam-221	745	4	t.	t.	PROPN
ejpam-221	745	5	e.	e.	PROPN
ejpam-221	745	6	hall	hall	PROPN
ejpam-221	745	7	.	.	PUNCT
ejpam-221	746	1	orthodox	orthodox	PROPN
ejpam-221	746	2	semigroups	semigroup	NOUN
ejpam-221	746	3	.	.	PUNCT
ejpam-221	747	1	pacific	pacific	PROPN
ejpam-221	747	2	j.	j.	PROPN
ejpam-221	747	3	math	math	PROPN
ejpam-221	747	4	.	.	PUNCT
ejpam-221	747	5	,	,	PUNCT
ejpam-221	748	1	39:677–686	39:677–686	NUM
ejpam-221	748	2	,	,	PUNCT
ejpam-221	748	3	1971	1971	NUM
ejpam-221	748	4	.	.	PUNCT
ejpam-221	749	1	[	[	X
ejpam-221	749	2	35	35	NUM
ejpam-221	749	3	]	]	X
ejpam-221	749	4	c.	c.	PROPN
ejpam-221	749	5	hollings	holling	NOUN
ejpam-221	749	6	.	.	PUNCT
ejpam-221	750	1	partial	partial	ADJ
ejpam-221	750	2	actions	action	NOUN
ejpam-221	750	3	of	of	ADP
ejpam-221	750	4	semigroups	semigroup	NOUN
ejpam-221	750	5	and	and	CCONJ
ejpam-221	750	6	monoids	monoid	NOUN
ejpam-221	750	7	.	.	PUNCT
ejpam-221	751	1	phd	phd	NOUN
ejpam-221	751	2	thesis	thesis	PROPN
ejpam-221	751	3	,	,	PUNCT
ejpam-221	751	4	university	university	PROPN
ejpam-221	751	5	of	of	ADP
ejpam-221	751	6	york	york	PROPN
ejpam-221	751	7	,	,	PUNCT
ejpam-221	751	8	2007	2007	NUM
ejpam-221	751	9	.	.	PUNCT
ejpam-221	752	1	[	[	X
ejpam-221	752	2	36	36	NUM
ejpam-221	752	3	]	]	X
ejpam-221	752	4	c.	c.	PROPN
ejpam-221	752	5	hollings	holling	NOUN
ejpam-221	752	6	.	.	PUNCT
ejpam-221	753	1	extending	extend	VERB
ejpam-221	753	2	the	the	DET
ejpam-221	753	3	ehresmann	ehresmann	PROPN
ejpam-221	753	4	-	-	PUNCT
ejpam-221	753	5	schein	schein	PROPN
ejpam-221	753	6	-	-	PUNCT
ejpam-221	753	7	nambooripad	nambooripad	NOUN
ejpam-221	753	8	theorem	theorem	PROPN
ejpam-221	753	9	.	.	PROPN
ejpam-221	753	10	submitted	submit	VERB
ejpam-221	753	11	.	.	PUNCT
ejpam-221	754	1	references	reference	NOUN
ejpam-221	754	2	55	55	NUM
ejpam-221	754	3	[	[	X
ejpam-221	754	4	37	37	NUM
ejpam-221	754	5	]	]	PUNCT
ejpam-221	754	6	j.	j.	PROPN
ejpam-221	754	7	m.	m.	PROPN
ejpam-221	754	8	howie	howie	PROPN
ejpam-221	754	9	.	.	PUNCT
ejpam-221	755	1	fundamentals	fundamental	NOUN
ejpam-221	755	2	of	of	ADP
ejpam-221	755	3	semigroup	semigroup	PROPN
ejpam-221	755	4	theory	theory	NOUN
ejpam-221	755	5	.	.	PUNCT
ejpam-221	756	1	lms	lm	NOUN
ejpam-221	756	2	monographs	monograph	NOUN
ejpam-221	756	3	no	no	INTJ
ejpam-221	756	4	.	.	PROPN
ejpam-221	756	5	12	12	NUM
ejpam-221	756	6	.	.	PUNCT
ejpam-221	757	1	clarendon	clarendon	PROPN
ejpam-221	757	2	press	press	PROPN
ejpam-221	757	3	,	,	PUNCT
ejpam-221	757	4	oxford	oxford	NOUN
ejpam-221	757	5	,	,	PUNCT
ejpam-221	757	6	1995	1995	NUM
ejpam-221	757	7	.	.	PUNCT
ejpam-221	758	1	[	[	X
ejpam-221	758	2	38	38	NUM
ejpam-221	758	3	]	]	PUNCT
ejpam-221	758	4	j.	j.	PROPN
ejpam-221	758	5	r.	r.	PROPN
ejpam-221	758	6	isbell	isbell	PROPN
ejpam-221	758	7	.	.	PUNCT
ejpam-221	759	1	beatific	beatific	PROPN
ejpam-221	759	2	semigroups	semigroup	NOUN
ejpam-221	759	3	.	.	PUNCT
ejpam-221	760	1	j.	j.	PROPN
ejpam-221	760	2	alg	alg	PROPN
ejpam-221	760	3	.	.	PROPN
ejpam-221	760	4	,	,	PUNCT
ejpam-221	760	5	23:228–238	23:228–238	PROPN
ejpam-221	760	6	,	,	PUNCT
ejpam-221	760	7	1972	1972	NUM
ejpam-221	760	8	.	.	PUNCT
ejpam-221	761	1	[	[	X
ejpam-221	761	2	39	39	NUM
ejpam-221	761	3	]	]	PUNCT
ejpam-221	761	4	m.	m.	PROPN
ejpam-221	761	5	jackson	jackson	PROPN
ejpam-221	761	6	and	and	CCONJ
ejpam-221	761	7	t.	t.	PROPN
ejpam-221	761	8	stokes	stokes	PROPN
ejpam-221	761	9	.	.	PUNCT
ejpam-221	762	1	an	an	DET
ejpam-221	762	2	invitation	invitation	NOUN
ejpam-221	762	3	to	to	ADP
ejpam-221	762	4	c	c	NOUN
ejpam-221	762	5	-	-	PUNCT
ejpam-221	762	6	semigroups	semigroup	NOUN
ejpam-221	762	7	.	.	PUNCT
ejpam-221	763	1	semigroup	semigroup	PROPN
ejpam-221	763	2	forum	forum	PROPN
ejpam-221	763	3	,	,	PUNCT
ejpam-221	763	4	62:279–310	62:279–310	PROPN
ejpam-221	763	5	,	,	PUNCT
ejpam-221	763	6	2001	2001	NUM
ejpam-221	763	7	.	.	PUNCT
ejpam-221	764	1	[	[	X
ejpam-221	764	2	40	40	NUM
ejpam-221	764	3	]	]	PUNCT
ejpam-221	764	4	m.	m.	PROPN
ejpam-221	764	5	jackson	jackson	PROPN
ejpam-221	764	6	and	and	CCONJ
ejpam-221	764	7	t.	t.	PROPN
ejpam-221	764	8	stokes	stokes	PROPN
ejpam-221	764	9	.	.	PUNCT
ejpam-221	765	1	algebras	algebras	PROPN
ejpam-221	765	2	of	of	ADP
ejpam-221	765	3	partial	partial	ADJ
ejpam-221	765	4	maps	map	NOUN
ejpam-221	765	5	.	.	PUNCT
ejpam-221	766	1	in	in	ADP
ejpam-221	766	2	proceedings	proceeding	NOUN
ejpam-221	766	3	of	of	ADP
ejpam-221	766	4	the	the	DET
ejpam-221	766	5	special	special	ADJ
ejpam-221	766	6	interest	interest	NOUN
ejpam-221	766	7	meeting	meeting	NOUN
ejpam-221	766	8	on	on	ADP
ejpam-221	766	9	semigroup	semigroup	PROPN
ejpam-221	766	10	theory	theory	NOUN
ejpam-221	766	11	and	and	CCONJ
ejpam-221	766	12	related	related	ADJ
ejpam-221	766	13	mathematics	mathematic	NOUN
ejpam-221	766	14	(	(	PUNCT
ejpam-221	766	15	sydney	sydney	NOUN
ejpam-221	766	16	,	,	PUNCT
ejpam-221	766	17	2005	2005	NUM
ejpam-221	766	18	)	)	PUNCT
ejpam-221	766	19	.	.	PUNCT
ejpam-221	767	1	sydney	sydney	PROPN
ejpam-221	767	2	university	university	PROPN
ejpam-221	767	3	press	press	NOUN
ejpam-221	767	4	,	,	PUNCT
ejpam-221	767	5	to	to	PART
ejpam-221	767	6	appear	appear	VERB
ejpam-221	767	7	.	.	PUNCT
ejpam-221	768	1	[	[	X
ejpam-221	768	2	41	41	NUM
ejpam-221	768	3	]	]	PUNCT
ejpam-221	768	4	j.	j.	PROPN
ejpam-221	768	5	p.	p.	PROPN
ejpam-221	768	6	jans	jans	PROPN
ejpam-221	768	7	.	.	PUNCT
ejpam-221	768	8	rings	ring	NOUN
ejpam-221	768	9	and	and	CCONJ
ejpam-221	768	10	homology	homology	PROPN
ejpam-221	768	11	.	.	PUNCT
ejpam-221	769	1	holt	holt	PROPN
ejpam-221	769	2	,	,	PUNCT
ejpam-221	769	3	rinehart	rinehart	PROPN
ejpam-221	769	4	and	and	CCONJ
ejpam-221	769	5	winston	winston	PROPN
ejpam-221	769	6	,	,	PUNCT
ejpam-221	769	7	1964	1964	NUM
ejpam-221	769	8	.	.	PUNCT
ejpam-221	770	1	[	[	X
ejpam-221	770	2	42	42	NUM
ejpam-221	770	3	]	]	PUNCT
ejpam-221	770	4	m.	m.	PROPN
ejpam-221	770	5	kilp	kilp	PROPN
ejpam-221	770	6	.	.	PUNCT
ejpam-221	771	1	commutative	commutative	PROPN
ejpam-221	771	2	monoids	monoid	NOUN
ejpam-221	771	3	all	all	PRON
ejpam-221	771	4	of	of	ADP
ejpam-221	771	5	whose	whose	DET
ejpam-221	771	6	principal	principal	ADJ
ejpam-221	771	7	ideals	ideal	NOUN
ejpam-221	771	8	are	be	AUX
ejpam-221	771	9	projective	projective	ADJ
ejpam-221	771	10	.	.	PUNCT
ejpam-221	772	1	semigroup	semigroup	PROPN
ejpam-221	772	2	forum	forum	PROPN
ejpam-221	772	3	,	,	PUNCT
ejpam-221	772	4	6:334–339	6:334–339	PROPN
ejpam-221	772	5	,	,	PUNCT
ejpam-221	772	6	1973	1973	NUM
ejpam-221	772	7	.	.	PUNCT
ejpam-221	773	1	[	[	X
ejpam-221	773	2	43	43	NUM
ejpam-221	773	3	]	]	X
ejpam-221	773	4	m.	m.	NOUN
ejpam-221	773	5	v.	v.	ADP
ejpam-221	773	6	lawson	lawson	PROPN
ejpam-221	773	7	.	.	PUNCT
ejpam-221	774	1	the	the	DET
ejpam-221	774	2	structure	structure	NOUN
ejpam-221	774	3	theory	theory	NOUN
ejpam-221	774	4	of	of	ADP
ejpam-221	774	5	abundant	abundant	ADJ
ejpam-221	774	6	semigroups	semigroup	NOUN
ejpam-221	774	7	.	.	PUNCT
ejpam-221	775	1	phd	phd	NOUN
ejpam-221	775	2	thesis	thesis	NOUN
ejpam-221	775	3	,	,	PUNCT
ejpam-221	775	4	university	university	PROPN
ejpam-221	775	5	of	of	ADP
ejpam-221	775	6	york	york	PROPN
ejpam-221	775	7	,	,	PUNCT
ejpam-221	775	8	1985	1985	NUM
ejpam-221	775	9	.	.	PUNCT
ejpam-221	776	1	[	[	X
ejpam-221	776	2	44	44	NUM
ejpam-221	776	3	]	]	PUNCT
ejpam-221	776	4	m.	m.	NOUN
ejpam-221	776	5	v.	v.	ADP
ejpam-221	776	6	lawson	lawson	PROPN
ejpam-221	776	7	.	.	PUNCT
ejpam-221	777	1	the	the	DET
ejpam-221	777	2	structure	structure	NOUN
ejpam-221	777	3	of	of	ADP
ejpam-221	777	4	type	type	NOUN
ejpam-221	777	5	a	a	DET
ejpam-221	777	6	semigroups	semigroup	NOUN
ejpam-221	777	7	.	.	PUNCT
ejpam-221	778	1	quart	quart	NOUN
ejpam-221	778	2	.	.	PUNCT
ejpam-221	779	1	j.	j.	PROPN
ejpam-221	779	2	math	math	PROPN
ejpam-221	779	3	.	.	PUNCT
ejpam-221	779	4	,	,	PUNCT
ejpam-221	779	5	oxford	oxford	PROPN
ejpam-221	779	6	(	(	PUNCT
ejpam-221	779	7	2	2	NUM
ejpam-221	779	8	)	)	PUNCT
ejpam-221	779	9	,	,	PUNCT
ejpam-221	779	10	37:279–298	37:279–298	NUM
ejpam-221	779	11	,	,	PUNCT
ejpam-221	779	12	1986	1986	NUM
ejpam-221	779	13	.	.	PUNCT
ejpam-221	780	1	[	[	X
ejpam-221	780	2	45	45	NUM
ejpam-221	780	3	]	]	PUNCT
ejpam-221	780	4	m.	m.	NOUN
ejpam-221	780	5	v.	v.	ADP
ejpam-221	780	6	lawson	lawson	PROPN
ejpam-221	780	7	.	.	PUNCT
ejpam-221	781	1	the	the	DET
ejpam-221	781	2	geometric	geometric	ADJ
ejpam-221	781	3	theory	theory	NOUN
ejpam-221	781	4	of	of	ADP
ejpam-221	781	5	inverse	inverse	NOUN
ejpam-221	781	6	semigroups	semigroup	NOUN
ejpam-221	782	1	i	i	PRON
ejpam-221	782	2	:	:	PUNCT
ejpam-221	782	3	e	e	X
ejpam-221	782	4	-	-	ADJ
ejpam-221	782	5	unitary	unitary	ADJ
ejpam-221	782	6	inverse	inverse	NOUN
ejpam-221	782	7	semigroups	semigroup	NOUN
ejpam-221	782	8	.	.	PUNCT
ejpam-221	783	1	j.	j.	PROPN
ejpam-221	783	2	pure	pure	PROPN
ejpam-221	783	3	appl	appl	PROPN
ejpam-221	783	4	.	.	PUNCT
ejpam-221	784	1	alg	alg	PROPN
ejpam-221	784	2	.	.	PROPN
ejpam-221	784	3	,	,	PUNCT
ejpam-221	784	4	67:151–177	67:151–177	PROPN
ejpam-221	784	5	,	,	PUNCT
ejpam-221	784	6	1990	1990	NUM
ejpam-221	784	7	.	.	PUNCT
ejpam-221	785	1	[	[	X
ejpam-221	785	2	46	46	NUM
ejpam-221	785	3	]	]	X
ejpam-221	785	4	m.	m.	NOUN
ejpam-221	785	5	v.	v.	ADP
ejpam-221	785	6	lawson	lawson	PROPN
ejpam-221	785	7	.	.	PUNCT
ejpam-221	786	1	rees	rees	PROPN
ejpam-221	786	2	matrix	matrix	NOUN
ejpam-221	786	3	semigroups	semigroup	NOUN
ejpam-221	786	4	.	.	PUNCT
ejpam-221	787	1	proc	proc	PROPN
ejpam-221	787	2	.	.	PUNCT
ejpam-221	788	1	edinburgh	edinburgh	PROPN
ejpam-221	788	2	math	math	PROPN
ejpam-221	788	3	.	.	PUNCT
ejpam-221	789	1	soc	soc	PROPN
ejpam-221	789	2	.	.	PUNCT
ejpam-221	789	3	,	,	PUNCT
ejpam-221	789	4	33:23–37	33:23–37	NUM
ejpam-221	789	5	,	,	PUNCT
ejpam-221	789	6	1990	1990	NUM
ejpam-221	789	7	.	.	PUNCT
ejpam-221	790	1	[	[	X
ejpam-221	790	2	47	47	NUM
ejpam-221	790	3	]	]	PUNCT
ejpam-221	790	4	m.	m.	NOUN
ejpam-221	790	5	v.	v.	ADP
ejpam-221	790	6	lawson	lawson	PROPN
ejpam-221	790	7	.	.	PUNCT
ejpam-221	791	1	semigroups	semigroup	NOUN
ejpam-221	791	2	and	and	CCONJ
ejpam-221	791	3	ordered	order	VERB
ejpam-221	791	4	categories	category	NOUN
ejpam-221	791	5	i	i	PRON
ejpam-221	791	6	:	:	PUNCT
ejpam-221	791	7	the	the	DET
ejpam-221	791	8	reduced	reduce	VERB
ejpam-221	791	9	case	case	NOUN
ejpam-221	791	10	.	.	PUNCT
ejpam-221	792	1	j.	j.	PROPN
ejpam-221	792	2	alg	alg	PROPN
ejpam-221	792	3	.	.	PROPN
ejpam-221	792	4	,	,	PUNCT
ejpam-221	792	5	141:422–462	141:422–462	NUM
ejpam-221	792	6	,	,	PUNCT
ejpam-221	792	7	1991	1991	NUM
ejpam-221	792	8	.	.	PUNCT
ejpam-221	793	1	[	[	X
ejpam-221	793	2	48	48	NUM
ejpam-221	793	3	]	]	PUNCT
ejpam-221	793	4	m.	m.	NOUN
ejpam-221	793	5	v.	v.	ADP
ejpam-221	793	6	lawson	lawson	PROPN
ejpam-221	793	7	.	.	PUNCT
ejpam-221	794	1	the	the	DET
ejpam-221	794	2	geometric	geometric	ADJ
ejpam-221	794	3	theory	theory	NOUN
ejpam-221	794	4	of	of	ADP
ejpam-221	794	5	inverse	inverse	NOUN
ejpam-221	794	6	semigroups	semigroups	PROPN
ejpam-221	794	7	ii	ii	PROPN
ejpam-221	794	8	:	:	PUNCT
ejpam-221	794	9	e	e	NOUN
ejpam-221	794	10	-	-	ADJ
ejpam-221	794	11	unitary	unitary	ADJ
ejpam-221	794	12	covers	cover	NOUN
ejpam-221	794	13	of	of	ADP
ejpam-221	794	14	inverse	inverse	NOUN
ejpam-221	794	15	semigroups	semigroup	NOUN
ejpam-221	794	16	.	.	PUNCT
ejpam-221	795	1	j.	j.	PROPN
ejpam-221	795	2	pure	pure	PROPN
ejpam-221	795	3	appl	appl	PROPN
ejpam-221	795	4	.	.	PUNCT
ejpam-221	796	1	alg	alg	PROPN
ejpam-221	796	2	.	.	PROPN
ejpam-221	796	3	,	,	PUNCT
ejpam-221	796	4	83:121–139	83:121–139	PROPN
ejpam-221	796	5	,	,	PUNCT
ejpam-221	796	6	1992	1992	NUM
ejpam-221	796	7	.	.	PUNCT
ejpam-221	797	1	[	[	X
ejpam-221	797	2	49	49	NUM
ejpam-221	797	3	]	]	PUNCT
ejpam-221	797	4	m.	m.	NOUN
ejpam-221	797	5	v.	v.	ADP
ejpam-221	797	6	lawson	lawson	PROPN
ejpam-221	797	7	.	.	PUNCT
ejpam-221	798	1	inverse	inverse	PROPN
ejpam-221	798	2	semigroups	semigroup	NOUN
ejpam-221	798	3	:	:	PUNCT
ejpam-221	798	4	the	the	DET
ejpam-221	798	5	theory	theory	NOUN
ejpam-221	798	6	of	of	ADP
ejpam-221	798	7	partial	partial	ADJ
ejpam-221	798	8	symmetries	symmetry	NOUN
ejpam-221	798	9	.	.	PUNCT
ejpam-221	799	1	world	world	PROPN
ejpam-221	799	2	scientific	scientific	PROPN
ejpam-221	799	3	,	,	PUNCT
ejpam-221	799	4	1998	1998	NUM
ejpam-221	799	5	.	.	PUNCT
ejpam-221	800	1	[	[	X
ejpam-221	800	2	50	50	NUM
ejpam-221	800	3	]	]	PUNCT
ejpam-221	800	4	e.	e.	PROPN
ejpam-221	800	5	s.	s.	PROPN
ejpam-221	800	6	lyapin	lyapin	PROPN
ejpam-221	800	7	.	.	PUNCT
ejpam-221	801	1	semigroups	semigroup	NOUN
ejpam-221	801	2	.	.	PUNCT
ejpam-221	802	1	translations	translation	NOUN
ejpam-221	802	2	of	of	ADP
ejpam-221	802	3	mathematical	mathematical	ADJ
ejpam-221	802	4	monographs	monograph	NOUN
ejpam-221	802	5	,	,	PUNCT
ejpam-221	802	6	volume	volume	NOUN
ejpam-221	802	7	3	3	NUM
ejpam-221	802	8	.	.	PUNCT
ejpam-221	802	9	american	american	PROPN
ejpam-221	802	10	mathematical	mathematical	PROPN
ejpam-221	802	11	society	society	NOUN
ejpam-221	802	12	,	,	PUNCT
ejpam-221	802	13	providence	providence	NOUN
ejpam-221	802	14	,	,	PUNCT
ejpam-221	802	15	r.i	r.i	PROPN
ejpam-221	802	16	.	.	PROPN
ejpam-221	802	17	,	,	PUNCT
ejpam-221	802	18	1963	1963	NUM
ejpam-221	802	19	.	.	PUNCT
ejpam-221	803	1	[	[	X
ejpam-221	803	2	51	51	NUM
ejpam-221	803	3	]	]	PUNCT
ejpam-221	803	4	e.	e.	PROPN
ejpam-221	803	5	manes	manes	PROPN
ejpam-221	803	6	.	.	PUNCT
ejpam-221	804	1	guarded	guard	VERB
ejpam-221	804	2	and	and	CCONJ
ejpam-221	804	3	banded	band	VERB
ejpam-221	804	4	semigroups	semigroup	NOUN
ejpam-221	804	5	.	.	PUNCT
ejpam-221	805	1	semigroup	semigroup	PROPN
ejpam-221	805	2	forum	forum	PROPN
ejpam-221	805	3	,	,	PUNCT
ejpam-221	805	4	72:94–120	72:94–120	NUM
ejpam-221	805	5	,	,	PUNCT
ejpam-221	805	6	2006	2006	NUM
ejpam-221	805	7	.	.	PUNCT
ejpam-221	806	1	[	[	X
ejpam-221	806	2	52	52	NUM
ejpam-221	806	3	]	]	PUNCT
ejpam-221	806	4	d.	d.	PROPN
ejpam-221	806	5	b.	b.	PROPN
ejpam-221	806	6	mcalister	mcalister	PROPN
ejpam-221	806	7	.	.	PUNCT
ejpam-221	807	1	groups	group	NOUN
ejpam-221	807	2	,	,	PUNCT
ejpam-221	807	3	semilattices	semilattice	NOUN
ejpam-221	807	4	and	and	CCONJ
ejpam-221	807	5	inverse	inverse	NOUN
ejpam-221	807	6	semigroups	semigroup	NOUN
ejpam-221	807	7	.	.	PUNCT
ejpam-221	808	1	trans	trans	PROPN
ejpam-221	808	2	.	.	PUNCT
ejpam-221	809	1	amer	amer	PROPN
ejpam-221	809	2	.	.	PUNCT
ejpam-221	809	3	math	math	PROPN
ejpam-221	809	4	.	.	PUNCT
ejpam-221	810	1	soc	soc	PROPN
ejpam-221	810	2	.	.	PUNCT
ejpam-221	810	3	,	,	PUNCT
ejpam-221	811	1	192:227	192:227	PROPN
ejpam-221	811	2	–	–	PUNCT
ejpam-221	811	3	244	244	NUM
ejpam-221	811	4	,	,	PUNCT
ejpam-221	811	5	1974	1974	NUM
ejpam-221	811	6	.	.	PUNCT
ejpam-221	812	1	[	[	X
ejpam-221	812	2	53	53	NUM
ejpam-221	812	3	]	]	PUNCT
ejpam-221	812	4	d.	d.	PROPN
ejpam-221	812	5	b.	b.	PROPN
ejpam-221	812	6	mcalister	mcalister	PROPN
ejpam-221	812	7	.	.	PUNCT
ejpam-221	813	1	groups	group	NOUN
ejpam-221	813	2	,	,	PUNCT
ejpam-221	813	3	semilattices	semilattice	NOUN
ejpam-221	813	4	and	and	CCONJ
ejpam-221	813	5	inverse	inverse	NOUN
ejpam-221	813	6	semigroups	semigroups	PROPN
ejpam-221	813	7	ii	ii	PROPN
ejpam-221	813	8	.	.	PUNCT
ejpam-221	814	1	trans	trans	PROPN
ejpam-221	814	2	.	.	PUNCT
ejpam-221	815	1	amer	amer	PROPN
ejpam-221	815	2	.	.	PUNCT
ejpam-221	815	3	math	math	PROPN
ejpam-221	815	4	.	.	PUNCT
ejpam-221	816	1	soc	soc	PROPN
ejpam-221	816	2	.	.	PUNCT
ejpam-221	816	3	,	,	PUNCT
ejpam-221	816	4	196:351–370	196:351–370	NUM
ejpam-221	816	5	,	,	PUNCT
ejpam-221	816	6	1974	1974	NUM
ejpam-221	816	7	.	.	PUNCT
ejpam-221	817	1	[	[	X
ejpam-221	817	2	54	54	NUM
ejpam-221	817	3	]	]	PUNCT
ejpam-221	817	4	d.	d.	PROPN
ejpam-221	817	5	b.	b.	PROPN
ejpam-221	817	6	mcalister	mcalister	PROPN
ejpam-221	817	7	.	.	PUNCT
ejpam-221	818	1	one	one	NUM
ejpam-221	818	2	-	-	PUNCT
ejpam-221	818	3	to	to	ADP
ejpam-221	818	4	-	-	PUNCT
ejpam-221	818	5	one	one	NUM
ejpam-221	818	6	partial	partial	ADJ
ejpam-221	818	7	right	right	ADJ
ejpam-221	818	8	translations	translation	NOUN
ejpam-221	818	9	of	of	ADP
ejpam-221	818	10	a	a	DET
ejpam-221	818	11	right	right	ADJ
ejpam-221	818	12	cancellative	cancellative	ADJ
ejpam-221	818	13	semigroup	semigroup	PROPN
ejpam-221	818	14	.	.	PUNCT
ejpam-221	819	1	j.	j.	PROPN
ejpam-221	819	2	alg	alg	PROPN
ejpam-221	819	3	.	.	PROPN
ejpam-221	819	4	,	,	PUNCT
ejpam-221	819	5	43:231–251	43:231–251	PROPN
ejpam-221	819	6	,	,	PUNCT
ejpam-221	819	7	1976	1976	NUM
ejpam-221	819	8	.	.	PUNCT
ejpam-221	820	1	[	[	X
ejpam-221	820	2	55	55	NUM
ejpam-221	820	3	]	]	PUNCT
ejpam-221	820	4	j.	j.	PROPN
ejpam-221	820	5	meakin	meakin	PROPN
ejpam-221	820	6	.	.	PUNCT
ejpam-221	821	1	on	on	ADP
ejpam-221	821	2	the	the	DET
ejpam-221	821	3	structure	structure	NOUN
ejpam-221	821	4	of	of	ADP
ejpam-221	821	5	inverse	inverse	NOUN
ejpam-221	821	6	semigroups	semigroup	NOUN
ejpam-221	821	7	.	.	PUNCT
ejpam-221	822	1	semigroup	semigroup	PROPN
ejpam-221	822	2	forum	forum	PROPN
ejpam-221	822	3	,	,	PUNCT
ejpam-221	822	4	12:6–14	12:6–14	NUM
ejpam-221	822	5	,	,	PUNCT
ejpam-221	822	6	1976	1976	NUM
ejpam-221	822	7	.	.	PUNCT
ejpam-221	823	1	references	reference	NOUN
ejpam-221	823	2	56	56	NUM
ejpam-221	823	3	[	[	X
ejpam-221	823	4	56	56	NUM
ejpam-221	823	5	]	]	X
ejpam-221	823	6	w.	w.	PROPN
ejpam-221	823	7	d.	d.	PROPN
ejpam-221	823	8	munn	munn	PROPN
ejpam-221	823	9	.	.	PUNCT
ejpam-221	824	1	a	a	DET
ejpam-221	824	2	certain	certain	ADJ
ejpam-221	824	3	sublattice	sublattice	NOUN
ejpam-221	824	4	of	of	ADP
ejpam-221	824	5	the	the	DET
ejpam-221	824	6	lattice	lattice	NOUN
ejpam-221	824	7	of	of	ADP
ejpam-221	824	8	congruences	congruence	NOUN
ejpam-221	824	9	on	on	ADP
ejpam-221	824	10	a	a	DET
ejpam-221	824	11	regular	regular	ADJ
ejpam-221	824	12	semigroup	semigroup	NOUN
ejpam-221	824	13	.	.	PUNCT
ejpam-221	825	1	proc	proc	PROPN
ejpam-221	825	2	.	.	PUNCT
ejpam-221	826	1	cam	cam	PROPN
ejpam-221	826	2	.	.	PUNCT
ejpam-221	827	1	phil	phil	PROPN
ejpam-221	827	2	.	.	PUNCT
ejpam-221	828	1	soc	soc	PROPN
ejpam-221	828	2	.	.	PUNCT
ejpam-221	828	3	,	,	PUNCT
ejpam-221	829	1	60:385–391	60:385–391	NUM
ejpam-221	829	2	,	,	PUNCT
ejpam-221	829	3	1964	1964	NUM
ejpam-221	829	4	.	.	PUNCT
ejpam-221	830	1	[	[	X
ejpam-221	830	2	57	57	NUM
ejpam-221	830	3	]	]	PUNCT
ejpam-221	830	4	w.	w.	PROPN
ejpam-221	830	5	d.	d.	PROPN
ejpam-221	830	6	munn	munn	PROPN
ejpam-221	830	7	.	.	PUNCT
ejpam-221	830	8	uniform	uniform	PROPN
ejpam-221	830	9	semilattices	semilattice	NOUN
ejpam-221	830	10	and	and	CCONJ
ejpam-221	830	11	bisimple	bisimple	ADJ
ejpam-221	830	12	inverse	inverse	NOUN
ejpam-221	830	13	semigroups	semigroup	NOUN
ejpam-221	830	14	.	.	PUNCT
ejpam-221	831	1	quart	quart	NOUN
ejpam-221	831	2	.	.	PUNCT
ejpam-221	832	1	j.	j.	PROPN
ejpam-221	832	2	math	math	PROPN
ejpam-221	832	3	.	.	PUNCT
ejpam-221	832	4	,	,	PUNCT
ejpam-221	832	5	oxford	oxford	PROPN
ejpam-221	832	6	(	(	PUNCT
ejpam-221	832	7	2	2	NUM
ejpam-221	832	8	)	)	PUNCT
ejpam-221	832	9	,	,	PUNCT
ejpam-221	832	10	17:151–159	17:151–159	NUM
ejpam-221	832	11	,	,	PUNCT
ejpam-221	832	12	1966	1966	NUM
ejpam-221	832	13	.	.	PUNCT
ejpam-221	833	1	[	[	X
ejpam-221	833	2	58	58	NUM
ejpam-221	833	3	]	]	PUNCT
ejpam-221	833	4	k.	k.	PROPN
ejpam-221	833	5	s.	s.	PROPN
ejpam-221	833	6	s.	s.	PROPN
ejpam-221	833	7	nambooripad	nambooripad	PROPN
ejpam-221	833	8	.	.	PUNCT
ejpam-221	834	1	structure	structure	NOUN
ejpam-221	834	2	of	of	ADP
ejpam-221	834	3	regular	regular	ADJ
ejpam-221	834	4	semigroups	semigroup	NOUN
ejpam-221	834	5	i.	i.	PROPN
ejpam-221	834	6	memoirs	memoir	NOUN
ejpam-221	834	7	of	of	ADP
ejpam-221	834	8	the	the	DET
ejpam-221	834	9	american	american	PROPN
ejpam-221	834	10	mathematical	mathematical	PROPN
ejpam-221	834	11	society	society	NOUN
ejpam-221	834	12	,	,	PUNCT
ejpam-221	834	13	22(224	22(224	ADV
ejpam-221	834	14	)	)	PUNCT
ejpam-221	834	15	,	,	PUNCT
ejpam-221	834	16	1979	1979	NUM
ejpam-221	834	17	.	.	PUNCT
ejpam-221	835	1	[	[	X
ejpam-221	835	2	59	59	NUM
ejpam-221	835	3	]	]	PUNCT
ejpam-221	835	4	f.	f.	PROPN
ejpam-221	835	5	pastijn	pastijn	PROPN
ejpam-221	835	6	.	.	PUNCT
ejpam-221	836	1	a	a	DET
ejpam-221	836	2	representation	representation	NOUN
ejpam-221	836	3	of	of	ADP
ejpam-221	836	4	a	a	DET
ejpam-221	836	5	semigroup	semigroup	NOUN
ejpam-221	836	6	by	by	ADP
ejpam-221	836	7	a	a	DET
ejpam-221	836	8	semigroup	semigroup	NOUN
ejpam-221	836	9	of	of	ADP
ejpam-221	836	10	matrices	matrix	NOUN
ejpam-221	836	11	over	over	ADP
ejpam-221	836	12	a	a	DET
ejpam-221	836	13	group	group	NOUN
ejpam-221	836	14	with	with	ADP
ejpam-221	836	15	zero	zero	NUM
ejpam-221	836	16	.	.	PUNCT
ejpam-221	837	1	semigroup	semigroup	PROPN
ejpam-221	837	2	forum	forum	PROPN
ejpam-221	837	3	,	,	PUNCT
ejpam-221	837	4	10:238–249	10:238–249	NUM
ejpam-221	837	5	,	,	PUNCT
ejpam-221	837	6	1975	1975	NUM
ejpam-221	837	7	.	.	PUNCT
ejpam-221	838	1	[	[	X
ejpam-221	838	2	60	60	NUM
ejpam-221	838	3	]	]	X
ejpam-221	838	4	g.	g.	PROPN
ejpam-221	838	5	b.	b.	PROPN
ejpam-221	838	6	preston	preston	PROPN
ejpam-221	838	7	.	.	PUNCT
ejpam-221	839	1	inverse	inverse	PROPN
ejpam-221	839	2	semi	semi	NOUN
ejpam-221	839	3	-	-	NOUN
ejpam-221	839	4	groups	group	NOUN
ejpam-221	839	5	.	.	PUNCT
ejpam-221	840	1	j.	j.	PROPN
ejpam-221	840	2	london	london	PROPN
ejpam-221	840	3	math	math	PROPN
ejpam-221	840	4	.	.	PUNCT
ejpam-221	841	1	soc	soc	PROPN
ejpam-221	841	2	.	.	PUNCT
ejpam-221	841	3	,	,	PUNCT
ejpam-221	842	1	29:396–403	29:396–403	NOUN
ejpam-221	842	2	,	,	PUNCT
ejpam-221	842	3	1954	1954	NUM
ejpam-221	842	4	.	.	PUNCT
ejpam-221	843	1	[	[	X
ejpam-221	843	2	61	61	NUM
ejpam-221	843	3	]	]	PUNCT
ejpam-221	843	4	g.	g.	PROPN
ejpam-221	843	5	b.	b.	PROPN
ejpam-221	843	6	preston	preston	PROPN
ejpam-221	843	7	.	.	PUNCT
ejpam-221	844	1	inverse	inverse	PROPN
ejpam-221	844	2	semi	semi	NOUN
ejpam-221	844	3	-	-	NOUN
ejpam-221	844	4	groups	group	NOUN
ejpam-221	844	5	with	with	ADP
ejpam-221	844	6	minimal	minimal	ADJ
ejpam-221	844	7	right	right	ADJ
ejpam-221	844	8	ideals	ideal	NOUN
ejpam-221	844	9	.	.	PUNCT
ejpam-221	845	1	j.	j.	PROPN
ejpam-221	845	2	london	london	PROPN
ejpam-221	845	3	math	math	PROPN
ejpam-221	845	4	.	.	PUNCT
ejpam-221	846	1	soc	soc	PROPN
ejpam-221	846	2	.	.	PROPN
ejpam-221	846	3	,	,	PUNCT
ejpam-221	847	1	29:404–411	29:404–411	PROPN
ejpam-221	847	2	,	,	PUNCT
ejpam-221	847	3	1954	1954	NUM
ejpam-221	847	4	.	.	PUNCT
ejpam-221	848	1	[	[	X
ejpam-221	848	2	62	62	NUM
ejpam-221	848	3	]	]	X
ejpam-221	848	4	g.	g.	PROPN
ejpam-221	848	5	b.	b.	PROPN
ejpam-221	848	6	preston	preston	PROPN
ejpam-221	848	7	.	.	PUNCT
ejpam-221	849	1	representations	representation	NOUN
ejpam-221	849	2	of	of	ADP
ejpam-221	849	3	inverse	inverse	NOUN
ejpam-221	849	4	semi	semi	NOUN
ejpam-221	849	5	-	-	NOUN
ejpam-221	849	6	groups	group	NOUN
ejpam-221	849	7	.	.	PUNCT
ejpam-221	850	1	j.	j.	PROPN
ejpam-221	850	2	london	london	PROPN
ejpam-221	850	3	math	math	PROPN
ejpam-221	850	4	.	.	PUNCT
ejpam-221	851	1	soc	soc	PROPN
ejpam-221	851	2	.	.	PUNCT
ejpam-221	851	3	,	,	PUNCT
ejpam-221	851	4	29:411–419	29:411–419	PROPN
ejpam-221	851	5	,	,	PUNCT
ejpam-221	851	6	1954	1954	NUM
ejpam-221	851	7	.	.	PUNCT
ejpam-221	852	1	[	[	X
ejpam-221	852	2	63	63	NUM
ejpam-221	852	3	]	]	PUNCT
ejpam-221	852	4	b.	b.	PROPN
ejpam-221	852	5	m.	m.	PROPN
ejpam-221	852	6	schein	schein	PROPN
ejpam-221	852	7	.	.	PUNCT
ejpam-221	853	1	on	on	ADP
ejpam-221	853	2	the	the	DET
ejpam-221	853	3	theory	theory	NOUN
ejpam-221	853	4	of	of	ADP
ejpam-221	853	5	generalised	generalised	ADJ
ejpam-221	853	6	heaps	heap	NOUN
ejpam-221	853	7	and	and	CCONJ
ejpam-221	853	8	generalised	generalised	ADJ
ejpam-221	853	9	groups	group	NOUN
ejpam-221	853	10	.	.	PUNCT
ejpam-221	854	1	in	in	ADP
ejpam-221	854	2	the	the	DET
ejpam-221	854	3	theory	theory	NOUN
ejpam-221	854	4	of	of	ADP
ejpam-221	854	5	semigroups	semigroup	NOUN
ejpam-221	854	6	and	and	CCONJ
ejpam-221	854	7	its	its	PRON
ejpam-221	854	8	applications	application	NOUN
ejpam-221	854	9	i	i	PRON
ejpam-221	854	10	,	,	PUNCT
ejpam-221	854	11	pages	page	NOUN
ejpam-221	854	12	286–324	286–324	NUM
ejpam-221	854	13	.	.	PUNCT
ejpam-221	855	1	university	university	NOUN
ejpam-221	855	2	of	of	ADP
ejpam-221	855	3	saratov	saratov	PROPN
ejpam-221	855	4	,	,	PUNCT
ejpam-221	855	5	1965	1965	NUM
ejpam-221	855	6	.	.	PUNCT
ejpam-221	856	1	[	[	X
ejpam-221	856	2	64	64	NUM
ejpam-221	856	3	]	]	X
ejpam-221	856	4	b.	b.	PROPN
ejpam-221	856	5	m.	m.	PROPN
ejpam-221	856	6	schein	schein	PROPN
ejpam-221	856	7	.	.	PUNCT
ejpam-221	857	1	relation	relation	NOUN
ejpam-221	857	2	algebras	algebra	NOUN
ejpam-221	857	3	and	and	CCONJ
ejpam-221	857	4	function	function	NOUN
ejpam-221	857	5	semigroups	semigroup	NOUN
ejpam-221	857	6	.	.	PUNCT
ejpam-221	858	1	semigroup	semigroup	PROPN
ejpam-221	858	2	forum	forum	PROPN
ejpam-221	858	3	,	,	PUNCT
ejpam-221	858	4	1:1–62	1:1–62	NUM
ejpam-221	858	5	,	,	PUNCT
ejpam-221	858	6	1970	1970	NUM
ejpam-221	858	7	.	.	PUNCT
ejpam-221	859	1	[	[	X
ejpam-221	859	2	65	65	NUM
ejpam-221	859	3	]	]	X
ejpam-221	859	4	b.	b.	PROPN
ejpam-221	859	5	m.	m.	PROPN
ejpam-221	859	6	schein	schein	PROPN
ejpam-221	859	7	.	.	PUNCT
ejpam-221	860	1	on	on	ADP
ejpam-221	860	2	the	the	DET
ejpam-221	860	3	theory	theory	NOUN
ejpam-221	860	4	of	of	ADP
ejpam-221	860	5	inverse	inverse	NOUN
ejpam-221	860	6	semigroups	semigroup	NOUN
ejpam-221	860	7	and	and	CCONJ
ejpam-221	860	8	generalised	generalised	ADJ
ejpam-221	860	9	grouds	groud	NOUN
ejpam-221	860	10	.	.	PUNCT
ejpam-221	861	1	american	american	PROPN
ejpam-221	861	2	mathematical	mathematical	ADJ
ejpam-221	861	3	society	society	NOUN
ejpam-221	861	4	translations	translation	NOUN
ejpam-221	861	5	(	(	PUNCT
ejpam-221	861	6	2	2	NUM
ejpam-221	861	7	)	)	PUNCT
ejpam-221	861	8	,	,	PUNCT
ejpam-221	861	9	113:89–122	113:89–122	NUM
ejpam-221	861	10	,	,	PUNCT
ejpam-221	861	11	1979	1979	NUM
ejpam-221	861	12	.	.	PUNCT
ejpam-221	862	1	[	[	X
ejpam-221	862	2	66	66	NUM
ejpam-221	862	3	]	]	PUNCT
ejpam-221	862	4	b.	b.	PROPN
ejpam-221	862	5	schweizer	schweizer	PROPN
ejpam-221	862	6	and	and	CCONJ
ejpam-221	862	7	a.	a.	NOUN
ejpam-221	862	8	sklar	sklar	PROPN
ejpam-221	862	9	.	.	PUNCT
ejpam-221	863	1	the	the	DET
ejpam-221	863	2	algebra	algebra	NOUN
ejpam-221	863	3	of	of	ADP
ejpam-221	863	4	functions	function	NOUN
ejpam-221	863	5	.	.	PUNCT
ejpam-221	864	1	math	math	NOUN
ejpam-221	864	2	.	.	PUNCT
ejpam-221	865	1	ann	ann	PROPN
ejpam-221	865	2	.	.	PROPN
ejpam-221	865	3	,	,	PUNCT
ejpam-221	865	4	139:366–382	139:366–382	NUM
ejpam-221	865	5	,	,	PUNCT
ejpam-221	865	6	1960	1960	NUM
ejpam-221	865	7	.	.	PUNCT
ejpam-221	866	1	[	[	X
ejpam-221	866	2	67	67	NUM
ejpam-221	866	3	]	]	X
ejpam-221	866	4	b.	b.	PROPN
ejpam-221	866	5	schweizer	schweizer	PROPN
ejpam-221	866	6	and	and	CCONJ
ejpam-221	866	7	a.	a.	NOUN
ejpam-221	866	8	sklar	sklar	PROPN
ejpam-221	866	9	.	.	PUNCT
ejpam-221	867	1	the	the	DET
ejpam-221	867	2	algebra	algebra	NOUN
ejpam-221	867	3	of	of	ADP
ejpam-221	867	4	functions	function	NOUN
ejpam-221	867	5	ii	ii	PROPN
ejpam-221	867	6	.	.	PUNCT
ejpam-221	867	7	math	math	PROPN
ejpam-221	867	8	.	.	PUNCT
ejpam-221	868	1	ann	ann	PROPN
ejpam-221	868	2	.	.	PROPN
ejpam-221	868	3	,	,	PUNCT
ejpam-221	868	4	143:440–447	143:440–447	NUM
ejpam-221	868	5	,	,	PUNCT
ejpam-221	868	6	1961	1961	NUM
ejpam-221	868	7	.	.	PUNCT
ejpam-221	869	1	[	[	X
ejpam-221	869	2	68	68	NUM
ejpam-221	869	3	]	]	X
ejpam-221	869	4	b.	b.	PROPN
ejpam-221	869	5	schweizer	schweizer	PROPN
ejpam-221	869	6	and	and	CCONJ
ejpam-221	869	7	a.	a.	NOUN
ejpam-221	869	8	sklar	sklar	PROPN
ejpam-221	869	9	.	.	PUNCT
ejpam-221	870	1	the	the	DET
ejpam-221	870	2	algebra	algebra	NOUN
ejpam-221	870	3	of	of	ADP
ejpam-221	870	4	functions	function	NOUN
ejpam-221	870	5	iii	iii	PROPN
ejpam-221	870	6	.	.	PUNCT
ejpam-221	870	7	math	math	PROPN
ejpam-221	870	8	.	.	PUNCT
ejpam-221	871	1	ann	ann	PROPN
ejpam-221	871	2	.	.	PROPN
ejpam-221	871	3	,	,	PUNCT
ejpam-221	871	4	161:171–196	161:171–196	NUM
ejpam-221	871	5	,	,	PUNCT
ejpam-221	871	6	1965	1965	NUM
ejpam-221	871	7	.	.	PUNCT
ejpam-221	872	1	[	[	X
ejpam-221	872	2	69	69	NUM
ejpam-221	872	3	]	]	PUNCT
ejpam-221	872	4	b.	b.	PROPN
ejpam-221	872	5	schweizer	schweizer	PROPN
ejpam-221	872	6	and	and	CCONJ
ejpam-221	872	7	a.	a.	PROPN
ejpam-221	872	8	sklar	sklar	PROPN
ejpam-221	872	9	.	.	PUNCT
ejpam-221	873	1	function	function	NOUN
ejpam-221	873	2	systems	system	NOUN
ejpam-221	873	3	.	.	PUNCT
ejpam-221	874	1	math	math	NOUN
ejpam-221	874	2	.	.	PUNCT
ejpam-221	875	1	ann	ann	PROPN
ejpam-221	875	2	.	.	PROPN
ejpam-221	875	3	,	,	PUNCT
ejpam-221	875	4	172:1–16	172:1–16	NUM
ejpam-221	875	5	,	,	PUNCT
ejpam-221	875	6	1967	1967	NUM
ejpam-221	875	7	.	.	PUNCT
ejpam-221	876	1	[	[	X
ejpam-221	876	2	70	70	NUM
ejpam-221	876	3	]	]	PUNCT
ejpam-221	876	4	k.	k.	PROPN
ejpam-221	876	5	shoji	shoji	PROPN
ejpam-221	876	6	.	.	PUNCT
ejpam-221	877	1	completely	completely	ADV
ejpam-221	877	2	right	right	ADJ
ejpam-221	877	3	injective	injective	ADJ
ejpam-221	877	4	semigroups	semigroup	NOUN
ejpam-221	877	5	.	.	PUNCT
ejpam-221	878	1	math	math	NOUN
ejpam-221	878	2	.	.	PUNCT
ejpam-221	879	1	japon	japon	PROPN
ejpam-221	879	2	.	.	PUNCT
ejpam-221	879	3	,	,	PUNCT
ejpam-221	880	1	24(6):609–615	24(6):609–615	NUM
ejpam-221	880	2	,	,	PUNCT
ejpam-221	880	3	1979/80	1979/80	NUM
ejpam-221	880	4	.	.	PUNCT
ejpam-221	881	1	[	[	X
ejpam-221	881	2	71	71	NUM
ejpam-221	881	3	]	]	X
ejpam-221	881	4	l.	l.	PROPN
ejpam-221	881	5	a.	a.	PROPN
ejpam-221	881	6	skornjakov	skornjakov	PROPN
ejpam-221	881	7	.	.	PUNCT
ejpam-221	882	1	on	on	ADP
ejpam-221	882	2	homological	homological	ADJ
ejpam-221	882	3	classification	classification	NOUN
ejpam-221	882	4	of	of	ADP
ejpam-221	882	5	monoids	monoid	NOUN
ejpam-221	882	6	.	.	PUNCT
ejpam-221	883	1	siberian	siberian	ADJ
ejpam-221	883	2	math	math	NOUN
ejpam-221	883	3	.	.	PUNCT
ejpam-221	884	1	j.	j.	PROPN
ejpam-221	884	2	,	,	PUNCT
ejpam-221	884	3	10:843–846	10:843–846	NUM
ejpam-221	884	4	,	,	PUNCT
ejpam-221	884	5	1969	1969	NUM
ejpam-221	884	6	.	.	PUNCT
ejpam-221	885	1	[	[	X
ejpam-221	885	2	72	72	NUM
ejpam-221	885	3	]	]	X
ejpam-221	885	4	è	è	X
ejpam-221	885	5	.	.	PUNCT
ejpam-221	885	6	g.	g.	PROPN
ejpam-221	885	7	šutov	šutov	PROPN
ejpam-221	885	8	.	.	PUNCT
ejpam-221	886	1	potential	potential	ADJ
ejpam-221	886	2	conjugacy	conjugacy	NOUN
ejpam-221	886	3	of	of	ADP
ejpam-221	886	4	elements	element	NOUN
ejpam-221	886	5	in	in	ADP
ejpam-221	886	6	semigroups	semigroup	NOUN
ejpam-221	886	7	(	(	PUNCT
ejpam-221	886	8	russian	russian	NOUN
ejpam-221	886	9	)	)	PUNCT
ejpam-221	886	10	.	.	PUNCT
ejpam-221	887	1	leningrad	leningrad	PROPN
ejpam-221	887	2	.	.	PUNCT
ejpam-221	888	1	gosud	gosud	PROPN
ejpam-221	888	2	.	.	PUNCT
ejpam-221	889	1	ped	ped	PROPN
ejpam-221	889	2	.	.	PROPN
ejpam-221	889	3	inst	inst	PROPN
ejpam-221	889	4	.	.	PUNCT
ejpam-221	890	1	uč.	uč.	PROPN
ejpam-221	890	2	zap	zap	PROPN
ejpam-221	890	3	.	.	PROPN
ejpam-221	890	4	,	,	PUNCT
ejpam-221	890	5	166:105–119	166:105–119	NUM
ejpam-221	890	6	,	,	PUNCT
ejpam-221	890	7	1958	1958	NUM
ejpam-221	890	8	.	.	PUNCT
ejpam-221	891	1	[	[	X
ejpam-221	891	2	73	73	NUM
ejpam-221	891	3	]	]	X
ejpam-221	891	4	è	è	X
ejpam-221	891	5	.	.	PUNCT
ejpam-221	891	6	g.	g.	PROPN
ejpam-221	891	7	šutov	šutov	PROPN
ejpam-221	891	8	.	.	PUNCT
ejpam-221	892	1	potential	potential	ADJ
ejpam-221	892	2	divisibility	divisibility	NOUN
ejpam-221	892	3	of	of	ADP
ejpam-221	892	4	elements	element	NOUN
ejpam-221	892	5	in	in	ADP
ejpam-221	892	6	semigroups	semigroup	NOUN
ejpam-221	892	7	(	(	PUNCT
ejpam-221	892	8	russian	russian	NOUN
ejpam-221	892	9	)	)	PUNCT
ejpam-221	892	10	.	.	PUNCT
ejpam-221	893	1	leningrad	leningrad	PROPN
ejpam-221	893	2	.	.	PUNCT
ejpam-221	894	1	gosud	gosud	PROPN
ejpam-221	894	2	.	.	PUNCT
ejpam-221	895	1	ped	ped	PROPN
ejpam-221	895	2	.	.	PROPN
ejpam-221	895	3	inst	inst	PROPN
ejpam-221	895	4	.	.	PUNCT
ejpam-221	896	1	uč.	uč.	PROPN
ejpam-221	896	2	zap	zap	PROPN
ejpam-221	896	3	.	.	PROPN
ejpam-221	896	4	,	,	PUNCT
ejpam-221	896	5	166:75–103	166:75–103	NUM
ejpam-221	896	6	,	,	PUNCT
ejpam-221	896	7	1958	1958	NUM
ejpam-221	896	8	.	.	PUNCT
ejpam-221	897	1	[	[	X
ejpam-221	897	2	74	74	NUM
ejpam-221	897	3	]	]	X
ejpam-221	897	4	è	è	X
ejpam-221	897	5	.	.	PUNCT
ejpam-221	897	6	g.	g.	PROPN
ejpam-221	897	7	šutov	šutov	PROPN
ejpam-221	897	8	.	.	PUNCT
ejpam-221	898	1	potential	potential	ADJ
ejpam-221	898	2	one	one	NUM
ejpam-221	898	3	-	-	PUNCT
ejpam-221	898	4	sided	sided	ADJ
ejpam-221	898	5	invertibility	invertibility	NOUN
ejpam-221	898	6	of	of	ADP
ejpam-221	898	7	elements	element	NOUN
ejpam-221	898	8	of	of	ADP
ejpam-221	898	9	semigroups	semigroup	NOUN
ejpam-221	898	10	(	(	PUNCT
ejpam-221	898	11	russian	russian	NOUN
ejpam-221	898	12	)	)	PUNCT
ejpam-221	898	13	.	.	PUNCT
ejpam-221	899	1	uč.	uč.	PROPN
ejpam-221	899	2	zap	zap	PROPN
ejpam-221	899	3	.	.	PUNCT
ejpam-221	899	4	udmurt	udmurt	PROPN
ejpam-221	899	5	.	.	PUNCT
ejpam-221	900	1	ped	ped	PROPN
ejpam-221	900	2	.	.	PROPN
ejpam-221	900	3	inst	inst	PROPN
ejpam-221	900	4	.	.	PROPN
ejpam-221	900	5	,	,	PUNCT
ejpam-221	900	6	12:24–36	12:24–36	NUM
ejpam-221	900	7	,	,	PUNCT
ejpam-221	900	8	1958	1958	NUM
ejpam-221	900	9	.	.	PUNCT
ejpam-221	901	1	[	[	X
ejpam-221	901	2	75	75	NUM
ejpam-221	901	3	]	]	X
ejpam-221	901	4	è	è	X
ejpam-221	901	5	.	.	PUNCT
ejpam-221	901	6	g.	g.	PROPN
ejpam-221	901	7	šutov	šutov	PROPN
ejpam-221	901	8	.	.	PUNCT
ejpam-221	902	1	potential	potential	ADJ
ejpam-221	902	2	stationarity	stationarity	NOUN
ejpam-221	902	3	of	of	ADP
ejpam-221	902	4	elements	element	NOUN
ejpam-221	902	5	of	of	ADP
ejpam-221	902	6	semigroups	semigroup	NOUN
ejpam-221	902	7	(	(	PUNCT
ejpam-221	902	8	russian	russian	NOUN
ejpam-221	902	9	)	)	PUNCT
ejpam-221	902	10	.	.	PUNCT
ejpam-221	903	1	uč.	uč.	PROPN
ejpam-221	903	2	zap	zap	PROPN
ejpam-221	903	3	.	.	PUNCT
ejpam-221	903	4	udmurt	udmurt	PROPN
ejpam-221	903	5	.	.	PUNCT
ejpam-221	904	1	ped	ped	PROPN
ejpam-221	904	2	.	.	PROPN
ejpam-221	904	3	inst	inst	PROPN
ejpam-221	904	4	.	.	PROPN
ejpam-221	904	5	,	,	PUNCT
ejpam-221	904	6	12:16–23	12:16–23	PROPN
ejpam-221	904	7	,	,	PUNCT
ejpam-221	904	8	1958	1958	NUM
ejpam-221	904	9	.	.	PUNCT
ejpam-221	905	1	references	reference	NOUN
ejpam-221	905	2	57	57	NUM
ejpam-221	906	1	[	[	X
ejpam-221	906	2	76	76	NUM
ejpam-221	906	3	]	]	X
ejpam-221	906	4	v.	v.	PROPN
ejpam-221	906	5	s.	s.	PROPN
ejpam-221	906	6	trokhimenko	trokhimenko	PROPN
ejpam-221	906	7	.	.	PUNCT
ejpam-221	907	1	menger	menger	PROPN
ejpam-221	907	2	’s	’s	PART
ejpam-221	907	3	function	function	NOUN
ejpam-221	907	4	systems	system	NOUN
ejpam-221	907	5	(	(	PUNCT
ejpam-221	907	6	russian	russian	PROPN
ejpam-221	907	7	)	)	PUNCT
ejpam-221	907	8	.	.	PUNCT
ejpam-221	908	1	izv	izv	PROPN
ejpam-221	908	2	.	.	PROPN
ejpam-221	908	3	vyssh	vyssh	PROPN
ejpam-221	908	4	.	.	PUNCT
ejpam-221	909	1	uchebn	uchebn	NOUN
ejpam-221	909	2	.	.	PUNCT
ejpam-221	910	1	zaved	zave	VERB
ejpam-221	910	2	.	.	PUNCT
ejpam-221	911	1	mat	mat	PROPN
ejpam-221	911	2	.	.	PROPN
ejpam-221	911	3	,	,	PUNCT
ejpam-221	911	4	11	11	NUM
ejpam-221	911	5	(	(	PUNCT
ejpam-221	911	6	138):71–78	138):71–78	NUM
ejpam-221	911	7	,	,	PUNCT
ejpam-221	911	8	1973	1973	NUM
ejpam-221	911	9	.	.	PUNCT
ejpam-221	912	1	[	[	X
ejpam-221	912	2	77	77	X
ejpam-221	912	3	]	]	X
ejpam-221	912	4	o.	o.	PROPN
ejpam-221	912	5	veblen	veblen	PROPN
ejpam-221	912	6	and	and	CCONJ
ejpam-221	912	7	j.	j.	PROPN
ejpam-221	912	8	h.	h.	PROPN
ejpam-221	912	9	c.	c.	PROPN
ejpam-221	912	10	whitehead	whitehead	PROPN
ejpam-221	912	11	.	.	PUNCT
ejpam-221	913	1	the	the	DET
ejpam-221	913	2	foundations	foundation	NOUN
ejpam-221	913	3	of	of	ADP
ejpam-221	913	4	differential	differential	ADJ
ejpam-221	913	5	geometry	geometry	NOUN
ejpam-221	913	6	.	.	PUNCT
ejpam-221	914	1	cambridge	cambridge	PROPN
ejpam-221	914	2	tract	tract	PROPN
ejpam-221	914	3	no	no	INTJ
ejpam-221	914	4	.	.	NOUN
ejpam-221	915	1	24	24	NUM
ejpam-221	915	2	.	.	PUNCT
ejpam-221	915	3	cambridge	cambridge	PROPN
ejpam-221	915	4	university	university	PROPN
ejpam-221	915	5	press	press	NOUN
ejpam-221	915	6	,	,	PUNCT
ejpam-221	915	7	1932	1932	NUM
ejpam-221	915	8	.	.	PUNCT
ejpam-221	916	1	[	[	X
ejpam-221	916	2	78	78	X
ejpam-221	916	3	]	]	X
ejpam-221	916	4	v.	v.	PROPN
ejpam-221	916	5	v.	v.	PROPN
ejpam-221	916	6	wagner	wagner	PROPN
ejpam-221	916	7	.	.	PUNCT
ejpam-221	917	1	generalised	generalise	VERB
ejpam-221	917	2	groups	group	NOUN
ejpam-221	917	3	(	(	PUNCT
ejpam-221	917	4	russian	russian	ADJ
ejpam-221	917	5	)	)	PUNCT
ejpam-221	917	6	.	.	PUNCT
ejpam-221	918	1	dokl	dokl	NOUN
ejpam-221	918	2	.	.	PUNCT
ejpam-221	919	1	acad	acad	PROPN
ejpam-221	919	2	.	.	PUNCT
ejpam-221	920	1	nauk	nauk	PROPN
ejpam-221	920	2	sssr	sssr	PROPN
ejpam-221	920	3	,	,	PUNCT
ejpam-221	920	4	84:1119–1122	84:1119–1122	NUM
ejpam-221	920	5	,	,	PUNCT
ejpam-221	920	6	1952	1952	NUM
ejpam-221	920	7	.	.	PUNCT
ejpam-221	921	1	[	[	X
ejpam-221	921	2	79	79	NUM
ejpam-221	921	3	]	]	X
ejpam-221	921	4	v.	v.	PROPN
ejpam-221	921	5	v.	v.	PROPN
ejpam-221	921	6	wagner	wagner	PROPN
ejpam-221	921	7	.	.	PUNCT
ejpam-221	922	1	the	the	DET
ejpam-221	922	2	theory	theory	NOUN
ejpam-221	922	3	of	of	ADP
ejpam-221	922	4	generalised	generalised	ADJ
ejpam-221	922	5	heaps	heap	NOUN
ejpam-221	922	6	and	and	CCONJ
ejpam-221	922	7	generalised	generalised	ADJ
ejpam-221	922	8	groups	group	NOUN
ejpam-221	922	9	(	(	PUNCT
ejpam-221	922	10	russian	russian	ADJ
ejpam-221	922	11	)	)	PUNCT
ejpam-221	922	12	.	.	PUNCT
ejpam-221	923	1	mat	mat	PROPN
ejpam-221	923	2	.	.	PUNCT
ejpam-221	923	3	sb	sb	PROPN
ejpam-221	923	4	.	.	PUNCT
ejpam-221	924	1	(	(	PUNCT
ejpam-221	924	2	n.	n.	PROPN
ejpam-221	924	3	s.	s.	PROPN
ejpam-221	924	4	)	)	PUNCT
ejpam-221	924	5	,	,	PUNCT
ejpam-221	924	6	32:545–632	32:545–632	NUM
ejpam-221	924	7	,	,	PUNCT
ejpam-221	924	8	1953	1953	NUM
ejpam-221	924	9	.	.	PUNCT