id	sid	tid	token	lemma	pos
ejpam-2231	1	1	compile	compile	NOUN
ejpam-2231	1	2	/	/	SYM
ejpam-2231	1	3	output.dvi	output.dvi	NOUN
ejpam-2231	1	4	european	european	ADJ
ejpam-2231	1	5	journal	journal	NOUN
ejpam-2231	1	6	of	of	ADP
ejpam-2231	1	7	pure	pure	ADJ
ejpam-2231	1	8	and	and	CCONJ
ejpam-2231	1	9	applied	apply	VERB
ejpam-2231	1	10	mathematics	mathematic	NOUN
ejpam-2231	1	11	vol	vol	NOUN
ejpam-2231	1	12	.	.	PROPN
ejpam-2231	2	1	9	9	NUM
ejpam-2231	2	2	,	,	PUNCT
ejpam-2231	2	3	no	no	INTJ
ejpam-2231	2	4	.	.	NOUN
ejpam-2231	2	5	3	3	NUM
ejpam-2231	2	6	,	,	PUNCT
ejpam-2231	2	7	2016	2016	NUM
ejpam-2231	2	8	,	,	PUNCT
ejpam-2231	2	9	277	277	NUM
ejpam-2231	2	10	-	-	SYM
ejpam-2231	2	11	291	291	NUM
ejpam-2231	2	12	issn	issn	PROPN
ejpam-2231	2	13	1307	1307	NUM
ejpam-2231	2	14	-	-	SYM
ejpam-2231	2	15	5543	5543	NUM
ejpam-2231	2	16	–	–	PUNCT
ejpam-2231	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2231	2	18	on	on	ADP
ejpam-2231	2	19	generalized	generalized	ADJ
ejpam-2231	2	20	ideals	ideal	NOUN
ejpam-2231	2	21	of	of	ADP
ejpam-2231	2	22	left	leave	VERB
ejpam-2231	3	1	almost	almost	ADV
ejpam-2231	3	2	semigroups	semigroup	NOUN
ejpam-2231	3	3	waqar	waqar	PROPN
ejpam-2231	3	4	khan1,2,3	khan1,2,3	PROPN
ejpam-2231	3	5	,	,	PUNCT
ejpam-2231	3	6	faisal	faisal	PROPN
ejpam-2231	3	7	yousafzai2,∗	yousafzai2,∗	PROPN
ejpam-2231	3	8	,	,	PUNCT
ejpam-2231	3	9	and	and	CCONJ
ejpam-2231	3	10	madad	madad	PROPN
ejpam-2231	3	11	khan3	khan3	NOUN
ejpam-2231	3	12	1	1	NUM
ejpam-2231	3	13	school	school	NOUN
ejpam-2231	3	14	of	of	ADP
ejpam-2231	3	15	mathematics	mathematic	NOUN
ejpam-2231	3	16	and	and	CCONJ
ejpam-2231	3	17	statistics	statistic	NOUN
ejpam-2231	3	18	,	,	PUNCT
ejpam-2231	3	19	southwest	southwest	PROPN
ejpam-2231	3	20	university	university	NOUN
ejpam-2231	3	21	,	,	PUNCT
ejpam-2231	3	22	beibei	beibei	PROPN
ejpam-2231	3	23	,	,	PUNCT
ejpam-2231	3	24	chongqing	chongqing	PROPN
ejpam-2231	3	25	,	,	PUNCT
ejpam-2231	3	26	china	china	PROPN
ejpam-2231	3	27	2	2	NUM
ejpam-2231	3	28	school	school	NOUN
ejpam-2231	3	29	of	of	ADP
ejpam-2231	3	30	mathematical	mathematical	ADJ
ejpam-2231	3	31	sciences	sciences	PROPN
ejpam-2231	3	32	,	,	PUNCT
ejpam-2231	3	33	university	university	NOUN
ejpam-2231	3	34	of	of	ADP
ejpam-2231	3	35	science	science	NOUN
ejpam-2231	3	36	and	and	CCONJ
ejpam-2231	3	37	technology	technology	NOUN
ejpam-2231	3	38	of	of	ADP
ejpam-2231	3	39	china	china	PROPN
ejpam-2231	3	40	,	,	PUNCT
ejpam-2231	3	41	hefei	hefei	PROPN
ejpam-2231	3	42	,	,	PUNCT
ejpam-2231	3	43	china	china	PROPN
ejpam-2231	3	44	3	3	NUM
ejpam-2231	3	45	department	department	NOUN
ejpam-2231	3	46	of	of	ADP
ejpam-2231	3	47	mathematics	mathematic	NOUN
ejpam-2231	3	48	,	,	PUNCT
ejpam-2231	3	49	comsats	comsats	PROPN
ejpam-2231	3	50	institute	institute	PROPN
ejpam-2231	3	51	of	of	ADP
ejpam-2231	3	52	information	information	PROPN
ejpam-2231	3	53	technology	technology	PROPN
ejpam-2231	3	54	,	,	PUNCT
ejpam-2231	3	55	abbottabad	abbottabad	PROPN
ejpam-2231	3	56	,	,	PUNCT
ejpam-2231	3	57	pakistan	pakistan	PROPN
ejpam-2231	3	58	abstract	abstract	NOUN
ejpam-2231	3	59	.	.	PUNCT
ejpam-2231	4	1	in	in	ADP
ejpam-2231	4	2	this	this	DET
ejpam-2231	4	3	paper	paper	NOUN
ejpam-2231	4	4	,	,	PUNCT
ejpam-2231	4	5	we	we	PRON
ejpam-2231	4	6	study	study	VERB
ejpam-2231	4	7	(	(	PUNCT
ejpam-2231	4	8	m	m	PROPN
ejpam-2231	4	9	,	,	PUNCT
ejpam-2231	4	10	n)-ideals	n)-ideal	NOUN
ejpam-2231	4	11	of	of	ADP
ejpam-2231	4	12	an	an	DET
ejpam-2231	4	13	la	la	ADJ
ejpam-2231	4	14	-semigroup	-semigroup	NOUN
ejpam-2231	4	15	in	in	ADP
ejpam-2231	4	16	detail	detail	NOUN
ejpam-2231	4	17	.	.	PUNCT
ejpam-2231	5	1	we	we	PRON
ejpam-2231	5	2	characterize	characterize	VERB
ejpam-2231	5	3	(	(	PUNCT
ejpam-2231	5	4	0,2)ideals	0,2)ideals	NUM
ejpam-2231	5	5	of	of	ADP
ejpam-2231	5	6	anla	anla	PROPN
ejpam-2231	5	7	-semigroup	-semigroup	PROPN
ejpam-2231	5	8	s	s	PART
ejpam-2231	5	9	and	and	CCONJ
ejpam-2231	5	10	prove	prove	VERB
ejpam-2231	5	11	that	that	SCONJ
ejpam-2231	5	12	a	a	PRON
ejpam-2231	5	13	is	be	AUX
ejpam-2231	5	14	a	a	DET
ejpam-2231	5	15	(	(	PUNCT
ejpam-2231	5	16	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	5	17	of	of	ADP
ejpam-2231	5	18	s	s	PRON
ejpam-2231	5	19	if	if	SCONJ
ejpam-2231	6	1	and	and	CCONJ
ejpam-2231	6	2	only	only	ADV
ejpam-2231	6	3	if	if	SCONJ
ejpam-2231	6	4	a	a	PRON
ejpam-2231	6	5	is	be	AUX
ejpam-2231	6	6	a	a	DET
ejpam-2231	6	7	left	left	ADJ
ejpam-2231	6	8	ideal	ideal	NOUN
ejpam-2231	6	9	of	of	ADP
ejpam-2231	6	10	some	some	DET
ejpam-2231	6	11	left	leave	VERB
ejpam-2231	6	12	ideal	ideal	NOUN
ejpam-2231	6	13	of	of	ADP
ejpam-2231	6	14	s.	s.	PROPN
ejpam-2231	6	15	we	we	PRON
ejpam-2231	6	16	also	also	ADV
ejpam-2231	6	17	show	show	VERB
ejpam-2231	6	18	that	that	SCONJ
ejpam-2231	6	19	an	an	DET
ejpam-2231	6	20	la	la	PROPN
ejpam-2231	6	21	-semigroup	-semigroup	NOUN
ejpam-2231	6	22	s	s	PART
ejpam-2231	6	23	is	be	AUX
ejpam-2231	6	24	0	0	NUM
ejpam-2231	6	25	−	−	PROPN
ejpam-2231	6	26	(	(	PUNCT
ejpam-2231	6	27	0,2)-bisimple	0,2)-bisimple	NUM
ejpam-2231	6	28	if	if	SCONJ
ejpam-2231	7	1	and	and	CCONJ
ejpam-2231	7	2	only	only	ADV
ejpam-2231	7	3	if	if	SCONJ
ejpam-2231	7	4	s	s	NOUN
ejpam-2231	7	5	is	be	AUX
ejpam-2231	7	6	right	right	ADJ
ejpam-2231	7	7	0	0	NOUN
ejpam-2231	7	8	-	-	NOUN
ejpam-2231	7	9	simple	simple	ADJ
ejpam-2231	7	10	.	.	PUNCT
ejpam-2231	8	1	furthermore	furthermore	ADV
ejpam-2231	8	2	we	we	PRON
ejpam-2231	8	3	study	study	VERB
ejpam-2231	8	4	0	0	NUM
ejpam-2231	8	5	-	-	PUNCT
ejpam-2231	8	6	minimal	minimal	ADJ
ejpam-2231	8	7	(	(	PUNCT
ejpam-2231	8	8	m	m	PROPN
ejpam-2231	8	9	,	,	PUNCT
ejpam-2231	8	10	n)-ideals	n)-ideal	NOUN
ejpam-2231	8	11	in	in	ADP
ejpam-2231	8	12	an	an	DET
ejpam-2231	8	13	la	la	PROPN
ejpam-2231	8	14	-semigroup	-semigroup	NOUN
ejpam-2231	8	15	s	s	PART
ejpam-2231	8	16	and	and	CCONJ
ejpam-2231	8	17	prove	prove	VERB
ejpam-2231	8	18	that	that	SCONJ
ejpam-2231	8	19	if	if	SCONJ
ejpam-2231	8	20	r	r	NOUN
ejpam-2231	8	21	,	,	PUNCT
ejpam-2231	8	22	(	(	PUNCT
ejpam-2231	8	23	l	l	NOUN
ejpam-2231	8	24	)	)	PUNCT
ejpam-2231	8	25	is	be	AUX
ejpam-2231	8	26	a	a	DET
ejpam-2231	8	27	0	0	NUM
ejpam-2231	8	28	-	-	PUNCT
ejpam-2231	8	29	minimal	minimal	ADJ
ejpam-2231	8	30	right	right	NOUN
ejpam-2231	8	31	(	(	PUNCT
ejpam-2231	8	32	le	le	PROPN
ejpam-2231	8	33	f	f	PROPN
ejpam-2231	8	34	t	t	PROPN
ejpam-2231	8	35	)	)	PUNCT
ejpam-2231	8	36	ideal	ideal	NOUN
ejpam-2231	8	37	of	of	ADP
ejpam-2231	8	38	s	s	PROPN
ejpam-2231	8	39	,	,	PUNCT
ejpam-2231	8	40	then	then	ADV
ejpam-2231	8	41	either	either	CCONJ
ejpam-2231	8	42	rm	rm	PROPN
ejpam-2231	8	43	ln	ln	NOUN
ejpam-2231	9	1	=	=	PUNCT
ejpam-2231	10	1	{	{	PUNCT
ejpam-2231	10	2	0	0	NUM
ejpam-2231	10	3	}	}	PUNCT
ejpam-2231	10	4	or	or	CCONJ
ejpam-2231	10	5	rm	rm	PROPN
ejpam-2231	10	6	ln	ln	PROPN
ejpam-2231	10	7	is	be	AUX
ejpam-2231	10	8	a	a	DET
ejpam-2231	10	9	0	0	NUM
ejpam-2231	10	10	-	-	PUNCT
ejpam-2231	10	11	minimal	minimal	ADJ
ejpam-2231	10	12	(	(	PUNCT
ejpam-2231	10	13	m	m	PROPN
ejpam-2231	10	14	,	,	PUNCT
ejpam-2231	10	15	n)-ideal	n)-ideal	NOUN
ejpam-2231	10	16	of	of	ADP
ejpam-2231	10	17	s	s	PRON
ejpam-2231	10	18	for	for	ADP
ejpam-2231	10	19	m	m	PRON
ejpam-2231	10	20	,	,	PUNCT
ejpam-2231	10	21	n≥	n≥	PROPN
ejpam-2231	10	22	3	3	X
ejpam-2231	10	23	.	.	PUNCT
ejpam-2231	11	1	finally	finally	ADV
ejpam-2231	11	2	we	we	PRON
ejpam-2231	11	3	discuss	discuss	VERB
ejpam-2231	11	4	(	(	PUNCT
ejpam-2231	11	5	m	m	PROPN
ejpam-2231	11	6	,	,	PUNCT
ejpam-2231	11	7	n)-ideals	n)-ideal	NOUN
ejpam-2231	11	8	in	in	ADP
ejpam-2231	11	9	an	an	DET
ejpam-2231	11	10	(	(	PUNCT
ejpam-2231	11	11	m	m	PROPN
ejpam-2231	11	12	,	,	PUNCT
ejpam-2231	11	13	n)-regularla	n)-regularla	X
ejpam-2231	11	14	-semigroup	-semigroup	NOUN
ejpam-2231	11	15	s	s	PART
ejpam-2231	11	16	and	and	CCONJ
ejpam-2231	11	17	show	show	VERB
ejpam-2231	11	18	that	that	SCONJ
ejpam-2231	11	19	s	s	VERB
ejpam-2231	11	20	is	be	AUX
ejpam-2231	11	21	(	(	PUNCT
ejpam-2231	11	22	0,1)-regular	0,1)-regular	NUM
ejpam-2231	11	23	if	if	SCONJ
ejpam-2231	11	24	and	and	CCONJ
ejpam-2231	11	25	only	only	ADV
ejpam-2231	11	26	if	if	SCONJ
ejpam-2231	11	27	l	l	NOUN
ejpam-2231	11	28	=	=	PUNCT
ejpam-2231	12	1	sl	sl	INTJ
ejpam-2231	12	2	where	where	SCONJ
ejpam-2231	12	3	l	l	NOUN
ejpam-2231	12	4	is	be	AUX
ejpam-2231	12	5	a	a	DET
ejpam-2231	12	6	(	(	PUNCT
ejpam-2231	12	7	0,1)-ideal	0,1)-ideal	NUM
ejpam-2231	12	8	of	of	ADP
ejpam-2231	12	9	s.	s.	PROPN
ejpam-2231	12	10	2010	2010	NUM
ejpam-2231	12	11	mathematics	mathematics	PROPN
ejpam-2231	12	12	subject	subject	NOUN
ejpam-2231	12	13	classifications	classification	NOUN
ejpam-2231	12	14	:	:	PUNCT
ejpam-2231	12	15	20m10	20m10	NUM
ejpam-2231	12	16	,	,	PUNCT
ejpam-2231	12	17	20n99	20n99	NUM
ejpam-2231	12	18	key	key	ADJ
ejpam-2231	12	19	words	word	NOUN
ejpam-2231	12	20	and	and	CCONJ
ejpam-2231	12	21	phrases	phrase	NOUN
ejpam-2231	12	22	:	:	PUNCT
ejpam-2231	12	23	la	la	ADJ
ejpam-2231	12	24	-semigroups	-semigroup	NOUN
ejpam-2231	12	25	,	,	PUNCT
ejpam-2231	12	26	left	leave	VERB
ejpam-2231	12	27	invertive	invertive	ADJ
ejpam-2231	12	28	law	law	NOUN
ejpam-2231	12	29	,	,	PUNCT
ejpam-2231	12	30	left	leave	VERB
ejpam-2231	12	31	identity	identity	NOUN
ejpam-2231	12	32	and	and	CCONJ
ejpam-2231	12	33	(	(	PUNCT
ejpam-2231	12	34	m	m	PROPN
ejpam-2231	12	35	,	,	PUNCT
ejpam-2231	12	36	n)-ideals	n)-ideal	NOUN
ejpam-2231	12	37	.	.	NOUN
ejpam-2231	13	1	1	1	X
ejpam-2231	13	2	.	.	X
ejpam-2231	13	3	introduction	introduction	NOUN
ejpam-2231	13	4	a	a	DET
ejpam-2231	13	5	left	left	NOUN
ejpam-2231	13	6	almost	almost	ADV
ejpam-2231	13	7	semigroup	semigroup	ADJ
ejpam-2231	13	8	(	(	PUNCT
ejpam-2231	13	9	la	la	PROPN
ejpam-2231	13	10	-semigroup	-semigroup	PROPN
ejpam-2231	13	11	)	)	PUNCT
ejpam-2231	13	12	is	be	AUX
ejpam-2231	13	13	a	a	DET
ejpam-2231	13	14	groupoid	groupoid	NOUN
ejpam-2231	13	15	ssatisfying	ssatisfye	VERB
ejpam-2231	13	16	the	the	DET
ejpam-2231	13	17	left	left	ADJ
ejpam-2231	13	18	invertive	invertive	ADJ
ejpam-2231	13	19	law	law	NOUN
ejpam-2231	13	20	(	(	PUNCT
ejpam-2231	13	21	ab)c	ab)c	PROPN
ejpam-2231	13	22	=	=	SYM
ejpam-2231	13	23	(	(	PUNCT
ejpam-2231	13	24	cb)a	cb)a	PROPN
ejpam-2231	13	25	for	for	ADP
ejpam-2231	13	26	all	all	DET
ejpam-2231	13	27	a	a	DET
ejpam-2231	13	28	,	,	PUNCT
ejpam-2231	13	29	b	b	NOUN
ejpam-2231	13	30	,	,	PUNCT
ejpam-2231	13	31	c	c	PROPN
ejpam-2231	13	32	∈	∈	PROPN
ejpam-2231	13	33	s.	s.	PROPN
ejpam-2231	13	34	this	this	PRON
ejpam-2231	13	35	left	leave	VERB
ejpam-2231	13	36	invertive	invertive	ADJ
ejpam-2231	13	37	law	law	NOUN
ejpam-2231	13	38	has	have	AUX
ejpam-2231	13	39	been	be	AUX
ejpam-2231	13	40	obtained	obtain	VERB
ejpam-2231	13	41	by	by	ADP
ejpam-2231	13	42	introducing	introduce	VERB
ejpam-2231	13	43	braces	brace	NOUN
ejpam-2231	13	44	on	on	ADP
ejpam-2231	13	45	the	the	DET
ejpam-2231	13	46	left	left	NOUN
ejpam-2231	13	47	of	of	ADP
ejpam-2231	13	48	ternary	ternary	ADJ
ejpam-2231	13	49	commutative	commutative	ADJ
ejpam-2231	13	50	law	law	NOUN
ejpam-2231	13	51	abc	abc	PROPN
ejpam-2231	13	52	=	=	SYM
ejpam-2231	13	53	cba	cba	PROPN
ejpam-2231	13	54	.	.	PUNCT
ejpam-2231	14	1	the	the	DET
ejpam-2231	14	2	concept	concept	NOUN
ejpam-2231	14	3	of	of	ADP
ejpam-2231	14	4	an	an	DET
ejpam-2231	14	5	la	la	ADJ
ejpam-2231	14	6	-semigroup	-semigroup	NOUN
ejpam-2231	14	7	was	be	AUX
ejpam-2231	14	8	first	first	ADV
ejpam-2231	14	9	given	give	VERB
ejpam-2231	14	10	by	by	ADP
ejpam-2231	14	11	kazim	kazim	PROPN
ejpam-2231	14	12	and	and	CCONJ
ejpam-2231	14	13	naseeruddin	naseeruddin	VERB
ejpam-2231	14	14	in	in	ADP
ejpam-2231	14	15	1972	1972	NUM
ejpam-2231	14	16	[	[	X
ejpam-2231	14	17	3	3	NUM
ejpam-2231	14	18	]	]	PUNCT
ejpam-2231	14	19	.	.	PUNCT
ejpam-2231	15	1	anla	anla	PROPN
ejpam-2231	15	2	-semigroup	-semigroup	PROPN
ejpam-2231	15	3	satisfies	satisfy	VERB
ejpam-2231	15	4	the	the	DET
ejpam-2231	15	5	medial	medial	ADJ
ejpam-2231	15	6	law	law	NOUN
ejpam-2231	15	7	(	(	PUNCT
ejpam-2231	15	8	ab)(cd	ab)(cd	PROPN
ejpam-2231	15	9	)	)	PUNCT
ejpam-2231	15	10	=	=	SYM
ejpam-2231	15	11	(	(	PUNCT
ejpam-2231	15	12	ac)(bd	ac)(bd	PROPN
ejpam-2231	15	13	)	)	PUNCT
ejpam-2231	15	14	for	for	ADP
ejpam-2231	15	15	all	all	DET
ejpam-2231	15	16	a	a	DET
ejpam-2231	15	17	,	,	PUNCT
ejpam-2231	15	18	b	b	NOUN
ejpam-2231	15	19	,	,	PUNCT
ejpam-2231	15	20	c	c	NOUN
ejpam-2231	15	21	,	,	PUNCT
ejpam-2231	15	22	d	d	PROPN
ejpam-2231	15	23	∈	∈	PROPN
ejpam-2231	15	24	s.	s.	PROPN
ejpam-2231	15	25	since	since	SCONJ
ejpam-2231	15	26	la	la	PROPN
ejpam-2231	15	27	-semigroups	-semigroup	NOUN
ejpam-2231	15	28	satisfy	satisfy	VERB
ejpam-2231	15	29	medial	medial	ADJ
ejpam-2231	15	30	law	law	NOUN
ejpam-2231	15	31	,	,	PUNCT
ejpam-2231	15	32	they	they	PRON
ejpam-2231	15	33	belong	belong	VERB
ejpam-2231	15	34	to	to	ADP
ejpam-2231	15	35	the	the	DET
ejpam-2231	15	36	class	class	NOUN
ejpam-2231	15	37	of	of	ADP
ejpam-2231	15	38	entropic	entropic	ADJ
ejpam-2231	15	39	groupoids	groupoid	NOUN
ejpam-2231	15	40	which	which	PRON
ejpam-2231	15	41	are	be	AUX
ejpam-2231	15	42	also	also	ADV
ejpam-2231	15	43	called	call	VERB
ejpam-2231	15	44	abelian	abelian	ADJ
ejpam-2231	15	45	quasigroups	quasigroup	NOUN
ejpam-2231	16	1	[	[	X
ejpam-2231	16	2	12	12	NUM
ejpam-2231	16	3	]	]	PUNCT
ejpam-2231	16	4	.	.	PUNCT
ejpam-2231	17	1	if	if	SCONJ
ejpam-2231	17	2	an	an	DET
ejpam-2231	17	3	la	la	PROPN
ejpam-2231	17	4	-semigroup	-semigroup	NOUN
ejpam-2231	17	5	s	s	PART
ejpam-2231	17	6	contains	contain	VERB
ejpam-2231	17	7	a	a	DET
ejpam-2231	17	8	left	left	ADJ
ejpam-2231	17	9	identity	identity	NOUN
ejpam-2231	17	10	(	(	PUNCT
ejpam-2231	17	11	unitary	unitary	ADJ
ejpam-2231	17	12	la	la	ADJ
ejpam-2231	17	13	-semigroup	-semigroup	NOUN
ejpam-2231	17	14	)	)	PUNCT
ejpam-2231	17	15	,	,	PUNCT
ejpam-2231	17	16	then	then	ADV
ejpam-2231	17	17	it	it	PRON
ejpam-2231	17	18	satisfies	satisfy	VERB
ejpam-2231	17	19	the	the	DET
ejpam-2231	17	20	paramedial	paramedial	ADJ
ejpam-2231	17	21	law	law	NOUN
ejpam-2231	17	22	(	(	PUNCT
ejpam-2231	17	23	ab)(cd	ab)(cd	PROPN
ejpam-2231	17	24	)	)	PUNCT
ejpam-2231	17	25	=	=	SYM
ejpam-2231	17	26	(	(	PUNCT
ejpam-2231	17	27	dc)(ba	dc)(ba	PROPN
ejpam-2231	17	28	)	)	PUNCT
ejpam-2231	17	29	and	and	CCONJ
ejpam-2231	17	30	the	the	DET
ejpam-2231	17	31	identity	identity	NOUN
ejpam-2231	17	32	a(bc	a(bc	NUM
ejpam-2231	17	33	)	)	PUNCT
ejpam-2231	17	34	=	=	SYM
ejpam-2231	17	35	b(ac	b(ac	X
ejpam-2231	17	36	)	)	PUNCT
ejpam-2231	17	37	for	for	ADP
ejpam-2231	17	38	all	all	DET
ejpam-2231	17	39	a	a	DET
ejpam-2231	17	40	,	,	PUNCT
ejpam-2231	17	41	b	b	NOUN
ejpam-2231	17	42	,	,	PUNCT
ejpam-2231	17	43	c	c	NOUN
ejpam-2231	17	44	,	,	PUNCT
ejpam-2231	17	45	d	d	PROPN
ejpam-2231	17	46	∈	∈	PROPN
ejpam-2231	17	47	s	s	PART
ejpam-2231	17	48	[	[	X
ejpam-2231	17	49	7	7	NUM
ejpam-2231	17	50	]	]	PUNCT
ejpam-2231	17	51	.	.	PUNCT
ejpam-2231	18	1	an	an	DET
ejpam-2231	18	2	la	la	PROPN
ejpam-2231	18	3	-semigroup	-semigroup	NOUN
ejpam-2231	18	4	is	be	AUX
ejpam-2231	18	5	a	a	DET
ejpam-2231	18	6	useful	useful	ADJ
ejpam-2231	18	7	algebraic	algebraic	ADJ
ejpam-2231	18	8	structure	structure	NOUN
ejpam-2231	18	9	,	,	PUNCT
ejpam-2231	18	10	midway	midway	ADV
ejpam-2231	18	11	between	between	ADP
ejpam-2231	18	12	a	a	DET
ejpam-2231	18	13	groupoid	groupoid	NOUN
ejpam-2231	18	14	and	and	CCONJ
ejpam-2231	18	15	a	a	DET
ejpam-2231	18	16	commutative	commutative	ADJ
ejpam-2231	18	17	semigroup	semigroup	NOUN
ejpam-2231	18	18	.	.	PUNCT
ejpam-2231	19	1	anla	anla	PROPN
ejpam-2231	19	2	-semigroup	-semigroup	PROPN
ejpam-2231	19	3	is	be	AUX
ejpam-2231	19	4	non	non	ADJ
ejpam-2231	19	5	-	-	ADJ
ejpam-2231	19	6	associative	associative	ADJ
ejpam-2231	19	7	and	and	CCONJ
ejpam-2231	19	8	non	non	ADJ
ejpam-2231	19	9	-	-	ADJ
ejpam-2231	19	10	commutative	commutative	ADJ
ejpam-2231	19	11	in	in	ADP
ejpam-2231	19	12	general	general	ADJ
ejpam-2231	19	13	,	,	PUNCT
ejpam-2231	19	14	however	however	ADV
ejpam-2231	19	15	,	,	PUNCT
ejpam-2231	19	16	there	there	PRON
ejpam-2231	19	17	is	be	VERB
ejpam-2231	19	18	a	a	DET
ejpam-2231	19	19	close	close	ADJ
ejpam-2231	19	20	relationship	relationship	NOUN
ejpam-2231	19	21	with	with	ADP
ejpam-2231	19	22	semigroup	semigroup	PROPN
ejpam-2231	19	23	as	as	ADV
ejpam-2231	19	24	well	well	ADV
ejpam-2231	19	25	as	as	ADP
ejpam-2231	19	26	with	with	ADP
ejpam-2231	19	27	commutative	commutative	ADJ
ejpam-2231	19	28	structures	structure	NOUN
ejpam-2231	19	29	.	.	PUNCT
ejpam-2231	20	1	it	it	PRON
ejpam-2231	20	2	has	have	AUX
ejpam-2231	20	3	been	be	AUX
ejpam-2231	20	4	investigated	investigate	VERB
ejpam-2231	20	5	in	in	ADP
ejpam-2231	20	6	[	[	X
ejpam-2231	20	7	7	7	X
ejpam-2231	20	8	]	]	PUNCT
ejpam-2231	20	9	that	that	SCONJ
ejpam-2231	20	10	if	if	SCONJ
ejpam-2231	20	11	an	an	DET
ejpam-2231	20	12	la	la	PROPN
ejpam-2231	20	13	-semigroup	-semigroup	NOUN
ejpam-2231	20	14	contains	contain	VERB
ejpam-2231	20	15	a	a	DET
ejpam-2231	20	16	right	right	ADJ
ejpam-2231	20	17	identity	identity	NOUN
ejpam-2231	20	18	,	,	PUNCT
ejpam-2231	20	19	then	then	ADV
ejpam-2231	20	20	it	it	PRON
ejpam-2231	20	21	becomes	become	VERB
ejpam-2231	20	22	a	a	DET
ejpam-2231	20	23	commutative	commutative	ADJ
ejpam-2231	20	24	semigroup	semigroup	NOUN
ejpam-2231	20	25	.	.	PUNCT
ejpam-2231	21	1	the	the	DET
ejpam-2231	21	2	connection	connection	NOUN
ejpam-2231	21	3	of	of	ADP
ejpam-2231	21	4	a	a	DET
ejpam-2231	21	5	commutative	commutative	ADJ
ejpam-2231	21	6	inverse	inverse	NOUN
ejpam-2231	21	7	semigroup	semigroup	NOUN
ejpam-2231	21	8	∗corresponding	∗corresponde	VERB
ejpam-2231	21	9	author	author	NOUN
ejpam-2231	21	10	.	.	PUNCT
ejpam-2231	22	1	email	email	NOUN
ejpam-2231	22	2	addresses	address	NOUN
ejpam-2231	22	3	:	:	PUNCT
ejpam-2231	23	1	wkyousafzai@163.com	wkyousafzai@163.com	PROPN
ejpam-2231	23	2	(	(	PUNCT
ejpam-2231	23	3	w.	w.	PROPN
ejpam-2231	23	4	khan	khan	PROPN
ejpam-2231	23	5	)	)	PUNCT
ejpam-2231	23	6	,	,	PUNCT
ejpam-2231	23	7	yousafzaimath@gmail.com	yousafzaimath@gmail.com	PROPN
ejpam-2231	23	8	(	(	PUNCT
ejpam-2231	23	9	f.	f.	PROPN
ejpam-2231	23	10	yousafzai	yousafzai	PROPN
ejpam-2231	23	11	)	)	PUNCT
ejpam-2231	23	12	,	,	PUNCT
ejpam-2231	23	13	madadmath@yahoo.com	madadmath@yahoo.com	X
ejpam-2231	24	1	(	(	PUNCT
ejpam-2231	24	2	m.	m.	PROPN
ejpam-2231	24	3	khan	khan	PROPN
ejpam-2231	24	4	)	)	PUNCT
ejpam-2231	24	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2231	25	1	277	277	NUM
ejpam-2231	25	2	c	c	NOUN
ejpam-2231	25	3	©	©	PROPN
ejpam-2231	25	4	2016	2016	NUM
ejpam-2231	25	5	ejpam	ejpam	VERB
ejpam-2231	25	6	all	all	DET
ejpam-2231	25	7	rights	right	NOUN
ejpam-2231	25	8	reserved	reserve	VERB
ejpam-2231	25	9	.	.	PUNCT
ejpam-2231	26	1	w.	w.	PROPN
ejpam-2231	26	2	khan	khan	PROPN
ejpam-2231	26	3	,	,	PUNCT
ejpam-2231	26	4	f.	f.	PROPN
ejpam-2231	26	5	yousafzai	yousafzai	PROPN
ejpam-2231	26	6	,	,	PUNCT
ejpam-2231	26	7	and	and	CCONJ
ejpam-2231	26	8	m.	m.	PROPN
ejpam-2231	26	9	khan	khan	PROPN
ejpam-2231	26	10	/	/	SYM
ejpam-2231	26	11	eur	eur	PROPN
ejpam-2231	26	12	.	.	PUNCT
ejpam-2231	27	1	j.	j.	PROPN
ejpam-2231	27	2	pure	pure	PROPN
ejpam-2231	27	3	appl	appl	PROPN
ejpam-2231	27	4	.	.	PROPN
ejpam-2231	27	5	math	math	PROPN
ejpam-2231	27	6	,	,	PUNCT
ejpam-2231	27	7	9	9	NUM
ejpam-2231	27	8	(	(	PUNCT
ejpam-2231	27	9	2016	2016	NUM
ejpam-2231	27	10	)	)	PUNCT
ejpam-2231	27	11	,	,	PUNCT
ejpam-2231	27	12	277	277	NUM
ejpam-2231	27	13	-	-	SYM
ejpam-2231	27	14	291	291	NUM
ejpam-2231	27	15	278	278	NUM
ejpam-2231	27	16	with	with	ADP
ejpam-2231	27	17	an	an	DET
ejpam-2231	27	18	la	la	PROPN
ejpam-2231	27	19	-semigroup	-semigroup	NOUN
ejpam-2231	27	20	has	have	AUX
ejpam-2231	27	21	been	be	AUX
ejpam-2231	27	22	given	give	VERB
ejpam-2231	27	23	by	by	ADP
ejpam-2231	27	24	yousafzai	yousafzai	PROPN
ejpam-2231	27	25	et	et	PROPN
ejpam-2231	27	26	al	al	PROPN
ejpam-2231	27	27	.	.	PUNCT
ejpam-2231	28	1	in	in	ADP
ejpam-2231	28	2	[	[	X
ejpam-2231	28	3	16	16	NUM
ejpam-2231	28	4	]	]	PUNCT
ejpam-2231	28	5	as	as	ADP
ejpam-2231	28	6	,	,	PUNCT
ejpam-2231	28	7	a	a	DET
ejpam-2231	28	8	commutative	commutative	ADJ
ejpam-2231	28	9	inverse	inverse	NOUN
ejpam-2231	28	10	semigroup	semigroup	NOUN
ejpam-2231	28	11	(	(	PUNCT
ejpam-2231	28	12	s	s	PROPN
ejpam-2231	28	13	,	,	PUNCT
ejpam-2231	28	14	·	·	PUNCT
ejpam-2231	28	15	)	)	PUNCT
ejpam-2231	28	16	becomes	become	VERB
ejpam-2231	28	17	an	an	DET
ejpam-2231	28	18	la	la	X
ejpam-2231	28	19	-semigroup	-semigroup	NOUN
ejpam-2231	28	20	(	(	PUNCT
ejpam-2231	28	21	s,∗	s,∗	PROPN
ejpam-2231	28	22	)	)	PUNCT
ejpam-2231	28	23	under	under	ADP
ejpam-2231	28	24	a	a	DET
ejpam-2231	28	25	∗	∗	NOUN
ejpam-2231	28	26	b	b	NOUN
ejpam-2231	28	27	=	=	SYM
ejpam-2231	28	28	ba−1r−1	ba−1r−1	PROPN
ejpam-2231	28	29	,	,	PUNCT
ejpam-2231	28	30	∀a	∀a	X
ejpam-2231	28	31	,	,	PUNCT
ejpam-2231	28	32	b	b	X
ejpam-2231	28	33	,	,	PUNCT
ejpam-2231	28	34	r	r	PROPN
ejpam-2231	28	35	∈	∈	PROPN
ejpam-2231	28	36	s.	s.	PROPN
ejpam-2231	28	37	an	an	DET
ejpam-2231	28	38	la	la	PROPN
ejpam-2231	28	39	-semigroup	-semigroup	NOUN
ejpam-2231	28	40	s	s	PART
ejpam-2231	28	41	with	with	ADP
ejpam-2231	28	42	left	left	ADJ
ejpam-2231	28	43	identity	identity	NOUN
ejpam-2231	28	44	becomes	become	VERB
ejpam-2231	28	45	a	a	DET
ejpam-2231	28	46	semigroup	semigroup	NOUN
ejpam-2231	28	47	under	under	ADP
ejpam-2231	28	48	the	the	DET
ejpam-2231	28	49	binary	binary	ADJ
ejpam-2231	28	50	operation	operation	NOUN
ejpam-2231	28	51	"	"	PUNCT
ejpam-2231	28	52	◦	◦	NOUN
ejpam-2231	28	53	e	e	NOUN
ejpam-2231	28	54	"	"	PUNCT
ejpam-2231	28	55	,	,	PUNCT
ejpam-2231	28	56	defined	define	VERB
ejpam-2231	28	57	as	as	ADP
ejpam-2231	28	58	x	x	X
ejpam-2231	28	59	◦	◦	NOUN
ejpam-2231	28	60	e	e	X
ejpam-2231	28	61	y	y	NOUN
ejpam-2231	28	62	=	=	SYM
ejpam-2231	28	63	(	(	PUNCT
ejpam-2231	28	64	xe)y	xe)y	PROPN
ejpam-2231	28	65	for	for	ADP
ejpam-2231	28	66	all	all	DET
ejpam-2231	28	67	x	x	SYM
ejpam-2231	28	68	,	,	PUNCT
ejpam-2231	28	69	y	y	PROPN
ejpam-2231	28	70	∈	∈	PROPN
ejpam-2231	28	71	s	s	PART
ejpam-2231	28	72	[	[	X
ejpam-2231	28	73	17	17	NUM
ejpam-2231	28	74	]	]	PUNCT
ejpam-2231	28	75	.	.	PUNCT
ejpam-2231	29	1	an	an	DET
ejpam-2231	29	2	la	la	PROPN
ejpam-2231	29	3	-semigroup	-semigroup	NOUN
ejpam-2231	29	4	is	be	AUX
ejpam-2231	29	5	the	the	DET
ejpam-2231	29	6	generalization	generalization	NOUN
ejpam-2231	29	7	of	of	ADP
ejpam-2231	29	8	a	a	DET
ejpam-2231	29	9	semigroup	semigroup	ADJ
ejpam-2231	29	10	theory	theory	NOUN
ejpam-2231	29	11	[	[	X
ejpam-2231	29	12	7	7	NUM
ejpam-2231	29	13	]	]	PUNCT
ejpam-2231	29	14	and	and	CCONJ
ejpam-2231	29	15	has	have	VERB
ejpam-2231	29	16	vast	vast	ADJ
ejpam-2231	29	17	applications	application	NOUN
ejpam-2231	29	18	in	in	ADP
ejpam-2231	29	19	collaboration	collaboration	NOUN
ejpam-2231	29	20	with	with	ADP
ejpam-2231	29	21	semigroups	semigroup	NOUN
ejpam-2231	29	22	like	like	ADP
ejpam-2231	29	23	other	other	ADJ
ejpam-2231	29	24	branches	branch	NOUN
ejpam-2231	29	25	of	of	ADP
ejpam-2231	29	26	mathematics	mathematic	NOUN
ejpam-2231	29	27	.	.	PUNCT
ejpam-2231	30	1	khan	khan	PROPN
ejpam-2231	30	2	et	et	PROPN
ejpam-2231	30	3	al	al	PROPN
ejpam-2231	30	4	.	.	PROPN
ejpam-2231	30	5	studied	study	VERB
ejpam-2231	30	6	an	an	DET
ejpam-2231	30	7	intra	intra	ADJ
ejpam-2231	30	8	-	-	ADJ
ejpam-2231	30	9	regular	regular	ADJ
ejpam-2231	30	10	class	class	NOUN
ejpam-2231	30	11	of	of	ADP
ejpam-2231	30	12	an	an	DET
ejpam-2231	30	13	la	la	ADJ
ejpam-2231	30	14	-semigroup	-semigroup	NOUN
ejpam-2231	30	15	in	in	ADP
ejpam-2231	30	16	[	[	X
ejpam-2231	30	17	4	4	NUM
ejpam-2231	30	18	]	]	PUNCT
ejpam-2231	30	19	and	and	CCONJ
ejpam-2231	30	20	proved	prove	VERB
ejpam-2231	30	21	some	some	DET
ejpam-2231	30	22	interesting	interesting	ADJ
ejpam-2231	30	23	problems	problem	NOUN
ejpam-2231	30	24	by	by	ADP
ejpam-2231	30	25	using	use	VERB
ejpam-2231	30	26	different	different	ADJ
ejpam-2231	30	27	ideals	ideal	NOUN
ejpam-2231	30	28	.	.	PUNCT
ejpam-2231	31	1	they	they	PRON
ejpam-2231	31	2	proved	prove	VERB
ejpam-2231	31	3	that	that	SCONJ
ejpam-2231	31	4	the	the	DET
ejpam-2231	31	5	set	set	NOUN
ejpam-2231	31	6	of	of	ADP
ejpam-2231	31	7	all	all	DET
ejpam-2231	31	8	two	two	NUM
ejpam-2231	31	9	-	-	PUNCT
ejpam-2231	31	10	sided	sided	ADJ
ejpam-2231	31	11	ideals	ideal	NOUN
ejpam-2231	31	12	of	of	ADP
ejpam-2231	31	13	intra	intra	ADJ
ejpam-2231	31	14	-	-	ADJ
ejpam-2231	31	15	regular	regular	ADJ
ejpam-2231	31	16	la	la	ADJ
ejpam-2231	31	17	-semigroup	-semigroup	NOUN
ejpam-2231	31	18	forms	form	VERB
ejpam-2231	31	19	a	a	DET
ejpam-2231	31	20	semilattice	semilattice	NOUN
ejpam-2231	31	21	structure	structure	NOUN
ejpam-2231	31	22	.	.	PUNCT
ejpam-2231	32	1	they	they	PRON
ejpam-2231	32	2	characterized	characterize	VERB
ejpam-2231	32	3	an	an	DET
ejpam-2231	32	4	intra	intra	ADJ
ejpam-2231	32	5	-	-	ADJ
ejpam-2231	32	6	regularla	regularla	ADJ
ejpam-2231	32	7	-semigroup	-semigroup	NOUN
ejpam-2231	32	8	by	by	ADP
ejpam-2231	32	9	using	use	VERB
ejpam-2231	32	10	left	leave	VERB
ejpam-2231	32	11	,	,	PUNCT
ejpam-2231	32	12	right	right	INTJ
ejpam-2231	32	13	,	,	PUNCT
ejpam-2231	32	14	two	two	NUM
ejpam-2231	32	15	-	-	PUNCT
ejpam-2231	32	16	sided	sided	ADJ
ejpam-2231	32	17	and	and	CCONJ
ejpam-2231	32	18	bi	bi	NOUN
ejpam-2231	32	19	-	-	NOUN
ejpam-2231	32	20	ideals	ideal	NOUN
ejpam-2231	32	21	.	.	PUNCT
ejpam-2231	33	1	an	an	DET
ejpam-2231	33	2	la	la	PROPN
ejpam-2231	33	3	-semigroup	-semigroup	NOUN
ejpam-2231	33	4	is	be	AUX
ejpam-2231	33	5	the	the	DET
ejpam-2231	33	6	generalization	generalization	NOUN
ejpam-2231	33	7	of	of	ADP
ejpam-2231	33	8	a	a	DET
ejpam-2231	33	9	semigroup	semigroup	ADJ
ejpam-2231	33	10	theory	theory	NOUN
ejpam-2231	33	11	[	[	X
ejpam-2231	33	12	7	7	NUM
ejpam-2231	33	13	]	]	PUNCT
ejpam-2231	33	14	.	.	PUNCT
ejpam-2231	34	1	many	many	ADJ
ejpam-2231	34	2	interesting	interesting	ADJ
ejpam-2231	34	3	results	result	NOUN
ejpam-2231	34	4	on	on	ADP
ejpam-2231	34	5	la	la	PRON
ejpam-2231	34	6	-semigroups	-semigroup	NOUN
ejpam-2231	34	7	have	have	AUX
ejpam-2231	34	8	been	be	AUX
ejpam-2231	34	9	investigated	investigate	VERB
ejpam-2231	34	10	in	in	ADP
ejpam-2231	34	11	[	[	X
ejpam-2231	34	12	5	5	NUM
ejpam-2231	34	13	,	,	PUNCT
ejpam-2231	34	14	9–11	9–11	NOUN
ejpam-2231	34	15	,	,	PUNCT
ejpam-2231	34	16	15	15	NUM
ejpam-2231	34	17	]	]	PUNCT
ejpam-2231	34	18	.	.	PUNCT
ejpam-2231	35	1	yaqoob	yaqoob	NOUN
ejpam-2231	35	2	,	,	PUNCT
ejpam-2231	35	3	corsini	corsini	PROPN
ejpam-2231	35	4	and	and	CCONJ
ejpam-2231	35	5	yousafzai	yousafzai	NOUN
ejpam-2231	36	1	[	[	X
ejpam-2231	36	2	13	13	NUM
ejpam-2231	36	3	]	]	PUNCT
ejpam-2231	36	4	extended	extend	VERB
ejpam-2231	36	5	the	the	DET
ejpam-2231	36	6	concept	concept	NOUN
ejpam-2231	36	7	of	of	ADP
ejpam-2231	36	8	la	la	NOUN
ejpam-2231	36	9	-	-	PUNCT
ejpam-2231	36	10	semigroups	semigroup	NOUN
ejpam-2231	36	11	and	and	CCONJ
ejpam-2231	36	12	introduced	introduce	VERB
ejpam-2231	36	13	a	a	DET
ejpam-2231	36	14	new	new	ADJ
ejpam-2231	36	15	structure	structure	NOUN
ejpam-2231	36	16	called	call	VERB
ejpam-2231	36	17	left	leave	VERB
ejpam-2231	36	18	almost	almost	ADV
ejpam-2231	36	19	semihypergroup	semihypergroup	ADV
ejpam-2231	36	20	.	.	PUNCT
ejpam-2231	37	1	further	further	ADJ
ejpam-2231	37	2	yaqoob	yaqoob	VERB
ejpam-2231	37	3	and	and	CCONJ
ejpam-2231	37	4	gulistan	gulistan	VERB
ejpam-2231	37	5	[	[	X
ejpam-2231	37	6	14	14	NUM
ejpam-2231	37	7	]	]	SYM
ejpam-2231	37	8	defined	define	VERB
ejpam-2231	37	9	partial	partial	ADJ
ejpam-2231	37	10	ordering	ordering	NOUN
ejpam-2231	37	11	on	on	ADP
ejpam-2231	37	12	left	left	ADJ
ejpam-2231	37	13	almost	almost	ADV
ejpam-2231	37	14	semihypergroups	semihypergroup	NOUN
ejpam-2231	37	15	.	.	PUNCT
ejpam-2231	38	1	gulistan	gulistan	PROPN
ejpam-2231	38	2	et	et	PROPN
ejpam-2231	38	3	al	al	PROPN
ejpam-2231	38	4	.	.	PUNCT
ejpam-2231	39	1	[	[	X
ejpam-2231	39	2	2	2	NUM
ejpam-2231	39	3	]	]	PUNCT
ejpam-2231	39	4	defined	define	VERB
ejpam-2231	39	5	hv	hv	NOUN
ejpam-2231	39	6	-	-	PUNCT
ejpam-2231	39	7	la	la	ADJ
ejpam-2231	39	8	semigroups	semigroup	NOUN
ejpam-2231	39	9	which	which	PRON
ejpam-2231	39	10	is	be	AUX
ejpam-2231	39	11	a	a	DET
ejpam-2231	39	12	new	new	ADJ
ejpam-2231	39	13	generalization	generalization	NOUN
ejpam-2231	39	14	of	of	ADP
ejpam-2231	39	15	la	la	PROPN
ejpam-2231	39	16	-semigroups	-semigroup	NOUN
ejpam-2231	39	17	and	and	CCONJ
ejpam-2231	39	18	la	la	ADJ
ejpam-2231	39	19	-semihypergroups	-semihypergroup	NOUN
ejpam-2231	39	20	.	.	PUNCT
ejpam-2231	40	1	2	2	NUM
ejpam-2231	40	2	.	.	NUM
ejpam-2231	40	3	preliminaries	preliminary	NOUN
ejpam-2231	40	4	and	and	CCONJ
ejpam-2231	40	5	examples	example	NOUN
ejpam-2231	40	6	if	if	SCONJ
ejpam-2231	40	7	s	s	VERB
ejpam-2231	40	8	is	be	AUX
ejpam-2231	40	9	an	an	DET
ejpam-2231	40	10	la	la	ADJ
ejpam-2231	40	11	-semigroup	-semigroup	NOUN
ejpam-2231	40	12	with	with	ADP
ejpam-2231	40	13	product	product	NOUN
ejpam-2231	40	14	·	·	PUNCT
ejpam-2231	40	15	:	:	PUNCT
ejpam-2231	40	16	s	s	VERB
ejpam-2231	40	17	×	×	NOUN
ejpam-2231	40	18	s	s	PART
ejpam-2231	40	19	−→	−→	NOUN
ejpam-2231	40	20	s	s	NOUN
ejpam-2231	40	21	,	,	PUNCT
ejpam-2231	40	22	then	then	ADV
ejpam-2231	41	1	ab	ab	PROPN
ejpam-2231	41	2	·	·	PUNCT
ejpam-2231	41	3	c	c	PROPN
ejpam-2231	41	4	and	and	CCONJ
ejpam-2231	41	5	(	(	PUNCT
ejpam-2231	41	6	ab)c	ab)c	PROPN
ejpam-2231	41	7	both	both	PRON
ejpam-2231	41	8	denote	denote	VERB
ejpam-2231	41	9	the	the	DET
ejpam-2231	41	10	product	product	NOUN
ejpam-2231	41	11	(	(	PUNCT
ejpam-2231	41	12	a	a	DET
ejpam-2231	41	13	·	·	SYM
ejpam-2231	41	14	b	b	NOUN
ejpam-2231	41	15	)	)	PUNCT
ejpam-2231	41	16	·	·	PUNCT
ejpam-2231	41	17	c.	c.	NOUN
ejpam-2231	41	18	if	if	SCONJ
ejpam-2231	41	19	there	there	PRON
ejpam-2231	41	20	is	be	VERB
ejpam-2231	41	21	an	an	DET
ejpam-2231	41	22	element	element	NOUN
ejpam-2231	41	23	0	0	NUM
ejpam-2231	41	24	of	of	ADP
ejpam-2231	41	25	an	an	DET
ejpam-2231	41	26	la	la	PROPN
ejpam-2231	41	27	-semigroup	-semigroup	NOUN
ejpam-2231	41	28	(	(	PUNCT
ejpam-2231	41	29	s	s	PROPN
ejpam-2231	41	30	,	,	PUNCT
ejpam-2231	41	31	·	·	PUNCT
ejpam-2231	41	32	)	)	PUNCT
ejpam-2231	42	1	such	such	ADJ
ejpam-2231	42	2	that	that	SCONJ
ejpam-2231	42	3	x	x	X
ejpam-2231	42	4	·	·	PUNCT
ejpam-2231	42	5	0	0	PUNCT
ejpam-2231	42	6	=	=	SYM
ejpam-2231	42	7	0	0	PUNCT
ejpam-2231	42	8	·	·	PUNCT
ejpam-2231	42	9	x	x	PUNCT
ejpam-2231	42	10	=	=	PUNCT
ejpam-2231	42	11	x	x	X
ejpam-2231	42	12	∀x	∀x	X
ejpam-2231	42	13	∈	∈	PROPN
ejpam-2231	42	14	s	s	NOUN
ejpam-2231	42	15	,	,	PUNCT
ejpam-2231	42	16	we	we	PRON
ejpam-2231	42	17	call	call	VERB
ejpam-2231	42	18	0	0	NUM
ejpam-2231	42	19	a	a	DET
ejpam-2231	42	20	zero	zero	NUM
ejpam-2231	42	21	element	element	NOUN
ejpam-2231	42	22	of	of	ADP
ejpam-2231	42	23	s.	s.	PROPN
ejpam-2231	42	24	example	example	PROPN
ejpam-2231	43	1	1	1	X
ejpam-2231	43	2	.	.	PUNCT
ejpam-2231	44	1	let	let	VERB
ejpam-2231	44	2	s	s	VERB
ejpam-2231	44	3	=	=	X
ejpam-2231	44	4	{	{	PUNCT
ejpam-2231	44	5	a	a	PRON
ejpam-2231	44	6	,	,	PUNCT
ejpam-2231	44	7	b	b	NOUN
ejpam-2231	44	8	,	,	PUNCT
ejpam-2231	44	9	c	c	NOUN
ejpam-2231	44	10	,	,	PUNCT
ejpam-2231	44	11	d	d	NOUN
ejpam-2231	44	12	,	,	PUNCT
ejpam-2231	44	13	e	e	NOUN
ejpam-2231	44	14	}	}	PUNCT
ejpam-2231	44	15	with	with	ADP
ejpam-2231	44	16	a	a	DET
ejpam-2231	44	17	left	left	ADJ
ejpam-2231	44	18	identity	identity	NOUN
ejpam-2231	44	19	d.	d.	NOUN
ejpam-2231	44	20	then	then	ADV
ejpam-2231	44	21	the	the	DET
ejpam-2231	44	22	following	follow	VERB
ejpam-2231	44	23	multiplication	multiplication	NOUN
ejpam-2231	44	24	table	table	NOUN
ejpam-2231	44	25	shows	show	VERB
ejpam-2231	44	26	that	that	SCONJ
ejpam-2231	44	27	(	(	PUNCT
ejpam-2231	44	28	s	s	X
ejpam-2231	44	29	,	,	PUNCT
ejpam-2231	44	30	·	·	PUNCT
ejpam-2231	44	31	)	)	PUNCT
ejpam-2231	44	32	is	be	AUX
ejpam-2231	44	33	a	a	DET
ejpam-2231	44	34	unitary	unitary	ADJ
ejpam-2231	44	35	la	la	ADJ
ejpam-2231	44	36	-semigroup	-semigroup	NOUN
ejpam-2231	44	37	with	with	ADP
ejpam-2231	44	38	a	a	DET
ejpam-2231	44	39	zero	zero	NUM
ejpam-2231	44	40	element	element	NOUN
ejpam-2231	44	41	a.	a.	NOUN
ejpam-2231	44	42	·	·	PUNCT
ejpam-2231	45	1	a	a	DET
ejpam-2231	45	2	b	b	X
ejpam-2231	45	3	c	c	NOUN
ejpam-2231	45	4	d	d	PROPN
ejpam-2231	45	5	e	e	X
ejpam-2231	45	6	a	a	DET
ejpam-2231	45	7	a	a	DET
ejpam-2231	45	8	a	a	DET
ejpam-2231	45	9	a	a	DET
ejpam-2231	45	10	a	a	DET
ejpam-2231	45	11	a	a	DET
ejpam-2231	45	12	b	b	NOUN
ejpam-2231	45	13	a	a	DET
ejpam-2231	45	14	e	e	NOUN
ejpam-2231	45	15	e	e	NOUN
ejpam-2231	45	16	c	c	NOUN
ejpam-2231	45	17	e	e	PROPN
ejpam-2231	45	18	c	c	PROPN
ejpam-2231	45	19	a	a	DET
ejpam-2231	45	20	e	e	X
ejpam-2231	45	21	e	e	X
ejpam-2231	45	22	b	b	PROPN
ejpam-2231	45	23	e	e	X
ejpam-2231	45	24	d	d	X
ejpam-2231	45	25	a	a	DET
ejpam-2231	45	26	b	b	NOUN
ejpam-2231	45	27	c	c	NOUN
ejpam-2231	45	28	d	d	X
ejpam-2231	45	29	e	e	X
ejpam-2231	45	30	e	e	X
ejpam-2231	45	31	a	a	DET
ejpam-2231	45	32	e	e	X
ejpam-2231	45	33	e	e	X
ejpam-2231	45	34	e	e	X
ejpam-2231	45	35	e	e	X
ejpam-2231	45	36	example	example	NOUN
ejpam-2231	45	37	2	2	NUM
ejpam-2231	45	38	.	.	PUNCT
ejpam-2231	46	1	let	let	VERB
ejpam-2231	46	2	s	s	VERB
ejpam-2231	46	3	=	=	X
ejpam-2231	46	4	{	{	PUNCT
ejpam-2231	46	5	a	a	PRON
ejpam-2231	46	6	,	,	PUNCT
ejpam-2231	46	7	b	b	NOUN
ejpam-2231	46	8	,	,	PUNCT
ejpam-2231	46	9	c	c	NOUN
ejpam-2231	46	10	,	,	PUNCT
ejpam-2231	46	11	d	d	NOUN
ejpam-2231	46	12	}	}	PUNCT
ejpam-2231	46	13	.	.	PUNCT
ejpam-2231	47	1	then	then	ADV
ejpam-2231	47	2	the	the	DET
ejpam-2231	47	3	following	follow	VERB
ejpam-2231	47	4	multiplication	multiplication	NOUN
ejpam-2231	47	5	table	table	NOUN
ejpam-2231	47	6	shows	show	VERB
ejpam-2231	47	7	that	that	SCONJ
ejpam-2231	47	8	(	(	PUNCT
ejpam-2231	47	9	s	s	X
ejpam-2231	47	10	,	,	PUNCT
ejpam-2231	47	11	·	·	PUNCT
ejpam-2231	47	12	)	)	PUNCT
ejpam-2231	47	13	is	be	AUX
ejpam-2231	47	14	an	an	DET
ejpam-2231	47	15	la	la	ADJ
ejpam-2231	47	16	-semigroup	-semigroup	NOUN
ejpam-2231	47	17	with	with	ADP
ejpam-2231	47	18	a	a	DET
ejpam-2231	47	19	zero	zero	NUM
ejpam-2231	47	20	element	element	NOUN
ejpam-2231	47	21	a.	a.	NOUN
ejpam-2231	47	22	·	·	PUNCT
ejpam-2231	48	1	a	a	DET
ejpam-2231	48	2	b	b	X
ejpam-2231	48	3	c	c	NOUN
ejpam-2231	48	4	d	d	NOUN
ejpam-2231	48	5	a	a	DET
ejpam-2231	48	6	a	a	DET
ejpam-2231	48	7	a	a	DET
ejpam-2231	48	8	a	a	DET
ejpam-2231	48	9	a	a	DET
ejpam-2231	48	10	b	b	NOUN
ejpam-2231	48	11	a	a	NOUN
ejpam-2231	48	12	d	d	X
ejpam-2231	48	13	d	d	X
ejpam-2231	48	14	c	c	PROPN
ejpam-2231	48	15	c	c	PROPN
ejpam-2231	48	16	a	a	DET
ejpam-2231	48	17	c	c	NOUN
ejpam-2231	48	18	c	c	NOUN
ejpam-2231	48	19	c	c	NOUN
ejpam-2231	49	1	d	d	NOUN
ejpam-2231	49	2	a	a	X
ejpam-2231	49	3	c	c	NOUN
ejpam-2231	49	4	c	c	NOUN
ejpam-2231	49	5	c	c	NOUN
ejpam-2231	49	6	the	the	DET
ejpam-2231	49	7	above	above	PROPN
ejpam-2231	49	8	la	la	PROPN
ejpam-2231	49	9	-semigroup	-semigroup	PROPN
ejpam-2231	49	10	s	s	PART
ejpam-2231	49	11	has	have	VERB
ejpam-2231	49	12	commutative	commutative	ADJ
ejpam-2231	49	13	powers	power	NOUN
ejpam-2231	49	14	,	,	PUNCT
ejpam-2231	49	15	that	that	PRON
ejpam-2231	49	16	is	be	AUX
ejpam-2231	49	17	aa	aa	NOUN
ejpam-2231	49	18	·	·	PUNCT
ejpam-2231	49	19	a	a	DET
ejpam-2231	49	20	=	=	X
ejpam-2231	49	21	a	a	DET
ejpam-2231	49	22	·	·	PUNCT
ejpam-2231	49	23	aa	aa	NOUN
ejpam-2231	49	24	for	for	ADP
ejpam-2231	49	25	all	all	DET
ejpam-2231	49	26	a	a	DET
ejpam-2231	49	27	∈	∈	NOUN
ejpam-2231	49	28	s	s	X
ejpam-2231	49	29	which	which	PRON
ejpam-2231	49	30	is	be	AUX
ejpam-2231	49	31	called	call	VERB
ejpam-2231	49	32	a	a	DET
ejpam-2231	49	33	locally	locally	ADV
ejpam-2231	49	34	associativela	associativela	NOUN
ejpam-2231	49	35	-semigroup	-semigroup	NOUN
ejpam-2231	49	36	[	[	X
ejpam-2231	49	37	8	8	NUM
ejpam-2231	49	38	]	]	PUNCT
ejpam-2231	49	39	.	.	PUNCT
ejpam-2231	50	1	note	note	VERB
ejpam-2231	50	2	that	that	SCONJ
ejpam-2231	50	3	s	s	VERB
ejpam-2231	50	4	has	have	VERB
ejpam-2231	50	5	no	no	DET
ejpam-2231	50	6	associative	associative	ADJ
ejpam-2231	50	7	powers	power	NOUN
ejpam-2231	50	8	for	for	ADP
ejpam-2231	50	9	all	all	DET
ejpam-2231	50	10	a	a	DET
ejpam-2231	50	11	∈	∈	NOUN
ejpam-2231	50	12	s	s	PART
ejpam-2231	50	13	because	because	SCONJ
ejpam-2231	50	14	(	(	PUNCT
ejpam-2231	50	15	bb	bb	INTJ
ejpam-2231	50	16	·	·	PUNCT
ejpam-2231	50	17	b)b	b)b	X
ejpam-2231	50	18	6=	6=	NUM
ejpam-2231	50	19	b(bb	b(bb	X
ejpam-2231	50	20	·	·	PUNCT
ejpam-2231	50	21	b	b	X
ejpam-2231	50	22	)	)	PUNCT
ejpam-2231	50	23	for	for	ADP
ejpam-2231	50	24	b	b	PROPN
ejpam-2231	50	25	∈	∈	PROPN
ejpam-2231	50	26	s.	s.	PROPN
ejpam-2231	50	27	w.	w.	PROPN
ejpam-2231	50	28	khan	khan	PROPN
ejpam-2231	50	29	,	,	PUNCT
ejpam-2231	50	30	f.	f.	PROPN
ejpam-2231	50	31	yousafzai	yousafzai	PROPN
ejpam-2231	50	32	,	,	PUNCT
ejpam-2231	50	33	and	and	CCONJ
ejpam-2231	50	34	m.	m.	PROPN
ejpam-2231	50	35	khan	khan	PROPN
ejpam-2231	50	36	/	/	SYM
ejpam-2231	50	37	eur	eur	PROPN
ejpam-2231	50	38	.	.	PUNCT
ejpam-2231	51	1	j.	j.	PROPN
ejpam-2231	51	2	pure	pure	PROPN
ejpam-2231	51	3	appl	appl	PROPN
ejpam-2231	51	4	.	.	PROPN
ejpam-2231	51	5	math	math	PROPN
ejpam-2231	51	6	,	,	PUNCT
ejpam-2231	51	7	9	9	NUM
ejpam-2231	51	8	(	(	PUNCT
ejpam-2231	51	9	2016	2016	NUM
ejpam-2231	51	10	)	)	PUNCT
ejpam-2231	51	11	,	,	PUNCT
ejpam-2231	51	12	277	277	NUM
ejpam-2231	51	13	-	-	SYM
ejpam-2231	51	14	291	291	NUM
ejpam-2231	51	15	279	279	NUM
ejpam-2231	51	16	assume	assume	VERB
ejpam-2231	51	17	that	that	SCONJ
ejpam-2231	51	18	s	s	VERB
ejpam-2231	51	19	is	be	AUX
ejpam-2231	51	20	an	an	DET
ejpam-2231	51	21	la	la	PROPN
ejpam-2231	51	22	-semigroup	-semigroup	NOUN
ejpam-2231	51	23	.	.	PUNCT
ejpam-2231	52	1	let	let	VERB
ejpam-2231	52	2	us	we	PRON
ejpam-2231	52	3	define	define	VERB
ejpam-2231	52	4	a1	a1	NOUN
ejpam-2231	52	5	=	=	SYM
ejpam-2231	52	6	a	a	NOUN
ejpam-2231	52	7	,	,	PUNCT
ejpam-2231	52	8	am+1	am+1	PROPN
ejpam-2231	52	9	=	=	PUNCT
ejpam-2231	52	10	ama	ama	PROPN
ejpam-2231	52	11	and	and	CCONJ
ejpam-2231	52	12	am	be	AUX
ejpam-2231	52	13	=	=	PUNCT
ejpam-2231	52	14	(	(	PUNCT
ejpam-2231	52	15	(	(	PUNCT
ejpam-2231	52	16	(	(	PUNCT
ejpam-2231	52	17	(	(	PUNCT
ejpam-2231	52	18	aa)a)a	aa)a)a	NOUN
ejpam-2231	52	19	)	)	PUNCT
ejpam-2231	52	20	.	.	PUNCT
ejpam-2231	52	21	.	.	PUNCT
ejpam-2231	53	1	.	.	PUNCT
ejpam-2231	53	2	a)a	a)a	PUNCT
ejpam-2231	54	1	=	=	SYM
ejpam-2231	54	2	am−1a	am−1a	PROPN
ejpam-2231	54	3	for	for	ADP
ejpam-2231	54	4	all	all	DET
ejpam-2231	54	5	a	a	DET
ejpam-2231	54	6	∈	∈	NOUN
ejpam-2231	54	7	s	s	VERB
ejpam-2231	54	8	where	where	SCONJ
ejpam-2231	54	9	m≥	m≥	ADJ
ejpam-2231	54	10	1	1	X
ejpam-2231	54	11	.	.	PUNCT
ejpam-2231	55	1	it	it	PRON
ejpam-2231	55	2	is	be	AUX
ejpam-2231	55	3	easy	easy	ADJ
ejpam-2231	55	4	to	to	PART
ejpam-2231	55	5	see	see	VERB
ejpam-2231	55	6	that	that	PRON
ejpam-2231	55	7	am	am	VERB
ejpam-2231	55	8	=	=	PUNCT
ejpam-2231	55	9	am−1a	am−1a	PROPN
ejpam-2231	55	10	=	=	SYM
ejpam-2231	55	11	aam−1	aam−1	PROPN
ejpam-2231	55	12	for	for	ADP
ejpam-2231	55	13	all	all	DET
ejpam-2231	55	14	a	a	DET
ejpam-2231	55	15	∈	∈	PROPN
ejpam-2231	55	16	s	s	PART
ejpam-2231	55	17	and	and	CCONJ
ejpam-2231	55	18	m	m	PROPN
ejpam-2231	55	19	≥	≥	NOUN
ejpam-2231	55	20	3	3	NUM
ejpam-2231	55	21	if	if	SCONJ
ejpam-2231	55	22	s	s	PROPN
ejpam-2231	55	23	has	have	VERB
ejpam-2231	55	24	a	a	DET
ejpam-2231	55	25	left	left	ADJ
ejpam-2231	55	26	identity	identity	NOUN
ejpam-2231	55	27	.	.	PUNCT
ejpam-2231	56	1	also	also	ADV
ejpam-2231	56	2	,	,	PUNCT
ejpam-2231	56	3	we	we	PRON
ejpam-2231	56	4	can	can	AUX
ejpam-2231	56	5	show	show	VERB
ejpam-2231	56	6	by	by	ADP
ejpam-2231	56	7	induction	induction	NOUN
ejpam-2231	56	8	,	,	PUNCT
ejpam-2231	56	9	(	(	PUNCT
ejpam-2231	56	10	ab)m	ab)m	X
ejpam-2231	56	11	=	=	SYM
ejpam-2231	56	12	am	be	AUX
ejpam-2231	56	13	bm	bm	NOUN
ejpam-2231	56	14	and	and	CCONJ
ejpam-2231	56	15	aman	aman	ADJ
ejpam-2231	56	16	=	=	SYM
ejpam-2231	56	17	am+n	am+n	ADJ
ejpam-2231	56	18	hold	hold	VERB
ejpam-2231	56	19	for	for	ADP
ejpam-2231	56	20	all	all	DET
ejpam-2231	56	21	a	a	DET
ejpam-2231	56	22	,	,	PUNCT
ejpam-2231	56	23	b	b	X
ejpam-2231	56	24	∈	∈	PROPN
ejpam-2231	56	25	s	s	X
ejpam-2231	56	26	and	and	CCONJ
ejpam-2231	56	27	m	m	PROPN
ejpam-2231	56	28	,	,	PUNCT
ejpam-2231	56	29	n≥	n≥	PROPN
ejpam-2231	56	30	3	3	X
ejpam-2231	56	31	.	.	PUNCT
ejpam-2231	57	1	a	a	DET
ejpam-2231	57	2	subset	subset	NOUN
ejpam-2231	57	3	a	a	PRON
ejpam-2231	57	4	of	of	ADP
ejpam-2231	57	5	an	an	DET
ejpam-2231	57	6	la	la	PROPN
ejpam-2231	57	7	-semigroup	-semigroup	NOUN
ejpam-2231	57	8	s	s	PART
ejpam-2231	57	9	is	be	AUX
ejpam-2231	57	10	called	call	VERB
ejpam-2231	57	11	a	a	DET
ejpam-2231	57	12	right	right	NOUN
ejpam-2231	57	13	(	(	PUNCT
ejpam-2231	57	14	left	left	ADJ
ejpam-2231	57	15	)	)	PUNCT
ejpam-2231	57	16	ideal	ideal	NOUN
ejpam-2231	57	17	of	of	ADP
ejpam-2231	57	18	s	s	PRON
ejpam-2231	57	19	if	if	SCONJ
ejpam-2231	57	20	as	as	ADP
ejpam-2231	57	21	⊆	⊆	X
ejpam-2231	57	22	a	a	PRON
ejpam-2231	57	23	(	(	PUNCT
ejpam-2231	57	24	sa⊆	sa⊆	NOUN
ejpam-2231	57	25	a	a	NOUN
ejpam-2231	57	26	)	)	PUNCT
ejpam-2231	57	27	,	,	PUNCT
ejpam-2231	57	28	and	and	CCONJ
ejpam-2231	57	29	is	be	AUX
ejpam-2231	57	30	called	call	VERB
ejpam-2231	57	31	an	an	DET
ejpam-2231	57	32	ideal	ideal	NOUN
ejpam-2231	57	33	of	of	ADP
ejpam-2231	57	34	s	s	PRON
ejpam-2231	57	35	if	if	SCONJ
ejpam-2231	57	36	it	it	PRON
ejpam-2231	57	37	is	be	AUX
ejpam-2231	57	38	both	both	PRON
ejpam-2231	57	39	left	left	ADJ
ejpam-2231	57	40	and	and	CCONJ
ejpam-2231	57	41	right	right	ADJ
ejpam-2231	57	42	ideal	ideal	NOUN
ejpam-2231	57	43	of	of	ADP
ejpam-2231	57	44	s.	s.	PROPN
ejpam-2231	57	45	a	a	DET
ejpam-2231	57	46	subset	subset	VERB
ejpam-2231	57	47	a	a	PRON
ejpam-2231	57	48	of	of	ADP
ejpam-2231	57	49	an	an	DET
ejpam-2231	57	50	la	la	PROPN
ejpam-2231	57	51	-semigroup	-semigroup	NOUN
ejpam-2231	57	52	s	s	PART
ejpam-2231	57	53	is	be	AUX
ejpam-2231	57	54	called	call	VERB
ejpam-2231	57	55	an	an	DET
ejpam-2231	57	56	la	la	NOUN
ejpam-2231	57	57	-subsemigroup	-subsemigroup	NOUN
ejpam-2231	57	58	of	of	ADP
ejpam-2231	57	59	s	s	PRON
ejpam-2231	58	1	if	if	SCONJ
ejpam-2231	58	2	a2	a2	PROPN
ejpam-2231	58	3	⊆	⊆	NUM
ejpam-2231	58	4	a.	a.	NOUN
ejpam-2231	58	5	the	the	DET
ejpam-2231	58	6	concept	concept	NOUN
ejpam-2231	58	7	of	of	ADP
ejpam-2231	58	8	(	(	PUNCT
ejpam-2231	58	9	m	m	PROPN
ejpam-2231	58	10	,	,	PUNCT
ejpam-2231	58	11	n)-ideals	n)-ideal	NOUN
ejpam-2231	58	12	of	of	ADP
ejpam-2231	58	13	a	a	DET
ejpam-2231	58	14	semigroup	semigroup	NOUN
ejpam-2231	58	15	and	and	CCONJ
ejpam-2231	58	16	an	an	DET
ejpam-2231	58	17	la	la	ADJ
ejpam-2231	58	18	-semigroup	-semigroup	NOUN
ejpam-2231	58	19	was	be	AUX
ejpam-2231	58	20	given	give	VERB
ejpam-2231	58	21	in	in	ADP
ejpam-2231	58	22	[	[	X
ejpam-2231	58	23	6	6	NUM
ejpam-2231	58	24	]	]	PUNCT
ejpam-2231	58	25	and	and	CCONJ
ejpam-2231	58	26	[	[	X
ejpam-2231	58	27	1	1	X
ejpam-2231	58	28	]	]	PUNCT
ejpam-2231	58	29	respectively	respectively	ADV
ejpam-2231	58	30	.	.	PUNCT
ejpam-2231	59	1	an	an	DET
ejpam-2231	59	2	la	la	ADV
ejpam-2231	59	3	-subsemigroup	-subsemigroup	NOUN
ejpam-2231	59	4	a	a	PRON
ejpam-2231	59	5	of	of	ADP
ejpam-2231	59	6	an	an	DET
ejpam-2231	59	7	la	la	PROPN
ejpam-2231	59	8	-semigroup	-semigroup	NOUN
ejpam-2231	59	9	s	s	PART
ejpam-2231	59	10	is	be	AUX
ejpam-2231	59	11	said	say	VERB
ejpam-2231	59	12	to	to	PART
ejpam-2231	59	13	be	be	AUX
ejpam-2231	59	14	an	an	DET
ejpam-2231	59	15	(	(	PUNCT
ejpam-2231	59	16	m	m	PROPN
ejpam-2231	59	17	,	,	PUNCT
ejpam-2231	59	18	n)-ideal	n)-ideal	NOUN
ejpam-2231	59	19	of	of	ADP
ejpam-2231	59	20	s	s	PRON
ejpam-2231	59	21	if	if	SCONJ
ejpam-2231	59	22	ams	am	NOUN
ejpam-2231	59	23	·	·	PUNCT
ejpam-2231	59	24	an	an	DET
ejpam-2231	59	25	⊆	⊆	NUM
ejpam-2231	59	26	a	a	DET
ejpam-2231	59	27	where	where	SCONJ
ejpam-2231	59	28	m	m	NOUN
ejpam-2231	59	29	,	,	PUNCT
ejpam-2231	59	30	n	n	PRON
ejpam-2231	59	31	are	be	AUX
ejpam-2231	59	32	non	non	ADJ
ejpam-2231	59	33	-	-	ADJ
ejpam-2231	59	34	negative	negative	ADJ
ejpam-2231	59	35	integers	integer	NOUN
ejpam-2231	59	36	such	such	ADJ
ejpam-2231	59	37	that	that	SCONJ
ejpam-2231	59	38	m=	m=	NOUN
ejpam-2231	59	39	n	n	PROPN
ejpam-2231	59	40	6=	6=	PROPN
ejpam-2231	59	41	0	0	NUM
ejpam-2231	59	42	.	.	PUNCT
ejpam-2231	60	1	here	here	ADV
ejpam-2231	60	2	am	be	AUX
ejpam-2231	60	3	or	or	CCONJ
ejpam-2231	60	4	an	an	PRON
ejpam-2231	60	5	are	be	AUX
ejpam-2231	60	6	suppressed	suppress	VERB
ejpam-2231	60	7	if	if	SCONJ
ejpam-2231	60	8	m=	m=	X
ejpam-2231	60	9	0	0	NUM
ejpam-2231	60	10	or	or	CCONJ
ejpam-2231	60	11	n=	n=	ADJ
ejpam-2231	60	12	0	0	NUM
ejpam-2231	60	13	,	,	PUNCT
ejpam-2231	60	14	that	that	PRON
ejpam-2231	60	15	is	be	AUX
ejpam-2231	60	16	a0s	a0s	PROPN
ejpam-2231	60	17	=	=	PUNCT
ejpam-2231	60	18	s	s	NOUN
ejpam-2231	60	19	or	or	CCONJ
ejpam-2231	60	20	sa0	sa0	NOUN
ejpam-2231	60	21	=	=	PUNCT
ejpam-2231	60	22	s.	s.	PROPN
ejpam-2231	60	23	note	note	VERB
ejpam-2231	60	24	that	that	SCONJ
ejpam-2231	60	25	if	if	SCONJ
ejpam-2231	60	26	m=	m=	VERB
ejpam-2231	60	27	n=	n=	ADJ
ejpam-2231	60	28	1	1	NUM
ejpam-2231	60	29	,	,	PUNCT
ejpam-2231	60	30	then	then	ADV
ejpam-2231	60	31	an	an	DET
ejpam-2231	60	32	(	(	PUNCT
ejpam-2231	60	33	m	m	PROPN
ejpam-2231	60	34	,	,	PUNCT
ejpam-2231	60	35	n)-ideal	n)-ideal	VERB
ejpam-2231	60	36	a	a	PRON
ejpam-2231	60	37	of	of	ADP
ejpam-2231	60	38	an	an	DET
ejpam-2231	60	39	la	la	PROPN
ejpam-2231	60	40	-semigroup	-semigroup	NOUN
ejpam-2231	60	41	s	s	PART
ejpam-2231	60	42	is	be	AUX
ejpam-2231	60	43	called	call	VERB
ejpam-2231	60	44	a	a	DET
ejpam-2231	60	45	bi	bi	NOUN
ejpam-2231	60	46	-	-	NOUN
ejpam-2231	60	47	ideal	ideal	NOUN
ejpam-2231	60	48	of	of	ADP
ejpam-2231	60	49	s.	s.	PROPN
ejpam-2231	60	50	if	if	SCONJ
ejpam-2231	60	51	we	we	PRON
ejpam-2231	60	52	take	take	VERB
ejpam-2231	60	53	m	m	VERB
ejpam-2231	60	54	=	=	NOUN
ejpam-2231	60	55	0	0	NUM
ejpam-2231	60	56	or	or	CCONJ
ejpam-2231	60	57	n	n	CCONJ
ejpam-2231	60	58	=	=	SYM
ejpam-2231	60	59	0	0	NUM
ejpam-2231	60	60	,	,	PUNCT
ejpam-2231	60	61	then	then	ADV
ejpam-2231	60	62	an	an	DET
ejpam-2231	60	63	(	(	PUNCT
ejpam-2231	60	64	m	m	PROPN
ejpam-2231	60	65	,	,	PUNCT
ejpam-2231	60	66	n)-ideal	n)-ideal	VERB
ejpam-2231	60	67	a	a	PRON
ejpam-2231	60	68	of	of	ADP
ejpam-2231	60	69	an	an	DET
ejpam-2231	60	70	la	la	PROPN
ejpam-2231	60	71	-semigroup	-semigroup	NOUN
ejpam-2231	60	72	s	s	PART
ejpam-2231	60	73	becomes	become	VERB
ejpam-2231	60	74	a	a	DET
ejpam-2231	60	75	left	left	NOUN
ejpam-2231	60	76	or	or	CCONJ
ejpam-2231	60	77	a	a	DET
ejpam-2231	60	78	right	right	ADJ
ejpam-2231	60	79	ideal	ideal	NOUN
ejpam-2231	60	80	of	of	ADP
ejpam-2231	60	81	s.	s.	PROPN
ejpam-2231	60	82	an	an	DET
ejpam-2231	60	83	(	(	PUNCT
ejpam-2231	60	84	m	m	PROPN
ejpam-2231	60	85	,	,	PUNCT
ejpam-2231	60	86	n)-ideal	n)-ideal	VERB
ejpam-2231	60	87	a	a	PRON
ejpam-2231	60	88	of	of	ADP
ejpam-2231	60	89	an	an	DET
ejpam-2231	60	90	la	la	PROPN
ejpam-2231	60	91	-semigroup	-semigroup	NOUN
ejpam-2231	60	92	s	s	PART
ejpam-2231	60	93	with	with	ADP
ejpam-2231	60	94	zero	zero	NUM
ejpam-2231	60	95	is	be	AUX
ejpam-2231	60	96	said	say	VERB
ejpam-2231	60	97	to	to	PART
ejpam-2231	60	98	be	be	AUX
ejpam-2231	60	99	0	0	NUM
ejpam-2231	60	100	-	-	NOUN
ejpam-2231	60	101	minimal	minimal	ADJ
ejpam-2231	60	102	if	if	SCONJ
ejpam-2231	60	103	a	a	PRON
ejpam-2231	60	104	6=	6=	NUM
ejpam-2231	60	105	{	{	PUNCT
ejpam-2231	60	106	0	0	NUM
ejpam-2231	60	107	}	}	PUNCT
ejpam-2231	60	108	and	and	CCONJ
ejpam-2231	60	109	{	{	PUNCT
ejpam-2231	60	110	0	0	X
ejpam-2231	60	111	}	}	PUNCT
ejpam-2231	60	112	is	be	AUX
ejpam-2231	60	113	the	the	DET
ejpam-2231	60	114	only	only	ADJ
ejpam-2231	60	115	(	(	PUNCT
ejpam-2231	60	116	m	m	PROPN
ejpam-2231	60	117	,	,	PUNCT
ejpam-2231	60	118	n)-ideal	n)-ideal	NOUN
ejpam-2231	60	119	of	of	ADP
ejpam-2231	60	120	s	s	PRON
ejpam-2231	60	121	properly	properly	ADV
ejpam-2231	60	122	contained	contain	VERB
ejpam-2231	60	123	in	in	ADP
ejpam-2231	60	124	a.	a.	NOUN
ejpam-2231	60	125	an	an	DET
ejpam-2231	60	126	la	la	PROPN
ejpam-2231	60	127	-semigroup	-semigroup	NOUN
ejpam-2231	60	128	s	s	PART
ejpam-2231	60	129	with	with	ADP
ejpam-2231	60	130	zero	zero	NUM
ejpam-2231	60	131	is	be	AUX
ejpam-2231	60	132	said	say	VERB
ejpam-2231	60	133	to	to	PART
ejpam-2231	60	134	be	be	AUX
ejpam-2231	60	135	0-(0,2)-bisimple	0-(0,2)-bisimple	NOUN
ejpam-2231	60	136	if	if	SCONJ
ejpam-2231	60	137	s2	s2	PROPN
ejpam-2231	60	138	6=	6=	PUNCT
ejpam-2231	60	139	{	{	PUNCT
ejpam-2231	60	140	0	0	NUM
ejpam-2231	60	141	}	}	PUNCT
ejpam-2231	60	142	and	and	CCONJ
ejpam-2231	60	143	{	{	PUNCT
ejpam-2231	60	144	0	0	X
ejpam-2231	60	145	}	}	PUNCT
ejpam-2231	60	146	is	be	AUX
ejpam-2231	60	147	the	the	DET
ejpam-2231	60	148	only	only	ADJ
ejpam-2231	60	149	proper	proper	ADJ
ejpam-2231	60	150	(	(	PUNCT
ejpam-2231	60	151	0,2)-bi	0,2)-bi	NUM
ejpam-2231	60	152	-	-	PUNCT
ejpam-2231	60	153	ideal	ideal	NOUN
ejpam-2231	60	154	of	of	ADP
ejpam-2231	60	155	s.	s.	PROPN
ejpam-2231	60	156	an	an	DET
ejpam-2231	60	157	la	la	PROPN
ejpam-2231	60	158	-semigroup	-semigroup	NOUN
ejpam-2231	60	159	s	s	PART
ejpam-2231	60	160	with	with	ADP
ejpam-2231	60	161	zero	zero	NUM
ejpam-2231	60	162	is	be	AUX
ejpam-2231	60	163	said	say	VERB
ejpam-2231	60	164	to	to	PART
ejpam-2231	60	165	be	be	AUX
ejpam-2231	60	166	nilpotent	nilpotent	ADJ
ejpam-2231	60	167	if	if	SCONJ
ejpam-2231	60	168	s	s	VERB
ejpam-2231	60	169	l	l	NOUN
ejpam-2231	60	170	=	=	PUNCT
ejpam-2231	60	171	{	{	PUNCT
ejpam-2231	60	172	0	0	NUM
ejpam-2231	60	173	}	}	PUNCT
ejpam-2231	60	174	for	for	ADP
ejpam-2231	60	175	some	some	DET
ejpam-2231	60	176	positive	positive	ADJ
ejpam-2231	60	177	integer	integer	NOUN
ejpam-2231	60	178	l.	l.	NOUN
ejpam-2231	60	179	let	let	VERB
ejpam-2231	60	180	m	m	PRON
ejpam-2231	60	181	,	,	PUNCT
ejpam-2231	60	182	n	n	PRON
ejpam-2231	60	183	be	be	AUX
ejpam-2231	60	184	non	non	ADJ
ejpam-2231	60	185	-	-	ADJ
ejpam-2231	60	186	negative	negative	ADJ
ejpam-2231	60	187	integers	integer	NOUN
ejpam-2231	60	188	and	and	CCONJ
ejpam-2231	60	189	s	s	AUX
ejpam-2231	60	190	be	be	AUX
ejpam-2231	60	191	an	an	DET
ejpam-2231	60	192	la	la	PROPN
ejpam-2231	60	193	-semigroup	-semigroup	NOUN
ejpam-2231	60	194	.	.	PUNCT
ejpam-2231	61	1	we	we	PRON
ejpam-2231	61	2	say	say	VERB
ejpam-2231	61	3	that	that	PRON
ejpam-2231	61	4	s	s	VERB
ejpam-2231	61	5	is	be	AUX
ejpam-2231	61	6	(	(	PUNCT
ejpam-2231	61	7	m	m	PROPN
ejpam-2231	61	8	,	,	PUNCT
ejpam-2231	61	9	n)regular	n)regular	ADJ
ejpam-2231	61	10	if	if	SCONJ
ejpam-2231	61	11	for	for	ADP
ejpam-2231	61	12	every	every	DET
ejpam-2231	61	13	element	element	NOUN
ejpam-2231	61	14	a	a	DET
ejpam-2231	61	15	∈	∈	NOUN
ejpam-2231	61	16	s	s	VERB
ejpam-2231	61	17	there	there	PRON
ejpam-2231	61	18	exists	exist	VERB
ejpam-2231	61	19	some	some	DET
ejpam-2231	61	20	x	x	SYM
ejpam-2231	61	21	∈	∈	NOUN
ejpam-2231	61	22	s	s	VERB
ejpam-2231	61	23	such	such	ADJ
ejpam-2231	61	24	that	that	SCONJ
ejpam-2231	61	25	a	a	DET
ejpam-2231	61	26	=	=	X
ejpam-2231	61	27	(	(	PUNCT
ejpam-2231	61	28	am	be	AUX
ejpam-2231	61	29	x)an	x)an	PROPN
ejpam-2231	61	30	.	.	PUNCT
ejpam-2231	62	1	note	note	VERB
ejpam-2231	62	2	that	that	SCONJ
ejpam-2231	62	3	a0	a0	PROPN
ejpam-2231	62	4	is	be	AUX
ejpam-2231	62	5	defined	define	VERB
ejpam-2231	62	6	as	as	ADP
ejpam-2231	62	7	an	an	DET
ejpam-2231	62	8	operator	operator	NOUN
ejpam-2231	62	9	element	element	NOUN
ejpam-2231	62	10	such	such	ADJ
ejpam-2231	62	11	that	that	DET
ejpam-2231	62	12	a0	a0	PROPN
ejpam-2231	62	13	y	y	PROPN
ejpam-2231	62	14	=	=	PROPN
ejpam-2231	62	15	y	y	PROPN
ejpam-2231	62	16	and	and	CCONJ
ejpam-2231	62	17	za0	za0	PROPN
ejpam-2231	63	1	=	=	SYM
ejpam-2231	63	2	z	z	NOUN
ejpam-2231	63	3	for	for	ADP
ejpam-2231	63	4	any	any	DET
ejpam-2231	63	5	y	y	NOUN
ejpam-2231	63	6	,	,	PUNCT
ejpam-2231	63	7	z	z	PROPN
ejpam-2231	63	8	∈	∈	PROPN
ejpam-2231	63	9	s.	s.	PROPN
ejpam-2231	63	10	3	3	NUM
ejpam-2231	63	11	.	.	NOUN
ejpam-2231	63	12	0	0	NUM
ejpam-2231	63	13	-	-	PUNCT
ejpam-2231	63	14	minimal	minimal	ADJ
ejpam-2231	63	15	(	(	PUNCT
ejpam-2231	63	16	0	0	NUM
ejpam-2231	63	17	,	,	PUNCT
ejpam-2231	63	18	2)-bi	2)-bi	NUM
ejpam-2231	63	19	-	-	PUNCT
ejpam-2231	63	20	ideals	ideal	NOUN
ejpam-2231	63	21	in	in	ADP
ejpam-2231	63	22	unitary	unitary	ADJ
ejpam-2231	63	23	la	la	ADJ
ejpam-2231	63	24	-semigroups	-semigroup	NOUN
ejpam-2231	63	25	if	if	SCONJ
ejpam-2231	63	26	s	s	VERB
ejpam-2231	63	27	is	be	AUX
ejpam-2231	63	28	a	a	DET
ejpam-2231	63	29	unitary	unitary	ADJ
ejpam-2231	63	30	la	la	ADJ
ejpam-2231	63	31	-semigroup	-semigroup	NOUN
ejpam-2231	63	32	,	,	PUNCT
ejpam-2231	63	33	then	then	ADV
ejpam-2231	63	34	it	it	PRON
ejpam-2231	63	35	is	be	AUX
ejpam-2231	63	36	easy	easy	ADJ
ejpam-2231	63	37	to	to	PART
ejpam-2231	63	38	see	see	VERB
ejpam-2231	63	39	that	that	DET
ejpam-2231	63	40	s2	s2	NOUN
ejpam-2231	63	41	=	=	SYM
ejpam-2231	63	42	s	s	PROPN
ejpam-2231	63	43	,	,	PUNCT
ejpam-2231	63	44	sa2	sa2	NOUN
ejpam-2231	63	45	=	=	SYM
ejpam-2231	63	46	a2s	a2s	NOUN
ejpam-2231	63	47	and	and	CCONJ
ejpam-2231	63	48	a⊆	a⊆	PROPN
ejpam-2231	63	49	sa	sa	PROPN
ejpam-2231	63	50	∀a	∀a	NOUN
ejpam-2231	63	51	⊆	⊆	NUM
ejpam-2231	63	52	s.	s.	PROPN
ejpam-2231	63	53	note	note	VERB
ejpam-2231	63	54	that	that	SCONJ
ejpam-2231	63	55	every	every	DET
ejpam-2231	63	56	right	right	ADJ
ejpam-2231	63	57	ideal	ideal	NOUN
ejpam-2231	63	58	of	of	ADP
ejpam-2231	63	59	a	a	DET
ejpam-2231	63	60	unitary	unitary	ADJ
ejpam-2231	63	61	la	la	PROPN
ejpam-2231	63	62	-semigroup	-semigroup	NOUN
ejpam-2231	63	63	s	s	PART
ejpam-2231	63	64	is	be	AUX
ejpam-2231	63	65	a	a	DET
ejpam-2231	63	66	left	left	ADJ
ejpam-2231	63	67	ideal	ideal	NOUN
ejpam-2231	63	68	of	of	ADP
ejpam-2231	63	69	s	s	PRON
ejpam-2231	63	70	but	but	CCONJ
ejpam-2231	63	71	the	the	DET
ejpam-2231	63	72	converse	converse	NOUN
ejpam-2231	63	73	is	be	AUX
ejpam-2231	63	74	not	not	PART
ejpam-2231	63	75	true	true	ADJ
ejpam-2231	63	76	in	in	ADP
ejpam-2231	63	77	general	general	ADJ
ejpam-2231	63	78	.	.	PUNCT
ejpam-2231	64	1	example	example	NOUN
ejpam-2231	64	2	1	1	NUM
ejpam-2231	64	3	shows	show	VERB
ejpam-2231	64	4	that	that	SCONJ
ejpam-2231	64	5	there	there	PRON
ejpam-2231	64	6	exists	exist	VERB
ejpam-2231	64	7	a	a	DET
ejpam-2231	64	8	subset	subset	NOUN
ejpam-2231	64	9	{	{	PUNCT
ejpam-2231	64	10	a	a	PRON
ejpam-2231	64	11	,	,	PUNCT
ejpam-2231	64	12	b	b	NOUN
ejpam-2231	64	13	,	,	PUNCT
ejpam-2231	64	14	e	e	NOUN
ejpam-2231	64	15	}	}	PUNCT
ejpam-2231	64	16	of	of	ADP
ejpam-2231	64	17	s	s	PRON
ejpam-2231	64	18	which	which	PRON
ejpam-2231	64	19	is	be	AUX
ejpam-2231	64	20	a	a	DET
ejpam-2231	64	21	left	left	ADJ
ejpam-2231	64	22	ideal	ideal	NOUN
ejpam-2231	64	23	of	of	ADP
ejpam-2231	64	24	s	s	NOUN
ejpam-2231	64	25	but	but	CCONJ
ejpam-2231	64	26	not	not	PART
ejpam-2231	64	27	a	a	DET
ejpam-2231	64	28	right	right	ADJ
ejpam-2231	64	29	ideal	ideal	NOUN
ejpam-2231	64	30	of	of	ADP
ejpam-2231	64	31	s.	s.	PROPN
ejpam-2231	64	32	it	it	PRON
ejpam-2231	64	33	is	be	AUX
ejpam-2231	64	34	easy	easy	ADJ
ejpam-2231	64	35	to	to	PART
ejpam-2231	64	36	see	see	VERB
ejpam-2231	64	37	that	that	DET
ejpam-2231	64	38	sa	sa	PROPN
ejpam-2231	64	39	and	and	CCONJ
ejpam-2231	64	40	sa2	sa2	PROPN
ejpam-2231	64	41	are	be	AUX
ejpam-2231	64	42	the	the	DET
ejpam-2231	64	43	left	left	ADJ
ejpam-2231	64	44	and	and	CCONJ
ejpam-2231	64	45	right	right	ADJ
ejpam-2231	64	46	ideals	ideal	NOUN
ejpam-2231	64	47	of	of	ADP
ejpam-2231	64	48	a	a	DET
ejpam-2231	64	49	unitary	unitary	ADJ
ejpam-2231	64	50	la	la	PROPN
ejpam-2231	64	51	-semigroup	-semigroup	NOUN
ejpam-2231	64	52	s.	s.	PROPN
ejpam-2231	64	53	thus	thus	ADV
ejpam-2231	64	54	sa2	sa2	PROPN
ejpam-2231	64	55	is	be	AUX
ejpam-2231	64	56	an	an	DET
ejpam-2231	64	57	ideal	ideal	NOUN
ejpam-2231	64	58	of	of	ADP
ejpam-2231	64	59	a	a	DET
ejpam-2231	64	60	unitary	unitary	ADJ
ejpam-2231	64	61	la	la	PROPN
ejpam-2231	64	62	-semigroup	-semigroup	NOUN
ejpam-2231	64	63	s.	s.	PROPN
ejpam-2231	64	64	lemma	lemma	PROPN
ejpam-2231	65	1	1	1	X
ejpam-2231	65	2	.	.	PUNCT
ejpam-2231	66	1	let	let	VERB
ejpam-2231	66	2	s	s	PRON
ejpam-2231	66	3	be	be	AUX
ejpam-2231	66	4	a	a	DET
ejpam-2231	66	5	unitary	unitary	ADJ
ejpam-2231	66	6	la	la	ADJ
ejpam-2231	66	7	-semigroup	-semigroup	NOUN
ejpam-2231	66	8	.	.	PUNCT
ejpam-2231	67	1	then	then	ADV
ejpam-2231	67	2	a	a	PRON
ejpam-2231	67	3	is	be	AUX
ejpam-2231	67	4	a	a	DET
ejpam-2231	67	5	(	(	PUNCT
ejpam-2231	67	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	67	7	of	of	ADP
ejpam-2231	67	8	s	s	PRON
ejpam-2231	67	9	if	if	SCONJ
ejpam-2231	67	10	and	and	CCONJ
ejpam-2231	67	11	only	only	ADV
ejpam-2231	67	12	if	if	SCONJ
ejpam-2231	67	13	a	a	PRON
ejpam-2231	67	14	is	be	AUX
ejpam-2231	67	15	an	an	DET
ejpam-2231	67	16	ideal	ideal	NOUN
ejpam-2231	67	17	of	of	ADP
ejpam-2231	67	18	some	some	DET
ejpam-2231	67	19	left	leave	VERB
ejpam-2231	67	20	ideal	ideal	NOUN
ejpam-2231	67	21	of	of	ADP
ejpam-2231	67	22	s.	s.	PROPN
ejpam-2231	67	23	proof	proof	PROPN
ejpam-2231	67	24	.	.	PUNCT
ejpam-2231	68	1	let	let	VERB
ejpam-2231	68	2	a	a	DET
ejpam-2231	68	3	be	be	AUX
ejpam-2231	68	4	a	a	DET
ejpam-2231	68	5	(	(	PUNCT
ejpam-2231	68	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	68	7	of	of	ADP
ejpam-2231	68	8	s	s	NOUN
ejpam-2231	68	9	,	,	PUNCT
ejpam-2231	68	10	then	then	ADV
ejpam-2231	68	11	sa	sa	PROPN
ejpam-2231	68	12	·	·	PUNCT
ejpam-2231	68	13	a=	a=	VERB
ejpam-2231	68	14	aa	aa	ADJ
ejpam-2231	68	15	·	·	PUNCT
ejpam-2231	68	16	s	s	PART
ejpam-2231	68	17	=	=	NOUN
ejpam-2231	68	18	sa2	sa2	PROPN
ejpam-2231	68	19	⊆	⊆	NUM
ejpam-2231	68	20	a	a	PRON
ejpam-2231	68	21	and	and	CCONJ
ejpam-2231	68	22	a	a	DET
ejpam-2231	68	23	·	·	PUNCT
ejpam-2231	68	24	sa=	sa=	NOUN
ejpam-2231	68	25	s	s	PART
ejpam-2231	68	26	·	·	PUNCT
ejpam-2231	68	27	aa=	aa=	VERB
ejpam-2231	68	28	ss	ss	PROPN
ejpam-2231	68	29	·	·	PUNCT
ejpam-2231	68	30	aa=	aa=	PROPN
ejpam-2231	68	31	sa2	sa2	NOUN
ejpam-2231	69	1	⊆	⊆	NUM
ejpam-2231	69	2	a.	a.	NOUN
ejpam-2231	69	3	hence	hence	ADV
ejpam-2231	69	4	a	a	PRON
ejpam-2231	69	5	is	be	AUX
ejpam-2231	69	6	an	an	DET
ejpam-2231	69	7	ideal	ideal	NOUN
ejpam-2231	69	8	of	of	ADP
ejpam-2231	69	9	a	a	DET
ejpam-2231	69	10	left	left	ADJ
ejpam-2231	69	11	ideal	ideal	NOUN
ejpam-2231	69	12	sa	sa	PROPN
ejpam-2231	69	13	of	of	ADP
ejpam-2231	69	14	s.	s.	PROPN
ejpam-2231	69	15	conversely	conversely	ADV
ejpam-2231	69	16	,	,	PUNCT
ejpam-2231	69	17	assume	assume	VERB
ejpam-2231	69	18	that	that	SCONJ
ejpam-2231	69	19	a	a	PRON
ejpam-2231	69	20	is	be	AUX
ejpam-2231	69	21	a	a	DET
ejpam-2231	69	22	left	left	ADJ
ejpam-2231	69	23	ideal	ideal	NOUN
ejpam-2231	69	24	of	of	ADP
ejpam-2231	69	25	a	a	DET
ejpam-2231	69	26	left	left	ADJ
ejpam-2231	69	27	ideal	ideal	NOUN
ejpam-2231	69	28	l	l	NOUN
ejpam-2231	69	29	of	of	ADP
ejpam-2231	69	30	s	s	PROPN
ejpam-2231	69	31	,	,	PUNCT
ejpam-2231	69	32	then	then	ADV
ejpam-2231	69	33	sa2	sa2	PROPN
ejpam-2231	69	34	=	=	SYM
ejpam-2231	69	35	aa	aa	PROPN
ejpam-2231	69	36	·	·	PUNCT
ejpam-2231	69	37	s	s	PART
ejpam-2231	69	38	=	=	X
ejpam-2231	69	39	sa	sa	PROPN
ejpam-2231	69	40	·	·	PUNCT
ejpam-2231	69	41	a⊆	a⊆	PROPN
ejpam-2231	69	42	sl	sl	PRON
ejpam-2231	69	43	·	·	PUNCT
ejpam-2231	69	44	a⊆	a⊆	NOUN
ejpam-2231	69	45	la⊆	la⊆	NOUN
ejpam-2231	69	46	a	a	PRON
ejpam-2231	69	47	,	,	PUNCT
ejpam-2231	69	48	and	and	CCONJ
ejpam-2231	69	49	clearly	clearly	ADV
ejpam-2231	69	50	a	a	PRON
ejpam-2231	69	51	is	be	AUX
ejpam-2231	69	52	an	an	DET
ejpam-2231	69	53	la	la	ADJ
ejpam-2231	69	54	-subsemigroup	-subsemigroup	NOUN
ejpam-2231	69	55	of	of	ADP
ejpam-2231	69	56	s	s	PRON
ejpam-2231	69	57	,	,	PUNCT
ejpam-2231	69	58	therefore	therefore	ADV
ejpam-2231	69	59	a	a	PRON
ejpam-2231	69	60	is	be	AUX
ejpam-2231	69	61	a	a	DET
ejpam-2231	69	62	(	(	PUNCT
ejpam-2231	69	63	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	69	64	of	of	ADP
ejpam-2231	69	65	s.	s.	PROPN
ejpam-2231	69	66	w.	w.	PROPN
ejpam-2231	69	67	khan	khan	PROPN
ejpam-2231	69	68	,	,	PUNCT
ejpam-2231	69	69	f.	f.	PROPN
ejpam-2231	69	70	yousafzai	yousafzai	PROPN
ejpam-2231	69	71	,	,	PUNCT
ejpam-2231	69	72	and	and	CCONJ
ejpam-2231	69	73	m.	m.	PROPN
ejpam-2231	69	74	khan	khan	PROPN
ejpam-2231	69	75	/	/	SYM
ejpam-2231	69	76	eur	eur	PROPN
ejpam-2231	69	77	.	.	PUNCT
ejpam-2231	70	1	j.	j.	PROPN
ejpam-2231	70	2	pure	pure	PROPN
ejpam-2231	70	3	appl	appl	PROPN
ejpam-2231	70	4	.	.	PROPN
ejpam-2231	70	5	math	math	PROPN
ejpam-2231	70	6	,	,	PUNCT
ejpam-2231	70	7	9	9	NUM
ejpam-2231	70	8	(	(	PUNCT
ejpam-2231	70	9	2016	2016	NUM
ejpam-2231	70	10	)	)	PUNCT
ejpam-2231	70	11	,	,	PUNCT
ejpam-2231	70	12	277	277	NUM
ejpam-2231	70	13	-	-	SYM
ejpam-2231	70	14	291	291	NUM
ejpam-2231	70	15	280	280	NUM
ejpam-2231	70	16	corollary	corollary	ADJ
ejpam-2231	70	17	1	1	NUM
ejpam-2231	70	18	.	.	PUNCT
ejpam-2231	71	1	let	let	VERB
ejpam-2231	71	2	s	s	PRON
ejpam-2231	71	3	be	be	AUX
ejpam-2231	71	4	a	a	DET
ejpam-2231	71	5	unitary	unitary	ADJ
ejpam-2231	71	6	la	la	ADJ
ejpam-2231	71	7	-semigroup	-semigroup	NOUN
ejpam-2231	71	8	.	.	PUNCT
ejpam-2231	72	1	then	then	ADV
ejpam-2231	72	2	a	a	PRON
ejpam-2231	72	3	is	be	AUX
ejpam-2231	72	4	a	a	DET
ejpam-2231	72	5	(	(	PUNCT
ejpam-2231	72	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	72	7	of	of	ADP
ejpam-2231	72	8	s	s	PRON
ejpam-2231	72	9	if	if	SCONJ
ejpam-2231	72	10	and	and	CCONJ
ejpam-2231	72	11	only	only	ADV
ejpam-2231	72	12	if	if	SCONJ
ejpam-2231	72	13	a	a	PRON
ejpam-2231	72	14	is	be	AUX
ejpam-2231	72	15	a	a	DET
ejpam-2231	72	16	left	left	ADJ
ejpam-2231	72	17	ideal	ideal	NOUN
ejpam-2231	72	18	of	of	ADP
ejpam-2231	72	19	some	some	DET
ejpam-2231	72	20	left	leave	VERB
ejpam-2231	72	21	ideal	ideal	NOUN
ejpam-2231	72	22	of	of	ADP
ejpam-2231	72	23	s.	s.	PROPN
ejpam-2231	72	24	lemma	lemma	PROPN
ejpam-2231	73	1	2	2	X
ejpam-2231	73	2	.	.	PUNCT
ejpam-2231	73	3	let	let	VERB
ejpam-2231	73	4	s	s	PRON
ejpam-2231	73	5	be	be	AUX
ejpam-2231	73	6	a	a	DET
ejpam-2231	73	7	unitary	unitary	ADJ
ejpam-2231	73	8	la	la	ADJ
ejpam-2231	73	9	-semigroup	-semigroup	NOUN
ejpam-2231	73	10	.	.	PUNCT
ejpam-2231	74	1	then	then	ADV
ejpam-2231	74	2	a	a	PRON
ejpam-2231	74	3	is	be	AUX
ejpam-2231	74	4	a	a	DET
ejpam-2231	74	5	(	(	PUNCT
ejpam-2231	74	6	0,2)-bi	0,2)-bi	NUM
ejpam-2231	74	7	-	-	PUNCT
ejpam-2231	74	8	ideal	ideal	NOUN
ejpam-2231	74	9	of	of	ADP
ejpam-2231	74	10	s	s	PRON
ejpam-2231	74	11	if	if	SCONJ
ejpam-2231	74	12	and	and	CCONJ
ejpam-2231	74	13	only	only	ADV
ejpam-2231	74	14	if	if	SCONJ
ejpam-2231	74	15	a	a	PRON
ejpam-2231	74	16	is	be	AUX
ejpam-2231	74	17	an	an	DET
ejpam-2231	74	18	ideal	ideal	NOUN
ejpam-2231	74	19	of	of	ADP
ejpam-2231	74	20	some	some	DET
ejpam-2231	74	21	right	right	ADJ
ejpam-2231	74	22	ideal	ideal	NOUN
ejpam-2231	74	23	of	of	ADP
ejpam-2231	74	24	s.	s.	PROPN
ejpam-2231	74	25	proof	proof	PROPN
ejpam-2231	74	26	.	.	PUNCT
ejpam-2231	75	1	let	let	VERB
ejpam-2231	75	2	a	a	DET
ejpam-2231	75	3	be	be	AUX
ejpam-2231	75	4	a	a	DET
ejpam-2231	75	5	(	(	PUNCT
ejpam-2231	75	6	0,2)-bi	0,2)-bi	NUM
ejpam-2231	75	7	-	-	PUNCT
ejpam-2231	75	8	ideal	ideal	NOUN
ejpam-2231	75	9	of	of	ADP
ejpam-2231	75	10	s	s	PROPN
ejpam-2231	75	11	,	,	PUNCT
ejpam-2231	75	12	then	then	ADV
ejpam-2231	75	13	sa2	sa2	PROPN
ejpam-2231	75	14	·	·	PUNCT
ejpam-2231	75	15	a	a	DET
ejpam-2231	75	16	=	=	ADJ
ejpam-2231	75	17	a2s	a2s	NOUN
ejpam-2231	75	18	·	·	PUNCT
ejpam-2231	75	19	a	a	DET
ejpam-2231	75	20	=	=	PUNCT
ejpam-2231	75	21	as	as	ADP
ejpam-2231	75	22	·	·	PUNCT
ejpam-2231	75	23	a2	a2	PROPN
ejpam-2231	75	24	⊆	⊆	NUM
ejpam-2231	75	25	sa2	sa2	NOUN
ejpam-2231	75	26	⊆	⊆	NUM
ejpam-2231	75	27	a	a	PRON
ejpam-2231	75	28	and	and	CCONJ
ejpam-2231	75	29	a	a	DET
ejpam-2231	75	30	·	·	PUNCT
ejpam-2231	75	31	sa2	sa2	NOUN
ejpam-2231	75	32	=	=	SYM
ejpam-2231	75	33	ss	ss	PROPN
ejpam-2231	75	34	·	·	PUNCT
ejpam-2231	75	35	aa2	aa2	X
ejpam-2231	76	1	=	=	SYM
ejpam-2231	76	2	a2a	a2a	PROPN
ejpam-2231	76	3	·	·	PUNCT
ejpam-2231	76	4	ss	ss	NOUN
ejpam-2231	76	5	=	=	PUNCT
ejpam-2231	76	6	sa	sa	PROPN
ejpam-2231	76	7	·	·	PUNCT
ejpam-2231	76	8	a2	a2	PROPN
ejpam-2231	76	9	⊆	⊆	NUM
ejpam-2231	76	10	sa2	sa2	NOUN
ejpam-2231	76	11	⊆	⊆	NUM
ejpam-2231	76	12	a.	a.	NOUN
ejpam-2231	76	13	hence	hence	ADV
ejpam-2231	76	14	a	a	PRON
ejpam-2231	76	15	is	be	AUX
ejpam-2231	76	16	an	an	DET
ejpam-2231	76	17	ideal	ideal	NOUN
ejpam-2231	76	18	of	of	ADP
ejpam-2231	76	19	some	some	DET
ejpam-2231	76	20	right	right	ADJ
ejpam-2231	76	21	ideal	ideal	ADJ
ejpam-2231	76	22	sa2	sa2	PROPN
ejpam-2231	76	23	of	of	ADP
ejpam-2231	76	24	s.	s.	PROPN
ejpam-2231	76	25	conversely	conversely	ADV
ejpam-2231	76	26	,	,	PUNCT
ejpam-2231	76	27	assume	assume	VERB
ejpam-2231	76	28	that	that	SCONJ
ejpam-2231	76	29	a	a	PRON
ejpam-2231	76	30	is	be	AUX
ejpam-2231	76	31	an	an	DET
ejpam-2231	76	32	ideal	ideal	NOUN
ejpam-2231	76	33	of	of	ADP
ejpam-2231	76	34	a	a	DET
ejpam-2231	76	35	right	right	ADJ
ejpam-2231	76	36	ideal	ideal	ADJ
ejpam-2231	76	37	r	r	NOUN
ejpam-2231	76	38	of	of	ADP
ejpam-2231	76	39	s	s	NOUN
ejpam-2231	76	40	,	,	PUNCT
ejpam-2231	76	41	then	then	ADV
ejpam-2231	76	42	sa2	sa2	PROPN
ejpam-2231	76	43	=	=	PUNCT
ejpam-2231	76	44	a	a	DET
ejpam-2231	76	45	·	·	PUNCT
ejpam-2231	76	46	sa=	sa=	NOUN
ejpam-2231	76	47	a	a	PRON
ejpam-2231	76	48	·	·	PUNCT
ejpam-2231	76	49	(	(	PUNCT
ejpam-2231	76	50	ss)a=	ss)a=	INTJ
ejpam-2231	76	51	a	a	PRON
ejpam-2231	76	52	·	·	PUNCT
ejpam-2231	76	53	(	(	PUNCT
ejpam-2231	76	54	as)s	as)s	PROPN
ejpam-2231	76	55	⊆	⊆	NUM
ejpam-2231	76	56	a	a	PRON
ejpam-2231	76	57	·	·	PUNCT
ejpam-2231	76	58	(	(	PUNCT
ejpam-2231	76	59	rs)r	rs)r	NOUN
ejpam-2231	76	60	⊆	⊆	NUM
ejpam-2231	76	61	ar	ar	NOUN
ejpam-2231	76	62	⊆	⊆	NUM
ejpam-2231	76	63	a	a	PRON
ejpam-2231	76	64	,	,	PUNCT
ejpam-2231	76	65	and	and	CCONJ
ejpam-2231	76	66	(	(	PUNCT
ejpam-2231	76	67	as)a⊆	as)a⊆	X
ejpam-2231	76	68	(	(	PUNCT
ejpam-2231	76	69	rs)a⊆	rs)a⊆	X
ejpam-2231	76	70	ra⊆	ra⊆	VERB
ejpam-2231	76	71	a	a	PRON
ejpam-2231	76	72	,	,	PUNCT
ejpam-2231	76	73	which	which	PRON
ejpam-2231	76	74	shows	show	VERB
ejpam-2231	76	75	that	that	SCONJ
ejpam-2231	76	76	a	a	PRON
ejpam-2231	76	77	is	be	AUX
ejpam-2231	76	78	a	a	DET
ejpam-2231	76	79	(	(	PUNCT
ejpam-2231	76	80	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	76	81	of	of	ADP
ejpam-2231	76	82	s.	s.	PROPN
ejpam-2231	76	83	theorem	theorem	VERB
ejpam-2231	76	84	1	1	X
ejpam-2231	76	85	.	.	PUNCT
ejpam-2231	77	1	let	let	VERB
ejpam-2231	77	2	s	s	PRON
ejpam-2231	77	3	be	be	AUX
ejpam-2231	77	4	a	a	DET
ejpam-2231	77	5	unitary	unitary	ADJ
ejpam-2231	77	6	la	la	ADJ
ejpam-2231	77	7	-semigroup	-semigroup	NOUN
ejpam-2231	77	8	.	.	PUNCT
ejpam-2231	78	1	then	then	ADV
ejpam-2231	78	2	the	the	DET
ejpam-2231	78	3	following	follow	VERB
ejpam-2231	78	4	statements	statement	NOUN
ejpam-2231	78	5	are	be	AUX
ejpam-2231	78	6	equivalent	equivalent	ADJ
ejpam-2231	78	7	.	.	PUNCT
ejpam-2231	79	1	(	(	PUNCT
ejpam-2231	79	2	i	i	NOUN
ejpam-2231	79	3	)	)	PUNCT
ejpam-2231	79	4	a	a	PRON
ejpam-2231	79	5	is	be	AUX
ejpam-2231	79	6	a	a	DET
ejpam-2231	79	7	(	(	PUNCT
ejpam-2231	79	8	1,2)-ideal	1,2)-ideal	NUM
ejpam-2231	79	9	of	of	ADP
ejpam-2231	79	10	s	s	PROPN
ejpam-2231	79	11	;	;	PUNCT
ejpam-2231	79	12	(	(	PUNCT
ejpam-2231	79	13	ii	ii	NOUN
ejpam-2231	79	14	)	)	PUNCT
ejpam-2231	79	15	a	a	PRON
ejpam-2231	79	16	is	be	AUX
ejpam-2231	79	17	a	a	DET
ejpam-2231	79	18	left	left	ADJ
ejpam-2231	79	19	ideal	ideal	NOUN
ejpam-2231	79	20	of	of	ADP
ejpam-2231	79	21	some	some	DET
ejpam-2231	79	22	bi	bi	NOUN
ejpam-2231	79	23	-	-	NOUN
ejpam-2231	79	24	ideal	ideal	NOUN
ejpam-2231	79	25	of	of	ADP
ejpam-2231	79	26	s	s	PROPN
ejpam-2231	79	27	;	;	PUNCT
ejpam-2231	79	28	(	(	PUNCT
ejpam-2231	79	29	iii	iii	X
ejpam-2231	79	30	)	)	PUNCT
ejpam-2231	79	31	a	a	PRON
ejpam-2231	79	32	is	be	AUX
ejpam-2231	79	33	a	a	DET
ejpam-2231	79	34	bi	bi	NOUN
ejpam-2231	79	35	-	-	NOUN
ejpam-2231	79	36	ideal	ideal	NOUN
ejpam-2231	79	37	of	of	ADP
ejpam-2231	79	38	some	some	DET
ejpam-2231	79	39	ideal	ideal	NOUN
ejpam-2231	79	40	of	of	ADP
ejpam-2231	79	41	s	s	PROPN
ejpam-2231	79	42	;	;	PUNCT
ejpam-2231	79	43	(	(	PUNCT
ejpam-2231	79	44	iv	iv	X
ejpam-2231	79	45	)	)	PUNCT
ejpam-2231	79	46	a	a	PRON
ejpam-2231	79	47	is	be	AUX
ejpam-2231	79	48	a	a	DET
ejpam-2231	79	49	(	(	PUNCT
ejpam-2231	79	50	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	79	51	of	of	ADP
ejpam-2231	79	52	some	some	DET
ejpam-2231	79	53	right	right	ADJ
ejpam-2231	79	54	ideal	ideal	NOUN
ejpam-2231	79	55	of	of	ADP
ejpam-2231	79	56	s	s	PROPN
ejpam-2231	79	57	;	;	PUNCT
ejpam-2231	79	58	(	(	PUNCT
ejpam-2231	79	59	v	v	NOUN
ejpam-2231	79	60	)	)	PUNCT
ejpam-2231	79	61	a	a	PRON
ejpam-2231	79	62	is	be	AUX
ejpam-2231	79	63	a	a	DET
ejpam-2231	79	64	left	left	ADJ
ejpam-2231	79	65	ideal	ideal	NOUN
ejpam-2231	79	66	of	of	ADP
ejpam-2231	79	67	some	some	PRON
ejpam-2231	79	68	(	(	PUNCT
ejpam-2231	79	69	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	79	70	of	of	ADP
ejpam-2231	79	71	s.	s.	PROPN
ejpam-2231	79	72	proof	proof	PROPN
ejpam-2231	79	73	.	.	PUNCT
ejpam-2231	80	1	(	(	PUNCT
ejpam-2231	80	2	i	i	NOUN
ejpam-2231	80	3	)	)	PUNCT
ejpam-2231	81	1	=	=	NOUN
ejpam-2231	81	2	⇒	⇒	NOUN
ejpam-2231	81	3	(	(	PUNCT
ejpam-2231	81	4	ii	ii	NOUN
ejpam-2231	81	5	)	)	PUNCT
ejpam-2231	81	6	.	.	PUNCT
ejpam-2231	82	1	it	it	PRON
ejpam-2231	82	2	is	be	AUX
ejpam-2231	82	3	easy	easy	ADJ
ejpam-2231	82	4	to	to	PART
ejpam-2231	82	5	see	see	VERB
ejpam-2231	82	6	that	that	SCONJ
ejpam-2231	82	7	sa2	sa2	NOUN
ejpam-2231	82	8	·	·	PUNCT
ejpam-2231	83	1	s	s	VERB
ejpam-2231	83	2	is	be	AUX
ejpam-2231	83	3	a	a	DET
ejpam-2231	83	4	bi	bi	NOUN
ejpam-2231	83	5	-	-	NOUN
ejpam-2231	83	6	ideal	ideal	NOUN
ejpam-2231	83	7	of	of	ADP
ejpam-2231	83	8	s.	s.	PROPN
ejpam-2231	83	9	let	let	VERB
ejpam-2231	83	10	a	a	DET
ejpam-2231	83	11	be	be	AUX
ejpam-2231	83	12	a	a	DET
ejpam-2231	83	13	(	(	PUNCT
ejpam-2231	83	14	1,2)-ideal	1,2)-ideal	NUM
ejpam-2231	83	15	of	of	ADP
ejpam-2231	83	16	s	s	PROPN
ejpam-2231	83	17	,	,	PUNCT
ejpam-2231	83	18	then	then	ADV
ejpam-2231	83	19	(	(	PUNCT
ejpam-2231	83	20	sa2	sa2	NOUN
ejpam-2231	83	21	·	·	PUNCT
ejpam-2231	83	22	s)a=(sa2	s)a=(sa2	NOUN
ejpam-2231	83	23	·	·	PUNCT
ejpam-2231	83	24	ss)a=	ss)a=	INTJ
ejpam-2231	83	25	(	(	PUNCT
ejpam-2231	83	26	ss	ss	NOUN
ejpam-2231	83	27	·	·	PUNCT
ejpam-2231	83	28	a2s)a=	a2s)a=	INTJ
ejpam-2231	83	29	(	(	PUNCT
ejpam-2231	83	30	s	s	X
ejpam-2231	83	31	·	·	PUNCT
ejpam-2231	83	32	a2s)a=	a2s)a=	INTJ
ejpam-2231	83	33	a2s	a2s	NOUN
ejpam-2231	83	34	·	·	PUNCT
ejpam-2231	83	35	a	a	DET
ejpam-2231	83	36	=	=	NOUN
ejpam-2231	83	37	as	as	ADP
ejpam-2231	83	38	·	·	PUNCT
ejpam-2231	83	39	a2	a2	PROPN
ejpam-2231	83	40	⊆	⊆	PROPN
ejpam-2231	83	41	a	a	PRON
ejpam-2231	83	42	,	,	PUNCT
ejpam-2231	83	43	which	which	PRON
ejpam-2231	83	44	shows	show	VERB
ejpam-2231	83	45	that	that	SCONJ
ejpam-2231	83	46	a	a	PRON
ejpam-2231	83	47	is	be	AUX
ejpam-2231	83	48	a	a	DET
ejpam-2231	83	49	left	left	ADJ
ejpam-2231	83	50	ideal	ideal	NOUN
ejpam-2231	83	51	of	of	ADP
ejpam-2231	83	52	a	a	DET
ejpam-2231	83	53	bi	bi	ADJ
ejpam-2231	83	54	-	-	ADJ
ejpam-2231	83	55	ideal	ideal	ADJ
ejpam-2231	83	56	sa2	sa2	NOUN
ejpam-2231	83	57	·	·	PUNCT
ejpam-2231	83	58	s	s	PROPN
ejpam-2231	83	59	of	of	ADP
ejpam-2231	83	60	s.	s.	PROPN
ejpam-2231	83	61	(	(	PUNCT
ejpam-2231	83	62	ii	ii	NOUN
ejpam-2231	83	63	)	)	PUNCT
ejpam-2231	83	64	=	=	NOUN
ejpam-2231	83	65	⇒	⇒	NOUN
ejpam-2231	83	66	(	(	PUNCT
ejpam-2231	83	67	iii	iii	NOUN
ejpam-2231	83	68	)	)	PUNCT
ejpam-2231	83	69	.	.	PUNCT
ejpam-2231	84	1	let	let	VERB
ejpam-2231	84	2	a	a	DET
ejpam-2231	84	3	be	be	AUX
ejpam-2231	84	4	a	a	DET
ejpam-2231	84	5	left	left	ADJ
ejpam-2231	84	6	ideal	ideal	NOUN
ejpam-2231	84	7	of	of	ADP
ejpam-2231	84	8	a	a	DET
ejpam-2231	84	9	bi	bi	ADJ
ejpam-2231	84	10	-	-	ADJ
ejpam-2231	84	11	ideal	ideal	ADJ
ejpam-2231	84	12	b	b	PROPN
ejpam-2231	84	13	of	of	ADP
ejpam-2231	84	14	s	s	PROPN
ejpam-2231	84	15	,	,	PUNCT
ejpam-2231	84	16	then	then	ADV
ejpam-2231	84	17	(	(	PUNCT
ejpam-2231	84	18	a	a	DET
ejpam-2231	84	19	·	·	PUNCT
ejpam-2231	84	20	sa2)a=(s	sa2)a=(s	PROPN
ejpam-2231	84	21	·	·	PUNCT
ejpam-2231	84	22	aa2)a⊆	aa2)a⊆	PUNCT
ejpam-2231	85	1	[	[	X
ejpam-2231	85	2	s(sa	s(sa	X
ejpam-2231	85	3	·	·	PUNCT
ejpam-2231	85	4	aa)]a=	aa)]a=	PROPN
ejpam-2231	85	5	[	[	X
ejpam-2231	85	6	s(aa	s(aa	X
ejpam-2231	85	7	·	·	PUNCT
ejpam-2231	85	8	as)]a	as)]a	PROPN
ejpam-2231	86	1	=[	=[	NOUN
ejpam-2231	86	2	aa	aa	NOUN
ejpam-2231	86	3	·	·	PUNCT
ejpam-2231	86	4	s(as)]a=	s(as)]a=	VERB
ejpam-2231	86	5	[	[	X
ejpam-2231	86	6	{	{	PUNCT
ejpam-2231	86	7	s(as	s(a	NOUN
ejpam-2231	86	8	)	)	PUNCT
ejpam-2231	86	9	·	·	PUNCT
ejpam-2231	86	10	a}a]a=	a}a]a=	PUNCT
ejpam-2231	87	1	[	[	X
ejpam-2231	87	2	(	(	PUNCT
ejpam-2231	87	3	as	as	ADP
ejpam-2231	87	4	·	·	PUNCT
ejpam-2231	87	5	a)a]a	a)a]a	X
ejpam-2231	87	6	⊆[(bs	⊆[(bs	PROPN
ejpam-2231	87	7	·	·	PUNCT
ejpam-2231	87	8	b)a]a⊆	b)a]a⊆	ADV
ejpam-2231	87	9	ba	ba	PROPN
ejpam-2231	87	10	·	·	PUNCT
ejpam-2231	87	11	a⊆	a⊆	VERB
ejpam-2231	87	12	a	a	PRON
ejpam-2231	87	13	,	,	PUNCT
ejpam-2231	87	14	which	which	PRON
ejpam-2231	87	15	shows	show	VERB
ejpam-2231	87	16	that	that	SCONJ
ejpam-2231	87	17	a	a	PRON
ejpam-2231	87	18	is	be	AUX
ejpam-2231	87	19	a	a	DET
ejpam-2231	87	20	bi	bi	NOUN
ejpam-2231	87	21	-	-	NOUN
ejpam-2231	87	22	ideal	ideal	NOUN
ejpam-2231	87	23	of	of	ADP
ejpam-2231	87	24	an	an	DET
ejpam-2231	87	25	ideal	ideal	ADJ
ejpam-2231	87	26	sa2	sa2	NOUN
ejpam-2231	87	27	of	of	ADP
ejpam-2231	87	28	s.	s.	PROPN
ejpam-2231	87	29	(	(	PUNCT
ejpam-2231	87	30	iii	iii	NOUN
ejpam-2231	87	31	)	)	PUNCT
ejpam-2231	88	1	=	=	NOUN
ejpam-2231	88	2	⇒	⇒	NOUN
ejpam-2231	88	3	(	(	PUNCT
ejpam-2231	88	4	iv	iv	NUM
ejpam-2231	88	5	)	)	PUNCT
ejpam-2231	88	6	.	.	PUNCT
ejpam-2231	89	1	let	let	VERB
ejpam-2231	89	2	a	a	PRON
ejpam-2231	89	3	be	be	AUX
ejpam-2231	89	4	a	a	DET
ejpam-2231	89	5	bi	bi	NOUN
ejpam-2231	89	6	-	-	NOUN
ejpam-2231	89	7	ideal	ideal	NOUN
ejpam-2231	89	8	of	of	ADP
ejpam-2231	89	9	an	an	DET
ejpam-2231	89	10	ideal	ideal	ADJ
ejpam-2231	89	11	i	i	PRON
ejpam-2231	89	12	of	of	ADP
ejpam-2231	89	13	s	s	PROPN
ejpam-2231	89	14	,	,	PUNCT
ejpam-2231	89	15	then	then	ADV
ejpam-2231	90	1	sa2	sa2	PROPN
ejpam-2231	90	2	·	·	PUNCT
ejpam-2231	90	3	a2	a2	PROPN
ejpam-2231	90	4	=(	=(	PROPN
ejpam-2231	90	5	a2	a2	PROPN
ejpam-2231	90	6	·	·	PUNCT
ejpam-2231	90	7	aa)s	aa)s	NUM
ejpam-2231	90	8	=	=	SYM
ejpam-2231	90	9	(	(	PUNCT
ejpam-2231	90	10	a	a	PRON
ejpam-2231	90	11	·	·	PUNCT
ejpam-2231	90	12	a2a)s	a2a)s	ADP
ejpam-2231	90	13	⊆	⊆	NUM
ejpam-2231	90	14	[	[	X
ejpam-2231	90	15	a	a	X
ejpam-2231	90	16	·	·	PUNCT
ejpam-2231	90	17	(	(	PUNCT
ejpam-2231	90	18	ai)a]s	ai)a]s	NOUN
ejpam-2231	90	19	=	=	SYM
ejpam-2231	90	20	aa	aa	PROPN
ejpam-2231	90	21	·	·	PUNCT
ejpam-2231	90	22	s	s	PART
ejpam-2231	90	23	=	=	X
ejpam-2231	90	24	sa	sa	X
ejpam-2231	90	25	·	·	PUNCT
ejpam-2231	90	26	a⊆	a⊆	PROPN
ejpam-2231	90	27	si	si	X
ejpam-2231	90	28	·	·	PUNCT
ejpam-2231	90	29	s	s	PROPN
ejpam-2231	90	30	⊆	⊆	NUM
ejpam-2231	90	31	i	i	PRON
ejpam-2231	90	32	,	,	PUNCT
ejpam-2231	90	33	which	which	PRON
ejpam-2231	90	34	shows	show	VERB
ejpam-2231	90	35	that	that	SCONJ
ejpam-2231	90	36	a	a	PRON
ejpam-2231	90	37	is	be	AUX
ejpam-2231	90	38	a	a	DET
ejpam-2231	90	39	(	(	PUNCT
ejpam-2231	90	40	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	90	41	of	of	ADP
ejpam-2231	90	42	a	a	DET
ejpam-2231	90	43	right	right	ADJ
ejpam-2231	90	44	ideal	ideal	ADJ
ejpam-2231	90	45	sa2	sa2	PROPN
ejpam-2231	90	46	of	of	ADP
ejpam-2231	90	47	s.	s.	PROPN
ejpam-2231	90	48	w.	w.	PROPN
ejpam-2231	90	49	khan	khan	PROPN
ejpam-2231	90	50	,	,	PUNCT
ejpam-2231	90	51	f.	f.	PROPN
ejpam-2231	90	52	yousafzai	yousafzai	PROPN
ejpam-2231	90	53	,	,	PUNCT
ejpam-2231	90	54	and	and	CCONJ
ejpam-2231	90	55	m.	m.	PROPN
ejpam-2231	90	56	khan	khan	PROPN
ejpam-2231	90	57	/	/	SYM
ejpam-2231	90	58	eur	eur	PROPN
ejpam-2231	90	59	.	.	PUNCT
ejpam-2231	91	1	j.	j.	PROPN
ejpam-2231	91	2	pure	pure	PROPN
ejpam-2231	91	3	appl	appl	PROPN
ejpam-2231	91	4	.	.	PROPN
ejpam-2231	91	5	math	math	PROPN
ejpam-2231	91	6	,	,	PUNCT
ejpam-2231	91	7	9	9	NUM
ejpam-2231	91	8	(	(	PUNCT
ejpam-2231	91	9	2016	2016	NUM
ejpam-2231	91	10	)	)	PUNCT
ejpam-2231	91	11	,	,	PUNCT
ejpam-2231	91	12	277	277	NUM
ejpam-2231	91	13	-	-	SYM
ejpam-2231	91	14	291	291	NUM
ejpam-2231	91	15	281	281	NUM
ejpam-2231	91	16	(	(	PUNCT
ejpam-2231	91	17	iv	iv	X
ejpam-2231	91	18	)	)	PUNCT
ejpam-2231	92	1	=	=	NOUN
ejpam-2231	92	2	⇒	⇒	NOUN
ejpam-2231	92	3	(	(	PUNCT
ejpam-2231	92	4	v	v	NOUN
ejpam-2231	92	5	)	)	PUNCT
ejpam-2231	92	6	.	.	PUNCT
ejpam-2231	93	1	it	it	PRON
ejpam-2231	93	2	is	be	AUX
ejpam-2231	93	3	easy	easy	ADJ
ejpam-2231	93	4	to	to	PART
ejpam-2231	93	5	see	see	VERB
ejpam-2231	93	6	that	that	DET
ejpam-2231	93	7	sa3	sa3	NOUN
ejpam-2231	93	8	is	be	AUX
ejpam-2231	93	9	a	a	DET
ejpam-2231	93	10	(	(	PUNCT
ejpam-2231	93	11	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	93	12	of	of	ADP
ejpam-2231	93	13	s.	s.	PROPN
ejpam-2231	93	14	let	let	VERB
ejpam-2231	93	15	a	a	DET
ejpam-2231	93	16	be	be	AUX
ejpam-2231	93	17	a	a	DET
ejpam-2231	93	18	(	(	PUNCT
ejpam-2231	93	19	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	93	20	of	of	ADP
ejpam-2231	93	21	a	a	DET
ejpam-2231	93	22	right	right	ADJ
ejpam-2231	93	23	ideal	ideal	ADJ
ejpam-2231	93	24	r	r	NOUN
ejpam-2231	93	25	of	of	ADP
ejpam-2231	93	26	s	s	PROPN
ejpam-2231	93	27	,	,	PUNCT
ejpam-2231	93	28	then	then	ADV
ejpam-2231	93	29	a	a	DET
ejpam-2231	93	30	·	·	PUNCT
ejpam-2231	93	31	sa3	sa3	ADJ
ejpam-2231	93	32	=	=	SYM
ejpam-2231	93	33	a(ss	a(ss	NOUN
ejpam-2231	93	34	·	·	PUNCT
ejpam-2231	93	35	a2a	a2a	NOUN
ejpam-2231	93	36	)	)	PUNCT
ejpam-2231	94	1	=	=	PUNCT
ejpam-2231	94	2	a(aa2	a(aa2	NOUN
ejpam-2231	94	3	·	·	PUNCT
ejpam-2231	94	4	s	s	X
ejpam-2231	94	5	)	)	PUNCT
ejpam-2231	94	6	⊆	⊆	NUM
ejpam-2231	94	7	a[(sa	a[(sa	NOUN
ejpam-2231	94	8	·	·	PUNCT
ejpam-2231	94	9	aa)s	aa)s	NUM
ejpam-2231	94	10	]	]	PUNCT
ejpam-2231	94	11	=	=	SYM
ejpam-2231	94	12	a[(aa	a[(aa	NOUN
ejpam-2231	94	13	·	·	PUNCT
ejpam-2231	94	14	as)s	as)s	PUNCT
ejpam-2231	94	15	]	]	X
ejpam-2231	95	1	=	=	X
ejpam-2231	95	2	(	(	PUNCT
ejpam-2231	95	3	aa)[(a	aa)[(a	PROPN
ejpam-2231	95	4	·	·	PUNCT
ejpam-2231	95	5	as)s	as)s	PROPN
ejpam-2231	95	6	]	]	X
ejpam-2231	95	7	=	=	PUNCT
ejpam-2231	96	1	[	[	X
ejpam-2231	96	2	s	s	X
ejpam-2231	96	3	·	·	PUNCT
ejpam-2231	96	4	a(as)]a2	a(as)]a2	NOUN
ejpam-2231	96	5	=	=	PUNCT
ejpam-2231	97	1	[	[	X
ejpam-2231	97	2	a	a	DET
ejpam-2231	97	3	·	·	PUNCT
ejpam-2231	97	4	s(as)]a2	s(as)]a2	PROPN
ejpam-2231	97	5	⊆rs	⊆rs	PROPN
ejpam-2231	97	6	·	·	PUNCT
ejpam-2231	97	7	a2	a2	PROPN
ejpam-2231	97	8	⊆	⊆	NUM
ejpam-2231	97	9	ra2	ra2	PROPN
ejpam-2231	97	10	⊆	⊆	NUM
ejpam-2231	97	11	a	a	PRON
ejpam-2231	97	12	,	,	PUNCT
ejpam-2231	97	13	which	which	PRON
ejpam-2231	97	14	shows	show	VERB
ejpam-2231	97	15	that	that	SCONJ
ejpam-2231	97	16	a	a	PRON
ejpam-2231	97	17	is	be	AUX
ejpam-2231	97	18	a	a	DET
ejpam-2231	97	19	left	left	ADJ
ejpam-2231	97	20	ideal	ideal	NOUN
ejpam-2231	97	21	of	of	ADP
ejpam-2231	97	22	a	a	DET
ejpam-2231	97	23	(	(	PUNCT
ejpam-2231	97	24	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	97	25	sa3	sa3	NOUN
ejpam-2231	97	26	of	of	ADP
ejpam-2231	97	27	s.	s.	PROPN
ejpam-2231	97	28	(	(	PUNCT
ejpam-2231	97	29	v	v	NOUN
ejpam-2231	97	30	)	)	PUNCT
ejpam-2231	97	31	=	=	NOUN
ejpam-2231	97	32	⇒	⇒	NOUN
ejpam-2231	97	33	(	(	PUNCT
ejpam-2231	97	34	i	i	NOUN
ejpam-2231	97	35	)	)	PUNCT
ejpam-2231	97	36	.	.	PUNCT
ejpam-2231	98	1	let	let	VERB
ejpam-2231	98	2	a	a	DET
ejpam-2231	98	3	be	be	AUX
ejpam-2231	98	4	a	a	DET
ejpam-2231	98	5	left	left	ADJ
ejpam-2231	98	6	ideal	ideal	NOUN
ejpam-2231	98	7	of	of	ADP
ejpam-2231	98	8	a	a	DET
ejpam-2231	98	9	(	(	PUNCT
ejpam-2231	98	10	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	98	11	o	o	NOUN
ejpam-2231	98	12	of	of	ADP
ejpam-2231	98	13	s	s	PROPN
ejpam-2231	98	14	,	,	PUNCT
ejpam-2231	98	15	then	then	ADV
ejpam-2231	98	16	as	as	ADP
ejpam-2231	98	17	·	·	PUNCT
ejpam-2231	98	18	a2	a2	PROPN
ejpam-2231	98	19	=	=	SYM
ejpam-2231	98	20	(	(	PUNCT
ejpam-2231	98	21	aa	aa	NOUN
ejpam-2231	98	22	·	·	PUNCT
ejpam-2231	98	23	ss)a=	ss)a=	ADJ
ejpam-2231	98	24	sa2	sa2	NOUN
ejpam-2231	98	25	·	·	PUNCT
ejpam-2231	98	26	a⊆	a⊆	PROPN
ejpam-2231	98	27	so2	so2	PROPN
ejpam-2231	98	28	·	·	PUNCT
ejpam-2231	98	29	a⊆	a⊆	VERB
ejpam-2231	98	30	oa⊆	oa⊆	ADP
ejpam-2231	98	31	a	a	PRON
ejpam-2231	98	32	,	,	PUNCT
ejpam-2231	98	33	which	which	PRON
ejpam-2231	98	34	shows	show	VERB
ejpam-2231	98	35	that	that	SCONJ
ejpam-2231	98	36	a	a	PRON
ejpam-2231	98	37	is	be	AUX
ejpam-2231	98	38	a	a	DET
ejpam-2231	98	39	(	(	PUNCT
ejpam-2231	98	40	1,2)-ideal	1,2)-ideal	NUM
ejpam-2231	98	41	of	of	ADP
ejpam-2231	98	42	s.	s.	PROPN
ejpam-2231	98	43	lemma	lemma	PROPN
ejpam-2231	99	1	3	3	X
ejpam-2231	99	2	.	.	PUNCT
ejpam-2231	99	3	let	let	VERB
ejpam-2231	99	4	s	s	PRON
ejpam-2231	99	5	be	be	AUX
ejpam-2231	99	6	a	a	DET
ejpam-2231	99	7	unitary	unitary	ADJ
ejpam-2231	99	8	la	la	ADJ
ejpam-2231	99	9	-semigroup	-semigroup	NOUN
ejpam-2231	99	10	and	and	CCONJ
ejpam-2231	99	11	a	a	DET
ejpam-2231	99	12	be	be	AUX
ejpam-2231	99	13	an	an	DET
ejpam-2231	99	14	idempotent	idempotent	ADJ
ejpam-2231	99	15	subset	subset	NOUN
ejpam-2231	99	16	of	of	ADP
ejpam-2231	99	17	s.	s.	PROPN
ejpam-2231	99	18	then	then	ADV
ejpam-2231	99	19	a	a	PRON
ejpam-2231	99	20	is	be	AUX
ejpam-2231	99	21	a	a	DET
ejpam-2231	99	22	(	(	PUNCT
ejpam-2231	99	23	1,2)-ideal	1,2)-ideal	NUM
ejpam-2231	99	24	of	of	ADP
ejpam-2231	99	25	s	s	PRON
ejpam-2231	99	26	if	if	SCONJ
ejpam-2231	100	1	and	and	CCONJ
ejpam-2231	100	2	only	only	ADV
ejpam-2231	100	3	if	if	SCONJ
ejpam-2231	100	4	there	there	PRON
ejpam-2231	100	5	exist	exist	VERB
ejpam-2231	100	6	a	a	DET
ejpam-2231	100	7	left	left	ADJ
ejpam-2231	100	8	ideal	ideal	NOUN
ejpam-2231	100	9	l	l	NOUN
ejpam-2231	100	10	and	and	CCONJ
ejpam-2231	100	11	a	a	DET
ejpam-2231	100	12	right	right	ADJ
ejpam-2231	100	13	ideal	ideal	ADJ
ejpam-2231	100	14	r	r	NOUN
ejpam-2231	100	15	of	of	ADP
ejpam-2231	100	16	s	s	PRON
ejpam-2231	100	17	such	such	ADJ
ejpam-2231	100	18	that	that	SCONJ
ejpam-2231	100	19	rl	rl	ADP
ejpam-2231	100	20	⊆	⊆	NUM
ejpam-2231	100	21	a⊆	a⊆	NOUN
ejpam-2231	100	22	r∩	r∩	PROPN
ejpam-2231	100	23	l.	l.	NOUN
ejpam-2231	100	24	proof	proof	PROPN
ejpam-2231	100	25	.	.	PUNCT
ejpam-2231	101	1	assume	assume	VERB
ejpam-2231	101	2	that	that	SCONJ
ejpam-2231	101	3	a	a	PRON
ejpam-2231	101	4	is	be	AUX
ejpam-2231	101	5	a	a	DET
ejpam-2231	101	6	(	(	PUNCT
ejpam-2231	101	7	1,2)-ideal	1,2)-ideal	NUM
ejpam-2231	101	8	of	of	ADP
ejpam-2231	101	9	s	s	PRON
ejpam-2231	101	10	such	such	ADJ
ejpam-2231	101	11	that	that	SCONJ
ejpam-2231	101	12	a	a	PRON
ejpam-2231	101	13	is	be	AUX
ejpam-2231	101	14	idempotent	idempotent	ADJ
ejpam-2231	101	15	.	.	PUNCT
ejpam-2231	102	1	setting	set	VERB
ejpam-2231	102	2	l	l	NOUN
ejpam-2231	102	3	=	=	PUNCT
ejpam-2231	102	4	sa	sa	PROPN
ejpam-2231	102	5	and	and	CCONJ
ejpam-2231	102	6	r=	r=	ADJ
ejpam-2231	102	7	sa2	sa2	PROPN
ejpam-2231	102	8	,	,	PUNCT
ejpam-2231	102	9	then	then	ADV
ejpam-2231	102	10	rl	rl	ADP
ejpam-2231	102	11	=	=	NOUN
ejpam-2231	102	12	sa2	sa2	PROPN
ejpam-2231	102	13	·	·	PUNCT
ejpam-2231	102	14	sa=	sa=	NOUN
ejpam-2231	102	15	a2s	a2s	NOUN
ejpam-2231	102	16	·	·	PUNCT
ejpam-2231	102	17	sa=	sa=	PROPN
ejpam-2231	102	18	(	(	PUNCT
ejpam-2231	102	19	sa	sa	NOUN
ejpam-2231	102	20	·	·	PUNCT
ejpam-2231	102	21	ss)a2	ss)a2	NOUN
ejpam-2231	103	1	=	=	SYM
ejpam-2231	103	2	(	(	PUNCT
ejpam-2231	103	3	ss	ss	NOUN
ejpam-2231	103	4	·	·	PUNCT
ejpam-2231	103	5	as)a2	as)a2	PROPN
ejpam-2231	103	6	=[	=[	VERB
ejpam-2231	103	7	s(aa	s(aa	PROPN
ejpam-2231	103	8	·	·	PUNCT
ejpam-2231	103	9	ss)]a2	ss)]a2	NOUN
ejpam-2231	103	10	=	=	PUNCT
ejpam-2231	104	1	[	[	X
ejpam-2231	104	2	s(ss	s(ss	X
ejpam-2231	104	3	·	·	PUNCT
ejpam-2231	104	4	aa)]a2	aa)]a2	NOUN
ejpam-2231	105	1	=	=	PUNCT
ejpam-2231	106	1	[	[	X
ejpam-2231	106	2	s{a(ss	s{a(ss	NOUN
ejpam-2231	106	3	·	·	PUNCT
ejpam-2231	106	4	a)}]a2	a)}]a2	NOUN
ejpam-2231	106	5	=[	=[	NOUN
ejpam-2231	106	6	a(s	a(	NOUN
ejpam-2231	106	7	·	·	PUNCT
ejpam-2231	106	8	sa)]a2	sa)]a2	NOUN
ejpam-2231	106	9	⊆	⊆	NUM
ejpam-2231	106	10	as	as	ADP
ejpam-2231	106	11	·	·	PUNCT
ejpam-2231	106	12	a2	a2	PROPN
ejpam-2231	106	13	⊆	⊆	NUM
ejpam-2231	106	14	a.	a.	NOUN
ejpam-2231	106	15	it	it	PRON
ejpam-2231	106	16	is	be	AUX
ejpam-2231	106	17	clear	clear	ADJ
ejpam-2231	106	18	that	that	SCONJ
ejpam-2231	106	19	a⊆	a⊆	NOUN
ejpam-2231	106	20	r∩	r∩	PROPN
ejpam-2231	106	21	l.	l.	NOUN
ejpam-2231	106	22	conversely	conversely	ADV
ejpam-2231	106	23	,	,	PUNCT
ejpam-2231	106	24	let	let	VERB
ejpam-2231	106	25	r	r	PRON
ejpam-2231	106	26	be	be	AUX
ejpam-2231	106	27	a	a	DET
ejpam-2231	106	28	right	right	ADJ
ejpam-2231	106	29	ideal	ideal	NOUN
ejpam-2231	106	30	and	and	CCONJ
ejpam-2231	106	31	l	l	NOUN
ejpam-2231	106	32	be	be	AUX
ejpam-2231	106	33	a	a	DET
ejpam-2231	106	34	left	left	ADJ
ejpam-2231	106	35	ideal	ideal	NOUN
ejpam-2231	106	36	of	of	ADP
ejpam-2231	106	37	s	s	PRON
ejpam-2231	106	38	such	such	ADJ
ejpam-2231	106	39	that	that	SCONJ
ejpam-2231	106	40	rl	rl	ADP
ejpam-2231	106	41	⊆	⊆	NUM
ejpam-2231	106	42	a⊆	a⊆	NOUN
ejpam-2231	106	43	r∩	r∩	PROPN
ejpam-2231	106	44	l	l	NOUN
ejpam-2231	106	45	,	,	PUNCT
ejpam-2231	106	46	then	then	ADV
ejpam-2231	106	47	as	as	ADP
ejpam-2231	106	48	·	·	PUNCT
ejpam-2231	106	49	a2	a2	PROPN
ejpam-2231	106	50	=	=	PUNCT
ejpam-2231	106	51	as	as	ADP
ejpam-2231	106	52	·	·	PUNCT
ejpam-2231	106	53	aa⊆	aa⊆	NOUN
ejpam-2231	106	54	rs	rs	NOUN
ejpam-2231	106	55	·	·	PUNCT
ejpam-2231	106	56	sl	sl	VERB
ejpam-2231	106	57	⊆	⊆	NUM
ejpam-2231	106	58	rl	rl	ADP
ejpam-2231	106	59	⊆	⊆	NUM
ejpam-2231	106	60	a.	a.	NOUN
ejpam-2231	106	61	assume	assume	VERB
ejpam-2231	106	62	that	that	SCONJ
ejpam-2231	106	63	s	s	VERB
ejpam-2231	106	64	is	be	AUX
ejpam-2231	106	65	a	a	DET
ejpam-2231	106	66	unitary	unitary	ADJ
ejpam-2231	106	67	la	la	ADJ
ejpam-2231	106	68	-semigroup	-semigroup	NOUN
ejpam-2231	106	69	with	with	ADP
ejpam-2231	106	70	zero	zero	NUM
ejpam-2231	106	71	.	.	PUNCT
ejpam-2231	107	1	then	then	ADV
ejpam-2231	107	2	it	it	PRON
ejpam-2231	107	3	is	be	AUX
ejpam-2231	107	4	easy	easy	ADJ
ejpam-2231	107	5	to	to	PART
ejpam-2231	107	6	see	see	VERB
ejpam-2231	107	7	that	that	SCONJ
ejpam-2231	107	8	every	every	DET
ejpam-2231	107	9	left	left	ADJ
ejpam-2231	107	10	(	(	PUNCT
ejpam-2231	107	11	right	right	ADJ
ejpam-2231	107	12	)	)	PUNCT
ejpam-2231	107	13	ideal	ideal	NOUN
ejpam-2231	107	14	of	of	ADP
ejpam-2231	107	15	s	s	PROPN
ejpam-2231	107	16	is	be	AUX
ejpam-2231	107	17	a	a	DET
ejpam-2231	107	18	(	(	PUNCT
ejpam-2231	107	19	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	107	20	of	of	ADP
ejpam-2231	107	21	s.	s.	PROPN
ejpam-2231	107	22	hence	hence	ADV
ejpam-2231	107	23	if	if	SCONJ
ejpam-2231	107	24	o	o	NOUN
ejpam-2231	107	25	is	be	AUX
ejpam-2231	107	26	a	a	DET
ejpam-2231	107	27	0	0	NUM
ejpam-2231	107	28	-	-	PUNCT
ejpam-2231	107	29	minimal	minimal	ADJ
ejpam-2231	107	30	(	(	PUNCT
ejpam-2231	107	31	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	107	32	of	of	ADP
ejpam-2231	107	33	s	s	PRON
ejpam-2231	107	34	and	and	CCONJ
ejpam-2231	107	35	a	a	PRON
ejpam-2231	107	36	is	be	AUX
ejpam-2231	107	37	a	a	DET
ejpam-2231	107	38	left	left	ADJ
ejpam-2231	107	39	(	(	PUNCT
ejpam-2231	107	40	right	right	ADJ
ejpam-2231	107	41	)	)	PUNCT
ejpam-2231	107	42	ideal	ideal	NOUN
ejpam-2231	107	43	of	of	ADP
ejpam-2231	107	44	s	s	PRON
ejpam-2231	107	45	contained	contain	VERB
ejpam-2231	107	46	in	in	ADP
ejpam-2231	107	47	o	o	NOUN
ejpam-2231	107	48	,	,	PUNCT
ejpam-2231	107	49	then	then	ADV
ejpam-2231	107	50	either	either	CCONJ
ejpam-2231	107	51	a=	a=	ADJ
ejpam-2231	107	52	{	{	PUNCT
ejpam-2231	107	53	0	0	NUM
ejpam-2231	107	54	}	}	PUNCT
ejpam-2231	107	55	or	or	CCONJ
ejpam-2231	107	56	a=	a=	PROPN
ejpam-2231	107	57	o.	o.	PROPN
ejpam-2231	107	58	lemma	lemma	PROPN
ejpam-2231	108	1	4	4	X
ejpam-2231	108	2	.	.	PUNCT
ejpam-2231	108	3	let	let	VERB
ejpam-2231	108	4	s	s	PRON
ejpam-2231	108	5	be	be	AUX
ejpam-2231	108	6	a	a	DET
ejpam-2231	108	7	unitary	unitary	ADJ
ejpam-2231	108	8	la	la	ADJ
ejpam-2231	108	9	-semigroup	-semigroup	NOUN
ejpam-2231	108	10	with	with	ADP
ejpam-2231	108	11	zero	zero	NUM
ejpam-2231	108	12	.	.	PUNCT
ejpam-2231	109	1	assume	assume	VERB
ejpam-2231	109	2	that	that	SCONJ
ejpam-2231	109	3	a	a	PRON
ejpam-2231	109	4	is	be	AUX
ejpam-2231	109	5	a	a	DET
ejpam-2231	109	6	0	0	NUM
ejpam-2231	109	7	-	-	PUNCT
ejpam-2231	109	8	minimal	minimal	ADJ
ejpam-2231	109	9	ideal	ideal	NOUN
ejpam-2231	109	10	of	of	ADP
ejpam-2231	109	11	s	s	PRON
ejpam-2231	109	12	and	and	CCONJ
ejpam-2231	109	13	o	o	PROPN
ejpam-2231	109	14	is	be	AUX
ejpam-2231	109	15	an	an	DET
ejpam-2231	109	16	la	la	ADJ
ejpam-2231	109	17	-subsemigroup	-subsemigroup	NOUN
ejpam-2231	109	18	of	of	ADP
ejpam-2231	109	19	a.	a.	NOUN
ejpam-2231	110	1	then	then	ADV
ejpam-2231	110	2	o	o	PROPN
ejpam-2231	110	3	is	be	AUX
ejpam-2231	110	4	a	a	DET
ejpam-2231	110	5	(	(	PUNCT
ejpam-2231	110	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	110	7	of	of	ADP
ejpam-2231	110	8	s	s	PRON
ejpam-2231	110	9	contained	contain	VERB
ejpam-2231	110	10	in	in	ADP
ejpam-2231	110	11	a	a	DET
ejpam-2231	110	12	if	if	NOUN
ejpam-2231	110	13	and	and	CCONJ
ejpam-2231	110	14	only	only	ADV
ejpam-2231	110	15	if	if	SCONJ
ejpam-2231	110	16	o2	o2	PROPN
ejpam-2231	110	17	=	=	SYM
ejpam-2231	110	18	{	{	PUNCT
ejpam-2231	110	19	0	0	NUM
ejpam-2231	110	20	}	}	PUNCT
ejpam-2231	110	21	or	or	CCONJ
ejpam-2231	110	22	o	o	NOUN
ejpam-2231	110	23	=	=	NOUN
ejpam-2231	110	24	a.	a.	NOUN
ejpam-2231	110	25	proof	proof	NOUN
ejpam-2231	110	26	.	.	PUNCT
ejpam-2231	111	1	let	let	VERB
ejpam-2231	111	2	o	o	NOUN
ejpam-2231	111	3	be	be	AUX
ejpam-2231	111	4	a	a	DET
ejpam-2231	111	5	(	(	PUNCT
ejpam-2231	111	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	111	7	of	of	ADP
ejpam-2231	111	8	s	s	PRON
ejpam-2231	111	9	contained	contain	VERB
ejpam-2231	111	10	in	in	ADP
ejpam-2231	111	11	a	a	DET
ejpam-2231	111	12	0	0	NUM
ejpam-2231	111	13	-	-	PUNCT
ejpam-2231	111	14	minimal	minimal	ADJ
ejpam-2231	111	15	ideal	ideal	NOUN
ejpam-2231	111	16	a	a	PRON
ejpam-2231	111	17	of	of	ADP
ejpam-2231	111	18	s.	s.	PROPN
ejpam-2231	111	19	then	then	ADV
ejpam-2231	111	20	so2	so2	PROPN
ejpam-2231	112	1	⊆	⊆	NUM
ejpam-2231	112	2	o	o	NOUN
ejpam-2231	112	3	⊆	⊆	NUM
ejpam-2231	112	4	a.	a.	NOUN
ejpam-2231	112	5	since	since	SCONJ
ejpam-2231	112	6	so2	so2	PROPN
ejpam-2231	112	7	is	be	AUX
ejpam-2231	112	8	an	an	DET
ejpam-2231	112	9	ideal	ideal	NOUN
ejpam-2231	112	10	of	of	ADP
ejpam-2231	112	11	s	s	PROPN
ejpam-2231	112	12	,	,	PUNCT
ejpam-2231	112	13	therefore	therefore	ADV
ejpam-2231	112	14	by	by	ADP
ejpam-2231	112	15	minimality	minimality	NOUN
ejpam-2231	112	16	of	of	ADP
ejpam-2231	112	17	a	a	DET
ejpam-2231	112	18	,	,	PUNCT
ejpam-2231	112	19	so2	so2	NOUN
ejpam-2231	112	20	=	=	PUNCT
ejpam-2231	112	21	{	{	PUNCT
ejpam-2231	112	22	0	0	NUM
ejpam-2231	112	23	}	}	PUNCT
ejpam-2231	112	24	or	or	CCONJ
ejpam-2231	112	25	so2	so2	NOUN
ejpam-2231	112	26	=	=	PUNCT
ejpam-2231	112	27	a.	a.	NOUN
ejpam-2231	112	28	if	if	SCONJ
ejpam-2231	112	29	so2	so2	PROPN
ejpam-2231	112	30	=	=	PUNCT
ejpam-2231	112	31	a	a	PROPN
ejpam-2231	112	32	,	,	PUNCT
ejpam-2231	112	33	then	then	ADV
ejpam-2231	112	34	a=	a=	PROPN
ejpam-2231	112	35	so2	so2	PROPN
ejpam-2231	112	36	⊆	⊆	NUM
ejpam-2231	112	37	o	o	NOUN
ejpam-2231	112	38	and	and	CCONJ
ejpam-2231	112	39	therefore	therefore	ADV
ejpam-2231	112	40	o	o	X
ejpam-2231	112	41	=	=	PUNCT
ejpam-2231	112	42	a.	a.	NOUN
ejpam-2231	112	43	let	let	VERB
ejpam-2231	112	44	so2	so2	PROPN
ejpam-2231	112	45	=	=	PUNCT
ejpam-2231	112	46	{	{	PUNCT
ejpam-2231	112	47	0	0	NUM
ejpam-2231	112	48	}	}	PUNCT
ejpam-2231	112	49	,	,	PUNCT
ejpam-2231	112	50	then	then	ADV
ejpam-2231	112	51	o2s	o2s	PROPN
ejpam-2231	112	52	=	=	PUNCT
ejpam-2231	112	53	so2	so2	PROPN
ejpam-2231	112	54	=	=	PUNCT
ejpam-2231	112	55	{	{	PUNCT
ejpam-2231	112	56	0	0	NUM
ejpam-2231	112	57	}	}	SYM
ejpam-2231	112	58	⊆	⊆	NUM
ejpam-2231	112	59	o2	o2	PROPN
ejpam-2231	112	60	,	,	PUNCT
ejpam-2231	112	61	which	which	PRON
ejpam-2231	112	62	shows	show	VERB
ejpam-2231	112	63	that	that	SCONJ
ejpam-2231	112	64	o2	o2	PROPN
ejpam-2231	112	65	is	be	AUX
ejpam-2231	112	66	a	a	DET
ejpam-2231	112	67	right	right	ADJ
ejpam-2231	112	68	ideal	ideal	NOUN
ejpam-2231	112	69	of	of	ADP
ejpam-2231	112	70	s	s	PROPN
ejpam-2231	112	71	,	,	PUNCT
ejpam-2231	112	72	and	and	CCONJ
ejpam-2231	112	73	hence	hence	ADV
ejpam-2231	112	74	an	an	DET
ejpam-2231	112	75	ideal	ideal	NOUN
ejpam-2231	112	76	of	of	ADP
ejpam-2231	112	77	s	s	PRON
ejpam-2231	112	78	contained	contain	VERB
ejpam-2231	112	79	in	in	ADP
ejpam-2231	112	80	a	a	PRON
ejpam-2231	112	81	,	,	PUNCT
ejpam-2231	112	82	therefore	therefore	ADV
ejpam-2231	112	83	by	by	ADP
ejpam-2231	112	84	minimality	minimality	NOUN
ejpam-2231	112	85	of	of	ADP
ejpam-2231	112	86	a	a	PRON
ejpam-2231	112	87	,	,	PUNCT
ejpam-2231	112	88	we	we	PRON
ejpam-2231	112	89	have	have	VERB
ejpam-2231	112	90	o2	o2	PROPN
ejpam-2231	112	91	=	=	SYM
ejpam-2231	112	92	{	{	PUNCT
ejpam-2231	112	93	0	0	NUM
ejpam-2231	112	94	}	}	PUNCT
ejpam-2231	112	95	or	or	CCONJ
ejpam-2231	112	96	o2	o2	PROPN
ejpam-2231	112	97	=	=	NOUN
ejpam-2231	112	98	a.	a.	NOUN
ejpam-2231	112	99	now	now	ADV
ejpam-2231	112	100	if	if	SCONJ
ejpam-2231	112	101	o2	o2	PROPN
ejpam-2231	112	102	=	=	SYM
ejpam-2231	112	103	a	a	NOUN
ejpam-2231	112	104	,	,	PUNCT
ejpam-2231	112	105	then	then	ADV
ejpam-2231	112	106	o	o	X
ejpam-2231	112	107	=	=	PUNCT
ejpam-2231	112	108	a.	a.	NOUN
ejpam-2231	112	109	conversely	conversely	ADV
ejpam-2231	112	110	,	,	PUNCT
ejpam-2231	112	111	let	let	VERB
ejpam-2231	112	112	o2	o2	PROPN
ejpam-2231	112	113	=	=	SYM
ejpam-2231	112	114	{	{	PUNCT
ejpam-2231	112	115	0	0	NUM
ejpam-2231	112	116	}	}	PUNCT
ejpam-2231	112	117	,	,	PUNCT
ejpam-2231	112	118	then	then	ADV
ejpam-2231	112	119	so2	so2	PROPN
ejpam-2231	112	120	=	=	PUNCT
ejpam-2231	113	1	o2s	o2s	PROPN
ejpam-2231	113	2	=	=	PUNCT
ejpam-2231	113	3	{	{	PUNCT
ejpam-2231	113	4	0}s	0}s	NUM
ejpam-2231	113	5	=	=	SYM
ejpam-2231	113	6	{	{	PUNCT
ejpam-2231	113	7	0	0	NUM
ejpam-2231	113	8	}	}	PUNCT
ejpam-2231	113	9	=	=	SYM
ejpam-2231	113	10	o2	o2	PROPN
ejpam-2231	113	11	.	.	PUNCT
ejpam-2231	114	1	now	now	ADV
ejpam-2231	114	2	if	if	SCONJ
ejpam-2231	114	3	o	o	PROPN
ejpam-2231	114	4	=	=	PUNCT
ejpam-2231	114	5	a	a	X
ejpam-2231	114	6	,	,	PUNCT
ejpam-2231	114	7	then	then	ADV
ejpam-2231	114	8	so2	so2	PROPN
ejpam-2231	114	9	=	=	SYM
ejpam-2231	114	10	ss	ss	PROPN
ejpam-2231	114	11	·	·	PUNCT
ejpam-2231	114	12	oo	oo	NOUN
ejpam-2231	114	13	=	=	X
ejpam-2231	114	14	sa	sa	NOUN
ejpam-2231	114	15	·	·	PUNCT
ejpam-2231	114	16	sa⊆	sa⊆	NOUN
ejpam-2231	114	17	a=	a=	ADV
ejpam-2231	114	18	o	o	NOUN
ejpam-2231	114	19	,	,	PUNCT
ejpam-2231	114	20	which	which	PRON
ejpam-2231	114	21	shows	show	VERB
ejpam-2231	114	22	that	that	SCONJ
ejpam-2231	114	23	o	o	NOUN
ejpam-2231	114	24	is	be	AUX
ejpam-2231	114	25	a	a	DET
ejpam-2231	114	26	(	(	PUNCT
ejpam-2231	114	27	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	114	28	of	of	ADP
ejpam-2231	114	29	s	s	PRON
ejpam-2231	114	30	contained	contain	VERB
ejpam-2231	114	31	in	in	ADP
ejpam-2231	114	32	a.	a.	PROPN
ejpam-2231	114	33	w.	w.	PROPN
ejpam-2231	114	34	khan	khan	PROPN
ejpam-2231	114	35	,	,	PUNCT
ejpam-2231	114	36	f.	f.	PROPN
ejpam-2231	114	37	yousafzai	yousafzai	PROPN
ejpam-2231	114	38	,	,	PUNCT
ejpam-2231	114	39	and	and	CCONJ
ejpam-2231	114	40	m.	m.	PROPN
ejpam-2231	114	41	khan	khan	PROPN
ejpam-2231	114	42	/	/	SYM
ejpam-2231	114	43	eur	eur	PROPN
ejpam-2231	114	44	.	.	PUNCT
ejpam-2231	115	1	j.	j.	PROPN
ejpam-2231	115	2	pure	pure	PROPN
ejpam-2231	115	3	appl	appl	PROPN
ejpam-2231	115	4	.	.	PROPN
ejpam-2231	115	5	math	math	PROPN
ejpam-2231	115	6	,	,	PUNCT
ejpam-2231	115	7	9	9	NUM
ejpam-2231	115	8	(	(	PUNCT
ejpam-2231	115	9	2016	2016	NUM
ejpam-2231	115	10	)	)	PUNCT
ejpam-2231	115	11	,	,	PUNCT
ejpam-2231	115	12	277	277	NUM
ejpam-2231	115	13	-	-	SYM
ejpam-2231	115	14	291	291	NUM
ejpam-2231	115	15	282	282	NUM
ejpam-2231	115	16	corollary	corollary	ADJ
ejpam-2231	115	17	2	2	NUM
ejpam-2231	115	18	.	.	PUNCT
ejpam-2231	116	1	let	let	VERB
ejpam-2231	116	2	s	s	PRON
ejpam-2231	116	3	be	be	AUX
ejpam-2231	116	4	a	a	DET
ejpam-2231	116	5	unitary	unitary	ADJ
ejpam-2231	116	6	la	la	ADJ
ejpam-2231	116	7	-semigroup	-semigroup	NOUN
ejpam-2231	116	8	with	with	ADP
ejpam-2231	116	9	zero	zero	NUM
ejpam-2231	116	10	.	.	PUNCT
ejpam-2231	117	1	assume	assume	VERB
ejpam-2231	117	2	that	that	SCONJ
ejpam-2231	117	3	a	a	PRON
ejpam-2231	117	4	is	be	AUX
ejpam-2231	117	5	a	a	DET
ejpam-2231	117	6	0	0	NUM
ejpam-2231	117	7	-	-	PUNCT
ejpam-2231	117	8	minimal	minimal	ADJ
ejpam-2231	117	9	left	leave	VERB
ejpam-2231	117	10	ideal	ideal	NOUN
ejpam-2231	117	11	of	of	ADP
ejpam-2231	117	12	s	s	PRON
ejpam-2231	117	13	and	and	CCONJ
ejpam-2231	117	14	o	o	PROPN
ejpam-2231	117	15	is	be	AUX
ejpam-2231	117	16	an	an	DET
ejpam-2231	117	17	la	la	ADJ
ejpam-2231	117	18	-subsemigroup	-subsemigroup	NOUN
ejpam-2231	117	19	of	of	ADP
ejpam-2231	117	20	a.	a.	NOUN
ejpam-2231	118	1	then	then	ADV
ejpam-2231	118	2	o	o	PROPN
ejpam-2231	118	3	is	be	AUX
ejpam-2231	118	4	a	a	DET
ejpam-2231	118	5	(	(	PUNCT
ejpam-2231	118	6	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	118	7	of	of	ADP
ejpam-2231	118	8	s	s	PRON
ejpam-2231	118	9	contained	contain	VERB
ejpam-2231	118	10	in	in	ADP
ejpam-2231	118	11	a	a	DET
ejpam-2231	118	12	if	if	NOUN
ejpam-2231	118	13	and	and	CCONJ
ejpam-2231	118	14	only	only	ADV
ejpam-2231	118	15	if	if	SCONJ
ejpam-2231	118	16	o2	o2	PROPN
ejpam-2231	118	17	=	=	SYM
ejpam-2231	118	18	{	{	PUNCT
ejpam-2231	118	19	0	0	NUM
ejpam-2231	118	20	}	}	PUNCT
ejpam-2231	118	21	or	or	CCONJ
ejpam-2231	118	22	o	o	NOUN
ejpam-2231	118	23	=	=	PUNCT
ejpam-2231	118	24	a.	a.	PROPN
ejpam-2231	118	25	lemma	lemma	PROPN
ejpam-2231	118	26	5	5	X
ejpam-2231	118	27	.	.	PUNCT
ejpam-2231	119	1	let	let	VERB
ejpam-2231	119	2	s	s	PRON
ejpam-2231	119	3	be	be	AUX
ejpam-2231	119	4	a	a	DET
ejpam-2231	119	5	unitary	unitary	ADJ
ejpam-2231	119	6	la	la	ADJ
ejpam-2231	119	7	-semigroup	-semigroup	NOUN
ejpam-2231	119	8	with	with	ADP
ejpam-2231	119	9	zero	zero	NUM
ejpam-2231	119	10	and	and	CCONJ
ejpam-2231	119	11	o	o	NOUN
ejpam-2231	119	12	be	be	AUX
ejpam-2231	119	13	a	a	DET
ejpam-2231	119	14	0	0	NUM
ejpam-2231	119	15	-	-	PUNCT
ejpam-2231	119	16	minimal	minimal	ADJ
ejpam-2231	119	17	(	(	PUNCT
ejpam-2231	119	18	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	119	19	of	of	ADP
ejpam-2231	119	20	s.	s.	PROPN
ejpam-2231	119	21	then	then	ADV
ejpam-2231	119	22	o2	o2	PROPN
ejpam-2231	119	23	=	=	SYM
ejpam-2231	119	24	{	{	PUNCT
ejpam-2231	119	25	0	0	NUM
ejpam-2231	119	26	}	}	PUNCT
ejpam-2231	119	27	or	or	CCONJ
ejpam-2231	119	28	o	o	NOUN
ejpam-2231	119	29	is	be	AUX
ejpam-2231	119	30	a	a	DET
ejpam-2231	119	31	0	0	NUM
ejpam-2231	119	32	-	-	PUNCT
ejpam-2231	119	33	minimal	minimal	ADJ
ejpam-2231	119	34	right	right	NOUN
ejpam-2231	119	35	(	(	PUNCT
ejpam-2231	119	36	le	le	PROPN
ejpam-2231	119	37	f	f	PROPN
ejpam-2231	119	38	t	t	PROPN
ejpam-2231	119	39	)	)	PUNCT
ejpam-2231	119	40	ideal	ideal	NOUN
ejpam-2231	119	41	of	of	ADP
ejpam-2231	119	42	s.	s.	PROPN
ejpam-2231	119	43	proof	proof	PROPN
ejpam-2231	119	44	.	.	PUNCT
ejpam-2231	120	1	let	let	VERB
ejpam-2231	120	2	o	o	NOUN
ejpam-2231	120	3	be	be	AUX
ejpam-2231	120	4	a	a	DET
ejpam-2231	120	5	0	0	NUM
ejpam-2231	120	6	-	-	PUNCT
ejpam-2231	120	7	minimal	minimal	ADJ
ejpam-2231	120	8	(	(	PUNCT
ejpam-2231	120	9	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	120	10	of	of	ADP
ejpam-2231	120	11	s	s	PROPN
ejpam-2231	120	12	,	,	PUNCT
ejpam-2231	120	13	then	then	ADV
ejpam-2231	120	14	s(o2)2	s(o2)2	PROPN
ejpam-2231	120	15	=	=	SYM
ejpam-2231	120	16	ss	ss	NOUN
ejpam-2231	120	17	·	·	SYM
ejpam-2231	120	18	o2o2	o2o2	NOUN
ejpam-2231	120	19	=	=	SYM
ejpam-2231	120	20	o2o2	o2o2	X
ejpam-2231	120	21	·	·	PUNCT
ejpam-2231	120	22	s	s	PART
ejpam-2231	120	23	=	=	PROPN
ejpam-2231	120	24	so2	so2	PROPN
ejpam-2231	120	25	·	·	PUNCT
ejpam-2231	120	26	o2	o2	PROPN
ejpam-2231	120	27	⊆	⊆	NUM
ejpam-2231	120	28	oo2	oo2	PROPN
ejpam-2231	120	29	⊆	⊆	NUM
ejpam-2231	120	30	o2	o2	PROPN
ejpam-2231	120	31	,	,	PUNCT
ejpam-2231	120	32	which	which	PRON
ejpam-2231	120	33	shows	show	VERB
ejpam-2231	120	34	that	that	SCONJ
ejpam-2231	120	35	o2	o2	PROPN
ejpam-2231	120	36	is	be	AUX
ejpam-2231	120	37	a	a	DET
ejpam-2231	120	38	(	(	PUNCT
ejpam-2231	120	39	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	120	40	of	of	ADP
ejpam-2231	120	41	s	s	PRON
ejpam-2231	120	42	contained	contain	VERB
ejpam-2231	120	43	in	in	ADP
ejpam-2231	120	44	o	o	NOUN
ejpam-2231	120	45	,	,	PUNCT
ejpam-2231	120	46	therefore	therefore	ADV
ejpam-2231	120	47	by	by	ADP
ejpam-2231	120	48	minimality	minimality	NOUN
ejpam-2231	120	49	of	of	ADP
ejpam-2231	120	50	o	o	PROPN
ejpam-2231	120	51	,	,	PUNCT
ejpam-2231	120	52	o2	o2	PROPN
ejpam-2231	120	53	=	=	SYM
ejpam-2231	120	54	{	{	PUNCT
ejpam-2231	120	55	0	0	NUM
ejpam-2231	120	56	}	}	PUNCT
ejpam-2231	120	57	or	or	CCONJ
ejpam-2231	120	58	o2	o2	PROPN
ejpam-2231	120	59	=	=	SYM
ejpam-2231	120	60	o.	o.	PROPN
ejpam-2231	120	61	suppose	suppose	VERB
ejpam-2231	120	62	that	that	SCONJ
ejpam-2231	120	63	o2	o2	PROPN
ejpam-2231	120	64	=	=	ADJ
ejpam-2231	120	65	o	o	NOUN
ejpam-2231	120	66	,	,	PUNCT
ejpam-2231	120	67	then	then	ADV
ejpam-2231	120	68	os	os	NOUN
ejpam-2231	120	69	=	=	PUNCT
ejpam-2231	120	70	oo	oo	INTJ
ejpam-2231	120	71	·	·	PUNCT
ejpam-2231	120	72	ss	ss	NOUN
ejpam-2231	120	73	=	=	PROPN
ejpam-2231	120	74	so2	so2	PROPN
ejpam-2231	120	75	⊆	⊆	NUM
ejpam-2231	120	76	o	o	NOUN
ejpam-2231	120	77	,	,	PUNCT
ejpam-2231	120	78	which	which	PRON
ejpam-2231	120	79	shows	show	VERB
ejpam-2231	120	80	that	that	SCONJ
ejpam-2231	120	81	o	o	NOUN
ejpam-2231	120	82	is	be	AUX
ejpam-2231	120	83	a	a	DET
ejpam-2231	120	84	right	right	ADJ
ejpam-2231	120	85	ideal	ideal	NOUN
ejpam-2231	120	86	of	of	ADP
ejpam-2231	120	87	s.	s.	PROPN
ejpam-2231	120	88	let	let	VERB
ejpam-2231	120	89	r	r	PRON
ejpam-2231	120	90	be	be	AUX
ejpam-2231	120	91	a	a	DET
ejpam-2231	120	92	right	right	ADJ
ejpam-2231	120	93	ideal	ideal	NOUN
ejpam-2231	120	94	of	of	ADP
ejpam-2231	120	95	s	s	PRON
ejpam-2231	120	96	contained	contain	VERB
ejpam-2231	120	97	in	in	ADP
ejpam-2231	120	98	o	o	NOUN
ejpam-2231	120	99	,	,	PUNCT
ejpam-2231	120	100	then	then	ADV
ejpam-2231	120	101	r2s	r2s	PROPN
ejpam-2231	120	102	=	=	SYM
ejpam-2231	120	103	rr	rr	X
ejpam-2231	120	104	·	·	PUNCT
ejpam-2231	120	105	s	s	PROPN
ejpam-2231	120	106	⊆	⊆	NUM
ejpam-2231	120	107	rs	rs	NOUN
ejpam-2231	120	108	·	·	PUNCT
ejpam-2231	120	109	s	s	PART
ejpam-2231	120	110	⊆	⊆	NUM
ejpam-2231	120	111	r.	r.	NOUN
ejpam-2231	120	112	thus	thus	ADV
ejpam-2231	120	113	r	r	NOUN
ejpam-2231	120	114	is	be	AUX
ejpam-2231	120	115	a	a	DET
ejpam-2231	120	116	(	(	PUNCT
ejpam-2231	120	117	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	120	118	of	of	ADP
ejpam-2231	120	119	s	s	PRON
ejpam-2231	120	120	contained	contain	VERB
ejpam-2231	120	121	in	in	ADP
ejpam-2231	120	122	o	o	NOUN
ejpam-2231	120	123	,	,	PUNCT
ejpam-2231	120	124	and	and	CCONJ
ejpam-2231	120	125	again	again	ADV
ejpam-2231	120	126	by	by	ADP
ejpam-2231	120	127	minimality	minimality	NOUN
ejpam-2231	120	128	of	of	ADP
ejpam-2231	120	129	o	o	PROPN
ejpam-2231	120	130	,	,	PUNCT
ejpam-2231	120	131	r=	r=	X
ejpam-2231	120	132	{	{	PUNCT
ejpam-2231	120	133	0	0	NUM
ejpam-2231	120	134	}	}	PUNCT
ejpam-2231	120	135	or	or	CCONJ
ejpam-2231	120	136	r=	r=	ADJ
ejpam-2231	121	1	o.	o.	NOUN
ejpam-2231	121	2	the	the	DET
ejpam-2231	121	3	following	follow	VERB
ejpam-2231	121	4	corollary	corollary	NOUN
ejpam-2231	121	5	follows	follow	VERB
ejpam-2231	121	6	from	from	ADP
ejpam-2231	121	7	lemma	lemma	PROPN
ejpam-2231	121	8	4	4	NUM
ejpam-2231	121	9	and	and	CCONJ
ejpam-2231	121	10	corollary	corollary	ADJ
ejpam-2231	121	11	2	2	NUM
ejpam-2231	121	12	.	.	PUNCT
ejpam-2231	121	13	corollary	corollary	ADJ
ejpam-2231	121	14	3	3	NUM
ejpam-2231	121	15	.	.	PUNCT
ejpam-2231	122	1	let	let	VERB
ejpam-2231	122	2	s	s	PRON
ejpam-2231	122	3	be	be	AUX
ejpam-2231	122	4	a	a	DET
ejpam-2231	122	5	unitary	unitary	ADJ
ejpam-2231	122	6	la	la	ADJ
ejpam-2231	122	7	-semigroup	-semigroup	NOUN
ejpam-2231	122	8	.	.	PUNCT
ejpam-2231	123	1	then	then	ADV
ejpam-2231	123	2	o	o	NOUN
ejpam-2231	123	3	is	be	AUX
ejpam-2231	123	4	a	a	DET
ejpam-2231	123	5	minimal	minimal	ADJ
ejpam-2231	123	6	(	(	PUNCT
ejpam-2231	123	7	0,2)-ideal	0,2)-ideal	NUM
ejpam-2231	123	8	of	of	ADP
ejpam-2231	123	9	s	s	PRON
ejpam-2231	123	10	if	if	SCONJ
ejpam-2231	123	11	and	and	CCONJ
ejpam-2231	123	12	only	only	ADV
ejpam-2231	123	13	if	if	SCONJ
ejpam-2231	123	14	o	o	NOUN
ejpam-2231	123	15	is	be	AUX
ejpam-2231	123	16	a	a	DET
ejpam-2231	123	17	minimal	minimal	ADJ
ejpam-2231	123	18	left	left	ADJ
ejpam-2231	123	19	ideal	ideal	NOUN
ejpam-2231	123	20	of	of	ADP
ejpam-2231	123	21	s.	s.	PROPN
ejpam-2231	123	22	theorem	theorem	VERB
ejpam-2231	123	23	2	2	X
ejpam-2231	123	24	.	.	PUNCT
ejpam-2231	124	1	let	let	VERB
ejpam-2231	124	2	s	s	PRON
ejpam-2231	124	3	be	be	AUX
ejpam-2231	124	4	a	a	DET
ejpam-2231	124	5	unitaryla	unitaryla	ADJ
ejpam-2231	124	6	-semigroup	-semigroup	NOUN
ejpam-2231	124	7	.	.	PUNCT
ejpam-2231	125	1	then	then	ADV
ejpam-2231	125	2	a	a	PRON
ejpam-2231	125	3	is	be	AUX
ejpam-2231	125	4	a	a	DET
ejpam-2231	125	5	minimal	minimal	ADJ
ejpam-2231	125	6	(	(	PUNCT
ejpam-2231	125	7	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	125	8	of	of	ADP
ejpam-2231	125	9	s	s	PRON
ejpam-2231	125	10	if	if	SCONJ
ejpam-2231	125	11	and	and	CCONJ
ejpam-2231	125	12	only	only	ADV
ejpam-2231	125	13	if	if	SCONJ
ejpam-2231	125	14	a	a	PRON
ejpam-2231	125	15	is	be	AUX
ejpam-2231	125	16	a	a	DET
ejpam-2231	125	17	minimal	minimal	ADJ
ejpam-2231	125	18	bi	bi	NOUN
ejpam-2231	125	19	-	-	NOUN
ejpam-2231	125	20	ideal	ideal	NOUN
ejpam-2231	125	21	of	of	ADP
ejpam-2231	125	22	s.	s.	PROPN
ejpam-2231	125	23	proof	proof	PROPN
ejpam-2231	125	24	.	.	PUNCT
ejpam-2231	126	1	let	let	VERB
ejpam-2231	126	2	a	a	DET
ejpam-2231	126	3	be	be	AUX
ejpam-2231	126	4	a	a	DET
ejpam-2231	126	5	minimal	minimal	ADJ
ejpam-2231	126	6	(	(	PUNCT
ejpam-2231	126	7	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	126	8	of	of	ADP
ejpam-2231	126	9	s.	s.	PROPN
ejpam-2231	127	1	then	then	ADV
ejpam-2231	128	1	[	[	X
ejpam-2231	128	2	(	(	PUNCT
ejpam-2231	128	3	a2s	a2s	PROPN
ejpam-2231	128	4	·	·	PUNCT
ejpam-2231	128	5	a)2s](a2s	a)2s](a2s	PROPN
ejpam-2231	128	6	·	·	PUNCT
ejpam-2231	128	7	a	a	X
ejpam-2231	128	8	)	)	PUNCT
ejpam-2231	128	9	=[	=[	NOUN
ejpam-2231	128	10	{	{	PUNCT
ejpam-2231	128	11	(	(	PUNCT
ejpam-2231	128	12	a2s	a2s	PROPN
ejpam-2231	128	13	·	·	PUNCT
ejpam-2231	128	14	a)(a2s	a)(a2s	NUM
ejpam-2231	128	15	·	·	PUNCT
ejpam-2231	128	16	a)}s](a2s	a)}s](a2s	NOUN
ejpam-2231	128	17	·	·	PUNCT
ejpam-2231	128	18	a	a	X
ejpam-2231	128	19	)	)	PUNCT
ejpam-2231	128	20	⊆[{(as	⊆[{(as	NOUN
ejpam-2231	128	21	·	·	PUNCT
ejpam-2231	128	22	a)(as	a)(as	X
ejpam-2231	128	23	·	·	PUNCT
ejpam-2231	128	24	a)}s](as	a)}s](as	ADJ
ejpam-2231	128	25	·	·	PUNCT
ejpam-2231	128	26	a	a	X
ejpam-2231	128	27	)	)	PUNCT
ejpam-2231	128	28	=[	=[	NOUN
ejpam-2231	128	29	{	{	PUNCT
ejpam-2231	128	30	(	(	PUNCT
ejpam-2231	128	31	as	as	ADP
ejpam-2231	128	32	·	·	PUNCT
ejpam-2231	128	33	as)(aa)}s](as	as)(aa)}s](as	X
ejpam-2231	128	34	·	·	PUNCT
ejpam-2231	128	35	a	a	X
ejpam-2231	128	36	)	)	PUNCT
ejpam-2231	128	37	=[	=[	NOUN
ejpam-2231	128	38	(	(	PUNCT
ejpam-2231	128	39	a2s	a2s	PROPN
ejpam-2231	128	40	·	·	PUNCT
ejpam-2231	128	41	aa)s](as	aa)s](as	PRON
ejpam-2231	128	42	·	·	PUNCT
ejpam-2231	128	43	a	a	X
ejpam-2231	128	44	)	)	PUNCT
ejpam-2231	128	45	⊆[(as	⊆[(as	PROPN
ejpam-2231	128	46	·	·	PUNCT
ejpam-2231	128	47	as)s](as	as)s](as	X
ejpam-2231	128	48	·	·	PUNCT
ejpam-2231	128	49	a	a	X
ejpam-2231	128	50	)	)	PUNCT
ejpam-2231	128	51	=(	=(	NOUN
ejpam-2231	128	52	a2s	a2s	PROPN
ejpam-2231	128	53	·	·	PUNCT
ejpam-2231	128	54	s)(as	s)(as	X
ejpam-2231	128	55	·	·	PUNCT
ejpam-2231	128	56	a	a	X
ejpam-2231	128	57	)	)	PUNCT
ejpam-2231	128	58	⊆(as	⊆(as	PROPN
ejpam-2231	128	59	·	·	PUNCT
ejpam-2231	128	60	s)(as	s)(as	X
ejpam-2231	128	61	·	·	PUNCT
ejpam-2231	128	62	a	a	X
ejpam-2231	128	63	)	)	PUNCT
ejpam-2231	128	64	=	=	SYM
ejpam-2231	128	65	(	(	PUNCT
ejpam-2231	128	66	as	as	ADP
ejpam-2231	128	67	·	·	PUNCT
ejpam-2231	128	68	as)(sa	as)(sa	NUM
ejpam-2231	128	69	)	)	PUNCT
ejpam-2231	128	70	=	=	ADJ
ejpam-2231	128	71	a2s	a2s	NOUN
ejpam-2231	128	72	·	·	PUNCT
ejpam-2231	128	73	sa=	sa=	NOUN
ejpam-2231	128	74	as	as	ADP
ejpam-2231	128	75	·	·	PUNCT
ejpam-2231	128	76	sa2	sa2	NOUN
ejpam-2231	128	77	=	=	SYM
ejpam-2231	128	78	(	(	PUNCT
ejpam-2231	128	79	sa2	sa2	PROPN
ejpam-2231	128	80	·	·	PUNCT
ejpam-2231	128	81	s)a	s)a	NOUN
ejpam-2231	128	82	=(	=(	PROPN
ejpam-2231	128	83	a2s	a2s	PROPN
ejpam-2231	128	84	·	·	PUNCT
ejpam-2231	128	85	s)a=	s)a=	NOUN
ejpam-2231	128	86	(	(	PUNCT
ejpam-2231	128	87	ss	ss	NOUN
ejpam-2231	128	88	·	·	PUNCT
ejpam-2231	128	89	aa)a=	aa)a=	NUM
ejpam-2231	128	90	a2s	a2s	PROPN
ejpam-2231	128	91	·	·	PUNCT
ejpam-2231	128	92	a	a	X
ejpam-2231	128	93	,	,	PUNCT
ejpam-2231	128	94	and	and	CCONJ
ejpam-2231	128	95	similarly	similarly	ADV
ejpam-2231	128	96	we	we	PRON
ejpam-2231	128	97	can	can	AUX
ejpam-2231	128	98	show	show	VERB
ejpam-2231	128	99	that	that	SCONJ
ejpam-2231	128	100	(	(	PUNCT
ejpam-2231	128	101	a2s	a2s	PROPN
ejpam-2231	128	102	·	·	SYM
ejpam-2231	128	103	a)2	a)2	PROPN
ejpam-2231	128	104	⊆	⊆	NUM
ejpam-2231	128	105	a2s	a2s	PROPN
ejpam-2231	128	106	·	·	PUNCT
ejpam-2231	128	107	a.	a.	NOUN
ejpam-2231	128	108	thus	thus	ADV
ejpam-2231	128	109	a2s	a2s	PROPN
ejpam-2231	128	110	·	·	PUNCT
ejpam-2231	128	111	a	a	PRON
ejpam-2231	128	112	is	be	AUX
ejpam-2231	128	113	a	a	DET
ejpam-2231	128	114	(	(	PUNCT
ejpam-2231	128	115	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	128	116	of	of	ADP
ejpam-2231	128	117	s	s	PRON
ejpam-2231	128	118	contained	contain	VERB
ejpam-2231	128	119	in	in	ADP
ejpam-2231	128	120	a	a	PRON
ejpam-2231	128	121	,	,	PUNCT
ejpam-2231	128	122	therefore	therefore	ADV
ejpam-2231	128	123	by	by	ADP
ejpam-2231	128	124	minimality	minimality	NOUN
ejpam-2231	128	125	of	of	ADP
ejpam-2231	128	126	a	a	DET
ejpam-2231	128	127	,	,	PUNCT
ejpam-2231	128	128	a2s	a2s	NOUN
ejpam-2231	128	129	·	·	PUNCT
ejpam-2231	128	130	a=	a=	VERB
ejpam-2231	128	131	a.	a.	NOUN
ejpam-2231	128	132	now	now	ADV
ejpam-2231	128	133	as	as	ADP
ejpam-2231	128	134	·	·	PUNCT
ejpam-2231	128	135	a=(as)(a2s	a=(as)(a2s	NOUN
ejpam-2231	128	136	·	·	PUNCT
ejpam-2231	128	137	a	a	X
ejpam-2231	128	138	)	)	PUNCT
ejpam-2231	128	139	=	=	SYM
ejpam-2231	129	1	[	[	X
ejpam-2231	129	2	(	(	PUNCT
ejpam-2231	129	3	a2s	a2s	PROPN
ejpam-2231	129	4	·	·	PUNCT
ejpam-2231	129	5	a)s]a=	a)s]a=	PROPN
ejpam-2231	129	6	(	(	PUNCT
ejpam-2231	129	7	sa	sa	X
ejpam-2231	129	8	·	·	PUNCT
ejpam-2231	129	9	a2s)a	a2s)a	PUNCT
ejpam-2231	130	1	=[	=[	NOUN
ejpam-2231	130	2	a2(sa	a2(sa	PROPN
ejpam-2231	130	3	·	·	PUNCT
ejpam-2231	130	4	s)]a⊆	s)]a⊆	PROPN
ejpam-2231	130	5	a2s	a2s	PROPN
ejpam-2231	130	6	·	·	PUNCT
ejpam-2231	130	7	a=	a=	VERB
ejpam-2231	130	8	a	a	X
ejpam-2231	130	9	,	,	PUNCT
ejpam-2231	130	10	it	it	PRON
ejpam-2231	130	11	follows	follow	VERB
ejpam-2231	130	12	that	that	SCONJ
ejpam-2231	130	13	a	a	PRON
ejpam-2231	130	14	is	be	AUX
ejpam-2231	130	15	a	a	DET
ejpam-2231	130	16	bi	bi	NOUN
ejpam-2231	130	17	-	-	NOUN
ejpam-2231	130	18	ideal	ideal	NOUN
ejpam-2231	130	19	of	of	ADP
ejpam-2231	130	20	s.	s.	PROPN
ejpam-2231	130	21	suppose	suppose	VERB
ejpam-2231	130	22	that	that	SCONJ
ejpam-2231	130	23	there	there	PRON
ejpam-2231	130	24	exists	exist	VERB
ejpam-2231	130	25	a	a	DET
ejpam-2231	130	26	bi	bi	ADJ
ejpam-2231	130	27	-	-	ADJ
ejpam-2231	130	28	ideal	ideal	ADJ
ejpam-2231	130	29	b	b	PROPN
ejpam-2231	130	30	of	of	ADP
ejpam-2231	130	31	s	s	PRON
ejpam-2231	130	32	contained	contain	VERB
ejpam-2231	130	33	in	in	ADP
ejpam-2231	130	34	a	a	PRON
ejpam-2231	130	35	,	,	PUNCT
ejpam-2231	130	36	then	then	ADV
ejpam-2231	130	37	b2s	b2s	PROPN
ejpam-2231	130	38	·	·	PUNCT
ejpam-2231	130	39	b	b	X
ejpam-2231	130	40	⊆	⊆	NUM
ejpam-2231	130	41	bs	bs	PROPN
ejpam-2231	130	42	·	·	PUNCT
ejpam-2231	130	43	b	b	X
ejpam-2231	130	44	⊆	⊆	NUM
ejpam-2231	130	45	b	b	NOUN
ejpam-2231	130	46	,	,	PUNCT
ejpam-2231	130	47	so	so	CCONJ
ejpam-2231	130	48	b	b	PROPN
ejpam-2231	130	49	is	be	AUX
ejpam-2231	130	50	a	a	DET
ejpam-2231	130	51	(	(	PUNCT
ejpam-2231	130	52	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	130	53	of	of	ADP
ejpam-2231	130	54	s	s	PRON
ejpam-2231	130	55	contained	contain	VERB
ejpam-2231	130	56	in	in	ADP
ejpam-2231	130	57	a	a	DET
ejpam-2231	130	58	,	,	PUNCT
ejpam-2231	130	59	therefore	therefore	ADV
ejpam-2231	130	60	b	b	X
ejpam-2231	130	61	=	=	SYM
ejpam-2231	130	62	a.	a.	PROPN
ejpam-2231	130	63	w.	w.	PROPN
ejpam-2231	130	64	khan	khan	PROPN
ejpam-2231	130	65	,	,	PUNCT
ejpam-2231	130	66	f.	f.	PROPN
ejpam-2231	130	67	yousafzai	yousafzai	PROPN
ejpam-2231	130	68	,	,	PUNCT
ejpam-2231	130	69	and	and	CCONJ
ejpam-2231	130	70	m.	m.	PROPN
ejpam-2231	130	71	khan	khan	PROPN
ejpam-2231	130	72	/	/	SYM
ejpam-2231	130	73	eur	eur	PROPN
ejpam-2231	130	74	.	.	PUNCT
ejpam-2231	131	1	j.	j.	PROPN
ejpam-2231	131	2	pure	pure	PROPN
ejpam-2231	131	3	appl	appl	PROPN
ejpam-2231	131	4	.	.	PROPN
ejpam-2231	131	5	math	math	PROPN
ejpam-2231	131	6	,	,	PUNCT
ejpam-2231	131	7	9	9	NUM
ejpam-2231	131	8	(	(	PUNCT
ejpam-2231	131	9	2016	2016	NUM
ejpam-2231	131	10	)	)	PUNCT
ejpam-2231	131	11	,	,	PUNCT
ejpam-2231	131	12	277	277	NUM
ejpam-2231	131	13	-	-	SYM
ejpam-2231	131	14	291	291	NUM
ejpam-2231	131	15	283	283	NUM
ejpam-2231	131	16	conversely	conversely	ADV
ejpam-2231	131	17	,	,	PUNCT
ejpam-2231	131	18	assume	assume	VERB
ejpam-2231	131	19	that	that	SCONJ
ejpam-2231	131	20	a	a	PRON
ejpam-2231	131	21	is	be	AUX
ejpam-2231	131	22	a	a	DET
ejpam-2231	131	23	minimal	minimal	ADJ
ejpam-2231	131	24	bi	bi	NOUN
ejpam-2231	131	25	-	-	NOUN
ejpam-2231	131	26	ideal	ideal	NOUN
ejpam-2231	131	27	of	of	ADP
ejpam-2231	131	28	s	s	PROPN
ejpam-2231	131	29	,	,	PUNCT
ejpam-2231	131	30	then	then	ADV
ejpam-2231	131	31	it	it	PRON
ejpam-2231	131	32	is	be	AUX
ejpam-2231	131	33	easy	easy	ADJ
ejpam-2231	131	34	to	to	PART
ejpam-2231	131	35	see	see	VERB
ejpam-2231	131	36	that	that	SCONJ
ejpam-2231	131	37	a	a	PRON
ejpam-2231	131	38	is	be	AUX
ejpam-2231	131	39	a	a	DET
ejpam-2231	131	40	(	(	PUNCT
ejpam-2231	131	41	2,1)ideal	2,1)ideal	NUM
ejpam-2231	131	42	of	of	ADP
ejpam-2231	131	43	s.	s.	PROPN
ejpam-2231	131	44	let	let	VERB
ejpam-2231	131	45	c	c	PRON
ejpam-2231	131	46	be	be	AUX
ejpam-2231	131	47	a	a	DET
ejpam-2231	131	48	(	(	PUNCT
ejpam-2231	131	49	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	131	50	of	of	ADP
ejpam-2231	131	51	s	s	PRON
ejpam-2231	131	52	contained	contain	VERB
ejpam-2231	131	53	in	in	ADP
ejpam-2231	131	54	a	a	PRON
ejpam-2231	131	55	,	,	PUNCT
ejpam-2231	131	56	then	then	ADV
ejpam-2231	131	57	[	[	X
ejpam-2231	131	58	(	(	PUNCT
ejpam-2231	131	59	c2s	c2s	X
ejpam-2231	131	60	·	·	PUNCT
ejpam-2231	131	61	c)s](c2s	c)s](c2s	ADJ
ejpam-2231	131	62	·	·	PUNCT
ejpam-2231	131	63	c	c	X
ejpam-2231	131	64	)	)	PUNCT
ejpam-2231	131	65	=(	=(	NOUN
ejpam-2231	131	66	sc	sc	X
ejpam-2231	131	67	·	·	PUNCT
ejpam-2231	131	68	c2s)(c2s	c2s)(c2s	PROPN
ejpam-2231	131	69	·	·	PUNCT
ejpam-2231	131	70	c	c	X
ejpam-2231	131	71	)	)	PUNCT
ejpam-2231	131	72	=	=	SYM
ejpam-2231	131	73	(	(	PUNCT
ejpam-2231	131	74	sc2	sc2	NOUN
ejpam-2231	131	75	·	·	PUNCT
ejpam-2231	132	1	cs)(c2s	cs)(c2	NOUN
ejpam-2231	132	2	·	·	PUNCT
ejpam-2231	132	3	c	c	X
ejpam-2231	132	4	)	)	PUNCT
ejpam-2231	132	5	=[	=[	NOUN
ejpam-2231	132	6	c(sc2	c(sc2	NOUN
ejpam-2231	132	7	·	·	PUNCT
ejpam-2231	132	8	s)](c2s	s)](c2s	PRON
ejpam-2231	132	9	·	·	PUNCT
ejpam-2231	132	10	c	c	X
ejpam-2231	132	11	)	)	PUNCT
ejpam-2231	133	1	=	=	NOUN
ejpam-2231	134	1	[	[	X
ejpam-2231	134	2	(	(	PUNCT
ejpam-2231	134	3	c2s	c2s	PROPN
ejpam-2231	134	4	·	·	PUNCT
ejpam-2231	134	5	c)(sc2	c)(sc2	NUM
ejpam-2231	134	6	·	·	PUNCT
ejpam-2231	134	7	ss)]c	ss)]c	PROPN
ejpam-2231	134	8	=[	=[	NOUN
ejpam-2231	134	9	(	(	PUNCT
ejpam-2231	134	10	c2s	c2s	PROPN
ejpam-2231	134	11	·	·	PUNCT
ejpam-2231	134	12	c)(s	c)(s	NOUN
ejpam-2231	134	13	·	·	PUNCT
ejpam-2231	134	14	c2s)]c	c2s)]c	NOUN
ejpam-2231	134	15	=	=	PUNCT
ejpam-2231	135	1	[	[	X
ejpam-2231	135	2	(	(	PUNCT
ejpam-2231	135	3	c2s	c2s	X
ejpam-2231	135	4	·	·	PUNCT
ejpam-2231	135	5	c)(c2s)]c	c)(c2s)]c	NOUN
ejpam-2231	135	6	=[	=[	NOUN
ejpam-2231	135	7	c2{(c2s	c2{(c2s	X
ejpam-2231	135	8	·	·	PUNCT
ejpam-2231	135	9	c)s}]c	c)s}]c	PROPN
ejpam-2231	135	10	⊆	⊆	NUM
ejpam-2231	135	11	c2s	c2	NOUN
ejpam-2231	135	12	·	·	PUNCT
ejpam-2231	135	13	c	c	X
ejpam-2231	135	14	.	.	PUNCT
ejpam-2231	136	1	this	this	PRON
ejpam-2231	136	2	shows	show	VERB
ejpam-2231	136	3	that	that	SCONJ
ejpam-2231	136	4	c2s	c2s	PROPN
ejpam-2231	136	5	·	·	PUNCT
ejpam-2231	136	6	c	c	NOUN
ejpam-2231	136	7	is	be	AUX
ejpam-2231	136	8	a	a	DET
ejpam-2231	136	9	bi	bi	NOUN
ejpam-2231	136	10	-	-	NOUN
ejpam-2231	136	11	ideal	ideal	NOUN
ejpam-2231	136	12	of	of	ADP
ejpam-2231	136	13	s	s	PROPN
ejpam-2231	136	14	,	,	PUNCT
ejpam-2231	136	15	and	and	CCONJ
ejpam-2231	136	16	by	by	ADP
ejpam-2231	136	17	minimality	minimality	NOUN
ejpam-2231	136	18	of	of	ADP
ejpam-2231	136	19	a	a	PRON
ejpam-2231	136	20	,	,	PUNCT
ejpam-2231	136	21	c2s	c2s	PROPN
ejpam-2231	136	22	·	·	PUNCT
ejpam-2231	136	23	c	c	X
ejpam-2231	136	24	=	=	PUNCT
ejpam-2231	136	25	a.	a.	NOUN
ejpam-2231	136	26	thus	thus	ADV
ejpam-2231	136	27	a	a	DET
ejpam-2231	136	28	=	=	PUNCT
ejpam-2231	136	29	c2s	c2s	ADJ
ejpam-2231	136	30	·	·	PUNCT
ejpam-2231	137	1	c	c	NOUN
ejpam-2231	137	2	⊆	⊆	NUM
ejpam-2231	137	3	c	c	NOUN
ejpam-2231	137	4	,	,	PUNCT
ejpam-2231	137	5	and	and	CCONJ
ejpam-2231	137	6	therefore	therefore	ADV
ejpam-2231	137	7	a	a	PRON
ejpam-2231	137	8	is	be	AUX
ejpam-2231	137	9	a	a	DET
ejpam-2231	137	10	minimal	minimal	ADJ
ejpam-2231	137	11	(	(	PUNCT
ejpam-2231	137	12	2,1)-ideal	2,1)-ideal	NUM
ejpam-2231	137	13	of	of	ADP
ejpam-2231	137	14	s.	s.	PROPN
ejpam-2231	137	15	theorem	theorem	VERB
ejpam-2231	137	16	3	3	X
ejpam-2231	137	17	.	.	PUNCT
ejpam-2231	137	18	let	let	VERB
ejpam-2231	137	19	a	a	PRON
ejpam-2231	137	20	be	be	AUX
ejpam-2231	137	21	a	a	DET
ejpam-2231	137	22	0	0	NUM
ejpam-2231	137	23	-	-	PUNCT
ejpam-2231	137	24	minimal	minimal	ADJ
ejpam-2231	137	25	(	(	PUNCT
ejpam-2231	137	26	0,2)-bi	0,2)-bi	NUM
ejpam-2231	137	27	-	-	PUNCT
ejpam-2231	137	28	ideal	ideal	NOUN
ejpam-2231	137	29	of	of	ADP
ejpam-2231	137	30	a	a	DET
ejpam-2231	137	31	unitary	unitary	ADJ
ejpam-2231	137	32	la	la	PROPN
ejpam-2231	137	33	-semigroup	-semigroup	NOUN
ejpam-2231	137	34	s	s	PART
ejpam-2231	137	35	with	with	ADP
ejpam-2231	137	36	zero	zero	NUM
ejpam-2231	137	37	.	.	PUNCT
ejpam-2231	138	1	then	then	ADV
ejpam-2231	138	2	exactly	exactly	ADV
ejpam-2231	138	3	one	one	NUM
ejpam-2231	138	4	of	of	ADP
ejpam-2231	138	5	the	the	DET
ejpam-2231	138	6	following	follow	VERB
ejpam-2231	138	7	cases	case	NOUN
ejpam-2231	138	8	occurs	occur	VERB
ejpam-2231	138	9	:	:	PUNCT
ejpam-2231	138	10	(	(	PUNCT
ejpam-2231	138	11	i	i	NOUN
ejpam-2231	138	12	)	)	PUNCT
ejpam-2231	138	13	a=	a=	VERB
ejpam-2231	138	14	{	{	PUNCT
ejpam-2231	138	15	0	0	NUM
ejpam-2231	138	16	,	,	PUNCT
ejpam-2231	138	17	a	a	PRON
ejpam-2231	138	18	}	}	PUNCT
ejpam-2231	138	19	,	,	PUNCT
ejpam-2231	138	20	a2	a2	PROPN
ejpam-2231	138	21	=	=	PUNCT
ejpam-2231	138	22	0	0	NUM
ejpam-2231	138	23	;	;	PUNCT
ejpam-2231	138	24	(	(	PUNCT
ejpam-2231	138	25	ii	ii	NOUN
ejpam-2231	138	26	)	)	PUNCT
ejpam-2231	138	27	∀a	∀a	NOUN
ejpam-2231	139	1	∈	∈	PROPN
ejpam-2231	139	2	a\{0	a\{0	PROPN
ejpam-2231	139	3	}	}	PUNCT
ejpam-2231	139	4	,	,	PUNCT
ejpam-2231	139	5	sa2	sa2	NOUN
ejpam-2231	139	6	=	=	NOUN
ejpam-2231	139	7	a.	a.	NOUN
ejpam-2231	139	8	proof	proof	NOUN
ejpam-2231	139	9	.	.	PUNCT
ejpam-2231	140	1	assume	assume	VERB
ejpam-2231	140	2	that	that	SCONJ
ejpam-2231	140	3	a	a	PRON
ejpam-2231	140	4	is	be	AUX
ejpam-2231	140	5	a	a	DET
ejpam-2231	140	6	0	0	NUM
ejpam-2231	140	7	-	-	PUNCT
ejpam-2231	140	8	minimal	minimal	ADJ
ejpam-2231	140	9	(	(	PUNCT
ejpam-2231	140	10	0,2)-bi	0,2)-bi	NUM
ejpam-2231	140	11	-	-	PUNCT
ejpam-2231	140	12	ideal	ideal	NOUN
ejpam-2231	140	13	of	of	ADP
ejpam-2231	140	14	s.	s.	PROPN
ejpam-2231	140	15	let	let	VERB
ejpam-2231	140	16	a	a	DET
ejpam-2231	140	17	∈	∈	PROPN
ejpam-2231	140	18	a\{0	a\{0	PROPN
ejpam-2231	140	19	}	}	PUNCT
ejpam-2231	140	20	,	,	PUNCT
ejpam-2231	140	21	then	then	ADV
ejpam-2231	140	22	sa2	sa2	PROPN
ejpam-2231	140	23	⊆	⊆	NUM
ejpam-2231	140	24	a.	a.	NOUN
ejpam-2231	140	25	also	also	ADV
ejpam-2231	140	26	sa2	sa2	PROPN
ejpam-2231	140	27	is	be	AUX
ejpam-2231	140	28	a	a	DET
ejpam-2231	140	29	(	(	PUNCT
ejpam-2231	140	30	0,2)-bi	0,2)-bi	NUM
ejpam-2231	140	31	-	-	PUNCT
ejpam-2231	140	32	ideal	ideal	NOUN
ejpam-2231	140	33	of	of	ADP
ejpam-2231	140	34	s	s	PROPN
ejpam-2231	140	35	,	,	PUNCT
ejpam-2231	140	36	therefore	therefore	ADV
ejpam-2231	140	37	sa2	sa2	PROPN
ejpam-2231	140	38	=	=	PUNCT
ejpam-2231	140	39	{	{	PUNCT
ejpam-2231	140	40	0	0	NUM
ejpam-2231	140	41	}	}	PUNCT
ejpam-2231	140	42	or	or	CCONJ
ejpam-2231	140	43	sa2	sa2	NOUN
ejpam-2231	140	44	=	=	PUNCT
ejpam-2231	140	45	a.	a.	NOUN
ejpam-2231	140	46	let	let	VERB
ejpam-2231	140	47	sa2	sa2	NOUN
ejpam-2231	140	48	=	=	PUNCT
ejpam-2231	140	49	{	{	PUNCT
ejpam-2231	140	50	0	0	NUM
ejpam-2231	140	51	}	}	PUNCT
ejpam-2231	140	52	.	.	PUNCT
ejpam-2231	141	1	since	since	SCONJ
ejpam-2231	141	2	a2	a2	PROPN
ejpam-2231	141	3	∈	∈	PROPN
ejpam-2231	141	4	a	a	PRON
ejpam-2231	141	5	,	,	PUNCT
ejpam-2231	141	6	we	we	PRON
ejpam-2231	141	7	have	have	VERB
ejpam-2231	141	8	either	either	CCONJ
ejpam-2231	141	9	a2	a2	PROPN
ejpam-2231	141	10	=	=	PUNCT
ejpam-2231	141	11	a	a	PRON
ejpam-2231	141	12	or	or	CCONJ
ejpam-2231	141	13	a2	a2	PROPN
ejpam-2231	141	14	=	=	SYM
ejpam-2231	141	15	0	0	NUM
ejpam-2231	141	16	or	or	CCONJ
ejpam-2231	141	17	a2	a2	PROPN
ejpam-2231	141	18	∈	∈	PROPN
ejpam-2231	141	19	a\{0	a\{0	PROPN
ejpam-2231	141	20	,	,	PUNCT
ejpam-2231	141	21	a	a	PRON
ejpam-2231	141	22	}	}	PUNCT
ejpam-2231	141	23	.	.	PUNCT
ejpam-2231	142	1	if	if	SCONJ
ejpam-2231	142	2	a2	a2	PROPN
ejpam-2231	142	3	=	=	SYM
ejpam-2231	142	4	a	a	PRON
ejpam-2231	142	5	,	,	PUNCT
ejpam-2231	142	6	then	then	ADV
ejpam-2231	142	7	a3	a3	NOUN
ejpam-2231	142	8	=	=	PUNCT
ejpam-2231	143	1	a2a	a2a	PROPN
ejpam-2231	143	2	=	=	PUNCT
ejpam-2231	143	3	a	a	PROPN
ejpam-2231	143	4	,	,	PUNCT
ejpam-2231	143	5	which	which	PRON
ejpam-2231	143	6	is	be	AUX
ejpam-2231	143	7	impossible	impossible	ADJ
ejpam-2231	143	8	because	because	SCONJ
ejpam-2231	143	9	a3	a3	PROPN
ejpam-2231	143	10	∈	∈	PROPN
ejpam-2231	143	11	a2s	a2s	PROPN
ejpam-2231	143	12	=	=	PUNCT
ejpam-2231	143	13	sa2	sa2	PROPN
ejpam-2231	143	14	=	=	PUNCT
ejpam-2231	143	15	{	{	PUNCT
ejpam-2231	143	16	0	0	NUM
ejpam-2231	143	17	}	}	PUNCT
ejpam-2231	143	18	.	.	PUNCT
ejpam-2231	144	1	let	let	VERB
ejpam-2231	144	2	a2	a2	PROPN
ejpam-2231	144	3	∈	∈	PROPN
ejpam-2231	144	4	a\{0	a\{0	PROPN
ejpam-2231	144	5	,	,	PUNCT
ejpam-2231	144	6	a	a	PRON
ejpam-2231	144	7	}	}	PUNCT
ejpam-2231	144	8	,	,	PUNCT
ejpam-2231	144	9	we	we	PRON
ejpam-2231	144	10	have	have	VERB
ejpam-2231	144	11	s	s	PRON
ejpam-2231	144	12	·	·	PUNCT
ejpam-2231	144	13	{	{	PUNCT
ejpam-2231	144	14	0	0	NUM
ejpam-2231	144	15	,	,	PUNCT
ejpam-2231	144	16	a2}{0	a2}{0	PROPN
ejpam-2231	144	17	,	,	PUNCT
ejpam-2231	144	18	a2}=	a2}=	PROPN
ejpam-2231	144	19	ss	ss	NOUN
ejpam-2231	144	20	·	·	PUNCT
ejpam-2231	144	21	a2a2	a2a2	PROPN
ejpam-2231	145	1	=	=	NOUN
ejpam-2231	145	2	sa2	sa2	PROPN
ejpam-2231	145	3	·	·	PUNCT
ejpam-2231	145	4	sa2	sa2	NOUN
ejpam-2231	145	5	=	=	SYM
ejpam-2231	145	6	{	{	PUNCT
ejpam-2231	145	7	0	0	NUM
ejpam-2231	145	8	}	}	PUNCT
ejpam-2231	145	9	⊆	⊆	NUM
ejpam-2231	145	10	{	{	PUNCT
ejpam-2231	145	11	0	0	NUM
ejpam-2231	145	12	,	,	PUNCT
ejpam-2231	145	13	a2	a2	PROPN
ejpam-2231	145	14	}	}	PUNCT
ejpam-2231	145	15	,	,	PUNCT
ejpam-2231	145	16	and	and	CCONJ
ejpam-2231	145	17	[	[	X
ejpam-2231	145	18	{	{	PUNCT
ejpam-2231	145	19	0	0	NUM
ejpam-2231	145	20	,	,	PUNCT
ejpam-2231	145	21	a2}s]{0	a2}s]{0	PROPN
ejpam-2231	145	22	,	,	PUNCT
ejpam-2231	145	23	a2}=	a2}=	NOUN
ejpam-2231	145	24	{	{	PUNCT
ejpam-2231	145	25	0	0	NUM
ejpam-2231	145	26	,	,	PUNCT
ejpam-2231	145	27	a2s}{0	a2s}{0	NOUN
ejpam-2231	145	28	,	,	PUNCT
ejpam-2231	145	29	a2}=	a2}=	PROPN
ejpam-2231	145	30	a2s	a2s	PROPN
ejpam-2231	145	31	·	·	PUNCT
ejpam-2231	145	32	a2	a2	PROPN
ejpam-2231	145	33	⊆	⊆	NUM
ejpam-2231	145	34	sa2	sa2	NOUN
ejpam-2231	145	35	=	=	PUNCT
ejpam-2231	145	36	{	{	PUNCT
ejpam-2231	145	37	0	0	NUM
ejpam-2231	145	38	}	}	PUNCT
ejpam-2231	145	39	⊆	⊆	NUM
ejpam-2231	145	40	{	{	PUNCT
ejpam-2231	145	41	0	0	NUM
ejpam-2231	145	42	,	,	PUNCT
ejpam-2231	145	43	a2	a2	PROPN
ejpam-2231	145	44	}	}	PUNCT
ejpam-2231	145	45	.	.	PUNCT
ejpam-2231	146	1	therefore	therefore	ADV
ejpam-2231	146	2	{	{	PUNCT
ejpam-2231	146	3	0	0	PROPN
ejpam-2231	146	4	,	,	PUNCT
ejpam-2231	146	5	a2	a2	PROPN
ejpam-2231	146	6	}	}	PUNCT
ejpam-2231	146	7	is	be	AUX
ejpam-2231	146	8	a	a	DET
ejpam-2231	146	9	(	(	PUNCT
ejpam-2231	146	10	0,2)-bi	0,2)-bi	NUM
ejpam-2231	146	11	-	-	PUNCT
ejpam-2231	146	12	ideal	ideal	NOUN
ejpam-2231	146	13	of	of	ADP
ejpam-2231	146	14	s	s	PRON
ejpam-2231	146	15	contained	contain	VERB
ejpam-2231	146	16	in	in	ADP
ejpam-2231	146	17	a.	a.	NOUN
ejpam-2231	146	18	we	we	PRON
ejpam-2231	146	19	observe	observe	VERB
ejpam-2231	146	20	that	that	SCONJ
ejpam-2231	146	21	{	{	PUNCT
ejpam-2231	146	22	0	0	NUM
ejpam-2231	146	23	,	,	PUNCT
ejpam-2231	146	24	a2	a2	PROPN
ejpam-2231	146	25	}	}	PUNCT
ejpam-2231	146	26	6=	6=	X
ejpam-2231	146	27	{	{	PUNCT
ejpam-2231	146	28	0	0	NUM
ejpam-2231	146	29	}	}	PUNCT
ejpam-2231	146	30	and	and	CCONJ
ejpam-2231	146	31	{	{	PUNCT
ejpam-2231	146	32	0	0	NUM
ejpam-2231	146	33	,	,	PUNCT
ejpam-2231	146	34	a2	a2	PROPN
ejpam-2231	146	35	}	}	PUNCT
ejpam-2231	146	36	6=	6=	ADP
ejpam-2231	146	37	a.	a.	NOUN
ejpam-2231	146	38	this	this	PRON
ejpam-2231	146	39	is	be	AUX
ejpam-2231	146	40	a	a	DET
ejpam-2231	146	41	contradiction	contradiction	NOUN
ejpam-2231	146	42	to	to	ADP
ejpam-2231	146	43	the	the	DET
ejpam-2231	146	44	fact	fact	NOUN
ejpam-2231	146	45	that	that	SCONJ
ejpam-2231	146	46	a	a	PRON
ejpam-2231	146	47	is	be	AUX
ejpam-2231	146	48	a	a	DET
ejpam-2231	146	49	0	0	NUM
ejpam-2231	146	50	-	-	PUNCT
ejpam-2231	146	51	minimal	minimal	ADJ
ejpam-2231	146	52	(	(	PUNCT
ejpam-2231	146	53	0,2)-bi	0,2)-bi	NUM
ejpam-2231	146	54	-	-	PUNCT
ejpam-2231	146	55	ideal	ideal	NOUN
ejpam-2231	146	56	of	of	ADP
ejpam-2231	146	57	s.	s.	PROPN
ejpam-2231	146	58	therefore	therefore	ADV
ejpam-2231	146	59	a2	a2	PROPN
ejpam-2231	146	60	=	=	SYM
ejpam-2231	146	61	0	0	PUNCT
ejpam-2231	146	62	and	and	CCONJ
ejpam-2231	146	63	a=	a=	VERB
ejpam-2231	146	64	{	{	PUNCT
ejpam-2231	146	65	0	0	NUM
ejpam-2231	146	66	,	,	PUNCT
ejpam-2231	146	67	a	a	PRON
ejpam-2231	146	68	}	}	PUNCT
ejpam-2231	146	69	.	.	PUNCT
ejpam-2231	147	1	if	if	SCONJ
ejpam-2231	147	2	sa2	sa2	PROPN
ejpam-2231	147	3	6=	6=	PROPN
ejpam-2231	147	4	{	{	PUNCT
ejpam-2231	147	5	0	0	NUM
ejpam-2231	147	6	}	}	PUNCT
ejpam-2231	147	7	,	,	PUNCT
ejpam-2231	147	8	then	then	ADV
ejpam-2231	147	9	sa2	sa2	PROPN
ejpam-2231	147	10	=	=	NOUN
ejpam-2231	147	11	a.	a.	NOUN
ejpam-2231	147	12	corollary	corollary	NOUN
ejpam-2231	147	13	4	4	X
ejpam-2231	147	14	.	.	PUNCT
ejpam-2231	147	15	let	let	VERB
ejpam-2231	147	16	a	a	PRON
ejpam-2231	147	17	be	be	AUX
ejpam-2231	147	18	a	a	DET
ejpam-2231	147	19	0	0	NUM
ejpam-2231	147	20	-	-	PUNCT
ejpam-2231	147	21	minimal	minimal	ADJ
ejpam-2231	147	22	(	(	PUNCT
ejpam-2231	147	23	0,2)-bi	0,2)-bi	NUM
ejpam-2231	147	24	-	-	PUNCT
ejpam-2231	147	25	ideal	ideal	NOUN
ejpam-2231	147	26	of	of	ADP
ejpam-2231	147	27	a	a	DET
ejpam-2231	147	28	unitary	unitary	ADJ
ejpam-2231	147	29	la	la	PROPN
ejpam-2231	147	30	-semigroup	-semigroup	NOUN
ejpam-2231	147	31	s	s	PART
ejpam-2231	147	32	with	with	ADP
ejpam-2231	147	33	zero	zero	NUM
ejpam-2231	147	34	such	such	ADJ
ejpam-2231	147	35	that	that	DET
ejpam-2231	147	36	a2	a2	PROPN
ejpam-2231	147	37	6=	6=	ADP
ejpam-2231	147	38	0	0	NUM
ejpam-2231	147	39	.	.	PUNCT
ejpam-2231	148	1	then	then	ADV
ejpam-2231	148	2	a=	a=	PROPN
ejpam-2231	148	3	sa2	sa2	PROPN
ejpam-2231	148	4	for	for	ADP
ejpam-2231	148	5	every	every	DET
ejpam-2231	148	6	a	a	DET
ejpam-2231	148	7	∈	∈	PROPN
ejpam-2231	148	8	a\{0	a\{0	PROPN
ejpam-2231	148	9	}	}	PUNCT
ejpam-2231	148	10	.	.	PUNCT
ejpam-2231	149	1	lemma	lemma	PROPN
ejpam-2231	149	2	6	6	NUM
ejpam-2231	149	3	.	.	PUNCT
ejpam-2231	150	1	let	let	VERB
ejpam-2231	150	2	s	s	PRON
ejpam-2231	150	3	be	be	AUX
ejpam-2231	150	4	a	a	DET
ejpam-2231	150	5	unitary	unitary	ADJ
ejpam-2231	150	6	la	la	ADJ
ejpam-2231	150	7	-semigroup	-semigroup	NOUN
ejpam-2231	150	8	.	.	PUNCT
ejpam-2231	151	1	then	then	ADV
ejpam-2231	151	2	every	every	DET
ejpam-2231	151	3	right	right	ADJ
ejpam-2231	151	4	ideal	ideal	NOUN
ejpam-2231	151	5	of	of	ADP
ejpam-2231	151	6	s	s	PROPN
ejpam-2231	151	7	is	be	AUX
ejpam-2231	151	8	a	a	DET
ejpam-2231	151	9	(	(	PUNCT
ejpam-2231	151	10	0,2)-bi	0,2)-bi	NUM
ejpam-2231	151	11	-	-	PUNCT
ejpam-2231	151	12	ideal	ideal	NOUN
ejpam-2231	151	13	of	of	ADP
ejpam-2231	151	14	s.	s.	PROPN
ejpam-2231	151	15	proof	proof	PROPN
ejpam-2231	151	16	.	.	PUNCT
ejpam-2231	152	1	assume	assume	VERB
ejpam-2231	152	2	that	that	SCONJ
ejpam-2231	152	3	a	a	PRON
ejpam-2231	152	4	is	be	AUX
ejpam-2231	152	5	a	a	DET
ejpam-2231	152	6	right	right	ADJ
ejpam-2231	152	7	ideal	ideal	NOUN
ejpam-2231	152	8	of	of	ADP
ejpam-2231	152	9	s	s	PROPN
ejpam-2231	152	10	,	,	PUNCT
ejpam-2231	152	11	then	then	ADV
ejpam-2231	152	12	sa2	sa2	PROPN
ejpam-2231	152	13	=	=	SYM
ejpam-2231	152	14	aa	aa	PROPN
ejpam-2231	152	15	·	·	PUNCT
ejpam-2231	152	16	ss	ss	NOUN
ejpam-2231	153	1	=	=	PUNCT
ejpam-2231	153	2	as	as	ADP
ejpam-2231	153	3	·	·	PUNCT
ejpam-2231	153	4	as	as	SCONJ
ejpam-2231	153	5	⊆	⊆	NUM
ejpam-2231	153	6	aa⊆	aa⊆	NOUN
ejpam-2231	153	7	as	as	ADP
ejpam-2231	153	8	⊆	⊆	X
ejpam-2231	153	9	a	a	PRON
ejpam-2231	153	10	,	,	PUNCT
ejpam-2231	153	11	as	as	SCONJ
ejpam-2231	153	12	·	·	PUNCT
ejpam-2231	153	13	a⊆	a⊆	VERB
ejpam-2231	153	14	a	a	PRON
ejpam-2231	153	15	,	,	PUNCT
ejpam-2231	153	16	and	and	CCONJ
ejpam-2231	153	17	clearly	clearly	ADV
ejpam-2231	153	18	a2	a2	VERB
ejpam-2231	153	19	⊆	⊆	NUM
ejpam-2231	153	20	a	a	PRON
ejpam-2231	153	21	,	,	PUNCT
ejpam-2231	153	22	therefore	therefore	ADV
ejpam-2231	153	23	a	a	PRON
ejpam-2231	153	24	is	be	AUX
ejpam-2231	153	25	a	a	DET
ejpam-2231	153	26	(	(	PUNCT
ejpam-2231	153	27	0,2)-bi	0,2)-bi	NUM
ejpam-2231	153	28	-	-	PUNCT
ejpam-2231	153	29	ideal	ideal	NOUN
ejpam-2231	153	30	of	of	ADP
ejpam-2231	153	31	s.	s.	PROPN
ejpam-2231	153	32	the	the	DET
ejpam-2231	153	33	converse	converse	NOUN
ejpam-2231	153	34	of	of	ADP
ejpam-2231	153	35	lemma	lemma	PROPN
ejpam-2231	153	36	6	6	NUM
ejpam-2231	153	37	is	be	AUX
ejpam-2231	153	38	not	not	PART
ejpam-2231	153	39	true	true	ADJ
ejpam-2231	153	40	in	in	ADP
ejpam-2231	153	41	general	general	ADJ
ejpam-2231	153	42	.	.	PUNCT
ejpam-2231	154	1	example	example	NOUN
ejpam-2231	155	1	1	1	NUM
ejpam-2231	155	2	showed	show	VERB
ejpam-2231	155	3	that	that	SCONJ
ejpam-2231	155	4	there	there	PRON
ejpam-2231	155	5	exists	exist	VERB
ejpam-2231	155	6	a	a	DET
ejpam-2231	155	7	(	(	PUNCT
ejpam-2231	155	8	0,2)-bi	0,2)-bi	NUM
ejpam-2231	155	9	-	-	PUNCT
ejpam-2231	155	10	ideal	ideal	NOUN
ejpam-2231	155	11	a=	a=	NOUN
ejpam-2231	155	12	{	{	PUNCT
ejpam-2231	155	13	a	a	X
ejpam-2231	155	14	,	,	PUNCT
ejpam-2231	155	15	c	c	NOUN
ejpam-2231	155	16	,	,	PUNCT
ejpam-2231	155	17	e	e	NOUN
ejpam-2231	155	18	}	}	PUNCT
ejpam-2231	155	19	of	of	ADP
ejpam-2231	155	20	s	s	PRON
ejpam-2231	155	21	which	which	PRON
ejpam-2231	155	22	is	be	AUX
ejpam-2231	155	23	not	not	PART
ejpam-2231	155	24	a	a	DET
ejpam-2231	155	25	right	right	ADJ
ejpam-2231	155	26	ideal	ideal	NOUN
ejpam-2231	155	27	of	of	ADP
ejpam-2231	155	28	s.	s.	PROPN
ejpam-2231	155	29	w.	w.	PROPN
ejpam-2231	155	30	khan	khan	PROPN
ejpam-2231	155	31	,	,	PUNCT
ejpam-2231	155	32	f.	f.	PROPN
ejpam-2231	155	33	yousafzai	yousafzai	PROPN
ejpam-2231	155	34	,	,	PUNCT
ejpam-2231	155	35	and	and	CCONJ
ejpam-2231	155	36	m.	m.	PROPN
ejpam-2231	155	37	khan	khan	PROPN
ejpam-2231	155	38	/	/	SYM
ejpam-2231	155	39	eur	eur	PROPN
ejpam-2231	155	40	.	.	PUNCT
ejpam-2231	156	1	j.	j.	PROPN
ejpam-2231	156	2	pure	pure	PROPN
ejpam-2231	156	3	appl	appl	PROPN
ejpam-2231	156	4	.	.	PROPN
ejpam-2231	156	5	math	math	PROPN
ejpam-2231	156	6	,	,	PUNCT
ejpam-2231	156	7	9	9	NUM
ejpam-2231	156	8	(	(	PUNCT
ejpam-2231	156	9	2016	2016	NUM
ejpam-2231	156	10	)	)	PUNCT
ejpam-2231	156	11	,	,	PUNCT
ejpam-2231	156	12	277	277	NUM
ejpam-2231	156	13	-	-	SYM
ejpam-2231	156	14	291	291	NUM
ejpam-2231	156	15	284	284	NUM
ejpam-2231	156	16	theorem	theorem	VERB
ejpam-2231	156	17	4	4	NUM
ejpam-2231	156	18	.	.	PUNCT
ejpam-2231	157	1	let	let	VERB
ejpam-2231	157	2	s	s	PRON
ejpam-2231	157	3	be	be	AUX
ejpam-2231	157	4	a	a	DET
ejpam-2231	157	5	unitaryla	unitaryla	ADJ
ejpam-2231	157	6	-semigroup	-semigroup	NOUN
ejpam-2231	157	7	with	with	ADP
ejpam-2231	157	8	zero	zero	NUM
ejpam-2231	157	9	.	.	PUNCT
ejpam-2231	158	1	then	then	ADV
ejpam-2231	158	2	sa2	sa2	PROPN
ejpam-2231	158	3	=	=	SYM
ejpam-2231	158	4	s	s	PART
ejpam-2231	158	5	∀a	∀a	NOUN
ejpam-2231	158	6	∈	∈	NOUN
ejpam-2231	158	7	s\{0	s\{0	PROPN
ejpam-2231	158	8	}	}	PUNCT
ejpam-2231	158	9	if	if	SCONJ
ejpam-2231	158	10	and	and	CCONJ
ejpam-2231	158	11	only	only	ADV
ejpam-2231	158	12	if	if	SCONJ
ejpam-2231	158	13	s	s	NOUN
ejpam-2231	158	14	is	be	AUX
ejpam-2231	158	15	0-(0,2)-bisimple	0-(0,2)-bisimple	ADJ
ejpam-2231	158	16	if	if	SCONJ
ejpam-2231	158	17	and	and	CCONJ
ejpam-2231	158	18	only	only	ADV
ejpam-2231	158	19	if	if	SCONJ
ejpam-2231	158	20	s	s	NOUN
ejpam-2231	158	21	is	be	AUX
ejpam-2231	158	22	right	right	ADJ
ejpam-2231	158	23	0	0	NOUN
ejpam-2231	158	24	-	-	NOUN
ejpam-2231	158	25	simple	simple	ADJ
ejpam-2231	158	26	.	.	PUNCT
ejpam-2231	159	1	proof	proof	NOUN
ejpam-2231	159	2	.	.	PUNCT
ejpam-2231	160	1	assume	assume	VERB
ejpam-2231	160	2	that	that	SCONJ
ejpam-2231	160	3	sa2	sa2	NOUN
ejpam-2231	160	4	=	=	SYM
ejpam-2231	160	5	s	s	PROPN
ejpam-2231	160	6	for	for	ADP
ejpam-2231	160	7	every	every	DET
ejpam-2231	160	8	a	a	DET
ejpam-2231	160	9	∈	∈	PROPN
ejpam-2231	160	10	s\{0	s\{0	NOUN
ejpam-2231	160	11	}	}	PUNCT
ejpam-2231	160	12	.	.	PUNCT
ejpam-2231	161	1	let	let	VERB
ejpam-2231	161	2	a	a	DET
ejpam-2231	161	3	be	be	AUX
ejpam-2231	161	4	a	a	DET
ejpam-2231	161	5	(	(	PUNCT
ejpam-2231	161	6	0,2)-bi	0,2)-bi	NUM
ejpam-2231	161	7	-	-	PUNCT
ejpam-2231	161	8	ideal	ideal	NOUN
ejpam-2231	161	9	of	of	ADP
ejpam-2231	161	10	s	s	PRON
ejpam-2231	161	11	such	such	ADJ
ejpam-2231	161	12	that	that	SCONJ
ejpam-2231	161	13	a	a	DET
ejpam-2231	161	14	6=	6=	NUM
ejpam-2231	161	15	{	{	PUNCT
ejpam-2231	161	16	0	0	NUM
ejpam-2231	161	17	}	}	PUNCT
ejpam-2231	161	18	.	.	PUNCT
ejpam-2231	162	1	let	let	VERB
ejpam-2231	162	2	a	a	DET
ejpam-2231	162	3	∈	∈	PROPN
ejpam-2231	162	4	a\{0	a\{0	PROPN
ejpam-2231	162	5	}	}	PUNCT
ejpam-2231	162	6	,	,	PUNCT
ejpam-2231	162	7	then	then	ADV
ejpam-2231	162	8	s	s	AUX
ejpam-2231	162	9	=	=	NOUN
ejpam-2231	162	10	sa2	sa2	NOUN
ejpam-2231	162	11	⊆	⊆	NUM
ejpam-2231	162	12	sa2	sa2	NOUN
ejpam-2231	162	13	⊆	⊆	NUM
ejpam-2231	162	14	a.	a.	NOUN
ejpam-2231	162	15	therefore	therefore	ADV
ejpam-2231	162	16	s	s	VERB
ejpam-2231	162	17	=	=	NOUN
ejpam-2231	162	18	a.	a.	NOUN
ejpam-2231	162	19	since	since	SCONJ
ejpam-2231	162	20	s	s	PART
ejpam-2231	162	21	=	=	NOUN
ejpam-2231	162	22	sa2	sa2	PROPN
ejpam-2231	162	23	⊆	⊆	NUM
ejpam-2231	162	24	ss	ss	NOUN
ejpam-2231	162	25	=	=	SYM
ejpam-2231	162	26	s2	s2	PROPN
ejpam-2231	162	27	,	,	PUNCT
ejpam-2231	162	28	we	we	PRON
ejpam-2231	162	29	have	have	VERB
ejpam-2231	162	30	s2	s2	NOUN
ejpam-2231	162	31	=	=	PUNCT
ejpam-2231	162	32	s	s	PROPN
ejpam-2231	162	33	6=	6=	X
ejpam-2231	162	34	{	{	PUNCT
ejpam-2231	162	35	0	0	NUM
ejpam-2231	162	36	}	}	PUNCT
ejpam-2231	162	37	.	.	PUNCT
ejpam-2231	163	1	thus	thus	ADV
ejpam-2231	163	2	s	s	X
ejpam-2231	163	3	is	be	AUX
ejpam-2231	163	4	0	0	NUM
ejpam-2231	163	5	−	−	PROPN
ejpam-2231	163	6	(	(	PUNCT
ejpam-2231	163	7	0,2)-bisimple	0,2)-bisimple	NUM
ejpam-2231	163	8	.	.	PUNCT
ejpam-2231	164	1	the	the	DET
ejpam-2231	164	2	converse	converse	NOUN
ejpam-2231	164	3	statement	statement	NOUN
ejpam-2231	164	4	follows	follow	VERB
ejpam-2231	164	5	from	from	ADP
ejpam-2231	164	6	corollary	corollary	ADJ
ejpam-2231	164	7	4	4	NUM
ejpam-2231	164	8	.	.	PUNCT
ejpam-2231	165	1	let	let	VERB
ejpam-2231	165	2	r	r	PRON
ejpam-2231	165	3	be	be	AUX
ejpam-2231	165	4	a	a	DET
ejpam-2231	165	5	right	right	ADJ
ejpam-2231	165	6	ideal	ideal	NOUN
ejpam-2231	165	7	of	of	ADP
ejpam-2231	165	8	0-(0,2)-bisimple	0-(0,2)-bisimple	NOUN
ejpam-2231	165	9	s.	s.	PROPN
ejpam-2231	165	10	then	then	ADV
ejpam-2231	165	11	by	by	ADP
ejpam-2231	165	12	lemma	lemma	PROPN
ejpam-2231	165	13	6	6	NUM
ejpam-2231	165	14	,	,	PUNCT
ejpam-2231	165	15	r	r	NOUN
ejpam-2231	165	16	is	be	AUX
ejpam-2231	165	17	a	a	DET
ejpam-2231	165	18	(	(	PUNCT
ejpam-2231	165	19	0,2)-bi	0,2)-bi	NUM
ejpam-2231	165	20	-	-	PUNCT
ejpam-2231	165	21	ideal	ideal	NOUN
ejpam-2231	165	22	of	of	ADP
ejpam-2231	165	23	s	s	PRON
ejpam-2231	165	24	and	and	CCONJ
ejpam-2231	165	25	so	so	ADV
ejpam-2231	165	26	r=	r=	ADJ
ejpam-2231	165	27	{	{	PUNCT
ejpam-2231	165	28	0	0	NUM
ejpam-2231	165	29	}	}	PUNCT
ejpam-2231	165	30	or	or	CCONJ
ejpam-2231	165	31	r=	r=	ADJ
ejpam-2231	165	32	s.	s.	PROPN
ejpam-2231	165	33	conversely	conversely	ADV
ejpam-2231	165	34	,	,	PUNCT
ejpam-2231	165	35	assume	assume	VERB
ejpam-2231	165	36	that	that	SCONJ
ejpam-2231	165	37	s	s	VERB
ejpam-2231	165	38	is	be	AUX
ejpam-2231	165	39	right	right	ADJ
ejpam-2231	165	40	0	0	NOUN
ejpam-2231	165	41	-	-	NOUN
ejpam-2231	165	42	simple	simple	ADJ
ejpam-2231	165	43	.	.	PUNCT
ejpam-2231	166	1	let	let	VERB
ejpam-2231	166	2	a	a	DET
ejpam-2231	166	3	∈	∈	PROPN
ejpam-2231	166	4	s\{0	s\{0	NOUN
ejpam-2231	166	5	}	}	PUNCT
ejpam-2231	166	6	,	,	PUNCT
ejpam-2231	166	7	then	then	ADV
ejpam-2231	166	8	sa2	sa2	PROPN
ejpam-2231	166	9	=	=	PUNCT
ejpam-2231	167	1	s.	s.	PROPN
ejpam-2231	167	2	hence	hence	ADV
ejpam-2231	167	3	s	s	VERB
ejpam-2231	167	4	is	be	AUX
ejpam-2231	167	5	0-(0,2)-bisimple	0-(0,2)-bisimple	NOUN
ejpam-2231	167	6	.	.	PUNCT
ejpam-2231	168	1	theorem	theorem	NOUN
ejpam-2231	168	2	5	5	NUM
ejpam-2231	168	3	.	.	PUNCT
ejpam-2231	169	1	let	let	VERB
ejpam-2231	169	2	a	a	PRON
ejpam-2231	169	3	be	be	AUX
ejpam-2231	169	4	a	a	DET
ejpam-2231	169	5	0	0	NUM
ejpam-2231	169	6	-	-	PUNCT
ejpam-2231	169	7	minimal	minimal	ADJ
ejpam-2231	169	8	(	(	PUNCT
ejpam-2231	169	9	0,2)-bi	0,2)-bi	NUM
ejpam-2231	169	10	-	-	PUNCT
ejpam-2231	169	11	ideal	ideal	NOUN
ejpam-2231	169	12	of	of	ADP
ejpam-2231	169	13	a	a	DET
ejpam-2231	169	14	unitary	unitary	ADJ
ejpam-2231	169	15	la	la	PROPN
ejpam-2231	169	16	-semigroup	-semigroup	NOUN
ejpam-2231	169	17	s	s	PART
ejpam-2231	169	18	with	with	ADP
ejpam-2231	169	19	zero	zero	NUM
ejpam-2231	169	20	.	.	PUNCT
ejpam-2231	170	1	then	then	ADV
ejpam-2231	170	2	either	either	CCONJ
ejpam-2231	170	3	a2	a2	PROPN
ejpam-2231	170	4	=	=	PUNCT
ejpam-2231	170	5	{	{	PUNCT
ejpam-2231	170	6	0	0	NUM
ejpam-2231	170	7	}	}	PUNCT
ejpam-2231	170	8	or	or	CCONJ
ejpam-2231	170	9	a	a	PRON
ejpam-2231	170	10	is	be	AUX
ejpam-2231	170	11	right	right	ADJ
ejpam-2231	170	12	0	0	NUM
ejpam-2231	170	13	-	-	NOUN
ejpam-2231	170	14	simple	simple	ADJ
ejpam-2231	170	15	.	.	PUNCT
ejpam-2231	171	1	proof	proof	NOUN
ejpam-2231	171	2	.	.	PUNCT
ejpam-2231	172	1	assume	assume	VERB
ejpam-2231	172	2	that	that	SCONJ
ejpam-2231	172	3	a	a	PRON
ejpam-2231	172	4	is	be	AUX
ejpam-2231	172	5	0	0	NUM
ejpam-2231	172	6	-	-	PUNCT
ejpam-2231	172	7	minimal	minimal	ADJ
ejpam-2231	172	8	(	(	PUNCT
ejpam-2231	172	9	0,2)-bi	0,2)-bi	NUM
ejpam-2231	172	10	-	-	PUNCT
ejpam-2231	172	11	ideal	ideal	NOUN
ejpam-2231	172	12	of	of	ADP
ejpam-2231	172	13	s	s	PRON
ejpam-2231	172	14	such	such	ADJ
ejpam-2231	172	15	that	that	DET
ejpam-2231	172	16	a2	a2	PROPN
ejpam-2231	172	17	6=	6=	PROPN
ejpam-2231	172	18	{	{	PUNCT
ejpam-2231	172	19	0	0	NUM
ejpam-2231	172	20	}	}	PUNCT
ejpam-2231	172	21	.	.	PUNCT
ejpam-2231	173	1	then	then	ADV
ejpam-2231	173	2	by	by	ADP
ejpam-2231	173	3	using	use	VERB
ejpam-2231	173	4	corollary	corollary	ADJ
ejpam-2231	173	5	4	4	NUM
ejpam-2231	173	6	,	,	PUNCT
ejpam-2231	173	7	sa2	sa2	NOUN
ejpam-2231	173	8	=	=	PUNCT
ejpam-2231	173	9	a	a	PRON
ejpam-2231	173	10	for	for	ADP
ejpam-2231	173	11	every	every	DET
ejpam-2231	173	12	a	a	DET
ejpam-2231	173	13	∈	∈	PROPN
ejpam-2231	173	14	a\{0	a\{0	PROPN
ejpam-2231	173	15	}	}	PUNCT
ejpam-2231	173	16	.	.	PUNCT
ejpam-2231	174	1	since	since	SCONJ
ejpam-2231	174	2	a2	a2	PROPN
ejpam-2231	174	3	∈	∈	PROPN
ejpam-2231	174	4	a\{0	a\{0	PROPN
ejpam-2231	174	5	}	}	PUNCT
ejpam-2231	174	6	for	for	ADP
ejpam-2231	174	7	every	every	DET
ejpam-2231	174	8	a	a	DET
ejpam-2231	174	9	∈	∈	PROPN
ejpam-2231	174	10	a\{0	a\{0	PROPN
ejpam-2231	174	11	}	}	PUNCT
ejpam-2231	174	12	,	,	PUNCT
ejpam-2231	174	13	we	we	PRON
ejpam-2231	174	14	have	have	VERB
ejpam-2231	174	15	a4	a4	NUM
ejpam-2231	174	16	=	=	SYM
ejpam-2231	174	17	(	(	PUNCT
ejpam-2231	174	18	a2)2	a2)2	X
ejpam-2231	174	19	∈	∈	PROPN
ejpam-2231	174	20	a\{0	a\{0	PROPN
ejpam-2231	174	21	}	}	PUNCT
ejpam-2231	174	22	for	for	ADP
ejpam-2231	174	23	every	every	DET
ejpam-2231	174	24	a	a	DET
ejpam-2231	174	25	∈	∈	PROPN
ejpam-2231	174	26	a\{0	a\{0	PROPN
ejpam-2231	174	27	}	}	PUNCT
ejpam-2231	174	28	.	.	PUNCT
ejpam-2231	175	1	let	let	VERB
ejpam-2231	175	2	a	a	DET
ejpam-2231	175	3	∈	∈	PROPN
ejpam-2231	175	4	a\{0	a\{0	PROPN
ejpam-2231	175	5	}	}	PUNCT
ejpam-2231	175	6	,	,	PUNCT
ejpam-2231	175	7	then	then	ADV
ejpam-2231	175	8	(	(	PUNCT
ejpam-2231	175	9	aa2)s	aa2)s	PROPN
ejpam-2231	175	10	·	·	PUNCT
ejpam-2231	175	11	aa2	aa2	PROPN
ejpam-2231	176	1	=	=	PRON
ejpam-2231	176	2	a2a	a2a	PROPN
ejpam-2231	176	3	·	·	PUNCT
ejpam-2231	176	4	s(aa2	s(aa2	NUM
ejpam-2231	176	5	)	)	PUNCT
ejpam-2231	176	6	=	=	PUNCT
ejpam-2231	177	1	[	[	X
ejpam-2231	177	2	(	(	PUNCT
ejpam-2231	177	3	s	s	X
ejpam-2231	177	4	·	·	PUNCT
ejpam-2231	177	5	aa2)a]a2	aa2)a]a2	NOUN
ejpam-2231	177	6	⊆	⊆	NUM
ejpam-2231	177	7	[	[	X
ejpam-2231	177	8	(	(	PUNCT
ejpam-2231	177	9	s	s	X
ejpam-2231	177	10	·	·	PUNCT
ejpam-2231	177	11	a)a]a2	a)a]a2	NOUN
ejpam-2231	177	12	=(	=(	PROPN
ejpam-2231	177	13	aa	aa	PROPN
ejpam-2231	177	14	·	·	PUNCT
ejpam-2231	177	15	ss)a2	ss)a2	NOUN
ejpam-2231	177	16	=	=	SYM
ejpam-2231	177	17	sa2	sa2	PROPN
ejpam-2231	177	18	·	·	PUNCT
ejpam-2231	177	19	a2	a2	PROPN
ejpam-2231	177	20	⊆	⊆	NUM
ejpam-2231	177	21	aa2	aa2	NOUN
ejpam-2231	177	22	,	,	PUNCT
ejpam-2231	177	23	and	and	CCONJ
ejpam-2231	177	24	s(aa2)2	s(aa2)2	NOUN
ejpam-2231	177	25	=	=	SYM
ejpam-2231	177	26	s(aa2	s(aa2	ADJ
ejpam-2231	177	27	·	·	PUNCT
ejpam-2231	177	28	aa2	aa2	X
ejpam-2231	177	29	)	)	PUNCT
ejpam-2231	177	30	=	=	SYM
ejpam-2231	177	31	s(a2a	s(a2a	PROPN
ejpam-2231	177	32	·	·	PUNCT
ejpam-2231	177	33	a2a	a2a	PROPN
ejpam-2231	177	34	)	)	PUNCT
ejpam-2231	177	35	=	=	X
ejpam-2231	177	36	s[a2(a2a	s[a2(a2a	X
ejpam-2231	177	37	·	·	PUNCT
ejpam-2231	177	38	a	a	X
ejpam-2231	177	39	)	)	PUNCT
ejpam-2231	177	40	]	]	PUNCT
ejpam-2231	178	1	=	=	X
ejpam-2231	178	2	(	(	PUNCT
ejpam-2231	178	3	aa)[s(a2a	aa)[s(a2a	PROPN
ejpam-2231	178	4	·	·	PUNCT
ejpam-2231	178	5	a	a	X
ejpam-2231	178	6	)	)	PUNCT
ejpam-2231	178	7	]	]	PUNCT
ejpam-2231	178	8	=	=	PUNCT
ejpam-2231	179	1	[	[	X
ejpam-2231	179	2	(	(	PUNCT
ejpam-2231	179	3	a2a	a2a	PROPN
ejpam-2231	179	4	·	·	PUNCT
ejpam-2231	179	5	a)s]a2	a)s]a2	NOUN
ejpam-2231	179	6	⊆(aa	⊆(aa	NOUN
ejpam-2231	179	7	·	·	SYM
ejpam-2231	179	8	ss)a2	ss)a2	NOUN
ejpam-2231	179	9	=	=	SYM
ejpam-2231	179	10	sa2	sa2	PROPN
ejpam-2231	179	11	·	·	PUNCT
ejpam-2231	179	12	a2	a2	PROPN
ejpam-2231	179	13	⊆	⊆	NUM
ejpam-2231	179	14	aa2	aa2	PROPN
ejpam-2231	179	15	,	,	PUNCT
ejpam-2231	179	16	which	which	PRON
ejpam-2231	179	17	shows	show	VERB
ejpam-2231	179	18	that	that	SCONJ
ejpam-2231	179	19	aa2	aa2	PROPN
ejpam-2231	179	20	is	be	AUX
ejpam-2231	179	21	a	a	DET
ejpam-2231	179	22	(	(	PUNCT
ejpam-2231	179	23	0,2)-bi	0,2)-bi	NUM
ejpam-2231	179	24	-	-	PUNCT
ejpam-2231	179	25	ideal	ideal	NOUN
ejpam-2231	179	26	of	of	ADP
ejpam-2231	179	27	s	s	PRON
ejpam-2231	179	28	contained	contain	VERB
ejpam-2231	179	29	in	in	ADP
ejpam-2231	179	30	a.	a.	NOUN
ejpam-2231	179	31	hence	hence	ADV
ejpam-2231	179	32	aa2	aa2	PROPN
ejpam-2231	179	33	=	=	PUNCT
ejpam-2231	179	34	{	{	PUNCT
ejpam-2231	179	35	0	0	NUM
ejpam-2231	179	36	}	}	PUNCT
ejpam-2231	179	37	or	or	CCONJ
ejpam-2231	179	38	aa2	aa2	NOUN
ejpam-2231	179	39	=	=	SYM
ejpam-2231	179	40	a.	a.	NOUN
ejpam-2231	179	41	since	since	SCONJ
ejpam-2231	179	42	a4	a4	NOUN
ejpam-2231	179	43	∈	∈	NOUN
ejpam-2231	179	44	aa2	aa2	NOUN
ejpam-2231	179	45	and	and	CCONJ
ejpam-2231	179	46	a4	a4	PROPN
ejpam-2231	179	47	∈	∈	PROPN
ejpam-2231	179	48	a\{0	a\{0	PROPN
ejpam-2231	179	49	}	}	PUNCT
ejpam-2231	179	50	,	,	PUNCT
ejpam-2231	179	51	we	we	PRON
ejpam-2231	179	52	get	get	VERB
ejpam-2231	179	53	aa2	aa2	NOUN
ejpam-2231	179	54	=	=	PUNCT
ejpam-2231	179	55	a.	a.	NOUN
ejpam-2231	179	56	thus	thus	ADV
ejpam-2231	179	57	by	by	ADP
ejpam-2231	179	58	using	use	VERB
ejpam-2231	179	59	theorem	theorem	NOUN
ejpam-2231	179	60	4	4	NUM
ejpam-2231	179	61	,	,	PUNCT
ejpam-2231	179	62	a	a	PRON
ejpam-2231	179	63	is	be	AUX
ejpam-2231	179	64	right	right	ADJ
ejpam-2231	179	65	0	0	NOUN
ejpam-2231	179	66	-	-	NOUN
ejpam-2231	179	67	simple	simple	ADJ
ejpam-2231	179	68	.	.	PUNCT
ejpam-2231	180	1	4	4	X
ejpam-2231	180	2	.	.	X
ejpam-2231	180	3	(	(	PUNCT
ejpam-2231	180	4	m	m	PROPN
ejpam-2231	180	5	,	,	PUNCT
ejpam-2231	180	6	n)-ideals	n)-ideal	NOUN
ejpam-2231	180	7	in	in	ADP
ejpam-2231	180	8	unitary	unitary	ADJ
ejpam-2231	180	9	la	la	ADJ
ejpam-2231	180	10	-semigroups	-semigroup	NOUN
ejpam-2231	180	11	in	in	ADP
ejpam-2231	180	12	this	this	DET
ejpam-2231	180	13	section	section	NOUN
ejpam-2231	180	14	,	,	PUNCT
ejpam-2231	180	15	we	we	PRON
ejpam-2231	180	16	characterize	characterize	VERB
ejpam-2231	180	17	a	a	DET
ejpam-2231	180	18	unitaryla	unitaryla	ADJ
ejpam-2231	180	19	-semigroup	-semigroup	NOUN
ejpam-2231	180	20	in	in	ADP
ejpam-2231	180	21	terms	term	NOUN
ejpam-2231	180	22	of	of	ADP
ejpam-2231	180	23	(	(	PUNCT
ejpam-2231	180	24	m	m	PROPN
ejpam-2231	180	25	,	,	PUNCT
ejpam-2231	180	26	n)-ideals	n)-ideal	NOUN
ejpam-2231	180	27	with	with	ADP
ejpam-2231	180	28	the	the	DET
ejpam-2231	180	29	assumption	assumption	NOUN
ejpam-2231	180	30	that	that	SCONJ
ejpam-2231	180	31	m	m	PRON
ejpam-2231	180	32	,	,	PUNCT
ejpam-2231	180	33	n≥	n≥	PROPN
ejpam-2231	180	34	3	3	X
ejpam-2231	180	35	.	.	PUNCT
ejpam-2231	181	1	if	if	SCONJ
ejpam-2231	181	2	we	we	PRON
ejpam-2231	181	3	take	take	VERB
ejpam-2231	181	4	m	m	PRON
ejpam-2231	181	5	,	,	PUNCT
ejpam-2231	181	6	n≥	n≥	PROPN
ejpam-2231	181	7	2	2	NUM
ejpam-2231	181	8	,	,	PUNCT
ejpam-2231	181	9	then	then	ADV
ejpam-2231	181	10	all	all	DET
ejpam-2231	181	11	the	the	DET
ejpam-2231	181	12	results	result	NOUN
ejpam-2231	181	13	of	of	ADP
ejpam-2231	181	14	this	this	DET
ejpam-2231	181	15	section	section	NOUN
ejpam-2231	181	16	can	can	AUX
ejpam-2231	181	17	be	be	AUX
ejpam-2231	181	18	trivially	trivially	ADV
ejpam-2231	181	19	followed	follow	VERB
ejpam-2231	181	20	for	for	ADP
ejpam-2231	181	21	a	a	DET
ejpam-2231	181	22	locally	locally	ADV
ejpam-2231	181	23	associative	associative	ADJ
ejpam-2231	181	24	unitary	unitary	ADJ
ejpam-2231	181	25	la	la	PROPN
ejpam-2231	181	26	-semigroup	-semigroup	NOUN
ejpam-2231	181	27	.	.	PUNCT
ejpam-2231	182	1	if	if	SCONJ
ejpam-2231	182	2	s	s	NOUN
ejpam-2231	182	3	is	be	AUX
ejpam-2231	182	4	a	a	DET
ejpam-2231	182	5	unitary	unitary	ADJ
ejpam-2231	182	6	la	la	ADJ
ejpam-2231	182	7	-semigroup	-semigroup	NOUN
ejpam-2231	182	8	,	,	PUNCT
ejpam-2231	182	9	then	then	ADV
ejpam-2231	182	10	it	it	PRON
ejpam-2231	182	11	is	be	AUX
ejpam-2231	182	12	easy	easy	ADJ
ejpam-2231	182	13	to	to	PART
ejpam-2231	182	14	see	see	VERB
ejpam-2231	182	15	that	that	PRON
ejpam-2231	182	16	sam	sam	PROPN
ejpam-2231	182	17	=	=	PUNCT
ejpam-2231	182	18	ams	am	NOUN
ejpam-2231	182	19	and	and	CCONJ
ejpam-2231	182	20	aman	aman	NOUN
ejpam-2231	182	21	=	=	PUNCT
ejpam-2231	182	22	anam	anam	PROPN
ejpam-2231	182	23	for	for	ADP
ejpam-2231	182	24	m	m	PRON
ejpam-2231	182	25	,	,	PUNCT
ejpam-2231	182	26	n≥	n≥	PROPN
ejpam-2231	182	27	3	3	NUM
ejpam-2231	182	28	such	such	ADJ
ejpam-2231	182	29	that	that	DET
ejpam-2231	182	30	a0	a0	NOUN
ejpam-2231	182	31	=	=	PUNCT
ejpam-2231	183	1	e	e	PROPN
ejpam-2231	183	2	if	if	SCONJ
ejpam-2231	183	3	occurs	occur	VERB
ejpam-2231	183	4	,	,	PUNCT
ejpam-2231	183	5	where	where	SCONJ
ejpam-2231	183	6	e	e	NOUN
ejpam-2231	183	7	is	be	AUX
ejpam-2231	183	8	a	a	DET
ejpam-2231	183	9	left	left	ADJ
ejpam-2231	183	10	identity	identity	NOUN
ejpam-2231	183	11	of	of	ADP
ejpam-2231	183	12	s.	s.	PROPN
ejpam-2231	183	13	lemma	lemma	PROPN
ejpam-2231	184	1	7	7	X
ejpam-2231	184	2	.	.	PUNCT
ejpam-2231	185	1	let	let	VERB
ejpam-2231	185	2	s	s	PRON
ejpam-2231	185	3	be	be	AUX
ejpam-2231	185	4	a	a	DET
ejpam-2231	185	5	unitary	unitary	ADJ
ejpam-2231	185	6	la	la	ADJ
ejpam-2231	185	7	-semigroup	-semigroup	NOUN
ejpam-2231	185	8	.	.	PUNCT
ejpam-2231	186	1	if	if	SCONJ
ejpam-2231	186	2	r	r	NOUN
ejpam-2231	186	3	and	and	CCONJ
ejpam-2231	186	4	l	l	NOUN
ejpam-2231	186	5	are	be	AUX
ejpam-2231	186	6	the	the	DET
ejpam-2231	186	7	right	right	NOUN
ejpam-2231	186	8	and	and	CCONJ
ejpam-2231	186	9	left	leave	VERB
ejpam-2231	186	10	ideals	ideal	NOUN
ejpam-2231	186	11	of	of	ADP
ejpam-2231	186	12	s	s	PRON
ejpam-2231	186	13	respectively	respectively	ADV
ejpam-2231	186	14	,	,	PUNCT
ejpam-2231	186	15	then	then	ADV
ejpam-2231	186	16	rl	rl	PROPN
ejpam-2231	186	17	is	be	AUX
ejpam-2231	186	18	an	an	DET
ejpam-2231	186	19	(	(	PUNCT
ejpam-2231	186	20	m	m	PROPN
ejpam-2231	186	21	,	,	PUNCT
ejpam-2231	186	22	n)-ideal	n)-ideal	NOUN
ejpam-2231	186	23	of	of	ADP
ejpam-2231	186	24	s.	s.	PROPN
ejpam-2231	186	25	w.	w.	PROPN
ejpam-2231	186	26	khan	khan	PROPN
ejpam-2231	186	27	,	,	PUNCT
ejpam-2231	186	28	f.	f.	PROPN
ejpam-2231	186	29	yousafzai	yousafzai	PROPN
ejpam-2231	186	30	,	,	PUNCT
ejpam-2231	186	31	and	and	CCONJ
ejpam-2231	186	32	m.	m.	PROPN
ejpam-2231	186	33	khan	khan	PROPN
ejpam-2231	186	34	/	/	SYM
ejpam-2231	186	35	eur	eur	PROPN
ejpam-2231	186	36	.	.	PUNCT
ejpam-2231	187	1	j.	j.	PROPN
ejpam-2231	187	2	pure	pure	PROPN
ejpam-2231	187	3	appl	appl	PROPN
ejpam-2231	187	4	.	.	PROPN
ejpam-2231	187	5	math	math	PROPN
ejpam-2231	187	6	,	,	PUNCT
ejpam-2231	187	7	9	9	NUM
ejpam-2231	187	8	(	(	PUNCT
ejpam-2231	187	9	2016	2016	NUM
ejpam-2231	187	10	)	)	PUNCT
ejpam-2231	187	11	,	,	PUNCT
ejpam-2231	187	12	277	277	NUM
ejpam-2231	187	13	-	-	SYM
ejpam-2231	187	14	291	291	NUM
ejpam-2231	187	15	285	285	NUM
ejpam-2231	187	16	proof	proof	NOUN
ejpam-2231	187	17	.	.	PUNCT
ejpam-2231	188	1	let	let	VERB
ejpam-2231	188	2	r	r	NOUN
ejpam-2231	188	3	and	and	CCONJ
ejpam-2231	188	4	l	l	NOUN
ejpam-2231	188	5	be	be	AUX
ejpam-2231	188	6	the	the	DET
ejpam-2231	188	7	right	right	NOUN
ejpam-2231	188	8	and	and	CCONJ
ejpam-2231	188	9	left	leave	VERB
ejpam-2231	188	10	ideals	ideal	NOUN
ejpam-2231	188	11	of	of	ADP
ejpam-2231	188	12	s	s	PRON
ejpam-2231	188	13	respectively	respectively	ADV
ejpam-2231	188	14	,	,	PUNCT
ejpam-2231	188	15	then	then	ADV
ejpam-2231	188	16	(	(	PUNCT
ejpam-2231	188	17	rl)ms	rl)ms	X
ejpam-2231	188	18	·	·	PUNCT
ejpam-2231	188	19	(	(	PUNCT
ejpam-2231	188	20	rl)n	rl)n	PROPN
ejpam-2231	188	21	=(	=(	NOUN
ejpam-2231	188	22	rm	rm	PROPN
ejpam-2231	188	23	lm	lm	INTJ
ejpam-2231	188	24	·	·	PUNCT
ejpam-2231	188	25	s)(rn	s)(rn	PROPN
ejpam-2231	189	1	ln	ln	X
ejpam-2231	189	2	)	)	PUNCT
ejpam-2231	189	3	=	=	SYM
ejpam-2231	189	4	(	(	PUNCT
ejpam-2231	189	5	rm	rm	PROPN
ejpam-2231	189	6	lm	lm	INTJ
ejpam-2231	189	7	·	·	PUNCT
ejpam-2231	189	8	rn)(sln	rn)(sln	NUM
ejpam-2231	189	9	)	)	PUNCT
ejpam-2231	189	10	=(	=(	NOUN
ejpam-2231	190	1	lmrm	lmrm	PROPN
ejpam-2231	190	2	·	·	PUNCT
ejpam-2231	190	3	rn)(sln	rn)(sln	X
ejpam-2231	190	4	)	)	PUNCT
ejpam-2231	190	5	=	=	SYM
ejpam-2231	190	6	(	(	PUNCT
ejpam-2231	190	7	rnrm	rnrm	X
ejpam-2231	190	8	·	·	PUNCT
ejpam-2231	190	9	lm)(sln	lm)(sln	NUM
ejpam-2231	190	10	)	)	PUNCT
ejpam-2231	190	11	=(	=(	NOUN
ejpam-2231	190	12	rmrn	rmrn	NOUN
ejpam-2231	190	13	·	·	PUNCT
ejpam-2231	190	14	lm)(sln	lm)(sln	X
ejpam-2231	190	15	)	)	PUNCT
ejpam-2231	190	16	=	=	SYM
ejpam-2231	191	1	(	(	PUNCT
ejpam-2231	191	2	rm+n	rm+n	INTJ
ejpam-2231	191	3	lm)(sln	lm)(sln	NOUN
ejpam-2231	191	4	)	)	PUNCT
ejpam-2231	192	1	=	=	NOUN
ejpam-2231	192	2	s(rm+n	s(rm+n	NOUN
ejpam-2231	192	3	lm	lm	INTJ
ejpam-2231	192	4	·	·	PUNCT
ejpam-2231	192	5	ln	ln	X
ejpam-2231	192	6	)	)	PUNCT
ejpam-2231	192	7	=	=	SYM
ejpam-2231	192	8	s(ln	s(ln	NOUN
ejpam-2231	192	9	lm	lm	NOUN
ejpam-2231	192	10	·	·	PUNCT
ejpam-2231	192	11	rm+n	rm+n	NUM
ejpam-2231	192	12	)	)	PUNCT
ejpam-2231	193	1	=	=	NOUN
ejpam-2231	193	2	ss	ss	X
ejpam-2231	193	3	·	·	PUNCT
ejpam-2231	193	4	lm+nrm+n	lm+nrm+n	SYM
ejpam-2231	194	1	=	=	SYM
ejpam-2231	194	2	slm+n	slm+n	PROPN
ejpam-2231	194	3	·	·	PUNCT
ejpam-2231	194	4	srm+n	srm+n	PUNCT
ejpam-2231	194	5	=	=	SYM
ejpam-2231	194	6	rm+ns	rm+ns	X
ejpam-2231	194	7	·	·	PUNCT
ejpam-2231	194	8	lm+ns	lm+n	NOUN
ejpam-2231	194	9	=	=	SYM
ejpam-2231	194	10	srm+n	srm+n	PROPN
ejpam-2231	194	11	·	·	PUNCT
ejpam-2231	195	1	slm+n	slm+n	PUNCT
ejpam-2231	195	2	,	,	PUNCT
ejpam-2231	195	3	and	and	CCONJ
ejpam-2231	195	4	srm+n	srm+n	PROPN
ejpam-2231	195	5	·	·	PUNCT
ejpam-2231	195	6	slm+n	slm+n	PUNCT
ejpam-2231	195	7	=(	=(	PROPN
ejpam-2231	195	8	s	s	PART
ejpam-2231	195	9	·	·	PUNCT
ejpam-2231	195	10	rm+n−1r)(s	rm+n−1r)(s	NOUN
ejpam-2231	195	11	·	·	PUNCT
ejpam-2231	195	12	lm+n−1	lm+n−1	PROPN
ejpam-2231	195	13	l	l	NOUN
ejpam-2231	195	14	)	)	PUNCT
ejpam-2231	196	1	=[	=[	NOUN
ejpam-2231	196	2	s(rm+n−2r	s(rm+n−2r	NOUN
ejpam-2231	196	3	·	·	PUNCT
ejpam-2231	196	4	r)][s(lm+n−2	r)][s(lm+n−2	NOUN
ejpam-2231	197	1	l	l	X
ejpam-2231	197	2	·	·	PUNCT
ejpam-2231	197	3	l	l	X
ejpam-2231	197	4	)	)	PUNCT
ejpam-2231	197	5	]	]	PUNCT
ejpam-2231	198	1	=	=	PUNCT
ejpam-2231	198	2	[	[	X
ejpam-2231	198	3	s(rr	s(rr	NUM
ejpam-2231	198	4	·	·	PUNCT
ejpam-2231	198	5	rm+n−2)][s(ll	rm+n−2)][s(ll	X
ejpam-2231	198	6	·	·	PUNCT
ejpam-2231	198	7	lm+n−2	lm+n−2	PROPN
ejpam-2231	198	8	)	)	PUNCT
ejpam-2231	198	9	]	]	PUNCT
ejpam-2231	198	10	⊆(ss	⊆(ss	X
ejpam-2231	198	11	·	·	PUNCT
ejpam-2231	198	12	rrm+n−2)(ss	rrm+n−2)(ss	ADP
ejpam-2231	198	13	·	·	PUNCT
ejpam-2231	198	14	llm+n−2	llm+n−2	NOUN
ejpam-2231	198	15	)	)	PUNCT
ejpam-2231	198	16	⊆(sr	⊆(sr	NOUN
ejpam-2231	198	17	·	·	PUNCT
ejpam-2231	198	18	srm+n−2)(sl	srm+n−2)(sl	NUM
ejpam-2231	198	19	·	·	SYM
ejpam-2231	198	20	slm+n−2	slm+n−2	PROPN
ejpam-2231	198	21	)	)	PUNCT
ejpam-2231	198	22	⊆(rm+n−2s	⊆(rm+n−2s	NOUN
ejpam-2231	198	23	·	·	PUNCT
ejpam-2231	198	24	rs)(l	rs)(l	NOUN
ejpam-2231	198	25	·	·	PUNCT
ejpam-2231	198	26	slm+n−2	slm+n−2	X
ejpam-2231	198	27	)	)	PUNCT
ejpam-2231	198	28	⊆(rm+n−2s	⊆(rm+n−2s	NOUN
ejpam-2231	198	29	·	·	PUNCT
ejpam-2231	198	30	r)(s	r)(s	NOUN
ejpam-2231	198	31	·	·	PUNCT
ejpam-2231	198	32	llm+n−2	llm+n−2	PROPN
ejpam-2231	198	33	)	)	PUNCT
ejpam-2231	198	34	=(	=(	NOUN
ejpam-2231	198	35	rs	rs	X
ejpam-2231	198	36	·	·	PUNCT
ejpam-2231	198	37	rm+n−2)(slm+n−1	rm+n−2)(slm+n−1	ADJ
ejpam-2231	198	38	)	)	PUNCT
ejpam-2231	198	39	⊆rrm+n−2	⊆rrm+n−2	NOUN
ejpam-2231	198	40	·	·	PUNCT
ejpam-2231	198	41	slm+n−1	slm+n−1	ADP
ejpam-2231	198	42	⊆srm+n−1	⊆srm+n−1	ADJ
ejpam-2231	198	43	·	·	PUNCT
ejpam-2231	198	44	slm+n−1	slm+n−1	NUM
ejpam-2231	198	45	,	,	PUNCT
ejpam-2231	198	46	therefore	therefore	ADV
ejpam-2231	198	47	(	(	PUNCT
ejpam-2231	198	48	rl)ms	rl)ms	X
ejpam-2231	198	49	·	·	PUNCT
ejpam-2231	198	50	(	(	PUNCT
ejpam-2231	198	51	rl)n	rl)n	PROPN
ejpam-2231	198	52	⊆srm+n	⊆srm+n	NUM
ejpam-2231	198	53	·	·	PUNCT
ejpam-2231	198	54	slm+n	slm+n	PUNCT
ejpam-2231	199	1	⊆	⊆	NUM
ejpam-2231	199	2	srm+n−1	srm+n−1	X
ejpam-2231	199	3	·	·	PUNCT
ejpam-2231	199	4	slm+n−1	slm+n−1	ADP
ejpam-2231	199	5	⊆	⊆	NUM
ejpam-2231	199	6	.	.	PUNCT
ejpam-2231	199	7	.	.	PUNCT
ejpam-2231	199	8	.	.	PUNCT
ejpam-2231	200	1	⊆	⊆	NUM
ejpam-2231	200	2	sr	sr	PROPN
ejpam-2231	200	3	·	·	PUNCT
ejpam-2231	200	4	sl	sl	PROPN
ejpam-2231	200	5	⊆(ss	⊆(ss	NUM
ejpam-2231	200	6	·	·	PUNCT
ejpam-2231	200	7	r)l	r)l	NOUN
ejpam-2231	200	8	=	=	SYM
ejpam-2231	200	9	(	(	PUNCT
ejpam-2231	200	10	rs	rs	X
ejpam-2231	200	11	·	·	PUNCT
ejpam-2231	200	12	s)l	s)l	ADJ
ejpam-2231	200	13	⊆	⊆	NUM
ejpam-2231	200	14	rl	rl	X
ejpam-2231	200	15	,	,	PUNCT
ejpam-2231	200	16	and	and	CCONJ
ejpam-2231	200	17	also	also	ADV
ejpam-2231	200	18	rl	rl	VERB
ejpam-2231	200	19	·	·	PUNCT
ejpam-2231	200	20	rl	rl	NOUN
ejpam-2231	200	21	=	=	SYM
ejpam-2231	200	22	lr	lr	X
ejpam-2231	200	23	·	·	PUNCT
ejpam-2231	200	24	lr=	lr=	NOUN
ejpam-2231	200	25	(	(	PUNCT
ejpam-2231	200	26	lr	lr	NOUN
ejpam-2231	200	27	·	·	PUNCT
ejpam-2231	200	28	r)l	r)l	NOUN
ejpam-2231	200	29	=	=	SYM
ejpam-2231	200	30	(	(	PUNCT
ejpam-2231	200	31	rr	rr	NOUN
ejpam-2231	200	32	·	·	PUNCT
ejpam-2231	200	33	l)l	l)l	X
ejpam-2231	200	34	⊆	⊆	NUM
ejpam-2231	200	35	(	(	PUNCT
ejpam-2231	200	36	rs	rs	NOUN
ejpam-2231	200	37	·	·	PUNCT
ejpam-2231	200	38	s)l	s)l	ADJ
ejpam-2231	200	39	⊆	⊆	NUM
ejpam-2231	200	40	rl	rl	X
ejpam-2231	200	41	.	.	PUNCT
ejpam-2231	201	1	this	this	PRON
ejpam-2231	201	2	shows	show	VERB
ejpam-2231	201	3	that	that	SCONJ
ejpam-2231	201	4	rl	rl	PROPN
ejpam-2231	201	5	is	be	AUX
ejpam-2231	201	6	an	an	DET
ejpam-2231	201	7	(	(	PUNCT
ejpam-2231	201	8	m	m	PROPN
ejpam-2231	201	9	,	,	PUNCT
ejpam-2231	201	10	n)-ideal	n)-ideal	NOUN
ejpam-2231	201	11	of	of	ADP
ejpam-2231	201	12	s.	s.	PROPN
ejpam-2231	201	13	theorem	theorem	VERB
ejpam-2231	201	14	6	6	NUM
ejpam-2231	201	15	.	.	PUNCT
ejpam-2231	202	1	let	let	VERB
ejpam-2231	202	2	s	s	PRON
ejpam-2231	202	3	be	be	AUX
ejpam-2231	202	4	a	a	DET
ejpam-2231	202	5	unitary	unitary	ADJ
ejpam-2231	202	6	la	la	ADJ
ejpam-2231	202	7	-semigroup	-semigroup	NOUN
ejpam-2231	202	8	with	with	ADP
ejpam-2231	202	9	zero	zero	NUM
ejpam-2231	202	10	.	.	PUNCT
ejpam-2231	203	1	if	if	SCONJ
ejpam-2231	203	2	s	s	PROPN
ejpam-2231	203	3	has	have	VERB
ejpam-2231	203	4	the	the	DET
ejpam-2231	203	5	property	property	NOUN
ejpam-2231	203	6	that	that	PRON
ejpam-2231	203	7	it	it	PRON
ejpam-2231	203	8	contains	contain	VERB
ejpam-2231	203	9	no	no	DET
ejpam-2231	203	10	non	non	ADJ
ejpam-2231	203	11	-	-	ADJ
ejpam-2231	203	12	zero	zero	ADJ
ejpam-2231	203	13	nilpotent	nilpotent	NOUN
ejpam-2231	203	14	(	(	PUNCT
ejpam-2231	203	15	m	m	NOUN
ejpam-2231	203	16	,	,	PUNCT
ejpam-2231	203	17	n)-ideals	n)-ideal	NOUN
ejpam-2231	203	18	and	and	CCONJ
ejpam-2231	203	19	r	r	NOUN
ejpam-2231	203	20	(	(	PUNCT
ejpam-2231	203	21	l	l	NOUN
ejpam-2231	203	22	)	)	PUNCT
ejpam-2231	203	23	is	be	AUX
ejpam-2231	203	24	a	a	DET
ejpam-2231	203	25	0	0	NUM
ejpam-2231	203	26	-	-	PUNCT
ejpam-2231	203	27	minimal	minimal	ADJ
ejpam-2231	203	28	right	right	NOUN
ejpam-2231	203	29	(	(	PUNCT
ejpam-2231	203	30	le	le	PROPN
ejpam-2231	203	31	f	f	PROPN
ejpam-2231	203	32	t	t	PROPN
ejpam-2231	203	33	)	)	PUNCT
ejpam-2231	203	34	ideal	ideal	NOUN
ejpam-2231	203	35	of	of	ADP
ejpam-2231	203	36	s	s	PROPN
ejpam-2231	203	37	,	,	PUNCT
ejpam-2231	203	38	then	then	ADV
ejpam-2231	203	39	either	either	CCONJ
ejpam-2231	203	40	rl	rl	ADP
ejpam-2231	203	41	=	=	SYM
ejpam-2231	203	42	{	{	PUNCT
ejpam-2231	203	43	0	0	NUM
ejpam-2231	203	44	}	}	PUNCT
ejpam-2231	203	45	or	or	CCONJ
ejpam-2231	203	46	rl	rl	PROPN
ejpam-2231	203	47	is	be	AUX
ejpam-2231	203	48	a	a	DET
ejpam-2231	203	49	0	0	NUM
ejpam-2231	203	50	-	-	PUNCT
ejpam-2231	203	51	minimal	minimal	ADJ
ejpam-2231	203	52	(	(	PUNCT
ejpam-2231	203	53	m	m	PROPN
ejpam-2231	203	54	,	,	PUNCT
ejpam-2231	203	55	n)-ideal	n)-ideal	NOUN
ejpam-2231	203	56	of	of	ADP
ejpam-2231	203	57	s.	s.	PROPN
ejpam-2231	203	58	proof	proof	PROPN
ejpam-2231	203	59	.	.	PUNCT
ejpam-2231	204	1	assume	assume	VERB
ejpam-2231	204	2	that	that	SCONJ
ejpam-2231	204	3	r(l	r(l	NOUN
ejpam-2231	204	4	)	)	PUNCT
ejpam-2231	204	5	is	be	AUX
ejpam-2231	204	6	a	a	DET
ejpam-2231	204	7	0	0	NUM
ejpam-2231	204	8	-	-	PUNCT
ejpam-2231	204	9	minimal	minimal	ADJ
ejpam-2231	204	10	right	right	NOUN
ejpam-2231	204	11	(	(	PUNCT
ejpam-2231	204	12	le	le	PROPN
ejpam-2231	204	13	f	f	PROPN
ejpam-2231	204	14	t	t	PROPN
ejpam-2231	204	15	)	)	PUNCT
ejpam-2231	204	16	ideal	ideal	NOUN
ejpam-2231	204	17	of	of	ADP
ejpam-2231	204	18	s	s	PRON
ejpam-2231	204	19	such	such	ADJ
ejpam-2231	204	20	that	that	PRON
ejpam-2231	204	21	rl	rl	ADP
ejpam-2231	204	22	6=	6=	PRON
ejpam-2231	204	23	{	{	PUNCT
ejpam-2231	204	24	0	0	NUM
ejpam-2231	204	25	}	}	PUNCT
ejpam-2231	204	26	,	,	PUNCT
ejpam-2231	204	27	then	then	ADV
ejpam-2231	204	28	by	by	ADP
ejpam-2231	204	29	lemma	lemma	PROPN
ejpam-2231	204	30	7	7	NUM
ejpam-2231	204	31	,	,	PUNCT
ejpam-2231	204	32	rl	rl	X
ejpam-2231	204	33	is	be	AUX
ejpam-2231	204	34	an	an	DET
ejpam-2231	204	35	(	(	PUNCT
ejpam-2231	204	36	m	m	PROPN
ejpam-2231	204	37	,	,	PUNCT
ejpam-2231	204	38	n)-ideal	n)-ideal	NOUN
ejpam-2231	204	39	of	of	ADP
ejpam-2231	204	40	s.	s.	PROPN
ejpam-2231	204	41	now	now	ADV
ejpam-2231	204	42	we	we	PRON
ejpam-2231	204	43	show	show	VERB
ejpam-2231	204	44	that	that	SCONJ
ejpam-2231	204	45	rl	rl	PROPN
ejpam-2231	204	46	is	be	AUX
ejpam-2231	204	47	a	a	DET
ejpam-2231	204	48	0	0	NUM
ejpam-2231	204	49	-	-	PUNCT
ejpam-2231	204	50	minimal	minimal	ADJ
ejpam-2231	204	51	(	(	PUNCT
ejpam-2231	204	52	m	m	PROPN
ejpam-2231	204	53	,	,	PUNCT
ejpam-2231	204	54	n)-ideal	n)-ideal	PROPN
ejpam-2231	204	55	of	of	ADP
ejpam-2231	204	56	s.	s.	PROPN
ejpam-2231	204	57	let	let	VERB
ejpam-2231	204	58	{	{	PUNCT
ejpam-2231	204	59	0	0	NUM
ejpam-2231	204	60	}	}	PUNCT
ejpam-2231	204	61	6=	6=	ADP
ejpam-2231	204	62	m	m	NOUN
ejpam-2231	204	63	⊆	⊆	NUM
ejpam-2231	204	64	rl	rl	PRON
ejpam-2231	204	65	be	be	AUX
ejpam-2231	204	66	an	an	DET
ejpam-2231	204	67	(	(	PUNCT
ejpam-2231	204	68	m	m	PROPN
ejpam-2231	204	69	,	,	PUNCT
ejpam-2231	204	70	n)-ideal	n)-ideal	NOUN
ejpam-2231	204	71	of	of	ADP
ejpam-2231	204	72	s.	s.	PROPN
ejpam-2231	204	73	note	note	VERB
ejpam-2231	204	74	that	that	SCONJ
ejpam-2231	204	75	since	since	SCONJ
ejpam-2231	204	76	rl	rl	ADP
ejpam-2231	204	77	⊆	⊆	NUM
ejpam-2231	204	78	r	r	NOUN
ejpam-2231	204	79	∩	∩	ADJ
ejpam-2231	204	80	l	l	NOUN
ejpam-2231	204	81	,	,	PUNCT
ejpam-2231	204	82	we	we	PRON
ejpam-2231	204	83	have	have	VERB
ejpam-2231	204	84	m	m	PROPN
ejpam-2231	204	85	⊆	⊆	NUM
ejpam-2231	204	86	r	r	NOUN
ejpam-2231	204	87	∩	∩	X
ejpam-2231	204	88	l.	l.	NOUN
ejpam-2231	204	89	hence	hence	ADV
ejpam-2231	204	90	m	m	VERB
ejpam-2231	204	91	⊆	⊆	NUM
ejpam-2231	204	92	r	r	NOUN
ejpam-2231	204	93	and	and	CCONJ
ejpam-2231	204	94	m	m	PROPN
ejpam-2231	204	95	⊆	⊆	NUM
ejpam-2231	204	96	l.	l.	NOUN
ejpam-2231	204	97	by	by	ADP
ejpam-2231	204	98	hypothesis	hypothesis	NOUN
ejpam-2231	204	99	,	,	PUNCT
ejpam-2231	204	100	m	m	VERB
ejpam-2231	204	101	m	m	VERB
ejpam-2231	204	102	6=	6=	PRON
ejpam-2231	204	103	{	{	PUNCT
ejpam-2231	204	104	0	0	NUM
ejpam-2231	204	105	}	}	PUNCT
ejpam-2231	204	106	and	and	CCONJ
ejpam-2231	204	107	m	m	PROPN
ejpam-2231	204	108	n	n	PRON
ejpam-2231	204	109	6=	6=	NUM
ejpam-2231	204	110	{	{	PUNCT
ejpam-2231	204	111	0	0	NUM
ejpam-2231	204	112	}	}	PUNCT
ejpam-2231	204	113	.	.	PUNCT
ejpam-2231	205	1	since	since	SCONJ
ejpam-2231	205	2	{	{	PUNCT
ejpam-2231	205	3	0	0	NUM
ejpam-2231	205	4	}	}	PUNCT
ejpam-2231	205	5	6=	6=	NUM
ejpam-2231	205	6	sm	sm	PROPN
ejpam-2231	205	7	m	m	NOUN
ejpam-2231	205	8	=	=	PROPN
ejpam-2231	205	9	m	m	VERB
ejpam-2231	205	10	ms	ms	NOUN
ejpam-2231	205	11	,	,	PUNCT
ejpam-2231	205	12	therefore	therefore	ADV
ejpam-2231	205	13	{	{	PUNCT
ejpam-2231	205	14	0	0	NUM
ejpam-2231	205	15	}	}	SYM
ejpam-2231	205	16	6	6	NUM
ejpam-2231	205	17	=	=	NOUN
ejpam-2231	205	18	m	m	NOUN
ejpam-2231	205	19	ms	ms	NOUN
ejpam-2231	205	20	⊆	⊆	NUM
ejpam-2231	205	21	rms	rm	NOUN
ejpam-2231	205	22	=	=	PUNCT
ejpam-2231	205	23	rm−1r	rm−1r	PROPN
ejpam-2231	205	24	·	·	PUNCT
ejpam-2231	205	25	s	s	PART
ejpam-2231	205	26	=	=	VERB
ejpam-2231	205	27	sr	sr	X
ejpam-2231	205	28	·	·	PUNCT
ejpam-2231	205	29	rm−1	rm−1	PROPN
ejpam-2231	205	30	=	=	SYM
ejpam-2231	205	31	sr	sr	PROPN
ejpam-2231	205	32	·	·	PUNCT
ejpam-2231	205	33	rm−2r	rm−2r	NOUN
ejpam-2231	205	34	w.	w.	PROPN
ejpam-2231	205	35	khan	khan	PROPN
ejpam-2231	205	36	,	,	PUNCT
ejpam-2231	205	37	f.	f.	PROPN
ejpam-2231	205	38	yousafzai	yousafzai	PROPN
ejpam-2231	205	39	,	,	PUNCT
ejpam-2231	205	40	and	and	CCONJ
ejpam-2231	205	41	m.	m.	PROPN
ejpam-2231	205	42	khan	khan	PROPN
ejpam-2231	205	43	/	/	SYM
ejpam-2231	205	44	eur	eur	PROPN
ejpam-2231	205	45	.	.	PUNCT
ejpam-2231	206	1	j.	j.	PROPN
ejpam-2231	206	2	pure	pure	PROPN
ejpam-2231	206	3	appl	appl	PROPN
ejpam-2231	206	4	.	.	PROPN
ejpam-2231	206	5	math	math	PROPN
ejpam-2231	206	6	,	,	PUNCT
ejpam-2231	206	7	9	9	NUM
ejpam-2231	206	8	(	(	PUNCT
ejpam-2231	206	9	2016	2016	NUM
ejpam-2231	206	10	)	)	PUNCT
ejpam-2231	206	11	,	,	PUNCT
ejpam-2231	206	12	277	277	NUM
ejpam-2231	206	13	-	-	SYM
ejpam-2231	206	14	291	291	NUM
ejpam-2231	206	15	286	286	NUM
ejpam-2231	206	16	=	=	SYM
ejpam-2231	206	17	rrm−2	rrm−2	NOUN
ejpam-2231	206	18	·	·	PUNCT
ejpam-2231	206	19	rs	rs	ADP
ejpam-2231	206	20	⊆	⊆	NUM
ejpam-2231	206	21	rrm−2	rrm−2	PROPN
ejpam-2231	206	22	·	·	PUNCT
ejpam-2231	206	23	r=	r=	PROPN
ejpam-2231	206	24	rm	rm	NOUN
ejpam-2231	206	25	,	,	PUNCT
ejpam-2231	206	26	and	and	CCONJ
ejpam-2231	206	27	rm	rm	NOUN
ejpam-2231	206	28	⊆srm	⊆srm	PROPN
ejpam-2231	207	1	=	=	PUNCT
ejpam-2231	207	2	ss	ss	PROPN
ejpam-2231	207	3	·	·	PUNCT
ejpam-2231	207	4	rrm−1	rrm−1	PROPN
ejpam-2231	207	5	=	=	PUNCT
ejpam-2231	207	6	rm−1r	rm−1r	PUNCT
ejpam-2231	207	7	·	·	PUNCT
ejpam-2231	207	8	s	s	X
ejpam-2231	207	9	=	=	PUNCT
ejpam-2231	207	10	(	(	PUNCT
ejpam-2231	207	11	rm−2r	rm−2r	NOUN
ejpam-2231	207	12	·	·	PUNCT
ejpam-2231	207	13	r)s	r)s	NOUN
ejpam-2231	207	14	=(	=(	X
ejpam-2231	207	15	rr	rr	NOUN
ejpam-2231	207	16	·	·	PUNCT
ejpam-2231	207	17	rm−2)s	rm−2)s	PUNCT
ejpam-2231	208	1	=	=	PUNCT
ejpam-2231	208	2	srm−2	srm−2	X
ejpam-2231	208	3	·	·	PUNCT
ejpam-2231	208	4	rr	rr	NOUN
ejpam-2231	208	5	⊆	⊆	NUM
ejpam-2231	208	6	srm−2	srm−2	NUM
ejpam-2231	208	7	·	·	PUNCT
ejpam-2231	208	8	r	r	NOUN
ejpam-2231	208	9	=(	=(	NOUN
ejpam-2231	208	10	ss	ss	NOUN
ejpam-2231	208	11	·	·	PUNCT
ejpam-2231	208	12	rm−3r)r=	rm−3r)r=	X
ejpam-2231	208	13	(	(	PUNCT
ejpam-2231	208	14	rrm−3	rrm−3	PROPN
ejpam-2231	208	15	·	·	PUNCT
ejpam-2231	208	16	ss)r=	ss)r=	PROPN
ejpam-2231	208	17	(	(	PUNCT
ejpam-2231	208	18	rs	rs	PROPN
ejpam-2231	208	19	·	·	PUNCT
ejpam-2231	208	20	rm−3s)r	rm−3s)r	PROPN
ejpam-2231	208	21	⊆(r	⊆(r	PROPN
ejpam-2231	208	22	·	·	PUNCT
ejpam-2231	208	23	rm−3s)r=	rm−3s)r=	X
ejpam-2231	208	24	(	(	PUNCT
ejpam-2231	208	25	rm−3	rm−3	NOUN
ejpam-2231	208	26	·	·	PUNCT
ejpam-2231	208	27	rs)r	rs)r	NOUN
ejpam-2231	208	28	⊆	⊆	NUM
ejpam-2231	208	29	rm−3r	rm−3r	PROPN
ejpam-2231	208	30	·	·	PUNCT
ejpam-2231	208	31	r=	r=	ADJ
ejpam-2231	208	32	rm−1	rm−1	NOUN
ejpam-2231	208	33	,	,	PUNCT
ejpam-2231	208	34	therefore	therefore	ADV
ejpam-2231	208	35	{	{	PUNCT
ejpam-2231	208	36	0	0	NUM
ejpam-2231	208	37	}	}	PUNCT
ejpam-2231	208	38	6=	6=	ADP
ejpam-2231	208	39	m	m	PROPN
ejpam-2231	208	40	ms	ms	PROPN
ejpam-2231	208	41	⊆	⊆	NUM
ejpam-2231	208	42	rm	rm	NOUN
ejpam-2231	208	43	⊆	⊆	NUM
ejpam-2231	208	44	rm−1	rm−1	PROPN
ejpam-2231	208	45	⊆	⊆	NUM
ejpam-2231	208	46	.	.	PUNCT
ejpam-2231	208	47	.	.	PUNCT
ejpam-2231	208	48	.	.	PUNCT
ejpam-2231	209	1	⊆	⊆	NUM
ejpam-2231	209	2	r.	r.	NOUN
ejpam-2231	209	3	it	it	PRON
ejpam-2231	209	4	is	be	AUX
ejpam-2231	209	5	easy	easy	ADJ
ejpam-2231	209	6	to	to	PART
ejpam-2231	209	7	see	see	VERB
ejpam-2231	209	8	that	that	SCONJ
ejpam-2231	209	9	m	m	PROPN
ejpam-2231	209	10	ms	ms	PROPN
ejpam-2231	209	11	is	be	AUX
ejpam-2231	209	12	a	a	DET
ejpam-2231	209	13	right	right	ADJ
ejpam-2231	209	14	ideal	ideal	NOUN
ejpam-2231	209	15	of	of	ADP
ejpam-2231	209	16	s.	s.	PROPN
ejpam-2231	209	17	thus	thus	ADV
ejpam-2231	209	18	m	m	VERB
ejpam-2231	209	19	ms	ms	NOUN
ejpam-2231	209	20	=	=	NOUN
ejpam-2231	209	21	r	r	NOUN
ejpam-2231	209	22	since	since	SCONJ
ejpam-2231	209	23	r	r	NOUN
ejpam-2231	209	24	is	be	AUX
ejpam-2231	209	25	0	0	NUM
ejpam-2231	209	26	-	-	PUNCT
ejpam-2231	209	27	minimal	minimal	ADJ
ejpam-2231	209	28	.	.	PUNCT
ejpam-2231	210	1	also	also	ADV
ejpam-2231	210	2	{	{	PUNCT
ejpam-2231	210	3	0	0	NUM
ejpam-2231	210	4	}	}	PUNCT
ejpam-2231	210	5	6=	6=	NUM
ejpam-2231	210	6	sm	sm	PROPN
ejpam-2231	210	7	n	n	PROPN
ejpam-2231	210	8	⊆	⊆	NUM
ejpam-2231	210	9	{	{	PUNCT
ejpam-2231	210	10	0	0	NUM
ejpam-2231	210	11	}	}	PUNCT
ejpam-2231	210	12	6=	6=	NUM
ejpam-2231	210	13	sln	sln	NOUN
ejpam-2231	210	14	=	=	SYM
ejpam-2231	210	15	s	s	PART
ejpam-2231	210	16	·	·	PUNCT
ejpam-2231	210	17	ln−1	ln−1	PROPN
ejpam-2231	210	18	l	l	NOUN
ejpam-2231	211	1	=	=	SYM
ejpam-2231	211	2	ln−1	ln−1	PROPN
ejpam-2231	211	3	·	·	PUNCT
ejpam-2231	211	4	sl	sl	PROPN
ejpam-2231	211	5	⊆	⊆	NUM
ejpam-2231	211	6	ln−1	ln−1	PROPN
ejpam-2231	211	7	l	l	NOUN
ejpam-2231	212	1	=	=	PUNCT
ejpam-2231	212	2	ln	ln	ADJ
ejpam-2231	212	3	,	,	PUNCT
ejpam-2231	212	4	and	and	CCONJ
ejpam-2231	212	5	ln	ln	ADJ
ejpam-2231	212	6	⊆sln	⊆sln	NOUN
ejpam-2231	212	7	=	=	SYM
ejpam-2231	212	8	ss	ss	NOUN
ejpam-2231	212	9	·	·	PUNCT
ejpam-2231	212	10	lln−1	lln−1	PROPN
ejpam-2231	212	11	=	=	SYM
ejpam-2231	212	12	ln−1	ln−1	PROPN
ejpam-2231	212	13	l	l	PROPN
ejpam-2231	212	14	·	·	PUNCT
ejpam-2231	212	15	s	s	X
ejpam-2231	212	16	=	=	PUNCT
ejpam-2231	212	17	(	(	PUNCT
ejpam-2231	212	18	ln−2	ln−2	PROPN
ejpam-2231	212	19	l	l	PROPN
ejpam-2231	212	20	·	·	PUNCT
ejpam-2231	212	21	l)s	l)s	X
ejpam-2231	212	22	=	=	PUNCT
ejpam-2231	212	23	sl	sl	INTJ
ejpam-2231	212	24	·	·	PUNCT
ejpam-2231	212	25	ln−2	ln−2	ADJ
ejpam-2231	212	26	l	l	X
ejpam-2231	212	27	⊆l	⊆l	NOUN
ejpam-2231	212	28	·	·	PUNCT
ejpam-2231	212	29	ln−2	ln−2	ADJ
ejpam-2231	212	30	l	l	NOUN
ejpam-2231	212	31	=	=	SYM
ejpam-2231	212	32	ln−2	ln−2	PROPN
ejpam-2231	212	33	·	·	PUNCT
ejpam-2231	212	34	ll	ll	PROPN
ejpam-2231	212	35	⊆	⊆	NUM
ejpam-2231	212	36	ln−2	ln−2	PROPN
ejpam-2231	212	37	l	l	PROPN
ejpam-2231	212	38	=	=	SYM
ejpam-2231	212	39	ln−1	ln−1	PROPN
ejpam-2231	212	40	⊆	⊆	NUM
ejpam-2231	212	41	.	.	PUNCT
ejpam-2231	212	42	.	.	PUNCT
ejpam-2231	212	43	.	.	PUNCT
ejpam-2231	213	1	⊆	⊆	NUM
ejpam-2231	213	2	l	l	NOUN
ejpam-2231	213	3	,	,	PUNCT
ejpam-2231	213	4	therefore	therefore	ADV
ejpam-2231	213	5	{	{	PUNCT
ejpam-2231	213	6	0	0	NUM
ejpam-2231	213	7	}	}	PUNCT
ejpam-2231	213	8	6=	6=	NUM
ejpam-2231	213	9	sm	sm	PROPN
ejpam-2231	213	10	n	n	PROPN
ejpam-2231	213	11	⊆	⊆	NUM
ejpam-2231	213	12	ln	ln	ADJ
ejpam-2231	213	13	⊆	⊆	NUM
ejpam-2231	213	14	ln−1	ln−1	PROPN
ejpam-2231	213	15	⊆	⊆	NUM
ejpam-2231	213	16	.	.	PUNCT
ejpam-2231	213	17	.	.	PUNCT
ejpam-2231	213	18	.	.	PUNCT
ejpam-2231	214	1	⊆	⊆	NUM
ejpam-2231	214	2	l.	l.	NOUN
ejpam-2231	214	3	it	it	PRON
ejpam-2231	214	4	is	be	AUX
ejpam-2231	214	5	easy	easy	ADJ
ejpam-2231	214	6	to	to	PART
ejpam-2231	214	7	see	see	VERB
ejpam-2231	214	8	that	that	SCONJ
ejpam-2231	214	9	sm	sm	PROPN
ejpam-2231	214	10	n	n	ADV
ejpam-2231	214	11	is	be	AUX
ejpam-2231	214	12	a	a	DET
ejpam-2231	214	13	left	left	ADJ
ejpam-2231	214	14	ideal	ideal	NOUN
ejpam-2231	214	15	of	of	ADP
ejpam-2231	214	16	s.	s.	PROPN
ejpam-2231	214	17	thus	thus	ADV
ejpam-2231	214	18	sm	sm	PROPN
ejpam-2231	214	19	n	n	NOUN
ejpam-2231	214	20	=	=	SYM
ejpam-2231	214	21	l	l	NOUN
ejpam-2231	214	22	since	since	SCONJ
ejpam-2231	214	23	l	l	PROPN
ejpam-2231	214	24	is	be	AUX
ejpam-2231	214	25	0	0	NUM
ejpam-2231	214	26	-	-	PUNCT
ejpam-2231	214	27	minimal	minimal	ADJ
ejpam-2231	214	28	.	.	PUNCT
ejpam-2231	215	1	therefore	therefore	ADV
ejpam-2231	215	2	m	m	VERB
ejpam-2231	215	3	⊆rl	⊆rl	NOUN
ejpam-2231	215	4	=	=	PUNCT
ejpam-2231	216	1	m	m	VERB
ejpam-2231	216	2	ms	ms	NOUN
ejpam-2231	216	3	·	·	PUNCT
ejpam-2231	216	4	sm	sm	PROPN
ejpam-2231	216	5	n	n	NOUN
ejpam-2231	216	6	=	=	NOUN
ejpam-2231	216	7	m	m	VERB
ejpam-2231	216	8	ns	ns	NUM
ejpam-2231	216	9	·	·	PUNCT
ejpam-2231	216	10	sm	sm	NOUN
ejpam-2231	216	11	m	m	NOUN
ejpam-2231	216	12	=	=	PUNCT
ejpam-2231	216	13	(	(	PUNCT
ejpam-2231	216	14	sm	sm	PROPN
ejpam-2231	216	15	m	m	PROPN
ejpam-2231	216	16	·	·	PUNCT
ejpam-2231	216	17	s)m	s)m	ADJ
ejpam-2231	216	18	n	n	PRON
ejpam-2231	216	19	=(	=(	NOUN
ejpam-2231	217	1	sm	sm	PROPN
ejpam-2231	217	2	m	m	PROPN
ejpam-2231	217	3	·	·	PUNCT
ejpam-2231	218	1	ss)m	ss)m	NUM
ejpam-2231	218	2	n	n	NOUN
ejpam-2231	218	3	=	=	SYM
ejpam-2231	218	4	(	(	PUNCT
ejpam-2231	218	5	s	s	X
ejpam-2231	218	6	·	·	PROPN
ejpam-2231	218	7	m	m	PROPN
ejpam-2231	218	8	ms)m	ms)m	PROPN
ejpam-2231	218	9	n	n	PROPN
ejpam-2231	218	10	=	=	PUNCT
ejpam-2231	218	11	(	(	PUNCT
ejpam-2231	218	12	m	m	VERB
ejpam-2231	218	13	m	m	VERB
ejpam-2231	218	14	·	·	PUNCT
ejpam-2231	219	1	ss)m	ss)m	ADJ
ejpam-2231	219	2	n	n	PRON
ejpam-2231	219	3	=	=	NOUN
ejpam-2231	219	4	m	m	PROPN
ejpam-2231	219	5	ms	ms	NOUN
ejpam-2231	219	6	·	·	PROPN
ejpam-2231	219	7	m	m	VERB
ejpam-2231	219	8	n	n	PRON
ejpam-2231	219	9	⊆	⊆	NUM
ejpam-2231	219	10	m	m	NOUN
ejpam-2231	219	11	.	.	PUNCT
ejpam-2231	220	1	thus	thus	ADV
ejpam-2231	220	2	m	m	ADV
ejpam-2231	220	3	=	=	SYM
ejpam-2231	220	4	rl	rl	PROPN
ejpam-2231	220	5	,	,	PUNCT
ejpam-2231	220	6	which	which	PRON
ejpam-2231	220	7	means	mean	VERB
ejpam-2231	220	8	that	that	SCONJ
ejpam-2231	220	9	rl	rl	PROPN
ejpam-2231	220	10	is	be	AUX
ejpam-2231	220	11	a	a	DET
ejpam-2231	220	12	0	0	NUM
ejpam-2231	220	13	-	-	PUNCT
ejpam-2231	220	14	minimal	minimal	ADJ
ejpam-2231	220	15	(	(	PUNCT
ejpam-2231	220	16	m	m	PROPN
ejpam-2231	220	17	,	,	PUNCT
ejpam-2231	220	18	n)-ideal	n)-ideal	NOUN
ejpam-2231	220	19	of	of	ADP
ejpam-2231	220	20	s.	s.	PROPN
ejpam-2231	220	21	theorem	theorem	VERB
ejpam-2231	220	22	7	7	NUM
ejpam-2231	220	23	.	.	PUNCT
ejpam-2231	221	1	let	let	VERB
ejpam-2231	221	2	s	s	PRON
ejpam-2231	221	3	be	be	AUX
ejpam-2231	221	4	a	a	DET
ejpam-2231	221	5	unitary	unitary	ADJ
ejpam-2231	221	6	la	la	ADJ
ejpam-2231	221	7	-semigroup	-semigroup	NOUN
ejpam-2231	221	8	.	.	PUNCT
ejpam-2231	222	1	if	if	SCONJ
ejpam-2231	222	2	r	r	NOUN
ejpam-2231	222	3	(	(	PUNCT
ejpam-2231	222	4	l	l	NOUN
ejpam-2231	222	5	)	)	PUNCT
ejpam-2231	222	6	is	be	AUX
ejpam-2231	222	7	a	a	DET
ejpam-2231	222	8	0	0	NUM
ejpam-2231	222	9	-	-	PUNCT
ejpam-2231	222	10	minimal	minimal	ADJ
ejpam-2231	222	11	right	right	NOUN
ejpam-2231	222	12	(	(	PUNCT
ejpam-2231	222	13	le	le	PROPN
ejpam-2231	222	14	f	f	PROPN
ejpam-2231	222	15	t	t	PROPN
ejpam-2231	222	16	)	)	PUNCT
ejpam-2231	222	17	ideal	ideal	NOUN
ejpam-2231	222	18	of	of	ADP
ejpam-2231	222	19	s	s	PROPN
ejpam-2231	222	20	,	,	PUNCT
ejpam-2231	222	21	then	then	ADV
ejpam-2231	222	22	either	either	CCONJ
ejpam-2231	222	23	rm	rm	PROPN
ejpam-2231	222	24	ln	ln	NOUN
ejpam-2231	223	1	=	=	PUNCT
ejpam-2231	224	1	{	{	PUNCT
ejpam-2231	224	2	0	0	NUM
ejpam-2231	224	3	}	}	PUNCT
ejpam-2231	224	4	or	or	CCONJ
ejpam-2231	224	5	rm	rm	PROPN
ejpam-2231	224	6	ln	ln	PROPN
ejpam-2231	224	7	is	be	AUX
ejpam-2231	224	8	a	a	DET
ejpam-2231	224	9	0	0	NUM
ejpam-2231	224	10	-	-	PUNCT
ejpam-2231	224	11	minimal	minimal	ADJ
ejpam-2231	224	12	(	(	PUNCT
ejpam-2231	224	13	m	m	PROPN
ejpam-2231	224	14	,	,	PUNCT
ejpam-2231	224	15	n)-ideal	n)-ideal	NOUN
ejpam-2231	224	16	of	of	ADP
ejpam-2231	224	17	s.	s.	PROPN
ejpam-2231	224	18	proof	proof	PROPN
ejpam-2231	224	19	.	.	PUNCT
ejpam-2231	225	1	assume	assume	VERB
ejpam-2231	225	2	that	that	SCONJ
ejpam-2231	225	3	r(l	r(l	NOUN
ejpam-2231	225	4	)	)	PUNCT
ejpam-2231	225	5	is	be	AUX
ejpam-2231	225	6	a	a	DET
ejpam-2231	225	7	0	0	NUM
ejpam-2231	225	8	-	-	PUNCT
ejpam-2231	225	9	minimal	minimal	ADJ
ejpam-2231	225	10	right	right	NOUN
ejpam-2231	225	11	(	(	PUNCT
ejpam-2231	225	12	le	le	PROPN
ejpam-2231	225	13	f	f	PROPN
ejpam-2231	225	14	t	t	PROPN
ejpam-2231	225	15	)	)	PUNCT
ejpam-2231	225	16	ideal	ideal	NOUN
ejpam-2231	225	17	of	of	ADP
ejpam-2231	225	18	s	s	PRON
ejpam-2231	225	19	such	such	ADJ
ejpam-2231	225	20	that	that	PRON
ejpam-2231	225	21	rm	rm	PROPN
ejpam-2231	225	22	ln	ln	PROPN
ejpam-2231	225	23	6=	6=	PROPN
ejpam-2231	225	24	{	{	PUNCT
ejpam-2231	225	25	0	0	NUM
ejpam-2231	225	26	}	}	PUNCT
ejpam-2231	225	27	,	,	PUNCT
ejpam-2231	225	28	then	then	ADV
ejpam-2231	225	29	rm	rm	PROPN
ejpam-2231	225	30	6=	6=	PROPN
ejpam-2231	225	31	{	{	PUNCT
ejpam-2231	225	32	0	0	NUM
ejpam-2231	225	33	}	}	PUNCT
ejpam-2231	225	34	and	and	CCONJ
ejpam-2231	225	35	ln	ln	ADJ
ejpam-2231	225	36	6=	6=	NOUN
ejpam-2231	225	37	{	{	PUNCT
ejpam-2231	225	38	0	0	NUM
ejpam-2231	225	39	}	}	PUNCT
ejpam-2231	225	40	.	.	PUNCT
ejpam-2231	226	1	hence	hence	ADV
ejpam-2231	226	2	{	{	PUNCT
ejpam-2231	226	3	0	0	NUM
ejpam-2231	226	4	}	}	PUNCT
ejpam-2231	226	5	6=	6=	NUM
ejpam-2231	226	6	rm	rm	NOUN
ejpam-2231	226	7	⊆	⊆	NUM
ejpam-2231	226	8	r	r	NOUN
ejpam-2231	226	9	and	and	CCONJ
ejpam-2231	226	10	{	{	PUNCT
ejpam-2231	226	11	0	0	NUM
ejpam-2231	226	12	}	}	PUNCT
ejpam-2231	226	13	6=	6=	NUM
ejpam-2231	226	14	ln	ln	ADP
ejpam-2231	226	15	⊆	⊆	NUM
ejpam-2231	226	16	l	l	NOUN
ejpam-2231	226	17	,	,	PUNCT
ejpam-2231	226	18	which	which	PRON
ejpam-2231	226	19	shows	show	VERB
ejpam-2231	226	20	that	that	SCONJ
ejpam-2231	226	21	rm	rm	NOUN
ejpam-2231	226	22	=	=	SYM
ejpam-2231	226	23	r	r	NOUN
ejpam-2231	226	24	and	and	CCONJ
ejpam-2231	226	25	ln	ln	NOUN
ejpam-2231	226	26	=	=	NOUN
ejpam-2231	226	27	l	l	NOUN
ejpam-2231	226	28	since	since	SCONJ
ejpam-2231	226	29	r	r	NOUN
ejpam-2231	226	30	(	(	PUNCT
ejpam-2231	226	31	l	l	NOUN
ejpam-2231	226	32	)	)	PUNCT
ejpam-2231	226	33	is	be	AUX
ejpam-2231	226	34	a	a	DET
ejpam-2231	226	35	0	0	NUM
ejpam-2231	226	36	-	-	PUNCT
ejpam-2231	226	37	minimal	minimal	ADJ
ejpam-2231	226	38	right	right	NOUN
ejpam-2231	226	39	(	(	PUNCT
ejpam-2231	226	40	le	le	PROPN
ejpam-2231	226	41	f	f	PROPN
ejpam-2231	226	42	t	t	PROPN
ejpam-2231	226	43	)	)	PUNCT
ejpam-2231	226	44	ideal	ideal	NOUN
ejpam-2231	226	45	of	of	ADP
ejpam-2231	226	46	s.	s.	PROPN
ejpam-2231	226	47	thus	thus	ADV
ejpam-2231	226	48	by	by	ADP
ejpam-2231	226	49	lemma	lemma	PROPN
ejpam-2231	226	50	7	7	NUM
ejpam-2231	226	51	,	,	PUNCT
ejpam-2231	226	52	rm	rm	PROPN
ejpam-2231	226	53	ln	ln	NOUN
ejpam-2231	227	1	=	=	PUNCT
ejpam-2231	227	2	rl	rl	PROPN
ejpam-2231	227	3	is	be	AUX
ejpam-2231	227	4	an	an	DET
ejpam-2231	227	5	(	(	PUNCT
ejpam-2231	227	6	m	m	PROPN
ejpam-2231	227	7	,	,	PUNCT
ejpam-2231	227	8	n)-ideal	n)-ideal	NOUN
ejpam-2231	227	9	of	of	ADP
ejpam-2231	227	10	s.	s.	PROPN
ejpam-2231	227	11	now	now	ADV
ejpam-2231	227	12	we	we	PRON
ejpam-2231	227	13	show	show	VERB
ejpam-2231	227	14	that	that	SCONJ
ejpam-2231	227	15	rm	rm	PROPN
ejpam-2231	227	16	ln	ln	PROPN
ejpam-2231	227	17	is	be	AUX
ejpam-2231	227	18	a	a	DET
ejpam-2231	227	19	0	0	NUM
ejpam-2231	227	20	-	-	PUNCT
ejpam-2231	227	21	minimal	minimal	ADJ
ejpam-2231	227	22	(	(	PUNCT
ejpam-2231	227	23	m	m	PROPN
ejpam-2231	227	24	,	,	PUNCT
ejpam-2231	227	25	n)-ideal	n)-ideal	PROPN
ejpam-2231	227	26	of	of	ADP
ejpam-2231	227	27	s.	s.	PROPN
ejpam-2231	227	28	let	let	VERB
ejpam-2231	227	29	{	{	PUNCT
ejpam-2231	227	30	0	0	NUM
ejpam-2231	227	31	}	}	PUNCT
ejpam-2231	227	32	6=	6=	ADP
ejpam-2231	227	33	m	m	PROPN
ejpam-2231	227	34	⊆	⊆	NUM
ejpam-2231	227	35	rm	rm	NOUN
ejpam-2231	227	36	ln	ln	NOUN
ejpam-2231	227	37	=	=	SYM
ejpam-2231	227	38	rl	rl	PROPN
ejpam-2231	227	39	⊆	⊆	NUM
ejpam-2231	227	40	r∩	r∩	PROPN
ejpam-2231	227	41	l	l	NOUN
ejpam-2231	227	42	be	be	AUX
ejpam-2231	227	43	an	an	DET
ejpam-2231	227	44	(	(	PUNCT
ejpam-2231	227	45	m	m	PROPN
ejpam-2231	227	46	,	,	PUNCT
ejpam-2231	227	47	n)-ideal	n)-ideal	NOUN
ejpam-2231	227	48	of	of	ADP
ejpam-2231	227	49	s.	s.	PROPN
ejpam-2231	227	50	hence	hence	ADV
ejpam-2231	227	51	{	{	PUNCT
ejpam-2231	227	52	0	0	NUM
ejpam-2231	227	53	}	}	PUNCT
ejpam-2231	227	54	6=	6=	NUM
ejpam-2231	227	55	sm2	sm2	NOUN
ejpam-2231	227	56	=	=	VERB
ejpam-2231	227	57	m	m	VERB
ejpam-2231	227	58	m	m	VERB
ejpam-2231	227	59	·	·	PUNCT
ejpam-2231	227	60	ss	ss	NOUN
ejpam-2231	228	1	=	=	PUNCT
ejpam-2231	228	2	ms	ms	PROPN
ejpam-2231	228	3	·	·	PUNCT
ejpam-2231	228	4	ms	ms	NOUN
ejpam-2231	228	5	⊆	⊆	NUM
ejpam-2231	228	6	rs	rs	NOUN
ejpam-2231	228	7	·	·	PUNCT
ejpam-2231	228	8	rs	rs	NOUN
ejpam-2231	228	9	⊆	⊆	NUM
ejpam-2231	228	10	r	r	NOUN
ejpam-2231	228	11	and	and	CCONJ
ejpam-2231	228	12	{	{	PUNCT
ejpam-2231	228	13	0	0	NUM
ejpam-2231	228	14	}	}	PUNCT
ejpam-2231	228	15	6=	6=	NUM
ejpam-2231	228	16	sm	sm	PROPN
ejpam-2231	228	17	⊆	⊆	NUM
ejpam-2231	228	18	sl	sl	PROPN
ejpam-2231	228	19	⊆	⊆	NUM
ejpam-2231	228	20	l.	l.	NOUN
ejpam-2231	228	21	thus	thus	ADV
ejpam-2231	228	22	r	r	NOUN
ejpam-2231	228	23	=	=	SYM
ejpam-2231	228	24	sm2	sm2	NOUN
ejpam-2231	228	25	=	=	VERB
ejpam-2231	228	26	m	m	VERB
ejpam-2231	228	27	m	m	VERB
ejpam-2231	228	28	·	·	PUNCT
ejpam-2231	228	29	ss	ss	NOUN
ejpam-2231	229	1	=	=	PUNCT
ejpam-2231	229	2	sm	sm	PROPN
ejpam-2231	229	3	·	·	PUNCT
ejpam-2231	229	4	m	m	PROPN
ejpam-2231	229	5	⊆	⊆	NUM
ejpam-2231	229	6	sm	sm	NOUN
ejpam-2231	229	7	and	and	CCONJ
ejpam-2231	229	8	sm	sm	PROPN
ejpam-2231	229	9	=	=	SYM
ejpam-2231	229	10	l	l	NOUN
ejpam-2231	229	11	since	since	SCONJ
ejpam-2231	229	12	r	r	NOUN
ejpam-2231	229	13	(	(	PUNCT
ejpam-2231	229	14	l	l	NOUN
ejpam-2231	229	15	)	)	PUNCT
ejpam-2231	229	16	is	be	AUX
ejpam-2231	229	17	a	a	DET
ejpam-2231	229	18	0	0	NUM
ejpam-2231	229	19	-	-	PUNCT
ejpam-2231	229	20	minimal	minimal	ADJ
ejpam-2231	229	21	right	right	NOUN
ejpam-2231	229	22	(	(	PUNCT
ejpam-2231	229	23	le	le	PROPN
ejpam-2231	229	24	f	f	PROPN
ejpam-2231	229	25	t	t	PROPN
ejpam-2231	229	26	)	)	PUNCT
ejpam-2231	229	27	ideal	ideal	NOUN
ejpam-2231	229	28	of	of	ADP
ejpam-2231	229	29	s.	s.	PROPN
ejpam-2231	229	30	therefore	therefore	ADV
ejpam-2231	229	31	m	m	VERB
ejpam-2231	229	32	⊆rm	⊆rm	DET
ejpam-2231	229	33	ln	ln	ADJ
ejpam-2231	229	34	⊆	⊆	NUM
ejpam-2231	229	35	(	(	PUNCT
ejpam-2231	229	36	sm)m(sm)n	sm)m(sm)n	X
ejpam-2231	229	37	=	=	SYM
ejpam-2231	229	38	smm	smm	X
ejpam-2231	229	39	m	m	PROPN
ejpam-2231	229	40	·	·	PUNCT
ejpam-2231	229	41	snm	snm	PROPN
ejpam-2231	229	42	n	n	PROPN
ejpam-2231	229	43	=	=	SYM
ejpam-2231	229	44	ss	ss	PROPN
ejpam-2231	229	45	·	·	PUNCT
ejpam-2231	229	46	m	m	VERB
ejpam-2231	229	47	mm	mm	INTJ
ejpam-2231	229	48	n	n	PROPN
ejpam-2231	229	49	=	=	NOUN
ejpam-2231	229	50	m	m	PROPN
ejpam-2231	229	51	nm	nm	ADJ
ejpam-2231	229	52	m	m	VERB
ejpam-2231	229	53	·	·	PUNCT
ejpam-2231	229	54	s	s	PART
ejpam-2231	230	1	=	=	X
ejpam-2231	230	2	sm	sm	PROPN
ejpam-2231	230	3	m	m	PROPN
ejpam-2231	230	4	·	·	PROPN
ejpam-2231	230	5	m	m	VERB
ejpam-2231	230	6	n	n	NOUN
ejpam-2231	230	7	=	=	NOUN
ejpam-2231	230	8	m	m	VERB
ejpam-2231	230	9	ms	ms	NOUN
ejpam-2231	230	10	·	·	PROPN
ejpam-2231	230	11	m	m	VERB
ejpam-2231	230	12	n	n	PRON
ejpam-2231	230	13	⊆	⊆	NUM
ejpam-2231	230	14	m	m	NOUN
ejpam-2231	230	15	,	,	PUNCT
ejpam-2231	230	16	thus	thus	ADV
ejpam-2231	230	17	m	m	ADJ
ejpam-2231	230	18	=	=	NOUN
ejpam-2231	230	19	rm	rm	PROPN
ejpam-2231	230	20	ln	ln	PROPN
ejpam-2231	230	21	,	,	PUNCT
ejpam-2231	230	22	which	which	PRON
ejpam-2231	230	23	shows	show	VERB
ejpam-2231	230	24	that	that	SCONJ
ejpam-2231	230	25	rm	rm	PROPN
ejpam-2231	230	26	ln	ln	PROPN
ejpam-2231	230	27	is	be	AUX
ejpam-2231	230	28	a	a	DET
ejpam-2231	230	29	0	0	NUM
ejpam-2231	230	30	-	-	PUNCT
ejpam-2231	230	31	minimal	minimal	ADJ
ejpam-2231	230	32	(	(	PUNCT
ejpam-2231	230	33	m	m	PROPN
ejpam-2231	230	34	,	,	PUNCT
ejpam-2231	230	35	n)-ideal	n)-ideal	NOUN
ejpam-2231	230	36	of	of	ADP
ejpam-2231	230	37	s.	s.	PROPN
ejpam-2231	230	38	w.	w.	PROPN
ejpam-2231	230	39	khan	khan	PROPN
ejpam-2231	230	40	,	,	PUNCT
ejpam-2231	230	41	f.	f.	PROPN
ejpam-2231	230	42	yousafzai	yousafzai	PROPN
ejpam-2231	230	43	,	,	PUNCT
ejpam-2231	230	44	and	and	CCONJ
ejpam-2231	230	45	m.	m.	PROPN
ejpam-2231	230	46	khan	khan	PROPN
ejpam-2231	230	47	/	/	SYM
ejpam-2231	230	48	eur	eur	PROPN
ejpam-2231	230	49	.	.	PUNCT
ejpam-2231	231	1	j.	j.	PROPN
ejpam-2231	231	2	pure	pure	PROPN
ejpam-2231	231	3	appl	appl	PROPN
ejpam-2231	231	4	.	.	PROPN
ejpam-2231	231	5	math	math	PROPN
ejpam-2231	231	6	,	,	PUNCT
ejpam-2231	231	7	9	9	NUM
ejpam-2231	231	8	(	(	PUNCT
ejpam-2231	231	9	2016	2016	NUM
ejpam-2231	231	10	)	)	PUNCT
ejpam-2231	231	11	,	,	PUNCT
ejpam-2231	231	12	277	277	NUM
ejpam-2231	231	13	-	-	SYM
ejpam-2231	231	14	291	291	NUM
ejpam-2231	231	15	287	287	NUM
ejpam-2231	231	16	theorem	theorem	NOUN
ejpam-2231	231	17	8	8	NUM
ejpam-2231	231	18	.	.	PUNCT
ejpam-2231	232	1	let	let	VERB
ejpam-2231	232	2	s	s	PRON
ejpam-2231	232	3	be	be	AUX
ejpam-2231	232	4	a	a	DET
ejpam-2231	232	5	unitary	unitary	ADJ
ejpam-2231	232	6	la	la	ADJ
ejpam-2231	232	7	-semigroup	-semigroup	NOUN
ejpam-2231	232	8	with	with	ADP
ejpam-2231	232	9	zero	zero	NUM
ejpam-2231	232	10	.	.	PUNCT
ejpam-2231	233	1	assume	assume	VERB
ejpam-2231	233	2	that	that	SCONJ
ejpam-2231	233	3	a	a	PRON
ejpam-2231	233	4	is	be	AUX
ejpam-2231	233	5	an	an	DET
ejpam-2231	233	6	(	(	PUNCT
ejpam-2231	233	7	m	m	PROPN
ejpam-2231	233	8	,	,	PUNCT
ejpam-2231	233	9	n)-ideal	n)-ideal	NOUN
ejpam-2231	233	10	of	of	ADP
ejpam-2231	233	11	s	s	PROPN
ejpam-2231	233	12	and	and	CCONJ
ejpam-2231	233	13	b	b	NOUN
ejpam-2231	233	14	is	be	AUX
ejpam-2231	233	15	an	an	DET
ejpam-2231	233	16	(	(	PUNCT
ejpam-2231	233	17	m	m	PROPN
ejpam-2231	233	18	,	,	PUNCT
ejpam-2231	233	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	233	20	of	of	ADP
ejpam-2231	233	21	a	a	DET
ejpam-2231	233	22	such	such	ADJ
ejpam-2231	233	23	that	that	DET
ejpam-2231	233	24	b	b	NOUN
ejpam-2231	233	25	is	be	AUX
ejpam-2231	233	26	idempotent	idempotent	ADJ
ejpam-2231	233	27	.	.	PUNCT
ejpam-2231	234	1	then	then	ADV
ejpam-2231	234	2	b	b	PROPN
ejpam-2231	234	3	is	be	AUX
ejpam-2231	234	4	an	an	DET
ejpam-2231	234	5	(	(	PUNCT
ejpam-2231	234	6	m	m	PROPN
ejpam-2231	234	7	,	,	PUNCT
ejpam-2231	234	8	n)-ideal	n)-ideal	NOUN
ejpam-2231	234	9	of	of	ADP
ejpam-2231	234	10	s.	s.	PROPN
ejpam-2231	234	11	proof	proof	PROPN
ejpam-2231	234	12	.	.	PUNCT
ejpam-2231	235	1	it	it	PRON
ejpam-2231	235	2	is	be	AUX
ejpam-2231	235	3	trivial	trivial	ADJ
ejpam-2231	235	4	that	that	SCONJ
ejpam-2231	235	5	b	b	PROPN
ejpam-2231	235	6	is	be	AUX
ejpam-2231	235	7	an	an	DET
ejpam-2231	235	8	la	la	PROPN
ejpam-2231	235	9	-subsemigroup	-subsemigroup	PROPN
ejpam-2231	235	10	s.	s.	PROPN
ejpam-2231	235	11	secondly	secondly	ADV
ejpam-2231	235	12	,	,	PUNCT
ejpam-2231	235	13	since	since	SCONJ
ejpam-2231	235	14	ams	am	NOUN
ejpam-2231	235	15	·	·	PUNCT
ejpam-2231	235	16	an	an	DET
ejpam-2231	235	17	⊆	⊆	NUM
ejpam-2231	235	18	a	a	PRON
ejpam-2231	235	19	and	and	CCONJ
ejpam-2231	235	20	bma	bma	PROPN
ejpam-2231	235	21	·	·	PUNCT
ejpam-2231	235	22	bn	bn	PROPN
ejpam-2231	235	23	⊆	⊆	NUM
ejpam-2231	235	24	b	b	NOUN
ejpam-2231	235	25	,	,	PUNCT
ejpam-2231	235	26	then	then	ADV
ejpam-2231	235	27	bms	bms	PROPN
ejpam-2231	235	28	·	·	PUNCT
ejpam-2231	235	29	bn	bn	NUM
ejpam-2231	236	1	=(	=(	NOUN
ejpam-2231	236	2	bmbm	bmbm	X
ejpam-2231	236	3	·	·	PUNCT
ejpam-2231	236	4	s)(bnbn	s)(bnbn	NUM
ejpam-2231	236	5	)	)	PUNCT
ejpam-2231	236	6	=	=	PRON
ejpam-2231	236	7	(	(	PUNCT
ejpam-2231	236	8	bnbn)(s	bnbn)(s	NOUN
ejpam-2231	236	9	·	·	SYM
ejpam-2231	236	10	bmbm	bmbm	NOUN
ejpam-2231	236	11	)	)	PUNCT
ejpam-2231	236	12	=[	=[	NOUN
ejpam-2231	236	13	(	(	PUNCT
ejpam-2231	236	14	s	s	X
ejpam-2231	236	15	·	·	PUNCT
ejpam-2231	236	16	bmbm)bn]bn	bmbm)bn]bn	X
ejpam-2231	236	17	=	=	PUNCT
ejpam-2231	237	1	[	[	X
ejpam-2231	237	2	(	(	PUNCT
ejpam-2231	237	3	bn	bn	INTJ
ejpam-2231	237	4	·	·	PUNCT
ejpam-2231	237	5	bmbm)(ss)]bn	bmbm)(ss)]bn	NOUN
ejpam-2231	237	6	=[	=[	NOUN
ejpam-2231	237	7	(	(	PUNCT
ejpam-2231	237	8	bm	bm	PROPN
ejpam-2231	237	9	·	·	PUNCT
ejpam-2231	237	10	bnbm)(ss)]bn	bnbm)(ss)]bn	PROPN
ejpam-2231	237	11	=	=	PUNCT
ejpam-2231	238	1	[	[	X
ejpam-2231	238	2	s(bnbm	s(bnbm	NOUN
ejpam-2231	238	3	·	·	PUNCT
ejpam-2231	238	4	bm)]bn	bm)]bn	PROPN
ejpam-2231	238	5	=[	=[	NOUN
ejpam-2231	238	6	s(bnbm	s(bnbm	NOUN
ejpam-2231	238	7	·	·	PUNCT
ejpam-2231	238	8	bm−1b)]bn	bm−1b)]bn	NOUN
ejpam-2231	238	9	=	=	PUNCT
ejpam-2231	239	1	[	[	X
ejpam-2231	239	2	s(bbm−1	s(bbm−1	X
ejpam-2231	239	3	·	·	PUNCT
ejpam-2231	239	4	bmbn)]bn	bmbn)]bn	PROPN
ejpam-2231	239	5	=[	=[	PROPN
ejpam-2231	239	6	s(bm	s(bm	X
ejpam-2231	239	7	·	·	PUNCT
ejpam-2231	239	8	bmbn)]bn	bmbn)]bn	PROPN
ejpam-2231	239	9	=	=	PUNCT
ejpam-2231	240	1	[	[	X
ejpam-2231	240	2	bm(ss	bm(ss	NOUN
ejpam-2231	240	3	·	·	PUNCT
ejpam-2231	240	4	bmbn)]bn	bmbn)]bn	PROPN
ejpam-2231	240	5	=[	=[	PROPN
ejpam-2231	240	6	bm(bnbm	bm(bnbm	PROPN
ejpam-2231	240	7	·	·	PUNCT
ejpam-2231	240	8	ss)]bn	ss)]bn	PROPN
ejpam-2231	240	9	=	=	PUNCT
ejpam-2231	241	1	[	[	X
ejpam-2231	241	2	bm(sbm	bm(sbm	NOUN
ejpam-2231	241	3	·	·	PUNCT
ejpam-2231	241	4	bn)]bn	bn)]bn	VERB
ejpam-2231	241	5	=[	=[	NOUN
ejpam-2231	241	6	bm{(ss	bm{(ss	NOUN
ejpam-2231	241	7	·	·	PUNCT
ejpam-2231	241	8	bm−1b)bn}]bn	bm−1b)bn}]bn	NOUN
ejpam-2231	241	9	=	=	PUNCT
ejpam-2231	242	1	[	[	X
ejpam-2231	242	2	bm(bms	bm(bms	X
ejpam-2231	242	3	·	·	PUNCT
ejpam-2231	242	4	bn)]bn	bn)]bn	VERB
ejpam-2231	242	5	⊆[bm(ams	⊆[bm(am	NOUN
ejpam-2231	242	6	·	·	PUNCT
ejpam-2231	243	1	an)]bn	an)]bn	PROPN
ejpam-2231	243	2	⊆	⊆	NUM
ejpam-2231	243	3	bma	bma	X
ejpam-2231	243	4	·	·	PUNCT
ejpam-2231	243	5	bn	bn	ADP
ejpam-2231	243	6	⊆	⊆	NUM
ejpam-2231	243	7	b	b	NOUN
ejpam-2231	243	8	,	,	PUNCT
ejpam-2231	243	9	which	which	PRON
ejpam-2231	243	10	shows	show	VERB
ejpam-2231	243	11	that	that	SCONJ
ejpam-2231	243	12	b	b	NOUN
ejpam-2231	243	13	is	be	AUX
ejpam-2231	243	14	an	an	DET
ejpam-2231	243	15	(	(	PUNCT
ejpam-2231	243	16	m	m	PROPN
ejpam-2231	243	17	,	,	PUNCT
ejpam-2231	243	18	n)-ideal	n)-ideal	NOUN
ejpam-2231	243	19	of	of	ADP
ejpam-2231	243	20	s.	s.	PROPN
ejpam-2231	243	21	lemma	lemma	PROPN
ejpam-2231	243	22	8	8	X
ejpam-2231	243	23	.	.	PUNCT
ejpam-2231	244	1	let	let	VERB
ejpam-2231	244	2	〈	〈	PROPN
ejpam-2231	244	3	a〉(m	a〉(m	NOUN
ejpam-2231	244	4	,	,	PUNCT
ejpam-2231	244	5	n	n	CCONJ
ejpam-2231	244	6	)	)	PUNCT
ejpam-2231	245	1	=	=	NOUN
ejpam-2231	245	2	ams	am	NOUN
ejpam-2231	245	3	·	·	PUNCT
ejpam-2231	245	4	an	an	X
ejpam-2231	245	5	,	,	PUNCT
ejpam-2231	245	6	then	then	ADV
ejpam-2231	245	7	〈	〈	PROPN
ejpam-2231	245	8	a〉(m	a〉(m	NOUN
ejpam-2231	245	9	,	,	PUNCT
ejpam-2231	245	10	n	n	CCONJ
ejpam-2231	245	11	)	)	PUNCT
ejpam-2231	245	12	is	be	AUX
ejpam-2231	245	13	an	an	DET
ejpam-2231	245	14	(	(	PUNCT
ejpam-2231	245	15	m	m	PROPN
ejpam-2231	245	16	,	,	PUNCT
ejpam-2231	245	17	n)-ideal	n)-ideal	NOUN
ejpam-2231	245	18	of	of	ADP
ejpam-2231	245	19	a	a	DET
ejpam-2231	245	20	unitary	unitary	ADJ
ejpam-2231	245	21	la	la	PROPN
ejpam-2231	245	22	-semigroup	-semigroup	NOUN
ejpam-2231	245	23	s.	s.	PROPN
ejpam-2231	245	24	proof	proof	PROPN
ejpam-2231	245	25	.	.	PUNCT
ejpam-2231	246	1	assume	assume	VERB
ejpam-2231	246	2	that	that	SCONJ
ejpam-2231	246	3	s	s	VERB
ejpam-2231	246	4	is	be	AUX
ejpam-2231	246	5	a	a	DET
ejpam-2231	246	6	unitaryla	unitaryla	ADJ
ejpam-2231	246	7	-semigroup	-semigroup	NOUN
ejpam-2231	246	8	and	and	CCONJ
ejpam-2231	246	9	m	m	PROPN
ejpam-2231	246	10	,	,	PUNCT
ejpam-2231	246	11	n	n	PRON
ejpam-2231	246	12	are	be	AUX
ejpam-2231	246	13	non	non	ADJ
ejpam-2231	246	14	-	-	ADJ
ejpam-2231	246	15	negative	negative	ADJ
ejpam-2231	246	16	integers	integer	NOUN
ejpam-2231	246	17	,	,	PUNCT
ejpam-2231	246	18	then	then	ADV
ejpam-2231	246	19	�	�	PROPN
ejpam-2231	246	20	{	{	PUNCT
ejpam-2231	246	21	〈	〈	NOUN
ejpam-2231	246	22	a〉(m	a〉(m	PROPN
ejpam-2231	246	23	,	,	PUNCT
ejpam-2231	246	24	n	n	CCONJ
ejpam-2231	246	25	)	)	PUNCT
ejpam-2231	246	26	}	}	PUNCT
ejpam-2231	246	27	mh	mh	PROPN
ejpam-2231	246	28	�	�	PROPN
ejpam-2231	246	29	{	{	PUNCT
ejpam-2231	246	30	〈	〈	PROPN
ejpam-2231	246	31	a〉(m	a〉(m	PROPN
ejpam-2231	246	32	,	,	PUNCT
ejpam-2231	246	33	n	n	CCONJ
ejpam-2231	246	34	)	)	PUNCT
ejpam-2231	246	35	}	}	PUNCT
ejpam-2231	246	36	n	n	PRON
ejpam-2231	246	37	=[	=[	NOUN
ejpam-2231	246	38	{	{	PUNCT
ejpam-2231	246	39	(	(	PUNCT
ejpam-2231	246	40	(	(	PUNCT
ejpam-2231	246	41	amh)an)}mh	amh)an)}mh	PROPN
ejpam-2231	246	42	]	]	X
ejpam-2231	246	43	{	{	PUNCT
ejpam-2231	246	44	(	(	PUNCT
ejpam-2231	246	45	amh)an}n	amh)an}n	NOUN
ejpam-2231	246	46	=[	=[	NOUN
ejpam-2231	246	47	{	{	PUNCT
ejpam-2231	246	48	(	(	PUNCT
ejpam-2231	246	49	ammhm)amn}h	ammhm)amn}h	NOUN
ejpam-2231	246	50	]	]	PUNCT
ejpam-2231	246	51	{	{	PUNCT
ejpam-2231	246	52	(	(	PUNCT
ejpam-2231	246	53	amnhn)ann	amnhn)ann	PROPN
ejpam-2231	246	54	}	}	PUNCT
ejpam-2231	246	55	=[	=[	NOUN
ejpam-2231	246	56	ann(amnhn)][h{(ammhm)amn	ann(amnhn)][h{(ammhm)amn	ADV
ejpam-2231	246	57	}	}	PUNCT
ejpam-2231	246	58	]	]	PUNCT
ejpam-2231	247	1	=	=	PUNCT
ejpam-2231	247	2	[	[	X
ejpam-2231	247	3	[	[	X
ejpam-2231	247	4	h{(ammhm)amn}](amnhn	h{(ammhm)amn}](amnhn	NOUN
ejpam-2231	247	5	)	)	PUNCT
ejpam-2231	247	6	]	]	PUNCT
ejpam-2231	248	1	ann	ann	PROPN
ejpam-2231	248	2	=[	=[	PROPN
ejpam-2231	248	3	amn[[h{(ammhm)amn}]hn	amn[[h{(ammhm)amn}]hn	PROPN
ejpam-2231	248	4	]	]	X
ejpam-2231	248	5	]	]	X
ejpam-2231	248	6	ann	ann	X
ejpam-2231	248	7	⊆(amnh)ann	⊆(amnh)ann	X
ejpam-2231	248	8	=	=	SYM
ejpam-2231	248	9	(	(	PUNCT
ejpam-2231	248	10	amnhn)ann	amnhn)ann	PROPN
ejpam-2231	248	11	=	=	PRON
ejpam-2231	248	12	{	{	PUNCT
ejpam-2231	248	13	(	(	PUNCT
ejpam-2231	248	14	amh)an}n	amh)an}n	NOUN
ejpam-2231	248	15	⊆	⊆	NUM
ejpam-2231	248	16	�	�	PROPN
ejpam-2231	248	17	〈	〈	PROPN
ejpam-2231	248	18	a〉(m	a〉(m	NOUN
ejpam-2231	248	19	,	,	PUNCT
ejpam-2231	248	20	n	n	CCONJ
ejpam-2231	248	21	)	)	PUNCT
ejpam-2231	248	22	�	�	PROPN
ejpam-2231	248	23	n	n	CCONJ
ejpam-2231	248	24	⊆	⊆	NUM
ejpam-2231	248	25	〈	〈	NOUN
ejpam-2231	248	26	a〉(m	a〉(m	NOUN
ejpam-2231	248	27	,	,	PUNCT
ejpam-2231	248	28	n	n	CCONJ
ejpam-2231	248	29	)	)	PUNCT
ejpam-2231	248	30	,	,	PUNCT
ejpam-2231	248	31	and	and	CCONJ
ejpam-2231	248	32	similarly	similarly	ADV
ejpam-2231	248	33	we	we	PRON
ejpam-2231	248	34	can	can	AUX
ejpam-2231	248	35	show	show	VERB
ejpam-2231	248	36	that	that	SCONJ
ejpam-2231	248	37	�	�	PROPN
ejpam-2231	248	38	〈	〈	PROPN
ejpam-2231	248	39	a〉(m	a〉(m	PROPN
ejpam-2231	248	40	,	,	PUNCT
ejpam-2231	248	41	n	n	CCONJ
ejpam-2231	248	42	)	)	PUNCT
ejpam-2231	248	43	�	�	PROPN
ejpam-2231	248	44	2	2	NUM
ejpam-2231	248	45	⊆	⊆	NUM
ejpam-2231	248	46	〈	〈	NOUN
ejpam-2231	248	47	a〉(m	a〉(m	NOUN
ejpam-2231	248	48	,	,	PUNCT
ejpam-2231	248	49	n	n	CCONJ
ejpam-2231	248	50	)	)	PUNCT
ejpam-2231	248	51	.	.	PUNCT
ejpam-2231	249	1	theorem	theorem	NOUN
ejpam-2231	249	2	9	9	NUM
ejpam-2231	249	3	.	.	PUNCT
ejpam-2231	250	1	let	let	VERB
ejpam-2231	250	2	s	s	PRON
ejpam-2231	250	3	be	be	AUX
ejpam-2231	250	4	a	a	DET
ejpam-2231	250	5	unitary	unitary	ADJ
ejpam-2231	250	6	la	la	ADJ
ejpam-2231	250	7	-semigroup	-semigroup	NOUN
ejpam-2231	250	8	and	and	CCONJ
ejpam-2231	250	9	〈	〈	PROPN
ejpam-2231	250	10	a〉(m	a〉(m	NOUN
ejpam-2231	250	11	,	,	PUNCT
ejpam-2231	250	12	n	n	CCONJ
ejpam-2231	250	13	)	)	PUNCT
ejpam-2231	250	14	be	be	AUX
ejpam-2231	250	15	an	an	DET
ejpam-2231	250	16	(	(	PUNCT
ejpam-2231	250	17	m	m	PROPN
ejpam-2231	250	18	,	,	PUNCT
ejpam-2231	250	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	250	20	of	of	ADP
ejpam-2231	250	21	s.	s.	PROPN
ejpam-2231	250	22	then	then	ADV
ejpam-2231	250	23	the	the	DET
ejpam-2231	250	24	following	follow	VERB
ejpam-2231	250	25	statements	statement	NOUN
ejpam-2231	250	26	hold	hold	VERB
ejpam-2231	250	27	:	:	PUNCT
ejpam-2231	250	28	(	(	PUNCT
ejpam-2231	250	29	i	i	NOUN
ejpam-2231	250	30	)	)	PUNCT
ejpam-2231	250	31	�	�	PROPN
ejpam-2231	250	32	〈	〈	NOUN
ejpam-2231	250	33	a〉(1,0	a〉(1,0	PROPN
ejpam-2231	250	34	)	)	PUNCT
ejpam-2231	250	35	�	�	PROPN
ejpam-2231	250	36	m	m	NOUN
ejpam-2231	250	37	s	s	PART
ejpam-2231	250	38	=	=	NOUN
ejpam-2231	250	39	ams	am	NOUN
ejpam-2231	250	40	;	;	PUNCT
ejpam-2231	250	41	(	(	PUNCT
ejpam-2231	250	42	ii	ii	NOUN
ejpam-2231	250	43	)	)	PUNCT
ejpam-2231	250	44	s	s	PART
ejpam-2231	250	45	�	�	PROPN
ejpam-2231	250	46	〈	〈	PROPN
ejpam-2231	250	47	a〉(0,1	a〉(0,1	NOUN
ejpam-2231	250	48	)	)	PUNCT
ejpam-2231	250	49	�	�	PROPN
ejpam-2231	250	50	n	n	NOUN
ejpam-2231	250	51	=	=	SYM
ejpam-2231	250	52	san	san	PROPN
ejpam-2231	250	53	;	;	PUNCT
ejpam-2231	250	54	(	(	PUNCT
ejpam-2231	250	55	iii	iii	X
ejpam-2231	250	56	)	)	PUNCT
ejpam-2231	250	57	�	�	PROPN
ejpam-2231	250	58	〈	〈	NOUN
ejpam-2231	250	59	a〉(1,0	a〉(1,0	PROPN
ejpam-2231	250	60	)	)	PUNCT
ejpam-2231	250	61	�	�	PROPN
ejpam-2231	250	62	m	m	PROPN
ejpam-2231	250	63	s	s	PART
ejpam-2231	250	64	·	·	PUNCT
ejpam-2231	250	65	�	�	PROPN
ejpam-2231	250	66	〈	〈	NOUN
ejpam-2231	250	67	a〉(0,1	a〉(0,1	NOUN
ejpam-2231	250	68	)	)	PUNCT
ejpam-2231	250	69	�	�	PROPN
ejpam-2231	250	70	n	n	NOUN
ejpam-2231	250	71	=	=	SYM
ejpam-2231	250	72	(	(	PUNCT
ejpam-2231	250	73	ams)an	ams)an	NOUN
ejpam-2231	250	74	.	.	PUNCT
ejpam-2231	251	1	w.	w.	PROPN
ejpam-2231	251	2	khan	khan	PROPN
ejpam-2231	251	3	,	,	PUNCT
ejpam-2231	251	4	f.	f.	PROPN
ejpam-2231	251	5	yousafzai	yousafzai	PROPN
ejpam-2231	251	6	,	,	PUNCT
ejpam-2231	251	7	and	and	CCONJ
ejpam-2231	251	8	m.	m.	PROPN
ejpam-2231	251	9	khan	khan	PROPN
ejpam-2231	251	10	/	/	SYM
ejpam-2231	251	11	eur	eur	PROPN
ejpam-2231	251	12	.	.	PUNCT
ejpam-2231	252	1	j.	j.	PROPN
ejpam-2231	252	2	pure	pure	PROPN
ejpam-2231	252	3	appl	appl	PROPN
ejpam-2231	252	4	.	.	PROPN
ejpam-2231	252	5	math	math	PROPN
ejpam-2231	252	6	,	,	PUNCT
ejpam-2231	252	7	9	9	NUM
ejpam-2231	252	8	(	(	PUNCT
ejpam-2231	252	9	2016	2016	NUM
ejpam-2231	252	10	)	)	PUNCT
ejpam-2231	252	11	,	,	PUNCT
ejpam-2231	252	12	277	277	NUM
ejpam-2231	252	13	-	-	SYM
ejpam-2231	252	14	291	291	NUM
ejpam-2231	252	15	288	288	NUM
ejpam-2231	252	16	proof	proof	NOUN
ejpam-2231	252	17	.	.	PUNCT
ejpam-2231	253	1	(	(	PUNCT
ejpam-2231	253	2	i	i	NOUN
ejpam-2231	253	3	)	)	PUNCT
ejpam-2231	253	4	.	.	PUNCT
ejpam-2231	254	1	as	as	ADP
ejpam-2231	254	2	〈	〈	NOUN
ejpam-2231	254	3	a〉(1,0	a〉(1,0	NOUN
ejpam-2231	254	4	)	)	PUNCT
ejpam-2231	254	5	=	=	PUNCT
ejpam-2231	254	6	as	as	SCONJ
ejpam-2231	254	7	,	,	PUNCT
ejpam-2231	254	8	we	we	PRON
ejpam-2231	254	9	have	have	VERB
ejpam-2231	254	10	�	�	PROPN
ejpam-2231	254	11	〈	〈	NOUN
ejpam-2231	254	12	a〉(1,0	a〉(1,0	PROPN
ejpam-2231	254	13	)	)	PUNCT
ejpam-2231	254	14	�	�	PROPN
ejpam-2231	254	15	m	m	PROPN
ejpam-2231	254	16	s	s	NOUN
ejpam-2231	254	17	=(	=(	NOUN
ejpam-2231	254	18	as)ms	as)ms	X
ejpam-2231	255	1	=	=	SYM
ejpam-2231	255	2	(	(	PUNCT
ejpam-2231	255	3	as)m−1(as	as)m−1(as	PROPN
ejpam-2231	255	4	)	)	PUNCT
ejpam-2231	255	5	·	·	PUNCT
ejpam-2231	255	6	s	s	PART
ejpam-2231	255	7	=	=	SYM
ejpam-2231	255	8	s(as	s(as	X
ejpam-2231	255	9	)	)	PUNCT
ejpam-2231	255	10	·	·	PUNCT
ejpam-2231	256	1	(	(	PUNCT
ejpam-2231	256	2	as)m−1	as)m−1	NOUN
ejpam-2231	256	3	=(	=(	ADV
ejpam-2231	256	4	as)(as)m−1	as)(as)m−1	PROPN
ejpam-2231	256	5	=	=	SYM
ejpam-2231	256	6	(	(	PUNCT
ejpam-2231	256	7	as)[(as)m−2(as	as)[(as)m−2(as	NOUN
ejpam-2231	256	8	)	)	PUNCT
ejpam-2231	256	9	]	]	PUNCT
ejpam-2231	257	1	=	=	X
ejpam-2231	257	2	(	(	PUNCT
ejpam-2231	257	3	as)m−2(as	as)m−2(as	PROPN
ejpam-2231	257	4	·	·	PUNCT
ejpam-2231	257	5	as	as	ADP
ejpam-2231	257	6	)	)	PUNCT
ejpam-2231	257	7	=	=	SYM
ejpam-2231	257	8	(	(	PUNCT
ejpam-2231	257	9	as)m−2(a2s	as)m−2(a2s	NOUN
ejpam-2231	257	10	)	)	PUNCT
ejpam-2231	257	11	=	=	PUNCT
ejpam-2231	257	12	.	.	PUNCT
ejpam-2231	257	13	.	.	PUNCT
ejpam-2231	258	1	.=	.=	VERB
ejpam-2231	259	1	¨	¨	X
ejpam-2231	259	2	(	(	PUNCT
ejpam-2231	259	3	as)m−(m−1)(am−1s	as)m−(m−1)(am−1s	NOUN
ejpam-2231	259	4	)	)	PUNCT
ejpam-2231	259	5	if	if	SCONJ
ejpam-2231	259	6	m	m	PROPN
ejpam-2231	259	7	is	be	AUX
ejpam-2231	259	8	odd	odd	ADJ
ejpam-2231	259	9	(	(	PUNCT
ejpam-2231	259	10	am−1s)(as)m−(m−1	am−1s)(as)m−(m−1	NOUN
ejpam-2231	259	11	)	)	PUNCT
ejpam-2231	259	12	if	if	SCONJ
ejpam-2231	259	13	m	m	NOUN
ejpam-2231	259	14	is	be	AUX
ejpam-2231	259	15	even	even	ADV
ejpam-2231	259	16	=	=	NOUN
ejpam-2231	259	17	ams	am	NOUN
ejpam-2231	259	18	.	.	PUNCT
ejpam-2231	260	1	analogously	analogously	ADV
ejpam-2231	260	2	,	,	PUNCT
ejpam-2231	260	3	we	we	PRON
ejpam-2231	260	4	can	can	AUX
ejpam-2231	260	5	prove	prove	VERB
ejpam-2231	260	6	(	(	PUNCT
ejpam-2231	260	7	ii	ii	NOUN
ejpam-2231	260	8	)	)	PUNCT
ejpam-2231	260	9	and	and	CCONJ
ejpam-2231	260	10	(	(	PUNCT
ejpam-2231	260	11	iii	iii	X
ejpam-2231	260	12	)	)	PUNCT
ejpam-2231	260	13	is	be	AUX
ejpam-2231	260	14	simple	simple	ADJ
ejpam-2231	260	15	.	.	PUNCT
ejpam-2231	261	1	corollary	corollary	ADJ
ejpam-2231	261	2	5	5	NUM
ejpam-2231	261	3	.	.	PUNCT
ejpam-2231	262	1	let	let	VERB
ejpam-2231	262	2	s	s	PRON
ejpam-2231	262	3	be	be	AUX
ejpam-2231	262	4	a	a	DET
ejpam-2231	262	5	unitary	unitary	ADJ
ejpam-2231	262	6	la	la	ADJ
ejpam-2231	262	7	-semigroup	-semigroup	NOUN
ejpam-2231	262	8	and	and	CCONJ
ejpam-2231	262	9	let	let	VERB
ejpam-2231	262	10	〈	〈	PROPN
ejpam-2231	262	11	a〉(m	a〉(m	NOUN
ejpam-2231	262	12	,	,	PUNCT
ejpam-2231	262	13	n	n	CCONJ
ejpam-2231	262	14	)	)	PUNCT
ejpam-2231	262	15	be	be	AUX
ejpam-2231	262	16	an	an	DET
ejpam-2231	262	17	(	(	PUNCT
ejpam-2231	262	18	m	m	PROPN
ejpam-2231	262	19	,	,	PUNCT
ejpam-2231	262	20	n)-ideal	n)-ideal	NOUN
ejpam-2231	262	21	of	of	ADP
ejpam-2231	262	22	s.	s.	PROPN
ejpam-2231	262	23	then	then	ADV
ejpam-2231	262	24	the	the	DET
ejpam-2231	262	25	following	follow	VERB
ejpam-2231	262	26	statements	statement	NOUN
ejpam-2231	262	27	hold	hold	VERB
ejpam-2231	262	28	:	:	PUNCT
ejpam-2231	262	29	(	(	PUNCT
ejpam-2231	262	30	i	i	NOUN
ejpam-2231	262	31	)	)	PUNCT
ejpam-2231	262	32	�	�	PROPN
ejpam-2231	262	33	〈	〈	NOUN
ejpam-2231	262	34	a〉(1,0	a〉(1,0	PROPN
ejpam-2231	262	35	)	)	PUNCT
ejpam-2231	262	36	�	�	PROPN
ejpam-2231	262	37	m	m	NOUN
ejpam-2231	262	38	s	s	PART
ejpam-2231	262	39	=	=	X
ejpam-2231	262	40	sam	sam	PROPN
ejpam-2231	262	41	;	;	PUNCT
ejpam-2231	262	42	(	(	PUNCT
ejpam-2231	262	43	ii	ii	NOUN
ejpam-2231	262	44	)	)	PUNCT
ejpam-2231	262	45	s	s	PART
ejpam-2231	262	46	�	�	PROPN
ejpam-2231	262	47	〈	〈	PROPN
ejpam-2231	262	48	a〉(0,1	a〉(0,1	NOUN
ejpam-2231	262	49	)	)	PUNCT
ejpam-2231	262	50	�	�	PROPN
ejpam-2231	262	51	n	n	NOUN
ejpam-2231	262	52	=	=	SYM
ejpam-2231	262	53	ans	ans	X
ejpam-2231	262	54	;	;	PUNCT
ejpam-2231	262	55	(	(	PUNCT
ejpam-2231	262	56	iii	iii	X
ejpam-2231	262	57	)	)	PUNCT
ejpam-2231	262	58	�	�	PROPN
ejpam-2231	262	59	〈	〈	NOUN
ejpam-2231	262	60	a〉(1,0	a〉(1,0	PROPN
ejpam-2231	262	61	)	)	PUNCT
ejpam-2231	262	62	�	�	PROPN
ejpam-2231	262	63	m	m	PROPN
ejpam-2231	262	64	s	s	PART
ejpam-2231	262	65	·	·	PUNCT
ejpam-2231	262	66	�	�	PROPN
ejpam-2231	262	67	〈	〈	NOUN
ejpam-2231	262	68	a〉(0,1	a〉(0,1	NOUN
ejpam-2231	262	69	)	)	PUNCT
ejpam-2231	262	70	�	�	PROPN
ejpam-2231	262	71	n	n	NOUN
ejpam-2231	262	72	=	=	SYM
ejpam-2231	262	73	(	(	PUNCT
ejpam-2231	262	74	sam)(ans	sam)(an	NOUN
ejpam-2231	262	75	)	)	PUNCT
ejpam-2231	262	76	.	.	PUNCT
ejpam-2231	263	1	let	let	VERB
ejpam-2231	263	2	l(0,n	l(0,n	ADJ
ejpam-2231	263	3	)	)	PUNCT
ejpam-2231	263	4	,	,	PUNCT
ejpam-2231	263	5	r(m,0	r(m,0	PROPN
ejpam-2231	263	6	)	)	PUNCT
ejpam-2231	263	7	and	and	CCONJ
ejpam-2231	263	8	a(m	a(m	PROPN
ejpam-2231	263	9	,	,	PUNCT
ejpam-2231	263	10	n	n	CCONJ
ejpam-2231	263	11	)	)	PUNCT
ejpam-2231	263	12	denote	denote	VERB
ejpam-2231	263	13	the	the	DET
ejpam-2231	263	14	sets	set	NOUN
ejpam-2231	263	15	of	of	ADP
ejpam-2231	263	16	(	(	PUNCT
ejpam-2231	263	17	0	0	NUM
ejpam-2231	263	18	,	,	PUNCT
ejpam-2231	263	19	n)-ideals	n)-ideal	NOUN
ejpam-2231	263	20	,	,	PUNCT
ejpam-2231	263	21	(	(	PUNCT
ejpam-2231	263	22	m	m	NOUN
ejpam-2231	263	23	,	,	PUNCT
ejpam-2231	263	24	0)-ideals	0)-ideal	NOUN
ejpam-2231	263	25	and	and	CCONJ
ejpam-2231	263	26	(	(	PUNCT
ejpam-2231	263	27	m	m	PROPN
ejpam-2231	263	28	,	,	PUNCT
ejpam-2231	263	29	n)-ideals	n)-ideal	NOUN
ejpam-2231	263	30	of	of	ADP
ejpam-2231	263	31	an	an	DET
ejpam-2231	263	32	la	la	PROPN
ejpam-2231	263	33	-semigroup	-semigroup	NOUN
ejpam-2231	263	34	s	s	PART
ejpam-2231	263	35	respectively	respectively	ADV
ejpam-2231	263	36	.	.	PUNCT
ejpam-2231	264	1	theorem	theorem	ADJ
ejpam-2231	264	2	10	10	NUM
ejpam-2231	264	3	.	.	PUNCT
ejpam-2231	265	1	if	if	SCONJ
ejpam-2231	265	2	s	s	PROPN
ejpam-2231	265	3	is	be	AUX
ejpam-2231	265	4	a	a	DET
ejpam-2231	265	5	unitary	unitary	ADJ
ejpam-2231	265	6	la	la	ADJ
ejpam-2231	265	7	-semigroup	-semigroup	NOUN
ejpam-2231	265	8	,	,	PUNCT
ejpam-2231	265	9	then	then	ADV
ejpam-2231	265	10	the	the	DET
ejpam-2231	265	11	following	following	ADJ
ejpam-2231	265	12	statements	statement	NOUN
ejpam-2231	265	13	hold	hold	VERB
ejpam-2231	265	14	:	:	PUNCT
ejpam-2231	265	15	(	(	PUNCT
ejpam-2231	265	16	i	i	NOUN
ejpam-2231	265	17	)	)	PUNCT
ejpam-2231	265	18	s	s	VERB
ejpam-2231	265	19	is	be	AUX
ejpam-2231	265	20	(	(	PUNCT
ejpam-2231	265	21	0,1)-regular	0,1)-regular	NUM
ejpam-2231	266	1	if	if	SCONJ
ejpam-2231	266	2	and	and	CCONJ
ejpam-2231	266	3	only	only	ADV
ejpam-2231	266	4	if	if	SCONJ
ejpam-2231	266	5	∀l	∀l	NOUN
ejpam-2231	266	6	∈	∈	PROPN
ejpam-2231	266	7	l(0,1	l(0,1	PROPN
ejpam-2231	266	8	)	)	PUNCT
ejpam-2231	266	9	,	,	PUNCT
ejpam-2231	266	10	l	l	NOUN
ejpam-2231	266	11	=	=	SYM
ejpam-2231	266	12	sl	sl	PROPN
ejpam-2231	266	13	;	;	PUNCT
ejpam-2231	266	14	(	(	PUNCT
ejpam-2231	266	15	ii	ii	NOUN
ejpam-2231	266	16	)	)	PUNCT
ejpam-2231	266	17	s	s	VERB
ejpam-2231	266	18	is	be	AUX
ejpam-2231	266	19	(	(	PUNCT
ejpam-2231	266	20	2,0)-regular	2,0)-regular	NUM
ejpam-2231	266	21	if	if	SCONJ
ejpam-2231	266	22	and	and	CCONJ
ejpam-2231	266	23	only	only	ADV
ejpam-2231	266	24	if	if	SCONJ
ejpam-2231	266	25	∀r	∀r	NOUN
ejpam-2231	266	26	∈r(2,0	∈r(2,0	PROPN
ejpam-2231	266	27	)	)	PUNCT
ejpam-2231	266	28	,	,	PUNCT
ejpam-2231	266	29	r=	r=	ADJ
ejpam-2231	266	30	r2s	r2	NOUN
ejpam-2231	266	31	such	such	ADJ
ejpam-2231	266	32	that	that	SCONJ
ejpam-2231	266	33	every	every	DET
ejpam-2231	266	34	r	r	NOUN
ejpam-2231	266	35	is	be	AUX
ejpam-2231	266	36	semiprime	semiprime	NOUN
ejpam-2231	266	37	;	;	PUNCT
ejpam-2231	266	38	(	(	PUNCT
ejpam-2231	266	39	iii	iii	X
ejpam-2231	266	40	)	)	PUNCT
ejpam-2231	266	41	s	s	VERB
ejpam-2231	266	42	is	be	AUX
ejpam-2231	266	43	(	(	PUNCT
ejpam-2231	266	44	0,2)-regular	0,2)-regular	NUM
ejpam-2231	266	45	if	if	SCONJ
ejpam-2231	266	46	and	and	CCONJ
ejpam-2231	266	47	only	only	ADV
ejpam-2231	266	48	if	if	SCONJ
ejpam-2231	266	49	∀u	∀u	NOUN
ejpam-2231	266	50	∈	∈	NUM
ejpam-2231	266	51	a(0,2	a(0,2	NOUN
ejpam-2231	266	52	)	)	PUNCT
ejpam-2231	266	53	,	,	PUNCT
ejpam-2231	266	54	u	u	NOUN
ejpam-2231	266	55	=	=	PUNCT
ejpam-2231	266	56	u2s	u2s	VERB
ejpam-2231	266	57	such	such	ADJ
ejpam-2231	266	58	that	that	SCONJ
ejpam-2231	266	59	every	every	DET
ejpam-2231	266	60	u	u	NOUN
ejpam-2231	266	61	is	be	AUX
ejpam-2231	266	62	semiprime	semiprime	NOUN
ejpam-2231	266	63	.	.	PUNCT
ejpam-2231	267	1	proof	proof	NOUN
ejpam-2231	267	2	.	.	PUNCT
ejpam-2231	268	1	(	(	PUNCT
ejpam-2231	268	2	i	i	NOUN
ejpam-2231	268	3	)	)	PUNCT
ejpam-2231	268	4	.	.	PUNCT
ejpam-2231	269	1	let	let	VERB
ejpam-2231	269	2	s	s	PRON
ejpam-2231	269	3	be	be	AUX
ejpam-2231	269	4	(	(	PUNCT
ejpam-2231	269	5	0,1)-regular	0,1)-regular	NUM
ejpam-2231	269	6	,	,	PUNCT
ejpam-2231	269	7	then	then	ADV
ejpam-2231	269	8	for	for	ADP
ejpam-2231	269	9	a	a	DET
ejpam-2231	269	10	∈	∈	NOUN
ejpam-2231	269	11	s	s	PART
ejpam-2231	269	12	there	there	PRON
ejpam-2231	269	13	exists	exist	VERB
ejpam-2231	269	14	x	x	X
ejpam-2231	269	15	∈	∈	NOUN
ejpam-2231	269	16	s	s	VERB
ejpam-2231	269	17	such	such	ADJ
ejpam-2231	269	18	that	that	SCONJ
ejpam-2231	269	19	a	a	DET
ejpam-2231	269	20	=	=	SYM
ejpam-2231	269	21	xa	xa	PROPN
ejpam-2231	269	22	.	.	PUNCT
ejpam-2231	270	1	since	since	SCONJ
ejpam-2231	270	2	l	l	PROPN
ejpam-2231	270	3	is	be	AUX
ejpam-2231	270	4	(	(	PUNCT
ejpam-2231	270	5	0,1)-ideal	0,1)-ideal	ADJ
ejpam-2231	270	6	,	,	PUNCT
ejpam-2231	270	7	therefore	therefore	ADV
ejpam-2231	270	8	sl	sl	VERB
ejpam-2231	270	9	⊆	⊆	NUM
ejpam-2231	270	10	l.	l.	NOUN
ejpam-2231	270	11	let	let	VERB
ejpam-2231	270	12	a	a	DET
ejpam-2231	270	13	∈	∈	PROPN
ejpam-2231	270	14	l	l	NOUN
ejpam-2231	270	15	,	,	PUNCT
ejpam-2231	270	16	then	then	ADV
ejpam-2231	270	17	a	a	DET
ejpam-2231	270	18	=	=	X
ejpam-2231	270	19	xa	xa	PROPN
ejpam-2231	270	20	∈	∈	PROPN
ejpam-2231	270	21	sl	sl	VERB
ejpam-2231	270	22	⊆	⊆	NUM
ejpam-2231	270	23	l.	l.	NOUN
ejpam-2231	270	24	hence	hence	ADV
ejpam-2231	270	25	l	l	NOUN
ejpam-2231	270	26	=	=	SYM
ejpam-2231	270	27	sl	sl	PROPN
ejpam-2231	270	28	.	.	PUNCT
ejpam-2231	270	29	converse	converse	NOUN
ejpam-2231	270	30	is	be	AUX
ejpam-2231	270	31	simple	simple	ADJ
ejpam-2231	270	32	.	.	PUNCT
ejpam-2231	271	1	(	(	PUNCT
ejpam-2231	271	2	ii	ii	NOUN
ejpam-2231	271	3	)	)	PUNCT
ejpam-2231	271	4	.	.	PUNCT
ejpam-2231	272	1	let	let	VERB
ejpam-2231	272	2	s	s	PRON
ejpam-2231	272	3	be	be	AUX
ejpam-2231	272	4	(	(	PUNCT
ejpam-2231	272	5	2,0)-regular	2,0)-regular	NUM
ejpam-2231	272	6	and	and	CCONJ
ejpam-2231	272	7	r	r	NOUN
ejpam-2231	272	8	be	be	VERB
ejpam-2231	272	9	(	(	PUNCT
ejpam-2231	272	10	2,0)-ideal	2,0)-ideal	NUM
ejpam-2231	272	11	of	of	ADP
ejpam-2231	272	12	s	s	PROPN
ejpam-2231	272	13	,	,	PUNCT
ejpam-2231	272	14	then	then	ADV
ejpam-2231	272	15	it	it	PRON
ejpam-2231	272	16	is	be	AUX
ejpam-2231	272	17	easy	easy	ADJ
ejpam-2231	272	18	to	to	PART
ejpam-2231	272	19	see	see	VERB
ejpam-2231	272	20	that	that	DET
ejpam-2231	272	21	r	r	NOUN
ejpam-2231	272	22	=	=	SYM
ejpam-2231	272	23	r2s	r2s	X
ejpam-2231	272	24	.	.	PUNCT
ejpam-2231	273	1	now	now	ADV
ejpam-2231	273	2	for	for	ADP
ejpam-2231	273	3	a	a	DET
ejpam-2231	273	4	∈	∈	NOUN
ejpam-2231	273	5	s	s	PART
ejpam-2231	273	6	there	there	PRON
ejpam-2231	273	7	exists	exist	VERB
ejpam-2231	273	8	x	x	X
ejpam-2231	273	9	∈	∈	NOUN
ejpam-2231	273	10	s	s	VERB
ejpam-2231	273	11	such	such	ADJ
ejpam-2231	273	12	that	that	SCONJ
ejpam-2231	273	13	a	a	DET
ejpam-2231	273	14	=	=	NOUN
ejpam-2231	273	15	a2	a2	PROPN
ejpam-2231	273	16	x	x	X
ejpam-2231	273	17	.	.	PUNCT
ejpam-2231	274	1	let	let	VERB
ejpam-2231	274	2	a2	a2	PROPN
ejpam-2231	274	3	∈	∈	PROPN
ejpam-2231	274	4	r	r	NOUN
ejpam-2231	274	5	,	,	PUNCT
ejpam-2231	274	6	then	then	ADV
ejpam-2231	274	7	a	a	DET
ejpam-2231	274	8	=	=	NOUN
ejpam-2231	274	9	a2	a2	PROPN
ejpam-2231	274	10	x	x	SYM
ejpam-2231	274	11	∈	∈	NOUN
ejpam-2231	274	12	rs	rs	NOUN
ejpam-2231	274	13	=	=	PUNCT
ejpam-2231	274	14	r2s	r2s	X
ejpam-2231	274	15	·	·	PUNCT
ejpam-2231	274	16	s	s	PART
ejpam-2231	274	17	=	=	PUNCT
ejpam-2231	274	18	ss	ss	NOUN
ejpam-2231	274	19	·	·	PUNCT
ejpam-2231	274	20	r2	r2	NOUN
ejpam-2231	274	21	=	=	PUNCT
ejpam-2231	274	22	r2s	r2s	X
ejpam-2231	274	23	=	=	SYM
ejpam-2231	274	24	r	r	NOUN
ejpam-2231	274	25	,	,	PUNCT
ejpam-2231	274	26	which	which	PRON
ejpam-2231	274	27	shows	show	VERB
ejpam-2231	274	28	that	that	SCONJ
ejpam-2231	274	29	every	every	PRON
ejpam-2231	274	30	(	(	PUNCT
ejpam-2231	274	31	2,0)-ideal	2,0)-ideal	NUM
ejpam-2231	274	32	is	be	AUX
ejpam-2231	274	33	semiprime	semiprime	NOUN
ejpam-2231	274	34	.	.	PUNCT
ejpam-2231	275	1	conversely	conversely	ADV
ejpam-2231	275	2	,	,	PUNCT
ejpam-2231	275	3	let	let	VERB
ejpam-2231	275	4	r	r	NOUN
ejpam-2231	275	5	=	=	NOUN
ejpam-2231	275	6	r2s	r2s	NOUN
ejpam-2231	275	7	for	for	ADP
ejpam-2231	275	8	every	every	DET
ejpam-2231	275	9	r	r	NOUN
ejpam-2231	275	10	∈	∈	PROPN
ejpam-2231	275	11	r(2,0	r(2,0	PROPN
ejpam-2231	275	12	)	)	PUNCT
ejpam-2231	275	13	.	.	PUNCT
ejpam-2231	276	1	since	since	SCONJ
ejpam-2231	276	2	sa2	sa2	PROPN
ejpam-2231	276	3	is	be	AUX
ejpam-2231	276	4	a	a	DET
ejpam-2231	276	5	(	(	PUNCT
ejpam-2231	276	6	2,0)-ideal	2,0)-ideal	NUM
ejpam-2231	276	7	of	of	ADP
ejpam-2231	276	8	s	s	PRON
ejpam-2231	276	9	such	such	ADJ
ejpam-2231	276	10	that	that	SCONJ
ejpam-2231	276	11	a2	a2	PROPN
ejpam-2231	276	12	∈	∈	PROPN
ejpam-2231	276	13	sa2	sa2	PROPN
ejpam-2231	276	14	,	,	PUNCT
ejpam-2231	276	15	therefore	therefore	ADV
ejpam-2231	276	16	a	a	DET
ejpam-2231	276	17	∈	∈	PROPN
ejpam-2231	276	18	sa2	sa2	NOUN
ejpam-2231	276	19	.	.	PUNCT
ejpam-2231	277	1	thus	thus	ADV
ejpam-2231	277	2	a	a	DET
ejpam-2231	277	3	∈sa2	∈sa2	NOUN
ejpam-2231	277	4	=	=	SYM
ejpam-2231	277	5	(	(	PUNCT
ejpam-2231	277	6	sa2)2s	sa2)2s	NOUN
ejpam-2231	277	7	=	=	SYM
ejpam-2231	277	8	(	(	PUNCT
ejpam-2231	277	9	sa2	sa2	NOUN
ejpam-2231	277	10	·	·	PUNCT
ejpam-2231	277	11	sa2)s	sa2)s	PROPN
ejpam-2231	278	1	=	=	CCONJ
ejpam-2231	278	2	(	(	PUNCT
ejpam-2231	278	3	a2s	a2s	PROPN
ejpam-2231	278	4	·	·	PUNCT
ejpam-2231	278	5	a2s)s	a2s)s	X
ejpam-2231	279	1	=	=	PUNCT
ejpam-2231	280	1	[	[	X
ejpam-2231	280	2	a2(a2s	a2(a2s	NOUN
ejpam-2231	280	3	·	·	PUNCT
ejpam-2231	280	4	s)]s	s)]s	NUM
ejpam-2231	280	5	=(	=(	NOUN
ejpam-2231	280	6	a2	a2	PROPN
ejpam-2231	280	7	·	·	PUNCT
ejpam-2231	280	8	sa2)s	sa2)s	PROPN
ejpam-2231	280	9	=	=	PUNCT
ejpam-2231	280	10	(	(	PUNCT
ejpam-2231	280	11	s	s	X
ejpam-2231	280	12	·	·	PUNCT
ejpam-2231	280	13	sa2)a2	sa2)a2	NUM
ejpam-2231	280	14	⊆	⊆	NUM
ejpam-2231	280	15	sa2	sa2	NOUN
ejpam-2231	280	16	=	=	SYM
ejpam-2231	280	17	a2s	a2s	PROPN
ejpam-2231	280	18	,	,	PUNCT
ejpam-2231	280	19	which	which	PRON
ejpam-2231	280	20	implies	imply	VERB
ejpam-2231	280	21	that	that	SCONJ
ejpam-2231	280	22	s	s	VERB
ejpam-2231	280	23	is	be	AUX
ejpam-2231	280	24	(	(	PUNCT
ejpam-2231	280	25	2,0)-regular	2,0)-regular	NUM
ejpam-2231	280	26	.	.	PUNCT
ejpam-2231	281	1	analogously	analogously	ADV
ejpam-2231	281	2	,	,	PUNCT
ejpam-2231	281	3	we	we	PRON
ejpam-2231	281	4	can	can	AUX
ejpam-2231	281	5	prove	prove	VERB
ejpam-2231	281	6	(	(	PUNCT
ejpam-2231	281	7	iii	iii	NOUN
ejpam-2231	281	8	)	)	PUNCT
ejpam-2231	281	9	.	.	PUNCT
ejpam-2231	282	1	w.	w.	PROPN
ejpam-2231	282	2	khan	khan	PROPN
ejpam-2231	282	3	,	,	PUNCT
ejpam-2231	282	4	f.	f.	PROPN
ejpam-2231	282	5	yousafzai	yousafzai	PROPN
ejpam-2231	282	6	,	,	PUNCT
ejpam-2231	282	7	and	and	CCONJ
ejpam-2231	282	8	m.	m.	PROPN
ejpam-2231	282	9	khan	khan	PROPN
ejpam-2231	282	10	/	/	SYM
ejpam-2231	282	11	eur	eur	PROPN
ejpam-2231	282	12	.	.	PUNCT
ejpam-2231	283	1	j.	j.	PROPN
ejpam-2231	283	2	pure	pure	PROPN
ejpam-2231	283	3	appl	appl	PROPN
ejpam-2231	283	4	.	.	PROPN
ejpam-2231	283	5	math	math	PROPN
ejpam-2231	283	6	,	,	PUNCT
ejpam-2231	283	7	9	9	NUM
ejpam-2231	283	8	(	(	PUNCT
ejpam-2231	283	9	2016	2016	NUM
ejpam-2231	283	10	)	)	PUNCT
ejpam-2231	283	11	,	,	PUNCT
ejpam-2231	283	12	277	277	NUM
ejpam-2231	283	13	-	-	SYM
ejpam-2231	283	14	291	291	NUM
ejpam-2231	283	15	289	289	NUM
ejpam-2231	283	16	lemma	lemma	PROPN
ejpam-2231	283	17	9	9	NUM
ejpam-2231	283	18	.	.	PUNCT
ejpam-2231	284	1	if	if	SCONJ
ejpam-2231	284	2	s	s	PROPN
ejpam-2231	284	3	is	be	AUX
ejpam-2231	284	4	a	a	DET
ejpam-2231	284	5	unitary	unitary	ADJ
ejpam-2231	284	6	la	la	ADJ
ejpam-2231	284	7	-semigroup	-semigroup	NOUN
ejpam-2231	284	8	,	,	PUNCT
ejpam-2231	284	9	then	then	ADV
ejpam-2231	284	10	the	the	DET
ejpam-2231	284	11	following	following	ADJ
ejpam-2231	284	12	statements	statement	NOUN
ejpam-2231	284	13	hold	hold	VERB
ejpam-2231	284	14	:	:	PUNCT
ejpam-2231	284	15	(	(	PUNCT
ejpam-2231	284	16	i	i	NOUN
ejpam-2231	284	17	)	)	PUNCT
ejpam-2231	284	18	if	if	SCONJ
ejpam-2231	284	19	s	s	VERB
ejpam-2231	284	20	is	be	AUX
ejpam-2231	284	21	(	(	PUNCT
ejpam-2231	284	22	0	0	NUM
ejpam-2231	284	23	,	,	PUNCT
ejpam-2231	284	24	n)-regular	n)-regular	X
ejpam-2231	284	25	,	,	PUNCT
ejpam-2231	284	26	then	then	ADV
ejpam-2231	284	27	∀l	∀l	NOUN
ejpam-2231	284	28	∈	∈	NOUN
ejpam-2231	284	29	l(0,n	l(0,n	NOUN
ejpam-2231	284	30	)	)	PUNCT
ejpam-2231	284	31	,	,	PUNCT
ejpam-2231	284	32	l	l	NOUN
ejpam-2231	285	1	=	=	SYM
ejpam-2231	285	2	sln	sln	PROPN
ejpam-2231	285	3	;	;	PUNCT
ejpam-2231	285	4	(	(	PUNCT
ejpam-2231	285	5	ii	ii	NOUN
ejpam-2231	285	6	)	)	PUNCT
ejpam-2231	285	7	if	if	SCONJ
ejpam-2231	285	8	s	s	VERB
ejpam-2231	285	9	is	be	AUX
ejpam-2231	285	10	(	(	PUNCT
ejpam-2231	285	11	m	m	PROPN
ejpam-2231	285	12	,	,	PUNCT
ejpam-2231	285	13	0)-regular	0)-regular	NUM
ejpam-2231	285	14	,	,	PUNCT
ejpam-2231	285	15	then	then	ADV
ejpam-2231	285	16	∀r	∀r	NOUN
ejpam-2231	285	17	∈r(m,0	∈r(m,0	NOUN
ejpam-2231	285	18	)	)	PUNCT
ejpam-2231	285	19	,	,	PUNCT
ejpam-2231	285	20	r=	r=	ADJ
ejpam-2231	285	21	rms	rm	NOUN
ejpam-2231	285	22	;	;	PUNCT
ejpam-2231	285	23	(	(	PUNCT
ejpam-2231	285	24	iii	iii	X
ejpam-2231	285	25	)	)	PUNCT
ejpam-2231	285	26	if	if	SCONJ
ejpam-2231	285	27	s	s	VERB
ejpam-2231	285	28	is	be	AUX
ejpam-2231	285	29	(	(	PUNCT
ejpam-2231	285	30	m	m	X
ejpam-2231	285	31	,	,	PUNCT
ejpam-2231	285	32	n)-regular	n)-regular	X
ejpam-2231	285	33	,	,	PUNCT
ejpam-2231	285	34	then	then	ADV
ejpam-2231	285	35	∀u	∀u	NOUN
ejpam-2231	285	36	∈	∈	PROPN
ejpam-2231	285	37	a(m	a(m	NOUN
ejpam-2231	285	38	,	,	PUNCT
ejpam-2231	285	39	n	n	CCONJ
ejpam-2231	285	40	)	)	PUNCT
ejpam-2231	285	41	,	,	PUNCT
ejpam-2231	285	42	u	u	NOUN
ejpam-2231	285	43	=	=	PUNCT
ejpam-2231	285	44	(	(	PUNCT
ejpam-2231	285	45	ums)un	ums)un	ADV
ejpam-2231	285	46	.	.	PUNCT
ejpam-2231	286	1	proof	proof	NOUN
ejpam-2231	286	2	.	.	PUNCT
ejpam-2231	287	1	it	it	PRON
ejpam-2231	287	2	is	be	AUX
ejpam-2231	287	3	simple	simple	ADJ
ejpam-2231	287	4	.	.	PUNCT
ejpam-2231	288	1	corollary	corollary	ADJ
ejpam-2231	288	2	6	6	NUM
ejpam-2231	288	3	.	.	PUNCT
ejpam-2231	289	1	if	if	SCONJ
ejpam-2231	289	2	s	s	PROPN
ejpam-2231	289	3	is	be	AUX
ejpam-2231	289	4	a	a	DET
ejpam-2231	289	5	unitary	unitary	ADJ
ejpam-2231	289	6	la	la	ADJ
ejpam-2231	289	7	-semigroup	-semigroup	NOUN
ejpam-2231	289	8	,	,	PUNCT
ejpam-2231	289	9	then	then	ADV
ejpam-2231	289	10	the	the	DET
ejpam-2231	289	11	following	following	ADJ
ejpam-2231	289	12	statements	statement	NOUN
ejpam-2231	289	13	hold	hold	VERB
ejpam-2231	289	14	:	:	PUNCT
ejpam-2231	289	15	(	(	PUNCT
ejpam-2231	289	16	i	i	NOUN
ejpam-2231	289	17	)	)	PUNCT
ejpam-2231	289	18	if	if	SCONJ
ejpam-2231	289	19	s	s	VERB
ejpam-2231	289	20	is	be	AUX
ejpam-2231	289	21	(	(	PUNCT
ejpam-2231	289	22	0	0	NUM
ejpam-2231	289	23	,	,	PUNCT
ejpam-2231	289	24	n)-regular	n)-regular	X
ejpam-2231	289	25	,	,	PUNCT
ejpam-2231	289	26	then	then	ADV
ejpam-2231	289	27	∀l	∀l	NOUN
ejpam-2231	289	28	∈	∈	NOUN
ejpam-2231	289	29	l(0,n	l(0,n	NOUN
ejpam-2231	289	30	)	)	PUNCT
ejpam-2231	289	31	,	,	PUNCT
ejpam-2231	289	32	l	l	NOUN
ejpam-2231	289	33	=	=	SYM
ejpam-2231	289	34	lns	lns	PROPN
ejpam-2231	289	35	;	;	PUNCT
ejpam-2231	289	36	(	(	PUNCT
ejpam-2231	289	37	ii	ii	NOUN
ejpam-2231	289	38	)	)	PUNCT
ejpam-2231	289	39	if	if	SCONJ
ejpam-2231	289	40	s	s	VERB
ejpam-2231	289	41	is	be	AUX
ejpam-2231	289	42	(	(	PUNCT
ejpam-2231	289	43	m	m	PROPN
ejpam-2231	289	44	,	,	PUNCT
ejpam-2231	289	45	0)-regular	0)-regular	NUM
ejpam-2231	289	46	,	,	PUNCT
ejpam-2231	289	47	then	then	ADV
ejpam-2231	289	48	∀r	∀r	NOUN
ejpam-2231	289	49	∈r(m,0	∈r(m,0	NOUN
ejpam-2231	289	50	)	)	PUNCT
ejpam-2231	289	51	,	,	PUNCT
ejpam-2231	289	52	r=	r=	PROPN
ejpam-2231	289	53	srm	srm	PROPN
ejpam-2231	289	54	;	;	PUNCT
ejpam-2231	289	55	(	(	PUNCT
ejpam-2231	289	56	iii	iii	X
ejpam-2231	289	57	)	)	PUNCT
ejpam-2231	289	58	if	if	SCONJ
ejpam-2231	289	59	s	s	VERB
ejpam-2231	289	60	is	be	AUX
ejpam-2231	289	61	(	(	PUNCT
ejpam-2231	289	62	m	m	X
ejpam-2231	289	63	,	,	PUNCT
ejpam-2231	289	64	n)-regular	n)-regular	X
ejpam-2231	289	65	,	,	PUNCT
ejpam-2231	289	66	then	then	ADV
ejpam-2231	289	67	∀u	∀u	NOUN
ejpam-2231	289	68	∈	∈	PROPN
ejpam-2231	289	69	a(m	a(m	NOUN
ejpam-2231	289	70	,	,	PUNCT
ejpam-2231	289	71	n	n	CCONJ
ejpam-2231	289	72	)	)	PUNCT
ejpam-2231	289	73	,	,	PUNCT
ejpam-2231	289	74	u	u	NOUN
ejpam-2231	290	1	=	=	PUNCT
ejpam-2231	290	2	um+ns	um+ns	PROPN
ejpam-2231	290	3	=	=	PUNCT
ejpam-2231	290	4	sum+n	sum+n	PROPN
ejpam-2231	290	5	.	.	PUNCT
ejpam-2231	290	6	theorem	theorem	VERB
ejpam-2231	290	7	11	11	NUM
ejpam-2231	290	8	.	.	PUNCT
ejpam-2231	291	1	let	let	VERB
ejpam-2231	291	2	s	s	PRON
ejpam-2231	291	3	be	be	AUX
ejpam-2231	291	4	a	a	DET
ejpam-2231	291	5	unitary	unitary	ADJ
ejpam-2231	291	6	(	(	PUNCT
ejpam-2231	291	7	m	m	PROPN
ejpam-2231	291	8	,	,	PUNCT
ejpam-2231	291	9	n)-regularla	n)-regularla	X
ejpam-2231	291	10	-semigroup	-semigroup	NOUN
ejpam-2231	291	11	such	such	ADJ
ejpam-2231	291	12	that	that	SCONJ
ejpam-2231	291	13	m=	m=	AUX
ejpam-2231	291	14	n.	n.	NOUN
ejpam-2231	291	15	then	then	ADV
ejpam-2231	291	16	for	for	ADP
ejpam-2231	291	17	every	every	DET
ejpam-2231	291	18	r	r	NOUN
ejpam-2231	291	19	∈r(m,0	∈r(m,0	NOUN
ejpam-2231	291	20	)	)	PUNCT
ejpam-2231	291	21	and	and	CCONJ
ejpam-2231	291	22	l	l	NOUN
ejpam-2231	291	23	∈	∈	PROPN
ejpam-2231	291	24	l(0,n	l(0,n	NOUN
ejpam-2231	291	25	)	)	PUNCT
ejpam-2231	291	26	,	,	PUNCT
ejpam-2231	291	27	r∩	r∩	AUX
ejpam-2231	291	28	l	l	NOUN
ejpam-2231	291	29	=	=	SYM
ejpam-2231	291	30	rm	rm	PROPN
ejpam-2231	291	31	l	l	PROPN
ejpam-2231	291	32	∩	∩	PROPN
ejpam-2231	291	33	rln	rln	PROPN
ejpam-2231	291	34	.	.	PUNCT
ejpam-2231	292	1	proof	proof	NOUN
ejpam-2231	292	2	.	.	PUNCT
ejpam-2231	293	1	it	it	PRON
ejpam-2231	293	2	is	be	AUX
ejpam-2231	293	3	simple	simple	ADJ
ejpam-2231	293	4	.	.	PUNCT
ejpam-2231	294	1	theorem	theorem	NOUN
ejpam-2231	294	2	12	12	NUM
ejpam-2231	294	3	.	.	PUNCT
ejpam-2231	295	1	let	let	VERB
ejpam-2231	295	2	s	s	PRON
ejpam-2231	295	3	be	be	AUX
ejpam-2231	295	4	a	a	DET
ejpam-2231	295	5	unitary	unitary	ADJ
ejpam-2231	295	6	(	(	PUNCT
ejpam-2231	295	7	m	m	PROPN
ejpam-2231	295	8	,	,	PUNCT
ejpam-2231	295	9	n)-regularla	n)-regularla	X
ejpam-2231	295	10	-semigroup	-semigroup	NOUN
ejpam-2231	295	11	.	.	PUNCT
ejpam-2231	296	1	if	if	SCONJ
ejpam-2231	296	2	m	m	PROPN
ejpam-2231	296	3	(	(	PUNCT
ejpam-2231	296	4	n	n	CCONJ
ejpam-2231	296	5	)	)	PUNCT
ejpam-2231	296	6	is	be	AUX
ejpam-2231	296	7	a	a	DET
ejpam-2231	296	8	0	0	NUM
ejpam-2231	296	9	-	-	PUNCT
ejpam-2231	296	10	minimal	minimal	ADJ
ejpam-2231	296	11	(	(	PUNCT
ejpam-2231	296	12	m	m	NOUN
ejpam-2231	296	13	,	,	PUNCT
ejpam-2231	296	14	0)ideal	0)ideal	ADJ
ejpam-2231	296	15	(	(	PUNCT
ejpam-2231	296	16	(	(	PUNCT
ejpam-2231	296	17	0	0	NUM
ejpam-2231	296	18	,	,	PUNCT
ejpam-2231	296	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	296	20	)	)	PUNCT
ejpam-2231	296	21	of	of	ADP
ejpam-2231	296	22	s	s	PRON
ejpam-2231	296	23	such	such	ADJ
ejpam-2231	296	24	that	that	SCONJ
ejpam-2231	296	25	mn	mn	PROPN
ejpam-2231	296	26	⊆	⊆	NUM
ejpam-2231	296	27	m	m	NOUN
ejpam-2231	296	28	∩	∩	NOUN
ejpam-2231	296	29	n	n	CCONJ
ejpam-2231	296	30	,	,	PUNCT
ejpam-2231	296	31	then	then	ADV
ejpam-2231	296	32	either	either	CCONJ
ejpam-2231	296	33	mn	mn	PROPN
ejpam-2231	296	34	=	=	PUNCT
ejpam-2231	296	35	{	{	PUNCT
ejpam-2231	296	36	0	0	NUM
ejpam-2231	296	37	}	}	PUNCT
ejpam-2231	296	38	or	or	CCONJ
ejpam-2231	296	39	mn	mn	PROPN
ejpam-2231	296	40	is	be	AUX
ejpam-2231	296	41	a	a	DET
ejpam-2231	296	42	0	0	NUM
ejpam-2231	296	43	-	-	PUNCT
ejpam-2231	296	44	minimal	minimal	ADJ
ejpam-2231	296	45	(	(	PUNCT
ejpam-2231	296	46	m	m	PROPN
ejpam-2231	296	47	,	,	PUNCT
ejpam-2231	296	48	n)-ideal	n)-ideal	NOUN
ejpam-2231	296	49	of	of	ADP
ejpam-2231	296	50	s.	s.	PROPN
ejpam-2231	296	51	proof	proof	PROPN
ejpam-2231	296	52	.	.	PUNCT
ejpam-2231	297	1	let	let	VERB
ejpam-2231	297	2	m	m	PROPN
ejpam-2231	297	3	(	(	PUNCT
ejpam-2231	297	4	n	n	CCONJ
ejpam-2231	297	5	)	)	PUNCT
ejpam-2231	297	6	be	be	AUX
ejpam-2231	297	7	a	a	DET
ejpam-2231	297	8	0	0	NUM
ejpam-2231	297	9	-	-	PUNCT
ejpam-2231	297	10	minimal	minimal	ADJ
ejpam-2231	297	11	(	(	PUNCT
ejpam-2231	297	12	m	m	PROPN
ejpam-2231	297	13	,	,	PUNCT
ejpam-2231	297	14	0)-ideal	0)-ideal	NUM
ejpam-2231	297	15	(	(	PUNCT
ejpam-2231	297	16	(	(	PUNCT
ejpam-2231	297	17	0	0	NUM
ejpam-2231	297	18	,	,	PUNCT
ejpam-2231	297	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	297	20	)	)	PUNCT
ejpam-2231	297	21	of	of	ADP
ejpam-2231	297	22	s.	s.	PROPN
ejpam-2231	297	23	let	let	VERB
ejpam-2231	297	24	o	o	PROPN
ejpam-2231	297	25	=	=	PROPN
ejpam-2231	297	26	mn	mn	PROPN
ejpam-2231	297	27	,	,	PUNCT
ejpam-2231	297	28	then	then	ADV
ejpam-2231	297	29	clearly	clearly	ADV
ejpam-2231	297	30	o2	o2	VERB
ejpam-2231	297	31	⊆	⊆	NUM
ejpam-2231	297	32	o.	o.	NOUN
ejpam-2231	297	33	moreover	moreover	ADV
ejpam-2231	297	34	oms	om	NOUN
ejpam-2231	297	35	·	·	PUNCT
ejpam-2231	297	36	on	on	ADP
ejpam-2231	297	37	=(	=(	NOUN
ejpam-2231	297	38	mn)ms	mn)ms	X
ejpam-2231	297	39	·	·	PUNCT
ejpam-2231	298	1	(	(	PUNCT
ejpam-2231	298	2	mn)n	mn)n	PROPN
ejpam-2231	298	3	=	=	SYM
ejpam-2231	298	4	(	(	PUNCT
ejpam-2231	298	5	m	m	PROPN
ejpam-2231	298	6	mn	mn	PROPN
ejpam-2231	298	7	m)s	m)s	ADJ
ejpam-2231	298	8	·	·	PUNCT
ejpam-2231	298	9	m	m	PROPN
ejpam-2231	298	10	nn	nn	PROPN
ejpam-2231	298	11	n	n	ADV
ejpam-2231	298	12	⊆	⊆	NUM
ejpam-2231	298	13	(	(	PUNCT
ejpam-2231	298	14	m	m	NOUN
ejpam-2231	298	15	ms)s	ms)s	NOUN
ejpam-2231	298	16	·	·	PUNCT
ejpam-2231	298	17	sn	sn	PROPN
ejpam-2231	298	18	n	n	PROPN
ejpam-2231	298	19	=	=	NOUN
ejpam-2231	298	20	sm	sm	PROPN
ejpam-2231	298	21	m	m	PROPN
ejpam-2231	298	22	·	·	PUNCT
ejpam-2231	298	23	sn	sn	PROPN
ejpam-2231	298	24	n	n	PROPN
ejpam-2231	298	25	=	=	NOUN
ejpam-2231	298	26	m	m	PROPN
ejpam-2231	298	27	ms	ms	NOUN
ejpam-2231	298	28	·	·	PUNCT
ejpam-2231	298	29	sn	sn	PROPN
ejpam-2231	298	30	n	n	PROPN
ejpam-2231	298	31	⊆	⊆	NUM
ejpam-2231	298	32	mn	mn	PROPN
ejpam-2231	298	33	=	=	SYM
ejpam-2231	298	34	o	o	NOUN
ejpam-2231	298	35	,	,	PUNCT
ejpam-2231	298	36	which	which	PRON
ejpam-2231	298	37	shows	show	VERB
ejpam-2231	298	38	that	that	SCONJ
ejpam-2231	298	39	o	o	NOUN
ejpam-2231	298	40	is	be	AUX
ejpam-2231	298	41	an	an	DET
ejpam-2231	298	42	(	(	PUNCT
ejpam-2231	298	43	m	m	PROPN
ejpam-2231	298	44	,	,	PUNCT
ejpam-2231	298	45	n)-ideal	n)-ideal	PROPN
ejpam-2231	298	46	of	of	ADP
ejpam-2231	298	47	s.	s.	PROPN
ejpam-2231	298	48	let	let	VERB
ejpam-2231	298	49	{	{	PUNCT
ejpam-2231	298	50	0	0	NUM
ejpam-2231	298	51	}	}	PUNCT
ejpam-2231	298	52	6=	6=	NUM
ejpam-2231	298	53	p	p	ADP
ejpam-2231	298	54	⊆	⊆	NUM
ejpam-2231	298	55	o	o	NOUN
ejpam-2231	298	56	be	be	AUX
ejpam-2231	298	57	a	a	DET
ejpam-2231	298	58	non	non	ADJ
ejpam-2231	298	59	-	-	ADJ
ejpam-2231	298	60	zero	zero	NUM
ejpam-2231	298	61	(	(	PUNCT
ejpam-2231	298	62	m	m	PROPN
ejpam-2231	298	63	,	,	PUNCT
ejpam-2231	298	64	n)-ideal	n)-ideal	NOUN
ejpam-2231	298	65	of	of	ADP
ejpam-2231	298	66	s.	s.	PROPN
ejpam-2231	298	67	since	since	SCONJ
ejpam-2231	298	68	s	s	PROPN
ejpam-2231	298	69	is	be	AUX
ejpam-2231	298	70	(	(	PUNCT
ejpam-2231	298	71	m	m	X
ejpam-2231	298	72	,	,	PUNCT
ejpam-2231	298	73	n)-regular	n)-regular	PRON
ejpam-2231	298	74	,	,	PUNCT
ejpam-2231	298	75	therefore	therefore	ADV
ejpam-2231	298	76	by	by	ADP
ejpam-2231	298	77	using	use	VERB
ejpam-2231	298	78	lemma	lemma	PROPN
ejpam-2231	298	79	9	9	NUM
ejpam-2231	298	80	,	,	PUNCT
ejpam-2231	298	81	we	we	PRON
ejpam-2231	298	82	have	have	VERB
ejpam-2231	298	83	{	{	PUNCT
ejpam-2231	298	84	0	0	NUM
ejpam-2231	298	85	}	}	SYM
ejpam-2231	298	86	6	6	NUM
ejpam-2231	298	87	=	=	NUM
ejpam-2231	298	88	p	p	NOUN
ejpam-2231	298	89	=	=	PUNCT
ejpam-2231	298	90	pms	pms	X
ejpam-2231	298	91	·	·	PUNCT
ejpam-2231	298	92	pn	pn	PROPN
ejpam-2231	299	1	=	=	SYM
ejpam-2231	299	2	(	(	PUNCT
ejpam-2231	299	3	pm	pm	NOUN
ejpam-2231	299	4	·	·	PUNCT
ejpam-2231	299	5	ss)pn	ss)pn	PUNCT
ejpam-2231	299	6	=	=	PUNCT
ejpam-2231	299	7	(	(	PUNCT
ejpam-2231	299	8	s	s	X
ejpam-2231	299	9	·	·	PUNCT
ejpam-2231	299	10	pms)pn	pms)pn	VERB
ejpam-2231	299	11	=	=	SYM
ejpam-2231	299	12	(	(	PUNCT
ejpam-2231	299	13	pn	pn	X
ejpam-2231	299	14	·	·	PUNCT
ejpam-2231	299	15	pms)(ss	pms)(ss	PROPN
ejpam-2231	299	16	)	)	PUNCT
ejpam-2231	299	17	=(	=(	NOUN
ejpam-2231	299	18	pns)(pms	pns)(pm	NOUN
ejpam-2231	299	19	·	·	PUNCT
ejpam-2231	299	20	s	s	X
ejpam-2231	299	21	)	)	PUNCT
ejpam-2231	299	22	=	=	SYM
ejpam-2231	299	23	pns	pns	PROPN
ejpam-2231	299	24	·	·	PUNCT
ejpam-2231	299	25	spm	spm	PROPN
ejpam-2231	299	26	=	=	SYM
ejpam-2231	299	27	pms	pms	PROPN
ejpam-2231	299	28	·	·	PUNCT
ejpam-2231	299	29	spn	spn	PROPN
ejpam-2231	299	30	.	.	PUNCT
ejpam-2231	300	1	hence	hence	ADV
ejpam-2231	300	2	pms	pms	PROPN
ejpam-2231	300	3	6=	6=	SYM
ejpam-2231	300	4	{	{	PUNCT
ejpam-2231	300	5	0	0	NUM
ejpam-2231	300	6	}	}	PUNCT
ejpam-2231	300	7	and	and	CCONJ
ejpam-2231	300	8	pms	pms	PROPN
ejpam-2231	300	9	6=	6=	SYM
ejpam-2231	300	10	{	{	PUNCT
ejpam-2231	300	11	0	0	NUM
ejpam-2231	300	12	}	}	PUNCT
ejpam-2231	300	13	.	.	PUNCT
ejpam-2231	301	1	further	far	ADV
ejpam-2231	301	2	p	p	NOUN
ejpam-2231	301	3	⊆	⊆	NUM
ejpam-2231	301	4	o	o	NOUN
ejpam-2231	301	5	=	=	SYM
ejpam-2231	301	6	mn	mn	PROPN
ejpam-2231	301	7	⊆	⊆	NUM
ejpam-2231	301	8	m	m	NOUN
ejpam-2231	301	9	∩	∩	NOUN
ejpam-2231	301	10	n	n	PRON
ejpam-2231	301	11	implies	imply	VERB
ejpam-2231	301	12	that	that	SCONJ
ejpam-2231	301	13	p	p	PROPN
ejpam-2231	301	14	⊆	⊆	NUM
ejpam-2231	301	15	m	m	NOUN
ejpam-2231	301	16	and	and	CCONJ
ejpam-2231	301	17	p	p	DET
ejpam-2231	301	18	⊆	⊆	NUM
ejpam-2231	301	19	n	n	NOUN
ejpam-2231	301	20	.	.	PUNCT
ejpam-2231	302	1	therefore	therefore	ADV
ejpam-2231	302	2	{	{	PUNCT
ejpam-2231	302	3	0	0	NUM
ejpam-2231	302	4	}	}	PUNCT
ejpam-2231	302	5	6=	6=	NUM
ejpam-2231	302	6	pms	pm	NOUN
ejpam-2231	302	7	⊆	⊆	NUM
ejpam-2231	302	8	m	m	NOUN
ejpam-2231	302	9	ms	ms	NOUN
ejpam-2231	302	10	⊆	⊆	NUM
ejpam-2231	302	11	m	m	NOUN
ejpam-2231	302	12	which	which	PRON
ejpam-2231	302	13	shows	show	VERB
ejpam-2231	302	14	that	that	SCONJ
ejpam-2231	302	15	pms	pm	NOUN
ejpam-2231	302	16	=	=	PUNCT
ejpam-2231	302	17	m	m	VERB
ejpam-2231	302	18	since	since	SCONJ
ejpam-2231	302	19	m	m	PROPN
ejpam-2231	302	20	is	be	AUX
ejpam-2231	302	21	0	0	NUM
ejpam-2231	302	22	-	-	PUNCT
ejpam-2231	302	23	minimal	minimal	ADJ
ejpam-2231	302	24	.	.	PUNCT
ejpam-2231	303	1	likewise	likewise	ADV
ejpam-2231	303	2	,	,	PUNCT
ejpam-2231	303	3	we	we	PRON
ejpam-2231	303	4	can	can	AUX
ejpam-2231	303	5	show	show	VERB
ejpam-2231	303	6	that	that	SCONJ
ejpam-2231	303	7	spn	spn	PROPN
ejpam-2231	303	8	=	=	PUNCT
ejpam-2231	303	9	n	n	PROPN
ejpam-2231	303	10	.	.	PUNCT
ejpam-2231	304	1	thus	thus	ADV
ejpam-2231	304	2	we	we	PRON
ejpam-2231	304	3	have	have	VERB
ejpam-2231	304	4	p	p	NOUN
ejpam-2231	304	5	⊆o	⊆o	NOUN
ejpam-2231	305	1	=	=	SYM
ejpam-2231	305	2	mn	mn	PROPN
ejpam-2231	305	3	=	=	SYM
ejpam-2231	305	4	pms	pms	PROPN
ejpam-2231	305	5	·	·	PUNCT
ejpam-2231	305	6	spn	spn	PROPN
ejpam-2231	305	7	=	=	SYM
ejpam-2231	305	8	pns	pns	PROPN
ejpam-2231	305	9	·	·	PUNCT
ejpam-2231	305	10	spm	spm	PROPN
ejpam-2231	305	11	=	=	SYM
ejpam-2231	305	12	(	(	PUNCT
ejpam-2231	305	13	spm	spm	PROPN
ejpam-2231	305	14	·	·	PUNCT
ejpam-2231	305	15	ss)pn	ss)pn	PUNCT
ejpam-2231	305	16	=(	=(	X
ejpam-2231	305	17	s	s	PART
ejpam-2231	305	18	·	·	PUNCT
ejpam-2231	305	19	pms)pn	pms)pn	ADJ
ejpam-2231	305	20	=	=	SYM
ejpam-2231	305	21	pms	pms	X
ejpam-2231	305	22	·	·	PUNCT
ejpam-2231	305	23	pn	pn	PROPN
ejpam-2231	305	24	⊆	⊆	NUM
ejpam-2231	306	1	p.	p.	NOUN
ejpam-2231	306	2	this	this	PRON
ejpam-2231	306	3	means	mean	VERB
ejpam-2231	306	4	that	that	SCONJ
ejpam-2231	306	5	p	p	PROPN
ejpam-2231	306	6	=	=	PROPN
ejpam-2231	306	7	mn	mn	PROPN
ejpam-2231	306	8	and	and	CCONJ
ejpam-2231	306	9	hence	hence	ADV
ejpam-2231	306	10	mn	mn	PROPN
ejpam-2231	306	11	is	be	AUX
ejpam-2231	306	12	0	0	NUM
ejpam-2231	306	13	-	-	PUNCT
ejpam-2231	306	14	minimal	minimal	ADJ
ejpam-2231	306	15	.	.	PUNCT
ejpam-2231	307	1	references	reference	NOUN
ejpam-2231	307	2	290	290	NUM
ejpam-2231	307	3	theorem	theorem	NOUN
ejpam-2231	307	4	13	13	NUM
ejpam-2231	307	5	.	.	PUNCT
ejpam-2231	308	1	let	let	VERB
ejpam-2231	308	2	s	s	PRON
ejpam-2231	308	3	be	be	AUX
ejpam-2231	308	4	a	a	DET
ejpam-2231	308	5	unitary	unitary	ADJ
ejpam-2231	308	6	(	(	PUNCT
ejpam-2231	308	7	m	m	PROPN
ejpam-2231	308	8	,	,	PUNCT
ejpam-2231	308	9	n)-regular	n)-regular	PUNCT
ejpam-2231	308	10	la	la	PROPN
ejpam-2231	308	11	-semigroup	-semigroup	PROPN
ejpam-2231	308	12	.	.	PUNCT
ejpam-2231	309	1	if	if	SCONJ
ejpam-2231	309	2	m	m	PROPN
ejpam-2231	309	3	(	(	PUNCT
ejpam-2231	309	4	n	n	CCONJ
ejpam-2231	309	5	)	)	PUNCT
ejpam-2231	309	6	is	be	AUX
ejpam-2231	309	7	a	a	DET
ejpam-2231	309	8	0	0	NUM
ejpam-2231	309	9	-	-	PUNCT
ejpam-2231	309	10	minimal	minimal	ADJ
ejpam-2231	309	11	(	(	PUNCT
ejpam-2231	309	12	m	m	PROPN
ejpam-2231	309	13	,	,	PUNCT
ejpam-2231	309	14	0)-ideal	0)-ideal	NUM
ejpam-2231	309	15	(	(	PUNCT
ejpam-2231	309	16	(	(	PUNCT
ejpam-2231	309	17	0	0	NUM
ejpam-2231	309	18	,	,	PUNCT
ejpam-2231	309	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	309	20	)	)	PUNCT
ejpam-2231	309	21	of	of	ADP
ejpam-2231	309	22	s	s	PROPN
ejpam-2231	309	23	,	,	PUNCT
ejpam-2231	309	24	then	then	ADV
ejpam-2231	309	25	either	either	CCONJ
ejpam-2231	309	26	m	m	VERB
ejpam-2231	309	27	∩n	∩n	NOUN
ejpam-2231	309	28	=	=	PUNCT
ejpam-2231	309	29	{	{	PUNCT
ejpam-2231	309	30	0	0	NUM
ejpam-2231	309	31	}	}	PUNCT
ejpam-2231	309	32	or	or	CCONJ
ejpam-2231	309	33	m	m	PROPN
ejpam-2231	309	34	∩n	∩n	NOUN
ejpam-2231	309	35	is	be	AUX
ejpam-2231	309	36	a	a	DET
ejpam-2231	309	37	0	0	NUM
ejpam-2231	309	38	-	-	PUNCT
ejpam-2231	309	39	minimal	minimal	ADJ
ejpam-2231	309	40	(	(	PUNCT
ejpam-2231	309	41	m	m	PROPN
ejpam-2231	309	42	,	,	PUNCT
ejpam-2231	309	43	n)-ideal	n)-ideal	NOUN
ejpam-2231	309	44	of	of	ADP
ejpam-2231	309	45	s.	s.	PROPN
ejpam-2231	309	46	proof	proof	PROPN
ejpam-2231	309	47	.	.	PUNCT
ejpam-2231	310	1	once	once	SCONJ
ejpam-2231	310	2	we	we	PRON
ejpam-2231	310	3	prove	prove	VERB
ejpam-2231	310	4	that	that	SCONJ
ejpam-2231	310	5	m	m	VERB
ejpam-2231	310	6	∩n	∩n	NOUN
ejpam-2231	310	7	is	be	AUX
ejpam-2231	310	8	an	an	DET
ejpam-2231	310	9	(	(	PUNCT
ejpam-2231	310	10	m	m	PROPN
ejpam-2231	310	11	,	,	PUNCT
ejpam-2231	310	12	n)-ideal	n)-ideal	NOUN
ejpam-2231	310	13	of	of	ADP
ejpam-2231	310	14	s	s	PROPN
ejpam-2231	310	15	,	,	PUNCT
ejpam-2231	310	16	the	the	DET
ejpam-2231	310	17	rest	rest	NOUN
ejpam-2231	310	18	of	of	ADP
ejpam-2231	310	19	the	the	DET
ejpam-2231	310	20	proof	proof	NOUN
ejpam-2231	310	21	is	be	AUX
ejpam-2231	310	22	same	same	ADJ
ejpam-2231	310	23	as	as	ADP
ejpam-2231	310	24	in	in	ADP
ejpam-2231	310	25	theorem	theorem	NOUN
ejpam-2231	310	26	11	11	NUM
ejpam-2231	310	27	.	.	PUNCT
ejpam-2231	311	1	let	let	VERB
ejpam-2231	311	2	o	o	NOUN
ejpam-2231	311	3	=	=	PUNCT
ejpam-2231	311	4	m	m	NOUN
ejpam-2231	311	5	∩	∩	ADJ
ejpam-2231	311	6	n	n	CCONJ
ejpam-2231	311	7	,	,	PUNCT
ejpam-2231	311	8	then	then	ADV
ejpam-2231	311	9	it	it	PRON
ejpam-2231	311	10	is	be	AUX
ejpam-2231	311	11	easy	easy	ADJ
ejpam-2231	311	12	to	to	PART
ejpam-2231	311	13	see	see	VERB
ejpam-2231	311	14	that	that	SCONJ
ejpam-2231	311	15	o2	o2	PROPN
ejpam-2231	311	16	⊆	⊆	NUM
ejpam-2231	311	17	o.	o.	NOUN
ejpam-2231	311	18	moreover	moreover	ADV
ejpam-2231	311	19	oms	om	NOUN
ejpam-2231	311	20	·	·	PUNCT
ejpam-2231	311	21	on	on	ADP
ejpam-2231	311	22	⊆	⊆	NUM
ejpam-2231	311	23	m	m	NOUN
ejpam-2231	311	24	ms	ms	PROPN
ejpam-2231	311	25	·	·	PUNCT
ejpam-2231	311	26	n	n	CCONJ
ejpam-2231	311	27	n	n	CCONJ
ejpam-2231	311	28	⊆	⊆	NUM
ejpam-2231	311	29	mn	mn	PROPN
ejpam-2231	311	30	n	n	CCONJ
ejpam-2231	311	31	⊆	⊆	NUM
ejpam-2231	311	32	sn	sn	NOUN
ejpam-2231	311	33	n	n	CCONJ
ejpam-2231	311	34	⊆	⊆	NUM
ejpam-2231	311	35	n	n	NOUN
ejpam-2231	311	36	.	.	PUNCT
ejpam-2231	312	1	but	but	CCONJ
ejpam-2231	312	2	,	,	PUNCT
ejpam-2231	312	3	we	we	PRON
ejpam-2231	312	4	also	also	ADV
ejpam-2231	312	5	have	have	VERB
ejpam-2231	312	6	oms	om	NOUN
ejpam-2231	312	7	·	·	PUNCT
ejpam-2231	312	8	on	on	ADP
ejpam-2231	312	9	⊆m	⊆m	NOUN
ejpam-2231	312	10	ms	ms	PROPN
ejpam-2231	312	11	·	·	PUNCT
ejpam-2231	312	12	n	n	CCONJ
ejpam-2231	312	13	n	n	NOUN
ejpam-2231	312	14	=	=	SYM
ejpam-2231	312	15	(	(	PUNCT
ejpam-2231	312	16	m	m	VERB
ejpam-2231	312	17	m	m	VERB
ejpam-2231	312	18	·	·	PUNCT
ejpam-2231	312	19	ss)n	ss)n	PROPN
ejpam-2231	312	20	n	n	NOUN
ejpam-2231	312	21	=	=	SYM
ejpam-2231	312	22	(	(	PUNCT
ejpam-2231	312	23	s	s	X
ejpam-2231	312	24	·	·	PROPN
ejpam-2231	312	25	m	m	PROPN
ejpam-2231	312	26	ms)n	ms)n	PROPN
ejpam-2231	312	27	n	n	PROPN
ejpam-2231	312	28	=	=	PUNCT
ejpam-2231	312	29	(	(	PUNCT
ejpam-2231	312	30	n	n	CCONJ
ejpam-2231	312	31	n	n	PRON
ejpam-2231	312	32	·	·	PUNCT
ejpam-2231	312	33	m	m	NOUN
ejpam-2231	312	34	ms)s	ms)s	ADJ
ejpam-2231	312	35	=(	=(	NOUN
ejpam-2231	312	36	m	m	VERB
ejpam-2231	312	37	m	m	PROPN
ejpam-2231	312	38	·	·	PUNCT
ejpam-2231	312	39	n	n	PRON
ejpam-2231	312	40	ns)(ss	ns)(ss	NUM
ejpam-2231	312	41	)	)	PUNCT
ejpam-2231	312	42	=	=	SYM
ejpam-2231	312	43	(	(	PUNCT
ejpam-2231	312	44	m	m	PROPN
ejpam-2231	312	45	ms)(n	ms)(n	NOUN
ejpam-2231	312	46	ns	ns	NUM
ejpam-2231	312	47	·	·	PUNCT
ejpam-2231	312	48	s	s	X
ejpam-2231	312	49	)	)	PUNCT
ejpam-2231	312	50	=	=	VERB
ejpam-2231	312	51	m	m	VERB
ejpam-2231	312	52	ms	ms	NOUN
ejpam-2231	312	53	·	·	PUNCT
ejpam-2231	312	54	sn	sn	PROPN
ejpam-2231	312	55	n	n	PROPN
ejpam-2231	312	56	=	=	NOUN
ejpam-2231	312	57	m	m	PROPN
ejpam-2231	312	58	ms	ms	NOUN
ejpam-2231	312	59	·	·	PUNCT
ejpam-2231	312	60	n	n	CCONJ
ejpam-2231	312	61	ns	ns	NUM
ejpam-2231	312	62	=	=	PUNCT
ejpam-2231	312	63	n	n	PROPN
ejpam-2231	312	64	n(m	n(m	PROPN
ejpam-2231	312	65	ms	ms	PROPN
ejpam-2231	312	66	·	·	PUNCT
ejpam-2231	312	67	s	s	X
ejpam-2231	312	68	)	)	PUNCT
ejpam-2231	312	69	=	=	SYM
ejpam-2231	312	70	n	n	CCONJ
ejpam-2231	312	71	n	n	CCONJ
ejpam-2231	312	72	·	·	PUNCT
ejpam-2231	313	1	sm	sm	PROPN
ejpam-2231	313	2	m	m	NOUN
ejpam-2231	313	3	=	=	SYM
ejpam-2231	313	4	n	n	PROPN
ejpam-2231	313	5	n	n	PRON
ejpam-2231	313	6	·	·	PUNCT
ejpam-2231	313	7	m	m	NOUN
ejpam-2231	313	8	ms	ms	NOUN
ejpam-2231	313	9	=	=	PROPN
ejpam-2231	313	10	m	m	PROPN
ejpam-2231	313	11	m	m	VERB
ejpam-2231	313	12	·	·	PUNCT
ejpam-2231	313	13	n	n	CCONJ
ejpam-2231	313	14	ns	ns	NUM
ejpam-2231	313	15	=	=	VERB
ejpam-2231	313	16	m	m	VERB
ejpam-2231	313	17	m	m	VERB
ejpam-2231	313	18	·	·	PUNCT
ejpam-2231	313	19	sn	sn	PROPN
ejpam-2231	313	20	n	n	PROPN
ejpam-2231	313	21	⊆	⊆	NUM
ejpam-2231	313	22	m	m	NOUN
ejpam-2231	313	23	mn	mn	PROPN
ejpam-2231	313	24	⊆	⊆	NUM
ejpam-2231	313	25	m	m	NOUN
ejpam-2231	313	26	ms	ms	NOUN
ejpam-2231	313	27	⊆	⊆	NUM
ejpam-2231	313	28	m	m	NOUN
ejpam-2231	313	29	.	.	PUNCT
ejpam-2231	314	1	thus	thus	ADV
ejpam-2231	314	2	oms	om	NOUN
ejpam-2231	314	3	·	·	PUNCT
ejpam-2231	314	4	on	on	ADP
ejpam-2231	314	5	⊆	⊆	NUM
ejpam-2231	314	6	m	m	NOUN
ejpam-2231	314	7	∩	∩	ADJ
ejpam-2231	314	8	n	n	NOUN
ejpam-2231	314	9	=	=	SYM
ejpam-2231	314	10	o	o	NOUN
ejpam-2231	314	11	and	and	CCONJ
ejpam-2231	314	12	therefore	therefore	ADV
ejpam-2231	314	13	o	o	PROPN
ejpam-2231	314	14	is	be	AUX
ejpam-2231	314	15	an	an	DET
ejpam-2231	314	16	(	(	PUNCT
ejpam-2231	314	17	m	m	PROPN
ejpam-2231	314	18	,	,	PUNCT
ejpam-2231	314	19	n)-ideal	n)-ideal	NOUN
ejpam-2231	314	20	of	of	ADP
ejpam-2231	314	21	s.	s.	PROPN
ejpam-2231	314	22	acknowledgements	acknowledgement	VERB
ejpam-2231	314	23	the	the	DET
ejpam-2231	314	24	work	work	NOUN
ejpam-2231	314	25	of	of	ADP
ejpam-2231	314	26	first	first	ADJ
ejpam-2231	314	27	author	author	NOUN
ejpam-2231	314	28	is	be	AUX
ejpam-2231	314	29	supported	support	VERB
ejpam-2231	314	30	by	by	ADP
ejpam-2231	314	31	the	the	DET
ejpam-2231	314	32	nnsf	nnsf	PROPN
ejpam-2231	314	33	(	(	PUNCT
ejpam-2231	314	34	grant	grant	VERB
ejpam-2231	314	35	no	no	NOUN
ejpam-2231	314	36	.	.	NOUN
ejpam-2231	314	37	11371335	11371335	NUM
ejpam-2231	314	38	)	)	PUNCT
ejpam-2231	314	39	grant	grant	NOUN
ejpam-2231	314	40	of	of	ADP
ejpam-2231	314	41	china	china	PROPN
ejpam-2231	314	42	.	.	PUNCT
ejpam-2231	315	1	the	the	DET
ejpam-2231	315	2	second	second	ADJ
ejpam-2231	315	3	author	author	NOUN
ejpam-2231	315	4	is	be	AUX
ejpam-2231	315	5	highly	highly	ADV
ejpam-2231	315	6	thankful	thankful	ADJ
ejpam-2231	315	7	to	to	ADP
ejpam-2231	315	8	cas	cas	PROPN
ejpam-2231	315	9	-	-	ADJ
ejpam-2231	315	10	twas	twas	PROPN
ejpam-2231	315	11	president	president	NOUN
ejpam-2231	315	12	’s	’s	PART
ejpam-2231	315	13	fellowship	fellowship	NOUN
ejpam-2231	315	14	.	.	PUNCT
ejpam-2231	316	1	references	reference	NOUN
ejpam-2231	316	2	[	[	X
ejpam-2231	316	3	1	1	NUM
ejpam-2231	316	4	]	]	PUNCT
ejpam-2231	316	5	m.	m.	NOUN
ejpam-2231	316	6	akram	akram	PROPN
ejpam-2231	316	7	,	,	PUNCT
ejpam-2231	316	8	n.	n.	NOUN
ejpam-2231	316	9	yaqoob	yaqoob	NOUN
ejpam-2231	316	10	,	,	PUNCT
ejpam-2231	316	11	and	and	CCONJ
ejpam-2231	316	12	m.	m.	PROPN
ejpam-2231	316	13	khan	khan	PROPN
ejpam-2231	316	14	.	.	PUNCT
ejpam-2231	317	1	on	on	ADP
ejpam-2231	317	2	(	(	PUNCT
ejpam-2231	317	3	m	m	PROPN
ejpam-2231	317	4	,	,	PUNCT
ejpam-2231	317	5	n)-ideals	n)-ideal	NOUN
ejpam-2231	317	6	in	in	ADP
ejpam-2231	317	7	la	la	NOUN
ejpam-2231	317	8	-	-	PUNCT
ejpam-2231	317	9	semigroups	semigroup	NOUN
ejpam-2231	317	10	,	,	PUNCT
ejpam-2231	317	11	applied	apply	VERB
ejpam-2231	317	12	mathematical	mathematical	ADJ
ejpam-2231	317	13	sciences	science	NOUN
ejpam-2231	317	14	,	,	PUNCT
ejpam-2231	317	15	7(44	7(44	NUM
ejpam-2231	317	16	)	)	PUNCT
ejpam-2231	317	17	,	,	PUNCT
ejpam-2231	317	18	2187	2187	NUM
ejpam-2231	317	19	-	-	SYM
ejpam-2231	317	20	2191	2191	NUM
ejpam-2231	317	21	.	.	PUNCT
ejpam-2231	318	1	2013	2013	NUM
ejpam-2231	318	2	.	.	PUNCT
ejpam-2231	319	1	[	[	X
ejpam-2231	319	2	2	2	NUM
ejpam-2231	319	3	]	]	PUNCT
ejpam-2231	319	4	m.	m.	NOUN
ejpam-2231	319	5	gulistan	gulistan	PROPN
ejpam-2231	319	6	,	,	PUNCT
ejpam-2231	319	7	n.	n.	PROPN
ejpam-2231	319	8	yaqoob	yaqoob	NOUN
ejpam-2231	319	9	,	,	PUNCT
ejpam-2231	319	10	and	and	CCONJ
ejpam-2231	319	11	m.	m.	PROPN
ejpam-2231	319	12	shahzad	shahzad	PROPN
ejpam-2231	319	13	.	.	PUNCT
ejpam-2231	320	1	a	a	DET
ejpam-2231	320	2	note	note	NOUN
ejpam-2231	320	3	on	on	ADP
ejpam-2231	320	4	hv	hv	PROPN
ejpam-2231	320	5	-	-	PUNCT
ejpam-2231	320	6	la	la	NOUN
ejpam-2231	320	7	-	-	PUNCT
ejpam-2231	320	8	semigroups	semigroup	NOUN
ejpam-2231	320	9	,	,	PUNCT
ejpam-2231	320	10	upb	upb	ADJ
ejpam-2231	320	11	scientific	scientific	ADJ
ejpam-2231	320	12	bulletin	bulletin	NOUN
ejpam-2231	320	13	,	,	PUNCT
ejpam-2231	320	14	series	series	NOUN
ejpam-2231	320	15	a	a	NOUN
ejpam-2231	320	16	,	,	PUNCT
ejpam-2231	320	17	77(3	77(3	PROPN
ejpam-2231	320	18	)	)	PUNCT
ejpam-2231	320	19	,	,	PUNCT
ejpam-2231	320	20	93	93	NUM
ejpam-2231	320	21	-	-	SYM
ejpam-2231	320	22	106	106	NUM
ejpam-2231	320	23	.	.	PUNCT
ejpam-2231	320	24	2015	2015	NUM
ejpam-2231	320	25	.	.	PUNCT
ejpam-2231	321	1	[	[	X
ejpam-2231	321	2	3	3	X
ejpam-2231	321	3	]	]	PUNCT
ejpam-2231	321	4	m.	m.	NOUN
ejpam-2231	321	5	a.	a.	PROPN
ejpam-2231	321	6	kazim	kazim	PROPN
ejpam-2231	321	7	and	and	CCONJ
ejpam-2231	321	8	m.	m.	PROPN
ejpam-2231	321	9	naseeruddin	naseeruddin	PROPN
ejpam-2231	321	10	.	.	PUNCT
ejpam-2231	322	1	on	on	ADP
ejpam-2231	322	2	almost	almost	ADV
ejpam-2231	322	3	semigroups	semigroup	NOUN
ejpam-2231	322	4	,	,	PUNCT
ejpam-2231	322	5	the	the	DET
ejpam-2231	322	6	aligarh	aligarh	NOUN
ejpam-2231	322	7	bulletin	bulletin	NOUN
ejpam-2231	322	8	of	of	ADP
ejpam-2231	322	9	mathematics	mathematic	NOUN
ejpam-2231	322	10	,	,	PUNCT
ejpam-2231	322	11	2	2	NUM
ejpam-2231	322	12	,	,	PUNCT
ejpam-2231	322	13	1	1	NUM
ejpam-2231	322	14	-	-	SYM
ejpam-2231	322	15	7	7	NUM
ejpam-2231	322	16	.	.	NOUN
ejpam-2231	322	17	1972	1972	NUM
ejpam-2231	322	18	.	.	PUNCT
ejpam-2231	323	1	[	[	X
ejpam-2231	323	2	4	4	X
ejpam-2231	323	3	]	]	X
ejpam-2231	323	4	m.	m.	NOUN
ejpam-2231	323	5	khan	khan	PROPN
ejpam-2231	323	6	and	and	CCONJ
ejpam-2231	323	7	n.	n.	PROPN
ejpam-2231	323	8	ahmad	ahmad	PROPN
ejpam-2231	323	9	.	.	PUNCT
ejpam-2231	324	1	characterizations	characterization	NOUN
ejpam-2231	324	2	of	of	ADP
ejpam-2231	324	3	left	leave	VERB
ejpam-2231	324	4	almost	almost	ADV
ejpam-2231	324	5	semigroups	semigroup	NOUN
ejpam-2231	324	6	by	by	ADP
ejpam-2231	324	7	their	their	PRON
ejpam-2231	324	8	ideals	ideal	NOUN
ejpam-2231	324	9	,	,	PUNCT
ejpam-2231	324	10	journal	journal	NOUN
ejpam-2231	324	11	of	of	ADP
ejpam-2231	324	12	advanced	advanced	ADJ
ejpam-2231	324	13	research	research	NOUN
ejpam-2231	324	14	in	in	ADP
ejpam-2231	324	15	pure	pure	ADJ
ejpam-2231	324	16	mathematics	mathematic	NOUN
ejpam-2231	324	17	,	,	PUNCT
ejpam-2231	324	18	2	2	NUM
ejpam-2231	324	19	,	,	PUNCT
ejpam-2231	324	20	61	61	NUM
ejpam-2231	324	21	-	-	SYM
ejpam-2231	324	22	63	63	NUM
ejpam-2231	324	23	.	.	PUNCT
ejpam-2231	324	24	2010	2010	NUM
ejpam-2231	324	25	.	.	PUNCT
ejpam-2231	325	1	[	[	X
ejpam-2231	325	2	5	5	NUM
ejpam-2231	325	3	]	]	PUNCT
ejpam-2231	325	4	m.	m.	NOUN
ejpam-2231	325	5	khan	khan	PROPN
ejpam-2231	325	6	,	,	PUNCT
ejpam-2231	325	7	f.	f.	PROPN
ejpam-2231	325	8	yousafzai	yousafzai	PROPN
ejpam-2231	325	9	,	,	PUNCT
ejpam-2231	325	10	and	and	CCONJ
ejpam-2231	325	11	v.	v.	PROPN
ejpam-2231	325	12	amjad	amjad	PROPN
ejpam-2231	325	13	.	.	PUNCT
ejpam-2231	326	1	on	on	ADP
ejpam-2231	326	2	some	some	DET
ejpam-2231	326	3	classes	class	NOUN
ejpam-2231	326	4	of	of	ADP
ejpam-2231	326	5	abel	abel	PROPN
ejpam-2231	326	6	-	-	PUNCT
ejpam-2231	326	7	grassmann	grassmann	PROPN
ejpam-2231	326	8	’s	’s	PART
ejpam-2231	326	9	groupoids	groupoid	NOUN
ejpam-2231	326	10	,	,	PUNCT
ejpam-2231	326	11	journal	journal	NOUN
ejpam-2231	326	12	of	of	ADP
ejpam-2231	326	13	advanced	advanced	ADJ
ejpam-2231	326	14	research	research	NOUN
ejpam-2231	326	15	in	in	ADP
ejpam-2231	326	16	pure	pure	ADJ
ejpam-2231	326	17	mathematics	mathematic	NOUN
ejpam-2231	326	18	,	,	PUNCT
ejpam-2231	326	19	3	3	NUM
ejpam-2231	326	20	,	,	PUNCT
ejpam-2231	326	21	109	109	NUM
ejpam-2231	326	22	-	-	SYM
ejpam-2231	326	23	119	119	NUM
ejpam-2231	326	24	.	.	PUNCT
ejpam-2231	326	25	2011	2011	NUM
ejpam-2231	326	26	.	.	PUNCT
ejpam-2231	327	1	[	[	X
ejpam-2231	327	2	6	6	NUM
ejpam-2231	327	3	]	]	PUNCT
ejpam-2231	327	4	s.	s.	PROPN
ejpam-2231	327	5	lajos	lajos	PROPN
ejpam-2231	327	6	.	.	PUNCT
ejpam-2231	328	1	generalized	generalized	ADJ
ejpam-2231	328	2	ideals	ideal	NOUN
ejpam-2231	328	3	in	in	ADP
ejpam-2231	328	4	semigroups	semigroup	NOUN
ejpam-2231	328	5	,	,	PUNCT
ejpam-2231	328	6	acta	acta	PROPN
ejpam-2231	328	7	scientiarum	scientiarum	PROPN
ejpam-2231	328	8	mathematicarum	mathematicarum	PROPN
ejpam-2231	328	9	,	,	PUNCT
ejpam-2231	328	10	22:217222	22:217222	PROPN
ejpam-2231	328	11	.	.	PROPN
ejpam-2231	328	12	1961	1961	NUM
ejpam-2231	328	13	.	.	PUNCT
ejpam-2231	329	1	[	[	X
ejpam-2231	329	2	7	7	X
ejpam-2231	329	3	]	]	X
ejpam-2231	329	4	q.	q.	PROPN
ejpam-2231	329	5	mushtaq	mushtaq	PROPN
ejpam-2231	329	6	and	and	CCONJ
ejpam-2231	329	7	s.	s.	PROPN
ejpam-2231	329	8	m.	m.	PROPN
ejpam-2231	329	9	yousuf	yousuf	PROPN
ejpam-2231	329	10	.	.	PUNCT
ejpam-2231	330	1	on	on	ADP
ejpam-2231	330	2	la	la	PROPN
ejpam-2231	330	3	-	-	PUNCT
ejpam-2231	330	4	semigroups	semigroup	NOUN
ejpam-2231	330	5	,	,	PUNCT
ejpam-2231	330	6	the	the	DET
ejpam-2231	330	7	aligarh	aligarh	NOUN
ejpam-2231	330	8	bulletin	bulletin	NOUN
ejpam-2231	330	9	of	of	ADP
ejpam-2231	330	10	mathematics	mathematic	NOUN
ejpam-2231	330	11	,	,	PUNCT
ejpam-2231	330	12	8	8	NUM
ejpam-2231	330	13	,	,	PUNCT
ejpam-2231	330	14	65	65	NUM
ejpam-2231	330	15	-	-	SYM
ejpam-2231	330	16	70	70	NUM
ejpam-2231	330	17	.	.	PUNCT
ejpam-2231	330	18	1978	1978	NUM
ejpam-2231	330	19	.	.	PUNCT
ejpam-2231	331	1	[	[	X
ejpam-2231	331	2	8	8	NUM
ejpam-2231	331	3	]	]	X
ejpam-2231	331	4	q.	q.	PROPN
ejpam-2231	331	5	mushtaq	mushtaq	PROPN
ejpam-2231	331	6	and	and	CCONJ
ejpam-2231	331	7	s.	s.	PROPN
ejpam-2231	331	8	m.	m.	PROPN
ejpam-2231	331	9	yusuf	yusuf	PROPN
ejpam-2231	331	10	.	.	PUNCT
ejpam-2231	332	1	on	on	ADP
ejpam-2231	332	2	locally	locally	ADV
ejpam-2231	332	3	associative	associative	ADJ
ejpam-2231	332	4	la	la	NOUN
ejpam-2231	332	5	-	-	PUNCT
ejpam-2231	332	6	semigroups	semigroup	NOUN
ejpam-2231	332	7	,	,	PUNCT
ejpam-2231	332	8	journal	journal	NOUN
ejpam-2231	332	9	of	of	ADP
ejpam-2231	332	10	natural	natural	ADJ
ejpam-2231	332	11	sciences	science	NOUN
ejpam-2231	332	12	and	and	CCONJ
ejpam-2231	332	13	mathematics	mathematic	NOUN
ejpam-2231	332	14	,	,	PUNCT
ejpam-2231	332	15	19:57	19:57	NUM
ejpam-2231	332	16	-	-	SYM
ejpam-2231	332	17	62	62	NUM
ejpam-2231	332	18	,	,	PUNCT
ejpam-2231	332	19	1979	1979	NUM
ejpam-2231	332	20	.	.	PUNCT
ejpam-2231	333	1	references	reference	NOUN
ejpam-2231	333	2	291	291	NUM
ejpam-2231	333	3	[	[	X
ejpam-2231	333	4	9	9	NUM
ejpam-2231	333	5	]	]	PUNCT
ejpam-2231	333	6	q.	q.	PROPN
ejpam-2231	333	7	mushtaq	mushtaq	PROPN
ejpam-2231	333	8	and	and	CCONJ
ejpam-2231	333	9	s.	s.	PROPN
ejpam-2231	333	10	m.	m.	PROPN
ejpam-2231	333	11	yusuf	yusuf	PROPN
ejpam-2231	333	12	.	.	PUNCT
ejpam-2231	334	1	on	on	ADP
ejpam-2231	334	2	la	la	PROPN
ejpam-2231	334	3	-	-	PUNCT
ejpam-2231	334	4	semigroup	semigroup	NOUN
ejpam-2231	334	5	defined	define	VERB
ejpam-2231	334	6	by	by	ADP
ejpam-2231	334	7	a	a	DET
ejpam-2231	334	8	commutative	commutative	ADJ
ejpam-2231	334	9	inverse	inverse	NOUN
ejpam-2231	334	10	semigroups	semigroup	NOUN
ejpam-2231	334	11	,	,	PUNCT
ejpam-2231	334	12	mathematicki	mathematicki	PROPN
ejpam-2231	334	13	vensik	vensik	NOUN
ejpam-2231	334	14	,	,	PUNCT
ejpam-2231	334	15	40	40	NUM
ejpam-2231	334	16	,	,	PUNCT
ejpam-2231	334	17	59	59	NUM
ejpam-2231	334	18	-	-	SYM
ejpam-2231	334	19	62	62	NUM
ejpam-2231	334	20	.	.	PUNCT
ejpam-2231	334	21	1988	1988	NUM
ejpam-2231	334	22	.	.	PUNCT
ejpam-2231	335	1	[	[	X
ejpam-2231	335	2	10	10	NUM
ejpam-2231	335	3	]	]	X
ejpam-2231	335	4	q.	q.	PROPN
ejpam-2231	335	5	mushtaq	mushtaq	PROPN
ejpam-2231	335	6	and	and	CCONJ
ejpam-2231	335	7	m.	m.	PROPN
ejpam-2231	335	8	s.	s.	PROPN
ejpam-2231	335	9	kamran	kamran	PROPN
ejpam-2231	335	10	.	.	PUNCT
ejpam-2231	336	1	on	on	ADP
ejpam-2231	336	2	la	la	NOUN
ejpam-2231	336	3	-	-	PUNCT
ejpam-2231	336	4	semigroups	semigroup	NOUN
ejpam-2231	336	5	with	with	ADP
ejpam-2231	336	6	weak	weak	ADJ
ejpam-2231	336	7	associative	associative	ADJ
ejpam-2231	336	8	law	law	NOUN
ejpam-2231	336	9	,	,	PUNCT
ejpam-2231	336	10	scientific	scientific	ADJ
ejpam-2231	336	11	khyber	khyber	PROPN
ejpam-2231	336	12	,	,	PUNCT
ejpam-2231	336	13	1	1	NUM
ejpam-2231	336	14	,	,	PUNCT
ejpam-2231	336	15	69	69	NUM
ejpam-2231	336	16	-	-	SYM
ejpam-2231	336	17	71	71	NUM
ejpam-2231	336	18	.	.	PUNCT
ejpam-2231	336	19	1989	1989	NUM
ejpam-2231	336	20	.	.	PUNCT
ejpam-2231	337	1	[	[	X
ejpam-2231	337	2	11	11	NUM
ejpam-2231	337	3	]	]	X
ejpam-2231	337	4	q.	q.	PROPN
ejpam-2231	337	5	mushtaq	mushtaq	PROPN
ejpam-2231	337	6	and	and	CCONJ
ejpam-2231	337	7	m.	m.	PROPN
ejpam-2231	337	8	khan	khan	PROPN
ejpam-2231	337	9	.	.	PUNCT
ejpam-2231	338	1	ideals	ideal	NOUN
ejpam-2231	338	2	in	in	ADP
ejpam-2231	338	3	left	left	ADJ
ejpam-2231	338	4	almost	almost	ADV
ejpam-2231	338	5	semigroups	semigroup	NOUN
ejpam-2231	338	6	,	,	PUNCT
ejpam-2231	338	7	proceedings	proceeding	NOUN
ejpam-2231	338	8	of	of	ADP
ejpam-2231	338	9	4th	4th	ADJ
ejpam-2231	338	10	international	international	ADJ
ejpam-2231	338	11	pure	pure	ADJ
ejpam-2231	338	12	mathematics	mathematic	NOUN
ejpam-2231	338	13	conference	conference	NOUN
ejpam-2231	338	14	,	,	PUNCT
ejpam-2231	338	15	65	65	NUM
ejpam-2231	338	16	-	-	SYM
ejpam-2231	338	17	77	77	NUM
ejpam-2231	338	18	.	.	PUNCT
ejpam-2231	338	19	2003	2003	NUM
ejpam-2231	338	20	.	.	PUNCT
ejpam-2231	339	1	[	[	X
ejpam-2231	339	2	12	12	NUM
ejpam-2231	339	3	]	]	PUNCT
ejpam-2231	339	4	n	n	CCONJ
ejpam-2231	339	5	stevanović	stevanović	NOUN
ejpam-2231	339	6	and	and	CCONJ
ejpam-2231	339	7	p	p	X
ejpam-2231	339	8	v	v	PROPN
ejpam-2231	339	9	protić.	protić.	PROPN
ejpam-2231	339	10	composition	composition	NOUN
ejpam-2231	339	11	of	of	ADP
ejpam-2231	339	12	abel	abel	PROPN
ejpam-2231	339	13	-	-	PUNCT
ejpam-2231	339	14	grassmann	grassmann	PROPN
ejpam-2231	339	15	’s	’s	PART
ejpam-2231	339	16	3	3	NUM
ejpam-2231	339	17	-	-	PUNCT
ejpam-2231	339	18	bands	band	NOUN
ejpam-2231	339	19	,	,	PUNCT
ejpam-2231	339	20	novi	novi	PROPN
ejpam-2231	339	21	sad	sad	PROPN
ejpam-2231	339	22	journal	journal	PROPN
ejpam-2231	339	23	of	of	ADP
ejpam-2231	339	24	mathematics	mathematic	NOUN
ejpam-2231	339	25	,	,	PUNCT
ejpam-2231	339	26	2(34	2(34	NUM
ejpam-2231	339	27	)	)	PUNCT
ejpam-2231	339	28	,	,	PUNCT
ejpam-2231	339	29	175	175	NUM
ejpam-2231	339	30	-	-	SYM
ejpam-2231	339	31	182	182	NUM
ejpam-2231	339	32	.	.	PUNCT
ejpam-2231	339	33	2004	2004	NUM
ejpam-2231	339	34	.	.	PUNCT
ejpam-2231	340	1	[	[	X
ejpam-2231	340	2	13	13	NUM
ejpam-2231	340	3	]	]	X
ejpam-2231	340	4	n.	n.	NOUN
ejpam-2231	340	5	yaqoob	yaqoob	NOUN
ejpam-2231	340	6	,	,	PUNCT
ejpam-2231	340	7	p.	p.	PROPN
ejpam-2231	340	8	corsini	corsini	PROPN
ejpam-2231	340	9	,	,	PUNCT
ejpam-2231	340	10	and	and	CCONJ
ejpam-2231	340	11	f.	f.	PROPN
ejpam-2231	340	12	yousafzai	yousafzai	PROPN
ejpam-2231	340	13	.	.	PUNCT
ejpam-2231	341	1	on	on	ADP
ejpam-2231	341	2	intra	intra	ADJ
ejpam-2231	341	3	-	-	ADJ
ejpam-2231	341	4	regular	regular	ADJ
ejpam-2231	341	5	left	leave	VERB
ejpam-2231	341	6	almost	almost	ADV
ejpam-2231	341	7	semihypergroups	semihypergroup	NOUN
ejpam-2231	341	8	with	with	ADP
ejpam-2231	341	9	pure	pure	ADJ
ejpam-2231	341	10	left	left	ADJ
ejpam-2231	341	11	identity	identity	NOUN
ejpam-2231	341	12	,	,	PUNCT
ejpam-2231	341	13	journal	journal	NOUN
ejpam-2231	341	14	of	of	ADP
ejpam-2231	341	15	mathematics	mathematic	NOUN
ejpam-2231	341	16	,	,	PUNCT
ejpam-2231	341	17	article	article	NOUN
ejpam-2231	341	18	i	i	PROPN
ejpam-2231	341	19	d	d	PROPN
ejpam-2231	341	20	510790:10	510790:10	NUM
ejpam-2231	341	21	,	,	PUNCT
ejpam-2231	341	22	2013	2013	NUM
ejpam-2231	341	23	.	.	PUNCT
ejpam-2231	342	1	[	[	X
ejpam-2231	342	2	14	14	NUM
ejpam-2231	342	3	]	]	X
ejpam-2231	342	4	n.	n.	NOUN
ejpam-2231	342	5	yaqoob	yaqoob	NOUN
ejpam-2231	342	6	and	and	CCONJ
ejpam-2231	342	7	m.	m.	NOUN
ejpam-2231	342	8	gulistan	gulistan	PROPN
ejpam-2231	342	9	.	.	PUNCT
ejpam-2231	343	1	partially	partially	ADV
ejpam-2231	343	2	ordered	order	VERB
ejpam-2231	343	3	left	leave	VERB
ejpam-2231	343	4	almost	almost	ADV
ejpam-2231	343	5	semihypergroups	semihypergroup	NOUN
ejpam-2231	343	6	,	,	PUNCT
ejpam-2231	343	7	journal	journal	NOUN
ejpam-2231	343	8	of	of	ADP
ejpam-2231	343	9	the	the	DET
ejpam-2231	343	10	egyptian	egyptian	PROPN
ejpam-2231	343	11	mathematical	mathematical	PROPN
ejpam-2231	343	12	society	society	NOUN
ejpam-2231	343	13	,	,	PUNCT
ejpam-2231	343	14	23	23	NUM
ejpam-2231	343	15	,	,	PUNCT
ejpam-2231	343	16	231	231	NUM
ejpam-2231	343	17	-	-	SYM
ejpam-2231	343	18	235	235	NUM
ejpam-2231	343	19	.	.	NOUN
ejpam-2231	343	20	2015	2015	NUM
ejpam-2231	343	21	.	.	PUNCT
ejpam-2231	344	1	[	[	X
ejpam-2231	344	2	15	15	NUM
ejpam-2231	344	3	]	]	X
ejpam-2231	344	4	n.	n.	NOUN
ejpam-2231	344	5	yaqoob	yaqoob	NOUN
ejpam-2231	344	6	.	.	PUNCT
ejpam-2231	345	1	interval	interval	NOUN
ejpam-2231	345	2	-	-	PUNCT
ejpam-2231	345	3	valued	value	VERB
ejpam-2231	345	4	intuitionistic	intuitionistic	ADJ
ejpam-2231	345	5	fuzzy	fuzzy	ADJ
ejpam-2231	345	6	ideals	ideal	NOUN
ejpam-2231	345	7	of	of	ADP
ejpam-2231	345	8	regular	regular	ADJ
ejpam-2231	345	9	la	la	NOUN
ejpam-2231	345	10	-	-	PUNCT
ejpam-2231	345	11	semigroups	semigroup	NOUN
ejpam-2231	345	12	,	,	PUNCT
ejpam-2231	345	13	thai	thai	PROPN
ejpam-2231	345	14	journal	journal	NOUN
ejpam-2231	345	15	of	of	ADP
ejpam-2231	345	16	mathematics	mathematic	NOUN
ejpam-2231	345	17	,	,	PUNCT
ejpam-2231	345	18	11(3	11(3	NUM
ejpam-2231	345	19	)	)	PUNCT
ejpam-2231	345	20	,	,	PUNCT
ejpam-2231	345	21	683	683	NUM
ejpam-2231	345	22	-	-	SYM
ejpam-2231	345	23	695	695	NUM
ejpam-2231	345	24	.	.	PUNCT
ejpam-2231	345	25	2013	2013	NUM
ejpam-2231	345	26	.	.	PUNCT
ejpam-2231	346	1	[	[	X
ejpam-2231	346	2	16	16	NUM
ejpam-2231	346	3	]	]	X
ejpam-2231	346	4	f.	f.	PROPN
ejpam-2231	346	5	yousafzai	yousafzai	PROPN
ejpam-2231	346	6	,	,	PUNCT
ejpam-2231	346	7	n.	n.	PROPN
ejpam-2231	346	8	yaqoob	yaqoob	NOUN
ejpam-2231	346	9	,	,	PUNCT
ejpam-2231	346	10	and	and	CCONJ
ejpam-2231	346	11	a.	a.	NOUN
ejpam-2231	346	12	ghareeb	ghareeb	PROPN
ejpam-2231	346	13	.	.	PUNCT
ejpam-2231	346	14	left	leave	VERB
ejpam-2231	346	15	regular	regular	ADJ
ejpam-2231	346	16	ag	ag	PROPN
ejpam-2231	346	17	-groupoids	-groupoid	NOUN
ejpam-2231	346	18	in	in	ADP
ejpam-2231	346	19	terms	term	NOUN
ejpam-2231	346	20	of	of	ADP
ejpam-2231	346	21	fuzzy	fuzzy	ADJ
ejpam-2231	346	22	interior	interior	ADJ
ejpam-2231	346	23	ideals	ideal	NOUN
ejpam-2231	346	24	,	,	PUNCT
ejpam-2231	346	25	afrika	afrika	ADJ
ejpam-2231	346	26	matematika	matematika	NOUN
ejpam-2231	346	27	,	,	PUNCT
ejpam-2231	346	28	24(4	24(4	NUM
ejpam-2231	346	29	)	)	PUNCT
ejpam-2231	346	30	,	,	PUNCT
ejpam-2231	346	31	577	577	NUM
ejpam-2231	346	32	-	-	SYM
ejpam-2231	346	33	587	587	NUM
ejpam-2231	346	34	.	.	PUNCT
ejpam-2231	347	1	2013	2013	NUM
ejpam-2231	347	2	.	.	PUNCT
ejpam-2231	348	1	[	[	X
ejpam-2231	348	2	17	17	NUM
ejpam-2231	348	3	]	]	X
ejpam-2231	348	4	f.	f.	PROPN
ejpam-2231	348	5	yousafzai	yousafzai	PROPN
ejpam-2231	348	6	,	,	PUNCT
ejpam-2231	348	7	a.	a.	PROPN
ejpam-2231	348	8	khan	khan	PROPN
ejpam-2231	348	9	,	,	PUNCT
ejpam-2231	348	10	and	and	CCONJ
ejpam-2231	348	11	b.	b.	PROPN
ejpam-2231	348	12	davvaz	davvaz	PROPN
ejpam-2231	348	13	.	.	PUNCT
ejpam-2231	349	1	on	on	ADP
ejpam-2231	349	2	fully	fully	ADV
ejpam-2231	349	3	regular	regular	ADJ
ejpam-2231	349	4	ag	ag	PROPN
ejpam-2231	349	5	-groupoids	-groupoids	PROPN
ejpam-2231	349	6	,	,	PUNCT
ejpam-2231	349	7	afrika	afrika	ADJ
ejpam-2231	349	8	mathematika	mathematika	NOUN
ejpam-2231	349	9	,	,	PUNCT
ejpam-2231	349	10	25	25	NUM
ejpam-2231	349	11	,	,	PUNCT
ejpam-2231	349	12	449	449	NUM
ejpam-2231	349	13	-	-	SYM
ejpam-2231	349	14	459	459	NUM
ejpam-2231	349	15	.	.	PUNCT
ejpam-2231	349	16	2014	2014	NUM
ejpam-2231	349	17	.	.	PUNCT