id	sid	tid	token	lemma	pos
ejpam-2311	1	1	european	european	PROPN
ejpam-2311	1	2	journal	journal	PROPN
ejpam-2311	1	3	of	of	ADP
ejpam-2311	1	4	pure	pure	ADJ
ejpam-2311	1	5	and	and	CCONJ
ejpam-2311	1	6	applied	apply	VERB
ejpam-2311	1	7	mathematics	mathematic	NOUN
ejpam-2311	1	8	vol	vol	NOUN
ejpam-2311	1	9	.	.	PUNCT
ejpam-2311	2	1	7	7	NUM
ejpam-2311	2	2	,	,	PUNCT
ejpam-2311	2	3	no	no	INTJ
ejpam-2311	2	4	.	.	NOUN
ejpam-2311	2	5	4	4	NUM
ejpam-2311	2	6	,	,	PUNCT
ejpam-2311	2	7	2014	2014	NUM
ejpam-2311	2	8	,	,	PUNCT
ejpam-2311	2	9	462	462	NUM
ejpam-2311	2	10	-	-	SYM
ejpam-2311	2	11	471	471	NUM
ejpam-2311	2	12	issn	issn	PROPN
ejpam-2311	2	13	1307	1307	NUM
ejpam-2311	2	14	-	-	SYM
ejpam-2311	2	15	5543	5543	NUM
ejpam-2311	2	16	–	–	PUNCT
ejpam-2311	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2311	2	18	characterization	characterization	NOUN
ejpam-2311	2	19	of	of	ADP
ejpam-2311	2	20	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	2	21	×	×	NOUN
ejpam-2311	2	22	k4	k4	NOUN
ejpam-2311	2	23	]	]	PUNCT
ejpam-2311	2	24	)	)	PUNCT
ejpam-2311	2	25	ismail	ismail	PROPN
ejpam-2311	2	26	gokhan	gokhan	PROPN
ejpam-2311	2	27	kelebek∗	kelebek∗	PROPN
ejpam-2311	2	28	,	,	PUNCT
ejpam-2311	2	29	tevfik	tevfik	PROPN
ejpam-2311	2	30	bilgin	bilgin	PROPN
ejpam-2311	2	31	department	department	PROPN
ejpam-2311	2	32	of	of	ADP
ejpam-2311	2	33	mathematics	mathematics	PROPN
ejpam-2311	2	34	,	,	PUNCT
ejpam-2311	2	35	fatih	fatih	PROPN
ejpam-2311	2	36	university	university	PROPN
ejpam-2311	2	37	,	,	PUNCT
ejpam-2311	2	38	istanbul	istanbul	PROPN
ejpam-2311	2	39	,	,	PUNCT
ejpam-2311	2	40	turkey	turkey	PROPN
ejpam-2311	2	41	abstract	abstract	NOUN
ejpam-2311	2	42	.	.	PUNCT
ejpam-2311	3	1	constructing	construct	VERB
ejpam-2311	3	2	the	the	DET
ejpam-2311	3	3	group	group	NOUN
ejpam-2311	3	4	of	of	ADP
ejpam-2311	3	5	units	unit	NOUN
ejpam-2311	3	6	u(zg	u(zg	NUM
ejpam-2311	3	7	)	)	PUNCT
ejpam-2311	3	8	of	of	ADP
ejpam-2311	3	9	the	the	DET
ejpam-2311	3	10	integral	integral	ADJ
ejpam-2311	3	11	group	group	NOUN
ejpam-2311	3	12	ring	ring	NOUN
ejpam-2311	3	13	zg	zg	PROPN
ejpam-2311	3	14	,	,	PUNCT
ejpam-2311	3	15	for	for	ADP
ejpam-2311	3	16	a	a	DET
ejpam-2311	3	17	finite	finite	ADJ
ejpam-2311	3	18	group	group	NOUN
ejpam-2311	3	19	g	g	NOUN
ejpam-2311	3	20	,	,	PUNCT
ejpam-2311	3	21	is	be	AUX
ejpam-2311	3	22	a	a	DET
ejpam-2311	3	23	classical	classical	ADJ
ejpam-2311	3	24	but	but	CCONJ
ejpam-2311	3	25	open	open	ADJ
ejpam-2311	3	26	problem	problem	NOUN
ejpam-2311	3	27	.	.	PUNCT
ejpam-2311	4	1	in	in	ADP
ejpam-2311	4	2	this	this	DET
ejpam-2311	4	3	study	study	NOUN
ejpam-2311	4	4	,	,	PUNCT
ejpam-2311	4	5	it	it	PRON
ejpam-2311	4	6	is	be	AUX
ejpam-2311	4	7	shown	show	VERB
ejpam-2311	4	8	that	that	SCONJ
ejpam-2311	4	9	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	4	10	×	×	NOUN
ejpam-2311	4	11	k4	k4	NOUN
ejpam-2311	4	12	]	]	PUNCT
ejpam-2311	4	13	)	)	PUNCT
ejpam-2311	5	1	=	=	SYM
ejpam-2311	5	2	u1(zcn)×	u1(zcn)×	PROPN
ejpam-2311	5	3	(	(	PUNCT
ejpam-2311	5	4	1	1	NUM
ejpam-2311	5	5	+	+	NUM
ejpam-2311	5	6	k	k	PROPN
ejpam-2311	5	7	x)×	x)×	SYM
ejpam-2311	5	8	(	(	PUNCT
ejpam-2311	5	9	1	1	NUM
ejpam-2311	5	10	+	+	NUM
ejpam-2311	5	11	k	k	NOUN
ejpam-2311	5	12	y)×	y)×	NOUN
ejpam-2311	5	13	(	(	PUNCT
ejpam-2311	5	14	1	1	NUM
ejpam-2311	5	15	+	+	NUM
ejpam-2311	5	16	k	k	PROPN
ejpam-2311	5	17	x	x	SYM
ejpam-2311	5	18	y	y	PROPN
ejpam-2311	5	19	)	)	PUNCT
ejpam-2311	5	20	.	.	PUNCT
ejpam-2311	6	1	this	this	DET
ejpam-2311	6	2	structure	structure	NOUN
ejpam-2311	6	3	theorem	theorem	NOUN
ejpam-2311	6	4	is	be	AUX
ejpam-2311	6	5	applied	apply	VERB
ejpam-2311	6	6	to	to	PART
ejpam-2311	6	7	give	give	VERB
ejpam-2311	6	8	precise	precise	ADJ
ejpam-2311	6	9	characterization	characterization	NOUN
ejpam-2311	6	10	of	of	ADP
ejpam-2311	6	11	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	6	12	×	×	NOUN
ejpam-2311	6	13	k4	k4	NOUN
ejpam-2311	6	14	]	]	PUNCT
ejpam-2311	6	15	)	)	PUNCT
ejpam-2311	6	16	for	for	ADP
ejpam-2311	6	17	cyclic	cyclic	ADJ
ejpam-2311	6	18	groups	group	NOUN
ejpam-2311	6	19	c5	c5	PROPN
ejpam-2311	6	20	and	and	CCONJ
ejpam-2311	6	21	c7	c7	PROPN
ejpam-2311	6	22	.	.	PROPN
ejpam-2311	7	1	2010	2010	NUM
ejpam-2311	7	2	mathematics	mathematic	NOUN
ejpam-2311	7	3	subject	subject	NOUN
ejpam-2311	7	4	classifications	classification	NOUN
ejpam-2311	7	5	:	:	PUNCT
ejpam-2311	7	6	16u60	16u60	NUM
ejpam-2311	7	7	,	,	PUNCT
ejpam-2311	7	8	16s34	16s34	NUM
ejpam-2311	7	9	key	key	ADJ
ejpam-2311	7	10	words	word	NOUN
ejpam-2311	7	11	and	and	CCONJ
ejpam-2311	7	12	phrases	phrase	NOUN
ejpam-2311	7	13	:	:	PUNCT
ejpam-2311	7	14	integral	integral	ADJ
ejpam-2311	7	15	group	group	NOUN
ejpam-2311	7	16	ring	ring	NOUN
ejpam-2311	7	17	,	,	PUNCT
ejpam-2311	7	18	unit	unit	NOUN
ejpam-2311	7	19	problem	problem	NOUN
ejpam-2311	7	20	,	,	PUNCT
ejpam-2311	7	21	generators	generator	NOUN
ejpam-2311	7	22	of	of	ADP
ejpam-2311	7	23	unit	unit	NOUN
ejpam-2311	7	24	group	group	NOUN
ejpam-2311	7	25	1	1	NUM
ejpam-2311	7	26	.	.	PUNCT
ejpam-2311	8	1	introduction	introduction	NOUN
ejpam-2311	8	2	let	let	VERB
ejpam-2311	8	3	us	we	PRON
ejpam-2311	8	4	denote	denote	VERB
ejpam-2311	8	5	za	za	PROPN
ejpam-2311	8	6	the	the	DET
ejpam-2311	8	7	integral	integral	ADJ
ejpam-2311	8	8	group	group	NOUN
ejpam-2311	8	9	ring	ring	NOUN
ejpam-2311	8	10	of	of	ADP
ejpam-2311	8	11	a	a	DET
ejpam-2311	8	12	finite	finite	ADJ
ejpam-2311	8	13	abelian	abelian	PROPN
ejpam-2311	8	14	group	group	PROPN
ejpam-2311	8	15	a	a	NOUN
ejpam-2311	8	16	with	with	ADP
ejpam-2311	8	17	the	the	DET
ejpam-2311	8	18	coefficients	coefficient	NOUN
ejpam-2311	8	19	from	from	ADP
ejpam-2311	8	20	the	the	DET
ejpam-2311	8	21	ring	ring	NOUN
ejpam-2311	8	22	of	of	ADP
ejpam-2311	8	23	integers	integer	NOUN
ejpam-2311	8	24	z.	z.	PROPN
ejpam-2311	8	25	let	let	VERB
ejpam-2311	8	26	u(za	u(za	PRON
ejpam-2311	8	27	)	)	PUNCT
ejpam-2311	8	28	be	be	AUX
ejpam-2311	8	29	the	the	DET
ejpam-2311	8	30	group	group	NOUN
ejpam-2311	8	31	of	of	ADP
ejpam-2311	8	32	units	unit	NOUN
ejpam-2311	8	33	in	in	ADP
ejpam-2311	8	34	za	za	PROPN
ejpam-2311	8	35	.	.	PUNCT
ejpam-2311	9	1	higman	higman	PROPN
ejpam-2311	10	1	[	[	X
ejpam-2311	10	2	4	4	NUM
ejpam-2311	10	3	]	]	PUNCT
ejpam-2311	10	4	obtained	obtain	VERB
ejpam-2311	10	5	the	the	DET
ejpam-2311	10	6	following	following	ADJ
ejpam-2311	10	7	result	result	NOUN
ejpam-2311	10	8	:	:	PUNCT
ejpam-2311	10	9	theorem	theorem	NOUN
ejpam-2311	10	10	1	1	NUM
ejpam-2311	10	11	.	.	PUNCT
ejpam-2311	11	1	if	if	SCONJ
ejpam-2311	11	2	a	a	PRON
ejpam-2311	11	3	is	be	AUX
ejpam-2311	11	4	a	a	DET
ejpam-2311	11	5	finite	finite	ADJ
ejpam-2311	11	6	abelian	abelian	PROPN
ejpam-2311	11	7	group	group	NOUN
ejpam-2311	11	8	then	then	ADV
ejpam-2311	11	9	u(za	u(za	NUM
ejpam-2311	11	10	)	)	PUNCT
ejpam-2311	12	1	=	=	SYM
ejpam-2311	12	2	±a×	±a×	NOUN
ejpam-2311	12	3	f	f	X
ejpam-2311	12	4	,	,	PUNCT
ejpam-2311	12	5	where	where	SCONJ
ejpam-2311	12	6	f	f	PROPN
ejpam-2311	12	7	is	be	AUX
ejpam-2311	12	8	a	a	DET
ejpam-2311	12	9	free	free	ADJ
ejpam-2311	12	10	abelian	abelian	ADJ
ejpam-2311	12	11	group	group	NOUN
ejpam-2311	12	12	.	.	PUNCT
ejpam-2311	13	1	here	here	ADV
ejpam-2311	13	2	torsion	torsion	NOUN
ejpam-2311	13	3	units	unit	NOUN
ejpam-2311	13	4	are	be	AUX
ejpam-2311	13	5	trivial	trivial	ADJ
ejpam-2311	13	6	,	,	PUNCT
ejpam-2311	13	7	torsion	torsion	NOUN
ejpam-2311	13	8	free	free	ADJ
ejpam-2311	13	9	units	unit	NOUN
ejpam-2311	13	10	are	be	AUX
ejpam-2311	13	11	finite	finite	ADJ
ejpam-2311	13	12	but	but	CCONJ
ejpam-2311	13	13	the	the	DET
ejpam-2311	13	14	rank	rank	NOUN
ejpam-2311	13	15	is	be	AUX
ejpam-2311	13	16	not	not	PART
ejpam-2311	13	17	determined	determine	VERB
ejpam-2311	13	18	.	.	PUNCT
ejpam-2311	14	1	the	the	DET
ejpam-2311	14	2	rank	rank	NOUN
ejpam-2311	14	3	of	of	ADP
ejpam-2311	14	4	torsion	torsion	NOUN
ejpam-2311	14	5	free	free	ADJ
ejpam-2311	14	6	part	part	NOUN
ejpam-2311	14	7	is	be	AUX
ejpam-2311	14	8	determined	determine	VERB
ejpam-2311	14	9	by	by	ADP
ejpam-2311	14	10	ayoub	ayoub	PROPN
ejpam-2311	14	11	and	and	CCONJ
ejpam-2311	14	12	ayoub	ayoub	PROPN
ejpam-2311	15	1	[	[	X
ejpam-2311	15	2	2	2	NUM
ejpam-2311	15	3	]	]	PUNCT
ejpam-2311	15	4	.	.	PUNCT
ejpam-2311	16	1	theorem	theorem	NOUN
ejpam-2311	16	2	2	2	NUM
ejpam-2311	16	3	.	.	PUNCT
ejpam-2311	17	1	if	if	SCONJ
ejpam-2311	17	2	a	a	PRON
ejpam-2311	17	3	is	be	AUX
ejpam-2311	17	4	a	a	DET
ejpam-2311	17	5	finite	finite	ADJ
ejpam-2311	17	6	abelian	abelian	PROPN
ejpam-2311	17	7	group	group	NOUN
ejpam-2311	17	8	then	then	ADV
ejpam-2311	17	9	u(za	u(za	NUM
ejpam-2311	17	10	)	)	PUNCT
ejpam-2311	18	1	=	=	SYM
ejpam-2311	18	2	±a×	±a×	NOUN
ejpam-2311	18	3	f	f	PROPN
ejpam-2311	18	4	with	with	ADP
ejpam-2311	18	5	the	the	DET
ejpam-2311	18	6	rank	rank	NOUN
ejpam-2311	18	7	ρ	ρ	PROPN
ejpam-2311	18	8	=	=	SYM
ejpam-2311	18	9	1	1	NUM
ejpam-2311	18	10	2	2	NUM
ejpam-2311	18	11	(	(	PUNCT
ejpam-2311	18	12	|a|+	|a|+	VERB
ejpam-2311	18	13	1	1	NUM
ejpam-2311	18	14	+	+	NOUN
ejpam-2311	18	15	n2	n2	ADJ
ejpam-2311	18	16	−	−	PROPN
ejpam-2311	18	17	2l	2l	NUM
ejpam-2311	18	18	)	)	PUNCT
ejpam-2311	18	19	,	,	PUNCT
ejpam-2311	18	20	(	(	PUNCT
ejpam-2311	18	21	1	1	X
ejpam-2311	18	22	)	)	PUNCT
ejpam-2311	18	23	where	where	SCONJ
ejpam-2311	18	24	n2	n2	NOUN
ejpam-2311	18	25	is	be	AUX
ejpam-2311	18	26	the	the	DET
ejpam-2311	18	27	number	number	NOUN
ejpam-2311	18	28	of	of	ADP
ejpam-2311	18	29	elements	element	NOUN
ejpam-2311	18	30	of	of	ADP
ejpam-2311	18	31	a	a	PRON
ejpam-2311	18	32	of	of	ADP
ejpam-2311	18	33	order	order	NOUN
ejpam-2311	18	34	2	2	NUM
ejpam-2311	18	35	and	and	CCONJ
ejpam-2311	18	36	l	l	NOUN
ejpam-2311	18	37	is	be	AUX
ejpam-2311	18	38	the	the	DET
ejpam-2311	18	39	number	number	NOUN
ejpam-2311	18	40	of	of	ADP
ejpam-2311	18	41	cyclic	cyclic	ADJ
ejpam-2311	18	42	subgroups	subgroup	NOUN
ejpam-2311	18	43	of	of	ADP
ejpam-2311	18	44	a.	a.	NOUN
ejpam-2311	18	45	∗corresponding	∗corresponde	VERB
ejpam-2311	18	46	author	author	NOUN
ejpam-2311	18	47	.	.	PUNCT
ejpam-2311	19	1	email	email	NOUN
ejpam-2311	19	2	addresses	address	NOUN
ejpam-2311	19	3	:	:	PUNCT
ejpam-2311	19	4	gkelebek@fatih.edu.tr	gkelebek@fatih.edu.tr	PROPN
ejpam-2311	19	5	(	(	PUNCT
ejpam-2311	19	6	i.g	i.g	PROPN
ejpam-2311	19	7	.	.	PROPN
ejpam-2311	19	8	kelebek	kelebek	PROPN
ejpam-2311	19	9	)	)	PUNCT
ejpam-2311	19	10	,	,	PUNCT
ejpam-2311	19	11	tbilgin@fatih.edu.tr	tbilgin@fatih.edu.tr	PROPN
ejpam-2311	19	12	(	(	PUNCT
ejpam-2311	19	13	t.	t.	NOUN
ejpam-2311	19	14	bilgin	bilgin	NOUN
ejpam-2311	19	15	)	)	PUNCT
ejpam-2311	19	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2311	20	1	462	462	NUM
ejpam-2311	21	1	c	c	X
ejpam-2311	21	2	©	©	PROPN
ejpam-2311	21	3	2014	2014	NUM
ejpam-2311	21	4	ejpam	ejpam	NOUN
ejpam-2311	21	5	all	all	DET
ejpam-2311	21	6	rights	right	NOUN
ejpam-2311	21	7	reserved	reserve	VERB
ejpam-2311	21	8	.	.	PUNCT
ejpam-2311	22	1	i.g	i.g	PROPN
ejpam-2311	22	2	.	.	PROPN
ejpam-2311	22	3	kelebek	kelebek	PROPN
ejpam-2311	22	4	,	,	PUNCT
ejpam-2311	22	5	t.	t.	PROPN
ejpam-2311	22	6	bilgin	bilgin	PROPN
ejpam-2311	22	7	/	/	SYM
ejpam-2311	22	8	eur	eur	PROPN
ejpam-2311	22	9	.	.	PUNCT
ejpam-2311	23	1	j.	j.	PROPN
ejpam-2311	23	2	pure	pure	PROPN
ejpam-2311	23	3	appl	appl	PROPN
ejpam-2311	23	4	.	.	PROPN
ejpam-2311	23	5	math	math	PROPN
ejpam-2311	23	6	,	,	PUNCT
ejpam-2311	23	7	7	7	NUM
ejpam-2311	23	8	(	(	PUNCT
ejpam-2311	23	9	2014	2014	NUM
ejpam-2311	23	10	)	)	PUNCT
ejpam-2311	23	11	,	,	PUNCT
ejpam-2311	23	12	462	462	NUM
ejpam-2311	23	13	-	-	SYM
ejpam-2311	23	14	471	471	NUM
ejpam-2311	23	15	463	463	NUM
ejpam-2311	23	16	the	the	DET
ejpam-2311	23	17	structures	structure	NOUN
ejpam-2311	23	18	of	of	ADP
ejpam-2311	23	19	the	the	DET
ejpam-2311	23	20	unit	unit	NOUN
ejpam-2311	23	21	groups	group	NOUN
ejpam-2311	23	22	for	for	ADP
ejpam-2311	23	23	zc5	zc5	PROPN
ejpam-2311	23	24	,	,	PUNCT
ejpam-2311	23	25	zc8	zc8	PROPN
ejpam-2311	23	26	were	be	AUX
ejpam-2311	23	27	given	give	VERB
ejpam-2311	23	28	by	by	ADP
ejpam-2311	23	29	karpilovsky	karpilovsky	NOUN
ejpam-2311	23	30	[	[	X
ejpam-2311	23	31	5	5	NUM
ejpam-2311	23	32	]	]	PUNCT
ejpam-2311	23	33	as	as	SCONJ
ejpam-2311	23	34	follows	follow	VERB
ejpam-2311	23	35	:	:	PUNCT
ejpam-2311	23	36	u(zc5	u(zc5	ADJ
ejpam-2311	23	37	)	)	PUNCT
ejpam-2311	23	38	=	=	NOUN
ejpam-2311	23	39	±	±	NOUN
ejpam-2311	23	40	c5×	c5×	NOUN
ejpam-2311	23	41	<	<	X
ejpam-2311	23	42	−1	−1	NOUN
ejpam-2311	23	43	+	+	CCONJ
ejpam-2311	23	44	a+	a+	PUNCT
ejpam-2311	23	45	a4	a4	NOUN
ejpam-2311	23	46	>	>	PUNCT
ejpam-2311	23	47	and	and	CCONJ
ejpam-2311	23	48	u(zc8	u(zc8	ADJ
ejpam-2311	23	49	)	)	PUNCT
ejpam-2311	23	50	=	=	NOUN
ejpam-2311	23	51	±	±	NUM
ejpam-2311	23	52	c8×	c8×	NOUN
ejpam-2311	23	53	<	<	X
ejpam-2311	23	54	2	2	NUM
ejpam-2311	23	55	+	+	NUM
ejpam-2311	23	56	(	(	PUNCT
ejpam-2311	23	57	a+	a+	PRON
ejpam-2311	23	58	a7)−	a7)−	NOUN
ejpam-2311	23	59	(	(	PUNCT
ejpam-2311	23	60	a3	a3	NOUN
ejpam-2311	23	61	+	+	CCONJ
ejpam-2311	23	62	a5)−	a5)−	X
ejpam-2311	23	63	a4	a4	NOUN
ejpam-2311	23	64	>	>	PUNCT
ejpam-2311	23	65	.	.	PUNCT
ejpam-2311	24	1	aleev	aleev	NOUN
ejpam-2311	24	2	and	and	CCONJ
ejpam-2311	24	3	panina	panina	ADJ
ejpam-2311	25	1	[	[	X
ejpam-2311	25	2	1	1	X
ejpam-2311	25	3	]	]	PUNCT
ejpam-2311	25	4	described	describe	VERB
ejpam-2311	25	5	the	the	DET
ejpam-2311	25	6	structure	structure	NOUN
ejpam-2311	25	7	of	of	ADP
ejpam-2311	25	8	u(zc7	u(zc7	NOUN
ejpam-2311	25	9	)	)	PUNCT
ejpam-2311	25	10	and	and	CCONJ
ejpam-2311	25	11	u(zc9	u(zc9	PROPN
ejpam-2311	25	12	):	):	PUNCT
ejpam-2311	25	13	u(zc7	u(zc7	NOUN
ejpam-2311	25	14	)	)	PUNCT
ejpam-2311	25	15	=	=	NUM
ejpam-2311	25	16	±	±	NUM
ejpam-2311	25	17	c7×	c7×	NOUN
ejpam-2311	25	18	<	<	X
ejpam-2311	25	19	−1	−1	PROPN
ejpam-2311	25	20	+	+	CCONJ
ejpam-2311	25	21	a+	a+	PUNCT
ejpam-2311	25	22	a6,−1	a6,−1	PROPN
ejpam-2311	25	23	+	+	CCONJ
ejpam-2311	26	1	2a2	2a2	NUM
ejpam-2311	26	2	−	−	NOUN
ejpam-2311	26	3	a3	a3	NOUN
ejpam-2311	26	4	−	−	PROPN
ejpam-2311	26	5	a4	a4	NOUN
ejpam-2311	26	6	+	+	CCONJ
ejpam-2311	26	7	2a5	2a5	NUM
ejpam-2311	26	8	>	>	X
ejpam-2311	26	9	and	and	CCONJ
ejpam-2311	26	10	u(zc9	u(zc9	ADJ
ejpam-2311	26	11	)	)	PUNCT
ejpam-2311	27	1	=	=	NOUN
ejpam-2311	27	2	±	±	NUM
ejpam-2311	27	3	c9×	c9×	NOUN
ejpam-2311	27	4	<	<	X
ejpam-2311	27	5	−1−	−1−	X
ejpam-2311	27	6	(	(	PUNCT
ejpam-2311	27	7	a+	a+	PUNCT
ejpam-2311	27	8	a8)−	a8)−	PROPN
ejpam-2311	27	9	(	(	PUNCT
ejpam-2311	27	10	a2	a2	PROPN
ejpam-2311	27	11	+	+	CCONJ
ejpam-2311	27	12	a7	a7	PROPN
ejpam-2311	27	13	)	)	PUNCT
ejpam-2311	28	1	+	+	CCONJ
ejpam-2311	28	2	2(a4	2(a4	NUM
ejpam-2311	28	3	+	+	CCONJ
ejpam-2311	28	4	a5	a5	NOUN
ejpam-2311	28	5	)	)	PUNCT
ejpam-2311	28	6	>	>	X
ejpam-2311	29	1	×	×	NOUN
ejpam-2311	29	2	<	<	X
ejpam-2311	29	3	−1−	−1−	X
ejpam-2311	29	4	(	(	PUNCT
ejpam-2311	29	5	a+	a+	X
ejpam-2311	29	6	a8	a8	PROPN
ejpam-2311	29	7	)	)	PUNCT
ejpam-2311	29	8	+	+	CCONJ
ejpam-2311	29	9	(	(	PUNCT
ejpam-2311	29	10	a2	a2	PROPN
ejpam-2311	29	11	+	+	CCONJ
ejpam-2311	29	12	a7	a7	PROPN
ejpam-2311	29	13	)	)	PUNCT
ejpam-2311	29	14	>	>	X
ejpam-2311	29	15	.	.	PUNCT
ejpam-2311	30	1	the	the	DET
ejpam-2311	30	2	unit	unit	NOUN
ejpam-2311	30	3	group	group	NOUN
ejpam-2311	30	4	u(zc12	u(zc12	PROPN
ejpam-2311	30	5	)	)	PUNCT
ejpam-2311	30	6	was	be	AUX
ejpam-2311	30	7	characterized	characterize	VERB
ejpam-2311	30	8	by	by	ADP
ejpam-2311	30	9	bilgin	bilgin	NOUN
ejpam-2311	30	10	[	[	X
ejpam-2311	30	11	3	3	NUM
ejpam-2311	30	12	]	]	PUNCT
ejpam-2311	30	13	as	as	ADP
ejpam-2311	30	14	,	,	PUNCT
ejpam-2311	30	15	u(zc12	u(zc12	NOUN
ejpam-2311	30	16	)	)	PUNCT
ejpam-2311	30	17	=	=	PUNCT
ejpam-2311	31	1	±c12×	±c12×	ADJ
ejpam-2311	31	2	<	<	X
ejpam-2311	31	3	3	3	NUM
ejpam-2311	31	4	+	+	NUM
ejpam-2311	31	5	2(a+	2(a+	NUM
ejpam-2311	31	6	a11	a11	NOUN
ejpam-2311	31	7	)	)	PUNCT
ejpam-2311	31	8	+	+	CCONJ
ejpam-2311	31	9	(	(	PUNCT
ejpam-2311	31	10	a2	a2	PROPN
ejpam-2311	31	11	+	+	CCONJ
ejpam-2311	31	12	a10)−	a10)−	PROPN
ejpam-2311	31	13	(	(	PUNCT
ejpam-2311	31	14	a4	a4	NOUN
ejpam-2311	31	15	+	+	CCONJ
ejpam-2311	31	16	a8)−	a8)−	PROPN
ejpam-2311	31	17	2(a5	2(a5	NUM
ejpam-2311	31	18	+	+	NUM
ejpam-2311	31	19	a7)−	a7)−	NOUN
ejpam-2311	31	20	2a6	2a6	PROPN
ejpam-2311	31	21	>	>	X
ejpam-2311	31	22	.	.	PUNCT
ejpam-2311	32	1	low	low	ADJ
ejpam-2311	33	1	[	[	X
ejpam-2311	33	2	6	6	NUM
ejpam-2311	33	3	]	]	PUNCT
ejpam-2311	33	4	gave	give	VERB
ejpam-2311	33	5	a	a	DET
ejpam-2311	33	6	generalization	generalization	NOUN
ejpam-2311	33	7	of	of	ADP
ejpam-2311	33	8	the	the	DET
ejpam-2311	33	9	structure	structure	NOUN
ejpam-2311	33	10	of	of	ADP
ejpam-2311	33	11	the	the	DET
ejpam-2311	33	12	the	the	DET
ejpam-2311	33	13	unit	unit	NOUN
ejpam-2311	33	14	group	group	NOUN
ejpam-2311	33	15	for	for	ADP
ejpam-2311	33	16	cn	cn	PROPN
ejpam-2311	33	17	×	×	PROPN
ejpam-2311	33	18	c2	c2	PROPN
ejpam-2311	33	19	using	use	VERB
ejpam-2311	33	20	exact	exact	ADJ
ejpam-2311	33	21	sequences	sequence	NOUN
ejpam-2311	33	22	.	.	PUNCT
ejpam-2311	34	1	remark	remark	PROPN
ejpam-2311	34	2	1	1	NUM
ejpam-2311	34	3	.	.	PUNCT
ejpam-2311	35	1	since	since	SCONJ
ejpam-2311	35	2	u(zg	u(zg	NUM
ejpam-2311	35	3	)	)	PUNCT
ejpam-2311	35	4	=	=	SYM
ejpam-2311	35	5	±u1(zg	±u1(zg	ADJ
ejpam-2311	35	6	)	)	PUNCT
ejpam-2311	35	7	,	,	PUNCT
ejpam-2311	35	8	we	we	PRON
ejpam-2311	35	9	will	will	AUX
ejpam-2311	35	10	use	use	VERB
ejpam-2311	35	11	u1(zg	u1(zg	PROPN
ejpam-2311	35	12	)	)	PUNCT
ejpam-2311	35	13	instead	instead	ADV
ejpam-2311	35	14	of	of	ADP
ejpam-2311	35	15	u(zg	u(zg	NUM
ejpam-2311	35	16	)	)	PUNCT
ejpam-2311	35	17	.	.	PUNCT
ejpam-2311	36	1	in	in	ADP
ejpam-2311	36	2	this	this	DET
ejpam-2311	36	3	study	study	NOUN
ejpam-2311	36	4	,	,	PUNCT
ejpam-2311	36	5	we	we	PRON
ejpam-2311	36	6	extend	extend	VERB
ejpam-2311	36	7	group	group	NOUN
ejpam-2311	36	8	epimorphisms	epimorphism	NOUN
ejpam-2311	36	9	linearly	linearly	ADV
ejpam-2311	36	10	over	over	ADP
ejpam-2311	36	11	z	z	NOUN
ejpam-2311	36	12	to	to	PART
ejpam-2311	36	13	ring	ring	VERB
ejpam-2311	36	14	epimorphisms	epimorphism	NOUN
ejpam-2311	36	15	in	in	ADP
ejpam-2311	36	16	the	the	DET
ejpam-2311	36	17	first	first	ADJ
ejpam-2311	36	18	place	place	NOUN
ejpam-2311	36	19	.	.	PUNCT
ejpam-2311	37	1	after	after	ADP
ejpam-2311	37	2	that	that	PRON
ejpam-2311	37	3	,	,	PUNCT
ejpam-2311	37	4	we	we	PRON
ejpam-2311	37	5	determine	determine	VERB
ejpam-2311	37	6	their	their	PRON
ejpam-2311	37	7	kernels	kernel	NOUN
ejpam-2311	37	8	to	to	PART
ejpam-2311	37	9	construct	construct	VERB
ejpam-2311	37	10	exact	exact	ADJ
ejpam-2311	37	11	sequences	sequence	NOUN
ejpam-2311	37	12	at	at	ADP
ejpam-2311	37	13	ring	ring	NOUN
ejpam-2311	37	14	level	level	NOUN
ejpam-2311	37	15	.	.	PUNCT
ejpam-2311	38	1	then	then	ADV
ejpam-2311	38	2	,	,	PUNCT
ejpam-2311	38	3	by	by	ADP
ejpam-2311	38	4	restricting	restrict	VERB
ejpam-2311	38	5	these	these	DET
ejpam-2311	38	6	exact	exact	ADJ
ejpam-2311	38	7	sequences	sequence	NOUN
ejpam-2311	38	8	to	to	ADP
ejpam-2311	38	9	unit	unit	NOUN
ejpam-2311	38	10	level	level	NOUN
ejpam-2311	38	11	,	,	PUNCT
ejpam-2311	38	12	we	we	PRON
ejpam-2311	38	13	characterize	characterize	VERB
ejpam-2311	38	14	u1(z[cn×	u1(z[cn×	PROPN
ejpam-2311	38	15	k4	k4	NOUN
ejpam-2311	38	16	]	]	PUNCT
ejpam-2311	38	17	)	)	PUNCT
ejpam-2311	38	18	as	as	ADP
ejpam-2311	38	19	an	an	DET
ejpam-2311	38	20	internal	internal	ADJ
ejpam-2311	38	21	direct	direct	ADJ
ejpam-2311	38	22	product	product	NOUN
ejpam-2311	38	23	of	of	ADP
ejpam-2311	38	24	four	four	NUM
ejpam-2311	38	25	subgroups	subgroup	NOUN
ejpam-2311	38	26	.	.	PUNCT
ejpam-2311	39	1	finally	finally	ADV
ejpam-2311	39	2	we	we	PRON
ejpam-2311	39	3	describe	describe	VERB
ejpam-2311	39	4	these	these	DET
ejpam-2311	39	5	subgroups	subgroup	NOUN
ejpam-2311	39	6	explicitly	explicitly	ADV
ejpam-2311	39	7	and	and	CCONJ
ejpam-2311	39	8	give	give	VERB
ejpam-2311	39	9	two	two	NUM
ejpam-2311	39	10	concrete	concrete	ADJ
ejpam-2311	39	11	examples	example	NOUN
ejpam-2311	39	12	for	for	ADP
ejpam-2311	39	13	cyclic	cyclic	ADJ
ejpam-2311	39	14	groups	group	NOUN
ejpam-2311	39	15	c5	c5	PROPN
ejpam-2311	39	16	and	and	CCONJ
ejpam-2311	39	17	c7	c7	PROPN
ejpam-2311	39	18	.	.	PROPN
ejpam-2311	40	1	2	2	X
ejpam-2311	40	2	.	.	X
ejpam-2311	40	3	main	main	ADJ
ejpam-2311	40	4	structure	structure	NOUN
ejpam-2311	40	5	theorem	theorem	NOUN
ejpam-2311	40	6	we	we	PRON
ejpam-2311	40	7	can	can	AUX
ejpam-2311	40	8	construct	construct	VERB
ejpam-2311	40	9	the	the	DET
ejpam-2311	40	10	following	follow	VERB
ejpam-2311	40	11	group	group	NOUN
ejpam-2311	40	12	epimorphisms	epimorphism	NOUN
ejpam-2311	40	13	by	by	ADP
ejpam-2311	40	14	using	use	VERB
ejpam-2311	40	15	abelian	abelian	PROPN
ejpam-2311	40	16	group	group	NOUN
ejpam-2311	40	17	cn	cn	PROPN
ejpam-2311	40	18	×	×	PROPN
ejpam-2311	40	19	k4	k4	NOUN
ejpam-2311	40	20	=	=	PROPN
ejpam-2311	40	21	<	<	X
ejpam-2311	40	22	a	a	X
ejpam-2311	40	23	,	,	PUNCT
ejpam-2311	40	24	x	x	X
ejpam-2311	40	25	,	,	PUNCT
ejpam-2311	40	26	y	y	PROPN
ejpam-2311	40	27	:	:	PUNCT
ejpam-2311	41	1	an	an	DET
ejpam-2311	41	2	=	=	X
ejpam-2311	41	3	x2	x2	NOUN
ejpam-2311	41	4	=	=	PUNCT
ejpam-2311	41	5	y2	y2	NOUN
ejpam-2311	41	6	=	=	SYM
ejpam-2311	41	7	1	1	NUM
ejpam-2311	41	8	,	,	PUNCT
ejpam-2311	41	9	ax	ax	NOUN
ejpam-2311	41	10	=	=	SYM
ejpam-2311	41	11	xa	xa	PROPN
ejpam-2311	41	12	,	,	PUNCT
ejpam-2311	41	13	a	a	DET
ejpam-2311	41	14	y	y	PROPN
ejpam-2311	41	15	=	=	SYM
ejpam-2311	41	16	ya	ya	PROPN
ejpam-2311	41	17	,	,	PUNCT
ejpam-2311	41	18	x	x	PROPN
ejpam-2311	41	19	y	y	NOUN
ejpam-2311	41	20	=	=	PUNCT
ejpam-2311	41	21	y	y	PROPN
ejpam-2311	41	22	x	x	SYM
ejpam-2311	41	23	>	>	X
ejpam-2311	41	24	as	as	SCONJ
ejpam-2311	41	25	follows	follow	VERB
ejpam-2311	41	26	:	:	PUNCT
ejpam-2311	41	27	πx	πx	NOUN
ejpam-2311	41	28	:	:	PUNCT
ejpam-2311	41	29	cn	cn	INTJ
ejpam-2311	41	30	×	×	NOUN
ejpam-2311	41	31	k4→	k4→	NOUN
ejpam-2311	42	1	cn	cn	PROPN
ejpam-2311	42	2	×	×	PROPN
ejpam-2311	42	3	y	y	PROPN
ejpam-2311	42	4	�	�	PROPN
ejpam-2311	42	5	,	,	PUNCT
ejpam-2311	42	6	πy	πy	INTJ
ejpam-2311	42	7	:	:	PUNCT
ejpam-2311	42	8	cn	cn	PROPN
ejpam-2311	42	9	×	×	NOUN
ejpam-2311	42	10	k4→	k4→	NOUN
ejpam-2311	42	11	cn	cn	PROPN
ejpam-2311	42	12	×	×	PROPN
ejpam-2311	42	13	〈	〈	PROPN
ejpam-2311	42	14	x	x	X
ejpam-2311	42	15	〉	〉	NOUN
ejpam-2311	42	16	a	a	DET
ejpam-2311	42	17	7→	7→	NUM
ejpam-2311	42	18	a	a	DET
ejpam-2311	42	19	a	a	DET
ejpam-2311	42	20	7→	7→	NUM
ejpam-2311	43	1	a	a	DET
ejpam-2311	43	2	x	x	SYM
ejpam-2311	43	3	7→	7→	NUM
ejpam-2311	43	4	1	1	NUM
ejpam-2311	43	5	x	x	SYM
ejpam-2311	43	6	7→	7→	NUM
ejpam-2311	43	7	x	x	SYM
ejpam-2311	43	8	y	y	NOUN
ejpam-2311	43	9	7→	7→	NUM
ejpam-2311	43	10	y	y	NOUN
ejpam-2311	43	11	y	y	PROPN
ejpam-2311	43	12	7→	7→	PROPN
ejpam-2311	43	13	1	1	NUM
ejpam-2311	43	14	.	.	PUNCT
ejpam-2311	44	1	if	if	SCONJ
ejpam-2311	44	2	we	we	PRON
ejpam-2311	44	3	denote	denote	VERB
ejpam-2311	44	4	the	the	DET
ejpam-2311	44	5	identity	identity	NOUN
ejpam-2311	44	6	map	map	NOUN
ejpam-2311	44	7	by	by	ADP
ejpam-2311	44	8	ι	ι	PROPN
ejpam-2311	44	9	,	,	PUNCT
ejpam-2311	44	10	then	then	ADV
ejpam-2311	44	11	we	we	PRON
ejpam-2311	44	12	get	get	VERB
ejpam-2311	44	13	the	the	DET
ejpam-2311	44	14	following	follow	VERB
ejpam-2311	44	15	exact	exact	ADJ
ejpam-2311	44	16	sequences	sequence	NOUN
ejpam-2311	44	17	:	:	PUNCT
ejpam-2311	44	18	〈	〈	ADJ
ejpam-2311	44	19	x	x	X
ejpam-2311	44	20	〉	〉	NOUN
ejpam-2311	44	21	ι	ι	PRON
ejpam-2311	44	22	−→	−→	ADJ
ejpam-2311	44	23	cn	cn	X
ejpam-2311	44	24	×	×	PROPN
ejpam-2311	44	25	k4	k4	PROPN
ejpam-2311	44	26	πx−→	πx−→	PROPN
ejpam-2311	44	27	cn	cn	INTJ
ejpam-2311	44	28	×	×	PROPN
ejpam-2311	44	29	y	y	PROPN
ejpam-2311	44	30	�	�	PROPN
ejpam-2311	44	31	,	,	PUNCT
ejpam-2311	44	32	y	y	PROPN
ejpam-2311	44	33	�	�	PROPN
ejpam-2311	45	1	ι	ι	ADP
ejpam-2311	45	2	−→	−→	ADJ
ejpam-2311	46	1	cn	cn	INTJ
ejpam-2311	46	2	×	×	NOUN
ejpam-2311	46	3	k4	k4	NOUN
ejpam-2311	46	4	πy	πy	VERB
ejpam-2311	46	5	−→	−→	NOUN
ejpam-2311	47	1	cn	cn	X
ejpam-2311	47	2	×	×	PROPN
ejpam-2311	47	3	〈	〈	NOUN
ejpam-2311	47	4	x	x	NOUN
ejpam-2311	47	5	〉	〉	NOUN
ejpam-2311	47	6	.	.	PUNCT
ejpam-2311	48	1	by	by	ADP
ejpam-2311	48	2	extending	extend	VERB
ejpam-2311	48	3	these	these	DET
ejpam-2311	48	4	epimorphisms	epimorphism	NOUN
ejpam-2311	48	5	linearly	linearly	ADV
ejpam-2311	48	6	over	over	ADP
ejpam-2311	48	7	z	z	PROPN
ejpam-2311	48	8	,	,	PUNCT
ejpam-2311	48	9	the	the	DET
ejpam-2311	48	10	following	follow	VERB
ejpam-2311	48	11	ring	ring	NOUN
ejpam-2311	48	12	epimorphisms	epimorphism	NOUN
ejpam-2311	48	13	are	be	AUX
ejpam-2311	48	14	obtained	obtain	VERB
ejpam-2311	48	15	:	:	PUNCT
ejpam-2311	48	16	i.g	i.g	PROPN
ejpam-2311	48	17	.	.	PROPN
ejpam-2311	48	18	kelebek	kelebek	PROPN
ejpam-2311	48	19	,	,	PUNCT
ejpam-2311	48	20	t.	t.	PROPN
ejpam-2311	48	21	bilgin	bilgin	PROPN
ejpam-2311	48	22	/	/	SYM
ejpam-2311	48	23	eur	eur	PROPN
ejpam-2311	48	24	.	.	PUNCT
ejpam-2311	49	1	j.	j.	PROPN
ejpam-2311	49	2	pure	pure	PROPN
ejpam-2311	49	3	appl	appl	PROPN
ejpam-2311	49	4	.	.	PROPN
ejpam-2311	49	5	math	math	PROPN
ejpam-2311	49	6	,	,	PUNCT
ejpam-2311	49	7	7	7	NUM
ejpam-2311	49	8	(	(	PUNCT
ejpam-2311	49	9	2014	2014	NUM
ejpam-2311	49	10	)	)	PUNCT
ejpam-2311	49	11	,	,	PUNCT
ejpam-2311	49	12	462	462	NUM
ejpam-2311	49	13	-	-	SYM
ejpam-2311	49	14	471	471	NUM
ejpam-2311	49	15	464	464	NUM
ejpam-2311	49	16	πx	πx	NOUN
ejpam-2311	49	17	:	:	PUNCT
ejpam-2311	49	18	z[cn	z[cn	NUM
ejpam-2311	49	19	×	×	NOUN
ejpam-2311	49	20	k4	k4	NOUN
ejpam-2311	49	21	]	]	X
ejpam-2311	49	22	−→	−→	NOUN
ejpam-2311	49	23	z[cn	z[cn	NOUN
ejpam-2311	49	24	×	×	PROPN
ejpam-2311	49	25	y	y	PROPN
ejpam-2311	49	26	�	�	PROPN
ejpam-2311	49	27	]	]	PUNCT
ejpam-2311	49	28	p0	p0	PROPN
ejpam-2311	49	29	+	+	CCONJ
ejpam-2311	49	30	p1	p1	PROPN
ejpam-2311	49	31	x	x	SYM
ejpam-2311	50	1	+	+	CCONJ
ejpam-2311	50	2	p2	p2	PROPN
ejpam-2311	50	3	y	y	PROPN
ejpam-2311	50	4	+	+	CCONJ
ejpam-2311	50	5	p3	p3	PROPN
ejpam-2311	50	6	x	x	SYM
ejpam-2311	50	7	y	y	PROPN
ejpam-2311	50	8	7→(p0	7→(p0	PROPN
ejpam-2311	50	9	+	+	CCONJ
ejpam-2311	50	10	p1	p1	NOUN
ejpam-2311	50	11	)	)	PUNCT
ejpam-2311	50	12	+	+	CCONJ
ejpam-2311	50	13	(	(	PUNCT
ejpam-2311	50	14	p2	p2	X
ejpam-2311	50	15	+	+	CCONJ
ejpam-2311	50	16	p3)y	p3)y	NOUN
ejpam-2311	50	17	πy	πy	NOUN
ejpam-2311	50	18	:	:	PUNCT
ejpam-2311	50	19	z[cn	z[cn	NUM
ejpam-2311	50	20	×	×	NOUN
ejpam-2311	50	21	k4	k4	NOUN
ejpam-2311	50	22	]	]	X
ejpam-2311	50	23	−→	−→	NOUN
ejpam-2311	50	24	z[cn	z[cn	NUM
ejpam-2311	50	25	×	×	NOUN
ejpam-2311	50	26	〈	〈	NOUN
ejpam-2311	50	27	x	x	X
ejpam-2311	50	28	〉	〉	NOUN
ejpam-2311	50	29	]	]	PUNCT
ejpam-2311	50	30	p0	p0	NOUN
ejpam-2311	50	31	+	+	CCONJ
ejpam-2311	50	32	p1	p1	PROPN
ejpam-2311	50	33	x	x	SYM
ejpam-2311	50	34	+	+	CCONJ
ejpam-2311	50	35	p2	p2	PROPN
ejpam-2311	50	36	y	y	PROPN
ejpam-2311	50	37	+	+	CCONJ
ejpam-2311	50	38	p3	p3	PROPN
ejpam-2311	50	39	x	x	SYM
ejpam-2311	50	40	y	y	PROPN
ejpam-2311	50	41	7→(p0	7→(p0	NOUN
ejpam-2311	50	42	+	+	CCONJ
ejpam-2311	50	43	p2	p2	NOUN
ejpam-2311	50	44	)	)	PUNCT
ejpam-2311	50	45	+	+	CCONJ
ejpam-2311	50	46	(	(	PUNCT
ejpam-2311	50	47	p1	p1	NOUN
ejpam-2311	50	48	+	+	CCONJ
ejpam-2311	50	49	p3)x	p3)x	PROPN
ejpam-2311	50	50	.	.	PUNCT
ejpam-2311	51	1	then	then	ADV
ejpam-2311	51	2	,	,	PUNCT
ejpam-2311	51	3	we	we	PRON
ejpam-2311	51	4	can	can	AUX
ejpam-2311	51	5	calculate	calculate	VERB
ejpam-2311	51	6	the	the	DET
ejpam-2311	51	7	kernels	kernel	NOUN
ejpam-2311	51	8	of	of	ADP
ejpam-2311	51	9	the	the	DET
ejpam-2311	51	10	epimorphisms	epimorphism	NOUN
ejpam-2311	51	11	.	.	PUNCT
ejpam-2311	52	1	n	n	PRON
ejpam-2311	53	1	x	x	X
ejpam-2311	53	2	=	=	NOUN
ejpam-2311	53	3	kerπx	kerπx	NOUN
ejpam-2311	53	4	=	=	SYM
ejpam-2311	53	5	�	�	PROPN
ejpam-2311	53	6	p	p	NOUN
ejpam-2311	53	7	=	=	PROPN
ejpam-2311	53	8	p0	p0	NOUN
ejpam-2311	53	9	+	+	CCONJ
ejpam-2311	53	10	p1	p1	PROPN
ejpam-2311	53	11	x	x	SYM
ejpam-2311	53	12	+	+	CCONJ
ejpam-2311	53	13	p2	p2	PROPN
ejpam-2311	53	14	y	y	PROPN
ejpam-2311	53	15	+	+	CCONJ
ejpam-2311	53	16	p3	p3	PROPN
ejpam-2311	53	17	x	x	SYM
ejpam-2311	53	18	y	y	PROPN
ejpam-2311	53	19	∈	∈	PROPN
ejpam-2311	53	20	zcn	zcn	NOUN
ejpam-2311	53	21	:	:	PUNCT
ejpam-2311	53	22	πx(p	πx(p	X
ejpam-2311	53	23	)	)	PUNCT
ejpam-2311	53	24	=	=	SYM
ejpam-2311	53	25	0	0	PUNCT
ejpam-2311	53	26	=	=	SYM
ejpam-2311	53	27	�	�	PROPN
ejpam-2311	53	28	p	p	NOUN
ejpam-2311	53	29	=	=	PROPN
ejpam-2311	53	30	p0	p0	NOUN
ejpam-2311	53	31	+	+	CCONJ
ejpam-2311	53	32	p1	p1	PROPN
ejpam-2311	53	33	x	x	SYM
ejpam-2311	53	34	+	+	CCONJ
ejpam-2311	53	35	p2	p2	PROPN
ejpam-2311	53	36	y	y	PROPN
ejpam-2311	53	37	+	+	CCONJ
ejpam-2311	53	38	p3	p3	PROPN
ejpam-2311	53	39	x	x	SYM
ejpam-2311	53	40	y	y	PROPN
ejpam-2311	53	41	∈	∈	PROPN
ejpam-2311	53	42	zcn	zcn	NOUN
ejpam-2311	53	43	:	:	PUNCT
ejpam-2311	53	44	(	(	PUNCT
ejpam-2311	53	45	p0	p0	NOUN
ejpam-2311	53	46	+	+	CCONJ
ejpam-2311	53	47	p1	p1	NOUN
ejpam-2311	53	48	)	)	PUNCT
ejpam-2311	53	49	+	+	CCONJ
ejpam-2311	53	50	(	(	PUNCT
ejpam-2311	53	51	p2	p2	X
ejpam-2311	53	52	+	+	CCONJ
ejpam-2311	53	53	p3)y	p3)y	NOUN
ejpam-2311	53	54	=	=	SYM
ejpam-2311	53	55	0	0	PUNCT
ejpam-2311	53	56	=	=	SYM
ejpam-2311	53	57	�	�	PROPN
ejpam-2311	53	58	p	p	NOUN
ejpam-2311	53	59	=	=	PROPN
ejpam-2311	53	60	p0	p0	NOUN
ejpam-2311	53	61	+	+	CCONJ
ejpam-2311	53	62	p1	p1	PROPN
ejpam-2311	53	63	x	x	SYM
ejpam-2311	53	64	+	+	CCONJ
ejpam-2311	53	65	p2	p2	PROPN
ejpam-2311	53	66	y	y	PROPN
ejpam-2311	53	67	+	+	CCONJ
ejpam-2311	53	68	p3	p3	PROPN
ejpam-2311	53	69	x	x	SYM
ejpam-2311	53	70	y	y	PROPN
ejpam-2311	53	71	∈	∈	PROPN
ejpam-2311	53	72	zcn	zcn	NOUN
ejpam-2311	53	73	:	:	PUNCT
ejpam-2311	53	74	p0	p0	NOUN
ejpam-2311	53	75	=	=	SYM
ejpam-2311	53	76	−p1	−p1	PROPN
ejpam-2311	53	77	,	,	PUNCT
ejpam-2311	53	78	p2	p2	X
ejpam-2311	53	79	=	=	SYM
ejpam-2311	53	80	−p3	−p3	PROPN
ejpam-2311	53	81	=	=	SYM
ejpam-2311	53	82	�	�	PROPN
ejpam-2311	53	83	(	(	PUNCT
ejpam-2311	53	84	x	x	SYM
ejpam-2311	53	85	−	−	PROPN
ejpam-2311	53	86	1)p1	1)p1	NUM
ejpam-2311	53	87	+	+	NUM
ejpam-2311	53	88	y(x	y(x	PROPN
ejpam-2311	53	89	−	−	PROPN
ejpam-2311	54	1	1)p3	1)p3	PROPN
ejpam-2311	54	2	:	:	PUNCT
ejpam-2311	54	3	p1	p1	PROPN
ejpam-2311	54	4	,	,	PUNCT
ejpam-2311	54	5	p3	p3	PROPN
ejpam-2311	54	6	∈	∈	PROPN
ejpam-2311	54	7	zcn	zcn	NOUN
ejpam-2311	54	8	=	=	SYM
ejpam-2311	54	9	�	�	PROPN
ejpam-2311	54	10	(	(	PUNCT
ejpam-2311	54	11	x	x	SYM
ejpam-2311	54	12	−	−	PROPN
ejpam-2311	54	13	1)[p1	1)[p1	NUM
ejpam-2311	54	14	+	+	NUM
ejpam-2311	54	15	yp3	yp3	PROPN
ejpam-2311	54	16	]	]	X
ejpam-2311	54	17	:	:	PUNCT
ejpam-2311	54	18	p1	p1	NOUN
ejpam-2311	54	19	,	,	PUNCT
ejpam-2311	54	20	p3	p3	PROPN
ejpam-2311	54	21	∈	∈	PROPN
ejpam-2311	54	22	zcn	zcn	NOUN
ejpam-2311	54	23	=(	=(	NOUN
ejpam-2311	54	24	x	x	SYM
ejpam-2311	54	25	−	−	PROPN
ejpam-2311	54	26	1)z[cn	1)z[cn	NUM
ejpam-2311	54	27	×	×	NOUN
ejpam-2311	54	28	y	y	PROPN
ejpam-2311	54	29	�	�	PROPN
ejpam-2311	54	30	]	]	PUNCT
ejpam-2311	54	31	.	.	PUNCT
ejpam-2311	55	1	similarly	similarly	ADV
ejpam-2311	55	2	n	n	CCONJ
ejpam-2311	55	3	y	y	NOUN
ejpam-2311	55	4	=	=	SYM
ejpam-2311	55	5	(	(	PUNCT
ejpam-2311	55	6	y	y	PROPN
ejpam-2311	55	7	−1)z[cn×〈x	−1)z[cn×〈x	PROPN
ejpam-2311	55	8	〉	〉	NOUN
ejpam-2311	55	9	]	]	PUNCT
ejpam-2311	55	10	.	.	PUNCT
ejpam-2311	56	1	by	by	ADP
ejpam-2311	56	2	restricting	restrict	VERB
ejpam-2311	56	3	πx	πx	PRON
ejpam-2311	56	4	and	and	CCONJ
ejpam-2311	56	5	πy	πy	VERB
ejpam-2311	56	6	to	to	ADP
ejpam-2311	56	7	the	the	DET
ejpam-2311	56	8	kernels	kernel	NOUN
ejpam-2311	56	9	n	n	CCONJ
ejpam-2311	56	10	y	y	PROPN
ejpam-2311	56	11	and	and	CCONJ
ejpam-2311	56	12	n	n	CCONJ
ejpam-2311	56	13	x	x	NOUN
ejpam-2311	56	14	we	we	PRON
ejpam-2311	56	15	get	get	VERB
ejpam-2311	56	16	the	the	DET
ejpam-2311	56	17	images	image	NOUN
ejpam-2311	57	1	k	k	X
ejpam-2311	57	2	y	y	PROPN
ejpam-2311	57	3	=	=	SYM
ejpam-2311	57	4	(	(	PUNCT
ejpam-2311	57	5	y	y	PROPN
ejpam-2311	57	6	−	−	PROPN
ejpam-2311	57	7	1)zcn	1)zcn	NUM
ejpam-2311	57	8	and	and	CCONJ
ejpam-2311	57	9	k	k	NOUN
ejpam-2311	57	10	x	x	SYM
ejpam-2311	57	11	=	=	PUNCT
ejpam-2311	57	12	(	(	PUNCT
ejpam-2311	57	13	x	x	SYM
ejpam-2311	57	14	−	−	PROPN
ejpam-2311	57	15	1)zcn	1)zcn	NUM
ejpam-2311	57	16	respectively	respectively	ADV
ejpam-2311	57	17	.	.	PUNCT
ejpam-2311	58	1	of	of	ADP
ejpam-2311	58	2	course	course	NOUN
ejpam-2311	58	3	,	,	PUNCT
ejpam-2311	58	4	k	k	PROPN
ejpam-2311	58	5	y	y	PROPN
ejpam-2311	58	6	is	be	AUX
ejpam-2311	58	7	the	the	DET
ejpam-2311	58	8	kernel	kernel	NOUN
ejpam-2311	58	9	of	of	ADP
ejpam-2311	58	10	πy	πy	NOUN
ejpam-2311	59	1	and	and	CCONJ
ejpam-2311	59	2	k	k	PROPN
ejpam-2311	59	3	x	x	X
ejpam-2311	59	4	is	be	AUX
ejpam-2311	59	5	also	also	ADV
ejpam-2311	59	6	the	the	DET
ejpam-2311	59	7	kernel	kernel	NOUN
ejpam-2311	59	8	of	of	ADP
ejpam-2311	59	9	πx	πx	X
ejpam-2311	59	10	.	.	PUNCT
ejpam-2311	60	1	on	on	ADP
ejpam-2311	60	2	the	the	DET
ejpam-2311	60	3	other	other	ADJ
ejpam-2311	60	4	hand	hand	NOUN
ejpam-2311	60	5	,	,	PUNCT
ejpam-2311	60	6	the	the	DET
ejpam-2311	60	7	ring	ring	NOUN
ejpam-2311	60	8	k	k	PROPN
ejpam-2311	60	9	x	x	PUNCT
ejpam-2311	60	10	y	y	PROPN
ejpam-2311	60	11	=	=	SYM
ejpam-2311	60	12	�	�	PROPN
ejpam-2311	60	13	(	(	PUNCT
ejpam-2311	60	14	x	x	PROPN
ejpam-2311	60	15	−	−	PROPN
ejpam-2311	61	1	1)(y	1)(y	NUM
ejpam-2311	61	2	−	−	PROPN
ejpam-2311	61	3	1)p3	1)p3	PROPN
ejpam-2311	61	4	:	:	PUNCT
ejpam-2311	61	5	p3	p3	PROPN
ejpam-2311	61	6	∈	∈	PROPN
ejpam-2311	61	7	zcn	zcn	NOUN
ejpam-2311	61	8	is	be	AUX
ejpam-2311	61	9	the	the	DET
ejpam-2311	61	10	kernel	kernel	NOUN
ejpam-2311	61	11	of	of	ADP
ejpam-2311	61	12	ring	ring	NOUN
ejpam-2311	61	13	epimorphism	epimorphism	NOUN
ejpam-2311	61	14	:	:	PUNCT
ejpam-2311	61	15	πy	πy	X
ejpam-2311	61	16	:	:	PUNCT
ejpam-2311	61	17	n	n	CCONJ
ejpam-2311	61	18	x	x	VERB
ejpam-2311	61	19	−→	−→	NOUN
ejpam-2311	61	20	k	k	NOUN
ejpam-2311	61	21	x	x	X
ejpam-2311	61	22	(	(	PUNCT
ejpam-2311	61	23	x	x	SYM
ejpam-2311	61	24	−	−	PROPN
ejpam-2311	62	1	1)[p1	1)[p1	NUM
ejpam-2311	62	2	+	+	NUM
ejpam-2311	62	3	yp3	yp3	PROPN
ejpam-2311	62	4	]	]	X
ejpam-2311	62	5	7→	7→	NUM
ejpam-2311	62	6	(	(	PUNCT
ejpam-2311	62	7	x	x	SYM
ejpam-2311	62	8	−	−	PROPN
ejpam-2311	62	9	1)[p1	1)[p1	PROPN
ejpam-2311	62	10	+	+	NUM
ejpam-2311	62	11	p3	p3	PROPN
ejpam-2311	62	12	]	]	PUNCT
ejpam-2311	62	13	,	,	PUNCT
ejpam-2311	62	14	while	while	SCONJ
ejpam-2311	62	15	k	k	PROPN
ejpam-2311	62	16	x	x	X
ejpam-2311	62	17	y	y	PROPN
ejpam-2311	62	18	is	be	AUX
ejpam-2311	62	19	the	the	DET
ejpam-2311	62	20	kernel	kernel	NOUN
ejpam-2311	62	21	of	of	ADP
ejpam-2311	62	22	another	another	DET
ejpam-2311	62	23	ring	ring	NOUN
ejpam-2311	62	24	epimorphism	epimorphism	NOUN
ejpam-2311	62	25	:	:	PUNCT
ejpam-2311	62	26	πx	πx	X
ejpam-2311	62	27	:	:	PUNCT
ejpam-2311	62	28	n	n	CCONJ
ejpam-2311	62	29	y	y	PROPN
ejpam-2311	62	30	−→	−→	NOUN
ejpam-2311	63	1	k	k	PROPN
ejpam-2311	63	2	y	y	PROPN
ejpam-2311	63	3	(	(	PUNCT
ejpam-2311	63	4	y	y	PROPN
ejpam-2311	63	5	−	−	PROPN
ejpam-2311	63	6	1)[p2	1)[p2	NUM
ejpam-2311	63	7	+	+	CCONJ
ejpam-2311	63	8	x	x	SYM
ejpam-2311	63	9	p3	p3	PROPN
ejpam-2311	63	10	]	]	PUNCT
ejpam-2311	63	11	7→	7→	NUM
ejpam-2311	63	12	(	(	PUNCT
ejpam-2311	63	13	y	y	PROPN
ejpam-2311	63	14	−	−	PROPN
ejpam-2311	63	15	1)[p2	1)[p2	PROPN
ejpam-2311	63	16	+	+	NUM
ejpam-2311	63	17	p3	p3	PROPN
ejpam-2311	63	18	]	]	PUNCT
ejpam-2311	63	19	.	.	PUNCT
ejpam-2311	64	1	hence	hence	ADV
ejpam-2311	64	2	,	,	PUNCT
ejpam-2311	64	3	we	we	PRON
ejpam-2311	64	4	have	have	VERB
ejpam-2311	64	5	the	the	DET
ejpam-2311	64	6	following	following	ADJ
ejpam-2311	64	7	commutative	commutative	ADJ
ejpam-2311	64	8	diagram	diagram	NOUN
ejpam-2311	64	9	at	at	ADP
ejpam-2311	64	10	ring	ring	NOUN
ejpam-2311	64	11	level	level	NOUN
ejpam-2311	64	12	:	:	PUNCT
ejpam-2311	65	1	k	k	X
ejpam-2311	65	2	x	x	PUNCT
ejpam-2311	65	3	y	y	NOUN
ejpam-2311	65	4	ι	ι	INTJ
ejpam-2311	65	5	−→	−→	NOUN
ejpam-2311	65	6	n	n	NOUN
ejpam-2311	65	7	x	x	NOUN
ejpam-2311	65	8	πy	πy	VERB
ejpam-2311	65	9	−→	−→	NOUN
ejpam-2311	66	1	k	k	NOUN
ejpam-2311	66	2	x	x	PUNCT
ejpam-2311	66	3	ı	ı	NOUN
ejpam-2311	66	4	↓	↓	PROPN
ejpam-2311	66	5	ı	ı	PROPN
ejpam-2311	66	6	↓	↓	PROPN
ejpam-2311	66	7	ı	ı	PROPN
ejpam-2311	66	8	↓	↓	PROPN
ejpam-2311	66	9	n	n	CCONJ
ejpam-2311	66	10	y	y	NOUN
ejpam-2311	66	11	ι	ι	INTJ
ejpam-2311	66	12	−→	−→	ADJ
ejpam-2311	66	13	z[cn	z[cn	NOUN
ejpam-2311	66	14	×	×	NOUN
ejpam-2311	66	15	k4	k4	NOUN
ejpam-2311	66	16	]	]	PUNCT
ejpam-2311	66	17	πy	πy	ADP
ejpam-2311	66	18	−→	−→	NOUN
ejpam-2311	66	19	z[cn	z[cn	NOUN
ejpam-2311	66	20	×	×	NOUN
ejpam-2311	66	21	〈	〈	NOUN
ejpam-2311	66	22	x	x	X
ejpam-2311	66	23	〉	〉	NOUN
ejpam-2311	66	24	]	]	PUNCT
ejpam-2311	66	25	πx	πx	ADP
ejpam-2311	66	26	↓	↓	PROPN
ejpam-2311	66	27	πx	πx	ADP
ejpam-2311	66	28	↓	↓	PROPN
ejpam-2311	66	29	πx	πx	ADP
ejpam-2311	66	30	↓	↓	PROPN
ejpam-2311	66	31	k	k	PROPN
ejpam-2311	66	32	y	y	PROPN
ejpam-2311	67	1	ι	ι	INTJ
ejpam-2311	67	2	−→	−→	ADJ
ejpam-2311	67	3	z[cn	z[cn	NOUN
ejpam-2311	67	4	×	×	NOUN
ejpam-2311	67	5	y	y	PROPN
ejpam-2311	67	6	�	�	PROPN
ejpam-2311	67	7	]	]	PUNCT
ejpam-2311	67	8	πy	πy	VERB
ejpam-2311	67	9	−→	−→	PROPN
ejpam-2311	67	10	zcn	zcn	PROPN
ejpam-2311	67	11	.	.	PUNCT
ejpam-2311	68	1	i.g	i.g	PROPN
ejpam-2311	68	2	.	.	PROPN
ejpam-2311	68	3	kelebek	kelebek	PROPN
ejpam-2311	68	4	,	,	PUNCT
ejpam-2311	68	5	t.	t.	PROPN
ejpam-2311	68	6	bilgin	bilgin	PROPN
ejpam-2311	68	7	/	/	SYM
ejpam-2311	68	8	eur	eur	PROPN
ejpam-2311	68	9	.	.	PUNCT
ejpam-2311	69	1	j.	j.	PROPN
ejpam-2311	69	2	pure	pure	PROPN
ejpam-2311	69	3	appl	appl	PROPN
ejpam-2311	69	4	.	.	PROPN
ejpam-2311	69	5	math	math	PROPN
ejpam-2311	69	6	,	,	PUNCT
ejpam-2311	69	7	7	7	NUM
ejpam-2311	69	8	(	(	PUNCT
ejpam-2311	69	9	2014	2014	NUM
ejpam-2311	69	10	)	)	PUNCT
ejpam-2311	69	11	,	,	PUNCT
ejpam-2311	69	12	462	462	NUM
ejpam-2311	69	13	-	-	SYM
ejpam-2311	69	14	471	471	NUM
ejpam-2311	69	15	465	465	NUM
ejpam-2311	69	16	theorem	theorem	NOUN
ejpam-2311	69	17	3	3	NUM
ejpam-2311	69	18	.	.	PUNCT
ejpam-2311	70	1	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	70	2	×	×	NOUN
ejpam-2311	70	3	k4	k4	NOUN
ejpam-2311	70	4	]	]	PUNCT
ejpam-2311	70	5	)	)	PUNCT
ejpam-2311	71	1	=	=	SYM
ejpam-2311	71	2	u1(zcn)×	u1(zcn)×	PROPN
ejpam-2311	71	3	(	(	PUNCT
ejpam-2311	71	4	1	1	NUM
ejpam-2311	71	5	+	+	NUM
ejpam-2311	71	6	k	k	PROPN
ejpam-2311	71	7	x)×	x)×	SYM
ejpam-2311	71	8	(	(	PUNCT
ejpam-2311	71	9	1	1	NUM
ejpam-2311	71	10	+	+	NUM
ejpam-2311	71	11	k	k	NOUN
ejpam-2311	71	12	y)×	y)×	NOUN
ejpam-2311	71	13	(	(	PUNCT
ejpam-2311	71	14	1	1	NUM
ejpam-2311	71	15	+	+	NUM
ejpam-2311	71	16	k	k	PROPN
ejpam-2311	71	17	x	x	SYM
ejpam-2311	71	18	y	y	PROPN
ejpam-2311	71	19	)	)	PUNCT
ejpam-2311	71	20	.	.	PUNCT
ejpam-2311	72	1	proof	proof	NOUN
ejpam-2311	72	2	.	.	PUNCT
ejpam-2311	73	1	by	by	ADP
ejpam-2311	73	2	restricting	restrict	VERB
ejpam-2311	73	3	πx	πx	PRON
ejpam-2311	73	4	and	and	CCONJ
ejpam-2311	73	5	πy	πy	VERB
ejpam-2311	73	6	to	to	ADP
ejpam-2311	73	7	the	the	DET
ejpam-2311	73	8	the	the	DET
ejpam-2311	73	9	unit	unit	NOUN
ejpam-2311	73	10	group	group	NOUN
ejpam-2311	73	11	u1(z[cn×k4	u1(z[cn×k4	ADP
ejpam-2311	73	12	]	]	PUNCT
ejpam-2311	73	13	)	)	PUNCT
ejpam-2311	73	14	,	,	PUNCT
ejpam-2311	73	15	we	we	PRON
ejpam-2311	73	16	get	get	VERB
ejpam-2311	73	17	the	the	DET
ejpam-2311	73	18	following	following	ADJ
ejpam-2311	73	19	commutative	commutative	ADJ
ejpam-2311	73	20	diagram	diagram	NOUN
ejpam-2311	73	21	for	for	ADP
ejpam-2311	73	22	groups	group	NOUN
ejpam-2311	73	23	.	.	PUNCT
ejpam-2311	74	1	1	1	NUM
ejpam-2311	74	2	+	+	NUM
ejpam-2311	74	3	k	k	NOUN
ejpam-2311	74	4	x	x	VERB
ejpam-2311	74	5	y	y	NOUN
ejpam-2311	74	6	ι	ι	INTJ
ejpam-2311	74	7	−→	−→	NOUN
ejpam-2311	74	8	1	1	NUM
ejpam-2311	74	9	+	+	NUM
ejpam-2311	74	10	n	n	NOUN
ejpam-2311	74	11	x	x	SYM
ejpam-2311	74	12	πy	πy	X
ejpam-2311	74	13	−→	−→	NOUN
ejpam-2311	74	14	1	1	NUM
ejpam-2311	74	15	+	+	NOUN
ejpam-2311	74	16	k	k	NOUN
ejpam-2311	74	17	x	x	SYM
ejpam-2311	74	18	ı	ı	PROPN
ejpam-2311	74	19	↓	↓	PROPN
ejpam-2311	74	20	ı	ı	PROPN
ejpam-2311	74	21	↓	↓	PROPN
ejpam-2311	74	22	ı	ı	PROPN
ejpam-2311	74	23	↓	↓	NOUN
ejpam-2311	74	24	1	1	NUM
ejpam-2311	74	25	+	+	PROPN
ejpam-2311	74	26	n	n	VERB
ejpam-2311	74	27	y	y	NOUN
ejpam-2311	74	28	ι	ι	INTJ
ejpam-2311	74	29	−→	−→	ADJ
ejpam-2311	74	30	u1(z[cn	u1(z[cn	PRON
ejpam-2311	74	31	×	×	NOUN
ejpam-2311	74	32	k4	k4	NOUN
ejpam-2311	74	33	]	]	PUNCT
ejpam-2311	74	34	)	)	PUNCT
ejpam-2311	74	35	πy	πy	AUX
ejpam-2311	74	36	−→	−→	ADJ
ejpam-2311	75	1	u1(z[cn	u1(z[cn	PRON
ejpam-2311	75	2	×	×	NOUN
ejpam-2311	75	3	〈	〈	NOUN
ejpam-2311	75	4	x	x	X
ejpam-2311	75	5	〉	〉	NOUN
ejpam-2311	75	6	]	]	PUNCT
ejpam-2311	75	7	)	)	PUNCT
ejpam-2311	75	8	πx	πx	ADP
ejpam-2311	75	9	↓	↓	PROPN
ejpam-2311	75	10	πx	πx	ADP
ejpam-2311	75	11	↓	↓	PROPN
ejpam-2311	75	12	πx	πx	ADP
ejpam-2311	75	13	↓	↓	PROPN
ejpam-2311	75	14	1	1	NUM
ejpam-2311	75	15	+	+	PROPN
ejpam-2311	75	16	k	k	PROPN
ejpam-2311	75	17	y	y	NOUN
ejpam-2311	75	18	ι	ι	INTJ
ejpam-2311	75	19	−→	−→	NOUN
ejpam-2311	75	20	u1(z[cn	u1(z[cn	PRON
ejpam-2311	75	21	×	×	NOUN
ejpam-2311	75	22	y	y	PROPN
ejpam-2311	75	23	�	�	PROPN
ejpam-2311	75	24	]	]	PUNCT
ejpam-2311	75	25	)	)	PUNCT
ejpam-2311	75	26	πy	πy	VERB
ejpam-2311	75	27	−→	−→	NOUN
ejpam-2311	75	28	u1(zcn	u1(zcn	NOUN
ejpam-2311	75	29	)	)	PUNCT
ejpam-2311	75	30	.	.	PUNCT
ejpam-2311	76	1	in	in	ADP
ejpam-2311	76	2	the	the	DET
ejpam-2311	76	3	diagram	diagram	NOUN
ejpam-2311	76	4	,	,	PUNCT
ejpam-2311	76	5	each	each	DET
ejpam-2311	76	6	row	row	NOUN
ejpam-2311	76	7	and	and	CCONJ
ejpam-2311	76	8	column	column	NOUN
ejpam-2311	76	9	are	be	AUX
ejpam-2311	76	10	exact	exact	ADJ
ejpam-2311	76	11	sequences	sequence	NOUN
ejpam-2311	76	12	.	.	PUNCT
ejpam-2311	77	1	if	if	SCONJ
ejpam-2311	77	2	we	we	PRON
ejpam-2311	77	3	define	define	VERB
ejpam-2311	77	4	τ	τ	PROPN
ejpam-2311	77	5	as	as	ADP
ejpam-2311	77	6	the	the	DET
ejpam-2311	77	7	identity	identity	NOUN
ejpam-2311	77	8	function	function	NOUN
ejpam-2311	77	9	in	in	ADP
ejpam-2311	77	10	the	the	DET
ejpam-2311	77	11	reverse	reverse	ADJ
ejpam-2311	77	12	directions	direction	NOUN
ejpam-2311	77	13	of	of	ADP
ejpam-2311	77	14	πx	πx	NOUN
ejpam-2311	77	15	and	and	CCONJ
ejpam-2311	77	16	πy	πy	INTJ
ejpam-2311	77	17	,	,	PUNCT
ejpam-2311	77	18	we	we	PRON
ejpam-2311	77	19	can	can	AUX
ejpam-2311	77	20	say	say	VERB
ejpam-2311	77	21	that	that	SCONJ
ejpam-2311	77	22	each	each	DET
ejpam-2311	77	23	exact	exact	ADJ
ejpam-2311	77	24	sequence	sequence	NOUN
ejpam-2311	77	25	splits	split	VERB
ejpam-2311	77	26	.	.	PUNCT
ejpam-2311	78	1	thus	thus	ADV
ejpam-2311	78	2	,	,	PUNCT
ejpam-2311	78	3	from	from	ADP
ejpam-2311	78	4	column	column	NOUN
ejpam-2311	78	5	-	-	PUNCT
ejpam-2311	78	6	wise	wise	ADJ
ejpam-2311	78	7	split	split	ADJ
ejpam-2311	78	8	-	-	PUNCT
ejpam-2311	78	9	short	short	ADJ
ejpam-2311	78	10	exact	exact	ADJ
ejpam-2311	78	11	sequences	sequence	NOUN
ejpam-2311	78	12	we	we	PRON
ejpam-2311	78	13	can	can	AUX
ejpam-2311	78	14	write	write	VERB
ejpam-2311	78	15	,	,	PUNCT
ejpam-2311	78	16	1	1	NUM
ejpam-2311	78	17	+	+	NUM
ejpam-2311	78	18	n	n	CCONJ
ejpam-2311	78	19	y	y	PROPN
ejpam-2311	78	20	=(	=(	NOUN
ejpam-2311	78	21	1	1	NUM
ejpam-2311	78	22	+	+	SYM
ejpam-2311	78	23	k	k	NOUN
ejpam-2311	78	24	x	x	X
ejpam-2311	78	25	y)×	y)×	NOUN
ejpam-2311	78	26	(	(	PUNCT
ejpam-2311	78	27	1	1	NUM
ejpam-2311	78	28	+	+	NUM
ejpam-2311	78	29	k	k	PROPN
ejpam-2311	78	30	y	y	PROPN
ejpam-2311	78	31	)	)	PUNCT
ejpam-2311	78	32	,	,	PUNCT
ejpam-2311	78	33	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	78	34	×	×	NOUN
ejpam-2311	78	35	k4	k4	NOUN
ejpam-2311	78	36	]	]	PUNCT
ejpam-2311	78	37	)	)	PUNCT
ejpam-2311	78	38	=(	=(	NOUN
ejpam-2311	78	39	1	1	NUM
ejpam-2311	78	40	+	+	NUM
ejpam-2311	78	41	n	n	NUM
ejpam-2311	78	42	x)×	x)×	NUM
ejpam-2311	79	1	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	79	2	×	×	PROPN
ejpam-2311	79	3	y	y	PROPN
ejpam-2311	79	4	�	�	PROPN
ejpam-2311	79	5	]	]	PUNCT
ejpam-2311	79	6	)	)	PUNCT
ejpam-2311	79	7	,	,	PUNCT
ejpam-2311	80	1	u1(z[cn	u1(z[cn	PRON
ejpam-2311	80	2	×	×	NOUN
ejpam-2311	80	3	〈	〈	NOUN
ejpam-2311	80	4	x	x	X
ejpam-2311	80	5	〉	〉	NOUN
ejpam-2311	80	6	]	]	PUNCT
ejpam-2311	80	7	)	)	PUNCT
ejpam-2311	80	8	=(	=(	NOUN
ejpam-2311	80	9	1	1	NUM
ejpam-2311	80	10	+	+	NUM
ejpam-2311	80	11	k	k	PROPN
ejpam-2311	80	12	x)×	x)×	NUM
ejpam-2311	80	13	u1(zcn	u1(zcn	NOUN
ejpam-2311	80	14	)	)	PUNCT
ejpam-2311	80	15	.	.	PUNCT
ejpam-2311	81	1	equivalently	equivalently	ADV
ejpam-2311	81	2	,	,	PUNCT
ejpam-2311	81	3	from	from	ADP
ejpam-2311	81	4	row	row	ADV
ejpam-2311	81	5	-	-	PUNCT
ejpam-2311	81	6	wise	wise	ADJ
ejpam-2311	81	7	split	split	ADJ
ejpam-2311	81	8	-	-	PUNCT
ejpam-2311	81	9	short	short	ADJ
ejpam-2311	81	10	exact	exact	ADJ
ejpam-2311	81	11	sequences	sequence	NOUN
ejpam-2311	81	12	we	we	PRON
ejpam-2311	81	13	get	get	VERB
ejpam-2311	81	14	1	1	NUM
ejpam-2311	81	15	+	+	CCONJ
ejpam-2311	81	16	n	n	CCONJ
ejpam-2311	81	17	x	x	ADJ
ejpam-2311	81	18	=(	=(	NOUN
ejpam-2311	81	19	1	1	NUM
ejpam-2311	81	20	+	+	SYM
ejpam-2311	81	21	k	k	NOUN
ejpam-2311	81	22	x	x	X
ejpam-2311	81	23	y)×	y)×	NOUN
ejpam-2311	81	24	(	(	PUNCT
ejpam-2311	81	25	1	1	NUM
ejpam-2311	81	26	+	+	NUM
ejpam-2311	81	27	k	k	PROPN
ejpam-2311	81	28	x	x	PROPN
ejpam-2311	81	29	)	)	PUNCT
ejpam-2311	81	30	,	,	PUNCT
ejpam-2311	81	31	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	81	32	×	×	NOUN
ejpam-2311	81	33	k4	k4	NOUN
ejpam-2311	81	34	]	]	PUNCT
ejpam-2311	81	35	)	)	PUNCT
ejpam-2311	81	36	=(	=(	NOUN
ejpam-2311	81	37	1	1	NUM
ejpam-2311	81	38	+	+	NUM
ejpam-2311	81	39	n	n	ADP
ejpam-2311	81	40	y)×	y)×	NOUN
ejpam-2311	81	41	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	81	42	×	×	NOUN
ejpam-2311	81	43	〈	〈	NOUN
ejpam-2311	81	44	x	x	X
ejpam-2311	81	45	〉	〉	NOUN
ejpam-2311	81	46	]	]	PUNCT
ejpam-2311	81	47	)	)	PUNCT
ejpam-2311	81	48	,	,	PUNCT
ejpam-2311	82	1	u1(z[cn	u1(z[cn	PRON
ejpam-2311	82	2	×	×	NOUN
ejpam-2311	82	3	y	y	PROPN
ejpam-2311	82	4	�	�	PROPN
ejpam-2311	82	5	]	]	PUNCT
ejpam-2311	82	6	)	)	PUNCT
ejpam-2311	82	7	=(	=(	NOUN
ejpam-2311	82	8	1	1	NUM
ejpam-2311	82	9	+	+	NUM
ejpam-2311	82	10	k	k	PROPN
ejpam-2311	82	11	y)×	y)×	NOUN
ejpam-2311	82	12	u1(zcn	u1(zcn	NOUN
ejpam-2311	82	13	)	)	PUNCT
ejpam-2311	82	14	.	.	PUNCT
ejpam-2311	83	1	finally	finally	ADV
ejpam-2311	83	2	,	,	PUNCT
ejpam-2311	83	3	the	the	DET
ejpam-2311	83	4	unit	unit	NOUN
ejpam-2311	83	5	group	group	NOUN
ejpam-2311	83	6	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	83	7	×	×	PROPN
ejpam-2311	83	8	k4	k4	NOUN
ejpam-2311	83	9	]	]	PUNCT
ejpam-2311	83	10	)	)	PUNCT
ejpam-2311	83	11	can	can	AUX
ejpam-2311	83	12	be	be	AUX
ejpam-2311	83	13	described	describe	VERB
ejpam-2311	83	14	as	as	ADP
ejpam-2311	83	15	an	an	DET
ejpam-2311	83	16	internal	internal	ADJ
ejpam-2311	83	17	direct	direct	ADJ
ejpam-2311	83	18	product	product	NOUN
ejpam-2311	83	19	of	of	ADP
ejpam-2311	83	20	four	four	NUM
ejpam-2311	83	21	subgroups	subgroup	NOUN
ejpam-2311	83	22	:	:	PUNCT
ejpam-2311	83	23	u1(z[cn	u1(z[cn	NUM
ejpam-2311	83	24	×	×	NOUN
ejpam-2311	83	25	k4	k4	NOUN
ejpam-2311	83	26	]	]	PUNCT
ejpam-2311	83	27	)	)	PUNCT
ejpam-2311	83	28	=(	=(	NOUN
ejpam-2311	83	29	1	1	NUM
ejpam-2311	83	30	+	+	NUM
ejpam-2311	83	31	n	n	NUM
ejpam-2311	83	32	x)×	x)×	NUM
ejpam-2311	84	1	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	84	2	×	×	PROPN
ejpam-2311	84	3	y	y	PROPN
ejpam-2311	84	4	�	�	PROPN
ejpam-2311	84	5	]	]	PUNCT
ejpam-2311	84	6	)	)	PUNCT
ejpam-2311	85	1	=	=	SYM
ejpam-2311	85	2	u1(zcn)×	u1(zcn)×	PROPN
ejpam-2311	85	3	(	(	PUNCT
ejpam-2311	85	4	1	1	NUM
ejpam-2311	85	5	+	+	NUM
ejpam-2311	85	6	k	k	PROPN
ejpam-2311	85	7	x)×	x)×	SYM
ejpam-2311	85	8	(	(	PUNCT
ejpam-2311	85	9	1	1	NUM
ejpam-2311	85	10	+	+	NUM
ejpam-2311	85	11	k	k	NOUN
ejpam-2311	85	12	y)×	y)×	NOUN
ejpam-2311	85	13	(	(	PUNCT
ejpam-2311	85	14	1	1	NUM
ejpam-2311	85	15	+	+	NUM
ejpam-2311	85	16	k	k	PROPN
ejpam-2311	85	17	x	x	SYM
ejpam-2311	85	18	y	y	PROPN
ejpam-2311	85	19	)	)	PUNCT
ejpam-2311	85	20	.	.	PUNCT
ejpam-2311	86	1	lemma	lemma	PROPN
ejpam-2311	86	2	1	1	X
ejpam-2311	86	3	.	.	PUNCT
ejpam-2311	87	1	in	in	ADP
ejpam-2311	87	2	u1(z[cn	u1(z[cn	PROPN
ejpam-2311	87	3	×	×	NOUN
ejpam-2311	87	4	k4	k4	NOUN
ejpam-2311	87	5	]	]	PUNCT
ejpam-2311	87	6	)	)	PUNCT
ejpam-2311	87	7	,	,	PUNCT
ejpam-2311	87	8	the	the	DET
ejpam-2311	87	9	subgroups	subgroup	NOUN
ejpam-2311	87	10	(	(	PUNCT
ejpam-2311	87	11	1	1	NUM
ejpam-2311	87	12	+	+	NUM
ejpam-2311	87	13	k	k	PROPN
ejpam-2311	87	14	x	x	PROPN
ejpam-2311	87	15	)	)	PUNCT
ejpam-2311	87	16	,	,	PUNCT
ejpam-2311	87	17	(	(	PUNCT
ejpam-2311	87	18	1	1	NUM
ejpam-2311	87	19	+	+	NUM
ejpam-2311	87	20	k	k	PROPN
ejpam-2311	87	21	y	y	PROPN
ejpam-2311	87	22	)	)	PUNCT
ejpam-2311	87	23	,	,	PUNCT
ejpam-2311	87	24	(	(	PUNCT
ejpam-2311	87	25	1	1	NUM
ejpam-2311	87	26	+	+	NUM
ejpam-2311	87	27	k	k	PROPN
ejpam-2311	87	28	x	x	SYM
ejpam-2311	87	29	y	y	X
ejpam-2311	87	30	)	)	PUNCT
ejpam-2311	87	31	satisfy	satisfy	VERB
ejpam-2311	87	32	the	the	DET
ejpam-2311	87	33	following	follow	VERB
ejpam-2311	87	34	conditions	condition	NOUN
ejpam-2311	87	35	.	.	PUNCT
ejpam-2311	88	1	(	(	PUNCT
ejpam-2311	88	2	i	i	NOUN
ejpam-2311	88	3	)	)	PUNCT
ejpam-2311	88	4	1	1	NUM
ejpam-2311	89	1	+	+	NUM
ejpam-2311	89	2	k	k	NOUN
ejpam-2311	89	3	x	x	SYM
ejpam-2311	89	4	=	=	PUNCT
ejpam-2311	89	5	{	{	PUNCT
ejpam-2311	89	6	1	1	NUM
ejpam-2311	89	7	+	+	NUM
ejpam-2311	89	8	(	(	PUNCT
ejpam-2311	89	9	x	x	SYM
ejpam-2311	89	10	−	−	PROPN
ejpam-2311	89	11	1)p	1)p	NUM
ejpam-2311	89	12	:	:	PUNCT
ejpam-2311	89	13	1−	1−	NUM
ejpam-2311	89	14	2p	2p	NUM
ejpam-2311	89	15	∈	∈	PROPN
ejpam-2311	89	16	u1(zcn	u1(zcn	NOUN
ejpam-2311	89	17	)	)	PUNCT
ejpam-2311	89	18	}	}	PUNCT
ejpam-2311	89	19	.	.	PUNCT
ejpam-2311	90	1	(	(	PUNCT
ejpam-2311	90	2	ii	ii	NOUN
ejpam-2311	90	3	)	)	PUNCT
ejpam-2311	90	4	1	1	NUM
ejpam-2311	91	1	+	+	NUM
ejpam-2311	91	2	k	k	PROPN
ejpam-2311	91	3	y	y	PROPN
ejpam-2311	91	4	=	=	PUNCT
ejpam-2311	91	5	{	{	PUNCT
ejpam-2311	91	6	1	1	NUM
ejpam-2311	91	7	+	+	CCONJ
ejpam-2311	91	8	(	(	PUNCT
ejpam-2311	91	9	y	y	PROPN
ejpam-2311	91	10	−	−	PROPN
ejpam-2311	91	11	1)p	1)p	NUM
ejpam-2311	91	12	:	:	PUNCT
ejpam-2311	91	13	1−	1−	NUM
ejpam-2311	91	14	2p	2p	NUM
ejpam-2311	91	15	∈	∈	PROPN
ejpam-2311	91	16	u1(zcn	u1(zcn	NOUN
ejpam-2311	91	17	)	)	PUNCT
ejpam-2311	91	18	}	}	PUNCT
ejpam-2311	91	19	.	.	PUNCT
ejpam-2311	92	1	(	(	PUNCT
ejpam-2311	92	2	iii	iii	NOUN
ejpam-2311	92	3	)	)	PUNCT
ejpam-2311	92	4	1	1	NUM
ejpam-2311	93	1	+	+	NUM
ejpam-2311	93	2	k	k	NOUN
ejpam-2311	93	3	x	x	SYM
ejpam-2311	93	4	y	y	PROPN
ejpam-2311	93	5	=	=	PUNCT
ejpam-2311	93	6	{	{	PUNCT
ejpam-2311	93	7	1	1	NUM
ejpam-2311	93	8	+	+	NUM
ejpam-2311	93	9	(	(	PUNCT
ejpam-2311	93	10	x	x	SYM
ejpam-2311	93	11	−	−	PROPN
ejpam-2311	93	12	1)(y	1)(y	NUM
ejpam-2311	94	1	−	−	NOUN
ejpam-2311	95	1	1)p	1)p	NUM
ejpam-2311	95	2	:	:	PUNCT
ejpam-2311	95	3	1	1	NUM
ejpam-2311	95	4	+	+	NUM
ejpam-2311	95	5	4p	4p	NUM
ejpam-2311	95	6	∈	∈	PROPN
ejpam-2311	95	7	u1(zcn	u1(zcn	NOUN
ejpam-2311	95	8	)	)	PUNCT
ejpam-2311	95	9	}	}	PUNCT
ejpam-2311	95	10	.	.	PUNCT
ejpam-2311	96	1	i.g	i.g	PROPN
ejpam-2311	96	2	.	.	PROPN
ejpam-2311	96	3	kelebek	kelebek	PROPN
ejpam-2311	96	4	,	,	PUNCT
ejpam-2311	96	5	t.	t.	PROPN
ejpam-2311	96	6	bilgin	bilgin	PROPN
ejpam-2311	96	7	/	/	SYM
ejpam-2311	96	8	eur	eur	PROPN
ejpam-2311	96	9	.	.	PUNCT
ejpam-2311	97	1	j.	j.	PROPN
ejpam-2311	97	2	pure	pure	PROPN
ejpam-2311	97	3	appl	appl	PROPN
ejpam-2311	97	4	.	.	PROPN
ejpam-2311	97	5	math	math	PROPN
ejpam-2311	97	6	,	,	PUNCT
ejpam-2311	97	7	7	7	NUM
ejpam-2311	97	8	(	(	PUNCT
ejpam-2311	97	9	2014	2014	NUM
ejpam-2311	97	10	)	)	PUNCT
ejpam-2311	97	11	,	,	PUNCT
ejpam-2311	97	12	462	462	NUM
ejpam-2311	97	13	-	-	SYM
ejpam-2311	97	14	471	471	NUM
ejpam-2311	97	15	466	466	NUM
ejpam-2311	97	16	proof	proof	NOUN
ejpam-2311	97	17	.	.	PUNCT
ejpam-2311	98	1	u	u	PROPN
ejpam-2311	98	2	∈	∈	PROPN
ejpam-2311	98	3	1+k	1+k	NUM
ejpam-2311	98	4	x	x	SYM
ejpam-2311	98	5	⇔	⇔	PROPN
ejpam-2311	98	6	u=	u=	PROPN
ejpam-2311	98	7	1+(x−1)p	1+(x−1)p	NUM
ejpam-2311	98	8	and	and	CCONJ
ejpam-2311	98	9	there	there	PRON
ejpam-2311	98	10	exists	exist	VERB
ejpam-2311	98	11	v	v	ADP
ejpam-2311	98	12	=	=	SYM
ejpam-2311	98	13	1+(x−1)q	1+(x−1)q	NOUN
ejpam-2311	98	14	for	for	ADP
ejpam-2311	98	15	some	some	DET
ejpam-2311	98	16	p	p	NOUN
ejpam-2311	98	17	,	,	PUNCT
ejpam-2311	98	18	q	q	PROPN
ejpam-2311	98	19	∈	∈	PROPN
ejpam-2311	98	20	zcn	zcn	NOUN
ejpam-2311	99	1	such	such	ADJ
ejpam-2311	99	2	that	that	DET
ejpam-2311	99	3	u.v	u.v	PROPN
ejpam-2311	99	4	=	=	NOUN
ejpam-2311	99	5	1	1	NUM
ejpam-2311	99	6	then	then	ADV
ejpam-2311	99	7	uv	uv	VERB
ejpam-2311	99	8	=	=	PUNCT
ejpam-2311	99	9	1⇔[1	1⇔[1	NUM
ejpam-2311	99	10	+	+	CCONJ
ejpam-2311	99	11	(	(	PUNCT
ejpam-2311	99	12	x	x	X
ejpam-2311	99	13	−	−	NOUN
ejpam-2311	99	14	1)p][1	1)p][1	NUM
ejpam-2311	99	15	+	+	SYM
ejpam-2311	99	16	(	(	PUNCT
ejpam-2311	99	17	x	x	SYM
ejpam-2311	99	18	−	−	NOUN
ejpam-2311	99	19	1)q	1)q	NOUN
ejpam-2311	99	20	]	]	X
ejpam-2311	99	21	=	=	SYM
ejpam-2311	99	22	1	1	NUM
ejpam-2311	99	23	⇔1	⇔1	NOUN
ejpam-2311	99	24	+	+	SYM
ejpam-2311	99	25	(	(	PUNCT
ejpam-2311	99	26	x	x	SYM
ejpam-2311	99	27	−	−	PROPN
ejpam-2311	99	28	1)[p	1)[p	NUM
ejpam-2311	100	1	+	+	NOUN
ejpam-2311	100	2	q−	q−	PROPN
ejpam-2311	100	3	2pq	2pq	NOUN
ejpam-2311	100	4	]	]	X
ejpam-2311	100	5	=	=	SYM
ejpam-2311	100	6	1	1	NUM
ejpam-2311	100	7	⇔p	⇔p	NOUN
ejpam-2311	100	8	+	+	NOUN
ejpam-2311	100	9	q−	q−	PROPN
ejpam-2311	100	10	2pq	2pq	NOUN
ejpam-2311	100	11	=	=	PUNCT
ejpam-2311	100	12	0	0	PROPN
ejpam-2311	101	1	⇔1−	⇔1−	NUM
ejpam-2311	101	2	2p	2p	NUM
ejpam-2311	101	3	−	−	PROPN
ejpam-2311	101	4	2q+	2q+	NUM
ejpam-2311	101	5	4pq	4pq	NOUN
ejpam-2311	101	6	=	=	NOUN
ejpam-2311	101	7	1	1	NUM
ejpam-2311	101	8	⇔(1−	⇔(1−	NOUN
ejpam-2311	101	9	2p)(1−	2p)(1−	NUM
ejpam-2311	101	10	2q	2q	NOUN
ejpam-2311	101	11	)	)	PUNCT
ejpam-2311	101	12	=	=	SYM
ejpam-2311	101	13	1	1	NUM
ejpam-2311	101	14	⇔1−	⇔1−	NUM
ejpam-2311	101	15	2p	2p	NUM
ejpam-2311	101	16	∈	∈	PROPN
ejpam-2311	101	17	u1(zcn	u1(zcn	NOUN
ejpam-2311	101	18	)	)	PUNCT
ejpam-2311	101	19	.	.	PUNCT
ejpam-2311	102	1	similarly	similarly	ADV
ejpam-2311	102	2	we	we	PRON
ejpam-2311	102	3	can	can	AUX
ejpam-2311	102	4	see	see	VERB
ejpam-2311	102	5	that	that	SCONJ
ejpam-2311	102	6	1	1	NUM
ejpam-2311	102	7	+	+	NUM
ejpam-2311	102	8	k	k	PROPN
ejpam-2311	102	9	y	y	PROPN
ejpam-2311	102	10	=	=	PUNCT
ejpam-2311	102	11	{	{	PUNCT
ejpam-2311	102	12	1	1	NUM
ejpam-2311	102	13	+	+	CCONJ
ejpam-2311	102	14	(	(	PUNCT
ejpam-2311	102	15	y	y	PROPN
ejpam-2311	102	16	−	−	PROPN
ejpam-2311	102	17	1)p	1)p	NUM
ejpam-2311	102	18	:	:	PUNCT
ejpam-2311	102	19	1−	1−	NUM
ejpam-2311	102	20	2p	2p	NUM
ejpam-2311	102	21	∈	∈	PROPN
ejpam-2311	102	22	u1(zcn	u1(zcn	NOUN
ejpam-2311	102	23	)	)	PUNCT
ejpam-2311	102	24	}	}	PUNCT
ejpam-2311	102	25	and	and	CCONJ
ejpam-2311	103	1	1	1	NUM
ejpam-2311	103	2	+	+	NUM
ejpam-2311	103	3	k	k	NOUN
ejpam-2311	103	4	x	x	SYM
ejpam-2311	103	5	y	y	PROPN
ejpam-2311	103	6	=	=	PUNCT
ejpam-2311	103	7	{	{	PUNCT
ejpam-2311	103	8	1	1	NUM
ejpam-2311	103	9	+	+	NUM
ejpam-2311	103	10	(	(	PUNCT
ejpam-2311	103	11	x	x	SYM
ejpam-2311	103	12	−	−	PROPN
ejpam-2311	103	13	1)(y	1)(y	NUM
ejpam-2311	103	14	−	−	NOUN
ejpam-2311	104	1	1)p	1)p	NUM
ejpam-2311	104	2	:	:	PUNCT
ejpam-2311	104	3	1	1	NUM
ejpam-2311	104	4	+	+	NUM
ejpam-2311	104	5	4p	4p	NUM
ejpam-2311	104	6	∈	∈	PROPN
ejpam-2311	104	7	u1(zcn	u1(zcn	NOUN
ejpam-2311	104	8	)	)	PUNCT
ejpam-2311	104	9	}	}	PUNCT
ejpam-2311	104	10	.	.	PUNCT
ejpam-2311	105	1	now	now	ADV
ejpam-2311	105	2	consider	consider	VERB
ejpam-2311	105	3	the	the	DET
ejpam-2311	105	4	surjective	surjective	ADJ
ejpam-2311	105	5	ring	ring	NOUN
ejpam-2311	105	6	homomorphism	homomorphism	PROPN
ejpam-2311	105	7	ρm	ρm	X
ejpam-2311	105	8	:	:	PUNCT
ejpam-2311	105	9	zcn	zcn	VERB
ejpam-2311	105	10	−→	−→	PROPN
ejpam-2311	105	11	zmcn	zmcn	NOUN
ejpam-2311	105	12	,	,	PUNCT
ejpam-2311	105	13	where	where	SCONJ
ejpam-2311	105	14	ρm	ρm	PROPN
ejpam-2311	105	15	reduces	reduce	VERB
ejpam-2311	105	16	the	the	DET
ejpam-2311	105	17	coefficients	coefficient	NOUN
ejpam-2311	105	18	modulo	modulo	ADJ
ejpam-2311	105	19	m.	m.	NOUN
ejpam-2311	105	20	if	if	SCONJ
ejpam-2311	105	21	we	we	PRON
ejpam-2311	105	22	denote	denote	VERB
ejpam-2311	105	23	the	the	DET
ejpam-2311	105	24	kernel	kernel	NOUN
ejpam-2311	105	25	of	of	ADP
ejpam-2311	105	26	ρm	ρm	NUM
ejpam-2311	105	27	by	by	ADP
ejpam-2311	105	28	mm	mm	PROPN
ejpam-2311	105	29	,	,	PUNCT
ejpam-2311	105	30	we	we	PRON
ejpam-2311	105	31	have	have	VERB
ejpam-2311	105	32	mm	mm	NOUN
ejpam-2311	105	33	=	=	SYM
ejpam-2311	105	34	(	(	PUNCT
ejpam-2311	105	35	mz)cn	mz)cn	X
ejpam-2311	105	36	and	and	CCONJ
ejpam-2311	105	37	the	the	DET
ejpam-2311	105	38	following	follow	VERB
ejpam-2311	105	39	exact	exact	ADJ
ejpam-2311	105	40	sequence	sequence	NOUN
ejpam-2311	105	41	is	be	AUX
ejpam-2311	105	42	obtained	obtain	VERB
ejpam-2311	105	43	at	at	ADP
ejpam-2311	105	44	ring	ring	NOUN
ejpam-2311	105	45	level	level	NOUN
ejpam-2311	105	46	:	:	PUNCT
ejpam-2311	105	47	mm	mm	PROPN
ejpam-2311	105	48	=	=	SYM
ejpam-2311	105	49	(	(	PUNCT
ejpam-2311	105	50	mz)cn	mz)cn	PROPN
ejpam-2311	105	51	ι	ι	PART
ejpam-2311	105	52	−→	−→	NOUN
ejpam-2311	105	53	zcn	zcn	NOUN
ejpam-2311	105	54	ρm−→	ρm−→	PROPN
ejpam-2311	105	55	zmcn	zmcn	PROPN
ejpam-2311	105	56	.	.	PUNCT
ejpam-2311	106	1	by	by	ADP
ejpam-2311	106	2	restricting	restrict	VERB
ejpam-2311	106	3	to	to	ADP
ejpam-2311	106	4	the	the	DET
ejpam-2311	106	5	unit	unit	NOUN
ejpam-2311	106	6	group	group	NOUN
ejpam-2311	106	7	u1(zcn	u1(zcn	PROPN
ejpam-2311	106	8	)	)	PUNCT
ejpam-2311	106	9	we	we	PRON
ejpam-2311	106	10	get	get	VERB
ejpam-2311	106	11	exact	exact	ADJ
ejpam-2311	106	12	sequence	sequence	NOUN
ejpam-2311	106	13	of	of	ADP
ejpam-2311	106	14	groups	group	NOUN
ejpam-2311	106	15	1+mm	1+mm	NUM
ejpam-2311	106	16	ι	ι	INTJ
ejpam-2311	106	17	−→	−→	NOUN
ejpam-2311	106	18	u1(zcn	u1(zcn	NOUN
ejpam-2311	106	19	)	)	PUNCT
ejpam-2311	106	20	ρm−→	ρm−→	NUM
ejpam-2311	106	21	u(zmcn	u(zmcn	NOUN
ejpam-2311	106	22	)	)	PUNCT
ejpam-2311	106	23	.	.	PUNCT
ejpam-2311	107	1	we	we	PRON
ejpam-2311	107	2	can	can	AUX
ejpam-2311	107	3	define	define	VERB
ejpam-2311	107	4	two	two	NUM
ejpam-2311	107	5	group	group	NOUN
ejpam-2311	107	6	isomorphisms	isomorphism	NOUN
ejpam-2311	107	7	,	,	PUNCT
ejpam-2311	107	8	σx	σx	X
ejpam-2311	107	9	:	:	PUNCT
ejpam-2311	107	10	cn	cn	PROPN
ejpam-2311	107	11	×	×	PROPN
ejpam-2311	107	12	k4→±cn	k4→±cn	ADJ
ejpam-2311	107	13	×	×	PROPN
ejpam-2311	107	14	y	y	PROPN
ejpam-2311	107	15	�	�	PROPN
ejpam-2311	107	16	,	,	PUNCT
ejpam-2311	107	17	σy	σy	X
ejpam-2311	107	18	:	:	PUNCT
ejpam-2311	107	19	cn	cn	PROPN
ejpam-2311	107	20	×	×	PROPN
ejpam-2311	107	21	k4→±cn	k4→±cn	ADJ
ejpam-2311	107	22	×	×	PROPN
ejpam-2311	107	23	〈	〈	NOUN
ejpam-2311	107	24	x	x	X
ejpam-2311	107	25	〉	〉	NOUN
ejpam-2311	107	26	a	a	DET
ejpam-2311	107	27	7→	7→	NUM
ejpam-2311	107	28	a	a	PRON
ejpam-2311	107	29	a	a	DET
ejpam-2311	107	30	7→	7→	NUM
ejpam-2311	107	31	a	a	DET
ejpam-2311	107	32	x	x	SYM
ejpam-2311	107	33	7→	7→	NUM
ejpam-2311	107	34	−1	−1	NOUN
ejpam-2311	107	35	x	x	NOUN
ejpam-2311	107	36	7→	7→	NUM
ejpam-2311	107	37	x	x	SYM
ejpam-2311	107	38	y	y	NOUN
ejpam-2311	107	39	7→	7→	NUM
ejpam-2311	107	40	y	y	NOUN
ejpam-2311	107	41	y	y	PROPN
ejpam-2311	107	42	7→	7→	PROPN
ejpam-2311	107	43	−1	−1	NOUN
ejpam-2311	107	44	by	by	ADP
ejpam-2311	107	45	extending	extend	VERB
ejpam-2311	107	46	these	these	DET
ejpam-2311	107	47	isomorphisms	isomorphism	NOUN
ejpam-2311	107	48	linearly	linearly	ADV
ejpam-2311	107	49	over	over	ADP
ejpam-2311	107	50	z	z	PROPN
ejpam-2311	107	51	,	,	PUNCT
ejpam-2311	107	52	we	we	PRON
ejpam-2311	107	53	get	get	VERB
ejpam-2311	107	54	the	the	DET
ejpam-2311	107	55	following	follow	VERB
ejpam-2311	107	56	ring	ring	NOUN
ejpam-2311	107	57	epimorphisms	epimorphism	NOUN
ejpam-2311	107	58	:	:	PUNCT
ejpam-2311	107	59	σx	σx	ADP
ejpam-2311	107	60	:	:	PUNCT
ejpam-2311	107	61	z[cn	z[cn	PROPN
ejpam-2311	107	62	×	×	NOUN
ejpam-2311	107	63	k4	k4	NOUN
ejpam-2311	107	64	]	]	X
ejpam-2311	107	65	−→	−→	NOUN
ejpam-2311	107	66	z[cn	z[cn	NOUN
ejpam-2311	107	67	×	×	PROPN
ejpam-2311	107	68	y	y	PROPN
ejpam-2311	107	69	�	�	PROPN
ejpam-2311	107	70	]	]	PUNCT
ejpam-2311	107	71	p0	p0	PROPN
ejpam-2311	107	72	+	+	CCONJ
ejpam-2311	107	73	p1	p1	PROPN
ejpam-2311	107	74	x	x	SYM
ejpam-2311	108	1	+	+	CCONJ
ejpam-2311	108	2	p2	p2	PROPN
ejpam-2311	108	3	y	y	PROPN
ejpam-2311	108	4	+	+	CCONJ
ejpam-2311	108	5	p3	p3	PROPN
ejpam-2311	108	6	x	x	SYM
ejpam-2311	108	7	y	y	PROPN
ejpam-2311	108	8	7→(p0	7→(p0	NUM
ejpam-2311	108	9	−	−	PROPN
ejpam-2311	108	10	p1	p1	PROPN
ejpam-2311	108	11	)	)	PUNCT
ejpam-2311	108	12	+	+	CCONJ
ejpam-2311	108	13	(	(	PUNCT
ejpam-2311	108	14	p2	p2	PROPN
ejpam-2311	108	15	−	−	PROPN
ejpam-2311	108	16	p3)y	p3)y	NOUN
ejpam-2311	108	17	,	,	PUNCT
ejpam-2311	108	18	σy	σy	X
ejpam-2311	108	19	:	:	PUNCT
ejpam-2311	108	20	z[cn	z[cn	NUM
ejpam-2311	108	21	×	×	NOUN
ejpam-2311	108	22	k4	k4	NOUN
ejpam-2311	108	23	]	]	X
ejpam-2311	108	24	−→	−→	NOUN
ejpam-2311	108	25	z[cn	z[cn	NUM
ejpam-2311	108	26	×	×	NOUN
ejpam-2311	108	27	〈	〈	NOUN
ejpam-2311	108	28	x	x	X
ejpam-2311	108	29	〉	〉	NOUN
ejpam-2311	108	30	]	]	PUNCT
ejpam-2311	108	31	p0	p0	NOUN
ejpam-2311	108	32	+	+	CCONJ
ejpam-2311	108	33	p1	p1	PROPN
ejpam-2311	108	34	x	x	SYM
ejpam-2311	108	35	+	+	CCONJ
ejpam-2311	108	36	p2	p2	PROPN
ejpam-2311	108	37	y	y	PROPN
ejpam-2311	108	38	+	+	CCONJ
ejpam-2311	108	39	p3	p3	PROPN
ejpam-2311	108	40	x	x	SYM
ejpam-2311	108	41	y	y	PROPN
ejpam-2311	108	42	7→(p0	7→(p0	NOUN
ejpam-2311	108	43	−	−	NOUN
ejpam-2311	108	44	p2	p2	NOUN
ejpam-2311	108	45	)	)	PUNCT
ejpam-2311	109	1	+	+	CCONJ
ejpam-2311	109	2	(	(	PUNCT
ejpam-2311	109	3	p1	p1	PROPN
ejpam-2311	109	4	−	−	PROPN
ejpam-2311	109	5	p3)x	p3)x	PROPN
ejpam-2311	109	6	.	.	PUNCT
ejpam-2311	110	1	this	this	PRON
ejpam-2311	110	2	leads	lead	VERB
ejpam-2311	110	3	to	to	ADP
ejpam-2311	110	4	the	the	DET
ejpam-2311	110	5	diagrams	diagram	NOUN
ejpam-2311	110	6	at	at	ADP
ejpam-2311	110	7	ring	ring	NOUN
ejpam-2311	110	8	level	level	NOUN
ejpam-2311	110	9	.	.	PUNCT
ejpam-2311	111	1	for	for	ADP
ejpam-2311	111	2	k	k	PROPN
ejpam-2311	111	3	x	x	X
ejpam-2311	111	4	we	we	PRON
ejpam-2311	111	5	write	write	VERB
ejpam-2311	111	6	k	k	PROPN
ejpam-2311	111	7	x	x	PUNCT
ejpam-2311	112	1	ι	ι	X
ejpam-2311	112	2	−→	−→	NOUN
ejpam-2311	112	3	z[cn×	z[cn×	PROPN
ejpam-2311	112	4	<	<	X
ejpam-2311	112	5	x	x	X
ejpam-2311	112	6	>	>	X
ejpam-2311	112	7	]	]	X
ejpam-2311	112	8	π	π	X
ejpam-2311	112	9	x−→	x−→	PROPN
ejpam-2311	112	10	zcn	zcn	PROPN
ejpam-2311	112	11	σx	σx	PROPN
ejpam-2311	112	12	↓	↓	PROPN
ejpam-2311	112	13	σx	σx	PROPN
ejpam-2311	112	14	↓	↓	PROPN
ejpam-2311	112	15	ρ2	ρ2	PROPN
ejpam-2311	112	16	↓	↓	NOUN
ejpam-2311	112	17	m2	m2	PROPN
ejpam-2311	112	18	ι	ι	PROPN
ejpam-2311	112	19	−→	−→	NOUN
ejpam-2311	112	20	zcn	zcn	NOUN
ejpam-2311	112	21	ρ2−→	ρ2−→	PROPN
ejpam-2311	112	22	z2cn	z2cn	NUM
ejpam-2311	112	23	,	,	PUNCT
ejpam-2311	112	24	i.g	i.g	PROPN
ejpam-2311	112	25	.	.	PROPN
ejpam-2311	112	26	kelebek	kelebek	PROPN
ejpam-2311	112	27	,	,	PUNCT
ejpam-2311	112	28	t.	t.	PROPN
ejpam-2311	112	29	bilgin	bilgin	PROPN
ejpam-2311	112	30	/	/	SYM
ejpam-2311	112	31	eur	eur	PROPN
ejpam-2311	112	32	.	.	PUNCT
ejpam-2311	113	1	j.	j.	PROPN
ejpam-2311	113	2	pure	pure	PROPN
ejpam-2311	113	3	appl	appl	PROPN
ejpam-2311	113	4	.	.	PROPN
ejpam-2311	113	5	math	math	PROPN
ejpam-2311	113	6	,	,	PUNCT
ejpam-2311	113	7	7	7	NUM
ejpam-2311	113	8	(	(	PUNCT
ejpam-2311	113	9	2014	2014	NUM
ejpam-2311	113	10	)	)	PUNCT
ejpam-2311	113	11	,	,	PUNCT
ejpam-2311	113	12	462	462	NUM
ejpam-2311	113	13	-	-	SYM
ejpam-2311	113	14	471	471	NUM
ejpam-2311	113	15	467	467	NUM
ejpam-2311	113	16	for	for	ADP
ejpam-2311	113	17	k	k	PROPN
ejpam-2311	113	18	y	y	PROPN
ejpam-2311	113	19	we	we	PRON
ejpam-2311	113	20	have	have	VERB
ejpam-2311	113	21	k	k	PROPN
ejpam-2311	113	22	y	y	PROPN
ejpam-2311	113	23	ι	ι	INTJ
ejpam-2311	113	24	−→	−→	NOUN
ejpam-2311	113	25	z[cn×	z[cn×	PROPN
ejpam-2311	113	26	<	<	X
ejpam-2311	113	27	y	y	PROPN
ejpam-2311	113	28	>	>	X
ejpam-2311	113	29	]	]	X
ejpam-2311	114	1	π	π	X
ejpam-2311	114	2	y	y	PROPN
ejpam-2311	114	3	−→	−→	NOUN
ejpam-2311	114	4	zcn	zcn	NOUN
ejpam-2311	114	5	σy	σy	PROPN
ejpam-2311	114	6	↓	↓	PROPN
ejpam-2311	114	7	σy	σy	PROPN
ejpam-2311	114	8	↓	↓	PROPN
ejpam-2311	114	9	ρ2	ρ2	PROPN
ejpam-2311	114	10	↓	↓	PROPN
ejpam-2311	114	11	m2	m2	PROPN
ejpam-2311	114	12	ι	ι	PROPN
ejpam-2311	114	13	−→	−→	NOUN
ejpam-2311	114	14	zcn	zcn	NOUN
ejpam-2311	114	15	ρ2−→	ρ2−→	NOUN
ejpam-2311	114	16	z2cn	z2cn	PUNCT
ejpam-2311	114	17	,	,	PUNCT
ejpam-2311	114	18	and	and	CCONJ
ejpam-2311	114	19	for	for	ADP
ejpam-2311	114	20	k	k	PROPN
ejpam-2311	114	21	x	x	X
ejpam-2311	114	22	y	y	VERB
ejpam-2311	114	23	we	we	PRON
ejpam-2311	114	24	get	get	VERB
ejpam-2311	114	25	k	k	NOUN
ejpam-2311	114	26	x	x	PUNCT
ejpam-2311	114	27	y	y	NOUN
ejpam-2311	114	28	ι	ι	INTJ
ejpam-2311	114	29	−→	−→	ADJ
ejpam-2311	114	30	z[cn	z[cn	NOUN
ejpam-2311	114	31	×	×	NOUN
ejpam-2311	114	32	k4	k4	PROPN
ejpam-2311	114	33	]	]	PUNCT
ejpam-2311	114	34	πxπy	πxπy	NOUN
ejpam-2311	114	35	−→	−→	NOUN
ejpam-2311	114	36	zcn	zcn	NOUN
ejpam-2311	114	37	σxσy	σxσy	NOUN
ejpam-2311	114	38	↓	↓	PROPN
ejpam-2311	114	39	σxσy	σxσy	PROPN
ejpam-2311	114	40	↓	↓	PROPN
ejpam-2311	114	41	ρ4	ρ4	ADV
ejpam-2311	114	42	↓	↓	PROPN
ejpam-2311	114	43	m4	m4	PROPN
ejpam-2311	114	44	ι	ι	PRON
ejpam-2311	114	45	−→	−→	NOUN
ejpam-2311	114	46	zcn	zcn	NOUN
ejpam-2311	114	47	ρ4−→	ρ4−→	X
ejpam-2311	114	48	z4cn	z4cn	X
ejpam-2311	114	49	.	.	PUNCT
ejpam-2311	115	1	corollary	corollary	ADJ
ejpam-2311	115	2	1	1	NUM
ejpam-2311	115	3	.	.	PUNCT
ejpam-2311	116	1	the	the	DET
ejpam-2311	116	2	following	follow	VERB
ejpam-2311	116	3	maps	map	NOUN
ejpam-2311	116	4	are	be	AUX
ejpam-2311	116	5	group	group	NOUN
ejpam-2311	116	6	isomorphisms	isomorphism	NOUN
ejpam-2311	116	7	:	:	PUNCT
ejpam-2311	116	8	(	(	PUNCT
ejpam-2311	116	9	i	i	NOUN
ejpam-2311	116	10	)	)	PUNCT
ejpam-2311	116	11	σx	σx	NOUN
ejpam-2311	116	12	:	:	PUNCT
ejpam-2311	117	1	1	1	NUM
ejpam-2311	117	2	+	+	SYM
ejpam-2311	117	3	k	k	NOUN
ejpam-2311	117	4	x	x	SYM
ejpam-2311	117	5	−→	−→	NOUN
ejpam-2311	117	6	1+m2	1+m2	NOUN
ejpam-2311	117	7	,	,	PUNCT
ejpam-2311	117	8	(	(	PUNCT
ejpam-2311	117	9	ii	ii	NOUN
ejpam-2311	117	10	)	)	PUNCT
ejpam-2311	117	11	σy	σy	NOUN
ejpam-2311	117	12	:	:	PUNCT
ejpam-2311	118	1	1	1	X
ejpam-2311	118	2	+	+	NUM
ejpam-2311	118	3	k	k	PROPN
ejpam-2311	118	4	y	y	NOUN
ejpam-2311	118	5	−→	−→	NOUN
ejpam-2311	118	6	1+m2	1+m2	NOUN
ejpam-2311	118	7	,	,	PUNCT
ejpam-2311	118	8	(	(	PUNCT
ejpam-2311	118	9	iii	iii	X
ejpam-2311	118	10	)	)	PUNCT
ejpam-2311	118	11	σxσy	σxσy	NOUN
ejpam-2311	118	12	:	:	PUNCT
ejpam-2311	118	13	1	1	NUM
ejpam-2311	118	14	+	+	NUM
ejpam-2311	118	15	k	k	NOUN
ejpam-2311	118	16	x	x	VERB
ejpam-2311	118	17	y	y	PROPN
ejpam-2311	118	18	−→	−→	NOUN
ejpam-2311	118	19	1+m4	1+m4	NOUN
ejpam-2311	118	20	.	.	PUNCT
ejpam-2311	119	1	proof	proof	NOUN
ejpam-2311	119	2	.	.	PUNCT
ejpam-2311	120	1	consider	consider	VERB
ejpam-2311	120	2	the	the	DET
ejpam-2311	120	3	following	follow	VERB
ejpam-2311	120	4	diagram	diagram	NOUN
ejpam-2311	120	5	1	1	NUM
ejpam-2311	120	6	+	+	SYM
ejpam-2311	120	7	k	k	NOUN
ejpam-2311	120	8	x	x	X
ejpam-2311	120	9	ι	ι	VERB
ejpam-2311	120	10	−→	−→	NOUN
ejpam-2311	120	11	u1(z[cn×	u1(z[cn×	NOUN
ejpam-2311	120	12	<	<	X
ejpam-2311	120	13	x	x	X
ejpam-2311	120	14	>	>	X
ejpam-2311	120	15	]	]	X
ejpam-2311	120	16	)	)	PUNCT
ejpam-2311	121	1	π	π	X
ejpam-2311	121	2	x−→	x−→	PROPN
ejpam-2311	121	3	u1(zcn	u1(zcn	NOUN
ejpam-2311	121	4	)	)	PUNCT
ejpam-2311	121	5	σx	σx	ADP
ejpam-2311	121	6	↓	↓	PROPN
ejpam-2311	121	7	σx	σx	PROPN
ejpam-2311	121	8	↓	↓	PROPN
ejpam-2311	121	9	ρ	ρ	PROPN
ejpam-2311	121	10	2	2	NUM
ejpam-2311	121	11	↓	↓	NOUN
ejpam-2311	121	12	1+m2	1+m2	NUM
ejpam-2311	121	13	ι	ι	X
ejpam-2311	121	14	−→	−→	ADJ
ejpam-2311	121	15	u1(zcn	u1(zcn	NOUN
ejpam-2311	121	16	)	)	PUNCT
ejpam-2311	121	17	ρ	ρ	PROPN
ejpam-2311	121	18	2−→	2−→	NUM
ejpam-2311	121	19	u1(z2cn	u1(z2cn	ADJ
ejpam-2311	121	20	)	)	PUNCT
ejpam-2311	121	21	.	.	PUNCT
ejpam-2311	122	1	here	here	ADV
ejpam-2311	122	2	if	if	SCONJ
ejpam-2311	122	3	we	we	PRON
ejpam-2311	122	4	restrict	restrict	VERB
ejpam-2311	122	5	the	the	DET
ejpam-2311	122	6	ring	ring	NOUN
ejpam-2311	122	7	homomorphism	homomorphism	NOUN
ejpam-2311	122	8	σx	σx	NOUN
ejpam-2311	122	9	to	to	ADP
ejpam-2311	122	10	the	the	DET
ejpam-2311	122	11	unit	unit	NOUN
ejpam-2311	122	12	group	group	NOUN
ejpam-2311	122	13	1	1	NUM
ejpam-2311	122	14	+	+	NUM
ejpam-2311	122	15	k	k	NOUN
ejpam-2311	122	16	x	x	X
ejpam-2311	122	17	,	,	PUNCT
ejpam-2311	122	18	we	we	PRON
ejpam-2311	122	19	get	get	VERB
ejpam-2311	122	20	the	the	DET
ejpam-2311	122	21	group	group	NOUN
ejpam-2311	122	22	homomorphism	homomorphism	NOUN
ejpam-2311	122	23	σx(1	σx(1	PROPN
ejpam-2311	122	24	+	+	PUNCT
ejpam-2311	122	25	(	(	PUNCT
ejpam-2311	122	26	x	x	SYM
ejpam-2311	122	27	−	−	PROPN
ejpam-2311	122	28	1)p	1)p	NUM
ejpam-2311	122	29	)	)	PUNCT
ejpam-2311	122	30	=	=	SYM
ejpam-2311	122	31	1−	1−	NUM
ejpam-2311	122	32	2p	2p	NUM
ejpam-2311	122	33	.	.	PUNCT
ejpam-2311	123	1	by	by	ADP
ejpam-2311	123	2	lemma	lemma	PROPN
ejpam-2311	123	3	1	1	PROPN
ejpam-2311	123	4	σx	σx	NOUN
ejpam-2311	123	5	is	be	AUX
ejpam-2311	123	6	surjective	surjective	ADJ
ejpam-2311	123	7	.	.	PUNCT
ejpam-2311	124	1	for	for	ADP
ejpam-2311	124	2	u	u	PROPN
ejpam-2311	124	3	∈	∈	PROPN
ejpam-2311	124	4	1	1	NUM
ejpam-2311	124	5	+	+	NUM
ejpam-2311	124	6	k	k	NOUN
ejpam-2311	124	7	x	x	X
ejpam-2311	124	8	,	,	PUNCT
ejpam-2311	124	9	u	u	PROPN
ejpam-2311	124	10	∈	∈	PROPN
ejpam-2311	124	11	kerσx⇔u=	kerσx⇔u=	NOUN
ejpam-2311	124	12	1	1	NUM
ejpam-2311	124	13	+	+	CCONJ
ejpam-2311	124	14	(	(	PUNCT
ejpam-2311	124	15	x	x	SYM
ejpam-2311	124	16	−	−	PROPN
ejpam-2311	124	17	1)p	1)p	NUM
ejpam-2311	124	18	and	and	CCONJ
ejpam-2311	124	19	σx(u	σx(u	PUNCT
ejpam-2311	124	20	)	)	PUNCT
ejpam-2311	124	21	=	=	SYM
ejpam-2311	124	22	1	1	NUM
ejpam-2311	124	23	⇔1−	⇔1−	NUM
ejpam-2311	124	24	2p=	2p=	NUM
ejpam-2311	124	25	1	1	NUM
ejpam-2311	124	26	and	and	CCONJ
ejpam-2311	124	27	p	p	PROPN
ejpam-2311	124	28	∈	∈	PROPN
ejpam-2311	124	29	zcn	zcn	NOUN
ejpam-2311	124	30	⇔p	⇔p	NOUN
ejpam-2311	124	31	=	=	SYM
ejpam-2311	124	32	0	0	NUM
ejpam-2311	124	33	⇔u=	⇔u=	NOUN
ejpam-2311	124	34	1	1	NUM
ejpam-2311	124	35	.	.	PUNCT
ejpam-2311	124	36	hence	hence	ADV
ejpam-2311	124	37	σx	σx	PROPN
ejpam-2311	124	38	is	be	AUX
ejpam-2311	124	39	injective	injective	ADJ
ejpam-2311	124	40	.	.	PUNCT
ejpam-2311	125	1	similarly	similarly	ADV
ejpam-2311	125	2	applying	apply	VERB
ejpam-2311	125	3	the	the	DET
ejpam-2311	125	4	same	same	ADJ
ejpam-2311	125	5	method	method	NOUN
ejpam-2311	125	6	to	to	PART
ejpam-2311	125	7	σy	σy	VERB
ejpam-2311	125	8	and	and	CCONJ
ejpam-2311	125	9	σxσy	σxσy	VERB
ejpam-2311	125	10	one	one	PRON
ejpam-2311	125	11	can	can	AUX
ejpam-2311	125	12	see	see	VERB
ejpam-2311	125	13	that	that	SCONJ
ejpam-2311	125	14	1	1	NUM
ejpam-2311	125	15	+	+	NUM
ejpam-2311	125	16	k	k	PROPN
ejpam-2311	125	17	y	y	PROPN
ejpam-2311	125	18	∼=	∼=	PROPN
ejpam-2311	125	19	1+m2	1+m2	NUM
ejpam-2311	125	20	and	and	CCONJ
ejpam-2311	125	21	1	1	NUM
ejpam-2311	125	22	+	+	NOUN
ejpam-2311	125	23	k	k	PROPN
ejpam-2311	125	24	x	x	SYM
ejpam-2311	125	25	y	y	PROPN
ejpam-2311	125	26	∼=	∼=	PROPN
ejpam-2311	125	27	1+m4	1+m4	NUM
ejpam-2311	125	28	respectively	respectively	ADV
ejpam-2311	125	29	.	.	PUNCT
ejpam-2311	126	1	remark	remark	PROPN
ejpam-2311	126	2	2	2	NUM
ejpam-2311	126	3	.	.	PUNCT
ejpam-2311	127	1	f	f	X
ejpam-2311	128	1	:	:	PUNCT
ejpam-2311	128	2	z[cn	z[cn	NUM
ejpam-2311	128	3	×	×	NOUN
ejpam-2311	128	4	k4	k4	NOUN
ejpam-2311	128	5	]	]	X
ejpam-2311	128	6	−→	−→	ADJ
ejpam-2311	128	7	z[cn	z[cn	NOUN
ejpam-2311	128	8	×	×	NOUN
ejpam-2311	128	9	k4	k4	NOUN
ejpam-2311	128	10	]	]	X
ejpam-2311	128	11	p0	p0	NOUN
ejpam-2311	128	12	+	+	CCONJ
ejpam-2311	128	13	p1	p1	PROPN
ejpam-2311	128	14	x	x	SYM
ejpam-2311	128	15	+	+	CCONJ
ejpam-2311	128	16	p2	p2	PROPN
ejpam-2311	128	17	y	y	PROPN
ejpam-2311	128	18	+	+	CCONJ
ejpam-2311	128	19	p3	p3	PROPN
ejpam-2311	128	20	x	x	SYM
ejpam-2311	128	21	y	y	PROPN
ejpam-2311	128	22	7→p0	7→p0	NUM
ejpam-2311	128	23	+	+	CCONJ
ejpam-2311	128	24	p2	p2	PROPN
ejpam-2311	128	25	x	x	PUNCT
ejpam-2311	129	1	+	+	CCONJ
ejpam-2311	129	2	p1	p1	PROPN
ejpam-2311	129	3	y	y	PROPN
ejpam-2311	129	4	+	+	CCONJ
ejpam-2311	129	5	p3	p3	PROPN
ejpam-2311	129	6	x	x	SYM
ejpam-2311	129	7	y	y	NOUN
ejpam-2311	129	8	is	be	AUX
ejpam-2311	129	9	a	a	DET
ejpam-2311	129	10	ring	ring	NOUN
ejpam-2311	129	11	isomorphism	isomorphism	NOUN
ejpam-2311	129	12	.	.	PUNCT
ejpam-2311	130	1	i.g	i.g	PROPN
ejpam-2311	130	2	.	.	PROPN
ejpam-2311	130	3	kelebek	kelebek	PROPN
ejpam-2311	130	4	,	,	PUNCT
ejpam-2311	130	5	t.	t.	PROPN
ejpam-2311	130	6	bilgin	bilgin	PROPN
ejpam-2311	130	7	/	/	SYM
ejpam-2311	130	8	eur	eur	PROPN
ejpam-2311	130	9	.	.	PUNCT
ejpam-2311	131	1	j.	j.	PROPN
ejpam-2311	131	2	pure	pure	PROPN
ejpam-2311	131	3	appl	appl	PROPN
ejpam-2311	131	4	.	.	PROPN
ejpam-2311	131	5	math	math	PROPN
ejpam-2311	131	6	,	,	PUNCT
ejpam-2311	131	7	7	7	NUM
ejpam-2311	131	8	(	(	PUNCT
ejpam-2311	131	9	2014	2014	NUM
ejpam-2311	131	10	)	)	PUNCT
ejpam-2311	131	11	,	,	PUNCT
ejpam-2311	131	12	462	462	NUM
ejpam-2311	131	13	-	-	SYM
ejpam-2311	131	14	471	471	NUM
ejpam-2311	131	15	468	468	NUM
ejpam-2311	131	16	3	3	NUM
ejpam-2311	131	17	.	.	PUNCT
ejpam-2311	131	18	applications	application	NOUN
ejpam-2311	131	19	theorem	theorem	VERB
ejpam-2311	131	20	4	4	NUM
ejpam-2311	131	21	.	.	PUNCT
ejpam-2311	131	22	u1(z[c5	u1(z[c5	PROPN
ejpam-2311	131	23	×	×	PROPN
ejpam-2311	131	24	k4	k4	PROPN
ejpam-2311	131	25	]	]	PUNCT
ejpam-2311	131	26	)	)	PUNCT
ejpam-2311	132	1	=	=	PRON
ejpam-2311	132	2	c5	c5	PROPN
ejpam-2311	132	3	×	×	PROPN
ejpam-2311	132	4	k4×	k4×	PROPN
ejpam-2311	132	5	<	<	X
ejpam-2311	132	6	v	v	X
ejpam-2311	132	7	>	>	X
ejpam-2311	132	8	×	×	NOUN
ejpam-2311	132	9	<	<	X
ejpam-2311	132	10	1	1	NUM
ejpam-2311	132	11	+	+	CCONJ
ejpam-2311	132	12	(	(	PUNCT
ejpam-2311	132	13	x	x	SYM
ejpam-2311	132	14	−	−	PROPN
ejpam-2311	132	15	1)p	1)p	NUM
ejpam-2311	132	16	>	>	X
ejpam-2311	132	17	×	×	NOUN
ejpam-2311	132	18	<	<	X
ejpam-2311	132	19	1	1	NUM
ejpam-2311	132	20	+	+	CCONJ
ejpam-2311	132	21	(	(	PUNCT
ejpam-2311	132	22	y	y	PROPN
ejpam-2311	132	23	−	−	PROPN
ejpam-2311	132	24	1)p	1)p	NUM
ejpam-2311	132	25	>	>	X
ejpam-2311	132	26	×	×	NOUN
ejpam-2311	132	27	<	<	X
ejpam-2311	132	28	1	1	NUM
ejpam-2311	132	29	+	+	CCONJ
ejpam-2311	132	30	(	(	PUNCT
ejpam-2311	132	31	x	x	SYM
ejpam-2311	132	32	−	−	PROPN
ejpam-2311	132	33	1)(y	1)(y	NUM
ejpam-2311	132	34	−	−	PROPN
ejpam-2311	132	35	1)q	1)q	NOUN
ejpam-2311	132	36	>	>	PUNCT
ejpam-2311	132	37	,	,	PUNCT
ejpam-2311	132	38	where	where	SCONJ
ejpam-2311	132	39	v	v	NOUN
ejpam-2311	132	40	=	=	SYM
ejpam-2311	132	41	−1	−1	NOUN
ejpam-2311	132	42	+	+	CCONJ
ejpam-2311	132	43	a+	a+	X
ejpam-2311	132	44	a4	a4	NOUN
ejpam-2311	132	45	,	,	PUNCT
ejpam-2311	132	46	p	p	NOUN
ejpam-2311	132	47	=	=	SYM
ejpam-2311	132	48	4−	4−	NUM
ejpam-2311	132	49	3(a+	3(a+	NUM
ejpam-2311	132	50	a4	a4	NOUN
ejpam-2311	132	51	)	)	PUNCT
ejpam-2311	132	52	+	+	CCONJ
ejpam-2311	132	53	(	(	PUNCT
ejpam-2311	132	54	a2	a2	PROPN
ejpam-2311	132	55	+	+	NUM
ejpam-2311	132	56	a3	a3	NOUN
ejpam-2311	132	57	)	)	PUNCT
ejpam-2311	132	58	and	and	CCONJ
ejpam-2311	132	59	q	q	NOUN
ejpam-2311	132	60	=	=	SYM
ejpam-2311	132	61	32−	32−	NUM
ejpam-2311	132	62	26(a+	26(a+	PROPN
ejpam-2311	132	63	a4	a4	NUM
ejpam-2311	132	64	)	)	PUNCT
ejpam-2311	132	65	+	+	SYM
ejpam-2311	132	66	10(a2	10(a2	NUM
ejpam-2311	132	67	+	+	NUM
ejpam-2311	132	68	a3	a3	NOUN
ejpam-2311	132	69	)	)	PUNCT
ejpam-2311	132	70	.	.	PUNCT
ejpam-2311	133	1	proof	proof	NOUN
ejpam-2311	133	2	.	.	PUNCT
ejpam-2311	134	1	karpilovsky	karpilovsky	PROPN
ejpam-2311	135	1	[	[	X
ejpam-2311	135	2	5	5	NUM
ejpam-2311	135	3	]	]	PUNCT
ejpam-2311	135	4	showed	show	VERB
ejpam-2311	135	5	if	if	SCONJ
ejpam-2311	135	6	c5	c5	PROPN
ejpam-2311	135	7	=	=	PROPN
ejpam-2311	135	8	<	<	X
ejpam-2311	135	9	a	a	DET
ejpam-2311	135	10	:	:	PUNCT
ejpam-2311	135	11	a5	a5	NOUN
ejpam-2311	135	12	=	=	SYM
ejpam-2311	135	13	1	1	X
ejpam-2311	135	14	>	>	PUNCT
ejpam-2311	135	15	then	then	ADV
ejpam-2311	135	16	u1(zc5	u1(zc5	ADJ
ejpam-2311	135	17	)	)	PUNCT
ejpam-2311	135	18	=	=	SYM
ejpam-2311	135	19	c5×	c5×	NOUN
ejpam-2311	135	20	<	<	X
ejpam-2311	135	21	v	v	X
ejpam-2311	135	22	>	>	X
ejpam-2311	135	23	,	,	PUNCT
ejpam-2311	135	24	where	where	SCONJ
ejpam-2311	135	25	v	v	NOUN
ejpam-2311	135	26	=	=	SYM
ejpam-2311	135	27	−1	−1	NOUN
ejpam-2311	135	28	+	+	CCONJ
ejpam-2311	135	29	a+	a+	PRON
ejpam-2311	135	30	a4	a4	NOUN
ejpam-2311	135	31	.	.	PUNCT
ejpam-2311	136	1	in	in	ADP
ejpam-2311	136	2	order	order	NOUN
ejpam-2311	136	3	to	to	PART
ejpam-2311	136	4	describe	describe	VERB
ejpam-2311	136	5	1	1	NUM
ejpam-2311	136	6	+	+	CCONJ
ejpam-2311	136	7	k	k	NOUN
ejpam-2311	136	8	x	x	VERB
ejpam-2311	136	9	consider	consider	VERB
ejpam-2311	136	10	the	the	DET
ejpam-2311	136	11	following	follow	VERB
ejpam-2311	136	12	commutative	commutative	ADJ
ejpam-2311	136	13	diagram	diagram	NOUN
ejpam-2311	136	14	:	:	PUNCT
ejpam-2311	136	15	1	1	X
ejpam-2311	136	16	+	+	NUM
ejpam-2311	136	17	k	k	NOUN
ejpam-2311	136	18	x	x	X
ejpam-2311	136	19	ι	ι	INTJ
ejpam-2311	136	20	−→	−→	NOUN
ejpam-2311	136	21	u1(z[c5×	u1(z[c5×	VERB
ejpam-2311	136	22	<	<	X
ejpam-2311	136	23	x	x	X
ejpam-2311	136	24	>	>	X
ejpam-2311	136	25	]	]	X
ejpam-2311	136	26	)	)	PUNCT
ejpam-2311	136	27	π	π	X
ejpam-2311	136	28	x−→	x−→	PUNCT
ejpam-2311	136	29	u1(zc5	u1(zc5	NOUN
ejpam-2311	136	30	)	)	PUNCT
ejpam-2311	136	31	σx	σx	ADP
ejpam-2311	136	32	↓	↓	PROPN
ejpam-2311	136	33	σx	σx	PROPN
ejpam-2311	136	34	↓	↓	PROPN
ejpam-2311	136	35	ρ2	ρ2	PROPN
ejpam-2311	136	36	↓	↓	NOUN
ejpam-2311	136	37	1+m2	1+m2	NUM
ejpam-2311	136	38	ι	ι	X
ejpam-2311	136	39	−→	−→	ADJ
ejpam-2311	136	40	u1(zc5	u1(zc5	NOUN
ejpam-2311	136	41	)	)	PUNCT
ejpam-2311	136	42	ρ2−→	ρ2−→	SYM
ejpam-2311	136	43	u1(z2c5	u1(z2c5	PROPN
ejpam-2311	136	44	)	)	PUNCT
ejpam-2311	136	45	ı	ı	PROPN
ejpam-2311	136	46	↑	↑	PROPN
ejpam-2311	136	47	ı	ı	PROPN
ejpam-2311	136	48	↑	↑	PROPN
ejpam-2311	136	49	ı	ı	PROPN
ejpam-2311	136	50	↑	↑	PROPN
ejpam-2311	136	51	(	(	PUNCT
ejpam-2311	136	52	1+m2)∩	1+m2)∩	NUM
ejpam-2311	136	53	f	f	NOUN
ejpam-2311	136	54	ι	ι	INTJ
ejpam-2311	136	55	−→	−→	NOUN
ejpam-2311	136	56	f	f	PROPN
ejpam-2311	136	57	ρ	ρ	X
ejpam-2311	136	58	2−→	2−→	PROPN
ejpam-2311	136	59	ρ2(f	ρ2(f	NUM
ejpam-2311	136	60	)	)	PUNCT
ejpam-2311	136	61	.	.	PUNCT
ejpam-2311	137	1	since	since	SCONJ
ejpam-2311	137	2	f	f	PROPN
ejpam-2311	137	3	=	=	PROPN
ejpam-2311	137	4	<	<	X
ejpam-2311	137	5	v	v	X
ejpam-2311	137	6	>	>	X
ejpam-2311	137	7	,	,	PUNCT
ejpam-2311	137	8	ρ2(f	ρ2(f	X
ejpam-2311	137	9	)	)	PUNCT
ejpam-2311	137	10	=	=	NOUN
ejpam-2311	137	11	<	<	X
ejpam-2311	137	12	1	1	NUM
ejpam-2311	137	13	+	+	CCONJ
ejpam-2311	137	14	a+	a+	PRON
ejpam-2311	137	15	a4	a4	NOUN
ejpam-2311	137	16	>	>	PUNCT
ejpam-2311	137	17	=	=	SYM
ejpam-2311	137	18	{	{	PUNCT
ejpam-2311	137	19	1	1	NUM
ejpam-2311	137	20	+	+	CCONJ
ejpam-2311	137	21	a+	a+	X
ejpam-2311	137	22	a4	a4	NOUN
ejpam-2311	137	23	,	,	PUNCT
ejpam-2311	137	24	1	1	NUM
ejpam-2311	137	25	+	+	NUM
ejpam-2311	137	26	a2	a2	PROPN
ejpam-2311	137	27	+	+	CCONJ
ejpam-2311	137	28	a3	a3	NOUN
ejpam-2311	137	29	,	,	PUNCT
ejpam-2311	137	30	1	1	NUM
ejpam-2311	137	31	}	}	PUNCT
ejpam-2311	137	32	.	.	PUNCT
ejpam-2311	138	1	so	so	ADV
ejpam-2311	138	2	,	,	PUNCT
ejpam-2311	138	3	we	we	PRON
ejpam-2311	138	4	get	get	VERB
ejpam-2311	138	5	(	(	PUNCT
ejpam-2311	138	6	1+m2)∩	1+m2)∩	NUM
ejpam-2311	138	7	f	f	X
ejpam-2311	138	8	=	=	SYM
ejpam-2311	138	9	kerρ2	kerρ2	NOUN
ejpam-2311	139	1	=	=	SYM
ejpam-2311	139	2	{	{	PUNCT
ejpam-2311	139	3	u	u	NOUN
ejpam-2311	139	4	∈	∈	PROPN
ejpam-2311	139	5	f	f	X
ejpam-2311	139	6	:	:	PUNCT
ejpam-2311	139	7	ρ2(u	ρ2(u	X
ejpam-2311	139	8	)	)	PUNCT
ejpam-2311	139	9	=	=	SYM
ejpam-2311	139	10	1}=	1}=	NUM
ejpam-2311	139	11	<	<	X
ejpam-2311	139	12	v3	v3	PROPN
ejpam-2311	139	13	>	>	X
ejpam-2311	139	14	.	.	PUNCT
ejpam-2311	140	1	on	on	ADP
ejpam-2311	140	2	the	the	DET
ejpam-2311	140	3	other	other	ADJ
ejpam-2311	140	4	hand	hand	NOUN
ejpam-2311	140	5	,	,	PUNCT
ejpam-2311	140	6	u	u	NOUN
ejpam-2311	140	7	∈	∈	PROPN
ejpam-2311	140	8	1	1	NUM
ejpam-2311	140	9	+	+	NUM
ejpam-2311	140	10	k	k	NOUN
ejpam-2311	140	11	x	x	X
ejpam-2311	140	12	⇒	⇒	NOUN
ejpam-2311	140	13	u	u	NOUN
ejpam-2311	140	14	=	=	PROPN
ejpam-2311	140	15	1	1	NUM
ejpam-2311	140	16	+	+	CCONJ
ejpam-2311	140	17	(	(	PUNCT
ejpam-2311	140	18	x	x	SYM
ejpam-2311	140	19	−	−	PROPN
ejpam-2311	140	20	1)p	1)p	NUM
ejpam-2311	140	21	,	,	PUNCT
ejpam-2311	140	22	(	(	PUNCT
ejpam-2311	140	23	p	p	NOUN
ejpam-2311	140	24	∈	∈	PROPN
ejpam-2311	140	25	zc5	zc5	PROPN
ejpam-2311	140	26	)	)	PUNCT
ejpam-2311	140	27	.	.	PUNCT
ejpam-2311	141	1	since	since	SCONJ
ejpam-2311	141	2	σx	σx	PROPN
ejpam-2311	141	3	is	be	AUX
ejpam-2311	141	4	an	an	DET
ejpam-2311	141	5	isomorphism	isomorphism	NOUN
ejpam-2311	141	6	and	and	CCONJ
ejpam-2311	141	7	σx(u	σx(u	PUNCT
ejpam-2311	141	8	)	)	PUNCT
ejpam-2311	142	1	=	=	SYM
ejpam-2311	142	2	1−	1−	NUM
ejpam-2311	142	3	2p	2p	NUM
ejpam-2311	142	4	,	,	PUNCT
ejpam-2311	142	5	we	we	PRON
ejpam-2311	142	6	conclude	conclude	VERB
ejpam-2311	142	7	that	that	SCONJ
ejpam-2311	142	8	1−	1−	NUM
ejpam-2311	142	9	2p	2p	NUM
ejpam-2311	142	10	=	=	SYM
ejpam-2311	142	11	v3	v3	PROPN
ejpam-2311	142	12	.	.	PUNCT
ejpam-2311	143	1	this	this	PRON
ejpam-2311	143	2	leads	lead	VERB
ejpam-2311	143	3	us	we	PRON
ejpam-2311	143	4	to	to	ADP
ejpam-2311	143	5	,	,	PUNCT
ejpam-2311	143	6	p	p	X
ejpam-2311	143	7	=	=	SYM
ejpam-2311	143	8	4−	4−	NUM
ejpam-2311	143	9	3(a+	3(a+	NUM
ejpam-2311	143	10	a4	a4	NOUN
ejpam-2311	143	11	)	)	PUNCT
ejpam-2311	144	1	+	+	CCONJ
ejpam-2311	144	2	(	(	PUNCT
ejpam-2311	144	3	a2	a2	PROPN
ejpam-2311	144	4	+	+	NUM
ejpam-2311	144	5	a3	a3	NOUN
ejpam-2311	144	6	)	)	PUNCT
ejpam-2311	144	7	.	.	PUNCT
ejpam-2311	145	1	consequently	consequently	ADV
ejpam-2311	145	2	we	we	PRON
ejpam-2311	145	3	get	get	VERB
ejpam-2311	145	4	the	the	DET
ejpam-2311	145	5	second	second	ADJ
ejpam-2311	145	6	generator	generator	NOUN
ejpam-2311	145	7	as	as	ADP
ejpam-2311	145	8	u=	u=	NOUN
ejpam-2311	145	9	1	1	NUM
ejpam-2311	145	10	+	+	CCONJ
ejpam-2311	145	11	(	(	PUNCT
ejpam-2311	145	12	x	x	SYM
ejpam-2311	145	13	−	−	NOUN
ejpam-2311	145	14	1)[4−	1)[4−	NUM
ejpam-2311	145	15	3(a+	3(a+	NUM
ejpam-2311	145	16	a4	a4	NOUN
ejpam-2311	145	17	)	)	PUNCT
ejpam-2311	146	1	+	+	CCONJ
ejpam-2311	146	2	(	(	PUNCT
ejpam-2311	146	3	a2	a2	PROPN
ejpam-2311	146	4	+	+	NUM
ejpam-2311	146	5	a3	a3	NOUN
ejpam-2311	146	6	)	)	PUNCT
ejpam-2311	146	7	]	]	PUNCT
ejpam-2311	146	8	.	.	PUNCT
ejpam-2311	147	1	by	by	ADP
ejpam-2311	147	2	remark	remark	NOUN
ejpam-2311	147	3	2	2	NUM
ejpam-2311	147	4	we	we	PRON
ejpam-2311	147	5	write	write	VERB
ejpam-2311	147	6	third	third	ADJ
ejpam-2311	147	7	generator	generator	NOUN
ejpam-2311	147	8	as	as	ADP
ejpam-2311	147	9	1	1	NUM
ejpam-2311	147	10	+	+	CCONJ
ejpam-2311	147	11	k	k	PROPN
ejpam-2311	147	12	y	y	NOUN
ejpam-2311	147	13	=	=	X
ejpam-2311	147	14	<	<	X
ejpam-2311	147	15	1	1	NUM
ejpam-2311	147	16	+	+	CCONJ
ejpam-2311	147	17	(	(	PUNCT
ejpam-2311	147	18	y	y	PROPN
ejpam-2311	147	19	−	−	PROPN
ejpam-2311	147	20	1)[4−	1)[4−	NUM
ejpam-2311	147	21	3(a+	3(a+	NUM
ejpam-2311	147	22	a4	a4	NOUN
ejpam-2311	147	23	)	)	PUNCT
ejpam-2311	147	24	+	+	CCONJ
ejpam-2311	147	25	(	(	PUNCT
ejpam-2311	147	26	a2	a2	PROPN
ejpam-2311	147	27	+	+	NUM
ejpam-2311	147	28	a3	a3	NOUN
ejpam-2311	147	29	)	)	PUNCT
ejpam-2311	147	30	]	]	PUNCT
ejpam-2311	147	31	>	>	X
ejpam-2311	147	32	.	.	PUNCT
ejpam-2311	148	1	in	in	ADP
ejpam-2311	148	2	order	order	NOUN
ejpam-2311	148	3	to	to	PART
ejpam-2311	148	4	construct	construct	VERB
ejpam-2311	148	5	1	1	NUM
ejpam-2311	148	6	+	+	NUM
ejpam-2311	148	7	k	k	PROPN
ejpam-2311	148	8	x	x	SYM
ejpam-2311	148	9	y	y	PROPN
ejpam-2311	148	10	,	,	PUNCT
ejpam-2311	148	11	consider	consider	VERB
ejpam-2311	148	12	the	the	DET
ejpam-2311	148	13	following	follow	VERB
ejpam-2311	148	14	commutative	commutative	ADJ
ejpam-2311	148	15	diagram	diagram	NOUN
ejpam-2311	148	16	:	:	PUNCT
ejpam-2311	148	17	1	1	NUM
ejpam-2311	148	18	+	+	NUM
ejpam-2311	148	19	k	k	NOUN
ejpam-2311	148	20	x	x	VERB
ejpam-2311	148	21	y	y	NOUN
ejpam-2311	148	22	ι	ι	INTJ
ejpam-2311	148	23	−→	−→	NOUN
ejpam-2311	148	24	1	1	NUM
ejpam-2311	148	25	+	+	NUM
ejpam-2311	148	26	n	n	CCONJ
ejpam-2311	148	27	y	y	PROPN
ejpam-2311	148	28	π	π	PROPN
ejpam-2311	148	29	x−→	x−→	PROPN
ejpam-2311	148	30	1	1	NUM
ejpam-2311	148	31	+	+	NUM
ejpam-2311	148	32	k	k	PROPN
ejpam-2311	148	33	y	y	PROPN
ejpam-2311	148	34	σxσy	σxσy	PROPN
ejpam-2311	148	35	↓	↓	PROPN
ejpam-2311	148	36	σxσy	σxσy	PROPN
ejpam-2311	148	37	↓	↓	PROPN
ejpam-2311	148	38	σy	σy	PROPN
ejpam-2311	148	39	↓	↓	PROPN
ejpam-2311	148	40	1+m4	1+m4	PROPN
ejpam-2311	149	1	ι	ι	X
ejpam-2311	149	2	−→	−→	ADJ
ejpam-2311	149	3	u1(zc5	u1(zc5	ADJ
ejpam-2311	149	4	)	)	PUNCT
ejpam-2311	149	5	ρ4−→	ρ4−→	SYM
ejpam-2311	149	6	u1(z4c5	u1(z4c5	NOUN
ejpam-2311	149	7	)	)	PUNCT
ejpam-2311	149	8	ı	ı	PROPN
ejpam-2311	149	9	↑	↑	PROPN
ejpam-2311	149	10	ı	ı	PROPN
ejpam-2311	149	11	↑	↑	PROPN
ejpam-2311	149	12	ı	ı	PROPN
ejpam-2311	149	13	↑	↑	PROPN
ejpam-2311	149	14	(	(	PUNCT
ejpam-2311	149	15	1+m4)∩	1+m4)∩	NUM
ejpam-2311	149	16	f	f	NOUN
ejpam-2311	150	1	ι	ι	INTJ
ejpam-2311	150	2	−→	−→	NOUN
ejpam-2311	150	3	f	f	X
ejpam-2311	150	4	ρ4−→	ρ4−→	PRON
ejpam-2311	150	5	ρ4(f	ρ4(f	NUM
ejpam-2311	150	6	)	)	PUNCT
ejpam-2311	150	7	.	.	PUNCT
ejpam-2311	151	1	as	as	ADP
ejpam-2311	151	2	f	f	PROPN
ejpam-2311	151	3	=	=	PROPN
ejpam-2311	151	4	<	<	X
ejpam-2311	151	5	v	v	X
ejpam-2311	151	6	>	>	X
ejpam-2311	151	7	and	and	CCONJ
ejpam-2311	151	8	ρ4(f	ρ4(f	NUM
ejpam-2311	151	9	)	)	PUNCT
ejpam-2311	151	10	=	=	NOUN
ejpam-2311	151	11	<	<	X
ejpam-2311	151	12	−1	−1	NOUN
ejpam-2311	151	13	+	+	CCONJ
ejpam-2311	151	14	a+	a+	PUNCT
ejpam-2311	151	15	a4	a4	NOUN
ejpam-2311	151	16	>	>	X
ejpam-2311	151	17	we	we	PRON
ejpam-2311	151	18	write	write	VERB
ejpam-2311	151	19	,	,	PUNCT
ejpam-2311	151	20	(	(	PUNCT
ejpam-2311	151	21	1+m4)∩	1+m4)∩	NUM
ejpam-2311	151	22	f	f	NOUN
ejpam-2311	151	23	=	=	PUNCT
ejpam-2311	151	24	kerρ4	kerρ4	NOUN
ejpam-2311	152	1	=	=	SYM
ejpam-2311	152	2	{	{	PUNCT
ejpam-2311	152	3	u	u	NOUN
ejpam-2311	152	4	∈	∈	PROPN
ejpam-2311	152	5	f	f	X
ejpam-2311	152	6	:	:	PUNCT
ejpam-2311	152	7	ρ4(u	ρ4(u	NOUN
ejpam-2311	152	8	)	)	PUNCT
ejpam-2311	152	9	=	=	SYM
ejpam-2311	153	1	1}=	1}=	NUM
ejpam-2311	153	2	<	<	X
ejpam-2311	153	3	v6	v6	NOUN
ejpam-2311	153	4	>	>	X
ejpam-2311	153	5	.	.	PUNCT
ejpam-2311	154	1	i.g	i.g	PROPN
ejpam-2311	154	2	.	.	PROPN
ejpam-2311	154	3	kelebek	kelebek	PROPN
ejpam-2311	154	4	,	,	PUNCT
ejpam-2311	154	5	t.	t.	PROPN
ejpam-2311	154	6	bilgin	bilgin	PROPN
ejpam-2311	154	7	/	/	SYM
ejpam-2311	154	8	eur	eur	PROPN
ejpam-2311	154	9	.	.	PUNCT
ejpam-2311	155	1	j.	j.	PROPN
ejpam-2311	155	2	pure	pure	PROPN
ejpam-2311	155	3	appl	appl	PROPN
ejpam-2311	155	4	.	.	PROPN
ejpam-2311	155	5	math	math	PROPN
ejpam-2311	155	6	,	,	PUNCT
ejpam-2311	155	7	7	7	NUM
ejpam-2311	155	8	(	(	PUNCT
ejpam-2311	155	9	2014	2014	NUM
ejpam-2311	155	10	)	)	PUNCT
ejpam-2311	155	11	,	,	PUNCT
ejpam-2311	155	12	462	462	NUM
ejpam-2311	155	13	-	-	SYM
ejpam-2311	155	14	471	471	NUM
ejpam-2311	155	15	469	469	NUM
ejpam-2311	155	16	for	for	ADP
ejpam-2311	155	17	u	u	PROPN
ejpam-2311	155	18	∈	∈	PROPN
ejpam-2311	155	19	1	1	NUM
ejpam-2311	155	20	+	+	NUM
ejpam-2311	155	21	k	k	PROPN
ejpam-2311	155	22	x	x	SYM
ejpam-2311	155	23	y	y	PROPN
ejpam-2311	155	24	⇒	⇒	VERB
ejpam-2311	155	25	u	u	NOUN
ejpam-2311	155	26	=	=	PROPN
ejpam-2311	155	27	1	1	NUM
ejpam-2311	155	28	+	+	CCONJ
ejpam-2311	155	29	(	(	PUNCT
ejpam-2311	155	30	x	x	SYM
ejpam-2311	155	31	−	−	PROPN
ejpam-2311	155	32	1)(y	1)(y	NUM
ejpam-2311	155	33	−	−	NOUN
ejpam-2311	155	34	1)q	1)q	NOUN
ejpam-2311	155	35	,	,	PUNCT
ejpam-2311	155	36	(	(	PUNCT
ejpam-2311	155	37	q	q	PROPN
ejpam-2311	155	38	∈	∈	PROPN
ejpam-2311	155	39	zc5	zc5	PROPN
ejpam-2311	155	40	)	)	PUNCT
ejpam-2311	155	41	.	.	PUNCT
ejpam-2311	156	1	since	since	SCONJ
ejpam-2311	156	2	σxσy	σxσy	NOUN
ejpam-2311	156	3	is	be	AUX
ejpam-2311	156	4	an	an	DET
ejpam-2311	156	5	isomorphism	isomorphism	NOUN
ejpam-2311	156	6	and	and	CCONJ
ejpam-2311	156	7	(	(	PUNCT
ejpam-2311	156	8	σxσy)(u	σxσy)(u	ADJ
ejpam-2311	156	9	)	)	PUNCT
ejpam-2311	156	10	=	=	SYM
ejpam-2311	157	1	1	1	NUM
ejpam-2311	157	2	+	+	NUM
ejpam-2311	157	3	4q	4q	NOUN
ejpam-2311	157	4	,	,	PUNCT
ejpam-2311	157	5	we	we	PRON
ejpam-2311	157	6	conclude	conclude	VERB
ejpam-2311	157	7	that	that	SCONJ
ejpam-2311	157	8	1	1	NUM
ejpam-2311	157	9	+	+	NUM
ejpam-2311	157	10	4q	4q	NOUN
ejpam-2311	157	11	=	=	SYM
ejpam-2311	157	12	v6	v6	NOUN
ejpam-2311	157	13	.	.	PUNCT
ejpam-2311	158	1	that	that	PRON
ejpam-2311	158	2	is	be	AUX
ejpam-2311	158	3	,	,	PUNCT
ejpam-2311	158	4	q	q	PROPN
ejpam-2311	158	5	=	=	SYM
ejpam-2311	158	6	32−	32−	NUM
ejpam-2311	158	7	26(a+	26(a+	PROPN
ejpam-2311	158	8	a4	a4	NUM
ejpam-2311	158	9	)	)	PUNCT
ejpam-2311	159	1	+	+	SYM
ejpam-2311	160	1	10(a2	10(a2	NUM
ejpam-2311	160	2	+	+	NUM
ejpam-2311	160	3	a3	a3	NOUN
ejpam-2311	160	4	)	)	PUNCT
ejpam-2311	161	1	,	,	PUNCT
ejpam-2311	161	2	then	then	ADV
ejpam-2311	161	3	the	the	DET
ejpam-2311	161	4	last	last	ADJ
ejpam-2311	161	5	generator	generator	NOUN
ejpam-2311	161	6	is	be	AUX
ejpam-2311	161	7	u=	u=	ADV
ejpam-2311	161	8	1	1	NUM
ejpam-2311	161	9	+	+	CCONJ
ejpam-2311	161	10	(	(	PUNCT
ejpam-2311	161	11	x	x	SYM
ejpam-2311	161	12	−	−	PROPN
ejpam-2311	161	13	1)(y	1)(y	NUM
ejpam-2311	161	14	−	−	PROPN
ejpam-2311	161	15	1)[32−	1)[32−	NUM
ejpam-2311	161	16	26(a+	26(a+	PROPN
ejpam-2311	161	17	a4	a4	NUM
ejpam-2311	161	18	)	)	PUNCT
ejpam-2311	161	19	+	+	SYM
ejpam-2311	162	1	10(a2	10(a2	NUM
ejpam-2311	162	2	+	+	NUM
ejpam-2311	162	3	a3	a3	NOUN
ejpam-2311	162	4	)	)	PUNCT
ejpam-2311	162	5	]	]	PUNCT
ejpam-2311	162	6	.	.	PUNCT
ejpam-2311	163	1	theorem	theorem	ADJ
ejpam-2311	163	2	5	5	NUM
ejpam-2311	163	3	.	.	NOUN
ejpam-2311	163	4	u1(z[c7	u1(z[c7	PROPN
ejpam-2311	163	5	×	×	PROPN
ejpam-2311	163	6	k4	k4	NOUN
ejpam-2311	163	7	]	]	PUNCT
ejpam-2311	163	8	)	)	PUNCT
ejpam-2311	164	1	=	=	PRON
ejpam-2311	164	2	c7	c7	PROPN
ejpam-2311	164	3	×	×	PROPN
ejpam-2311	164	4	k4×	k4×	PROPN
ejpam-2311	164	5	<	<	X
ejpam-2311	164	6	v1	v1	PROPN
ejpam-2311	164	7	,	,	PUNCT
ejpam-2311	164	8	v2	v2	PROPN
ejpam-2311	164	9	>	>	X
ejpam-2311	164	10	×	×	NOUN
ejpam-2311	164	11	<	<	X
ejpam-2311	164	12	1	1	NUM
ejpam-2311	164	13	+	+	CCONJ
ejpam-2311	164	14	(	(	PUNCT
ejpam-2311	164	15	x	x	SYM
ejpam-2311	164	16	−	−	PROPN
ejpam-2311	164	17	1)p1	1)p1	PROPN
ejpam-2311	164	18	>	>	SYM
ejpam-2311	164	19	×	×	NOUN
ejpam-2311	164	20	<	<	X
ejpam-2311	164	21	1	1	NUM
ejpam-2311	164	22	+	+	CCONJ
ejpam-2311	164	23	(	(	PUNCT
ejpam-2311	164	24	x	x	SYM
ejpam-2311	164	25	−	−	PROPN
ejpam-2311	164	26	1)p2	1)p2	NUM
ejpam-2311	164	27	>	>	X
ejpam-2311	164	28	×	×	NOUN
ejpam-2311	164	29	<	<	X
ejpam-2311	164	30	1	1	NUM
ejpam-2311	164	31	+	+	CCONJ
ejpam-2311	164	32	(	(	PUNCT
ejpam-2311	164	33	y	y	PROPN
ejpam-2311	164	34	−	−	PROPN
ejpam-2311	164	35	1)p1	1)p1	PROPN
ejpam-2311	164	36	>	>	SYM
ejpam-2311	164	37	×	×	NOUN
ejpam-2311	164	38	<	<	X
ejpam-2311	164	39	1	1	NUM
ejpam-2311	164	40	+	+	CCONJ
ejpam-2311	164	41	(	(	PUNCT
ejpam-2311	164	42	y	y	PROPN
ejpam-2311	164	43	−	−	PROPN
ejpam-2311	164	44	1)p2	1)p2	PROPN
ejpam-2311	164	45	>	>	X
ejpam-2311	164	46	×	×	NOUN
ejpam-2311	164	47	<	<	X
ejpam-2311	164	48	1	1	NUM
ejpam-2311	164	49	+	+	CCONJ
ejpam-2311	164	50	(	(	PUNCT
ejpam-2311	164	51	x	x	SYM
ejpam-2311	164	52	−	−	PROPN
ejpam-2311	164	53	1)(y	1)(y	NUM
ejpam-2311	164	54	−	−	PROPN
ejpam-2311	164	55	1)q1	1)q1	NUM
ejpam-2311	164	56	>	>	SYM
ejpam-2311	164	57	×	×	NOUN
ejpam-2311	164	58	<	<	X
ejpam-2311	164	59	1	1	NUM
ejpam-2311	164	60	+	+	CCONJ
ejpam-2311	164	61	(	(	PUNCT
ejpam-2311	164	62	x	x	SYM
ejpam-2311	164	63	−	−	PROPN
ejpam-2311	164	64	1)(y	1)(y	NUM
ejpam-2311	164	65	−	−	PROPN
ejpam-2311	165	1	1)q2	1)q2	NUM
ejpam-2311	165	2	>	>	PUNCT
ejpam-2311	165	3	,	,	PUNCT
ejpam-2311	165	4	where	where	SCONJ
ejpam-2311	165	5	v1	v1	VERB
ejpam-2311	165	6	=	=	NOUN
ejpam-2311	165	7	−	−	PROPN
ejpam-2311	165	8	1	1	NUM
ejpam-2311	165	9	+	+	NUM
ejpam-2311	165	10	(	(	PUNCT
ejpam-2311	165	11	a+	a+	X
ejpam-2311	165	12	a6	a6	NOUN
ejpam-2311	165	13	)	)	PUNCT
ejpam-2311	165	14	,	,	PUNCT
ejpam-2311	165	15	v2	v2	PROPN
ejpam-2311	165	16	=	=	NOUN
ejpam-2311	165	17	−	−	PROPN
ejpam-2311	165	18	1	1	NUM
ejpam-2311	165	19	+	+	CCONJ
ejpam-2311	165	20	(	(	PUNCT
ejpam-2311	165	21	a2	a2	PROPN
ejpam-2311	165	22	+	+	CCONJ
ejpam-2311	165	23	a6	a6	NOUN
ejpam-2311	165	24	)	)	PUNCT
ejpam-2311	165	25	,	,	PUNCT
ejpam-2311	165	26	p1	p1	NOUN
ejpam-2311	165	27	=	=	SYM
ejpam-2311	165	28	−	−	PROPN
ejpam-2311	165	29	4	4	NUM
ejpam-2311	165	30	+	+	NUM
ejpam-2311	165	31	(	(	PUNCT
ejpam-2311	165	32	a+	a+	X
ejpam-2311	165	33	a6	a6	NOUN
ejpam-2311	165	34	)	)	PUNCT
ejpam-2311	166	1	+	+	CCONJ
ejpam-2311	166	2	4(a2	4(a2	NUM
ejpam-2311	166	3	+	+	CCONJ
ejpam-2311	166	4	a5)−	a5)−	ADP
ejpam-2311	166	5	3(a3	3(a3	NUM
ejpam-2311	166	6	+	+	SYM
ejpam-2311	166	7	a4	a4	NOUN
ejpam-2311	166	8	)	)	PUNCT
ejpam-2311	166	9	,	,	PUNCT
ejpam-2311	166	10	p2	p2	PROPN
ejpam-2311	166	11	=	=	SYM
ejpam-2311	166	12	4−	4−	PROPN
ejpam-2311	166	13	(	(	PUNCT
ejpam-2311	166	14	a+	a+	PUNCT
ejpam-2311	166	15	a6)−	a6)−	PROPN
ejpam-2311	166	16	3(a2	3(a2	PROPN
ejpam-2311	166	17	+	+	CCONJ
ejpam-2311	166	18	a5	a5	NOUN
ejpam-2311	166	19	)	)	PUNCT
ejpam-2311	166	20	+	+	CCONJ
ejpam-2311	166	21	2(a3	2(a3	NUM
ejpam-2311	166	22	+	+	NUM
ejpam-2311	166	23	a4	a4	NOUN
ejpam-2311	166	24	)	)	PUNCT
ejpam-2311	166	25	,	,	PUNCT
ejpam-2311	166	26	q1	q1	PROPN
ejpam-2311	166	27	=	=	SYM
ejpam-2311	166	28	72−	72−	PROPN
ejpam-2311	166	29	16(a+	16(a+	NOUN
ejpam-2311	166	30	a6)−	a6)−	PROPN
ejpam-2311	166	31	65(a2	65(a2	NUM
ejpam-2311	166	32	+	+	CCONJ
ejpam-2311	166	33	a5	a5	NOUN
ejpam-2311	166	34	)	)	PUNCT
ejpam-2311	166	35	+	+	NUM
ejpam-2311	166	36	45(a3	45(a3	X
ejpam-2311	166	37	+	+	NUM
ejpam-2311	166	38	a4	a4	NOUN
ejpam-2311	166	39	)	)	PUNCT
ejpam-2311	166	40	,	,	PUNCT
ejpam-2311	166	41	q2	q2	NOUN
ejpam-2311	166	42	=	=	NOUN
ejpam-2311	166	43	40−	40−	PROPN
ejpam-2311	166	44	9(a+	9(a+	NOUN
ejpam-2311	167	1	a6)−	a6)−	ADJ
ejpam-2311	167	2	36(a2	36(a2	X
ejpam-2311	167	3	+	+	CCONJ
ejpam-2311	167	4	a5	a5	NUM
ejpam-2311	167	5	)	)	PUNCT
ejpam-2311	167	6	+	+	CCONJ
ejpam-2311	167	7	25(a3	25(a3	NUM
ejpam-2311	167	8	+	+	NUM
ejpam-2311	167	9	a4	a4	NOUN
ejpam-2311	167	10	)	)	PUNCT
ejpam-2311	167	11	.	.	PUNCT
ejpam-2311	168	1	proof	proof	NOUN
ejpam-2311	168	2	.	.	PUNCT
ejpam-2311	169	1	let	let	VERB
ejpam-2311	169	2	c7	c7	PROPN
ejpam-2311	170	1	=	=	PROPN
ejpam-2311	170	2	<	<	X
ejpam-2311	170	3	a	a	PRON
ejpam-2311	170	4	:	:	PUNCT
ejpam-2311	170	5	a7	a7	PROPN
ejpam-2311	170	6	=	=	SYM
ejpam-2311	170	7	1	1	NUM
ejpam-2311	170	8	>	>	PUNCT
ejpam-2311	170	9	.	.	PUNCT
ejpam-2311	171	1	aleev	aleev	NOUN
ejpam-2311	171	2	and	and	CCONJ
ejpam-2311	171	3	panina	panina	ADJ
ejpam-2311	172	1	[	[	X
ejpam-2311	172	2	1	1	X
ejpam-2311	172	3	]	]	PUNCT
ejpam-2311	172	4	showed	show	VERB
ejpam-2311	172	5	that	that	SCONJ
ejpam-2311	172	6	,	,	PUNCT
ejpam-2311	172	7	u1(zc7	u1(zc7	NOUN
ejpam-2311	172	8	)	)	PUNCT
ejpam-2311	172	9	=	=	PUNCT
ejpam-2311	172	10	c7×	c7×	VERB
ejpam-2311	172	11	<	<	X
ejpam-2311	172	12	−1	−1	NOUN
ejpam-2311	172	13	+	+	CCONJ
ejpam-2311	172	14	a+	a+	PUNCT
ejpam-2311	172	15	a6,−1	a6,−1	PROPN
ejpam-2311	172	16	+	+	CCONJ
ejpam-2311	173	1	2a2	2a2	NUM
ejpam-2311	173	2	−	−	NOUN
ejpam-2311	173	3	a3	a3	NOUN
ejpam-2311	173	4	−	−	PROPN
ejpam-2311	173	5	a4	a4	NOUN
ejpam-2311	173	6	+	+	CCONJ
ejpam-2311	173	7	2a5	2a5	NUM
ejpam-2311	173	8	>	>	X
ejpam-2311	173	9	.	.	PUNCT
ejpam-2311	174	1	since	since	SCONJ
ejpam-2311	174	2	(	(	PUNCT
ejpam-2311	174	3	−1	−1	NOUN
ejpam-2311	174	4	+	+	CCONJ
ejpam-2311	174	5	a+	a+	PUNCT
ejpam-2311	174	6	a6)2(−1	a6)2(−1	NOUN
ejpam-2311	174	7	+	+	NUM
ejpam-2311	174	8	a2	a2	PROPN
ejpam-2311	174	9	+	+	CCONJ
ejpam-2311	174	10	a5	a5	NOUN
ejpam-2311	174	11	)	)	PUNCT
ejpam-2311	174	12	=	=	SYM
ejpam-2311	174	13	−1	−1	NOUN
ejpam-2311	174	14	+	+	NUM
ejpam-2311	174	15	2a2	2a2	NUM
ejpam-2311	174	16	−	−	NOUN
ejpam-2311	174	17	a3	a3	NOUN
ejpam-2311	174	18	−	−	PROPN
ejpam-2311	174	19	a4	a4	PROPN
ejpam-2311	174	20	+	+	CCONJ
ejpam-2311	174	21	2a5	2a5	NUM
ejpam-2311	174	22	,	,	PUNCT
ejpam-2311	174	23	we	we	PRON
ejpam-2311	174	24	can	can	AUX
ejpam-2311	174	25	write	write	VERB
ejpam-2311	174	26	<	<	X
ejpam-2311	174	27	−1	−1	NOUN
ejpam-2311	174	28	+	+	CCONJ
ejpam-2311	174	29	a+	a+	PUNCT
ejpam-2311	174	30	a6,−1	a6,−1	PROPN
ejpam-2311	174	31	+	+	CCONJ
ejpam-2311	174	32	2a2	2a2	NUM
ejpam-2311	174	33	−	−	NOUN
ejpam-2311	174	34	a3	a3	NOUN
ejpam-2311	174	35	−	−	PROPN
ejpam-2311	174	36	a4	a4	PROPN
ejpam-2311	174	37	+	+	CCONJ
ejpam-2311	174	38	2a5	2a5	NUM
ejpam-2311	174	39	>	>	PUNCT
ejpam-2311	175	1	=	=	X
ejpam-2311	175	2	<	<	X
ejpam-2311	175	3	−1	−1	NOUN
ejpam-2311	175	4	+	+	NOUN
ejpam-2311	175	5	a+	a+	PUNCT
ejpam-2311	175	6	a6,−1	a6,−1	PROPN
ejpam-2311	175	7	+	+	SYM
ejpam-2311	175	8	a2	a2	PROPN
ejpam-2311	175	9	+	+	CCONJ
ejpam-2311	175	10	a5	a5	PROPN
ejpam-2311	175	11	>	>	PUNCT
ejpam-2311	175	12	.	.	PUNCT
ejpam-2311	176	1	take	take	VERB
ejpam-2311	176	2	v1	v1	NOUN
ejpam-2311	176	3	=	=	SYM
ejpam-2311	176	4	−1	−1	NOUN
ejpam-2311	176	5	+	+	CCONJ
ejpam-2311	176	6	(	(	PUNCT
ejpam-2311	176	7	a+	a+	X
ejpam-2311	176	8	a6	a6	NOUN
ejpam-2311	176	9	)	)	PUNCT
ejpam-2311	176	10	and	and	CCONJ
ejpam-2311	176	11	v2	v2	NOUN
ejpam-2311	176	12	=	=	SYM
ejpam-2311	176	13	−1	−1	NOUN
ejpam-2311	176	14	+	+	CCONJ
ejpam-2311	176	15	(	(	PUNCT
ejpam-2311	176	16	a2	a2	PROPN
ejpam-2311	176	17	+	+	CCONJ
ejpam-2311	176	18	a6	a6	NOUN
ejpam-2311	176	19	)	)	PUNCT
ejpam-2311	176	20	.	.	PUNCT
ejpam-2311	177	1	to	to	PART
ejpam-2311	177	2	describe	describe	VERB
ejpam-2311	177	3	1	1	NUM
ejpam-2311	177	4	+	+	SYM
ejpam-2311	177	5	k	k	NOUN
ejpam-2311	177	6	x	x	X
ejpam-2311	177	7	,	,	PUNCT
ejpam-2311	177	8	consider	consider	VERB
ejpam-2311	177	9	the	the	DET
ejpam-2311	177	10	following	follow	VERB
ejpam-2311	177	11	commutative	commutative	ADJ
ejpam-2311	177	12	diagram	diagram	NOUN
ejpam-2311	177	13	:	:	PUNCT
ejpam-2311	178	1	1	1	X
ejpam-2311	178	2	+	+	NUM
ejpam-2311	178	3	k	k	NOUN
ejpam-2311	178	4	x	x	X
ejpam-2311	178	5	ι	ι	INTJ
ejpam-2311	178	6	−→	−→	NOUN
ejpam-2311	178	7	u1(z[c7×	u1(z[c7×	VERB
ejpam-2311	178	8	<	<	X
ejpam-2311	178	9	x	x	X
ejpam-2311	178	10	>	>	X
ejpam-2311	178	11	]	]	X
ejpam-2311	178	12	)	)	PUNCT
ejpam-2311	179	1	π	π	X
ejpam-2311	179	2	x−→	x−→	X
ejpam-2311	179	3	u1(zc7	u1(zc7	PROPN
ejpam-2311	179	4	)	)	PUNCT
ejpam-2311	179	5	σx	σx	ADP
ejpam-2311	179	6	↓	↓	PROPN
ejpam-2311	179	7	σx	σx	PROPN
ejpam-2311	179	8	↓	↓	PROPN
ejpam-2311	179	9	ρ2	ρ2	PROPN
ejpam-2311	179	10	↓	↓	NOUN
ejpam-2311	179	11	1+m2	1+m2	NUM
ejpam-2311	179	12	ι	ι	X
ejpam-2311	179	13	−→	−→	PROPN
ejpam-2311	179	14	u1(zc7	u1(zc7	NOUN
ejpam-2311	179	15	)	)	PUNCT
ejpam-2311	179	16	ρ2−→	ρ2−→	SYM
ejpam-2311	179	17	u1(z2c7	u1(z2c7	PROPN
ejpam-2311	179	18	)	)	PUNCT
ejpam-2311	179	19	ı	ı	PROPN
ejpam-2311	179	20	↑	↑	PROPN
ejpam-2311	179	21	ı	ı	PROPN
ejpam-2311	179	22	↑	↑	PROPN
ejpam-2311	179	23	ı	ı	PROPN
ejpam-2311	179	24	↑	↑	PROPN
ejpam-2311	179	25	(	(	PUNCT
ejpam-2311	179	26	1+m2)∩	1+m2)∩	NUM
ejpam-2311	179	27	f	f	NOUN
ejpam-2311	179	28	ι	ι	INTJ
ejpam-2311	179	29	−→	−→	NOUN
ejpam-2311	179	30	f	f	PROPN
ejpam-2311	179	31	ρ	ρ	X
ejpam-2311	179	32	2−→	2−→	PROPN
ejpam-2311	179	33	ρ2(f	ρ2(f	NUM
ejpam-2311	179	34	)	)	PUNCT
ejpam-2311	179	35	i.g	i.g	PROPN
ejpam-2311	179	36	.	.	PROPN
ejpam-2311	179	37	kelebek	kelebek	PROPN
ejpam-2311	179	38	,	,	PUNCT
ejpam-2311	179	39	t.	t.	PROPN
ejpam-2311	179	40	bilgin	bilgin	PROPN
ejpam-2311	179	41	/	/	SYM
ejpam-2311	179	42	eur	eur	PROPN
ejpam-2311	179	43	.	.	PUNCT
ejpam-2311	180	1	j.	j.	PROPN
ejpam-2311	180	2	pure	pure	PROPN
ejpam-2311	180	3	appl	appl	PROPN
ejpam-2311	180	4	.	.	PROPN
ejpam-2311	180	5	math	math	PROPN
ejpam-2311	180	6	,	,	PUNCT
ejpam-2311	180	7	7	7	NUM
ejpam-2311	180	8	(	(	PUNCT
ejpam-2311	180	9	2014	2014	NUM
ejpam-2311	180	10	)	)	PUNCT
ejpam-2311	180	11	,	,	PUNCT
ejpam-2311	180	12	462	462	NUM
ejpam-2311	180	13	-	-	SYM
ejpam-2311	180	14	471	471	NUM
ejpam-2311	180	15	470	470	NUM
ejpam-2311	180	16	f	f	NOUN
ejpam-2311	180	17	=	=	NOUN
ejpam-2311	180	18	<	<	X
ejpam-2311	180	19	v1	v1	PROPN
ejpam-2311	180	20	,	,	PUNCT
ejpam-2311	180	21	v2	v2	PROPN
ejpam-2311	180	22	>	>	X
ejpam-2311	180	23	implies	imply	VERB
ejpam-2311	180	24	ρ2(f	ρ2(f	NUM
ejpam-2311	180	25	)	)	PUNCT
ejpam-2311	180	26	=	=	NOUN
ejpam-2311	180	27	<	<	X
ejpam-2311	180	28	ρ2(v1	ρ2(v1	NOUN
ejpam-2311	180	29	)	)	PUNCT
ejpam-2311	180	30	,	,	PUNCT
ejpam-2311	180	31	ρ2(v2)>=	ρ2(v2)>=	NOUN
ejpam-2311	180	32	<	<	X
ejpam-2311	180	33	1	1	NUM
ejpam-2311	180	34	+	+	CCONJ
ejpam-2311	180	35	a+	a+	X
ejpam-2311	180	36	a6	a6	NOUN
ejpam-2311	180	37	,	,	PUNCT
ejpam-2311	180	38	1	1	NUM
ejpam-2311	180	39	+	+	NUM
ejpam-2311	180	40	a2	a2	PROPN
ejpam-2311	180	41	+	+	CCONJ
ejpam-2311	180	42	a5	a5	PROPN
ejpam-2311	180	43	>	>	PUNCT
ejpam-2311	180	44	.	.	PUNCT
ejpam-2311	181	1	since	since	SCONJ
ejpam-2311	181	2	(	(	PUNCT
ejpam-2311	181	3	1	1	NUM
ejpam-2311	181	4	+	+	NUM
ejpam-2311	181	5	a+	a+	PUNCT
ejpam-2311	181	6	a6)(1	a6)(1	PROPN
ejpam-2311	181	7	+	+	NUM
ejpam-2311	181	8	a2	a2	PROPN
ejpam-2311	181	9	+	+	CCONJ
ejpam-2311	181	10	a5)3	a5)3	ADJ
ejpam-2311	181	11	=	=	SYM
ejpam-2311	181	12	1	1	NUM
ejpam-2311	181	13	and	and	CCONJ
ejpam-2311	181	14	(	(	PUNCT
ejpam-2311	181	15	1	1	NUM
ejpam-2311	181	16	+	+	NUM
ejpam-2311	181	17	a+	a+	PUNCT
ejpam-2311	181	18	a6)3(1	a6)3(1	PROPN
ejpam-2311	181	19	+	+	NUM
ejpam-2311	181	20	a2	a2	NOUN
ejpam-2311	181	21	+	+	CCONJ
ejpam-2311	181	22	a5)2	a5)2	PUNCT
ejpam-2311	181	23	=	=	SYM
ejpam-2311	181	24	1	1	X
ejpam-2311	181	25	.	.	PUNCT
ejpam-2311	181	26	the	the	DET
ejpam-2311	181	27	kernel	kernel	NOUN
ejpam-2311	181	28	of	of	ADP
ejpam-2311	181	29	ρ2	ρ2	PROPN
ejpam-2311	181	30	is	be	AUX
ejpam-2311	181	31	(	(	PUNCT
ejpam-2311	181	32	1+m2)∩	1+m2)∩	NUM
ejpam-2311	181	33	f	f	NOUN
ejpam-2311	182	1	=	=	X
ejpam-2311	182	2	<	<	X
ejpam-2311	182	3	v1v3	v1v3	PROPN
ejpam-2311	182	4	2	2	NUM
ejpam-2311	182	5	,	,	PUNCT
ejpam-2311	182	6	v3	v3	PROPN
ejpam-2311	182	7	1	1	NUM
ejpam-2311	183	1	v2	v2	PROPN
ejpam-2311	183	2	2	2	NUM
ejpam-2311	183	3	>	>	PUNCT
ejpam-2311	183	4	.	.	PUNCT
ejpam-2311	184	1	on	on	ADP
ejpam-2311	184	2	the	the	DET
ejpam-2311	184	3	other	other	ADJ
ejpam-2311	184	4	hand	hand	NOUN
ejpam-2311	184	5	,	,	PUNCT
ejpam-2311	184	6	u	u	NOUN
ejpam-2311	184	7	∈	∈	PROPN
ejpam-2311	184	8	1	1	NUM
ejpam-2311	184	9	+	+	NUM
ejpam-2311	184	10	k	k	NOUN
ejpam-2311	184	11	x	x	X
ejpam-2311	184	12	⇒	⇒	NOUN
ejpam-2311	184	13	u	u	NOUN
ejpam-2311	184	14	=	=	PROPN
ejpam-2311	184	15	1	1	NUM
ejpam-2311	184	16	+	+	CCONJ
ejpam-2311	184	17	(	(	PUNCT
ejpam-2311	184	18	x	x	SYM
ejpam-2311	184	19	−	−	PROPN
ejpam-2311	184	20	1)p	1)p	NUM
ejpam-2311	184	21	,	,	PUNCT
ejpam-2311	184	22	(	(	PUNCT
ejpam-2311	184	23	p	p	NOUN
ejpam-2311	184	24	∈	∈	PROPN
ejpam-2311	184	25	zc7	zc7	NOUN
ejpam-2311	184	26	)	)	PUNCT
ejpam-2311	184	27	.	.	PUNCT
ejpam-2311	185	1	since	since	SCONJ
ejpam-2311	185	2	σx	σx	PROPN
ejpam-2311	185	3	is	be	AUX
ejpam-2311	185	4	an	an	DET
ejpam-2311	185	5	isomorphism	isomorphism	NOUN
ejpam-2311	185	6	and	and	CCONJ
ejpam-2311	185	7	σx(u	σx(u	PUNCT
ejpam-2311	185	8	)	)	PUNCT
ejpam-2311	186	1	=	=	SYM
ejpam-2311	186	2	1−	1−	NUM
ejpam-2311	186	3	2p	2p	NUM
ejpam-2311	186	4	,	,	PUNCT
ejpam-2311	186	5	we	we	PRON
ejpam-2311	186	6	conclude	conclude	VERB
ejpam-2311	186	7	that	that	SCONJ
ejpam-2311	186	8	1−	1−	NUM
ejpam-2311	186	9	2p1	2p1	NUM
ejpam-2311	186	10	=	=	SYM
ejpam-2311	186	11	v1v3	v1v3	PROPN
ejpam-2311	186	12	2	2	NUM
ejpam-2311	186	13	1−	1−	NUM
ejpam-2311	186	14	2p2	2p2	NUM
ejpam-2311	186	15	=	=	SYM
ejpam-2311	187	1	v3	v3	PROPN
ejpam-2311	187	2	1	1	NUM
ejpam-2311	187	3	v2	v2	PROPN
ejpam-2311	187	4	2	2	NUM
ejpam-2311	187	5	�	�	PROPN
ejpam-2311	187	6	⇒	⇒	NOUN
ejpam-2311	187	7	p1	p1	NOUN
ejpam-2311	187	8	=	=	SYM
ejpam-2311	187	9	−4	−4	PROPN
ejpam-2311	187	10	+	+	CCONJ
ejpam-2311	187	11	(	(	PUNCT
ejpam-2311	187	12	a+	a+	X
ejpam-2311	187	13	a6	a6	NOUN
ejpam-2311	187	14	)	)	PUNCT
ejpam-2311	188	1	+	+	CCONJ
ejpam-2311	188	2	4(a2	4(a2	NUM
ejpam-2311	188	3	+	+	CCONJ
ejpam-2311	188	4	a5)−	a5)−	ADP
ejpam-2311	188	5	3(a3	3(a3	NUM
ejpam-2311	188	6	+	+	SYM
ejpam-2311	188	7	a4	a4	NOUN
ejpam-2311	188	8	)	)	PUNCT
ejpam-2311	188	9	p2	p2	PROPN
ejpam-2311	188	10	=	=	SYM
ejpam-2311	188	11	4−	4−	PROPN
ejpam-2311	188	12	(	(	PUNCT
ejpam-2311	188	13	a+	a+	PUNCT
ejpam-2311	188	14	a6)−	a6)−	PROPN
ejpam-2311	188	15	3(a2	3(a2	PROPN
ejpam-2311	188	16	+	+	CCONJ
ejpam-2311	188	17	a5	a5	NOUN
ejpam-2311	188	18	)	)	PUNCT
ejpam-2311	189	1	+	+	CCONJ
ejpam-2311	189	2	2(a3	2(a3	NUM
ejpam-2311	189	3	+	+	SYM
ejpam-2311	189	4	a4	a4	NOUN
ejpam-2311	189	5	)	)	PUNCT
ejpam-2311	189	6	�	�	PROPN
ejpam-2311	189	7	.	.	PUNCT
ejpam-2311	190	1	hence	hence	ADV
ejpam-2311	190	2	1	1	NUM
ejpam-2311	190	3	+	+	SYM
ejpam-2311	190	4	k	k	NOUN
ejpam-2311	190	5	x	x	SYM
ejpam-2311	190	6	=	=	X
ejpam-2311	190	7	<	<	X
ejpam-2311	190	8	1	1	NUM
ejpam-2311	190	9	+	+	CCONJ
ejpam-2311	190	10	(	(	PUNCT
ejpam-2311	190	11	x	x	SYM
ejpam-2311	190	12	−	−	PROPN
ejpam-2311	190	13	1)p1	1)p1	NUM
ejpam-2311	190	14	,	,	PUNCT
ejpam-2311	190	15	1	1	NUM
ejpam-2311	190	16	+	+	CCONJ
ejpam-2311	190	17	(	(	PUNCT
ejpam-2311	190	18	x	x	SYM
ejpam-2311	190	19	−	−	PROPN
ejpam-2311	190	20	1)p2	1)p2	NUM
ejpam-2311	190	21	>	>	X
ejpam-2311	190	22	.	.	PUNCT
ejpam-2311	191	1	by	by	ADP
ejpam-2311	191	2	remark	remark	NOUN
ejpam-2311	191	3	2	2	NUM
ejpam-2311	191	4	we	we	PRON
ejpam-2311	191	5	have	have	VERB
ejpam-2311	191	6	1+k	1+k	NUM
ejpam-2311	191	7	y	y	SYM
ejpam-2311	192	1	=	=	PROPN
ejpam-2311	192	2	<	<	X
ejpam-2311	192	3	1+(y	1+(y	NUM
ejpam-2311	192	4	−1)p1	−1)p1	ADJ
ejpam-2311	192	5	,	,	PUNCT
ejpam-2311	192	6	1+(y	1+(y	NUM
ejpam-2311	192	7	−1)p2	−1)p2	NOUN
ejpam-2311	192	8	>	>	PUNCT
ejpam-2311	192	9	.	.	PUNCT
ejpam-2311	193	1	in	in	ADP
ejpam-2311	193	2	order	order	NOUN
ejpam-2311	193	3	to	to	PART
ejpam-2311	193	4	construct	construct	VERB
ejpam-2311	193	5	1+k	1+k	NUM
ejpam-2311	193	6	x	x	X
ejpam-2311	193	7	y	y	NOUN
ejpam-2311	193	8	consider	consider	VERB
ejpam-2311	193	9	the	the	DET
ejpam-2311	193	10	following	follow	VERB
ejpam-2311	193	11	commutative	commutative	ADJ
ejpam-2311	193	12	diagram	diagram	NOUN
ejpam-2311	193	13	:	:	PUNCT
ejpam-2311	193	14	1	1	X
ejpam-2311	193	15	+	+	NUM
ejpam-2311	193	16	k	k	NOUN
ejpam-2311	193	17	x	x	VERB
ejpam-2311	193	18	y	y	NOUN
ejpam-2311	193	19	ι	ι	INTJ
ejpam-2311	193	20	−→	−→	NOUN
ejpam-2311	193	21	1	1	NUM
ejpam-2311	193	22	+	+	NUM
ejpam-2311	193	23	n	n	CCONJ
ejpam-2311	193	24	y	y	PROPN
ejpam-2311	193	25	π	π	PROPN
ejpam-2311	193	26	x−→	x−→	PROPN
ejpam-2311	193	27	1	1	NUM
ejpam-2311	193	28	+	+	NUM
ejpam-2311	193	29	k	k	PROPN
ejpam-2311	193	30	y	y	PROPN
ejpam-2311	193	31	σxσy	σxσy	PROPN
ejpam-2311	193	32	↓	↓	PROPN
ejpam-2311	193	33	σxσy	σxσy	PROPN
ejpam-2311	193	34	↓	↓	PROPN
ejpam-2311	193	35	σy	σy	PROPN
ejpam-2311	193	36	↓	↓	PROPN
ejpam-2311	193	37	1+m4	1+m4	PROPN
ejpam-2311	193	38	ι	ι	X
ejpam-2311	193	39	−→	−→	NOUN
ejpam-2311	193	40	u1(zc7	u1(zc7	NOUN
ejpam-2311	193	41	)	)	PUNCT
ejpam-2311	193	42	ρ4−→	ρ4−→	ADP
ejpam-2311	193	43	u1(z4c7	u1(z4c7	NOUN
ejpam-2311	193	44	)	)	PUNCT
ejpam-2311	193	45	ı	ı	PROPN
ejpam-2311	193	46	↑	↑	PROPN
ejpam-2311	193	47	ı	ı	PROPN
ejpam-2311	193	48	↑	↑	PROPN
ejpam-2311	193	49	ı	ı	PROPN
ejpam-2311	193	50	↑	↑	PROPN
ejpam-2311	193	51	(	(	PUNCT
ejpam-2311	193	52	1+m4)∩	1+m4)∩	NUM
ejpam-2311	193	53	f	f	NOUN
ejpam-2311	193	54	ι	ι	INTJ
ejpam-2311	193	55	−→	−→	NOUN
ejpam-2311	193	56	f	f	X
ejpam-2311	193	57	ρ4−→	ρ4−→	PRON
ejpam-2311	193	58	ρ4(f	ρ4(f	NUM
ejpam-2311	193	59	)	)	PUNCT
ejpam-2311	193	60	since	since	SCONJ
ejpam-2311	193	61	f	f	PROPN
ejpam-2311	193	62	=	=	PROPN
ejpam-2311	193	63	<	<	X
ejpam-2311	193	64	v1	v1	PROPN
ejpam-2311	193	65	,	,	PUNCT
ejpam-2311	193	66	v2	v2	PROPN
ejpam-2311	193	67	>	>	X
ejpam-2311	193	68	,	,	PUNCT
ejpam-2311	193	69	ρ4(f	ρ4(f	NUM
ejpam-2311	193	70	)	)	PUNCT
ejpam-2311	194	1	=	=	NOUN
ejpam-2311	194	2	<	<	X
ejpam-2311	194	3	−1	−1	NOUN
ejpam-2311	194	4	+	+	NOUN
ejpam-2311	194	5	a+	a+	PUNCT
ejpam-2311	194	6	a6,−1	a6,−1	PROPN
ejpam-2311	194	7	+	+	SYM
ejpam-2311	194	8	a2	a2	PROPN
ejpam-2311	194	9	+	+	CCONJ
ejpam-2311	194	10	a5	a5	PROPN
ejpam-2311	194	11	>	>	PUNCT
ejpam-2311	194	12	.	.	PUNCT
ejpam-2311	195	1	then	then	ADV
ejpam-2311	195	2	,	,	PUNCT
ejpam-2311	195	3	the	the	DET
ejpam-2311	195	4	kernel	kernel	NOUN
ejpam-2311	195	5	of	of	ADP
ejpam-2311	195	6	ρ4	ρ4	ADV
ejpam-2311	195	7	is	be	AUX
ejpam-2311	195	8	(	(	PUNCT
ejpam-2311	195	9	−1	−1	NOUN
ejpam-2311	195	10	+	+	CCONJ
ejpam-2311	195	11	a+	a+	PUNCT
ejpam-2311	195	12	a6)2(−1	a6)2(−1	NOUN
ejpam-2311	195	13	+	+	NUM
ejpam-2311	195	14	a2	a2	PROPN
ejpam-2311	195	15	+	+	CCONJ
ejpam-2311	195	16	a5)6	a5)6	PUNCT
ejpam-2311	195	17	=	=	SYM
ejpam-2311	195	18	1	1	NUM
ejpam-2311	195	19	(	(	PUNCT
ejpam-2311	195	20	−1	−1	NOUN
ejpam-2311	195	21	+	+	CCONJ
ejpam-2311	195	22	a+	a+	PUNCT
ejpam-2311	195	23	a6)6(−1	a6)6(−1	PROPN
ejpam-2311	195	24	+	+	NUM
ejpam-2311	195	25	a2	a2	PROPN
ejpam-2311	195	26	+	+	CCONJ
ejpam-2311	195	27	a5)4	a5)4	PART
ejpam-2311	195	28	=	=	SYM
ejpam-2311	195	29	1	1	NUM
ejpam-2311	195	30	�	�	PROPN
ejpam-2311	195	31	⇒	⇒	NOUN
ejpam-2311	195	32	(	(	PUNCT
ejpam-2311	195	33	1+m4	1+m4	NUM
ejpam-2311	195	34	)	)	PUNCT
ejpam-2311	196	1	=	=	NOUN
ejpam-2311	196	2	<	<	X
ejpam-2311	196	3	v2	v2	PROPN
ejpam-2311	196	4	1	1	NUM
ejpam-2311	196	5	v6	v6	NOUN
ejpam-2311	196	6	2	2	NUM
ejpam-2311	196	7	,	,	PUNCT
ejpam-2311	196	8	v6	v6	NOUN
ejpam-2311	196	9	1	1	NUM
ejpam-2311	196	10	v4	v4	PROPN
ejpam-2311	196	11	2	2	NUM
ejpam-2311	196	12	>	>	PUNCT
ejpam-2311	196	13	.	.	PUNCT
ejpam-2311	197	1	for	for	ADP
ejpam-2311	197	2	u	u	PROPN
ejpam-2311	197	3	∈	∈	PROPN
ejpam-2311	197	4	1	1	NUM
ejpam-2311	197	5	+	+	NUM
ejpam-2311	197	6	k	k	PROPN
ejpam-2311	197	7	x	x	SYM
ejpam-2311	197	8	y	y	PROPN
ejpam-2311	197	9	⇒	⇒	VERB
ejpam-2311	197	10	u	u	NOUN
ejpam-2311	197	11	=	=	PROPN
ejpam-2311	197	12	1	1	NUM
ejpam-2311	197	13	+	+	CCONJ
ejpam-2311	197	14	(	(	PUNCT
ejpam-2311	197	15	x	x	SYM
ejpam-2311	197	16	−	−	PROPN
ejpam-2311	197	17	1)(y	1)(y	NUM
ejpam-2311	197	18	−	−	NOUN
ejpam-2311	197	19	1)q	1)q	NOUN
ejpam-2311	197	20	,	,	PUNCT
ejpam-2311	197	21	(	(	PUNCT
ejpam-2311	197	22	q	q	PROPN
ejpam-2311	197	23	∈	∈	PROPN
ejpam-2311	197	24	zc7	zc7	NOUN
ejpam-2311	197	25	)	)	PUNCT
ejpam-2311	197	26	.	.	PUNCT
ejpam-2311	198	1	since	since	SCONJ
ejpam-2311	198	2	σxσy	σxσy	NOUN
ejpam-2311	198	3	is	be	AUX
ejpam-2311	198	4	an	an	DET
ejpam-2311	198	5	isomorphism	isomorphism	NOUN
ejpam-2311	198	6	and	and	CCONJ
ejpam-2311	198	7	(	(	PUNCT
ejpam-2311	198	8	σxσy)(u	σxσy)(u	ADJ
ejpam-2311	198	9	)	)	PUNCT
ejpam-2311	198	10	=	=	SYM
ejpam-2311	199	1	1	1	NUM
ejpam-2311	199	2	+	+	NUM
ejpam-2311	199	3	4q	4q	NOUN
ejpam-2311	199	4	,	,	PUNCT
ejpam-2311	199	5	we	we	PRON
ejpam-2311	199	6	conclude	conclude	VERB
ejpam-2311	199	7	that	that	SCONJ
ejpam-2311	199	8	1	1	NUM
ejpam-2311	199	9	+	+	NUM
ejpam-2311	199	10	4q1	4q1	NUM
ejpam-2311	199	11	=	=	SYM
ejpam-2311	199	12	v2	v2	PROPN
ejpam-2311	199	13	1	1	NUM
ejpam-2311	199	14	v6	v6	NOUN
ejpam-2311	199	15	2	2	NUM
ejpam-2311	199	16	1	1	NUM
ejpam-2311	199	17	+	+	NUM
ejpam-2311	199	18	4q2	4q2	NUM
ejpam-2311	199	19	=	=	SYM
ejpam-2311	199	20	v6	v6	NOUN
ejpam-2311	199	21	1	1	NUM
ejpam-2311	199	22	v4	v4	PROPN
ejpam-2311	199	23	2	2	NUM
ejpam-2311	199	24	�	�	PROPN
ejpam-2311	199	25	⇒	⇒	PROPN
ejpam-2311	199	26	q1	q1	PROPN
ejpam-2311	199	27	=	=	SYM
ejpam-2311	199	28	72−	72−	PROPN
ejpam-2311	199	29	16(a+	16(a+	NOUN
ejpam-2311	200	1	a6)−	a6)−	PROPN
ejpam-2311	200	2	65(a2	65(a2	NUM
ejpam-2311	200	3	+	+	CCONJ
ejpam-2311	200	4	a5	a5	NOUN
ejpam-2311	200	5	)	)	PUNCT
ejpam-2311	200	6	+	+	NUM
ejpam-2311	200	7	45(a3	45(a3	X
ejpam-2311	200	8	+	+	NUM
ejpam-2311	200	9	a4	a4	NOUN
ejpam-2311	200	10	)	)	PUNCT
ejpam-2311	200	11	,	,	PUNCT
ejpam-2311	200	12	q2	q2	NOUN
ejpam-2311	200	13	=	=	SYM
ejpam-2311	200	14	40−	40−	PROPN
ejpam-2311	201	1	9(a+	9(a+	NOUN
ejpam-2311	202	1	a6)−	a6)−	ADJ
ejpam-2311	202	2	36(a2	36(a2	X
ejpam-2311	202	3	+	+	CCONJ
ejpam-2311	202	4	a5	a5	NUM
ejpam-2311	202	5	)	)	PUNCT
ejpam-2311	202	6	+	+	CCONJ
ejpam-2311	202	7	25(a3	25(a3	NUM
ejpam-2311	202	8	+	+	NUM
ejpam-2311	202	9	a4	a4	NOUN
ejpam-2311	202	10	)	)	PUNCT
ejpam-2311	202	11	.	.	PUNCT
ejpam-2311	203	1	thus	thus	ADV
ejpam-2311	203	2	1	1	NUM
ejpam-2311	203	3	+	+	NUM
ejpam-2311	203	4	k	k	NOUN
ejpam-2311	203	5	x	x	SYM
ejpam-2311	203	6	y	y	PROPN
ejpam-2311	203	7	=	=	X
ejpam-2311	203	8	<	<	X
ejpam-2311	203	9	1	1	NUM
ejpam-2311	203	10	+	+	CCONJ
ejpam-2311	203	11	(	(	PUNCT
ejpam-2311	203	12	x	x	SYM
ejpam-2311	203	13	−	−	PROPN
ejpam-2311	203	14	1)(y	1)(y	NUM
ejpam-2311	203	15	−	−	PROPN
ejpam-2311	203	16	1)q1	1)q1	NUM
ejpam-2311	203	17	,	,	PUNCT
ejpam-2311	203	18	1	1	NUM
ejpam-2311	203	19	+	+	CCONJ
ejpam-2311	203	20	(	(	PUNCT
ejpam-2311	203	21	x	x	SYM
ejpam-2311	203	22	−	−	PROPN
ejpam-2311	203	23	1)(y	1)(y	NUM
ejpam-2311	204	1	−	−	PROPN
ejpam-2311	204	2	1)q2	1)q2	NUM
ejpam-2311	204	3	>	>	X
ejpam-2311	204	4	.	.	PUNCT
ejpam-2311	205	1	references	reference	NOUN
ejpam-2311	205	2	471	471	NUM
ejpam-2311	205	3	references	reference	NOUN
ejpam-2311	205	4	[	[	X
ejpam-2311	205	5	1	1	NUM
ejpam-2311	205	6	]	]	X
ejpam-2311	205	7	r	r	NOUN
ejpam-2311	205	8	zh	zh	X
ejpam-2311	205	9	aleev	aleev	VERB
ejpam-2311	206	1	and	and	CCONJ
ejpam-2311	206	2	l	l	NOUN
ejpam-2311	206	3	v	v	NOUN
ejpam-2311	206	4	panina	panina	ADJ
ejpam-2311	206	5	.	.	PUNCT
ejpam-2311	207	1	the	the	DET
ejpam-2311	207	2	units	unit	NOUN
ejpam-2311	207	3	of	of	ADP
ejpam-2311	207	4	cyclic	cyclic	ADJ
ejpam-2311	207	5	groups	group	NOUN
ejpam-2311	207	6	of	of	ADP
ejpam-2311	207	7	orders	order	NOUN
ejpam-2311	207	8	7	7	NUM
ejpam-2311	207	9	and	and	CCONJ
ejpam-2311	207	10	9	9	NUM
ejpam-2311	207	11	.	.	PUNCT
ejpam-2311	207	12	izvestiya	izvestiya	PROPN
ejpam-2311	207	13	vysshikh	vysshikh	PROPN
ejpam-2311	207	14	uchebnykh	uchebnykh	ADJ
ejpam-2311	207	15	zavedenii	zavedenii	NOUN
ejpam-2311	207	16	.	.	PUNCT
ejpam-2311	208	1	matematika	matematika	PROPN
ejpam-2311	208	2	,	,	PUNCT
ejpam-2311	208	3	11:81–84	11:81–84	NOUN
ejpam-2311	208	4	,	,	PUNCT
ejpam-2311	208	5	1999	1999	NUM
ejpam-2311	208	6	.	.	PUNCT
ejpam-2311	209	1	[	[	X
ejpam-2311	209	2	2	2	NUM
ejpam-2311	209	3	]	]	X
ejpam-2311	209	4	r	r	NOUN
ejpam-2311	209	5	g	g	PROPN
ejpam-2311	209	6	ayoub	ayoub	PROPN
ejpam-2311	209	7	and	and	CCONJ
ejpam-2311	209	8	c	c	PROPN
ejpam-2311	209	9	ayoub	ayoub	PROPN
ejpam-2311	209	10	.	.	PUNCT
ejpam-2311	210	1	on	on	ADP
ejpam-2311	210	2	the	the	DET
ejpam-2311	210	3	group	group	NOUN
ejpam-2311	210	4	ring	ring	NOUN
ejpam-2311	210	5	of	of	ADP
ejpam-2311	210	6	a	a	DET
ejpam-2311	210	7	finite	finite	ADJ
ejpam-2311	210	8	abelian	abelian	PROPN
ejpam-2311	210	9	group	group	PROPN
ejpam-2311	210	10	.	.	PUNCT
ejpam-2311	211	1	bulletin	bulletin	NOUN
ejpam-2311	211	2	of	of	ADP
ejpam-2311	211	3	australian	australian	ADJ
ejpam-2311	211	4	mathematics	mathematic	NOUN
ejpam-2311	211	5	society	society	NOUN
ejpam-2311	211	6	,	,	PUNCT
ejpam-2311	211	7	1:245–261	1:245–261	NUM
ejpam-2311	211	8	,	,	PUNCT
ejpam-2311	211	9	1969	1969	NUM
ejpam-2311	211	10	.	.	PUNCT
ejpam-2311	212	1	[	[	X
ejpam-2311	212	2	3	3	NUM
ejpam-2311	212	3	]	]	PUNCT
ejpam-2311	212	4	t	t	NOUN
ejpam-2311	212	5	bilgin	bilgin	NOUN
ejpam-2311	212	6	.	.	PUNCT
ejpam-2311	213	1	characterization	characterization	NOUN
ejpam-2311	213	2	of	of	ADP
ejpam-2311	213	3	u1(z[c12	u1(z[c12	NOUN
ejpam-2311	213	4	]	]	PUNCT
ejpam-2311	213	5	)	)	PUNCT
ejpam-2311	213	6	.	.	PUNCT
ejpam-2311	214	1	international	international	ADJ
ejpam-2311	214	2	journal	journal	NOUN
ejpam-2311	214	3	of	of	ADP
ejpam-2311	214	4	pure	pure	ADJ
ejpam-2311	214	5	and	and	CCONJ
ejpam-2311	214	6	applied	applied	ADJ
ejpam-2311	214	7	mathematics	mathematic	NOUN
ejpam-2311	214	8	,	,	PUNCT
ejpam-2311	214	9	14:531–535	14:531–535	PROPN
ejpam-2311	214	10	,	,	PUNCT
ejpam-2311	214	11	2004	2004	NUM
ejpam-2311	214	12	.	.	PUNCT
ejpam-2311	215	1	[	[	X
ejpam-2311	215	2	4	4	NUM
ejpam-2311	215	3	]	]	PUNCT
ejpam-2311	215	4	g	g	PROPN
ejpam-2311	215	5	higman	higman	NOUN
ejpam-2311	215	6	.	.	PUNCT
ejpam-2311	216	1	the	the	DET
ejpam-2311	216	2	units	unit	NOUN
ejpam-2311	216	3	of	of	ADP
ejpam-2311	216	4	group	group	NOUN
ejpam-2311	216	5	rings	ring	NOUN
ejpam-2311	216	6	.	.	PUNCT
ejpam-2311	217	1	proceedings	proceeding	NOUN
ejpam-2311	217	2	of	of	ADP
ejpam-2311	217	3	london	london	PROPN
ejpam-2311	217	4	mathematical	mathematical	ADJ
ejpam-2311	217	5	society	society	NOUN
ejpam-2311	217	6	,	,	PUNCT
ejpam-2311	217	7	46(2	46(2	NOUN
ejpam-2311	217	8	)	)	PUNCT
ejpam-2311	217	9	,	,	PUNCT
ejpam-2311	217	10	1940	1940	NUM
ejpam-2311	217	11	.	.	PUNCT
ejpam-2311	218	1	[	[	X
ejpam-2311	218	2	5	5	NUM
ejpam-2311	218	3	]	]	PUNCT
ejpam-2311	218	4	g	g	PROPN
ejpam-2311	218	5	karpilovsky	karpilovsky	NOUN
ejpam-2311	218	6	.	.	PUNCT
ejpam-2311	219	1	commutative	commutative	ADJ
ejpam-2311	219	2	group	group	PROPN
ejpam-2311	219	3	algebras	algebras	PROPN
ejpam-2311	219	4	.	.	PUNCT
ejpam-2311	219	5	marcel	marcel	PROPN
ejpam-2311	219	6	dekker	dekker	PROPN
ejpam-2311	219	7	,	,	PUNCT
ejpam-2311	219	8	new	new	PROPN
ejpam-2311	219	9	york	york	PROPN
ejpam-2311	219	10	,	,	PUNCT
ejpam-2311	219	11	1983	1983	NUM
ejpam-2311	219	12	.	.	PUNCT
ejpam-2311	220	1	[	[	X
ejpam-2311	220	2	6	6	NUM
ejpam-2311	220	3	]	]	X
ejpam-2311	220	4	r	r	NOUN
ejpam-2311	220	5	m	m	NOUN
ejpam-2311	220	6	low	low	ADJ
ejpam-2311	220	7	.	.	PUNCT
ejpam-2311	221	1	on	on	ADP
ejpam-2311	221	2	the	the	DET
ejpam-2311	221	3	units	unit	NOUN
ejpam-2311	221	4	of	of	ADP
ejpam-2311	221	5	integral	integral	ADJ
ejpam-2311	221	6	group	group	NOUN
ejpam-2311	221	7	ring	ring	NOUN
ejpam-2311	221	8	z[g	z[g	PROPN
ejpam-2311	221	9	×	×	PROPN
ejpam-2311	221	10	cp	cp	NOUN
ejpam-2311	221	11	]	]	PUNCT
ejpam-2311	221	12	.	.	PUNCT
ejpam-2311	222	1	journal	journal	PROPN
ejpam-2311	222	2	of	of	ADP
ejpam-2311	222	3	algebra	algebra	PROPN
ejpam-2311	222	4	and	and	CCONJ
ejpam-2311	222	5	its	its	PRON
ejpam-2311	222	6	applications	application	NOUN
ejpam-2311	222	7	,	,	PUNCT
ejpam-2311	222	8	7:393–403	7:393–403	NOUN
ejpam-2311	222	9	,	,	PUNCT
ejpam-2311	222	10	2008	2008	NUM
ejpam-2311	222	11	.	.	PUNCT