id	sid	tid	token	lemma	pos
ejpam-1097	1	1	2_talebi.dvi	2_talebi.dvi	NUM
ejpam-1097	1	2	european	european	ADJ
ejpam-1097	1	3	journal	journal	NOUN
ejpam-1097	1	4	of	of	ADP
ejpam-1097	1	5	pure	pure	ADJ
ejpam-1097	1	6	and	and	CCONJ
ejpam-1097	1	7	applied	apply	VERB
ejpam-1097	1	8	mathematics	mathematic	NOUN
ejpam-1097	1	9	vol	vol	NOUN
ejpam-1097	1	10	.	.	PROPN
ejpam-1097	2	1	5	5	NUM
ejpam-1097	2	2	,	,	PUNCT
ejpam-1097	2	3	no	no	INTJ
ejpam-1097	2	4	.	.	NOUN
ejpam-1097	2	5	2	2	NUM
ejpam-1097	2	6	,	,	PUNCT
ejpam-1097	2	7	2012	2012	NUM
ejpam-1097	2	8	,	,	PUNCT
ejpam-1097	2	9	108	108	NUM
ejpam-1097	2	10	-	-	SYM
ejpam-1097	2	11	115	115	NUM
ejpam-1097	2	12	issn	issn	PROPN
ejpam-1097	2	13	1307	1307	NUM
ejpam-1097	2	14	-	-	SYM
ejpam-1097	2	15	5543	5543	NUM
ejpam-1097	2	16	–	–	PUNCT
ejpam-1097	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1097	2	18	a	a	DET
ejpam-1097	2	19	generalization	generalization	NOUN
ejpam-1097	2	20	of	of	ADP
ejpam-1097	2	21	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	2	22	modules	module	NOUN
ejpam-1097	2	23	tayyebeh	tayyebeh	NOUN
ejpam-1097	2	24	amouzegar1	amouzegar1	PROPN
ejpam-1097	2	25	,	,	PUNCT
ejpam-1097	2	26	yahya	yahya	PROPN
ejpam-1097	2	27	talebi	talebi	PROPN
ejpam-1097	2	28	2,∗	2,∗	NUM
ejpam-1097	2	29	1	1	NUM
ejpam-1097	2	30	department	department	NOUN
ejpam-1097	2	31	of	of	ADP
ejpam-1097	2	32	mathematics	mathematic	NOUN
ejpam-1097	2	33	,	,	PUNCT
ejpam-1097	2	34	quchan	quchan	PROPN
ejpam-1097	2	35	institute	institute	PROPN
ejpam-1097	2	36	of	of	ADP
ejpam-1097	2	37	engineering	engineering	NOUN
ejpam-1097	2	38	and	and	CCONJ
ejpam-1097	2	39	technology	technology	NOUN
ejpam-1097	2	40	,	,	PUNCT
ejpam-1097	2	41	quchan	quchan	PROPN
ejpam-1097	2	42	,	,	PUNCT
ejpam-1097	2	43	iran	iran	PROPN
ejpam-1097	2	44	2	2	NUM
ejpam-1097	2	45	department	department	NOUN
ejpam-1097	2	46	of	of	ADP
ejpam-1097	2	47	mathematics	mathematic	NOUN
ejpam-1097	2	48	,	,	PUNCT
ejpam-1097	2	49	faculty	faculty	NOUN
ejpam-1097	2	50	of	of	ADP
ejpam-1097	2	51	mathematical	mathematical	ADJ
ejpam-1097	2	52	sciences	sciences	PROPN
ejpam-1097	2	53	,	,	PUNCT
ejpam-1097	2	54	university	university	NOUN
ejpam-1097	2	55	of	of	ADP
ejpam-1097	2	56	mazandaran	mazandaran	PROPN
ejpam-1097	2	57	,	,	PUNCT
ejpam-1097	2	58	babolsar	babolsar	PROPN
ejpam-1097	2	59	,	,	PUNCT
ejpam-1097	2	60	iran	iran	PROPN
ejpam-1097	2	61	abstract	abstract	NOUN
ejpam-1097	2	62	.	.	PUNCT
ejpam-1097	3	1	let	let	VERB
ejpam-1097	3	2	m	m	PRON
ejpam-1097	3	3	and	and	CCONJ
ejpam-1097	3	4	x	x	PART
ejpam-1097	3	5	be	be	AUX
ejpam-1097	3	6	r	r	NOUN
ejpam-1097	3	7	-	-	PUNCT
ejpam-1097	3	8	modules	module	NOUN
ejpam-1097	3	9	.	.	PUNCT
ejpam-1097	4	1	we	we	PRON
ejpam-1097	4	2	define	define	VERB
ejpam-1097	4	3	the	the	DET
ejpam-1097	4	4	x	x	X
ejpam-1097	4	5	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	4	6	modules	module	NOUN
ejpam-1097	4	7	via	via	ADP
ejpam-1097	4	8	the	the	DET
ejpam-1097	4	9	classb(m	classb(m	NOUN
ejpam-1097	4	10	,	,	PUNCT
ejpam-1097	4	11	x	x	PUNCT
ejpam-1097	4	12	)	)	PUNCT
ejpam-1097	4	13	as	as	ADP
ejpam-1097	4	14	a	a	DET
ejpam-1097	4	15	generalization	generalization	NOUN
ejpam-1097	4	16	of⊕-supplemented	of⊕-supplemente	VERB
ejpam-1097	4	17	modules	module	NOUN
ejpam-1097	4	18	.	.	PUNCT
ejpam-1097	5	1	we	we	PRON
ejpam-1097	5	2	show	show	VERB
ejpam-1097	5	3	that	that	SCONJ
ejpam-1097	5	4	any	any	DET
ejpam-1097	5	5	finite	finite	ADJ
ejpam-1097	5	6	direct	direct	ADJ
ejpam-1097	5	7	sum	sum	NOUN
ejpam-1097	5	8	of	of	ADP
ejpam-1097	5	9	x	x	PUNCT
ejpam-1097	5	10	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	5	11	modules	module	NOUN
ejpam-1097	5	12	is	be	AUX
ejpam-1097	5	13	x	x	PUNCT
ejpam-1097	5	14	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	5	15	.	.	PUNCT
ejpam-1097	6	1	it	it	PRON
ejpam-1097	6	2	is	be	AUX
ejpam-1097	6	3	given	give	VERB
ejpam-1097	6	4	a	a	DET
ejpam-1097	6	5	number	number	NOUN
ejpam-1097	6	6	of	of	ADP
ejpam-1097	6	7	necessary	necessary	ADJ
ejpam-1097	6	8	and	and	CCONJ
ejpam-1097	6	9	sufficient	sufficient	ADJ
ejpam-1097	6	10	conditions	condition	NOUN
ejpam-1097	6	11	for	for	ADP
ejpam-1097	6	12	every	every	DET
ejpam-1097	6	13	direct	direct	ADJ
ejpam-1097	6	14	summand	summand	NOUN
ejpam-1097	6	15	of	of	ADP
ejpam-1097	6	16	an	an	DET
ejpam-1097	6	17	x	x	NOUN
ejpam-1097	6	18	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	6	19	module	module	NOUN
ejpam-1097	6	20	to	to	PART
ejpam-1097	6	21	be	be	AUX
ejpam-1097	6	22	x	x	PUNCT
ejpam-1097	6	23	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	6	24	.	.	PUNCT
ejpam-1097	6	25	2010	2010	NUM
ejpam-1097	6	26	mathematics	mathematic	NOUN
ejpam-1097	6	27	subject	subject	NOUN
ejpam-1097	6	28	classifications	classification	NOUN
ejpam-1097	6	29	:	:	PUNCT
ejpam-1097	6	30	16d90	16d90	NUM
ejpam-1097	6	31	,	,	PUNCT
ejpam-1097	6	32	16d99	16d99	NUM
ejpam-1097	6	33	key	key	ADJ
ejpam-1097	6	34	words	word	NOUN
ejpam-1097	6	35	and	and	CCONJ
ejpam-1097	6	36	phrases	phrase	NOUN
ejpam-1097	6	37	:	:	PUNCT
ejpam-1097	6	38	x	x	X
ejpam-1097	6	39	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	6	40	module	module	NOUN
ejpam-1097	6	41	,	,	PUNCT
ejpam-1097	6	42	completely	completely	ADV
ejpam-1097	6	43	x	x	NUM
ejpam-1097	6	44	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	6	45	module	module	NOUN
ejpam-1097	6	46	,	,	PUNCT
ejpam-1097	6	47	hollow	hollow	ADJ
ejpam-1097	6	48	module	module	NOUN
ejpam-1097	6	49	1	1	NUM
ejpam-1097	6	50	.	.	PUNCT
ejpam-1097	6	51	introduction	introduction	NOUN
ejpam-1097	6	52	throughout	throughout	ADP
ejpam-1097	6	53	this	this	DET
ejpam-1097	6	54	paper	paper	NOUN
ejpam-1097	6	55	r	r	NOUN
ejpam-1097	6	56	will	will	AUX
ejpam-1097	6	57	denote	denote	VERB
ejpam-1097	6	58	an	an	DET
ejpam-1097	6	59	arbitrary	arbitrary	ADJ
ejpam-1097	6	60	associative	associative	ADJ
ejpam-1097	6	61	ring	ring	NOUN
ejpam-1097	6	62	with	with	ADP
ejpam-1097	6	63	identity	identity	NOUN
ejpam-1097	6	64	and	and	CCONJ
ejpam-1097	6	65	m	m	VERB
ejpam-1097	6	66	a	a	DET
ejpam-1097	6	67	unitary	unitary	ADJ
ejpam-1097	6	68	r	r	NOUN
ejpam-1097	6	69	-	-	PUNCT
ejpam-1097	6	70	module	module	NOUN
ejpam-1097	6	71	.	.	PUNCT
ejpam-1097	7	1	a	a	DET
ejpam-1097	7	2	submodule	submodule	NOUN
ejpam-1097	7	3	n	n	PROPN
ejpam-1097	7	4	of	of	ADP
ejpam-1097	7	5	m	m	PROPN
ejpam-1097	7	6	is	be	AUX
ejpam-1097	7	7	called	call	VERB
ejpam-1097	7	8	small	small	ADJ
ejpam-1097	7	9	in	in	ADP
ejpam-1097	7	10	m	m	PROPN
ejpam-1097	7	11	(	(	PUNCT
ejpam-1097	7	12	notation	notation	NOUN
ejpam-1097	7	13	n	n	CCONJ
ejpam-1097	7	14	≪	≪	NOUN
ejpam-1097	7	15	m	m	NOUN
ejpam-1097	7	16	)	)	PUNCT
ejpam-1097	7	17	if	if	SCONJ
ejpam-1097	7	18	∀l	∀l	NOUN
ejpam-1097	7	19	�	�	PROPN
ejpam-1097	7	20	m	m	PROPN
ejpam-1097	7	21	,	,	PUNCT
ejpam-1097	7	22	l	l	PROPN
ejpam-1097	7	23	+	+	CCONJ
ejpam-1097	7	24	n	n	CCONJ
ejpam-1097	7	25	6=	6=	NUM
ejpam-1097	7	26	m	m	NOUN
ejpam-1097	7	27	.	.	PUNCT
ejpam-1097	8	1	a	a	DET
ejpam-1097	8	2	non	non	ADJ
ejpam-1097	8	3	-	-	ADJ
ejpam-1097	8	4	zero	zero	NUM
ejpam-1097	8	5	module	module	NOUN
ejpam-1097	8	6	m	m	NOUN
ejpam-1097	8	7	is	be	AUX
ejpam-1097	8	8	called	call	VERB
ejpam-1097	8	9	hollow	hollow	ADJ
ejpam-1097	8	10	if	if	SCONJ
ejpam-1097	8	11	every	every	DET
ejpam-1097	8	12	proper	proper	ADJ
ejpam-1097	8	13	submodule	submodule	NOUN
ejpam-1097	8	14	is	be	AUX
ejpam-1097	8	15	small	small	ADJ
ejpam-1097	8	16	in	in	ADP
ejpam-1097	8	17	m	m	PROPN
ejpam-1097	8	18	.	.	PUNCT
ejpam-1097	9	1	let	let	VERB
ejpam-1097	9	2	k	k	NOUN
ejpam-1097	9	3	and	and	CCONJ
ejpam-1097	9	4	n	n	CCONJ
ejpam-1097	9	5	be	be	VERB
ejpam-1097	9	6	submodules	submodule	NOUN
ejpam-1097	9	7	of	of	ADP
ejpam-1097	9	8	m	m	PRON
ejpam-1097	9	9	.	.	PUNCT
ejpam-1097	10	1	k	k	PROPN
ejpam-1097	10	2	is	be	AUX
ejpam-1097	10	3	called	call	VERB
ejpam-1097	10	4	a	a	DET
ejpam-1097	10	5	supplement	supplement	NOUN
ejpam-1097	10	6	of	of	ADP
ejpam-1097	10	7	n	n	PROPN
ejpam-1097	10	8	in	in	ADP
ejpam-1097	10	9	m	m	PROPN
ejpam-1097	10	10	if	if	SCONJ
ejpam-1097	10	11	m	m	VERB
ejpam-1097	10	12	=	=	SYM
ejpam-1097	10	13	k	k	PROPN
ejpam-1097	11	1	+	+	CCONJ
ejpam-1097	11	2	n	n	PROPN
ejpam-1097	11	3	and	and	CCONJ
ejpam-1097	11	4	k	k	PROPN
ejpam-1097	11	5	is	be	AUX
ejpam-1097	11	6	minimal	minimal	ADJ
ejpam-1097	11	7	with	with	ADP
ejpam-1097	11	8	respect	respect	NOUN
ejpam-1097	11	9	to	to	ADP
ejpam-1097	11	10	this	this	DET
ejpam-1097	11	11	property	property	NOUN
ejpam-1097	11	12	,	,	PUNCT
ejpam-1097	11	13	or	or	CCONJ
ejpam-1097	11	14	equivalently	equivalently	ADV
ejpam-1097	11	15	,	,	PUNCT
ejpam-1097	12	1	m	m	VERB
ejpam-1097	12	2	=	=	SYM
ejpam-1097	12	3	k	k	PROPN
ejpam-1097	13	1	+	+	CCONJ
ejpam-1097	13	2	n	n	PROPN
ejpam-1097	13	3	and	and	CCONJ
ejpam-1097	13	4	k	k	PROPN
ejpam-1097	13	5	∩	∩	PROPN
ejpam-1097	13	6	n	n	CCONJ
ejpam-1097	13	7	≪	≪	ADJ
ejpam-1097	13	8	k	k	PROPN
ejpam-1097	13	9	.	.	PUNCT
ejpam-1097	14	1	a	a	DET
ejpam-1097	14	2	submodule	submodule	NOUN
ejpam-1097	14	3	k	k	PROPN
ejpam-1097	14	4	of	of	ADP
ejpam-1097	14	5	m	m	PROPN
ejpam-1097	14	6	is	be	AUX
ejpam-1097	14	7	called	call	VERB
ejpam-1097	14	8	a	a	DET
ejpam-1097	14	9	supplement	supplement	NOUN
ejpam-1097	14	10	in	in	ADP
ejpam-1097	14	11	m	m	AUX
ejpam-1097	14	12	provided	provide	VERB
ejpam-1097	14	13	there	there	PRON
ejpam-1097	14	14	exists	exist	VERB
ejpam-1097	14	15	a	a	DET
ejpam-1097	14	16	submodule	submodule	NOUN
ejpam-1097	14	17	n	n	PROPN
ejpam-1097	14	18	of	of	ADP
ejpam-1097	14	19	m	m	PRON
ejpam-1097	14	20	such	such	ADJ
ejpam-1097	14	21	that	that	SCONJ
ejpam-1097	14	22	k	k	PROPN
ejpam-1097	14	23	is	be	AUX
ejpam-1097	14	24	a	a	DET
ejpam-1097	14	25	supplement	supplement	NOUN
ejpam-1097	14	26	of	of	ADP
ejpam-1097	14	27	n	n	PROPN
ejpam-1097	14	28	in	in	ADP
ejpam-1097	14	29	m	m	PROPN
ejpam-1097	14	30	.	.	PUNCT
ejpam-1097	15	1	following	follow	VERB
ejpam-1097	15	2	[	[	X
ejpam-1097	15	3	9	9	NUM
ejpam-1097	15	4	]	]	PUNCT
ejpam-1097	15	5	,	,	PUNCT
ejpam-1097	15	6	a	a	DET
ejpam-1097	15	7	module	module	NOUN
ejpam-1097	15	8	m	m	VERB
ejpam-1097	15	9	is	be	AUX
ejpam-1097	15	10	called	call	VERB
ejpam-1097	15	11	supplemented	supplement	VERB
ejpam-1097	15	12	if	if	SCONJ
ejpam-1097	15	13	every	every	DET
ejpam-1097	15	14	submodule	submodule	NOUN
ejpam-1097	15	15	of	of	ADP
ejpam-1097	15	16	m	m	PROPN
ejpam-1097	15	17	has	have	VERB
ejpam-1097	15	18	a	a	DET
ejpam-1097	15	19	supplement	supplement	NOUN
ejpam-1097	15	20	in	in	ADP
ejpam-1097	15	21	m	m	PROPN
ejpam-1097	15	22	.	.	PUNCT
ejpam-1097	16	1	according	accord	VERB
ejpam-1097	16	2	to	to	ADP
ejpam-1097	16	3	[	[	X
ejpam-1097	16	4	6	6	NUM
ejpam-1097	16	5	]	]	PUNCT
ejpam-1097	16	6	,	,	PUNCT
ejpam-1097	16	7	a	a	DET
ejpam-1097	16	8	module	module	NOUN
ejpam-1097	16	9	m	m	VERB
ejpam-1097	16	10	is	be	AUX
ejpam-1097	16	11	called	call	VERB
ejpam-1097	16	12	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	16	13	if	if	SCONJ
ejpam-1097	16	14	every	every	DET
ejpam-1097	16	15	submodule	submodule	NOUN
ejpam-1097	16	16	of	of	ADP
ejpam-1097	16	17	m	m	PROPN
ejpam-1097	16	18	has	have	VERB
ejpam-1097	16	19	a	a	DET
ejpam-1097	16	20	supplement	supplement	NOUN
ejpam-1097	16	21	that	that	PRON
ejpam-1097	16	22	is	be	AUX
ejpam-1097	16	23	a	a	DET
ejpam-1097	16	24	direct	direct	ADJ
ejpam-1097	16	25	summand	summand	NOUN
ejpam-1097	16	26	of	of	ADP
ejpam-1097	16	27	m	m	PROPN
ejpam-1097	16	28	.	.	PUNCT
ejpam-1097	17	1	a	a	DET
ejpam-1097	17	2	module	module	NOUN
ejpam-1097	17	3	m	m	VERB
ejpam-1097	17	4	is	be	AUX
ejpam-1097	17	5	called	call	VERB
ejpam-1097	17	6	completely	completely	ADV
ejpam-1097	17	7	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	17	8	if	if	SCONJ
ejpam-1097	17	9	every	every	DET
ejpam-1097	17	10	direct	direct	ADJ
ejpam-1097	17	11	summand	summand	NOUN
ejpam-1097	17	12	of	of	ADP
ejpam-1097	17	13	m	m	PROPN
ejpam-1097	17	14	is	be	AUX
ejpam-1097	17	15	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	17	16	[	[	PUNCT
ejpam-1097	17	17	see	see	VERB
ejpam-1097	17	18	4	4	NUM
ejpam-1097	17	19	]	]	PUNCT
ejpam-1097	17	20	.	.	PUNCT
ejpam-1097	18	1	let	let	VERB
ejpam-1097	18	2	m	m	PRON
ejpam-1097	18	3	and	and	CCONJ
ejpam-1097	18	4	x	x	PART
ejpam-1097	18	5	be	be	AUX
ejpam-1097	18	6	r	r	NOUN
ejpam-1097	18	7	-	-	PUNCT
ejpam-1097	18	8	modules	module	NOUN
ejpam-1097	18	9	.	.	PUNCT
ejpam-1097	19	1	in	in	ADP
ejpam-1097	19	2	[	[	X
ejpam-1097	19	3	5	5	NUM
ejpam-1097	19	4	]	]	PUNCT
ejpam-1097	19	5	,	,	PUNCT
ejpam-1097	19	6	keskin	keskin	PROPN
ejpam-1097	19	7	tütüncü	tütüncü	PROPN
ejpam-1097	19	8	and	and	CCONJ
ejpam-1097	19	9	harmancı	harmancı	PROPN
ejpam-1097	19	10	defined	define	VERB
ejpam-1097	19	11	the	the	DET
ejpam-1097	19	12	family	family	NOUN
ejpam-1097	19	13	b(m	b(m	NOUN
ejpam-1097	19	14	,	,	PUNCT
ejpam-1097	19	15	x	x	X
ejpam-1097	19	16	)	)	PUNCT
ejpam-1097	20	1	=	=	PRON
ejpam-1097	20	2	{	{	PUNCT
ejpam-1097	20	3	a≤	a≤	ADP
ejpam-1097	20	4	m	m	PROPN
ejpam-1097	20	5	|	|	NOUN
ejpam-1097	20	6	∃y	∃y	PROPN
ejpam-1097	20	7	≤	≤	NUM
ejpam-1097	20	8	x	x	X
ejpam-1097	20	9	,	,	PUNCT
ejpam-1097	20	10	∃	∃	PROPN
ejpam-1097	20	11	f	f	PROPN
ejpam-1097	20	12	∈	∈	PROPN
ejpam-1097	20	13	hom(m	hom(m	PROPN
ejpam-1097	20	14	,	,	PUNCT
ejpam-1097	20	15	x	x	PROPN
ejpam-1097	20	16	/	/	SYM
ejpam-1097	20	17	y	y	PROPN
ejpam-1097	20	18	)	)	PUNCT
ejpam-1097	20	19	,	,	PUNCT
ejpam-1097	20	20	ker	ker	PROPN
ejpam-1097	20	21	f	f	X
ejpam-1097	20	22	/a≪	/a≪	PUNCT
ejpam-1097	21	1	m	m	PROPN
ejpam-1097	21	2	/	/	SYM
ejpam-1097	21	3	a	a	PRON
ejpam-1097	21	4	}	}	PUNCT
ejpam-1097	21	5	and	and	CCONJ
ejpam-1097	21	6	used	use	VERB
ejpam-1097	21	7	this	this	DET
ejpam-1097	21	8	class	class	NOUN
ejpam-1097	21	9	to	to	PART
ejpam-1097	21	10	define	define	VERB
ejpam-1097	21	11	b(m	b(m	PROPN
ejpam-1097	21	12	,	,	PUNCT
ejpam-1097	21	13	x	x	X
ejpam-1097	21	14	)	)	PUNCT
ejpam-1097	21	15	-projective	-projective	ADJ
ejpam-1097	21	16	modules	module	NOUN
ejpam-1097	21	17	as	as	ADP
ejpam-1097	21	18	a	a	DET
ejpam-1097	21	19	generalization	generalization	NOUN
ejpam-1097	21	20	of	of	ADP
ejpam-1097	21	21	projective	projective	ADJ
ejpam-1097	21	22	modules	module	NOUN
ejpam-1097	21	23	.	.	PUNCT
ejpam-1097	22	1	in	in	ADP
ejpam-1097	22	2	this	this	DET
ejpam-1097	22	3	paper	paper	NOUN
ejpam-1097	22	4	we	we	PRON
ejpam-1097	22	5	define	define	VERB
ejpam-1097	22	6	x	x	PUNCT
ejpam-1097	22	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	22	8	modules	module	NOUN
ejpam-1097	22	9	and	and	CCONJ
ejpam-1097	22	10	completely	completely	ADV
ejpam-1097	22	11	x	x	NUM
ejpam-1097	22	12	-⊕-supplemented	-⊕-supplemented	ADJ
ejpam-1097	22	13	modules	module	NOUN
ejpam-1097	22	14	via	via	ADP
ejpam-1097	22	15	the	the	DET
ejpam-1097	22	16	class	class	NOUN
ejpam-1097	22	17	∗corresponding	∗corresponding	NOUN
ejpam-1097	22	18	author	author	NOUN
ejpam-1097	22	19	.	.	PUNCT
ejpam-1097	23	1	email	email	NOUN
ejpam-1097	23	2	addresses	address	NOUN
ejpam-1097	23	3	:	:	PUNCT
ejpam-1097	23	4	t.amoozegar	t.amoozegar	NUM
ejpam-1097	23	5	�	�	NOUN
ejpam-1097	23	6	yahoo	yahoo	PROPN
ejpam-1097	23	7	.	.	PUNCT
ejpam-1097	24	1	om	om	PROPN
ejpam-1097	24	2	(	(	PUNCT
ejpam-1097	24	3	t.	t.	NOUN
ejpam-1097	24	4	amouzegar	amouzegar	NOUN
ejpam-1097	24	5	)	)	PUNCT
ejpam-1097	24	6	,	,	PUNCT
ejpam-1097	24	7	talebi	talebi	PROPN
ejpam-1097	24	8	�	�	PROPN
ejpam-1097	24	9	umz.a	umz.a	PROPN
ejpam-1097	24	10	.ir	.ir	PUNCT
ejpam-1097	24	11	(	(	PUNCT
ejpam-1097	24	12	y.	y.	NOUN
ejpam-1097	24	13	talebi	talebi	PROPN
ejpam-1097	24	14	)	)	PUNCT
ejpam-1097	24	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1097	25	1	108	108	NUM
ejpam-1097	25	2	c	c	NOUN
ejpam-1097	25	3	©	©	PROPN
ejpam-1097	25	4	2012	2012	NUM
ejpam-1097	25	5	ejpam	ejpam	VERB
ejpam-1097	25	6	all	all	DET
ejpam-1097	25	7	rights	right	NOUN
ejpam-1097	25	8	reserved	reserve	VERB
ejpam-1097	25	9	.	.	PUNCT
ejpam-1097	26	1	t.	t.	PROPN
ejpam-1097	26	2	amouzegar	amouzegar	NOUN
ejpam-1097	26	3	,	,	PUNCT
ejpam-1097	26	4	y.	y.	PROPN
ejpam-1097	26	5	talebi	talebi	PROPN
ejpam-1097	26	6	/	/	SYM
ejpam-1097	26	7	eur	eur	PROPN
ejpam-1097	26	8	.	.	PUNCT
ejpam-1097	27	1	j.	j.	PROPN
ejpam-1097	27	2	pure	pure	PROPN
ejpam-1097	27	3	appl	appl	PROPN
ejpam-1097	27	4	.	.	PROPN
ejpam-1097	27	5	math	math	PROPN
ejpam-1097	27	6	,	,	PUNCT
ejpam-1097	27	7	5	5	NUM
ejpam-1097	27	8	(	(	PUNCT
ejpam-1097	27	9	2012	2012	NUM
ejpam-1097	27	10	)	)	PUNCT
ejpam-1097	27	11	,	,	PUNCT
ejpam-1097	27	12	108	108	NUM
ejpam-1097	27	13	-	-	SYM
ejpam-1097	27	14	115	115	NUM
ejpam-1097	27	15	109	109	NUM
ejpam-1097	27	16	b(m	b(m	NOUN
ejpam-1097	27	17	,	,	PUNCT
ejpam-1097	27	18	x	x	PUNCT
ejpam-1097	27	19	)	)	PUNCT
ejpam-1097	27	20	as	as	ADP
ejpam-1097	27	21	generalizations	generalization	NOUN
ejpam-1097	27	22	of	of	ADP
ejpam-1097	27	23	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	27	24	modules	module	NOUN
ejpam-1097	27	25	and	and	CCONJ
ejpam-1097	27	26	completely	completely	ADV
ejpam-1097	27	27	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	27	28	modules	module	NOUN
ejpam-1097	27	29	respectively	respectively	ADV
ejpam-1097	27	30	.	.	PUNCT
ejpam-1097	28	1	let	let	VERB
ejpam-1097	28	2	a	a	PRON
ejpam-1097	28	3	and	and	CCONJ
ejpam-1097	28	4	p	p	NOUN
ejpam-1097	28	5	be	be	AUX
ejpam-1097	28	6	submodules	submodule	NOUN
ejpam-1097	28	7	of	of	ADP
ejpam-1097	28	8	m	m	PROPN
ejpam-1097	28	9	with	with	ADP
ejpam-1097	28	10	p	p	PROPN
ejpam-1097	28	11	∈	∈	PROPN
ejpam-1097	28	12	b(m	b(m	PROPN
ejpam-1097	28	13	,	,	PUNCT
ejpam-1097	28	14	x	x	PROPN
ejpam-1097	28	15	)	)	PUNCT
ejpam-1097	28	16	.	.	PUNCT
ejpam-1097	29	1	following	follow	VERB
ejpam-1097	29	2	[	[	X
ejpam-1097	29	3	7	7	NUM
ejpam-1097	29	4	]	]	PUNCT
ejpam-1097	29	5	,	,	PUNCT
ejpam-1097	29	6	p	p	PROPN
ejpam-1097	29	7	is	be	AUX
ejpam-1097	29	8	called	call	VERB
ejpam-1097	29	9	an	an	DET
ejpam-1097	29	10	x	x	NOUN
ejpam-1097	29	11	supplement	supplement	NOUN
ejpam-1097	29	12	of	of	ADP
ejpam-1097	29	13	a	a	PRON
ejpam-1097	29	14	in	in	ADP
ejpam-1097	29	15	m	m	PROPN
ejpam-1097	29	16	if	if	SCONJ
ejpam-1097	29	17	it	it	PRON
ejpam-1097	29	18	is	be	AUX
ejpam-1097	29	19	minimal	minimal	ADJ
ejpam-1097	29	20	with	with	ADP
ejpam-1097	29	21	the	the	DET
ejpam-1097	29	22	property	property	NOUN
ejpam-1097	29	23	m	m	NOUN
ejpam-1097	29	24	=	=	PUNCT
ejpam-1097	29	25	a+	a+	PUNCT
ejpam-1097	29	26	p.	p.	NOUN
ejpam-1097	29	27	equivalently	equivalently	ADV
ejpam-1097	29	28	,	,	PUNCT
ejpam-1097	29	29	if	if	SCONJ
ejpam-1097	29	30	m	m	ADV
ejpam-1097	29	31	=	=	VERB
ejpam-1097	29	32	a+	a+	PUNCT
ejpam-1097	29	33	p	p	NOUN
ejpam-1097	29	34	and	and	CCONJ
ejpam-1097	29	35	a	a	DET
ejpam-1097	29	36	∩	∩	ADJ
ejpam-1097	29	37	p	p	NOUN
ejpam-1097	29	38	≪	≪	NOUN
ejpam-1097	29	39	p.	p.	NOUN
ejpam-1097	29	40	a	a	DET
ejpam-1097	29	41	module	module	NOUN
ejpam-1097	29	42	m	m	VERB
ejpam-1097	29	43	is	be	AUX
ejpam-1097	29	44	called	call	VERB
ejpam-1097	29	45	x	x	PUNCT
ejpam-1097	29	46	-supplemented	-supplemente	VERB
ejpam-1097	29	47	if	if	SCONJ
ejpam-1097	29	48	every	every	DET
ejpam-1097	29	49	submodule	submodule	NOUN
ejpam-1097	29	50	n	n	PROPN
ejpam-1097	29	51	of	of	ADP
ejpam-1097	29	52	m	m	PROPN
ejpam-1097	29	53	with	with	ADP
ejpam-1097	29	54	n	n	PRON
ejpam-1097	29	55	∈	∈	PROPN
ejpam-1097	29	56	b(m	b(m	PROPN
ejpam-1097	29	57	,	,	PUNCT
ejpam-1097	29	58	x	x	X
ejpam-1097	29	59	)	)	PUNCT
ejpam-1097	29	60	has	have	VERB
ejpam-1097	29	61	an	an	DET
ejpam-1097	29	62	x	x	SYM
ejpam-1097	29	63	-supplement	-supplement	NOUN
ejpam-1097	29	64	in	in	ADP
ejpam-1097	29	65	m	m	PROPN
ejpam-1097	29	66	.	.	PUNCT
ejpam-1097	30	1	we	we	PRON
ejpam-1097	30	2	say	say	VERB
ejpam-1097	30	3	that	that	SCONJ
ejpam-1097	30	4	a	a	DET
ejpam-1097	30	5	module	module	NOUN
ejpam-1097	30	6	m	m	NOUN
ejpam-1097	30	7	is	be	AUX
ejpam-1097	30	8	x	x	PUNCT
ejpam-1097	30	9	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	30	10	if	if	SCONJ
ejpam-1097	30	11	every	every	DET
ejpam-1097	30	12	submodule	submodule	NOUN
ejpam-1097	30	13	n	n	PROPN
ejpam-1097	30	14	of	of	ADP
ejpam-1097	30	15	m	m	PROPN
ejpam-1097	30	16	with	with	ADP
ejpam-1097	30	17	n	n	PRON
ejpam-1097	30	18	∈	∈	PROPN
ejpam-1097	30	19	b(m	b(m	PROPN
ejpam-1097	30	20	,	,	PUNCT
ejpam-1097	30	21	x	x	PROPN
ejpam-1097	30	22	)	)	PUNCT
ejpam-1097	30	23	,	,	PUNCT
ejpam-1097	30	24	has	have	VERB
ejpam-1097	30	25	an	an	DET
ejpam-1097	30	26	x	x	SYM
ejpam-1097	30	27	-supplement	-supplement	NOUN
ejpam-1097	30	28	that	that	PRON
ejpam-1097	30	29	is	be	AUX
ejpam-1097	30	30	a	a	DET
ejpam-1097	30	31	direct	direct	ADJ
ejpam-1097	30	32	summand	summand	NOUN
ejpam-1097	30	33	of	of	ADP
ejpam-1097	30	34	m	m	PROPN
ejpam-1097	30	35	.	.	PUNCT
ejpam-1097	31	1	we	we	PRON
ejpam-1097	31	2	prove	prove	VERB
ejpam-1097	31	3	some	some	DET
ejpam-1097	31	4	results	result	NOUN
ejpam-1097	31	5	on	on	ADP
ejpam-1097	31	6	these	these	DET
ejpam-1097	31	7	classes	class	NOUN
ejpam-1097	31	8	of	of	ADP
ejpam-1097	31	9	modules	module	NOUN
ejpam-1097	31	10	.	.	PUNCT
ejpam-1097	32	1	in	in	ADP
ejpam-1097	32	2	section	section	NOUN
ejpam-1097	32	3	2	2	NUM
ejpam-1097	32	4	,	,	PUNCT
ejpam-1097	32	5	we	we	PRON
ejpam-1097	32	6	recall	recall	VERB
ejpam-1097	32	7	some	some	DET
ejpam-1097	32	8	notions	notion	NOUN
ejpam-1097	32	9	and	and	CCONJ
ejpam-1097	32	10	results	result	NOUN
ejpam-1097	32	11	that	that	SCONJ
ejpam-1097	32	12	they	they	PRON
ejpam-1097	32	13	are	be	AUX
ejpam-1097	32	14	used	use	VERB
ejpam-1097	32	15	in	in	ADP
ejpam-1097	32	16	this	this	DET
ejpam-1097	32	17	paper	paper	NOUN
ejpam-1097	32	18	.	.	PUNCT
ejpam-1097	33	1	in	in	ADP
ejpam-1097	33	2	section	section	NOUN
ejpam-1097	33	3	3	3	NUM
ejpam-1097	33	4	,	,	PUNCT
ejpam-1097	33	5	we	we	PRON
ejpam-1097	33	6	give	give	VERB
ejpam-1097	33	7	a	a	DET
ejpam-1097	33	8	characterization	characterization	NOUN
ejpam-1097	33	9	of	of	ADP
ejpam-1097	33	10	x	x	SYM
ejpam-1097	33	11	-⊕supplemented	-⊕supplemented	ADJ
ejpam-1097	33	12	modules	module	NOUN
ejpam-1097	33	13	.	.	PUNCT
ejpam-1097	34	1	it	it	PRON
ejpam-1097	34	2	is	be	AUX
ejpam-1097	34	3	shown	show	VERB
ejpam-1097	34	4	that	that	SCONJ
ejpam-1097	34	5	any	any	DET
ejpam-1097	34	6	finite	finite	ADJ
ejpam-1097	34	7	direct	direct	ADJ
ejpam-1097	34	8	sum	sum	NOUN
ejpam-1097	34	9	of	of	ADP
ejpam-1097	34	10	x	x	PUNCT
ejpam-1097	34	11	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	34	12	modules	module	NOUN
ejpam-1097	34	13	is	be	AUX
ejpam-1097	34	14	x	x	PUNCT
ejpam-1097	34	15	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	34	16	.	.	PUNCT
ejpam-1097	35	1	we	we	PRON
ejpam-1097	35	2	give	give	VERB
ejpam-1097	35	3	a	a	DET
ejpam-1097	35	4	number	number	NOUN
ejpam-1097	35	5	of	of	ADP
ejpam-1097	35	6	necessary	necessary	ADJ
ejpam-1097	35	7	and	and	CCONJ
ejpam-1097	35	8	sufficient	sufficient	ADJ
ejpam-1097	35	9	conditions	condition	NOUN
ejpam-1097	35	10	for	for	SCONJ
ejpam-1097	35	11	every	every	DET
ejpam-1097	35	12	direct	direct	ADJ
ejpam-1097	35	13	summand	summand	NOUN
ejpam-1097	35	14	of	of	ADP
ejpam-1097	35	15	an	an	DET
ejpam-1097	35	16	x	x	NOUN
ejpam-1097	35	17	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	35	18	module	module	NOUN
ejpam-1097	35	19	to	to	PART
ejpam-1097	35	20	be	be	AUX
ejpam-1097	35	21	x	x	PUNCT
ejpam-1097	35	22	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	35	23	.	.	PUNCT
ejpam-1097	36	1	we	we	PRON
ejpam-1097	36	2	show	show	VERB
ejpam-1097	36	3	that	that	SCONJ
ejpam-1097	36	4	the	the	DET
ejpam-1097	36	5	direct	direct	ADJ
ejpam-1097	36	6	sum	sum	NOUN
ejpam-1097	36	7	of	of	ADP
ejpam-1097	36	8	any	any	DET
ejpam-1097	36	9	finite	finite	ADJ
ejpam-1097	36	10	family	family	NOUN
ejpam-1097	36	11	mi	mi	PROPN
ejpam-1097	36	12	of	of	ADP
ejpam-1097	36	13	relatively	relatively	ADV
ejpam-1097	36	14	b	b	NOUN
ejpam-1097	36	15	-	-	PUNCT
ejpam-1097	36	16	projective	projective	ADJ
ejpam-1097	36	17	modules	module	NOUN
ejpam-1097	36	18	is	be	AUX
ejpam-1097	36	19	x	x	PRON
ejpam-1097	36	20	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	36	21	if	if	SCONJ
ejpam-1097	36	22	and	and	CCONJ
ejpam-1097	36	23	only	only	ADV
ejpam-1097	36	24	if	if	SCONJ
ejpam-1097	36	25	every	every	DET
ejpam-1097	36	26	mi	mi	NOUN
ejpam-1097	36	27	is	be	AUX
ejpam-1097	36	28	x	x	PUNCT
ejpam-1097	36	29	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	36	30	.	.	PUNCT
ejpam-1097	37	1	in	in	ADP
ejpam-1097	37	2	section	section	NOUN
ejpam-1097	37	3	4	4	NUM
ejpam-1097	37	4	,	,	PUNCT
ejpam-1097	37	5	we	we	PRON
ejpam-1097	37	6	prove	prove	VERB
ejpam-1097	37	7	the	the	DET
ejpam-1097	37	8	equivalence	equivalence	NOUN
ejpam-1097	37	9	of	of	ADP
ejpam-1097	37	10	two	two	NUM
ejpam-1097	37	11	conditions	condition	NOUN
ejpam-1097	37	12	for	for	ADP
ejpam-1097	37	13	a	a	DET
ejpam-1097	37	14	module	module	NOUN
ejpam-1097	37	15	with	with	ADP
ejpam-1097	37	16	finite	finite	PROPN
ejpam-1097	37	17	goldie	goldie	PROPN
ejpam-1097	37	18	dimension	dimension	PROPN
ejpam-1097	37	19	:	:	PUNCT
ejpam-1097	37	20	one	one	NUM
ejpam-1097	37	21	saying	say	VERB
ejpam-1097	37	22	that	that	SCONJ
ejpam-1097	37	23	every	every	DET
ejpam-1097	37	24	direct	direct	ADJ
ejpam-1097	37	25	summand	summand	NOUN
ejpam-1097	37	26	n	n	PROPN
ejpam-1097	37	27	of	of	ADP
ejpam-1097	37	28	m	m	PROPN
ejpam-1097	37	29	with	with	ADP
ejpam-1097	37	30	n	n	PRON
ejpam-1097	37	31	∈	∈	PROPN
ejpam-1097	37	32	b(m	b(m	PROPN
ejpam-1097	37	33	,	,	PUNCT
ejpam-1097	37	34	x	x	X
ejpam-1097	37	35	)	)	PUNCT
ejpam-1097	37	36	is	be	AUX
ejpam-1097	37	37	a	a	DET
ejpam-1097	37	38	finite	finite	ADJ
ejpam-1097	37	39	direct	direct	ADJ
ejpam-1097	37	40	sum	sum	NOUN
ejpam-1097	37	41	of	of	ADP
ejpam-1097	37	42	x	x	PUNCT
ejpam-1097	37	43	-hollow	-hollow	ADJ
ejpam-1097	37	44	modules	module	NOUN
ejpam-1097	37	45	,	,	PUNCT
ejpam-1097	37	46	and	and	CCONJ
ejpam-1097	37	47	the	the	DET
ejpam-1097	37	48	other	other	ADJ
ejpam-1097	37	49	stating	state	VERB
ejpam-1097	37	50	that	that	SCONJ
ejpam-1097	37	51	m	m	PROPN
ejpam-1097	37	52	is	be	AUX
ejpam-1097	37	53	a	a	DET
ejpam-1097	37	54	completely	completely	ADV
ejpam-1097	37	55	x	x	SYM
ejpam-1097	37	56	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	37	57	module	module	NOUN
ejpam-1097	37	58	.	.	PUNCT
ejpam-1097	38	1	2	2	X
ejpam-1097	38	2	.	.	X
ejpam-1097	38	3	preliminaries	preliminary	NOUN
ejpam-1097	38	4	let	let	VERB
ejpam-1097	38	5	m	m	PRON
ejpam-1097	38	6	be	be	AUX
ejpam-1097	38	7	a	a	DET
ejpam-1097	38	8	module	module	NOUN
ejpam-1097	38	9	and	and	CCONJ
ejpam-1097	38	10	n	n	PRON
ejpam-1097	38	11	≤	≤	NOUN
ejpam-1097	38	12	m	m	VERB
ejpam-1097	38	13	.	.	PUNCT
ejpam-1097	39	1	n	n	PROPN
ejpam-1097	39	2	is	be	AUX
ejpam-1097	39	3	called	call	VERB
ejpam-1097	39	4	a	a	DET
ejpam-1097	39	5	coclosed	coclose	VERB
ejpam-1097	39	6	submodule	submodule	NOUN
ejpam-1097	39	7	in	in	ADP
ejpam-1097	39	8	m	m	PROPN
ejpam-1097	39	9	if	if	SCONJ
ejpam-1097	39	10	whenever	whenever	SCONJ
ejpam-1097	39	11	n	n	CCONJ
ejpam-1097	39	12	/	/	SYM
ejpam-1097	39	13	k	k	PROPN
ejpam-1097	39	14	≪	≪	PROPN
ejpam-1097	39	15	m	m	PROPN
ejpam-1097	39	16	/	/	SYM
ejpam-1097	39	17	k	k	PROPN
ejpam-1097	39	18	then	then	ADV
ejpam-1097	39	19	n	n	PROPN
ejpam-1097	39	20	=	=	SYM
ejpam-1097	39	21	k	k	PROPN
ejpam-1097	39	22	.	.	PUNCT
ejpam-1097	40	1	let	let	VERB
ejpam-1097	40	2	m	m	PRON
ejpam-1097	40	3	be	be	AUX
ejpam-1097	40	4	a	a	DET
ejpam-1097	40	5	module	module	NOUN
ejpam-1097	40	6	and	and	CCONJ
ejpam-1097	40	7	b	b	NOUN
ejpam-1097	40	8	≤	≤	NOUN
ejpam-1097	40	9	a	a	DET
ejpam-1097	40	10	≤	≤	NUM
ejpam-1097	40	11	m	m	NOUN
ejpam-1097	40	12	.	.	PUNCT
ejpam-1097	41	1	if	if	SCONJ
ejpam-1097	41	2	b	b	PROPN
ejpam-1097	41	3	is	be	AUX
ejpam-1097	41	4	coclosed	coclose	VERB
ejpam-1097	41	5	in	in	ADP
ejpam-1097	41	6	m	m	PROPN
ejpam-1097	41	7	and	and	CCONJ
ejpam-1097	41	8	a	a	PRON
ejpam-1097	41	9	/	/	SYM
ejpam-1097	41	10	b	b	NOUN
ejpam-1097	41	11	≪	≪	PROPN
ejpam-1097	41	12	m	m	PROPN
ejpam-1097	41	13	/	/	SYM
ejpam-1097	41	14	b	b	NOUN
ejpam-1097	41	15	,	,	PUNCT
ejpam-1097	41	16	then	then	ADV
ejpam-1097	41	17	b	b	PROPN
ejpam-1097	41	18	is	be	AUX
ejpam-1097	41	19	called	call	VERB
ejpam-1097	41	20	an	an	DET
ejpam-1097	41	21	co	co	NOUN
ejpam-1097	41	22	-	-	NOUN
ejpam-1097	41	23	closure	closure	NOUN
ejpam-1097	41	24	of	of	ADP
ejpam-1097	41	25	a	a	PRON
ejpam-1097	41	26	in	in	ADP
ejpam-1097	41	27	m	m	PROPN
ejpam-1097	41	28	.	.	PUNCT
ejpam-1097	42	1	a	a	DET
ejpam-1097	42	2	non	non	ADJ
ejpam-1097	42	3	-	-	ADJ
ejpam-1097	42	4	zero	zero	NUM
ejpam-1097	42	5	module	module	NOUN
ejpam-1097	42	6	m	m	NOUN
ejpam-1097	42	7	is	be	AUX
ejpam-1097	42	8	called	call	VERB
ejpam-1097	42	9	local	local	ADJ
ejpam-1097	42	10	if	if	SCONJ
ejpam-1097	42	11	the	the	DET
ejpam-1097	42	12	sum	sum	NOUN
ejpam-1097	42	13	of	of	ADP
ejpam-1097	42	14	all	all	DET
ejpam-1097	42	15	proper	proper	ADJ
ejpam-1097	42	16	submodules	submodule	NOUN
ejpam-1097	42	17	of	of	ADP
ejpam-1097	42	18	m	m	PROPN
ejpam-1097	42	19	is	be	AUX
ejpam-1097	42	20	also	also	ADV
ejpam-1097	42	21	a	a	DET
ejpam-1097	42	22	proper	proper	ADJ
ejpam-1097	42	23	submodule	submodule	NOUN
ejpam-1097	42	24	of	of	ADP
ejpam-1097	42	25	m	m	PROPN
ejpam-1097	42	26	.	.	PUNCT
ejpam-1097	43	1	every	every	DET
ejpam-1097	43	2	local	local	ADJ
ejpam-1097	43	3	module	module	NOUN
ejpam-1097	43	4	is	be	AUX
ejpam-1097	43	5	hollow	hollow	ADJ
ejpam-1097	43	6	and	and	CCONJ
ejpam-1097	43	7	hollow	hollow	ADJ
ejpam-1097	43	8	modules	module	NOUN
ejpam-1097	43	9	are	be	AUX
ejpam-1097	43	10	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	43	11	.	.	PUNCT
ejpam-1097	44	1	a	a	DET
ejpam-1097	44	2	submodule	submodule	NOUN
ejpam-1097	44	3	k	k	PROPN
ejpam-1097	44	4	of	of	ADP
ejpam-1097	44	5	m	m	PROPN
ejpam-1097	44	6	is	be	AUX
ejpam-1097	44	7	called	call	VERB
ejpam-1097	44	8	essential	essential	ADJ
ejpam-1097	44	9	in	in	ADP
ejpam-1097	44	10	m	m	PROPN
ejpam-1097	44	11	(	(	PUNCT
ejpam-1097	44	12	notation	notation	NOUN
ejpam-1097	44	13	k	k	PROPN
ejpam-1097	44	14	≤e	≤e	PROPN
ejpam-1097	44	15	m	m	PROPN
ejpam-1097	44	16	)	)	PUNCT
ejpam-1097	44	17	if	if	SCONJ
ejpam-1097	44	18	k∩a	k∩a	PROPN
ejpam-1097	44	19	6=	6=	ADP
ejpam-1097	44	20	0	0	NUM
ejpam-1097	44	21	for	for	ADP
ejpam-1097	44	22	any	any	DET
ejpam-1097	44	23	nonzero	nonzero	NOUN
ejpam-1097	44	24	submodule	submodule	NOUN
ejpam-1097	44	25	a	a	PRON
ejpam-1097	44	26	of	of	ADP
ejpam-1097	44	27	m	m	PROPN
ejpam-1097	44	28	.	.	PUNCT
ejpam-1097	44	29	recall	recall	VERB
ejpam-1097	44	30	that	that	SCONJ
ejpam-1097	44	31	a	a	DET
ejpam-1097	44	32	module	module	NOUN
ejpam-1097	44	33	m	m	VERB
ejpam-1097	44	34	is	be	AUX
ejpam-1097	44	35	said	say	VERB
ejpam-1097	44	36	to	to	PART
ejpam-1097	44	37	have	have	VERB
ejpam-1097	44	38	the	the	DET
ejpam-1097	44	39	summand	summand	NOUN
ejpam-1097	44	40	sum	sum	NOUN
ejpam-1097	44	41	property	property	NOUN
ejpam-1097	44	42	(	(	PUNCT
ejpam-1097	44	43	ssp	ssp	NOUN
ejpam-1097	44	44	)	)	PUNCT
ejpam-1097	44	45	if	if	SCONJ
ejpam-1097	44	46	the	the	DET
ejpam-1097	44	47	sum	sum	NOUN
ejpam-1097	44	48	of	of	ADP
ejpam-1097	44	49	two	two	NUM
ejpam-1097	44	50	direct	direct	ADJ
ejpam-1097	44	51	summands	summand	NOUN
ejpam-1097	44	52	is	be	AUX
ejpam-1097	44	53	again	again	ADV
ejpam-1097	44	54	a	a	DET
ejpam-1097	44	55	direct	direct	ADJ
ejpam-1097	44	56	summand	summand	NOUN
ejpam-1097	44	57	.	.	PUNCT
ejpam-1097	45	1	a	a	DET
ejpam-1097	45	2	module	module	NOUN
ejpam-1097	45	3	m	m	NOUN
ejpam-1097	45	4	is	be	AUX
ejpam-1097	45	5	said	say	VERB
ejpam-1097	45	6	to	to	PART
ejpam-1097	45	7	have	have	VERB
ejpam-1097	45	8	the	the	DET
ejpam-1097	45	9	(	(	PUNCT
ejpam-1097	45	10	finite	finite	PROPN
ejpam-1097	45	11	)	)	PUNCT
ejpam-1097	45	12	internal	internal	ADJ
ejpam-1097	45	13	exchange	exchange	NOUN
ejpam-1097	45	14	property	property	NOUN
ejpam-1097	45	15	if	if	SCONJ
ejpam-1097	45	16	for	for	SCONJ
ejpam-1097	45	17	every	every	DET
ejpam-1097	45	18	(	(	PUNCT
ejpam-1097	45	19	finite	finite	PROPN
ejpam-1097	45	20	)	)	PUNCT
ejpam-1097	45	21	index	index	NOUN
ejpam-1097	45	22	set	set	VERB
ejpam-1097	45	23	i	i	PRON
ejpam-1097	45	24	,	,	PUNCT
ejpam-1097	45	25	whenever	whenever	SCONJ
ejpam-1097	45	26	m	m	VERB
ejpam-1097	45	27	=	=	VERB
ejpam-1097	45	28	⊕i∈iai	⊕i∈iai	VERB
ejpam-1097	45	29	for	for	ADP
ejpam-1097	45	30	modules	module	NOUN
ejpam-1097	45	31	ai	ai	VERB
ejpam-1097	45	32	,	,	PUNCT
ejpam-1097	45	33	then	then	ADV
ejpam-1097	45	34	for	for	ADP
ejpam-1097	45	35	every	every	DET
ejpam-1097	45	36	direct	direct	ADJ
ejpam-1097	45	37	summand	summand	NOUN
ejpam-1097	45	38	k	k	PROPN
ejpam-1097	45	39	of	of	ADP
ejpam-1097	45	40	m	m	PRON
ejpam-1097	45	41	there	there	ADV
ejpam-1097	45	42	exist	exist	VERB
ejpam-1097	45	43	submodules	submodule	NOUN
ejpam-1097	45	44	bi	bi	NOUN
ejpam-1097	45	45	of	of	ADP
ejpam-1097	45	46	ai	ai	VERB
ejpam-1097	45	47	such	such	ADJ
ejpam-1097	45	48	that	that	SCONJ
ejpam-1097	45	49	m	m	VERB
ejpam-1097	45	50	=	=	ADJ
ejpam-1097	45	51	k⊕	k⊕	NOUN
ejpam-1097	45	52	(	(	PUNCT
ejpam-1097	45	53	⊕i∈i	⊕i∈i	X
ejpam-1097	45	54	bi	bi	NOUN
ejpam-1097	45	55	)	)	PUNCT
ejpam-1097	45	56	.	.	PUNCT
ejpam-1097	46	1	the	the	DET
ejpam-1097	46	2	notation	notation	NOUN
ejpam-1097	46	3	n	n	PROPN
ejpam-1097	46	4	≤⊕	≤⊕	NOUN
ejpam-1097	46	5	m	m	VERB
ejpam-1097	46	6	denotes	denote	NOUN
ejpam-1097	46	7	that	that	SCONJ
ejpam-1097	46	8	n	n	VERB
ejpam-1097	46	9	is	be	AUX
ejpam-1097	46	10	a	a	DET
ejpam-1097	46	11	direct	direct	ADJ
ejpam-1097	46	12	summand	summand	NOUN
ejpam-1097	46	13	of	of	ADP
ejpam-1097	46	14	m	m	PROPN
ejpam-1097	46	15	.	.	PUNCT
ejpam-1097	47	1	n	n	CCONJ
ejpam-1097	47	2	ã	ã	X
ejpam-1097	47	3	m	m	NOUN
ejpam-1097	47	4	means	mean	VERB
ejpam-1097	47	5	that	that	SCONJ
ejpam-1097	47	6	n	n	PRON
ejpam-1097	47	7	is	be	AUX
ejpam-1097	47	8	a	a	DET
ejpam-1097	47	9	fully	fully	ADV
ejpam-1097	47	10	invariant	invariant	ADJ
ejpam-1097	47	11	submodule	submodule	NOUN
ejpam-1097	47	12	of	of	ADP
ejpam-1097	47	13	m	m	PROPN
ejpam-1097	47	14	(	(	PUNCT
ejpam-1097	47	15	i.e.	i.e.	X
ejpam-1097	47	16	,	,	PUNCT
ejpam-1097	47	17	∀φ	∀φ	NOUN
ejpam-1097	47	18	∈	∈	NOUN
ejpam-1097	47	19	endr(m),φ(n	endr(m),φ(n	X
ejpam-1097	47	20	)	)	PUNCT
ejpam-1097	47	21	⊆	⊆	NUM
ejpam-1097	47	22	n	n	CCONJ
ejpam-1097	47	23	)	)	PUNCT
ejpam-1097	47	24	.	.	PUNCT
ejpam-1097	48	1	lemma	lemma	PROPN
ejpam-1097	48	2	1	1	X
ejpam-1097	48	3	.	.	PUNCT
ejpam-1097	49	1	let	let	VERB
ejpam-1097	49	2	m	m	PRON
ejpam-1097	49	3	,	,	PUNCT
ejpam-1097	49	4	n	n	PROPN
ejpam-1097	49	5	and	and	CCONJ
ejpam-1097	49	6	x	x	PART
ejpam-1097	49	7	be	be	AUX
ejpam-1097	49	8	r	r	NOUN
ejpam-1097	49	9	-	-	PUNCT
ejpam-1097	49	10	modules	module	NOUN
ejpam-1097	49	11	.	.	PUNCT
ejpam-1097	50	1	then	then	ADV
ejpam-1097	50	2	the	the	DET
ejpam-1097	50	3	following	follow	VERB
ejpam-1097	50	4	hold	hold	NOUN
ejpam-1097	50	5	:	:	PUNCT
ejpam-1097	50	6	(	(	PUNCT
ejpam-1097	50	7	1	1	X
ejpam-1097	50	8	)	)	PUNCT
ejpam-1097	50	9	if	if	SCONJ
ejpam-1097	50	10	a∈b(m	a∈b(m	NOUN
ejpam-1097	50	11	,	,	PUNCT
ejpam-1097	50	12	x	x	X
ejpam-1097	50	13	)	)	PUNCT
ejpam-1097	50	14	and	and	CCONJ
ejpam-1097	50	15	b	b	X
ejpam-1097	50	16	≤	≤	NOUN
ejpam-1097	50	17	a	a	PRON
ejpam-1097	50	18	with	with	ADP
ejpam-1097	50	19	a	a	DET
ejpam-1097	50	20	/	/	SYM
ejpam-1097	50	21	b≪	b≪	NOUN
ejpam-1097	50	22	m	m	PROPN
ejpam-1097	50	23	/	/	SYM
ejpam-1097	50	24	b	b	PROPN
ejpam-1097	50	25	,	,	PUNCT
ejpam-1097	50	26	then	then	ADV
ejpam-1097	50	27	b	b	PROPN
ejpam-1097	50	28	∈b(m	∈b(m	PROPN
ejpam-1097	50	29	,	,	PUNCT
ejpam-1097	50	30	x	x	PROPN
ejpam-1097	50	31	)	)	PUNCT
ejpam-1097	50	32	.	.	PUNCT
ejpam-1097	51	1	(	(	PUNCT
ejpam-1097	51	2	2	2	X
ejpam-1097	51	3	)	)	PUNCT
ejpam-1097	51	4	let	let	AUX
ejpam-1097	51	5	h	h	NOUN
ejpam-1097	51	6	:	:	PUNCT
ejpam-1097	51	7	m	m	VERB
ejpam-1097	51	8	→	→	SYM
ejpam-1097	51	9	n	n	CCONJ
ejpam-1097	51	10	be	be	AUX
ejpam-1097	51	11	an	an	DET
ejpam-1097	51	12	epimorphism	epimorphism	NOUN
ejpam-1097	51	13	and	and	CCONJ
ejpam-1097	51	14	a∈b(m	a∈b(m	NOUN
ejpam-1097	51	15	,	,	PUNCT
ejpam-1097	51	16	x	x	PUNCT
ejpam-1097	51	17	)	)	PUNCT
ejpam-1097	51	18	with	with	ADP
ejpam-1097	51	19	ker	ker	PROPN
ejpam-1097	51	20	h≤	h≤	PROPN
ejpam-1097	51	21	a.	a.	NOUN
ejpam-1097	51	22	then	then	ADV
ejpam-1097	51	23	h(a	h(a	PROPN
ejpam-1097	51	24	)	)	PUNCT
ejpam-1097	51	25	∈	∈	PROPN
ejpam-1097	51	26	b(n	b(n	PROPN
ejpam-1097	51	27	,	,	PUNCT
ejpam-1097	51	28	x	x	NOUN
ejpam-1097	51	29	)	)	PUNCT
ejpam-1097	51	30	.	.	PUNCT
ejpam-1097	52	1	conversely	conversely	ADV
ejpam-1097	52	2	,	,	PUNCT
ejpam-1097	52	3	if	if	SCONJ
ejpam-1097	52	4	h(a	h(a	PROPN
ejpam-1097	52	5	)	)	PUNCT
ejpam-1097	52	6	∈b(n	∈b(n	PROPN
ejpam-1097	52	7	,	,	PUNCT
ejpam-1097	52	8	x	x	PUNCT
ejpam-1097	52	9	)	)	PUNCT
ejpam-1097	52	10	and	and	CCONJ
ejpam-1097	52	11	ker	ker	X
ejpam-1097	53	1	h≤	h≤	PRON
ejpam-1097	53	2	a	a	PRON
ejpam-1097	53	3	,	,	PUNCT
ejpam-1097	53	4	then	then	ADV
ejpam-1097	53	5	a∈b(m	a∈b(m	VERB
ejpam-1097	53	6	,	,	PUNCT
ejpam-1097	53	7	x	x	X
ejpam-1097	53	8	)	)	PUNCT
ejpam-1097	53	9	.	.	PUNCT
ejpam-1097	54	1	(	(	PUNCT
ejpam-1097	54	2	3	3	X
ejpam-1097	54	3	)	)	PUNCT
ejpam-1097	54	4	let	let	VERB
ejpam-1097	54	5	b	b	NOUN
ejpam-1097	54	6	≤	≤	NUM
ejpam-1097	54	7	a≤	a≤	DET
ejpam-1097	54	8	m.	m.	NOUN
ejpam-1097	54	9	then	then	ADV
ejpam-1097	54	10	a∈	a∈	PROPN
ejpam-1097	54	11	b(m	b(m	PROPN
ejpam-1097	54	12	,	,	PUNCT
ejpam-1097	54	13	x	x	SYM
ejpam-1097	54	14	)	)	PUNCT
ejpam-1097	54	15	if	if	SCONJ
ejpam-1097	54	16	and	and	CCONJ
ejpam-1097	54	17	only	only	ADV
ejpam-1097	54	18	if	if	SCONJ
ejpam-1097	54	19	a	a	DET
ejpam-1097	54	20	/	/	SYM
ejpam-1097	54	21	b	b	NOUN
ejpam-1097	54	22	∈b(m	∈b(m	PROPN
ejpam-1097	54	23	/	/	SYM
ejpam-1097	54	24	b	b	PROPN
ejpam-1097	54	25	,	,	PUNCT
ejpam-1097	54	26	x	x	NOUN
ejpam-1097	54	27	)	)	PUNCT
ejpam-1097	54	28	.	.	PUNCT
ejpam-1097	55	1	(	(	PUNCT
ejpam-1097	55	2	4	4	X
ejpam-1097	55	3	)	)	PUNCT
ejpam-1097	55	4	let	let	VERB
ejpam-1097	55	5	h	h	NOUN
ejpam-1097	55	6	:	:	PUNCT
ejpam-1097	55	7	n	n	X
ejpam-1097	55	8	→	→	PUNCT
ejpam-1097	55	9	m	m	AUX
ejpam-1097	55	10	be	be	AUX
ejpam-1097	55	11	an	an	DET
ejpam-1097	55	12	epimorphism	epimorphism	NOUN
ejpam-1097	55	13	and	and	CCONJ
ejpam-1097	55	14	a∈b(m	a∈b(m	NOUN
ejpam-1097	55	15	,	,	PUNCT
ejpam-1097	55	16	x	x	PROPN
ejpam-1097	55	17	)	)	PUNCT
ejpam-1097	55	18	.	.	PUNCT
ejpam-1097	56	1	then	then	ADV
ejpam-1097	56	2	h−1(a	h−1(a	PROPN
ejpam-1097	56	3	)	)	PUNCT
ejpam-1097	57	1	∈b(n	∈b(n	PROPN
ejpam-1097	57	2	,	,	PUNCT
ejpam-1097	57	3	x	x	PROPN
ejpam-1097	57	4	)	)	PUNCT
ejpam-1097	57	5	.	.	PUNCT
ejpam-1097	58	1	t.	t.	PROPN
ejpam-1097	58	2	amouzegar	amouzegar	NOUN
ejpam-1097	58	3	,	,	PUNCT
ejpam-1097	58	4	y.	y.	PROPN
ejpam-1097	58	5	talebi	talebi	PROPN
ejpam-1097	58	6	/	/	SYM
ejpam-1097	58	7	eur	eur	PROPN
ejpam-1097	58	8	.	.	PUNCT
ejpam-1097	59	1	j.	j.	PROPN
ejpam-1097	59	2	pure	pure	PROPN
ejpam-1097	59	3	appl	appl	PROPN
ejpam-1097	59	4	.	.	PROPN
ejpam-1097	59	5	math	math	PROPN
ejpam-1097	59	6	,	,	PUNCT
ejpam-1097	59	7	5	5	NUM
ejpam-1097	59	8	(	(	PUNCT
ejpam-1097	59	9	2012	2012	NUM
ejpam-1097	59	10	)	)	PUNCT
ejpam-1097	59	11	,	,	PUNCT
ejpam-1097	59	12	108	108	NUM
ejpam-1097	59	13	-	-	SYM
ejpam-1097	59	14	115	115	NUM
ejpam-1097	59	15	110	110	NUM
ejpam-1097	59	16	proof	proof	NOUN
ejpam-1097	59	17	.	.	PUNCT
ejpam-1097	60	1	see	see	VERB
ejpam-1097	60	2	[	[	X
ejpam-1097	60	3	5	5	NUM
ejpam-1097	60	4	,	,	PUNCT
ejpam-1097	60	5	lemma	lemma	PROPN
ejpam-1097	60	6	2.2	2.2	NUM
ejpam-1097	60	7	]	]	PUNCT
ejpam-1097	60	8	.	.	PUNCT
ejpam-1097	61	1	lemma	lemma	PROPN
ejpam-1097	61	2	2	2	X
ejpam-1097	61	3	.	.	PUNCT
ejpam-1097	62	1	let	let	VERB
ejpam-1097	62	2	m	m	PRON
ejpam-1097	62	3	and	and	CCONJ
ejpam-1097	62	4	x	x	PART
ejpam-1097	62	5	be	be	AUX
ejpam-1097	62	6	r	r	NOUN
ejpam-1097	62	7	-	-	PUNCT
ejpam-1097	62	8	modules	module	NOUN
ejpam-1097	62	9	.	.	PUNCT
ejpam-1097	63	1	then	then	ADV
ejpam-1097	63	2	the	the	DET
ejpam-1097	63	3	following	follow	VERB
ejpam-1097	63	4	hold	hold	NOUN
ejpam-1097	63	5	:	:	PUNCT
ejpam-1097	63	6	(	(	PUNCT
ejpam-1097	63	7	1	1	X
ejpam-1097	63	8	)	)	PUNCT
ejpam-1097	63	9	let	let	VERB
ejpam-1097	63	10	m	m	NOUN
ejpam-1097	63	11	=	=	SYM
ejpam-1097	63	12	a+	a+	PUNCT
ejpam-1097	63	13	b.	b.	NOUN
ejpam-1097	64	1	if	if	SCONJ
ejpam-1097	64	2	b	b	PROPN
ejpam-1097	64	3	∈	∈	PROPN
ejpam-1097	64	4	b(m	b(m	PROPN
ejpam-1097	64	5	,	,	PUNCT
ejpam-1097	64	6	x	x	PROPN
ejpam-1097	64	7	)	)	PUNCT
ejpam-1097	64	8	,	,	PUNCT
ejpam-1097	64	9	then	then	ADV
ejpam-1097	64	10	a∩	a∩	PROPN
ejpam-1097	64	11	b	b	PROPN
ejpam-1097	64	12	∈	∈	PROPN
ejpam-1097	64	13	b(m	b(m	PROPN
ejpam-1097	64	14	,	,	PUNCT
ejpam-1097	64	15	x	x	NOUN
ejpam-1097	64	16	)	)	PUNCT
ejpam-1097	64	17	.	.	PUNCT
ejpam-1097	65	1	(	(	PUNCT
ejpam-1097	65	2	2	2	X
ejpam-1097	65	3	)	)	PUNCT
ejpam-1097	65	4	let	let	VERB
ejpam-1097	65	5	m	m	NOUN
ejpam-1097	65	6	=	=	PROPN
ejpam-1097	65	7	⊕	⊕	PROPN
ejpam-1097	65	8	i∈i	i∈i	PROPN
ejpam-1097	65	9	mi	mi	PROPN
ejpam-1097	65	10	.	.	PUNCT
ejpam-1097	66	1	if	if	SCONJ
ejpam-1097	66	2	ni	ni	PROPN
ejpam-1097	66	3	∈b(mi	∈b(mi	PROPN
ejpam-1097	66	4	,	,	PUNCT
ejpam-1097	66	5	x	x	PROPN
ejpam-1097	66	6	)	)	PUNCT
ejpam-1097	66	7	,	,	PUNCT
ejpam-1097	66	8	for	for	ADP
ejpam-1097	66	9	every	every	DET
ejpam-1097	66	10	i	i	NOUN
ejpam-1097	66	11	∈	∈	PROPN
ejpam-1097	66	12	i	i	PRON
ejpam-1097	66	13	.	.	PUNCT
ejpam-1097	67	1	then	then	ADV
ejpam-1097	67	2	⊕i∈i	⊕i∈i	NUM
ejpam-1097	67	3	ni	ni	PROPN
ejpam-1097	67	4	∈b(m	∈b(m	PROPN
ejpam-1097	67	5	,	,	PUNCT
ejpam-1097	67	6	x	x	PROPN
ejpam-1097	67	7	)	)	PUNCT
ejpam-1097	67	8	.	.	PUNCT
ejpam-1097	68	1	(	(	PUNCT
ejpam-1097	68	2	3	3	X
ejpam-1097	68	3	)	)	PUNCT
ejpam-1097	68	4	let	let	VERB
ejpam-1097	68	5	m	m	NOUN
ejpam-1097	68	6	=	=	PUNCT
ejpam-1097	68	7	m1	m1	PROPN
ejpam-1097	68	8	⊕m2	⊕m2	NUM
ejpam-1097	68	9	.	.	PUNCT
ejpam-1097	69	1	if	if	SCONJ
ejpam-1097	69	2	a∈b(m	a∈b(m	NOUN
ejpam-1097	69	3	,	,	PUNCT
ejpam-1097	69	4	x	x	X
ejpam-1097	69	5	)	)	PUNCT
ejpam-1097	69	6	,	,	PUNCT
ejpam-1097	69	7	then	then	ADV
ejpam-1097	69	8	a+mi	a+mi	X
ejpam-1097	69	9	∈	∈	PROPN
ejpam-1097	69	10	b(m	b(m	PROPN
ejpam-1097	69	11	,	,	PUNCT
ejpam-1097	69	12	x	x	X
ejpam-1097	69	13	)	)	PUNCT
ejpam-1097	69	14	for	for	ADP
ejpam-1097	69	15	i	i	PROPN
ejpam-1097	69	16	=	=	SYM
ejpam-1097	69	17	1,2	1,2	NUM
ejpam-1097	69	18	.	.	PUNCT
ejpam-1097	70	1	proof	proof	NOUN
ejpam-1097	70	2	.	.	PUNCT
ejpam-1097	71	1	(	(	PUNCT
ejpam-1097	71	2	1	1	X
ejpam-1097	71	3	)	)	PUNCT
ejpam-1097	71	4	let	let	VERB
ejpam-1097	71	5	m	m	VERB
ejpam-1097	71	6	=	=	PRON
ejpam-1097	71	7	a+	a+	PUNCT
ejpam-1097	71	8	b	b	PROPN
ejpam-1097	71	9	and	and	CCONJ
ejpam-1097	71	10	b	b	PROPN
ejpam-1097	71	11	∈	∈	PROPN
ejpam-1097	71	12	b(m	b(m	PROPN
ejpam-1097	71	13	,	,	PUNCT
ejpam-1097	71	14	x	x	PROPN
ejpam-1097	71	15	)	)	PUNCT
ejpam-1097	71	16	.	.	PUNCT
ejpam-1097	72	1	there	there	PRON
ejpam-1097	72	2	exist	exist	VERB
ejpam-1097	72	3	y	y	PROPN
ejpam-1097	72	4	≤	≤	NUM
ejpam-1097	72	5	x	x	PUNCT
ejpam-1097	72	6	and	and	CCONJ
ejpam-1097	72	7	f	f	X
ejpam-1097	72	8	:	:	PUNCT
ejpam-1097	72	9	m	m	VERB
ejpam-1097	72	10	→	→	SYM
ejpam-1097	72	11	x	x	X
ejpam-1097	72	12	/	/	SYM
ejpam-1097	72	13	y	y	PRON
ejpam-1097	72	14	such	such	ADJ
ejpam-1097	72	15	that	that	DET
ejpam-1097	72	16	ker	ker	PROPN
ejpam-1097	73	1	f	f	X
ejpam-1097	73	2	/b≪	/b≪	PUNCT
ejpam-1097	73	3	m	m	AUX
ejpam-1097	73	4	/	/	SYM
ejpam-1097	73	5	b.	b.	PROPN
ejpam-1097	73	6	consider	consider	VERB
ejpam-1097	73	7	the	the	DET
ejpam-1097	73	8	isomorphism	isomorphism	NOUN
ejpam-1097	73	9	α	α	NOUN
ejpam-1097	73	10	:	:	PUNCT
ejpam-1097	73	11	m	m	PROPN
ejpam-1097	73	12	/	/	SYM
ejpam-1097	73	13	b	b	PROPN
ejpam-1097	73	14	→	→	SYM
ejpam-1097	73	15	a/(a∩	a/(a∩	PROPN
ejpam-1097	73	16	b	b	PROPN
ejpam-1097	73	17	)	)	PUNCT
ejpam-1097	73	18	.	.	PUNCT
ejpam-1097	74	1	then	then	ADV
ejpam-1097	74	2	α(ker	α(ker	VERB
ejpam-1097	74	3	f	f	PROPN
ejpam-1097	74	4	/b	/b	PUNCT
ejpam-1097	74	5	)	)	PUNCT
ejpam-1097	75	1	=	=	PUNCT
ejpam-1097	75	2	ker	ker	NOUN
ejpam-1097	76	1	f	f	X
ejpam-1097	76	2	/(a∩	/(a∩	PROPN
ejpam-1097	76	3	b	b	PROPN
ejpam-1097	76	4	)	)	PUNCT
ejpam-1097	76	5	.	.	PUNCT
ejpam-1097	77	1	hence	hence	ADV
ejpam-1097	77	2	ker	ker	PROPN
ejpam-1097	78	1	f	f	PROPN
ejpam-1097	78	2	/(a∩	/(a∩	PROPN
ejpam-1097	78	3	b)≪	b)≪	PROPN
ejpam-1097	78	4	m/(a∩	m/(a∩	PROPN
ejpam-1097	78	5	b	b	PROPN
ejpam-1097	78	6	)	)	PUNCT
ejpam-1097	78	7	.	.	PUNCT
ejpam-1097	79	1	therefore	therefore	ADV
ejpam-1097	79	2	a∩	a∩	PROPN
ejpam-1097	79	3	b	b	PROPN
ejpam-1097	79	4	∈b(m	∈b(m	PROPN
ejpam-1097	79	5	,	,	PUNCT
ejpam-1097	79	6	x	x	PROPN
ejpam-1097	79	7	)	)	PUNCT
ejpam-1097	79	8	.	.	PUNCT
ejpam-1097	80	1	(	(	PUNCT
ejpam-1097	80	2	2	2	X
ejpam-1097	80	3	)	)	PUNCT
ejpam-1097	80	4	since	since	SCONJ
ejpam-1097	80	5	ni	ni	PROPN
ejpam-1097	80	6	∈b(mi	∈b(mi	PROPN
ejpam-1097	80	7	,	,	PUNCT
ejpam-1097	80	8	x	x	PROPN
ejpam-1097	80	9	)	)	PUNCT
ejpam-1097	80	10	,	,	PUNCT
ejpam-1097	80	11	there	there	PRON
ejpam-1097	80	12	exist	exist	VERB
ejpam-1097	80	13	a	a	DET
ejpam-1097	80	14	submodule	submodule	NOUN
ejpam-1097	80	15	y	y	PROPN
ejpam-1097	80	16	of	of	ADP
ejpam-1097	80	17	x	x	PROPN
ejpam-1097	80	18	and	and	CCONJ
ejpam-1097	80	19	a	a	DET
ejpam-1097	80	20	homomorphism	homomorphism	PROPN
ejpam-1097	80	21	fi	fi	NOUN
ejpam-1097	80	22	:	:	PUNCT
ejpam-1097	80	23	mi	mi	PROPN
ejpam-1097	80	24	→	→	SYM
ejpam-1097	80	25	x	x	PROPN
ejpam-1097	80	26	/	/	SYM
ejpam-1097	80	27	y	y	PROPN
ejpam-1097	80	28	such	such	ADJ
ejpam-1097	80	29	that	that	DET
ejpam-1097	80	30	ker	ker	PROPN
ejpam-1097	80	31	fi	fi	PROPN
ejpam-1097	80	32	/	/	PROPN
ejpam-1097	80	33	ni	ni	PROPN
ejpam-1097	80	34	≪	≪	PROPN
ejpam-1097	80	35	mi	mi	PROPN
ejpam-1097	80	36	/	/	SYM
ejpam-1097	80	37	ni	ni	PROPN
ejpam-1097	80	38	.	.	PROPN
ejpam-1097	80	39	put	put	VERB
ejpam-1097	80	40	f	f	NOUN
ejpam-1097	80	41	=	=	PUNCT
ejpam-1097	80	42	⊕i∈i	⊕i∈i	NUM
ejpam-1097	80	43	fi	fi	NOUN
ejpam-1097	80	44	.	.	PUNCT
ejpam-1097	81	1	then	then	ADV
ejpam-1097	81	2	f	f	X
ejpam-1097	81	3	:	:	PUNCT
ejpam-1097	81	4	m	m	VERB
ejpam-1097	81	5	→	→	SYM
ejpam-1097	81	6	x	x	X
ejpam-1097	81	7	/	/	SYM
ejpam-1097	81	8	y	y	PRON
ejpam-1097	81	9	such	such	ADJ
ejpam-1097	81	10	that	that	DET
ejpam-1097	81	11	ker	ker	PROPN
ejpam-1097	82	1	f	f	X
ejpam-1097	82	2	/⊕i∈i	/⊕i∈i	PUNCT
ejpam-1097	82	3	ni	ni	PROPN
ejpam-1097	82	4	≪	≪	PUNCT
ejpam-1097	82	5	m/⊕i∈i	m/⊕i∈i	NUM
ejpam-1097	82	6	ni	ni	NOUN
ejpam-1097	82	7	.	.	PROPN
ejpam-1097	82	8	thus	thus	ADV
ejpam-1097	82	9	⊕i∈i	⊕i∈i	NUM
ejpam-1097	82	10	ni	ni	PROPN
ejpam-1097	82	11	∈	∈	PROPN
ejpam-1097	82	12	b(m	b(m	PROPN
ejpam-1097	82	13	,	,	PUNCT
ejpam-1097	82	14	x	x	NOUN
ejpam-1097	82	15	)	)	PUNCT
ejpam-1097	82	16	.	.	PUNCT
ejpam-1097	83	1	(	(	PUNCT
ejpam-1097	83	2	3	3	X
ejpam-1097	83	3	)	)	PUNCT
ejpam-1097	83	4	by	by	ADP
ejpam-1097	83	5	lemma	lemma	PROPN
ejpam-1097	83	6	1	1	NUM
ejpam-1097	83	7	and	and	CCONJ
ejpam-1097	83	8	[	[	X
ejpam-1097	83	9	5	5	NUM
ejpam-1097	83	10	,	,	PUNCT
ejpam-1097	83	11	lemma	lemma	PROPN
ejpam-1097	83	12	3.5	3.5	NUM
ejpam-1097	83	13	]	]	PUNCT
ejpam-1097	83	14	.	.	PUNCT
ejpam-1097	84	1	3	3	X
ejpam-1097	84	2	.	.	X
ejpam-1097	84	3	x	x	SYM
ejpam-1097	84	4	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	84	5	modules	module	NOUN
ejpam-1097	84	6	let	let	VERB
ejpam-1097	84	7	x	x	PRON
ejpam-1097	84	8	and	and	CCONJ
ejpam-1097	84	9	m	m	AUX
ejpam-1097	84	10	be	be	VERB
ejpam-1097	84	11	r	r	NOUN
ejpam-1097	84	12	-	-	PUNCT
ejpam-1097	84	13	modules	module	NOUN
ejpam-1097	84	14	.	.	PUNCT
ejpam-1097	85	1	we	we	PRON
ejpam-1097	85	2	recall	recall	VERB
ejpam-1097	85	3	that	that	SCONJ
ejpam-1097	85	4	a	a	DET
ejpam-1097	85	5	module	module	NOUN
ejpam-1097	85	6	m	m	NOUN
ejpam-1097	85	7	is	be	AUX
ejpam-1097	85	8	x	x	PUNCT
ejpam-1097	85	9	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	85	10	if	if	SCONJ
ejpam-1097	85	11	every	every	DET
ejpam-1097	85	12	submodule	submodule	NOUN
ejpam-1097	85	13	n	n	PROPN
ejpam-1097	85	14	of	of	ADP
ejpam-1097	85	15	m	m	PROPN
ejpam-1097	85	16	with	with	ADP
ejpam-1097	85	17	n	n	PRON
ejpam-1097	85	18	∈	∈	PROPN
ejpam-1097	85	19	b(m	b(m	PROPN
ejpam-1097	85	20	,	,	PUNCT
ejpam-1097	85	21	x	x	PROPN
ejpam-1097	85	22	)	)	PUNCT
ejpam-1097	85	23	,	,	PUNCT
ejpam-1097	85	24	has	have	VERB
ejpam-1097	85	25	an	an	DET
ejpam-1097	85	26	x	x	SYM
ejpam-1097	85	27	-supplement	-supplement	NOUN
ejpam-1097	85	28	that	that	PRON
ejpam-1097	85	29	is	be	AUX
ejpam-1097	85	30	a	a	DET
ejpam-1097	85	31	direct	direct	ADJ
ejpam-1097	85	32	summand	summand	NOUN
ejpam-1097	85	33	of	of	ADP
ejpam-1097	85	34	m	m	PROPN
ejpam-1097	85	35	.	.	PUNCT
ejpam-1097	86	1	clearly	clearly	ADV
ejpam-1097	86	2	x	x	SYM
ejpam-1097	86	3	-hollow	-hollow	ADJ
ejpam-1097	86	4	modules	module	NOUN
ejpam-1097	86	5	are	be	AUX
ejpam-1097	86	6	x	x	PUNCT
ejpam-1097	86	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	86	8	.	.	PUNCT
ejpam-1097	87	1	it	it	PRON
ejpam-1097	87	2	is	be	AUX
ejpam-1097	87	3	obvious	obvious	ADJ
ejpam-1097	87	4	that	that	SCONJ
ejpam-1097	87	5	x	x	X
ejpam-1097	87	6	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	87	7	modules	module	NOUN
ejpam-1097	87	8	are	be	AUX
ejpam-1097	87	9	x	x	PUNCT
ejpam-1097	87	10	-supplemented	-supplemented	ADJ
ejpam-1097	87	11	.	.	PUNCT
ejpam-1097	88	1	proposition	proposition	NOUN
ejpam-1097	88	2	1	1	NUM
ejpam-1097	88	3	.	.	PUNCT
ejpam-1097	89	1	let	let	VERB
ejpam-1097	89	2	m	m	PRON
ejpam-1097	89	3	be	be	AUX
ejpam-1097	89	4	a	a	DET
ejpam-1097	89	5	module	module	NOUN
ejpam-1097	89	6	such	such	ADJ
ejpam-1097	89	7	that	that	SCONJ
ejpam-1097	89	8	every	every	DET
ejpam-1097	89	9	submodule	submodule	NOUN
ejpam-1097	89	10	a	a	PRON
ejpam-1097	89	11	of	of	ADP
ejpam-1097	89	12	m	m	PROPN
ejpam-1097	89	13	with	with	ADP
ejpam-1097	89	14	a	a	DET
ejpam-1097	89	15	∈	∈	PROPN
ejpam-1097	89	16	b(m	b(m	NOUN
ejpam-1097	89	17	,	,	PUNCT
ejpam-1097	89	18	x	x	X
ejpam-1097	89	19	)	)	PUNCT
ejpam-1097	89	20	has	have	VERB
ejpam-1097	89	21	a	a	DET
ejpam-1097	89	22	co	co	NOUN
ejpam-1097	89	23	-	-	NOUN
ejpam-1097	89	24	closure	closure	NOUN
ejpam-1097	89	25	in	in	ADP
ejpam-1097	89	26	m.	m.	NOUN
ejpam-1097	89	27	then	then	ADV
ejpam-1097	89	28	the	the	DET
ejpam-1097	89	29	following	follow	VERB
ejpam-1097	89	30	statements	statement	NOUN
ejpam-1097	89	31	are	be	AUX
ejpam-1097	89	32	equivalent	equivalent	ADJ
ejpam-1097	89	33	:	:	PUNCT
ejpam-1097	89	34	(	(	PUNCT
ejpam-1097	89	35	1	1	X
ejpam-1097	89	36	)	)	PUNCT
ejpam-1097	89	37	m	m	VERB
ejpam-1097	89	38	is	be	AUX
ejpam-1097	89	39	x	x	PUNCT
ejpam-1097	89	40	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	89	41	.	.	PUNCT
ejpam-1097	90	1	(	(	PUNCT
ejpam-1097	90	2	2	2	X
ejpam-1097	90	3	)	)	PUNCT
ejpam-1097	90	4	any	any	DET
ejpam-1097	90	5	coclosed	coclosed	ADJ
ejpam-1097	90	6	submodule	submodule	NOUN
ejpam-1097	90	7	h	h	NOUN
ejpam-1097	90	8	of	of	ADP
ejpam-1097	90	9	m	m	PROPN
ejpam-1097	90	10	with	with	ADP
ejpam-1097	90	11	h	h	PROPN
ejpam-1097	90	12	∈	∈	PROPN
ejpam-1097	90	13	b(m	b(m	PROPN
ejpam-1097	90	14	,	,	PUNCT
ejpam-1097	90	15	x	x	PROPN
ejpam-1097	90	16	)	)	PUNCT
ejpam-1097	90	17	,	,	PUNCT
ejpam-1097	90	18	has	have	VERB
ejpam-1097	90	19	an	an	DET
ejpam-1097	90	20	x	x	SYM
ejpam-1097	90	21	-supplement	-supplement	NOUN
ejpam-1097	90	22	that	that	PRON
ejpam-1097	90	23	is	be	AUX
ejpam-1097	90	24	a	a	DET
ejpam-1097	90	25	direct	direct	ADJ
ejpam-1097	90	26	summand	summand	NOUN
ejpam-1097	90	27	of	of	ADP
ejpam-1097	90	28	m.	m.	NOUN
ejpam-1097	90	29	(	(	PUNCT
ejpam-1097	90	30	3	3	NUM
ejpam-1097	90	31	)	)	PUNCT
ejpam-1097	90	32	for	for	ADP
ejpam-1097	90	33	any	any	DET
ejpam-1097	90	34	submodule	submodule	NOUN
ejpam-1097	90	35	n	n	PROPN
ejpam-1097	90	36	of	of	ADP
ejpam-1097	90	37	m	m	PROPN
ejpam-1097	90	38	with	with	ADP
ejpam-1097	90	39	n	n	PROPN
ejpam-1097	90	40	∈b(m	∈b(m	PROPN
ejpam-1097	90	41	,	,	PUNCT
ejpam-1097	90	42	x	x	PROPN
ejpam-1097	90	43	)	)	PUNCT
ejpam-1097	90	44	,	,	PUNCT
ejpam-1097	90	45	there	there	PRON
ejpam-1097	90	46	exists	exist	VERB
ejpam-1097	90	47	a	a	DET
ejpam-1097	90	48	direct	direct	ADJ
ejpam-1097	90	49	summand	summand	NOUN
ejpam-1097	90	50	k	k	PROPN
ejpam-1097	90	51	of	of	ADP
ejpam-1097	90	52	m	m	PROPN
ejpam-1097	90	53	with	with	ADP
ejpam-1097	90	54	k	k	PROPN
ejpam-1097	90	55	∈b(m	∈b(m	PROPN
ejpam-1097	90	56	,	,	PUNCT
ejpam-1097	90	57	x	x	X
ejpam-1097	90	58	)	)	PUNCT
ejpam-1097	90	59	such	such	ADJ
ejpam-1097	90	60	that	that	SCONJ
ejpam-1097	90	61	m	m	VERB
ejpam-1097	90	62	=	=	SYM
ejpam-1097	90	63	n	n	PROPN
ejpam-1097	90	64	+	+	CCONJ
ejpam-1097	90	65	k	k	PROPN
ejpam-1097	90	66	and	and	CCONJ
ejpam-1097	90	67	n	n	PROPN
ejpam-1097	90	68	∩	∩	X
ejpam-1097	90	69	k	k	X
ejpam-1097	90	70	≪	≪	PUNCT
ejpam-1097	90	71	m.	m.	NOUN
ejpam-1097	90	72	(	(	PUNCT
ejpam-1097	90	73	4	4	NUM
ejpam-1097	90	74	)	)	PUNCT
ejpam-1097	90	75	for	for	ADP
ejpam-1097	90	76	any	any	DET
ejpam-1097	90	77	coclosed	coclosed	ADJ
ejpam-1097	90	78	submodule	submodule	NOUN
ejpam-1097	90	79	h	h	NOUN
ejpam-1097	90	80	of	of	ADP
ejpam-1097	90	81	m	m	PROPN
ejpam-1097	90	82	with	with	ADP
ejpam-1097	90	83	h	h	PROPN
ejpam-1097	90	84	∈	∈	PROPN
ejpam-1097	90	85	b(m	b(m	PROPN
ejpam-1097	90	86	,	,	PUNCT
ejpam-1097	90	87	x	x	PROPN
ejpam-1097	90	88	)	)	PUNCT
ejpam-1097	90	89	,	,	PUNCT
ejpam-1097	90	90	there	there	PRON
ejpam-1097	90	91	exists	exist	VERB
ejpam-1097	90	92	a	a	DET
ejpam-1097	90	93	direct	direct	ADJ
ejpam-1097	90	94	summand	summand	NOUN
ejpam-1097	90	95	k	k	PROPN
ejpam-1097	90	96	of	of	ADP
ejpam-1097	90	97	m	m	PROPN
ejpam-1097	90	98	with	with	ADP
ejpam-1097	90	99	k	k	PROPN
ejpam-1097	90	100	∈b(m	∈b(m	PROPN
ejpam-1097	90	101	,	,	PUNCT
ejpam-1097	90	102	x	x	X
ejpam-1097	90	103	)	)	PUNCT
ejpam-1097	91	1	such	such	ADJ
ejpam-1097	91	2	that	that	SCONJ
ejpam-1097	91	3	m	m	VERB
ejpam-1097	92	1	=	=	ADJ
ejpam-1097	92	2	h	h	PROPN
ejpam-1097	93	1	+	+	CCONJ
ejpam-1097	93	2	k	k	PROPN
ejpam-1097	93	3	and	and	CCONJ
ejpam-1097	93	4	h	h	PROPN
ejpam-1097	93	5	∩	∩	NOUN
ejpam-1097	93	6	k	k	X
ejpam-1097	93	7	≪	≪	PUNCT
ejpam-1097	93	8	m.	m.	NOUN
ejpam-1097	93	9	proof	proof	NOUN
ejpam-1097	93	10	.	.	PUNCT
ejpam-1097	94	1	(	(	PUNCT
ejpam-1097	94	2	1)⇔	1)⇔	NUM
ejpam-1097	94	3	(	(	PUNCT
ejpam-1097	94	4	3	3	NUM
ejpam-1097	94	5	)	)	PUNCT
ejpam-1097	94	6	,	,	PUNCT
ejpam-1097	94	7	(	(	PUNCT
ejpam-1097	94	8	2)⇔	2)⇔	NUM
ejpam-1097	94	9	(	(	PUNCT
ejpam-1097	94	10	4	4	NUM
ejpam-1097	94	11	)	)	PUNCT
ejpam-1097	94	12	,	,	PUNCT
ejpam-1097	94	13	(	(	PUNCT
ejpam-1097	94	14	1)⇒	1)⇒	NUM
ejpam-1097	94	15	(	(	PUNCT
ejpam-1097	94	16	2	2	NUM
ejpam-1097	94	17	)	)	PUNCT
ejpam-1097	94	18	and	and	CCONJ
ejpam-1097	94	19	(	(	PUNCT
ejpam-1097	94	20	3)⇒	3)⇒	NUM
ejpam-1097	94	21	(	(	PUNCT
ejpam-1097	94	22	4	4	NUM
ejpam-1097	94	23	)	)	PUNCT
ejpam-1097	94	24	are	be	AUX
ejpam-1097	94	25	clear	clear	ADJ
ejpam-1097	94	26	.	.	PUNCT
ejpam-1097	95	1	(	(	PUNCT
ejpam-1097	95	2	4	4	X
ejpam-1097	95	3	)	)	PUNCT
ejpam-1097	95	4	⇒	⇒	NOUN
ejpam-1097	95	5	(	(	PUNCT
ejpam-1097	95	6	1	1	X
ejpam-1097	95	7	)	)	PUNCT
ejpam-1097	95	8	let	let	VERB
ejpam-1097	95	9	a	a	DET
ejpam-1097	95	10	∈	∈	PROPN
ejpam-1097	95	11	b(m	b(m	NOUN
ejpam-1097	95	12	,	,	PUNCT
ejpam-1097	95	13	x	x	NOUN
ejpam-1097	95	14	)	)	PUNCT
ejpam-1097	95	15	.	.	PUNCT
ejpam-1097	96	1	by	by	ADP
ejpam-1097	96	2	assumption	assumption	NOUN
ejpam-1097	96	3	,	,	PUNCT
ejpam-1097	96	4	there	there	PRON
ejpam-1097	96	5	exists	exist	VERB
ejpam-1097	96	6	a	a	DET
ejpam-1097	96	7	coclosed	coclosed	ADJ
ejpam-1097	96	8	submodule	submodule	PROPN
ejpam-1097	96	9	b	b	PROPN
ejpam-1097	96	10	of	of	ADP
ejpam-1097	96	11	m	m	PRON
ejpam-1097	96	12	such	such	ADJ
ejpam-1097	96	13	that	that	DET
ejpam-1097	96	14	b	b	X
ejpam-1097	96	15	≤	≤	NOUN
ejpam-1097	96	16	a	a	PRON
ejpam-1097	96	17	and	and	CCONJ
ejpam-1097	96	18	a	a	PRON
ejpam-1097	96	19	/	/	SYM
ejpam-1097	96	20	b≪	b≪	PROPN
ejpam-1097	96	21	m	m	PROPN
ejpam-1097	96	22	/	/	SYM
ejpam-1097	96	23	b.	b.	PROPN
ejpam-1097	96	24	by	by	ADP
ejpam-1097	96	25	lemma	lemma	PROPN
ejpam-1097	96	26	1	1	NUM
ejpam-1097	96	27	,	,	PUNCT
ejpam-1097	96	28	b	b	PROPN
ejpam-1097	96	29	∈	∈	PROPN
ejpam-1097	96	30	b(m	b(m	PROPN
ejpam-1097	96	31	,	,	PUNCT
ejpam-1097	96	32	x	x	PROPN
ejpam-1097	96	33	)	)	PUNCT
ejpam-1097	96	34	.	.	PUNCT
ejpam-1097	97	1	therefore	therefore	ADV
ejpam-1097	97	2	there	there	PRON
ejpam-1097	97	3	exists	exist	VERB
ejpam-1097	97	4	a	a	DET
ejpam-1097	97	5	direct	direct	ADJ
ejpam-1097	97	6	summand	summand	NOUN
ejpam-1097	97	7	k	k	PROPN
ejpam-1097	97	8	of	of	ADP
ejpam-1097	97	9	m	m	PROPN
ejpam-1097	97	10	with	with	ADP
ejpam-1097	97	11	k	k	PROPN
ejpam-1097	97	12	∈	∈	PROPN
ejpam-1097	97	13	b(m	b(m	PROPN
ejpam-1097	97	14	,	,	PUNCT
ejpam-1097	97	15	x	x	X
ejpam-1097	97	16	)	)	PUNCT
ejpam-1097	97	17	such	such	ADJ
ejpam-1097	97	18	that	that	SCONJ
ejpam-1097	97	19	m	m	VERB
ejpam-1097	97	20	=	=	SYM
ejpam-1097	97	21	b	b	PROPN
ejpam-1097	97	22	+	+	CCONJ
ejpam-1097	97	23	k	k	PROPN
ejpam-1097	97	24	and	and	CCONJ
ejpam-1097	97	25	b	b	PROPN
ejpam-1097	97	26	∩	∩	PROPN
ejpam-1097	97	27	k	k	PROPN
ejpam-1097	97	28	≪	≪	PROPN
ejpam-1097	97	29	m	m	PRON
ejpam-1097	97	30	.	.	PUNCT
ejpam-1097	98	1	hence	hence	ADV
ejpam-1097	98	2	k	k	PROPN
ejpam-1097	98	3	is	be	AUX
ejpam-1097	98	4	an	an	DET
ejpam-1097	98	5	x	x	SYM
ejpam-1097	98	6	-supplement	-supplement	NOUN
ejpam-1097	98	7	of	of	ADP
ejpam-1097	98	8	b	b	NOUN
ejpam-1097	98	9	in	in	ADP
ejpam-1097	98	10	m	m	PROPN
ejpam-1097	98	11	.	.	PUNCT
ejpam-1097	99	1	note	note	VERB
ejpam-1097	99	2	that	that	SCONJ
ejpam-1097	99	3	m	m	VERB
ejpam-1097	99	4	=	=	SYM
ejpam-1097	99	5	a+	a+	PUNCT
ejpam-1097	99	6	k	k	PROPN
ejpam-1097	99	7	.	.	PUNCT
ejpam-1097	100	1	assume	assume	VERB
ejpam-1097	100	2	that	that	SCONJ
ejpam-1097	100	3	k	k	PROPN
ejpam-1097	101	1	′	′	NOUN
ejpam-1097	101	2	<	<	X
ejpam-1097	101	3	k	k	PROPN
ejpam-1097	101	4	and	and	CCONJ
ejpam-1097	101	5	m	m	PROPN
ejpam-1097	101	6	=	=	SYM
ejpam-1097	101	7	a+	a+	PUNCT
ejpam-1097	101	8	k	k	PROPN
ejpam-1097	101	9	′.	′.	PROPN
ejpam-1097	101	10	then	then	ADV
ejpam-1097	101	11	m	m	VERB
ejpam-1097	101	12	6=	6=	NUM
ejpam-1097	101	13	b+	b+	X
ejpam-1097	101	14	k	k	X
ejpam-1097	101	15	′	′	NOUN
ejpam-1097	102	1	and	and	CCONJ
ejpam-1097	102	2	so	so	ADV
ejpam-1097	102	3	m	m	PROPN
ejpam-1097	102	4	6=	6=	NUM
ejpam-1097	102	5	a+	a+	PUNCT
ejpam-1097	103	1	k	k	PROPN
ejpam-1097	103	2	′	′	VERB
ejpam-1097	103	3	since	since	SCONJ
ejpam-1097	103	4	a	a	DET
ejpam-1097	103	5	/	/	SYM
ejpam-1097	103	6	b≪	b≪	PROPN
ejpam-1097	103	7	m	m	PROPN
ejpam-1097	103	8	/	/	SYM
ejpam-1097	103	9	b.	b.	PROPN
ejpam-1097	104	1	thus	thus	ADV
ejpam-1097	104	2	k	k	PROPN
ejpam-1097	104	3	is	be	AUX
ejpam-1097	104	4	an	an	DET
ejpam-1097	104	5	x	x	SYM
ejpam-1097	104	6	-supplement	-supplement	NOUN
ejpam-1097	104	7	of	of	ADP
ejpam-1097	104	8	a	a	PRON
ejpam-1097	104	9	in	in	ADP
ejpam-1097	104	10	m	m	PROPN
ejpam-1097	104	11	.	.	PUNCT
ejpam-1097	105	1	t.	t.	PROPN
ejpam-1097	105	2	amouzegar	amouzegar	NOUN
ejpam-1097	105	3	,	,	PUNCT
ejpam-1097	105	4	y.	y.	PROPN
ejpam-1097	105	5	talebi	talebi	PROPN
ejpam-1097	105	6	/	/	SYM
ejpam-1097	105	7	eur	eur	PROPN
ejpam-1097	105	8	.	.	PUNCT
ejpam-1097	106	1	j.	j.	PROPN
ejpam-1097	106	2	pure	pure	PROPN
ejpam-1097	106	3	appl	appl	PROPN
ejpam-1097	106	4	.	.	PROPN
ejpam-1097	106	5	math	math	PROPN
ejpam-1097	106	6	,	,	PUNCT
ejpam-1097	106	7	5	5	NUM
ejpam-1097	106	8	(	(	PUNCT
ejpam-1097	106	9	2012	2012	NUM
ejpam-1097	106	10	)	)	PUNCT
ejpam-1097	106	11	,	,	PUNCT
ejpam-1097	106	12	108	108	NUM
ejpam-1097	106	13	-	-	SYM
ejpam-1097	106	14	115	115	NUM
ejpam-1097	106	15	111	111	NUM
ejpam-1097	106	16	theorem	theorem	NOUN
ejpam-1097	106	17	1	1	NUM
ejpam-1097	106	18	.	.	PUNCT
ejpam-1097	107	1	any	any	DET
ejpam-1097	107	2	finite	finite	ADJ
ejpam-1097	107	3	direct	direct	ADJ
ejpam-1097	107	4	sum	sum	NOUN
ejpam-1097	107	5	of	of	ADP
ejpam-1097	107	6	x	x	PUNCT
ejpam-1097	107	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	107	8	modules	module	NOUN
ejpam-1097	107	9	is	be	AUX
ejpam-1097	107	10	x	x	PUNCT
ejpam-1097	107	11	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	107	12	.	.	PUNCT
ejpam-1097	108	1	proof	proof	NOUN
ejpam-1097	108	2	.	.	PUNCT
ejpam-1097	109	1	let	let	VERB
ejpam-1097	109	2	m	m	NOUN
ejpam-1097	109	3	=	=	VERB
ejpam-1097	109	4	m1	m1	PROPN
ejpam-1097	109	5	⊕	⊕	PROPN
ejpam-1097	109	6	m2	m2	PROPN
ejpam-1097	109	7	where	where	SCONJ
ejpam-1097	109	8	m1	m1	PROPN
ejpam-1097	109	9	and	and	CCONJ
ejpam-1097	109	10	m2	m2	PROPN
ejpam-1097	109	11	are	be	AUX
ejpam-1097	109	12	x	x	INTJ
ejpam-1097	109	13	-⊕-supplemented	-⊕-supplemented	ADJ
ejpam-1097	109	14	modules	module	NOUN
ejpam-1097	109	15	.	.	PUNCT
ejpam-1097	110	1	let	let	VERB
ejpam-1097	110	2	n	n	PRON
ejpam-1097	110	3	be	be	AUX
ejpam-1097	110	4	any	any	DET
ejpam-1097	110	5	submodule	submodule	NOUN
ejpam-1097	110	6	of	of	ADP
ejpam-1097	110	7	m	m	PROPN
ejpam-1097	110	8	with	with	ADP
ejpam-1097	110	9	n	n	PRON
ejpam-1097	110	10	∈	∈	PROPN
ejpam-1097	110	11	b(m	b(m	PROPN
ejpam-1097	110	12	,	,	PUNCT
ejpam-1097	110	13	x	x	PROPN
ejpam-1097	110	14	)	)	PUNCT
ejpam-1097	110	15	.	.	PUNCT
ejpam-1097	111	1	we	we	PRON
ejpam-1097	111	2	have	have	VERB
ejpam-1097	111	3	n	n	PROPN
ejpam-1097	111	4	+	+	NUM
ejpam-1097	112	1	m2	m2	PROPN
ejpam-1097	112	2	=	=	PROPN
ejpam-1097	112	3	m2	m2	PROPN
ejpam-1097	112	4	⊕	⊕	PROPN
ejpam-1097	112	5	[	[	X
ejpam-1097	112	6	(	(	PUNCT
ejpam-1097	112	7	n	n	CCONJ
ejpam-1097	112	8	+	+	CCONJ
ejpam-1097	112	9	m2	m2	PROPN
ejpam-1097	112	10	)	)	PUNCT
ejpam-1097	112	11	∩	∩	NOUN
ejpam-1097	112	12	m1	m1	NOUN
ejpam-1097	112	13	]	]	PUNCT
ejpam-1097	112	14	.	.	PUNCT
ejpam-1097	113	1	since	since	SCONJ
ejpam-1097	113	2	n	n	PROPN
ejpam-1097	113	3	∈b(m	∈b(m	PROPN
ejpam-1097	113	4	,	,	PUNCT
ejpam-1097	113	5	x	x	PROPN
ejpam-1097	113	6	)	)	PUNCT
ejpam-1097	113	7	,	,	PUNCT
ejpam-1097	113	8	n	n	PROPN
ejpam-1097	113	9	+	+	NOUN
ejpam-1097	113	10	m2	m2	PROPN
ejpam-1097	113	11	∈b(m	∈b(m	PROPN
ejpam-1097	113	12	,	,	PUNCT
ejpam-1097	113	13	x	x	X
ejpam-1097	113	14	)	)	PUNCT
ejpam-1097	113	15	by	by	ADP
ejpam-1097	113	16	lemma	lemma	PROPN
ejpam-1097	113	17	2	2	NUM
ejpam-1097	113	18	.	.	PUNCT
ejpam-1097	113	19	from	from	ADP
ejpam-1097	113	20	[	[	X
ejpam-1097	113	21	7	7	NUM
ejpam-1097	113	22	,	,	PUNCT
ejpam-1097	113	23	lemma	lemma	PROPN
ejpam-1097	113	24	3.1	3.1	NUM
ejpam-1097	113	25	]	]	PUNCT
ejpam-1097	113	26	,	,	PUNCT
ejpam-1097	113	27	(	(	PUNCT
ejpam-1097	113	28	n+m2)∩m1	n+m2)∩m1	PROPN
ejpam-1097	113	29	∈b(m1	∈b(m1	PROPN
ejpam-1097	113	30	,	,	PUNCT
ejpam-1097	113	31	x	x	PRON
ejpam-1097	113	32	)	)	PUNCT
ejpam-1097	113	33	.	.	PUNCT
ejpam-1097	114	1	since	since	SCONJ
ejpam-1097	114	2	m1	m1	PROPN
ejpam-1097	114	3	is	be	AUX
ejpam-1097	114	4	x	x	PUNCT
ejpam-1097	114	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	114	6	,	,	PUNCT
ejpam-1097	114	7	there	there	PRON
ejpam-1097	114	8	exists	exist	VERB
ejpam-1097	114	9	a	a	DET
ejpam-1097	114	10	direct	direct	ADJ
ejpam-1097	114	11	summand	summand	NOUN
ejpam-1097	114	12	k1	k1	NOUN
ejpam-1097	114	13	of	of	ADP
ejpam-1097	114	14	m1	m1	PROPN
ejpam-1097	114	15	with	with	ADP
ejpam-1097	114	16	k1	k1	PROPN
ejpam-1097	114	17	∈b(m1	∈b(m1	NOUN
ejpam-1097	114	18	,	,	PUNCT
ejpam-1097	114	19	x	x	PUNCT
ejpam-1097	114	20	)	)	PUNCT
ejpam-1097	114	21	such	such	ADJ
ejpam-1097	114	22	that	that	SCONJ
ejpam-1097	114	23	[	[	X
ejpam-1097	114	24	(	(	PUNCT
ejpam-1097	114	25	n	n	X
ejpam-1097	114	26	+	+	NOUN
ejpam-1097	114	27	m2)∩m1]+k1	m2)∩m1]+k1	NOUN
ejpam-1097	114	28	=	=	SYM
ejpam-1097	114	29	m1	m1	PROPN
ejpam-1097	114	30	and	and	CCONJ
ejpam-1097	114	31	(	(	PUNCT
ejpam-1097	114	32	n	n	X
ejpam-1097	114	33	+	+	PROPN
ejpam-1097	114	34	m2)∩k1≪	m2)∩k1≪	PROPN
ejpam-1097	114	35	k1	k1	NOUN
ejpam-1097	114	36	.	.	PUNCT
ejpam-1097	115	1	by	by	ADP
ejpam-1097	115	2	lemma	lemma	PROPN
ejpam-1097	115	3	2	2	PROPN
ejpam-1097	115	4	and	and	CCONJ
ejpam-1097	115	5	[	[	X
ejpam-1097	115	6	7	7	NUM
ejpam-1097	115	7	,	,	PUNCT
ejpam-1097	115	8	lemma	lemma	PROPN
ejpam-1097	115	9	3.1	3.1	NUM
ejpam-1097	115	10	]	]	PUNCT
ejpam-1097	115	11	,	,	PUNCT
ejpam-1097	115	12	(	(	PUNCT
ejpam-1097	115	13	n+k1)∩m2	n+k1)∩m2	PROPN
ejpam-1097	115	14	∈	∈	PROPN
ejpam-1097	115	15	b(m2	b(m2	NOUN
ejpam-1097	115	16	,	,	PUNCT
ejpam-1097	115	17	x	x	PUNCT
ejpam-1097	115	18	)	)	PUNCT
ejpam-1097	115	19	.	.	PUNCT
ejpam-1097	116	1	thus	thus	ADV
ejpam-1097	116	2	there	there	PRON
ejpam-1097	116	3	exists	exist	VERB
ejpam-1097	116	4	a	a	DET
ejpam-1097	116	5	direct	direct	ADJ
ejpam-1097	116	6	summand	summand	NOUN
ejpam-1097	116	7	k2	k2	PROPN
ejpam-1097	116	8	of	of	ADP
ejpam-1097	116	9	m2	m2	PROPN
ejpam-1097	116	10	with	with	ADP
ejpam-1097	116	11	k2	k2	PROPN
ejpam-1097	116	12	∈b(m2	∈b(m2	PROPN
ejpam-1097	116	13	,	,	PUNCT
ejpam-1097	116	14	x	x	PUNCT
ejpam-1097	116	15	)	)	PUNCT
ejpam-1097	116	16	such	such	ADJ
ejpam-1097	116	17	that	that	SCONJ
ejpam-1097	116	18	[	[	X
ejpam-1097	116	19	(	(	PUNCT
ejpam-1097	116	20	n	n	NOUN
ejpam-1097	116	21	+	+	NUM
ejpam-1097	116	22	k1)∩m2	k1)∩m2	PROPN
ejpam-1097	116	23	]	]	X
ejpam-1097	116	24	+	+	CCONJ
ejpam-1097	116	25	k2	k2	PROPN
ejpam-1097	116	26	=	=	SYM
ejpam-1097	116	27	m2	m2	PROPN
ejpam-1097	116	28	and	and	CCONJ
ejpam-1097	116	29	(	(	PUNCT
ejpam-1097	116	30	n	n	NOUN
ejpam-1097	116	31	+	+	NUM
ejpam-1097	116	32	k1)∩	k1)∩	PROPN
ejpam-1097	116	33	k2≪	k2≪	PROPN
ejpam-1097	116	34	k2	k2	PROPN
ejpam-1097	116	35	.	.	PUNCT
ejpam-1097	117	1	let	let	VERB
ejpam-1097	117	2	k	k	PROPN
ejpam-1097	117	3	=	=	SYM
ejpam-1097	117	4	k1	k1	PROPN
ejpam-1097	117	5	⊕	⊕	PROPN
ejpam-1097	117	6	k2	k2	PROPN
ejpam-1097	117	7	,	,	PUNCT
ejpam-1097	117	8	then	then	ADV
ejpam-1097	117	9	k	k	PROPN
ejpam-1097	117	10	is	be	AUX
ejpam-1097	117	11	a	a	DET
ejpam-1097	117	12	direct	direct	ADJ
ejpam-1097	117	13	summand	summand	NOUN
ejpam-1097	117	14	of	of	ADP
ejpam-1097	117	15	m	m	PROPN
ejpam-1097	117	16	and	and	CCONJ
ejpam-1097	117	17	k	k	PROPN
ejpam-1097	117	18	∈	∈	PROPN
ejpam-1097	117	19	b(m	b(m	PROPN
ejpam-1097	117	20	,	,	PUNCT
ejpam-1097	117	21	x	x	SYM
ejpam-1097	117	22	)	)	PUNCT
ejpam-1097	117	23	(	(	PUNCT
ejpam-1097	117	24	lemma	lemma	PROPN
ejpam-1097	117	25	2	2	NUM
ejpam-1097	117	26	)	)	PUNCT
ejpam-1097	117	27	.	.	PUNCT
ejpam-1097	118	1	moreover	moreover	ADV
ejpam-1097	118	2	,	,	PUNCT
ejpam-1097	118	3	m1	m1	PROPN
ejpam-1097	118	4	≤	≤	PUNCT
ejpam-1097	118	5	n	n	PROPN
ejpam-1097	118	6	+	+	NUM
ejpam-1097	118	7	m2	m2	PROPN
ejpam-1097	118	8	+	+	CCONJ
ejpam-1097	118	9	k1	k1	PROPN
ejpam-1097	118	10	and	and	CCONJ
ejpam-1097	118	11	m2	m2	PROPN
ejpam-1097	118	12	≤	≤	PROPN
ejpam-1097	118	13	n	n	CCONJ
ejpam-1097	118	14	+	+	CCONJ
ejpam-1097	118	15	k1	k1	NOUN
ejpam-1097	118	16	+	+	X
ejpam-1097	118	17	k2	k2	NOUN
ejpam-1097	118	18	.	.	PUNCT
ejpam-1097	119	1	hence	hence	ADV
ejpam-1097	119	2	m	m	VERB
ejpam-1097	119	3	=	=	SYM
ejpam-1097	119	4	n	n	PROPN
ejpam-1097	119	5	+	+	CCONJ
ejpam-1097	119	6	k1	k1	NOUN
ejpam-1097	119	7	+	+	CCONJ
ejpam-1097	119	8	k2	k2	NOUN
ejpam-1097	119	9	=	=	SYM
ejpam-1097	119	10	n	n	PROPN
ejpam-1097	119	11	+	+	X
ejpam-1097	119	12	k	k	X
ejpam-1097	119	13	.	.	PUNCT
ejpam-1097	120	1	since	since	SCONJ
ejpam-1097	120	2	n	n	NOUN
ejpam-1097	120	3	∩	∩	NOUN
ejpam-1097	120	4	(	(	PUNCT
ejpam-1097	120	5	k1+k2)≤	k1+k2)≤	X
ejpam-1097	120	6	(	(	PUNCT
ejpam-1097	120	7	n	n	X
ejpam-1097	120	8	+	+	PROPN
ejpam-1097	120	9	k1)∩k2+(n+k2)∩k1	k1)∩k2+(n+k2)∩k1	PROPN
ejpam-1097	120	10	,	,	PUNCT
ejpam-1097	120	11	n	n	PRON
ejpam-1097	120	12	∩	∩	NOUN
ejpam-1097	120	13	(	(	PUNCT
ejpam-1097	120	14	k1+k2)≤	k1+k2)≤	X
ejpam-1097	120	15	(	(	PUNCT
ejpam-1097	120	16	n	n	X
ejpam-1097	120	17	+	+	PROPN
ejpam-1097	120	18	k1)∩k2+(n+m2)∩k1	k1)∩k2+(n+m2)∩k1	PROPN
ejpam-1097	120	19	.	.	PUNCT
ejpam-1097	121	1	as	as	ADP
ejpam-1097	121	2	(	(	PUNCT
ejpam-1097	121	3	n	n	X
ejpam-1097	121	4	+	+	PROPN
ejpam-1097	121	5	m2)∩k1≪	m2)∩k1≪	NOUN
ejpam-1097	121	6	k1	k1	NOUN
ejpam-1097	121	7	and	and	CCONJ
ejpam-1097	121	8	(	(	PUNCT
ejpam-1097	121	9	n	n	NOUN
ejpam-1097	121	10	+	+	NUM
ejpam-1097	121	11	k1)∩	k1)∩	PROPN
ejpam-1097	121	12	k2≪	k2≪	PROPN
ejpam-1097	121	13	k2	k2	PROPN
ejpam-1097	121	14	,	,	PUNCT
ejpam-1097	121	15	(	(	PUNCT
ejpam-1097	121	16	n	n	X
ejpam-1097	121	17	∩k)≪	∩k)≪	PROPN
ejpam-1097	121	18	k	k	PROPN
ejpam-1097	121	19	.	.	PUNCT
ejpam-1097	122	1	thus	thus	ADV
ejpam-1097	122	2	m	m	NOUN
ejpam-1097	122	3	is	be	AUX
ejpam-1097	122	4	x	x	PUNCT
ejpam-1097	122	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	122	6	.	.	PUNCT
ejpam-1097	122	7	corollary	corollary	ADJ
ejpam-1097	122	8	1	1	NUM
ejpam-1097	122	9	.	.	PUNCT
ejpam-1097	123	1	any	any	DET
ejpam-1097	123	2	finite	finite	ADJ
ejpam-1097	123	3	direct	direct	ADJ
ejpam-1097	123	4	sum	sum	NOUN
ejpam-1097	123	5	of	of	ADP
ejpam-1097	123	6	x	x	PUNCT
ejpam-1097	123	7	-hollow	-hollow	ADJ
ejpam-1097	123	8	modules	module	NOUN
ejpam-1097	123	9	is	be	AUX
ejpam-1097	123	10	x	x	PUNCT
ejpam-1097	123	11	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	123	12	.	.	PUNCT
ejpam-1097	124	1	lemma	lemma	PROPN
ejpam-1097	124	2	3	3	X
ejpam-1097	124	3	.	.	PUNCT
ejpam-1097	125	1	let	let	VERB
ejpam-1097	125	2	m	m	PRON
ejpam-1097	125	3	=	=	PRON
ejpam-1097	125	4	n⊕n	n⊕n	ADJ
ejpam-1097	125	5	′	′	NUM
ejpam-1097	125	6	be	be	AUX
ejpam-1097	125	7	a	a	DET
ejpam-1097	125	8	module	module	NOUN
ejpam-1097	125	9	.	.	PUNCT
ejpam-1097	126	1	assume	assume	VERB
ejpam-1097	126	2	that	that	SCONJ
ejpam-1097	126	3	a	a	PRON
ejpam-1097	126	4	is	be	AUX
ejpam-1097	126	5	a	a	DET
ejpam-1097	126	6	submodule	submodule	NOUN
ejpam-1097	126	7	of	of	ADP
ejpam-1097	126	8	n	n	PROPN
ejpam-1097	126	9	and	and	CCONJ
ejpam-1097	126	10	k	k	PROPN
ejpam-1097	126	11	a	a	DET
ejpam-1097	126	12	submodule	submodule	NOUN
ejpam-1097	126	13	of	of	ADP
ejpam-1097	126	14	m.	m.	NOUN
ejpam-1097	126	15	if	if	SCONJ
ejpam-1097	126	16	k	k	PROPN
ejpam-1097	126	17	∩	∩	X
ejpam-1097	126	18	(	(	PUNCT
ejpam-1097	126	19	a⊕	a⊕	NOUN
ejpam-1097	126	20	n	n	ADP
ejpam-1097	126	21	′)≪	′)≪	PROPN
ejpam-1097	126	22	k	k	NOUN
ejpam-1097	126	23	,	,	PUNCT
ejpam-1097	126	24	then	then	ADV
ejpam-1097	126	25	a∩	a∩	PROPN
ejpam-1097	126	26	(	(	PUNCT
ejpam-1097	126	27	k	k	X
ejpam-1097	126	28	+	+	CCONJ
ejpam-1097	126	29	n	n	CCONJ
ejpam-1097	126	30	′)≪	′)≪	PROPN
ejpam-1097	126	31	n	n	NOUN
ejpam-1097	126	32	∩	∩	NOUN
ejpam-1097	126	33	(	(	PUNCT
ejpam-1097	126	34	k	k	X
ejpam-1097	126	35	+	+	PROPN
ejpam-1097	126	36	n	n	NUM
ejpam-1097	126	37	′	′	NUM
ejpam-1097	126	38	)	)	PUNCT
ejpam-1097	126	39	.	.	PUNCT
ejpam-1097	127	1	proof	proof	NOUN
ejpam-1097	127	2	.	.	PUNCT
ejpam-1097	128	1	let	let	VERB
ejpam-1097	128	2	π	π	NOUN
ejpam-1097	128	3	be	be	AUX
ejpam-1097	128	4	the	the	DET
ejpam-1097	128	5	projection	projection	NOUN
ejpam-1097	128	6	n	n	PROPN
ejpam-1097	128	7	⊕	⊕	PROPN
ejpam-1097	128	8	n	n	ADV
ejpam-1097	128	9	′	′	NUM
ejpam-1097	128	10	→	→	SYM
ejpam-1097	128	11	n	n	CCONJ
ejpam-1097	128	12	.	.	PUNCT
ejpam-1097	129	1	since	since	SCONJ
ejpam-1097	129	2	k	k	PROPN
ejpam-1097	129	3	∩	∩	PROPN
ejpam-1097	129	4	π−1(a	π−1(a	PROPN
ejpam-1097	129	5	)	)	PUNCT
ejpam-1097	130	1	=	=	SYM
ejpam-1097	130	2	k	k	PROPN
ejpam-1097	130	3	∩	∩	NOUN
ejpam-1097	130	4	(	(	PUNCT
ejpam-1097	130	5	a⊕	a⊕	PROPN
ejpam-1097	130	6	n	n	PRON
ejpam-1097	130	7	′	′	NUM
ejpam-1097	130	8	)	)	PUNCT
ejpam-1097	130	9	≪	≪	PUNCT
ejpam-1097	130	10	k	k	PROPN
ejpam-1097	130	11	,	,	PUNCT
ejpam-1097	130	12	π(k∩π−1(a	π(k∩π−1(a	PROPN
ejpam-1097	130	13	)	)	PUNCT
ejpam-1097	130	14	)	)	PUNCT
ejpam-1097	130	15	=	=	PRON
ejpam-1097	130	16	π(k)∩a≪	π(k)∩a≪	PROPN
ejpam-1097	130	17	π(k	π(k	NOUN
ejpam-1097	130	18	)	)	PUNCT
ejpam-1097	130	19	.	.	PUNCT
ejpam-1097	131	1	but	but	CCONJ
ejpam-1097	131	2	π(k	π(k	NUM
ejpam-1097	131	3	)	)	PUNCT
ejpam-1097	131	4	=	=	SYM
ejpam-1097	131	5	n∩(k+n	n∩(k+n	NOUN
ejpam-1097	131	6	′	′	NOUN
ejpam-1097	131	7	)	)	PUNCT
ejpam-1097	131	8	.	.	PUNCT
ejpam-1097	132	1	hence	hence	ADV
ejpam-1097	132	2	a∩(k+n	a∩(k+n	VERB
ejpam-1097	132	3	′)≪	′)≪	NOUN
ejpam-1097	132	4	n∩(k+n	n∩(k+n	NOUN
ejpam-1097	132	5	′	′	NOUN
ejpam-1097	132	6	)	)	PUNCT
ejpam-1097	132	7	.	.	PUNCT
ejpam-1097	133	1	following	follow	VERB
ejpam-1097	133	2	[	[	X
ejpam-1097	133	3	5	5	NUM
ejpam-1097	133	4	]	]	PUNCT
ejpam-1097	133	5	,	,	PUNCT
ejpam-1097	133	6	an	an	DET
ejpam-1097	133	7	r	r	NOUN
ejpam-1097	133	8	-	-	PUNCT
ejpam-1097	133	9	module	module	NOUN
ejpam-1097	133	10	n	n	NOUN
ejpam-1097	133	11	is	be	AUX
ejpam-1097	133	12	called	call	VERB
ejpam-1097	133	13	b(m	b(m	PROPN
ejpam-1097	133	14	,	,	PUNCT
ejpam-1097	133	15	x	x	X
ejpam-1097	133	16	)	)	PUNCT
ejpam-1097	133	17	-projective	-projective	ADJ
ejpam-1097	133	18	if	if	SCONJ
ejpam-1097	133	19	for	for	ADP
ejpam-1097	133	20	any	any	DET
ejpam-1097	133	21	submodule	submodule	NOUN
ejpam-1097	133	22	a	a	PRON
ejpam-1097	133	23	of	of	ADP
ejpam-1097	133	24	m	m	PROPN
ejpam-1097	133	25	with	with	ADP
ejpam-1097	133	26	a	a	DET
ejpam-1097	133	27	∈	∈	PROPN
ejpam-1097	133	28	b(m	b(m	NOUN
ejpam-1097	133	29	,	,	PUNCT
ejpam-1097	133	30	x	x	PROPN
ejpam-1097	133	31	)	)	PUNCT
ejpam-1097	133	32	,	,	PUNCT
ejpam-1097	133	33	any	any	DET
ejpam-1097	133	34	homomorphism	homomorphism	PROPN
ejpam-1097	133	35	φ	φ	X
ejpam-1097	133	36	:	:	PUNCT
ejpam-1097	133	37	n	n	PROPN
ejpam-1097	133	38	→	→	SYM
ejpam-1097	133	39	m	m	NOUN
ejpam-1097	133	40	/	/	SYM
ejpam-1097	133	41	a	a	PRON
ejpam-1097	133	42	can	can	AUX
ejpam-1097	133	43	be	be	AUX
ejpam-1097	133	44	lifted	lift	VERB
ejpam-1097	133	45	to	to	ADP
ejpam-1097	133	46	a	a	DET
ejpam-1097	133	47	homomorphism	homomorphism	NOUN
ejpam-1097	133	48	ψ	ψ	X
ejpam-1097	133	49	:	:	PUNCT
ejpam-1097	133	50	n	n	X
ejpam-1097	133	51	→	→	SYM
ejpam-1097	133	52	m	m	NOUN
ejpam-1097	133	53	.	.	PUNCT
ejpam-1097	134	1	two	two	NUM
ejpam-1097	134	2	r	r	NOUN
ejpam-1097	134	3	-	-	PUNCT
ejpam-1097	134	4	modules	module	NOUN
ejpam-1097	134	5	m1	m1	NOUN
ejpam-1097	134	6	and	and	CCONJ
ejpam-1097	134	7	m2	m2	PROPN
ejpam-1097	134	8	are	be	AUX
ejpam-1097	134	9	called	call	VERB
ejpam-1097	134	10	relatively	relatively	ADV
ejpam-1097	134	11	b	b	NOUN
ejpam-1097	134	12	-	-	PUNCT
ejpam-1097	134	13	projective	projective	ADJ
ejpam-1097	134	14	if	if	SCONJ
ejpam-1097	134	15	m1	m1	PROPN
ejpam-1097	134	16	is	be	AUX
ejpam-1097	134	17	b(m2	b(m2	ADJ
ejpam-1097	134	18	,	,	PUNCT
ejpam-1097	134	19	x	x	X
ejpam-1097	134	20	)	)	PUNCT
ejpam-1097	134	21	projective	projective	NOUN
ejpam-1097	134	22	and	and	CCONJ
ejpam-1097	134	23	m2	m2	PROPN
ejpam-1097	134	24	is	be	AUX
ejpam-1097	134	25	b(m1	b(m1	NOUN
ejpam-1097	134	26	,	,	PUNCT
ejpam-1097	134	27	x	x	X
ejpam-1097	134	28	)	)	PUNCT
ejpam-1097	134	29	-projective	-projective	NOUN
ejpam-1097	134	30	.	.	PUNCT
ejpam-1097	135	1	theorem	theorem	NOUN
ejpam-1097	135	2	2	2	NUM
ejpam-1097	135	3	.	.	PUNCT
ejpam-1097	136	1	let	let	VERB
ejpam-1097	136	2	m	m	VERB
ejpam-1097	136	3	=	=	VERB
ejpam-1097	136	4	⊕n	⊕n	NOUN
ejpam-1097	136	5	i=1	i=1	PROPN
ejpam-1097	136	6	mi	mi	PROPN
ejpam-1097	136	7	be	be	AUX
ejpam-1097	136	8	a	a	DET
ejpam-1097	136	9	finite	finite	ADJ
ejpam-1097	136	10	direct	direct	ADJ
ejpam-1097	136	11	sum	sum	NOUN
ejpam-1097	136	12	of	of	ADP
ejpam-1097	136	13	relativelyb	relativelyb	NOUN
ejpam-1097	136	14	-	-	PUNCT
ejpam-1097	136	15	projective	projective	ADJ
ejpam-1097	136	16	modules	module	NOUN
ejpam-1097	136	17	mi	mi	PROPN
ejpam-1097	136	18	and	and	CCONJ
ejpam-1097	136	19	let	let	VERB
ejpam-1097	136	20	m	m	PRON
ejpam-1097	136	21	have	have	VERB
ejpam-1097	136	22	the	the	DET
ejpam-1097	136	23	summand	summand	NOUN
ejpam-1097	136	24	sum	sum	NOUN
ejpam-1097	136	25	property	property	NOUN
ejpam-1097	136	26	.	.	PUNCT
ejpam-1097	137	1	then	then	ADV
ejpam-1097	137	2	the	the	DET
ejpam-1097	137	3	module	module	NOUN
ejpam-1097	137	4	m	m	NOUN
ejpam-1097	137	5	is	be	AUX
ejpam-1097	137	6	x	x	PUNCT
ejpam-1097	137	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	137	8	if	if	SCONJ
ejpam-1097	137	9	and	and	CCONJ
ejpam-1097	137	10	only	only	ADV
ejpam-1097	137	11	if	if	SCONJ
ejpam-1097	137	12	mi	mi	PROPN
ejpam-1097	137	13	is	be	AUX
ejpam-1097	137	14	x	x	PUNCT
ejpam-1097	137	15	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	137	16	for	for	ADP
ejpam-1097	137	17	all	all	PRON
ejpam-1097	137	18	1≤	1≤	NUM
ejpam-1097	137	19	i	i	PRON
ejpam-1097	137	20	≤	≤	ADJ
ejpam-1097	137	21	n.	n.	NOUN
ejpam-1097	137	22	proof	proof	NOUN
ejpam-1097	137	23	.	.	PUNCT
ejpam-1097	138	1	the	the	DET
ejpam-1097	138	2	sufficiency	sufficiency	NOUN
ejpam-1097	138	3	is	be	AUX
ejpam-1097	138	4	proved	prove	VERB
ejpam-1097	138	5	in	in	ADP
ejpam-1097	138	6	theorem	theorem	NOUN
ejpam-1097	138	7	1	1	NUM
ejpam-1097	138	8	.	.	PUNCT
ejpam-1097	139	1	conversely	conversely	ADV
ejpam-1097	139	2	,	,	PUNCT
ejpam-1097	139	3	we	we	PRON
ejpam-1097	139	4	only	only	ADV
ejpam-1097	139	5	prove	prove	VERB
ejpam-1097	139	6	m1	m1	PROPN
ejpam-1097	139	7	is	be	AUX
ejpam-1097	139	8	x	x	PRON
ejpam-1097	139	9	-⊕supplemented	-⊕supplemented	ADJ
ejpam-1097	139	10	.	.	PUNCT
ejpam-1097	140	1	let	let	VERB
ejpam-1097	140	2	a	a	DET
ejpam-1097	140	3	∈	∈	NOUN
ejpam-1097	140	4	b(m1	b(m1	NOUN
ejpam-1097	140	5	,	,	PUNCT
ejpam-1097	140	6	x	x	NOUN
ejpam-1097	140	7	)	)	PUNCT
ejpam-1097	140	8	.	.	PUNCT
ejpam-1097	141	1	by	by	ADP
ejpam-1097	141	2	lemma	lemma	PROPN
ejpam-1097	141	3	1	1	NUM
ejpam-1097	141	4	,	,	PUNCT
ejpam-1097	141	5	a⊕	a⊕	PROPN
ejpam-1097	141	6	m2	m2	PROPN
ejpam-1097	141	7	∈	∈	PROPN
ejpam-1097	141	8	b(m	b(m	PROPN
ejpam-1097	141	9	,	,	PUNCT
ejpam-1097	141	10	x	x	PROPN
ejpam-1097	141	11	)	)	PUNCT
ejpam-1097	141	12	.	.	PUNCT
ejpam-1097	142	1	since	since	SCONJ
ejpam-1097	142	2	m	m	PROPN
ejpam-1097	142	3	is	be	AUX
ejpam-1097	142	4	x	x	PRON
ejpam-1097	142	5	-⊕supplemented	-⊕supplemented	ADJ
ejpam-1097	142	6	,	,	PUNCT
ejpam-1097	142	7	there	there	PRON
ejpam-1097	142	8	exists	exist	VERB
ejpam-1097	142	9	b	b	PROPN
ejpam-1097	142	10	∈	∈	PROPN
ejpam-1097	142	11	b(m	b(m	PROPN
ejpam-1097	142	12	,	,	PUNCT
ejpam-1097	142	13	x	x	X
ejpam-1097	142	14	)	)	PUNCT
ejpam-1097	142	15	such	such	ADJ
ejpam-1097	142	16	that	that	SCONJ
ejpam-1097	142	17	m	m	VERB
ejpam-1097	142	18	=	=	X
ejpam-1097	142	19	(	(	PUNCT
ejpam-1097	142	20	a⊕m2	a⊕m2	ADJ
ejpam-1097	142	21	)	)	PUNCT
ejpam-1097	143	1	+	+	CCONJ
ejpam-1097	143	2	b	b	X
ejpam-1097	143	3	,	,	PUNCT
ejpam-1097	143	4	(	(	PUNCT
ejpam-1097	143	5	a⊕m2)∩	a⊕m2)∩	PROPN
ejpam-1097	143	6	b≪	b≪	PROPN
ejpam-1097	143	7	b	b	PROPN
ejpam-1097	143	8	and	and	CCONJ
ejpam-1097	143	9	b	b	PROPN
ejpam-1097	143	10	is	be	AUX
ejpam-1097	143	11	a	a	DET
ejpam-1097	143	12	direct	direct	ADJ
ejpam-1097	143	13	summand	summand	NOUN
ejpam-1097	143	14	of	of	ADP
ejpam-1097	143	15	m	m	PROPN
ejpam-1097	143	16	.	.	PUNCT
ejpam-1097	144	1	by	by	ADP
ejpam-1097	144	2	lemma	lemma	PROPN
ejpam-1097	144	3	2	2	NUM
ejpam-1097	144	4	,	,	PUNCT
ejpam-1097	144	5	m2	m2	PROPN
ejpam-1097	144	6	+	+	PROPN
ejpam-1097	144	7	b	b	PROPN
ejpam-1097	144	8	∈b(m	∈b(m	PROPN
ejpam-1097	144	9	,	,	PUNCT
ejpam-1097	144	10	x	x	PROPN
ejpam-1097	144	11	)	)	PUNCT
ejpam-1097	144	12	.	.	PUNCT
ejpam-1097	145	1	clearly	clearly	ADV
ejpam-1097	145	2	m	m	VERB
ejpam-1097	145	3	=	=	ADJ
ejpam-1097	145	4	m1	m1	PROPN
ejpam-1097	145	5	+	+	PROPN
ejpam-1097	145	6	m2	m2	PROPN
ejpam-1097	145	7	+	+	X
ejpam-1097	145	8	b.	b.	PROPN
ejpam-1097	145	9	by	by	ADP
ejpam-1097	145	10	[	[	X
ejpam-1097	145	11	5	5	NUM
ejpam-1097	145	12	,	,	PUNCT
ejpam-1097	145	13	proposition	proposition	NOUN
ejpam-1097	145	14	2.5	2.5	NUM
ejpam-1097	145	15	]	]	PUNCT
ejpam-1097	145	16	,	,	PUNCT
ejpam-1097	145	17	there	there	PRON
ejpam-1097	145	18	exists	exist	VERB
ejpam-1097	145	19	t	t	PROPN
ejpam-1097	145	20	≤	≤	PROPN
ejpam-1097	145	21	m2	m2	PROPN
ejpam-1097	146	1	+	+	CCONJ
ejpam-1097	146	2	b	b	X
ejpam-1097	146	3	such	such	ADJ
ejpam-1097	146	4	that	that	SCONJ
ejpam-1097	146	5	m	m	PROPN
ejpam-1097	146	6	=	=	SYM
ejpam-1097	146	7	m1	m1	PROPN
ejpam-1097	146	8	⊕	⊕	PROPN
ejpam-1097	146	9	t	t	PROPN
ejpam-1097	146	10	.	.	PUNCT
ejpam-1097	147	1	thus	thus	ADV
ejpam-1097	147	2	b	b	X
ejpam-1097	147	3	+	+	NOUN
ejpam-1097	147	4	m2	m2	PROPN
ejpam-1097	147	5	=	=	SYM
ejpam-1097	147	6	(	(	PUNCT
ejpam-1097	147	7	m1	m1	PROPN
ejpam-1097	147	8	∩	∩	NOUN
ejpam-1097	147	9	(	(	PUNCT
ejpam-1097	147	10	b+m2))⊕	b+m2))⊕	NOUN
ejpam-1097	147	11	t	t	NOUN
ejpam-1097	147	12	.	.	PUNCT
ejpam-1097	148	1	now	now	ADV
ejpam-1097	148	2	m1	m1	PROPN
ejpam-1097	148	3	=	=	SYM
ejpam-1097	148	4	a+	a+	PUNCT
ejpam-1097	148	5	(	(	PUNCT
ejpam-1097	148	6	(	(	PUNCT
ejpam-1097	148	7	b+m2)∩m1	b+m2)∩m1	PROPN
ejpam-1097	148	8	)	)	PUNCT
ejpam-1097	148	9	and	and	CCONJ
ejpam-1097	148	10	since	since	SCONJ
ejpam-1097	148	11	(	(	PUNCT
ejpam-1097	148	12	a⊕m2)∩	a⊕m2)∩	PROPN
ejpam-1097	148	13	b≪	b≪	PROPN
ejpam-1097	148	14	b	b	PROPN
ejpam-1097	148	15	,	,	PUNCT
ejpam-1097	148	16	by	by	ADP
ejpam-1097	148	17	lemma	lemma	PROPN
ejpam-1097	148	18	3	3	NUM
ejpam-1097	148	19	,	,	PUNCT
ejpam-1097	148	20	a∩	a∩	PROPN
ejpam-1097	148	21	(	(	PUNCT
ejpam-1097	148	22	m1	m1	PROPN
ejpam-1097	148	23	∩	∩	NOUN
ejpam-1097	148	24	(	(	PUNCT
ejpam-1097	148	25	b	b	X
ejpam-1097	148	26	+	+	PUNCT
ejpam-1097	148	27	m2))≪	m2))≪	PROPN
ejpam-1097	148	28	m1	m1	NOUN
ejpam-1097	148	29	∩	∩	NOUN
ejpam-1097	148	30	(	(	PUNCT
ejpam-1097	148	31	b	b	PROPN
ejpam-1097	148	32	+	+	CCONJ
ejpam-1097	148	33	m2	m2	NOUN
ejpam-1097	148	34	)	)	PUNCT
ejpam-1097	148	35	.	.	PUNCT
ejpam-1097	149	1	as	as	SCONJ
ejpam-1097	149	2	m	m	PROPN
ejpam-1097	149	3	has	have	VERB
ejpam-1097	149	4	the	the	DET
ejpam-1097	149	5	summand	summand	NOUN
ejpam-1097	149	6	sum	sum	NOUN
ejpam-1097	149	7	property	property	NOUN
ejpam-1097	149	8	,	,	PUNCT
ejpam-1097	149	9	b	b	PROPN
ejpam-1097	150	1	+	+	CCONJ
ejpam-1097	150	2	m2	m2	PROPN
ejpam-1097	150	3	is	be	AUX
ejpam-1097	150	4	a	a	DET
ejpam-1097	150	5	direct	direct	ADJ
ejpam-1097	150	6	summand	summand	NOUN
ejpam-1097	150	7	of	of	ADP
ejpam-1097	150	8	m	m	PROPN
ejpam-1097	150	9	.	.	PUNCT
ejpam-1097	151	1	thus	thus	ADV
ejpam-1097	151	2	(	(	PUNCT
ejpam-1097	151	3	b	b	X
ejpam-1097	151	4	+	+	CCONJ
ejpam-1097	151	5	m2	m2	PROPN
ejpam-1097	151	6	)	)	PUNCT
ejpam-1097	151	7	∩	∩	ADJ
ejpam-1097	151	8	m1	m1	PROPN
ejpam-1097	151	9	≤	≤	PROPN
ejpam-1097	151	10	⊕	⊕	PROPN
ejpam-1097	151	11	m	m	PROPN
ejpam-1097	151	12	and	and	CCONJ
ejpam-1097	151	13	so	so	ADV
ejpam-1097	151	14	(	(	PUNCT
ejpam-1097	151	15	b	b	PROPN
ejpam-1097	151	16	+	+	CCONJ
ejpam-1097	151	17	m2	m2	PROPN
ejpam-1097	151	18	)	)	PUNCT
ejpam-1097	151	19	∩	∩	NOUN
ejpam-1097	151	20	m1	m1	PROPN
ejpam-1097	151	21	is	be	AUX
ejpam-1097	151	22	a	a	DET
ejpam-1097	151	23	direct	direct	ADJ
ejpam-1097	151	24	summand	summand	NOUN
ejpam-1097	151	25	of	of	ADP
ejpam-1097	151	26	m1	m1	PROPN
ejpam-1097	151	27	.	.	PUNCT
ejpam-1097	152	1	by	by	ADP
ejpam-1097	152	2	[	[	X
ejpam-1097	152	3	7	7	NUM
ejpam-1097	152	4	,	,	PUNCT
ejpam-1097	152	5	lemma	lemma	PROPN
ejpam-1097	152	6	3.1	3.1	NUM
ejpam-1097	152	7	(	(	PUNCT
ejpam-1097	152	8	1	1	NUM
ejpam-1097	152	9	)	)	PUNCT
ejpam-1097	152	10	]	]	PUNCT
ejpam-1097	152	11	,	,	PUNCT
ejpam-1097	152	12	(	(	PUNCT
ejpam-1097	152	13	b	b	X
ejpam-1097	152	14	+	+	CCONJ
ejpam-1097	152	15	m2	m2	PROPN
ejpam-1097	152	16	)	)	PUNCT
ejpam-1097	152	17	∩	∩	ADJ
ejpam-1097	152	18	m1	m1	PROPN
ejpam-1097	152	19	∈	∈	PROPN
ejpam-1097	152	20	b(m1	b(m1	NOUN
ejpam-1097	152	21	,	,	PUNCT
ejpam-1097	152	22	x	x	NOUN
ejpam-1097	152	23	)	)	PUNCT
ejpam-1097	152	24	.	.	PUNCT
ejpam-1097	153	1	hence	hence	ADV
ejpam-1097	153	2	m1	m1	PROPN
ejpam-1097	153	3	is	be	AUX
ejpam-1097	153	4	x	x	PUNCT
ejpam-1097	153	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	153	6	.	.	PUNCT
ejpam-1097	153	7	proposition	proposition	NOUN
ejpam-1097	153	8	2	2	NUM
ejpam-1097	153	9	.	.	PUNCT
ejpam-1097	154	1	let	let	AUX
ejpam-1097	154	2	m	m	PRON
ejpam-1097	154	3	and	and	CCONJ
ejpam-1097	154	4	n	n	AUX
ejpam-1097	154	5	be	be	VERB
ejpam-1097	154	6	r	r	NOUN
ejpam-1097	154	7	-	-	PUNCT
ejpam-1097	154	8	modules	module	NOUN
ejpam-1097	154	9	and	and	CCONJ
ejpam-1097	154	10	h	h	NOUN
ejpam-1097	154	11	:	:	PUNCT
ejpam-1097	154	12	m	m	VERB
ejpam-1097	154	13	→	→	SYM
ejpam-1097	154	14	n	n	CCONJ
ejpam-1097	154	15	be	be	AUX
ejpam-1097	154	16	an	an	DET
ejpam-1097	154	17	epimorphism	epimorphism	NOUN
ejpam-1097	154	18	such	such	ADJ
ejpam-1097	154	19	that	that	DET
ejpam-1097	154	20	ker	ker	PROPN
ejpam-1097	154	21	hã	hã	INTJ
ejpam-1097	154	22	m.	m.	NOUN
ejpam-1097	154	23	if	if	SCONJ
ejpam-1097	154	24	m	m	NOUN
ejpam-1097	154	25	is	be	AUX
ejpam-1097	154	26	x	x	PUNCT
ejpam-1097	154	27	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	154	28	,	,	PUNCT
ejpam-1097	154	29	then	then	ADV
ejpam-1097	154	30	n	n	PRON
ejpam-1097	154	31	is	be	AUX
ejpam-1097	154	32	x	x	PUNCT
ejpam-1097	154	33	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	154	34	.	.	PUNCT
ejpam-1097	155	1	t.	t.	PROPN
ejpam-1097	155	2	amouzegar	amouzegar	NOUN
ejpam-1097	155	3	,	,	PUNCT
ejpam-1097	155	4	y.	y.	PROPN
ejpam-1097	155	5	talebi	talebi	PROPN
ejpam-1097	155	6	/	/	SYM
ejpam-1097	155	7	eur	eur	PROPN
ejpam-1097	155	8	.	.	PUNCT
ejpam-1097	156	1	j.	j.	PROPN
ejpam-1097	156	2	pure	pure	PROPN
ejpam-1097	156	3	appl	appl	PROPN
ejpam-1097	156	4	.	.	PROPN
ejpam-1097	156	5	math	math	PROPN
ejpam-1097	156	6	,	,	PUNCT
ejpam-1097	156	7	5	5	NUM
ejpam-1097	156	8	(	(	PUNCT
ejpam-1097	156	9	2012	2012	NUM
ejpam-1097	156	10	)	)	PUNCT
ejpam-1097	156	11	,	,	PUNCT
ejpam-1097	156	12	108	108	NUM
ejpam-1097	156	13	-	-	SYM
ejpam-1097	156	14	115	115	NUM
ejpam-1097	156	15	112	112	NUM
ejpam-1097	156	16	proof	proof	NOUN
ejpam-1097	156	17	.	.	PUNCT
ejpam-1097	157	1	let	let	VERB
ejpam-1097	157	2	a	a	DET
ejpam-1097	157	3	∈	∈	PROPN
ejpam-1097	157	4	b(n	b(n	NOUN
ejpam-1097	157	5	,	,	PUNCT
ejpam-1097	157	6	x	x	NOUN
ejpam-1097	157	7	)	)	PUNCT
ejpam-1097	157	8	.	.	PUNCT
ejpam-1097	158	1	by	by	ADP
ejpam-1097	158	2	lemma	lemma	PROPN
ejpam-1097	158	3	1	1	NUM
ejpam-1097	158	4	,	,	PUNCT
ejpam-1097	158	5	h−1(a	h−1(a	PROPN
ejpam-1097	158	6	)	)	PUNCT
ejpam-1097	158	7	∈	∈	PROPN
ejpam-1097	158	8	b(m	b(m	PROPN
ejpam-1097	158	9	,	,	PUNCT
ejpam-1097	158	10	x	x	PROPN
ejpam-1097	158	11	)	)	PUNCT
ejpam-1097	158	12	.	.	PUNCT
ejpam-1097	159	1	since	since	SCONJ
ejpam-1097	159	2	m	m	PROPN
ejpam-1097	159	3	is	be	AUX
ejpam-1097	159	4	x	x	PUNCT
ejpam-1097	159	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	159	6	,	,	PUNCT
ejpam-1097	159	7	there	there	PRON
ejpam-1097	159	8	exist	exist	VERB
ejpam-1097	159	9	submodules	submodule	NOUN
ejpam-1097	159	10	h	h	NOUN
ejpam-1097	159	11	and	and	CCONJ
ejpam-1097	159	12	h	h	NOUN
ejpam-1097	159	13	′	′	NUM
ejpam-1097	159	14	of	of	ADP
ejpam-1097	159	15	m	m	PRON
ejpam-1097	159	16	such	such	ADJ
ejpam-1097	159	17	that	that	SCONJ
ejpam-1097	159	18	m	m	PROPN
ejpam-1097	159	19	=	=	NOUN
ejpam-1097	159	20	h	h	NOUN
ejpam-1097	159	21	⊕h	⊕h	PROPN
ejpam-1097	159	22	′	′	NUM
ejpam-1097	159	23	,	,	PUNCT
ejpam-1097	159	24	m	m	PROPN
ejpam-1097	159	25	=	=	PUNCT
ejpam-1097	159	26	h−1(a)+h	h−1(a)+h	NOUN
ejpam-1097	159	27	and	and	CCONJ
ejpam-1097	159	28	h−1(a)∩h	h−1(a)∩h	NOUN
ejpam-1097	159	29	≪	≪	PUNCT
ejpam-1097	159	30	h.	h.	PROPN
ejpam-1097	159	31	now	now	ADV
ejpam-1097	159	32	n	n	PROPN
ejpam-1097	159	33	=	=	PUNCT
ejpam-1097	159	34	a+	a+	PUNCT
ejpam-1097	159	35	h(h	h(h	X
ejpam-1097	159	36	)	)	PUNCT
ejpam-1097	159	37	and	and	CCONJ
ejpam-1097	159	38	since	since	SCONJ
ejpam-1097	159	39	h−1(a)∩h	h−1(a)∩h	NOUN
ejpam-1097	159	40	≪	≪	NOUN
ejpam-1097	159	41	h	h	NOUN
ejpam-1097	159	42	,	,	PUNCT
ejpam-1097	159	43	h(h−1(a	h(h−1(a	PROPN
ejpam-1097	159	44	)	)	PUNCT
ejpam-1097	159	45	∩	∩	ADJ
ejpam-1097	159	46	h	h	NOUN
ejpam-1097	159	47	)	)	PUNCT
ejpam-1097	159	48	=	=	SYM
ejpam-1097	160	1	a∩	a∩	PROPN
ejpam-1097	160	2	h(h	h(h	X
ejpam-1097	160	3	)	)	PUNCT
ejpam-1097	160	4	≪	≪	PUNCT
ejpam-1097	160	5	h(h	h(h	NOUN
ejpam-1097	160	6	)	)	PUNCT
ejpam-1097	160	7	.	.	PUNCT
ejpam-1097	161	1	moreover	moreover	ADV
ejpam-1097	161	2	,	,	PUNCT
ejpam-1097	161	3	since	since	SCONJ
ejpam-1097	161	4	ker	ker	PROPN
ejpam-1097	161	5	h	h	PROPN
ejpam-1097	162	1	ã	ã	X
ejpam-1097	162	2	m	m	NOUN
ejpam-1097	162	3	,	,	PUNCT
ejpam-1097	162	4	n	n	PROPN
ejpam-1097	162	5	=	=	SYM
ejpam-1097	162	6	h(h)⊕	h(h)⊕	NOUN
ejpam-1097	162	7	h(h	h(h	PROPN
ejpam-1097	162	8	′	′	NOUN
ejpam-1097	162	9	)	)	PUNCT
ejpam-1097	162	10	.	.	PUNCT
ejpam-1097	163	1	therefore	therefore	ADV
ejpam-1097	163	2	h(h	h(h	X
ejpam-1097	163	3	)	)	PUNCT
ejpam-1097	163	4	is	be	AUX
ejpam-1097	163	5	an	an	DET
ejpam-1097	163	6	x	x	SYM
ejpam-1097	163	7	-supplement	-supplement	NOUN
ejpam-1097	163	8	of	of	ADP
ejpam-1097	163	9	a	a	PRON
ejpam-1097	163	10	in	in	ADP
ejpam-1097	163	11	n	n	NOUN
ejpam-1097	164	1	and	and	CCONJ
ejpam-1097	164	2	it	it	PRON
ejpam-1097	164	3	is	be	AUX
ejpam-1097	164	4	a	a	DET
ejpam-1097	164	5	direct	direct	ADJ
ejpam-1097	164	6	summand	summand	NOUN
ejpam-1097	164	7	of	of	ADP
ejpam-1097	164	8	n	n	PROPN
ejpam-1097	164	9	.	.	PUNCT
ejpam-1097	165	1	hence	hence	ADV
ejpam-1097	165	2	n	n	ADV
ejpam-1097	165	3	is	be	AUX
ejpam-1097	165	4	x	x	PUNCT
ejpam-1097	165	5	-⊕supplemented	-⊕supplemented	ADJ
ejpam-1097	165	6	.	.	PUNCT
ejpam-1097	166	1	corollary	corollary	ADJ
ejpam-1097	166	2	2	2	NUM
ejpam-1097	166	3	.	.	PUNCT
ejpam-1097	167	1	let	let	VERB
ejpam-1097	167	2	m	m	PRON
ejpam-1097	167	3	be	be	AUX
ejpam-1097	167	4	an	an	DET
ejpam-1097	167	5	r	r	NOUN
ejpam-1097	167	6	-	-	PUNCT
ejpam-1097	167	7	module	module	NOUN
ejpam-1097	167	8	and	and	CCONJ
ejpam-1097	167	9	n	n	CCONJ
ejpam-1097	167	10	be	be	AUX
ejpam-1097	167	11	a	a	DET
ejpam-1097	167	12	fully	fully	ADV
ejpam-1097	167	13	invariant	invariant	ADJ
ejpam-1097	167	14	submodule	submodule	NOUN
ejpam-1097	167	15	of	of	ADP
ejpam-1097	167	16	m.	m.	NOUN
ejpam-1097	167	17	if	if	SCONJ
ejpam-1097	167	18	m	m	NOUN
ejpam-1097	167	19	is	be	AUX
ejpam-1097	167	20	x	x	PRON
ejpam-1097	167	21	-⊕supplemented	-⊕supplemented	ADJ
ejpam-1097	167	22	,	,	PUNCT
ejpam-1097	167	23	then	then	ADV
ejpam-1097	167	24	m	m	PROPN
ejpam-1097	167	25	/	/	SYM
ejpam-1097	167	26	n	n	PROPN
ejpam-1097	167	27	is	be	AUX
ejpam-1097	167	28	x	x	PUNCT
ejpam-1097	167	29	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	167	30	.	.	PUNCT
ejpam-1097	168	1	proof	proof	NOUN
ejpam-1097	168	2	.	.	PUNCT
ejpam-1097	169	1	by	by	ADP
ejpam-1097	169	2	proposition	proposition	NOUN
ejpam-1097	169	3	2	2	NUM
ejpam-1097	169	4	.	.	X
ejpam-1097	169	5	recall	recall	VERB
ejpam-1097	169	6	that	that	SCONJ
ejpam-1097	169	7	a	a	DET
ejpam-1097	169	8	module	module	NOUN
ejpam-1097	169	9	m	m	NOUN
ejpam-1097	169	10	is	be	AUX
ejpam-1097	169	11	a	a	DET
ejpam-1097	169	12	duo	duo	NOUN
ejpam-1097	169	13	module	module	NOUN
ejpam-1097	169	14	,	,	PUNCT
ejpam-1097	169	15	if	if	SCONJ
ejpam-1097	169	16	every	every	DET
ejpam-1097	169	17	submodule	submodule	NOUN
ejpam-1097	169	18	of	of	ADP
ejpam-1097	169	19	m	m	PROPN
ejpam-1097	169	20	is	be	AUX
ejpam-1097	169	21	a	a	DET
ejpam-1097	169	22	fully	fully	ADV
ejpam-1097	169	23	invariant	invariant	ADJ
ejpam-1097	169	24	submodule	submodule	NOUN
ejpam-1097	169	25	of	of	ADP
ejpam-1097	169	26	m	m	PROPN
ejpam-1097	169	27	.	.	PUNCT
ejpam-1097	170	1	corollary	corollary	ADJ
ejpam-1097	170	2	3	3	X
ejpam-1097	170	3	.	.	PUNCT
ejpam-1097	171	1	let	let	VERB
ejpam-1097	171	2	m	m	PRON
ejpam-1097	171	3	be	be	AUX
ejpam-1097	171	4	an	an	DET
ejpam-1097	171	5	x	x	ADV
ejpam-1097	171	6	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	171	7	duo	duo	NOUN
ejpam-1097	171	8	module	module	NOUN
ejpam-1097	171	9	,	,	PUNCT
ejpam-1097	171	10	then	then	ADV
ejpam-1097	171	11	every	every	DET
ejpam-1097	171	12	direct	direct	ADJ
ejpam-1097	171	13	summand	summand	NOUN
ejpam-1097	171	14	of	of	ADP
ejpam-1097	171	15	m	m	PROPN
ejpam-1097	171	16	is	be	AUX
ejpam-1097	171	17	x	x	PUNCT
ejpam-1097	171	18	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	171	19	.	.	PUNCT
ejpam-1097	172	1	proof	proof	NOUN
ejpam-1097	172	2	.	.	PUNCT
ejpam-1097	173	1	by	by	ADP
ejpam-1097	173	2	corollary	corollary	ADJ
ejpam-1097	173	3	2	2	NUM
ejpam-1097	173	4	.	.	PUNCT
ejpam-1097	173	5	definition	definition	NOUN
ejpam-1097	173	6	1	1	NUM
ejpam-1097	173	7	.	.	PUNCT
ejpam-1097	174	1	a	a	DET
ejpam-1097	174	2	module	module	NOUN
ejpam-1097	174	3	m	m	NOUN
ejpam-1097	174	4	is	be	AUX
ejpam-1097	174	5	said	say	VERB
ejpam-1097	174	6	to	to	PART
ejpam-1097	174	7	have	have	VERB
ejpam-1097	174	8	the	the	DET
ejpam-1097	174	9	(	(	PUNCT
ejpam-1097	174	10	finite	finite	PROPN
ejpam-1097	174	11	)	)	PUNCT
ejpam-1097	174	12	strong	strong	ADJ
ejpam-1097	174	13	internal	internal	ADJ
ejpam-1097	174	14	exchange	exchange	NOUN
ejpam-1097	174	15	property	property	NOUN
ejpam-1097	174	16	if	if	SCONJ
ejpam-1097	174	17	for	for	SCONJ
ejpam-1097	174	18	every	every	DET
ejpam-1097	174	19	(	(	PUNCT
ejpam-1097	174	20	finite	finite	PROPN
ejpam-1097	174	21	)	)	PUNCT
ejpam-1097	174	22	index	index	NOUN
ejpam-1097	174	23	set	set	VERB
ejpam-1097	174	24	i	i	PRON
ejpam-1097	174	25	,	,	PUNCT
ejpam-1097	174	26	whenever	whenever	SCONJ
ejpam-1097	174	27	m	m	VERB
ejpam-1097	174	28	=	=	ADJ
ejpam-1097	174	29	k+(⊕i∈iai	k+(⊕i∈iai	PROPN
ejpam-1097	174	30	)	)	PUNCT
ejpam-1097	174	31	for	for	ADP
ejpam-1097	174	32	a	a	DET
ejpam-1097	174	33	direct	direct	ADJ
ejpam-1097	174	34	summand	summand	NOUN
ejpam-1097	174	35	k	k	PROPN
ejpam-1097	174	36	of	of	ADP
ejpam-1097	174	37	m	m	PROPN
ejpam-1097	174	38	and	and	CCONJ
ejpam-1097	174	39	modules	module	NOUN
ejpam-1097	174	40	ai	ai	VERB
ejpam-1097	174	41	,	,	PUNCT
ejpam-1097	174	42	then	then	ADV
ejpam-1097	174	43	m	m	VERB
ejpam-1097	174	44	=	=	SYM
ejpam-1097	174	45	k	k	PROPN
ejpam-1097	174	46	⊕	⊕	PROPN
ejpam-1097	174	47	(	(	PUNCT
ejpam-1097	174	48	⊕i∈i	⊕i∈i	X
ejpam-1097	174	49	bi	bi	NOUN
ejpam-1097	174	50	)	)	PUNCT
ejpam-1097	174	51	for	for	ADP
ejpam-1097	174	52	submodules	submodule	NOUN
ejpam-1097	174	53	bi	bi	NOUN
ejpam-1097	174	54	of	of	ADP
ejpam-1097	174	55	ai	ai	PROPN
ejpam-1097	174	56	.	.	PUNCT
ejpam-1097	175	1	it	it	PRON
ejpam-1097	175	2	is	be	AUX
ejpam-1097	175	3	clear	clear	ADJ
ejpam-1097	175	4	that	that	SCONJ
ejpam-1097	175	5	if	if	SCONJ
ejpam-1097	175	6	a	a	DET
ejpam-1097	175	7	module	module	NOUN
ejpam-1097	175	8	m	m	VERB
ejpam-1097	175	9	has	have	VERB
ejpam-1097	175	10	the	the	DET
ejpam-1097	175	11	(	(	PUNCT
ejpam-1097	175	12	finite	finite	PROPN
ejpam-1097	175	13	)	)	PUNCT
ejpam-1097	175	14	strong	strong	ADJ
ejpam-1097	175	15	internal	internal	ADJ
ejpam-1097	175	16	exchange	exchange	NOUN
ejpam-1097	175	17	property	property	NOUN
ejpam-1097	175	18	,	,	PUNCT
ejpam-1097	175	19	then	then	ADV
ejpam-1097	175	20	m	m	PROPN
ejpam-1097	175	21	has	have	VERB
ejpam-1097	175	22	the	the	DET
ejpam-1097	175	23	(	(	PUNCT
ejpam-1097	175	24	finite	finite	ADJ
ejpam-1097	175	25	)	)	PUNCT
ejpam-1097	175	26	internal	internal	ADJ
ejpam-1097	175	27	exchange	exchange	NOUN
ejpam-1097	175	28	property	property	NOUN
ejpam-1097	175	29	.	.	PUNCT
ejpam-1097	176	1	theorem	theorem	NOUN
ejpam-1097	176	2	3	3	X
ejpam-1097	176	3	.	.	PUNCT
ejpam-1097	177	1	let	let	VERB
ejpam-1097	177	2	m	m	PRON
ejpam-1097	177	3	be	be	AUX
ejpam-1097	177	4	an	an	DET
ejpam-1097	177	5	x	x	NOUN
ejpam-1097	177	6	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	177	7	module	module	NOUN
ejpam-1097	177	8	with	with	ADP
ejpam-1097	177	9	the	the	DET
ejpam-1097	177	10	finite	finite	ADJ
ejpam-1097	177	11	strong	strong	ADJ
ejpam-1097	177	12	internal	internal	ADJ
ejpam-1097	177	13	exchange	exchange	NOUN
ejpam-1097	177	14	property	property	NOUN
ejpam-1097	177	15	.	.	PUNCT
ejpam-1097	178	1	then	then	ADV
ejpam-1097	178	2	any	any	DET
ejpam-1097	178	3	direct	direct	ADJ
ejpam-1097	178	4	summand	summand	NOUN
ejpam-1097	178	5	of	of	ADP
ejpam-1097	178	6	m	m	PROPN
ejpam-1097	178	7	is	be	AUX
ejpam-1097	178	8	x	x	PUNCT
ejpam-1097	178	9	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	178	10	.	.	PUNCT
ejpam-1097	179	1	proof	proof	NOUN
ejpam-1097	179	2	.	.	PUNCT
ejpam-1097	180	1	let	let	VERB
ejpam-1097	180	2	n	n	PRON
ejpam-1097	180	3	be	be	AUX
ejpam-1097	180	4	a	a	DET
ejpam-1097	180	5	direct	direct	ADJ
ejpam-1097	180	6	summand	summand	NOUN
ejpam-1097	180	7	of	of	ADP
ejpam-1097	180	8	m	m	PROPN
ejpam-1097	180	9	.	.	PUNCT
ejpam-1097	181	1	thus	thus	ADV
ejpam-1097	181	2	m	m	VERB
ejpam-1097	181	3	=	=	SYM
ejpam-1097	181	4	n	n	PRON
ejpam-1097	181	5	⊕	⊕	PROPN
ejpam-1097	181	6	n	n	ADV
ejpam-1097	181	7	′	′	NUM
ejpam-1097	181	8	for	for	ADP
ejpam-1097	181	9	some	some	DET
ejpam-1097	181	10	submodule	submodule	NOUN
ejpam-1097	181	11	n	n	PART
ejpam-1097	181	12	′of	′of	PROPN
ejpam-1097	181	13	m	m	VERB
ejpam-1097	181	14	.	.	PUNCT
ejpam-1097	182	1	let	let	VERB
ejpam-1097	182	2	a	a	DET
ejpam-1097	182	3	∈	∈	PROPN
ejpam-1097	182	4	b(n	b(n	NOUN
ejpam-1097	182	5	,	,	PUNCT
ejpam-1097	182	6	x	x	NOUN
ejpam-1097	182	7	)	)	PUNCT
ejpam-1097	182	8	.	.	PUNCT
ejpam-1097	183	1	by	by	ADP
ejpam-1097	183	2	lemma	lemma	PROPN
ejpam-1097	183	3	1	1	NUM
ejpam-1097	183	4	,	,	PUNCT
ejpam-1097	183	5	a⊕	a⊕	PRON
ejpam-1097	183	6	n	n	CCONJ
ejpam-1097	183	7	′	′	NUM
ejpam-1097	183	8	∈	∈	PROPN
ejpam-1097	183	9	b(m	b(m	PROPN
ejpam-1097	183	10	,	,	PUNCT
ejpam-1097	183	11	x	x	PROPN
ejpam-1097	183	12	)	)	PUNCT
ejpam-1097	183	13	.	.	PUNCT
ejpam-1097	184	1	since	since	SCONJ
ejpam-1097	184	2	m	m	PROPN
ejpam-1097	184	3	is	be	AUX
ejpam-1097	184	4	x	x	PUNCT
ejpam-1097	184	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	184	6	,	,	PUNCT
ejpam-1097	184	7	there	there	PRON
ejpam-1097	184	8	exists	exist	VERB
ejpam-1097	184	9	a	a	DET
ejpam-1097	184	10	direct	direct	ADJ
ejpam-1097	184	11	summand	summand	NOUN
ejpam-1097	184	12	k	k	PROPN
ejpam-1097	184	13	of	of	ADP
ejpam-1097	184	14	m	m	PROPN
ejpam-1097	184	15	with	with	ADP
ejpam-1097	184	16	k	k	PROPN
ejpam-1097	184	17	∈	∈	PROPN
ejpam-1097	184	18	b(m	b(m	PROPN
ejpam-1097	184	19	,	,	PUNCT
ejpam-1097	184	20	x	x	X
ejpam-1097	184	21	)	)	PUNCT
ejpam-1097	184	22	such	such	ADJ
ejpam-1097	184	23	that	that	SCONJ
ejpam-1097	184	24	m	m	VERB
ejpam-1097	185	1	=	=	SYM
ejpam-1097	185	2	k	k	X
ejpam-1097	186	1	+	+	CCONJ
ejpam-1097	186	2	(	(	PUNCT
ejpam-1097	186	3	a⊕	a⊕	PROPN
ejpam-1097	186	4	n	n	NOUN
ejpam-1097	186	5	′	′	NUM
ejpam-1097	186	6	)	)	PUNCT
ejpam-1097	186	7	and	and	CCONJ
ejpam-1097	186	8	(	(	PUNCT
ejpam-1097	186	9	a⊕n	a⊕n	PROPN
ejpam-1097	186	10	′)∩k	′)∩k	PROPN
ejpam-1097	186	11	≪	≪	PROPN
ejpam-1097	186	12	k	k	PROPN
ejpam-1097	186	13	.	.	PUNCT
ejpam-1097	187	1	since	since	SCONJ
ejpam-1097	187	2	m	m	PROPN
ejpam-1097	187	3	has	have	VERB
ejpam-1097	187	4	the	the	DET
ejpam-1097	187	5	finite	finite	ADJ
ejpam-1097	187	6	strong	strong	ADJ
ejpam-1097	187	7	internal	internal	ADJ
ejpam-1097	187	8	exchange	exchange	NOUN
ejpam-1097	187	9	property	property	NOUN
ejpam-1097	187	10	,	,	PUNCT
ejpam-1097	187	11	m	m	VERB
ejpam-1097	187	12	=	=	SYM
ejpam-1097	187	13	k	k	X
ejpam-1097	187	14	⊕n1⊕n	⊕n1⊕n	PUNCT
ejpam-1097	187	15	′1	′1	ADP
ejpam-1097	187	16	such	such	ADJ
ejpam-1097	187	17	that	that	SCONJ
ejpam-1097	187	18	n1	n1	PROPN
ejpam-1097	187	19	⊆	⊆	NUM
ejpam-1097	187	20	a	a	PRON
ejpam-1097	187	21	and	and	CCONJ
ejpam-1097	187	22	n	n	CCONJ
ejpam-1097	187	23	′1	′1	ADP
ejpam-1097	187	24	⊆	⊆	NUM
ejpam-1097	187	25	n	n	DET
ejpam-1097	187	26	′.	′.	NOUN
ejpam-1097	187	27	by	by	ADP
ejpam-1097	187	28	modularity	modularity	NOUN
ejpam-1097	187	29	,	,	PUNCT
ejpam-1097	187	30	n	n	PROPN
ejpam-1097	187	31	=	=	SYM
ejpam-1097	187	32	n1⊕	n1⊕	PROPN
ejpam-1097	187	33	(	(	PUNCT
ejpam-1097	187	34	n	n	X
ejpam-1097	187	35	∩	∩	NOUN
ejpam-1097	187	36	(	(	PUNCT
ejpam-1097	187	37	k	k	PROPN
ejpam-1097	187	38	⊕	⊕	PROPN
ejpam-1097	187	39	n	n	PRON
ejpam-1097	187	40	′1	′1	NOUN
ejpam-1097	187	41	)	)	PUNCT
ejpam-1097	187	42	)	)	PUNCT
ejpam-1097	187	43	.	.	PUNCT
ejpam-1097	188	1	by	by	ADP
ejpam-1097	188	2	lemma	lemma	PROPN
ejpam-1097	188	3	2	2	PROPN
ejpam-1097	188	4	and	and	CCONJ
ejpam-1097	188	5	[	[	X
ejpam-1097	188	6	7	7	NUM
ejpam-1097	188	7	,	,	PUNCT
ejpam-1097	188	8	lemma	lemma	PROPN
ejpam-1097	188	9	3.1	3.1	NUM
ejpam-1097	188	10	]	]	PUNCT
ejpam-1097	188	11	,	,	PUNCT
ejpam-1097	188	12	n	n	CCONJ
ejpam-1097	188	13	∩	∩	NOUN
ejpam-1097	188	14	(	(	PUNCT
ejpam-1097	188	15	k	k	PROPN
ejpam-1097	188	16	⊕	⊕	PROPN
ejpam-1097	188	17	n	n	PRON
ejpam-1097	188	18	′1	′1	NOUN
ejpam-1097	188	19	)	)	PUNCT
ejpam-1097	188	20	∈	∈	PROPN
ejpam-1097	188	21	b(n	b(n	NOUN
ejpam-1097	188	22	,	,	PUNCT
ejpam-1097	188	23	x	x	PROPN
ejpam-1097	188	24	)	)	PUNCT
ejpam-1097	188	25	.	.	PUNCT
ejpam-1097	189	1	as	as	ADP
ejpam-1097	189	2	m	m	PROPN
ejpam-1097	189	3	=	=	PRON
ejpam-1097	189	4	a+	a+	PUNCT
ejpam-1097	189	5	(	(	PUNCT
ejpam-1097	189	6	k	k	PROPN
ejpam-1097	189	7	⊕	⊕	PROPN
ejpam-1097	189	8	n	n	PRON
ejpam-1097	189	9	′1	′1	NOUN
ejpam-1097	189	10	)	)	PUNCT
ejpam-1097	189	11	,	,	PUNCT
ejpam-1097	189	12	n	n	NOUN
ejpam-1097	189	13	=	=	PRON
ejpam-1097	189	14	a+	a+	PUNCT
ejpam-1097	189	15	(	(	PUNCT
ejpam-1097	189	16	n	n	CCONJ
ejpam-1097	189	17	∩	∩	NOUN
ejpam-1097	189	18	(	(	PUNCT
ejpam-1097	189	19	k	k	PROPN
ejpam-1097	189	20	′	′	PROPN
ejpam-1097	189	21	⊕	⊕	PROPN
ejpam-1097	189	22	n	n	PRON
ejpam-1097	189	23	′1	′1	NOUN
ejpam-1097	189	24	)	)	PUNCT
ejpam-1097	189	25	.	.	PUNCT
ejpam-1097	190	1	since	since	SCONJ
ejpam-1097	190	2	(	(	PUNCT
ejpam-1097	190	3	a⊕n	a⊕n	PROPN
ejpam-1097	190	4	′)∩k	′)∩k	PROPN
ejpam-1097	190	5	≪	≪	PROPN
ejpam-1097	190	6	k	k	X
ejpam-1097	190	7	,	,	PUNCT
ejpam-1097	190	8	by	by	ADP
ejpam-1097	190	9	lemma	lemma	PROPN
ejpam-1097	190	10	3	3	NUM
ejpam-1097	190	11	,	,	PUNCT
ejpam-1097	190	12	a∩(k⊕n	a∩(k⊕n	ADP
ejpam-1097	190	13	′)≪	′)≪	NOUN
ejpam-1097	190	14	n	n	CCONJ
ejpam-1097	190	15	∩(k⊕n	∩(k⊕n	PROPN
ejpam-1097	190	16	′	′	NUM
ejpam-1097	190	17	)	)	PUNCT
ejpam-1097	190	18	.	.	PUNCT
ejpam-1097	191	1	thus	thus	ADV
ejpam-1097	191	2	a∩(k⊕n	a∩(k⊕n	X
ejpam-1097	191	3	′1)≪	′1)≪	PROPN
ejpam-1097	191	4	n	n	ADV
ejpam-1097	191	5	∩(k⊕n	∩(k⊕n	PROPN
ejpam-1097	191	6	′	′	NUM
ejpam-1097	191	7	)	)	PUNCT
ejpam-1097	191	8	.	.	PUNCT
ejpam-1097	192	1	since	since	SCONJ
ejpam-1097	192	2	n	n	NOUN
ejpam-1097	192	3	∩	∩	NOUN
ejpam-1097	192	4	(	(	PUNCT
ejpam-1097	192	5	k	k	PROPN
ejpam-1097	192	6	⊕	⊕	PROPN
ejpam-1097	192	7	n	n	PROPN
ejpam-1097	192	8	′1)≤	′1)≤	PROPN
ejpam-1097	192	9	⊕	⊕	PROPN
ejpam-1097	192	10	m	m	PROPN
ejpam-1097	192	11	,	,	PUNCT
ejpam-1097	192	12	a∩	a∩	PROPN
ejpam-1097	192	13	(	(	PUNCT
ejpam-1097	192	14	k	k	PROPN
ejpam-1097	192	15	⊕	⊕	PROPN
ejpam-1097	192	16	n	n	CCONJ
ejpam-1097	192	17	′1)≪	′1)≪	PROPN
ejpam-1097	192	18	n	n	PART
ejpam-1097	192	19	∩	∩	NOUN
ejpam-1097	192	20	(	(	PUNCT
ejpam-1097	192	21	k	k	PROPN
ejpam-1097	192	22	⊕	⊕	PROPN
ejpam-1097	192	23	n	n	PRON
ejpam-1097	192	24	′1	′1	NOUN
ejpam-1097	192	25	)	)	PUNCT
ejpam-1097	192	26	.	.	PUNCT
ejpam-1097	193	1	hence	hence	ADV
ejpam-1097	193	2	n	n	ADV
ejpam-1097	193	3	is	be	AUX
ejpam-1097	193	4	x	x	PUNCT
ejpam-1097	193	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	193	6	.	.	PUNCT
ejpam-1097	194	1	if	if	SCONJ
ejpam-1097	194	2	in	in	ADP
ejpam-1097	194	3	setb(m	setb(m	PROPN
ejpam-1097	194	4	,	,	PUNCT
ejpam-1097	194	5	x	x	PROPN
ejpam-1097	194	6	)	)	PUNCT
ejpam-1097	194	7	,	,	PUNCT
ejpam-1097	194	8	we	we	PRON
ejpam-1097	194	9	take	take	VERB
ejpam-1097	194	10	x	x	ADJ
ejpam-1097	194	11	=	=	VERB
ejpam-1097	194	12	m	m	X
ejpam-1097	194	13	,	,	PUNCT
ejpam-1097	194	14	thenb(m	thenb(m	ADV
ejpam-1097	194	15	,	,	PUNCT
ejpam-1097	194	16	x	x	PUNCT
ejpam-1097	194	17	)	)	PUNCT
ejpam-1097	194	18	coincides	coincide	VERB
ejpam-1097	194	19	with	with	ADP
ejpam-1097	194	20	the	the	DET
ejpam-1097	194	21	set	set	NOUN
ejpam-1097	194	22	of	of	ADP
ejpam-1097	194	23	all	all	DET
ejpam-1097	194	24	submodules	submodule	NOUN
ejpam-1097	194	25	of	of	ADP
ejpam-1097	194	26	m	m	PROPN
ejpam-1097	194	27	.	.	PUNCT
ejpam-1097	195	1	therefore	therefore	ADV
ejpam-1097	195	2	we	we	PRON
ejpam-1097	195	3	obtain	obtain	VERB
ejpam-1097	195	4	the	the	DET
ejpam-1097	195	5	following	follow	VERB
ejpam-1097	195	6	corollary	corollary	ADJ
ejpam-1097	195	7	:	:	PUNCT
ejpam-1097	195	8	corollary	corollary	ADJ
ejpam-1097	195	9	4	4	X
ejpam-1097	195	10	.	.	PUNCT
ejpam-1097	196	1	let	let	VERB
ejpam-1097	196	2	m	m	PRON
ejpam-1097	196	3	be	be	AUX
ejpam-1097	196	4	a	a	DET
ejpam-1097	196	5	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	196	6	module	module	NOUN
ejpam-1097	196	7	with	with	ADP
ejpam-1097	196	8	the	the	DET
ejpam-1097	196	9	finite	finite	ADJ
ejpam-1097	196	10	strong	strong	ADJ
ejpam-1097	196	11	internal	internal	ADJ
ejpam-1097	196	12	exchange	exchange	NOUN
ejpam-1097	196	13	property	property	NOUN
ejpam-1097	196	14	.	.	PUNCT
ejpam-1097	197	1	then	then	ADV
ejpam-1097	197	2	any	any	DET
ejpam-1097	197	3	direct	direct	ADJ
ejpam-1097	197	4	summand	summand	NOUN
ejpam-1097	197	5	of	of	ADP
ejpam-1097	197	6	m	m	PROPN
ejpam-1097	197	7	is	be	AUX
ejpam-1097	197	8	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	197	9	.	.	PUNCT
ejpam-1097	198	1	t.	t.	NOUN
ejpam-1097	198	2	amouzegar	amouzegar	NOUN
ejpam-1097	198	3	,	,	PUNCT
ejpam-1097	198	4	y.	y.	PROPN
ejpam-1097	198	5	talebi	talebi	PROPN
ejpam-1097	198	6	/	/	SYM
ejpam-1097	198	7	eur	eur	PROPN
ejpam-1097	198	8	.	.	PUNCT
ejpam-1097	199	1	j.	j.	PROPN
ejpam-1097	199	2	pure	pure	PROPN
ejpam-1097	199	3	appl	appl	PROPN
ejpam-1097	199	4	.	.	PROPN
ejpam-1097	199	5	math	math	PROPN
ejpam-1097	199	6	,	,	PUNCT
ejpam-1097	199	7	5	5	NUM
ejpam-1097	199	8	(	(	PUNCT
ejpam-1097	199	9	2012	2012	NUM
ejpam-1097	199	10	)	)	PUNCT
ejpam-1097	199	11	,	,	PUNCT
ejpam-1097	199	12	108	108	NUM
ejpam-1097	199	13	-	-	SYM
ejpam-1097	199	14	115	115	NUM
ejpam-1097	199	15	113	113	NUM
ejpam-1097	199	16	4	4	NUM
ejpam-1097	199	17	.	.	PUNCT
ejpam-1097	200	1	completely	completely	ADV
ejpam-1097	200	2	x	x	SYM
ejpam-1097	200	3	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	200	4	modules	module	NOUN
ejpam-1097	200	5	let	let	VERB
ejpam-1097	200	6	x	x	PRON
ejpam-1097	200	7	and	and	CCONJ
ejpam-1097	200	8	m	m	AUX
ejpam-1097	200	9	be	be	VERB
ejpam-1097	200	10	r	r	NOUN
ejpam-1097	200	11	-	-	PUNCT
ejpam-1097	200	12	modules	module	NOUN
ejpam-1097	200	13	.	.	PUNCT
ejpam-1097	201	1	we	we	PRON
ejpam-1097	201	2	call	call	VERB
ejpam-1097	201	3	a	a	DET
ejpam-1097	201	4	module	module	NOUN
ejpam-1097	201	5	m	m	VERB
ejpam-1097	201	6	completely	completely	ADV
ejpam-1097	201	7	x	x	ADP
ejpam-1097	201	8	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	201	9	if	if	SCONJ
ejpam-1097	201	10	every	every	DET
ejpam-1097	201	11	direct	direct	ADJ
ejpam-1097	201	12	summand	summand	NOUN
ejpam-1097	201	13	n	n	PROPN
ejpam-1097	201	14	of	of	ADP
ejpam-1097	201	15	m	m	PROPN
ejpam-1097	201	16	with	with	ADP
ejpam-1097	201	17	n	n	PROPN
ejpam-1097	201	18	∈b(m	∈b(m	PROPN
ejpam-1097	201	19	,	,	PUNCT
ejpam-1097	201	20	x	x	PUNCT
ejpam-1097	201	21	)	)	PUNCT
ejpam-1097	201	22	is	be	AUX
ejpam-1097	201	23	x	x	PUNCT
ejpam-1097	201	24	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	201	25	.	.	PUNCT
ejpam-1097	202	1	recall	recall	VERB
ejpam-1097	202	2	that	that	SCONJ
ejpam-1097	202	3	a	a	DET
ejpam-1097	202	4	module	module	NOUN
ejpam-1097	202	5	m	m	VERB
ejpam-1097	202	6	has	have	VERB
ejpam-1097	202	7	b(m	b(m	PROPN
ejpam-1097	202	8	,	,	PUNCT
ejpam-1097	202	9	x	x	NOUN
ejpam-1097	202	10	)	)	PUNCT
ejpam-1097	202	11	-(d3	-(d3	NUM
ejpam-1097	202	12	)	)	PUNCT
ejpam-1097	202	13	condition	condition	NOUN
ejpam-1097	202	14	if	if	SCONJ
ejpam-1097	202	15	for	for	ADP
ejpam-1097	202	16	all	all	DET
ejpam-1097	202	17	a	a	DET
ejpam-1097	202	18	∈	∈	PROPN
ejpam-1097	202	19	b(m	b(m	NOUN
ejpam-1097	202	20	,	,	PUNCT
ejpam-1097	202	21	x	x	SYM
ejpam-1097	202	22	)	)	PUNCT
ejpam-1097	202	23	and	and	CCONJ
ejpam-1097	202	24	direct	direct	ADJ
ejpam-1097	202	25	summand	summand	PROPN
ejpam-1097	202	26	b	b	PROPN
ejpam-1097	202	27	of	of	ADP
ejpam-1097	202	28	m	m	PRON
ejpam-1097	202	29	,	,	PUNCT
ejpam-1097	202	30	if	if	SCONJ
ejpam-1097	202	31	a	a	PRON
ejpam-1097	202	32	is	be	AUX
ejpam-1097	202	33	a	a	DET
ejpam-1097	202	34	direct	direct	ADJ
ejpam-1097	202	35	summand	summand	NOUN
ejpam-1097	202	36	of	of	ADP
ejpam-1097	202	37	m	m	PROPN
ejpam-1097	202	38	and	and	CCONJ
ejpam-1097	202	39	m	m	PROPN
ejpam-1097	202	40	=	=	SYM
ejpam-1097	202	41	a+	a+	PUNCT
ejpam-1097	202	42	b	b	NOUN
ejpam-1097	202	43	then	then	ADV
ejpam-1097	202	44	a	a	DET
ejpam-1097	202	45	∩	∩	ADJ
ejpam-1097	202	46	b	b	NOUN
ejpam-1097	202	47	is	be	AUX
ejpam-1097	202	48	a	a	DET
ejpam-1097	202	49	direct	direct	ADJ
ejpam-1097	202	50	summand	summand	NOUN
ejpam-1097	202	51	of	of	ADP
ejpam-1097	202	52	m	m	PROPN
ejpam-1097	203	1	[	[	X
ejpam-1097	203	2	5	5	NUM
ejpam-1097	203	3	]	]	PUNCT
ejpam-1097	203	4	.	.	PUNCT
ejpam-1097	204	1	proposition	proposition	NOUN
ejpam-1097	204	2	3	3	X
ejpam-1097	204	3	.	.	PUNCT
ejpam-1097	205	1	let	let	VERB
ejpam-1097	205	2	m	m	PRON
ejpam-1097	205	3	be	be	AUX
ejpam-1097	205	4	an	an	DET
ejpam-1097	205	5	x	x	NOUN
ejpam-1097	205	6	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	205	7	module	module	NOUN
ejpam-1097	205	8	with	with	ADP
ejpam-1097	205	9	b(m	b(m	PROPN
ejpam-1097	205	10	,	,	PUNCT
ejpam-1097	205	11	x	x	NOUN
ejpam-1097	205	12	)	)	PUNCT
ejpam-1097	205	13	-(d3	-(d3	NUM
ejpam-1097	205	14	)	)	PUNCT
ejpam-1097	205	15	.	.	PUNCT
ejpam-1097	206	1	then	then	ADV
ejpam-1097	206	2	m	m	PROPN
ejpam-1097	206	3	is	be	AUX
ejpam-1097	206	4	completely	completely	ADV
ejpam-1097	206	5	x	x	SYM
ejpam-1097	206	6	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	206	7	.	.	PUNCT
ejpam-1097	207	1	proof	proof	NOUN
ejpam-1097	207	2	.	.	PUNCT
ejpam-1097	208	1	let	let	VERB
ejpam-1097	208	2	n	n	PRON
ejpam-1097	208	3	be	be	AUX
ejpam-1097	208	4	a	a	DET
ejpam-1097	208	5	direct	direct	ADJ
ejpam-1097	208	6	summand	summand	NOUN
ejpam-1097	208	7	of	of	ADP
ejpam-1097	208	8	m	m	PROPN
ejpam-1097	208	9	and	and	CCONJ
ejpam-1097	208	10	a	a	DET
ejpam-1097	208	11	a	a	DET
ejpam-1097	208	12	submodule	submodule	NOUN
ejpam-1097	208	13	of	of	ADP
ejpam-1097	208	14	n	n	PRON
ejpam-1097	208	15	such	such	ADJ
ejpam-1097	208	16	that	that	SCONJ
ejpam-1097	208	17	n	n	NUM
ejpam-1097	208	18	∈	∈	PROPN
ejpam-1097	208	19	b(m	b(m	PROPN
ejpam-1097	208	20	,	,	PUNCT
ejpam-1097	208	21	x	x	PROPN
ejpam-1097	208	22	)	)	PUNCT
ejpam-1097	208	23	and	and	CCONJ
ejpam-1097	208	24	a	a	DET
ejpam-1097	208	25	∈	∈	PROPN
ejpam-1097	208	26	b(n	b(n	NOUN
ejpam-1097	208	27	,	,	PUNCT
ejpam-1097	208	28	x	x	PROPN
ejpam-1097	208	29	)	)	PUNCT
ejpam-1097	208	30	.	.	PUNCT
ejpam-1097	209	1	we	we	PRON
ejpam-1097	209	2	show	show	VERB
ejpam-1097	209	3	that	that	SCONJ
ejpam-1097	209	4	a	a	PRON
ejpam-1097	209	5	has	have	VERB
ejpam-1097	209	6	an	an	DET
ejpam-1097	209	7	x	x	SYM
ejpam-1097	209	8	-supplement	-supplement	NOUN
ejpam-1097	209	9	in	in	ADP
ejpam-1097	209	10	n	n	CCONJ
ejpam-1097	209	11	that	that	PRON
ejpam-1097	209	12	is	be	AUX
ejpam-1097	209	13	a	a	DET
ejpam-1097	209	14	direct	direct	ADJ
ejpam-1097	209	15	summand	summand	NOUN
ejpam-1097	209	16	of	of	ADP
ejpam-1097	209	17	n	n	PROPN
ejpam-1097	209	18	.	.	PUNCT
ejpam-1097	210	1	we	we	PRON
ejpam-1097	210	2	have	have	VERB
ejpam-1097	210	3	m	m	NOUN
ejpam-1097	210	4	=	=	SYM
ejpam-1097	210	5	n	n	PROPN
ejpam-1097	210	6	⊕	⊕	PROPN
ejpam-1097	210	7	n	n	ADV
ejpam-1097	210	8	′	′	NUM
ejpam-1097	210	9	for	for	ADP
ejpam-1097	210	10	some	some	DET
ejpam-1097	210	11	submodule	submodule	NOUN
ejpam-1097	210	12	n	n	DET
ejpam-1097	210	13	′	′	NOUN
ejpam-1097	210	14	of	of	ADP
ejpam-1097	210	15	m	m	PROPN
ejpam-1097	210	16	.	.	PUNCT
ejpam-1097	211	1	let	let	VERB
ejpam-1097	212	1	π	π	NOUN
ejpam-1097	212	2	:	:	PUNCT
ejpam-1097	212	3	m	m	VERB
ejpam-1097	212	4	→	→	SYM
ejpam-1097	212	5	n	n	CCONJ
ejpam-1097	212	6	be	be	AUX
ejpam-1097	212	7	the	the	DET
ejpam-1097	212	8	projection	projection	NOUN
ejpam-1097	212	9	along	along	ADP
ejpam-1097	212	10	n	n	PRON
ejpam-1097	212	11	′.	′.	NOUN
ejpam-1097	212	12	since	since	SCONJ
ejpam-1097	212	13	a∈b(n	a∈b(n	PROPN
ejpam-1097	212	14	,	,	PUNCT
ejpam-1097	212	15	x	x	X
ejpam-1097	212	16	)	)	PUNCT
ejpam-1097	212	17	,	,	PUNCT
ejpam-1097	212	18	by	by	ADP
ejpam-1097	212	19	lemma	lemma	PROPN
ejpam-1097	212	20	1(4	1(4	NUM
ejpam-1097	212	21	)	)	PUNCT
ejpam-1097	212	22	,	,	PUNCT
ejpam-1097	212	23	a⊕	a⊕	PROPN
ejpam-1097	212	24	n	n	NOUN
ejpam-1097	212	25	′	′	NUM
ejpam-1097	212	26	=	=	PUNCT
ejpam-1097	212	27	π−1(a	π−1(a	PROPN
ejpam-1097	212	28	)	)	PUNCT
ejpam-1097	213	1	∈b(m	∈b(m	ADJ
ejpam-1097	213	2	,	,	PUNCT
ejpam-1097	213	3	x	x	PROPN
ejpam-1097	213	4	)	)	PUNCT
ejpam-1097	213	5	.	.	PUNCT
ejpam-1097	214	1	since	since	SCONJ
ejpam-1097	214	2	m	m	PROPN
ejpam-1097	214	3	=	=	SYM
ejpam-1097	214	4	a+	a+	PUNCT
ejpam-1097	214	5	n	n	PROPN
ejpam-1097	214	6	+	+	CCONJ
ejpam-1097	214	7	n	n	PRON
ejpam-1097	214	8	′	′	NUM
ejpam-1097	214	9	,	,	PUNCT
ejpam-1097	214	10	a=	a=	X
ejpam-1097	214	11	(	(	PUNCT
ejpam-1097	214	12	a⊕	a⊕	NOUN
ejpam-1097	214	13	n	n	ADP
ejpam-1097	214	14	′)∩	′)∩	NOUN
ejpam-1097	214	15	n	n	DET
ejpam-1097	214	16	∈	∈	PROPN
ejpam-1097	214	17	b(m	b(m	PROPN
ejpam-1097	214	18	,	,	PUNCT
ejpam-1097	214	19	x	x	SYM
ejpam-1097	214	20	)	)	PUNCT
ejpam-1097	214	21	(	(	PUNCT
ejpam-1097	214	22	lemma	lemma	PROPN
ejpam-1097	214	23	2	2	NUM
ejpam-1097	214	24	)	)	PUNCT
ejpam-1097	214	25	.	.	PUNCT
ejpam-1097	215	1	since	since	SCONJ
ejpam-1097	215	2	m	m	PROPN
ejpam-1097	215	3	is	be	AUX
ejpam-1097	215	4	x	x	PUNCT
ejpam-1097	215	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	215	6	,	,	PUNCT
ejpam-1097	215	7	there	there	PRON
ejpam-1097	215	8	exists	exist	VERB
ejpam-1097	215	9	a	a	DET
ejpam-1097	215	10	direct	direct	ADJ
ejpam-1097	215	11	summand	summand	NOUN
ejpam-1097	215	12	b	b	PROPN
ejpam-1097	215	13	of	of	ADP
ejpam-1097	215	14	m	m	PROPN
ejpam-1097	215	15	with	with	ADP
ejpam-1097	215	16	b	b	PROPN
ejpam-1097	215	17	∈b(m	∈b(m	PROPN
ejpam-1097	215	18	,	,	PUNCT
ejpam-1097	215	19	x	x	PROPN
ejpam-1097	215	20	)	)	PUNCT
ejpam-1097	215	21	such	such	ADJ
ejpam-1097	215	22	that	that	SCONJ
ejpam-1097	215	23	m	m	VERB
ejpam-1097	215	24	=	=	SYM
ejpam-1097	215	25	a+b	a+b	NUM
ejpam-1097	215	26	and	and	CCONJ
ejpam-1097	215	27	a∩b≪	a∩b≪	DET
ejpam-1097	215	28	b.	b.	PROPN
ejpam-1097	215	29	then	then	ADV
ejpam-1097	215	30	n	n	PROPN
ejpam-1097	215	31	=	=	SYM
ejpam-1097	215	32	a+(n∩b	a+(n∩b	PROPN
ejpam-1097	215	33	)	)	PUNCT
ejpam-1097	215	34	.	.	PUNCT
ejpam-1097	216	1	again	again	ADV
ejpam-1097	216	2	by	by	ADP
ejpam-1097	216	3	lemma	lemma	PROPN
ejpam-1097	216	4	2	2	NUM
ejpam-1097	216	5	,	,	PUNCT
ejpam-1097	216	6	n	n	PRON
ejpam-1097	216	7	∩	∩	NOUN
ejpam-1097	216	8	b	b	PROPN
ejpam-1097	216	9	∈	∈	PROPN
ejpam-1097	216	10	b(m	b(m	PROPN
ejpam-1097	216	11	,	,	PUNCT
ejpam-1097	216	12	x	x	PROPN
ejpam-1097	216	13	)	)	PUNCT
ejpam-1097	216	14	.	.	PUNCT
ejpam-1097	217	1	furthermore	furthermore	ADV
ejpam-1097	217	2	n	n	PRON
ejpam-1097	217	3	∩	∩	NOUN
ejpam-1097	217	4	b	b	NOUN
ejpam-1097	217	5	is	be	AUX
ejpam-1097	217	6	a	a	DET
ejpam-1097	217	7	direct	direct	ADJ
ejpam-1097	217	8	summand	summand	NOUN
ejpam-1097	217	9	of	of	ADP
ejpam-1097	217	10	m	m	PROPN
ejpam-1097	217	11	because	because	SCONJ
ejpam-1097	217	12	m	m	PROPN
ejpam-1097	217	13	has	have	VERB
ejpam-1097	217	14	b(m	b(m	PROPN
ejpam-1097	217	15	,	,	PUNCT
ejpam-1097	217	16	x	x	NOUN
ejpam-1097	217	17	)	)	PUNCT
ejpam-1097	217	18	-(d3	-(d3	NUM
ejpam-1097	217	19	)	)	PUNCT
ejpam-1097	217	20	.	.	PUNCT
ejpam-1097	218	1	then	then	ADV
ejpam-1097	218	2	a∩	a∩	PROPN
ejpam-1097	218	3	(	(	PUNCT
ejpam-1097	218	4	n	n	CCONJ
ejpam-1097	218	5	∩	∩	ADJ
ejpam-1097	218	6	b	b	X
ejpam-1097	218	7	)	)	PUNCT
ejpam-1097	219	1	=	=	SYM
ejpam-1097	219	2	a∩	a∩	PROPN
ejpam-1097	219	3	b	b	NOUN
ejpam-1097	219	4	is	be	AUX
ejpam-1097	219	5	small	small	ADJ
ejpam-1097	219	6	in	in	ADP
ejpam-1097	219	7	n	n	PRON
ejpam-1097	219	8	∩	∩	ADJ
ejpam-1097	219	9	b	b	NOUN
ejpam-1097	219	10	and	and	CCONJ
ejpam-1097	219	11	by	by	ADP
ejpam-1097	219	12	[	[	X
ejpam-1097	219	13	7	7	NUM
ejpam-1097	219	14	,	,	PUNCT
ejpam-1097	219	15	lemma	lemma	PROPN
ejpam-1097	219	16	3.1	3.1	NUM
ejpam-1097	219	17	]	]	PUNCT
ejpam-1097	219	18	,	,	PUNCT
ejpam-1097	219	19	n	n	SYM
ejpam-1097	219	20	∩	∩	PROPN
ejpam-1097	219	21	b	b	PROPN
ejpam-1097	219	22	∈b(n	∈b(n	PROPN
ejpam-1097	219	23	,	,	PUNCT
ejpam-1097	219	24	x	x	PROPN
ejpam-1097	219	25	)	)	PUNCT
ejpam-1097	219	26	.	.	PUNCT
ejpam-1097	220	1	let	let	VERB
ejpam-1097	220	2	x	x	PRON
ejpam-1097	220	3	and	and	CCONJ
ejpam-1097	220	4	m	m	AUX
ejpam-1097	220	5	be	be	VERB
ejpam-1097	220	6	r	r	NOUN
ejpam-1097	220	7	-	-	PUNCT
ejpam-1097	220	8	modules	module	NOUN
ejpam-1097	220	9	.	.	PUNCT
ejpam-1097	221	1	we	we	PRON
ejpam-1097	221	2	say	say	VERB
ejpam-1097	221	3	n	n	DET
ejpam-1097	221	4	∈	∈	PROPN
ejpam-1097	221	5	b(m	b(m	PROPN
ejpam-1097	221	6	,	,	PUNCT
ejpam-1097	221	7	x	x	X
ejpam-1097	221	8	)	)	PUNCT
ejpam-1097	221	9	is	be	AUX
ejpam-1097	221	10	semisimple	semisimple	NOUN
ejpam-1097	221	11	relative	relative	ADJ
ejpam-1097	221	12	to	to	ADP
ejpam-1097	221	13	the	the	DET
ejpam-1097	221	14	class	class	NOUN
ejpam-1097	221	15	b(m	b(m	PROPN
ejpam-1097	221	16	,	,	PUNCT
ejpam-1097	221	17	x	x	X
ejpam-1097	221	18	)	)	PUNCT
ejpam-1097	221	19	if	if	SCONJ
ejpam-1097	221	20	,	,	PUNCT
ejpam-1097	221	21	for	for	ADP
ejpam-1097	221	22	every	every	DET
ejpam-1097	221	23	submodule	submodule	NOUN
ejpam-1097	221	24	k	k	PROPN
ejpam-1097	221	25	of	of	ADP
ejpam-1097	221	26	n	n	PROPN
ejpam-1097	221	27	with	with	ADP
ejpam-1097	221	28	k	k	PROPN
ejpam-1097	221	29	∈	∈	PROPN
ejpam-1097	221	30	b(n	b(n	PROPN
ejpam-1097	221	31	,	,	PUNCT
ejpam-1097	221	32	x	x	PROPN
ejpam-1097	221	33	)	)	PUNCT
ejpam-1097	221	34	,	,	PUNCT
ejpam-1097	221	35	there	there	PRON
ejpam-1097	221	36	exists	exist	VERB
ejpam-1097	221	37	a	a	DET
ejpam-1097	221	38	submodule	submodule	NOUN
ejpam-1097	221	39	k	k	NOUN
ejpam-1097	221	40	′	′	NOUN
ejpam-1097	221	41	of	of	ADP
ejpam-1097	221	42	n	n	PROPN
ejpam-1097	221	43	with	with	ADP
ejpam-1097	221	44	k	k	PROPN
ejpam-1097	221	45	′	′	PROPN
ejpam-1097	221	46	∈	∈	PROPN
ejpam-1097	221	47	b(n	b(n	NOUN
ejpam-1097	221	48	,	,	PUNCT
ejpam-1097	221	49	x	x	PUNCT
ejpam-1097	221	50	)	)	PUNCT
ejpam-1097	221	51	such	such	ADJ
ejpam-1097	221	52	that	that	SCONJ
ejpam-1097	221	53	n	n	NOUN
ejpam-1097	221	54	=	=	SYM
ejpam-1097	221	55	k	k	PROPN
ejpam-1097	221	56	⊕	⊕	PROPN
ejpam-1097	221	57	k	k	PROPN
ejpam-1097	221	58	′.	′.	PROPN
ejpam-1097	221	59	it	it	PRON
ejpam-1097	221	60	is	be	AUX
ejpam-1097	221	61	clear	clear	ADJ
ejpam-1097	221	62	that	that	SCONJ
ejpam-1097	221	63	every	every	DET
ejpam-1097	221	64	semisimple	semisimple	NOUN
ejpam-1097	221	65	module	module	NOUN
ejpam-1097	221	66	relative	relative	ADJ
ejpam-1097	221	67	to	to	ADP
ejpam-1097	221	68	the	the	DET
ejpam-1097	221	69	classb(m	classb(m	NOUN
ejpam-1097	221	70	,	,	PUNCT
ejpam-1097	221	71	x	x	X
ejpam-1097	221	72	)	)	PUNCT
ejpam-1097	221	73	is	be	AUX
ejpam-1097	221	74	x	x	PUNCT
ejpam-1097	221	75	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	221	76	.	.	PUNCT
ejpam-1097	222	1	lemma	lemma	PROPN
ejpam-1097	222	2	4	4	X
ejpam-1097	222	3	.	.	PUNCT
ejpam-1097	223	1	let	let	VERB
ejpam-1097	223	2	m	m	PRON
ejpam-1097	223	3	be	be	AUX
ejpam-1097	223	4	an	an	DET
ejpam-1097	223	5	x	x	SYM
ejpam-1097	223	6	-supplemented	-supplemente	VERB
ejpam-1097	223	7	module	module	NOUN
ejpam-1097	223	8	and	and	CCONJ
ejpam-1097	223	9	let	let	VERB
ejpam-1097	223	10	n	n	PRON
ejpam-1097	223	11	be	be	AUX
ejpam-1097	223	12	a	a	DET
ejpam-1097	223	13	submodule	submodule	NOUN
ejpam-1097	223	14	of	of	ADP
ejpam-1097	223	15	m	m	PRON
ejpam-1097	223	16	such	such	ADJ
ejpam-1097	223	17	that	that	SCONJ
ejpam-1097	223	18	n	n	CCONJ
ejpam-1097	223	19	∩	∩	X
ejpam-1097	223	20	rad(m	rad(m	NUM
ejpam-1097	223	21	)	)	PUNCT
ejpam-1097	223	22	=	=	SYM
ejpam-1097	223	23	0	0	NUM
ejpam-1097	223	24	and	and	CCONJ
ejpam-1097	223	25	n	n	PROPN
ejpam-1097	223	26	∈b(m	∈b(m	PROPN
ejpam-1097	223	27	,	,	PUNCT
ejpam-1097	223	28	x	x	PROPN
ejpam-1097	223	29	)	)	PUNCT
ejpam-1097	223	30	.	.	PUNCT
ejpam-1097	224	1	then	then	ADV
ejpam-1097	224	2	n	n	PRON
ejpam-1097	224	3	is	be	AUX
ejpam-1097	224	4	semisimple	semisimple	NOUN
ejpam-1097	224	5	relative	relative	ADJ
ejpam-1097	224	6	to	to	ADP
ejpam-1097	224	7	the	the	DET
ejpam-1097	224	8	classb(m	classb(m	NOUN
ejpam-1097	224	9	,	,	PUNCT
ejpam-1097	224	10	x	x	X
ejpam-1097	224	11	)	)	PUNCT
ejpam-1097	224	12	.	.	PUNCT
ejpam-1097	225	1	proof	proof	NOUN
ejpam-1097	225	2	.	.	PUNCT
ejpam-1097	226	1	we	we	PRON
ejpam-1097	226	2	have	have	VERB
ejpam-1097	226	3	to	to	PART
ejpam-1097	226	4	prove	prove	VERB
ejpam-1097	226	5	that	that	SCONJ
ejpam-1097	226	6	m	m	PROPN
ejpam-1097	226	7	/	/	SYM
ejpam-1097	226	8	rad(m	rad(m	PROPN
ejpam-1097	226	9	)	)	PUNCT
ejpam-1097	226	10	contains	contain	VERB
ejpam-1097	226	11	no	no	DET
ejpam-1097	226	12	non	non	ADJ
ejpam-1097	226	13	-	-	ADJ
ejpam-1097	226	14	zero	zero	ADJ
ejpam-1097	226	15	small	small	ADJ
ejpam-1097	226	16	submodule	submodule	NOUN
ejpam-1097	226	17	k	k	PROPN
ejpam-1097	226	18	/	/	SYM
ejpam-1097	226	19	rad(m	rad(m	NOUN
ejpam-1097	226	20	)	)	PUNCT
ejpam-1097	226	21	with	with	ADP
ejpam-1097	226	22	k	k	PROPN
ejpam-1097	226	23	/	/	SYM
ejpam-1097	226	24	rad(m	rad(m	NOUN
ejpam-1097	226	25	)	)	PUNCT
ejpam-1097	226	26	∈b(m	∈b(m	PROPN
ejpam-1097	226	27	/	/	SYM
ejpam-1097	226	28	rad(m	rad(m	PROPN
ejpam-1097	226	29	)	)	PUNCT
ejpam-1097	226	30	,	,	PUNCT
ejpam-1097	226	31	x	x	X
ejpam-1097	226	32	)	)	PUNCT
ejpam-1097	226	33	.	.	PUNCT
ejpam-1097	227	1	let	let	VERB
ejpam-1097	227	2	k	k	X
ejpam-1097	227	3	/	/	SYM
ejpam-1097	227	4	rad(m)≪	rad(m)≪	PROPN
ejpam-1097	227	5	m	m	PROPN
ejpam-1097	227	6	/	/	SYM
ejpam-1097	227	7	rad(m	rad(m	NOUN
ejpam-1097	227	8	)	)	PUNCT
ejpam-1097	227	9	and	and	CCONJ
ejpam-1097	227	10	k	k	ADJ
ejpam-1097	227	11	/	/	SYM
ejpam-1097	227	12	rad(m	rad(m	PROPN
ejpam-1097	227	13	)	)	PUNCT
ejpam-1097	227	14	∈	∈	PROPN
ejpam-1097	227	15	b(m	b(m	PROPN
ejpam-1097	227	16	/	/	SYM
ejpam-1097	227	17	rad(m	rad(m	PROPN
ejpam-1097	227	18	)	)	PUNCT
ejpam-1097	227	19	,	,	PUNCT
ejpam-1097	227	20	x	x	X
ejpam-1097	227	21	)	)	PUNCT
ejpam-1097	227	22	.	.	PUNCT
ejpam-1097	228	1	from	from	ADP
ejpam-1097	228	2	lemma	lemma	PROPN
ejpam-1097	228	3	1	1	NUM
ejpam-1097	228	4	,	,	PUNCT
ejpam-1097	228	5	k	k	PROPN
ejpam-1097	228	6	∈	∈	PROPN
ejpam-1097	228	7	b(m	b(m	PROPN
ejpam-1097	228	8	,	,	PUNCT
ejpam-1097	228	9	x	x	NOUN
ejpam-1097	228	10	)	)	PUNCT
ejpam-1097	228	11	.	.	PUNCT
ejpam-1097	229	1	by	by	ADP
ejpam-1097	229	2	hypothesis	hypothesis	NOUN
ejpam-1097	229	3	,	,	PUNCT
ejpam-1097	229	4	there	there	PRON
ejpam-1097	229	5	exists	exist	VERB
ejpam-1097	229	6	a	a	DET
ejpam-1097	229	7	submodule	submodule	PROPN
ejpam-1097	229	8	b	b	PROPN
ejpam-1097	229	9	of	of	ADP
ejpam-1097	229	10	m	m	PROPN
ejpam-1097	229	11	with	with	ADP
ejpam-1097	229	12	b	b	PROPN
ejpam-1097	229	13	∈	∈	PROPN
ejpam-1097	229	14	b(m	b(m	PROPN
ejpam-1097	229	15	,	,	PUNCT
ejpam-1097	229	16	x	x	X
ejpam-1097	229	17	)	)	PUNCT
ejpam-1097	229	18	such	such	ADJ
ejpam-1097	229	19	that	that	SCONJ
ejpam-1097	229	20	m	m	VERB
ejpam-1097	230	1	=	=	SYM
ejpam-1097	230	2	k	k	PROPN
ejpam-1097	231	1	+	+	CCONJ
ejpam-1097	231	2	b	b	PROPN
ejpam-1097	231	3	and	and	CCONJ
ejpam-1097	231	4	k	k	PROPN
ejpam-1097	231	5	∩	∩	PROPN
ejpam-1097	231	6	b	b	PROPN
ejpam-1097	231	7	≪	≪	X
ejpam-1097	231	8	b.	b.	NOUN
ejpam-1097	231	9	as	as	ADP
ejpam-1097	231	10	k	k	PROPN
ejpam-1097	231	11	/	/	SYM
ejpam-1097	231	12	rad(m	rad(m	NOUN
ejpam-1097	231	13	)	)	PUNCT
ejpam-1097	231	14	≪	≪	PUNCT
ejpam-1097	231	15	m	m	PROPN
ejpam-1097	231	16	/	/	SYM
ejpam-1097	231	17	rad(m	rad(m	ADJ
ejpam-1097	231	18	)	)	PUNCT
ejpam-1097	231	19	,	,	PUNCT
ejpam-1097	231	20	rad(m	rad(m	NOUN
ejpam-1097	231	21	)	)	PUNCT
ejpam-1097	231	22	=	=	SYM
ejpam-1097	231	23	k	k	PROPN
ejpam-1097	231	24	.	.	PUNCT
ejpam-1097	232	1	thus	thus	ADV
ejpam-1097	232	2	every	every	DET
ejpam-1097	232	3	submodule	submodule	NOUN
ejpam-1097	232	4	k	k	PROPN
ejpam-1097	232	5	/	/	SYM
ejpam-1097	232	6	rad(m	rad(m	NOUN
ejpam-1097	232	7	)	)	PUNCT
ejpam-1097	232	8	of	of	ADP
ejpam-1097	232	9	m	m	PROPN
ejpam-1097	232	10	/	/	SYM
ejpam-1097	232	11	rad(m	rad(m	NOUN
ejpam-1097	232	12	)	)	PUNCT
ejpam-1097	232	13	with	with	ADP
ejpam-1097	232	14	k	k	PROPN
ejpam-1097	232	15	/	/	SYM
ejpam-1097	232	16	rad(m	rad(m	NOUN
ejpam-1097	232	17	)	)	PUNCT
ejpam-1097	232	18	∈b(m	∈b(m	PROPN
ejpam-1097	232	19	/	/	SYM
ejpam-1097	232	20	rad(m	rad(m	PROPN
ejpam-1097	232	21	)	)	PUNCT
ejpam-1097	232	22	,	,	PUNCT
ejpam-1097	232	23	x	x	X
ejpam-1097	232	24	)	)	PUNCT
ejpam-1097	232	25	is	be	AUX
ejpam-1097	232	26	a	a	DET
ejpam-1097	232	27	direct	direct	ADJ
ejpam-1097	232	28	summand	summand	NOUN
ejpam-1097	232	29	of	of	ADP
ejpam-1097	232	30	m	m	PROPN
ejpam-1097	232	31	/	/	SYM
ejpam-1097	232	32	rad(m	rad(m	PROPN
ejpam-1097	232	33	)	)	PUNCT
ejpam-1097	232	34	.	.	PUNCT
ejpam-1097	233	1	hence	hence	ADV
ejpam-1097	233	2	m	m	PROPN
ejpam-1097	233	3	/	/	SYM
ejpam-1097	233	4	rad(m	rad(m	PROPN
ejpam-1097	233	5	)	)	PUNCT
ejpam-1097	233	6	is	be	AUX
ejpam-1097	233	7	semisimple	semisimple	NOUN
ejpam-1097	233	8	relative	relative	ADJ
ejpam-1097	233	9	to	to	ADP
ejpam-1097	233	10	the	the	DET
ejpam-1097	233	11	class	class	NOUN
ejpam-1097	233	12	b(m	b(m	PROPN
ejpam-1097	233	13	/	/	SYM
ejpam-1097	233	14	rad(m	rad(m	PROPN
ejpam-1097	233	15	)	)	PUNCT
ejpam-1097	233	16	,	,	PUNCT
ejpam-1097	233	17	x	x	X
ejpam-1097	233	18	)	)	PUNCT
ejpam-1097	233	19	.	.	PUNCT
ejpam-1097	234	1	hence	hence	ADV
ejpam-1097	234	2	n	n	PROPN
ejpam-1097	234	3	is	be	AUX
ejpam-1097	234	4	semisimple	semisimple	NOUN
ejpam-1097	234	5	relative	relative	ADJ
ejpam-1097	234	6	to	to	ADP
ejpam-1097	234	7	the	the	DET
ejpam-1097	234	8	classb(m	classb(m	NOUN
ejpam-1097	234	9	,	,	PUNCT
ejpam-1097	234	10	x	x	X
ejpam-1097	234	11	)	)	PUNCT
ejpam-1097	234	12	.	.	PUNCT
ejpam-1097	235	1	proposition	proposition	NOUN
ejpam-1097	235	2	4	4	NUM
ejpam-1097	235	3	.	.	PUNCT
ejpam-1097	236	1	let	let	VERB
ejpam-1097	236	2	m	m	PRON
ejpam-1097	236	3	be	be	AUX
ejpam-1097	236	4	an	an	DET
ejpam-1097	236	5	x	x	SYM
ejpam-1097	236	6	-supplemented	-supplemente	VERB
ejpam-1097	236	7	module	module	NOUN
ejpam-1097	236	8	and	and	CCONJ
ejpam-1097	236	9	suppose	suppose	VERB
ejpam-1097	237	1	that	that	SCONJ
ejpam-1097	237	2	for	for	ADP
ejpam-1097	237	3	every	every	DET
ejpam-1097	237	4	submodule	submodule	NOUN
ejpam-1097	237	5	n	n	PROPN
ejpam-1097	237	6	of	of	ADP
ejpam-1097	237	7	m	m	PRON
ejpam-1097	237	8	such	such	ADJ
ejpam-1097	237	9	that	that	SCONJ
ejpam-1097	237	10	n	n	CCONJ
ejpam-1097	237	11	∩	∩	X
ejpam-1097	237	12	rad(m	rad(m	NUM
ejpam-1097	237	13	)	)	PUNCT
ejpam-1097	237	14	=	=	SYM
ejpam-1097	237	15	0	0	NUM
ejpam-1097	238	1	we	we	PRON
ejpam-1097	238	2	have	have	VERB
ejpam-1097	238	3	n	n	NUM
ejpam-1097	238	4	∈	∈	PROPN
ejpam-1097	238	5	b(m	b(m	PROPN
ejpam-1097	238	6	,	,	PUNCT
ejpam-1097	238	7	x	x	PROPN
ejpam-1097	238	8	)	)	PUNCT
ejpam-1097	238	9	.	.	PUNCT
ejpam-1097	239	1	then	then	ADV
ejpam-1097	239	2	m	m	VERB
ejpam-1097	239	3	=	=	SYM
ejpam-1097	239	4	m1	m1	PROPN
ejpam-1097	239	5	⊕	⊕	PROPN
ejpam-1097	239	6	m2	m2	PROPN
ejpam-1097	239	7	,	,	PUNCT
ejpam-1097	239	8	where	where	SCONJ
ejpam-1097	239	9	m1	m1	PROPN
ejpam-1097	239	10	is	be	AUX
ejpam-1097	239	11	a	a	DET
ejpam-1097	239	12	semisimple	semisimple	NOUN
ejpam-1097	239	13	module	module	NOUN
ejpam-1097	239	14	relative	relative	ADJ
ejpam-1097	239	15	to	to	ADP
ejpam-1097	239	16	the	the	DET
ejpam-1097	239	17	classb(m	classb(m	NOUN
ejpam-1097	239	18	,	,	PUNCT
ejpam-1097	239	19	x	x	PUNCT
ejpam-1097	239	20	)	)	PUNCT
ejpam-1097	239	21	and	and	CCONJ
ejpam-1097	239	22	rad(m2	rad(m2	NOUN
ejpam-1097	239	23	)	)	PUNCT
ejpam-1097	239	24	essential	essential	ADJ
ejpam-1097	239	25	in	in	ADP
ejpam-1097	239	26	m2	m2	PROPN
ejpam-1097	239	27	.	.	PUNCT
ejpam-1097	240	1	proof	proof	NOUN
ejpam-1097	240	2	.	.	PUNCT
ejpam-1097	241	1	let	let	VERB
ejpam-1097	241	2	m1	m1	PROPN
ejpam-1097	241	3	be	be	AUX
ejpam-1097	241	4	a	a	DET
ejpam-1097	241	5	complement	complement	NOUN
ejpam-1097	241	6	of	of	ADP
ejpam-1097	241	7	rad(m	rad(m	NOUN
ejpam-1097	241	8	)	)	PUNCT
ejpam-1097	241	9	in	in	ADP
ejpam-1097	241	10	m	m	PROPN
ejpam-1097	241	11	,	,	PUNCT
ejpam-1097	241	12	hence	hence	ADV
ejpam-1097	241	13	rad(m)⊕	rad(m)⊕	NOUN
ejpam-1097	241	14	m1	m1	PROPN
ejpam-1097	241	15	is	be	AUX
ejpam-1097	241	16	essential	essential	ADJ
ejpam-1097	241	17	in	in	ADP
ejpam-1097	241	18	m	m	PROPN
ejpam-1097	241	19	.	.	PUNCT
ejpam-1097	242	1	since	since	SCONJ
ejpam-1097	242	2	m	m	PROPN
ejpam-1097	242	3	is	be	AUX
ejpam-1097	242	4	x	x	PUNCT
ejpam-1097	242	5	-supplemented	-supplemented	ADJ
ejpam-1097	242	6	,	,	PUNCT
ejpam-1097	242	7	there	there	PRON
ejpam-1097	242	8	exists	exist	VERB
ejpam-1097	242	9	a	a	DET
ejpam-1097	242	10	submodule	submodule	NOUN
ejpam-1097	242	11	m2	m2	PROPN
ejpam-1097	242	12	of	of	ADP
ejpam-1097	242	13	m	m	PROPN
ejpam-1097	242	14	such	such	ADJ
ejpam-1097	242	15	that	that	SCONJ
ejpam-1097	242	16	m	m	PROPN
ejpam-1097	242	17	=	=	SYM
ejpam-1097	242	18	m1	m1	PROPN
ejpam-1097	242	19	+	+	CCONJ
ejpam-1097	242	20	m2	m2	PROPN
ejpam-1097	242	21	,	,	PUNCT
ejpam-1097	242	22	m1	m1	PROPN
ejpam-1097	242	23	∩	∩	NOUN
ejpam-1097	242	24	m2	m2	PROPN
ejpam-1097	242	25	≪	≪	PUNCT
ejpam-1097	242	26	m2	m2	PROPN
ejpam-1097	242	27	and	and	CCONJ
ejpam-1097	242	28	m2	m2	PROPN
ejpam-1097	242	29	∈	∈	PROPN
ejpam-1097	242	30	b(m	b(m	PROPN
ejpam-1097	242	31	,	,	PUNCT
ejpam-1097	242	32	x	x	PROPN
ejpam-1097	242	33	)	)	PUNCT
ejpam-1097	242	34	.	.	PUNCT
ejpam-1097	243	1	then	then	ADV
ejpam-1097	243	2	m1	m1	PROPN
ejpam-1097	243	3	∩	∩	NOUN
ejpam-1097	243	4	m2	m2	PROPN
ejpam-1097	243	5	is	be	AUX
ejpam-1097	243	6	a	a	DET
ejpam-1097	243	7	submodule	submodule	NOUN
ejpam-1097	243	8	of	of	ADP
ejpam-1097	243	9	both	both	DET
ejpam-1097	243	10	t.	t.	NOUN
ejpam-1097	243	11	amouzegar	amouzegar	NOUN
ejpam-1097	243	12	,	,	PUNCT
ejpam-1097	243	13	y.	y.	PROPN
ejpam-1097	243	14	talebi	talebi	PROPN
ejpam-1097	243	15	/	/	SYM
ejpam-1097	243	16	eur	eur	PROPN
ejpam-1097	243	17	.	.	PUNCT
ejpam-1097	244	1	j.	j.	PROPN
ejpam-1097	244	2	pure	pure	PROPN
ejpam-1097	244	3	appl	appl	PROPN
ejpam-1097	244	4	.	.	PROPN
ejpam-1097	244	5	math	math	PROPN
ejpam-1097	244	6	,	,	PUNCT
ejpam-1097	244	7	5	5	NUM
ejpam-1097	244	8	(	(	PUNCT
ejpam-1097	244	9	2012	2012	NUM
ejpam-1097	244	10	)	)	PUNCT
ejpam-1097	244	11	,	,	PUNCT
ejpam-1097	244	12	108	108	NUM
ejpam-1097	244	13	-	-	SYM
ejpam-1097	244	14	115	115	NUM
ejpam-1097	244	15	114	114	NUM
ejpam-1097	244	16	rad(m	rad(m	NOUN
ejpam-1097	244	17	)	)	PUNCT
ejpam-1097	244	18	and	and	CCONJ
ejpam-1097	244	19	m1	m1	NOUN
ejpam-1097	244	20	.	.	PUNCT
ejpam-1097	245	1	it	it	PRON
ejpam-1097	245	2	follows	follow	VERB
ejpam-1097	245	3	that	that	SCONJ
ejpam-1097	245	4	m	m	VERB
ejpam-1097	245	5	=	=	ADJ
ejpam-1097	245	6	m1⊕m2	m1⊕m2	PROPN
ejpam-1097	245	7	,	,	PUNCT
ejpam-1097	245	8	rad(m	rad(m	PROPN
ejpam-1097	245	9	)	)	PUNCT
ejpam-1097	245	10	=	=	SYM
ejpam-1097	245	11	rad(m2	rad(m2	NOUN
ejpam-1097	245	12	)	)	PUNCT
ejpam-1097	245	13	is	be	AUX
ejpam-1097	245	14	essential	essential	ADJ
ejpam-1097	245	15	in	in	ADP
ejpam-1097	245	16	m2	m2	PROPN
ejpam-1097	245	17	,	,	PUNCT
ejpam-1097	245	18	and	and	CCONJ
ejpam-1097	245	19	by	by	ADP
ejpam-1097	245	20	lemma	lemma	PROPN
ejpam-1097	245	21	4	4	NUM
ejpam-1097	245	22	,	,	PUNCT
ejpam-1097	245	23	m1	m1	PROPN
ejpam-1097	245	24	is	be	AUX
ejpam-1097	245	25	semisimple	semisimple	NOUN
ejpam-1097	245	26	relative	relative	ADJ
ejpam-1097	245	27	to	to	ADP
ejpam-1097	245	28	the	the	DET
ejpam-1097	245	29	classb(m	classb(m	NOUN
ejpam-1097	245	30	,	,	PUNCT
ejpam-1097	245	31	x	x	PROPN
ejpam-1097	245	32	)	)	PUNCT
ejpam-1097	245	33	.	.	PUNCT
ejpam-1097	246	1	a	a	DET
ejpam-1097	246	2	module	module	NOUN
ejpam-1097	246	3	m	m	NOUN
ejpam-1097	246	4	is	be	AUX
ejpam-1097	246	5	said	say	VERB
ejpam-1097	246	6	to	to	PART
ejpam-1097	246	7	be	be	AUX
ejpam-1097	246	8	finite	finite	ADJ
ejpam-1097	246	9	goldie	goldie	PROPN
ejpam-1097	246	10	-	-	PUNCT
ejpam-1097	246	11	dimensional	dimensional	ADJ
ejpam-1097	246	12	provided	provide	VERB
ejpam-1097	246	13	m	m	NOUN
ejpam-1097	246	14	contains	contain	VERB
ejpam-1097	246	15	no	no	DET
ejpam-1097	246	16	infinite	infinite	ADJ
ejpam-1097	246	17	independent	independent	ADJ
ejpam-1097	246	18	families	family	NOUN
ejpam-1097	246	19	of	of	ADP
ejpam-1097	246	20	nonzero	nonzero	PROPN
ejpam-1097	246	21	submodules	submodule	NOUN
ejpam-1097	246	22	.	.	PUNCT
ejpam-1097	247	1	theorem	theorem	NOUN
ejpam-1097	247	2	4	4	NUM
ejpam-1097	247	3	.	.	PUNCT
ejpam-1097	247	4	consider	consider	VERB
ejpam-1097	247	5	the	the	DET
ejpam-1097	247	6	following	follow	VERB
ejpam-1097	247	7	conditions	condition	NOUN
ejpam-1097	247	8	for	for	ADP
ejpam-1097	247	9	a	a	DET
ejpam-1097	247	10	projective	projective	ADJ
ejpam-1097	247	11	module	module	NOUN
ejpam-1097	247	12	m	m	PROPN
ejpam-1097	247	13	:	:	PUNCT
ejpam-1097	247	14	(	(	PUNCT
ejpam-1097	247	15	i	i	NOUN
ejpam-1097	247	16	)	)	PUNCT
ejpam-1097	248	1	m	m	VERB
ejpam-1097	248	2	is	be	AUX
ejpam-1097	248	3	a	a	DET
ejpam-1097	248	4	direct	direct	ADJ
ejpam-1097	248	5	sum	sum	NOUN
ejpam-1097	248	6	of	of	ADP
ejpam-1097	248	7	x	x	X
ejpam-1097	248	8	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	248	9	modules	module	NOUN
ejpam-1097	248	10	and	and	CCONJ
ejpam-1097	248	11	rad(m	rad(m	NUM
ejpam-1097	248	12	)	)	PUNCT
ejpam-1097	248	13	has	have	AUX
ejpam-1097	248	14	finite	finite	PROPN
ejpam-1097	248	15	goldie	goldie	PROPN
ejpam-1097	248	16	dimension	dimension	PROPN
ejpam-1097	248	17	.	.	PUNCT
ejpam-1097	249	1	(	(	PUNCT
ejpam-1097	249	2	ii	ii	X
ejpam-1097	249	3	)	)	PUNCT
ejpam-1097	249	4	m	m	PROPN
ejpam-1097	250	1	=	=	SYM
ejpam-1097	250	2	m1	m1	PROPN
ejpam-1097	250	3	⊕m2	⊕m2	NUM
ejpam-1097	250	4	such	such	ADJ
ejpam-1097	250	5	that	that	DET
ejpam-1097	250	6	m1	m1	PROPN
ejpam-1097	250	7	is	be	AUX
ejpam-1097	250	8	semisimple	semisimple	NOUN
ejpam-1097	250	9	relative	relative	ADJ
ejpam-1097	250	10	to	to	ADP
ejpam-1097	250	11	the	the	DET
ejpam-1097	250	12	class	class	NOUN
ejpam-1097	250	13	b(m	b(m	PROPN
ejpam-1097	250	14	,	,	PUNCT
ejpam-1097	250	15	x	x	SYM
ejpam-1097	250	16	)	)	PUNCT
ejpam-1097	250	17	and	and	CCONJ
ejpam-1097	250	18	m2	m2	PROPN
ejpam-1097	250	19	has	have	AUX
ejpam-1097	250	20	finite	finite	PROPN
ejpam-1097	250	21	goldie	goldie	PROPN
ejpam-1097	250	22	dimension	dimension	PROPN
ejpam-1097	250	23	and	and	CCONJ
ejpam-1097	250	24	m2	m2	PROPN
ejpam-1097	250	25	is	be	AUX
ejpam-1097	250	26	a	a	DET
ejpam-1097	250	27	(	(	PUNCT
ejpam-1097	250	28	finite	finite	NOUN
ejpam-1097	250	29	)	)	PUNCT
ejpam-1097	250	30	direct	direct	ADJ
ejpam-1097	250	31	sum	sum	NOUN
ejpam-1097	250	32	of	of	ADP
ejpam-1097	250	33	local	local	ADJ
ejpam-1097	250	34	modules	module	NOUN
ejpam-1097	250	35	.	.	PUNCT
ejpam-1097	251	1	if	if	SCONJ
ejpam-1097	251	2	for	for	ADP
ejpam-1097	251	3	every	every	DET
ejpam-1097	251	4	submodule	submodule	NOUN
ejpam-1097	251	5	n	n	PROPN
ejpam-1097	251	6	of	of	ADP
ejpam-1097	251	7	a	a	DET
ejpam-1097	251	8	direct	direct	ADJ
ejpam-1097	251	9	summand	summand	NOUN
ejpam-1097	251	10	mi	mi	PROPN
ejpam-1097	251	11	of	of	ADP
ejpam-1097	251	12	m	m	PROPN
ejpam-1097	251	13	such	such	ADJ
ejpam-1097	251	14	that	that	SCONJ
ejpam-1097	251	15	n	n	ADP
ejpam-1097	251	16	∩	∩	NOUN
ejpam-1097	251	17	rad(mi	rad(mi	NOUN
ejpam-1097	251	18	)	)	PUNCT
ejpam-1097	251	19	=	=	SYM
ejpam-1097	251	20	0	0	NUM
ejpam-1097	251	21	we	we	PRON
ejpam-1097	251	22	have	have	VERB
ejpam-1097	251	23	n	n	PRON
ejpam-1097	251	24	∈b(mi	∈b(mi	NOUN
ejpam-1097	251	25	,	,	PUNCT
ejpam-1097	251	26	x	x	SYM
ejpam-1097	251	27	)	)	PUNCT
ejpam-1097	251	28	,	,	PUNCT
ejpam-1097	251	29	then	then	ADV
ejpam-1097	251	30	(	(	PUNCT
ejpam-1097	251	31	i)⇒	i)⇒	PROPN
ejpam-1097	251	32	(	(	PUNCT
ejpam-1097	251	33	ii	ii	NOUN
ejpam-1097	251	34	)	)	PUNCT
ejpam-1097	251	35	holds	hold	VERB
ejpam-1097	251	36	and	and	CCONJ
ejpam-1097	251	37	if	if	SCONJ
ejpam-1097	251	38	for	for	ADP
ejpam-1097	251	39	every	every	DET
ejpam-1097	251	40	small	small	ADJ
ejpam-1097	251	41	submodule	submodule	NOUN
ejpam-1097	251	42	n	n	PROPN
ejpam-1097	251	43	of	of	ADP
ejpam-1097	251	44	m1	m1	NOUN
ejpam-1097	251	45	we	we	PRON
ejpam-1097	251	46	have	have	VERB
ejpam-1097	251	47	n	n	ADV
ejpam-1097	251	48	∈b(m1	∈b(m1	NOUN
ejpam-1097	251	49	,	,	PUNCT
ejpam-1097	251	50	x	x	X
ejpam-1097	251	51	)	)	PUNCT
ejpam-1097	251	52	,	,	PUNCT
ejpam-1097	251	53	then	then	ADV
ejpam-1097	251	54	(	(	PUNCT
ejpam-1097	251	55	ii)⇒	ii)⇒	PROPN
ejpam-1097	251	56	(	(	PUNCT
ejpam-1097	251	57	i	i	NOUN
ejpam-1097	251	58	)	)	PUNCT
ejpam-1097	251	59	holds	hold	VERB
ejpam-1097	251	60	.	.	PUNCT
ejpam-1097	252	1	proof	proof	NOUN
ejpam-1097	252	2	.	.	PUNCT
ejpam-1097	253	1	(	(	PUNCT
ejpam-1097	253	2	i	i	NOUN
ejpam-1097	253	3	)	)	PUNCT
ejpam-1097	253	4	⇒	⇒	PROPN
ejpam-1097	253	5	(	(	PUNCT
ejpam-1097	253	6	ii	ii	NOUN
ejpam-1097	253	7	)	)	PUNCT
ejpam-1097	253	8	let	let	VERB
ejpam-1097	253	9	m	m	NOUN
ejpam-1097	253	10	=	=	PROPN
ejpam-1097	253	11	⊕	⊕	PROPN
ejpam-1097	253	12	i∈i	i∈i	ADJ
ejpam-1097	253	13	mi	mi	PROPN
ejpam-1097	253	14	and	and	CCONJ
ejpam-1097	253	15	mi	mi	PROPN
ejpam-1097	253	16	is	be	AUX
ejpam-1097	253	17	x	x	PUNCT
ejpam-1097	253	18	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	253	19	for	for	ADP
ejpam-1097	253	20	every	every	DET
ejpam-1097	253	21	i	i	NOUN
ejpam-1097	253	22	∈	∈	PROPN
ejpam-1097	253	23	i	i	PRON
ejpam-1097	253	24	.	.	PUNCT
ejpam-1097	254	1	since	since	SCONJ
ejpam-1097	254	2	rad(m	rad(m	NUM
ejpam-1097	254	3	)	)	PUNCT
ejpam-1097	254	4	=	=	SYM
ejpam-1097	254	5	⊕i∈irad(mi	⊕i∈irad(mi	PROPN
ejpam-1097	254	6	)	)	PUNCT
ejpam-1097	254	7	,	,	PUNCT
ejpam-1097	254	8	then	then	ADV
ejpam-1097	254	9	there	there	PRON
ejpam-1097	254	10	is	be	VERB
ejpam-1097	254	11	a	a	DET
ejpam-1097	254	12	finite	finite	NOUN
ejpam-1097	254	13	subset	subset	NOUN
ejpam-1097	254	14	j	j	PROPN
ejpam-1097	254	15	of	of	ADP
ejpam-1097	254	16	i	i	PRON
ejpam-1097	254	17	such	such	ADJ
ejpam-1097	254	18	that	that	DET
ejpam-1097	254	19	rad(mi	rad(mi	NOUN
ejpam-1097	254	20	)	)	PUNCT
ejpam-1097	254	21	=	=	SYM
ejpam-1097	254	22	0	0	NUM
ejpam-1097	255	1	for	for	ADP
ejpam-1097	255	2	all	all	PRON
ejpam-1097	255	3	i	i	PRON
ejpam-1097	255	4	∈	∈	VERB
ejpam-1097	256	1	i	i	PRON
ejpam-1097	256	2	\	\	PROPN
ejpam-1097	256	3	j	j	PROPN
ejpam-1097	256	4	.	.	PUNCT
ejpam-1097	257	1	therefore	therefore	ADV
ejpam-1097	257	2	mi	mi	PROPN
ejpam-1097	257	3	is	be	AUX
ejpam-1097	257	4	semisimple	semisimple	NOUN
ejpam-1097	257	5	relative	relative	ADJ
ejpam-1097	257	6	to	to	ADP
ejpam-1097	257	7	b(m	b(m	PROPN
ejpam-1097	257	8	,	,	PUNCT
ejpam-1097	257	9	x	x	PUNCT
ejpam-1097	257	10	)	)	PUNCT
ejpam-1097	257	11	for	for	ADP
ejpam-1097	257	12	all	all	PRON
ejpam-1097	257	13	i	i	PRON
ejpam-1097	257	14	∈	∈	VERB
ejpam-1097	258	1	i	i	PRON
ejpam-1097	258	2	\	\	PROPN
ejpam-1097	258	3	j	j	PROPN
ejpam-1097	258	4	.	.	PUNCT
ejpam-1097	259	1	hence	hence	ADV
ejpam-1097	259	2	there	there	PRON
ejpam-1097	259	3	is	be	VERB
ejpam-1097	259	4	a	a	DET
ejpam-1097	259	5	submodule	submodule	NOUN
ejpam-1097	259	6	m1	m1	NOUN
ejpam-1097	259	7	semisimple	semisimple	NOUN
ejpam-1097	259	8	relative	relative	ADJ
ejpam-1097	259	9	to	to	ADP
ejpam-1097	259	10	b(m	b(m	PROPN
ejpam-1097	259	11	,	,	PUNCT
ejpam-1097	259	12	x	x	PUNCT
ejpam-1097	259	13	)	)	PUNCT
ejpam-1097	259	14	such	such	ADJ
ejpam-1097	259	15	that	that	SCONJ
ejpam-1097	259	16	m	m	PROPN
ejpam-1097	259	17	=	=	SYM
ejpam-1097	259	18	m1	m1	PROPN
ejpam-1097	259	19	⊕	⊕	PROPN
ejpam-1097	259	20	(	(	PUNCT
ejpam-1097	259	21	⊕	⊕	PROPN
ejpam-1097	259	22	j∈j	j∈j	PROPN
ejpam-1097	259	23	m	m	PROPN
ejpam-1097	259	24	j	j	PROPN
ejpam-1097	259	25	)	)	PUNCT
ejpam-1097	259	26	.	.	PUNCT
ejpam-1097	260	1	by	by	ADP
ejpam-1097	260	2	proposition	proposition	NOUN
ejpam-1097	260	3	4	4	NUM
ejpam-1097	260	4	,	,	PUNCT
ejpam-1097	260	5	without	without	ADP
ejpam-1097	260	6	loss	loss	NOUN
ejpam-1097	260	7	of	of	ADP
ejpam-1097	260	8	generality	generality	NOUN
ejpam-1097	260	9	,	,	PUNCT
ejpam-1097	260	10	we	we	PRON
ejpam-1097	260	11	may	may	AUX
ejpam-1097	260	12	assume	assume	VERB
ejpam-1097	260	13	rad(m	rad(m	PROPN
ejpam-1097	260	14	j	j	PROPN
ejpam-1097	260	15	)	)	PUNCT
ejpam-1097	260	16	is	be	AUX
ejpam-1097	260	17	essential	essential	ADJ
ejpam-1097	260	18	in	in	ADP
ejpam-1097	260	19	m	m	PROPN
ejpam-1097	260	20	j	j	NOUN
ejpam-1097	260	21	(	(	PUNCT
ejpam-1097	260	22	j	j	PROPN
ejpam-1097	260	23	∈	∈	PROPN
ejpam-1097	260	24	j	j	PROPN
ejpam-1097	260	25	)	)	PUNCT
ejpam-1097	260	26	.	.	PUNCT
ejpam-1097	261	1	then	then	ADV
ejpam-1097	261	2	m	m	PROPN
ejpam-1097	261	3	j	j	PROPN
ejpam-1097	261	4	(	(	PUNCT
ejpam-1097	261	5	j	j	PROPN
ejpam-1097	261	6	∈	∈	PROPN
ejpam-1097	261	7	j	j	PROPN
ejpam-1097	261	8	)	)	PUNCT
ejpam-1097	261	9	has	have	VERB
ejpam-1097	261	10	finite	finite	PROPN
ejpam-1097	261	11	goldie	goldie	PROPN
ejpam-1097	261	12	dimension	dimension	PROPN
ejpam-1097	261	13	by	by	ADP
ejpam-1097	261	14	[	[	X
ejpam-1097	261	15	3	3	NUM
ejpam-1097	261	16	,	,	PUNCT
ejpam-1097	261	17	proposition	proposition	NOUN
ejpam-1097	261	18	3.20	3.20	NUM
ejpam-1097	261	19	]	]	PUNCT
ejpam-1097	261	20	.	.	PUNCT
ejpam-1097	262	1	next	next	ADV
ejpam-1097	262	2	we	we	PRON
ejpam-1097	262	3	prove	prove	VERB
ejpam-1097	262	4	that	that	SCONJ
ejpam-1097	262	5	each	each	DET
ejpam-1097	262	6	m	m	VERB
ejpam-1097	262	7	j	j	NOUN
ejpam-1097	262	8	,	,	PUNCT
ejpam-1097	262	9	for	for	ADP
ejpam-1097	262	10	j	j	PROPN
ejpam-1097	262	11	∈	∈	PROPN
ejpam-1097	262	12	j	j	PROPN
ejpam-1097	262	13	,	,	PUNCT
ejpam-1097	262	14	is	be	AUX
ejpam-1097	262	15	local	local	ADJ
ejpam-1097	262	16	or	or	CCONJ
ejpam-1097	262	17	a	a	DET
ejpam-1097	262	18	finite	finite	ADJ
ejpam-1097	262	19	direct	direct	ADJ
ejpam-1097	262	20	sum	sum	NOUN
ejpam-1097	262	21	of	of	ADP
ejpam-1097	262	22	local	local	ADJ
ejpam-1097	262	23	modules	module	NOUN
ejpam-1097	262	24	.	.	PUNCT
ejpam-1097	263	1	set	set	VERB
ejpam-1097	263	2	h	h	NOUN
ejpam-1097	264	1	=	=	PROPN
ejpam-1097	264	2	m	m	PROPN
ejpam-1097	264	3	j	j	NOUN
ejpam-1097	264	4	for	for	ADP
ejpam-1097	264	5	any	any	DET
ejpam-1097	264	6	j	j	PROPN
ejpam-1097	264	7	∈	∈	PROPN
ejpam-1097	264	8	j	j	PROPN
ejpam-1097	264	9	.	.	PUNCT
ejpam-1097	265	1	first	first	ADV
ejpam-1097	265	2	,	,	PUNCT
ejpam-1097	265	3	note	note	VERB
ejpam-1097	265	4	that	that	SCONJ
ejpam-1097	265	5	rad(h	rad(h	NOUN
ejpam-1097	265	6	)	)	PUNCT
ejpam-1097	265	7	6=	6=	NUM
ejpam-1097	265	8	h	h	NOUN
ejpam-1097	265	9	because	because	SCONJ
ejpam-1097	265	10	h	h	NOUN
ejpam-1097	265	11	is	be	AUX
ejpam-1097	265	12	projective	projective	ADJ
ejpam-1097	266	1	[	[	X
ejpam-1097	266	2	1	1	NUM
ejpam-1097	266	3	,	,	PUNCT
ejpam-1097	266	4	proposition	proposition	NOUN
ejpam-1097	266	5	17.14	17.14	NUM
ejpam-1097	266	6	]	]	PUNCT
ejpam-1097	266	7	.	.	PUNCT
ejpam-1097	267	1	assume	assume	VERB
ejpam-1097	267	2	that	that	SCONJ
ejpam-1097	267	3	h	h	NOUN
ejpam-1097	267	4	has	have	VERB
ejpam-1097	267	5	goldie	goldie	PROPN
ejpam-1097	267	6	dimension	dimension	PROPN
ejpam-1097	267	7	1	1	NUM
ejpam-1097	267	8	,	,	PUNCT
ejpam-1097	267	9	and	and	CCONJ
ejpam-1097	267	10	take	take	VERB
ejpam-1097	267	11	some	some	DET
ejpam-1097	267	12	x	x	SYM
ejpam-1097	267	13	∈	∈	PROPN
ejpam-1097	267	14	h	h	NOUN
ejpam-1097	267	15	\rad(h	\rad(h	NOUN
ejpam-1097	267	16	)	)	PUNCT
ejpam-1097	267	17	.	.	PUNCT
ejpam-1097	268	1	since	since	SCONJ
ejpam-1097	268	2	h	h	NOUN
ejpam-1097	268	3	is	be	AUX
ejpam-1097	268	4	x	x	PUNCT
ejpam-1097	268	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	268	6	,	,	PUNCT
ejpam-1097	268	7	there	there	PRON
ejpam-1097	268	8	is	be	VERB
ejpam-1097	268	9	a	a	DET
ejpam-1097	268	10	submodule	submodule	NOUN
ejpam-1097	268	11	k	k	NOUN
ejpam-1097	268	12	of	of	ADP
ejpam-1097	268	13	h	h	PROPN
ejpam-1097	268	14	with	with	ADP
ejpam-1097	268	15	k	k	PROPN
ejpam-1097	268	16	∈	∈	PROPN
ejpam-1097	268	17	b(h	b(h	PROPN
ejpam-1097	268	18	,	,	PUNCT
ejpam-1097	268	19	x	x	PUNCT
ejpam-1097	268	20	)	)	PUNCT
ejpam-1097	268	21	such	such	ADJ
ejpam-1097	268	22	that	that	PRON
ejpam-1097	268	23	h	h	NOUN
ejpam-1097	268	24	=	=	SYM
ejpam-1097	268	25	xr+	xr+	PROPN
ejpam-1097	268	26	k	k	PROPN
ejpam-1097	268	27	,	,	PUNCT
ejpam-1097	268	28	xr∩	xr∩	PROPN
ejpam-1097	269	1	k	k	PROPN
ejpam-1097	269	2	≪	≪	PUNCT
ejpam-1097	269	3	k	k	NOUN
ejpam-1097	269	4	and	and	CCONJ
ejpam-1097	269	5	h	h	NOUN
ejpam-1097	269	6	=	=	SYM
ejpam-1097	269	7	k	k	PROPN
ejpam-1097	269	8	⊕	⊕	PROPN
ejpam-1097	269	9	k1	k1	PROPN
ejpam-1097	269	10	for	for	ADP
ejpam-1097	269	11	some	some	DET
ejpam-1097	269	12	submodule	submodule	NOUN
ejpam-1097	269	13	k1	k1	NOUN
ejpam-1097	269	14	of	of	ADP
ejpam-1097	269	15	m	m	PROPN
ejpam-1097	269	16	.	.	PUNCT
ejpam-1097	270	1	then	then	ADV
ejpam-1097	270	2	k	k	PROPN
ejpam-1097	270	3	=	=	SYM
ejpam-1097	270	4	0	0	NUM
ejpam-1097	270	5	or	or	CCONJ
ejpam-1097	270	6	k1	k1	NOUN
ejpam-1097	270	7	=	=	SYM
ejpam-1097	270	8	0	0	PROPN
ejpam-1097	270	9	.	.	PUNCT
ejpam-1097	271	1	if	if	SCONJ
ejpam-1097	271	2	k1	k1	NOUN
ejpam-1097	271	3	=	=	SYM
ejpam-1097	271	4	0	0	NUM
ejpam-1097	271	5	,	,	PUNCT
ejpam-1097	271	6	then	then	ADV
ejpam-1097	271	7	xr⊆	xr⊆	PROPN
ejpam-1097	271	8	rad(h	rad(h	NOUN
ejpam-1097	271	9	)	)	PUNCT
ejpam-1097	271	10	which	which	PRON
ejpam-1097	271	11	is	be	AUX
ejpam-1097	271	12	a	a	DET
ejpam-1097	271	13	contradiction	contradiction	NOUN
ejpam-1097	271	14	.	.	PUNCT
ejpam-1097	272	1	hence	hence	ADV
ejpam-1097	272	2	k	k	PROPN
ejpam-1097	273	1	=	=	PUNCT
ejpam-1097	273	2	0	0	NUM
ejpam-1097	273	3	and	and	CCONJ
ejpam-1097	273	4	h	h	NOUN
ejpam-1097	273	5	=	=	SYM
ejpam-1097	273	6	xr	xr	PROPN
ejpam-1097	273	7	.	.	PUNCT
ejpam-1097	274	1	it	it	PRON
ejpam-1097	274	2	follows	follow	VERB
ejpam-1097	274	3	that	that	SCONJ
ejpam-1097	274	4	h	h	NOUN
ejpam-1097	274	5	is	be	AUX
ejpam-1097	274	6	local	local	ADJ
ejpam-1097	274	7	.	.	PUNCT
ejpam-1097	275	1	let	let	VERB
ejpam-1097	275	2	n	n	CCONJ
ejpam-1097	275	3	>	>	X
ejpam-1097	275	4	1	1	NUM
ejpam-1097	275	5	be	be	AUX
ejpam-1097	275	6	a	a	DET
ejpam-1097	275	7	positive	positive	ADJ
ejpam-1097	275	8	integer	integer	NOUN
ejpam-1097	275	9	and	and	CCONJ
ejpam-1097	275	10	assume	assume	VERB
ejpam-1097	275	11	that	that	SCONJ
ejpam-1097	275	12	each	each	DET
ejpam-1097	275	13	m	m	VERB
ejpam-1097	275	14	j	j	PROPN
ejpam-1097	275	15	having	have	VERB
ejpam-1097	275	16	goldie	goldie	PROPN
ejpam-1097	275	17	dimension	dimension	PROPN
ejpam-1097	275	18	k	k	PROPN
ejpam-1097	276	1	(	(	PUNCT
ejpam-1097	276	2	1≤	1≤	NOUN
ejpam-1097	276	3	k	k	X
ejpam-1097	276	4	<	<	X
ejpam-1097	276	5	n	n	CCONJ
ejpam-1097	276	6	)	)	PUNCT
ejpam-1097	276	7	is	be	AUX
ejpam-1097	276	8	local	local	ADJ
ejpam-1097	276	9	or	or	CCONJ
ejpam-1097	276	10	a	a	DET
ejpam-1097	276	11	finite	finite	ADJ
ejpam-1097	276	12	direct	direct	ADJ
ejpam-1097	276	13	sum	sum	NOUN
ejpam-1097	276	14	of	of	ADP
ejpam-1097	276	15	local	local	ADJ
ejpam-1097	276	16	submodules	submodule	NOUN
ejpam-1097	276	17	.	.	PUNCT
ejpam-1097	277	1	let	let	VERB
ejpam-1097	277	2	j	j	PROPN
ejpam-1097	277	3	∈	∈	PROPN
ejpam-1097	277	4	j	j	PROPN
ejpam-1097	277	5	and	and	CCONJ
ejpam-1097	277	6	h	h	NOUN
ejpam-1097	278	1	=	=	NOUN
ejpam-1097	278	2	m	m	VERB
ejpam-1097	278	3	j	j	NOUN
ejpam-1097	278	4	and	and	CCONJ
ejpam-1097	278	5	assume	assume	VERB
ejpam-1097	278	6	h	h	NOUN
ejpam-1097	278	7	has	have	AUX
ejpam-1097	278	8	goldie	goldie	PROPN
ejpam-1097	278	9	dimension	dimension	PROPN
ejpam-1097	278	10	n.	n.	PROPN
ejpam-1097	278	11	suppose	suppose	VERB
ejpam-1097	278	12	that	that	SCONJ
ejpam-1097	278	13	h	h	NOUN
ejpam-1097	278	14	is	be	AUX
ejpam-1097	278	15	not	not	PART
ejpam-1097	278	16	local	local	ADJ
ejpam-1097	278	17	.	.	PUNCT
ejpam-1097	279	1	let	let	VERB
ejpam-1097	279	2	x	x	PUNCT
ejpam-1097	279	3	∈	∈	PROPN
ejpam-1097	279	4	h	h	NOUN
ejpam-1097	279	5	\	\	NOUN
ejpam-1097	279	6	rad(h	rad(h	PROPN
ejpam-1097	279	7	)	)	PUNCT
ejpam-1097	279	8	such	such	ADJ
ejpam-1097	279	9	that	that	DET
ejpam-1097	279	10	h	h	PROPN
ejpam-1097	279	11	6=	6=	ADP
ejpam-1097	279	12	xr	xr	PROPN
ejpam-1097	279	13	.	.	PUNCT
ejpam-1097	280	1	since	since	SCONJ
ejpam-1097	280	2	h	h	NOUN
ejpam-1097	280	3	is	be	AUX
ejpam-1097	280	4	x	x	PUNCT
ejpam-1097	280	5	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	280	6	,	,	PUNCT
ejpam-1097	280	7	there	there	PRON
ejpam-1097	280	8	exist	exist	VERB
ejpam-1097	280	9	submodules	submodule	NOUN
ejpam-1097	280	10	k	k	PROPN
ejpam-1097	280	11	,	,	PUNCT
ejpam-1097	280	12	k1	k1	PROPN
ejpam-1097	280	13	of	of	ADP
ejpam-1097	280	14	h	h	NOUN
ejpam-1097	280	15	with	with	ADP
ejpam-1097	280	16	k	k	PROPN
ejpam-1097	280	17	∈	∈	PROPN
ejpam-1097	280	18	b(h	b(h	PROPN
ejpam-1097	280	19	,	,	PUNCT
ejpam-1097	280	20	x	x	PUNCT
ejpam-1097	280	21	)	)	PUNCT
ejpam-1097	280	22	such	such	ADJ
ejpam-1097	280	23	that	that	DET
ejpam-1097	280	24	h	h	NOUN
ejpam-1097	281	1	=	=	SYM
ejpam-1097	281	2	xr+	xr+	PROPN
ejpam-1097	282	1	k	k	PROPN
ejpam-1097	283	1	=	=	SYM
ejpam-1097	283	2	k	k	PROPN
ejpam-1097	283	3	⊕	⊕	PROPN
ejpam-1097	283	4	k1	k1	PROPN
ejpam-1097	283	5	and	and	CCONJ
ejpam-1097	283	6	xr∩	xr∩	PROPN
ejpam-1097	284	1	k	k	PROPN
ejpam-1097	284	2	≪	≪	PROPN
ejpam-1097	284	3	k	k	X
ejpam-1097	284	4	.	.	PUNCT
ejpam-1097	285	1	it	it	PRON
ejpam-1097	285	2	is	be	AUX
ejpam-1097	285	3	clear	clear	ADJ
ejpam-1097	285	4	that	that	SCONJ
ejpam-1097	285	5	k1	k1	PROPN
ejpam-1097	285	6	6=	6=	ADP
ejpam-1097	285	7	0	0	NUM
ejpam-1097	285	8	.	.	PUNCT
ejpam-1097	286	1	also	also	ADV
ejpam-1097	286	2	k	k	PROPN
ejpam-1097	286	3	6=	6=	PROPN
ejpam-1097	286	4	0	0	NUM
ejpam-1097	286	5	.	.	PUNCT
ejpam-1097	287	1	since	since	SCONJ
ejpam-1097	287	2	projective	projective	ADJ
ejpam-1097	287	3	modules	module	NOUN
ejpam-1097	287	4	satisfy	satisfy	VERB
ejpam-1097	287	5	(	(	PUNCT
ejpam-1097	287	6	d3	d3	PROPN
ejpam-1097	287	7	)	)	PUNCT
ejpam-1097	287	8	,	,	PUNCT
ejpam-1097	287	9	and	and	CCONJ
ejpam-1097	287	10	so	so	ADV
ejpam-1097	287	11	they	they	PRON
ejpam-1097	287	12	satisfy	satisfy	VERB
ejpam-1097	287	13	b(m	b(m	PROPN
ejpam-1097	287	14	,	,	PUNCT
ejpam-1097	287	15	x	x	NOUN
ejpam-1097	287	16	)	)	PUNCT
ejpam-1097	287	17	-(d3	-(d3	NUM
ejpam-1097	287	18	)	)	PUNCT
ejpam-1097	287	19	.	.	PUNCT
ejpam-1097	288	1	by	by	ADP
ejpam-1097	288	2	proposition	proposition	NOUN
ejpam-1097	288	3	3	3	NUM
ejpam-1097	288	4	,	,	PUNCT
ejpam-1097	288	5	we	we	PRON
ejpam-1097	288	6	obtain	obtain	VERB
ejpam-1097	288	7	that	that	SCONJ
ejpam-1097	288	8	any	any	DET
ejpam-1097	288	9	direct	direct	ADJ
ejpam-1097	288	10	summand	summand	NOUN
ejpam-1097	288	11	of	of	ADP
ejpam-1097	288	12	m	m	PROPN
ejpam-1097	288	13	is	be	AUX
ejpam-1097	288	14	x	x	PUNCT
ejpam-1097	288	15	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	288	16	.	.	PUNCT
ejpam-1097	289	1	thus	thus	ADV
ejpam-1097	289	2	k	k	PROPN
ejpam-1097	289	3	and	and	CCONJ
ejpam-1097	289	4	k1	k1	PROPN
ejpam-1097	289	5	are	be	AUX
ejpam-1097	289	6	x	x	X
ejpam-1097	289	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	289	8	.	.	PUNCT
ejpam-1097	290	1	by	by	ADP
ejpam-1097	290	2	induction	induction	NOUN
ejpam-1097	290	3	,	,	PUNCT
ejpam-1097	290	4	k	k	PROPN
ejpam-1097	290	5	and	and	CCONJ
ejpam-1097	290	6	k1	k1	PROPN
ejpam-1097	290	7	are	be	AUX
ejpam-1097	290	8	local	local	ADJ
ejpam-1097	290	9	or	or	CCONJ
ejpam-1097	290	10	finite	finite	VERB
ejpam-1097	290	11	direct	direct	ADJ
ejpam-1097	290	12	sum	sum	NOUN
ejpam-1097	290	13	of	of	ADP
ejpam-1097	290	14	local	local	ADJ
ejpam-1097	290	15	submodules	submodule	NOUN
ejpam-1097	290	16	.	.	PUNCT
ejpam-1097	291	1	this	this	PRON
ejpam-1097	291	2	completes	complete	VERB
ejpam-1097	291	3	the	the	DET
ejpam-1097	291	4	proof	proof	NOUN
ejpam-1097	291	5	of	of	ADP
ejpam-1097	291	6	(	(	PUNCT
ejpam-1097	291	7	i)⇒	i)⇒	PROPN
ejpam-1097	291	8	(	(	PUNCT
ejpam-1097	291	9	ii	ii	NOUN
ejpam-1097	291	10	)	)	PUNCT
ejpam-1097	291	11	.	.	PUNCT
ejpam-1097	292	1	(	(	PUNCT
ejpam-1097	292	2	ii)⇒	ii)⇒	PROPN
ejpam-1097	292	3	(	(	PUNCT
ejpam-1097	292	4	i	i	NOUN
ejpam-1097	292	5	)	)	PUNCT
ejpam-1097	292	6	it	it	PRON
ejpam-1097	292	7	is	be	AUX
ejpam-1097	292	8	clear	clear	ADJ
ejpam-1097	292	9	.	.	PUNCT
ejpam-1097	293	1	lemma	lemma	PROPN
ejpam-1097	293	2	5	5	X
ejpam-1097	293	3	.	.	PUNCT
ejpam-1097	294	1	let	let	VERB
ejpam-1097	294	2	m	m	PRON
ejpam-1097	294	3	be	be	AUX
ejpam-1097	294	4	an	an	DET
ejpam-1097	294	5	indecomposable	indecomposable	ADJ
ejpam-1097	294	6	module	module	NOUN
ejpam-1097	294	7	.	.	PUNCT
ejpam-1097	295	1	then	then	ADV
ejpam-1097	295	2	m	m	PROPN
ejpam-1097	295	3	is	be	AUX
ejpam-1097	295	4	x	x	X
ejpam-1097	295	5	-hollow	-hollow	PROPN
ejpam-1097	295	6	if	if	SCONJ
ejpam-1097	296	1	and	and	CCONJ
ejpam-1097	296	2	only	only	ADV
ejpam-1097	296	3	if	if	SCONJ
ejpam-1097	296	4	m	m	NOUN
ejpam-1097	296	5	is	be	AUX
ejpam-1097	296	6	completely	completely	ADV
ejpam-1097	296	7	x	x	SYM
ejpam-1097	296	8	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	296	9	.	.	PUNCT
ejpam-1097	297	1	proof	proof	NOUN
ejpam-1097	297	2	.	.	PUNCT
ejpam-1097	298	1	let	let	VERB
ejpam-1097	298	2	m	m	PRON
ejpam-1097	298	3	be	be	AUX
ejpam-1097	298	4	completely	completely	ADV
ejpam-1097	298	5	x	x	SYM
ejpam-1097	298	6	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	298	7	.	.	PUNCT
ejpam-1097	299	1	if	if	SCONJ
ejpam-1097	299	2	n	n	NUM
ejpam-1097	299	3	∈	∈	PROPN
ejpam-1097	299	4	b(m	b(m	PROPN
ejpam-1097	299	5	,	,	PUNCT
ejpam-1097	299	6	x	x	X
ejpam-1097	299	7	)	)	PUNCT
ejpam-1097	299	8	is	be	AUX
ejpam-1097	299	9	a	a	DET
ejpam-1097	299	10	proper	proper	ADJ
ejpam-1097	299	11	submodule	submodule	NOUN
ejpam-1097	299	12	of	of	ADP
ejpam-1097	299	13	m	m	PROPN
ejpam-1097	299	14	,	,	PUNCT
ejpam-1097	299	15	then	then	ADV
ejpam-1097	299	16	there	there	PRON
ejpam-1097	299	17	exists	exist	VERB
ejpam-1097	299	18	an	an	DET
ejpam-1097	299	19	x	x	SYM
ejpam-1097	299	20	-supplement	-supplement	NOUN
ejpam-1097	299	21	a	a	PRON
ejpam-1097	299	22	of	of	ADP
ejpam-1097	299	23	m	m	PRON
ejpam-1097	299	24	such	such	ADJ
ejpam-1097	299	25	that	that	SCONJ
ejpam-1097	299	26	a	a	PRON
ejpam-1097	299	27	is	be	AUX
ejpam-1097	299	28	direct	direct	ADJ
ejpam-1097	299	29	summand	summand	NOUN
ejpam-1097	299	30	of	of	ADP
ejpam-1097	299	31	m	m	PROPN
ejpam-1097	299	32	.	.	PUNCT
ejpam-1097	300	1	by	by	ADP
ejpam-1097	300	2	hypothesis	hypothesis	NOUN
ejpam-1097	300	3	we	we	PRON
ejpam-1097	300	4	have	have	VERB
ejpam-1097	300	5	a	a	DET
ejpam-1097	300	6	=	=	NOUN
ejpam-1097	300	7	m	m	NOUN
ejpam-1097	300	8	.	.	PUNCT
ejpam-1097	301	1	thus	thus	ADV
ejpam-1097	301	2	n	n	CCONJ
ejpam-1097	301	3	=	=	SYM
ejpam-1097	301	4	n	n	NOUN
ejpam-1097	301	5	∩	∩	X
ejpam-1097	301	6	m	m	NOUN
ejpam-1097	301	7	=	=	SYM
ejpam-1097	301	8	n	n	NOUN
ejpam-1097	301	9	∩	∩	NOUN
ejpam-1097	301	10	a	a	DET
ejpam-1097	301	11	≪	≪	ADJ
ejpam-1097	301	12	m	m	NOUN
ejpam-1097	301	13	.	.	PUNCT
ejpam-1097	302	1	therefore	therefore	ADV
ejpam-1097	302	2	m	m	PROPN
ejpam-1097	302	3	is	be	AUX
ejpam-1097	302	4	x	x	X
ejpam-1097	302	5	-hollow	-hollow	PROPN
ejpam-1097	302	6	.	.	PUNCT
ejpam-1097	303	1	conversely	conversely	ADV
ejpam-1097	303	2	,	,	PUNCT
ejpam-1097	303	3	if	if	SCONJ
ejpam-1097	303	4	m	m	PROPN
ejpam-1097	303	5	is	be	AUX
ejpam-1097	303	6	x	x	X
ejpam-1097	303	7	-hollow	-hollow	PROPN
ejpam-1097	303	8	and	and	CCONJ
ejpam-1097	303	9	n	n	PRON
ejpam-1097	303	10	∈	∈	PROPN
ejpam-1097	303	11	b(m	b(m	PROPN
ejpam-1097	303	12	,	,	PUNCT
ejpam-1097	303	13	x	x	X
ejpam-1097	303	14	)	)	PUNCT
ejpam-1097	303	15	then	then	ADV
ejpam-1097	303	16	n	n	CCONJ
ejpam-1097	303	17	≪	≪	NOUN
ejpam-1097	303	18	m	m	PRON
ejpam-1097	303	19	.	.	PUNCT
ejpam-1097	304	1	since	since	SCONJ
ejpam-1097	304	2	m	m	PROPN
ejpam-1097	304	3	∈	∈	PROPN
ejpam-1097	304	4	b(m	b(m	PROPN
ejpam-1097	304	5	,	,	PUNCT
ejpam-1097	304	6	x	x	PROPN
ejpam-1097	304	7	)	)	PUNCT
ejpam-1097	304	8	,	,	PUNCT
ejpam-1097	304	9	m	m	PROPN
ejpam-1097	304	10	is	be	AUX
ejpam-1097	304	11	an	an	DET
ejpam-1097	304	12	x	x	SYM
ejpam-1097	304	13	-supplement	-supplement	NOUN
ejpam-1097	304	14	of	of	ADP
ejpam-1097	304	15	n	n	NOUN
ejpam-1097	304	16	in	in	ADP
ejpam-1097	304	17	m	m	PROPN
ejpam-1097	304	18	.	.	PUNCT
ejpam-1097	305	1	references	reference	NOUN
ejpam-1097	305	2	115	115	NUM
ejpam-1097	305	3	proposition	proposition	NOUN
ejpam-1097	305	4	5	5	NUM
ejpam-1097	305	5	.	.	PUNCT
ejpam-1097	306	1	let	let	VERB
ejpam-1097	306	2	m	m	VERB
ejpam-1097	306	3	=	=	VERB
ejpam-1097	306	4	u	u	PROPN
ejpam-1097	306	5	⊕	⊕	PROPN
ejpam-1097	306	6	v	v	ADP
ejpam-1097	306	7	such	such	DET
ejpam-1097	306	8	that	that	PRON
ejpam-1097	306	9	u	u	NOUN
ejpam-1097	306	10	and	and	CCONJ
ejpam-1097	306	11	v	v	NOUN
ejpam-1097	306	12	have	have	VERB
ejpam-1097	306	13	local	local	ADJ
ejpam-1097	306	14	endomorphism	endomorphism	NOUN
ejpam-1097	306	15	rings	ring	NOUN
ejpam-1097	306	16	.	.	PUNCT
ejpam-1097	307	1	then	then	ADV
ejpam-1097	307	2	m	m	PROPN
ejpam-1097	307	3	is	be	AUX
ejpam-1097	307	4	completely	completely	ADV
ejpam-1097	307	5	x	x	SYM
ejpam-1097	307	6	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	307	7	if	if	SCONJ
ejpam-1097	308	1	and	and	CCONJ
ejpam-1097	308	2	only	only	ADV
ejpam-1097	308	3	if	if	SCONJ
ejpam-1097	308	4	u	u	NOUN
ejpam-1097	308	5	and	and	CCONJ
ejpam-1097	308	6	v	v	NOUN
ejpam-1097	308	7	are	be	AUX
ejpam-1097	308	8	x	x	X
ejpam-1097	308	9	-hollow	-hollow	ADJ
ejpam-1097	308	10	modules	module	NOUN
ejpam-1097	308	11	.	.	PUNCT
ejpam-1097	309	1	proof	proof	NOUN
ejpam-1097	309	2	.	.	PUNCT
ejpam-1097	310	1	the	the	DET
ejpam-1097	310	2	necessity	necessity	NOUN
ejpam-1097	310	3	is	be	AUX
ejpam-1097	310	4	clear	clear	ADJ
ejpam-1097	310	5	from	from	ADP
ejpam-1097	310	6	lemma	lemma	PROPN
ejpam-1097	310	7	5	5	NUM
ejpam-1097	310	8	.	.	PUNCT
ejpam-1097	311	1	conversely	conversely	ADV
ejpam-1097	311	2	,	,	PUNCT
ejpam-1097	311	3	let	let	VERB
ejpam-1097	311	4	k	k	PROPN
ejpam-1097	311	5	∈	∈	PROPN
ejpam-1097	311	6	b(m	b(m	PROPN
ejpam-1097	311	7	,	,	PUNCT
ejpam-1097	311	8	x	x	X
ejpam-1097	311	9	)	)	PUNCT
ejpam-1097	311	10	be	be	AUX
ejpam-1097	311	11	a	a	DET
ejpam-1097	311	12	direct	direct	ADJ
ejpam-1097	311	13	summand	summand	NOUN
ejpam-1097	311	14	of	of	ADP
ejpam-1097	311	15	m	m	PROPN
ejpam-1097	311	16	.	.	PUNCT
ejpam-1097	312	1	if	if	SCONJ
ejpam-1097	312	2	k	k	PROPN
ejpam-1097	312	3	=	=	VERB
ejpam-1097	312	4	m	m	VERB
ejpam-1097	312	5	then	then	ADV
ejpam-1097	312	6	by	by	ADP
ejpam-1097	312	7	corollary	corollary	ADJ
ejpam-1097	312	8	1	1	NUM
ejpam-1097	312	9	,	,	PUNCT
ejpam-1097	312	10	k	k	X
ejpam-1097	312	11	is	be	AUX
ejpam-1097	312	12	x	x	PUNCT
ejpam-1097	312	13	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	312	14	.	.	PUNCT
ejpam-1097	313	1	assume	assume	VERB
ejpam-1097	313	2	k	k	PROPN
ejpam-1097	313	3	6=	6=	PROPN
ejpam-1097	313	4	m	m	PROPN
ejpam-1097	313	5	.	.	PUNCT
ejpam-1097	314	1	then	then	ADV
ejpam-1097	314	2	either	either	CCONJ
ejpam-1097	314	3	k	k	PROPN
ejpam-1097	314	4	∼=	∼=	PROPN
ejpam-1097	314	5	u	u	NOUN
ejpam-1097	314	6	or	or	CCONJ
ejpam-1097	314	7	k	k	NOUN
ejpam-1097	314	8	∼=	∼=	PROPN
ejpam-1097	314	9	v	v	NOUN
ejpam-1097	314	10	[	[	PUNCT
ejpam-1097	314	11	1	1	NUM
ejpam-1097	314	12	,	,	PUNCT
ejpam-1097	314	13	corollary	corollary	NOUN
ejpam-1097	314	14	12.7	12.7	NUM
ejpam-1097	314	15	]	]	PUNCT
ejpam-1097	314	16	.	.	PUNCT
ejpam-1097	315	1	in	in	ADP
ejpam-1097	315	2	either	either	DET
ejpam-1097	315	3	case	case	NOUN
ejpam-1097	315	4	k	k	PROPN
ejpam-1097	315	5	is	be	AUX
ejpam-1097	315	6	x	x	PUNCT
ejpam-1097	315	7	-⊕-supplemented	-⊕-supplemented	PUNCT
ejpam-1097	315	8	.	.	PUNCT
ejpam-1097	316	1	thus	thus	ADV
ejpam-1097	316	2	m	m	NOUN
ejpam-1097	316	3	is	be	AUX
ejpam-1097	316	4	completely	completely	ADV
ejpam-1097	316	5	x	x	SYM
ejpam-1097	316	6	-⊕-supplemented	-⊕-supplemented	X
ejpam-1097	316	7	.	.	PUNCT
ejpam-1097	316	8	theorem	theorem	NOUN
ejpam-1097	316	9	5	5	NUM
ejpam-1097	316	10	.	.	PUNCT
ejpam-1097	317	1	let	let	VERB
ejpam-1097	317	2	m	m	PRON
ejpam-1097	317	3	be	be	AUX
ejpam-1097	317	4	a	a	DET
ejpam-1097	317	5	non	non	ADJ
ejpam-1097	317	6	-	-	ADJ
ejpam-1097	317	7	zero	zero	NUM
ejpam-1097	317	8	module	module	NOUN
ejpam-1097	317	9	with	with	ADP
ejpam-1097	317	10	finite	finite	PROPN
ejpam-1097	317	11	goldie	goldie	PROPN
ejpam-1097	317	12	dimension	dimension	PROPN
ejpam-1097	317	13	.	.	PUNCT
ejpam-1097	318	1	then	then	ADV
ejpam-1097	318	2	the	the	DET
ejpam-1097	318	3	following	follow	VERB
ejpam-1097	318	4	statements	statement	NOUN
ejpam-1097	318	5	are	be	AUX
ejpam-1097	318	6	equivalent	equivalent	ADJ
ejpam-1097	318	7	:	:	PUNCT
ejpam-1097	318	8	(	(	PUNCT
ejpam-1097	318	9	i	i	NOUN
ejpam-1097	318	10	)	)	PUNCT
ejpam-1097	318	11	every	every	DET
ejpam-1097	318	12	direct	direct	ADJ
ejpam-1097	318	13	summand	summand	NOUN
ejpam-1097	318	14	n	n	PROPN
ejpam-1097	318	15	of	of	ADP
ejpam-1097	318	16	m	m	PROPN
ejpam-1097	318	17	with	with	ADP
ejpam-1097	318	18	n	n	PRON
ejpam-1097	318	19	∈	∈	PROPN
ejpam-1097	318	20	b(m	b(m	PROPN
ejpam-1097	318	21	,	,	PUNCT
ejpam-1097	318	22	x	x	X
ejpam-1097	318	23	)	)	PUNCT
ejpam-1097	318	24	is	be	AUX
ejpam-1097	318	25	a	a	DET
ejpam-1097	318	26	finite	finite	ADJ
ejpam-1097	318	27	direct	direct	ADJ
ejpam-1097	318	28	sum	sum	NOUN
ejpam-1097	318	29	of	of	ADP
ejpam-1097	318	30	x	x	PUNCT
ejpam-1097	318	31	-hollow	-hollow	ADJ
ejpam-1097	318	32	modules	module	NOUN
ejpam-1097	318	33	.	.	PUNCT
ejpam-1097	319	1	(	(	PUNCT
ejpam-1097	319	2	ii	ii	NOUN
ejpam-1097	319	3	)	)	PUNCT
ejpam-1097	319	4	m	m	VERB
ejpam-1097	319	5	is	be	AUX
ejpam-1097	319	6	a	a	DET
ejpam-1097	319	7	completely	completely	ADV
ejpam-1097	319	8	x	x	SYM
ejpam-1097	319	9	-⊕-supplemented	-⊕-supplemente	VERB
ejpam-1097	319	10	module	module	NOUN
ejpam-1097	319	11	.	.	PUNCT
ejpam-1097	320	1	proof	proof	NOUN
ejpam-1097	320	2	.	.	PUNCT
ejpam-1097	321	1	(	(	PUNCT
ejpam-1097	321	2	i)⇒	i)⇒	PROPN
ejpam-1097	321	3	(	(	PUNCT
ejpam-1097	321	4	ii	ii	NOUN
ejpam-1097	321	5	)	)	PUNCT
ejpam-1097	321	6	it	it	PRON
ejpam-1097	321	7	is	be	AUX
ejpam-1097	321	8	clear	clear	ADJ
ejpam-1097	321	9	by	by	ADP
ejpam-1097	321	10	corollary	corollary	ADJ
ejpam-1097	321	11	1	1	NUM
ejpam-1097	321	12	.	.	PUNCT
ejpam-1097	321	13	(	(	PUNCT
ejpam-1097	321	14	ii)⇒	ii)⇒	PROPN
ejpam-1097	321	15	(	(	PUNCT
ejpam-1097	321	16	i	i	NOUN
ejpam-1097	321	17	)	)	PUNCT
ejpam-1097	321	18	let	let	VERB
ejpam-1097	321	19	n	n	PRON
ejpam-1097	321	20	be	be	AUX
ejpam-1097	321	21	a	a	DET
ejpam-1097	321	22	direct	direct	ADJ
ejpam-1097	321	23	summand	summand	NOUN
ejpam-1097	321	24	of	of	ADP
ejpam-1097	321	25	m	m	PROPN
ejpam-1097	321	26	with	with	ADP
ejpam-1097	321	27	n	n	PRON
ejpam-1097	321	28	∈	∈	PROPN
ejpam-1097	321	29	b(m	b(m	PROPN
ejpam-1097	321	30	,	,	PUNCT
ejpam-1097	321	31	x	x	PROPN
ejpam-1097	321	32	)	)	PUNCT
ejpam-1097	321	33	.	.	PUNCT
ejpam-1097	322	1	since	since	SCONJ
ejpam-1097	322	2	n	n	NUM
ejpam-1097	322	3	has	have	VERB
ejpam-1097	322	4	finite	finite	PROPN
ejpam-1097	322	5	goldie	goldie	PROPN
ejpam-1097	322	6	dimension	dimension	PROPN
ejpam-1097	322	7	,	,	PUNCT
ejpam-1097	322	8	n	n	PRON
ejpam-1097	322	9	has	have	VERB
ejpam-1097	322	10	a	a	DET
ejpam-1097	322	11	decomposition	decomposition	NOUN
ejpam-1097	322	12	n	n	PROPN
ejpam-1097	322	13	=	=	SYM
ejpam-1097	322	14	l1	l1	PROPN
ejpam-1097	322	15	⊕	⊕	PROPN
ejpam-1097	322	16	.	.	PUNCT
ejpam-1097	322	17	.	.	PUNCT
ejpam-1097	323	1	.	.	PUNCT
ejpam-1097	324	1	⊕	⊕	PROPN
ejpam-1097	325	1	ln	ln	PROPN
ejpam-1097	325	2	,	,	PUNCT
ejpam-1097	325	3	where	where	SCONJ
ejpam-1097	325	4	each	each	DET
ejpam-1097	325	5	li	li	PROPN
ejpam-1097	325	6	is	be	AUX
ejpam-1097	325	7	indecomposable	indecomposable	ADJ
ejpam-1097	325	8	for	for	ADP
ejpam-1097	325	9	1≤	1≤	NUM
ejpam-1097	325	10	i	i	PROPN
ejpam-1097	325	11	≤	≤	PROPN
ejpam-1097	326	1	n.	n.	NOUN
ejpam-1097	326	2	thus	thus	ADV
ejpam-1097	326	3	each	each	DET
ejpam-1097	326	4	li	li	NOUN
ejpam-1097	327	1	(	(	PUNCT
ejpam-1097	327	2	1≤	1≤	INTJ
ejpam-1097	327	3	i	i	NOUN
ejpam-1097	327	4	≤	≤	PROPN
ejpam-1097	327	5	n	n	CCONJ
ejpam-1097	327	6	)	)	PUNCT
ejpam-1097	327	7	is	be	AUX
ejpam-1097	327	8	x	x	X
ejpam-1097	327	9	-hollow	-hollow	PROPN
ejpam-1097	327	10	from	from	ADP
ejpam-1097	327	11	lemma	lemma	PROPN
ejpam-1097	327	12	5	5	NUM
ejpam-1097	327	13	.	.	PUNCT
ejpam-1097	327	14	references	reference	NOUN
ejpam-1097	328	1	[	[	X
ejpam-1097	328	2	1	1	NUM
ejpam-1097	328	3	]	]	X
ejpam-1097	328	4	f	f	PROPN
ejpam-1097	328	5	anderson	anderson	PROPN
ejpam-1097	328	6	and	and	CCONJ
ejpam-1097	328	7	k	k	PROPN
ejpam-1097	328	8	fuller	full	ADJ
ejpam-1097	328	9	.	.	PUNCT
ejpam-1097	329	1	rings	ring	NOUN
ejpam-1097	329	2	and	and	CCONJ
ejpam-1097	329	3	categories	category	NOUN
ejpam-1097	329	4	of	of	ADP
ejpam-1097	329	5	modules	module	NOUN
ejpam-1097	329	6	.	.	PUNCT
ejpam-1097	330	1	springer	springer	NOUN
ejpam-1097	330	2	-	-	PUNCT
ejpam-1097	330	3	verlog	verlog	PROPN
ejpam-1097	330	4	,	,	PUNCT
ejpam-1097	330	5	new	new	PROPN
ejpam-1097	330	6	york	york	PROPN
ejpam-1097	330	7	,	,	PUNCT
ejpam-1097	330	8	1992	1992	NUM
ejpam-1097	330	9	.	.	PUNCT
ejpam-1097	331	1	[	[	X
ejpam-1097	331	2	2	2	NUM
ejpam-1097	331	3	]	]	X
ejpam-1097	331	4	c	c	PROPN
ejpam-1097	331	5	chang	chang	PROPN
ejpam-1097	331	6	.	.	PUNCT
ejpam-1097	332	1	x	x	PUNCT
ejpam-1097	332	2	-lifting	-lifte	VERB
ejpam-1097	332	3	modules	module	NOUN
ejpam-1097	332	4	over	over	ADP
ejpam-1097	332	5	right	right	ADJ
ejpam-1097	332	6	perfect	perfect	ADJ
ejpam-1097	332	7	rings	ring	NOUN
ejpam-1097	332	8	.	.	PUNCT
ejpam-1097	333	1	bull	bull	NOUN
ejpam-1097	333	2	.	.	PUNCT
ejpam-1097	334	1	korean	korean	ADJ
ejpam-1097	334	2	math	math	PROPN
ejpam-1097	334	3	.	.	PUNCT
ejpam-1097	335	1	soc	soc	PROPN
ejpam-1097	335	2	,	,	PUNCT
ejpam-1097	335	3	45(1):5966	45(1):5966	NUM
ejpam-1097	335	4	,	,	PUNCT
ejpam-1097	335	5	2008	2008	NUM
ejpam-1097	335	6	.	.	PUNCT
ejpam-1097	336	1	[	[	X
ejpam-1097	336	2	3	3	NUM
ejpam-1097	336	3	]	]	X
ejpam-1097	336	4	k	k	PROPN
ejpam-1097	336	5	goodearl	goodearl	PROPN
ejpam-1097	336	6	.	.	PROPN
ejpam-1097	336	7	ring	ring	PROPN
ejpam-1097	336	8	theory	theory	PROPN
ejpam-1097	336	9	,	,	PUNCT
ejpam-1097	336	10	nonsingular	nonsingular	ADJ
ejpam-1097	336	11	rings	ring	NOUN
ejpam-1097	336	12	and	and	CCONJ
ejpam-1097	336	13	modules	module	NOUN
ejpam-1097	336	14	.	.	PUNCT
ejpam-1097	337	1	marcel	marcel	PROPN
ejpam-1097	337	2	dekker	dekker	PROPN
ejpam-1097	337	3	,	,	PUNCT
ejpam-1097	337	4	inc	inc	PROPN
ejpam-1097	337	5	.	.	PROPN
ejpam-1097	337	6	,	,	PUNCT
ejpam-1097	337	7	new	new	PROPN
ejpam-1097	337	8	york	york	PROPN
ejpam-1097	337	9	and	and	CCONJ
ejpam-1097	337	10	basel	basel	PROPN
ejpam-1097	337	11	,	,	PUNCT
ejpam-1097	337	12	1976	1976	NUM
ejpam-1097	337	13	.	.	PUNCT
ejpam-1097	338	1	[	[	X
ejpam-1097	338	2	4	4	X
ejpam-1097	338	3	]	]	X
ejpam-1097	338	4	a	a	DET
ejpam-1097	338	5	harmancı	harmancı	NOUN
ejpam-1097	338	6	,	,	PUNCT
ejpam-1097	338	7	d	d	PROPN
ejpam-1097	338	8	tütüncü	tütüncü	PRON
ejpam-1097	338	9	and	and	CCONJ
ejpam-1097	338	10	p	p	PROPN
ejpam-1097	338	11	smith	smith	PROPN
ejpam-1097	338	12	.	.	PUNCT
ejpam-1097	339	1	on	on	ADP
ejpam-1097	339	2	⊕-supplemented	⊕-supplemente	VERB
ejpam-1097	339	3	modules	module	NOUN
ejpam-1097	339	4	.	.	PUNCT
ejpam-1097	340	1	acta	acta	PROPN
ejpam-1097	340	2	math	math	PROPN
ejpam-1097	340	3	.	.	PUNCT
ejpam-1097	341	1	hungar	hungar	PROPN
ejpam-1097	341	2	,	,	PUNCT
ejpam-1097	341	3	83:161	83:161	NUM
ejpam-1097	341	4	-	-	SYM
ejpam-1097	341	5	169	169	NUM
ejpam-1097	341	6	,	,	PUNCT
ejpam-1097	341	7	1999	1999	NUM
ejpam-1097	341	8	.	.	PUNCT
ejpam-1097	342	1	[	[	X
ejpam-1097	342	2	5	5	NUM
ejpam-1097	342	3	]	]	X
ejpam-1097	342	4	d	d	X
ejpam-1097	342	5	tütüncü	tütüncü	PROPN
ejpam-1097	342	6	and	and	CCONJ
ejpam-1097	342	7	a	a	DET
ejpam-1097	342	8	harmancı	harmancı	NOUN
ejpam-1097	342	9	.	.	PUNCT
ejpam-1097	343	1	a	a	DET
ejpam-1097	343	2	relative	relative	ADJ
ejpam-1097	343	3	version	version	NOUN
ejpam-1097	343	4	of	of	ADP
ejpam-1097	343	5	the	the	DET
ejpam-1097	343	6	lifting	lift	VERB
ejpam-1097	343	7	property	property	NOUN
ejpam-1097	343	8	of	of	ADP
ejpam-1097	343	9	modules	module	NOUN
ejpam-1097	343	10	.	.	PUNCT
ejpam-1097	344	1	algebra	algebra	PROPN
ejpam-1097	344	2	colloq	colloq	PROPN
ejpam-1097	344	3	,	,	PUNCT
ejpam-1097	344	4	11(3):361	11(3):361	PROPN
ejpam-1097	344	5	-	-	SYM
ejpam-1097	344	6	370	370	NUM
ejpam-1097	344	7	,	,	PUNCT
ejpam-1097	344	8	2004	2004	NUM
ejpam-1097	344	9	.	.	PUNCT
ejpam-1097	345	1	[	[	X
ejpam-1097	345	2	6	6	NUM
ejpam-1097	345	3	]	]	X
ejpam-1097	345	4	s	s	VERB
ejpam-1097	345	5	mohamed	mohamed	PROPN
ejpam-1097	345	6	and	and	CCONJ
ejpam-1097	345	7	b	b	PROPN
ejpam-1097	345	8	müller	müller	PROPN
ejpam-1097	345	9	.	.	PUNCT
ejpam-1097	346	1	continuous	continuous	ADJ
ejpam-1097	346	2	and	and	CCONJ
ejpam-1097	346	3	discrete	discrete	ADJ
ejpam-1097	346	4	modules	module	NOUN
ejpam-1097	346	5	.	.	PUNCT
ejpam-1097	347	1	london	london	PROPN
ejpam-1097	347	2	math	math	PROPN
ejpam-1097	347	3	.	.	PUNCT
ejpam-1097	348	1	soc	soc	PROPN
ejpam-1097	348	2	.	.	PUNCT
ejpam-1097	349	1	lecture	lecture	NOUN
ejpam-1097	349	2	notes	note	NOUN
ejpam-1097	349	3	series	series	PROPN
ejpam-1097	349	4	147	147	NUM
ejpam-1097	349	5	,	,	PUNCT
ejpam-1097	349	6	cambridge	cambridge	PROPN
ejpam-1097	349	7	,	,	PUNCT
ejpam-1097	349	8	university	university	NOUN
ejpam-1097	349	9	press	press	NOUN
ejpam-1097	349	10	,	,	PUNCT
ejpam-1097	349	11	1990	1990	NUM
ejpam-1097	349	12	.	.	PUNCT
ejpam-1097	350	1	[	[	X
ejpam-1097	350	2	7	7	X
ejpam-1097	350	3	]	]	PUNCT
ejpam-1097	350	4	n	n	PRON
ejpam-1097	350	5	orhan	orhan	NOUN
ejpam-1097	350	6	and	and	CCONJ
ejpam-1097	350	7	d	d	PROPN
ejpam-1097	350	8	tütüncü	tütüncü	PROPN
ejpam-1097	350	9	.	.	PUNCT
ejpam-1097	351	1	characterizations	characterization	NOUN
ejpam-1097	351	2	of	of	ADP
ejpam-1097	351	3	lifting	lift	VERB
ejpam-1097	351	4	modules	module	NOUN
ejpam-1097	351	5	in	in	ADP
ejpam-1097	351	6	terms	term	NOUN
ejpam-1097	351	7	of	of	ADP
ejpam-1097	351	8	cojective	cojective	ADJ
ejpam-1097	351	9	modules	module	NOUN
ejpam-1097	351	10	and	and	CCONJ
ejpam-1097	351	11	the	the	DET
ejpam-1097	351	12	class	class	NOUN
ejpam-1097	351	13	ofb(m	ofb(m	PROPN
ejpam-1097	351	14	,	,	PUNCT
ejpam-1097	351	15	x	x	PROPN
ejpam-1097	351	16	)	)	PUNCT
ejpam-1097	351	17	,	,	PUNCT
ejpam-1097	351	18	international	international	ADJ
ejpam-1097	351	19	j.	j.	PROPN
ejpam-1097	351	20	mathematics	mathematics	PROPN
ejpam-1097	351	21	6:647	6:647	PROPN
ejpam-1097	351	22	-	-	SYM
ejpam-1097	351	23	660	660	NUM
ejpam-1097	351	24	,	,	PUNCT
ejpam-1097	351	25	2005	2005	NUM
ejpam-1097	351	26	.	.	PUNCT
ejpam-1097	352	1	[	[	X
ejpam-1097	352	2	8	8	X
ejpam-1097	352	3	]	]	X
ejpam-1097	352	4	p	p	X
ejpam-1097	352	5	smith	smith	PROPN
ejpam-1097	352	6	.	.	PUNCT
ejpam-1097	353	1	modules	module	NOUN
ejpam-1097	353	2	for	for	ADP
ejpam-1097	353	3	which	which	PRON
ejpam-1097	353	4	every	every	DET
ejpam-1097	353	5	submodules	submodule	NOUN
ejpam-1097	353	6	has	have	VERB
ejpam-1097	353	7	a	a	DET
ejpam-1097	353	8	unique	unique	ADJ
ejpam-1097	353	9	closure	closure	NOUN
ejpam-1097	353	10	.	.	PUNCT
ejpam-1097	354	1	ring	ring	NOUN
ejpam-1097	354	2	theory	theory	NOUN
ejpam-1097	354	3	,	,	PUNCT
ejpam-1097	354	4	world	world	PROPN
ejpam-1097	354	5	sci	sci	PROPN
ejpam-1097	354	6	.	.	PROPN
ejpam-1097	354	7	,	,	PUNCT
ejpam-1097	354	8	pages	page	NOUN
ejpam-1097	354	9	302	302	NUM
ejpam-1097	354	10	-	-	SYM
ejpam-1097	354	11	313	313	NUM
ejpam-1097	354	12	,	,	PUNCT
ejpam-1097	354	13	singapore	singapore	PROPN
ejpam-1097	354	14	,	,	PUNCT
ejpam-1097	354	15	1993	1993	NUM
ejpam-1097	354	16	.	.	PUNCT
ejpam-1097	355	1	[	[	X
ejpam-1097	355	2	9	9	NUM
ejpam-1097	355	3	]	]	SYM
ejpam-1097	355	4	r	r	NOUN
ejpam-1097	355	5	wisbauer	wisbauer	NOUN
ejpam-1097	355	6	.	.	PUNCT
ejpam-1097	356	1	foundations	foundation	NOUN
ejpam-1097	356	2	of	of	ADP
ejpam-1097	356	3	module	module	NOUN
ejpam-1097	356	4	and	and	CCONJ
ejpam-1097	356	5	ring	ring	NOUN
ejpam-1097	356	6	theory	theory	NOUN
ejpam-1097	356	7	.	.	PUNCT
ejpam-1097	357	1	gordon	gordon	PROPN
ejpam-1097	357	2	and	and	CCONJ
ejpam-1097	357	3	breach	breach	NOUN
ejpam-1097	357	4	,	,	PUNCT
ejpam-1097	357	5	reading	reading	NOUN
ejpam-1097	357	6	,	,	PUNCT
ejpam-1097	357	7	1991	1991	NUM
ejpam-1097	357	8	.	.	PUNCT