id	sid	tid	token	lemma	pos
iajs-219	1	1	microsoft	microsoft	PROPN
iajs-219	1	2	word	word	NOUN
iajs-219	1	3	147	147	NUM
iajs-219	1	4	-	-	SYM
iajs-219	1	5	154	154	NUM
iajs-219	1	6	147	147	NUM
iajs-219	1	7	|	|	NOUN
iajs-219	1	8	mathematics	mathematic	NOUN
iajs-219	1	9	٢٠١٥	٢٠١٥	NUM
iajs-219	1	10	)	)	PUNCT
iajs-219	1	11	عام	عام	ADP
iajs-219	1	12	٢العدد	٢العدد	PROPN
iajs-219	1	13	(	(	PUNCT
iajs-219	1	14	٢٨المجلد	٢٨المجلد	NUM
iajs-219	1	15	والتطبيقية	والتطبيقية	PROPN
iajs-219	1	16	الھيثم	الھيثم	NOUN
iajs-219	1	17	للعلوم	للعلوم	PROPN
iajs-219	1	18	الصرفة	الصرفة	NOUN
iajs-219	1	19	ابنمجلة	ابنمجلة	VERB
iajs-219	1	20	ibn	ibn	PROPN
iajs-219	1	21	al	al	PROPN
iajs-219	1	22	-	-	PUNCT
iajs-219	1	23	haitham	haitham	PROPN
iajs-219	1	24	.	.	PUNCT
iajs-219	2	1	j.	j.	PROPN
iajs-219	2	2	for	for	ADP
iajs-219	2	3	pure	pure	PROPN
iajs-219	2	4	&	&	CCONJ
iajs-219	2	5	appl	appl	PROPN
iajs-219	2	6	.	.	PUNCT
iajs-219	3	1	sci	sci	PROPN
iajs-219	3	2	.	.	PUNCT
iajs-219	3	3	vol	vol	NOUN
iajs-219	3	4	.	.	PROPN
iajs-219	4	1	28	28	NUM
iajs-219	4	2	(	(	PUNCT
iajs-219	4	3	٢	٢	NOUN
iajs-219	4	4	)	)	PUNCT
iajs-219	4	5	2015	2015	NUM
iajs-219	4	6	purely	purely	ADV
iajs-219	4	7	goldie	goldie	X
iajs-219	4	8	extending	extend	VERB
iajs-219	4	9	modules	module	NOUN
iajs-219	4	10	saad	saad	PROPN
iajs-219	4	11	a.	a.	PROPN
iajs-219	4	12	al	al	PROPN
iajs-219	4	13	-	-	PUNCT
iajs-219	4	14	saadi	saadi	PROPN
iajs-219	4	15	ikbal	ikbal	PROPN
iajs-219	4	16	a.	a.	PROPN
iajs-219	4	17	omer	omer	PROPN
iajs-219	4	18	dep	dep	PROPN
iajs-219	4	19	.	.	PROPN
iajs-219	4	20	of	of	ADP
iajs-219	4	21	mathematics	mathematics	PROPN
iajs-219	4	22	/college	/college	PROPN
iajs-219	4	23	of	of	ADP
iajs-219	4	24	science	science	PROPN
iajs-219	4	25	/	/	SYM
iajs-219	4	26	university	university	PROPN
iajs-219	4	27	of	of	ADP
iajs-219	4	28	al	al	PROPN
iajs-219	4	29	mustansiriyah	mustansiriyah	PROPN
iajs-219	4	30	received	receive	VERB
iajs-219	4	31	in	in	ADP
iajs-219	4	32	:	:	PUNCT
iajs-219	4	33	4	4	NUM
iajs-219	4	34	march	march	NOUN
iajs-219	4	35	2015	2015	NUM
iajs-219	4	36	,	,	PUNCT
iajs-219	4	37	accepted	accept	VERB
iajs-219	4	38	in	in	ADP
iajs-219	4	39	:	:	PUNCT
iajs-219	4	40	13	13	NUM
iajs-219	4	41	april	april	PROPN
iajs-219	4	42	2015	2015	NUM
iajs-219	4	43	abstract	abstract	NOUN
iajs-219	4	44	an	an	DET
iajs-219	4	45	-module	-module	NOUN
iajs-219	4	46	is	be	AUX
iajs-219	4	47	extending	extend	VERB
iajs-219	4	48	if	if	SCONJ
iajs-219	4	49	every	every	DET
iajs-219	4	50	submodule	submodule	NOUN
iajs-219	4	51	of	of	ADP
iajs-219	4	52	is	be	AUX
iajs-219	4	53	essential	essential	ADJ
iajs-219	4	54	in	in	ADP
iajs-219	4	55	a	a	DET
iajs-219	4	56	direct	direct	ADJ
iajs-219	4	57	summand	summand	NOUN
iajs-219	4	58	of	of	ADP
iajs-219	4	59	.	.	PUNCT
iajs-219	5	1	following	follow	VERB
iajs-219	5	2	clark	clark	PROPN
iajs-219	5	3	,	,	PUNCT
iajs-219	5	4	an	an	DET
iajs-219	5	5	-module	-module	NOUN
iajs-219	5	6	is	be	AUX
iajs-219	5	7	purely	purely	ADV
iajs-219	5	8	extending	extend	VERB
iajs-219	5	9	if	if	SCONJ
iajs-219	5	10	every	every	DET
iajs-219	5	11	submodule	submodule	NOUN
iajs-219	5	12	of	of	ADP
iajs-219	5	13	is	be	AUX
iajs-219	5	14	essential	essential	ADJ
iajs-219	5	15	in	in	ADP
iajs-219	5	16	a	a	DET
iajs-219	5	17	pure	pure	ADJ
iajs-219	5	18	submodule	submodule	NOUN
iajs-219	5	19	of	of	ADP
iajs-219	5	20	.	.	PUNCT
iajs-219	6	1	it	it	PRON
iajs-219	6	2	is	be	AUX
iajs-219	6	3	clear	clear	ADJ
iajs-219	6	4	purely	purely	ADV
iajs-219	6	5	extending	extend	VERB
iajs-219	6	6	is	be	AUX
iajs-219	6	7	generalization	generalization	NOUN
iajs-219	6	8	of	of	ADP
iajs-219	6	9	extending	extend	VERB
iajs-219	6	10	modules	module	NOUN
iajs-219	6	11	.	.	PUNCT
iajs-219	7	1	following	follow	VERB
iajs-219	7	2	birkenmeier	birkenmeier	PROPN
iajs-219	7	3	and	and	CCONJ
iajs-219	7	4	tercan	tercan	PROPN
iajs-219	7	5	,	,	PUNCT
iajs-219	7	6	an	an	DET
iajs-219	7	7	-module	-module	NOUN
iajs-219	7	8	is	be	AUX
iajs-219	7	9	goldie	goldie	NOUN
iajs-219	7	10	extending	extend	VERB
iajs-219	7	11	if	if	SCONJ
iajs-219	7	12	,	,	PUNCT
iajs-219	7	13	for	for	ADP
iajs-219	7	14	each	each	DET
iajs-219	7	15	submodule	submodule	NOUN
iajs-219	7	16	of	of	ADP
iajs-219	7	17	,	,	PUNCT
iajs-219	7	18	there	there	PRON
iajs-219	7	19	is	be	VERB
iajs-219	7	20	a	a	DET
iajs-219	7	21	direct	direct	ADJ
iajs-219	7	22	summand	summand	NOUN
iajs-219	7	23	d	d	PROPN
iajs-219	7	24	of	of	ADP
iajs-219	7	25	such	such	ADJ
iajs-219	7	26	that	that	PRON
iajs-219	7	27	.	.	PUNCT
iajs-219	8	1	in	in	ADP
iajs-219	8	2	this	this	DET
iajs-219	8	3	paper	paper	NOUN
iajs-219	8	4	,	,	PUNCT
iajs-219	8	5	we	we	PRON
iajs-219	8	6	introduce	introduce	VERB
iajs-219	8	7	and	and	CCONJ
iajs-219	8	8	study	study	VERB
iajs-219	8	9	class	class	NOUN
iajs-219	8	10	of	of	ADP
iajs-219	8	11	modules	module	NOUN
iajs-219	8	12	which	which	PRON
iajs-219	8	13	are	be	AUX
iajs-219	8	14	proper	proper	ADJ
iajs-219	8	15	generalization	generalization	NOUN
iajs-219	8	16	of	of	ADP
iajs-219	8	17	both	both	CCONJ
iajs-219	8	18	the	the	DET
iajs-219	8	19	purely	purely	ADV
iajs-219	8	20	extending	extend	VERB
iajs-219	8	21	modules	module	NOUN
iajs-219	8	22	and	and	CCONJ
iajs-219	8	23	-extending	-extending	NOUN
iajs-219	8	24	modules	module	NOUN
iajs-219	8	25	.	.	PUNCT
iajs-219	9	1	we	we	PRON
iajs-219	9	2	call	call	VERB
iajs-219	9	3	an	an	DET
iajs-219	9	4	-module	-module	NOUN
iajs-219	9	5	is	be	AUX
iajs-219	9	6	purely	purely	ADV
iajs-219	9	7	goldie	goldie	PROPN
iajs-219	9	8	extending	extend	VERB
iajs-219	9	9	if	if	SCONJ
iajs-219	9	10	,	,	PUNCT
iajs-219	9	11	for	for	ADP
iajs-219	9	12	each	each	PRON
iajs-219	9	13	,	,	PUNCT
iajs-219	9	14	there	there	PRON
iajs-219	9	15	is	be	VERB
iajs-219	9	16	a	a	DET
iajs-219	9	17	pure	pure	ADJ
iajs-219	9	18	submodule	submodule	NOUN
iajs-219	9	19	p	p	NOUN
iajs-219	9	20	of	of	ADP
iajs-219	9	21	such	such	ADJ
iajs-219	9	22	that	that	PRON
iajs-219	9	23	.	.	PUNCT
iajs-219	10	1	many	many	ADJ
iajs-219	10	2	characterizations	characterization	NOUN
iajs-219	10	3	and	and	CCONJ
iajs-219	10	4	properties	property	NOUN
iajs-219	10	5	of	of	ADP
iajs-219	10	6	purely	purely	ADV
iajs-219	10	7	goldie	goldie	PROPN
iajs-219	10	8	extending	extend	VERB
iajs-219	10	9	modules	module	NOUN
iajs-219	10	10	are	be	AUX
iajs-219	10	11	given	give	VERB
iajs-219	10	12	.	.	PUNCT
iajs-219	11	1	also	also	ADV
iajs-219	11	2	,	,	PUNCT
iajs-219	11	3	we	we	PRON
iajs-219	11	4	discuss	discuss	VERB
iajs-219	11	5	when	when	SCONJ
iajs-219	11	6	a	a	DET
iajs-219	11	7	direct	direct	ADJ
iajs-219	11	8	sum	sum	NOUN
iajs-219	11	9	of	of	ADP
iajs-219	11	10	purely	purely	ADV
iajs-219	11	11	goldie	goldie	PROPN
iajs-219	11	12	extending	extend	VERB
iajs-219	11	13	modules	module	NOUN
iajs-219	11	14	is	be	AUX
iajs-219	11	15	purely	purely	ADV
iajs-219	11	16	goldie	goldie	PROPN
iajs-219	11	17	extending	extending	NOUN
iajs-219	11	18	and	and	CCONJ
iajs-219	11	19	moreover	moreover	ADV
iajs-219	11	20	we	we	PRON
iajs-219	11	21	give	give	VERB
iajs-219	11	22	a	a	DET
iajs-219	11	23	sufficient	sufficient	ADJ
iajs-219	11	24	condition	condition	NOUN
iajs-219	11	25	to	to	PART
iajs-219	11	26	make	make	VERB
iajs-219	11	27	this	this	DET
iajs-219	11	28	property	property	NOUN
iajs-219	11	29	of	of	ADP
iajs-219	11	30	purely	purely	ADV
iajs-219	11	31	goldie	goldie	PROPN
iajs-219	11	32	extending	extend	VERB
iajs-219	11	33	modules	module	NOUN
iajs-219	11	34	is	be	AUX
iajs-219	11	35	valid	valid	ADJ
iajs-219	11	36	.	.	PUNCT
iajs-219	12	1	key	key	ADJ
iajs-219	12	2	words	word	NOUN
iajs-219	12	3	:	:	PUNCT
iajs-219	12	4	extending	extend	VERB
iajs-219	12	5	module	module	NOUN
iajs-219	12	6	,	,	PUNCT
iajs-219	12	7	purely	purely	ADV
iajs-219	12	8	extending	extend	VERB
iajs-219	12	9	module	module	NOUN
iajs-219	12	10	,	,	PUNCT
iajs-219	12	11	-extending	-extending	NOUN
iajs-219	12	12	module	module	NOUN
iajs-219	12	13	,	,	PUNCT
iajs-219	12	14	purely	purely	ADV
iajs-219	12	15	goldie	goldie	PROPN
iajs-219	12	16	extending	extending	NOUN
iajs-219	12	17	.	.	PUNCT
iajs-219	13	1	148	148	NUM
iajs-219	13	2	|	|	NOUN
iajs-219	13	3	mathematics	mathematic	NOUN
iajs-219	13	4	٢٠١٥	٢٠١٥	NUM
iajs-219	13	5	)	)	PUNCT
iajs-219	13	6	عام	عام	ADP
iajs-219	13	7	٢العدد	٢العدد	PROPN
iajs-219	13	8	(	(	PUNCT
iajs-219	13	9	٢٨المجلد	٢٨المجلد	NUM
iajs-219	13	10	والتطبيقية	والتطبيقية	PROPN
iajs-219	13	11	الھيثم	الھيثم	NOUN
iajs-219	13	12	للعلوم	للعلوم	PROPN
iajs-219	13	13	الصرفة	الصرفة	NOUN
iajs-219	13	14	ابنمجلة	ابنمجلة	VERB
iajs-219	13	15	ibn	ibn	PROPN
iajs-219	13	16	al	al	PROPN
iajs-219	13	17	-	-	PUNCT
iajs-219	13	18	haitham	haitham	PROPN
iajs-219	13	19	.	.	PUNCT
iajs-219	14	1	j.	j.	PROPN
iajs-219	14	2	for	for	ADP
iajs-219	14	3	pure	pure	PROPN
iajs-219	14	4	&	&	CCONJ
iajs-219	14	5	appl	appl	PROPN
iajs-219	14	6	.	.	PUNCT
iajs-219	15	1	sci	sci	PROPN
iajs-219	15	2	.	.	PUNCT
iajs-219	15	3	vol	vol	NOUN
iajs-219	15	4	.	.	PROPN
iajs-219	16	1	28	28	NUM
iajs-219	16	2	(	(	PUNCT
iajs-219	16	3	٢	٢	NOUN
iajs-219	16	4	)	)	PUNCT
iajs-219	16	5	2015	2015	NUM
iajs-219	16	6	introduction	introduction	NOUN
iajs-219	16	7	throughout	throughout	ADP
iajs-219	16	8	all	all	DET
iajs-219	16	9	rings	ring	NOUN
iajs-219	16	10	are	be	AUX
iajs-219	16	11	associative	associative	ADJ
iajs-219	16	12	and	and	CCONJ
iajs-219	16	13	r	r	NOUN
iajs-219	16	14	denotes	denote	VERB
iajs-219	16	15	a	a	DET
iajs-219	16	16	ring	ring	NOUN
iajs-219	16	17	with	with	ADP
iajs-219	16	18	identity	identity	NOUN
iajs-219	16	19	and	and	CCONJ
iajs-219	16	20	all	all	DET
iajs-219	16	21	modules	module	NOUN
iajs-219	16	22	are	be	AUX
iajs-219	16	23	unitary	unitary	ADJ
iajs-219	16	24	r	r	NOUN
iajs-219	16	25	-	-	PUNCT
iajs-219	16	26	modules	module	NOUN
iajs-219	16	27	.	.	PUNCT
iajs-219	17	1	a	a	DET
iajs-219	17	2	submodule	submodule	NOUN
iajs-219	17	3	of	of	ADP
iajs-219	17	4	a	a	DET
iajs-219	17	5	module	module	NOUN
iajs-219	17	6	is	be	AUX
iajs-219	17	7	called	call	VERB
iajs-219	17	8	essential	essential	ADJ
iajs-219	17	9	if	if	SCONJ
iajs-219	17	10	every	every	DET
iajs-219	17	11	non	non	ADJ
iajs-219	17	12	-	-	ADJ
iajs-219	17	13	zero	zero	NUM
iajs-219	17	14	submodule	submodule	NOUN
iajs-219	17	15	of	of	ADP
iajs-219	17	16	intersects	intersect	NOUN
iajs-219	17	17	nontrivially	nontrivially	ADV
iajs-219	17	18	(	(	PUNCT
iajs-219	17	19	notionally	notionally	ADV
iajs-219	17	20	,	,	PUNCT
iajs-219	17	21	e	e	NOUN
iajs-219	17	22	m	m	PROPN
iajs-219	17	23	)	)	PUNCT
iajs-219	17	24	.	.	PUNCT
iajs-219	18	1	also	also	ADV
iajs-219	18	2	,	,	PUNCT
iajs-219	18	3	a	a	DET
iajs-219	18	4	submodule	submodule	NOUN
iajs-219	18	5	of	of	ADP
iajs-219	18	6	is	be	AUX
iajs-219	18	7	closed	close	VERB
iajs-219	18	8	in	in	ADP
iajs-219	18	9	,	,	PUNCT
iajs-219	18	10	if	if	SCONJ
iajs-219	18	11	it	it	PRON
iajs-219	18	12	has	have	VERB
iajs-219	18	13	no	no	DET
iajs-219	18	14	proper	proper	ADJ
iajs-219	18	15	essential	essential	ADJ
iajs-219	18	16	extension	extension	NOUN
iajs-219	18	17	in	in	ADP
iajs-219	18	18	[	[	X
iajs-219	18	19	1	1	NUM
iajs-219	18	20	]	]	PUNCT
iajs-219	18	21	.	.	PUNCT
iajs-219	19	1	recall	recall	VERB
iajs-219	19	2	that	that	SCONJ
iajs-219	19	3	a	a	DET
iajs-219	19	4	module	module	NOUN
iajs-219	19	5	m	m	VERB
iajs-219	19	6	is	be	AUX
iajs-219	19	7	extending	extend	VERB
iajs-219	19	8	if	if	SCONJ
iajs-219	19	9	every	every	DET
iajs-219	19	10	submodule	submodule	NOUN
iajs-219	19	11	of	of	ADP
iajs-219	19	12	is	be	AUX
iajs-219	19	13	essential	essential	ADJ
iajs-219	19	14	in	in	ADP
iajs-219	19	15	a	a	DET
iajs-219	19	16	direct	direct	ADJ
iajs-219	19	17	summand	summand	NOUN
iajs-219	19	18	of	of	ADP
iajs-219	19	19	.	.	PUNCT
iajs-219	20	1	equivalently	equivalently	ADV
iajs-219	20	2	,	,	PUNCT
iajs-219	20	3	every	every	DET
iajs-219	20	4	closed	closed	ADJ
iajs-219	20	5	submodule	submodule	NOUN
iajs-219	20	6	of	of	ADP
iajs-219	20	7	m	m	PROPN
iajs-219	20	8	is	be	AUX
iajs-219	20	9	direct	direct	ADJ
iajs-219	20	10	summand	summand	NOUN
iajs-219	20	11	[	[	X
iajs-219	20	12	1	1	NUM
iajs-219	20	13	]	]	PUNCT
iajs-219	20	14	.	.	PUNCT
iajs-219	21	1	many	many	ADJ
iajs-219	21	2	generalizations	generalization	NOUN
iajs-219	21	3	of	of	ADP
iajs-219	21	4	extending	extend	VERB
iajs-219	21	5	modules	module	NOUN
iajs-219	21	6	are	be	AUX
iajs-219	21	7	extensively	extensively	ADV
iajs-219	21	8	studied	study	VERB
iajs-219	21	9	.	.	PUNCT
iajs-219	22	1	following	follow	VERB
iajs-219	22	2	fuchs	fuchs	PROPN
iajs-219	22	3	[	[	X
iajs-219	22	4	2	2	NUM
iajs-219	22	5	]	]	PUNCT
iajs-219	22	6	and	and	CCONJ
iajs-219	22	7	clark	clark	NOUN
iajs-219	22	8	[	[	X
iajs-219	22	9	3	3	NUM
iajs-219	22	10	]	]	PUNCT
iajs-219	22	11	,	,	PUNCT
iajs-219	22	12	an	an	DET
iajs-219	22	13	-module	-module	NOUN
iajs-219	22	14	is	be	AUX
iajs-219	22	15	purely	purely	ADV
iajs-219	22	16	extending	extend	VERB
iajs-219	22	17	if	if	SCONJ
iajs-219	22	18	every	every	DET
iajs-219	22	19	submodule	submodule	NOUN
iajs-219	22	20	of	of	ADP
iajs-219	22	21	is	be	AUX
iajs-219	22	22	essentialin	essentialin	NOUN
iajs-219	22	23	a	a	DET
iajs-219	22	24	pure	pure	ADJ
iajs-219	22	25	submodule	submodule	NOUN
iajs-219	22	26	of	of	ADP
iajs-219	22	27	m	m	PROPN
iajs-219	22	28	(	(	PUNCT
iajs-219	22	29	recall	recall	VERB
iajs-219	22	30	that	that	SCONJ
iajs-219	22	31	a	a	DET
iajs-219	22	32	submodule	submodule	NOUN
iajs-219	22	33	n	n	PROPN
iajs-219	22	34	of	of	ADP
iajs-219	22	35	an	an	DET
iajs-219	22	36	r	r	NOUN
iajs-219	22	37	-	-	PUNCT
iajs-219	22	38	module	module	NOUN
iajs-219	22	39	m	m	NOUN
iajs-219	22	40	is	be	AUX
iajs-219	22	41	pure	pure	ADJ
iajs-219	22	42	if	if	SCONJ
iajs-219	22	43	im∩n	im∩n	PROPN
iajs-219	22	44	=	=	NOUN
iajs-219	22	45	in	in	ADP
iajs-219	22	46	for	for	ADP
iajs-219	22	47	every	every	DET
iajs-219	22	48	finitely	finitely	ADV
iajs-219	22	49	generated	generate	VERB
iajs-219	22	50	ideal	ideal	NOUN
iajs-219	22	51	i	i	PRON
iajs-219	22	52	of	of	ADP
iajs-219	22	53	r	r	NOUN
iajs-219	22	54	)	)	PUNCT
iajs-219	22	55	.	.	PUNCT
iajs-219	23	1	also	also	ADV
iajs-219	23	2	in	in	ADP
iajs-219	23	3	[	[	X
iajs-219	23	4	4	4	NUM
iajs-219	23	5	]	]	PUNCT
iajs-219	23	6	,	,	PUNCT
iajs-219	23	7	the	the	DET
iajs-219	23	8	following	follow	VERB
iajs-219	23	9	relations	relation	NOUN
iajs-219	23	10	on	on	ADP
iajs-219	23	11	the	the	DET
iajs-219	23	12	set	set	NOUN
iajs-219	23	13	of	of	ADP
iajs-219	23	14	submodules	submodule	NOUN
iajs-219	23	15	of	of	ADP
iajs-219	23	16	an	an	DET
iajs-219	23	17	r	r	NOUN
iajs-219	23	18	-	-	PUNCT
iajs-219	23	19	module	module	NOUN
iajs-219	23	20	m	m	NOUN
iajs-219	23	21	are	be	AUX
iajs-219	23	22	considered	consider	VERB
iajs-219	23	23	.	.	PUNCT
iajs-219	24	1	(	(	PUNCT
iajs-219	24	2	1	1	X
iajs-219	24	3	)	)	PUNCT
iajs-219	24	4	if	if	SCONJ
iajs-219	24	5	and	and	CCONJ
iajs-219	24	6	only	only	ADV
iajs-219	24	7	if	if	SCONJ
iajs-219	24	8	there	there	PRON
iajs-219	24	9	exists	exist	VERB
iajs-219	24	10	a	a	DET
iajs-219	24	11	submodule	submodule	NOUN
iajs-219	24	12	of	of	ADP
iajs-219	24	13	such	such	ADJ
iajs-219	24	14	that	that	SCONJ
iajs-219	24	15	e	e	PROPN
iajs-219	24	16	a	a	PROPN
iajs-219	24	17	and	and	CCONJ
iajs-219	24	18	e	e	X
iajs-219	24	19	a	a	X
iajs-219	24	20	;	;	PUNCT
iajs-219	24	21	(	(	PUNCT
iajs-219	24	22	ii	ii	NOUN
iajs-219	24	23	)	)	PUNCT
iajs-219	24	24	if	if	SCONJ
iajs-219	24	25	and	and	CCONJ
iajs-219	24	26	only	only	ADV
iajs-219	24	27	if	if	SCONJ
iajs-219	24	28	∩	∩	NOUN
iajs-219	24	29	e	e	NOUN
iajs-219	24	30	x	x	NOUN
iajs-219	24	31	and	and	CCONJ
iajs-219	24	32	∩	∩	NOUN
iajs-219	24	33	e	e	X
iajs-219	24	34	y.	y.	NOUN
iajs-219	24	35	following	follow	VERB
iajs-219	24	36	[	[	X
iajs-219	24	37	4	4	NUM
iajs-219	24	38	]	]	PUNCT
iajs-219	24	39	,	,	PUNCT
iajs-219	24	40	is	be	AUX
iajs-219	24	41	reflexive	reflexive	ADJ
iajs-219	24	42	and	and	CCONJ
iajs-219	24	43	symmetric	symmetric	ADJ
iajs-219	24	44	,	,	PUNCT
iajs-219	24	45	but	but	CCONJ
iajs-219	24	46	it	it	PRON
iajs-219	24	47	may	may	AUX
iajs-219	24	48	not	not	PART
iajs-219	24	49	be	be	AUX
iajs-219	24	50	transitive	transitive	ADJ
iajs-219	24	51	.	.	PUNCT
iajs-219	25	1	also	also	ADV
iajs-219	25	2	,	,	PUNCT
iajs-219	25	3	is	be	AUX
iajs-219	25	4	an	an	DET
iajs-219	25	5	equivalence	equivalence	NOUN
iajs-219	25	6	relation	relation	NOUN
iajs-219	25	7	.	.	PUNCT
iajs-219	26	1	moreover	moreover	ADV
iajs-219	26	2	,	,	PUNCT
iajs-219	26	3	an	an	DET
iajs-219	26	4	r	r	NOUN
iajs-219	26	5	-	-	PUNCT
iajs-219	26	6	module	module	NOUN
iajs-219	26	7	is	be	AUX
iajs-219	26	8	extending	extend	VERB
iajs-219	26	9	if	if	SCONJ
iajs-219	26	10	and	and	CCONJ
iajs-219	26	11	only	only	ADV
iajs-219	26	12	if	if	SCONJ
iajs-219	26	13	for	for	ADP
iajs-219	26	14	each	each	DET
iajs-219	26	15	submodule	submodule	NOUN
iajs-219	26	16	of	of	ADP
iajs-219	26	17	,	,	PUNCT
iajs-219	26	18	there	there	PRON
iajs-219	26	19	exists	exist	VERB
iajs-219	26	20	a	a	DET
iajs-219	26	21	direct	direct	ADJ
iajs-219	26	22	summand	summand	NOUN
iajs-219	26	23	of	of	ADP
iajs-219	26	24	such	such	DET
iajs-219	26	25	that	that	SCONJ
iajs-219	27	1	[	[	X
iajs-219	27	2	4	4	NUM
iajs-219	27	3	]	]	PUNCT
iajs-219	27	4	.	.	PUNCT
iajs-219	28	1	in	in	ADP
iajs-219	28	2	2009	2009	NUM
iajs-219	28	3	birkenmeier	birkenmeier	NOUN
iajs-219	28	4	and	and	CCONJ
iajs-219	28	5	tercan	tercan	NOUN
iajs-219	28	6	[	[	X
iajs-219	28	7	4	4	NUM
iajs-219	28	8	]	]	PUNCT
iajs-219	28	9	,	,	PUNCT
iajs-219	28	10	an	an	DET
iajs-219	28	11	module	module	NOUN
iajs-219	28	12	is	be	AUX
iajs-219	28	13	called	call	VERB
iajs-219	28	14	goldie	goldie	PROPN
iajs-219	28	15	extending	extending	PROPN
iajs-219	28	16	(	(	PUNCT
iajs-219	28	17	shortly	shortly	ADV
iajs-219	28	18	,	,	PUNCT
iajs-219	28	19	-extending	-extending	NOUN
iajs-219	28	20	)	)	PUNCT
iajs-219	28	21	if	if	SCONJ
iajs-219	28	22	,	,	PUNCT
iajs-219	28	23	for	for	ADP
iajs-219	28	24	each	each	DET
iajs-219	28	25	submodule	submodule	NOUN
iajs-219	28	26	of	of	ADP
iajs-219	28	27	,	,	PUNCT
iajs-219	28	28	there	there	PRON
iajs-219	28	29	is	be	VERB
iajs-219	28	30	a	a	DET
iajs-219	28	31	direct	direct	ADJ
iajs-219	28	32	summand	summand	NOUN
iajs-219	28	33	d	d	PROPN
iajs-219	28	34	of	of	ADP
iajs-219	28	35	such	such	ADJ
iajs-219	28	36	that	that	PRON
iajs-219	28	37	.	.	PUNCT
iajs-219	29	1	in	in	ADP
iajs-219	29	2	section	section	NOUN
iajs-219	29	3	one	one	NUM
iajs-219	29	4	,	,	PUNCT
iajs-219	29	5	we	we	PRON
iajs-219	29	6	introduce	introduce	VERB
iajs-219	29	7	purely	purely	ADV
iajs-219	29	8	-extending	-extende	VERB
iajs-219	29	9	modules	module	NOUN
iajs-219	29	10	.	.	PUNCT
iajs-219	30	1	an	an	DET
iajs-219	30	2	r	r	NOUN
iajs-219	30	3	-	-	PUNCT
iajs-219	30	4	module	module	NOUN
iajs-219	30	5	m	m	NOUN
iajs-219	30	6	is	be	AUX
iajs-219	30	7	-extending	-extending	ADJ
iajs-219	30	8	if	if	SCONJ
iajs-219	30	9	,	,	PUNCT
iajs-219	30	10	for	for	ADP
iajs-219	30	11	each	each	PRON
iajs-219	30	12	,	,	PUNCT
iajs-219	30	13	there	there	PRON
iajs-219	30	14	is	be	VERB
iajs-219	30	15	a	a	DET
iajs-219	30	16	pure	pure	ADJ
iajs-219	30	17	submodule	submodule	NOUN
iajs-219	30	18	p	p	NOUN
iajs-219	30	19	of	of	ADP
iajs-219	30	20	such	such	ADJ
iajs-219	30	21	that	that	PRON
iajs-219	30	22	.	.	PUNCT
iajs-219	31	1	it	it	PRON
iajs-219	31	2	is	be	AUX
iajs-219	31	3	clear	clear	ADJ
iajs-219	31	4	that	that	SCONJ
iajs-219	31	5	every	every	DET
iajs-219	31	6	extending	extending	NOUN
iajs-219	31	7	(	(	PUNCT
iajs-219	31	8	purely	purely	ADV
iajs-219	31	9	extending	extending	ADJ
iajs-219	31	10	)	)	PUNCT
iajs-219	31	11	module	module	NOUN
iajs-219	31	12	is	be	AUX
iajs-219	31	13	purely	purely	ADV
iajs-219	31	14	-extending	-extende	VERB
iajs-219	31	15	module	module	NOUN
iajs-219	31	16	and	and	CCONJ
iajs-219	31	17	the	the	DET
iajs-219	31	18	converse	converse	NOUN
iajs-219	31	19	is	be	AUX
iajs-219	31	20	not	not	PART
iajs-219	31	21	true	true	ADJ
iajs-219	31	22	in	in	ADP
iajs-219	31	23	general	general	ADJ
iajs-219	31	24	.	.	PUNCT
iajs-219	32	1	additional	additional	ADJ
iajs-219	32	2	conditions	condition	NOUN
iajs-219	32	3	are	be	AUX
iajs-219	32	4	given	give	VERB
iajs-219	32	5	to	to	PART
iajs-219	32	6	make	make	VERB
iajs-219	32	7	the	the	DET
iajs-219	32	8	converse	converse	NOUN
iajs-219	32	9	true	true	ADJ
iajs-219	32	10	.	.	PUNCT
iajs-219	33	1	in	in	ADP
iajs-219	33	2	fact	fact	NOUN
iajs-219	33	3	we	we	PRON
iajs-219	33	4	prove	prove	VERB
iajs-219	33	5	that	that	PRON
iajs-219	33	6	:	:	PUNCT
iajs-219	33	7	let	let	AUX
iajs-219	33	8	be	be	AUX
iajs-219	33	9	a	a	DET
iajs-219	33	10	pure	pure	ADJ
iajs-219	33	11	split	split	NOUN
iajs-219	33	12	.	.	PUNCT
iajs-219	34	1	then	then	ADV
iajs-219	34	2	is	be	AUX
iajs-219	34	3	a	a	DET
iajs-219	34	4	purely	purely	ADV
iajs-219	34	5	-extending	-extende	VERB
iajs-219	34	6	module	module	NOUN
iajs-219	34	7	if	if	SCONJ
iajs-219	34	8	and	and	CCONJ
iajs-219	34	9	only	only	ADV
iajs-219	34	10	if	if	SCONJ
iajs-219	34	11	is	be	AUX
iajs-219	34	12	a	a	DET
iajs-219	34	13	–	–	PUNCT
iajs-219	34	14	extending	extend	VERB
iajs-219	34	15	module	module	NOUN
iajs-219	34	16	.	.	PUNCT
iajs-219	35	1	moreover	moreover	ADV
iajs-219	35	2	,	,	PUNCT
iajs-219	35	3	the	the	DET
iajs-219	35	4	hereditary	hereditary	ADJ
iajs-219	35	5	property	property	NOUN
iajs-219	35	6	of	of	ADP
iajs-219	35	7	purely	purely	ADV
iajs-219	35	8	-extending	-extende	VERB
iajs-219	35	9	modules	module	NOUN
iajs-219	35	10	is	be	AUX
iajs-219	35	11	discussed	discuss	VERB
iajs-219	35	12	.	.	PUNCT
iajs-219	36	1	we	we	PRON
iajs-219	36	2	call	call	VERB
iajs-219	36	3	an	an	DET
iajs-219	36	4	r	r	NOUN
iajs-219	36	5	-	-	PUNCT
iajs-219	36	6	module	module	NOUN
iajs-219	36	7	m	m	NOUN
iajs-219	36	8	is	be	AUX
iajs-219	36	9	purely	purely	ADV
iajs-219	36	10	-extending	-extending	ADJ
iajs-219	36	11	if	if	SCONJ
iajs-219	36	12	every	every	DET
iajs-219	36	13	direct	direct	ADJ
iajs-219	36	14	summand	summand	NOUN
iajs-219	36	15	of	of	ADP
iajs-219	36	16	m	m	PROPN
iajs-219	36	17	is	be	AUX
iajs-219	36	18	purely	purely	ADV
iajs-219	36	19	–	–	PUNCT
iajs-219	36	20	extending	extending	ADJ
iajs-219	36	21	.	.	PUNCT
iajs-219	37	1	we	we	PRON
iajs-219	37	2	do	do	AUX
iajs-219	37	3	not	not	PART
iajs-219	37	4	know	know	VERB
iajs-219	37	5	whether	whether	SCONJ
iajs-219	37	6	every	every	DET
iajs-219	37	7	purely	purely	ADV
iajs-219	37	8	–	–	PUNCT
iajs-219	37	9	extending	extend	VERB
iajs-219	37	10	module	module	NOUN
iajs-219	37	11	is	be	AUX
iajs-219	37	12	purely	purely	ADV
iajs-219	37	13	extending	extend	VERB
iajs-219	37	14	.	.	PUNCT
iajs-219	38	1	indeed	indeed	ADV
iajs-219	38	2	,	,	PUNCT
iajs-219	38	3	we	we	PRON
iajs-219	38	4	conclude	conclude	VERB
iajs-219	38	5	that	that	SCONJ
iajs-219	38	6	every	every	DET
iajs-219	38	7	purely	purely	ADV
iajs-219	38	8	extending	extend	VERB
iajs-219	38	9	module	module	NOUN
iajs-219	38	10	is	be	AUX
iajs-219	38	11	purely	purely	ADV
iajs-219	38	12	-extending	-extende	VERB
iajs-219	38	13	.	.	PUNCT
iajs-219	39	1	finally	finally	ADV
iajs-219	39	2	,	,	PUNCT
iajs-219	39	3	we	we	PRON
iajs-219	39	4	prove	prove	VERB
iajs-219	39	5	that	that	SCONJ
iajs-219	39	6	an	an	DET
iajs-219	39	7	z	z	NOUN
iajs-219	39	8	-	-	PUNCT
iajs-219	39	9	module	module	NOUN
iajs-219	39	10	is	be	AUX
iajs-219	39	11	extending	extend	VERB
iajs-219	39	12	if	if	SCONJ
iajs-219	39	13	and	and	CCONJ
iajs-219	39	14	only	only	ADV
iajs-219	39	15	if	if	SCONJ
iajs-219	39	16	m	m	NOUN
iajs-219	39	17	is	be	AUX
iajs-219	39	18	a	a	DET
iajs-219	39	19	purely	purely	ADV
iajs-219	39	20	extending	extend	VERB
iajs-219	39	21	and	and	CCONJ
iajs-219	39	22	is	be	AUX
iajs-219	39	23	a	a	DET
iajs-219	39	24	-extending	-extending	NOUN
iajs-219	39	25	.	.	PUNCT
iajs-219	40	1	in	in	ADP
iajs-219	40	2	section	section	NOUN
iajs-219	40	3	two	two	NUM
iajs-219	40	4	,	,	PUNCT
iajs-219	40	5	various	various	ADJ
iajs-219	40	6	characterizations	characterization	NOUN
iajs-219	40	7	of	of	ADP
iajs-219	40	8	purely	purely	ADV
iajs-219	40	9	-extending	-extende	VERB
iajs-219	40	10	modules	module	NOUN
iajs-219	40	11	are	be	AUX
iajs-219	40	12	given	give	VERB
iajs-219	40	13	.	.	PUNCT
iajs-219	41	1	for	for	ADP
iajs-219	41	2	example	example	NOUN
iajs-219	41	3	,	,	PUNCT
iajs-219	41	4	we	we	PRON
iajs-219	41	5	prove	prove	VERB
iajs-219	41	6	that	that	SCONJ
iajs-219	41	7	an	an	DET
iajs-219	41	8	-module	-module	NOUN
iajs-219	41	9	is	be	AUX
iajs-219	41	10	purely	purely	ADV
iajs-219	41	11	-extending	-extending	ADJ
iajs-219	41	12	if	if	SCONJ
iajs-219	41	13	and	and	CCONJ
iajs-219	41	14	only	only	ADV
iajs-219	41	15	if	if	SCONJ
iajs-219	41	16	every	every	DET
iajs-219	41	17	direct	direct	ADJ
iajs-219	41	18	summand	summand	NOUN
iajs-219	41	19	of	of	ADP
iajs-219	41	20	the	the	DET
iajs-219	41	21	injective	injective	ADJ
iajs-219	41	22	hull	hull	NOUN
iajs-219	41	23	of	of	ADP
iajs-219	41	24	,	,	PUNCT
iajs-219	41	25	there	there	PRON
iajs-219	41	26	exists	exist	VERB
iajs-219	41	27	a	a	DET
iajs-219	41	28	pure	pure	ADJ
iajs-219	41	29	submodule	submodule	NOUN
iajs-219	41	30	of	of	ADP
iajs-219	41	31	such	such	ADJ
iajs-219	41	32	that	that	DET
iajs-219	41	33	∩	∩	NOUN
iajs-219	41	34	)	)	PUNCT
iajs-219	41	35	.	.	PUNCT
iajs-219	42	1	on	on	ADP
iajs-219	42	2	other	other	ADJ
iajs-219	42	3	direction	direction	NOUN
iajs-219	42	4	,	,	PUNCT
iajs-219	42	5	the	the	DET
iajs-219	42	6	direct	direct	ADJ
iajs-219	42	7	sum	sum	NOUN
iajs-219	42	8	property	property	NOUN
iajs-219	42	9	of	of	ADP
iajs-219	42	10	purely	purely	ADV
iajs-219	42	11	–	–	PUNCT
iajs-219	42	12	extending	extend	VERB
iajs-219	42	13	modules	module	NOUN
iajs-219	42	14	is	be	AUX
iajs-219	42	15	discussed	discuss	VERB
iajs-219	42	16	.	.	PUNCT
iajs-219	43	1	we	we	PRON
iajs-219	43	2	prove	prove	VERB
iajs-219	43	3	that	that	SCONJ
iajs-219	43	4	,	,	PUNCT
iajs-219	43	5	if	if	SCONJ
iajs-219	43	6	is	be	AUX
iajs-219	43	7	purely	purely	ADV
iajs-219	43	8	-extending	-extende	VERB
iajs-219	43	9	module	module	NOUN
iajs-219	43	10	for	for	ADP
iajs-219	43	11	each	each	DET
iajs-219	43	12	∈	∈	PROPN
iajs-219	43	13	and	and	CCONJ
iajs-219	43	14	every	every	DET
iajs-219	43	15	closed	closed	ADJ
iajs-219	43	16	submodule	submodule	NOUN
iajs-219	43	17	of	of	ADP
iajs-219	43	18	=	=	PROPN
iajs-219	43	19	⊕	⊕	PROPN
iajs-219	43	20	∈	∈	PROPN
iajs-219	43	21	is	be	AUX
iajs-219	43	22	fully	fully	ADV
iajs-219	43	23	invariant	invariant	ADJ
iajs-219	43	24	,	,	PUNCT
iajs-219	43	25	then	then	ADV
iajs-219	43	26	=	=	PROPN
iajs-219	43	27	⊕	⊕	PROPN
iajs-219	43	28	∈	∈	PROPN
iajs-219	43	29	is	be	AUX
iajs-219	43	30	purely	purely	ADV
iajs-219	43	31	-extending	-extende	VERB
iajs-219	43	32	module	module	NOUN
iajs-219	43	33	.	.	PUNCT
iajs-219	44	1	1	1	X
iajs-219	44	2	.	.	X
iajs-219	44	3	purely	purely	ADV
iajs-219	44	4	goldie	goldie	PROPN
iajs-219	44	5	extending	extend	VERB
iajs-219	44	6	modules	module	NOUN
iajs-219	44	7	.	.	PUNCT
iajs-219	45	1	recall	recall	VERB
iajs-219	45	2	that	that	SCONJ
iajs-219	45	3	an	an	DET
iajs-219	45	4	-module	-module	NOUN
iajs-219	45	5	is	be	AUX
iajs-219	45	6	-extending	-extending	ADJ
iajs-219	45	7	if	if	SCONJ
iajs-219	45	8	,	,	PUNCT
iajs-219	45	9	for	for	ADP
iajs-219	45	10	each	each	DET
iajs-219	45	11	submodule	submodule	NOUN
iajs-219	45	12	of	of	ADP
iajs-219	45	13	,	,	PUNCT
iajs-219	45	14	there	there	PRON
iajs-219	45	15	is	be	VERB
iajs-219	45	16	a	a	DET
iajs-219	45	17	direct	direct	ADJ
iajs-219	45	18	summand	summand	NOUN
iajs-219	45	19	d	d	PROPN
iajs-219	45	20	of	of	ADP
iajs-219	45	21	such	such	ADJ
iajs-219	45	22	that	that	PRON
iajs-219	45	23	.	.	PUNCT
iajs-219	46	1	equivalently	equivalently	ADV
iajs-219	46	2	,	,	PUNCT
iajs-219	46	3	is	be	AUX
iajs-219	46	4	goldie	goldie	PROPN
iajs-219	46	5	extending	extend	VERB
iajs-219	46	6	if	if	SCONJ
iajs-219	46	7	and	and	CCONJ
iajs-219	46	8	only	only	ADV
iajs-219	46	9	if	if	SCONJ
iajs-219	46	10	for	for	ADP
iajs-219	46	11	each	each	DET
iajs-219	46	12	closed	closed	ADJ
iajs-219	46	13	submodule	submodule	NOUN
iajs-219	46	14	c	c	PROPN
iajs-219	46	15	of	of	ADP
iajs-219	46	16	,	,	PUNCT
iajs-219	46	17	there	there	PRON
iajs-219	46	18	is	be	VERB
iajs-219	46	19	a	a	DET
iajs-219	46	20	direct	direct	ADJ
iajs-219	46	21	summand	summand	NOUN
iajs-219	46	22	d	d	NOUN
iajs-219	46	23	of	of	ADP
iajs-219	46	24	such	such	ADJ
iajs-219	46	25	that	that	SCONJ
iajs-219	46	26	[	[	X
iajs-219	46	27	4	4	NUM
iajs-219	46	28	]	]	PUNCT
iajs-219	46	29	,	,	PUNCT
iajs-219	46	30	also	also	ADV
iajs-219	46	31	,	,	PUNCT
iajs-219	46	32	an	an	DET
iajs-219	46	33	module	module	NOUN
iajs-219	46	34	is	be	AUX
iajs-219	46	35	purely	purely	ADV
iajs-219	46	36	extending	extend	VERB
iajs-219	46	37	module	module	NOUN
iajs-219	46	38	if	if	SCONJ
iajs-219	46	39	every	every	DET
iajs-219	46	40	submodule	submodule	NOUN
iajs-219	46	41	of	of	ADP
iajs-219	46	42	is	be	AUX
iajs-219	46	43	essential	essential	ADJ
iajs-219	46	44	in	in	ADP
iajs-219	46	45	a	a	DET
iajs-219	46	46	pure	pure	ADJ
iajs-219	46	47	submodule	submodule	NOUN
iajs-219	46	48	of	of	ADP
iajs-219	46	49	[	[	X
iajs-219	46	50	3	3	NUM
iajs-219	46	51	]	]	PUNCT
iajs-219	46	52	.	.	PUNCT
iajs-219	47	1	we	we	PRON
iajs-219	47	2	introduce	introduce	VERB
iajs-219	47	3	and	and	CCONJ
iajs-219	47	4	study	study	VERB
iajs-219	47	5	the	the	DET
iajs-219	47	6	class	class	NOUN
iajs-219	47	7	of	of	ADP
iajs-219	47	8	modules	module	NOUN
iajs-219	47	9	which	which	PRON
iajs-219	47	10	is	be	AUX
iajs-219	47	11	a	a	DET
iajs-219	47	12	generalization	generalization	NOUN
iajs-219	47	13	of	of	ADP
iajs-219	47	14	both	both	PRON
iajs-219	47	15	-extending	-extende	VERB
iajs-219	47	16	modules	module	NOUN
iajs-219	47	17	and	and	CCONJ
iajs-219	47	18	purely	purely	ADV
iajs-219	47	19	extending	extend	VERB
iajs-219	47	20	modules	module	NOUN
iajs-219	47	21	.	.	PUNCT
iajs-219	48	1	149	149	NUM
iajs-219	48	2	|	|	ADV
iajs-219	48	3	mathematics	mathematic	NOUN
iajs-219	48	4	٢٠١٥	٢٠١٥	NUM
iajs-219	48	5	)	)	PUNCT
iajs-219	48	6	عام	عام	ADP
iajs-219	48	7	٢العدد	٢العدد	PROPN
iajs-219	48	8	(	(	PUNCT
iajs-219	48	9	٢٨المجلد	٢٨المجلد	NUM
iajs-219	48	10	والتطبيقية	والتطبيقية	PROPN
iajs-219	48	11	الھيثم	الھيثم	NOUN
iajs-219	48	12	للعلوم	للعلوم	PROPN
iajs-219	48	13	الصرفة	الصرفة	NOUN
iajs-219	48	14	ابنمجلة	ابنمجلة	VERB
iajs-219	48	15	ibn	ibn	PROPN
iajs-219	48	16	al	al	PROPN
iajs-219	48	17	-	-	PUNCT
iajs-219	48	18	haitham	haitham	PROPN
iajs-219	48	19	.	.	PUNCT
iajs-219	49	1	j.	j.	PROPN
iajs-219	49	2	for	for	ADP
iajs-219	49	3	pure	pure	PROPN
iajs-219	49	4	&	&	CCONJ
iajs-219	49	5	appl	appl	PROPN
iajs-219	49	6	.	.	PUNCT
iajs-219	50	1	sci	sci	PROPN
iajs-219	50	2	.	.	PUNCT
iajs-219	50	3	vol	vol	NOUN
iajs-219	50	4	.	.	PROPN
iajs-219	51	1	28	28	NUM
iajs-219	51	2	(	(	PUNCT
iajs-219	51	3	٢	٢	NOUN
iajs-219	51	4	)	)	PUNCT
iajs-219	51	5	2015	2015	NUM
iajs-219	51	6	definition	definition	NOUN
iajs-219	51	7	(	(	PUNCT
iajs-219	51	8	1.1	1.1	NUM
iajs-219	51	9	)	)	PUNCT
iajs-219	51	10	an	an	DET
iajs-219	51	11	-module	-module	NOUN
iajs-219	51	12	is	be	AUX
iajs-219	51	13	called	call	VERB
iajs-219	51	14	purely	purely	ADV
iajs-219	51	15	goldie	goldie	PROPN
iajs-219	51	16	extending	extending	NOUN
iajs-219	51	17	(	(	PUNCT
iajs-219	51	18	shortly	shortly	ADV
iajs-219	51	19	,	,	PUNCT
iajs-219	51	20	purely	purely	ADV
iajs-219	51	21	-extending	-extending	NOUN
iajs-219	51	22	)	)	PUNCT
iajs-219	51	23	if	if	SCONJ
iajs-219	51	24	,	,	PUNCT
iajs-219	51	25	for	for	ADP
iajs-219	51	26	each	each	PRON
iajs-219	51	27	,	,	PUNCT
iajs-219	51	28	there	there	PRON
iajs-219	51	29	is	be	VERB
iajs-219	51	30	a	a	DET
iajs-219	51	31	pure	pure	ADJ
iajs-219	51	32	submodule	submodule	NOUN
iajs-219	51	33	p	p	NOUN
iajs-219	51	34	of	of	ADP
iajs-219	51	35	such	such	ADJ
iajs-219	51	36	that	that	PRON
iajs-219	51	37	.	.	PUNCT
iajs-219	52	1	remarks	remark	NOUN
iajs-219	52	2	and	and	CCONJ
iajs-219	52	3	examples	example	NOUN
iajs-219	52	4	(	(	PUNCT
iajs-219	52	5	1.2	1.2	NUM
iajs-219	52	6	)	)	PUNCT
iajs-219	52	7	1	1	NUM
iajs-219	52	8	)	)	PUNCT
iajs-219	52	9	every	every	DET
iajs-219	52	10	purely	purely	ADV
iajs-219	52	11	extending	extend	VERB
iajs-219	52	12	module	module	NOUN
iajs-219	52	13	is	be	AUX
iajs-219	52	14	a	a	DET
iajs-219	52	15	purely	purely	ADV
iajs-219	52	16	-extending	-extending	ADJ
iajs-219	52	17	,	,	PUNCT
iajs-219	52	18	but	but	CCONJ
iajs-219	52	19	the	the	DET
iajs-219	52	20	converse	converse	NOUN
iajs-219	52	21	is	be	AUX
iajs-219	52	22	not	not	PART
iajs-219	52	23	true	true	ADJ
iajs-219	52	24	in	in	ADP
iajs-219	52	25	general	general	ADJ
iajs-219	52	26	.	.	PUNCT
iajs-219	53	1	for	for	ADP
iajs-219	53	2	example	example	NOUN
iajs-219	53	3	,	,	PUNCT
iajs-219	53	4	the	the	DET
iajs-219	53	5	z	z	NOUN
iajs-219	53	6	-	-	PUNCT
iajs-219	53	7	module	module	NOUN
iajs-219	53	8	⊕	⊕	PROPN
iajs-219	53	9	is	be	AUX
iajs-219	53	10	a	a	DET
iajs-219	53	11	purely	purely	ADV
iajs-219	53	12	–	–	PUNCT
iajs-219	53	13	extending	extend	VERB
iajs-219	53	14	since	since	SCONJ
iajs-219	53	15	is	be	AUX
iajs-219	53	16	-extending	-extende	VERB
iajs-219	53	17	[	[	X
iajs-219	53	18	4	4	NUM
iajs-219	53	19	]	]	PUNCT
iajs-219	53	20	.	.	PUNCT
iajs-219	54	1	but	but	CCONJ
iajs-219	54	2	by	by	ADP
iajs-219	54	3	[	[	X
iajs-219	54	4	4	4	NUM
iajs-219	54	5	,	,	PUNCT
iajs-219	54	6	example	example	NOUN
iajs-219	54	7	(	(	PUNCT
iajs-219	54	8	3.20	3.20	NUM
iajs-219	54	9	)	)	PUNCT
iajs-219	54	10	]	]	PUNCT
iajs-219	54	11	and	and	CCONJ
iajs-219	54	12	proposition	proposition	NOUN
iajs-219	54	13	(	(	PUNCT
iajs-219	54	14	1.14	1.14	NUM
iajs-219	54	15	)	)	PUNCT
iajs-219	54	16	,	,	PUNCT
iajs-219	54	17	⊕	⊕	PROPN
iajs-219	54	18	is	be	AUX
iajs-219	54	19	not	not	PART
iajs-219	54	20	purely	purely	ADV
iajs-219	54	21	extending	extend	VERB
iajs-219	54	22	z	z	NOUN
iajs-219	54	23	-	-	NOUN
iajs-219	54	24	module	module	NOUN
iajs-219	54	25	.	.	NOUN
iajs-219	55	1	2	2	NUM
iajs-219	55	2	)	)	PUNCT
iajs-219	55	3	every	every	DET
iajs-219	55	4	extending	extend	VERB
iajs-219	55	5	module	module	NOUN
iajs-219	55	6	is	be	AUX
iajs-219	55	7	purely	purely	ADV
iajs-219	55	8	-extending	-extending	ADJ
iajs-219	55	9	,	,	PUNCT
iajs-219	55	10	but	but	CCONJ
iajs-219	55	11	the	the	DET
iajs-219	55	12	converse	converse	NOUN
iajs-219	55	13	is	be	AUX
iajs-219	55	14	not	not	PART
iajs-219	55	15	true	true	ADJ
iajs-219	55	16	in	in	ADP
iajs-219	55	17	general	general	ADJ
iajs-219	55	18	.	.	PUNCT
iajs-219	56	1	for	for	ADP
iajs-219	56	2	example	example	NOUN
iajs-219	56	3	,	,	PUNCT
iajs-219	56	4	by	by	ADP
iajs-219	56	5	[	[	X
iajs-219	56	6	5	5	NUM
iajs-219	56	7	,	,	PUNCT
iajs-219	56	8	example	example	NOUN
iajs-219	56	9	(	(	PUNCT
iajs-219	56	10	3.4	3.4	NUM
iajs-219	56	11	)	)	PUNCT
iajs-219	56	12	]	]	PUNCT
iajs-219	56	13	,	,	PUNCT
iajs-219	56	14	the	the	DET
iajs-219	56	15	z	z	NOUN
iajs-219	56	16	-	-	PUNCT
iajs-219	56	17	module	module	NOUN
iajs-219	56	18	⊕	⊕	PROPN
iajs-219	56	19	∈	∈	PROPN
iajs-219	56	20	z	z	NOUN
iajs-219	56	21	is	be	AUX
iajs-219	56	22	purely	purely	ADV
iajs-219	56	23	extending	extend	VERB
iajs-219	57	1	but	but	CCONJ
iajs-219	57	2	it	it	PRON
iajs-219	57	3	is	be	AUX
iajs-219	57	4	not	not	PART
iajs-219	57	5	extending	extend	VERB
iajs-219	57	6	.	.	PUNCT
iajs-219	58	1	so	so	ADV
iajs-219	58	2	m	m	VERB
iajs-219	58	3	is	be	AUX
iajs-219	58	4	a	a	DET
iajs-219	58	5	purely	purely	ADV
iajs-219	58	6	–	–	PUNCT
iajs-219	58	7	extending	extend	VERB
iajs-219	58	8	while	while	NOUN
iajs-219	58	9	,	,	PUNCT
iajs-219	58	10	by	by	ADP
iajs-219	58	11	proposition	proposition	NOUN
iajs-219	58	12	(	(	PUNCT
iajs-219	58	13	1.14	1.14	NUM
iajs-219	58	14	)	)	PUNCT
iajs-219	58	15	,	,	PUNCT
iajs-219	58	16	m	m	PROPN
iajs-219	58	17	is	be	AUX
iajs-219	58	18	not	not	PART
iajs-219	58	19	-extending	-extende	VERB
iajs-219	58	20	.	.	PUNCT
iajs-219	59	1	3	3	X
iajs-219	59	2	)	)	PUNCT
iajs-219	59	3	every	every	DET
iajs-219	59	4	uniform	uniform	NOUN
iajs-219	59	5	module	module	NOUN
iajs-219	59	6	is	be	AUX
iajs-219	59	7	purely	purely	ADV
iajs-219	59	8	-extending	-extending	ADJ
iajs-219	59	9	,	,	PUNCT
iajs-219	59	10	but	but	CCONJ
iajs-219	59	11	the	the	DET
iajs-219	59	12	converse	converse	NOUN
iajs-219	59	13	is	be	AUX
iajs-219	59	14	not	not	PART
iajs-219	59	15	true	true	ADJ
iajs-219	59	16	in	in	ADP
iajs-219	59	17	general	general	ADJ
iajs-219	59	18	.	.	PUNCT
iajs-219	60	1	for	for	ADP
iajs-219	60	2	example	example	NOUN
iajs-219	60	3	,	,	PUNCT
iajs-219	60	4	as	as	SCONJ
iajs-219	60	5	z	z	NOUN
iajs-219	60	6	-	-	PUNCT
iajs-219	60	7	module	module	NOUN
iajs-219	60	8	is	be	AUX
iajs-219	60	9	purely	purely	ADV
iajs-219	60	10	extending	extend	VERB
iajs-219	61	1	but	but	CCONJ
iajs-219	61	2	it	it	PRON
iajs-219	61	3	is	be	AUX
iajs-219	61	4	not	not	PART
iajs-219	61	5	uniform	uniform	ADJ
iajs-219	61	6	.	.	PUNCT
iajs-219	62	1	recall	recall	VERB
iajs-219	62	2	that	that	SCONJ
iajs-219	62	3	an	an	DET
iajs-219	62	4	-module	-module	NOUN
iajs-219	62	5	is	be	AUX
iajs-219	62	6	a	a	DET
iajs-219	62	7	pure	pure	ADJ
iajs-219	62	8	-	-	PUNCT
iajs-219	62	9	split	split	NOUN
iajs-219	62	10	if	if	SCONJ
iajs-219	62	11	every	every	DET
iajs-219	62	12	pure	pure	ADJ
iajs-219	62	13	submodule	submodule	NOUN
iajs-219	62	14	of	of	ADP
iajs-219	62	15	is	be	AUX
iajs-219	62	16	a	a	DET
iajs-219	62	17	direct	direct	ADJ
iajs-219	62	18	summand	summand	NOUN
iajs-219	62	19	[	[	X
iajs-219	62	20	6].the	6].the	DET
iajs-219	62	21	following	follow	VERB
iajs-219	62	22	proposition	proposition	NOUN
iajs-219	62	23	gives	give	VERB
iajs-219	62	24	conditions	condition	NOUN
iajs-219	62	25	under	under	ADP
iajs-219	62	26	which	which	PRON
iajs-219	62	27	the	the	DET
iajs-219	62	28	concepts	concept	NOUN
iajs-219	62	29	of	of	ADP
iajs-219	62	30	extending	extend	VERB
iajs-219	62	31	modules	module	NOUN
iajs-219	62	32	and	and	CCONJ
iajs-219	62	33	purely	purely	ADV
iajs-219	62	34	extending	extend	VERB
iajs-219	62	35	modules	module	NOUN
iajs-219	62	36	are	be	AUX
iajs-219	62	37	equivalent	equivalent	ADJ
iajs-219	62	38	.	.	PUNCT
iajs-219	63	1	proposition	proposition	NOUN
iajs-219	63	2	(	(	PUNCT
iajs-219	63	3	1.3	1.3	NUM
iajs-219	63	4	):	):	PUNCT
iajs-219	63	5	let	let	VERB
iajs-219	63	6	is	be	AUX
iajs-219	63	7	a	a	DET
iajs-219	63	8	pure	pure	ADJ
iajs-219	63	9	split	split	ADJ
iajs-219	63	10	-module	-module	NOUN
iajs-219	63	11	.	.	PUNCT
iajs-219	64	1	then	then	ADV
iajs-219	64	2	is	be	AUX
iajs-219	64	3	a	a	DET
iajs-219	64	4	purely	purely	ADV
iajs-219	64	5	-extending	-extending	ADJ
iajs-219	64	6	if	if	SCONJ
iajs-219	64	7	and	and	CCONJ
iajs-219	64	8	only	only	ADV
iajs-219	64	9	if	if	SCONJ
iajs-219	64	10	is	be	AUX
iajs-219	64	11	a	a	DET
iajs-219	64	12	extending	extending	NOUN
iajs-219	64	13	.	.	PUNCT
iajs-219	65	1	∎	∎	PROPN
iajs-219	65	2	following	follow	VERB
iajs-219	65	3	[	[	X
iajs-219	65	4	7	7	NUM
iajs-219	65	5	]	]	PUNCT
iajs-219	65	6	,	,	PUNCT
iajs-219	65	7	a	a	DET
iajs-219	65	8	non	non	ADJ
iajs-219	65	9	-	-	ADJ
iajs-219	65	10	zero	zero	NUM
iajs-219	65	11	-module	-module	NOUN
iajs-219	65	12	is	be	AUX
iajs-219	65	13	pure	pure	ADJ
iajs-219	65	14	-	-	PUNCT
iajs-219	65	15	simple	simple	ADJ
iajs-219	65	16	if	if	SCONJ
iajs-219	65	17	the	the	DET
iajs-219	65	18	only	only	ADJ
iajs-219	65	19	pure	pure	ADJ
iajs-219	65	20	submodules	submodule	NOUN
iajs-219	65	21	of	of	ADP
iajs-219	65	22	are	be	AUX
iajs-219	65	23	0	0	NUM
iajs-219	65	24	and	and	CCONJ
iajs-219	65	25	itself	itself	PRON
iajs-219	65	26	.	.	PUNCT
iajs-219	66	1	proposition	proposition	NOUN
iajs-219	66	2	(	(	PUNCT
iajs-219	66	3	1.4	1.4	NUM
iajs-219	66	4	)	)	PUNCT
iajs-219	66	5	let	let	AUX
iajs-219	66	6	be	be	AUX
iajs-219	66	7	a	a	DET
iajs-219	66	8	puresimple	puresimple	ADJ
iajs-219	66	9	-module	-module	NOUN
iajs-219	66	10	.	.	PUNCT
iajs-219	67	1	then	then	ADV
iajs-219	67	2	is	be	AUX
iajs-219	67	3	a	a	DET
iajs-219	67	4	purely	purely	ADV
iajs-219	67	5	extending	extend	VERB
iajs-219	67	6	if	if	SCONJ
iajs-219	67	7	and	and	CCONJ
iajs-219	67	8	only	only	ADV
iajs-219	67	9	if	if	SCONJ
iajs-219	67	10	is	be	AUX
iajs-219	67	11	a	a	DET
iajs-219	67	12	uniform	uniform	ADJ
iajs-219	67	13	module	module	NOUN
iajs-219	67	14	.	.	PUNCT
iajs-219	68	1	proof:(⟹	proof:(⟹	NOUN
iajs-219	68	2	)	)	PUNCT
iajs-219	68	3	let	let	AUX
iajs-219	68	4	be	be	AUX
iajs-219	68	5	a	a	DET
iajs-219	68	6	submodule	submodule	NOUN
iajs-219	68	7	of	of	ADP
iajs-219	68	8	.	.	PUNCT
iajs-219	69	1	by	by	ADP
iajs-219	69	2	assumption	assumption	NOUN
iajs-219	69	3	,	,	PUNCT
iajs-219	69	4	there	there	PRON
iajs-219	69	5	is	be	VERB
iajs-219	69	6	a	a	DET
iajs-219	69	7	pure	pure	ADJ
iajs-219	69	8	submodule	submodule	NOUN
iajs-219	69	9	p	p	NOUN
iajs-219	69	10	of	of	ADP
iajs-219	69	11	such	such	ADJ
iajs-219	69	12	that	that	DET
iajs-219	69	13	β	β	NOUN
iajs-219	69	14	.	.	PUNCT
iajs-219	70	1	so	so	ADV
iajs-219	70	2	,	,	PUNCT
iajs-219	70	3	∩	∩	NOUN
iajs-219	70	4	is	be	AUX
iajs-219	70	5	essential	essential	ADJ
iajs-219	70	6	in	in	ADP
iajs-219	70	7	.but	.but	PUNCT
iajs-219	70	8	is	be	AUX
iajs-219	70	9	a	a	DET
iajs-219	70	10	puresimple	puresimple	NOUN
iajs-219	70	11	then	then	ADV
iajs-219	70	12	=	=	PUNCT
iajs-219	70	13	,	,	PUNCT
iajs-219	70	14	then	then	ADV
iajs-219	70	15	is	be	AUX
iajs-219	70	16	essential	essential	ADJ
iajs-219	70	17	in	in	ADP
iajs-219	70	18	.	.	PUNCT
iajs-219	71	1	thus	thus	ADV
iajs-219	71	2	,	,	PUNCT
iajs-219	71	3	is	be	AUX
iajs-219	71	4	a	a	DET
iajs-219	71	5	uniform	uniform	ADJ
iajs-219	71	6	module	module	NOUN
iajs-219	71	7	.	.	PUNCT
iajs-219	72	1	(	(	PUNCT
iajs-219	72	2	⟸	⟸	X
iajs-219	72	3	)	)	PUNCT
iajs-219	72	4	let	let	AUX
iajs-219	72	5	be	be	AUX
iajs-219	72	6	a	a	DET
iajs-219	72	7	submodule	submodule	NOUN
iajs-219	72	8	of	of	ADP
iajs-219	72	9	.	.	PUNCT
iajs-219	73	1	since	since	SCONJ
iajs-219	73	2	is	be	AUX
iajs-219	73	3	a	a	DET
iajs-219	73	4	uniform	uniform	ADJ
iajs-219	73	5	module	module	NOUN
iajs-219	73	6	,	,	PUNCT
iajs-219	73	7	then	then	ADV
iajs-219	73	8	is	be	AUX
iajs-219	73	9	essential	essential	ADJ
iajs-219	73	10	in	in	ADP
iajs-219	73	11	,	,	PUNCT
iajs-219	73	12	but	but	CCONJ
iajs-219	73	13	is	be	AUX
iajs-219	73	14	a	a	DET
iajs-219	73	15	pure	pure	ADJ
iajs-219	73	16	submodule	submodule	NOUN
iajs-219	73	17	of	of	ADP
iajs-219	73	18	,	,	PUNCT
iajs-219	73	19	then	then	ADV
iajs-219	73	20	β	β	X
iajs-219	73	21	.	.	PUNCT
iajs-219	74	1	hence	hence	ADV
iajs-219	74	2	,	,	PUNCT
iajs-219	74	3	is	be	AUX
iajs-219	74	4	a	a	DET
iajs-219	74	5	purely	purely	ADV
iajs-219	74	6	extending	extending	ADJ
iajs-219	74	7	.	.	PUNCT
iajs-219	75	1	∎	∎	PROPN
iajs-219	75	2	corollary	corollary	ADJ
iajs-219	75	3	(	(	PUNCT
iajs-219	75	4	1.5	1.5	NUM
iajs-219	75	5	)	)	PUNCT
iajs-219	75	6	let	let	AUX
iajs-219	75	7	be	be	AUX
iajs-219	75	8	a	a	DET
iajs-219	75	9	puresimple	puresimple	ADJ
iajs-219	75	10	-module	-module	NOUN
iajs-219	75	11	.	.	PUNCT
iajs-219	76	1	then	then	ADV
iajs-219	76	2	the	the	DET
iajs-219	76	3	following	follow	VERB
iajs-219	76	4	statements	statement	NOUN
iajs-219	76	5	are	be	AUX
iajs-219	76	6	equivalent	equivalent	ADJ
iajs-219	76	7	.	.	PUNCT
iajs-219	77	1	(	(	PUNCT
iajs-219	77	2	1	1	X
iajs-219	77	3	)	)	PUNCT
iajs-219	77	4	is	be	AUX
iajs-219	77	5	a	a	DET
iajs-219	77	6	purely	purely	ADV
iajs-219	77	7	extending	extend	VERB
iajs-219	77	8	module	module	NOUN
iajs-219	77	9	.	.	PUNCT
iajs-219	78	1	(	(	PUNCT
iajs-219	78	2	2	2	X
iajs-219	78	3	)	)	PUNCT
iajs-219	78	4	is	be	AUX
iajs-219	78	5	a	a	DET
iajs-219	78	6	purely	purely	ADV
iajs-219	78	7	-extending	-extende	VERB
iajs-219	78	8	module	module	NOUN
iajs-219	78	9	.	.	PUNCT
iajs-219	79	1	(	(	PUNCT
iajs-219	79	2	3	3	X
iajs-219	79	3	)	)	PUNCT
iajs-219	79	4	is	be	AUX
iajs-219	79	5	uniform	uniform	ADJ
iajs-219	79	6	module	module	NOUN
iajs-219	79	7	.	.	PUNCT
iajs-219	80	1	following	follow	VERB
iajs-219	80	2	[	[	X
iajs-219	80	3	4	4	NUM
iajs-219	80	4	]	]	PUNCT
iajs-219	80	5	,	,	PUNCT
iajs-219	80	6	a	a	DET
iajs-219	80	7	submodule	submodule	NOUN
iajs-219	80	8	of	of	ADP
iajs-219	80	9	-extending	-extending	NOUN
iajs-219	80	10	module	module	NOUN
iajs-219	80	11	need	need	VERB
iajs-219	80	12	not	not	PART
iajs-219	80	13	to	to	PART
iajs-219	80	14	be	be	AUX
iajs-219	80	15	-extending	-extende	VERB
iajs-219	80	16	.	.	PUNCT
iajs-219	81	1	moreover	moreover	ADV
iajs-219	81	2	,	,	PUNCT
iajs-219	81	3	a	a	DET
iajs-219	81	4	submodule	submodule	NOUN
iajs-219	81	5	of	of	ADP
iajs-219	81	6	purely	purely	ADV
iajs-219	81	7	extending	extend	VERB
iajs-219	81	8	module	module	NOUN
iajs-219	81	9	need	need	AUX
iajs-219	81	10	not	not	PART
iajs-219	81	11	to	to	PART
iajs-219	81	12	be	be	AUX
iajs-219	81	13	purely	purely	ADV
iajs-219	81	14	extending	extend	VERB
iajs-219	81	15	[	[	X
iajs-219	81	16	5	5	NUM
iajs-219	81	17	]	]	PUNCT
iajs-219	81	18	.	.	PUNCT
iajs-219	82	1	in	in	ADP
iajs-219	82	2	fact	fact	NOUN
iajs-219	82	3	,	,	PUNCT
iajs-219	82	4	we	we	PRON
iajs-219	82	5	do	do	AUX
iajs-219	82	6	not	not	PART
iajs-219	82	7	know	know	VERB
iajs-219	82	8	whether	whether	SCONJ
iajs-219	82	9	a	a	DET
iajs-219	82	10	submodule	submodule	NOUN
iajs-219	82	11	of	of	ADP
iajs-219	82	12	a	a	DET
iajs-219	82	13	purely	purely	ADV
iajs-219	82	14	-extending	-extende	VERB
iajs-219	82	15	module	module	NOUN
iajs-219	82	16	is	be	AUX
iajs-219	82	17	purely	purely	ADV
iajs-219	82	18	-extending	-extende	VERB
iajs-219	82	19	.	.	PUNCT
iajs-219	83	1	indeed	indeed	ADV
iajs-219	83	2	,	,	PUNCT
iajs-219	83	3	we	we	PRON
iajs-219	83	4	have	have	VERB
iajs-219	83	5	the	the	DET
iajs-219	83	6	following	follow	VERB
iajs-219	83	7	result	result	NOUN
iajs-219	83	8	.	.	PUNCT
iajs-219	84	1	proposition	proposition	NOUN
iajs-219	84	2	(	(	PUNCT
iajs-219	84	3	1.6	1.6	NUM
iajs-219	84	4	)	)	PUNCT
iajs-219	84	5	every	every	DET
iajs-219	84	6	submodule	submodule	NOUN
iajs-219	84	7	of	of	ADP
iajs-219	84	8	a	a	DET
iajs-219	84	9	purely	purely	ADV
iajs-219	84	10	-extending	-extending	ADJ
iajs-219	84	11	-module	-module	NOUN
iajs-219	84	12	with	with	ADP
iajs-219	84	13	the	the	DET
iajs-219	84	14	property	property	NOUN
iajs-219	84	15	that	that	PRON
iajs-219	84	16	the	the	DET
iajs-219	84	17	intersection	intersection	NOUN
iajs-219	84	18	of	of	ADP
iajs-219	84	19	with	with	ADP
iajs-219	84	20	any	any	DET
iajs-219	84	21	pure	pure	ADJ
iajs-219	84	22	submodule	submodule	NOUN
iajs-219	84	23	of	of	ADP
iajs-219	84	24	is	be	AUX
iajs-219	84	25	a	a	DET
iajs-219	84	26	pure	pure	ADJ
iajs-219	84	27	submodule	submodule	NOUN
iajs-219	84	28	of	of	ADP
iajs-219	84	29	is	be	AUX
iajs-219	84	30	purely	purely	ADV
iajs-219	84	31	extending	extend	VERB
iajs-219	84	32	.	.	PUNCT
iajs-219	85	1	150	150	NUM
iajs-219	86	1	|	|	ADV
iajs-219	86	2	mathematics	mathematic	NOUN
iajs-219	86	3	٢٠١٥	٢٠١٥	NUM
iajs-219	86	4	)	)	PUNCT
iajs-219	86	5	عام	عام	ADP
iajs-219	86	6	٢العدد	٢العدد	PROPN
iajs-219	86	7	(	(	PUNCT
iajs-219	86	8	٢٨المجلد	٢٨المجلد	NUM
iajs-219	86	9	والتطبيقية	والتطبيقية	PROPN
iajs-219	86	10	الھيثم	الھيثم	NOUN
iajs-219	86	11	للعلوم	للعلوم	PROPN
iajs-219	86	12	الصرفة	الصرفة	NOUN
iajs-219	86	13	ابنمجلة	ابنمجلة	VERB
iajs-219	86	14	ibn	ibn	PROPN
iajs-219	86	15	al	al	PROPN
iajs-219	86	16	-	-	PUNCT
iajs-219	86	17	haitham	haitham	PROPN
iajs-219	86	18	.	.	PUNCT
iajs-219	87	1	j.	j.	PROPN
iajs-219	87	2	for	for	ADP
iajs-219	87	3	pure	pure	PROPN
iajs-219	87	4	&	&	CCONJ
iajs-219	87	5	appl	appl	PROPN
iajs-219	87	6	.	.	PUNCT
iajs-219	88	1	sci	sci	PROPN
iajs-219	88	2	.	.	PUNCT
iajs-219	88	3	vol	vol	NOUN
iajs-219	88	4	.	.	PROPN
iajs-219	89	1	28	28	NUM
iajs-219	89	2	(	(	PUNCT
iajs-219	89	3	٢	٢	NOUN
iajs-219	89	4	)	)	PUNCT
iajs-219	89	5	2015	2015	NUM
iajs-219	89	6	proof	proof	NOUN
iajs-219	89	7	:	:	PUNCT
iajs-219	89	8	let	let	AUX
iajs-219	89	9	be	be	AUX
iajs-219	89	10	a	a	DET
iajs-219	89	11	submodule	submodule	NOUN
iajs-219	89	12	of	of	ADP
iajs-219	89	13	.	.	PUNCT
iajs-219	90	1	since	since	SCONJ
iajs-219	90	2	is	be	AUX
iajs-219	90	3	a	a	DET
iajs-219	90	4	purely	purely	ADV
iajs-219	90	5	-extending	-extending	NOUN
iajs-219	90	6	,	,	PUNCT
iajs-219	90	7	then	then	ADV
iajs-219	90	8	there	there	PRON
iajs-219	90	9	is	be	VERB
iajs-219	90	10	a	a	DET
iajs-219	90	11	pure	pure	ADJ
iajs-219	90	12	submodule	submodule	NOUN
iajs-219	90	13	of	of	ADP
iajs-219	90	14	such	such	ADJ
iajs-219	90	15	that	that	PRON
iajs-219	90	16	.	.	PUNCT
iajs-219	91	1	by	by	ADP
iajs-219	91	2	assumption	assumption	NOUN
iajs-219	91	3	,	,	PUNCT
iajs-219	91	4	∩	∩	NOUN
iajs-219	91	5	is	be	AUX
iajs-219	91	6	a	a	DET
iajs-219	91	7	pure	pure	ADJ
iajs-219	91	8	submoduleof	submoduleof	NOUN
iajs-219	91	9	.but	.but	NOUN
iajs-219	91	10	,	,	PUNCT
iajs-219	91	11	∩	∩	PROPN
iajs-219	91	12	≤e	≤e	VERB
iajs-219	91	13	p	p	NOUN
iajs-219	91	14	and	and	CCONJ
iajs-219	91	15	∩	∩	NOUN
iajs-219	91	16	≤e	≤e	VERB
iajs-219	91	17	a	a	DET
iajs-219	91	18	,	,	PUNCT
iajs-219	91	19	so	so	SCONJ
iajs-219	91	20	∩	∩	ADJ
iajs-219	91	21	∩	∩	NOUN
iajs-219	91	22	≤e	≤e	VERB
iajs-219	91	23	∩	∩	NOUN
iajs-219	91	24	and	and	CCONJ
iajs-219	91	25	∩	∩	NOUN
iajs-219	91	26	∩	∩	NOUN
iajs-219	91	27	≤e	≤e	VERB
iajs-219	91	28	∩	∩	NOUN
iajs-219	91	29	=	=	NOUN
iajs-219	91	30	a.	a.	NOUN
iajs-219	91	31	therefore	therefore	ADV
iajs-219	91	32	,	,	PUNCT
iajs-219	91	33	∩	∩	NOUN
iajs-219	91	34	.	.	PUNCT
iajs-219	92	1	thus	thus	ADV
iajs-219	92	2	,	,	PUNCT
iajs-219	92	3	is	be	AUX
iajs-219	92	4	purely	purely	ADV
iajs-219	92	5	-extending	-extende	VERB
iajs-219	92	6	module	module	NOUN
iajs-219	92	7	.	.	PUNCT
iajs-219	93	1	∎	∎	VERB
iajs-219	93	2	from	from	ADP
iajs-219	93	3	[	[	X
iajs-219	93	4	4	4	NUM
iajs-219	93	5	]	]	PUNCT
iajs-219	93	6	,	,	PUNCT
iajs-219	93	7	recall	recall	VERB
iajs-219	93	8	that	that	PRON
iajs-219	93	9	is	be	AUX
iajs-219	93	10	-extending	-extende	VERB
iajs-219	93	11	module	module	NOUN
iajs-219	93	12	if	if	SCONJ
iajs-219	93	13	every	every	DET
iajs-219	93	14	direct	direct	ADJ
iajs-219	93	15	summand	summand	NOUN
iajs-219	93	16	of	of	ADP
iajs-219	93	17	is	be	AUX
iajs-219	93	18	extending.this	extending.this	NUM
iajs-219	93	19	lead	lead	NOUN
iajs-219	93	20	us	we	PRON
iajs-219	93	21	to	to	PART
iajs-219	93	22	introduce	introduce	VERB
iajs-219	93	23	the	the	DET
iajs-219	93	24	following	following	NOUN
iajs-219	93	25	.	.	PUNCT
iajs-219	94	1	definition	definition	NOUN
iajs-219	94	2	(	(	PUNCT
iajs-219	94	3	1.7	1.7	NUM
iajs-219	94	4	):	):	PUNCT
iajs-219	94	5	an	an	DET
iajs-219	94	6	-module	-module	NOUN
iajs-219	94	7	is	be	AUX
iajs-219	94	8	called	call	VERB
iajs-219	94	9	purely	purely	ADV
iajs-219	94	10	-extending	-extending	ADJ
iajs-219	94	11	if	if	SCONJ
iajs-219	94	12	every	every	DET
iajs-219	94	13	direct	direct	ADJ
iajs-219	94	14	summand	summand	NOUN
iajs-219	94	15	of	of	ADP
iajs-219	94	16	is	be	AUX
iajs-219	94	17	purely	purely	ADV
iajs-219	94	18	extending	extend	VERB
iajs-219	94	19	.	.	PUNCT
iajs-219	95	1	in	in	ADP
iajs-219	95	2	fact	fact	NOUN
iajs-219	95	3	,	,	PUNCT
iajs-219	95	4	we	we	PRON
iajs-219	95	5	do	do	AUX
iajs-219	95	6	not	not	PART
iajs-219	95	7	know	know	VERB
iajs-219	95	8	whether	whether	SCONJ
iajs-219	95	9	,	,	PUNCT
iajs-219	95	10	every	every	DET
iajs-219	95	11	purely	purely	ADV
iajs-219	95	12	-extending	-extending	ADJ
iajs-219	95	13	module	module	NOUN
iajs-219	95	14	is	be	AUX
iajs-219	95	15	purely	purely	ADV
iajs-219	95	16	extending	extend	VERB
iajs-219	95	17	.	.	PUNCT
iajs-219	96	1	in	in	ADP
iajs-219	96	2	fact	fact	NOUN
iajs-219	96	3	,	,	PUNCT
iajs-219	96	4	we	we	PRON
iajs-219	96	5	have	have	VERB
iajs-219	96	6	the	the	DET
iajs-219	96	7	following	follow	VERB
iajs-219	96	8	result	result	NOUN
iajs-219	96	9	.	.	PUNCT
iajs-219	97	1	proposition	proposition	NOUN
iajs-219	97	2	(	(	PUNCT
iajs-219	97	3	1.8	1.8	NUM
iajs-219	97	4	):	):	PUNCT
iajs-219	97	5	every	every	DET
iajs-219	97	6	purely	purely	ADV
iajs-219	97	7	extending	extend	VERB
iajs-219	97	8	module	module	NOUN
iajs-219	97	9	is	be	AUX
iajs-219	97	10	purely	purely	ADV
iajs-219	97	11	-extending	-extende	VERB
iajs-219	97	12	module	module	NOUN
iajs-219	97	13	.	.	PUNCT
iajs-219	98	1	proof	proof	NOUN
iajs-219	98	2	:	:	PUNCT
iajs-219	98	3	let	let	AUX
iajs-219	98	4	be	be	AUX
iajs-219	98	5	a	a	DET
iajs-219	98	6	direct	direct	ADJ
iajs-219	98	7	summand	summand	NOUN
iajs-219	98	8	of	of	ADP
iajs-219	98	9	a	a	DET
iajs-219	98	10	purely	purely	ADV
iajs-219	98	11	extending	extend	VERB
iajs-219	98	12	module	module	NOUN
iajs-219	98	13	.	.	PUNCT
iajs-219	99	1	by	by	ADP
iajs-219	99	2	[	[	X
iajs-219	99	3	5	5	NUM
iajs-219	99	4	]	]	PUNCT
iajs-219	99	5	,	,	PUNCT
iajs-219	99	6	is	be	AUX
iajs-219	99	7	purely	purely	ADV
iajs-219	99	8	extending	extend	VERB
iajs-219	99	9	module	module	NOUN
iajs-219	99	10	.	.	PUNCT
iajs-219	100	1	hence	hence	ADV
iajs-219	100	2	is	be	AUX
iajs-219	100	3	purely	purely	ADV
iajs-219	100	4	-extending	-extende	VERB
iajs-219	100	5	module	module	NOUN
iajs-219	100	6	.	.	PUNCT
iajs-219	101	1	thus	thus	ADV
iajs-219	101	2	,	,	PUNCT
iajs-219	101	3	is	be	AUX
iajs-219	101	4	a	a	DET
iajs-219	101	5	purely	purely	ADV
iajs-219	101	6	extending	extending	ADJ
iajs-219	101	7	.	.	PUNCT
iajs-219	102	1	∎	∎	PROPN
iajs-219	102	2	but	but	CCONJ
iajs-219	102	3	the	the	DET
iajs-219	102	4	converse	converse	NOUN
iajs-219	102	5	of	of	ADP
iajs-219	102	6	proposition	proposition	NOUN
iajs-219	102	7	(	(	PUNCT
iajs-219	102	8	1.8	1.8	NUM
iajs-219	102	9	)	)	PUNCT
iajs-219	102	10	is	be	AUX
iajs-219	102	11	not	not	PART
iajs-219	102	12	true	true	ADJ
iajs-219	102	13	in	in	ADP
iajs-219	102	14	general	general	ADJ
iajs-219	102	15	,	,	PUNCT
iajs-219	102	16	for	for	ADP
iajs-219	102	17	example	example	NOUN
iajs-219	102	18	,	,	PUNCT
iajs-219	102	19	the	the	DET
iajs-219	102	20	zmodule	zmodule	PROPN
iajs-219	102	21	⊕	⊕	PROPN
iajs-219	102	22	(	(	PUNCT
iajs-219	102	23	for	for	ADP
iajs-219	102	24	any	any	DET
iajs-219	102	25	prime	prime	ADJ
iajs-219	102	26	number	number	NOUN
iajs-219	102	27	)	)	PUNCT
iajs-219	102	28	is	be	AUX
iajs-219	102	29	not	not	PART
iajs-219	102	30	purely	purely	ADV
iajs-219	102	31	extending	extend	VERB
iajs-219	102	32	by	by	ADP
iajs-219	102	33	(	(	PUNCT
iajs-219	102	34	1.2	1.2	NUM
iajs-219	102	35	)	)	PUNCT
iajs-219	102	36	,	,	PUNCT
iajs-219	102	37	but	but	CCONJ
iajs-219	102	38	is	be	AUX
iajs-219	102	39	purely	purely	ADV
iajs-219	102	40	-extending	-extending	ADJ
iajs-219	102	41	,	,	PUNCT
iajs-219	102	42	since	since	SCONJ
iajs-219	102	43	the	the	DET
iajs-219	102	44	only	only	ADJ
iajs-219	102	45	direct	direct	ADJ
iajs-219	102	46	summands	summand	NOUN
iajs-219	102	47	of	of	ADP
iajs-219	102	48	,	,	PUNCT
iajs-219	102	49	(	(	PUNCT
iajs-219	102	50	⊕0	⊕0	PROPN
iajs-219	102	51	,	,	PUNCT
iajs-219	102	52	(	(	PUNCT
iajs-219	102	53	0⊕	0⊕	NUM
iajs-219	102	54	)	)	PUNCT
iajs-219	102	55	,	,	PUNCT
iajs-219	102	56	(	(	PUNCT
iajs-219	102	57	0⊕	0⊕	NUM
iajs-219	102	58	0	0	NUM
iajs-219	102	59	and	and	CCONJ
iajs-219	102	60	,	,	PUNCT
iajs-219	102	61	which	which	PRON
iajs-219	102	62	are	be	AUX
iajs-219	102	63	purely	purely	ADV
iajs-219	102	64	-extending	-extende	VERB
iajs-219	102	65	.	.	PUNCT
iajs-219	103	1	recall	recall	VERB
iajs-219	103	2	that	that	SCONJ
iajs-219	103	3	an	an	DET
iajs-219	103	4	r	r	NOUN
iajs-219	103	5	-	-	PUNCT
iajs-219	103	6	module	module	NOUN
iajs-219	103	7	m	m	NOUN
iajs-219	103	8	has	have	VERB
iajs-219	103	9	the	the	DET
iajs-219	103	10	pure	pure	ADJ
iajs-219	103	11	intersection	intersection	NOUN
iajs-219	103	12	property	property	NOUN
iajs-219	103	13	(	(	PUNCT
iajs-219	103	14	pip	pip	NOUN
iajs-219	103	15	)	)	PUNCT
iajs-219	103	16	if	if	SCONJ
iajs-219	103	17	the	the	DET
iajs-219	103	18	intersection	intersection	NOUN
iajs-219	103	19	of	of	ADP
iajs-219	103	20	any	any	DET
iajs-219	103	21	two	two	NUM
iajs-219	103	22	pure	pure	ADJ
iajs-219	103	23	submodule	submodule	NOUN
iajs-219	103	24	of	of	ADP
iajs-219	103	25	m	m	PROPN
iajs-219	103	26	is	be	AUX
iajs-219	103	27	pure	pure	ADJ
iajs-219	104	1	[	[	X
iajs-219	104	2	8	8	NUM
iajs-219	104	3	]	]	PUNCT
iajs-219	104	4	.	.	PUNCT
iajs-219	105	1	proposition	proposition	NOUN
iajs-219	105	2	(	(	PUNCT
iajs-219	105	3	1.9	1.9	NUM
iajs-219	105	4	)	)	PUNCT
iajs-219	105	5	:	:	PUNCT
iajs-219	105	6	let	let	AUX
iajs-219	105	7	be	be	AUX
iajs-219	105	8	a	a	DET
iajs-219	105	9	purely	purely	ADV
iajs-219	105	10	-extending	-extending	NOUN
iajs-219	105	11	and	and	CCONJ
iajs-219	105	12	has	have	VERB
iajs-219	105	13	the	the	PRON
iajs-219	105	14	.	.	PUNCT
iajs-219	106	1	then	then	ADV
iajs-219	106	2	is	be	AUX
iajs-219	106	3	a	a	DET
iajs-219	106	4	purely	purely	ADV
iajs-219	106	5	-extending	-extending	ADJ
iajs-219	106	6	.	.	PUNCT
iajs-219	107	1	proof	proof	NOUN
iajs-219	107	2	:	:	PUNCT
iajs-219	107	3	let	let	AUX
iajs-219	107	4	be	be	AUX
iajs-219	107	5	a	a	DET
iajs-219	107	6	direct	direct	ADJ
iajs-219	107	7	summand	summand	NOUN
iajs-219	107	8	of	of	ADP
iajs-219	107	9	and	and	CCONJ
iajs-219	107	10	be	be	AUX
iajs-219	107	11	a	a	DET
iajs-219	107	12	submodule	submodule	NOUN
iajs-219	107	13	of	of	ADP
iajs-219	107	14	.	.	PUNCT
iajs-219	108	1	since	since	SCONJ
iajs-219	108	2	is	be	AUX
iajs-219	108	3	a	a	DET
iajs-219	108	4	purely	purely	ADV
iajs-219	108	5	extending	extending	ADJ
iajs-219	108	6	,	,	PUNCT
iajs-219	108	7	then	then	ADV
iajs-219	108	8	there	there	PRON
iajs-219	108	9	is	be	VERB
iajs-219	108	10	a	a	DET
iajs-219	108	11	pure	pure	ADJ
iajs-219	108	12	submodule	submodule	NOUN
iajs-219	108	13	of	of	ADP
iajs-219	108	14	such	such	ADJ
iajs-219	108	15	that	that	PRON
iajs-219	108	16	.	.	PUNCT
iajs-219	109	1	but	but	CCONJ
iajs-219	109	2	satisfies	satisfie	NOUN
iajs-219	109	3	,	,	PUNCT
iajs-219	109	4	then	then	ADV
iajs-219	109	5	∩	∩	NOUN
iajs-219	109	6	is	be	AUX
iajs-219	109	7	a	a	DET
iajs-219	109	8	pure	pure	ADJ
iajs-219	109	9	submodule	submodule	NOUN
iajs-219	109	10	of	of	ADP
iajs-219	109	11	.	.	PUNCT
iajs-219	110	1	but	but	CCONJ
iajs-219	110	2	∩	∩	NOUN
iajs-219	110	3	⊆	⊆	NUM
iajs-219	110	4	n	n	CCONJ
iajs-219	110	5	,	,	PUNCT
iajs-219	110	6	hence	hence	ADV
iajs-219	110	7	∩	∩	NOUN
iajs-219	110	8	is	be	AUX
iajs-219	110	9	a	a	DET
iajs-219	110	10	pure	pure	ADJ
iajs-219	110	11	submodule	submodule	NOUN
iajs-219	110	12	of	of	ADP
iajs-219	110	13	.therefore	.therefore	NOUN
iajs-219	110	14	,	,	PUNCT
iajs-219	110	15	∩	∩	NOUN
iajs-219	110	16	∩	∩	NOUN
iajs-219	110	17	by	by	ADP
iajs-219	110	18	[	[	PUNCT
iajs-219	110	19	9	9	NUM
iajs-219	110	20	]	]	PUNCT
iajs-219	110	21	,	,	PUNCT
iajs-219	110	22	and	and	CCONJ
iajs-219	110	23	so	so	ADV
iajs-219	110	24	is	be	AUX
iajs-219	110	25	a	a	DET
iajs-219	110	26	purely	purely	ADV
iajs-219	110	27	-extending	-extending	ADJ
iajs-219	110	28	.	.	PUNCT
iajs-219	111	1	∎	∎	PROPN
iajs-219	111	2	corollary	corollary	ADJ
iajs-219	111	3	(	(	PUNCT
iajs-219	111	4	1.10	1.10	NUM
iajs-219	111	5	)	)	PUNCT
iajs-219	111	6	:	:	PUNCT
iajs-219	111	7	let	let	VERB
iajs-219	111	8	be	be	AUX
iajs-219	111	9	a	a	DET
iajs-219	111	10	prime	prime	ADJ
iajs-219	111	11	module	module	NOUN
iajs-219	111	12	over	over	ADP
iajs-219	111	13	a	a	DET
iajs-219	111	14	bezout	bezout	NOUN
iajs-219	111	15	domain	domain	NOUN
iajs-219	111	16	.	.	PUNCT
iajs-219	112	1	if	if	SCONJ
iajs-219	112	2	is	be	AUX
iajs-219	112	3	a	a	DET
iajs-219	112	4	purely	purely	ADV
iajs-219	112	5	-extending	-extende	VERB
iajs-219	112	6	module	module	NOUN
iajs-219	112	7	,	,	PUNCT
iajs-219	112	8	then	then	ADV
iajs-219	112	9	is	be	AUX
iajs-219	112	10	a	a	DET
iajs-219	112	11	purely	purely	ADV
iajs-219	112	12	-extending	-extending	ADJ
iajs-219	112	13	.	.	PUNCT
iajs-219	113	1	∎	∎	PROPN
iajs-219	113	2	recall	recall	VERB
iajs-219	113	3	that	that	SCONJ
iajs-219	113	4	an	an	DET
iajs-219	113	5	-module	-module	NOUN
iajs-219	113	6	is	be	AUX
iajs-219	113	7	a	a	DET
iajs-219	113	8	multiplication	multiplication	NOUN
iajs-219	113	9	if	if	SCONJ
iajs-219	113	10	for	for	ADP
iajs-219	113	11	each	each	DET
iajs-219	113	12	submodule	submodule	NOUN
iajs-219	113	13	of	of	ADP
iajs-219	113	14	,	,	PUNCT
iajs-219	113	15	there	there	PRON
iajs-219	113	16	exists	exist	VERB
iajs-219	113	17	an	an	DET
iajs-219	113	18	ideal	ideal	NOUN
iajs-219	113	19	of	of	ADP
iajs-219	113	20	such	such	ADJ
iajs-219	113	21	that	that	PRON
iajs-219	113	22	=	=	PUNCT
iajs-219	114	1	[	[	X
iajs-219	114	2	10	10	NUM
iajs-219	114	3	]	]	PUNCT
iajs-219	114	4	.	.	PUNCT
iajs-219	115	1	since	since	SCONJ
iajs-219	115	2	every	every	DET
iajs-219	115	3	multiplication	multiplication	NOUN
iajs-219	115	4	module	module	NOUN
iajs-219	115	5	has	have	VERB
iajs-219	115	6	the	the	DET
iajs-219	115	7	[	[	NOUN
iajs-219	115	8	8	8	NUM
iajs-219	115	9	]	]	PUNCT
iajs-219	115	10	.	.	PUNCT
iajs-219	116	1	thus	thus	ADV
iajs-219	116	2	,	,	PUNCT
iajs-219	116	3	we	we	PRON
iajs-219	116	4	have	have	VERB
iajs-219	116	5	the	the	DET
iajs-219	116	6	next	next	ADJ
iajs-219	116	7	corollary	corollary	NOUN
iajs-219	116	8	.	.	PUNCT
iajs-219	117	1	corollary	corollary	NOUN
iajs-219	117	2	(	(	PUNCT
iajs-219	117	3	1.11	1.11	NUM
iajs-219	117	4	):	):	PUNCT
iajs-219	117	5	let	let	VERB
iajs-219	117	6	be	be	AUX
iajs-219	117	7	a	a	DET
iajs-219	117	8	multiplication	multiplication	NOUN
iajs-219	117	9	purely	purely	ADV
iajs-219	117	10	-extending	-extende	VERB
iajs-219	117	11	module	module	NOUN
iajs-219	117	12	.	.	PUNCT
iajs-219	118	1	then	then	ADV
iajs-219	118	2	is	be	AUX
iajs-219	118	3	a	a	DET
iajs-219	118	4	purely	purely	ADV
iajs-219	118	5	extending	extending	ADJ
iajs-219	118	6	.	.	PUNCT
iajs-219	119	1	∎	∎	PROPN
iajs-219	119	2	corollary	corollary	ADJ
iajs-219	119	3	(	(	PUNCT
iajs-219	119	4	1.12	1.12	NUM
iajs-219	119	5	)	)	PUNCT
iajs-219	119	6	:	:	PUNCT
iajs-219	119	7	let	let	VERB
iajs-219	119	8	is	be	AUX
iajs-219	119	9	cyclic	cyclic	ADJ
iajs-219	119	10	module	module	NOUN
iajs-219	119	11	over	over	ADP
iajs-219	119	12	a	a	DET
iajs-219	119	13	commutative	commutative	ADJ
iajs-219	119	14	ring	ring	NOUN
iajs-219	119	15	.	.	PUNCT
iajs-219	120	1	if	if	SCONJ
iajs-219	120	2	is	be	AUX
iajs-219	120	3	a	a	DET
iajs-219	120	4	purely	purely	ADV
iajs-219	120	5	-extending	-extending	NOUN
iajs-219	120	6	,	,	PUNCT
iajs-219	120	7	then	then	ADV
iajs-219	120	8	is	be	AUX
iajs-219	120	9	purely	purely	ADV
iajs-219	120	10	-extending	-extending	ADJ
iajs-219	120	11	.	.	PUNCT
iajs-219	121	1	∎	∎	PROPN
iajs-219	121	2	corollary	corollary	ADJ
iajs-219	121	3	(	(	PUNCT
iajs-219	121	4	1.13	1.13	NUM
iajs-219	121	5	)	)	PUNCT
iajs-219	121	6	:	:	PUNCT
iajs-219	121	7	let	let	VERB
iajs-219	121	8	be	be	AUX
iajs-219	121	9	a	a	DET
iajs-219	121	10	purely	purely	ADV
iajs-219	121	11	-extending	-extending	ADJ
iajs-219	121	12	commutative	commutative	ADJ
iajs-219	121	13	ring	ring	NOUN
iajs-219	121	14	,	,	PUNCT
iajs-219	121	15	then	then	ADV
iajs-219	121	16	is	be	AUX
iajs-219	121	17	a	a	DET
iajs-219	121	18	purely	purely	ADV
iajs-219	121	19	extending	extending	ADJ
iajs-219	121	20	.	.	PUNCT
iajs-219	122	1	∎	∎	PROPN
iajs-219	122	2	151	151	NUM
iajs-219	122	3	|	|	NOUN
iajs-219	122	4	mathematics	mathematic	NOUN
iajs-219	122	5	٢٠١٥	٢٠١٥	NUM
iajs-219	122	6	)	)	PUNCT
iajs-219	122	7	عام	عام	ADP
iajs-219	122	8	٢العدد	٢العدد	PROPN
iajs-219	122	9	(	(	PUNCT
iajs-219	122	10	٢٨المجلد	٢٨المجلد	NUM
iajs-219	122	11	والتطبيقية	والتطبيقية	PROPN
iajs-219	122	12	الھيثم	الھيثم	NOUN
iajs-219	122	13	للعلوم	للعلوم	PROPN
iajs-219	122	14	الصرفة	الصرفة	NOUN
iajs-219	122	15	ابنمجلة	ابنمجلة	VERB
iajs-219	122	16	ibn	ibn	PROPN
iajs-219	122	17	al	al	PROPN
iajs-219	122	18	-	-	PUNCT
iajs-219	122	19	haitham	haitham	PROPN
iajs-219	122	20	.	.	PUNCT
iajs-219	123	1	j.	j.	PROPN
iajs-219	123	2	for	for	ADP
iajs-219	123	3	pure	pure	PROPN
iajs-219	123	4	&	&	CCONJ
iajs-219	123	5	appl	appl	PROPN
iajs-219	123	6	.	.	PUNCT
iajs-219	124	1	sci	sci	PROPN
iajs-219	124	2	.	.	PUNCT
iajs-219	124	3	vol	vol	NOUN
iajs-219	124	4	.	.	PROPN
iajs-219	125	1	28	28	NUM
iajs-219	125	2	(	(	PUNCT
iajs-219	125	3	٢	٢	PROPN
iajs-219	125	4	)	)	PUNCT
iajs-219	125	5	2015	2015	NUM
iajs-219	125	6	the	the	DET
iajs-219	125	7	following	following	ADJ
iajs-219	125	8	result	result	NOUN
iajs-219	125	9	gives	give	VERB
iajs-219	125	10	a	a	DET
iajs-219	125	11	characterization	characterization	NOUN
iajs-219	125	12	of	of	ADP
iajs-219	125	13	extending	extend	VERB
iajs-219	125	14	abelian	abelian	ADJ
iajs-219	125	15	groups	group	NOUN
iajs-219	125	16	.	.	PUNCT
iajs-219	126	1	proposition	proposition	NOUN
iajs-219	126	2	(	(	PUNCT
iajs-219	126	3	1.14	1.14	NUM
iajs-219	126	4	):	):	PUNCT
iajs-219	126	5	a	a	DET
iajs-219	126	6	-module	-module	NOUN
iajs-219	126	7	is	be	AUX
iajs-219	126	8	extending	extend	VERB
iajs-219	126	9	module	module	NOUN
iajs-219	126	10	if	if	SCONJ
iajs-219	126	11	and	and	CCONJ
iajs-219	126	12	only	only	ADV
iajs-219	126	13	if	if	SCONJ
iajs-219	126	14	is	be	AUX
iajs-219	126	15	a	a	DET
iajs-219	126	16	purely	purely	ADV
iajs-219	126	17	extending	extend	VERB
iajs-219	126	18	and	and	CCONJ
iajs-219	126	19	is	be	AUX
iajs-219	126	20	a	a	DET
iajs-219	126	21	extending	extending	NOUN
iajs-219	126	22	as	as	ADP
iajs-219	126	23	-module	-module	NOUN
iajs-219	126	24	.	.	PUNCT
iajs-219	127	1	proof	proof	NOUN
iajs-219	127	2	:	:	PUNCT
iajs-219	127	3	(	(	PUNCT
iajs-219	127	4	⟹	⟹	X
iajs-219	127	5	)	)	PUNCT
iajs-219	127	6	it	it	PRON
iajs-219	127	7	is	be	AUX
iajs-219	127	8	clear	clear	ADJ
iajs-219	127	9	that	that	SCONJ
iajs-219	127	10	.	.	PUNCT
iajs-219	128	1	(	(	PUNCT
iajs-219	128	2	⟸	⟸	X
iajs-219	128	3	)	)	PUNCT
iajs-219	128	4	let	let	AUX
iajs-219	128	5	be	be	AUX
iajs-219	128	6	a	a	DET
iajs-219	128	7	closed	closed	ADJ
iajs-219	128	8	submodule	submodule	NOUN
iajs-219	128	9	of	of	ADP
iajs-219	128	10	.	.	PUNCT
iajs-219	129	1	since	since	SCONJ
iajs-219	129	2	is	be	AUX
iajs-219	129	3	a	a	DET
iajs-219	129	4	purely	purely	ADV
iajs-219	129	5	extending	extending	ADJ
iajs-219	129	6	,	,	PUNCT
iajs-219	129	7	then	then	ADV
iajs-219	129	8	is	be	AUX
iajs-219	129	9	a	a	DET
iajs-219	129	10	pure	pure	ADJ
iajs-219	129	11	submodule	submodule	NOUN
iajs-219	129	12	of	of	ADP
iajs-219	129	13	by	by	ADP
iajs-219	129	14	[	[	X
iajs-219	129	15	5	5	NUM
iajs-219	129	16	]	]	PUNCT
iajs-219	129	17	.	.	PUNCT
iajs-219	130	1	also	also	ADV
iajs-219	130	2	,	,	PUNCT
iajs-219	130	3	since	since	SCONJ
iajs-219	130	4	is	be	AUX
iajs-219	130	5	a	a	DET
iajs-219	130	6	-extending	-extending	NOUN
iajs-219	130	7	as	as	ADP
iajs-219	130	8	-module	-module	NOUN
iajs-219	130	9	by	by	ADP
iajs-219	130	10	[	[	X
iajs-219	130	11	4	4	NUM
iajs-219	130	12	]	]	PUNCT
iajs-219	130	13	,	,	PUNCT
iajs-219	130	14	then	then	ADV
iajs-219	130	15	is	be	AUX
iajs-219	130	16	a	a	DET
iajs-219	130	17	direct	direct	ADJ
iajs-219	130	18	summand	summand	NOUN
iajs-219	130	19	of	of	ADP
iajs-219	130	20	.therefore	.therefore	NOUN
iajs-219	130	21	,	,	PUNCT
iajs-219	130	22	is	be	AUX
iajs-219	130	23	extending	extend	VERB
iajs-219	130	24	module	module	NOUN
iajs-219	130	25	.	.	PUNCT
iajs-219	131	1	∎	∎	PROPN
iajs-219	131	2	2	2	NUM
iajs-219	131	3	.	.	PUNCT
iajs-219	131	4	characterizations	characterization	NOUN
iajs-219	131	5	of	of	ADP
iajs-219	131	6	purely	purely	ADV
iajs-219	131	7	goldie	goldie	PROPN
iajs-219	131	8	extending	extend	VERB
iajs-219	131	9	modules	module	NOUN
iajs-219	131	10	it	it	PRON
iajs-219	131	11	is	be	AUX
iajs-219	131	12	known	know	VERB
iajs-219	131	13	that	that	PRON
iajs-219	131	14	is	be	AUX
iajs-219	131	15	a	a	DET
iajs-219	131	16	purely	purely	ADV
iajs-219	131	17	extending	extend	VERB
iajs-219	131	18	module	module	NOUN
iajs-219	131	19	if	if	SCONJ
iajs-219	131	20	and	and	CCONJ
iajs-219	131	21	only	only	ADV
iajs-219	131	22	if	if	SCONJ
iajs-219	131	23	every	every	DET
iajs-219	131	24	closed	closed	ADJ
iajs-219	131	25	submodule	submodule	NOUN
iajs-219	131	26	in	in	ADP
iajs-219	131	27	is	be	AUX
iajs-219	131	28	a	a	DET
iajs-219	131	29	pure	pure	ADJ
iajs-219	131	30	in	in	ADP
iajs-219	131	31	[	[	X
iajs-219	131	32	5	5	NUM
iajs-219	131	33	]	]	PUNCT
iajs-219	131	34	.	.	PUNCT
iajs-219	132	1	also	also	ADV
iajs-219	132	2	from	from	ADP
iajs-219	132	3	[	[	X
iajs-219	132	4	4	4	NUM
iajs-219	132	5	]	]	PUNCT
iajs-219	132	6	,	,	PUNCT
iajs-219	132	7	is	be	AUX
iajs-219	132	8	-extending	-extende	VERB
iajs-219	132	9	module	module	NOUN
iajs-219	132	10	if	if	SCONJ
iajs-219	132	11	and	and	CCONJ
iajs-219	132	12	only	only	ADV
iajs-219	132	13	if	if	SCONJ
iajs-219	132	14	for	for	ADP
iajs-219	132	15	every	every	DET
iajs-219	132	16	closed	closed	ADJ
iajs-219	132	17	submodule	submodule	NOUN
iajs-219	132	18	of	of	ADP
iajs-219	132	19	m	m	PROPN
iajs-219	132	20	,	,	PUNCT
iajs-219	132	21	there	there	PRON
iajs-219	132	22	is	be	VERB
iajs-219	132	23	a	a	DET
iajs-219	132	24	direct	direct	ADJ
iajs-219	132	25	summand	summand	NOUN
iajs-219	132	26	of	of	ADP
iajs-219	132	27	such	such	ADJ
iajs-219	132	28	that	that	PRON
iajs-219	132	29	.	.	PUNCT
iajs-219	133	1	here	here	ADV
iajs-219	133	2	,	,	PUNCT
iajs-219	133	3	we	we	PRON
iajs-219	133	4	give	give	VERB
iajs-219	133	5	analogous	analogous	ADJ
iajs-219	133	6	characterization	characterization	NOUN
iajs-219	133	7	of	of	ADP
iajs-219	133	8	purely	purely	ADV
iajs-219	133	9	-extending	-extende	VERB
iajs-219	133	10	modules	module	NOUN
iajs-219	133	11	.	.	PUNCT
iajs-219	134	1	proposition	proposition	NOUN
iajs-219	134	2	(	(	PUNCT
iajs-219	134	3	2.1	2.1	NUM
iajs-219	134	4	):	):	PUNCT
iajs-219	134	5	an	an	DET
iajs-219	134	6	-module	-module	NOUN
iajs-219	134	7	is	be	AUX
iajs-219	134	8	purely	purely	ADV
iajs-219	134	9	-extending	-extending	ADJ
iajs-219	134	10	if	if	SCONJ
iajs-219	134	11	and	and	CCONJ
iajs-219	134	12	only	only	ADV
iajs-219	134	13	if	if	SCONJ
iajs-219	134	14	for	for	ADP
iajs-219	134	15	every	every	DET
iajs-219	134	16	closed	closed	ADJ
iajs-219	134	17	submodule	submodule	NOUN
iajs-219	134	18	of	of	ADP
iajs-219	134	19	,	,	PUNCT
iajs-219	134	20	there	there	PRON
iajs-219	134	21	is	be	VERB
iajs-219	134	22	a	a	DET
iajs-219	134	23	pure	pure	ADJ
iajs-219	134	24	submodule	submodule	NOUN
iajs-219	134	25	of	of	ADP
iajs-219	134	26	such	such	ADJ
iajs-219	134	27	that	that	PRON
iajs-219	134	28	.	.	PUNCT
iajs-219	135	1	proof	proof	NOUN
iajs-219	135	2	:	:	PUNCT
iajs-219	135	3	(	(	PUNCT
iajs-219	135	4	⟹	⟹	X
iajs-219	135	5	)	)	PUNCT
iajs-219	135	6	it	it	PRON
iajs-219	135	7	is	be	AUX
iajs-219	135	8	clear	clear	ADJ
iajs-219	135	9	.	.	PUNCT
iajs-219	136	1	(	(	PUNCT
iajs-219	136	2	⟸	⟸	X
iajs-219	136	3	)	)	PUNCT
iajs-219	136	4	let	let	AUX
iajs-219	136	5	be	be	AUX
iajs-219	136	6	a	a	DET
iajs-219	136	7	submodule	submodule	NOUN
iajs-219	136	8	of	of	ADP
iajs-219	136	9	.by	.by	PROPN
iajs-219	136	10	zorn	zorn	PROPN
iajs-219	136	11	's	's	PART
iajs-219	136	12	lemma	lemma	PROPN
iajs-219	136	13	,	,	PUNCT
iajs-219	136	14	there	there	PRON
iajs-219	136	15	exists	exist	VERB
iajs-219	136	16	a	a	DET
iajs-219	136	17	closed	closed	ADJ
iajs-219	136	18	submodule	submodule	NOUN
iajs-219	136	19	of	of	ADP
iajs-219	136	20	such	such	ADJ
iajs-219	136	21	that	that	PRON
iajs-219	136	22	is	be	AUX
iajs-219	136	23	essential	essential	ADJ
iajs-219	136	24	in	in	ADP
iajs-219	136	25	.	.	PUNCT
iajs-219	137	1	so	so	ADV
iajs-219	137	2	,	,	PUNCT
iajs-219	137	3	we	we	PRON
iajs-219	137	4	have	have	VERB
iajs-219	137	5	a	a	DET
iajs-219	137	6	.by	.by	PROPN
iajs-219	137	7	assumption	assumption	NOUN
iajs-219	137	8	,	,	PUNCT
iajs-219	137	9	there	there	PRON
iajs-219	137	10	exists	exist	VERB
iajs-219	137	11	a	a	DET
iajs-219	137	12	pure	pure	ADJ
iajs-219	137	13	submodule	submodule	NOUN
iajs-219	137	14	of	of	ADP
iajs-219	137	15	such	such	ADJ
iajs-219	137	16	that	that	PRON
iajs-219	137	17	.	.	PUNCT
iajs-219	138	1	since	since	SCONJ
iajs-219	138	2	is	be	AUX
iajs-219	138	3	transitive	transitive	ADJ
iajs-219	138	4	relation	relation	NOUN
iajs-219	138	5	,	,	PUNCT
iajs-219	138	6	then	then	ADV
iajs-219	138	7	a	a	DET
iajs-219	138	8	.therefore	.therefore	NOUN
iajs-219	138	9	,	,	PUNCT
iajs-219	138	10	is	be	AUX
iajs-219	138	11	purely	purely	ADV
iajs-219	138	12	-extending	-extende	VERB
iajs-219	138	13	module	module	NOUN
iajs-219	138	14	.	.	PUNCT
iajs-219	139	1	∎	∎	NOUN
iajs-219	139	2	proposition	proposition	NOUN
iajs-219	139	3	(	(	PUNCT
iajs-219	139	4	2.2	2.2	NUM
iajs-219	139	5	):	):	PUNCT
iajs-219	139	6	an	an	DET
iajs-219	139	7	-module	-module	NOUN
iajs-219	139	8	is	be	AUX
iajs-219	139	9	purely	purely	ADV
iajs-219	139	10	-extending	-extending	ADJ
iajs-219	139	11	if	if	SCONJ
iajs-219	139	12	and	and	CCONJ
iajs-219	139	13	only	only	ADV
iajs-219	139	14	if	if	SCONJ
iajs-219	139	15	every	every	DET
iajs-219	139	16	direct	direct	ADJ
iajs-219	139	17	summand	summand	NOUN
iajs-219	139	18	of	of	ADP
iajs-219	139	19	the	the	DET
iajs-219	139	20	injective	injective	ADJ
iajs-219	139	21	hull	hull	NOUN
iajs-219	139	22	,	,	PUNCT
iajs-219	139	23	there	there	PRON
iajs-219	139	24	exists	exist	VERB
iajs-219	139	25	a	a	DET
iajs-219	139	26	pure	pure	ADJ
iajs-219	139	27	submodule	submodule	NOUN
iajs-219	139	28	of	of	ADP
iajs-219	139	29	such	such	ADJ
iajs-219	139	30	that	that	DET
iajs-219	139	31	∩	∩	NOUN
iajs-219	139	32	)	)	PUNCT
iajs-219	139	33	.	.	PUNCT
iajs-219	140	1	proof	proof	NOUN
iajs-219	140	2	:	:	PUNCT
iajs-219	140	3	(	(	PUNCT
iajs-219	140	4	⟹	⟹	X
iajs-219	140	5	)	)	PUNCT
iajs-219	140	6	let	let	AUX
iajs-219	140	7	be	be	AUX
iajs-219	140	8	a	a	DET
iajs-219	140	9	direct	direct	ADJ
iajs-219	140	10	summand	summand	NOUN
iajs-219	140	11	of	of	ADP
iajs-219	140	12	the	the	DET
iajs-219	140	13	injective	injective	ADJ
iajs-219	140	14	hull	hull	NOUN
iajs-219	140	15	of	of	ADP
iajs-219	140	16	,	,	PUNCT
iajs-219	140	17	then	then	ADV
iajs-219	140	18	(	(	PUNCT
iajs-219	140	19	∩	∩	NOUN
iajs-219	140	20	is	be	AUX
iajs-219	140	21	a	a	DET
iajs-219	140	22	submodule	submodule	NOUN
iajs-219	140	23	of	of	ADP
iajs-219	140	24	,	,	PUNCT
iajs-219	140	25	since	since	SCONJ
iajs-219	140	26	is	be	AUX
iajs-219	140	27	purely	purely	ADV
iajs-219	140	28	-extending	-extending	ADJ
iajs-219	140	29	,	,	PUNCT
iajs-219	140	30	then	then	ADV
iajs-219	140	31	there	there	PRON
iajs-219	140	32	exists	exist	VERB
iajs-219	140	33	a	a	DET
iajs-219	140	34	pure	pure	ADJ
iajs-219	140	35	submodule	submodule	NOUN
iajs-219	140	36	of	of	ADP
iajs-219	140	37	such	such	ADJ
iajs-219	140	38	that	that	DET
iajs-219	140	39	∩	∩	NOUN
iajs-219	140	40	.	.	PUNCT
iajs-219	141	1	(	(	PUNCT
iajs-219	141	2	⟸	⟸	X
iajs-219	141	3	)	)	PUNCT
iajs-219	141	4	let	let	VERB
iajs-219	141	5	is	be	AUX
iajs-219	141	6	a	a	DET
iajs-219	141	7	submodule	submodule	NOUN
iajs-219	141	8	of	of	ADP
iajs-219	141	9	and	and	CCONJ
iajs-219	141	10	let	let	VERB
iajs-219	141	11	be	be	AUX
iajs-219	141	12	a	a	DET
iajs-219	141	13	relative	relative	ADJ
iajs-219	141	14	complement	complement	NOUN
iajs-219	141	15	of	of	ADP
iajs-219	141	16	such	such	ADJ
iajs-219	141	17	that	that	SCONJ
iajs-219	141	18	⨁	⨁	PROPN
iajs-219	141	19	is	be	AUX
iajs-219	141	20	essential	essential	ADJ
iajs-219	141	21	in	in	ADP
iajs-219	141	22	[	[	X
iajs-219	141	23	11	11	NUM
iajs-219	141	24	]	]	PUNCT
iajs-219	141	25	.	.	PUNCT
iajs-219	142	1	since	since	SCONJ
iajs-219	142	2	is	be	AUX
iajs-219	142	3	essential	essential	ADJ
iajs-219	142	4	in	in	ADP
iajs-219	142	5	,	,	PUNCT
iajs-219	142	6	then	then	ADV
iajs-219	142	7	⨁	⨁	PROPN
iajs-219	142	8	is	be	AUX
iajs-219	142	9	essential	essential	ADJ
iajs-219	142	10	in	in	ADP
iajs-219	142	11	.	.	PUNCT
iajs-219	143	1	thus	thus	ADV
iajs-219	143	2	,	,	PUNCT
iajs-219	143	3	⨁	⨁	PROPN
iajs-219	143	4	⨁	⨁	PROPN
iajs-219	143	5	)	)	PUNCT
iajs-219	143	6	=	=	PUNCT
iajs-219	144	1	[	[	X
iajs-219	144	2	10	10	NUM
iajs-219	144	3	]	]	PUNCT
iajs-219	144	4	.	.	PUNCT
iajs-219	145	1	by	by	ADP
iajs-219	145	2	hypothesis	hypothesis	NOUN
iajs-219	145	3	,	,	PUNCT
iajs-219	145	4	there	there	PRON
iajs-219	145	5	exists	exist	VERB
iajs-219	145	6	a	a	DET
iajs-219	145	7	pure	pure	ADJ
iajs-219	145	8	submodule	submodule	NOUN
iajs-219	145	9	of	of	ADP
iajs-219	145	10	such	such	ADJ
iajs-219	145	11	that	that	PRON
iajs-219	145	12	(	(	PUNCT
iajs-219	145	13	∩	∩	NOUN
iajs-219	145	14	)	)	PUNCT
iajs-219	145	15	.	.	PUNCT
iajs-219	146	1	but	but	CCONJ
iajs-219	146	2	is	be	AUX
iajs-219	146	3	essential	essential	ADJ
iajs-219	146	4	in	in	ADP
iajs-219	146	5	.	.	PUNCT
iajs-219	147	1	therefore	therefore	ADV
iajs-219	147	2	,	,	PUNCT
iajs-219	147	3	∩	∩	NOUN
iajs-219	147	4	≤e	≤e	VERB
iajs-219	147	5	∩	∩	NOUN
iajs-219	147	6	.	.	PUNCT
iajs-219	148	1	but	but	CCONJ
iajs-219	148	2	∩	∩	NOUN
iajs-219	148	3	=	=	SYM
iajs-219	148	4	∩	∩	NOUN
iajs-219	148	5	∩	∩	NOUN
iajs-219	148	6	∩	∩	NOUN
iajs-219	148	7	≤e	≤e	VERB
iajs-219	148	8	∩	∩	NOUN
iajs-219	148	9	and	and	CCONJ
iajs-219	148	10	∩	∩	NOUN
iajs-219	148	11	=	=	SYM
iajs-219	148	12	∩	∩	NOUN
iajs-219	148	13	∩	∩	NOUN
iajs-219	148	14	∩	∩	NOUN
iajs-219	148	15	≤e	≤e	VERB
iajs-219	148	16	∩	∩	NOUN
iajs-219	148	17	.	.	PUNCT
iajs-219	149	1	so	so	ADV
iajs-219	149	2	,	,	PUNCT
iajs-219	149	3	∩	∩	ADJ
iajs-219	149	4	)	)	PUNCT
iajs-219	149	5	∩	∩	NOUN
iajs-219	149	6	.	.	PUNCT
iajs-219	150	1	since	since	SCONJ
iajs-219	150	2	is	be	AUX
iajs-219	150	3	transitive	transitive	ADJ
iajs-219	150	4	,	,	PUNCT
iajs-219	150	5	then	then	ADV
iajs-219	150	6	∩	∩	NOUN
iajs-219	150	7	.	.	PUNCT
iajs-219	151	1	so	so	ADV
iajs-219	151	2	is	be	AUX
iajs-219	151	3	purely	purely	ADV
iajs-219	151	4	-extending	-extending	ADJ
iajs-219	151	5	.	.	PUNCT
iajs-219	152	1	∎	∎	NOUN
iajs-219	152	2	proposition	proposition	NOUN
iajs-219	152	3	(	(	PUNCT
iajs-219	152	4	2.3	2.3	NUM
iajs-219	152	5	):	):	PUNCT
iajs-219	152	6	the	the	DET
iajs-219	152	7	following	following	ADJ
iajs-219	152	8	statements	statement	NOUN
iajs-219	152	9	are	be	AUX
iajs-219	152	10	equivalent	equivalent	ADJ
iajs-219	152	11	for	for	ADP
iajs-219	152	12	an	an	DET
iajs-219	152	13	an	an	DET
iajs-219	152	14	module	module	NOUN
iajs-219	152	15	:	:	PUNCT
iajs-219	152	16	(	(	PUNCT
iajs-219	152	17	1	1	X
iajs-219	152	18	)	)	PUNCT
iajs-219	152	19	is	be	AUX
iajs-219	152	20	purely	purely	ADV
iajs-219	152	21	–	–	PUNCT
iajs-219	152	22	extending	extend	VERB
iajs-219	152	23	module	module	NOUN
iajs-219	152	24	.	.	PUNCT
iajs-219	153	1	(	(	PUNCT
iajs-219	153	2	2	2	X
iajs-219	153	3	)	)	PUNCT
iajs-219	153	4	for	for	ADP
iajs-219	153	5	each	each	PRON
iajs-219	153	6	is	be	AUX
iajs-219	153	7	a	a	DET
iajs-219	153	8	submodule	submodule	NOUN
iajs-219	153	9	of	of	ADP
iajs-219	153	10	,	,	PUNCT
iajs-219	153	11	there	there	PRON
iajs-219	153	12	exists	exist	VERB
iajs-219	153	13	a	a	DET
iajs-219	153	14	submodule	submodule	NOUN
iajs-219	153	15	of	of	ADP
iajs-219	153	16	and	and	CCONJ
iajs-219	153	17	a	a	DET
iajs-219	153	18	pure	pure	ADJ
iajs-219	153	19	submodule	submodule	NOUN
iajs-219	153	20	of	of	ADP
iajs-219	153	21	,	,	PUNCT
iajs-219	153	22	such	such	ADJ
iajs-219	153	23	that	that	PRON
iajs-219	153	24	and	and	CCONJ
iajs-219	153	25	.	.	PUNCT
iajs-219	154	1	proof	proof	NOUN
iajs-219	154	2	:	:	PUNCT
iajs-219	154	3	(	(	PUNCT
iajs-219	154	4	1)⟹(2	1)⟹(2	NUM
iajs-219	154	5	)	)	PUNCT
iajs-219	154	6	let	let	AUX
iajs-219	154	7	be	be	AUX
iajs-219	154	8	a	a	DET
iajs-219	154	9	submodule	submodule	NOUN
iajs-219	154	10	of	of	ADP
iajs-219	154	11	.	.	PUNCT
iajs-219	155	1	then	then	ADV
iajs-219	155	2	there	there	PRON
iajs-219	155	3	exists	exist	VERB
iajs-219	155	4	a	a	DET
iajs-219	155	5	pure	pure	ADJ
iajs-219	155	6	submodule	submodule	NOUN
iajs-219	155	7	of	of	ADP
iajs-219	155	8	such	such	ADJ
iajs-219	155	9	that	that	PRON
iajs-219	155	10	,	,	PUNCT
iajs-219	155	11	so	so	SCONJ
iajs-219	155	12	∩	∩	NOUN
iajs-219	155	13	and	and	CCONJ
iajs-219	155	14	∩	∩	NOUN
iajs-219	155	15	.	.	PUNCT
iajs-219	156	1	the	the	DET
iajs-219	156	2	proof	proof	NOUN
iajs-219	156	3	is	be	AUX
iajs-219	156	4	complete	complete	ADJ
iajs-219	156	5	put	put	NOUN
iajs-219	156	6	∩	∩	NOUN
iajs-219	156	7	.	.	PUNCT
iajs-219	157	1	(	(	PUNCT
iajs-219	157	2	2)⟹(1	2)⟹(1	NUM
iajs-219	157	3	)	)	PUNCT
iajs-219	157	4	let	let	AUX
iajs-219	157	5	be	be	AUX
iajs-219	157	6	a	a	DET
iajs-219	157	7	submodule	submodule	NOUN
iajs-219	157	8	of	of	ADP
iajs-219	157	9	.	.	PUNCT
iajs-219	158	1	by	by	ADP
iajs-219	158	2	(	(	PUNCT
iajs-219	158	3	2	2	NUM
iajs-219	158	4	)	)	PUNCT
iajs-219	158	5	,	,	PUNCT
iajs-219	158	6	there	there	PRON
iajs-219	158	7	exists	exist	VERB
iajs-219	158	8	a	a	DET
iajs-219	158	9	submodule	submodule	NOUN
iajs-219	158	10	of	of	ADP
iajs-219	158	11	and	and	CCONJ
iajs-219	158	12	a	a	DET
iajs-219	158	13	pure	pure	ADJ
iajs-219	158	14	submodule	submodule	NOUN
iajs-219	158	15	of	of	ADP
iajs-219	158	16	such	such	ADJ
iajs-219	158	17	that	that	PRON
iajs-219	158	18	and	and	CCONJ
iajs-219	158	19	.	.	PUNCT
iajs-219	159	1	now	now	ADV
iajs-219	159	2	,	,	PUNCT
iajs-219	159	3	since	since	SCONJ
iajs-219	159	4	∩	∩	NOUN
iajs-219	159	5	and	and	CCONJ
iajs-219	159	6	∩	∩	NOUN
iajs-219	159	7	then	then	ADV
iajs-219	159	8	∩	∩	ADJ
iajs-219	159	9	and	and	CCONJ
iajs-219	159	10	∩	∩	NOUN
iajs-219	159	11	.	.	PUNCT
iajs-219	160	1	so	so	ADV
iajs-219	160	2	and	and	CCONJ
iajs-219	160	3	so	so	ADV
iajs-219	160	4	is	be	AUX
iajs-219	160	5	purely	purely	ADV
iajs-219	160	6	–	–	PUNCT
iajs-219	160	7	extending	extend	VERB
iajs-219	160	8	module	module	NOUN
iajs-219	160	9	.	.	PUNCT
iajs-219	161	1	∎	∎	PROPN
iajs-219	161	2	following	follow	VERB
iajs-219	161	3	[	[	X
iajs-219	161	4	4	4	NUM
iajs-219	161	5	]	]	PUNCT
iajs-219	161	6	,	,	PUNCT
iajs-219	161	7	a	a	DET
iajs-219	161	8	direct	direct	ADJ
iajs-219	161	9	sum	sum	NOUN
iajs-219	161	10	of	of	ADP
iajs-219	161	11	-extending	-extende	VERB
iajs-219	161	12	modules	module	NOUN
iajs-219	161	13	need	need	AUX
iajs-219	161	14	not	not	PART
iajs-219	161	15	be	be	AUX
iajs-219	161	16	-extending	-extende	VERB
iajs-219	161	17	module	module	NOUN
iajs-219	161	18	.	.	PUNCT
iajs-219	162	1	also	also	ADV
iajs-219	162	2	,	,	PUNCT
iajs-219	162	3	a	a	DET
iajs-219	162	4	direct	direct	ADJ
iajs-219	162	5	sum	sum	NOUN
iajs-219	162	6	of	of	ADP
iajs-219	162	7	purely	purely	ADV
iajs-219	162	8	extending	extend	VERB
iajs-219	162	9	modules	module	NOUN
iajs-219	162	10	need	need	AUX
iajs-219	162	11	not	not	PART
iajs-219	162	12	be	be	AUX
iajs-219	162	13	purely	purely	ADV
iajs-219	162	14	extending	extend	VERB
iajs-219	162	15	module	module	NOUN
iajs-219	162	16	[	[	X
iajs-219	162	17	5	5	NUM
iajs-219	162	18	]	]	PUNCT
iajs-219	162	19	.	.	PUNCT
iajs-219	163	1	here	here	ADV
iajs-219	163	2	,	,	PUNCT
iajs-219	163	3	we	we	PRON
iajs-219	163	4	discuss	discuss	VERB
iajs-219	163	5	when	when	SCONJ
iajs-219	163	6	a	a	DET
iajs-219	163	7	direct	direct	ADJ
iajs-219	163	8	sum	sum	NOUN
iajs-219	163	9	of	of	ADP
iajs-219	163	10	purely	purely	ADV
iajs-219	163	11	-extending	-extende	VERB
iajs-219	163	12	modules	module	NOUN
iajs-219	163	13	is	be	AUX
iajs-219	163	14	a	a	DET
iajs-219	163	15	purely	purely	ADV
iajs-219	163	16	-extending	-extending	ADJ
iajs-219	163	17	.	.	PUNCT
iajs-219	163	18	152	152	NUM
iajs-219	164	1	|	|	NOUN
iajs-219	164	2	mathematics	mathematic	NOUN
iajs-219	164	3	٢٠١٥	٢٠١٥	NUM
iajs-219	164	4	)	)	PUNCT
iajs-219	164	5	عام	عام	ADP
iajs-219	164	6	٢العدد	٢العدد	PROPN
iajs-219	164	7	(	(	PUNCT
iajs-219	164	8	٢٨المجلد	٢٨المجلد	NUM
iajs-219	164	9	والتطبيقية	والتطبيقية	PROPN
iajs-219	164	10	الھيثم	الھيثم	NOUN
iajs-219	164	11	للعلوم	للعلوم	PROPN
iajs-219	164	12	الصرفة	الصرفة	NOUN
iajs-219	164	13	ابنمجلة	ابنمجلة	VERB
iajs-219	164	14	ibn	ibn	PROPN
iajs-219	164	15	al	al	PROPN
iajs-219	164	16	-	-	PUNCT
iajs-219	164	17	haitham	haitham	PROPN
iajs-219	164	18	.	.	PUNCT
iajs-219	165	1	j.	j.	PROPN
iajs-219	165	2	for	for	ADP
iajs-219	165	3	pure	pure	PROPN
iajs-219	165	4	&	&	CCONJ
iajs-219	165	5	appl	appl	PROPN
iajs-219	165	6	.	.	PUNCT
iajs-219	166	1	sci	sci	PROPN
iajs-219	166	2	.	.	PUNCT
iajs-219	166	3	vol	vol	NOUN
iajs-219	166	4	.	.	PROPN
iajs-219	167	1	28	28	NUM
iajs-219	167	2	(	(	PUNCT
iajs-219	167	3	٢	٢	NOUN
iajs-219	167	4	)	)	PUNCT
iajs-219	167	5	2015	2015	NUM
iajs-219	167	6	recall	recall	VERB
iajs-219	167	7	that	that	SCONJ
iajs-219	167	8	a	a	DET
iajs-219	167	9	submodule	submodule	NOUN
iajs-219	167	10	n	n	PROPN
iajs-219	167	11	of	of	ADP
iajs-219	167	12	an	an	DET
iajs-219	167	13	r	r	NOUN
iajs-219	167	14	-module	-module	NOUN
iajs-219	167	15	m	m	NOUN
iajs-219	167	16	is	be	AUX
iajs-219	167	17	fully	fully	ADV
iajs-219	167	18	invariant	invariant	ADJ
iajs-219	167	19	if	if	SCONJ
iajs-219	167	20	f	f	PROPN
iajs-219	167	21	(	(	PUNCT
iajs-219	167	22	n	n	CCONJ
iajs-219	167	23	)	)	PUNCT
iajs-219	167	24			PROPN
iajs-219	167	25	n	n	INTJ
iajs-219	167	26	for	for	ADP
iajs-219	167	27	each	each	DET
iajs-219	167	28	r	r	NOUN
iajs-219	167	29	-	-	PUNCT
iajs-219	167	30	endomorphism	endomorphism	PROPN
iajs-219	167	31	f	f	PROPN
iajs-219	167	32	of	of	ADP
iajs-219	167	33	m	m	PROPN
iajs-219	167	34	[	[	X
iajs-219	167	35	12	12	NUM
iajs-219	167	36	]	]	PUNCT
iajs-219	167	37	.	.	PUNCT
iajs-219	168	1	m	m	PROPN
iajs-219	168	2	is	be	AUX
iajs-219	168	3	called	call	VERB
iajs-219	168	4	duo	duo	NOUN
iajs-219	168	5	if	if	SCONJ
iajs-219	168	6	every	every	DET
iajs-219	168	7	submodule	submodule	NOUN
iajs-219	168	8	of	of	ADP
iajs-219	168	9	m	m	PROPN
iajs-219	168	10	is	be	AUX
iajs-219	168	11	fully	fully	ADV
iajs-219	168	12	invariant	invariant	ADJ
iajs-219	169	1	[	[	PUNCT
iajs-219	169	2	13	13	NUM
iajs-219	169	3	]	]	PUNCT
iajs-219	169	4	.	.	PUNCT
iajs-219	170	1	proposition	proposition	NOUN
iajs-219	170	2	(	(	PUNCT
iajs-219	170	3	2.4	2.4	NUM
iajs-219	170	4	)	)	PUNCT
iajs-219	170	5	let	let	VERB
iajs-219	170	6	is	be	AUX
iajs-219	170	7	purely	purely	ADV
iajs-219	170	8	-extending	-extende	VERB
iajs-219	170	9	r	r	NOUN
iajs-219	170	10	-	-	PUNCT
iajs-219	170	11	module	module	NOUN
iajs-219	170	12	for	for	ADP
iajs-219	170	13	each	each	DET
iajs-219	170	14	∈	∈	NOUN
iajs-219	170	15	such	such	ADJ
iajs-219	170	16	that	that	SCONJ
iajs-219	170	17	every	every	DET
iajs-219	170	18	closed	closed	ADJ
iajs-219	170	19	submodule	submodule	NOUN
iajs-219	170	20	of	of	ADP
iajs-219	170	21	=	=	PROPN
iajs-219	170	22	⊕	⊕	PROPN
iajs-219	170	23	∈	∈	PROPN
iajs-219	170	24	is	be	AUX
iajs-219	170	25	fully	fully	ADV
iajs-219	170	26	invariant	invariant	ADJ
iajs-219	170	27	,	,	PUNCT
iajs-219	170	28	then	then	ADV
iajs-219	170	29	=	=	PROPN
iajs-219	170	30	⊕	⊕	PROPN
iajs-219	170	31	∈	∈	PROPN
iajs-219	170	32	is	be	AUX
iajs-219	170	33	purely	purely	ADV
iajs-219	170	34	-extending	-extende	VERB
iajs-219	170	35	module	module	NOUN
iajs-219	170	36	.	.	PUNCT
iajs-219	171	1	proof	proof	NOUN
iajs-219	171	2	:	:	PUNCT
iajs-219	171	3	let	let	AUX
iajs-219	171	4	be	be	AUX
iajs-219	171	5	a	a	DET
iajs-219	171	6	closed	closed	ADJ
iajs-219	171	7	submodule	submodule	NOUN
iajs-219	171	8	of	of	ADP
iajs-219	171	9	and	and	CCONJ
iajs-219	171	10	let	let	VERB
iajs-219	171	11	:	:	PUNCT
iajs-219	171	12	⟶	⟶	ADJ
iajs-219	171	13	be	be	AUX
iajs-219	171	14	the	the	DET
iajs-219	171	15	natural	natural	ADJ
iajs-219	171	16	projection	projection	NOUN
iajs-219	171	17	on	on	ADP
iajs-219	171	18	for	for	ADP
iajs-219	171	19	each	each	DET
iajs-219	171	20	∈	∈	NOUN
iajs-219	171	21	.	.	PUNCT
iajs-219	172	1	let	let	VERB
iajs-219	172	2	∈	∈	PRON
iajs-219	172	3	,	,	PUNCT
iajs-219	172	4	so	so	CCONJ
iajs-219	172	5	∑	∑	PUNCT
iajs-219	172	6	∈	∈	PROPN
iajs-219	172	7	,	,	PUNCT
iajs-219	172	8	where	where	SCONJ
iajs-219	172	9	∈	∈	NOUN
iajs-219	172	10	and	and	CCONJ
iajs-219	172	11	hence	hence	ADV
iajs-219	172	12	(	(	PUNCT
iajs-219	172	13	)	)	PUNCT
iajs-219	172	14	=	=	PUNCT
iajs-219	172	15	.	.	PUNCT
iajs-219	173	1	now	now	ADV
iajs-219	173	2	,	,	PUNCT
iajs-219	173	3	since	since	SCONJ
iajs-219	173	4	is	be	AUX
iajs-219	173	5	closed	close	VERB
iajs-219	173	6	submodule	submodule	NOUN
iajs-219	173	7	of	of	ADP
iajs-219	173	8	,	,	PUNCT
iajs-219	173	9	then	then	ADV
iajs-219	173	10	by	by	ADP
iajs-219	173	11	hypothesis	hypothesis	NOUN
iajs-219	173	12	,	,	PUNCT
iajs-219	173	13	is	be	AUX
iajs-219	173	14	fully	fully	ADV
iajs-219	173	15	invariant	invariant	ADJ
iajs-219	173	16	and	and	CCONJ
iajs-219	173	17	hence	hence	ADV
iajs-219	173	18	(	(	PUNCT
iajs-219	173	19	)	)	PUNCT
iajs-219	173	20	⊆	⊆	NUM
iajs-219	173	21	∩	∩	NOUN
iajs-219	173	22	.	.	PUNCT
iajs-219	174	1	so	so	ADV
iajs-219	174	2	(	(	PUNCT
iajs-219	174	3	)	)	PUNCT
iajs-219	174	4	=	=	SYM
iajs-219	174	5	∈	∈	PROPN
iajs-219	174	6	∩	∩	NOUN
iajs-219	174	7	and	and	CCONJ
iajs-219	174	8	hence	hence	ADV
iajs-219	174	9	∈⊕	∈⊕	NOUN
iajs-219	174	10	∈	∈	PROPN
iajs-219	174	11	∩	∩	NOUN
iajs-219	174	12	.	.	PUNCT
iajs-219	175	1	thus	thus	ADV
iajs-219	175	2	⊆⊕	⊆⊕	NUM
iajs-219	175	3	∈	∈	NOUN
iajs-219	175	4	∩	∩	NOUN
iajs-219	175	5	)	)	PUNCT
iajs-219	175	6	.	.	PUNCT
iajs-219	176	1	also	also	ADV
iajs-219	176	2	,	,	PUNCT
iajs-219	176	3	⊕	⊕	PROPN
iajs-219	176	4	∈	∈	PROPN
iajs-219	176	5	∩	∩	NOUN
iajs-219	176	6	)	)	PUNCT
iajs-219	176	7	⊆	⊆	NUM
iajs-219	176	8	and	and	CCONJ
iajs-219	176	9	so	so	ADV
iajs-219	176	10	⊕	⊕	PROPN
iajs-219	176	11	∈	∈	PROPN
iajs-219	176	12	∩	∩	NOUN
iajs-219	176	13	)	)	PUNCT
iajs-219	176	14	.	.	PUNCT
iajs-219	177	1	since	since	SCONJ
iajs-219	177	2	∩	∩	NOUN
iajs-219	177	3	)	)	PUNCT
iajs-219	177	4	⊆	⊆	NUM
iajs-219	177	5	and	and	CCONJ
iajs-219	177	6	by	by	ADP
iajs-219	177	7	purely	purely	ADV
iajs-219	177	8	extending	extend	VERB
iajs-219	177	9	property	property	NOUN
iajs-219	177	10	of	of	ADP
iajs-219	177	11	,	,	PUNCT
iajs-219	177	12	then	then	ADV
iajs-219	177	13	there	there	PRON
iajs-219	177	14	is	be	VERB
iajs-219	177	15	a	a	DET
iajs-219	177	16	pure	pure	ADJ
iajs-219	177	17	submodule	submodule	NOUN
iajs-219	177	18	of	of	ADP
iajs-219	177	19	such	such	ADJ
iajs-219	177	20	that	that	DET
iajs-219	177	21	∩	∩	NOUN
iajs-219	177	22	,	,	PUNCT
iajs-219	177	23	∀	∀	X
iajs-219	177	24	∈	∈	PROPN
iajs-219	177	25	.	.	PUNCT
iajs-219	178	1	now	now	ADV
iajs-219	178	2	,	,	PUNCT
iajs-219	178	3	since	since	SCONJ
iajs-219	178	4	is	be	AUX
iajs-219	178	5	a	a	DET
iajs-219	178	6	pure	pure	ADJ
iajs-219	178	7	submodule	submodule	NOUN
iajs-219	178	8	of	of	ADP
iajs-219	178	9	,	,	PUNCT
iajs-219	178	10	∀	∀	X
iajs-219	178	11	∈	∈	NOUN
iajs-219	178	12	,	,	PUNCT
iajs-219	178	13	then	then	ADV
iajs-219	178	14	⊕	⊕	PROPN
iajs-219	178	15	∈	∈	PROPN
iajs-219	178	16	is	be	AUX
iajs-219	178	17	a	a	DET
iajs-219	178	18	pure	pure	ADJ
iajs-219	178	19	submodule	submodule	NOUN
iajs-219	178	20	in	in	ADP
iajs-219	178	21	⊕	⊕	PROPN
iajs-219	178	22	∈	∈	PROPN
iajs-219	179	1	[	[	X
iajs-219	179	2	8].so	8].so	NUM
iajs-219	179	3	,	,	PUNCT
iajs-219	179	4	⊕	⊕	PROPN
iajs-219	179	5	∈	∈	PROPN
iajs-219	179	6	∩	∩	NOUN
iajs-219	179	7	⊕	⊕	PROPN
iajs-219	179	8	∈	∈	PROPN
iajs-219	180	1	[	[	X
iajs-219	180	2	9].thus	9].thus	NUM
iajs-219	180	3	,	,	PUNCT
iajs-219	180	4	is	be	AUX
iajs-219	180	5	purely	purely	ADV
iajs-219	180	6	-extending	-extende	VERB
iajs-219	180	7	module	module	NOUN
iajs-219	180	8	.	.	PUNCT
iajs-219	181	1	∎	∎	PROPN
iajs-219	181	2	corollary	corollary	ADJ
iajs-219	181	3	(	(	PUNCT
iajs-219	181	4	2.5	2.5	NUM
iajs-219	181	5	)	)	PUNCT
iajs-219	181	6	:	:	PUNCT
iajs-219	181	7	let	let	VERB
iajs-219	181	8	⨁	⨁	PROPN
iajs-219	181	9	be	be	AUX
iajs-219	181	10	a	a	DET
iajs-219	181	11	duo	duo	NOUN
iajs-219	181	12	module	module	NOUN
iajs-219	181	13	such	such	ADJ
iajs-219	181	14	that	that	PRON
iajs-219	181	15	and	and	CCONJ
iajs-219	181	16	are	be	AUX
iajs-219	181	17	purely	purely	ADV
iajs-219	181	18	-extending	-extende	VERB
iajs-219	181	19	modules	module	NOUN
iajs-219	181	20	.	.	PUNCT
iajs-219	182	1	then	then	ADV
iajs-219	182	2	is	be	AUX
iajs-219	182	3	a	a	DET
iajs-219	182	4	purely	purely	ADV
iajs-219	182	5	-extending	-extending	ADJ
iajs-219	182	6	.	.	PUNCT
iajs-219	183	1	∎	∎	VERB
iajs-219	183	2	by	by	ADP
iajs-219	183	3	the	the	DET
iajs-219	183	4	same	same	ADJ
iajs-219	183	5	argument	argument	NOUN
iajs-219	183	6	of	of	ADP
iajs-219	183	7	the	the	DET
iajs-219	183	8	proof	proof	ADJ
iajs-219	183	9	proposition	proposition	NOUN
iajs-219	183	10	(	(	PUNCT
iajs-219	183	11	2.4	2.4	NUM
iajs-219	183	12	)	)	PUNCT
iajs-219	183	13	,	,	PUNCT
iajs-219	183	14	one	one	PRON
iajs-219	183	15	can	can	AUX
iajs-219	183	16	get	get	VERB
iajs-219	183	17	the	the	DET
iajs-219	183	18	following	follow	VERB
iajs-219	183	19	result	result	NOUN
iajs-219	183	20	.	.	PUNCT
iajs-219	184	1	firstly	firstly	ADV
iajs-219	184	2	,	,	PUNCT
iajs-219	184	3	recall	recall	VERB
iajs-219	184	4	that	that	SCONJ
iajs-219	184	5	an	an	DET
iajs-219	184	6	rmodule	rmodule	NOUN
iajs-219	184	7	m	m	VERB
iajs-219	184	8	is	be	AUX
iajs-219	184	9	distributive	distributive	ADJ
iajs-219	184	10	if	if	SCONJ
iajs-219	184	11	for	for	ADP
iajs-219	184	12	all	all	DET
iajs-219	184	13	submodules	submodule	NOUN
iajs-219	184	14	k	k	NOUN
iajs-219	184	15	,	,	PUNCT
iajs-219	184	16	l	l	PROPN
iajs-219	184	17	and	and	CCONJ
iajs-219	184	18	n	n	PROPN
iajs-219	184	19	of	of	ADP
iajs-219	184	20	m	m	PROPN
iajs-219	184	21	,	,	PUNCT
iajs-219	184	22	k	k	PROPN
iajs-219	184	23	∩	∩	X
iajs-219	184	24	(	(	PUNCT
iajs-219	184	25	l	l	NOUN
iajs-219	184	26	+	+	NUM
iajs-219	184	27	n	n	CCONJ
iajs-219	184	28	)	)	PUNCT
iajs-219	184	29	=	=	SYM
iajs-219	184	30	(	(	PUNCT
iajs-219	184	31	k	k	X
iajs-219	184	32	∩	∩	X
iajs-219	184	33	l)+	l)+	X
iajs-219	184	34	(	(	PUNCT
iajs-219	184	35	k	k	PROPN
iajs-219	184	36	∩	∩	PROPN
iajs-219	184	37	n)[14	n)[14	PROPN
iajs-219	184	38	]	]	PUNCT
iajs-219	184	39	.	.	PUNCT
iajs-219	185	1	proposition	proposition	NOUN
iajs-219	185	2	(	(	PUNCT
iajs-219	185	3	2.6	2.6	NUM
iajs-219	185	4	)	)	PUNCT
iajs-219	185	5	let	let	VERB
iajs-219	185	6	⨁	⨁	PROPN
iajs-219	185	7	be	be	AUX
iajs-219	185	8	a	a	DET
iajs-219	185	9	distributive	distributive	ADJ
iajs-219	185	10	module	module	NOUN
iajs-219	185	11	such	such	ADJ
iajs-219	185	12	that	that	PRON
iajs-219	185	13	and	and	CCONJ
iajs-219	185	14	are	be	AUX
iajs-219	185	15	purely	purely	ADV
iajs-219	185	16	-extending	-extende	VERB
iajs-219	185	17	modules	module	NOUN
iajs-219	185	18	.	.	PUNCT
iajs-219	186	1	then	then	ADV
iajs-219	186	2	is	be	AUX
iajs-219	186	3	a	a	DET
iajs-219	186	4	purely	purely	ADV
iajs-219	186	5	-extending	-extending	ADJ
iajs-219	186	6	.	.	PUNCT
iajs-219	187	1	proof	proof	NOUN
iajs-219	187	2	:	:	PUNCT
iajs-219	187	3	let	let	VERB
iajs-219	187	4	is	be	AUX
iajs-219	187	5	a	a	DET
iajs-219	187	6	submodule	submodule	NOUN
iajs-219	187	7	of	of	ADP
iajs-219	187	8	⨁	⨁	PROPN
iajs-219	187	9	since	since	SCONJ
iajs-219	187	10	is	be	AUX
iajs-219	187	11	a	a	DET
iajs-219	187	12	distributive	distributive	ADJ
iajs-219	187	13	module	module	NOUN
iajs-219	187	14	so	so	SCONJ
iajs-219	187	15	a	a	DET
iajs-219	187	16	a⋂m	a⋂m	PROPN
iajs-219	187	17	a⋂	a⋂	NOUN
iajs-219	187	18	⨁	⨁	PROPN
iajs-219	187	19	a⋂	a⋂	NOUN
iajs-219	187	20	⨁	⨁	NUM
iajs-219	187	21	a⋂	a⋂	NOUN
iajs-219	187	22	.	.	PUNCT
iajs-219	188	1	but	but	CCONJ
iajs-219	188	2	and	and	CCONJ
iajs-219	188	3	are	be	AUX
iajs-219	188	4	purely	purely	ADV
iajs-219	188	5	extending	extend	VERB
iajs-219	188	6	,	,	PUNCT
iajs-219	188	7	then	then	ADV
iajs-219	188	8	there	there	PRON
iajs-219	188	9	are	be	VERB
iajs-219	188	10	a	a	DET
iajs-219	188	11	pure	pure	ADJ
iajs-219	188	12	submodule	submodule	NOUN
iajs-219	188	13	of	of	ADP
iajs-219	188	14	such	such	ADJ
iajs-219	188	15	that	that	SCONJ
iajs-219	188	16	a⋂	a⋂	NOUN
iajs-219	188	17	and	and	CCONJ
iajs-219	188	18	pure	pure	ADJ
iajs-219	188	19	submodule	submodule	NOUN
iajs-219	188	20	of	of	ADP
iajs-219	188	21	such	such	ADJ
iajs-219	188	22	that	that	DET
iajs-219	188	23	a⋂	a⋂	NOUN
iajs-219	188	24	.	.	PUNCT
iajs-219	189	1	so	so	ADV
iajs-219	189	2	,	,	PUNCT
iajs-219	189	3	a	a	DET
iajs-219	189	4	a⋂	a⋂	NOUN
iajs-219	189	5	⨁	⨁	PROPN
iajs-219	189	6	a⋂	a⋂	NOUN
iajs-219	189	7	⨁	⨁	PROPN
iajs-219	189	8	by	by	ADP
iajs-219	189	9	[	[	X
iajs-219	189	10	9	9	NUM
iajs-219	189	11	]	]	PUNCT
iajs-219	189	12	and	and	CCONJ
iajs-219	189	13	by	by	ADP
iajs-219	189	14	[	[	X
iajs-219	189	15	8	8	NUM
iajs-219	189	16	]	]	X
iajs-219	189	17	⨁	⨁	PROPN
iajs-219	189	18	is	be	AUX
iajs-219	189	19	a	a	DET
iajs-219	189	20	pure	pure	ADJ
iajs-219	189	21	submodule	submodule	NOUN
iajs-219	189	22	of	of	ADP
iajs-219	189	23	⨁	⨁	PROPN
iajs-219	189	24	.	.	PUNCT
iajs-219	190	1	thus	thus	ADV
iajs-219	190	2	,	,	PUNCT
iajs-219	190	3	is	be	AUX
iajs-219	190	4	a	a	DET
iajs-219	190	5	purely	purely	ADV
iajs-219	190	6	-extending	-extending	ADJ
iajs-219	190	7	.	.	PUNCT
iajs-219	191	1	∎	∎	NOUN
iajs-219	191	2	proposition	proposition	NOUN
iajs-219	191	3	(	(	PUNCT
iajs-219	191	4	2.7	2.7	NUM
iajs-219	191	5	):	):	PUNCT
iajs-219	191	6	let	let	VERB
iajs-219	191	7	and	and	CCONJ
iajs-219	191	8	be	be	AUX
iajs-219	191	9	purely	purely	ADV
iajs-219	191	10	-extending	-extende	VERB
iajs-219	191	11	-modules	-module	NOUN
iajs-219	191	12	such	such	ADJ
iajs-219	191	13	that	that	PRON
iajs-219	191	14	.	.	PUNCT
iajs-219	192	1	then	then	ADV
iajs-219	192	2	⊕	⊕	PROPN
iajs-219	192	3	is	be	AUX
iajs-219	192	4	a	a	DET
iajs-219	192	5	purely	purely	ADV
iajs-219	192	6	-extending	-extende	VERB
iajs-219	192	7	module	module	NOUN
iajs-219	192	8	.	.	PUNCT
iajs-219	193	1	proof	proof	NOUN
iajs-219	193	2	:	:	PUNCT
iajs-219	193	3	let	let	VERB
iajs-219	193	4	(	(	PUNCT
iajs-219	193	5	≠0	≠0	VERB
iajs-219	193	6	)	)	PUNCT
iajs-219	193	7	be	be	VERB
iajs-219	193	8	a	a	DET
iajs-219	193	9	submodule	submodule	NOUN
iajs-219	193	10	of	of	ADP
iajs-219	193	11	⊕	⊕	PROPN
iajs-219	193	12	.	.	PUNCT
iajs-219	194	1	since	since	SCONJ
iajs-219	194	2	,	,	PUNCT
iajs-219	194	3	then	then	ADV
iajs-219	194	4	⊕	⊕	PROPN
iajs-219	194	5	,	,	PUNCT
iajs-219	194	6	where	where	SCONJ
iajs-219	194	7	is	be	AUX
iajs-219	194	8	a	a	DET
iajs-219	194	9	submodule	submodule	NOUN
iajs-219	194	10	of	of	ADP
iajs-219	194	11	and	and	CCONJ
iajs-219	194	12	is	be	AUX
iajs-219	194	13	a	a	DET
iajs-219	194	14	submodule	submodule	NOUN
iajs-219	194	15	of	of	ADP
iajs-219	194	16	[	[	X
iajs-219	194	17	15	15	NUM
iajs-219	194	18	]	]	PUNCT
iajs-219	194	19	.	.	PUNCT
iajs-219	195	1	since	since	SCONJ
iajs-219	195	2	(	(	PUNCT
iajs-219	195	3	≠0	≠0	NOUN
iajs-219	195	4	)	)	PUNCT
iajs-219	195	5	then	then	ADV
iajs-219	195	6	(	(	PUNCT
iajs-219	195	7	≠0	≠0	NOUN
iajs-219	195	8	)	)	PUNCT
iajs-219	195	9	or	or	CCONJ
iajs-219	195	10	(	(	PUNCT
iajs-219	195	11	≠0).if	≠0).if	NOUN
iajs-219	195	12	≠0	≠0	NOUN
iajs-219	195	13	and	and	CCONJ
iajs-219	195	14	=	=	NOUN
iajs-219	195	15	0	0	NUM
iajs-219	195	16	,	,	PUNCT
iajs-219	195	17	then	then	ADV
iajs-219	195	18	=	=	PUNCT
iajs-219	195	19	is	be	AUX
iajs-219	195	20	a	a	DET
iajs-219	195	21	submodule	submodule	NOUN
iajs-219	195	22	of	of	ADP
iajs-219	195	23	.	.	PUNCT
iajs-219	196	1	but	but	CCONJ
iajs-219	196	2	m	m	PROPN
iajs-219	196	3	is	be	AUX
iajs-219	196	4	purely	purely	ADV
iajs-219	196	5	-extending	-extending	ADJ
iajs-219	196	6	and	and	CCONJ
iajs-219	196	7	hence	hence	ADV
iajs-219	196	8	there	there	PRON
iajs-219	196	9	is	be	VERB
iajs-219	196	10	a	a	DET
iajs-219	196	11	pure	pure	ADJ
iajs-219	196	12	submodule	submodule	NOUN
iajs-219	196	13	of	of	ADP
iajs-219	196	14	such	such	ADJ
iajs-219	196	15	that	that	PRON
iajs-219	196	16	.	.	PUNCT
iajs-219	197	1	since	since	SCONJ
iajs-219	197	2	is	be	AUX
iajs-219	197	3	a	a	DET
iajs-219	197	4	direct	direct	ADJ
iajs-219	197	5	summand	summand	NOUN
iajs-219	197	6	of	of	ADP
iajs-219	197	7	⊕	⊕	PROPN
iajs-219	197	8	,	,	PUNCT
iajs-219	197	9	then	then	ADV
iajs-219	197	10	is	be	AUX
iajs-219	197	11	a	a	DET
iajs-219	197	12	pure	pure	ADJ
iajs-219	197	13	submodule	submodule	NOUN
iajs-219	197	14	of	of	ADP
iajs-219	197	15	⊕	⊕	PROPN
iajs-219	197	16	,	,	PUNCT
iajs-219	197	17	(	(	PUNCT
iajs-219	197	18	by	by	ADP
iajs-219	197	19	[	[	X
iajs-219	197	20	16	16	NUM
iajs-219	197	21	]	]	PUNCT
iajs-219	197	22	)	)	PUNCT
iajs-219	197	23	,	,	PUNCT
iajs-219	197	24	then	then	ADV
iajs-219	197	25	pure	pure	ADJ
iajs-219	197	26	submodule	submodule	NOUN
iajs-219	197	27	of	of	ADP
iajs-219	197	28	⊕	⊕	PROPN
iajs-219	197	29	.thus	.thus	PROPN
iajs-219	197	30	⊕	⊕	PROPN
iajs-219	197	31	is	be	AUX
iajs-219	197	32	a	a	DET
iajs-219	197	33	purely	purely	ADV
iajs-219	197	34	-extending	-extende	VERB
iajs-219	197	35	module	module	NOUN
iajs-219	197	36	.	.	PUNCT
iajs-219	198	1	by	by	ADP
iajs-219	198	2	the	the	DET
iajs-219	198	3	similar	similar	ADJ
iajs-219	198	4	way	way	NOUN
iajs-219	198	5	if	if	SCONJ
iajs-219	198	6	=	=	NOUN
iajs-219	198	7	0	0	NUM
iajs-219	198	8	and	and	CCONJ
iajs-219	198	9	≠0	≠0	NOUN
iajs-219	198	10	,	,	PUNCT
iajs-219	198	11	then	then	ADV
iajs-219	198	12	⊕	⊕	PROPN
iajs-219	198	13	is	be	AUX
iajs-219	198	14	a	a	DET
iajs-219	198	15	purely	purely	ADV
iajs-219	198	16	-extending	-extende	VERB
iajs-219	198	17	module	module	NOUN
iajs-219	198	18	.	.	PUNCT
iajs-219	199	1	if	if	SCONJ
iajs-219	199	2	(	(	PUNCT
iajs-219	199	3	≠0	≠0	NOUN
iajs-219	199	4	)	)	PUNCT
iajs-219	199	5	and	and	CCONJ
iajs-219	199	6	(	(	PUNCT
iajs-219	199	7	≠0	≠0	NOUN
iajs-219	199	8	)	)	PUNCT
iajs-219	199	9	,	,	PUNCT
iajs-219	199	10	since	since	SCONJ
iajs-219	199	11	and	and	CCONJ
iajs-219	199	12	are	be	AUX
iajs-219	199	13	purely	purely	ADV
iajs-219	199	14	extending	extend	VERB
iajs-219	199	15	modules	module	NOUN
iajs-219	199	16	,	,	PUNCT
iajs-219	199	17	then	then	ADV
iajs-219	199	18	there	there	PRON
iajs-219	199	19	is	be	VERB
iajs-219	199	20	a	a	DET
iajs-219	199	21	pure	pure	ADJ
iajs-219	199	22	submodule	submodule	NOUN
iajs-219	199	23	of	of	ADP
iajs-219	199	24	such	such	ADJ
iajs-219	199	25	that	that	PRON
iajs-219	199	26	,	,	PUNCT
iajs-219	199	27	and	and	CCONJ
iajs-219	199	28	there	there	PRON
iajs-219	199	29	is	be	VERB
iajs-219	199	30	a	a	DET
iajs-219	199	31	pure	pure	ADJ
iajs-219	199	32	submodule	submodule	NOUN
iajs-219	199	33	of	of	ADP
iajs-219	199	34	such	such	ADJ
iajs-219	199	35	that	that	PRON
iajs-219	199	36	.	.	PUNCT
iajs-219	200	1	but	but	CCONJ
iajs-219	200	2	⊕	⊕	PROPN
iajs-219	200	3	is	be	AUX
iajs-219	200	4	a	a	DET
iajs-219	200	5	pure	pure	ADJ
iajs-219	200	6	submodule	submodule	NOUN
iajs-219	200	7	of	of	ADP
iajs-219	200	8	⊕	⊕	PROPN
iajs-219	200	9	[	[	X
iajs-219	200	10	8	8	NUM
iajs-219	200	11	]	]	PUNCT
iajs-219	200	12	and	and	CCONJ
iajs-219	200	13	by	by	ADP
iajs-219	200	14	[	[	PUNCT
iajs-219	200	15	9	9	NUM
iajs-219	200	16	]	]	PUNCT
iajs-219	200	17	,	,	PUNCT
iajs-219	200	18	(	(	PUNCT
iajs-219	200	19	⊕	⊕	PROPN
iajs-219	200	20	⊕	⊕	PROPN
iajs-219	200	21	.	.	PUNCT
iajs-219	201	1	therefore	therefore	ADV
iajs-219	201	2	,	,	PUNCT
iajs-219	201	3	⊕	⊕	PROPN
iajs-219	201	4	is	be	AUX
iajs-219	201	5	a	a	DET
iajs-219	201	6	purely	purely	ADV
iajs-219	201	7	-extending	-extende	VERB
iajs-219	201	8	module	module	NOUN
iajs-219	201	9	.	.	PUNCT
iajs-219	202	1	∎	∎	PROPN
iajs-219	202	2	153	153	NUM
iajs-219	202	3	|	|	NOUN
iajs-219	202	4	mathematics	mathematic	NOUN
iajs-219	202	5	٢٠١٥	٢٠١٥	NUM
iajs-219	202	6	)	)	PUNCT
iajs-219	202	7	عام	عام	ADP
iajs-219	202	8	٢العدد	٢العدد	PROPN
iajs-219	202	9	(	(	PUNCT
iajs-219	202	10	٢٨المجلد	٢٨المجلد	NUM
iajs-219	202	11	والتطبيقية	والتطبيقية	PROPN
iajs-219	202	12	الھيثم	الھيثم	NOUN
iajs-219	202	13	للعلوم	للعلوم	PROPN
iajs-219	202	14	الصرفة	الصرفة	NOUN
iajs-219	202	15	ابنمجلة	ابنمجلة	VERB
iajs-219	202	16	ibn	ibn	PROPN
iajs-219	202	17	al	al	PROPN
iajs-219	202	18	-	-	PUNCT
iajs-219	202	19	haitham	haitham	PROPN
iajs-219	202	20	.	.	PUNCT
iajs-219	203	1	j.	j.	PROPN
iajs-219	203	2	for	for	ADP
iajs-219	203	3	pure	pure	PROPN
iajs-219	203	4	&	&	CCONJ
iajs-219	203	5	appl	appl	PROPN
iajs-219	203	6	.	.	PUNCT
iajs-219	204	1	sci	sci	PROPN
iajs-219	204	2	.	.	PUNCT
iajs-219	204	3	vol	vol	NOUN
iajs-219	204	4	.	.	PROPN
iajs-219	205	1	28	28	NUM
iajs-219	205	2	(	(	PUNCT
iajs-219	205	3	٢	٢	NOUN
iajs-219	205	4	)	)	PUNCT
iajs-219	205	5	2015	2015	NUM
iajs-219	205	6	references	reference	NOUN
iajs-219	205	7	1	1	NUM
iajs-219	205	8	.	.	PUNCT
iajs-219	205	9	dung	dung	NOUN
iajs-219	205	10	,	,	PUNCT
iajs-219	205	11	n.v	n.v	PROPN
iajs-219	205	12	.	.	PROPN
iajs-219	205	13	;	;	PUNCT
iajs-219	205	14	huynh	huynh	PROPN
iajs-219	205	15	,	,	PUNCT
iajs-219	205	16	d.v	d.v	PROPN
iajs-219	205	17	.	.	PROPN
iajs-219	205	18	;	;	PUNCT
iajs-219	205	19	smith	smith	PROPN
iajs-219	205	20	,	,	PUNCT
iajs-219	205	21	p.f	p.f	PROPN
iajs-219	205	22	.	.	PROPN
iajs-219	205	23	and	and	CCONJ
iajs-219	205	24	wisbauer	wisbauer	PROPN
iajs-219	205	25	r.	r.	PROPN
iajs-219	205	26	:	:	PUNCT
iajs-219	205	27	(	(	PUNCT
iajs-219	205	28	1994	1994	NUM
iajs-219	205	29	)	)	PUNCT
iajs-219	205	30	,	,	PUNCT
iajs-219	205	31	extending	extend	VERB
iajs-219	205	32	modules	module	NOUN
iajs-219	205	33	,	,	PUNCT
iajs-219	205	34	john	john	PROPN
iajs-219	205	35	wiley	wiley	PROPN
iajs-219	205	36	and	and	CCONJ
iajs-219	205	37	sons	son	NOUN
iajs-219	205	38	,	,	PUNCT
iajs-219	205	39	inc	inc	PROPN
iajs-219	205	40	.	.	PROPN
iajs-219	205	41	new	new	PROPN
iajs-219	205	42	york	york	PROPN
iajs-219	205	43	.	.	PUNCT
iajs-219	206	1	2	2	X
iajs-219	206	2	.	.	X
iajs-219	206	3	fuchs	fuchs	PROPN
iajs-219	206	4	,	,	PUNCT
iajs-219	206	5	l.	l.	PROPN
iajs-219	206	6	:	:	PUNCT
iajs-219	206	7	(	(	PUNCT
iajs-219	206	8	1995	1995	NUM
iajs-219	206	9	)	)	PUNCT
iajs-219	206	10	,	,	PUNCT
iajs-219	206	11	notes	note	NOUN
iajs-219	206	12	on	on	ADP
iajs-219	206	13	generalized	generalized	ADJ
iajs-219	206	14	continuous	continuous	ADJ
iajs-219	206	15	modules	module	NOUN
iajs-219	206	16	,	,	PUNCT
iajs-219	206	17	preprint	preprint	NOUN
iajs-219	206	18	.	.	PUNCT
iajs-219	207	1	3	3	X
iajs-219	207	2	.	.	X
iajs-219	207	3	clark	clark	PROPN
iajs-219	207	4	,	,	PUNCT
iajs-219	207	5	j.	j.	PROPN
iajs-219	207	6	:	:	PUNCT
iajs-219	207	7	(	(	PUNCT
iajs-219	207	8	1999	1999	NUM
iajs-219	207	9	)	)	PUNCT
iajs-219	207	10	,	,	PUNCT
iajs-219	207	11	on	on	ADP
iajs-219	207	12	purely	purely	ADV
iajs-219	207	13	extending	extend	VERB
iajs-219	207	14	modules	module	NOUN
iajs-219	207	15	,	,	PUNCT
iajs-219	207	16	in	in	ADP
iajs-219	207	17	abelian	abelian	ADJ
iajs-219	207	18	groups	group	NOUN
iajs-219	207	19	an	an	DET
iajs-219	207	20	modules	module	NOUN
iajs-219	207	21	.	.	PUNCT
iajs-219	208	1	proceedings	proceeding	NOUN
iajs-219	208	2	of	of	ADP
iajs-219	208	3	the	the	DET
iajs-219	208	4	international	international	ADJ
iajs-219	208	5	conference	conference	NOUN
iajs-219	208	6	in	in	ADP
iajs-219	208	7	dublin	dublin	PROPN
iajs-219	208	8	,	,	PUNCT
iajs-219	208	9	ireland	ireland	PROPN
iajs-219	208	10	,	,	PUNCT
iajs-219	208	11	august	august	PROPN
iajs-219	208	12	10	10	NUM
iajs-219	208	13	-	-	SYM
iajs-219	208	14	14	14	NUM
iajs-219	208	15	,	,	PUNCT
iajs-219	208	16	1998	1998	NUM
iajs-219	208	17	(	(	PUNCT
iajs-219	208	18	ed	ed	NOUN
iajs-219	208	19	.	.	PUNCT
iajs-219	209	1	by	by	ADP
iajs-219	209	2	eklof	eklof	PROPN
iajs-219	209	3	,	,	PUNCT
iajs-219	209	4	paul	paul	PROPN
iajs-219	209	5	c	c	PROPN
iajs-219	209	6	,	,	PUNCT
iajs-219	209	7	etal	etal	NOUN
iajs-219	209	8	.	.	PUNCT
iajs-219	209	9	)	)	PUNCT
iajs-219	209	10	,	,	PUNCT
iajs-219	209	11	basel	basel	PROPN
iajs-219	209	12	,	,	PUNCT
iajs-219	209	13	birkhasure	birkhasure	NOUN
iajs-219	209	14	,	,	PUNCT
iajs-219	209	15	trends	trend	NOUN
iajs-219	209	16	in	in	ADP
iajs-219	209	17	mathematics	mathematic	NOUN
iajs-219	209	18	,	,	PUNCT
iajs-219	209	19	353	353	NUM
iajs-219	209	20	-	-	SYM
iajs-219	209	21	358	358	NUM
iajs-219	209	22	.	.	PUNCT
iajs-219	210	1	4	4	X
iajs-219	210	2	.	.	X
iajs-219	210	3	akalan	akalan	PROPN
iajs-219	210	4	,	,	PUNCT
iajs-219	210	5	e.	e.	PROPN
iajs-219	210	6	,	,	PUNCT
iajs-219	210	7	birkenmeier	birkenmeier	PROPN
iajs-219	210	8	g.	g.	PROPN
iajs-219	210	9	f.	f.	PROPN
iajs-219	210	10	and	and	CCONJ
iajs-219	210	11	tercan	tercan	PROPN
iajs-219	210	12	a.	a.	NOUN
iajs-219	210	13	,	,	PUNCT
iajs-219	210	14	(	(	PUNCT
iajs-219	210	15	2009	2009	NUM
iajs-219	210	16	)	)	PUNCT
iajs-219	210	17	,	,	PUNCT
iajs-219	210	18	goldie	goldie	PROPN
iajs-219	210	19	extending	extend	VERB
iajs-219	210	20	modules	module	NOUN
iajs-219	210	21	,	,	PUNCT
iajs-219	210	22	comm	comm	NOUN
iajs-219	210	23	.	.	PUNCT
iajs-219	211	1	algebra	algebra	NOUN
iajs-219	211	2	37	37	NUM
iajs-219	211	3	:	:	SYM
iajs-219	211	4	2	2	NUM
iajs-219	211	5	,	,	PUNCT
iajs-219	211	6	663	663	NUM
iajs-219	211	7	-	-	SYM
iajs-219	211	8	683	683	NUM
iajs-219	211	9	.	.	PUNCT
iajs-219	212	1	5	5	NUM
iajs-219	212	2	.	.	X
iajs-219	212	3	alzubaidey	alzubaidey	PROPN
iajs-219	212	4	,	,	PUNCT
iajs-219	212	5	z.	z.	PROPN
iajs-219	212	6	t.	t.	PROPN
iajs-219	212	7	:	:	PUNCT
iajs-219	212	8	(	(	PUNCT
iajs-219	212	9	2005	2005	NUM
iajs-219	212	10	)	)	PUNCT
iajs-219	212	11	,	,	PUNCT
iajs-219	212	12	on	on	ADP
iajs-219	212	13	purely	purely	ADV
iajs-219	212	14	extending	extend	VERB
iajs-219	212	15	modules	module	NOUN
iajs-219	212	16	,	,	PUNCT
iajs-219	212	17	msc	msc	PROPN
iajs-219	212	18	.	.	PROPN
iajs-219	213	1	thesis	thesis	PROPN
iajs-219	213	2	,	,	PUNCT
iajs-219	213	3	univ	univ	PROPN
iajs-219	213	4	.	.	PROPN
iajs-219	213	5	of	of	ADP
iajs-219	213	6	baghdad	baghdad	PROPN
iajs-219	213	7	.	.	PUNCT
iajs-219	214	1	6	6	NUM
iajs-219	214	2	.	.	X
iajs-219	214	3	azumaya	azumaya	PROPN
iajs-219	214	4	,	,	PUNCT
iajs-219	214	5	g.	g.	PROPN
iajs-219	214	6	and	and	CCONJ
iajs-219	214	7	faccini	faccini	PROPN
iajs-219	214	8	a.	a.	NOUN
iajs-219	214	9	:	:	PUNCT
iajs-219	214	10	(	(	PUNCT
iajs-219	214	11	1989	1989	NUM
iajs-219	214	12	)	)	PUNCT
iajs-219	214	13	,	,	PUNCT
iajs-219	214	14	rings	ring	NOUN
iajs-219	214	15	of	of	ADP
iajs-219	214	16	pure	pure	ADJ
iajs-219	214	17	global	global	ADJ
iajs-219	214	18	dimension	dimension	NOUN
iajs-219	214	19	zero	zero	NUM
iajs-219	214	20	and	and	CCONJ
iajs-219	214	21	mittagleffler	mittagleffler	NOUN
iajs-219	214	22	modules	module	NOUN
iajs-219	214	23	,	,	PUNCT
iajs-219	214	24	j.pure	j.pure	NOUN
iajs-219	214	25	appl	appl	NOUN
iajs-219	214	26	.	.	PUNCT
iajs-219	215	1	algbra	algbra	PROPN
iajs-219	215	2	,	,	PUNCT
iajs-219	215	3	62	62	NUM
iajs-219	215	4	,	,	PUNCT
iajs-219	215	5	109	109	NUM
iajs-219	215	6	-	-	SYM
iajs-219	215	7	122	122	NUM
iajs-219	215	8	.	.	PUNCT
iajs-219	216	1	7	7	X
iajs-219	216	2	.	.	X
iajs-219	216	3	fieldhouse	fieldhouse	PROPN
iajs-219	216	4	,	,	PUNCT
iajs-219	216	5	d.j	d.j	PROPN
iajs-219	216	6	.	.	PROPN
iajs-219	216	7	:	:	PUNCT
iajs-219	216	8	(	(	PUNCT
iajs-219	216	9	1969	1969	NUM
iajs-219	216	10	)	)	PUNCT
iajs-219	216	11	,	,	PUNCT
iajs-219	216	12	pure	pure	ADJ
iajs-219	216	13	theories	theory	NOUN
iajs-219	216	14	,	,	PUNCT
iajs-219	216	15	math	math	NOUN
iajs-219	216	16	.	.	PUNCT
iajs-219	217	1	ann	ann	PROPN
iajs-219	217	2	.	.	PROPN
iajs-219	218	1	184	184	NUM
iajs-219	218	2	,	,	PUNCT
iajs-219	218	3	1	1	NUM
iajs-219	218	4	-	-	SYM
iajs-219	218	5	18	18	NUM
iajs-219	218	6	.	.	NOUN
iajs-219	218	7	8	8	NUM
iajs-219	218	8	.	.	PUNCT
iajs-219	218	9	albahraany	albahraany	PROPN
iajs-219	218	10	b.h	b.h	PROPN
iajs-219	218	11	.	.	PUNCT
iajs-219	218	12	:	:	PUNCT
iajs-219	219	1	(	(	PUNCT
iajs-219	219	2	2000	2000	NUM
iajs-219	219	3	)	)	PUNCT
iajs-219	219	4	,	,	PUNCT
iajs-219	219	5	modules	module	NOUN
iajs-219	219	6	with	with	ADP
iajs-219	219	7	pure	pure	ADJ
iajs-219	219	8	intersection	intersection	NOUN
iajs-219	219	9	property	property	NOUN
iajs-219	219	10	,	,	PUNCT
iajs-219	219	11	ph.d	ph.d	PROPN
iajs-219	219	12	.	.	PUNCT
iajs-219	220	1	thesis	thesis	PROPN
iajs-219	220	2	,	,	PUNCT
iajs-219	220	3	univ	univ	PROPN
iajs-219	220	4	.	.	PROPN
iajs-219	220	5	of	of	ADP
iajs-219	220	6	baghdad	baghdad	PROPN
iajs-219	220	7	.	.	PUNCT
iajs-219	221	1	9	9	X
iajs-219	221	2	.	.	X
iajs-219	221	3	enas	ena	NOUN
iajs-219	221	4	,	,	PUNCT
iajs-219	221	5	m.	m.	NOUN
iajs-219	221	6	kamil	kamil	PROPN
iajs-219	221	7	:	:	PUNCT
iajs-219	221	8	(	(	PUNCT
iajs-219	221	9	2014	2014	NUM
iajs-219	221	10	)	)	PUNCT
iajs-219	221	11	,	,	PUNCT
iajs-219	221	12	goldie	goldie	PROPN
iajs-219	221	13	extending	extending	PROPN
iajs-219	221	14	(	(	PUNCT
iajs-219	221	15	lifting	lifting	NOUN
iajs-219	221	16	)	)	PUNCT
iajs-219	221	17	modules	module	NOUN
iajs-219	221	18	,	,	PUNCT
iajs-219	221	19	msc	msc	PROPN
iajs-219	221	20	.	.	PROPN
iajs-219	222	1	thesis	thesis	PROPN
iajs-219	222	2	,	,	PUNCT
iajs-219	222	3	univ	univ	PROPN
iajs-219	222	4	.	.	PROPN
iajs-219	222	5	of	of	ADP
iajs-219	222	6	baghdad	baghdad	PROPN
iajs-219	222	7	.	.	PUNCT
iajs-219	223	1	10	10	NUM
iajs-219	223	2	.	.	PUNCT
iajs-219	223	3	barnad	barnad	NOUN
iajs-219	223	4	,	,	PUNCT
iajs-219	223	5	a.	a.	NOUN
iajs-219	223	6	:	:	PUNCT
iajs-219	223	7	(	(	PUNCT
iajs-219	223	8	1981	1981	NUM
iajs-219	223	9	)	)	PUNCT
iajs-219	223	10	,	,	PUNCT
iajs-219	223	11	multiplication	multiplication	NOUN
iajs-219	223	12	modules	module	NOUN
iajs-219	223	13	,	,	PUNCT
iajs-219	223	14	j.	j.	PROPN
iajs-219	223	15	algebra	algebra	PROPN
iajs-219	223	16	71	71	NUM
iajs-219	223	17	,	,	PUNCT
iajs-219	223	18	174178	174178	NUM
iajs-219	223	19	.	.	PUNCT
iajs-219	224	1	11	11	NUM
iajs-219	224	2	.	.	X
iajs-219	225	1	anderson	anderson	PROPN
iajs-219	225	2	,	,	PUNCT
iajs-219	225	3	f.w	f.w	PROPN
iajs-219	225	4	.	.	PROPN
iajs-219	225	5	and	and	CCONJ
iajs-219	225	6	fuller	full	ADJ
iajs-219	225	7	k.r	k.r	PROPN
iajs-219	225	8	.	.	PROPN
iajs-219	225	9	:	:	PUNCT
iajs-219	225	10	rings	ring	NOUN
iajs-219	225	11	and	and	CCONJ
iajs-219	225	12	categories	category	NOUN
iajs-219	225	13	of	of	ADP
iajs-219	225	14	modules	module	NOUN
iajs-219	225	15	,	,	PUNCT
iajs-219	225	16	springer	springer	NOUN
iajs-219	225	17	-	-	PUNCT
iajs-219	225	18	verlag	verlag	PROPN
iajs-219	225	19	.	.	PUNCT
iajs-219	226	1	new	new	PROPN
iajs-219	226	2	york	york	PROPN
iajs-219	226	3	1973	1973	NUM
iajs-219	226	4	.	.	PUNCT
iajs-219	227	1	12	12	NUM
iajs-219	227	2	.	.	PUNCT
iajs-219	227	3	wisbauer	wisbauer	NOUN
iajs-219	227	4	,	,	PUNCT
iajs-219	227	5	r.	r.	PROPN
iajs-219	227	6	:	:	PUNCT
iajs-219	227	7	(	(	PUNCT
iajs-219	227	8	1991	1991	NUM
iajs-219	227	9	)	)	PUNCT
iajs-219	227	10	,	,	PUNCT
iajs-219	227	11	foundations	foundation	NOUN
iajs-219	227	12	of	of	ADP
iajs-219	227	13	module	module	NOUN
iajs-219	227	14	and	and	CCONJ
iajs-219	227	15	ring	ring	NOUN
iajs-219	227	16	theory	theory	NOUN
iajs-219	227	17	,	,	PUNCT
iajs-219	227	18	reading	read	VERB
iajs-219	227	19	:	:	PUNCT
iajs-219	227	20	gordon	gordon	PROPN
iajs-219	227	21	and	and	CCONJ
iajs-219	227	22	breach	breach	VERB
iajs-219	227	23	science	science	NOUN
iajs-219	227	24	publishers	publisher	NOUN
iajs-219	227	25	.	.	PUNCT
iajs-219	228	1	13	13	NUM
iajs-219	228	2	.	.	X
iajs-219	229	1	lam	lam	PROPN
iajs-219	229	2	,	,	PUNCT
iajs-219	229	3	t.y	t.y	PROPN
iajs-219	229	4	.	.	PROPN
iajs-219	229	5	:	:	PUNCT
iajs-219	229	6	(	(	PUNCT
iajs-219	229	7	1988	1988	NUM
iajs-219	229	8	)	)	PUNCT
iajs-219	229	9	,	,	PUNCT
iajs-219	229	10	lectures	lecture	VERB
iajs-219	229	11	on	on	ADP
iajs-219	229	12	modules	module	NOUN
iajs-219	229	13	and	and	CCONJ
iajs-219	229	14	rings	ring	NOUN
iajs-219	229	15	,	,	PUNCT
iajs-219	229	16	springer	springer	NOUN
iajs-219	229	17	-	-	PUNCT
iajs-219	229	18	verlag	verlag	PROPN
iajs-219	229	19	,	,	PUNCT
iajs-219	229	20	berin	berin	NOUN
iajs-219	229	21	,	,	PUNCT
iajs-219	229	22	heidelberg	heidelberg	PROPN
iajs-219	229	23	.	.	PUNCT
iajs-219	230	1	new	new	PROPN
iajs-219	230	2	york	york	PROPN
iajs-219	230	3	.	.	PUNCT
iajs-219	231	1	14	14	NUM
iajs-219	231	2	.	.	PUNCT
iajs-219	231	3	erdogdu	erdogdu	PROPN
iajs-219	231	4	,	,	PUNCT
iajs-219	231	5	v.	v.	CCONJ
iajs-219	231	6	:	:	PUNCT
iajs-219	231	7	(	(	PUNCT
iajs-219	231	8	1987	1987	NUM
iajs-219	231	9	)	)	PUNCT
iajs-219	231	10	,	,	PUNCT
iajs-219	231	11	distributive	distributive	ADJ
iajs-219	231	12	modules	module	NOUN
iajs-219	231	13	,	,	PUNCT
iajs-219	231	14	can	can	AUX
iajs-219	231	15	.	.	PUNCT
iajs-219	232	1	math	math	NOUN
iajs-219	232	2	.	.	PUNCT
iajs-219	233	1	bull	bull	PROPN
iajs-219	233	2	30	30	NUM
iajs-219	233	3	,	,	PUNCT
iajs-219	233	4	248	248	NUM
iajs-219	233	5	-	-	SYM
iajs-219	233	6	254	254	NUM
iajs-219	233	7	.	.	PUNCT
iajs-219	233	8	15	15	NUM
iajs-219	233	9	.	.	PUNCT
iajs-219	233	10	abbas	abbas	PROPN
iajs-219	233	11	,	,	PUNCT
iajs-219	233	12	m.	m.	NOUN
iajs-219	233	13	s.	s.	PROPN
iajs-219	233	14	:	:	PUNCT
iajs-219	233	15	(	(	PUNCT
iajs-219	233	16	1991	1991	NUM
iajs-219	233	17	)	)	PUNCT
iajs-219	233	18	,	,	PUNCT
iajs-219	233	19	on	on	ADP
iajs-219	233	20	fully	fully	ADV
iajs-219	233	21	stable	stable	ADJ
iajs-219	233	22	modules	module	NOUN
iajs-219	233	23	,	,	PUNCT
iajs-219	233	24	ph.d	ph.d	PROPN
iajs-219	233	25	.	.	PUNCT
iajs-219	234	1	thesis	thesis	PROPN
iajs-219	234	2	,	,	PUNCT
iajs-219	234	3	univ	univ	PROPN
iajs-219	234	4	.	.	PROPN
iajs-219	234	5	of	of	ADP
iajs-219	234	6	baghdad	baghdad	PROPN
iajs-219	234	7	.	.	PUNCT
iajs-219	235	1	16.yaseen	16.yaseen	NUM
iajs-219	235	2	,	,	PUNCT
iajs-219	235	3	s.h	s.h	PROPN
iajs-219	235	4	.	.	PROPN
iajs-219	235	5	:	:	PUNCT
iajs-219	235	6	(	(	PUNCT
iajs-219	235	7	1993	1993	NUM
iajs-219	235	8	)	)	PUNCT
iajs-219	235	9	,	,	PUNCT
iajs-219	235	10	f	f	X
iajs-219	235	11	-	-	PUNCT
iajs-219	235	12	regular	regular	ADJ
iajs-219	235	13	modules	module	NOUN
iajs-219	235	14	,	,	PUNCT
iajs-219	235	15	m.sc	m.sc	PROPN
iajs-219	235	16	.	.	PUNCT
iajs-219	236	1	thesis	thesis	NOUN
iajs-219	236	2	,	,	PUNCT
iajs-219	236	3	university	university	NOUN
iajs-219	236	4	of	of	ADP
iajs-219	236	5	baghdad	baghdad	PROPN
iajs-219	236	6	.	.	PUNCT
iajs-219	237	1	154	154	NUM
iajs-219	237	2	|	|	NOUN
iajs-219	237	3	mathematics	mathematic	NOUN
iajs-219	237	4	٢٠١٥	٢٠١٥	NUM
iajs-219	237	5	)	)	PUNCT
iajs-219	237	6	عام	عام	ADP
iajs-219	237	7	٢العدد	٢العدد	PROPN
iajs-219	237	8	(	(	PUNCT
iajs-219	237	9	٢٨المجلد	٢٨المجلد	NUM
iajs-219	237	10	والتطبيقية	والتطبيقية	PROPN
iajs-219	237	11	الھيثم	الھيثم	NOUN
iajs-219	237	12	للعلوم	للعلوم	PROPN
iajs-219	237	13	الصرفة	الصرفة	NOUN
iajs-219	237	14	ابنمجلة	ابنمجلة	VERB
iajs-219	237	15	ibn	ibn	PROPN
iajs-219	237	16	al	al	PROPN
iajs-219	237	17	-	-	PUNCT
iajs-219	237	18	haitham	haitham	PROPN
iajs-219	237	19	.	.	PUNCT
iajs-219	238	1	j.	j.	PROPN
iajs-219	238	2	for	for	ADP
iajs-219	238	3	pure	pure	PROPN
iajs-219	238	4	&	&	CCONJ
iajs-219	238	5	appl	appl	PROPN
iajs-219	238	6	.	.	PUNCT
iajs-219	239	1	sci	sci	PROPN
iajs-219	239	2	.	.	PUNCT
iajs-219	239	3	vol	vol	NOUN
iajs-219	239	4	.	.	PROPN
iajs-219	240	1	28	28	NUM
iajs-219	240	2	(	(	PUNCT
iajs-219	240	3	٢	٢	NOUN
iajs-219	240	4	)	)	PUNCT
iajs-219	240	5	2015	2015	NUM
iajs-219	240	6	-مقاسات	-مقاسات	NOUN
iajs-219	240	7	التوسع	التوسع	VERB
iajs-219	240	8	النقية	النقية	NOUN
iajs-219	240	9	من	من	PRON
iajs-219	240	10	النمط	النمط	NOUN
iajs-219	240	11	سعد	سعد	NOUN
iajs-219	240	12	عبد	عبد	PROPN
iajs-219	240	13	الكاظم	الكاظم	PROPN
iajs-219	240	14	الساعدي	الساعدي	PROPN
iajs-219	240	15	قبال	قبال	PROPN
iajs-219	240	16	احمد	احمد	PROPN
iajs-219	240	17	عمرإ	عمرإ	PROPN
iajs-219	240	18	المستنصرية	المستنصرية	NOUN
iajs-219	240	19	العلوم	العلوم	PROPN
iajs-219	240	20	/	/	SYM
iajs-219	240	21	الجامعةقسم	الجامعةقسم	VERB
iajs-219	240	22	الرياضيات/	الرياضيات/	NUM
iajs-219	240	23	كلية	كلية	NOUN
iajs-219	240	24	٢٠١٥نيسان	٢٠١٥نيسان	NOUN
iajs-219	240	25	١٣في	١٣في	NOUN
iajs-219	240	26	:	:	PUNCT
iajs-219	240	27	البحث	البحث	PROPN
iajs-219	240	28	قبل	قبل	PROPN
iajs-219	240	29	،	،	PROPN
iajs-219	240	30	٢٠١٥أذار	٢٠١٥أذار	PROPN
iajs-219	240	31	٤	٤	PROPN
iajs-219	241	1	:	:	PUNCT
iajs-219	241	2	في	في	ADP
iajs-219	241	3	البحث	البحث	PROPN
iajs-219	241	4	استلم	استلم	PROPN
iajs-219	241	5	الخالصة	الخالصة	PROPN
iajs-219	241	6	يكون	يكون	PROPN
iajs-219	241	7	mبأنه	mبأنه	PROPN
iajs-219	241	8	توسع	توسع	PROPN
iajs-219	241	9	إذا	إذا	VERB
iajs-219	241	10	كان	كان	PROPN
iajs-219	241	11	كل	كل	PROPN
iajs-219	241	12	مقاس	مقاس	PROPN
iajs-219	241	13	جزئي	جزئي	NOUN
iajs-219	241	14	من	من	PRON
iajs-219	241	15	mيقال	mيقال	PROPN
iajs-219	241	16	للمقاس	للمقاس	ADJ
iajs-219	241	17	r.مقاسا	r.مقاسا	NOUN
iajs-219	241	18	ً	ً	NOUN
iajs-219	241	19	معرفا	معرفا	PROPN
iajs-219	241	20	ًعلى	ًعلى	VERB
iajs-219	241	21	mحلقة	mحلقة	NOUN
iajs-219	242	1	و	و	PRON
iajs-219	242	2	rلتكن	rلتكن	NOUN
iajs-219	242	3	يكون	يكون	PROPN
iajs-219	242	4	mبأنه	mبأنه	PROPN
iajs-219	242	5	توسع	توسع	PROPN
iajs-219	242	6	نقي	نقي	NOUN
iajs-219	242	7	إذا	إذا	NUM
iajs-219	242	8	كان	كان	PROPN
iajs-219	242	9	كل	كل	PROPN
iajs-219	242	10	مقاس	مقاس	PROPN
iajs-219	242	11	جزئي	جزئي	NOUN
iajs-219	242	12	من	من	PRON
iajs-219	242	13	m.	m.	NOUN
iajs-219	242	14	تبعاً	تبعاً	PROPN
iajs-219	242	15	كالرك	كالرك	PROPN
iajs-219	242	16	،	،	PROPN
iajs-219	242	17	يقال	يقال	PROPN
iajs-219	242	18	للمقاس	للمقاس	PROPN
iajs-219	242	19	mجوھريا	mجوھريا	NOUN
iajs-219	242	20	ً	ً	NOUN
iajs-219	242	21	من	من	PRON
iajs-219	242	22	مركبة	مركبة	PROPN
iajs-219	242	23	جمع	جمع	NOUN
iajs-219	242	24	مباشرمن	مباشرمن	NOUN
iajs-219	242	25	.	.	PUNCT
iajs-219	243	1	-	-	INTJ
iajs-219	243	2	.	.	PUNCT
iajs-219	244	1	من	من	NUM
iajs-219	244	2	جھة	جھة	PROPN
iajs-219	244	3	اخرى	اخرى	PROPN
iajs-219	244	4	،	،	PROPN
iajs-219	244	5	بركانمير	بركانمير	PROPN
iajs-219	244	6	و	و	PRON
iajs-219	244	7	تيركان	تيركان	VERB
iajs-219	244	8	عرضا	عرضا	PROPN
iajs-219	244	9	مفھوم	مفھوم	PROPN
iajs-219	244	10	مقاسات	مقاسات	PROPN
iajs-219	244	11	التوسع	التوسع	VERB
iajs-219	244	12	من	من	PRON
iajs-219	244	13	النمطmجوھريا	النمطmجوھريا	PROPN
iajs-219	244	14	ً	ً	PROPN
iajs-219	244	15	من	من	NOUN
iajs-219	244	16	مقاس	مقاس	PROPN
iajs-219	244	17	جزئي	جزئي	NOUN
iajs-219	244	18	نقي	نقي	NOUN
iajs-219	244	19	من	من	PROPN
iajs-219	244	20	بحيث	بحيث	PROPN
iajs-219	244	21	mمن	mمن	PROPN
iajs-219	244	22	dيوجد	dيوجد	PROPN
iajs-219	244	23	مركبة	مركبة	PROPN
iajs-219	244	24	جمع	جمع	NOUN
iajs-219	244	25	مباشر	مباشر	PROPN
iajs-219	244	26	mمن	mمن	VERB
iajs-219	244	27	xأذا	xأذا	PROPN
iajs-219	244	28	كان	كان	PROPN
iajs-219	244	29	لكل	لكل	PROPN
iajs-219	244	30	مقاس	مقاس	PROPN
iajs-219	244	31	جزئي	جزئي	NOUN
iajs-219	244	32	بأنه	بأنه	PROPN
iajs-219	244	33	توسع	توسع	PROPN
iajs-219	244	34	من	من	PRON
iajs-219	244	35	النمط	النمط	PROPN
iajs-219	244	36	mيقال	mيقال	PROPN
iajs-219	244	37	للمقاس	للمقاس	PROPN
iajs-219	244	38	.	.	PUNCT
iajs-219	245	1	في	في	PRON
iajs-219	245	2	ھذا	ھذا	NOUN
iajs-219	245	3	البحث	البحث	PROPN
iajs-219	245	4	،	،	PROPN
iajs-219	245	5	تم	تم	PUNCT
iajs-219	246	1	عرض	عرض	PROPN
iajs-219	247	1	و	و	PRON
iajs-219	247	2	دراسة	دراسة	PROPN
iajs-219	247	3	صنف	صنف	VERB
iajs-219	247	4	من	من	DET
iajs-219	247	5	المقاسات	المقاسات	PROPN
iajs-219	247	6	كتعميم	كتعميم	VERB
iajs-219	247	7	فعلي	فعلي	NOUN
iajs-219	247	8	لكل	لكل	PRON
iajs-219	247	9	من	من	INTJ
iajs-219	247	10	صنف	صنف	PROPN
iajs-219	247	11	مقاسات	مقاسات	PROPN
iajs-219	247	12	التوسع	التوسع	VERB
iajs-219	247	13	النقية	النقية	PROPN
iajs-219	247	14	mمن	mمن	PROPN
iajs-219	247	15	xإذا	xإذا	NOUN
iajs-219	247	16	كان	كان	PROPN
iajs-219	247	17	لكل	لكل	PROPN
iajs-219	247	18	مقاس	مقاس	PROPN
iajs-219	247	19	جزئي	جزئي	NOUN
iajs-219	247	20	-بأنه	-بأنه	PROPN
iajs-219	247	21	توسع	توسع	NOUN
iajs-219	247	22	نقي	نقي	NOUN
iajs-219	247	23	من	من	PRON
iajs-219	247	24	النمط	النمط	PROPN
iajs-219	247	25	m.	m.	PROPN
iajs-219	247	26	نقول	نقول	PROPN
iajs-219	247	27	عن	عن	PROPN
iajs-219	247	28	المقاس	المقاس	PROPN
iajs-219	247	29	-ومقاسات	-ومقاسات	PROPN
iajs-219	247	30	التوسع	التوسع	NOUN
iajs-219	247	31	من	من	ADP
iajs-219	247	32	النمط	النمط	NOUN
iajs-219	247	33	.	.	PUNCT
iajs-219	248	1	تم	تم	PROPN
iajs-219	248	2	أعطاء	أعطاء	PROPN
iajs-219	249	1	العديد	العديد	PROPN
iajs-219	250	1	من	من	INTJ
iajs-219	250	2	التشخيصات	التشخيصات	ADV
iajs-219	251	1	و	و	PRON
iajs-219	251	2	النتائج	النتائج	PROPN
iajs-219	251	3	و	و	PRON
iajs-219	251	4	الخواص	الخواص	NOUN
iajs-219	251	5	لمقاسات	لمقاسات	PROPN
iajs-219	251	6	التوسع	التوسع	PROPN
iajs-219	251	7	بحيث	بحيث	PROPN
iajs-219	251	8	mن	mن	PROPN
iajs-219	251	9	م	م	PROPN
iajs-219	251	10	pيوجد	pيوجد	PROPN
iajs-219	251	11	مقاس	مقاس	PROPN
iajs-219	251	12	جزئي	جزئي	NOUN
iajs-219	251	13	نقي	نقي	NOUN
iajs-219	251	14	مقاس	مقاس	PROPN
iajs-219	251	15	توسع	توسع	PROPN
iajs-219	251	16	–	–	PUNCT
iajs-219	251	17	.	.	PUNCT
iajs-219	252	1	وكذلك	وكذلك	PROPN
iajs-219	252	2	تم	تم	PROPN
iajs-219	252	3	مناقشة	مناقشة	PROPN
iajs-219	253	1	متى	متى	PROPN
iajs-219	253	2	تكون	تكون	VERB
iajs-219	253	3	مركبة	مركبة	PROPN
iajs-219	253	4	الجمع	الجمع	PROPN
iajs-219	253	5	المباشرلمقاسات	المباشرلمقاسات	PROPN
iajs-219	253	6	التوسع	التوسع	ADP
iajs-219	253	7	النقية	النقية	NOUN
iajs-219	253	8	من	من	PRON
iajs-219	253	9	النمط	النمط	NOUN
iajs-219	253	10	-النقية	-النقية	PROPN
iajs-219	253	11	من	من	NOUN
iajs-219	253	12	النمط	النمط	NOUN
iajs-219	253	13	.	.	PUNCT
iajs-219	254	1	–	–	PUNCT
iajs-219	254	2	صية	صية	PROPN
iajs-219	254	3	متحققة	متحققة	PROPN
iajs-219	254	4	لمقاسات	لمقاسات	PROPN
iajs-219	254	5	التوسع	التوسع	VERB
iajs-219	254	6	النقية	النقية	PROPN
iajs-219	254	7	من	من	PRON
iajs-219	254	8	النمط	النمط	NOUN
iajs-219	254	9	.	.	PUNCT
iajs-219	255	1	أكثر	أكثر	PROPN
iajs-219	255	2	من	من	PRON
iajs-219	255	3	ذلك	ذلك	PROPN
iajs-219	255	4	،	،	PROPN
iajs-219	255	5	تم	تم	PROPN
iajs-219	255	6	تقديم	تقديم	PROPN
iajs-219	255	7	شروط	شروط	PROPN
iajs-219	255	8	كافية	كافية	PROPN
iajs-219	255	9	لجعل	لجعل	VERB
iajs-219	255	10	ھذه	ھذه	PROPN
iajs-219	255	11	الخا	الخا	NOUN
iajs-219	255	12	نقي	نقي	NOUN
iajs-219	255	13	من	من	PROPN
iajs-219	255	14	النمط	النمط	PROPN
iajs-219	255	15	،	،	PROPN
iajs-219	255	16	مقاسات	مقاسات	PROPN
iajs-219	255	17	التوسع	التوسع	VERB
iajs-219	255	18	النقية	النقية	PROPN
iajs-219	255	19	من	من	DET
iajs-219	255	20	النمط	النمط	NOUN
iajs-219	255	21	مقاسات	مقاسات	PROPN
iajs-219	255	22	التوسع	التوسع	VERB
iajs-219	255	23	من	من	ADP
iajs-219	255	24	النمط	النمط	PROPN
iajs-219	255	25	النقية،مقاسات	النقية،مقاسات	NOUN
iajs-219	255	26	التوسع	التوسع	ADP
iajs-219	255	27	التوسع،مقاسات	التوسع،مقاسات	PROPN
iajs-219	255	28	:	:	PUNCT
iajs-219	255	29	المفتاحيةالكلمات	المفتاحيةالكلمات	ADJ
iajs-219	255	30	–	–	PUNCT
iajs-219	255	31	.	.	PUNCT