id	sid	tid	token	lemma	pos
iajs-117	1	1	microsoft	microsoft	PROPN
iajs-117	1	2	word	word	PROPN
iajs-117	1	3	282	282	NUM
iajs-117	1	4	-	-	SYM
iajs-117	1	5	291	291	NUM
iajs-117	1	6	mathematics	mathematic	NOUN
iajs-117	1	7	|	|	ADV
iajs-117	1	8	282	282	NUM
iajs-117	1	9	2016	2016	NUM
iajs-117	1	10	)	)	PUNCT
iajs-117	1	11	عام	عام	ADP
iajs-117	1	12	2العدد	2العدد	NUM
iajs-117	1	13	(	(	PUNCT
iajs-117	1	14	29مجلة	29مجلة	NUM
iajs-117	1	15	إبن	إبن	VERB
iajs-117	1	16	الهيثم	الهيثم	ADJ
iajs-117	1	17	للعلوم	للعلوم	NOUN
iajs-117	1	18	الصرفة	الصرفة	NOUN
iajs-117	2	1	و	و	PRON
iajs-117	2	2	التطبيقية	التطبيقية	ADV
iajs-117	2	3	المجلد	المجلد	VERB
iajs-117	2	4	ibn	ibn	PROPN
iajs-117	2	5	al	al	PROPN
iajs-117	2	6	-	-	PUNCT
iajs-117	2	7	haitham	haitham	PROPN
iajs-117	2	8	jour	jour	X
iajs-117	2	9	.	.	PROPN
iajs-117	3	1	for	for	ADP
iajs-117	3	2	pure	pure	ADJ
iajs-117	3	3	&	&	CCONJ
iajs-117	3	4	appl	appl	PROPN
iajs-117	3	5	.	.	PUNCT
iajs-117	4	1	sci	sci	PROPN
iajs-117	4	2	.	.	PUNCT
iajs-117	4	3	vol	vol	NOUN
iajs-117	4	4	.	.	PROPN
iajs-117	4	5	29	29	NUM
iajs-117	4	6	(	(	PUNCT
iajs-117	4	7	2	2	NUM
iajs-117	4	8	)	)	SYM
iajs-117	4	9	2016	2016	NUM
iajs-117	4	10	-prime	-prime	NOUN
iajs-117	4	11	submodules	submodule	NOUN
iajs-117	4	12	nuhad	nuhad	VERB
iajs-117	4	13	s.	s.	PROPN
iajs-117	4	14	al	al	PROPN
iajs-117	4	15	-	-	PUNCT
iajs-117	4	16	mothafar	mothafar	PROPN
iajs-117	4	17	dept	dept	NOUN
iajs-117	4	18	.	.	PROPN
iajs-117	5	1	of	of	ADP
iajs-117	5	2	mathematics	mathematics	PROPN
iajs-117	5	3	/	/	SYM
iajs-117	5	4	college	college	PROPN
iajs-117	5	5	of	of	ADP
iajs-117	5	6	science/	science/	NUM
iajs-117	5	7	university	university	NOUN
iajs-117	5	8	of	of	ADP
iajs-117	5	9	baghdad	baghdad	PROPN
iajs-117	5	10	.	.	PUNCT
iajs-117	6	1	adwia	adwia	VERB
iajs-117	6	2	j.	j.	PROPN
iajs-117	6	3	abdil	abdil	PROPN
iajs-117	6	4	.al	.al	PROPN
iajs-117	6	5	-	-	PUNCT
iajs-117	6	6	khalik	khalik	PROPN
iajs-117	6	7	dept	dept	NOUN
iajs-117	6	8	.	.	PROPN
iajs-117	6	9	of	of	ADP
iajs-117	6	10	mathematics	mathematics	PROPN
iajs-117	6	11	/	/	SYM
iajs-117	6	12	college	college	NOUN
iajs-117	6	13	of	of	ADP
iajs-117	6	14	science/	science/	NUM
iajs-117	6	15	al	al	PROPN
iajs-117	6	16	-	-	PUNCT
iajs-117	6	17	mustansiriya	mustansiriya	PROPN
iajs-117	6	18	university	university	NOUN
iajs-117	6	19	.	.	PUNCT
iajs-117	7	1	received	receive	VERB
iajs-117	7	2	in:6/	in:6/	PROPN
iajs-117	7	3	march	march	PROPN
iajs-117	7	4	/2016,accepted	/2016,accepte	VERB
iajs-117	7	5	in:5	in:5	PROPN
iajs-117	7	6	/	/	SYM
iajs-117	7	7	june	june	PROPN
iajs-117	7	8	/2016	/2016	PUNCT
iajs-117	8	1	abstract	abstract	ADV
iajs-117	8	2	let	let	VERB
iajs-117	8	3	r	r	PRON
iajs-117	8	4	be	be	AUX
iajs-117	8	5	a	a	DET
iajs-117	8	6	commutative	commutative	ADJ
iajs-117	8	7	ring	ring	NOUN
iajs-117	8	8	with	with	ADP
iajs-117	8	9	identity	identity	NOUN
iajs-117	8	10	and	and	CCONJ
iajs-117	8	11	m	m	AUX
iajs-117	8	12	be	be	AUX
iajs-117	8	13	an	an	DET
iajs-117	8	14	unitary	unitary	ADJ
iajs-117	8	15	r	r	NOUN
iajs-117	8	16	-	-	PUNCT
iajs-117	8	17	module	module	NOUN
iajs-117	8	18	.	.	PUNCT
iajs-117	9	1	let	let	VERB
iajs-117	9	2	(m	(m	PRON
iajs-117	9	3	)	)	PUNCT
iajs-117	9	4	be	be	AUX
iajs-117	9	5	the	the	DET
iajs-117	9	6	set	set	NOUN
iajs-117	9	7	of	of	ADP
iajs-117	9	8	all	all	DET
iajs-117	9	9	submodules	submodule	NOUN
iajs-117	9	10	of	of	ADP
iajs-117	9	11	m	m	PROPN
iajs-117	9	12	,	,	PUNCT
iajs-117	9	13	and	and	CCONJ
iajs-117	9	14			NOUN
iajs-117	9	15	:	:	PUNCT
iajs-117	9	16	(m	(m	PROPN
iajs-117	9	17	)	)	PUNCT
iajs-117	9	18			PROPN
iajs-117	9	19	(m	(m	PROPN
iajs-117	9	20	)	)	PUNCT
iajs-117	9	21			NOUN
iajs-117	9	22	{	{	PUNCT
iajs-117	9	23			NOUN
iajs-117	9	24	}	}	PUNCT
iajs-117	9	25	be	be	AUX
iajs-117	9	26	a	a	DET
iajs-117	9	27	function	function	NOUN
iajs-117	9	28	.	.	PUNCT
iajs-117	10	1	we	we	PRON
iajs-117	10	2	say	say	VERB
iajs-117	10	3	that	that	SCONJ
iajs-117	10	4	a	a	DET
iajs-117	10	5	proper	proper	ADJ
iajs-117	10	6	submodule	submodule	NOUN
iajs-117	10	7	p	p	NOUN
iajs-117	10	8	of	of	ADP
iajs-117	10	9	m	m	PROPN
iajs-117	10	10	is	be	AUX
iajs-117	10	11	-prime	-prime	ADJ
iajs-117	10	12	if	if	SCONJ
iajs-117	10	13	for	for	ADP
iajs-117	10	14	each	each	DET
iajs-117	10	15	r	r	NOUN
iajs-117	10	16			NOUN
iajs-117	10	17	r	r	NOUN
iajs-117	10	18	and	and	CCONJ
iajs-117	10	19	x	x	PROPN
iajs-117	10	20			NOUN
iajs-117	10	21	m	m	VERB
iajs-117	10	22	,	,	PUNCT
iajs-117	10	23	if	if	SCONJ
iajs-117	10	24	rx	rx	VERB
iajs-117	10	25			PROPN
iajs-117	10	26	p	p	NOUN
iajs-117	10	27	,	,	PUNCT
iajs-117	10	28	then	then	ADV
iajs-117	10	29	either	either	CCONJ
iajs-117	10	30	x	x	SYM
iajs-117	10	31			NOUN
iajs-117	10	32	p	p	X
iajs-117	10	33	+	+	CCONJ
iajs-117	10	34	(p	(p	X
iajs-117	10	35	)	)	PUNCT
iajs-117	10	36	or	or	CCONJ
iajs-117	10	37	r	r	NOUN
iajs-117	10	38	m	m	NOUN
iajs-117	10	39			PROPN
iajs-117	10	40	p	p	X
iajs-117	10	41	+	+	X
iajs-117	10	42	(p	(p	NOUN
iajs-117	10	43	)	)	PUNCT
iajs-117	10	44	.	.	PUNCT
iajs-117	11	1	some	some	PRON
iajs-117	11	2	of	of	ADP
iajs-117	11	3	the	the	DET
iajs-117	11	4	properties	property	NOUN
iajs-117	11	5	of	of	ADP
iajs-117	11	6	this	this	DET
iajs-117	11	7	concept	concept	NOUN
iajs-117	11	8	will	will	AUX
iajs-117	11	9	be	be	AUX
iajs-117	11	10	investigated	investigate	VERB
iajs-117	11	11	.	.	PUNCT
iajs-117	12	1	some	some	DET
iajs-117	12	2	characterizations	characterization	NOUN
iajs-117	12	3	of	of	ADP
iajs-117	12	4	-prime	-prime	ADJ
iajs-117	12	5	submodules	submodule	NOUN
iajs-117	12	6	will	will	AUX
iajs-117	12	7	be	be	AUX
iajs-117	12	8	given	give	VERB
iajs-117	12	9	,	,	PUNCT
iajs-117	12	10	and	and	CCONJ
iajs-117	12	11	we	we	PRON
iajs-117	12	12	show	show	VERB
iajs-117	12	13	that	that	SCONJ
iajs-117	12	14	under	under	ADP
iajs-117	12	15	some	some	DET
iajs-117	12	16	assumptions	assumption	NOUN
iajs-117	12	17	prime	prime	ADJ
iajs-117	12	18	submodules	submodule	NOUN
iajs-117	12	19	and	and	CCONJ
iajs-117	12	20	-prime	-prime	ADJ
iajs-117	12	21	submodules	submodule	NOUN
iajs-117	12	22	are	be	AUX
iajs-117	12	23	coincide	coincide	ADJ
iajs-117	12	24	.	.	PUNCT
iajs-117	13	1	key	key	ADJ
iajs-117	13	2	words	word	NOUN
iajs-117	13	3	:	:	PUNCT
iajs-117	13	4	prime	prime	ADJ
iajs-117	13	5	submodule	submodule	NOUN
iajs-117	13	6	,	,	PUNCT
iajs-117	13	7	weakly	weakly	ADJ
iajs-117	13	8	prime	prime	ADJ
iajs-117	13	9	submodules	submodule	NOUN
iajs-117	13	10	,	,	PUNCT
iajs-117	13	11	-prime	-prime	PROPN
iajs-117	13	12	submodules	submodule	NOUN
iajs-117	13	13	.	.	PUNCT
iajs-117	14	1	mathematics	mathematic	NOUN
iajs-117	14	2	|	|	ADV
iajs-117	14	3	283	283	NUM
iajs-117	14	4	2016	2016	NUM
iajs-117	14	5	)	)	PUNCT
iajs-117	14	6	عام	عام	ADP
iajs-117	14	7	2العدد	2العدد	NUM
iajs-117	14	8	(	(	PUNCT
iajs-117	14	9	29لمجلد	29لمجلد	NUM
iajs-117	14	10	ا	ا	X
iajs-117	14	11	مجلة	مجلة	NOUN
iajs-117	14	12	إبن	إبن	VERB
iajs-117	14	13	الهيثم	الهيثم	ADJ
iajs-117	14	14	للعلوم	للعلوم	NOUN
iajs-117	14	15	الصرفة	الصرفة	NOUN
iajs-117	15	1	و	و	PRON
iajs-117	15	2	التطبيقية	التطبيقية	ADJ
iajs-117	15	3	ibn	ibn	PROPN
iajs-117	15	4	al	al	PROPN
iajs-117	15	5	-	-	PUNCT
iajs-117	15	6	haitham	haitham	PROPN
iajs-117	15	7	jour	jour	X
iajs-117	15	8	.	.	PROPN
iajs-117	15	9	for	for	ADP
iajs-117	15	10	pure	pure	ADJ
iajs-117	15	11	&	&	CCONJ
iajs-117	15	12	appl	appl	PROPN
iajs-117	15	13	.	.	PUNCT
iajs-117	16	1	sci	sci	PROPN
iajs-117	16	2	.	.	PUNCT
iajs-117	16	3	vol	vol	NOUN
iajs-117	16	4	.	.	PROPN
iajs-117	16	5	29	29	NUM
iajs-117	16	6	(	(	PUNCT
iajs-117	16	7	2	2	NUM
iajs-117	16	8	)	)	PUNCT
iajs-117	16	9	2016	2016	NUM
iajs-117	16	10	1introduction	1introduction	NUM
iajs-117	16	11	throughout	throughout	ADP
iajs-117	16	12	this	this	DET
iajs-117	16	13	paper	paper	NOUN
iajs-117	16	14	,	,	PUNCT
iajs-117	16	15	r	r	NOUN
iajs-117	16	16	is	be	AUX
iajs-117	16	17	a	a	DET
iajs-117	16	18	commutative	commutative	ADJ
iajs-117	16	19	ring	ring	NOUN
iajs-117	16	20	with	with	ADP
iajs-117	16	21	identity	identity	NOUN
iajs-117	16	22	and	and	CCONJ
iajs-117	16	23	m	m	NOUN
iajs-117	16	24	is	be	AUX
iajs-117	16	25	an	an	DET
iajs-117	16	26	unitary	unitary	ADJ
iajs-117	16	27	rmodule	rmodule	NOUN
iajs-117	16	28	.	.	PUNCT
iajs-117	17	1	a	a	DET
iajs-117	17	2	proper	proper	ADJ
iajs-117	17	3	ideal	ideal	NOUN
iajs-117	17	4	p	p	NOUN
iajs-117	17	5	of	of	ADP
iajs-117	17	6	a	a	DET
iajs-117	17	7	ring	ring	NOUN
iajs-117	17	8	r	r	NOUN
iajs-117	17	9	is	be	AUX
iajs-117	17	10	prime	prime	ADJ
iajs-117	17	11	if	if	SCONJ
iajs-117	17	12	for	for	ADP
iajs-117	17	13	all	all	DET
iajs-117	17	14	elements	element	NOUN
iajs-117	17	15	a	a	DET
iajs-117	17	16	,	,	PUNCT
iajs-117	17	17	b	b	PROPN
iajs-117	17	18			PROPN
iajs-117	17	19	r	r	NOUN
iajs-117	17	20	,	,	PUNCT
iajs-117	17	21	ab	ab	PROPN
iajs-117	17	22			PROPN
iajs-117	17	23	p	p	PROPN
iajs-117	17	24	implies	imply	VERB
iajs-117	17	25	either	either	CCONJ
iajs-117	17	26	a	a	DET
iajs-117	17	27			NOUN
iajs-117	17	28	p	p	NOUN
iajs-117	17	29	or	or	CCONJ
iajs-117	17	30	b	b	NOUN
iajs-117	17	31			NOUN
iajs-117	17	32	p	p	X
iajs-117	17	33	[	[	PUNCT
iajs-117	17	34	1	1	NUM
iajs-117	17	35	,	,	PUNCT
iajs-117	17	36	p.40].in	p.40].in	PROPN
iajs-117	17	37	the	the	DET
iajs-117	17	38	theory	theory	NOUN
iajs-117	17	39	of	of	ADP
iajs-117	17	40	rings	ring	NOUN
iajs-117	17	41	,	,	PUNCT
iajs-117	17	42	prime	prime	ADJ
iajs-117	17	43	ideals	ideal	NOUN
iajs-117	17	44	play	play	VERB
iajs-117	17	45	important	important	ADJ
iajs-117	17	46	roles	role	NOUN
iajs-117	17	47	.	.	PUNCT
iajs-117	18	1	one	one	NUM
iajs-117	18	2	of	of	ADP
iajs-117	18	3	the	the	DET
iajs-117	18	4	natural	natural	ADJ
iajs-117	18	5	generalizations	generalization	NOUN
iajs-117	18	6	of	of	ADP
iajs-117	18	7	prime	prime	ADJ
iajs-117	18	8	ideals	ideal	NOUN
iajs-117	18	9	which	which	PRON
iajs-117	18	10	have	have	AUX
iajs-117	18	11	attracted	attract	VERB
iajs-117	18	12	the	the	DET
iajs-117	18	13	interest	interest	NOUN
iajs-117	18	14	of	of	ADP
iajs-117	18	15	several	several	ADJ
iajs-117	18	16	authors	author	NOUN
iajs-117	18	17	in	in	ADP
iajs-117	18	18	the	the	DET
iajs-117	18	19	last	last	ADJ
iajs-117	18	20	two	two	NUM
iajs-117	18	21	decades	decade	NOUN
iajs-117	18	22	is	be	AUX
iajs-117	18	23	the	the	DET
iajs-117	18	24	notion	notion	NOUN
iajs-117	18	25	of	of	ADP
iajs-117	18	26	prime	prime	PROPN
iajs-117	18	27	submodule,[2],[3],[4	submodule,[2],[3],[4	PROPN
iajs-117	18	28	]	]	PUNCT
iajs-117	18	29	.	.	PUNCT
iajs-117	19	1	these	these	PRON
iajs-117	19	2	have	have	AUX
iajs-117	19	3	led	lead	VERB
iajs-117	19	4	to	to	ADP
iajs-117	19	5	more	more	ADJ
iajs-117	19	6	information	information	NOUN
iajs-117	19	7	on	on	ADP
iajs-117	19	8	the	the	DET
iajs-117	19	9	structure	structure	NOUN
iajs-117	19	10	of	of	ADP
iajs-117	19	11	the	the	DET
iajs-117	19	12	r	r	NOUN
iajs-117	19	13	-	-	PUNCT
iajs-117	19	14	module	module	NOUN
iajs-117	19	15	m.	m.	NOUN
iajs-117	19	16	for	for	ADP
iajs-117	19	17	an	an	DET
iajs-117	19	18	ideal	ideal	ADJ
iajs-117	19	19	i	i	PRON
iajs-117	19	20	of	of	ADP
iajs-117	19	21	r	r	NOUN
iajs-117	19	22	and	and	CCONJ
iajs-117	19	23	a	a	DET
iajs-117	19	24	submodule	submodule	NOUN
iajs-117	19	25	n	n	PROPN
iajs-117	19	26	of	of	ADP
iajs-117	19	27	m	m	VERB
iajs-117	19	28	let	let	VERB
iajs-117	19	29	i	i	PRON
iajs-117	19	30	denote	denote	VERB
iajs-117	19	31	the	the	DET
iajs-117	19	32	radical	radical	NOUN
iajs-117	19	33	of	of	ADP
iajs-117	19	34	i	i	PROPN
iajs-117	19	35	,	,	PUNCT
iajs-117	19	36	and	and	CCONJ
iajs-117	19	37	[	[	X
iajs-117	19	38	n	n	X
iajs-117	19	39	r	r	NOUN
iajs-117	19	40	:	:	PUNCT
iajs-117	19	41	m	m	VERB
iajs-117	19	42	]	]	X
iajs-117	19	43	=	=	PUNCT
iajs-117	19	44	{	{	PUNCT
iajs-117	19	45	r	r	NOUN
iajs-117	19	46			PROPN
iajs-117	19	47	r	r	NOUN
iajs-117	19	48	,	,	PUNCT
iajs-117	19	49	rm	rm	PROPN
iajs-117	19	50			PROPN
iajs-117	19	51	n	n	CCONJ
iajs-117	19	52	}	}	PUNCT
iajs-117	19	53	which	which	PRON
iajs-117	19	54	is	be	AUX
iajs-117	19	55	clearly	clearly	ADV
iajs-117	19	56	an	an	DET
iajs-117	19	57	ideal	ideal	NOUN
iajs-117	19	58	of	of	ADP
iajs-117	19	59	r.	r.	PROPN
iajs-117	19	60	a	a	DET
iajs-117	19	61	proper	proper	ADJ
iajs-117	19	62	submodule	submodule	NOUN
iajs-117	19	63	p	p	NOUN
iajs-117	19	64	of	of	ADP
iajs-117	19	65	m	m	PROPN
iajs-117	19	66	is	be	AUX
iajs-117	19	67	called	call	VERB
iajs-117	19	68	a	a	DET
iajs-117	19	69	prime	prime	ADJ
iajs-117	19	70	submodule	submodule	NOUN
iajs-117	19	71	if	if	SCONJ
iajs-117	19	72	r	r	NOUN
iajs-117	19	73			NOUN
iajs-117	19	74	r	r	NOUN
iajs-117	19	75	and	and	CCONJ
iajs-117	19	76	x	x	NOUN
iajs-117	19	77			NOUN
iajs-117	19	78	m	m	VERB
iajs-117	19	79	with	with	ADP
iajs-117	19	80	rx	rx	ADJ
iajs-117	19	81			PROPN
iajs-117	19	82	p	p	PROPN
iajs-117	19	83	implies	imply	VERB
iajs-117	19	84	that	that	SCONJ
iajs-117	19	85	r	r	NOUN
iajs-117	19	86			NOUN
iajs-117	20	1	[	[	X
iajs-117	20	2	p	p	X
iajs-117	20	3	:	:	PUNCT
iajs-117	20	4	m	m	X
iajs-117	20	5	]	]	X
iajs-117	20	6	or	or	CCONJ
iajs-117	20	7	x	x	ADJ
iajs-117	20	8			NOUN
iajs-117	20	9	p,[3	p,[3	PROPN
iajs-117	20	10	]	]	PUNCT
iajs-117	20	11	.	.	PUNCT
iajs-117	21	1	there	there	PRON
iajs-117	21	2	are	be	VERB
iajs-117	21	3	several	several	ADJ
iajs-117	21	4	generalization	generalization	NOUN
iajs-117	21	5	of	of	ADP
iajs-117	21	6	the	the	DET
iajs-117	21	7	notion	notion	NOUN
iajs-117	21	8	of	of	ADP
iajs-117	21	9	a	a	DET
iajs-117	21	10	prime	prime	ADJ
iajs-117	21	11	submodules	submodule	NOUN
iajs-117	21	12	,	,	PUNCT
iajs-117	21	13	such	such	ADJ
iajs-117	21	14	as	as	ADP
iajs-117	21	15	ebrahimi	ebrahimi	PROPN
iajs-117	21	16	atani	atani	PROPN
iajs-117	21	17	,	,	PUNCT
iajs-117	21	18	f.	f.	PROPN
iajs-117	21	19	farzalipour	farzalipour	PROPN
iajs-117	21	20	,	,	PUNCT
iajs-117	21	21	introduced	introduce	VERB
iajs-117	21	22	and	and	CCONJ
iajs-117	21	23	studied	study	VERB
iajs-117	21	24	weakly	weakly	ADJ
iajs-117	21	25	prime	prime	ADJ
iajs-117	21	26	submodules	submodule	NOUN
iajs-117	21	27	,	,	PUNCT
iajs-117	21	28	where	where	SCONJ
iajs-117	21	29	a	a	DET
iajs-117	21	30	proper	proper	ADJ
iajs-117	21	31	submodule	submodule	NOUN
iajs-117	21	32	n	n	PROPN
iajs-117	21	33	of	of	ADP
iajs-117	21	34	m	m	PROPN
iajs-117	21	35	is	be	AUX
iajs-117	21	36	said	say	VERB
iajs-117	21	37	to	to	PART
iajs-117	21	38	be	be	AUX
iajs-117	21	39	weakly	weakly	ADJ
iajs-117	21	40	prime	prime	ADJ
iajs-117	21	41	submodule	submodule	NOUN
iajs-117	21	42	of	of	ADP
iajs-117	21	43	m	m	PROPN
iajs-117	21	44	if	if	SCONJ
iajs-117	21	45	r	r	NOUN
iajs-117	21	46			NOUN
iajs-117	21	47	r	r	NOUN
iajs-117	21	48	and	and	CCONJ
iajs-117	21	49	x	x	NOUN
iajs-117	21	50			PROPN
iajs-117	21	51	m	m	VERB
iajs-117	21	52	0	0	NUM
iajs-117	21	53			NOUN
iajs-117	21	54	rx	rx	VERB
iajs-117	21	55			PROPN
iajs-117	21	56	n	n	ADP
iajs-117	21	57	gives	give	VERB
iajs-117	21	58	that	that	DET
iajs-117	21	59	r	r	NOUN
iajs-117	21	60			NOUN
iajs-117	21	61	[	[	PUNCT
iajs-117	21	62	n	n	X
iajs-117	21	63	:	:	PUNCT
iajs-117	21	64	m	m	X
iajs-117	21	65	]	]	X
iajs-117	21	66	or	or	CCONJ
iajs-117	21	67	x	x	ADJ
iajs-117	21	68			NOUN
iajs-117	21	69	n	n	CCONJ
iajs-117	21	70	,	,	PUNCT
iajs-117	21	71	[	[	X
iajs-117	21	72	5	5	NUM
iajs-117	21	73	]	]	PUNCT
iajs-117	21	74	.	.	PUNCT
iajs-117	22	1	khaksari	khaksari	PROPN
iajs-117	22	2	and	and	CCONJ
iajs-117	22	3	jafari	jafari	PROPN
iajs-117	22	4	extended	extend	VERB
iajs-117	22	5	the	the	DET
iajs-117	22	6	notion	notion	NOUN
iajs-117	22	7	of	of	ADP
iajs-117	22	8	prime	prime	ADJ
iajs-117	22	9	submodule	submodule	NOUN
iajs-117	22	10	to	to	PART
iajs-117	22	11	-prime.let	-prime.let	PROPN
iajs-117	22	12	m	m	AUX
iajs-117	22	13	be	be	AUX
iajs-117	22	14	an	an	DET
iajs-117	22	15	r	r	NOUN
iajs-117	22	16	-	-	PUNCT
iajs-117	22	17	module	module	NOUN
iajs-117	22	18	and	and	CCONJ
iajs-117	22	19	(m	(m	NOUN
iajs-117	22	20	)	)	PUNCT
iajs-117	22	21	be	be	VERB
iajs-117	22	22	the	the	DET
iajs-117	22	23	set	set	NOUN
iajs-117	22	24	of	of	ADP
iajs-117	22	25	all	all	DET
iajs-117	22	26	submodules	submodule	NOUN
iajs-117	22	27	of	of	ADP
iajs-117	22	28	m	m	NOUN
iajs-117	22	29	and	and	CCONJ
iajs-117	22	30			NOUN
iajs-117	22	31	:	:	PUNCT
iajs-117	22	32	(m	(m	NUM
iajs-117	22	33	)	)	PUNCT
iajs-117	22	34			PROPN
iajs-117	22	35	(m	(m	PROPN
iajs-117	22	36	)	)	PUNCT
iajs-117	22	37			NOUN
iajs-117	22	38	{	{	PUNCT
iajs-117	22	39			NOUN
iajs-117	22	40	}	}	PUNCT
iajs-117	22	41	be	be	AUX
iajs-117	22	42	a	a	DET
iajs-117	22	43	function	function	NOUN
iajs-117	22	44	.	.	PUNCT
iajs-117	23	1	a	a	DET
iajs-117	23	2	proper	proper	ADJ
iajs-117	23	3	submodule	submodule	NOUN
iajs-117	23	4	p	p	NOUN
iajs-117	23	5	of	of	ADP
iajs-117	23	6	m	m	PROPN
iajs-117	23	7	is	be	AUX
iajs-117	23	8	said	say	VERB
iajs-117	23	9	to	to	PART
iajs-117	23	10	be	be	AUX
iajs-117	23	11	-prime	-prime	NOUN
iajs-117	23	12	if	if	SCONJ
iajs-117	23	13	r	r	NOUN
iajs-117	23	14			NOUN
iajs-117	23	15	r	r	NOUN
iajs-117	23	16	and	and	CCONJ
iajs-117	23	17	x	x	PROPN
iajs-117	23	18			NOUN
iajs-117	23	19	m	m	VERB
iajs-117	23	20	,	,	PUNCT
iajs-117	23	21	rx	rx	VERB
iajs-117	23	22			NOUN
iajs-117	23	23	p\(p	p\(p	NOUN
iajs-117	23	24	)	)	PUNCT
iajs-117	23	25	implies	imply	VERB
iajs-117	23	26	that	that	SCONJ
iajs-117	23	27	r	r	NOUN
iajs-117	23	28			NOUN
iajs-117	24	1	[	[	X
iajs-117	24	2	p	p	X
iajs-117	24	3	:	:	PUNCT
iajs-117	24	4	m	m	X
iajs-117	24	5	]	]	X
iajs-117	24	6	or	or	CCONJ
iajs-117	24	7	x	x	ADJ
iajs-117	24	8			NOUN
iajs-117	24	9	p	p	X
iajs-117	25	1	[	[	X
iajs-117	25	2	6	6	NUM
iajs-117	25	3	]	]	PUNCT
iajs-117	25	4	.	.	PUNCT
iajs-117	26	1	in	in	ADP
iajs-117	26	2	this	this	DET
iajs-117	26	3	paper	paper	NOUN
iajs-117	26	4	,	,	PUNCT
iajs-117	26	5	we	we	PRON
iajs-117	26	6	define	define	VERB
iajs-117	26	7	and	and	CCONJ
iajs-117	26	8	study	study	VERB
iajs-117	26	9	the	the	DET
iajs-117	26	10	notion	notion	NOUN
iajs-117	26	11	of	of	ADP
iajs-117	26	12	-prime	-prime	ADJ
iajs-117	26	13	submodules	submodule	NOUN
iajs-117	26	14	.	.	PUNCT
iajs-117	27	1	let	let	VERB
iajs-117	27	2	(m	(m	PRON
iajs-117	27	3	)	)	PUNCT
iajs-117	27	4	be	be	AUX
iajs-117	27	5	the	the	DET
iajs-117	27	6	set	set	NOUN
iajs-117	27	7	of	of	ADP
iajs-117	27	8	all	all	DET
iajs-117	27	9	submodules	submodule	NOUN
iajs-117	27	10	of	of	ADP
iajs-117	27	11	m	m	PROPN
iajs-117	27	12	and	and	CCONJ
iajs-117	27	13			NOUN
iajs-117	27	14	:	:	PUNCT
iajs-117	27	15	(m	(m	PROPN
iajs-117	27	16	)	)	PUNCT
iajs-117	27	17			PROPN
iajs-117	27	18	(m	(m	PROPN
iajs-117	27	19	)	)	PUNCT
iajs-117	27	20			NOUN
iajs-117	27	21	{	{	PUNCT
iajs-117	27	22			NOUN
iajs-117	27	23	}	}	PUNCT
iajs-117	27	24	be	be	AUX
iajs-117	27	25	a	a	DET
iajs-117	27	26	function	function	NOUN
iajs-117	27	27	.	.	PUNCT
iajs-117	28	1	a	a	DET
iajs-117	28	2	proper	proper	ADJ
iajs-117	28	3	submodule	submodule	NOUN
iajs-117	28	4	p	p	NOUN
iajs-117	28	5	of	of	ADP
iajs-117	28	6	m	m	PROPN
iajs-117	28	7	is	be	AUX
iajs-117	28	8	said	say	VERB
iajs-117	28	9	to	to	PART
iajs-117	28	10	be	be	AUX
iajs-117	28	11	-prime	-prime	ADJ
iajs-117	28	12	if	if	SCONJ
iajs-117	28	13	for	for	ADP
iajs-117	28	14	each	each	DET
iajs-117	28	15	r	r	NOUN
iajs-117	28	16			NOUN
iajs-117	28	17	r	r	NOUN
iajs-117	28	18	and	and	CCONJ
iajs-117	28	19	x	x	PROPN
iajs-117	28	20			NOUN
iajs-117	28	21	m	m	VERB
iajs-117	28	22	,	,	PUNCT
iajs-117	28	23	if	if	SCONJ
iajs-117	28	24	rx	rx	VERB
iajs-117	28	25			PROPN
iajs-117	28	26	p	p	NOUN
iajs-117	28	27	,	,	PUNCT
iajs-117	28	28	then	then	ADV
iajs-117	28	29	either	either	CCONJ
iajs-117	28	30	x	x	SYM
iajs-117	28	31			NOUN
iajs-117	28	32	p	p	X
iajs-117	28	33	+	+	CCONJ
iajs-117	28	34	(p	(p	X
iajs-117	28	35	)	)	PUNCT
iajs-117	28	36	or	or	CCONJ
iajs-117	28	37	r	r	NOUN
iajs-117	28	38	m	m	NOUN
iajs-117	28	39			PROPN
iajs-117	28	40	p	p	X
iajs-117	28	41	+	+	X
iajs-117	28	42	(p	(p	X
iajs-117	28	43	)	)	PUNCT
iajs-117	28	44	.	.	PUNCT
iajs-117	29	1	2	2	NUM
iajs-117	29	2	-	-	PUNCT
iajs-117	29	3	basic	basic	ADJ
iajs-117	29	4	properties	property	NOUN
iajs-117	29	5	of	of	ADP
iajs-117	29	6	-prime	-prime	ADJ
iajs-117	29	7	submodules	submodule	NOUN
iajs-117	29	8	first	first	ADV
iajs-117	29	9	we	we	PRON
iajs-117	29	10	give	give	VERB
iajs-117	29	11	the	the	DET
iajs-117	29	12	following	follow	VERB
iajs-117	29	13	definition	definition	NOUN
iajs-117	29	14	.	.	PUNCT
iajs-117	30	1	definition	definition	NOUN
iajs-117	30	2	(	(	PUNCT
iajs-117	30	3	2.1	2.1	NUM
iajs-117	30	4	):	):	PUNCT
iajs-117	30	5	let	let	VERB
iajs-117	30	6	m	m	PRON
iajs-117	30	7	be	be	AUX
iajs-117	30	8	an	an	DET
iajs-117	30	9	r	r	NOUN
iajs-117	30	10	-	-	PUNCT
iajs-117	30	11	module	module	NOUN
iajs-117	30	12	and	and	CCONJ
iajs-117	30	13	(m	(m	NOUN
iajs-117	30	14	)	)	PUNCT
iajs-117	30	15	be	be	VERB
iajs-117	30	16	the	the	DET
iajs-117	30	17	set	set	NOUN
iajs-117	30	18	of	of	ADP
iajs-117	30	19	all	all	DET
iajs-117	30	20	submodules	submodule	NOUN
iajs-117	30	21	of	of	ADP
iajs-117	30	22	m.	m.	NOUN
iajs-117	30	23	let	let	VERB
iajs-117	30	24	:(m	:(m	PROPN
iajs-117	30	25	)	)	PUNCT
iajs-117	30	26	(m	(m	PROPN
iajs-117	30	27	)	)	PUNCT
iajs-117	30	28			NOUN
iajs-117	30	29	{	{	PUNCT
iajs-117	30	30			NOUN
iajs-117	30	31	}	}	PUNCT
iajs-117	30	32	be	be	AUX
iajs-117	30	33	a	a	DET
iajs-117	30	34	function	function	NOUN
iajs-117	30	35	.	.	PUNCT
iajs-117	31	1	a	a	DET
iajs-117	31	2	proper	proper	ADJ
iajs-117	31	3	submodule	submodule	NOUN
iajs-117	31	4	n	n	PROPN
iajs-117	31	5	of	of	ADP
iajs-117	31	6	m	m	PROPN
iajs-117	31	7	is	be	AUX
iajs-117	31	8	said	say	VERB
iajs-117	31	9	to	to	PART
iajs-117	31	10	be	be	AUX
iajs-117	31	11	-prime	-prime	ADJ
iajs-117	31	12	if	if	SCONJ
iajs-117	31	13	for	for	ADP
iajs-117	31	14	each	each	DET
iajs-117	31	15	r	r	NOUN
iajs-117	31	16			NOUN
iajs-117	31	17	r	r	NOUN
iajs-117	31	18	and	and	CCONJ
iajs-117	31	19	x	x	PROPN
iajs-117	31	20			NOUN
iajs-117	31	21	m	m	VERB
iajs-117	31	22	,	,	PUNCT
iajs-117	31	23	if	if	SCONJ
iajs-117	31	24	rx	rx	VERB
iajs-117	31	25			NOUN
iajs-117	31	26	n	n	CCONJ
iajs-117	31	27	,	,	PUNCT
iajs-117	31	28	then	then	ADV
iajs-117	31	29	x	x	SYM
iajs-117	31	30			PROPN
iajs-117	31	31	n	n	PROPN
iajs-117	31	32	+	+	CCONJ
iajs-117	31	33	(n	(n	X
iajs-117	31	34	)	)	PUNCT
iajs-117	31	35	or	or	CCONJ
iajs-117	31	36	r	r	NOUN
iajs-117	31	37	m	m	NOUN
iajs-117	31	38			PROPN
iajs-117	31	39	n	n	PROPN
iajs-117	31	40	+	+	CCONJ
iajs-117	31	41	(n	(n	X
iajs-117	31	42	)	)	PUNCT
iajs-117	31	43	.	.	PUNCT
iajs-117	32	1	remarks	remark	NOUN
iajs-117	32	2	and	and	CCONJ
iajs-117	32	3	examples	example	NOUN
iajs-117	32	4	(	(	PUNCT
iajs-117	32	5	2.2	2.2	NUM
iajs-117	32	6	)	)	PUNCT
iajs-117	32	7	(	(	PUNCT
iajs-117	32	8	1	1	X
iajs-117	32	9	)	)	PUNCT
iajs-117	32	10	it	it	PRON
iajs-117	32	11	is	be	AUX
iajs-117	32	12	clear	clear	ADJ
iajs-117	32	13	that	that	SCONJ
iajs-117	32	14	every	every	DET
iajs-117	32	15	prime	prime	ADJ
iajs-117	32	16	submodule	submodule	NOUN
iajs-117	32	17	of	of	ADP
iajs-117	32	18	an	an	DET
iajs-117	32	19	r	r	NOUN
iajs-117	32	20	-	-	PUNCT
iajs-117	32	21	module	module	NOUN
iajs-117	32	22	m	m	NOUN
iajs-117	32	23	is	be	AUX
iajs-117	32	24	-prime	-prime	ADJ
iajs-117	32	25	submodule	submodule	NOUN
iajs-117	32	26	of	of	ADP
iajs-117	32	27	m	m	PROPN
iajs-117	32	28	,	,	PUNCT
iajs-117	32	29	but	but	CCONJ
iajs-117	32	30	the	the	DET
iajs-117	32	31	convers	conver	NOUN
iajs-117	32	32	is	be	AUX
iajs-117	32	33	not	not	PART
iajs-117	32	34	true	true	ADJ
iajs-117	32	35	in	in	ADP
iajs-117	32	36	general	general	ADJ
iajs-117	32	37	for	for	ADP
iajs-117	32	38	example	example	NOUN
iajs-117	32	39	:	:	PUNCT
iajs-117	32	40	let	let	VERB
iajs-117	32	41	m	m	VERB
iajs-117	32	42	=	=	VERB
iajs-117	32	43	z8	z8	NOUN
iajs-117	32	44	as	as	ADP
iajs-117	32	45	a	a	DET
iajs-117	32	46	z	z	NOUN
iajs-117	32	47	-	-	PUNCT
iajs-117	32	48	module	module	NOUN
iajs-117	32	49	,	,	PUNCT
iajs-117	32	50	n	n	NOUN
iajs-117	32	51	=	=	SYM
iajs-117	32	52			PROPN
iajs-117	33	1	4	4	NUM
iajs-117	33	2	.	.	NOUN
iajs-117	33	3	then	then	ADV
iajs-117	33	4	n	n	PRON
iajs-117	33	5	is	be	AUX
iajs-117	33	6	not	not	PART
iajs-117	33	7	prime	prime	ADJ
iajs-117	33	8	submodule	submodule	NOUN
iajs-117	33	9	of	of	ADP
iajs-117	33	10	m	m	PROPN
iajs-117	33	11	.	.	PUNCT
iajs-117	34	1	but	but	CCONJ
iajs-117	34	2	n	n	PRON
iajs-117	34	3	is	be	AUX
iajs-117	34	4	-prime	-prime	PROPN
iajs-117	34	5	submodule	submodule	NOUN
iajs-117	34	6	of	of	ADP
iajs-117	34	7	m.	m.	NOUN
iajs-117	34	8	proof	proof	NOUN
iajs-117	34	9	:	:	PUNCT
iajs-117	34	10	let	let	VERB
iajs-117	34	11			NOUN
iajs-117	34	12	:	:	PUNCT
iajs-117	34	13	(z8	(z8	NOUN
iajs-117	34	14	)	)	PUNCT
iajs-117	34	15	(z8	(z8	NOUN
iajs-117	34	16	)	)	PUNCT
iajs-117	34	17			NOUN
iajs-117	34	18	{	{	PUNCT
iajs-117	34	19			NOUN
iajs-117	34	20	}	}	PUNCT
iajs-117	34	21	,	,	PUNCT
iajs-117	34	22	where	where	SCONJ
iajs-117	34	23	(n	(n	X
iajs-117	34	24	)	)	PUNCT
iajs-117	34	25	=	=	SYM
iajs-117	35	1	n	n	PROPN
iajs-117	35	2	+	+	CCONJ
iajs-117	35	3			PROPN
iajs-117	35	4	2	2	NUM
iajs-117	35	5			NOUN
iajs-117	35	6	,	,	PUNCT
iajs-117	35	7			NOUN
iajs-117	35	8	n	n	PRON
iajs-117	35	9			PROPN
iajs-117	35	10	m	m	PROPN
iajs-117	35	11	,	,	PUNCT
iajs-117	35	12	then	then	ADV
iajs-117	35	13	for	for	ADP
iajs-117	35	14	each	each	DET
iajs-117	35	15	r	r	PROPN
iajs-117	35	16	z	z	PROPN
iajs-117	35	17	,	,	PUNCT
iajs-117	35	18	̅	̅	NUM
iajs-117	35	19	z8	z8	NOUN
iajs-117	35	20	,	,	PUNCT
iajs-117	35	21	if	if	SCONJ
iajs-117	35	22	r	r	NOUN
iajs-117	35	23	̅	̅	NUM
iajs-117	35	24	n	n	NOUN
iajs-117	35	25	,	,	PUNCT
iajs-117	35	26	then	then	ADV
iajs-117	35	27	̅	̅	NUM
iajs-117	35	28	n	n	PRON
iajs-117	35	29	+	+	NUM
iajs-117	35	30	(n	(n	X
iajs-117	35	31	)	)	PUNCT
iajs-117	35	32	=	=	SYM
iajs-117	36	1	n	n	PROPN
iajs-117	36	2	+	+	NUM
iajs-117	36	3	n	n	CCONJ
iajs-117	36	4	+	+	CCONJ
iajs-117	36	5			PROPN
iajs-117	36	6	2	2	NUM
iajs-117	36	7			NOUN
iajs-117	36	8	=	=	PUNCT
iajs-117	36	9			PROPN
iajs-117	36	10	2	2	NUM
iajs-117	37	1			NOUN
iajs-117	37	2	or	or	CCONJ
iajs-117	37	3	r	r	NOUN
iajs-117	37	4	z8	z8	NOUN
iajs-117	37	5			PROPN
iajs-117	37	6	n	n	PROPN
iajs-117	37	7	+	+	CCONJ
iajs-117	37	8	(n	(n	X
iajs-117	37	9	)	)	PUNCT
iajs-117	38	1	=	=	SYM
iajs-117	38	2	n	n	NOUN
iajs-117	38	3	+	+	NUM
iajs-117	38	4	n	n	CCONJ
iajs-117	38	5	+	+	CCONJ
iajs-117	38	6			PROPN
iajs-117	38	7	2	2	NUM
iajs-117	38	8			NOUN
iajs-117	38	9	=	=	PUNCT
iajs-117	38	10			PROPN
iajs-117	38	11	2	2	NUM
iajs-117	38	12			NOUN
iajs-117	38	13	.therefore	.therefore	ADP
iajs-117	39	1	n	n	PROPN
iajs-117	39	2	=	=	SYM
iajs-117	39	3			PROPN
iajs-117	39	4	4	4	NUM
iajs-117	39	5			PRON
iajs-117	39	6	is	be	AUX
iajs-117	39	7	a	a	DET
iajs-117	39	8	-prime	-prime	ADJ
iajs-117	39	9	submodule	submodule	NOUN
iajs-117	39	10	of	of	ADP
iajs-117	39	11	z8	z8	PROPN
iajs-117	39	12	.	.	PUNCT
iajs-117	40	1	(	(	PUNCT
iajs-117	40	2	2	2	X
iajs-117	40	3	)	)	PUNCT
iajs-117	40	4	if	if	SCONJ
iajs-117	40	5	(n	(n	NOUN
iajs-117	40	6	)	)	PUNCT
iajs-117	40	7			PROPN
iajs-117	40	8	n	n	PROPN
iajs-117	40	9	or	or	CCONJ
iajs-117	40	10	(n	(n	NOUN
iajs-117	40	11	)	)	PUNCT
iajs-117	41	1	=	=	SYM
iajs-117	41	2	0	0	NUM
iajs-117	41	3	,	,	PUNCT
iajs-117	41	4	then	then	ADV
iajs-117	41	5	every	every	DET
iajs-117	41	6	-prime	-prime	ADJ
iajs-117	41	7	submodule	submodule	NOUN
iajs-117	41	8	of	of	ADP
iajs-117	41	9	m	m	PROPN
iajs-117	41	10	is	be	AUX
iajs-117	41	11	a	a	DET
iajs-117	41	12	prime	prime	ADJ
iajs-117	41	13	submodule	submodule	NOUN
iajs-117	41	14	.	.	PUNCT
iajs-117	42	1	(	(	PUNCT
iajs-117	42	2	3	3	X
iajs-117	42	3	)	)	PUNCT
iajs-117	42	4	let	let	VERB
iajs-117	42	5	n	n	PRON
iajs-117	42	6	,	,	PUNCT
iajs-117	42	7	w	w	PROPN
iajs-117	42	8	be	be	AUX
iajs-117	42	9	two	two	NUM
iajs-117	42	10	submodules	submodule	NOUN
iajs-117	42	11	of	of	ADP
iajs-117	42	12	an	an	DET
iajs-117	42	13	rmodule	rmodule	NOUN
iajs-117	42	14	m	m	NOUN
iajs-117	42	15	and	and	CCONJ
iajs-117	42	16	nw	nw	ADJ
iajs-117	42	17	.	.	PUNCT
iajs-117	43	1	if	if	SCONJ
iajs-117	43	2	n	n	NOUN
iajs-117	43	3	is	be	AUX
iajs-117	43	4	-prime	-prime	PROPN
iajs-117	43	5	submodule	submodule	NOUN
iajs-117	43	6	of	of	ADP
iajs-117	43	7	m	m	PROPN
iajs-117	43	8	and	and	CCONJ
iajs-117	43	9	(n	(n	PROPN
iajs-117	43	10	)	)	PUNCT
iajs-117	43	11			PROPN
iajs-117	43	12			PROPN
iajs-117	43	13	'	'	PUNCT
iajs-117	43	14	(	(	PUNCT
iajs-117	43	15	n	n	CCONJ
iajs-117	43	16	)	)	PUNCT
iajs-117	43	17	,	,	PUNCT
iajs-117	43	18	where	where	SCONJ
iajs-117	43	19			NOUN
iajs-117	43	20	'	'	PUNCT
iajs-117	43	21	:	:	PUNCT
iajs-117	43	22	(w	(w	NUM
iajs-117	43	23	)	)	PUNCT
iajs-117	43	24			PROPN
iajs-117	43	25	(w	(w	NUM
iajs-117	43	26	)	)	PUNCT
iajs-117	43	27			NOUN
iajs-117	43	28	{	{	PUNCT
iajs-117	43	29			NOUN
iajs-117	43	30	}	}	PUNCT
iajs-117	43	31	and	and	CCONJ
iajs-117	43	32			NOUN
iajs-117	43	33	:	:	PUNCT
iajs-117	43	34	(m	(m	PROPN
iajs-117	43	35	)	)	PUNCT
iajs-117	43	36			PROPN
iajs-117	43	37	(m	(m	PROPN
iajs-117	43	38	)	)	PUNCT
iajs-117	43	39			NOUN
iajs-117	43	40	{	{	PUNCT
iajs-117	43	41			NOUN
iajs-117	43	42	}	}	PUNCT
iajs-117	43	43	,	,	PUNCT
iajs-117	43	44	then	then	ADV
iajs-117	43	45	n	n	PRON
iajs-117	43	46	is	be	AUX
iajs-117	43	47	'-prime	'-prime	ADV
iajs-117	43	48	submodule	submodule	NOUN
iajs-117	43	49	of	of	ADP
iajs-117	43	50	w	w	PROPN
iajs-117	43	51	.	.	PUNCT
iajs-117	44	1	proof	proof	NOUN
iajs-117	44	2	:	:	PUNCT
iajs-117	44	3	let	let	VERB
iajs-117	44	4	rr	rr	CCONJ
iajs-117	44	5	,	,	PUNCT
iajs-117	44	6	mw	mw	VERB
iajs-117	44	7	such	such	ADJ
iajs-117	44	8	that	that	DET
iajs-117	44	9	rm	rm	PROPN
iajs-117	44	10	n	n	PROPN
iajs-117	44	11	.	.	PUNCT
iajs-117	45	1	since	since	SCONJ
iajs-117	45	2	n	n	NUM
iajs-117	45	3	is	be	AUX
iajs-117	45	4	-prime	-prime	PROPN
iajs-117	45	5	submodule	submodule	NOUN
iajs-117	45	6	of	of	ADP
iajs-117	45	7	m	m	PROPN
iajs-117	45	8	,	,	PUNCT
iajs-117	45	9	so	so	ADV
iajs-117	45	10	either	either	CCONJ
iajs-117	45	11	m	m	PROPN
iajs-117	45	12	n	n	NOUN
iajs-117	45	13	+	+	CCONJ
iajs-117	45	14	(n	(n	X
iajs-117	45	15	)	)	PUNCT
iajs-117	45	16	or	or	CCONJ
iajs-117	45	17	r	r	NOUN
iajs-117	45	18	m	m	NOUN
iajs-117	45	19			PROPN
iajs-117	45	20	n	n	PROPN
iajs-117	45	21	+	+	CCONJ
iajs-117	45	22	(n	(n	X
iajs-117	45	23	)	)	PUNCT
iajs-117	45	24	.	.	PUNCT
iajs-117	46	1	but	but	CCONJ
iajs-117	46	2	(n	(n	X
iajs-117	46	3	)	)	PUNCT
iajs-117	46	4			PROPN
iajs-117	46	5			PROPN
iajs-117	46	6	'	'	PUNCT
iajs-117	46	7	(	(	PUNCT
iajs-117	46	8	n	n	CCONJ
iajs-117	46	9	)	)	PUNCT
iajs-117	46	10	,	,	PUNCT
iajs-117	46	11	so	so	CCONJ
iajs-117	46	12	either	either	CCONJ
iajs-117	46	13	m	m	PROPN
iajs-117	46	14	n	n	NOUN
iajs-117	47	1	+	+	CCONJ
iajs-117	48	1			NOUN
iajs-117	48	2	'	'	PUNCT
iajs-117	48	3	(	(	PUNCT
iajs-117	48	4	n	n	CCONJ
iajs-117	48	5	)	)	PUNCT
iajs-117	48	6	or	or	CCONJ
iajs-117	48	7	r	r	NOUN
iajs-117	48	8	m	m	NOUN
iajs-117	48	9			PROPN
iajs-117	48	10	n	n	PROPN
iajs-117	48	11	+	+	CCONJ
iajs-117	48	12			NOUN
iajs-117	48	13	'	'	PUNCT
iajs-117	48	14	(	(	PUNCT
iajs-117	48	15	n	n	CCONJ
iajs-117	48	16	)	)	PUNCT
iajs-117	48	17	,	,	PUNCT
iajs-117	48	18	so	so	CCONJ
iajs-117	48	19	either	either	CCONJ
iajs-117	48	20	mn	mn	PROPN
iajs-117	49	1	+	+	CCONJ
iajs-117	49	2			NOUN
iajs-117	49	3	'	'	PUNCT
iajs-117	49	4	(	(	PUNCT
iajs-117	49	5	n	n	CCONJ
iajs-117	49	6	)	)	PUNCT
iajs-117	49	7	or	or	CCONJ
iajs-117	49	8	r	r	NOUN
iajs-117	49	9	w	w	NOUN
iajs-117	49	10			PROPN
iajs-117	50	1	n	n	PROPN
iajs-117	50	2	+	+	CCONJ
iajs-117	50	3			NOUN
iajs-117	50	4	'	'	PUNCT
iajs-117	50	5	(	(	PUNCT
iajs-117	50	6	n	n	CCONJ
iajs-117	50	7	)	)	PUNCT
iajs-117	50	8	.therefore	.therefore	PUNCT
iajs-117	51	1	n	n	ADV
iajs-117	51	2	is	be	AUX
iajs-117	51	3	'-prime	'-prime	X
iajs-117	51	4	submodule	submodule	NOUN
iajs-117	51	5	of	of	ADP
iajs-117	51	6	w	w	PROPN
iajs-117	51	7	.	.	PUNCT
iajs-117	52	1	(	(	PUNCT
iajs-117	52	2	4	4	X
iajs-117	52	3	)	)	PUNCT
iajs-117	52	4	given	give	VERB
iajs-117	52	5	two	two	NUM
iajs-117	52	6	functions	function	NOUN
iajs-117	52	7	,	,	NOUN
iajs-117	52	8	'	'	PUNCT
iajs-117	52	9	:	:	PUNCT
iajs-117	52	10	(m	(m	PROPN
iajs-117	52	11	)	)	PUNCT
iajs-117	52	12			PROPN
iajs-117	52	13	(m	(m	PROPN
iajs-117	52	14	)	)	PUNCT
iajs-117	52	15			NOUN
iajs-117	52	16	{	{	PUNCT
iajs-117	52	17	}such	}such	ADP
iajs-117	52	18	that	that	DET
iajs-117	52	19			NOUN
iajs-117	52	20			NUM
iajs-117	52	21			NOUN
iajs-117	52	22	'	'	PUNCT
iajs-117	52	23	and	and	CCONJ
iajs-117	52	24	(n	(n	NOUN
iajs-117	52	25	)	)	PUNCT
iajs-117	53	1			PROPN
iajs-117	53	2			PROPN
iajs-117	53	3	'	'	PUNCT
iajs-117	53	4	(	(	PUNCT
iajs-117	53	5	n	n	CCONJ
iajs-117	53	6	)	)	PUNCT
iajs-117	53	7	for	for	ADP
iajs-117	53	8	each	each	DET
iajs-117	53	9	n	n	DET
iajs-117	53	10	(m	(m	NOUN
iajs-117	53	11	)	)	PUNCT
iajs-117	53	12	.	.	PUNCT
iajs-117	54	1	if	if	SCONJ
iajs-117	54	2	n	n	PRON
iajs-117	54	3	is	be	AUX
iajs-117	54	4	a	a	DET
iajs-117	54	5	-prime	-prime	ADJ
iajs-117	54	6	submodule	submodule	NOUN
iajs-117	54	7	of	of	ADP
iajs-117	54	8	m	m	PROPN
iajs-117	54	9	implies	imply	VERB
iajs-117	54	10	n	n	AUX
iajs-117	54	11	is	be	AUX
iajs-117	54	12	'-prime	'-prime	ADV
iajs-117	54	13	submodule	submodule	NOUN
iajs-117	54	14	of	of	ADP
iajs-117	54	15	m	m	PROPN
iajs-117	54	16	.	.	PUNCT
iajs-117	55	1	proof	proof	NOUN
iajs-117	55	2	:	:	PUNCT
iajs-117	55	3	let	let	VERB
iajs-117	55	4	rr	rr	CCONJ
iajs-117	55	5	,	,	PUNCT
iajs-117	55	6	mm	mm	NUM
iajs-117	55	7	such	such	ADJ
iajs-117	55	8	that	that	DET
iajs-117	55	9	rm	rm	PROPN
iajs-117	55	10	n	n	PROPN
iajs-117	55	11	.	.	PUNCT
iajs-117	56	1	since	since	SCONJ
iajs-117	56	2	n	n	NUM
iajs-117	56	3	is	be	AUX
iajs-117	56	4	-prime	-prime	PROPN
iajs-117	56	5	submodule	submodule	NOUN
iajs-117	56	6	of	of	ADP
iajs-117	56	7	m	m	PROPN
iajs-117	56	8	,	,	PUNCT
iajs-117	56	9	so	so	ADV
iajs-117	56	10	either	either	CCONJ
iajs-117	56	11	m	m	PROPN
iajs-117	56	12	n	n	NOUN
iajs-117	56	13	+	+	CCONJ
iajs-117	56	14	(n	(n	X
iajs-117	56	15	)	)	PUNCT
iajs-117	56	16	or	or	CCONJ
iajs-117	56	17	r	r	NOUN
iajs-117	56	18	m	m	NOUN
iajs-117	56	19			PROPN
iajs-117	56	20	n	n	PROPN
iajs-117	56	21	+	+	CCONJ
iajs-117	56	22	(n	(n	X
iajs-117	56	23	)	)	PUNCT
iajs-117	56	24	.	.	PUNCT
iajs-117	57	1	but	but	CCONJ
iajs-117	57	2	(n	(n	X
iajs-117	57	3	)	)	PUNCT
iajs-117	57	4			PROPN
iajs-117	57	5			PROPN
iajs-117	57	6	'	'	PUNCT
iajs-117	57	7	(	(	PUNCT
iajs-117	57	8	n	n	CCONJ
iajs-117	57	9	)	)	PUNCT
iajs-117	57	10	,	,	PUNCT
iajs-117	57	11	so	so	CCONJ
iajs-117	57	12	either	either	CCONJ
iajs-117	57	13	m	m	PROPN
iajs-117	57	14	n	n	NOUN
iajs-117	58	1	+	+	CCONJ
iajs-117	59	1			NOUN
iajs-117	59	2	'	'	PUNCT
iajs-117	59	3	(	(	PUNCT
iajs-117	59	4	n	n	CCONJ
iajs-117	59	5	)	)	PUNCT
iajs-117	59	6	or	or	CCONJ
iajs-117	59	7	r	r	NOUN
iajs-117	59	8	m	m	NOUN
iajs-117	59	9			PROPN
iajs-117	59	10	n	n	PROPN
iajs-117	59	11	+	+	CCONJ
iajs-117	59	12			NOUN
iajs-117	59	13	'	'	PUNCT
iajs-117	59	14	(	(	PUNCT
iajs-117	59	15	n	n	CCONJ
iajs-117	59	16	)	)	PUNCT
iajs-117	59	17	.	.	PUNCT
iajs-117	60	1	therefore	therefore	ADV
iajs-117	60	2	n	n	PRON
iajs-117	60	3	is	be	AUX
iajs-117	60	4	'-prime	'-prime	ADV
iajs-117	60	5	submodule	submodule	NOUN
iajs-117	60	6	of	of	ADP
iajs-117	60	7	m	m	PROPN
iajs-117	60	8	.	.	PUNCT
iajs-117	61	1	mathematics	mathematic	NOUN
iajs-117	61	2	|	|	ADV
iajs-117	61	3	284	284	NUM
iajs-117	61	4	2016	2016	NUM
iajs-117	61	5	)	)	PUNCT
iajs-117	61	6	عام	عام	ADP
iajs-117	61	7	2العدد	2العدد	NUM
iajs-117	61	8	(	(	PUNCT
iajs-117	61	9	29لمجلد	29لمجلد	NUM
iajs-117	61	10	ا	ا	X
iajs-117	61	11	مجلة	مجلة	NOUN
iajs-117	61	12	إبن	إبن	VERB
iajs-117	61	13	الهيثم	الهيثم	ADJ
iajs-117	61	14	للعلوم	للعلوم	NOUN
iajs-117	61	15	الصرفة	الصرفة	NOUN
iajs-117	62	1	و	و	PRON
iajs-117	62	2	التطبيقية	التطبيقية	ADJ
iajs-117	62	3	ibn	ibn	PROPN
iajs-117	62	4	al	al	PROPN
iajs-117	62	5	-	-	PUNCT
iajs-117	62	6	haitham	haitham	PROPN
iajs-117	62	7	jour	jour	X
iajs-117	62	8	.	.	PROPN
iajs-117	62	9	for	for	ADP
iajs-117	62	10	pure	pure	ADJ
iajs-117	62	11	&	&	CCONJ
iajs-117	62	12	appl	appl	PROPN
iajs-117	62	13	.	.	PUNCT
iajs-117	63	1	sci	sci	PROPN
iajs-117	63	2	.	.	PUNCT
iajs-117	63	3	vol	vol	NOUN
iajs-117	63	4	.	.	PROPN
iajs-117	63	5	29	29	NUM
iajs-117	63	6	(	(	PUNCT
iajs-117	63	7	2	2	NUM
iajs-117	63	8	)	)	PUNCT
iajs-117	63	9	2016	2016	NUM
iajs-117	63	10	(	(	PUNCT
iajs-117	63	11	5	5	X
iajs-117	63	12	)	)	PUNCT
iajs-117	63	13	let	let	VERB
iajs-117	63	14	n	n	PRON
iajs-117	63	15	and	and	CCONJ
iajs-117	63	16	w	w	PROPN
iajs-117	63	17	be	be	AUX
iajs-117	63	18	two	two	NUM
iajs-117	63	19	submodules	submodule	NOUN
iajs-117	63	20	of	of	ADP
iajs-117	63	21	an	an	DET
iajs-117	63	22	r	r	NOUN
iajs-117	63	23	–	–	PUNCT
iajs-117	63	24	module	module	NOUN
iajs-117	63	25	m	m	NOUN
iajs-117	63	26	such	such	ADJ
iajs-117	63	27	that	that	SCONJ
iajs-117	63	28	nw	nw	NOUN
iajs-117	63	29	.	.	PUNCT
iajs-117	64	1	if	if	SCONJ
iajs-117	64	2	n	n	PRON
iajs-117	64	3	is	be	AUX
iajs-117	64	4	-prime	-prime	PROPN
iajs-117	64	5	submodule	submodule	NOUN
iajs-117	64	6	of	of	ADP
iajs-117	64	7	m	m	PRON
iajs-117	64	8	then	then	ADV
iajs-117	64	9	it	it	PRON
iajs-117	64	10	is	be	AUX
iajs-117	64	11	not	not	PART
iajs-117	64	12	necessary	necessary	ADJ
iajs-117	64	13	that	that	SCONJ
iajs-117	64	14	w	w	NOUN
iajs-117	64	15	is	be	AUX
iajs-117	64	16	-prime	-prime	PROPN
iajs-117	64	17	submodule	submodule	NOUN
iajs-117	64	18	of	of	ADP
iajs-117	64	19	m	m	PRON
iajs-117	64	20	as	as	SCONJ
iajs-117	64	21	the	the	DET
iajs-117	64	22	following	following	ADJ
iajs-117	64	23	example	example	NOUN
iajs-117	64	24	explains	explain	VERB
iajs-117	64	25	:	:	PUNCT
iajs-117	64	26	consider	consider	VERB
iajs-117	64	27	the	the	DET
iajs-117	64	28	z	z	NOUN
iajs-117	64	29	–	–	PUNCT
iajs-117	64	30	module	module	NOUN
iajs-117	64	31	z	z	NOUN
iajs-117	64	32	,	,	PUNCT
iajs-117	64	33	the	the	DET
iajs-117	64	34	submodule	submodule	NOUN
iajs-117	64	35	2z	2z	NUM
iajs-117	64	36	is	be	AUX
iajs-117	64	37	-prime	-prime	ADJ
iajs-117	64	38	submodule	submodule	NOUN
iajs-117	64	39	of	of	ADP
iajs-117	64	40	z(since	z(since	NOUN
iajs-117	64	41	it	it	PRON
iajs-117	64	42	is	be	AUX
iajs-117	64	43	prime	prime	ADJ
iajs-117	64	44	)	)	PUNCT
iajs-117	65	1	but	but	CCONJ
iajs-117	65	2	2z	2z	NUM
iajs-117	65	3			PROPN
iajs-117	65	4	30z	30z	NOUN
iajs-117	65	5	and	and	CCONJ
iajs-117	65	6	30z	30z	NOUN
iajs-117	65	7	is	be	AUX
iajs-117	65	8	not	not	PART
iajs-117	65	9	-prime	-prime	ADV
iajs-117	65	10	submodule	submodule	NOUN
iajs-117	65	11	of	of	ADP
iajs-117	65	12	z	z	PROPN
iajs-117	65	13	.since	.since	NOUN
iajs-117	65	14	if	if	SCONJ
iajs-117	65	15	(n	(n	X
iajs-117	65	16	)	)	PUNCT
iajs-117	65	17	=	=	SYM
iajs-117	65	18	n	n	X
iajs-117	65	19	,	,	PUNCT
iajs-117	65	20			VERB
iajs-117	65	21	n	n	ADV
iajs-117	65	22	m	m	PROPN
iajs-117	65	23	and	and	CCONJ
iajs-117	65	24	6.5	6.5	NUM
iajs-117	65	25	=	=	SYM
iajs-117	65	26	30	30	NUM
iajs-117	65	27			NOUN
iajs-117	65	28	30z	30z	NOUN
iajs-117	65	29	but	but	CCONJ
iajs-117	65	30	5	5	NUM
iajs-117	65	31	30z	30z	NOUN
iajs-117	65	32	+30z	+30z	PUNCT
iajs-117	66	1	=	=	NOUN
iajs-117	66	2	30z	30z	NOUN
iajs-117	66	3	and	and	CCONJ
iajs-117	66	4	6z	6z	NUM
iajs-117	66	5	⊈	⊈	PROPN
iajs-117	66	6	30	30	NUM
iajs-117	66	7	z	z	NOUN
iajs-117	66	8	+30z	+30z	PUNCT
iajs-117	66	9	=	=	NOUN
iajs-117	66	10	30z	30z	X
iajs-117	66	11	.	.	PUNCT
iajs-117	67	1	(	(	PUNCT
iajs-117	67	2	6	6	X
iajs-117	67	3	)	)	PUNCT
iajs-117	67	4	let	let	VERB
iajs-117	67	5	m	m	NOUN
iajs-117	67	6	=	=	VERB
iajs-117	67	7	z4	z4	PROPN
iajs-117	67	8	as	as	ADP
iajs-117	67	9	z	z	NOUN
iajs-117	67	10	-	-	PUNCT
iajs-117	67	11	module	module	NOUN
iajs-117	67	12	,	,	PUNCT
iajs-117	67	13	n	n	NOUN
iajs-117	67	14	=	=	SYM
iajs-117	67	15	{	{	PUNCT
iajs-117	67	16	0	0	NUM
iajs-117	67	17	,	,	PUNCT
iajs-117	67	18	2}.since	2}.since	NUM
iajs-117	67	19	n	n	X
iajs-117	67	20	is	be	AUX
iajs-117	67	21	prime	prime	ADJ
iajs-117	67	22	,	,	PUNCT
iajs-117	67	23	then	then	ADV
iajs-117	67	24	n	n	PRON
iajs-117	67	25	is	be	AUX
iajs-117	67	26	-prime	-prime	ADJ
iajs-117	67	27	submodule	submodule	NOUN
iajs-117	67	28	of	of	ADP
iajs-117	67	29	m.	m.	NOUN
iajs-117	67	30	(	(	PUNCT
iajs-117	67	31	7	7	X
iajs-117	67	32	)	)	PUNCT
iajs-117	67	33	let	let	VERB
iajs-117	67	34	m	m	VERB
iajs-117	67	35	=	=	VERB
iajs-117	67	36	z12	z12	NUM
iajs-117	67	37	as	as	ADP
iajs-117	67	38	a	a	DET
iajs-117	67	39	z	z	NOUN
iajs-117	67	40	–	–	PUNCT
iajs-117	67	41	module	module	NOUN
iajs-117	67	42	and	and	CCONJ
iajs-117	67	43	n	n	NOUN
iajs-117	67	44	=	=	NOUN
iajs-117	67	45	6	6	NOUN
iajs-117	67	46	and	and	CCONJ
iajs-117	67	47	let	let	VERB
iajs-117	67	48			NOUN
iajs-117	67	49	:	:	PUNCT
iajs-117	67	50	(z12	(z12	NOUN
iajs-117	67	51	)	)	PUNCT
iajs-117	67	52	(z12	(z12	NOUN
iajs-117	67	53	)	)	PUNCT
iajs-117	67	54			NOUN
iajs-117	67	55	{	{	PUNCT
iajs-117	67	56			NOUN
iajs-117	67	57	}	}	PUNCT
iajs-117	67	58	.	.	PUNCT
iajs-117	68	1	if	if	SCONJ
iajs-117	68	2	(n	(n	X
iajs-117	68	3	)	)	PUNCT
iajs-117	68	4	=	=	SYM
iajs-117	68	5	n+	n+	NUM
iajs-117	68	6			PROPN
iajs-117	68	7	2	2	NUM
iajs-117	68	8			PROPN
iajs-117	68	9	,	,	PUNCT
iajs-117	68	10			NOUN
iajs-117	68	11	n	n	PRON
iajs-117	68	12	{6	{6	NOUN
iajs-117	68	13			NOUN
iajs-117	68	14	,	,	PUNCT
iajs-117	68	15			PROPN
iajs-117	68	16	2	2	NUM
iajs-117	68	17			INTJ
iajs-117	68	18	,	,	PUNCT
iajs-117	68	19			PROPN
iajs-117	68	20	4	4	NUM
iajs-117	68	21	,	,	NOUN
iajs-117	68	22	0	0	NUM
iajs-117	68	23			PROPN
iajs-117	68	24	}	}	PUNCT
iajs-117	68	25	and	and	CCONJ
iajs-117	68	26	(n	(n	X
iajs-117	68	27	)	)	PUNCT
iajs-117	68	28	=	=	SYM
iajs-117	69	1	n	n	X
iajs-117	69	2	where	where	SCONJ
iajs-117	69	3	n	n	ADP
iajs-117	69	4	{m	{m	NOUN
iajs-117	69	5	,	,	PUNCT
iajs-117	69	6	3}.therefore	3}.therefore	NOUN
iajs-117	69	7	6	6	NOUN
iajs-117	69	8	=	=	SYM
iajs-117	69	9	6	6	NOUN
iajs-117	69	10	+	+	NUM
iajs-117	69	11	2	2	NOUN
iajs-117	69	12	=	=	SYM
iajs-117	69	13	2	2	NOUN
iajs-117	69	14	and	and	CCONJ
iajs-117	69	15			NOUN
iajs-117	69	16	x	x	PROPN
iajs-117	69	17	z12	z12	PROPN
iajs-117	69	18	,	,	PUNCT
iajs-117	69	19	rz	rz	PROPN
iajs-117	69	20	then	then	ADV
iajs-117	69	21	either	either	CCONJ
iajs-117	69	22	x	x	PROPN
iajs-117	69	23	6	6	PROPN
iajs-117	69	24	+	+	CCONJ
iajs-117	69	25	2	2	NOUN
iajs-117	69	26	=	=	SYM
iajs-117	69	27	2	2	NOUN
iajs-117	69	28	or	or	CCONJ
iajs-117	69	29	r	r	NOUN
iajs-117	69	30	z12	z12	NUM
iajs-117	69	31			PROPN
iajs-117	69	32	6	6	NOUN
iajs-117	69	33	+	+	PUNCT
iajs-117	69	34	2	2	NOUN
iajs-117	69	35	=	=	SYM
iajs-117	69	36	2	2	NOUN
iajs-117	69	37	.	.	PUNCT
iajs-117	70	1	hence	hence	ADV
iajs-117	70	2	n	n	PRON
iajs-117	70	3	is	be	AUX
iajs-117	70	4	a	a	DET
iajs-117	70	5	-prime	-prime	ADJ
iajs-117	70	6	submodule	submodule	NOUN
iajs-117	70	7	of	of	ADP
iajs-117	70	8	m.	m.	NOUN
iajs-117	70	9	(	(	PUNCT
iajs-117	70	10	8)	8)	NUM
iajs-117	70	11	{	{	PUNCT
iajs-117	70	12	0	0	NUM
iajs-117	70	13	}	}	PUNCT
iajs-117	70	14	is	be	AUX
iajs-117	70	15	the	the	DET
iajs-117	70	16	only	only	ADJ
iajs-117	70	17	-prime	-prime	NOUN
iajs-117	70	18	submoduleof	submoduleof	X
iajs-117	70	19	a	a	DET
iajs-117	70	20	simple	simple	ADJ
iajs-117	70	21	modules.therefore	modules.therefore	NOUN
iajs-117	70	22	(	(	PUNCT
iajs-117	70	23	0	0	NUM
iajs-117	70	24	)	)	PUNCT
iajs-117	70	25	of	of	ADP
iajs-117	70	26	a	a	DET
iajs-117	70	27	simple	simple	ADJ
iajs-117	70	28	zmodule	zmodule	NOUN
iajs-117	70	29	zp	zp	PROPN
iajs-117	70	30	(	(	PUNCT
iajs-117	70	31	p	p	NOUN
iajs-117	70	32	is	be	AUX
iajs-117	70	33	prime	prime	ADJ
iajs-117	70	34	)	)	PUNCT
iajs-117	70	35	is	be	AUX
iajs-117	70	36	-prime	-prime	ADJ
iajs-117	70	37	submodule	submodule	NOUN
iajs-117	70	38	.	.	PUNCT
iajs-117	71	1	(	(	PUNCT
iajs-117	71	2	9	9	X
iajs-117	71	3	)	)	PUNCT
iajs-117	71	4	let	let	VERB
iajs-117	71	5	m	m	NOUN
iajs-117	71	6	=	=	NOUN
iajs-117	71	7	z	z	PROPN
iajs-117	71	8			PROPN
iajs-117	71	9	z	z	PROPN
iajs-117	71	10	as	as	ADP
iajs-117	71	11	a	a	DET
iajs-117	71	12	z	z	NOUN
iajs-117	71	13	-	-	PUNCT
iajs-117	71	14	module	module	NOUN
iajs-117	71	15	,	,	PUNCT
iajs-117	71	16	n	n	NOUN
iajs-117	71	17	=	=	SYM
iajs-117	71	18	2z(0	2z(0	NUM
iajs-117	71	19	)	)	PUNCT
iajs-117	71	20	and	and	CCONJ
iajs-117	71	21	let	let	VERB
iajs-117	71	22	:(m	:(m	ADJ
iajs-117	71	23	)	)	PUNCT
iajs-117	71	24			PROPN
iajs-117	71	25	(m	(m	PROPN
iajs-117	71	26	)	)	PUNCT
iajs-117	71	27			NOUN
iajs-117	71	28	{	{	PUNCT
iajs-117	71	29	}.if	}.if	NOUN
iajs-117	71	30	(n	(n	X
iajs-117	71	31	)	)	PUNCT
iajs-117	71	32	=	=	SYM
iajs-117	71	33	n	n	CCONJ
iajs-117	71	34	,	,	PUNCT
iajs-117	71	35			NOUN
iajs-117	71	36	n	n	PRON
iajs-117	71	37			PROPN
iajs-117	71	38	m	m	PROPN
iajs-117	71	39	,	,	PUNCT
iajs-117	71	40	then	then	ADV
iajs-117	71	41	n	n	PRON
iajs-117	71	42	is	be	AUX
iajs-117	71	43	not	not	PART
iajs-117	71	44	-prime	-prime	ADJ
iajs-117	71	45	submodule	submodule	NOUN
iajs-117	71	46	of	of	ADP
iajs-117	71	47	m.	m.	NOUN
iajs-117	71	48	(	(	PUNCT
iajs-117	71	49	10	10	NUM
iajs-117	71	50	)	)	PUNCT
iajs-117	71	51	i	i	PRON
iajs-117	71	52	is	be	AUX
iajs-117	71	53	a	a	DET
iajs-117	71	54	-prime	-prime	ADJ
iajs-117	71	55	ideal	ideal	NOUN
iajs-117	71	56	of	of	ADP
iajs-117	71	57	r	r	NOUN
iajs-117	71	58	if	if	SCONJ
iajs-117	72	1	and	and	CCONJ
iajs-117	72	2	only	only	ADV
iajs-117	72	3	if	if	SCONJ
iajs-117	72	4	i	i	PRON
iajs-117	72	5	is	be	AUX
iajs-117	72	6	a	a	DET
iajs-117	72	7	-prime	-prime	ADJ
iajs-117	72	8	submodule	submodule	NOUN
iajs-117	72	9	of	of	ADP
iajs-117	72	10	r.	r.	PROPN
iajs-117	72	11	now	now	ADV
iajs-117	72	12	,	,	PUNCT
iajs-117	72	13	if	if	SCONJ
iajs-117	72	14	n	n	PRON
iajs-117	72	15	is	be	AUX
iajs-117	72	16	a	a	DET
iajs-117	72	17	prime	prime	ADJ
iajs-117	72	18	submodule	submodule	NOUN
iajs-117	72	19	,	,	PUNCT
iajs-117	72	20	then	then	ADV
iajs-117	72	21	sometimes	sometimes	ADV
iajs-117	72	22	n	n	PRON
iajs-117	72	23	is	be	AUX
iajs-117	72	24	called	call	VERB
iajs-117	72	25	p	p	NOUN
iajs-117	72	26	–	–	PUNCT
iajs-117	72	27	prime	prime	ADJ
iajs-117	72	28	submodule	submodule	NOUN
iajs-117	72	29	,	,	PUNCT
iajs-117	72	30	where	where	SCONJ
iajs-117	72	31	p	p	NOUN
iajs-117	73	1	=	=	PUNCT
iajs-117	74	1	[	[	X
iajs-117	74	2	n	n	X
iajs-117	74	3	:	:	PUNCT
iajs-117	74	4	m	m	X
iajs-117	74	5	]	]	X
iajs-117	74	6	,	,	PUNCT
iajs-117	74	7	[	[	X
iajs-117	74	8	4	4	NUM
iajs-117	74	9	]	]	PUNCT
iajs-117	74	10	.	.	PUNCT
iajs-117	75	1	for	for	ADP
iajs-117	75	2	a	a	DET
iajs-117	75	3	-prime	-prime	NOUN
iajs-117	75	4	,	,	PUNCT
iajs-117	75	5	we	we	PRON
iajs-117	75	6	called	call	VERB
iajs-117	75	7	p-prime	p-prime	NOUN
iajs-117	75	8	submodule	submodule	NOUN
iajs-117	75	9	,	,	PUNCT
iajs-117	75	10	where	where	SCONJ
iajs-117	75	11	p	p	NOUN
iajs-117	75	12	=	=	X
iajs-117	76	1	[	[	X
iajs-117	76	2	n	n	X
iajs-117	76	3	+	+	NOUN
iajs-117	76	4	(n	(n	X
iajs-117	76	5	)	)	PUNCT
iajs-117	76	6	:	:	PUNCT
iajs-117	76	7	m	m	VERB
iajs-117	76	8	]	]	X
iajs-117	76	9	.	.	PUNCT
iajs-117	77	1	the	the	DET
iajs-117	77	2	following	follow	VERB
iajs-117	77	3	theorem	theorem	NOUN
iajs-117	77	4	gives	give	VERB
iajs-117	77	5	some	some	DET
iajs-117	77	6	characterizations	characterization	NOUN
iajs-117	77	7	for	for	ADP
iajs-117	77	8	-prime	-prime	ADJ
iajs-117	77	9	submodules	submodule	NOUN
iajs-117	77	10	.	.	PUNCT
iajs-117	78	1	theorem(2.3	theorem(2.3	NOUN
iajs-117	78	2	):	):	PUNCT
iajs-117	78	3	let	let	VERB
iajs-117	78	4	n	n	PRON
iajs-117	78	5	be	be	AUX
iajs-117	78	6	a	a	DET
iajs-117	78	7	proper	proper	ADJ
iajs-117	78	8	submodule	submodule	NOUN
iajs-117	78	9	of	of	ADP
iajs-117	78	10	an	an	DET
iajs-117	78	11	rmodule	rmodule	NOUN
iajs-117	78	12	m	m	PROPN
iajs-117	78	13	and	and	CCONJ
iajs-117	78	14	p=	p=	ADJ
iajs-117	78	15	n	n	CCONJ
iajs-117	78	16			NOUN
iajs-117	78	17	n	n	NOUN
iajs-117	78	18	:	:	PUNCT
iajs-117	78	19	m	m	VERB
iajs-117	78	20	.then	.then	ADJ
iajs-117	78	21	,	,	PUNCT
iajs-117	78	22	the	the	DET
iajs-117	78	23	following	follow	VERB
iajs-117	78	24	statements	statement	NOUN
iajs-117	78	25	are	be	AUX
iajs-117	78	26	equivalent	equivalent	ADJ
iajs-117	78	27	:	:	PUNCT
iajs-117	78	28	1	1	X
iajs-117	78	29	.	.	X
iajs-117	78	30	n	n	PRON
iajs-117	78	31	is	be	AUX
iajs-117	78	32	-prime	-prime	PROPN
iajs-117	78	33	submodule	submodule	NOUN
iajs-117	78	34	of	of	ADP
iajs-117	78	35	m.	m.	NOUN
iajs-117	78	36	2	2	NUM
iajs-117	78	37	.	.	PUNCT
iajs-117	79	1	for	for	ADP
iajs-117	79	2	every	every	DET
iajs-117	79	3	submodule	submodule	NOUN
iajs-117	79	4	k	k	PROPN
iajs-117	79	5	of	of	ADP
iajs-117	79	6	m	m	PROPN
iajs-117	79	7	and	and	CCONJ
iajs-117	79	8	for	for	ADP
iajs-117	79	9	every	every	DET
iajs-117	79	10	an	an	DET
iajs-117	79	11	ideal	ideal	NOUN
iajs-117	79	12	i	i	PRON
iajs-117	79	13	of	of	ADP
iajs-117	79	14	r	r	NOUN
iajs-117	79	15	such	such	ADJ
iajs-117	79	16	that	that	SCONJ
iajs-117	79	17	ik	ik	X
iajs-117	79	18	n	n	CCONJ
iajs-117	79	19	,	,	PUNCT
iajs-117	79	20	implies	imply	VERB
iajs-117	79	21	that	that	SCONJ
iajs-117	79	22	either	either	CCONJ
iajs-117	79	23	k	k	CCONJ
iajs-117	79	24	n	n	PRON
iajs-117	79	25			NOUN
iajs-117	79	26	n	n	NOUN
iajs-117	79	27	or	or	CCONJ
iajs-117	79	28	i	i	VERB
iajs-117	79	29	p	p	PROPN
iajs-117	79	30	n	n	PRON
iajs-117	79	31			NOUN
iajs-117	79	32	n	n	NOUN
iajs-117	79	33	:	:	PUNCT
iajs-117	79	34	m	m	X
iajs-117	79	35	.	.	PUNCT
iajs-117	80	1	proof	proof	NOUN
iajs-117	80	2	:	:	PUNCT
iajs-117	80	3	(	(	PUNCT
iajs-117	80	4	1	1	X
iajs-117	80	5	)	)	PUNCT
iajs-117	80	6	(2	(2	NOUN
iajs-117	80	7	):	):	PUNCT
iajs-117	80	8	let	let	VERB
iajs-117	80	9	ik	ik	X
iajs-117	80	10	n	n	CCONJ
iajs-117	80	11	,	,	PUNCT
iajs-117	80	12	where	where	SCONJ
iajs-117	80	13	i	i	PRON
iajs-117	80	14	be	be	VERB
iajs-117	80	15	an	an	DET
iajs-117	80	16	ideal	ideal	NOUN
iajs-117	80	17	of	of	ADP
iajs-117	80	18	r	r	NOUN
iajs-117	80	19	and	and	CCONJ
iajs-117	80	20	k	k	PROPN
iajs-117	80	21	be	be	AUX
iajs-117	80	22	a	a	DET
iajs-117	80	23	submodule	submodule	NOUN
iajs-117	80	24	of	of	ADP
iajs-117	80	25	m.	m.	NOUN
iajs-117	80	26	suppose	suppose	VERB
iajs-117	80	27	k⊈	k⊈	NOUN
iajs-117	80	28	n	n	NOUN
iajs-117	80	29	+	+	CCONJ
iajs-117	80	30	(n	(n	NOUN
iajs-117	80	31	)	)	PUNCT
iajs-117	80	32	,	,	PUNCT
iajs-117	80	33	then	then	ADV
iajs-117	80	34	there	there	PRON
iajs-117	80	35	exists	exist	VERB
iajs-117	80	36	k	k	PROPN
iajs-117	80	37	k	k	PROPN
iajs-117	80	38	such	such	ADJ
iajs-117	80	39	that	that	SCONJ
iajs-117	80	40	kn	kn	PROPN
iajs-117	80	41	+	+	NUM
iajs-117	80	42	(n	(n	X
iajs-117	80	43	)	)	PUNCT
iajs-117	80	44	.	.	PUNCT
iajs-117	81	1	it	it	PRON
iajs-117	81	2	is	be	AUX
iajs-117	81	3	clear	clear	ADJ
iajs-117	81	4	that	that	SCONJ
iajs-117	81	5	for	for	ADP
iajs-117	81	6	each	each	DET
iajs-117	81	7	y	y	NOUN
iajs-117	81	8	i	i	PRON
iajs-117	81	9	,	,	PUNCT
iajs-117	81	10	thus	thus	ADV
iajs-117	81	11	ykn	ykn	X
iajs-117	81	12	.	.	PUNCT
iajs-117	82	1	but	but	CCONJ
iajs-117	82	2	n	n	PRON
iajs-117	82	3	is	be	AUX
iajs-117	82	4	-prime	-prime	PROPN
iajs-117	82	5	submodule	submodule	NOUN
iajs-117	82	6	of	of	ADP
iajs-117	82	7	m	m	PROPN
iajs-117	82	8	and	and	CCONJ
iajs-117	82	9	kn	kn	PROPN
iajs-117	82	10	+	+	CCONJ
iajs-117	82	11	(n	(n	X
iajs-117	82	12	)	)	PUNCT
iajs-117	82	13	,	,	PUNCT
iajs-117	82	14	hence	hence	ADV
iajs-117	82	15	y	y	PROPN
iajs-117	82	16	p=	p=	PROPN
iajs-117	83	1	[	[	X
iajs-117	83	2	n	n	NOUN
iajs-117	83	3	+	+	CCONJ
iajs-117	83	4	(n	(n	NOUN
iajs-117	83	5	):	):	PUNCT
iajs-117	83	6	m	m	PRON
iajs-117	83	7	]	]	X
iajs-117	83	8	.	.	PUNCT
iajs-117	84	1	therefore	therefore	ADV
iajs-117	84	2	i	i	VERB
iajs-117	84	3	p	p	PROPN
iajs-117	84	4	.	.	PUNCT
iajs-117	85	1	(	(	PUNCT
iajs-117	85	2	2	2	NUM
iajs-117	85	3	)	)	PUNCT
iajs-117	85	4	)	)	PUNCT
iajs-117	86	1	(1	(1	NOUN
iajs-117	86	2	):	):	PUNCT
iajs-117	86	3	let	let	VERB
iajs-117	86	4	r	r	NOUN
iajs-117	86	5			NOUN
iajs-117	86	6	r	r	NOUN
iajs-117	86	7	,	,	PUNCT
iajs-117	86	8	m	m	VERB
iajs-117	86	9			NOUN
iajs-117	86	10	m	m	VERB
iajs-117	86	11	such	such	ADJ
iajs-117	86	12	that	that	SCONJ
iajs-117	86	13	rm	rm	PROPN
iajs-117	86	14	n	n	PROPN
iajs-117	86	15	.	.	PUNCT
iajs-117	87	1	then	then	ADV
iajs-117	87	2	<	<	X
iajs-117	87	3	r	r	X
iajs-117	87	4	>	>	X
iajs-117	87	5	<	<	X
iajs-117	87	6	m	m	PROPN
iajs-117	87	7	>	>	X
iajs-117	87	8			PROPN
iajs-117	87	9	n.	n.	PROPN
iajs-117	88	1	so	so	ADV
iajs-117	88	2	either	either	CCONJ
iajs-117	88	3	<	<	X
iajs-117	88	4	m	m	X
iajs-117	88	5	>	>	X
iajs-117	88	6			PROPN
iajs-117	88	7	n	n	PROPN
iajs-117	88	8	+	+	CCONJ
iajs-117	88	9	(n	(n	X
iajs-117	88	10	)	)	PUNCT
iajs-117	88	11	or	or	CCONJ
iajs-117	88	12	<	<	X
iajs-117	88	13	r	r	X
iajs-117	88	14	>	>	X
iajs-117	88	15			PROPN
iajs-117	88	16	p=	p=	PROPN
iajs-117	88	17	n	n	CCONJ
iajs-117	88	18			NOUN
iajs-117	88	19	n	n	NOUN
iajs-117	88	20	:	:	PUNCT
iajs-117	88	21	m	m	NOUN
iajs-117	88	22	by(2	by(2	NOUN
iajs-117	88	23	)	)	PUNCT
iajs-117	88	24	)	)	PUNCT
iajs-117	88	25	;	;	PUNCT
iajs-117	89	1	i.e.	i.e.	X
iajs-117	89	2	,	,	PUNCT
iajs-117	89	3	either	either	CCONJ
iajs-117	89	4	mn	mn	PROPN
iajs-117	89	5	+	+	NUM
iajs-117	89	6	(n	(n	X
iajs-117	89	7	)	)	PUNCT
iajs-117	89	8	or	or	CCONJ
iajs-117	89	9	r	r	NOUN
iajs-117	89	10			NOUN
iajs-117	89	11	p=	p=	NOUN
iajs-117	89	12	n	n	CCONJ
iajs-117	89	13			NOUN
iajs-117	89	14	n	n	NOUN
iajs-117	89	15	:	:	PUNCT
iajs-117	89	16	m	m	X
iajs-117	89	17	.	.	PUNCT
iajs-117	90	1	therefore	therefore	ADV
iajs-117	90	2	n	n	PRON
iajs-117	90	3	is	be	AUX
iajs-117	90	4	-prime	-prime	PROPN
iajs-117	90	5	submodule	submodule	NOUN
iajs-117	90	6	of	of	ADP
iajs-117	90	7	m	m	PROPN
iajs-117	90	8	.	.	PUNCT
iajs-117	91	1	we	we	PRON
iajs-117	91	2	can	can	AUX
iajs-117	91	3	give	give	VERB
iajs-117	91	4	the	the	DET
iajs-117	91	5	following	follow	VERB
iajs-117	91	6	result	result	NOUN
iajs-117	91	7	.	.	PUNCT
iajs-117	92	1	proposition	proposition	NOUN
iajs-117	92	2	(	(	PUNCT
iajs-117	92	3	2.4	2.4	NUM
iajs-117	92	4	):	):	PUNCT
iajs-117	92	5	let	let	VERB
iajs-117	92	6	n	n	PRON
iajs-117	92	7	be	be	AUX
iajs-117	92	8	a	a	DET
iajs-117	92	9	proper	proper	ADJ
iajs-117	92	10	submodule	submodule	NOUN
iajs-117	92	11	of	of	ADP
iajs-117	92	12	an	an	DET
iajs-117	92	13	rmodule	rmodule	NOUN
iajs-117	92	14	m	m	NOUN
iajs-117	92	15	.	.	PUNCT
iajs-117	93	1	if	if	SCONJ
iajs-117	93	2	n	n	PRON
iajs-117	93	3			NOUN
iajs-117	93	4	n	n	NOUN
iajs-117	93	5	:	:	PUNCT
iajs-117	93	6	m	m	VERB
iajs-117	93	7	=	=	PUNCT
iajs-117	94	1	[	[	X
iajs-117	94	2	n+	n+	NUM
iajs-117	94	3			NOUN
iajs-117	94	4	(	(	PUNCT
iajs-117	94	5	n	n	CCONJ
iajs-117	94	6	)	)	PUNCT
iajs-117	94	7	:	:	PUNCT
iajs-117	95	1	k	k	X
iajs-117	95	2	]	]	X
iajs-117	95	3	for	for	ADP
iajs-117	95	4	each	each	DET
iajs-117	95	5	submodule	submodule	NOUN
iajs-117	95	6	k	k	PROPN
iajs-117	95	7	of	of	ADP
iajs-117	95	8	m	m	PROPN
iajs-117	95	9	such	such	ADJ
iajs-117	95	10	that	that	SCONJ
iajs-117	95	11	k⊋	k⊋	PROPN
iajs-117	95	12	n	n	NOUN
iajs-117	95	13	+	+	CCONJ
iajs-117	95	14	(n	(n	X
iajs-117	95	15	)	)	PUNCT
iajs-117	95	16	,	,	PUNCT
iajs-117	95	17	then	then	ADV
iajs-117	95	18	n	n	PRON
iajs-117	95	19	is	be	AUX
iajs-117	95	20	-prime	-prime	ADJ
iajs-117	95	21	submodule	submodule	NOUN
iajs-117	95	22	of	of	ADP
iajs-117	95	23	m.	m.	NOUN
iajs-117	95	24	proof	proof	NOUN
iajs-117	95	25	:	:	PUNCT
iajs-117	95	26	let	let	VERB
iajs-117	95	27	r	r	NOUN
iajs-117	95	28			NOUN
iajs-117	95	29	r	r	NOUN
iajs-117	95	30	,	,	PUNCT
iajs-117	95	31	m	m	VERB
iajs-117	95	32			NOUN
iajs-117	95	33	m	m	VERB
iajs-117	95	34	such	such	ADJ
iajs-117	95	35	that	that	DET
iajs-117	95	36	rm	rm	PROPN
iajs-117	95	37	n	n	NOUN
iajs-117	95	38	and	and	CCONJ
iajs-117	95	39	suppose	suppose	VERB
iajs-117	95	40	m	m	PROPN
iajs-117	95	41	n	n	PROPN
iajs-117	95	42	+	+	CCONJ
iajs-117	95	43	(n	(n	X
iajs-117	95	44	)	)	PUNCT
iajs-117	95	45	.	.	PUNCT
iajs-117	96	1	let	let	VERB
iajs-117	96	2	k=	k=	INTJ
iajs-117	97	1	n	n	ADV
iajs-117	97	2	+	+	CCONJ
iajs-117	97	3	(n)+	(n)+	PROPN
iajs-117	97	4	<	<	X
iajs-117	97	5	m	m	NOUN
iajs-117	97	6	>	>	X
iajs-117	97	7	,	,	PUNCT
iajs-117	97	8	then	then	ADV
iajs-117	97	9	k⊋	k⊋	PROPN
iajs-117	97	10	n	n	NOUN
iajs-117	97	11	+	+	CCONJ
iajs-117	97	12	(n	(n	X
iajs-117	97	13	)	)	PUNCT
iajs-117	97	14	,	,	PUNCT
iajs-117	97	15	mk	mk	PUNCT
iajs-117	97	16	and	and	CCONJ
iajs-117	97	17	so	so	ADV
iajs-117	97	18	r	r	ADJ
iajs-117	98	1	[	[	X
iajs-117	98	2	n	n	CCONJ
iajs-117	98	3	:	:	PUNCT
iajs-117	98	4	k	k	X
iajs-117	98	5	]	]	X
iajs-117	98	6			PROPN
iajs-117	98	7	[	[	X
iajs-117	98	8	n	n	X
iajs-117	98	9	+	+	X
iajs-117	98	10	(n):k	(n):k	NOUN
iajs-117	98	11	]	]	X
iajs-117	98	12	=	=	SYM
iajs-117	98	13	n	n	PART
iajs-117	98	14			NOUN
iajs-117	98	15	n	n	NOUN
iajs-117	98	16	:	:	PUNCT
iajs-117	98	17	m	m	PROPN
iajs-117	98	18	.it	.it	PUNCT
iajs-117	98	19	follows	follow	VERB
iajs-117	98	20	that	that	SCONJ
iajs-117	98	21	r	r	ADJ
iajs-117	98	22	n	n	CCONJ
iajs-117	98	23			NOUN
iajs-117	98	24	n	n	NOUN
iajs-117	98	25	:	:	PUNCT
iajs-117	98	26	m	m	VERB
iajs-117	98	27	and	and	CCONJ
iajs-117	98	28	hence	hence	ADV
iajs-117	98	29	n	n	PRON
iajs-117	98	30	is	be	AUX
iajs-117	98	31	-prime	-prime	ADJ
iajs-117	98	32	.	.	PUNCT
iajs-117	99	1	however	however	ADV
iajs-117	99	2	,	,	PUNCT
iajs-117	99	3	we	we	PRON
iajs-117	99	4	can	can	AUX
iajs-117	99	5	give	give	VERB
iajs-117	99	6	another	another	DET
iajs-117	99	7	corollary	corollary	NOUN
iajs-117	99	8	of	of	ADP
iajs-117	99	9	proposition	proposition	NOUN
iajs-117	99	10	(	(	PUNCT
iajs-117	99	11	2.4	2.4	NUM
iajs-117	99	12	)	)	PUNCT
iajs-117	99	13	.	.	PUNCT
iajs-117	100	1	but	but	CCONJ
iajs-117	100	2	first	first	ADV
iajs-117	100	3	we	we	PRON
iajs-117	100	4	state	state	VERB
iajs-117	100	5	and	and	CCONJ
iajs-117	100	6	prove	prove	VERB
iajs-117	100	7	the	the	DET
iajs-117	100	8	following	follow	VERB
iajs-117	100	9	lemma	lemma	PROPN
iajs-117	100	10	which	which	PRON
iajs-117	100	11	we	we	PRON
iajs-117	100	12	needed	need	VERB
iajs-117	100	13	.	.	PUNCT
iajs-117	101	1	mathematics	mathematic	NOUN
iajs-117	101	2	|	|	ADV
iajs-117	101	3	285	285	NUM
iajs-117	101	4	2016	2016	NUM
iajs-117	101	5	)	)	PUNCT
iajs-117	101	6	عام	عام	ADP
iajs-117	101	7	2العدد	2العدد	NUM
iajs-117	101	8	(	(	PUNCT
iajs-117	101	9	29لمجلد	29لمجلد	NUM
iajs-117	101	10	ا	ا	X
iajs-117	101	11	مجلة	مجلة	NOUN
iajs-117	101	12	إبن	إبن	VERB
iajs-117	101	13	الهيثم	الهيثم	ADJ
iajs-117	101	14	للعلوم	للعلوم	NOUN
iajs-117	101	15	الصرفة	الصرفة	NOUN
iajs-117	102	1	و	و	PRON
iajs-117	102	2	التطبيقية	التطبيقية	ADJ
iajs-117	102	3	ibn	ibn	PROPN
iajs-117	102	4	al	al	PROPN
iajs-117	102	5	-	-	PUNCT
iajs-117	102	6	haitham	haitham	PROPN
iajs-117	102	7	jour	jour	X
iajs-117	102	8	.	.	PROPN
iajs-117	102	9	for	for	ADP
iajs-117	102	10	pure	pure	ADJ
iajs-117	102	11	&	&	CCONJ
iajs-117	102	12	appl	appl	PROPN
iajs-117	102	13	.	.	PUNCT
iajs-117	103	1	sci	sci	PROPN
iajs-117	103	2	.	.	PUNCT
iajs-117	103	3	vol	vol	NOUN
iajs-117	103	4	.	.	PROPN
iajs-117	103	5	29	29	NUM
iajs-117	103	6	(	(	PUNCT
iajs-117	103	7	2	2	NUM
iajs-117	103	8	)	)	PUNCT
iajs-117	103	9	2016	2016	NUM
iajs-117	103	10	lemma	lemma	X
iajs-117	103	11	(	(	PUNCT
iajs-117	103	12	2.5	2.5	NUM
iajs-117	103	13	)	)	PUNCT
iajs-117	103	14	let	let	VERB
iajs-117	103	15	n	n	PRON
iajs-117	103	16	be	be	AUX
iajs-117	103	17	a	a	DET
iajs-117	103	18	proper	proper	ADJ
iajs-117	103	19	submodule	submodule	NOUN
iajs-117	103	20	of	of	ADP
iajs-117	103	21	an	an	DET
iajs-117	103	22	rmodule	rmodule	NOUN
iajs-117	103	23	m	m	NOUN
iajs-117	103	24	.	.	PUNCT
iajs-117	104	1	if	if	SCONJ
iajs-117	104	2	n	n	PRON
iajs-117	104	3			NOUN
iajs-117	104	4	n	n	NOUN
iajs-117	104	5	:	:	PUNCT
iajs-117	104	6	m	m	VERB
iajs-117	104	7	n	n	ADV
iajs-117	104	8			NOUN
iajs-117	104	9	n	n	CCONJ
iajs-117	104	10	∶	∶	NOUN
iajs-117	104	11	c	c	NOUN
iajs-117	104	12	for	for	ADP
iajs-117	104	13	each	each	DET
iajs-117	104	14	c	c	NOUN
iajs-117	104	15	m	m	NOUN
iajs-117	104	16	\	\	PROPN
iajs-117	104	17	n	n	PROPN
iajs-117	104	18	+	+	CCONJ
iajs-117	104	19	(n	(n	X
iajs-117	104	20	)	)	PUNCT
iajs-117	104	21	,	,	PUNCT
iajs-117	104	22	then	then	ADV
iajs-117	104	23	n	n	CCONJ
iajs-117	104	24			NOUN
iajs-117	104	25	n	n	NOUN
iajs-117	104	26	:	:	PUNCT
iajs-117	104	27	m	m	VERB
iajs-117	104	28	=	=	PUNCT
iajs-117	105	1	[	[	X
iajs-117	105	2	n+(n	n+(n	PROPN
iajs-117	105	3	)	)	PUNCT
iajs-117	105	4	:	:	PUNCT
iajs-117	106	1	k	k	X
iajs-117	106	2	]	]	X
iajs-117	106	3	for	for	ADP
iajs-117	106	4	each	each	DET
iajs-117	106	5	submodule	submodule	NOUN
iajs-117	106	6	k	k	PROPN
iajs-117	106	7	of	of	ADP
iajs-117	106	8	m	m	PROPN
iajs-117	106	9	such	such	ADJ
iajs-117	106	10	that	that	SCONJ
iajs-117	106	11	k⊋	k⊋	PROPN
iajs-117	106	12	n	n	NOUN
iajs-117	106	13	+	+	CCONJ
iajs-117	106	14	(n	(n	X
iajs-117	106	15	)	)	PUNCT
iajs-117	106	16	.	.	PUNCT
iajs-117	107	1	proof	proof	NOUN
iajs-117	107	2	:	:	PUNCT
iajs-117	107	3	since	since	SCONJ
iajs-117	107	4	k	k	PROPN
iajs-117	107	5			PROPN
iajs-117	107	6	m	m	VERB
iajs-117	107	7	so	so	ADV
iajs-117	107	8	n	n	ADV
iajs-117	107	9			NOUN
iajs-117	107	10	n	n	NOUN
iajs-117	107	11	:	:	PUNCT
iajs-117	107	12	m	m	VERB
iajs-117	107	13			PROPN
iajs-117	108	1	[	[	X
iajs-117	108	2	n+	n+	NUM
iajs-117	108	3	(n	(n	X
iajs-117	108	4	)	)	PUNCT
iajs-117	108	5	:	:	PUNCT
iajs-117	109	1	k	k	X
iajs-117	109	2	]	]	PUNCT
iajs-117	109	3	.let	.let	PUNCT
iajs-117	110	1	r	r	NOUN
iajs-117	110	2			PROPN
iajs-117	110	3	n	n	CCONJ
iajs-117	110	4			NOUN
iajs-117	110	5	n	n	PRON
iajs-117	110	6	∶	∶	NOUN
iajs-117	110	7	k	k	NOUN
iajs-117	110	8	,	,	PUNCT
iajs-117	110	9	hence	hence	ADV
iajs-117	110	10	r	r	NOUN
iajs-117	110	11	k	k	NOUN
iajs-117	110	12			PROPN
iajs-117	110	13	n	n	PROPN
iajs-117	110	14	+	+	CCONJ
iajs-117	110	15	(n	(n	X
iajs-117	110	16	)	)	PUNCT
iajs-117	110	17	.	.	PUNCT
iajs-117	111	1	but	but	CCONJ
iajs-117	111	2	n	n	PROPN
iajs-117	111	3	+	+	CCONJ
iajs-117	111	4	(n	(n	X
iajs-117	111	5	)	)	PUNCT
iajs-117	111	6	⊊	⊊	VERB
iajs-117	111	7	k	k	PROPN
iajs-117	111	8	,	,	PUNCT
iajs-117	111	9	implies	imply	VERB
iajs-117	111	10	that	that	SCONJ
iajs-117	111	11	there	there	PRON
iajs-117	111	12	exists	exist	VERB
iajs-117	111	13	xk	xk	PROPN
iajs-117	111	14	and	and	CCONJ
iajs-117	111	15	x	x	PART
iajs-117	111	16	n	n	PROPN
iajs-117	111	17	+	+	CCONJ
iajs-117	111	18	(n).hence	(n).hence	CCONJ
iajs-117	111	19	rx	rx	VERB
iajs-117	111	20			PROPN
iajs-117	111	21	n+(n	n+(n	PROPN
iajs-117	111	22	)	)	PUNCT
iajs-117	111	23	and	and	CCONJ
iajs-117	111	24	then	then	ADV
iajs-117	111	25	r	r	NOUN
iajs-117	111	26	[n+(n	[n+(n	NUM
iajs-117	111	27	)	)	PUNCT
iajs-117	111	28	:	:	PUNCT
iajs-117	112	1	x	x	X
iajs-117	112	2	]	]	X
iajs-117	112	3	=	=	PUNCT
iajs-117	112	4	[	[	X
iajs-117	112	5	n+	n+	NUM
iajs-117	112	6	(n	(n	X
iajs-117	112	7	)	)	PUNCT
iajs-117	112	8	:	:	PUNCT
iajs-117	112	9	m	m	X
iajs-117	112	10	]	]	X
iajs-117	112	11	,	,	PUNCT
iajs-117	112	12	which	which	PRON
iajs-117	112	13	implies	imply	VERB
iajs-117	112	14	that	that	SCONJ
iajs-117	112	15	r	r	NOUN
iajs-117	112	16			NOUN
iajs-117	112	17	n	n	CCONJ
iajs-117	112	18			NOUN
iajs-117	112	19	n	n	PRON
iajs-117	112	20	∶	∶	NOUN
iajs-117	112	21	k	k	PROPN
iajs-117	112	22			PROPN
iajs-117	112	23	n	n	INTJ
iajs-117	112	24			NOUN
iajs-117	112	25	n	n	NOUN
iajs-117	112	26	:	:	PUNCT
iajs-117	112	27	m	m	NOUN
iajs-117	112	28	.therefore	.therefore	ADP
iajs-117	112	29	n	n	ADV
iajs-117	112	30			NOUN
iajs-117	112	31	n	n	NOUN
iajs-117	112	32	:	:	PUNCT
iajs-117	112	33	m	m	VERB
iajs-117	112	34	=	=	PUNCT
iajs-117	113	1	[	[	X
iajs-117	113	2	n+	n+	NUM
iajs-117	113	3	(n	(n	NOUN
iajs-117	113	4	):	):	PUNCT
iajs-117	113	5	k	k	X
iajs-117	113	6	]	]	X
iajs-117	113	7	for	for	ADP
iajs-117	113	8	each	each	DET
iajs-117	113	9	submodule	submodule	NOUN
iajs-117	113	10	k	k	PROPN
iajs-117	113	11	of	of	ADP
iajs-117	113	12	m	m	PROPN
iajs-117	113	13	such	such	ADJ
iajs-117	113	14	that	that	SCONJ
iajs-117	113	15	k⊋	k⊋	PROPN
iajs-117	113	16	n	n	NOUN
iajs-117	113	17	+	+	CCONJ
iajs-117	113	18	(n	(n	X
iajs-117	113	19	)	)	PUNCT
iajs-117	113	20	.	.	PUNCT
iajs-117	114	1	corollary	corollary	ADJ
iajs-117	114	2	(	(	PUNCT
iajs-117	114	3	2.6	2.6	NUM
iajs-117	114	4	):	):	PUNCT
iajs-117	114	5	let	let	VERB
iajs-117	114	6	n	n	PRON
iajs-117	114	7	be	be	AUX
iajs-117	114	8	a	a	DET
iajs-117	114	9	proper	proper	ADJ
iajs-117	114	10	submodule	submodule	NOUN
iajs-117	114	11	of	of	ADP
iajs-117	114	12	an	an	DET
iajs-117	114	13	rmodule	rmodule	NOUN
iajs-117	114	14	m	m	NOUN
iajs-117	114	15	.	.	PUNCT
iajs-117	115	1	if	if	SCONJ
iajs-117	115	2	n	n	PRON
iajs-117	115	3			NOUN
iajs-117	115	4	:	:	PUNCT
iajs-117	115	5	m	m	VERB
iajs-117	115	6	n	n	VERB
iajs-117	115	7			NOUN
iajs-117	115	8	n	n	CCONJ
iajs-117	115	9	∶	∶	NOUN
iajs-117	115	10	c	c	NOUN
iajs-117	115	11	for	for	ADP
iajs-117	115	12	each	each	DET
iajs-117	115	13	c	c	NOUN
iajs-117	115	14	m	m	NOUN
iajs-117	115	15	\	\	PROPN
iajs-117	115	16	n	n	PROPN
iajs-117	115	17	+	+	CCONJ
iajs-117	115	18	(n	(n	X
iajs-117	115	19	)	)	PUNCT
iajs-117	115	20	,	,	PUNCT
iajs-117	115	21	then	then	ADV
iajs-117	115	22	n	n	PRON
iajs-117	115	23	is	be	AUX
iajs-117	115	24	-prime	-prime	ADJ
iajs-117	115	25	submodule	submodule	NOUN
iajs-117	115	26	of	of	ADP
iajs-117	115	27	m.	m.	NOUN
iajs-117	115	28	now	now	ADV
iajs-117	115	29	,	,	PUNCT
iajs-117	115	30	the	the	DET
iajs-117	115	31	following	follow	VERB
iajs-117	115	32	proposition	proposition	NOUN
iajs-117	115	33	shows	show	VERB
iajs-117	115	34	that	that	SCONJ
iajs-117	115	35	under	under	ADP
iajs-117	115	36	the	the	DET
iajs-117	115	37	condition	condition	NOUN
iajs-117	115	38	(n	(n	X
iajs-117	115	39	)	)	PUNCT
iajs-117	115	40			PROPN
iajs-117	115	41	n	n	PROPN
iajs-117	115	42	for	for	ADP
iajs-117	115	43	all	all	DET
iajs-117	115	44	submodule	submodule	NOUN
iajs-117	115	45	n	n	PROPN
iajs-117	115	46	of	of	ADP
iajs-117	115	47	m	m	PROPN
iajs-117	115	48	the	the	DET
iajs-117	115	49	convers	conver	NOUN
iajs-117	115	50	of	of	ADP
iajs-117	115	51	proposition	proposition	NOUN
iajs-117	115	52	(	(	PUNCT
iajs-117	115	53	2.4	2.4	NUM
iajs-117	115	54	)	)	PUNCT
iajs-117	115	55	is	be	AUX
iajs-117	115	56	true	true	ADJ
iajs-117	115	57	.	.	PUNCT
iajs-117	116	1	proposition(2.7	proposition(2.7	NOUN
iajs-117	116	2	):	):	PUNCT
iajs-117	116	3	if	if	SCONJ
iajs-117	116	4	n	n	PRON
iajs-117	116	5	is	be	AUX
iajs-117	116	6	a	a	DET
iajs-117	116	7	-prime	-prime	ADJ
iajs-117	116	8	submodule	submodule	NOUN
iajs-117	116	9	of	of	ADP
iajs-117	116	10	an	an	DET
iajs-117	116	11	r	r	NOUN
iajs-117	116	12	–	–	PUNCT
iajs-117	116	13	module	module	NOUN
iajs-117	116	14	m	m	NOUN
iajs-117	116	15	and	and	CCONJ
iajs-117	116	16	(n	(n	NOUN
iajs-117	116	17	)	)	PUNCT
iajs-117	117	1			PROPN
iajs-117	117	2	n	n	INTJ
iajs-117	117	3	,	,	PUNCT
iajs-117	117	4	then	then	ADV
iajs-117	117	5	n	n	PRON
iajs-117	117	6			NOUN
iajs-117	117	7	:	:	PUNCT
iajs-117	117	8	m	m	VERB
iajs-117	117	9	=	=	PUNCT
iajs-117	118	1	[	[	X
iajs-117	118	2	n+	n+	NUM
iajs-117	118	3	(n	(n	X
iajs-117	118	4	)	)	PUNCT
iajs-117	118	5	:	:	PUNCT
iajs-117	119	1	k	k	X
iajs-117	119	2	]	]	X
iajs-117	119	3	for	for	ADP
iajs-117	119	4	each	each	DET
iajs-117	119	5	submodule	submodule	NOUN
iajs-117	119	6	k	k	PROPN
iajs-117	119	7	of	of	ADP
iajs-117	119	8	m	m	PROPN
iajs-117	119	9	such	such	ADJ
iajs-117	119	10	that	that	SCONJ
iajs-117	119	11	k	k	PROPN
iajs-117	119	12	⊋	⊋	PROPN
iajs-117	119	13	n	n	PROPN
iajs-117	119	14	+	+	CCONJ
iajs-117	119	15	(n	(n	X
iajs-117	119	16	)	)	PUNCT
iajs-117	119	17	.	.	PUNCT
iajs-117	120	1	proof	proof	NOUN
iajs-117	120	2	:	:	PUNCT
iajs-117	120	3	since	since	SCONJ
iajs-117	120	4	n	n	PRON
iajs-117	120	5	is	be	AUX
iajs-117	120	6	a	a	DET
iajs-117	120	7	-prime	-prime	ADJ
iajs-117	120	8	submodule	submodule	NOUN
iajs-117	120	9	of	of	ADP
iajs-117	120	10	m	m	PROPN
iajs-117	120	11	and	and	CCONJ
iajs-117	120	12	(n	(n	PROPN
iajs-117	120	13	)	)	PUNCT
iajs-117	121	1			PROPN
iajs-117	121	2	n	n	INTJ
iajs-117	121	3	,	,	PUNCT
iajs-117	121	4	so	so	ADV
iajs-117	121	5	by	by	ADP
iajs-117	121	6	(	(	PUNCT
iajs-117	121	7	remark	remark	NOUN
iajs-117	121	8	2.2,(2	2.2,(2	NUM
iajs-117	121	9	)	)	PUNCT
iajs-117	121	10	)	)	PUNCT
iajs-117	122	1	n	n	CCONJ
iajs-117	122	2	is	be	AUX
iajs-117	122	3	a	a	DET
iajs-117	122	4	prime	prime	ADJ
iajs-117	122	5	submodule	submodule	NOUN
iajs-117	122	6	.hence	.hence	PUNCT
iajs-117	123	1	[	[	X
iajs-117	123	2	n	n	X
iajs-117	123	3	:	:	PUNCT
iajs-117	123	4	m	m	VERB
iajs-117	123	5	]	]	X
iajs-117	124	1	=	=	PUNCT
iajs-117	125	1	[	[	X
iajs-117	125	2	n	n	CCONJ
iajs-117	125	3	:	:	PUNCT
iajs-117	125	4	k	k	X
iajs-117	125	5	]	]	X
iajs-117	125	6	,	,	PUNCT
iajs-117	125	7	for	for	ADP
iajs-117	125	8	each	each	DET
iajs-117	125	9	submodule	submodule	NOUN
iajs-117	125	10	k	k	PROPN
iajs-117	125	11	of	of	ADP
iajs-117	125	12	m	m	PROPN
iajs-117	125	13	such	such	ADJ
iajs-117	125	14	that	that	SCONJ
iajs-117	125	15	k	k	PROPN
iajs-117	125	16	⊋	⊋	PROPN
iajs-117	125	17	n,[2	n,[2	PROPN
iajs-117	125	18	]	]	PUNCT
iajs-117	125	19	.	.	PUNCT
iajs-117	126	1	since	since	SCONJ
iajs-117	126	2	(n	(n	PROPN
iajs-117	126	3	)	)	PUNCT
iajs-117	126	4			PROPN
iajs-117	126	5	n	n	INTJ
iajs-117	126	6	,	,	PUNCT
iajs-117	126	7	then	then	ADV
iajs-117	126	8	n	n	PRON
iajs-117	126	9			NOUN
iajs-117	126	10	:	:	PUNCT
iajs-117	126	11	m	m	VERB
iajs-117	126	12	=	=	PUNCT
iajs-117	127	1	[	[	X
iajs-117	127	2	n+	n+	NUM
iajs-117	127	3	(n	(n	X
iajs-117	127	4	)	)	PUNCT
iajs-117	127	5	:	:	PUNCT
iajs-117	128	1	k	k	X
iajs-117	128	2	]	]	X
iajs-117	128	3	for	for	ADP
iajs-117	128	4	each	each	DET
iajs-117	128	5	submodule	submodule	NOUN
iajs-117	128	6	k	k	PROPN
iajs-117	128	7	of	of	ADP
iajs-117	128	8	m	m	PROPN
iajs-117	128	9	such	such	ADJ
iajs-117	128	10	that	that	SCONJ
iajs-117	128	11	k	k	PROPN
iajs-117	128	12	⊋	⊋	PROPN
iajs-117	128	13	n	n	PROPN
iajs-117	128	14	+	+	CCONJ
iajs-117	128	15	(n	(n	X
iajs-117	128	16	)	)	PUNCT
iajs-117	128	17	.	.	PUNCT
iajs-117	129	1	it	it	PRON
iajs-117	129	2	is	be	AUX
iajs-117	129	3	well	well	ADV
iajs-117	129	4	know	know	ADJ
iajs-117	129	5	if	if	SCONJ
iajs-117	129	6	n	n	PRON
iajs-117	129	7	is	be	AUX
iajs-117	129	8	a	a	DET
iajs-117	129	9	prime	prime	ADJ
iajs-117	129	10	submodule	submodule	NOUN
iajs-117	129	11	of	of	ADP
iajs-117	129	12	an	an	DET
iajs-117	129	13	r	r	NOUN
iajs-117	129	14	–	–	PUNCT
iajs-117	129	15	module	module	NOUN
iajs-117	129	16	,	,	PUNCT
iajs-117	129	17	then	then	ADV
iajs-117	129	18	[	[	X
iajs-117	129	19	n	n	X
iajs-117	129	20	:	:	PUNCT
iajs-117	129	21	m	m	X
iajs-117	129	22	]	]	X
iajs-117	129	23	is	be	AUX
iajs-117	129	24	a	a	DET
iajs-117	129	25	prime	prime	ADJ
iajs-117	129	26	ideal	ideal	NOUN
iajs-117	129	27	of	of	ADP
iajs-117	129	28	r	r	NOUN
iajs-117	129	29	,	,	PUNCT
iajs-117	129	30	see	see	VERB
iajs-117	129	31	[	[	X
iajs-117	129	32	4	4	NUM
iajs-117	129	33	]	]	PUNCT
iajs-117	129	34	.	.	PUNCT
iajs-117	130	1	but	but	CCONJ
iajs-117	130	2	for	for	ADP
iajs-117	130	3	a	a	DET
iajs-117	130	4	-prime	-prime	NOUN
iajs-117	130	5	we	we	PRON
iajs-117	130	6	have	have	AUX
iajs-117	130	7	:	:	PUNCT
iajs-117	130	8	remark(2.8	remark(2.8	VERB
iajs-117	130	9	):	):	PUNCT
iajs-117	130	10	(	(	PUNCT
iajs-117	130	11	1	1	X
iajs-117	130	12	)	)	PUNCT
iajs-117	130	13	if	if	SCONJ
iajs-117	130	14	n	n	PRON
iajs-117	130	15	is	be	AUX
iajs-117	130	16	-prime	-prime	PROPN
iajs-117	130	17	submodule	submodule	NOUN
iajs-117	130	18	of	of	ADP
iajs-117	130	19	m	m	PROPN
iajs-117	130	20	,	,	PUNCT
iajs-117	130	21	then	then	ADV
iajs-117	130	22	it	it	PRON
iajs-117	130	23	is	be	AUX
iajs-117	130	24	not	not	PART
iajs-117	130	25	necessarily	necessarily	ADV
iajs-117	130	26	that	that	SCONJ
iajs-117	130	27	[	[	X
iajs-117	130	28	n	n	CCONJ
iajs-117	130	29	:	:	PUNCT
iajs-117	130	30	m	m	VERB
iajs-117	130	31	]	]	X
iajs-117	130	32	is	be	AUX
iajs-117	130	33	a	a	DET
iajs-117	130	34	prime	prime	ADJ
iajs-117	130	35	ideal	ideal	NOUN
iajs-117	130	36	of	of	ADP
iajs-117	130	37	r	r	NOUN
iajs-117	130	38	,	,	PUNCT
iajs-117	130	39	for	for	ADP
iajs-117	130	40	example	example	NOUN
iajs-117	130	41	:	:	PUNCT
iajs-117	130	42	let	let	VERB
iajs-117	130	43	m	m	VERB
iajs-117	130	44	=	=	VERB
iajs-117	130	45	z8	z8	NOUN
iajs-117	130	46	as	as	ADP
iajs-117	130	47	a	a	DET
iajs-117	130	48	z	z	NOUN
iajs-117	130	49	-	-	PUNCT
iajs-117	130	50	module	module	NOUN
iajs-117	130	51	,	,	PUNCT
iajs-117	130	52	n	n	NOUN
iajs-117	130	53	=	=	SYM
iajs-117	130	54			PROPN
iajs-117	130	55	4	4	NUM
iajs-117	130	56	.	.	NOUN
iajs-117	130	57	then	then	ADV
iajs-117	130	58	n	n	PRON
iajs-117	130	59	is	be	AUX
iajs-117	130	60	prime	prime	PROPN
iajs-117	130	61	submodule	submodule	NOUN
iajs-117	130	62	of	of	ADP
iajs-117	130	63	m	m	PRON
iajs-117	130	64	by	by	ADP
iajs-117	130	65	(	(	PUNCT
iajs-117	130	66	remark	remark	NOUN
iajs-117	130	67	2.2,(1	2.2,(1	NUM
iajs-117	130	68	)	)	PUNCT
iajs-117	130	69	)	)	PUNCT
iajs-117	130	70	.	.	PUNCT
iajs-117	131	1	but	but	CCONJ
iajs-117	131	2	[	[	X
iajs-117	131	3			PROPN
iajs-117	131	4	4	4	NUM
iajs-117	131	5			ADJ
iajs-117	131	6	:	:	PUNCT
iajs-117	131	7	z8	z8	NOUN
iajs-117	131	8	]	]	X
iajs-117	131	9	=	=	SYM
iajs-117	131	10	4z	4z	NOUN
iajs-117	131	11	is	be	AUX
iajs-117	131	12	not	not	PART
iajs-117	131	13	-prime	-prime	ADJ
iajs-117	131	14	submodule	submodule	NOUN
iajs-117	131	15	of	of	ADP
iajs-117	131	16	z	z	PROPN
iajs-117	131	17	,	,	PUNCT
iajs-117	131	18	where	where	SCONJ
iajs-117	131	19	(i	(i	NOUN
iajs-117	131	20	)	)	PUNCT
iajs-117	132	1	=	=	PUNCT
iajs-117	132	2	i	i	PRON
iajs-117	132	3	for	for	ADP
iajs-117	132	4	each	each	DET
iajs-117	132	5	i	i	PRON
iajs-117	132	6	an	an	DET
iajs-117	132	7	ideal	ideal	NOUN
iajs-117	132	8	of	of	ADP
iajs-117	132	9	z	z	PROPN
iajs-117	132	10	and	and	CCONJ
iajs-117	132	11			NOUN
iajs-117	132	12	:	:	PUNCT
iajs-117	132	13	(z	(z	NUM
iajs-117	132	14	)	)	PUNCT
iajs-117	132	15			PROPN
iajs-117	132	16	(z	(z	NUM
iajs-117	132	17	)	)	PUNCT
iajs-117	132	18			NOUN
iajs-117	132	19	{	{	PUNCT
iajs-117	132	20			NOUN
iajs-117	132	21	}	}	PUNCT
iajs-117	132	22	be	be	AUX
iajs-117	132	23	a	a	DET
iajs-117	132	24	function	function	NOUN
iajs-117	132	25	.	.	PUNCT
iajs-117	133	1	now	now	ADV
iajs-117	133	2	,	,	PUNCT
iajs-117	133	3	the	the	DET
iajs-117	133	4	following	follow	VERB
iajs-117	133	5	proposition	proposition	NOUN
iajs-117	133	6	shows	show	VERB
iajs-117	133	7	that	that	SCONJ
iajs-117	133	8	under	under	ADP
iajs-117	133	9	the	the	DET
iajs-117	133	10	condition	condition	NOUN
iajs-117	133	11	(n	(n	X
iajs-117	133	12	)	)	PUNCT
iajs-117	133	13			PROPN
iajs-117	133	14	n	n	PROPN
iajs-117	133	15	for	for	ADP
iajs-117	133	16	all	all	DET
iajs-117	133	17	submodule	submodule	NOUN
iajs-117	133	18	n	n	PROPN
iajs-117	133	19	of	of	ADP
iajs-117	133	20	m	m	PRON
iajs-117	133	21	the	the	DET
iajs-117	133	22	above	above	ADJ
iajs-117	133	23	statement	statement	NOUN
iajs-117	133	24	is	be	AUX
iajs-117	133	25	true	true	ADJ
iajs-117	133	26	.	.	PUNCT
iajs-117	134	1	proposition(2.9	proposition(2.9	ADJ
iajs-117	134	2	):	):	PUNCT
iajs-117	134	3	if	if	SCONJ
iajs-117	134	4	n	n	PRON
iajs-117	134	5	is	be	AUX
iajs-117	134	6	a	a	DET
iajs-117	134	7	-prime	-prime	ADJ
iajs-117	134	8	submodule	submodule	NOUN
iajs-117	134	9	of	of	ADP
iajs-117	134	10	an	an	DET
iajs-117	134	11	r	r	NOUN
iajs-117	134	12	–	–	PUNCT
iajs-117	134	13	module	module	NOUN
iajs-117	134	14	m	m	NOUN
iajs-117	134	15	and	and	CCONJ
iajs-117	134	16	(n	(n	NOUN
iajs-117	134	17	)	)	PUNCT
iajs-117	135	1			PROPN
iajs-117	135	2	n	n	PROPN
iajs-117	135	3	,	,	PUNCT
iajs-117	135	4	then	then	ADV
iajs-117	135	5	n	n	CCONJ
iajs-117	135	6	:	:	PUNCT
iajs-117	135	7	m	m	VERB
iajs-117	135	8	is	be	AUX
iajs-117	135	9	a	a	DET
iajs-117	135	10			NUM
iajs-117	135	11	prime	prime	ADJ
iajs-117	135	12	ideal	ideal	NOUN
iajs-117	135	13	of	of	ADP
iajs-117	135	14	r.	r.	PROPN
iajs-117	135	15	proof	proof	NOUN
iajs-117	135	16	:	:	PUNCT
iajs-117	135	17	since	since	SCONJ
iajs-117	135	18	n	n	PRON
iajs-117	135	19	is	be	AUX
iajs-117	135	20	a	a	DET
iajs-117	135	21	-prime	-prime	ADJ
iajs-117	135	22	submodule	submodule	NOUN
iajs-117	135	23	of	of	ADP
iajs-117	135	24	an	an	DET
iajs-117	135	25	r	r	NOUN
iajs-117	135	26	–	–	PUNCT
iajs-117	135	27	module	module	NOUN
iajs-117	135	28	m	m	NOUN
iajs-117	135	29	and	and	CCONJ
iajs-117	135	30	(n	(n	NOUN
iajs-117	135	31	)	)	PUNCT
iajs-117	135	32			PROPN
iajs-117	135	33	n	n	CCONJ
iajs-117	135	34	,	,	PUNCT
iajs-117	135	35	so	so	ADV
iajs-117	135	36	n	n	PRON
iajs-117	135	37	is	be	AUX
iajs-117	135	38	a	a	DET
iajs-117	135	39	prime	prime	ADJ
iajs-117	135	40	submodule	submodule	NOUN
iajs-117	135	41	by	by	ADP
iajs-117	135	42	(	(	PUNCT
iajs-117	135	43	2.2,(2	2.2,(2	NUM
iajs-117	135	44	)	)	PUNCT
iajs-117	135	45	)	)	PUNCT
iajs-117	135	46	,	,	PUNCT
iajs-117	135	47	then	then	ADV
iajs-117	135	48	[	[	X
iajs-117	135	49	n	n	X
iajs-117	135	50	:	:	PUNCT
iajs-117	135	51	m	m	VERB
iajs-117	135	52	]	]	X
iajs-117	135	53	is	be	AUX
iajs-117	135	54	a	a	DET
iajs-117	135	55	prime	prime	ADJ
iajs-117	135	56	ideal	ideal	NOUN
iajs-117	135	57	of	of	ADP
iajs-117	135	58	r	r	NOUN
iajs-117	135	59	and	and	CCONJ
iajs-117	135	60	hence	hence	ADV
iajs-117	135	61	is	be	AUX
iajs-117	135	62	a	a	DET
iajs-117	135	63	-prime	-prime	ADJ
iajs-117	135	64	ideal	ideal	NOUN
iajs-117	135	65	of	of	ADP
iajs-117	135	66	r.	r.	PROPN
iajs-117	135	67	(	(	PUNCT
iajs-117	135	68	.2	.2	NUM
iajs-117	135	69	,	,	PUNCT
iajs-117	135	70	2	2	NUM
iajs-117	135	71	)	)	PUNCT
iajs-117	135	72	,	,	PUNCT
iajs-117	135	73	then	then	ADV
iajs-117	135	74	n	n	CCONJ
iajs-117	135	75	:	:	PUNCT
iajs-117	135	76	m	m	VERB
iajs-117	135	77	is	be	AUX
iajs-117	135	78	a	a	DET
iajs-117	135	79	remark	remark	NOUN
iajs-117	135	80	(	(	PUNCT
iajs-117	135	81	2.10	2.10	NUM
iajs-117	135	82	):	):	PUNCT
iajs-117	135	83	if	if	SCONJ
iajs-117	135	84	[	[	X
iajs-117	135	85	n	n	X
iajs-117	135	86	:	:	PUNCT
iajs-117	135	87	m	m	X
iajs-117	135	88	]	]	X
iajs-117	135	89	is	be	AUX
iajs-117	135	90	prime	prime	PROPN
iajs-117	135	91	ideal	ideal	NOUN
iajs-117	135	92	of	of	ADP
iajs-117	135	93	r	r	NOUN
iajs-117	135	94	,	,	PUNCT
iajs-117	135	95	then	then	ADV
iajs-117	135	96	it	it	PRON
iajs-117	135	97	is	be	AUX
iajs-117	135	98	not	not	PART
iajs-117	135	99	necessarily	necessarily	ADV
iajs-117	135	100	that	that	PRON
iajs-117	135	101	n	n	ADV
iajs-117	135	102	is	be	AUX
iajs-117	135	103	-prime	-prime	PROPN
iajs-117	135	104	submodule	submodule	NOUN
iajs-117	135	105	of	of	ADP
iajs-117	135	106	m	m	PROPN
iajs-117	135	107	,	,	PUNCT
iajs-117	135	108	for	for	ADP
iajs-117	135	109	example	example	NOUN
iajs-117	135	110	:	:	PUNCT
iajs-117	135	111	let	let	VERB
iajs-117	135	112	m	m	VERB
iajs-117	135	113	=	=	NOUN
iajs-117	135	114	z	z	PROPN
iajs-117	135	115			PROPN
iajs-117	135	116	z	z	PROPN
iajs-117	135	117	as	as	ADP
iajs-117	135	118	a	a	DET
iajs-117	135	119	z	z	NOUN
iajs-117	135	120	-	-	PUNCT
iajs-117	135	121	module	module	NOUN
iajs-117	135	122	,	,	PUNCT
iajs-117	135	123	n	n	NOUN
iajs-117	135	124	=	=	SYM
iajs-117	135	125	2z(0	2z(0	NUM
iajs-117	135	126	)	)	PUNCT
iajs-117	135	127	,	,	PUNCT
iajs-117	135	128	n	n	PRON
iajs-117	135	129	is	be	AUX
iajs-117	135	130	not	not	PART
iajs-117	135	131	-prime	-prime	ADJ
iajs-117	135	132	submodule	submodule	NOUN
iajs-117	135	133	of	of	ADP
iajs-117	135	134	m	m	PRON
iajs-117	135	135	,	,	PUNCT
iajs-117	135	136	by	by	ADP
iajs-117	135	137	(	(	PUNCT
iajs-117	135	138	2.2,9	2.2,9	NOUN
iajs-117	135	139	)	)	PUNCT
iajs-117	135	140	.	.	PUNCT
iajs-117	136	1	but	but	CCONJ
iajs-117	137	1	[	[	X
iajs-117	137	2	n	n	X
iajs-117	137	3	:	:	PUNCT
iajs-117	137	4	m	m	VERB
iajs-117	137	5	]	]	X
iajs-117	137	6	=	=	PUNCT
iajs-117	138	1	[	[	X
iajs-117	138	2	2z	2z	NUM
iajs-117	138	3			ADJ
iajs-117	138	4	(	(	PUNCT
iajs-117	138	5	0	0	NUM
iajs-117	138	6	)	)	PUNCT
iajs-117	138	7	:	:	PUNCT
iajs-117	138	8	z	z	PROPN
iajs-117	138	9			PROPN
iajs-117	138	10	z	z	X
iajs-117	138	11	]	]	PUNCT
iajs-117	139	1	=	=	SYM
iajs-117	139	2	0	0	PUNCT
iajs-117	139	3	is	be	AUX
iajs-117	139	4	a	a	DET
iajs-117	139	5	prime	prime	ADJ
iajs-117	139	6	ideal	ideal	NOUN
iajs-117	139	7	of	of	ADP
iajs-117	139	8	z	z	NOUN
iajs-117	139	9	and	and	CCONJ
iajs-117	139	10	hence	hence	ADV
iajs-117	139	11	is	be	AUX
iajs-117	139	12			NUM
iajs-117	139	13	prime	prime	ADJ
iajs-117	139	14	ideal	ideal	NOUN
iajs-117	139	15	of	of	ADP
iajs-117	139	16	z	z	NOUN
iajs-117	139	17	,	,	PUNCT
iajs-117	139	18	where	where	SCONJ
iajs-117	139	19	(i	(i	NOUN
iajs-117	139	20	)	)	PUNCT
iajs-117	140	1	=	=	PUNCT
iajs-117	140	2	i	i	PRON
iajs-117	140	3	for	for	ADP
iajs-117	140	4	each	each	DET
iajs-117	140	5	i	i	PRON
iajs-117	140	6	an	an	DET
iajs-117	140	7	ideal	ideal	NOUN
iajs-117	140	8	of	of	ADP
iajs-117	140	9	z	z	PROPN
iajs-117	140	10	and	and	CCONJ
iajs-117	140	11			NOUN
iajs-117	140	12	:	:	PUNCT
iajs-117	140	13	(z	(z	NUM
iajs-117	140	14	)	)	PUNCT
iajs-117	140	15			PROPN
iajs-117	140	16	(z	(z	NUM
iajs-117	140	17	)	)	PUNCT
iajs-117	140	18			NOUN
iajs-117	140	19	{	{	PUNCT
iajs-117	140	20			NOUN
iajs-117	140	21	}	}	PUNCT
iajs-117	140	22	be	be	AUX
iajs-117	140	23	a	a	DET
iajs-117	140	24	function	function	NOUN
iajs-117	140	25	.	.	PUNCT
iajs-117	141	1	now	now	ADV
iajs-117	141	2	,	,	PUNCT
iajs-117	141	3	we	we	PRON
iajs-117	141	4	shall	shall	AUX
iajs-117	141	5	give	give	VERB
iajs-117	141	6	characterization	characterization	NOUN
iajs-117	141	7	of	of	ADP
iajs-117	141	8	-prime	-prime	ADJ
iajs-117	141	9	submoules	submoule	NOUN
iajs-117	141	10	,	,	PUNCT
iajs-117	141	11	but	but	CCONJ
iajs-117	141	12	first	first	ADV
iajs-117	141	13	recall	recall	VERB
iajs-117	141	14	the	the	DET
iajs-117	141	15	following	following	NOUN
iajs-117	141	16	:	:	PUNCT
iajs-117	141	17	let	let	VERB
iajs-117	141	18	r	r	NOUN
iajs-117	141	19	be	be	AUX
iajs-117	141	20	any	any	DET
iajs-117	141	21	ring	ring	NOUN
iajs-117	141	22	.	.	PUNCT
iajs-117	142	1	a	a	DET
iajs-117	142	2	subset	subset	NOUN
iajs-117	142	3	s	s	NOUN
iajs-117	142	4	of	of	ADP
iajs-117	142	5	r	r	NOUN
iajs-117	142	6	is	be	AUX
iajs-117	142	7	called	call	VERB
iajs-117	142	8	multiplicatively	multiplicatively	ADV
iajs-117	142	9	closed	close	VERB
iajs-117	142	10	if	if	SCONJ
iajs-117	142	11	1	1	NUM
iajs-117	142	12	s	s	NOUN
iajs-117	142	13	and	and	CCONJ
iajs-117	142	14	ab	ab	PROPN
iajs-117	142	15			PROPN
iajs-117	142	16	s	s	PART
iajs-117	142	17	for	for	ADP
iajs-117	142	18	every	every	PRON
iajs-117	142	19	a	a	DET
iajs-117	142	20	,	,	PUNCT
iajs-117	142	21	bs	bs	PROPN
iajs-117	142	22	.	.	NOUN
iajs-117	143	1	we	we	PRON
iajs-117	143	2	know	know	VERB
iajs-117	143	3	that	that	SCONJ
iajs-117	143	4	every	every	DET
iajs-117	143	5	proper	proper	ADJ
iajs-117	143	6	ideal	ideal	NOUN
iajs-117	143	7	p	p	NOUN
iajs-117	143	8	in	in	ADP
iajs-117	143	9	r	r	NOUN
iajs-117	143	10	is	be	AUX
iajs-117	143	11	prime	prime	ADJ
iajs-117	143	12	if	if	SCONJ
iajs-117	143	13	and	and	CCONJ
iajs-117	143	14	only	only	ADV
iajs-117	143	15	if	if	SCONJ
iajs-117	143	16	r	r	X
iajs-117	143	17	-	-	PUNCT
iajs-117	143	18	p	p	NOUN
iajs-117	143	19	is	be	AUX
iajs-117	143	20	mathematics	mathematic	NOUN
iajs-117	143	21	|	|	ADV
iajs-117	143	22	286	286	NUM
iajs-117	143	23	2016	2016	NUM
iajs-117	143	24	)	)	PUNCT
iajs-117	143	25	عام	عام	ADP
iajs-117	143	26	2العدد	2العدد	NUM
iajs-117	143	27	(	(	PUNCT
iajs-117	143	28	29لمجلد	29لمجلد	NUM
iajs-117	143	29	ا	ا	X
iajs-117	143	30	مجلة	مجلة	NOUN
iajs-117	143	31	إبن	إبن	VERB
iajs-117	143	32	الهيثم	الهيثم	ADJ
iajs-117	143	33	للعلوم	للعلوم	NOUN
iajs-117	143	34	الصرفة	الصرفة	NOUN
iajs-117	143	35	و	و	PRON
iajs-117	143	36	التطبيقية	التطبيقية	ADJ
iajs-117	143	37	ibn	ibn	PROPN
iajs-117	143	38	al	al	PROPN
iajs-117	143	39	-	-	PUNCT
iajs-117	143	40	haitham	haitham	PROPN
iajs-117	143	41	jour	jour	X
iajs-117	143	42	.	.	PROPN
iajs-117	144	1	for	for	ADP
iajs-117	144	2	pure	pure	ADJ
iajs-117	144	3	&	&	CCONJ
iajs-117	144	4	appl	appl	PROPN
iajs-117	144	5	.	.	PUNCT
iajs-117	145	1	sci	sci	PROPN
iajs-117	145	2	.	.	PUNCT
iajs-117	145	3	vol	vol	NOUN
iajs-117	145	4	.	.	PROPN
iajs-117	145	5	29	29	NUM
iajs-117	145	6	(	(	PUNCT
iajs-117	145	7	2	2	NUM
iajs-117	145	8	)	)	PUNCT
iajs-117	145	9	2016	2016	NUM
iajs-117	145	10	multiplicatively	multiplicatively	ADV
iajs-117	145	11	closed	close	VERB
iajs-117	145	12	subset	subset	NOUN
iajs-117	145	13	of	of	ADP
iajs-117	145	14	r,[1,p.42	r,[1,p.42	NOUN
iajs-117	145	15	]	]	X
iajs-117	145	16	.	.	PUNCT
iajs-117	146	1	and	and	CCONJ
iajs-117	146	2	if	if	SCONJ
iajs-117	146	3	n	n	PRON
iajs-117	146	4	is	be	AUX
iajs-117	146	5	a	a	DET
iajs-117	146	6	submodule	submodule	NOUN
iajs-117	146	7	of	of	ADP
iajs-117	146	8	an	an	DET
iajs-117	146	9	r	r	NOUN
iajs-117	146	10	-	-	PUNCT
iajs-117	146	11	module	module	NOUN
iajs-117	146	12	m	m	NOUN
iajs-117	146	13	and	and	CCONJ
iajs-117	146	14	s	s	VERB
iajs-117	146	15	is	be	AUX
iajs-117	146	16	multiplicatively	multiplicatively	ADV
iajs-117	146	17	closed	close	VERB
iajs-117	146	18	sub	sub	NOUN
iajs-117	146	19	set	set	NOUN
iajs-117	146	20	of	of	ADP
iajs-117	146	21	r	r	NOUN
iajs-117	146	22	,	,	PUNCT
iajs-117	146	23	then	then	ADV
iajs-117	146	24	n(s	n(s	PROPN
iajs-117	146	25	)	)	PUNCT
iajs-117	147	1	=	=	NOUN
iajs-117	147	2	{	{	PUNCT
iajs-117	147	3	x	x	PROPN
iajs-117	147	4	m:	m:	PROPN
iajs-117	147	5	t	t	PROPN
iajs-117	147	6			PROPN
iajs-117	147	7	s	s	PROPN
iajs-117	147	8	,	,	PUNCT
iajs-117	147	9	such	such	ADJ
iajs-117	147	10	that	that	SCONJ
iajs-117	147	11	tx	tx	NOUN
iajs-117	147	12	n}be	n}be	PROPN
iajs-117	147	13	a	a	DET
iajs-117	147	14	submodule	submodule	NOUN
iajs-117	147	15	of	of	ADP
iajs-117	147	16	m	m	PROPN
iajs-117	147	17	and	and	CCONJ
iajs-117	147	18	n	n	ADV
iajs-117	147	19	n(s	n(s	PROPN
iajs-117	147	20	)	)	PUNCT
iajs-117	147	21	.	.	PUNCT
iajs-117	148	1	proposition	proposition	NOUN
iajs-117	148	2	(	(	PUNCT
iajs-117	148	3	2.11	2.11	NUM
iajs-117	148	4	):	):	PUNCT
iajs-117	148	5	let	let	VERB
iajs-117	148	6	n	n	PRON
iajs-117	148	7	be	be	AUX
iajs-117	148	8	a	a	DET
iajs-117	148	9	proper	proper	ADJ
iajs-117	148	10	submodule	submodule	NOUN
iajs-117	148	11	of	of	ADP
iajs-117	148	12	an	an	DET
iajs-117	148	13	rmodule	rmodule	NOUN
iajs-117	148	14	m	m	NOUN
iajs-117	148	15	.if	.if	PUNCT
iajs-117	149	1	[	[	X
iajs-117	149	2	n	n	X
iajs-117	149	3	+	+	CCONJ
iajs-117	149	4	(n):m	(n):m	NOUN
iajs-117	149	5	]	]	PUNCT
iajs-117	149	6	is	be	AUX
iajs-117	149	7	a	a	DET
iajs-117	149	8	prime	prime	ADJ
iajs-117	149	9	ideal	ideal	NOUN
iajs-117	149	10	of	of	ADP
iajs-117	149	11	r	r	NOUN
iajs-117	149	12	and	and	CCONJ
iajs-117	149	13	n(s	n(s	PROPN
iajs-117	149	14	)	)	PUNCT
iajs-117	149	15			PROPN
iajs-117	149	16	n	n	PROPN
iajs-117	149	17	+	+	CCONJ
iajs-117	149	18	(n	(n	NOUN
iajs-117	149	19	)	)	PUNCT
iajs-117	149	20	for	for	ADP
iajs-117	149	21	each	each	DET
iajs-117	149	22	multiplicatively	multiplicatively	ADV
iajs-117	149	23	closed	close	VERB
iajs-117	149	24	subset	subset	NOUN
iajs-117	149	25	of	of	ADP
iajs-117	149	26	r	r	NOUN
iajs-117	149	27	such	such	ADJ
iajs-117	149	28	that	that	DET
iajs-117	149	29	s	s	X
iajs-117	149	30			NOUN
iajs-117	149	31	[	[	X
iajs-117	149	32	n	n	CCONJ
iajs-117	149	33	+	+	CCONJ
iajs-117	149	34	(n):m	(n):m	NOUN
iajs-117	149	35	]	]	X
iajs-117	149	36	=	=	SYM
iajs-117	150	1	,then	,then	PROPN
iajs-117	150	2	n	n	NUM
iajs-117	150	3	is	be	AUX
iajs-117	150	4	-prime	-prime	PROPN
iajs-117	150	5	submodule	submodule	NOUN
iajs-117	150	6	of	of	ADP
iajs-117	150	7	m	m	PROPN
iajs-117	150	8	.	.	PUNCT
iajs-117	151	1	proof	proof	NOUN
iajs-117	151	2	:	:	PUNCT
iajs-117	151	3	let	let	VERB
iajs-117	151	4	r	r	NOUN
iajs-117	151	5			NOUN
iajs-117	151	6	r	r	NOUN
iajs-117	151	7	,	,	PUNCT
iajs-117	151	8	m	m	VERB
iajs-117	151	9			NOUN
iajs-117	151	10	m	m	VERB
iajs-117	151	11	such	such	ADJ
iajs-117	151	12	that	that	DET
iajs-117	151	13	rm	rm	PROPN
iajs-117	151	14	n	n	NOUN
iajs-117	151	15	and	and	CCONJ
iajs-117	151	16	suppose	suppose	VERB
iajs-117	151	17	m	m	PROPN
iajs-117	151	18	n	n	PROPN
iajs-117	151	19	+	+	CCONJ
iajs-117	151	20	(n	(n	X
iajs-117	151	21	)	)	PUNCT
iajs-117	151	22	,	,	PUNCT
iajs-117	151	23	r	r	NOUN
iajs-117	151	24			NOUN
iajs-117	151	25	[	[	X
iajs-117	151	26	n	n	CCONJ
iajs-117	151	27	+	+	CCONJ
iajs-117	151	28	(n):m	(n):m	NOUN
iajs-117	151	29	]	]	PUNCT
iajs-117	151	30	.	.	PUNCT
iajs-117	152	1	consider	consider	VERB
iajs-117	152	2	the	the	DET
iajs-117	152	3	set	set	NOUN
iajs-117	152	4	s	s	PART
iajs-117	152	5	=	=	NOUN
iajs-117	152	6	{	{	PUNCT
iajs-117	152	7	1,r	1,r	NUM
iajs-117	152	8	,	,	PUNCT
iajs-117	152	9	r	r	NOUN
iajs-117	152	10	2	2	NUM
iajs-117	152	11	,	,	PUNCT
iajs-117	152	12	…	…	PUNCT
iajs-117	152	13	…	…	PUNCT
iajs-117	152	14	…	…	PUNCT
iajs-117	152	15	.},this	.},this	PRON
iajs-117	152	16	is	be	AUX
iajs-117	152	17	multiplicatively	multiplicatively	ADV
iajs-117	152	18	closed	close	VERB
iajs-117	152	19	subset	subset	NOUN
iajs-117	152	20	of	of	ADP
iajs-117	152	21	r	r	NOUN
iajs-117	153	1	and	and	CCONJ
iajs-117	153	2	it	it	PRON
iajs-117	153	3	is	be	AUX
iajs-117	153	4	clear	clear	ADJ
iajs-117	153	5	that	that	SCONJ
iajs-117	153	6	s	s	VERB
iajs-117	153	7	[n	[n	PROPN
iajs-117	153	8	+	+	CCONJ
iajs-117	153	9	(n):m	(n):m	NOUN
iajs-117	153	10	]	]	X
iajs-117	153	11			NOUN
iajs-117	153	12	,	,	PUNCT
iajs-117	153	13	since	since	SCONJ
iajs-117	153	14	n	n	PROPN
iajs-117	153	15			NOUN
iajs-117	153	16	n	n	NOUN
iajs-117	153	17	:	:	PUNCT
iajs-117	153	18	m	m	VERB
iajs-117	153	19	is	be	AUX
iajs-117	153	20	a	a	DET
iajs-117	153	21	prime	prime	ADJ
iajs-117	153	22	ideal	ideal	NOUN
iajs-117	153	23	of	of	ADP
iajs-117	153	24	r.	r.	PROPN
iajs-117	153	25	but	but	CCONJ
iajs-117	153	26	m	m	PROPN
iajs-117	153	27	n	n	PROPN
iajs-117	153	28	+	+	CCONJ
iajs-117	153	29	(n	(n	X
iajs-117	153	30	)	)	PUNCT
iajs-117	153	31	implies	imply	VERB
iajs-117	153	32	that	that	SCONJ
iajs-117	153	33	m	m	PROPN
iajs-117	153	34	n(s	n(s	PROPN
iajs-117	153	35	)	)	PUNCT
iajs-117	154	1	and	and	CCONJ
iajs-117	154	2	so	so	ADV
iajs-117	154	3	r	r	NOUN
iajs-117	154	4	m	m	NOUN
iajs-117	154	5	n	n	PROPN
iajs-117	154	6	which	which	PRON
iajs-117	154	7	is	be	AUX
iajs-117	154	8	a	a	DET
iajs-117	154	9	contradiction	contradiction	NOUN
iajs-117	154	10	.therefore	.therefore	ADP
iajs-117	154	11	either	either	CCONJ
iajs-117	154	12	m	m	PROPN
iajs-117	154	13	n	n	NOUN
iajs-117	154	14	+	+	CCONJ
iajs-117	154	15	(n	(n	X
iajs-117	154	16	)	)	PUNCT
iajs-117	154	17	or	or	CCONJ
iajs-117	154	18	r[n	r[n	PROPN
iajs-117	154	19	+	+	CCONJ
iajs-117	154	20	(n):m	(n):m	NOUN
iajs-117	154	21	]	]	PUNCT
iajs-117	154	22	and	and	CCONJ
iajs-117	154	23	hence	hence	ADV
iajs-117	154	24	n	n	PRON
iajs-117	154	25	is	be	AUX
iajs-117	154	26	-prime	-prime	ADJ
iajs-117	154	27	submodule	submodule	NOUN
iajs-117	154	28	of	of	ADP
iajs-117	154	29	m	m	PROPN
iajs-117	154	30	.	.	PUNCT
iajs-117	155	1	conversely	conversely	ADV
iajs-117	155	2	,	,	PUNCT
iajs-117	155	3	if	if	SCONJ
iajs-117	155	4	n	n	PRON
iajs-117	155	5	is	be	AUX
iajs-117	155	6	-prime	-prime	PROPN
iajs-117	155	7	submodule	submodule	NOUN
iajs-117	155	8	of	of	ADP
iajs-117	155	9	m	m	PROPN
iajs-117	155	10	,	,	PUNCT
iajs-117	155	11	to	to	PART
iajs-117	155	12	prove	prove	VERB
iajs-117	155	13	n(s	n(s	NOUN
iajs-117	155	14	)	)	PUNCT
iajs-117	155	15			PROPN
iajs-117	155	16	n	n	PROPN
iajs-117	155	17	+	+	CCONJ
iajs-117	155	18	(n	(n	X
iajs-117	155	19	)	)	PUNCT
iajs-117	155	20	.	.	PUNCT
iajs-117	156	1	let	let	VERB
iajs-117	156	2	x	x	PRON
iajs-117	156	3			PROPN
iajs-117	156	4	n(s	n(s	PROPN
iajs-117	156	5	)	)	PUNCT
iajs-117	156	6	,	,	PUNCT
iajs-117	156	7	so	so	CCONJ
iajs-117	156	8	there	there	PRON
iajs-117	156	9	exists	exist	VERB
iajs-117	156	10	t	t	NOUN
iajs-117	156	11	s	s	NOUN
iajs-117	156	12	such	such	ADJ
iajs-117	156	13	that	that	PRON
iajs-117	156	14	tx	tx	PROPN
iajs-117	156	15			PROPN
iajs-117	156	16	n	n	PROPN
iajs-117	156	17	.	.	PUNCT
iajs-117	157	1	but	but	CCONJ
iajs-117	157	2	n	n	PRON
iajs-117	157	3	is	be	AUX
iajs-117	157	4	-prime	-prime	PROPN
iajs-117	157	5	submodule	submodule	NOUN
iajs-117	157	6	of	of	ADP
iajs-117	157	7	m	m	PROPN
iajs-117	157	8	,	,	PUNCT
iajs-117	157	9	so	so	ADV
iajs-117	157	10	either	either	CCONJ
iajs-117	157	11	x	x	PUNCT
iajs-117	157	12			NOUN
iajs-117	157	13	n	n	PROPN
iajs-117	157	14	+	+	CCONJ
iajs-117	157	15	(n	(n	X
iajs-117	157	16	)	)	PUNCT
iajs-117	157	17	or	or	CCONJ
iajs-117	157	18	t	t	PROPN
iajs-117	157	19	n	n	CCONJ
iajs-117	157	20			NOUN
iajs-117	157	21	n	n	NOUN
iajs-117	157	22	:	:	PUNCT
iajs-117	157	23	m	m	NOUN
iajs-117	157	24	.	.	PUNCT
iajs-117	158	1	but	but	CCONJ
iajs-117	158	2	t	t	PROPN
iajs-117	158	3			NOUN
iajs-117	158	4	n	n	CCONJ
iajs-117	158	5			NOUN
iajs-117	158	6	n	n	NOUN
iajs-117	158	7	:	:	PUNCT
iajs-117	158	8	m	m	VERB
iajs-117	158	9	implies	imply	VERB
iajs-117	158	10	that	that	SCONJ
iajs-117	158	11	s	s	VERB
iajs-117	158	12			PUNCT
iajs-117	158	13	n	n	NOUN
iajs-117	158	14			NOUN
iajs-117	158	15	n	n	NOUN
iajs-117	158	16	:	:	PUNCT
iajs-117	158	17	m	m	VERB
iajs-117	158	18	=	=	NOUN
iajs-117	158	19			NOUN
iajs-117	158	20	which	which	PRON
iajs-117	158	21	is	be	AUX
iajs-117	158	22	a	a	DET
iajs-117	158	23	contradiction	contradiction	NOUN
iajs-117	158	24	.thus	.thus	PRON
iajs-117	158	25	,	,	PUNCT
iajs-117	158	26	xn	xn	PUNCT
iajs-117	159	1	+	+	NOUN
iajs-117	159	2	(n	(n	X
iajs-117	159	3	)	)	PUNCT
iajs-117	159	4	and	and	CCONJ
iajs-117	159	5	hence	hence	ADV
iajs-117	159	6	n(s	n(s	PROPN
iajs-117	159	7	)	)	PUNCT
iajs-117	159	8	n+	n+	PROPN
iajs-117	159	9	(n	(n	PROPN
iajs-117	159	10	)	)	PUNCT
iajs-117	159	11	.	.	PUNCT
iajs-117	160	1	proposition	proposition	NOUN
iajs-117	160	2	(	(	PUNCT
iajs-117	160	3	2.12	2.12	NUM
iajs-117	160	4	):	):	PUNCT
iajs-117	160	5	if	if	SCONJ
iajs-117	160	6	[	[	X
iajs-117	160	7	n	n	X
iajs-117	160	8	+	+	CCONJ
iajs-117	160	9	(n):m	(n):m	NOUN
iajs-117	160	10	]	]	PUNCT
iajs-117	160	11	is	be	AUX
iajs-117	160	12	maximal	maximal	ADJ
iajs-117	160	13	ideal	ideal	NOUN
iajs-117	160	14	of	of	ADP
iajs-117	160	15	r	r	NOUN
iajs-117	160	16	,	,	PUNCT
iajs-117	160	17	then	then	ADV
iajs-117	160	18	n	n	PRON
iajs-117	160	19	is	be	AUX
iajs-117	160	20	-prime	-prime	PROPN
iajs-117	160	21	submodule	submodule	NOUN
iajs-117	160	22	of	of	ADP
iajs-117	160	23	m	m	PROPN
iajs-117	160	24	.	.	PUNCT
iajs-117	161	1	proof	proof	NOUN
iajs-117	161	2	:	:	PUNCT
iajs-117	161	3	let	let	VERB
iajs-117	161	4	r	r	NOUN
iajs-117	161	5			NOUN
iajs-117	161	6	r	r	NOUN
iajs-117	161	7	,	,	PUNCT
iajs-117	161	8	m	m	VERB
iajs-117	161	9			NOUN
iajs-117	161	10	m	m	VERB
iajs-117	161	11	such	such	ADJ
iajs-117	161	12	that	that	DET
iajs-117	161	13	rm	rm	PROPN
iajs-117	161	14	n	n	PROPN
iajs-117	161	15	.if	.if	PUNCT
iajs-117	162	1	r	r	NOUN
iajs-117	162	2			NOUN
iajs-117	162	3	n	n	CCONJ
iajs-117	162	4			NOUN
iajs-117	162	5	n	n	NOUN
iajs-117	162	6	:	:	PUNCT
iajs-117	162	7	m	m	INTJ
iajs-117	162	8	,	,	PUNCT
iajs-117	162	9	then	then	ADV
iajs-117	162	10	r=	r=	VERB
iajs-117	162	11	<	<	X
iajs-117	162	12	r	r	X
iajs-117	162	13	>	>	X
iajs-117	162	14	+	+	PROPN
iajs-117	162	15	n	n	CCONJ
iajs-117	162	16			NOUN
iajs-117	162	17	n	n	NOUN
iajs-117	162	18	:	:	PUNCT
iajs-117	162	19	m	m	NOUN
iajs-117	162	20	.therefore	.therefore	ADV
iajs-117	162	21	there	there	ADV
iajs-117	162	22	exist	exist	VERB
iajs-117	162	23	sr	sr	PUNCT
iajs-117	162	24	and	and	CCONJ
iajs-117	162	25	k	k	PROPN
iajs-117	163	1	n	n	CCONJ
iajs-117	163	2			NOUN
iajs-117	163	3	n	n	NOUN
iajs-117	163	4	:	:	PUNCT
iajs-117	163	5	m	m	VERB
iajs-117	163	6	such	such	ADJ
iajs-117	163	7	that	that	SCONJ
iajs-117	163	8	1	1	NUM
iajs-117	163	9	=	=	SYM
iajs-117	163	10	s	s	NOUN
iajs-117	163	11	r	r	NOUN
iajs-117	163	12	+	+	PROPN
iajs-117	163	13	k	k	PROPN
iajs-117	164	1	and	and	CCONJ
iajs-117	164	2	so	so	ADV
iajs-117	164	3	m=	m=	X
iajs-117	164	4	srm	srm	NOUN
iajs-117	164	5	+	+	ADJ
iajs-117	164	6	km	km	PROPN
iajs-117	164	7			NOUN
iajs-117	164	8	n	n	CCONJ
iajs-117	164	9	+	+	CCONJ
iajs-117	164	10	(n	(n	NOUN
iajs-117	164	11	)	)	PUNCT
iajs-117	164	12	.therefore	.therefore	PUNCT
iajs-117	165	1	n	n	ADV
iajs-117	165	2	is	be	AUX
iajs-117	165	3	-prime	-prime	ADJ
iajs-117	165	4	submodule	submodule	NOUN
iajs-117	165	5	of	of	ADP
iajs-117	165	6	m.	m.	NOUN
iajs-117	165	7	proposition	proposition	NOUN
iajs-117	165	8	(	(	PUNCT
iajs-117	165	9	2.13	2.13	NUM
iajs-117	165	10	):	):	PUNCT
iajs-117	165	11	let	let	VERB
iajs-117	165	12	n	n	PRON
iajs-117	165	13	be	be	AUX
iajs-117	165	14	a	a	DET
iajs-117	165	15	proper	proper	ADJ
iajs-117	165	16	submodule	submodule	NOUN
iajs-117	165	17	of	of	ADP
iajs-117	165	18	an	an	DET
iajs-117	165	19	rmodule	rmodule	NOUN
iajs-117	165	20	m	m	VERB
iajs-117	165	21	such	such	ADJ
iajs-117	165	22	that	that	SCONJ
iajs-117	166	1	[	[	X
iajs-117	166	2	k	k	X
iajs-117	166	3	:	:	PUNCT
iajs-117	166	4	m	m	VERB
iajs-117	166	5	]	]	X
iajs-117	166	6	⊈	⊈	PUNCT
iajs-117	167	1	[	[	X
iajs-117	167	2	n+	n+	ADP
iajs-117	167	3	(n):m	(n):m	NOUN
iajs-117	167	4	]	]	PUNCT
iajs-117	167	5	for	for	ADP
iajs-117	167	6	each	each	DET
iajs-117	167	7	submodule	submodule	NOUN
iajs-117	167	8	k	k	PROPN
iajs-117	167	9	of	of	ADP
iajs-117	167	10	m	m	PROPN
iajs-117	167	11	and	and	CCONJ
iajs-117	167	12	containing	contain	VERB
iajs-117	167	13	n+	n+	NUM
iajs-117	167	14	(n	(n	X
iajs-117	167	15	)	)	PUNCT
iajs-117	167	16	properly	properly	ADV
iajs-117	167	17	.if	.if	PUNCT
iajs-117	168	1	[	[	X
iajs-117	168	2	n	n	X
iajs-117	168	3	+	+	CCONJ
iajs-117	168	4	(n):m	(n):m	NOUN
iajs-117	168	5	]	]	PUNCT
iajs-117	168	6	is	be	AUX
iajs-117	168	7	a	a	DET
iajs-117	168	8	prime	prime	ADJ
iajs-117	168	9	ideal	ideal	NOUN
iajs-117	168	10	of	of	ADP
iajs-117	168	11	r	r	NOUN
iajs-117	168	12	,	,	PUNCT
iajs-117	168	13	then	then	ADV
iajs-117	168	14	n	n	PRON
iajs-117	168	15	is	be	AUX
iajs-117	168	16	-prime	-prime	PROPN
iajs-117	168	17	submodule	submodule	NOUN
iajs-117	168	18	of	of	ADP
iajs-117	168	19	m	m	PROPN
iajs-117	168	20	.	.	PUNCT
iajs-117	169	1	proof	proof	NOUN
iajs-117	169	2	:	:	PUNCT
iajs-117	169	3	suppose	suppose	VERB
iajs-117	169	4	[	[	X
iajs-117	169	5	n	n	X
iajs-117	169	6	+	+	NUM
iajs-117	169	7	(n):m	(n):m	NOUN
iajs-117	169	8	]	]	PUNCT
iajs-117	169	9	is	be	AUX
iajs-117	169	10	a	a	DET
iajs-117	169	11	prime	prime	ADJ
iajs-117	169	12	ideal	ideal	NOUN
iajs-117	169	13	of	of	ADP
iajs-117	169	14	r	r	NOUN
iajs-117	169	15	,	,	PUNCT
iajs-117	169	16	to	to	PART
iajs-117	169	17	prove	prove	VERB
iajs-117	169	18	n	n	PRON
iajs-117	169	19	is	be	AUX
iajs-117	169	20	-prime	-prime	ADJ
iajs-117	169	21	submodule	submodule	NOUN
iajs-117	169	22	of	of	ADP
iajs-117	169	23	m.	m.	NOUN
iajs-117	169	24	let	let	VERB
iajs-117	169	25	r	r	NOUN
iajs-117	169	26			NOUN
iajs-117	169	27	r	r	NOUN
iajs-117	169	28	,	,	PUNCT
iajs-117	169	29	m	m	VERB
iajs-117	169	30			NOUN
iajs-117	169	31	m	m	VERB
iajs-117	169	32	such	such	ADJ
iajs-117	169	33	that	that	DET
iajs-117	169	34	rm	rm	PROPN
iajs-117	169	35	n	n	NOUN
iajs-117	169	36	and	and	CCONJ
iajs-117	169	37	suppose	suppose	VERB
iajs-117	169	38	m	m	PROPN
iajs-117	169	39	n	n	PROPN
iajs-117	169	40	+	+	CCONJ
iajs-117	169	41	(n	(n	X
iajs-117	169	42	)	)	PUNCT
iajs-117	169	43	.	.	PUNCT
iajs-117	170	1	let	let	VERB
iajs-117	170	2	k	k	NOUN
iajs-117	170	3	=	=	PUNCT
iajs-117	170	4	n	n	PROPN
iajs-117	170	5	+	+	CCONJ
iajs-117	170	6	(n	(n	X
iajs-117	170	7	)	)	PUNCT
iajs-117	171	1	+	+	CCONJ
iajs-117	171	2	<	<	X
iajs-117	171	3	m	m	X
iajs-117	171	4	>	>	X
iajs-117	171	5	,	,	PUNCT
iajs-117	171	6	it	it	PRON
iajs-117	171	7	is	be	AUX
iajs-117	171	8	clear	clear	ADJ
iajs-117	171	9	that	that	SCONJ
iajs-117	171	10	n	n	PROPN
iajs-117	171	11	+	+	PROPN
iajs-117	171	12	(n)⊊	(n)⊊	PROPN
iajs-117	171	13	k	k	NOUN
iajs-117	171	14	,	,	PUNCT
iajs-117	171	15	and	and	CCONJ
iajs-117	171	16	so	so	ADV
iajs-117	172	1	[	[	X
iajs-117	172	2	k	k	X
iajs-117	172	3	:	:	PUNCT
iajs-117	172	4	m	m	VERB
iajs-117	172	5	]	]	X
iajs-117	172	6	⊈	⊈	PROPN
iajs-117	173	1	[	[	X
iajs-117	173	2	n+	n+	NUM
iajs-117	173	3	(n	(n	NOUN
iajs-117	173	4	):	):	PUNCT
iajs-117	173	5	m].then	m].then	ADV
iajs-117	173	6	there	there	PRON
iajs-117	173	7	exists	exist	VERB
iajs-117	173	8	s	s	PROPN
iajs-117	174	1	[	[	X
iajs-117	174	2	k	k	X
iajs-117	174	3	:	:	PUNCT
iajs-117	174	4	m	m	X
iajs-117	174	5	]	]	X
iajs-117	174	6	and	and	CCONJ
iajs-117	174	7	s	s	X
iajs-117	174	8			X
iajs-117	175	1	[	[	X
iajs-117	175	2	n	n	X
iajs-117	175	3	+	+	CCONJ
iajs-117	175	4	(n):m].thus	(n):m].thu	NOUN
iajs-117	175	5	,	,	PUNCT
iajs-117	175	6	sm	sm	PROPN
iajs-117	175	7			PROPN
iajs-117	175	8	k	k	PROPN
iajs-117	175	9	and	and	CCONJ
iajs-117	175	10	sm	sm	PRON
iajs-117	175	11	⊈	⊈	PROPN
iajs-117	175	12	n+	n+	PUNCT
iajs-117	175	13	(n).but	(n).but	NOUN
iajs-117	175	14	,	,	PUNCT
iajs-117	175	15	sm	sm	PROPN
iajs-117	175	16			PROPN
iajs-117	175	17	k	k	PROPN
iajs-117	175	18	implies	imply	VERB
iajs-117	175	19	,	,	PUNCT
iajs-117	175	20	r	r	PROPN
iajs-117	175	21	s	s	NOUN
iajs-117	175	22	m	m	NOUN
iajs-117	175	23			PROPN
iajs-117	175	24	r	r	NOUN
iajs-117	175	25	k	k	NOUN
iajs-117	175	26	=	=	SYM
iajs-117	175	27	r	r	NOUN
iajs-117	175	28	(	(	PUNCT
iajs-117	175	29	n	n	X
iajs-117	175	30	+	+	CCONJ
iajs-117	175	31	(n	(n	X
iajs-117	175	32	)	)	PUNCT
iajs-117	176	1	+	+	CCONJ
iajs-117	176	2	<	<	X
iajs-117	176	3	m	m	X
iajs-117	176	4	>	>	X
iajs-117	176	5	)	)	PUNCT
iajs-117	176	6			PROPN
iajs-117	176	7	n	n	PROPN
iajs-117	176	8	+	+	CCONJ
iajs-117	176	9	(n	(n	X
iajs-117	176	10	)	)	PUNCT
iajs-117	176	11	and	and	CCONJ
iajs-117	176	12	rs	rs	X
iajs-117	177	1	[	[	X
iajs-117	177	2	n	n	X
iajs-117	177	3	+	+	CCONJ
iajs-117	177	4	(n):m	(n):m	NOUN
iajs-117	177	5	]	]	PUNCT
iajs-117	177	6	.	.	PUNCT
iajs-117	178	1	since	since	SCONJ
iajs-117	178	2	[	[	X
iajs-117	178	3	n	n	X
iajs-117	178	4	+	+	CCONJ
iajs-117	178	5	(n):m	(n):m	NOUN
iajs-117	178	6	]	]	PUNCT
iajs-117	178	7	is	be	AUX
iajs-117	178	8	a	a	DET
iajs-117	178	9	prime	prime	ADJ
iajs-117	178	10	ideal	ideal	NOUN
iajs-117	178	11	of	of	ADP
iajs-117	178	12	r	r	NOUN
iajs-117	178	13	and	and	CCONJ
iajs-117	178	14	s	s	NOUN
iajs-117	178	15			NOUN
iajs-117	178	16	[	[	X
iajs-117	178	17	n	n	X
iajs-117	178	18	+	+	CCONJ
iajs-117	178	19	(n):m	(n):m	NOUN
iajs-117	178	20	]	]	PUNCT
iajs-117	178	21	,	,	PUNCT
iajs-117	178	22	so	so	ADV
iajs-117	178	23	r	r	ADJ
iajs-117	178	24	[	[	X
iajs-117	178	25	n	n	X
iajs-117	178	26	+	+	CCONJ
iajs-117	178	27	(n):m	(n):m	NOUN
iajs-117	178	28	]	]	PUNCT
iajs-117	178	29	.	.	PUNCT
iajs-117	179	1	therefore	therefore	ADV
iajs-117	179	2	n	n	PRON
iajs-117	179	3	is	be	AUX
iajs-117	179	4	-prime	-prime	PROPN
iajs-117	179	5	submodule	submodule	NOUN
iajs-117	179	6	of	of	ADP
iajs-117	179	7	m	m	PROPN
iajs-117	179	8	.	.	PUNCT
iajs-117	180	1	recall	recall	VERB
iajs-117	180	2	that	that	SCONJ
iajs-117	180	3	an	an	DET
iajs-117	180	4	rmodule	rmodule	NOUN
iajs-117	180	5	m	m	VERB
iajs-117	180	6	is	be	AUX
iajs-117	180	7	called	call	VERB
iajs-117	180	8	mulitplication	mulitplication	NOUN
iajs-117	180	9	module	module	NOUN
iajs-117	180	10	if	if	SCONJ
iajs-117	180	11	for	for	ADP
iajs-117	180	12	every	every	DET
iajs-117	180	13	submodule	submodule	NOUN
iajs-117	180	14	n	n	PROPN
iajs-117	180	15	of	of	ADP
iajs-117	180	16	m	m	PRON
iajs-117	180	17	,	,	PUNCT
iajs-117	180	18	there	there	PRON
iajs-117	180	19	exists	exist	VERB
iajs-117	180	20	an	an	DET
iajs-117	180	21	ideal	ideal	NOUN
iajs-117	180	22	i	i	PRON
iajs-117	180	23	of	of	ADP
iajs-117	180	24	r	r	NOUN
iajs-117	181	1	such	such	ADJ
iajs-117	181	2	that	that	SCONJ
iajs-117	181	3	im	im	NOUN
iajs-117	181	4	=	=	NOUN
iajs-117	181	5	n	n	PRON
iajs-117	181	6	,	,	PUNCT
iajs-117	181	7	equivalently	equivalently	ADV
iajs-117	181	8	;	;	PUNCT
iajs-117	181	9	for	for	ADP
iajs-117	181	10	every	every	DET
iajs-117	181	11	submodule	submodule	NOUN
iajs-117	181	12	n	n	PROPN
iajs-117	181	13	of	of	ADP
iajs-117	181	14	m	m	PRON
iajs-117	181	15	n=[n	n=[n	NOUN
iajs-117	181	16	:	:	PUNCT
iajs-117	181	17	m]m	m]m	NOUN
iajs-117	181	18	,	,	PUNCT
iajs-117	181	19	see[7	see[7	NOUN
iajs-117	181	20	]	]	PUNCT
iajs-117	181	21	.	.	PUNCT
iajs-117	182	1	corollary	corollary	ADJ
iajs-117	182	2	(	(	PUNCT
iajs-117	182	3	2.14	2.14	NUM
iajs-117	182	4	):	):	PUNCT
iajs-117	182	5	let	let	VERB
iajs-117	182	6	n	n	PRON
iajs-117	182	7	be	be	AUX
iajs-117	182	8	a	a	DET
iajs-117	182	9	proper	proper	ADJ
iajs-117	182	10	submodule	submodule	NOUN
iajs-117	182	11	of	of	ADP
iajs-117	182	12	a	a	DET
iajs-117	182	13	mulitplication	mulitplication	NOUN
iajs-117	182	14	rmodule	rmodule	NOUN
iajs-117	182	15	m.	m.	NOUN
iajs-117	182	16	then	then	ADV
iajs-117	182	17	n	n	PRON
iajs-117	182	18	is	be	AUX
iajs-117	182	19	-prime	-prime	PROPN
iajs-117	182	20	submodule	submodule	NOUN
iajs-117	182	21	of	of	ADP
iajs-117	182	22	m	m	PRON
iajs-117	182	23	if	if	SCONJ
iajs-117	182	24	[	[	X
iajs-117	182	25	n	n	X
iajs-117	182	26	+	+	CCONJ
iajs-117	182	27	(n):m	(n):m	NOUN
iajs-117	182	28	]	]	PUNCT
iajs-117	182	29	is	be	AUX
iajs-117	182	30	a	a	DET
iajs-117	182	31	prime	prime	ADJ
iajs-117	182	32	ideal	ideal	NOUN
iajs-117	182	33	of	of	ADP
iajs-117	182	34	r.	r.	PROPN
iajs-117	182	35	proof	proof	NOUN
iajs-117	182	36	:	:	PUNCT
iajs-117	182	37	suppose	suppose	VERB
iajs-117	182	38	[	[	X
iajs-117	182	39	n	n	X
iajs-117	182	40	+	+	NUM
iajs-117	182	41	(n):m	(n):m	NOUN
iajs-117	182	42	]	]	PUNCT
iajs-117	182	43	is	be	AUX
iajs-117	182	44	a	a	DET
iajs-117	182	45	prime	prime	ADJ
iajs-117	182	46	ideal	ideal	NOUN
iajs-117	182	47	of	of	ADP
iajs-117	182	48	r	r	NOUN
iajs-117	182	49	,	,	PUNCT
iajs-117	182	50	to	to	PART
iajs-117	182	51	prove	prove	VERB
iajs-117	182	52	n	n	PRON
iajs-117	182	53	is	be	AUX
iajs-117	182	54	-prime	-prime	ADJ
iajs-117	182	55	submodule	submodule	NOUN
iajs-117	182	56	of	of	ADP
iajs-117	182	57	m.	m.	NOUN
iajs-117	182	58	let	let	VERB
iajs-117	182	59	r	r	NOUN
iajs-117	182	60			NOUN
iajs-117	182	61	r	r	NOUN
iajs-117	182	62	,	,	PUNCT
iajs-117	182	63	m	m	VERB
iajs-117	182	64			NOUN
iajs-117	182	65	m	m	VERB
iajs-117	182	66	such	such	ADJ
iajs-117	182	67	that	that	DET
iajs-117	182	68	rm	rm	PROPN
iajs-117	182	69	n	n	NOUN
iajs-117	182	70	and	and	CCONJ
iajs-117	182	71	suppose	suppose	VERB
iajs-117	182	72	m	m	PROPN
iajs-117	182	73	n	n	PROPN
iajs-117	182	74	+	+	CCONJ
iajs-117	182	75	(n	(n	X
iajs-117	182	76	)	)	PUNCT
iajs-117	182	77	.	.	PUNCT
iajs-117	183	1	let	let	VERB
iajs-117	183	2	k	k	NOUN
iajs-117	183	3	=	=	PUNCT
iajs-117	183	4	n	n	PROPN
iajs-117	183	5	+	+	CCONJ
iajs-117	183	6	(n	(n	X
iajs-117	183	7	)	)	PUNCT
iajs-117	184	1	+	+	CCONJ
iajs-117	184	2	<	<	X
iajs-117	184	3	m>,it	m>,it	X
iajs-117	184	4	is	be	AUX
iajs-117	184	5	clear	clear	ADJ
iajs-117	184	6	that	that	SCONJ
iajs-117	184	7	n	n	PROPN
iajs-117	184	8	+	+	CCONJ
iajs-117	184	9	(n	(n	ADJ
iajs-117	184	10	)	)	PUNCT
iajs-117	184	11	⊊k	⊊k	NOUN
iajs-117	184	12	.	.	PUNCT
iajs-117	185	1	since	since	SCONJ
iajs-117	185	2	m	m	PROPN
iajs-117	185	3	is	be	AUX
iajs-117	185	4	mulitplication	mulitplication	NOUN
iajs-117	185	5	,	,	PUNCT
iajs-117	185	6	so	so	CCONJ
iajs-117	186	1	[	[	X
iajs-117	186	2	k	k	X
iajs-117	186	3	:	:	PUNCT
iajs-117	186	4	m	m	VERB
iajs-117	186	5	]	]	X
iajs-117	186	6	⊈	⊈	PUNCT
iajs-117	187	1	[	[	X
iajs-117	187	2	n+	n+	ADP
iajs-117	187	3	(n):m	(n):m	NOUN
iajs-117	187	4	]	]	X
iajs-117	187	5	by[9,remark	by[9,remark	NOUN
iajs-117	187	6	(	(	PUNCT
iajs-117	187	7	2	2	NUM
iajs-117	187	8	-	-	SYM
iajs-117	187	9	15),chapter	15),chapter	NUM
iajs-117	187	10	one	one	NOUN
iajs-117	187	11	]	]	PUNCT
iajs-117	187	12	.	.	PUNCT
iajs-117	188	1	then	then	ADV
iajs-117	188	2	there	there	PRON
iajs-117	188	3	exists	exist	VERB
iajs-117	188	4	s	s	PROPN
iajs-117	189	1	[	[	X
iajs-117	189	2	k	k	X
iajs-117	189	3	:	:	PUNCT
iajs-117	189	4	m	m	X
iajs-117	189	5	]	]	X
iajs-117	189	6	and	and	CCONJ
iajs-117	189	7	s	s	X
iajs-117	189	8			X
iajs-117	190	1	[	[	X
iajs-117	190	2	n	n	X
iajs-117	190	3	+	+	CCONJ
iajs-117	190	4	(n):m].thus	(n):m].thu	NOUN
iajs-117	190	5	,	,	PUNCT
iajs-117	190	6	sm	sm	PROPN
iajs-117	190	7			PROPN
iajs-117	190	8	k	k	PROPN
iajs-117	190	9	and	and	CCONJ
iajs-117	190	10	sm	sm	PRON
iajs-117	190	11	⊈	⊈	PROPN
iajs-117	190	12	n+	n+	PUNCT
iajs-117	190	13	(n).but	(n).but	NOUN
iajs-117	190	14	,	,	PUNCT
iajs-117	190	15	sm	sm	PROPN
iajs-117	190	16			PROPN
iajs-117	190	17	k	k	PROPN
iajs-117	190	18	implies	imply	VERB
iajs-117	190	19	r	r	NOUN
iajs-117	190	20	s	s	NOUN
iajs-117	190	21	m	m	NOUN
iajs-117	190	22			PROPN
iajs-117	190	23	r	r	NOUN
iajs-117	190	24	k	k	NOUN
iajs-117	190	25	=	=	SYM
iajs-117	190	26	r	r	NOUN
iajs-117	190	27	(	(	PUNCT
iajs-117	190	28	n	n	X
iajs-117	190	29	+	+	CCONJ
iajs-117	190	30	(n	(n	X
iajs-117	190	31	)	)	PUNCT
iajs-117	191	1	+	+	CCONJ
iajs-117	191	2	<	<	X
iajs-117	191	3	m	m	X
iajs-117	191	4	>	>	X
iajs-117	191	5	)	)	PUNCT
iajs-117	191	6			PROPN
iajs-117	191	7	n	n	PROPN
iajs-117	191	8	+	+	CCONJ
iajs-117	191	9	(n	(n	X
iajs-117	191	10	)	)	PUNCT
iajs-117	191	11	and	and	CCONJ
iajs-117	191	12	rs	rs	X
iajs-117	192	1	[	[	X
iajs-117	192	2	n	n	X
iajs-117	192	3	+	+	CCONJ
iajs-117	192	4	(n):m	(n):m	NOUN
iajs-117	192	5	]	]	PUNCT
iajs-117	192	6	.	.	PUNCT
iajs-117	193	1	since	since	SCONJ
iajs-117	193	2	[	[	X
iajs-117	193	3	n	n	X
iajs-117	193	4	+	+	CCONJ
iajs-117	193	5	(n):m	(n):m	NOUN
iajs-117	193	6	]	]	PUNCT
iajs-117	193	7	is	be	AUX
iajs-117	193	8	a	a	DET
iajs-117	193	9	prime	prime	ADJ
iajs-117	193	10	ideal	ideal	NOUN
iajs-117	193	11	of	of	ADP
iajs-117	193	12	r	r	NOUN
iajs-117	193	13	and	and	CCONJ
iajs-117	193	14	s	s	NOUN
iajs-117	193	15			NOUN
iajs-117	193	16	[	[	X
iajs-117	193	17	n	n	X
iajs-117	193	18	+	+	CCONJ
iajs-117	193	19	(n):m	(n):m	NOUN
iajs-117	193	20	]	]	PUNCT
iajs-117	193	21	,	,	PUNCT
iajs-117	193	22	so	so	ADV
iajs-117	193	23	r	r	ADJ
iajs-117	193	24	[	[	X
iajs-117	193	25	n	n	X
iajs-117	193	26	+	+	CCONJ
iajs-117	193	27	(n):m	(n):m	NOUN
iajs-117	193	28	]	]	X
iajs-117	193	29	.therefore	.therefore	PUNCT
iajs-117	193	30	n	n	ADV
iajs-117	193	31	is	be	AUX
iajs-117	193	32	-prime	-prime	PROPN
iajs-117	193	33	submodule	submodule	NOUN
iajs-117	193	34	of	of	ADP
iajs-117	193	35	m	m	PROPN
iajs-117	193	36	.	.	PUNCT
iajs-117	194	1	mathematics	mathematic	NOUN
iajs-117	194	2	|	|	ADV
iajs-117	194	3	287	287	NUM
iajs-117	194	4	2016	2016	NUM
iajs-117	194	5	)	)	PUNCT
iajs-117	194	6	عام	عام	ADP
iajs-117	194	7	2العدد	2العدد	NUM
iajs-117	194	8	(	(	PUNCT
iajs-117	194	9	29لمجلد	29لمجلد	NUM
iajs-117	194	10	ا	ا	X
iajs-117	194	11	مجلة	مجلة	NOUN
iajs-117	194	12	إبن	إبن	VERB
iajs-117	194	13	الهيثم	الهيثم	ADJ
iajs-117	194	14	للعلوم	للعلوم	NOUN
iajs-117	194	15	الصرفة	الصرفة	NOUN
iajs-117	195	1	و	و	PRON
iajs-117	195	2	التطبيقية	التطبيقية	ADJ
iajs-117	195	3	ibn	ibn	PROPN
iajs-117	195	4	al	al	PROPN
iajs-117	195	5	-	-	PUNCT
iajs-117	195	6	haitham	haitham	PROPN
iajs-117	195	7	jour	jour	X
iajs-117	195	8	.	.	PROPN
iajs-117	195	9	for	for	ADP
iajs-117	195	10	pure	pure	ADJ
iajs-117	195	11	&	&	CCONJ
iajs-117	195	12	appl	appl	PROPN
iajs-117	195	13	.	.	PUNCT
iajs-117	196	1	sci	sci	PROPN
iajs-117	196	2	.	.	PUNCT
iajs-117	196	3	vol	vol	NOUN
iajs-117	196	4	.	.	PROPN
iajs-117	196	5	29	29	NUM
iajs-117	196	6	(	(	PUNCT
iajs-117	196	7	2	2	NUM
iajs-117	196	8	)	)	PUNCT
iajs-117	196	9	2016	2016	NUM
iajs-117	196	10	as	as	ADP
iajs-117	196	11	anther	anther	ADJ
iajs-117	196	12	consequence	consequence	NOUN
iajs-117	196	13	of	of	ADP
iajs-117	196	14	(	(	PUNCT
iajs-117	196	15	2.13	2.13	NUM
iajs-117	196	16	)	)	PUNCT
iajs-117	196	17	,	,	PUNCT
iajs-117	196	18	we	we	PRON
iajs-117	196	19	have	have	VERB
iajs-117	196	20	the	the	DET
iajs-117	196	21	following	follow	VERB
iajs-117	196	22	result	result	NOUN
iajs-117	196	23	:	:	PUNCT
iajs-117	196	24	corollary	corollary	ADJ
iajs-117	196	25	(	(	PUNCT
iajs-117	196	26	2.15	2.15	NUM
iajs-117	196	27	):	):	PUNCT
iajs-117	196	28	let	let	VERB
iajs-117	196	29	n	n	PRON
iajs-117	196	30	be	be	AUX
iajs-117	196	31	a	a	DET
iajs-117	196	32	proper	proper	ADJ
iajs-117	196	33	submodule	submodule	NOUN
iajs-117	196	34	of	of	ADP
iajs-117	196	35	a	a	DET
iajs-117	196	36	cyclic	cyclic	ADJ
iajs-117	196	37	rmodule	rmodule	NOUN
iajs-117	196	38	m.	m.	NOUN
iajs-117	196	39	then	then	ADV
iajs-117	196	40	n	n	PRON
iajs-117	196	41	is	be	AUX
iajs-117	196	42	-prime	-prime	PROPN
iajs-117	196	43	submodule	submodule	NOUN
iajs-117	196	44	of	of	ADP
iajs-117	196	45	m	m	PRON
iajs-117	196	46	if	if	SCONJ
iajs-117	196	47	[	[	X
iajs-117	196	48	n	n	X
iajs-117	196	49	+	+	CCONJ
iajs-117	196	50	(n):m	(n):m	NOUN
iajs-117	196	51	]	]	PUNCT
iajs-117	196	52	is	be	AUX
iajs-117	196	53	a	a	DET
iajs-117	196	54	prime	prime	ADJ
iajs-117	196	55	ideal	ideal	NOUN
iajs-117	196	56	of	of	ADP
iajs-117	196	57	r.	r.	PROPN
iajs-117	196	58	proof	proof	NOUN
iajs-117	196	59	:	:	PUNCT
iajs-117	196	60	since	since	SCONJ
iajs-117	196	61	m	m	PROPN
iajs-117	196	62	is	be	AUX
iajs-117	196	63	cyclic	cyclic	ADJ
iajs-117	196	64	,	,	PUNCT
iajs-117	196	65	then	then	ADV
iajs-117	196	66	m	m	VERB
iajs-117	196	67	is	be	AUX
iajs-117	196	68	a	a	DET
iajs-117	196	69	mulitplication	mulitplication	NOUN
iajs-117	196	70	.	.	PUNCT
iajs-117	197	1	hence	hence	ADV
iajs-117	197	2	the	the	DET
iajs-117	197	3	result	result	NOUN
iajs-117	197	4	follows	follow	VERB
iajs-117	197	5	immediately	immediately	ADV
iajs-117	197	6	from	from	ADP
iajs-117	197	7	corollary	corollary	ADJ
iajs-117	197	8	(	(	PUNCT
iajs-117	197	9	2.14	2.14	NUM
iajs-117	197	10	)	)	PUNCT
iajs-117	197	11	.	.	PUNCT
iajs-117	198	1	recall	recall	VERB
iajs-117	198	2	that	that	SCONJ
iajs-117	198	3	an	an	DET
iajs-117	198	4	r	r	NOUN
iajs-117	198	5	–	–	PUNCT
iajs-117	198	6	module	module	NOUN
iajs-117	198	7	m	m	NOUN
iajs-117	198	8	is	be	AUX
iajs-117	198	9	said	say	VERB
iajs-117	198	10	to	to	PART
iajs-117	198	11	be	be	AUX
iajs-117	198	12	bounded	bound	VERB
iajs-117	198	13	module	module	NOUN
iajs-117	198	14	if	if	SCONJ
iajs-117	198	15	there	there	PRON
iajs-117	198	16	exists	exist	VERB
iajs-117	198	17	an	an	DET
iajs-117	198	18	element	element	NOUN
iajs-117	198	19	x	x	PRON
iajs-117	198	20			PROPN
iajs-117	198	21	m	m	VERB
iajs-117	198	22	such	such	ADJ
iajs-117	198	23	that	that	DET
iajs-117	198	24	annm	annm	NOUN
iajs-117	198	25	=	=	SYM
iajs-117	198	26	ann(x	ann(x	PROPN
iajs-117	198	27	)	)	PUNCT
iajs-117	198	28	,	,	PUNCT
iajs-117	198	29	where	where	SCONJ
iajs-117	198	30	annm	annm	NOUN
iajs-117	198	31	=	=	PRON
iajs-117	198	32	{	{	PUNCT
iajs-117	198	33	r	r	NOUN
iajs-117	198	34			NOUN
iajs-117	198	35	r	r	NOUN
iajs-117	198	36	:	:	PUNCT
iajs-117	198	37	rm	rm	NOUN
iajs-117	198	38	=	=	SYM
iajs-117	198	39	0	0	PROPN
iajs-117	198	40	,	,	PUNCT
iajs-117	198	41			NOUN
iajs-117	198	42	m	m	PROPN
iajs-117	198	43	m	m	PROPN
iajs-117	198	44	}	}	PUNCT
iajs-117	198	45	,	,	PUNCT
iajs-117	198	46	[	[	X
iajs-117	198	47	8].and	8].and	NUM
iajs-117	198	48	an	an	DET
iajs-117	198	49	rmodule	rmodule	NOUN
iajs-117	198	50	m	m	VERB
iajs-117	198	51	is	be	AUX
iajs-117	198	52	said	say	VERB
iajs-117	198	53	to	to	PART
iajs-117	198	54	be	be	AUX
iajs-117	198	55	fully	fully	ADV
iajs-117	198	56	stable	stable	ADJ
iajs-117	198	57	if	if	SCONJ
iajs-117	198	58	each	each	DET
iajs-117	198	59	submodule	submodule	NOUN
iajs-117	198	60	is	be	AUX
iajs-117	198	61	stable	stable	ADJ
iajs-117	198	62	,	,	PUNCT
iajs-117	198	63	where	where	SCONJ
iajs-117	198	64	a	a	DET
iajs-117	198	65	submodule	submodule	NOUN
iajs-117	198	66	n	n	PROPN
iajs-117	198	67	of	of	ADP
iajs-117	198	68	an	an	DET
iajs-117	198	69	r	r	NOUN
iajs-117	198	70	–	–	PUNCT
iajs-117	198	71	module	module	NOUN
iajs-117	198	72	m	m	NOUN
iajs-117	198	73	is	be	AUX
iajs-117	198	74	said	say	VERB
iajs-117	198	75	to	to	PART
iajs-117	198	76	be	be	AUX
iajs-117	198	77	stable	stable	ADJ
iajs-117	198	78	if	if	SCONJ
iajs-117	198	79	f(n	f(n	PROPN
iajs-117	198	80	)	)	PUNCT
iajs-117	198	81			PROPN
iajs-117	198	82	n	n	CCONJ
iajs-117	198	83	for	for	ADP
iajs-117	198	84	each	each	DET
iajs-117	198	85	f	f	PROPN
iajs-117	198	86			PROPN
iajs-117	198	87	hom(n	hom(n	PROPN
iajs-117	198	88	,	,	PUNCT
iajs-117	198	89	m	m	NOUN
iajs-117	198	90	)	)	PUNCT
iajs-117	198	91	,	,	PUNCT
iajs-117	199	1	[	[	X
iajs-117	199	2	9	9	NUM
iajs-117	199	3	]	]	PUNCT
iajs-117	199	4	.	.	PUNCT
iajs-117	200	1	corollary	corollary	ADJ
iajs-117	200	2	(	(	PUNCT
iajs-117	200	3	2.16	2.16	NUM
iajs-117	200	4	):	):	PUNCT
iajs-117	200	5	let	let	VERB
iajs-117	200	6	n	n	PRON
iajs-117	200	7	be	be	AUX
iajs-117	200	8	a	a	DET
iajs-117	200	9	proper	proper	ADJ
iajs-117	200	10	submodule	submodule	NOUN
iajs-117	200	11	of	of	ADP
iajs-117	200	12	a	a	DET
iajs-117	200	13	bounded	bound	VERB
iajs-117	200	14	fully	fully	ADV
iajs-117	200	15	stable	stable	ADJ
iajs-117	200	16	rmodule	rmodule	NOUN
iajs-117	200	17	m.	m.	NOUN
iajs-117	200	18	then	then	ADV
iajs-117	200	19	n	n	PRON
iajs-117	200	20	is	be	AUX
iajs-117	200	21	-prime	-prime	PROPN
iajs-117	200	22	submodule	submodule	NOUN
iajs-117	200	23	of	of	ADP
iajs-117	200	24	m	m	PRON
iajs-117	200	25	if	if	SCONJ
iajs-117	200	26	[	[	X
iajs-117	200	27	n	n	X
iajs-117	200	28	+	+	CCONJ
iajs-117	200	29	(n):m	(n):m	NOUN
iajs-117	200	30	]	]	PUNCT
iajs-117	200	31	is	be	AUX
iajs-117	200	32	a	a	DET
iajs-117	200	33	prime	prime	ADJ
iajs-117	200	34	ideal	ideal	NOUN
iajs-117	200	35	of	of	ADP
iajs-117	200	36	r.	r.	PROPN
iajs-117	200	37	proof	proof	NOUN
iajs-117	200	38	:	:	PUNCT
iajs-117	200	39	since	since	SCONJ
iajs-117	200	40	m	m	PROPN
iajs-117	200	41	is	be	AUX
iajs-117	200	42	bounded	bound	VERB
iajs-117	200	43	fully	fully	ADV
iajs-117	200	44	stable	stable	ADJ
iajs-117	200	45	rmodule	rmodule	NOUN
iajs-117	200	46	,	,	PUNCT
iajs-117	200	47	then	then	ADV
iajs-117	200	48	m	m	VERB
iajs-117	200	49	is	be	AUX
iajs-117	200	50	a	a	DET
iajs-117	200	51	cyclic	cyclic	ADJ
iajs-117	200	52	rmodule	rmodule	NOUN
iajs-117	200	53	by	by	ADP
iajs-117	200	54	[	[	X
iajs-117	200	55	10,prop.1.1.4,ch.1	10,prop.1.1.4,ch.1	NUM
iajs-117	200	56	]	]	PUNCT
iajs-117	200	57	.	.	PUNCT
iajs-117	201	1	hence	hence	ADV
iajs-117	201	2	the	the	DET
iajs-117	201	3	result	result	NOUN
iajs-117	201	4	follows	follow	VERB
iajs-117	201	5	immediately	immediately	ADV
iajs-117	201	6	from	from	ADP
iajs-117	201	7	corollary	corollary	ADJ
iajs-117	201	8	(	(	PUNCT
iajs-117	201	9	2.15	2.15	NUM
iajs-117	201	10	)	)	PUNCT
iajs-117	201	11	.	.	PUNCT
iajs-117	202	1	proposition	proposition	NOUN
iajs-117	202	2	(	(	PUNCT
iajs-117	202	3	2.17	2.17	NUM
iajs-117	202	4	):	):	PUNCT
iajs-117	202	5	let	let	VERB
iajs-117	202	6	m	m	PRON
iajs-117	202	7	be	be	AUX
iajs-117	202	8	an	an	DET
iajs-117	202	9	r	r	NOUN
iajs-117	202	10	-	-	PUNCT
iajs-117	202	11	module	module	NOUN
iajs-117	202	12	and	and	CCONJ
iajs-117	202	13	n	n	CCONJ
iajs-117	202	14	,	,	PUNCT
iajs-117	202	15	l	l	X
iajs-117	202	16	be	be	VERB
iajs-117	202	17	two	two	NUM
iajs-117	202	18	submodules	submodule	NOUN
iajs-117	202	19	of	of	ADP
iajs-117	202	20	m	m	PROPN
iajs-117	202	21	.if	.if	PUNCT
iajs-117	203	1	k	k	X
iajs-117	203	2	be	be	AUX
iajs-117	203	3	a	a	DET
iajs-117	203	4	p-prime	p-prime	NOUN
iajs-117	203	5	submodule	submodule	NOUN
iajs-117	203	6	of	of	ADP
iajs-117	203	7	m	m	PRON
iajs-117	203	8	such	such	ADJ
iajs-117	203	9	that	that	SCONJ
iajs-117	203	10	n	n	CCONJ
iajs-117	203	11			PUNCT
iajs-117	203	12	l	l	NOUN
iajs-117	203	13			PROPN
iajs-117	203	14	k	k	PROPN
iajs-117	203	15	,	,	PUNCT
iajs-117	203	16	then	then	ADV
iajs-117	203	17	l	l	PROPN
iajs-117	203	18			PROPN
iajs-117	204	1	k	k	PROPN
iajs-117	204	2	+	+	CCONJ
iajs-117	204	3	(k	(k	NOUN
iajs-117	204	4	)	)	PUNCT
iajs-117	204	5	or	or	CCONJ
iajs-117	204	6	[	[	X
iajs-117	204	7	n	n	CCONJ
iajs-117	204	8	:	:	PUNCT
iajs-117	204	9	m	m	VERB
iajs-117	204	10	]	]	X
iajs-117	204	11			PROPN
iajs-117	205	1	p	p	X
iajs-117	205	2	k	k	PROPN
iajs-117	205	3			NOUN
iajs-117	205	4	n	n	PROPN
iajs-117	205	5	:	:	PUNCT
iajs-117	205	6	m	m	X
iajs-117	205	7	.	.	PUNCT
iajs-117	206	1	proof	proof	NOUN
iajs-117	206	2	:	:	PUNCT
iajs-117	206	3	suppose	suppose	VERB
iajs-117	206	4	[	[	X
iajs-117	206	5	n	n	NUM
iajs-117	206	6	:	:	PUNCT
iajs-117	206	7	m]⊈	m]⊈	VERB
iajs-117	206	8	k	k	PROPN
iajs-117	206	9			NOUN
iajs-117	206	10	n	n	PROPN
iajs-117	206	11	:	:	PUNCT
iajs-117	206	12	m	m	VERB
iajs-117	206	13	=	=	NOUN
iajs-117	206	14	p	p	ADJ
iajs-117	206	15	,	,	PUNCT
iajs-117	206	16	so	so	SCONJ
iajs-117	206	17	there	there	PRON
iajs-117	206	18	exists	exist	VERB
iajs-117	206	19	s	s	PART
iajs-117	206	20			NOUN
iajs-117	206	21	[	[	X
iajs-117	206	22	n	n	CCONJ
iajs-117	206	23	:	:	PUNCT
iajs-117	206	24	m	m	PART
iajs-117	206	25	]	]	PUNCT
iajs-117	206	26	and	and	CCONJ
iajs-117	206	27	s	s	PROPN
iajs-117	206	28	p	p	PROPN
iajs-117	206	29	k	k	PROPN
iajs-117	206	30			NOUN
iajs-117	206	31	n	n	PROPN
iajs-117	206	32	:	:	PUNCT
iajs-117	206	33	m	m	VERB
iajs-117	206	34	.	.	PUNCT
iajs-117	207	1	let	let	VERB
iajs-117	207	2	t	t	PROPN
iajs-117	207	3	l	l	PROPN
iajs-117	207	4	,	,	PUNCT
iajs-117	207	5	then	then	ADV
iajs-117	207	6	st	st	PROPN
iajs-117	207	7			PROPN
iajs-117	207	8	l	l	PROPN
iajs-117	207	9	n	n	NOUN
iajs-117	207	10	and	and	CCONJ
iajs-117	207	11	so	so	ADV
iajs-117	207	12	st	st	PROPN
iajs-117	207	13			PROPN
iajs-117	207	14	k.	k.	PROPN
iajs-117	208	1	but	but	CCONJ
iajs-117	208	2	k	k	PROPN
iajs-117	208	3	is	be	AUX
iajs-117	208	4	p-prime	p-prime	NOUN
iajs-117	208	5	submodule	submodule	NOUN
iajs-117	208	6	of	of	ADP
iajs-117	208	7	m	m	PROPN
iajs-117	208	8	and	and	CCONJ
iajs-117	208	9	s	s	PROPN
iajs-117	208	10	k	k	PROPN
iajs-117	208	11			NOUN
iajs-117	209	1	n	n	PROPN
iajs-117	209	2	:	:	PUNCT
iajs-117	209	3	m	m	X
iajs-117	209	4	.	.	PUNCT
iajs-117	210	1	therefore	therefore	ADV
iajs-117	210	2	t	t	PROPN
iajs-117	210	3	k	k	PROPN
iajs-117	211	1	+	+	CCONJ
iajs-117	212	1	(k	(k	NOUN
iajs-117	212	2	)	)	PUNCT
iajs-117	212	3	,	,	PUNCT
iajs-117	212	4	thus	thus	ADV
iajs-117	212	5	l	l	NOUN
iajs-117	212	6			PROPN
iajs-117	212	7	k	k	PROPN
iajs-117	212	8	+	+	CCONJ
iajs-117	212	9	(k	(k	NOUN
iajs-117	212	10	)	)	PUNCT
iajs-117	212	11	.	.	PUNCT
iajs-117	213	1	corollary	corollary	ADJ
iajs-117	213	2	(	(	PUNCT
iajs-117	213	3	2.18	2.18	NUM
iajs-117	213	4	):	):	PUNCT
iajs-117	213	5	let	let	VERB
iajs-117	213	6	a	a	DET
iajs-117	213	7	an	an	DET
iajs-117	213	8	ideal	ideal	NOUN
iajs-117	213	9	of	of	ADP
iajs-117	213	10	a	a	DET
iajs-117	213	11	ring	ring	NOUN
iajs-117	213	12	r	r	NOUN
iajs-117	213	13	and	and	CCONJ
iajs-117	213	14	n	n	CCONJ
iajs-117	213	15	be	be	VERB
iajs-117	213	16	a	a	DET
iajs-117	213	17	submodule	submodule	NOUN
iajs-117	213	18	of	of	ADP
iajs-117	213	19	m	m	PROPN
iajs-117	213	20	.	.	PUNCT
iajs-117	214	1	if	if	SCONJ
iajs-117	214	2	k	k	PROPN
iajs-117	214	3	is	be	AUX
iajs-117	214	4	a	a	DET
iajs-117	214	5	p-prime	p-prime	NOUN
iajs-117	214	6	submodule	submodule	NOUN
iajs-117	214	7	of	of	ADP
iajs-117	214	8	m	m	PRON
iajs-117	214	9	such	such	ADJ
iajs-117	214	10	that	that	PRON
iajs-117	214	11	am	be	AUX
iajs-117	214	12			PUNCT
iajs-117	214	13	n	n	PRON
iajs-117	214	14			PROPN
iajs-117	214	15	k	k	PROPN
iajs-117	214	16	,	,	PUNCT
iajs-117	214	17	then	then	ADV
iajs-117	214	18	either	either	CCONJ
iajs-117	214	19	am	am	PROPN
iajs-117	214	20	k	k	PROPN
iajs-117	215	1	+	+	PUNCT
iajs-117	215	2	(k	(k	NOUN
iajs-117	215	3	)	)	PUNCT
iajs-117	215	4	or	or	CCONJ
iajs-117	215	5	n	n	CCONJ
iajs-117	215	6			PROPN
iajs-117	215	7	k	k	PROPN
iajs-117	215	8	+	+	CCONJ
iajs-117	215	9	(k	(k	NOUN
iajs-117	215	10	)	)	PUNCT
iajs-117	215	11	.	.	PUNCT
iajs-117	216	1	proposition	proposition	NOUN
iajs-117	216	2	(	(	PUNCT
iajs-117	216	3	2.19	2.19	NUM
iajs-117	216	4	):	):	PUNCT
iajs-117	216	5	let	let	VERB
iajs-117	216	6	m	m	PRON
iajs-117	216	7	be	be	AUX
iajs-117	216	8	an	an	DET
iajs-117	216	9	r	r	NOUN
iajs-117	216	10	-	-	PUNCT
iajs-117	216	11	module	module	NOUN
iajs-117	216	12	and	and	CCONJ
iajs-117	216	13	n	n	CCONJ
iajs-117	216	14	be	be	VERB
iajs-117	216	15	a	a	DET
iajs-117	216	16	submodules	submodule	NOUN
iajs-117	216	17	of	of	ADP
iajs-117	216	18	m	m	PROPN
iajs-117	216	19	.if	.if	PUNCT
iajs-117	217	1	p	p	X
iajs-117	217	2	=	=	PUNCT
iajs-117	217	3	n	n	PROPN
iajs-117	217	4			NOUN
iajs-117	217	5	n	n	NOUN
iajs-117	217	6	:	:	PUNCT
iajs-117	217	7	m	m	VERB
iajs-117	217	8	is	be	AUX
iajs-117	217	9	a	a	DET
iajs-117	217	10	prime	prime	ADJ
iajs-117	217	11	ideal	ideal	NOUN
iajs-117	217	12	of	of	ADP
iajs-117	217	13	r	r	NOUN
iajs-117	217	14	,	,	PUNCT
iajs-117	217	15	then	then	ADV
iajs-117	217	16	n	n	CCONJ
iajs-117	217	17			NOUN
iajs-117	217	18	n	n	NOUN
iajs-117	217	19	:	:	PUNCT
iajs-117	217	20	m	m	VERB
iajs-117	217	21	n	n	ADV
iajs-117	217	22			NOUN
iajs-117	217	23	n	n	NOUN
iajs-117	217	24	:	:	PUNCT
iajs-117	217	25	rm	rm	NOUN
iajs-117	217	26	,	,	PUNCT
iajs-117	217	27			NOUN
iajs-117	217	28	r	r	NOUN
iajs-117	217	29			NOUN
iajs-117	217	30	n	n	NOUN
iajs-117	217	31			NOUN
iajs-117	217	32	n	n	NOUN
iajs-117	217	33	:	:	PUNCT
iajs-117	217	34	m	m	X
iajs-117	217	35	.	.	PUNCT
iajs-117	218	1	proof	proof	NOUN
iajs-117	218	2	:	:	PUNCT
iajs-117	218	3	since	since	SCONJ
iajs-117	218	4	rm	rm	PROPN
iajs-117	218	5	m	m	VERB
iajs-117	218	6	,	,	PUNCT
iajs-117	218	7	so	so	ADV
iajs-117	218	8	n	n	CCONJ
iajs-117	218	9			NOUN
iajs-117	218	10	n	n	NOUN
iajs-117	218	11	:	:	PUNCT
iajs-117	218	12	m	m	VERB
iajs-117	218	13			ADJ
iajs-117	218	14	n	n	PRON
iajs-117	218	15			NOUN
iajs-117	218	16	n	n	NOUN
iajs-117	218	17	:	:	PUNCT
iajs-117	218	18	rm	rm	NOUN
iajs-117	218	19	.	.	PUNCT
iajs-117	219	1	let	let	VERB
iajs-117	219	2	a	a	DET
iajs-117	219	3			NOUN
iajs-117	219	4	n	n	CCONJ
iajs-117	219	5			NOUN
iajs-117	219	6	n	n	PROPN
iajs-117	219	7	:	:	PUNCT
iajs-117	219	8	rm	rm	NOUN
iajs-117	219	9	,	,	PUNCT
iajs-117	219	10	so	so	CCONJ
iajs-117	219	11	ar	ar	PROPN
iajs-117	219	12	m	m	PROPN
iajs-117	219	13			PROPN
iajs-117	219	14	n	n	INTJ
iajs-117	219	15			NOUN
iajs-117	219	16	n	n	NOUN
iajs-117	219	17	.which	.which	PRON
iajs-117	219	18	means	mean	VERB
iajs-117	219	19	that	that	SCONJ
iajs-117	219	20	ar	ar	VERB
iajs-117	219	21			PROPN
iajs-117	219	22	n	n	CCONJ
iajs-117	219	23			NOUN
iajs-117	219	24	n	n	NOUN
iajs-117	219	25	:	:	PUNCT
iajs-117	219	26	m	m	NOUN
iajs-117	219	27	.	.	PUNCT
iajs-117	220	1	but	but	CCONJ
iajs-117	220	2	n	n	PRON
iajs-117	220	3			NOUN
iajs-117	220	4	n	n	NOUN
iajs-117	220	5	:	:	PUNCT
iajs-117	220	6	m	m	VERB
iajs-117	220	7	is	be	AUX
iajs-117	220	8	a	a	DET
iajs-117	220	9	prime	prime	ADJ
iajs-117	220	10	ideal	ideal	NOUN
iajs-117	220	11	of	of	ADP
iajs-117	220	12	r	r	NOUN
iajs-117	220	13	,	,	PUNCT
iajs-117	220	14	so	so	CCONJ
iajs-117	220	15	either	either	CCONJ
iajs-117	220	16	a	a	DET
iajs-117	220	17			NOUN
iajs-117	220	18	n	n	CCONJ
iajs-117	220	19			NOUN
iajs-117	220	20	n	n	NOUN
iajs-117	220	21	:	:	PUNCT
iajs-117	220	22	m	m	NOUN
iajs-117	220	23	or	or	CCONJ
iajs-117	220	24	r	r	ADJ
iajs-117	220	25	n	n	DET
iajs-117	220	26			NOUN
iajs-117	220	27	n	n	NOUN
iajs-117	220	28	:	:	PUNCT
iajs-117	220	29	m	m	NOUN
iajs-117	220	30	,	,	PUNCT
iajs-117	220	31	but	but	CCONJ
iajs-117	220	32	r	r	NOUN
iajs-117	220	33			NOUN
iajs-117	220	34	n	n	CCONJ
iajs-117	220	35			NOUN
iajs-117	220	36	n	n	NOUN
iajs-117	220	37	:	:	PUNCT
iajs-117	220	38	m	m	INTJ
iajs-117	220	39	,	,	PUNCT
iajs-117	220	40	so	so	ADV
iajs-117	220	41	a	a	DET
iajs-117	220	42			NOUN
iajs-117	220	43	n	n	CCONJ
iajs-117	220	44			NOUN
iajs-117	220	45	n	n	NOUN
iajs-117	220	46	:	:	PUNCT
iajs-117	220	47	m	m	NOUN
iajs-117	220	48	.	.	PUNCT
iajs-117	221	1	thus	thus	ADV
iajs-117	221	2	n	n	PRON
iajs-117	221	3			NOUN
iajs-117	221	4	n	n	NOUN
iajs-117	221	5	:	:	PUNCT
iajs-117	221	6	m	m	VERB
iajs-117	221	7	n	n	ADV
iajs-117	221	8			NOUN
iajs-117	221	9	n	n	NOUN
iajs-117	221	10	:	:	PUNCT
iajs-117	221	11	rm	rm	NOUN
iajs-117	221	12	,	,	PUNCT
iajs-117	221	13			NOUN
iajs-117	221	14	r	r	NOUN
iajs-117	221	15			NOUN
iajs-117	221	16	n	n	NOUN
iajs-117	221	17			NOUN
iajs-117	221	18	n	n	NOUN
iajs-117	221	19	:	:	PUNCT
iajs-117	221	20	m	m	VERB
iajs-117	221	21	.	.	PUNCT
iajs-117	222	1	now	now	ADV
iajs-117	222	2	,	,	PUNCT
iajs-117	222	3	we	we	PRON
iajs-117	222	4	can	can	AUX
iajs-117	222	5	give	give	VERB
iajs-117	222	6	the	the	DET
iajs-117	222	7	following	follow	VERB
iajs-117	222	8	proposition	proposition	NOUN
iajs-117	222	9	:	:	PUNCT
iajs-117	222	10	proposition	proposition	NOUN
iajs-117	222	11	(	(	PUNCT
iajs-117	222	12	2.20	2.20	NUM
iajs-117	222	13	):	):	PUNCT
iajs-117	222	14	let	let	VERB
iajs-117	222	15	n	n	PRON
iajs-117	222	16	be	be	AUX
iajs-117	222	17	a	a	DET
iajs-117	222	18	submodule	submodule	NOUN
iajs-117	222	19	of	of	ADP
iajs-117	222	20	an	an	DET
iajs-117	222	21	r	r	NOUN
iajs-117	222	22	–	–	PUNCT
iajs-117	222	23	module	module	NOUN
iajs-117	222	24	m	m	NOUN
iajs-117	222	25	and	and	CCONJ
iajs-117	222	26	p	p	NOUN
iajs-117	222	27	=	=	NOUN
iajs-117	222	28	n	n	PROPN
iajs-117	222	29			NOUN
iajs-117	222	30	n	n	NOUN
iajs-117	222	31	:	:	PUNCT
iajs-117	222	32	m	m	VERB
iajs-117	222	33	.	.	PUNCT
iajs-117	223	1	if	if	SCONJ
iajs-117	223	2	the	the	DET
iajs-117	223	3	ideal	ideal	NOUN
iajs-117	223	4	=	=	SYM
iajs-117	223	5	n	n	CCONJ
iajs-117	223	6			NOUN
iajs-117	223	7	n	n	NOUN
iajs-117	223	8	:	:	PUNCT
iajs-117	223	9	e	e	X
iajs-117	223	10	=	=	PUNCT
iajs-117	223	11	p	p	X
iajs-117	223	12	,	,	PUNCT
iajs-117	223	13	for	for	ADP
iajs-117	223	14	each	each	DET
iajs-117	223	15	e	e	NOUN
iajs-117	223	16			NOUN
iajs-117	223	17	m	m	VERB
iajs-117	223	18	,	,	PUNCT
iajs-117	223	19	e	e	PROPN
iajs-117	223	20			NOUN
iajs-117	223	21	n	n	PROPN
iajs-117	223	22	+	+	CCONJ
iajs-117	223	23	(n	(n	X
iajs-117	223	24	)	)	PUNCT
iajs-117	223	25	,	,	PUNCT
iajs-117	223	26	then	then	ADV
iajs-117	223	27	n	n	PRON
iajs-117	223	28	is	be	AUX
iajs-117	223	29	a	a	DET
iajs-117	223	30	prime	prime	PROPN
iajs-117	223	31	submodule	submodule	NOUN
iajs-117	223	32	of	of	ADP
iajs-117	223	33	m	m	PROPN
iajs-117	223	34	.	.	PUNCT
iajs-117	224	1	proof	proof	NOUN
iajs-117	224	2	:	:	PUNCT
iajs-117	224	3	let	let	VERB
iajs-117	224	4	r	r	ADJ
iajs-117	224	5	r	r	NOUN
iajs-117	224	6	,	,	PUNCT
iajs-117	224	7	x	x	SYM
iajs-117	224	8			PROPN
iajs-117	224	9	m	m	VERB
iajs-117	224	10	such	such	ADJ
iajs-117	224	11	that	that	SCONJ
iajs-117	224	12	rx	rx	VERB
iajs-117	224	13			NOUN
iajs-117	224	14	n	n	DET
iajs-117	224	15	and	and	CCONJ
iajs-117	224	16	suppose	suppose	VERB
iajs-117	224	17	x	x	PUNCT
iajs-117	224	18	n	n	PROPN
iajs-117	224	19	+	+	CCONJ
iajs-117	224	20	(n	(n	X
iajs-117	224	21	)	)	PUNCT
iajs-117	224	22	.	.	PUNCT
iajs-117	225	1	thus	thus	ADV
iajs-117	225	2	r	r	VERB
iajs-117	225	3			NOUN
iajs-117	225	4	n	n	CCONJ
iajs-117	225	5			NOUN
iajs-117	225	6	n	n	PROPN
iajs-117	225	7	:	:	PUNCT
iajs-117	225	8	x	x	X
iajs-117	225	9	.	.	PUNCT
iajs-117	226	1	but	but	CCONJ
iajs-117	226	2	n	n	PRON
iajs-117	226	3			NOUN
iajs-117	226	4	n	n	NOUN
iajs-117	226	5	:	:	PUNCT
iajs-117	226	6			PROPN
iajs-117	226	7	x	x	PUNCT
iajs-117	227	1	=	=	PUNCT
iajs-117	227	2	p	p	X
iajs-117	227	3	,	,	PUNCT
iajs-117	227	4	so	so	CCONJ
iajs-117	227	5	r	r	NOUN
iajs-117	227	6			PROPN
iajs-117	227	7	p	p	X
iajs-117	227	8	.	.	PUNCT
iajs-117	228	1	therefore	therefore	ADV
iajs-117	228	2	n	n	PROPN
iajs-117	228	3	is	be	AUX
iajs-117	228	4	a	a	DET
iajs-117	228	5			NUM
iajs-117	228	6	prime	prime	ADJ
iajs-117	228	7	submodule	submodule	NOUN
iajs-117	228	8	of	of	ADP
iajs-117	228	9	m	m	PROPN
iajs-117	228	10	.	.	PUNCT
iajs-117	229	1	however	however	ADV
iajs-117	229	2	,	,	PUNCT
iajs-117	229	3	we	we	PRON
iajs-117	229	4	can	can	AUX
iajs-117	229	5	give	give	VERB
iajs-117	229	6	a	a	DET
iajs-117	229	7	corollary	corollary	NOUN
iajs-117	229	8	of	of	ADP
iajs-117	229	9	proposition	proposition	NOUN
iajs-117	229	10	(	(	PUNCT
iajs-117	229	11	2.20).but	2.20).but	NUM
iajs-117	229	12	first	first	ADV
iajs-117	229	13	we	we	PRON
iajs-117	229	14	state	state	VERB
iajs-117	229	15	and	and	CCONJ
iajs-117	229	16	prove	prove	VERB
iajs-117	229	17	the	the	DET
iajs-117	229	18	following	follow	VERB
iajs-117	229	19	lemma	lemma	PROPN
iajs-117	229	20	which	which	PRON
iajs-117	229	21	is	be	AUX
iajs-117	229	22	needed	need	VERB
iajs-117	229	23	.	.	PUNCT
iajs-117	230	1	mathematics	mathematic	NOUN
iajs-117	230	2	|	|	ADV
iajs-117	230	3	288	288	NUM
iajs-117	230	4	2016	2016	NUM
iajs-117	230	5	)	)	PUNCT
iajs-117	230	6	عام	عام	ADP
iajs-117	230	7	2العدد	2العدد	NUM
iajs-117	230	8	(	(	PUNCT
iajs-117	230	9	29لمجلد	29لمجلد	NUM
iajs-117	230	10	ا	ا	X
iajs-117	230	11	مجلة	مجلة	NOUN
iajs-117	230	12	إبن	إبن	VERB
iajs-117	230	13	الهيثم	الهيثم	ADJ
iajs-117	230	14	للعلوم	للعلوم	NOUN
iajs-117	230	15	الصرفة	الصرفة	NOUN
iajs-117	231	1	و	و	PRON
iajs-117	231	2	التطبيقية	التطبيقية	ADJ
iajs-117	231	3	ibn	ibn	PROPN
iajs-117	231	4	al	al	PROPN
iajs-117	231	5	-	-	PUNCT
iajs-117	231	6	haitham	haitham	PROPN
iajs-117	231	7	jour	jour	X
iajs-117	231	8	.	.	PROPN
iajs-117	231	9	for	for	ADP
iajs-117	231	10	pure	pure	ADJ
iajs-117	231	11	&	&	CCONJ
iajs-117	231	12	appl	appl	PROPN
iajs-117	231	13	.	.	PUNCT
iajs-117	232	1	sci	sci	PROPN
iajs-117	232	2	.	.	PUNCT
iajs-117	232	3	vol	vol	NOUN
iajs-117	232	4	.	.	PROPN
iajs-117	233	1	29	29	NUM
iajs-117	233	2	(	(	PUNCT
iajs-117	233	3	2	2	NUM
iajs-117	233	4	)	)	PUNCT
iajs-117	233	5	2016	2016	NUM
iajs-117	233	6	lemma	lemma	PROPN
iajs-117	233	7	(	(	PUNCT
iajs-117	233	8	2.21	2.21	NUM
iajs-117	233	9	):	):	PUNCT
iajs-117	233	10	let	let	VERB
iajs-117	233	11	n	n	PRON
iajs-117	233	12	be	be	AUX
iajs-117	233	13	a	a	DET
iajs-117	233	14	submodule	submodule	NOUN
iajs-117	233	15	of	of	ADP
iajs-117	233	16	an	an	DET
iajs-117	233	17	r	r	NOUN
iajs-117	233	18	–	–	PUNCT
iajs-117	233	19	module	module	NOUN
iajs-117	233	20	m	m	NOUN
iajs-117	233	21	.	.	PUNCT
iajs-117	234	1	if	if	SCONJ
iajs-117	234	2	the	the	DET
iajs-117	234	3	submodule	submodule	NOUN
iajs-117	234	4	n	n	CCONJ
iajs-117	234	5			NOUN
iajs-117	234	6	n	n	NOUN
iajs-117	234	7	:	:	PUNCT
iajs-117	234	8			PROPN
iajs-117	234	9	r	r	X
iajs-117	234	10	=	=	PUNCT
iajs-117	234	11	n	n	PROPN
iajs-117	234	12	+	+	NOUN
iajs-117	234	13			NOUN
iajs-117	234	14	(	(	PUNCT
iajs-117	234	15	n	n	CCONJ
iajs-117	234	16	)	)	PUNCT
iajs-117	234	17	,	,	PUNCT
iajs-117	234	18	for	for	ADP
iajs-117	234	19	each	each	DET
iajs-117	234	20	r	r	NOUN
iajs-117	234	21			NOUN
iajs-117	234	22	r	r	NOUN
iajs-117	234	23	,	,	PUNCT
iajs-117	234	24	r	r	NOUN
iajs-117	234	25	p	p	ADV
iajs-117	234	26	,	,	PUNCT
iajs-117	234	27	then	then	ADV
iajs-117	234	28	the	the	DET
iajs-117	234	29	ideal	ideal	NOUN
iajs-117	234	30	p	p	X
iajs-117	234	31	=	=	PUNCT
iajs-117	234	32	n	n	PROPN
iajs-117	234	33			NOUN
iajs-117	234	34	n	n	NOUN
iajs-117	234	35	:	:	PUNCT
iajs-117	234	36	e	e	X
iajs-117	234	37	,	,	PUNCT
iajs-117	234	38	for	for	ADP
iajs-117	234	39	each	each	DET
iajs-117	234	40	e	e	NOUN
iajs-117	234	41			NOUN
iajs-117	234	42	m	m	VERB
iajs-117	234	43	;	;	PUNCT
iajs-117	234	44	e	e	X
iajs-117	234	45			NOUN
iajs-117	234	46	n	n	PROPN
iajs-117	234	47	+	+	CCONJ
iajs-117	234	48	(n	(n	X
iajs-117	234	49	)	)	PUNCT
iajs-117	234	50	.	.	PUNCT
iajs-117	235	1	proof	proof	NOUN
iajs-117	235	2	:	:	PUNCT
iajs-117	235	3	let	let	VERB
iajs-117	235	4	e	e	PRON
iajs-117	235	5			NOUN
iajs-117	235	6	m	m	VERB
iajs-117	235	7	;	;	PUNCT
iajs-117	235	8	e	e	X
iajs-117	235	9	n	n	PROPN
iajs-117	235	10	+	+	CCONJ
iajs-117	235	11	(n	(n	X
iajs-117	235	12	)	)	PUNCT
iajs-117	235	13	.	.	PUNCT
iajs-117	236	1	it	it	PRON
iajs-117	236	2	is	be	AUX
iajs-117	236	3	clear	clear	ADJ
iajs-117	236	4	that	that	SCONJ
iajs-117	236	5	p	p	PROPN
iajs-117	236	6			PROPN
iajs-117	236	7	n	n	CCONJ
iajs-117	236	8			NOUN
iajs-117	236	9	n	n	NOUN
iajs-117	236	10	:	:	PUNCT
iajs-117	236	11	e	e	X
iajs-117	236	12	.	.	PUNCT
iajs-117	237	1	let	let	VERB
iajs-117	237	2	r	r	NOUN
iajs-117	237	3			PROPN
iajs-117	237	4	n	n	CCONJ
iajs-117	237	5			NOUN
iajs-117	237	6	n	n	NOUN
iajs-117	237	7	:	:	PUNCT
iajs-117	237	8	e	e	X
iajs-117	237	9	,	,	PUNCT
iajs-117	237	10	then	then	ADV
iajs-117	237	11	re	re	VERB
iajs-117	237	12			NOUN
iajs-117	237	13	n	n	PROPN
iajs-117	237	14	+	+	CCONJ
iajs-117	237	15	(n	(n	X
iajs-117	237	16	)	)	PUNCT
iajs-117	237	17	.	.	PUNCT
iajs-117	238	1	suppose	suppose	VERB
iajs-117	238	2	r	r	NOUN
iajs-117	238	3			NOUN
iajs-117	238	4	p	p	NOUN
iajs-117	238	5	=	=	PUNCT
iajs-117	238	6	n	n	NOUN
iajs-117	238	7			NOUN
iajs-117	238	8	n	n	NOUN
iajs-117	238	9	:	:	PUNCT
iajs-117	238	10	:	:	PUNCT
iajs-117	238	11	m	m	VERB
iajs-117	238	12	.since	.since	NOUN
iajs-117	238	13	n	n	ADV
iajs-117	238	14			NOUN
iajs-117	238	15	n	n	NOUN
iajs-117	238	16	:	:	PUNCT
iajs-117	238	17			PROPN
iajs-117	238	18	r	r	X
iajs-117	239	1	=	=	SYM
iajs-117	239	2	n+(n	n+(n	PROPN
iajs-117	239	3	)	)	PUNCT
iajs-117	239	4	and	and	CCONJ
iajs-117	239	5	e	e	ADP
iajs-117	239	6			NOUN
iajs-117	240	1	[	[	X
iajs-117	240	2	n+	n+	NUM
iajs-117	240	3	(n	(n	X
iajs-117	240	4	)	)	PUNCT
iajs-117	240	5	:	:	PUNCT
iajs-117	240	6			PROPN
iajs-117	240	7	r	r	NOUN
iajs-117	240	8			PROPN
iajs-117	240	9	]	]	X
iajs-117	240	10	,	,	PUNCT
iajs-117	240	11	so	so	CCONJ
iajs-117	240	12	e	e	ADP
iajs-117	240	13			NOUN
iajs-117	240	14	n+	n+	X
iajs-117	240	15	(	(	PUNCT
iajs-117	240	16	n	n	CCONJ
iajs-117	240	17	)	)	PUNCT
iajs-117	240	18	which	which	PRON
iajs-117	240	19	a	a	PRON
iajs-117	240	20	contradicts	contradict	VERB
iajs-117	240	21	our	our	PRON
iajs-117	240	22	assumption	assumption	NOUN
iajs-117	240	23	.	.	PUNCT
iajs-117	241	1	thus	thus	ADV
iajs-117	241	2	r	r	VERB
iajs-117	241	3			NOUN
iajs-117	241	4	p	p	NOUN
iajs-117	241	5	for	for	ADP
iajs-117	241	6	each	each	DET
iajs-117	241	7	e	e	NOUN
iajs-117	241	8			NOUN
iajs-117	241	9	m	m	AUX
iajs-117	241	10	such	such	ADJ
iajs-117	241	11	that	that	SCONJ
iajs-117	241	12	e	e	PROPN
iajs-117	241	13			NOUN
iajs-117	241	14	n	n	X
iajs-117	241	15	+	+	ADP
iajs-117	241	16	(n).therefore	(n).therefore	X
iajs-117	241	17	p	p	NOUN
iajs-117	241	18	=	=	PUNCT
iajs-117	241	19	n	n	PROPN
iajs-117	241	20			NOUN
iajs-117	241	21	n	n	NOUN
iajs-117	241	22	:	:	PUNCT
iajs-117	241	23	:	:	PUNCT
iajs-117	241	24	e	e	X
iajs-117	241	25	.	.	PUNCT
iajs-117	242	1	corollary	corollary	ADJ
iajs-117	242	2	(	(	PUNCT
iajs-117	242	3	2.22	2.22	NUM
iajs-117	242	4	):	):	PUNCT
iajs-117	242	5	let	let	VERB
iajs-117	242	6	n	n	PRON
iajs-117	242	7	be	be	AUX
iajs-117	242	8	a	a	DET
iajs-117	242	9	submodule	submodule	NOUN
iajs-117	242	10	of	of	ADP
iajs-117	242	11	an	an	DET
iajs-117	242	12	r	r	NOUN
iajs-117	242	13	–	–	PUNCT
iajs-117	242	14	module	module	NOUN
iajs-117	242	15	m	m	NOUN
iajs-117	242	16	and	and	CCONJ
iajs-117	242	17	p	p	NOUN
iajs-117	242	18	=	=	NOUN
iajs-117	242	19	n	n	PROPN
iajs-117	242	20			NOUN
iajs-117	242	21	n	n	NOUN
iajs-117	242	22	:	:	PUNCT
iajs-117	242	23	m	m	VERB
iajs-117	242	24	.	.	PUNCT
iajs-117	243	1	if	if	SCONJ
iajs-117	243	2	the	the	DET
iajs-117	243	3	submodule	submodule	NOUN
iajs-117	243	4	n	n	CCONJ
iajs-117	243	5			NOUN
iajs-117	243	6	n	n	NOUN
iajs-117	243	7	:	:	PUNCT
iajs-117	243	8			PROPN
iajs-117	243	9	r	r	X
iajs-117	243	10	=	=	PUNCT
iajs-117	243	11	n	n	PROPN
iajs-117	243	12	+	+	NOUN
iajs-117	243	13			NOUN
iajs-117	243	14	(	(	PUNCT
iajs-117	243	15	n	n	CCONJ
iajs-117	243	16	)	)	PUNCT
iajs-117	243	17	,	,	PUNCT
iajs-117	243	18	for	for	ADP
iajs-117	243	19	each	each	DET
iajs-117	243	20	r	r	NOUN
iajs-117	243	21			NOUN
iajs-117	243	22	r	r	NOUN
iajs-117	243	23	,	,	PUNCT
iajs-117	243	24	then	then	ADV
iajs-117	243	25	n	n	PRON
iajs-117	243	26	is	be	AUX
iajs-117	243	27	a	a	DET
iajs-117	243	28	prime	prime	PROPN
iajs-117	243	29	submodule	submodule	NOUN
iajs-117	243	30	of	of	ADP
iajs-117	243	31	m	m	PROPN
iajs-117	243	32	.	.	PUNCT
iajs-117	244	1	note	note	VERB
iajs-117	244	2	that	that	SCONJ
iajs-117	244	3	,	,	PUNCT
iajs-117	244	4	the	the	DET
iajs-117	244	5	intersection	intersection	NOUN
iajs-117	244	6	of	of	ADP
iajs-117	244	7	two	two	NUM
iajs-117	244	8	-prime	-prime	ADJ
iajs-117	244	9	submodules	submodule	NOUN
iajs-117	244	10	of	of	ADP
iajs-117	244	11	an	an	DET
iajs-117	244	12	r	r	NOUN
iajs-117	244	13	–	–	PUNCT
iajs-117	244	14	module	module	NOUN
iajs-117	244	15	m	m	PRON
iajs-117	244	16	need	need	AUX
iajs-117	244	17	not	not	PART
iajs-117	244	18	be	be	AUX
iajs-117	244	19	a	a	DET
iajs-117	244	20	-prime	-prime	ADJ
iajs-117	244	21	submodule	submodule	NOUN
iajs-117	244	22	of	of	ADP
iajs-117	244	23	m	m	PROPN
iajs-117	244	24	,	,	PUNCT
iajs-117	244	25	for	for	ADP
iajs-117	244	26	example	example	NOUN
iajs-117	244	27	:	:	PUNCT
iajs-117	244	28	the	the	DET
iajs-117	244	29	z	z	NOUN
iajs-117	244	30	-	-	PUNCT
iajs-117	244	31	module	module	NOUN
iajs-117	244	32	z6	z6	NOUN
iajs-117	244	33	has	have	VERB
iajs-117	244	34	two	two	NUM
iajs-117	244	35	-prime	-prime	ADJ
iajs-117	244	36	submodules	submodule	NOUN
iajs-117	244	37	,	,	PUNCT
iajs-117	244	38	n1	n1	PROPN
iajs-117	244	39	=	=	SYM
iajs-117	244	40			PROPN
iajs-117	244	41	2	2	NUM
iajs-117	244	42	and	and	CCONJ
iajs-117	244	43	n2	n2	ADJ
iajs-117	244	44	=	=	SYM
iajs-117	244	45			PROPN
iajs-117	245	1	3	3	NUM
iajs-117	245	2			NOUN
iajs-117	245	3	but	but	CCONJ
iajs-117	245	4	n1	n1	NOUN
iajs-117	245	5	n2	n2	NOUN
iajs-117	245	6	=	=	PUNCT
iajs-117	245	7	0	0	X
iajs-117	245	8			PROPN
iajs-117	245	9	is	be	AUX
iajs-117	245	10	not	not	PART
iajs-117	245	11	a	a	DET
iajs-117	245	12	-prime	-prime	ADJ
iajs-117	245	13	submodule	submodule	NOUN
iajs-117	245	14	of	of	ADP
iajs-117	245	15	z6	z6	PROPN
iajs-117	245	16	,	,	PUNCT
iajs-117	245	17	where	where	SCONJ
iajs-117	245	18	(n	(n	X
iajs-117	245	19	)	)	PUNCT
iajs-117	245	20	=	=	SYM
iajs-117	245	21	n	n	CCONJ
iajs-117	245	22	,	,	PUNCT
iajs-117	245	23			NOUN
iajs-117	245	24	n	n	PRON
iajs-117	245	25			PROPN
iajs-117	245	26	m	m	PROPN
iajs-117	245	27	.	.	PUNCT
iajs-117	246	1	however	however	ADV
iajs-117	246	2	,	,	PUNCT
iajs-117	246	3	we	we	PRON
iajs-117	246	4	have	have	VERB
iajs-117	246	5	the	the	DET
iajs-117	246	6	following	follow	VERB
iajs-117	246	7	proposition	proposition	NOUN
iajs-117	246	8	:	:	PUNCT
iajs-117	246	9	proposition	proposition	NOUN
iajs-117	246	10	(	(	PUNCT
iajs-117	246	11	2.23	2.23	NUM
iajs-117	246	12	):	):	PUNCT
iajs-117	246	13	let	let	VERB
iajs-117	246	14	k	k	PROPN
iajs-117	246	15	is	be	AUX
iajs-117	246	16	a	a	DET
iajs-117	246	17	-prime	-prime	NOUN
iajs-117	246	18	of	of	ADP
iajs-117	246	19	an	an	DET
iajs-117	246	20	r	r	NOUN
iajs-117	246	21	-	-	PUNCT
iajs-117	246	22	module	module	NOUN
iajs-117	246	23	m	m	NOUN
iajs-117	246	24	and	and	CCONJ
iajs-117	246	25	let	let	VERB
iajs-117	246	26	n	n	PRON
iajs-117	246	27	<	<	X
iajs-117	246	28	m	m	VERB
iajs-117	246	29	such	such	ADJ
iajs-117	246	30	that	that	PRON
iajs-117	246	31	(k	(k	NOUN
iajs-117	246	32	)	)	PUNCT
iajs-117	246	33			PROPN
iajs-117	246	34	k.	k.	PROPN
iajs-117	247	1	then	then	ADV
iajs-117	247	2	either	either	CCONJ
iajs-117	247	3	n	n	PRON
iajs-117	247	4			PROPN
iajs-117	247	5	k	k	PROPN
iajs-117	247	6	or	or	CCONJ
iajs-117	247	7	k	k	PROPN
iajs-117	247	8			PUNCT
iajs-117	248	1	n	n	CCONJ
iajs-117	248	2	is	be	AUX
iajs-117	248	3	a	a	DET
iajs-117	248	4	'-prime	'-prime	NOUN
iajs-117	248	5	in	in	ADP
iajs-117	248	6	n	n	CCONJ
iajs-117	248	7	,	,	PUNCT
iajs-117	248	8	where	where	SCONJ
iajs-117	248	9			NOUN
iajs-117	248	10	'	'	PUNCT
iajs-117	248	11	:	:	PUNCT
iajs-117	248	12	(n	(n	PROPN
iajs-117	248	13	)	)	PUNCT
iajs-117	248	14			PROPN
iajs-117	248	15	(n	(n	PROPN
iajs-117	248	16	)	)	PUNCT
iajs-117	248	17			NOUN
iajs-117	248	18	{	{	PUNCT
iajs-117	248	19			NOUN
iajs-117	248	20	}	}	PUNCT
iajs-117	248	21	and	and	NOUN
iajs-117	248	22	:	:	PUNCT
iajs-117	248	23	(m	(m	X
iajs-117	248	24	)	)	PUNCT
iajs-117	248	25			PROPN
iajs-117	248	26	(m	(m	PROPN
iajs-117	248	27	)	)	PUNCT
iajs-117	248	28			NOUN
iajs-117	248	29	{	{	PUNCT
iajs-117	248	30			NOUN
iajs-117	248	31	}	}	PUNCT
iajs-117	248	32	.	.	PUNCT
iajs-117	249	1	proof	proof	NOUN
iajs-117	249	2	:	:	PUNCT
iajs-117	249	3	since	since	SCONJ
iajs-117	249	4	k	k	PROPN
iajs-117	249	5	is	be	AUX
iajs-117	249	6	a	a	DET
iajs-117	249	7	-prime	-prime	NOUN
iajs-117	249	8	of	of	ADP
iajs-117	249	9	an	an	DET
iajs-117	249	10	r	r	NOUN
iajs-117	249	11	-	-	PUNCT
iajs-117	249	12	module	module	NOUN
iajs-117	249	13	m	m	NOUN
iajs-117	249	14	and	and	CCONJ
iajs-117	249	15	(k	(k	NOUN
iajs-117	249	16	)	)	PUNCT
iajs-117	249	17			PROPN
iajs-117	249	18	k	k	PROPN
iajs-117	249	19	,	,	PUNCT
iajs-117	249	20	so	so	ADV
iajs-117	249	21	k	k	PROPN
iajs-117	249	22	is	be	AUX
iajs-117	249	23	a	a	DET
iajs-117	249	24	prime	prime	NOUN
iajs-117	249	25	by	by	ADP
iajs-117	249	26	(	(	PUNCT
iajs-117	249	27	2.2,(1	2.2,(1	NUM
iajs-117	249	28	)	)	PUNCT
iajs-117	249	29	)	)	PUNCT
iajs-117	249	30	.	.	PUNCT
iajs-117	250	1	hence	hence	ADV
iajs-117	250	2	either	either	CCONJ
iajs-117	250	3	n	n	PRON
iajs-117	250	4			PROPN
iajs-117	250	5	k	k	PROPN
iajs-117	250	6	or	or	CCONJ
iajs-117	250	7	k	k	PROPN
iajs-117	250	8			PUNCT
iajs-117	250	9	n	n	CCONJ
iajs-117	250	10	is	be	AUX
iajs-117	250	11	a	a	DET
iajs-117	250	12	prime	prime	NOUN
iajs-117	250	13	in	in	ADP
iajs-117	250	14	n,[11	n,[11	NUM
iajs-117	250	15	]	]	PUNCT
iajs-117	250	16	.	.	PUNCT
iajs-117	251	1	therefore	therefore	ADV
iajs-117	251	2	either	either	CCONJ
iajs-117	251	3	n	n	PRON
iajs-117	251	4			PROPN
iajs-117	251	5	k	k	PROPN
iajs-117	251	6	or	or	CCONJ
iajs-117	251	7	k	k	PROPN
iajs-117	251	8			PUNCT
iajs-117	251	9	n	n	CCONJ
iajs-117	251	10	is	be	AUX
iajs-117	251	11	a	a	DET
iajs-117	251	12	'prime	'prime	PROPN
iajs-117	251	13	in	in	ADP
iajs-117	251	14	n.	n.	NOUN
iajs-117	251	15	proposition	proposition	NOUN
iajs-117	251	16	(	(	PUNCT
iajs-117	251	17	2.24	2.24	NUM
iajs-117	251	18	):	):	PUNCT
iajs-117	251	19	let	let	VERB
iajs-117	251	20	p	p	PRON
iajs-117	251	21	be	be	AUX
iajs-117	251	22	an	an	DET
iajs-117	251	23	ideal	ideal	NOUN
iajs-117	251	24	of	of	ADP
iajs-117	251	25	a	a	DET
iajs-117	251	26	ring	ring	NOUN
iajs-117	251	27	r	r	NOUN
iajs-117	251	28	and	and	CCONJ
iajs-117	251	29	m	m	VERB
iajs-117	251	30	be	be	VERB
iajs-117	251	31	an	an	DET
iajs-117	251	32	r	r	NOUN
iajs-117	251	33	–	–	PUNCT
iajs-117	251	34	module	module	NOUN
iajs-117	251	35	.	.	PUNCT
iajs-117	252	1	then	then	ADV
iajs-117	252	2	a	a	DET
iajs-117	252	3	proper	proper	ADJ
iajs-117	252	4	submodule	submodule	NOUN
iajs-117	252	5	n	n	PROPN
iajs-117	252	6	of	of	ADP
iajs-117	252	7	m	m	PROPN
iajs-117	252	8	is	be	AUX
iajs-117	252	9	a	a	DET
iajs-117	252	10	p	p	NOUN
iajs-117	252	11			NOUN
iajs-117	252	12	prime	prime	NOUN
iajs-117	252	13	if	if	SCONJ
iajs-117	252	14	and	and	CCONJ
iajs-117	252	15	only	only	ADV
iajs-117	252	16	if	if	SCONJ
iajs-117	252	17	1	1	NUM
iajs-117	252	18	.	.	X
iajs-117	253	1	p	p	X
iajs-117	253	2			PROPN
iajs-117	253	3	n	n	CCONJ
iajs-117	253	4			NOUN
iajs-117	253	5	n	n	NOUN
iajs-117	253	6	:	:	PUNCT
iajs-117	253	7	m	m	NOUN
iajs-117	253	8	,	,	PUNCT
iajs-117	253	9	and	and	CCONJ
iajs-117	253	10	2	2	NUM
iajs-117	253	11	.	.	X
iajs-117	253	12	cm	cm	PROPN
iajs-117	253	13			CCONJ
iajs-117	253	14	n	n	CCONJ
iajs-117	253	15	,	,	PUNCT
iajs-117	253	16	for	for	ADP
iajs-117	253	17	all	all	DET
iajs-117	253	18	c	c	NOUN
iajs-117	253	19			PROPN
iajs-117	253	20	r	r	NOUN
iajs-117	253	21	\	\	PROPN
iajs-117	253	22	p	p	NOUN
iajs-117	253	23	,	,	PUNCT
iajs-117	253	24	m	m	PROPN
iajs-117	253	25			NOUN
iajs-117	253	26	m	m	VERB
iajs-117	253	27	\	\	PROPN
iajs-117	253	28	n	n	PROPN
iajs-117	253	29	+	+	ADJ
iajs-117	253	30			NOUN
iajs-117	253	31	(	(	PUNCT
iajs-117	253	32	n	n	CCONJ
iajs-117	253	33	)	)	PUNCT
iajs-117	253	34	.	.	PUNCT
iajs-117	254	1	proof	proof	NOUN
iajs-117	254	2	:	:	PUNCT
iajs-117	254	3	suppose	suppose	VERB
iajs-117	254	4	n	n	PRON
iajs-117	254	5	is	be	AUX
iajs-117	254	6	a	a	DET
iajs-117	254	7	p	p	NOUN
iajs-117	255	1			NOUN
iajs-117	255	2	prime	prime	NOUN
iajs-117	255	3	.	.	PUNCT
iajs-117	256	1	to	to	PART
iajs-117	256	2	prove	prove	VERB
iajs-117	256	3	that	that	SCONJ
iajs-117	256	4	(	(	PUNCT
iajs-117	256	5	1	1	X
iajs-117	256	6	)	)	PUNCT
iajs-117	256	7	and	and	CCONJ
iajs-117	256	8	(	(	PUNCT
iajs-117	256	9	2	2	X
iajs-117	256	10	)	)	PUNCT
iajs-117	256	11	are	be	AUX
iajs-117	256	12	hold	hold	ADJ
iajs-117	256	13	.	.	PUNCT
iajs-117	257	1	it	it	PRON
iajs-117	257	2	is	be	AUX
iajs-117	257	3	clear	clear	ADJ
iajs-117	257	4	that	that	SCONJ
iajs-117	257	5	p	p	PROPN
iajs-117	257	6	=	=	PUNCT
iajs-117	257	7	n	n	PROPN
iajs-117	257	8			NOUN
iajs-117	257	9	n	n	NOUN
iajs-117	257	10	:	:	PUNCT
iajs-117	257	11	m	m	NOUN
iajs-117	257	12	.therefore	.therefore	ADP
iajs-117	258	1	p	p	X
iajs-117	258	2			PROPN
iajs-117	258	3	n	n	INTJ
iajs-117	258	4			NOUN
iajs-117	258	5	n	n	NOUN
iajs-117	258	6	:	:	PUNCT
iajs-117	258	7	m	m	VERB
iajs-117	258	8	.	.	PUNCT
iajs-117	259	1	now	now	ADV
iajs-117	259	2	if	if	SCONJ
iajs-117	259	3	c	c	PROPN
iajs-117	259	4			NOUN
iajs-117	259	5	r	r	NOUN
iajs-117	259	6	\	\	PROPN
iajs-117	259	7	p	p	NOUN
iajs-117	259	8	and	and	CCONJ
iajs-117	259	9	m	m	PROPN
iajs-117	259	10			NOUN
iajs-117	259	11	m	m	VERB
iajs-117	259	12	\	\	PROPN
iajs-117	259	13	n	n	PROPN
iajs-117	259	14	+	+	ADJ
iajs-117	259	15			NOUN
iajs-117	259	16	(	(	PUNCT
iajs-117	259	17	n	n	CCONJ
iajs-117	259	18	)	)	PUNCT
iajs-117	259	19	,	,	PUNCT
iajs-117	259	20	then	then	ADV
iajs-117	259	21	c[n	c[n	PROPN
iajs-117	259	22	+	+	CCONJ
iajs-117	259	23	(n):m	(n):m	NOUN
iajs-117	259	24	]	]	PUNCT
iajs-117	259	25	and	and	CCONJ
iajs-117	259	26	m	m	PROPN
iajs-117	259	27	n	n	PROPN
iajs-117	259	28	+	+	CCONJ
iajs-117	259	29	n	n	NUM
iajs-117	259	30	)	)	PUNCT
iajs-117	259	31	,	,	PUNCT
iajs-117	259	32	hence	hence	ADV
iajs-117	259	33	cm	cm	NOUN
iajs-117	259	34			VERB
iajs-117	259	35	n.	n.	NOUN
iajs-117	259	36	conversely	conversely	ADV
iajs-117	259	37	,	,	PUNCT
iajs-117	259	38	let	let	VERB
iajs-117	259	39	c	c	NOUN
iajs-117	259	40			NOUN
iajs-117	259	41	r	r	NOUN
iajs-117	259	42	and	and	CCONJ
iajs-117	259	43	m	m	PROPN
iajs-117	259	44			NOUN
iajs-117	259	45	m	m	VERB
iajs-117	259	46	such	such	ADJ
iajs-117	259	47	that	that	SCONJ
iajs-117	259	48	m	m	VERB
iajs-117	259	49	n	n	PROPN
iajs-117	259	50	+	+	CCONJ
iajs-117	259	51	(n	(n	X
iajs-117	259	52	)	)	PUNCT
iajs-117	259	53	and	and	CCONJ
iajs-117	259	54	c	c	PROPN
iajs-117	259	55	[n	[n	PROPN
iajs-117	259	56	+	+	CCONJ
iajs-117	259	57	(n):m	(n):m	NOUN
iajs-117	259	58	]	]	PUNCT
iajs-117	259	59	.	.	PUNCT
iajs-117	260	1	since	since	SCONJ
iajs-117	260	2	p	p	NOUN
iajs-117	260	3			PROPN
iajs-117	260	4	[	[	X
iajs-117	260	5	n	n	X
iajs-117	260	6	+	+	CCONJ
iajs-117	260	7	(n):m	(n):m	NOUN
iajs-117	260	8	]	]	PUNCT
iajs-117	260	9	,	,	PUNCT
iajs-117	260	10	then	then	ADV
iajs-117	260	11	m	m	VERB
iajs-117	260	12			PROPN
iajs-117	260	13	m	m	VERB
iajs-117	260	14	\	\	PROPN
iajs-117	260	15	n	n	PROPN
iajs-117	260	16	+	+	ADJ
iajs-117	260	17			NOUN
iajs-117	260	18	(	(	PUNCT
iajs-117	260	19	n	n	CCONJ
iajs-117	260	20	)	)	PUNCT
iajs-117	260	21	and	and	CCONJ
iajs-117	260	22	c	c	NOUN
iajs-117	260	23			NOUN
iajs-117	260	24	p	p	X
iajs-117	260	25	.therefore	.therefore	PUNCT
iajs-117	260	26	,	,	PUNCT
iajs-117	260	27	c	c	PROPN
iajs-117	260	28			PROPN
iajs-117	260	29	r	r	NOUN
iajs-117	260	30	\	\	NOUN
iajs-117	260	31	p.	p.	NOUN
iajs-117	260	32	hence	hence	ADV
iajs-117	260	33	cm	cm	PROPN
iajs-117	260	34			NUM
iajs-117	260	35	n	n	CCONJ
iajs-117	260	36	,	,	PUNCT
iajs-117	260	37	which	which	PRON
iajs-117	260	38	implies	imply	VERB
iajs-117	260	39	that	that	SCONJ
iajs-117	260	40	n	n	X
iajs-117	260	41	is	be	AUX
iajs-117	260	42	a	a	DET
iajs-117	260	43	p	p	NOUN
iajs-117	261	1			NOUN
iajs-117	261	2	prime	prime	NOUN
iajs-117	261	3	.	.	PUNCT
iajs-117	262	1	proposition	proposition	NOUN
iajs-117	262	2	(	(	PUNCT
iajs-117	262	3	2.25	2.25	NUM
iajs-117	262	4	):	):	PUNCT
iajs-117	262	5	let	let	VERB
iajs-117	262	6			NOUN
iajs-117	262	7	:	:	PUNCT
iajs-117	262	8	m	m	VERB
iajs-117	262	9			PROPN
iajs-117	262	10	m	m	VERB
iajs-117	262	11	'	'	PUNCT
iajs-117	262	12	be	be	VERB
iajs-117	262	13	an	an	DET
iajs-117	262	14	homomorphism	homomorphism	NOUN
iajs-117	262	15	.	.	PUNCT
iajs-117	263	1	if	if	SCONJ
iajs-117	263	2	n	n	PRON
iajs-117	263	3	is	be	AUX
iajs-117	263	4			PRON
iajs-117	263	5	'	'	PUNCT
iajs-117	263	6	prime	prime	ADJ
iajs-117	263	7	submodule	submodule	NOUN
iajs-117	263	8	of	of	ADP
iajs-117	263	9	an	an	DET
iajs-117	263	10	r	r	NOUN
iajs-117	263	11	-	-	PUNCT
iajs-117	263	12	module	module	NOUN
iajs-117	263	13	m	m	NOUN
iajs-117	263	14	'	'	PUNCT
iajs-117	263	15	,	,	PUNCT
iajs-117	263	16	such	such	ADJ
iajs-117	263	17	that	that	SCONJ
iajs-117	263	18			NOUN
iajs-117	263	19	(	(	PUNCT
iajs-117	263	20	m	m	NOUN
iajs-117	263	21	)	)	PUNCT
iajs-117	263	22	⊈	⊈	PROPN
iajs-117	263	23	n	n	PROPN
iajs-117	263	24	and	and	CCONJ
iajs-117	263	25	(	(	NOUN
iajs-117	263	26	–	–	PUNCT
iajs-117	263	27	1(n))=	1(n))=	NUM
iajs-117	263	28			NOUN
iajs-117	263	29	–	–	PUNCT
iajs-117	263	30	1(	1(	NOUN
iajs-117	263	31	'	'	PUNCT
iajs-117	263	32	(	(	PUNCT
iajs-117	263	33	n	n	CCONJ
iajs-117	263	34	)	)	PUNCT
iajs-117	263	35	)	)	PUNCT
iajs-117	263	36	,	,	PUNCT
iajs-117	263	37	then	then	ADV
iajs-117	263	38			NOUN
iajs-117	263	39	–	–	PUNCT
iajs-117	263	40	1(n	1(n	NUM
iajs-117	263	41	)	)	PUNCT
iajs-117	263	42	is	be	AUX
iajs-117	263	43	-prime	-prime	ADJ
iajs-117	263	44	submodule	submodule	NOUN
iajs-117	263	45	of	of	ADP
iajs-117	263	46	m	m	PROPN
iajs-117	263	47	,	,	PUNCT
iajs-117	263	48	where	where	SCONJ
iajs-117	263	49	:(m	:(m	ADJ
iajs-117	263	50	)	)	PUNCT
iajs-117	263	51			PROPN
iajs-117	263	52	(m	(m	PROPN
iajs-117	263	53	)	)	PUNCT
iajs-117	263	54			NOUN
iajs-117	263	55	{	{	PUNCT
iajs-117	263	56			NOUN
iajs-117	263	57	}	}	PUNCT
iajs-117	263	58	and	and	CCONJ
iajs-117	263	59			NOUN
iajs-117	263	60	'	'	PUNCT
iajs-117	263	61	:	:	PUNCT
iajs-117	263	62	(m	(m	NOUN
iajs-117	263	63	'	'	NUM
iajs-117	263	64	)	)	PUNCT
iajs-117	263	65			PROPN
iajs-117	263	66	(m	(m	PROPN
iajs-117	263	67	'	'	NOUN
iajs-117	263	68	)	)	PUNCT
iajs-117	263	69			NOUN
iajs-117	263	70	{	{	PUNCT
iajs-117	263	71			NOUN
iajs-117	263	72	}	}	PUNCT
iajs-117	263	73	.	.	PUNCT
iajs-117	264	1	proof	proof	NOUN
iajs-117	264	2	:	:	PUNCT
iajs-117	264	3	first	first	ADV
iajs-117	264	4	,	,	PUNCT
iajs-117	264	5	we	we	PRON
iajs-117	264	6	must	must	AUX
iajs-117	264	7	show	show	VERB
iajs-117	264	8	that	that	SCONJ
iajs-117	264	9			NOUN
iajs-117	264	10	–	–	PUNCT
iajs-117	264	11	1(n	1(n	NUM
iajs-117	264	12	)	)	PUNCT
iajs-117	264	13	is	be	AUX
iajs-117	264	14	a	a	DET
iajs-117	264	15	proper	proper	ADJ
iajs-117	264	16	submodule	submodule	NOUN
iajs-117	264	17	of	of	ADP
iajs-117	264	18	m.	m.	NOUN
iajs-117	264	19	suppose	suppose	VERB
iajs-117	264	20	that	that	SCONJ
iajs-117	264	21			NOUN
iajs-117	264	22	–	–	PUNCT
iajs-117	264	23	1(n	1(n	NUM
iajs-117	264	24	)	)	PUNCT
iajs-117	264	25	=	=	SYM
iajs-117	264	26	m	m	PROPN
iajs-117	264	27	,	,	PUNCT
iajs-117	264	28	then	then	ADV
iajs-117	264	29	(m	(m	ADJ
iajs-117	264	30	)	)	PUNCT
iajs-117	264	31			PROPN
iajs-117	264	32	n	n	CCONJ
iajs-117	264	33	,	,	PUNCT
iajs-117	264	34	which	which	PRON
iajs-117	264	35	a	a	DET
iajs-117	264	36	contradiction	contradiction	NOUN
iajs-117	264	37	to	to	ADP
iajs-117	264	38	the	the	DET
iajs-117	264	39	assumption	assumption	NOUN
iajs-117	264	40	.	.	PUNCT
iajs-117	265	1	let	let	VERB
iajs-117	265	2	r	r	NOUN
iajs-117	265	3			NOUN
iajs-117	265	4	r	r	NOUN
iajs-117	265	5	,	,	PUNCT
iajs-117	265	6	m	m	VERB
iajs-117	265	7			NOUN
iajs-117	265	8	m	m	VERB
iajs-117	265	9	such	such	ADJ
iajs-117	265	10	that	that	SCONJ
iajs-117	265	11	rm	rm	PROPN
iajs-117	265	12			NOUN
iajs-117	265	13	–	–	PUNCT
iajs-117	265	14	1(n	1(n	NUM
iajs-117	265	15	)	)	PUNCT
iajs-117	265	16	.then	.then	PUNCT
iajs-117	266	1	r	r	NOUN
iajs-117	266	2	(	(	PUNCT
iajs-117	266	3	m	m	NOUN
iajs-117	266	4	)	)	PUNCT
iajs-117	266	5			NOUN
iajs-117	266	6	n	n	CCONJ
iajs-117	266	7	and	and	CCONJ
iajs-117	266	8	n	n	PROPN
iajs-117	266	9	is	be	AUX
iajs-117	266	10			PRON
iajs-117	266	11	'	'	PUNCT
iajs-117	266	12	‐	‐	ADJ
iajs-117	266	13	prime	prime	ADJ
iajs-117	266	14	submodule	submodule	NOUN
iajs-117	266	15	of	of	ADP
iajs-117	266	16	an	an	DET
iajs-117	266	17	r‐module	r‐module	NOUN
iajs-117	266	18	m	m	PRON
iajs-117	266	19	'	'	NUM
iajs-117	266	20	,	,	PUNCT
iajs-117	266	21	then	then	ADV
iajs-117	266	22	either	either	CCONJ
iajs-117	266	23			NOUN
iajs-117	266	24	m	m	VERB
iajs-117	266	25			NOUN
iajs-117	266	26	n	n	CCONJ
iajs-117	266	27			NOUN
iajs-117	266	28	'	'	PUNCT
iajs-117	266	29	n	n	CCONJ
iajs-117	266	30	or	or	CCONJ
iajs-117	266	31	r	r	NOUN
iajs-117	266	32	m	m	PROPN
iajs-117	266	33	'	'	PART
iajs-117	266	34			PROPN
iajs-117	266	35	n	n	CCONJ
iajs-117	266	36			NOUN
iajs-117	266	37	'	'	PUNCT
iajs-117	266	38	n	n	NOUN
iajs-117	266	39	.	.	PUNCT
iajs-117	267	1	if	if	SCONJ
iajs-117	267	2			NOUN
iajs-117	267	3	m	m	VERB
iajs-117	267	4	n	n	NOUN
iajs-117	267	5			NOUN
iajs-117	267	6	'	'	PUNCT
iajs-117	267	7	n	n	NOUN
iajs-117	267	8	,	,	PUNCT
iajs-117	267	9	then	then	ADV
iajs-117	267	10	m	m	PROPN
iajs-117	267	11	–	–	PUNCT
iajs-117	267	12	1	1	NUM
iajs-117	267	13	n	n	DET
iajs-117	267	14			NOUN
iajs-117	267	15	–	–	PUNCT
iajs-117	267	16	1	1	NUM
iajs-117	267	17			NOUN
iajs-117	267	18	'	'	PUNCT
iajs-117	267	19	n	n	NOUN
iajs-117	267	20	and	and	CCONJ
iajs-117	267	21	hence	hence	ADV
iajs-117	267	22	m	m	VERB
iajs-117	267	23			NOUN
iajs-117	267	24			NOUN
iajs-117	267	25	–	–	PUNCT
iajs-117	267	26	1	1	NUM
iajs-117	267	27	n	n	ADP
iajs-117	267	28			NOUN
iajs-117	267	29			NOUN
iajs-117	267	30	–	–	PUNCT
iajs-117	267	31	1	1	NUM
iajs-117	267	32	n	n	NOUN
iajs-117	267	33	.	.	PUNCT
iajs-117	268	1	if	if	SCONJ
iajs-117	268	2	r	r	PROPN
iajs-117	268	3	m	m	VERB
iajs-117	268	4	'	'	PART
iajs-117	268	5			PROPN
iajs-117	268	6	n	n	CCONJ
iajs-117	268	7			NOUN
iajs-117	268	8	'	'	PUNCT
iajs-117	268	9	n	n	NOUN
iajs-117	268	10	,	,	PUNCT
iajs-117	268	11	then	then	ADV
iajs-117	268	12	r	r	PROPN
iajs-117	268	13	m	m	PROPN
iajs-117	268	14			PROPN
iajs-117	268	15	n	n	PRON
iajs-117	268	16			NOUN
iajs-117	268	17	'	'	PUNCT
iajs-117	268	18	n	n	PRON
iajs-117	268	19	mathematics	mathematic	NOUN
iajs-117	268	20	|	|	ADV
iajs-117	268	21	289	289	NUM
iajs-117	268	22	2016	2016	NUM
iajs-117	268	23	)	)	PUNCT
iajs-117	269	1	عام	عام	ADP
iajs-117	269	2	2العدد	2العدد	NUM
iajs-117	269	3	(	(	PUNCT
iajs-117	269	4	29لمجلد	29لمجلد	NUM
iajs-117	269	5	ا	ا	X
iajs-117	269	6	مجلة	مجلة	NOUN
iajs-117	269	7	إبن	إبن	VERB
iajs-117	269	8	الهيثم	الهيثم	ADJ
iajs-117	269	9	للعلوم	للعلوم	NOUN
iajs-117	269	10	الصرفة	الصرفة	NOUN
iajs-117	270	1	و	و	PRON
iajs-117	270	2	التطبيقية	التطبيقية	ADJ
iajs-117	270	3	ibn	ibn	PROPN
iajs-117	270	4	al	al	PROPN
iajs-117	270	5	-	-	PUNCT
iajs-117	270	6	haitham	haitham	PROPN
iajs-117	270	7	jour	jour	X
iajs-117	270	8	.	.	PROPN
iajs-117	270	9	for	for	ADP
iajs-117	270	10	pure	pure	ADJ
iajs-117	270	11	&	&	CCONJ
iajs-117	270	12	appl	appl	PROPN
iajs-117	270	13	.	.	PUNCT
iajs-117	271	1	sci	sci	PROPN
iajs-117	271	2	.	.	PUNCT
iajs-117	271	3	vol	vol	NOUN
iajs-117	271	4	.	.	PROPN
iajs-117	271	5	29	29	NUM
iajs-117	271	6	(	(	PUNCT
iajs-117	271	7	2	2	NUM
iajs-117	271	8	)	)	PUNCT
iajs-117	271	9	2016	2016	NUM
iajs-117	271	10	since	since	SCONJ
iajs-117	271	11			NOUN
iajs-117	271	12	m	m	VERB
iajs-117	271	13			PROPN
iajs-117	271	14	m	m	PROPN
iajs-117	271	15	'	'	NUM
iajs-117	271	16	.	.	PUNCT
iajs-117	272	1	this	this	PRON
iajs-117	272	2	implies	imply	VERB
iajs-117	272	3	r	r	NOUN
iajs-117	272	4	m	m	VERB
iajs-117	272	5			PROPN
iajs-117	272	6			NOUN
iajs-117	272	7	–	–	PUNCT
iajs-117	272	8	1	1	NUM
iajs-117	272	9	n	n	PRON
iajs-117	272	10			NOUN
iajs-117	272	11	–	–	PUNCT
iajs-117	272	12	1	1	NUM
iajs-117	272	13			NOUN
iajs-117	272	14	'	'	PUNCT
iajs-117	272	15	n	n	CCONJ
iajs-117	272	16			NOUN
iajs-117	272	17	–	–	PUNCT
iajs-117	272	18	1	1	NUM
iajs-117	272	19	n	n	ADP
iajs-117	272	20			NOUN
iajs-117	272	21			NOUN
iajs-117	272	22	–	–	PUNCT
iajs-117	272	23	1	1	NUM
iajs-117	272	24	n	n	NOUN
iajs-117	272	25	.therefore	.therefore	NOUN
iajs-117	272	26			NOUN
iajs-117	272	27	–	–	PUNCT
iajs-117	272	28	1	1	NUM
iajs-117	272	29	n	n	PRON
iajs-117	272	30	is	be	AUX
iajs-117	272	31	‐prime	‐prime	PROPN
iajs-117	272	32	submodule	submodule	NOUN
iajs-117	272	33	of	of	ADP
iajs-117	272	34	m.	m.	NOUN
iajs-117	272	35	theorem	theorem	PROPN
iajs-117	272	36	(	(	PUNCT
iajs-117	272	37	2.26	2.26	NUM
iajs-117	272	38	):	):	PUNCT
iajs-117	272	39	let	let	VERB
iajs-117	272	40	f	f	X
iajs-117	272	41	:	:	PUNCT
iajs-117	272	42	m	m	VERB
iajs-117	272	43			PROPN
iajs-117	272	44	m	m	VERB
iajs-117	272	45	'	'	PUNCT
iajs-117	272	46	be	be	VERB
iajs-117	272	47	an	an	DET
iajs-117	272	48	epimorphism	epimorphism	NOUN
iajs-117	272	49	and	and	CCONJ
iajs-117	272	50	let	let	VERB
iajs-117	272	51	n	n	PRON
iajs-117	272	52	<	<	X
iajs-117	272	53	m	m	VERB
iajs-117	272	54	such	such	ADJ
iajs-117	272	55	that	that	DET
iajs-117	272	56	ker	ker	PROPN
iajs-117	272	57	f	f	PROPN
iajs-117	272	58			PROPN
iajs-117	272	59	n.	n.	NOUN
iajs-117	272	60	if	if	SCONJ
iajs-117	272	61	n	n	PRON
iajs-117	272	62	is	be	AUX
iajs-117	272	63	a	a	DET
iajs-117	272	64	-prime	-prime	ADJ
iajs-117	272	65	submodule	submodule	NOUN
iajs-117	272	66	of	of	ADP
iajs-117	272	67	an	an	DET
iajs-117	272	68	rmodule	rmodule	NOUN
iajs-117	272	69	m	m	PROPN
iajs-117	272	70	and	and	CCONJ
iajs-117	272	71			NOUN
iajs-117	272	72	'	'	PUNCT
iajs-117	272	73	(	(	PUNCT
iajs-117	272	74	f	f	X
iajs-117	272	75	(	(	PUNCT
iajs-117	272	76	n	n	CCONJ
iajs-117	272	77	)	)	PUNCT
iajs-117	272	78	)	)	PUNCT
iajs-117	273	1	=	=	SYM
iajs-117	273	2	f	f	PROPN
iajs-117	273	3	(	(	PUNCT
iajs-117	273	4	(n	(n	PROPN
iajs-117	273	5	)	)	PUNCT
iajs-117	273	6	)	)	PUNCT
iajs-117	273	7	,	,	PUNCT
iajs-117	273	8	then	then	ADV
iajs-117	273	9	f	f	PROPN
iajs-117	273	10	(	(	PUNCT
iajs-117	273	11	n	n	CCONJ
iajs-117	273	12	)	)	PUNCT
iajs-117	273	13	is	be	AUX
iajs-117	273	14	a	a	DET
iajs-117	273	15	'-prime	'-prime	ADJ
iajs-117	273	16	submodule	submodule	NOUN
iajs-117	273	17	of	of	ADP
iajs-117	273	18	a	a	DET
iajs-117	273	19	module	module	NOUN
iajs-117	273	20	of	of	ADP
iajs-117	273	21	m	m	NOUN
iajs-117	273	22	'	'	PUNCT
iajs-117	273	23	,	,	PUNCT
iajs-117	273	24	where	where	SCONJ
iajs-117	273	25	:(m	:(m	ADJ
iajs-117	273	26	)	)	PUNCT
iajs-117	273	27			PROPN
iajs-117	273	28	(m	(m	PROPN
iajs-117	273	29	)	)	PUNCT
iajs-117	273	30			NOUN
iajs-117	273	31	{	{	PUNCT
iajs-117	273	32			NOUN
iajs-117	273	33	}	}	PUNCT
iajs-117	273	34	and	and	CCONJ
iajs-117	273	35			NOUN
iajs-117	273	36	'	'	PUNCT
iajs-117	273	37	:	:	PUNCT
iajs-117	273	38	(m	(m	NOUN
iajs-117	273	39	'	'	NUM
iajs-117	273	40	)	)	PUNCT
iajs-117	273	41			PROPN
iajs-117	273	42	(m	(m	PROPN
iajs-117	273	43	'	'	NOUN
iajs-117	273	44	)	)	PUNCT
iajs-117	273	45			NOUN
iajs-117	273	46	{	{	PUNCT
iajs-117	273	47			NOUN
iajs-117	273	48	}	}	PUNCT
iajs-117	273	49	.	.	PUNCT
iajs-117	274	1	proof	proof	NOUN
iajs-117	274	2	:	:	PUNCT
iajs-117	274	3	first	first	ADV
iajs-117	274	4	,	,	PUNCT
iajs-117	274	5	we	we	PRON
iajs-117	274	6	must	must	AUX
iajs-117	274	7	show	show	VERB
iajs-117	274	8	that	that	SCONJ
iajs-117	274	9	f	f	PROPN
iajs-117	274	10	(	(	PUNCT
iajs-117	274	11	n	n	CCONJ
iajs-117	274	12	)	)	PUNCT
iajs-117	274	13	is	be	AUX
iajs-117	274	14	a	a	DET
iajs-117	274	15	proper	proper	ADJ
iajs-117	274	16	submodule	submodule	NOUN
iajs-117	274	17	of	of	ADP
iajs-117	274	18	a	a	DET
iajs-117	274	19	module	module	NOUN
iajs-117	274	20	m	m	NOUN
iajs-117	274	21	'	'	PUNCT
iajs-117	274	22	.	.	PUNCT
iajs-117	275	1	suppose	suppose	VERB
iajs-117	276	1	f	f	PROPN
iajs-117	276	2	(	(	PUNCT
iajs-117	276	3	n	n	CCONJ
iajs-117	276	4	)	)	PUNCT
iajs-117	276	5	=	=	PUNCT
iajs-117	276	6	m	m	NOUN
iajs-117	276	7	'	'	NUM
iajs-117	276	8	.	.	PUNCT
iajs-117	277	1	but	but	CCONJ
iajs-117	277	2	f	f	PROPN
iajs-117	277	3	is	be	AUX
iajs-117	277	4	an	an	DET
iajs-117	277	5	epimorphism	epimorphism	NOUN
iajs-117	277	6	,	,	PUNCT
iajs-117	277	7	thus	thus	ADV
iajs-117	277	8	f	f	X
iajs-117	277	9	(	(	PUNCT
iajs-117	277	10	n	n	CCONJ
iajs-117	277	11	)	)	PUNCT
iajs-117	277	12	=	=	SYM
iajs-117	277	13	f	f	PROPN
iajs-117	277	14	(	(	PUNCT
iajs-117	277	15	m	m	PROPN
iajs-117	277	16	)	)	PUNCT
iajs-117	277	17	and	and	CCONJ
iajs-117	277	18	hence	hence	ADV
iajs-117	277	19	m	m	VERB
iajs-117	277	20	=	=	SYM
iajs-117	277	21	n	n	PROPN
iajs-117	277	22	+	+	CCONJ
iajs-117	277	23	ker	ker	PROPN
iajs-117	277	24	f.	f.	PROPN
iajs-117	278	1	this	this	PRON
iajs-117	278	2	implies	imply	VERB
iajs-117	278	3	that	that	SCONJ
iajs-117	278	4	m	m	VERB
iajs-117	278	5	=	=	PUNCT
iajs-117	278	6	n.	n.	VERB
iajs-117	278	7	a	a	DET
iajs-117	278	8	contradiction	contradiction	NOUN
iajs-117	278	9	.	.	PUNCT
iajs-117	279	1	now	now	ADV
iajs-117	279	2	,	,	PUNCT
iajs-117	279	3	let	let	VERB
iajs-117	279	4	r	r	NOUN
iajs-117	279	5	m	m	NOUN
iajs-117	279	6	'	'	PART
iajs-117	279	7			PROPN
iajs-117	279	8	f	f	X
iajs-117	279	9	(	(	PUNCT
iajs-117	279	10	n	n	CCONJ
iajs-117	279	11	)	)	PUNCT
iajs-117	279	12	,	,	PUNCT
iajs-117	279	13	where	where	SCONJ
iajs-117	279	14	r	r	NOUN
iajs-117	279	15			NOUN
iajs-117	279	16	r	r	NOUN
iajs-117	279	17	and	and	CCONJ
iajs-117	279	18	m	m	PROPN
iajs-117	279	19	'	'	PART
iajs-117	279	20			PROPN
iajs-117	279	21	m	m	NOUN
iajs-117	279	22	'	'	PUNCT
iajs-117	279	23	,	,	PUNCT
iajs-117	279	24	m'=	m'=	PROPN
iajs-117	279	25	f	f	X
iajs-117	279	26	(	(	PUNCT
iajs-117	279	27	m	m	PROPN
iajs-117	279	28	)	)	PUNCT
iajs-117	279	29	for	for	ADP
iajs-117	279	30	some	some	DET
iajs-117	279	31	m	m	NOUN
iajs-117	279	32	m	m	ADJ
iajs-117	279	33	since	since	SCONJ
iajs-117	279	34	f	f	PROPN
iajs-117	279	35	is	be	AUX
iajs-117	279	36	an	an	DET
iajs-117	279	37	epimorphism	epimorphism	NOUN
iajs-117	279	38	.	.	PUNCT
iajs-117	280	1	then	then	ADV
iajs-117	280	2	r	r	NOUN
iajs-117	280	3	f	f	X
iajs-117	280	4	(	(	PUNCT
iajs-117	280	5	m	m	NOUN
iajs-117	280	6	)	)	PUNCT
iajs-117	280	7			NOUN
iajs-117	280	8	f	f	PROPN
iajs-117	280	9	(	(	PUNCT
iajs-117	280	10	n),so	n),so	X
iajs-117	280	11	f	f	X
iajs-117	280	12	(	(	PUNCT
iajs-117	280	13	r	r	NOUN
iajs-117	280	14	m)=	m)=	NOUN
iajs-117	280	15	f	f	PROPN
iajs-117	280	16	(	(	PUNCT
iajs-117	280	17	n	n	CCONJ
iajs-117	280	18	)	)	PUNCT
iajs-117	280	19	for	for	ADP
iajs-117	280	20	some	some	DET
iajs-117	280	21	n	n	PROPN
iajs-117	280	22	n	n	CCONJ
iajs-117	280	23	and	and	CCONJ
iajs-117	280	24	hence	hence	ADV
iajs-117	280	25	f	f	PROPN
iajs-117	280	26	(	(	PUNCT
iajs-117	280	27	r	r	NOUN
iajs-117	280	28	m	m	PROPN
iajs-117	280	29	)	)	PUNCT
iajs-117	280	30	f	f	PROPN
iajs-117	280	31	(	(	PUNCT
iajs-117	280	32	n	n	CCONJ
iajs-117	280	33	)	)	PUNCT
iajs-117	280	34	=	=	SYM
iajs-117	280	35	0	0	PUNCT
iajs-117	281	1	.thus	.thus	INTJ
iajs-117	281	2	we	we	PRON
iajs-117	281	3	get	get	VERB
iajs-117	281	4	that	that	DET
iajs-117	281	5	rm	rm	PROPN
iajs-117	281	6	-	-	PUNCT
iajs-117	281	7	n	n	PROPN
iajs-117	281	8			NOUN
iajs-117	281	9	ker	ker	X
iajs-117	282	1	f	f	PROPN
iajs-117	282	2			PROPN
iajs-117	282	3	n	n	X
iajs-117	282	4	which	which	PRON
iajs-117	282	5	implies	imply	VERB
iajs-117	282	6	that	that	SCONJ
iajs-117	282	7	rm	rm	PROPN
iajs-117	282	8	n	n	PROPN
iajs-117	282	9	.but	.but	PUNCT
iajs-117	283	1	n	n	PRON
iajs-117	283	2	is	be	AUX
iajs-117	283	3	a	a	DET
iajs-117	283	4	-prime	-prime	NOUN
iajs-117	283	5	,	,	PUNCT
iajs-117	283	6	so	so	CCONJ
iajs-117	283	7	either	either	CCONJ
iajs-117	283	8	m	m	PROPN
iajs-117	283	9	n	n	NOUN
iajs-117	283	10	+	+	CCONJ
iajs-117	283	11	(n	(n	X
iajs-117	283	12	)	)	PUNCT
iajs-117	283	13	or	or	CCONJ
iajs-117	283	14	r	r	NOUN
iajs-117	283	15	m	m	NOUN
iajs-117	283	16			PROPN
iajs-117	283	17	n	n	PROPN
iajs-117	283	18	+	+	CCONJ
iajs-117	283	19	(n	(n	NOUN
iajs-117	283	20	)	)	PUNCT
iajs-117	283	21	.	.	PUNCT
iajs-117	284	1	if	if	SCONJ
iajs-117	284	2	m	m	PROPN
iajs-117	284	3	n	n	NOUN
iajs-117	284	4	+	+	X
iajs-117	284	5	(n),then	(n),then	X
iajs-117	284	6	f	f	X
iajs-117	284	7	(	(	PUNCT
iajs-117	284	8	m	m	PROPN
iajs-117	284	9	)	)	PUNCT
iajs-117	284	10			NOUN
iajs-117	284	11	f	f	X
iajs-117	284	12	(	(	PUNCT
iajs-117	284	13	n	n	CCONJ
iajs-117	284	14	)	)	PUNCT
iajs-117	285	1	+	+	CCONJ
iajs-117	285	2	f	f	X
iajs-117	285	3	(	(	PUNCT
iajs-117	285	4	(n));that	(n));that	PRON
iajs-117	285	5	is	be	AUX
iajs-117	285	6	m'	m'	PROPN
iajs-117	285	7	f	f	PROPN
iajs-117	285	8	(	(	PUNCT
iajs-117	285	9	n	n	CCONJ
iajs-117	285	10	)	)	PUNCT
iajs-117	286	1	+	+	CCONJ
iajs-117	286	2	f	f	X
iajs-117	286	3	(	(	PUNCT
iajs-117	286	4	(n	(n	X
iajs-117	286	5	)	)	PUNCT
iajs-117	286	6	)	)	PUNCT
iajs-117	287	1	=	=	SYM
iajs-117	287	2	f	f	X
iajs-117	287	3	(	(	PUNCT
iajs-117	287	4	n	n	CCONJ
iajs-117	287	5	)	)	PUNCT
iajs-117	287	6	+	+	CCONJ
iajs-117	287	7			NOUN
iajs-117	287	8	'	'	PUNCT
iajs-117	287	9	(	(	PUNCT
iajs-117	287	10	f	f	X
iajs-117	287	11	(	(	PUNCT
iajs-117	287	12	n	n	CCONJ
iajs-117	287	13	)	)	PUNCT
iajs-117	287	14	)	)	PUNCT
iajs-117	287	15	.	.	PUNCT
iajs-117	288	1	if	if	SCONJ
iajs-117	288	2	r	r	NOUN
iajs-117	288	3	m	m	VERB
iajs-117	288	4			ADJ
iajs-117	288	5	n	n	PROPN
iajs-117	288	6	+	+	CCONJ
iajs-117	289	1	(n),then	(n),then	X
iajs-117	289	2	r	r	NOUN
iajs-117	289	3	f	f	X
iajs-117	289	4	(	(	PUNCT
iajs-117	289	5	m	m	PROPN
iajs-117	289	6	)	)	PUNCT
iajs-117	289	7			PROPN
iajs-117	289	8	f	f	PROPN
iajs-117	289	9	(	(	PUNCT
iajs-117	289	10	n	n	CCONJ
iajs-117	289	11	)	)	PUNCT
iajs-117	290	1	+	+	CCONJ
iajs-117	290	2	f	f	X
iajs-117	290	3	(	(	PUNCT
iajs-117	290	4	(n	(n	X
iajs-117	290	5	)	)	PUNCT
iajs-117	290	6	)	)	PUNCT
iajs-117	291	1	=	=	SYM
iajs-117	291	2	f	f	X
iajs-117	291	3	(	(	PUNCT
iajs-117	291	4	n	n	CCONJ
iajs-117	291	5	)	)	PUNCT
iajs-117	291	6	+	+	CCONJ
iajs-117	291	7			NOUN
iajs-117	291	8	'	'	PUNCT
iajs-117	291	9	(	(	PUNCT
iajs-117	291	10	f	f	X
iajs-117	291	11	(	(	PUNCT
iajs-117	291	12	n	n	CCONJ
iajs-117	291	13	)	)	PUNCT
iajs-117	291	14	implies	imply	VERB
iajs-117	291	15	that	that	SCONJ
iajs-117	291	16	r	r	PROPN
iajs-117	291	17	m	m	NOUN
iajs-117	291	18	'	'	PART
iajs-117	291	19			PROPN
iajs-117	291	20	f	f	PROPN
iajs-117	291	21	(	(	PUNCT
iajs-117	291	22	n	n	CCONJ
iajs-117	291	23	)	)	PUNCT
iajs-117	291	24	+	+	CCONJ
iajs-117	291	25			NOUN
iajs-117	291	26	'	'	PUNCT
iajs-117	291	27	(	(	PUNCT
iajs-117	291	28	f	f	X
iajs-117	291	29	(	(	PUNCT
iajs-117	291	30	n	n	CCONJ
iajs-117	291	31	)	)	PUNCT
iajs-117	291	32	.	.	PUNCT
iajs-117	292	1	corollary	corollary	ADJ
iajs-117	292	2	(	(	PUNCT
iajs-117	292	3	2.27	2.27	NUM
iajs-117	292	4	):	):	PUNCT
iajs-117	292	5	let	let	VERB
iajs-117	292	6	m	m	PRON
iajs-117	292	7	be	be	AUX
iajs-117	292	8	an	an	DET
iajs-117	292	9	r	r	NOUN
iajs-117	292	10	-	-	PUNCT
iajs-117	292	11	module	module	NOUN
iajs-117	292	12	,	,	PUNCT
iajs-117	292	13	let	let	VERB
iajs-117	292	14	k	k	PRON
iajs-117	292	15	<	<	X
iajs-117	292	16	n	n	X
iajs-117	292	17	<	<	X
iajs-117	292	18	m	m	NOUN
iajs-117	293	1	and	and	CCONJ
iajs-117	293	2	n	n	PRON
iajs-117	293	3	be	be	VERB
iajs-117	293	4	a	a	DET
iajs-117	293	5	-prime	-prime	NOUN
iajs-117	293	6	of	of	ADP
iajs-117	293	7	m.	m.	NOUN
iajs-117	293	8	then	then	ADV
iajs-117	293	9	n	n	CCONJ
iajs-117	293	10	/	/	SYM
iajs-117	293	11	k	k	PROPN
iajs-117	293	12	is	be	AUX
iajs-117	293	13	a	a	DET
iajs-117	293	14	'prime	'prime	PROPN
iajs-117	293	15	submodule	submodule	NOUN
iajs-117	293	16	of	of	ADP
iajs-117	293	17	m	m	PROPN
iajs-117	293	18	/	/	SYM
iajs-117	293	19	k	k	NOUN
iajs-117	293	20	,	,	PUNCT
iajs-117	293	21	where	where	SCONJ
iajs-117	293	22			NOUN
iajs-117	293	23	'	'	PUNCT
iajs-117	293	24	:	:	PUNCT
iajs-117	294	1			NUM
iajs-117	294	2	(	(	PUNCT
iajs-117	294	3	m/	m/	NOUN
iajs-117	294	4	k	k	NOUN
iajs-117	294	5	)	)	PUNCT
iajs-117	294	6			PUNCT
iajs-117	295	1			NUM
iajs-117	295	2	(	(	PUNCT
iajs-117	295	3	m/	m/	NOUN
iajs-117	295	4	k	k	NOUN
iajs-117	295	5	)	)	PUNCT
iajs-117	295	6	.	.	PUNCT
iajs-117	296	1	proof	proof	NOUN
iajs-117	296	2	:	:	PUNCT
iajs-117	296	3	let	let	VERB
iajs-117	296	4	:m	:m	PROPN
iajs-117	296	5			PROPN
iajs-117	296	6	m	m	PROPN
iajs-117	296	7	/	/	SYM
iajs-117	296	8	k	k	PROPN
iajs-117	296	9	be	be	VERB
iajs-117	296	10	the	the	DET
iajs-117	296	11	natural	natural	ADJ
iajs-117	296	12	mapping	mapping	NOUN
iajs-117	296	13	,	,	PUNCT
iajs-117	296	14	then	then	ADV
iajs-117	296	15	the	the	DET
iajs-117	296	16	result	result	NOUN
iajs-117	296	17	follows	follow	VERB
iajs-117	296	18	by	by	ADP
iajs-117	296	19	proposition(2.26	proposition(2.26	NOUN
iajs-117	296	20	)	)	PUNCT
iajs-117	296	21	.	.	PUNCT
iajs-117	297	1	proposition	proposition	NOUN
iajs-117	297	2	(	(	PUNCT
iajs-117	297	3	2.28	2.28	NUM
iajs-117	297	4	):	):	PUNCT
iajs-117	297	5	let	let	VERB
iajs-117	297	6	m	m	PRON
iajs-117	297	7	be	be	AUX
iajs-117	297	8	an	an	DET
iajs-117	297	9	r	r	NOUN
iajs-117	297	10	-	-	PUNCT
iajs-117	297	11	module	module	NOUN
iajs-117	297	12	and	and	CCONJ
iajs-117	297	13	let	let	VERB
iajs-117	297	14	k	k	PRON
iajs-117	297	15	<	<	X
iajs-117	297	16	n	n	X
iajs-117	297	17	<	<	X
iajs-117	297	18	m	m	PROPN
iajs-117	297	19	.if	.if	PUNCT
iajs-117	298	1	n	n	PRON
iajs-117	298	2	is	be	AUX
iajs-117	298	3	a	a	DET
iajs-117	298	4	-prime	-prime	ADJ
iajs-117	298	5	submodule	submodule	NOUN
iajs-117	298	6	of	of	ADP
iajs-117	298	7	m	m	PROPN
iajs-117	298	8	,	,	PUNCT
iajs-117	298	9	then	then	ADV
iajs-117	298	10	n	n	CCONJ
iajs-117	298	11	/	/	SYM
iajs-117	298	12	k	k	PROPN
iajs-117	298	13	is	be	AUX
iajs-117	298	14	a	a	DET
iajs-117	298	15	'-prime	'-prime	ADJ
iajs-117	298	16	submodule	submodule	NOUN
iajs-117	298	17	of	of	ADP
iajs-117	298	18	m	m	PROPN
iajs-117	298	19	/	/	SYM
iajs-117	298	20	k	k	NOUN
iajs-117	298	21	,	,	PUNCT
iajs-117	299	1	where	where	SCONJ
iajs-117	299	2			NOUN
iajs-117	299	3	'	'	PUNCT
iajs-117	299	4	:	:	PUNCT
iajs-117	299	5			NUM
iajs-117	299	6	(	(	PUNCT
iajs-117	299	7	m/	m/	NOUN
iajs-117	299	8	k	k	NOUN
iajs-117	299	9	)	)	PUNCT
iajs-117	299	10			PUNCT
iajs-117	300	1			NUM
iajs-117	300	2	(	(	PUNCT
iajs-117	300	3	m/	m/	NOUN
iajs-117	300	4	k	k	NOUN
iajs-117	300	5	)	)	PUNCT
iajs-117	300	6	and	and	CCONJ
iajs-117	300	7			NOUN
iajs-117	300	8	'	'	PUNCT
iajs-117	300	9	(	(	PUNCT
iajs-117	300	10	n	n	CCONJ
iajs-117	300	11	/	/	SYM
iajs-117	300	12	k	k	NOUN
iajs-117	300	13	)	)	PUNCT
iajs-117	300	14	=	=	SYM
iajs-117	300	15	(n	(n	X
iajs-117	300	16	)	)	PUNCT
iajs-117	300	17	/k	/k	PUNCT
iajs-117	300	18	.	.	PUNCT
iajs-117	301	1	proof	proof	NOUN
iajs-117	301	2	:	:	PUNCT
iajs-117	301	3	let	let	VERB
iajs-117	301	4	rr	rr	PUNCT
iajs-117	301	5	and	and	CCONJ
iajs-117	301	6	m	m	PROPN
iajs-117	301	7			NOUN
iajs-117	301	8	n	n	CCONJ
iajs-117	301	9	/	/	SYM
iajs-117	301	10	k	k	NOUN
iajs-117	301	11	with	with	ADP
iajs-117	301	12	r	r	PROPN
iajs-117	301	13	m	m	VERB
iajs-117	301	14			NOUN
iajs-117	301	15	[	[	X
iajs-117	301	16	n	n	X
iajs-117	301	17	/	/	SYM
iajs-117	301	18	k	k	X
iajs-117	301	19	]	]	X
iajs-117	301	20	,	,	PUNCT
iajs-117	301	21	where	where	SCONJ
iajs-117	301	22	m=	m=	X
iajs-117	301	23	m+k	m+k	NUM
iajs-117	301	24	,	,	PUNCT
iajs-117	301	25	for	for	ADP
iajs-117	301	26	some	some	DET
iajs-117	301	27	m	m	ADJ
iajs-117	301	28	m	m	NOUN
iajs-117	301	29	.	.	PUNCT
iajs-117	302	1	so	so	ADV
iajs-117	302	2	we	we	PRON
iajs-117	302	3	have	have	VERB
iajs-117	302	4	rm	rm	PROPN
iajs-117	302	5			PROPN
iajs-117	302	6	n	n	PROPN
iajs-117	302	7	,	,	PUNCT
iajs-117	302	8	which	which	PRON
iajs-117	302	9	gives	give	VERB
iajs-117	302	10	that	that	SCONJ
iajs-117	302	11	either	either	CCONJ
iajs-117	302	12	m	m	PROPN
iajs-117	302	13	n	n	PROPN
iajs-117	302	14	+	+	CCONJ
iajs-117	302	15	(n	(n	X
iajs-117	302	16	)	)	PUNCT
iajs-117	302	17	or	or	CCONJ
iajs-117	302	18	r	r	NOUN
iajs-117	302	19	m	m	NOUN
iajs-117	302	20			PROPN
iajs-117	302	21	n	n	PROPN
iajs-117	302	22	+	+	CCONJ
iajs-117	302	23	(n	(n	NOUN
iajs-117	302	24	)	)	PUNCT
iajs-117	302	25	.therefor	.therefor	PUNCT
iajs-117	302	26	either	either	CCONJ
iajs-117	302	27	m	m	PROPN
iajs-117	302	28	+	+	PROPN
iajs-117	302	29	k	k	NOUN
iajs-117	302	30			NOUN
iajs-117	302	31	(	(	PUNCT
iajs-117	302	32	n	n	PROPN
iajs-117	302	33	+	+	CCONJ
iajs-117	302	34	(n	(n	X
iajs-117	302	35	)	)	PUNCT
iajs-117	302	36	)	)	PUNCT
iajs-117	302	37	/k	/k	PUNCT
iajs-117	303	1	=[	=[	NOUN
iajs-117	303	2	n	n	NOUN
iajs-117	303	3	/k	/k	AUX
iajs-117	303	4	]	]	X
iajs-117	304	1	+	+	PROPN
iajs-117	304	2	[	[	PUNCT
iajs-117	304	3	(n	(n	X
iajs-117	304	4	)	)	PUNCT
iajs-117	304	5	/k	/k	PUNCT
iajs-117	304	6	]	]	PUNCT
iajs-117	304	7	=	=	PUNCT
iajs-117	305	1	[	[	X
iajs-117	305	2	n	n	X
iajs-117	305	3	/	/	SYM
iajs-117	305	4	k	k	X
iajs-117	305	5	]	]	X
iajs-117	305	6	+	+	CCONJ
iajs-117	305	7	[	[	PUNCT
iajs-117	305	8			NOUN
iajs-117	305	9	'	'	PUNCT
iajs-117	305	10	(	(	PUNCT
iajs-117	305	11	n	n	CCONJ
iajs-117	305	12	/	/	SYM
iajs-117	305	13	k	k	NOUN
iajs-117	305	14	)	)	PUNCT
iajs-117	305	15	]	]	PUNCT
iajs-117	305	16	or	or	CCONJ
iajs-117	305	17	r	r	NOUN
iajs-117	305	18	[	[	X
iajs-117	305	19	m	m	NOUN
iajs-117	305	20	/k	/k	ADJ
iajs-117	305	21	]	]	X
iajs-117	305	22			PROPN
iajs-117	305	23	[	[	X
iajs-117	305	24	(	(	PUNCT
iajs-117	305	25	n	n	X
iajs-117	305	26	+	+	CCONJ
iajs-117	305	27	(n	(n	NOUN
iajs-117	305	28	)	)	PUNCT
iajs-117	305	29	)	)	PUNCT
iajs-117	305	30	/	/	PUNCT
iajs-117	306	1	k	k	X
iajs-117	306	2	]	]	PUNCT
iajs-117	307	1			PROPN
iajs-117	307	2	[	[	PUNCT
iajs-117	307	3	n	n	X
iajs-117	307	4	/k	/k	NOUN
iajs-117	307	5	]	]	X
iajs-117	308	1	+	+	PROPN
iajs-117	308	2	[	[	PUNCT
iajs-117	308	3	(n	(n	X
iajs-117	308	4	)	)	PUNCT
iajs-117	308	5	/k	/k	PUNCT
iajs-117	308	6	]	]	PUNCT
iajs-117	308	7	=	=	PUNCT
iajs-117	309	1	[	[	X
iajs-117	309	2	n	n	X
iajs-117	309	3	/	/	SYM
iajs-117	309	4	k	k	X
iajs-117	309	5	]	]	X
iajs-117	309	6	+	+	CCONJ
iajs-117	309	7	[	[	PUNCT
iajs-117	309	8			NOUN
iajs-117	309	9	'	'	PUNCT
iajs-117	309	10	(	(	PUNCT
iajs-117	309	11	n	n	CCONJ
iajs-117	309	12	/	/	SYM
iajs-117	309	13	k	k	NOUN
iajs-117	309	14	)	)	PUNCT
iajs-117	309	15	]	]	PUNCT
iajs-117	309	16	.hence	.hence	ADP
iajs-117	309	17	either	either	CCONJ
iajs-117	309	18	m	m	VERB
iajs-117	309	19			NOUN
iajs-117	309	20	[	[	X
iajs-117	309	21	n	n	X
iajs-117	309	22	/	/	SYM
iajs-117	309	23	k	k	X
iajs-117	309	24	]	]	X
iajs-117	309	25	+	+	CCONJ
iajs-117	309	26	[	[	PUNCT
iajs-117	309	27			NOUN
iajs-117	309	28	'	'	PUNCT
iajs-117	309	29	(	(	PUNCT
iajs-117	309	30	n	n	CCONJ
iajs-117	309	31	/	/	SYM
iajs-117	309	32	k	k	NOUN
iajs-117	309	33	)	)	PUNCT
iajs-117	309	34	]	]	PUNCT
iajs-117	309	35	or	or	CCONJ
iajs-117	309	36	r	r	NOUN
iajs-117	309	37	[	[	X
iajs-117	309	38	m	m	NOUN
iajs-117	309	39	/k	/k	ADJ
iajs-117	309	40	]	]	X
iajs-117	309	41			PROPN
iajs-117	310	1	[	[	X
iajs-117	310	2	n	n	X
iajs-117	310	3	/	/	SYM
iajs-117	310	4	k	k	X
iajs-117	310	5	]	]	X
iajs-117	310	6	+	+	CCONJ
iajs-117	310	7	[	[	PUNCT
iajs-117	310	8			NOUN
iajs-117	310	9	'	'	PUNCT
iajs-117	310	10	(	(	PUNCT
iajs-117	310	11	n	n	CCONJ
iajs-117	310	12	/	/	SYM
iajs-117	310	13	k	k	NOUN
iajs-117	310	14	)	)	PUNCT
iajs-117	310	15	]	]	PUNCT
iajs-117	310	16	.therefore	.therefore	ADP
iajs-117	310	17	n	n	PROPN
iajs-117	310	18	/	/	SYM
iajs-117	310	19	k	k	PROPN
iajs-117	310	20	is	be	AUX
iajs-117	310	21	a	a	DET
iajs-117	310	22	'-prime	'-prime	ADJ
iajs-117	310	23	submodule	submodule	NOUN
iajs-117	310	24	of	of	ADP
iajs-117	310	25	m	m	PROPN
iajs-117	310	26	/	/	PUNCT
iajs-117	310	27	k.	k.	PROPN
iajs-117	310	28	let	let	VERB
iajs-117	310	29	r1	r1	PROPN
iajs-117	310	30	,	,	PUNCT
iajs-117	310	31	r2	r2	PROPN
iajs-117	310	32	be	be	AUX
iajs-117	310	33	two	two	NUM
iajs-117	310	34	commutative	commutative	ADJ
iajs-117	310	35	rings	ring	NOUN
iajs-117	310	36	with	with	ADP
iajs-117	310	37	identity	identity	NOUN
iajs-117	310	38	and	and	CCONJ
iajs-117	310	39	m1	m1	NOUN
iajs-117	310	40	,	,	PUNCT
iajs-117	310	41	m2	m2	PROPN
iajs-117	310	42	be	be	AUX
iajs-117	310	43	r1	r1	NOUN
iajs-117	310	44	and	and	CCONJ
iajs-117	310	45	r2	r2	NOUN
iajs-117	310	46	–	–	PUNCT
iajs-117	310	47	module	module	NOUN
iajs-117	310	48	respectively	respectively	ADV
iajs-117	310	49	,	,	PUNCT
iajs-117	310	50	put	put	VERB
iajs-117	310	51	r	r	NOUN
iajs-117	310	52	=	=	SYM
iajs-117	310	53	r1	r1	PROPN
iajs-117	310	54	r2	r2	PROPN
iajs-117	310	55	.	.	PUNCT
iajs-117	311	1	then	then	ADV
iajs-117	311	2	m	m	VERB
iajs-117	311	3	=	=	ADJ
iajs-117	311	4	m1	m1	PROPN
iajs-117	311	5			PROPN
iajs-117	311	6	m2	m2	PROPN
iajs-117	311	7	is	be	AUX
iajs-117	311	8	an	an	DET
iajs-117	311	9	r	r	NOUN
iajs-117	311	10	–	–	PUNCT
iajs-117	311	11	module	module	NOUN
iajs-117	311	12	and	and	CCONJ
iajs-117	311	13	each	each	DET
iajs-117	311	14	submodule	submodule	NOUN
iajs-117	311	15	of	of	ADP
iajs-117	311	16	m	m	PROPN
iajs-117	311	17	is	be	AUX
iajs-117	311	18	of	of	ADP
iajs-117	311	19	the	the	DET
iajs-117	311	20	form	form	NOUN
iajs-117	311	21	n	n	NOUN
iajs-117	311	22	=	=	SYM
iajs-117	311	23	n1	n1	PROPN
iajs-117	311	24			NOUN
iajs-117	311	25	n2	n2	PROPN
iajs-117	311	26	for	for	ADP
iajs-117	311	27	some	some	DET
iajs-117	311	28	n1	n1	NOUN
iajs-117	311	29	of	of	ADP
iajs-117	311	30	m1	m1	PROPN
iajs-117	311	31	and	and	CCONJ
iajs-117	311	32	n2	n2	NOUN
iajs-117	311	33	of	of	ADP
iajs-117	311	34	m2	m2	PROPN
iajs-117	311	35	.furthermore	.furthermore	PUNCT
iajs-117	311	36	n	n	NOUN
iajs-117	311	37	=	=	SYM
iajs-117	311	38	n1	n1	PROPN
iajs-117	311	39			NOUN
iajs-117	311	40	n2	n2	PROPN
iajs-117	311	41	is	be	AUX
iajs-117	311	42	a	a	DET
iajs-117	311	43	prime	prime	ADJ
iajs-117	311	44	submodule	submodule	NOUN
iajs-117	311	45	of	of	ADP
iajs-117	311	46	m	m	PROPN
iajs-117	311	47	if	if	SCONJ
iajs-117	312	1	and	and	CCONJ
iajs-117	312	2	only	only	ADV
iajs-117	312	3	if	if	SCONJ
iajs-117	312	4	n	n	NOUN
iajs-117	312	5	=	=	SYM
iajs-117	312	6	n1	n1	PROPN
iajs-117	312	7	m2	m2	PROPN
iajs-117	312	8	or	or	CCONJ
iajs-117	312	9	n	n	NOUN
iajs-117	312	10	=	=	PROPN
iajs-117	312	11	m1	m1	PROPN
iajs-117	312	12	n2	n2	PROPN
iajs-117	313	1	for	for	ADP
iajs-117	313	2	some	some	DET
iajs-117	313	3	prime	prime	ADJ
iajs-117	313	4	submodules	submodule	NOUN
iajs-117	313	5	n1	n1	NOUN
iajs-117	313	6	of	of	ADP
iajs-117	313	7	m1	m1	PROPN
iajs-117	313	8	and	and	CCONJ
iajs-117	313	9	n2	n2	NOUN
iajs-117	313	10	of	of	ADP
iajs-117	313	11	m2	m2	PROPN
iajs-117	313	12	.	.	PUNCT
iajs-117	314	1	theorem	theorem	PROPN
iajs-117	314	2	(	(	PUNCT
iajs-117	314	3	2.29	2.29	NUM
iajs-117	314	4	):	):	PUNCT
iajs-117	314	5	let	let	VERB
iajs-117	314	6	r	r	NOUN
iajs-117	314	7	=	=	SYM
iajs-117	314	8	r1	r1	PROPN
iajs-117	314	9	r2	r2	NOUN
iajs-117	314	10	that	that	PRON
iajs-117	314	11	each	each	DET
iajs-117	314	12	ri	ri	PROPN
iajs-117	314	13	is	be	AUX
iajs-117	314	14	a	a	DET
iajs-117	314	15	commutative	commutative	ADJ
iajs-117	314	16	rings	ring	NOUN
iajs-117	314	17	with	with	ADP
iajs-117	314	18	identity	identity	NOUN
iajs-117	314	19	.	.	PUNCT
iajs-117	315	1	let	let	VERB
iajs-117	315	2	mi	mi	PROPN
iajs-117	315	3	be	be	AUX
iajs-117	315	4	ri	ri	PROPN
iajs-117	315	5	–	–	PUNCT
iajs-117	315	6	module	module	NOUN
iajs-117	315	7	and	and	CCONJ
iajs-117	315	8	m	m	NOUN
iajs-117	315	9	=	=	ADJ
iajs-117	315	10	m1	m1	PROPN
iajs-117	315	11			PROPN
iajs-117	315	12	m2	m2	PROPN
iajs-117	315	13	with	with	ADP
iajs-117	315	14	(	(	PUNCT
iajs-117	315	15	r1	r1	PROPN
iajs-117	315	16	,	,	PUNCT
iajs-117	315	17	r2	r2	PROPN
iajs-117	315	18	)	)	PUNCT
iajs-117	315	19	(	(	PUNCT
iajs-117	315	20	m1,m2	m1,m2	PROPN
iajs-117	315	21	)	)	PUNCT
iajs-117	315	22	=	=	NOUN
iajs-117	315	23	(	(	PUNCT
iajs-117	315	24	r1m1,r2m2	r1m1,r2m2	NOUN
iajs-117	315	25	)	)	PUNCT
iajs-117	315	26	,	,	PUNCT
iajs-117	315	27	be	be	AUX
iajs-117	315	28	an	an	DET
iajs-117	315	29	r	r	NOUN
iajs-117	315	30	–	–	PUNCT
iajs-117	315	31	module	module	NOUN
iajs-117	315	32	,	,	PUNCT
iajs-117	315	33	where	where	SCONJ
iajs-117	315	34	ri	ri	PROPN
iajs-117	315	35			PROPN
iajs-117	315	36	ri	ri	PROPN
iajs-117	315	37	,	,	PUNCT
iajs-117	315	38	mi	mi	PROPN
iajs-117	315	39			PROPN
iajs-117	315	40	mi	mi	PROPN
iajs-117	315	41	,	,	PUNCT
iajs-117	315	42	and	and	CCONJ
iajs-117	315	43	let	let	VERB
iajs-117	315	44	i	i	PRON
iajs-117	315	45	:	:	PUNCT
iajs-117	316	1			NUM
iajs-117	316	2	(	(	PUNCT
iajs-117	316	3	mi	mi	PROPN
iajs-117	316	4	)	)	PUNCT
iajs-117	316	5			PROPN
iajs-117	317	1			NUM
iajs-117	317	2	(	(	PUNCT
iajs-117	317	3	mi	mi	PROPN
iajs-117	317	4	)	)	PUNCT
iajs-117	317	5			NOUN
iajs-117	317	6	{	{	PUNCT
iajs-117	317	7			NOUN
iajs-117	317	8	}	}	PUNCT
iajs-117	317	9	be	be	AUX
iajs-117	317	10	functions	function	NOUN
iajs-117	317	11	,	,	PUNCT
iajs-117	317	12			NOUN
iajs-117	317	13	=	=	SYM
iajs-117	317	14	1	1	PROPN
iajs-117	317	15	2	2	NOUN
iajs-117	317	16	.	.	PUNCT
iajs-117	318	1	then	then	ADV
iajs-117	318	2	we	we	PRON
iajs-117	318	3	have	have	VERB
iajs-117	318	4	:	:	PUNCT
iajs-117	318	5	1	1	X
iajs-117	318	6	)	)	PUNCT
iajs-117	318	7	n1	n1	PROPN
iajs-117	318	8			PROPN
iajs-117	318	9	n2	n2	PROPN
iajs-117	318	10	is	be	AUX
iajs-117	318	11	a	a	DET
iajs-117	318	12	prime	prime	PROPN
iajs-117	318	13	submodule	submodule	NOUN
iajs-117	318	14	,	,	PUNCT
iajs-117	318	15	where	where	SCONJ
iajs-117	318	16	ni	ni	PROPN
iajs-117	318	17	is	be	AUX
iajs-117	318	18	a	a	DET
iajs-117	318	19	i	i	NOUN
iajs-117	318	20	–	–	PUNCT
iajs-117	318	21	prime	prime	ADJ
iajs-117	318	22	submodule	submodule	NOUN
iajs-117	318	23	of	of	ADP
iajs-117	318	24	mi	mi	PROPN
iajs-117	318	25	,	,	PUNCT
iajs-117	318	26	with	with	ADP
iajs-117	318	27	ni	ni	PROPN
iajs-117	318	28			PROPN
iajs-117	318	29	i	i	PROPN
iajs-117	318	30	(	(	PUNCT
iajs-117	318	31	ni	ni	PROPN
iajs-117	318	32	)	)	PUNCT
iajs-117	318	33	.	.	PUNCT
iajs-117	319	1	2	2	X
iajs-117	319	2	)	)	PUNCT
iajs-117	319	3	n1	n1	PROPN
iajs-117	319	4	m2	m2	PROPN
iajs-117	319	5	is	be	AUX
iajs-117	319	6	a	a	DET
iajs-117	319	7	prime	prime	PROPN
iajs-117	319	8	submodule	submodule	NOUN
iajs-117	319	9	of	of	ADP
iajs-117	319	10	m	m	PROPN
iajs-117	319	11	,	,	PUNCT
iajs-117	319	12	where	where	SCONJ
iajs-117	319	13	n1	n1	PROPN
iajs-117	319	14	is	be	AUX
iajs-117	319	15	a	a	DET
iajs-117	319	16	prime	prime	ADJ
iajs-117	319	17	submodule	submodule	NOUN
iajs-117	319	18	of	of	ADP
iajs-117	319	19	m1	m1	PROPN
iajs-117	319	20	.	.	PUNCT
iajs-117	320	1	3	3	X
iajs-117	320	2	)	)	PUNCT
iajs-117	320	3	n1	n1	PROPN
iajs-117	320	4	m2	m2	PROPN
iajs-117	320	5	is	be	AUX
iajs-117	320	6	a	a	DET
iajs-117	320	7	prime	prime	PROPN
iajs-117	320	8	submodule	submodule	NOUN
iajs-117	320	9	of	of	ADP
iajs-117	320	10	m	m	PROPN
iajs-117	320	11	,	,	PUNCT
iajs-117	320	12	wheren1	wheren1	ADJ
iajs-117	320	13	is	be	AUX
iajs-117	320	14	a	a	DET
iajs-117	320	15	1prime	1prime	ADJ
iajs-117	320	16	submodule	submodule	NOUN
iajs-117	320	17	of	of	ADP
iajs-117	320	18	m1	m1	PROPN
iajs-117	320	19	and	and	CCONJ
iajs-117	320	20	2	2	NOUN
iajs-117	320	21	(	(	PUNCT
iajs-117	320	22	m2	m2	PROPN
iajs-117	320	23	)	)	PUNCT
iajs-117	321	1	=	=	PROPN
iajs-117	321	2	m2	m2	PROPN
iajs-117	321	3	.	.	PUNCT
iajs-117	322	1	mathematics	mathematic	NOUN
iajs-117	322	2	|	|	ADV
iajs-117	322	3	290	290	NUM
iajs-117	322	4	2016	2016	NUM
iajs-117	322	5	)	)	PUNCT
iajs-117	322	6	عام	عام	ADP
iajs-117	322	7	2العدد	2العدد	NUM
iajs-117	322	8	(	(	PUNCT
iajs-117	322	9	29لمجلد	29لمجلد	NUM
iajs-117	322	10	ا	ا	X
iajs-117	322	11	مجلة	مجلة	NOUN
iajs-117	322	12	إبن	إبن	VERB
iajs-117	322	13	الهيثم	الهيثم	ADJ
iajs-117	322	14	للعلوم	للعلوم	NOUN
iajs-117	322	15	الصرفة	الصرفة	NOUN
iajs-117	323	1	و	و	PRON
iajs-117	323	2	التطبيقية	التطبيقية	ADJ
iajs-117	323	3	ibn	ibn	PROPN
iajs-117	323	4	al	al	PROPN
iajs-117	323	5	-	-	PUNCT
iajs-117	323	6	haitham	haitham	PROPN
iajs-117	323	7	jour	jour	X
iajs-117	323	8	.	.	PROPN
iajs-117	323	9	for	for	ADP
iajs-117	323	10	pure	pure	ADJ
iajs-117	323	11	&	&	CCONJ
iajs-117	323	12	appl	appl	PROPN
iajs-117	323	13	.	.	PUNCT
iajs-117	324	1	sci	sci	PROPN
iajs-117	324	2	.	.	PUNCT
iajs-117	324	3	vol	vol	NOUN
iajs-117	324	4	.	.	PROPN
iajs-117	324	5	29	29	NUM
iajs-117	324	6	(	(	PUNCT
iajs-117	324	7	2	2	NUM
iajs-117	324	8	)	)	PUNCT
iajs-117	324	9	2016	2016	NUM
iajs-117	324	10	4	4	NUM
iajs-117	324	11	)	)	PUNCT
iajs-117	324	12	m1	m1	PROPN
iajs-117	324	13			PROPN
iajs-117	324	14	n2	n2	PROPN
iajs-117	324	15	is	be	AUX
iajs-117	324	16	a	a	DET
iajs-117	324	17	prime	prime	PROPN
iajs-117	324	18	submodule	submodule	NOUN
iajs-117	324	19	of	of	ADP
iajs-117	324	20	m	m	PROPN
iajs-117	324	21	,	,	PUNCT
iajs-117	324	22	wheren2	wheren2	NOUN
iajs-117	324	23	is	be	AUX
iajs-117	324	24	a	a	DET
iajs-117	324	25	prime	prime	ADJ
iajs-117	324	26	submodule	submodule	NOUN
iajs-117	324	27	of	of	ADP
iajs-117	324	28	m2	m2	PROPN
iajs-117	324	29	.	.	PUNCT
iajs-117	325	1	5	5	X
iajs-117	325	2	)	)	PUNCT
iajs-117	325	3	m1	m1	PROPN
iajs-117	325	4	n2	n2	PROPN
iajs-117	325	5	is	be	AUX
iajs-117	325	6	a	a	DET
iajs-117	325	7	prime	prime	PROPN
iajs-117	325	8	submodule	submodule	NOUN
iajs-117	325	9	of	of	ADP
iajs-117	325	10	m	m	PROPN
iajs-117	325	11	,	,	PUNCT
iajs-117	325	12	where	where	SCONJ
iajs-117	325	13	n2	n2	NOUN
iajs-117	325	14	is	be	AUX
iajs-117	325	15	a	a	DET
iajs-117	325	16	2prime	2prime	NOUN
iajs-117	325	17	submodule	submodule	NOUN
iajs-117	325	18	of	of	ADP
iajs-117	325	19	m2	m2	PROPN
iajs-117	325	20	and	and	CCONJ
iajs-117	325	21	1	1	PROPN
iajs-117	325	22	(	(	PUNCT
iajs-117	325	23	m1	m1	PROPN
iajs-117	325	24	)	)	PUNCT
iajs-117	326	1	=	=	SYM
iajs-117	326	2	m1	m1	NOUN
iajs-117	326	3	.	.	PUNCT
iajs-117	327	1	proof	proof	NOUN
iajs-117	327	2	:	:	PUNCT
iajs-117	327	3	(	(	PUNCT
iajs-117	327	4	1	1	X
iajs-117	327	5	)	)	PUNCT
iajs-117	327	6	suppose	suppose	VERB
iajs-117	327	7	ni	ni	PROPN
iajs-117	327	8	is	be	AUX
iajs-117	327	9	a	a	DET
iajs-117	327	10	i	i	NOUN
iajs-117	327	11	–	–	PUNCT
iajs-117	327	12	prime	prime	ADJ
iajs-117	327	13	submodule	submodule	NOUN
iajs-117	327	14	of	of	ADP
iajs-117	327	15	mi	mi	PROPN
iajs-117	327	16	,	,	PUNCT
iajs-117	327	17	with	with	ADP
iajs-117	327	18	ni	ni	PROPN
iajs-117	327	19			PROPN
iajs-117	327	20	i	i	PROPN
iajs-117	327	21	(	(	PUNCT
iajs-117	327	22	ni	ni	PROPN
iajs-117	327	23	)	)	PUNCT
iajs-117	327	24	and	and	CCONJ
iajs-117	327	25	let	let	VERB
iajs-117	327	26	(	(	PUNCT
iajs-117	327	27	r1	r1	NOUN
iajs-117	327	28	,	,	PUNCT
iajs-117	327	29	r2	r2	PROPN
iajs-117	327	30	)	)	PUNCT
iajs-117	327	31	(	(	PUNCT
iajs-117	327	32	m1,m2	m1,m2	PROPN
iajs-117	327	33	)	)	PUNCT
iajs-117	328	1	=	=	PRON
iajs-117	328	2	(	(	PUNCT
iajs-117	328	3	r1m1,r2m2	r1m1,r2m2	X
iajs-117	328	4	)	)	PUNCT
iajs-117	328	5			NOUN
iajs-117	328	6	n1	n1	PROPN
iajs-117	328	7			PROPN
iajs-117	328	8	n2	n2	PROPN
iajs-117	328	9	,	,	PUNCT
iajs-117	328	10	then	then	ADV
iajs-117	328	11	r1m1	r1m1	VERB
iajs-117	328	12			NOUN
iajs-117	328	13	n1	n1	PROPN
iajs-117	328	14	and	and	CCONJ
iajs-117	328	15	r2m2	r2m2	ADJ
iajs-117	328	16			PROPN
iajs-117	328	17	n2	n2	NOUN
iajs-117	328	18	and	and	CCONJ
iajs-117	328	19	since	since	SCONJ
iajs-117	328	20	ni	ni	PROPN
iajs-117	328	21	is	be	AUX
iajs-117	328	22	a	a	DET
iajs-117	328	23	i	i	NOUN
iajs-117	328	24	–	–	PUNCT
iajs-117	328	25	prime	prime	ADJ
iajs-117	328	26	submodule	submodule	NOUN
iajs-117	328	27	of	of	ADP
iajs-117	328	28	mi	mi	PROPN
iajs-117	328	29	,	,	PUNCT
iajs-117	328	30	so	so	ADV
iajs-117	328	31	either	either	CCONJ
iajs-117	328	32	r1	r1	PROPN
iajs-117	328	33			PROPN
iajs-117	328	34	[	[	PUNCT
iajs-117	328	35	n1	n1	PROPN
iajs-117	328	36	+	+	CCONJ
iajs-117	328	37	1	1	PROPN
iajs-117	328	38	(	(	PUNCT
iajs-117	328	39	n1	n1	PROPN
iajs-117	328	40	):	):	PUNCT
iajs-117	328	41	m1	m1	PROPN
iajs-117	328	42	]	]	PUNCT
iajs-117	328	43	and	and	CCONJ
iajs-117	328	44	.	.	PUNCT
iajs-117	329	1	r2	r2	PROPN
iajs-117	329	2			PROPN
iajs-117	329	3	[	[	PUNCT
iajs-117	329	4	n2	n2	NOUN
iajs-117	329	5	+	+	CCONJ
iajs-117	329	6	2	2	PROPN
iajs-117	329	7	(	(	PUNCT
iajs-117	329	8	n2	n2	NOUN
iajs-117	329	9	)	)	PUNCT
iajs-117	329	10	:	:	PUNCT
iajs-117	330	1	m2	m2	PROPN
iajs-117	330	2	]	]	PUNCT
iajs-117	330	3	or	or	CCONJ
iajs-117	330	4	m1	m1	PROPN
iajs-117	330	5			PROPN
iajs-117	330	6	n1	n1	PROPN
iajs-117	330	7	+	+	CCONJ
iajs-117	330	8	1	1	PROPN
iajs-117	330	9	(	(	PUNCT
iajs-117	330	10	n1	n1	PROPN
iajs-117	330	11	)	)	PUNCT
iajs-117	330	12	and	and	CCONJ
iajs-117	330	13	m2	m2	PROPN
iajs-117	330	14			PROPN
iajs-117	330	15	n2	n2	NOUN
iajs-117	330	16	+	+	CCONJ
iajs-117	330	17	2	2	PROPN
iajs-117	330	18	(	(	PUNCT
iajs-117	330	19	n2	n2	NOUN
iajs-117	330	20	)	)	PUNCT
iajs-117	330	21	.	.	PUNCT
iajs-117	331	1	hence	hence	ADV
iajs-117	331	2	either	either	CCONJ
iajs-117	331	3	(	(	PUNCT
iajs-117	331	4	r1	r1	PROPN
iajs-117	331	5	,	,	PUNCT
iajs-117	331	6	r2	r2	PROPN
iajs-117	331	7	)	)	PUNCT
iajs-117	331	8			NOUN
iajs-117	331	9	[	[	PUNCT
iajs-117	331	10	n1	n1	PROPN
iajs-117	331	11	+	+	CCONJ
iajs-117	331	12	1	1	PROPN
iajs-117	331	13	(	(	PUNCT
iajs-117	331	14	n1	n1	PROPN
iajs-117	331	15	):	):	PUNCT
iajs-117	331	16	m1	m1	PROPN
iajs-117	331	17	]	]	PUNCT
iajs-117	331	18			PROPN
iajs-117	331	19	[	[	PUNCT
iajs-117	331	20	n2	n2	NOUN
iajs-117	331	21	+	+	CCONJ
iajs-117	331	22	2	2	PROPN
iajs-117	331	23	(	(	PUNCT
iajs-117	331	24	n2	n2	NOUN
iajs-117	331	25	)	)	PUNCT
iajs-117	331	26	:	:	PUNCT
iajs-117	332	1	m2	m2	PROPN
iajs-117	332	2	]	]	PUNCT
iajs-117	333	1	=	=	PUNCT
iajs-117	334	1	[	[	X
iajs-117	334	2	1	1	X
iajs-117	334	3	(	(	PUNCT
iajs-117	334	4	n1	n1	PROPN
iajs-117	334	5	):	):	PUNCT
iajs-117	334	6	m1	m1	PROPN
iajs-117	334	7	]	]	PUNCT
iajs-117	334	8			X
iajs-117	335	1	[	[	X
iajs-117	335	2	2	2	X
iajs-117	335	3	(	(	PUNCT
iajs-117	335	4	n2	n2	NOUN
iajs-117	335	5	)	)	PUNCT
iajs-117	335	6	:	:	PUNCT
iajs-117	336	1	m2	m2	PROPN
iajs-117	336	2	]	]	PUNCT
iajs-117	337	1	=	=	PUNCT
iajs-117	338	1	[	[	X
iajs-117	338	2	1	1	X
iajs-117	338	3	(	(	PUNCT
iajs-117	338	4	n1	n1	ADJ
iajs-117	338	5	)	)	PUNCT
iajs-117	338	6	2	2	NOUN
iajs-117	338	7	(	(	PUNCT
iajs-117	338	8	n2	n2	PROPN
iajs-117	338	9	)	)	PUNCT
iajs-117	338	10	:	:	PUNCT
iajs-117	338	11	m1	m1	PROPN
iajs-117	338	12			PROPN
iajs-117	338	13	m2	m2	PROPN
iajs-117	338	14	]	]	PUNCT
iajs-117	338	15	=	=	PUNCT
iajs-117	339	1	[	[	X
iajs-117	339	2	n1	n1	PROPN
iajs-117	339	3			NOUN
iajs-117	339	4	n2	n2	PROPN
iajs-117	339	5	+	+	PROPN
iajs-117	339	6			PROPN
iajs-117	339	7	(	(	PUNCT
iajs-117	339	8	n1	n1	PROPN
iajs-117	339	9			PROPN
iajs-117	339	10	n2	n2	PROPN
iajs-117	339	11	)	)	PUNCT
iajs-117	339	12	:	:	PUNCT
iajs-117	340	1	m1	m1	PROPN
iajs-117	340	2			PROPN
iajs-117	340	3	m2	m2	PROPN
iajs-117	340	4	]	]	PUNCT
iajs-117	340	5	or	or	CCONJ
iajs-117	340	6	(	(	PUNCT
iajs-117	340	7	m1,m2	m1,m2	PROPN
iajs-117	340	8	)	)	PUNCT
iajs-117	340	9	=	=	PUNCT
iajs-117	341	1	[	[	X
iajs-117	341	2	n1	n1	NOUN
iajs-117	341	3	+	+	NUM
iajs-117	341	4	1	1	X
iajs-117	341	5	(	(	PUNCT
iajs-117	341	6	n1	n1	NOUN
iajs-117	341	7	)	)	PUNCT
iajs-117	341	8	]	]	PUNCT
iajs-117	342	1			PROPN
iajs-117	342	2	[	[	PUNCT
iajs-117	342	3	n2	n2	NOUN
iajs-117	342	4	+	+	CCONJ
iajs-117	342	5	2	2	PROPN
iajs-117	342	6	(	(	PUNCT
iajs-117	342	7	n2	n2	NOUN
iajs-117	342	8	)	)	PUNCT
iajs-117	342	9	]	]	PUNCT
iajs-117	343	1	=	=	PUNCT
iajs-117	343	2	[	[	X
iajs-117	343	3	1	1	X
iajs-117	343	4	(	(	PUNCT
iajs-117	343	5	n1	n1	ADJ
iajs-117	343	6	)	)	PUNCT
iajs-117	343	7	2	2	NOUN
iajs-117	343	8	(	(	PUNCT
iajs-117	343	9	n2	n2	PROPN
iajs-117	343	10	)	)	PUNCT
iajs-117	343	11			PROPN
iajs-117	344	1	[	[	X
iajs-117	344	2	n1	n1	NOUN
iajs-117	344	3			NOUN
iajs-117	344	4	n2	n2	PROPN
iajs-117	344	5	]	]	PUNCT
iajs-117	345	1	+	+	CCONJ
iajs-117	345	2	[	[	PUNCT
iajs-117	345	3			NOUN
iajs-117	345	4	(	(	PUNCT
iajs-117	345	5	n1	n1	PROPN
iajs-117	345	6			PROPN
iajs-117	345	7	n2	n2	PROPN
iajs-117	345	8	)	)	PUNCT
iajs-117	345	9	]	]	PUNCT
iajs-117	345	10	.	.	PUNCT
iajs-117	346	1	therefore	therefore	ADV
iajs-117	346	2	n1	n1	PROPN
iajs-117	346	3			PROPN
iajs-117	346	4	n2	n2	PROPN
iajs-117	346	5	is	be	AUX
iajs-117	346	6	a	a	DET
iajs-117	346	7	prime	prime	PROPN
iajs-117	346	8	submodule	submodule	NOUN
iajs-117	346	9	.	.	PUNCT
iajs-117	347	1	(	(	PUNCT
iajs-117	347	2	2	2	X
iajs-117	347	3	)	)	PUNCT
iajs-117	347	4	if	if	SCONJ
iajs-117	347	5	n1	n1	PROPN
iajs-117	347	6	is	be	AUX
iajs-117	347	7	a	a	DET
iajs-117	347	8	prime	prime	ADJ
iajs-117	347	9	submodule	submodule	NOUN
iajs-117	347	10	of	of	ADP
iajs-117	347	11	m1	m1	PROPN
iajs-117	347	12	,	,	PUNCT
iajs-117	347	13	then	then	ADV
iajs-117	347	14	n1	n1	PROPN
iajs-117	347	15	m2	m2	PROPN
iajs-117	347	16	is	be	AUX
iajs-117	347	17	a	a	DET
iajs-117	347	18	prime	prime	ADJ
iajs-117	347	19	submodule	submodule	NOUN
iajs-117	347	20	of	of	ADP
iajs-117	347	21	m	m	PRON
iajs-117	347	22	by	by	ADP
iajs-117	347	23	[	[	X
iajs-117	347	24	6,th.2.14,p.1446	6,th.2.14,p.1446	X
iajs-117	347	25	]	]	PUNCT
iajs-117	347	26	and	and	CCONJ
iajs-117	347	27	hence	hence	ADV
iajs-117	347	28	n1	n1	PROPN
iajs-117	347	29	m2	m2	PROPN
iajs-117	347	30	is	be	AUX
iajs-117	347	31	a	a	DET
iajs-117	347	32	prime	prime	PROPN
iajs-117	347	33	submodule	submodule	NOUN
iajs-117	347	34	of	of	ADP
iajs-117	347	35	m	m	PRON
iajs-117	347	36	by	by	ADP
iajs-117	347	37	(	(	PUNCT
iajs-117	347	38	2.2,(1	2.2,(1	NUM
iajs-117	347	39	)	)	PUNCT
iajs-117	347	40	)	)	PUNCT
iajs-117	347	41	.	.	PUNCT
iajs-117	348	1	3	3	X
iajs-117	348	2	)	)	PUNCT
iajs-117	348	3	let	let	VERB
iajs-117	348	4	n1	n1	PROPN
iajs-117	348	5	is	be	AUX
iajs-117	348	6	a	a	DET
iajs-117	348	7	1prime	1prime	ADJ
iajs-117	348	8	submodule	submodule	NOUN
iajs-117	348	9	of	of	ADP
iajs-117	348	10	m1	m1	PROPN
iajs-117	348	11	and	and	CCONJ
iajs-117	348	12	2	2	NOUN
iajs-117	348	13	(	(	PUNCT
iajs-117	348	14	m2	m2	PROPN
iajs-117	348	15	)	)	PUNCT
iajs-117	349	1	=	=	PROPN
iajs-117	349	2	m2	m2	PROPN
iajs-117	349	3	.let	.let	PROPN
iajs-117	349	4	(	(	PUNCT
iajs-117	349	5	r1	r1	PROPN
iajs-117	349	6	,	,	PUNCT
iajs-117	349	7	r2)	r2)	NOUN
iajs-117	349	8	r	r	NOUN
iajs-117	349	9	and	and	CCONJ
iajs-117	349	10	(	(	PUNCT
iajs-117	349	11	m1,m2	m1,m2	PROPN
iajs-117	349	12	)	)	PUNCT
iajs-117	349	13			NOUN
iajs-117	349	14	m	m	AUX
iajs-117	349	15	be	be	VERB
iajs-117	349	16	such	such	ADJ
iajs-117	349	17	that	that	SCONJ
iajs-117	349	18	(	(	PUNCT
iajs-117	349	19	r1	r1	PROPN
iajs-117	349	20	,	,	PUNCT
iajs-117	349	21	r2	r2	PROPN
iajs-117	349	22	)	)	PUNCT
iajs-117	349	23	(	(	PUNCT
iajs-117	349	24	m1,m2	m1,m2	PROPN
iajs-117	349	25	)	)	PUNCT
iajs-117	349	26	=	=	NOUN
iajs-117	349	27	(	(	PUNCT
iajs-117	349	28	r1m1,r2m2	r1m1,r2m2	NOUN
iajs-117	349	29	)	)	PUNCT
iajs-117	349	30	n1	n1	NUM
iajs-117	350	1	m2	m2	PROPN
iajs-117	350	2	.	.	PUNCT
iajs-117	351	1	then	then	ADV
iajs-117	351	2	r1m1	r1m1	VERB
iajs-117	351	3			PROPN
iajs-117	351	4	n1	n1	PROPN
iajs-117	351	5	and	and	CCONJ
iajs-117	351	6	r2m2	r2m2	ADJ
iajs-117	351	7			NOUN
iajs-117	351	8	m2	m2	PROPN
iajs-117	351	9	and	and	CCONJ
iajs-117	351	10	since	since	SCONJ
iajs-117	351	11	n1	n1	PROPN
iajs-117	351	12	is	be	AUX
iajs-117	351	13	a	a	DET
iajs-117	351	14	1	1	NOUN
iajs-117	351	15	–	–	PUNCT
iajs-117	351	16	prime	prime	ADJ
iajs-117	351	17	submodule	submodule	NOUN
iajs-117	351	18	of	of	ADP
iajs-117	351	19	m1	m1	PROPN
iajs-117	351	20	,	,	PUNCT
iajs-117	351	21	so	so	ADV
iajs-117	351	22	either	either	CCONJ
iajs-117	351	23	r1	r1	PROPN
iajs-117	351	24			PROPN
iajs-117	351	25	[	[	PUNCT
iajs-117	351	26	n1	n1	PROPN
iajs-117	351	27	+	+	CCONJ
iajs-117	351	28	1	1	PROPN
iajs-117	351	29	(	(	PUNCT
iajs-117	351	30	n1	n1	PROPN
iajs-117	351	31	):	):	PUNCT
iajs-117	351	32	m1	m1	PROPN
iajs-117	351	33	]	]	PUNCT
iajs-117	351	34	or	or	CCONJ
iajs-117	351	35	m1	m1	PROPN
iajs-117	351	36			PROPN
iajs-117	351	37	n1	n1	PROPN
iajs-117	351	38	+	+	CCONJ
iajs-117	351	39	1	1	PROPN
iajs-117	351	40	(	(	PUNCT
iajs-117	351	41	n1	n1	PROPN
iajs-117	351	42	)	)	PUNCT
iajs-117	351	43	.so	.so	PUNCT
iajs-117	352	1	either	either	CCONJ
iajs-117	352	2	(	(	PUNCT
iajs-117	352	3	r1	r1	PROPN
iajs-117	352	4	,	,	PUNCT
iajs-117	352	5	r2	r2	PROPN
iajs-117	352	6	)	)	PUNCT
iajs-117	352	7			NOUN
iajs-117	352	8	[	[	PUNCT
iajs-117	352	9	n1	n1	PROPN
iajs-117	352	10	+	+	CCONJ
iajs-117	352	11	1	1	PROPN
iajs-117	352	12	(	(	PUNCT
iajs-117	352	13	n1	n1	PROPN
iajs-117	352	14	):	):	PUNCT
iajs-117	352	15	m1	m1	PROPN
iajs-117	352	16	]	]	PUNCT
iajs-117	352	17			X
iajs-117	353	1	[	[	X
iajs-117	353	2	m	m	PROPN
iajs-117	353	3	2	2	NUM
iajs-117	353	4	:	:	PUNCT
iajs-117	353	5	m2	m2	PROPN
iajs-117	353	6	]	]	PUNCT
iajs-117	353	7	or	or	CCONJ
iajs-117	353	8	(	(	PUNCT
iajs-117	353	9	m1,m2	m1,m2	PROPN
iajs-117	353	10	)	)	PUNCT
iajs-117	353	11			NOUN
iajs-117	354	1	[	[	X
iajs-117	354	2	n1	n1	NOUN
iajs-117	354	3	+	+	NUM
iajs-117	354	4	1	1	X
iajs-117	354	5	(	(	PUNCT
iajs-117	354	6	n1	n1	NOUN
iajs-117	354	7	)	)	PUNCT
iajs-117	354	8	]	]	PUNCT
iajs-117	355	1			PROPN
iajs-117	355	2	m2	m2	PROPN
iajs-117	355	3	.	.	PUNCT
iajs-117	356	1	hence	hence	ADV
iajs-117	356	2	either	either	CCONJ
iajs-117	356	3	(	(	PUNCT
iajs-117	356	4	r1	r1	PROPN
iajs-117	356	5	,	,	PUNCT
iajs-117	356	6	r2	r2	PROPN
iajs-117	356	7	)	)	PUNCT
iajs-117	356	8			NOUN
iajs-117	357	1	[	[	X
iajs-117	357	2	(	(	PUNCT
iajs-117	357	3	n1	n1	PROPN
iajs-117	357	4	+	+	CCONJ
iajs-117	357	5	1	1	PROPN
iajs-117	357	6	(	(	PUNCT
iajs-117	357	7	n1	n1	PROPN
iajs-117	357	8	)	)	PUNCT
iajs-117	357	9	)	)	PUNCT
iajs-117	358	1			PROPN
iajs-117	358	2	m	m	PROPN
iajs-117	358	3	2	2	NUM
iajs-117	358	4	:	:	PUNCT
iajs-117	358	5	m1	m1	PROPN
iajs-117	358	6			NOUN
iajs-117	358	7	m	m	PROPN
iajs-117	358	8	2	2	NUM
iajs-117	358	9	]	]	PUNCT
iajs-117	358	10	=	=	PUNCT
iajs-117	359	1	[	[	X
iajs-117	359	2	n1	n1	PROPN
iajs-117	359	3			NOUN
iajs-117	359	4	m2	m2	PROPN
iajs-117	359	5	+	+	PROPN
iajs-117	359	6			PROPN
iajs-117	359	7	(	(	PUNCT
iajs-117	359	8	n1	n1	PROPN
iajs-117	359	9			PROPN
iajs-117	359	10	m2	m2	PROPN
iajs-117	359	11	)	)	PUNCT
iajs-117	359	12	:	:	PUNCT
iajs-117	359	13	m1	m1	PROPN
iajs-117	359	14			PROPN
iajs-117	359	15	m	m	PROPN
iajs-117	359	16	2	2	NUM
iajs-117	359	17	]	]	PUNCT
iajs-117	359	18	or	or	CCONJ
iajs-117	359	19	(	(	PUNCT
iajs-117	359	20	m1,m2	m1,m2	PROPN
iajs-117	359	21	)	)	PUNCT
iajs-117	359	22			NOUN
iajs-117	360	1	[	[	X
iajs-117	360	2	n1	n1	PROPN
iajs-117	360	3			NOUN
iajs-117	360	4	m2	m2	PROPN
iajs-117	360	5	+	+	PROPN
iajs-117	360	6	1	1	PROPN
iajs-117	360	7	(	(	PUNCT
iajs-117	360	8	n1	n1	PROPN
iajs-117	360	9	)	)	PUNCT
iajs-117	360	10			NOUN
iajs-117	360	11	2(n2	2(n2	PROPN
iajs-117	360	12	)	)	PUNCT
iajs-117	360	13	]	]	PUNCT
iajs-117	361	1	=	=	SYM
iajs-117	361	2	n	n	SYM
iajs-117	361	3	1	1	NUM
iajs-117	361	4			NOUN
iajs-117	361	5	m2	m2	PROPN
iajs-117	361	6	+	+	PROPN
iajs-117	361	7			PROPN
iajs-117	361	8	(	(	PUNCT
iajs-117	361	9	n1	n1	PROPN
iajs-117	361	10			NOUN
iajs-117	361	11	m2).therefore	m2).therefore	PROPN
iajs-117	361	12	n1	n1	PROPN
iajs-117	361	13			PROPN
iajs-117	361	14	m2	m2	PROPN
iajs-117	361	15	is	be	AUX
iajs-117	361	16	a	a	DET
iajs-117	361	17	prime	prime	PROPN
iajs-117	361	18	submodule	submodule	NOUN
iajs-117	361	19	of	of	ADP
iajs-117	361	20	m	m	PROPN
iajs-117	361	21	.	.	PUNCT
iajs-117	362	1	parts	part	NOUN
iajs-117	362	2	(	(	PUNCT
iajs-117	362	3	4	4	NUM
iajs-117	362	4	)	)	PUNCT
iajs-117	362	5	,	,	PUNCT
iajs-117	362	6	(	(	PUNCT
iajs-117	362	7	5	5	X
iajs-117	362	8	)	)	PUNCT
iajs-117	362	9	are	be	AUX
iajs-117	362	10	proved	prove	VERB
iajs-117	362	11	similar	similar	ADJ
iajs-117	362	12	to	to	ADP
iajs-117	362	13	(	(	PUNCT
iajs-117	362	14	2	2	NUM
iajs-117	362	15	)	)	PUNCT
iajs-117	362	16	,	,	PUNCT
iajs-117	362	17	(	(	PUNCT
iajs-117	362	18	3	3	X
iajs-117	362	19	)	)	PUNCT
iajs-117	362	20	respectively	respectively	ADV
iajs-117	362	21	.	.	PUNCT
iajs-117	363	1	references	reference	NOUN
iajs-117	363	2	1	1	NUM
iajs-117	363	3	.	.	PUNCT
iajs-117	364	1	larsen	larsen	PROPN
iajs-117	364	2	,	,	PUNCT
iajs-117	364	3	m.d	m.d	PROPN
iajs-117	364	4	.	.	PROPN
iajs-117	364	5	and	and	CCONJ
iajs-117	364	6	mccarlthy	mccarlthy	ADJ
iajs-117	364	7	,	,	PUNCT
iajs-117	364	8	p.j	p.j	PROPN
iajs-117	364	9	.	.	PROPN
iajs-117	364	10	,	,	PUNCT
iajs-117	364	11	(	(	PUNCT
iajs-117	364	12	1971	1971	NUM
iajs-117	364	13	)	)	PUNCT
iajs-117	364	14	,	,	PUNCT
iajs-117	364	15	multiplication	multiplication	NOUN
iajs-117	364	16	theory	theory	NOUN
iajs-117	364	17	of	of	ADP
iajs-117	364	18	ideals	ideal	NOUN
iajs-117	364	19	,	,	PUNCT
iajs-117	364	20	academic	academic	ADJ
iajs-117	364	21	press	press	NOUN
iajs-117	364	22	,	,	PUNCT
iajs-117	364	23	new	new	PROPN
iajs-117	364	24	york	york	PROPN
iajs-117	364	25	.	.	PUNCT
iajs-117	365	1	2	2	X
iajs-117	365	2	.	.	X
iajs-117	365	3	mccasland	mccasland	NOUN
iajs-117	365	4	,	,	PUNCT
iajs-117	365	5	r	r	NOUN
iajs-117	365	6	.l	.l	PROPN
iajs-117	365	7	.	.	PUNCT
iajs-117	366	1	and	and	CCONJ
iajs-117	366	2	smith	smith	PROPN
iajs-117	366	3	,	,	PUNCT
iajs-117	366	4	p.f	p.f	PROPN
iajs-117	366	5	.	.	PROPN
iajs-117	366	6	,	,	PUNCT
iajs-117	366	7	(	(	PUNCT
iajs-117	366	8	1993	1993	NUM
iajs-117	366	9	)	)	PUNCT
iajs-117	366	10	,	,	PUNCT
iajs-117	366	11	prime	prime	ADJ
iajs-117	366	12	submodules	submodule	NOUN
iajs-117	366	13	of	of	ADP
iajs-117	366	14	noetherian	noetherian	ADJ
iajs-117	366	15	modules	module	NOUN
iajs-117	366	16	,	,	PUNCT
iajs-117	366	17	rocky	rocky	ADJ
iajs-117	366	18	mtn.j	mtn.j	PROPN
iajs-117	366	19	.	.	PUNCT
iajs-117	366	20	,23	,23	PROPN
iajs-117	366	21	,	,	PUNCT
iajs-117	366	22	1041	1041	NUM
iajs-117	366	23	-	-	SYM
iajs-117	366	24	1062	1062	NUM
iajs-117	366	25	.	.	PUNCT
iajs-117	367	1	3	3	X
iajs-117	367	2	.	.	X
iajs-117	367	3	l	l	NOUN
iajs-117	367	4	,	,	PUNCT
iajs-117	367	5	u	u	NOUN
iajs-117	367	6	,	,	PUNCT
iajs-117	367	7	c.p	c.p	PROPN
iajs-117	367	8	.	.	PROPN
iajs-117	367	9	,	,	PUNCT
iajs-117	367	10	(	(	PUNCT
iajs-117	367	11	1981),prime	1981),prime	NUM
iajs-117	367	12	submodule	submodule	NOUN
iajs-117	367	13	of	of	ADP
iajs-117	367	14	modules	module	NOUN
iajs-117	367	15	,	,	PUNCT
iajs-117	367	16	commutative	commutative	ADJ
iajs-117	367	17	mathematics	mathematic	NOUN
iajs-117	367	18	,	,	PUNCT
iajs-117	367	19	university	university	NOUN
iajs-117	367	20	spatula	spatula	NOUN
iajs-117	367	21	,	,	PUNCT
iajs-117	367	22	33,16	33,16	NUM
iajs-117	367	23	-	-	SYM
iajs-117	367	24	69	69	NUM
iajs-117	367	25	.	.	PUNCT
iajs-117	368	1	4	4	X
iajs-117	368	2	.	.	X
iajs-117	368	3	saymeh	saymeh	PROPN
iajs-117	368	4	,	,	PUNCT
iajs-117	368	5	s.	s.	PROPN
iajs-117	368	6	a.	a.	PROPN
iajs-117	368	7	,(1979	,(1979	PROPN
iajs-117	368	8	)	)	PUNCT
iajs-117	368	9	,	,	PUNCT
iajs-117	368	10	on	on	ADP
iajs-117	368	11	prime	prime	ADJ
iajs-117	368	12	r	r	NOUN
iajs-117	368	13	-	-	PUNCT
iajs-117	368	14	submodules	submodules	NOUN
iajs-117	368	15	,	,	PUNCT
iajs-117	368	16	univ	univ	PROPN
iajs-117	368	17	.	.	PUNCT
iajs-117	369	1	nac	nac	PROPN
iajs-117	369	2	.	.	PROPN
iajs-117	369	3	tucuman	tucuman	PROPN
iajs-117	369	4	rev	rev	PROPN
iajs-117	369	5	.	.	PROPN
iajs-117	369	6	ser	ser	PROPN
iajs-117	369	7	.	.	PROPN
iajs-117	370	1	,	,	PUNCT
iajs-117	370	2	a	a	DET
iajs-117	370	3	29	29	NUM
iajs-117	370	4	,	,	PUNCT
iajs-117	370	5	121	121	NUM
iajs-117	370	6	-	-	SYM
iajs-117	370	7	136	136	NUM
iajs-117	370	8	.	.	PUNCT
iajs-117	371	1	5	5	NUM
iajs-117	371	2	.	.	NUM
iajs-117	371	3	atani	atani	PROPN
iajs-117	371	4	,	,	PUNCT
iajs-117	371	5	s.e	s.e	PROPN
iajs-117	371	6	.	.	PROPN
iajs-117	371	7	and	and	CCONJ
iajs-117	371	8	farzalipouur	farzalipouur	PROPN
iajs-117	371	9	,	,	PUNCT
iajs-117	371	10	f.	f.	PROPN
iajs-117	371	11	,(2007	,(2007	PROPN
iajs-117	371	12	)	)	PUNCT
iajs-117	371	13	,	,	PUNCT
iajs-117	371	14	on	on	ADP
iajs-117	371	15	weakly	weakly	ADJ
iajs-117	371	16	prime	prime	ADJ
iajs-117	371	17	submodules	submodule	NOUN
iajs-117	371	18	,	,	PUNCT
iajs-117	371	19	tamkang	tamkang	PROPN
iajs-117	371	20	journal	journal	PROPN
iajs-117	371	21	of	of	ADP
iajs-117	371	22	mathematics,38(3),247	mathematics,38(3),247	NOUN
iajs-117	371	23	-	-	PUNCT
iajs-117	371	24	252	252	NUM
iajs-117	371	25	.	.	NOUN
iajs-117	371	26	6	6	NUM
iajs-117	371	27	.	.	X
iajs-117	371	28	khaksari	khaksari	PROPN
iajs-117	371	29	,	,	PUNCT
iajs-117	371	30	a.	a.	NOUN
iajs-117	371	31	and	and	CCONJ
iajs-117	371	32	jafari	jafari	PROPN
iajs-117	371	33	,	,	PUNCT
iajs-117	371	34	a.	a.	NOUN
iajs-117	371	35	,	,	PUNCT
iajs-117	371	36	(	(	PUNCT
iajs-117	371	37	2011),	2011),	NUM
iajs-117	371	38	-prime	-prime	NOUN
iajs-117	371	39	submodules	submodule	NOUN
iajs-117	371	40	,	,	PUNCT
iajs-117	371	41	international	international	ADJ
iajs-117	371	42	journal	journal	NOUN
iajs-117	371	43	of	of	ADP
iajs-117	371	44	algebra	algebra	PROPN
iajs-117	371	45	,	,	PUNCT
iajs-117	371	46	5	5	NUM
iajs-117	371	47	(	(	PUNCT
iajs-117	371	48	20	20	NUM
iajs-117	371	49	)	)	PUNCT
iajs-117	371	50	,	,	PUNCT
iajs-117	371	51	1443	1443	NUM
iajs-117	371	52	-	-	SYM
iajs-117	371	53	1440	1440	NUM
iajs-117	371	54	.	.	PUNCT
iajs-117	372	1	7	7	X
iajs-117	372	2	.	.	X
iajs-117	372	3	eibast	eibast	PROPN
iajs-117	372	4	z.a.and	z.a.and	PROPN
iajs-117	372	5	smith	smith	PROPN
iajs-117	373	1	p.f	p.f	PROPN
iajs-117	373	2	.	.	PROPN
iajs-117	373	3	,(1988),multiplication	,(1988),multiplication	NOUN
iajs-117	373	4	modules	module	NOUN
iajs-117	373	5	,	,	PUNCT
iajs-117	373	6	comm	comm	NOUN
iajs-117	373	7	.	.	PUNCT
iajs-117	374	1	in	in	ADP
iajs-117	374	2	algebra,16,755	algebra,16,755	PROPN
iajs-117	374	3	779	779	NUM
iajs-117	374	4	.	.	NOUN
iajs-117	374	5	8	8	NUM
iajs-117	374	6	.	.	X
iajs-117	374	7	faith	faith	NOUN
iajs-117	374	8	,	,	PUNCT
iajs-117	374	9	c.	c.	PROPN
iajs-117	374	10	,	,	PUNCT
iajs-117	374	11	(	(	PUNCT
iajs-117	374	12	1976	1976	NUM
iajs-117	374	13	)	)	PUNCT
iajs-117	374	14	,	,	PUNCT
iajs-117	374	15	ring	ring	NOUN
iajs-117	374	16	theory	theory	NOUN
iajs-117	374	17	,	,	PUNCT
iajs-117	374	18	springerverlag	springerverlag	NOUN
iajs-117	374	19	,	,	PUNCT
iajs-117	374	20	berlin	berlin	PROPN
iajs-117	374	21	heidelberg	heidelberg	PROPN
iajs-117	374	22	,	,	PUNCT
iajs-117	374	23	new	new	PROPN
iajs-117	374	24	york	york	PROPN
iajs-117	374	25	.	.	PUNCT
iajs-117	375	1	9	9	NUM
iajs-117	375	2	.	.	X
iajs-117	375	3	abbas	abbas	PROPN
iajs-117	375	4	,	,	PUNCT
iajs-117	375	5	m.s	m.s	PROPN
iajs-117	375	6	.	.	PROPN
iajs-117	375	7	,	,	PUNCT
iajs-117	375	8	(	(	PUNCT
iajs-117	375	9	1990),on	1990),on	NOUN
iajs-117	375	10	fully	fully	ADV
iajs-117	375	11	stable	stable	ADJ
iajs-117	375	12	modules	module	NOUN
iajs-117	375	13	,	,	PUNCT
iajs-117	375	14	ph.d	ph.d	PROPN
iajs-117	375	15	.	.	PUNCT
iajs-117	376	1	thesis	thesis	NOUN
iajs-117	376	2	,	,	PUNCT
iajs-117	376	3	university	university	NOUN
iajs-117	376	4	of	of	ADP
iajs-117	376	5	baghdad	baghdad	PROPN
iajs-117	376	6	.	.	PUNCT
iajs-117	377	1	10	10	NUM
iajs-117	377	2	.	.	X
iajs-117	378	1	ameen	ameen	PROPN
iajs-117	378	2	,	,	PUNCT
iajs-117	378	3	sh	sh	PROPN
iajs-117	378	4	.	.	PROPN
iajs-117	378	5	a.	a.	PROPN
iajs-117	378	6	,	,	PUNCT
iajs-117	378	7	(	(	PUNCT
iajs-117	378	8	2002	2002	NUM
iajs-117	378	9	)	)	PUNCT
iajs-117	378	10	,	,	PUNCT
iajs-117	378	11	bounded	bounded	ADJ
iajs-117	378	12	modules	module	NOUN
iajs-117	378	13	,	,	PUNCT
iajs-117	378	14	msc	msc	PROPN
iajs-117	378	15	.	.	PROPN
iajs-117	378	16	thesis	thesis	PROPN
iajs-117	378	17	,	,	PUNCT
iajs-117	378	18	university	university	NOUN
iajs-117	378	19	of	of	ADP
iajs-117	378	20	baghdad	baghdad	PROPN
iajs-117	378	21	.	.	PUNCT
iajs-117	378	22	)	)	PUNCT
iajs-117	378	23	،	،	PROPN
iajs-117	378	24	الموديوالت	الموديوالت	X
iajs-117	378	25	الجزئية	الجزئية	PROPN
iajs-117	378	26	االولية	االولية	NOUN
iajs-117	378	27	والموديوالت	والموديوالت	ADV
iajs-117	378	28	الجزئية	الجزئية	VERB
iajs-117	378	29	شبه	شبه	VERB
iajs-117	378	30	االولية،رسالة	االولية،رسالة	NOUN
iajs-117	378	31	ماجستير	ماجستير	NOUN
iajs-117	378	32	,	,	PUNCT
iajs-117	378	33	1996.عذاب	1996.عذاب	NUM
iajs-117	378	34	،	،	NOUN
iajs-117	378	35	ايمان	ايمان	NOUN
iajs-117	378	36	علي	علي	NOUN
iajs-117	378	37	,	,	PUNCT
iajs-117	378	38	(	(	PUNCT
iajs-117	378	39	11	11	NUM
iajs-117	378	40	0	0	NUM
iajs-117	378	41	0جامعةبغداد	0جامعةبغداد	NUM
iajs-117	378	42	mathematics	mathematic	NOUN
iajs-117	378	43	|	|	ADV
iajs-117	378	44	291	291	NUM
iajs-117	378	45	2016	2016	NUM
iajs-117	378	46	)	)	PUNCT
iajs-117	378	47	عام	عام	ADP
iajs-117	378	48	2العدد	2العدد	NUM
iajs-117	378	49	(	(	PUNCT
iajs-117	378	50	29لمجلد	29لمجلد	NUM
iajs-117	378	51	ا	ا	X
iajs-117	378	52	مجلة	مجلة	NOUN
iajs-117	378	53	إبن	إبن	VERB
iajs-117	378	54	الهيثم	الهيثم	ADJ
iajs-117	378	55	للعلوم	للعلوم	NOUN
iajs-117	378	56	الصرفة	الصرفة	NOUN
iajs-117	379	1	و	و	PRON
iajs-117	379	2	التطبيقية	التطبيقية	ADJ
iajs-117	379	3	ibn	ibn	PROPN
iajs-117	379	4	al	al	PROPN
iajs-117	379	5	-	-	PUNCT
iajs-117	379	6	haitham	haitham	PROPN
iajs-117	379	7	jour	jour	X
iajs-117	379	8	.	.	PROPN
iajs-117	379	9	for	for	ADP
iajs-117	379	10	pure	pure	ADJ
iajs-117	379	11	&	&	CCONJ
iajs-117	379	12	appl	appl	PROPN
iajs-117	379	13	.	.	PUNCT
iajs-117	380	1	sci	sci	PROPN
iajs-117	380	2	.	.	PUNCT
iajs-117	380	3	vol	vol	NOUN
iajs-117	380	4	.	.	PROPN
iajs-117	380	5	29	29	NUM
iajs-117	380	6	(	(	PUNCT
iajs-117	380	7	2	2	NUM
iajs-117	380	8	)	)	PUNCT
iajs-117	380	9	2016	2016	NUM
iajs-117	380	10	--المقاسات	--المقاسات	PROPN
iajs-117	380	11	الجزئية	الجزئية	VERB
iajs-117	380	12	األولية	األولية	NOUN
iajs-117	380	13	من	من	DET
iajs-117	380	14	النمط	النمط	NOUN
iajs-117	380	15	نهاد	نهاد	NOUN
iajs-117	380	16	سالم	سالم	VERB
iajs-117	380	17	المظفر	المظفر	ADJ
iajs-117	380	18	جامعة	جامعة	NOUN
iajs-117	380	19	بغداد	بغداد	PROPN
iajs-117	380	20	/كلية	/كلية	NOUN
iajs-117	380	21	العلوم	العلوم	PROPN
iajs-117	380	22	/قسم	/قسم	PUNCT
iajs-117	380	23	الرياضيات	الرياضيات	PROPN
iajs-117	380	24	عدويه	عدويه	PROPN
iajs-117	380	25	جاسم	جاسم	NOUN
iajs-117	380	26	عبدالخالق	عبدالخالق	NOUN
iajs-117	380	27	الجامعة	الجامعة	VERB
iajs-117	381	1	المستنصرية	المستنصرية	PROPN
iajs-117	381	2	/كلية	/كلية	NOUN
iajs-117	381	3	العلوم	العلوم	PROPN
iajs-117	381	4	/قسم	/قسم	PROPN
iajs-117	381	5	الرياضيات	الرياضيات	NOUN
iajs-117	381	6	2016حزيران//5،قبل	2016حزيران//5،قبل	PROPN
iajs-117	381	7	في:2016اذار//9استلم	في:2016اذار//9استلم	PROPN
iajs-117	382	1	في	في	PROPN
iajs-117	382	2	:	:	PUNCT
iajs-117	382	3	خالصةال	خالصةال	PROPN
iajs-117	382	4	مجموعة	مجموعة	PROPN
iajs-117	382	5	كل	كل	PROPN
iajs-117	382	6	المقاسات	المقاسات	PROPN
iajs-117	382	7	(m	(m	PROPN
iajs-117	382	8	)	)	PUNCT
iajs-117	382	9	.	.	PUNCT
iajs-117	383	1	لتكن	لتكن	PROPN
iajs-117	383	2	rمقاساً	rمقاساً	PROPN
iajs-117	383	3	معرفا	معرفا	PROPN
iajs-117	383	4	ً	ً	PROPN
iajs-117	383	5	على	على	NOUN
iajs-117	383	6	الحلقة	الحلقة	PROPN
iajs-117	383	7	mحلقة	mحلقة	PROPN
iajs-117	383	8	ابدالية	ابدالية	NOUN
iajs-117	383	9	ذات	ذات	VERB
iajs-117	383	10	عنصر	عنصر	PROPN
iajs-117	383	11	محايد	محايد	NOUN
iajs-117	383	12	،	،	NOUN
iajs-117	383	13	وليكن	وليكن	PROPN
iajs-117	384	1	rلتكن	rلتكن	NOUN
iajs-117	384	2	هو	هو	PRON
iajs-117	384	3	مقاس	مقاس	PROPN
iajs-117	384	4	mمن	mمن	NOUN
iajs-117	384	5	pدالة	pدالة	NOUN
iajs-117	384	6	.	.	PUNCT
iajs-117	385	1	في	في	PRON
iajs-117	385	2	هذا	هذا	NOUN
iajs-117	385	3	البحث	البحث	PROPN
iajs-117	385	4	،	،	PROPN
iajs-117	385	5	نقول	نقول	PROPN
iajs-117	385	6	ان	ان	PROPN
iajs-117	385	7	المقاس	المقاس	PROPN
iajs-117	385	8	الجزئي	الجزئي	PROPN
iajs-117	385	9			NOUN
iajs-117	385	10	:	:	PUNCT
iajs-117	385	11	(m	(m	PROPN
iajs-117	385	12	)	)	PUNCT
iajs-117	385	13			PROPN
iajs-117	385	14	(m	(m	PROPN
iajs-117	385	15	)	)	PUNCT
iajs-117	385	16			NOUN
iajs-117	385	17	{	{	PUNCT
iajs-117	385	18	}ولتكن	}ولتكن	PROPN
iajs-117	385	19	mالجزئية	mالجزئية	NOUN
iajs-117	385	20	من	من	PROPN
iajs-117	385	21	p	p	NOUN
iajs-117	385	22	+	+	CCONJ
iajs-117	385	23	(p	(p	ADJ
iajs-117	385	24	)	)	PUNCT
iajs-117	385	25	m	m	PROPN
iajs-117	385	26	،	،	PROPN
iajs-117	385	27	فانه	فانه	PROPN
iajs-117	385	28	يؤدي	يؤدي	NOUN
iajs-117	385	29	الى	الى	AUX
iajs-117	385	30	اما	اما	AUX
iajs-117	385	31	rx	rx	VERB
iajs-117	385	32			NOUN
iajs-117	385	33	pا	pا	VERB
iajs-117	385	34	ذ	ذ	ADP
iajs-117	385	35	ان	ان	INTJ
iajs-117	385	36	r	r	PROPN
iajs-117	385	37	r	r	NOUN
iajs-117	385	38	,	,	PUNCT
iajs-117	385	39			NOUN
iajs-117	385	40	m	m	VERB
iajs-117	385	41	mا	mا	NOUN
iajs-117	385	42	ذا	ذا	PROPN
iajs-117	385	43	كان	كان	PROPN
iajs-117	385	44	لكل	لكل	PRON
iajs-117	385	45			NOUN
iajs-117	385	46	--جزئي	--جزئي	NOUN
iajs-117	385	47	أولي	أولي	NOUN
iajs-117	385	48	من	من	PROPN
iajs-117	385	49	النمط	النمط	PROPN
iajs-117	385	50	لقد	لقد	PROPN
iajs-117	385	51	درسنا	درسنا	ADV
iajs-117	385	52	واعطينا	واعطينا	VERB
iajs-117	385	53	بعض	بعض	NOUN
iajs-117	386	1	خواص	خواص	ADV
iajs-117	386	2	و	و	PRON
iajs-117	386	3	مميزات	مميزات	ADJ
iajs-117	386	4	هذا	هذا	NOUN
iajs-117	386	5	النوع	النوع	NOUN
iajs-117	386	6	من	من	DET
iajs-117	386	7	المقاسات	المقاسات	PROPN
iajs-117	386	8	الجزئية	الجزئية	PROPN
iajs-117	386	9	وبرهنا	وبرهنا	PROPN
iajs-117	386	10	تحت	تحت	VERB
iajs-117	386	11			PROPN
iajs-117	386	12	r	r	NOUN
iajs-117	386	13	0	0	PUNCT
iajs-117	387	1	[	[	X
iajs-117	387	2	p	p	X
iajs-117	387	3	+	+	CCONJ
iajs-117	387	4	(p	(p	X
iajs-117	387	5	):	):	PUNCT
iajs-117	387	6	m]أو	m]أو	PROPN
iajs-117	387	7	0شروط	0شروط	PROPN
iajs-117	387	8	معينة	معينة	NOUN
iajs-117	387	9	ان	ان	SCONJ
iajs-117	387	10	المقاسات	المقاسات	PROPN
iajs-117	387	11	الجزئية	الجزئية	PROPN
iajs-117	387	12	االولية	االولية	NOUN
iajs-117	387	13	وهذا	وهذا	VERB
iajs-117	387	14	النوع	النوع	PROPN
iajs-117	387	15	من	من	DET
iajs-117	387	16	المقاسات	المقاسات	PROPN
iajs-117	387	17	الجزئية	الجزئية	PROPN
iajs-117	387	18	تكون	تكون	VERB
iajs-117	387	19	متكافئة	متكافئة	ADJ
iajs-117	387	20	0	0	PUNCT
iajs-117	387	21	-ية	-ية	PUNCT
iajs-117	387	22	االولية	االولية	NOUN
iajs-117	387	23	من	من	DET
iajs-117	387	24	النمط	النمط	PROPN
iajs-117	387	25	المقاسات	المقاسات	PROPN
iajs-117	387	26	الجزئية	الجزئية	VERB
iajs-117	387	27	االولية	االولية	PROPN
iajs-117	387	28	،	،	PROPN
iajs-117	387	29	المقاسات	المقاسات	PROPN
iajs-117	387	30	الجزئية	الجزئية	VERB
iajs-117	387	31	الضعيفة	الضعيفة	PROPN
iajs-117	387	32	،	،	PROPN
iajs-117	387	33	المقاسات	المقاسات	PROPN
iajs-117	387	34	الجزئ	الجزئ	PROPN
iajs-117	387	35	:	:	PUNCT
iajs-117	387	36	الكلمات	الكلمات	VERB
iajs-117	387	37	المفتاحية	المفتاحية	NOUN