id	sid	tid	token	lemma	pos
iajs-704	1	1	مجلة	مجلة	VERB
iajs-704	1	2	إبن	إبن	VERB
iajs-704	1	3	الھیثم	الھیثم	NOUN
iajs-704	1	4	للعلوم	للعلوم	NOUN
iajs-704	1	5	الصرفة	الصرفة	NOUN
iajs-704	1	6	و	و	PRON
iajs-704	1	7	التطبیقیة	التطبیقیة	PROPN
iajs-704	1	8	2012	2012	NUM
iajs-704	1	9	السنة	السنة	NOUN
iajs-704	1	10	25	25	NUM
iajs-704	1	11	المجلد	المجلد	NOUN
iajs-704	1	12	1	1	NUM
iajs-704	1	13	العدد	العدد	PROPN
iajs-704	1	14	ibn	ibn	PROPN
iajs-704	1	15	al	al	PROPN
iajs-704	1	16	-	-	PUNCT
iajs-704	1	17	haitham	haitham	PROPN
iajs-704	1	18	journal	journal	PROPN
iajs-704	1	19	for	for	ADP
iajs-704	1	20	pure	pure	ADJ
iajs-704	1	21	and	and	CCONJ
iajs-704	1	22	applied	apply	VERB
iajs-704	1	23	science	science	NOUN
iajs-704	1	24	no	no	NOUN
iajs-704	1	25	.	.	NOUN
iajs-704	1	26	1	1	NUM
iajs-704	1	27	vol	vol	NOUN
iajs-704	1	28	.	.	PUNCT
iajs-704	2	1	25	25	NUM
iajs-704	2	2	year	year	NOUN
iajs-704	2	3	2012	2012	NUM
iajs-704	2	4	on	on	ADP
iajs-704	2	5	weakly	weakly	ADJ
iajs-704	2	6	quasi	quasi	ADJ
iajs-704	2	7	-	-	ADJ
iajs-704	2	8	prime	prime	ADJ
iajs-704	2	9	module	module	NOUN
iajs-704	2	10	m.	m.	NOUN
iajs-704	2	11	a.	a.	PROPN
iajs-704	2	12	hassin	hassin	PROPN
iajs-704	2	13	department	department	PROPN
iajs-704	2	14	of	of	ADP
iajs-704	2	15	mathematical	mathematical	PROPN
iajs-704	2	16	,	,	PUNCT
iajs-704	2	17	college	college	NOUN
iajs-704	2	18	of	of	ADP
iajs-704	2	19	basic	basic	ADJ
iajs-704	2	20	education	education	NOUN
iajs-704	2	21	,	,	PUNCT
iajs-704	2	22	university	university	NOUN
iajs-704	2	23	of	of	ADP
iajs-704	2	24	al	al	PROPN
iajs-704	2	25	-	-	PUNCT
iajs-704	2	26	mustansriyah	mustansriyah	PROPN
iajs-704	2	27	received	receive	VERB
iajs-704	2	28	in	in	ADP
iajs-704	2	29	:	:	PUNCT
iajs-704	2	30	3	3	NUM
iajs-704	2	31	april	april	PROPN
iajs-704	2	32	2011	2011	NUM
iajs-704	2	33	accepted	accept	VERB
iajs-704	2	34	in	in	ADP
iajs-704	2	35	:	:	PUNCT
iajs-704	2	36	18	18	NUM
iajs-704	2	37	october	october	PROPN
iajs-704	2	38	2011	2011	NUM
iajs-704	2	39	abstract	abstract	NOUN
iajs-704	2	40	in	in	ADP
iajs-704	2	41	this	this	DET
iajs-704	2	42	work	work	NOUN
iajs-704	2	43	we	we	PRON
iajs-704	2	44	shall	shall	AUX
iajs-704	2	45	introduce	introduce	VERB
iajs-704	2	46	the	the	DET
iajs-704	2	47	concept	concept	NOUN
iajs-704	2	48	of	of	ADP
iajs-704	2	49	weakly	weakly	ADJ
iajs-704	2	50	quasi	quasi	ADJ
iajs-704	2	51	-	-	ADJ
iajs-704	2	52	prime	prime	ADJ
iajs-704	2	53	modules	module	NOUN
iajs-704	2	54	and	and	CCONJ
iajs-704	2	55	give	give	VERB
iajs-704	2	56	some	some	DET
iajs-704	2	57	properties	property	NOUN
iajs-704	2	58	of	of	ADP
iajs-704	2	59	this	this	DET
iajs-704	2	60	type	type	NOUN
iajs-704	2	61	of	of	ADP
iajs-704	2	62	modules	module	NOUN
iajs-704	2	63	.	.	PUNCT
iajs-704	3	1	key	key	ADJ
iajs-704	3	2	words	word	NOUN
iajs-704	3	3	:	:	PUNCT
iajs-704	3	4	prime	prime	ADJ
iajs-704	3	5	module	module	NOUN
iajs-704	3	6	,	,	PUNCT
iajs-704	3	7	quasi	quasi	ADJ
iajs-704	3	8	-	-	ADJ
iajs-704	3	9	prime	prime	ADJ
iajs-704	3	10	module	module	NOUN
iajs-704	3	11	,	,	PUNCT
iajs-704	3	12	weakly	weakly	ADJ
iajs-704	3	13	quasi	quasi	ADJ
iajs-704	3	14	-	-	ADJ
iajs-704	3	15	prime	prime	ADJ
iajs-704	3	16	module	module	NOUN
iajs-704	3	17	.	.	PUNCT
iajs-704	4	1	1introduction	1introduction	NUM
iajs-704	4	2	let	let	VERB
iajs-704	4	3	r	r	NOUN
iajs-704	4	4	be	be	AUX
iajs-704	4	5	a	a	DET
iajs-704	4	6	commutative	commutative	ADJ
iajs-704	4	7	ring	ring	NOUN
iajs-704	4	8	with	with	ADP
iajs-704	4	9	unity	unity	NOUN
iajs-704	4	10	,	,	PUNCT
iajs-704	4	11	and	and	CCONJ
iajs-704	4	12	let	let	VERB
iajs-704	4	13	m	m	PRON
iajs-704	4	14	be	be	AUX
iajs-704	4	15	an	an	DET
iajs-704	4	16	r	r	NOUN
iajs-704	4	17	-	-	PUNCT
iajs-704	4	18	module	module	NOUN
iajs-704	4	19	,	,	PUNCT
iajs-704	4	20	we	we	PRON
iajs-704	4	21	introduce	introduce	VERB
iajs-704	4	22	that	that	SCONJ
iajs-704	4	23	an	an	DET
iajs-704	4	24	r	r	NOUN
iajs-704	4	25	-	-	PUNCT
iajs-704	4	26	module	module	NOUN
iajs-704	4	27	m	m	NOUN
iajs-704	4	28	is	be	AUX
iajs-704	4	29	called	call	VERB
iajs-704	4	30	weakly	weakly	ADJ
iajs-704	4	31	quasi	quasi	ADJ
iajs-704	4	32	–	–	PUNCT
iajs-704	4	33	prime	prime	ADJ
iajs-704	4	34	module	module	NOUN
iajs-704	4	35	if	if	SCONJ
iajs-704	4	36	annrm	annrm	NOUN
iajs-704	4	37	=	=	SYM
iajs-704	4	38	annrrm	annrrm	NOUN
iajs-704	4	39	for	for	ADP
iajs-704	4	40	every	every	DET
iajs-704	4	41	r	r	NOUN
iajs-704	4	42	annrm	annrm	NOUN
iajs-704	4	43	,	,	PUNCT
iajs-704	4	44	where	where	SCONJ
iajs-704	4	45	annrm	annrm	NOUN
iajs-704	4	46	=	=	PUNCT
iajs-704	4	47	{	{	PUNCT
iajs-704	4	48	r	r	NOUN
iajs-704	4	49	:	:	PUNCT
iajs-704	4	50	rr	rr	NUM
iajs-704	4	51	and	and	CCONJ
iajs-704	4	52	rm	rm	X
iajs-704	4	53	=	=	PUNCT
iajs-704	4	54	0	0	NUM
iajs-704	4	55	}	}	PUNCT
iajs-704	4	56	.	.	PUNCT
iajs-704	5	1	the	the	DET
iajs-704	5	2	main	main	ADJ
iajs-704	5	3	purpose	purpose	NOUN
iajs-704	5	4	of	of	ADP
iajs-704	5	5	this	this	DET
iajs-704	5	6	work	work	NOUN
iajs-704	5	7	is	be	AUX
iajs-704	5	8	to	to	PART
iajs-704	5	9	investigate	investigate	VERB
iajs-704	5	10	the	the	DET
iajs-704	5	11	properties	property	NOUN
iajs-704	5	12	of	of	ADP
iajs-704	5	13	weakly	weakly	ADJ
iajs-704	5	14	quasi	quasi	ADJ
iajs-704	5	15	-	-	ADJ
iajs-704	5	16	prime	prime	ADJ
iajs-704	5	17	modules	module	NOUN
iajs-704	5	18	,	,	PUNCT
iajs-704	5	19	and	and	CCONJ
iajs-704	5	20	we	we	PRON
iajs-704	5	21	give	give	VERB
iajs-704	5	22	several	several	ADJ
iajs-704	5	23	characterizations	characterization	NOUN
iajs-704	5	24	of	of	ADP
iajs-704	5	25	weakly	weakly	ADJ
iajs-704	5	26	quasi	quasi	ADJ
iajs-704	5	27	-	-	ADJ
iajs-704	5	28	prime	prime	ADJ
iajs-704	5	29	modules	module	NOUN
iajs-704	5	30	.	.	PUNCT
iajs-704	6	1	recall	recall	VERB
iajs-704	6	2	that	that	SCONJ
iajs-704	6	3	an	an	DET
iajs-704	6	4	r	r	NOUN
iajs-704	6	5	-	-	PUNCT
iajs-704	6	6	module	module	NOUN
iajs-704	6	7	is	be	AUX
iajs-704	6	8	called	call	VERB
iajs-704	6	9	prime	prime	NOUN
iajs-704	6	10	if	if	SCONJ
iajs-704	6	11	annrm	annrm	NOUN
iajs-704	6	12	=	=	SYM
iajs-704	6	13	annrn	annrn	NOUN
iajs-704	6	14	for	for	ADP
iajs-704	6	15	every	every	DET
iajs-704	6	16	non	non	ADJ
iajs-704	6	17	-	-	ADJ
iajs-704	6	18	zero	zero	NUM
iajs-704	6	19	submodule	submodule	NOUN
iajs-704	6	20	n	n	PROPN
iajs-704	6	21	of	of	ADP
iajs-704	6	22	m	m	PROPN
iajs-704	6	23	and	and	CCONJ
iajs-704	6	24	annrm	annrm	NOUN
iajs-704	6	25	=	=	SYM
iajs-704	6	26	{	{	PUNCT
iajs-704	6	27	r	r	NOUN
iajs-704	6	28	:	:	PUNCT
iajs-704	6	29	rr	rr	NUM
iajs-704	6	30	and	and	CCONJ
iajs-704	6	31	rm	rm	X
iajs-704	6	32	=	=	PUNCT
iajs-704	6	33	0	0	NUM
iajs-704	6	34	}	}	PUNCT
iajs-704	6	35	,	,	PUNCT
iajs-704	6	36	[	[	X
iajs-704	6	37	1	1	NUM
iajs-704	6	38	]	]	PUNCT
iajs-704	6	39	.	.	PUNCT
iajs-704	7	1	a	a	DET
iajs-704	7	2	submodule	submodule	PROPN
iajs-704	7	3	n	n	PROPN
iajs-704	7	4	of	of	ADP
iajs-704	7	5	m	m	PROPN
iajs-704	7	6	is	be	AUX
iajs-704	7	7	said	say	VERB
iajs-704	7	8	to	to	PART
iajs-704	7	9	be	be	AUX
iajs-704	7	10	prime	prime	ADJ
iajs-704	7	11	if	if	SCONJ
iajs-704	7	12	a	a	DET
iajs-704	7	13	m	m	NOUN
iajs-704	7	14			NOUN
iajs-704	7	15	n	n	CCONJ
iajs-704	7	16	for	for	ADP
iajs-704	7	17	a	a	DET
iajs-704	7	18			NOUN
iajs-704	7	19	r	r	NOUN
iajs-704	7	20	,	,	PUNCT
iajs-704	7	21	m	m	VERB
iajs-704	7	22			NOUN
iajs-704	7	23	m	m	PROPN
iajs-704	7	24	,	,	PUNCT
iajs-704	7	25	then	then	ADV
iajs-704	7	26	either	either	CCONJ
iajs-704	7	27	m	m	VERB
iajs-704	7	28			NOUN
iajs-704	7	29	n	n	CCONJ
iajs-704	7	30	or	or	CCONJ
iajs-704	7	31	a	a	DET
iajs-704	7	32			NOUN
iajs-704	7	33	[	[	X
iajs-704	7	34	n	n	CCONJ
iajs-704	7	35	:	:	PUNCT
iajs-704	7	36	m	m	VERB
iajs-704	7	37	]	]	X
iajs-704	7	38	where	where	SCONJ
iajs-704	7	39	[	[	X
iajs-704	7	40	n	n	CCONJ
iajs-704	7	41	:	:	PUNCT
iajs-704	7	42	m	m	VERB
iajs-704	7	43	]	]	X
iajs-704	8	1	=	=	X
iajs-704	8	2	{	{	PUNCT
iajs-704	8	3	r	r	NOUN
iajs-704	8	4	:	:	PUNCT
iajs-704	8	5	rr	rr	NUM
iajs-704	8	6	,	,	PUNCT
iajs-704	8	7	rm	rm	PROPN
iajs-704	8	8			PROPN
iajs-704	8	9	n	n	CCONJ
iajs-704	8	10	}	}	PUNCT
iajs-704	8	11	,	,	PUNCT
iajs-704	8	12	[	[	X
iajs-704	8	13	1	1	NUM
iajs-704	8	14	]	]	PUNCT
iajs-704	8	15	,	,	PUNCT
iajs-704	8	16	[	[	X
iajs-704	8	17	2	2	NUM
iajs-704	8	18	]	]	PUNCT
iajs-704	8	19	.	.	PUNCT
iajs-704	9	1	it	it	PRON
iajs-704	9	2	was	be	AUX
iajs-704	9	3	shown	show	VERB
iajs-704	9	4	that	that	SCONJ
iajs-704	9	5	in	in	ADP
iajs-704	9	6	[	[	X
iajs-704	9	7	1	1	NUM
iajs-704	9	8	]	]	X
iajs-704	9	9	m	m	VERB
iajs-704	9	10	is	be	AUX
iajs-704	9	11	prime	prime	ADJ
iajs-704	9	12	module	module	NOUN
iajs-704	9	13	iff	iff	PROPN
iajs-704	9	14	(	(	PUNCT
iajs-704	9	15	0	0	NUM
iajs-704	9	16	)	)	PUNCT
iajs-704	9	17	is	be	AUX
iajs-704	9	18	p	p	PROPN
iajs-704	9	19	rime	rime	NOUN
iajs-704	9	20	submodule	submodule	NOUN
iajs-704	9	21	.	.	PUNCT
iajs-704	10	1	the	the	DET
iajs-704	10	2	concept	concept	NOUN
iajs-704	10	3	of	of	ADP
iajs-704	10	4	quasi	quasi	ADJ
iajs-704	10	5	-	-	ADJ
iajs-704	10	6	prime	prime	ADJ
iajs-704	10	7	module	module	NOUN
iajs-704	10	8	is	be	AUX
iajs-704	10	9	introduced	introduce	VERB
iajs-704	10	10	in	in	ADP
iajs-704	10	11	[	[	X
iajs-704	10	12	3	3	NUM
iajs-704	10	13	]	]	PUNCT
iajs-704	10	14	where	where	SCONJ
iajs-704	10	15	an	an	DET
iajs-704	10	16	r	r	NOUN
iajs-704	10	17	-	-	PUNCT
iajs-704	10	18	module	module	NOUN
iajs-704	10	19	m	m	NOUN
iajs-704	10	20	is	be	AUX
iajs-704	10	21	quasi	quasi	ADJ
iajs-704	10	22	-	-	ADJ
iajs-704	10	23	prime	prime	ADJ
iajs-704	10	24	module	module	NOUN
iajs-704	10	25	if	if	SCONJ
iajs-704	10	26	annrn	annrn	NOUN
iajs-704	10	27	is	be	AUX
iajs-704	10	28	prime	prime	ADJ
iajs-704	10	29	ideal	ideal	NOUN
iajs-704	10	30	for	for	ADP
iajs-704	10	31	every	every	DET
iajs-704	10	32	nonzero	nonzero	PROPN
iajs-704	10	33	submodule	submodule	PROPN
iajs-704	10	34	n	n	PROPN
iajs-704	10	35	of	of	ADP
iajs-704	10	36	m.	m.	NOUN
iajs-704	10	37	if	if	SCONJ
iajs-704	10	38	m	m	NOUN
iajs-704	10	39	is	be	AUX
iajs-704	10	40	quasi	quasi	ADJ
iajs-704	10	41	-	-	ADJ
iajs-704	10	42	prime	prime	ADJ
iajs-704	10	43	module	module	NOUN
iajs-704	10	44	then	then	ADV
iajs-704	10	45	annrm	annrm	NOUN
iajs-704	10	46	=	=	SYM
iajs-704	10	47	annrrm	annrrm	PROPN
iajs-704	10	48			PROPN
iajs-704	10	49	r	r	NOUN
iajs-704	10	50			NOUN
iajs-704	10	51	annrm	annrm	NOUN
iajs-704	10	52	,	,	PUNCT
iajs-704	10	53	[	[	X
iajs-704	10	54	3	3	NUM
iajs-704	10	55	]	]	PUNCT
iajs-704	10	56	.	.	PUNCT
iajs-704	11	1	but	but	CCONJ
iajs-704	11	2	the	the	DET
iajs-704	11	3	converse	converse	NOUN
iajs-704	11	4	is	be	AUX
iajs-704	11	5	not	not	PART
iajs-704	11	6	true	true	ADJ
iajs-704	11	7	for	for	ADP
iajs-704	11	8	example	example	NOUN
iajs-704	11	9	:	:	PUNCT
iajs-704	11	10	let	let	VERB
iajs-704	11	11	m	m	PRON
iajs-704	11	12	=	=	VERB
iajs-704	11	13			VERB
iajs-704	11	14	p	p	X
iajs-704	11	15	z	z	NOUN
iajs-704	11	16	as	as	SCONJ
iajs-704	11	17	z	z	NOUN
iajs-704	11	18	-	-	PUNCT
iajs-704	11	19	module	module	NOUN
iajs-704	11	20	is	be	AUX
iajs-704	11	21	not	not	PART
iajs-704	11	22	quasi	quasi	ADJ
iajs-704	11	23	-	-	ADJ
iajs-704	11	24	prime	prime	ADJ
iajs-704	11	25	module	module	NOUN
iajs-704	11	26	since	since	SCONJ
iajs-704	11	27	if	if	SCONJ
iajs-704	11	28	n	n	PROPN
iajs-704	11	29	=	=	SYM
iajs-704	11	30	<	<	X
iajs-704	11	31	1	1	NUM
iajs-704	11	32	/	/	SYM
iajs-704	11	33	p	p	NOUN
iajs-704	11	34	2	2	NUM
iajs-704	11	35	+	+	CCONJ
iajs-704	11	36	z	z	NOUN
iajs-704	11	37	>	>	SYM
iajs-704	11	38			NUM
iajs-704	11	39			VERB
iajs-704	11	40	p	p	NOUN
iajs-704	11	41	z	z	NOUN
iajs-704	11	42	.	.	PUNCT
iajs-704	12	1	so	so	ADV
iajs-704	12	2	annrn	annrn	NOUN
iajs-704	13	1	=	=	PUNCT
iajs-704	13	2	p2z	p2z	PROPN
iajs-704	13	3	is	be	AUX
iajs-704	13	4	not	not	PART
iajs-704	13	5	prime	prime	ADJ
iajs-704	13	6	ideal	ideal	NOUN
iajs-704	13	7	in	in	ADP
iajs-704	13	8	z.	z.	PROPN
iajs-704	13	9	but	but	CCONJ
iajs-704	13	10	ann	ann	PROPN
iajs-704	13	11	p	p	PROPN
iajs-704	13	12	z	z	PROPN
iajs-704	13	13	=	=	SYM
iajs-704	13	14	0	0	NUM
iajs-704	13	15	and	and	CCONJ
iajs-704	13	16			NOUN
iajs-704	13	17	r	r	NOUN
iajs-704	13	18			NOUN
iajs-704	13	19	0	0	NUM
iajs-704	13	20	,	,	PUNCT
iajs-704	13	21	let	let	VERB
iajs-704	13	22	a	a	DET
iajs-704	13	23			NOUN
iajs-704	14	1	ann	ann	PROPN
iajs-704	14	2	r	r	NOUN
iajs-704	14	3	p	p	PROPN
iajs-704	14	4	z	z	PROPN
iajs-704	15	1	so	so	ADV
iajs-704	15	2	a	a	DET
iajs-704	15	3	r	r	NOUN
iajs-704	15	4	p	p	NOUN
iajs-704	15	5	z	z	NOUN
iajs-704	15	6			NOUN
iajs-704	15	7	=	=	SYM
iajs-704	15	8	0	0	NUM
iajs-704	15	9	,	,	PUNCT
iajs-704	15	10	so	so	ADV
iajs-704	15	11	a	a	DET
iajs-704	15	12	r	r	NOUN
iajs-704	15	13			PROPN
iajs-704	15	14	ann	ann	PROPN
iajs-704	15	15	p	p	PROPN
iajs-704	15	16	z	z	PROPN
iajs-704	15	17	.	.	PUNCT
iajs-704	16	1	a	a	DET
iajs-704	16	2	r	r	NOUN
iajs-704	16	3	=	=	SYM
iajs-704	16	4	0	0	NUM
iajs-704	16	5	,	,	PUNCT
iajs-704	16	6	but	but	CCONJ
iajs-704	16	7	r	r	NOUN
iajs-704	16	8			NOUN
iajs-704	16	9	0	0	NUM
iajs-704	17	1	so	so	ADV
iajs-704	17	2	a	a	DET
iajs-704	17	3	=	=	SYM
iajs-704	17	4	0	0	NUM
iajs-704	18	1	so	so	ADV
iajs-704	18	2	ann	ann	PROPN
iajs-704	18	3	r	r	PROPN
iajs-704	18	4	p	p	ADJ
iajs-704	18	5	z	z	PROPN
iajs-704	18	6	=	=	SYM
iajs-704	18	7	0	0	PROPN
iajs-704	18	8	.	.	PUNCT
iajs-704	19	1	then	then	ADV
iajs-704	19	2	ann	ann	PROPN
iajs-704	19	3	p	p	PROPN
iajs-704	19	4	z	z	PROPN
iajs-704	20	1	=	=	SYM
iajs-704	20	2	ann	ann	PROPN
iajs-704	20	3	r	r	NOUN
iajs-704	20	4	p	p	ADJ
iajs-704	20	5	z	z	NOUN
iajs-704	20	6	.	.	PUNCT
iajs-704	21	1	2weakly	2weakly	NUM
iajs-704	21	2	quasi	quasi	ADJ
iajs-704	21	3	-	-	ADJ
iajs-704	21	4	prime	prime	ADJ
iajs-704	21	5	module	module	NOUN
iajs-704	21	6	in	in	ADP
iajs-704	21	7	this	this	DET
iajs-704	21	8	section	section	NOUN
iajs-704	21	9	we	we	PRON
iajs-704	21	10	introduce	introduce	VERB
iajs-704	21	11	the	the	DET
iajs-704	21	12	concept	concept	NOUN
iajs-704	21	13	of	of	ADP
iajs-704	21	14	weakly	weakly	ADJ
iajs-704	21	15	quasi	quasi	ADJ
iajs-704	21	16	-	-	ADJ
iajs-704	21	17	prime	prime	ADJ
iajs-704	21	18	module	module	NOUN
iajs-704	21	19	and	and	CCONJ
iajs-704	21	20	give	give	VERB
iajs-704	21	21	several	several	ADJ
iajs-704	21	22	results	result	NOUN
iajs-704	21	23	about	about	ADP
iajs-704	21	24	it	it	PRON
iajs-704	21	25	.	.	PUNCT
iajs-704	22	1	2.1	2.1	NUM
iajs-704	22	2	definition	definition	NOUN
iajs-704	22	3	:	:	PUNCT
iajs-704	22	4	an	an	DET
iajs-704	22	5	r	r	NOUN
iajs-704	22	6	-	-	PUNCT
iajs-704	22	7	module	module	NOUN
iajs-704	22	8	m	m	NOUN
iajs-704	22	9	is	be	AUX
iajs-704	22	10	called	call	VERB
iajs-704	22	11	weakly	weakly	ADJ
iajs-704	22	12	quasi	quasi	ADJ
iajs-704	22	13	-	-	ADJ
iajs-704	22	14	prime	prime	ADJ
iajs-704	22	15	module	module	NOUN
iajs-704	22	16	(	(	PUNCT
iajs-704	22	17	briefly	briefly	NOUN
iajs-704	22	18	w.q.p	w.q.p	NOUN
iajs-704	22	19	)	)	PUNCT
iajs-704	22	20	if	if	SCONJ
iajs-704	22	21	annrm	annrm	NOUN
iajs-704	22	22	=	=	SYM
iajs-704	22	23	annrrm	annrrm	NOUN
iajs-704	22	24	for	for	SCONJ
iajs-704	22	25	every	every	DET
iajs-704	22	26	r	r	NOUN
iajs-704	22	27	ann	ann	PROPN
iajs-704	22	28	rm	rm	PROPN
iajs-704	22	29	.	.	PROPN
iajs-704	22	30	recall	recall	VERB
iajs-704	22	31	that	that	SCONJ
iajs-704	22	32	if	if	SCONJ
iajs-704	22	33	r	r	NOUN
iajs-704	22	34	is	be	AUX
iajs-704	22	35	an	an	DET
iajs-704	22	36	integral	integral	ADJ
iajs-704	22	37	domain	domain	NOUN
iajs-704	22	38	,	,	PUNCT
iajs-704	22	39	an	an	DET
iajs-704	22	40	r	r	NOUN
iajs-704	22	41	-	-	PUNCT
iajs-704	22	42	module	module	NOUN
iajs-704	22	43	m	m	NOUN
iajs-704	22	44	is	be	AUX
iajs-704	22	45	said	say	VERB
iajs-704	22	46	to	to	PART
iajs-704	22	47	be	be	AUX
iajs-704	22	48	divisible	divisible	ADJ
iajs-704	22	49	iff	iff	PROPN
iajs-704	22	50	rm	rm	PROPN
iajs-704	22	51	=	=	PROPN
iajs-704	22	52	m	m	PROPN
iajs-704	22	53	for	for	ADP
iajs-704	22	54	every	every	DET
iajs-704	22	55	nonzero	nonzero	NOUN
iajs-704	22	56	element	element	NOUN
iajs-704	22	57	r	r	NOUN
iajs-704	22	58	in	in	ADP
iajs-704	22	59	r	r	NOUN
iajs-704	22	60	,	,	PUNCT
iajs-704	22	61	[	[	X
iajs-704	22	62	4,p.35	4,p.35	NOUN
iajs-704	22	63	]	]	X
iajs-704	22	64	.	.	PUNCT
iajs-704	23	1	2.2	2.2	NUM
iajs-704	23	2	examples	example	NOUN
iajs-704	23	3	and	and	CCONJ
iajs-704	23	4	remarks	remark	VERB
iajs-704	23	5	:	:	PUNCT
iajs-704	23	6	مجلة	مجلة	ADJ
iajs-704	23	7	إبن	إبن	VERB
iajs-704	23	8	الھیثم	الھیثم	NOUN
iajs-704	23	9	للعلوم	للعلوم	NOUN
iajs-704	23	10	الصرفة	الصرفة	NOUN
iajs-704	23	11	و	و	PRON
iajs-704	23	12	التطبیقیة	التطبیقیة	PROPN
iajs-704	23	13	2012	2012	NUM
iajs-704	23	14	السنة	السنة	NOUN
iajs-704	23	15	25	25	NUM
iajs-704	23	16	المجلد	المجلد	NOUN
iajs-704	23	17	1	1	NUM
iajs-704	23	18	العدد	العدد	PROPN
iajs-704	23	19	ibn	ibn	PROPN
iajs-704	23	20	al	al	PROPN
iajs-704	23	21	-	-	PUNCT
iajs-704	23	22	haitham	haitham	PROPN
iajs-704	23	23	journal	journal	PROPN
iajs-704	23	24	for	for	ADP
iajs-704	23	25	pure	pure	ADJ
iajs-704	23	26	and	and	CCONJ
iajs-704	23	27	applied	apply	VERB
iajs-704	23	28	science	science	NOUN
iajs-704	23	29	no	no	NOUN
iajs-704	23	30	.	.	NOUN
iajs-704	23	31	1	1	NUM
iajs-704	23	32	vol	vol	NOUN
iajs-704	23	33	.	.	PUNCT
iajs-704	24	1	25	25	NUM
iajs-704	24	2	year	year	NOUN
iajs-704	24	3	2012	2012	NUM
iajs-704	24	4	1	1	NUM
iajs-704	24	5	.	.	PUNCT
iajs-704	25	1	if	if	SCONJ
iajs-704	25	2	m	m	NOUN
iajs-704	25	3	is	be	AUX
iajs-704	25	4	divisible	divisible	ADJ
iajs-704	25	5	over	over	ADP
iajs-704	25	6	integral	integral	ADJ
iajs-704	25	7	domain	domain	NOUN
iajs-704	25	8	then	then	ADV
iajs-704	25	9	m	m	PROPN
iajs-704	25	10	is	be	AUX
iajs-704	25	11	w.q.p	w.q.p	NOUN
iajs-704	25	12	.	.	PROPN
iajs-704	26	1	2	2	X
iajs-704	26	2	.	.	X
iajs-704	27	1	every	every	DET
iajs-704	27	2	quasi	quasi	ADJ
iajs-704	27	3	-	-	ADJ
iajs-704	27	4	prime	prime	ADJ
iajs-704	27	5	is	be	AUX
iajs-704	27	6	w.q.p	w.q.p	NOUN
iajs-704	27	7	but	but	CCONJ
iajs-704	27	8	the	the	DET
iajs-704	27	9	converse	converse	NOUN
iajs-704	27	10	is	be	AUX
iajs-704	27	11	not	not	PART
iajs-704	27	12	true	true	ADJ
iajs-704	27	13	(	(	PUNCT
iajs-704	27	14	see	see	VERB
iajs-704	27	15	the	the	DET
iajs-704	27	16	example	example	NOUN
iajs-704	27	17	in	in	ADP
iajs-704	27	18	the	the	DET
iajs-704	27	19	introduction	introduction	NOUN
iajs-704	27	20	)	)	PUNCT
iajs-704	27	21	.	.	PUNCT
iajs-704	28	1	3	3	X
iajs-704	28	2	.	.	X
iajs-704	28	3	z	z	NOUN
iajs-704	28	4	as	as	SCONJ
iajs-704	28	5	z	z	NOUN
iajs-704	28	6	-	-	PUNCT
iajs-704	28	7	module	module	NOUN
iajs-704	28	8	is	be	AUX
iajs-704	28	9	w.q.p	w.q.p	NOUN
iajs-704	28	10	module	module	NOUN
iajs-704	28	11	since	since	SCONJ
iajs-704	28	12	annrz	annrz	PROPN
iajs-704	28	13	=	=	SYM
iajs-704	28	14	0	0	PUNCT
iajs-704	29	1	=	=	SYM
iajs-704	29	2	annr	annr	NOUN
iajs-704	29	3	rz	rz	NOUN
iajs-704	29	4	,	,	PUNCT
iajs-704	29	5			NOUN
iajs-704	29	6	r	r	PROPN
iajs-704	29	7	annrz	annrz	NOUN
iajs-704	29	8	.	.	PUNCT
iajs-704	30	1	4	4	X
iajs-704	30	2	.	.	X
iajs-704	30	3	z4	z4	PROPN
iajs-704	30	4	as	as	SCONJ
iajs-704	30	5	z	z	NOUN
iajs-704	30	6	-	-	PUNCT
iajs-704	30	7	module	module	NOUN
iajs-704	30	8	is	be	AUX
iajs-704	30	9	not	not	PART
iajs-704	30	10	w.q.p	w.q.p	NOUN
iajs-704	30	11	module	module	NOUN
iajs-704	30	12	since	since	SCONJ
iajs-704	30	13	annrz4	annrz4	PROPN
iajs-704	30	14	=	=	SYM
iajs-704	30	15	4z	4z	NOUN
iajs-704	30	16	and	and	CCONJ
iajs-704	30	17	annr2z	annr2z	NOUN
iajs-704	30	18	=	=	SYM
iajs-704	30	19	annr	annr	NOUN
iajs-704	30	20	(	(	PUNCT
iajs-704	30	21	2	2	NUM
iajs-704	30	22	)	)	PUNCT
iajs-704	30	23	=	=	NOUN
iajs-704	30	24	2z	2z	NUM
iajs-704	30	25	.	.	PUNCT
iajs-704	31	1	thus	thus	ADV
iajs-704	31	2	z4	z4	PROPN
iajs-704	31	3	as	as	SCONJ
iajs-704	31	4	z	z	NOUN
iajs-704	31	5	-	-	PUNCT
iajs-704	31	6	module	module	NOUN
iajs-704	31	7	is	be	AUX
iajs-704	31	8	not	not	PART
iajs-704	31	9	w.q.p	w.q.p	NOUN
iajs-704	31	10	module	module	NOUN
iajs-704	31	11	.	.	PUNCT
iajs-704	32	1	5	5	NUM
iajs-704	32	2	.	.	X
iajs-704	32	3	z6	z6	PROPN
iajs-704	32	4	as	as	SCONJ
iajs-704	32	5	z	z	NOUN
iajs-704	32	6	-	-	PUNCT
iajs-704	32	7	module	module	NOUN
iajs-704	32	8	is	be	AUX
iajs-704	32	9	not	not	PART
iajs-704	32	10	w.q.p	w.q.p	NOUN
iajs-704	32	11	module	module	NOUN
iajs-704	32	12	since	since	SCONJ
iajs-704	32	13	annz6	annz6	PROPN
iajs-704	33	1	=	=	SYM
iajs-704	33	2	6z	6z	NOUN
iajs-704	33	3	and	and	CCONJ
iajs-704	33	4	ann2z6	ann2z6	NOUN
iajs-704	33	5	=	=	SYM
iajs-704	33	6	ann	ann	PROPN
iajs-704	33	7	(	(	PUNCT
iajs-704	33	8	2	2	NUM
iajs-704	33	9	)	)	PUNCT
iajs-704	33	10	=	=	SYM
iajs-704	33	11	3z	3z	NUM
iajs-704	33	12	,	,	PUNCT
iajs-704	33	13	so	so	ADV
iajs-704	33	14	annz6	annz6	PROPN
iajs-704	33	15	ann	ann	PROPN
iajs-704	33	16	2z6	2z6	NUM
iajs-704	33	17	.	.	PUNCT
iajs-704	34	1	6	6	NUM
iajs-704	34	2	.	.	X
iajs-704	34	3	zn	zn	PROPN
iajs-704	34	4	as	as	ADP
iajs-704	34	5	z	z	NOUN
iajs-704	34	6	-	-	PUNCT
iajs-704	34	7	module	module	NOUN
iajs-704	34	8	is	be	AUX
iajs-704	34	9	w.q.p	w.q.p	NOUN
iajs-704	34	10	module	module	NOUN
iajs-704	34	11	iff	iff	PROPN
iajs-704	34	12	n	n	PRON
iajs-704	34	13	is	be	AUX
iajs-704	34	14	prime	prime	ADJ
iajs-704	34	15	.	.	PUNCT
iajs-704	35	1	7	7	X
iajs-704	35	2	.	.	X
iajs-704	35	3	let	let	VERB
iajs-704	35	4	m	m	PRON
iajs-704	35	5	=	=	VERB
iajs-704	35	6	zzp	zzp	NOUN
iajs-704	35	7	;	;	PUNCT
iajs-704	35	8	p	p	PRON
iajs-704	35	9	is	be	AUX
iajs-704	35	10	prime	prime	ADJ
iajs-704	35	11	number	number	NOUN
iajs-704	35	12	is	be	AUX
iajs-704	35	13	w.q.p	w.q.p	NOUN
iajs-704	35	14	module	module	NOUN
iajs-704	35	15	since	since	SCONJ
iajs-704	35	16	annm	annm	NOUN
iajs-704	35	17	=	=	SYM
iajs-704	35	18	ann	ann	PROPN
iajs-704	35	19	rm	rm	PROPN
iajs-704	35	20	=	=	NOUN
iajs-704	35	21	0	0	PROPN
iajs-704	35	22	for	for	ADP
iajs-704	35	23	each	each	PRON
iajs-704	35	24	r	r	NOUN
iajs-704	35	25			NOUN
iajs-704	35	26	ann(z	ann(z	PROPN
iajs-704	35	27	zp	zp	PROPN
iajs-704	35	28	)	)	PUNCT
iajs-704	35	29	.	.	PUNCT
iajs-704	36	1	8	8	X
iajs-704	36	2	.	.	X
iajs-704	37	1			VERB
iajs-704	37	2	p	p	X
iajs-704	37	3	z	z	NOUN
iajs-704	37	4	is	be	AUX
iajs-704	37	5	w.q.p	w.q.p	NOUN
iajs-704	37	6	module	module	NOUN
iajs-704	37	7	since	since	SCONJ
iajs-704	37	8	ann	ann	PROPN
iajs-704	37	9			PROPN
iajs-704	37	10	p	p	NOUN
iajs-704	37	11	z	z	NOUN
iajs-704	37	12	=	=	SYM
iajs-704	37	13	ann	ann	PROPN
iajs-704	37	14	r	r	NOUN
iajs-704	37	15			NOUN
iajs-704	37	16	p	p	NOUN
iajs-704	37	17	z	z	NOUN
iajs-704	37	18	=	=	SYM
iajs-704	37	19	0	0	NUM
iajs-704	37	20	.	.	X
iajs-704	37	21	2.3	2.3	NUM
iajs-704	37	22	note	note	NOUN
iajs-704	37	23	:	:	PUNCT
iajs-704	37	24	let	let	VERB
iajs-704	37	25	m	m	PRON
iajs-704	37	26	be	be	AUX
iajs-704	37	27	w.q.p	w.q.p	NOUN
iajs-704	37	28	over	over	ADP
iajs-704	37	29	integral	integral	ADJ
iajs-704	37	30	domain	domain	NOUN
iajs-704	37	31	in	in	ADP
iajs-704	37	32	r.	r.	PROPN
iajs-704	37	33	then	then	ADV
iajs-704	37	34	every	every	DET
iajs-704	37	35	divisible	divisible	ADJ
iajs-704	37	36	submodule	submodule	NOUN
iajs-704	37	37	of	of	ADP
iajs-704	37	38	w.q.p	w.q.p	PROPN
iajs-704	37	39	module	module	NOUN
iajs-704	37	40	.	.	PUNCT
iajs-704	38	1	recall	recall	VERB
iajs-704	38	2	that	that	SCONJ
iajs-704	38	3	a	a	DET
iajs-704	38	4	proper	proper	ADJ
iajs-704	38	5	submodule	submodule	NOUN
iajs-704	38	6	n	n	PROPN
iajs-704	38	7	of	of	ADP
iajs-704	38	8	m	m	PROPN
iajs-704	38	9	is	be	AUX
iajs-704	38	10	called	call	VERB
iajs-704	38	11	semi	semi	ADJ
iajs-704	38	12	-	-	ADJ
iajs-704	38	13	prime	prime	ADJ
iajs-704	38	14	submodule	submodule	NOUN
iajs-704	38	15	if	if	SCONJ
iajs-704	38	16	every	every	DET
iajs-704	38	17	r	r	NOUN
iajs-704	38	18			NOUN
iajs-704	38	19	r	r	NOUN
iajs-704	38	20	,	,	PUNCT
iajs-704	38	21	x	x	SYM
iajs-704	38	22			PROPN
iajs-704	38	23	m	m	PROPN
iajs-704	38	24	,	,	PUNCT
iajs-704	38	25	k	k	PROPN
iajs-704	38	26			PROPN
iajs-704	38	27	z+	z+	NUM
iajs-704	38	28	,	,	PUNCT
iajs-704	38	29	such	such	ADJ
iajs-704	38	30	that	that	SCONJ
iajs-704	38	31	rkx	rkx	PROPN
iajs-704	38	32			PROPN
iajs-704	38	33	n	n	CCONJ
iajs-704	38	34	,	,	PUNCT
iajs-704	38	35	then	then	ADV
iajs-704	38	36	rx	rx	VERB
iajs-704	38	37			PROPN
iajs-704	38	38	n	n	CCONJ
iajs-704	38	39	,	,	PUNCT
iajs-704	38	40	[	[	X
iajs-704	38	41	4,p	4,p	NUM
iajs-704	38	42	.50	.50	NUM
iajs-704	38	43	]	]	PUNCT
iajs-704	38	44	.	.	PUNCT
iajs-704	39	1	2.4	2.4	NUM
iajs-704	39	2	proposition	proposition	NOUN
iajs-704	39	3	:	:	PUNCT
iajs-704	39	4	let	let	VERB
iajs-704	39	5	m	m	PRON
iajs-704	39	6	be	be	AUX
iajs-704	39	7	divisible	divisible	ADJ
iajs-704	39	8	and	and	CCONJ
iajs-704	39	9	(	(	PUNCT
iajs-704	39	10	0	0	NUM
iajs-704	39	11	)	)	PUNCT
iajs-704	39	12	submodule	submodule	NOUN
iajs-704	39	13	of	of	ADP
iajs-704	39	14	m	m	PROPN
iajs-704	39	15	is	be	AUX
iajs-704	39	16	semi	semi	ADJ
iajs-704	39	17	-	-	ADJ
iajs-704	39	18	prime	prime	ADJ
iajs-704	39	19	submodule	submodule	NOUN
iajs-704	39	20	,	,	PUNCT
iajs-704	39	21	then	then	ADV
iajs-704	39	22	the	the	DET
iajs-704	39	23	following	following	ADJ
iajs-704	39	24	statements	statement	NOUN
iajs-704	39	25	are	be	AUX
iajs-704	39	26	equivalent	equivalent	ADJ
iajs-704	39	27	1	1	NUM
iajs-704	39	28	.	.	PUNCT
iajs-704	40	1	m	m	PROPN
iajs-704	40	2	is	be	AUX
iajs-704	40	3	prime	prime	ADJ
iajs-704	40	4	module	module	NOUN
iajs-704	40	5	,	,	PUNCT
iajs-704	40	6	2	2	NUM
iajs-704	40	7	.	.	X
iajs-704	41	1	m	m	PROPN
iajs-704	41	2	is	be	AUX
iajs-704	41	3	q.p	q.p	PROPN
iajs-704	41	4	module	module	NOUN
iajs-704	41	5	,	,	PUNCT
iajs-704	41	6	3	3	NUM
iajs-704	41	7	.	.	X
iajs-704	42	1	m	m	PROPN
iajs-704	42	2	is	be	AUX
iajs-704	42	3	w.q.p	w.q.p	NOUN
iajs-704	42	4	module	module	NOUN
iajs-704	42	5	.	.	PUNCT
iajs-704	43	1	proof	proof	NOUN
iajs-704	43	2	:(	:(	PROPN
iajs-704	43	3	1	1	X
iajs-704	43	4	)	)	PUNCT
iajs-704	43	5	→	→	X
iajs-704	43	6	(	(	PUNCT
iajs-704	43	7	2	2	NUM
iajs-704	43	8	)	)	PUNCT
iajs-704	43	9	,	,	PUNCT
iajs-704	43	10	by	by	ADP
iajs-704	43	11	[	[	X
iajs-704	43	12	2,p10	2,p10	NUM
iajs-704	43	13	]	]	X
iajs-704	43	14	(	(	PUNCT
iajs-704	43	15	2	2	NUM
iajs-704	43	16	)	)	PUNCT
iajs-704	43	17	→	→	X
iajs-704	43	18	(	(	PUNCT
iajs-704	43	19	3	3	NUM
iajs-704	43	20	)	)	PUNCT
iajs-704	43	21	,	,	PUNCT
iajs-704	43	22	by	by	ADP
iajs-704	43	23	[	[	X
iajs-704	43	24	2,p20	2,p20	NOUN
iajs-704	43	25	]	]	SYM
iajs-704	43	26	(	(	PUNCT
iajs-704	43	27	3	3	NUM
iajs-704	43	28	)	)	PUNCT
iajs-704	43	29	→	→	X
iajs-704	43	30	(	(	PUNCT
iajs-704	43	31	1	1	NUM
iajs-704	43	32	)	)	PUNCT
iajs-704	43	33	to	to	PART
iajs-704	43	34	prove	prove	VERB
iajs-704	43	35	m	m	NOUN
iajs-704	43	36	is	be	AUX
iajs-704	43	37	prime	prime	ADJ
iajs-704	43	38	module	module	NOUN
iajs-704	43	39	,	,	PUNCT
iajs-704	43	40	i.e.	i.e.	X
iajs-704	43	41	to	to	PART
iajs-704	43	42	show	show	VERB
iajs-704	43	43	that	that	SCONJ
iajs-704	43	44	(	(	PUNCT
iajs-704	43	45	0	0	NUM
iajs-704	43	46	)	)	PUNCT
iajs-704	43	47	is	be	AUX
iajs-704	43	48	p	p	PROPN
iajs-704	43	49	rime	rime	NOUN
iajs-704	43	50	submodule	submodule	NOUN
iajs-704	43	51	.	.	PUNCT
iajs-704	44	1	let	let	VERB
iajs-704	44	2	rm	rm	PROPN
iajs-704	44	3	=	=	PUNCT
iajs-704	44	4	0	0	PROPN
iajs-704	44	5	,	,	PUNCT
iajs-704	44	6	r	r	NOUN
iajs-704	44	7			PROPN
iajs-704	44	8	r	r	NOUN
iajs-704	44	9	,	,	PUNCT
iajs-704	44	10	m	m	VERB
iajs-704	44	11			NOUN
iajs-704	44	12	m	m	PROPN
iajs-704	44	13	,	,	PUNCT
iajs-704	44	14	to	to	PART
iajs-704	44	15	prove	prove	VERB
iajs-704	44	16	either	either	DET
iajs-704	44	17	m	m	PROPN
iajs-704	44	18	=	=	SYM
iajs-704	44	19	0	0	NUM
iajs-704	44	20	or	or	CCONJ
iajs-704	44	21	r	r	NOUN
iajs-704	44	22			NOUN
iajs-704	44	23	annrm	annrm	NOUN
iajs-704	44	24	.	.	PUNCT
iajs-704	45	1	suppose	suppose	VERB
iajs-704	45	2	r	r	NOUN
iajs-704	45	3			NOUN
iajs-704	45	4	annrm	annrm	NOUN
iajs-704	45	5	,	,	PUNCT
iajs-704	45	6	so	so	SCONJ
iajs-704	45	7	we	we	PRON
iajs-704	45	8	must	must	AUX
iajs-704	45	9	prove	prove	VERB
iajs-704	45	10	that	that	SCONJ
iajs-704	45	11	m	m	VERB
iajs-704	45	12	=	=	NOUN
iajs-704	45	13	0	0	X
iajs-704	45	14	.	.	PUNCT
iajs-704	46	1	since	since	SCONJ
iajs-704	46	2	r	r	NOUN
iajs-704	46	3			NOUN
iajs-704	46	4	annrm	annrm	NOUN
iajs-704	46	5	,	,	PUNCT
iajs-704	46	6	rm	rm	PROPN
iajs-704	46	7			PROPN
iajs-704	46	8	0	0	NUM
iajs-704	46	9	.	.	PUNCT
iajs-704	46	10	hence	hence	ADV
iajs-704	46	11	rm	rm	PROPN
iajs-704	46	12	=	=	PUNCT
iajs-704	46	13	m	m	PROPN
iajs-704	46	14	,	,	PUNCT
iajs-704	46	15	because	because	SCONJ
iajs-704	46	16	m	m	PROPN
iajs-704	46	17	is	be	AUX
iajs-704	46	18	divisible	divisible	ADJ
iajs-704	46	19	.	.	PUNCT
iajs-704	47	1	thus	thus	ADV
iajs-704	47	2	m	m	PROPN
iajs-704	47	3	=	=	SYM
iajs-704	47	4	rm1	rm1	PROPN
iajs-704	47	5	for	for	ADP
iajs-704	47	6	some	some	DET
iajs-704	47	7	m1	m1	PROPN
iajs-704	47	8			NOUN
iajs-704	47	9	m.	m.	NOUN
iajs-704	47	10	since	since	SCONJ
iajs-704	47	11	rm	rm	PROPN
iajs-704	47	12	=	=	PUNCT
iajs-704	47	13	r(rm1	r(rm1	NOUN
iajs-704	47	14	)	)	PUNCT
iajs-704	47	15	=	=	SYM
iajs-704	48	1	0	0	NUM
iajs-704	48	2	,	,	PUNCT
iajs-704	48	3	that	that	PRON
iajs-704	48	4	is	be	AUX
iajs-704	48	5	r2m1	r2m1	ADV
iajs-704	48	6	=	=	SYM
iajs-704	48	7	0	0	NUM
iajs-704	48	8	which	which	PRON
iajs-704	48	9	implies	imply	VERB
iajs-704	48	10	that	that	PRON
iajs-704	48	11	rm1	rm1	PROPN
iajs-704	48	12	=	=	SYM
iajs-704	48	13	0	0	PROPN
iajs-704	48	14	,	,	PUNCT
iajs-704	48	15	since	since	SCONJ
iajs-704	48	16	(	(	PUNCT
iajs-704	48	17	0	0	NUM
iajs-704	48	18	)	)	PUNCT
iajs-704	48	19	submodule	submodule	NOUN
iajs-704	48	20	of	of	ADP
iajs-704	48	21	m	m	PROPN
iajs-704	48	22	is	be	AUX
iajs-704	48	23	semi	semi	ADJ
iajs-704	48	24	-	-	ADJ
iajs-704	48	25	prime	prime	ADJ
iajs-704	48	26	.	.	PUNCT
iajs-704	49	1	thus	thus	ADV
iajs-704	49	2	m	m	VERB
iajs-704	49	3	=	=	ADJ
iajs-704	49	4	0	0	NUM
iajs-704	49	5	.	.	X
iajs-704	49	6	2.5	2.5	NUM
iajs-704	49	7	remark	remark	NOUN
iajs-704	49	8	:	:	PUNCT
iajs-704	49	9	the	the	DET
iajs-704	49	10	condition	condition	NOUN
iajs-704	49	11	in	in	ADP
iajs-704	49	12	proposition	proposition	NOUN
iajs-704	49	13	2.4	2.4	NUM
iajs-704	49	14	is	be	AUX
iajs-704	49	15	necessary	necessary	ADJ
iajs-704	49	16	as	as	SCONJ
iajs-704	49	17	the	the	DET
iajs-704	49	18	following	follow	VERB
iajs-704	49	19	example	example	NOUN
iajs-704	49	20	shows	show	VERB
iajs-704	49	21	:	:	PUNCT
iajs-704	49	22			VERB
iajs-704	49	23	p	p	ADP
iajs-704	49	24	z	z	NOUN
iajs-704	49	25	is	be	AUX
iajs-704	49	26	not	not	PART
iajs-704	49	27	q.p	q.p	PROPN
iajs-704	49	28	since	since	SCONJ
iajs-704	49	29	if	if	SCONJ
iajs-704	49	30	n	n	NOUN
iajs-704	49	31	=	=	SYM
iajs-704	49	32	2	2	NUM
iajs-704	49	33	1	1	NUM
iajs-704	49	34	p	p	NOUN
iajs-704	50	1	+	+	NOUN
iajs-704	50	2	z	z	NOUN
iajs-704	50	3	then	then	ADV
iajs-704	50	4	ann	ann	PROPN
iajs-704	50	5	n	n	PROPN
iajs-704	50	6	=	=	PUNCT
iajs-704	50	7	p2z	p2z	PROPN
iajs-704	50	8	is	be	AUX
iajs-704	50	9	not	not	PART
iajs-704	50	10	prime	prime	ADJ
iajs-704	50	11	ideal	ideal	NOUN
iajs-704	50	12	,	,	PUNCT
iajs-704	50	13	but	but	CCONJ
iajs-704	50	14			VERB
iajs-704	50	15	p	p	X
iajs-704	50	16	z	z	NOUN
iajs-704	50	17	is	be	AUX
iajs-704	50	18	w.q.p	w.q.p	NOUN
iajs-704	50	19	module	module	NOUN
iajs-704	50	20	(	(	PUNCT
iajs-704	50	21	see	see	VERB
iajs-704	50	22	the	the	DET
iajs-704	50	23	example	example	NOUN
iajs-704	50	24	in	in	ADP
iajs-704	50	25	the	the	DET
iajs-704	50	26	introduction	introduction	NOUN
iajs-704	50	27	)	)	PUNCT
iajs-704	50	28	.	.	PUNCT
iajs-704	51	1	2.6	2.6	NUM
iajs-704	51	2	theorem	theorem	VERB
iajs-704	51	3	:	:	PUNCT
iajs-704	51	4	let	let	VERB
iajs-704	51	5	m	m	PRON
iajs-704	51	6	be	be	AUX
iajs-704	51	7	a	a	DET
iajs-704	51	8	module	module	NOUN
iajs-704	51	9	over	over	ADP
iajs-704	51	10	an	an	DET
iajs-704	51	11	integral	integral	ADJ
iajs-704	51	12	domain	domain	NOUN
iajs-704	51	13	r	r	NOUN
iajs-704	51	14	and	and	CCONJ
iajs-704	51	15	every	every	DET
iajs-704	51	16	submodule	submodule	NOUN
iajs-704	51	17	of	of	ADP
iajs-704	51	18	m	m	PROPN
iajs-704	51	19	is	be	AUX
iajs-704	51	20	divisible	divisible	ADJ
iajs-704	51	21	then	then	ADV
iajs-704	51	22	ann	ann	PROPN
iajs-704	51	23	(	(	PUNCT
iajs-704	51	24	rm	rm	PROPN
iajs-704	51	25	)	)	PUNCT
iajs-704	51	26	=	=	NOUN
iajs-704	51	27	ann	ann	X
iajs-704	51	28	(	(	PUNCT
iajs-704	51	29	m	m	PROPN
iajs-704	51	30	)	)	PUNCT
iajs-704	51	31	,	,	PUNCT
iajs-704	51	32	for	for	ADP
iajs-704	51	33	each	each	DET
iajs-704	51	34	r	r	NOUN
iajs-704	51	35			NOUN
iajs-704	51	36	ann	ann	PROPN
iajs-704	51	37	(	(	PUNCT
iajs-704	51	38	m	m	PROPN
iajs-704	51	39	)	)	PUNCT
iajs-704	51	40	.	.	PUNCT
iajs-704	52	1	proof	proof	NOUN
iajs-704	52	2	:	:	PUNCT
iajs-704	52	3	since	since	SCONJ
iajs-704	52	4	(	(	PUNCT
iajs-704	52	5	rm	rm	NOUN
iajs-704	52	6	)	)	PUNCT
iajs-704	52	7			PROPN
iajs-704	52	8	(	(	PUNCT
iajs-704	52	9	m	m	NOUN
iajs-704	52	10	)	)	PUNCT
iajs-704	52	11	,	,	PUNCT
iajs-704	52	12	so	so	ADV
iajs-704	52	13	ann(m	ann(m	PROPN
iajs-704	52	14	)	)	PUNCT
iajs-704	52	15			PROPN
iajs-704	52	16	ann	ann	PROPN
iajs-704	52	17	(	(	PUNCT
iajs-704	52	18	rm	rm	PROPN
iajs-704	52	19	)	)	PUNCT
iajs-704	52	20	…	…	PUNCT
iajs-704	52	21	(	(	PUNCT
iajs-704	52	22	1	1	NUM
iajs-704	52	23	)	)	PUNCT
iajs-704	52	24	to	to	PART
iajs-704	52	25	prove	prove	VERB
iajs-704	52	26	ann	ann	PROPN
iajs-704	52	27	(	(	PUNCT
iajs-704	52	28	rm	rm	PROPN
iajs-704	52	29	)	)	PUNCT
iajs-704	52	30			PROPN
iajs-704	52	31	ann	ann	PROPN
iajs-704	52	32	(	(	PUNCT
iajs-704	52	33	m	m	PROPN
iajs-704	52	34	)	)	PUNCT
iajs-704	52	35	let	let	VERB
iajs-704	52	36	x	x	PUNCT
iajs-704	52	37			PROPN
iajs-704	52	38	ann	ann	PROPN
iajs-704	52	39	(	(	PUNCT
iajs-704	52	40	rm	rm	PROPN
iajs-704	52	41	)	)	PUNCT
iajs-704	52	42	so	so	ADV
iajs-704	52	43	x	x	X
iajs-704	52	44	(	(	PUNCT
iajs-704	52	45	rm	rm	NOUN
iajs-704	52	46	)	)	PUNCT
iajs-704	52	47	=	=	NOUN
iajs-704	53	1	0	0	X
iajs-704	53	2	.	.	PUNCT
iajs-704	54	1	since	since	SCONJ
iajs-704	54	2	every	every	DET
iajs-704	54	3	submodule	submodule	NOUN
iajs-704	54	4	of	of	ADP
iajs-704	54	5	m	m	PROPN
iajs-704	54	6	is	be	AUX
iajs-704	54	7	divisible	divisible	ADJ
iajs-704	54	8	,	,	PUNCT
iajs-704	54	9	(	(	PUNCT
iajs-704	54	10	rm	rm	NOUN
iajs-704	54	11	)	)	PUNCT
iajs-704	54	12	=	=	PUNCT
iajs-704	54	13	(	(	PUNCT
iajs-704	54	14	m	m	NOUN
iajs-704	54	15	)	)	PUNCT
iajs-704	54	16	and	and	CCONJ
iajs-704	55	1	so	so	ADV
iajs-704	55	2	xm	xm	PROPN
iajs-704	55	3	=	=	PUNCT
iajs-704	55	4	0	0	NUM
iajs-704	55	5	which	which	PRON
iajs-704	55	6	implies	imply	VERB
iajs-704	55	7	x	x	PUNCT
iajs-704	55	8			PROPN
iajs-704	55	9	ann	ann	PROPN
iajs-704	55	10	(	(	PUNCT
iajs-704	55	11	m	m	PROPN
iajs-704	55	12	)	)	PUNCT
iajs-704	55	13	.	.	PUNCT
iajs-704	56	1	thus	thus	ADV
iajs-704	56	2	ann(rm	ann(rm	ADV
iajs-704	56	3	)	)	PUNCT
iajs-704	56	4			PROPN
iajs-704	56	5	ann(m	ann(m	PROPN
iajs-704	56	6	)	)	PUNCT
iajs-704	56	7	…	…	PUNCT
iajs-704	56	8	(	(	PUNCT
iajs-704	56	9	2	2	NUM
iajs-704	56	10	)	)	PUNCT
iajs-704	56	11	from	from	ADP
iajs-704	56	12	(	(	PUNCT
iajs-704	56	13	1	1	NUM
iajs-704	56	14	)	)	PUNCT
iajs-704	56	15	and	and	CCONJ
iajs-704	56	16	(	(	PUNCT
iajs-704	56	17	2	2	NUM
iajs-704	56	18	)	)	PUNCT
iajs-704	56	19	,	,	PUNCT
iajs-704	56	20	we	we	PRON
iajs-704	56	21	have	have	VERB
iajs-704	56	22	ann	ann	PROPN
iajs-704	56	23	(	(	PUNCT
iajs-704	56	24	m	m	NOUN
iajs-704	56	25	)	)	PUNCT
iajs-704	56	26	=	=	SYM
iajs-704	57	1	ann(rm	ann(rm	NOUN
iajs-704	57	2	)	)	PUNCT
iajs-704	57	3	,	,	PUNCT
iajs-704	57	4	for	for	ADP
iajs-704	57	5	each	each	DET
iajs-704	57	6	r	r	NOUN
iajs-704	57	7			NOUN
iajs-704	57	8	ann	ann	PROPN
iajs-704	57	9	(	(	PUNCT
iajs-704	57	10	m	m	PROPN
iajs-704	57	11	)	)	PUNCT
iajs-704	57	12	.	.	PUNCT
iajs-704	58	1	recall	recall	VERB
iajs-704	58	2	that	that	SCONJ
iajs-704	58	3	an	an	DET
iajs-704	58	4	r	r	NOUN
iajs-704	58	5	-	-	PUNCT
iajs-704	58	6	module	module	NOUN
iajs-704	58	7	m	m	NOUN
iajs-704	58	8	is	be	AUX
iajs-704	58	9	called	call	VERB
iajs-704	58	10	multiplication	multiplication	NOUN
iajs-704	58	11	r	r	NOUN
iajs-704	58	12	-	-	PUNCT
iajs-704	58	13	module	module	NOUN
iajs-704	58	14	if	if	SCONJ
iajs-704	58	15	for	for	ADP
iajs-704	58	16	every	every	DET
iajs-704	58	17	submodule	submodule	NOUN
iajs-704	58	18	n	n	PROPN
iajs-704	58	19	of	of	ADP
iajs-704	58	20	m	m	PROPN
iajs-704	58	21	,	,	PUNCT
iajs-704	58	22	there	there	PRON
iajs-704	58	23	exists	exist	VERB
iajs-704	58	24	an	an	DET
iajs-704	58	25	ideal	ideal	NOUN
iajs-704	58	26	i	i	PRON
iajs-704	58	27	of	of	ADP
iajs-704	58	28	r	r	NOUN
iajs-704	59	1	such	such	ADJ
iajs-704	59	2	that	that	SCONJ
iajs-704	59	3	i	i	PRON
iajs-704	59	4	m	m	VERB
iajs-704	59	5	=	=	VERB
iajs-704	59	6	n.	n.	ADJ
iajs-704	59	7	مجلة	مجلة	NOUN
iajs-704	59	8	إبن	إبن	VERB
iajs-704	59	9	الھیثم	الھیثم	NOUN
iajs-704	59	10	للعلوم	للعلوم	NOUN
iajs-704	59	11	الصرفة	الصرفة	NOUN
iajs-704	59	12	و	و	PRON
iajs-704	59	13	التطبیقیة	التطبیقیة	PROPN
iajs-704	59	14	2012	2012	NUM
iajs-704	59	15	السنة	السنة	NOUN
iajs-704	60	1	25	25	NUM
iajs-704	60	2	المجلد	المجلد	NOUN
iajs-704	60	3	1	1	NUM
iajs-704	60	4	العدد	العدد	PROPN
iajs-704	60	5	ibn	ibn	PROPN
iajs-704	60	6	al	al	PROPN
iajs-704	60	7	-	-	PUNCT
iajs-704	60	8	haitham	haitham	PROPN
iajs-704	60	9	journal	journal	PROPN
iajs-704	60	10	for	for	ADP
iajs-704	60	11	pure	pure	ADJ
iajs-704	60	12	and	and	CCONJ
iajs-704	60	13	applied	apply	VERB
iajs-704	60	14	science	science	NOUN
iajs-704	60	15	no	no	NOUN
iajs-704	60	16	.	.	NOUN
iajs-704	60	17	1	1	NUM
iajs-704	60	18	vol	vol	NOUN
iajs-704	60	19	.	.	PUNCT
iajs-704	61	1	25	25	NUM
iajs-704	61	2	year	year	NOUN
iajs-704	61	3	2012	2012	NUM
iajs-704	61	4	2.7	2.7	NUM
iajs-704	61	5	theorem	theorem	VERB
iajs-704	61	6	:	:	PUNCT
iajs-704	61	7	let	let	VERB
iajs-704	61	8	m	m	PRON
iajs-704	61	9	be	be	AUX
iajs-704	61	10	multiplication	multiplication	NOUN
iajs-704	61	11	w.q.p	w.q.p	NOUN
iajs-704	61	12	r	r	NOUN
iajs-704	61	13	-	-	PUNCT
iajs-704	61	14	module	module	NOUN
iajs-704	61	15	.	.	PUNCT
iajs-704	62	1	then	then	ADV
iajs-704	62	2	every	every	DET
iajs-704	62	3	submodule	submodule	NOUN
iajs-704	62	4	of	of	ADP
iajs-704	62	5	m	m	PROPN
iajs-704	62	6	is	be	AUX
iajs-704	62	7	w,.q.p	w,.q.p	NOUN
iajs-704	62	8	module	module	NOUN
iajs-704	62	9	.	.	PUNCT
iajs-704	63	1	proof	proof	NOUN
iajs-704	63	2	:	:	PUNCT
iajs-704	63	3	let	let	VERB
iajs-704	63	4	n	n	PRON
iajs-704	63	5	be	be	AUX
iajs-704	63	6	submodule	submodule	NOUN
iajs-704	63	7	of	of	ADP
iajs-704	63	8	m	m	PROPN
iajs-704	63	9	,	,	PUNCT
iajs-704	63	10	since	since	SCONJ
iajs-704	63	11	m	m	PROPN
iajs-704	63	12	is	be	AUX
iajs-704	63	13	multiplication	multiplication	NOUN
iajs-704	63	14	r	r	NOUN
iajs-704	63	15	-	-	PUNCT
iajs-704	63	16	module	module	NOUN
iajs-704	63	17	,	,	PUNCT
iajs-704	63	18	so	so	SCONJ
iajs-704	63	19	n	n	NOUN
iajs-704	63	20	=	=	VERB
iajs-704	64	1	i	i	NOUN
iajs-704	64	2	m	m	PROPN
iajs-704	64	3	;	;	PUNCT
iajs-704	64	4	i	i	PRON
iajs-704	64	5	be	be	VERB
iajs-704	64	6	ideal	ideal	ADJ
iajs-704	64	7	of	of	ADP
iajs-704	64	8	ring	ring	PROPN
iajs-704	64	9	r.	r.	PROPN
iajs-704	64	10	to	to	PART
iajs-704	64	11	prove	prove	VERB
iajs-704	64	12	n	n	PROPN
iajs-704	64	13	is	be	AUX
iajs-704	64	14	w.q.p	w.q.p	NOUN
iajs-704	64	15	module	module	NOUN
iajs-704	64	16	.	.	PUNCT
iajs-704	65	1	to	to	PART
iajs-704	65	2	prove	prove	VERB
iajs-704	65	3	annrn	annrn	NOUN
iajs-704	66	1	=	=	SYM
iajs-704	66	2	annrrn	annrrn	NOUN
iajs-704	66	3	,	,	PUNCT
iajs-704	66	4			NOUN
iajs-704	66	5	r	r	ADJ
iajs-704	66	6	annrn	annrn	NOUN
iajs-704	66	7	since	since	SCONJ
iajs-704	66	8	rn	rn	PROPN
iajs-704	66	9			PROPN
iajs-704	66	10	n	n	PROPN
iajs-704	66	11	so	so	ADV
iajs-704	66	12	annrn	annrn	NOUN
iajs-704	66	13			PROPN
iajs-704	66	14	annrrn	annrrn	PROPN
iajs-704	66	15	…	…	PUNCT
iajs-704	66	16	(	(	PUNCT
iajs-704	66	17	1	1	NUM
iajs-704	66	18	)	)	PUNCT
iajs-704	66	19	to	to	PART
iajs-704	66	20	prove	prove	VERB
iajs-704	66	21	annrrn	annrrn	PROPN
iajs-704	66	22			PROPN
iajs-704	66	23	annrn	annrn	NOUN
iajs-704	66	24	.	.	PUNCT
iajs-704	67	1	let	let	VERB
iajs-704	67	2	x	x	PRON
iajs-704	67	3			NOUN
iajs-704	67	4	annrrn	annrrn	NOUN
iajs-704	67	5	so	so	ADV
iajs-704	67	6	xrn	xrn	ADV
iajs-704	67	7	=	=	SYM
iajs-704	68	1	0	0	X
iajs-704	68	2	.	.	PUNCT
iajs-704	69	1	since	since	SCONJ
iajs-704	69	2	m	m	PROPN
iajs-704	69	3	is	be	AUX
iajs-704	69	4	multiplication	multiplication	NOUN
iajs-704	69	5	so	so	SCONJ
iajs-704	69	6	there	there	PRON
iajs-704	69	7	exists	exist	VERB
iajs-704	69	8	an	an	DET
iajs-704	69	9	ideal	ideal	NOUN
iajs-704	69	10	i	i	PRON
iajs-704	69	11	of	of	ADP
iajs-704	69	12	r	r	NOUN
iajs-704	70	1	such	such	ADJ
iajs-704	70	2	that	that	SCONJ
iajs-704	70	3	n	n	NOUN
iajs-704	70	4	=	=	SYM
iajs-704	70	5	i	i	PRON
iajs-704	70	6	m.	m.	NOUN
iajs-704	70	7	thus	thus	ADV
iajs-704	70	8	xrim	xrim	PROPN
iajs-704	71	1	=	=	SYM
iajs-704	71	2	0	0	NUM
iajs-704	71	3	;	;	PUNCT
iajs-704	71	4	that	that	PRON
iajs-704	71	5	is	be	AUX
iajs-704	71	6	xi	xi	ADP
iajs-704	71	7			PROPN
iajs-704	71	8	annrrm	annrrm	PROPN
iajs-704	71	9	=	=	SYM
iajs-704	71	10	annrm	annrm	NOUN
iajs-704	71	11	,	,	PUNCT
iajs-704	71	12	hence	hence	ADV
iajs-704	71	13	xim	xim	PROPN
iajs-704	71	14	=	=	SYM
iajs-704	71	15	0	0	NUM
iajs-704	71	16	;	;	PUNCT
iajs-704	71	17	so	so	ADV
iajs-704	71	18	xn	xn	PUNCT
iajs-704	72	1	=	=	SYM
iajs-704	72	2	0	0	NUM
iajs-704	72	3	which	which	PRON
iajs-704	72	4	implies	imply	VERB
iajs-704	72	5	x	x	PUNCT
iajs-704	72	6			NOUN
iajs-704	72	7	annrn	annrn	NOUN
iajs-704	72	8	.	.	PUNCT
iajs-704	73	1	thus	thus	ADV
iajs-704	73	2	annrrn	annrrn	PRON
iajs-704	73	3			PROPN
iajs-704	73	4	annrn	annrn	NOUN
iajs-704	73	5	…	…	PUNCT
iajs-704	73	6	(	(	PUNCT
iajs-704	73	7	2	2	NUM
iajs-704	73	8	)	)	PUNCT
iajs-704	73	9	from	from	ADP
iajs-704	73	10	(	(	PUNCT
iajs-704	73	11	1	1	NUM
iajs-704	73	12	)	)	PUNCT
iajs-704	73	13	and	and	CCONJ
iajs-704	73	14	(	(	PUNCT
iajs-704	73	15	2	2	X
iajs-704	73	16	)	)	PUNCT
iajs-704	73	17	we	we	PRON
iajs-704	73	18	have	have	VERB
iajs-704	73	19	annrn	annrn	NOUN
iajs-704	73	20	=	=	PUNCT
iajs-704	74	1	annrrn	annrrn	NOUN
iajs-704	74	2	so	so	ADV
iajs-704	74	3	n	n	PROPN
iajs-704	74	4	is	be	AUX
iajs-704	74	5	w.q.p	w.q.p	NOUN
iajs-704	74	6	module	module	NOUN
iajs-704	74	7	.	.	PUNCT
iajs-704	75	1	2.8	2.8	NUM
iajs-704	75	2	proposition	proposition	NOUN
iajs-704	75	3	:	:	PUNCT
iajs-704	75	4	let	let	VERB
iajs-704	75	5	m	m	PRON
iajs-704	75	6	be	be	AUX
iajs-704	75	7	cyclic	cyclic	ADJ
iajs-704	75	8	w.q.p	w.q.p	NOUN
iajs-704	75	9	r	r	NOUN
iajs-704	75	10	-	-	PUNCT
iajs-704	75	11	module	module	NOUN
iajs-704	75	12	.	.	PUNCT
iajs-704	76	1	then	then	ADV
iajs-704	76	2	m	m	PROPN
iajs-704	76	3	is	be	AUX
iajs-704	76	4	q.p	q.p	PROPN
iajs-704	76	5	module	module	NOUN
iajs-704	76	6	.	.	PUNCT
iajs-704	77	1	proof	proof	NOUN
iajs-704	77	2	:	:	PUNCT
iajs-704	77	3	let	let	VERB
iajs-704	77	4	m	m	PRON
iajs-704	77	5	be	be	AUX
iajs-704	77	6	cyclic	cyclic	ADJ
iajs-704	77	7	so	so	SCONJ
iajs-704	77	8	there	there	PRON
iajs-704	77	9	exist	exist	VERB
iajs-704	77	10	x	x	PUNCT
iajs-704	77	11			NOUN
iajs-704	77	12	m	m	NOUN
iajs-704	77	13	;	;	PUNCT
iajs-704	77	14	m	m	VERB
iajs-704	77	15	=	=	SYM
iajs-704	77	16	(	(	PUNCT
iajs-704	77	17	x	x	NOUN
iajs-704	77	18	)	)	PUNCT
iajs-704	77	19	,	,	PUNCT
iajs-704	77	20	let	let	VERB
iajs-704	77	21	y	y	PRON
iajs-704	77	22			PROPN
iajs-704	77	23	m	m	PROPN
iajs-704	77	24	,	,	PUNCT
iajs-704	77	25	to	to	PART
iajs-704	77	26	prove	prove	VERB
iajs-704	77	27	annry	annry	NOUN
iajs-704	77	28	is	be	AUX
iajs-704	77	29	prime	prime	ADJ
iajs-704	77	30	ideal	ideal	NOUN
iajs-704	77	31	,	,	PUNCT
iajs-704	77	32	so	so	ADV
iajs-704	77	33	y	y	PROPN
iajs-704	77	34	=	=	PUNCT
iajs-704	77	35	rx	rx	PROPN
iajs-704	77	36	;	;	PUNCT
iajs-704	77	37	r	r	NOUN
iajs-704	77	38			PROPN
iajs-704	77	39	r	r	NOUN
iajs-704	77	40	,	,	PUNCT
iajs-704	77	41	let	let	VERB
iajs-704	77	42	a	a	DET
iajs-704	77	43	,	,	PUNCT
iajs-704	77	44	b	b	PROPN
iajs-704	77	45			PROPN
iajs-704	77	46	annry	annry	NOUN
iajs-704	77	47	,	,	PUNCT
iajs-704	77	48	to	to	PART
iajs-704	77	49	prove	prove	VERB
iajs-704	77	50	either	either	CCONJ
iajs-704	77	51	a	a	DET
iajs-704	77	52			NOUN
iajs-704	77	53	annry	annry	NOUN
iajs-704	77	54	or	or	CCONJ
iajs-704	77	55	b	b	NOUN
iajs-704	77	56			NOUN
iajs-704	77	57	annry	annry	NOUN
iajs-704	77	58	.	.	PUNCT
iajs-704	78	1	since	since	SCONJ
iajs-704	78	2	ab	ab	PROPN
iajs-704	78	3			PROPN
iajs-704	78	4	annry	annry	NOUN
iajs-704	78	5	=	=	NOUN
iajs-704	78	6	annrrx	annrrx	NOUN
iajs-704	78	7	,	,	PUNCT
iajs-704	78	8	so	so	ADV
iajs-704	78	9	abrx	abrx	ADJ
iajs-704	78	10	=	=	NOUN
iajs-704	78	11	0	0	X
iajs-704	78	12	.	.	PUNCT
iajs-704	78	13	suppose	suppose	VERB
iajs-704	78	14	b	b	X
iajs-704	78	15			NOUN
iajs-704	78	16	annry	annry	NOUN
iajs-704	78	17	=	=	NOUN
iajs-704	78	18	annrrx	annrrx	NOUN
iajs-704	78	19	,	,	PUNCT
iajs-704	78	20	i.e	i.e	PRON
iajs-704	78	21	brx	brx	ADJ
iajs-704	78	22	≠	≠	PROPN
iajs-704	78	23	0	0	NUM
iajs-704	78	24	,	,	PUNCT
iajs-704	78	25	so	so	SCONJ
iajs-704	78	26	ab	ab	PROPN
iajs-704	78	27			PROPN
iajs-704	78	28	annr(rx	annr(rx	PROPN
iajs-704	78	29	)	)	PUNCT
iajs-704	78	30	=	=	SYM
iajs-704	78	31	annr(x	annr(x	NOUN
iajs-704	78	32	)	)	PUNCT
iajs-704	78	33	,	,	PUNCT
iajs-704	78	34	since	since	SCONJ
iajs-704	78	35	m	m	PROPN
iajs-704	78	36	is	be	AUX
iajs-704	78	37	w.q.p	w.q.p	NOUN
iajs-704	78	38	module	module	NOUN
iajs-704	78	39	,	,	PUNCT
iajs-704	78	40	so	so	ADV
iajs-704	78	41	abx	abx	NOUN
iajs-704	78	42	=	=	SYM
iajs-704	78	43	0	0	NUM
iajs-704	78	44	which	which	PRON
iajs-704	78	45	implies	imply	VERB
iajs-704	78	46	that	that	SCONJ
iajs-704	78	47	a	a	DET
iajs-704	78	48	annrbx=	annrbx=	ADJ
iajs-704	78	49	annr(x	annr(x	NOUN
iajs-704	78	50	)	)	PUNCT
iajs-704	78	51	(	(	PUNCT
iajs-704	78	52	since	since	SCONJ
iajs-704	78	53	m	m	PROPN
iajs-704	78	54	is	be	AUX
iajs-704	78	55	w.q.p	w.q.p	NOUN
iajs-704	78	56	)	)	PUNCT
iajs-704	78	57	.	.	PUNCT
iajs-704	79	1	thus	thus	ADV
iajs-704	79	2	ax	ax	NOUN
iajs-704	79	3	=	=	SYM
iajs-704	79	4	0	0	NUM
iajs-704	79	5	which	which	PRON
iajs-704	79	6	implies	imply	VERB
iajs-704	79	7	rax	rax	NOUN
iajs-704	79	8	=	=	SYM
iajs-704	79	9	r.0	r.0	PROPN
iajs-704	79	10	=	=	SYM
iajs-704	79	11	0	0	PUNCT
iajs-704	80	1	so	so	ADV
iajs-704	80	2	a	a	DET
iajs-704	80	3			NOUN
iajs-704	80	4	ann	ann	PROPN
iajs-704	80	5	(	(	PUNCT
iajs-704	80	6	rx	rx	PROPN
iajs-704	80	7	)	)	PUNCT
iajs-704	80	8	which	which	PRON
iajs-704	80	9	means	mean	VERB
iajs-704	80	10	a	a	DET
iajs-704	80	11			NOUN
iajs-704	80	12	annry	annry	NOUN
iajs-704	80	13	.	.	PUNCT
iajs-704	81	1	2.9	2.9	NUM
iajs-704	81	2	theorem	theorem	VERB
iajs-704	81	3	:	:	PUNCT
iajs-704	81	4	let	let	VERB
iajs-704	81	5	m	m	PRON
iajs-704	81	6	be	be	AUX
iajs-704	81	7	cyclic	cyclic	ADJ
iajs-704	81	8	r	r	NOUN
iajs-704	81	9	-	-	PUNCT
iajs-704	81	10	module	module	NOUN
iajs-704	81	11	then	then	ADV
iajs-704	81	12	the	the	DET
iajs-704	81	13	following	following	ADJ
iajs-704	81	14	statements	statement	NOUN
iajs-704	81	15	are	be	AUX
iajs-704	81	16	equivalent	equivalent	ADJ
iajs-704	81	17	1	1	NUM
iajs-704	81	18	.	.	PUNCT
iajs-704	82	1	m	m	PROPN
iajs-704	82	2	is	be	AUX
iajs-704	82	3	prime	prime	ADJ
iajs-704	82	4	module	module	NOUN
iajs-704	82	5	2	2	NUM
iajs-704	82	6	.	.	PUNCT
iajs-704	82	7	annrm	annrm	NOUN
iajs-704	82	8	=	=	SYM
iajs-704	82	9	annrim	annrim	NOUN
iajs-704	82	10	;	;	PUNCT
iajs-704	83	1	i	i	PRON
iajs-704	83	2	⊈	⊈	PROPN
iajs-704	83	3	annrn	annrn	NOUN
iajs-704	83	4	3	3	NUM
iajs-704	83	5	.	.	PUNCT
iajs-704	83	6	m	m	PROPN
iajs-704	83	7	is	be	AUX
iajs-704	83	8	w.q.p	w.q.p	NOUN
iajs-704	83	9	module	module	NOUN
iajs-704	83	10	.	.	PUNCT
iajs-704	84	1	proof	proof	NOUN
iajs-704	84	2	:	:	PUNCT
iajs-704	84	3	to	to	PART
iajs-704	84	4	prove	prove	VERB
iajs-704	84	5	(	(	PUNCT
iajs-704	84	6	1	1	NUM
iajs-704	84	7	)	)	PUNCT
iajs-704	84	8	→	→	X
iajs-704	84	9	(	(	PUNCT
iajs-704	84	10	2	2	X
iajs-704	84	11	)	)	PUNCT
iajs-704	84	12	it	it	PRON
iajs-704	84	13	is	be	AUX
iajs-704	84	14	clear	clear	ADJ
iajs-704	84	15	by	by	ADP
iajs-704	84	16	definition	definition	NOUN
iajs-704	84	17	of	of	ADP
iajs-704	84	18	prime	prime	ADJ
iajs-704	84	19	submodules	submodule	NOUN
iajs-704	84	20	.	.	PUNCT
iajs-704	85	1	(	(	PUNCT
iajs-704	85	2	2	2	X
iajs-704	85	3	)	)	PUNCT
iajs-704	85	4			NOUN
iajs-704	85	5	(	(	PUNCT
iajs-704	85	6	3	3	X
iajs-704	85	7	)	)	PUNCT
iajs-704	85	8	it	it	PRON
iajs-704	85	9	is	be	AUX
iajs-704	85	10	obvious	obvious	ADJ
iajs-704	85	11	.	.	PUNCT
iajs-704	86	1	to	to	PART
iajs-704	86	2	prove	prove	VERB
iajs-704	86	3	(	(	PUNCT
iajs-704	86	4	3	3	NUM
iajs-704	86	5	)	)	PUNCT
iajs-704	86	6			NOUN
iajs-704	87	1	(	(	PUNCT
iajs-704	87	2	1	1	NUM
iajs-704	87	3	)	)	PUNCT
iajs-704	87	4	,	,	PUNCT
iajs-704	87	5	to	to	PART
iajs-704	87	6	prove	prove	VERB
iajs-704	87	7	m	m	NOUN
iajs-704	87	8	is	be	AUX
iajs-704	87	9	prime	prime	ADJ
iajs-704	87	10	module	module	NOUN
iajs-704	87	11	.	.	PUNCT
iajs-704	88	1	by	by	ADP
iajs-704	88	2	proposition	proposition	NOUN
iajs-704	88	3	(	(	PUNCT
iajs-704	88	4	2.8	2.8	NUM
iajs-704	88	5	)	)	PUNCT
iajs-704	88	6	we	we	PRON
iajs-704	88	7	have	have	VERB
iajs-704	88	8	m	m	PROPN
iajs-704	88	9	is	be	AUX
iajs-704	88	10	q.p	q.p	PROPN
iajs-704	88	11	module	module	NOUN
iajs-704	88	12	which	which	PRON
iajs-704	88	13	implies	imply	VERB
iajs-704	88	14	that	that	SCONJ
iajs-704	88	15	annrm	annrm	NOUN
iajs-704	88	16	is	be	AUX
iajs-704	88	17	prime	prime	ADJ
iajs-704	88	18	ideal	ideal	ADJ
iajs-704	88	19	,	,	PUNCT
iajs-704	88	20	see	see	VERB
iajs-704	88	21	[	[	X
iajs-704	88	22	3,p.14	3,p.14	NUM
iajs-704	88	23	]	]	PUNCT
iajs-704	88	24	and	and	CCONJ
iajs-704	88	25	by	by	ADP
iajs-704	88	26	[	[	X
iajs-704	88	27	3,p.8	3,p.8	NUM
iajs-704	88	28	]	]	X
iajs-704	88	29	we	we	PRON
iajs-704	88	30	get	get	VERB
iajs-704	88	31	m	m	NOUN
iajs-704	88	32	is	be	AUX
iajs-704	88	33	a	a	DET
iajs-704	88	34	prime	prime	ADJ
iajs-704	88	35	module	module	NOUN
iajs-704	88	36	.	.	PUNCT
iajs-704	89	1	2.10	2.10	NUM
iajs-704	89	2	theorem	theorem	VERB
iajs-704	89	3	:	:	PUNCT
iajs-704	89	4	the	the	DET
iajs-704	89	5	direct	direct	ADJ
iajs-704	89	6	sum	sum	NOUN
iajs-704	89	7	of	of	ADP
iajs-704	89	8	two	two	NUM
iajs-704	89	9	w.q.p	w.q.p	NOUN
iajs-704	89	10	r	r	NOUN
iajs-704	89	11	-	-	PUNCT
iajs-704	89	12	module	module	NOUN
iajs-704	89	13	is	be	AUX
iajs-704	89	14	also	also	ADV
iajs-704	89	15	w.q.p	w.q.p	NOUN
iajs-704	89	16	r	r	NOUN
iajs-704	89	17	-	-	PUNCT
iajs-704	89	18	module	module	NOUN
iajs-704	89	19	.	.	PUNCT
iajs-704	90	1	proof	proof	NOUN
iajs-704	90	2	:	:	PUNCT
iajs-704	90	3	let	let	VERB
iajs-704	90	4	m	m	VERB
iajs-704	90	5	=	=	VERB
iajs-704	90	6	m	m	PROPN
iajs-704	90	7	1	1	NUM
iajs-704	90	8			ADJ
iajs-704	90	9	m	m	VERB
iajs-704	90	10	2	2	NUM
iajs-704	90	11	where	where	SCONJ
iajs-704	90	12	m	m	VERB
iajs-704	90	13	1	1	NUM
iajs-704	90	14	and	and	CCONJ
iajs-704	90	15	m	m	PROPN
iajs-704	90	16	2	2	NUM
iajs-704	90	17	are	be	AUX
iajs-704	90	18	two	two	NUM
iajs-704	90	19	w.q.p	w.q.p	NOUN
iajs-704	90	20	module	module	NOUN
iajs-704	90	21	,	,	PUNCT
iajs-704	90	22	to	to	PART
iajs-704	90	23	prove	prove	VERB
iajs-704	90	24	m	m	NOUN
iajs-704	90	25	is	be	AUX
iajs-704	90	26	w.q.p	w.q.p	NOUN
iajs-704	90	27	module	module	NOUN
iajs-704	90	28	,	,	PUNCT
iajs-704	90	29	i.e	i.e	X
iajs-704	90	30	to	to	PART
iajs-704	90	31	prove	prove	VERB
iajs-704	90	32	annrm	annrm	NOUN
iajs-704	90	33	=	=	SYM
iajs-704	90	34	annrrm	annrrm	NOUN
iajs-704	90	35	,	,	PUNCT
iajs-704	90	36	for	for	ADP
iajs-704	90	37	all	all	DET
iajs-704	90	38	r	r	NOUN
iajs-704	90	39			NOUN
iajs-704	90	40	annrm	annrm	NOUN
iajs-704	90	41	.	.	PUNCT
iajs-704	91	1	annrrm	annrrm	NOUN
iajs-704	91	2	=	=	PUNCT
iajs-704	91	3	annrr(m	annrr(m	NOUN
iajs-704	91	4	1	1	NUM
iajs-704	91	5			PROPN
iajs-704	91	6	m	m	VERB
iajs-704	91	7	2	2	NUM
iajs-704	91	8	)	)	PUNCT
iajs-704	92	1	=	=	SYM
iajs-704	92	2	annr(rm	annr(rm	PROPN
iajs-704	92	3	1	1	NUM
iajs-704	92	4			PROPN
iajs-704	92	5	rm	rm	NOUN
iajs-704	92	6	2	2	NUM
iajs-704	92	7	)	)	PUNCT
iajs-704	92	8	,	,	PUNCT
iajs-704	92	9	see	see	VERB
iajs-704	92	10	[	[	X
iajs-704	92	11	2	2	NUM
iajs-704	92	12	,	,	PUNCT
iajs-704	92	13	p.80	p.80	ADP
iajs-704	92	14	]	]	X
iajs-704	92	15	=	=	SYM
iajs-704	92	16	annrrm	annrrm	PROPN
iajs-704	92	17	1	1	NUM
iajs-704	92	18			NOUN
iajs-704	92	19	annrrm	annrrm	NOUN
iajs-704	92	20	2	2	NUM
iajs-704	92	21	,	,	PUNCT
iajs-704	92	22	see	see	VERB
iajs-704	92	23	[	[	X
iajs-704	92	24	2	2	NUM
iajs-704	92	25	,	,	PUNCT
iajs-704	92	26	p.83	p.83	PROPN
iajs-704	92	27	]	]	X
iajs-704	92	28	=	=	SYM
iajs-704	92	29	annrm	annrm	NOUN
iajs-704	92	30	1	1	NUM
iajs-704	92	31			PUNCT
iajs-704	92	32	annrm	annrm	NOUN
iajs-704	92	33	2	2	NUM
iajs-704	92	34	,	,	PUNCT
iajs-704	92	35	since	since	SCONJ
iajs-704	92	36	m	m	PROPN
iajs-704	92	37	1	1	NUM
iajs-704	92	38	and	and	CCONJ
iajs-704	92	39	m2	m2	PROPN
iajs-704	92	40	are	be	AUX
iajs-704	92	41	w.q.p	w.q.p	NOUN
iajs-704	93	1	=	=	PUNCT
iajs-704	93	2	annr(m	annr(m	NUM
iajs-704	93	3	1	1	NUM
iajs-704	93	4			VERB
iajs-704	93	5	m	m	VERB
iajs-704	93	6	2	2	NUM
iajs-704	93	7	)	)	PUNCT
iajs-704	93	8	=	=	SYM
iajs-704	93	9	annrm	annrm	PROPN
iajs-704	93	10	2.11	2.11	NUM
iajs-704	93	11	corollary	corollary	NOUN
iajs-704	93	12	:	:	PUNCT
iajs-704	93	13	let	let	VERB
iajs-704	93	14	m	m	PRON
iajs-704	93	15	be	be	AUX
iajs-704	93	16	an	an	DET
iajs-704	93	17	r	r	NOUN
iajs-704	93	18	-	-	PUNCT
iajs-704	93	19	module	module	NOUN
iajs-704	93	20	if	if	SCONJ
iajs-704	93	21	m	m	NOUN
iajs-704	93	22	is	be	AUX
iajs-704	93	23	w.q.p	w.q.p	NOUN
iajs-704	93	24	module	module	NOUN
iajs-704	93	25	then	then	ADV
iajs-704	93	26	for	for	ADP
iajs-704	93	27	any	any	DET
iajs-704	93	28	positive	positive	ADJ
iajs-704	93	29	integer	integer	NOUN
iajs-704	93	30	n	n	CCONJ
iajs-704	93	31	,	,	PUNCT
iajs-704	93	32	m	m	VERB
iajs-704	93	33	n	n	VERB
iajs-704	93	34	is	be	AUX
iajs-704	93	35	w.q.p	w.q.p	NOUN
iajs-704	93	36	module	module	NOUN
iajs-704	93	37	where	where	SCONJ
iajs-704	93	38	m	m	VERB
iajs-704	93	39	n	n	VERB
iajs-704	93	40	is	be	AUX
iajs-704	93	41	the	the	DET
iajs-704	93	42	direct	direct	ADJ
iajs-704	93	43	sum	sum	NOUN
iajs-704	93	44	of	of	ADP
iajs-704	93	45	n	n	NOUN
iajs-704	93	46	copies	copy	NOUN
iajs-704	93	47	of	of	ADP
iajs-704	93	48	m	m	PROPN
iajs-704	93	49	.	.	PUNCT
iajs-704	94	1	2.12	2.12	NUM
iajs-704	94	2	remark	remark	NOUN
iajs-704	94	3	:	:	PUNCT
iajs-704	94	4	مجلة	مجلة	NOUN
iajs-704	94	5	إبن	إبن	VERB
iajs-704	94	6	الھیثم	الھیثم	NOUN
iajs-704	94	7	للعلوم	للعلوم	NOUN
iajs-704	94	8	الصرفة	الصرفة	NOUN
iajs-704	94	9	و	و	PRON
iajs-704	94	10	التطبیقیة	التطبیقیة	PROPN
iajs-704	94	11	2012	2012	NUM
iajs-704	94	12	السنة	السنة	NOUN
iajs-704	94	13	25	25	NUM
iajs-704	94	14	المجلد	المجلد	NOUN
iajs-704	94	15	1	1	NUM
iajs-704	94	16	العدد	العدد	PROPN
iajs-704	94	17	ibn	ibn	PROPN
iajs-704	94	18	al	al	PROPN
iajs-704	94	19	-	-	PUNCT
iajs-704	94	20	haitham	haitham	PROPN
iajs-704	94	21	journal	journal	PROPN
iajs-704	94	22	for	for	ADP
iajs-704	94	23	pure	pure	ADJ
iajs-704	94	24	and	and	CCONJ
iajs-704	94	25	applied	apply	VERB
iajs-704	94	26	science	science	NOUN
iajs-704	94	27	no	no	NOUN
iajs-704	94	28	.	.	NOUN
iajs-704	94	29	1	1	NUM
iajs-704	94	30	vol	vol	NOUN
iajs-704	94	31	.	.	PUNCT
iajs-704	94	32	25	25	NUM
iajs-704	94	33	year	year	NOUN
iajs-704	94	34	2012	2012	NUM
iajs-704	94	35	a	a	DET
iajs-704	94	36	direct	direct	ADJ
iajs-704	94	37	summand	summand	NOUN
iajs-704	94	38	of	of	ADP
iajs-704	94	39	w.q.p	w.q.p	NOUN
iajs-704	94	40	module	module	NOUN
iajs-704	94	41	is	be	AUX
iajs-704	94	42	need	need	AUX
iajs-704	94	43	not	not	PART
iajs-704	94	44	be	be	AUX
iajs-704	94	45	w.q.p	w.q.p	NOUN
iajs-704	94	46	module	module	NOUN
iajs-704	94	47	.	.	PUNCT
iajs-704	95	1	for	for	ADP
iajs-704	95	2	example	example	NOUN
iajs-704	95	3	:	:	PUNCT
iajs-704	95	4	let	let	VERB
iajs-704	95	5	m	m	VERB
iajs-704	95	6	=	=	SYM
iajs-704	96	1	z	z	PROPN
iajs-704	96	2			PROPN
iajs-704	96	3	z4	z4	PROPN
iajs-704	96	4	so	so	SCONJ
iajs-704	96	5	annrm	annrm	PROPN
iajs-704	96	6	=	=	SYM
iajs-704	96	7	annrrm	annrrm	PROPN
iajs-704	96	8			PROPN
iajs-704	96	9	r	r	NOUN
iajs-704	96	10			NOUN
iajs-704	96	11	annrm	annrm	NOUN
iajs-704	96	12	.	.	PUNCT
iajs-704	97	1	but	but	CCONJ
iajs-704	97	2	z4	z4	PROPN
iajs-704	97	3	is	be	AUX
iajs-704	97	4	not	not	PART
iajs-704	97	5	w.q.p	w.q.p	NOUN
iajs-704	97	6	module	module	NOUN
iajs-704	97	7	,	,	PUNCT
iajs-704	97	8	(	(	PUNCT
iajs-704	97	9	see	see	VERB
iajs-704	97	10	remarks	remark	NOUN
iajs-704	97	11	and	and	CCONJ
iajs-704	97	12	examples	example	NOUN
iajs-704	97	13	(	(	PUNCT
iajs-704	97	14	2.2(4	2.2(4	NUM
iajs-704	97	15	)	)	PUNCT
iajs-704	97	16	)	)	PUNCT
iajs-704	97	17	.	.	PUNCT
iajs-704	98	1	2.13	2.13	NUM
iajs-704	98	2	theorem	theorem	VERB
iajs-704	98	3	:	:	PUNCT
iajs-704	98	4	let	let	VERB
iajs-704	98	5	m	m	PROPN
iajs-704	98	6	1	1	NUM
iajs-704	98	7	;	;	PUNCT
iajs-704	98	8	m	m	VERB
iajs-704	98	9	2	2	NUM
iajs-704	98	10	then	then	ADV
iajs-704	98	11	m1	m1	PROPN
iajs-704	98	12	is	be	AUX
iajs-704	98	13	w.q.p	w.q.p	PROPN
iajs-704	98	14	iff	iff	PROPN
iajs-704	98	15	m2	m2	PROPN
iajs-704	98	16	is	be	AUX
iajs-704	98	17	w.q.p	w.q.p	NOUN
iajs-704	98	18	.	.	PUNCT
iajs-704	99	1	proof	proof	NOUN
iajs-704	99	2	:	:	PUNCT
iajs-704	99	3			NOUN
iajs-704	99	4	let	let	VERB
iajs-704	99	5	f	f	X
iajs-704	99	6	:	:	PUNCT
iajs-704	99	7	m	m	PROPN
iajs-704	99	8	1	1	NUM
iajs-704	99	9	→	→	SYM
iajs-704	99	10	m	m	NUM
iajs-704	99	11	2	2	NUM
iajs-704	99	12	be	be	VERB
iajs-704	99	13	1	1	NUM
iajs-704	99	14	-	-	SYM
iajs-704	99	15	1	1	NUM
iajs-704	99	16	and	and	CCONJ
iajs-704	99	17	onto	onto	ADP
iajs-704	99	18	and	and	CCONJ
iajs-704	99	19	homomorphisim	homomorphisim	NOUN
iajs-704	99	20	and	and	CCONJ
iajs-704	99	21	m2	m2	PROPN
iajs-704	99	22	is	be	AUX
iajs-704	99	23	w.q.p	w.q.p	NOUN
iajs-704	99	24	.	.	PUNCT
iajs-704	100	1	to	to	PART
iajs-704	100	2	prove	prove	VERB
iajs-704	100	3	m	m	PROPN
iajs-704	100	4	1	1	NUM
iajs-704	100	5	=	=	SYM
iajs-704	100	6	f	f	X
iajs-704	100	7	–	–	PUNCT
iajs-704	100	8	1(m	1(m	NUM
iajs-704	100	9	2	2	NUM
iajs-704	100	10	)	)	PUNCT
iajs-704	100	11	is	be	AUX
iajs-704	100	12	w.q.p	w.q.p	NOUN
iajs-704	100	13	module	module	NOUN
iajs-704	100	14	,	,	PUNCT
iajs-704	100	15	that	that	PRON
iajs-704	100	16	is	be	AUX
iajs-704	100	17	to	to	PART
iajs-704	100	18	prove	prove	VERB
iajs-704	100	19	annrrf	annrrf	VERB
iajs-704	100	20	–	–	PUNCT
iajs-704	100	21	1(m	1(m	NUM
iajs-704	100	22	2	2	NUM
iajs-704	100	23	)	)	PUNCT
iajs-704	100	24			PROPN
iajs-704	100	25	annrf	annrf	ADJ
iajs-704	100	26	–	–	PUNCT
iajs-704	100	27	1(m	1(m	NUM
iajs-704	100	28	2	2	NUM
iajs-704	100	29	)	)	PUNCT
iajs-704	100	30	;	;	PUNCT
iajs-704	100	31	rannrf	rannrf	NUM
iajs-704	100	32	–	–	PUNCT
iajs-704	100	33	1(m2	1(m2	NUM
iajs-704	100	34	)	)	PUNCT
iajs-704	100	35	,	,	PUNCT
iajs-704	100	36	let	let	VERB
iajs-704	100	37	x	x	PUNCT
iajs-704	100	38			NOUN
iajs-704	100	39	annr	annr	NOUN
iajs-704	100	40	r	r	NOUN
iajs-704	100	41	f	f	PROPN
iajs-704	100	42	–	–	PUNCT
iajs-704	100	43	1(m	1(m	NUM
iajs-704	100	44	2	2	NUM
iajs-704	100	45	)	)	PUNCT
iajs-704	101	1	so	so	ADV
iajs-704	101	2	xrf	xrf	PROPN
iajs-704	101	3	–	–	PUNCT
iajs-704	101	4	1(m	1(m	NUM
iajs-704	101	5	2	2	NUM
iajs-704	101	6	)	)	PUNCT
iajs-704	101	7	=	=	SYM
iajs-704	101	8	0	0	PUNCT
iajs-704	102	1	and	and	CCONJ
iajs-704	102	2	since	since	SCONJ
iajs-704	102	3	f	f	PROPN
iajs-704	102	4	–	–	PUNCT
iajs-704	102	5	1is	1is	ADJ
iajs-704	102	6	homomorphisim	homomorphisim	NOUN
iajs-704	103	1	so	so	SCONJ
iajs-704	103	2	f	f	PROPN
iajs-704	103	3	–	–	PUNCT
iajs-704	103	4	1(xrm	1(xrm	NUM
iajs-704	103	5	2	2	NUM
iajs-704	103	6	)	)	PUNCT
iajs-704	103	7	=	=	PUNCT
iajs-704	103	8	f-1(0	f-1(0	X
iajs-704	103	9	)	)	PUNCT
iajs-704	103	10	and	and	CCONJ
iajs-704	103	11	since	since	SCONJ
iajs-704	103	12	f	f	PROPN
iajs-704	103	13	–	–	PUNCT
iajs-704	103	14	1	1	NUM
iajs-704	103	15	is	be	AUX
iajs-704	103	16	1	1	NUM
iajs-704	103	17	-	-	SYM
iajs-704	103	18	1	1	NUM
iajs-704	103	19	so	so	ADV
iajs-704	103	20	xrm	xrm	NOUN
iajs-704	103	21	2	2	NUM
iajs-704	103	22	=	=	SYM
iajs-704	103	23	0	0	NUM
iajs-704	103	24	which	which	PRON
iajs-704	103	25	mean	mean	VERB
iajs-704	103	26	x	x	SYM
iajs-704	103	27			PROPN
iajs-704	103	28	annrrm	annrrm	NOUN
iajs-704	103	29	2	2	NUM
iajs-704	103	30	but	but	CCONJ
iajs-704	103	31	m	m	PRON
iajs-704	103	32	2	2	NUM
iajs-704	103	33	is	be	AUX
iajs-704	103	34	w.q.p	w.q.p	NOUN
iajs-704	103	35	module	module	NOUN
iajs-704	103	36	and	and	CCONJ
iajs-704	103	37	rannrm	rannrm	PROPN
iajs-704	103	38	2	2	NUM
iajs-704	103	39	then	then	ADV
iajs-704	103	40	xm	xm	PROPN
iajs-704	103	41	2	2	NUM
iajs-704	103	42	=	=	SYM
iajs-704	103	43	0	0	NUM
iajs-704	103	44	which	which	PRON
iajs-704	103	45	implies	imply	VERB
iajs-704	103	46	f	f	PROPN
iajs-704	103	47	–	–	PUNCT
iajs-704	103	48	1	1	NUM
iajs-704	103	49	(	(	PUNCT
iajs-704	103	50	xm	xm	PROPN
iajs-704	103	51	2	2	NUM
iajs-704	103	52	)	)	PUNCT
iajs-704	103	53	=	=	SYM
iajs-704	103	54	f	f	X
iajs-704	103	55	–	–	PUNCT
iajs-704	103	56	1	1	NUM
iajs-704	103	57	(	(	PUNCT
iajs-704	103	58	0	0	NUM
iajs-704	103	59	)	)	PUNCT
iajs-704	103	60	,	,	PUNCT
iajs-704	103	61	but	but	CCONJ
iajs-704	103	62	f	f	X
iajs-704	103	63	–	–	PUNCT
iajs-704	103	64	1	1	NUM
iajs-704	103	65	is	be	AUX
iajs-704	103	66	homomorphisim	homomorphisim	NOUN
iajs-704	104	1	so	so	SCONJ
iajs-704	104	2	x	x	SYM
iajs-704	104	3	f	f	X
iajs-704	104	4	–	–	PUNCT
iajs-704	104	5	1	1	NUM
iajs-704	104	6	(	(	PUNCT
iajs-704	104	7	m	m	NOUN
iajs-704	104	8	2	2	NUM
iajs-704	104	9	)	)	PUNCT
iajs-704	104	10	=	=	SYM
iajs-704	104	11	0	0	NUM
iajs-704	104	12	implies	imply	VERB
iajs-704	104	13	x	x	PUNCT
iajs-704	104	14			NOUN
iajs-704	104	15	annrf	annrf	ADJ
iajs-704	104	16	–	–	PUNCT
iajs-704	104	17	1	1	NUM
iajs-704	104	18	(	(	PUNCT
iajs-704	104	19	m	m	NOUN
iajs-704	104	20	2	2	NUM
iajs-704	104	21	)	)	PUNCT
iajs-704	104	22	so	so	ADV
iajs-704	105	1	annrr	annrr	PROPN
iajs-704	105	2	f	f	PROPN
iajs-704	105	3	–	–	PUNCT
iajs-704	105	4	1(m	1(m	NUM
iajs-704	105	5	2	2	NUM
iajs-704	105	6	)	)	PUNCT
iajs-704	105	7			PROPN
iajs-704	105	8	annr	annr	PROPN
iajs-704	105	9	f	f	PROPN
iajs-704	105	10	–	–	PUNCT
iajs-704	105	11	1(m	1(m	NUM
iajs-704	105	12	2	2	NUM
iajs-704	105	13	)	)	PUNCT
iajs-704	105	14	…	…	PUNCT
iajs-704	105	15	(	(	PUNCT
iajs-704	105	16	1	1	NUM
iajs-704	105	17	)	)	PUNCT
iajs-704	105	18	and	and	CCONJ
iajs-704	105	19	since	since	SCONJ
iajs-704	105	20	r	r	PROPN
iajs-704	105	21	f	f	PROPN
iajs-704	105	22	–	–	PUNCT
iajs-704	105	23	1(m	1(m	NUM
iajs-704	105	24	2	2	NUM
iajs-704	105	25	)	)	PUNCT
iajs-704	105	26			PROPN
iajs-704	105	27	f	f	PROPN
iajs-704	105	28	–	–	PUNCT
iajs-704	105	29	1(m	1(m	NUM
iajs-704	105	30	2	2	NUM
iajs-704	105	31	)	)	PUNCT
iajs-704	105	32	,	,	PUNCT
iajs-704	105	33	so	so	ADV
iajs-704	105	34	annrf	annrf	ADJ
iajs-704	105	35	–	–	PUNCT
iajs-704	105	36	1(m	1(m	NUM
iajs-704	105	37	2	2	NUM
iajs-704	105	38	)	)	PUNCT
iajs-704	105	39			PROPN
iajs-704	105	40	annrr	annrr	PROPN
iajs-704	105	41	f	f	PROPN
iajs-704	105	42	–	–	PUNCT
iajs-704	105	43	1(m	1(m	NUM
iajs-704	105	44	2	2	NUM
iajs-704	105	45	)	)	PUNCT
iajs-704	105	46	…	…	PUNCT
iajs-704	105	47	(	(	PUNCT
iajs-704	105	48	2	2	NUM
iajs-704	105	49	)	)	PUNCT
iajs-704	105	50	from	from	ADP
iajs-704	105	51	(	(	PUNCT
iajs-704	105	52	1	1	NUM
iajs-704	105	53	)	)	PUNCT
iajs-704	105	54	and	and	CCONJ
iajs-704	105	55	(	(	PUNCT
iajs-704	105	56	2	2	X
iajs-704	105	57	)	)	PUNCT
iajs-704	105	58	we	we	PRON
iajs-704	105	59	have	have	VERB
iajs-704	105	60	annrf	annrf	ADJ
iajs-704	105	61	–	–	PUNCT
iajs-704	105	62	1(m	1(m	NUM
iajs-704	105	63	2	2	NUM
iajs-704	105	64	)	)	PUNCT
iajs-704	105	65	=	=	PUNCT
iajs-704	105	66	annrrf	annrrf	VERB
iajs-704	105	67	–	–	PUNCT
iajs-704	105	68	1(m	1(m	NUM
iajs-704	105	69	2	2	NUM
iajs-704	105	70	)	)	PUNCT
iajs-704	105	71	.	.	PUNCT
iajs-704	106	1	so	so	ADV
iajs-704	106	2	f	f	PROPN
iajs-704	106	3	–	–	PUNCT
iajs-704	106	4	1(m	1(m	NUM
iajs-704	106	5	2	2	NUM
iajs-704	106	6	)	)	PUNCT
iajs-704	106	7	is	be	AUX
iajs-704	106	8	w.q.p	w.q.p	NOUN
iajs-704	106	9	module	module	NOUN
iajs-704	106	10	.	.	PUNCT
iajs-704	107	1			PROPN
iajs-704	107	2	clearly	clearly	ADV
iajs-704	107	3	.	.	PUNCT
iajs-704	108	1	2.14	2.14	NUM
iajs-704	108	2	note	note	NOUN
iajs-704	108	3	:	:	PUNCT
iajs-704	108	4	the	the	DET
iajs-704	108	5	condition	condition	NOUN
iajs-704	108	6	"	"	PUNCT
iajs-704	108	7	isomorphism	isomorphism	NOUN
iajs-704	108	8	"	"	PUNCT
iajs-704	108	9	in	in	ADP
iajs-704	108	10	theorem	theorem	NOUN
iajs-704	108	11	2.13	2.13	NUM
iajs-704	108	12	is	be	AUX
iajs-704	108	13	necessary	necessary	ADJ
iajs-704	108	14	as	as	SCONJ
iajs-704	108	15	the	the	DET
iajs-704	108	16	following	follow	VERB
iajs-704	108	17	example	example	NOUN
iajs-704	108	18	shows	show	VERB
iajs-704	108	19	example	example	NOUN
iajs-704	108	20	:	:	PUNCT
iajs-704	108	21	let	let	VERB
iajs-704	108	22			ADJ
iajs-704	108	23	:	:	PUNCT
iajs-704	108	24	z	z	PROPN
iajs-704	108	25			PROPN
iajs-704	108	26	z	z	PROPN
iajs-704	108	27	⁄	⁄	PROPN
iajs-704	108	28	(	(	PUNCT
iajs-704	108	29	4	4	NUM
iajs-704	108	30	)	)	PUNCT
iajs-704	108	31	;	;	PUNCT
iajs-704	108	32	z4	z4	X
iajs-704	108	33	,	,	PUNCT
iajs-704	108	34	where	where	SCONJ
iajs-704	108	35	z	z	NOUN
iajs-704	108	36	is	be	AUX
iajs-704	108	37	w.q.p	w.q.p	NOUN
iajs-704	108	38	,	,	PUNCT
iajs-704	108	39	but	but	CCONJ
iajs-704	108	40	z4	z4	PROPN
iajs-704	108	41	is	be	AUX
iajs-704	108	42	not	not	PART
iajs-704	108	43	w.q.p	w.q.p	NOUN
iajs-704	108	44	.	.	PUNCT
iajs-704	109	1	it	it	PRON
iajs-704	109	2	is	be	AUX
iajs-704	109	3	known	know	VERB
iajs-704	109	4	that	that	SCONJ
iajs-704	109	5	,	,	PUNCT
iajs-704	109	6	if	if	SCONJ
iajs-704	109	7	m	m	NOUN
iajs-704	109	8	is	be	AUX
iajs-704	109	9	an	an	DET
iajs-704	109	10	r	r	NOUN
iajs-704	109	11	-	-	PUNCT
iajs-704	109	12	module	module	NOUN
iajs-704	109	13	and	and	CCONJ
iajs-704	109	14	i	i	PRON
iajs-704	109	15	is	be	AUX
iajs-704	109	16	an	an	DET
iajs-704	109	17	ideal	ideal	NOUN
iajs-704	109	18	of	of	ADP
iajs-704	109	19	r	r	NOUN
iajs-704	109	20	which	which	PRON
iajs-704	109	21	is	be	AUX
iajs-704	109	22	contained	contain	VERB
iajs-704	109	23	in	in	ADP
iajs-704	109	24	annrm	annrm	NOUN
iajs-704	109	25	then	then	ADV
iajs-704	109	26	m	m	VERB
iajs-704	109	27	is	be	AUX
iajs-704	109	28	r	r	NOUN
iajs-704	109	29	/	/	SYM
iajs-704	109	30	i	i	NOUN
iajs-704	109	31	-	-	PUNCT
iajs-704	109	32	module	module	NOUN
iajs-704	109	33	,	,	PUNCT
iajs-704	109	34	by	by	ADP
iajs-704	109	35	taking	take	VERB
iajs-704	109	36	(	(	PUNCT
iajs-704	109	37	r	r	NOUN
iajs-704	109	38	+	+	NUM
iajs-704	109	39	1)x	1)x	NUM
iajs-704	109	40	=	=	SYM
iajs-704	109	41	rx	rx	VERB
iajs-704	109	42	x	x	NOUN
iajs-704	109	43			NOUN
iajs-704	109	44	m	m	NOUN
iajs-704	109	45	,	,	PUNCT
iajs-704	109	46	r	r	NOUN
iajs-704	109	47			PROPN
iajs-704	109	48	r	r	NOUN
iajs-704	109	49	,	,	PUNCT
iajs-704	109	50	see	see	VERB
iajs-704	109	51	[	[	X
iajs-704	109	52	5,p.40	5,p.40	NOUN
iajs-704	109	53	]	]	PUNCT
iajs-704	109	54	.	.	PUNCT
iajs-704	110	1	now	now	ADV
iajs-704	110	2	,	,	PUNCT
iajs-704	110	3	we	we	PRON
iajs-704	110	4	give	give	VERB
iajs-704	110	5	the	the	DET
iajs-704	110	6	following	follow	VERB
iajs-704	110	7	result	result	NOUN
iajs-704	110	8	.	.	PUNCT
iajs-704	111	1	2.15	2.15	NUM
iajs-704	111	2	theorem	theorem	NOUN
iajs-704	111	3	:	:	PUNCT
iajs-704	111	4	let	let	VERB
iajs-704	111	5	m	m	PRON
iajs-704	111	6	be	be	AUX
iajs-704	111	7	an	an	DET
iajs-704	111	8	r	r	NOUN
iajs-704	111	9	-	-	PUNCT
iajs-704	111	10	module	module	NOUN
iajs-704	111	11	and	and	CCONJ
iajs-704	111	12	let	let	VERB
iajs-704	111	13	i	i	PRON
iajs-704	111	14	be	be	AUX
iajs-704	111	15	an	an	DET
iajs-704	111	16	ideal	ideal	NOUN
iajs-704	111	17	of	of	ADP
iajs-704	111	18	r	r	NOUN
iajs-704	111	19	,	,	PUNCT
iajs-704	111	20	which	which	PRON
iajs-704	111	21	is	be	AUX
iajs-704	111	22	contained	contain	VERB
iajs-704	111	23	in	in	ADP
iajs-704	111	24	annrm	annrm	NOUN
iajs-704	111	25	.	.	PUNCT
iajs-704	112	1	then	then	ADV
iajs-704	112	2	m	m	PROPN
iajs-704	112	3	is	be	AUX
iajs-704	112	4	w.q.p	w.q.p	NOUN
iajs-704	112	5	r	r	NOUN
iajs-704	112	6	-	-	PUNCT
iajs-704	112	7	module	module	NOUN
iajs-704	112	8	iff	iff	PROPN
iajs-704	112	9	m	m	PROPN
iajs-704	112	10	is	be	AUX
iajs-704	112	11	w.q.p	w.q.p	ADP
iajs-704	112	12	r	r	NOUN
iajs-704	112	13	/	/	SYM
iajs-704	112	14	i	i	NOUN
iajs-704	112	15	-	-	PUNCT
iajs-704	112	16	module	module	NOUN
iajs-704	112	17	.	.	PUNCT
iajs-704	113	1	proof	proof	NOUN
iajs-704	113	2	:	:	PUNCT
iajs-704	113	3			NOUN
iajs-704	113	4	to	to	PART
iajs-704	113	5	prove	prove	VERB
iajs-704	113	6	m	m	NOUN
iajs-704	113	7	is	be	AUX
iajs-704	113	8	w.q.p	w.q.p	ADP
iajs-704	113	9	r	r	NOUN
iajs-704	113	10	/	/	SYM
iajs-704	113	11	i	i	NOUN
iajs-704	113	12	-	-	PUNCT
iajs-704	113	13	module	module	NOUN
iajs-704	113	14	,	,	PUNCT
iajs-704	113	15	i.e.	i.e.	X
iajs-704	113	16	to	to	PART
iajs-704	113	17	prove	prove	VERB
iajs-704	113	18	annr	annr	NOUN
iajs-704	113	19	/	/	SYM
iajs-704	113	20	im	im	NOUN
iajs-704	113	21	=	=	NOUN
iajs-704	113	22	annr	annr	NOUN
iajs-704	113	23	/	/	SYM
iajs-704	113	24	i(r	i(r	PROPN
iajs-704	113	25	+	+	NOUN
iajs-704	113	26	1)m	1)m	NUM
iajs-704	113	27	.	.	PUNCT
iajs-704	114	1	since	since	SCONJ
iajs-704	114	2	(	(	PUNCT
iajs-704	114	3	r	r	NOUN
iajs-704	114	4	+	+	NUM
iajs-704	114	5	1)m	1)m	NUM
iajs-704	114	6			NOUN
iajs-704	114	7	m	m	VERB
iajs-704	114	8	so	so	ADV
iajs-704	114	9	annr	annr	ADJ
iajs-704	114	10	/	/	SYM
iajs-704	114	11	im	im	CCONJ
iajs-704	114	12			PROPN
iajs-704	114	13	annr	annr	NOUN
iajs-704	114	14	/	/	SYM
iajs-704	114	15	i(r	i(r	PROPN
iajs-704	114	16	+	+	CCONJ
iajs-704	114	17	1)m	1)m	NUM
iajs-704	114	18	…	…	PUNCT
iajs-704	114	19	(	(	PUNCT
iajs-704	114	20	1	1	NUM
iajs-704	114	21	)	)	PUNCT
iajs-704	114	22	to	to	PART
iajs-704	114	23	prove	prove	VERB
iajs-704	114	24	annr	annr	NOUN
iajs-704	114	25	/	/	SYM
iajs-704	114	26	i(r	i(r	PROPN
iajs-704	114	27	+	+	CCONJ
iajs-704	114	28	1)m	1)m	NUM
iajs-704	114	29			ADJ
iajs-704	114	30	annr	annr	NOUN
iajs-704	114	31	/	/	SYM
iajs-704	114	32	im	im	NOUN
iajs-704	114	33	let	let	VERB
iajs-704	114	34	x	x	PUNCT
iajs-704	114	35			NOUN
iajs-704	114	36	annr	annr	NOUN
iajs-704	114	37	/	/	SYM
iajs-704	114	38	i(r	i(r	PROPN
iajs-704	115	1	+	+	CCONJ
iajs-704	115	2	1)m	1)m	NUM
iajs-704	116	1	so	so	ADV
iajs-704	116	2	x(r	x(r	PROPN
iajs-704	116	3	+	+	CCONJ
iajs-704	116	4	1)m	1)m	NUM
iajs-704	116	5	=	=	SYM
iajs-704	116	6	0	0	NUM
iajs-704	116	7	,	,	PUNCT
iajs-704	116	8	which	which	PRON
iajs-704	116	9	implies	imply	VERB
iajs-704	116	10	(	(	PUNCT
iajs-704	116	11	xr	xr	PROPN
iajs-704	116	12	+	+	NOUN
iajs-704	116	13	1)m	1)m	PROPN
iajs-704	116	14	=	=	SYM
iajs-704	116	15	0	0	NUM
iajs-704	117	1	so	so	CCONJ
iajs-704	117	2	(	(	PUNCT
iajs-704	117	3	xr)m	xr)m	X
iajs-704	117	4	=	=	SYM
iajs-704	117	5	0	0	PUNCT
iajs-704	117	6	(	(	PUNCT
iajs-704	117	7	by	by	ADP
iajs-704	117	8	definition	definition	NOUN
iajs-704	117	9	)	)	PUNCT
iajs-704	117	10	,	,	PUNCT
iajs-704	117	11	so	so	CCONJ
iajs-704	117	12	x	x	SYM
iajs-704	117	13			NOUN
iajs-704	117	14	annrrm	annrrm	NOUN
iajs-704	117	15	=	=	SYM
iajs-704	117	16	annrm	annrm	NOUN
iajs-704	117	17	(	(	PUNCT
iajs-704	117	18	since	since	SCONJ
iajs-704	117	19	m	m	PROPN
iajs-704	117	20	is	be	AUX
iajs-704	117	21	w.q.p	w.q.p	NOUN
iajs-704	117	22	r	r	NOUN
iajs-704	117	23	-	-	PUNCT
iajs-704	117	24	module	module	NOUN
iajs-704	117	25	)	)	PUNCT
iajs-704	117	26	.	.	PUNCT
iajs-704	118	1	x	x	X
iajs-704	118	2			NOUN
iajs-704	118	3	annr	annr	NOUN
iajs-704	118	4	/	/	SYM
iajs-704	118	5	im	im	INTJ
iajs-704	118	6	(	(	PUNCT
iajs-704	118	7	since	since	SCONJ
iajs-704	118	8	i	i	PRON
iajs-704	118	9			VERB
iajs-704	118	10	annr	annr	PROPN
iajs-704	118	11	/	/	SYM
iajs-704	118	12	im	im	NOUN
iajs-704	118	13	)	)	PUNCT
iajs-704	118	14	,	,	PUNCT
iajs-704	118	15	so	so	ADV
iajs-704	118	16	annr	annr	NOUN
iajs-704	118	17	/	/	SYM
iajs-704	118	18	i(r	i(r	PROPN
iajs-704	118	19	+	+	CCONJ
iajs-704	118	20	1)m	1)m	NUM
iajs-704	118	21			ADJ
iajs-704	118	22	annr	annr	NOUN
iajs-704	118	23	/	/	SYM
iajs-704	118	24	im	im	NOUN
iajs-704	118	25	…	…	PUNCT
iajs-704	118	26	(	(	PUNCT
iajs-704	118	27	2	2	NUM
iajs-704	118	28	)	)	PUNCT
iajs-704	118	29	from	from	ADP
iajs-704	118	30	(	(	PUNCT
iajs-704	118	31	1	1	NUM
iajs-704	118	32	)	)	PUNCT
iajs-704	118	33	and	and	CCONJ
iajs-704	118	34	(	(	PUNCT
iajs-704	118	35	2	2	X
iajs-704	118	36	)	)	PUNCT
iajs-704	118	37	we	we	PRON
iajs-704	118	38	have	have	VERB
iajs-704	118	39	annr	annr	NOUN
iajs-704	118	40	/	/	SYM
iajs-704	118	41	im	im	NOUN
iajs-704	118	42	=	=	NOUN
iajs-704	118	43	annr	annr	NOUN
iajs-704	118	44	/	/	SYM
iajs-704	118	45	i(r	i(r	PROPN
iajs-704	118	46	+	+	NOUN
iajs-704	118	47	1)m	1)m	NUM
iajs-704	118	48	.	.	PUNCT
iajs-704	119	1			PROPN
iajs-704	120	1	if	if	SCONJ
iajs-704	120	2	m	m	PROPN
iajs-704	120	3	is	be	AUX
iajs-704	120	4	w.q.p	w.q.p	ADP
iajs-704	120	5	r	r	PROPN
iajs-704	120	6	/	/	SYM
iajs-704	120	7	i	i	NOUN
iajs-704	120	8	-	-	PUNCT
iajs-704	120	9	module	module	NOUN
iajs-704	120	10	then	then	ADV
iajs-704	120	11	m	m	VERB
iajs-704	120	12	is	be	AUX
iajs-704	120	13	w.q.p	w.q.p	NOUN
iajs-704	120	14	r	r	NOUN
iajs-704	120	15	-	-	PUNCT
iajs-704	120	16	module	module	NOUN
iajs-704	120	17	,	,	PUNCT
iajs-704	120	18	i.e.	i.e.	X
iajs-704	120	19	to	to	PART
iajs-704	120	20	prove	prove	VERB
iajs-704	120	21	annrm	annrm	NOUN
iajs-704	120	22	=	=	SYM
iajs-704	120	23	annrrm	annrrm	PROPN
iajs-704	120	24	,	,	PUNCT
iajs-704	120	25			NOUN
iajs-704	120	26	r	r	NOUN
iajs-704	120	27			NOUN
iajs-704	120	28	annrm	annrm	NOUN
iajs-704	120	29	.	.	PUNCT
iajs-704	121	1	since	since	SCONJ
iajs-704	121	2	rm	rm	PROPN
iajs-704	121	3			PROPN
iajs-704	121	4	m	m	PROPN
iajs-704	121	5	so	so	ADV
iajs-704	121	6	annrm	annrm	PROPN
iajs-704	121	7			PROPN
iajs-704	121	8	annrrm	annrrm	PROPN
iajs-704	121	9	…	…	PUNCT
iajs-704	121	10	(	(	PUNCT
iajs-704	121	11	1	1	NUM
iajs-704	121	12	)	)	PUNCT
iajs-704	121	13	to	to	PART
iajs-704	121	14	prove	prove	VERB
iajs-704	121	15	annrrm	annrrm	ADJ
iajs-704	121	16			PROPN
iajs-704	121	17	annrm	annrm	PROPN
iajs-704	121	18	let	let	VERB
iajs-704	121	19	x	x	PUNCT
iajs-704	121	20			PROPN
iajs-704	121	21	annrrm	annrrm	NOUN
iajs-704	121	22	so	so	SCONJ
iajs-704	121	23	(	(	PUNCT
iajs-704	121	24	xr)m	xr)m	X
iajs-704	121	25	=	=	SYM
iajs-704	121	26	0	0	NUM
iajs-704	121	27	implies	imply	VERB
iajs-704	121	28	that	that	SCONJ
iajs-704	121	29	(	(	PUNCT
iajs-704	121	30	xr	xr	PROPN
iajs-704	121	31	+	+	NOUN
iajs-704	121	32	1)m	1)m	PROPN
iajs-704	121	33	=	=	SYM
iajs-704	121	34	0	0	NUM
iajs-704	121	35	,	,	PUNCT
iajs-704	121	36	so	so	ADV
iajs-704	121	37	x(r	x(r	PROPN
iajs-704	121	38	+	+	CCONJ
iajs-704	121	39	1)m	1)m	NUM
iajs-704	121	40	=	=	SYM
iajs-704	121	41	0	0	NUM
iajs-704	121	42	,	,	PUNCT
iajs-704	121	43	hence	hence	ADV
iajs-704	121	44	x	x	PUNCT
iajs-704	121	45			NOUN
iajs-704	121	46	annr	annr	NOUN
iajs-704	121	47	/	/	SYM
iajs-704	121	48	i(r	i(r	PROPN
iajs-704	121	49	+	+	CCONJ
iajs-704	122	1	1)m	1)m	NUM
iajs-704	122	2	=	=	SYM
iajs-704	122	3	annr	annr	NOUN
iajs-704	122	4	/	/	SYM
iajs-704	122	5	im	im	NOUN
iajs-704	122	6	(	(	PUNCT
iajs-704	122	7	since	since	SCONJ
iajs-704	122	8	m	m	PROPN
iajs-704	122	9	is	be	AUX
iajs-704	122	10	w.q.p	w.q.p	ADP
iajs-704	122	11	r	r	NOUN
iajs-704	122	12	/	/	SYM
iajs-704	122	13	i	i	NOUN
iajs-704	122	14	-	-	PUNCT
iajs-704	122	15	module	module	NOUN
iajs-704	122	16	)	)	PUNCT
iajs-704	122	17	.	.	PUNCT
iajs-704	123	1	thus	thus	ADV
iajs-704	123	2	x	x	SYM
iajs-704	123	3			NOUN
iajs-704	123	4	annr	annr	NOUN
iajs-704	123	5	/	/	SYM
iajs-704	123	6	im	im	NOUN
iajs-704	123	7	,	,	PUNCT
iajs-704	123	8	which	which	PRON
iajs-704	123	9	implies	imply	VERB
iajs-704	123	10	that	that	SCONJ
iajs-704	123	11	x	x	SYM
iajs-704	123	12			PROPN
iajs-704	123	13	annrm	annrm	NOUN
iajs-704	123	14	(	(	PUNCT
iajs-704	123	15	since	since	SCONJ
iajs-704	123	16	i	i	PRON
iajs-704	123	17			PROPN
iajs-704	123	18	annrm	annrm	PROPN
iajs-704	123	19	)	)	PUNCT
iajs-704	123	20	,	,	PUNCT
iajs-704	123	21	so	so	ADV
iajs-704	123	22	annrrm	annrrm	PROPN
iajs-704	123	23			PROPN
iajs-704	123	24	annrm	annrm	PROPN
iajs-704	123	25	…	…	PUNCT
iajs-704	123	26	(	(	PUNCT
iajs-704	123	27	2	2	NUM
iajs-704	123	28	)	)	PUNCT
iajs-704	123	29	مجلة	مجلة	NOUN
iajs-704	123	30	إبن	إبن	NOUN
iajs-704	123	31	الھیثم	الھیثم	NOUN
iajs-704	123	32	للعلوم	للعلوم	NOUN
iajs-704	123	33	الصرفة	الصرفة	NOUN
iajs-704	123	34	و	و	PRON
iajs-704	123	35	التطبیقیة	التطبیقیة	PROPN
iajs-704	123	36	2012	2012	NUM
iajs-704	123	37	السنة	السنة	NOUN
iajs-704	124	1	25	25	NUM
iajs-704	124	2	المجلد	المجلد	NOUN
iajs-704	124	3	1	1	NUM
iajs-704	124	4	العدد	العدد	PROPN
iajs-704	124	5	ibn	ibn	PROPN
iajs-704	124	6	al	al	PROPN
iajs-704	124	7	-	-	PUNCT
iajs-704	124	8	haitham	haitham	PROPN
iajs-704	124	9	journal	journal	PROPN
iajs-704	124	10	for	for	ADP
iajs-704	124	11	pure	pure	ADJ
iajs-704	124	12	and	and	CCONJ
iajs-704	124	13	applied	apply	VERB
iajs-704	124	14	science	science	NOUN
iajs-704	124	15	no	no	NOUN
iajs-704	124	16	.	.	NOUN
iajs-704	124	17	1	1	NUM
iajs-704	124	18	vol	vol	NOUN
iajs-704	124	19	.	.	PUNCT
iajs-704	125	1	25	25	NUM
iajs-704	125	2	year	year	NOUN
iajs-704	125	3	2012	2012	NUM
iajs-704	125	4	from	from	ADP
iajs-704	125	5	(	(	PUNCT
iajs-704	125	6	1	1	NUM
iajs-704	125	7	)	)	PUNCT
iajs-704	125	8	and	and	CCONJ
iajs-704	125	9	(	(	PUNCT
iajs-704	125	10	2	2	X
iajs-704	125	11	)	)	PUNCT
iajs-704	125	12	we	we	PRON
iajs-704	125	13	have	have	AUX
iajs-704	125	14	annrm	annrm	NOUN
iajs-704	125	15	=	=	SYM
iajs-704	125	16	annrrm	annrrm	PROPN
iajs-704	125	17	.	.	PUNCT
iajs-704	126	1	so	so	ADV
iajs-704	126	2	m	m	PROPN
iajs-704	126	3	is	be	AUX
iajs-704	126	4	w.q.p	w.q.p	NOUN
iajs-704	126	5	module	module	NOUN
iajs-704	126	6	.	.	PUNCT
iajs-704	127	1	recall	recall	VERB
iajs-704	127	2	that	that	SCONJ
iajs-704	127	3	a	a	DET
iajs-704	127	4	subset	subset	NOUN
iajs-704	127	5	s	s	NOUN
iajs-704	127	6	of	of	ADP
iajs-704	127	7	a	a	DET
iajs-704	127	8	ring	ring	NOUN
iajs-704	127	9	r	r	NOUN
iajs-704	127	10	is	be	AUX
iajs-704	127	11	called	call	VERB
iajs-704	127	12	multiplicatively	multiplicatively	ADV
iajs-704	127	13	closed	close	VERB
iajs-704	127	14	if	if	SCONJ
iajs-704	127	15	1	1	NUM
iajs-704	127	16			NOUN
iajs-704	127	17	s	s	NOUN
iajs-704	127	18	and	and	CCONJ
iajs-704	127	19	ab	ab	ADV
iajs-704	127	20			NOUN
iajs-704	127	21	s	s	VERB
iajs-704	127	22	for	for	ADP
iajs-704	127	23	every	every	DET
iajs-704	127	24	a	a	PROPN
iajs-704	127	25	,	,	PUNCT
iajs-704	127	26	b	b	PROPN
iajs-704	127	27			PROPN
iajs-704	127	28	s.	s.	PROPN
iajs-704	128	1	we	we	PRON
iajs-704	128	2	know	know	VERB
iajs-704	128	3	that	that	SCONJ
iajs-704	128	4	every	every	DET
iajs-704	128	5	proper	proper	ADJ
iajs-704	128	6	ideal	ideal	NOUN
iajs-704	128	7	p	p	NOUN
iajs-704	128	8	in	in	ADP
iajs-704	128	9	r	r	NOUN
iajs-704	128	10	is	be	AUX
iajs-704	128	11	prime	prime	ADJ
iajs-704	128	12	if	if	SCONJ
iajs-704	128	13	and	and	CCONJ
iajs-704	128	14	only	only	ADV
iajs-704	128	15	if	if	SCONJ
iajs-704	128	16	r	r	X
iajs-704	128	17	-	-	PUNCT
iajs-704	128	18	p	p	NOUN
iajs-704	128	19	is	be	AUX
iajs-704	128	20	multiplicatively	multiplicatively	ADV
iajs-704	128	21	closed	closed	ADJ
iajs-704	128	22	,	,	PUNCT
iajs-704	128	23	see	see	VERB
iajs-704	128	24	[	[	X
iajs-704	128	25	4,p.42	4,p.42	X
iajs-704	128	26	]	]	PUNCT
iajs-704	128	27	.	.	PUNCT
iajs-704	129	1	let	let	VERB
iajs-704	129	2	m	m	PRON
iajs-704	129	3	be	be	AUX
iajs-704	129	4	a	a	DET
iajs-704	129	5	module	module	NOUN
iajs-704	129	6	on	on	ADP
iajs-704	129	7	the	the	DET
iajs-704	129	8	ring	ring	NOUN
iajs-704	129	9	r	r	NOUN
iajs-704	129	10	and	and	CCONJ
iajs-704	129	11	s	s	VERB
iajs-704	129	12	be	be	AUX
iajs-704	129	13	a	a	DET
iajs-704	129	14	multiplicatively	multiplicatively	ADV
iajs-704	129	15	closed	close	VERB
iajs-704	129	16	on	on	ADP
iajs-704	129	17	r	r	NOUN
iajs-704	129	18	such	such	ADJ
iajs-704	129	19	that	that	DET
iajs-704	129	20	s	s	X
iajs-704	129	21			NOUN
iajs-704	129	22	0	0	PUNCT
iajs-704	129	23	and	and	CCONJ
iajs-704	129	24	let	let	VERB
iajs-704	129	25	rs	rs	INTJ
iajs-704	129	26	be	be	AUX
iajs-704	129	27	the	the	DET
iajs-704	129	28	set	set	NOUN
iajs-704	129	29	of	of	ADP
iajs-704	129	30	all	all	DET
iajs-704	129	31	fractional	fractional	ADJ
iajs-704	129	32	r	r	NOUN
iajs-704	129	33	/	/	SYM
iajs-704	129	34	s	s	NOUN
iajs-704	129	35	where	where	SCONJ
iajs-704	129	36	r	r	NOUN
iajs-704	129	37			NOUN
iajs-704	129	38	r	r	NOUN
iajs-704	129	39	and	and	CCONJ
iajs-704	129	40	s	s	PROPN
iajs-704	129	41			NOUN
iajs-704	129	42	s	s	PART
iajs-704	129	43	and	and	CCONJ
iajs-704	129	44	m	m	PROPN
iajs-704	129	45	s	s	PART
iajs-704	129	46	be	be	AUX
iajs-704	129	47	the	the	DET
iajs-704	129	48	set	set	NOUN
iajs-704	129	49	of	of	ADP
iajs-704	129	50	all	all	DET
iajs-704	129	51	fractional	fractional	ADJ
iajs-704	129	52	x	x	X
iajs-704	129	53	/	/	SYM
iajs-704	129	54	s	s	PROPN
iajs-704	129	55	where	where	SCONJ
iajs-704	129	56	x	x	SYM
iajs-704	129	57			NOUN
iajs-704	129	58	m	m	PROPN
iajs-704	129	59	,	,	PUNCT
iajs-704	129	60	s	s	VERB
iajs-704	129	61			NOUN
iajs-704	129	62	s	s	PART
iajs-704	129	63	;	;	PUNCT
iajs-704	129	64	x1	x1	PROPN
iajs-704	129	65	/	/	SYM
iajs-704	129	66	s1	s1	NOUN
iajs-704	129	67	=	=	SYM
iajs-704	129	68	x2	x2	PROPN
iajs-704	129	69	/	/	SYM
iajs-704	129	70	s2	s2	NOUN
iajs-704	129	71	if	if	SCONJ
iajs-704	129	72	and	and	CCONJ
iajs-704	129	73	only	only	ADV
iajs-704	129	74	if	if	SCONJ
iajs-704	129	75	there	there	PRON
iajs-704	129	76	exists	exist	VERB
iajs-704	129	77	t	t	PROPN
iajs-704	129	78			PROPN
iajs-704	129	79	s	s	VERB
iajs-704	129	80	such	such	ADJ
iajs-704	129	81	that	that	SCONJ
iajs-704	129	82	t(s1x2	t(s1x2	PROPN
iajs-704	129	83	–	–	PUNCT
iajs-704	129	84	s2x1	s2x1	X
iajs-704	129	85	)	)	PUNCT
iajs-704	129	86	=	=	SYM
iajs-704	130	1	0	0	X
iajs-704	130	2	.	.	PUNCT
iajs-704	131	1	so	so	ADV
iajs-704	131	2	,	,	PUNCT
iajs-704	131	3	can	can	AUX
iajs-704	131	4	make	make	VERB
iajs-704	131	5	m	m	NOUN
iajs-704	131	6	s	s	NOUN
iajs-704	131	7	into	into	ADP
iajs-704	131	8	rs	rs	NOUN
iajs-704	131	9	-	-	PUNCT
iajs-704	131	10	module	module	NOUN
iajs-704	131	11	by	by	ADP
iajs-704	131	12	setting	set	VERB
iajs-704	131	13	x	x	X
iajs-704	131	14	/	/	SYM
iajs-704	131	15	s	s	PART
iajs-704	131	16	+	+	NOUN
iajs-704	131	17	y	y	PROPN
iajs-704	131	18	/	/	SYM
iajs-704	131	19	t	t	PROPN
iajs-704	131	20	=	=	SYM
iajs-704	131	21	(	(	PUNCT
iajs-704	131	22	tx	tx	PROPN
iajs-704	131	23	+	+	CCONJ
iajs-704	131	24	sy	sy	PROPN
iajs-704	131	25	)	)	PUNCT
iajs-704	131	26	/st	/st	PROPN
iajs-704	131	27	,	,	PUNCT
iajs-704	131	28	r	r	NOUN
iajs-704	131	29	/	/	SYM
iajs-704	131	30	tx	tx	PROPN
iajs-704	131	31	/	/	SYM
iajs-704	131	32	s	s	PART
iajs-704	131	33	=	=	VERB
iajs-704	131	34	rx	rx	VERB
iajs-704	131	35	/	/	SYM
iajs-704	131	36	ts	ts	ADP
iajs-704	131	37	for	for	ADP
iajs-704	131	38	every	every	DET
iajs-704	131	39	x	x	PROPN
iajs-704	131	40	,	,	PUNCT
iajs-704	131	41	y	y	PROPN
iajs-704	131	42			PROPN
iajs-704	131	43	m	m	VERB
iajs-704	131	44	and	and	CCONJ
iajs-704	131	45	for	for	ADP
iajs-704	131	46	every	every	DET
iajs-704	131	47	r	r	NOUN
iajs-704	131	48			NOUN
iajs-704	131	49	r	r	NOUN
iajs-704	131	50	,	,	PUNCT
iajs-704	131	51	s	s	PROPN
iajs-704	131	52	,	,	PUNCT
iajs-704	131	53	t	t	PROPN
iajs-704	131	54			PROPN
iajs-704	131	55	s.	s.	PROPN
iajs-704	132	1	if	if	SCONJ
iajs-704	132	2	s	s	VERB
iajs-704	132	3	=	=	SYM
iajs-704	132	4	r	r	X
iajs-704	132	5	-	-	PUNCT
iajs-704	132	6	p	p	NOUN
iajs-704	132	7	where	where	SCONJ
iajs-704	132	8	p	p	NOUN
iajs-704	132	9	is	be	AUX
iajs-704	132	10	a	a	DET
iajs-704	132	11	prime	prime	ADJ
iajs-704	132	12	ideal	ideal	NOUN
iajs-704	132	13	we	we	PRON
iajs-704	132	14	use	use	VERB
iajs-704	132	15	m	m	PRON
iajs-704	132	16	p	p	X
iajs-704	132	17	instead	instead	ADV
iajs-704	132	18	of	of	ADP
iajs-704	132	19	m	m	PRON
iajs-704	132	20	s	s	PART
iajs-704	132	21	and	and	CCONJ
iajs-704	132	22	rp	rp	NOUN
iajs-704	132	23	instead	instead	ADV
iajs-704	132	24	of	of	ADP
iajs-704	132	25	rs	rs	X
iajs-704	132	26	.	.	PUNCT
iajs-704	133	1	a	a	DET
iajs-704	133	2	ring	ring	NOUN
iajs-704	133	3	in	in	ADP
iajs-704	133	4	which	which	PRON
iajs-704	133	5	there	there	PRON
iajs-704	133	6	is	be	VERB
iajs-704	133	7	only	only	ADV
iajs-704	133	8	one	one	NUM
iajs-704	133	9	maximal	maximal	ADJ
iajs-704	133	10	ideal	ideal	NOUN
iajs-704	133	11	is	be	AUX
iajs-704	133	12	called	call	VERB
iajs-704	133	13	local	local	ADJ
iajs-704	133	14	ring	ring	NOUN
iajs-704	133	15	,	,	PUNCT
iajs-704	133	16	see	see	VERB
iajs-704	133	17	[	[	X
iajs-704	133	18	4,p.50	4,p.50	NOUN
iajs-704	133	19	]	]	X
iajs-704	133	20	,	,	PUNCT
iajs-704	133	21	hence	hence	ADV
iajs-704	133	22	rp	rp	NOUN
iajs-704	133	23	is	be	AUX
iajs-704	133	24	often	often	ADV
iajs-704	133	25	called	call	VERB
iajs-704	133	26	the	the	DET
iajs-704	133	27	localization	localization	NOUN
iajs-704	133	28	of	of	ADP
iajs-704	133	29	r	r	NOUN
iajs-704	133	30	,	,	PUNCT
iajs-704	133	31	similar	similar	ADJ
iajs-704	133	32	m	m	PROPN
iajs-704	133	33	p	p	NOUN
iajs-704	133	34	is	be	AUX
iajs-704	133	35	the	the	DET
iajs-704	133	36	localization	localization	NOUN
iajs-704	133	37	of	of	ADP
iajs-704	133	38	m	m	NOUN
iajs-704	133	39	at	at	ADP
iajs-704	133	40	p.	p.	NOUN
iajs-704	134	1	so	so	ADV
iajs-704	134	2	we	we	PRON
iajs-704	134	3	can	can	AUX
iajs-704	134	4	define	define	VERB
iajs-704	134	5	the	the	DET
iajs-704	134	6	two	two	NUM
iajs-704	134	7	maps	map	NOUN
iajs-704	134	8	:r	:r	PROPN
iajs-704	134	9			PROPN
iajs-704	134	10	rs	rs	PROPN
iajs-704	134	11	,	,	PUNCT
iajs-704	134	12	such	such	ADJ
iajs-704	134	13	that	that	SCONJ
iajs-704	134	14	(r	(r	PROPN
iajs-704	134	15	)	)	PUNCT
iajs-704	135	1	=	=	SYM
iajs-704	135	2	r	r	NOUN
iajs-704	135	3	/1	/1	NOUN
iajs-704	135	4	,	,	PUNCT
iajs-704	135	5	rr	rr	PROPN
iajs-704	135	6	,	,	PUNCT
iajs-704	135	7	:m	:m	X
iajs-704	135	8			PROPN
iajs-704	135	9	m	m	NOUN
iajs-704	135	10	s	s	PROPN
iajs-704	135	11	,	,	PUNCT
iajs-704	135	12	such	such	ADJ
iajs-704	135	13	that	that	DET
iajs-704	135	14	(m	(m	NOUN
iajs-704	135	15	)	)	PUNCT
iajs-704	136	1	=	=	PUNCT
iajs-704	137	1	m	m	AUX
iajs-704	137	2	/1	/1	ADJ
iajs-704	137	3	,	,	PUNCT
iajs-704	137	4	mm	mm	VERB
iajs-704	137	5	,	,	PUNCT
iajs-704	137	6	see	see	VERB
iajs-704	137	7	[	[	X
iajs-704	137	8	5,p.69	5,p.69	NOUN
iajs-704	137	9	]	]	PUNCT
iajs-704	137	10	.	.	PUNCT
iajs-704	138	1	through	through	ADP
iajs-704	138	2	this	this	DET
iajs-704	138	3	paper	paper	NOUN
iajs-704	138	4	s	s	PART
iajs-704	138	5	–	–	PUNCT
iajs-704	138	6	1r	1r	NUM
iajs-704	138	7	and	and	CCONJ
iajs-704	138	8	s	s	PART
iajs-704	138	9	–	–	PUNCT
iajs-704	138	10	1	1	NUM
iajs-704	138	11	m	m	NOUN
iajs-704	138	12	represent	represent	VERB
iajs-704	138	13	rs	rs	NOUN
iajs-704	138	14	and	and	CCONJ
iajs-704	138	15	ms	ms	NOUN
iajs-704	138	16	respectively	respectively	ADV
iajs-704	138	17	.	.	PUNCT
iajs-704	139	1	2.16	2.16	NUM
iajs-704	139	2	proposition	proposition	NOUN
iajs-704	139	3	:	:	PUNCT
iajs-704	139	4	let	let	VERB
iajs-704	139	5	m	m	PRON
iajs-704	139	6	be	be	AUX
iajs-704	139	7	w.q.p	w.q.p	NOUN
iajs-704	139	8	r	r	NOUN
iajs-704	139	9	-	-	PUNCT
iajs-704	139	10	module	module	NOUN
iajs-704	139	11	then	then	ADV
iajs-704	139	12	s	s	PART
iajs-704	139	13	–	–	PUNCT
iajs-704	139	14	1	1	NUM
iajs-704	139	15	m	m	NOUN
iajs-704	139	16	is	be	AUX
iajs-704	139	17	w.q.p	w.q.p	NOUN
iajs-704	139	18	s	s	PART
iajs-704	139	19	–	–	PUNCT
iajs-704	139	20	1r	1r	NUM
iajs-704	139	21	-	-	PUNCT
iajs-704	139	22	module	module	NOUN
iajs-704	139	23	for	for	ADP
iajs-704	139	24	each	each	DET
iajs-704	139	25	multiplicatively	multiplicatively	ADV
iajs-704	139	26	closed	close	VERB
iajs-704	139	27	set	set	VERB
iajs-704	139	28	s	s	PROPN
iajs-704	139	29	of	of	ADP
iajs-704	139	30	r.	r.	PROPN
iajs-704	139	31	proof	proof	NOUN
iajs-704	139	32	:	:	PUNCT
iajs-704	139	33	to	to	PART
iajs-704	139	34	prove	prove	VERB
iajs-704	139	35	1	1	NUM
iajs-704	139	36	s	s	PART
iajs-704	139	37	rann	rann	PROPN
iajs-704	139	38			PROPN
iajs-704	139	39	s	s	PART
iajs-704	139	40	–	–	PUNCT
iajs-704	139	41	1	1	NUM
iajs-704	139	42	m	m	NOUN
iajs-704	139	43	=	=	SYM
iajs-704	139	44	1	1	NUM
iajs-704	139	45	s	s	PART
iajs-704	139	46	rann	rann	PROPN
iajs-704	139	47			PROPN
iajs-704	139	48	r	r	PROPN
iajs-704	139	49	/	/	SYM
iajs-704	139	50	t	t	NOUN
iajs-704	139	51	s	s	PART
iajs-704	139	52	–	–	PUNCT
iajs-704	139	53	1	1	NUM
iajs-704	139	54	m	m	NOUN
iajs-704	139	55			NOUN
iajs-704	139	56	r	r	PROPN
iajs-704	139	57	t	t	PROPN
iajs-704	139	58			NOUN
iajs-704	139	59	1	1	NUM
iajs-704	139	60	s	s	PART
iajs-704	139	61	rann	rann	PROPN
iajs-704	139	62			PROPN
iajs-704	139	63	s	s	PART
iajs-704	139	64	–	–	PUNCT
iajs-704	139	65	1	1	NUM
iajs-704	139	66	m	m	NOUN
iajs-704	139	67	,	,	PUNCT
iajs-704	139	68	since	since	SCONJ
iajs-704	139	69	r	r	NOUN
iajs-704	139	70	/	/	SYM
iajs-704	139	71	t	t	NOUN
iajs-704	139	72	s	s	PART
iajs-704	139	73	–	–	PUNCT
iajs-704	139	74	1	1	NUM
iajs-704	139	75	m	m	NOUN
iajs-704	139	76			PROPN
iajs-704	139	77	s	s	PART
iajs-704	139	78	–	–	PUNCT
iajs-704	139	79	1	1	NUM
iajs-704	139	80	m	m	NOUN
iajs-704	139	81	so	so	ADV
iajs-704	139	82	1	1	NUM
iajs-704	139	83	s	s	PART
iajs-704	139	84	rann	rann	PROPN
iajs-704	139	85			PROPN
iajs-704	139	86	s	s	PART
iajs-704	139	87	–	–	PUNCT
iajs-704	139	88	1	1	NUM
iajs-704	139	89	m	m	NOUN
iajs-704	139	90			PROPN
iajs-704	139	91	1	1	NUM
iajs-704	139	92	s	s	PART
iajs-704	139	93	rann	rann	PROPN
iajs-704	139	94			PROPN
iajs-704	139	95	r	r	PROPN
iajs-704	139	96	/	/	SYM
iajs-704	139	97	t	t	NOUN
iajs-704	139	98	s	s	PART
iajs-704	139	99	–	–	PUNCT
iajs-704	139	100	1	1	NUM
iajs-704	139	101	m	m	NOUN
iajs-704	139	102	…	…	PUNCT
iajs-704	139	103	(	(	PUNCT
iajs-704	139	104	1	1	NUM
iajs-704	139	105	)	)	PUNCT
iajs-704	139	106	to	to	PART
iajs-704	139	107	prove	prove	VERB
iajs-704	139	108	1	1	NUM
iajs-704	139	109	s	s	PART
iajs-704	139	110	rann	rann	PROPN
iajs-704	139	111			PROPN
iajs-704	139	112	r	r	PROPN
iajs-704	139	113	/	/	SYM
iajs-704	139	114	t	t	NOUN
iajs-704	139	115	s	s	PART
iajs-704	139	116	–	–	PUNCT
iajs-704	139	117	1	1	NUM
iajs-704	139	118	m	m	NOUN
iajs-704	139	119			PROPN
iajs-704	139	120	1	1	NUM
iajs-704	139	121	s	s	PART
iajs-704	139	122	rann	rann	PROPN
iajs-704	139	123			PROPN
iajs-704	139	124	s	s	PART
iajs-704	139	125	–	–	PUNCT
iajs-704	139	126	1	1	NUM
iajs-704	139	127	m	m	NOUN
iajs-704	139	128	let	let	VERB
iajs-704	139	129	y	y	PRON
iajs-704	139	130	/	/	SYM
iajs-704	139	131	t	t	PROPN
iajs-704	139	132	'	'	PUNCT
iajs-704	139	133			NOUN
iajs-704	139	134	1	1	NUM
iajs-704	139	135	s	s	PART
iajs-704	139	136	rann	rann	PROPN
iajs-704	139	137			PROPN
iajs-704	139	138	r	r	PROPN
iajs-704	139	139	/	/	SYM
iajs-704	139	140	t	t	NOUN
iajs-704	139	141	s	s	PART
iajs-704	139	142	–	–	PUNCT
iajs-704	139	143	1	1	NUM
iajs-704	139	144	m	m	NOUN
iajs-704	139	145	so	so	ADV
iajs-704	139	146	y	y	PROPN
iajs-704	139	147	/	/	SYM
iajs-704	139	148	t	t	PROPN
iajs-704	139	149	'	'	PUNCT
iajs-704	139	150	r	r	PROPN
iajs-704	139	151	/	/	SYM
iajs-704	139	152	t	t	PROPN
iajs-704	139	153	s	s	PART
iajs-704	139	154	–	–	PUNCT
iajs-704	139	155	1	1	NUM
iajs-704	139	156	m	m	NOUN
iajs-704	139	157	=	=	NUM
iajs-704	139	158	0	0	NUM
iajs-704	139	159	which	which	PRON
iajs-704	139	160	implies	imply	VERB
iajs-704	139	161	that	that	SCONJ
iajs-704	139	162	yr	yr	PROPN
iajs-704	139	163	/	/	SYM
iajs-704	139	164	tt	tt	PROPN
iajs-704	139	165	's	's	PART
iajs-704	139	166	–	–	PUNCT
iajs-704	139	167	1	1	NUM
iajs-704	139	168	m	m	NOUN
iajs-704	139	169	=	=	NOUN
iajs-704	139	170	0	0	NUM
iajs-704	139	171	where	where	SCONJ
iajs-704	139	172	yr	yr	VERB
iajs-704	139	173			PROPN
iajs-704	139	174	m	m	PROPN
iajs-704	139	175	,	,	PUNCT
iajs-704	139	176	tt	tt	PROPN
iajs-704	139	177	'	'	PUNCT
iajs-704	139	178			PROPN
iajs-704	139	179	s	s	VERB
iajs-704	139	180	so	so	SCONJ
iajs-704	139	181	yr/	yr/	PROPN
iajs-704	139	182	tt	tt	PROPN
iajs-704	139	183	's	's	PART
iajs-704	139	184	–	–	PUNCT
iajs-704	139	185	1	1	NUM
iajs-704	139	186	m	m	NOUN
iajs-704	139	187	=	=	NUM
iajs-704	139	188	0	0	NUM
iajs-704	139	189	which	which	PRON
iajs-704	139	190	implies	imply	VERB
iajs-704	139	191	that	that	SCONJ
iajs-704	139	192	yr/	yr/	PROPN
iajs-704	139	193	tt	tt	PROPN
iajs-704	139	194	'	'	VERB
iajs-704	139	195	m	m	PROPN
iajs-704	139	196	/	/	SYM
iajs-704	139	197	s	s	PART
iajs-704	139	198	=	=	SYM
iajs-704	139	199	0	0	PROPN
iajs-704	139	200	so	so	ADV
iajs-704	139	201	yrm	yrm	NOUN
iajs-704	139	202	=	=	SYM
iajs-704	139	203	0	0	X
iajs-704	139	204	.	.	PUNCT
iajs-704	140	1	hence	hence	ADV
iajs-704	140	2	y	y	PROPN
iajs-704	140	3			PROPN
iajs-704	140	4	annrrm	annrrm	PROPN
iajs-704	140	5	=	=	SYM
iajs-704	140	6	annrm	annrm	NOUN
iajs-704	140	7	.	.	PUNCT
iajs-704	141	1	since	since	SCONJ
iajs-704	141	2	y	y	PROPN
iajs-704	141	3			PROPN
iajs-704	141	4	annrm	annrm	NOUN
iajs-704	141	5	so	so	SCONJ
iajs-704	141	6	ym	ym	PROPN
iajs-704	142	1	=	=	NOUN
iajs-704	142	2	0	0	X
iajs-704	142	3	.	.	PUNCT
iajs-704	143	1	thus	thus	ADV
iajs-704	143	2	ym	ym	PROPN
iajs-704	143	3	/	/	SYM
iajs-704	143	4	ts	ts	X
iajs-704	143	5	=	=	PUNCT
iajs-704	143	6	0	0	PROPN
iajs-704	144	1	so	so	ADV
iajs-704	144	2	y	y	PROPN
iajs-704	144	3	/	/	SYM
iajs-704	144	4	ts	ts	PUNCT
iajs-704	144	5	–	–	PUNCT
iajs-704	144	6	1	1	NUM
iajs-704	144	7	m	m	NOUN
iajs-704	144	8	=	=	SYM
iajs-704	144	9	0	0	NUM
iajs-704	144	10	,	,	PUNCT
iajs-704	144	11	y	y	PROPN
iajs-704	144	12	/	/	SYM
iajs-704	144	13	t	t	NOUN
iajs-704	144	14	annrs	annrs	VERB
iajs-704	144	15	–	–	PUNCT
iajs-704	144	16	1	1	NUM
iajs-704	144	17	m	m	NOUN
iajs-704	144	18	,	,	PUNCT
iajs-704	144	19	hence	hence	ADV
iajs-704	144	20	1	1	NUM
iajs-704	144	21	s	s	PART
iajs-704	144	22	rann	rann	PROPN
iajs-704	144	23			PROPN
iajs-704	144	24	r	r	PROPN
iajs-704	144	25	/	/	SYM
iajs-704	144	26	t	t	NOUN
iajs-704	144	27	s	s	PART
iajs-704	144	28	–	–	PUNCT
iajs-704	144	29	1	1	NUM
iajs-704	144	30	m	m	NOUN
iajs-704	144	31			PROPN
iajs-704	144	32	1	1	NUM
iajs-704	144	33	s	s	PART
iajs-704	144	34	rann	rann	PROPN
iajs-704	144	35			PROPN
iajs-704	144	36	s	s	PART
iajs-704	144	37	–	–	PUNCT
iajs-704	144	38	1	1	NUM
iajs-704	144	39	m	m	NOUN
iajs-704	144	40	…	…	PUNCT
iajs-704	144	41	(	(	PUNCT
iajs-704	144	42	2	2	NUM
iajs-704	144	43	)	)	PUNCT
iajs-704	144	44	from	from	ADP
iajs-704	144	45	(	(	PUNCT
iajs-704	144	46	1	1	NUM
iajs-704	144	47	)	)	PUNCT
iajs-704	144	48	and	and	CCONJ
iajs-704	144	49	(	(	PUNCT
iajs-704	144	50	2	2	X
iajs-704	144	51	)	)	PUNCT
iajs-704	144	52	we	we	PRON
iajs-704	144	53	have	have	VERB
iajs-704	144	54	1	1	NUM
iajs-704	144	55	s	s	PART
iajs-704	145	1	rann	rann	PROPN
iajs-704	145	2			PROPN
iajs-704	145	3	s	s	PART
iajs-704	145	4	–	–	PUNCT
iajs-704	145	5	1	1	NUM
iajs-704	145	6	m	m	NOUN
iajs-704	145	7	=	=	NUM
iajs-704	145	8	1	1	NUM
iajs-704	145	9	s	s	PART
iajs-704	145	10	rann	rann	PROPN
iajs-704	145	11			PROPN
iajs-704	145	12	r	r	PROPN
iajs-704	145	13	/	/	SYM
iajs-704	145	14	t	t	NOUN
iajs-704	145	15	s	s	PART
iajs-704	145	16	–	–	PUNCT
iajs-704	145	17	1	1	NUM
iajs-704	145	18	m	m	NOUN
iajs-704	145	19	,	,	PUNCT
iajs-704	145	20	so	so	SCONJ
iajs-704	145	21	s	s	X
iajs-704	145	22	–	–	PUNCT
iajs-704	145	23	1	1	NUM
iajs-704	145	24	m	m	NOUN
iajs-704	145	25	is	be	AUX
iajs-704	145	26	w.q.p	w.q.p	NOUN
iajs-704	145	27	module	module	NOUN
iajs-704	145	28	.	.	PUNCT
iajs-704	146	1	references	reference	NOUN
iajs-704	146	2	:	:	PUNCT
iajs-704	147	1	1	1	X
iajs-704	147	2	.	.	X
iajs-704	147	3	al	al	PROPN
iajs-704	147	4	-	-	PUNCT
iajs-704	147	5	bahraany	bahraany	PROPN
iajs-704	147	6	,	,	PUNCT
iajs-704	147	7	b.	b.	PROPN
iajs-704	147	8	,	,	PUNCT
iajs-704	147	9	(	(	PUNCT
iajs-704	147	10	1996	1996	NUM
iajs-704	147	11	)	)	PUNCT
iajs-704	147	12	,	,	PUNCT
iajs-704	147	13	note	note	VERB
iajs-704	147	14	on	on	ADP
iajs-704	147	15	prime	prime	ADJ
iajs-704	147	16	modules	module	NOUN
iajs-704	147	17	and	and	CCONJ
iajs-704	147	18	pure	pure	ADJ
iajs-704	147	19	submodule	submodule	NOUN
iajs-704	147	20	,	,	PUNCT
iajs-704	147	21	j.science	j.science	NOUN
iajs-704	147	22	,	,	PUNCT
iajs-704	147	23	37	37	NUM
iajs-704	147	24	,	,	PUNCT
iajs-704	147	25	.	.	PUNCT
iajs-704	148	1	1431	1431	NUM
iajs-704	148	2	–	–	PUNCT
iajs-704	148	3	1441	1441	NUM
iajs-704	148	4	.	.	PUNCT
iajs-704	149	1	2	2	NUM
iajs-704	149	2	.	.	X
iajs-704	149	3	anderson	anderson	PROPN
iajs-704	149	4	,	,	PUNCT
iajs-704	149	5	f.w	f.w	PROPN
iajs-704	149	6	.	.	PROPN
iajs-704	149	7	and	and	CCONJ
iajs-704	149	8	fuller	full	ADJ
iajs-704	149	9	,	,	PUNCT
iajs-704	149	10	r.r	r.r	PROPN
iajs-704	149	11	.	.	PROPN
iajs-704	149	12	,	,	PUNCT
iajs-704	149	13	(	(	PUNCT
iajs-704	149	14	1973	1973	NUM
iajs-704	149	15	)	)	PUNCT
iajs-704	149	16	,	,	PUNCT
iajs-704	149	17	rings	ring	NOUN
iajs-704	149	18	and	and	CCONJ
iajs-704	149	19	categories	category	NOUN
iajs-704	149	20	of	of	ADP
iajs-704	149	21	m	m	PROPN
iajs-704	149	22	module	module	NOUN
iajs-704	149	23	,	,	PUNCT
iajs-704	149	24	university	university	NOUN
iajs-704	149	25	of	of	ADP
iajs-704	149	26	oregon	oregon	PROPN
iajs-704	149	27	.	.	PUNCT
iajs-704	150	1	3	3	X
iajs-704	150	2	.	.	X
iajs-704	150	3	abdul	abdul	PROPN
iajs-704	150	4	razak	razak	PROPN
iajs-704	150	5	,	,	PUNCT
iajs-704	150	6	h.m	h.m	PROPN
iajs-704	150	7	.	.	PROPN
iajs-704	150	8	,	,	PUNCT
iajs-704	150	9	(	(	PUNCT
iajs-704	150	10	1999	1999	NUM
iajs-704	150	11	)	)	PUNCT
iajs-704	150	12	,	,	PUNCT
iajs-704	150	13	quasi	quasi	ADJ
iajs-704	150	14	prime	prime	ADJ
iajs-704	150	15	module	module	NOUN
iajs-704	150	16	and	and	CCONJ
iajs-704	150	17	quasi	quasi	ADJ
iajs-704	150	18	-	-	ADJ
iajs-704	150	19	prime	prime	ADJ
iajs-704	150	20	submodule	submodule	NOUN
iajs-704	150	21	.	.	PUNCT
iajs-704	151	1	m.sc	m.sc	PROPN
iajs-704	151	2	.	.	PUNCT
iajs-704	152	1	thesis	thesis	NOUN
iajs-704	152	2	,	,	PUNCT
iajs-704	152	3	university	university	NOUN
iajs-704	152	4	of	of	ADP
iajs-704	152	5	baghdad	baghdad	PROPN
iajs-704	152	6	.	.	PUNCT
iajs-704	153	1	4	4	X
iajs-704	153	2	.	.	X
iajs-704	153	3	sharpe	sharpe	PROPN
iajs-704	153	4	,	,	PUNCT
iajs-704	153	5	d.w	d.w	PROPN
iajs-704	153	6	.	.	PROPN
iajs-704	153	7	and	and	CCONJ
iajs-704	153	8	vamos	vamos	PROPN
iajs-704	153	9	,	,	PUNCT
iajs-704	153	10	p.	p.	NOUN
iajs-704	153	11	,	,	PUNCT
iajs-704	153	12	(	(	PUNCT
iajs-704	153	13	1972	1972	NUM
iajs-704	153	14	)	)	PUNCT
iajs-704	153	15	,	,	PUNCT
iajs-704	153	16	injective	injective	ADJ
iajs-704	153	17	modules	module	NOUN
iajs-704	153	18	,	,	PUNCT
iajs-704	153	19	cambridge	cambridge	PROPN
iajs-704	153	20	university	university	PROPN
iajs-704	153	21	,	,	PUNCT
iajs-704	153	22	press	press	NOUN
iajs-704	153	23	.	.	PUNCT
iajs-704	154	1	5	5	X
iajs-704	154	2	.	.	X
iajs-704	154	3	larsen	larsen	PROPN
iajs-704	154	4	,	,	PUNCT
iajs-704	154	5	m.d	m.d	PROPN
iajs-704	154	6	.	.	PROPN
iajs-704	154	7	and	and	CCONJ
iajs-704	154	8	mccarl	mccarl	PROPN
iajs-704	154	9	,	,	PUNCT
iajs-704	154	10	p.j	p.j	PROPN
iajs-704	154	11	.	.	PROPN
iajs-704	154	12	,	,	PUNCT
iajs-704	154	13	(	(	PUNCT
iajs-704	154	14	1971	1971	NUM
iajs-704	154	15	)	)	PUNCT
iajs-704	154	16	,	,	PUNCT
iajs-704	154	17	multiplicative	multiplicative	ADJ
iajs-704	154	18	theory	theory	NOUN
iajs-704	154	19	of	of	ADP
iajs-704	154	20	ideals	ideal	NOUN
iajs-704	154	21	,	,	PUNCT
iajs-704	154	22	academic	academic	ADJ
iajs-704	154	23	press	press	NOUN
iajs-704	154	24	,	,	PUNCT
iajs-704	154	25	new	new	PROPN
iajs-704	154	26	york	york	PROPN
iajs-704	154	27	.	.	PUNCT
iajs-704	155	1	مجلة	مجلة	PROPN
iajs-704	155	2	إبن	إبن	VERB
iajs-704	155	3	الھیثم	الھیثم	NOUN
iajs-704	155	4	للعلوم	للعلوم	NOUN
iajs-704	155	5	الصرفة	الصرفة	NOUN
iajs-704	155	6	و	و	PRON
iajs-704	155	7	التطبیقیة	التطبیقیة	PROPN
iajs-704	155	8	2012	2012	NUM
iajs-704	155	9	السنة	السنة	NOUN
iajs-704	156	1	25	25	NUM
iajs-704	156	2	المجلد	المجلد	NOUN
iajs-704	156	3	1	1	NUM
iajs-704	156	4	العدد	العدد	PROPN
iajs-704	156	5	ibn	ibn	PROPN
iajs-704	156	6	al	al	PROPN
iajs-704	156	7	-	-	PUNCT
iajs-704	156	8	haitham	haitham	PROPN
iajs-704	156	9	journal	journal	PROPN
iajs-704	156	10	for	for	ADP
iajs-704	156	11	pure	pure	ADJ
iajs-704	156	12	and	and	CCONJ
iajs-704	156	13	applied	apply	VERB
iajs-704	156	14	science	science	NOUN
iajs-704	156	15	no	no	NOUN
iajs-704	156	16	.	.	NOUN
iajs-704	156	17	1	1	NUM
iajs-704	156	18	vol	vol	NOUN
iajs-704	156	19	.	.	PUNCT
iajs-704	157	1	25	25	NUM
iajs-704	157	2	year	year	NOUN
iajs-704	157	3	2012	2012	NUM
iajs-704	157	4	حول	حول	NOUN
iajs-704	157	5	المودیوالت	المودیوالت	PROPN
iajs-704	157	6	الشبه	الشبه	PROPN
iajs-704	157	7	األولیه	األولیه	PROPN
iajs-704	157	8	الضعیفة	الضعیفة	VERB
iajs-704	157	9	منتهى	منتهى	PROPN
iajs-704	157	10	عبد	عبد	PROPN
iajs-704	157	11	الرزاق	الرزاق	NOUN
iajs-704	157	12	حسن	حسن	NOUN
iajs-704	158	1	قسم	قسم	PROPN
iajs-704	158	2	الریاضیات	الریاضیات	PROPN
iajs-704	158	3	،	،	PROPN
iajs-704	158	4	كلیة	كلیة	PROPN
iajs-704	158	5	التربیة	التربیة	PROPN
iajs-704	158	6	االساسیة	االساسیة	PROPN
iajs-704	158	7	،	،	PROPN
iajs-704	158	8	الجامعة	الجامعة	PROPN
iajs-704	158	9	المستنصریة	المستنصریة	PROPN
iajs-704	158	10	2011	2011	NUM
iajs-704	158	11	تشرین	تشرین	NOUN
iajs-704	158	12	االول	االول	NOUN
iajs-704	158	13	18	18	NUM
iajs-704	158	14	:	:	PUNCT
iajs-704	158	15	قبل	قبل	PROPN
iajs-704	158	16	البحث	البحث	PROPN
iajs-704	158	17	في2011	في2011	PROPN
iajs-704	158	18	نیسان	نیسان	NOUN
iajs-704	158	19	3	3	NUM
iajs-704	158	20	:	:	PUNCT
iajs-704	158	21	استلم	استلم	PROPN
iajs-704	158	22	البحث	البحث	VERB
iajs-704	158	23	في	في	ADP
iajs-704	158	24	الخالصة	الخالصة	PROPN
iajs-704	158	25	ُوقـد	ُوقـد	PROPN
iajs-704	158	26	برهنـت	برهنـت	NOUN
iajs-704	158	27	بعـض	بعـض	NOUN
iajs-704	158	28	الخـواص	الخـواص	PROPN
iajs-704	158	29	لهـذا	لهـذا	PROPN
iajs-704	158	30	النـوع	النـوع	PROPN
iajs-704	158	31	مـن	مـن	PROPN
iajs-704	158	32	.	.	PUNCT
iajs-704	159	1	ُ	ُ	PROPN
iajs-704	159	2	قدمت	قدمت	PROPN
iajs-704	159	3	تعریف	تعریف	PROPN
iajs-704	159	4	جدید	جدید	PROPN
iajs-704	159	5	وهو	وهو	PROPN
iajs-704	159	6	المودیوالت	المودیوالت	PROPN
iajs-704	159	7	الشبه	الشبه	PROPN
iajs-704	159	8	أولیه	أولیه	PROPN
iajs-704	159	9	الـضعیفة	الـضعیفة	VERB
iajs-704	159	10	في	في	ADP
iajs-704	159	11	هذا	هذا	NOUN
iajs-704	159	12	العمل	العمل	NOUN
iajs-704	159	13	.المودیوالت	.المودیوالت	X
iajs-704	159	14	.	.	PUNCT
iajs-704	160	1	المودیول	المودیول	VERB
iajs-704	160	2	األولي	األولي	PROPN
iajs-704	160	3	،	،	PROPN
iajs-704	160	4	المودیول	المودیول	PROPN
iajs-704	160	5	الشبه	الشبه	PROPN
iajs-704	160	6	األولي	األولي	PROPN
iajs-704	160	7	،	،	PROPN
iajs-704	160	8	المودیول	المودیول	PROPN
iajs-704	160	9	الشبه	الشبه	NOUN
iajs-704	160	10	األولي	األولي	NOUN
iajs-704	160	11	الضعیف	الضعیف	PROPN
iajs-704	160	12	:	:	PUNCT
iajs-704	160	13	الكلمات	الكلمات	VERB
iajs-704	160	14	المفتاحیة	المفتاحیة	ADV