id	sid	tid	token	lemma	pos
iajs-695	1	1	مجلة	مجلة	VERB
iajs-695	1	2	إبن	إبن	VERB
iajs-695	1	3	الھیثم	الھیثم	NOUN
iajs-695	1	4	للعلوم	للعلوم	NOUN
iajs-695	1	5	الصرفة	الصرفة	NOUN
iajs-695	1	6	و	و	PRON
iajs-695	1	7	التطبیقیة	التطبیقیة	PROPN
iajs-695	1	8	2012	2012	NUM
iajs-695	1	9	السنة	السنة	NOUN
iajs-695	1	10	25	25	NUM
iajs-695	1	11	المجلد	المجلد	NOUN
iajs-695	1	12	1	1	NUM
iajs-695	1	13	العدد	العدد	PROPN
iajs-695	1	14	ibn	ibn	PROPN
iajs-695	1	15	al	al	PROPN
iajs-695	1	16	-	-	PUNCT
iajs-695	1	17	haitham	haitham	PROPN
iajs-695	1	18	journal	journal	PROPN
iajs-695	1	19	for	for	ADP
iajs-695	1	20	pure	pure	ADJ
iajs-695	1	21	and	and	CCONJ
iajs-695	1	22	applied	apply	VERB
iajs-695	1	23	science	science	NOUN
iajs-695	1	24	no	no	NOUN
iajs-695	1	25	.	.	NOUN
iajs-695	1	26	1	1	NUM
iajs-695	1	27	vol	vol	NOUN
iajs-695	1	28	.	.	PUNCT
iajs-695	2	1	25	25	NUM
iajs-695	2	2	year	year	NOUN
iajs-695	2	3	2012	2012	NUM
iajs-695	2	4	strongly	strongly	ADV
iajs-695	2	5	essentially	essentially	ADV
iajs-695	2	6	quasi	quasi	ADJ
iajs-695	2	7	-	-	ADJ
iajs-695	2	8	dedekind	dedekind	ADJ
iajs-695	2	9	modules	module	NOUN
iajs-695	2	10	i.	i.	PROPN
iajs-695	2	11	m.a.hadi	m.a.hadi	PROPN
iajs-695	2	12	,	,	PUNCT
iajs-695	2	13	t.y.ghawi	t.y.ghawi	ADJ
iajs-695	2	14	department	department	NOUN
iajs-695	2	15	of	of	ADP
iajs-695	2	16	mathematics	mathematics	PROPN
iajs-695	2	17	,	,	PUNCT
iajs-695	2	18	college	college	NOUN
iajs-695	2	19	of	of	ADP
iajs-695	2	20	education	education	PROPN
iajs-695	2	21	ibn	ibn	PROPN
iajs-695	2	22	-	-	PUNCT
iajs-695	2	23	al	al	PROPN
iajs-695	2	24	-	-	PUNCT
iajs-695	2	25	haitham	haitham	PROPN
iajs-695	2	26	,	,	PUNCT
iajs-695	2	27	university	university	PROPN
iajs-695	2	28	of	of	ADP
iajs-695	2	29	baghdad	baghdad	PROPN
iajs-695	2	30	department	department	PROPN
iajs-695	2	31	of	of	ADP
iajs-695	2	32	mathematics	mathematics	PROPN
iajs-695	2	33	,	,	PUNCT
iajs-695	2	34	college	college	NOUN
iajs-695	2	35	of	of	ADP
iajs-695	2	36	education	education	NOUN
iajs-695	2	37	,	,	PUNCT
iajs-695	2	38	university	university	PROPN
iajs-695	2	39	of	of	ADP
iajs-695	2	40	al	al	PROPN
iajs-695	2	41	qadisiya	qadisiya	PROPN
iajs-695	2	42	received	receive	VERB
iajs-695	2	43	in	in	ADP
iajs-695	2	44	:	:	PUNCT
iajs-695	2	45	5	5	NUM
iajs-695	2	46	april	april	PROPN
iajs-695	2	47	2011	2011	NUM
iajs-695	2	48	,	,	PUNCT
iajs-695	2	49	accepted	accept	VERB
iajs-695	2	50	in	in	ADP
iajs-695	2	51	:	:	PUNCT
iajs-695	2	52	13july	13july	NUM
iajs-695	2	53	2011	2011	NUM
iajs-695	2	54	abstract	abstract	NOUN
iajs-695	2	55	let	let	VERB
iajs-695	2	56	r	r	PRON
iajs-695	2	57	be	be	AUX
iajs-695	2	58	a	a	DET
iajs-695	2	59	commutative	commutative	ADJ
iajs-695	2	60	ring	ring	NOUN
iajs-695	2	61	with	with	ADP
iajs-695	2	62	unity	unity	NOUN
iajs-695	2	63	.	.	PUNCT
iajs-695	3	1	in	in	ADP
iajs-695	3	2	this	this	DET
iajs-695	3	3	paper	paper	NOUN
iajs-695	3	4	we	we	PRON
iajs-695	3	5	introduce	introduce	VERB
iajs-695	3	6	and	and	CCONJ
iajs-695	3	7	study	study	VERB
iajs-695	3	8	the	the	DET
iajs-695	3	9	concept	concept	NOUN
iajs-695	3	10	of	of	ADP
iajs-695	3	11	strongly	strongly	ADV
iajs-695	3	12	essentially	essentially	ADV
iajs-695	3	13	quasi	quasi	ADJ
iajs-695	3	14	-	-	ADJ
iajs-695	3	15	dedekind	dedekind	ADJ
iajs-695	3	16	module	module	NOUN
iajs-695	3	17	as	as	ADP
iajs-695	3	18	a	a	DET
iajs-695	3	19	generalization	generalization	NOUN
iajs-695	3	20	of	of	ADP
iajs-695	3	21	essentially	essentially	ADV
iajs-695	3	22	quasidedekind	quasidedekind	VERB
iajs-695	3	23	module	module	NOUN
iajs-695	3	24	.	.	PUNCT
iajs-695	4	1	a	a	DET
iajs-695	4	2	unitary	unitary	ADJ
iajs-695	4	3	r	r	NOUN
iajs-695	4	4	-	-	PUNCT
iajs-695	4	5	module	module	NOUN
iajs-695	4	6	m	m	NOUN
iajs-695	4	7	is	be	AUX
iajs-695	4	8	called	call	VERB
iajs-695	4	9	a	a	DET
iajs-695	4	10	strongly	strongly	ADV
iajs-695	4	11	essentially	essentially	ADV
iajs-695	4	12	quasi	quasi	ADJ
iajs-695	4	13	-	-	ADJ
iajs-695	4	14	dedekind	dedekind	ADJ
iajs-695	4	15	module	module	NOUN
iajs-695	4	16	if	if	SCONJ
iajs-695	4	17	0	0	NUM
iajs-695	4	18	)	)	PUNCT
iajs-695	4	19	,	,	PUNCT
iajs-695	4	20	(	(	PUNCT
iajs-695	4	21	mnmhom	mnmhom	PUNCT
iajs-695	4	22	for	for	ADP
iajs-695	4	23	all	all	DET
iajs-695	4	24	semiessential	semiessential	ADJ
iajs-695	4	25	submodules	submodule	NOUN
iajs-695	4	26	n	n	PROPN
iajs-695	4	27	of	of	ADP
iajs-695	4	28	m.	m.	NOUN
iajs-695	4	29	where	where	SCONJ
iajs-695	4	30	a	a	DET
iajs-695	4	31	submodule	submodule	NOUN
iajs-695	4	32	n	n	PROPN
iajs-695	4	33	of	of	ADP
iajs-695	4	34	an	an	DET
iajs-695	4	35	r	r	NOUN
iajs-695	4	36	-	-	PUNCT
iajs-695	4	37	module	module	NOUN
iajs-695	4	38	m	m	NOUN
iajs-695	4	39	is	be	AUX
iajs-695	4	40	called	call	VERB
iajs-695	4	41	semiessential	semiessential	ADJ
iajs-695	4	42	if	if	SCONJ
iajs-695	4	43	,	,	PUNCT
iajs-695	4	44	0	0	PROPN
iajs-695	4	45	pn	pn	PROPN
iajs-695	4	46	for	for	ADP
iajs-695	4	47	all	all	DET
iajs-695	4	48	nonzero	nonzero	ADJ
iajs-695	4	49	prime	prime	ADJ
iajs-695	4	50	submodules	submodule	NOUN
iajs-695	4	51	p	p	NOUN
iajs-695	4	52	of	of	ADP
iajs-695	4	53	m	m	PROPN
iajs-695	4	54	.	.	PUNCT
iajs-695	5	1	key	key	ADJ
iajs-695	5	2	words	word	NOUN
iajs-695	5	3	:	:	PUNCT
iajs-695	5	4	essentially	essentially	ADV
iajs-695	5	5	quasi	quasi	ADJ
iajs-695	5	6	-	-	ADJ
iajs-695	5	7	dedekind	dedekind	ADJ
iajs-695	5	8	modules	module	NOUN
iajs-695	5	9	;	;	PUNCT
iajs-695	5	10	strongly	strongly	ADV
iajs-695	5	11	essentially	essentially	ADV
iajs-695	5	12	quasi	quasi	ADJ
iajs-695	5	13	-	-	ADJ
iajs-695	5	14	dedekind	dedekind	ADJ
iajs-695	5	15	modules	module	NOUN
iajs-695	5	16	,	,	PUNCT
iajs-695	5	17	semiessential	semiessential	ADJ
iajs-695	5	18	submodules	submodule	NOUN
iajs-695	5	19	,	,	PUNCT
iajs-695	5	20	multiplication	multiplication	NOUN
iajs-695	5	21	modules	module	NOUN
iajs-695	5	22	.	.	PUNCT
iajs-695	6	1	1	1	X
iajs-695	6	2	.	.	X
iajs-695	6	3	introduction	introduction	NOUN
iajs-695	6	4	let	let	VERB
iajs-695	6	5	r	r	PRON
iajs-695	6	6	be	be	AUX
iajs-695	6	7	a	a	DET
iajs-695	6	8	commutative	commutative	ADJ
iajs-695	6	9	ring	ring	NOUN
iajs-695	6	10	with	with	ADP
iajs-695	6	11	unity	unity	NOUN
iajs-695	6	12	and	and	CCONJ
iajs-695	6	13	m	m	AUX
iajs-695	6	14	be	be	AUX
iajs-695	6	15	an	an	DET
iajs-695	6	16	r	r	NOUN
iajs-695	6	17	-	-	PUNCT
iajs-695	6	18	module	module	NOUN
iajs-695	6	19	.	.	PUNCT
iajs-695	7	1	mijbass	mijbass	PROPN
iajs-695	7	2	a.s	a.s	PROPN
iajs-695	7	3	in	in	ADP
iajs-695	7	4	[	[	X
iajs-695	7	5	7	7	NUM
iajs-695	7	6	]	]	PUNCT
iajs-695	7	7	introduced	introduce	VERB
iajs-695	7	8	and	and	CCONJ
iajs-695	7	9	studied	study	VERB
iajs-695	7	10	the	the	DET
iajs-695	7	11	concept	concept	NOUN
iajs-695	7	12	of	of	ADP
iajs-695	7	13	quasi	quasi	NOUN
iajs-695	7	14	-	-	ADJ
iajs-695	7	15	dedekind	dedekind	ADJ
iajs-695	7	16	,	,	PUNCT
iajs-695	7	17	where	where	SCONJ
iajs-695	7	18	an	an	DET
iajs-695	7	19	r	r	NOUN
iajs-695	7	20	-	-	PUNCT
iajs-695	7	21	module	module	NOUN
iajs-695	7	22	m	m	NOUN
iajs-695	7	23	is	be	AUX
iajs-695	7	24	called	call	VERB
iajs-695	7	25	quasidedekind	quasidedekind	NOUN
iajs-695	7	26	if	if	SCONJ
iajs-695	7	27	,	,	PUNCT
iajs-695	7	28	0	0	NUM
iajs-695	7	29	)	)	PUNCT
iajs-695	7	30	,	,	PUNCT
iajs-695	7	31	(	(	PUNCT
iajs-695	7	32	mnmhom	mnmhom	PUNCT
iajs-695	7	33	for	for	ADP
iajs-695	7	34	all	all	DET
iajs-695	7	35	nonzero	nonzero	PROPN
iajs-695	7	36	submodules	submodule	NOUN
iajs-695	7	37	n	n	PROPN
iajs-695	7	38	of	of	ADP
iajs-695	7	39	m.	m.	NOUN
iajs-695	7	40	ghawi	ghawi	VERB
iajs-695	7	41	th.y	th.y	NOUN
iajs-695	7	42	.	.	PUNCT
iajs-695	8	1	in	in	ADP
iajs-695	8	2	[	[	X
iajs-695	8	3	4	4	X
iajs-695	8	4	]	]	PUNCT
iajs-695	8	5	introduced	introduce	VERB
iajs-695	8	6	and	and	CCONJ
iajs-695	8	7	studied	study	VERB
iajs-695	8	8	the	the	DET
iajs-695	8	9	concept	concept	NOUN
iajs-695	8	10	of	of	ADP
iajs-695	8	11	essentially	essentially	ADV
iajs-695	8	12	quasi	quasi	ADJ
iajs-695	8	13	-	-	ADJ
iajs-695	8	14	dedekind	dedekind	ADJ
iajs-695	8	15	,	,	PUNCT
iajs-695	8	16	where	where	SCONJ
iajs-695	8	17	an	an	DET
iajs-695	8	18	r	r	NOUN
iajs-695	8	19	-	-	PUNCT
iajs-695	8	20	module	module	NOUN
iajs-695	8	21	m	m	NOUN
iajs-695	8	22	is	be	AUX
iajs-695	8	23	called	call	VERB
iajs-695	8	24	essentially	essentially	ADV
iajs-695	8	25	quasi	quasi	ADJ
iajs-695	8	26	-	-	NOUN
iajs-695	8	27	dedekind	dedekind	ADJ
iajs-695	8	28	if	if	SCONJ
iajs-695	8	29	,	,	PUNCT
iajs-695	8	30	0	0	NUM
iajs-695	8	31	)	)	PUNCT
iajs-695	8	32	,	,	PUNCT
iajs-695	8	33	(	(	PUNCT
iajs-695	8	34	mnmhom	mnmhom	PUNCT
iajs-695	8	35	for	for	ADP
iajs-695	8	36	all	all	DET
iajs-695	8	37	essential	essential	ADJ
iajs-695	8	38	submodules	submodule	NOUN
iajs-695	8	39	n	n	PROPN
iajs-695	8	40	of	of	ADP
iajs-695	8	41	m	m	PROPN
iajs-695	8	42	(	(	PUNCT
iajs-695	8	43	n	n	PROPN
iajs-695	8	44	e	e	PRON
iajs-695	8	45	m	m	NOUN
iajs-695	8	46	)	)	PUNCT
iajs-695	8	47	.	.	PUNCT
iajs-695	9	1	in	in	ADP
iajs-695	9	2	this	this	DET
iajs-695	9	3	paper	paper	NOUN
iajs-695	9	4	we	we	PRON
iajs-695	9	5	give	give	VERB
iajs-695	9	6	a	a	DET
iajs-695	9	7	generalization	generalization	NOUN
iajs-695	9	8	of	of	ADP
iajs-695	9	9	essentially	essentially	ADV
iajs-695	9	10	quasi	quasi	ADJ
iajs-695	9	11	-	-	NOUN
iajs-695	9	12	dedekind	dedekind	ADJ
iajs-695	9	13	which	which	PRON
iajs-695	9	14	we	we	PRON
iajs-695	9	15	call	call	VERB
iajs-695	9	16	it	it	PRON
iajs-695	9	17	strongly	strongly	ADV
iajs-695	9	18	essentially	essentially	ADV
iajs-695	9	19	quasi	quasi	ADJ
iajs-695	9	20	-	-	ADJ
iajs-695	9	21	dedekind	dedekind	ADJ
iajs-695	9	22	,	,	PUNCT
iajs-695	9	23	where	where	SCONJ
iajs-695	9	24	an	an	DET
iajs-695	9	25	r	r	NOUN
iajs-695	9	26	-	-	PUNCT
iajs-695	9	27	module	module	NOUN
iajs-695	9	28	m	m	NOUN
iajs-695	9	29	is	be	AUX
iajs-695	9	30	called	call	VERB
iajs-695	9	31	strongly	strongly	ADV
iajs-695	9	32	essentially	essentially	ADV
iajs-695	9	33	quasi	quasi	ADJ
iajs-695	9	34	-	-	NOUN
iajs-695	9	35	dedekind	dedekind	ADJ
iajs-695	9	36	if	if	SCONJ
iajs-695	9	37	,	,	PUNCT
iajs-695	9	38	0	0	NUM
iajs-695	9	39	)	)	PUNCT
iajs-695	9	40	,	,	PUNCT
iajs-695	9	41	(	(	PUNCT
iajs-695	9	42	mnmhom	mnmhom	PUNCT
iajs-695	9	43	for	for	ADP
iajs-695	9	44	all	all	DET
iajs-695	9	45	n	n	PRON
iajs-695	9	46	se	se	NOUN
iajs-695	9	47	m.	m.	NOUN
iajs-695	9	48	in	in	ADP
iajs-695	9	49	fact	fact	NOUN
iajs-695	9	50	a	a	DET
iajs-695	9	51	submodule	submodule	NOUN
iajs-695	9	52	n	n	PROPN
iajs-695	9	53	of	of	ADP
iajs-695	9	54	m	m	PROPN
iajs-695	9	55	is	be	AUX
iajs-695	9	56	called	call	VERB
iajs-695	9	57	semiessential	semiessential	NOUN
iajs-695	9	58	in	in	ADP
iajs-695	9	59	m	m	PROPN
iajs-695	9	60	and	and	CCONJ
iajs-695	9	61	denoted	denote	VERB
iajs-695	9	62	by	by	ADP
iajs-695	9	63	(	(	PUNCT
iajs-695	9	64	n	n	PROPN
iajs-695	9	65	se	se	PROPN
iajs-695	9	66	m	m	PROPN
iajs-695	9	67	)	)	PUNCT
iajs-695	9	68	if	if	SCONJ
iajs-695	9	69	,	,	PUNCT
iajs-695	9	70	0	0	PROPN
iajs-695	9	71	pn	pn	PROPN
iajs-695	9	72	for	for	ADP
iajs-695	9	73	all	all	DET
iajs-695	9	74	nonzero	nonzero	ADJ
iajs-695	9	75	prime	prime	ADJ
iajs-695	9	76	submodules	submodule	NOUN
iajs-695	9	77	p	p	NOUN
iajs-695	9	78	of	of	ADP
iajs-695	9	79	m	m	PROPN
iajs-695	10	1	[	[	X
iajs-695	10	2	1	1	NUM
iajs-695	10	3	]	]	PUNCT
iajs-695	10	4	,	,	PUNCT
iajs-695	10	5	provided	provide	VERB
iajs-695	10	6	that	that	SCONJ
iajs-695	10	7	m	m	PROPN
iajs-695	10	8	has	have	AUX
iajs-695	10	9	nonzero	nonzero	PROPN
iajs-695	10	10	prime	prime	ADJ
iajs-695	10	11	submodule	submodule	NOUN
iajs-695	10	12	.	.	PUNCT
iajs-695	11	1	in	in	ADP
iajs-695	11	2	this	this	DET
iajs-695	11	3	paper	paper	NOUN
iajs-695	11	4	we	we	PRON
iajs-695	11	5	present	present	VERB
iajs-695	11	6	the	the	DET
iajs-695	11	7	basic	basic	ADJ
iajs-695	11	8	properties	property	NOUN
iajs-695	11	9	of	of	ADP
iajs-695	11	10	strongly	strongly	ADV
iajs-695	11	11	essentially	essentially	ADV
iajs-695	11	12	quasi	quasi	ADJ
iajs-695	11	13	-	-	ADJ
iajs-695	11	14	dedekind	dedekind	ADJ
iajs-695	11	15	and	and	CCONJ
iajs-695	11	16	some	some	DET
iajs-695	11	17	relationships	relationship	NOUN
iajs-695	11	18	with	with	ADP
iajs-695	11	19	other	other	ADJ
iajs-695	11	20	modules	module	NOUN
iajs-695	11	21	.	.	PUNCT
iajs-695	12	1	next	next	ADJ
iajs-695	12	2	throughout	throughout	ADP
iajs-695	12	3	this	this	DET
iajs-695	12	4	paper	paper	NOUN
iajs-695	12	5	,	,	PUNCT
iajs-695	12	6	m	m	VERB
iajs-695	12	7	has	have	VERB
iajs-695	12	8	a	a	DET
iajs-695	12	9	nonzero	nonzero	ADJ
iajs-695	12	10	prime	prime	ADJ
iajs-695	12	11	submodules	submodule	NOUN
iajs-695	12	12	.	.	PUNCT
iajs-695	13	1	1.1	1.1	NUM
iajs-695	13	2	definition	definition	NOUN
iajs-695	13	3	an	an	DET
iajs-695	13	4	r	r	NOUN
iajs-695	13	5	-	-	PUNCT
iajs-695	13	6	module	module	NOUN
iajs-695	13	7	m	m	NOUN
iajs-695	13	8	is	be	AUX
iajs-695	13	9	called	call	VERB
iajs-695	13	10	strongly	strongly	ADV
iajs-695	13	11	essentially	essentially	ADV
iajs-695	13	12	quasi	quasi	ADJ
iajs-695	13	13	-	-	NOUN
iajs-695	13	14	dedekind	dedekind	ADJ
iajs-695	13	15	if	if	SCONJ
iajs-695	13	16	,	,	PUNCT
iajs-695	13	17	0	0	NUM
iajs-695	13	18	)	)	PUNCT
iajs-695	13	19	,	,	PUNCT
iajs-695	13	20	(	(	PUNCT
iajs-695	13	21	mnmhom	mnmhom	PUNCT
iajs-695	13	22	for	for	ADP
iajs-695	13	23	all	all	DET
iajs-695	13	24	semiessential	semiessential	ADJ
iajs-695	13	25	submodules	submodule	NOUN
iajs-695	13	26	n	n	PROPN
iajs-695	13	27	of	of	ADP
iajs-695	13	28	m.	m.	NOUN
iajs-695	13	29	مجلة	مجلة	PROPN
iajs-695	13	30	إبن	إبن	VERB
iajs-695	13	31	الھیثم	الھیثم	NOUN
iajs-695	13	32	للعلوم	للعلوم	NOUN
iajs-695	13	33	الصرفة	الصرفة	NOUN
iajs-695	13	34	و	و	PRON
iajs-695	13	35	التطبیقیة	التطبیقیة	PROPN
iajs-695	13	36	2012	2012	NUM
iajs-695	13	37	السنة	السنة	NOUN
iajs-695	13	38	25	25	NUM
iajs-695	13	39	المجلد	المجلد	NOUN
iajs-695	13	40	1	1	NUM
iajs-695	13	41	العدد	العدد	PROPN
iajs-695	13	42	ibn	ibn	PROPN
iajs-695	13	43	al	al	PROPN
iajs-695	13	44	-	-	PUNCT
iajs-695	13	45	haitham	haitham	PROPN
iajs-695	13	46	journal	journal	PROPN
iajs-695	13	47	for	for	ADP
iajs-695	13	48	pure	pure	ADJ
iajs-695	13	49	and	and	CCONJ
iajs-695	13	50	applied	apply	VERB
iajs-695	13	51	science	science	NOUN
iajs-695	13	52	no	no	NOUN
iajs-695	13	53	.	.	NOUN
iajs-695	13	54	1	1	NUM
iajs-695	13	55	vol	vol	NOUN
iajs-695	13	56	.	.	PUNCT
iajs-695	14	1	25	25	NUM
iajs-695	14	2	year	year	NOUN
iajs-695	14	3	2012	2012	NUM
iajs-695	14	4	1.2	1.2	NUM
iajs-695	14	5	remarks	remark	NOUN
iajs-695	14	6	and	and	CCONJ
iajs-695	14	7	examples	example	NOUN
iajs-695	14	8	:	:	PUNCT
iajs-695	14	9	1it	1it	NOUN
iajs-695	14	10	is	be	AUX
iajs-695	14	11	clear	clear	ADJ
iajs-695	14	12	that	that	SCONJ
iajs-695	14	13	if	if	SCONJ
iajs-695	14	14	m	m	NOUN
iajs-695	14	15	is	be	AUX
iajs-695	14	16	a	a	DET
iajs-695	14	17	strongly	strongly	ADV
iajs-695	14	18	essentially	essentially	ADV
iajs-695	14	19	quasi	quasi	ADJ
iajs-695	14	20	-	-	ADJ
iajs-695	14	21	dedekind	dedekind	ADJ
iajs-695	14	22	r	r	NOUN
iajs-695	14	23	-	-	PUNCT
iajs-695	14	24	module	module	NOUN
iajs-695	14	25	,	,	PUNCT
iajs-695	14	26	then	then	ADV
iajs-695	14	27	m	m	NOUN
iajs-695	14	28	is	be	AUX
iajs-695	14	29	an	an	DET
iajs-695	14	30	essentially	essentially	ADV
iajs-695	14	31	quasi	quasi	ADJ
iajs-695	14	32	-	-	ADJ
iajs-695	14	33	dedekind	dedekind	ADJ
iajs-695	14	34	r	r	NOUN
iajs-695	14	35	-	-	NOUN
iajs-695	14	36	module	module	NOUN
iajs-695	14	37	,	,	PUNCT
iajs-695	14	38	since	since	SCONJ
iajs-695	14	39	every	every	DET
iajs-695	14	40	essential	essential	ADJ
iajs-695	14	41	submodule	submodule	NOUN
iajs-695	14	42	is	be	AUX
iajs-695	14	43	semiessential	semiessential	ADJ
iajs-695	14	44	submodule	submodule	NOUN
iajs-695	14	45	.	.	PUNCT
iajs-695	15	1	2every	2every	NUM
iajs-695	15	2	quasi	quasi	ADJ
iajs-695	15	3	-	-	ADJ
iajs-695	15	4	dedekind	dedekind	ADJ
iajs-695	15	5	r	r	NOUN
iajs-695	15	6	-	-	PUNCT
iajs-695	15	7	module	module	NOUN
iajs-695	15	8	is	be	AUX
iajs-695	15	9	a	a	DET
iajs-695	15	10	strongly	strongly	ADV
iajs-695	15	11	essentially	essentially	ADV
iajs-695	15	12	quasi	quasi	ADJ
iajs-695	15	13	-	-	ADJ
iajs-695	15	14	dedekind	dedekind	ADJ
iajs-695	15	15	r	r	NOUN
iajs-695	15	16	-	-	PUNCT
iajs-695	15	17	module	module	NOUN
iajs-695	15	18	,	,	PUNCT
iajs-695	15	19	but	but	CCONJ
iajs-695	15	20	the	the	DET
iajs-695	15	21	converse	converse	NOUN
iajs-695	15	22	is	be	AUX
iajs-695	15	23	not	not	PART
iajs-695	15	24	true	true	ADJ
iajs-695	15	25	in	in	ADP
iajs-695	15	26	general	general	ADJ
iajs-695	15	27	,	,	PUNCT
iajs-695	15	28	for	for	ADP
iajs-695	15	29	example	example	NOUN
iajs-695	15	30	:	:	PUNCT
iajs-695	15	31	z6	z6	PROPN
iajs-695	15	32	as	as	SCONJ
iajs-695	15	33	zmodule	zmodule	NOUN
iajs-695	15	34	is	be	AUX
iajs-695	15	35	strongly	strongly	ADV
iajs-695	15	36	essentially	essentially	ADV
iajs-695	15	37	quasi	quasi	ADJ
iajs-695	15	38	-	-	ADJ
iajs-695	15	39	dedekind	dedekind	ADJ
iajs-695	15	40	,	,	PUNCT
iajs-695	15	41	but	but	CCONJ
iajs-695	15	42	it	it	PRON
iajs-695	15	43	is	be	AUX
iajs-695	15	44	not	not	PART
iajs-695	15	45	quasi	quasi	ADJ
iajs-695	15	46	-	-	ADJ
iajs-695	15	47	dedekind	dedekind	ADJ
iajs-695	15	48	,	,	PUNCT
iajs-695	15	49	since	since	SCONJ
iajs-695	15	50	0)),2	0)),2	PROPN
iajs-695	15	51	(	(	PUNCT
iajs-695	15	52	(	(	PUNCT
iajs-695	15	53	266	266	NUM
iajs-695	15	54			NUM
iajs-695	15	55	zzzhom	zzzhom	NOUN
iajs-695	15	56	.	.	PUNCT
iajs-695	16	1	3each	3each	NUM
iajs-695	16	2	of	of	ADP
iajs-695	16	3	z	z	PROPN
iajs-695	16	4	,	,	PUNCT
iajs-695	16	5	z6	z6	PROPN
iajs-695	16	6	,	,	PUNCT
iajs-695	16	7	z10	z10	NOUN
iajs-695	16	8	is	be	AUX
iajs-695	16	9	strongly	strongly	ADV
iajs-695	16	10	essentially	essentially	ADV
iajs-695	16	11	quasi	quasi	ADJ
iajs-695	16	12	-	-	NOUN
iajs-695	16	13	dedekind	dedekind	ADJ
iajs-695	16	14	as	as	ADP
iajs-695	16	15	z	z	NOUN
iajs-695	16	16	-	-	NOUN
iajs-695	16	17	module	module	NOUN
iajs-695	16	18	.	.	PUNCT
iajs-695	17	1	4each	4each	PRON
iajs-695	17	2	of	of	ADP
iajs-695	17	3	z4	z4	PROPN
iajs-695	17	4	,	,	PUNCT
iajs-695	17	5	z8	z8	PROPN
iajs-695	17	6	,	,	PUNCT
iajs-695	17	7	z12	z12	PROPN
iajs-695	17	8	,	,	PUNCT
iajs-695	17	9	z16	z16	PROPN
iajs-695	17	10	is	be	AUX
iajs-695	17	11	not	not	PART
iajs-695	17	12	strongly	strongly	ADV
iajs-695	17	13	essentially	essentially	ADV
iajs-695	17	14	quasi	quasi	ADJ
iajs-695	17	15	-	-	NOUN
iajs-695	17	16	dedekind	dedekind	ADJ
iajs-695	17	17	as	as	ADP
iajs-695	17	18	z	z	NOUN
iajs-695	17	19	-	-	NOUN
iajs-695	17	20	module	module	NOUN
iajs-695	17	21	.	.	PUNCT
iajs-695	18	1	5	5	NUM
iajs-695	19	1	p	p	NOUN
iajs-695	19	2	z	z	NOUN
iajs-695	19	3			NOUN
iajs-695	19	4	is	be	AUX
iajs-695	19	5	not	not	PART
iajs-695	19	6	strongly	strongly	ADV
iajs-695	19	7	essentially	essentially	ADV
iajs-695	19	8	quasi	quasi	ADJ
iajs-695	19	9	-	-	NOUN
iajs-695	19	10	dedekind	dedekind	ADJ
iajs-695	19	11	as	as	ADP
iajs-695	19	12	z	z	NOUN
iajs-695	19	13	-	-	NOUN
iajs-695	19	14	module	module	NOUN
iajs-695	19	15	,	,	PUNCT
iajs-695	19	16	for	for	ADP
iajs-695	19	17	all	all	DET
iajs-695	19	18	prime	prime	ADJ
iajs-695	19	19	numbers	number	NOUN
iajs-695	19	20	p.	p.	PROPN
iajs-695	19	21	62zz	62zz	PROPN
iajs-695	20	1			ADJ
iajs-695	20	2	is	be	AUX
iajs-695	20	3	not	not	PART
iajs-695	20	4	essentially	essentially	ADV
iajs-695	20	5	quasi	quasi	ADJ
iajs-695	20	6	-	-	ADJ
iajs-695	20	7	dedekind	dedekind	ADJ
iajs-695	20	8	as	as	ADP
iajs-695	20	9	z	z	NOUN
iajs-695	20	10	-	-	PUNCT
iajs-695	20	11	module	module	NOUN
iajs-695	20	12	,	,	PUNCT
iajs-695	20	13	see	see	VERB
iajs-695	20	14	[	[	X
iajs-695	20	15	4	4	NUM
iajs-695	20	16	,	,	PUNCT
iajs-695	20	17	remark	remark	VERB
iajs-695	20	18	1.2.14	1.2.14	NUM
iajs-695	20	19	]	]	PUNCT
iajs-695	20	20	,	,	PUNCT
iajs-695	20	21	so	so	CCONJ
iajs-695	20	22	it	it	PRON
iajs-695	20	23	is	be	AUX
iajs-695	20	24	not	not	PART
iajs-695	20	25	strongly	strongly	ADV
iajs-695	20	26	essentially	essentially	ADV
iajs-695	20	27	quasi	quasi	ADJ
iajs-695	20	28	-	-	NOUN
iajs-695	20	29	dedekind	dedekind	ADJ
iajs-695	20	30	as	as	ADP
iajs-695	20	31	z	z	NOUN
iajs-695	20	32	-	-	NOUN
iajs-695	20	33	module	module	NOUN
iajs-695	20	34	.	.	PUNCT
iajs-695	21	1	7let	7let	NUM
iajs-695	21	2	n	n	NUM
iajs-695	21	3			NUM
iajs-695	21	4	m	m	NOUN
iajs-695	21	5	and	and	CCONJ
iajs-695	21	6	m	m	NOUN
iajs-695	21	7	/	/	SYM
iajs-695	21	8	n	n	PROPN
iajs-695	21	9	is	be	AUX
iajs-695	21	10	a	a	DET
iajs-695	21	11	strongly	strongly	ADV
iajs-695	21	12	essentially	essentially	ADV
iajs-695	21	13	quasi	quasi	ADJ
iajs-695	21	14	-	-	ADJ
iajs-695	21	15	dedekind	dedekind	ADJ
iajs-695	21	16	r	r	NOUN
iajs-695	21	17	-	-	PUNCT
iajs-695	21	18	module	module	NOUN
iajs-695	21	19	,	,	PUNCT
iajs-695	21	20	then	then	ADV
iajs-695	21	21	it	it	PRON
iajs-695	21	22	is	be	AUX
iajs-695	21	23	not	not	PART
iajs-695	21	24	necessarily	necessarily	ADV
iajs-695	21	25	that	that	PRON
iajs-695	21	26	m	m	VERB
iajs-695	21	27	is	be	AUX
iajs-695	21	28	a	a	DET
iajs-695	21	29	strongly	strongly	ADV
iajs-695	21	30	essentially	essentially	ADV
iajs-695	21	31	quasi	quasi	ADJ
iajs-695	21	32	-	-	ADJ
iajs-695	21	33	dedekind	dedekind	ADJ
iajs-695	21	34	r	r	NOUN
iajs-695	21	35	-	-	NOUN
iajs-695	21	36	module	module	NOUN
iajs-695	21	37	;	;	PUNCT
iajs-695	21	38	for	for	ADP
iajs-695	21	39	example	example	NOUN
iajs-695	21	40	:	:	PUNCT
iajs-695	21	41	let	let	VERB
iajs-695	21	42	m	m	VERB
iajs-695	21	43	=	=	VERB
iajs-695	21	44	z12	z12	NUM
iajs-695	21	45	as	as	ADP
iajs-695	21	46	z	z	NOUN
iajs-695	21	47	-	-	PUNCT
iajs-695	21	48	module	module	NOUN
iajs-695	21	49	and	and	CCONJ
iajs-695	21	50	let	let	VERB
iajs-695	21	51	n	n	PROPN
iajs-695	21	52	=	=	SYM
iajs-695	21	53	12(6	12(6	NUM
iajs-695	21	54	)	)	PUNCT
iajs-695	21	55	z	z	PROPN
iajs-695	21	56	,	,	PUNCT
iajs-695	21	57	then	then	ADV
iajs-695	21	58	12	12	NUM
iajs-695	21	59	6z	6z	NOUN
iajs-695	21	60	n	n	PRON
iajs-695	21	61	z	z	NOUN
iajs-695	21	62	is	be	AUX
iajs-695	21	63	a	a	DET
iajs-695	21	64	strongly	strongly	ADV
iajs-695	21	65	essentially	essentially	ADV
iajs-695	21	66	quasi	quasi	ADJ
iajs-695	21	67	-	-	ADJ
iajs-695	21	68	dedekind	dedekind	ADJ
iajs-695	21	69	z	z	NOUN
iajs-695	21	70	-	-	NOUN
iajs-695	21	71	module	module	NOUN
iajs-695	21	72	,	,	PUNCT
iajs-695	21	73	but	but	CCONJ
iajs-695	21	74	z12	z12	NOUN
iajs-695	21	75	is	be	AUX
iajs-695	21	76	not	not	PART
iajs-695	21	77	strongly	strongly	ADV
iajs-695	21	78	essentially	essentially	ADV
iajs-695	21	79	quasi	quasi	ADJ
iajs-695	21	80	-	-	NOUN
iajs-695	21	81	dedekind	dedekind	ADJ
iajs-695	21	82	as	as	ADP
iajs-695	21	83	z	z	NOUN
iajs-695	21	84	-	-	PUNCT
iajs-695	21	85	module	module	NOUN
iajs-695	21	86	.	.	PUNCT
iajs-695	22	1	recall	recall	VERB
iajs-695	22	2	that	that	SCONJ
iajs-695	22	3	a	a	DET
iajs-695	22	4	nonzero	nonzero	ADJ
iajs-695	22	5	r	r	NOUN
iajs-695	22	6	-	-	PUNCT
iajs-695	22	7	module	module	NOUN
iajs-695	22	8	m	m	NOUN
iajs-695	22	9	is	be	AUX
iajs-695	22	10	called	call	VERB
iajs-695	22	11	semi	semi	ADJ
iajs-695	22	12	-	-	ADJ
iajs-695	22	13	uniform	uniform	ADJ
iajs-695	22	14	,	,	PUNCT
iajs-695	22	15	if	if	SCONJ
iajs-695	22	16	every	every	DET
iajs-695	22	17	nonzero	nonzero	ADJ
iajs-695	22	18	r	r	NOUN
iajs-695	22	19	-	-	PUNCT
iajs-695	22	20	submodule	submodule	NOUN
iajs-695	22	21	of	of	ADP
iajs-695	22	22	m	m	PROPN
iajs-695	22	23	is	be	AUX
iajs-695	22	24	a	a	DET
iajs-695	22	25	semiessential	semiessential	ADJ
iajs-695	22	26	submodule	submodule	NOUN
iajs-695	22	27	of	of	ADP
iajs-695	22	28	m	m	PROPN
iajs-695	22	29	[	[	X
iajs-695	22	30	1	1	NUM
iajs-695	22	31	]	]	PUNCT
iajs-695	22	32	.	.	PUNCT
iajs-695	23	1	1.3	1.3	NUM
iajs-695	23	2	proposition	proposition	NOUN
iajs-695	23	3	:	:	PUNCT
iajs-695	23	4	let	let	VERB
iajs-695	23	5	m	m	PRON
iajs-695	23	6	be	be	AUX
iajs-695	23	7	a	a	DET
iajs-695	23	8	semi	semi	ADJ
iajs-695	23	9	-	-	ADJ
iajs-695	23	10	uniform	uniform	ADJ
iajs-695	23	11	r	r	NOUN
iajs-695	23	12	-	-	PUNCT
iajs-695	23	13	module	module	NOUN
iajs-695	23	14	.	.	PUNCT
iajs-695	24	1	then	then	ADV
iajs-695	24	2	m	m	PROPN
iajs-695	24	3	is	be	AUX
iajs-695	24	4	a	a	DET
iajs-695	24	5	quasi	quasi	ADJ
iajs-695	24	6	-	-	ADJ
iajs-695	24	7	dedekind	dedekind	ADJ
iajs-695	24	8	r	r	NOUN
iajs-695	24	9	-	-	PUNCT
iajs-695	24	10	module	module	NOUN
iajs-695	24	11	if	if	SCONJ
iajs-695	24	12	and	and	CCONJ
iajs-695	24	13	only	only	ADV
iajs-695	24	14	if	if	SCONJ
iajs-695	24	15	m	m	NOUN
iajs-695	24	16	is	be	AUX
iajs-695	24	17	a	a	DET
iajs-695	24	18	strongly	strongly	ADV
iajs-695	24	19	essentially	essentially	ADV
iajs-695	24	20	quasi	quasi	ADJ
iajs-695	24	21	-	-	ADJ
iajs-695	24	22	dedekind	dedekind	ADJ
iajs-695	24	23	r	r	NOUN
iajs-695	24	24	-	-	PUNCT
iajs-695	24	25	module	module	NOUN
iajs-695	24	26	.	.	PUNCT
iajs-695	25	1	proof	proof	NOUN
iajs-695	25	2	:	:	PUNCT
iajs-695	25	3	it	it	PRON
iajs-695	25	4	is	be	AUX
iajs-695	25	5	clear	clear	ADJ
iajs-695	25	6	.	.	PUNCT
iajs-695	26	1	1.4	1.4	NUM
iajs-695	26	2	corollary	corollary	NOUN
iajs-695	26	3	:	:	PUNCT
iajs-695	26	4	let	let	VERB
iajs-695	26	5	m	m	PRON
iajs-695	26	6	be	be	AUX
iajs-695	26	7	a	a	DET
iajs-695	26	8	uniform	uniform	ADJ
iajs-695	26	9	r	r	NOUN
iajs-695	26	10	-	-	PUNCT
iajs-695	26	11	module	module	NOUN
iajs-695	26	12	.the	.the	NOUN
iajs-695	26	13	following	follow	VERB
iajs-695	26	14	statements	statement	NOUN
iajs-695	26	15	are	be	AUX
iajs-695	26	16	equivalent	equivalent	ADJ
iajs-695	26	17	:	:	PUNCT
iajs-695	26	18	1	1	NUM
iajs-695	26	19	m	m	NOUN
iajs-695	26	20	is	be	AUX
iajs-695	26	21	a	a	DET
iajs-695	26	22	quasi	quasi	ADJ
iajs-695	26	23	-	-	ADJ
iajs-695	26	24	dedekind	dedekind	ADJ
iajs-695	26	25	r	r	NOUN
iajs-695	26	26	-	-	NOUN
iajs-695	26	27	module	module	NOUN
iajs-695	26	28	.	.	PUNCT
iajs-695	27	1	2	2	NUM
iajs-695	27	2	m	m	NOUN
iajs-695	27	3	is	be	AUX
iajs-695	27	4	a	a	DET
iajs-695	27	5	strongly	strongly	ADV
iajs-695	27	6	essentially	essentially	ADV
iajs-695	27	7	quasi	quasi	ADJ
iajs-695	27	8	-	-	ADJ
iajs-695	27	9	dedekind	dedekind	ADJ
iajs-695	27	10	r	r	NOUN
iajs-695	27	11	-	-	NOUN
iajs-695	27	12	module	module	NOUN
iajs-695	27	13	.	.	PUNCT
iajs-695	28	1	3	3	NUM
iajs-695	28	2	m	m	NOUN
iajs-695	28	3	is	be	AUX
iajs-695	28	4	an	an	DET
iajs-695	28	5	essentially	essentially	ADV
iajs-695	28	6	quasi	quasi	ADJ
iajs-695	28	7	-	-	ADJ
iajs-695	28	8	dedekind	dedekind	ADJ
iajs-695	28	9	r	r	NOUN
iajs-695	28	10	-	-	PUNCT
iajs-695	28	11	module	module	NOUN
iajs-695	28	12	.	.	PUNCT
iajs-695	29	1	proof	proof	NOUN
iajs-695	29	2	:	:	PUNCT
iajs-695	29	3	it	it	PRON
iajs-695	29	4	is	be	AUX
iajs-695	29	5	clear	clear	ADJ
iajs-695	29	6	.	.	PUNCT
iajs-695	30	1	the	the	DET
iajs-695	30	2	following	follow	VERB
iajs-695	30	3	is	be	AUX
iajs-695	30	4	a	a	DET
iajs-695	30	5	characterization	characterization	NOUN
iajs-695	30	6	of	of	ADP
iajs-695	30	7	strongly	strongly	ADV
iajs-695	30	8	essentially	essentially	ADV
iajs-695	30	9	quasi	quasi	ADJ
iajs-695	30	10	-	-	ADJ
iajs-695	30	11	dedekind	dedekind	ADJ
iajs-695	30	12	module	module	NOUN
iajs-695	30	13	.	.	PUNCT
iajs-695	31	1	1.5	1.5	NUM
iajs-695	31	2	theorem	theorem	NOUN
iajs-695	31	3	:	:	PUNCT
iajs-695	31	4	let	let	VERB
iajs-695	31	5	m	m	PRON
iajs-695	31	6	be	be	AUX
iajs-695	31	7	an	an	DET
iajs-695	31	8	r	r	NOUN
iajs-695	31	9	-	-	PUNCT
iajs-695	31	10	module	module	NOUN
iajs-695	31	11	m	m	NOUN
iajs-695	31	12	is	be	AUX
iajs-695	31	13	strongly	strongly	ADV
iajs-695	31	14	essentially	essentially	ADV
iajs-695	31	15	quasi	quasi	ADJ
iajs-695	31	16	-	-	NOUN
iajs-695	31	17	dedekind	dedekind	ADJ
iajs-695	31	18	if	if	SCONJ
iajs-695	31	19	and	and	CCONJ
iajs-695	31	20	only	only	ADV
iajs-695	31	21	if	if	SCONJ
iajs-695	31	22	for	for	ADP
iajs-695	31	23	each	each	PRON
iajs-695	31	24	)	)	PUNCT
iajs-695	31	25	(	(	PUNCT
iajs-695	31	26	mendf	mendf	ADJ
iajs-695	31	27	r	r	NOUN
iajs-695	31	28	,	,	PUNCT
iajs-695	31	29	0f	0f	NUM
iajs-695	31	30	implies	imply	VERB
iajs-695	31	31	kerf	kerf	NOUN
iajs-695	31	32	se	se	PROPN
iajs-695	31	33	m	m	PROPN
iajs-695	31	34	.	.	PUNCT
iajs-695	32	1	proof	proof	NOUN
iajs-695	32	2	:	:	PUNCT
iajs-695	32	3			NOUN
iajs-695	32	4	)	)	PUNCT
iajs-695	32	5	suppose	suppose	VERB
iajs-695	32	6	that	that	SCONJ
iajs-695	32	7	m	m	PROPN
iajs-695	32	8	is	be	AUX
iajs-695	32	9	a	a	DET
iajs-695	32	10	strongly	strongly	ADV
iajs-695	32	11	essentially	essentially	ADV
iajs-695	32	12	quasi	quasi	ADJ
iajs-695	32	13	-	-	ADJ
iajs-695	32	14	dedekind	dedekind	ADJ
iajs-695	32	15	r	r	NOUN
iajs-695	32	16	-	-	PUNCT
iajs-695	32	17	module	module	NOUN
iajs-695	32	18	.let	.let	NOUN
iajs-695	32	19	)	)	PUNCT
iajs-695	33	1	(	(	PUNCT
iajs-695	33	2	mendf	mendf	ADJ
iajs-695	33	3	r	r	NOUN
iajs-695	33	4	,	,	PUNCT
iajs-695	33	5	0f	0f	NUM
iajs-695	33	6	.	.	PUNCT
iajs-695	34	1	to	to	PART
iajs-695	34	2	prove	prove	VERB
iajs-695	34	3	that	that	SCONJ
iajs-695	34	4	kerf	kerf	NOUN
iajs-695	34	5	se	se	PROPN
iajs-695	34	6	m.	m.	NOUN
iajs-695	34	7	assume	assume	VERB
iajs-695	34	8	that	that	SCONJ
iajs-695	34	9	kerf	kerf	NOUN
iajs-695	34	10	se	se	PROPN
iajs-695	34	11	m	m	PROPN
iajs-695	34	12	,	,	PUNCT
iajs-695	34	13	define	define	VERB
iajs-695	34	14	mkerfmg	mkerfmg	NOUN
iajs-695	34	15			NUM
iajs-695	34	16	:	:	PUNCT
iajs-695	34	17	by	by	ADP
iajs-695	34	18	g	g	PROPN
iajs-695	34	19	(	(	PUNCT
iajs-695	34	20	m+kerf	m+kerf	PROPN
iajs-695	35	1	)	)	PUNCT
iajs-695	35	2	=	=	SYM
iajs-695	35	3	f(m	f(m	PROPN
iajs-695	35	4	)	)	PUNCT
iajs-695	35	5	for	for	ADP
iajs-695	35	6	all	all	DET
iajs-695	35	7	mm	mm	NOUN
iajs-695	35	8	.	.	PUNCT
iajs-695	36	1	it	it	PRON
iajs-695	36	2	is	be	AUX
iajs-695	36	3	clear	clear	ADJ
iajs-695	36	4	that	that	SCONJ
iajs-695	36	5	g	g	PROPN
iajs-695	36	6	is	be	AUX
iajs-695	36	7	well	well	ADV
iajs-695	36	8	-	-	PUNCT
iajs-695	36	9	defined	define	VERB
iajs-695	36	10	and	and	CCONJ
iajs-695	36	11	0g	0g	NUM
iajs-695	36	12	,	,	PUNCT
iajs-695	36	13	hence	hence	ADV
iajs-695	36	14	0	0	NUM
iajs-695	36	15	)	)	PUNCT
iajs-695	36	16	,	,	PUNCT
iajs-695	36	17	(	(	PUNCT
iajs-695	36	18	mkerfmhom	mkerfmhom	X
iajs-695	36	19	which	which	PRON
iajs-695	36	20	is	be	AUX
iajs-695	36	21	a	a	DET
iajs-695	36	22	contradiction	contradiction	NOUN
iajs-695	36	23	.	.	PUNCT
iajs-695	37	1			NOUN
iajs-695	37	2	)	)	PUNCT
iajs-695	37	3	assume	assume	VERB
iajs-695	37	4	that	that	SCONJ
iajs-695	37	5	there	there	PRON
iajs-695	37	6	exists	exist	VERB
iajs-695	37	7	mnmh	mnmh	NOUN
iajs-695	37	8			NOUN
iajs-695	37	9	:	:	PUNCT
iajs-695	37	10	,	,	PUNCT
iajs-695	37	11	0h	0h	NUM
iajs-695	37	12	,	,	PUNCT
iajs-695	37	13	for	for	ADP
iajs-695	37	14	some	some	DET
iajs-695	37	15	n	n	PRON
iajs-695	37	16	se	se	NOUN
iajs-695	37	17	m.	m.	NOUN
iajs-695	37	18	consider	consider	VERB
iajs-695	37	19	the	the	DET
iajs-695	37	20	following	following	NOUN
iajs-695	37	21	:	:	PUNCT
iajs-695	37	22	mnmm	mnmm	PROPN
iajs-695	37	23	h	h	INTJ
iajs-695	37	24	,	,	PUNCT
iajs-695	37	25	where	where	SCONJ
iajs-695	37	26			PROPN
iajs-695	37	27	is	be	AUX
iajs-695	37	28	the	the	DET
iajs-695	37	29	natural	natural	ADJ
iajs-695	37	30	projective	projective	ADJ
iajs-695	37	31	mapping	mapping	NOUN
iajs-695	37	32	,	,	PUNCT
iajs-695	37	33	then	then	ADV
iajs-695	37	34	مجلة	مجلة	VERB
iajs-695	37	35	إبن	إبن	VERB
iajs-695	37	36	الھیثم	الھیثم	NOUN
iajs-695	37	37	للعلوم	للعلوم	NOUN
iajs-695	37	38	الصرفة	الصرفة	NOUN
iajs-695	37	39	و	و	PRON
iajs-695	37	40	التطبیقیة	التطبیقیة	PROPN
iajs-695	37	41	2012	2012	NUM
iajs-695	37	42	السنة	السنة	NOUN
iajs-695	38	1	25	25	NUM
iajs-695	38	2	المجلد	المجلد	NOUN
iajs-695	38	3	1	1	NUM
iajs-695	38	4	العدد	العدد	PROPN
iajs-695	38	5	ibn	ibn	PROPN
iajs-695	38	6	al	al	PROPN
iajs-695	38	7	-	-	PUNCT
iajs-695	38	8	haitham	haitham	PROPN
iajs-695	38	9	journal	journal	PROPN
iajs-695	38	10	for	for	ADP
iajs-695	38	11	pure	pure	ADJ
iajs-695	38	12	and	and	CCONJ
iajs-695	38	13	applied	apply	VERB
iajs-695	38	14	science	science	NOUN
iajs-695	38	15	no	no	NOUN
iajs-695	38	16	.	.	NOUN
iajs-695	38	17	1	1	NUM
iajs-695	38	18	vol	vol	NOUN
iajs-695	38	19	.	.	PUNCT
iajs-695	39	1	25	25	NUM
iajs-695	39	2	year	year	NOUN
iajs-695	39	3	2012	2012	NUM
iajs-695	39	4	)	)	PUNCT
iajs-695	39	5	(	(	PUNCT
iajs-695	39	6	mendho	mendho	VERB
iajs-695	39	7	r	r	X
iajs-695	39	8			X
iajs-695	39	9			PROPN
iajs-695	39	10	and	and	CCONJ
iajs-695	39	11	0	0	PROPN
iajs-695	39	12	.	.	PUNCT
iajs-695	40	1	since	since	SCONJ
iajs-695	40	2	n	n	NOUN
iajs-695	40	3			PROPN
iajs-695	40	4	ker	ker	PROPN
iajs-695	40	5	and	and	CCONJ
iajs-695	40	6	n	n	PROPN
iajs-695	40	7	se	se	PROPN
iajs-695	40	8	m	m	PROPN
iajs-695	40	9	,	,	PUNCT
iajs-695	40	10	thus	thus	ADV
iajs-695	40	11	ker	ker	PROPN
iajs-695	40	12	se	se	PROPN
iajs-695	40	13	m.	m.	NOUN
iajs-695	40	14	since	since	SCONJ
iajs-695	40	15	(	(	PUNCT
iajs-695	40	16	for	for	ADP
iajs-695	40	17	any	any	DET
iajs-695	40	18	prime	prime	ADJ
iajs-695	40	19	submodule	submodule	NOUN
iajs-695	40	20	p	p	PROPN
iajs-695	40	21	of	of	ADP
iajs-695	40	22	m	m	PROPN
iajs-695	40	23	,	,	PUNCT
iajs-695	40	24	pn	pn	PROPN
iajs-695	40	25			PROPN
iajs-695	40	26	(	(	PUNCT
iajs-695	40	27	0	0	NUM
iajs-695	40	28	)	)	PUNCT
iajs-695	40	29	)	)	PUNCT
iajs-695	40	30	.	.	PUNCT
iajs-695	41	1	but	but	CCONJ
iajs-695	41	2	this	this	PRON
iajs-695	41	3	is	be	AUX
iajs-695	41	4	contradiction	contradiction	NOUN
iajs-695	41	5	.	.	PUNCT
iajs-695	42	1	1.6	1.6	NUM
iajs-695	42	2	proposition	proposition	NOUN
iajs-695	42	3	:	:	PUNCT
iajs-695	42	4	let	let	VERB
iajs-695	42	5	m	m	PRON
iajs-695	42	6	be	be	AUX
iajs-695	42	7	an	an	DET
iajs-695	42	8	r	r	NOUN
iajs-695	42	9	-	-	PUNCT
iajs-695	42	10	module	module	NOUN
iajs-695	42	11	and	and	CCONJ
iajs-695	42	12	let	let	VERB
iajs-695	42	13	r	r	NOUN
iajs-695	42	14	=	=	SYM
iajs-695	42	15	r	r	NOUN
iajs-695	42	16	/	/	SYM
iajs-695	42	17	j	j	PROPN
iajs-695	42	18	,	,	PUNCT
iajs-695	42	19	mannj	mannj	NOUN
iajs-695	42	20	r	r	NOUN
iajs-695	42	21	,	,	PUNCT
iajs-695	42	22	then	then	ADV
iajs-695	42	23	m	m	VERB
iajs-695	42	24	is	be	AUX
iajs-695	42	25	a	a	DET
iajs-695	42	26	strongly	strongly	ADV
iajs-695	42	27	essentially	essentially	ADV
iajs-695	42	28	quasi	quasi	ADJ
iajs-695	42	29	-	-	ADJ
iajs-695	42	30	dedekind	dedekind	ADJ
iajs-695	42	31	r	r	NOUN
iajs-695	42	32	-	-	PUNCT
iajs-695	42	33	module	module	NOUN
iajs-695	42	34	if	if	SCONJ
iajs-695	42	35	and	and	CCONJ
iajs-695	42	36	only	only	ADV
iajs-695	42	37	if	if	SCONJ
iajs-695	42	38	m	m	NOUN
iajs-695	42	39	is	be	AUX
iajs-695	42	40	a	a	DET
iajs-695	42	41	strongly	strongly	ADV
iajs-695	42	42	essentially	essentially	ADV
iajs-695	42	43	quasi	quasi	ADJ
iajs-695	42	44	-	-	ADJ
iajs-695	42	45	dedekind	dedekind	ADJ
iajs-695	42	46	r	r	NOUN
iajs-695	42	47	-module	-module	NOUN
iajs-695	42	48	.	.	PUNCT
iajs-695	43	1	proof	proof	NOUN
iajs-695	43	2	:	:	PUNCT
iajs-695	43	3	since	since	SCONJ
iajs-695	43	4	)	)	PUNCT
iajs-695	43	5	,	,	PUNCT
iajs-695	43	6	(	(	PUNCT
iajs-695	43	7	mnmhom	mnmhom	NOUN
iajs-695	43	8	r	r	NOUN
iajs-695	43	9	=	=	PUNCT
iajs-695	43	10	)	)	PUNCT
iajs-695	43	11	,	,	PUNCT
iajs-695	43	12	(	(	PUNCT
iajs-695	43	13	mnmhomr	mnmhomr	NOUN
iajs-695	43	14	for	for	ADP
iajs-695	43	15	all	all	DET
iajs-695	43	16	n	n	PRON
iajs-695	43	17			NUM
iajs-695	43	18	m	m	NOUN
iajs-695	43	19	,	,	PUNCT
iajs-695	43	20	by	by	ADP
iajs-695	43	21	[	[	X
iajs-695	43	22	6	6	NUM
iajs-695	43	23	,	,	PUNCT
iajs-695	43	24	p.51	p.51	PROPN
iajs-695	43	25	]	]	X
iajs-695	43	26	the	the	DET
iajs-695	43	27	result	result	NOUN
iajs-695	43	28	follows	follow	VERB
iajs-695	43	29	easily	easily	ADV
iajs-695	43	30	.	.	PUNCT
iajs-695	44	1	recall	recall	VERB
iajs-695	44	2	that	that	SCONJ
iajs-695	44	3	an	an	DET
iajs-695	44	4	injective	injective	ADJ
iajs-695	44	5	r	r	NOUN
iajs-695	44	6	-	-	PUNCT
iajs-695	44	7	module	module	NOUN
iajs-695	44	8	e	e	NOUN
iajs-695	44	9	(	(	PUNCT
iajs-695	44	10	m	m	NOUN
iajs-695	44	11	)	)	PUNCT
iajs-695	44	12	is	be	AUX
iajs-695	44	13	called	call	VERB
iajs-695	44	14	an	an	DET
iajs-695	44	15	injective	injective	ADJ
iajs-695	44	16	hull	hull	NOUN
iajs-695	44	17	(	(	PUNCT
iajs-695	44	18	injective	injective	ADJ
iajs-695	44	19	envelope	envelope	NOUN
iajs-695	44	20	)	)	PUNCT
iajs-695	44	21	of	of	ADP
iajs-695	44	22	an	an	DET
iajs-695	44	23	r	r	NOUN
iajs-695	44	24	-	-	PUNCT
iajs-695	44	25	module	module	NOUN
iajs-695	44	26	m	m	NOUN
iajs-695	44	27	if	if	SCONJ
iajs-695	44	28	,	,	PUNCT
iajs-695	44	29	there	there	PRON
iajs-695	44	30	exists	exist	VERB
iajs-695	44	31	a	a	DET
iajs-695	44	32	monomorphism	monomorphism	NOUN
iajs-695	44	33	f	f	X
iajs-695	44	34	:	:	PUNCT
iajs-695	44	35	m	m	AUX
iajs-695	44	36			X
iajs-695	44	37	e(m	e(m	NOUN
iajs-695	44	38	)	)	PUNCT
iajs-695	44	39	such	such	ADJ
iajs-695	44	40	that	that	SCONJ
iajs-695	44	41	imf	imf	PROPN
iajs-695	44	42	e	e	SYM
iajs-695	44	43	e(m	e(m	PROPN
iajs-695	44	44	)	)	PUNCT
iajs-695	45	1	[	[	X
iajs-695	45	2	6	6	NUM
iajs-695	45	3	,	,	PUNCT
iajs-695	45	4	p.142	p.142	PRON
iajs-695	45	5	]	]	PUNCT
iajs-695	45	6	.	.	PUNCT
iajs-695	46	1	and	and	CCONJ
iajs-695	46	2	recall	recall	VERB
iajs-695	46	3	that	that	SCONJ
iajs-695	46	4	a	a	DET
iajs-695	46	5	quasi	quasi	ADJ
iajs-695	46	6	-	-	ADJ
iajs-695	46	7	injective	injective	ADJ
iajs-695	46	8	r	r	NOUN
iajs-695	46	9	-	-	PUNCT
iajs-695	46	10	module	module	NOUN
iajs-695	46	11	m	m	NOUN
iajs-695	46	12	is	be	AUX
iajs-695	46	13	called	call	VERB
iajs-695	46	14	a	a	DET
iajs-695	46	15	quasi	quasi	ADJ
iajs-695	46	16	-	-	ADJ
iajs-695	46	17	injective	injective	ADJ
iajs-695	46	18	hull	hull	NOUN
iajs-695	46	19	(	(	PUNCT
iajs-695	46	20	quasi	quasi	ADJ
iajs-695	46	21	-	-	ADJ
iajs-695	46	22	injective	injective	ADJ
iajs-695	46	23	envelope	envelope	NOUN
iajs-695	46	24	)	)	PUNCT
iajs-695	46	25	of	of	ADP
iajs-695	46	26	an	an	DET
iajs-695	46	27	r	r	NOUN
iajs-695	46	28	-	-	PUNCT
iajs-695	46	29	module	module	NOUN
iajs-695	46	30	m	m	NOUN
iajs-695	46	31	if	if	SCONJ
iajs-695	46	32	,	,	PUNCT
iajs-695	46	33	there	there	PRON
iajs-695	46	34	exists	exist	VERB
iajs-695	46	35	a	a	DET
iajs-695	46	36	monomorphism	monomorphism	NOUN
iajs-695	46	37	g	g	NOUN
iajs-695	46	38	:	:	PUNCT
iajs-695	46	39	m	m	VERB
iajs-695	46	40			VERB
iajs-695	46	41	m	m	VERB
iajs-695	46	42	such	such	ADJ
iajs-695	46	43	that	that	SCONJ
iajs-695	46	44	img	img	VERB
iajs-695	47	1	e	e	INTJ
iajs-695	47	2	m	m	VERB
iajs-695	47	3	[	[	X
iajs-695	47	4	11	11	NUM
iajs-695	47	5	]	]	PUNCT
iajs-695	47	6	.	.	PUNCT
iajs-695	48	1	to	to	PART
iajs-695	48	2	prove	prove	VERB
iajs-695	48	3	the	the	DET
iajs-695	48	4	next	next	ADJ
iajs-695	48	5	result	result	NOUN
iajs-695	48	6	,	,	PUNCT
iajs-695	48	7	we	we	PRON
iajs-695	48	8	state	state	VERB
iajs-695	48	9	and	and	CCONJ
iajs-695	48	10	prove	prove	VERB
iajs-695	48	11	the	the	DET
iajs-695	48	12	following	follow	VERB
iajs-695	48	13	lemma	lemma	PROPN
iajs-695	48	14	:	:	PUNCT
iajs-695	48	15	1.7	1.7	NUM
iajs-695	48	16	lemma	lemma	PROPN
iajs-695	48	17	:	:	PUNCT
iajs-695	48	18	let	let	VERB
iajs-695	48	19	m	m	PRON
iajs-695	48	20	be	be	AUX
iajs-695	48	21	an	an	DET
iajs-695	48	22	r	r	NOUN
iajs-695	48	23	-	-	PUNCT
iajs-695	48	24	module	module	NOUN
iajs-695	48	25	and	and	CCONJ
iajs-695	48	26	let	let	VERB
iajs-695	48	27	a	a	DET
iajs-695	48	28			NUM
iajs-695	48	29	m	m	NOUN
iajs-695	48	30	,	,	PUNCT
iajs-695	48	31	b	b	X
iajs-695	48	32			NUM
iajs-695	48	33	m.	m.	NOUN
iajs-695	48	34	if	if	SCONJ
iajs-695	48	35	a	a	DET
iajs-695	48	36	se	se	PROPN
iajs-695	48	37	b	b	NOUN
iajs-695	48	38	se	se	PROPN
iajs-695	48	39	m	m	VERB
iajs-695	48	40	then	then	ADV
iajs-695	48	41	a	a	DET
iajs-695	48	42	se	se	NOUN
iajs-695	48	43	m.	m.	NOUN
iajs-695	48	44	proof	proof	NOUN
iajs-695	48	45	:	:	PUNCT
iajs-695	48	46	let	let	VERB
iajs-695	48	47	p	p	PRON
iajs-695	48	48	be	be	AUX
iajs-695	48	49	a	a	DET
iajs-695	48	50	nonzero	nonzero	ADJ
iajs-695	48	51	prime	prime	ADJ
iajs-695	48	52	submodule	submodule	NOUN
iajs-695	48	53	in	in	ADP
iajs-695	48	54	m	m	PROPN
iajs-695	48	55	,	,	PUNCT
iajs-695	48	56	then	then	ADV
iajs-695	48	57	0	0	NUM
iajs-695	48	58			PROPN
iajs-695	48	59	pb	pb	NOUN
iajs-695	48	60	is	be	AUX
iajs-695	48	61	prime	prime	ADJ
iajs-695	48	62	in	in	ADP
iajs-695	48	63	b	b	NOUN
iajs-695	48	64	and	and	CCONJ
iajs-695	48	65	to	to	PART
iajs-695	48	66	show	show	VERB
iajs-695	48	67	this	this	PRON
iajs-695	48	68	:	:	PUNCT
iajs-695	48	69	let	let	VERB
iajs-695	48	70	x	x	X
iajs-695	48	71	b	b	PROPN
iajs-695	48	72	,	,	PUNCT
iajs-695	48	73	r	r	NOUN
iajs-695	48	74	r	r	NOUN
iajs-695	48	75	.	.	PUNCT
iajs-695	49	1	if	if	SCONJ
iajs-695	49	2	rx	rx	VERB
iajs-695	49	3			PROPN
iajs-695	49	4	pb	pb	PROPN
iajs-695	49	5	,	,	PUNCT
iajs-695	49	6	then	then	ADV
iajs-695	49	7	rx	rx	VERB
iajs-695	49	8			PROPN
iajs-695	49	9	p	p	NOUN
iajs-695	49	10	and	and	CCONJ
iajs-695	49	11	rx	rx	VERB
iajs-695	49	12			PROPN
iajs-695	49	13	b.	b.	PROPN
iajs-695	50	1	now	now	ADV
iajs-695	50	2	rx	rx	VERB
iajs-695	50	3			PROPN
iajs-695	50	4	p	p	PROPN
iajs-695	50	5	implies	imply	VERB
iajs-695	50	6	either	either	CCONJ
iajs-695	50	7	x	x	SYM
iajs-695	50	8	p	p	NOUN
iajs-695	50	9	or	or	CCONJ
iajs-695	50	10	r	r	NOUN
iajs-695	50	11			NOUN
iajs-695	50	12	[	[	PUNCT
iajs-695	50	13	p	p	X
iajs-695	50	14	:	:	PUNCT
iajs-695	50	15	m	m	VERB
iajs-695	50	16	]	]	X
iajs-695	50	17	,	,	PUNCT
iajs-695	50	18	since	since	SCONJ
iajs-695	50	19	p	p	NOUN
iajs-695	50	20	is	be	AUX
iajs-695	50	21	prime	prime	ADJ
iajs-695	50	22	in	in	ADP
iajs-695	50	23	m.	m.	NOUN
iajs-695	50	24	if	if	SCONJ
iajs-695	50	25	x	x	PRON
iajs-695	50	26	p	p	NOUN
iajs-695	50	27	,	,	PUNCT
iajs-695	50	28	then	then	ADV
iajs-695	50	29	x	x	SYM
iajs-695	50	30			PROPN
iajs-695	50	31	pb	pb	PROPN
iajs-695	50	32	.	.	PUNCT
iajs-695	51	1	and	and	CCONJ
iajs-695	51	2	if	if	SCONJ
iajs-695	51	3	r	r	NOUN
iajs-695	51	4			NOUN
iajs-695	51	5	[	[	PUNCT
iajs-695	51	6	p	p	X
iajs-695	51	7	:	:	PUNCT
iajs-695	51	8	m	m	PROPN
iajs-695	51	9	]	]	X
iajs-695	51	10	,	,	PUNCT
iajs-695	51	11	then	then	ADV
iajs-695	51	12	rm	rm	PROPN
iajs-695	51	13	p	p	NUM
iajs-695	51	14	,	,	PUNCT
iajs-695	51	15	but	but	CCONJ
iajs-695	51	16	rb	rb	PROPN
iajs-695	51	17			PROPN
iajs-695	51	18	rm	rm	PROPN
iajs-695	51	19			PROPN
iajs-695	51	20	p	p	PROPN
iajs-695	51	21	,	,	PUNCT
iajs-695	51	22	then	then	ADV
iajs-695	51	23	rb	rb	VERB
iajs-695	51	24			PROPN
iajs-695	51	25	p	p	PROPN
iajs-695	51	26	and	and	CCONJ
iajs-695	51	27	also	also	ADV
iajs-695	51	28	rb	rb	ADJ
iajs-695	51	29			PROPN
iajs-695	51	30	b	b	PROPN
iajs-695	51	31	,	,	PUNCT
iajs-695	51	32	hence	hence	ADV
iajs-695	51	33	rb	rb	PROPN
iajs-695	51	34			PROPN
iajs-695	51	35	pb	pb	PROPN
iajs-695	51	36	.	.	PUNCT
iajs-695	52	1	thus	thus	ADV
iajs-695	52	2	r	r	VERB
iajs-695	52	3			NOUN
iajs-695	52	4	[	[	PUNCT
iajs-695	52	5	pb	pb	NOUN
iajs-695	52	6	:	:	PUNCT
iajs-695	52	7	b	b	NOUN
iajs-695	52	8	]	]	X
iajs-695	52	9	,	,	PUNCT
iajs-695	52	10	so	so	SCONJ
iajs-695	52	11	that	that	SCONJ
iajs-695	52	12	pb	pb	NOUN
iajs-695	52	13	is	be	AUX
iajs-695	52	14	prime	prime	ADJ
iajs-695	52	15	in	in	ADP
iajs-695	52	16	b.	b.	PROPN
iajs-695	52	17	it	it	PRON
iajs-695	52	18	follows	follow	VERB
iajs-695	52	19	that	that	SCONJ
iajs-695	52	20	a	a	PROPN
iajs-695	52	21	(	(	PUNCT
iajs-695	52	22	pb	pb	PROPN
iajs-695	52	23	)	)	PUNCT
iajs-695	52	24			NOUN
iajs-695	52	25	0	0	NUM
iajs-695	52	26	and	and	CCONJ
iajs-695	52	27	hence	hence	ADV
iajs-695	52	28	ap	ap	NOUN
iajs-695	52	29			VERB
iajs-695	52	30	0	0	X
iajs-695	52	31	.	.	PUNCT
iajs-695	53	1	therefore	therefore	ADV
iajs-695	53	2	a	a	DET
iajs-695	53	3	se	se	PROPN
iajs-695	53	4	m.	m.	NOUN
iajs-695	53	5	1.8	1.8	NUM
iajs-695	53	6	proposition	proposition	NOUN
iajs-695	53	7	:	:	PUNCT
iajs-695	53	8	let	let	VERB
iajs-695	53	9	m	m	PRON
iajs-695	53	10	be	be	AUX
iajs-695	53	11	an	an	DET
iajs-695	53	12	r	r	NOUN
iajs-695	53	13	-	-	PUNCT
iajs-695	53	14	module	module	NOUN
iajs-695	53	15	.	.	PUNCT
iajs-695	54	1	if	if	SCONJ
iajs-695	54	2	m	m	NOUN
iajs-695	54	3	is	be	AUX
iajs-695	54	4	a	a	DET
iajs-695	54	5	strongly	strongly	ADV
iajs-695	54	6	essentially	essentially	ADV
iajs-695	54	7	quasi	quasi	ADJ
iajs-695	54	8	-	-	ADJ
iajs-695	54	9	dedekind	dedekind	ADJ
iajs-695	54	10	r	r	NOUN
iajs-695	54	11	-	-	PUNCT
iajs-695	54	12	module	module	NOUN
iajs-695	54	13	,	,	PUNCT
iajs-695	54	14	then	then	ADV
iajs-695	54	15	m	m	NOUN
iajs-695	54	16	is	be	AUX
iajs-695	54	17	a	a	DET
iajs-695	54	18	strongly	strongly	ADV
iajs-695	54	19	essentially	essentially	ADV
iajs-695	54	20	quasi	quasi	ADJ
iajs-695	54	21	-	-	ADJ
iajs-695	54	22	dedekind	dedekind	ADJ
iajs-695	54	23	r	r	NOUN
iajs-695	54	24	-	-	PUNCT
iajs-695	54	25	module	module	NOUN
iajs-695	54	26	.	.	PUNCT
iajs-695	55	1	proof	proof	NOUN
iajs-695	55	2	:	:	PUNCT
iajs-695	55	3	let	let	VERB
iajs-695	55	4	)	)	PUNCT
iajs-695	55	5	(	(	PUNCT
iajs-695	55	6	mendf	mendf	ADJ
iajs-695	55	7	r	r	NOUN
iajs-695	55	8	,	,	PUNCT
iajs-695	55	9	f	f	PROPN
iajs-695	55	10	0	0	NUM
iajs-695	55	11	.	.	PUNCT
iajs-695	56	1	to	to	PART
iajs-695	56	2	prove	prove	VERB
iajs-695	56	3	that	that	SCONJ
iajs-695	56	4	kerf	kerf	NOUN
iajs-695	56	5	se	se	PROPN
iajs-695	56	6	m.	m.	NOUN
iajs-695	56	7	since	since	SCONJ
iajs-695	56	8	m	m	PROPN
iajs-695	56	9	is	be	AUX
iajs-695	56	10	quasiinjective	quasiinjective	ADJ
iajs-695	56	11	r	r	NOUN
iajs-695	56	12	-	-	PUNCT
iajs-695	56	13	module	module	NOUN
iajs-695	56	14	,	,	PUNCT
iajs-695	56	15	then	then	ADV
iajs-695	56	16	there	there	PRON
iajs-695	56	17	exists	exist	VERB
iajs-695	56	18	g	g	NOUN
iajs-695	56	19	:	:	PUNCT
iajs-695	56	20	m	m	VERB
iajs-695	56	21			ADJ
iajs-695	56	22	m	m	PROPN
iajs-695	56	23	,	,	PUNCT
iajs-695	56	24	g	g	PROPN
iajs-695	56	25			PROPN
iajs-695	56	26	0	0	NUM
iajs-695	57	1	such	such	ADJ
iajs-695	57	2	that	that	SCONJ
iajs-695	57	3	g	g	PROPN
iajs-695	57	4	o	o	X
iajs-695	57	5	i	i	PRON
iajs-695	57	6	=	=	VERB
iajs-695	58	1	i	i	PRON
iajs-695	58	2	o	o	NOUN
iajs-695	59	1	f	f	X
iajs-695	59	2	(	(	PUNCT
iajs-695	59	3	where	where	SCONJ
iajs-695	59	4	i	i	PRON
iajs-695	59	5	is	be	AUX
iajs-695	59	6	the	the	DET
iajs-695	59	7	inclusion	inclusion	NOUN
iajs-695	59	8	mapping	mapping	NOUN
iajs-695	59	9	)	)	PUNCT
iajs-695	59	10	.	.	PUNCT
iajs-695	60	1	i	i	PRON
iajs-695	60	2	f	f	VERB
iajs-695	61	1	i	i	PRON
iajs-695	61	2	m	m	VERB
iajs-695	61	3	m	m	VERB
iajs-695	61	4	g	g	NOUN
iajs-695	61	5	m	m	VERB
iajs-695	61	6	m	m	VERB
iajs-695	61	7	مجلة	مجلة	ADJ
iajs-695	61	8	إبن	إبن	VERB
iajs-695	61	9	الھیثم	الھیثم	NOUN
iajs-695	61	10	للعلوم	للعلوم	NOUN
iajs-695	61	11	الصرفة	الصرفة	NOUN
iajs-695	61	12	و	و	PRON
iajs-695	61	13	التطبیقیة	التطبیقیة	PROPN
iajs-695	61	14	2012	2012	NUM
iajs-695	61	15	السنة	السنة	NOUN
iajs-695	62	1	25	25	NUM
iajs-695	62	2	المجلد	المجلد	NOUN
iajs-695	62	3	1	1	NUM
iajs-695	62	4	العدد	العدد	PROPN
iajs-695	62	5	ibn	ibn	PROPN
iajs-695	62	6	al	al	PROPN
iajs-695	62	7	-	-	PUNCT
iajs-695	62	8	haitham	haitham	PROPN
iajs-695	62	9	journal	journal	PROPN
iajs-695	62	10	for	for	ADP
iajs-695	62	11	pure	pure	ADJ
iajs-695	62	12	and	and	CCONJ
iajs-695	62	13	applied	apply	VERB
iajs-695	62	14	science	science	NOUN
iajs-695	62	15	no	no	NOUN
iajs-695	62	16	.	.	NOUN
iajs-695	62	17	1	1	NUM
iajs-695	62	18	vol	vol	NOUN
iajs-695	62	19	.	.	PUNCT
iajs-695	63	1	25	25	NUM
iajs-695	63	2	year	year	NOUN
iajs-695	63	3	2012	2012	NUM
iajs-695	64	1	but	but	CCONJ
iajs-695	64	2	m	m	NOUN
iajs-695	64	3	is	be	AUX
iajs-695	64	4	a	a	DET
iajs-695	64	5	strongly	strongly	ADV
iajs-695	64	6	essentially	essentially	ADV
iajs-695	64	7	quasi	quasi	ADJ
iajs-695	64	8	-	-	ADJ
iajs-695	64	9	dedekind	dedekind	ADJ
iajs-695	64	10	r	r	NOUN
iajs-695	64	11	-	-	PUNCT
iajs-695	64	12	module	module	NOUN
iajs-695	64	13	,	,	PUNCT
iajs-695	64	14	so	so	SCONJ
iajs-695	64	15	kerg	kerg	PROPN
iajs-695	64	16	se	se	PROPN
iajs-695	64	17	m	m	PROPN
iajs-695	64	18	,	,	PUNCT
iajs-695	64	19	but	but	CCONJ
iajs-695	64	20	kerf	kerf	NOUN
iajs-695	64	21			PROPN
iajs-695	64	22	kerg	kerg	PROPN
iajs-695	64	23	,	,	PUNCT
iajs-695	64	24	then	then	ADV
iajs-695	64	25	kerf	kerf	VERB
iajs-695	64	26			NUM
iajs-695	64	27	se	se	X
iajs-695	64	28	m	m	PROPN
iajs-695	64	29	,	,	PUNCT
iajs-695	64	30	and	and	CCONJ
iajs-695	64	31	since	since	SCONJ
iajs-695	64	32	m	m	PROPN
iajs-695	64	33	e	e	NOUN
iajs-695	64	34	m	m	VERB
iajs-695	64	35	;	;	PUNCT
iajs-695	64	36	that	that	PRON
iajs-695	64	37	is	be	AUX
iajs-695	64	38	m	m	VERB
iajs-695	64	39	se	se	NOUN
iajs-695	64	40	m	m	NOUN
iajs-695	64	41	,	,	PUNCT
iajs-695	64	42	then	then	ADV
iajs-695	64	43	by	by	ADP
iajs-695	64	44	(	(	PUNCT
iajs-695	64	45	lemma	lemma	PROPN
iajs-695	64	46	1.7	1.7	NUM
iajs-695	64	47	)	)	PUNCT
iajs-695	64	48	kerf	kerf	NOUN
iajs-695	64	49	se	se	PROPN
iajs-695	64	50	m	m	VERB
iajs-695	64	51	which	which	PRON
iajs-695	64	52	implies	imply	VERB
iajs-695	64	53	kerg	kerg	PROPN
iajs-695	64	54	se	se	PROPN
iajs-695	64	55	m	m	PROPN
iajs-695	64	56	which	which	PRON
iajs-695	64	57	is	be	AUX
iajs-695	64	58	a	a	DET
iajs-695	64	59	contradiction	contradiction	NOUN
iajs-695	64	60	.	.	PUNCT
iajs-695	65	1	thus	thus	ADV
iajs-695	65	2	m	m	NOUN
iajs-695	65	3	is	be	AUX
iajs-695	65	4	a	a	PRON
iajs-695	65	5	strongly	strongly	ADV
iajs-695	65	6	essentially	essentially	ADV
iajs-695	65	7	quasidedekind	quasidedekind	VERB
iajs-695	65	8	r	r	NOUN
iajs-695	65	9	-	-	PUNCT
iajs-695	65	10	module	module	NOUN
iajs-695	65	11	.	.	PUNCT
iajs-695	66	1	the	the	DET
iajs-695	66	2	following	follow	VERB
iajs-695	66	3	results	result	NOUN
iajs-695	66	4	follow	follow	VERB
iajs-695	66	5	directly	directly	ADV
iajs-695	66	6	by	by	ADP
iajs-695	66	7	(	(	PUNCT
iajs-695	66	8	prop	prop	NOUN
iajs-695	66	9	.	.	PUNCT
iajs-695	66	10	1.8	1.8	NUM
iajs-695	66	11	)	)	PUNCT
iajs-695	66	12	.	.	PUNCT
iajs-695	67	1	1.9	1.9	NUM
iajs-695	67	2	corollary	corollary	NOUN
iajs-695	67	3	:	:	PUNCT
iajs-695	67	4	let	let	VERB
iajs-695	67	5	m	m	PRON
iajs-695	67	6	be	be	AUX
iajs-695	67	7	a	a	DET
iajs-695	67	8	strongly	strongly	ADV
iajs-695	67	9	essentially	essentially	ADV
iajs-695	67	10	quasi	quasi	ADJ
iajs-695	67	11	-	-	ADJ
iajs-695	67	12	dedekind	dedekind	ADJ
iajs-695	67	13	and	and	CCONJ
iajs-695	67	14	quasi	quasi	ADJ
iajs-695	67	15	-	-	ADJ
iajs-695	67	16	injective	injective	ADJ
iajs-695	67	17	r	r	NOUN
iajs-695	67	18	-	-	PUNCT
iajs-695	67	19	module	module	NOUN
iajs-695	67	20	.	.	PUNCT
iajs-695	68	1	if	if	SCONJ
iajs-695	68	2	n	n	PROPN
iajs-695	68	3	se	se	NOUN
iajs-695	68	4	m	m	VERB
iajs-695	68	5	then	then	ADV
iajs-695	68	6	n	n	PRON
iajs-695	68	7	is	be	AUX
iajs-695	68	8	a	a	DET
iajs-695	68	9	strongly	strongly	ADV
iajs-695	68	10	essentially	essentially	ADV
iajs-695	68	11	quasi	quasi	ADJ
iajs-695	68	12	-	-	ADJ
iajs-695	68	13	dedekind	dedekind	ADJ
iajs-695	68	14	r	r	NOUN
iajs-695	68	15	-	-	NOUN
iajs-695	68	16	module	module	NOUN
iajs-695	68	17	.	.	PUNCT
iajs-695	69	1	1.10	1.10	NUM
iajs-695	69	2	corollary	corollary	NOUN
iajs-695	69	3	:	:	PUNCT
iajs-695	69	4	let	let	VERB
iajs-695	69	5	m	m	PRON
iajs-695	69	6	be	be	AUX
iajs-695	69	7	an	an	DET
iajs-695	69	8	r	r	NOUN
iajs-695	69	9	-	-	PUNCT
iajs-695	69	10	module	module	NOUN
iajs-695	69	11	.	.	PUNCT
iajs-695	70	1	if	if	SCONJ
iajs-695	70	2	e(m	e(m	PROPN
iajs-695	70	3	)	)	PUNCT
iajs-695	70	4	is	be	AUX
iajs-695	70	5	a	a	DET
iajs-695	70	6	strongly	strongly	ADV
iajs-695	70	7	essentially	essentially	ADV
iajs-695	70	8	quasi	quasi	ADJ
iajs-695	70	9	-	-	ADJ
iajs-695	70	10	dedekind	dedekind	ADJ
iajs-695	70	11	r	r	NOUN
iajs-695	70	12	-	-	PUNCT
iajs-695	70	13	module	module	NOUN
iajs-695	70	14	then	then	ADV
iajs-695	70	15	m	m	VERB
iajs-695	70	16	is	be	AUX
iajs-695	70	17	a	a	DET
iajs-695	70	18	strongly	strongly	ADV
iajs-695	70	19	essentially	essentially	ADV
iajs-695	70	20	quasi	quasi	ADJ
iajs-695	70	21	-	-	ADJ
iajs-695	70	22	dedekind	dedekind	ADJ
iajs-695	70	23	r	r	NOUN
iajs-695	70	24	-	-	NOUN
iajs-695	70	25	module	module	NOUN
iajs-695	70	26	.	.	PUNCT
iajs-695	71	1	the	the	DET
iajs-695	71	2	converse	converse	NOUN
iajs-695	71	3	of	of	ADP
iajs-695	71	4	(	(	PUNCT
iajs-695	71	5	coro	coro	X
iajs-695	71	6	.	.	NOUN
iajs-695	71	7	1.10	1.10	NUM
iajs-695	71	8	)	)	PUNCT
iajs-695	71	9	is	be	AUX
iajs-695	71	10	not	not	PART
iajs-695	71	11	true	true	ADJ
iajs-695	71	12	in	in	ADP
iajs-695	71	13	general	general	ADJ
iajs-695	71	14	,	,	PUNCT
iajs-695	71	15	as	as	SCONJ
iajs-695	71	16	the	the	DET
iajs-695	71	17	following	follow	VERB
iajs-695	71	18	example	example	NOUN
iajs-695	71	19	shows	show	VERB
iajs-695	71	20	:	:	PUNCT
iajs-695	71	21	1.11	1.11	NUM
iajs-695	71	22	example	example	NOUN
iajs-695	71	23	:	:	PUNCT
iajs-695	71	24	it	it	PRON
iajs-695	71	25	is	be	AUX
iajs-695	71	26	well	well	ADV
iajs-695	71	27	known	know	VERB
iajs-695	71	28	that	that	SCONJ
iajs-695	71	29	z2	z2	PROPN
iajs-695	71	30	as	as	ADP
iajs-695	71	31	z	z	NOUN
iajs-695	71	32	-	-	PUNCT
iajs-695	71	33	module	module	NOUN
iajs-695	71	34	is	be	AUX
iajs-695	71	35	a	a	DET
iajs-695	71	36	strongly	strongly	ADV
iajs-695	71	37	essentially	essentially	ADV
iajs-695	71	38	quasi	quasi	ADJ
iajs-695	71	39	-	-	ADJ
iajs-695	71	40	dedekind	dedekind	ADJ
iajs-695	71	41	.	.	PUNCT
iajs-695	72	1	but	but	CCONJ
iajs-695	72	2	e(z2	e(z2	NOUN
iajs-695	72	3	)	)	PUNCT
iajs-695	73	1	=	=	SYM
iajs-695	73	2	z2	z2	PROPN
iajs-695	73	3	∞	∞	PROPN
iajs-695	73	4	is	be	AUX
iajs-695	73	5	not	not	PART
iajs-695	73	6	strongly	strongly	ADV
iajs-695	73	7	essentially	essentially	ADV
iajs-695	73	8	quasi	quasi	ADJ
iajs-695	73	9	-	-	NOUN
iajs-695	73	10	dedekind	dedekind	ADJ
iajs-695	73	11	as	as	ADP
iajs-695	73	12	z	z	NOUN
iajs-695	73	13	-	-	NOUN
iajs-695	73	14	module	module	NOUN
iajs-695	73	15	.	.	PUNCT
iajs-695	74	1	1.12	1.12	NUM
iajs-695	74	2	remark	remark	NOUN
iajs-695	74	3	:	:	PUNCT
iajs-695	74	4	let	let	VERB
iajs-695	74	5	m	m	PRON
iajs-695	74	6	be	be	AUX
iajs-695	74	7	an	an	DET
iajs-695	74	8	r	r	NOUN
iajs-695	74	9	-	-	PUNCT
iajs-695	74	10	module	module	NOUN
iajs-695	74	11	.	.	PUNCT
iajs-695	75	1	if	if	SCONJ
iajs-695	75	2	n	n	NOUN
iajs-695	75	3			NOUN
iajs-695	75	4	m	m	VERB
iajs-695	75	5	is	be	AUX
iajs-695	75	6	a	a	DET
iajs-695	75	7	strongly	strongly	ADV
iajs-695	75	8	essentially	essentially	ADV
iajs-695	75	9	quasi	quasi	ADJ
iajs-695	75	10	-	-	ADJ
iajs-695	75	11	dedekind	dedekind	ADJ
iajs-695	75	12	r	r	NOUN
iajs-695	75	13	-	-	PUNCT
iajs-695	75	14	module	module	NOUN
iajs-695	75	15	then	then	ADV
iajs-695	75	16	it	it	PRON
iajs-695	75	17	is	be	AUX
iajs-695	75	18	not	not	PART
iajs-695	75	19	necessarily	necessarily	ADV
iajs-695	75	20	that	that	ADV
iajs-695	75	21	m	m	PROPN
iajs-695	75	22	/	/	SYM
iajs-695	75	23	n	n	PROPN
iajs-695	75	24	is	be	AUX
iajs-695	75	25	a	a	DET
iajs-695	75	26	strongly	strongly	ADV
iajs-695	75	27	essentially	essentially	ADV
iajs-695	75	28	quasi	quasi	ADJ
iajs-695	75	29	-	-	ADJ
iajs-695	75	30	dedekind	dedekind	ADJ
iajs-695	75	31	r	r	NOUN
iajs-695	75	32	-	-	PUNCT
iajs-695	75	33	module	module	NOUN
iajs-695	75	34	,	,	PUNCT
iajs-695	75	35	consider	consider	VERB
iajs-695	75	36	the	the	DET
iajs-695	75	37	following	follow	VERB
iajs-695	75	38	example	example	NOUN
iajs-695	75	39	:	:	PUNCT
iajs-695	75	40	1.13	1.13	NUM
iajs-695	75	41	example	example	NOUN
iajs-695	75	42	:	:	PUNCT
iajs-695	75	43	let	let	VERB
iajs-695	75	44	m	m	VERB
iajs-695	75	45	=	=	VERB
iajs-695	75	46	z	z	NOUN
iajs-695	75	47	as	as	ADP
iajs-695	75	48	z	z	NOUN
iajs-695	75	49	-	-	PUNCT
iajs-695	75	50	module	module	NOUN
iajs-695	75	51	,	,	PUNCT
iajs-695	75	52	and	and	CCONJ
iajs-695	75	53	let	let	VERB
iajs-695	75	54	n	n	NOUN
iajs-695	75	55	=	=	NOUN
iajs-695	75	56	4z	4z	X
iajs-695	75	57			NOUN
iajs-695	75	58	z	z	NOUN
iajs-695	75	59	=	=	PUNCT
iajs-695	75	60	m.	m.	NOUN
iajs-695	75	61	it	it	PRON
iajs-695	75	62	is	be	AUX
iajs-695	75	63	clear	clear	ADJ
iajs-695	75	64	that	that	SCONJ
iajs-695	75	65	n	n	ADV
iajs-695	75	66	se	se	NOUN
iajs-695	75	67	m	m	VERB
iajs-695	75	68	and	and	CCONJ
iajs-695	75	69	m	m	PROPN
iajs-695	75	70	is	be	AUX
iajs-695	75	71	strongly	strongly	ADV
iajs-695	75	72	essentially	essentially	ADV
iajs-695	75	73	quasi	quasi	ADJ
iajs-695	75	74	-	-	ADJ
iajs-695	75	75	dedekind	dedekind	ADJ
iajs-695	75	76	and	and	CCONJ
iajs-695	75	77	quasi	quasi	ADJ
iajs-695	75	78	-	-	ADJ
iajs-695	75	79	injective	injective	ADJ
iajs-695	75	80	as	as	ADP
iajs-695	75	81	z	z	NOUN
iajs-695	75	82	-	-	PUNCT
iajs-695	75	83	module	module	NOUN
iajs-695	75	84	,	,	PUNCT
iajs-695	75	85	so	so	ADV
iajs-695	75	86	by	by	ADP
iajs-695	75	87	(	(	PUNCT
iajs-695	75	88	coro.1.9	coro.1.9	PROPN
iajs-695	75	89	)	)	PUNCT
iajs-695	75	90	n	n	PRON
iajs-695	75	91	is	be	AUX
iajs-695	75	92	strongly	strongly	ADV
iajs-695	75	93	essentially	essentially	ADV
iajs-695	75	94	quasi	quasi	ADJ
iajs-695	75	95	-	-	NOUN
iajs-695	75	96	dedekind	dedekind	ADJ
iajs-695	75	97	as	as	ADP
iajs-695	75	98	z	z	NOUN
iajs-695	75	99	-	-	PUNCT
iajs-695	75	100	module	module	NOUN
iajs-695	75	101	,	,	PUNCT
iajs-695	75	102	but	but	CCONJ
iajs-695	75	103	m	m	PROPN
iajs-695	75	104	/	/	SYM
iajs-695	75	105	n	n	PROPN
iajs-695	75	106	=	=	SYM
iajs-695	75	107	z/4z	z/4z	NUM
iajs-695	75	108			PROPN
iajs-695	75	109	z4	z4	PROPN
iajs-695	75	110	is	be	AUX
iajs-695	75	111	not	not	PART
iajs-695	75	112	strongly	strongly	ADV
iajs-695	75	113	essentially	essentially	ADV
iajs-695	75	114	quasi	quasi	ADJ
iajs-695	75	115	-	-	NOUN
iajs-695	75	116	dedekind	dedekind	ADJ
iajs-695	75	117	as	as	ADP
iajs-695	75	118	z	z	NOUN
iajs-695	75	119	-	-	PUNCT
iajs-695	75	120	module	module	NOUN
iajs-695	75	121	(	(	PUNCT
iajs-695	75	122	see	see	VERB
iajs-695	75	123	,	,	PUNCT
iajs-695	75	124	rem.and.ex(1.2)(4	rem.and.ex(1.2)(4	NOUN
iajs-695	75	125	)	)	PUNCT
iajs-695	75	126	)	)	PUNCT
iajs-695	75	127	.	.	PUNCT
iajs-695	76	1	recall	recall	VERB
iajs-695	76	2	that	that	SCONJ
iajs-695	76	3	a	a	DET
iajs-695	76	4	nonzero	nonzero	ADJ
iajs-695	76	5	r	r	NOUN
iajs-695	76	6	-	-	PUNCT
iajs-695	76	7	module	module	NOUN
iajs-695	76	8	m	m	NOUN
iajs-695	76	9	is	be	AUX
iajs-695	76	10	called	call	VERB
iajs-695	76	11	compressible	compressible	ADJ
iajs-695	76	12	if	if	SCONJ
iajs-695	76	13	,	,	PUNCT
iajs-695	76	14	m	m	AUX
iajs-695	76	15	embedded	embed	VERB
iajs-695	76	16	in	in	ADP
iajs-695	76	17	each	each	PRON
iajs-695	76	18	of	of	ADP
iajs-695	76	19	its	its	PRON
iajs-695	76	20	nonzero	nonzero	ADJ
iajs-695	76	21	submodules	submodule	NOUN
iajs-695	77	1	[	[	X
iajs-695	77	2	2	2	NUM
iajs-695	77	3	]	]	PUNCT
iajs-695	77	4	.	.	PUNCT
iajs-695	78	1	1.14	1.14	NUM
iajs-695	78	2	proposition	proposition	NOUN
iajs-695	78	3	:	:	PUNCT
iajs-695	78	4	let	let	VERB
iajs-695	78	5	m	m	PRON
iajs-695	78	6	be	be	AUX
iajs-695	78	7	a	a	DET
iajs-695	78	8	multiplication	multiplication	NOUN
iajs-695	78	9	r	r	NOUN
iajs-695	78	10	-	-	PUNCT
iajs-695	78	11	module	module	NOUN
iajs-695	78	12	,	,	PUNCT
iajs-695	78	13	n	n	CCONJ
iajs-695	78	14	≨	≨	PROPN
iajs-695	78	15	m.	m.	NOUN
iajs-695	78	16	if	if	SCONJ
iajs-695	78	17	n	n	PRON
iajs-695	78	18	is	be	AUX
iajs-695	78	19	a	a	DET
iajs-695	78	20	prime	prime	ADJ
iajs-695	78	21	r	r	NOUN
iajs-695	78	22	-	-	PUNCT
iajs-695	78	23	submodule	submodule	NOUN
iajs-695	78	24	of	of	ADP
iajs-695	78	25	m	m	PROPN
iajs-695	78	26	,	,	PUNCT
iajs-695	78	27	then	then	ADV
iajs-695	78	28	m	m	PROPN
iajs-695	78	29	/	/	SYM
iajs-695	78	30	n	n	PROPN
iajs-695	78	31	is	be	AUX
iajs-695	78	32	a	a	DET
iajs-695	78	33	strongly	strongly	ADV
iajs-695	78	34	essentially	essentially	ADV
iajs-695	78	35	quasi	quasi	ADJ
iajs-695	78	36	-	-	ADJ
iajs-695	78	37	dedekind	dedekind	ADJ
iajs-695	78	38	r	r	NOUN
iajs-695	78	39	-	-	PUNCT
iajs-695	78	40	module	module	NOUN
iajs-695	78	41	.	.	PUNCT
iajs-695	79	1	proof	proof	NOUN
iajs-695	79	2	:	:	PUNCT
iajs-695	79	3	since	since	SCONJ
iajs-695	79	4	n	n	NOUN
iajs-695	79	5	is	be	AUX
iajs-695	79	6	a	a	DET
iajs-695	79	7	prime	prime	ADJ
iajs-695	79	8	submodule	submodule	NOUN
iajs-695	79	9	of	of	ADP
iajs-695	79	10	m	m	PROPN
iajs-695	79	11	,	,	PUNCT
iajs-695	79	12	so	so	ADV
iajs-695	79	13	by	by	ADP
iajs-695	79	14	[	[	X
iajs-695	79	15	12	12	NUM
iajs-695	79	16	,	,	PUNCT
iajs-695	79	17	coro	coro	NOUN
iajs-695	79	18	.	.	PUNCT
iajs-695	79	19	4.18	4.18	NUM
iajs-695	79	20	,	,	PUNCT
iajs-695	79	21	ch.1	ch.1	PROPN
iajs-695	79	22	]	]	X
iajs-695	79	23	m	m	PROPN
iajs-695	79	24	/	/	SYM
iajs-695	79	25	n	n	PROPN
iajs-695	79	26	is	be	AUX
iajs-695	79	27	a	a	DET
iajs-695	79	28	compressible	compressible	ADJ
iajs-695	79	29	r	r	NOUN
iajs-695	79	30	-	-	PUNCT
iajs-695	79	31	module	module	NOUN
iajs-695	79	32	,	,	PUNCT
iajs-695	79	33	thus	thus	ADV
iajs-695	79	34	by	by	ADP
iajs-695	79	35	[	[	X
iajs-695	79	36	7,prop	7,prop	NUM
iajs-695	79	37	2.6	2.6	NUM
iajs-695	79	38	,	,	PUNCT
iajs-695	79	39	p.30	p.30	X
iajs-695	79	40	]	]	X
iajs-695	79	41	m	m	PROPN
iajs-695	79	42	/	/	SYM
iajs-695	79	43	n	n	PROPN
iajs-695	79	44	is	be	AUX
iajs-695	79	45	a	a	DET
iajs-695	79	46	quasi	quasi	ADJ
iajs-695	79	47	-	-	ADJ
iajs-695	79	48	dedekind	dedekind	ADJ
iajs-695	79	49	r	r	NOUN
iajs-695	79	50	-	-	PUNCT
iajs-695	79	51	module	module	NOUN
iajs-695	79	52	.	.	PUNCT
iajs-695	80	1	therefore	therefore	ADV
iajs-695	80	2	by	by	ADP
iajs-695	80	3	(	(	PUNCT
iajs-695	80	4	rem.and.ex(1.2)(2	rem.and.ex(1.2)(2	NOUN
iajs-695	80	5	)	)	PUNCT
iajs-695	80	6	)	)	PUNCT
iajs-695	80	7	m	m	PROPN
iajs-695	80	8	/	/	SYM
iajs-695	80	9	n	n	PROPN
iajs-695	80	10	is	be	AUX
iajs-695	80	11	a	a	DET
iajs-695	80	12	strongly	strongly	ADV
iajs-695	80	13	essentially	essentially	ADV
iajs-695	80	14	quasi	quasi	ADJ
iajs-695	80	15	-	-	ADJ
iajs-695	80	16	dedekind	dedekind	ADJ
iajs-695	80	17	r	r	NOUN
iajs-695	80	18	-	-	PUNCT
iajs-695	80	19	module	module	NOUN
iajs-695	80	20	.	.	PUNCT
iajs-695	81	1	مجلة	مجلة	NOUN
iajs-695	81	2	إبن	إبن	VERB
iajs-695	81	3	الھیثم	الھیثم	NOUN
iajs-695	81	4	للعلوم	للعلوم	NOUN
iajs-695	81	5	الصرفة	الصرفة	NOUN
iajs-695	81	6	و	و	PRON
iajs-695	81	7	التطبیقیة	التطبیقیة	PROPN
iajs-695	81	8	2012	2012	NUM
iajs-695	81	9	السنة	السنة	NOUN
iajs-695	82	1	25	25	NUM
iajs-695	82	2	المجلد	المجلد	NOUN
iajs-695	82	3	1	1	NUM
iajs-695	82	4	العدد	العدد	PROPN
iajs-695	82	5	ibn	ibn	PROPN
iajs-695	82	6	al	al	PROPN
iajs-695	82	7	-	-	PUNCT
iajs-695	82	8	haitham	haitham	PROPN
iajs-695	82	9	journal	journal	PROPN
iajs-695	82	10	for	for	ADP
iajs-695	82	11	pure	pure	ADJ
iajs-695	82	12	and	and	CCONJ
iajs-695	82	13	applied	apply	VERB
iajs-695	82	14	science	science	NOUN
iajs-695	82	15	no	no	NOUN
iajs-695	82	16	.	.	NOUN
iajs-695	82	17	1	1	NUM
iajs-695	82	18	vol	vol	NOUN
iajs-695	82	19	.	.	PUNCT
iajs-695	83	1	25	25	NUM
iajs-695	83	2	year	year	NOUN
iajs-695	83	3	2012	2012	NUM
iajs-695	83	4	to	to	PART
iajs-695	83	5	prove	prove	VERB
iajs-695	83	6	our	our	PRON
iajs-695	83	7	next	next	ADJ
iajs-695	83	8	result	result	NOUN
iajs-695	83	9	,	,	PUNCT
iajs-695	83	10	we	we	PRON
iajs-695	83	11	need	need	VERB
iajs-695	83	12	the	the	DET
iajs-695	83	13	following	follow	VERB
iajs-695	83	14	lemma	lemma	PROPN
iajs-695	83	15	:	:	PUNCT
iajs-695	83	16	1.15	1.15	NUM
iajs-695	83	17	lemma	lemma	PROPN
iajs-695	83	18	:	:	PUNCT
iajs-695	83	19	let	let	VERB
iajs-695	83	20	m	m	PRON
iajs-695	83	21	,	,	PUNCT
iajs-695	83	22	n	n	PRON
iajs-695	83	23	be	be	AUX
iajs-695	83	24	an	an	DET
iajs-695	83	25	r	r	NOUN
iajs-695	83	26	-	-	PUNCT
iajs-695	83	27	modules	module	NOUN
iajs-695	83	28	,	,	PUNCT
iajs-695	83	29	let	let	VERB
iajs-695	83	30	f	f	PRON
iajs-695	83	31	:	:	PUNCT
iajs-695	83	32	m	m	VERB
iajs-695	83	33			PRON
iajs-695	83	34	n	n	AUX
iajs-695	83	35	be	be	AUX
iajs-695	83	36	a	a	DET
iajs-695	83	37	monomorphism	monomorphism	NOUN
iajs-695	83	38	.	.	PUNCT
iajs-695	84	1	let	let	VERB
iajs-695	84	2	k	k	PROPN
iajs-695	84	3			PROPN
iajs-695	84	4	m	m	PRON
iajs-695	84	5	,	,	PUNCT
iajs-695	84	6	a	a	DET
iajs-695	84	7			NOUN
iajs-695	84	8	n	n	CCONJ
iajs-695	84	9	,	,	PUNCT
iajs-695	84	10	then	then	ADV
iajs-695	84	11	:	:	PUNCT
iajs-695	84	12	(	(	PUNCT
iajs-695	84	13	1	1	X
iajs-695	84	14	)	)	PUNCT
iajs-695	84	15	k	k	PROPN
iajs-695	84	16	se	se	PROPN
iajs-695	84	17	m	m	VERB
iajs-695	84	18	implies	imply	VERB
iajs-695	84	19	f	f	PROPN
iajs-695	84	20	(	(	PUNCT
iajs-695	84	21	k	k	NOUN
iajs-695	84	22	)	)	PUNCT
iajs-695	84	23	se	se	PROPN
iajs-695	84	24	n.	n.	NOUN
iajs-695	84	25	(	(	PUNCT
iajs-695	84	26	2	2	NUM
iajs-695	84	27	)	)	PUNCT
iajs-695	84	28	a	a	DET
iajs-695	84	29	se	se	PROPN
iajs-695	84	30	n	n	PROPN
iajs-695	84	31	implies	imply	VERB
iajs-695	84	32	)	)	PUNCT
iajs-695	84	33	(	(	PUNCT
iajs-695	84	34	1	1	NUM
iajs-695	84	35	af	af	PROPN
iajs-695	84	36			PROPN
iajs-695	84	37	se	se	PROPN
iajs-695	84	38	m	m	PROPN
iajs-695	84	39	,	,	PUNCT
iajs-695	84	40	if	if	SCONJ
iajs-695	84	41	f	f	PROPN
iajs-695	84	42	is	be	AUX
iajs-695	84	43	an	an	DET
iajs-695	84	44	epimorphism	epimorphism	NOUN
iajs-695	84	45	and	and	CCONJ
iajs-695	84	46	kerf	kerf	NOUN
iajs-695	84	47			PROPN
iajs-695	84	48	p	p	X
iajs-695	84	49	,	,	PUNCT
iajs-695	84	50	where	where	SCONJ
iajs-695	84	51	p	p	NOUN
iajs-695	84	52	is	be	AUX
iajs-695	84	53	any	any	DET
iajs-695	84	54	prime	prime	ADJ
iajs-695	84	55	submodule	submodule	NOUN
iajs-695	84	56	of	of	ADP
iajs-695	84	57	m.	m.	NOUN
iajs-695	84	58	proof	proof	NOUN
iajs-695	84	59	:	:	PUNCT
iajs-695	84	60	(	(	PUNCT
iajs-695	84	61	1	1	X
iajs-695	84	62	)	)	PUNCT
iajs-695	84	63	suppose	suppose	VERB
iajs-695	84	64	that	that	SCONJ
iajs-695	84	65	there	there	PRON
iajs-695	84	66	exists	exist	VERB
iajs-695	84	67	a	a	DET
iajs-695	84	68	nonzero	nonzero	PROPN
iajs-695	84	69	prime	prime	PROPN
iajs-695	84	70	submodule	submodule	PROPN
iajs-695	84	71	w	w	PROPN
iajs-695	84	72	of	of	ADP
iajs-695	84	73	n	n	PRON
iajs-695	84	74	such	such	ADJ
iajs-695	84	75	that	that	SCONJ
iajs-695	84	76	f(k	f(k	PROPN
iajs-695	84	77	)	)	PUNCT
iajs-695	84	78	w	w	NOUN
iajs-695	84	79	=	=	PUNCT
iajs-695	84	80	0	0	PROPN
iajs-695	84	81	.	.	PUNCT
iajs-695	85	1	but	but	CCONJ
iajs-695	85	2	k	k	NOUN
iajs-695	85	3	=	=	PUNCT
iajs-695	85	4	)	)	PUNCT
iajs-695	85	5	)	)	PUNCT
iajs-695	85	6	(	(	PUNCT
iajs-695	85	7	(	(	PUNCT
iajs-695	85	8	1	1	NUM
iajs-695	85	9	kff	kff	PROPN
iajs-695	85	10			PROPN
iajs-695	85	11	,	,	PUNCT
iajs-695	85	12	since	since	SCONJ
iajs-695	85	13	f	f	PROPN
iajs-695	85	14	is	be	AUX
iajs-695	85	15	a	a	DET
iajs-695	85	16	monomorphism	monomorphism	NOUN
iajs-695	85	17	.	.	PUNCT
iajs-695	86	1	hence	hence	ADV
iajs-695	86	2	k	k	X
iajs-695	86	3			PUNCT
iajs-695	86	4	)	)	PUNCT
iajs-695	86	5	(	(	PUNCT
iajs-695	86	6	1	1	NUM
iajs-695	86	7	wf	wf	PROPN
iajs-695	86	8			PROPN
iajs-695	86	9	=	=	PUNCT
iajs-695	86	10	)	)	PUNCT
iajs-695	86	11	)	)	PUNCT
iajs-695	86	12	(	(	PUNCT
iajs-695	86	13	(	(	PUNCT
iajs-695	86	14	1	1	NUM
iajs-695	86	15	kff	kff	PROPN
iajs-695	86	16			PROPN
iajs-695	86	17			NUM
iajs-695	86	18	)	)	PUNCT
iajs-695	86	19	(	(	PUNCT
iajs-695	86	20	1	1	NUM
iajs-695	86	21	wf	wf	PROPN
iajs-695	86	22			PROPN
iajs-695	86	23	=	=	PUNCT
iajs-695	86	24	)	)	PUNCT
iajs-695	86	25	)	)	PUNCT
iajs-695	86	26	(	(	PUNCT
iajs-695	86	27	(	(	PUNCT
iajs-695	86	28	1	1	NUM
iajs-695	86	29	wkff	wkff	ADJ
iajs-695	86	30			X
iajs-695	86	31	=	=	SYM
iajs-695	86	32	)	)	PUNCT
iajs-695	86	33	0(1f	0(1f	NOUN
iajs-695	87	1	=	=	NOUN
iajs-695	87	2	kerf	kerf	NOUN
iajs-695	87	3	=	=	SYM
iajs-695	87	4	{	{	PUNCT
iajs-695	87	5	0	0	NUM
iajs-695	87	6	}	}	PUNCT
iajs-695	87	7	.	.	PUNCT
iajs-695	88	1	but	but	CCONJ
iajs-695	88	2	)	)	PUNCT
iajs-695	88	3	(	(	PUNCT
iajs-695	88	4	1	1	NUM
iajs-695	88	5	wf	wf	PROPN
iajs-695	88	6			PROPN
iajs-695	88	7	is	be	AUX
iajs-695	88	8	a	a	DET
iajs-695	88	9	nonzero	nonzero	ADJ
iajs-695	88	10	prime	prime	ADJ
iajs-695	88	11	submodule	submodule	NOUN
iajs-695	88	12	of	of	ADP
iajs-695	88	13	m	m	PROPN
iajs-695	88	14	,	,	PUNCT
iajs-695	88	15	so	so	ADV
iajs-695	88	16	k	k	PROPN
iajs-695	88	17	≰se	≰se	PROPN
iajs-695	88	18	m	m	PROPN
iajs-695	88	19	which	which	PRON
iajs-695	88	20	is	be	AUX
iajs-695	88	21	a	a	DET
iajs-695	88	22	contradiction	contradiction	NOUN
iajs-695	88	23	.	.	PUNCT
iajs-695	89	1	(	(	PUNCT
iajs-695	89	2	2	2	X
iajs-695	89	3	)	)	PUNCT
iajs-695	89	4	the	the	DET
iajs-695	89	5	proof	proof	NOUN
iajs-695	89	6	is	be	AUX
iajs-695	89	7	similarly	similarly	ADV
iajs-695	89	8	.	.	PUNCT
iajs-695	90	1	1.16	1.16	NUM
iajs-695	90	2	proposition	proposition	NOUN
iajs-695	90	3	:	:	PUNCT
iajs-695	90	4	let	let	VERB
iajs-695	90	5	m	m	PRON
iajs-695	90	6			PROPN
iajs-695	90	7	n.	n.	NOUN
iajs-695	90	8	then	then	ADV
iajs-695	90	9	m	m	VERB
iajs-695	90	10	is	be	AUX
iajs-695	90	11	a	a	DET
iajs-695	90	12	strongly	strongly	ADV
iajs-695	90	13	essentially	essentially	ADV
iajs-695	90	14	quasi	quasi	ADJ
iajs-695	90	15	-	-	ADJ
iajs-695	90	16	dedekind	dedekind	ADJ
iajs-695	90	17	r	r	NOUN
iajs-695	90	18	-	-	PUNCT
iajs-695	90	19	module	module	NOUN
iajs-695	90	20	if	if	SCONJ
iajs-695	90	21	and	and	CCONJ
iajs-695	90	22	only	only	ADV
iajs-695	90	23	if	if	SCONJ
iajs-695	90	24	n	n	PRON
iajs-695	90	25	is	be	AUX
iajs-695	90	26	a	a	DET
iajs-695	90	27	strongly	strongly	ADV
iajs-695	90	28	essentially	essentially	ADV
iajs-695	90	29	quasi	quasi	ADJ
iajs-695	90	30	-	-	ADJ
iajs-695	90	31	dedekind	dedekind	ADJ
iajs-695	90	32	r	r	NOUN
iajs-695	90	33	-	-	PUNCT
iajs-695	90	34	module	module	NOUN
iajs-695	90	35	.	.	PUNCT
iajs-695	91	1	proof	proof	NOUN
iajs-695	91	2	:	:	PUNCT
iajs-695	91	3			NOUN
iajs-695	91	4	)	)	PUNCT
iajs-695	91	5	let	let	VERB
iajs-695	91	6			NOUN
iajs-695	91	7	:	:	PUNCT
iajs-695	91	8	m	m	VERB
iajs-695	91	9			PRON
iajs-695	91	10	n	n	AUX
iajs-695	91	11	be	be	AUX
iajs-695	91	12	an	an	DET
iajs-695	91	13	isomorphism	isomorphism	NOUN
iajs-695	91	14	.	.	PUNCT
iajs-695	92	1	suppose	suppose	VERB
iajs-695	92	2	that	that	SCONJ
iajs-695	92	3	m	m	PROPN
iajs-695	92	4	is	be	AUX
iajs-695	92	5	a	a	DET
iajs-695	92	6	strongly	strongly	ADV
iajs-695	92	7	essentially	essentially	ADV
iajs-695	92	8	quasi	quasi	ADJ
iajs-695	92	9	-	-	ADJ
iajs-695	92	10	dedekind	dedekind	ADJ
iajs-695	92	11	r	r	NOUN
iajs-695	92	12	-	-	PUNCT
iajs-695	92	13	module	module	NOUN
iajs-695	92	14	.	.	PUNCT
iajs-695	93	1	let	let	VERB
iajs-695	93	2	fendr(n	fendr(n	X
iajs-695	93	3	)	)	PUNCT
iajs-695	93	4	,	,	PUNCT
iajs-695	93	5	f	f	PROPN
iajs-695	93	6			PROPN
iajs-695	93	7	0	0	NUM
iajs-695	93	8	.	.	PUNCT
iajs-695	94	1	to	to	PART
iajs-695	94	2	prove	prove	VERB
iajs-695	94	3	that	that	DET
iajs-695	94	4	kerf	kerf	NOUN
iajs-695	94	5	≰se	≰se	PROPN
iajs-695	94	6	n	n	CCONJ
iajs-695	94	7	,	,	PUNCT
iajs-695	94	8	consider	consider	VERB
iajs-695	94	9	the	the	DET
iajs-695	94	10	following	following	NOUN
iajs-695	94	11	:	:	PUNCT
iajs-695	94	12	m	m	VERB
iajs-695	94	13			PROPN
iajs-695	94	14	n	n	NUM
iajs-695	94	15			ADP
iajs-695	94	16	f	f	PROPN
iajs-695	94	17	n	n	CCONJ
iajs-695	94	18			PRON
iajs-695	94	19	1	1	ADJ
iajs-695	94	20			NOUN
iajs-695	94	21	m	m	VERB
iajs-695	94	22	,	,	PUNCT
iajs-695	94	23	let	let	VERB
iajs-695	94	24	h=	h=	ADJ
iajs-695	94	25	-1o	-1o	PROPN
iajs-695	94	26	f	f	PROPN
iajs-695	94	27	o	o	ADV
iajs-695	94	28	endr(m	endr(m	NOUN
iajs-695	94	29	)	)	PUNCT
iajs-695	94	30	,	,	PUNCT
iajs-695	94	31	h	h	PROPN
iajs-695	94	32			NOUN
iajs-695	94	33	0	0	NUM
iajs-695	94	34	since	since	SCONJ
iajs-695	94	35	h(m	h(m	ADJ
iajs-695	94	36	)	)	PUNCT
iajs-695	94	37	=	=	NOUN
iajs-695	95	1			NOUN
iajs-695	95	2	-1∘	-1∘	PROPN
iajs-695	95	3	f	f	PROPN
iajs-695	95	4	∘	∘	NOUN
iajs-695	95	5	(	(	PUNCT
iajs-695	95	6	m	m	NOUN
iajs-695	95	7	)	)	PUNCT
iajs-695	95	8			PROPN
iajs-695	95	9			PROPN
iajs-695	95	10	-1	-1	PUNCT
iajs-695	95	11	(	(	PUNCT
iajs-695	95	12	f(n	f(n	PROPN
iajs-695	95	13	)	)	PUNCT
iajs-695	95	14	)	)	PUNCT
iajs-695	96	1			PROPN
iajs-695	96	2			PROPN
iajs-695	96	3	-1	-1	PUNCT
iajs-695	96	4	(	(	PUNCT
iajs-695	96	5	n	n	CCONJ
iajs-695	96	6	)	)	PUNCT
iajs-695	96	7			NOUN
iajs-695	96	8	0	0	NUM
iajs-695	96	9	.then	.then	PROPN
iajs-695	96	10	kerh	kerh	PROPN
iajs-695	96	11	≰se	≰se	PROPN
iajs-695	96	12	m	m	PROPN
iajs-695	96	13	,	,	PUNCT
iajs-695	96	14	since	since	SCONJ
iajs-695	96	15	m	m	PROPN
iajs-695	96	16	is	be	AUX
iajs-695	96	17	a	a	DET
iajs-695	96	18	strongly	strongly	ADV
iajs-695	96	19	essentially	essentially	ADV
iajs-695	96	20	quasi	quasi	ADJ
iajs-695	96	21	-	-	ADJ
iajs-695	96	22	dedekind	dedekind	ADJ
iajs-695	96	23	r	r	NOUN
iajs-695	96	24	-	-	NOUN
iajs-695	96	25	module	module	NOUN
iajs-695	96	26	.	.	PUNCT
iajs-695	97	1	we	we	PRON
iajs-695	97	2	claim	claim	VERB
iajs-695	97	3	that	that	SCONJ
iajs-695	97	4	kerf	kerf	NOUN
iajs-695	97	5	=	=	SYM
iajs-695	97	6	{	{	PUNCT
iajs-695	97	7	yn:	yn:	PROPN
iajs-695	97	8	-1(y	-1(y	PROPN
iajs-695	97	9	)	)	PUNCT
iajs-695	97	10			PROPN
iajs-695	97	11	kerh	kerh	PROPN
iajs-695	97	12	}	}	PUNCT
iajs-695	97	13	.	.	PUNCT
iajs-695	98	1	to	to	PART
iajs-695	98	2	prove	prove	VERB
iajs-695	98	3	our	our	PRON
iajs-695	98	4	assertion	assertion	NOUN
iajs-695	98	5	.	.	PUNCT
iajs-695	99	1	let	let	VERB
iajs-695	99	2	y	y	PRON
iajs-695	99	3	kerf	kerf	VERB
iajs-695	99	4	,	,	PUNCT
iajs-695	99	5	then	then	ADV
iajs-695	99	6	f(y	f(y	NOUN
iajs-695	99	7	)	)	PUNCT
iajs-695	100	1	=	=	SYM
iajs-695	100	2	0	0	X
iajs-695	100	3	.	.	PUNCT
iajs-695	101	1	h(	h(	PROPN
iajs-695	102	1	-1(y))=	-1(y))=	PROPN
iajs-695	102	2			NOUN
iajs-695	102	3	-1∘	-1∘	PROPN
iajs-695	102	4	f∘	f∘	NOUN
iajs-695	102	5	(	(	PUNCT
iajs-695	102	6			NOUN
iajs-695	102	7	-1(y))=	-1(y))=	PUNCT
iajs-695	102	8	-1∘	-1∘	PROPN
iajs-695	102	9	f	f	PROPN
iajs-695	102	10	(	(	PUNCT
iajs-695	102	11	y)=	y)=	NOUN
iajs-695	102	12	-1	-1	INTJ
iajs-695	102	13	(	(	PUNCT
iajs-695	102	14	0)=0	0)=0	NUM
iajs-695	102	15	.	.	PUNCT
iajs-695	103	1	thus	thus	ADV
iajs-695	103	2	for	for	ADP
iajs-695	103	3	each	each	DET
iajs-695	103	4	y	y	PROPN
iajs-695	103	5	kerf	kerf	NOUN
iajs-695	103	6	,	,	PUNCT
iajs-695	103	7	then	then	ADV
iajs-695	103	8			PROPN
iajs-695	103	9	-1(y	-1(y	PROPN
iajs-695	103	10	)	)	PUNCT
iajs-695	103	11			NOUN
iajs-695	103	12	kerh	kerh	NOUN
iajs-695	103	13	and	and	CCONJ
iajs-695	103	14	hence	hence	ADV
iajs-695	103	15			NOUN
iajs-695	103	16	-1(kerf)kerh	-1(kerf)kerh	PUNCT
iajs-695	103	17	≰se	≰se	PROPN
iajs-695	103	18	m	m	VERB
iajs-695	103	19	this	this	PRON
iajs-695	103	20	implies	imply	VERB
iajs-695	103	21			NOUN
iajs-695	103	22	-1(kerf	-1(kerf	NOUN
iajs-695	103	23	)	)	PUNCT
iajs-695	103	24	≰se	≰se	PROPN
iajs-695	103	25	m	m	PROPN
iajs-695	103	26	,	,	PUNCT
iajs-695	103	27	so	so	ADV
iajs-695	103	28	by	by	ADP
iajs-695	103	29	(	(	PUNCT
iajs-695	103	30	lemma.(1.16)(2	lemma.(1.16)(2	PROPN
iajs-695	103	31	)	)	PUNCT
iajs-695	103	32	)	)	PUNCT
iajs-695	103	33	kerf	kerf	NOUN
iajs-695	103	34	≰se	≰se	PROPN
iajs-695	103	35	n.	n.	PROPN
iajs-695	103	36	therefore	therefore	ADV
iajs-695	103	37	n	n	ADV
iajs-695	103	38	is	be	AUX
iajs-695	103	39	a	a	DET
iajs-695	103	40	strongly	strongly	ADV
iajs-695	103	41	essentially	essentially	ADV
iajs-695	103	42	quasi	quasi	ADJ
iajs-695	103	43	-	-	ADJ
iajs-695	103	44	dedekind	dedekind	ADJ
iajs-695	103	45	r	r	NOUN
iajs-695	103	46	-	-	NOUN
iajs-695	103	47	module	module	NOUN
iajs-695	103	48	.	.	PUNCT
iajs-695	104	1			NOUN
iajs-695	104	2	)	)	PUNCT
iajs-695	104	3	the	the	DET
iajs-695	104	4	proof	proof	NOUN
iajs-695	104	5	of	of	ADP
iajs-695	104	6	the	the	DET
iajs-695	104	7	converse	converse	NOUN
iajs-695	104	8	is	be	AUX
iajs-695	104	9	similarly	similarly	ADV
iajs-695	104	10	.	.	PUNCT
iajs-695	105	1	1.17	1.17	NUM
iajs-695	105	2	theorem	theorem	NOUN
iajs-695	105	3	:	:	PUNCT
iajs-695	105	4	let	let	VERB
iajs-695	105	5	m	m	PRON
iajs-695	105	6	be	be	AUX
iajs-695	105	7	an	an	DET
iajs-695	105	8	r	r	NOUN
iajs-695	105	9	-	-	PUNCT
iajs-695	105	10	module	module	NOUN
iajs-695	105	11	such	such	ADJ
iajs-695	105	12	that	that	SCONJ
iajs-695	105	13	m	m	PROPN
iajs-695	105	14	/	/	SYM
iajs-695	105	15	v	v	PROPN
iajs-695	105	16	is	be	AUX
iajs-695	105	17	projective	projective	ADJ
iajs-695	105	18	r	r	NOUN
iajs-695	105	19	-	-	PUNCT
iajs-695	105	20	module	module	NOUN
iajs-695	105	21	,	,	PUNCT
iajs-695	105	22	for	for	ADP
iajs-695	105	23	all	all	PRON
iajs-695	105	24	v	v	PRON
iajs-695	105	25	se	se	PROPN
iajs-695	105	26	m.	m.	NOUN
iajs-695	105	27	if	if	SCONJ
iajs-695	105	28	m	m	NOUN
iajs-695	105	29	is	be	AUX
iajs-695	105	30	a	a	DET
iajs-695	105	31	strongly	strongly	ADV
iajs-695	105	32	essentially	essentially	ADV
iajs-695	105	33	quasi	quasi	ADJ
iajs-695	105	34	-	-	ADJ
iajs-695	105	35	dedekind	dedekind	ADJ
iajs-695	105	36	r	r	NOUN
iajs-695	105	37	-	-	PUNCT
iajs-695	105	38	module	module	NOUN
iajs-695	105	39	,	,	PUNCT
iajs-695	105	40	then	then	ADV
iajs-695	105	41	m	m	PROPN
iajs-695	105	42	/	/	SYM
iajs-695	105	43	n	n	PROPN
iajs-695	105	44	is	be	AUX
iajs-695	105	45	a	a	DET
iajs-695	105	46	strongly	strongly	ADV
iajs-695	105	47	essentially	essentially	ADV
iajs-695	105	48	quasidedekind	quasidedekind	VERB
iajs-695	105	49	r	r	NOUN
iajs-695	105	50	-	-	PUNCT
iajs-695	105	51	module	module	NOUN
iajs-695	105	52	for	for	ADP
iajs-695	105	53	all	all	PRON
iajs-695	105	54	n	n	DET
iajs-695	105	55	m	m	PROPN
iajs-695	105	56	.	.	PROPN
iajs-695	105	57	provided	provide	VERB
iajs-695	105	58	n	n	NUM
iajs-695	105	59	se	se	PROPN
iajs-695	105	60	m.	m.	NOUN
iajs-695	105	61	proof	proof	NOUN
iajs-695	105	62	:	:	PUNCT
iajs-695	105	63	to	to	PART
iajs-695	105	64	prove	prove	VERB
iajs-695	105	65	that	that	SCONJ
iajs-695	105	66	m	m	NOUN
iajs-695	105	67	/	/	SYM
iajs-695	105	68	n	n	PROPN
iajs-695	105	69	is	be	AUX
iajs-695	105	70	strongly	strongly	ADV
iajs-695	105	71	essentially	essentially	ADV
iajs-695	105	72	quasi	quasi	ADJ
iajs-695	105	73	-	-	ADJ
iajs-695	105	74	dedekind	dedekind	ADJ
iajs-695	105	75	,	,	PUNCT
iajs-695	105	76	we	we	PRON
iajs-695	105	77	must	must	AUX
iajs-695	105	78	prove	prove	VERB
iajs-695	105	79	that	that	PRON
iajs-695	105	80	)	)	PUNCT
iajs-695	105	81	,	,	PUNCT
iajs-695	105	82	(	(	PUNCT
iajs-695	105	83	n	n	X
iajs-695	105	84	m	m	PROPN
iajs-695	105	85	nu	nu	INTJ
iajs-695	105	86	nm	nm	ADV
iajs-695	105	87	hom	hom	NOUN
iajs-695	106	1	=	=	SYM
iajs-695	106	2	0	0	NUM
iajs-695	106	3	for	for	SCONJ
iajs-695	106	4	all	all	DET
iajs-695	106	5	u	u	NOUN
iajs-695	106	6	/	/	SYM
iajs-695	106	7	n	n	PROPN
iajs-695	106	8	se	se	PROPN
iajs-695	106	9	m	m	PROPN
iajs-695	106	10	/	/	SYM
iajs-695	106	11	n.	n.	NOUN
iajs-695	106	12	by	by	ADP
iajs-695	106	13	3rd	3rd	PROPN
iajs-695	106	14	isomorphism	isomorphism	NOUN
iajs-695	106	15	theorem	theorem	VERB
iajs-695	106	16	u	u	PROPN
iajs-695	106	17	m	m	PROPN
iajs-695	106	18	n	n	ADP
iajs-695	106	19	u	u	NOUN
iajs-695	106	20	n	n	NOUN
iajs-695	106	21	m	m	VERB
iajs-695	106	22			NOUN
iajs-695	106	23	,	,	PUNCT
iajs-695	106	24	so	so	ADV
iajs-695	106	25	its	its	PRON
iajs-695	106	26	enough	enough	ADJ
iajs-695	106	27	to	to	PART
iajs-695	106	28	show	show	VERB
iajs-695	106	29	that	that	SCONJ
iajs-695	106	30	hom	hom	PROPN
iajs-695	106	31	(	(	PUNCT
iajs-695	106	32	m	m	PROPN
iajs-695	106	33	/	/	SYM
iajs-695	106	34	u	u	PROPN
iajs-695	106	35	,	,	PUNCT
iajs-695	106	36	m	m	PROPN
iajs-695	106	37	/	/	SYM
iajs-695	106	38	n)=	n)=	NOUN
iajs-695	106	39	0	0	NUM
iajs-695	106	40	.	.	PUNCT
iajs-695	107	1	let	let	VERB
iajs-695	107	2	f	f	PROPN
iajs-695	107	3			PROPN
iajs-695	107	4	hom	hom	PROPN
iajs-695	107	5	(	(	PUNCT
iajs-695	107	6	m	m	PROPN
iajs-695	107	7	/	/	SYM
iajs-695	107	8	u	u	PROPN
iajs-695	107	9	,	,	PUNCT
iajs-695	107	10	m	m	PROPN
iajs-695	107	11	/	/	SYM
iajs-695	107	12	n	n	PROPN
iajs-695	107	13	)	)	PUNCT
iajs-695	107	14	,	,	PUNCT
iajs-695	107	15	f	f	PROPN
iajs-695	107	16			PROPN
iajs-695	107	17	0	0	NUM
iajs-695	107	18	.hence	.hence	PUNCT
iajs-695	107	19	there	there	PRON
iajs-695	107	20	exists	exist	VERB
iajs-695	107	21	g	g	NOUN
iajs-695	107	22	:	:	PUNCT
iajs-695	107	23	m	m	PROPN
iajs-695	107	24	/	/	SYM
iajs-695	107	25	u	u	X
iajs-695	107	26			VERB
iajs-695	107	27	m	m	VERB
iajs-695	107	28	such	such	ADJ
iajs-695	107	29	that	that	PRON
iajs-695	107	30			ADJ
iajs-695	107	31	og	og	NOUN
iajs-695	107	32	=	=	SYM
iajs-695	107	33	f	f	PROPN
iajs-695	107	34	,	,	PUNCT
iajs-695	107	35	since	since	SCONJ
iajs-695	107	36	m	m	PROPN
iajs-695	107	37	/	/	SYM
iajs-695	107	38	u	u	NOUN
iajs-695	107	39	is	be	AUX
iajs-695	107	40	projective	projective	ADJ
iajs-695	107	41	.	.	PUNCT
iajs-695	108	1	مجلة	مجلة	VERB
iajs-695	108	2	إبن	إبن	VERB
iajs-695	108	3	الھیثم	الھیثم	NOUN
iajs-695	108	4	للعلوم	للعلوم	NOUN
iajs-695	108	5	الصرفة	الصرفة	NOUN
iajs-695	108	6	و	و	PRON
iajs-695	108	7	التطبیقیة	التطبیقیة	PROPN
iajs-695	108	8	2012	2012	NUM
iajs-695	108	9	السنة	السنة	NOUN
iajs-695	109	1	25	25	NUM
iajs-695	109	2	المجلد	المجلد	NOUN
iajs-695	109	3	1	1	NUM
iajs-695	109	4	العدد	العدد	PROPN
iajs-695	109	5	ibn	ibn	PROPN
iajs-695	109	6	al	al	PROPN
iajs-695	109	7	-	-	PUNCT
iajs-695	109	8	haitham	haitham	PROPN
iajs-695	109	9	journal	journal	PROPN
iajs-695	109	10	for	for	ADP
iajs-695	109	11	pure	pure	ADJ
iajs-695	109	12	and	and	CCONJ
iajs-695	109	13	applied	apply	VERB
iajs-695	109	14	science	science	NOUN
iajs-695	109	15	no	no	NOUN
iajs-695	109	16	.	.	NOUN
iajs-695	109	17	1	1	NUM
iajs-695	109	18	vol	vol	NOUN
iajs-695	109	19	.	.	PUNCT
iajs-695	110	1	25	25	NUM
iajs-695	110	2	year	year	NOUN
iajs-695	110	3	2012	2012	NUM
iajs-695	110	4	so	so	ADV
iajs-695	110	5	g	g	PROPN
iajs-695	110	6			PROPN
iajs-695	110	7	0	0	NUM
iajs-695	110	8	,	,	PUNCT
iajs-695	110	9	thus	thus	ADV
iajs-695	110	10	0	0	NUM
iajs-695	110	11	)	)	PUNCT
iajs-695	110	12	,	,	PUNCT
iajs-695	110	13	(	(	PUNCT
iajs-695	110	14	mumhom	mumhom	X
iajs-695	110	15	.	.	PUNCT
iajs-695	111	1	u	u	PROPN
iajs-695	111	2	se	se	PROPN
iajs-695	111	3	m	m	PROPN
iajs-695	111	4	,	,	PUNCT
iajs-695	111	5	because	because	SCONJ
iajs-695	111	6	nu	nu	PROPN
iajs-695	111	7			PROPN
iajs-695	111	8	.	.	PUNCT
iajs-695	112	1	thus	thus	ADV
iajs-695	112	2	m	m	NOUN
iajs-695	112	3	is	be	AUX
iajs-695	112	4	not	not	PART
iajs-695	112	5	strongly	strongly	ADV
iajs-695	112	6	essentially	essentially	ADV
iajs-695	112	7	quasi	quasi	ADJ
iajs-695	112	8	-	-	ADJ
iajs-695	112	9	dedekind	dedekind	ADJ
iajs-695	112	10	r	r	NOUN
iajs-695	112	11	-	-	PUNCT
iajs-695	112	12	module	module	NOUN
iajs-695	112	13	,	,	PUNCT
iajs-695	112	14	so	so	SCONJ
iajs-695	112	15	we	we	PRON
iajs-695	112	16	get	get	VERB
iajs-695	112	17	a	a	DET
iajs-695	112	18	contradiction	contradiction	NOUN
iajs-695	112	19	.thus	.thus	PRON
iajs-695	112	20	m	m	PROPN
iajs-695	112	21	/	/	SYM
iajs-695	112	22	n	n	PROPN
iajs-695	112	23	must	must	AUX
iajs-695	112	24	be	be	AUX
iajs-695	112	25	a	a	DET
iajs-695	112	26	strongly	strongly	ADV
iajs-695	112	27	essentially	essentially	ADV
iajs-695	112	28	quasi	quasi	ADJ
iajs-695	112	29	-	-	ADJ
iajs-695	112	30	dedekind	dedekind	ADJ
iajs-695	112	31	r	r	NOUN
iajs-695	112	32	-	-	NOUN
iajs-695	112	33	module	module	NOUN
iajs-695	112	34	.	.	PUNCT
iajs-695	113	1	to	to	PART
iajs-695	113	2	prove	prove	VERB
iajs-695	113	3	the	the	DET
iajs-695	113	4	next	next	ADJ
iajs-695	113	5	theorem	theorem	NOUN
iajs-695	113	6	we	we	PRON
iajs-695	113	7	need	need	VERB
iajs-695	113	8	the	the	DET
iajs-695	113	9	following	follow	VERB
iajs-695	113	10	lemma	lemma	PROPN
iajs-695	113	11	:	:	PUNCT
iajs-695	113	12	1.18	1.18	NUM
iajs-695	113	13	lemma	lemma	PROPN
iajs-695	113	14	:	:	PUNCT
iajs-695	113	15	let	let	VERB
iajs-695	113	16	m1	m1	PROPN
iajs-695	113	17	,	,	PUNCT
iajs-695	113	18	m2	m2	PROPN
iajs-695	113	19	be	be	VERB
iajs-695	113	20	r	r	NOUN
iajs-695	113	21	-	-	PUNCT
iajs-695	113	22	modules	module	NOUN
iajs-695	113	23	.	.	PUNCT
iajs-695	114	1	if	if	SCONJ
iajs-695	114	2	a	a	DET
iajs-695	114	3	se	se	PROPN
iajs-695	114	4	m1	m1	NOUN
iajs-695	114	5	,	,	PUNCT
iajs-695	114	6	b	b	PROPN
iajs-695	114	7	se	se	PROPN
iajs-695	114	8	m2	m2	PROPN
iajs-695	114	9	then	then	ADV
iajs-695	114	10	ba	ba	PROPN
iajs-695	114	11	se	se	PROPN
iajs-695	114	12	21	21	NUM
iajs-695	114	13	mm	mm	NOUN
iajs-695	114	14			PROPN
iajs-695	114	15	.	.	PUNCT
iajs-695	115	1	proof	proof	NOUN
iajs-695	115	2	:	:	PUNCT
iajs-695	115	3	let	let	VERB
iajs-695	115	4	p	p	PRON
iajs-695	115	5	be	be	AUX
iajs-695	115	6	prime	prime	ADJ
iajs-695	115	7	in	in	ADP
iajs-695	115	8	21	21	NUM
iajs-695	115	9	mm	mm	NOUN
iajs-695	115	10			PROPN
iajs-695	115	11	,	,	PUNCT
iajs-695	115	12	then	then	ADV
iajs-695	115	13	by	by	ADP
iajs-695	115	14	[	[	X
iajs-695	115	15	5	5	X
iajs-695	115	16	]	]	X
iajs-695	115	17	p	p	NOUN
iajs-695	115	18	=	=	SYM
iajs-695	115	19	21	21	NUM
iajs-695	115	20	pp	pp	ADV
iajs-695	115	21			ADJ
iajs-695	115	22	,	,	PUNCT
iajs-695	115	23	such	such	ADJ
iajs-695	115	24	that	that	SCONJ
iajs-695	115	25	either	either	DET
iajs-695	115	26	p1	p1	NOUN
iajs-695	115	27	,	,	PUNCT
iajs-695	115	28	p2	p2	X
iajs-695	115	29	prime	prime	NOUN
iajs-695	115	30	in	in	ADP
iajs-695	115	31	m1	m1	PROPN
iajs-695	115	32	,	,	PUNCT
iajs-695	115	33	m2	m2	PROPN
iajs-695	115	34	respectively	respectively	ADV
iajs-695	115	35	,	,	PUNCT
iajs-695	115	36	so	so	ADV
iajs-695	115	37	0	0	NUM
iajs-695	115	38	)	)	PUNCT
iajs-695	115	39	(	(	PUNCT
iajs-695	115	40	)	)	PUNCT
iajs-695	115	41	(	(	PUNCT
iajs-695	115	42	)	)	PUNCT
iajs-695	115	43	(	(	PUNCT
iajs-695	115	44	)	)	PUNCT
iajs-695	115	45	(	(	PUNCT
iajs-695	115	46	2121	2121	NUM
iajs-695	115	47			NOUN
iajs-695	115	48	pbpappba	pbpappba	NOUN
iajs-695	115	49	.	.	PUNCT
iajs-695	116	1	or	or	CCONJ
iajs-695	116	2	,	,	PUNCT
iajs-695	116	3	p	p	X
iajs-695	116	4	=	=	SYM
iajs-695	116	5	21	21	NUM
iajs-695	116	6	mp	mp	NOUN
iajs-695	116	7			PROPN
iajs-695	116	8	,	,	PUNCT
iajs-695	116	9	then	then	ADV
iajs-695	116	10	0	0	NUM
iajs-695	116	11	)	)	PUNCT
iajs-695	116	12	(	(	PUNCT
iajs-695	116	13	)	)	PUNCT
iajs-695	116	14	(	(	PUNCT
iajs-695	116	15	)	)	PUNCT
iajs-695	116	16	(	(	PUNCT
iajs-695	116	17	)	)	PUNCT
iajs-695	116	18	(	(	PUNCT
iajs-695	116	19	12121	12121	NUM
iajs-695	116	20			NOUN
iajs-695	116	21	bpambpampba	bpambpampba	NOUN
iajs-695	116	22	.	.	PUNCT
iajs-695	117	1	or	or	CCONJ
iajs-695	117	2	,	,	PUNCT
iajs-695	117	3	p	p	X
iajs-695	117	4	=	=	SYM
iajs-695	117	5	21	21	NUM
iajs-695	117	6	pm	pm	NOUN
iajs-695	117	7			ADJ
iajs-695	117	8	,	,	PUNCT
iajs-695	117	9	then	then	ADV
iajs-695	117	10	0	0	NUM
iajs-695	117	11	)	)	PUNCT
iajs-695	117	12	(	(	PUNCT
iajs-695	117	13	)	)	PUNCT
iajs-695	117	14	(	(	PUNCT
iajs-695	117	15	)	)	PUNCT
iajs-695	117	16	(	(	PUNCT
iajs-695	117	17	)	)	PUNCT
iajs-695	117	18	(	(	PUNCT
iajs-695	117	19	22121	22121	NUM
iajs-695	117	20			AUX
iajs-695	117	21	pbapbmapmba	pbapbmapmba	ADV
iajs-695	117	22	.	.	PUNCT
iajs-695	118	1	1.19	1.19	NUM
iajs-695	118	2	theorem	theorem	VERB
iajs-695	118	3	:	:	PUNCT
iajs-695	118	4	a	a	DET
iajs-695	118	5	direct	direct	ADJ
iajs-695	118	6	summand	summand	NOUN
iajs-695	118	7	of	of	ADP
iajs-695	118	8	a	a	DET
iajs-695	118	9	strongly	strongly	ADV
iajs-695	118	10	essentially	essentially	ADV
iajs-695	118	11	quasi	quasi	ADJ
iajs-695	118	12	-	-	ADJ
iajs-695	118	13	dedekind	dedekind	ADJ
iajs-695	118	14	r	r	NOUN
iajs-695	118	15	-	-	PUNCT
iajs-695	118	16	module	module	NOUN
iajs-695	118	17	is	be	AUX
iajs-695	118	18	a	a	DET
iajs-695	118	19	strongly	strongly	ADV
iajs-695	118	20	essentially	essentially	ADV
iajs-695	118	21	quasi	quasi	ADJ
iajs-695	118	22	-	-	ADJ
iajs-695	118	23	dedekind	dedekind	ADJ
iajs-695	118	24	r	r	NOUN
iajs-695	118	25	-	-	PUNCT
iajs-695	118	26	module	module	NOUN
iajs-695	118	27	.	.	PUNCT
iajs-695	119	1	proof	proof	NOUN
iajs-695	119	2	:	:	PUNCT
iajs-695	119	3	let	let	VERB
iajs-695	119	4	21	21	NUM
iajs-695	119	5	mmm	mmm	NOUN
iajs-695	119	6			NOUN
iajs-695	119	7	.	.	PUNCT
iajs-695	120	1	to	to	PART
iajs-695	120	2	prove	prove	VERB
iajs-695	120	3	m1	m1	PROPN
iajs-695	120	4	is	be	AUX
iajs-695	120	5	a	a	DET
iajs-695	120	6	strongly	strongly	ADV
iajs-695	120	7	essentially	essentially	ADV
iajs-695	120	8	quasi	quasi	ADJ
iajs-695	120	9	-	-	ADJ
iajs-695	120	10	dedekind	dedekind	ADJ
iajs-695	120	11	r	r	NOUN
iajs-695	120	12	-	-	PUNCT
iajs-695	120	13	module	module	NOUN
iajs-695	120	14	.	.	PUNCT
iajs-695	121	1	let	let	VERB
iajs-695	121	2	0	0	NUM
iajs-695	121	3	)	)	PUNCT
iajs-695	121	4	,	,	PUNCT
iajs-695	121	5	(	(	PUNCT
iajs-695	121	6	1	1	NUM
iajs-695	121	7			NOUN
iajs-695	121	8	fmendf	fmendf	ADJ
iajs-695	121	9	r	r	NOUN
iajs-695	121	10	,	,	PUNCT
iajs-695	121	11	we	we	PRON
iajs-695	121	12	have	have	VERB
iajs-695	121	13	the	the	DET
iajs-695	121	14	following	follow	VERB
iajs-695	121	15	diagram	diagram	NOUN
iajs-695	121	16	:	:	PUNCT
iajs-695	121	17	211121	211121	NUM
iajs-695	121	18	mmmmmm	mmmmmm	NOUN
iajs-695	122	1	if	if	SCONJ
iajs-695	122	2			PROPN
iajs-695	122	3			ADP
iajs-695	122	4	r	r	PROPN
iajs-695	123	1	i	i	PRON
iajs-695	123	2	f	f	NOUN
iajs-695	123	3	end	end	VERB
iajs-695	123	4	(	(	PUNCT
iajs-695	123	5	m)o	m)o	NOUN
iajs-695	123	6	o	o	NOUN
iajs-695	123	7	.if	.if	PROPN
iajs-695	124	1	1i	1i	NOUN
iajs-695	124	2	f	f	X
iajs-695	124	3	(	(	PUNCT
iajs-695	124	4	m	m	PROPN
iajs-695	124	5	)	)	PUNCT
iajs-695	125	1	i	i	PRON
iajs-695	125	2	f(m	f(m	PROPN
iajs-695	125	3	)	)	PUNCT
iajs-695	125	4			ADP
iajs-695	125	5			PROPN
iajs-695	125	6	o	o	NUM
iajs-695	126	1	o	o	NOUN
iajs-695	126	2	o	o	NOUN
iajs-695	126	3	0	0	NUM
iajs-695	126	4	)	)	PUNCT
iajs-695	126	5	(	(	PUNCT
iajs-695	126	6	)	)	PUNCT
iajs-695	126	7	)	)	PUNCT
iajs-695	126	8	(	(	PUNCT
iajs-695	126	9	(	(	PUNCT
iajs-695	126	10	11	11	NUM
iajs-695	126	11			ADP
iajs-695	126	12	mfmfi	mfmfi	NOUN
iajs-695	126	13	,	,	PUNCT
iajs-695	126	14	then	then	ADV
iajs-695	126	15	ker(i	ker(i	PROPN
iajs-695	126	16	f	f	PROPN
iajs-695	126	17	)	)	PUNCT
iajs-695	126	18	o	o	PROPN
iajs-695	127	1	o	o	PROPN
iajs-695	127	2	≰sem	≰sem	NOUN
iajs-695	127	3	.	.	PUNCT
iajs-695	128	1	ker(i	ker(i	PROPN
iajs-695	128	2	f	f	PROPN
iajs-695	128	3	)	)	PUNCT
iajs-695	128	4	o	o	NUM
iajs-695	128	5	o	o	X
iajs-695	128	6	=	=	PUNCT
iajs-695	128	7	{	{	PUNCT
iajs-695	128	8	m1+m2	m1+m2	NOUN
iajs-695	128	9	:	:	PUNCT
iajs-695	128	10	}	}	PUNCT
iajs-695	128	11	0	0	NUM
iajs-695	128	12	)	)	PUNCT
iajs-695	128	13	,	,	PUNCT
iajs-695	128	14	(	(	PUNCT
iajs-695	128	15	21	21	NUM
iajs-695	128	16	mmiofo	mmiofo	NOUN
iajs-695	128	17	=	=	SYM
iajs-695	128	18	{	{	PUNCT
iajs-695	128	19	m1+m2	m1+m2	NOUN
iajs-695	128	20	:	:	PUNCT
iajs-695	128	21	1i	1i	NUM
iajs-695	128	22	f	f	X
iajs-695	128	23	(	(	PUNCT
iajs-695	128	24	m	m	PROPN
iajs-695	128	25	)	)	PUNCT
iajs-695	128	26	0}o	0}o	NUM
iajs-695	129	1	=	=	NOUN
iajs-695	129	2	{	{	PUNCT
iajs-695	129	3	m1+m2	m1+m2	NOUN
iajs-695	129	4	:	:	PUNCT
iajs-695	129	5	}	}	PUNCT
iajs-695	129	6	0	0	NUM
iajs-695	129	7	)	)	PUNCT
iajs-695	129	8	(	(	PUNCT
iajs-695	129	9	1	1	NUM
iajs-695	129	10	mf	mf	NOUN
iajs-695	129	11	=	=	SYM
iajs-695	129	12	2mkerf	2mkerf	NUM
iajs-695	129	13			ADJ
iajs-695	129	14	≰se	≰se	NOUN
iajs-695	129	15	21	21	NUM
iajs-695	129	16	mm	mm	NOUN
iajs-695	129	17			PROPN
iajs-695	129	18	.	.	PUNCT
iajs-695	130	1	but	but	CCONJ
iajs-695	130	2	m2se	m2se	NUM
iajs-695	130	3	m2	m2	PROPN
iajs-695	130	4	,	,	PUNCT
iajs-695	130	5	so	so	ADV
iajs-695	130	6	kerf	kerf	NOUN
iajs-695	130	7	≰se	≰se	NOUN
iajs-695	130	8	1	1	NUM
iajs-695	130	9	m	m	NOUN
iajs-695	130	10	,	,	PUNCT
iajs-695	130	11	by	by	ADP
iajs-695	130	12	(	(	PUNCT
iajs-695	130	13	lemma	lemma	PROPN
iajs-695	130	14	1.18	1.18	NUM
iajs-695	130	15	)	)	PUNCT
iajs-695	130	16	.	.	PUNCT
iajs-695	131	1	the	the	DET
iajs-695	131	2	converse	converse	NOUN
iajs-695	131	3	of	of	ADP
iajs-695	131	4	(	(	PUNCT
iajs-695	131	5	theorem	theorem	NOUN
iajs-695	131	6	1.19	1.19	NUM
iajs-695	131	7	)	)	PUNCT
iajs-695	131	8	is	be	AUX
iajs-695	131	9	not	not	PART
iajs-695	131	10	true	true	ADJ
iajs-695	131	11	in	in	ADP
iajs-695	131	12	general	general	ADJ
iajs-695	131	13	,	,	PUNCT
iajs-695	131	14	consider	consider	VERB
iajs-695	131	15	the	the	DET
iajs-695	131	16	following	follow	VERB
iajs-695	131	17	example	example	NOUN
iajs-695	131	18	:	:	PUNCT
iajs-695	131	19	1.20	1.20	NUM
iajs-695	131	20	example	example	NOUN
iajs-695	131	21	:	:	PUNCT
iajs-695	131	22	we	we	PRON
iajs-695	131	23	know	know	VERB
iajs-695	131	24	that	that	SCONJ
iajs-695	131	25	each	each	PRON
iajs-695	131	26	of	of	ADP
iajs-695	131	27	z	z	PROPN
iajs-695	131	28	,	,	PUNCT
iajs-695	131	29	z6	z6	PROPN
iajs-695	131	30	as	as	ADP
iajs-695	131	31	z	z	NOUN
iajs-695	131	32	-	-	PUNCT
iajs-695	131	33	module	module	NOUN
iajs-695	131	34	is	be	AUX
iajs-695	131	35	strongly	strongly	ADV
iajs-695	131	36	essentially	essentially	ADV
iajs-695	131	37	quasi	quasi	ADJ
iajs-695	131	38	-	-	ADJ
iajs-695	131	39	dedekind	dedekind	ADJ
iajs-695	131	40	.	.	PUNCT
iajs-695	132	1	but	but	CCONJ
iajs-695	132	2	6z	6z	NOUN
iajs-695	132	3	z	z	NOUN
iajs-695	132	4	is	be	AUX
iajs-695	132	5	not	not	PART
iajs-695	132	6	strongly	strongly	ADV
iajs-695	132	7	essentially	essentially	ADV
iajs-695	132	8	quasi	quasi	ADJ
iajs-695	132	9	-	-	NOUN
iajs-695	132	10	dedekind	dedekind	ADJ
iajs-695	132	11	as	as	ADP
iajs-695	132	12	z	z	NOUN
iajs-695	132	13	-	-	NOUN
iajs-695	132	14	module	module	NOUN
iajs-695	132	15	,	,	PUNCT
iajs-695	132	16	since	since	SCONJ
iajs-695	132	17	6z	6z	NUM
iajs-695	132	18	z	z	NOUN
iajs-695	132	19	is	be	AUX
iajs-695	132	20	not	not	PART
iajs-695	132	21	essentially	essentially	ADV
iajs-695	132	22	quasi	quasi	ADJ
iajs-695	132	23	-	-	ADJ
iajs-695	132	24	dedekind	dedekind	ADJ
iajs-695	132	25	.	.	PUNCT
iajs-695	133	1	m	m	VERB
iajs-695	133	2	u	u	NOUN
iajs-695	133	3	m	m	VERB
iajs-695	133	4	n	n	ADV
iajs-695	133	5	m	m	NOUN
iajs-695	133	6	0	0	NUM
iajs-695	134	1	g	g	PROPN
iajs-695	134	2			PROPN
iajs-695	134	3	f	f	PROPN
iajs-695	134	4	مجلة	مجلة	NOUN
iajs-695	134	5	إبن	إبن	VERB
iajs-695	134	6	الھیثم	الھیثم	NOUN
iajs-695	134	7	للعلوم	للعلوم	NOUN
iajs-695	134	8	الصرفة	الصرفة	NOUN
iajs-695	134	9	و	و	PRON
iajs-695	134	10	التطبیقیة	التطبیقیة	PROPN
iajs-695	134	11	2012	2012	NUM
iajs-695	134	12	السنة	السنة	NOUN
iajs-695	135	1	25	25	NUM
iajs-695	135	2	المجلد	المجلد	NOUN
iajs-695	135	3	1	1	NUM
iajs-695	135	4	العدد	العدد	PROPN
iajs-695	135	5	ibn	ibn	PROPN
iajs-695	135	6	al	al	PROPN
iajs-695	135	7	-	-	PUNCT
iajs-695	135	8	haitham	haitham	PROPN
iajs-695	135	9	journal	journal	PROPN
iajs-695	135	10	for	for	ADP
iajs-695	135	11	pure	pure	ADJ
iajs-695	135	12	and	and	CCONJ
iajs-695	135	13	applied	apply	VERB
iajs-695	135	14	science	science	NOUN
iajs-695	135	15	no	no	NOUN
iajs-695	135	16	.	.	NOUN
iajs-695	135	17	1	1	NUM
iajs-695	135	18	vol	vol	NOUN
iajs-695	135	19	.	.	PUNCT
iajs-695	136	1	25	25	NUM
iajs-695	136	2	year	year	NOUN
iajs-695	136	3	2012	2012	NUM
iajs-695	136	4	recall	recall	VERB
iajs-695	136	5	that	that	SCONJ
iajs-695	136	6	a	a	DET
iajs-695	136	7	nonzero	nonzero	PROPN
iajs-695	136	8	submodule	submodule	PROPN
iajs-695	136	9	n	n	PROPN
iajs-695	136	10	of	of	ADP
iajs-695	136	11	an	an	DET
iajs-695	136	12	r	r	NOUN
iajs-695	136	13	-	-	PUNCT
iajs-695	136	14	module	module	NOUN
iajs-695	136	15	m	m	NOUN
iajs-695	136	16	is	be	AUX
iajs-695	136	17	called	call	VERB
iajs-695	136	18	quasi	quasi	ADJ
iajs-695	136	19	-	-	ADJ
iajs-695	136	20	invertible	invertible	ADJ
iajs-695	136	21	if	if	SCONJ
iajs-695	136	22	hom(mn	hom(mn	NOUN
iajs-695	136	23	,	,	PUNCT
iajs-695	136	24	m	m	NOUN
iajs-695	136	25	)	)	PUNCT
iajs-695	137	1	=	=	SYM
iajs-695	137	2	0	0	NUM
iajs-695	137	3	,	,	PUNCT
iajs-695	137	4	[	[	X
iajs-695	137	5	7	7	NUM
iajs-695	137	6	]	]	PUNCT
iajs-695	137	7	.	.	PUNCT
iajs-695	138	1	1.21	1.21	NUM
iajs-695	138	2	proposition	proposition	NOUN
iajs-695	138	3	:	:	PUNCT
iajs-695	138	4	if	if	SCONJ
iajs-695	138	5	m	m	NOUN
iajs-695	138	6	be	be	VERB
iajs-695	138	7	a	a	DET
iajs-695	138	8	strongly	strongly	ADV
iajs-695	138	9	essentially	essentially	ADV
iajs-695	138	10	quasi	quasi	ADJ
iajs-695	138	11	-	-	ADJ
iajs-695	138	12	dedekind	dedekind	ADJ
iajs-695	138	13	r	r	NOUN
iajs-695	138	14	-	-	PUNCT
iajs-695	138	15	module	module	NOUN
iajs-695	138	16	.	.	PUNCT
iajs-695	139	1	then	then	ADV
iajs-695	139	2	nannmann	nannmann	PROPN
iajs-695	139	3	rr	rr	PROPN
iajs-695	139	4			PROPN
iajs-695	139	5	for	for	ADP
iajs-695	139	6	all	all	DET
iajs-695	139	7	n	n	PRON
iajs-695	139	8	se	se	NOUN
iajs-695	139	9	m.	m.	NOUN
iajs-695	139	10	proof	proof	NOUN
iajs-695	139	11	:	:	PUNCT
iajs-695	139	12	suppose	suppose	VERB
iajs-695	139	13	that	that	SCONJ
iajs-695	139	14	m	m	PROPN
iajs-695	139	15	is	be	AUX
iajs-695	139	16	a	a	DET
iajs-695	139	17	strongly	strongly	ADV
iajs-695	139	18	essentially	essentially	ADV
iajs-695	139	19	quasi	quasi	ADJ
iajs-695	139	20	-	-	ADJ
iajs-695	139	21	dedekind	dedekind	ADJ
iajs-695	139	22	r	r	NOUN
iajs-695	139	23	-	-	PUNCT
iajs-695	139	24	module	module	NOUN
iajs-695	139	25	,	,	PUNCT
iajs-695	139	26	then	then	ADV
iajs-695	139	27	0	0	NUM
iajs-695	139	28	)	)	PUNCT
iajs-695	139	29	,	,	PUNCT
iajs-695	139	30	(	(	PUNCT
iajs-695	139	31	mnmhom	mnmhom	PUNCT
iajs-695	139	32	for	for	ADP
iajs-695	139	33	all	all	DET
iajs-695	139	34	n	n	PRON
iajs-695	139	35	se	se	PROPN
iajs-695	139	36	m	m	NOUN
iajs-695	139	37	,	,	PUNCT
iajs-695	139	38	hence	hence	ADV
iajs-695	139	39	n	n	PRON
iajs-695	139	40	is	be	AUX
iajs-695	139	41	a	a	DET
iajs-695	139	42	quasi	quasi	ADJ
iajs-695	139	43	-	-	ADJ
iajs-695	139	44	invertible	invertible	ADJ
iajs-695	139	45	submodule	submodule	NOUN
iajs-695	139	46	of	of	ADP
iajs-695	139	47	m	m	PROPN
iajs-695	139	48	,	,	PUNCT
iajs-695	139	49	for	for	ADP
iajs-695	139	50	all	all	DET
iajs-695	139	51	n	n	PRON
iajs-695	139	52	se	se	NOUN
iajs-695	139	53	m	m	NOUN
iajs-695	139	54	.	.	PUNCT
iajs-695	140	1	thus	thus	ADV
iajs-695	140	2	by	by	ADP
iajs-695	140	3	[	[	X
iajs-695	140	4	7	7	NUM
iajs-695	140	5	,	,	PUNCT
iajs-695	140	6	prop	prop	NOUN
iajs-695	140	7	.1.4	.1.4	PROPN
iajs-695	140	8	]	]	PUNCT
iajs-695	140	9	nannmann	nannmann	PROPN
iajs-695	140	10	rr	rr	NOUN
iajs-695	140	11			PROPN
iajs-695	140	12	for	for	ADP
iajs-695	140	13	all	all	DET
iajs-695	140	14	n	n	PRON
iajs-695	140	15	se	se	PROPN
iajs-695	140	16	m.	m.	NOUN
iajs-695	140	17	to	to	PART
iajs-695	140	18	prove	prove	VERB
iajs-695	140	19	the	the	DET
iajs-695	140	20	following	follow	VERB
iajs-695	140	21	proposition	proposition	NOUN
iajs-695	140	22	,	,	PUNCT
iajs-695	140	23	we	we	PRON
iajs-695	140	24	need	need	VERB
iajs-695	140	25	to	to	PART
iajs-695	140	26	prove	prove	VERB
iajs-695	140	27	the	the	DET
iajs-695	140	28	following	follow	VERB
iajs-695	140	29	lemma	lemma	PROPN
iajs-695	140	30	:	:	PUNCT
iajs-695	140	31	1.22	1.22	NUM
iajs-695	140	32	lemma	lemma	PROPN
iajs-695	140	33	:	:	PUNCT
iajs-695	140	34	let	let	VERB
iajs-695	140	35	m	m	PRON
iajs-695	140	36	be	be	AUX
iajs-695	140	37	a	a	DET
iajs-695	140	38	faithful	faithful	ADJ
iajs-695	140	39	multiplication	multiplication	NOUN
iajs-695	140	40	r	r	NOUN
iajs-695	140	41	-	-	NOUN
iajs-695	140	42	module	module	NOUN
iajs-695	140	43	.	.	PUNCT
iajs-695	141	1	then	then	ADV
iajs-695	141	2	n	n	ADV
iajs-695	141	3	se	se	NOUN
iajs-695	141	4	m	m	VERB
iajs-695	141	5	if	if	SCONJ
iajs-695	141	6	and	and	CCONJ
iajs-695	141	7	only	only	ADV
iajs-695	141	8	if	if	SCONJ
iajs-695	141	9	[	[	X
iajs-695	141	10	n	n	X
iajs-695	141	11	:	:	PUNCT
iajs-695	141	12	m	m	X
iajs-695	141	13	]	]	X
iajs-695	141	14	se	se	PROPN
iajs-695	141	15	r.	r.	PROPN
iajs-695	141	16	proof	proof	NOUN
iajs-695	141	17	:	:	PUNCT
iajs-695	141	18			NOUN
iajs-695	141	19	)	)	PUNCT
iajs-695	141	20	if	if	SCONJ
iajs-695	141	21	n	n	NUM
iajs-695	141	22	se	se	PROPN
iajs-695	141	23	m.	m.	NOUN
iajs-695	141	24	let	let	VERB
iajs-695	141	25	p	p	PRON
iajs-695	141	26	be	be	AUX
iajs-695	141	27	any	any	DET
iajs-695	141	28	nonzero	nonzero	ADJ
iajs-695	141	29	prime	prime	ADJ
iajs-695	141	30	ideal	ideal	NOUN
iajs-695	141	31	in	in	ADP
iajs-695	141	32	r.	r.	PROPN
iajs-695	141	33	then	then	ADV
iajs-695	141	34	by	by	ADP
iajs-695	141	35	[	[	X
iajs-695	141	36	3	3	NUM
iajs-695	141	37	,	,	PUNCT
iajs-695	141	38	lemma	lemma	PROPN
iajs-695	141	39	2.10	2.10	NUM
iajs-695	141	40	]	]	PUNCT
iajs-695	141	41	pm	pm	NOUN
iajs-695	141	42	is	be	AUX
iajs-695	141	43	a	a	DET
iajs-695	141	44	nonzero	nonzero	ADJ
iajs-695	141	45	prime	prime	ADJ
iajs-695	141	46	submodul	submodul	NOUN
iajs-695	141	47	in	in	ADP
iajs-695	141	48	m	m	PROPN
iajs-695	141	49	,	,	PUNCT
iajs-695	141	50	hence	hence	ADV
iajs-695	141	51	n	n	CCONJ
iajs-695	141	52	pm	pm	PROPN
iajs-695	141	53	0	0	NUM
iajs-695	141	54	;	;	PUNCT
iajs-695	141	55	that	that	PRON
iajs-695	141	56	is	be	AUX
iajs-695	141	57	[	[	X
iajs-695	141	58	(	(	PUNCT
iajs-695	141	59	n	n	NUM
iajs-695	141	60	:	:	X
iajs-695	141	61	m)m	m)m	X
iajs-695	141	62	]	]	X
iajs-695	141	63	pm	pm	PROPN
iajs-695	141	64	0	0	NUM
iajs-695	141	65	,	,	PUNCT
iajs-695	141	66	and	and	CCONJ
iajs-695	141	67	since	since	SCONJ
iajs-695	141	68	m	m	PROPN
iajs-695	141	69	is	be	AUX
iajs-695	141	70	a	a	DET
iajs-695	141	71	faithful	faithful	ADJ
iajs-695	141	72	multiplication	multiplication	NOUN
iajs-695	141	73	r	r	NOUN
iajs-695	141	74	-	-	NOUN
iajs-695	141	75	module	module	NOUN
iajs-695	141	76	,	,	PUNCT
iajs-695	141	77	[	[	PUNCT
iajs-695	141	78	(	(	PUNCT
iajs-695	141	79	n	n	CCONJ
iajs-695	141	80	:	:	PUNCT
iajs-695	141	81	m	m	X
iajs-695	141	82	)	)	PUNCT
iajs-695	141	83	p	p	PROPN
iajs-695	141	84	]	]	X
iajs-695	141	85	m	m	VERB
iajs-695	141	86			NOUN
iajs-695	141	87	0	0	NUM
iajs-695	141	88	,	,	PUNCT
iajs-695	141	89	by	by	ADP
iajs-695	141	90	[	[	X
iajs-695	141	91	3	3	NUM
iajs-695	141	92	]	]	PUNCT
iajs-695	141	93	.	.	PUNCT
iajs-695	142	1	thus	thus	ADV
iajs-695	142	2	[	[	X
iajs-695	142	3	n	n	X
iajs-695	142	4	:	:	PUNCT
iajs-695	142	5	m	m	PART
iajs-695	142	6	]	]	X
iajs-695	142	7	p	p	PROPN
iajs-695	142	8			PROPN
iajs-695	142	9	0	0	NUM
iajs-695	142	10	,	,	PUNCT
iajs-695	142	11	so	so	SCONJ
iajs-695	142	12	[	[	X
iajs-695	142	13	n	n	NUM
iajs-695	142	14	:	:	PUNCT
iajs-695	142	15	m	m	VERB
iajs-695	142	16	]	]	X
iajs-695	142	17	se	se	PROPN
iajs-695	142	18	r	r	NOUN
iajs-695	142	19	.	.	PUNCT
iajs-695	143	1			NOUN
iajs-695	143	2	)	)	PUNCT
iajs-695	143	3	if	if	SCONJ
iajs-695	143	4	[	[	X
iajs-695	143	5	n	n	X
iajs-695	143	6	:	:	PUNCT
iajs-695	143	7	m	m	X
iajs-695	143	8	]	]	X
iajs-695	143	9	se	se	NOUN
iajs-695	143	10	r	r	NOUN
iajs-695	143	11	.let	.let	PUNCT
iajs-695	144	1	p	p	X
iajs-695	144	2	be	be	AUX
iajs-695	144	3	any	any	DET
iajs-695	144	4	nonzero	nonzero	ADJ
iajs-695	144	5	prime	prime	ADJ
iajs-695	144	6	submodule	submodule	NOUN
iajs-695	144	7	in	in	ADP
iajs-695	144	8	m	m	PROPN
iajs-695	144	9	,	,	PUNCT
iajs-695	144	10	then	then	ADV
iajs-695	144	11	by	by	ADP
iajs-695	144	12	[	[	X
iajs-695	144	13	3	3	NUM
iajs-695	144	14	,	,	PUNCT
iajs-695	144	15	prop	prop	NOUN
iajs-695	144	16	.2.8,ch1	.2.8,ch1	SYM
iajs-695	144	17	]	]	X
iajs-695	145	1	[	[	X
iajs-695	145	2	p	p	X
iajs-695	145	3	:	:	PUNCT
iajs-695	145	4	m	m	X
iajs-695	145	5	]	]	X
iajs-695	145	6	is	be	AUX
iajs-695	145	7	prime	prime	ADJ
iajs-695	145	8	ideal	ideal	NOUN
iajs-695	145	9	in	in	ADP
iajs-695	145	10	r	r	NOUN
iajs-695	145	11	,	,	PUNCT
iajs-695	145	12	and	and	CCONJ
iajs-695	145	13	since	since	SCONJ
iajs-695	145	14	[	[	X
iajs-695	145	15	n	n	X
iajs-695	145	16	:	:	PUNCT
iajs-695	145	17	m	m	SYM
iajs-695	145	18	]	]	X
iajs-695	145	19	se	se	PROPN
iajs-695	145	20	r	r	NOUN
iajs-695	145	21	,	,	PUNCT
iajs-695	145	22	we	we	PRON
iajs-695	145	23	have	have	VERB
iajs-695	145	24	[	[	X
iajs-695	145	25	n	n	NUM
iajs-695	145	26	:	:	PUNCT
iajs-695	145	27	m	m	PART
iajs-695	145	28	]	]	X
iajs-695	145	29			PUNCT
iajs-695	146	1	[	[	X
iajs-695	146	2	p	p	X
iajs-695	146	3	:	:	PUNCT
iajs-695	146	4	m	m	PART
iajs-695	146	5	]	]	X
iajs-695	146	6			NOUN
iajs-695	146	7	0	0	NUM
iajs-695	146	8	which	which	PRON
iajs-695	146	9	implies	imply	VERB
iajs-695	146	10	(	(	PUNCT
iajs-695	146	11	[	[	X
iajs-695	146	12	n	n	CCONJ
iajs-695	146	13	:	:	PUNCT
iajs-695	146	14	m	m	PART
iajs-695	146	15	]	]	X
iajs-695	146	16			PUNCT
iajs-695	147	1	[	[	X
iajs-695	147	2	p	p	X
iajs-695	147	3	:	:	PUNCT
iajs-695	147	4	m])m	m])m	PROPN
iajs-695	147	5			NOUN
iajs-695	147	6	0	0	NUM
iajs-695	147	7	,	,	PUNCT
iajs-695	147	8	so	so	SCONJ
iajs-695	147	9	that	that	SCONJ
iajs-695	147	10	by	by	ADP
iajs-695	147	11	[	[	X
iajs-695	147	12	3	3	X
iajs-695	147	13	]	]	X
iajs-695	147	14	[	[	X
iajs-695	147	15	n	n	NUM
iajs-695	147	16	:	:	PUNCT
iajs-695	147	17	m]m	m]m	VERB
iajs-695	148	1	[	[	X
iajs-695	148	2	p	p	X
iajs-695	148	3	:	:	PUNCT
iajs-695	148	4	m	m	ADJ
iajs-695	148	5	]	]	X
iajs-695	148	6	m	m	VERB
iajs-695	148	7			NOUN
iajs-695	148	8	0	0	NUM
iajs-695	148	9	,	,	PUNCT
iajs-695	148	10	thus	thus	ADV
iajs-695	148	11	n	n	ADV
iajs-695	148	12	p	p	PROPN
iajs-695	148	13			NOUN
iajs-695	148	14	0	0	NUM
iajs-695	148	15	;	;	PUNCT
iajs-695	148	16	that	that	PRON
iajs-695	148	17	is	be	AUX
iajs-695	148	18	n	n	PRON
iajs-695	148	19	se	se	X
iajs-695	148	20	m.	m.	NOUN
iajs-695	148	21	1.23	1.23	NUM
iajs-695	148	22	proposition	proposition	NOUN
iajs-695	148	23	:	:	PUNCT
iajs-695	148	24	let	let	VERB
iajs-695	148	25	m	m	PRON
iajs-695	148	26	be	be	AUX
iajs-695	148	27	a	a	DET
iajs-695	148	28	faithful	faithful	ADJ
iajs-695	148	29	multiplication	multiplication	NOUN
iajs-695	148	30	r	r	NOUN
iajs-695	148	31	-	-	NOUN
iajs-695	148	32	module	module	NOUN
iajs-695	148	33	.	.	PUNCT
iajs-695	149	1	if	if	SCONJ
iajs-695	149	2	m	m	NOUN
iajs-695	149	3	is	be	AUX
iajs-695	149	4	a	a	DET
iajs-695	149	5	strongly	strongly	ADV
iajs-695	149	6	essentially	essentially	ADV
iajs-695	149	7	quasi	quasi	ADJ
iajs-695	149	8	-	-	ADJ
iajs-695	149	9	dedekind	dedekind	ADJ
iajs-695	149	10	r	r	NOUN
iajs-695	149	11	-	-	PUNCT
iajs-695	149	12	module	module	NOUN
iajs-695	149	13	,	,	PUNCT
iajs-695	149	14	then	then	ADV
iajs-695	149	15	r	r	NOUN
iajs-695	149	16	is	be	AUX
iajs-695	149	17	a	a	DET
iajs-695	149	18	strongly	strongly	ADV
iajs-695	149	19	essentially	essentially	ADV
iajs-695	149	20	quasi	quasi	ADJ
iajs-695	149	21	-	-	ADJ
iajs-695	149	22	dedekind	dedekind	ADJ
iajs-695	149	23	r	r	NOUN
iajs-695	149	24	-	-	PUNCT
iajs-695	149	25	module	module	NOUN
iajs-695	149	26	.	.	PUNCT
iajs-695	150	1	proof	proof	NOUN
iajs-695	150	2	:	:	PUNCT
iajs-695	150	3	let	let	VERB
iajs-695	150	4	f	f	PRON
iajs-695	150	5	:	:	PUNCT
iajs-695	150	6	r	r	X
iajs-695	150	7			NOUN
iajs-695	150	8	r	r	NOUN
iajs-695	150	9	,	,	PUNCT
iajs-695	150	10	f	f	PROPN
iajs-695	150	11			PROPN
iajs-695	150	12	0	0	NUM
iajs-695	150	13	.	.	PUNCT
iajs-695	151	1	for	for	ADP
iajs-695	151	2	any	any	DET
iajs-695	151	3	rr	rr	NOUN
iajs-695	151	4	,	,	PUNCT
iajs-695	151	5	f	f	X
iajs-695	151	6	(	(	PUNCT
iajs-695	151	7	r	r	NOUN
iajs-695	151	8	)	)	PUNCT
iajs-695	151	9	=	=	SYM
iajs-695	151	10	r	r	NOUN
iajs-695	151	11	f(1	f(1	PROPN
iajs-695	151	12	)	)	PUNCT
iajs-695	151	13	=	=	SYM
iajs-695	151	14	ra	ra	PROPN
iajs-695	151	15	,	,	PUNCT
iajs-695	151	16	where	where	SCONJ
iajs-695	151	17	a	a	DET
iajs-695	151	18	=	=	SYM
iajs-695	151	19	f(1	f(1	PROPN
iajs-695	151	20	)	)	PUNCT
iajs-695	151	21	.	.	PUNCT
iajs-695	152	1	define	define	VERB
iajs-695	152	2	g	g	NOUN
iajs-695	152	3	:	:	PUNCT
iajs-695	152	4	m	m	VERB
iajs-695	152	5			VERB
iajs-695	152	6	m	m	VERB
iajs-695	152	7	by	by	ADP
iajs-695	152	8	g(m	g(m	NOUN
iajs-695	152	9	)	)	PUNCT
iajs-695	152	10	=	=	PRON
iajs-695	152	11	am	be	AUX
iajs-695	152	12	for	for	ADP
iajs-695	152	13	each	each	DET
iajs-695	152	14	mm	mm	PROPN
iajs-695	152	15	.	.	PUNCT
iajs-695	153	1	g	g	PROPN
iajs-695	153	2	is	be	AUX
iajs-695	153	3	well	well	ADV
iajs-695	153	4	-	-	PUNCT
iajs-695	153	5	defined	define	VERB
iajs-695	153	6	and	and	CCONJ
iajs-695	153	7	g	g	PROPN
iajs-695	153	8			NOUN
iajs-695	153	9	0	0	NUM
iajs-695	153	10	,	,	PUNCT
iajs-695	153	11	hence	hence	ADV
iajs-695	153	12	kerg	kerg	PROPN
iajs-695	153	13	≰se	≰se	PROPN
iajs-695	153	14	m.	m.	NOUN
iajs-695	153	15	but	but	CCONJ
iajs-695	153	16	kerg	kerg	PROPN
iajs-695	153	17	=	=	PUNCT
iajs-695	154	1	[	[	X
iajs-695	154	2	kerg	kerg	PROPN
iajs-695	154	3	:	:	PUNCT
iajs-695	154	4	m]m	m]m	NOUN
iajs-695	154	5	,	,	PUNCT
iajs-695	154	6	since	since	SCONJ
iajs-695	154	7	m	m	PROPN
iajs-695	154	8	is	be	AUX
iajs-695	154	9	a	a	DET
iajs-695	154	10	multiplication	multiplication	NOUN
iajs-695	154	11	r	r	NOUN
iajs-695	154	12	-	-	NOUN
iajs-695	154	13	module	module	NOUN
iajs-695	154	14	.	.	PUNCT
iajs-695	155	1	however	however	ADV
iajs-695	155	2	we	we	PRON
iajs-695	155	3	can	can	AUX
iajs-695	155	4	show	show	VERB
iajs-695	155	5	that	that	SCONJ
iajs-695	155	6	[	[	X
iajs-695	155	7	kerg	kerg	X
iajs-695	155	8	:	:	PUNCT
iajs-695	155	9	m	m	VERB
iajs-695	155	10	]	]	X
iajs-695	155	11	=	=	SYM
iajs-695	155	12	kerf	kerf	NOUN
iajs-695	155	13	as	as	ADP
iajs-695	155	14	the	the	DET
iajs-695	155	15	following	following	NOUN
iajs-695	155	16	:	:	PUNCT
iajs-695	155	17	let	let	VERB
iajs-695	155	18	r	r	NOUN
iajs-695	155	19	[kerg	[kerg	ADP
iajs-695	155	20	:	:	PUNCT
iajs-695	155	21	m	m	X
iajs-695	155	22	]	]	PUNCT
iajs-695	155	23	implies	imply	VERB
iajs-695	155	24	rm	rm	PROPN
iajs-695	155	25	kerg	kerg	PROPN
iajs-695	155	26	,	,	PUNCT
iajs-695	155	27	so	so	ADV
iajs-695	155	28	g(rm	g(rm	NOUN
iajs-695	155	29	)	)	PUNCT
iajs-695	155	30	=	=	SYM
iajs-695	155	31	0	0	NUM
iajs-695	155	32	,	,	PUNCT
iajs-695	155	33	hence	hence	ADV
iajs-695	155	34	arm	arm	VERB
iajs-695	155	35	=	=	SYM
iajs-695	155	36	0	0	NUM
iajs-695	155	37	;	;	PUNCT
iajs-695	155	38	that	that	PRON
iajs-695	155	39	is	be	AUX
iajs-695	155	40	ar	ar	NOUN
iajs-695	155	41	annrm	annrm	PROPN
iajs-695	155	42	=	=	SYM
iajs-695	155	43	0	0	NUM
iajs-695	155	44	,	,	PUNCT
iajs-695	155	45	thus	thus	ADV
iajs-695	155	46	f(r	f(r	NOUN
iajs-695	155	47	)	)	PUNCT
iajs-695	156	1	=	=	SYM
iajs-695	156	2	ar	ar	NOUN
iajs-695	156	3	=	=	SYM
iajs-695	156	4	0	0	PROPN
iajs-695	156	5	,	,	PUNCT
iajs-695	156	6	hence	hence	ADV
iajs-695	156	7	r	r	NOUN
iajs-695	156	8	kerf	kerf	NOUN
iajs-695	156	9	.	.	PUNCT
iajs-695	157	1	now	now	ADV
iajs-695	157	2	,	,	PUNCT
iajs-695	157	3	let	let	VERB
iajs-695	157	4	rkerf	rkerf	PROPN
iajs-695	157	5	,	,	PUNCT
iajs-695	157	6	then	then	ADV
iajs-695	157	7	ar	ar	PROPN
iajs-695	157	8	=	=	SYM
iajs-695	157	9	f(r	f(r	X
iajs-695	157	10	)	)	PUNCT
iajs-695	158	1	=	=	SYM
iajs-695	158	2	0	0	NUM
iajs-695	158	3	,	,	PUNCT
iajs-695	158	4	so	so	ADV
iajs-695	158	5	arm	arm	NOUN
iajs-695	158	6	=	=	SYM
iajs-695	158	7	0	0	NUM
iajs-695	158	8	;	;	PUNCT
iajs-695	158	9	that	that	PRON
iajs-695	158	10	is	be	AUX
iajs-695	158	11	g(rm	g(rm	NOUN
iajs-695	158	12	)	)	PUNCT
iajs-695	158	13	=	=	SYM
iajs-695	158	14	0	0	NUM
iajs-695	158	15	,	,	PUNCT
iajs-695	158	16	thus	thus	ADV
iajs-695	158	17	rm	rm	PROPN
iajs-695	158	18	kerg	kerg	PROPN
iajs-695	158	19	and	and	CCONJ
iajs-695	158	20	hence	hence	ADV
iajs-695	158	21	r	r	NOUN
iajs-695	158	22	[kerg	[kerg	PROPN
iajs-695	158	23	:	:	PUNCT
iajs-695	158	24	m	m	VERB
iajs-695	158	25	]	]	X
iajs-695	158	26	.	.	PUNCT
iajs-695	159	1	therefore	therefore	ADV
iajs-695	159	2	[	[	X
iajs-695	159	3	kerg	kerg	X
iajs-695	159	4	:	:	PUNCT
iajs-695	159	5	m	m	VERB
iajs-695	159	6	]	]	X
iajs-695	159	7	=	=	SYM
iajs-695	159	8	kerf	kerf	NOUN
iajs-695	159	9	.	.	PUNCT
iajs-695	160	1	but	but	CCONJ
iajs-695	160	2	kerg	kerg	PROPN
iajs-695	160	3	≰se	≰se	PROPN
iajs-695	160	4	m	m	PROPN
iajs-695	160	5	,	,	PUNCT
iajs-695	160	6	implies	imply	VERB
iajs-695	160	7	by	by	ADP
iajs-695	160	8	(	(	PUNCT
iajs-695	160	9	lemma	lemma	PROPN
iajs-695	160	10	(	(	PUNCT
iajs-695	160	11	1.22	1.22	NUM
iajs-695	160	12	)	)	PUNCT
iajs-695	160	13	)	)	PUNCT
iajs-695	161	1	[	[	PUNCT
iajs-695	161	2	kerg	kerg	PROPN
iajs-695	161	3	:	:	PUNCT
iajs-695	161	4	m	m	VERB
iajs-695	161	5	]	]	PUNCT
iajs-695	161	6	≰	≰	AUX
iajs-695	161	7	se	se	X
iajs-695	161	8	r	r	NOUN
iajs-695	161	9	,	,	PUNCT
iajs-695	161	10	thus	thus	ADV
iajs-695	161	11	kerf	kerf	NOUN
iajs-695	161	12	≰se	≰se	NOUN
iajs-695	161	13	r	r	NOUN
iajs-695	161	14	and	and	CCONJ
iajs-695	161	15	hence	hence	ADV
iajs-695	161	16	r	r	NOUN
iajs-695	161	17	is	be	AUX
iajs-695	161	18	a	a	DET
iajs-695	161	19	strongly	strongly	ADV
iajs-695	161	20	essentially	essentially	ADV
iajs-695	161	21	quasi	quasi	ADJ
iajs-695	161	22	-	-	ADJ
iajs-695	161	23	dedekind	dedekind	ADJ
iajs-695	161	24	r	r	NOUN
iajs-695	161	25	-	-	PUNCT
iajs-695	161	26	module	module	NOUN
iajs-695	161	27	.	.	PUNCT
iajs-695	162	1	recall	recall	VERB
iajs-695	162	2	that	that	SCONJ
iajs-695	162	3	an	an	DET
iajs-695	162	4	r	r	NOUN
iajs-695	162	5	-	-	PUNCT
iajs-695	162	6	module	module	NOUN
iajs-695	162	7	m	m	NOUN
iajs-695	162	8	is	be	AUX
iajs-695	162	9	called	call	VERB
iajs-695	162	10	scalar	scalar	ADJ
iajs-695	162	11	if	if	SCONJ
iajs-695	162	12	for	for	SCONJ
iajs-695	162	13	each	each	DET
iajs-695	162	14	f	f	PROPN
iajs-695	162	15			PROPN
iajs-695	162	16	endr(m	endr(m	PROPN
iajs-695	162	17	)	)	PUNCT
iajs-695	162	18	,	,	PUNCT
iajs-695	162	19	there	there	PRON
iajs-695	162	20	exists	exist	VERB
iajs-695	162	21	rr	rr	PUNCT
iajs-695	162	22	such	such	ADJ
iajs-695	162	23	that	that	DET
iajs-695	162	24	f(a	f(a	NOUN
iajs-695	162	25	)	)	PUNCT
iajs-695	163	1	=	=	SYM
iajs-695	163	2	ar	ar	NOUN
iajs-695	163	3	for	for	ADP
iajs-695	163	4	all	all	DET
iajs-695	163	5	am	am	PROPN
iajs-695	164	1	[	[	X
iajs-695	164	2	10	10	NUM
iajs-695	164	3	,	,	PUNCT
iajs-695	164	4	p.8	p.8	NOUN
iajs-695	164	5	]	]	PUNCT
iajs-695	164	6	.	.	PUNCT
iajs-695	165	1	1.24	1.24	NUM
iajs-695	165	2	proposition	proposition	NOUN
iajs-695	165	3	:	:	PUNCT
iajs-695	165	4	let	let	VERB
iajs-695	165	5	m	m	PRON
iajs-695	165	6	be	be	AUX
iajs-695	165	7	a	a	DET
iajs-695	165	8	finitely	finitely	ADV
iajs-695	165	9	generated	generate	VERB
iajs-695	165	10	faithful	faithful	ADJ
iajs-695	165	11	multiplication	multiplication	NOUN
iajs-695	165	12	r	r	NOUN
iajs-695	165	13	-	-	NOUN
iajs-695	165	14	module	module	NOUN
iajs-695	165	15	.	.	PUNCT
iajs-695	166	1	if	if	SCONJ
iajs-695	166	2	r	r	NOUN
iajs-695	166	3	is	be	AUX
iajs-695	166	4	a	a	DET
iajs-695	166	5	strongly	strongly	ADV
iajs-695	166	6	essentially	essentially	ADV
iajs-695	166	7	quasi	quasi	ADJ
iajs-695	166	8	-	-	ADJ
iajs-695	166	9	dedekind	dedekind	ADJ
iajs-695	166	10	r	r	NOUN
iajs-695	166	11	-	-	PUNCT
iajs-695	166	12	module	module	NOUN
iajs-695	166	13	,	,	PUNCT
iajs-695	166	14	then	then	ADV
iajs-695	166	15	m	m	NOUN
iajs-695	166	16	is	be	AUX
iajs-695	166	17	a	a	DET
iajs-695	166	18	strongly	strongly	ADV
iajs-695	166	19	essentially	essentially	ADV
iajs-695	166	20	quasi	quasi	ADJ
iajs-695	166	21	-	-	ADJ
iajs-695	166	22	dedekind	dedekind	ADJ
iajs-695	166	23	r	r	NOUN
iajs-695	166	24	-	-	PUNCT
iajs-695	166	25	module	module	NOUN
iajs-695	166	26	.	.	PUNCT
iajs-695	167	1	مجلة	مجلة	NOUN
iajs-695	167	2	إبن	إبن	VERB
iajs-695	167	3	الھیثم	الھیثم	NOUN
iajs-695	167	4	للعلوم	للعلوم	NOUN
iajs-695	167	5	الصرفة	الصرفة	NOUN
iajs-695	167	6	و	و	PRON
iajs-695	167	7	التطبیقیة	التطبیقیة	PROPN
iajs-695	167	8	2012	2012	NUM
iajs-695	167	9	السنة	السنة	NOUN
iajs-695	168	1	25	25	NUM
iajs-695	168	2	المجلد	المجلد	NOUN
iajs-695	168	3	1	1	NUM
iajs-695	168	4	العدد	العدد	PROPN
iajs-695	168	5	ibn	ibn	PROPN
iajs-695	168	6	al	al	PROPN
iajs-695	168	7	-	-	PUNCT
iajs-695	168	8	haitham	haitham	PROPN
iajs-695	168	9	journal	journal	PROPN
iajs-695	168	10	for	for	ADP
iajs-695	168	11	pure	pure	ADJ
iajs-695	168	12	and	and	CCONJ
iajs-695	168	13	applied	apply	VERB
iajs-695	168	14	science	science	NOUN
iajs-695	168	15	no	no	NOUN
iajs-695	168	16	.	.	NOUN
iajs-695	168	17	1	1	NUM
iajs-695	168	18	vol	vol	NOUN
iajs-695	168	19	.	.	PUNCT
iajs-695	169	1	25	25	NUM
iajs-695	169	2	year	year	NOUN
iajs-695	169	3	2012	2012	NUM
iajs-695	169	4	proof	proof	NOUN
iajs-695	169	5	:	:	PUNCT
iajs-695	169	6	since	since	SCONJ
iajs-695	169	7	m	m	PROPN
iajs-695	169	8	is	be	AUX
iajs-695	169	9	a	a	DET
iajs-695	169	10	finitely	finitely	ADV
iajs-695	169	11	generated	generate	VERB
iajs-695	169	12	multiplication	multiplication	NOUN
iajs-695	169	13	r	r	NOUN
iajs-695	169	14	-	-	PUNCT
iajs-695	169	15	module	module	NOUN
iajs-695	169	16	,	,	PUNCT
iajs-695	169	17	then	then	ADV
iajs-695	169	18	by	by	ADP
iajs-695	169	19	[	[	X
iajs-695	169	20	9,th.2.3	9,th.2.3	NUM
iajs-695	169	21	]	]	X
iajs-695	169	22	m	m	VERB
iajs-695	169	23	is	be	AUX
iajs-695	169	24	a	a	DET
iajs-695	169	25	scalar	scalar	ADJ
iajs-695	169	26	r	r	NOUN
iajs-695	169	27	-	-	PUNCT
iajs-695	169	28	module	module	NOUN
iajs-695	169	29	,	,	PUNCT
iajs-695	169	30	so	so	SCONJ
iajs-695	169	31	for	for	ADP
iajs-695	169	32	each	each	DET
iajs-695	169	33	f	f	PROPN
iajs-695	169	34	endr(m	endr(m	NOUN
iajs-695	169	35	)	)	PUNCT
iajs-695	169	36	,	,	PUNCT
iajs-695	169	37	there	there	PRON
iajs-695	169	38	exists	exist	VERB
iajs-695	169	39	rr	rr	PUNCT
iajs-695	169	40	such	such	ADJ
iajs-695	169	41	that	that	SCONJ
iajs-695	169	42	f(m	f(m	PROPN
iajs-695	169	43	)	)	PUNCT
iajs-695	169	44	=	=	SYM
iajs-695	169	45	rm	rm	PROPN
iajs-695	169	46	,	,	PUNCT
iajs-695	169	47	for	for	ADP
iajs-695	169	48	all	all	DET
iajs-695	169	49	mm	mm	NOUN
iajs-695	169	50	.	.	PUNCT
iajs-695	170	1	define	define	VERB
iajs-695	170	2	g	g	NOUN
iajs-695	170	3	:	:	PUNCT
iajs-695	170	4	r	r	NOUN
iajs-695	170	5			NOUN
iajs-695	170	6	r	r	NOUN
iajs-695	170	7	by	by	ADP
iajs-695	170	8	g(a	g(a	PROPN
iajs-695	170	9	)	)	PUNCT
iajs-695	171	1	=	=	SYM
iajs-695	171	2	ra	ra	PROPN
iajs-695	171	3	,	,	PUNCT
iajs-695	171	4	for	for	ADP
iajs-695	171	5	all	all	DET
iajs-695	171	6	ar	ar	PROPN
iajs-695	171	7	,	,	PUNCT
iajs-695	171	8	kerg	kerg	PROPN
iajs-695	171	9	≰se	≰se	PROPN
iajs-695	171	10	r	r	NOUN
iajs-695	171	11	,	,	PUNCT
iajs-695	171	12	since	since	SCONJ
iajs-695	171	13	r	r	NOUN
iajs-695	171	14	is	be	AUX
iajs-695	171	15	a	a	DET
iajs-695	171	16	strongly	strongly	ADV
iajs-695	171	17	essentially	essentially	ADV
iajs-695	171	18	quasi	quasi	ADJ
iajs-695	171	19	-	-	ADJ
iajs-695	171	20	dedekind	dedekind	ADJ
iajs-695	171	21	r	r	NOUN
iajs-695	171	22	-	-	PUNCT
iajs-695	171	23	module	module	NOUN
iajs-695	171	24	.	.	PUNCT
iajs-695	172	1	but	but	CCONJ
iajs-695	172	2	kerf	kerf	NOUN
iajs-695	172	3	=	=	SYM
iajs-695	173	1	[	[	X
iajs-695	173	2	kerf	kerf	NOUN
iajs-695	173	3	:	:	PUNCT
iajs-695	173	4	m	m	NOUN
iajs-695	173	5	]	]	X
iajs-695	173	6	m	m	VERB
iajs-695	173	7	,	,	PUNCT
iajs-695	173	8	also	also	ADV
iajs-695	173	9	by	by	ADP
iajs-695	173	10	the	the	DET
iajs-695	173	11	same	same	ADJ
iajs-695	173	12	argument	argument	NOUN
iajs-695	173	13	of	of	ADP
iajs-695	173	14	the	the	DET
iajs-695	173	15	proof	proof	NOUN
iajs-695	173	16	of	of	ADP
iajs-695	173	17	(	(	PUNCT
iajs-695	173	18	prop	prop	PROPN
iajs-695	173	19	.1.23	.1.23	PROPN
iajs-695	173	20	)	)	PUNCT
iajs-695	173	21	,	,	PUNCT
iajs-695	173	22	we	we	PRON
iajs-695	173	23	get	get	VERB
iajs-695	173	24	kerg	kerg	PROPN
iajs-695	173	25	=	=	PUNCT
iajs-695	174	1	[	[	PUNCT
iajs-695	174	2	kerf	kerf	NOUN
iajs-695	174	3	:	:	PUNCT
iajs-695	174	4	m	m	VERB
iajs-695	174	5	]	]	PUNCT
iajs-695	174	6	,	,	PUNCT
iajs-695	174	7	but	but	CCONJ
iajs-695	174	8	kerg	kerg	PROPN
iajs-695	174	9	≰se	≰se	PROPN
iajs-695	174	10	r	r	NOUN
iajs-695	174	11	,	,	PUNCT
iajs-695	174	12	so	so	CCONJ
iajs-695	174	13	[	[	X
iajs-695	174	14	kerf	kerf	NOUN
iajs-695	174	15	:	:	PUNCT
iajs-695	174	16	m	m	NOUN
iajs-695	174	17	]	]	X
iajs-695	174	18	≰se	≰se	PROPN
iajs-695	174	19	r	r	NOUN
iajs-695	174	20	which	which	PRON
iajs-695	174	21	implies	imply	VERB
iajs-695	174	22	kerf	kerf	NOUN
iajs-695	174	23	≰se	≰se	PROPN
iajs-695	174	24	m	m	PRON
iajs-695	174	25	,	,	PUNCT
iajs-695	174	26	by	by	ADP
iajs-695	174	27	(	(	PUNCT
iajs-695	174	28	lemma	lemma	PROPN
iajs-695	174	29	1.22	1.22	NUM
iajs-695	174	30	)	)	PUNCT
iajs-695	174	31	.	.	PUNCT
iajs-695	175	1	thus	thus	ADV
iajs-695	175	2	m	m	NOUN
iajs-695	175	3	is	be	AUX
iajs-695	175	4	a	a	DET
iajs-695	175	5	strongly	strongly	ADV
iajs-695	175	6	essentially	essentially	ADV
iajs-695	175	7	quasi	quasi	ADJ
iajs-695	175	8	-	-	ADJ
iajs-695	175	9	dedekind	dedekind	ADJ
iajs-695	175	10	r	r	NOUN
iajs-695	175	11	-	-	PUNCT
iajs-695	175	12	module	module	NOUN
iajs-695	175	13	.	.	PUNCT
iajs-695	176	1	by	by	ADP
iajs-695	176	2	combining	combine	VERB
iajs-695	176	3	(	(	PUNCT
iajs-695	176	4	prop	prop	NOUN
iajs-695	176	5	1.23	1.23	NUM
iajs-695	176	6	)	)	PUNCT
iajs-695	176	7	and	and	CCONJ
iajs-695	176	8	(	(	PUNCT
iajs-695	176	9	prop	prop	NOUN
iajs-695	176	10	1.24	1.24	NUM
iajs-695	176	11	)	)	PUNCT
iajs-695	176	12	,	,	PUNCT
iajs-695	176	13	we	we	PRON
iajs-695	176	14	get	get	VERB
iajs-695	176	15	the	the	DET
iajs-695	176	16	following	follow	VERB
iajs-695	176	17	result	result	NOUN
iajs-695	176	18	:	:	PUNCT
iajs-695	176	19	1.25	1.25	NUM
iajs-695	176	20	corollary	corollary	NOUN
iajs-695	176	21	:	:	PUNCT
iajs-695	176	22	let	let	VERB
iajs-695	176	23	m	m	PRON
iajs-695	176	24	be	be	AUX
iajs-695	176	25	a	a	DET
iajs-695	176	26	finitely	finitely	ADV
iajs-695	176	27	generated	generate	VERB
iajs-695	176	28	faithful	faithful	ADJ
iajs-695	176	29	multiplication	multiplication	NOUN
iajs-695	176	30	r	r	NOUN
iajs-695	176	31	-	-	PUNCT
iajs-695	176	32	module.m	module.m	PROPN
iajs-695	176	33	is	be	AUX
iajs-695	176	34	a	a	DET
iajs-695	176	35	strongly	strongly	ADV
iajs-695	176	36	essentially	essentially	ADV
iajs-695	176	37	quasi	quasi	ADJ
iajs-695	176	38	-	-	ADJ
iajs-695	176	39	dedekind	dedekind	ADJ
iajs-695	176	40	r	r	NOUN
iajs-695	176	41	-	-	PUNCT
iajs-695	176	42	module	module	NOUN
iajs-695	176	43	if	if	SCONJ
iajs-695	176	44	and	and	CCONJ
iajs-695	176	45	only	only	ADV
iajs-695	176	46	if	if	SCONJ
iajs-695	176	47	r	r	NOUN
iajs-695	176	48	is	be	AUX
iajs-695	176	49	a	a	DET
iajs-695	176	50	strongly	strongly	ADV
iajs-695	176	51	essentially	essentially	ADV
iajs-695	176	52	quasi	quasi	ADJ
iajs-695	176	53	-	-	ADJ
iajs-695	176	54	dedekind	dedekind	ADJ
iajs-695	176	55	r	r	NOUN
iajs-695	176	56	-	-	NOUN
iajs-695	176	57	module	module	NOUN
iajs-695	176	58	.	.	PUNCT
iajs-695	177	1	we	we	PRON
iajs-695	177	2	end	end	VERB
iajs-695	177	3	this	this	DET
iajs-695	177	4	paper	paper	NOUN
iajs-695	177	5	with	with	ADP
iajs-695	177	6	the	the	DET
iajs-695	177	7	following	follow	VERB
iajs-695	177	8	corollary	corollary	NOUN
iajs-695	177	9	:	:	PUNCT
iajs-695	177	10	1.26	1.26	NUM
iajs-695	177	11	corollary	corollary	NOUN
iajs-695	177	12	:	:	PUNCT
iajs-695	177	13	let	let	VERB
iajs-695	177	14	m	m	PRON
iajs-695	177	15	be	be	AUX
iajs-695	177	16	a	a	DET
iajs-695	177	17	finitely	finitely	ADV
iajs-695	177	18	generated	generate	VERB
iajs-695	177	19	faithful	faithful	ADJ
iajs-695	177	20	multiplication	multiplication	NOUN
iajs-695	177	21	r	r	NOUN
iajs-695	177	22	-	-	NOUN
iajs-695	177	23	module	module	NOUN
iajs-695	177	24	.	.	PUNCT
iajs-695	178	1	if	if	SCONJ
iajs-695	178	2	r	r	NOUN
iajs-695	178	3	is	be	AUX
iajs-695	178	4	a	a	DET
iajs-695	178	5	strongly	strongly	ADV
iajs-695	178	6	essentially	essentially	ADV
iajs-695	178	7	quasi	quasi	ADJ
iajs-695	178	8	-	-	ADJ
iajs-695	178	9	dedekind	dedekind	ADJ
iajs-695	178	10	r	r	NOUN
iajs-695	178	11	-	-	PUNCT
iajs-695	178	12	module	module	NOUN
iajs-695	178	13	,	,	PUNCT
iajs-695	178	14	then	then	ADV
iajs-695	178	15	endr(m	endr(m	PROPN
iajs-695	178	16	)	)	PUNCT
iajs-695	178	17	is	be	AUX
iajs-695	178	18	a	a	DET
iajs-695	178	19	strongly	strongly	ADV
iajs-695	178	20	essentially	essentially	ADV
iajs-695	178	21	quasi	quasi	ADJ
iajs-695	178	22	-	-	ADJ
iajs-695	178	23	dedekind	dedekind	ADJ
iajs-695	178	24	ring	ring	NOUN
iajs-695	178	25	.	.	PUNCT
iajs-695	179	1	proof	proof	NOUN
iajs-695	179	2	:	:	PUNCT
iajs-695	179	3	since	since	SCONJ
iajs-695	179	4	m	m	PROPN
iajs-695	179	5	is	be	AUX
iajs-695	179	6	a	a	DET
iajs-695	179	7	finitely	finitely	ADV
iajs-695	179	8	generated	generate	VERB
iajs-695	179	9	multiplication	multiplication	NOUN
iajs-695	179	10	r	r	NOUN
iajs-695	179	11	-	-	NOUN
iajs-695	179	12	module	module	NOUN
iajs-695	179	13	,	,	PUNCT
iajs-695	179	14	then	then	ADV
iajs-695	179	15	by	by	ADP
iajs-695	179	16	[	[	PUNCT
iajs-695	179	17	9,i.2.3	9,i.2.3	NUM
iajs-695	179	18	]	]	X
iajs-695	179	19	m	m	VERB
iajs-695	179	20	is	be	AUX
iajs-695	179	21	a	a	DET
iajs-695	179	22	scalar	scalar	ADJ
iajs-695	179	23	r	r	NOUN
iajs-695	179	24	-	-	PUNCT
iajs-695	179	25	module	module	NOUN
iajs-695	179	26	.	.	PUNCT
iajs-695	180	1	then	then	ADV
iajs-695	180	2	by	by	ADP
iajs-695	180	3	[	[	X
iajs-695	180	4	8	8	NUM
iajs-695	180	5	,	,	PUNCT
iajs-695	180	6	lemma	lemma	PROPN
iajs-695	180	7	6.2	6.2	NUM
iajs-695	180	8	,	,	PUNCT
iajs-695	180	9	ch.3	ch.3	PROPN
iajs-695	180	10	]	]	PUNCT
iajs-695	180	11	endr(m	endr(m	PROPN
iajs-695	180	12	)	)	PUNCT
iajs-695	180	13			PROPN
iajs-695	180	14	r	r	X
iajs-695	180	15	/	/	SYM
iajs-695	180	16	annrm	annrm	NOUN
iajs-695	180	17			PROPN
iajs-695	180	18	r	r	NOUN
iajs-695	180	19	,	,	PUNCT
iajs-695	180	20	but	but	CCONJ
iajs-695	180	21	r	r	NOUN
iajs-695	180	22	is	be	AUX
iajs-695	180	23	a	a	DET
iajs-695	180	24	strongly	strongly	ADV
iajs-695	180	25	essentially	essentially	ADV
iajs-695	180	26	quasi	quasi	ADJ
iajs-695	180	27	-	-	ADJ
iajs-695	180	28	dedekind	dedekind	ADJ
iajs-695	180	29	ring	ring	NOUN
iajs-695	180	30	,	,	PUNCT
iajs-695	180	31	thus	thus	ADV
iajs-695	180	32	by	by	ADP
iajs-695	180	33	prop	prop	NOUN
iajs-695	180	34	.1.16	.1.16	PROPN
iajs-695	180	35	endr(m	endr(m	PROPN
iajs-695	180	36	)	)	PUNCT
iajs-695	180	37	is	be	AUX
iajs-695	180	38	a	a	PRON
iajs-695	180	39	strongly	strongly	ADV
iajs-695	180	40	essentially	essentially	ADV
iajs-695	180	41	quasidedekind	quasidedekind	VERB
iajs-695	180	42	ring	ring	NOUN
iajs-695	180	43	.	.	PUNCT
iajs-695	181	1	references	reference	NOUN
iajs-695	181	2	1	1	NUM
iajs-695	181	3	.	.	PUNCT
iajs-695	182	1	al	al	PROPN
iajs-695	182	2	-	-	PUNCT
iajs-695	182	3	daban	daban	PROPN
iajs-695	182	4	,	,	PUNCT
iajs-695	182	5	n.k.(2005)semi	n.k.(2005)semi	ADJ
iajs-695	182	6	-	-	ADJ
iajs-695	182	7	essential	essential	ADJ
iajs-695	182	8	submodules	submodule	NOUN
iajs-695	182	9	and	and	CCONJ
iajs-695	182	10	semi	semi	ADJ
iajs-695	182	11	-	-	ADJ
iajs-695	182	12	uniform	uniform	ADJ
iajs-695	182	13	modules	module	NOUN
iajs-695	182	14	,	,	PUNCT
iajs-695	182	15	m.sc.thesis	m.sc.thesis	NOUN
iajs-695	182	16	,	,	PUNCT
iajs-695	182	17	college	college	NOUN
iajs-695	182	18	of	of	ADP
iajs-695	182	19	education	education	NOUN
iajs-695	182	20	,	,	PUNCT
iajs-695	182	21	university	university	NOUN
iajs-695	182	22	of	of	ADP
iajs-695	182	23	tikret	tikret	NOUN
iajs-695	182	24	.	.	PUNCT
iajs-695	183	1	2	2	X
iajs-695	183	2	.	.	X
iajs-695	183	3	desale	desale	NOUN
iajs-695	183	4	,	,	PUNCT
iajs-695	183	5	g.and	g.and	PROPN
iajs-695	183	6	nicholson	nicholson	PROPN
iajs-695	183	7	,	,	PUNCT
iajs-695	183	8	w.k	w.k	PROPN
iajs-695	183	9	.	.	PROPN
iajs-695	183	10	(	(	PUNCT
iajs-695	183	11	1981	1981	NUM
iajs-695	183	12	)	)	PUNCT
iajs-695	183	13	endoprimitive	endoprimitive	ADJ
iajs-695	183	14	rings	ring	NOUN
iajs-695	183	15	,	,	PUNCT
iajs-695	183	16	j.algebra	j.algebra	PROPN
iajs-695	183	17	,	,	PUNCT
iajs-695	183	18	70	70	NUM
iajs-695	183	19	:	:	PUNCT
iajs-695	183	20	548	548	NUM
iajs-695	183	21	-	-	SYM
iajs-695	183	22	560	560	NUM
iajs-695	183	23	.	.	NOUN
iajs-695	184	1	3	3	NUM
iajs-695	184	2	.	.	X
iajs-695	185	1	el	el	NOUN
iajs-695	185	2	-	-	PUNCT
iajs-695	185	3	bast	bast	NOUN
iajs-695	185	4	,	,	PUNCT
iajs-695	185	5	z.a.and	z.a.and	PROPN
iajs-695	185	6	smith	smith	PROPN
iajs-695	186	1	p.f	p.f	PROPN
iajs-695	186	2	.	.	PROPN
iajs-695	186	3	,	,	PUNCT
iajs-695	186	4	(	(	PUNCT
iajs-695	186	5	1988	1988	NUM
iajs-695	186	6	)	)	PUNCT
iajs-695	186	7	,	,	PUNCT
iajs-695	186	8	multiplication	multiplication	NOUN
iajs-695	186	9	modules	module	NOUN
iajs-695	186	10	,	,	PUNCT
iajs-695	186	11	comm	comm	NOUN
iajs-695	186	12	.	.	PUNCT
iajs-695	187	1	in	in	ADP
iajs-695	187	2	algebra	algebra	NOUN
iajs-695	187	3	,	,	PUNCT
iajs-695	187	4	16	16	NUM
iajs-695	187	5	:	:	PUNCT
iajs-695	187	6	755	755	NUM
iajs-695	187	7	–	–	PUNCT
iajs-695	187	8	779	779	NUM
iajs-695	187	9	.	.	NOUN
iajs-695	187	10	4	4	NUM
iajs-695	187	11	.	.	X
iajs-695	187	12	ghawi	ghawi	PROPN
iajs-695	187	13	,	,	PUNCT
iajs-695	187	14	i.y	i.y	PROPN
iajs-695	187	15	.	.	PUNCT
iajs-695	188	1	(	(	PUNCT
iajs-695	188	2	2010	2010	NUM
iajs-695	188	3	)	)	PUNCT
iajs-695	188	4	,	,	PUNCT
iajs-695	188	5	some	some	DET
iajs-695	188	6	generalizations	generalization	NOUN
iajs-695	188	7	of	of	ADP
iajs-695	188	8	quasi	quasi	ADJ
iajs-695	188	9	-	-	ADJ
iajs-695	188	10	dedekind	dedekind	ADJ
iajs-695	188	11	modules	module	NOUN
iajs-695	188	12	,	,	PUNCT
iajs-695	188	13	m.sc	m.sc	PROPN
iajs-695	188	14	.	.	PUNCT
iajs-695	189	1	thesis	thesis	NOUN
iajs-695	189	2	,	,	PUNCT
iajs-695	189	3	college	college	NOUN
iajs-695	189	4	of	of	ADP
iajs-695	189	5	education	education	PROPN
iajs-695	189	6	ibn	ibn	PROPN
iajs-695	189	7	l	l	PROPN
iajs-695	189	8	-	-	PROPN
iajs-695	189	9	haitham	haitham	PROPN
iajs-695	189	10	,	,	PUNCT
iajs-695	189	11	university	university	NOUN
iajs-695	189	12	of	of	ADP
iajs-695	189	13	baghdad	baghdad	PROPN
iajs-695	189	14	.	.	PUNCT
iajs-695	190	1	5	5	X
iajs-695	190	2	.	.	X
iajs-695	190	3	hadi	hadi	PROPN
iajs-695	190	4	,	,	PUNCT
iajs-695	190	5	i.m	i.m	PROPN
iajs-695	190	6	-	-	PUNCT
iajs-695	190	7	a.	a.	NOUN
iajs-695	190	8	(	(	PUNCT
iajs-695	190	9	2003	2003	NUM
iajs-695	190	10	)	)	PUNCT
iajs-695	190	11	,	,	PUNCT
iajs-695	190	12	piecewise	piecewise	NOUN
iajs-695	190	13	noetherian	noetherian	ADJ
iajs-695	190	14	modules	module	NOUN
iajs-695	190	15	,	,	PUNCT
iajs-695	190	16	ph.d.thesis	ph.d.thesis	PROPN
iajs-695	190	17	,	,	PUNCT
iajs-695	190	18	college	college	NOUN
iajs-695	190	19	of	of	ADP
iajs-695	190	20	education	education	PROPN
iajs-695	190	21	ibn	ibn	PROPN
iajs-695	190	22	al	al	PROPN
iajs-695	190	23	-	-	PUNCT
iajs-695	190	24	haitham	haitham	PROPN
iajs-695	190	25	,	,	PUNCT
iajs-695	190	26	university	university	NOUN
iajs-695	190	27	of	of	ADP
iajs-695	190	28	baghdad	baghdad	PROPN
iajs-695	190	29	.	.	PUNCT
iajs-695	191	1	6	6	NUM
iajs-695	191	2	.	.	X
iajs-695	191	3	kasch	kasch	PROPN
iajs-695	191	4	,	,	PUNCT
iajs-695	191	5	f.	f.	PROPN
iajs-695	191	6	(	(	PUNCT
iajs-695	191	7	1982	1982	NUM
iajs-695	191	8	)	)	PUNCT
iajs-695	191	9	,	,	PUNCT
iajs-695	191	10	m	m	VERB
iajs-695	191	11	odules	odule	NOUN
iajs-695	191	12	and	and	CCONJ
iajs-695	191	13	rings	ring	NOUN
iajs-695	191	14	,	,	PUNCT
iajs-695	191	15	academic	academic	ADJ
iajs-695	191	16	press	press	NOUN
iajs-695	191	17	,	,	PUNCT
iajs-695	191	18	london	london	PROPN
iajs-695	191	19	.	.	PUNCT
iajs-695	192	1	7	7	X
iajs-695	192	2	.	.	X
iajs-695	192	3	mijbass	mijbass	PROPN
iajs-695	192	4	,	,	PUNCT
iajs-695	192	5	a.s	a.s	PROPN
iajs-695	192	6	.	.	PROPN
iajs-695	192	7	(	(	PUNCT
iajs-695	192	8	1997	1997	NUM
iajs-695	192	9	)	)	PUNCT
iajs-695	192	10	,	,	PUNCT
iajs-695	192	11	quasi	quasi	ADJ
iajs-695	192	12	-	-	ADJ
iajs-695	192	13	dedekind	dedekind	ADJ
iajs-695	192	14	modules	module	NOUN
iajs-695	192	15	,	,	PUNCT
iajs-695	192	16	ph.d.thesis	ph.d.thesis	PROPN
iajs-695	192	17	,	,	PUNCT
iajs-695	192	18	college	college	NOUN
iajs-695	192	19	of	of	ADP
iajs-695	192	20	science	science	NOUN
iajs-695	192	21	,	,	PUNCT
iajs-695	192	22	university	university	NOUN
iajs-695	192	23	of	of	ADP
iajs-695	192	24	baghdad	baghdad	PROPN
iajs-695	192	25	.	.	PUNCT
iajs-695	193	1	8	8	NUM
iajs-695	193	2	.	.	X
iajs-695	193	3	mohamed	mohamed	PROPN
iajs-695	193	4	–	–	PUNCT
iajs-695	193	5	ali	ali	PROPN
iajs-695	193	6	,	,	PUNCT
iajs-695	193	7	e.a	e.a	PROPN
iajs-695	193	8	.	.	PROPN
iajs-695	193	9	(	(	PUNCT
iajs-695	193	10	2006	2006	NUM
iajs-695	193	11	)	)	PUNCT
iajs-695	193	12	,	,	PUNCT
iajs-695	193	13	on	on	ADP
iajs-695	193	14	ikeda	ikeda	NOUN
iajs-695	193	15	-	-	PUNCT
iajs-695	193	16	nakayama	nakayama	NOUN
iajs-695	193	17	modules	module	NOUN
iajs-695	193	18	,	,	PUNCT
iajs-695	193	19	ph.d.thesis	ph.d.thesis	PROPN
iajs-695	193	20	,	,	PUNCT
iajs-695	193	21	college	college	NOUN
iajs-695	193	22	of	of	ADP
iajs-695	193	23	education	education	PROPN
iajs-695	193	24	ibn	ibn	PROPN
iajs-695	193	25	al	al	PROPN
iajs-695	193	26	-	-	PUNCT
iajs-695	193	27	haitham	haitham	PROPN
iajs-695	193	28	,	,	PUNCT
iajs-695	193	29	university	university	NOUN
iajs-695	193	30	of	of	ADP
iajs-695	193	31	baghdad	baghdad	PROPN
iajs-695	193	32	.	.	PUNCT
iajs-695	194	1	9	9	X
iajs-695	194	2	.	.	X
iajs-695	194	3	naoum	naoum	PROPN
iajs-695	194	4	,	,	PUNCT
iajs-695	194	5	a.g	a.g	PROPN
iajs-695	194	6	.	.	PROPN
iajs-695	194	7	(	(	PUNCT
iajs-695	194	8	1990	1990	NUM
iajs-695	194	9	)	)	PUNCT
iajs-695	194	10	,	,	PUNCT
iajs-695	194	11	on	on	ADP
iajs-695	194	12	the	the	DET
iajs-695	194	13	ring	ring	NOUN
iajs-695	194	14	of	of	ADP
iajs-695	194	15	endomorphisms	endomorphism	NOUN
iajs-695	194	16	of	of	ADP
iajs-695	194	17	a	a	DET
iajs-695	194	18	finitely	finitely	ADV
iajs-695	194	19	generated	generate	VERB
iajs-695	194	20	multiplication	multiplication	NOUN
iajs-695	194	21	modules	module	NOUN
iajs-695	194	22	,	,	PUNCT
iajs-695	194	23	periodica	periodica	NOUN
iajs-695	194	24	math	math	NOUN
iajs-695	194	25	,	,	PUNCT
iajs-695	194	26	hungarica	hungarica	PROPN
iajs-695	194	27	,	,	PUNCT
iajs-695	194	28	21(3):249	21(3):249	PROPN
iajs-695	194	29	–	–	PUNCT
iajs-695	194	30	255	255	NUM
iajs-695	194	31	.	.	X
iajs-695	194	32	10	10	NUM
iajs-695	194	33	.	.	PUNCT
iajs-695	194	34	shihab	shihab	PROPN
iajs-695	194	35	b.n	b.n	PROPN
iajs-695	194	36	.	.	PROPN
iajs-695	194	37	(	(	PUNCT
iajs-695	194	38	2004	2004	NUM
iajs-695	194	39	)	)	PUNCT
iajs-695	194	40	,	,	PUNCT
iajs-695	194	41	scalar	scalar	ADJ
iajs-695	194	42	reflexive	reflexive	ADJ
iajs-695	194	43	modules	module	NOUN
iajs-695	194	44	,	,	PUNCT
iajs-695	194	45	ph.d.thesis	ph.d.thesis	PROPN
iajs-695	194	46	,	,	PUNCT
iajs-695	194	47	college	college	NOUN
iajs-695	194	48	of	of	ADP
iajs-695	194	49	education	education	PROPN
iajs-695	194	50	ibn	ibn	PROPN
iajs-695	194	51	al	al	PROPN
iajs-695	194	52	-	-	PUNCT
iajs-695	194	53	haitham	haitham	PROPN
iajs-695	194	54	,	,	PUNCT
iajs-695	194	55	university	university	NOUN
iajs-695	194	56	of	of	ADP
iajs-695	194	57	baghdad	baghdad	PROPN
iajs-695	194	58	.	.	PUNCT
iajs-695	195	1	11	11	NUM
iajs-695	195	2	.	.	PUNCT
iajs-695	196	1	zelmanowitz	zelmanowitz	NOUN
iajs-695	196	2	,	,	PUNCT
iajs-695	196	3	j.m	j.m	PROPN
iajs-695	196	4	.	.	PUNCT
iajs-695	197	1	(	(	PUNCT
iajs-695	197	2	1986	1986	NUM
iajs-695	197	3	)	)	PUNCT
iajs-695	197	4	,	,	PUNCT
iajs-695	197	5	representation	representation	NOUN
iajs-695	197	6	of	of	ADP
iajs-695	197	7	rings	ring	NOUN
iajs-695	197	8	with	with	ADP
iajs-695	197	9	faithful	faithful	ADJ
iajs-695	197	10	polyform	polyform	NOUN
iajs-695	197	11	modules	module	NOUN
iajs-695	197	12	,	,	PUNCT
iajs-695	197	13	comm	comm	NOUN
iajs-695	197	14	.	.	PUNCT
iajs-695	198	1	in	in	ADP
iajs-695	198	2	algebra,.14	algebra,.14	PROPN
iajs-695	198	3	(	(	PUNCT
iajs-695	198	4	6):1141	6):1141	NUM
iajs-695	198	5	–	–	PUNCT
iajs-695	198	6	1169	1169	NUM
iajs-695	198	7	.	.	PUNCT
iajs-695	198	8	،	،	PROPN
iajs-695	198	9	رسـالة	رسـالة	PROPN
iajs-695	198	10	ماجـستیر	ماجـستیر	PROPN
iajs-695	198	11	،	،	PROPN
iajs-695	198	12	حول	حول	PROPN
iajs-695	198	13	المودیـوالت	المودیـوالت	PROPN
iajs-695	198	14	الجزئیـة	الجزئیـة	PROPN
iajs-695	198	15	األولیـة	األولیـة	PROPN
iajs-695	198	16	والمودیـوالت	والمودیـوالت	PROPN
iajs-695	198	17	الجزئیـة	الجزئیـة	PROPN
iajs-695	198	18	شـبھ	شـبھ	PROPN
iajs-695	198	19	االولیـة،)1996	االولیـة،)1996	X
iajs-695	198	20	(	(	PUNCT
iajs-695	198	21	،	،	X
iajs-695	198	22	یمان	یمان	NOUN
iajs-695	198	23	علي	علي	NOUN
iajs-695	198	24	عذابإ	عذابإ	VERB
iajs-695	198	25	.12	.12	NUM
iajs-695	198	26	.جامعة	.جامعة	ADP
iajs-695	198	27	بغداد	بغداد	PROPN
iajs-695	198	28	،	،	PROPN
iajs-695	198	29	كلیة	كلیة	PROPN
iajs-695	198	30	العلوم	العلوم	NOUN
iajs-695	198	31	مجلة	مجلة	VERB
iajs-695	198	32	إبن	إبن	NOUN
iajs-695	198	33	الھیثم	الھیثم	NOUN
iajs-695	198	34	للعلوم	للعلوم	NOUN
iajs-695	198	35	الصرفة	الصرفة	NOUN
iajs-695	198	36	و	و	PRON
iajs-695	198	37	التطبیقیة	التطبیقیة	PROPN
iajs-695	198	38	2012	2012	NUM
iajs-695	198	39	السنة	السنة	NOUN
iajs-695	198	40	25	25	NUM
iajs-695	198	41	المجلد	المجلد	NOUN
iajs-695	198	42	1	1	NUM
iajs-695	198	43	العدد	العدد	PROPN
iajs-695	198	44	ibn	ibn	PROPN
iajs-695	198	45	al	al	PROPN
iajs-695	198	46	-	-	PUNCT
iajs-695	198	47	haitham	haitham	PROPN
iajs-695	198	48	journal	journal	PROPN
iajs-695	198	49	for	for	ADP
iajs-695	198	50	pure	pure	ADJ
iajs-695	198	51	and	and	CCONJ
iajs-695	198	52	applied	apply	VERB
iajs-695	198	53	science	science	NOUN
iajs-695	198	54	no	no	NOUN
iajs-695	198	55	.	.	NOUN
iajs-695	198	56	1	1	NUM
iajs-695	198	57	vol	vol	NOUN
iajs-695	198	58	.	.	PUNCT
iajs-695	199	1	25	25	NUM
iajs-695	199	2	year	year	NOUN
iajs-695	199	3	2012	2012	NUM
iajs-695	199	4	بقوة	بقوة	ADJ
iajs-695	199	5	دیدیكاندیة	دیدیكاندیة	NOUN
iajs-695	199	6	الواسعة	الواسعة	NOUN
iajs-695	199	7	-	-	PUNCT
iajs-695	199	8	المقاسات	المقاسات	PROPN
iajs-695	199	9	شبھ	شبھ	PROPN
iajs-695	199	10	ثائر	ثائر	PROPN
iajs-695	199	11	یونس	یونس	NOUN
iajs-695	199	12	غاوي	غاوي	PROPN
iajs-695	199	13	،	،	PROPN
iajs-695	199	14	هاديإنعام	هاديإنعام	PROPN
iajs-695	199	15	محمد	محمد	PROPN
iajs-695	199	16	علي	علي	NOUN
iajs-695	199	17	جامعة	جامعة	PROPN
iajs-695	199	18	بغداد	بغداد	PROPN
iajs-695	199	19	،	،	PROPN
iajs-695	199	20	ابن	ابن	PROPN
iajs-695	199	21	الهیثم	الهیثم	PROPN
iajs-695	199	22	-لیة	-لیة	ADJ
iajs-695	199	23	التربیةك	التربیةك	PROPN
iajs-695	199	24	،	،	PROPN
iajs-695	199	25	قسم	قسم	PROPN
iajs-695	199	26	الریاضیات	الریاضیات	PROPN
iajs-695	199	27	جامعة	جامعة	PROPN
iajs-695	199	28	القادسیة،كلیة	القادسیة،كلیة	PROPN
iajs-695	199	29	التربیة	التربیة	NOUN
iajs-695	199	30	،	،	PROPN
iajs-695	199	31	قسم	قسم	PROPN
iajs-695	199	32	الریاضیات	الریاضیات	VERB
iajs-695	199	33	2011تموز	2011تموز	NUM
iajs-695	199	34	13	13	NUM
iajs-695	199	35	:	:	PUNCT
iajs-695	199	36	،	،	PROPN
iajs-695	200	1	قبل	قبل	PROPN
iajs-695	200	2	البحث	البحث	VERB
iajs-695	200	3	في	في	ADP
iajs-695	200	4	2011	2011	NUM
iajs-695	200	5	نیسان	نیسان	NOUN
iajs-695	200	6	5	5	NUM
iajs-695	200	7	:	:	PUNCT
iajs-695	200	8	استلم	استلم	PROPN
iajs-695	200	9	البحث	البحث	VERB
iajs-695	200	10	في	في	ADP
iajs-695	200	11	الخالصة	الخالصة	PROPN
iajs-695	200	12	واسـعة	واسـعة	PROPN
iajs-695	201	1	دیدیكاندیـة	دیدیكاندیـة	PROPN
iajs-695	201	2	ال-ّفـي	ال-ّفـي	PROPN
iajs-695	201	3	هـذا	هـذا	NOUN
iajs-695	201	4	البحـث	البحـث	VERB
iajs-695	201	5	قـدمنا	قـدمنا	PROPN
iajs-695	201	6	ودرسـنا	ودرسـنا	PROPN
iajs-695	202	1	مفهـوم	مفهـوم	PROPN
iajs-695	202	2	المقاسـات	المقاسـات	PROPN
iajs-695	202	3	شـبه	شـبه	PROPN
iajs-695	202	4	.	.	PUNCT
iajs-695	203	1	عنـصر	عنـصر	NOUN
iajs-695	203	2	محایـد	محایـد	PROPN
iajs-695	204	1	ا	ا	ADP
iajs-695	204	2	حلقة	حلقة	PROPN
iajs-695	204	3	أبدالیـة	أبدالیـة	ADJ
iajs-695	204	4	ذrلتكن	ذrلتكن	NOUN
iajs-695	204	5	دیدیكانـدي	دیدیكانـدي	VERB
iajs-695	205	1	واسـع	واسـع	PROPN
iajs-695	205	2	بقـوة	بقـوة	NOUN
iajs-695	205	3	إذا	إذا	NOUN
iajs-695	205	4	-ًمقاسـا	-ًمقاسـا	NOUN
iajs-695	205	5	شـبهr	شـبهr	ADJ
iajs-695	205	6	علـى	علـى	VERB
iajs-695	205	7	mّ	mّ	PROPN
iajs-695	205	8	یـسمى	یـسمى	VERB
iajs-695	205	9	المقـاس	المقـاس	PROPN
iajs-695	205	10	اذ	اذ	PROPN
iajs-695	205	11	،	،	PROPN
iajs-695	206	1	دیدیكاندیـة	دیدیكاندیـة	PROPN
iajs-695	206	2	الواسـعة	الواسـعة	PROPN
iajs-695	206	3	-	-	PUNCT
iajs-695	206	4	بقوة	بقوة	ADJ
iajs-695	206	5	كأعمـام	كأعمـام	PROPN
iajs-695	206	6	إلـى	إلـى	PROPN
iajs-695	206	7	المقاسـات	المقاسـات	PROPN
iajs-695	206	8	شـبه	شـبه	PROPN
iajs-695	206	9	)	)	PUNCT
iajs-695	206	10	,	,	PUNCT
iajs-695	206	11	(	(	PUNCT
iajs-695	206	12	0كـان	0كـان	PROPN
iajs-695	206	13	mnmhom	mnmhom	PUNCT
iajs-695	206	14	لكـل	لكـل	NOUN
iajs-695	206	15	مقـاس	مقـاس	VERB
iajs-695	206	16	جزئـي	جزئـي	ADJ
iajs-695	206	17	شـبه	شـبه	PROPN
iajs-695	206	18	واسـع	واسـع	PROPN
iajs-695	207	1	n	n	PROPN
iajs-695	207	2	فـيm	فـيm	NOUN
iajs-695	207	3	.	.	PUNCT
iajs-695	208	1	یطلـق	یطلـق	NOUN
iajs-695	208	2	علـى	علـى	ADP
iajs-695	208	3	مقـاس	مقـاس	PROPN
iajs-695	208	4	جزئـيn	جزئـيn	PROPN
iajs-695	208	5	مـن	مـن	VERB
iajs-695	208	6	مقـاس	مقـاس	PROPN
iajs-695	208	7	mعلـىr	mعلـىr	NOUN
iajs-695	208	8	0	0	NUM
iajs-695	208	9	شــبه	شــبه	PROPN
iajs-695	209	1	واسـع	واسـع	ADJ
iajs-695	209	2	إذا	إذا	NOUN
iajs-695	209	3	كــان	كــان	PROPN
iajs-695	209	4	pn	pn	PROPN
iajs-695	209	5	لكــل	لكــل	PROPN
iajs-695	209	6	مقــاس	مقــاس	NOUN
iajs-695	209	7	جزئــي	جزئــي	VERB
iajs-695	209	8	أولــي	أولــي	PROPN
iajs-695	209	9	غیـر	غیـر	PROPN
iajs-695	209	10	صــفري	صــفري	VERB
iajs-695	209	11	p	p	NOUN
iajs-695	209	12	فــي	فــي	ADJ
iajs-695	209	13	m	m	NOUN
iajs-695	209	14	.	.	PUNCT
iajs-695	210	1	علــى	علــى	PROPN
iajs-695	210	2	شــرط	شــرط	PROPN
iajs-695	210	3	انm	انm	PROPN
iajs-695	210	4	ـا	ـا	PROPN
iajs-695	210	5	لهـ	لهـ	NOUN
iajs-695	210	6	.	.	PUNCT
iajs-695	211	1	صفریةمقاسات	صفریةمقاسات	PROPN
iajs-695	211	2	أولیة	أولیة	PROPN
iajs-695	211	3	غیر	غیر	PROPN
iajs-695	211	4	وة	وة	PROPN
iajs-695	211	5	،	،	PROPN
iajs-695	211	6	المقاسـات	المقاسـات	PROPN
iajs-695	211	7	الجزئیـة	الجزئیـة	PROPN
iajs-695	211	8	شـبھ	شـبھ	PROPN
iajs-695	212	1	ة	ة	ADP
iajs-695	212	2	المقاسـات	المقاسـات	PROPN
iajs-695	212	3	شـبھ	شـبھ	PROPN
iajs-695	212	4	الدیدكاندیـھ	الدیدكاندیـھ	PROPN
iajs-695	212	5	الواسـعة	الواسـعة	PROPN
iajs-695	212	6	،	،	PROPN
iajs-695	212	7	المقاسـات	المقاسـات	PROPN
iajs-695	212	8	شـبھ	شـبھ	PROPN
iajs-695	212	9	الدیدكاندیـ	الدیدكاندیـ	PROPN
iajs-695	212	10	:	:	PUNCT
iajs-695	212	11	الكلمات	الكلمات	ADJ
iajs-695	212	12	المفتاحیة	المفتاحیة	ADJ
iajs-695	212	13	الواسـعة	الواسـعة	PROPN
iajs-695	212	14	بـق	بـق	PROPN
iajs-695	212	15	.الواسعة	.الواسعة	PROPN
iajs-695	212	16	،	،	PROPN
iajs-695	212	17	المقاسات	المقاسات	PROPN
iajs-695	212	18	الجدائیة	الجدائیة	PROPN
iajs-695	212	19	مجلة	مجلة	PROPN
iajs-695	212	20	إبن	إبن	VERB
iajs-695	212	21	الھیثم	الھیثم	NOUN
iajs-695	212	22	للعلوم	للعلوم	NOUN
iajs-695	212	23	الصرفة	الصرفة	NOUN
iajs-695	212	24	و	و	PRON
iajs-695	212	25	التطبیقیة	التطبیقیة	PROPN
iajs-695	212	26	2012	2012	NUM
iajs-695	212	27	السنة	السنة	NOUN
iajs-695	213	1	25	25	NUM
iajs-695	213	2	المجلد	المجلد	NOUN
iajs-695	213	3	1	1	NUM
iajs-695	213	4	العدد	العدد	PROPN
iajs-695	213	5	ibn	ibn	PROPN
iajs-695	213	6	al	al	PROPN
iajs-695	213	7	-	-	PUNCT
iajs-695	213	8	haitham	haitham	PROPN
iajs-695	213	9	journal	journal	PROPN
iajs-695	213	10	for	for	ADP
iajs-695	213	11	pure	pure	ADJ
iajs-695	213	12	and	and	CCONJ
iajs-695	213	13	applied	apply	VERB
iajs-695	213	14	science	science	NOUN
iajs-695	213	15	no	no	NOUN
iajs-695	213	16	.	.	NOUN
iajs-695	213	17	1	1	NUM
iajs-695	213	18	vol	vol	NOUN
iajs-695	213	19	.	.	PUNCT
iajs-695	214	1	25	25	NUM
iajs-695	214	2	year	year	NOUN
iajs-695	214	3	2012	2012	NUM