id	sid	tid	token	lemma	pos
iajs-653	1	1	إبن	إبن	VERB
iajs-653	1	2	الهيثم	الهيثم	ADJ
iajs-653	1	3	للعلوم	للعلوم	NOUN
iajs-653	1	4	الصرفة	الصرفة	NOUN
iajs-653	1	5	و	و	PRON
iajs-653	1	6	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	1	7	2012	2012	NUM
iajs-653	1	8	السنة	السنة	NOUN
iajs-653	1	9	25	25	NUM
iajs-653	2	1	المجلد	المجلد	NOUN
iajs-653	3	1	2	2	NUM
iajs-653	4	1	العدد	العدد	PROPN
iajs-653	4	2	ibn	ibn	PROPN
iajs-653	4	3	al	al	PROPN
iajs-653	4	4	-	-	PUNCT
iajs-653	4	5	haitham	haitham	PROPN
iajs-653	4	6	journal	journal	PROPN
iajs-653	4	7	for	for	ADP
iajs-653	4	8	pure	pure	ADJ
iajs-653	4	9	and	and	CCONJ
iajs-653	4	10	applied	apply	VERB
iajs-653	4	11	science	science	NOUN
iajs-653	4	12	no	no	NOUN
iajs-653	4	13	.	.	NOUN
iajs-653	4	14	2	2	NUM
iajs-653	4	15	vol	vol	NOUN
iajs-653	4	16	.	.	PUNCT
iajs-653	5	1	25	25	NUM
iajs-653	5	2	year	year	NOUN
iajs-653	5	3	2012	2012	NUM
iajs-653	5	4	purely	purely	ADV
iajs-653	5	5	co	co	ADJ
iajs-653	5	6	-	-	ADJ
iajs-653	5	7	hopfian	hopfian	ADJ
iajs-653	5	8	modules	module	NOUN
iajs-653	5	9	z.	z.	PROPN
iajs-653	5	10	t.salman	t.salman	NOUN
iajs-653	5	11	department	department	PROPN
iajs-653	5	12	of	of	ADP
iajs-653	5	13	mathematics	mathematics	PROPN
iajs-653	5	14	,	,	PUNCT
iajs-653	5	15	college	college	NOUN
iajs-653	5	16	of	of	ADP
iajs-653	5	17	science	science	NOUN
iajs-653	5	18	,	,	PUNCT
iajs-653	5	19	university	university	PROPN
iajs-653	5	20	of	of	ADP
iajs-653	5	21	baghdad	baghdad	PROPN
iajs-653	5	22	received	receive	VERB
iajs-653	5	23	in	in	ADP
iajs-653	5	24	:	:	PUNCT
iajs-653	5	25	22	22	NUM
iajs-653	5	26	septembre	septembre	PROPN
iajs-653	5	27	2011	2011	NUM
iajs-653	5	28	accepted	accept	VERB
iajs-653	5	29	in	in	ADP
iajs-653	5	30	:	:	PUNCT
iajs-653	5	31	11january	11january	NUM
iajs-653	5	32	2012	2012	NUM
iajs-653	5	33	abstract	abstract	NOUN
iajs-653	5	34	let	let	VERB
iajs-653	5	35	r	r	PRON
iajs-653	5	36	be	be	AUX
iajs-653	5	37	an	an	DET
iajs-653	5	38	associative	associative	ADJ
iajs-653	5	39	ring	ring	NOUN
iajs-653	5	40	with	with	ADP
iajs-653	5	41	identity	identity	NOUN
iajs-653	5	42	and	and	CCONJ
iajs-653	5	43	m	m	PROPN
iajs-653	5	44	a	a	DET
iajs-653	5	45	non	non	X
iajs-653	5	46	–	–	PUNCT
iajs-653	5	47	zero	zero	NUM
iajs-653	5	48	unitary	unitary	ADJ
iajs-653	5	49	r-module.in	r-module.in	NUM
iajs-653	5	50	this	this	DET
iajs-653	5	51	paper	paper	NOUN
iajs-653	5	52	we	we	PRON
iajs-653	5	53	introduce	introduce	VERB
iajs-653	5	54	the	the	DET
iajs-653	5	55	definition	definition	NOUN
iajs-653	5	56	of	of	ADP
iajs-653	5	57	purely	purely	ADV
iajs-653	5	58	co	co	ADJ
iajs-653	5	59	-	-	ADJ
iajs-653	5	60	hopfian	hopfian	ADJ
iajs-653	5	61	module	module	NOUN
iajs-653	5	62	,	,	PUNCT
iajs-653	5	63	where	where	SCONJ
iajs-653	5	64	an	an	DET
iajs-653	5	65	r	r	NOUN
iajs-653	5	66	-	-	PUNCT
iajs-653	5	67	module	module	NOUN
iajs-653	5	68	m	m	NOUN
iajs-653	5	69	is	be	AUX
iajs-653	5	70	said	say	VERB
iajs-653	5	71	to	to	PART
iajs-653	5	72	be	be	AUX
iajs-653	5	73	purely	purely	ADV
iajs-653	5	74	co	co	ADJ
iajs-653	5	75	-	-	NOUN
iajs-653	5	76	hopfian	hopfian	ADJ
iajs-653	5	77	if	if	SCONJ
iajs-653	5	78	for	for	ADP
iajs-653	5	79	any	any	DET
iajs-653	5	80	monomorphism	monomorphism	NOUN
iajs-653	5	81	f	f	PROPN
iajs-653	5	82	î	î	PROPN
iajs-653	5	83	end	end	NOUN
iajs-653	5	84	(	(	PUNCT
iajs-653	5	85	m	m	NOUN
iajs-653	5	86	)	)	PUNCT
iajs-653	5	87	,	,	PUNCT
iajs-653	5	88	imf	imf	PROPN
iajs-653	5	89	is	be	AUX
iajs-653	5	90	pure	pure	ADJ
iajs-653	5	91	in	in	ADP
iajs-653	5	92	m	m	PROPN
iajs-653	5	93	and	and	CCONJ
iajs-653	5	94	we	we	PRON
iajs-653	5	95	give	give	VERB
iajs-653	5	96	some	some	DET
iajs-653	5	97	properties	property	NOUN
iajs-653	5	98	of	of	ADP
iajs-653	5	99	this	this	DET
iajs-653	5	100	kind	kind	NOUN
iajs-653	5	101	of	of	ADP
iajs-653	5	102	modules	module	NOUN
iajs-653	5	103	.	.	PUNCT
iajs-653	6	1	keywords	keyword	NOUN
iajs-653	6	2	:	:	PUNCT
iajs-653	6	3	co	co	ADJ
iajs-653	6	4	-	-	ADJ
iajs-653	6	5	hopfian	hopfian	ADJ
iajs-653	6	6	module	module	NOUN
iajs-653	6	7	,	,	PUNCT
iajs-653	6	8	semi	semi	ADV
iajs-653	6	9	co	co	ADJ
iajs-653	6	10	-	-	ADJ
iajs-653	6	11	hopfian	hopfian	ADJ
iajs-653	6	12	module	module	NOUN
iajs-653	6	13	,	,	PUNCT
iajs-653	6	14	purely	purely	ADV
iajs-653	6	15	co	co	ADJ
iajs-653	6	16	-	-	ADJ
iajs-653	6	17	hopfian	hopfian	ADJ
iajs-653	6	18	module	module	NOUN
iajs-653	6	19	introduction	introduction	NOUN
iajs-653	6	20	and	and	CCONJ
iajs-653	6	21	preliminaries	preliminary	NOUN
iajs-653	6	22	let	let	VERB
iajs-653	6	23	r	r	PRON
iajs-653	6	24	be	be	AUX
iajs-653	6	25	an	an	DET
iajs-653	6	26	associative	associative	ADJ
iajs-653	6	27	ring	ring	NOUN
iajs-653	6	28	with	with	ADP
iajs-653	6	29	identity	identity	NOUN
iajs-653	6	30	and	and	CCONJ
iajs-653	6	31	m	m	PROPN
iajs-653	6	32	a	a	DET
iajs-653	6	33	non	non	X
iajs-653	6	34	–	–	PUNCT
iajs-653	6	35	zero	zero	NUM
iajs-653	6	36	unitary	unitary	ADJ
iajs-653	6	37	r	r	NOUN
iajs-653	6	38	–	–	PUNCT
iajs-653	6	39	module	module	NOUN
iajs-653	6	40	,	,	PUNCT
iajs-653	6	41	recall	recall	VERB
iajs-653	6	42	that	that	SCONJ
iajs-653	6	43	a	a	DET
iajs-653	6	44	module	module	NOUN
iajs-653	6	45	m	m	VERB
iajs-653	6	46	is	be	AUX
iajs-653	6	47	called	call	VERB
iajs-653	6	48	co	co	NOUN
iajs-653	6	49	-	-	NOUN
iajs-653	6	50	hopfian	hopfian	ADJ
iajs-653	6	51	if	if	SCONJ
iajs-653	6	52	any	any	DET
iajs-653	6	53	injective	injective	ADJ
iajs-653	6	54	endomorphism	endomorphism	NOUN
iajs-653	6	55	of	of	ADP
iajs-653	6	56	m	m	PROPN
iajs-653	6	57	is	be	AUX
iajs-653	6	58	an	an	DET
iajs-653	6	59	isomorphism	isomorphism	NOUN
iajs-653	6	60	[	[	X
iajs-653	6	61	1].a	1].a	NUM
iajs-653	6	62	module	module	NOUN
iajs-653	6	63	m	m	VERB
iajs-653	6	64	is	be	AUX
iajs-653	6	65	called	call	VERB
iajs-653	6	66	semi	semi	ADV
iajs-653	6	67	co	co	NOUN
iajs-653	6	68	-	-	NOUN
iajs-653	6	69	hopfian	hopfian	ADJ
iajs-653	6	70	if	if	SCONJ
iajs-653	6	71	any	any	DET
iajs-653	6	72	injective	injective	ADJ
iajs-653	6	73	endomorphism	endomorphism	NOUN
iajs-653	6	74	of	of	ADP
iajs-653	6	75	m	m	PROPN
iajs-653	6	76	has	have	VERB
iajs-653	6	77	a	a	DET
iajs-653	6	78	direct	direct	ADJ
iajs-653	6	79	summand	summand	NOUN
iajs-653	6	80	image	image	NOUN
iajs-653	6	81	that	that	PRON
iajs-653	6	82	means	mean	VERB
iajs-653	6	83	any	any	DET
iajs-653	6	84	injective	injective	ADJ
iajs-653	6	85	endomorphism	endomorphism	NOUN
iajs-653	6	86	of	of	ADP
iajs-653	6	87	m	m	PROPN
iajs-653	6	88	splits	split	VERB
iajs-653	6	89	[	[	X
iajs-653	6	90	1].a	1].a	NUM
iajs-653	6	91	ring	ring	NOUN
iajs-653	6	92	r	r	NOUN
iajs-653	6	93	is	be	AUX
iajs-653	6	94	semi	semi	ADV
iajs-653	6	95	cohopfian	cohopfian	ADJ
iajs-653	6	96	if	if	SCONJ
iajs-653	6	97	r	r	NOUN
iajs-653	6	98	is	be	AUX
iajs-653	6	99	semi	semi	ADV
iajs-653	6	100	co	co	ADJ
iajs-653	6	101	-	-	ADJ
iajs-653	6	102	hopfian	hopfian	ADJ
iajs-653	6	103	r	r	NOUN
iajs-653	6	104	module	module	NOUN
iajs-653	6	105	.	.	PUNCT
iajs-653	7	1	clearly	clearly	ADV
iajs-653	7	2	,	,	PUNCT
iajs-653	7	3	any	any	DET
iajs-653	7	4	co	co	NOUN
iajs-653	7	5	-	-	NOUN
iajs-653	7	6	hopfian	hopfian	ADJ
iajs-653	7	7	is	be	AUX
iajs-653	7	8	semi	semi	ADV
iajs-653	7	9	co	co	ADJ
iajs-653	7	10	-	-	ADJ
iajs-653	7	11	hopfian	hopfian	ADJ
iajs-653	7	12	but	but	CCONJ
iajs-653	7	13	the	the	DET
iajs-653	7	14	converse	converse	NOUN
iajs-653	7	15	is	be	AUX
iajs-653	7	16	not	not	PART
iajs-653	7	17	true	true	ADJ
iajs-653	7	18	in	in	ADP
iajs-653	7	19	general	general	ADJ
iajs-653	7	20	as	as	ADP
iajs-653	7	21	,	,	PUNCT
iajs-653	7	22	for	for	ADP
iajs-653	7	23	example	example	NOUN
iajs-653	7	24	m	m	ADJ
iajs-653	7	25	=	=	SYM
iajs-653	7	26	q	q	PROPN
iajs-653	8	1	n	n	PROPN
iajs-653	8	2	=	=	SYM
iajs-653	8	3	q	q	X
iajs-653	8	4	å	å	PROPN
iajs-653	8	5	q	q	X
iajs-653	8	6	å	å	PROPN
iajs-653	8	7	.	.	PUNCT
iajs-653	8	8	.	.	PUNCT
iajs-653	8	9	.	.	PUNCT
iajs-653	9	1	,	,	PUNCT
iajs-653	9	2	as	as	SCONJ
iajs-653	9	3	z	z	NOUN
iajs-653	9	4	-	-	PUNCT
iajs-653	9	5	module	module	NOUN
iajs-653	9	6	is	be	AUX
iajs-653	9	7	semi	semi	ADV
iajs-653	9	8	co	co	ADJ
iajs-653	9	9	-	-	NOUN
iajs-653	9	10	hopfian	hopfian	ADJ
iajs-653	10	1	but	but	CCONJ
iajs-653	10	2	it	it	PRON
iajs-653	10	3	is	be	AUX
iajs-653	10	4	not	not	PART
iajs-653	10	5	co	co	ADJ
iajs-653	10	6	-	-	NOUN
iajs-653	10	7	hopfian	hopfian	ADJ
iajs-653	10	8	[	[	X
iajs-653	10	9	1	1	NUM
iajs-653	10	10	]	]	PUNCT
iajs-653	10	11	.	.	PUNCT
iajs-653	11	1	a	a	DET
iajs-653	11	2	submodule	submodule	PROPN
iajs-653	11	3	n	n	PROPN
iajs-653	11	4	of	of	ADP
iajs-653	11	5	m	m	PROPN
iajs-653	11	6	is	be	AUX
iajs-653	11	7	called	call	VERB
iajs-653	11	8	pure	pure	ADJ
iajs-653	11	9	if	if	SCONJ
iajs-653	11	10	im∩n	im∩n	PROPN
iajs-653	11	11	=	=	NOUN
iajs-653	11	12	in	in	ADP
iajs-653	11	13	for	for	ADP
iajs-653	11	14	each	each	DET
iajs-653	11	15	ideal	ideal	NOUN
iajs-653	11	16	of	of	ADP
iajs-653	11	17	r,[8].it	r,[8].it	PROPN
iajs-653	11	18	is	be	AUX
iajs-653	11	19	well	well	ADV
iajs-653	11	20	–	–	PUNCT
iajs-653	11	21	known	know	VERB
iajs-653	11	22	every	every	DET
iajs-653	11	23	direct	direct	ADJ
iajs-653	11	24	summand	summand	NOUN
iajs-653	11	25	of	of	ADP
iajs-653	11	26	a	a	DET
iajs-653	11	27	module	module	NOUN
iajs-653	11	28	m	m	NOUN
iajs-653	11	29	is	be	AUX
iajs-653	11	30	pure	pure	ADJ
iajs-653	11	31	submodule	submodule	NOUN
iajs-653	11	32	but	but	CCONJ
iajs-653	11	33	the	the	DET
iajs-653	11	34	converse	converse	NOUN
iajs-653	11	35	is	be	AUX
iajs-653	11	36	not	not	PART
iajs-653	11	37	true	true	ADJ
iajs-653	11	38	in	in	ADP
iajs-653	11	39	general	general	ADJ
iajs-653	11	40	[	[	X
iajs-653	11	41	2].this	2].this	PROPN
iajs-653	11	42	leads	lead	VERB
iajs-653	11	43	us	we	PRON
iajs-653	11	44	to	to	PART
iajs-653	11	45	introduce	introduce	VERB
iajs-653	11	46	the	the	DET
iajs-653	11	47	following	following	ADJ
iajs-653	11	48	concept	concept	NOUN
iajs-653	11	49	,	,	PUNCT
iajs-653	11	50	namely	namely	ADV
iajs-653	11	51	purely	purely	ADV
iajs-653	11	52	co	co	ADJ
iajs-653	11	53	-	-	ADJ
iajs-653	11	54	hopfian	hopfian	ADJ
iajs-653	11	55	module	module	NOUN
iajs-653	11	56	.	.	PUNCT
iajs-653	12	1	definition	definition	NOUN
iajs-653	12	2	1.1	1.1	NUM
iajs-653	12	3	an	an	DET
iajs-653	12	4	rmodule	rmodule	NOUN
iajs-653	12	5	m	m	VERB
iajs-653	12	6	is	be	AUX
iajs-653	12	7	called	call	VERB
iajs-653	12	8	purely	purely	ADV
iajs-653	12	9	co	co	ADJ
iajs-653	12	10	-	-	NOUN
iajs-653	12	11	hopfian	hopfian	ADJ
iajs-653	12	12	if	if	SCONJ
iajs-653	12	13	for	for	ADP
iajs-653	12	14	any	any	DET
iajs-653	12	15	monomorphism	monomorphism	NOUN
iajs-653	12	16	f	f	PROPN
iajs-653	12	17	î	î	PROPN
iajs-653	12	18	end	end	NOUN
iajs-653	12	19	(	(	PUNCT
iajs-653	12	20	m	m	NOUN
iajs-653	12	21	)	)	PUNCT
iajs-653	12	22	,	,	PUNCT
iajs-653	12	23	imf	imf	PROPN
iajs-653	12	24	is	be	AUX
iajs-653	12	25	pure	pure	ADJ
iajs-653	12	26	in	in	ADP
iajs-653	12	27	m.	m.	NOUN
iajs-653	12	28	remarks	remark	NOUN
iajs-653	12	29	and	and	CCONJ
iajs-653	12	30	examples	example	NOUN
iajs-653	12	31	1.2	1.2	NUM
iajs-653	12	32	1	1	NUM
iajs-653	12	33	.	.	PUNCT
iajs-653	13	1	every	every	DET
iajs-653	13	2	semi	semi	ADJ
iajs-653	13	3	co	co	ADJ
iajs-653	13	4	-	-	ADJ
iajs-653	13	5	hopfian	hopfian	ADJ
iajs-653	13	6	module	module	NOUN
iajs-653	13	7	is	be	AUX
iajs-653	13	8	purely	purely	ADV
iajs-653	13	9	co	co	ADJ
iajs-653	13	10	-	-	NOUN
iajs-653	13	11	hopfian	hopfian	ADJ
iajs-653	13	12	.	.	PUNCT
iajs-653	14	1	2	2	X
iajs-653	14	2	.	.	X
iajs-653	14	3	every	every	DET
iajs-653	14	4	fregular	fregular	ADJ
iajs-653	14	5	module	module	NOUN
iajs-653	14	6	m	m	NOUN
iajs-653	14	7	is	be	AUX
iajs-653	14	8	purely	purely	ADV
iajs-653	14	9	co	co	ADJ
iajs-653	14	10	-	-	ADJ
iajs-653	14	11	hopfian	hopfian	ADJ
iajs-653	14	12	,	,	PUNCT
iajs-653	14	13	where	where	SCONJ
iajs-653	14	14	m	m	NOUN
iajs-653	14	15	is	be	AUX
iajs-653	14	16	fregular	fregular	ADJ
iajs-653	14	17	if	if	SCONJ
iajs-653	14	18	every	every	DET
iajs-653	14	19	submodule	submodule	NOUN
iajs-653	14	20	of	of	ADP
iajs-653	14	21	m	m	PROPN
iajs-653	14	22	is	be	AUX
iajs-653	14	23	pure,[3	pure,[3	VERB
iajs-653	14	24	]	]	PUNCT
iajs-653	14	25	.	.	PUNCT
iajs-653	15	1	3	3	X
iajs-653	15	2	.	.	X
iajs-653	15	3	every	every	DET
iajs-653	15	4	semi	semi	ADJ
iajs-653	15	5	simple	simple	ADJ
iajs-653	15	6	r	r	NOUN
iajs-653	15	7	-	-	PUNCT
iajs-653	15	8	module	module	NOUN
iajs-653	15	9	is	be	AUX
iajs-653	15	10	purely	purely	ADV
iajs-653	15	11	co	co	ADJ
iajs-653	15	12	-	-	NOUN
iajs-653	15	13	hopfian	hopfian	ADJ
iajs-653	15	14	.	.	PUNCT
iajs-653	16	1	4	4	X
iajs-653	16	2	.	.	X
iajs-653	16	3	if	if	SCONJ
iajs-653	16	4	m	m	NOUN
iajs-653	16	5	is	be	AUX
iajs-653	16	6	pure	pure	ADJ
iajs-653	16	7	simple	simple	ADJ
iajs-653	16	8	(	(	PUNCT
iajs-653	16	9	that	that	PRON
iajs-653	16	10	means	mean	VERB
iajs-653	16	11	m	m	VERB
iajs-653	16	12	has	have	VERB
iajs-653	16	13	only	only	ADV
iajs-653	16	14	two	two	NUM
iajs-653	16	15	pure	pure	ADJ
iajs-653	16	16	submodules	submodule	NOUN
iajs-653	16	17	0	0	NUM
iajs-653	16	18	,	,	PUNCT
iajs-653	16	19	m	m	NOUN
iajs-653	16	20	)	)	PUNCT
iajs-653	16	21	[	[	PUNCT
iajs-653	16	22	2	2	NUM
iajs-653	16	23	]	]	PUNCT
iajs-653	16	24	,	,	PUNCT
iajs-653	16	25	then	then	ADV
iajs-653	16	26	m	m	NOUN
iajs-653	16	27	is	be	AUX
iajs-653	16	28	purely	purely	ADV
iajs-653	16	29	co	co	ADJ
iajs-653	16	30	-	-	NOUN
iajs-653	16	31	hopfian	hopfian	ADJ
iajs-653	16	32	.	.	PUNCT
iajs-653	17	1	icmma	icmma	PROPN
iajs-653	17	2	1.3	1.3	NUM
iajs-653	17	3	the	the	DET
iajs-653	17	4	following	following	NOUN
iajs-653	17	5	are	be	AUX
iajs-653	17	6	equivalent	equivalent	ADJ
iajs-653	17	7	for	for	ADP
iajs-653	17	8	an	an	DET
iajs-653	17	9	r	r	NOUN
iajs-653	17	10	-	-	PUNCT
iajs-653	17	11	module	module	NOUN
iajs-653	17	12	m	m	NOUN
iajs-653	17	13	:	:	PUNCT
iajs-653	17	14	1	1	X
iajs-653	17	15	.	.	X
iajs-653	17	16	m	m	PROPN
iajs-653	17	17	is	be	AUX
iajs-653	17	18	purely	purely	ADV
iajs-653	17	19	co	co	ADJ
iajs-653	17	20	-	-	NOUN
iajs-653	17	21	hopfian	hopfian	ADJ
iajs-653	17	22	.	.	PUNCT
iajs-653	18	1	2	2	X
iajs-653	18	2	.	.	X
iajs-653	18	3	any	any	DET
iajs-653	18	4	submodule	submodule	NOUN
iajs-653	18	5	n	n	PROPN
iajs-653	18	6	of	of	ADP
iajs-653	18	7	m	m	PRON
iajs-653	18	8	such	such	ADJ
iajs-653	18	9	that	that	SCONJ
iajs-653	18	10	n	n	NOUN
iajs-653	18	11	@	@	ADP
iajs-653	18	12	m	m	PROPN
iajs-653	18	13	,	,	PUNCT
iajs-653	18	14	n	n	PRON
iajs-653	18	15	is	be	AUX
iajs-653	18	16	pure	pure	ADJ
iajs-653	18	17	in	in	ADP
iajs-653	18	18	m.	m.	NOUN
iajs-653	18	19	proof	proof	NOUN
iajs-653	18	20	(	(	PUNCT
iajs-653	18	21	1)→(2	1)→(2	NUM
iajs-653	18	22	)	)	PUNCT
iajs-653	18	23	let	let	VERB
iajs-653	18	24	n	n	PRON
iajs-653	18	25	≤	≤	NOUN
iajs-653	18	26	m	m	PROPN
iajs-653	18	27	,	,	PUNCT
iajs-653	18	28	n	n	CCONJ
iajs-653	18	29	@	@	ADP
iajs-653	18	30	m.	m.	NOUN
iajs-653	18	31	then	then	ADV
iajs-653	18	32	there	there	PRON
iajs-653	18	33	exists	exist	VERB
iajs-653	18	34	α	α	NOUN
iajs-653	18	35	:	:	PUNCT
iajs-653	18	36	m	m	NOUN
iajs-653	18	37	→	→	SYM
iajs-653	18	38	n	n	CCONJ
iajs-653	18	39	,	,	PUNCT
iajs-653	18	40	α	α	PROPN
iajs-653	18	41	is	be	AUX
iajs-653	18	42	an	an	DET
iajs-653	18	43	isomorphism	isomorphism	NOUN
iajs-653	18	44	.	.	PUNCT
iajs-653	19	1	hence	hence	ADV
iajs-653	19	2	m	m	PROPN
iajs-653	19	3	a¾¾	a¾¾	ADJ
iajs-653	19	4	®	®	PROPN
iajs-653	19	5	n	n	PRON
iajs-653	19	6	i¾¾	i¾¾	NOUN
iajs-653	19	7	®	®	NOUN
iajs-653	19	8	m	m	VERB
iajs-653	19	9	where	where	SCONJ
iajs-653	19	10	i	i	PRON
iajs-653	19	11	:	:	PUNCT
iajs-653	19	12	n	n	X
iajs-653	19	13	→	→	PUNCT
iajs-653	19	14	m	m	VERB
iajs-653	19	15	is	be	AUX
iajs-653	19	16	the	the	DET
iajs-653	19	17	inclusion	inclusion	NOUN
iajs-653	19	18	map	map	NOUN
iajs-653	19	19	,	,	PUNCT
iajs-653	19	20	and	and	CCONJ
iajs-653	19	21	this	this	PRON
iajs-653	19	22	implies	imply	VERB
iajs-653	19	23	iоa	iоa	PRON
iajs-653	19	24	î	î	PROPN
iajs-653	19	25	end	end	NOUN
iajs-653	19	26	(	(	PUNCT
iajs-653	19	27	m	m	PROPN
iajs-653	19	28	)	)	PUNCT
iajs-653	19	29	,	,	PUNCT
iajs-653	19	30	i	i	PRON
iajs-653	19	31	оa	оa	VERB
iajs-653	19	32	is	be	AUX
iajs-653	19	33	monomorphism	monomorphism	NOUN
iajs-653	19	34	.	.	PUNCT
iajs-653	20	1	so	so	ADV
iajs-653	20	2	(	(	PUNCT
iajs-653	20	3	i	i	PRON
iajs-653	20	4	о	о	PROPN
iajs-653	20	5	α	α	NOUN
iajs-653	20	6	)	)	PUNCT
iajs-653	20	7	(	(	PUNCT
iajs-653	20	8	m	m	PROPN
iajs-653	20	9	)	)	PUNCT
iajs-653	20	10	is	be	AUX
iajs-653	20	11	pure	pure	ADJ
iajs-653	20	12	in	in	ADP
iajs-653	20	13	m	m	PROPN
iajs-653	20	14	.	.	PUNCT
iajs-653	21	1	thus	thus	ADV
iajs-653	21	2	i	i	PRON
iajs-653	21	3	(	(	PUNCT
iajs-653	21	4	α	α	PROPN
iajs-653	21	5	(	(	PUNCT
iajs-653	21	6	m	m	NOUN
iajs-653	21	7	)	)	PUNCT
iajs-653	21	8	)	)	PUNCT
iajs-653	22	1	=	=	PUNCT
iajs-653	22	2	i	i	PROPN
iajs-653	22	3	(	(	PUNCT
iajs-653	22	4	n	n	CCONJ
iajs-653	22	5	)	)	PUNCT
iajs-653	22	6	=	=	PRON
iajs-653	23	1	n	n	X
iajs-653	23	2	is	be	AUX
iajs-653	23	3	pure	pure	ADJ
iajs-653	23	4	in	in	ADP
iajs-653	23	5	m.	m.	NOUN
iajs-653	23	6	(	(	PUNCT
iajs-653	23	7	2)→(1	2)→(1	NUM
iajs-653	23	8	):	):	PUNCT
iajs-653	23	9	let	let	VERB
iajs-653	23	10	f	f	PROPN
iajs-653	23	11	î	î	PROPN
iajs-653	23	12	end	end	NOUN
iajs-653	23	13	(	(	PUNCT
iajs-653	23	14	m	m	NOUN
iajs-653	23	15	)	)	PUNCT
iajs-653	23	16	,	,	PUNCT
iajs-653	23	17	f	f	PROPN
iajs-653	23	18	is	be	AUX
iajs-653	23	19	monomorphism	monomorphism	NOUN
iajs-653	23	20	.	.	PUNCT
iajs-653	24	1	hence	hence	ADV
iajs-653	24	2	f(m	f(m	PROPN
iajs-653	24	3	)	)	PUNCT
iajs-653	24	4	@	@	ADP
iajs-653	24	5	m	m	PROPN
iajs-653	24	6	and	and	CCONJ
iajs-653	24	7	so	so	ADV
iajs-653	24	8	by	by	ADP
iajs-653	24	9	(	(	PUNCT
iajs-653	24	10	2	2	NUM
iajs-653	24	11	)	)	PUNCT
iajs-653	24	12	,	,	PUNCT
iajs-653	24	13	f	f	PROPN
iajs-653	24	14	(	(	PUNCT
iajs-653	24	15	m	m	PROPN
iajs-653	24	16	)	)	PUNCT
iajs-653	24	17	is	be	AUX
iajs-653	24	18	pure	pure	ADJ
iajs-653	24	19	in	in	ADP
iajs-653	24	20	m.	m.	NOUN
iajs-653	24	21	إبن	إبن	VERB
iajs-653	24	22	الهيثم	الهيثم	ADJ
iajs-653	24	23	للعلوم	للعلوم	NOUN
iajs-653	24	24	الصرفة	الصرفة	NOUN
iajs-653	24	25	و	و	PRON
iajs-653	24	26	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	24	27	2012	2012	NUM
iajs-653	24	28	السنة	السنة	NOUN
iajs-653	25	1	25	25	NUM
iajs-653	25	2	المجلد	المجلد	NOUN
iajs-653	25	3	2	2	NUM
iajs-653	25	4	العدد	العدد	PROPN
iajs-653	25	5	ibn	ibn	PROPN
iajs-653	25	6	al	al	PROPN
iajs-653	25	7	-	-	PUNCT
iajs-653	25	8	haitham	haitham	PROPN
iajs-653	25	9	journal	journal	PROPN
iajs-653	25	10	for	for	ADP
iajs-653	25	11	pure	pure	ADJ
iajs-653	25	12	and	and	CCONJ
iajs-653	25	13	applied	apply	VERB
iajs-653	25	14	science	science	NOUN
iajs-653	25	15	no	no	NOUN
iajs-653	25	16	.	.	NOUN
iajs-653	25	17	2	2	NUM
iajs-653	25	18	vol	vol	NOUN
iajs-653	25	19	.	.	PUNCT
iajs-653	26	1	25	25	NUM
iajs-653	26	2	year	year	NOUN
iajs-653	26	3	2012	2012	NUM
iajs-653	26	4	proposition	proposition	NOUN
iajs-653	26	5	1.4	1.4	NUM
iajs-653	26	6	the	the	DET
iajs-653	26	7	following	following	NOUN
iajs-653	26	8	are	be	AUX
iajs-653	26	9	equivalent	equivalent	ADJ
iajs-653	26	10	for	for	ADP
iajs-653	26	11	a	a	DET
iajs-653	26	12	ring	ring	NOUN
iajs-653	26	13	r	r	NOUN
iajs-653	26	14	1	1	NUM
iajs-653	26	15	.	.	PUNCT
iajs-653	27	1	r	r	NOUN
iajs-653	27	2	is	be	AUX
iajs-653	27	3	purely	purely	ADV
iajs-653	27	4	co	co	ADJ
iajs-653	27	5	-	-	NOUN
iajs-653	27	6	hopfian	hopfian	ADJ
iajs-653	27	7	.	.	PUNCT
iajs-653	28	1	2	2	X
iajs-653	28	2	.	.	X
iajs-653	28	3	r	r	NOUN
iajs-653	28	4	is	be	AUX
iajs-653	28	5	semi	semi	ADV
iajs-653	28	6	co	co	ADJ
iajs-653	28	7	-	-	ADJ
iajs-653	28	8	hopfian	hopfian	ADJ
iajs-653	28	9	.	.	PUNCT
iajs-653	29	1	proof	proof	NOUN
iajs-653	29	2	(	(	PUNCT
iajs-653	29	3	1)→(2	1)→(2	NUM
iajs-653	29	4	)	)	PUNCT
iajs-653	29	5	let	let	VERB
iajs-653	29	6	f	f	X
iajs-653	29	7	:	:	PUNCT
iajs-653	29	8	r	r	NOUN
iajs-653	29	9	→	→	SYM
iajs-653	29	10	r	r	NOUN
iajs-653	29	11	,	,	PUNCT
iajs-653	29	12	f	f	PROPN
iajs-653	29	13	is	be	AUX
iajs-653	29	14	r	r	NOUN
iajs-653	29	15	-	-	PUNCT
iajs-653	29	16	monomorphism	monomorphism	NOUN
iajs-653	29	17	.	.	PUNCT
iajs-653	30	1	hence	hence	ADV
iajs-653	30	2	f	f	PROPN
iajs-653	30	3	(	(	PUNCT
iajs-653	30	4	r	r	NOUN
iajs-653	30	5	)	)	PUNCT
iajs-653	30	6	=	=	NOUN
iajs-653	31	1	<	<	X
iajs-653	31	2	a	a	X
iajs-653	31	3	>	>	X
iajs-653	31	4	for	for	ADP
iajs-653	31	5	some	some	PRON
iajs-653	31	6	a	a	DET
iajs-653	31	7	¹	¹	NUM
iajs-653	31	8	0	0	NUM
iajs-653	31	9	î	î	PROPN
iajs-653	31	10	r.	r.	PROPN
iajs-653	31	11	since	since	SCONJ
iajs-653	31	12	r	r	NOUN
iajs-653	31	13	is	be	AUX
iajs-653	31	14	purely	purely	ADV
iajs-653	31	15	co	co	ADJ
iajs-653	31	16	-	-	NOUN
iajs-653	31	17	hopfian	hopfian	ADJ
iajs-653	31	18	,	,	PUNCT
iajs-653	31	19	<	<	X
iajs-653	31	20	a	a	X
iajs-653	31	21	>	>	X
iajs-653	31	22	is	be	AUX
iajs-653	31	23	pure	pure	ADJ
iajs-653	31	24	ideal	ideal	NOUN
iajs-653	31	25	at	at	ADP
iajs-653	31	26	r	r	NOUN
iajs-653	31	27	,	,	PUNCT
iajs-653	31	28	hence	hence	ADV
iajs-653	31	29	<	<	X
iajs-653	31	30	a	a	X
iajs-653	31	31	>	>	X
iajs-653	31	32	=	=	PUNCT
iajs-653	31	33	<	<	X
iajs-653	31	34	a2	a2	PROPN
iajs-653	31	35	>	>	X
iajs-653	31	36	(	(	PUNCT
iajs-653	31	37	since	since	SCONJ
iajs-653	31	38	<	<	X
iajs-653	31	39	a	a	X
iajs-653	31	40	>	>	X
iajs-653	31	41	i	i	PRON
iajs-653	31	42	<	<	X
iajs-653	31	43	a	a	X
iajs-653	31	44	>	>	X
iajs-653	32	1	=	=	X
iajs-653	32	2	<	<	X
iajs-653	32	3	a	a	X
iajs-653	32	4	>	>	X
iajs-653	32	5	<	<	X
iajs-653	32	6	a	a	X
iajs-653	32	7	>	>	X
iajs-653	32	8	)	)	PUNCT
iajs-653	32	9	.thus	.thus	PRON
iajs-653	32	10	a	a	DET
iajs-653	32	11	=	=	X
iajs-653	32	12	ra2	ra2	PROPN
iajs-653	32	13	for	for	ADP
iajs-653	32	14	some	some	DET
iajs-653	32	15	r	r	NOUN
iajs-653	32	16	î	î	PROPN
iajs-653	32	17	r	r	NOUN
iajs-653	32	18	,	,	PUNCT
iajs-653	32	19	this	this	PRON
iajs-653	32	20	implies	imply	VERB
iajs-653	32	21	ra	ra	PROPN
iajs-653	32	22	is	be	AUX
iajs-653	32	23	idempotent	idempotent	ADJ
iajs-653	32	24	and	and	CCONJ
iajs-653	33	1	<	<	X
iajs-653	33	2	a	a	X
iajs-653	33	3	>	>	X
iajs-653	33	4	=	=	PUNCT
iajs-653	33	5	<	<	X
iajs-653	33	6	ra	ra	X
iajs-653	33	7	>	>	PUNCT
iajs-653	33	8	.	.	PUNCT
iajs-653	34	1	it	it	PRON
iajs-653	34	2	follows	follow	VERB
iajs-653	34	3	that	that	SCONJ
iajs-653	34	4	<	<	X
iajs-653	34	5	a	a	X
iajs-653	34	6	>	>	X
iajs-653	34	7	is	be	AUX
iajs-653	34	8	a	a	DET
iajs-653	34	9	direct	direct	ADJ
iajs-653	34	10	summand	summand	NOUN
iajs-653	34	11	.	.	PUNCT
iajs-653	35	1	the	the	DET
iajs-653	35	2	proof	proof	NOUN
iajs-653	35	3	of	of	ADP
iajs-653	35	4	the	the	DET
iajs-653	35	5	part	part	NOUN
iajs-653	35	6	(	(	PUNCT
iajs-653	35	7	2)→(1	2)→(1	NUM
iajs-653	35	8	)	)	PUNCT
iajs-653	35	9	is	be	AUX
iajs-653	35	10	clear	clear	ADJ
iajs-653	35	11	.	.	PUNCT
iajs-653	36	1	by	by	ADP
iajs-653	36	2	combining	combine	VERB
iajs-653	36	3	proposition	proposition	NOUN
iajs-653	36	4	1.4	1.4	NUM
iajs-653	36	5	and	and	CCONJ
iajs-653	36	6	proposition	proposition	NOUN
iajs-653	36	7	2.3	2.3	NUM
iajs-653	36	8	from	from	ADP
iajs-653	36	9	[	[	X
iajs-653	36	10	1	1	X
iajs-653	36	11	]	]	PUNCT
iajs-653	36	12	we	we	PRON
iajs-653	36	13	get	get	VERB
iajs-653	36	14	the	the	DET
iajs-653	36	15	following	follow	VERB
iajs-653	36	16	result	result	NOUN
iajs-653	36	17	.	.	PUNCT
iajs-653	37	1	corollary	corollary	ADJ
iajs-653	37	2	1.5	1.5	NUM
iajs-653	37	3	the	the	DET
iajs-653	37	4	following	following	NOUN
iajs-653	37	5	are	be	AUX
iajs-653	37	6	equivalent	equivalent	ADJ
iajs-653	37	7	for	for	ADP
iajs-653	37	8	any	any	DET
iajs-653	37	9	a	a	DET
iajs-653	37	10	ring	ring	NOUN
iajs-653	37	11	r	r	NOUN
iajs-653	37	12	:	:	PUNCT
iajs-653	38	1	1	1	X
iajs-653	38	2	.	.	X
iajs-653	38	3	r	r	NOUN
iajs-653	38	4	is	be	AUX
iajs-653	38	5	purely	purely	ADV
iajs-653	38	6	co	co	ADJ
iajs-653	38	7	-	-	NOUN
iajs-653	38	8	hopfian	hopfian	ADJ
iajs-653	38	9	.	.	PUNCT
iajs-653	39	1	2	2	X
iajs-653	39	2	.	.	X
iajs-653	39	3	r	r	NOUN
iajs-653	39	4	is	be	AUX
iajs-653	39	5	semi	semi	ADV
iajs-653	39	6	co	co	ADJ
iajs-653	39	7	-	-	ADJ
iajs-653	39	8	hopfian	hopfian	ADJ
iajs-653	39	9	.	.	PUNCT
iajs-653	40	1	3	3	X
iajs-653	40	2	.	.	X
iajs-653	40	3	ann	ann	PROPN
iajs-653	40	4	(	(	PUNCT
iajs-653	40	5	a	a	X
iajs-653	40	6	)	)	PUNCT
iajs-653	40	7	=	=	SYM
iajs-653	40	8	0	0	NUM
iajs-653	40	9	,	,	PUNCT
iajs-653	40	10	a	a	DET
iajs-653	40	11	î	î	NOUN
iajs-653	40	12	r	r	NOUN
iajs-653	40	13	then	then	ADV
iajs-653	40	14	<	<	X
iajs-653	40	15	a	a	X
iajs-653	40	16	>	>	X
iajs-653	40	17	is	be	AUX
iajs-653	40	18	a	a	DET
iajs-653	40	19	direct	direct	ADJ
iajs-653	40	20	summand	summand	NOUN
iajs-653	40	21	.	.	PUNCT
iajs-653	41	1	4	4	X
iajs-653	41	2	.	.	X
iajs-653	42	1	if	if	SCONJ
iajs-653	42	2	ann	ann	PROPN
iajs-653	42	3	(	(	PUNCT
iajs-653	42	4	a	a	PROPN
iajs-653	42	5	)	)	PUNCT
iajs-653	42	6	=	=	SYM
iajs-653	42	7	0	0	NUM
iajs-653	42	8	,	,	PUNCT
iajs-653	42	9	a	a	DET
iajs-653	42	10	î	î	NOUN
iajs-653	42	11	r	r	NOUN
iajs-653	42	12	then	then	ADV
iajs-653	42	13	<	<	X
iajs-653	42	14	a	a	X
iajs-653	42	15	>	>	X
iajs-653	42	16	=	=	PUNCT
iajs-653	42	17	r	r	NOUN
iajs-653	42	18	.	.	PUNCT
iajs-653	43	1	5	5	X
iajs-653	43	2	.	.	X
iajs-653	44	1	every	every	DET
iajs-653	44	2	r	r	NOUN
iajs-653	44	3	–	–	PUNCT
iajs-653	44	4	isomorphism	isomorphism	NOUN
iajs-653	44	5	<	<	X
iajs-653	44	6	a	a	X
iajs-653	44	7	>	>	X
iajs-653	44	8	→	→	SYM
iajs-653	44	9	r	r	NOUN
iajs-653	44	10	,	,	PUNCT
iajs-653	44	11	a	a	DET
iajs-653	44	12	î	î	PROPN
iajs-653	44	13	r	r	NOUN
iajs-653	44	14	,	,	PUNCT
iajs-653	44	15	extends	extend	VERB
iajs-653	44	16	to	to	ADP
iajs-653	44	17	r.	r.	NOUN
iajs-653	44	18	proof	proof	NOUN
iajs-653	44	19	(	(	PUNCT
iajs-653	44	20	1	1	X
iajs-653	44	21	)	)	PUNCT
iajs-653	44	22	↔	↔	NOUN
iajs-653	44	23	(	(	PUNCT
iajs-653	44	24	2	2	NUM
iajs-653	44	25	):	):	PUNCT
iajs-653	44	26	see	see	VERB
iajs-653	44	27	proposition	proposition	NOUN
iajs-653	44	28	1.4	1.4	NUM
iajs-653	44	29	(	(	PUNCT
iajs-653	44	30	2	2	NUM
iajs-653	44	31	)	)	PUNCT
iajs-653	44	32	↔(3	↔(3	NOUN
iajs-653	44	33	)	)	PUNCT
iajs-653	44	34	↔(4	↔(4	NOUN
iajs-653	44	35	)	)	PUNCT
iajs-653	44	36	↔(5	↔(5	NOUN
iajs-653	44	37	):	):	PUNCT
iajs-653	44	38	(	(	PUNCT
iajs-653	44	39	see	see	VERB
iajs-653	44	40	proposition	proposition	NOUN
iajs-653	44	41	2.3	2.3	NUM
iajs-653	44	42	)	)	PUNCT
iajs-653	44	43	,	,	PUNCT
iajs-653	45	1	[	[	X
iajs-653	45	2	1	1	NUM
iajs-653	45	3	]	]	PUNCT
iajs-653	45	4	.	.	PUNCT
iajs-653	46	1	corollary	corollary	ADJ
iajs-653	46	2	1.6	1.6	NUM
iajs-653	46	3	if	if	SCONJ
iajs-653	46	4	r	r	NOUN
iajs-653	46	5	is	be	AUX
iajs-653	46	6	a	a	DET
iajs-653	46	7	ring	ring	NOUN
iajs-653	46	8	with	with	ADP
iajs-653	46	9	two	two	NUM
iajs-653	46	10	idempotent	idempotent	NOUN
iajs-653	46	11	0,1	0,1	NUM
iajs-653	46	12	then	then	ADV
iajs-653	46	13	the	the	DET
iajs-653	46	14	following	follow	VERB
iajs-653	46	15	statement	statement	NOUN
iajs-653	46	16	are	be	AUX
iajs-653	46	17	equivalent	equivalent	ADJ
iajs-653	46	18	:	:	PUNCT
iajs-653	46	19	1	1	X
iajs-653	46	20	.	.	X
iajs-653	46	21	r	r	NOUN
iajs-653	46	22	is	be	AUX
iajs-653	46	23	co	co	ADJ
iajs-653	46	24	-	-	NOUN
iajs-653	46	25	hopfian	hopfian	ADJ
iajs-653	46	26	.	.	PUNCT
iajs-653	47	1	2	2	X
iajs-653	47	2	.	.	X
iajs-653	47	3	r	r	NOUN
iajs-653	47	4	is	be	AUX
iajs-653	47	5	semi	semi	ADV
iajs-653	47	6	co	co	ADJ
iajs-653	47	7	-	-	ADJ
iajs-653	47	8	hopfian	hopfian	ADJ
iajs-653	47	9	.	.	PUNCT
iajs-653	48	1	3	3	X
iajs-653	48	2	.	.	X
iajs-653	48	3	r	r	NOUN
iajs-653	48	4	is	be	AUX
iajs-653	48	5	purely	purely	ADV
iajs-653	48	6	co	co	ADJ
iajs-653	48	7	-	-	NOUN
iajs-653	48	8	hopfian	hopfian	ADJ
iajs-653	48	9	.	.	PUNCT
iajs-653	49	1	proof	proof	NOUN
iajs-653	49	2	(	(	PUNCT
iajs-653	49	3	1	1	NUM
iajs-653	49	4	)	)	PUNCT
iajs-653	49	5	→	→	X
iajs-653	49	6	(	(	PUNCT
iajs-653	49	7	2	2	NUM
iajs-653	49	8	):	):	PUNCT
iajs-653	49	9	it	it	PRON
iajs-653	49	10	is	be	AUX
iajs-653	49	11	clear	clear	ADJ
iajs-653	49	12	(	(	PUNCT
iajs-653	49	13	2	2	NUM
iajs-653	49	14	)	)	PUNCT
iajs-653	49	15	↔	↔	NOUN
iajs-653	49	16	(	(	PUNCT
iajs-653	49	17	3	3	NUM
iajs-653	49	18	)	)	PUNCT
iajs-653	49	19	:	:	PUNCT
iajs-653	49	20	by	by	ADP
iajs-653	49	21	proposition	proposition	NOUN
iajs-653	49	22	1.4	1.4	NUM
iajs-653	49	23	(	(	PUNCT
iajs-653	49	24	3)→(2	3)→(2	NUM
iajs-653	49	25	):	):	PUNCT
iajs-653	49	26	let	let	VERB
iajs-653	49	27	f	f	NOUN
iajs-653	49	28	:	:	PUNCT
iajs-653	49	29	r	r	NOUN
iajs-653	49	30	→	→	SYM
iajs-653	49	31	r	r	NOUN
iajs-653	49	32	,	,	PUNCT
iajs-653	49	33	f	f	PROPN
iajs-653	49	34	is	be	AUX
iajs-653	49	35	monomorphism	monomorphism	NOUN
iajs-653	50	1	then	then	ADV
iajs-653	50	2	f	f	PROPN
iajs-653	50	3	(	(	PUNCT
iajs-653	50	4	r	r	NOUN
iajs-653	50	5	)	)	PUNCT
iajs-653	51	1	=	=	PUNCT
iajs-653	51	2	<	<	X
iajs-653	51	3	a	a	X
iajs-653	51	4	>	>	X
iajs-653	51	5	for	for	ADP
iajs-653	51	6	some	some	PRON
iajs-653	51	7	a	a	DET
iajs-653	51	8	î	î	PROPN
iajs-653	51	9	r	r	NOUN
iajs-653	51	10	,	,	PUNCT
iajs-653	51	11	a	a	DET
iajs-653	51	12	¹	¹	PROPN
iajs-653	51	13	0	0	NUM
iajs-653	51	14	,	,	PUNCT
iajs-653	51	15	but	but	CCONJ
iajs-653	51	16	i	i	PRON
iajs-653	52	1	=	=	X
iajs-653	52	2	<	<	X
iajs-653	52	3	a	a	X
iajs-653	52	4	>	>	X
iajs-653	52	5	is	be	AUX
iajs-653	52	6	a	a	DET
iajs-653	52	7	direct	direct	ADJ
iajs-653	52	8	summand	summand	NOUN
iajs-653	52	9	of	of	ADP
iajs-653	52	10	r	r	NOUN
iajs-653	52	11	(	(	PUNCT
iajs-653	52	12	since	since	SCONJ
iajs-653	52	13	r	r	NOUN
iajs-653	52	14	is	be	AUX
iajs-653	52	15	semi	semi	ADV
iajs-653	52	16	co	co	ADJ
iajs-653	52	17	-	-	ADJ
iajs-653	52	18	hopfian	hopfian	ADJ
iajs-653	52	19	)	)	PUNCT
iajs-653	52	20	then	then	ADV
iajs-653	52	21	<	<	X
iajs-653	52	22	a	a	X
iajs-653	52	23	>	>	X
iajs-653	52	24	is	be	AUX
iajs-653	52	25	generated	generate	VERB
iajs-653	52	26	by	by	ADP
iajs-653	52	27	idempotent	idempotent	NOUN
iajs-653	52	28	.	.	PUNCT
iajs-653	53	1	since	since	SCONJ
iajs-653	53	2	a	a	DET
iajs-653	53	3	¹	¹	PROPN
iajs-653	53	4	0	0	NUM
iajs-653	53	5	,	,	PUNCT
iajs-653	53	6	hence	hence	ADV
iajs-653	53	7	a	a	DET
iajs-653	53	8	=	=	SYM
iajs-653	53	9	1	1	NUM
iajs-653	53	10	and	and	CCONJ
iajs-653	53	11	<	<	X
iajs-653	53	12	a	a	DET
iajs-653	53	13	>	>	X
iajs-653	53	14	=	=	NOUN
iajs-653	54	1	r.thus	r.thu	NOUN
iajs-653	54	2	f	f	PROPN
iajs-653	54	3	is	be	AUX
iajs-653	54	4	onto	onto	ADP
iajs-653	55	1	and	and	CCONJ
iajs-653	55	2	we	we	PRON
iajs-653	55	3	get	get	VERB
iajs-653	55	4	r	r	NOUN
iajs-653	55	5	is	be	AUX
iajs-653	55	6	cohopfian	cohopfian	ADJ
iajs-653	55	7	.	.	PUNCT
iajs-653	56	1	recall	recall	VERB
iajs-653	56	2	that	that	DET
iajs-653	56	3	module	module	NOUN
iajs-653	56	4	m	m	VERB
iajs-653	56	5	has	have	VERB
iajs-653	56	6	c2	c2	PROPN
iajs-653	56	7	if	if	SCONJ
iajs-653	56	8	for	for	ADP
iajs-653	56	9	any	any	DET
iajs-653	56	10	submodule	submodule	NOUN
iajs-653	56	11	n	n	PROPN
iajs-653	56	12	of	of	ADP
iajs-653	56	13	m	m	PRON
iajs-653	56	14	which	which	PRON
iajs-653	56	15	is	be	AUX
iajs-653	56	16	isomorphic	isomorphic	ADJ
iajs-653	56	17	to	to	ADP
iajs-653	56	18	a	a	DET
iajs-653	56	19	direct	direct	ADJ
iajs-653	56	20	summand	summand	NOUN
iajs-653	56	21	of	of	ADP
iajs-653	56	22	m	m	PROPN
iajs-653	56	23	,	,	PUNCT
iajs-653	56	24	is	be	AUX
iajs-653	56	25	a	a	DET
iajs-653	56	26	direct	direct	ADJ
iajs-653	56	27	summand	summand	NOUN
iajs-653	56	28	of	of	ADP
iajs-653	56	29	m	m	PROPN
iajs-653	56	30	[	[	X
iajs-653	56	31	4	4	NUM
iajs-653	56	32	]	]	PUNCT
iajs-653	56	33	.	.	PUNCT
iajs-653	57	1	corollary	corollary	ADJ
iajs-653	57	2	1.7	1.7	NUM
iajs-653	57	3	if	if	SCONJ
iajs-653	57	4	r	r	NOUN
iajs-653	57	5	is	be	AUX
iajs-653	57	6	a	a	DET
iajs-653	57	7	ring	ring	NOUN
iajs-653	57	8	only	only	ADV
iajs-653	57	9	idempotent	idempotent	ADJ
iajs-653	57	10	0	0	PUNCT
iajs-653	57	11	and	and	CCONJ
iajs-653	57	12	1	1	NUM
iajs-653	57	13	the	the	DET
iajs-653	57	14	following	follow	VERB
iajs-653	57	15	equivalent	equivalent	NOUN
iajs-653	57	16	:	:	PUNCT
iajs-653	57	17	1	1	X
iajs-653	57	18	.	.	X
iajs-653	57	19	r	r	NOUN
iajs-653	57	20	has	have	VERB
iajs-653	57	21	c2	c2	PROPN
iajs-653	57	22	.	.	PUNCT
iajs-653	58	1	2	2	X
iajs-653	58	2	.	.	X
iajs-653	58	3	r	r	NOUN
iajs-653	58	4	is	be	AUX
iajs-653	58	5	co	co	ADJ
iajs-653	58	6	-	-	NOUN
iajs-653	58	7	hopfian	hopfian	ADJ
iajs-653	58	8	.	.	PUNCT
iajs-653	59	1	3	3	X
iajs-653	59	2	.	.	X
iajs-653	59	3	r	r	NOUN
iajs-653	59	4	is	be	AUX
iajs-653	59	5	purely	purely	ADV
iajs-653	59	6	co	co	ADJ
iajs-653	59	7	-	-	NOUN
iajs-653	59	8	hopfian	hopfian	ADJ
iajs-653	59	9	.	.	PUNCT
iajs-653	60	1	4	4	X
iajs-653	60	2	.	.	X
iajs-653	60	3	r	r	NOUN
iajs-653	60	4	is	be	AUX
iajs-653	60	5	semi	semi	ADV
iajs-653	60	6	co	co	ADJ
iajs-653	60	7	-	-	ADJ
iajs-653	60	8	hopfian	hopfian	ADJ
iajs-653	60	9	.	.	PUNCT
iajs-653	61	1	proof	proof	NOUN
iajs-653	61	2	(	(	PUNCT
iajs-653	61	3	1	1	NUM
iajs-653	61	4	)	)	PUNCT
iajs-653	61	5	→	→	X
iajs-653	61	6	(	(	PUNCT
iajs-653	61	7	2	2	X
iajs-653	61	8	)	)	PUNCT
iajs-653	61	9	let	let	VERB
iajs-653	61	10	f	f	X
iajs-653	61	11	:	:	PUNCT
iajs-653	61	12	r	r	NOUN
iajs-653	61	13	→	→	SYM
iajs-653	61	14	r	r	NOUN
iajs-653	61	15	be	be	VERB
iajs-653	61	16	monomorphism	monomorphism	NOUN
iajs-653	61	17	.	.	PUNCT
iajs-653	62	1	to	to	PART
iajs-653	62	2	prove	prove	VERB
iajs-653	62	3	that	that	SCONJ
iajs-653	62	4	r	r	NOUN
iajs-653	62	5	is	be	AUX
iajs-653	62	6	co	co	ADJ
iajs-653	62	7	-	-	NOUN
iajs-653	62	8	hopfian	hopfian	ADJ
iajs-653	62	9	,	,	PUNCT
iajs-653	62	10	we	we	PRON
iajs-653	62	11	must	must	AUX
iajs-653	62	12	prove	prove	VERB
iajs-653	62	13	f	f	PROPN
iajs-653	62	14	is	be	AUX
iajs-653	62	15	an	an	DET
iajs-653	62	16	isomorphism.since	isomorphism.since	NOUN
iajs-653	62	17	f	f	NOUN
iajs-653	62	18	is	be	AUX
iajs-653	62	19	monomorphism	monomorphism	NOUN
iajs-653	62	20	,	,	PUNCT
iajs-653	62	21	f	f	PROPN
iajs-653	62	22	(	(	PUNCT
iajs-653	62	23	r	r	NOUN
iajs-653	62	24	)	)	PUNCT
iajs-653	62	25	@	@	ADP
iajs-653	62	26	r	r	NOUN
iajs-653	62	27	.	.	PUNCT
iajs-653	63	1	but	but	CCONJ
iajs-653	63	2	r	r	NOUN
iajs-653	63	3	is	be	AUX
iajs-653	63	4	c2	c2	PROPN
iajs-653	63	5	by	by	ADP
iajs-653	63	6	(	(	PUNCT
iajs-653	63	7	1	1	NUM
iajs-653	63	8	)	)	PUNCT
iajs-653	63	9	and	and	CCONJ
iajs-653	63	10	r	r	NOUN
iajs-653	63	11	is	be	AUX
iajs-653	63	12	direct	direct	ADJ
iajs-653	63	13	إبن	إبن	NOUN
iajs-653	63	14	الهيثم	الهيثم	ADJ
iajs-653	63	15	للعلوم	للعلوم	NOUN
iajs-653	63	16	الصرفة	الصرفة	NOUN
iajs-653	63	17	و	و	PRON
iajs-653	63	18	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	63	19	2012	2012	NUM
iajs-653	63	20	السنة	السنة	NOUN
iajs-653	64	1	25	25	NUM
iajs-653	64	2	المجلد	المجلد	NOUN
iajs-653	64	3	2	2	NUM
iajs-653	64	4	العدد	العدد	PROPN
iajs-653	64	5	ibn	ibn	PROPN
iajs-653	64	6	al	al	PROPN
iajs-653	64	7	-	-	PUNCT
iajs-653	64	8	haitham	haitham	PROPN
iajs-653	64	9	journal	journal	PROPN
iajs-653	64	10	for	for	ADP
iajs-653	64	11	pure	pure	ADJ
iajs-653	64	12	and	and	CCONJ
iajs-653	64	13	applied	apply	VERB
iajs-653	64	14	science	science	NOUN
iajs-653	64	15	no	no	NOUN
iajs-653	64	16	.	.	NOUN
iajs-653	64	17	2	2	NUM
iajs-653	64	18	vol	vol	NOUN
iajs-653	64	19	.	.	PUNCT
iajs-653	65	1	25	25	NUM
iajs-653	65	2	year	year	NOUN
iajs-653	65	3	2012	2012	NUM
iajs-653	65	4	summand	summand	NOUN
iajs-653	65	5	of	of	ADP
iajs-653	65	6	r	r	NOUN
iajs-653	65	7	,	,	PUNCT
iajs-653	65	8	hence	hence	ADV
iajs-653	65	9	f(r	f(r	NOUN
iajs-653	65	10	)	)	PUNCT
iajs-653	65	11	is	be	AUX
iajs-653	65	12	direct	direct	ADJ
iajs-653	65	13	summand	summand	NOUN
iajs-653	65	14	of	of	ADP
iajs-653	65	15	r.it	r.it	PROPN
iajs-653	65	16	follows	follow	VERB
iajs-653	65	17	that	that	SCONJ
iajs-653	65	18	f	f	PROPN
iajs-653	65	19	(	(	PUNCT
iajs-653	65	20	r	r	NOUN
iajs-653	65	21	)	)	PUNCT
iajs-653	65	22	is	be	AUX
iajs-653	65	23	generated	generate	VERB
iajs-653	65	24	by	by	ADP
iajs-653	65	25	idempotent.since	idempotent.since	NOUN
iajs-653	65	26	r	r	NOUN
iajs-653	65	27	has	have	VERB
iajs-653	65	28	only	only	ADV
iajs-653	65	29	2	2	NUM
iajs-653	65	30	–	–	PUNCT
iajs-653	65	31	idempotent	idempotent	ADJ
iajs-653	65	32	namely	namely	ADV
iajs-653	65	33	0	0	NUM
iajs-653	65	34	,	,	PUNCT
iajs-653	65	35	1	1	NUM
iajs-653	65	36	and	and	CCONJ
iajs-653	65	37	f	f	PROPN
iajs-653	65	38	(	(	PUNCT
iajs-653	65	39	r	r	NOUN
iajs-653	65	40	)	)	PUNCT
iajs-653	65	41	¹	¹	X
iajs-653	65	42	0	0	NUM
iajs-653	65	43	,	,	PUNCT
iajs-653	65	44	then	then	ADV
iajs-653	65	45	f	f	PROPN
iajs-653	65	46	(	(	PUNCT
iajs-653	65	47	r	r	NOUN
iajs-653	65	48	)	)	PUNCT
iajs-653	66	1	=	=	PUNCT
iajs-653	66	2	<	<	X
iajs-653	66	3	1	1	NUM
iajs-653	66	4	>	>	X
iajs-653	66	5	thus	thus	ADV
iajs-653	66	6	f	f	X
iajs-653	66	7	(	(	PUNCT
iajs-653	66	8	r	r	NOUN
iajs-653	66	9	)	)	PUNCT
iajs-653	66	10	=	=	SYM
iajs-653	66	11	r	r	NOUN
iajs-653	66	12	and	and	CCONJ
iajs-653	66	13	so	so	SCONJ
iajs-653	66	14	that	that	SCONJ
iajs-653	66	15	f	f	PROPN
iajs-653	66	16	is	be	AUX
iajs-653	66	17	an	an	DET
iajs-653	66	18	isomorphism	isomorphism	NOUN
iajs-653	66	19	.	.	PUNCT
iajs-653	67	1	(	(	PUNCT
iajs-653	67	2	2	2	X
iajs-653	67	3	)	)	PUNCT
iajs-653	67	4	→	→	X
iajs-653	67	5	(	(	PUNCT
iajs-653	67	6	3	3	NUM
iajs-653	67	7	:	:	PUNCT
iajs-653	67	8	it	it	PRON
iajs-653	67	9	is	be	AUX
iajs-653	67	10	clear	clear	ADJ
iajs-653	67	11	.	.	PUNCT
iajs-653	68	1	(	(	PUNCT
iajs-653	68	2	3	3	NUM
iajs-653	68	3	)	)	PUNCT
iajs-653	68	4	→	→	X
iajs-653	68	5	(	(	PUNCT
iajs-653	68	6	4):it	4):it	NUM
iajs-653	68	7	follows	follow	VERB
iajs-653	68	8	by	by	ADP
iajs-653	68	9	proposition	proposition	NOUN
iajs-653	68	10	(	(	PUNCT
iajs-653	68	11	1.4	1.4	NUM
iajs-653	68	12	)	)	PUNCT
iajs-653	68	13	.	.	PUNCT
iajs-653	69	1	(	(	PUNCT
iajs-653	69	2	4	4	NUM
iajs-653	69	3	)	)	PUNCT
iajs-653	69	4	→	→	X
iajs-653	69	5	(	(	PUNCT
iajs-653	69	6	1	1	NUM
iajs-653	69	7	):	):	PUNCT
iajs-653	69	8	it	it	PRON
iajs-653	69	9	follows	follow	VERB
iajs-653	69	10	by	by	ADP
iajs-653	69	11	proposition	proposition	NOUN
iajs-653	69	12	2.4	2.4	NUM
iajs-653	70	1	[	[	SYM
iajs-653	70	2	1	1	NUM
iajs-653	70	3	]	]	PUNCT
iajs-653	70	4	.	.	PUNCT
iajs-653	71	1	corollary	corollary	ADJ
iajs-653	71	2	1.8	1.8	NUM
iajs-653	71	3	let	let	VERB
iajs-653	71	4	r	r	NOUN
iajs-653	71	5	be	be	AUX
iajs-653	71	6	an	an	DET
iajs-653	71	7	integral	integral	ADJ
iajs-653	71	8	domain	domain	NOUN
iajs-653	71	9	.	.	PUNCT
iajs-653	72	1	then	then	ADV
iajs-653	72	2	the	the	DET
iajs-653	72	3	following	follow	VERB
iajs-653	72	4	are	be	AUX
iajs-653	72	5	equivalent	equivalent	ADJ
iajs-653	72	6	:	:	PUNCT
iajs-653	72	7	1	1	X
iajs-653	72	8	.	.	X
iajs-653	72	9	r	r	NOUN
iajs-653	72	10	is	be	AUX
iajs-653	72	11	co	co	ADJ
iajs-653	72	12	-	-	NOUN
iajs-653	72	13	hopfian	hopfian	ADJ
iajs-653	72	14	.	.	PUNCT
iajs-653	73	1	2	2	X
iajs-653	73	2	.	.	X
iajs-653	73	3	r	r	NOUN
iajs-653	73	4	is	be	AUX
iajs-653	73	5	semi	semi	ADV
iajs-653	73	6	co	co	ADJ
iajs-653	73	7	-	-	ADJ
iajs-653	73	8	hopfian	hopfian	ADJ
iajs-653	73	9	.	.	PUNCT
iajs-653	74	1	3	3	X
iajs-653	74	2	.	.	X
iajs-653	74	3	r	r	NOUN
iajs-653	74	4	is	be	AUX
iajs-653	74	5	purely	purely	ADV
iajs-653	74	6	co	co	ADJ
iajs-653	74	7	-	-	NOUN
iajs-653	74	8	hopfian	hopfian	ADJ
iajs-653	74	9	.	.	PUNCT
iajs-653	75	1	4	4	X
iajs-653	75	2	.	.	X
iajs-653	75	3	r	r	NOUN
iajs-653	75	4	is	be	AUX
iajs-653	75	5	field	field	NOUN
iajs-653	75	6	.	.	PUNCT
iajs-653	76	1	proof	proof	NOUN
iajs-653	76	2	(	(	PUNCT
iajs-653	76	3	1	1	X
iajs-653	76	4	)	)	PUNCT
iajs-653	76	5	↔	↔	NOUN
iajs-653	76	6	(	(	PUNCT
iajs-653	76	7	2	2	NUM
iajs-653	76	8	)	)	PUNCT
iajs-653	76	9	↔	↔	NOUN
iajs-653	76	10	(	(	PUNCT
iajs-653	76	11	3	3	NUM
iajs-653	76	12	)	)	PUNCT
iajs-653	76	13	:	:	PUNCT
iajs-653	76	14	it	it	PRON
iajs-653	76	15	follows	follow	VERB
iajs-653	76	16	by	by	ADP
iajs-653	76	17	corollary	corollary	ADJ
iajs-653	76	18	1.6	1.6	NUM
iajs-653	76	19	(	(	PUNCT
iajs-653	76	20	1	1	NUM
iajs-653	76	21	)	)	PUNCT
iajs-653	76	22	→	→	X
iajs-653	76	23	(	(	PUNCT
iajs-653	76	24	4	4	NUM
iajs-653	76	25	)	)	PUNCT
iajs-653	76	26	:	:	PUNCT
iajs-653	76	27	let	let	VERB
iajs-653	76	28	a	a	DET
iajs-653	76	29	î	î	PROPN
iajs-653	76	30	r	r	NOUN
iajs-653	76	31	,	,	PUNCT
iajs-653	76	32	a	a	DET
iajs-653	76	33	¹	¹	PROPN
iajs-653	76	34	0	0	NUM
iajs-653	76	35	then	then	ADV
iajs-653	76	36	ann	ann	PROPN
iajs-653	76	37	(	(	PUNCT
iajs-653	76	38	a	a	X
iajs-653	76	39	)	)	PUNCT
iajs-653	77	1	=	=	SYM
iajs-653	77	2	0	0	PUNCT
iajs-653	78	1	since	since	SCONJ
iajs-653	78	2	r	r	NOUN
iajs-653	78	3	is	be	AUX
iajs-653	78	4	an	an	DET
iajs-653	78	5	integral	integral	ADJ
iajs-653	78	6	domain	domain	NOUN
iajs-653	78	7	.	.	PUNCT
iajs-653	79	1	by	by	ADP
iajs-653	79	2	corollary	corollary	ADJ
iajs-653	79	3	1.5	1.5	NUM
iajs-653	79	4	,	,	PUNCT
iajs-653	79	5	<	<	X
iajs-653	79	6	a	a	PRON
iajs-653	79	7	>	>	X
iajs-653	79	8	=	=	PUNCT
iajs-653	79	9	r.	r.	PROPN
iajs-653	79	10	hence	hence	ADV
iajs-653	79	11	a	a	PRON
iajs-653	79	12	is	be	AUX
iajs-653	79	13	an	an	DET
iajs-653	79	14	invertible	invertible	ADJ
iajs-653	79	15	element.then	element.then	NOUN
iajs-653	79	16	r	r	NOUN
iajs-653	79	17	is	be	AUX
iajs-653	79	18	a	a	DET
iajs-653	79	19	field	field	NOUN
iajs-653	79	20	.	.	PUNCT
iajs-653	80	1	(	(	PUNCT
iajs-653	80	2	4	4	NUM
iajs-653	80	3	)	)	PUNCT
iajs-653	80	4	→	→	X
iajs-653	80	5	(	(	PUNCT
iajs-653	80	6	1	1	NUM
iajs-653	80	7	)	)	PUNCT
iajs-653	80	8	:	:	PUNCT
iajs-653	80	9	since	since	SCONJ
iajs-653	80	10	r	r	NOUN
iajs-653	80	11	is	be	AUX
iajs-653	80	12	a	a	DET
iajs-653	80	13	field	field	NOUN
iajs-653	80	14	,	,	PUNCT
iajs-653	80	15	r	r	NOUN
iajs-653	80	16	has	have	VERB
iajs-653	80	17	only	only	ADV
iajs-653	80	18	two	two	NUM
iajs-653	80	19	ideals	ideal	NOUN
iajs-653	80	20	namely	namely	ADV
iajs-653	80	21	r	r	NOUN
iajs-653	80	22	,	,	PUNCT
iajs-653	80	23	(	(	PUNCT
iajs-653	80	24	0	0	NUM
iajs-653	80	25	)	)	PUNCT
iajs-653	80	26	.	.	PUNCT
iajs-653	81	1	hence	hence	ADV
iajs-653	81	2	for	for	ADP
iajs-653	81	3	any	any	PRON
iajs-653	81	4	f	f	NOUN
iajs-653	81	5	:	:	PUNCT
iajs-653	81	6	r	r	NOUN
iajs-653	81	7	→	→	SYM
iajs-653	81	8	r	r	NOUN
iajs-653	81	9	,	,	PUNCT
iajs-653	81	10	f	f	PROPN
iajs-653	81	11	is	be	AUX
iajs-653	81	12	r	r	NOUN
iajs-653	81	13	–	–	PUNCT
iajs-653	81	14	monomorphism	monomorphism	NOUN
iajs-653	81	15	f	f	X
iajs-653	81	16	(	(	PUNCT
iajs-653	81	17	r	r	NOUN
iajs-653	81	18	)	)	PUNCT
iajs-653	81	19	¹	¹	NUM
iajs-653	81	20	0	0	NUM
iajs-653	81	21	.	.	PUNCT
iajs-653	82	1	hence	hence	ADV
iajs-653	82	2	f	f	PROPN
iajs-653	82	3	(	(	PUNCT
iajs-653	82	4	r	r	NOUN
iajs-653	82	5	)	)	PUNCT
iajs-653	82	6	=	=	NOUN
iajs-653	83	1	r.thus	r.thu	NOUN
iajs-653	83	2	f	f	PROPN
iajs-653	83	3	is	be	AUX
iajs-653	83	4	onto	onto	ADP
iajs-653	83	5	then	then	ADV
iajs-653	83	6	r	r	NOUN
iajs-653	83	7	is	be	AUX
iajs-653	83	8	co	co	ADJ
iajs-653	83	9	-	-	ADJ
iajs-653	83	10	hopfian	hopfian	ADJ
iajs-653	83	11	.	.	PUNCT
iajs-653	84	1	proposition	proposition	NOUN
iajs-653	84	2	1.9	1.9	NUM
iajs-653	84	3	any	any	DET
iajs-653	84	4	direct	direct	ADJ
iajs-653	84	5	summand	summand	NOUN
iajs-653	84	6	of	of	ADP
iajs-653	84	7	purely	purely	ADV
iajs-653	84	8	co	co	ADJ
iajs-653	84	9	-	-	ADJ
iajs-653	84	10	hopfian	hopfian	ADJ
iajs-653	84	11	module	module	NOUN
iajs-653	84	12	is	be	AUX
iajs-653	84	13	purely	purely	ADV
iajs-653	84	14	co	co	ADJ
iajs-653	84	15	-	-	NOUN
iajs-653	84	16	hopfian	hopfian	ADJ
iajs-653	84	17	.	.	PUNCT
iajs-653	85	1	proof	proof	NOUN
iajs-653	85	2	let	let	VERB
iajs-653	85	3	n	n	PRON
iajs-653	85	4	be	be	AUX
iajs-653	85	5	a	a	DET
iajs-653	85	6	direct	direct	ADJ
iajs-653	85	7	summand	summand	NOUN
iajs-653	85	8	of	of	ADP
iajs-653	85	9	m	m	PROPN
iajs-653	85	10	,	,	PUNCT
iajs-653	85	11	so	so	ADV
iajs-653	85	12	m	m	NOUN
iajs-653	85	13	=	=	SYM
iajs-653	85	14	n	n	CCONJ
iajs-653	85	15	å	å	PROPN
iajs-653	85	16	a	a	NOUN
iajs-653	85	17	for	for	ADP
iajs-653	85	18	some	some	DET
iajs-653	85	19	submodule	submodule	NOUN
iajs-653	85	20	a	a	PRON
iajs-653	85	21	of	of	ADP
iajs-653	85	22	m	m	PROPN
iajs-653	85	23	.let	.let	PUNCT
iajs-653	86	1	f	f	X
iajs-653	86	2	:	:	PUNCT
iajs-653	86	3	n	n	X
iajs-653	86	4	→	→	SYM
iajs-653	86	5	n	n	CCONJ
iajs-653	86	6	be	be	AUX
iajs-653	86	7	monomorphism	monomorphism	NOUN
iajs-653	86	8	.	.	PUNCT
iajs-653	87	1	define	define	VERB
iajs-653	87	2	g	g	NOUN
iajs-653	87	3	:	:	PUNCT
iajs-653	87	4	m	m	VERB
iajs-653	87	5	→m	→m	PUNCT
iajs-653	87	6	by	by	ADP
iajs-653	87	7	g(n+a	g(n+a	PROPN
iajs-653	87	8	)	)	PUNCT
iajs-653	88	1	=	=	SYM
iajs-653	88	2	f	f	X
iajs-653	88	3	(	(	PUNCT
iajs-653	88	4	n	n	NOUN
iajs-653	88	5	)	)	PUNCT
iajs-653	88	6	+	+	NOUN
iajs-653	88	7	a	a	PRON
iajs-653	88	8	where	where	SCONJ
iajs-653	88	9	n	n	VERB
iajs-653	88	10	î	î	PROPN
iajs-653	88	11	n	n	PROPN
iajs-653	88	12	,	,	PUNCT
iajs-653	88	13	a	a	DET
iajs-653	88	14	îa	îa	NOUN
iajs-653	88	15	it	it	PRON
iajs-653	88	16	is	be	AUX
iajs-653	88	17	easy	easy	ADJ
iajs-653	88	18	to	to	PART
iajs-653	88	19	see	see	VERB
iajs-653	88	20	that	that	SCONJ
iajs-653	88	21	g	g	PROPN
iajs-653	88	22	is	be	AUX
iajs-653	88	23	monomorphism	monomorphism	NOUN
iajs-653	88	24	hence	hence	ADV
iajs-653	88	25	g	g	PROPN
iajs-653	88	26	(	(	PUNCT
iajs-653	88	27	m	m	PROPN
iajs-653	88	28	)	)	PUNCT
iajs-653	89	1	=	=	SYM
iajs-653	89	2	f	f	X
iajs-653	89	3	(	(	PUNCT
iajs-653	89	4	a	a	NOUN
iajs-653	89	5	)	)	PUNCT
iajs-653	89	6	å	å	PROPN
iajs-653	89	7	n	n	NOUN
iajs-653	89	8	.	.	PUNCT
iajs-653	90	1	since	since	SCONJ
iajs-653	90	2	m	m	PROPN
iajs-653	90	3	is	be	AUX
iajs-653	90	4	purely	purely	ADV
iajs-653	90	5	co	co	ADJ
iajs-653	90	6	-	-	ADJ
iajs-653	90	7	hopfian	hopfian	ADJ
iajs-653	90	8	,	,	PUNCT
iajs-653	90	9	g	g	PROPN
iajs-653	90	10	(	(	PUNCT
iajs-653	90	11	m	m	NOUN
iajs-653	90	12	)	)	PUNCT
iajs-653	90	13	is	be	AUX
iajs-653	90	14	pure	pure	ADJ
iajs-653	90	15	in	in	ADP
iajs-653	90	16	m.to	m.to	PROPN
iajs-653	90	17	prove	prove	VERB
iajs-653	90	18	f	f	PROPN
iajs-653	90	19	(	(	PUNCT
iajs-653	90	20	n	n	CCONJ
iajs-653	90	21	)	)	PUNCT
iajs-653	90	22	pure	pure	ADJ
iajs-653	90	23	in	in	ADP
iajs-653	90	24	n	n	CCONJ
iajs-653	90	25	,	,	PUNCT
iajs-653	90	26	let	let	VERB
iajs-653	90	27	i	i	PRON
iajs-653	90	28	be	be	AUX
iajs-653	90	29	any	any	DET
iajs-653	90	30	ideal	ideal	NOUN
iajs-653	90	31	of	of	ADP
iajs-653	90	32	r	r	NOUN
iajs-653	90	33	,	,	PUNCT
iajs-653	90	34	i	i	PRON
iajs-653	90	35	m	m	VERB
iajs-653	90	36	∩	∩	ADJ
iajs-653	90	37	g	g	PROPN
iajs-653	90	38	(	(	PUNCT
iajs-653	90	39	m	m	PROPN
iajs-653	90	40	)	)	PUNCT
iajs-653	91	1	=	=	SYM
iajs-653	92	1	i	i	PRON
iajs-653	92	2	g	g	PROPN
iajs-653	92	3	(	(	PUNCT
iajs-653	92	4	m	m	PROPN
iajs-653	92	5	)	)	PUNCT
iajs-653	92	6	,	,	PUNCT
iajs-653	92	7	i	i	PRON
iajs-653	92	8	(	(	PUNCT
iajs-653	92	9	n	n	CCONJ
iajs-653	92	10	å	å	PROPN
iajs-653	92	11	a	a	PRON
iajs-653	92	12	)	)	PUNCT
iajs-653	92	13	∩	∩	NOUN
iajs-653	92	14	(	(	PUNCT
iajs-653	92	15	f	f	X
iajs-653	92	16	(	(	PUNCT
iajs-653	92	17	n	n	CCONJ
iajs-653	92	18	)	)	PUNCT
iajs-653	92	19	å	å	PROPN
iajs-653	92	20	a	a	NOUN
iajs-653	92	21	)	)	PUNCT
iajs-653	93	1	=	=	SYM
iajs-653	93	2	i	i	PRON
iajs-653	93	3	(	(	PUNCT
iajs-653	93	4	f	f	PROPN
iajs-653	93	5	(	(	PUNCT
iajs-653	93	6	n	n	PROPN
iajs-653	93	7	)	)	PUNCT
iajs-653	93	8	å	å	PROPN
iajs-653	93	9	a	a	NOUN
iajs-653	93	10	)	)	PUNCT
iajs-653	93	11	,	,	PUNCT
iajs-653	93	12	(	(	PUNCT
iajs-653	93	13	in	in	ADP
iajs-653	93	14	å	å	PROPN
iajs-653	93	15	i	i	PRON
iajs-653	93	16	a	a	NOUN
iajs-653	93	17	)	)	PUNCT
iajs-653	93	18	∩	∩	NOUN
iajs-653	93	19	(	(	PUNCT
iajs-653	93	20	f	f	X
iajs-653	93	21	(	(	PUNCT
iajs-653	93	22	n	n	PROPN
iajs-653	93	23	)	)	PUNCT
iajs-653	93	24	å	å	PROPN
iajs-653	93	25	a	a	DET
iajs-653	93	26	)	)	PUNCT
iajs-653	93	27	=(	=(	NOUN
iajs-653	93	28	in	in	ADP
iajs-653	93	29	∩	∩	ADJ
iajs-653	93	30	f	f	X
iajs-653	93	31	(	(	PUNCT
iajs-653	93	32	n	n	CCONJ
iajs-653	93	33	)	)	PUNCT
iajs-653	93	34	)	)	PUNCT
iajs-653	94	1	å	å	PROPN
iajs-653	94	2	(	(	PUNCT
iajs-653	94	3	ia	ia	PROPN
iajs-653	94	4	∩	∩	PROPN
iajs-653	94	5	a)=	a)=	PROPN
iajs-653	95	1	i	i	PRON
iajs-653	95	2	f	f	PROPN
iajs-653	95	3	(	(	PUNCT
iajs-653	95	4	n	n	CCONJ
iajs-653	95	5	)	)	PUNCT
iajs-653	95	6	å	å	PROPN
iajs-653	95	7	ia	ia	NOUN
iajs-653	95	8	,	,	PUNCT
iajs-653	95	9	(	(	PUNCT
iajs-653	95	10	in	in	ADP
iajs-653	95	11	∩	∩	ADJ
iajs-653	95	12	f	f	X
iajs-653	95	13	(	(	PUNCT
iajs-653	95	14	n	n	NOUN
iajs-653	95	15	)	)	PUNCT
iajs-653	95	16	)	)	PUNCT
iajs-653	96	1	å	å	PROPN
iajs-653	96	2	ia	ia	NOUN
iajs-653	96	3	=	=	SYM
iajs-653	96	4	if	if	SCONJ
iajs-653	96	5	(	(	PUNCT
iajs-653	96	6	n	n	NOUN
iajs-653	96	7	)	)	PUNCT
iajs-653	96	8	å	å	PROPN
iajs-653	96	9	ia	ia	PROPN
iajs-653	96	10	,	,	PUNCT
iajs-653	96	11	in	in	ADP
iajs-653	96	12	∩	∩	ADJ
iajs-653	96	13	f	f	X
iajs-653	96	14	(	(	PUNCT
iajs-653	96	15	n	n	NOUN
iajs-653	96	16	)	)	PUNCT
iajs-653	96	17	=	=	SYM
iajs-653	96	18	if	if	SCONJ
iajs-653	96	19	(	(	PUNCT
iajs-653	96	20	n	n	NOUN
iajs-653	96	21	)	)	PUNCT
iajs-653	96	22	.	.	PUNCT
iajs-653	97	1	thus	thus	ADV
iajs-653	97	2	f(n)is	f(n)is	CCONJ
iajs-653	97	3	pure	pure	ADJ
iajs-653	97	4	in	in	ADP
iajs-653	97	5	n	n	PRON
iajs-653	97	6	and	and	CCONJ
iajs-653	97	7	so	so	ADV
iajs-653	97	8	n	n	ADV
iajs-653	97	9	is	be	AUX
iajs-653	97	10	purely	purely	ADV
iajs-653	97	11	copfian	copfian	ADJ
iajs-653	97	12	.	.	PUNCT
iajs-653	98	1	recall	recall	VERB
iajs-653	98	2	that	that	SCONJ
iajs-653	98	3	a	a	DET
iajs-653	98	4	submodule	submodule	NOUN
iajs-653	98	5	n	n	PROPN
iajs-653	98	6	of	of	ADP
iajs-653	98	7	m	m	PROPN
iajs-653	98	8	is	be	AUX
iajs-653	98	9	a	a	DET
iajs-653	98	10	nonsummand	nonsummand	NOUN
iajs-653	98	11	if	if	SCONJ
iajs-653	98	12	n	n	PRON
iajs-653	98	13	is	be	AUX
iajs-653	98	14	not	not	PART
iajs-653	98	15	direct	direct	ADJ
iajs-653	98	16	summand	summand	NOUN
iajs-653	98	17	of	of	ADP
iajs-653	98	18	m	m	PROPN
iajs-653	99	1	[	[	X
iajs-653	99	2	1	1	NUM
iajs-653	99	3	]	]	PUNCT
iajs-653	99	4	.	.	PUNCT
iajs-653	100	1	proposition	proposition	NOUN
iajs-653	100	2	1.10	1.10	NUM
iajs-653	100	3	let	let	VERB
iajs-653	100	4	m	m	PRON
iajs-653	100	5	be	be	AUX
iajs-653	100	6	an	an	DET
iajs-653	100	7	rmodule	rmodule	NOUN
iajs-653	100	8	such	such	ADJ
iajs-653	100	9	that	that	SCONJ
iajs-653	100	10	every	every	DET
iajs-653	100	11	non	non	ADJ
iajs-653	100	12	summand	summand	NOUN
iajs-653	100	13	n	n	PROPN
iajs-653	100	14	of	of	ADP
iajs-653	100	15	m	m	PROPN
iajs-653	100	16	is	be	AUX
iajs-653	100	17	purely	purely	ADV
iajs-653	100	18	co	co	ADJ
iajs-653	100	19	-	-	NOUN
iajs-653	100	20	hopfian	hopfian	ADJ
iajs-653	100	21	,	,	PUNCT
iajs-653	100	22	if	if	SCONJ
iajs-653	100	23	for	for	ADP
iajs-653	100	24	any	any	DET
iajs-653	100	25	non	non	ADJ
iajs-653	100	26	–	–	PUNCT
iajs-653	100	27	summand	summand	NOUN
iajs-653	100	28	submodule	submodule	PROPN
iajs-653	100	29	n	n	PROPN
iajs-653	100	30	of	of	ADP
iajs-653	100	31	m	m	PROPN
iajs-653	100	32	,	,	PUNCT
iajs-653	100	33	n	n	PRON
iajs-653	100	34	is	be	AUX
iajs-653	100	35	purely	purely	ADV
iajs-653	100	36	co	co	ADJ
iajs-653	100	37	-	-	NOUN
iajs-653	100	38	hopfian	hopfian	ADJ
iajs-653	100	39	,	,	PUNCT
iajs-653	100	40	then	then	ADV
iajs-653	100	41	m	m	VERB
iajs-653	100	42	is	be	AUX
iajs-653	100	43	purely	purely	ADV
iajs-653	100	44	cohopfian	cohopfian	ADJ
iajs-653	100	45	.	.	PUNCT
iajs-653	101	1	proof	proof	NOUN
iajs-653	101	2	suppose	suppose	VERB
iajs-653	101	3	m	m	NOUN
iajs-653	101	4	is	be	AUX
iajs-653	101	5	not	not	PART
iajs-653	101	6	purely	purely	ADV
iajs-653	101	7	co	co	ADJ
iajs-653	101	8	-	-	NOUN
iajs-653	101	9	hopfian	hopfian	ADJ
iajs-653	101	10	then	then	ADV
iajs-653	101	11	there	there	PRON
iajs-653	101	12	exists	exist	VERB
iajs-653	101	13	n	n	PRON
iajs-653	101	14	<	<	X
iajs-653	101	15	m	m	PROPN
iajs-653	101	16	,	,	PUNCT
iajs-653	101	17	n	n	CCONJ
iajs-653	101	18	@	@	ADP
iajs-653	101	19	m	m	PROPN
iajs-653	101	20	,	,	PUNCT
iajs-653	101	21	n	n	PRON
iajs-653	101	22	is	be	AUX
iajs-653	101	23	not	not	PART
iajs-653	101	24	pure	pure	ADJ
iajs-653	101	25	in	in	ADP
iajs-653	101	26	m	m	PROPN
iajs-653	101	27	by	by	ADP
iajs-653	101	28	lemma	lemma	PROPN
iajs-653	101	29	(	(	PUNCT
iajs-653	101	30	1.3	1.3	NUM
iajs-653	101	31	)	)	PUNCT
iajs-653	101	32	.	.	PUNCT
iajs-653	102	1	but	but	CCONJ
iajs-653	102	2	n	n	PRON
iajs-653	102	3	is	be	AUX
iajs-653	102	4	not	not	PART
iajs-653	102	5	pure	pure	ADJ
iajs-653	102	6	implies	implie	NOUN
iajs-653	102	7	n	n	VERB
iajs-653	102	8	is	be	AUX
iajs-653	102	9	not	not	PART
iajs-653	102	10	summand	summand	NOUN
iajs-653	102	11	.	.	PUNCT
iajs-653	103	1	hence	hence	ADV
iajs-653	103	2	by	by	ADP
iajs-653	103	3	hypothesis	hypothesis	NOUN
iajs-653	103	4	n	n	AUX
iajs-653	103	5	is	be	AUX
iajs-653	103	6	purely	purely	ADV
iajs-653	103	7	co	co	ADJ
iajs-653	103	8	-	-	NOUN
iajs-653	103	9	hopfian	hopfian	ADJ
iajs-653	103	10	which	which	PRON
iajs-653	103	11	implies	imply	VERB
iajs-653	103	12	m	m	VERB
iajs-653	103	13	is	be	AUX
iajs-653	103	14	purely	purely	ADV
iajs-653	103	15	co	co	ADJ
iajs-653	103	16	-	-	NOUN
iajs-653	103	17	hopfian	hopfian	ADJ
iajs-653	103	18	which	which	PRON
iajs-653	103	19	is	be	AUX
iajs-653	103	20	a	a	DET
iajs-653	103	21	contradiction	contradiction	NOUN
iajs-653	103	22	.	.	PUNCT
iajs-653	104	1	recall	recall	VERB
iajs-653	104	2	that	that	PRON
iajs-653	104	3	m	m	PROPN
iajs-653	104	4	is	be	AUX
iajs-653	104	5	fully	fully	ADV
iajs-653	104	6	stable	stable	ADJ
iajs-653	104	7	if	if	SCONJ
iajs-653	104	8	for	for	ADP
iajs-653	104	9	any	any	DET
iajs-653	104	10	submodule	submodule	NOUN
iajs-653	104	11	n	n	PROPN
iajs-653	104	12	of	of	ADP
iajs-653	104	13	m	m	PROPN
iajs-653	104	14	,	,	PUNCT
iajs-653	105	1	f	f	X
iajs-653	105	2	:	:	PUNCT
iajs-653	105	3	n	n	X
iajs-653	105	4	→	→	SYM
iajs-653	105	5	m	m	NOUN
iajs-653	105	6	is	be	AUX
iajs-653	105	7	then	then	ADV
iajs-653	105	8	f	f	PROPN
iajs-653	105	9	(	(	PUNCT
iajs-653	105	10	n	n	CCONJ
iajs-653	105	11	)	)	PUNCT
iajs-653	105	12	£	£	SYM
iajs-653	105	13	n	n	NOUN
iajs-653	106	1	[	[	X
iajs-653	106	2	5	5	NUM
iajs-653	106	3	]	]	PUNCT
iajs-653	106	4	.	.	PUNCT
iajs-653	107	1	proposition	proposition	NOUN
iajs-653	107	2	1.11	1.11	NUM
iajs-653	107	3	let	let	VERB
iajs-653	107	4	m	m	NOUN
iajs-653	107	5	=	=	SYM
iajs-653	107	6	m1	m1	PROPN
iajs-653	107	7	å	å	PROPN
iajs-653	107	8	m2	m2	PROPN
iajs-653	107	9	,	,	PUNCT
iajs-653	107	10	m	m	VERB
iajs-653	107	11	is	be	AUX
iajs-653	107	12	fully	fully	ADV
iajs-653	107	13	stable.then	stable.then	NOUN
iajs-653	107	14	m	m	NOUN
iajs-653	107	15	is	be	AUX
iajs-653	107	16	purely	purely	ADV
iajs-653	107	17	co	co	ADJ
iajs-653	107	18	-	-	NOUN
iajs-653	107	19	hopfian	hopfian	ADJ
iajs-653	107	20	if	if	SCONJ
iajs-653	107	21	and	and	CCONJ
iajs-653	107	22	only	only	ADV
iajs-653	107	23	if	if	SCONJ
iajs-653	107	24	m1	m1	PROPN
iajs-653	107	25	,	,	PUNCT
iajs-653	107	26	m2	m2	PROPN
iajs-653	107	27	are	be	AUX
iajs-653	107	28	purely	purely	ADV
iajs-653	107	29	co	co	ADJ
iajs-653	107	30	-	-	ADJ
iajs-653	107	31	hopfian	hopfian	ADJ
iajs-653	107	32	proof	proof	NOUN
iajs-653	107	33	إبن	إبن	VERB
iajs-653	107	34	الهيثم	الهيثم	ADJ
iajs-653	107	35	للعلوم	للعلوم	NOUN
iajs-653	107	36	الصرفة	الصرفة	NOUN
iajs-653	107	37	و	و	PRON
iajs-653	107	38	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	107	39	2012	2012	NUM
iajs-653	107	40	السنة	السنة	NOUN
iajs-653	108	1	25	25	NUM
iajs-653	108	2	المجلد	المجلد	NOUN
iajs-653	108	3	2	2	NUM
iajs-653	108	4	العدد	العدد	PROPN
iajs-653	108	5	ibn	ibn	PROPN
iajs-653	108	6	al	al	PROPN
iajs-653	108	7	-	-	PUNCT
iajs-653	108	8	haitham	haitham	PROPN
iajs-653	108	9	journal	journal	PROPN
iajs-653	108	10	for	for	ADP
iajs-653	108	11	pure	pure	ADJ
iajs-653	108	12	and	and	CCONJ
iajs-653	108	13	applied	apply	VERB
iajs-653	108	14	science	science	NOUN
iajs-653	108	15	no	no	NOUN
iajs-653	108	16	.	.	NOUN
iajs-653	108	17	2	2	NUM
iajs-653	108	18	vol	vol	NOUN
iajs-653	108	19	.	.	PUNCT
iajs-653	109	1	25	25	NUM
iajs-653	109	2	year	year	NOUN
iajs-653	109	3	2012	2012	NUM
iajs-653	109	4	it	it	PRON
iajs-653	109	5	follows	follow	VERB
iajs-653	109	6	by	by	ADP
iajs-653	109	7	proposition	proposition	NOUN
iajs-653	109	8	1.9.conversely	1.9.conversely	NUM
iajs-653	109	9	,	,	PUNCT
iajs-653	109	10	let	let	VERB
iajs-653	109	11	f	f	X
iajs-653	109	12	:	:	PUNCT
iajs-653	109	13	m	m	VERB
iajs-653	109	14	→	→	NOUN
iajs-653	109	15	m	m	VERB
iajs-653	109	16	be	be	VERB
iajs-653	109	17	monomorphism	monomorphism	NOUN
iajs-653	109	18	put	put	VERB
iajs-653	109	19	f1	f1	NOUN
iajs-653	109	20	=	=	SYM
iajs-653	110	1	f	f	X
iajs-653	110	2	│	│	ADJ
iajs-653	110	3	m1	m1	NOUN
iajs-653	110	4	,	,	PUNCT
iajs-653	110	5	f2	f2	PROPN
iajs-653	110	6	=	=	SYM
iajs-653	110	7	f	f	X
iajs-653	110	8	│	│	ADJ
iajs-653	110	9	m2	m2	PROPN
iajs-653	110	10	.since	.since	NOUN
iajs-653	110	11	m	m	VERB
iajs-653	110	12	is	be	AUX
iajs-653	110	13	fully	fully	ADV
iajs-653	110	14	stable	stable	ADJ
iajs-653	110	15	,	,	PUNCT
iajs-653	110	16	f1(m1	f1(m1	NOUN
iajs-653	110	17	)	)	PUNCT
iajs-653	110	18	£	£	NOUN
iajs-653	110	19	m1	m1	NOUN
iajs-653	110	20	and	and	CCONJ
iajs-653	110	21	f2	f2	PROPN
iajs-653	110	22	(	(	PUNCT
iajs-653	110	23	m2	m2	PROPN
iajs-653	110	24	)	)	PUNCT
iajs-653	110	25	£	£	PROPN
iajs-653	110	26	m2	m2	PROPN
iajs-653	110	27	.	.	PUNCT
iajs-653	111	1	since	since	SCONJ
iajs-653	111	2	f	f	PROPN
iajs-653	111	3	is	be	AUX
iajs-653	111	4	monomorphism	monomorphism	NOUN
iajs-653	111	5	,	,	PUNCT
iajs-653	111	6	f1	f1	NOUN
iajs-653	111	7	,	,	PUNCT
iajs-653	111	8	f2	f2	PROPN
iajs-653	111	9	are	be	AUX
iajs-653	111	10	monomorphism	monomorphism	NOUN
iajs-653	111	11	.	.	PUNCT
iajs-653	112	1	hence	hence	ADV
iajs-653	112	2	f1	f1	PROPN
iajs-653	112	3	(	(	PUNCT
iajs-653	112	4	m1	m1	PROPN
iajs-653	112	5	)	)	PUNCT
iajs-653	112	6	,	,	PUNCT
iajs-653	112	7	f2	f2	PROPN
iajs-653	112	8	(	(	PUNCT
iajs-653	112	9	m2	m2	PROPN
iajs-653	112	10	)	)	PUNCT
iajs-653	112	11	are	be	AUX
iajs-653	112	12	pure	pure	ADJ
iajs-653	112	13	in	in	ADP
iajs-653	112	14	m1	m1	PROPN
iajs-653	112	15	,	,	PUNCT
iajs-653	112	16	m2	m2	PROPN
iajs-653	112	17	respectively	respectively	ADV
iajs-653	112	18	.	.	PUNCT
iajs-653	113	1	hencef1	hencef1	NOUN
iajs-653	113	2	(	(	PUNCT
iajs-653	113	3	m1	m1	NOUN
iajs-653	113	4	)	)	PUNCT
iajs-653	113	5	å	å	PROPN
iajs-653	113	6	f2	f2	PROPN
iajs-653	113	7	(	(	PUNCT
iajs-653	113	8	m2	m2	PROPN
iajs-653	113	9	)	)	PUNCT
iajs-653	113	10	is	be	AUX
iajs-653	113	11	pure	pure	ADJ
iajs-653	113	12	in	in	ADP
iajs-653	113	13	m	m	PROPN
iajs-653	113	14	[	[	X
iajs-653	113	15	2	2	NUM
iajs-653	113	16	]	]	PUNCT
iajs-653	113	17	.	.	PUNCT
iajs-653	114	1	but	but	CCONJ
iajs-653	114	2	it	it	PRON
iajs-653	114	3	is	be	AUX
iajs-653	114	4	easy	easy	ADJ
iajs-653	114	5	to	to	PART
iajs-653	114	6	see	see	VERB
iajs-653	114	7	that	that	SCONJ
iajs-653	114	8	f	f	PROPN
iajs-653	114	9	(	(	PUNCT
iajs-653	114	10	m	m	NOUN
iajs-653	114	11	)	)	PUNCT
iajs-653	114	12	=	=	SYM
iajs-653	114	13	f1	f1	NOUN
iajs-653	114	14	(	(	PUNCT
iajs-653	114	15	m1	m1	NOUN
iajs-653	114	16	)	)	PUNCT
iajs-653	114	17	å	å	PROPN
iajs-653	114	18	f2	f2	PROPN
iajs-653	114	19	(	(	PUNCT
iajs-653	114	20	m2	m2	PROPN
iajs-653	114	21	)	)	PUNCT
iajs-653	114	22	.	.	PUNCT
iajs-653	115	1	thus	thus	ADV
iajs-653	115	2	f(m)is	f(m)is	VERB
iajs-653	115	3	pure	pure	ADJ
iajs-653	115	4	in	in	ADP
iajs-653	115	5	m	m	PROPN
iajs-653	115	6	.	.	PUNCT
iajs-653	116	1	corollary	corollary	ADJ
iajs-653	116	2	1	1	NUM
iajs-653	116	3	.	.	PROPN
iajs-653	116	4	12	12	NUM
iajs-653	116	5	let	let	VERB
iajs-653	116	6	m=	m=	PART
iajs-653	116	7	å	å	PROPN
iajs-653	116	8	iî	iî	PROPN
iajs-653	116	9	i	i	PROPN
iajs-653	116	10	mi	mi	PROPN
iajs-653	116	11	,	,	PUNCT
iajs-653	116	12	m	m	VERB
iajs-653	116	13	is	be	AUX
iajs-653	116	14	fully	fully	ADV
iajs-653	116	15	stable	stable	ADJ
iajs-653	116	16	m	m	NOUN
iajs-653	116	17	is	be	AUX
iajs-653	116	18	purely	purely	ADV
iajs-653	116	19	co	co	ADJ
iajs-653	116	20	-	-	NOUN
iajs-653	116	21	hopfian	hopfian	ADJ
iajs-653	116	22	if	if	SCONJ
iajs-653	116	23	and	and	CCONJ
iajs-653	116	24	only	only	ADV
iajs-653	116	25	if	if	SCONJ
iajs-653	116	26	mi	mi	PROPN
iajs-653	116	27	is	be	AUX
iajs-653	116	28	purely	purely	ADV
iajs-653	116	29	co	co	ADJ
iajs-653	116	30	-	-	NOUN
iajs-653	116	31	hopfian	hopfian	ADJ
iajs-653	116	32	for	for	ADP
iajs-653	116	33	all	all	PRON
iajs-653	117	1	i	i	PRON
iajs-653	117	2	î	î	VERB
iajs-653	117	3	i	i	PRON
iajs-653	117	4	.	.	PUNCT
iajs-653	118	1	recall	recall	VERB
iajs-653	118	2	that	that	PRON
iajs-653	118	3	m	m	PROPN
iajs-653	118	4	is	be	AUX
iajs-653	118	5	torsion	torsion	NOUN
iajs-653	118	6	free	free	ADJ
iajs-653	118	7	if	if	SCONJ
iajs-653	118	8	rm	rm	PROPN
iajs-653	118	9	=	=	NOUN
iajs-653	118	10	0	0	PUNCT
iajs-653	119	1	then	then	ADV
iajs-653	119	2	r	r	NOUN
iajs-653	119	3	=	=	SYM
iajs-653	119	4	0	0	NUM
iajs-653	119	5	or	or	CCONJ
iajs-653	119	6	m	m	PROPN
iajs-653	119	7	=	=	NOUN
iajs-653	119	8	0	0	NUM
iajs-653	120	1	for	for	ADP
iajs-653	120	2	any	any	DET
iajs-653	120	3	r	r	NOUN
iajs-653	120	4	î	î	PROPN
iajs-653	120	5	r	r	NOUN
iajs-653	120	6	,	,	PUNCT
iajs-653	120	7	m	m	VERB
iajs-653	120	8	î	î	PROPN
iajs-653	120	9	m.	m.	NOUN
iajs-653	120	10	note	note	NOUN
iajs-653	120	11	that	that	SCONJ
iajs-653	120	12	torsion	torsion	NOUN
iajs-653	120	13	free	free	ADJ
iajs-653	120	14	module	module	NOUN
iajs-653	120	15	needs	need	VERB
iajs-653	120	16	not	not	PART
iajs-653	120	17	purely	purely	ADV
iajs-653	120	18	co	co	ADJ
iajs-653	120	19	-	-	ADJ
iajs-653	120	20	hopfian	hopfian	ADJ
iajs-653	120	21	,	,	PUNCT
iajs-653	120	22	for	for	ADP
iajs-653	120	23	example	example	NOUN
iajs-653	120	24	z	z	PROPN
iajs-653	120	25	as	as	ADP
iajs-653	120	26	z	z	NOUN
iajs-653	120	27	-	-	NOUN
iajs-653	120	28	module	module	NOUN
iajs-653	120	29	.	.	PUNCT
iajs-653	121	1	now	now	ADV
iajs-653	121	2	we	we	PRON
iajs-653	121	3	have	have	VERB
iajs-653	121	4	the	the	DET
iajs-653	121	5	following	following	ADJ
iajs-653	121	6	result	result	NOUN
iajs-653	121	7	which	which	PRON
iajs-653	121	8	improves	improve	VERB
iajs-653	121	9	proposition	proposition	NOUN
iajs-653	121	10	2.13	2.13	NUM
iajs-653	121	11	in	in	ADP
iajs-653	121	12	[	[	X
iajs-653	121	13	1].which	1].which	NUM
iajs-653	121	14	states	state	VERB
iajs-653	121	15	that	that	SCONJ
iajs-653	121	16	,	,	PUNCT
iajs-653	121	17	let	let	VERB
iajs-653	121	18	r	r	PRON
iajs-653	121	19	be	be	AUX
iajs-653	121	20	a	a	DET
iajs-653	121	21	commutative	commutative	ADJ
iajs-653	121	22	domain	domain	NOUN
iajs-653	121	23	and	and	CCONJ
iajs-653	121	24	let	let	VERB
iajs-653	121	25	m	m	PRON
iajs-653	121	26	be	be	AUX
iajs-653	121	27	a	a	DET
iajs-653	121	28	torsion	torsion	NOUN
iajs-653	121	29	free	free	ADJ
iajs-653	121	30	semi	semi	ADJ
iajs-653	121	31	co	co	ADJ
iajs-653	121	32	-	-	ADJ
iajs-653	121	33	hopfian	hopfian	ADJ
iajs-653	121	34	r	r	NOUN
iajs-653	121	35	-	-	PUNCT
iajs-653	121	36	module	module	NOUN
iajs-653	121	37	.then	.then	AUX
iajs-653	122	1	m	m	VERB
iajs-653	122	2	is	be	AUX
iajs-653	122	3	injective	injective	ADJ
iajs-653	122	4	.	.	PUNCT
iajs-653	123	1	proposition	proposition	NOUN
iajs-653	123	2	1.13	1.13	NUM
iajs-653	123	3	let	let	VERB
iajs-653	123	4	r	r	PRON
iajs-653	123	5	be	be	AUX
iajs-653	123	6	an	an	DET
iajs-653	123	7	integral	integral	ADJ
iajs-653	123	8	domain	domain	NOUN
iajs-653	123	9	and	and	CCONJ
iajs-653	123	10	let	let	VERB
iajs-653	123	11	m	m	PRON
iajs-653	123	12	be	be	AUX
iajs-653	123	13	a	a	DET
iajs-653	123	14	torsion	torsion	NOUN
iajs-653	123	15	free	free	ADJ
iajs-653	123	16	purely	purely	ADV
iajs-653	123	17	co	co	ADJ
iajs-653	123	18	-	-	NOUN
iajs-653	123	19	hopfian	hopfian	ADJ
iajs-653	123	20	r	r	NOUN
iajs-653	123	21	–	–	PUNCT
iajs-653	123	22	module	module	NOUN
iajs-653	123	23	.then	.then	AUX
iajs-653	123	24	m	m	VERB
iajs-653	123	25	is	be	AUX
iajs-653	123	26	injective	injective	ADJ
iajs-653	123	27	r	r	NOUN
iajs-653	123	28	-	-	PUNCT
iajs-653	123	29	module	module	NOUN
iajs-653	123	30	.	.	PUNCT
iajs-653	124	1	proof	proof	NOUN
iajs-653	124	2	let	let	VERB
iajs-653	124	3	a	a	DET
iajs-653	124	4	î	î	PROPN
iajs-653	124	5	r	r	NOUN
iajs-653	124	6	,	,	PUNCT
iajs-653	124	7	a	a	DET
iajs-653	124	8	¹	¹	PROPN
iajs-653	124	9	0	0	NUM
iajs-653	124	10	.	.	PUNCT
iajs-653	125	1	define	define	VERB
iajs-653	125	2	f	f	PROPN
iajs-653	125	3	:	:	PUNCT
iajs-653	125	4	m	m	VERB
iajs-653	125	5	→	→	SYM
iajs-653	125	6	m	m	VERB
iajs-653	125	7	by	by	ADP
iajs-653	125	8	f	f	PROPN
iajs-653	125	9	(	(	PUNCT
iajs-653	125	10	m	m	PROPN
iajs-653	125	11	)	)	PUNCT
iajs-653	126	1	=	=	PRON
iajs-653	126	2	am	be	AUX
iajs-653	126	3	,	,	PUNCT
iajs-653	126	4	for	for	ADP
iajs-653	126	5	all	all	DET
iajs-653	126	6	a	a	DET
iajs-653	126	7	î	î	PROPN
iajs-653	126	8	m	m	NOUN
iajs-653	126	9	.	.	PUNCT
iajs-653	127	1	then	then	ADV
iajs-653	127	2	f	f	PROPN
iajs-653	127	3	is	be	AUX
iajs-653	127	4	monomorphism	monomorphism	NOUN
iajs-653	127	5	,	,	PUNCT
iajs-653	127	6	hence	hence	ADV
iajs-653	127	7	f	f	PROPN
iajs-653	127	8	(	(	PUNCT
iajs-653	127	9	m	m	PROPN
iajs-653	127	10	)	)	PUNCT
iajs-653	128	1	=	=	PRON
iajs-653	128	2	am	be	AUX
iajs-653	128	3	is	be	AUX
iajs-653	128	4	pure	pure	ADJ
iajs-653	128	5	submodule	submodule	NOUN
iajs-653	128	6	in	in	ADP
iajs-653	128	7	m	m	PROPN
iajs-653	128	8	since	since	SCONJ
iajs-653	128	9	m	m	PROPN
iajs-653	128	10	is	be	AUX
iajs-653	128	11	purely	purely	ADV
iajs-653	128	12	cohopfian.thus	cohopfian.thus	X
iajs-653	128	13	i	i	PRON
iajs-653	128	14	m	m	VERB
iajs-653	128	15	i	i	PRON
iajs-653	128	16	f	f	X
iajs-653	128	17	(	(	PUNCT
iajs-653	128	18	m	m	PROPN
iajs-653	128	19	)	)	PUNCT
iajs-653	129	1	=	=	SYM
iajs-653	130	1	i	i	PRON
iajs-653	130	2	f	f	X
iajs-653	130	3	(	(	PUNCT
iajs-653	130	4	m	m	PROPN
iajs-653	130	5	)	)	PUNCT
iajs-653	130	6	for	for	ADP
iajs-653	130	7	any	any	DET
iajs-653	130	8	ideal	ideal	NOUN
iajs-653	130	9	i	i	PRON
iajs-653	130	10	of	of	ADP
iajs-653	130	11	r.	r.	PROPN
iajs-653	130	12	take	take	VERB
iajs-653	130	13	i	i	PRON
iajs-653	130	14	=	=	X
iajs-653	130	15	<	<	X
iajs-653	130	16	a	a	X
iajs-653	130	17	>	>	X
iajs-653	130	18	.	.	PUNCT
iajs-653	131	1	hence	hence	ADV
iajs-653	131	2	(	(	PUNCT
iajs-653	131	3	a	a	X
iajs-653	131	4	)	)	PUNCT
iajs-653	131	5	m	m	VERB
iajs-653	131	6	i	i	PRON
iajs-653	131	7	am	be	AUX
iajs-653	131	8	=	=	PUNCT
iajs-653	131	9	(	(	PUNCT
iajs-653	131	10	a	a	NOUN
iajs-653	131	11	)	)	PUNCT
iajs-653	131	12	.	.	PUNCT
iajs-653	132	1	am	be	AUX
iajs-653	132	2	thus	thus	ADV
iajs-653	132	3	am	be	AUX
iajs-653	132	4	=	=	SYM
iajs-653	132	5	a2	a2	PROPN
iajs-653	132	6	m	m	NOUN
iajs-653	132	7	.now	.now	NOUN
iajs-653	132	8	for	for	ADP
iajs-653	132	9	any	any	DET
iajs-653	132	10	m	m	NOUN
iajs-653	132	11	î	î	PROPN
iajs-653	132	12	m	m	PROPN
iajs-653	132	13	,	,	PUNCT
iajs-653	132	14	am	be	AUX
iajs-653	132	15	=	=	SYM
iajs-653	132	16	a2m1	a2m1	ADJ
iajs-653	132	17	,	,	PUNCT
iajs-653	132	18	so	so	SCONJ
iajs-653	132	19	a	a	DET
iajs-653	132	20	(	(	PUNCT
iajs-653	132	21	m	m	PROPN
iajs-653	132	22	–	–	PUNCT
iajs-653	132	23	am1	am1	PROPN
iajs-653	132	24	)	)	PUNCT
iajs-653	132	25	=	=	SYM
iajs-653	132	26	0.hence	0.hence	NOUN
iajs-653	132	27	mam1=0	mam1=0	NOUN
iajs-653	132	28	since	since	SCONJ
iajs-653	132	29	m	m	PROPN
iajs-653	132	30	is	be	AUX
iajs-653	132	31	torsion	torsion	NOUN
iajs-653	132	32	free	free	ADJ
iajs-653	132	33	and	and	CCONJ
iajs-653	132	34	so	so	ADV
iajs-653	132	35	m	m	PROPN
iajs-653	132	36	=	=	SYM
iajs-653	132	37	am1	am1	PROPN
iajs-653	132	38	.	.	PUNCT
iajs-653	133	1	thus	thus	ADV
iajs-653	133	2	we	we	PRON
iajs-653	133	3	have	have	VERB
iajs-653	133	4	m	m	NOUN
iajs-653	133	5	=	=	NOUN
iajs-653	133	6	am	be	AUX
iajs-653	133	7	,	,	PUNCT
iajs-653	133	8	that	that	PRON
iajs-653	133	9	is	be	AUX
iajs-653	133	10	m	m	VERB
iajs-653	133	11	divisible	divisible	ADJ
iajs-653	133	12	torsion	torsion	NOUN
iajs-653	133	13	free	free	ADJ
iajs-653	133	14	,	,	PUNCT
iajs-653	133	15	hence	hence	ADV
iajs-653	133	16	m	m	VERB
iajs-653	133	17	is	be	AUX
iajs-653	133	18	injective	injective	ADJ
iajs-653	133	19	.	.	PUNCT
iajs-653	134	1	proposition	proposition	NOUN
iajs-653	134	2	1.14	1.14	NUM
iajs-653	134	3	if	if	SCONJ
iajs-653	134	4	m	m	PROPN
iajs-653	134	5	has	have	VERB
iajs-653	134	6	dcc	dcc	PROPN
iajs-653	134	7	on	on	ADP
iajs-653	134	8	non	non	PRON
iajs-653	134	9	pure	pure	ADJ
iajs-653	134	10	submodule	submodule	NOUN
iajs-653	134	11	(	(	PUNCT
iajs-653	134	12	that	that	DET
iajs-653	134	13	means	mean	VERB
iajs-653	134	14	has	have	AUX
iajs-653	134	15	dcc	dcc	PROPN
iajs-653	134	16	on	on	ADP
iajs-653	134	17	not	not	PART
iajs-653	134	18	pure	pure	ADJ
iajs-653	134	19	submodule	submodule	NOUN
iajs-653	134	20	)	)	PUNCT
iajs-653	134	21	,	,	PUNCT
iajs-653	134	22	then	then	ADV
iajs-653	134	23	m	m	NOUN
iajs-653	134	24	is	be	AUX
iajs-653	134	25	purely	purely	ADV
iajs-653	134	26	co	co	ADJ
iajs-653	134	27	-	-	NOUN
iajs-653	134	28	hopfian	hopfian	ADJ
iajs-653	134	29	.	.	PUNCT
iajs-653	135	1	proof	proof	NOUN
iajs-653	135	2	suppose	suppose	VERB
iajs-653	135	3	m	m	NOUN
iajs-653	135	4	is	be	AUX
iajs-653	135	5	not	not	PART
iajs-653	135	6	purely	purely	ADV
iajs-653	135	7	co	co	ADJ
iajs-653	135	8	-	-	NOUN
iajs-653	135	9	hopfian	hopfian	ADJ
iajs-653	135	10	,	,	PUNCT
iajs-653	135	11	then	then	ADV
iajs-653	135	12	by	by	ADP
iajs-653	135	13	lemma	lemma	PROPN
iajs-653	135	14	1.3	1.3	NUM
iajs-653	135	15	,	,	PUNCT
iajs-653	135	16	there	there	ADV
iajs-653	135	17	existsm1	existsm1	NOUN
iajs-653	136	1	(	(	PUNCT
iajs-653	136	2	not	not	PART
iajs-653	136	3	pure	pure	ADJ
iajs-653	136	4	submodule	submodule	NOUN
iajs-653	136	5	of	of	ADP
iajs-653	136	6	m	m	PROPN
iajs-653	136	7	)	)	PUNCT
iajs-653	136	8	such	such	ADJ
iajs-653	136	9	that	that	DET
iajs-653	136	10	m1	m1	PROPN
iajs-653	136	11	@	@	ADP
iajs-653	136	12	m.	m.	NOUN
iajs-653	136	13	hence	hence	ADV
iajs-653	136	14	m1	m1	PROPN
iajs-653	136	15	is	be	AUX
iajs-653	136	16	not	not	PART
iajs-653	136	17	purely	purely	ADV
iajs-653	136	18	co	co	ADJ
iajs-653	136	19	-	-	NOUN
iajs-653	136	20	hopfian	hopfian	ADJ
iajs-653	136	21	and	and	CCONJ
iajs-653	136	22	,	,	PUNCT
iajs-653	136	23	so	so	ADV
iajs-653	136	24	there	there	PRON
iajs-653	136	25	exists	exist	VERB
iajs-653	136	26	m2	m2	PROPN
iajs-653	136	27	submodule	submodule	PROPN
iajs-653	136	28	of	of	ADP
iajs-653	136	29	m1	m1	PROPN
iajs-653	136	30	which	which	PRON
iajs-653	136	31	is	be	AUX
iajs-653	136	32	not	not	PART
iajs-653	136	33	pure	pure	ADJ
iajs-653	136	34	of	of	ADP
iajs-653	136	35	m2	m2	PROPN
iajs-653	136	36	@	@	ADP
iajs-653	136	37	m1	m1	PROPN
iajs-653	136	38	.	.	PUNCT
iajs-653	137	1	by	by	ADP
iajs-653	137	2	repeating	repeat	VERB
iajs-653	137	3	this	this	DET
iajs-653	137	4	argument	argument	NOUN
iajs-653	137	5	we	we	PRON
iajs-653	137	6	have	have	AUX
iajs-653	137	7	strictly	strictly	ADV
iajs-653	137	8	descending	descend	VERB
iajs-653	137	9	chain	chain	NOUN
iajs-653	137	10	m1	m1	PROPN
iajs-653	137	11	é	é	PROPN
iajs-653	138	1	m2	m2	PROPN
iajs-653	138	2	é	é	PROPN
iajs-653	138	3	…	…	PUNCT
iajs-653	138	4	moreover	moreover	ADV
iajs-653	138	5	mi	mi	PROPN
iajs-653	138	6	is	be	AUX
iajs-653	138	7	not	not	PART
iajs-653	138	8	pure	pure	ADJ
iajs-653	138	9	in	in	ADP
iajs-653	138	10	m	m	PROPN
iajs-653	138	11	,	,	PUNCT
iajs-653	138	12	for	for	ADP
iajs-653	138	13	all	all	DET
iajs-653	138	14	i	i	PRON
iajs-653	138	15	=	=	NOUN
iajs-653	138	16	1	1	NUM
iajs-653	138	17	,	,	PUNCT
iajs-653	138	18	2	2	NUM
iajs-653	138	19	,	,	PUNCT
iajs-653	138	20	……	……	NOUN
iajs-653	138	21	.	.	PUNCT
iajs-653	139	1	to	to	PART
iajs-653	139	2	show	show	VERB
iajs-653	139	3	this	this	DET
iajs-653	139	4	m1	m1	NOUN
iajs-653	139	5	is	be	AUX
iajs-653	139	6	not	not	PART
iajs-653	139	7	pure	pure	ADJ
iajs-653	139	8	in	in	ADP
iajs-653	139	9	m	m	PROPN
iajs-653	139	10	(	(	PUNCT
iajs-653	139	11	by	by	ADP
iajs-653	139	12	proof	proof	NOUN
iajs-653	139	13	)	)	PUNCT
iajs-653	139	14	.	.	PUNCT
iajs-653	140	1	if	if	SCONJ
iajs-653	140	2	m2	m2	PROPN
iajs-653	140	3	pure	pure	ADJ
iajs-653	140	4	in	in	ADP
iajs-653	140	5	m	m	PROPN
iajs-653	140	6	,	,	PUNCT
iajs-653	140	7	then	then	ADV
iajs-653	140	8	m1	m1	PROPN
iajs-653	140	9	pure	pure	ADJ
iajs-653	140	10	in	in	ADP
iajs-653	140	11	m	m	PROPN
iajs-653	140	12	[	[	X
iajs-653	140	13	2,rem.7.2(1	2,rem.7.2(1	NOUN
iajs-653	140	14	)	)	PUNCT
iajs-653	140	15	]	]	PUNCT
iajs-653	140	16	,	,	PUNCT
iajs-653	140	17	which	which	PRON
iajs-653	140	18	is	be	AUX
iajs-653	140	19	a	a	DET
iajs-653	140	20	contradiction	contradiction	NOUN
iajs-653	140	21	.	.	PUNCT
iajs-653	141	1	thus	thus	ADV
iajs-653	141	2	m2	m2	PROPN
iajs-653	141	3	is	be	AUX
iajs-653	141	4	not	not	PART
iajs-653	141	5	pure	pure	ADJ
iajs-653	141	6	in	in	ADP
iajs-653	141	7	m.similarly	m.similarly	ADV
iajs-653	141	8	mi	mi	PROPN
iajs-653	141	9	is	be	AUX
iajs-653	141	10	not	not	PART
iajs-653	141	11	pure	pure	ADJ
iajs-653	141	12	in	in	ADP
iajs-653	141	13	m	m	PROPN
iajs-653	141	14	,	,	PUNCT
iajs-653	141	15	for	for	ADP
iajs-653	141	16	all	all	DET
iajs-653	141	17	i	i	PRON
iajs-653	141	18	=	=	NOUN
iajs-653	141	19	3	3	NUM
iajs-653	141	20	,	,	PUNCT
iajs-653	141	21	4	4	NUM
iajs-653	141	22	,	,	PUNCT
iajs-653	141	23	…	…	PUNCT
iajs-653	141	24	.	.	PUNCT
iajs-653	142	1	thus	thus	ADV
iajs-653	142	2	m1	m1	PROPN
iajs-653	142	3	é	é	PROPN
iajs-653	142	4	m2	m2	PROPN
iajs-653	142	5	é	é	PROPN
iajs-653	142	6	…	…	PUNCT
iajs-653	142	7	.	.	PUNCT
iajs-653	143	1	is	be	AUX
iajs-653	143	2	strictly	strictly	ADV
iajs-653	143	3	descending	descend	VERB
iajs-653	143	4	chain	chain	NOUN
iajs-653	143	5	of	of	ADP
iajs-653	143	6	non	non	ADJ
iajs-653	143	7	pure	pure	ADJ
iajs-653	143	8	submodule	submodule	NOUN
iajs-653	143	9	of	of	ADP
iajs-653	143	10	m	m	PROPN
iajs-653	143	11	,	,	PUNCT
iajs-653	143	12	which	which	PRON
iajs-653	143	13	is	be	AUX
iajs-653	143	14	a	a	DET
iajs-653	143	15	contradiction.thus	contradiction.thus	PROPN
iajs-653	143	16	m	m	NOUN
iajs-653	143	17	is	be	AUX
iajs-653	143	18	purely	purely	ADV
iajs-653	143	19	co	co	ADJ
iajs-653	143	20	-	-	ADJ
iajs-653	143	21	hopfian	hopfian	ADJ
iajs-653	143	22	.	.	PUNCT
iajs-653	144	1	remark	remark	NOUN
iajs-653	144	2	1.15	1.15	NUM
iajs-653	144	3	the	the	DET
iajs-653	144	4	endomorphism	endomorphism	PROPN
iajs-653	144	5	ring	ring	NOUN
iajs-653	144	6	of	of	ADP
iajs-653	144	7	purely	purely	ADV
iajs-653	144	8	co	co	ADJ
iajs-653	144	9	-	-	ADJ
iajs-653	144	10	hopfian	hopfian	ADJ
iajs-653	144	11	module	module	NOUN
iajs-653	144	12	need	need	AUX
iajs-653	144	13	not	not	PART
iajs-653	144	14	be	be	AUX
iajs-653	144	15	purely	purely	ADV
iajs-653	144	16	co	co	ADJ
iajs-653	144	17	-	-	NOUN
iajs-653	144	18	hopfian	hopfian	ADJ
iajs-653	144	19	.	.	PUNCT
iajs-653	145	1	example	example	NOUN
iajs-653	145	2	1.16	1.16	NUM
iajs-653	145	3	the	the	DET
iajs-653	145	4	z	z	NOUN
iajs-653	145	5	–	–	PUNCT
iajs-653	145	6	module	module	NOUN
iajs-653	145	7	zp	zp	NOUN
iajs-653	146	1	¥	¥	PROPN
iajs-653	146	2	is	be	AUX
iajs-653	146	3	co	co	ADJ
iajs-653	146	4	-	-	NOUN
iajs-653	146	5	hopfian	hopfian	ADJ
iajs-653	146	6	.	.	PUNCT
iajs-653	147	1	s	s	PART
iajs-653	148	1	=	=	VERB
iajs-653	148	2	end	end	NOUN
iajs-653	148	3	(	(	PUNCT
iajs-653	148	4	zp	zp	NOUN
iajs-653	148	5	¥	¥	PROPN
iajs-653	148	6	)	)	PUNCT
iajs-653	148	7	is	be	AUX
iajs-653	148	8	the	the	DET
iajs-653	148	9	integral	integral	ADJ
iajs-653	148	10	domain	domain	NOUN
iajs-653	148	11	of	of	ADP
iajs-653	148	12	p	p	NOUN
iajs-653	148	13	-	-	PUNCT
iajs-653	148	14	adic	adic	ADJ
iajs-653	148	15	integers	integer	NOUN
iajs-653	148	16	is	be	AUX
iajs-653	148	17	not	not	PART
iajs-653	148	18	co	co	ADJ
iajs-653	148	19	-	-	NOUN
iajs-653	148	20	hopfian	hopfian	ADJ
iajs-653	148	21	[	[	X
iajs-653	148	22	6	6	NUM
iajs-653	148	23	]	]	PUNCT
iajs-653	148	24	,	,	PUNCT
iajs-653	148	25	then	then	ADV
iajs-653	148	26	s	s	VERB
iajs-653	148	27	is	be	AUX
iajs-653	148	28	not	not	PART
iajs-653	148	29	purely	purely	ADV
iajs-653	148	30	co	co	ADJ
iajs-653	148	31	-	-	NOUN
iajs-653	148	32	hopfian	hopfian	ADJ
iajs-653	148	33	by	by	ADP
iajs-653	148	34	corollary	corollary	ADJ
iajs-653	148	35	(	(	PUNCT
iajs-653	148	36	1.6	1.6	NUM
iajs-653	148	37	)	)	PUNCT
iajs-653	148	38	.	.	PUNCT
iajs-653	149	1	recall	recall	VERB
iajs-653	149	2	that	that	SCONJ
iajs-653	149	3	an	an	DET
iajs-653	149	4	r	r	NOUN
iajs-653	149	5	-	-	PUNCT
iajs-653	149	6	module	module	NOUN
iajs-653	149	7	m	m	NOUN
iajs-653	149	8	is	be	AUX
iajs-653	149	9	called	call	VERB
iajs-653	149	10	multiplication	multiplication	NOUN
iajs-653	149	11	module	module	NOUN
iajs-653	149	12	if	if	SCONJ
iajs-653	149	13	for	for	ADP
iajs-653	149	14	each	each	DET
iajs-653	149	15	n≤m	n≤m	NOUN
iajs-653	149	16	,	,	PUNCT
iajs-653	149	17	there	there	PRON
iajs-653	149	18	exists	exist	VERB
iajs-653	149	19	ideal	ideal	ADJ
iajs-653	149	20	i	i	PRON
iajs-653	149	21	of	of	ADP
iajs-653	149	22	r	r	NOUN
iajs-653	149	23	such	such	ADJ
iajs-653	149	24	that	that	SCONJ
iajs-653	149	25	n	n	CCONJ
iajs-653	149	26	=	=	NOUN
iajs-653	149	27	im	im	X
iajs-653	149	28	.	.	PUNCT
iajs-653	150	1	equivalently	equivalently	ADV
iajs-653	150	2	,	,	PUNCT
iajs-653	150	3	mis	mis	NOUN
iajs-653	150	4	multiplication	multiplication	NOUN
iajs-653	150	5	if	if	SCONJ
iajs-653	150	6	for	for	ADP
iajs-653	150	7	each	each	DET
iajs-653	150	8	n≤m	n≤m	NOUN
iajs-653	150	9	,	,	PUNCT
iajs-653	150	10	n=(n	n=(n	NOUN
iajs-653	150	11	:	:	PUNCT
iajs-653	150	12	m)m	m)m	NOUN
iajs-653	150	13	,	,	PUNCT
iajs-653	150	14	where	where	SCONJ
iajs-653	150	15	(	(	PUNCT
iajs-653	150	16	n	n	NUM
iajs-653	150	17	:	:	PUNCT
iajs-653	150	18	m)={r	m)={r	PROPN
iajs-653	150	19	:	:	PUNCT
iajs-653	150	20	rîr	rîr	PROPN
iajs-653	150	21	,	,	PUNCT
iajs-653	150	22	rmín}[7	rmín}[7	PROPN
iajs-653	150	23	]	]	PUNCT
iajs-653	150	24	.	.	PUNCT
iajs-653	151	1	theorem	theorem	NOUN
iajs-653	151	2	1.17	1.17	NUM
iajs-653	151	3	let	let	VERB
iajs-653	151	4	m	m	PRON
iajs-653	151	5	be	be	AUX
iajs-653	151	6	a	a	DET
iajs-653	151	7	faithful	faithful	ADJ
iajs-653	151	8	finitely	finitely	ADV
iajs-653	151	9	generated	generate	VERB
iajs-653	151	10	multiplication	multiplication	NOUN
iajs-653	151	11	r	r	NOUN
iajs-653	151	12	–	–	PUNCT
iajs-653	151	13	module	module	NOUN
iajs-653	151	14	the	the	DET
iajs-653	151	15	following	following	ADJ
iajs-653	151	16	statements	statement	NOUN
iajs-653	151	17	are	be	AUX
iajs-653	151	18	equivalent	equivalent	ADJ
iajs-653	151	19	:	:	PUNCT
iajs-653	152	1	1	1	X
iajs-653	152	2	.	.	X
iajs-653	152	3	m	m	PROPN
iajs-653	152	4	is	be	AUX
iajs-653	152	5	purely	purely	ADV
iajs-653	152	6	co	co	ADJ
iajs-653	152	7	-	-	NOUN
iajs-653	152	8	hopfian	hopfian	ADJ
iajs-653	152	9	.	.	PUNCT
iajs-653	153	1	2	2	X
iajs-653	153	2	.	.	X
iajs-653	153	3	r	r	NOUN
iajs-653	153	4	is	be	AUX
iajs-653	153	5	semi	semi	ADV
iajs-653	153	6	co	co	ADJ
iajs-653	153	7	-	-	ADJ
iajs-653	153	8	hopfian	hopfian	ADJ
iajs-653	153	9	.	.	PUNCT
iajs-653	154	1	إبن	إبن	VERB
iajs-653	154	2	الهيثم	الهيثم	ADJ
iajs-653	154	3	للعلوم	للعلوم	NOUN
iajs-653	154	4	الصرفة	الصرفة	NOUN
iajs-653	154	5	و	و	PRON
iajs-653	154	6	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	154	7	2012	2012	NUM
iajs-653	154	8	السنة	السنة	NOUN
iajs-653	155	1	25	25	NUM
iajs-653	155	2	المجلد	المجلد	NOUN
iajs-653	155	3	2	2	NUM
iajs-653	155	4	العدد	العدد	PROPN
iajs-653	155	5	ibn	ibn	PROPN
iajs-653	155	6	al	al	PROPN
iajs-653	155	7	-	-	PUNCT
iajs-653	155	8	haitham	haitham	PROPN
iajs-653	155	9	journal	journal	PROPN
iajs-653	155	10	for	for	ADP
iajs-653	155	11	pure	pure	ADJ
iajs-653	155	12	and	and	CCONJ
iajs-653	155	13	applied	apply	VERB
iajs-653	155	14	science	science	NOUN
iajs-653	155	15	no	no	NOUN
iajs-653	155	16	.	.	NOUN
iajs-653	155	17	2	2	NUM
iajs-653	155	18	vol	vol	NOUN
iajs-653	155	19	.	.	PUNCT
iajs-653	156	1	25	25	NUM
iajs-653	156	2	year	year	NOUN
iajs-653	156	3	2012	2012	NUM
iajs-653	156	4	3	3	NUM
iajs-653	156	5	.	.	PUNCT
iajs-653	157	1	r	r	NOUN
iajs-653	157	2	is	be	AUX
iajs-653	157	3	purely	purely	ADV
iajs-653	157	4	co	co	ADJ
iajs-653	157	5	-	-	NOUN
iajs-653	157	6	hopfian	hopfian	ADJ
iajs-653	157	7	.	.	PUNCT
iajs-653	158	1	4	4	X
iajs-653	158	2	.	.	X
iajs-653	158	3	m	m	PROPN
iajs-653	158	4	is	be	AUX
iajs-653	158	5	co	co	ADJ
iajs-653	158	6	-	-	ADJ
iajs-653	158	7	hopfian	hopfian	ADJ
iajs-653	158	8	.	.	PUNCT
iajs-653	159	1	5	5	X
iajs-653	159	2	.	.	X
iajs-653	159	3	m	m	PROPN
iajs-653	159	4	is	be	AUX
iajs-653	159	5	semi	semi	ADV
iajs-653	159	6	co	co	ADJ
iajs-653	159	7	-	-	ADJ
iajs-653	159	8	hopfian	hopfian	ADJ
iajs-653	159	9	.	.	PUNCT
iajs-653	160	1	proof	proof	NOUN
iajs-653	160	2	(	(	PUNCT
iajs-653	160	3	1	1	NUM
iajs-653	160	4	)	)	PUNCT
iajs-653	160	5	→(2	→(2	NUM
iajs-653	160	6	):	):	PUNCT
iajs-653	160	7	let	let	VERB
iajs-653	160	8	a	a	DET
iajs-653	160	9	îr	îr	NOUN
iajs-653	160	10	,	,	PUNCT
iajs-653	160	11	annra	annra	NOUN
iajs-653	160	12	=	=	NOUN
iajs-653	160	13	0	0	X
iajs-653	161	1	.	.	PUNCT
iajs-653	161	2	define	define	VERB
iajs-653	161	3	f	f	PROPN
iajs-653	161	4	:	:	PUNCT
iajs-653	161	5	m	m	VERB
iajs-653	161	6	→	→	SYM
iajs-653	161	7	m	m	VERB
iajs-653	161	8	by	by	ADP
iajs-653	161	9	f	f	PROPN
iajs-653	161	10	(	(	PUNCT
iajs-653	161	11	m	m	PROPN
iajs-653	161	12	)	)	PUNCT
iajs-653	162	1	=	=	PRON
iajs-653	162	2	am	be	AUX
iajs-653	162	3	for	for	ADP
iajs-653	162	4	any	any	DET
iajs-653	162	5	mîm	mîm	NOUN
iajs-653	162	6	.we	.we	PUNCT
iajs-653	162	7	can	can	AUX
iajs-653	162	8	see	see	VERB
iajs-653	162	9	that	that	SCONJ
iajs-653	162	10	f	f	PROPN
iajs-653	162	11	is	be	AUX
iajs-653	162	12	monomorphism	monomorphism	NOUN
iajs-653	162	13	as	as	SCONJ
iajs-653	162	14	follows	follow	VERB
iajs-653	162	15	,	,	PUNCT
iajs-653	162	16	let	let	VERB
iajs-653	162	17	m	m	PRON
iajs-653	162	18	î	î	NOUN
iajs-653	162	19	kerf	kerf	NOUN
iajs-653	162	20	then	then	ADV
iajs-653	162	21	am	be	AUX
iajs-653	162	22	=	=	NUM
iajs-653	162	23	0	0	NUM
iajs-653	163	1	and	and	CCONJ
iajs-653	163	2	so	so	ADV
iajs-653	163	3	m	m	VERB
iajs-653	163	4	î	î	PROPN
iajs-653	163	5	annm	annm	NOUN
iajs-653	163	6	(	(	PUNCT
iajs-653	163	7	a	a	PRON
iajs-653	163	8	)	)	PUNCT
iajs-653	163	9	.	.	PUNCT
iajs-653	164	1	but	but	CCONJ
iajs-653	164	2	annm	annm	NOUN
iajs-653	164	3	(	(	PUNCT
iajs-653	164	4	a	a	X
iajs-653	164	5	)	)	PUNCT
iajs-653	164	6	=	=	SYM
iajs-653	164	7	(	(	PUNCT
iajs-653	164	8	annr	annr	NOUN
iajs-653	164	9	(	(	PUNCT
iajs-653	164	10	a	a	NOUN
iajs-653	164	11	)	)	PUNCT
iajs-653	164	12	)	)	PUNCT
iajs-653	165	1	m	m	VERB
iajs-653	165	2	.hence	.hence	ADP
iajs-653	165	3	m	m	VERB
iajs-653	165	4	î	î	X
iajs-653	165	5	(	(	PUNCT
iajs-653	165	6	annra	annra	NOUN
iajs-653	165	7	)	)	PUNCT
iajs-653	165	8	m	m	PROPN
iajs-653	166	1	=	=	NOUN
iajs-653	166	2	0	0	NUM
iajs-653	166	3	.	.	PUNCT
iajs-653	167	1	m	m	VERB
iajs-653	167	2	=	=	SYM
iajs-653	167	3	0	0	NUM
iajs-653	167	4	,	,	PUNCT
iajs-653	167	5	then	then	ADV
iajs-653	167	6	we	we	PRON
iajs-653	167	7	get	get	VERB
iajs-653	167	8	m	m	NOUN
iajs-653	167	9	=	=	PUNCT
iajs-653	168	1	0.now	0.now	ADJ
iajs-653	168	2	f	f	X
iajs-653	168	3	(	(	PUNCT
iajs-653	168	4	m	m	PROPN
iajs-653	168	5	)	)	PUNCT
iajs-653	168	6	=	=	PUNCT
iajs-653	169	1	a	a	DET
iajs-653	169	2	m	m	NOUN
iajs-653	169	3	is	be	AUX
iajs-653	169	4	pure	pure	ADJ
iajs-653	169	5	in	in	ADP
iajs-653	169	6	m.	m.	NOUN
iajs-653	169	7	hence	hence	ADV
iajs-653	169	8	<	<	X
iajs-653	169	9	a	a	X
iajs-653	169	10	>	>	X
iajs-653	169	11	is	be	AUX
iajs-653	169	12	pure	pure	ADJ
iajs-653	169	13	in	in	ADP
iajs-653	169	14	r	r	NOUN
iajs-653	169	15	,	,	PUNCT
iajs-653	169	16	since	since	SCONJ
iajs-653	169	17	m	m	PROPN
iajs-653	169	18	is	be	AUX
iajs-653	169	19	faithful	faithful	ADJ
iajs-653	169	20	finitely	finitely	ADV
iajs-653	169	21	generated	generate	VERB
iajs-653	169	22	multiplication	multiplication	NOUN
iajs-653	170	1	.thus	.thus	ADP
iajs-653	170	2	<	<	X
iajs-653	170	3	a	a	X
iajs-653	170	4	>	>	X
iajs-653	170	5	=	=	X
iajs-653	170	6	<	<	X
iajs-653	170	7	a	a	DET
iajs-653	170	8	2	2	NUM
iajs-653	170	9	>	>	X
iajs-653	170	10	so	so	SCONJ
iajs-653	170	11	a	a	DET
iajs-653	170	12	=	=	PUNCT
iajs-653	170	13	ra2	ra2	PROPN
iajs-653	170	14	,	,	PUNCT
iajs-653	170	15	which	which	PRON
iajs-653	170	16	implies	imply	VERB
iajs-653	170	17	a	a	DET
iajs-653	170	18	(	(	PUNCT
iajs-653	170	19	1ra	1ra	NOUN
iajs-653	170	20	)	)	PUNCT
iajs-653	170	21	=	=	SYM
iajs-653	170	22	0	0	NUM
iajs-653	170	23	,	,	PUNCT
iajs-653	170	24	since	since	SCONJ
iajs-653	170	25	ann	ann	PROPN
iajs-653	170	26	(	(	PUNCT
iajs-653	170	27	a	a	PROPN
iajs-653	170	28	)	)	PUNCT
iajs-653	170	29	=	=	SYM
iajs-653	170	30	0	0	NUM
iajs-653	170	31	,	,	PUNCT
iajs-653	170	32	1	1	NUM
iajs-653	170	33	-	-	NUM
iajs-653	170	34	ra	ra	NOUN
iajs-653	170	35	=	=	NOUN
iajs-653	170	36	0	0	NUM
iajs-653	170	37	,	,	PUNCT
iajs-653	170	38	1	1	NUM
iajs-653	170	39	=	=	SYM
iajs-653	170	40	ra	ra	PROPN
iajs-653	170	41	,	,	PUNCT
iajs-653	170	42	that	that	PRON
iajs-653	170	43	is	be	AUX
iajs-653	170	44	a	a	PRON
iajs-653	170	45	is	be	AUX
iajs-653	170	46	an	an	DET
iajs-653	170	47	inevitable	inevitable	ADJ
iajs-653	170	48	element	element	NOUN
iajs-653	170	49	,	,	PUNCT
iajs-653	170	50	so	so	SCONJ
iajs-653	170	51	<	<	X
iajs-653	170	52	a	a	X
iajs-653	170	53	>	>	X
iajs-653	170	54	=	=	PUNCT
iajs-653	170	55	r	r	NOUN
iajs-653	170	56	.	.	PUNCT
iajs-653	171	1	(	(	PUNCT
iajs-653	171	2	2	2	X
iajs-653	171	3	)	)	PUNCT
iajs-653	171	4	↔(3	↔(3	NOUN
iajs-653	171	5	):	):	PUNCT
iajs-653	171	6	it	it	PRON
iajs-653	171	7	follows	follow	VERB
iajs-653	171	8	by	by	ADP
iajs-653	171	9	proposition	proposition	NOUN
iajs-653	171	10	(	(	PUNCT
iajs-653	171	11	1.4	1.4	NUM
iajs-653	171	12	)	)	PUNCT
iajs-653	171	13	.	.	PUNCT
iajs-653	172	1	(	(	PUNCT
iajs-653	172	2	3	3	X
iajs-653	172	3	)	)	PUNCT
iajs-653	172	4	→	→	X
iajs-653	172	5	(	(	PUNCT
iajs-653	172	6	4	4	NUM
iajs-653	172	7	):	):	PUNCT
iajs-653	172	8	let	let	VERB
iajs-653	172	9	f	f	PRON
iajs-653	172	10	:	:	PUNCT
iajs-653	172	11	m	m	AUX
iajs-653	172	12	→	→	NOUN
iajs-653	172	13	m	m	VERB
iajs-653	172	14	be	be	VERB
iajs-653	172	15	monomorphism	monomorphism	NOUN
iajs-653	172	16	,	,	PUNCT
iajs-653	172	17	since	since	SCONJ
iajs-653	172	18	m	m	PROPN
iajs-653	172	19	is	be	AUX
iajs-653	172	20	finitely	finitely	ADV
iajs-653	172	21	generated	generate	VERB
iajs-653	172	22	multiplication	multiplication	NOUN
iajs-653	172	23	,	,	PUNCT
iajs-653	172	24	then	then	ADV
iajs-653	172	25	m	m	VERB
iajs-653	172	26	is	be	AUX
iajs-653	172	27	a	a	DET
iajs-653	172	28	scalar	scalar	ADJ
iajs-653	172	29	module	module	NOUN
iajs-653	172	30	,	,	PUNCT
iajs-653	172	31	there	there	PRON
iajs-653	172	32	exists	exist	VERB
iajs-653	172	33	a	a	DET
iajs-653	172	34	î	î	PROPN
iajs-653	172	35	r	r	NOUN
iajs-653	172	36	,	,	PUNCT
iajs-653	172	37	a	a	DET
iajs-653	172	38	¹	¹	PROPN
iajs-653	172	39	0such	0such	X
iajs-653	173	1	that	that	PRON
iajs-653	173	2	,	,	PUNCT
iajs-653	173	3	f	f	PROPN
iajs-653	173	4	(	(	PUNCT
iajs-653	173	5	m	m	PROPN
iajs-653	173	6	)	)	PUNCT
iajs-653	173	7	=	=	PRON
iajs-653	173	8	am	be	AUX
iajs-653	173	9	for	for	ADP
iajs-653	173	10	all	all	DET
iajs-653	173	11	m	m	VERB
iajs-653	173	12	î	î	NOUN
iajs-653	173	13	m	m	PRON
iajs-653	173	14	[	[	X
iajs-653	173	15	8	8	NUM
iajs-653	173	16	]	]	PUNCT
iajs-653	173	17	.	.	PUNCT
iajs-653	174	1	since	since	SCONJ
iajs-653	174	2	kerf	kerf	NOUN
iajs-653	174	3	=	=	SYM
iajs-653	174	4	{	{	PUNCT
iajs-653	174	5	0	0	NUM
iajs-653	174	6	}	}	PUNCT
iajs-653	174	7	,	,	PUNCT
iajs-653	174	8	annma	annma	PROPN
iajs-653	174	9	=	=	SYM
iajs-653	174	10	0	0	X
iajs-653	174	11	.	.	PUNCT
iajs-653	174	12	[	[	PUNCT
iajs-653	174	13	to	to	PART
iajs-653	174	14	prove	prove	VERB
iajs-653	174	15	this	this	PRON
iajs-653	174	16	.	.	PUNCT
iajs-653	175	1	since	since	SCONJ
iajs-653	175	2	annm(a	annm(a	PROPN
iajs-653	175	3	)	)	PUNCT
iajs-653	175	4	=	=	PRON
iajs-653	175	5	{	{	PUNCT
iajs-653	175	6	m	m	VERB
iajs-653	175	7	:	:	PUNCT
iajs-653	175	8	am	be	AUX
iajs-653	175	9	=	=	NOUN
iajs-653	175	10	0	0	PUNCT
iajs-653	175	11	}	}	PUNCT
iajs-653	175	12	=	=	SYM
iajs-653	175	13	{	{	PUNCT
iajs-653	175	14	m	m	VERB
iajs-653	175	15	:	:	PUNCT
iajs-653	175	16	f	f	X
iajs-653	175	17	(	(	PUNCT
iajs-653	175	18	m	m	PROPN
iajs-653	175	19	)	)	PUNCT
iajs-653	176	1	=	=	SYM
iajs-653	176	2	0	0	PUNCT
iajs-653	177	1	}	}	PUNCT
iajs-653	177	2	=	=	SYM
iajs-653	177	3	{	{	PUNCT
iajs-653	177	4	m	m	VERB
iajs-653	177	5	:	:	PUNCT
iajs-653	177	6	m	m	VERB
iajs-653	177	7	=	=	NOUN
iajs-653	177	8	0	0	NUM
iajs-653	177	9	}	}	PUNCT
iajs-653	177	10	]	]	PUNCT
iajs-653	177	11	.but	.but	PUNCT
iajs-653	178	1	annma	annma	PROPN
iajs-653	178	2	=	=	PUNCT
iajs-653	178	3	(	(	PUNCT
iajs-653	178	4	annra	annra	NOUN
iajs-653	178	5	)	)	PUNCT
iajs-653	178	6	m	m	PROPN
iajs-653	178	7	,	,	PUNCT
iajs-653	178	8	so	so	ADV
iajs-653	178	9	annr(a	annr(a	ADJ
iajs-653	178	10	)	)	PUNCT
iajs-653	178	11	.m	.m	PUNCT
iajs-653	179	1	=	=	PUNCT
iajs-653	179	2	0	0	NUM
iajs-653	179	3	.thus	.thus	SYM
iajs-653	179	4	annr(a	annr(a	ADJ
iajs-653	179	5	)	)	PUNCT
iajs-653	179	6	í	í	NOUN
iajs-653	179	7	annm	annm	NOUN
iajs-653	179	8	=	=	SYM
iajs-653	179	9	0	0	NUM
iajs-653	179	10	.it	.it	PUNCT
iajs-653	179	11	follows	follow	VERB
iajs-653	179	12	that	that	SCONJ
iajs-653	179	13	annr(a	annr(a	NOUN
iajs-653	179	14	)	)	PUNCT
iajs-653	179	15	=	=	SYM
iajs-653	180	1	0	0	X
iajs-653	180	2	.	.	PUNCT
iajs-653	181	1	but	but	CCONJ
iajs-653	181	2	r	r	NOUN
iajs-653	181	3	is	be	AUX
iajs-653	181	4	purely	purely	ADV
iajs-653	181	5	co	co	ADJ
iajs-653	181	6	-	-	NOUN
iajs-653	181	7	hopfian	hopfian	ADJ
iajs-653	181	8	so	so	SCONJ
iajs-653	181	9	<	<	X
iajs-653	181	10	a	a	X
iajs-653	181	11	>	>	X
iajs-653	181	12	=	=	PUNCT
iajs-653	181	13	r	r	NOUN
iajs-653	181	14	by	by	ADP
iajs-653	181	15	corollary	corollary	ADJ
iajs-653	181	16	(	(	PUNCT
iajs-653	181	17	1.5	1.5	NUM
iajs-653	181	18	)	)	PUNCT
iajs-653	181	19	.	.	PUNCT
iajs-653	182	1	(	(	PUNCT
iajs-653	182	2	4	4	NUM
iajs-653	182	3	)	)	PUNCT
iajs-653	182	4	→(5	→(5	NUM
iajs-653	182	5	):	):	PUNCT
iajs-653	182	6	it	it	PRON
iajs-653	182	7	is	be	AUX
iajs-653	182	8	clear	clear	ADJ
iajs-653	182	9	any	any	DET
iajs-653	182	10	co	co	NOUN
iajs-653	182	11	-	-	NOUN
iajs-653	182	12	hopfian	hopfian	ADJ
iajs-653	182	13	is	be	AUX
iajs-653	182	14	semi	semi	ADV
iajs-653	182	15	co	co	ADJ
iajs-653	182	16	-	-	ADJ
iajs-653	182	17	hopfian	hopfian	ADJ
iajs-653	182	18	by	by	ADP
iajs-653	182	19	[	[	PUNCT
iajs-653	182	20	1	1	NUM
iajs-653	182	21	]	]	PUNCT
iajs-653	182	22	.	.	PUNCT
iajs-653	183	1	(	(	PUNCT
iajs-653	183	2	5	5	NUM
iajs-653	183	3	)	)	PUNCT
iajs-653	183	4	→	→	X
iajs-653	183	5	(	(	PUNCT
iajs-653	183	6	1	1	NUM
iajs-653	183	7	):	):	PUNCT
iajs-653	183	8	by	by	ADP
iajs-653	183	9	[	[	PUNCT
iajs-653	183	10	remark	remark	NOUN
iajs-653	183	11	and	and	CCONJ
iajs-653	183	12	examples	example	NOUN
iajs-653	183	13	1.2	1.2	NUM
iajs-653	183	14	]	]	PUNCT
iajs-653	183	15	corollary	corollary	NOUN
iajs-653	183	16	1.18	1.18	NUM
iajs-653	183	17	let	let	VERB
iajs-653	183	18	m	m	PRON
iajs-653	183	19	be	be	AUX
iajs-653	183	20	a	a	DET
iajs-653	183	21	faithful	faithful	ADJ
iajs-653	183	22	finitely	finitely	ADV
iajs-653	183	23	generated	generate	VERB
iajs-653	183	24	multiplication	multiplication	NOUN
iajs-653	183	25	r	r	NOUN
iajs-653	183	26	-	-	PUNCT
iajs-653	183	27	module	module	NOUN
iajs-653	183	28	then	then	ADV
iajs-653	183	29	the	the	DET
iajs-653	183	30	following	following	NOUN
iajs-653	183	31	are	be	AUX
iajs-653	183	32	equivalent	equivalent	ADJ
iajs-653	183	33	:	:	PUNCT
iajs-653	183	34	1	1	X
iajs-653	183	35	.	.	X
iajs-653	183	36	m	m	PROPN
iajs-653	183	37	is	be	AUX
iajs-653	183	38	purely	purely	ADV
iajs-653	183	39	co	co	ADJ
iajs-653	183	40	-	-	ADJ
iajs-653	183	41	hopfian	hopfian	ADJ
iajs-653	183	42	module	module	NOUN
iajs-653	183	43	.	.	PUNCT
iajs-653	184	1	2	2	X
iajs-653	184	2	.	.	X
iajs-653	184	3	end	end	NOUN
iajs-653	184	4	r	r	NOUN
iajs-653	184	5	m	m	VERB
iajs-653	184	6	is	be	AUX
iajs-653	184	7	purely	purely	ADV
iajs-653	184	8	co	co	ADJ
iajs-653	184	9	-	-	ADJ
iajs-653	184	10	hopfian	hopfian	ADJ
iajs-653	184	11	ring	ring	NOUN
iajs-653	184	12	(	(	PUNCT
iajs-653	184	13	semi	semi	ADV
iajs-653	184	14	co	co	VERB
iajs-653	184	15	-	-	ADJ
iajs-653	184	16	hopfian	hopfian	ADJ
iajs-653	184	17	,	,	PUNCT
iajs-653	184	18	co	co	ADJ
iajs-653	184	19	-	-	NOUN
iajs-653	184	20	hopfian	hopfian	ADJ
iajs-653	184	21	)	)	PUNCT
iajs-653	184	22	proof	proof	NOUN
iajs-653	184	23	(	(	PUNCT
iajs-653	184	24	1	1	X
iajs-653	184	25	)	)	PUNCT
iajs-653	184	26	↔	↔	NOUN
iajs-653	184	27	(	(	PUNCT
iajs-653	184	28	2	2	NUM
iajs-653	184	29	)	)	PUNCT
iajs-653	184	30	since	since	SCONJ
iajs-653	184	31	m	m	PROPN
iajs-653	184	32	is	be	AUX
iajs-653	184	33	a	a	DET
iajs-653	184	34	finitely	finitely	ADV
iajs-653	184	35	generated	generate	VERB
iajs-653	184	36	multiplication	multiplication	NOUN
iajs-653	184	37	r	r	NOUN
iajs-653	184	38	-	-	PUNCT
iajs-653	184	39	module	module	NOUN
iajs-653	184	40	m	m	NOUN
iajs-653	184	41	is	be	AUX
iajs-653	184	42	a	a	DET
iajs-653	184	43	scalar	scalar	ADJ
iajs-653	184	44	module	module	NOUN
iajs-653	184	45	by	by	ADP
iajs-653	184	46	[	[	X
iajs-653	184	47	8,prop.1.1.10].hence	8,prop.1.1.10].hence	NUM
iajs-653	184	48	end	end	NOUN
iajs-653	184	49	m	m	VERB
iajs-653	184	50	@	@	ADP
iajs-653	184	51	r	r	NOUN
iajs-653	184	52	by	by	ADP
iajs-653	184	53	[	[	X
iajs-653	184	54	9,lemma	9,lemma	NUM
iajs-653	184	55	6.1,ch.3].thus	6.1,ch.3].thus	NUM
iajs-653	184	56	by	by	ADP
iajs-653	184	57	previous	previous	ADJ
iajs-653	184	58	theorem	theorem	NOUN
iajs-653	184	59	we	we	PRON
iajs-653	184	60	obtained	obtain	VERB
iajs-653	184	61	the	the	DET
iajs-653	184	62	result	result	NOUN
iajs-653	184	63	.	.	PUNCT
iajs-653	185	1	references	reference	NOUN
iajs-653	185	2	1aydogdu	1aydogdu	NUM
iajs-653	185	3	,	,	PUNCT
iajs-653	185	4	p.ozcan	p.ozcan	ADJ
iajs-653	185	5	,	,	PUNCT
iajs-653	185	6	a.	a.	NOUN
iajs-653	185	7	cigdem	cigdem	PROPN
iajs-653	185	8	;	;	PUNCT
iajs-653	185	9	10(2008	10(2008	NUM
iajs-653	185	10	)	)	PUNCT
iajs-653	185	11	,	,	PUNCT
iajs-653	185	12	semi	semi	ADV
iajs-653	185	13	co	co	VERB
iajs-653	185	14	-	-	ADJ
iajs-653	185	15	hopfian	hopfian	ADJ
iajs-653	185	16	and	and	CCONJ
iajs-653	185	17	semi	semi	ADJ
iajs-653	185	18	hopfian	hopfian	ADJ
iajs-653	185	19	modules	module	NOUN
iajs-653	185	20	.	.	PUNCT
iajs-653	186	1	east	east	PROPN
iajs-653	186	2	-	-	PUNCT
iajs-653	186	3	west	west	PROPN
iajs-653	186	4	j.	j.	PROPN
iajs-653	186	5	math	math	PROPN
iajs-653	186	6	.	.	PUNCT
iajs-653	186	7	,	,	PUNCT
iajs-653	187	1	no	no	INTJ
iajs-653	187	2	.	.	NOUN
iajs-653	187	3	1	1	NUM
iajs-653	187	4	:	:	PUNCT
iajs-653	187	5	55	55	NUM
iajs-653	187	6	-	-	SYM
iajs-653	187	7	70	70	NUM
iajs-653	187	8	.	.	PUNCT
iajs-653	188	1	2yaseen	2yaseen	NUM
iajs-653	188	2	,	,	PUNCT
iajs-653	188	3	s.m	s.m	PROPN
iajs-653	188	4	.	.	PROPN
iajs-653	188	5	,msc.thesis,(1993),on	,msc.thesis,(1993),on	PUNCT
iajs-653	189	1	f	f	X
iajs-653	189	2	-	-	PUNCT
iajs-653	189	3	regular	regular	ADJ
iajs-653	189	4	modules	module	NOUN
iajs-653	189	5	,	,	PUNCT
iajs-653	189	6	university	university	NOUN
iajs-653	189	7	of	of	ADP
iajs-653	189	8	baghdad	baghdad	PROPN
iajs-653	189	9	,	,	PUNCT
iajs-653	189	10	college	college	NOUN
iajs-653	189	11	of	of	ADP
iajs-653	189	12	science	science	NOUN
iajs-653	189	13	.	.	PUNCT
iajs-653	190	1	3fieldhouse	3fieldhouse	NUM
iajs-653	190	2	,	,	PUNCT
iajs-653	190	3	d.j.(1969	d.j.(1969	PROPN
iajs-653	190	4	)	)	PUNCT
iajs-653	190	5	,	,	PUNCT
iajs-653	190	6	pure	pure	ADJ
iajs-653	190	7	theorie	theorie	NOUN
iajs-653	190	8	,	,	PUNCT
iajs-653	190	9	math.ann	math.ann	X
iajs-653	190	10	.	.	NOUN
iajs-653	190	11	184:1	184:1	NUM
iajs-653	190	12	-	-	SYM
iajs-653	190	13	18	18	NUM
iajs-653	190	14	.	.	PUNCT
iajs-653	191	1	4mohamed	4mohamed	NUM
iajs-653	191	2	,	,	PUNCT
iajs-653	191	3	s.h	s.h	PROPN
iajs-653	191	4	.	.	PROPN
iajs-653	191	5	,and	,and	PUNCT
iajs-653	191	6	muller	muller	PROPN
iajs-653	191	7	b.j	b.j	PROPN
iajs-653	191	8	.	.	PROPN
iajs-653	191	9	,(1990	,(1990	PROPN
iajs-653	191	10	)	)	PUNCT
iajs-653	191	11	,	,	PUNCT
iajs-653	191	12	continuous	continuous	ADJ
iajs-653	191	13	and	and	CCONJ
iajs-653	191	14	discrete	discrete	ADJ
iajs-653	191	15	module	module	NOUN
iajs-653	191	16	,	,	PUNCT
iajs-653	191	17	london	london	PROPN
iajs-653	191	18	math	math	PROPN
iajs-653	191	19	.	.	PUNCT
iajs-653	192	1	soc	soc	PROPN
iajs-653	192	2	.	.	PUNCT
iajs-653	193	1	lns	lns	PROPN
iajs-653	193	2	147	147	NUM
iajs-653	193	3	cambridge	cambridge	PROPN
iajs-653	193	4	univ.press	univ.press	PROPN
iajs-653	193	5	,	,	PUNCT
iajs-653	193	6	cambridge	cambridge	NOUN
iajs-653	193	7	.	.	PUNCT
iajs-653	194	1	5abbas	5abbas	NUM
iajs-653	194	2	,	,	PUNCT
iajs-653	194	3	m.s	m.s	PROPN
iajs-653	194	4	,	,	PUNCT
iajs-653	194	5	(	(	PUNCT
iajs-653	194	6	1990	1990	NUM
iajs-653	194	7	)	)	PUNCT
iajs-653	194	8	,	,	PUNCT
iajs-653	194	9	on	on	ADP
iajs-653	194	10	fully	fully	ADV
iajs-653	194	11	stable	stable	ADJ
iajs-653	194	12	module	module	NOUN
iajs-653	194	13	,	,	PUNCT
iajs-653	194	14	ph.d	ph.d	PROPN
iajs-653	194	15	.	.	PUNCT
iajs-653	195	1	thesis	thesis	NOUN
iajs-653	195	2	.university	.university	NOUN
iajs-653	195	3	of	of	ADP
iajs-653	195	4	baghdad	baghdad	PROPN
iajs-653	195	5	.	.	PUNCT
iajs-653	196	1	6lam	6lam	NUM
iajs-653	196	2	,	,	PUNCT
iajs-653	196	3	t.y	t.y	PROPN
iajs-653	196	4	.	.	PROPN
iajs-653	196	5	,3(2004	,3(2004	PUNCT
iajs-653	196	6	)	)	PUNCT
iajs-653	196	7	acrash	acrash	NOUN
iajs-653	196	8	course	course	NOUN
iajs-653	196	9	on	on	ADP
iajs-653	196	10	stable	stable	ADJ
iajs-653	196	11	range	range	NOUN
iajs-653	196	12	,	,	PUNCT
iajs-653	196	13	cancellation	cancellation	NOUN
iajs-653	196	14	,	,	PUNCT
iajs-653	196	15	substitution	substitution	NOUN
iajs-653	196	16	and	and	CCONJ
iajs-653	196	17	exchange	exchange	NOUN
iajs-653	196	18	.	.	PUNCT
iajs-653	197	1	j.algebra	j.algebra	PROPN
iajs-653	197	2	appl	appl	PROPN
iajs-653	197	3	.	.	PROPN
iajs-653	197	4	,	,	PUNCT
iajs-653	197	5	no	no	INTJ
iajs-653	197	6	.	.	PUNCT
iajs-653	198	1	3:301	3:301	NUM
iajs-653	198	2	-	-	SYM
iajs-653	198	3	343	343	NUM
iajs-653	198	4	.	.	PUNCT
iajs-653	199	1	7el.bast	7el.bast	NUM
iajs-653	199	2	,	,	PUNCT
iajs-653	199	3	abd	abd	PROPN
iajs-653	199	4	,	,	PUNCT
iajs-653	199	5	z	z	PROPN
iajs-653	199	6	and	and	CCONJ
iajs-653	199	7	p.f	p.f	PROPN
iajs-653	199	8	.	.	PROPN
iajs-653	199	9	smith	smith	PROPN
iajs-653	199	10	(	(	PUNCT
iajs-653	199	11	1988	1988	NUM
iajs-653	199	12	)	)	PUNCT
iajs-653	199	13	,	,	PUNCT
iajs-653	199	14	multiplication	multiplication	NOUN
iajs-653	199	15	modules	module	NOUN
iajs-653	199	16	,	,	PUNCT
iajs-653	199	17	comm	comm	NOUN
iajs-653	199	18	.	.	PUNCT
iajs-653	200	1	algebra	algebra	NOUN
iajs-653	200	2	,	,	PUNCT
iajs-653	200	3	16(4	16(4	NUM
iajs-653	200	4	):	):	PUNCT
iajs-653	200	5	755	755	NUM
iajs-653	200	6	-	-	SYM
iajs-653	200	7	779	779	NUM
iajs-653	200	8	.	.	PUNCT
iajs-653	201	1	8shihab	8shihab	PROPN
iajs-653	201	2	b.n	b.n	PROPN
iajs-653	201	3	.	.	PROPN
iajs-653	201	4	,	,	PUNCT
iajs-653	201	5	(	(	PUNCT
iajs-653	201	6	2004	2004	NUM
iajs-653	201	7	)	)	PUNCT
iajs-653	201	8	,	,	PUNCT
iajs-653	201	9	scalar	scalar	ADJ
iajs-653	201	10	reflexive	reflexive	ADJ
iajs-653	201	11	module	module	NOUN
iajs-653	201	12	,	,	PUNCT
iajs-653	201	13	ph.d	ph.d	PROPN
iajs-653	201	14	.	.	PUNCT
iajs-653	202	1	thesis	thesis	NOUN
iajs-653	202	2	.university	.university	NOUN
iajs-653	202	3	of	of	ADP
iajs-653	202	4	baghdad	baghdad	PROPN
iajs-653	202	5	college	college	PROPN
iajs-653	202	6	of	of	ADP
iajs-653	202	7	science	science	NOUN
iajs-653	202	8	.	.	PUNCT
iajs-653	203	1	9mohammed	9mohammed	NUM
iajs-653	203	2	ali	ali	PROPN
iajs-653	203	3	,	,	PUNCT
iajs-653	203	4	e.a.al	e.a.al	PROPN
iajs-653	203	5	-	-	PUNCT
iajs-653	203	6	am	be	AUX
iajs-653	203	7	.(2006	.(2006	NUM
iajs-653	203	8	)	)	PUNCT
iajs-653	203	9	,	,	PUNCT
iajs-653	203	10	on	on	ADP
iajs-653	203	11	ikeda	ikeda	PROPN
iajs-653	203	12	nakayma	nakayma	PROPN
iajs-653	203	13	module	module	NOUN
iajs-653	203	14	,	,	PUNCT
iajs-653	203	15	ph.d	ph.d	PROPN
iajs-653	203	16	.	.	PUNCT
iajs-653	204	1	thesis	thesis	NOUN
iajs-653	204	2	.university	.university	NOUN
iajs-653	204	3	of	of	ADP
iajs-653	204	4	baghdad	baghdad	PROPN
iajs-653	204	5	.	.	PUNCT
iajs-653	205	1	إبن	إبن	VERB
iajs-653	205	2	الهيثم	الهيثم	ADJ
iajs-653	205	3	للعلوم	للعلوم	NOUN
iajs-653	205	4	الصرفة	الصرفة	NOUN
iajs-653	205	5	و	و	PRON
iajs-653	205	6	التطبيقيةمجلة	التطبيقيةمجلة	VERB
iajs-653	205	7	2012	2012	NUM
iajs-653	205	8	السنة	السنة	NOUN
iajs-653	206	1	25	25	NUM
iajs-653	207	1	المجلد	المجلد	NOUN
iajs-653	207	2	2	2	NUM
iajs-653	207	3	العدد	العدد	PROPN
iajs-653	207	4	ibn	ibn	PROPN
iajs-653	207	5	al	al	PROPN
iajs-653	207	6	-	-	PUNCT
iajs-653	207	7	haitham	haitham	PROPN
iajs-653	207	8	journal	journal	PROPN
iajs-653	207	9	for	for	ADP
iajs-653	207	10	pure	pure	ADJ
iajs-653	207	11	and	and	CCONJ
iajs-653	207	12	applied	apply	VERB
iajs-653	207	13	science	science	NOUN
iajs-653	207	14	no	no	NOUN
iajs-653	207	15	.	.	NOUN
iajs-653	207	16	2	2	NUM
iajs-653	207	17	vol	vol	NOUN
iajs-653	207	18	.	.	PUNCT
iajs-653	208	1	25	25	NUM
iajs-653	208	2	year	year	NOUN
iajs-653	208	3	2012	2012	NUM
iajs-653	208	4	ةالنقي	ةالنقي	PROPN
iajs-653	208	5	éالمضادةالمقاسات	éالمضادةالمقاسات	PROPN
iajs-653	208	6	الهوبفيني	الهوبفيني	PROPN
iajs-653	208	7	زينب	زينب	ADJ
iajs-653	208	8	طالب	طالب	NOUN
iajs-653	208	9	سلمان	سلمان	NOUN
iajs-653	208	10	قسم	قسم	DET
iajs-653	208	11	الرياضيات	الرياضيات	PROPN
iajs-653	208	12	،	،	PROPN
iajs-653	208	13	كلية	كلية	PROPN
iajs-653	208	14	العلوم	العلوم	PROPN
iajs-653	208	15	،	،	PROPN
iajs-653	208	16	جامعة	جامعة	PROPN
iajs-653	208	17	بغداد	بغداد	PROPN
iajs-653	208	18	2012	2012	NUM
iajs-653	208	19	كانون	كانون	NOUN
iajs-653	208	20	الثاني	الثاني	PROPN
iajs-653	208	21	11	11	NUM
iajs-653	208	22	:	:	PUNCT
iajs-653	208	23	قبل	قبل	NOUN
iajs-653	208	24	البحث	البحث	VERB
iajs-653	208	25	في	في	ADP
iajs-653	208	26	2011ايلول	2011ايلول	PROPN
iajs-653	208	27	22	22	NUM
iajs-653	208	28	:	:	PUNCT
iajs-653	208	29	استلم	استلم	PROPN
iajs-653	208	30	البحث	البحث	VERB
iajs-653	208	31	في	في	ADP
iajs-653	208	32	ةالخالص	ةالخالص	NOUN
iajs-653	208	33	.	.	PUNCT
iajs-653	209	1	في	في	PRON
iajs-653	209	2	هذا	هذا	NOUN
iajs-653	209	3	البحث	البحث	NOUN
iajs-653	209	4	نقدم	نقدم	NOUN
iajs-653	209	5	مفهوم	مفهوم	NOUN
iajs-653	209	6	مقاسا	مقاسا	NOUN
iajs-653	209	7	احاديا	احاديا	VERB
iajs-653	209	8	غير	غير	AUX
iajs-653	209	9	صفري	صفري	VERB
iajs-653	209	10	معرفا	معرفا	PROPN
iajs-653	209	11	عليها	عليها	PROPN
iajs-653	209	12	mحلقه	mحلقه	PROPN
iajs-653	209	13	تجميعيه	تجميعيه	ADJ
iajs-653	209	14	ذا	ذا	PROPN
iajs-653	209	15	عنصر	عنصر	PROPN
iajs-653	209	16	محايد	محايد	NOUN
iajs-653	209	17	،	،	X
iajs-653	209	18	rلتكن	rلتكن	PROPN
iajs-653	209	19	f	f	PROPN
iajs-653	209	20	î	î	PROPN
iajs-653	209	21	end	end	NOUN
iajs-653	209	22	(	(	PUNCT
iajs-653	209	23	m	m	NOUN
iajs-653	209	24	)	)	PUNCT
iajs-653	209	25	مقاسا	مقاسا	NOUN
iajs-653	209	26	هوبفينيا	هوبفينيا	PROPN
iajs-653	209	27	مضادا	مضادا	VERB
iajs-653	209	28	اذا	اذا	NOUN
iajs-653	209	29	كان	كان	PROPN
iajs-653	209	30	لكل	لكل	NUM
iajs-653	209	31	rعلى	rعلى	PROPN
iajs-653	209	32	حلقه	حلقه	NOUN
iajs-653	209	33	mيقال	mيقال	PROPN
iajs-653	209	34	عن	عن	PROPN
iajs-653	209	35	مقاس	مقاس	PROPN
iajs-653	209	36	¡	¡	PROPN
iajs-653	209	37	ðç	ðç	PROPN
iajs-653	209	38	ةالنقي	ةالنقي	PROPN
iajs-653	209	39	éالمضادةالمقاسات	éالمضادةالمقاسات	PROPN
iajs-653	209	40	الهوفيني	الهوفيني	PROPN
iajs-653	209	41	¡	¡	PROPN
iajs-653	210	1	f	f	PROPN
iajs-653	210	2	فان	فان	PROPN
iajs-653	210	3	ةمتباين	ةمتباين	PROPN
iajs-653	210	4	ةدالimf	ةدالimf	PROPN
iajs-653	210	5	نقي	نقي	PROPN
iajs-653	210	6	فيm	فيm	ADV
iajs-653	210	7	واعطينا	واعطينا	PROPN
iajs-653	210	8	بعض	بعض	NOUN
iajs-653	210	9	خواص	خواص	ADV
iajs-653	210	10	هذا	هذا	VERB
iajs-653	210	11	النوع	النوع	PROPN
iajs-653	210	12	من	من	DET
iajs-653	210	13	المقاسات	المقاسات	PROPN
iajs-653	210	14	.	.	PUNCT
iajs-653	210	15	.	.	PUNCT
iajs-653	211	1	éمضاد	éمضاد	VERB
iajs-653	211	2	ة	ة	PROPN
iajs-653	211	3	،	،	PROPN
iajs-653	211	4	مقاسات	مقاسات	PROPN
iajs-653	211	5	هوفيني	هوفيني	PROPN
iajs-653	211	6	éمضاد	éمضاد	VERB
iajs-653	211	7	ةهوفيني	ةهوفيني	PROPN
iajs-653	211	8	ة	ة	PROPN
iajs-653	211	9	،	،	PROPN
iajs-653	211	10	مقاسات	مقاسات	PROPN
iajs-653	211	11	شب	شب	ADP
iajs-653	211	12	ةنقي	ةنقي	PROPN
iajs-653	211	13	éمضاد	éمضاد	PROPN
iajs-653	211	14	ةمقاسات	ةمقاسات	NOUN
iajs-653	211	15	هوفيني	هوفيني	ADV
iajs-653	211	16	:	:	PUNCT
iajs-653	211	17	ةالكلمات	ةالكلمات	VERB
iajs-653	211	18	المفتاحي	المفتاحي	ADJ