id	sid	tid	token	lemma	pos
iajs-156	1	1	microsoft	microsoft	PROPN
iajs-156	1	2	word	word	NOUN
iajs-156	1	3	235	235	NUM
iajs-156	1	4	-	-	SYM
iajs-156	1	5	244	244	NUM
iajs-156	1	6	235	235	NUM
iajs-156	1	7	|	|	NOUN
iajs-156	1	8	mathematics	mathematic	NOUN
iajs-156	1	9	2015	2015	NUM
iajs-156	1	10	)	)	PUNCT
iajs-156	1	11	عام	عام	ADP
iajs-156	1	12	3العدد	3العدد	NUM
iajs-156	1	13	(	(	PUNCT
iajs-156	1	14	28مجلة	28مجلة	X
iajs-156	1	15	إبن	إبن	VERB
iajs-156	1	16	الھيثم	الھيثم	NOUN
iajs-156	1	17	للعلوم	للعلوم	NOUN
iajs-156	1	18	الصرفة	الصرفة	NOUN
iajs-156	2	1	و	و	PRON
iajs-156	2	2	التطبيقية	التطبيقية	ADV
iajs-156	2	3	المجلد	المجلد	VERB
iajs-156	2	4	ibn	ibn	PROPN
iajs-156	2	5	al	al	PROPN
iajs-156	2	6	-	-	PUNCT
iajs-156	2	7	haitham	haitham	PROPN
iajs-156	2	8	jour	jour	X
iajs-156	2	9	.	.	PROPN
iajs-156	3	1	for	for	ADP
iajs-156	3	2	pure	pure	ADJ
iajs-156	3	3	&	&	CCONJ
iajs-156	3	4	appl	appl	PROPN
iajs-156	3	5	.	.	PUNCT
iajs-156	4	1	sci	sci	PROPN
iajs-156	4	2	.	.	PUNCT
iajs-156	4	3	vol	vol	NOUN
iajs-156	4	4	.	.	PROPN
iajs-156	5	1	28	28	NUM
iajs-156	5	2	(	(	PUNCT
iajs-156	5	3	3	3	NUM
iajs-156	5	4	)	)	PUNCT
iajs-156	5	5	2015	2015	NUM
iajs-156	5	6	2	2	NUM
iajs-156	5	7	-	-	PUNCT
iajs-156	5	8	regular	regular	ADJ
iajs-156	5	9	modules	module	NOUN
iajs-156	5	10	ii	ii	PROPN
iajs-156	5	11	nuhad	nuhad	VERB
iajs-156	5	12	s.al	s.al	ADJ
iajs-156	5	13	-	-	PUNCT
iajs-156	5	14	mothafar	mothafar	PROPN
iajs-156	5	15	dept	dept	NOUN
iajs-156	5	16	.	.	PUNCT
iajs-156	6	1	of	of	ADP
iajs-156	6	2	mathematic/	mathematic/	NUM
iajs-156	6	3	college	college	NOUN
iajs-156	6	4	of	of	ADP
iajs-156	6	5	science/	science/	NUM
iajs-156	6	6	university	university	PROPN
iajs-156	6	7	of	of	ADP
iajs-156	6	8	baghdad	baghdad	PROPN
iajs-156	6	9	ghaleb	ghaleb	PROPN
iajs-156	6	10	a.	a.	PROPN
iajs-156	6	11	humod	humod	PROPN
iajs-156	6	12	dept	dept	PROPN
iajs-156	6	13	.	.	PROPN
iajs-156	7	1	of	of	ADP
iajs-156	7	2	mathematic/	mathematic/	NUM
iajs-156	7	3	college	college	NOUN
iajs-156	7	4	of	of	ADP
iajs-156	7	5	education	education	NOUN
iajs-156	7	6	for	for	ADP
iajs-156	7	7	pure	pure	ADJ
iajs-156	7	8	science	science	NOUN
iajs-156	7	9	(	(	PUNCT
iajs-156	7	10	ibn	ibn	PROPN
iajs-156	7	11	al	al	PROPN
iajs-156	7	12	-	-	PUNCT
iajs-156	7	13	haitham)/	haitham)/	PROPN
iajs-156	7	14	university	university	NOUN
iajs-156	7	15	of	of	ADP
iajs-156	7	16	baghdad	baghdad	PROPN
iajs-156	7	17	received	receive	VERB
iajs-156	7	18	in:28	in:28	PROPN
iajs-156	7	19	/	/	SYM
iajs-156	7	20	march/2015,accepted	march/2015,accepte	VERB
iajs-156	7	21	in:7	in:7	PROPN
iajs-156	7	22	/	/	SYM
iajs-156	7	23	june/2015	june/2015	PROPN
iajs-156	7	24	abstract	abstract	VERB
iajs-156	7	25	an	an	DET
iajs-156	7	26	r	r	NOUN
iajs-156	7	27	-	-	PUNCT
iajs-156	7	28	module	module	NOUN
iajs-156	7	29	m	m	NOUN
iajs-156	7	30	is	be	AUX
iajs-156	7	31	called	call	VERB
iajs-156	7	32	a	a	DET
iajs-156	7	33	2	2	NUM
iajs-156	7	34	-	-	PUNCT
iajs-156	7	35	regular	regular	ADJ
iajs-156	7	36	module	module	NOUN
iajs-156	7	37	if	if	SCONJ
iajs-156	7	38	every	every	DET
iajs-156	7	39	submodule	submodule	NOUN
iajs-156	7	40	n	n	PROPN
iajs-156	7	41	of	of	ADP
iajs-156	7	42	m	m	PROPN
iajs-156	7	43	is	be	AUX
iajs-156	7	44	2	2	NUM
iajs-156	7	45	-	-	PUNCT
iajs-156	7	46	pure	pure	ADJ
iajs-156	7	47	submodule	submodule	NOUN
iajs-156	7	48	,	,	PUNCT
iajs-156	7	49	where	where	SCONJ
iajs-156	7	50	a	a	DET
iajs-156	7	51	submodule	submodule	NOUN
iajs-156	7	52	n	n	PROPN
iajs-156	7	53	of	of	ADP
iajs-156	7	54	m	m	PROPN
iajs-156	7	55	is	be	AUX
iajs-156	7	56	2	2	NUM
iajs-156	7	57	-	-	ADJ
iajs-156	7	58	pure	pure	ADJ
iajs-156	7	59	in	in	ADP
iajs-156	7	60	m	m	PROPN
iajs-156	7	61	if	if	SCONJ
iajs-156	7	62	for	for	ADP
iajs-156	7	63	every	every	DET
iajs-156	7	64	ideal	ideal	NOUN
iajs-156	7	65	i	i	PRON
iajs-156	7	66	of	of	ADP
iajs-156	7	67	r	r	NOUN
iajs-156	7	68	,	,	PUNCT
iajs-156	7	69	i2mn	i2mn	NOUN
iajs-156	7	70	=	=	SYM
iajs-156	7	71	i2n	i2n	NOUN
iajs-156	7	72	,	,	PUNCT
iajs-156	7	73	[	[	X
iajs-156	7	74	1	1	NUM
iajs-156	7	75	]	]	PUNCT
iajs-156	7	76	.	.	PUNCT
iajs-156	8	1	this	this	DET
iajs-156	8	2	paper	paper	NOUN
iajs-156	8	3	is	be	AUX
iajs-156	8	4	a	a	DET
iajs-156	8	5	continuation	continuation	NOUN
iajs-156	8	6	of	of	ADP
iajs-156	8	7	[	[	X
iajs-156	8	8	1	1	NUM
iajs-156	8	9	]	]	PUNCT
iajs-156	8	10	.	.	PUNCT
iajs-156	9	1	we	we	PRON
iajs-156	9	2	give	give	VERB
iajs-156	9	3	some	some	DET
iajs-156	9	4	conditions	condition	NOUN
iajs-156	9	5	to	to	PART
iajs-156	9	6	characterize	characterize	VERB
iajs-156	9	7	this	this	DET
iajs-156	9	8	class	class	NOUN
iajs-156	9	9	of	of	ADP
iajs-156	9	10	modules	module	NOUN
iajs-156	9	11	,	,	PUNCT
iajs-156	9	12	also	also	ADV
iajs-156	9	13	many	many	ADJ
iajs-156	9	14	relationships	relationship	NOUN
iajs-156	9	15	with	with	ADP
iajs-156	9	16	other	other	ADJ
iajs-156	9	17	related	related	ADJ
iajs-156	9	18	concepts	concept	NOUN
iajs-156	9	19	are	be	AUX
iajs-156	9	20	introduced	introduce	VERB
iajs-156	9	21	.	.	PUNCT
iajs-156	10	1	key	key	ADJ
iajs-156	10	2	words	word	NOUN
iajs-156	10	3	:	:	PUNCT
iajs-156	10	4	2	2	NUM
iajs-156	10	5	-	-	PUNCT
iajs-156	10	6	pure	pure	ADJ
iajs-156	10	7	submodules	submodule	NOUN
iajs-156	10	8	,	,	PUNCT
iajs-156	10	9	2	2	NUM
iajs-156	10	10	-	-	PUNCT
iajs-156	10	11	regular	regular	ADJ
iajs-156	10	12	modules	module	NOUN
iajs-156	10	13	,	,	PUNCT
iajs-156	10	14	pure	pure	ADJ
iajs-156	10	15	submodule	submodule	NOUN
iajs-156	10	16	,	,	PUNCT
iajs-156	10	17	regular	regular	ADJ
iajs-156	10	18	modules	module	NOUN
iajs-156	10	19	.	.	PUNCT
iajs-156	11	1	236	236	NUM
iajs-156	11	2	|	|	NOUN
iajs-156	11	3	mathematics	mathematic	NOUN
iajs-156	11	4	2015	2015	NUM
iajs-156	11	5	)	)	PUNCT
iajs-156	11	6	عام	عام	ADP
iajs-156	11	7	3العدد	3العدد	NUM
iajs-156	11	8	(	(	PUNCT
iajs-156	11	9	28مجلة	28مجلة	X
iajs-156	11	10	إبن	إبن	VERB
iajs-156	11	11	الھيثم	الھيثم	NOUN
iajs-156	11	12	للعلوم	للعلوم	NOUN
iajs-156	11	13	الصرفة	الصرفة	NOUN
iajs-156	12	1	و	و	PRON
iajs-156	12	2	التطبيقية	التطبيقية	ADV
iajs-156	12	3	المجلد	المجلد	VERB
iajs-156	12	4	ibn	ibn	PROPN
iajs-156	12	5	al	al	PROPN
iajs-156	12	6	-	-	PUNCT
iajs-156	12	7	haitham	haitham	PROPN
iajs-156	12	8	jour	jour	X
iajs-156	12	9	.	.	PROPN
iajs-156	13	1	for	for	ADP
iajs-156	13	2	pure	pure	ADJ
iajs-156	13	3	&	&	CCONJ
iajs-156	13	4	appl	appl	PROPN
iajs-156	13	5	.	.	PUNCT
iajs-156	14	1	sci	sci	PROPN
iajs-156	14	2	.	.	PUNCT
iajs-156	14	3	vol	vol	NOUN
iajs-156	14	4	.	.	PROPN
iajs-156	15	1	28	28	NUM
iajs-156	15	2	(	(	PUNCT
iajs-156	15	3	3	3	NUM
iajs-156	15	4	)	)	PUNCT
iajs-156	15	5	2015	2015	NUM
iajs-156	15	6	0introduction	0introduction	NUM
iajs-156	15	7	throughout	throughout	ADP
iajs-156	15	8	this	this	DET
iajs-156	15	9	paper	paper	NOUN
iajs-156	15	10	,	,	PUNCT
iajs-156	15	11	r	r	NOUN
iajs-156	15	12	is	be	AUX
iajs-156	15	13	a	a	DET
iajs-156	15	14	commutative	commutative	ADJ
iajs-156	15	15	ring	ring	NOUN
iajs-156	15	16	with	with	ADP
iajs-156	15	17	identity	identity	NOUN
iajs-156	15	18	and	and	CCONJ
iajs-156	15	19	all	all	DET
iajs-156	15	20	r	r	NOUN
iajs-156	15	21	-	-	PUNCT
iajs-156	15	22	modules	module	NOUN
iajs-156	15	23	are	be	AUX
iajs-156	15	24	unitary	unitary	ADJ
iajs-156	15	25	.	.	PUNCT
iajs-156	16	1	a	a	DET
iajs-156	16	2	submodule	submodule	NOUN
iajs-156	16	3	n	n	PROPN
iajs-156	16	4	of	of	ADP
iajs-156	16	5	an	an	DET
iajs-156	16	6	r	r	NOUN
iajs-156	16	7	-	-	PUNCT
iajs-156	16	8	module	module	NOUN
iajs-156	16	9	m	m	NOUN
iajs-156	16	10	is	be	AUX
iajs-156	16	11	called	call	VERB
iajs-156	16	12	2	2	NUM
iajs-156	16	13	-	-	PUNCT
iajs-156	16	14	pure	pure	ADJ
iajs-156	16	15	submodule	submodule	NOUN
iajs-156	16	16	if	if	SCONJ
iajs-156	16	17	for	for	ADP
iajs-156	16	18	every	every	DET
iajs-156	16	19	ideal	ideal	NOUN
iajs-156	16	20	i	i	PRON
iajs-156	16	21	of	of	ADP
iajs-156	16	22	r	r	NOUN
iajs-156	16	23	,	,	PUNCT
iajs-156	16	24	i2mn	i2mn	NOUN
iajs-156	16	25	=	=	PUNCT
iajs-156	16	26	i2n	i2n	NOUN
iajs-156	16	27	.	.	PUNCT
iajs-156	17	1	if	if	SCONJ
iajs-156	17	2	every	every	DET
iajs-156	17	3	submodule	submodule	NOUN
iajs-156	17	4	of	of	ADP
iajs-156	17	5	m	m	PROPN
iajs-156	17	6	is	be	AUX
iajs-156	17	7	2	2	NUM
iajs-156	17	8	-	-	PUNCT
iajs-156	17	9	pure	pure	ADJ
iajs-156	17	10	,	,	PUNCT
iajs-156	17	11	then	then	ADV
iajs-156	17	12	m	m	VERB
iajs-156	17	13	is	be	AUX
iajs-156	17	14	said	say	VERB
iajs-156	17	15	to	to	PART
iajs-156	17	16	be	be	AUX
iajs-156	17	17	2	2	NUM
iajs-156	17	18	-	-	PUNCT
iajs-156	17	19	regular	regular	ADJ
iajs-156	17	20	module	module	NOUN
iajs-156	17	21	.	.	PUNCT
iajs-156	18	1	this	this	DET
iajs-156	18	2	work	work	NOUN
iajs-156	18	3	consists	consist	VERB
iajs-156	18	4	of	of	ADP
iajs-156	18	5	two	two	NUM
iajs-156	18	6	sections	section	NOUN
iajs-156	18	7	.	.	PUNCT
iajs-156	19	1	in	in	ADP
iajs-156	19	2	the	the	DET
iajs-156	19	3	first	first	ADJ
iajs-156	19	4	section	section	NOUN
iajs-156	19	5	we	we	PRON
iajs-156	19	6	give	give	VERB
iajs-156	19	7	some	some	DET
iajs-156	19	8	properties	property	NOUN
iajs-156	19	9	of	of	ADP
iajs-156	19	10	2	2	NUM
iajs-156	19	11	-	-	PUNCT
iajs-156	19	12	regular	regular	ADJ
iajs-156	19	13	rings	ring	NOUN
iajs-156	19	14	.	.	PUNCT
iajs-156	20	1	next	next	ADV
iajs-156	20	2	we	we	PRON
iajs-156	20	3	present	present	VERB
iajs-156	20	4	a	a	DET
iajs-156	20	5	characterization	characterization	NOUN
iajs-156	20	6	of	of	ADP
iajs-156	20	7	2	2	NUM
iajs-156	20	8	-	-	PUNCT
iajs-156	20	9	regular	regular	ADJ
iajs-156	20	10	modules	module	NOUN
iajs-156	20	11	.	.	PUNCT
iajs-156	21	1	in	in	ADP
iajs-156	21	2	the	the	DET
iajs-156	21	3	second	second	ADJ
iajs-156	21	4	section	section	NOUN
iajs-156	21	5	we	we	PRON
iajs-156	21	6	illustrate	illustrate	VERB
iajs-156	21	7	some	some	DET
iajs-156	21	8	relationships	relationship	NOUN
iajs-156	21	9	between	between	ADP
iajs-156	21	10	the	the	DET
iajs-156	21	11	concept	concept	NOUN
iajs-156	21	12	2	2	NUM
iajs-156	21	13	-	-	PUNCT
iajs-156	21	14	regular	regular	ADJ
iajs-156	21	15	modules	module	NOUN
iajs-156	21	16	and	and	CCONJ
iajs-156	21	17	other	other	ADJ
iajs-156	21	18	modules	module	NOUN
iajs-156	21	19	such	such	ADJ
iajs-156	21	20	as	as	ADP
iajs-156	21	21	semiprime	semiprime	NOUN
iajs-156	21	22	divisible	divisible	ADJ
iajs-156	21	23	,	,	PUNCT
iajs-156	21	24	projective	projective	ADJ
iajs-156	21	25	and	and	CCONJ
iajs-156	21	26	multiplication	multiplication	NOUN
iajs-156	21	27	modules	module	NOUN
iajs-156	21	28	.	.	PUNCT
iajs-156	22	1	12	12	NUM
iajs-156	22	2	-	-	PUNCT
iajs-156	22	3	regular	regular	ADJ
iajs-156	22	4	modules	module	NOUN
iajs-156	22	5	in	in	ADP
iajs-156	22	6	this	this	DET
iajs-156	22	7	section	section	NOUN
iajs-156	22	8	,	,	PUNCT
iajs-156	22	9	we	we	PRON
iajs-156	22	10	first	first	ADV
iajs-156	22	11	define	define	VERB
iajs-156	22	12	2	2	NUM
iajs-156	22	13	-	-	PUNCT
iajs-156	22	14	regular	regular	ADJ
iajs-156	22	15	rings	ring	NOUN
iajs-156	22	16	and	and	CCONJ
iajs-156	22	17	study	study	VERB
iajs-156	22	18	some	some	PRON
iajs-156	22	19	of	of	ADP
iajs-156	22	20	its	its	PRON
iajs-156	22	21	properties	property	NOUN
iajs-156	22	22	.	.	PUNCT
iajs-156	23	1	next	next	ADV
iajs-156	23	2	we	we	PRON
iajs-156	23	3	consider	consider	VERB
iajs-156	23	4	some	some	DET
iajs-156	23	5	conditions	condition	NOUN
iajs-156	23	6	to	to	PART
iajs-156	23	7	characterize	characterize	VERB
iajs-156	23	8	2	2	NUM
iajs-156	23	9	-	-	PUNCT
iajs-156	23	10	regular	regular	ADJ
iajs-156	23	11	modules	module	NOUN
iajs-156	23	12	.	.	PUNCT
iajs-156	24	1	definition	definition	NOUN
iajs-156	24	2	(	(	PUNCT
iajs-156	24	3	1.1	1.1	NUM
iajs-156	24	4	):	):	PUNCT
iajs-156	24	5	[	[	X
iajs-156	24	6	1	1	X
iajs-156	24	7	]	]	PUNCT
iajs-156	24	8	an	an	DET
iajs-156	24	9	ideal	ideal	NOUN
iajs-156	24	10	i	i	PRON
iajs-156	24	11	of	of	ADP
iajs-156	24	12	a	a	DET
iajs-156	24	13	ring	ring	NOUN
iajs-156	24	14	r	r	NOUN
iajs-156	24	15	is	be	AUX
iajs-156	24	16	called	call	VERB
iajs-156	24	17	2	2	NUM
iajs-156	24	18	-	-	PUNCT
iajs-156	24	19	pure	pure	ADJ
iajs-156	24	20	ideal	ideal	NOUN
iajs-156	24	21	of	of	ADP
iajs-156	24	22	r	r	NOUN
iajs-156	24	23	if	if	SCONJ
iajs-156	24	24	for	for	ADP
iajs-156	24	25	each	each	DET
iajs-156	24	26	ideal	ideal	ADJ
iajs-156	24	27	j	j	PROPN
iajs-156	24	28	of	of	ADP
iajs-156	24	29	r	r	PROPN
iajs-156	24	30	,	,	PUNCT
iajs-156	24	31	j2	j2	PROPN
iajs-156	24	32			PUNCT
iajs-156	24	33	i	i	PROPN
iajs-156	24	34	=	=	SYM
iajs-156	24	35	j2i	j2i	PROPN
iajs-156	24	36	.	.	PUNCT
iajs-156	25	1	if	if	SCONJ
iajs-156	25	2	every	every	DET
iajs-156	25	3	ideal	ideal	NOUN
iajs-156	25	4	of	of	ADP
iajs-156	25	5	a	a	DET
iajs-156	25	6	ring	ring	NOUN
iajs-156	25	7	r	r	NOUN
iajs-156	25	8	is	be	AUX
iajs-156	25	9	2	2	NUM
iajs-156	25	10	-	-	PUNCT
iajs-156	25	11	pure	pure	ADJ
iajs-156	25	12	ideal	ideal	NOUN
iajs-156	25	13	,	,	PUNCT
iajs-156	25	14	then	then	ADV
iajs-156	25	15	we	we	PRON
iajs-156	25	16	say	say	VERB
iajs-156	25	17	r	r	NOUN
iajs-156	25	18	is	be	AUX
iajs-156	25	19	2	2	NUM
iajs-156	25	20	-	-	PUNCT
iajs-156	25	21	regular	regular	ADJ
iajs-156	25	22	ring	ring	NOUN
iajs-156	25	23	.	.	PUNCT
iajs-156	26	1	remarks	remark	NOUN
iajs-156	26	2	and	and	CCONJ
iajs-156	26	3	examples	example	NOUN
iajs-156	26	4	(	(	PUNCT
iajs-156	26	5	1.2	1.2	NUM
iajs-156	26	6	):	):	PUNCT
iajs-156	26	7	(	(	PUNCT
iajs-156	26	8	1	1	X
iajs-156	26	9	)	)	PUNCT
iajs-156	26	10	it	it	PRON
iajs-156	26	11	is	be	AUX
iajs-156	26	12	clear	clear	ADJ
iajs-156	26	13	every	every	PRON
iajs-156	26	14	(	(	PUNCT
iajs-156	26	15	von	von	PROPN
iajs-156	26	16	neumman	neumman	PROPN
iajs-156	26	17	)	)	PUNCT
iajs-156	26	18	regular	regular	ADJ
iajs-156	26	19	ring	ring	NOUN
iajs-156	26	20	is	be	AUX
iajs-156	26	21	2	2	NUM
iajs-156	26	22	-	-	PUNCT
iajs-156	26	23	regular	regular	ADJ
iajs-156	26	24	ring	ring	NOUN
iajs-156	26	25	,	,	PUNCT
iajs-156	26	26	but	but	CCONJ
iajs-156	26	27	the	the	DET
iajs-156	26	28	converse	converse	NOUN
iajs-156	26	29	is	be	AUX
iajs-156	26	30	not	not	PART
iajs-156	26	31	true	true	ADJ
iajs-156	26	32	,	,	PUNCT
iajs-156	26	33	for	for	ADP
iajs-156	26	34	example	example	NOUN
iajs-156	26	35	:	:	PUNCT
iajs-156	26	36	the	the	DET
iajs-156	26	37	ring	ring	NOUN
iajs-156	26	38	z4	z4	PROPN
iajs-156	26	39	is	be	AUX
iajs-156	26	40	2	2	NUM
iajs-156	26	41	-	-	PUNCT
iajs-156	26	42	regular	regular	ADJ
iajs-156	26	43	ring	ring	NOUN
iajs-156	26	44	,	,	PUNCT
iajs-156	26	45	since	since	SCONJ
iajs-156	26	46	every	every	DET
iajs-156	26	47	ideal	ideal	NOUN
iajs-156	26	48	of	of	ADP
iajs-156	26	49	z4	z4	PROPN
iajs-156	26	50	is	be	AUX
iajs-156	26	51	2	2	NUM
iajs-156	26	52	-	-	PUNCT
iajs-156	26	53	pure	pure	ADJ
iajs-156	26	54	.	.	PUNCT
iajs-156	27	1	but	but	CCONJ
iajs-156	27	2	z4	z4	PROPN
iajs-156	27	3	is	be	AUX
iajs-156	27	4	not	not	PART
iajs-156	27	5	regular	regular	ADJ
iajs-156	27	6	since	since	SCONJ
iajs-156	27	7	the	the	DET
iajs-156	27	8	ideal	ideal	NOUN
iajs-156	27	9	{	{	PUNCT
iajs-156	27	10	0	0	NUM
iajs-156	27	11	,	,	PUNCT
iajs-156	27	12	2	2	NUM
iajs-156	27	13	}	}	PUNCT
iajs-156	27	14	is	be	AUX
iajs-156	27	15	not	not	PART
iajs-156	27	16	pure	pure	ADJ
iajs-156	27	17	because	because	SCONJ
iajs-156	27	18	{	{	PUNCT
iajs-156	27	19	0	0	NUM
iajs-156	27	20	,	,	PUNCT
iajs-156	27	21	2	2	NUM
iajs-156	27	22	}	}	PUNCT
iajs-156	27	23	{	{	PUNCT
iajs-156	27	24	0	0	NUM
iajs-156	27	25	,	,	PUNCT
iajs-156	27	26	2	2	NUM
iajs-156	27	27	}	}	PUNCT
iajs-156	27	28	{	{	PUNCT
iajs-156	27	29	0	0	NUM
iajs-156	27	30	,	,	PUNCT
iajs-156	27	31	2}	2}	NOUN
iajs-156	27	32			NOUN
iajs-156	27	33	,	,	PUNCT
iajs-156	27	34	on	on	ADP
iajs-156	27	35	the	the	DET
iajs-156	27	36	other	other	ADJ
iajs-156	27	37	hand	hand	NOUN
iajs-156	27	38	{	{	PUNCT
iajs-156	27	39	0	0	NUM
iajs-156	27	40	,	,	PUNCT
iajs-156	27	41	2	2	NUM
iajs-156	27	42	}	}	PUNCT
iajs-156	27	43	{	{	PUNCT
iajs-156	27	44	0	0	NUM
iajs-156	27	45	,	,	PUNCT
iajs-156	27	46	2	2	NUM
iajs-156	27	47	}	}	PUNCT
iajs-156	27	48	{	{	PUNCT
iajs-156	27	49	0}	0}	NUM
iajs-156	27	50			PROPN
iajs-156	27	51	implies	imply	VERB
iajs-156	27	52	{	{	PUNCT
iajs-156	27	53	0	0	NUM
iajs-156	27	54	,	,	PUNCT
iajs-156	27	55	2	2	NUM
iajs-156	27	56	}	}	PUNCT
iajs-156	27	57	{	{	PUNCT
iajs-156	27	58	0	0	NUM
iajs-156	27	59	,	,	PUNCT
iajs-156	27	60	2	2	NUM
iajs-156	27	61	}	}	PUNCT
iajs-156	27	62	{	{	PUNCT
iajs-156	27	63	0	0	NUM
iajs-156	27	64	,	,	PUNCT
iajs-156	27	65	2	2	NUM
iajs-156	27	66	}	}	PUNCT
iajs-156	27	67	{	{	PUNCT
iajs-156	27	68	0	0	NUM
iajs-156	27	69	,	,	PUNCT
iajs-156	27	70	2}	2}	NOUN
iajs-156	27	71			PROPN
iajs-156	27	72			PROPN
iajs-156	27	73	.	.	PUNCT
iajs-156	28	1	(	(	PUNCT
iajs-156	28	2	2	2	X
iajs-156	28	3	)	)	PUNCT
iajs-156	28	4	it	it	PRON
iajs-156	28	5	is	be	AUX
iajs-156	28	6	clear	clear	ADJ
iajs-156	28	7	that	that	SCONJ
iajs-156	28	8	{	{	PUNCT
iajs-156	28	9	0	0	NUM
iajs-156	28	10	}	}	PUNCT
iajs-156	28	11	and	and	CCONJ
iajs-156	28	12	r	r	NOUN
iajs-156	28	13	are	be	AUX
iajs-156	28	14	always	always	ADV
iajs-156	28	15	2	2	NUM
iajs-156	28	16	-	-	PUNCT
iajs-156	28	17	pure	pure	ADJ
iajs-156	28	18	ideals	ideal	NOUN
iajs-156	28	19	of	of	ADP
iajs-156	28	20	any	any	DET
iajs-156	28	21	ring	ring	NOUN
iajs-156	28	22	r.	r.	NOUN
iajs-156	28	23	(	(	PUNCT
iajs-156	28	24	3	3	X
iajs-156	28	25	)	)	PUNCT
iajs-156	28	26	every	every	DET
iajs-156	28	27	field	field	NOUN
iajs-156	28	28	is	be	AUX
iajs-156	28	29	2	2	NUM
iajs-156	28	30	-	-	PUNCT
iajs-156	28	31	regular	regular	ADJ
iajs-156	28	32	ring	ring	NOUN
iajs-156	28	33	.	.	PUNCT
iajs-156	29	1	(	(	PUNCT
iajs-156	29	2	4	4	X
iajs-156	29	3	)	)	PUNCT
iajs-156	29	4	let	let	VERB
iajs-156	29	5	r	r	PRON
iajs-156	29	6	be	be	AUX
iajs-156	29	7	an	an	DET
iajs-156	29	8	integral	integral	ADJ
iajs-156	29	9	domain	domain	NOUN
iajs-156	29	10	.	.	PUNCT
iajs-156	30	1	if	if	SCONJ
iajs-156	30	2	r	r	NOUN
iajs-156	30	3	is	be	AUX
iajs-156	30	4	2	2	NUM
iajs-156	30	5	-	-	PUNCT
iajs-156	30	6	regular	regular	ADJ
iajs-156	30	7	ring	ring	NOUN
iajs-156	30	8	,	,	PUNCT
iajs-156	30	9	then	then	ADV
iajs-156	30	10	r	r	NOUN
iajs-156	30	11	is	be	AUX
iajs-156	30	12	a	a	DET
iajs-156	30	13	field	field	NOUN
iajs-156	30	14	.	.	PUNCT
iajs-156	31	1	proof	proof	NOUN
iajs-156	31	2	:	:	PUNCT
iajs-156	31	3	let	let	VERB
iajs-156	31	4	i	i	PRON
iajs-156	31	5	be	be	AUX
iajs-156	31	6	an	an	DET
iajs-156	31	7	ideal	ideal	NOUN
iajs-156	31	8	of	of	ADP
iajs-156	31	9	r.	r.	PROPN
iajs-156	31	10	since	since	SCONJ
iajs-156	31	11	r	r	NOUN
iajs-156	31	12	is	be	AUX
iajs-156	31	13	2	2	NUM
iajs-156	31	14	-	-	PUNCT
iajs-156	31	15	regular	regular	ADJ
iajs-156	31	16	ring	ring	NOUN
iajs-156	31	17	then	then	ADV
iajs-156	31	18	j2	j2	PROPN
iajs-156	31	19			PUNCT
iajs-156	31	20	i	i	NOUN
iajs-156	31	21	=	=	PUNCT
iajs-156	31	22	j2i	j2i	PROPN
iajs-156	31	23	for	for	ADP
iajs-156	31	24	every	every	DET
iajs-156	31	25	ideal	ideal	ADJ
iajs-156	31	26	j	j	PROPN
iajs-156	31	27	of	of	ADP
iajs-156	31	28	r.	r.	PROPN
iajs-156	31	29	if	if	SCONJ
iajs-156	31	30	we	we	PRON
iajs-156	31	31	take	take	VERB
iajs-156	31	32	j	j	NOUN
iajs-156	32	1	=	=	PRON
iajs-156	32	2	i	i	PRON
iajs-156	32	3	implies	imply	VERB
iajs-156	32	4	i2	i2	PROPN
iajs-156	32	5	=	=	SYM
iajs-156	32	6	i3	i3	PROPN
iajs-156	32	7	.	.	PUNCT
iajs-156	33	1	thus	thus	ADV
iajs-156	33	2	for	for	SCONJ
iajs-156	33	3	each	each	DET
iajs-156	33	4	element	element	NOUN
iajs-156	33	5	0	0	NUM
iajs-156	33	6			VERB
iajs-156	33	7	a	a	DET
iajs-156	33	8			NOUN
iajs-156	33	9	r	r	NOUN
iajs-156	33	10	,	,	PUNCT
iajs-156	33	11	<	<	X
iajs-156	33	12	a	a	DET
iajs-156	33	13	>	>	SYM
iajs-156	33	14	2	2	NUM
iajs-156	33	15	=	=	SYM
iajs-156	33	16	<	<	X
iajs-156	33	17	a	a	X
iajs-156	33	18	>	>	X
iajs-156	33	19	3	3	NUM
iajs-156	33	20	,	,	PUNCT
iajs-156	33	21	hence	hence	ADV
iajs-156	33	22	a2	a2	PROPN
iajs-156	33	23			NOUN
iajs-156	33	24	<	<	X
iajs-156	33	25	a	a	X
iajs-156	33	26	>	>	X
iajs-156	33	27	3	3	X
iajs-156	33	28	.	.	PUNCT
iajs-156	34	1	let	let	VERB
iajs-156	34	2	a2	a2	PROPN
iajs-156	34	3	=	=	SYM
iajs-156	34	4	r	r	NOUN
iajs-156	34	5	a3	a3	NOUN
iajs-156	34	6	for	for	ADP
iajs-156	34	7	some	some	DET
iajs-156	34	8	r	r	NOUN
iajs-156	34	9			NOUN
iajs-156	34	10	r	r	NOUN
iajs-156	34	11	,	,	PUNCT
iajs-156	34	12	then	then	ADV
iajs-156	34	13	a2(1	a2(1	PROPN
iajs-156	34	14	–	–	PUNCT
iajs-156	34	15	ra	ra	NOUN
iajs-156	34	16	)	)	PUNCT
iajs-156	34	17	=	=	SYM
iajs-156	34	18	0	0	PUNCT
iajs-156	35	1	but	but	CCONJ
iajs-156	35	2	r	r	NOUN
iajs-156	35	3	is	be	AUX
iajs-156	35	4	domain	domain	NOUN
iajs-156	35	5	and	and	CCONJ
iajs-156	35	6	a	a	DET
iajs-156	35	7			NOUN
iajs-156	35	8	0	0	NUM
iajs-156	35	9	implies	imply	VERB
iajs-156	35	10	1	1	NUM
iajs-156	35	11	–	–	PUNCT
iajs-156	35	12	ra	ra	PROPN
iajs-156	35	13	=	=	SYM
iajs-156	35	14	0	0	PROPN
iajs-156	35	15	,	,	PUNCT
iajs-156	35	16	thus	thus	ADV
iajs-156	35	17	1	1	NUM
iajs-156	35	18	=	=	SYM
iajs-156	35	19	ra	ra	PROPN
iajs-156	35	20	.	.	PUNCT
iajs-156	36	1	therefore	therefore	ADV
iajs-156	36	2	a	a	PRON
iajs-156	36	3	is	be	AUX
iajs-156	36	4	an	an	DET
iajs-156	36	5	invertible	invertible	ADJ
iajs-156	36	6	element	element	NOUN
iajs-156	36	7	of	of	ADP
iajs-156	36	8	r.	r.	PROPN
iajs-156	36	9	thus	thus	ADV
iajs-156	36	10	r	r	NOUN
iajs-156	36	11	is	be	AUX
iajs-156	36	12	a	a	DET
iajs-156	36	13	field	field	NOUN
iajs-156	36	14	(	(	PUNCT
iajs-156	36	15	5	5	NUM
iajs-156	36	16	)	)	PUNCT
iajs-156	36	17	if	if	SCONJ
iajs-156	36	18	r	r	NOUN
iajs-156	36	19	is	be	AUX
iajs-156	36	20	a	a	DET
iajs-156	36	21	2	2	NUM
iajs-156	36	22	-	-	PUNCT
iajs-156	36	23	regular	regular	ADJ
iajs-156	36	24	ring	ring	NOUN
iajs-156	36	25	then	then	ADV
iajs-156	36	26	every	every	DET
iajs-156	36	27	prime	prime	ADJ
iajs-156	36	28	ideal	ideal	NOUN
iajs-156	36	29	of	of	ADP
iajs-156	36	30	r	r	NOUN
iajs-156	36	31	is	be	AUX
iajs-156	36	32	a	a	DET
iajs-156	36	33	maximal	maximal	ADJ
iajs-156	36	34	ideal	ideal	NOUN
iajs-156	36	35	.	.	PUNCT
iajs-156	37	1	proof	proof	NOUN
iajs-156	37	2	:	:	PUNCT
iajs-156	37	3	let	let	VERB
iajs-156	37	4	i	i	PRON
iajs-156	37	5	be	be	AUX
iajs-156	37	6	a	a	DET
iajs-156	37	7	prime	prime	ADJ
iajs-156	37	8	ideal	ideal	NOUN
iajs-156	37	9	of	of	ADP
iajs-156	37	10	r.	r.	PROPN
iajs-156	37	11	since	since	SCONJ
iajs-156	37	12	r	r	NOUN
iajs-156	37	13	is	be	AUX
iajs-156	37	14	a	a	DET
iajs-156	37	15	2	2	NUM
iajs-156	37	16	-	-	PUNCT
iajs-156	37	17	regular	regular	ADJ
iajs-156	37	18	ring	ring	NOUN
iajs-156	37	19	then	then	ADV
iajs-156	37	20	r	r	VERB
iajs-156	37	21	i	i	PRON
iajs-156	37	22	is	be	AUX
iajs-156	37	23	2	2	NUM
iajs-156	37	24	-	-	PUNCT
iajs-156	37	25	regular	regular	ADJ
iajs-156	37	26	by	by	ADP
iajs-156	37	27	[	[	X
iajs-156	37	28	1,cor.3.2	1,cor.3.2	NOUN
iajs-156	37	29	]	]	PUNCT
iajs-156	37	30	.	.	PUNCT
iajs-156	38	1	but	but	CCONJ
iajs-156	38	2	r	r	NOUN
iajs-156	38	3	i	i	PRON
iajs-156	38	4	is	be	AUX
iajs-156	38	5	a	a	DET
iajs-156	38	6	domain	domain	NOUN
iajs-156	38	7	since	since	SCONJ
iajs-156	38	8	i	i	PRON
iajs-156	38	9	is	be	AUX
iajs-156	38	10	a	a	DET
iajs-156	38	11	prime	prime	ADJ
iajs-156	38	12	ideal	ideal	NOUN
iajs-156	38	13	.	.	PUNCT
iajs-156	39	1	thus	thus	ADV
iajs-156	39	2	r	r	NOUN
iajs-156	39	3	i	i	PRON
iajs-156	39	4	is	be	AUX
iajs-156	39	5	a	a	DET
iajs-156	39	6	field	field	NOUN
iajs-156	39	7	by	by	ADP
iajs-156	39	8	the	the	DET
iajs-156	39	9	above	above	ADJ
iajs-156	39	10	remark	remark	NOUN
iajs-156	39	11	.	.	PUNCT
iajs-156	40	1	therefore	therefore	ADV
iajs-156	40	2	i	i	PRON
iajs-156	40	3	is	be	AUX
iajs-156	40	4	a	a	DET
iajs-156	40	5	maximal	maximal	ADJ
iajs-156	40	6	ideal	ideal	NOUN
iajs-156	40	7	.	.	PUNCT
iajs-156	41	1	(	(	PUNCT
iajs-156	41	2	6	6	NUM
iajs-156	41	3	)	)	PUNCT
iajs-156	41	4	every	every	DET
iajs-156	41	5	2	2	NUM
iajs-156	41	6	-	-	PUNCT
iajs-156	41	7	regular	regular	ADJ
iajs-156	41	8	ring	ring	NOUN
iajs-156	41	9	is	be	AUX
iajs-156	41	10	nearly	nearly	ADV
iajs-156	41	11	regular	regular	ADJ
iajs-156	41	12	,	,	PUNCT
iajs-156	41	13	where	where	SCONJ
iajs-156	41	14	a	a	DET
iajs-156	41	15	ring	ring	NOUN
iajs-156	41	16	r	r	NOUN
iajs-156	41	17	is	be	AUX
iajs-156	41	18	called	call	VERB
iajs-156	41	19	nearly	nearly	ADV
iajs-156	41	20	regular	regular	ADJ
iajs-156	41	21	if	if	SCONJ
iajs-156	41	22	r	r	NOUN
iajs-156	41	23	j(r	j(r	PROPN
iajs-156	41	24	)	)	PUNCT
iajs-156	41	25	is	be	AUX
iajs-156	41	26	regular	regular	ADJ
iajs-156	41	27	ring	ring	NOUN
iajs-156	41	28	,	,	PUNCT
iajs-156	41	29	see	see	VERB
iajs-156	41	30	[	[	X
iajs-156	41	31	2	2	NUM
iajs-156	41	32	]	]	PUNCT
iajs-156	41	33	,	,	PUNCT
iajs-156	41	34	where	where	SCONJ
iajs-156	41	35	j(r	j(r	NOUN
iajs-156	41	36	)	)	PUNCT
iajs-156	42	1	=	=	NOUN
iajs-156	42	2	the	the	DET
iajs-156	42	3	intersection	intersection	NOUN
iajs-156	42	4	of	of	ADP
iajs-156	42	5	all	all	DET
iajs-156	42	6	maximal	maximal	ADJ
iajs-156	42	7	ideals	ideal	NOUN
iajs-156	42	8	of	of	ADP
iajs-156	42	9	r.	r.	PROPN
iajs-156	42	10	proof	proof	NOUN
iajs-156	42	11	:	:	PUNCT
iajs-156	42	12	237	237	NUM
iajs-156	42	13	|	|	NOUN
iajs-156	42	14	mathematics	mathematic	NOUN
iajs-156	42	15	2015	2015	NUM
iajs-156	42	16	)	)	PUNCT
iajs-156	42	17	عام	عام	ADP
iajs-156	42	18	3العدد	3العدد	NUM
iajs-156	42	19	(	(	PUNCT
iajs-156	42	20	28مجلة	28مجلة	X
iajs-156	42	21	إبن	إبن	VERB
iajs-156	42	22	الھيثم	الھيثم	NOUN
iajs-156	42	23	للعلوم	للعلوم	NOUN
iajs-156	42	24	الصرفة	الصرفة	NOUN
iajs-156	43	1	و	و	PRON
iajs-156	43	2	التطبيقية	التطبيقية	ADV
iajs-156	43	3	المجلد	المجلد	VERB
iajs-156	43	4	ibn	ibn	PROPN
iajs-156	43	5	al	al	PROPN
iajs-156	43	6	-	-	PUNCT
iajs-156	43	7	haitham	haitham	PROPN
iajs-156	43	8	jour	jour	X
iajs-156	43	9	.	.	PROPN
iajs-156	44	1	for	for	ADP
iajs-156	44	2	pure	pure	ADJ
iajs-156	44	3	&	&	CCONJ
iajs-156	44	4	appl	appl	PROPN
iajs-156	44	5	.	.	PUNCT
iajs-156	45	1	sci	sci	PROPN
iajs-156	45	2	.	.	PUNCT
iajs-156	45	3	vol	vol	NOUN
iajs-156	45	4	.	.	PROPN
iajs-156	46	1	28	28	NUM
iajs-156	46	2	(	(	PUNCT
iajs-156	46	3	3	3	NUM
iajs-156	46	4	)	)	PUNCT
iajs-156	46	5	2015	2015	NUM
iajs-156	46	6	let	let	VERB
iajs-156	46	7	r	r	PRON
iajs-156	46	8	be	be	AUX
iajs-156	46	9	a	a	DET
iajs-156	46	10	2	2	NUM
iajs-156	46	11	-	-	PUNCT
iajs-156	46	12	regular	regular	ADJ
iajs-156	46	13	ring	ring	NOUN
iajs-156	46	14	.	.	PUNCT
iajs-156	47	1	then	then	ADV
iajs-156	47	2	r	r	PROPN
iajs-156	47	3	j(r	j(r	PROPN
iajs-156	47	4	)	)	PUNCT
iajs-156	47	5	is	be	AUX
iajs-156	47	6	2	2	NUM
iajs-156	47	7	-	-	PUNCT
iajs-156	47	8	regular	regular	ADJ
iajs-156	47	9	by	by	ADP
iajs-156	47	10	corollary	corollary	ADJ
iajs-156	47	11	(	(	PUNCT
iajs-156	47	12	1.2.3	1.2.3	NUM
iajs-156	47	13	)	)	PUNCT
iajs-156	47	14	.	.	PUNCT
iajs-156	48	1	so	so	ADV
iajs-156	48	2	by	by	ADP
iajs-156	48	3	above	above	ADP
iajs-156	48	4	remark	remark	NOUN
iajs-156	48	5	(	(	PUNCT
iajs-156	48	6	5	5	NUM
iajs-156	48	7	)	)	PUNCT
iajs-156	48	8	,	,	PUNCT
iajs-156	48	9	every	every	DET
iajs-156	48	10	prime	prime	ADJ
iajs-156	48	11	ideal	ideal	NOUN
iajs-156	48	12	of	of	ADP
iajs-156	48	13	r	r	PROPN
iajs-156	48	14	j(r	j(r	PROPN
iajs-156	48	15	)	)	PUNCT
iajs-156	48	16	is	be	AUX
iajs-156	48	17	a	a	DET
iajs-156	48	18	maximal	maximal	ADJ
iajs-156	48	19	ideal	ideal	NOUN
iajs-156	48	20	and	and	CCONJ
iajs-156	48	21	since	since	SCONJ
iajs-156	48	22	r	r	PROPN
iajs-156	48	23	j	j	PROPN
iajs-156	48	24	0	0	NUM
iajs-156	48	25	j(r	j(r	PROPN
iajs-156	48	26	)	)	PUNCT
iajs-156	48	27			NOUN
iajs-156	48	28			PROPN
iajs-156	48	29			PUNCT
iajs-156	48	30			PROPN
iajs-156	48	31			PROPN
iajs-156	48	32			NOUN
iajs-156	48	33	,	,	PUNCT
iajs-156	48	34	therefore	therefore	ADV
iajs-156	48	35	by	by	ADP
iajs-156	48	36	[	[	X
iajs-156	48	37	3	3	NUM
iajs-156	48	38	]	]	PUNCT
iajs-156	48	39	,	,	PUNCT
iajs-156	48	40	r	r	PROPN
iajs-156	48	41	j(r	j(r	PROPN
iajs-156	48	42	)	)	PUNCT
iajs-156	48	43	is	be	AUX
iajs-156	48	44	regular	regular	ADJ
iajs-156	48	45	.	.	PUNCT
iajs-156	49	1	proposition	proposition	NOUN
iajs-156	49	2	(	(	PUNCT
iajs-156	49	3	1.3	1.3	NUM
iajs-156	49	4	):	):	PUNCT
iajs-156	49	5	let	let	VERB
iajs-156	49	6	m	m	PRON
iajs-156	49	7	be	be	AUX
iajs-156	49	8	2	2	NUM
iajs-156	49	9	-	-	PUNCT
iajs-156	49	10	regular	regular	ADJ
iajs-156	49	11	r	r	NOUN
iajs-156	49	12	-	-	PUNCT
iajs-156	49	13	module	module	NOUN
iajs-156	49	14	then	then	ADV
iajs-156	49	15	for	for	ADP
iajs-156	49	16	every	every	DET
iajs-156	49	17	element	element	NOUN
iajs-156	49	18	x	x	ADJ
iajs-156	49	19	of	of	ADP
iajs-156	49	20	mand	mand	NOUN
iajs-156	49	21	every	every	DET
iajs-156	49	22	element	element	NOUN
iajs-156	49	23	r	r	NOUN
iajs-156	49	24			NOUN
iajs-156	49	25	r	r	NOUN
iajs-156	49	26	,	,	PUNCT
iajs-156	49	27	r2x	r2x	NOUN
iajs-156	49	28	=	=	SYM
iajs-156	49	29	r2tr2x	r2tr2x	NOUN
iajs-156	49	30	for	for	ADP
iajs-156	49	31	some	some	DET
iajs-156	49	32	t	t	NOUN
iajs-156	49	33			PROPN
iajs-156	49	34	r.	r.	PROPN
iajs-156	49	35	proof	proof	PROPN
iajs-156	49	36	:	:	PUNCT
iajs-156	49	37	let	let	VERB
iajs-156	49	38	x	x	PRON
iajs-156	49	39	be	be	AUX
iajs-156	49	40	an	an	DET
iajs-156	49	41	element	element	NOUN
iajs-156	49	42	of	of	ADP
iajs-156	49	43	m	m	PROPN
iajs-156	49	44	and	and	CCONJ
iajs-156	49	45	r	r	NOUN
iajs-156	49	46	be	be	AUX
iajs-156	49	47	an	an	DET
iajs-156	49	48	element	element	NOUN
iajs-156	49	49	of	of	ADP
iajs-156	49	50	r.	r.	PROPN
iajs-156	49	51	since	since	SCONJ
iajs-156	49	52	r2x	r2x	PROPN
iajs-156	49	53			NOUN
iajs-156	49	54	r2	r2	PROPN
iajs-156	49	55	m	m	PROPN
iajs-156	49	56	and	and	CCONJ
iajs-156	49	57	r2x	r2x	VERB
iajs-156	49	58			NOUN
iajs-156	49	59	<	<	X
iajs-156	49	60	r2x	r2x	X
iajs-156	49	61	>	>	X
iajs-156	49	62	implies	imply	VERB
iajs-156	49	63	r2x	r2x	PROPN
iajs-156	49	64			NOUN
iajs-156	49	65	r2	r2	PROPN
iajs-156	49	66	m	m	VERB
iajs-156	49	67			PUNCT
iajs-156	49	68	<	<	X
iajs-156	49	69	r2x	r2x	X
iajs-156	49	70	>	>	X
iajs-156	49	71	.	.	PUNCT
iajs-156	50	1	but	but	CCONJ
iajs-156	50	2	m	m	PROPN
iajs-156	50	3	is	be	AUX
iajs-156	50	4	2	2	NUM
iajs-156	50	5	-	-	PUNCT
iajs-156	50	6	regular	regular	ADJ
iajs-156	50	7	,	,	PUNCT
iajs-156	50	8	then	then	ADV
iajs-156	50	9	r2m	r2m	NOUN
iajs-156	50	10	<	<	X
iajs-156	50	11	r2x	r2x	X
iajs-156	50	12	>	>	PUNCT
iajs-156	50	13	=	=	NOUN
iajs-156	50	14	r2	r2	PROPN
iajs-156	50	15	<	<	X
iajs-156	50	16	r2x	r2x	X
iajs-156	50	17	>	>	X
iajs-156	50	18	.	.	PUNCT
iajs-156	51	1	thus	thus	ADV
iajs-156	51	2	,	,	PUNCT
iajs-156	51	3	r2xr2	r2xr2	NOUN
iajs-156	51	4	<	<	X
iajs-156	51	5	r2x	r2x	X
iajs-156	51	6	>	>	X
iajs-156	51	7	implies	imply	VERB
iajs-156	51	8	r2x	r2x	PROPN
iajs-156	51	9	=	=	NOUN
iajs-156	51	10	r2	r2	PROPN
iajs-156	51	11	t	t	PROPN
iajs-156	51	12	r2x	r2x	NOUN
iajs-156	51	13	for	for	ADP
iajs-156	51	14	some	some	DET
iajs-156	51	15	tr	tr	NOUN
iajs-156	51	16	.	.	PUNCT
iajs-156	52	1	proposition	proposition	NOUN
iajs-156	52	2	(	(	PUNCT
iajs-156	52	3	1.4	1.4	NUM
iajs-156	52	4	):	):	PUNCT
iajs-156	52	5	let	let	VERB
iajs-156	52	6	m	m	PRON
iajs-156	52	7	be	be	AUX
iajs-156	52	8	a	a	DET
iajs-156	52	9	module	module	NOUN
iajs-156	52	10	over	over	ADP
iajs-156	52	11	principal	principal	ADJ
iajs-156	52	12	ideal	ideal	NOUN
iajs-156	52	13	ring	ring	PROPN
iajs-156	52	14	r.	r.	PROPN
iajs-156	52	15	if	if	SCONJ
iajs-156	52	16	for	for	ADP
iajs-156	52	17	every	every	DET
iajs-156	52	18	element	element	NOUN
iajs-156	52	19	x	x	ADJ
iajs-156	52	20	of	of	ADP
iajs-156	52	21	m	m	PROPN
iajs-156	52	22	and	and	CCONJ
iajs-156	52	23	every	every	DET
iajs-156	52	24	element	element	NOUN
iajs-156	52	25	r	r	NOUN
iajs-156	52	26			NOUN
iajs-156	52	27	r	r	NOUN
iajs-156	52	28	,	,	PUNCT
iajs-156	52	29	r2x	r2x	NOUN
iajs-156	52	30	=	=	SYM
iajs-156	52	31	r2tr2x	r2tr2x	NOUN
iajs-156	52	32	for	for	ADP
iajs-156	52	33	some	some	DET
iajs-156	52	34	t	t	NOUN
iajs-156	52	35			NOUN
iajs-156	52	36	r	r	NOUN
iajs-156	52	37	implies	imply	VERB
iajs-156	52	38	m	m	VERB
iajs-156	52	39	is	be	AUX
iajs-156	52	40	a	a	DET
iajs-156	52	41	2	2	NUM
iajs-156	52	42	-	-	PUNCT
iajs-156	52	43	regular	regular	ADJ
iajs-156	52	44	module	module	NOUN
iajs-156	52	45	.	.	PUNCT
iajs-156	53	1	proof	proof	NOUN
iajs-156	53	2	:	:	PUNCT
iajs-156	53	3	let	let	VERB
iajs-156	53	4	n	n	PRON
iajs-156	53	5	be	be	AUX
iajs-156	53	6	a	a	DET
iajs-156	53	7	submodule	submodule	NOUN
iajs-156	53	8	of	of	ADP
iajs-156	53	9	m	m	PROPN
iajs-156	53	10	and	and	CCONJ
iajs-156	53	11	i	i	PRON
iajs-156	53	12	is	be	AUX
iajs-156	53	13	an	an	DET
iajs-156	53	14	ideal	ideal	NOUN
iajs-156	53	15	of	of	ADP
iajs-156	53	16	r.	r.	PROPN
iajs-156	53	17	first	first	PROPN
iajs-156	53	18	,	,	PUNCT
iajs-156	53	19	to	to	PART
iajs-156	53	20	prove	prove	VERB
iajs-156	53	21	r2	r2	PROPN
iajs-156	53	22	m	m	PROPN
iajs-156	53	23			PUNCT
iajs-156	53	24	n	n	NOUN
iajs-156	53	25	=	=	PUNCT
iajs-156	53	26	r2n	r2n	NOUN
iajs-156	53	27	for	for	ADP
iajs-156	53	28	every	every	DET
iajs-156	53	29	element	element	NOUN
iajs-156	53	30	r	r	NOUN
iajs-156	53	31			PROPN
iajs-156	53	32	r.	r.	PROPN
iajs-156	53	33	let	let	VERB
iajs-156	53	34	x	x	PUNCT
iajs-156	53	35			PROPN
iajs-156	53	36	r2	r2	PROPN
iajs-156	53	37	m	m	VERB
iajs-156	53	38			PUNCT
iajs-156	53	39	n	n	PRON
iajs-156	53	40	implies	imply	VERB
iajs-156	53	41	x	x	PUNCT
iajs-156	53	42			NOUN
iajs-156	53	43	r2	r2	PROPN
iajs-156	53	44	m	m	PROPN
iajs-156	53	45	,	,	PUNCT
iajs-156	53	46	x	x	SYM
iajs-156	53	47			PROPN
iajs-156	53	48	n.	n.	NOUN
iajs-156	53	49	thus	thus	ADV
iajs-156	53	50	x	x	X
iajs-156	53	51	=	=	PUNCT
iajs-156	53	52	r2	r2	PROPN
iajs-156	53	53	m	m	VERB
iajs-156	53	54	for	for	ADP
iajs-156	53	55	some	some	DET
iajs-156	53	56	m	m	PROPN
iajs-156	53	57			NOUN
iajs-156	53	58	m.	m.	NOUN
iajs-156	53	59	then	then	ADV
iajs-156	53	60	x	x	X
iajs-156	53	61	=	=	PUNCT
iajs-156	53	62	r2tr2	r2tr2	NOUN
iajs-156	53	63	m	m	VERB
iajs-156	53	64	for	for	ADP
iajs-156	53	65	some	some	DET
iajs-156	53	66	t	t	NOUN
iajs-156	53	67			NOUN
iajs-156	53	68	r	r	NOUN
iajs-156	53	69	by	by	ADP
iajs-156	53	70	hypothesis	hypothesis	NOUN
iajs-156	53	71	.	.	PUNCT
iajs-156	54	1	hence	hence	ADV
iajs-156	54	2	x	x	PUNCT
iajs-156	54	3			NOUN
iajs-156	54	4	r2n	r2n	NOUN
iajs-156	54	5	.	.	PUNCT
iajs-156	55	1	but	but	CCONJ
iajs-156	55	2	r	r	NOUN
iajs-156	55	3	is	be	AUX
iajs-156	55	4	a	a	DET
iajs-156	55	5	principal	principal	ADJ
iajs-156	55	6	ideal	ideal	ADJ
iajs-156	55	7	ring	ring	NOUN
iajs-156	55	8	.	.	PUNCT
iajs-156	56	1	therefore	therefore	ADV
iajs-156	56	2	i2	i2	PROPN
iajs-156	56	3	m	m	PROPN
iajs-156	56	4			PUNCT
iajs-156	56	5	n	n	NOUN
iajs-156	56	6	=	=	PUNCT
iajs-156	56	7	i2n	i2n	NOUN
iajs-156	56	8	.	.	PUNCT
iajs-156	57	1	proposition	proposition	NOUN
iajs-156	57	2	(	(	PUNCT
iajs-156	57	3	1.5	1.5	NUM
iajs-156	57	4	):	):	PUNCT
iajs-156	57	5	let	let	VERB
iajs-156	57	6	m	m	PRON
iajs-156	57	7	be	be	AUX
iajs-156	57	8	a	a	DET
iajs-156	57	9	cyclic	cyclic	ADJ
iajs-156	57	10	r	r	NOUN
iajs-156	57	11	-	-	PUNCT
iajs-156	57	12	module	module	NOUN
iajs-156	57	13	.	.	PUNCT
iajs-156	58	1	if	if	SCONJ
iajs-156	58	2	for	for	ADP
iajs-156	58	3	every	every	DET
iajs-156	58	4	element	element	NOUN
iajs-156	58	5	x	x	ADJ
iajs-156	58	6	of	of	ADP
iajs-156	58	7	m	m	PROPN
iajs-156	58	8	and	and	CCONJ
iajs-156	58	9	every	every	DET
iajs-156	58	10	element	element	NOUN
iajs-156	58	11	r	r	NOUN
iajs-156	58	12	of	of	ADP
iajs-156	58	13	r	r	NOUN
iajs-156	58	14	,	,	PUNCT
iajs-156	58	15	r2x	r2x	NOUN
iajs-156	58	16	=	=	SYM
iajs-156	58	17	r2tr2x	r2tr2x	NOUN
iajs-156	58	18	for	for	ADP
iajs-156	58	19	some	some	DET
iajs-156	58	20	t	t	NOUN
iajs-156	58	21			NOUN
iajs-156	58	22	r	r	NOUN
iajs-156	58	23	,	,	PUNCT
iajs-156	58	24	implies	imply	VERB
iajs-156	58	25	m	m	VERB
iajs-156	58	26	is	be	AUX
iajs-156	58	27	a	a	DET
iajs-156	58	28	2	2	NUM
iajs-156	58	29	-	-	PUNCT
iajs-156	58	30	regular	regular	ADJ
iajs-156	58	31	module	module	NOUN
iajs-156	58	32	.	.	PUNCT
iajs-156	59	1	proof	proof	NOUN
iajs-156	59	2	:	:	PUNCT
iajs-156	59	3	let	let	VERB
iajs-156	59	4	m	m	VERB
iajs-156	59	5	=	=	NOUN
iajs-156	59	6	rm	rm	NOUN
iajs-156	59	7	be	be	AUX
iajs-156	59	8	a	a	DET
iajs-156	59	9	cyclic	cyclic	ADJ
iajs-156	59	10	module	module	NOUN
iajs-156	59	11	for	for	ADP
iajs-156	59	12	some	some	DET
iajs-156	59	13	m	m	PROPN
iajs-156	59	14			NOUN
iajs-156	59	15	m.	m.	NOUN
iajs-156	59	16	let	let	VERB
iajs-156	59	17	n	n	PRON
iajs-156	59	18	be	be	AUX
iajs-156	59	19	a	a	DET
iajs-156	59	20	submodule	submodule	NOUN
iajs-156	59	21	of	of	ADP
iajs-156	59	22	m	m	PROPN
iajs-156	60	1	and	and	CCONJ
iajs-156	60	2	i	i	PRON
iajs-156	60	3	is	be	AUX
iajs-156	60	4	an	an	DET
iajs-156	60	5	ideal	ideal	NOUN
iajs-156	60	6	of	of	ADP
iajs-156	60	7	r.	r.	PROPN
iajs-156	60	8	let	let	VERB
iajs-156	60	9	y	y	PROPN
iajs-156	60	10			PROPN
iajs-156	60	11	i2	i2	PROPN
iajs-156	60	12	m	m	PROPN
iajs-156	60	13			PUNCT
iajs-156	61	1	n	n	CCONJ
iajs-156	61	2	then	then	ADV
iajs-156	61	3	y	y	PROPN
iajs-156	61	4			PROPN
iajs-156	61	5	i2	i2	PROPN
iajs-156	61	6	m	m	PROPN
iajs-156	61	7	and	and	CCONJ
iajs-156	61	8	y	y	PROPN
iajs-156	61	9			PROPN
iajs-156	61	10	n.	n.	PROPN
iajs-156	61	11	thus	thus	ADV
iajs-156	61	12	y	y	PROPN
iajs-156	61	13	=	=	SYM
iajs-156	61	14	r2	r2	PROPN
iajs-156	61	15	m	m	NOUN
iajs-156	61	16	=	=	ADJ
iajs-156	61	17	r2tr2	r2tr2	ADJ
iajs-156	61	18	m	m	PROPN
iajs-156	61	19			NOUN
iajs-156	61	20	r2n	r2n	NOUN
iajs-156	61	21	for	for	ADP
iajs-156	61	22	some	some	DET
iajs-156	61	23	t	t	NOUN
iajs-156	61	24			NOUN
iajs-156	61	25	r	r	NOUN
iajs-156	61	26	and	and	CCONJ
iajs-156	61	27	r	r	PROPN
iajs-156	61	28			PROPN
iajs-156	61	29	i.	i.	NOUN
iajs-156	61	30	therefore	therefore	ADV
iajs-156	61	31	y	y	PROPN
iajs-156	61	32			PROPN
iajs-156	61	33	i2n	i2n	NOUN
iajs-156	61	34	implies	imply	VERB
iajs-156	61	35	m	m	PROPN
iajs-156	61	36	is	be	AUX
iajs-156	61	37	2	2	NUM
iajs-156	61	38	-	-	PUNCT
iajs-156	61	39	regular	regular	ADJ
iajs-156	61	40	.	.	PUNCT
iajs-156	62	1	the	the	DET
iajs-156	62	2	proof	proof	NOUN
iajs-156	62	3	of	of	ADP
iajs-156	62	4	the	the	DET
iajs-156	62	5	following	following	ADJ
iajs-156	62	6	result	result	NOUN
iajs-156	62	7	is	be	AUX
iajs-156	62	8	similar	similar	ADJ
iajs-156	62	9	to	to	ADP
iajs-156	62	10	that	that	PRON
iajs-156	62	11	of	of	ADP
iajs-156	62	12	propositions	proposition	NOUN
iajs-156	62	13	(	(	PUNCT
iajs-156	62	14	1.3	1.3	NUM
iajs-156	62	15	)	)	PUNCT
iajs-156	62	16	and	and	CCONJ
iajs-156	62	17	(	(	PUNCT
iajs-156	62	18	1.4	1.4	NUM
iajs-156	62	19	)	)	PUNCT
iajs-156	62	20	.	.	PUNCT
iajs-156	63	1	corollary	corollary	ADJ
iajs-156	63	2	(	(	PUNCT
iajs-156	63	3	1.6	1.6	NUM
iajs-156	63	4	):	):	PUNCT
iajs-156	63	5	let	let	VERB
iajs-156	63	6	r	r	PRON
iajs-156	63	7	be	be	AUX
iajs-156	63	8	a	a	DET
iajs-156	63	9	2	2	NUM
iajs-156	63	10	-	-	PUNCT
iajs-156	63	11	regular	regular	ADJ
iajs-156	63	12	ring	ring	NOUN
iajs-156	63	13	then	then	ADV
iajs-156	63	14	for	for	ADP
iajs-156	63	15	every	every	DET
iajs-156	63	16	element	element	NOUN
iajs-156	63	17	a	a	DET
iajs-156	63	18			NOUN
iajs-156	63	19	r	r	NOUN
iajs-156	63	20	,	,	PUNCT
iajs-156	63	21	a2	a2	PROPN
iajs-156	63	22	=	=	SYM
iajs-156	63	23	a2	a2	PROPN
iajs-156	63	24	t	t	PROPN
iajs-156	63	25	a2	a2	PROPN
iajs-156	63	26	for	for	ADP
iajs-156	63	27	some	some	DET
iajs-156	63	28	t	t	NOUN
iajs-156	63	29			NOUN
iajs-156	63	30	r	r	NOUN
iajs-156	63	31	,	,	PUNCT
iajs-156	63	32	and	and	CCONJ
iajs-156	63	33	the	the	DET
iajs-156	63	34	converse	converse	NOUN
iajs-156	63	35	is	be	AUX
iajs-156	63	36	true	true	ADJ
iajs-156	63	37	if	if	SCONJ
iajs-156	63	38	r	r	NOUN
iajs-156	63	39	is	be	AUX
iajs-156	63	40	a	a	DET
iajs-156	63	41	principal	principal	ADJ
iajs-156	63	42	ideal	ideal	ADJ
iajs-156	63	43	ring	ring	NOUN
iajs-156	63	44	.	.	PUNCT
iajs-156	64	1	proposition	proposition	NOUN
iajs-156	64	2	(	(	PUNCT
iajs-156	64	3	1.7	1.7	NUM
iajs-156	64	4	):	):	PUNCT
iajs-156	64	5	let	let	VERB
iajs-156	64	6	r	r	PRON
iajs-156	64	7	be	be	AUX
iajs-156	64	8	a	a	DET
iajs-156	64	9	principal	principal	ADJ
iajs-156	64	10	ideal	ideal	ADJ
iajs-156	64	11	ring	ring	NOUN
iajs-156	64	12	and	and	CCONJ
iajs-156	64	13	m	m	AUX
iajs-156	64	14	be	be	AUX
iajs-156	64	15	an	an	DET
iajs-156	64	16	r	r	NOUN
iajs-156	64	17	-	-	PUNCT
iajs-156	64	18	module	module	NOUN
iajs-156	64	19	.	.	PUNCT
iajs-156	65	1	the	the	DET
iajs-156	65	2	following	follow	VERB
iajs-156	65	3	statements	statement	NOUN
iajs-156	65	4	are	be	AUX
iajs-156	65	5	equivalent	equivalent	ADJ
iajs-156	65	6	:	:	PUNCT
iajs-156	65	7	(	(	PUNCT
iajs-156	65	8	1	1	X
iajs-156	65	9	)	)	PUNCT
iajs-156	65	10	m	m	VERB
iajs-156	65	11	is	be	AUX
iajs-156	65	12	2	2	NUM
iajs-156	65	13	-	-	PUNCT
iajs-156	65	14	regular	regular	ADJ
iajs-156	65	15	module	module	NOUN
iajs-156	65	16	.	.	PUNCT
iajs-156	66	1	(	(	PUNCT
iajs-156	66	2	2	2	X
iajs-156	66	3	)	)	PUNCT
iajs-156	66	4	r	r	NOUN
iajs-156	66	5	r	r	NOUN
iajs-156	66	6	ann(x	ann(x	PROPN
iajs-156	66	7	)	)	PUNCT
iajs-156	66	8	is	be	AUX
iajs-156	66	9	2	2	NUM
iajs-156	66	10	-	-	PUNCT
iajs-156	66	11	regular	regular	ADJ
iajs-156	66	12	for	for	ADP
iajs-156	66	13	every	every	DET
iajs-156	66	14	element	element	NOUN
iajs-156	66	15	x	x	PUNCT
iajs-156	66	16	of	of	ADP
iajs-156	66	17	m.	m.	NOUN
iajs-156	66	18	(	(	PUNCT
iajs-156	66	19	3	3	NUM
iajs-156	66	20	)	)	PUNCT
iajs-156	66	21	for	for	ADP
iajs-156	66	22	every	every	DET
iajs-156	66	23	element	element	NOUN
iajs-156	66	24	x	x	ADJ
iajs-156	66	25	of	of	ADP
iajs-156	66	26	m	m	PROPN
iajs-156	66	27	and	and	CCONJ
iajs-156	66	28	every	every	DET
iajs-156	66	29	element	element	NOUN
iajs-156	66	30	r	r	NOUN
iajs-156	66	31	of	of	ADP
iajs-156	66	32	r	r	NOUN
iajs-156	66	33	,	,	PUNCT
iajs-156	66	34	r2x	r2x	NOUN
iajs-156	66	35	=	=	SYM
iajs-156	66	36	r2tr2x	r2tr2x	NOUN
iajs-156	66	37	for	for	ADP
iajs-156	66	38	some	some	DET
iajs-156	66	39	t	t	NOUN
iajs-156	66	40			PROPN
iajs-156	66	41	r.	r.	PROPN
iajs-156	66	42	238	238	NUM
iajs-156	66	43	|	|	NOUN
iajs-156	66	44	mathematics	mathematic	NOUN
iajs-156	66	45	2015	2015	NUM
iajs-156	66	46	)	)	PUNCT
iajs-156	66	47	عام	عام	ADP
iajs-156	66	48	3العدد	3العدد	NUM
iajs-156	66	49	(	(	PUNCT
iajs-156	66	50	28مجلة	28مجلة	X
iajs-156	66	51	إبن	إبن	VERB
iajs-156	66	52	الھيثم	الھيثم	NOUN
iajs-156	66	53	للعلوم	للعلوم	NOUN
iajs-156	66	54	الصرفة	الصرفة	NOUN
iajs-156	67	1	و	و	PRON
iajs-156	67	2	التطبيقية	التطبيقية	ADV
iajs-156	67	3	المجلد	المجلد	VERB
iajs-156	67	4	ibn	ibn	PROPN
iajs-156	67	5	al	al	PROPN
iajs-156	67	6	-	-	PUNCT
iajs-156	67	7	haitham	haitham	PROPN
iajs-156	67	8	jour	jour	X
iajs-156	67	9	.	.	PROPN
iajs-156	68	1	for	for	ADP
iajs-156	68	2	pure	pure	ADJ
iajs-156	68	3	&	&	CCONJ
iajs-156	68	4	appl	appl	PROPN
iajs-156	68	5	.	.	PUNCT
iajs-156	69	1	sci	sci	PROPN
iajs-156	69	2	.	.	PUNCT
iajs-156	69	3	vol	vol	NOUN
iajs-156	69	4	.	.	PROPN
iajs-156	70	1	28	28	NUM
iajs-156	70	2	(	(	PUNCT
iajs-156	70	3	3	3	NUM
iajs-156	70	4	)	)	PUNCT
iajs-156	70	5	2015	2015	NUM
iajs-156	70	6	proof	proof	NOUN
iajs-156	70	7	:	:	PUNCT
iajs-156	70	8	(	(	PUNCT
iajs-156	70	9	1	1	X
iajs-156	70	10	)	)	PUNCT
iajs-156	70	11			NOUN
iajs-156	70	12	(	(	PUNCT
iajs-156	70	13	3	3	X
iajs-156	70	14	)	)	PUNCT
iajs-156	70	15	it	it	PRON
iajs-156	70	16	follows	follow	VERB
iajs-156	70	17	by	by	ADP
iajs-156	70	18	proposition	proposition	NOUN
iajs-156	70	19	(	(	PUNCT
iajs-156	70	20	1.3	1.3	NUM
iajs-156	70	21	)	)	PUNCT
iajs-156	70	22	.	.	PUNCT
iajs-156	71	1	(	(	PUNCT
iajs-156	71	2	3	3	X
iajs-156	71	3	)	)	PUNCT
iajs-156	71	4			NOUN
iajs-156	71	5	(	(	PUNCT
iajs-156	71	6	1	1	X
iajs-156	71	7	)	)	PUNCT
iajs-156	71	8	by	by	ADP
iajs-156	71	9	proposition	proposition	NOUN
iajs-156	71	10	(	(	PUNCT
iajs-156	71	11	1.4	1.4	NUM
iajs-156	71	12	)	)	PUNCT
iajs-156	71	13	.	.	PUNCT
iajs-156	72	1	(	(	PUNCT
iajs-156	72	2	1	1	X
iajs-156	72	3	)	)	PUNCT
iajs-156	72	4			NOUN
iajs-156	72	5	(	(	PUNCT
iajs-156	72	6	2	2	X
iajs-156	72	7	)	)	PUNCT
iajs-156	72	8	let	let	VERB
iajs-156	72	9	r	r	NOUN
iajs-156	72	10	+	+	CCONJ
iajs-156	72	11	r	r	NOUN
iajs-156	72	12	ann(x	ann(x	PROPN
iajs-156	72	13	)	)	PUNCT
iajs-156	72	14			NOUN
iajs-156	72	15	r	r	NOUN
iajs-156	72	16	r	r	NOUN
iajs-156	72	17	ann(x	ann(x	PROPN
iajs-156	72	18	)	)	PUNCT
iajs-156	73	1	where	where	SCONJ
iajs-156	73	2	x	x	PUNCT
iajs-156	73	3			NOUN
iajs-156	73	4	m	m	VERB
iajs-156	73	5	and	and	CCONJ
iajs-156	73	6	r	r	PROPN
iajs-156	73	7			PROPN
iajs-156	73	8	r.	r.	PROPN
iajs-156	73	9	since	since	SCONJ
iajs-156	73	10	m	m	PROPN
iajs-156	73	11	is	be	AUX
iajs-156	73	12	2	2	NUM
iajs-156	73	13	-	-	PUNCT
iajs-156	73	14	regular	regular	ADJ
iajs-156	73	15	,	,	PUNCT
iajs-156	73	16	then	then	ADV
iajs-156	73	17	r2x	r2x	VERB
iajs-156	73	18	=	=	SYM
iajs-156	73	19	r2tr2x	r2tr2x	NOUN
iajs-156	73	20	for	for	ADP
iajs-156	73	21	some	some	DET
iajs-156	73	22	t	t	NOUN
iajs-156	73	23			PROPN
iajs-156	73	24	r.	r.	PROPN
iajs-156	73	25	thus	thus	ADV
iajs-156	73	26	r2	r2	PROPN
iajs-156	73	27	–	–	PUNCT
iajs-156	73	28	r2tr2	r2tr2	ADJ
iajs-156	73	29			NOUN
iajs-156	73	30	r	r	NOUN
iajs-156	73	31	ann(x	ann(x	PROPN
iajs-156	73	32	)	)	PUNCT
iajs-156	73	33	implies	imply	VERB
iajs-156	73	34	r	r	NOUN
iajs-156	73	35	r	r	NOUN
iajs-156	73	36	ann(x	ann(x	PROPN
iajs-156	73	37	)	)	PUNCT
iajs-156	73	38	is	be	AUX
iajs-156	73	39	2	2	NUM
iajs-156	73	40	-	-	PUNCT
iajs-156	73	41	regular	regular	ADJ
iajs-156	73	42	.	.	PUNCT
iajs-156	74	1	(	(	PUNCT
iajs-156	74	2	2	2	X
iajs-156	74	3	)	)	PUNCT
iajs-156	74	4			NOUN
iajs-156	74	5	(	(	PUNCT
iajs-156	74	6	1	1	X
iajs-156	74	7	)	)	PUNCT
iajs-156	74	8	let	let	VERB
iajs-156	74	9	x	x	PRON
iajs-156	74	10			NOUN
iajs-156	74	11	m	m	PRON
iajs-156	74	12	and	and	CCONJ
iajs-156	74	13	r	r	PROPN
iajs-156	74	14			PROPN
iajs-156	74	15	r.	r.	PROPN
iajs-156	74	16	since	since	SCONJ
iajs-156	74	17	r	r	NOUN
iajs-156	74	18	r	r	NOUN
iajs-156	74	19	ann(x	ann(x	PROPN
iajs-156	74	20	)	)	PUNCT
iajs-156	74	21	is	be	AUX
iajs-156	74	22	2	2	NUM
iajs-156	74	23	-	-	PUNCT
iajs-156	74	24	regular	regular	ADJ
iajs-156	74	25	,	,	PUNCT
iajs-156	74	26	then	then	ADV
iajs-156	74	27	r2	r2	PROPN
iajs-156	74	28	+	+	CCONJ
iajs-156	74	29	r	r	NOUN
iajs-156	74	30	ann(x	ann(x	PROPN
iajs-156	74	31	)	)	PUNCT
iajs-156	74	32	=	=	SYM
iajs-156	74	33	(	(	PUNCT
iajs-156	74	34	r2	r2	PROPN
iajs-156	74	35	+	+	CCONJ
iajs-156	74	36	r	r	NOUN
iajs-156	74	37	ann(x	ann(x	PROPN
iajs-156	74	38	)	)	PUNCT
iajs-156	74	39	(	(	PUNCT
iajs-156	74	40	t	t	NOUN
iajs-156	74	41	+	+	CCONJ
iajs-156	74	42	r	r	NOUN
iajs-156	74	43	ann(x	ann(x	PROPN
iajs-156	74	44	)	)	PUNCT
iajs-156	74	45	)	)	PUNCT
iajs-156	75	1	(	(	PUNCT
iajs-156	75	2	r2	r2	NOUN
iajs-156	75	3	+	+	CCONJ
iajs-156	75	4	r	r	NOUN
iajs-156	75	5	ann(x	ann(x	PROPN
iajs-156	75	6	)	)	PUNCT
iajs-156	75	7	)	)	PUNCT
iajs-156	75	8	for	for	ADP
iajs-156	75	9	some	some	DET
iajs-156	75	10	t	t	PROPN
iajs-156	75	11			PROPN
iajs-156	75	12	r.	r.	PROPN
iajs-156	75	13	thus	thus	ADV
iajs-156	75	14	r2x	r2x	PROPN
iajs-156	75	15	=	=	PUNCT
iajs-156	75	16	r2tr2x	r2tr2x	NOUN
iajs-156	75	17	implies	imply	VERB
iajs-156	75	18	m	m	PROPN
iajs-156	75	19	is	be	AUX
iajs-156	75	20	2	2	NUM
iajs-156	75	21	-	-	PUNCT
iajs-156	75	22	regular	regular	ADJ
iajs-156	75	23	.	.	PUNCT
iajs-156	76	1	we	we	PRON
iajs-156	76	2	have	have	VERB
iajs-156	76	3	the	the	DET
iajs-156	76	4	following	follow	VERB
iajs-156	76	5	results	result	NOUN
iajs-156	76	6	:	:	PUNCT
iajs-156	76	7	corollary	corollary	ADJ
iajs-156	76	8	(	(	PUNCT
iajs-156	76	9	1.8	1.8	NUM
iajs-156	76	10	):	):	PUNCT
iajs-156	76	11	let	let	VERB
iajs-156	76	12	r	r	PRON
iajs-156	76	13	be	be	AUX
iajs-156	76	14	a	a	DET
iajs-156	76	15	principal	principal	ADJ
iajs-156	76	16	ideal	ideal	ADJ
iajs-156	76	17	ring	ring	NOUN
iajs-156	76	18	.	.	PUNCT
iajs-156	77	1	then	then	ADV
iajs-156	77	2	r	r	NOUN
iajs-156	77	3	is	be	AUX
iajs-156	77	4	2	2	NUM
iajs-156	77	5	-	-	PUNCT
iajs-156	77	6	regular	regular	ADJ
iajs-156	77	7	if	if	SCONJ
iajs-156	78	1	and	and	CCONJ
iajs-156	78	2	only	only	ADV
iajs-156	78	3	if	if	SCONJ
iajs-156	78	4	all	all	DET
iajs-156	78	5	r	r	NOUN
iajs-156	78	6	-	-	PUNCT
iajs-156	78	7	modules	module	NOUN
iajs-156	78	8	are	be	AUX
iajs-156	78	9	2	2	NUM
iajs-156	78	10	-	-	PUNCT
iajs-156	78	11	regular	regular	ADJ
iajs-156	78	12	.	.	PUNCT
iajs-156	79	1	proof	proof	NOUN
iajs-156	79	2	:	:	PUNCT
iajs-156	79	3	(	(	PUNCT
iajs-156	79	4			NOUN
iajs-156	79	5	)	)	PUNCT
iajs-156	79	6	let	let	VERB
iajs-156	79	7	r	r	NOUN
iajs-156	79	8	be	be	AUX
iajs-156	79	9	2	2	NUM
iajs-156	79	10	-	-	PUNCT
iajs-156	79	11	regular	regular	ADJ
iajs-156	79	12	ring	ring	NOUN
iajs-156	79	13	and	and	CCONJ
iajs-156	79	14	m	m	NOUN
iajs-156	79	15	is	be	AUX
iajs-156	79	16	an	an	DET
iajs-156	79	17	r	r	NOUN
iajs-156	79	18	-	-	PUNCT
iajs-156	79	19	module	module	NOUN
iajs-156	79	20	.	.	PUNCT
iajs-156	80	1	then	then	ADV
iajs-156	80	2	r	r	NOUN
iajs-156	80	3	r	r	NOUN
iajs-156	80	4	ann(x	ann(x	PROPN
iajs-156	80	5	)	)	PUNCT
iajs-156	80	6	is	be	AUX
iajs-156	80	7	2	2	NUM
iajs-156	80	8	-	-	PUNCT
iajs-156	80	9	regular	regular	ADJ
iajs-156	80	10	for	for	ADP
iajs-156	80	11	every	every	DET
iajs-156	80	12	element	element	NOUN
iajs-156	80	13	x	x	PUNCT
iajs-156	80	14			PROPN
iajs-156	80	15	m	m	VERB
iajs-156	80	16	by	by	ADP
iajs-156	80	17	[	[	X
iajs-156	80	18	1,cor.(3.3	1,cor.(3.3	NUM
iajs-156	80	19	)	)	PUNCT
iajs-156	80	20	]	]	PUNCT
iajs-156	80	21	.	.	PUNCT
iajs-156	81	1	therefore	therefore	ADV
iajs-156	81	2	m	m	PROPN
iajs-156	81	3	is	be	AUX
iajs-156	81	4	2	2	NUM
iajs-156	81	5	-	-	PUNCT
iajs-156	81	6	regular	regular	ADJ
iajs-156	81	7	by	by	ADP
iajs-156	81	8	proposition	proposition	NOUN
iajs-156	81	9	(	(	PUNCT
iajs-156	81	10	1.7	1.7	NUM
iajs-156	81	11	)	)	PUNCT
iajs-156	81	12	.	.	PUNCT
iajs-156	82	1	(	(	PUNCT
iajs-156	82	2			NOUN
iajs-156	82	3	)	)	PUNCT
iajs-156	82	4	assume	assume	VERB
iajs-156	82	5	all	all	DET
iajs-156	82	6	r	r	NOUN
iajs-156	82	7	-	-	PUNCT
iajs-156	82	8	modules	module	NOUN
iajs-156	82	9	are	be	AUX
iajs-156	82	10	2	2	NUM
iajs-156	82	11	-	-	PUNCT
iajs-156	82	12	regular	regular	ADJ
iajs-156	82	13	.	.	PUNCT
iajs-156	83	1	thus	thus	ADV
iajs-156	83	2	r	r	NOUN
iajs-156	83	3	is	be	AUX
iajs-156	83	4	2	2	NUM
iajs-156	83	5	-	-	PUNCT
iajs-156	83	6	regular	regular	ADJ
iajs-156	83	7	r	r	NOUN
iajs-156	83	8	-	-	PUNCT
iajs-156	83	9	module	module	NOUN
iajs-156	83	10	.	.	PUNCT
iajs-156	84	1	by	by	ADP
iajs-156	84	2	proposition	proposition	NOUN
iajs-156	84	3	(	(	PUNCT
iajs-156	84	4	1.7	1.7	NUM
iajs-156	84	5	)	)	PUNCT
iajs-156	84	6	,	,	PUNCT
iajs-156	84	7	r	r	NOUN
iajs-156	84	8	r	r	NOUN
iajs-156	84	9	ann(x	ann(x	PROPN
iajs-156	84	10	)	)	PUNCT
iajs-156	84	11	is	be	AUX
iajs-156	84	12	2	2	NUM
iajs-156	84	13	-	-	PUNCT
iajs-156	84	14	regular	regular	ADJ
iajs-156	84	15	for	for	ADP
iajs-156	84	16	some	some	DET
iajs-156	84	17	every	every	DET
iajs-156	84	18	element	element	NOUN
iajs-156	84	19	x	x	X
iajs-156	84	20			NOUN
iajs-156	84	21	r	r	NOUN
iajs-156	84	22	,	,	PUNCT
iajs-156	84	23	so	so	CCONJ
iajs-156	84	24	if	if	SCONJ
iajs-156	84	25	take	take	VERB
iajs-156	84	26	x	x	NOUN
iajs-156	84	27	=	=	SYM
iajs-156	84	28	1	1	NUM
iajs-156	84	29			NOUN
iajs-156	84	30	r	r	NOUN
iajs-156	84	31	implies	imply	VERB
iajs-156	84	32	r	r	NOUN
iajs-156	84	33	r	r	NOUN
iajs-156	84	34	r	r	NOUN
iajs-156	84	35	r	r	NOUN
iajs-156	84	36	ann(x	ann(x	PROPN
iajs-156	84	37	)	)	PUNCT
iajs-156	84	38	0	0	NUM
iajs-156	85	1			NUM
iajs-156	85	2			PROPN
iajs-156	85	3			PROPN
iajs-156	85	4			INTJ
iajs-156	85	5	,	,	PUNCT
iajs-156	85	6	therefore	therefore	ADV
iajs-156	85	7	r	r	NOUN
iajs-156	85	8	is	be	AUX
iajs-156	85	9	2	2	NUM
iajs-156	85	10	-	-	PUNCT
iajs-156	85	11	regular	regular	ADJ
iajs-156	85	12	.	.	PUNCT
iajs-156	86	1	corollary	corollary	NOUN
iajs-156	86	2	(	(	PUNCT
iajs-156	86	3	1.9	1.9	NUM
iajs-156	86	4	):	):	PUNCT
iajs-156	86	5	let	let	VERB
iajs-156	86	6	r	r	PRON
iajs-156	86	7	be	be	AUX
iajs-156	86	8	a	a	DET
iajs-156	86	9	principal	principal	ADJ
iajs-156	86	10	ideal	ideal	ADJ
iajs-156	86	11	ring	ring	NOUN
iajs-156	86	12	.	.	PUNCT
iajs-156	87	1	then	then	ADV
iajs-156	87	2	r	r	NOUN
iajs-156	87	3	is	be	AUX
iajs-156	87	4	a	a	DET
iajs-156	87	5	2	2	NUM
iajs-156	87	6	-	-	PUNCT
iajs-156	87	7	regular	regular	NOUN
iajs-156	87	8	if	if	SCONJ
iajs-156	88	1	and	and	CCONJ
iajs-156	88	2	only	only	ADV
iajs-156	88	3	if	if	SCONJ
iajs-156	88	4	r	r	NOUN
iajs-156	88	5	is	be	AUX
iajs-156	88	6	2	2	NUM
iajs-156	88	7	-	-	PUNCT
iajs-156	88	8	regular	regular	ADJ
iajs-156	88	9	r	r	NOUN
iajs-156	88	10	-	-	PUNCT
iajs-156	88	11	module	module	NOUN
iajs-156	88	12	.	.	PUNCT
iajs-156	89	1	proof	proof	NOUN
iajs-156	89	2	:	:	PUNCT
iajs-156	89	3	by	by	ADP
iajs-156	89	4	the	the	DET
iajs-156	89	5	same	same	ADJ
iajs-156	89	6	argument	argument	NOUN
iajs-156	89	7	of	of	ADP
iajs-156	89	8	corollary	corollary	ADJ
iajs-156	89	9	(	(	PUNCT
iajs-156	89	10	1.8	1.8	NUM
iajs-156	89	11	)	)	PUNCT
iajs-156	89	12	.	.	PUNCT
iajs-156	90	1	corollary	corollary	ADJ
iajs-156	90	2	(	(	PUNCT
iajs-156	90	3	1	1	NUM
iajs-156	90	4	.	.	NOUN
iajs-156	90	5	10	10	NUM
iajs-156	90	6	):	):	PUNCT
iajs-156	90	7	let	let	VERB
iajs-156	90	8	r	r	PRON
iajs-156	90	9	be	be	AUX
iajs-156	90	10	a	a	DET
iajs-156	90	11	principal	principal	ADJ
iajs-156	90	12	ideal	ideal	ADJ
iajs-156	90	13	ring	ring	NOUN
iajs-156	90	14	.	.	PUNCT
iajs-156	91	1	if	if	SCONJ
iajs-156	91	2	r	r	NOUN
iajs-156	91	3	r	r	NOUN
iajs-156	91	4	ann(m	ann(m	NOUN
iajs-156	91	5	)	)	PUNCT
iajs-156	91	6	is	be	AUX
iajs-156	91	7	2	2	NUM
iajs-156	91	8	-	-	PUNCT
iajs-156	91	9	regular	regular	ADJ
iajs-156	91	10	then	then	ADV
iajs-156	91	11	m	m	VERB
iajs-156	91	12	is	be	AUX
iajs-156	91	13	2	2	NUM
iajs-156	91	14	-	-	PUNCT
iajs-156	91	15	regular	regular	ADJ
iajs-156	91	16	r	r	NOUN
iajs-156	91	17	-	-	PUNCT
iajs-156	91	18	module	module	NOUN
iajs-156	91	19	.	.	PUNCT
iajs-156	92	1	proof	proof	NOUN
iajs-156	92	2	:	:	PUNCT
iajs-156	92	3	let	let	VERB
iajs-156	92	4	x	x	PRON
iajs-156	92	5	be	be	AUX
iajs-156	92	6	a	a	DET
iajs-156	92	7	non	non	ADJ
iajs-156	92	8	-	-	ADJ
iajs-156	92	9	zero	zero	NUM
iajs-156	92	10	element	element	NOUN
iajs-156	92	11	of	of	ADP
iajs-156	92	12	m.	m.	NOUN
iajs-156	92	13	since	since	SCONJ
iajs-156	92	14	r	r	NOUN
iajs-156	92	15	r	r	NOUN
iajs-156	92	16	ann(m	ann(m	NOUN
iajs-156	92	17	)	)	PUNCT
iajs-156	92	18	ann(x)	ann(x)	PUNCT
iajs-156	92	19	,	,	PUNCT
iajs-156	92	20	there	there	PRON
iajs-156	92	21	exists	exist	VERB
iajs-156	92	22	an	an	DET
iajs-156	92	23	epimorphism	epimorphism	NOUN
iajs-156	92	24	f	f	X
iajs-156	92	25	:	:	PUNCT
iajs-156	92	26	r	r	NOUN
iajs-156	92	27	r	r	NOUN
iajs-156	92	28	r	r	NOUN
iajs-156	92	29	r	r	NOUN
iajs-156	92	30	ann(m	ann(m	NOUN
iajs-156	92	31	)	)	PUNCT
iajs-156	92	32	ann(x	ann(x	PROPN
iajs-156	92	33	)	)	PUNCT
iajs-156	92	34			NOUN
iajs-156	92	35	defined	define	VERB
iajs-156	92	36	by	by	ADP
iajs-156	92	37	f	f	PROPN
iajs-156	92	38	(	(	PUNCT
iajs-156	92	39	r	r	NOUN
iajs-156	92	40	+	+	NOUN
iajs-156	92	41	r	r	NOUN
iajs-156	92	42	ann(m	ann(m	NOUN
iajs-156	92	43	)	)	PUNCT
iajs-156	92	44	)	)	PUNCT
iajs-156	93	1	=	=	PUNCT
iajs-156	94	1	r	r	NOUN
iajs-156	94	2	+	+	NOUN
iajs-156	94	3	r	r	NOUN
iajs-156	94	4	ann(x	ann(x	PROPN
iajs-156	94	5	)	)	PUNCT
iajs-156	94	6	.	.	PUNCT
iajs-156	95	1	therefore	therefore	ADV
iajs-156	95	2	r	r	NOUN
iajs-156	95	3	r	r	NOUN
iajs-156	95	4	ann(x	ann(x	PROPN
iajs-156	95	5	)	)	PUNCT
iajs-156	95	6	is	be	AUX
iajs-156	95	7	2	2	NUM
iajs-156	95	8	-	-	PUNCT
iajs-156	95	9	regular	regular	ADJ
iajs-156	95	10	by	by	ADP
iajs-156	95	11	[	[	NOUN
iajs-156	95	12	1,cor.(3.3	1,cor.(3.3	NUM
iajs-156	95	13	)	)	PUNCT
iajs-156	95	14	]	]	PUNCT
iajs-156	95	15	.	.	PUNCT
iajs-156	96	1	then	then	ADV
iajs-156	96	2	m	m	PROPN
iajs-156	96	3	is	be	AUX
iajs-156	96	4	2	2	NUM
iajs-156	96	5	-	-	PUNCT
iajs-156	96	6	regular	regular	ADJ
iajs-156	96	7	by	by	ADP
iajs-156	96	8	proposition	proposition	NOUN
iajs-156	96	9	(	(	PUNCT
iajs-156	96	10	1.7	1.7	NUM
iajs-156	96	11	)	)	PUNCT
iajs-156	96	12	.	.	PUNCT
iajs-156	97	1	239	239	NUM
iajs-156	97	2	|	|	ADV
iajs-156	97	3	mathematics	mathematic	NOUN
iajs-156	97	4	2015	2015	NUM
iajs-156	97	5	)	)	PUNCT
iajs-156	97	6	عام	عام	ADP
iajs-156	97	7	3العدد	3العدد	NUM
iajs-156	97	8	(	(	PUNCT
iajs-156	97	9	28مجلة	28مجلة	X
iajs-156	97	10	إبن	إبن	VERB
iajs-156	97	11	الھيثم	الھيثم	NOUN
iajs-156	97	12	للعلوم	للعلوم	NOUN
iajs-156	97	13	الصرفة	الصرفة	NOUN
iajs-156	98	1	و	و	PRON
iajs-156	98	2	التطبيقية	التطبيقية	ADV
iajs-156	98	3	المجلد	المجلد	VERB
iajs-156	98	4	ibn	ibn	PROPN
iajs-156	98	5	al	al	PROPN
iajs-156	98	6	-	-	PUNCT
iajs-156	98	7	haitham	haitham	PROPN
iajs-156	98	8	jour	jour	X
iajs-156	98	9	.	.	PROPN
iajs-156	99	1	for	for	ADP
iajs-156	99	2	pure	pure	ADJ
iajs-156	99	3	&	&	CCONJ
iajs-156	99	4	appl	appl	PROPN
iajs-156	99	5	.	.	PUNCT
iajs-156	100	1	sci	sci	PROPN
iajs-156	100	2	.	.	PUNCT
iajs-156	100	3	vol	vol	NOUN
iajs-156	100	4	.	.	PROPN
iajs-156	101	1	28	28	NUM
iajs-156	101	2	(	(	PUNCT
iajs-156	101	3	3	3	NUM
iajs-156	101	4	)	)	PUNCT
iajs-156	101	5	2015	2015	NUM
iajs-156	101	6	2regular	2regular	NUM
iajs-156	101	7	modules	module	NOUN
iajs-156	101	8	and	and	CCONJ
iajs-156	101	9	other	other	ADJ
iajs-156	101	10	related	related	ADJ
iajs-156	101	11	modules	module	NOUN
iajs-156	101	12	in	in	ADP
iajs-156	101	13	this	this	DET
iajs-156	101	14	section	section	NOUN
iajs-156	101	15	,	,	PUNCT
iajs-156	101	16	we	we	PRON
iajs-156	101	17	study	study	VERB
iajs-156	101	18	the	the	DET
iajs-156	101	19	relationships	relationship	NOUN
iajs-156	101	20	between	between	ADP
iajs-156	101	21	2	2	NUM
iajs-156	101	22	-	-	PUNCT
iajs-156	101	23	regular	regular	ADJ
iajs-156	101	24	modules	module	NOUN
iajs-156	101	25	and	and	CCONJ
iajs-156	101	26	other	other	ADJ
iajs-156	101	27	modules	module	NOUN
iajs-156	101	28	such	such	ADJ
iajs-156	101	29	as	as	ADP
iajs-156	101	30	semiprime	semiprime	NOUN
iajs-156	101	31	,	,	PUNCT
iajs-156	101	32	divisible	divisible	ADJ
iajs-156	101	33	,	,	PUNCT
iajs-156	101	34	projective	projective	ADJ
iajs-156	101	35	and	and	CCONJ
iajs-156	101	36	multiplication	multiplication	NOUN
iajs-156	101	37	modules	module	NOUN
iajs-156	101	38	.	.	PUNCT
iajs-156	102	1	recall	recall	VERB
iajs-156	102	2	that	that	SCONJ
iajs-156	102	3	a	a	DET
iajs-156	102	4	proper	proper	ADJ
iajs-156	102	5	submodule	submodule	NOUN
iajs-156	102	6	n	n	PROPN
iajs-156	102	7	of	of	ADP
iajs-156	102	8	an	an	DET
iajs-156	102	9	r	r	NOUN
iajs-156	102	10	-	-	PUNCT
iajs-156	102	11	module	module	NOUN
iajs-156	102	12	m	m	NOUN
iajs-156	102	13	is	be	AUX
iajs-156	102	14	called	call	VERB
iajs-156	102	15	a	a	DET
iajs-156	102	16	semiprime	semiprime	NOUN
iajs-156	102	17	submodule	submodule	NOUN
iajs-156	102	18	if	if	SCONJ
iajs-156	102	19	for	for	ADP
iajs-156	102	20	every	every	DET
iajs-156	102	21	r	r	NOUN
iajs-156	102	22			NOUN
iajs-156	102	23	r	r	NOUN
iajs-156	102	24	,	,	PUNCT
iajs-156	102	25	x	x	SYM
iajs-156	102	26			PROPN
iajs-156	102	27	m	m	PROPN
iajs-156	102	28	,	,	PUNCT
iajs-156	102	29	k	k	PROPN
iajs-156	102	30			PROPN
iajs-156	102	31	z+	z+	NUM
iajs-156	102	32	such	such	ADJ
iajs-156	102	33	that	that	SCONJ
iajs-156	102	34	rkx	rkx	PROPN
iajs-156	102	35			NOUN
iajs-156	103	1	n	n	PRON
iajs-156	103	2	implies	imply	VERB
iajs-156	103	3	rx	rx	VERB
iajs-156	103	4			NOUN
iajs-156	103	5	n	n	PRON
iajs-156	103	6	implies	imply	VERB
iajs-156	103	7	rx	rx	VERB
iajs-156	103	8			PROPN
iajs-156	103	9	n	n	CCONJ
iajs-156	103	10	,	,	PUNCT
iajs-156	103	11	see	see	VERB
iajs-156	103	12	[	[	X
iajs-156	103	13	4	4	NUM
iajs-156	103	14	]	]	X
iajs-156	103	15	.	.	PUNCT
iajs-156	104	1	equivalently	equivalently	ADV
iajs-156	104	2	,	,	PUNCT
iajs-156	104	3	a	a	DET
iajs-156	104	4	proper	proper	ADJ
iajs-156	104	5	submodule	submodule	NOUN
iajs-156	104	6	n	n	PROPN
iajs-156	104	7	of	of	ADP
iajs-156	104	8	m	m	PROPN
iajs-156	104	9	is	be	AUX
iajs-156	104	10	semiprime	semiprime	ADJ
iajs-156	104	11	if	if	SCONJ
iajs-156	104	12	for	for	SCONJ
iajs-156	104	13	every	every	DET
iajs-156	104	14	r	r	NOUN
iajs-156	104	15			NOUN
iajs-156	104	16	r	r	NOUN
iajs-156	104	17	,	,	PUNCT
iajs-156	104	18	x	x	SYM
iajs-156	104	19			NOUN
iajs-156	104	20	m	m	VERB
iajs-156	104	21	such	such	ADJ
iajs-156	104	22	that	that	DET
iajs-156	104	23	r2x	r2x	PROPN
iajs-156	104	24			NOUN
iajs-156	104	25	n	n	PRON
iajs-156	104	26	implies	imply	VERB
iajs-156	104	27	rx	rx	VERB
iajs-156	104	28			PROPN
iajs-156	104	29	n	n	CCONJ
iajs-156	104	30	,	,	PUNCT
iajs-156	104	31	see	see	VERB
iajs-156	104	32	[	[	X
iajs-156	104	33	5	5	NUM
iajs-156	104	34	]	]	PUNCT
iajs-156	104	35	.	.	PUNCT
iajs-156	105	1	an	an	DET
iajs-156	105	2	r	r	NOUN
iajs-156	105	3	-	-	PUNCT
iajs-156	105	4	module	module	NOUN
iajs-156	105	5	m	m	NOUN
iajs-156	105	6	is	be	AUX
iajs-156	105	7	called	call	VERB
iajs-156	105	8	semiprime	semiprime	NOUN
iajs-156	105	9	if	if	SCONJ
iajs-156	105	10	<	<	X
iajs-156	105	11	0	0	NUM
iajs-156	105	12	>	>	X
iajs-156	105	13	is	be	AUX
iajs-156	105	14	a	a	DET
iajs-156	105	15	semiprime	semiprime	NOUN
iajs-156	105	16	submodule	submodule	NOUN
iajs-156	105	17	of	of	ADP
iajs-156	105	18	m.	m.	NOUN
iajs-156	105	19	the	the	DET
iajs-156	105	20	proof	proof	NOUN
iajs-156	105	21	of	of	ADP
iajs-156	105	22	the	the	DET
iajs-156	105	23	following	following	ADJ
iajs-156	105	24	result	result	NOUN
iajs-156	105	25	follows	follow	VERB
iajs-156	105	26	by	by	ADP
iajs-156	105	27	[	[	X
iajs-156	105	28	5	5	NUM
iajs-156	105	29	]	]	PUNCT
iajs-156	105	30	.	.	PUNCT
iajs-156	106	1	proposition	proposition	NOUN
iajs-156	106	2	(	(	PUNCT
iajs-156	106	3	2.1	2.1	NUM
iajs-156	106	4	):	):	PUNCT
iajs-156	106	5	let	let	VERB
iajs-156	106	6	r	r	PRON
iajs-156	106	7	be	be	AUX
iajs-156	106	8	a	a	DET
iajs-156	106	9	principal	principal	ADJ
iajs-156	106	10	ideal	ideal	ADJ
iajs-156	106	11	ring	ring	NOUN
iajs-156	106	12	and	and	CCONJ
iajs-156	106	13	m	m	NOUN
iajs-156	106	14	is	be	AUX
iajs-156	106	15	an	an	DET
iajs-156	106	16	r	r	NOUN
iajs-156	106	17	-	-	PUNCT
iajs-156	106	18	module	module	NOUN
iajs-156	106	19	.	.	PUNCT
iajs-156	107	1	if	if	SCONJ
iajs-156	107	2	every	every	DET
iajs-156	107	3	proper	proper	ADJ
iajs-156	107	4	submodule	submodule	NOUN
iajs-156	107	5	of	of	ADP
iajs-156	107	6	m	m	PROPN
iajs-156	107	7	is	be	AUX
iajs-156	107	8	semiprime	semiprime	NOUN
iajs-156	107	9	then	then	ADV
iajs-156	107	10	m	m	VERB
iajs-156	107	11	is	be	AUX
iajs-156	107	12	a	a	DET
iajs-156	107	13	2	2	NUM
iajs-156	107	14	-	-	PUNCT
iajs-156	107	15	regular	regular	ADJ
iajs-156	107	16	module	module	NOUN
iajs-156	107	17	.	.	PUNCT
iajs-156	108	1	the	the	DET
iajs-156	108	2	converse	converse	NOUN
iajs-156	108	3	is	be	AUX
iajs-156	108	4	not	not	PART
iajs-156	108	5	true	true	ADJ
iajs-156	108	6	,	,	PUNCT
iajs-156	108	7	for	for	ADP
iajs-156	108	8	example	example	NOUN
iajs-156	108	9	:	:	PUNCT
iajs-156	108	10	the	the	DET
iajs-156	108	11	module	module	NOUN
iajs-156	108	12	z4	z4	PROPN
iajs-156	108	13	as	as	ADP
iajs-156	108	14	z	z	NOUN
iajs-156	108	15	-	-	PUNCT
iajs-156	108	16	module	module	NOUN
iajs-156	108	17	is	be	AUX
iajs-156	108	18	2	2	NUM
iajs-156	108	19	-	-	PUNCT
iajs-156	108	20	regular	regular	ADJ
iajs-156	108	21	but	but	CCONJ
iajs-156	108	22	<	<	X
iajs-156	108	23	0	0	NUM
iajs-156	108	24	>	>	X
iajs-156	108	25	is	be	AUX
iajs-156	108	26	not	not	PART
iajs-156	108	27	semiprime	semiprime	NOUN
iajs-156	108	28	.	.	PUNCT
iajs-156	109	1	the	the	DET
iajs-156	109	2	following	follow	VERB
iajs-156	109	3	proposition	proposition	NOUN
iajs-156	109	4	gives	give	VERB
iajs-156	109	5	a	a	DET
iajs-156	109	6	partial	partial	ADJ
iajs-156	109	7	converse	converse	NOUN
iajs-156	109	8	of	of	ADP
iajs-156	109	9	proposition	proposition	NOUN
iajs-156	109	10	(	(	PUNCT
iajs-156	109	11	2.1	2.1	NUM
iajs-156	109	12	)	)	PUNCT
iajs-156	109	13	.	.	PUNCT
iajs-156	110	1	proposition	proposition	NOUN
iajs-156	110	2	(	(	PUNCT
iajs-156	110	3	2.2	2.2	NUM
iajs-156	110	4	):	):	PUNCT
iajs-156	110	5	let	let	VERB
iajs-156	110	6	m	m	PRON
iajs-156	110	7	be	be	AUX
iajs-156	110	8	2	2	NUM
iajs-156	110	9	-	-	PUNCT
iajs-156	110	10	regular	regular	ADJ
iajs-156	110	11	and	and	CCONJ
iajs-156	110	12	semiprime	semiprime	NOUN
iajs-156	110	13	r	r	NOUN
iajs-156	110	14	-	-	PUNCT
iajs-156	110	15	module	module	NOUN
iajs-156	110	16	then	then	ADV
iajs-156	110	17	every	every	DET
iajs-156	110	18	proper	proper	ADJ
iajs-156	110	19	submodule	submodule	NOUN
iajs-156	110	20	of	of	ADP
iajs-156	110	21	m	m	PROPN
iajs-156	110	22	is	be	AUX
iajs-156	110	23	semiprime	semiprime	NOUN
iajs-156	110	24	.	.	PUNCT
iajs-156	111	1	proof	proof	NOUN
iajs-156	111	2	:	:	PUNCT
iajs-156	111	3	let	let	VERB
iajs-156	111	4	n	n	PRON
iajs-156	111	5	be	be	AUX
iajs-156	111	6	a	a	DET
iajs-156	111	7	proper	proper	ADJ
iajs-156	111	8	submodule	submodule	NOUN
iajs-156	111	9	of	of	ADP
iajs-156	111	10	m	m	PROPN
iajs-156	111	11	and	and	CCONJ
iajs-156	111	12	r2x	r2x	VERB
iajs-156	111	13			NOUN
iajs-156	111	14	n	n	CCONJ
iajs-156	111	15	where	where	SCONJ
iajs-156	111	16	r	r	NOUN
iajs-156	111	17			NOUN
iajs-156	111	18	r	r	NOUN
iajs-156	111	19	,	,	PUNCT
iajs-156	111	20	x	x	SYM
iajs-156	111	21			NOUN
iajs-156	111	22	m	m	VERB
iajs-156	111	23	implies	imply	VERB
iajs-156	111	24	r2x	r2x	PROPN
iajs-156	111	25			NOUN
iajs-156	111	26	r2	r2	PROPN
iajs-156	111	27	m	m	PROPN
iajs-156	111	28			PUNCT
iajs-156	111	29	n	n	NOUN
iajs-156	111	30	=	=	PUNCT
iajs-156	111	31	r2n	r2n	NOUN
iajs-156	111	32	since	since	SCONJ
iajs-156	111	33	m	m	PROPN
iajs-156	111	34	is	be	AUX
iajs-156	111	35	2	2	NUM
iajs-156	111	36	-	-	PUNCT
iajs-156	111	37	regular	regular	ADJ
iajs-156	111	38	.	.	PUNCT
iajs-156	112	1	then	then	ADV
iajs-156	112	2	r2x	r2x	VERB
iajs-156	112	3	=	=	PUNCT
iajs-156	112	4	r2n	r2n	NOUN
iajs-156	112	5	for	for	ADP
iajs-156	112	6	some	some	DET
iajs-156	112	7	n	n	ADJ
iajs-156	112	8			NOUN
iajs-156	112	9	n	n	CCONJ
iajs-156	112	10	,	,	PUNCT
iajs-156	112	11	thus	thus	ADV
iajs-156	112	12	r2(x	r2(x	X
iajs-156	112	13	–	–	PUNCT
iajs-156	112	14	n	n	CCONJ
iajs-156	112	15	)	)	PUNCT
iajs-156	112	16			NOUN
iajs-156	112	17	<	<	X
iajs-156	112	18	0	0	NUM
iajs-156	112	19	>	>	X
iajs-156	112	20	.	.	PUNCT
iajs-156	113	1	but	but	CCONJ
iajs-156	113	2	<	<	X
iajs-156	113	3	0	0	NUM
iajs-156	113	4	>	>	X
iajs-156	113	5	is	be	AUX
iajs-156	113	6	semiprime	semiprime	NOUN
iajs-156	113	7	,	,	PUNCT
iajs-156	113	8	hence	hence	ADV
iajs-156	113	9	rx	rx	VERB
iajs-156	113	10	=	=	PROPN
iajs-156	113	11	rn	rn	PROPN
iajs-156	113	12			PROPN
iajs-156	113	13	n.	n.	PROPN
iajs-156	113	14	therefore	therefore	ADV
iajs-156	113	15	n	n	ADV
iajs-156	113	16	is	be	AUX
iajs-156	113	17	semiprime	semiprime	NOUN
iajs-156	113	18	submodule	submodule	NOUN
iajs-156	113	19	of	of	ADP
iajs-156	113	20	m.	m.	NOUN
iajs-156	113	21	before	before	SCONJ
iajs-156	113	22	we	we	PRON
iajs-156	113	23	give	give	VERB
iajs-156	113	24	a	a	DET
iajs-156	113	25	consequence	consequence	NOUN
iajs-156	113	26	of	of	ADP
iajs-156	113	27	proposition	proposition	NOUN
iajs-156	113	28	(	(	PUNCT
iajs-156	113	29	2.2	2.2	NUM
iajs-156	113	30	)	)	PUNCT
iajs-156	113	31	,	,	PUNCT
iajs-156	113	32	we	we	PRON
iajs-156	113	33	need	need	VERB
iajs-156	113	34	the	the	DET
iajs-156	113	35	following	follow	VERB
iajs-156	113	36	lemma	lemma	PROPN
iajs-156	113	37	:	:	PUNCT
iajs-156	113	38	lemma	lemma	PROPN
iajs-156	113	39	(	(	PUNCT
iajs-156	113	40	2.3	2.3	NUM
iajs-156	113	41	):	):	PUNCT
iajs-156	113	42	let	let	VERB
iajs-156	113	43	m	m	PRON
iajs-156	113	44	be	be	AUX
iajs-156	113	45	2	2	NUM
iajs-156	113	46	-	-	PUNCT
iajs-156	113	47	regular	regular	ADJ
iajs-156	113	48	and	and	CCONJ
iajs-156	113	49	semiprime	semiprime	NOUN
iajs-156	113	50	r	r	NOUN
iajs-156	113	51	-	-	PUNCT
iajs-156	113	52	module	module	NOUN
iajs-156	113	53	then	then	ADV
iajs-156	113	54	j(r)m	j(r)m	PROPN
iajs-156	113	55	=	=	PUNCT
iajs-156	114	1	<	<	X
iajs-156	114	2	0	0	NUM
iajs-156	114	3	>	>	X
iajs-156	114	4	.	.	PUNCT
iajs-156	115	1	proof	proof	NOUN
iajs-156	115	2	:	:	PUNCT
iajs-156	115	3	let	let	VERB
iajs-156	115	4	r	r	NOUN
iajs-156	115	5			NOUN
iajs-156	115	6	j(r	j(r	PROPN
iajs-156	115	7	)	)	PUNCT
iajs-156	115	8	and	and	CCONJ
iajs-156	115	9	x	x	SYM
iajs-156	115	10			NOUN
iajs-156	115	11	m	m	VERB
iajs-156	115	12	then	then	ADV
iajs-156	115	13	r2x	r2x	PROPN
iajs-156	115	14	=	=	NOUN
iajs-156	115	15	r2tr2x	r2tr2x	NOUN
iajs-156	115	16	for	for	ADP
iajs-156	115	17	some	some	DET
iajs-156	115	18	t	t	NOUN
iajs-156	115	19			NOUN
iajs-156	115	20	r	r	NOUN
iajs-156	115	21	since	since	SCONJ
iajs-156	115	22	m	m	PROPN
iajs-156	115	23	is	be	AUX
iajs-156	115	24	2	2	NUM
iajs-156	115	25	-	-	PUNCT
iajs-156	115	26	regular	regular	ADJ
iajs-156	115	27	,	,	PUNCT
iajs-156	115	28	r2x(1	r2x(1	PROPN
iajs-156	115	29	–	–	PUNCT
iajs-156	115	30	r2t)=0	r2t)=0	PROPN
iajs-156	115	31	implies	imply	VERB
iajs-156	115	32	1	1	NUM
iajs-156	115	33	–	–	PUNCT
iajs-156	115	34	r2	r2	PROPN
iajs-156	115	35	t	t	PROPN
iajs-156	115	36	is	be	AUX
iajs-156	115	37	invertible	invertible	ADJ
iajs-156	115	38	in	in	ADP
iajs-156	115	39	r.	r.	PROPN
iajs-156	115	40	then	then	ADV
iajs-156	115	41	r2x	r2x	VERB
iajs-156	115	42	=	=	SYM
iajs-156	115	43	0	0	NUM
iajs-156	115	44	,	,	PUNCT
iajs-156	115	45	but	but	CCONJ
iajs-156	115	46	m	m	PROPN
iajs-156	115	47	is	be	AUX
iajs-156	115	48	semiprime	semiprime	NOUN
iajs-156	115	49	thus	thus	ADV
iajs-156	115	50	rx	rx	VERB
iajs-156	115	51	=	=	SYM
iajs-156	115	52	0	0	X
iajs-156	115	53	.	.	PUNCT
iajs-156	116	1	therefore	therefore	ADV
iajs-156	116	2	j(r)m	j(r)m	PROPN
iajs-156	116	3	=	=	PUNCT
iajs-156	117	1	<	<	X
iajs-156	117	2	0	0	NUM
iajs-156	117	3	>	>	X
iajs-156	117	4	.	.	PUNCT
iajs-156	118	1	recall	recall	VERB
iajs-156	118	2	that	that	SCONJ
iajs-156	118	3	an	an	DET
iajs-156	118	4	r	r	NOUN
iajs-156	118	5	-	-	PUNCT
iajs-156	118	6	module	module	NOUN
iajs-156	118	7	m	m	NOUN
iajs-156	118	8	is	be	AUX
iajs-156	118	9	called	call	VERB
iajs-156	118	10	semisimple	semisimple	NOUN
iajs-156	118	11	if	if	SCONJ
iajs-156	118	12	every	every	DET
iajs-156	118	13	submodule	submodule	NOUN
iajs-156	118	14	of	of	ADP
iajs-156	118	15	m	m	PROPN
iajs-156	118	16	is	be	AUX
iajs-156	118	17	a	a	DET
iajs-156	118	18	summand	summand	NOUN
iajs-156	118	19	.	.	PUNCT
iajs-156	119	1	the	the	DET
iajs-156	119	2	sum	sum	NOUN
iajs-156	119	3	of	of	ADP
iajs-156	119	4	all	all	DET
iajs-156	119	5	simple	simple	ADJ
iajs-156	119	6	submodules	submodule	NOUN
iajs-156	119	7	of	of	ADP
iajs-156	119	8	a	a	DET
iajs-156	119	9	module	module	NOUN
iajs-156	119	10	m	m	VERB
iajs-156	119	11	is	be	AUX
iajs-156	119	12	called	call	VERB
iajs-156	119	13	the	the	DET
iajs-156	119	14	socle	socle	NOUN
iajs-156	119	15	of	of	ADP
iajs-156	119	16	m	m	PROPN
iajs-156	119	17	is	be	AUX
iajs-156	119	18	denoted	denote	VERB
iajs-156	119	19	by	by	ADP
iajs-156	119	20	soc(m	soc(m	PROPN
iajs-156	119	21	)	)	PUNCT
iajs-156	119	22	,	,	PUNCT
iajs-156	119	23	moreover	moreover	ADV
iajs-156	119	24	if	if	SCONJ
iajs-156	119	25	soc(m	soc(m	PROPN
iajs-156	119	26	)	)	PUNCT
iajs-156	119	27	=	=	SYM
iajs-156	119	28	0	0	NUM
iajs-156	119	29	,	,	PUNCT
iajs-156	119	30	then	then	ADV
iajs-156	119	31	m	m	PROPN
iajs-156	119	32	has	have	VERB
iajs-156	119	33	no	no	DET
iajs-156	119	34	simple	simple	ADJ
iajs-156	119	35	submodule	submodule	NOUN
iajs-156	119	36	and	and	CCONJ
iajs-156	119	37	if	if	SCONJ
iajs-156	119	38	soc(m	soc(m	PROPN
iajs-156	119	39	)	)	PUNCT
iajs-156	120	1	=	=	PUNCT
iajs-156	121	1	m	m	VERB
iajs-156	121	2	then	then	ADV
iajs-156	121	3	m	m	VERB
iajs-156	121	4	is	be	AUX
iajs-156	121	5	semisimple	semisimple	NOUN
iajs-156	121	6	module	module	NOUN
iajs-156	121	7	,	,	PUNCT
iajs-156	121	8	see	see	VERB
iajs-156	121	9	[	[	X
iajs-156	121	10	6	6	NUM
iajs-156	121	11	]	]	PUNCT
iajs-156	121	12	.	.	PUNCT
iajs-156	122	1	a	a	DET
iajs-156	122	2	commutative	commutative	ADJ
iajs-156	122	3	ring	ring	NOUN
iajs-156	122	4	is	be	AUX
iajs-156	122	5	a	a	DET
iajs-156	122	6	local	local	ADJ
iajs-156	122	7	ring	ring	NOUN
iajs-156	122	8	in	in	ADP
iajs-156	122	9	case	case	NOUN
iajs-156	122	10	it	it	PRON
iajs-156	122	11	has	have	VERB
iajs-156	122	12	a	a	DET
iajs-156	122	13	unique	unique	ADJ
iajs-156	122	14	maximal	maximal	ADJ
iajs-156	122	15	ideal	ideal	NOUN
iajs-156	122	16	,	,	PUNCT
iajs-156	122	17	see	see	VERB
iajs-156	122	18	[	[	X
iajs-156	122	19	7	7	NUM
iajs-156	122	20	]	]	PUNCT
iajs-156	122	21	.	.	PUNCT
iajs-156	123	1	corollary	corollary	ADJ
iajs-156	123	2	(	(	PUNCT
iajs-156	123	3	2.4	2.4	NUM
iajs-156	123	4	):	):	PUNCT
iajs-156	123	5	let	let	VERB
iajs-156	123	6	r	r	PRON
iajs-156	123	7	be	be	AUX
iajs-156	123	8	a	a	DET
iajs-156	123	9	local	local	ADJ
iajs-156	123	10	ring	ring	NOUN
iajs-156	123	11	and	and	CCONJ
iajs-156	123	12	m	m	NOUN
iajs-156	123	13	is	be	AUX
iajs-156	123	14	2	2	NUM
iajs-156	123	15	-	-	PUNCT
iajs-156	123	16	regular	regular	ADJ
iajs-156	123	17	and	and	CCONJ
iajs-156	123	18	semiprime	semiprime	NOUN
iajs-156	123	19	r	r	NOUN
iajs-156	123	20	-	-	PUNCT
iajs-156	123	21	module	module	NOUN
iajs-156	123	22	then	then	ADV
iajs-156	123	23	m	m	VERB
iajs-156	123	24	is	be	AUX
iajs-156	123	25	a	a	DET
iajs-156	123	26	semisimple	semisimple	NOUN
iajs-156	123	27	and	and	CCONJ
iajs-156	123	28	hence	hence	ADV
iajs-156	123	29	is	be	AUX
iajs-156	123	30	regular	regular	ADJ
iajs-156	123	31	.	.	PUNCT
iajs-156	124	1	240	240	NUM
iajs-156	124	2	|	|	NOUN
iajs-156	124	3	mathematics	mathematic	NOUN
iajs-156	124	4	2015	2015	NUM
iajs-156	124	5	)	)	PUNCT
iajs-156	124	6	عام	عام	ADP
iajs-156	124	7	3العدد	3العدد	NUM
iajs-156	124	8	(	(	PUNCT
iajs-156	124	9	28مجلة	28مجلة	X
iajs-156	124	10	إبن	إبن	VERB
iajs-156	124	11	الھيثم	الھيثم	NOUN
iajs-156	124	12	للعلوم	للعلوم	NOUN
iajs-156	124	13	الصرفة	الصرفة	NOUN
iajs-156	125	1	و	و	PRON
iajs-156	125	2	التطبيقية	التطبيقية	ADV
iajs-156	125	3	المجلد	المجلد	VERB
iajs-156	125	4	ibn	ibn	PROPN
iajs-156	125	5	al	al	PROPN
iajs-156	125	6	-	-	PUNCT
iajs-156	125	7	haitham	haitham	PROPN
iajs-156	125	8	jour	jour	X
iajs-156	125	9	.	.	PROPN
iajs-156	126	1	for	for	ADP
iajs-156	126	2	pure	pure	ADJ
iajs-156	126	3	&	&	CCONJ
iajs-156	126	4	appl	appl	PROPN
iajs-156	126	5	.	.	PUNCT
iajs-156	127	1	sci	sci	PROPN
iajs-156	127	2	.	.	PUNCT
iajs-156	127	3	vol	vol	NOUN
iajs-156	127	4	.	.	PROPN
iajs-156	128	1	28	28	NUM
iajs-156	128	2	(	(	PUNCT
iajs-156	128	3	3	3	NUM
iajs-156	128	4	)	)	PUNCT
iajs-156	128	5	2015	2015	NUM
iajs-156	128	6	proof	proof	NOUN
iajs-156	128	7	:	:	PUNCT
iajs-156	128	8	since	since	SCONJ
iajs-156	128	9	r	r	NOUN
iajs-156	128	10	is	be	AUX
iajs-156	128	11	a	a	DET
iajs-156	128	12	local	local	ADJ
iajs-156	128	13	ring	ring	NOUN
iajs-156	128	14	,	,	PUNCT
iajs-156	128	15	then	then	ADV
iajs-156	128	16	r	r	PROPN
iajs-156	128	17	j(r	j(r	PROPN
iajs-156	128	18	)	)	PUNCT
iajs-156	128	19	is	be	AUX
iajs-156	128	20	a	a	DET
iajs-156	128	21	simple	simple	ADJ
iajs-156	128	22	ring	ring	NOUN
iajs-156	128	23	and	and	CCONJ
iajs-156	128	24	hence	hence	ADV
iajs-156	128	25	is	be	AUX
iajs-156	128	26	semisimple	semisimple	ADJ
iajs-156	128	27	.	.	PUNCT
iajs-156	129	1	by	by	ADP
iajs-156	129	2	[	[	X
iajs-156	129	3	6	6	NUM
iajs-156	129	4	]	]	PUNCT
iajs-156	129	5	,	,	PUNCT
iajs-156	129	6	soc(m	soc(m	PROPN
iajs-156	129	7	)	)	PUNCT
iajs-156	129	8	=	=	PUNCT
iajs-156	130	1	m	m	VERB
iajs-156	130	2	ann(j(r	ann(j(r	NOUN
iajs-156	130	3	)	)	PUNCT
iajs-156	130	4	)	)	PUNCT
iajs-156	131	1	=	=	PRON
iajs-156	131	2	{	{	PUNCT
iajs-156	131	3	m	m	PROPN
iajs-156	131	4			NOUN
iajs-156	131	5	m	m	PROPN
iajs-156	131	6	;	;	PUNCT
iajs-156	131	7	mj(r	mj(r	NOUN
iajs-156	131	8	)	)	PUNCT
iajs-156	131	9	=	=	PUNCT
iajs-156	132	1	0	0	NUM
iajs-156	132	2	}	}	PUNCT
iajs-156	132	3	.	.	PUNCT
iajs-156	133	1	but	but	CCONJ
iajs-156	133	2	j(r)m	j(r)m	PROPN
iajs-156	133	3	=	=	PUNCT
iajs-156	134	1	<	<	X
iajs-156	134	2	0	0	NUM
iajs-156	134	3	>	>	X
iajs-156	134	4	by	by	ADP
iajs-156	134	5	lemma	lemma	PROPN
iajs-156	134	6	(	(	PUNCT
iajs-156	134	7	2.3	2.3	NUM
iajs-156	134	8	)	)	PUNCT
iajs-156	134	9	,	,	PUNCT
iajs-156	134	10	thus	thus	ADV
iajs-156	134	11	soc(m	soc(m	PROPN
iajs-156	134	12	)	)	PUNCT
iajs-156	134	13	=	=	VERB
iajs-156	135	1	m.	m.	NOUN
iajs-156	135	2	therefore	therefore	ADV
iajs-156	135	3	m	m	PROPN
iajs-156	135	4	is	be	AUX
iajs-156	135	5	semisimple	semisimple	ADJ
iajs-156	135	6	.	.	PUNCT
iajs-156	136	1	now	now	ADV
iajs-156	136	2	,	,	PUNCT
iajs-156	136	3	we	we	PRON
iajs-156	136	4	have	have	VERB
iajs-156	136	5	the	the	DET
iajs-156	136	6	following	following	NOUN
iajs-156	136	7	:	:	PUNCT
iajs-156	136	8	proposition	proposition	NOUN
iajs-156	136	9	(	(	PUNCT
iajs-156	136	10	2.5	2.5	NUM
iajs-156	136	11	):	):	PUNCT
iajs-156	136	12	let	let	VERB
iajs-156	136	13	n	n	PRON
iajs-156	136	14	be	be	AUX
iajs-156	136	15	a	a	DET
iajs-156	136	16	semiprime	semiprime	NOUN
iajs-156	136	17	submodule	submodule	NOUN
iajs-156	136	18	of	of	ADP
iajs-156	136	19	an	an	DET
iajs-156	136	20	r	r	NOUN
iajs-156	136	21	-	-	PUNCT
iajs-156	136	22	module	module	NOUN
iajs-156	136	23	m	m	NOUN
iajs-156	136	24	and	and	CCONJ
iajs-156	136	25	k	k	PROPN
iajs-156	136	26	is	be	AUX
iajs-156	136	27	a	a	DET
iajs-156	136	28	2	2	NUM
iajs-156	136	29	-	-	PUNCT
iajs-156	136	30	pure	pure	ADJ
iajs-156	136	31	submodule	submodule	NOUN
iajs-156	136	32	of	of	ADP
iajs-156	136	33	m	m	PROPN
iajs-156	136	34	containing	contain	VERB
iajs-156	136	35	n	n	CCONJ
iajs-156	136	36	,	,	PUNCT
iajs-156	136	37	then	then	ADV
iajs-156	136	38	k	k	PROPN
iajs-156	136	39	n	n	PROPN
iajs-156	136	40	is	be	AUX
iajs-156	136	41	semiprime	semiprime	NOUN
iajs-156	136	42	submodule	submodule	NOUN
iajs-156	136	43	in	in	ADP
iajs-156	136	44	m	m	PROPN
iajs-156	136	45	n	n	NOUN
iajs-156	136	46	.	.	PUNCT
iajs-156	137	1	proof	proof	NOUN
iajs-156	137	2	:	:	PUNCT
iajs-156	137	3	let	let	VERB
iajs-156	137	4	r2(x	r2(x	PRON
iajs-156	137	5	+	+	NOUN
iajs-156	137	6	n	n	CCONJ
iajs-156	137	7	)	)	PUNCT
iajs-156	137	8			NOUN
iajs-156	137	9	k	k	PROPN
iajs-156	137	10	n	n	CCONJ
iajs-156	137	11	for	for	ADP
iajs-156	137	12	some	some	DET
iajs-156	137	13	r	r	NOUN
iajs-156	137	14			NOUN
iajs-156	137	15	r	r	NOUN
iajs-156	137	16	and	and	CCONJ
iajs-156	137	17	x	x	SYM
iajs-156	137	18	+	+	CCONJ
iajs-156	137	19	n	n	CCONJ
iajs-156	137	20			NOUN
iajs-156	137	21	m	m	VERB
iajs-156	137	22	n	n	NUM
iajs-156	137	23	.	.	PUNCT
iajs-156	138	1	then	then	ADV
iajs-156	138	2	r2x	r2x	VERB
iajs-156	138	3			PROPN
iajs-156	138	4	k	k	PROPN
iajs-156	138	5	,	,	PUNCT
iajs-156	138	6	imples	imple	VERB
iajs-156	138	7	r2x	r2x	PROPN
iajs-156	138	8			NOUN
iajs-156	138	9	r2	r2	PROPN
iajs-156	138	10	m	m	PROPN
iajs-156	138	11			PUNCT
iajs-156	138	12	k	k	NOUN
iajs-156	139	1	=	=	PUNCT
iajs-156	139	2	r2k	r2k	NOUN
iajs-156	139	3	since	since	SCONJ
iajs-156	139	4	k	k	PROPN
iajs-156	139	5	is	be	AUX
iajs-156	139	6	2	2	NUM
iajs-156	139	7	-	-	ADJ
iajs-156	139	8	pure	pure	ADJ
iajs-156	139	9	in	in	ADP
iajs-156	139	10	m.	m.	NOUN
iajs-156	139	11	let	let	VERB
iajs-156	139	12	r2x	r2x	VERB
iajs-156	139	13	=	=	PUNCT
iajs-156	139	14	r2	r2	PROPN
iajs-156	139	15	m	m	VERB
iajs-156	139	16	for	for	ADP
iajs-156	139	17	some	some	DET
iajs-156	139	18	m	m	PROPN
iajs-156	139	19			NOUN
iajs-156	139	20	k.	k.	PROPN
iajs-156	140	1	thus	thus	ADV
iajs-156	140	2	r2(x	r2(x	X
iajs-156	140	3	–	–	PUNCT
iajs-156	140	4	m	m	NOUN
iajs-156	140	5	)	)	PUNCT
iajs-156	140	6	=	=	SYM
iajs-156	140	7	0	0	NUM
iajs-156	140	8			NOUN
iajs-156	140	9	n	n	CCONJ
iajs-156	140	10	implies	imply	VERB
iajs-156	140	11	r(x	r(x	PROPN
iajs-156	140	12	–	–	PUNCT
iajs-156	140	13	m	m	NOUN
iajs-156	140	14	)	)	PUNCT
iajs-156	140	15			NOUN
iajs-156	140	16	n	n	CCONJ
iajs-156	140	17	since	since	SCONJ
iajs-156	140	18	n	n	ADV
iajs-156	140	19	is	be	AUX
iajs-156	140	20	semiprime	semiprime	NOUN
iajs-156	140	21	submodule	submodule	NOUN
iajs-156	140	22	in	in	ADP
iajs-156	140	23	m	m	PROPN
iajs-156	140	24	,	,	PUNCT
iajs-156	140	25	hence	hence	ADV
iajs-156	140	26	r(x	r(x	NOUN
iajs-156	140	27	+	+	CCONJ
iajs-156	140	28	n	n	CCONJ
iajs-156	140	29	)	)	PUNCT
iajs-156	140	30	=	=	SYM
iajs-156	140	31	rm	rm	PROPN
iajs-156	140	32	+	+	CCONJ
iajs-156	140	33	n	n	CCONJ
iajs-156	140	34			NOUN
iajs-156	140	35	k	k	PROPN
iajs-156	140	36	n	n	PROPN
iajs-156	140	37	.	.	PUNCT
iajs-156	141	1	therefore	therefore	ADV
iajs-156	141	2	k	k	PROPN
iajs-156	141	3	n	n	PROPN
iajs-156	141	4	is	be	AUX
iajs-156	141	5	semiprime	semiprime	NOUN
iajs-156	141	6	submodule	submodule	NOUN
iajs-156	141	7	in	in	ADP
iajs-156	141	8	m	m	PROPN
iajs-156	141	9	n	n	NOUN
iajs-156	141	10	.	.	PUNCT
iajs-156	142	1	corollary	corollary	ADJ
iajs-156	142	2	(	(	PUNCT
iajs-156	142	3	2.6	2.6	NUM
iajs-156	142	4	):	):	PUNCT
iajs-156	142	5	let	let	VERB
iajs-156	142	6	n	n	PRON
iajs-156	142	7	be	be	AUX
iajs-156	142	8	a	a	DET
iajs-156	142	9	semiprime	semiprime	NOUN
iajs-156	142	10	submodule	submodule	NOUN
iajs-156	142	11	of	of	ADP
iajs-156	142	12	an	an	DET
iajs-156	142	13	r	r	NOUN
iajs-156	142	14	-	-	PUNCT
iajs-156	142	15	module	module	NOUN
iajs-156	142	16	m	m	NOUN
iajs-156	142	17	and	and	CCONJ
iajs-156	142	18	k	k	PROPN
iajs-156	142	19	is	be	AUX
iajs-156	142	20	a	a	DET
iajs-156	142	21	2	2	NUM
iajs-156	142	22	-	-	PUNCT
iajs-156	142	23	pure	pure	ADJ
iajs-156	142	24	in	in	ADP
iajs-156	142	25	m	m	PROPN
iajs-156	142	26	with	with	ADP
iajs-156	143	1	n	n	PROPN
iajs-156	143	2			PROPN
iajs-156	143	3	k	k	PROPN
iajs-156	143	4	then	then	ADV
iajs-156	143	5	k	k	PROPN
iajs-156	143	6	is	be	AUX
iajs-156	143	7	semiprime	semiprime	NOUN
iajs-156	143	8	submodule	submodule	NOUN
iajs-156	143	9	in	in	ADP
iajs-156	143	10	m.	m.	NOUN
iajs-156	143	11	proof	proof	NOUN
iajs-156	143	12	:	:	PUNCT
iajs-156	143	13	let	let	VERB
iajs-156	143	14	r2x	r2x	VERB
iajs-156	143	15			PROPN
iajs-156	143	16	k	k	PROPN
iajs-156	143	17	for	for	ADP
iajs-156	143	18	some	some	DET
iajs-156	143	19	r	r	NOUN
iajs-156	143	20			NOUN
iajs-156	143	21	r	r	NOUN
iajs-156	143	22	and	and	CCONJ
iajs-156	143	23	x	x	PROPN
iajs-156	143	24			NOUN
iajs-156	143	25	m.	m.	NOUN
iajs-156	144	1	thus	thus	ADV
iajs-156	144	2	r2(x	r2(x	X
iajs-156	144	3	+	+	CCONJ
iajs-156	144	4	n	n	CCONJ
iajs-156	144	5	)	)	PUNCT
iajs-156	144	6			NOUN
iajs-156	144	7	k	k	NOUN
iajs-156	144	8	n	n	CCONJ
iajs-156	144	9	,	,	PUNCT
iajs-156	144	10	but	but	CCONJ
iajs-156	144	11	k	k	PROPN
iajs-156	144	12	n	n	PROPN
iajs-156	144	13	is	be	AUX
iajs-156	144	14	semiprime	semiprime	NOUN
iajs-156	144	15	in	in	ADP
iajs-156	144	16	m	m	PROPN
iajs-156	144	17	k	k	NOUN
iajs-156	144	18	by	by	ADP
iajs-156	144	19	proposition	proposition	NOUN
iajs-156	144	20	(	(	PUNCT
iajs-156	144	21	2.5	2.5	NUM
iajs-156	144	22	)	)	PUNCT
iajs-156	144	23	therefore	therefore	ADV
iajs-156	144	24	r(x	r(x	PROPN
iajs-156	144	25	+	+	CCONJ
iajs-156	144	26	n	n	CCONJ
iajs-156	144	27	)	)	PUNCT
iajs-156	144	28			NOUN
iajs-156	144	29	k	k	PROPN
iajs-156	145	1	n	n	PROPN
iajs-156	145	2	.	.	PUNCT
iajs-156	146	1	hence	hence	ADV
iajs-156	146	2	rx	rx	VERB
iajs-156	146	3			PROPN
iajs-156	146	4	k	k	PROPN
iajs-156	146	5	,	,	PUNCT
iajs-156	146	6	that	that	PRON
iajs-156	146	7	is	is	ADV
iajs-156	146	8	k	k	PROPN
iajs-156	146	9	is	be	AUX
iajs-156	146	10	semiprime	semiprime	NOUN
iajs-156	146	11	in	in	ADP
iajs-156	146	12	m.	m.	NOUN
iajs-156	146	13	let	let	VERB
iajs-156	146	14	r	r	PRON
iajs-156	146	15	be	be	AUX
iajs-156	146	16	an	an	DET
iajs-156	146	17	integral	integral	ADJ
iajs-156	146	18	domain	domain	NOUN
iajs-156	146	19	,	,	PUNCT
iajs-156	146	20	an	an	DET
iajs-156	146	21	r	r	NOUN
iajs-156	146	22	-	-	PUNCT
iajs-156	146	23	module	module	NOUN
iajs-156	146	24	m	m	NOUN
iajs-156	146	25	is	be	AUX
iajs-156	146	26	said	say	VERB
iajs-156	146	27	to	to	PART
iajs-156	146	28	be	be	AUX
iajs-156	146	29	divisible	divisible	ADJ
iajs-156	146	30	if	if	SCONJ
iajs-156	146	31	and	and	CCONJ
iajs-156	146	32	only	only	ADV
iajs-156	146	33	if	if	SCONJ
iajs-156	146	34	rm	rm	PROPN
iajs-156	146	35	=	=	VERB
iajs-156	146	36	m	m	VERB
iajs-156	146	37	for	for	ADP
iajs-156	146	38	every	every	DET
iajs-156	146	39	non	non	ADJ
iajs-156	146	40	-	-	ADJ
iajs-156	146	41	zero	zero	NUM
iajs-156	146	42	element	element	NOUN
iajs-156	146	43	r	r	NOUN
iajs-156	146	44	of	of	ADP
iajs-156	146	45	r	r	NOUN
iajs-156	146	46	,	,	PUNCT
iajs-156	146	47	see	see	VERB
iajs-156	146	48	[	[	X
iajs-156	146	49	8	8	NUM
iajs-156	146	50	]	]	PUNCT
iajs-156	146	51	.	.	PUNCT
iajs-156	147	1	an	an	DET
iajs-156	147	2	r	r	NOUN
iajs-156	147	3	-	-	PUNCT
iajs-156	147	4	module	module	NOUN
iajs-156	147	5	m	m	NOUN
iajs-156	147	6	is	be	AUX
iajs-156	147	7	said	say	VERB
iajs-156	147	8	to	to	PART
iajs-156	147	9	be	be	AUX
iajs-156	147	10	a	a	DET
iajs-156	147	11	prime	prime	ADJ
iajs-156	147	12	module	module	NOUN
iajs-156	147	13	if	if	SCONJ
iajs-156	147	14	r	r	NOUN
iajs-156	147	15	r	r	NOUN
iajs-156	147	16	ann(m	ann(m	NOUN
iajs-156	147	17	)	)	PUNCT
iajs-156	147	18	ann(n)	ann(n)	PROPN
iajs-156	147	19	for	for	ADP
iajs-156	147	20	every	every	DET
iajs-156	147	21	non	non	ADJ
iajs-156	147	22	-	-	ADJ
iajs-156	147	23	zero	zero	NUM
iajs-156	147	24	submodule	submodule	NOUN
iajs-156	147	25	n	n	PROPN
iajs-156	147	26	of	of	ADP
iajs-156	147	27	m	m	PRON
iajs-156	147	28	,	,	PUNCT
iajs-156	147	29	see	see	VERB
iajs-156	147	30	[	[	X
iajs-156	147	31	9	9	NUM
iajs-156	147	32	]	]	PUNCT
iajs-156	147	33	.	.	PUNCT
iajs-156	148	1	proposition	proposition	NOUN
iajs-156	148	2	(	(	PUNCT
iajs-156	148	3	2.7	2.7	NUM
iajs-156	148	4	):	):	PUNCT
iajs-156	148	5	let	let	VERB
iajs-156	148	6	m	m	PRON
iajs-156	148	7	be	be	AUX
iajs-156	148	8	a	a	DET
iajs-156	148	9	module	module	NOUN
iajs-156	148	10	over	over	ADP
iajs-156	148	11	a	a	DET
iajs-156	148	12	principal	principal	ADJ
iajs-156	148	13	ideal	ideal	ADJ
iajs-156	148	14	domain	domain	NOUN
iajs-156	148	15	r	r	NOUN
iajs-156	148	16	and	and	CCONJ
iajs-156	148	17	n	n	PROPN
iajs-156	148	18	is	be	AUX
iajs-156	148	19	a	a	DET
iajs-156	148	20	divisible	divisible	ADJ
iajs-156	148	21	r	r	NOUN
iajs-156	148	22	-	-	PUNCT
iajs-156	148	23	submodule	submodule	NOUN
iajs-156	148	24	of	of	ADP
iajs-156	148	25	m	m	PROPN
iajs-156	148	26	then	then	ADV
iajs-156	148	27	n	n	PRON
iajs-156	148	28	is	be	AUX
iajs-156	148	29	a	a	DET
iajs-156	148	30	2	2	NUM
iajs-156	148	31	-	-	PUNCT
iajs-156	148	32	pure	pure	ADJ
iajs-156	148	33	submodule	submodule	NOUN
iajs-156	148	34	in	in	ADP
iajs-156	148	35	m.	m.	NOUN
iajs-156	148	36	proof	proof	NOUN
iajs-156	148	37	:	:	PUNCT
iajs-156	148	38	since	since	SCONJ
iajs-156	148	39	n	n	PRON
iajs-156	148	40	is	be	AUX
iajs-156	148	41	divisible	divisible	ADJ
iajs-156	148	42	then	then	ADV
iajs-156	148	43	for	for	ADP
iajs-156	148	44	each	each	DET
iajs-156	148	45	rr	rr	NUM
iajs-156	148	46	,	,	PUNCT
iajs-156	148	47	r2n	r2n	NOUN
iajs-156	148	48	=	=	NOUN
iajs-156	148	49	n.	n.	NOUN
iajs-156	148	50	therefore	therefore	ADV
iajs-156	148	51	n	n	CCONJ
iajs-156	148	52			PUNCT
iajs-156	148	53	r2	r2	NOUN
iajs-156	148	54	m	m	NOUN
iajs-156	148	55	=	=	NOUN
iajs-156	148	56	r2n	r2n	NOUN
iajs-156	148	57	.	.	PUNCT
iajs-156	149	1	241	241	NUM
iajs-156	150	1	|	|	ADV
iajs-156	150	2	mathematics	mathematic	NOUN
iajs-156	150	3	2015	2015	NUM
iajs-156	150	4	)	)	PUNCT
iajs-156	150	5	عام	عام	ADP
iajs-156	150	6	3العدد	3العدد	NUM
iajs-156	150	7	(	(	PUNCT
iajs-156	150	8	28مجلة	28مجلة	X
iajs-156	150	9	إبن	إبن	VERB
iajs-156	150	10	الھيثم	الھيثم	NOUN
iajs-156	150	11	للعلوم	للعلوم	NOUN
iajs-156	150	12	الصرفة	الصرفة	NOUN
iajs-156	151	1	و	و	PRON
iajs-156	151	2	التطبيقية	التطبيقية	ADV
iajs-156	151	3	المجلد	المجلد	VERB
iajs-156	151	4	ibn	ibn	PROPN
iajs-156	151	5	al	al	PROPN
iajs-156	151	6	-	-	PUNCT
iajs-156	151	7	haitham	haitham	PROPN
iajs-156	151	8	jour	jour	X
iajs-156	151	9	.	.	PROPN
iajs-156	152	1	for	for	ADP
iajs-156	152	2	pure	pure	ADJ
iajs-156	152	3	&	&	CCONJ
iajs-156	152	4	appl	appl	PROPN
iajs-156	152	5	.	.	PUNCT
iajs-156	153	1	sci	sci	PROPN
iajs-156	153	2	.	.	PUNCT
iajs-156	153	3	vol	vol	NOUN
iajs-156	153	4	.	.	PROPN
iajs-156	154	1	28	28	NUM
iajs-156	154	2	(	(	PUNCT
iajs-156	154	3	3	3	NUM
iajs-156	154	4	)	)	PUNCT
iajs-156	154	5	2015	2015	NUM
iajs-156	154	6	remark	remark	NOUN
iajs-156	154	7	(	(	PUNCT
iajs-156	154	8	2.8	2.8	NUM
iajs-156	154	9	):	):	PUNCT
iajs-156	154	10	the	the	DET
iajs-156	154	11	converse	converse	NOUN
iajs-156	154	12	of	of	ADP
iajs-156	154	13	proposition	proposition	NOUN
iajs-156	154	14	(	(	PUNCT
iajs-156	154	15	2.7	2.7	NUM
iajs-156	154	16	)	)	PUNCT
iajs-156	154	17	is	be	AUX
iajs-156	154	18	not	not	PART
iajs-156	154	19	true	true	ADJ
iajs-156	154	20	,	,	PUNCT
iajs-156	154	21	for	for	ADP
iajs-156	154	22	example	example	NOUN
iajs-156	154	23	:	:	PUNCT
iajs-156	154	24	the	the	DET
iajs-156	154	25	submodule	submodule	NOUN
iajs-156	154	26	{	{	PUNCT
iajs-156	154	27	0	0	NUM
iajs-156	154	28	,	,	PUNCT
iajs-156	154	29	2	2	NUM
iajs-156	154	30	}	}	PUNCT
iajs-156	154	31	of	of	ADP
iajs-156	154	32	the	the	DET
iajs-156	154	33	module	module	NOUN
iajs-156	154	34	z4	z4	NOUN
iajs-156	154	35	as	as	ADP
iajs-156	154	36	z	z	NOUN
iajs-156	154	37	-	-	PUNCT
iajs-156	154	38	module	module	NOUN
iajs-156	154	39	where	where	SCONJ
iajs-156	154	40	{	{	PUNCT
iajs-156	154	41	0	0	NUM
iajs-156	154	42	,	,	PUNCT
iajs-156	154	43	2	2	NUM
iajs-156	154	44	}	}	PUNCT
iajs-156	154	45	is	be	AUX
iajs-156	154	46	2	2	NUM
iajs-156	154	47	-	-	ADJ
iajs-156	154	48	pure	pure	ADJ
iajs-156	154	49	in	in	ADP
iajs-156	154	50	z4	z4	PROPN
iajs-156	154	51	,	,	PUNCT
iajs-156	154	52	but	but	CCONJ
iajs-156	154	53	is	be	AUX
iajs-156	154	54	not	not	PART
iajs-156	154	55	divisible	divisible	ADJ
iajs-156	154	56	since	since	SCONJ
iajs-156	154	57	there	there	PRON
iajs-156	154	58	exists	exist	VERB
iajs-156	154	59	2	2	NUM
iajs-156	154	60			NOUN
iajs-156	154	61	z	z	NOUN
iajs-156	154	62	and	and	CCONJ
iajs-156	154	63	2{0	2{0	NUM
iajs-156	154	64	,	,	PUNCT
iajs-156	154	65	2	2	NUM
iajs-156	154	66	}	}	PUNCT
iajs-156	154	67	=	=	PRON
iajs-156	154	68	{	{	PUNCT
iajs-156	154	69	0	0	NUM
iajs-156	154	70	}	}	PUNCT
iajs-156	154	71	.	.	PUNCT
iajs-156	155	1	that	that	PRON
iajs-156	155	2	is	be	AUX
iajs-156	155	3	2{0	2{0	NUM
iajs-156	155	4	,	,	PUNCT
iajs-156	155	5	2	2	NUM
iajs-156	155	6	}	}	PUNCT
iajs-156	155	7			NOUN
iajs-156	155	8	{	{	PUNCT
iajs-156	155	9	0	0	NUM
iajs-156	155	10	,	,	PUNCT
iajs-156	155	11	2	2	NUM
iajs-156	155	12	}	}	PUNCT
iajs-156	155	13	.	.	PUNCT
iajs-156	156	1	the	the	DET
iajs-156	156	2	following	follow	VERB
iajs-156	156	3	proposition	proposition	NOUN
iajs-156	156	4	gives	give	VERB
iajs-156	156	5	a	a	DET
iajs-156	156	6	condition	condition	NOUN
iajs-156	156	7	under	under	ADP
iajs-156	156	8	which	which	PRON
iajs-156	156	9	the	the	DET
iajs-156	156	10	converse	converse	NOUN
iajs-156	156	11	of	of	ADP
iajs-156	156	12	proposition	proposition	NOUN
iajs-156	156	13	(	(	PUNCT
iajs-156	156	14	2.7	2.7	NUM
iajs-156	156	15	)	)	PUNCT
iajs-156	156	16	is	be	AUX
iajs-156	156	17	true	true	ADJ
iajs-156	156	18	.	.	PUNCT
iajs-156	157	1	proposition	proposition	NOUN
iajs-156	157	2	(	(	PUNCT
iajs-156	157	3	2.9	2.9	NUM
iajs-156	157	4	):	):	PUNCT
iajs-156	157	5	let	let	VERB
iajs-156	157	6	m	m	PRON
iajs-156	157	7	be	be	AUX
iajs-156	157	8	divisible	divisible	ADJ
iajs-156	157	9	module	module	NOUN
iajs-156	157	10	over	over	ADP
iajs-156	157	11	a	a	DET
iajs-156	157	12	principal	principal	ADJ
iajs-156	157	13	ideal	ideal	ADJ
iajs-156	157	14	domain	domain	NOUN
iajs-156	157	15	r	r	NOUN
iajs-156	157	16	and	and	CCONJ
iajs-156	157	17	n	n	PROPN
iajs-156	157	18	is	be	AUX
iajs-156	157	19	a	a	DET
iajs-156	157	20	2	2	NUM
iajs-156	157	21	-	-	PUNCT
iajs-156	157	22	pure	pure	ADJ
iajs-156	157	23	in	in	ADP
iajs-156	157	24	m	m	PROPN
iajs-156	157	25	then	then	ADV
iajs-156	157	26	n	n	ADV
iajs-156	157	27	is	be	AUX
iajs-156	157	28	divisible	divisible	ADJ
iajs-156	157	29	.	.	PUNCT
iajs-156	158	1	proof	proof	NOUN
iajs-156	158	2	:	:	PUNCT
iajs-156	158	3	assume	assume	VERB
iajs-156	158	4	n	n	PRON
iajs-156	158	5	is	be	AUX
iajs-156	158	6	2	2	NUM
iajs-156	158	7	-	-	ADJ
iajs-156	158	8	pure	pure	ADJ
iajs-156	158	9	in	in	ADP
iajs-156	158	10	m	m	PROPN
iajs-156	158	11	,	,	PUNCT
iajs-156	158	12	let	let	VERB
iajs-156	158	13	m	m	PRON
iajs-156	158	14			NOUN
iajs-156	158	15	n	n	CCONJ
iajs-156	158	16	and	and	CCONJ
iajs-156	158	17	r	r	PROPN
iajs-156	158	18			PROPN
iajs-156	158	19	r.	r.	PROPN
iajs-156	158	20	since	since	SCONJ
iajs-156	158	21	m	m	PROPN
iajs-156	158	22	is	be	AUX
iajs-156	158	23	divisible	divisible	ADJ
iajs-156	158	24	implies	imply	VERB
iajs-156	158	25	m	m	PROPN
iajs-156	158	26	=	=	VERB
iajs-156	158	27	r2x	r2x	NOUN
iajs-156	158	28	for	for	ADP
iajs-156	158	29	some	some	DET
iajs-156	158	30	x	x	SYM
iajs-156	158	31			NOUN
iajs-156	158	32	m.	m.	NOUN
iajs-156	158	33	but	but	CCONJ
iajs-156	158	34	m	m	NOUN
iajs-156	158	35	=	=	VERB
iajs-156	158	36	r2x	r2x	ADJ
iajs-156	158	37			NOUN
iajs-156	158	38	r2	r2	PROPN
iajs-156	158	39	m	m	PROPN
iajs-156	158	40			PUNCT
iajs-156	159	1	n	n	NOUN
iajs-156	159	2	=	=	PRON
iajs-156	159	3	r2n	r2n	X
iajs-156	159	4			PROPN
iajs-156	159	5	rn	rn	PROPN
iajs-156	159	6	.	.	PROPN
iajs-156	160	1	therefore	therefore	ADV
iajs-156	160	2	n	n	PROPN
iajs-156	160	3	=	=	SYM
iajs-156	160	4	rn	rn	PROPN
iajs-156	160	5	.	.	PROPN
iajs-156	161	1	as	as	ADP
iajs-156	161	2	an	an	DET
iajs-156	161	3	immediate	immediate	ADJ
iajs-156	161	4	consequence	consequence	NOUN
iajs-156	161	5	we	we	PRON
iajs-156	161	6	have	have	VERB
iajs-156	161	7	the	the	DET
iajs-156	161	8	following	follow	VERB
iajs-156	161	9	:	:	PUNCT
iajs-156	161	10	corollary	corollary	ADJ
iajs-156	161	11	(	(	PUNCT
iajs-156	161	12	2.10	2.10	NUM
iajs-156	161	13	):	):	PUNCT
iajs-156	161	14	let	let	VERB
iajs-156	161	15	r	r	PRON
iajs-156	161	16	be	be	AUX
iajs-156	161	17	a	a	DET
iajs-156	161	18	principal	principal	ADJ
iajs-156	161	19	ideal	ideal	ADJ
iajs-156	161	20	domain	domain	NOUN
iajs-156	161	21	and	and	CCONJ
iajs-156	161	22	every	every	DET
iajs-156	161	23	proper	proper	ADJ
iajs-156	161	24	submodule	submodule	NOUN
iajs-156	161	25	of	of	ADP
iajs-156	161	26	an	an	DET
iajs-156	161	27	r	r	NOUN
iajs-156	161	28	-	-	PUNCT
iajs-156	161	29	module	module	NOUN
iajs-156	161	30	m	m	NOUN
iajs-156	161	31	is	be	AUX
iajs-156	161	32	divisible	divisible	ADJ
iajs-156	161	33	then	then	ADV
iajs-156	161	34	m	m	VERB
iajs-156	161	35	is	be	AUX
iajs-156	161	36	2	2	NUM
iajs-156	161	37	-	-	PUNCT
iajs-156	161	38	regular	regular	ADJ
iajs-156	161	39	.	.	PUNCT
iajs-156	162	1	the	the	DET
iajs-156	162	2	converse	converse	NOUN
iajs-156	162	3	is	be	AUX
iajs-156	162	4	true	true	ADJ
iajs-156	162	5	if	if	SCONJ
iajs-156	162	6	m	m	NOUN
iajs-156	162	7	is	be	AUX
iajs-156	162	8	divisible	divisible	ADJ
iajs-156	162	9	.	.	PUNCT
iajs-156	163	1	proof	proof	NOUN
iajs-156	163	2	:	:	PUNCT
iajs-156	163	3	follows	follow	VERB
iajs-156	163	4	by	by	ADP
iajs-156	163	5	propositions	proposition	NOUN
iajs-156	163	6	(	(	PUNCT
iajs-156	163	7	2.7	2.7	NUM
iajs-156	163	8	)	)	PUNCT
iajs-156	163	9	and	and	CCONJ
iajs-156	163	10	(	(	PUNCT
iajs-156	163	11	2.9	2.9	NUM
iajs-156	163	12	)	)	PUNCT
iajs-156	163	13	.	.	PUNCT
iajs-156	164	1	corollary	corollary	ADJ
iajs-156	164	2	(	(	PUNCT
iajs-156	164	3	2.11	2.11	NUM
iajs-156	164	4	):	):	PUNCT
iajs-156	164	5	let	let	VERB
iajs-156	164	6	r	r	PRON
iajs-156	164	7	be	be	AUX
iajs-156	164	8	a	a	DET
iajs-156	164	9	principal	principal	ADJ
iajs-156	164	10	ideal	ideal	ADJ
iajs-156	164	11	domain	domain	NOUN
iajs-156	164	12	and	and	CCONJ
iajs-156	164	13	m	m	NOUN
iajs-156	164	14	is	be	AUX
iajs-156	164	15	2	2	NUM
iajs-156	164	16	-	-	PUNCT
iajs-156	164	17	regular	regular	ADJ
iajs-156	164	18	and	and	CCONJ
iajs-156	164	19	divisible	divisible	ADJ
iajs-156	164	20	r	r	NOUN
iajs-156	164	21	-	-	PUNCT
iajs-156	164	22	module	module	NOUN
iajs-156	164	23	then	then	ADV
iajs-156	164	24	m	m	VERB
iajs-156	164	25	is	be	AUX
iajs-156	164	26	prime	prime	ADJ
iajs-156	164	27	module	module	NOUN
iajs-156	164	28	.	.	PUNCT
iajs-156	165	1	proof	proof	NOUN
iajs-156	165	2	:	:	PUNCT
iajs-156	165	3	by	by	ADP
iajs-156	165	4	above	above	ADP
iajs-156	165	5	corollary	corollary	ADJ
iajs-156	165	6	(	(	PUNCT
iajs-156	165	7	2.10	2.10	NUM
iajs-156	165	8	)	)	PUNCT
iajs-156	165	9	,	,	PUNCT
iajs-156	165	10	every	every	DET
iajs-156	165	11	submodule	submodule	NOUN
iajs-156	165	12	n	n	PROPN
iajs-156	165	13	of	of	ADP
iajs-156	165	14	m	m	PROPN
iajs-156	165	15	is	be	AUX
iajs-156	165	16	divisible	divisible	ADJ
iajs-156	165	17	.	.	PUNCT
iajs-156	166	1	thus	thus	ADV
iajs-156	166	2	rn	rn	PROPN
iajs-156	166	3	=	=	PROPN
iajs-156	166	4	n	n	PROPN
iajs-156	166	5	for	for	ADP
iajs-156	166	6	every	every	DET
iajs-156	166	7	r	r	NOUN
iajs-156	166	8			PROPN
iajs-156	166	9	r.	r.	X
iajs-156	166	10	therefore	therefore	ADV
iajs-156	166	11	r	r	NOUN
iajs-156	166	12	r	r	NOUN
iajs-156	166	13	ann(n	ann(n	PROPN
iajs-156	166	14	)	)	PUNCT
iajs-156	166	15	ann(m	ann(m	PROPN
iajs-156	166	16	)	)	PUNCT
iajs-156	166	17	0	0	NUM
iajs-156	166	18			ADJ
iajs-156	166	19			X
iajs-156	166	20	.	.	PUNCT
iajs-156	167	1	hence	hence	ADV
iajs-156	167	2	m	m	PROPN
iajs-156	167	3	is	be	AUX
iajs-156	167	4	prime	prime	ADJ
iajs-156	167	5	module	module	NOUN
iajs-156	167	6	.	.	PUNCT
iajs-156	168	1	corollary	corollary	NOUN
iajs-156	168	2	(	(	PUNCT
iajs-156	168	3	2.12	2.12	NUM
iajs-156	168	4	):	):	PUNCT
iajs-156	168	5	let	let	VERB
iajs-156	168	6	r	r	PRON
iajs-156	168	7	be	be	AUX
iajs-156	168	8	a	a	DET
iajs-156	168	9	principal	principal	ADJ
iajs-156	168	10	ideal	ideal	ADJ
iajs-156	168	11	domain	domain	NOUN
iajs-156	168	12	and	and	CCONJ
iajs-156	168	13	m	m	NOUN
iajs-156	168	14	is	be	AUX
iajs-156	168	15	2	2	NUM
iajs-156	168	16	-	-	PUNCT
iajs-156	168	17	regular	regular	ADJ
iajs-156	168	18	injective	injective	ADJ
iajs-156	168	19	r	r	NOUN
iajs-156	168	20	-	-	PUNCT
iajs-156	168	21	module	module	NOUN
iajs-156	168	22	then	then	ADV
iajs-156	168	23	m	m	VERB
iajs-156	168	24	is	be	AUX
iajs-156	168	25	prime	prime	ADJ
iajs-156	168	26	module	module	NOUN
iajs-156	168	27	.	.	PUNCT
iajs-156	169	1	proof	proof	NOUN
iajs-156	169	2	:	:	PUNCT
iajs-156	169	3	clear	clear	ADJ
iajs-156	169	4	we	we	PRON
iajs-156	169	5	give	give	VERB
iajs-156	169	6	the	the	DET
iajs-156	169	7	following	follow	VERB
iajs-156	169	8	theorem	theorem	PROPN
iajs-156	169	9	.	.	PUNCT
iajs-156	170	1	theorem	theorem	PROPN
iajs-156	170	2	(	(	PUNCT
iajs-156	170	3	2.13	2.13	NUM
iajs-156	170	4	):	):	PUNCT
iajs-156	170	5	let	let	VERB
iajs-156	170	6	r	r	PRON
iajs-156	170	7	be	be	AUX
iajs-156	170	8	any	any	DET
iajs-156	170	9	ring	ring	NOUN
iajs-156	170	10	.	.	PUNCT
iajs-156	171	1	the	the	DET
iajs-156	171	2	following	follow	VERB
iajs-156	171	3	statements	statement	NOUN
iajs-156	171	4	are	be	AUX
iajs-156	171	5	equivalent	equivalent	ADJ
iajs-156	171	6	:	:	PUNCT
iajs-156	171	7	(	(	PUNCT
iajs-156	171	8	1	1	X
iajs-156	171	9	)	)	PUNCT
iajs-156	171	10			NOUN
iajs-156	171	11	r	r	NOUN
iajs-156	171	12	is	be	AUX
iajs-156	171	13	2	2	NUM
iajs-156	171	14	-	-	PUNCT
iajs-156	171	15	regular	regular	ADJ
iajs-156	171	16	r	r	NOUN
iajs-156	171	17	-	-	PUNCT
iajs-156	171	18	module	module	NOUN
iajs-156	171	19	for	for	ADP
iajs-156	171	20	any	any	DET
iajs-156	171	21	index	index	NOUN
iajs-156	171	22	set	set	VERB
iajs-156	171	23	.	.	NOUN
iajs-156	171	24	(	(	PUNCT
iajs-156	171	25	2	2	X
iajs-156	171	26	)	)	PUNCT
iajs-156	171	27	every	every	DET
iajs-156	171	28	projective	projective	ADJ
iajs-156	171	29	r	r	NOUN
iajs-156	171	30	-	-	PUNCT
iajs-156	171	31	module	module	NOUN
iajs-156	171	32	is	be	AUX
iajs-156	171	33	2	2	NUM
iajs-156	171	34	-	-	PUNCT
iajs-156	171	35	regulaar	regulaar	NOUN
iajs-156	171	36	module	module	NOUN
iajs-156	171	37	.	.	PUNCT
iajs-156	172	1	proof	proof	NOUN
iajs-156	172	2	:	:	PUNCT
iajs-156	172	3	242	242	NUM
iajs-156	172	4	|	|	NOUN
iajs-156	172	5	mathematics	mathematic	NOUN
iajs-156	172	6	2015	2015	NUM
iajs-156	172	7	)	)	PUNCT
iajs-156	172	8	عام	عام	ADP
iajs-156	172	9	3العدد	3العدد	NUM
iajs-156	172	10	(	(	PUNCT
iajs-156	172	11	28مجلة	28مجلة	X
iajs-156	172	12	إبن	إبن	VERB
iajs-156	172	13	الھيثم	الھيثم	NOUN
iajs-156	172	14	للعلوم	للعلوم	NOUN
iajs-156	172	15	الصرفة	الصرفة	NOUN
iajs-156	173	1	و	و	PRON
iajs-156	173	2	التطبيقية	التطبيقية	ADV
iajs-156	173	3	المجلد	المجلد	VERB
iajs-156	173	4	ibn	ibn	PROPN
iajs-156	173	5	al	al	PROPN
iajs-156	173	6	-	-	PUNCT
iajs-156	173	7	haitham	haitham	PROPN
iajs-156	173	8	jour	jour	X
iajs-156	173	9	.	.	PROPN
iajs-156	174	1	for	for	ADP
iajs-156	174	2	pure	pure	ADJ
iajs-156	174	3	&	&	CCONJ
iajs-156	174	4	appl	appl	PROPN
iajs-156	174	5	.	.	PUNCT
iajs-156	175	1	sci	sci	PROPN
iajs-156	175	2	.	.	PUNCT
iajs-156	175	3	vol	vol	NOUN
iajs-156	175	4	.	.	PROPN
iajs-156	176	1	28	28	NUM
iajs-156	176	2	(	(	PUNCT
iajs-156	176	3	3	3	NUM
iajs-156	176	4	)	)	PUNCT
iajs-156	176	5	2015	2015	NUM
iajs-156	176	6	(	(	PUNCT
iajs-156	176	7	1	1	NUM
iajs-156	176	8	)	)	PUNCT
iajs-156	176	9			NOUN
iajs-156	176	10	(	(	PUNCT
iajs-156	176	11	2	2	X
iajs-156	176	12	)	)	PUNCT
iajs-156	176	13	let	let	VERB
iajs-156	176	14	m	m	PRON
iajs-156	176	15	be	be	AUX
iajs-156	176	16	projective	projective	ADJ
iajs-156	176	17	r	r	NOUN
iajs-156	176	18	-	-	PUNCT
iajs-156	176	19	module	module	NOUN
iajs-156	176	20	then	then	ADV
iajs-156	176	21	there	there	PRON
iajs-156	176	22	exists	exist	VERB
iajs-156	176	23	a	a	DET
iajs-156	176	24	free	free	ADJ
iajs-156	176	25	r	r	NOUN
iajs-156	176	26	-	-	PUNCT
iajs-156	176	27	module	module	NOUN
iajs-156	176	28	f	f	NOUN
iajs-156	176	29	and	and	CCONJ
iajs-156	176	30	an	an	DET
iajs-156	176	31	repimorphism	repimorphism	NOUN
iajs-156	176	32	f	f	NOUN
iajs-156	176	33	:	:	PUNCT
iajs-156	177	1	f	f	PROPN
iajs-156	177	2			PROPN
iajs-156	177	3	m	m	PROPN
iajs-156	177	4	,	,	PUNCT
iajs-156	177	5	and	and	CCONJ
iajs-156	177	6	f	f	PROPN
iajs-156	177	7			PROPN
iajs-156	177	8			NOUN
iajs-156	177	9	r	r	NUM
iajs-156	177	10	where	where	SCONJ
iajs-156	177	11			NOUN
iajs-156	177	12	is	be	AUX
iajs-156	177	13	an	an	DET
iajs-156	177	14	index	index	NOUN
iajs-156	177	15	set	set	NOUN
iajs-156	177	16	.	.	PUNCT
iajs-156	178	1	we	we	PRON
iajs-156	178	2	have	have	VERB
iajs-156	178	3	the	the	DET
iajs-156	178	4	following	follow	VERB
iajs-156	178	5	short	short	ADJ
iajs-156	178	6	exact	exact	ADJ
iajs-156	178	7	sequence	sequence	NOUN
iajs-156	178	8	i0	i0	PROPN
iajs-156	178	9	ker	ker	PROPN
iajs-156	179	1	r	r	NOUN
iajs-156	179	2	m	m	VERB
iajs-156	179	3	0ff	0ff	NOUN
iajs-156	179	4			NOUN
iajs-156	179	5			ADJ
iajs-156	179	6			NUM
iajs-156	179	7			PROPN
iajs-156	179	8			PROPN
iajs-156	179	9	where	where	SCONJ
iajs-156	179	10	i	i	PRON
iajs-156	179	11	is	be	AUX
iajs-156	179	12	the	the	DET
iajs-156	179	13	inclusion	inclusion	NOUN
iajs-156	179	14	mapping	mapping	NOUN
iajs-156	179	15	.	.	PUNCT
iajs-156	180	1	since	since	SCONJ
iajs-156	180	2	m	m	PROPN
iajs-156	180	3	is	be	AUX
iajs-156	180	4	projective	projective	ADJ
iajs-156	180	5	,	,	PUNCT
iajs-156	180	6	the	the	DET
iajs-156	180	7	sequence	sequence	NOUN
iajs-156	180	8	is	be	AUX
iajs-156	180	9	split	split	ADJ
iajs-156	180	10	implies	imply	VERB
iajs-156	180	11	that	that	SCONJ
iajs-156	180	12			NOUN
iajs-156	180	13	r	r	X
iajs-156	180	14			PROPN
iajs-156	180	15	ker	ker	PROPN
iajs-156	181	1	f	f	PROPN
iajs-156	181	2			PROPN
iajs-156	181	3	m.	m.	NOUN
iajs-156	181	4	but	but	CCONJ
iajs-156	181	5			NOUN
iajs-156	181	6	r	r	NOUN
iajs-156	181	7	is	be	AUX
iajs-156	181	8	2	2	NUM
iajs-156	181	9	-	-	PUNCT
iajs-156	181	10	regular	regular	ADJ
iajs-156	181	11	r	r	NOUN
iajs-156	181	12	-	-	PUNCT
iajs-156	181	13	module	module	NOUN
iajs-156	181	14	.	.	PUNCT
iajs-156	182	1	therefore	therefore	ADV
iajs-156	182	2	by	by	ADP
iajs-156	182	3	[	[	X
iajs-156	182	4	1,cor.(3.4	1,cor.(3.4	NUM
iajs-156	182	5	)	)	PUNCT
iajs-156	182	6	]	]	PUNCT
iajs-156	183	1	m	m	VERB
iajs-156	183	2	is	be	AUX
iajs-156	183	3	2	2	NUM
iajs-156	183	4	-	-	PUNCT
iajs-156	183	5	regular	regular	ADJ
iajs-156	183	6	module	module	NOUN
iajs-156	183	7	.	.	PUNCT
iajs-156	184	1	(	(	PUNCT
iajs-156	184	2	2	2	NUM
iajs-156	184	3	)	)	PUNCT
iajs-156	184	4			NOUN
iajs-156	184	5	(	(	PUNCT
iajs-156	184	6	1	1	X
iajs-156	184	7	)	)	PUNCT
iajs-156	184	8	assume	assume	VERB
iajs-156	184	9	that	that	SCONJ
iajs-156	184	10	every	every	DET
iajs-156	184	11	projective	projective	ADJ
iajs-156	184	12	r	r	NOUN
iajs-156	184	13	-	-	PUNCT
iajs-156	184	14	module	module	NOUN
iajs-156	184	15	is	be	AUX
iajs-156	184	16	2	2	NUM
iajs-156	184	17	-	-	PUNCT
iajs-156	184	18	regular	regular	ADJ
iajs-156	184	19	module	module	NOUN
iajs-156	184	20	.	.	PUNCT
iajs-156	185	1	since	since	SCONJ
iajs-156	185	2	r	r	NOUN
iajs-156	185	3	is	be	AUX
iajs-156	185	4	projective	projective	ADJ
iajs-156	185	5	r	r	NOUN
iajs-156	185	6	-	-	PUNCT
iajs-156	185	7	module	module	NOUN
iajs-156	185	8	,	,	PUNCT
iajs-156	185	9	then	then	ADV
iajs-156	185	10			NOUN
iajs-156	185	11	r	r	PRON
iajs-156	185	12	is	be	AUX
iajs-156	185	13	projective	projective	ADJ
iajs-156	185	14	because	because	SCONJ
iajs-156	185	15	the	the	DET
iajs-156	185	16	direct	direct	ADJ
iajs-156	185	17	sum	sum	NOUN
iajs-156	185	18	of	of	ADP
iajs-156	185	19	projective	projective	ADJ
iajs-156	185	20	modules	module	NOUN
iajs-156	185	21	is	be	AUX
iajs-156	185	22	projective	projective	ADJ
iajs-156	185	23	.	.	PUNCT
iajs-156	186	1	therefore	therefore	ADV
iajs-156	186	2			NOUN
iajs-156	186	3	r	r	NOUN
iajs-156	186	4	is	be	AUX
iajs-156	186	5	2	2	NUM
iajs-156	186	6	-	-	PUNCT
iajs-156	186	7	regular	regular	ADJ
iajs-156	186	8	r	r	NOUN
iajs-156	186	9	-	-	PUNCT
iajs-156	186	10	module	module	NOUN
iajs-156	186	11	for	for	ADP
iajs-156	186	12	any	any	DET
iajs-156	186	13	index	index	NOUN
iajs-156	186	14	set	set	VERB
iajs-156	186	15	.	.	NOUN
iajs-156	186	16	recall	recall	VERB
iajs-156	186	17	that	that	SCONJ
iajs-156	186	18	an	an	DET
iajs-156	186	19	r	r	NOUN
iajs-156	186	20	-	-	PUNCT
iajs-156	186	21	module	module	NOUN
iajs-156	186	22	m	m	NOUN
iajs-156	186	23	is	be	AUX
iajs-156	186	24	called	call	VERB
iajs-156	186	25	multiplication	multiplication	NOUN
iajs-156	186	26	module	module	NOUN
iajs-156	186	27	if	if	SCONJ
iajs-156	186	28	for	for	ADP
iajs-156	186	29	every	every	DET
iajs-156	186	30	submodule	submodule	NOUN
iajs-156	186	31	n	n	PROPN
iajs-156	186	32	of	of	ADP
iajs-156	186	33	m	m	VERB
iajs-156	186	34	there	there	PRON
iajs-156	186	35	exists	exist	VERB
iajs-156	186	36	an	an	DET
iajs-156	186	37	ideal	ideal	NOUN
iajs-156	186	38	i	i	PRON
iajs-156	186	39	of	of	ADP
iajs-156	186	40	r	r	NOUN
iajs-156	187	1	such	such	ADJ
iajs-156	187	2	that	that	SCONJ
iajs-156	187	3	n	n	NOUN
iajs-156	187	4	=	=	VERB
iajs-156	187	5	i	i	NOUN
iajs-156	187	6	m	m	VERB
iajs-156	187	7	,	,	PUNCT
iajs-156	187	8	see	see	VERB
iajs-156	187	9	[	[	X
iajs-156	187	10	10	10	NUM
iajs-156	187	11	]	]	X
iajs-156	187	12	we	we	PRON
iajs-156	187	13	have	have	VERB
iajs-156	187	14	the	the	DET
iajs-156	187	15	following	following	NOUN
iajs-156	187	16	:	:	PUNCT
iajs-156	187	17	proposition	proposition	NOUN
iajs-156	187	18	(	(	PUNCT
iajs-156	187	19	2.14	2.14	NUM
iajs-156	187	20	):	):	PUNCT
iajs-156	187	21	if	if	SCONJ
iajs-156	187	22	m	m	NOUN
iajs-156	187	23	is	be	AUX
iajs-156	187	24	a	a	DET
iajs-156	187	25	finitely	finitely	ADV
iajs-156	187	26	generated	generate	VERB
iajs-156	187	27	faithful	faithful	ADJ
iajs-156	187	28	multiplication	multiplication	NOUN
iajs-156	187	29	r	r	NOUN
iajs-156	187	30	-	-	NOUN
iajs-156	187	31	module	module	NOUN
iajs-156	187	32	.	.	PUNCT
iajs-156	188	1	the	the	DET
iajs-156	188	2	following	follow	VERB
iajs-156	188	3	statements	statement	NOUN
iajs-156	188	4	are	be	AUX
iajs-156	188	5	equivalent	equivalent	ADJ
iajs-156	188	6	:	:	PUNCT
iajs-156	188	7	(	(	PUNCT
iajs-156	188	8	1	1	X
iajs-156	188	9	)	)	PUNCT
iajs-156	188	10	r	r	NOUN
iajs-156	188	11	is	be	AUX
iajs-156	188	12	2	2	NUM
iajs-156	188	13	-	-	PUNCT
iajs-156	188	14	regular	regular	ADJ
iajs-156	188	15	ring	ring	NOUN
iajs-156	188	16	.	.	PUNCT
iajs-156	189	1	(	(	PUNCT
iajs-156	189	2	2	2	X
iajs-156	189	3	)	)	PUNCT
iajs-156	189	4	m	m	VERB
iajs-156	189	5	is	be	AUX
iajs-156	189	6	2	2	NUM
iajs-156	189	7	-	-	PUNCT
iajs-156	189	8	regular	regular	ADJ
iajs-156	189	9	r	r	NOUN
iajs-156	189	10	-	-	PUNCT
iajs-156	189	11	module	module	NOUN
iajs-156	189	12	.	.	PUNCT
iajs-156	190	1	proof	proof	NOUN
iajs-156	190	2	:	:	PUNCT
iajs-156	190	3	(	(	PUNCT
iajs-156	190	4	1	1	X
iajs-156	190	5	)	)	PUNCT
iajs-156	190	6			NOUN
iajs-156	190	7	(	(	PUNCT
iajs-156	190	8	2	2	X
iajs-156	190	9	)	)	PUNCT
iajs-156	190	10	let	let	VERB
iajs-156	190	11	n	n	PRON
iajs-156	190	12	be	be	AUX
iajs-156	190	13	a	a	DET
iajs-156	190	14	submodule	submodule	NOUN
iajs-156	190	15	of	of	ADP
iajs-156	190	16	m	m	PROPN
iajs-156	191	1	and	and	CCONJ
iajs-156	191	2	i	i	PRON
iajs-156	191	3	is	be	AUX
iajs-156	191	4	an	an	DET
iajs-156	191	5	ideal	ideal	NOUN
iajs-156	191	6	of	of	ADP
iajs-156	191	7	r.	r.	PROPN
iajs-156	191	8	since	since	SCONJ
iajs-156	191	9	i2	i2	PROPN
iajs-156	191	10	m	m	PROPN
iajs-156	191	11			PUNCT
iajs-156	191	12	n	n	PROPN
iajs-156	191	13	=	=	SYM
iajs-156	191	14	i2	i2	PROPN
iajs-156	191	15	m	m	PROPN
iajs-156	191	16			ADJ
iajs-156	191	17	jm	jm	NOUN
iajs-156	191	18	for	for	ADP
iajs-156	191	19	some	some	DET
iajs-156	191	20	ideal	ideal	ADJ
iajs-156	191	21	j	j	PROPN
iajs-156	191	22	of	of	ADP
iajs-156	191	23	r	r	NOUN
iajs-156	191	24	=	=	PUNCT
iajs-156	191	25	(	(	PUNCT
iajs-156	191	26	i2	i2	PROPN
iajs-156	191	27			PUNCT
iajs-156	191	28	j)m	j)m	NOUN
iajs-156	191	29	since	since	SCONJ
iajs-156	191	30	m	m	PROPN
iajs-156	191	31	is	be	AUX
iajs-156	191	32	faithful	faithful	ADJ
iajs-156	191	33	multiplication	multiplication	NOUN
iajs-156	191	34	,	,	PUNCT
iajs-156	191	35	see	see	VERB
iajs-156	191	36	[	[	X
iajs-156	191	37	10	10	NUM
iajs-156	191	38	]	]	X
iajs-156	191	39	=	=	SYM
iajs-156	191	40	(	(	PUNCT
iajs-156	191	41	i2j)m	i2j)m	NOUN
iajs-156	191	42	since	since	SCONJ
iajs-156	191	43	r	r	NOUN
iajs-156	191	44	is	be	AUX
iajs-156	191	45	2	2	NUM
iajs-156	191	46	-	-	PUNCT
iajs-156	191	47	regular	regular	ADJ
iajs-156	191	48	=	=	PUNCT
iajs-156	191	49	i2(jm	i2(jm	PROPN
iajs-156	191	50	)	)	PUNCT
iajs-156	192	1	=	=	PRON
iajs-156	193	1	i2n	i2n	PRON
iajs-156	193	2	therefore	therefore	ADV
iajs-156	193	3	m	m	VERB
iajs-156	193	4	is	be	AUX
iajs-156	193	5	2	2	NUM
iajs-156	193	6	-	-	PUNCT
iajs-156	193	7	regular	regular	ADJ
iajs-156	193	8	.	.	PUNCT
iajs-156	194	1	(	(	PUNCT
iajs-156	194	2	2	2	X
iajs-156	194	3	)	)	PUNCT
iajs-156	194	4			NOUN
iajs-156	194	5	(	(	PUNCT
iajs-156	194	6	1	1	X
iajs-156	194	7	)	)	PUNCT
iajs-156	194	8	let	let	VERB
iajs-156	194	9	i	i	PRON
iajs-156	194	10	and	and	CCONJ
iajs-156	194	11	j	j	PROPN
iajs-156	194	12	be	be	VERB
iajs-156	194	13	ideals	ideal	NOUN
iajs-156	194	14	of	of	ADP
iajs-156	194	15	r.	r.	PROPN
iajs-156	194	16	since	since	SCONJ
iajs-156	194	17	(	(	PUNCT
iajs-156	194	18	i2	i2	PROPN
iajs-156	194	19			PUNCT
iajs-156	194	20	j)m	j)m	NOUN
iajs-156	194	21	=	=	SYM
iajs-156	194	22	i2	i2	PROPN
iajs-156	194	23	m	m	PROPN
iajs-156	194	24			PUNCT
iajs-156	194	25	jm	jm	NOUN
iajs-156	194	26	because	because	SCONJ
iajs-156	194	27	m	m	PROPN
iajs-156	194	28	is	be	AUX
iajs-156	194	29	faithful	faithful	ADJ
iajs-156	194	30	multiplication	multiplication	NOUN
iajs-156	194	31	=	=	SYM
iajs-156	194	32	i2(jm	i2(jm	PROPN
iajs-156	194	33	)	)	PUNCT
iajs-156	194	34	since	since	SCONJ
iajs-156	194	35	m	m	PROPN
iajs-156	194	36	is	be	AUX
iajs-156	194	37	2	2	NUM
iajs-156	194	38	-	-	PUNCT
iajs-156	194	39	regular	regular	ADJ
iajs-156	194	40	=	=	NOUN
iajs-156	194	41	(	(	PUNCT
iajs-156	194	42	i2j)m	i2j)m	X
iajs-156	194	43	thus	thus	ADV
iajs-156	194	44	i2	i2	X
iajs-156	194	45			PUNCT
iajs-156	194	46	j	j	NOUN
iajs-156	195	1	=	=	PUNCT
iajs-156	195	2	i2j	i2j	ADV
iajs-156	195	3	since	since	SCONJ
iajs-156	195	4	m	m	PROPN
iajs-156	195	5	is	be	AUX
iajs-156	195	6	finitely	finitely	ADV
iajs-156	195	7	generated	generate	VERB
iajs-156	195	8	faithful	faithful	ADJ
iajs-156	195	9	multiplication	multiplication	NOUN
iajs-156	195	10	,	,	PUNCT
iajs-156	195	11	see	see	VERB
iajs-156	195	12	[	[	X
iajs-156	195	13	10	10	NUM
iajs-156	195	14	]	]	PUNCT
iajs-156	195	15	.	.	PUNCT
iajs-156	196	1	therefore	therefore	ADV
iajs-156	196	2	r	r	NOUN
iajs-156	196	3	is	be	AUX
iajs-156	196	4	2	2	NUM
iajs-156	196	5	-	-	PUNCT
iajs-156	196	6	regular	regular	ADJ
iajs-156	196	7	ring	ring	NOUN
iajs-156	196	8	.	.	PUNCT
iajs-156	197	1	recall	recall	VERB
iajs-156	197	2	that	that	SCONJ
iajs-156	197	3	an	an	DET
iajs-156	197	4	r	r	NOUN
iajs-156	197	5	-	-	PUNCT
iajs-156	197	6	module	module	NOUN
iajs-156	197	7	m	m	NOUN
iajs-156	197	8	is	be	AUX
iajs-156	197	9	said	say	VERB
iajs-156	197	10	to	to	PART
iajs-156	197	11	be	be	AUX
iajs-156	197	12	i	i	NOUN
iajs-156	197	13	-	-	PUNCT
iajs-156	197	14	multiplication	multiplication	NOUN
iajs-156	197	15	module	module	NOUN
iajs-156	197	16	if	if	SCONJ
iajs-156	197	17	each	each	DET
iajs-156	197	18	submodule	submodule	NOUN
iajs-156	197	19	n	n	PROPN
iajs-156	197	20	of	of	ADP
iajs-156	197	21	m	m	PRON
iajs-156	197	22	of	of	ADP
iajs-156	197	23	the	the	DET
iajs-156	197	24	form	form	NOUN
iajs-156	197	25	jm	jm	PROPN
iajs-156	197	26	for	for	ADP
iajs-156	197	27	some	some	DET
iajs-156	197	28	idempotent	idempotent	ADJ
iajs-156	197	29	ideal	ideal	NOUN
iajs-156	197	30	j	j	PROPN
iajs-156	197	31	of	of	ADP
iajs-156	197	32	r	r	PROPN
iajs-156	197	33	,	,	PUNCT
iajs-156	197	34	see	see	VERB
iajs-156	197	35	[	[	X
iajs-156	197	36	11	11	NUM
iajs-156	197	37	]	]	PUNCT
iajs-156	197	38	.	.	PUNCT
iajs-156	198	1	it	it	PRON
iajs-156	198	2	is	be	AUX
iajs-156	198	3	clear	clear	ADJ
iajs-156	198	4	that	that	SCONJ
iajs-156	198	5	every	every	DET
iajs-156	198	6	i	i	PROPN
iajs-156	198	7	-	-	PUNCT
iajs-156	198	8	miltiplication	miltiplication	NOUN
iajs-156	198	9	module	module	NOUN
iajs-156	198	10	is	be	AUX
iajs-156	198	11	multiplication	multiplication	NOUN
iajs-156	198	12	but	but	CCONJ
iajs-156	198	13	not	not	PART
iajs-156	198	14	the	the	DET
iajs-156	198	15	converse	converse	NOUN
iajs-156	198	16	.	.	PUNCT
iajs-156	199	1	clearly	clearly	ADV
iajs-156	199	2	the	the	DET
iajs-156	199	3	two	two	NUM
iajs-156	199	4	concepts	concept	NOUN
iajs-156	199	5	multiplication	multiplication	NOUN
iajs-156	199	6	and	and	CCONJ
iajs-156	199	7	i	i	NOUN
iajs-156	199	8	-	-	PUNCT
iajs-156	199	9	multiplication	multiplication	NOUN
iajs-156	199	10	modules	module	NOUN
iajs-156	199	11	are	be	AUX
iajs-156	199	12	equivalent	equivalent	ADJ
iajs-156	199	13	over	over	ADP
iajs-156	199	14	regular	regular	ADJ
iajs-156	199	15	rings	ring	NOUN
iajs-156	199	16	.	.	PUNCT
iajs-156	200	1	however	however	ADV
iajs-156	200	2	we	we	PRON
iajs-156	200	3	have	have	VERB
iajs-156	200	4	the	the	DET
iajs-156	200	5	following	following	NOUN
iajs-156	200	6	:	:	PUNCT
iajs-156	200	7	proposition	proposition	NOUN
iajs-156	200	8	(	(	PUNCT
iajs-156	200	9	2.15	2.15	NUM
iajs-156	200	10	):	):	PUNCT
iajs-156	200	11	if	if	SCONJ
iajs-156	200	12	m	m	NOUN
iajs-156	200	13	is	be	AUX
iajs-156	200	14	i	i	NOUN
iajs-156	200	15	-	-	PUNCT
iajs-156	200	16	multiplication	multiplication	NOUN
iajs-156	200	17	and	and	CCONJ
iajs-156	200	18	2	2	NUM
iajs-156	200	19	-	-	PUNCT
iajs-156	200	20	regular	regular	ADJ
iajs-156	200	21	r	r	NOUN
iajs-156	200	22	-	-	PUNCT
iajs-156	200	23	module	module	NOUN
iajs-156	200	24	then	then	ADV
iajs-156	200	25	m	m	VERB
iajs-156	200	26	is	be	AUX
iajs-156	200	27	regular	regular	ADJ
iajs-156	200	28	module	module	NOUN
iajs-156	200	29	.	.	PUNCT
iajs-156	201	1	proof	proof	NOUN
iajs-156	201	2	:	:	PUNCT
iajs-156	201	3	let	let	VERB
iajs-156	201	4	n	n	PRON
iajs-156	201	5	be	be	AUX
iajs-156	201	6	a	a	DET
iajs-156	201	7	submodule	submodule	NOUN
iajs-156	201	8	of	of	ADP
iajs-156	201	9	m	m	PROPN
iajs-156	201	10	and	and	CCONJ
iajs-156	201	11	i	i	PRON
iajs-156	201	12	is	be	AUX
iajs-156	201	13	an	an	DET
iajs-156	201	14	ideal	ideal	NOUN
iajs-156	201	15	of	of	ADP
iajs-156	201	16	r.	r.	PROPN
iajs-156	201	17	since	since	SCONJ
iajs-156	201	18	243	243	NUM
iajs-156	201	19	|	|	NOUN
iajs-156	201	20	mathematics	mathematic	NOUN
iajs-156	201	21	2015	2015	NUM
iajs-156	201	22	)	)	PUNCT
iajs-156	201	23	عام	عام	ADP
iajs-156	201	24	3العدد	3العدد	NUM
iajs-156	201	25	(	(	PUNCT
iajs-156	201	26	28مجلة	28مجلة	X
iajs-156	201	27	إبن	إبن	VERB
iajs-156	202	1	الھيثم	الھيثم	NOUN
iajs-156	202	2	للعلوم	للعلوم	NOUN
iajs-156	202	3	الصرفة	الصرفة	NOUN
iajs-156	203	1	و	و	PRON
iajs-156	203	2	التطبيقية	التطبيقية	ADV
iajs-156	203	3	المجلد	المجلد	VERB
iajs-156	203	4	ibn	ibn	PROPN
iajs-156	203	5	al	al	PROPN
iajs-156	203	6	-	-	PUNCT
iajs-156	203	7	haitham	haitham	PROPN
iajs-156	203	8	jour	jour	X
iajs-156	203	9	.	.	PROPN
iajs-156	204	1	for	for	ADP
iajs-156	204	2	pure	pure	ADJ
iajs-156	204	3	&	&	CCONJ
iajs-156	204	4	appl	appl	PROPN
iajs-156	204	5	.	.	PUNCT
iajs-156	205	1	sci	sci	PROPN
iajs-156	205	2	.	.	PUNCT
iajs-156	205	3	vol	vol	NOUN
iajs-156	205	4	.	.	PROPN
iajs-156	206	1	28	28	NUM
iajs-156	206	2	(	(	PUNCT
iajs-156	206	3	3	3	NUM
iajs-156	206	4	)	)	PUNCT
iajs-156	206	5	2015	2015	NUM
iajs-156	207	1	i	i	PRON
iajs-156	207	2	m	m	VERB
iajs-156	207	3			PUNCT
iajs-156	208	1	n	n	PROPN
iajs-156	208	2	=	=	X
iajs-156	209	1	i	i	PRON
iajs-156	209	2	m	m	VERB
iajs-156	209	3			PUNCT
iajs-156	209	4	jm	jm	X
iajs-156	209	5	=	=	PUNCT
iajs-156	209	6	i	i	PROPN
iajs-156	209	7	m	m	VERB
iajs-156	209	8			PUNCT
iajs-156	209	9	j2	j2	PROPN
iajs-156	209	10	m	m	PROPN
iajs-156	209	11	for	for	ADP
iajs-156	209	12	some	some	DET
iajs-156	209	13	idempotent	idempotent	ADJ
iajs-156	209	14	j	j	PROPN
iajs-156	209	15	=	=	SYM
iajs-156	209	16	j2	j2	PROPN
iajs-156	209	17	=	=	SYM
iajs-156	209	18	j2(im	j2(im	PROPN
iajs-156	209	19	)	)	PUNCT
iajs-156	209	20	since	since	SCONJ
iajs-156	209	21	m	m	PROPN
iajs-156	209	22	is	be	AUX
iajs-156	209	23	2	2	NUM
iajs-156	209	24	-	-	PUNCT
iajs-156	209	25	regular	regular	ADJ
iajs-156	209	26	=	=	NOUN
iajs-156	209	27	(	(	PUNCT
iajs-156	209	28	i2j)m	i2j)m	NOUN
iajs-156	209	29	since	since	SCONJ
iajs-156	209	30	r	r	NOUN
iajs-156	209	31	is	be	AUX
iajs-156	209	32	2	2	NUM
iajs-156	209	33	-	-	PUNCT
iajs-156	209	34	regular	regular	ADJ
iajs-156	209	35	=	=	PUNCT
iajs-156	209	36	i(j2	i(j2	NOUN
iajs-156	209	37	m	m	PROPN
iajs-156	209	38	)	)	PUNCT
iajs-156	210	1	=	=	SYM
iajs-156	211	1	i(jm	i(jm	PROPN
iajs-156	211	2	)	)	PUNCT
iajs-156	212	1	=	=	NOUN
iajs-156	212	2	in	in	ADP
iajs-156	212	3	therefore	therefore	ADV
iajs-156	212	4	m	m	PROPN
iajs-156	212	5	is	be	AUX
iajs-156	212	6	regular	regular	ADJ
iajs-156	212	7	module	module	NOUN
iajs-156	212	8	.	.	PUNCT
iajs-156	213	1	proposition	proposition	NOUN
iajs-156	213	2	(	(	PUNCT
iajs-156	213	3	2.16	2.16	NUM
iajs-156	213	4	):	):	PUNCT
iajs-156	213	5	if	if	SCONJ
iajs-156	213	6	m	m	NOUN
iajs-156	213	7	is	be	AUX
iajs-156	213	8	i	i	NOUN
iajs-156	213	9	-	-	PUNCT
iajs-156	213	10	multiplication	multiplication	NOUN
iajs-156	213	11	and	and	CCONJ
iajs-156	213	12	2	2	NUM
iajs-156	213	13	-	-	PUNCT
iajs-156	213	14	regular	regular	ADJ
iajs-156	213	15	r	r	NOUN
iajs-156	213	16	-	-	PUNCT
iajs-156	213	17	module	module	NOUN
iajs-156	213	18	then	then	ADV
iajs-156	213	19	every	every	DET
iajs-156	213	20	submodule	submodule	NOUN
iajs-156	213	21	n	n	PROPN
iajs-156	213	22	of	of	ADP
iajs-156	213	23	m	m	PROPN
iajs-156	213	24	is	be	AUX
iajs-156	213	25	i	i	NOUN
iajs-156	213	26	-	-	PUNCT
iajs-156	213	27	multiplication	multiplication	NOUN
iajs-156	213	28	as	as	ADP
iajs-156	213	29	r	r	NOUN
iajs-156	213	30	-	-	PUNCT
iajs-156	213	31	module	module	NOUN
iajs-156	213	32	.	.	PUNCT
iajs-156	214	1	proof	proof	NOUN
iajs-156	214	2	:	:	PUNCT
iajs-156	214	3	let	let	VERB
iajs-156	214	4	n	n	PRON
iajs-156	214	5	be	be	AUX
iajs-156	214	6	a	a	DET
iajs-156	214	7	submodule	submodule	NOUN
iajs-156	214	8	of	of	ADP
iajs-156	214	9	m	m	PROPN
iajs-156	214	10	and	and	CCONJ
iajs-156	214	11	k	k	PROPN
iajs-156	214	12	is	be	AUX
iajs-156	214	13	any	any	DET
iajs-156	214	14	submodule	submodule	NOUN
iajs-156	214	15	in	in	ADP
iajs-156	214	16	n	n	CCONJ
iajs-156	214	17	,	,	PUNCT
iajs-156	214	18	then	then	ADV
iajs-156	214	19	k	k	PROPN
iajs-156	214	20	is	be	AUX
iajs-156	214	21	a	a	DET
iajs-156	214	22	submodule	submodule	NOUN
iajs-156	214	23	of	of	ADP
iajs-156	214	24	m	m	PROPN
iajs-156	214	25	and	and	CCONJ
iajs-156	214	26	k	k	PROPN
iajs-156	215	1	=	=	PUNCT
iajs-156	215	2	i	i	NOUN
iajs-156	215	3	m	m	NOUN
iajs-156	215	4	=	=	VERB
iajs-156	215	5	i2	i2	PROPN
iajs-156	215	6	m	m	PROPN
iajs-156	215	7	for	for	ADP
iajs-156	215	8	some	some	DET
iajs-156	215	9	idempotent	idempotent	ADJ
iajs-156	215	10	ideal	ideal	NOUN
iajs-156	215	11	i	i	PRON
iajs-156	215	12	of	of	ADP
iajs-156	215	13	r.	r.	PROPN
iajs-156	215	14	since	since	SCONJ
iajs-156	215	15	k	k	PROPN
iajs-156	215	16	=	=	PROPN
iajs-156	215	17	n	n	PROPN
iajs-156	215	18			PUNCT
iajs-156	215	19	k	k	NOUN
iajs-156	215	20	=	=	PUNCT
iajs-156	215	21	n	n	PROPN
iajs-156	215	22			NOUN
iajs-156	215	23	i2	i2	PROPN
iajs-156	215	24	m	m	NOUN
iajs-156	215	25	=	=	ADJ
iajs-156	215	26	i2n	i2n	NOUN
iajs-156	215	27	because	because	SCONJ
iajs-156	215	28	m	m	PROPN
iajs-156	215	29	is	be	AUX
iajs-156	215	30	2	2	NUM
iajs-156	215	31	-	-	PUNCT
iajs-156	215	32	regular	regular	ADJ
iajs-156	215	33	=	=	NOUN
iajs-156	215	34	in	in	ADP
iajs-156	215	35	thus	thus	ADV
iajs-156	215	36	n	n	ADV
iajs-156	215	37	is	be	AUX
iajs-156	215	38	i	i	NOUN
iajs-156	215	39	-	-	PUNCT
iajs-156	215	40	multiplication	multiplication	NOUN
iajs-156	215	41	r	r	NOUN
iajs-156	215	42	-	-	PUNCT
iajs-156	215	43	module	module	NOUN
iajs-156	215	44	.	.	PUNCT
iajs-156	216	1	references	reference	NOUN
iajs-156	216	2	1	1	NUM
iajs-156	216	3	.	.	PUNCT
iajs-156	216	4	nuhad	nuhad	PROPN
iajs-156	216	5	,	,	PUNCT
iajs-156	216	6	s.al	s.al	ADJ
iajs-156	216	7	-	-	PUNCT
iajs-156	216	8	mothafar	mothafar	NOUN
iajs-156	216	9	and	and	CCONJ
iajs-156	216	10	ghaleb	ghaleb	NOUN
iajs-156	216	11	,	,	PUNCT
iajs-156	216	12	a.humod	a.humod	ADJ
iajs-156	216	13	,	,	PUNCT
iajs-156	216	14	2	2	NUM
iajs-156	216	15	-	-	PUNCT
iajs-156	216	16	regular	regular	ADJ
iajs-156	216	17	modules	module	NOUN
iajs-156	216	18	,	,	PUNCT
iajs-156	216	19	to	to	PART
iajs-156	216	20	appear	appear	VERB
iajs-156	216	21	.	.	PUNCT
iajs-156	217	1	2	2	X
iajs-156	217	2	.	.	X
iajs-156	217	3	naoum	naoum	PROPN
iajs-156	217	4	,	,	PUNCT
iajs-156	217	5	a.g	a.g	PROPN
iajs-156	217	6	.	.	PROPN
iajs-156	217	7	and	and	CCONJ
iajs-156	217	8	nuhad	nuhad	PROPN
iajs-156	217	9	,	,	PUNCT
iajs-156	217	10	s.al	s.al	PROPN
iajs-156	217	11	-	-	NOUN
iajs-156	217	12	mothafar	mothafar	ADJ
iajs-156	217	13	,	,	PUNCT
iajs-156	217	14	(	(	PUNCT
iajs-156	217	15	1994),nearly	1994),nearly	NUM
iajs-156	217	16	regular	regular	ADJ
iajs-156	217	17	ring	ring	NOUN
iajs-156	217	18	and	and	CCONJ
iajs-156	217	19	nearly	nearly	ADV
iajs-156	217	20	regular	regular	ADJ
iajs-156	217	21	modules	module	NOUN
iajs-156	217	22	,	,	PUNCT
iajs-156	217	23	mutah	mutah	PROPN
iajs-156	217	24	.	.	PUNCT
iajs-156	218	1	journal	journal	PROPN
iajs-156	218	2	for	for	ADP
iajs-156	218	3	research	research	NOUN
iajs-156	218	4	and	and	CCONJ
iajs-156	218	5	studies	study	NOUN
iajs-156	218	6	,	,	PUNCT
iajs-156	218	7	9	9	NUM
iajs-156	218	8	,	,	PUNCT
iajs-156	218	9	6	6	NUM
iajs-156	218	10	.	.	NOUN
iajs-156	218	11	3	3	NUM
iajs-156	218	12	.	.	X
iajs-156	218	13	aziz	aziz	PROPN
iajs-156	218	14	,	,	PUNCT
iajs-156	218	15	b.b	b.b	PROPN
iajs-156	218	16	.	.	PROPN
iajs-156	218	17	,	,	PUNCT
iajs-156	218	18	(	(	PUNCT
iajs-156	218	19	1975	1975	NUM
iajs-156	218	20	)	)	PUNCT
iajs-156	218	21	,	,	PUNCT
iajs-156	218	22	regular	regular	ADJ
iajs-156	218	23	rings	ring	NOUN
iajs-156	218	24	and	and	CCONJ
iajs-156	218	25	bear	bear	NOUN
iajs-156	218	26	rings	ring	NOUN
iajs-156	218	27	,	,	PUNCT
iajs-156	218	28	m.sc.thesis	m.sc.thesis	NOUN
iajs-156	218	29	,	,	PUNCT
iajs-156	218	30	university	university	NOUN
iajs-156	218	31	of	of	ADP
iajs-156	218	32	baghdad	baghdad	PROPN
iajs-156	218	33	.	.	PUNCT
iajs-156	219	1	4	4	NUM
iajs-156	219	2	.	.	PUNCT
iajs-156	219	3	.duns	.dun	NOUN
iajs-156	219	4	,	,	PUNCT
iajs-156	219	5	(	(	PUNCT
iajs-156	219	6	1988	1988	NUM
iajs-156	219	7	)	)	PUNCT
iajs-156	219	8	,	,	PUNCT
iajs-156	219	9	modules	module	NOUN
iajs-156	219	10	and	and	CCONJ
iajs-156	219	11	one	one	NUM
iajs-156	219	12	-	-	PUNCT
iajs-156	219	13	sided	sided	ADJ
iajs-156	219	14	ideal	ideal	NOUN
iajs-156	219	15	in	in	ADP
iajs-156	219	16	ring	ring	NOUN
iajs-156	219	17	theory	theory	NOUN
iajs-156	219	18	and	and	CCONJ
iajs-156	219	19	algebra	algebra	NOUN
iajs-156	219	20	,	,	PUNCT
iajs-156	219	21	19	19	NUM
iajs-156	219	22	,	,	PUNCT
iajs-156	219	23	755	755	NUM
iajs-156	219	24	-	-	SYM
iajs-156	219	25	779	779	NUM
iajs-156	219	26	.	.	NOUN
iajs-156	219	27	5	5	NUM
iajs-156	219	28	.	.	NOUN
iajs-156	219	29	athab	athab	PROPN
iajs-156	219	30	,	,	PUNCT
iajs-156	219	31	e.a	e.a	PROPN
iajs-156	219	32	.	.	PROPN
iajs-156	219	33	,	,	PUNCT
iajs-156	219	34	(	(	PUNCT
iajs-156	219	35	1996	1996	NUM
iajs-156	219	36	)	)	PUNCT
iajs-156	219	37	,	,	PUNCT
iajs-156	219	38	prime	prime	ADJ
iajs-156	219	39	submodules	submodule	NOUN
iajs-156	219	40	and	and	CCONJ
iajs-156	219	41	semiprime	semiprime	NOUN
iajs-156	219	42	submodules	submodule	NOUN
iajs-156	219	43	,	,	PUNCT
iajs-156	219	44	m.sc	m.sc	PROPN
iajs-156	219	45	.	.	PUNCT
iajs-156	220	1	thesis	thesis	NOUN
iajs-156	220	2	,	,	PUNCT
iajs-156	220	3	university	university	NOUN
iajs-156	220	4	of	of	ADP
iajs-156	220	5	baghdad	baghdad	PROPN
iajs-156	220	6	,	,	PUNCT
iajs-156	220	7	iraq	iraq	PROPN
iajs-156	220	8	.	.	PUNCT
iajs-156	221	1	6	6	X
iajs-156	221	2	.	.	X
iajs-156	221	3	kasch	kasch	PROPN
iajs-156	221	4	,	,	PUNCT
iajs-156	221	5	f.	f.	PROPN
iajs-156	221	6	,	,	PUNCT
iajs-156	221	7	(	(	PUNCT
iajs-156	221	8	1982	1982	NUM
iajs-156	221	9	)	)	PUNCT
iajs-156	221	10	,	,	PUNCT
iajs-156	221	11	modules	module	NOUN
iajs-156	221	12	and	and	CCONJ
iajs-156	221	13	rings	ring	NOUN
iajs-156	221	14	,	,	PUNCT
iajs-156	221	15	academic	academic	ADJ
iajs-156	221	16	press	press	NOUN
iajs-156	221	17	,	,	PUNCT
iajs-156	221	18	new	new	PROPN
iajs-156	221	19	york	york	PROPN
iajs-156	221	20	.	.	PUNCT
iajs-156	222	1	7	7	X
iajs-156	222	2	.	.	X
iajs-156	222	3	anderson	anderson	PROPN
iajs-156	222	4	,	,	PUNCT
iajs-156	222	5	f.w	f.w	PROPN
iajs-156	222	6	.	.	PROPN
iajs-156	222	7	and	and	CCONJ
iajs-156	222	8	fuller	full	ADJ
iajs-156	222	9	k.r	k.r	PROPN
iajs-156	222	10	.	.	PROPN
iajs-156	222	11	,	,	PUNCT
iajs-156	222	12	(	(	PUNCT
iajs-156	222	13	1992	1992	NUM
iajs-156	222	14	)	)	PUNCT
iajs-156	222	15	,	,	PUNCT
iajs-156	222	16	rings	ring	NOUN
iajs-156	222	17	and	and	CCONJ
iajs-156	222	18	categories	category	NOUN
iajs-156	222	19	of	of	ADP
iajs-156	222	20	modules	module	NOUN
iajs-156	222	21	,	,	PUNCT
iajs-156	222	22	springer	springer	NOUN
iajs-156	222	23	verlag	verlag	PROPN
iajs-156	222	24	,	,	PUNCT
iajs-156	222	25	new	new	PROPN
iajs-156	222	26	york	york	PROPN
iajs-156	222	27	.	.	PROPN
iajs-156	223	1	8	8	X
iajs-156	223	2	.	.	X
iajs-156	223	3	sharp	sharp	ADJ
iajs-156	223	4	,	,	PUNCT
iajs-156	223	5	d.w	d.w	PROPN
iajs-156	223	6	.	.	PROPN
iajs-156	223	7	and	and	CCONJ
iajs-156	223	8	vamos	vamos	PROPN
iajs-156	223	9	,	,	PUNCT
iajs-156	223	10	p.	p.	NOUN
iajs-156	223	11	,	,	PUNCT
iajs-156	223	12	(	(	PUNCT
iajs-156	223	13	1972	1972	NUM
iajs-156	223	14	)	)	PUNCT
iajs-156	223	15	,	,	PUNCT
iajs-156	223	16	injective	injective	ADJ
iajs-156	223	17	modules	module	NOUN
iajs-156	223	18	,	,	PUNCT
iajs-156	223	19	combrdige	combrdige	PROPN
iajs-156	223	20	university	university	NOUN
iajs-156	223	21	,	,	PUNCT
iajs-156	223	22	press	press	NOUN
iajs-156	223	23	.	.	PUNCT
iajs-156	224	1	9	9	X
iajs-156	224	2	.	.	X
iajs-156	224	3	desale	desale	NOUN
iajs-156	224	4	,	,	PUNCT
iajs-156	224	5	g.and	g.and	PROPN
iajs-156	224	6	nicholson	nicholson	PROPN
iajs-156	224	7	,	,	PUNCT
iajs-156	224	8	w.k	w.k	PROPN
iajs-156	224	9	.	.	PROPN
iajs-156	224	10	,	,	PUNCT
iajs-156	224	11	(	(	PUNCT
iajs-156	224	12	1981	1981	NUM
iajs-156	224	13	)	)	PUNCT
iajs-156	224	14	,	,	PUNCT
iajs-156	224	15	endoprimitive	endoprimitive	ADJ
iajs-156	224	16	rings	ring	NOUN
iajs-156	224	17	,	,	PUNCT
iajs-156	224	18	j.algebra	j.algebra	PROPN
iajs-156	224	19	,	,	PUNCT
iajs-156	224	20	70	70	NUM
iajs-156	224	21	,	,	PUNCT
iajs-156	224	22	548	548	NUM
iajs-156	224	23	-	-	SYM
iajs-156	224	24	560	560	NUM
iajs-156	224	25	.	.	NOUN
iajs-156	224	26	10	10	NUM
iajs-156	224	27	.	.	PUNCT
iajs-156	225	1	el	el	NOUN
iajs-156	225	2	-	-	PUNCT
iajs-156	225	3	bast	bast	NOUN
iajs-156	225	4	,	,	PUNCT
iajs-156	225	5	z.a	z.a	PROPN
iajs-156	225	6	.	.	PROPN
iajs-156	225	7	,	,	PUNCT
iajs-156	225	8	and	and	CCONJ
iajs-156	225	9	smith	smith	PROPN
iajs-156	225	10	,	,	PUNCT
iajs-156	225	11	p.f	p.f	PROPN
iajs-156	225	12	.	.	PROPN
iajs-156	225	13	,	,	PUNCT
iajs-156	225	14	(	(	PUNCT
iajs-156	225	15	1988	1988	NUM
iajs-156	225	16	)	)	PUNCT
iajs-156	225	17	,	,	PUNCT
iajs-156	225	18	multiplication	multiplication	NOUN
iajs-156	225	19	modules	module	NOUN
iajs-156	225	20	,	,	PUNCT
iajs-156	225	21	commun	commun	PROPN
iajs-156	225	22	.	.	PUNCT
iajs-156	226	1	algebra	algebra	PROPN
iajs-156	226	2	,	,	PUNCT
iajs-156	226	3	16	16	NUM
iajs-156	226	4	,	,	PUNCT
iajs-156	226	5	4	4	NUM
iajs-156	226	6	,	,	PUNCT
iajs-156	226	7	755	755	NUM
iajs-156	226	8	-	-	SYM
iajs-156	226	9	779	779	NUM
iajs-156	226	10	.	.	PROPN
iajs-156	226	11	11	11	NUM
iajs-156	226	12	.	.	PUNCT
iajs-156	227	1	abbas	abbas	PROPN
iajs-156	227	2	,	,	PUNCT
iajs-156	227	3	m.s	m.s	PROPN
iajs-156	227	4	.	.	PROPN
iajs-156	227	5	,	,	PUNCT
iajs-156	227	6	(	(	PUNCT
iajs-156	227	7	1990	1990	NUM
iajs-156	227	8	)	)	PUNCT
iajs-156	227	9	,	,	PUNCT
iajs-156	227	10	on	on	ADP
iajs-156	227	11	fully	fully	ADV
iajs-156	227	12	stable	stable	ADJ
iajs-156	227	13	modules	module	NOUN
iajs-156	227	14	,	,	PUNCT
iajs-156	227	15	ph.d	ph.d	PROPN
iajs-156	227	16	.	.	PUNCT
iajs-156	228	1	thesis	thesis	NOUN
iajs-156	228	2	,	,	PUNCT
iajs-156	228	3	university	university	NOUN
iajs-156	228	4	of	of	ADP
iajs-156	228	5	baghdad	baghdad	PROPN
iajs-156	228	6	,	,	PUNCT
iajs-156	228	7	iraq	iraq	PROPN
iajs-156	228	8	.	.	PUNCT
iajs-156	229	1	244	244	NUM
iajs-156	230	1	|	|	ADV
iajs-156	230	2	mathematics	mathematic	NOUN
iajs-156	230	3	2015	2015	NUM
iajs-156	230	4	)	)	PUNCT
iajs-156	230	5	عام	عام	ADP
iajs-156	230	6	3العدد	3العدد	NUM
iajs-156	230	7	(	(	PUNCT
iajs-156	230	8	28مجلة	28مجلة	X
iajs-156	230	9	إبن	إبن	VERB
iajs-156	230	10	الھيثم	الھيثم	NOUN
iajs-156	230	11	للعلوم	للعلوم	NOUN
iajs-156	230	12	الصرفة	الصرفة	NOUN
iajs-156	231	1	و	و	PRON
iajs-156	231	2	التطبيقية	التطبيقية	ADV
iajs-156	231	3	المجلد	المجلد	VERB
iajs-156	231	4	ibn	ibn	PROPN
iajs-156	231	5	al	al	PROPN
iajs-156	231	6	-	-	PUNCT
iajs-156	231	7	haitham	haitham	PROPN
iajs-156	231	8	jour	jour	X
iajs-156	231	9	.	.	PROPN
iajs-156	232	1	for	for	ADP
iajs-156	232	2	pure	pure	ADJ
iajs-156	232	3	&	&	CCONJ
iajs-156	232	4	appl	appl	PROPN
iajs-156	232	5	.	.	PUNCT
iajs-156	233	1	sci	sci	PROPN
iajs-156	233	2	.	.	PUNCT
iajs-156	233	3	vol	vol	NOUN
iajs-156	233	4	.	.	PROPN
iajs-156	234	1	28	28	NUM
iajs-156	234	2	(	(	PUNCT
iajs-156	234	3	3	3	NUM
iajs-156	234	4	)	)	PUNCT
iajs-156	235	1	2015	2015	NUM
iajs-156	235	2	ii	ii	NOUN
iajs-156	235	3	2	2	NUM
iajs-156	235	4	-	-	PUNCT
iajs-156	235	5	المقاسات	المقاسات	PROPN
iajs-156	235	6	المنتظمة	المنتظمة	NOUN
iajs-156	235	7	من	من	DET
iajs-156	235	8	النمط	النمط	NOUN
iajs-156	235	9	نھاد	نھاد	NOUN
iajs-156	235	10	سالم	سالم	VERB
iajs-156	235	11	عبد	عبد	PROPN
iajs-156	235	12	الكريم	الكريم	PROPN
iajs-156	235	13	جامعة	جامعة	PROPN
iajs-156	235	14	بغداد	بغداد	PROPN
iajs-156	235	15	/كلية	/كلية	PROPN
iajs-156	235	16	العلوم	العلوم	PROPN
iajs-156	235	17	/قسم	/قسم	PUNCT
iajs-156	235	18	الرياضيات	الرياضيات	PROPN
iajs-156	235	19	غالب	غالب	NOUN
iajs-156	235	20	أحمد	أحمد	NOUN
iajs-156	235	21	حمود	حمود	VERB
iajs-156	235	22	جامعة	جامعة	PROPN
iajs-156	235	23	بغداد	بغداد	PROPN
iajs-156	235	24	/	/	SYM
iajs-156	235	25	)	)	PUNCT
iajs-156	235	26	ابن	ابن	PROPN
iajs-156	235	27	الھيثم(كلية	الھيثم(كلية	PROPN
iajs-156	235	28	التربية	التربية	NOUN
iajs-156	235	29	للعلوم	للعلوم	NOUN
iajs-156	235	30	الصرفة	الصرفة	NOUN
iajs-156	235	31	/قسم	/قسم	PUNCT
iajs-156	236	1	الرياضيات	الرياضيات	NOUN
iajs-156	236	2	2015	2015	NUM
iajs-156	236	3	/	/	SYM
iajs-156	236	4	حزيران/7،قبل	حزيران/7،قبل	NOUN
iajs-156	236	5	البحث	البحث	NOUN
iajs-156	236	6	في:2015	في:2015	PROPN
iajs-156	236	7	/	/	SYM
iajs-156	236	8	نيسان/	نيسان/	NUM
iajs-156	236	9	28استلم	28استلم	NUM
iajs-156	236	10	البحث	البحث	NOUN
iajs-156	236	11	في	في	PROPN
iajs-156	236	12	:	:	PUNCT
iajs-156	236	13	خالصةال	خالصةال	ADJ
iajs-156	236	14	اذا	اذا	PROPN
iajs-156	236	15	كان	كان	PROPN
iajs-156	236	16	كل	كل	PROPN
iajs-156	236	17	مقاس	مقاس	NOUN
iajs-156	236	18	2	2	NUM
iajs-156	236	19	–	–	PUNCT
iajs-156	236	20	بأنه	بأنه	NOUN
iajs-156	236	21	منتظم	منتظم	PROPN
iajs-156	236	22	من	من	PRON
iajs-156	236	23	النمط	النمط	PROPN
iajs-156	236	24	mحلقة	mحلقة	PROPN
iajs-156	236	25	إبدالية	إبدالية	NOUN
iajs-156	236	26	ذات	ذات	NOUN
iajs-156	236	27	محايد	محايد	NOUN
iajs-156	236	28	.	.	PUNCT
iajs-156	237	1	يقال	يقال	NOUN
iajs-156	237	2	ان	ان	PROPN
iajs-156	237	3	المقاس	المقاس	PROPN
iajs-156	237	4	rإذ	rإذ	NOUN
iajs-156	237	5	rمقاسا	rمقاسا	NOUN
iajs-156	237	6	ً	ً	NOUN
iajs-156	237	7	على	على	NOUN
iajs-156	237	8	mليكن	mليكن	NOUN
iajs-156	237	9	اذا	اذا	NOUN
iajs-156	237	10	حقق	حقق	X
iajs-156	237	11	mفي	mفي	X
iajs-156	237	12	2	2	NUM
iajs-156	237	13	-	-	PUNCT
iajs-156	237	14	بأنه	بأنه	NOUN
iajs-156	237	15	نقي	نقي	NOUN
iajs-156	237	16	من	من	PRON
iajs-156	237	17	النمط	النمط	PROPN
iajs-156	237	18	nإذ	nإذ	NOUN
iajs-156	237	19	يقال	يقال	NOUN
iajs-156	237	20	عن	عن	PROPN
iajs-156	237	21	المقاس	المقاس	NOUN
iajs-156	237	22	الجزئي	الجزئي	NOUN
iajs-156	237	23	2	2	NUM
iajs-156	237	24	-	-	PUNCT
iajs-156	237	25	ھو	ھو	NOUN
iajs-156	237	26	مقاس	مقاس	NOUN
iajs-156	237	27	جزئي	جزئي	NOUN
iajs-156	237	28	نقي	نقي	NOUN
iajs-156	237	29	من	من	PROPN
iajs-156	237	30	النمط	النمط	PROPN
iajs-156	237	31	mجزئي	mجزئي	NOUN
iajs-156	237	32	في	في	X
iajs-156	237	33	n2n	n2n	ADV
iajs-156	237	34	=	=	PUNCT
iajs-156	237	35	im2i	im2i	ADJ
iajs-156	237	36	لكل	لكل	PRON
iajs-156	237	37	مثاليi	مثاليi	X
iajs-156	237	38	فيr	فيr	PROPN
iajs-156	237	39	،	،	X
iajs-156	237	40	[	[	X
iajs-156	237	41	1	1	NUM
iajs-156	237	42	]	]	PUNCT
iajs-156	237	43	.	.	PUNCT
iajs-156	238	1	تمييزاً	تمييزاً	VERB
iajs-156	238	2	.	.	PUNCT
iajs-156	239	1	في	في	DET
iajs-156	239	2	القسم	القسم	PROPN
iajs-156	239	3	االول	االول	INTJ
iajs-156	239	4	من	من	INTJ
iajs-156	239	5	ھذا	ھذا	NOUN
iajs-156	239	6	البحث	البحث	ADV
iajs-156	239	7	أعطينا	أعطينا	VERB
iajs-156	240	1	[	[	X
iajs-156	240	2	1	1	NUM
iajs-156	240	3	]	]	SYM
iajs-156	240	4	2	2	NUM
iajs-156	240	5	-	-	PUNCT
iajs-156	240	6	في	في	NOUN
iajs-156	240	7	ھذا	ھذا	NOUN
iajs-156	240	8	البحث	البحث	PROPN
iajs-156	240	9	نستمر	نستمر	PROPN
iajs-156	240	10	بدراسة	بدراسة	PROPN
iajs-156	240	11	مفھوم	مفھوم	NOUN
iajs-156	240	12	االنتظام	االنتظام	ADP
iajs-156	240	13	من	من	PRON
iajs-156	240	14	النمط	النمط	PROPN
iajs-156	240	15	وانواع	وانواع	PROPN
iajs-156	240	16	اخرى	اخرى	VERB
iajs-156	240	17	من	من	PROPN
iajs-156	240	18	2-	2-	PROPN
iajs-156	240	19	.	.	PUNCT
iajs-156	241	1	في	في	DET
iajs-156	241	2	القسم	القسم	PROPN
iajs-156	241	3	الثاني	الثاني	PROPN
iajs-156	241	4	درسنا	درسنا	PROPN
iajs-156	241	5	العالقة	العالقة	PROPN
iajs-156	241	6	بين	بين	AUX
iajs-156	241	7	المقاسات	المقاسات	PROPN
iajs-156	241	8	المنتظمة	المنتظمة	VERB
iajs-156	241	9	من	من	PRON
iajs-156	241	10	النمط2	النمط2	PROPN
iajs-156	241	11	-	-	PUNCT
iajs-156	241	12	للمقاسات	للمقاسات	NOUN
iajs-156	241	13	المنتظمة	المنتظمة	NOUN
iajs-156	241	14	من	من	PRON
iajs-156	241	15	النمط	النمط	PROPN
iajs-156	241	16	المقاسات	المقاسات	PROPN
iajs-156	241	17	.	.	PUNCT
iajs-156	242	1	،	،	PROPN
iajs-156	242	2	المقاسات	المقاسات	PROPN
iajs-156	242	3	الجزئية	الجزئية	VERB
iajs-156	242	4	النقية	النقية	NOUN
iajs-156	242	5	،	،	X
iajs-156	242	6	2	2	NUM
iajs-156	242	7	–	–	PUNCT
iajs-156	242	8	،	،	NOUN
iajs-156	242	9	المقاسات	المقاسات	PROPN
iajs-156	242	10	النتظمة	النتظمة	VERB
iajs-156	242	11	من	من	DET
iajs-156	242	12	النمط	النمط	NOUN
iajs-156	242	13	2	2	NUM
iajs-156	242	14	–	–	PUNCT
iajs-156	242	15	المقاسات	المقاسات	NOUN
iajs-156	242	16	الجزئية	الجزئية	VERB
iajs-156	242	17	النقية	النقية	NOUN
iajs-156	242	18	من	من	DET
iajs-156	242	19	النمط	النمط	NOUN
iajs-156	242	20	:	:	PUNCT
iajs-156	242	21	الكلمات	الكلمات	VERB
iajs-156	242	22	المفتاحية	المفتاحية	VERB
iajs-156	242	23	المنتظمة.المقاسات	المنتظمة.المقاسات	PRON