id	sid	tid	token	lemma	pos
iajs-154	1	1	microsoft	microsoft	PROPN
iajs-154	1	2	word	word	NOUN
iajs-154	1	3	214	214	NUM
iajs-154	1	4	-	-	SYM
iajs-154	1	5	222	222	NUM
iajs-154	1	6	214	214	NUM
iajs-154	1	7	|	|	NOUN
iajs-154	1	8	mathematics	mathematic	NOUN
iajs-154	1	9	2015	2015	NUM
iajs-154	1	10	)	)	PUNCT
iajs-154	1	11	عام	عام	ADP
iajs-154	1	12	3العدد	3العدد	NUM
iajs-154	1	13	(	(	PUNCT
iajs-154	1	14	28مجلة	28مجلة	X
iajs-154	1	15	إبن	إبن	VERB
iajs-154	1	16	الهيثم	الهيثم	ADJ
iajs-154	1	17	للعلوم	للعلوم	NOUN
iajs-154	1	18	الصرفة	الصرفة	NOUN
iajs-154	2	1	و	و	PRON
iajs-154	2	2	التطبيقية	التطبيقية	ADV
iajs-154	2	3	المجلد	المجلد	VERB
iajs-154	2	4	ibn	ibn	PROPN
iajs-154	2	5	al	al	PROPN
iajs-154	2	6	-	-	PUNCT
iajs-154	2	7	haitham	haitham	PROPN
iajs-154	2	8	jour	jour	X
iajs-154	2	9	.	.	PROPN
iajs-154	3	1	for	for	ADP
iajs-154	3	2	pure	pure	ADJ
iajs-154	3	3	&	&	CCONJ
iajs-154	3	4	appl	appl	PROPN
iajs-154	3	5	.	.	PUNCT
iajs-154	4	1	sci	sci	PROPN
iajs-154	4	2	.	.	PUNCT
iajs-154	4	3	vol	vol	NOUN
iajs-154	4	4	.	.	PROPN
iajs-154	5	1	28	28	NUM
iajs-154	5	2	(	(	PUNCT
iajs-154	5	3	3	3	NUM
iajs-154	5	4	)	)	PUNCT
iajs-154	5	5	2015	2015	NUM
iajs-154	5	6	on	on	ADP
iajs-154	5	7	e	e	ADJ
iajs-154	5	8	-	-	ADJ
iajs-154	5	9	small	small	ADJ
iajs-154	5	10	submodules	submodule	NOUN
iajs-154	5	11	inaam	inaam	PROPN
iajs-154	5	12	m.a	m.a	PROPN
iajs-154	5	13	.	.	PROPN
iajs-154	5	14	hadi	hadi	PROPN
iajs-154	5	15	sameeah	sameeah	PROPN
iajs-154	5	16	h.	h.	PROPN
iajs-154	5	17	aidi	aidi	PROPN
iajs-154	5	18	dept	dept	PROPN
iajs-154	5	19	.	.	PROPN
iajs-154	6	1	of	of	ADP
iajs-154	6	2	mathematics/	mathematics/	NUM
iajs-154	6	3	college	college	NOUN
iajs-154	6	4	of	of	ADP
iajs-154	6	5	education	education	NOUN
iajs-154	6	6	for	for	ADP
iajs-154	6	7	pure	pure	ADJ
iajs-154	6	8	science	science	NOUN
iajs-154	6	9	(	(	PUNCT
iajs-154	6	10	ibn	ibn	PROPN
iajs-154	6	11	al	al	PROPN
iajs-154	6	12	-	-	PUNCT
iajs-154	6	13	haitham	haitham	PROPN
iajs-154	6	14	)	)	PUNCT
iajs-154	6	15	university	university	PROPN
iajs-154	6	16	of	of	ADP
iajs-154	6	17	baghdad	baghdad	PROPN
iajs-154	6	18	received	receive	VERB
iajs-154	6	19	in	in	ADP
iajs-154	6	20	:3	:3	PRON
iajs-154	6	21	/	/	SYM
iajs-154	6	22	june/2015,accepted	june/2015,accepte	VERB
iajs-154	6	23	in	in	ADP
iajs-154	6	24	:	:	PUNCT
iajs-154	6	25	20	20	NUM
iajs-154	6	26	/	/	SYM
iajs-154	6	27	september/2015	september/2015	NOUN
iajs-154	6	28	abstract	abstract	ADV
iajs-154	6	29	let	let	VERB
iajs-154	6	30	m	m	PRON
iajs-154	6	31	be	be	AUX
iajs-154	6	32	an	an	DET
iajs-154	6	33	r	r	NOUN
iajs-154	6	34	-	-	PUNCT
iajs-154	6	35	module	module	NOUN
iajs-154	6	36	,	,	PUNCT
iajs-154	6	37	where	where	SCONJ
iajs-154	6	38	r	r	NOUN
iajs-154	6	39	is	be	AUX
iajs-154	6	40	a	a	DET
iajs-154	6	41	commutative	commutative	ADJ
iajs-154	6	42	ring	ring	NOUN
iajs-154	6	43	with	with	ADP
iajs-154	6	44	unity	unity	NOUN
iajs-154	6	45	.	.	PUNCT
iajs-154	7	1	a	a	DET
iajs-154	7	2	submodule	submodule	NOUN
iajs-154	7	3	n	n	PROPN
iajs-154	7	4	of	of	ADP
iajs-154	7	5	m	m	PROPN
iajs-154	7	6	is	be	AUX
iajs-154	7	7	called	call	VERB
iajs-154	7	8	e	e	NOUN
iajs-154	7	9	-	-	ADJ
iajs-154	7	10	small	small	ADJ
iajs-154	7	11	(	(	PUNCT
iajs-154	7	12	denoted	denote	VERB
iajs-154	7	13	by	by	ADP
iajs-154	7	14	n	n	ADP
iajs-154	7	15	e	e	PROPN
iajs-154	7	16			PROPN
iajs-154	7	17	m	m	VERB
iajs-154	7	18	)	)	PUNCT
iajs-154	7	19	if	if	SCONJ
iajs-154	7	20	n	n	PROPN
iajs-154	8	1	+	+	X
iajs-154	8	2	k	k	X
iajs-154	8	3	=	=	SYM
iajs-154	8	4	m	m	PROPN
iajs-154	8	5	,	,	PUNCT
iajs-154	8	6	where	where	SCONJ
iajs-154	8	7	k	k	PROPN
iajs-154	8	8	e	e	PROPN
iajs-154	8	9			PROPN
iajs-154	8	10	m	m	VERB
iajs-154	8	11	implies	imply	VERB
iajs-154	8	12	k	k	X
iajs-154	8	13	=	=	PUNCT
iajs-154	8	14	m.	m.	NOUN
iajs-154	8	15	we	we	PRON
iajs-154	8	16	give	give	VERB
iajs-154	8	17	many	many	ADJ
iajs-154	8	18	properties	property	NOUN
iajs-154	8	19	related	relate	VERB
iajs-154	8	20	with	with	ADP
iajs-154	8	21	this	this	DET
iajs-154	8	22	type	type	NOUN
iajs-154	8	23	of	of	ADP
iajs-154	8	24	submodules	submodule	NOUN
iajs-154	8	25	.	.	PUNCT
iajs-154	9	1	keywords	keyword	NOUN
iajs-154	9	2	:	:	PUNCT
iajs-154	9	3	small	small	ADJ
iajs-154	9	4	submodule	submodule	NOUN
iajs-154	9	5	,	,	PUNCT
iajs-154	9	6	-small	-small	NOUN
iajs-154	9	7	submodule	submodule	NOUN
iajs-154	9	8	,	,	PUNCT
iajs-154	9	9	e	e	ADJ
iajs-154	9	10	-	-	ADJ
iajs-154	9	11	small	small	ADJ
iajs-154	9	12	submodule	submodule	NOUN
iajs-154	9	13	,	,	PUNCT
iajs-154	9	14	and	and	CCONJ
iajs-154	9	15	e	e	X
iajs-154	9	16	-	-	ADJ
iajs-154	9	17	coclosed	coclose	VERB
iajs-154	9	18	submodule	submodule	NOUN
iajs-154	9	19	.	.	PUNCT
iajs-154	10	1	215	215	NUM
iajs-154	10	2	|	|	NOUN
iajs-154	10	3	mathematics	mathematic	NOUN
iajs-154	10	4	2015	2015	NUM
iajs-154	10	5	)	)	PUNCT
iajs-154	10	6	عام	عام	ADP
iajs-154	10	7	3العدد	3العدد	NUM
iajs-154	10	8	(	(	PUNCT
iajs-154	10	9	28مجلة	28مجلة	X
iajs-154	10	10	إبن	إبن	VERB
iajs-154	10	11	الهيثم	الهيثم	ADJ
iajs-154	10	12	للعلوم	للعلوم	NOUN
iajs-154	10	13	الصرفة	الصرفة	NOUN
iajs-154	11	1	و	و	PRON
iajs-154	11	2	التطبيقية	التطبيقية	ADV
iajs-154	11	3	المجلد	المجلد	VERB
iajs-154	11	4	ibn	ibn	PROPN
iajs-154	11	5	al	al	PROPN
iajs-154	11	6	-	-	PUNCT
iajs-154	11	7	haitham	haitham	PROPN
iajs-154	11	8	jour	jour	X
iajs-154	11	9	.	.	PROPN
iajs-154	12	1	for	for	ADP
iajs-154	12	2	pure	pure	ADJ
iajs-154	12	3	&	&	CCONJ
iajs-154	12	4	appl	appl	PROPN
iajs-154	12	5	.	.	PUNCT
iajs-154	13	1	sci	sci	PROPN
iajs-154	13	2	.	.	PUNCT
iajs-154	13	3	vol	vol	NOUN
iajs-154	13	4	.	.	PROPN
iajs-154	14	1	28	28	NUM
iajs-154	14	2	(	(	PUNCT
iajs-154	14	3	3	3	NUM
iajs-154	14	4	)	)	PUNCT
iajs-154	14	5	2015	2015	NUM
iajs-154	14	6	1introduction	1introduction	NUM
iajs-154	14	7	throughout	throughout	ADP
iajs-154	14	8	this	this	DET
iajs-154	14	9	work	work	NOUN
iajs-154	14	10	,	,	PUNCT
iajs-154	14	11	r	r	NOUN
iajs-154	14	12	is	be	AUX
iajs-154	14	13	a	a	DET
iajs-154	14	14	commutative	commutative	ADJ
iajs-154	14	15	ring	ring	NOUN
iajs-154	14	16	with	with	ADP
iajs-154	14	17	unity	unity	NOUN
iajs-154	14	18	and	and	CCONJ
iajs-154	14	19	m	m	NOUN
iajs-154	14	20	is	be	AUX
iajs-154	14	21	an	an	DET
iajs-154	14	22	r	r	NOUN
iajs-154	14	23	-	-	PUNCT
iajs-154	14	24	module	module	NOUN
iajs-154	14	25	.	.	PUNCT
iajs-154	15	1	a	a	DET
iajs-154	15	2	proper	proper	ADJ
iajs-154	15	3	submodule	submodule	NOUN
iajs-154	15	4	n	n	PROPN
iajs-154	15	5	of	of	ADP
iajs-154	15	6	m	m	PROPN
iajs-154	15	7	is	be	AUX
iajs-154	15	8	called	call	VERB
iajs-154	15	9	small	small	ADJ
iajs-154	15	10	(	(	PUNCT
iajs-154	15	11	n	n	CCONJ
iajs-154	15	12	≪	≪	ADJ
iajs-154	15	13	m	m	NOUN
iajs-154	15	14	)	)	PUNCT
iajs-154	15	15	,	,	PUNCT
iajs-154	15	16	if	if	SCONJ
iajs-154	15	17	n	n	PROPN
iajs-154	16	1	+	+	X
iajs-154	16	2	k	k	X
iajs-154	16	3	=	=	PUNCT
iajs-154	16	4	m	m	VERB
iajs-154	16	5	where	where	SCONJ
iajs-154	16	6	k	k	PROPN
iajs-154	16	7			PROPN
iajs-154	16	8	m	m	VERB
iajs-154	16	9	implies	imply	VERB
iajs-154	16	10	k	k	PROPN
iajs-154	16	11	=	=	PUNCT
iajs-154	16	12	m	m	PROPN
iajs-154	16	13	,	,	PUNCT
iajs-154	16	14	[	[	X
iajs-154	16	15	1	1	NUM
iajs-154	16	16	]	]	PUNCT
iajs-154	16	17	.	.	PUNCT
iajs-154	17	1	a	a	DET
iajs-154	17	2	submodule	submodule	PROPN
iajs-154	17	3	n	n	PROPN
iajs-154	17	4	of	of	ADP
iajs-154	17	5	m	m	PROPN
iajs-154	17	6	is	be	AUX
iajs-154	17	7	called	call	VERB
iajs-154	17	8	-small	-small	NOUN
iajs-154	17	9	if	if	SCONJ
iajs-154	17	10	n	n	PROPN
iajs-154	17	11	+	+	X
iajs-154	18	1	k	k	X
iajs-154	18	2	=	=	NOUN
iajs-154	18	3	m	m	VERB
iajs-154	18	4	with	with	ADP
iajs-154	18	5	m	m	PROPN
iajs-154	18	6	k	k	NOUN
iajs-154	18	7	is	be	AUX
iajs-154	18	8	singular	singular	ADJ
iajs-154	18	9	implies	imply	VERB
iajs-154	18	10	,	,	PUNCT
iajs-154	18	11	k	k	PROPN
iajs-154	18	12	=	=	PUNCT
iajs-154	18	13	m	m	PROPN
iajs-154	18	14	,	,	PUNCT
iajs-154	18	15	[	[	X
iajs-154	18	16	2	2	NUM
iajs-154	18	17	]	]	PUNCT
iajs-154	18	18	.	.	PUNCT
iajs-154	19	1	a	a	DET
iajs-154	19	2	submodule	submodule	PROPN
iajs-154	19	3	n	n	PROPN
iajs-154	19	4	of	of	ADP
iajs-154	19	5	m	m	PROPN
iajs-154	19	6	is	be	AUX
iajs-154	19	7	called	call	VERB
iajs-154	19	8	essential	essential	ADJ
iajs-154	19	9	(	(	PUNCT
iajs-154	19	10	n	n	CCONJ
iajs-154	19	11	e	e	X
iajs-154	19	12	m	m	X
iajs-154	19	13	)	)	PUNCT
iajs-154	19	14	if	if	SCONJ
iajs-154	19	15	n	n	CCONJ
iajs-154	19	16			PROPN
iajs-154	19	17	w	w	PROPN
iajs-154	19	18			PROPN
iajs-154	19	19	(	(	PUNCT
iajs-154	19	20	0	0	NUM
iajs-154	19	21	)	)	PUNCT
iajs-154	19	22	for	for	ADP
iajs-154	19	23	any	any	DET
iajs-154	19	24	non	non	ADJ
iajs-154	19	25	zero	zero	NUM
iajs-154	19	26	submodule	submodule	PROPN
iajs-154	19	27	w	w	PROPN
iajs-154	19	28	of	of	ADP
iajs-154	19	29	m	m	PRON
iajs-154	19	30	,	,	PUNCT
iajs-154	19	31	[	[	X
iajs-154	19	32	3	3	NUM
iajs-154	19	33	]	]	PUNCT
iajs-154	19	34	.	.	PUNCT
iajs-154	20	1	an	an	DET
iajs-154	20	2	r	r	NOUN
iajs-154	20	3	-	-	PUNCT
iajs-154	20	4	module	module	NOUN
iajs-154	20	5	m	m	NOUN
iajs-154	20	6	is	be	AUX
iajs-154	20	7	called	call	VERB
iajs-154	20	8	singular	singular	ADJ
iajs-154	20	9	(	(	PUNCT
iajs-154	20	10	non	non	X
iajs-154	20	11	singular	singular	PROPN
iajs-154	20	12	)	)	PUNCT
iajs-154	20	13	if	if	SCONJ
iajs-154	20	14	z(m	z(m	NOUN
iajs-154	20	15	)	)	PUNCT
iajs-154	21	1	=	=	SYM
iajs-154	21	2	m	m	PROPN
iajs-154	21	3	(	(	PUNCT
iajs-154	21	4	z(m	z(m	PROPN
iajs-154	21	5	)	)	PUNCT
iajs-154	21	6	=(	=(	NOUN
iajs-154	21	7	0	0	NUM
iajs-154	21	8	)	)	PUNCT
iajs-154	21	9	)	)	PUNCT
iajs-154	21	10	,	,	PUNCT
iajs-154	21	11	where	where	SCONJ
iajs-154	21	12	z(m	z(m	NOUN
iajs-154	21	13	)	)	PUNCT
iajs-154	21	14	=	=	PRON
iajs-154	21	15	{	{	PUNCT
iajs-154	21	16	x	x	X
iajs-154	21	17			NOUN
iajs-154	21	18	m	m	ADP
iajs-154	21	19	:	:	PUNCT
iajs-154	21	20	r	r	NOUN
iajs-154	21	21	ann	ann	X
iajs-154	21	22	(	(	PUNCT
iajs-154	21	23	x	x	NOUN
iajs-154	21	24	)	)	PUNCT
iajs-154	21	25			NOUN
iajs-154	21	26	r	r	NOUN
iajs-154	21	27	}	}	PUNCT
iajs-154	21	28	.	.	PUNCT
iajs-154	22	1	zhou	zhou	PROPN
iajs-154	22	2	and	and	CCONJ
iajs-154	22	3	zhang	zhang	PROPN
iajs-154	22	4	in	in	ADP
iajs-154	22	5	[	[	X
iajs-154	22	6	4	4	NUM
iajs-154	22	7	]	]	PUNCT
iajs-154	22	8	introduce	introduce	VERB
iajs-154	22	9	a	a	DET
iajs-154	22	10	new	new	ADJ
iajs-154	22	11	type	type	NOUN
iajs-154	22	12	of	of	ADP
iajs-154	22	13	small	small	ADJ
iajs-154	22	14	submodule	submodule	NOUN
iajs-154	22	15	namely	namely	ADV
iajs-154	22	16	e	e	NOUN
iajs-154	22	17	-	-	ADJ
iajs-154	22	18	small	small	ADJ
iajs-154	22	19	submodule	submodule	NOUN
iajs-154	22	20	and	and	CCONJ
iajs-154	22	21	give	give	VERB
iajs-154	22	22	some	some	DET
iajs-154	22	23	basic	basic	ADJ
iajs-154	22	24	properties	property	NOUN
iajs-154	22	25	of	of	ADP
iajs-154	22	26	this	this	DET
iajs-154	22	27	kind	kind	NOUN
iajs-154	22	28	of	of	ADP
iajs-154	22	29	submodules	submodules	NOUN
iajs-154	22	30	.	.	PUNCT
iajs-154	23	1	in	in	ADP
iajs-154	23	2	this	this	DET
iajs-154	23	3	paper	paper	NOUN
iajs-154	23	4	,	,	PUNCT
iajs-154	23	5	we	we	PRON
iajs-154	23	6	continuo	continuo	VERB
iajs-154	23	7	the	the	DET
iajs-154	23	8	work	work	NOUN
iajs-154	23	9	of	of	ADP
iajs-154	23	10	zhou	zhou	PROPN
iajs-154	24	1	[	[	X
iajs-154	24	2	4	4	NUM
iajs-154	24	3	]	]	PUNCT
iajs-154	24	4	and	and	CCONJ
iajs-154	24	5	give	give	VERB
iajs-154	24	6	many	many	ADJ
iajs-154	24	7	other	other	ADJ
iajs-154	24	8	properties	property	NOUN
iajs-154	24	9	of	of	ADP
iajs-154	24	10	esmall	esmall	NOUN
iajs-154	24	11	submodule	submodule	NOUN
iajs-154	24	12	and	and	CCONJ
iajs-154	24	13	study	study	VERB
iajs-154	24	14	the	the	DET
iajs-154	24	15	behavior	behavior	NOUN
iajs-154	24	16	of	of	ADP
iajs-154	24	17	e	e	NOUN
iajs-154	24	18	-	-	ADJ
iajs-154	24	19	small	small	ADJ
iajs-154	24	20	submodules	submodule	NOUN
iajs-154	24	21	in	in	ADP
iajs-154	24	22	certain	certain	ADJ
iajs-154	24	23	class	class	NOUN
iajs-154	24	24	of	of	ADP
iajs-154	24	25	module	module	NOUN
iajs-154	24	26	.	.	PUNCT
iajs-154	25	1	2preliminary	2preliminary	NUM
iajs-154	25	2	definition	definition	NOUN
iajs-154	25	3	(	(	PUNCT
iajs-154	25	4	2.1	2.1	NUM
iajs-154	25	5	):	):	PUNCT
iajs-154	25	6	[	[	X
iajs-154	25	7	4	4	X
iajs-154	25	8	]	]	PUNCT
iajs-154	25	9	let	let	VERB
iajs-154	25	10	n	n	PRON
iajs-154	25	11	be	be	AUX
iajs-154	25	12	a	a	DET
iajs-154	25	13	submodule	submodule	NOUN
iajs-154	25	14	of	of	ADP
iajs-154	25	15	a	a	DET
iajs-154	25	16	module	module	NOUN
iajs-154	25	17	m.	m.	NOUN
iajs-154	25	18	n	n	PRON
iajs-154	25	19	is	be	AUX
iajs-154	25	20	said	say	VERB
iajs-154	25	21	to	to	PART
iajs-154	25	22	be	be	AUX
iajs-154	25	23	e	e	NOUN
iajs-154	25	24	-	-	NOUN
iajs-154	25	25	small	small	ADJ
iajs-154	25	26	in	in	ADP
iajs-154	25	27	m	m	PROPN
iajs-154	25	28	(	(	PUNCT
iajs-154	25	29	denoted	denote	VERB
iajs-154	25	30	by	by	ADP
iajs-154	25	31	n	n	X
iajs-154	25	32	e	e	NOUN
iajs-154	25	33	m	m	PROPN
iajs-154	25	34	)	)	PUNCT
iajs-154	25	35	,	,	PUNCT
iajs-154	25	36	if	if	SCONJ
iajs-154	25	37	n	n	PROPN
iajs-154	25	38	+	+	NOUN
iajs-154	25	39	l	l	NOUN
iajs-154	25	40	=	=	NOUN
iajs-154	25	41	m	m	NOUN
iajs-154	25	42	with	with	ADP
iajs-154	25	43	l	l	NOUN
iajs-154	25	44	e	e	NOUN
iajs-154	25	45			NOUN
iajs-154	25	46	m	m	VERB
iajs-154	25	47	implies	imply	VERB
iajs-154	25	48	l	l	NOUN
iajs-154	25	49	=	=	PUNCT
iajs-154	25	50	m.	m.	NOUN
iajs-154	25	51	remark	remark	NOUN
iajs-154	25	52	(	(	PUNCT
iajs-154	25	53	2.2	2.2	NUM
iajs-154	25	54	):	):	PUNCT
iajs-154	25	55	obviously	obviously	ADV
iajs-154	25	56	,	,	PUNCT
iajs-154	25	57	every	every	DET
iajs-154	25	58	small	small	ADJ
iajs-154	25	59	(	(	PUNCT
iajs-154	25	60	-small	-small	NOUN
iajs-154	25	61	)	)	PUNCT
iajs-154	25	62	submodule	submodule	NOUN
iajs-154	25	63	of	of	ADP
iajs-154	25	64	an	an	DET
iajs-154	25	65	r	r	NOUN
iajs-154	25	66	-	-	PUNCT
iajs-154	25	67	module	module	NOUN
iajs-154	25	68	m	m	NOUN
iajs-154	25	69	is	be	AUX
iajs-154	25	70	e	e	ADJ
iajs-154	25	71	-	-	ADJ
iajs-154	25	72	small	small	ADJ
iajs-154	26	1	[	[	X
iajs-154	26	2	4	4	NUM
iajs-154	26	3	]	]	PUNCT
iajs-154	26	4	,	,	PUNCT
iajs-154	26	5	but	but	CCONJ
iajs-154	26	6	the	the	DET
iajs-154	26	7	converses	converse	NOUN
iajs-154	26	8	are	be	AUX
iajs-154	26	9	not	not	PART
iajs-154	26	10	true	true	ADJ
iajs-154	26	11	in	in	ADP
iajs-154	26	12	general	general	ADJ
iajs-154	26	13	,	,	PUNCT
iajs-154	26	14	for	for	ADP
iajs-154	26	15	example	example	NOUN
iajs-154	26	16	:	:	PUNCT
iajs-154	26	17	in	in	ADP
iajs-154	26	18	the	the	DET
iajs-154	26	19	z	z	NOUN
iajs-154	26	20	-	-	PUNCT
iajs-154	26	21	module	module	NOUN
iajs-154	26	22	z12	z12	NOUN
iajs-154	26	23	,	,	PUNCT
iajs-154	27	1	the	the	DET
iajs-154	27	2	submodule	submodule	NOUN
iajs-154	27	3	n	n	NOUN
iajs-154	27	4	=	=	SYM
iajs-154	27	5	12	12	NUM
iajs-154	27	6	e	e	NOUN
iajs-154	27	7	2	2	NUM
iajs-154	27	8	z	z	X
iajs-154	27	9			PROPN
iajs-154	27	10	but	but	CCONJ
iajs-154	27	11	n	n	CCONJ
iajs-154	27	12			PROPN
iajs-154	27	13	z12	z12	PROPN
iajs-154	27	14	,	,	PUNCT
iajs-154	27	15	also	also	ADV
iajs-154	27	16	n	n	PROPN
iajs-154	27	17	δ	δ	PROPN
iajs-154	27	18			PROPN
iajs-154	27	19	z12	z12	PROPN
iajs-154	27	20	.	.	PUNCT
iajs-154	27	21	also	also	ADV
iajs-154	27	22	,	,	PUNCT
iajs-154	27	23	in	in	ADP
iajs-154	27	24	the	the	DET
iajs-154	27	25	z	z	NOUN
iajs-154	27	26	-	-	PUNCT
iajs-154	27	27	module	module	NOUN
iajs-154	27	28	z6	z6	NOUN
iajs-154	27	29	,	,	PUNCT
iajs-154	27	30	n	n	NOUN
iajs-154	27	31	=	=	SYM
iajs-154	27	32	6	6	NUM
iajs-154	27	33	e	e	NOUN
iajs-154	27	34	3	3	NUM
iajs-154	27	35	z	z	X
iajs-154	27	36			PROPN
iajs-154	27	37	,	,	PUNCT
iajs-154	27	38	but	but	CCONJ
iajs-154	27	39	n	n	CCONJ
iajs-154	27	40	δ	δ	PROPN
iajs-154	27	41			PROPN
iajs-154	27	42	z6	z6	PROPN
iajs-154	27	43	and	and	CCONJ
iajs-154	27	44	n	n	CCONJ
iajs-154	27	45			PROPN
iajs-154	27	46	z6	z6	PROPN
iajs-154	27	47	,	,	PUNCT
iajs-154	27	48	[	[	X
iajs-154	27	49	4	4	NUM
iajs-154	27	50	]	]	PUNCT
iajs-154	27	51	.	.	PUNCT
iajs-154	28	1	proposition	proposition	NOUN
iajs-154	28	2	(	(	PUNCT
iajs-154	28	3	2.3	2.3	NUM
iajs-154	28	4	):	):	PUNCT
iajs-154	29	1	[	[	X
iajs-154	29	2	4,proposition	4,proposition	NUM
iajs-154	29	3	2.3	2.3	NUM
iajs-154	29	4	]	]	PUNCT
iajs-154	29	5	let	let	VERB
iajs-154	29	6	n	n	PRON
iajs-154	29	7	be	be	AUX
iajs-154	29	8	a	a	DET
iajs-154	29	9	submodule	submodule	NOUN
iajs-154	29	10	of	of	ADP
iajs-154	29	11	m.	m.	NOUN
iajs-154	29	12	the	the	DET
iajs-154	29	13	following	follow	VERB
iajs-154	29	14	statements	statement	NOUN
iajs-154	29	15	are	be	AUX
iajs-154	29	16	equivalent	equivalent	ADJ
iajs-154	29	17	:	:	PUNCT
iajs-154	29	18	(	(	PUNCT
iajs-154	29	19	1	1	X
iajs-154	29	20	)	)	PUNCT
iajs-154	29	21	n	n	NOUN
iajs-154	29	22	e	e	NOUN
iajs-154	29	23			NOUN
iajs-154	29	24	m	m	VERB
iajs-154	29	25	(	(	PUNCT
iajs-154	29	26	2	2	NUM
iajs-154	29	27	)	)	PUNCT
iajs-154	29	28	if	if	SCONJ
iajs-154	29	29	x	x	PROPN
iajs-154	29	30	+	+	NUM
iajs-154	29	31	n	n	PROPN
iajs-154	29	32	=	=	SYM
iajs-154	29	33	m	m	PROPN
iajs-154	29	34	,	,	PUNCT
iajs-154	29	35	then	then	ADV
iajs-154	29	36	x	x	PUNCT
iajs-154	29	37			NOUN
iajs-154	29	38	m	m	PUNCT
iajs-154	29	39	with	with	ADP
iajs-154	29	40	m	m	PROPN
iajs-154	29	41	x	x	PUNCT
iajs-154	29	42	a	a	DET
iajs-154	29	43	semisimple	semisimple	NOUN
iajs-154	29	44	module	module	NOUN
iajs-154	29	45	.	.	PUNCT
iajs-154	30	1	where	where	SCONJ
iajs-154	30	2	x	x	PUNCT
iajs-154	30	3			NUM
iajs-154	30	4	m	m	PROPN
iajs-154	30	5	,	,	PUNCT
iajs-154	30	6	means	mean	VERB
iajs-154	30	7	there	there	PRON
iajs-154	30	8	exists	exist	VERB
iajs-154	30	9	w	w	PROPN
iajs-154	30	10			NOUN
iajs-154	30	11	m	m	VERB
iajs-154	30	12	such	such	ADJ
iajs-154	30	13	that	that	SCONJ
iajs-154	30	14	w	w	PROPN
iajs-154	30	15			ADJ
iajs-154	30	16	x	x	PUNCT
iajs-154	31	1	=	=	VERB
iajs-154	31	2	m.	m.	NOUN
iajs-154	31	3	corollary	corollary	NOUN
iajs-154	31	4	(	(	PUNCT
iajs-154	31	5	2.4	2.4	NUM
iajs-154	31	6	):	):	PUNCT
iajs-154	31	7	[	[	X
iajs-154	31	8	4	4	X
iajs-154	31	9	]	]	X
iajs-154	31	10	if	if	SCONJ
iajs-154	31	11	m	m	NOUN
iajs-154	31	12	is	be	AUX
iajs-154	31	13	a	a	DET
iajs-154	31	14	projective	projective	ADJ
iajs-154	31	15	module	module	NOUN
iajs-154	31	16	,	,	PUNCT
iajs-154	31	17	then	then	ADV
iajs-154	31	18	every	every	DET
iajs-154	31	19	e	e	ADJ
iajs-154	31	20	-	-	ADJ
iajs-154	31	21	small	small	ADJ
iajs-154	31	22	submodule	submodule	NOUN
iajs-154	31	23	n	n	PROPN
iajs-154	31	24	of	of	ADP
iajs-154	31	25	m	m	PROPN
iajs-154	31	26	is	be	AUX
iajs-154	31	27	-small	-small	PROPN
iajs-154	31	28	.	.	PUNCT
iajs-154	32	1	the	the	DET
iajs-154	32	2	next	next	ADJ
iajs-154	32	3	proposition	proposition	NOUN
iajs-154	32	4	explains	explain	VERB
iajs-154	32	5	how	how	SCONJ
iajs-154	32	6	close	close	ADJ
iajs-154	32	7	the	the	DET
iajs-154	32	8	notion	notion	NOUN
iajs-154	32	9	of	of	ADP
iajs-154	32	10	e	e	NOUN
iajs-154	32	11	-	-	ADJ
iajs-154	32	12	small	small	ADJ
iajs-154	32	13	submodules	submodule	NOUN
iajs-154	32	14	to	to	ADP
iajs-154	32	15	small	small	ADJ
iajs-154	32	16	submodules	submodule	NOUN
iajs-154	32	17	.	.	PUNCT
iajs-154	33	1	proposition	proposition	NOUN
iajs-154	33	2	(	(	PUNCT
iajs-154	33	3	2.5	2.5	NUM
iajs-154	33	4	):	):	PUNCT
iajs-154	34	1	[	[	X
iajs-154	34	2	4,proposition	4,proposition	NUM
iajs-154	34	3	2.5	2.5	NUM
iajs-154	34	4	]	]	PUNCT
iajs-154	34	5	let	let	VERB
iajs-154	34	6	m	m	PRON
iajs-154	34	7	be	be	AUX
iajs-154	34	8	an	an	DET
iajs-154	34	9	r	r	NOUN
iajs-154	34	10	-	-	PUNCT
iajs-154	34	11	module	module	NOUN
iajs-154	34	12	(	(	PUNCT
iajs-154	34	13	1	1	X
iajs-154	34	14	)	)	PUNCT
iajs-154	34	15	assume	assume	VERB
iajs-154	34	16	n	n	CCONJ
iajs-154	34	17	,	,	PUNCT
iajs-154	34	18	k	k	PROPN
iajs-154	34	19	,	,	PUNCT
iajs-154	34	20	l	l	NOUN
iajs-154	34	21	are	be	AUX
iajs-154	34	22	submodules	submodule	NOUN
iajs-154	34	23	of	of	ADP
iajs-154	34	24	m	m	PROPN
iajs-154	34	25	with	with	ADP
iajs-154	34	26	k	k	PROPN
iajs-154	34	27			PROPN
iajs-154	34	28	n	n	CCONJ
iajs-154	34	29	:	:	PUNCT
iajs-154	34	30	(	(	PUNCT
iajs-154	34	31	a	a	X
iajs-154	34	32	)	)	PUNCT
iajs-154	34	33	if	if	SCONJ
iajs-154	34	34	n	n	NUM
iajs-154	34	35	e	e	NOUN
iajs-154	34	36			NOUN
iajs-154	34	37	m	m	PROPN
iajs-154	34	38	,	,	PUNCT
iajs-154	34	39	then	then	ADV
iajs-154	34	40	k	k	PROPN
iajs-154	34	41	e	e	PROPN
iajs-154	34	42			NOUN
iajs-154	34	43	m	m	VERB
iajs-154	34	44	and	and	CCONJ
iajs-154	34	45	e	e	PROPN
iajs-154	34	46	n	n	CCONJ
iajs-154	34	47	m	m	VERB
iajs-154	34	48	k	k	NOUN
iajs-154	35	1	k	k	PROPN
iajs-154	35	2			PROPN
iajs-154	35	3	.	.	PUNCT
iajs-154	36	1	(	(	PUNCT
iajs-154	36	2	b	b	X
iajs-154	36	3	)	)	PUNCT
iajs-154	36	4	n	n	NOUN
iajs-154	36	5	+	+	NOUN
iajs-154	36	6	l	l	NOUN
iajs-154	36	7	e	e	NOUN
iajs-154	37	1			NOUN
iajs-154	37	2	m	m	VERB
iajs-154	37	3	if	if	SCONJ
iajs-154	37	4	and	and	CCONJ
iajs-154	37	5	only	only	ADV
iajs-154	37	6	if	if	SCONJ
iajs-154	37	7	n	n	NUM
iajs-154	37	8	e	e	VERB
iajs-154	37	9			NOUN
iajs-154	37	10	m	m	VERB
iajs-154	37	11	and	and	CCONJ
iajs-154	37	12	l	l	NOUN
iajs-154	38	1	e	e	NOUN
iajs-154	38	2			PROPN
iajs-154	38	3	m.	m.	NOUN
iajs-154	38	4	216	216	NUM
iajs-154	38	5	|	|	NOUN
iajs-154	38	6	mathematics	mathematic	NOUN
iajs-154	38	7	2015	2015	NUM
iajs-154	38	8	)	)	PUNCT
iajs-154	38	9	عام	عام	ADP
iajs-154	38	10	3العدد	3العدد	NUM
iajs-154	38	11	(	(	PUNCT
iajs-154	38	12	28مجلة	28مجلة	X
iajs-154	38	13	إبن	إبن	VERB
iajs-154	38	14	الهيثم	الهيثم	ADJ
iajs-154	38	15	للعلوم	للعلوم	NOUN
iajs-154	38	16	الصرفة	الصرفة	NOUN
iajs-154	39	1	و	و	PRON
iajs-154	39	2	التطبيقية	التطبيقية	ADV
iajs-154	39	3	المجلد	المجلد	VERB
iajs-154	39	4	ibn	ibn	PROPN
iajs-154	39	5	al	al	PROPN
iajs-154	39	6	-	-	PUNCT
iajs-154	39	7	haitham	haitham	PROPN
iajs-154	39	8	jour	jour	X
iajs-154	39	9	.	.	PROPN
iajs-154	40	1	for	for	ADP
iajs-154	40	2	pure	pure	ADJ
iajs-154	40	3	&	&	CCONJ
iajs-154	40	4	appl	appl	PROPN
iajs-154	40	5	.	.	PUNCT
iajs-154	41	1	sci	sci	PROPN
iajs-154	41	2	.	.	PUNCT
iajs-154	41	3	vol	vol	NOUN
iajs-154	41	4	.	.	PROPN
iajs-154	42	1	28	28	NUM
iajs-154	42	2	(	(	PUNCT
iajs-154	42	3	3	3	NUM
iajs-154	42	4	)	)	PUNCT
iajs-154	42	5	2015	2015	NUM
iajs-154	42	6	(	(	PUNCT
iajs-154	42	7	2	2	NUM
iajs-154	42	8	)	)	PUNCT
iajs-154	42	9	if	if	SCONJ
iajs-154	42	10	k	k	PROPN
iajs-154	42	11	e	e	PROPN
iajs-154	43	1			VERB
iajs-154	43	2	m	m	VERB
iajs-154	43	3	and	and	CCONJ
iajs-154	43	4	f	f	X
iajs-154	43	5	:	:	PUNCT
iajs-154	43	6	m	m	VERB
iajs-154	43	7			PROPN
iajs-154	43	8	n	n	PRON
iajs-154	43	9	is	be	AUX
iajs-154	43	10	a	a	DET
iajs-154	43	11	homeomorphism	homeomorphism	NOUN
iajs-154	43	12	,	,	PUNCT
iajs-154	43	13	then	then	ADV
iajs-154	43	14	f	f	PROPN
iajs-154	43	15	(	(	PUNCT
iajs-154	43	16	k	k	NOUN
iajs-154	43	17	)	)	PUNCT
iajs-154	43	18	e	e	NOUN
iajs-154	44	1			PROPN
iajs-154	44	2	n.	n.	PROPN
iajs-154	44	3	in	in	ADP
iajs-154	44	4	particular	particular	ADJ
iajs-154	44	5	,	,	PUNCT
iajs-154	44	6	if	if	SCONJ
iajs-154	44	7	k	k	PROPN
iajs-154	44	8	e	e	PROPN
iajs-154	44	9	m	m	PROPN
iajs-154	44	10			NOUN
iajs-154	44	11	n	n	CCONJ
iajs-154	44	12	,	,	PUNCT
iajs-154	44	13	then	then	ADV
iajs-154	44	14	k	k	PROPN
iajs-154	44	15	e	e	PROPN
iajs-154	44	16			PROPN
iajs-154	44	17	n.	n.	NOUN
iajs-154	44	18	(	(	PUNCT
iajs-154	44	19	3	3	X
iajs-154	44	20	)	)	PUNCT
iajs-154	44	21	assume	assume	VERB
iajs-154	44	22	that	that	SCONJ
iajs-154	44	23	k1	k1	PROPN
iajs-154	44	24			PROPN
iajs-154	44	25	m1	m1	PROPN
iajs-154	44	26	<	<	X
iajs-154	44	27	m	m	PROPN
iajs-154	44	28	,	,	PUNCT
iajs-154	44	29	k2	k2	ADJ
iajs-154	44	30			PROPN
iajs-154	44	31	m2	m2	PROPN
iajs-154	44	32			PROPN
iajs-154	44	33	m	m	VERB
iajs-154	44	34	and	and	CCONJ
iajs-154	44	35	m	m	PROPN
iajs-154	44	36	=	=	ADJ
iajs-154	44	37	m1	m1	PROPN
iajs-154	44	38			PROPN
iajs-154	44	39	m2	m2	PROPN
iajs-154	44	40	,	,	PUNCT
iajs-154	44	41	then	then	ADV
iajs-154	44	42	k1	k1	PROPN
iajs-154	44	43			PROPN
iajs-154	44	44	k2	k2	PROPN
iajs-154	44	45	e	e	PROPN
iajs-154	44	46			PROPN
iajs-154	44	47	m1	m1	PROPN
iajs-154	44	48			PROPN
iajs-154	44	49	m2	m2	PROPN
iajs-154	45	1	if	if	SCONJ
iajs-154	45	2	and	and	CCONJ
iajs-154	45	3	only	only	ADV
iajs-154	45	4	if	if	SCONJ
iajs-154	45	5	k1	k1	PROPN
iajs-154	45	6	e	e	NOUN
iajs-154	45	7			PROPN
iajs-154	45	8	m1	m1	PROPN
iajs-154	45	9	and	and	CCONJ
iajs-154	45	10	k2	k2	PROPN
iajs-154	45	11	e	e	PROPN
iajs-154	45	12			PROPN
iajs-154	45	13	m2	m2	PROPN
iajs-154	45	14	.	.	PUNCT
iajs-154	46	1	3main	3main	NUM
iajs-154	46	2	results	result	VERB
iajs-154	46	3	proposition	proposition	NOUN
iajs-154	46	4	(	(	PUNCT
iajs-154	46	5	3.1	3.1	NUM
iajs-154	46	6	):	):	PUNCT
iajs-154	46	7	let	let	VERB
iajs-154	46	8	m	m	PRON
iajs-154	46	9	be	be	AUX
iajs-154	46	10	an	an	DET
iajs-154	46	11	r	r	NOUN
iajs-154	46	12	-	-	PUNCT
iajs-154	46	13	module	module	NOUN
iajs-154	46	14	,	,	PUNCT
iajs-154	46	15	let	let	VERB
iajs-154	46	16	m	m	PRON
iajs-154	46	17			PROPN
iajs-154	46	18	m.	m.	NOUN
iajs-154	46	19	then	then	ADV
iajs-154	46	20	rm	rm	PROPN
iajs-154	46	21	e	e	PROPN
iajs-154	46	22			PROPN
iajs-154	46	23	m	m	VERB
iajs-154	46	24	if	if	SCONJ
iajs-154	46	25	and	and	CCONJ
iajs-154	46	26	only	only	ADV
iajs-154	46	27	if	if	SCONJ
iajs-154	46	28	there	there	PRON
iajs-154	46	29	exists	exist	VERB
iajs-154	46	30	an	an	DET
iajs-154	46	31	essential	essential	ADJ
iajs-154	46	32	maximal	maximal	ADJ
iajs-154	46	33	submodule	submodule	NOUN
iajs-154	46	34	n	n	PROPN
iajs-154	46	35	with	with	ADP
iajs-154	46	36	m	m	PROPN
iajs-154	46	37			ADJ
iajs-154	46	38	n.	n.	NOUN
iajs-154	46	39	proof	proof	NOUN
iajs-154	46	40	:	:	PUNCT
iajs-154	46	41	(	(	PUNCT
iajs-154	46	42			NOUN
iajs-154	46	43	)	)	PUNCT
iajs-154	46	44	suppose	suppose	VERB
iajs-154	46	45	there	there	PRON
iajs-154	46	46	exists	exist	VERB
iajs-154	46	47	an	an	DET
iajs-154	46	48	essential	essential	ADJ
iajs-154	46	49	maximal	maximal	ADJ
iajs-154	46	50	submodule	submodule	NOUN
iajs-154	46	51	n	n	PRON
iajs-154	46	52	such	such	ADJ
iajs-154	46	53	that	that	SCONJ
iajs-154	46	54	m	m	PROPN
iajs-154	46	55			ADJ
iajs-154	46	56	n.	n.	NOUN
iajs-154	46	57	hence	hence	ADV
iajs-154	46	58	m	m	VERB
iajs-154	46	59	=	=	SYM
iajs-154	46	60	rm	rm	PROPN
iajs-154	46	61	+	+	CCONJ
iajs-154	46	62	n	n	PROPN
iajs-154	46	63	and	and	CCONJ
iajs-154	46	64	so	so	ADV
iajs-154	46	65	rm	rm	PROPN
iajs-154	46	66	e	e	PROPN
iajs-154	46	67			PROPN
iajs-154	46	68	m.	m.	NOUN
iajs-154	46	69	(	(	PUNCT
iajs-154	46	70			NOUN
iajs-154	46	71	)	)	PUNCT
iajs-154	46	72	suppose	suppose	VERB
iajs-154	46	73	rm	rm	PROPN
iajs-154	46	74	e	e	PROPN
iajs-154	46	75			PROPN
iajs-154	46	76	m.	m.	NOUN
iajs-154	46	77	hence	hence	ADV
iajs-154	46	78	there	there	PRON
iajs-154	46	79	exists	exist	VERB
iajs-154	46	80	an	an	DET
iajs-154	46	81	essential	essential	ADJ
iajs-154	46	82	submodule	submodule	NOUN
iajs-154	46	83	w	w	PROPN
iajs-154	46	84	(	(	PUNCT
iajs-154	46	85	w	w	PROPN
iajs-154	46	86			PROPN
iajs-154	46	87	m	m	NOUN
iajs-154	46	88	)	)	PUNCT
iajs-154	46	89	such	such	ADJ
iajs-154	46	90	that	that	SCONJ
iajs-154	46	91	m	m	VERB
iajs-154	46	92	=	=	SYM
iajs-154	46	93	rm	rm	PROPN
iajs-154	46	94	+	+	CCONJ
iajs-154	46	95	w.	w.	PROPN
iajs-154	46	96	let	let	VERB
iajs-154	46	97	c	c	NOUN
iajs-154	46	98	=	=	PRON
iajs-154	46	99	{	{	PUNCT
iajs-154	46	100	n	n	PROPN
iajs-154	46	101	e	e	NOUN
iajs-154	46	102			NOUN
iajs-154	46	103	m	m	VERB
iajs-154	46	104	:	:	PUNCT
iajs-154	46	105	rm	rm	NOUN
iajs-154	46	106	+	+	CCONJ
iajs-154	46	107	n	n	PROPN
iajs-154	46	108	=	=	SYM
iajs-154	46	109	m	m	NOUN
iajs-154	46	110	}	}	PUNCT
iajs-154	46	111	.	.	PUNCT
iajs-154	47	1	then	then	ADV
iajs-154	47	2	b	b	PROPN
iajs-154	47	3			PROPN
iajs-154	47	4	.	.	PUNCT
iajs-154	47	5	by	by	ADP
iajs-154	47	6	zorn	zorn	PROPN
iajs-154	47	7	's	's	PART
iajs-154	47	8	lemma	lemma	PROPN
iajs-154	47	9	,	,	PUNCT
iajs-154	47	10	there	there	PRON
iajs-154	47	11	exists	exist	VERB
iajs-154	47	12	a	a	DET
iajs-154	47	13	maximal	maximal	ADJ
iajs-154	47	14	element	element	NOUN
iajs-154	47	15	n	n	CCONJ
iajs-154	47	16	in	in	ADP
iajs-154	47	17	c	c	PROPN
iajs-154	47	18	such	such	ADJ
iajs-154	47	19	that	that	DET
iajs-154	47	20	rm	rm	NOUN
iajs-154	47	21	+	+	CCONJ
iajs-154	47	22	n	n	PROPN
iajs-154	47	23	=	=	NOUN
iajs-154	47	24	m.	m.	NOUN
iajs-154	47	25	we	we	PRON
iajs-154	47	26	claim	claim	VERB
iajs-154	47	27	that	that	SCONJ
iajs-154	47	28	n	n	PRON
iajs-154	47	29	is	be	AUX
iajs-154	47	30	a	a	DET
iajs-154	47	31	maximal	maximal	ADJ
iajs-154	47	32	submodule	submodule	NOUN
iajs-154	47	33	.	.	PUNCT
iajs-154	48	1	suppose	suppose	VERB
iajs-154	48	2	n	n	PRON
iajs-154	48	3	is	be	AUX
iajs-154	48	4	not	not	PART
iajs-154	48	5	maximal	maximal	ADJ
iajs-154	48	6	,	,	PUNCT
iajs-154	48	7	so	so	SCONJ
iajs-154	48	8	there	there	PRON
iajs-154	48	9	exists	exist	VERB
iajs-154	48	10	a	a	DET
iajs-154	48	11	submodule	submodule	NOUN
iajs-154	48	12	k	k	PROPN
iajs-154	48	13	of	of	ADP
iajs-154	48	14	m	m	PROPN
iajs-154	48	15	with	with	ADP
iajs-154	48	16	n	n	CCONJ
iajs-154	48	17			PROPN
iajs-154	48	18	k	k	PROPN
iajs-154	48	19			PROPN
iajs-154	48	20	m.	m.	NOUN
iajs-154	48	21	but	but	CCONJ
iajs-154	48	22	n	n	PROPN
iajs-154	48	23	e	e	PROPN
iajs-154	48	24			NUM
iajs-154	48	25	m	m	NOUN
iajs-154	48	26	,	,	PUNCT
iajs-154	48	27	so	so	ADV
iajs-154	48	28	k	k	PROPN
iajs-154	48	29	e	e	PROPN
iajs-154	48	30			PROPN
iajs-154	48	31	m	m	VERB
iajs-154	48	32	and	and	CCONJ
iajs-154	48	33	m	m	PROPN
iajs-154	48	34	=	=	ADJ
iajs-154	48	35	rm	rm	PROPN
iajs-154	48	36	+	+	CCONJ
iajs-154	48	37	n	n	CCONJ
iajs-154	48	38			PROPN
iajs-154	48	39	rm	rm	PROPN
iajs-154	48	40	+	+	CCONJ
iajs-154	48	41	k	k	X
iajs-154	48	42	,	,	PUNCT
iajs-154	48	43	thus	thus	ADV
iajs-154	48	44	rm	rm	NOUN
iajs-154	48	45	+	+	CCONJ
iajs-154	48	46	k	k	X
iajs-154	49	1	=	=	VERB
iajs-154	49	2	m	m	ADJ
iajs-154	49	3	and	and	CCONJ
iajs-154	49	4	hence	hence	ADV
iajs-154	49	5	k	k	PROPN
iajs-154	49	6			PROPN
iajs-154	49	7	c.	c.	PROPN
iajs-154	50	1	but	but	CCONJ
iajs-154	50	2	this	this	PRON
iajs-154	50	3	contradicts	contradict	VERB
iajs-154	50	4	the	the	DET
iajs-154	50	5	maximality	maximality	NOUN
iajs-154	50	6	of	of	ADP
iajs-154	50	7	n.	n.	NOUN
iajs-154	50	8	therefore	therefore	ADV
iajs-154	50	9	n	n	ADV
iajs-154	50	10	is	be	AUX
iajs-154	50	11	a	a	DET
iajs-154	50	12	maximal	maximal	ADJ
iajs-154	50	13	submodule	submodule	NOUN
iajs-154	50	14	,	,	PUNCT
iajs-154	50	15	and	and	CCONJ
iajs-154	50	16	n	n	DET
iajs-154	50	17	e	e	NOUN
iajs-154	50	18	m	m	PROPN
iajs-154	50	19	with	with	ADP
iajs-154	50	20	mn	mn	PROPN
iajs-154	50	21	.	.	PROPN
iajs-154	50	22	proposition	proposition	NOUN
iajs-154	50	23	(	(	PUNCT
iajs-154	50	24	3.2	3.2	NUM
iajs-154	50	25	):	):	PUNCT
iajs-154	50	26	let	let	VERB
iajs-154	50	27	m	m	PRON
iajs-154	50	28	be	be	AUX
iajs-154	50	29	an	an	DET
iajs-154	50	30	r	r	NOUN
iajs-154	50	31	-	-	PUNCT
iajs-154	50	32	module	module	NOUN
iajs-154	50	33	,	,	PUNCT
iajs-154	50	34	let	let	VERB
iajs-154	50	35	k	k	PROPN
iajs-154	50	36			PROPN
iajs-154	50	37	n	n	PRON
iajs-154	50	38			NOUN
iajs-154	50	39	m	m	VERB
iajs-154	50	40	be	be	VERB
iajs-154	50	41	submodules	submodule	NOUN
iajs-154	50	42	of	of	ADP
iajs-154	50	43	m.	m.	NOUN
iajs-154	50	44	if	if	SCONJ
iajs-154	50	45	k	k	PROPN
iajs-154	50	46	e	e	PROPN
iajs-154	50	47			VERB
iajs-154	50	48	m	m	VERB
iajs-154	50	49	and	and	CCONJ
iajs-154	50	50	n	n	CCONJ
iajs-154	50	51			NUM
iajs-154	50	52	m	m	PUNCT
iajs-154	50	53	,	,	PUNCT
iajs-154	50	54	then	then	ADV
iajs-154	50	55	k	k	PROPN
iajs-154	50	56	e	e	PROPN
iajs-154	50	57			PROPN
iajs-154	50	58	n.	n.	PROPN
iajs-154	50	59	proof	proof	NOUN
iajs-154	50	60	:	:	PUNCT
iajs-154	50	61	since	since	SCONJ
iajs-154	50	62	n	n	PROPN
iajs-154	50	63			NUM
iajs-154	50	64	m	m	PUNCT
iajs-154	50	65	,	,	PUNCT
iajs-154	50	66	then	then	ADV
iajs-154	50	67	m	m	VERB
iajs-154	50	68	=	=	SYM
iajs-154	50	69	n	n	X
iajs-154	50	70			ADJ
iajs-154	50	71	w	w	NOUN
iajs-154	50	72	for	for	ADP
iajs-154	50	73	some	some	DET
iajs-154	50	74	w	w	NOUN
iajs-154	50	75			PROPN
iajs-154	50	76	m.	m.	NOUN
iajs-154	50	77	to	to	PART
iajs-154	50	78	prove	prove	VERB
iajs-154	50	79	k	k	PROPN
iajs-154	50	80	e	e	PROPN
iajs-154	50	81			PROPN
iajs-154	50	82	n.	n.	PROPN
iajs-154	50	83	assume	assume	VERB
iajs-154	51	1	n	n	PROPN
iajs-154	51	2	=	=	PROPN
iajs-154	51	3	k	k	PROPN
iajs-154	51	4	+	+	CCONJ
iajs-154	51	5	u	u	NOUN
iajs-154	51	6	for	for	ADP
iajs-154	51	7	some	some	DET
iajs-154	51	8	u	u	NOUN
iajs-154	51	9	e	e	NOUN
iajs-154	51	10			NOUN
iajs-154	51	11	n.	n.	NOUN
iajs-154	51	12	then	then	ADV
iajs-154	51	13	m	m	VERB
iajs-154	51	14	=	=	PUNCT
iajs-154	51	15	(	(	PUNCT
iajs-154	51	16	k	k	X
iajs-154	51	17	+	+	NUM
iajs-154	51	18	u	u	NOUN
iajs-154	51	19	)	)	PUNCT
iajs-154	51	20			PROPN
iajs-154	51	21	w	w	PROPN
iajs-154	51	22	=	=	PUNCT
iajs-154	51	23	k	k	PROPN
iajs-154	52	1	+	+	CCONJ
iajs-154	52	2	(	(	PUNCT
iajs-154	52	3	u	u	PROPN
iajs-154	52	4			PROPN
iajs-154	52	5	w	w	PROPN
iajs-154	52	6	)	)	PUNCT
iajs-154	52	7	.	.	PUNCT
iajs-154	53	1	we	we	PRON
iajs-154	53	2	claim	claim	VERB
iajs-154	53	3	that	that	SCONJ
iajs-154	53	4	(	(	PUNCT
iajs-154	53	5	u	u	NOUN
iajs-154	53	6			PROPN
iajs-154	53	7	w	w	PROPN
iajs-154	53	8	)	)	PUNCT
iajs-154	53	9	e	e	NOUN
iajs-154	53	10			NUM
iajs-154	53	11	m.	m.	NOUN
iajs-154	53	12	to	to	PART
iajs-154	53	13	see	see	VERB
iajs-154	53	14	this	this	PRON
iajs-154	53	15	:	:	PUNCT
iajs-154	53	16	let	let	VERB
iajs-154	53	17	m	m	PRON
iajs-154	53	18			ADJ
iajs-154	53	19	m	m	ADJ
iajs-154	53	20	and	and	CCONJ
iajs-154	53	21	m	m	PROPN
iajs-154	53	22			NOUN
iajs-154	53	23	0	0	NUM
iajs-154	53	24	.	.	PUNCT
iajs-154	54	1	as	as	ADP
iajs-154	54	2	m	m	PROPN
iajs-154	54	3	=	=	SYM
iajs-154	54	4	n	n	PROPN
iajs-154	54	5			PROPN
iajs-154	54	6	w	w	PROPN
iajs-154	54	7	,	,	PUNCT
iajs-154	54	8	m	m	VERB
iajs-154	54	9	=	=	SYM
iajs-154	54	10	n	n	PROPN
iajs-154	54	11	+	+	CCONJ
iajs-154	54	12	w	w	NOUN
iajs-154	54	13	for	for	ADP
iajs-154	54	14	some	some	DET
iajs-154	54	15	n	n	ADJ
iajs-154	54	16			NOUN
iajs-154	54	17	n	n	CCONJ
iajs-154	54	18	,	,	PUNCT
iajs-154	54	19	w	w	ADP
iajs-154	54	20			PROPN
iajs-154	54	21	w.	w.	PROPN
iajs-154	54	22	if	if	SCONJ
iajs-154	54	23	n	n	PROPN
iajs-154	54	24			NOUN
iajs-154	54	25	0	0	NUM
iajs-154	54	26	,	,	PUNCT
iajs-154	54	27	then	then	ADV
iajs-154	54	28	there	there	PRON
iajs-154	54	29	exists	exist	VERB
iajs-154	54	30	r	r	NOUN
iajs-154	54	31			NOUN
iajs-154	54	32	r\{0	r\{0	PROPN
iajs-154	54	33	}	}	PUNCT
iajs-154	54	34	such	such	ADJ
iajs-154	54	35	that	that	SCONJ
iajs-154	54	36	0	0	NUM
iajs-154	54	37			PROPN
iajs-154	54	38	rn	rn	PROPN
iajs-154	54	39			PROPN
iajs-154	54	40	u	u	PROPN
iajs-154	54	41	,	,	PUNCT
iajs-154	54	42	hence	hence	ADV
iajs-154	54	43	rm	rm	NOUN
iajs-154	54	44	=	=	SYM
iajs-154	54	45	rn	rn	PROPN
iajs-154	54	46	+	+	PROPN
iajs-154	54	47	rw	rw	PROPN
iajs-154	54	48			NOUN
iajs-154	54	49	0	0	PUNCT
iajs-154	55	1	(	(	PUNCT
iajs-154	55	2	because	because	SCONJ
iajs-154	55	3	if	if	SCONJ
iajs-154	55	4	rm	rm	PROPN
iajs-154	55	5	=	=	SYM
iajs-154	55	6	0	0	PROPN
iajs-154	55	7	,	,	PUNCT
iajs-154	55	8	then	then	ADV
iajs-154	55	9	rn	rn	PROPN
iajs-154	55	10	=	=	SYM
iajs-154	55	11	–	–	PUNCT
iajs-154	55	12	rw	rw	NOUN
iajs-154	55	13			PROPN
iajs-154	55	14	n	n	CCONJ
iajs-154	55	15			PUNCT
iajs-154	55	16	w	w	NOUN
iajs-154	55	17	=	=	SYM
iajs-154	55	18	(	(	PUNCT
iajs-154	55	19	0	0	NUM
iajs-154	55	20	)	)	PUNCT
iajs-154	55	21	and	and	CCONJ
iajs-154	55	22	hence	hence	ADV
iajs-154	55	23	rn	rn	PROPN
iajs-154	55	24	=	=	PROPN
iajs-154	55	25	0	0	NUM
iajs-154	55	26	which	which	PRON
iajs-154	55	27	is	be	AUX
iajs-154	55	28	a	a	DET
iajs-154	55	29	contradiction	contradiction	NOUN
iajs-154	55	30	)	)	PUNCT
iajs-154	55	31	.	.	PUNCT
iajs-154	56	1	thus	thus	ADV
iajs-154	56	2	0	0	NUM
iajs-154	56	3			PROPN
iajs-154	56	4	rm	rm	PROPN
iajs-154	56	5			PROPN
iajs-154	56	6	(	(	PUNCT
iajs-154	56	7	u	u	PROPN
iajs-154	56	8			PROPN
iajs-154	56	9	w	w	PROPN
iajs-154	56	10	)	)	PUNCT
iajs-154	56	11	.	.	PUNCT
iajs-154	57	1	now	now	ADV
iajs-154	57	2	if	if	SCONJ
iajs-154	57	3	n	n	PROPN
iajs-154	57	4	=	=	SYM
iajs-154	57	5	0	0	NUM
iajs-154	57	6	,	,	PUNCT
iajs-154	57	7	then	then	ADV
iajs-154	57	8	m	m	VERB
iajs-154	57	9	=	=	SYM
iajs-154	57	10	w	w	PROPN
iajs-154	58	1	and	and	CCONJ
iajs-154	58	2	so	so	ADV
iajs-154	58	3	0	0	NUM
iajs-154	58	4			NOUN
iajs-154	58	5	1m	1m	NUM
iajs-154	58	6	=	=	SYM
iajs-154	58	7	1w	1w	NUM
iajs-154	58	8			NOUN
iajs-154	58	9	w	w	ADP
iajs-154	58	10			PROPN
iajs-154	58	11	(	(	PUNCT
iajs-154	58	12	u	u	NOUN
iajs-154	58	13			PROPN
iajs-154	58	14	w	w	PROPN
iajs-154	58	15	)	)	PUNCT
iajs-154	58	16	.	.	PUNCT
iajs-154	59	1	therefore	therefore	ADV
iajs-154	59	2	(	(	PUNCT
iajs-154	59	3	u	u	NOUN
iajs-154	59	4			PROPN
iajs-154	59	5	w	w	PROPN
iajs-154	59	6	)	)	PUNCT
iajs-154	59	7	e	e	NOUN
iajs-154	59	8			NUM
iajs-154	59	9	m.	m.	NOUN
iajs-154	59	10	since	since	SCONJ
iajs-154	59	11	k	k	PROPN
iajs-154	59	12	e	e	PROPN
iajs-154	59	13			PROPN
iajs-154	59	14	m	m	VERB
iajs-154	59	15	,	,	PUNCT
iajs-154	59	16	we	we	PRON
iajs-154	59	17	get	get	VERB
iajs-154	59	18	u	u	PRON
iajs-154	59	19			ADJ
iajs-154	59	20	w	w	PROPN
iajs-154	59	21	=	=	PROPN
iajs-154	59	22	m.	m.	NOUN
iajs-154	59	23	now	now	ADV
iajs-154	59	24	,	,	PUNCT
iajs-154	59	25	assume	assume	VERB
iajs-154	59	26	x	x	PUNCT
iajs-154	59	27			NOUN
iajs-154	59	28	n	n	CCONJ
iajs-154	59	29			NOUN
iajs-154	59	30	m	m	NOUN
iajs-154	59	31	,	,	PUNCT
iajs-154	59	32	so	so	SCONJ
iajs-154	59	33	that	that	SCONJ
iajs-154	59	34	x	x	NOUN
iajs-154	59	35	=	=	SYM
iajs-154	59	36	u1	u1	NOUN
iajs-154	59	37	+	+	CCONJ
iajs-154	59	38	w1	w1	NOUN
iajs-154	59	39	for	for	ADP
iajs-154	59	40	some	some	DET
iajs-154	59	41	u1	u1	NOUN
iajs-154	59	42			PROPN
iajs-154	59	43	u	u	PROPN
iajs-154	59	44	,	,	PUNCT
iajs-154	59	45	w1	w1	PROPN
iajs-154	59	46			PROPN
iajs-154	59	47	w.	w.	PROPN
iajs-154	60	1	it	it	PRON
iajs-154	60	2	follows	follow	VERB
iajs-154	60	3	that	that	SCONJ
iajs-154	60	4	x	x	X
iajs-154	60	5	–	–	PUNCT
iajs-154	60	6	u1	u1	NOUN
iajs-154	60	7	=	=	SYM
iajs-154	60	8	w	w	NOUN
iajs-154	60	9			NOUN
iajs-154	60	10	(	(	PUNCT
iajs-154	60	11	n	n	CCONJ
iajs-154	60	12			X
iajs-154	60	13	w	w	NOUN
iajs-154	60	14	)	)	PUNCT
iajs-154	60	15	=	=	SYM
iajs-154	60	16	(	(	PUNCT
iajs-154	60	17	0	0	NUM
iajs-154	60	18	)	)	PUNCT
iajs-154	60	19	,	,	PUNCT
iajs-154	60	20	hence	hence	ADV
iajs-154	60	21	x	x	PUNCT
iajs-154	60	22	=	=	SYM
iajs-154	60	23	u1	u1	PROPN
iajs-154	60	24			NOUN
iajs-154	60	25	u.	u.	VERB
iajs-154	60	26	thus	thus	ADV
iajs-154	60	27	n	n	PROPN
iajs-154	60	28	=	=	SYM
iajs-154	60	29	u	u	PROPN
iajs-154	60	30	and	and	CCONJ
iajs-154	60	31	k	k	PROPN
iajs-154	60	32	e	e	PROPN
iajs-154	61	1			PROPN
iajs-154	61	2	n.	n.	PROPN
iajs-154	61	3	217	217	NUM
iajs-154	62	1	|	|	NOUN
iajs-154	62	2	mathematics	mathematic	NOUN
iajs-154	62	3	2015	2015	NUM
iajs-154	62	4	)	)	PUNCT
iajs-154	62	5	عام	عام	ADP
iajs-154	62	6	3العدد	3العدد	NUM
iajs-154	62	7	(	(	PUNCT
iajs-154	62	8	28مجلة	28مجلة	X
iajs-154	62	9	إبن	إبن	VERB
iajs-154	62	10	الهيثم	الهيثم	ADJ
iajs-154	62	11	للعلوم	للعلوم	NOUN
iajs-154	62	12	الصرفة	الصرفة	NOUN
iajs-154	63	1	و	و	PRON
iajs-154	63	2	التطبيقية	التطبيقية	ADV
iajs-154	63	3	المجلد	المجلد	VERB
iajs-154	63	4	ibn	ibn	PROPN
iajs-154	63	5	al	al	PROPN
iajs-154	63	6	-	-	PUNCT
iajs-154	63	7	haitham	haitham	PROPN
iajs-154	63	8	jour	jour	X
iajs-154	63	9	.	.	PROPN
iajs-154	64	1	for	for	ADP
iajs-154	64	2	pure	pure	ADJ
iajs-154	64	3	&	&	CCONJ
iajs-154	64	4	appl	appl	PROPN
iajs-154	64	5	.	.	PUNCT
iajs-154	65	1	sci	sci	PROPN
iajs-154	65	2	.	.	PUNCT
iajs-154	65	3	vol	vol	NOUN
iajs-154	65	4	.	.	PROPN
iajs-154	66	1	28	28	NUM
iajs-154	66	2	(	(	PUNCT
iajs-154	66	3	3	3	NUM
iajs-154	66	4	)	)	PUNCT
iajs-154	66	5	2015	2015	NUM
iajs-154	66	6	recall	recall	VERB
iajs-154	66	7	that	that	SCONJ
iajs-154	66	8	a	a	DET
iajs-154	66	9	submodule	submodule	NOUN
iajs-154	66	10	n	n	PROPN
iajs-154	66	11	of	of	ADP
iajs-154	66	12	an	an	DET
iajs-154	66	13	r	r	NOUN
iajs-154	66	14	-	-	PUNCT
iajs-154	66	15	module	module	NOUN
iajs-154	66	16	m	m	NOUN
iajs-154	66	17	is	be	AUX
iajs-154	66	18	called	call	VERB
iajs-154	66	19	coclosed	coclose	VERB
iajs-154	66	20	whenever	whenever	SCONJ
iajs-154	66	21	k	k	PROPN
iajs-154	66	22			PROPN
iajs-154	66	23	n	n	CCONJ
iajs-154	66	24	,	,	PUNCT
iajs-154	66	25	n	n	PRON
iajs-154	66	26	m	m	VERB
iajs-154	66	27	k	k	NOUN
iajs-154	66	28	k	k	PROPN
iajs-154	66	29			PROPN
iajs-154	66	30	implies	imply	VERB
iajs-154	66	31	n	n	NOUN
iajs-154	66	32	=	=	SYM
iajs-154	66	33	k	k	PROPN
iajs-154	67	1	[	[	X
iajs-154	67	2	5	5	NUM
iajs-154	67	3	]	]	PUNCT
iajs-154	67	4	,	,	PUNCT
iajs-154	67	5	[	[	X
iajs-154	67	6	6	6	NUM
iajs-154	67	7	]	]	PUNCT
iajs-154	67	8	.	.	PUNCT
iajs-154	68	1	hasan	hasan	PROPN
iajs-154	68	2	in	in	ADP
iajs-154	68	3	[	[	X
iajs-154	68	4	7	7	NUM
iajs-154	68	5	]	]	PUNCT
iajs-154	68	6	,	,	PUNCT
iajs-154	68	7	gave	give	VERB
iajs-154	68	8	the	the	DET
iajs-154	68	9	following	follow	VERB
iajs-154	68	10	definition	definition	NOUN
iajs-154	68	11	:	:	PUNCT
iajs-154	68	12	definition	definition	NOUN
iajs-154	68	13	(	(	PUNCT
iajs-154	68	14	3.3	3.3	NUM
iajs-154	68	15	):	):	PUNCT
iajs-154	68	16	let	let	VERB
iajs-154	68	17	n	n	PRON
iajs-154	68	18	be	be	AUX
iajs-154	68	19	a	a	DET
iajs-154	68	20	submodule	submodule	NOUN
iajs-154	68	21	of	of	ADP
iajs-154	68	22	an	an	DET
iajs-154	68	23	r	r	NOUN
iajs-154	68	24	-	-	PUNCT
iajs-154	68	25	module	module	NOUN
iajs-154	68	26	m.	m.	NOUN
iajs-154	68	27	n	n	CCONJ
iajs-154	68	28	is	be	AUX
iajs-154	68	29	called	call	VERB
iajs-154	68	30	e	e	ADJ
iajs-154	68	31	-	-	VERB
iajs-154	68	32	coclosed	coclosed	ADJ
iajs-154	68	33	if	if	SCONJ
iajs-154	68	34	whenever	whenever	SCONJ
iajs-154	68	35	k	k	PROPN
iajs-154	68	36			NOUN
iajs-154	68	37	n	n	CCONJ
iajs-154	68	38	,	,	PUNCT
iajs-154	68	39	e	e	X
iajs-154	68	40	n	n	X
iajs-154	68	41	m	m	VERB
iajs-154	68	42	k	k	NOUN
iajs-154	69	1	k	k	PROPN
iajs-154	70	1			PROPN
iajs-154	70	2	,	,	PUNCT
iajs-154	70	3	then	then	ADV
iajs-154	70	4	n	n	PROPN
iajs-154	70	5	=	=	SYM
iajs-154	70	6	k.	k.	PROPN
iajs-154	70	7	remarks	remark	VERB
iajs-154	70	8	(	(	PUNCT
iajs-154	70	9	3.4	3.4	NUM
iajs-154	70	10	):	):	PUNCT
iajs-154	70	11	(	(	PUNCT
iajs-154	70	12	1	1	X
iajs-154	70	13	)	)	PUNCT
iajs-154	70	14	it	it	PRON
iajs-154	70	15	is	be	AUX
iajs-154	70	16	known	know	VERB
iajs-154	70	17	that	that	SCONJ
iajs-154	70	18	every	every	DET
iajs-154	70	19	direct	direct	ADJ
iajs-154	70	20	summand	summand	NOUN
iajs-154	70	21	is	be	AUX
iajs-154	70	22	coclosed	coclose	VERB
iajs-154	70	23	.	.	PUNCT
iajs-154	71	1	however	however	ADV
iajs-154	71	2	a	a	DET
iajs-154	71	3	direct	direct	ADJ
iajs-154	71	4	summand	summand	NOUN
iajs-154	71	5	may	may	AUX
iajs-154	71	6	not	not	PART
iajs-154	71	7	be	be	AUX
iajs-154	71	8	e	e	VERB
iajs-154	71	9	-	-	VERB
iajs-154	71	10	coclosed	coclose	VERB
iajs-154	71	11	for	for	ADP
iajs-154	71	12	example	example	NOUN
iajs-154	71	13	:	:	PUNCT
iajs-154	71	14	let	let	VERB
iajs-154	71	15	m	m	PRON
iajs-154	71	16	be	be	AUX
iajs-154	71	17	the	the	DET
iajs-154	71	18	z	z	NOUN
iajs-154	71	19	-	-	PUNCT
iajs-154	71	20	module	module	NOUN
iajs-154	71	21	z6	z6	NOUN
iajs-154	71	22	,	,	PUNCT
iajs-154	71	23	let	let	VERB
iajs-154	71	24	n	n	PRON
iajs-154	71	25	=	=	SYM
iajs-154	71	26	2	2	NUM
iajs-154	71	27	m	m	NOUN
iajs-154	71	28			VERB
iajs-154	71	29	.	.	PUNCT
iajs-154	72	1	e	e	X
iajs-154	72	2	n	n	X
iajs-154	72	3	m	m	VERB
iajs-154	72	4	0	0	NUM
iajs-154	73	1	(	(	PUNCT
iajs-154	73	2	0)	0)	PROPN
iajs-154	73	3			VERB
iajs-154	73	4			PROPN
iajs-154	73	5	,	,	PUNCT
iajs-154	73	6	but	but	CCONJ
iajs-154	73	7	n	n	PRON
iajs-154	73	8			NOUN
iajs-154	73	9	0	0	PUNCT
iajs-154	74	1			INTJ
iajs-154	74	2	.	.	PUNCT
iajs-154	75	1	(	(	PUNCT
iajs-154	75	2	2	2	X
iajs-154	75	3	)	)	PUNCT
iajs-154	75	4	it	it	PRON
iajs-154	75	5	is	be	AUX
iajs-154	75	6	clear	clear	ADJ
iajs-154	75	7	that	that	SCONJ
iajs-154	75	8	every	every	DET
iajs-154	75	9	e	e	ADJ
iajs-154	75	10	-	-	ADJ
iajs-154	75	11	coclosed	coclosed	ADJ
iajs-154	75	12	submodule	submodule	NOUN
iajs-154	75	13	is	be	AUX
iajs-154	75	14	coclosed	coclose	VERB
iajs-154	75	15	,	,	PUNCT
iajs-154	75	16	but	but	CCONJ
iajs-154	75	17	the	the	DET
iajs-154	75	18	converse	converse	NOUN
iajs-154	75	19	is	be	AUX
iajs-154	75	20	true	true	ADJ
iajs-154	75	21	by	by	ADP
iajs-154	75	22	the	the	DET
iajs-154	75	23	same	same	ADJ
iajs-154	75	24	example	example	NOUN
iajs-154	75	25	in	in	ADP
iajs-154	75	26	(	(	PUNCT
iajs-154	75	27	1	1	NUM
iajs-154	75	28	)	)	PUNCT
iajs-154	75	29	,	,	PUNCT
iajs-154	75	30	n	n	PRON
iajs-154	75	31	is	be	AUX
iajs-154	75	32	coclosed	coclose	VERB
iajs-154	75	33	and	and	CCONJ
iajs-154	75	34	it	it	PRON
iajs-154	75	35	is	be	AUX
iajs-154	75	36	not	not	PART
iajs-154	75	37	e	e	VERB
iajs-154	75	38	-	-	VERB
iajs-154	75	39	coclosed	coclosed	ADJ
iajs-154	75	40	.	.	PUNCT
iajs-154	76	1	proposition	proposition	NOUN
iajs-154	76	2	(	(	PUNCT
iajs-154	76	3	3.5	3.5	NUM
iajs-154	76	4	):	):	PUNCT
iajs-154	76	5	[	[	X
iajs-154	76	6	7,lemma	7,lemma	X
iajs-154	76	7	4.2.8	4.2.8	NUM
iajs-154	76	8	]	]	X
iajs-154	76	9	let	let	VERB
iajs-154	76	10	a	a	PRON
iajs-154	76	11	be	be	AUX
iajs-154	76	12	a	a	DET
iajs-154	76	13	submodule	submodule	NOUN
iajs-154	76	14	of	of	ADP
iajs-154	76	15	an	an	DET
iajs-154	76	16	r	r	NOUN
iajs-154	76	17	-	-	PUNCT
iajs-154	76	18	module	module	NOUN
iajs-154	76	19	m.	m.	NOUN
iajs-154	76	20	if	if	SCONJ
iajs-154	76	21	a	a	PRON
iajs-154	76	22	is	be	AUX
iajs-154	76	23	e	e	NOUN
iajs-154	76	24	-	-	VERB
iajs-154	76	25	coclosed	coclosed	ADJ
iajs-154	76	26	,	,	PUNCT
iajs-154	76	27	then	then	ADV
iajs-154	76	28	for	for	ADP
iajs-154	76	29	each	each	DET
iajs-154	76	30	x	x	ADP
iajs-154	76	31			NOUN
iajs-154	76	32	a	a	PRON
iajs-154	76	33	,	,	PUNCT
iajs-154	76	34	x	x	SYM
iajs-154	76	35	e	e	X
iajs-154	76	36			NOUN
iajs-154	76	37	m	m	VERB
iajs-154	76	38	implies	imply	VERB
iajs-154	76	39	x	x	X
iajs-154	76	40	e	e	X
iajs-154	76	41			NOUN
iajs-154	76	42	a.	a.	NOUN
iajs-154	76	43	proof	proof	NOUN
iajs-154	76	44	:	:	PUNCT
iajs-154	76	45	to	to	PART
iajs-154	76	46	prove	prove	VERB
iajs-154	76	47	x	x	X
iajs-154	76	48	e	e	X
iajs-154	76	49			PROPN
iajs-154	76	50	a.	a.	NOUN
iajs-154	76	51	assume	assume	VERB
iajs-154	77	1	a	a	PRON
iajs-154	77	2	=	=	PUNCT
iajs-154	77	3	x	x	SYM
iajs-154	78	1	+	+	NUM
iajs-154	78	2	y	y	PROPN
iajs-154	78	3	for	for	ADP
iajs-154	78	4	some	some	DET
iajs-154	78	5	y	y	PROPN
iajs-154	78	6	e	e	NOUN
iajs-154	78	7			NUM
iajs-154	78	8	a.	a.	NOUN
iajs-154	78	9	we	we	PRON
iajs-154	78	10	claim	claim	VERB
iajs-154	78	11	that	that	SCONJ
iajs-154	78	12	e	e	PROPN
iajs-154	78	13	a	a	DET
iajs-154	78	14	m	m	NOUN
iajs-154	78	15	y	y	NOUN
iajs-154	78	16	y	y	PROPN
iajs-154	78	17			PROPN
iajs-154	78	18	.	.	PUNCT
iajs-154	79	1	to	to	PART
iajs-154	79	2	see	see	VERB
iajs-154	79	3	this	this	PRON
iajs-154	79	4	,	,	PUNCT
iajs-154	79	5	let	let	VERB
iajs-154	79	6	m	m	PRON
iajs-154	79	7	a	a	DET
iajs-154	79	8	c	c	NOUN
iajs-154	79	9	y	y	PROPN
iajs-154	79	10	y	y	PROPN
iajs-154	79	11	y	y	PROPN
iajs-154	79	12			PROPN
iajs-154	79	13			ADJ
iajs-154	79	14	for	for	ADP
iajs-154	79	15	some	some	DET
iajs-154	79	16	e	e	NOUN
iajs-154	79	17	c	c	NOUN
iajs-154	79	18	m	m	VERB
iajs-154	79	19	y	y	PROPN
iajs-154	79	20	y	y	PROPN
iajs-154	79	21			PROPN
iajs-154	79	22	.	.	PUNCT
iajs-154	80	1	then	then	ADV
iajs-154	80	2	m	m	VERB
iajs-154	80	3	=	=	SYM
iajs-154	80	4	a	a	PRON
iajs-154	80	5	+	+	X
iajs-154	80	6	c	c	X
iajs-154	80	7	,	,	PUNCT
iajs-154	80	8	so	so	ADV
iajs-154	80	9	m	m	VERB
iajs-154	80	10	=	=	NOUN
iajs-154	80	11	x	x	SYM
iajs-154	80	12	+	+	CCONJ
iajs-154	80	13	y+	y+	NUM
iajs-154	80	14	c	c	PROPN
iajs-154	80	15	implies	imply	VERB
iajs-154	80	16	m	m	NOUN
iajs-154	80	17	=	=	ADJ
iajs-154	80	18	x	x	X
iajs-154	80	19	+	+	CCONJ
iajs-154	80	20	c.	c.	NOUN
iajs-154	80	21	since	since	SCONJ
iajs-154	80	22	e	e	PROPN
iajs-154	80	23	c	c	PROPN
iajs-154	80	24	m	m	VERB
iajs-154	80	25	y	y	PROPN
iajs-154	80	26	y	y	PROPN
iajs-154	80	27			PROPN
iajs-154	80	28	,	,	PUNCT
iajs-154	80	29	we	we	PRON
iajs-154	80	30	have	have	VERB
iajs-154	80	31	e	e	PROPN
iajs-154	80	32	c	c	NOUN
iajs-154	80	33	m	m	X
iajs-154	80	34	.	.	PUNCT
iajs-154	81	1	hence	hence	ADV
iajs-154	81	2	c	c	X
iajs-154	82	1	=	=	PUNCT
iajs-154	82	2	m	m	VERB
iajs-154	82	3	since	since	SCONJ
iajs-154	82	4	x	x	X
iajs-154	82	5	e	e	PROPN
iajs-154	82	6			PROPN
iajs-154	82	7	m.	m.	NOUN
iajs-154	82	8	this	this	PRON
iajs-154	82	9	implies	imply	VERB
iajs-154	82	10	m	m	PROPN
iajs-154	82	11	c	c	NOUN
iajs-154	82	12	y	y	PROPN
iajs-154	82	13	y	y	PROPN
iajs-154	82	14			PROPN
iajs-154	82	15	and	and	CCONJ
iajs-154	82	16	e	e	X
iajs-154	82	17	a	a	DET
iajs-154	82	18	m	m	VERB
iajs-154	82	19	y	y	NOUN
iajs-154	82	20	y	y	PROPN
iajs-154	83	1			PROPN
iajs-154	83	2	.	.	PUNCT
iajs-154	84	1	but	but	CCONJ
iajs-154	84	2	a	a	PRON
iajs-154	84	3	is	be	AUX
iajs-154	84	4	e	e	VERB
iajs-154	84	5	-	-	VERB
iajs-154	84	6	coclosed	coclosed	ADJ
iajs-154	84	7	in	in	ADP
iajs-154	84	8	m	m	PROPN
iajs-154	84	9	,	,	PUNCT
iajs-154	84	10	so	so	SCONJ
iajs-154	84	11	that	that	SCONJ
iajs-154	84	12	y	y	NOUN
iajs-154	84	13	=	=	PUNCT
iajs-154	84	14	a.	a.	NOUN
iajs-154	84	15	thus	thus	ADV
iajs-154	84	16	x	x	X
iajs-154	84	17	e	e	X
iajs-154	84	18			NUM
iajs-154	84	19	a.	a.	NOUN
iajs-154	84	20	proposition	proposition	NOUN
iajs-154	84	21	(	(	PUNCT
iajs-154	84	22	3.6	3.6	NUM
iajs-154	84	23	):	):	PUNCT
iajs-154	84	24	let	let	VERB
iajs-154	84	25	m	m	PRON
iajs-154	84	26	be	be	AUX
iajs-154	84	27	a	a	DET
iajs-154	84	28	non	non	ADJ
iajs-154	84	29	singular	singular	ADJ
iajs-154	84	30	r	r	NOUN
iajs-154	84	31	-	-	NOUN
iajs-154	84	32	module	module	NOUN
iajs-154	84	33	.	.	PUNCT
iajs-154	85	1	a	a	DET
iajs-154	85	2	proper	proper	ADJ
iajs-154	85	3	submodule	submodule	NOUN
iajs-154	85	4	n	n	PROPN
iajs-154	85	5	of	of	ADP
iajs-154	85	6	m	m	PROPN
iajs-154	85	7	is	be	AUX
iajs-154	85	8	e	e	ADJ
iajs-154	85	9	-	-	NOUN
iajs-154	85	10	small	small	ADJ
iajs-154	85	11	if	if	SCONJ
iajs-154	86	1	and	and	CCONJ
iajs-154	86	2	only	only	ADV
iajs-154	86	3	if	if	SCONJ
iajs-154	86	4	it	it	PRON
iajs-154	86	5	is	be	AUX
iajs-154	86	6	-small	-small	PROPN
iajs-154	86	7	.	.	PUNCT
iajs-154	87	1	proof	proof	NOUN
iajs-154	87	2	:	:	PUNCT
iajs-154	87	3	(	(	PUNCT
iajs-154	87	4			NOUN
iajs-154	87	5	)	)	PUNCT
iajs-154	87	6	it	it	PRON
iajs-154	87	7	is	be	AUX
iajs-154	87	8	clear	clear	ADJ
iajs-154	87	9	by	by	ADP
iajs-154	87	10	remark	remark	NOUN
iajs-154	87	11	(	(	PUNCT
iajs-154	87	12	2.2	2.2	NUM
iajs-154	87	13	)	)	PUNCT
iajs-154	87	14	.	.	PUNCT
iajs-154	88	1	(	(	PUNCT
iajs-154	88	2			NOUN
iajs-154	88	3	)	)	PUNCT
iajs-154	88	4	let	let	VERB
iajs-154	88	5	n	n	PRON
iajs-154	88	6	<	<	X
iajs-154	88	7	m.	m.	NOUN
iajs-154	88	8	assume	assume	VERB
iajs-154	88	9	n	n	PROPN
iajs-154	89	1	+	+	CCONJ
iajs-154	89	2	k	k	X
iajs-154	89	3	=	=	NOUN
iajs-154	89	4	m	m	VERB
iajs-154	89	5	with	with	ADP
iajs-154	89	6	m	m	PROPN
iajs-154	89	7	k	k	NOUN
iajs-154	89	8	is	be	AUX
iajs-154	89	9	singular	singular	ADJ
iajs-154	89	10	.	.	PUNCT
iajs-154	90	1	since	since	SCONJ
iajs-154	90	2	m	m	PROPN
iajs-154	90	3	is	be	AUX
iajs-154	90	4	nonsingular	nonsingular	ADJ
iajs-154	90	5	,	,	PUNCT
iajs-154	90	6	then	then	ADV
iajs-154	90	7	by	by	ADP
iajs-154	90	8	[	[	X
iajs-154	90	9	8	8	NUM
iajs-154	90	10	,	,	PUNCT
iajs-154	90	11	proposition	proposition	NOUN
iajs-154	90	12	1.21,p.32	1.21,p.32	NUM
iajs-154	90	13	]	]	PUNCT
iajs-154	90	14	,	,	PUNCT
iajs-154	90	15	k	k	PROPN
iajs-154	90	16	e	e	PROPN
iajs-154	90	17			NUM
iajs-154	90	18	m.	m.	NOUN
iajs-154	90	19	but	but	CCONJ
iajs-154	90	20	n	n	CCONJ
iajs-154	90	21	e	e	PROPN
iajs-154	90	22			PROPN
iajs-154	90	23	m	m	PROPN
iajs-154	90	24	,	,	PUNCT
iajs-154	90	25	so	so	ADV
iajs-154	90	26	k	k	PROPN
iajs-154	90	27	=	=	PUNCT
iajs-154	90	28	m.	m.	NOUN
iajs-154	90	29	thus	thus	ADV
iajs-154	91	1	n	n	NUM
iajs-154	91	2	δ	δ	PROPN
iajs-154	91	3			PROPN
iajs-154	91	4	m.	m.	NOUN
iajs-154	91	5	proposition	proposition	NOUN
iajs-154	91	6	(	(	PUNCT
iajs-154	91	7	3.7	3.7	NUM
iajs-154	91	8	):	):	PUNCT
iajs-154	91	9	let	let	VERB
iajs-154	91	10	m	m	PRON
iajs-154	91	11	be	be	AUX
iajs-154	91	12	an	an	DET
iajs-154	91	13	indecomposable	indecomposable	ADJ
iajs-154	91	14	r	r	NOUN
iajs-154	91	15	-	-	PUNCT
iajs-154	91	16	module	module	NOUN
iajs-154	91	17	.	.	PUNCT
iajs-154	92	1	a	a	DET
iajs-154	92	2	proper	proper	ADJ
iajs-154	92	3	submodule	submodule	NOUN
iajs-154	92	4	n	n	PROPN
iajs-154	92	5	of	of	ADP
iajs-154	92	6	m	m	PROPN
iajs-154	92	7	is	be	AUX
iajs-154	92	8	small	small	ADJ
iajs-154	92	9	if	if	SCONJ
iajs-154	93	1	and	and	CCONJ
iajs-154	93	2	only	only	ADV
iajs-154	93	3	if	if	SCONJ
iajs-154	93	4	it	it	PRON
iajs-154	93	5	is	be	AUX
iajs-154	93	6	e	e	ADJ
iajs-154	93	7	-	-	ADJ
iajs-154	93	8	small	small	ADJ
iajs-154	93	9	.	.	PUNCT
iajs-154	94	1	proof	proof	NOUN
iajs-154	94	2	:	:	PUNCT
iajs-154	94	3	(	(	PUNCT
iajs-154	94	4			NOUN
iajs-154	94	5	)	)	PUNCT
iajs-154	94	6	it	it	PRON
iajs-154	94	7	is	be	AUX
iajs-154	94	8	clear	clear	ADJ
iajs-154	94	9	by	by	ADP
iajs-154	94	10	remark	remark	NOUN
iajs-154	94	11	(	(	PUNCT
iajs-154	94	12	2.2	2.2	NUM
iajs-154	94	13	)	)	PUNCT
iajs-154	94	14	.	.	PUNCT
iajs-154	95	1	218	218	NUM
iajs-154	95	2	|	|	ADV
iajs-154	95	3	mathematics	mathematic	NOUN
iajs-154	95	4	2015	2015	NUM
iajs-154	95	5	)	)	PUNCT
iajs-154	95	6	عام	عام	ADP
iajs-154	95	7	3العدد	3العدد	NUM
iajs-154	95	8	(	(	PUNCT
iajs-154	95	9	28مجلة	28مجلة	X
iajs-154	95	10	إبن	إبن	VERB
iajs-154	95	11	الهيثم	الهيثم	ADJ
iajs-154	95	12	للعلوم	للعلوم	NOUN
iajs-154	95	13	الصرفة	الصرفة	NOUN
iajs-154	96	1	و	و	PRON
iajs-154	96	2	التطبيقية	التطبيقية	ADV
iajs-154	96	3	المجلد	المجلد	VERB
iajs-154	96	4	ibn	ibn	PROPN
iajs-154	96	5	al	al	PROPN
iajs-154	96	6	-	-	PUNCT
iajs-154	96	7	haitham	haitham	PROPN
iajs-154	96	8	jour	jour	X
iajs-154	96	9	.	.	PROPN
iajs-154	97	1	for	for	ADP
iajs-154	97	2	pure	pure	ADJ
iajs-154	97	3	&	&	CCONJ
iajs-154	97	4	appl	appl	PROPN
iajs-154	97	5	.	.	PUNCT
iajs-154	98	1	sci	sci	PROPN
iajs-154	98	2	.	.	PUNCT
iajs-154	98	3	vol	vol	NOUN
iajs-154	98	4	.	.	PROPN
iajs-154	99	1	28	28	NUM
iajs-154	99	2	(	(	PUNCT
iajs-154	99	3	3	3	NUM
iajs-154	99	4	)	)	PUNCT
iajs-154	99	5	2015	2015	NUM
iajs-154	99	6	(	(	PUNCT
iajs-154	99	7			NOUN
iajs-154	99	8	)	)	PUNCT
iajs-154	99	9	let	let	VERB
iajs-154	99	10	n	n	PRON
iajs-154	99	11	<	<	X
iajs-154	99	12	m.	m.	NOUN
iajs-154	99	13	assume	assume	VERB
iajs-154	99	14	n	n	PROPN
iajs-154	100	1	+	+	CCONJ
iajs-154	100	2	k	k	X
iajs-154	100	3	=	=	NOUN
iajs-154	100	4	m	m	VERB
iajs-154	100	5	with	with	ADP
iajs-154	100	6	k	k	PROPN
iajs-154	100	7			PROPN
iajs-154	100	8	m.	m.	NOUN
iajs-154	100	9	since	since	SCONJ
iajs-154	100	10	n	n	NUM
iajs-154	100	11	e	e	NOUN
iajs-154	100	12			PROPN
iajs-154	100	13	m	m	PROPN
iajs-154	100	14	,	,	PUNCT
iajs-154	100	15	then	then	ADV
iajs-154	100	16	by	by	ADP
iajs-154	100	17	proposition	proposition	NOUN
iajs-154	100	18	(	(	PUNCT
iajs-154	100	19	2.3	2.3	NUM
iajs-154	100	20	)	)	PUNCT
iajs-154	100	21	,	,	PUNCT
iajs-154	100	22	k	k	PROPN
iajs-154	100	23			NUM
iajs-154	100	24	m	m	PUNCT
iajs-154	100	25	and	and	CCONJ
iajs-154	100	26	m	m	NOUN
iajs-154	100	27	x	x	VERB
iajs-154	100	28	is	be	AUX
iajs-154	100	29	semisimple	semisimple	ADJ
iajs-154	100	30	.	.	PUNCT
iajs-154	101	1	but	but	CCONJ
iajs-154	101	2	m	m	PROPN
iajs-154	101	3	is	be	AUX
iajs-154	101	4	indecomposable	indecomposable	ADJ
iajs-154	101	5	and	and	CCONJ
iajs-154	101	6	k	k	PROPN
iajs-154	101	7			PROPN
iajs-154	101	8	(	(	PUNCT
iajs-154	101	9	0	0	NUM
iajs-154	101	10	)	)	PUNCT
iajs-154	101	11	,	,	PUNCT
iajs-154	101	12	so	so	CCONJ
iajs-154	102	1	k	k	PROPN
iajs-154	102	2	=	=	PUNCT
iajs-154	102	3	m.	m.	NOUN
iajs-154	102	4	thus	thus	ADV
iajs-154	102	5	n	n	NUM
iajs-154	102	6			PROPN
iajs-154	102	7	m.	m.	NOUN
iajs-154	102	8	now	now	ADV
iajs-154	102	9	we	we	PRON
iajs-154	102	10	get	get	VERB
iajs-154	102	11	the	the	DET
iajs-154	102	12	following	follow	VERB
iajs-154	102	13	corollaries	corollary	NOUN
iajs-154	102	14	.	.	PUNCT
iajs-154	103	1	corollary	corollary	ADJ
iajs-154	103	2	(	(	PUNCT
iajs-154	103	3	3.8	3.8	NUM
iajs-154	103	4	):	):	PUNCT
iajs-154	103	5	let	let	VERB
iajs-154	103	6	m	m	PRON
iajs-154	103	7	be	be	AUX
iajs-154	103	8	a	a	DET
iajs-154	103	9	an	an	DET
iajs-154	103	10	indecomposable	indecomposable	ADJ
iajs-154	103	11	r	r	NOUN
iajs-154	103	12	-	-	PUNCT
iajs-154	103	13	module	module	NOUN
iajs-154	103	14	and	and	CCONJ
iajs-154	103	15	let	let	VERB
iajs-154	103	16	n	n	PRON
iajs-154	103	17	<	<	X
iajs-154	103	18	m.	m.	NOUN
iajs-154	103	19	the	the	DET
iajs-154	103	20	following	follow	VERB
iajs-154	103	21	statements	statement	NOUN
iajs-154	103	22	are	be	AUX
iajs-154	103	23	equivalent	equivalent	ADJ
iajs-154	103	24	:	:	PUNCT
iajs-154	103	25	(	(	PUNCT
iajs-154	103	26	1	1	X
iajs-154	103	27	)	)	PUNCT
iajs-154	103	28	n	n	NOUN
iajs-154	104	1			PROPN
iajs-154	104	2	m.	m.	NOUN
iajs-154	104	3	(	(	PUNCT
iajs-154	104	4	2	2	NUM
iajs-154	104	5	)	)	PUNCT
iajs-154	104	6	n	n	CCONJ
iajs-154	104	7	δ	δ	PROPN
iajs-154	104	8			PROPN
iajs-154	104	9	m.	m.	NOUN
iajs-154	104	10	(	(	PUNCT
iajs-154	104	11	3	3	NUM
iajs-154	104	12	)	)	PUNCT
iajs-154	104	13	n	n	NOUN
iajs-154	104	14	e	e	X
iajs-154	104	15			NOUN
iajs-154	104	16	m.	m.	NOUN
iajs-154	104	17	since	since	SCONJ
iajs-154	104	18	every	every	DET
iajs-154	104	19	uniform	uniform	NOUN
iajs-154	104	20	module	module	NOUN
iajs-154	104	21	is	be	AUX
iajs-154	104	22	indecomposable	indecomposable	ADJ
iajs-154	104	23	we	we	PRON
iajs-154	104	24	have	have	VERB
iajs-154	104	25	the	the	DET
iajs-154	104	26	following	following	ADJ
iajs-154	104	27	result	result	NOUN
iajs-154	104	28	which	which	PRON
iajs-154	104	29	follows	follow	VERB
iajs-154	104	30	directly	directly	ADV
iajs-154	104	31	by	by	ADP
iajs-154	104	32	corollary	corollary	ADJ
iajs-154	104	33	(	(	PUNCT
iajs-154	104	34	3.8	3.8	NUM
iajs-154	104	35	)	)	PUNCT
iajs-154	104	36	.	.	PUNCT
iajs-154	105	1	corollary	corollary	NOUN
iajs-154	105	2	(	(	PUNCT
iajs-154	105	3	3.9	3.9	NUM
iajs-154	105	4	):	):	PUNCT
iajs-154	105	5	let	let	VERB
iajs-154	105	6	m	m	PRON
iajs-154	105	7	be	be	AUX
iajs-154	105	8	uniform	uniform	ADJ
iajs-154	105	9	r	r	NOUN
iajs-154	105	10	-	-	PUNCT
iajs-154	105	11	module	module	NOUN
iajs-154	105	12	and	and	CCONJ
iajs-154	105	13	let	let	VERB
iajs-154	105	14	n	n	PRON
iajs-154	105	15	<	<	X
iajs-154	105	16	m.	m.	NOUN
iajs-154	105	17	then	then	ADV
iajs-154	105	18	the	the	DET
iajs-154	105	19	following	follow	VERB
iajs-154	105	20	statements	statement	NOUN
iajs-154	105	21	are	be	AUX
iajs-154	105	22	equivalent	equivalent	ADJ
iajs-154	105	23	:	:	PUNCT
iajs-154	105	24	(	(	PUNCT
iajs-154	105	25	1	1	X
iajs-154	105	26	)	)	PUNCT
iajs-154	105	27	n	n	NOUN
iajs-154	106	1			PROPN
iajs-154	106	2	m.	m.	NOUN
iajs-154	106	3	(	(	PUNCT
iajs-154	106	4	2	2	NUM
iajs-154	106	5	)	)	PUNCT
iajs-154	106	6	n	n	CCONJ
iajs-154	106	7	δ	δ	PROPN
iajs-154	106	8			PROPN
iajs-154	106	9	m.	m.	NOUN
iajs-154	106	10	(	(	PUNCT
iajs-154	106	11	3	3	NUM
iajs-154	106	12	)	)	PUNCT
iajs-154	106	13	n	n	NOUN
iajs-154	106	14	e	e	ADP
iajs-154	106	15			PROPN
iajs-154	106	16	m.	m.	NOUN
iajs-154	106	17	recall	recall	VERB
iajs-154	106	18	that	that	PRON
iajs-154	106	19	for	for	ADP
iajs-154	106	20	an	an	DET
iajs-154	106	21	r	r	NOUN
iajs-154	106	22	-	-	PUNCT
iajs-154	106	23	module	module	NOUN
iajs-154	106	24	m	m	NOUN
iajs-154	106	25	,	,	PUNCT
iajs-154	106	26	if	if	SCONJ
iajs-154	106	27	m	m	PROPN
iajs-154	106	28	has	have	VERB
iajs-154	106	29	maximal	maximal	ADJ
iajs-154	106	30	submodule	submodule	NOUN
iajs-154	106	31	.	.	PUNCT
iajs-154	107	1	then	then	ADV
iajs-154	107	2	e	e	X
iajs-154	107	3	rad	rad	PROPN
iajs-154	107	4	m={n	m={n	PROPN
iajs-154	107	5	e	e	PROPN
iajs-154	107	6			PROPN
iajs-154	107	7	mn	mn	PRON
iajs-154	107	8	is	be	AUX
iajs-154	107	9	maximal	maximal	ADJ
iajs-154	107	10	in	in	ADP
iajs-154	107	11	m	m	NOUN
iajs-154	107	12	}	}	PUNCT
iajs-154	107	13	,	,	PUNCT
iajs-154	107	14	and	and	CCONJ
iajs-154	107	15	if	if	SCONJ
iajs-154	107	16	m	m	PROPN
iajs-154	107	17	has	have	VERB
iajs-154	107	18	no	no	DET
iajs-154	107	19	maximal	maximal	ADJ
iajs-154	107	20	submodule	submodule	NOUN
iajs-154	107	21	,	,	PUNCT
iajs-154	107	22	e	e	PROPN
iajs-154	107	23	rad	rad	NOUN
iajs-154	107	24	m	m	PROPN
iajs-154	107	25	=	=	NOUN
iajs-154	107	26	m	m	PROPN
iajs-154	107	27	,	,	PUNCT
iajs-154	107	28	[	[	X
iajs-154	107	29	4	4	NUM
iajs-154	107	30	]	]	PUNCT
iajs-154	107	31	.	.	PUNCT
iajs-154	108	1	the	the	DET
iajs-154	108	2	following	follow	VERB
iajs-154	108	3	is	be	AUX
iajs-154	108	4	a	a	DET
iajs-154	108	5	characterization	characterization	NOUN
iajs-154	108	6	of	of	ADP
iajs-154	108	7	e	e	PROPN
iajs-154	108	8	rad	rad	PROPN
iajs-154	108	9	m.	m.	PROPN
iajs-154	108	10	theorem	theorem	PROPN
iajs-154	108	11	(	(	PUNCT
iajs-154	108	12	3.10	3.10	NUM
iajs-154	108	13	):	):	PUNCT
iajs-154	108	14	[	[	X
iajs-154	108	15	4,theorem	4,theorem	NUM
iajs-154	108	16	2.10	2.10	NUM
iajs-154	108	17	]	]	PUNCT
iajs-154	108	18	let	let	VERB
iajs-154	108	19	m	m	PRON
iajs-154	108	20	be	be	AUX
iajs-154	108	21	an	an	DET
iajs-154	108	22	r	r	NOUN
iajs-154	108	23	-	-	PUNCT
iajs-154	108	24	module	module	NOUN
iajs-154	108	25	.	.	PUNCT
iajs-154	109	1	then	then	ADV
iajs-154	109	2	ee	ee	PROPN
iajs-154	109	3	rad(m	rad(m	PROPN
iajs-154	109	4	)	)	PUNCT
iajs-154	109	5	{	{	PUNCT
iajs-154	110	1	n	n	NOUN
iajs-154	110	2	m	m	VERB
iajs-154	110	3	n	n	PRON
iajs-154	110	4	m}	m}	NOUN
iajs-154	110	5			X
iajs-154	110	6			NUM
iajs-154	110	7			PRON
iajs-154	110	8	.	.	PUNCT
iajs-154	111	1	corollary	corollary	ADJ
iajs-154	111	2	(	(	PUNCT
iajs-154	111	3	3.11	3.11	NUM
iajs-154	111	4	):	):	PUNCT
iajs-154	112	1	[	[	X
iajs-154	112	2	4,corollary	4,corollary	NUM
iajs-154	112	3	2.11	2.11	NUM
iajs-154	112	4	]	]	PUNCT
iajs-154	112	5	let	let	VERB
iajs-154	112	6	m	m	PRON
iajs-154	112	7	and	and	CCONJ
iajs-154	112	8	n	n	AUX
iajs-154	112	9	be	be	VERB
iajs-154	112	10	r	r	NOUN
iajs-154	112	11	-	-	PUNCT
iajs-154	112	12	modules	module	NOUN
iajs-154	112	13	.	.	PUNCT
iajs-154	113	1	(	(	PUNCT
iajs-154	113	2	1	1	X
iajs-154	113	3	)	)	PUNCT
iajs-154	113	4	if	if	SCONJ
iajs-154	113	5	f	f	PROPN
iajs-154	113	6	:	:	PUNCT
iajs-154	113	7	m	m	VERB
iajs-154	113	8			ADJ
iajs-154	113	9	n	n	PRON
iajs-154	113	10	is	be	AUX
iajs-154	113	11	an	an	DET
iajs-154	113	12	r	r	NOUN
iajs-154	113	13	-	-	PUNCT
iajs-154	113	14	homeomorphism	homeomorphism	NOUN
iajs-154	113	15	,	,	PUNCT
iajs-154	113	16	then	then	ADV
iajs-154	113	17	e	e	X
iajs-154	113	18	e	e	X
iajs-154	113	19	(	(	PUNCT
iajs-154	113	20	rad(m	rad(m	NOUN
iajs-154	113	21	)	)	PUNCT
iajs-154	113	22	)	)	PUNCT
iajs-154	113	23	rad(n)f	rad(n)f	NOUN
iajs-154	113	24			PROPN
iajs-154	113	25	.	.	PUNCT
iajs-154	114	1	(	(	PUNCT
iajs-154	114	2	2	2	X
iajs-154	114	3	)	)	PUNCT
iajs-154	114	4	if	if	SCONJ
iajs-154	114	5	every	every	DET
iajs-154	114	6	proper	proper	ADJ
iajs-154	114	7	essential	essential	ADJ
iajs-154	114	8	submodule	submodule	NOUN
iajs-154	114	9	of	of	ADP
iajs-154	114	10	m	m	PROPN
iajs-154	114	11	is	be	AUX
iajs-154	114	12	contained	contain	VERB
iajs-154	114	13	in	in	ADP
iajs-154	114	14	a	a	DET
iajs-154	114	15	maximal	maximal	ADJ
iajs-154	114	16	submodule	submodule	NOUN
iajs-154	114	17	of	of	ADP
iajs-154	114	18	m	m	PROPN
iajs-154	114	19	,	,	PUNCT
iajs-154	114	20	then	then	ADV
iajs-154	114	21	e	e	PROPN
iajs-154	114	22	rad(m	rad(m	PROPN
iajs-154	114	23	)	)	PUNCT
iajs-154	114	24	is	be	AUX
iajs-154	114	25	the	the	DET
iajs-154	114	26	largest	large	ADJ
iajs-154	114	27	e	e	ADJ
iajs-154	114	28	-	-	ADJ
iajs-154	114	29	small	small	ADJ
iajs-154	114	30	submodule	submodule	NOUN
iajs-154	114	31	of	of	ADP
iajs-154	114	32	m.	m.	NOUN
iajs-154	114	33	219	219	NUM
iajs-154	114	34	|	|	NOUN
iajs-154	114	35	mathematics	mathematic	NOUN
iajs-154	114	36	2015	2015	NUM
iajs-154	114	37	)	)	PUNCT
iajs-154	114	38	عام	عام	ADP
iajs-154	114	39	3العدد	3العدد	NUM
iajs-154	114	40	(	(	PUNCT
iajs-154	114	41	28مجلة	28مجلة	X
iajs-154	114	42	إبن	إبن	VERB
iajs-154	114	43	الهيثم	الهيثم	ADJ
iajs-154	114	44	للعلوم	للعلوم	NOUN
iajs-154	114	45	الصرفة	الصرفة	NOUN
iajs-154	115	1	و	و	PRON
iajs-154	115	2	التطبيقية	التطبيقية	ADV
iajs-154	115	3	المجلد	المجلد	VERB
iajs-154	115	4	ibn	ibn	PROPN
iajs-154	115	5	al	al	PROPN
iajs-154	115	6	-	-	PUNCT
iajs-154	115	7	haitham	haitham	PROPN
iajs-154	115	8	jour	jour	X
iajs-154	115	9	.	.	PROPN
iajs-154	116	1	for	for	ADP
iajs-154	116	2	pure	pure	ADJ
iajs-154	116	3	&	&	CCONJ
iajs-154	116	4	appl	appl	PROPN
iajs-154	116	5	.	.	PUNCT
iajs-154	117	1	sci	sci	PROPN
iajs-154	117	2	.	.	PUNCT
iajs-154	117	3	vol	vol	NOUN
iajs-154	117	4	.	.	PROPN
iajs-154	118	1	28	28	NUM
iajs-154	118	2	(	(	PUNCT
iajs-154	118	3	3	3	NUM
iajs-154	118	4	)	)	PUNCT
iajs-154	118	5	2015	2015	NUM
iajs-154	118	6	recall	recall	VERB
iajs-154	118	7	that	that	SCONJ
iajs-154	118	8	an	an	DET
iajs-154	118	9	r	r	NOUN
iajs-154	118	10	-	-	PUNCT
iajs-154	118	11	module	module	NOUN
iajs-154	118	12	m	m	NOUN
iajs-154	118	13	is	be	AUX
iajs-154	118	14	called	call	VERB
iajs-154	118	15	multiplication	multiplication	NOUN
iajs-154	118	16	if	if	SCONJ
iajs-154	118	17	for	for	ADP
iajs-154	118	18	each	each	DET
iajs-154	118	19	n	n	PRON
iajs-154	118	20			NOUN
iajs-154	118	21	m	m	NOUN
iajs-154	118	22	,	,	PUNCT
iajs-154	118	23	there	there	PRON
iajs-154	118	24	exists	exist	VERB
iajs-154	118	25	an	an	DET
iajs-154	118	26	ideal	ideal	NOUN
iajs-154	118	27	i	i	PRON
iajs-154	118	28	of	of	ADP
iajs-154	118	29	r	r	NOUN
iajs-154	119	1	such	such	ADJ
iajs-154	119	2	that	that	SCONJ
iajs-154	119	3	n	n	NOUN
iajs-154	119	4	=	=	SYM
iajs-154	119	5	i	i	PRON
iajs-154	119	6	m.	m.	NOUN
iajs-154	119	7	equivalently	equivalently	ADV
iajs-154	119	8	m	m	VERB
iajs-154	119	9	is	be	AUX
iajs-154	119	10	multiplication	multiplication	NOUN
iajs-154	119	11	if	if	SCONJ
iajs-154	119	12	for	for	ADP
iajs-154	119	13	each	each	DET
iajs-154	119	14	n	n	PRON
iajs-154	119	15			NUM
iajs-154	119	16	m	m	NOUN
iajs-154	119	17	,	,	PUNCT
iajs-154	119	18	n	n	NOUN
iajs-154	119	19	=	=	SYM
iajs-154	119	20	(	(	PUNCT
iajs-154	119	21	n	n	CCONJ
iajs-154	119	22	:	:	PUNCT
iajs-154	119	23	m)m	m)m	NOUN
iajs-154	119	24	,	,	PUNCT
iajs-154	119	25	where	where	SCONJ
iajs-154	119	26	(	(	PUNCT
iajs-154	119	27	n	n	NOUN
iajs-154	119	28	r	r	NOUN
iajs-154	119	29	:	:	PUNCT
iajs-154	119	30	m	m	X
iajs-154	119	31	)	)	PUNCT
iajs-154	120	1	=	=	PRON
iajs-154	120	2	{	{	PUNCT
iajs-154	120	3	r	r	NOUN
iajs-154	120	4			NOUN
iajs-154	120	5	r	r	NOUN
iajs-154	120	6	:	:	PUNCT
iajs-154	120	7	rm	rm	PROPN
iajs-154	120	8			PROPN
iajs-154	120	9	n	n	CCONJ
iajs-154	120	10	}	}	PUNCT
iajs-154	120	11	,	,	PUNCT
iajs-154	120	12	[	[	X
iajs-154	120	13	9	9	NUM
iajs-154	120	14	]	]	PUNCT
iajs-154	120	15	.	.	PUNCT
iajs-154	121	1	corollary	corollary	ADJ
iajs-154	121	2	(	(	PUNCT
iajs-154	121	3	3.12	3.12	NUM
iajs-154	121	4	):	):	PUNCT
iajs-154	121	5	let	let	VERB
iajs-154	121	6	m	m	PRON
iajs-154	121	7	be	be	AUX
iajs-154	121	8	a	a	DET
iajs-154	121	9	finitely	finitely	ADV
iajs-154	121	10	generated	generate	VERB
iajs-154	121	11	or	or	CCONJ
iajs-154	121	12	multiplication	multiplication	NOUN
iajs-154	121	13	r	r	NOUN
iajs-154	121	14	-	-	NOUN
iajs-154	121	15	module	module	NOUN
iajs-154	121	16	.	.	PUNCT
iajs-154	122	1	then	then	ADV
iajs-154	122	2	e	e	PROPN
iajs-154	122	3	rad(m	rad(m	PROPN
iajs-154	122	4	)	)	PUNCT
iajs-154	122	5	is	be	AUX
iajs-154	122	6	the	the	DET
iajs-154	122	7	largest	large	ADJ
iajs-154	122	8	e	e	ADJ
iajs-154	122	9	-	-	ADJ
iajs-154	122	10	small	small	ADJ
iajs-154	122	11	submodule	submodule	NOUN
iajs-154	122	12	of	of	ADP
iajs-154	122	13	m.	m.	NOUN
iajs-154	122	14	proof	proof	NOUN
iajs-154	122	15	:	:	PUNCT
iajs-154	122	16	since	since	SCONJ
iajs-154	122	17	m	m	PROPN
iajs-154	122	18	is	be	AUX
iajs-154	122	19	finitely	finitely	ADV
iajs-154	122	20	generated	generate	VERB
iajs-154	122	21	or	or	CCONJ
iajs-154	122	22	multiplication	multiplication	NOUN
iajs-154	122	23	,	,	PUNCT
iajs-154	122	24	then	then	ADV
iajs-154	122	25	every	every	DET
iajs-154	122	26	proper	proper	ADJ
iajs-154	122	27	submodule	submodule	NOUN
iajs-154	122	28	is	be	AUX
iajs-154	122	29	contained	contain	VERB
iajs-154	122	30	in	in	ADP
iajs-154	122	31	maximal	maximal	ADJ
iajs-154	122	32	submodule	submodule	NOUN
iajs-154	122	33	.	.	PUNCT
iajs-154	123	1	hence	hence	ADV
iajs-154	123	2	the	the	DET
iajs-154	123	3	result	result	NOUN
iajs-154	123	4	is	be	AUX
iajs-154	123	5	followed	follow	VERB
iajs-154	123	6	by	by	ADP
iajs-154	123	7	corollary	corollary	ADJ
iajs-154	123	8	(	(	PUNCT
iajs-154	123	9	3.11	3.11	NUM
iajs-154	123	10	)	)	PUNCT
iajs-154	123	11	.	.	PUNCT
iajs-154	124	1	proposition	proposition	NOUN
iajs-154	124	2	(	(	PUNCT
iajs-154	124	3	3.13	3.13	NUM
iajs-154	124	4	):	):	PUNCT
iajs-154	124	5	let	let	VERB
iajs-154	124	6	m	m	PRON
iajs-154	124	7	be	be	AUX
iajs-154	124	8	an	an	DET
iajs-154	124	9	module	module	NOUN
iajs-154	124	10	,	,	PUNCT
iajs-154	124	11	let	let	VERB
iajs-154	124	12	m	m	PRON
iajs-154	124	13			PROPN
iajs-154	124	14	m	m	VERB
iajs-154	124	15	then	then	ADV
iajs-154	124	16	rm	rm	PROPN
iajs-154	124	17	e	e	PROPN
iajs-154	124	18	m	m	PROPN
iajs-154	124	19	if	if	SCONJ
iajs-154	124	20	and	and	CCONJ
iajs-154	124	21	only	only	ADV
iajs-154	124	22	if	if	SCONJ
iajs-154	124	23	m	m	VERB
iajs-154	124	24			NOUN
iajs-154	124	25	e	e	X
iajs-154	124	26	rad(m	rad(m	PROPN
iajs-154	124	27	)	)	PUNCT
iajs-154	124	28	.	.	PUNCT
iajs-154	125	1	proof	proof	NOUN
iajs-154	125	2	:	:	PUNCT
iajs-154	125	3	suppose	suppose	VERB
iajs-154	125	4	rm	rm	PROPN
iajs-154	125	5	e	e	PROPN
iajs-154	125	6	m	m	PROPN
iajs-154	125	7	,	,	PUNCT
iajs-154	125	8	then	then	ADV
iajs-154	125	9	rm	rm	PROPN
iajs-154	125	10	e	e	PROPN
iajs-154	125	11	rad	rad	PROPN
iajs-154	125	12	m	m	X
iajs-154	125	13	,	,	PUNCT
iajs-154	125	14	hence	hence	ADV
iajs-154	125	15	m	m	VERB
iajs-154	125	16			NOUN
iajs-154	125	17	e	e	X
iajs-154	125	18	rad(m	rad(m	PROPN
iajs-154	125	19	)	)	PUNCT
iajs-154	125	20	.	.	PUNCT
iajs-154	126	1	conversely	conversely	ADV
iajs-154	126	2	,	,	PUNCT
iajs-154	126	3	let	let	VERB
iajs-154	126	4	m	m	PRON
iajs-154	126	5			NOUN
iajs-154	126	6	e	e	X
iajs-154	126	7	rad(m	rad(m	PROPN
iajs-154	126	8	)	)	PUNCT
iajs-154	126	9	.	.	PUNCT
iajs-154	127	1	assume	assume	VERB
iajs-154	128	1	e	e	X
iajs-154	128	2	rad	rad	PROPN
iajs-154	128	3	(	(	PUNCT
iajs-154	128	4	m	m	NOUN
iajs-154	128	5	)	)	PUNCT
iajs-154	128	6	m	m	PROPN
iajs-154	128	7	.	.	PUNCT
iajs-154	129	1	suppose	suppose	VERB
iajs-154	129	2	rm	rm	PROPN
iajs-154	129	3	e	e	PROPN
iajs-154	129	4	m	m	PROPN
iajs-154	129	5	,	,	PUNCT
iajs-154	129	6	then	then	ADV
iajs-154	129	7	by	by	ADP
iajs-154	129	8	proposition(3.1	proposition(3.1	PROPN
iajs-154	129	9	)	)	PUNCT
iajs-154	129	10	,	,	PUNCT
iajs-154	129	11	there	there	PRON
iajs-154	129	12	exists	exist	VERB
iajs-154	129	13	an	an	DET
iajs-154	129	14	essential	essential	ADJ
iajs-154	129	15	maximal	maximal	ADJ
iajs-154	129	16	submodule	submodule	NOUN
iajs-154	129	17	n	n	PROPN
iajs-154	129	18	in	in	ADP
iajs-154	129	19	m	m	PROPN
iajs-154	129	20	and	and	CCONJ
iajs-154	129	21	m	m	PROPN
iajs-154	129	22			ADJ
iajs-154	129	23	n.	n.	NOUN
iajs-154	129	24	hence	hence	ADV
iajs-154	129	25	m	m	VERB
iajs-154	129	26			NOUN
iajs-154	129	27	e	e	X
iajs-154	129	28	rad(m	rad(m	PROPN
iajs-154	129	29	)	)	PUNCT
iajs-154	129	30	which	which	PRON
iajs-154	129	31	is	be	AUX
iajs-154	129	32	a	a	DET
iajs-154	129	33	contradiction	contradiction	NOUN
iajs-154	129	34	.	.	PUNCT
iajs-154	130	1	thus	thus	ADV
iajs-154	130	2	rm	rm	PROPN
iajs-154	130	3	e	e	PROPN
iajs-154	130	4	m	m	PROPN
iajs-154	130	5	.	.	PUNCT
iajs-154	131	1	if	if	SCONJ
iajs-154	131	2	e	e	PROPN
iajs-154	131	3	rad	rad	PROPN
iajs-154	131	4	(	(	PUNCT
iajs-154	131	5	m	m	NOUN
iajs-154	131	6	)	)	PUNCT
iajs-154	131	7	m	m	NOUN
iajs-154	131	8	,	,	PUNCT
iajs-154	131	9	then	then	ADV
iajs-154	131	10	m	m	PROPN
iajs-154	131	11	has	have	VERB
iajs-154	131	12	no	no	DET
iajs-154	131	13	essential	essential	ADJ
iajs-154	131	14	maximal	maximal	ADJ
iajs-154	131	15	submodule	submodule	NOUN
iajs-154	131	16	.	.	PUNCT
iajs-154	132	1	hence	hence	ADV
iajs-154	132	2	for	for	ADP
iajs-154	132	3	each	each	DET
iajs-154	132	4	m	m	PROPN
iajs-154	132	5			PROPN
iajs-154	132	6	m	m	PROPN
iajs-154	132	7	,	,	PUNCT
iajs-154	132	8	rm	rm	PROPN
iajs-154	132	9	e	e	X
iajs-154	132	10	m	m	X
iajs-154	132	11	(	(	PUNCT
iajs-154	132	12	by	by	ADP
iajs-154	132	13	proposition	proposition	NOUN
iajs-154	132	14	(	(	PUNCT
iajs-154	132	15	3.1	3.1	NUM
iajs-154	132	16	)	)	PUNCT
iajs-154	132	17	)	)	PUNCT
iajs-154	132	18	.	.	PUNCT
iajs-154	133	1	proposition	proposition	NOUN
iajs-154	133	2	(	(	PUNCT
iajs-154	133	3	3.14	3.14	NUM
iajs-154	133	4	):	):	PUNCT
iajs-154	133	5	an	an	DET
iajs-154	133	6	arbitrary	arbitrary	ADJ
iajs-154	133	7	sum	sum	NOUN
iajs-154	133	8	of	of	ADP
iajs-154	133	9	e	e	ADJ
iajs-154	133	10	-	-	ADJ
iajs-154	133	11	small	small	ADJ
iajs-154	133	12	submodules	submodule	NOUN
iajs-154	133	13	of	of	ADP
iajs-154	133	14	a	a	DET
iajs-154	133	15	module	module	NOUN
iajs-154	133	16	m	m	NOUN
iajs-154	133	17	is	be	AUX
iajs-154	133	18	an	an	DET
iajs-154	133	19	e	e	ADJ
iajs-154	133	20	-	-	ADJ
iajs-154	133	21	small	small	ADJ
iajs-154	133	22	submodule	submodule	NOUN
iajs-154	133	23	of	of	ADP
iajs-154	133	24	m	m	PROPN
iajs-154	133	25	if	if	SCONJ
iajs-154	134	1	and	and	CCONJ
iajs-154	134	2	only	only	ADV
iajs-154	134	3	if	if	SCONJ
iajs-154	134	4	ee	ee	PROPN
iajs-154	134	5	rad(m	rad(m	PROPN
iajs-154	134	6	)	)	PUNCT
iajs-154	134	7	m	m	NOUN
iajs-154	134	8	.	.	PUNCT
iajs-154	135	1	proof	proof	NOUN
iajs-154	135	2	:	:	PUNCT
iajs-154	135	3	(	(	PUNCT
iajs-154	135	4			NOUN
iajs-154	135	5	)	)	PUNCT
iajs-154	135	6	since	since	SCONJ
iajs-154	135	7	e	e	PROPN
iajs-154	135	8	rad(m	rad(m	PROPN
iajs-154	135	9	)	)	PUNCT
iajs-154	135	10	=	=	NOUN
iajs-154	136	1	the	the	DET
iajs-154	136	2	sum	sum	NOUN
iajs-154	136	3	of	of	ADP
iajs-154	136	4	all	all	DET
iajs-154	136	5	e	e	ADJ
iajs-154	136	6	-	-	ADJ
iajs-154	136	7	small	small	ADJ
iajs-154	136	8	submodules	submodule	NOUN
iajs-154	136	9	(	(	PUNCT
iajs-154	136	10	by	by	ADP
iajs-154	136	11	theorem	theorem	NOUN
iajs-154	136	12	(	(	PUNCT
iajs-154	136	13	3.10	3.10	NUM
iajs-154	136	14	)	)	PUNCT
iajs-154	136	15	)	)	PUNCT
iajs-154	136	16	,	,	PUNCT
iajs-154	136	17	ee	ee	PROPN
iajs-154	136	18	rad(m	rad(m	PROPN
iajs-154	136	19	)	)	PUNCT
iajs-154	136	20	m	m	NOUN
iajs-154	136	21	.	.	PUNCT
iajs-154	137	1	(	(	PUNCT
iajs-154	137	2			NOUN
iajs-154	137	3	)	)	PUNCT
iajs-154	137	4	suppose	suppose	VERB
iajs-154	137	5	ee	ee	ADP
iajs-154	137	6	rad(m	rad(m	PROPN
iajs-154	137	7	)	)	PUNCT
iajs-154	137	8	m	m	NOUN
iajs-154	137	9	.	.	PUNCT
iajs-154	138	1	let	let	VERB
iajs-154	138	2	{	{	PUNCT
iajs-154	138	3	k}	k}	PROPN
iajs-154	138	4	be	be	AUX
iajs-154	138	5	a	a	DET
iajs-154	138	6	family	family	NOUN
iajs-154	138	7	of	of	ADP
iajs-154	138	8	e	e	NOUN
iajs-154	138	9	-	-	ADJ
iajs-154	138	10	small	small	ADJ
iajs-154	138	11	submodules	submodule	NOUN
iajs-154	138	12	of	of	ADP
iajs-154	138	13	m.	m.	NOUN
iajs-154	139	1	α	α	PROPN
iajs-154	139	2	eeα	eeα	PROPN
iajs-154	139	3	k	k	PROPN
iajs-154	139	4	rad(m	rad(m	PROPN
iajs-154	139	5	)	)	PUNCT
iajs-154	139	6	m	m	VERB
iajs-154	139	7			PROPN
iajs-154	139	8			PROPN
iajs-154	139	9			PROPN
iajs-154	139	10	.	.	PUNCT
iajs-154	140	1	therefore	therefore	ADV
iajs-154	140	2	α	α	INTJ
iajs-154	140	3	eα	eα	VERB
iajs-154	140	4	k	k	NOUN
iajs-154	140	5	m	m	PROPN
iajs-154	140	6			ADJ
iajs-154	140	7			X
iajs-154	140	8			NUM
iajs-154	140	9	by	by	ADP
iajs-154	140	10	proposition	proposition	NOUN
iajs-154	140	11	(	(	PUNCT
iajs-154	140	12	2.5	2.5	NUM
iajs-154	140	13	(	(	PUNCT
iajs-154	140	14	a	a	NOUN
iajs-154	140	15	)	)	PUNCT
iajs-154	140	16	)	)	PUNCT
iajs-154	140	17	.	.	PUNCT
iajs-154	141	1	proposition	proposition	NOUN
iajs-154	141	2	(	(	PUNCT
iajs-154	141	3	3.15	3.15	NUM
iajs-154	141	4	):	):	PUNCT
iajs-154	141	5	let	let	VERB
iajs-154	141	6	m	m	PRON
iajs-154	141	7	be	be	AUX
iajs-154	141	8	an	an	DET
iajs-154	141	9	r	r	NOUN
iajs-154	141	10	-	-	PUNCT
iajs-154	141	11	module	module	NOUN
iajs-154	141	12	.	.	PUNCT
iajs-154	142	1	then	then	ADV
iajs-154	142	2	e	e	PROPN
iajs-154	142	3	rad(m	rad(m	PROPN
iajs-154	142	4	)	)	PUNCT
iajs-154	142	5	m	m	NOUN
iajs-154	142	6	if	if	SCONJ
iajs-154	142	7	and	and	CCONJ
iajs-154	142	8	only	only	ADV
iajs-154	142	9	if	if	SCONJ
iajs-154	142	10	all	all	DET
iajs-154	142	11	finitely	finitely	ADV
iajs-154	142	12	generated	generate	VERB
iajs-154	142	13	submodules	submodule	NOUN
iajs-154	142	14	are	be	AUX
iajs-154	142	15	e	e	ADJ
iajs-154	142	16	-	-	ADJ
iajs-154	142	17	small	small	ADJ
iajs-154	142	18	submodules	submodule	NOUN
iajs-154	142	19	of	of	ADP
iajs-154	142	20	m.	m.	NOUN
iajs-154	142	21	proof	proof	NOUN
iajs-154	142	22	:	:	PUNCT
iajs-154	142	23	(	(	PUNCT
iajs-154	142	24			NOUN
iajs-154	142	25	)	)	PUNCT
iajs-154	142	26	suppose	suppose	VERB
iajs-154	142	27	e	e	X
iajs-154	142	28	rad(m	rad(m	NOUN
iajs-154	142	29	)	)	PUNCT
iajs-154	142	30	m	m	NOUN
iajs-154	142	31	and	and	CCONJ
iajs-154	142	32	let	let	VERB
iajs-154	142	33	n	n	PRON
iajs-154	142	34	be	be	AUX
iajs-154	142	35	a	a	DET
iajs-154	142	36	finitely	finitely	ADV
iajs-154	142	37	generated	generate	VERB
iajs-154	142	38	submodule	submodule	NOUN
iajs-154	142	39	of	of	ADP
iajs-154	142	40	m.	m.	NOUN
iajs-154	142	41	hence	hence	ADV
iajs-154	142	42	1	1	NUM
iajs-154	142	43	nn	nn	INTJ
iajs-154	142	44	rx	rx	VERB
iajs-154	142	45	...	...	PUNCT
iajs-154	142	46	rx	rx	PROPN
iajs-154	142	47			ADV
iajs-154	142	48			PUNCT
iajs-154	142	49	where	where	SCONJ
iajs-154	142	50	x1	x1	PROPN
iajs-154	142	51	,	,	PUNCT
iajs-154	142	52	…	…	PUNCT
iajs-154	142	53	,	,	PUNCT
iajs-154	142	54	xn	xn	PROPN
iajs-154	142	55			NOUN
iajs-154	142	56	m	m	VERB
iajs-154	142	57	=	=	SYM
iajs-154	142	58	e	e	X
iajs-154	142	59	rad(m	rad(m	PROPN
iajs-154	142	60	)	)	PUNCT
iajs-154	142	61	,	,	PUNCT
iajs-154	142	62	then	then	ADV
iajs-154	142	63	by	by	ADP
iajs-154	142	64	proposition	proposition	NOUN
iajs-154	142	65	(	(	PUNCT
iajs-154	142	66	3.13	3.13	NUM
iajs-154	142	67	)	)	PUNCT
iajs-154	142	68	,	,	PUNCT
iajs-154	142	69	i	i	PRON
iajs-154	142	70	e	e	AUX
iajs-154	142	71	rx	rx	VERB
iajs-154	142	72	m	m	NOUN
iajs-154	142	73	and	and	CCONJ
iajs-154	142	74	by	by	ADP
iajs-154	142	75	proposition	proposition	NOUN
iajs-154	142	76	(	(	PUNCT
iajs-154	142	77	2.5(1.b	2.5(1.b	NUM
iajs-154	142	78	)	)	PUNCT
iajs-154	142	79	)	)	PUNCT
iajs-154	143	1	e	e	NOUN
iajs-154	143	2	n	n	PRON
iajs-154	143	3	m	m	NOUN
iajs-154	143	4	.	.	PUNCT
iajs-154	144	1	220	220	NUM
iajs-154	144	2	|	|	NOUN
iajs-154	144	3	mathematics	mathematic	NOUN
iajs-154	144	4	2015	2015	NUM
iajs-154	144	5	)	)	PUNCT
iajs-154	144	6	عام	عام	ADP
iajs-154	144	7	3العدد	3العدد	NUM
iajs-154	144	8	(	(	PUNCT
iajs-154	144	9	28مجلة	28مجلة	X
iajs-154	144	10	إبن	إبن	VERB
iajs-154	144	11	الهيثم	الهيثم	ADJ
iajs-154	144	12	للعلوم	للعلوم	NOUN
iajs-154	144	13	الصرفة	الصرفة	NOUN
iajs-154	145	1	و	و	PRON
iajs-154	145	2	التطبيقية	التطبيقية	ADV
iajs-154	145	3	المجلد	المجلد	VERB
iajs-154	145	4	ibn	ibn	PROPN
iajs-154	145	5	al	al	PROPN
iajs-154	145	6	-	-	PUNCT
iajs-154	145	7	haitham	haitham	PROPN
iajs-154	145	8	jour	jour	X
iajs-154	145	9	.	.	PROPN
iajs-154	146	1	for	for	ADP
iajs-154	146	2	pure	pure	ADJ
iajs-154	146	3	&	&	CCONJ
iajs-154	146	4	appl	appl	PROPN
iajs-154	146	5	.	.	PUNCT
iajs-154	147	1	sci	sci	PROPN
iajs-154	147	2	.	.	PUNCT
iajs-154	147	3	vol	vol	NOUN
iajs-154	147	4	.	.	PROPN
iajs-154	148	1	28	28	NUM
iajs-154	148	2	(	(	PUNCT
iajs-154	148	3	3	3	NUM
iajs-154	148	4	)	)	PUNCT
iajs-154	148	5	2015	2015	NUM
iajs-154	148	6	(	(	PUNCT
iajs-154	148	7			NOUN
iajs-154	148	8	)	)	PUNCT
iajs-154	148	9	let	let	VERB
iajs-154	148	10	m	m	PRON
iajs-154	148	11			PROPN
iajs-154	148	12	m.	m.	NOUN
iajs-154	148	13	then	then	ADV
iajs-154	148	14	<	<	X
iajs-154	148	15	m	m	VERB
iajs-154	148	16	>	>	X
iajs-154	148	17	=	=	PUNCT
iajs-154	148	18	rm	rm	PROPN
iajs-154	148	19	is	be	AUX
iajs-154	148	20	finitely	finitely	ADV
iajs-154	148	21	generated	generate	VERB
iajs-154	148	22	,	,	PUNCT
iajs-154	148	23	so	so	ADV
iajs-154	148	24	by	by	ADP
iajs-154	148	25	hypothesis	hypothesis	NOUN
iajs-154	148	26	,	,	PUNCT
iajs-154	148	27	e	e	PROPN
iajs-154	148	28	rm	rm	NOUN
iajs-154	148	29	m	m	PROPN
iajs-154	148	30	and	and	CCONJ
iajs-154	148	31	hence	hence	ADV
iajs-154	148	32	<	<	X
iajs-154	148	33	m	m	X
iajs-154	148	34	>	>	X
iajs-154	148	35	e	e	NOUN
iajs-154	148	36	rad(m)	rad(m)	NOUN
iajs-154	148	37	.	.	PUNCT
iajs-154	149	1	thus	thus	ADV
iajs-154	149	2	e	e	X
iajs-154	149	3	m	m	NOUN
iajs-154	149	4	rad(m)	rad(m)	NOUN
iajs-154	149	5	.	.	PUNCT
iajs-154	150	1	next	next	ADV
iajs-154	150	2	(	(	PUNCT
iajs-154	150	3	3.16	3.16	NUM
iajs-154	150	4	):	):	PUNCT
iajs-154	150	5	it	it	PRON
iajs-154	150	6	is	be	AUX
iajs-154	150	7	known	know	VERB
iajs-154	150	8	that	that	SCONJ
iajs-154	150	9	for	for	ADP
iajs-154	150	10	a	a	DET
iajs-154	150	11	module	module	NOUN
iajs-154	150	12	m	m	NOUN
iajs-154	150	13	,	,	PUNCT
iajs-154	150	14	if	if	SCONJ
iajs-154	150	15	rad(m	rad(m	NUM
iajs-154	150	16	)	)	PUNCT
iajs-154	150	17	m	m	NOUN
iajs-154	150	18	then	then	ADV
iajs-154	150	19	m	m	PROPN
iajs-154	150	20	/	/	SYM
iajs-154	150	21	rad	rad	VERB
iajs-154	150	22	m	m	VERB
iajs-154	150	23	has	have	VERB
iajs-154	150	24	no	no	DET
iajs-154	150	25	nonzero	nonzero	ADJ
iajs-154	150	26	small	small	ADJ
iajs-154	150	27	submodulele	submodulele	NOUN
iajs-154	150	28	.	.	PUNCT
iajs-154	151	1	however	however	ADV
iajs-154	151	2	this	this	DET
iajs-154	151	3	statement	statement	NOUN
iajs-154	151	4	can	can	AUX
iajs-154	151	5	not	not	PART
iajs-154	151	6	be	be	AUX
iajs-154	151	7	generalized	generalize	VERB
iajs-154	151	8	for	for	ADP
iajs-154	151	9	e	e	PROPN
iajs-154	151	10	rad(m	rad(m	PROPN
iajs-154	151	11	)	)	PUNCT
iajs-154	151	12	,	,	PUNCT
iajs-154	151	13	as	as	SCONJ
iajs-154	151	14	the	the	DET
iajs-154	151	15	following	follow	VERB
iajs-154	151	16	example	example	NOUN
iajs-154	151	17	shows	show	NOUN
iajs-154	151	18	.	.	PUNCT
iajs-154	152	1	example	example	NOUN
iajs-154	152	2	(	(	PUNCT
iajs-154	152	3	3.17	3.17	NUM
iajs-154	152	4	):	):	PUNCT
iajs-154	152	5	consider	consider	VERB
iajs-154	152	6	the	the	DET
iajs-154	152	7	z	z	NOUN
iajs-154	152	8	-	-	PUNCT
iajs-154	152	9	module	module	NOUN
iajs-154	152	10	z24	z24	NOUN
iajs-154	152	11	24	24	NUM
iajs-154	152	12	24	24	NUM
iajs-154	152	13	ee	ee	PROPN
iajs-154	152	14	rad(z	rad(z	PROPN
iajs-154	152	15	)	)	PUNCT
iajs-154	152	16	2	2	NUM
iajs-154	152	17	z	z	NOUN
iajs-154	152	18			PROPN
iajs-154	152	19	.	.	PUNCT
iajs-154	153	1	but	but	CCONJ
iajs-154	153	2	24	24	NUM
iajs-154	153	3	2	2	NUM
iajs-154	153	4	z	z	NOUN
iajs-154	153	5	z	z	NOUN
iajs-154	154	1	2	2	NUM
iajs-154	154	2			INTJ
iajs-154	154	3			NOUN
iajs-154	154	4	and	and	CCONJ
iajs-154	154	5	2	2	NUM
iajs-154	154	6	2	2	NUM
iajs-154	154	7	e	e	NOUN
iajs-154	154	8	z	z	PROPN
iajs-154	154	9	z	z	PROPN
iajs-154	154	10	.	.	PUNCT
iajs-154	155	1	proposition	proposition	NOUN
iajs-154	155	2	(	(	PUNCT
iajs-154	155	3	3.18	3.18	NUM
iajs-154	155	4	):	):	PUNCT
iajs-154	155	5	let	let	VERB
iajs-154	155	6	m	m	PRON
iajs-154	155	7	be	be	AUX
iajs-154	155	8	a	a	DET
iajs-154	155	9	faithful	faithful	ADJ
iajs-154	155	10	finitely	finitely	ADV
iajs-154	155	11	generated	generate	VERB
iajs-154	155	12	multiplication	multiplication	NOUN
iajs-154	155	13	r	r	NOUN
iajs-154	155	14	-	-	PUNCT
iajs-154	155	15	module	module	NOUN
iajs-154	155	16	,	,	PUNCT
iajs-154	155	17	let	let	VERB
iajs-154	155	18	n	n	PRON
iajs-154	155	19	<	<	X
iajs-154	155	20	m.	m.	NOUN
iajs-154	155	21	then	then	ADV
iajs-154	155	22	the	the	DET
iajs-154	155	23	following	follow	VERB
iajs-154	155	24	statements	statement	NOUN
iajs-154	155	25	are	be	AUX
iajs-154	155	26	equivalent	equivalent	ADJ
iajs-154	155	27	e	e	NOUN
iajs-154	155	28	n	n	PRON
iajs-154	155	29	m	m	NOUN
iajs-154	155	30	if	if	SCONJ
iajs-154	155	31	and	and	CCONJ
iajs-154	155	32	only	only	ADV
iajs-154	155	33	if	if	SCONJ
iajs-154	155	34	(	(	PUNCT
iajs-154	155	35	n	n	NUM
iajs-154	155	36	:	:	PUNCT
iajs-154	155	37	m	m	X
iajs-154	155	38	)	)	PUNCT
iajs-154	155	39	e	e	X
iajs-154	155	40	r	r	X
iajs-154	155	41	.	.	PUNCT
iajs-154	156	1	proof	proof	NOUN
iajs-154	156	2	:	:	PUNCT
iajs-154	156	3	(	(	PUNCT
iajs-154	156	4			NOUN
iajs-154	156	5	)	)	PUNCT
iajs-154	156	6	assume	assume	VERB
iajs-154	156	7	(	(	PUNCT
iajs-154	156	8	n	n	NUM
iajs-154	156	9	:	:	PUNCT
iajs-154	156	10	m	m	VERB
iajs-154	156	11	)	)	PUNCT
iajs-154	157	1	+	+	CCONJ
iajs-154	157	2	k	k	X
iajs-154	157	3	=	=	SYM
iajs-154	157	4	r	r	NOUN
iajs-154	157	5	with	with	ADP
iajs-154	157	6	k	k	PROPN
iajs-154	157	7	e	e	PROPN
iajs-154	157	8	r	r	NOUN
iajs-154	157	9	.	.	PUNCT
iajs-154	158	1	then	then	ADV
iajs-154	158	2	(	(	PUNCT
iajs-154	158	3	n	n	CCONJ
iajs-154	158	4	:	:	X
iajs-154	158	5	m)m	m)m	X
iajs-154	159	1	+	+	CCONJ
iajs-154	159	2	km	km	NOUN
iajs-154	159	3	=	=	SYM
iajs-154	159	4	m	m	NOUN
iajs-154	159	5	,	,	PUNCT
iajs-154	159	6	thus	thus	ADV
iajs-154	159	7	n	n	PROPN
iajs-154	159	8	+	+	CCONJ
iajs-154	159	9	km	km	NOUN
iajs-154	159	10	=	=	SYM
iajs-154	159	11	m.	m.	NOUN
iajs-154	160	1	but	but	CCONJ
iajs-154	160	2	k	k	PROPN
iajs-154	160	3	e	e	PROPN
iajs-154	160	4	r	r	NOUN
iajs-154	160	5	,	,	PUNCT
iajs-154	160	6	so	so	CCONJ
iajs-154	160	7	by	by	ADP
iajs-154	160	8	[	[	X
iajs-154	160	9	9,theorem	9,theorem	NOUN
iajs-154	160	10	2.13	2.13	NUM
iajs-154	160	11	]	]	PUNCT
iajs-154	160	12	,	,	PUNCT
iajs-154	160	13	km	km	PROPN
iajs-154	160	14	e	e	NOUN
iajs-154	160	15			NOUN
iajs-154	160	16	m	m	VERB
iajs-154	160	17	and	and	CCONJ
iajs-154	160	18	since	since	SCONJ
iajs-154	160	19	n	n	NUM
iajs-154	160	20	e	e	NOUN
iajs-154	160	21			NOUN
iajs-154	160	22	m	m	VERB
iajs-154	160	23	,	,	PUNCT
iajs-154	160	24	we	we	PRON
iajs-154	160	25	get	get	VERB
iajs-154	160	26	km	km	NOUN
iajs-154	160	27	=	=	PUNCT
iajs-154	160	28	m.	m.	NOUN
iajs-154	160	29	therefore	therefore	ADV
iajs-154	160	30	k	k	PROPN
iajs-154	161	1	=	=	PUNCT
iajs-154	161	2	r	r	NOUN
iajs-154	161	3	by	by	ADP
iajs-154	161	4	[	[	X
iajs-154	161	5	9,theorem	9,theorem	NOUN
iajs-154	161	6	3.1	3.1	NUM
iajs-154	161	7	]	]	PUNCT
iajs-154	161	8	.	.	PUNCT
iajs-154	162	1	(	(	PUNCT
iajs-154	162	2			NOUN
iajs-154	162	3	)	)	PUNCT
iajs-154	162	4	assume	assume	VERB
iajs-154	162	5	n	n	PROPN
iajs-154	163	1	+	+	CCONJ
iajs-154	163	2	k	k	X
iajs-154	163	3	=	=	NOUN
iajs-154	163	4	m	m	VERB
iajs-154	163	5	with	with	ADP
iajs-154	163	6	k	k	PROPN
iajs-154	163	7	e	e	PROPN
iajs-154	163	8			PROPN
iajs-154	163	9	m.	m.	NOUN
iajs-154	163	10	since	since	SCONJ
iajs-154	163	11	m	m	PROPN
iajs-154	163	12	is	be	AUX
iajs-154	163	13	multiplication	multiplication	NOUN
iajs-154	163	14	n	n	NOUN
iajs-154	163	15	=	=	SYM
iajs-154	163	16	(	(	PUNCT
iajs-154	163	17	n	n	CCONJ
iajs-154	163	18	:	:	PUNCT
iajs-154	163	19	m)m	m)m	X
iajs-154	163	20	,	,	PUNCT
iajs-154	163	21	k	k	X
iajs-154	163	22	=	=	PRON
iajs-154	163	23	(	(	PUNCT
iajs-154	163	24	k	k	NOUN
iajs-154	163	25	:	:	PUNCT
iajs-154	163	26	m)m	m)m	NOUN
iajs-154	163	27	,	,	PUNCT
iajs-154	163	28	and	and	CCONJ
iajs-154	163	29	er	er	INTJ
iajs-154	163	30	(	(	PUNCT
iajs-154	163	31	k	k	NOUN
iajs-154	163	32	:	:	PUNCT
iajs-154	163	33	m	m	X
iajs-154	163	34	)	)	PUNCT
iajs-154	163	35	r	r	NOUN
iajs-154	163	36	by	by	ADP
iajs-154	163	37	[	[	X
iajs-154	163	38	1,theorem	1,theorem	NUM
iajs-154	163	39	2.13	2.13	NUM
iajs-154	163	40	]	]	PUNCT
iajs-154	163	41	.	.	PUNCT
iajs-154	164	1	thus	thus	ADV
iajs-154	164	2	(	(	PUNCT
iajs-154	164	3	n	n	NUM
iajs-154	164	4	:	:	X
iajs-154	164	5	m)m	m)m	X
iajs-154	165	1	+	+	CCONJ
iajs-154	165	2	k	k	X
iajs-154	165	3	:	:	X
iajs-154	165	4	m)m	m)m	X
iajs-154	165	5	=	=	SYM
iajs-154	165	6	m	m	NOUN
iajs-154	165	7	and	and	CCONJ
iajs-154	165	8	since	since	SCONJ
iajs-154	165	9	m	m	PROPN
iajs-154	165	10	is	be	AUX
iajs-154	165	11	a	a	DET
iajs-154	165	12	finitely	finitely	ADV
iajs-154	165	13	generated	generate	VERB
iajs-154	165	14	faithful	faithful	ADJ
iajs-154	165	15	multiplication	multiplication	NOUN
iajs-154	165	16	r	r	NOUN
iajs-154	165	17	-	-	PUNCT
iajs-154	165	18	module	module	NOUN
iajs-154	165	19	,	,	PUNCT
iajs-154	165	20	then	then	ADV
iajs-154	165	21	(	(	PUNCT
iajs-154	165	22	n	n	CCONJ
iajs-154	165	23	:	:	PUNCT
iajs-154	165	24	m	m	VERB
iajs-154	165	25	)	)	PUNCT
iajs-154	166	1	+	+	CCONJ
iajs-154	166	2	(	(	PUNCT
iajs-154	166	3	k	k	NOUN
iajs-154	166	4	:	:	PUNCT
iajs-154	166	5	m	m	VERB
iajs-154	166	6	)	)	PUNCT
iajs-154	166	7	=	=	SYM
iajs-154	166	8	r.	r.	NOUN
iajs-154	166	9	as	as	ADP
iajs-154	166	10	(	(	PUNCT
iajs-154	166	11	n	n	NUM
iajs-154	166	12	:	:	PUNCT
iajs-154	166	13	m	m	X
iajs-154	166	14	)	)	PUNCT
iajs-154	166	15	e	e	NOUN
iajs-154	166	16	r	r	NOUN
iajs-154	166	17	and	and	CCONJ
iajs-154	166	18	e	e	X
iajs-154	166	19	(	(	PUNCT
iajs-154	166	20	k	k	NOUN
iajs-154	166	21	:	:	PUNCT
iajs-154	166	22	m	m	X
iajs-154	166	23	)	)	PUNCT
iajs-154	166	24	r	r	NOUN
iajs-154	166	25	,	,	PUNCT
iajs-154	166	26	we	we	PRON
iajs-154	166	27	have	have	VERB
iajs-154	166	28	(	(	PUNCT
iajs-154	166	29	k	k	NOUN
iajs-154	166	30	:	:	PUNCT
iajs-154	166	31	m	m	VERB
iajs-154	166	32	)	)	PUNCT
iajs-154	167	1	=	=	PUNCT
iajs-154	167	2	r.	r.	NOUN
iajs-154	167	3	it	it	PRON
iajs-154	167	4	follows	follow	VERB
iajs-154	167	5	that	that	SCONJ
iajs-154	167	6	k	k	PROPN
iajs-154	167	7	=	=	PUNCT
iajs-154	167	8	m	m	PROPN
iajs-154	167	9	,	,	PUNCT
iajs-154	167	10	and	and	CCONJ
iajs-154	167	11	n	n	PRON
iajs-154	167	12	e	e	NOUN
iajs-154	167	13			PROPN
iajs-154	167	14	m.	m.	NOUN
iajs-154	167	15	corollary	corollary	NOUN
iajs-154	167	16	(	(	PUNCT
iajs-154	167	17	3.19	3.19	NUM
iajs-154	167	18	):	):	PUNCT
iajs-154	167	19	let	let	VERB
iajs-154	167	20	m	m	PRON
iajs-154	167	21	be	be	AUX
iajs-154	167	22	a	a	DET
iajs-154	167	23	faithful	faithful	ADJ
iajs-154	167	24	finitely	finitely	ADV
iajs-154	167	25	generated	generate	VERB
iajs-154	167	26	multiplication	multiplication	NOUN
iajs-154	167	27	r	r	NOUN
iajs-154	167	28	-	-	PUNCT
iajs-154	167	29	module	module	NOUN
iajs-154	167	30	,	,	PUNCT
iajs-154	167	31	let	let	VERB
iajs-154	167	32	n	n	PRON
iajs-154	167	33	<	<	X
iajs-154	167	34	m.	m.	NOUN
iajs-154	167	35	the	the	DET
iajs-154	167	36	following	follow	VERB
iajs-154	167	37	statements	statement	NOUN
iajs-154	167	38	are	be	AUX
iajs-154	167	39	equivalent	equivalent	ADJ
iajs-154	167	40	:	:	PUNCT
iajs-154	167	41	(	(	PUNCT
iajs-154	167	42	1	1	X
iajs-154	167	43	)	)	PUNCT
iajs-154	167	44	n	n	NOUN
iajs-154	167	45	e	e	NOUN
iajs-154	167	46			PROPN
iajs-154	167	47	m.	m.	NOUN
iajs-154	167	48	(	(	PUNCT
iajs-154	167	49	2	2	NUM
iajs-154	167	50	)	)	PUNCT
iajs-154	167	51	(	(	PUNCT
iajs-154	167	52	n	n	CCONJ
iajs-154	167	53	:	:	PUNCT
iajs-154	167	54	m	m	X
iajs-154	167	55	)	)	PUNCT
iajs-154	168	1	e	e	X
iajs-154	168	2			PROPN
iajs-154	168	3	r.	r.	PROPN
iajs-154	168	4	(	(	PUNCT
iajs-154	168	5	3	3	NUM
iajs-154	168	6	)	)	PUNCT
iajs-154	168	7	n	n	NOUN
iajs-154	168	8	=	=	SYM
iajs-154	168	9	i	i	PRON
iajs-154	168	10	m	m	VERB
iajs-154	168	11	for	for	ADP
iajs-154	168	12	some	some	PRON
iajs-154	169	1	i	i	PRON
iajs-154	169	2	e	e	PROPN
iajs-154	169	3			PROPN
iajs-154	169	4	r.	r.	PROPN
iajs-154	169	5	references	reference	NOUN
iajs-154	169	6	1	1	NUM
iajs-154	169	7	.	.	PUNCT
iajs-154	170	1	fleury	fleury	PROPN
iajs-154	170	2	,	,	PUNCT
iajs-154	170	3	p.	p.	PROPN
iajs-154	170	4	,	,	PUNCT
iajs-154	170	5	(	(	PUNCT
iajs-154	170	6	1974	1974	NUM
iajs-154	170	7	)	)	PUNCT
iajs-154	170	8	,	,	PUNCT
iajs-154	170	9	hollow	hollow	ADJ
iajs-154	170	10	modules	module	NOUN
iajs-154	170	11	and	and	CCONJ
iajs-154	170	12	local	local	ADJ
iajs-154	170	13	endomorphism	endomorphism	NOUN
iajs-154	170	14	rings	ring	NOUN
iajs-154	170	15	,	,	PUNCT
iajs-154	170	16	pac.j.math	pac.j.math	NOUN
iajs-154	170	17	.	.	PROPN
iajs-154	170	18	,	,	PUNCT
iajs-154	170	19	53	53	NUM
iajs-154	170	20	,	,	PUNCT
iajs-154	170	21	379	379	NUM
iajs-154	170	22	-	-	SYM
iajs-154	170	23	385	385	NUM
iajs-154	170	24	.	.	PUNCT
iajs-154	171	1	2	2	NUM
iajs-154	171	2	.	.	X
iajs-154	171	3	zhou	zhou	PROPN
iajs-154	171	4	,	,	PUNCT
iajs-154	171	5	y.q	y.q	PROPN
iajs-154	171	6	.	.	PROPN
iajs-154	171	7	,	,	PUNCT
iajs-154	171	8	(	(	PUNCT
iajs-154	171	9	2000	2000	NUM
iajs-154	171	10	)	)	PUNCT
iajs-154	171	11	,	,	PUNCT
iajs-154	171	12	generalizations	generalization	NOUN
iajs-154	171	13	of	of	ADP
iajs-154	171	14	perfect	perfect	ADJ
iajs-154	171	15	semiperfect	semiperfect	NOUN
iajs-154	171	16	and	and	CCONJ
iajs-154	171	17	semiregular	semiregular	NOUN
iajs-154	171	18	rings	ring	NOUN
iajs-154	171	19	,	,	PUNCT
iajs-154	171	20	algebra	algebra	PROPN
iajs-154	171	21	college	college	NOUN
iajs-154	171	22	,	,	PUNCT
iajs-154	171	23	7	7	NUM
iajs-154	171	24	,	,	PUNCT
iajs-154	171	25	305	305	NUM
iajs-154	171	26	-	-	SYM
iajs-154	171	27	318	318	NUM
iajs-154	171	28	.	.	PUNCT
iajs-154	172	1	3	3	X
iajs-154	172	2	.	.	X
iajs-154	172	3	kasch	kasch	PROPN
iajs-154	172	4	,	,	PUNCT
iajs-154	172	5	f.	f.	PROPN
iajs-154	172	6	,	,	PUNCT
iajs-154	172	7	(	(	PUNCT
iajs-154	172	8	1982	1982	NUM
iajs-154	172	9	)	)	PUNCT
iajs-154	172	10	,	,	PUNCT
iajs-154	172	11	modules	module	NOUN
iajs-154	172	12	and	and	CCONJ
iajs-154	172	13	rings	ring	NOUN
iajs-154	172	14	,	,	PUNCT
iajs-154	172	15	academic	academic	ADJ
iajs-154	172	16	press	press	NOUN
iajs-154	172	17	,	,	PUNCT
iajs-154	172	18	inc	inc	PROPN
iajs-154	172	19	-	-	PROPN
iajs-154	172	20	london	london	PROPN
iajs-154	172	21	.	.	PUNCT
iajs-154	173	1	4	4	X
iajs-154	173	2	.	.	X
iajs-154	173	3	zhou	zhou	PROPN
iajs-154	173	4	,	,	PUNCT
iajs-154	173	5	d.x	d.x	PROPN
iajs-154	173	6	.	.	PROPN
iajs-154	173	7	and	and	CCONJ
iajs-154	173	8	zhang	zhang	PROPN
iajs-154	173	9	,	,	PUNCT
iajs-154	173	10	x.r	x.r	PROPN
iajs-154	173	11	.	.	PROPN
iajs-154	173	12	,	,	PUNCT
iajs-154	173	13	(	(	PUNCT
iajs-154	173	14	2011	2011	NUM
iajs-154	173	15	)	)	PUNCT
iajs-154	173	16	,	,	PUNCT
iajs-154	173	17	small	small	ADJ
iajs-154	173	18	-	-	PUNCT
iajs-154	173	19	essential	essential	ADJ
iajs-154	173	20	submodules	submodule	NOUN
iajs-154	173	21	and	and	CCONJ
iajs-154	173	22	morita	morita	PROPN
iajs-154	173	23	duality	duality	PROPN
iajs-154	173	24	,	,	PUNCT
iajs-154	173	25	southeast	southeast	ADJ
iajs-154	173	26	asian	asian	ADJ
iajs-154	173	27	bull	bull	NOUN
iajs-154	173	28	.	.	PUNCT
iajs-154	174	1	math	math	NOUN
iajs-154	174	2	.	.	PUNCT
iajs-154	174	3	,	,	PUNCT
iajs-154	174	4	35	35	NUM
iajs-154	174	5	,	,	PUNCT
iajs-154	174	6	1051	1051	NUM
iajs-154	174	7	-	-	SYM
iajs-154	174	8	1062	1062	NUM
iajs-154	174	9	.	.	PUNCT
iajs-154	175	1	221	221	NUM
iajs-154	175	2	|	|	NOUN
iajs-154	175	3	mathematics	mathematic	NOUN
iajs-154	175	4	2015	2015	NUM
iajs-154	175	5	)	)	PUNCT
iajs-154	175	6	عام	عام	ADP
iajs-154	175	7	3العدد	3العدد	NUM
iajs-154	175	8	(	(	PUNCT
iajs-154	175	9	28مجلة	28مجلة	X
iajs-154	175	10	إبن	إبن	VERB
iajs-154	175	11	الهيثم	الهيثم	ADJ
iajs-154	175	12	للعلوم	للعلوم	NOUN
iajs-154	175	13	الصرفة	الصرفة	NOUN
iajs-154	176	1	و	و	PRON
iajs-154	176	2	التطبيقية	التطبيقية	ADV
iajs-154	176	3	المجلد	المجلد	VERB
iajs-154	176	4	ibn	ibn	PROPN
iajs-154	176	5	al	al	PROPN
iajs-154	176	6	-	-	PUNCT
iajs-154	176	7	haitham	haitham	PROPN
iajs-154	176	8	jour	jour	X
iajs-154	176	9	.	.	PROPN
iajs-154	177	1	for	for	ADP
iajs-154	177	2	pure	pure	ADJ
iajs-154	177	3	&	&	CCONJ
iajs-154	177	4	appl	appl	PROPN
iajs-154	177	5	.	.	PUNCT
iajs-154	178	1	sci	sci	PROPN
iajs-154	178	2	.	.	PUNCT
iajs-154	178	3	vol	vol	NOUN
iajs-154	178	4	.	.	PROPN
iajs-154	179	1	28	28	NUM
iajs-154	179	2	(	(	PUNCT
iajs-154	179	3	3	3	NUM
iajs-154	179	4	)	)	PUNCT
iajs-154	179	5	2015	2015	NUM
iajs-154	179	6	5	5	NUM
iajs-154	179	7	.	.	PUNCT
iajs-154	180	1	golan	golan	PROPN
iajs-154	180	2	,	,	PUNCT
iajs-154	180	3	j.s	j.s	PROPN
iajs-154	180	4	.	.	PROPN
iajs-154	180	5	,	,	PUNCT
iajs-154	180	6	(	(	PUNCT
iajs-154	180	7	1971	1971	NUM
iajs-154	180	8	)	)	PUNCT
iajs-154	180	9	,	,	PUNCT
iajs-154	180	10	quasi	quasi	ADJ
iajs-154	180	11	-	-	ADJ
iajs-154	180	12	semiperfect	semiperfect	ADJ
iajs-154	180	13	modules	module	NOUN
iajs-154	180	14	,	,	PUNCT
iajs-154	180	15	quart	quart	NOUN
iajs-154	180	16	,	,	PUNCT
iajs-154	180	17	j.math.oxford	j.math.oxford	PROPN
iajs-154	180	18	,	,	PUNCT
iajs-154	180	19	2	2	NUM
iajs-154	180	20	,	,	PUNCT
iajs-154	180	21	22173	22173	NUM
iajs-154	180	22	-	-	SYM
iajs-154	180	23	182	182	NUM
iajs-154	180	24	.	.	PUNCT
iajs-154	181	1	6	6	NUM
iajs-154	181	2	.	.	X
iajs-154	182	1	lomp	lomp	PROPN
iajs-154	182	2	,	,	PUNCT
iajs-154	182	3	c.	c.	PROPN
iajs-154	182	4	,	,	PUNCT
iajs-154	182	5	(	(	PUNCT
iajs-154	182	6	1991	1991	NUM
iajs-154	182	7	)	)	PUNCT
iajs-154	182	8	,	,	PUNCT
iajs-154	182	9	on	on	ADP
iajs-154	182	10	dual	dual	ADJ
iajs-154	182	11	goldie	goldie	PROPN
iajs-154	182	12	dimension	dimension	PROPN
iajs-154	182	13	,	,	PUNCT
iajs-154	182	14	diplama	diplama	NOUN
iajs-154	182	15	thesis	thesis	NOUN
iajs-154	182	16	,	,	PUNCT
iajs-154	182	17	univ	univ	PROPN
iajs-154	182	18	.	.	PROPN
iajs-154	182	19	of	of	ADP
iajs-154	182	20	dussel	dussel	PROPN
iajs-154	182	21	dorf	dorf	PROPN
iajs-154	182	22	.	.	PUNCT
iajs-154	183	1	7	7	X
iajs-154	183	2	.	.	X
iajs-154	183	3	marhoon	marhoon	NOUN
iajs-154	183	4	,	,	PUNCT
iajs-154	183	5	h.k	h.k	PROPN
iajs-154	183	6	.	.	PROPN
iajs-154	183	7	,	,	PUNCT
iajs-154	183	8	(	(	PUNCT
iajs-154	183	9	2014	2014	NUM
iajs-154	183	10	)	)	PUNCT
iajs-154	183	11	some	some	DET
iajs-154	183	12	generalizations	generalization	NOUN
iajs-154	183	13	of	of	ADP
iajs-154	183	14	monoform	monoform	NOUN
iajs-154	183	15	modules	module	NOUN
iajs-154	183	16	,	,	PUNCT
iajs-154	183	17	ms.c	ms.c	ADJ
iajs-154	183	18	thesis	thesis	NOUN
iajs-154	183	19	,	,	PUNCT
iajs-154	183	20	university	university	NOUN
iajs-154	183	21	of	of	ADP
iajs-154	183	22	baghdad	baghdad	PROPN
iajs-154	183	23	.	.	PUNCT
iajs-154	184	1	8	8	X
iajs-154	184	2	.	.	X
iajs-154	184	3	goodearl	goodearl	PROPN
iajs-154	184	4	,	,	PUNCT
iajs-154	184	5	k.r	k.r	PROPN
iajs-154	184	6	.	.	PROPN
iajs-154	184	7	,	,	PUNCT
iajs-154	184	8	(	(	PUNCT
iajs-154	184	9	1976	1976	NUM
iajs-154	184	10	)	)	PUNCT
iajs-154	184	11	,	,	PUNCT
iajs-154	184	12	ring	ring	NOUN
iajs-154	184	13	theory	theory	NOUN
iajs-154	184	14	nonsingular	nonsingular	PROPN
iajs-154	184	15	rings	ring	NOUN
iajs-154	184	16	and	and	CCONJ
iajs-154	184	17	modules	module	NOUN
iajs-154	184	18	,	,	PUNCT
iajs-154	184	19	marcel	marcel	PROPN
iajs-154	184	20	dekkl	dekkl	PROPN
iajs-154	184	21	.	.	PUNCT
iajs-154	185	1	9	9	X
iajs-154	185	2	.	.	X
iajs-154	186	1	elbast	elbast	ADJ
iajs-154	186	2	,	,	PUNCT
iajs-154	186	3	z.a	z.a	PROPN
iajs-154	186	4	.	.	PROPN
iajs-154	186	5	and	and	CCONJ
iajs-154	186	6	smith	smith	PROPN
iajs-154	186	7	,	,	PUNCT
iajs-154	186	8	p.f	p.f	PROPN
iajs-154	186	9	.	.	PROPN
iajs-154	186	10	,	,	PUNCT
iajs-154	186	11	(	(	PUNCT
iajs-154	186	12	1988	1988	NUM
iajs-154	186	13	)	)	PUNCT
iajs-154	186	14	,	,	PUNCT
iajs-154	186	15	multiplication	multiplication	NOUN
iajs-154	186	16	modules	module	NOUN
iajs-154	186	17	,	,	PUNCT
iajs-154	186	18	commuinication	commuinication	NOUN
iajs-154	186	19	in	in	ADP
iajs-154	186	20	algebra	algebra	NOUN
iajs-154	186	21	,	,	PUNCT
iajs-154	186	22	10	10	NUM
iajs-154	186	23	,	,	PUNCT
iajs-154	186	24	4	4	NUM
iajs-154	186	25	.	.	NOUN
iajs-154	186	26	222	222	NUM
iajs-154	186	27	|	|	ADV
iajs-154	186	28	mathematics	mathematic	NOUN
iajs-154	186	29	2015	2015	NUM
iajs-154	186	30	)	)	PUNCT
iajs-154	186	31	عام	عام	ADP
iajs-154	186	32	3العدد	3العدد	NUM
iajs-154	186	33	(	(	PUNCT
iajs-154	186	34	28مجلة	28مجلة	X
iajs-154	186	35	إبن	إبن	VERB
iajs-154	186	36	الهيثم	الهيثم	ADJ
iajs-154	186	37	للعلوم	للعلوم	NOUN
iajs-154	186	38	الصرفة	الصرفة	NOUN
iajs-154	187	1	و	و	PRON
iajs-154	187	2	التطبيقية	التطبيقية	ADV
iajs-154	187	3	المجلد	المجلد	VERB
iajs-154	187	4	ibn	ibn	PROPN
iajs-154	187	5	al	al	PROPN
iajs-154	187	6	-	-	PUNCT
iajs-154	187	7	haitham	haitham	PROPN
iajs-154	187	8	jour	jour	X
iajs-154	187	9	.	.	PROPN
iajs-154	188	1	for	for	ADP
iajs-154	188	2	pure	pure	ADJ
iajs-154	188	3	&	&	CCONJ
iajs-154	188	4	appl	appl	PROPN
iajs-154	188	5	.	.	PUNCT
iajs-154	189	1	sci	sci	PROPN
iajs-154	189	2	.	.	PUNCT
iajs-154	189	3	vol	vol	NOUN
iajs-154	189	4	.	.	PROPN
iajs-154	190	1	28	28	NUM
iajs-154	190	2	(	(	PUNCT
iajs-154	190	3	3	3	NUM
iajs-154	190	4	)	)	PUNCT
iajs-154	190	5	2015	2015	NUM
iajs-154	191	1	e	e	NOUN
iajs-154	191	2	-	-	NOUN
iajs-154	191	3	الجزئية	الجزئية	ADJ
iajs-154	191	4	الصغيرة	الصغيرة	NOUN
iajs-154	191	5	من	من	DET
iajs-154	191	6	النمط	النمط	PROPN
iajs-154	191	7	حول	حول	PROPN
iajs-154	191	8	المقاسات	المقاسات	PROPN
iajs-154	191	9	أنعام	أنعام	PROPN
iajs-154	191	10	محمد	محمد	PROPN
iajs-154	191	11	علي	علي	NOUN
iajs-154	191	12	هادي	هادي	NOUN
iajs-154	191	13	سميعة	سميعة	NOUN
iajs-154	191	14	حسون	حسون	PROPN
iajs-154	191	15	عيدي	عيدي	PROPN
iajs-154	191	16	جامعة	جامعة	PROPN
iajs-154	191	17	بغداد	بغداد	PROPN
iajs-154	191	18	/)ابن	/)ابن	SYM
iajs-154	191	19	الهيثم	الهيثم	PROPN
iajs-154	191	20	(	(	PUNCT
iajs-154	191	21	كلية	كلية	NOUN
iajs-154	191	22	التربية	التربية	NOUN
iajs-154	191	23	للعلوم	للعلوم	NOUN
iajs-154	191	24	الصرفة	الصرفة	NOUN
iajs-154	191	25	/قسم	/قسم	PUNCT
iajs-154	192	1	الرياضيات	الرياضيات	NOUN
iajs-154	192	2	2015	2015	NUM
iajs-154	192	3	/	/	SYM
iajs-154	192	4	أيلول/20قبل	أيلول/20قبل	PROPN
iajs-154	192	5	البحث	البحث	VERB
iajs-154	192	6	في	في	ADP
iajs-154	192	7	:	:	PUNCT
iajs-154	192	8	،	،	NOUN
iajs-154	192	9	2015	2015	NUM
iajs-154	192	10	/	/	SYM
iajs-154	192	11	حزيران/3استلم	حزيران/3استلم	PUNCT
iajs-154	192	12	البحث	البحث	NOUN
iajs-154	192	13	في	في	PROPN
iajs-154	192	14	:	:	PUNCT
iajs-154	192	15	خالصةال	خالصةال	PROPN
iajs-154	192	16	(	(	PUNCT
iajs-154	192	17	يرمز	يرمز	INTJ
iajs-154	192	18	له	له	X
iajs-154	192	19	e	e	PROPN
iajs-154	192	20	–	–	PUNCT
iajs-154	192	21	يسمى	يسمى	NOUN
iajs-154	192	22	مقاسا	مقاسا	NOUN
iajs-154	192	23	ً	ً	NOUN
iajs-154	192	24	جزئيا	جزئيا	NOUN
iajs-154	192	25	ً	ً	NOUN
iajs-154	192	26	من	من	DET
iajs-154	192	27	النمط	النمط	PROPN
iajs-154	192	28	mفي	mفي	PROPN
iajs-154	192	29	nحلقة	nحلقة	PROPN
iajs-154	192	30	ابدالية	ابدالية	PROPN
iajs-154	192	31	ذات	ذات	NOUN
iajs-154	192	32	محايد	محايد	NOUN
iajs-154	192	33	.	.	PUNCT
iajs-154	193	1	المقاس	المقاس	PROPN
iajs-154	193	2	r	r	PROPN
iajs-154	193	3	،	،	NOUN
iajs-154	193	4	إذ	إذ	NOUN
iajs-154	193	5	rمقاسا	rمقاسا	NOUN
iajs-154	193	6	ً	ً	NOUN
iajs-154	193	7	على	على	NOUN
iajs-154	193	8	mليكن	mليكن	NOUN
iajs-154	193	9	mبالرمز	mبالرمز	PROPN
iajs-154	193	10	e	e	NOUN
iajs-154	193	11	n	n	PROPN
iajs-154	193	12	اذا	اذا	NOUN
iajs-154	193	13	كان	كان	NOUN
iajs-154	193	14	(	(	PUNCT
iajs-154	193	15	n	n	PROPN
iajs-154	193	16	+	+	CCONJ
iajs-154	193	17	k	k	NOUN
iajs-154	193	18	=	=	PUNCT
iajs-154	193	19	m	m	VERB
iajs-154	193	20	إذ	إذ	NOUN
iajs-154	193	21	،	،	NOUN
iajs-154	193	22	m	m	VERB
iajs-154	193	23	e	e	NOUN
iajs-154	193	24	k	k	PROPN
iajs-154	193	25	تؤدي	تؤدي	ADJ
iajs-154	193	26	الىk	الىk	NOUN
iajs-154	193	27	=	=	PUNCT
iajs-154	194	1	m	m	PROPN
iajs-154	194	2	اعطينا	اعطينا	NOUN
iajs-154	195	1	العديد	العديد	INTJ
iajs-154	195	2	من	من	INTJ
iajs-154	196	1	الخواص	الخواص	INTJ
iajs-154	196	2	المتعلقة	المتعلقة	INTJ
iajs-154	196	3	لهذا	لهذا	X
iajs-154	196	4	.	.	PUNCT
iajs-154	197	1	النمط	النمط	PROPN
iajs-154	198	1	من	من	PRON
iajs-154	198	2	المقاسات	المقاسات	PROPN
iajs-154	198	3	الجزئية	الجزئية	PROPN
iajs-154	198	4	.	.	PUNCT
iajs-154	199	1	،	،	PROPN
iajs-154	199	2	e	e	X
iajs-154	199	3	–	–	PUNCT
iajs-154	199	4	،	،	PROPN
iajs-154	199	5	مقاس	مقاس	PROPN
iajs-154	199	6	جزئي	جزئي	NOUN
iajs-154	199	7	صغير	صغير	PROPN
iajs-154	199	8	من	من	NUM
iajs-154	199	9	النمط	النمط	PROPN
iajs-154	199	10			NUM
iajs-154	199	11	-مقاس	-مقاس	PROPN
iajs-154	199	12	جزئي	جزئي	NOUN
iajs-154	199	13	صغير	صغير	PROPN
iajs-154	199	14	،	،	PROPN
iajs-154	199	15	مقاس	مقاس	PROPN
iajs-154	199	16	جزئي	جزئي	NOUN
iajs-154	199	17	صغير	صغير	PROPN
iajs-154	199	18	من	من	PROPN
iajs-154	199	19	النمط	النمط	NOUN
iajs-154	199	20	:	:	PUNCT
iajs-154	199	21	المفتاحيةالكلمات	المفتاحيةالكلمات	ADJ
iajs-154	199	22	.e	.e	PROPN
iajs-154	199	23	-و	-و	PUNCT
iajs-154	199	24	مقاس	مقاس	PROPN
iajs-154	199	25	جزئي	جزئي	NOUN
iajs-154	199	26	ضد	ضد	PROPN
iajs-154	199	27	مغلق	مغلق	PROPN
iajs-154	199	28	من	من	PROPN
iajs-154	199	29	النمط	النمط	NOUN