id	sid	tid	token	lemma	pos
iajs-1071	1	1	conseguences	conseguence	NOUN
iajs-1071	1	2	of	of	ADP
iajs-1071	1	3	soil	soil	NOUN
iajs-1071	1	4	crude	crude	ADJ
iajs-1071	1	5	oil	oil	NOUN
iajs-1071	1	6	pollution	pollution	NOUN
iajs-1071	1	7	on	on	ADP
iajs-1071	1	8	some	some	DET
iajs-1071	1	9	wood	wood	NOUN
iajs-1071	1	10	properties	property	NOUN
iajs-1071	1	11	of	of	ADP
iajs-1071	1	12	olive	olive	NOUN
iajs-1071	1	13	trees	tree	NOUN
iajs-1071	1	14	mathematics	mathematic	NOUN
iajs-1071	1	15	|	|	ADV
iajs-1071	1	16	192	192	NUM
iajs-1071	1	17	2012	2012	NUM
iajs-1071	1	18	(	(	PUNCT
iajs-1071	1	19	عام	عام	PROPN
iajs-1071	1	20	1	1	NUM
iajs-1071	1	21	)	)	PUNCT
iajs-1071	1	22	(	(	PUNCT
iajs-1071	1	23	العدد	العدد	PROPN
iajs-1071	1	24	30مجلة	30مجلة	NUM
iajs-1071	1	25	إبن	إبن	VERB
iajs-1071	1	26	الهيثم	الهيثم	ADJ
iajs-1071	1	27	للعلوم	للعلوم	NOUN
iajs-1071	1	28	الصرفة	الصرفة	NOUN
iajs-1071	2	1	و	و	PRON
iajs-1071	2	2	التطبيقية	التطبيقية	ADV
iajs-1071	2	3	المجلد	المجلد	ADV
iajs-1071	2	4	)	)	PUNCT
iajs-1071	3	1	ibn	ibn	PROPN
iajs-1071	3	2	al	al	PROPN
iajs-1071	3	3	-	-	PUNCT
iajs-1071	3	4	haitham	haitham	PROPN
iajs-1071	3	5	j.	j.	PROPN
iajs-1071	3	6	for	for	ADP
iajs-1071	3	7	pure	pure	PROPN
iajs-1071	3	8	&	&	CCONJ
iajs-1071	3	9	appl	appl	PROPN
iajs-1071	3	10	.	.	PUNCT
iajs-1071	4	1	sci	sci	PROPN
iajs-1071	4	2	.	.	PUNCT
iajs-1071	5	1	vol.30	vol.30	NOUN
iajs-1071	5	2	(	(	PUNCT
iajs-1071	5	3	1	1	NUM
iajs-1071	5	4	)	)	PUNCT
iajs-1071	5	5	2017	2017	NUM
iajs-1071	5	6	quasi	quasi	ADJ
iajs-1071	5	7	-	-	ADJ
iajs-1071	5	8	fully	fully	ADV
iajs-1071	5	9	cancellation	cancellation	NOUN
iajs-1071	5	10	fuzzy	fuzzy	ADJ
iajs-1071	5	11	modules	module	NOUN
iajs-1071	5	12	hatem	hatem	PROPN
iajs-1071	5	13	yahya	yahya	PROPN
iajs-1071	5	14	khalaf	khalaf	PROPN
iajs-1071	5	15	department	department	PROPN
iajs-1071	5	16	of	of	ADP
iajs-1071	5	17	mathematics/	mathematics/	PROPN
iajs-1071	5	18	college	college	NOUN
iajs-1071	5	19	of	of	ADP
iajs-1071	5	20	education(ibn	education(ibn	PROPN
iajs-1071	5	21	-	-	PUNCT
iajs-1071	5	22	al	al	PROPN
iajs-1071	5	23	-	-	PUNCT
iajs-1071	5	24	haitham	haitham	PROPN
iajs-1071	5	25	)	)	PUNCT
iajs-1071	5	26	,	,	PUNCT
iajs-1071	5	27	university	university	NOUN
iajs-1071	5	28	of	of	ADP
iajs-1071	5	29	baghdad	baghdad	PROPN
iajs-1071	5	30	hadi	hadi	PROPN
iajs-1071	5	31	ghali	ghali	PROPN
iajs-1071	5	32	rashed	rashe	VERB
iajs-1071	5	33	al	al	PROPN
iajs-1071	5	34	-	-	PUNCT
iajs-1071	5	35	rusafa	rusafa	PROPN
iajs-1071	5	36	the	the	DET
iajs-1071	5	37	first	first	ADJ
iajs-1071	5	38	education/	education/	PROPN
iajs-1071	5	39	ministry	ministry	PROPN
iajs-1071	5	40	of	of	ADP
iajs-1071	5	41	education	education	PROPN
iajs-1071	5	42	received	receive	VERB
iajs-1071	5	43	in	in	ADP
iajs-1071	5	44	5	5	NUM
iajs-1071	5	45	/	/	SYM
iajs-1071	5	46	december	december	PROPN
iajs-1071	5	47	/2016	/2016	PUNCT
iajs-1071	5	48	accepted	accept	VERB
iajs-1071	5	49	in	in	ADP
iajs-1071	5	50	:	:	PUNCT
iajs-1071	5	51	28	28	NUM
iajs-1071	5	52	/	/	SYM
iajs-1071	5	53	decmber/2016	decmber/2016	PROPN
iajs-1071	5	54	abstract	abstract	ADV
iajs-1071	5	55	in	in	ADP
iajs-1071	5	56	this	this	DET
iajs-1071	5	57	paper	paper	NOUN
iajs-1071	5	58	it	it	PRON
iajs-1071	5	59	was	be	AUX
iajs-1071	5	60	presented	present	VERB
iajs-1071	5	61	the	the	DET
iajs-1071	5	62	idea	idea	NOUN
iajs-1071	5	63	quasi	quasi	ADJ
iajs-1071	5	64	-	-	ADJ
iajs-1071	5	65	fully	fully	ADV
iajs-1071	5	66	cancellation	cancellation	NOUN
iajs-1071	5	67	fuzzy	fuzzy	ADJ
iajs-1071	5	68	modules	module	NOUN
iajs-1071	5	69	and	and	CCONJ
iajs-1071	5	70	we	we	PRON
iajs-1071	5	71	will	will	AUX
iajs-1071	5	72	denote	denote	VERB
iajs-1071	5	73	it	it	PRON
iajs-1071	5	74	by	by	ADP
iajs-1071	5	75	q	q	NOUN
iajs-1071	5	76	-	-	PUNCT
iajs-1071	5	77	fcf(m	fcf(m	NOUN
iajs-1071	5	78	)	)	PUNCT
iajs-1071	5	79	,	,	PUNCT
iajs-1071	6	1	condition	condition	NOUN
iajs-1071	6	2	universalistic	universalistic	ADJ
iajs-1071	6	3	idea	idea	NOUN
iajs-1071	6	4	quasi	quasi	ADJ
iajs-1071	6	5	-	-	ADJ
iajs-1071	6	6	fully	fully	ADV
iajs-1071	6	7	cancellation	cancellation	NOUN
iajs-1071	6	8	modules	module	NOUN
iajs-1071	6	9	it	it	PRON
iajs-1071	6	10	.has	.has	PUNCT
iajs-1071	6	11	been	be	AUX
iajs-1071	6	12	circulated	circulate	VERB
iajs-1071	6	13	to	to	ADP
iajs-1071	6	14	this	this	DET
iajs-1071	6	15	idea	idea	NOUN
iajs-1071	6	16	quasi	quasi	NOUN
iajs-1071	6	17	-	-	ADJ
iajs-1071	6	18	max	max	ADJ
iajs-1071	6	19	fully	fully	ADV
iajs-1071	6	20	cancellation	cancellation	NOUN
iajs-1071	6	21	fuzzy	fuzzy	ADJ
iajs-1071	6	22	modules	module	NOUN
iajs-1071	6	23	and	and	CCONJ
iajs-1071	6	24	we	we	PRON
iajs-1071	6	25	will	will	AUX
iajs-1071	6	26	denote	denote	VERB
iajs-1071	6	27	it	it	PRON
iajs-1071	6	28	by	by	ADP
iajs-1071	6	29	q	q	NOUN
iajs-1071	6	30	-	-	PUNCT
iajs-1071	6	31	mfcf(m	mfcf(m	NOUN
iajs-1071	6	32	)	)	PUNCT
iajs-1071	6	33	.	.	PUNCT
iajs-1071	7	1	lot	lot	NOUN
iajs-1071	7	2	of	of	ADP
iajs-1071	7	3	results	result	NOUN
iajs-1071	7	4	and	and	CCONJ
iajs-1071	7	5	properties	property	NOUN
iajs-1071	7	6	have	have	AUX
iajs-1071	7	7	been	be	AUX
iajs-1071	7	8	studied	study	VERB
iajs-1071	7	9	in	in	ADP
iajs-1071	7	10	this	this	DET
iajs-1071	7	11	research	research	NOUN
iajs-1071	7	12	.	.	PUNCT
iajs-1071	8	1	key	key	ADJ
iajs-1071	8	2	word	word	NOUN
iajs-1071	8	3	:	:	PUNCT
iajs-1071	8	4	q	q	X
iajs-1071	8	5	-	-	PUNCT
iajs-1071	8	6	fcf(m	fcf(m	NOUN
iajs-1071	8	7	)	)	PUNCT
iajs-1071	8	8	,	,	PUNCT
iajs-1071	8	9	q	q	NOUN
iajs-1071	8	10	-	-	PUNCT
iajs-1071	8	11	mfcf(m	mfcf(m	NOUN
iajs-1071	8	12	)	)	PUNCT
iajs-1071	8	13	,	,	PUNCT
iajs-1071	8	14	direct	direct	ADJ
iajs-1071	8	15	sum	sum	NOUN
iajs-1071	8	16	q	q	NOUN
iajs-1071	8	17	-	-	PUNCT
iajs-1071	8	18	fcf(m	fcf(m	NOUN
iajs-1071	8	19	)	)	PUNCT
iajs-1071	8	20	.	.	PUNCT
iajs-1071	9	1	mathematics	mathematic	NOUN
iajs-1071	9	2	|	|	ADV
iajs-1071	9	3	193	193	NUM
iajs-1071	9	4	2012	2012	NUM
iajs-1071	9	5	(	(	PUNCT
iajs-1071	9	6	عام	عام	PROPN
iajs-1071	9	7	1	1	NUM
iajs-1071	9	8	)	)	PUNCT
iajs-1071	9	9	(	(	PUNCT
iajs-1071	9	10	العدد	العدد	PROPN
iajs-1071	9	11	30مجلة	30مجلة	NUM
iajs-1071	9	12	إبن	إبن	VERB
iajs-1071	9	13	الهيثم	الهيثم	ADJ
iajs-1071	9	14	للعلوم	للعلوم	NOUN
iajs-1071	9	15	الصرفة	الصرفة	NOUN
iajs-1071	10	1	و	و	PRON
iajs-1071	10	2	التطبيقية	التطبيقية	ADV
iajs-1071	10	3	المجلد	المجلد	ADV
iajs-1071	10	4	)	)	PUNCT
iajs-1071	11	1	ibn	ibn	PROPN
iajs-1071	11	2	al	al	PROPN
iajs-1071	11	3	-	-	PUNCT
iajs-1071	11	4	haitham	haitham	PROPN
iajs-1071	11	5	j.	j.	PROPN
iajs-1071	11	6	for	for	ADP
iajs-1071	11	7	pure	pure	PROPN
iajs-1071	11	8	&	&	CCONJ
iajs-1071	11	9	appl	appl	PROPN
iajs-1071	11	10	.	.	PUNCT
iajs-1071	12	1	sci	sci	PROPN
iajs-1071	12	2	.	.	PUNCT
iajs-1071	13	1	vol.30	vol.30	NOUN
iajs-1071	13	2	(	(	PUNCT
iajs-1071	13	3	1	1	NUM
iajs-1071	13	4	)	)	PUNCT
iajs-1071	13	5	2017	2017	NUM
iajs-1071	13	6	introduction	introduction	NOUN
iajs-1071	13	7	let	let	VERB
iajs-1071	13	8	r	r	PRON
iajs-1071	13	9	be	be	AUX
iajs-1071	13	10	a	a	DET
iajs-1071	13	11	commutative	commutative	ADJ
iajs-1071	13	12	ring	ring	NOUN
iajs-1071	13	13	with	with	ADP
iajs-1071	13	14	identity	identity	NOUN
iajs-1071	13	15	.	.	PUNCT
iajs-1071	14	1	let	let	VERB
iajs-1071	14	2	x	x	PRON
iajs-1071	14	3	be	be	AUX
iajs-1071	14	4	a	a	DET
iajs-1071	14	5	fuzzy	fuzzy	ADJ
iajs-1071	14	6	module	module	NOUN
iajs-1071	14	7	of	of	ADP
iajs-1071	14	8	an	an	DET
iajs-1071	14	9	r	r	NOUN
iajs-1071	14	10	-	-	PUNCT
iajs-1071	14	11	module	module	NOUN
iajs-1071	14	12	m	m	NOUN
iajs-1071	14	13	and	and	CCONJ
iajs-1071	14	14	we	we	PRON
iajs-1071	14	15	will	will	AUX
iajs-1071	14	16	denote	denote	VERB
iajs-1071	14	17	it	it	PRON
iajs-1071	14	18	by	by	ADP
iajs-1071	14	19	(	(	PUNCT
iajs-1071	14	20	x	x	INTJ
iajs-1071	14	21	be	be	AUX
iajs-1071	14	22	f(m	f(m	PROPN
iajs-1071	14	23	)	)	PUNCT
iajs-1071	14	24	)	)	PUNCT
iajs-1071	14	25	.	.	PUNCT
iajs-1071	15	1	x	x	PUNCT
iajs-1071	15	2	is	be	AUX
iajs-1071	15	3	called	call	VERB
iajs-1071	15	4	q	q	NOUN
iajs-1071	15	5	-	-	PUNCT
iajs-1071	15	6	fcf(m	fcf(m	NOUN
iajs-1071	15	7	)	)	PUNCT
iajs-1071	15	8	,	,	PUNCT
iajs-1071	15	9	if	if	SCONJ
iajs-1071	15	10	for	for	ADP
iajs-1071	15	11	every	every	DET
iajs-1071	15	12	fuzzy	fuzzy	ADJ
iajs-1071	15	13	ideal	ideal	NOUN
iajs-1071	15	14	i	i	PRON
iajs-1071	15	15	of	of	ADP
iajs-1071	15	16	r	r	NOUN
iajs-1071	15	17	and	and	CCONJ
iajs-1071	15	18	two	two	NUM
iajs-1071	15	19	every	every	DET
iajs-1071	15	20	fuzzy	fuzzy	ADJ
iajs-1071	15	21	submodules	submodule	NOUN
iajs-1071	15	22	a	a	PRON
iajs-1071	15	23	and	and	CCONJ
iajs-1071	15	24	b	b	NOUN
iajs-1071	15	25	of	of	ADP
iajs-1071	15	26	x	x	SYM
iajs-1071	15	27	,	,	PUNCT
iajs-1071	15	28	if	if	SCONJ
iajs-1071	15	29	ia	ia	PROPN
iajs-1071	15	30	=	=	NOUN
iajs-1071	15	31	ib	ib	X
iajs-1071	15	32	,	,	PUNCT
iajs-1071	15	33	then	then	ADV
iajs-1071	15	34	a+(fanni)=b+(f	a+(fanni)=b+(f	PROPN
iajs-1071	15	35	-	-	PUNCT
iajs-1071	15	36	anni	anni	NOUN
iajs-1071	15	37	)	)	PUNCT
iajs-1071	15	38	where	where	SCONJ
iajs-1071	15	39	f	f	X
iajs-1071	15	40	-	-	PUNCT
iajs-1071	15	41	anni	anni	PROPN
iajs-1071	15	42	is	be	AUX
iajs-1071	15	43	a	a	DET
iajs-1071	15	44	fuzzy	fuzzy	ADJ
iajs-1071	15	45	submodule	submodule	NOUN
iajs-1071	15	46	of	of	ADP
iajs-1071	15	47	x	x	PUNCT
iajs-1071	15	48	and	and	CCONJ
iajs-1071	15	49	define	define	VERB
iajs-1071	15	50	by	by	ADP
iajs-1071	15	51	f	f	PROPN
iajs-1071	15	52	-	-	PUNCT
iajs-1071	15	53	anni	anni	PROPN
iajs-1071	15	54	=	=	PROPN
iajs-1071	15	55	{	{	PUNCT
iajs-1071	15	56	xt	xt	NOUN
iajs-1071	15	57	x	x	SYM
iajs-1071	15	58	:	:	PUNCT
iajs-1071	15	59	ixt=01	ixt=01	NOUN
iajs-1071	15	60	}	}	PUNCT
iajs-1071	15	61	see	see	VERB
iajs-1071	15	62	definition	definition	NOUN
iajs-1071	15	63	(	(	PUNCT
iajs-1071	15	64	1.1	1.1	NUM
iajs-1071	15	65	)	)	PUNCT
iajs-1071	15	66	.	.	PUNCT
iajs-1071	16	1	and	and	CCONJ
iajs-1071	16	2	x	x	X
iajs-1071	16	3	is	be	AUX
iajs-1071	16	4	called	call	VERB
iajs-1071	16	5	q	q	NOUN
iajs-1071	16	6	-	-	PUNCT
iajs-1071	16	7	mfcf(m	mfcf(m	NOUN
iajs-1071	16	8	)	)	PUNCT
iajs-1071	16	9	if	if	SCONJ
iajs-1071	16	10	for	for	ADP
iajs-1071	16	11	every	every	DET
iajs-1071	16	12	maximal	maximal	ADJ
iajs-1071	16	13	fuzzy	fuzzy	ADJ
iajs-1071	16	14	ideal	ideal	NOUN
iajs-1071	16	15	of	of	ADP
iajs-1071	16	16	r	r	NOUN
iajs-1071	16	17	and	and	CCONJ
iajs-1071	16	18	for	for	ADP
iajs-1071	16	19	every	every	DET
iajs-1071	16	20	two	two	NUM
iajs-1071	16	21	fuzzy	fuzzy	ADJ
iajs-1071	16	22	submodules	submodule	NOUN
iajs-1071	16	23	a	a	PRON
iajs-1071	16	24	and	and	CCONJ
iajs-1071	16	25	b	b	NOUN
iajs-1071	16	26	of	of	ADP
iajs-1071	16	27	x	x	SYM
iajs-1071	16	28	such	such	ADJ
iajs-1071	16	29	that	that	SCONJ
iajs-1071	16	30	ia	ia	PROPN
iajs-1071	16	31	=	=	NOUN
iajs-1071	16	32	ib	ib	NOUN
iajs-1071	16	33	implies	imply	VERB
iajs-1071	16	34	that	that	SCONJ
iajs-1071	16	35	a+(f	a+(f	NOUN
iajs-1071	16	36	-	-	PUNCT
iajs-1071	16	37	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	16	38	-	-	PUNCT
iajs-1071	16	39	annxi	annxi	NOUN
iajs-1071	16	40	)	)	PUNCT
iajs-1071	16	41	see	see	VERB
iajs-1071	16	42	(	(	PUNCT
iajs-1071	16	43	2.1	2.1	NUM
iajs-1071	16	44	)	)	PUNCT
iajs-1071	16	45	.	.	PUNCT
iajs-1071	17	1	clearly	clearly	ADV
iajs-1071	17	2	,	,	PUNCT
iajs-1071	17	3	every	every	DET
iajs-1071	17	4	q	q	NOUN
iajs-1071	17	5	-	-	PUNCT
iajs-1071	17	6	fcf(m	fcf(m	NOUN
iajs-1071	17	7	)	)	PUNCT
iajs-1071	17	8	is	be	AUX
iajs-1071	17	9	q	q	ADJ
iajs-1071	17	10	-	-	PUNCT
iajs-1071	17	11	mfcf(m	mfcf(m	NOUN
iajs-1071	17	12	)	)	PUNCT
iajs-1071	17	13	see	see	NOUN
iajs-1071	17	14	(	(	PUNCT
iajs-1071	17	15	remark(2.3)(1	remark(2.3)(1	NOUN
iajs-1071	17	16	)	)	PUNCT
iajs-1071	17	17	)	)	PUNCT
iajs-1071	18	1	and	and	CCONJ
iajs-1071	18	2	every	every	DET
iajs-1071	18	3	fully	fully	ADV
iajs-1071	18	4	cancellation	cancellation	NOUN
iajs-1071	18	5	fuzzy	fuzzy	ADJ
iajs-1071	18	6	module	module	NOUN
iajs-1071	18	7	is	be	AUX
iajs-1071	18	8	q	q	NOUN
iajs-1071	18	9	-	-	PUNCT
iajs-1071	18	10	fcf(m	fcf(m	NOUN
iajs-1071	18	11	)	)	PUNCT
iajs-1071	18	12	.	.	PUNCT
iajs-1071	19	1	see	see	VERB
iajs-1071	19	2	(	(	PUNCT
iajs-1071	19	3	remark(1.3)(1	remark(1.3)(1	NOUN
iajs-1071	19	4	)	)	PUNCT
iajs-1071	19	5	)	)	PUNCT
iajs-1071	20	1	but	but	CCONJ
iajs-1071	20	2	the	the	DET
iajs-1071	20	3	convers	conver	NOUN
iajs-1071	20	4	is	be	AUX
iajs-1071	20	5	not	not	PART
iajs-1071	20	6	true	true	ADJ
iajs-1071	20	7	ingenarl	ingenarl	NOUN
iajs-1071	20	8	see	see	NOUN
iajs-1071	20	9	(	(	PUNCT
iajs-1071	20	10	remark(1.6	remark(1.6	PROPN
iajs-1071	20	11	)	)	PUNCT
iajs-1071	20	12	)	)	PUNCT
iajs-1071	21	1	and	and	CCONJ
iajs-1071	21	2	,	,	PUNCT
iajs-1071	21	3	if	if	SCONJ
iajs-1071	21	4	x	x	PRON
iajs-1071	21	5	is	be	AUX
iajs-1071	21	6	multiplication	multiplication	NOUN
iajs-1071	21	7	and	and	CCONJ
iajs-1071	21	8	naturally	naturally	ADV
iajs-1071	21	9	cancellation	cancellation	NOUN
iajs-1071	21	10	fuzzy	fuzzy	ADJ
iajs-1071	21	11	module	module	NOUN
iajs-1071	21	12	or	or	CCONJ
iajs-1071	21	13	(	(	PUNCT
iajs-1071	21	14	fuzzy	fuzzy	ADJ
iajs-1071	21	15	principle	principle	NOUN
iajs-1071	21	16	ideal	ideal	NOUN
iajs-1071	21	17	)	)	PUNCT
iajs-1071	21	18	,	,	PUNCT
iajs-1071	21	19	then	then	ADV
iajs-1071	21	20	x	x	PUNCT
iajs-1071	21	21	is	be	AUX
iajs-1071	21	22	q	q	NOUN
iajs-1071	21	23	-	-	PUNCT
iajs-1071	21	24	fcf(m	fcf(m	NOUN
iajs-1071	21	25	)	)	PUNCT
iajs-1071	21	26	.	.	PUNCT
iajs-1071	22	1	see	see	VERB
iajs-1071	22	2	proposition	proposition	NOUN
iajs-1071	22	3	(	(	PUNCT
iajs-1071	22	4	1.4	1.4	NUM
iajs-1071	22	5	)	)	PUNCT
iajs-1071	22	6	and	and	CCONJ
iajs-1071	22	7	proposition	proposition	NOUN
iajs-1071	22	8	(	(	PUNCT
iajs-1071	22	9	1.5	1.5	NUM
iajs-1071	22	10	)	)	PUNCT
iajs-1071	22	11	.	.	PUNCT
iajs-1071	23	1	in	in	ADP
iajs-1071	23	2	this	this	DET
iajs-1071	23	3	chapter	chapter	NOUN
iajs-1071	23	4	,	,	PUNCT
iajs-1071	23	5	we	we	PRON
iajs-1071	23	6	will	will	AUX
iajs-1071	23	7	study	study	VERB
iajs-1071	23	8	in	in	ADP
iajs-1071	23	9	details	detail	NOUN
iajs-1071	23	10	the	the	DET
iajs-1071	23	11	concept	concept	NOUN
iajs-1071	23	12	of	of	ADP
iajs-1071	23	13	q	q	ADJ
iajs-1071	23	14	-	-	PUNCT
iajs-1071	23	15	fcf(m).this	fcf(m).this	ADJ
iajs-1071	23	16	chapter	chapter	NOUN
iajs-1071	23	17	consists	consist	VERB
iajs-1071	23	18	of	of	ADP
iajs-1071	23	19	three	three	NUM
iajs-1071	23	20	parts	part	NOUN
iajs-1071	23	21	.	.	PUNCT
iajs-1071	24	1	in	in	ADP
iajs-1071	24	2	part	part	NOUN
iajs-1071	24	3	one	one	NOUN
iajs-1071	24	4	we	we	PRON
iajs-1071	24	5	give	give	VERB
iajs-1071	24	6	some	some	DET
iajs-1071	24	7	basic	basic	ADJ
iajs-1071	24	8	propositions	proposition	NOUN
iajs-1071	24	9	of	of	ADP
iajs-1071	24	10	q	q	NOUN
iajs-1071	24	11	-	-	PUNCT
iajs-1071	24	12	mfcf(m	mfcf(m	NOUN
iajs-1071	24	13	)	)	PUNCT
iajs-1071	24	14	.	.	PUNCT
iajs-1071	25	1	it	it	PRON
iajs-1071	25	2	turns	turn	VERB
iajs-1071	25	3	out	out	ADP
iajs-1071	25	4	that	that	SCONJ
iajs-1071	25	5	a	a	DET
iajs-1071	25	6	fuzzy	fuzzy	ADJ
iajs-1071	25	7	module	module	NOUN
iajs-1071	25	8	x	x	PUNCT
iajs-1071	25	9	is	be	AUX
iajs-1071	25	10	quasi	quasi	ADJ
iajs-1071	25	11	-	-	ADJ
iajs-1071	25	12	fully	fully	ADV
iajs-1071	25	13	cancellation	cancellation	NOUN
iajs-1071	25	14	(	(	PUNCT
iajs-1071	25	15	quasi	quasi	ADJ
iajs-1071	25	16	-	-	ADJ
iajs-1071	25	17	max	max	ADJ
iajs-1071	25	18	fully	fully	ADV
iajs-1071	25	19	cancellation	cancellation	NOUN
iajs-1071	25	20	)	)	PUNCT
iajs-1071	25	21	if	if	SCONJ
iajs-1071	25	22	and	and	CCONJ
iajs-1071	25	23	only	only	ADV
iajs-1071	25	24	if	if	SCONJ
iajs-1071	25	25	i	i	PRON
iajs-1071	25	26	ik	ik	VERB
iajs-1071	25	27	,	,	PUNCT
iajs-1071	25	28	then	then	ADV
iajs-1071	25	29	h	h	PROPN
iajs-1071	25	30	k+(f	k+(f	NOUN
iajs-1071	25	31	-	-	PUNCT
iajs-1071	25	32	annxi	annxi	NOUN
iajs-1071	25	33	)	)	PUNCT
iajs-1071	25	34	,	,	PUNCT
iajs-1071	25	35	where	where	SCONJ
iajs-1071	25	36	h	h	NOUN
iajs-1071	25	37	and	and	CCONJ
iajs-1071	25	38	k	k	PROPN
iajs-1071	25	39	are	be	AUX
iajs-1071	25	40	fuzzy	fuzzy	ADJ
iajs-1071	25	41	submodules	submodule	NOUN
iajs-1071	25	42	of	of	ADP
iajs-1071	25	43	x	x	PUNCT
iajs-1071	25	44	and	and	CCONJ
iajs-1071	25	45	i	i	PRON
iajs-1071	25	46	be	be	VERB
iajs-1071	25	47	a	a	DET
iajs-1071	25	48	fuzzy	fuzzy	ADJ
iajs-1071	25	49	ideal	ideal	NOUN
iajs-1071	25	50	(	(	PUNCT
iajs-1071	25	51	fuzzy	fuzzy	ADJ
iajs-1071	25	52	maximal	maximal	ADJ
iajs-1071	25	53	ideal	ideal	NOUN
iajs-1071	25	54	)	)	PUNCT
iajs-1071	25	55	of	of	ADP
iajs-1071	25	56	r.	r.	PROPN
iajs-1071	25	57	equivalently	equivalently	ADV
iajs-1071	25	58	,	,	PUNCT
iajs-1071	25	59	i(ht	i(ht	NOUN
iajs-1071	25	60	)	)	PUNCT
iajs-1071	25	61	il	il	PROPN
iajs-1071	25	62	,	,	PUNCT
iajs-1071	25	63	then	then	ADV
iajs-1071	25	64	ht	ht	PROPN
iajs-1071	25	65	l+(f	l+(f	PROPN
iajs-1071	25	66	-	-	PUNCT
iajs-1071	25	67	annxi	annxi	NOUN
iajs-1071	25	68	)	)	PUNCT
iajs-1071	25	69	,	,	PUNCT
iajs-1071	25	70	where	where	SCONJ
iajs-1071	25	71	ht	ht	INTJ
iajs-1071	25	72	x	x	PUNCT
iajs-1071	25	73	if	if	SCONJ
iajs-1071	25	74	and	and	CCONJ
iajs-1071	25	75	only	only	ADV
iajs-1071	25	76	if	if	SCONJ
iajs-1071	25	77	(	(	PUNCT
iajs-1071	25	78	ih	ih	NOUN
iajs-1071	25	79	:	:	PUNCT
iajs-1071	25	80	i)=h+(f	i)=h+(f	NOUN
iajs-1071	25	81	-	-	PUNCT
iajs-1071	25	82	annxi	annxi	NOUN
iajs-1071	25	83	)	)	PUNCT
iajs-1071	25	84	where	where	SCONJ
iajs-1071	25	85	l	l	NOUN
iajs-1071	25	86	is	be	AUX
iajs-1071	25	87	a	a	DET
iajs-1071	25	88	fuzzy	fuzzy	ADJ
iajs-1071	25	89	submodule	submodule	NOUN
iajs-1071	25	90	.	.	PUNCT
iajs-1071	26	1	and	and	CCONJ
iajs-1071	26	2	ht	ht	PROPN
iajs-1071	26	3	is	be	AUX
iajs-1071	26	4	a	a	DET
iajs-1071	26	5	fuzzy	fuzzy	ADJ
iajs-1071	26	6	singleton	singleton	NOUN
iajs-1071	26	7	of	of	ADP
iajs-1071	26	8	r	r	NOUN
iajs-1071	26	9	,	,	PUNCT
iajs-1071	26	10	see	see	VERB
iajs-1071	26	11	proposition	proposition	NOUN
iajs-1071	26	12	(	(	PUNCT
iajs-1071	26	13	1.7	1.7	NUM
iajs-1071	26	14	)	)	PUNCT
iajs-1071	26	15	and	and	CCONJ
iajs-1071	26	16	proposition	proposition	NOUN
iajs-1071	26	17	(	(	PUNCT
iajs-1071	26	18	2.9).and	2.9).and	NUM
iajs-1071	26	19	fully	fully	ADV
iajs-1071	26	20	cancellation	cancellation	NOUN
iajs-1071	26	21	fuzzy	fuzzy	ADJ
iajs-1071	26	22	module	module	NOUN
iajs-1071	26	23	is	be	AUX
iajs-1071	26	24	equivalent	equivalent	ADJ
iajs-1071	26	25	quasi	quasi	ADJ
iajs-1071	26	26	-	-	ADJ
iajs-1071	26	27	fully	fully	ADJ
iajs-1071	26	28	cancellation	cancellation	NOUN
iajs-1071	26	29	in	in	ADP
iajs-1071	26	30	the	the	DET
iajs-1071	26	31	class	class	NOUN
iajs-1071	26	32	x	x	PUNCT
iajs-1071	26	33	is	be	AUX
iajs-1071	26	34	torsion	torsion	NOUN
iajs-1071	26	35	free	free	ADJ
iajs-1071	26	36	fuzzy	fuzzy	ADJ
iajs-1071	26	37	module	module	NOUN
iajs-1071	26	38	over	over	ADP
iajs-1071	26	39	a	a	DET
iajs-1071	26	40	fuzzy	fuzzy	ADJ
iajs-1071	26	41	integral	integral	ADJ
iajs-1071	26	42	domain	domain	NOUN
iajs-1071	26	43	r	r	NOUN
iajs-1071	26	44	see	see	NOUN
iajs-1071	26	45	proposition	proposition	NOUN
iajs-1071	26	46	(	(	PUNCT
iajs-1071	26	47	1.4	1.4	NUM
iajs-1071	26	48	)	)	PUNCT
iajs-1071	26	49	.	.	PUNCT
iajs-1071	27	1	part	part	NOUN
iajs-1071	27	2	two	two	NUM
iajs-1071	27	3	is	be	AUX
iajs-1071	27	4	devoted	devote	VERB
iajs-1071	27	5	to	to	PART
iajs-1071	27	6	study	study	VERB
iajs-1071	27	7	the	the	DET
iajs-1071	27	8	relation	relation	NOUN
iajs-1071	27	9	between	between	ADP
iajs-1071	27	10	max	max	PROPN
iajs-1071	27	11	-	-	PUNCT
iajs-1071	27	12	fully	fully	ADV
iajs-1071	27	13	cancellation	cancellation	NOUN
iajs-1071	27	14	fuzzy	fuzzy	ADJ
iajs-1071	27	15	module	module	NOUN
iajs-1071	27	16	and	and	CCONJ
iajs-1071	27	17	q	q	NOUN
iajs-1071	27	18	-	-	PUNCT
iajs-1071	27	19	mfcf(m	mfcf(m	NOUN
iajs-1071	27	20	)	)	PUNCT
iajs-1071	27	21	but	but	CCONJ
iajs-1071	27	22	the	the	DET
iajs-1071	27	23	convers	conver	NOUN
iajs-1071	27	24	is	be	AUX
iajs-1071	27	25	not	not	PART
iajs-1071	27	26	true	true	ADJ
iajs-1071	27	27	see	see	NOUN
iajs-1071	27	28	remark	remark	NOUN
iajs-1071	27	29	(	(	PUNCT
iajs-1071	27	30	2.7	2.7	NUM
iajs-1071	27	31	)	)	PUNCT
iajs-1071	27	32	and	and	CCONJ
iajs-1071	27	33	example	example	NOUN
iajs-1071	27	34	(	(	PUNCT
iajs-1071	27	35	2.8	2.8	NUM
iajs-1071	27	36	)	)	PUNCT
iajs-1071	27	37	.	.	PUNCT
iajs-1071	28	1	part	part	NOUN
iajs-1071	28	2	three	three	NUM
iajs-1071	28	3	is	be	AUX
iajs-1071	28	4	study	study	VERB
iajs-1071	28	5	the	the	DET
iajs-1071	28	6	concepts	concept	NOUN
iajs-1071	28	7	the	the	DET
iajs-1071	28	8	direct	direct	ADJ
iajs-1071	28	9	sum	sum	NOUN
iajs-1071	28	10	of	of	ADP
iajs-1071	28	11	q	q	NOUN
iajs-1071	28	12	-	-	PUNCT
iajs-1071	28	13	fcf(m	fcf(m	NOUN
iajs-1071	28	14	)	)	PUNCT
iajs-1071	28	15	which	which	PRON
iajs-1071	28	16	is	be	AUX
iajs-1071	28	17	mentioned	mention	VERB
iajs-1071	28	18	in	in	ADP
iajs-1071	28	19	chapter	chapter	NOUN
iajs-1071	28	20	one	one	NUM
iajs-1071	28	21	section	section	NOUN
iajs-1071	28	22	five	five	NUM
iajs-1071	28	23	.	.	PUNCT
iajs-1071	29	1	and	and	CCONJ
iajs-1071	29	2	naturally	naturally	ADV
iajs-1071	29	3	cancellation	cancellation	VERB
iajs-1071	29	4	fuzzy	fuzzy	ADJ
iajs-1071	29	5	module	module	NOUN
iajs-1071	29	6	x	x	PRON
iajs-1071	29	7	is	be	AUX
iajs-1071	29	8	equivalent	equivalent	ADJ
iajs-1071	29	9	to	to	ADP
iajs-1071	29	10	quasi	quasi	ADJ
iajs-1071	29	11	-	-	ADJ
iajs-1071	29	12	fully	fully	ADV
iajs-1071	29	13	cancellation	cancellation	NOUN
iajs-1071	29	14	if	if	SCONJ
iajs-1071	29	15	x	x	PRON
iajs-1071	29	16	is	be	AUX
iajs-1071	29	17	multiplication	multiplication	NOUN
iajs-1071	29	18	fuzzy	fuzzy	ADJ
iajs-1071	29	19	module	module	NOUN
iajs-1071	29	20	.	.	PUNCT
iajs-1071	30	1	§	§	PROPN
iajs-1071	30	2	1	1	NUM
iajs-1071	30	3	.	.	PUNCT
iajs-1071	30	4	quasi	quasi	ADJ
iajs-1071	30	5	-	-	ADJ
iajs-1071	30	6	fully	fully	ADV
iajs-1071	30	7	cancellation	cancellation	NOUN
iajs-1071	30	8	fuzzy	fuzzy	ADJ
iajs-1071	30	9	modules	module	NOUN
iajs-1071	30	10	in	in	ADP
iajs-1071	30	11	this	this	DET
iajs-1071	30	12	part	part	NOUN
iajs-1071	30	13	we	we	PRON
iajs-1071	30	14	give	give	VERB
iajs-1071	30	15	the	the	DET
iajs-1071	30	16	concept	concept	NOUN
iajs-1071	30	17	of	of	ADP
iajs-1071	30	18	q	q	NOUN
iajs-1071	30	19	-	-	PUNCT
iajs-1071	30	20	fcf(m	fcf(m	NOUN
iajs-1071	30	21	)	)	PUNCT
iajs-1071	30	22	this	this	DET
iajs-1071	30	23	concept	concept	NOUN
iajs-1071	30	24	is	be	AUX
iajs-1071	30	25	generalization	generalization	NOUN
iajs-1071	30	26	of	of	ADP
iajs-1071	30	27	concept	concept	NOUN
iajs-1071	30	28	quasi	quasi	ADJ
iajs-1071	30	29	-	-	ADJ
iajs-1071	30	30	fully	fully	ADV
iajs-1071	30	31	cancellation	cancellation	NOUN
iajs-1071	30	32	modules[1	modules[1	NOUN
iajs-1071	30	33	]	]	PUNCT
iajs-1071	30	34	,	,	PUNCT
iajs-1071	30	35	and	and	CCONJ
iajs-1071	30	36	we	we	PRON
iajs-1071	30	37	give	give	VERB
iajs-1071	30	38	a	a	DET
iajs-1071	30	39	some	some	DET
iajs-1071	30	40	basic	basic	ADJ
iajs-1071	30	41	results	result	NOUN
iajs-1071	30	42	and	and	CCONJ
iajs-1071	30	43	properties	property	NOUN
iajs-1071	30	44	of	of	ADP
iajs-1071	30	45	this	this	DET
iajs-1071	30	46	concept	concept	NOUN
iajs-1071	30	47	.	.	PUNCT
iajs-1071	31	1	also	also	ADV
iajs-1071	31	2	,	,	PUNCT
iajs-1071	31	3	relationships	relationship	NOUN
iajs-1071	31	4	between	between	ADP
iajs-1071	31	5	the	the	DET
iajs-1071	31	6	class	class	NOUN
iajs-1071	31	7	of	of	ADP
iajs-1071	31	8	q	q	NOUN
iajs-1071	31	9	-	-	PUNCT
iajs-1071	31	10	fcf(m)and	fcf(m)and	ADJ
iajs-1071	31	11	other	other	ADJ
iajs-1071	31	12	types	type	NOUN
iajs-1071	31	13	of	of	ADP
iajs-1071	31	14	modules	module	NOUN
iajs-1071	31	15	are	be	AUX
iajs-1071	31	16	established	establish	VERB
iajs-1071	31	17	.	.	PUNCT
iajs-1071	31	18	"	"	PUNCT
iajs-1071	31	19	recall	recall	VERB
iajs-1071	31	20	that	that	SCONJ
iajs-1071	31	21	an	an	DET
iajs-1071	31	22	r	r	NOUN
iajs-1071	31	23	-	-	PUNCT
iajs-1071	31	24	module	module	NOUN
iajs-1071	31	25	m	m	NOUN
iajs-1071	31	26	is	be	AUX
iajs-1071	31	27	called	call	VERB
iajs-1071	31	28	quasi	quasi	ADJ
iajs-1071	31	29	-	-	ADJ
iajs-1071	31	30	fully	fully	ADV
iajs-1071	31	31	cancellation	cancellation	NOUN
iajs-1071	31	32	produle	produle	NOUN
iajs-1071	31	33	.	.	PUNCT
iajs-1071	32	1	if	if	SCONJ
iajs-1071	32	2	for	for	ADP
iajs-1071	32	3	every	every	DET
iajs-1071	32	4	ideal	ideal	NOUN
iajs-1071	32	5	i	i	PRON
iajs-1071	32	6	of	of	ADP
iajs-1071	32	7	r	r	NOUN
iajs-1071	32	8	and	and	CCONJ
iajs-1071	32	9	for	for	ADP
iajs-1071	32	10	every	every	DET
iajs-1071	32	11	two	two	NUM
iajs-1071	32	12	submodules	submodule	NOUN
iajs-1071	32	13	a	a	PRON
iajs-1071	32	14	,	,	PUNCT
iajs-1071	32	15	b	b	NOUN
iajs-1071	32	16	of	of	ADP
iajs-1071	32	17	m.	m.	NOUN
iajs-1071	32	18	such	such	ADJ
iajs-1071	32	19	that	that	SCONJ
iajs-1071	32	20	ia	ia	PROPN
iajs-1071	32	21	=	=	NOUN
iajs-1071	32	22	ib	ib	NOUN
iajs-1071	32	23	implies	imply	VERB
iajs-1071	32	24	a+annmi	a+annmi	PROPN
iajs-1071	33	1	=	=	PRON
iajs-1071	33	2	b+annmi	b+annmi	PROPN
iajs-1071	33	3	(	(	PUNCT
iajs-1071	33	4	where	where	SCONJ
iajs-1071	33	5	annmi={m	annmi={m	PROPN
iajs-1071	33	6	m	m	PROPN
iajs-1071	33	7	,	,	PUNCT
iajs-1071	33	8	im=0}.[1	im=0}.[1	PROPN
iajs-1071	33	9	]	]	PUNCT
iajs-1071	33	10	"	"	PUNCT
iajs-1071	33	11	here	here	ADV
iajs-1071	33	12	,	,	PUNCT
iajs-1071	33	13	we	we	PRON
iajs-1071	33	14	introduce	introduce	VERB
iajs-1071	33	15	the	the	DET
iajs-1071	33	16	principle	principle	ADJ
iajs-1071	33	17	definition	definition	NOUN
iajs-1071	33	18	of	of	ADP
iajs-1071	33	19	our	our	PRON
iajs-1071	33	20	work	work	NOUN
iajs-1071	33	21	.	.	PUNCT
iajs-1071	34	1	definition	definition	NOUN
iajs-1071	34	2	1.1	1.1	NUM
iajs-1071	34	3	:	:	PUNCT
iajs-1071	34	4	let	let	VERB
iajs-1071	34	5	x	x	SYM
iajs-1071	34	6	bef(m	bef(m	PROPN
iajs-1071	34	7	)	)	PUNCT
iajs-1071	34	8	.	.	PUNCT
iajs-1071	35	1	x	x	PUNCT
iajs-1071	35	2	is	be	AUX
iajs-1071	35	3	called	call	VERB
iajs-1071	35	4	q	q	NOUN
iajs-1071	35	5	-	-	PUNCT
iajs-1071	35	6	fcf(m	fcf(m	NOUN
iajs-1071	35	7	)	)	PUNCT
iajs-1071	35	8	for	for	ADP
iajs-1071	35	9	every	every	DET
iajs-1071	35	10	fuzzy	fuzzy	ADJ
iajs-1071	35	11	ideal	ideal	NOUN
iajs-1071	35	12	i	i	PRON
iajs-1071	35	13	of	of	ADP
iajs-1071	35	14	r	r	NOUN
iajs-1071	35	15	and	and	CCONJ
iajs-1071	35	16	for	for	ADP
iajs-1071	35	17	every	every	DET
iajs-1071	35	18	fuzzy	fuzzy	ADJ
iajs-1071	35	19	submodules	submodule	NOUN
iajs-1071	35	20	a	a	PRON
iajs-1071	35	21	and	and	CCONJ
iajs-1071	35	22	b	b	NOUN
iajs-1071	35	23	of	of	ADP
iajs-1071	35	24	x	x	SYM
iajs-1071	35	25	,	,	PUNCT
iajs-1071	35	26	if	if	SCONJ
iajs-1071	35	27	ia	ia	PROPN
iajs-1071	35	28	=	=	NOUN
iajs-1071	35	29	ib	ib	X
iajs-1071	35	30	,	,	PUNCT
iajs-1071	35	31	then	then	ADV
iajs-1071	35	32	a+f	a+f	PROPN
iajs-1071	35	33	-	-	PUNCT
iajs-1071	35	34	annxi	annxi	NOUN
iajs-1071	35	35	=	=	SYM
iajs-1071	35	36	b+f	b+f	NOUN
iajs-1071	35	37	-	-	PUNCT
iajs-1071	35	38	annxi	annxi	NOUN
iajs-1071	35	39	where	where	SCONJ
iajs-1071	35	40	f	f	X
iajs-1071	35	41	-	-	PUNCT
iajs-1071	35	42	anni	anni	PROPN
iajs-1071	35	43	is	be	AUX
iajs-1071	35	44	a	a	DET
iajs-1071	35	45	fuzzy	fuzzy	ADJ
iajs-1071	35	46	submodule	submodule	NOUN
iajs-1071	35	47	of	of	ADP
iajs-1071	35	48	x.	x.	NOUN
iajs-1071	35	49	and	and	CCONJ
iajs-1071	35	50	definition	definition	NOUN
iajs-1071	35	51	by	by	ADP
iajs-1071	35	52	{	{	PUNCT
iajs-1071	35	53	xt	xt	PROPN
iajs-1071	35	54	x	x	NOUN
iajs-1071	35	55	:	:	PUNCT
iajs-1071	35	56	i.xt=01	i.xt=01	NOUN
iajs-1071	35	57	}	}	PUNCT
iajs-1071	35	58	.	.	PUNCT
iajs-1071	36	1	t	t	PROPN
iajs-1071	36	2	(	(	PUNCT
iajs-1071	36	3	0,1	0,1	NOUN
iajs-1071	36	4	]	]	PUNCT
iajs-1071	36	5	.	.	PUNCT
iajs-1071	37	1	proposition	proposition	NOUN
iajs-1071	37	2	1.2	1.2	NUM
iajs-1071	37	3	:	:	PUNCT
iajs-1071	37	4	let	let	VERB
iajs-1071	37	5	x	x	SYM
iajs-1071	37	6	bef(m	bef(m	PROPN
iajs-1071	37	7	)	)	PUNCT
iajs-1071	37	8	.	.	PUNCT
iajs-1071	38	1	such	such	ADJ
iajs-1071	38	2	that	that	PRON
iajs-1071	38	3	(	(	PUNCT
iajs-1071	38	4	f	f	X
iajs-1071	38	5	-	-	PUNCT
iajs-1071	38	6	annx)t	annx)t	NOUN
iajs-1071	38	7	=	=	SYM
iajs-1071	38	8	f	f	X
iajs-1071	38	9	-	-	PUNCT
iajs-1071	38	10	annxt	annxt	ADJ
iajs-1071	38	11	.	.	PUNCT
iajs-1071	39	1	then	then	ADV
iajs-1071	39	2	x	x	X
iajs-1071	39	3	is	be	AUX
iajs-1071	39	4	a	a	DET
iajs-1071	39	5	q	q	NOUN
iajs-1071	39	6	-	-	PUNCT
iajs-1071	39	7	fcf(m)if	fcf(m)if	NOUN
iajs-1071	39	8	and	and	CCONJ
iajs-1071	39	9	only	only	ADV
iajs-1071	39	10	if	if	SCONJ
iajs-1071	39	11	xt	xt	PROPN
iajs-1071	39	12	is	be	AUX
iajs-1071	39	13	a	a	DET
iajs-1071	39	14	quasi	quasi	ADJ
iajs-1071	39	15	-	-	ADJ
iajs-1071	39	16	fully	fully	ADV
iajs-1071	39	17	cancellation	cancellation	NOUN
iajs-1071	39	18	module	module	NOUN
iajs-1071	39	19	,	,	PUNCT
iajs-1071	39	20	t	t	PROPN
iajs-1071	39	21	(	(	PUNCT
iajs-1071	39	22	0,1	0,1	NOUN
iajs-1071	39	23	]	]	PUNCT
iajs-1071	39	24	.	.	PUNCT
iajs-1071	40	1	mathematics	mathematic	NOUN
iajs-1071	40	2	|	|	ADV
iajs-1071	40	3	194	194	NUM
iajs-1071	40	4	2012	2012	NUM
iajs-1071	40	5	(	(	PUNCT
iajs-1071	40	6	عام	عام	PROPN
iajs-1071	40	7	1	1	NUM
iajs-1071	40	8	)	)	PUNCT
iajs-1071	40	9	(	(	PUNCT
iajs-1071	40	10	العدد	العدد	PROPN
iajs-1071	40	11	30مجلة	30مجلة	NUM
iajs-1071	40	12	إبن	إبن	VERB
iajs-1071	40	13	الهيثم	الهيثم	ADJ
iajs-1071	40	14	للعلوم	للعلوم	NOUN
iajs-1071	40	15	الصرفة	الصرفة	NOUN
iajs-1071	41	1	و	و	PRON
iajs-1071	41	2	التطبيقية	التطبيقية	ADV
iajs-1071	41	3	المجلد	المجلد	ADV
iajs-1071	41	4	)	)	PUNCT
iajs-1071	42	1	ibn	ibn	PROPN
iajs-1071	42	2	al	al	PROPN
iajs-1071	42	3	-	-	PUNCT
iajs-1071	42	4	haitham	haitham	PROPN
iajs-1071	42	5	j.	j.	PROPN
iajs-1071	42	6	for	for	ADP
iajs-1071	42	7	pure	pure	PROPN
iajs-1071	42	8	&	&	CCONJ
iajs-1071	42	9	appl	appl	PROPN
iajs-1071	42	10	.	.	PUNCT
iajs-1071	43	1	sci	sci	PROPN
iajs-1071	43	2	.	.	PUNCT
iajs-1071	44	1	vol.30	vol.30	NOUN
iajs-1071	44	2	(	(	PUNCT
iajs-1071	44	3	1	1	NUM
iajs-1071	44	4	)	)	PUNCT
iajs-1071	44	5	2017	2017	NUM
iajs-1071	44	6	proof	proof	NOUN
iajs-1071	44	7	:	:	PUNCT
iajs-1071	44	8	let	let	VERB
iajs-1071	44	9	x	x	SYM
iajs-1071	44	10	bef(m	bef(m	PROPN
iajs-1071	44	11	)	)	PUNCT
iajs-1071	44	12	.	.	PUNCT
iajs-1071	45	1	let	let	VERB
iajs-1071	45	2	n	n	PRON
iajs-1071	45	3	and	and	CCONJ
iajs-1071	45	4	k	k	PROPN
iajs-1071	45	5	be	be	AUX
iajs-1071	45	6	two	two	NUM
iajs-1071	45	7	submodules	submodule	NOUN
iajs-1071	45	8	of	of	ADP
iajs-1071	45	9	m	m	PRON
iajs-1071	45	10	,	,	PUNCT
iajs-1071	45	11	and	and	CCONJ
iajs-1071	45	12	let	let	VERB
iajs-1071	45	13	j	j	PROPN
iajs-1071	45	14	be	be	AUX
iajs-1071	45	15	an	an	DET
iajs-1071	45	16	ideal	ideal	NOUN
iajs-1071	45	17	of	of	ADP
iajs-1071	45	18	r.	r.	PROPN
iajs-1071	45	19	such	such	ADJ
iajs-1071	45	20	that	that	SCONJ
iajs-1071	45	21	jn	jn	PROPN
iajs-1071	45	22	=	=	PROPN
iajs-1071	45	23	jk	jk	PROPN
iajs-1071	45	24	.	.	PUNCT
iajs-1071	46	1	now	now	ADV
iajs-1071	46	2	,	,	PUNCT
iajs-1071	46	3	define	define	VERB
iajs-1071	46	4	:	:	PUNCT
iajs-1071	46	5	a	a	X
iajs-1071	46	6	:	:	PUNCT
iajs-1071	46	7	m	m	VERB
iajs-1071	46	8	[	[	X
iajs-1071	46	9	0,1	0,1	NUM
iajs-1071	46	10	]	]	PUNCT
iajs-1071	46	11	,	,	PUNCT
iajs-1071	46	12	b	b	X
iajs-1071	46	13	:	:	PUNCT
iajs-1071	47	1	[	[	X
iajs-1071	47	2	0,1	0,1	NUM
iajs-1071	47	3	]	]	PUNCT
iajs-1071	47	4	by	by	ADP
iajs-1071	47	5	a(x)=	a(x)=	PROPN
iajs-1071	47	6	{	{	PUNCT
iajs-1071	47	7	t	t	PROPN
iajs-1071	47	8	(	(	PUNCT
iajs-1071	47	9	0,1	0,1	NUM
iajs-1071	47	10	]	]	PUNCT
iajs-1071	47	11	b(x)=	b(x)=	PROPN
iajs-1071	47	12	{	{	PUNCT
iajs-1071	47	13	t	t	PROPN
iajs-1071	47	14	(	(	PUNCT
iajs-1071	47	15	0,1	0,1	NOUN
iajs-1071	47	16	]	]	PUNCT
iajs-1071	47	17	and	and	CCONJ
iajs-1071	47	18	define	define	VERB
iajs-1071	47	19	:	:	PUNCT
iajs-1071	47	20	i	i	PRON
iajs-1071	47	21	:	:	PUNCT
iajs-1071	47	22	r	r	NOUN
iajs-1071	47	23	[	[	X
iajs-1071	47	24	0,1	0,1	NUM
iajs-1071	47	25	]	]	PUNCT
iajs-1071	47	26	by	by	ADP
iajs-1071	47	27	i(x)=	i(x)=	PROPN
iajs-1071	47	28	{	{	PUNCT
iajs-1071	47	29	t	t	PROPN
iajs-1071	47	30	(	(	PUNCT
iajs-1071	47	31	0,1	0,1	NUM
iajs-1071	47	32	]	]	PUNCT
iajs-1071	47	33	it	it	PRON
iajs-1071	47	34	is	be	AUX
iajs-1071	47	35	clear	clear	ADJ
iajs-1071	47	36	that	that	SCONJ
iajs-1071	47	37	a	a	PRON
iajs-1071	47	38	and	and	CCONJ
iajs-1071	47	39	b	b	NOUN
iajs-1071	47	40	are	be	AUX
iajs-1071	47	41	fuzzy	fuzzy	ADJ
iajs-1071	47	42	submodules	submodule	NOUN
iajs-1071	47	43	of	of	ADP
iajs-1071	47	44	x	x	PUNCT
iajs-1071	48	1	and	and	CCONJ
iajs-1071	48	2	i	i	PRON
iajs-1071	48	3	be	be	VERB
iajs-1071	48	4	a	a	DET
iajs-1071	48	5	fuzzy	fuzzy	ADJ
iajs-1071	48	6	ideal	ideal	NOUN
iajs-1071	48	7	of	of	ADP
iajs-1071	48	8	r.	r.	PROPN
iajs-1071	48	9	also	also	ADV
iajs-1071	48	10	,	,	PUNCT
iajs-1071	48	11	at	at	ADP
iajs-1071	48	12	=	=	NOUN
iajs-1071	48	13	n	n	CCONJ
iajs-1071	48	14	,	,	PUNCT
iajs-1071	48	15	bt	bt	PROPN
iajs-1071	48	16	=	=	PROPN
iajs-1071	48	17	k	k	NOUN
iajs-1071	48	18	and	and	CCONJ
iajs-1071	48	19	it	it	PRON
iajs-1071	48	20	=	=	ADJ
iajs-1071	48	21	j	j	PROPN
iajs-1071	48	22	;	;	PUNCT
iajs-1071	48	23	t	t	PROPN
iajs-1071	48	24	(	(	PUNCT
iajs-1071	48	25	0,1	0,1	NUM
iajs-1071	48	26	]	]	PUNCT
iajs-1071	48	27	,	,	PUNCT
iajs-1071	48	28	jn	jn	PROPN
iajs-1071	48	29	=	=	PROPN
iajs-1071	48	30	jk	jk	PROPN
iajs-1071	48	31	,	,	PUNCT
iajs-1071	48	32	then	then	ADV
iajs-1071	48	33	itat=	itat=	NOUN
iajs-1071	48	34	itbt	itbt	VERB
iajs-1071	48	35	therefore	therefore	ADV
iajs-1071	48	36	(	(	PUNCT
iajs-1071	48	37	ia)t=(ib)t	ia)t=(ib)t	PROPN
iajs-1071	48	38	t	t	PROPN
iajs-1071	48	39	(	(	PUNCT
iajs-1071	48	40	0,1	0,1	NOUN
iajs-1071	48	41	]	]	PUNCT
iajs-1071	48	42	.	.	PUNCT
iajs-1071	49	1	thus	thus	ADV
iajs-1071	49	2	ia	ia	PROPN
iajs-1071	49	3	=	=	PROPN
iajs-1071	49	4	ib	ib	NOUN
iajs-1071	49	5	.	.	PUNCT
iajs-1071	50	1	butx	butx	PROPN
iajs-1071	50	2	is	be	AUX
iajs-1071	50	3	a	a	DET
iajs-1071	50	4	q	q	NOUN
iajs-1071	50	5	-	-	PUNCT
iajs-1071	50	6	fcf(m	fcf(m	NOUN
iajs-1071	50	7	)	)	PUNCT
iajs-1071	50	8	.	.	PUNCT
iajs-1071	51	1	then	then	ADV
iajs-1071	51	2	we	we	PRON
iajs-1071	51	3	get	get	VERB
iajs-1071	51	4	a+f	a+f	NOUN
iajs-1071	51	5	-	-	PUNCT
iajs-1071	51	6	annxi	annxi	NOUN
iajs-1071	51	7	=	=	NOUN
iajs-1071	51	8	b+f	b+f	NOUN
iajs-1071	51	9	-	-	PUNCT
iajs-1071	51	10	annxi	annxi	NOUN
iajs-1071	51	11	hence	hence	ADV
iajs-1071	51	12	(	(	PUNCT
iajs-1071	51	13	a+f	a+f	PROPN
iajs-1071	51	14	-	-	PUNCT
iajs-1071	51	15	annxi)t=(b+f	annxi)t=(b+f	NOUN
iajs-1071	51	16	-	-	PUNCT
iajs-1071	51	17	annxi)t	annxi)t	NOUN
iajs-1071	51	18	.	.	PUNCT
iajs-1071	52	1	t	t	PROPN
iajs-1071	52	2	(	(	PUNCT
iajs-1071	52	3	0,1	0,1	NUM
iajs-1071	52	4	]	]	PUNCT
iajs-1071	52	5	but	but	CCONJ
iajs-1071	52	6	(	(	PUNCT
iajs-1071	52	7	f	f	X
iajs-1071	52	8	-	-	PUNCT
iajs-1071	52	9	annxi)t	annxi)t	NOUN
iajs-1071	52	10	=	=	NOUN
iajs-1071	52	11	fannmit	fannmit	X
iajs-1071	52	12	t	t	PROPN
iajs-1071	52	13	(	(	PUNCT
iajs-1071	52	14	0,1	0,1	NOUN
iajs-1071	52	15	]	]	PUNCT
iajs-1071	52	16	see[5,proposition.(2.2	see[5,proposition.(2.2	NOUN
iajs-1071	52	17	)	)	PUNCT
iajs-1071	52	18	]	]	PUNCT
iajs-1071	53	1	so	so	ADV
iajs-1071	53	2	,	,	PUNCT
iajs-1071	53	3	at+f	at+f	PROPN
iajs-1071	53	4	-	-	PUNCT
iajs-1071	53	5	annit	annit	VERB
iajs-1071	53	6	=	=	PROPN
iajs-1071	53	7	bt+f	bt+f	NOUN
iajs-1071	53	8	-	-	PUNCT
iajs-1071	53	9	annit	annit	NOUN
iajs-1071	53	10	.	.	PUNCT
iajs-1071	54	1	therefore	therefore	ADV
iajs-1071	54	2	n+f	n+f	ADV
iajs-1071	54	3	-	-	PUNCT
iajs-1071	54	4	annj	annj	NOUN
iajs-1071	54	5	=	=	NOUN
iajs-1071	54	6	k+f	k+f	NUM
iajs-1071	54	7	-	-	PUNCT
iajs-1071	54	8	annj	annj	NOUN
iajs-1071	54	9	.	.	PUNCT
iajs-1071	55	1	thus	thus	ADV
iajs-1071	55	2	xt	xt	PROPN
iajs-1071	55	3	is	be	AUX
iajs-1071	55	4	quasi	quasi	ADJ
iajs-1071	55	5	-	-	ADJ
iajs-1071	55	6	fully	fully	ADV
iajs-1071	55	7	cancellation	cancellation	NOUN
iajs-1071	55	8	module	module	NOUN
iajs-1071	55	9	.	.	PUNCT
iajs-1071	56	1	another	another	DET
iajs-1071	56	2	side	side	NOUN
iajs-1071	56	3	,	,	PUNCT
iajs-1071	56	4	let	let	VERB
iajs-1071	56	5	a	a	DET
iajs-1071	56	6	,	,	PUNCT
iajs-1071	56	7	b	b	NOUN
iajs-1071	56	8	be	be	AUX
iajs-1071	56	9	two	two	NUM
iajs-1071	56	10	fuzzy	fuzzy	ADJ
iajs-1071	56	11	submodules	submodule	NOUN
iajs-1071	56	12	of	of	ADP
iajs-1071	56	13	x	x	PUNCT
iajs-1071	56	14	and	and	CCONJ
iajs-1071	56	15	let	let	VERB
iajs-1071	56	16	i	i	PRON
iajs-1071	56	17	be	be	AUX
iajs-1071	56	18	a	a	DET
iajs-1071	56	19	fuzzy	fuzzy	ADJ
iajs-1071	56	20	ideal	ideal	NOUN
iajs-1071	56	21	of	of	ADP
iajs-1071	56	22	r.	r.	PROPN
iajs-1071	56	23	such	such	ADJ
iajs-1071	56	24	that	that	SCONJ
iajs-1071	56	25	ia	ia	PROPN
iajs-1071	56	26	=	=	NOUN
iajs-1071	56	27	ib	ib	NOUN
iajs-1071	56	28	.	.	PUNCT
iajs-1071	56	29	to	to	PART
iajs-1071	56	30	prove	prove	VERB
iajs-1071	56	31	a+f	a+f	PROPN
iajs-1071	56	32	-	-	PUNCT
iajs-1071	56	33	anni	anni	PROPN
iajs-1071	56	34	=	=	PROPN
iajs-1071	56	35	b+f	b+f	PROPN
iajs-1071	56	36	-	-	PUNCT
iajs-1071	56	37	anni	anni	PROPN
iajs-1071	56	38	.	.	PUNCT
iajs-1071	57	1	now	now	ADV
iajs-1071	57	2	,	,	PUNCT
iajs-1071	57	3	since	since	SCONJ
iajs-1071	57	4	ia	ia	PROPN
iajs-1071	57	5	=	=	NOUN
iajs-1071	57	6	ib	ib	X
iajs-1071	57	7	,	,	PUNCT
iajs-1071	57	8	then	then	ADV
iajs-1071	57	9	(	(	PUNCT
iajs-1071	57	10	ia)t=(ib)t	ia)t=(ib)t	PROPN
iajs-1071	57	11	t	t	PROPN
iajs-1071	57	12	(	(	PUNCT
iajs-1071	57	13	0,1	0,1	NUM
iajs-1071	57	14	]	]	PUNCT
iajs-1071	57	15	,	,	PUNCT
iajs-1071	57	16	so	so	CCONJ
iajs-1071	57	17	,	,	PUNCT
iajs-1071	57	18	itat=	itat=	NOUN
iajs-1071	57	19	itbt	itbt	VERB
iajs-1071	57	20	but	but	CCONJ
iajs-1071	57	21	xt	xt	PROPN
iajs-1071	57	22	is	be	AUX
iajs-1071	57	23	a	a	DET
iajs-1071	57	24	quasi	quasi	ADJ
iajs-1071	57	25	-	-	ADJ
iajs-1071	57	26	fully	fully	ADV
iajs-1071	57	27	cancellation	cancellation	NOUN
iajs-1071	57	28	module	module	NOUN
iajs-1071	57	29	.	.	PUNCT
iajs-1071	58	1	then	then	ADV
iajs-1071	58	2	at+f	at+f	PROPN
iajs-1071	58	3	-	-	PUNCT
iajs-1071	58	4	annit	annit	VERB
iajs-1071	58	5	=	=	PROPN
iajs-1071	58	6	bt+f	bt+f	NOUN
iajs-1071	58	7	-	-	PUNCT
iajs-1071	58	8	annit	annit	NOUN
iajs-1071	58	9	.	.	PUNCT
iajs-1071	59	1	but	but	CCONJ
iajs-1071	59	2	(	(	PUNCT
iajs-1071	59	3	f	f	X
iajs-1071	59	4	-	-	PUNCT
iajs-1071	59	5	anni)t	anni)t	NOUN
iajs-1071	59	6	=	=	SYM
iajs-1071	59	7	f	f	X
iajs-1071	59	8	-	-	PUNCT
iajs-1071	59	9	sannit	sannit	VERB
iajs-1071	59	10	t	t	PROPN
iajs-1071	59	11	(	(	PUNCT
iajs-1071	59	12	0,1	0,1	NOUN
iajs-1071	59	13	]	]	PUNCT
iajs-1071	59	14	which	which	PRON
iajs-1071	59	15	implies	imply	VERB
iajs-1071	59	16	at+(f	at+(f	NOUN
iajs-1071	59	17	-	-	PUNCT
iajs-1071	59	18	anni)t	anni)t	NOUN
iajs-1071	59	19	=	=	SYM
iajs-1071	59	20	bt+(f	bt+(f	NOUN
iajs-1071	59	21	-	-	PUNCT
iajs-1071	59	22	anni)t	anni)t	NOUN
iajs-1071	59	23	.	.	PUNCT
iajs-1071	60	1	so	so	ADV
iajs-1071	60	2	(	(	PUNCT
iajs-1071	60	3	a+f	a+f	PROPN
iajs-1071	60	4	-	-	PUNCT
iajs-1071	60	5	annxi)t=(b+f	annxi)t=(b+f	NOUN
iajs-1071	60	6	-	-	PUNCT
iajs-1071	60	7	annxi)t	annxi)t	NOUN
iajs-1071	60	8	.	.	PUNCT
iajs-1071	60	9	,	,	PUNCT
iajs-1071	60	10	by	by	ADP
iajs-1071	60	11	[	[	X
iajs-1071	60	12	2	2	NUM
iajs-1071	60	13	,	,	PUNCT
iajs-1071	60	14	remark	remark	NOUN
iajs-1071	60	15	(	(	PUNCT
iajs-1071	60	16	1.1.7	1.1.7	NUM
iajs-1071	60	17	)	)	PUNCT
iajs-1071	60	18	]	]	PUNCT
iajs-1071	60	19	.	.	PUNCT
iajs-1071	61	1	thus	thus	ADV
iajs-1071	61	2	a+f	a+f	NUM
iajs-1071	61	3	-	-	PUNCT
iajs-1071	61	4	annxi	annxi	NOUN
iajs-1071	61	5	=	=	SYM
iajs-1071	61	6	b+f	b+f	NOUN
iajs-1071	61	7	-	-	PUNCT
iajs-1071	61	8	annxi	annxi	NOUN
iajs-1071	61	9	.	.	PUNCT
iajs-1071	62	1	therefore	therefore	ADV
iajs-1071	62	2	x	x	X
iajs-1071	62	3	is	be	AUX
iajs-1071	62	4	q	q	NOUN
iajs-1071	62	5	-	-	PUNCT
iajs-1071	62	6	fcf(m	fcf(m	NOUN
iajs-1071	62	7	)	)	PUNCT
iajs-1071	62	8	.	.	PUNCT
iajs-1071	63	1	remarks	remark	NOUN
iajs-1071	63	2	and	and	CCONJ
iajs-1071	63	3	examples	example	NOUN
iajs-1071	63	4	1.3	1.3	NUM
iajs-1071	63	5	:	:	PUNCT
iajs-1071	63	6	(	(	PUNCT
iajs-1071	63	7	1	1	X
iajs-1071	63	8	)	)	PUNCT
iajs-1071	63	9	every	every	DET
iajs-1071	63	10	fully	fully	ADV
iajs-1071	63	11	cancellation	cancellation	NOUN
iajs-1071	63	12	fuzzy	fuzzy	ADJ
iajs-1071	63	13	module	module	NOUN
iajs-1071	63	14	is	be	AUX
iajs-1071	63	15	q	q	NOUN
iajs-1071	63	16	-	-	PUNCT
iajs-1071	63	17	fcf(m	fcf(m	NOUN
iajs-1071	63	18	)	)	PUNCT
iajs-1071	63	19	.	.	PUNCT
iajs-1071	64	1	but	but	CCONJ
iajs-1071	64	2	the	the	DET
iajs-1071	64	3	converse	converse	NOUN
iajs-1071	64	4	is	be	AUX
iajs-1071	64	5	not	not	PART
iajs-1071	64	6	true	true	ADJ
iajs-1071	64	7	ingeneral	ingeneral	NOUN
iajs-1071	64	8	by	by	ADP
iajs-1071	64	9	the	the	DET
iajs-1071	64	10	following	follow	VERB
iajs-1071	64	11	example	example	NOUN
iajs-1071	64	12	:	:	PUNCT
iajs-1071	64	13	let	let	VERB
iajs-1071	64	14	m	m	PRON
iajs-1071	64	15	=	=	VERB
iajs-1071	64	16	z4	z4	X
iajs-1071	64	17	is	be	AUX
iajs-1071	64	18	a	a	DET
iajs-1071	64	19	z	z	NOUN
iajs-1071	64	20	-	-	PUNCT
iajs-1071	64	21	module	module	NOUN
iajs-1071	64	22	.	.	PUNCT
iajs-1071	65	1	letx	letx	PROPN
iajs-1071	65	2	:	:	PUNCT
iajs-1071	66	1	m	m	VERB
iajs-1071	67	1	[	[	X
iajs-1071	67	2	0,1	0,1	NUM
iajs-1071	67	3	]	]	PUNCT
iajs-1071	67	4	define	define	NOUN
iajs-1071	67	5	by	by	ADP
iajs-1071	67	6	x(x)=	x(x)=	PROPN
iajs-1071	67	7	{	{	PUNCT
iajs-1071	67	8	let	let	VERB
iajs-1071	67	9	a	a	DET
iajs-1071	67	10	:	:	PUNCT
iajs-1071	67	11	(	(	PUNCT
iajs-1071	67	12	̅	̅	NOUN
iajs-1071	67	13	[	[	X
iajs-1071	67	14	0,1	0,1	NUM
iajs-1071	67	15	]	]	PUNCT
iajs-1071	67	16	define	define	NOUN
iajs-1071	67	17	by	by	ADP
iajs-1071	67	18	a(x)=	a(x)=	ADJ
iajs-1071	67	19	{	{	PUNCT
iajs-1071	67	20	̅	̅	NOUN
iajs-1071	67	21	t	t	PROPN
iajs-1071	67	22	(	(	PUNCT
iajs-1071	67	23	0,1	0,1	NOUN
iajs-1071	67	24	]	]	PUNCT
iajs-1071	67	25	let	let	VERB
iajs-1071	67	26	b	b	NOUN
iajs-1071	67	27	:	:	PUNCT
iajs-1071	67	28	z4	z4	PROPN
iajs-1071	67	29	[	[	X
iajs-1071	67	30	0,1	0,1	NUM
iajs-1071	67	31	]	]	PUNCT
iajs-1071	67	32	define	define	NOUN
iajs-1071	67	33	by	by	ADP
iajs-1071	67	34	b(x)=	b(x)=	PROPN
iajs-1071	67	35	{	{	PUNCT
iajs-1071	67	36	t	t	PROPN
iajs-1071	67	37	(	(	PUNCT
iajs-1071	67	38	0,1	0,1	NOUN
iajs-1071	67	39	]	]	PUNCT
iajs-1071	67	40	define	define	VERB
iajs-1071	68	1	i	i	PRON
iajs-1071	68	2	:	:	PUNCT
iajs-1071	68	3	(	(	PUNCT
iajs-1071	68	4	[	[	X
iajs-1071	68	5	0,1	0,1	NOUN
iajs-1071	68	6	]	]	PUNCT
iajs-1071	68	7	define	define	NOUN
iajs-1071	68	8	by	by	ADP
iajs-1071	68	9	i(x)=	i(x)=	PROPN
iajs-1071	68	10	{	{	PUNCT
iajs-1071	68	11	t	t	PROPN
iajs-1071	68	12	(	(	PUNCT
iajs-1071	68	13	0,1	0,1	NUM
iajs-1071	68	14	]	]	PUNCT
iajs-1071	68	15	it	it	PRON
iajs-1071	68	16	is	be	AUX
iajs-1071	68	17	clear	clear	ADJ
iajs-1071	68	18	that	that	SCONJ
iajs-1071	68	19	a	a	PRON
iajs-1071	68	20	and	and	CCONJ
iajs-1071	68	21	b	b	NOUN
iajs-1071	68	22	are	be	AUX
iajs-1071	68	23	fuzzy	fuzzy	ADJ
iajs-1071	68	24	submodules	submodule	NOUN
iajs-1071	68	25	of	of	ADP
iajs-1071	68	26	x	x	PUNCT
iajs-1071	69	1	and	and	CCONJ
iajs-1071	69	2	i	i	PRON
iajs-1071	69	3	is	be	AUX
iajs-1071	69	4	a	a	DET
iajs-1071	69	5	fuzzy	fuzzy	ADJ
iajs-1071	69	6	ideal	ideal	NOUN
iajs-1071	69	7	of	of	ADP
iajs-1071	69	8	r	r	NOUN
iajs-1071	69	9	mathematics	mathematic	NOUN
iajs-1071	69	10	|	|	ADV
iajs-1071	69	11	195	195	NUM
iajs-1071	69	12	2012	2012	NUM
iajs-1071	69	13	(	(	PUNCT
iajs-1071	69	14	عام	عام	PROPN
iajs-1071	69	15	1	1	NUM
iajs-1071	69	16	)	)	PUNCT
iajs-1071	69	17	(	(	PUNCT
iajs-1071	69	18	العدد	العدد	PROPN
iajs-1071	69	19	30مجلة	30مجلة	NUM
iajs-1071	69	20	إبن	إبن	VERB
iajs-1071	69	21	الهيثم	الهيثم	ADJ
iajs-1071	69	22	للعلوم	للعلوم	NOUN
iajs-1071	69	23	الصرفة	الصرفة	NOUN
iajs-1071	70	1	و	و	PRON
iajs-1071	70	2	التطبيقية	التطبيقية	ADV
iajs-1071	70	3	المجلد	المجلد	ADV
iajs-1071	70	4	)	)	PUNCT
iajs-1071	71	1	ibn	ibn	PROPN
iajs-1071	71	2	al	al	PROPN
iajs-1071	71	3	-	-	PUNCT
iajs-1071	71	4	haitham	haitham	PROPN
iajs-1071	71	5	j.	j.	PROPN
iajs-1071	71	6	for	for	ADP
iajs-1071	71	7	pure	pure	PROPN
iajs-1071	71	8	&	&	CCONJ
iajs-1071	71	9	appl	appl	PROPN
iajs-1071	71	10	.	.	PUNCT
iajs-1071	72	1	sci	sci	PROPN
iajs-1071	72	2	.	.	PUNCT
iajs-1071	73	1	vol.30	vol.30	NOUN
iajs-1071	73	2	(	(	PUNCT
iajs-1071	73	3	1	1	NUM
iajs-1071	73	4	)	)	PUNCT
iajs-1071	73	5	2017	2017	NUM
iajs-1071	73	6	m	m	NOUN
iajs-1071	73	7	=	=	NOUN
iajs-1071	73	8	z4	z4	NOUN
iajs-1071	73	9	=	=	SYM
iajs-1071	73	10	xt	xt	NOUN
iajs-1071	73	11	is	be	AUX
iajs-1071	73	12	not	not	PART
iajs-1071	73	13	fully	fully	ADV
iajs-1071	73	14	cancellation	cancellation	NOUN
iajs-1071	73	15	module	module	NOUN
iajs-1071	73	16	by	by	ADP
iajs-1071	73	17	[	[	X
iajs-1071	73	18	3	3	NUM
iajs-1071	73	19	,	,	PUNCT
iajs-1071	73	20	remark	remark	NOUN
iajs-1071	73	21	and	and	CCONJ
iajs-1071	73	22	examples	example	NOUN
iajs-1071	73	23	(	(	PUNCT
iajs-1071	73	24	2.3)(2	2.3)(2	NUM
iajs-1071	73	25	)	)	PUNCT
iajs-1071	73	26	]	]	PUNCT
iajs-1071	73	27	.	.	PUNCT
iajs-1071	74	1	since	since	SCONJ
iajs-1071	74	2	(	(	PUNCT
iajs-1071	74	3	(	(	PUNCT
iajs-1071	74	4	̅	̅	NOUN
iajs-1071	74	5	=	=	SYM
iajs-1071	74	6	(	(	PUNCT
iajs-1071	74	7	z4=0	z4=0	PROPN
iajs-1071	74	8	,	,	PUNCT
iajs-1071	74	9	but	but	CCONJ
iajs-1071	74	10	(	(	PUNCT
iajs-1071	74	11	̅	̅	NOUN
iajs-1071	74	12	≠z4	≠z4	PROPN
iajs-1071	74	13	.	.	PROPN
iajs-1071	74	14	implies	imply	VERB
iajs-1071	74	15	that	that	SCONJ
iajs-1071	74	16	x	x	PRON
iajs-1071	74	17	is	be	AUX
iajs-1071	74	18	not	not	PART
iajs-1071	74	19	fully	fully	ADV
iajs-1071	74	20	cancellation	cancellation	NOUN
iajs-1071	74	21	fuzzy	fuzzy	ADJ
iajs-1071	74	22	module	module	NOUN
iajs-1071	74	23	by	by	ADP
iajs-1071	74	24	[	[	X
iajs-1071	74	25	4	4	NUM
iajs-1071	74	26	,	,	PUNCT
iajs-1071	74	27	proposition	proposition	NOUN
iajs-1071	74	28	(	(	PUNCT
iajs-1071	74	29	1.2,2	1.2,2	NUM
iajs-1071	74	30	)	)	PUNCT
iajs-1071	74	31	]	]	PUNCT
iajs-1071	74	32	.	.	PUNCT
iajs-1071	75	1	hence	hence	ADV
iajs-1071	75	2	it=	it=	PROPN
iajs-1071	75	3	(	(	PUNCT
iajs-1071	75	4	,	,	PUNCT
iajs-1071	75	5	at=	at=	PROPN
iajs-1071	75	6	(	(	PUNCT
iajs-1071	75	7	̅	̅	NOUN
iajs-1071	75	8	and	and	CCONJ
iajs-1071	75	9	bt	bt	NOUN
iajs-1071	75	10	=	=	NOUN
iajs-1071	75	11	z4	z4	X
iajs-1071	75	12	.	.	PUNCT
iajs-1071	76	1	so	so	ADV
iajs-1071	76	2	itat=	itat=	PROPN
iajs-1071	76	3	itbt	itbt	VERB
iajs-1071	76	4	(	(	PUNCT
iajs-1071	76	5	since	since	SCONJ
iajs-1071	76	6	(	(	PUNCT
iajs-1071	76	7	(	(	PUNCT
iajs-1071	76	8	̅	̅	NOUN
iajs-1071	76	9	=(	=(	ADJ
iajs-1071	76	10	z4=	z4=	NOUN
iajs-1071	76	11	̅	̅	NOUN
iajs-1071	76	12	also	also	ADV
iajs-1071	76	13	,	,	PUNCT
iajs-1071	76	14	annit	annit	X
iajs-1071	76	15	=	=	NOUN
iajs-1071	76	16	ann	ann	X
iajs-1071	76	17	(	(	PUNCT
iajs-1071	76	18	=	=	NOUN
iajs-1071	76	19	z4	z4	PROPN
iajs-1071	76	20	then	then	ADV
iajs-1071	76	21	at+annit=	at+annit=	PROPN
iajs-1071	76	22	(	(	PUNCT
iajs-1071	76	23	̅	̅	NOUN
iajs-1071	76	24	+	+	NOUN
iajs-1071	76	25	z4	z4	X
iajs-1071	76	26	=	=	SYM
iajs-1071	76	27	z4	z4	PROPN
iajs-1071	76	28	also	also	ADV
iajs-1071	76	29	,	,	PUNCT
iajs-1071	76	30	bt+annit	bt+annit	ADJ
iajs-1071	76	31	=	=	ADJ
iajs-1071	76	32	z4+z4	z4+z4	NOUN
iajs-1071	76	33	=	=	PROPN
iajs-1071	76	34	z4	z4	PROPN
iajs-1071	76	35	then	then	ADV
iajs-1071	76	36	xt	xt	NOUN
iajs-1071	76	37	=	=	NOUN
iajs-1071	76	38	m	m	VERB
iajs-1071	76	39	is	be	AUX
iajs-1071	76	40	quasi	quasi	ADJ
iajs-1071	76	41	-	-	ADJ
iajs-1071	76	42	fully	fully	ADV
iajs-1071	76	43	cancellation	cancellation	NOUN
iajs-1071	76	44	module	module	NOUN
iajs-1071	76	45	.	.	PUNCT
iajs-1071	77	1	and	and	CCONJ
iajs-1071	77	2	by	by	ADP
iajs-1071	77	3	proposition	proposition	NOUN
iajs-1071	77	4	(	(	PUNCT
iajs-1071	77	5	1.2	1.2	NUM
iajs-1071	77	6	)	)	PUNCT
iajs-1071	77	7	.	.	PUNCT
iajs-1071	78	1	x	x	PUNCT
iajs-1071	78	2	is	be	AUX
iajs-1071	78	3	q	q	NOUN
iajs-1071	78	4	-	-	PUNCT
iajs-1071	78	5	fcf(m	fcf(m	NOUN
iajs-1071	78	6	)	)	PUNCT
iajs-1071	78	7	.	.	PUNCT
iajs-1071	79	1	(	(	PUNCT
iajs-1071	79	2	2	2	X
iajs-1071	79	3	)	)	PUNCT
iajs-1071	79	4	any	any	DET
iajs-1071	79	5	fuzzy	fuzzy	ADJ
iajs-1071	79	6	module	module	NOUN
iajs-1071	79	7	of	of	ADP
iajs-1071	79	8	a	a	DET
iajs-1071	79	9	z	z	NOUN
iajs-1071	79	10	-	-	PUNCT
iajs-1071	79	11	module	module	NOUN
iajs-1071	79	12	z	z	NOUN
iajs-1071	79	13	is	be	AUX
iajs-1071	79	14	q	q	NOUN
iajs-1071	79	15	-	-	PUNCT
iajs-1071	79	16	fcf(m	fcf(m	NOUN
iajs-1071	79	17	)	)	PUNCT
iajs-1071	79	18	.	.	PUNCT
iajs-1071	80	1	proof	proof	NOUN
iajs-1071	80	2	:	:	PUNCT
iajs-1071	80	3	by[4	by[4	NUM
iajs-1071	80	4	,	,	PUNCT
iajs-1071	80	5	remark	remark	NOUN
iajs-1071	80	6	and	and	CCONJ
iajs-1071	80	7	examples	example	NOUN
iajs-1071	80	8	(	(	PUNCT
iajs-1071	80	9	1.2.3)(1	1.2.3)(1	NUM
iajs-1071	80	10	)	)	PUNCT
iajs-1071	80	11	]	]	PUNCT
iajs-1071	81	1	we	we	PRON
iajs-1071	81	2	get	get	VERB
iajs-1071	81	3	x	x	PUNCT
iajs-1071	81	4	is	be	AUX
iajs-1071	81	5	fully	fully	ADV
iajs-1071	81	6	cancellation	cancellation	NOUN
iajs-1071	81	7	fuzzy	fuzzy	ADJ
iajs-1071	81	8	module	module	NOUN
iajs-1071	81	9	.	.	PUNCT
iajs-1071	82	1	and	and	CCONJ
iajs-1071	82	2	by	by	ADP
iajs-1071	82	3	(	(	PUNCT
iajs-1071	82	4	1	1	X
iajs-1071	82	5	)	)	PUNCT
iajs-1071	82	6	we	we	PRON
iajs-1071	82	7	interduce	interduce	VERB
iajs-1071	82	8	x	x	VERB
iajs-1071	82	9	is	be	AUX
iajs-1071	82	10	q	q	NOUN
iajs-1071	82	11	-	-	PUNCT
iajs-1071	82	12	fcf(m	fcf(m	NOUN
iajs-1071	82	13	)	)	PUNCT
iajs-1071	82	14	.	.	PUNCT
iajs-1071	83	1	(	(	PUNCT
iajs-1071	83	2	3	3	X
iajs-1071	83	3	)	)	PUNCT
iajs-1071	83	4	every	every	DET
iajs-1071	83	5	fuzzy	fuzzy	ADJ
iajs-1071	83	6	submodule	submodule	NOUN
iajs-1071	83	7	of	of	ADP
iajs-1071	83	8	q	q	NOUN
iajs-1071	83	9	-	-	PUNCT
iajs-1071	83	10	fcf(m	fcf(m	NOUN
iajs-1071	83	11	)	)	PUNCT
iajs-1071	83	12	is	be	AUX
iajs-1071	83	13	quasi	quasi	ADJ
iajs-1071	83	14	-	-	ADJ
iajs-1071	83	15	fully	fully	ADV
iajs-1071	83	16	cancellation	cancellation	NOUN
iajs-1071	83	17	.	.	PUNCT
iajs-1071	84	1	proof	proof	NOUN
iajs-1071	84	2	:	:	PUNCT
iajs-1071	84	3	let	let	VERB
iajs-1071	84	4	x	x	PRON
iajs-1071	84	5	be	be	AUX
iajs-1071	84	6	a	a	DET
iajs-1071	84	7	q	q	NOUN
iajs-1071	84	8	-	-	PUNCT
iajs-1071	84	9	fcf(m	fcf(m	NOUN
iajs-1071	84	10	)	)	PUNCT
iajs-1071	84	11	of	of	ADP
iajs-1071	84	12	an	an	DET
iajs-1071	84	13	r	r	NOUN
iajs-1071	84	14	-	-	PUNCT
iajs-1071	84	15	module	module	NOUN
iajs-1071	84	16	m.	m.	NOUN
iajs-1071	84	17	let	let	VERB
iajs-1071	84	18	n	n	PRON
iajs-1071	84	19	,	,	PUNCT
iajs-1071	84	20	k	k	X
iajs-1071	84	21	be	be	VERB
iajs-1071	84	22	two	two	NUM
iajs-1071	84	23	submodules	submodule	NOUN
iajs-1071	84	24	of	of	ADP
iajs-1071	84	25	m	m	PROPN
iajs-1071	84	26	and	and	CCONJ
iajs-1071	84	27	j	j	PROPN
iajs-1071	84	28	be	be	AUX
iajs-1071	84	29	an	an	DET
iajs-1071	84	30	ideal	ideal	NOUN
iajs-1071	84	31	of	of	ADP
iajs-1071	84	32	r.	r.	PROPN
iajs-1071	84	33	let	let	VERB
iajs-1071	84	34	c	c	PRON
iajs-1071	84	35	be	be	AUX
iajs-1071	84	36	a	a	DET
iajs-1071	84	37	fuzzy	fuzzy	ADJ
iajs-1071	84	38	submodule	submodule	NOUN
iajs-1071	84	39	of	of	ADP
iajs-1071	84	40	x	x	X
iajs-1071	84	41	.	.	PUNCT
iajs-1071	85	1	to	to	PART
iajs-1071	85	2	prove	prove	VERB
iajs-1071	85	3	c	c	PROPN
iajs-1071	85	4	is	be	AUX
iajs-1071	85	5	q	q	NOUN
iajs-1071	85	6	-	-	PUNCT
iajs-1071	85	7	fcf(m	fcf(m	NOUN
iajs-1071	85	8	)	)	PUNCT
iajs-1071	85	9	.	.	PUNCT
iajs-1071	86	1	define	define	NOUN
iajs-1071	86	2	:	:	PUNCT
iajs-1071	86	3	c	c	X
iajs-1071	86	4	:	:	PUNCT
iajs-1071	86	5	m	m	VERB
iajs-1071	86	6	[	[	X
iajs-1071	86	7	0,1	0,1	NUM
iajs-1071	86	8	]	]	PUNCT
iajs-1071	86	9	by	by	ADP
iajs-1071	86	10	c(x)=	c(x)=	PROPN
iajs-1071	86	11	{	{	PUNCT
iajs-1071	86	12	define	define	VERB
iajs-1071	86	13	a	a	DET
iajs-1071	86	14	:	:	PUNCT
iajs-1071	86	15	n	n	PRON
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iajs-1071	86	17	0,1	0,1	NUM
iajs-1071	86	18	]	]	PUNCT
iajs-1071	86	19	by	by	ADP
iajs-1071	86	20	a(x)=	a(x)=	PROPN
iajs-1071	86	21	{	{	PUNCT
iajs-1071	86	22	t	t	PROPN
iajs-1071	86	23	(	(	PUNCT
iajs-1071	86	24	0,1	0,1	NOUN
iajs-1071	86	25	]	]	PUNCT
iajs-1071	86	26	define	define	VERB
iajs-1071	86	27	b	b	NOUN
iajs-1071	86	28	:	:	PUNCT
iajs-1071	87	1	[	[	X
iajs-1071	87	2	0,1	0,1	NUM
iajs-1071	87	3	]	]	PUNCT
iajs-1071	87	4	by	by	ADP
iajs-1071	87	5	b(x)=	b(x)=	PROPN
iajs-1071	87	6	{	{	PUNCT
iajs-1071	87	7	t	t	PROPN
iajs-1071	87	8	(	(	PUNCT
iajs-1071	87	9	0,1	0,1	NOUN
iajs-1071	87	10	]	]	PUNCT
iajs-1071	87	11	define	define	VERB
iajs-1071	87	12	i	i	PRON
iajs-1071	87	13	:	:	PUNCT
iajs-1071	87	14	j	j	PROPN
iajs-1071	88	1	[	[	X
iajs-1071	88	2	0,1	0,1	NUM
iajs-1071	88	3	]	]	PUNCT
iajs-1071	88	4	by	by	ADP
iajs-1071	88	5	i(x)=	i(x)=	PROPN
iajs-1071	88	6	{	{	PUNCT
iajs-1071	88	7	t	t	PROPN
iajs-1071	88	8	(	(	PUNCT
iajs-1071	88	9	0,1	0,1	NUM
iajs-1071	88	10	]	]	PUNCT
iajs-1071	88	11	it	it	PRON
iajs-1071	88	12	is	be	AUX
iajs-1071	88	13	clear	clear	ADJ
iajs-1071	88	14	that	that	SCONJ
iajs-1071	88	15	a	a	DET
iajs-1071	88	16	,	,	PUNCT
iajs-1071	88	17	b	b	NOUN
iajs-1071	88	18	are	be	AUX
iajs-1071	88	19	fuzzy	fuzzy	ADJ
iajs-1071	88	20	submodules	submodule	NOUN
iajs-1071	88	21	of	of	ADP
iajs-1071	88	22	c	c	PROPN
iajs-1071	89	1	and	and	CCONJ
iajs-1071	89	2	i	i	PRON
iajs-1071	89	3	is	be	AUX
iajs-1071	89	4	a	a	DET
iajs-1071	89	5	fuzzy	fuzzy	ADJ
iajs-1071	89	6	ideal	ideal	NOUN
iajs-1071	89	7	of	of	ADP
iajs-1071	89	8	r.	r.	PROPN
iajs-1071	89	9	also	also	ADV
iajs-1071	89	10	,	,	PUNCT
iajs-1071	89	11	it	it	PRON
iajs-1071	89	12	=	=	PUNCT
iajs-1071	89	13	j	j	PROPN
iajs-1071	89	14	,	,	PUNCT
iajs-1071	89	15	at	at	ADP
iajs-1071	89	16	=	=	NOUN
iajs-1071	89	17	n	n	X
iajs-1071	89	18	,	,	PUNCT
iajs-1071	89	19	bt	bt	PROPN
iajs-1071	89	20	=	=	PROPN
iajs-1071	89	21	k	k	X
iajs-1071	89	22	,	,	PUNCT
iajs-1071	89	23	ct	ct	PROPN
iajs-1071	89	24	=	=	NOUN
iajs-1071	89	25	m.	m.	NOUN
iajs-1071	89	26	since	since	SCONJ
iajs-1071	89	27	x	x	PRON
iajs-1071	89	28	is	be	AUX
iajs-1071	89	29	q	q	NOUN
iajs-1071	89	30	-	-	PUNCT
iajs-1071	89	31	fcf(m	fcf(m	NOUN
iajs-1071	89	32	)	)	PUNCT
iajs-1071	89	33	.	.	PUNCT
iajs-1071	90	1	then	then	ADV
iajs-1071	90	2	xt	xt	PROPN
iajs-1071	90	3	is	be	AUX
iajs-1071	90	4	quasi	quasi	ADJ
iajs-1071	90	5	-	-	ADJ
iajs-1071	90	6	fully	fully	ADV
iajs-1071	90	7	cancellation	cancellation	NOUN
iajs-1071	90	8	module.by	module.by	NOUN
iajs-1071	90	9	proposition	proposition	NOUN
iajs-1071	90	10	(	(	PUNCT
iajs-1071	90	11	1.2	1.2	NUM
iajs-1071	90	12	)	)	PUNCT
iajs-1071	90	13	.	.	PUNCT
iajs-1071	91	1	since	since	SCONJ
iajs-1071	91	2	c	c	PROPN
iajs-1071	91	3	is	be	AUX
iajs-1071	91	4	a	a	DET
iajs-1071	91	5	fuzzy	fuzzy	ADJ
iajs-1071	91	6	submodule	submodule	NOUN
iajs-1071	91	7	of	of	ADP
iajs-1071	91	8	x.	x.	NOUN
iajs-1071	91	9	then	then	ADV
iajs-1071	91	10	ct	ct	PROPN
iajs-1071	91	11	is	be	AUX
iajs-1071	91	12	a	a	DET
iajs-1071	91	13	submodule	submodule	NOUN
iajs-1071	91	14	of	of	ADP
iajs-1071	91	15	xt	xt	PROPN
iajs-1071	91	16	and	and	CCONJ
iajs-1071	91	17	by	by	ADP
iajs-1071	91	18	[	[	PUNCT
iajs-1071	91	19	3	3	NUM
iajs-1071	91	20	,	,	PUNCT
iajs-1071	91	21	remark	remark	NOUN
iajs-1071	91	22	and	and	CCONJ
iajs-1071	91	23	examples	example	NOUN
iajs-1071	91	24	(	(	PUNCT
iajs-1071	91	25	2.2	2.2	NUM
iajs-1071	91	26	)	)	PUNCT
iajs-1071	91	27	]	]	PUNCT
iajs-1071	91	28	,	,	PUNCT
iajs-1071	91	29	we	we	PRON
iajs-1071	91	30	get	get	VERB
iajs-1071	91	31	ct	ct	PROPN
iajs-1071	91	32	is	be	AUX
iajs-1071	91	33	quasi	quasi	ADJ
iajs-1071	91	34	-	-	ADJ
iajs-1071	91	35	fully	fully	ADV
iajs-1071	91	36	cancellation	cancellation	NOUN
iajs-1071	91	37	module	module	NOUN
iajs-1071	91	38	.	.	PUNCT
iajs-1071	92	1	therefore	therefore	ADV
iajs-1071	92	2	c	c	PROPN
iajs-1071	92	3	is	be	AUX
iajs-1071	92	4	q	q	NOUN
iajs-1071	92	5	-	-	PUNCT
iajs-1071	92	6	fcf(m	fcf(m	NOUN
iajs-1071	92	7	)	)	PUNCT
iajs-1071	92	8	.	.	PUNCT
iajs-1071	93	1	by	by	ADP
iajs-1071	93	2	proposition(1.2	proposition(1.2	NOUN
iajs-1071	93	3	)	)	PUNCT
iajs-1071	93	4	mathematics	mathematic	NOUN
iajs-1071	93	5	|	|	ADV
iajs-1071	93	6	196	196	NUM
iajs-1071	93	7	2012	2012	NUM
iajs-1071	93	8	(	(	PUNCT
iajs-1071	93	9	عام	عام	PROPN
iajs-1071	93	10	1	1	NUM
iajs-1071	93	11	)	)	PUNCT
iajs-1071	93	12	(	(	PUNCT
iajs-1071	93	13	العدد	العدد	PROPN
iajs-1071	93	14	30مجلة	30مجلة	NUM
iajs-1071	93	15	إبن	إبن	VERB
iajs-1071	93	16	الهيثم	الهيثم	ADJ
iajs-1071	93	17	للعلوم	للعلوم	NOUN
iajs-1071	93	18	الصرفة	الصرفة	NOUN
iajs-1071	93	19	و	و	PRON
iajs-1071	93	20	التطبيقية	التطبيقية	ADV
iajs-1071	93	21	المجلد	المجلد	ADV
iajs-1071	93	22	)	)	PUNCT
iajs-1071	94	1	ibn	ibn	PROPN
iajs-1071	94	2	al	al	PROPN
iajs-1071	94	3	-	-	PUNCT
iajs-1071	94	4	haitham	haitham	PROPN
iajs-1071	94	5	j.	j.	PROPN
iajs-1071	94	6	for	for	ADP
iajs-1071	94	7	pure	pure	PROPN
iajs-1071	94	8	&	&	CCONJ
iajs-1071	94	9	appl	appl	PROPN
iajs-1071	94	10	.	.	PUNCT
iajs-1071	95	1	sci	sci	PROPN
iajs-1071	95	2	.	.	PUNCT
iajs-1071	96	1	vol.30	vol.30	NOUN
iajs-1071	96	2	(	(	PUNCT
iajs-1071	96	3	1	1	NUM
iajs-1071	96	4	)	)	PUNCT
iajs-1071	96	5	2017	2017	NUM
iajs-1071	96	6	(	(	PUNCT
iajs-1071	96	7	4	4	X
iajs-1071	96	8	)	)	PUNCT
iajs-1071	96	9	let	let	VERB
iajs-1071	96	10	x1and	x1and	PROPN
iajs-1071	97	1	x2	x2	PRON
iajs-1071	97	2	be	be	AUX
iajs-1071	97	3	two	two	NUM
iajs-1071	97	4	fuzzy	fuzzy	ADJ
iajs-1071	97	5	modules	module	NOUN
iajs-1071	97	6	of	of	ADP
iajs-1071	97	7	an	an	DET
iajs-1071	97	8	r	r	NOUN
iajs-1071	97	9	-	-	PUNCT
iajs-1071	97	10	module	module	NOUN
iajs-1071	97	11	m1	m1	NOUN
iajs-1071	97	12	,	,	PUNCT
iajs-1071	97	13	m2	m2	PROPN
iajs-1071	97	14	respectivly	respectivly	VERB
iajs-1071	97	15	such	such	ADJ
iajs-1071	97	16	that	that	DET
iajs-1071	97	17	m1	m1	PROPN
iajs-1071	97	18	m2.then	m2.then	SCONJ
iajs-1071	97	19	x1	x1	PROPN
iajs-1071	97	20	is	be	AUX
iajs-1071	97	21	q	q	NOUN
iajs-1071	97	22	-	-	PUNCT
iajs-1071	97	23	fcf(m)if	fcf(m)if	NOUN
iajs-1071	97	24	and	and	CCONJ
iajs-1071	97	25	only	only	ADV
iajs-1071	97	26	if	if	SCONJ
iajs-1071	97	27	x2	x2	PRON
iajs-1071	97	28	is	be	AUX
iajs-1071	97	29	q	q	NOUN
iajs-1071	97	30	-	-	PUNCT
iajs-1071	97	31	fcf(m	fcf(m	NOUN
iajs-1071	97	32	)	)	PUNCT
iajs-1071	97	33	.	.	PUNCT
iajs-1071	98	1	proof	proof	NOUN
iajs-1071	98	2	:	:	PUNCT
iajs-1071	98	3	(	(	PUNCT
iajs-1071	98	4	)	)	PUNCT
iajs-1071	98	5	let	let	VERB
iajs-1071	98	6	x1	x1	NOUN
iajs-1071	98	7	:	:	PUNCT
iajs-1071	98	8	m1	m1	PROPN
iajs-1071	99	1	[	[	X
iajs-1071	99	2	0,1	0,1	NUM
iajs-1071	99	3	]	]	PUNCT
iajs-1071	99	4	define	define	NOUN
iajs-1071	99	5	by	by	ADP
iajs-1071	99	6	x1(x)=	x1(x)=	PROPN
iajs-1071	99	7	{	{	PUNCT
iajs-1071	99	8	let	let	VERB
iajs-1071	99	9	x2	x2	PRON
iajs-1071	99	10	:	:	PUNCT
iajs-1071	99	11	m2	m2	PROPN
iajs-1071	100	1	[	[	X
iajs-1071	100	2	0,1	0,1	NUM
iajs-1071	100	3	]	]	PUNCT
iajs-1071	100	4	define	define	NOUN
iajs-1071	100	5	by	by	ADP
iajs-1071	100	6	x2(x)=	x2(x)=	NOUN
iajs-1071	100	7	{	{	PUNCT
iajs-1071	100	8	it	it	PRON
iajs-1071	100	9	is	be	AUX
iajs-1071	100	10	clear	clear	ADJ
iajs-1071	100	11	that	that	SCONJ
iajs-1071	100	12	x1	x1	PROPN
iajs-1071	100	13	and	and	CCONJ
iajs-1071	100	14	x2	x2	PROPN
iajs-1071	100	15	are	be	AUX
iajs-1071	100	16	fuzzy	fuzzy	ADJ
iajs-1071	100	17	modules	module	NOUN
iajs-1071	100	18	of	of	ADP
iajs-1071	100	19	m1	m1	PROPN
iajs-1071	100	20	and	and	CCONJ
iajs-1071	100	21	m2	m2	PROPN
iajs-1071	100	22	respectively	respectively	ADV
iajs-1071	100	23	.	.	PUNCT
iajs-1071	101	1	since	since	SCONJ
iajs-1071	101	2	(	(	PUNCT
iajs-1071	101	3	x1)t	x1)t	NOUN
iajs-1071	101	4	=	=	PROPN
iajs-1071	101	5	m1	m1	PROPN
iajs-1071	101	6	,	,	PUNCT
iajs-1071	101	7	(	(	PUNCT
iajs-1071	101	8	x2)t	x2)t	PROPN
iajs-1071	101	9	=	=	PROPN
iajs-1071	101	10	m2	m2	PROPN
iajs-1071	101	11	and	and	CCONJ
iajs-1071	101	12	m1	m1	PROPN
iajs-1071	101	13	m2	m2	PROPN
iajs-1071	101	14	,	,	PUNCT
iajs-1071	101	15	t	t	PROPN
iajs-1071	101	16	(	(	PUNCT
iajs-1071	101	17	0,1	0,1	NUM
iajs-1071	101	18	]	]	PUNCT
iajs-1071	101	19	,	,	PUNCT
iajs-1071	101	20	then	then	ADV
iajs-1071	101	21	m2	m2	PROPN
iajs-1071	101	22	is	be	AUX
iajs-1071	101	23	quasi	quasi	ADJ
iajs-1071	101	24	-	-	ADJ
iajs-1071	101	25	fully	fully	ADV
iajs-1071	101	26	cancellation	cancellation	NOUN
iajs-1071	101	27	module	module	NOUN
iajs-1071	101	28	by	by	ADP
iajs-1071	101	29	[	[	PUNCT
iajs-1071	101	30	3	3	NUM
iajs-1071	101	31	,	,	PUNCT
iajs-1071	101	32	remark	remark	NOUN
iajs-1071	101	33	and	and	CCONJ
iajs-1071	101	34	examples	example	NOUN
iajs-1071	101	35	(	(	PUNCT
iajs-1071	101	36	2.2	2.2	NUM
iajs-1071	101	37	)	)	PUNCT
iajs-1071	101	38	.	.	PUNCT
iajs-1071	102	1	(	(	PUNCT
iajs-1071	102	2	5	5	NUM
iajs-1071	102	3	)	)	PUNCT
iajs-1071	102	4	]	]	PUNCT
iajs-1071	102	5	then	then	ADV
iajs-1071	102	6	x2	x2	PROPN
iajs-1071	102	7	is	be	AUX
iajs-1071	102	8	q	q	NOUN
iajs-1071	102	9	-	-	PUNCT
iajs-1071	102	10	fcf(m	fcf(m	NOUN
iajs-1071	102	11	)	)	PUNCT
iajs-1071	102	12	by	by	ADP
iajs-1071	102	13	proposition	proposition	NOUN
iajs-1071	102	14	(	(	PUNCT
iajs-1071	102	15	1.2	1.2	NUM
iajs-1071	102	16	)	)	PUNCT
iajs-1071	102	17	.	.	PUNCT
iajs-1071	103	1	conversely	conversely	ADV
iajs-1071	103	2	:	:	PUNCT
iajs-1071	103	3	it	it	PRON
iajs-1071	103	4	is	be	AUX
iajs-1071	103	5	clear	clear	ADJ
iajs-1071	103	6	.	.	PUNCT
iajs-1071	104	1	proposition	proposition	NOUN
iajs-1071	104	2	1.4	1.4	NUM
iajs-1071	104	3	:	:	PUNCT
iajs-1071	104	4	let	let	VERB
iajs-1071	104	5	x	x	PRON
iajs-1071	104	6	be	be	AUX
iajs-1071	104	7	a	a	DET
iajs-1071	104	8	multiplication	multiplication	NOUN
iajs-1071	104	9	and	and	CCONJ
iajs-1071	104	10	naturally	naturally	ADV
iajs-1071	104	11	cancellation	cancellation	NOUN
iajs-1071	104	12	fuzzy	fuzzy	ADJ
iajs-1071	104	13	module	module	NOUN
iajs-1071	104	14	of	of	ADP
iajs-1071	104	15	an	an	DET
iajs-1071	104	16	r	r	NOUN
iajs-1071	104	17	-	-	PUNCT
iajs-1071	104	18	module	module	NOUN
iajs-1071	104	19	m	m	NOUN
iajs-1071	104	20	then	then	ADV
iajs-1071	104	21	x	x	VERB
iajs-1071	104	22	is	be	AUX
iajs-1071	104	23	q	q	NOUN
iajs-1071	104	24	-	-	PUNCT
iajs-1071	104	25	fcf(m	fcf(m	NOUN
iajs-1071	104	26	)	)	PUNCT
iajs-1071	104	27	.	.	PUNCT
iajs-1071	105	1	proof	proof	NOUN
iajs-1071	105	2	:	:	PUNCT
iajs-1071	105	3	since	since	SCONJ
iajs-1071	105	4	x	x	PRON
iajs-1071	105	5	is	be	AUX
iajs-1071	105	6	multiplication	multiplication	NOUN
iajs-1071	105	7	and	and	CCONJ
iajs-1071	105	8	naturally	naturally	ADV
iajs-1071	105	9	cancellation	cancellation	NOUN
iajs-1071	105	10	fuzzy	fuzzy	ADJ
iajs-1071	105	11	module	module	NOUN
iajs-1071	105	12	,	,	PUNCT
iajs-1071	105	13	then	then	ADV
iajs-1071	105	14	by[4	by[4	PROPN
iajs-1071	105	15	,	,	PUNCT
iajs-1071	105	16	theorem	theorem	VERB
iajs-1071	105	17	(	(	PUNCT
iajs-1071	105	18	1.4.3	1.4.3	NUM
iajs-1071	105	19	)	)	PUNCT
iajs-1071	105	20	]	]	PUNCT
iajs-1071	105	21	.	.	PUNCT
iajs-1071	106	1	we	we	PRON
iajs-1071	106	2	obtian	obtian	ADV
iajs-1071	106	3	x	x	VERB
iajs-1071	106	4	is	be	AUX
iajs-1071	106	5	fully	fully	ADV
iajs-1071	106	6	cancellation	cancellation	NOUN
iajs-1071	106	7	fuzzy	fuzzy	ADJ
iajs-1071	106	8	module	module	NOUN
iajs-1071	106	9	and	and	CCONJ
iajs-1071	106	10	by	by	ADP
iajs-1071	106	11	remark	remark	NOUN
iajs-1071	106	12	and	and	CCONJ
iajs-1071	106	13	examples	example	NOUN
iajs-1071	106	14	(	(	PUNCT
iajs-1071	106	15	(	(	PUNCT
iajs-1071	106	16	1.3	1.3	NUM
iajs-1071	106	17	)	)	PUNCT
iajs-1071	106	18	(	(	PUNCT
iajs-1071	106	19	1	1	NUM
iajs-1071	106	20	)	)	PUNCT
iajs-1071	106	21	)	)	PUNCT
iajs-1071	106	22	.	.	PUNCT
iajs-1071	107	1	x	x	PUNCT
iajs-1071	107	2	is	be	AUX
iajs-1071	107	3	q	q	NOUN
iajs-1071	107	4	-	-	PUNCT
iajs-1071	107	5	fcf(m	fcf(m	NOUN
iajs-1071	107	6	)	)	PUNCT
iajs-1071	107	7	.	.	PUNCT
iajs-1071	108	1	proposition	proposition	NOUN
iajs-1071	108	2	1.5	1.5	NUM
iajs-1071	108	3	:	:	PUNCT
iajs-1071	108	4	let	let	VERB
iajs-1071	108	5	x	x	PRON
iajs-1071	108	6	be	be	AUX
iajs-1071	108	7	a	a	DET
iajs-1071	108	8	fuzzy	fuzzy	ADJ
iajs-1071	108	9	torsion	torsion	NOUN
iajs-1071	108	10	free	free	ADJ
iajs-1071	108	11	module	module	NOUN
iajs-1071	108	12	over	over	ADP
iajs-1071	108	13	a	a	DET
iajs-1071	108	14	fuzzy	fuzzy	ADJ
iajs-1071	108	15	integral	integral	ADJ
iajs-1071	108	16	domain	domain	NOUN
iajs-1071	108	17	r.	r.	NOUN
iajs-1071	108	18	if	if	SCONJ
iajs-1071	108	19	x	x	PRON
iajs-1071	108	20	is	be	AUX
iajs-1071	108	21	quasi	quasi	ADJ
iajs-1071	108	22	-	-	ADJ
iajs-1071	108	23	fully	fully	ADV
iajs-1071	108	24	cancellation	cancellation	NOUN
iajs-1071	108	25	modules	module	NOUN
iajs-1071	108	26	,	,	PUNCT
iajs-1071	108	27	then	then	ADV
iajs-1071	108	28	x	x	PUNCT
iajs-1071	108	29	is	be	AUX
iajs-1071	108	30	fully	fully	ADV
iajs-1071	108	31	cancellation	cancellation	NOUN
iajs-1071	108	32	.	.	PUNCT
iajs-1071	109	1	proof	proof	NOUN
iajs-1071	109	2	:	:	PUNCT
iajs-1071	109	3	let	let	VERB
iajs-1071	109	4	x	x	PRON
iajs-1071	109	5	be	be	AUX
iajs-1071	109	6	a	a	DET
iajs-1071	109	7	fuzzy	fuzzy	ADJ
iajs-1071	109	8	torsion	torsion	NOUN
iajs-1071	109	9	free	free	ADJ
iajs-1071	109	10	module	module	NOUN
iajs-1071	109	11	and	and	CCONJ
iajs-1071	109	12	r	r	NOUN
iajs-1071	109	13	be	be	VERB
iajs-1071	109	14	a	a	DET
iajs-1071	109	15	fuzzy	fuzzy	ADJ
iajs-1071	109	16	integral	integral	ADJ
iajs-1071	109	17	domain	domain	NOUN
iajs-1071	109	18	.	.	PUNCT
iajs-1071	109	19	suppose	suppose	VERB
iajs-1071	110	1	that	that	SCONJ
iajs-1071	110	2	ia	ia	PROPN
iajs-1071	110	3	=	=	NOUN
iajs-1071	110	4	ib	ib	X
iajs-1071	110	5	where	where	SCONJ
iajs-1071	110	6	a	a	DET
iajs-1071	110	7	,	,	PUNCT
iajs-1071	110	8	b	b	NOUN
iajs-1071	110	9	are	be	AUX
iajs-1071	110	10	two	two	NUM
iajs-1071	110	11	fuzzy	fuzzy	ADJ
iajs-1071	110	12	submodules	submodule	NOUN
iajs-1071	110	13	of	of	ADP
iajs-1071	110	14	x	x	PUNCT
iajs-1071	111	1	and	and	CCONJ
iajs-1071	111	2	i	i	PRON
iajs-1071	111	3	be	be	VERB
iajs-1071	111	4	a	a	DET
iajs-1071	111	5	fuzzy	fuzzy	ADJ
iajs-1071	111	6	ideal	ideal	NOUN
iajs-1071	111	7	of	of	ADP
iajs-1071	111	8	r.	r.	PROPN
iajs-1071	111	9	since	since	SCONJ
iajs-1071	111	10	x	x	PROPN
iajs-1071	111	11	is	be	AUX
iajs-1071	111	12	quasi	quasi	ADJ
iajs-1071	111	13	-	-	ADJ
iajs-1071	111	14	fully	fully	ADV
iajs-1071	111	15	cancellation	cancellation	NOUN
iajs-1071	111	16	,	,	PUNCT
iajs-1071	111	17	then	then	ADV
iajs-1071	111	18	a+(f	a+(f	NOUN
iajs-1071	111	19	-	-	PUNCT
iajs-1071	111	20	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	111	21	-	-	PUNCT
iajs-1071	111	22	annxi	annxi	NOUN
iajs-1071	111	23	)	)	PUNCT
iajs-1071	111	24	.	.	PUNCT
iajs-1071	112	1	now	now	ADV
iajs-1071	112	2	,	,	PUNCT
iajs-1071	112	3	let	let	VERB
iajs-1071	112	4	xt	xt	ADP
iajs-1071	112	5	f	f	X
iajs-1071	112	6	-	-	PUNCT
iajs-1071	112	7	annxi	annxi	NOUN
iajs-1071	112	8	,	,	PUNCT
iajs-1071	112	9	then	then	ADV
iajs-1071	112	10	ixt=01	ixt=01	PROPN
iajs-1071	112	11	t	t	PROPN
iajs-1071	112	12	(	(	PUNCT
iajs-1071	112	13	0,1	0,1	NUM
iajs-1071	112	14	]	]	PUNCT
iajs-1071	112	15	and	and	CCONJ
iajs-1071	112	16	hence	hence	ADV
iajs-1071	112	17	xt=01	xt=01	PROPN
iajs-1071	112	18	for	for	ADP
iajs-1071	112	19	each	each	DET
iajs-1071	112	20	fuzzy	fuzzy	ADJ
iajs-1071	112	21	singleton	singleton	NOUN
iajs-1071	112	22	of	of	ADP
iajs-1071	112	23	i	i	PRON
iajs-1071	112	24	,	,	PUNCT
iajs-1071	112	25	(	(	PUNCT
iajs-1071	112	26	0,1	0,1	NOUN
iajs-1071	112	27	]	]	PUNCT
iajs-1071	112	28	.	.	PUNCT
iajs-1071	113	1	≠01	≠01	NUM
iajs-1071	113	2	(	(	PUNCT
iajs-1071	113	3	since	since	SCONJ
iajs-1071	113	4	r	r	NOUN
iajs-1071	113	5	is	be	AUX
iajs-1071	113	6	integral	integral	ADJ
iajs-1071	113	7	domain	domain	NOUN
iajs-1071	113	8	)	)	PUNCT
iajs-1071	113	9	.	.	PUNCT
iajs-1071	114	1	then	then	ADV
iajs-1071	114	2	i≠01	i≠01	X
iajs-1071	114	3	.	.	PUNCT
iajs-1071	115	1	therefore	therefore	ADV
iajs-1071	115	2	xt=01	xt=01	PROPN
iajs-1071	115	3	(	(	PUNCT
iajs-1071	115	4	since	since	SCONJ
iajs-1071	115	5	x	x	PRON
iajs-1071	115	6	is	be	AUX
iajs-1071	115	7	a	a	DET
iajs-1071	115	8	fuzzy	fuzzy	ADJ
iajs-1071	115	9	torsion	torsion	NOUN
iajs-1071	115	10	free	free	ADJ
iajs-1071	115	11	)	)	PUNCT
iajs-1071	115	12	.	.	PUNCT
iajs-1071	116	1	then	then	ADV
iajs-1071	116	2	f	f	X
iajs-1071	116	3	-	-	PUNCT
iajs-1071	116	4	annxi=01.thus	annxi=01.thus	PROPN
iajs-1071	116	5	a	a	DET
iajs-1071	116	6	=	=	NOUN
iajs-1071	116	7	b	b	NOUN
iajs-1071	116	8	and	and	CCONJ
iajs-1071	116	9	hence	hence	ADV
iajs-1071	116	10	x	x	PRON
iajs-1071	116	11	is	be	AUX
iajs-1071	116	12	a	a	DET
iajs-1071	116	13	fully	fully	ADV
iajs-1071	116	14	cancellation	cancellation	NOUN
iajs-1071	116	15	fuzzy	fuzzy	ADJ
iajs-1071	116	16	module	module	NOUN
iajs-1071	116	17	.	.	PUNCT
iajs-1071	117	1	mathematics	mathematic	NOUN
iajs-1071	117	2	|	|	ADV
iajs-1071	117	3	197	197	NUM
iajs-1071	117	4	2012	2012	NUM
iajs-1071	117	5	(	(	PUNCT
iajs-1071	117	6	عام	عام	PROPN
iajs-1071	117	7	1	1	NUM
iajs-1071	117	8	)	)	PUNCT
iajs-1071	117	9	(	(	PUNCT
iajs-1071	117	10	العدد	العدد	PROPN
iajs-1071	117	11	30مجلة	30مجلة	NUM
iajs-1071	117	12	إبن	إبن	VERB
iajs-1071	117	13	الهيثم	الهيثم	ADJ
iajs-1071	117	14	للعلوم	للعلوم	NOUN
iajs-1071	117	15	الصرفة	الصرفة	NOUN
iajs-1071	118	1	و	و	PRON
iajs-1071	118	2	التطبيقية	التطبيقية	ADV
iajs-1071	118	3	المجلد	المجلد	ADV
iajs-1071	118	4	)	)	PUNCT
iajs-1071	119	1	ibn	ibn	PROPN
iajs-1071	119	2	al	al	PROPN
iajs-1071	119	3	-	-	PUNCT
iajs-1071	119	4	haitham	haitham	PROPN
iajs-1071	119	5	j.	j.	PROPN
iajs-1071	119	6	for	for	ADP
iajs-1071	119	7	pure	pure	PROPN
iajs-1071	119	8	&	&	CCONJ
iajs-1071	119	9	appl	appl	PROPN
iajs-1071	119	10	.	.	PUNCT
iajs-1071	120	1	sci	sci	PROPN
iajs-1071	120	2	.	.	PUNCT
iajs-1071	121	1	vol.30	vol.30	NOUN
iajs-1071	121	2	(	(	PUNCT
iajs-1071	121	3	1	1	NUM
iajs-1071	121	4	)	)	PUNCT
iajs-1071	121	5	2017	2017	NUM
iajs-1071	121	6	proposition	proposition	NOUN
iajs-1071	121	7	1.6	1.6	NUM
iajs-1071	121	8	:	:	PUNCT
iajs-1071	121	9	let	let	VERB
iajs-1071	121	10	x	x	PRON
iajs-1071	121	11	be	be	AUX
iajs-1071	121	12	f(m	f(m	PROPN
iajs-1071	121	13	)	)	PUNCT
iajs-1071	121	14	and	and	CCONJ
iajs-1071	121	15	let	let	VERB
iajs-1071	121	16	r	r	PRON
iajs-1071	121	17	be	be	AUX
iajs-1071	121	18	a	a	DET
iajs-1071	121	19	fuzzy	fuzzy	ADJ
iajs-1071	121	20	principle	principle	ADJ
iajs-1071	121	21	ideal	ideal	ADJ
iajs-1071	121	22	ring	ring	NOUN
iajs-1071	121	23	.	.	PUNCT
iajs-1071	122	1	then	then	ADV
iajs-1071	122	2	x	x	X
iajs-1071	122	3	is	be	AUX
iajs-1071	122	4	a	a	DET
iajs-1071	122	5	quasi	quasi	ADJ
iajs-1071	122	6	-	-	ADJ
iajs-1071	122	7	fully	fully	ADV
iajs-1071	122	8	cancellation	cancellation	NOUN
iajs-1071	122	9	module	module	NOUN
iajs-1071	122	10	.	.	PUNCT
iajs-1071	123	1	proof	proof	NOUN
iajs-1071	123	2	:	:	PUNCT
iajs-1071	123	3	let	let	VERB
iajs-1071	123	4	a	a	PRON
iajs-1071	123	5	and	and	CCONJ
iajs-1071	123	6	b	b	NOUN
iajs-1071	123	7	be	be	AUX
iajs-1071	123	8	two	two	NUM
iajs-1071	123	9	fuzzy	fuzzy	ADJ
iajs-1071	123	10	submodules	submodule	NOUN
iajs-1071	123	11	of	of	ADP
iajs-1071	123	12	x.	x.	NOUN
iajs-1071	123	13	let	let	VERB
iajs-1071	123	14	i	i	PRON
iajs-1071	123	15	be	be	AUX
iajs-1071	123	16	a	a	DET
iajs-1071	123	17	fuzzy	fuzzy	ADJ
iajs-1071	123	18	ideal	ideal	NOUN
iajs-1071	123	19	of	of	ADP
iajs-1071	123	20	a	a	DET
iajs-1071	123	21	fuzzy	fuzzy	ADJ
iajs-1071	123	22	principle	principle	NOUN
iajs-1071	123	23	ideal	ideal	NOUN
iajs-1071	123	24	ring	ring	PROPN
iajs-1071	123	25	r.	r.	PROPN
iajs-1071	123	26	suppose	suppose	VERB
iajs-1071	123	27	that	that	SCONJ
iajs-1071	123	28	ia	ia	PROPN
iajs-1071	123	29	=	=	PROPN
iajs-1071	123	30	ib	ib	VERB
iajs-1071	123	31	.	.	PUNCT
iajs-1071	124	1	we	we	PRON
iajs-1071	124	2	show	show	VERB
iajs-1071	124	3	that	that	SCONJ
iajs-1071	124	4	a+(f	a+(f	NOUN
iajs-1071	124	5	-	-	PUNCT
iajs-1071	124	6	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	124	7	-	-	PUNCT
iajs-1071	124	8	annxi	annxi	NOUN
iajs-1071	124	9	)	)	PUNCT
iajs-1071	124	10	since	since	SCONJ
iajs-1071	124	11	r	r	NOUN
iajs-1071	124	12	is	be	AUX
iajs-1071	124	13	a	a	DET
iajs-1071	124	14	fuzzy	fuzzy	ADJ
iajs-1071	124	15	principle	principle	ADJ
iajs-1071	124	16	ideal	ideal	NOUN
iajs-1071	124	17	ring	ring	NOUN
iajs-1071	124	18	,	,	PUNCT
iajs-1071	124	19	then	then	ADV
iajs-1071	124	20	i=	i=	PROPN
iajs-1071	124	21	(	(	PUNCT
iajs-1071	124	22	)	)	PUNCT
iajs-1071	124	23	,	,	PUNCT
iajs-1071	124	24	where	where	SCONJ
iajs-1071	124	25	be	be	AUX
iajs-1071	124	26	a	a	DET
iajs-1071	124	27	fuzzy	fuzzy	ADJ
iajs-1071	124	28	singleton	singleton	NOUN
iajs-1071	124	29	of	of	ADP
iajs-1071	124	30	r	r	PROPN
iajs-1071	124	31	,	,	PUNCT
iajs-1071	124	32	(	(	PUNCT
iajs-1071	124	33	0,1	0,1	NOUN
iajs-1071	124	34	]	]	PUNCT
iajs-1071	124	35	.	.	PUNCT
iajs-1071	125	1	then	then	ADV
iajs-1071	125	2	(	(	PUNCT
iajs-1071	125	3	)	)	PUNCT
iajs-1071	125	4	a=	a=	PROPN
iajs-1071	125	5	(	(	PUNCT
iajs-1071	125	6	)	)	PUNCT
iajs-1071	125	7	b	b	NOUN
iajs-1071	125	8	and	and	CCONJ
iajs-1071	125	9	hence	hence	ADV
iajs-1071	125	10	.at=	.at=	NOUN
iajs-1071	125	11	.bs	.bs	PUNCT
iajs-1071	126	1	where	where	SCONJ
iajs-1071	126	2	at	at	ADP
iajs-1071	126	3	a	a	PRON
iajs-1071	126	4	and	and	CCONJ
iajs-1071	126	5	bs	bs	PROPN
iajs-1071	126	6	b	b	PROPN
iajs-1071	126	7	(	(	PUNCT
iajs-1071	126	8	0,1	0,1	NOUN
iajs-1071	126	9	]	]	PUNCT
iajs-1071	126	10	.	.	PUNCT
iajs-1071	127	1	now	now	ADV
iajs-1071	127	2	,	,	PUNCT
iajs-1071	127	3	.at	.at	PUNCT
iajs-1071	128	1	.bs=01	.bs=01	PUNCT
iajs-1071	128	2	then	then	ADV
iajs-1071	128	3	(	(	PUNCT
iajs-1071	128	4	ra	ra	NOUN
iajs-1071	128	5	-	-	PUNCT
iajs-1071	128	6	rb	rb	NOUN
iajs-1071	128	7	)	)	PUNCT
iajs-1071	128	8	=	=	NOUN
iajs-1071	128	9	0	0	NUM
iajs-1071	128	10	≤	≤	NUM
iajs-1071	128	11	01	01	NUM
iajs-1071	129	1	where	where	SCONJ
iajs-1071	129	2	=	=	NOUN
iajs-1071	129	3	min	min	NOUN
iajs-1071	129	4	{	{	PUNCT
iajs-1071	129	5	,	,	PUNCT
iajs-1071	129	6	t	t	PROPN
iajs-1071	129	7	,	,	PUNCT
iajs-1071	129	8	s	s	PART
iajs-1071	129	9	}	}	PUNCT
iajs-1071	129	10	.	.	PUNCT
iajs-1071	130	1	therefore	therefore	ADV
iajs-1071	130	2	(	(	PUNCT
iajs-1071	130	3	a	a	PROPN
iajs-1071	130	4	-	-	PUNCT
iajs-1071	130	5	b	b	NOUN
iajs-1071	130	6	)	)	PUNCT
iajs-1071	131	1	=	=	NOUN
iajs-1071	131	2	01,and	01,and	NOUN
iajs-1071	132	1	hence	hence	ADV
iajs-1071	132	2	(	(	PUNCT
iajs-1071	132	3	at	at	ADP
iajs-1071	132	4	-	-	PUNCT
iajs-1071	132	5	bs)=01	bs)=01	PROPN
iajs-1071	132	6	.thus	.thus	PUNCT
iajs-1071	132	7	at	at	ADP
iajs-1071	132	8	-	-	PUNCT
iajs-1071	132	9	bs	bs	ADJ
iajs-1071	132	10	f	f	NOUN
iajs-1071	132	11	-	-	PUNCT
iajs-1071	132	12	annxi	annxi	NOUN
iajs-1071	132	13	.	.	PUNCT
iajs-1071	133	1	but	but	CCONJ
iajs-1071	133	2	at	at	ADP
iajs-1071	133	3	=	=	ADJ
iajs-1071	133	4	bs+	bs+	NOUN
iajs-1071	133	5	at	at	ADP
iajs-1071	133	6	-	-	PUNCT
iajs-1071	133	7	bs	bs	NOUN
iajs-1071	133	8	b+(f	b+(f	NOUN
iajs-1071	133	9	-	-	PUNCT
iajs-1071	133	10	annxi	annxi	NOUN
iajs-1071	133	11	)	)	PUNCT
iajs-1071	133	12	.	.	PUNCT
iajs-1071	134	1	then	then	ADV
iajs-1071	134	2	a	a	DET
iajs-1071	134	3	b+(f	b+(f	NOUN
iajs-1071	134	4	-	-	PUNCT
iajs-1071	134	5	annxi	annxi	NOUN
iajs-1071	134	6	)	)	PUNCT
iajs-1071	134	7	hence	hence	ADV
iajs-1071	134	8	a+(f	a+(f	NOUN
iajs-1071	134	9	-	-	PUNCT
iajs-1071	134	10	annxi	annxi	NOUN
iajs-1071	134	11	)	)	PUNCT
iajs-1071	134	12	b+(f	b+(f	NOUN
iajs-1071	134	13	-	-	PUNCT
iajs-1071	134	14	annxi	annxi	NOUN
iajs-1071	134	15	)	)	PUNCT
iajs-1071	134	16	similarly	similarly	ADV
iajs-1071	134	17	:	:	PUNCT
iajs-1071	134	18	b+(f	b+(f	NOUN
iajs-1071	134	19	-	-	PUNCT
iajs-1071	134	20	annxi	annxi	NOUN
iajs-1071	134	21	)	)	PUNCT
iajs-1071	134	22	a+(f	a+(f	NOUN
iajs-1071	134	23	-	-	PUNCT
iajs-1071	134	24	annxi	annxi	NOUN
iajs-1071	134	25	)	)	PUNCT
iajs-1071	134	26	thus	thus	ADV
iajs-1071	134	27	a+(f	a+(f	NOUN
iajs-1071	134	28	-	-	PUNCT
iajs-1071	134	29	annxi)=	annxi)=	PRON
iajs-1071	134	30	b+(f	b+(f	NOUN
iajs-1071	134	31	-	-	PUNCT
iajs-1071	134	32	annxi	annxi	NOUN
iajs-1071	134	33	)	)	PUNCT
iajs-1071	134	34	and	and	CCONJ
iajs-1071	134	35	hence	hence	ADV
iajs-1071	134	36	x	x	PRON
iajs-1071	134	37	is	be	AUX
iajs-1071	134	38	q	q	NOUN
iajs-1071	134	39	-	-	PUNCT
iajs-1071	134	40	fcf(m	fcf(m	NOUN
iajs-1071	134	41	)	)	PUNCT
iajs-1071	134	42	.	.	PUNCT
iajs-1071	135	1	remark	remark	VERB
iajs-1071	135	2	1.7	1.7	NUM
iajs-1071	135	3	:	:	PUNCT
iajs-1071	135	4	the	the	DET
iajs-1071	135	5	converse	converse	NOUN
iajs-1071	135	6	of	of	ADP
iajs-1071	135	7	remark	remark	NOUN
iajs-1071	135	8	and	and	CCONJ
iajs-1071	135	9	examples	example	NOUN
iajs-1071	135	10	(	(	PUNCT
iajs-1071	135	11	(	(	PUNCT
iajs-1071	135	12	1.3)(1	1.3)(1	NUM
iajs-1071	135	13	)	)	PUNCT
iajs-1071	135	14	)	)	PUNCT
iajs-1071	136	1	is	be	AUX
iajs-1071	136	2	not	not	PART
iajs-1071	136	3	true	true	ADJ
iajs-1071	136	4	in	in	ADP
iajs-1071	136	5	general	general	ADJ
iajs-1071	136	6	by	by	ADP
iajs-1071	136	7	the	the	DET
iajs-1071	136	8	following	follow	VERB
iajs-1071	136	9	example	example	NOUN
iajs-1071	136	10	:	:	PUNCT
iajs-1071	136	11	let	let	VERB
iajs-1071	136	12	m	m	PRON
iajs-1071	136	13	=	=	VERB
iajs-1071	136	14	zp∞	zp∞	PROPN
iajs-1071	136	15	and	and	CCONJ
iajs-1071	136	16	r	r	NOUN
iajs-1071	136	17	=	=	NOUN
iajs-1071	136	18	z	z	AUX
iajs-1071	136	19	define	define	NOUN
iajs-1071	136	20	by	by	ADP
iajs-1071	136	21	x	x	NOUN
iajs-1071	136	22	:	:	PUNCT
iajs-1071	136	23	m	m	VERB
iajs-1071	136	24	[	[	X
iajs-1071	136	25	0,1	0,1	NUM
iajs-1071	136	26	]	]	PUNCT
iajs-1071	136	27	such	such	ADJ
iajs-1071	136	28	that	that	SCONJ
iajs-1071	136	29	x(x	x(x	NOUN
iajs-1071	136	30	)	)	PUNCT
iajs-1071	137	1	=	=	NOUN
iajs-1071	137	2	{	{	PUNCT
iajs-1071	137	3	it	it	PRON
iajs-1071	137	4	is	be	AUX
iajs-1071	137	5	clear	clear	ADJ
iajs-1071	137	6	that	that	SCONJ
iajs-1071	137	7	t	t	PROPN
iajs-1071	137	8	(	(	PUNCT
iajs-1071	137	9	0,1	0,1	PROPN
iajs-1071	137	10	]	]	PUNCT
iajs-1071	137	11	,	,	PUNCT
iajs-1071	137	12	xt	xt	X
iajs-1071	137	13	=	=	NOUN
iajs-1071	137	14	m	m	NOUN
iajs-1071	137	15	and	and	CCONJ
iajs-1071	137	16	m	m	VERB
iajs-1071	137	17	is	be	AUX
iajs-1071	137	18	not	not	PART
iajs-1071	137	19	fully	fully	ADV
iajs-1071	137	20	cancellation	cancellation	NOUN
iajs-1071	137	21	module	module	NOUN
iajs-1071	137	22	[	[	X
iajs-1071	137	23	3	3	NUM
iajs-1071	137	24	,	,	PUNCT
iajs-1071	137	25	examples	example	NOUN
iajs-1071	137	26	(	(	PUNCT
iajs-1071	137	27	2.5)(2	2.5)(2	NUM
iajs-1071	137	28	)	)	PUNCT
iajs-1071	137	29	]	]	PUNCT
iajs-1071	137	30	.	.	PUNCT
iajs-1071	138	1	thus	thus	ADV
iajs-1071	138	2	x	x	PRON
iajs-1071	138	3	is	be	AUX
iajs-1071	138	4	not	not	PART
iajs-1071	138	5	fully	fully	ADV
iajs-1071	138	6	cancellation	cancellation	NOUN
iajs-1071	138	7	fuzzy	fuzzy	ADJ
iajs-1071	138	8	module	module	NOUN
iajs-1071	138	9	by	by	ADP
iajs-1071	138	10	proposition	proposition	NOUN
iajs-1071	138	11	(	(	PUNCT
iajs-1071	138	12	1.2	1.2	NUM
iajs-1071	138	13	)	)	PUNCT
iajs-1071	138	14	.	.	PUNCT
iajs-1071	139	1	proposition	proposition	NOUN
iajs-1071	139	2	1.8	1.8	NUM
iajs-1071	139	3	:	:	PUNCT
iajs-1071	139	4	let	let	VERB
iajs-1071	139	5	x	x	PRON
iajs-1071	139	6	be	be	AUX
iajs-1071	139	7	f(m	f(m	PROPN
iajs-1071	139	8	)	)	PUNCT
iajs-1071	139	9	and	and	CCONJ
iajs-1071	139	10	let	let	VERB
iajs-1071	139	11	h	h	NOUN
iajs-1071	139	12	,	,	PUNCT
iajs-1071	139	13	k	k	PROPN
iajs-1071	139	14	and	and	CCONJ
iajs-1071	139	15	l	l	NOUN
iajs-1071	139	16	are	be	AUX
iajs-1071	139	17	fuzzy	fuzzy	ADJ
iajs-1071	139	18	submodules	submodule	NOUN
iajs-1071	139	19	of	of	ADP
iajs-1071	139	20	x.	x.	NOUN
iajs-1071	139	21	let	let	VERB
iajs-1071	139	22	i	i	PRON
iajs-1071	139	23	be	be	AUX
iajs-1071	139	24	a	a	DET
iajs-1071	139	25	fuzzy	fuzzy	ADJ
iajs-1071	139	26	ideal	ideal	NOUN
iajs-1071	139	27	of	of	ADP
iajs-1071	139	28	r.	r.	PROPN
iajs-1071	139	29	then	then	ADV
iajs-1071	139	30	the	the	DET
iajs-1071	139	31	following	follow	VERB
iajs-1071	139	32	statements	statement	NOUN
iajs-1071	139	33	are	be	AUX
iajs-1071	139	34	equivalent	equivalent	ADJ
iajs-1071	139	35	:	:	PUNCT
iajs-1071	139	36	1x	1x	NUM
iajs-1071	139	37	is	be	AUX
iajs-1071	139	38	a	a	DET
iajs-1071	139	39	q	q	NOUN
iajs-1071	139	40	-	-	PUNCT
iajs-1071	139	41	fcf(m	fcf(m	NOUN
iajs-1071	139	42	)	)	PUNCT
iajs-1071	139	43	.	.	PUNCT
iajs-1071	140	1	mathematics	mathematic	NOUN
iajs-1071	140	2	|	|	ADV
iajs-1071	140	3	198	198	NUM
iajs-1071	140	4	2012	2012	NUM
iajs-1071	140	5	(	(	PUNCT
iajs-1071	140	6	عام	عام	PROPN
iajs-1071	140	7	1	1	NUM
iajs-1071	140	8	)	)	PUNCT
iajs-1071	140	9	(	(	PUNCT
iajs-1071	140	10	العدد	العدد	PROPN
iajs-1071	140	11	30مجلة	30مجلة	NUM
iajs-1071	140	12	إبن	إبن	VERB
iajs-1071	140	13	الهيثم	الهيثم	ADJ
iajs-1071	140	14	للعلوم	للعلوم	NOUN
iajs-1071	140	15	الصرفة	الصرفة	NOUN
iajs-1071	141	1	و	و	PRON
iajs-1071	141	2	التطبيقية	التطبيقية	ADV
iajs-1071	141	3	المجلد	المجلد	ADV
iajs-1071	141	4	)	)	PUNCT
iajs-1071	142	1	ibn	ibn	PROPN
iajs-1071	142	2	al	al	PROPN
iajs-1071	142	3	-	-	PUNCT
iajs-1071	142	4	haitham	haitham	PROPN
iajs-1071	142	5	j.	j.	PROPN
iajs-1071	142	6	for	for	ADP
iajs-1071	142	7	pure	pure	PROPN
iajs-1071	142	8	&	&	CCONJ
iajs-1071	142	9	appl	appl	PROPN
iajs-1071	142	10	.	.	PUNCT
iajs-1071	143	1	sci	sci	PROPN
iajs-1071	143	2	.	.	PUNCT
iajs-1071	144	1	vol.30	vol.30	NOUN
iajs-1071	144	2	(	(	PUNCT
iajs-1071	144	3	1	1	NUM
iajs-1071	144	4	)	)	PUNCT
iajs-1071	144	5	2017	2017	NUM
iajs-1071	144	6	2if	2if	NOUN
iajs-1071	144	7	ih	ih	ADP
iajs-1071	144	8	ik	ik	PROPN
iajs-1071	144	9	,	,	PUNCT
iajs-1071	144	10	then	then	ADV
iajs-1071	144	11	h	h	PROPN
iajs-1071	144	12	k+(f	k+(f	NOUN
iajs-1071	144	13	-	-	PUNCT
iajs-1071	144	14	annxi	annxi	NOUN
iajs-1071	144	15	)	)	PUNCT
iajs-1071	144	16	.	.	PUNCT
iajs-1071	145	1	3i(ht	3i(ht	NUM
iajs-1071	145	2	)	)	PUNCT
iajs-1071	145	3	il	il	PROPN
iajs-1071	145	4	,	,	PUNCT
iajs-1071	145	5	then	then	ADV
iajs-1071	145	6	ht	ht	PROPN
iajs-1071	145	7	l+(f	l+(f	PROPN
iajs-1071	145	8	-	-	PUNCT
iajs-1071	145	9	annxi	annxi	NOUN
iajs-1071	145	10	)	)	PUNCT
iajs-1071	145	11	,	,	PUNCT
iajs-1071	145	12	where	where	SCONJ
iajs-1071	145	13	ht	ht	PROPN
iajs-1071	145	14	x.	x.	NOUN
iajs-1071	145	15	(	(	PUNCT
iajs-1071	145	16	0,1	0,1	NOUN
iajs-1071	145	17	]	]	PUNCT
iajs-1071	145	18	.	.	PUNCT
iajs-1071	146	1	4(ih	4(ih	NOUN
iajs-1071	146	2	:	:	PUNCT
iajs-1071	146	3	xi)=h+(f	xi)=h+(f	PROPN
iajs-1071	146	4	-	-	PUNCT
iajs-1071	146	5	annxi	annxi	NOUN
iajs-1071	146	6	)	)	PUNCT
iajs-1071	146	7	.	.	PUNCT
iajs-1071	147	1	proof	proof	NOUN
iajs-1071	147	2	:	:	PUNCT
iajs-1071	147	3	(	(	PUNCT
iajs-1071	147	4	1	1	X
iajs-1071	147	5	)	)	PUNCT
iajs-1071	147	6	(	(	PUNCT
iajs-1071	147	7	2	2	X
iajs-1071	147	8	)	)	PUNCT
iajs-1071	147	9	let	let	VERB
iajs-1071	147	10	x	x	PRON
iajs-1071	147	11	be	be	AUX
iajs-1071	147	12	a	a	DET
iajs-1071	147	13	q	q	NOUN
iajs-1071	147	14	-	-	PUNCT
iajs-1071	147	15	fcf(m	fcf(m	NOUN
iajs-1071	147	16	)	)	PUNCT
iajs-1071	147	17	and	and	CCONJ
iajs-1071	147	18	let	let	VERB
iajs-1071	147	19	ih	ih	PRON
iajs-1071	147	20	ik	ik	PROPN
iajs-1071	147	21	.	.	PROPN
iajs-1071	147	22	then	then	ADV
iajs-1071	147	23	ik	ik	PROPN
iajs-1071	147	24	ih+ik	ih+ik	PROPN
iajs-1071	147	25	=	=	SYM
iajs-1071	147	26	i(h+k	i(h+k	NOUN
iajs-1071	147	27	)	)	PUNCT
iajs-1071	147	28	by	by	ADP
iajs-1071	147	29	[	[	X
iajs-1071	147	30	5,proposition	5,proposition	NUM
iajs-1071	147	31	(	(	PUNCT
iajs-1071	147	32	2.6	2.6	NUM
iajs-1071	147	33	)	)	PUNCT
iajs-1071	147	34	]	]	PUNCT
iajs-1071	147	35	.	.	PUNCT
iajs-1071	148	1	hence	hence	ADV
iajs-1071	148	2	k+(f	k+(f	PROPN
iajs-1071	148	3	-	-	PUNCT
iajs-1071	148	4	annxi)=(h+k)+(f	annxi)=(h+k)+(f	NOUN
iajs-1071	148	5	-	-	PUNCT
iajs-1071	148	6	annxi	annxi	NOUN
iajs-1071	148	7	)	)	PUNCT
iajs-1071	149	1	(	(	PUNCT
iajs-1071	149	2	since	since	SCONJ
iajs-1071	149	3	x	x	PRON
iajs-1071	149	4	is	be	AUX
iajs-1071	149	5	q	q	NOUN
iajs-1071	149	6	-	-	PUNCT
iajs-1071	149	7	fcf(m	fcf(m	NOUN
iajs-1071	149	8	)	)	PUNCT
iajs-1071	149	9	)	)	PUNCT
iajs-1071	149	10	.	.	PUNCT
iajs-1071	150	1	therefore	therefore	ADV
iajs-1071	150	2	h	h	X
iajs-1071	150	3	k+(f	k+(f	NOUN
iajs-1071	150	4	-	-	PUNCT
iajs-1071	150	5	annxi	annxi	NOUN
iajs-1071	150	6	)	)	PUNCT
iajs-1071	150	7	.	.	PUNCT
iajs-1071	151	1	(	(	PUNCT
iajs-1071	151	2	2	2	X
iajs-1071	151	3	)	)	PUNCT
iajs-1071	151	4	(	(	PUNCT
iajs-1071	151	5	3	3	X
iajs-1071	151	6	)	)	PUNCT
iajs-1071	151	7	let	let	VERB
iajs-1071	151	8	i(ht	i(ht	NOUN
iajs-1071	151	9	)	)	PUNCT
iajs-1071	151	10	il	il	PROPN
iajs-1071	151	11	,	,	PUNCT
iajs-1071	151	12	where	where	SCONJ
iajs-1071	151	13	ht	ht	PROPN
iajs-1071	151	14	h	h	NOUN
iajs-1071	151	15	and	and	CCONJ
iajs-1071	151	16	by	by	ADP
iajs-1071	151	17	(	(	PUNCT
iajs-1071	151	18	2	2	X
iajs-1071	151	19	)	)	PUNCT
iajs-1071	151	20	we	we	PRON
iajs-1071	151	21	have	have	VERB
iajs-1071	151	22	(	(	PUNCT
iajs-1071	151	23	ht	ht	X
iajs-1071	151	24	)	)	PUNCT
iajs-1071	151	25	l+(f	l+(f	PROPN
iajs-1071	151	26	-	-	PUNCT
iajs-1071	151	27	annxi	annxi	NOUN
iajs-1071	151	28	)	)	PUNCT
iajs-1071	151	29	.	.	PUNCT
iajs-1071	152	1	thus	thus	ADV
iajs-1071	152	2	ht	ht	PROPN
iajs-1071	152	3	l+(f	l+(f	PROPN
iajs-1071	152	4	-	-	PUNCT
iajs-1071	152	5	annxi	annxi	NOUN
iajs-1071	152	6	)	)	PUNCT
iajs-1071	152	7	.	.	PUNCT
iajs-1071	153	1	(	(	PUNCT
iajs-1071	153	2	3	3	X
iajs-1071	153	3	)	)	PUNCT
iajs-1071	153	4	(	(	PUNCT
iajs-1071	153	5	4	4	X
iajs-1071	153	6	)	)	PUNCT
iajs-1071	153	7	let	let	VERB
iajs-1071	153	8	xt	xt	X
iajs-1071	153	9	(	(	PUNCT
iajs-1071	153	10	ih	ih	X
iajs-1071	153	11	:	:	PUNCT
iajs-1071	153	12	xi	xi	NUM
iajs-1071	153	13	)	)	PUNCT
iajs-1071	153	14	,	,	PUNCT
iajs-1071	153	15	(	(	PUNCT
iajs-1071	153	16	0,1	0,1	NOUN
iajs-1071	153	17	]	]	PUNCT
iajs-1071	153	18	,	,	PUNCT
iajs-1071	153	19	then	then	ADV
iajs-1071	153	20	ixt	ixt	VERB
iajs-1071	153	21	ih	ih	NOUN
iajs-1071	153	22	and	and	CCONJ
iajs-1071	153	23	by	by	ADP
iajs-1071	153	24	(	(	PUNCT
iajs-1071	153	25	3	3	NUM
iajs-1071	153	26	)	)	PUNCT
iajs-1071	153	27	xt	xt	ADP
iajs-1071	153	28	h+(f	h+(f	NOUN
iajs-1071	153	29	-	-	PUNCT
iajs-1071	153	30	annxi	annxi	NOUN
iajs-1071	153	31	)	)	PUNCT
iajs-1071	153	32	.	.	PUNCT
iajs-1071	154	1	therefore	therefore	ADV
iajs-1071	154	2	(	(	PUNCT
iajs-1071	154	3	ih	ih	NOUN
iajs-1071	154	4	:	:	PUNCT
iajs-1071	154	5	xi	xi	ADJ
iajs-1071	154	6	)	)	PUNCT
iajs-1071	154	7	h+(f	h+(f	NOUN
iajs-1071	154	8	-	-	PUNCT
iajs-1071	154	9	annxi	annxi	NOUN
iajs-1071	154	10	)	)	PUNCT
iajs-1071	154	11	.	.	PUNCT
iajs-1071	155	1	conversely	conversely	ADV
iajs-1071	155	2	,	,	PUNCT
iajs-1071	155	3	let	let	VERB
iajs-1071	155	4	h+(f	h+(f	NOUN
iajs-1071	155	5	-	-	PUNCT
iajs-1071	155	6	annxi	annxi	NOUN
iajs-1071	155	7	)	)	PUNCT
iajs-1071	155	8	,	,	PUNCT
iajs-1071	155	9	(	(	PUNCT
iajs-1071	155	10	0,1	0,1	NOUN
iajs-1071	155	11	]	]	PUNCT
iajs-1071	155	12	.	.	PUNCT
iajs-1071	156	1	then	then	ADV
iajs-1071	156	2	=	=	SYM
iajs-1071	156	3	ht+ms	ht+ms	NOUN
iajs-1071	156	4	,	,	PUNCT
iajs-1071	156	5	where	where	SCONJ
iajs-1071	156	6	ht	ht	PROPN
iajs-1071	156	7	h	h	PROPN
iajs-1071	156	8	and	and	CCONJ
iajs-1071	156	9	ms	ms	NOUN
iajs-1071	156	10	(	(	PUNCT
iajs-1071	156	11	f	f	NOUN
iajs-1071	156	12	-	-	PUNCT
iajs-1071	156	13	annxi	annxi	NOUN
iajs-1071	156	14	)	)	PUNCT
iajs-1071	156	15	,	,	PUNCT
iajs-1071	156	16	(	(	PUNCT
iajs-1071	156	17	0,1	0,1	NOUN
iajs-1071	156	18	]	]	PUNCT
iajs-1071	156	19	.	.	PUNCT
iajs-1071	157	1	thus	thus	ADV
iajs-1071	157	2	i	i	PRON
iajs-1071	157	3	=	=	AUX
iajs-1071	157	4	iht	iht	VERB
iajs-1071	157	5	+	+	NOUN
iajs-1071	157	6	ims	ims	NOUN
iajs-1071	157	7	.	.	PUNCT
iajs-1071	158	1	but	but	CCONJ
iajs-1071	158	2	ims=01	ims=01	PROPN
iajs-1071	158	3	therefore	therefore	ADV
iajs-1071	158	4	i	i	PRON
iajs-1071	158	5	=	=	AUX
iajs-1071	158	6	iht	iht	VERB
iajs-1071	158	7	ih	ih	NOUN
iajs-1071	158	8	.	.	PUNCT
iajs-1071	159	1	then	then	ADV
iajs-1071	159	2	(	(	PUNCT
iajs-1071	159	3	ih	ih	NOUN
iajs-1071	159	4	:	:	PUNCT
iajs-1071	159	5	xi	xi	NUM
iajs-1071	159	6	)	)	PUNCT
iajs-1071	159	7	.	.	PUNCT
iajs-1071	160	1	thus	thus	ADV
iajs-1071	160	2	h+(f	h+(f	NOUN
iajs-1071	160	3	-	-	PUNCT
iajs-1071	160	4	annxi	annxi	NOUN
iajs-1071	160	5	)	)	PUNCT
iajs-1071	161	1	(	(	PUNCT
iajs-1071	161	2	ih	ih	NOUN
iajs-1071	161	3	:	:	PUNCT
iajs-1071	161	4	xi	xi	NUM
iajs-1071	161	5	)	)	PUNCT
iajs-1071	161	6	.	.	PUNCT
iajs-1071	162	1	and	and	CCONJ
iajs-1071	162	2	hence	hence	ADV
iajs-1071	162	3	(	(	PUNCT
iajs-1071	162	4	ih	ih	NOUN
iajs-1071	162	5	:	:	PUNCT
iajs-1071	162	6	xi)=	xi)=	PROPN
iajs-1071	162	7	h+(f	h+(f	NOUN
iajs-1071	162	8	-	-	PUNCT
iajs-1071	162	9	annxi	annxi	NOUN
iajs-1071	162	10	)	)	PUNCT
iajs-1071	162	11	.	.	PUNCT
iajs-1071	163	1	(	(	PUNCT
iajs-1071	163	2	4	4	X
iajs-1071	163	3	)	)	PUNCT
iajs-1071	163	4	(	(	PUNCT
iajs-1071	163	5	1	1	X
iajs-1071	163	6	)	)	PUNCT
iajs-1071	163	7	let	let	VERB
iajs-1071	163	8	ih	ih	PRON
iajs-1071	163	9	=	=	NOUN
iajs-1071	163	10	ik	ik	X
iajs-1071	163	11	we	we	PRON
iajs-1071	163	12	want	want	VERB
iajs-1071	163	13	to	to	PART
iajs-1071	163	14	prove	prove	VERB
iajs-1071	163	15	x	x	PUNCT
iajs-1071	163	16	is	be	AUX
iajs-1071	163	17	q	q	NOUN
iajs-1071	163	18	-	-	PUNCT
iajs-1071	163	19	fcf(m	fcf(m	NOUN
iajs-1071	163	20	)	)	PUNCT
iajs-1071	163	21	.	.	PUNCT
iajs-1071	164	1	i.e	i.e	PRON
iajs-1071	164	2	to	to	PART
iajs-1071	164	3	prove	prove	VERB
iajs-1071	164	4	h+(f	h+(f	NOUN
iajs-1071	164	5	-	-	PUNCT
iajs-1071	164	6	annxi)=k+(f	annxi)=k+(f	NOUN
iajs-1071	164	7	-	-	PUNCT
iajs-1071	164	8	annxi	annxi	NOUN
iajs-1071	164	9	)	)	PUNCT
iajs-1071	165	1	k	k	PROPN
iajs-1071	165	2	(	(	PUNCT
iajs-1071	165	3	ih	ih	NOUN
iajs-1071	165	4	:	:	PUNCT
iajs-1071	165	5	xi	xi	NUM
iajs-1071	165	6	)	)	PUNCT
iajs-1071	165	7	and	and	CCONJ
iajs-1071	165	8	by	by	ADP
iajs-1071	165	9	(	(	PUNCT
iajs-1071	165	10	4	4	X
iajs-1071	165	11	)	)	PUNCT
iajs-1071	165	12	we	we	PRON
iajs-1071	165	13	get	get	VERB
iajs-1071	165	14	(	(	PUNCT
iajs-1071	165	15	ih	ih	NOUN
iajs-1071	165	16	:	:	PUNCT
iajs-1071	165	17	xi	xi	ADJ
iajs-1071	165	18	)	)	PUNCT
iajs-1071	165	19	=	=	SYM
iajs-1071	166	1	h+(f	h+(f	NOUN
iajs-1071	166	2	-	-	PUNCT
iajs-1071	166	3	annxi	annxi	NOUN
iajs-1071	166	4	)	)	PUNCT
iajs-1071	166	5	.	.	PUNCT
iajs-1071	167	1	hence	hence	ADV
iajs-1071	167	2	k	k	X
iajs-1071	167	3	h+(f	h+(f	NOUN
iajs-1071	167	4	-	-	PUNCT
iajs-1071	167	5	annxi	annxi	NOUN
iajs-1071	167	6	)	)	PUNCT
iajs-1071	167	7	.	.	PUNCT
iajs-1071	168	1	therefore	therefore	ADV
iajs-1071	168	2	k+(f	k+(f	NOUN
iajs-1071	168	3	-	-	PUNCT
iajs-1071	168	4	annxi	annxi	NOUN
iajs-1071	168	5	)	)	PUNCT
iajs-1071	168	6	h+(f	h+(f	NOUN
iajs-1071	168	7	-	-	PUNCT
iajs-1071	168	8	annxi	annxi	NOUN
iajs-1071	168	9	)	)	PUNCT
iajs-1071	168	10	.	.	PUNCT
iajs-1071	169	1	similarly	similarly	ADV
iajs-1071	169	2	:	:	PUNCT
iajs-1071	169	3	h	h	PROPN
iajs-1071	169	4	(	(	PUNCT
iajs-1071	169	5	ik	ik	ADJ
iajs-1071	169	6	:	:	PUNCT
iajs-1071	169	7	xi	xi	NUM
iajs-1071	169	8	)	)	PUNCT
iajs-1071	169	9	and	and	CCONJ
iajs-1071	169	10	by	by	ADP
iajs-1071	169	11	(	(	PUNCT
iajs-1071	169	12	4	4	NUM
iajs-1071	169	13	)	)	PUNCT
iajs-1071	169	14	,	,	PUNCT
iajs-1071	169	15	we	we	PRON
iajs-1071	169	16	obtain(ik	obtain(ik	PROPN
iajs-1071	169	17	:	:	PUNCT
iajs-1071	169	18	xi)=	xi)=	PROPN
iajs-1071	170	1	k+(f	k+(f	PROPN
iajs-1071	170	2	-	-	PUNCT
iajs-1071	170	3	annxi	annxi	NOUN
iajs-1071	170	4	)	)	PUNCT
iajs-1071	170	5	,	,	PUNCT
iajs-1071	170	6	then	then	ADV
iajs-1071	170	7	h	h	PROPN
iajs-1071	170	8	k+(f	k+(f	NOUN
iajs-1071	170	9	-	-	PUNCT
iajs-1071	170	10	annxi	annxi	NOUN
iajs-1071	170	11	)	)	PUNCT
iajs-1071	170	12	.	.	PUNCT
iajs-1071	171	1	therefore	therefore	ADV
iajs-1071	171	2	h+(f	h+(f	NOUN
iajs-1071	171	3	-	-	PUNCT
iajs-1071	171	4	annxi)=k+(f	annxi)=k+(f	NOUN
iajs-1071	171	5	-	-	PUNCT
iajs-1071	171	6	annxi	annxi	NOUN
iajs-1071	171	7	)	)	PUNCT
iajs-1071	171	8	.	.	PUNCT
iajs-1071	172	1	thus	thus	ADV
iajs-1071	172	2	x	x	X
iajs-1071	172	3	is	be	AUX
iajs-1071	172	4	q	q	NOUN
iajs-1071	172	5	-	-	PUNCT
iajs-1071	172	6	fcf(m	fcf(m	NOUN
iajs-1071	172	7	)	)	PUNCT
iajs-1071	172	8	.	.	PUNCT
iajs-1071	173	1	proposition	proposition	NOUN
iajs-1071	173	2	1.9	1.9	NUM
iajs-1071	173	3	:	:	PUNCT
iajs-1071	173	4	let	let	VERB
iajs-1071	173	5	x	x	PRON
iajs-1071	173	6	be	be	AUX
iajs-1071	173	7	f(m).then	f(m).then	PROPN
iajs-1071	173	8	x	x	PRON
iajs-1071	173	9	is	be	AUX
iajs-1071	173	10	q	q	ADJ
iajs-1071	173	11	-	-	PUNCT
iajs-1071	173	12	fcf(m	fcf(m	NOUN
iajs-1071	173	13	)	)	PUNCT
iajs-1071	174	1	if	if	SCONJ
iajs-1071	174	2	and	and	CCONJ
iajs-1071	174	3	only	only	ADV
iajs-1071	174	4	if	if	SCONJ
iajs-1071	174	5	(	(	PUNCT
iajs-1071	174	6	(	(	PUNCT
iajs-1071	174	7	a+(f	a+(f	NOUN
iajs-1071	174	8	-	-	PUNCT
iajs-1071	174	9	annxi):b)=(ia	annxi):b)=(ia	ADJ
iajs-1071	174	10	:	:	PUNCT
iajs-1071	174	11	rib	rib	NOUN
iajs-1071	174	12	)	)	PUNCT
iajs-1071	174	13	where	where	SCONJ
iajs-1071	174	14	i	i	PRON
iajs-1071	174	15	be	be	VERB
iajs-1071	174	16	a	a	DET
iajs-1071	174	17	fuzzy	fuzzy	ADJ
iajs-1071	174	18	ideal	ideal	NOUN
iajs-1071	174	19	of	of	ADP
iajs-1071	174	20	r	r	NOUN
iajs-1071	174	21	and	and	CCONJ
iajs-1071	174	22	a	a	DET
iajs-1071	174	23	,	,	PUNCT
iajs-1071	174	24	b	b	NOUN
iajs-1071	174	25	are	be	AUX
iajs-1071	174	26	two	two	NUM
iajs-1071	174	27	fuzzy	fuzzy	ADJ
iajs-1071	174	28	submodules	submodule	NOUN
iajs-1071	174	29	of	of	ADP
iajs-1071	174	30	x.	x.	NOUN
iajs-1071	174	31	proof	proof	NOUN
iajs-1071	174	32	:	:	PUNCT
iajs-1071	174	33	(	(	PUNCT
iajs-1071	174	34	)	)	PUNCT
iajs-1071	174	35	let	let	VERB
iajs-1071	174	36	xt	xt	X
iajs-1071	174	37	(	(	PUNCT
iajs-1071	174	38	(	(	PUNCT
iajs-1071	174	39	a+(f	a+(f	NOUN
iajs-1071	174	40	-	-	PUNCT
iajs-1071	174	41	annxi):b	annxi):b	ADJ
iajs-1071	174	42	)	)	PUNCT
iajs-1071	174	43	,	,	PUNCT
iajs-1071	174	44	(	(	PUNCT
iajs-1071	174	45	0,1	0,1	NOUN
iajs-1071	174	46	]	]	PUNCT
iajs-1071	174	47	.	.	PUNCT
iajs-1071	175	1	mathematics	mathematic	NOUN
iajs-1071	175	2	|	|	ADV
iajs-1071	175	3	199	199	NUM
iajs-1071	175	4	2012	2012	NUM
iajs-1071	175	5	(	(	PUNCT
iajs-1071	175	6	عام	عام	PROPN
iajs-1071	175	7	1	1	NUM
iajs-1071	175	8	)	)	PUNCT
iajs-1071	175	9	(	(	PUNCT
iajs-1071	175	10	العدد	العدد	PROPN
iajs-1071	175	11	30مجلة	30مجلة	NUM
iajs-1071	175	12	إبن	إبن	VERB
iajs-1071	175	13	الهيثم	الهيثم	ADJ
iajs-1071	175	14	للعلوم	للعلوم	NOUN
iajs-1071	175	15	الصرفة	الصرفة	NOUN
iajs-1071	176	1	و	و	PRON
iajs-1071	176	2	التطبيقية	التطبيقية	ADV
iajs-1071	176	3	المجلد	المجلد	ADV
iajs-1071	176	4	)	)	PUNCT
iajs-1071	177	1	ibn	ibn	PROPN
iajs-1071	177	2	al	al	PROPN
iajs-1071	177	3	-	-	PUNCT
iajs-1071	177	4	haitham	haitham	PROPN
iajs-1071	177	5	j.	j.	PROPN
iajs-1071	177	6	for	for	ADP
iajs-1071	177	7	pure	pure	PROPN
iajs-1071	177	8	&	&	CCONJ
iajs-1071	177	9	appl	appl	PROPN
iajs-1071	177	10	.	.	PUNCT
iajs-1071	178	1	sci	sci	PROPN
iajs-1071	178	2	.	.	PUNCT
iajs-1071	179	1	vol.30	vol.30	NOUN
iajs-1071	179	2	(	(	PUNCT
iajs-1071	179	3	1	1	NUM
iajs-1071	179	4	)	)	PUNCT
iajs-1071	179	5	2017	2017	NUM
iajs-1071	179	6	then	then	ADV
iajs-1071	179	7	xtb	xtb	PROPN
iajs-1071	180	1	(	(	PUNCT
iajs-1071	180	2	f	f	NOUN
iajs-1071	180	3	-	-	PUNCT
iajs-1071	180	4	annxi	annxi	NOUN
iajs-1071	180	5	)	)	PUNCT
iajs-1071	180	6	and	and	CCONJ
iajs-1071	180	7	hence	hence	ADV
iajs-1071	180	8	xt	xt	PUNCT
iajs-1071	180	9	bs	bs	PROPN
iajs-1071	180	10	a+(f	a+(f	NOUN
iajs-1071	180	11	-	-	PUNCT
iajs-1071	180	12	annxi	annxi	NOUN
iajs-1071	180	13	)	)	PUNCT
iajs-1071	181	1	for	for	ADP
iajs-1071	181	2	and	and	CCONJ
iajs-1071	181	3	bs	bs	PROPN
iajs-1071	181	4	b	b	PROPN
iajs-1071	181	5	,	,	PUNCT
iajs-1071	181	6	(	(	PUNCT
iajs-1071	181	7	0,1	0,1	NOUN
iajs-1071	181	8	]	]	PUNCT
iajs-1071	181	9	.	.	PUNCT
iajs-1071	182	1	thus	thus	ADV
iajs-1071	182	2	xtib	xtib	PROPN
iajs-1071	182	3	ia	ia	PROPN
iajs-1071	182	4	.	.	PUNCT
iajs-1071	183	1	then	then	ADV
iajs-1071	183	2	xt	xt	PROPN
iajs-1071	183	3	(	(	PUNCT
iajs-1071	183	4	ia	ia	PROPN
iajs-1071	183	5	:	:	PUNCT
iajs-1071	183	6	rib	rib	NOUN
iajs-1071	183	7	)	)	PUNCT
iajs-1071	183	8	.	.	PUNCT
iajs-1071	184	1	therefore	therefore	ADV
iajs-1071	184	2	(	(	PUNCT
iajs-1071	184	3	(	(	PUNCT
iajs-1071	184	4	a+(f	a+(f	NOUN
iajs-1071	184	5	-	-	PUNCT
iajs-1071	184	6	annxi):b	annxi):b	ADJ
iajs-1071	184	7	)	)	PUNCT
iajs-1071	184	8	(	(	PUNCT
iajs-1071	184	9	ia	ia	PROPN
iajs-1071	184	10	:	:	PUNCT
iajs-1071	184	11	rib	rib	NOUN
iajs-1071	184	12	)	)	PUNCT
iajs-1071	184	13	.	.	PUNCT
iajs-1071	185	1	now	now	ADV
iajs-1071	185	2	,	,	PUNCT
iajs-1071	185	3	let	let	VERB
iajs-1071	185	4	xt	xt	PROPN
iajs-1071	185	5	(	(	PUNCT
iajs-1071	185	6	ia	ia	PROPN
iajs-1071	185	7	:	:	PUNCT
iajs-1071	185	8	rib	rib	NOUN
iajs-1071	185	9	)	)	PUNCT
iajs-1071	185	10	,	,	PUNCT
iajs-1071	185	11	then	then	ADV
iajs-1071	185	12	xtib	xtib	PROPN
iajs-1071	185	13	ia	ia	PROPN
iajs-1071	185	14	and	and	CCONJ
iajs-1071	185	15	by	by	ADP
iajs-1071	185	16	proposition	proposition	NOUN
iajs-1071	185	17	(	(	PUNCT
iajs-1071	185	18	1.7),we	1.7),we	NUM
iajs-1071	185	19	get	get	VERB
iajs-1071	185	20	xtb	xtb	PRON
iajs-1071	185	21	a+(f	a+(f	NOUN
iajs-1071	185	22	-	-	PUNCT
iajs-1071	185	23	annxi	annxi	NOUN
iajs-1071	185	24	)	)	PUNCT
iajs-1071	185	25	and	and	CCONJ
iajs-1071	185	26	hence	hence	ADV
iajs-1071	185	27	xt	xt	PROPN
iajs-1071	186	1	(	(	PUNCT
iajs-1071	186	2	(	(	PUNCT
iajs-1071	186	3	a+(f	a+(f	NOUN
iajs-1071	186	4	-	-	PUNCT
iajs-1071	186	5	annxi):b	annxi):b	ADJ
iajs-1071	186	6	)	)	PUNCT
iajs-1071	186	7	.	.	PUNCT
iajs-1071	187	1	thus	thus	ADV
iajs-1071	187	2	(	(	PUNCT
iajs-1071	187	3	ia	ia	NOUN
iajs-1071	187	4	:	:	NOUN
iajs-1071	187	5	rib	rib	NOUN
iajs-1071	187	6	)	)	PUNCT
iajs-1071	187	7	(	(	PUNCT
iajs-1071	187	8	(	(	PUNCT
iajs-1071	187	9	a+(f	a+(f	NOUN
iajs-1071	187	10	-	-	PUNCT
iajs-1071	187	11	annxi):b	annxi):b	ADJ
iajs-1071	187	12	)	)	PUNCT
iajs-1071	187	13	.	.	PUNCT
iajs-1071	188	1	therefore	therefore	ADV
iajs-1071	188	2	(	(	PUNCT
iajs-1071	188	3	(	(	PUNCT
iajs-1071	188	4	a+(f	a+(f	NOUN
iajs-1071	188	5	-	-	PUNCT
iajs-1071	188	6	annxi):b)=(ia	annxi):b)=(ia	ADJ
iajs-1071	188	7	:	:	PUNCT
iajs-1071	188	8	rib	rib	NOUN
iajs-1071	188	9	)	)	PUNCT
iajs-1071	188	10	.	.	PUNCT
iajs-1071	189	1	on	on	ADP
iajs-1071	189	2	the	the	DET
iajs-1071	189	3	other	other	ADJ
iajs-1071	189	4	side	side	NOUN
iajs-1071	189	5	:	:	PUNCT
iajs-1071	189	6	suppose	suppose	VERB
iajs-1071	189	7	ib	ib	PROPN
iajs-1071	189	8	ia	ia	PROPN
iajs-1071	189	9	,	,	PUNCT
iajs-1071	189	10	where	where	SCONJ
iajs-1071	189	11	i	i	PRON
iajs-1071	189	12	be	be	VERB
iajs-1071	189	13	a	a	DET
iajs-1071	189	14	fuzzy	fuzzy	ADJ
iajs-1071	189	15	ideal	ideal	NOUN
iajs-1071	189	16	of	of	ADP
iajs-1071	189	17	r	r	NOUN
iajs-1071	189	18	and	and	CCONJ
iajs-1071	189	19	a	a	DET
iajs-1071	189	20	,	,	PUNCT
iajs-1071	189	21	b	b	NOUN
iajs-1071	189	22	are	be	AUX
iajs-1071	189	23	two	two	NUM
iajs-1071	189	24	fuzzy	fuzzy	ADJ
iajs-1071	189	25	submodules	submodule	NOUN
iajs-1071	189	26	of	of	ADP
iajs-1071	189	27	x.	x.	NOUN
iajs-1071	189	28	then	then	ADV
iajs-1071	189	29	(	(	PUNCT
iajs-1071	189	30	ia	ia	NOUN
iajs-1071	189	31	:	:	PUNCT
iajs-1071	189	32	rib)=r	rib)=r	ADJ
iajs-1071	189	33	.	.	PUNCT
iajs-1071	190	1	but	but	CCONJ
iajs-1071	190	2	(	(	PUNCT
iajs-1071	190	3	(	(	PUNCT
iajs-1071	190	4	a+(f	a+(f	NOUN
iajs-1071	190	5	-	-	PUNCT
iajs-1071	190	6	annxi):b)=(ia	annxi):b)=(ia	ADJ
iajs-1071	190	7	:	:	PUNCT
iajs-1071	190	8	rib	rib	NOUN
iajs-1071	190	9	)	)	PUNCT
iajs-1071	190	10	.	.	PUNCT
iajs-1071	191	1	then	then	ADV
iajs-1071	191	2	(	(	PUNCT
iajs-1071	191	3	(	(	PUNCT
iajs-1071	191	4	a+(f	a+(f	NOUN
iajs-1071	191	5	-	-	PUNCT
iajs-1071	191	6	annxi):b)=r	annxi):b)=r	PROPN
iajs-1071	191	7	,	,	PUNCT
iajs-1071	191	8	it	it	PRON
iajs-1071	191	9	follows	follow	VERB
iajs-1071	191	10	that	that	SCONJ
iajs-1071	191	11	b	b	PROPN
iajs-1071	191	12	a+(f	a+(f	PROPN
iajs-1071	191	13	-	-	PUNCT
iajs-1071	191	14	anni	anni	NOUN
iajs-1071	191	15	)	)	PUNCT
iajs-1071	191	16	.	.	PUNCT
iajs-1071	192	1	thus	thus	ADV
iajs-1071	192	2	x	x	X
iajs-1071	192	3	is	be	AUX
iajs-1071	192	4	q	q	NOUN
iajs-1071	192	5	-	-	PUNCT
iajs-1071	192	6	fcf(m	fcf(m	NOUN
iajs-1071	192	7	)	)	PUNCT
iajs-1071	192	8	.	.	PUNCT
iajs-1071	193	1	§	§	PROPN
iajs-1071	193	2	2	2	NUM
iajs-1071	193	3	.	.	PUNCT
iajs-1071	193	4	quasi	quasi	ADJ
iajs-1071	193	5	-	-	ADJ
iajs-1071	193	6	max	max	ADJ
iajs-1071	193	7	fully	fully	ADV
iajs-1071	193	8	cancellation	cancellation	NOUN
iajs-1071	193	9	fuzzy	fuzzy	ADJ
iajs-1071	193	10	modules	module	NOUN
iajs-1071	193	11	as	as	SCONJ
iajs-1071	193	12	we	we	PRON
iajs-1071	193	13	have	have	AUX
iajs-1071	193	14	mentioned	mention	VERB
iajs-1071	193	15	in	in	ADP
iajs-1071	193	16	section	section	NOUN
iajs-1071	193	17	one	one	NUM
iajs-1071	193	18	,	,	PUNCT
iajs-1071	193	19	that	that	SCONJ
iajs-1071	193	20	every	every	DET
iajs-1071	193	21	fully	fully	ADV
iajs-1071	193	22	cancellation	cancellation	NOUN
iajs-1071	193	23	fuzzy	fuzzy	ADJ
iajs-1071	193	24	module	module	NOUN
iajs-1071	193	25	is	be	AUX
iajs-1071	193	26	qfcf(m	qfcf(m	NOUN
iajs-1071	193	27	)	)	PUNCT
iajs-1071	193	28	and	and	CCONJ
iajs-1071	193	29	the	the	DET
iajs-1071	193	30	converse	converse	NOUN
iajs-1071	193	31	is	be	AUX
iajs-1071	193	32	not	not	PART
iajs-1071	193	33	to	to	PART
iajs-1071	193	34	be	be	AUX
iajs-1071	193	35	true	true	ADJ
iajs-1071	193	36	in	in	ADP
iajs-1071	193	37	general	general	ADJ
iajs-1071	193	38	.	.	PUNCT
iajs-1071	194	1	in	in	ADP
iajs-1071	194	2	this	this	DET
iajs-1071	194	3	section	section	NOUN
iajs-1071	194	4	,	,	PUNCT
iajs-1071	194	5	we	we	PRON
iajs-1071	194	6	introduce	introduce	VERB
iajs-1071	194	7	the	the	DET
iajs-1071	194	8	concept	concept	NOUN
iajs-1071	194	9	of	of	ADP
iajs-1071	194	10	q	q	NOUN
iajs-1071	194	11	-	-	PUNCT
iajs-1071	194	12	mfcf(m	mfcf(m	NOUN
iajs-1071	194	13	)	)	PUNCT
iajs-1071	194	14	and	and	CCONJ
iajs-1071	194	15	to	to	PART
iajs-1071	194	16	show	show	VERB
iajs-1071	194	17	that	that	SCONJ
iajs-1071	194	18	every	every	DET
iajs-1071	194	19	max	max	PROPN
iajs-1071	194	20	-	-	PUNCT
iajs-1071	194	21	fully	fully	ADV
iajs-1071	194	22	cancellation	cancellation	NOUN
iajs-1071	194	23	fuzzy	fuzzy	ADJ
iajs-1071	194	24	module	module	NOUN
iajs-1071	194	25	is	be	AUX
iajs-1071	194	26	q	q	NOUN
iajs-1071	194	27	-	-	PUNCT
iajs-1071	194	28	fcf(m	fcf(m	NOUN
iajs-1071	194	29	)	)	PUNCT
iajs-1071	194	30	but	but	CCONJ
iajs-1071	194	31	the	the	DET
iajs-1071	194	32	converse	converse	NOUN
iajs-1071	194	33	is	be	AUX
iajs-1071	194	34	not	not	PART
iajs-1071	194	35	true	true	ADJ
iajs-1071	194	36	.	.	PUNCT
iajs-1071	195	1	morevore	morevore	NOUN
iajs-1071	195	2	,	,	PUNCT
iajs-1071	195	3	we	we	PRON
iajs-1071	195	4	prove	prove	VERB
iajs-1071	195	5	that	that	SCONJ
iajs-1071	195	6	in	in	ADP
iajs-1071	195	7	the	the	DET
iajs-1071	195	8	class	class	NOUN
iajs-1071	195	9	of	of	ADP
iajs-1071	195	10	faithful	faithful	ADJ
iajs-1071	195	11	fuzzy	fuzzy	ADJ
iajs-1071	195	12	module	module	NOUN
iajs-1071	195	13	,	,	PUNCT
iajs-1071	195	14	the	the	DET
iajs-1071	195	15	two	two	NUM
iajs-1071	195	16	concepts	concept	NOUN
iajs-1071	195	17	max	max	PROPN
iajs-1071	195	18	-	-	PUNCT
iajs-1071	195	19	fully	fully	ADV
iajs-1071	195	20	cancellation	cancellation	NOUN
iajs-1071	195	21	fuzzy	fuzzy	ADJ
iajs-1071	195	22	module	module	NOUN
iajs-1071	195	23	and	and	CCONJ
iajs-1071	195	24	q	q	NOUN
iajs-1071	195	25	-	-	PUNCT
iajs-1071	195	26	mfcf(m	mfcf(m	NOUN
iajs-1071	195	27	)	)	PUNCT
iajs-1071	195	28	are	be	AUX
iajs-1071	195	29	equivalent	equivalent	ADJ
iajs-1071	195	30	.	.	PUNCT
iajs-1071	195	31	"	"	PUNCT
iajs-1071	196	1	recall	recall	VERB
iajs-1071	196	2	that	that	SCONJ
iajs-1071	196	3	an	an	DET
iajs-1071	196	4	r	r	NOUN
iajs-1071	196	5	-	-	PUNCT
iajs-1071	196	6	module	module	NOUN
iajs-1071	196	7	m	m	NOUN
iajs-1071	196	8	is	be	AUX
iajs-1071	196	9	called	call	VERB
iajs-1071	196	10	quasi	quasi	ADJ
iajs-1071	196	11	-	-	ADJ
iajs-1071	196	12	max	max	ADJ
iajs-1071	196	13	fully	fully	ADV
iajs-1071	196	14	cancellation	cancellation	NOUN
iajs-1071	196	15	module	module	NOUN
iajs-1071	196	16	if	if	SCONJ
iajs-1071	196	17	for	for	ADP
iajs-1071	196	18	every	every	DET
iajs-1071	196	19	maximal	maximal	ADJ
iajs-1071	196	20	ideal	ideal	NOUN
iajs-1071	196	21	i	i	PRON
iajs-1071	196	22	of	of	ADP
iajs-1071	196	23	r	r	NOUN
iajs-1071	196	24	and	and	CCONJ
iajs-1071	196	25	for	for	SCONJ
iajs-1071	196	26	every	every	DET
iajs-1071	196	27	two	two	NUM
iajs-1071	196	28	submodules	submodule	NOUN
iajs-1071	196	29	n	n	PRON
iajs-1071	196	30	and	and	CCONJ
iajs-1071	196	31	k	k	X
iajs-1071	196	32	of	of	ADP
iajs-1071	196	33	m	m	PRON
iajs-1071	196	34	such	such	ADJ
iajs-1071	196	35	that	that	SCONJ
iajs-1071	196	36	in	in	ADP
iajs-1071	196	37	=	=	NOUN
iajs-1071	196	38	ik	ik	PROPN
iajs-1071	196	39	implies	imply	VERB
iajs-1071	196	40	n+annmi	n+annmi	PROPN
iajs-1071	197	1	=	=	SYM
iajs-1071	197	2	k+annmi	k+annmi	PROPN
iajs-1071	198	1	[	[	X
iajs-1071	198	2	6	6	NUM
iajs-1071	198	3	]	]	PUNCT
iajs-1071	198	4	.	.	PUNCT
iajs-1071	198	5	"	"	PUNCT
iajs-1071	199	1	we	we	PRON
iajs-1071	199	2	shall	shall	AUX
iajs-1071	199	3	fuzzify	fuzzify	VERB
iajs-1071	199	4	this	this	DET
iajs-1071	199	5	concepts	concept	NOUN
iajs-1071	199	6	as	as	SCONJ
iajs-1071	199	7	follows	follow	VERB
iajs-1071	199	8	:	:	PUNCT
iajs-1071	199	9	definition	definition	NOUN
iajs-1071	199	10	2.1	2.1	NUM
iajs-1071	199	11	:	:	PUNCT
iajs-1071	199	12	let	let	VERB
iajs-1071	199	13	x	x	PRON
iajs-1071	199	14	be	be	AUX
iajs-1071	199	15	f(m	f(m	PROPN
iajs-1071	199	16	)	)	PUNCT
iajs-1071	199	17	.	.	PUNCT
iajs-1071	200	1	x	x	PUNCT
iajs-1071	200	2	is	be	AUX
iajs-1071	200	3	called	call	VERB
iajs-1071	200	4	q	q	NOUN
iajs-1071	200	5	-	-	PUNCT
iajs-1071	200	6	mfcf(m	mfcf(m	NOUN
iajs-1071	200	7	)	)	PUNCT
iajs-1071	200	8	if	if	SCONJ
iajs-1071	200	9	for	for	ADP
iajs-1071	200	10	every	every	DET
iajs-1071	200	11	maximal	maximal	ADJ
iajs-1071	200	12	fuzzy	fuzzy	ADJ
iajs-1071	200	13	ideal	ideal	NOUN
iajs-1071	200	14	of	of	ADP
iajs-1071	200	15	r	r	NOUN
iajs-1071	200	16	and	and	CCONJ
iajs-1071	200	17	for	for	ADP
iajs-1071	200	18	every	every	DET
iajs-1071	200	19	two	two	NUM
iajs-1071	200	20	fuzzy	fuzzy	ADJ
iajs-1071	200	21	submodules	submodule	NOUN
iajs-1071	200	22	a	a	PRON
iajs-1071	200	23	and	and	CCONJ
iajs-1071	200	24	b	b	NOUN
iajs-1071	200	25	of	of	ADP
iajs-1071	200	26	x	x	SYM
iajs-1071	200	27	such	such	ADJ
iajs-1071	200	28	that	that	SCONJ
iajs-1071	200	29	ia	ia	PROPN
iajs-1071	200	30	=	=	NOUN
iajs-1071	200	31	ib	ib	NOUN
iajs-1071	200	32	implies	imply	VERB
iajs-1071	200	33	that	that	SCONJ
iajs-1071	200	34	a+(f	a+(f	NOUN
iajs-1071	200	35	-	-	PUNCT
iajs-1071	200	36	annxi)=b+(fannxi	annxi)=b+(fannxi	NOUN
iajs-1071	200	37	)	)	PUNCT
iajs-1071	200	38	.	.	PUNCT
iajs-1071	201	1	next	next	ADV
iajs-1071	201	2	,	,	PUNCT
iajs-1071	201	3	we	we	PRON
iajs-1071	201	4	have	have	VERB
iajs-1071	201	5	the	the	DET
iajs-1071	201	6	following	follow	VERB
iajs-1071	201	7	proposition	proposition	NOUN
iajs-1071	201	8	.	.	PUNCT
iajs-1071	202	1	proposition	proposition	NOUN
iajs-1071	202	2	2.2	2.2	NUM
iajs-1071	202	3	:	:	PUNCT
iajs-1071	202	4	let	let	VERB
iajs-1071	202	5	x	x	PRON
iajs-1071	202	6	be	be	AUX
iajs-1071	202	7	f(m	f(m	PROPN
iajs-1071	202	8	)	)	PUNCT
iajs-1071	202	9	and	and	CCONJ
iajs-1071	202	10	let	let	VERB
iajs-1071	202	11	i	i	PRON
iajs-1071	202	12	be	be	AUX
iajs-1071	202	13	a	a	DET
iajs-1071	202	14	maximal	maximal	ADJ
iajs-1071	202	15	fuzzy	fuzzy	ADJ
iajs-1071	202	16	ideal	ideal	NOUN
iajs-1071	202	17	of	of	ADP
iajs-1071	202	18	r.	r.	PROPN
iajs-1071	202	19	such	such	ADJ
iajs-1071	202	20	that	that	SCONJ
iajs-1071	202	21	(	(	PUNCT
iajs-1071	202	22	f	f	X
iajs-1071	202	23	-	-	PUNCT
iajs-1071	202	24	anni)t	anni)t	NOUN
iajs-1071	202	25	=	=	SYM
iajs-1071	202	26	f	f	X
iajs-1071	202	27	-	-	PUNCT
iajs-1071	202	28	annit	annit	VERB
iajs-1071	202	29	,	,	PUNCT
iajs-1071	202	30	then	then	ADV
iajs-1071	202	31	x	x	PUNCT
iajs-1071	202	32	is	be	AUX
iajs-1071	202	33	a	a	DET
iajs-1071	202	34	q	q	NOUN
iajs-1071	202	35	-	-	PUNCT
iajs-1071	202	36	mfcf(m	mfcf(m	NOUN
iajs-1071	202	37	)	)	PUNCT
iajs-1071	202	38	if	if	SCONJ
iajs-1071	202	39	and	and	CCONJ
iajs-1071	202	40	only	only	ADV
iajs-1071	202	41	if	if	SCONJ
iajs-1071	202	42	xt	xt	PROPN
iajs-1071	202	43	is	be	AUX
iajs-1071	202	44	a	a	DET
iajs-1071	202	45	quasi	quasi	NOUN
iajs-1071	202	46	-	-	ADJ
iajs-1071	202	47	max	max	ADJ
iajs-1071	202	48	fully	fully	ADV
iajs-1071	202	49	cancellation	cancellation	NOUN
iajs-1071	202	50	module	module	NOUN
iajs-1071	202	51	t	t	PROPN
iajs-1071	202	52	(	(	PUNCT
iajs-1071	202	53	0,1	0,1	NOUN
iajs-1071	202	54	]	]	PUNCT
iajs-1071	202	55	.	.	PUNCT
iajs-1071	203	1	proof	proof	NOUN
iajs-1071	203	2	:	:	PUNCT
iajs-1071	203	3	it	it	PRON
iajs-1071	203	4	is	be	AUX
iajs-1071	203	5	similar	similar	ADJ
iajs-1071	203	6	of	of	ADP
iajs-1071	203	7	proof	proof	NOUN
iajs-1071	203	8	of	of	ADP
iajs-1071	203	9	proposition	proposition	NOUN
iajs-1071	203	10	(	(	PUNCT
iajs-1071	203	11	1.2	1.2	NUM
iajs-1071	203	12	)	)	PUNCT
iajs-1071	203	13	only	only	ADV
iajs-1071	203	14	we	we	PRON
iajs-1071	203	15	take	take	VERB
iajs-1071	203	16	i	i	PRON
iajs-1071	203	17	maximal	maximal	ADJ
iajs-1071	203	18	fuzzy	fuzzy	ADJ
iajs-1071	203	19	ideal	ideal	NOUN
iajs-1071	203	20	.	.	PUNCT
iajs-1071	204	1	mathematics	mathematic	NOUN
iajs-1071	204	2	|	|	ADV
iajs-1071	204	3	200	200	NUM
iajs-1071	204	4	2012	2012	NUM
iajs-1071	204	5	(	(	PUNCT
iajs-1071	204	6	عام	عام	PROPN
iajs-1071	204	7	1	1	NUM
iajs-1071	204	8	)	)	PUNCT
iajs-1071	204	9	(	(	PUNCT
iajs-1071	204	10	العدد	العدد	PROPN
iajs-1071	204	11	30مجلة	30مجلة	NUM
iajs-1071	204	12	إبن	إبن	VERB
iajs-1071	204	13	الهيثم	الهيثم	ADJ
iajs-1071	204	14	للعلوم	للعلوم	NOUN
iajs-1071	204	15	الصرفة	الصرفة	NOUN
iajs-1071	205	1	و	و	PRON
iajs-1071	205	2	التطبيقية	التطبيقية	ADV
iajs-1071	205	3	المجلد	المجلد	ADV
iajs-1071	205	4	)	)	PUNCT
iajs-1071	206	1	ibn	ibn	PROPN
iajs-1071	206	2	al	al	PROPN
iajs-1071	206	3	-	-	PUNCT
iajs-1071	206	4	haitham	haitham	PROPN
iajs-1071	206	5	j.	j.	PROPN
iajs-1071	206	6	for	for	ADP
iajs-1071	206	7	pure	pure	PROPN
iajs-1071	206	8	&	&	CCONJ
iajs-1071	206	9	appl	appl	PROPN
iajs-1071	206	10	.	.	PUNCT
iajs-1071	207	1	sci	sci	PROPN
iajs-1071	207	2	.	.	PUNCT
iajs-1071	208	1	vol.30	vol.30	NOUN
iajs-1071	208	2	(	(	PUNCT
iajs-1071	208	3	1	1	NUM
iajs-1071	208	4	)	)	PUNCT
iajs-1071	208	5	2017	2017	NUM
iajs-1071	208	6	remarks	remark	NOUN
iajs-1071	208	7	and	and	CCONJ
iajs-1071	208	8	examples	example	NOUN
iajs-1071	208	9	2.3	2.3	NUM
iajs-1071	208	10	:	:	PUNCT
iajs-1071	208	11	(	(	PUNCT
iajs-1071	208	12	1	1	X
iajs-1071	208	13	)	)	PUNCT
iajs-1071	208	14	every	every	DET
iajs-1071	208	15	q	q	NOUN
iajs-1071	208	16	-	-	PUNCT
iajs-1071	208	17	fcf(m	fcf(m	NOUN
iajs-1071	208	18	)	)	PUNCT
iajs-1071	208	19	is	be	AUX
iajs-1071	208	20	a	a	DET
iajs-1071	208	21	q	q	NOUN
iajs-1071	208	22	-	-	PUNCT
iajs-1071	208	23	mfcf(m	mfcf(m	NOUN
iajs-1071	208	24	)	)	PUNCT
iajs-1071	208	25	.	.	PUNCT
iajs-1071	209	1	proof	proof	NOUN
iajs-1071	209	2	:	:	PUNCT
iajs-1071	209	3	it	it	PRON
iajs-1071	209	4	is	be	AUX
iajs-1071	209	5	clear	clear	ADJ
iajs-1071	209	6	.	.	PUNCT
iajs-1071	210	1	(	(	PUNCT
iajs-1071	210	2	2	2	X
iajs-1071	210	3	)	)	PUNCT
iajs-1071	210	4	a	a	DET
iajs-1071	210	5	fuzzy	fuzzy	ADJ
iajs-1071	210	6	module	module	NOUN
iajs-1071	210	7	x	x	PUNCT
iajs-1071	210	8	of	of	ADP
iajs-1071	210	9	an	an	DET
iajs-1071	210	10	z6	z6	NOUN
iajs-1071	210	11	-	-	PUNCT
iajs-1071	210	12	module	module	NOUN
iajs-1071	210	13	z6	z6	NOUN
iajs-1071	210	14	is	be	AUX
iajs-1071	210	15	q	q	NOUN
iajs-1071	210	16	-	-	PUNCT
iajs-1071	210	17	mfcf(m	mfcf(m	NOUN
iajs-1071	210	18	)	)	PUNCT
iajs-1071	210	19	.	.	PUNCT
iajs-1071	211	1	proof	proof	NOUN
iajs-1071	211	2	:	:	PUNCT
iajs-1071	211	3	let	let	VERB
iajs-1071	211	4	m	m	NOUN
iajs-1071	211	5	=	=	NOUN
iajs-1071	211	6	z6	z6	PROPN
iajs-1071	211	7	and	and	CCONJ
iajs-1071	211	8	x	x	X
iajs-1071	211	9	:	:	PUNCT
iajs-1071	211	10	m	m	VERB
iajs-1071	211	11	[	[	X
iajs-1071	211	12	0,1	0,1	NUM
iajs-1071	211	13	]	]	PUNCT
iajs-1071	211	14	such	such	ADJ
iajs-1071	211	15	that	that	SCONJ
iajs-1071	211	16	x(x	x(x	NOUN
iajs-1071	211	17	)	)	PUNCT
iajs-1071	212	1	=	=	NOUN
iajs-1071	212	2	{	{	PUNCT
iajs-1071	212	3	define	define	NOUN
iajs-1071	212	4	:	:	PUNCT
iajs-1071	212	5	i	i	PRON
iajs-1071	212	6	:(	:(	PUNCT
iajs-1071	212	7	̅	̅	X
iajs-1071	212	8	[	[	X
iajs-1071	212	9	0,1	0,1	NUM
iajs-1071	212	10	]	]	PUNCT
iajs-1071	212	11	by	by	ADP
iajs-1071	212	12	i(r	i(r	PROPN
iajs-1071	212	13	)	)	PUNCT
iajs-1071	212	14	=	=	NOUN
iajs-1071	212	15	{	{	PUNCT
iajs-1071	212	16	̅	̅	NOUN
iajs-1071	212	17	,	,	PUNCT
iajs-1071	212	18	t	t	PROPN
iajs-1071	212	19	(	(	PUNCT
iajs-1071	212	20	0,1	0,1	NOUN
iajs-1071	212	21	]	]	PUNCT
iajs-1071	212	22	.	.	PUNCT
iajs-1071	213	1	define	define	NOUN
iajs-1071	213	2	:	:	PUNCT
iajs-1071	213	3	a	a	DET
iajs-1071	213	4	:(	:(	X
iajs-1071	213	5	̅	̅	NOUN
iajs-1071	213	6	[	[	X
iajs-1071	213	7	0,1	0,1	NUM
iajs-1071	213	8	]	]	PUNCT
iajs-1071	213	9	by	by	ADP
iajs-1071	213	10	a(x	a(x	NOUN
iajs-1071	213	11	)	)	PUNCT
iajs-1071	213	12	=	=	NOUN
iajs-1071	213	13	{	{	PUNCT
iajs-1071	213	14	̅	̅	NOUN
iajs-1071	213	15	define	define	NOUN
iajs-1071	213	16	:	:	PUNCT
iajs-1071	213	17	b	b	X
iajs-1071	213	18	:	:	PUNCT
iajs-1071	213	19	z6	z6	PROPN
iajs-1071	214	1	[	[	X
iajs-1071	214	2	0,1	0,1	NUM
iajs-1071	214	3	]	]	PUNCT
iajs-1071	214	4	by	by	ADP
iajs-1071	214	5	b(x	b(x	NOUN
iajs-1071	214	6	)	)	PUNCT
iajs-1071	214	7	=	=	NOUN
iajs-1071	214	8	{	{	PUNCT
iajs-1071	214	9	it	it	PRON
iajs-1071	214	10	is	be	AUX
iajs-1071	214	11	clear	clear	ADJ
iajs-1071	214	12	that	that	SCONJ
iajs-1071	214	13	at=	at=	NOUN
iajs-1071	214	14	(	(	PUNCT
iajs-1071	214	15	̅	̅	NOUN
iajs-1071	214	16	,	,	PUNCT
iajs-1071	214	17	bt	bt	NOUN
iajs-1071	214	18	=	=	NOUN
iajs-1071	214	19	z6	z6	PROPN
iajs-1071	214	20	and	and	CCONJ
iajs-1071	214	21	it=	it=	PROPN
iajs-1071	214	22	(	(	PUNCT
iajs-1071	214	23	̅	̅	NOUN
iajs-1071	214	24	is	be	AUX
iajs-1071	214	25	a	a	DET
iajs-1071	214	26	maximal	maximal	ADJ
iajs-1071	214	27	ideal	ideal	NOUN
iajs-1071	214	28	and	and	CCONJ
iajs-1071	214	29	xt	xt	NOUN
iajs-1071	214	30	=	=	PROPN
iajs-1071	214	31	m	m	PROPN
iajs-1071	214	32	,	,	PUNCT
iajs-1071	214	33	t	t	PROPN
iajs-1071	214	34	(	(	PUNCT
iajs-1071	214	35	0,1	0,1	NOUN
iajs-1071	214	36	]	]	PUNCT
iajs-1071	214	37	.	.	PUNCT
iajs-1071	215	1	now	now	ADV
iajs-1071	215	2	,	,	PUNCT
iajs-1071	215	3	itat=	itat=	NOUN
iajs-1071	215	4	(	(	PUNCT
iajs-1071	215	5	̅	̅	NOUN
iajs-1071	215	6	̅	̅	NOUN
iajs-1071	215	7	=	=	SYM
iajs-1071	215	8	(	(	PUNCT
iajs-1071	215	9	̅	̅	NOUN
iajs-1071	215	10	=	=	SYM
iajs-1071	215	11	itbt=	itbt=	X
iajs-1071	215	12	(	(	PUNCT
iajs-1071	215	13	̅	̅	NOUN
iajs-1071	215	14	similarly	similarly	ADV
iajs-1071	215	15	if	if	SCONJ
iajs-1071	215	16	at=(0	at=(0	ADJ
iajs-1071	215	17	)	)	PUNCT
iajs-1071	215	18	,	,	PUNCT
iajs-1071	215	19	bt=	bt=	NOUN
iajs-1071	215	20	(	(	PUNCT
iajs-1071	215	21	̅	̅	NOUN
iajs-1071	215	22	since	since	SCONJ
iajs-1071	215	23	itat=	itat=	NOUN
iajs-1071	215	24	(	(	PUNCT
iajs-1071	215	25	̅	̅	NOUN
iajs-1071	215	26	̅	̅	NOUN
iajs-1071	215	27	=	=	SYM
iajs-1071	215	28	(	(	PUNCT
iajs-1071	215	29	̅	̅	NOUN
iajs-1071	215	30	̅	̅	NOUN
iajs-1071	215	31	=	=	SYM
iajs-1071	215	32	itbt=	itbt=	X
iajs-1071	215	33	(	(	PUNCT
iajs-1071	215	34	̅	̅	NOUN
iajs-1071	215	35	where	where	SCONJ
iajs-1071	215	36	(	(	PUNCT
iajs-1071	215	37	0	0	NUM
iajs-1071	215	38	)	)	PUNCT
iajs-1071	215	39	,	,	PUNCT
iajs-1071	215	40	̅̅̅	̅̅̅	PROPN
iajs-1071	215	41	̅	̅	NOUN
iajs-1071	215	42	are	be	AUX
iajs-1071	215	43	submodules	submodule	NOUN
iajs-1071	215	44	of	of	ADP
iajs-1071	215	45	m	m	NOUN
iajs-1071	215	46	=	=	NOUN
iajs-1071	215	47	z6	z6	PROPN
iajs-1071	215	48	then	then	ADV
iajs-1071	215	49	we	we	PRON
iajs-1071	215	50	obtain	obtain	VERB
iajs-1071	215	51	̅	̅	NOUN
iajs-1071	215	52	+	+	ADJ
iajs-1071	215	53	annm	annm	ADJ
iajs-1071	215	54	̅	̅	NOUN
iajs-1071	215	55	=	=	SYM
iajs-1071	215	56	̅	̅	NOUN
iajs-1071	215	57	+	+	NOUN
iajs-1071	215	58	annm	annm	ADJ
iajs-1071	215	59	̅	̅	NOUN
iajs-1071	215	60	=	=	SYM
iajs-1071	215	61	̅	̅	NOUN
iajs-1071	215	62	thus	thus	ADV
iajs-1071	215	63	m	m	VERB
iajs-1071	215	64	is	be	AUX
iajs-1071	215	65	q	q	ADJ
iajs-1071	215	66	-	-	PUNCT
iajs-1071	215	67	mfc(m).therefore	mfc(m).therefore	NOUN
iajs-1071	215	68	x	x	NOUN
iajs-1071	215	69	is	be	AUX
iajs-1071	215	70	q	q	NOUN
iajs-1071	215	71	-	-	PUNCT
iajs-1071	215	72	mfcf(m	mfcf(m	NOUN
iajs-1071	215	73	)	)	PUNCT
iajs-1071	215	74	.	.	PUNCT
iajs-1071	216	1	by	by	ADP
iajs-1071	216	2	proposition	proposition	NOUN
iajs-1071	216	3	(	(	PUNCT
iajs-1071	216	4	2.2	2.2	NUM
iajs-1071	216	5	)	)	PUNCT
iajs-1071	216	6	.	.	PUNCT
iajs-1071	217	1	(	(	PUNCT
iajs-1071	217	2	3	3	X
iajs-1071	217	3	)	)	PUNCT
iajs-1071	217	4	the	the	DET
iajs-1071	217	5	fuzzy	fuzzy	ADJ
iajs-1071	217	6	module	module	NOUN
iajs-1071	217	7	x	x	PUNCT
iajs-1071	217	8	of	of	ADP
iajs-1071	217	9	an	an	DET
iajs-1071	217	10	z4	z4	NOUN
iajs-1071	217	11	-	-	PUNCT
iajs-1071	217	12	module	module	NOUN
iajs-1071	217	13	z4	z4	NOUN
iajs-1071	217	14	is	be	AUX
iajs-1071	217	15	a	a	DET
iajs-1071	217	16	q	q	NOUN
iajs-1071	217	17	-	-	PUNCT
iajs-1071	217	18	fcf(m	fcf(m	NOUN
iajs-1071	217	19	)	)	PUNCT
iajs-1071	217	20	.	.	PUNCT
iajs-1071	218	1	proof	proof	NOUN
iajs-1071	218	2	:	:	PUNCT
iajs-1071	218	3	by	by	ADP
iajs-1071	218	4	remark	remark	NOUN
iajs-1071	218	5	and	and	CCONJ
iajs-1071	218	6	examples	example	NOUN
iajs-1071	218	7	(	(	PUNCT
iajs-1071	218	8	(	(	PUNCT
iajs-1071	218	9	1.3)(2	1.3)(2	NUM
iajs-1071	218	10	)	)	PUNCT
iajs-1071	218	11	)	)	PUNCT
iajs-1071	218	12	.	.	PUNCT
iajs-1071	219	1	we	we	PRON
iajs-1071	219	2	have	have	AUX
iajs-1071	219	3	z4	z4	PROPN
iajs-1071	219	4	is	be	AUX
iajs-1071	219	5	quasi	quasi	ADJ
iajs-1071	219	6	max	max	PROPN
iajs-1071	219	7	fully	fully	ADV
iajs-1071	219	8	cancellation	cancellation	NOUN
iajs-1071	219	9	module	module	NOUN
iajs-1071	219	10	and	and	CCONJ
iajs-1071	219	11	by	by	ADP
iajs-1071	219	12	proposition	proposition	NOUN
iajs-1071	219	13	(	(	PUNCT
iajs-1071	219	14	2.2	2.2	NUM
iajs-1071	219	15	)	)	PUNCT
iajs-1071	219	16	we	we	PRON
iajs-1071	219	17	get	get	VERB
iajs-1071	219	18	the	the	DET
iajs-1071	219	19	result	result	NOUN
iajs-1071	219	20	.	.	PUNCT
iajs-1071	220	1	(	(	PUNCT
iajs-1071	220	2	4	4	X
iajs-1071	220	3	)	)	PUNCT
iajs-1071	220	4	let	let	VERB
iajs-1071	220	5	x1	x1	PROPN
iajs-1071	220	6	and	and	CCONJ
iajs-1071	220	7	x2	x2	PROPN
iajs-1071	220	8	be	be	VERB
iajs-1071	220	9	a	a	DET
iajs-1071	220	10	fuzzy	fuzzy	ADJ
iajs-1071	220	11	modules	module	NOUN
iajs-1071	220	12	of	of	ADP
iajs-1071	220	13	an	an	DET
iajs-1071	220	14	r	r	NOUN
iajs-1071	220	15	-	-	PUNCT
iajs-1071	220	16	module	module	NOUN
iajs-1071	220	17	m1,m2	m1,m2	PROPN
iajs-1071	220	18	respectively	respectively	ADV
iajs-1071	220	19	.	.	PUNCT
iajs-1071	221	1	if	if	SCONJ
iajs-1071	221	2	m1	m1	PROPN
iajs-1071	221	3	is	be	AUX
iajs-1071	221	4	a	a	DET
iajs-1071	221	5	q	q	ADJ
iajs-1071	221	6	-	-	ADJ
iajs-1071	221	7	mfc(m)and	mfc(m)and	NOUN
iajs-1071	221	8	m1	m1	PROPN
iajs-1071	221	9	m2	m2	PROPN
iajs-1071	221	10	,	,	PUNCT
iajs-1071	221	11	then	then	ADV
iajs-1071	221	12	x1	x1	PROPN
iajs-1071	221	13	is	be	AUX
iajs-1071	221	14	a	a	DET
iajs-1071	221	15	q	q	NOUN
iajs-1071	221	16	-	-	PUNCT
iajs-1071	221	17	mfcf(m	mfcf(m	NOUN
iajs-1071	221	18	)	)	PUNCT
iajs-1071	221	19	if	if	SCONJ
iajs-1071	222	1	and	and	CCONJ
iajs-1071	222	2	only	only	ADV
iajs-1071	222	3	if	if	SCONJ
iajs-1071	222	4	x2	x2	PRON
iajs-1071	222	5	is	be	AUX
iajs-1071	222	6	a	a	DET
iajs-1071	222	7	q	q	NOUN
iajs-1071	222	8	-	-	PUNCT
iajs-1071	222	9	mfcf(m	mfcf(m	NOUN
iajs-1071	222	10	)	)	PUNCT
iajs-1071	222	11	.	.	PUNCT
iajs-1071	223	1	proof	proof	NOUN
iajs-1071	223	2	:	:	PUNCT
iajs-1071	223	3	(	(	PUNCT
iajs-1071	223	4	)	)	PUNCT
iajs-1071	223	5	let	let	VERB
iajs-1071	223	6	x1	x1	NOUN
iajs-1071	223	7	:	:	PUNCT
iajs-1071	223	8	m1	m1	PROPN
iajs-1071	224	1	[	[	X
iajs-1071	224	2	0,1	0,1	NUM
iajs-1071	224	3	]	]	PUNCT
iajs-1071	224	4	define	define	NOUN
iajs-1071	224	5	by	by	ADP
iajs-1071	224	6	x1(x	x1(x	PROPN
iajs-1071	224	7	)	)	PUNCT
iajs-1071	225	1	=	=	NOUN
iajs-1071	225	2	{	{	PUNCT
iajs-1071	225	3	let	let	VERB
iajs-1071	225	4	x2	x2	PRON
iajs-1071	225	5	:	:	PUNCT
iajs-1071	225	6	m2	m2	PROPN
iajs-1071	226	1	[	[	X
iajs-1071	226	2	0,1	0,1	NUM
iajs-1071	226	3	]	]	PUNCT
iajs-1071	226	4	define	define	NOUN
iajs-1071	226	5	by	by	ADP
iajs-1071	226	6	x2(x	x2(x	PROPN
iajs-1071	226	7	)	)	PUNCT
iajs-1071	227	1	=	=	NOUN
iajs-1071	227	2	{	{	PUNCT
iajs-1071	227	3	clear	clear	ADJ
iajs-1071	227	4	that	that	SCONJ
iajs-1071	227	5	(	(	PUNCT
iajs-1071	227	6	x1)t	x1)t	PROPN
iajs-1071	227	7	=	=	NOUN
iajs-1071	227	8	m1	m1	PROPN
iajs-1071	227	9	,	,	PUNCT
iajs-1071	227	10	is	be	AUX
iajs-1071	227	11	a	a	DET
iajs-1071	227	12	quasi	quasi	NOUN
iajs-1071	227	13	-	-	ADJ
iajs-1071	227	14	max	max	ADJ
iajs-1071	227	15	fully	fully	ADV
iajs-1071	227	16	cancellation	cancellation	NOUN
iajs-1071	227	17	module	module	NOUN
iajs-1071	227	18	,	,	PUNCT
iajs-1071	227	19	then	then	ADV
iajs-1071	227	20	x1	x1	PROPN
iajs-1071	227	21	is	be	AUX
iajs-1071	227	22	a	a	DET
iajs-1071	227	23	q	q	NOUN
iajs-1071	227	24	-	-	PUNCT
iajs-1071	227	25	mfcf(m	mfcf(m	NOUN
iajs-1071	227	26	)	)	PUNCT
iajs-1071	227	27	by	by	ADP
iajs-1071	227	28	proposition	proposition	NOUN
iajs-1071	227	29	(	(	PUNCT
iajs-1071	227	30	2.7	2.7	NUM
iajs-1071	227	31	)	)	PUNCT
iajs-1071	227	32	.	.	PUNCT
iajs-1071	228	1	but	but	CCONJ
iajs-1071	228	2	m1	m1	PROPN
iajs-1071	228	3	m2	m2	PROPN
iajs-1071	228	4	,	,	PUNCT
iajs-1071	228	5	then	then	ADV
iajs-1071	228	6	m1	m1	PROPN
iajs-1071	228	7	is	be	AUX
iajs-1071	228	8	a	a	DET
iajs-1071	228	9	quasi	quasi	NOUN
iajs-1071	228	10	-	-	ADJ
iajs-1071	228	11	max	max	ADJ
iajs-1071	228	12	fully	fully	ADV
iajs-1071	228	13	cancellation	cancellation	NOUN
iajs-1071	228	14	module	module	NOUN
iajs-1071	228	15	by	by	ADP
iajs-1071	228	16	[	[	X
iajs-1071	228	17	6	6	NUM
iajs-1071	228	18	,	,	PUNCT
iajs-1071	228	19	remark	remark	NOUN
iajs-1071	228	20	and	and	CCONJ
iajs-1071	228	21	examples	example	NOUN
iajs-1071	228	22	(	(	PUNCT
iajs-1071	228	23	1.3)(4	1.3)(4	NUM
iajs-1071	228	24	)	)	PUNCT
iajs-1071	228	25	]	]	PUNCT
iajs-1071	229	1	therefore	therefore	ADV
iajs-1071	229	2	x2	x2	PROPN
iajs-1071	229	3	is	be	AUX
iajs-1071	229	4	a	a	DET
iajs-1071	229	5	q	q	NOUN
iajs-1071	229	6	-	-	PUNCT
iajs-1071	229	7	mfcf(m	mfcf(m	NOUN
iajs-1071	229	8	)	)	PUNCT
iajs-1071	229	9	.	.	PUNCT
iajs-1071	230	1	mathematics	mathematic	NOUN
iajs-1071	230	2	|	|	ADV
iajs-1071	230	3	201	201	NUM
iajs-1071	230	4	2012	2012	NUM
iajs-1071	230	5	(	(	PUNCT
iajs-1071	230	6	عام	عام	PROPN
iajs-1071	230	7	1	1	NUM
iajs-1071	230	8	)	)	PUNCT
iajs-1071	230	9	(	(	PUNCT
iajs-1071	230	10	العدد	العدد	PROPN
iajs-1071	230	11	30مجلة	30مجلة	NUM
iajs-1071	230	12	إبن	إبن	VERB
iajs-1071	230	13	الهيثم	الهيثم	ADJ
iajs-1071	230	14	للعلوم	للعلوم	NOUN
iajs-1071	230	15	الصرفة	الصرفة	NOUN
iajs-1071	231	1	و	و	PRON
iajs-1071	231	2	التطبيقية	التطبيقية	ADV
iajs-1071	231	3	المجلد	المجلد	ADV
iajs-1071	231	4	)	)	PUNCT
iajs-1071	232	1	ibn	ibn	PROPN
iajs-1071	232	2	al	al	PROPN
iajs-1071	232	3	-	-	PUNCT
iajs-1071	232	4	haitham	haitham	PROPN
iajs-1071	232	5	j.	j.	PROPN
iajs-1071	232	6	for	for	ADP
iajs-1071	232	7	pure	pure	PROPN
iajs-1071	232	8	&	&	CCONJ
iajs-1071	232	9	appl	appl	PROPN
iajs-1071	232	10	.	.	PUNCT
iajs-1071	233	1	sci	sci	PROPN
iajs-1071	233	2	.	.	PUNCT
iajs-1071	234	1	vol.30	vol.30	NOUN
iajs-1071	234	2	(	(	PUNCT
iajs-1071	234	3	1	1	NUM
iajs-1071	234	4	)	)	PUNCT
iajs-1071	234	5	2017	2017	NUM
iajs-1071	234	6	conversely	conversely	ADV
iajs-1071	234	7	:	:	PUNCT
iajs-1071	234	8	it	it	PRON
iajs-1071	234	9	is	be	AUX
iajs-1071	234	10	clear	clear	ADJ
iajs-1071	234	11	.	.	PUNCT
iajs-1071	235	1	(	(	PUNCT
iajs-1071	235	2	5	5	X
iajs-1071	235	3	)	)	PUNCT
iajs-1071	235	4	let	let	VERB
iajs-1071	235	5	x	x	PRON
iajs-1071	235	6	be	be	AUX
iajs-1071	235	7	f(m).and	f(m).and	PROPN
iajs-1071	235	8	let	let	VERB
iajs-1071	235	9	c	c	PRON
iajs-1071	235	10	be	be	AUX
iajs-1071	235	11	a	a	DET
iajs-1071	235	12	fuzzy	fuzzy	ADJ
iajs-1071	235	13	submodule	submodule	NOUN
iajs-1071	235	14	of	of	ADP
iajs-1071	235	15	x	x	PRON
iajs-1071	235	16	,	,	PUNCT
iajs-1071	235	17	then	then	ADV
iajs-1071	235	18	c	c	PROPN
iajs-1071	235	19	is	be	AUX
iajs-1071	235	20	q	q	NOUN
iajs-1071	235	21	-	-	PUNCT
iajs-1071	235	22	mfcf(m	mfcf(m	NOUN
iajs-1071	235	23	)	)	PUNCT
iajs-1071	235	24	.	.	PUNCT
iajs-1071	236	1	proof	proof	NOUN
iajs-1071	236	2	:	:	PUNCT
iajs-1071	236	3	the	the	DET
iajs-1071	236	4	prove	prove	NOUN
iajs-1071	236	5	is	be	AUX
iajs-1071	236	6	similar	similar	ADJ
iajs-1071	236	7	of	of	ADP
iajs-1071	236	8	remarks	remark	NOUN
iajs-1071	236	9	and	and	CCONJ
iajs-1071	236	10	examples	example	NOUN
iajs-1071	236	11	(	(	PUNCT
iajs-1071	236	12	1.3)(4	1.3)(4	NUM
iajs-1071	236	13	)	)	PUNCT
iajs-1071	236	14	)	)	PUNCT
iajs-1071	237	1	only	only	ADV
iajs-1071	237	2	we	we	PRON
iajs-1071	237	3	take	take	VERB
iajs-1071	237	4	the	the	DET
iajs-1071	237	5	ideal	ideal	NOUN
iajs-1071	237	6	of	of	ADP
iajs-1071	237	7	a	a	DET
iajs-1071	237	8	ring	ring	NOUN
iajs-1071	237	9	r	r	NOUN
iajs-1071	237	10	in	in	ADP
iajs-1071	237	11	maximal	maximal	ADJ
iajs-1071	237	12	fuzzy	fuzzy	ADJ
iajs-1071	237	13	ideal	ideal	NOUN
iajs-1071	237	14	.	.	PUNCT
iajs-1071	238	1	the	the	DET
iajs-1071	238	2	following	follow	VERB
iajs-1071	238	3	lemmas	lemma	NOUN
iajs-1071	238	4	are	be	AUX
iajs-1071	238	5	needed	need	VERB
iajs-1071	238	6	to	to	PART
iajs-1071	238	7	prove	prove	VERB
iajs-1071	238	8	next	next	ADJ
iajs-1071	238	9	proposition	proposition	NOUN
iajs-1071	238	10	.	.	PUNCT
iajs-1071	239	1	lemma	lemma	PROPN
iajs-1071	239	2	2.4	2.4	NUM
iajs-1071	239	3	:	:	PUNCT
iajs-1071	239	4	let	let	VERB
iajs-1071	239	5	x	x	PRON
iajs-1071	239	6	be	be	AUX
iajs-1071	239	7	f(m	f(m	PROPN
iajs-1071	239	8	)	)	PUNCT
iajs-1071	239	9	and	and	CCONJ
iajs-1071	239	10	let	let	VERB
iajs-1071	239	11	a	a	DET
iajs-1071	239	12	,	,	PUNCT
iajs-1071	239	13	b	b	NOUN
iajs-1071	239	14	and	and	CCONJ
iajs-1071	239	15	c	c	PROPN
iajs-1071	239	16	are	be	AUX
iajs-1071	239	17	fuzzy	fuzzy	ADJ
iajs-1071	239	18	submodules	submodule	NOUN
iajs-1071	239	19	of	of	ADP
iajs-1071	239	20	x	x	SYM
iajs-1071	239	21	such	such	ADJ
iajs-1071	239	22	that	that	SCONJ
iajs-1071	239	23	c	c	PROPN
iajs-1071	239	24	b.then	b.then	PRON
iajs-1071	239	25	c+(b	c+(b	NOUN
iajs-1071	239	26	a)=(c+a	a)=(c+a	PROPN
iajs-1071	239	27	)	)	PUNCT
iajs-1071	239	28	b.	b.	PROPN
iajs-1071	239	29	proof	proof	NOUN
iajs-1071	239	30	:	:	PUNCT
iajs-1071	239	31	first	first	ADV
iajs-1071	239	32	to	to	PART
iajs-1071	239	33	show	show	VERB
iajs-1071	239	34	that	that	SCONJ
iajs-1071	239	35	c+(b	c+(b	NOUN
iajs-1071	239	36	a	a	NOUN
iajs-1071	239	37	)	)	PUNCT
iajs-1071	239	38	,	,	PUNCT
iajs-1071	239	39	(	(	PUNCT
iajs-1071	239	40	since	since	SCONJ
iajs-1071	239	41	c	c	PROPN
iajs-1071	239	42	b	b	PROPN
iajs-1071	239	43	and	and	CCONJ
iajs-1071	239	44	b	b	PROPN
iajs-1071	239	45	a	a	DET
iajs-1071	239	46	b	b	NOUN
iajs-1071	239	47	)	)	PUNCT
iajs-1071	239	48	then	then	ADV
iajs-1071	239	49	c+(b	c+(b	ADP
iajs-1071	239	50	a	a	NOUN
iajs-1071	239	51	)	)	PUNCT
iajs-1071	239	52	b	b	NOUN
iajs-1071	239	53	by	by	ADP
iajs-1071	239	54	[	[	X
iajs-1071	239	55	2	2	NUM
iajs-1071	239	56	]	]	PUNCT
iajs-1071	239	57	.	.	PUNCT
iajs-1071	240	1	further	further	PROPN
iajs-1071	240	2	c	c	PROPN
iajs-1071	240	3	c+a	c+a	PUNCT
iajs-1071	240	4	,	,	PUNCT
iajs-1071	240	5	b	b	PROPN
iajs-1071	240	6	a	a	DET
iajs-1071	240	7	c+a	c+a	PROPN
iajs-1071	240	8	.	.	PUNCT
iajs-1071	241	1	thus	thus	ADV
iajs-1071	241	2	c+(b	c+(b	ADP
iajs-1071	241	3	a	a	NOUN
iajs-1071	241	4	)	)	PUNCT
iajs-1071	241	5	c+a	c+a	NUM
iajs-1071	241	6	therefore	therefore	ADV
iajs-1071	241	7	c+(b	c+(b	X
iajs-1071	241	8	a	a	NOUN
iajs-1071	241	9	)	)	PUNCT
iajs-1071	241	10	b	b	NOUN
iajs-1071	241	11	(	(	PUNCT
iajs-1071	241	12	c+a	c+a	PROPN
iajs-1071	241	13	)	)	PUNCT
iajs-1071	241	14	.	.	PUNCT
iajs-1071	242	1	conversely	conversely	ADV
iajs-1071	242	2	:	:	PUNCT
iajs-1071	242	3	to	to	PART
iajs-1071	242	4	show	show	VERB
iajs-1071	242	5	that	that	SCONJ
iajs-1071	242	6	c+	c+	NOUN
iajs-1071	242	7	(	(	PUNCT
iajs-1071	242	8	b	b	NOUN
iajs-1071	242	9	a	a	NOUN
iajs-1071	242	10	)	)	PUNCT
iajs-1071	242	11	let	let	VERB
iajs-1071	242	12	bt	bt	PROPN
iajs-1071	242	13	t	t	PROPN
iajs-1071	242	14	(	(	PUNCT
iajs-1071	242	15	0,1	0,1	NOUN
iajs-1071	242	16	]	]	PUNCT
iajs-1071	242	17	.	.	PUNCT
iajs-1071	243	1	then	then	ADV
iajs-1071	243	2	bt=	bt=	PROPN
iajs-1071	243	3	+	+	X
iajs-1071	243	4	for	for	ADP
iajs-1071	243	5	some	some	DET
iajs-1071	243	6	fuzzy	fuzzy	ADJ
iajs-1071	243	7	singletons	singleton	NOUN
iajs-1071	243	8	c	c	NOUN
iajs-1071	243	9	,	,	PUNCT
iajs-1071	243	10	a	a	DET
iajs-1071	243	11	(	(	PUNCT
iajs-1071	243	12	0,1	0,1	NUM
iajs-1071	243	13	]	]	PUNCT
iajs-1071	243	14	.	.	PUNCT
iajs-1071	244	1	hence	hence	ADV
iajs-1071	244	2	bt=(c+a)t	bt=(c+a)t	ADV
iajs-1071	244	3	where	where	SCONJ
iajs-1071	244	4	t	t	PROPN
iajs-1071	244	5	=	=	SYM
iajs-1071	244	6	min	min	NOUN
iajs-1071	244	7	{	{	PUNCT
iajs-1071	244	8	}	}	PUNCT
iajs-1071	244	9	.	.	PUNCT
iajs-1071	245	1	then	then	ADV
iajs-1071	245	2	b	b	X
iajs-1071	245	3	=	=	NOUN
iajs-1071	245	4	c+a	c+a	NOUN
iajs-1071	245	5	by[7	by[7	NOUN
iajs-1071	245	6	,	,	PUNCT
iajs-1071	245	7	definition	definition	NOUN
iajs-1071	245	8	(	(	PUNCT
iajs-1071	245	9	1.1.3)(3	1.1.3)(3	NUM
iajs-1071	245	10	)	)	PUNCT
iajs-1071	245	11	]	]	PUNCT
iajs-1071	245	12	.	.	PUNCT
iajs-1071	246	1	hence	hence	ADV
iajs-1071	246	2	a	a	DET
iajs-1071	246	3	=	=	ADJ
iajs-1071	246	4	b	b	NOUN
iajs-1071	246	5	-	-	PUNCT
iajs-1071	246	6	c	c	NOUN
iajs-1071	246	7	and	and	CCONJ
iajs-1071	246	8	=	=	X
iajs-1071	246	9	bt	bt	NOUN
iajs-1071	246	10	thus	thus	ADV
iajs-1071	246	11	b	b	X
iajs-1071	246	12	(	(	PUNCT
iajs-1071	246	13	since	since	SCONJ
iajs-1071	246	14	bt	bt	PROPN
iajs-1071	246	15	b	b	PROPN
iajs-1071	246	16	and	and	CCONJ
iajs-1071	246	17	c	c	PROPN
iajs-1071	246	18	b	b	PROPN
iajs-1071	246	19	)	)	PUNCT
iajs-1071	246	20	hence	hence	ADV
iajs-1071	246	21	b	b	X
iajs-1071	246	22	a	a	PRON
iajs-1071	246	23	and	and	CCONJ
iajs-1071	246	24	so	so	ADV
iajs-1071	246	25	bt=	bt=	NOUN
iajs-1071	246	26	+	+	CCONJ
iajs-1071	246	27	c+	c+	X
iajs-1071	246	28	(	(	PUNCT
iajs-1071	246	29	b	b	NOUN
iajs-1071	246	30	a	a	NOUN
iajs-1071	246	31	)	)	PUNCT
iajs-1071	246	32	.	.	PUNCT
iajs-1071	247	1	therefore	therefore	ADV
iajs-1071	247	2	c+(b	c+(b	VERB
iajs-1071	247	3	a)=(c+a	a)=(c+a	PROPN
iajs-1071	247	4	)	)	PUNCT
iajs-1071	247	5	b.	b.	PROPN
iajs-1071	248	1	lemma	lemma	PROPN
iajs-1071	248	2	2.5	2.5	NUM
iajs-1071	248	3	:	:	PUNCT
iajs-1071	248	4	let	let	VERB
iajs-1071	248	5	a	a	PRON
iajs-1071	248	6	be	be	AUX
iajs-1071	248	7	a	a	DET
iajs-1071	248	8	fuzzy	fuzzy	ADJ
iajs-1071	248	9	submodule	submodule	NOUN
iajs-1071	248	10	of	of	ADP
iajs-1071	248	11	a	a	DET
iajs-1071	248	12	fuzzy	fuzzy	ADJ
iajs-1071	248	13	module	module	NOUN
iajs-1071	248	14	x	x	PUNCT
iajs-1071	248	15	of	of	ADP
iajs-1071	248	16	an	an	DET
iajs-1071	248	17	r	r	NOUN
iajs-1071	248	18	-	-	PUNCT
iajs-1071	248	19	module	module	NOUN
iajs-1071	248	20	m	m	NOUN
iajs-1071	248	21	,	,	PUNCT
iajs-1071	248	22	let	let	VERB
iajs-1071	248	23	i	i	PRON
iajs-1071	248	24	be	be	AUX
iajs-1071	248	25	any	any	DET
iajs-1071	248	26	fuzzy	fuzzy	ADJ
iajs-1071	248	27	ideal	ideal	NOUN
iajs-1071	248	28	of	of	ADP
iajs-1071	248	29	r	r	NOUN
iajs-1071	248	30	,	,	PUNCT
iajs-1071	248	31	then	then	ADV
iajs-1071	248	32	f	f	X
iajs-1071	248	33	-	-	PUNCT
iajs-1071	248	34	annai	annai	ADP
iajs-1071	248	35	=	=	ADJ
iajs-1071	248	36	f	f	NOUN
iajs-1071	248	37	-	-	PUNCT
iajs-1071	248	38	annxi	annxi	NOUN
iajs-1071	248	39	a.	a.	NOUN
iajs-1071	248	40	proof	proof	NOUN
iajs-1071	248	41	:	:	PUNCT
iajs-1071	248	42	since	since	SCONJ
iajs-1071	248	43	f	f	NOUN
iajs-1071	248	44	-	-	PUNCT
iajs-1071	248	45	annai	annai	ADV
iajs-1071	248	46	is	be	AUX
iajs-1071	248	47	a	a	DET
iajs-1071	248	48	fuzzy	fuzzy	ADJ
iajs-1071	248	49	submodule	submodule	NOUN
iajs-1071	248	50	of	of	ADP
iajs-1071	248	51	a	a	DET
iajs-1071	248	52	fuzzy	fuzzy	ADJ
iajs-1071	248	53	submodule	submodule	NOUN
iajs-1071	248	54	a.	a.	NOUN
iajs-1071	248	55	then	then	ADV
iajs-1071	248	56	f	f	X
iajs-1071	248	57	-	-	PUNCT
iajs-1071	248	58	annxi	annxi	NOUN
iajs-1071	248	59	is	be	AUX
iajs-1071	248	60	a	a	DET
iajs-1071	248	61	fuzzy	fuzzy	ADJ
iajs-1071	248	62	submodule	submodule	NOUN
iajs-1071	248	63	of	of	ADP
iajs-1071	248	64	x	x	PROPN
iajs-1071	248	65	.	.	PUNCT
iajs-1071	249	1	and	and	CCONJ
iajs-1071	249	2	f	f	X
iajs-1071	249	3	-	-	PUNCT
iajs-1071	249	4	annxi	annxi	NOUN
iajs-1071	249	5	a	a	DET
iajs-1071	249	6	f	f	NOUN
iajs-1071	249	7	-	-	PUNCT
iajs-1071	249	8	annai	annai	ADV
iajs-1071	249	9	conversely	conversely	ADV
iajs-1071	249	10	:	:	PUNCT
iajs-1071	249	11	to	to	PART
iajs-1071	249	12	show	show	VERB
iajs-1071	249	13	that	that	SCONJ
iajs-1071	249	14	f	f	X
iajs-1071	249	15	-	-	PUNCT
iajs-1071	249	16	annai	annai	ADV
iajs-1071	249	17	f	f	NOUN
iajs-1071	249	18	-	-	PUNCT
iajs-1071	249	19	annxi	annxi	NOUN
iajs-1071	249	20	a	a	PRON
iajs-1071	249	21	?	?	PUNCT
iajs-1071	250	1	mathematics	mathematic	NOUN
iajs-1071	250	2	|	|	ADV
iajs-1071	250	3	202	202	NUM
iajs-1071	250	4	2012	2012	NUM
iajs-1071	250	5	(	(	PUNCT
iajs-1071	250	6	عام	عام	PROPN
iajs-1071	250	7	1	1	NUM
iajs-1071	250	8	)	)	PUNCT
iajs-1071	250	9	(	(	PUNCT
iajs-1071	250	10	العدد	العدد	PROPN
iajs-1071	250	11	30مجلة	30مجلة	NUM
iajs-1071	250	12	إبن	إبن	VERB
iajs-1071	250	13	الهيثم	الهيثم	ADJ
iajs-1071	250	14	للعلوم	للعلوم	NOUN
iajs-1071	250	15	الصرفة	الصرفة	NOUN
iajs-1071	251	1	و	و	PRON
iajs-1071	251	2	التطبيقية	التطبيقية	ADV
iajs-1071	251	3	المجلد	المجلد	ADV
iajs-1071	251	4	)	)	PUNCT
iajs-1071	252	1	ibn	ibn	PROPN
iajs-1071	252	2	al	al	PROPN
iajs-1071	252	3	-	-	PUNCT
iajs-1071	252	4	haitham	haitham	PROPN
iajs-1071	252	5	j.	j.	PROPN
iajs-1071	252	6	for	for	ADP
iajs-1071	252	7	pure	pure	PROPN
iajs-1071	252	8	&	&	CCONJ
iajs-1071	252	9	appl	appl	PROPN
iajs-1071	252	10	.	.	PUNCT
iajs-1071	253	1	sci	sci	PROPN
iajs-1071	253	2	.	.	PUNCT
iajs-1071	254	1	vol.30	vol.30	NOUN
iajs-1071	254	2	(	(	PUNCT
iajs-1071	254	3	1	1	X
iajs-1071	254	4	)	)	PUNCT
iajs-1071	254	5	2017	2017	NUM
iajs-1071	254	6	let	let	VERB
iajs-1071	254	7	xt	xt	PROPN
iajs-1071	255	1	f	f	X
iajs-1071	255	2	-	-	PUNCT
iajs-1071	255	3	annai	annai	PROPN
iajs-1071	255	4	,	,	PUNCT
iajs-1071	255	5	where	where	SCONJ
iajs-1071	255	6	xt	xt	ADP
iajs-1071	255	7	a	a	PRON
iajs-1071	255	8	,	,	PUNCT
iajs-1071	255	9	t	t	PROPN
iajs-1071	255	10	(	(	PUNCT
iajs-1071	255	11	0,1	0,1	NOUN
iajs-1071	255	12	]	]	PUNCT
iajs-1071	255	13	.	.	PUNCT
iajs-1071	256	1	then	then	ADV
iajs-1071	256	2	xti=01	xti=01	PROPN
iajs-1071	256	3	01=01	01=01	NOUN
iajs-1071	257	1	a	a	DET
iajs-1071	257	2	=	=	NOUN
iajs-1071	257	3	xti	xti	X
iajs-1071	257	4	a	a	DET
iajs-1071	257	5	=	=	ADJ
iajs-1071	257	6	f	f	X
iajs-1071	257	7	-	-	PUNCT
iajs-1071	257	8	annai	annai	NOUN
iajs-1071	257	9	a	a	PRON
iajs-1071	257	10	but	but	ADV
iajs-1071	257	11	xt	xt	ADP
iajs-1071	257	12	a	a	DET
iajs-1071	257	13	x	x	X
iajs-1071	257	14	xt	xt	PROPN
iajs-1071	257	15	x.	x.	NOUN
iajs-1071	258	1	thus	thus	ADV
iajs-1071	258	2	f	f	X
iajs-1071	258	3	-	-	PUNCT
iajs-1071	258	4	annxi	annxi	NOUN
iajs-1071	258	5	a=01=	a=01=	PROPN
iajs-1071	259	1	xti=	xti=	PROPN
iajs-1071	260	1	f	f	X
iajs-1071	260	2	-	-	PUNCT
iajs-1071	260	3	annai	annai	ADV
iajs-1071	260	4	now	now	ADV
iajs-1071	260	5	,	,	PUNCT
iajs-1071	260	6	we	we	PRON
iajs-1071	260	7	have	have	VERB
iajs-1071	260	8	the	the	DET
iajs-1071	260	9	following	follow	VERB
iajs-1071	260	10	proposition	proposition	NOUN
iajs-1071	260	11	.	.	PUNCT
iajs-1071	261	1	proposition	proposition	NOUN
iajs-1071	261	2	2.6	2.6	NUM
iajs-1071	261	3	:	:	PUNCT
iajs-1071	261	4	let	let	VERB
iajs-1071	261	5	a	a	PRON
iajs-1071	261	6	be	be	AUX
iajs-1071	261	7	a	a	DET
iajs-1071	261	8	fuzzy	fuzzy	ADJ
iajs-1071	261	9	submodule	submodule	NOUN
iajs-1071	261	10	of	of	ADP
iajs-1071	261	11	a	a	DET
iajs-1071	261	12	q	q	NOUN
iajs-1071	261	13	-	-	PUNCT
iajs-1071	261	14	mfcf(m	mfcf(m	NOUN
iajs-1071	261	15	)	)	PUNCT
iajs-1071	261	16	x	x	NOUN
iajs-1071	261	17	,	,	PUNCT
iajs-1071	261	18	then	then	ADV
iajs-1071	261	19	a	a	PRON
iajs-1071	261	20	is	be	AUX
iajs-1071	261	21	a	a	DET
iajs-1071	261	22	q	q	NOUN
iajs-1071	261	23	-	-	PUNCT
iajs-1071	261	24	mfcf(m	mfcf(m	NOUN
iajs-1071	261	25	)	)	PUNCT
iajs-1071	261	26	.	.	PUNCT
iajs-1071	262	1	proof	proof	NOUN
iajs-1071	262	2	:	:	PUNCT
iajs-1071	262	3	let	let	VERB
iajs-1071	262	4	b	b	X
iajs-1071	262	5	,	,	PUNCT
iajs-1071	262	6	c	c	PROPN
iajs-1071	262	7	are	be	AUX
iajs-1071	262	8	two	two	NUM
iajs-1071	262	9	fuzzy	fuzzy	ADJ
iajs-1071	262	10	submodules	submodule	NOUN
iajs-1071	262	11	of	of	ADP
iajs-1071	262	12	a	a	DET
iajs-1071	262	13	fuzzy	fuzzy	ADJ
iajs-1071	262	14	submodule	submodule	NOUN
iajs-1071	262	15	a	a	NOUN
iajs-1071	262	16	and	and	CCONJ
iajs-1071	262	17	let	let	VERB
iajs-1071	262	18	i	i	PRON
iajs-1071	262	19	be	be	AUX
iajs-1071	262	20	a	a	DET
iajs-1071	262	21	maximal	maximal	ADJ
iajs-1071	262	22	fuzzy	fuzzy	ADJ
iajs-1071	262	23	ideal	ideal	NOUN
iajs-1071	262	24	of	of	ADP
iajs-1071	262	25	r.	r.	PROPN
iajs-1071	262	26	such	such	ADJ
iajs-1071	262	27	that	that	SCONJ
iajs-1071	262	28	ib	ib	PROPN
iajs-1071	262	29	=	=	PROPN
iajs-1071	262	30	ic	ic	PROPN
iajs-1071	262	31	,	,	PUNCT
iajs-1071	262	32	then	then	ADV
iajs-1071	262	33	b	b	X
iajs-1071	262	34	,	,	PUNCT
iajs-1071	262	35	c	c	PROPN
iajs-1071	262	36	are	be	AUX
iajs-1071	262	37	fuzzy	fuzzy	ADJ
iajs-1071	262	38	submodules	submodule	NOUN
iajs-1071	262	39	of	of	ADP
iajs-1071	262	40	x.	x.	NOUN
iajs-1071	262	41	since	since	SCONJ
iajs-1071	262	42	x	x	PRON
iajs-1071	262	43	is	be	AUX
iajs-1071	262	44	a	a	DET
iajs-1071	262	45	q	q	NOUN
iajs-1071	262	46	-	-	PUNCT
iajs-1071	262	47	mfcf(m	mfcf(m	NOUN
iajs-1071	262	48	)	)	PUNCT
iajs-1071	262	49	then	then	ADV
iajs-1071	262	50	b+(f	b+(f	PROPN
iajs-1071	262	51	-	-	PUNCT
iajs-1071	262	52	annxi)=c+(f	annxi)=c+(f	NOUN
iajs-1071	262	53	-	-	NOUN
iajs-1071	262	54	annxi	annxi	NOUN
iajs-1071	262	55	)	)	PUNCT
iajs-1071	262	56	.	.	PUNCT
iajs-1071	263	1	but	but	CCONJ
iajs-1071	263	2	f	f	X
iajs-1071	263	3	-	-	PUNCT
iajs-1071	263	4	annai	annai	ADP
iajs-1071	263	5	=	=	ADJ
iajs-1071	263	6	f	f	NOUN
iajs-1071	263	7	-	-	PUNCT
iajs-1071	263	8	annxi	annxi	NOUN
iajs-1071	263	9	a	a	X
iajs-1071	263	10	by	by	ADP
iajs-1071	263	11	lemma	lemma	PROPN
iajs-1071	263	12	(	(	PUNCT
iajs-1071	263	13	2.5	2.5	NUM
iajs-1071	263	14	)	)	PUNCT
iajs-1071	263	15	.	.	PUNCT
iajs-1071	264	1	hence	hence	ADV
iajs-1071	264	2	b+	b+	VERB
iajs-1071	264	3	f	f	X
iajs-1071	264	4	-	-	PUNCT
iajs-1071	264	5	annai	annai	ADP
iajs-1071	264	6	=	=	SYM
iajs-1071	264	7	b+((f	b+((f	NOUN
iajs-1071	264	8	-	-	NOUN
iajs-1071	264	9	annxi	annxi	NOUN
iajs-1071	264	10	)	)	PUNCT
iajs-1071	264	11	a	a	DET
iajs-1071	264	12	)	)	PUNCT
iajs-1071	264	13	=(	=(	NOUN
iajs-1071	264	14	b+(f	b+(f	NOUN
iajs-1071	264	15	-	-	NOUN
iajs-1071	264	16	annxi	annxi	NOUN
iajs-1071	264	17	)	)	PUNCT
iajs-1071	264	18	)	)	PUNCT
iajs-1071	265	1	a	a	PRON
iajs-1071	265	2	by	by	ADP
iajs-1071	265	3	lemma	lemma	PROPN
iajs-1071	265	4	(	(	PUNCT
iajs-1071	265	5	2.4	2.4	NUM
iajs-1071	265	6	)	)	PUNCT
iajs-1071	265	7	.	.	PUNCT
iajs-1071	266	1	=(	=(	PROPN
iajs-1071	266	2	c+(f	c+(f	NOUN
iajs-1071	266	3	-	-	PUNCT
iajs-1071	266	4	annxi	annxi	NOUN
iajs-1071	266	5	)	)	PUNCT
iajs-1071	266	6	)	)	PUNCT
iajs-1071	267	1	a	a	DET
iajs-1071	267	2	=	=	NUM
iajs-1071	267	3	c+((f	c+((f	NOUN
iajs-1071	267	4	-	-	NOUN
iajs-1071	267	5	annxi	annxi	NOUN
iajs-1071	267	6	)	)	PUNCT
iajs-1071	267	7	a	a	X
iajs-1071	267	8	)	)	PUNCT
iajs-1071	267	9	by	by	ADP
iajs-1071	267	10	lemma	lemma	PROPN
iajs-1071	267	11	(	(	PUNCT
iajs-1071	267	12	2.4	2.4	NUM
iajs-1071	267	13	)	)	PUNCT
iajs-1071	267	14	=	=	NOUN
iajs-1071	267	15	c+	c+	X
iajs-1071	267	16	(	(	PUNCT
iajs-1071	267	17	f	f	NOUN
iajs-1071	267	18	-	-	PUNCT
iajs-1071	267	19	annai	annai	ADV
iajs-1071	267	20	)	)	PUNCT
iajs-1071	267	21	by	by	ADP
iajs-1071	267	22	lemma	lemma	PROPN
iajs-1071	267	23	(	(	PUNCT
iajs-1071	267	24	2.5	2.5	NUM
iajs-1071	267	25	)	)	PUNCT
iajs-1071	267	26	thus	thus	ADV
iajs-1071	267	27	a	a	PRON
iajs-1071	267	28	is	be	AUX
iajs-1071	267	29	a	a	DET
iajs-1071	267	30	q	q	NOUN
iajs-1071	267	31	-	-	PUNCT
iajs-1071	267	32	mfcf(m	mfcf(m	NOUN
iajs-1071	267	33	)	)	PUNCT
iajs-1071	267	34	.	.	PUNCT
iajs-1071	268	1	remark	remark	VERB
iajs-1071	268	2	2.7	2.7	NUM
iajs-1071	268	3	:	:	PUNCT
iajs-1071	268	4	every	every	DET
iajs-1071	268	5	max	max	PROPN
iajs-1071	268	6	-	-	PUNCT
iajs-1071	268	7	fully	fully	ADV
iajs-1071	268	8	cancellation	cancellation	NOUN
iajs-1071	268	9	fuzzy	fuzzy	ADJ
iajs-1071	268	10	module	module	NOUN
iajs-1071	268	11	is	be	AUX
iajs-1071	268	12	q	q	NOUN
iajs-1071	268	13	-	-	PUNCT
iajs-1071	268	14	mfcf(m	mfcf(m	NOUN
iajs-1071	268	15	)	)	PUNCT
iajs-1071	268	16	.	.	PUNCT
iajs-1071	269	1	proof	proof	NOUN
iajs-1071	269	2	:	:	PUNCT
iajs-1071	269	3	it	it	PRON
iajs-1071	269	4	is	be	AUX
iajs-1071	269	5	clear	clear	ADJ
iajs-1071	269	6	.	.	PUNCT
iajs-1071	270	1	the	the	DET
iajs-1071	270	2	converse	converse	NOUN
iajs-1071	270	3	of	of	ADP
iajs-1071	270	4	remark	remark	NOUN
iajs-1071	270	5	(	(	PUNCT
iajs-1071	270	6	2.7	2.7	NUM
iajs-1071	270	7	)	)	PUNCT
iajs-1071	270	8	is	be	AUX
iajs-1071	270	9	not	not	PART
iajs-1071	270	10	true	true	ADJ
iajs-1071	270	11	in	in	ADP
iajs-1071	270	12	general	general	ADJ
iajs-1071	270	13	for	for	ADP
iajs-1071	270	14	example	example	NOUN
iajs-1071	270	15	:	:	PUNCT
iajs-1071	270	16	let	let	VERB
iajs-1071	270	17	m	m	NOUN
iajs-1071	270	18	=	=	NOUN
iajs-1071	270	19	z6	z6	PROPN
iajs-1071	270	20	,	,	PUNCT
iajs-1071	270	21	r	r	PROPN
iajs-1071	270	22	=	=	SYM
iajs-1071	270	23	z6	z6	NOUN
iajs-1071	270	24	let	let	VERB
iajs-1071	270	25	x	x	PRON
iajs-1071	270	26	:	:	PUNCT
iajs-1071	270	27	m	m	VERB
iajs-1071	270	28	[	[	X
iajs-1071	270	29	0,1	0,1	NUM
iajs-1071	270	30	]	]	PUNCT
iajs-1071	270	31	define	define	NOUN
iajs-1071	270	32	by	by	ADP
iajs-1071	270	33	x(x	x(x	NOUN
iajs-1071	270	34	)	)	PUNCT
iajs-1071	271	1	=	=	NOUN
iajs-1071	271	2	{	{	PUNCT
iajs-1071	271	3	xt	xt	ADP
iajs-1071	271	4	=	=	PROPN
iajs-1071	271	5	m	m	PROPN
iajs-1071	271	6	t	t	NOUN
iajs-1071	271	7	(	(	PUNCT
iajs-1071	271	8	0,1	0,1	NUM
iajs-1071	271	9	]	]	PUNCT
iajs-1071	271	10	,	,	PUNCT
iajs-1071	271	11	then	then	ADV
iajs-1071	271	12	x	x	PUNCT
iajs-1071	271	13	is	be	AUX
iajs-1071	271	14	a	a	DET
iajs-1071	271	15	q	q	NOUN
iajs-1071	271	16	-	-	PUNCT
iajs-1071	271	17	mfcf(m	mfcf(m	NOUN
iajs-1071	271	18	)	)	PUNCT
iajs-1071	271	19	by	by	ADP
iajs-1071	271	20	remark((1.3)(1	remark((1.3)(1	NOUN
iajs-1071	271	21	)	)	PUNCT
iajs-1071	271	22	)	)	PUNCT
iajs-1071	271	23	and	and	CCONJ
iajs-1071	271	24	it	it	PRON
iajs-1071	271	25	is	be	AUX
iajs-1071	271	26	not	not	PART
iajs-1071	271	27	max	max	PROPN
iajs-1071	271	28	-	-	PUNCT
iajs-1071	271	29	fully	fully	ADV
iajs-1071	271	30	cancellation	cancellation	NOUN
iajs-1071	271	31	fuzzy	fuzzy	ADJ
iajs-1071	271	32	module	module	NOUN
iajs-1071	271	33	since	since	SCONJ
iajs-1071	271	34	let	let	VERB
iajs-1071	271	35	i	i	PRON
iajs-1071	271	36	:(	:(	PUNCT
iajs-1071	271	37	̅	̅	X
iajs-1071	271	38	[	[	X
iajs-1071	271	39	0,1	0,1	NUM
iajs-1071	271	40	]	]	PUNCT
iajs-1071	271	41	define	define	NOUN
iajs-1071	271	42	by	by	ADP
iajs-1071	271	43	i(r	i(r	PROPN
iajs-1071	271	44	)	)	PUNCT
iajs-1071	272	1	=	=	NOUN
iajs-1071	272	2	{	{	PUNCT
iajs-1071	272	3	̅	̅	NOUN
iajs-1071	272	4	,	,	PUNCT
iajs-1071	272	5	t	t	PROPN
iajs-1071	272	6	(	(	PUNCT
iajs-1071	272	7	0,1	0,1	NOUN
iajs-1071	272	8	]	]	PUNCT
iajs-1071	272	9	.	.	PUNCT
iajs-1071	273	1	and	and	CCONJ
iajs-1071	273	2	a	a	DET
iajs-1071	273	3	:(	:(	X
iajs-1071	273	4	̅	̅	NOUN
iajs-1071	273	5	[	[	X
iajs-1071	273	6	0,1	0,1	NUM
iajs-1071	273	7	]	]	PUNCT
iajs-1071	273	8	define	define	NOUN
iajs-1071	273	9	by	by	ADP
iajs-1071	273	10	a(x	a(x	NOUN
iajs-1071	273	11	)	)	PUNCT
iajs-1071	273	12	=	=	NOUN
iajs-1071	273	13	{	{	PUNCT
iajs-1071	273	14	̅	̅	NOUN
iajs-1071	273	15	mathematics	mathematic	NOUN
iajs-1071	273	16	|	|	ADV
iajs-1071	273	17	203	203	NUM
iajs-1071	273	18	2012	2012	NUM
iajs-1071	273	19	(	(	PUNCT
iajs-1071	273	20	عام	عام	PROPN
iajs-1071	273	21	1	1	NUM
iajs-1071	273	22	)	)	PUNCT
iajs-1071	273	23	(	(	PUNCT
iajs-1071	273	24	العدد	العدد	PROPN
iajs-1071	273	25	30مجلة	30مجلة	NUM
iajs-1071	273	26	إبن	إبن	VERB
iajs-1071	273	27	الهيثم	الهيثم	ADJ
iajs-1071	273	28	للعلوم	للعلوم	NOUN
iajs-1071	273	29	الصرفة	الصرفة	NOUN
iajs-1071	274	1	و	و	PRON
iajs-1071	274	2	التطبيقية	التطبيقية	ADV
iajs-1071	274	3	المجلد	المجلد	ADV
iajs-1071	274	4	)	)	PUNCT
iajs-1071	275	1	ibn	ibn	PROPN
iajs-1071	275	2	al	al	PROPN
iajs-1071	275	3	-	-	PUNCT
iajs-1071	275	4	haitham	haitham	PROPN
iajs-1071	275	5	j.	j.	PROPN
iajs-1071	275	6	for	for	ADP
iajs-1071	275	7	pure	pure	PROPN
iajs-1071	275	8	&	&	CCONJ
iajs-1071	275	9	appl	appl	PROPN
iajs-1071	275	10	.	.	PUNCT
iajs-1071	276	1	sci	sci	PROPN
iajs-1071	276	2	.	.	PUNCT
iajs-1071	277	1	vol.30	vol.30	NOUN
iajs-1071	277	2	(	(	PUNCT
iajs-1071	277	3	1	1	NUM
iajs-1071	277	4	)	)	PUNCT
iajs-1071	277	5	2017	2017	NUM
iajs-1071	277	6	also	also	ADV
iajs-1071	277	7	,	,	PUNCT
iajs-1071	277	8	b	b	X
iajs-1071	277	9	:(	:(	X
iajs-1071	277	10	̅	̅	NOUN
iajs-1071	277	11	[	[	X
iajs-1071	277	12	0,1	0,1	NUM
iajs-1071	277	13	]	]	PUNCT
iajs-1071	277	14	define	define	NOUN
iajs-1071	277	15	by	by	ADP
iajs-1071	277	16	b(x	b(x	NOUN
iajs-1071	277	17	)	)	PUNCT
iajs-1071	277	18	=	=	NOUN
iajs-1071	277	19	{	{	PUNCT
iajs-1071	277	20	̅	̅	NOUN
iajs-1071	277	21	,	,	PUNCT
iajs-1071	277	22	t	t	PROPN
iajs-1071	277	23	(	(	PUNCT
iajs-1071	277	24	0,1	0,1	NUM
iajs-1071	277	25	]	]	PUNCT
iajs-1071	277	26	.	.	PUNCT
iajs-1071	278	1	it	it	PRON
iajs-1071	278	2	is	be	AUX
iajs-1071	278	3	clear	clear	ADJ
iajs-1071	278	4	that	that	SCONJ
iajs-1071	278	5	a	a	DET
iajs-1071	278	6	,	,	PUNCT
iajs-1071	278	7	b	b	NOUN
iajs-1071	278	8	are	be	AUX
iajs-1071	278	9	fuzzy	fuzzy	ADJ
iajs-1071	278	10	suodules	suodule	NOUN
iajs-1071	278	11	of	of	ADP
iajs-1071	278	12	x	x	PUNCT
iajs-1071	278	13	and	and	CCONJ
iajs-1071	278	14	i	i	PRON
iajs-1071	278	15	is	be	AUX
iajs-1071	278	16	a	a	DET
iajs-1071	278	17	fuzzy	fuzzy	ADJ
iajs-1071	278	18	ideal	ideal	NOUN
iajs-1071	278	19	of	of	ADP
iajs-1071	278	20	r.	r.	PROPN
iajs-1071	278	21	ia	ia	PROPN
iajs-1071	278	22	=	=	PROPN
iajs-1071	278	23	ib	ib	NOUN
iajs-1071	278	24	itat	itat	NOUN
iajs-1071	278	25	=	=	PUNCT
iajs-1071	278	26	itbt	itbt	NOUN
iajs-1071	278	27	.	.	PUNCT
iajs-1071	279	1	(	(	PUNCT
iajs-1071	279	2	̅	̅	X
iajs-1071	279	3	(	(	PUNCT
iajs-1071	279	4	̅	̅	NOUN
iajs-1071	279	5	̅	̅	NOUN
iajs-1071	279	6	̅	̅	NOUN
iajs-1071	279	7	̅	̅	NOUN
iajs-1071	279	8	,	,	PUNCT
iajs-1071	279	9	but	but	CCONJ
iajs-1071	279	10	(	(	PUNCT
iajs-1071	279	11	̅	̅	X
iajs-1071	279	12	(	(	PUNCT
iajs-1071	279	13	̅	̅	NOUN
iajs-1071	279	14	then	then	ADV
iajs-1071	279	15	at≠bt	at≠bt	PROPN
iajs-1071	279	16	a≠b	a≠b	NOUN
iajs-1071	279	17	.	.	PUNCT
iajs-1071	280	1	thus	thus	ADV
iajs-1071	280	2	x	x	PRON
iajs-1071	280	3	is	be	AUX
iajs-1071	280	4	not	not	PART
iajs-1071	280	5	max	max	PROPN
iajs-1071	280	6	-	-	PUNCT
iajs-1071	280	7	fully	fully	ADV
iajs-1071	280	8	cancellation	cancellation	NOUN
iajs-1071	280	9	fuzzy	fuzzy	ADJ
iajs-1071	280	10	module	module	NOUN
iajs-1071	280	11	.	.	PUNCT
iajs-1071	281	1	the	the	DET
iajs-1071	281	2	convers	conver	NOUN
iajs-1071	281	3	of	of	ADP
iajs-1071	281	4	remark	remark	NOUN
iajs-1071	281	5	(	(	PUNCT
iajs-1071	281	6	2.7	2.7	NUM
iajs-1071	281	7	)	)	PUNCT
iajs-1071	281	8	is	be	AUX
iajs-1071	281	9	true	true	ADJ
iajs-1071	281	10	under	under	ADP
iajs-1071	281	11	the	the	DET
iajs-1071	281	12	following	follow	VERB
iajs-1071	281	13	conditions	condition	NOUN
iajs-1071	281	14	.	.	PUNCT
iajs-1071	282	1	proposition	proposition	NOUN
iajs-1071	282	2	2.8	2.8	NUM
iajs-1071	282	3	:	:	PUNCT
iajs-1071	282	4	let	let	VERB
iajs-1071	282	5	x	x	PRON
iajs-1071	282	6	be	be	AUX
iajs-1071	282	7	f(m	f(m	PROPN
iajs-1071	282	8	)	)	PUNCT
iajs-1071	282	9	and	and	CCONJ
iajs-1071	282	10	let	let	VERB
iajs-1071	282	11	f	f	X
iajs-1071	282	12	-	-	PUNCT
iajs-1071	282	13	annxi=01	annxi=01	ADJ
iajs-1071	282	14	be	be	AUX
iajs-1071	282	15	(	(	PUNCT
iajs-1071	282	16	f	f	NOUN
iajs-1071	282	17	-	-	PUNCT
iajs-1071	282	18	faithful	faithful	ADJ
iajs-1071	282	19	)	)	PUNCT
iajs-1071	282	20	for	for	ADP
iajs-1071	282	21	every	every	DET
iajs-1071	282	22	non	non	ADJ
iajs-1071	282	23	-	-	ADJ
iajs-1071	282	24	empty	empty	ADJ
iajs-1071	282	25	fuzzy	fuzzy	ADJ
iajs-1071	282	26	ideal	ideal	NOUN
iajs-1071	282	27	i	i	PRON
iajs-1071	282	28	of	of	ADP
iajs-1071	282	29	r.	r.	PROPN
iajs-1071	282	30	then	then	ADV
iajs-1071	282	31	every	every	DET
iajs-1071	282	32	q	q	NOUN
iajs-1071	282	33	-	-	PUNCT
iajs-1071	282	34	mfcf(m	mfcf(m	NOUN
iajs-1071	282	35	)	)	PUNCT
iajs-1071	282	36	is	be	AUX
iajs-1071	282	37	max	max	PROPN
iajs-1071	282	38	-	-	PUNCT
iajs-1071	282	39	fully	fully	ADV
iajs-1071	282	40	cancellation	cancellation	NOUN
iajs-1071	282	41	fuzzy	fuzzy	ADJ
iajs-1071	282	42	module	module	NOUN
iajs-1071	282	43	.	.	PUNCT
iajs-1071	283	1	proof	proof	NOUN
iajs-1071	283	2	:	:	PUNCT
iajs-1071	283	3	let	let	VERB
iajs-1071	283	4	i	i	PRON
iajs-1071	283	5	be	be	AUX
iajs-1071	283	6	a	a	DET
iajs-1071	283	7	maximal	maximal	ADJ
iajs-1071	283	8	fuzzy	fuzzy	ADJ
iajs-1071	283	9	ideal	ideal	NOUN
iajs-1071	283	10	of	of	ADP
iajs-1071	283	11	r.	r.	PROPN
iajs-1071	283	12	and	and	CCONJ
iajs-1071	283	13	let	let	VERB
iajs-1071	283	14	a	a	DET
iajs-1071	283	15	,	,	PUNCT
iajs-1071	283	16	b	b	NOUN
iajs-1071	283	17	be	be	AUX
iajs-1071	283	18	two	two	NUM
iajs-1071	283	19	fuzzy	fuzzy	ADJ
iajs-1071	283	20	submodules	submodule	NOUN
iajs-1071	283	21	of	of	ADP
iajs-1071	283	22	x	x	SYM
iajs-1071	283	23	such	such	ADJ
iajs-1071	283	24	that	that	SCONJ
iajs-1071	283	25	ia	ia	PROPN
iajs-1071	283	26	=	=	NOUN
iajs-1071	283	27	ib	ib	NOUN
iajs-1071	283	28	since	since	SCONJ
iajs-1071	283	29	x	x	PRON
iajs-1071	283	30	is	be	AUX
iajs-1071	283	31	q	q	NOUN
iajs-1071	283	32	-	-	PUNCT
iajs-1071	283	33	mfcf(m	mfcf(m	NOUN
iajs-1071	283	34	)	)	PUNCT
iajs-1071	283	35	,	,	PUNCT
iajs-1071	283	36	then	then	ADV
iajs-1071	283	37	a+(f	a+(f	NOUN
iajs-1071	283	38	-	-	PUNCT
iajs-1071	283	39	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	283	40	-	-	PUNCT
iajs-1071	283	41	annxi	annxi	NOUN
iajs-1071	283	42	)	)	PUNCT
iajs-1071	283	43	.	.	PUNCT
iajs-1071	284	1	but	but	CCONJ
iajs-1071	284	2	(	(	PUNCT
iajs-1071	284	3	f	f	X
iajs-1071	284	4	-	-	PUNCT
iajs-1071	284	5	annxi)=01	annxi)=01	NOUN
iajs-1071	284	6	.	.	PUNCT
iajs-1071	285	1	thus	thus	ADV
iajs-1071	285	2	a	a	DET
iajs-1071	285	3	=	=	SYM
iajs-1071	285	4	b	b	NOUN
iajs-1071	285	5	then	then	ADV
iajs-1071	285	6	x	x	VERB
iajs-1071	285	7	is	be	AUX
iajs-1071	285	8	max	max	PROPN
iajs-1071	285	9	-	-	PUNCT
iajs-1071	285	10	fully	fully	ADV
iajs-1071	285	11	cancellation	cancellation	NOUN
iajs-1071	285	12	fuzzy	fuzzy	ADJ
iajs-1071	285	13	module	module	NOUN
iajs-1071	285	14	.	.	PUNCT
iajs-1071	286	1	the	the	DET
iajs-1071	286	2	following	follow	VERB
iajs-1071	286	3	is	be	AUX
iajs-1071	286	4	characterization	characterization	NOUN
iajs-1071	286	5	of	of	ADP
iajs-1071	286	6	q	q	NOUN
iajs-1071	286	7	-	-	PUNCT
iajs-1071	286	8	mfcf(m	mfcf(m	NOUN
iajs-1071	286	9	)	)	PUNCT
iajs-1071	286	10	.	.	PUNCT
iajs-1071	287	1	theorem	theorem	VERB
iajs-1071	287	2	2.9	2.9	NUM
iajs-1071	287	3	:	:	PUNCT
iajs-1071	287	4	let	let	VERB
iajs-1071	287	5	x	x	PRON
iajs-1071	287	6	be	be	AUX
iajs-1071	287	7	f(m	f(m	PROPN
iajs-1071	287	8	)	)	PUNCT
iajs-1071	287	9	,	,	PUNCT
iajs-1071	287	10	let	let	VERB
iajs-1071	287	11	a	a	DET
iajs-1071	287	12	,	,	PUNCT
iajs-1071	287	13	b	b	NOUN
iajs-1071	287	14	be	be	AUX
iajs-1071	287	15	two	two	NUM
iajs-1071	287	16	fuzzy	fuzzy	ADJ
iajs-1071	287	17	submodules	submodule	NOUN
iajs-1071	287	18	of	of	ADP
iajs-1071	287	19	x	x	PUNCT
iajs-1071	287	20	and	and	CCONJ
iajs-1071	287	21	let	let	VERB
iajs-1071	287	22	i	i	PRON
iajs-1071	287	23	be	be	AUX
iajs-1071	287	24	a	a	DET
iajs-1071	287	25	maximal	maximal	ADJ
iajs-1071	287	26	fuzzy	fuzzy	ADJ
iajs-1071	287	27	ideal	ideal	NOUN
iajs-1071	287	28	of	of	ADP
iajs-1071	287	29	r.	r.	PROPN
iajs-1071	287	30	then	then	ADV
iajs-1071	287	31	the	the	DET
iajs-1071	287	32	following	follow	VERB
iajs-1071	287	33	statements	statement	NOUN
iajs-1071	287	34	are	be	AUX
iajs-1071	287	35	equivalent	equivalent	ADJ
iajs-1071	287	36	:	:	PUNCT
iajs-1071	287	37	(	(	PUNCT
iajs-1071	287	38	1	1	X
iajs-1071	287	39	)	)	PUNCT
iajs-1071	287	40	x	x	X
iajs-1071	287	41	is	be	AUX
iajs-1071	287	42	a	a	DET
iajs-1071	287	43	q	q	NOUN
iajs-1071	287	44	-	-	PUNCT
iajs-1071	287	45	mfcf(m	mfcf(m	NOUN
iajs-1071	287	46	)	)	PUNCT
iajs-1071	287	47	.	.	PUNCT
iajs-1071	288	1	(	(	PUNCT
iajs-1071	288	2	2	2	X
iajs-1071	288	3	)	)	PUNCT
iajs-1071	288	4	if	if	SCONJ
iajs-1071	288	5	ia	ia	PROPN
iajs-1071	288	6	ib	ib	PROPN
iajs-1071	288	7	,	,	PUNCT
iajs-1071	288	8	then	then	ADV
iajs-1071	288	9	a	a	DET
iajs-1071	288	10	b+(f	b+(f	NOUN
iajs-1071	288	11	-	-	NOUN
iajs-1071	288	12	annxi	annxi	NOUN
iajs-1071	288	13	)	)	PUNCT
iajs-1071	288	14	.	.	PUNCT
iajs-1071	289	1	(	(	PUNCT
iajs-1071	289	2	3	3	X
iajs-1071	289	3	)	)	PUNCT
iajs-1071	289	4	if	if	SCONJ
iajs-1071	289	5	i(xt	i(xt	NOUN
iajs-1071	289	6	)	)	PUNCT
iajs-1071	289	7	ib	ib	NOUN
iajs-1071	289	8	,	,	PUNCT
iajs-1071	289	9	then	then	ADV
iajs-1071	289	10	xt	xt	ADP
iajs-1071	289	11	b+(f	b+(f	NOUN
iajs-1071	289	12	-	-	PUNCT
iajs-1071	289	13	annxi).where	annxi).where	NOUN
iajs-1071	289	14	xt	xt	X
iajs-1071	289	15	x.	x.	NOUN
iajs-1071	289	16	(	(	PUNCT
iajs-1071	289	17	4	4	NUM
iajs-1071	289	18	)	)	PUNCT
iajs-1071	289	19	(	(	PUNCT
iajs-1071	289	20	ia	ia	PROPN
iajs-1071	289	21	:	:	PUNCT
iajs-1071	289	22	xi)=	xi)=	PROPN
iajs-1071	289	23	b+(f	b+(f	NOUN
iajs-1071	289	24	-	-	NOUN
iajs-1071	289	25	annxi	annxi	NOUN
iajs-1071	289	26	)	)	PUNCT
iajs-1071	289	27	.	.	PUNCT
iajs-1071	290	1	proof	proof	NOUN
iajs-1071	290	2	:	:	PUNCT
iajs-1071	290	3	compare	compare	VERB
iajs-1071	290	4	this	this	DET
iajs-1071	290	5	proof	proof	NOUN
iajs-1071	290	6	with	with	ADP
iajs-1071	290	7	the	the	DET
iajs-1071	290	8	proof	proof	NOUN
iajs-1071	290	9	of	of	ADP
iajs-1071	290	10	proposition	proposition	NOUN
iajs-1071	290	11	(	(	PUNCT
iajs-1071	290	12	1.7	1.7	NUM
iajs-1071	290	13	)	)	PUNCT
iajs-1071	290	14	.	.	PUNCT
iajs-1071	291	1	the	the	DET
iajs-1071	291	2	next	next	ADJ
iajs-1071	291	3	result	result	NOUN
iajs-1071	291	4	gives	give	VERB
iajs-1071	291	5	another	another	DET
iajs-1071	291	6	characterization	characterization	NOUN
iajs-1071	291	7	for	for	ADP
iajs-1071	291	8	q	q	NOUN
iajs-1071	291	9	-	-	PUNCT
iajs-1071	291	10	mfcf(m	mfcf(m	NOUN
iajs-1071	291	11	)	)	PUNCT
iajs-1071	291	12	.	.	PUNCT
iajs-1071	292	1	proposition	proposition	NOUN
iajs-1071	292	2	2.10	2.10	NUM
iajs-1071	292	3	:	:	PUNCT
iajs-1071	292	4	let	let	VERB
iajs-1071	292	5	x	x	PRON
iajs-1071	292	6	be	be	AUX
iajs-1071	292	7	f(m).then	f(m).then	PROPN
iajs-1071	292	8	for	for	ADP
iajs-1071	292	9	any	any	DET
iajs-1071	292	10	maximal	maximal	ADJ
iajs-1071	292	11	fuzzy	fuzzy	ADJ
iajs-1071	292	12	ideal	ideal	NOUN
iajs-1071	292	13	i	i	PRON
iajs-1071	292	14	of	of	ADP
iajs-1071	292	15	r	r	NOUN
iajs-1071	292	16	the	the	DET
iajs-1071	292	17	following	following	ADJ
iajs-1071	292	18	statements	statement	NOUN
iajs-1071	292	19	are	be	AUX
iajs-1071	292	20	equivalent	equivalent	ADJ
iajs-1071	292	21	:	:	PUNCT
iajs-1071	292	22	(	(	PUNCT
iajs-1071	292	23	1	1	X
iajs-1071	292	24	)	)	PUNCT
iajs-1071	292	25	x	x	X
iajs-1071	292	26	is	be	AUX
iajs-1071	292	27	q	q	NOUN
iajs-1071	292	28	-	-	PUNCT
iajs-1071	292	29	mfcf(m	mfcf(m	NOUN
iajs-1071	292	30	)	)	PUNCT
iajs-1071	292	31	.	.	PUNCT
iajs-1071	293	1	(	(	PUNCT
iajs-1071	293	2	2	2	X
iajs-1071	293	3	)	)	PUNCT
iajs-1071	293	4	for	for	ADP
iajs-1071	293	5	every	every	DET
iajs-1071	293	6	fuzzy	fuzzy	ADJ
iajs-1071	293	7	submodules	submodule	NOUN
iajs-1071	293	8	a	a	PRON
iajs-1071	293	9	,	,	PUNCT
iajs-1071	293	10	b	b	PROPN
iajs-1071	293	11	of	of	ADP
iajs-1071	293	12	x	x	PRON
iajs-1071	293	13	then	then	ADV
iajs-1071	293	14	(	(	PUNCT
iajs-1071	293	15	(	(	PUNCT
iajs-1071	293	16	a+(f	a+(f	NOUN
iajs-1071	293	17	-	-	PUNCT
iajs-1071	293	18	annxi)):b)=(ia	annxi)):b)=(ia	VERB
iajs-1071	293	19	:	:	PUNCT
iajs-1071	293	20	ib	ib	PROPN
iajs-1071	293	21	)	)	PUNCT
iajs-1071	293	22	.	.	PUNCT
iajs-1071	294	1	mathematics	mathematic	NOUN
iajs-1071	294	2	|	|	ADV
iajs-1071	294	3	204	204	NUM
iajs-1071	294	4	2012	2012	NUM
iajs-1071	294	5	(	(	PUNCT
iajs-1071	294	6	عام	عام	PROPN
iajs-1071	294	7	1	1	NUM
iajs-1071	294	8	)	)	PUNCT
iajs-1071	294	9	(	(	PUNCT
iajs-1071	294	10	العدد	العدد	PROPN
iajs-1071	294	11	30مجلة	30مجلة	NUM
iajs-1071	294	12	إبن	إبن	VERB
iajs-1071	294	13	الهيثم	الهيثم	ADJ
iajs-1071	294	14	للعلوم	للعلوم	NOUN
iajs-1071	294	15	الصرفة	الصرفة	NOUN
iajs-1071	295	1	و	و	PRON
iajs-1071	295	2	التطبيقية	التطبيقية	ADV
iajs-1071	295	3	المجلد	المجلد	ADV
iajs-1071	295	4	)	)	PUNCT
iajs-1071	296	1	ibn	ibn	PROPN
iajs-1071	296	2	al	al	PROPN
iajs-1071	296	3	-	-	PUNCT
iajs-1071	296	4	haitham	haitham	PROPN
iajs-1071	296	5	j.	j.	PROPN
iajs-1071	296	6	for	for	ADP
iajs-1071	296	7	pure	pure	PROPN
iajs-1071	296	8	&	&	CCONJ
iajs-1071	296	9	appl	appl	PROPN
iajs-1071	296	10	.	.	PUNCT
iajs-1071	297	1	sci	sci	PROPN
iajs-1071	297	2	.	.	PUNCT
iajs-1071	298	1	vol.30	vol.30	NOUN
iajs-1071	298	2	(	(	PUNCT
iajs-1071	298	3	1	1	NUM
iajs-1071	298	4	)	)	PUNCT
iajs-1071	298	5	2017	2017	NUM
iajs-1071	298	6	proof	proof	NOUN
iajs-1071	298	7	:	:	PUNCT
iajs-1071	298	8	it	it	PRON
iajs-1071	298	9	is	be	AUX
iajs-1071	298	10	similar	similar	ADJ
iajs-1071	298	11	proof	proof	NOUN
iajs-1071	298	12	of	of	ADP
iajs-1071	298	13	proposition	proposition	NOUN
iajs-1071	298	14	(	(	PUNCT
iajs-1071	298	15	1.8	1.8	NUM
iajs-1071	298	16	)	)	PUNCT
iajs-1071	298	17	.	.	PUNCT
iajs-1071	299	1	§	§	PROPN
iajs-1071	299	2	3	3	NUM
iajs-1071	299	3	.	.	PUNCT
iajs-1071	300	1	the	the	DET
iajs-1071	300	2	direct	direct	ADJ
iajs-1071	300	3	sum	sum	NOUN
iajs-1071	300	4	of	of	ADP
iajs-1071	300	5	quasi	quasi	ADJ
iajs-1071	300	6	-	-	ADJ
iajs-1071	300	7	fully	fully	ADV
iajs-1071	300	8	cancellation	cancellation	NOUN
iajs-1071	300	9	fuzzy	fuzzy	ADJ
iajs-1071	300	10	modules	module	NOUN
iajs-1071	300	11	and	and	CCONJ
iajs-1071	300	12	its	its	PRON
iajs-1071	300	13	generalization	generalization	NOUN
iajs-1071	300	14	in	in	ADP
iajs-1071	300	15	this	this	DET
iajs-1071	300	16	part	part	NOUN
iajs-1071	300	17	we	we	PRON
iajs-1071	300	18	study	study	VERB
iajs-1071	300	19	the	the	DET
iajs-1071	300	20	direct	direct	ADJ
iajs-1071	300	21	sum	sum	NOUN
iajs-1071	300	22	of	of	ADP
iajs-1071	300	23	two	two	NUM
iajs-1071	300	24	q	q	NOUN
iajs-1071	300	25	-	-	PUNCT
iajs-1071	300	26	fcf(m	fcf(m	NOUN
iajs-1071	300	27	)	)	PUNCT
iajs-1071	300	28	and	and	CCONJ
iajs-1071	300	29	we	we	PRON
iajs-1071	300	30	prove	prove	VERB
iajs-1071	300	31	some	some	DET
iajs-1071	300	32	results	result	NOUN
iajs-1071	300	33	about	about	ADP
iajs-1071	300	34	it	it	PRON
iajs-1071	300	35	.	.	PUNCT
iajs-1071	301	1	also	also	ADV
iajs-1071	301	2	,	,	PUNCT
iajs-1071	301	3	we	we	PRON
iajs-1071	301	4	study	study	VERB
iajs-1071	301	5	its	its	PRON
iajs-1071	301	6	generalizations	generalization	NOUN
iajs-1071	301	7	.	.	PUNCT
iajs-1071	302	1	first	first	ADV
iajs-1071	302	2	,	,	PUNCT
iajs-1071	302	3	we	we	PRON
iajs-1071	302	4	give	give	VERB
iajs-1071	302	5	the	the	DET
iajs-1071	302	6	following	follow	VERB
iajs-1071	302	7	lemma	lemma	PROPN
iajs-1071	302	8	,	,	PUNCT
iajs-1071	302	9	which	which	PRON
iajs-1071	302	10	is	be	AUX
iajs-1071	302	11	needed	need	VERB
iajs-1071	302	12	in	in	ADP
iajs-1071	302	13	the	the	DET
iajs-1071	302	14	next	next	ADJ
iajs-1071	302	15	our	our	PRON
iajs-1071	302	16	proposition	proposition	NOUN
iajs-1071	302	17	.	.	PUNCT
iajs-1071	303	1	lemma	lemma	PROPN
iajs-1071	303	2	3.1	3.1	NUM
iajs-1071	303	3	:	:	PUNCT
iajs-1071	303	4	let	let	VERB
iajs-1071	303	5	x	x	PRON
iajs-1071	303	6	be	be	AUX
iajs-1071	303	7	f(m	f(m	PROPN
iajs-1071	303	8	)	)	PUNCT
iajs-1071	303	9	,	,	PUNCT
iajs-1071	303	10	m	m	NOUN
iajs-1071	303	11	=	=	PROPN
iajs-1071	303	12	m1	m1	PROPN
iajs-1071	303	13	m2	m2	PROPN
iajs-1071	303	14	where	where	SCONJ
iajs-1071	303	15	m1	m1	PROPN
iajs-1071	303	16	,	,	PUNCT
iajs-1071	303	17	m2	m2	PROPN
iajs-1071	303	18	are	be	AUX
iajs-1071	303	19	submodules	submodule	NOUN
iajs-1071	303	20	of	of	ADP
iajs-1071	303	21	m	m	PRON
iajs-1071	303	22	,	,	PUNCT
iajs-1071	303	23	if	if	SCONJ
iajs-1071	303	24	x	x	NOUN
iajs-1071	303	25	=	=	NOUN
iajs-1071	303	26	a1	a1	NOUN
iajs-1071	303	27	a2	a2	NOUN
iajs-1071	303	28	,	,	PUNCT
iajs-1071	303	29	where	where	SCONJ
iajs-1071	303	30	a1	a1	NOUN
iajs-1071	303	31	,	,	PUNCT
iajs-1071	303	32	a2	a2	PROPN
iajs-1071	303	33	are	be	AUX
iajs-1071	303	34	fuzzy	fuzzy	ADJ
iajs-1071	303	35	submodules	submodule	NOUN
iajs-1071	303	36	of	of	ADP
iajs-1071	303	37	x	x	X
iajs-1071	303	38	,	,	PUNCT
iajs-1071	303	39	then	then	ADV
iajs-1071	303	40	f	f	X
iajs-1071	303	41	-	-	PUNCT
iajs-1071	303	42	annxi	annxi	NOUN
iajs-1071	303	43	=	=	SYM
iajs-1071	303	44	f	f	NOUN
iajs-1071	303	45	-	-	PUNCT
iajs-1071	303	46	anna1i	anna1i	VERB
iajs-1071	303	47	f	f	PROPN
iajs-1071	303	48	-	-	PUNCT
iajs-1071	303	49	anna2i	anna2i	NOUN
iajs-1071	303	50	where	where	SCONJ
iajs-1071	303	51	i	i	PRON
iajs-1071	303	52	is	be	AUX
iajs-1071	303	53	a	a	DET
iajs-1071	303	54	fuzzy	fuzzy	ADJ
iajs-1071	303	55	ideal	ideal	NOUN
iajs-1071	303	56	of	of	ADP
iajs-1071	303	57	r.	r.	PROPN
iajs-1071	303	58	proof	proof	NOUN
iajs-1071	303	59	:	:	PUNCT
iajs-1071	303	60	we	we	PRON
iajs-1071	303	61	must	must	AUX
iajs-1071	303	62	prove	prove	VERB
iajs-1071	303	63	that	that	SCONJ
iajs-1071	303	64	f	f	NOUN
iajs-1071	303	65	-	-	PUNCT
iajs-1071	303	66	annxi	annxi	NOUN
iajs-1071	303	67	f	f	NOUN
iajs-1071	303	68	-	-	PUNCT
iajs-1071	303	69	anna1i	anna1i	VERB
iajs-1071	303	70	f	f	PROPN
iajs-1071	303	71	-	-	PUNCT
iajs-1071	303	72	anna2i	anna2i	NOUN
iajs-1071	303	73	let	let	VERB
iajs-1071	303	74	xt	xt	VERB
iajs-1071	303	75	f	f	X
iajs-1071	303	76	-	-	PUNCT
iajs-1071	303	77	annxi	annxi	NOUN
iajs-1071	303	78	,	,	PUNCT
iajs-1071	303	79	then	then	ADV
iajs-1071	303	80	ixt=01	ixt=01	PROPN
iajs-1071	303	81	and	and	CCONJ
iajs-1071	303	82	xt	xt	ADP
iajs-1071	303	83	x	x	PROPN
iajs-1071	303	84	,	,	PUNCT
iajs-1071	303	85	t	t	PROPN
iajs-1071	303	86	since	since	SCONJ
iajs-1071	303	87	xt	xt	PROPN
iajs-1071	304	1	x	x	SYM
iajs-1071	304	2	x	x	X
iajs-1071	304	3	xt	xt	X
iajs-1071	304	4	=	=	ADJ
iajs-1071	304	5	m=	m=	VERB
iajs-1071	304	6	m1	m1	PROPN
iajs-1071	304	7	m2	m2	PROPN
iajs-1071	304	8	.	.	PUNCT
iajs-1071	305	1	then	then	ADV
iajs-1071	305	2	x	x	X
iajs-1071	305	3	=	=	NOUN
iajs-1071	305	4	x1+x2	x1+x2	PROPN
iajs-1071	305	5	for	for	ADP
iajs-1071	305	6	some	some	DET
iajs-1071	305	7	x1	x1	PROPN
iajs-1071	305	8	m1	m1	NOUN
iajs-1071	305	9	,	,	PUNCT
iajs-1071	305	10	x2	x2	PROPN
iajs-1071	305	11	m2	m2	PROPN
iajs-1071	305	12	define	define	VERB
iajs-1071	305	13	i	i	PRON
iajs-1071	305	14	:	:	PUNCT
iajs-1071	305	15	j	j	PROPN
iajs-1071	306	1	[	[	X
iajs-1071	306	2	0,1	0,1	NUM
iajs-1071	306	3	]	]	PUNCT
iajs-1071	306	4	by	by	ADP
iajs-1071	306	5	i(x	i(x	PROPN
iajs-1071	306	6	)	)	PUNCT
iajs-1071	306	7	=	=	NOUN
iajs-1071	306	8	{	{	PUNCT
iajs-1071	306	9	,	,	PUNCT
iajs-1071	306	10	t	t	PROPN
iajs-1071	306	11	(	(	PUNCT
iajs-1071	306	12	0,1	0,1	NOUN
iajs-1071	306	13	]	]	PUNCT
iajs-1071	306	14	.	.	PUNCT
iajs-1071	307	1	be	be	AUX
iajs-1071	307	2	a	a	DET
iajs-1071	307	3	fuzzy	fuzzy	ADJ
iajs-1071	307	4	ideal	ideal	NOUN
iajs-1071	307	5	of	of	ADP
iajs-1071	307	6	r.	r.	PROPN
iajs-1071	307	7	it	it	PRON
iajs-1071	307	8	is	be	AUX
iajs-1071	307	9	clear	clear	ADJ
iajs-1071	307	10	tat	tat	ADJ
iajs-1071	307	11	it	it	PRON
iajs-1071	308	1	=	=	PUNCT
iajs-1071	308	2	j	j	PROPN
iajs-1071	308	3	then	then	ADV
iajs-1071	308	4	j.x	j.x	PROPN
iajs-1071	308	5	=	=	NOUN
iajs-1071	308	6	j(x1+x2)=0	j(x1+x2)=0	NOUN
iajs-1071	308	7	(	(	PUNCT
iajs-1071	308	8	since	since	SCONJ
iajs-1071	308	9	+	+	X
iajs-1071	308	10	on	on	ADP
iajs-1071	308	11	m	m	PROPN
iajs-1071	308	12	is	be	AUX
iajs-1071	308	13	a	a	DET
iajs-1071	308	14	direct	direct	ADJ
iajs-1071	308	15	sum	sum	NOUN
iajs-1071	308	16	)	)	PUNCT
iajs-1071	308	17	it	it	PRON
iajs-1071	308	18	follows	follow	VERB
iajs-1071	308	19	that	that	SCONJ
iajs-1071	308	20	:	:	PUNCT
iajs-1071	308	21	jx1	jx1	NOUN
iajs-1071	308	22	=	=	SYM
iajs-1071	308	23	jx2=0	jx2=0	PROPN
iajs-1071	308	24	.	.	PUNCT
iajs-1071	309	1	(	(	PUNCT
iajs-1071	309	2	jx1)t=(jx2)t=0	jx1)t=(jx2)t=0	PUNCT
iajs-1071	309	3	t	t	X
iajs-1071	309	4	≤	≤	NUM
iajs-1071	309	5	01	01	NUM
iajs-1071	309	6	t	t	NOUN
iajs-1071	309	7	(	(	PUNCT
iajs-1071	309	8	0,1	0,1	NOUN
iajs-1071	309	9	]	]	PUNCT
iajs-1071	309	10	.	.	PUNCT
iajs-1071	310	1	it(x1)t	it(x1)t	PROPN
iajs-1071	311	1	=	=	SYM
iajs-1071	311	2	it(x2)t=0	it(x2)t=0	PROPN
iajs-1071	311	3	t	t	X
iajs-1071	311	4	(	(	PUNCT
iajs-1071	311	5	since	since	SCONJ
iajs-1071	311	6	j	j	PROPN
iajs-1071	311	7	=	=	PROPN
iajs-1071	311	8	it	it	PRON
iajs-1071	311	9	)	)	PUNCT
iajs-1071	311	10	.	.	PUNCT
iajs-1071	312	1	i(x1)t	i(x1)t	PROPN
iajs-1071	312	2	=	=	SYM
iajs-1071	312	3	i(x2)t=0	i(x2)t=0	PROPN
iajs-1071	312	4	t.	t.	NOUN
iajs-1071	312	5	thus	thus	ADV
iajs-1071	312	6	(	(	PUNCT
iajs-1071	312	7	x1)t	x1)t	NOUN
iajs-1071	312	8	f	f	PROPN
iajs-1071	312	9	-	-	PUNCT
iajs-1071	312	10	anna1i	anna1i	VERB
iajs-1071	312	11	and	and	CCONJ
iajs-1071	312	12	(	(	PUNCT
iajs-1071	312	13	x2)t	x2)t	PROPN
iajs-1071	312	14	f	f	PROPN
iajs-1071	312	15	-	-	PUNCT
iajs-1071	312	16	anna2i	anna2i	PROPN
iajs-1071	312	17	.	.	PUNCT
iajs-1071	312	18	.	.	PUNCT
iajs-1071	313	1	therefore	therefore	ADV
iajs-1071	313	2	xt=(x1)t+(x2)t	xt=(x1)t+(x2)t	PROPN
iajs-1071	313	3	f	f	X
iajs-1071	313	4	-	-	PUNCT
iajs-1071	313	5	anna1i	anna1i	VERB
iajs-1071	313	6	f	f	PROPN
iajs-1071	313	7	-	-	PUNCT
iajs-1071	313	8	anna2i	anna2i	NOUN
iajs-1071	313	9	.	.	PUNCT
iajs-1071	314	1	conversely	conversely	ADV
iajs-1071	314	2	:	:	PUNCT
iajs-1071	314	3	let	let	VERB
iajs-1071	314	4	xt	xt	X
iajs-1071	314	5	f	f	VERB
iajs-1071	314	6	-	-	PUNCT
iajs-1071	314	7	anna1i	anna1i	VERB
iajs-1071	314	8	f	f	PROPN
iajs-1071	314	9	-	-	PUNCT
iajs-1071	314	10	anna2i	anna2i	PROPN
iajs-1071	314	11	then	then	ADV
iajs-1071	314	12	xt	xt	PROPN
iajs-1071	315	1	(	(	PUNCT
iajs-1071	315	2	(	(	PUNCT
iajs-1071	315	3	x1	x1	INTJ
iajs-1071	315	4	,	,	PUNCT
iajs-1071	315	5	(	(	PUNCT
iajs-1071	315	6	x2)s	x2)s	ADV
iajs-1071	315	7	)	)	PUNCT
iajs-1071	315	8	where	where	SCONJ
iajs-1071	315	9	(	(	PUNCT
iajs-1071	315	10	x1	x1	PROPN
iajs-1071	315	11	f	f	NOUN
iajs-1071	315	12	-	-	PUNCT
iajs-1071	315	13	anna1i	anna1i	VERB
iajs-1071	315	14	and	and	CCONJ
iajs-1071	315	15	(	(	PUNCT
iajs-1071	315	16	x2)s	x2)s	ADJ
iajs-1071	315	17	f	f	X
iajs-1071	315	18	-	-	PUNCT
iajs-1071	315	19	anna2i	anna2i	PROPN
iajs-1071	315	20	(	(	PUNCT
iajs-1071	315	21	0,1	0,1	NOUN
iajs-1071	315	22	]	]	PUNCT
iajs-1071	315	23	.	.	PUNCT
iajs-1071	316	1	thus	thus	ADV
iajs-1071	316	2	i(x1	i(x1	ADJ
iajs-1071	316	3	=	=	SYM
iajs-1071	316	4	01	01	NUM
iajs-1071	316	5	and	and	CCONJ
iajs-1071	316	6	i(x2)s=01	i(x2)s=01	NOUN
iajs-1071	316	7	.	.	PUNCT
iajs-1071	317	1	therefore	therefore	ADV
iajs-1071	317	2	i(x1	i(x1	PROPN
iajs-1071	317	3	+	+	X
iajs-1071	317	4	i(x2)s=01	i(x2)s=01	NOUN
iajs-1071	317	5	,	,	PUNCT
iajs-1071	317	6	and	and	CCONJ
iajs-1071	317	7	hence	hence	ADV
iajs-1071	317	8	i((x1	i((x1	ADJ
iajs-1071	317	9	+	+	CCONJ
iajs-1071	317	10	(	(	PUNCT
iajs-1071	317	11	x2)s)=01	x2)s)=01	INTJ
iajs-1071	317	12	then	then	ADV
iajs-1071	318	1	[	[	X
iajs-1071	318	2	j(x1+x2	j(x1+x2	NOUN
iajs-1071	318	3	)	)	PUNCT
iajs-1071	318	4	=	=	SYM
iajs-1071	318	5	≤	≤	NUM
iajs-1071	318	6	01	01	NUM
iajs-1071	318	7	where	where	SCONJ
iajs-1071	318	8	=	=	PRON
iajs-1071	318	9	min	min	X
iajs-1071	318	10	{	{	PUNCT
iajs-1071	318	11	t	t	PROPN
iajs-1071	318	12	,	,	PUNCT
iajs-1071	318	13	s	s	PART
iajs-1071	318	14	,	,	PUNCT
iajs-1071	318	15	}	}	PUNCT
iajs-1071	318	16	implies	imply	VERB
iajs-1071	318	17	,	,	PUNCT
iajs-1071	318	18	j(x1+x2)=0	j(x1+x2)=0	NOUN
iajs-1071	318	19	therefore	therefore	ADV
iajs-1071	318	20	jx=0	jx=0	PROPN
iajs-1071	318	21	and	and	CCONJ
iajs-1071	318	22	hence	hence	ADV
iajs-1071	318	23	i(xt)=01	i(xt)=01	VERB
iajs-1071	318	24	mathematics	mathematic	NOUN
iajs-1071	318	25	|	|	ADV
iajs-1071	318	26	205	205	NUM
iajs-1071	318	27	2012	2012	NUM
iajs-1071	318	28	(	(	PUNCT
iajs-1071	318	29	عام	عام	PROPN
iajs-1071	318	30	1	1	NUM
iajs-1071	318	31	)	)	PUNCT
iajs-1071	318	32	(	(	PUNCT
iajs-1071	318	33	العدد	العدد	PROPN
iajs-1071	318	34	30مجلة	30مجلة	NUM
iajs-1071	318	35	إبن	إبن	VERB
iajs-1071	318	36	الهيثم	الهيثم	ADJ
iajs-1071	318	37	للعلوم	للعلوم	NOUN
iajs-1071	318	38	الصرفة	الصرفة	NOUN
iajs-1071	319	1	و	و	PRON
iajs-1071	319	2	التطبيقية	التطبيقية	ADV
iajs-1071	319	3	المجلد	المجلد	ADV
iajs-1071	319	4	)	)	PUNCT
iajs-1071	320	1	ibn	ibn	PROPN
iajs-1071	320	2	al	al	PROPN
iajs-1071	320	3	-	-	PUNCT
iajs-1071	320	4	haitham	haitham	PROPN
iajs-1071	320	5	j.	j.	PROPN
iajs-1071	320	6	for	for	ADP
iajs-1071	320	7	pure	pure	PROPN
iajs-1071	320	8	&	&	CCONJ
iajs-1071	320	9	appl	appl	PROPN
iajs-1071	320	10	.	.	PUNCT
iajs-1071	321	1	sci	sci	PROPN
iajs-1071	321	2	.	.	PUNCT
iajs-1071	322	1	vol.30	vol.30	NOUN
iajs-1071	322	2	(	(	PUNCT
iajs-1071	322	3	1	1	NUM
iajs-1071	322	4	)	)	PUNCT
iajs-1071	322	5	2017	2017	NUM
iajs-1071	322	6	hence	hence	ADV
iajs-1071	322	7	xt	xt	PUNCT
iajs-1071	323	1	f	f	X
iajs-1071	323	2	-	-	PUNCT
iajs-1071	323	3	annxi	annxi	NOUN
iajs-1071	323	4	.therefore	.therefore	ADP
iajs-1071	324	1	f	f	X
iajs-1071	324	2	-	-	PUNCT
iajs-1071	324	3	annxi=	annxi=	PRON
iajs-1071	324	4	f	f	NOUN
iajs-1071	324	5	-	-	PUNCT
iajs-1071	324	6	anna1i	anna1i	VERB
iajs-1071	324	7	f	f	PROPN
iajs-1071	324	8	-	-	PUNCT
iajs-1071	324	9	anna2i	anna2i	NOUN
iajs-1071	324	10	proposition	proposition	NOUN
iajs-1071	324	11	3.2	3.2	NUM
iajs-1071	324	12	:	:	PUNCT
iajs-1071	324	13	let	let	VERB
iajs-1071	324	14	x	x	PRON
iajs-1071	324	15	be	be	AUX
iajs-1071	324	16	f(m	f(m	PROPN
iajs-1071	324	17	)	)	PUNCT
iajs-1071	324	18	and	and	CCONJ
iajs-1071	324	19	let	let	VERB
iajs-1071	324	20	x=	x=	PROPN
iajs-1071	324	21	a1	a1	PROPN
iajs-1071	324	22	a2	a2	PROPN
iajs-1071	324	23	,	,	PUNCT
iajs-1071	324	24	where	where	SCONJ
iajs-1071	324	25	a1	a1	NOUN
iajs-1071	324	26	and	and	CCONJ
iajs-1071	324	27	a2	a2	PROPN
iajs-1071	324	28	be	be	VERB
iajs-1071	324	29	two	two	NUM
iajs-1071	324	30	fuzzy	fuzzy	ADJ
iajs-1071	324	31	submodules	submodule	NOUN
iajs-1071	324	32	of	of	ADP
iajs-1071	324	33	x.	x.	NOUN
iajs-1071	324	34	such	such	ADJ
iajs-1071	324	35	that	that	SCONJ
iajs-1071	324	36	f	f	NOUN
iajs-1071	324	37	-	-	PUNCT
iajs-1071	324	38	anna1i	anna1i	VERB
iajs-1071	324	39	f	f	NOUN
iajs-1071	324	40	-	-	PUNCT
iajs-1071	324	41	anna2i=	anna2i=	VERB
iajs-1071	324	42	r	r	NOUN
iajs-1071	324	43	where	where	SCONJ
iajs-1071	324	44	r(x)=1	r(x)=1	NOUN
iajs-1071	324	45	;	;	PUNCT
iajs-1071	324	46	x	x	SYM
iajs-1071	324	47	r.	r.	PROPN
iajs-1071	324	48	then	then	ADV
iajs-1071	324	49	a1	a1	PROPN
iajs-1071	324	50	and	and	CCONJ
iajs-1071	324	51	a2	a2	PROPN
iajs-1071	324	52	are	be	AUX
iajs-1071	324	53	q	q	ADJ
iajs-1071	324	54	-	-	PUNCT
iajs-1071	324	55	fcf(m	fcf(m	NOUN
iajs-1071	324	56	)	)	PUNCT
iajs-1071	324	57	.	.	PUNCT
iajs-1071	325	1	proof	proof	NOUN
iajs-1071	325	2	:	:	PUNCT
iajs-1071	325	3	(	(	PUNCT
iajs-1071	325	4	)	)	PUNCT
iajs-1071	325	5	let	let	VERB
iajs-1071	325	6	i	i	PRON
iajs-1071	325	7	be	be	AUX
iajs-1071	325	8	a	a	DET
iajs-1071	325	9	non	non	ADJ
iajs-1071	325	10	-	-	ADJ
iajs-1071	325	11	empty	empty	ADJ
iajs-1071	325	12	fuzzy	fuzzy	ADJ
iajs-1071	325	13	ideal	ideal	NOUN
iajs-1071	325	14	of	of	ADP
iajs-1071	325	15	r	r	NOUN
iajs-1071	325	16	and	and	CCONJ
iajs-1071	325	17	let	let	VERB
iajs-1071	325	18	a	a	PRON
iajs-1071	325	19	and	and	CCONJ
iajs-1071	325	20	b	b	NOUN
iajs-1071	325	21	are	be	AUX
iajs-1071	325	22	fuzzy	fuzzy	ADJ
iajs-1071	325	23	submodules	submodule	NOUN
iajs-1071	325	24	of	of	ADP
iajs-1071	325	25	x.	x.	NOUN
iajs-1071	325	26	suppose	suppose	VERB
iajs-1071	325	27	that	that	SCONJ
iajs-1071	325	28	ia	ia	PROPN
iajs-1071	325	29	=	=	NOUN
iajs-1071	325	30	ib	ib	X
iajs-1071	325	31	we	we	PRON
iajs-1071	325	32	show	show	VERB
iajs-1071	325	33	that	that	SCONJ
iajs-1071	325	34	a+(f	a+(f	NOUN
iajs-1071	325	35	-	-	PUNCT
iajs-1071	325	36	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	325	37	-	-	PUNCT
iajs-1071	325	38	annxi	annxi	NOUN
iajs-1071	325	39	)	)	PUNCT
iajs-1071	325	40	since	since	SCONJ
iajs-1071	325	41	(	(	PUNCT
iajs-1071	325	42	f	f	X
iajs-1071	325	43	-	-	PUNCT
iajs-1071	325	44	anna1)+	anna1)+	ADJ
iajs-1071	325	45	(	(	PUNCT
iajs-1071	325	46	f	f	X
iajs-1071	325	47	-	-	PUNCT
iajs-1071	325	48	anna2)=	anna2)=	NOUN
iajs-1071	325	49	r	r	NOUN
iajs-1071	325	50	,	,	PUNCT
iajs-1071	325	51	then	then	ADV
iajs-1071	325	52	by	by	ADP
iajs-1071	325	53	[	[	X
iajs-1071	325	54	4,lemma	4,lemma	X
iajs-1071	325	55	(	(	PUNCT
iajs-1071	325	56	1.5.5	1.5.5	NUM
iajs-1071	325	57	)	)	PUNCT
iajs-1071	325	58	]	]	PUNCT
iajs-1071	325	59	we	we	PRON
iajs-1071	325	60	get	get	VERB
iajs-1071	325	61	,	,	PUNCT
iajs-1071	325	62	a=	a=	ADV
iajs-1071	325	63	a1	a1	NOUN
iajs-1071	325	64	a2	a2	PROPN
iajs-1071	325	65	and	and	CCONJ
iajs-1071	325	66	b=	b=	NOUN
iajs-1071	325	67	b1	b1	NOUN
iajs-1071	325	68	b2	b2	NOUN
iajs-1071	325	69	for	for	ADP
iajs-1071	325	70	some	some	DET
iajs-1071	325	71	fuzzy	fuzzy	ADJ
iajs-1071	325	72	submodules	submodule	NOUN
iajs-1071	325	73	a1	a1	NOUN
iajs-1071	325	74	,	,	PUNCT
iajs-1071	325	75	a2	a2	PROPN
iajs-1071	325	76	of	of	ADP
iajs-1071	325	77	a	a	PRON
iajs-1071	325	78	and	and	CCONJ
iajs-1071	325	79	for	for	ADP
iajs-1071	325	80	some	some	DET
iajs-1071	325	81	fuzzy	fuzzy	ADJ
iajs-1071	325	82	submodules	submodule	NOUN
iajs-1071	325	83	b1	b1	NOUN
iajs-1071	325	84	,	,	PUNCT
iajs-1071	325	85	b2	b2	NOUN
iajs-1071	325	86	of	of	ADP
iajs-1071	325	87	b.	b.	PROPN
iajs-1071	325	88	now	now	ADV
iajs-1071	325	89	,	,	PUNCT
iajs-1071	325	90	i	i	PRON
iajs-1071	325	91	(	(	PUNCT
iajs-1071	325	92	a1	a1	NOUN
iajs-1071	325	93	a2	a2	PROPN
iajs-1071	325	94	)	)	PUNCT
iajs-1071	326	1	=	=	NOUN
iajs-1071	326	2	i	i	PROPN
iajs-1071	326	3	(	(	PUNCT
iajs-1071	326	4	b1	b1	NOUN
iajs-1071	326	5	b2	b2	NOUN
iajs-1071	326	6	)	)	PUNCT
iajs-1071	326	7	.	.	PUNCT
iajs-1071	327	1	hence	hence	ADV
iajs-1071	327	2	(	(	PUNCT
iajs-1071	327	3	ia1	ia1	NOUN
iajs-1071	327	4	,	,	PUNCT
iajs-1071	327	5	ia2)=(ib1	ia2)=(ib1	NOUN
iajs-1071	327	6	,	,	PUNCT
iajs-1071	327	7	ib2	ib2	NOUN
iajs-1071	327	8	)	)	PUNCT
iajs-1071	327	9	.	.	PUNCT
iajs-1071	328	1	[	[	PUNCT
iajs-1071	328	2	7	7	NUM
iajs-1071	328	3	,	,	PUNCT
iajs-1071	328	4	proposition	proposition	NOUN
iajs-1071	328	5	(	(	PUNCT
iajs-1071	328	6	3.2.4	3.2.4	NUM
iajs-1071	328	7	)	)	PUNCT
iajs-1071	328	8	]	]	PUNCT
iajs-1071	328	9	which	which	PRON
iajs-1071	328	10	implies	imply	VERB
iajs-1071	328	11	that	that	SCONJ
iajs-1071	328	12	,	,	PUNCT
iajs-1071	328	13	ia1	ia1	PROPN
iajs-1071	328	14	=	=	NOUN
iajs-1071	328	15	ib1	ib1	NOUN
iajs-1071	328	16	and	and	CCONJ
iajs-1071	328	17	ia2	ia2	NOUN
iajs-1071	328	18	=	=	NOUN
iajs-1071	328	19	ib2	ib2	NOUN
iajs-1071	328	20	but	but	CCONJ
iajs-1071	328	21	a1	a1	NOUN
iajs-1071	328	22	and	and	CCONJ
iajs-1071	328	23	a2	a2	PROPN
iajs-1071	328	24	are	be	AUX
iajs-1071	328	25	q	q	ADJ
iajs-1071	328	26	-	-	PUNCT
iajs-1071	328	27	fcf(m	fcf(m	NOUN
iajs-1071	328	28	)	)	PUNCT
iajs-1071	328	29	.	.	PUNCT
iajs-1071	329	1	thus	thus	ADV
iajs-1071	329	2	a1+(f	a1+(f	PROPN
iajs-1071	329	3	-	-	PUNCT
iajs-1071	329	4	anna1i)=b1+(f	anna1i)=b1+(f	NOUN
iajs-1071	329	5	-	-	PUNCT
iajs-1071	329	6	anna1i	anna1i	VERB
iajs-1071	329	7	)	)	PUNCT
iajs-1071	329	8	and	and	CCONJ
iajs-1071	329	9	a2+(f	a2+(f	PROPN
iajs-1071	329	10	-	-	PUNCT
iajs-1071	329	11	anna2i)=b2+(f	anna2i)=b2+(f	NOUN
iajs-1071	329	12	-	-	PUNCT
iajs-1071	329	13	anna2i	anna2i	NOUN
iajs-1071	329	14	)	)	PUNCT
iajs-1071	330	1	it	it	PRON
iajs-1071	330	2	follows	follow	VERB
iajs-1071	330	3	that	that	SCONJ
iajs-1071	330	4	,	,	PUNCT
iajs-1071	330	5	a1+a2+(f	a1+a2+(f	ADJ
iajs-1071	330	6	-	-	ADJ
iajs-1071	330	7	anna1i)+(f	anna1i)+(f	ADJ
iajs-1071	330	8	-	-	PUNCT
iajs-1071	330	9	anna2i)=	anna2i)=	PROPN
iajs-1071	330	10	b1+b2+(f	b1+b2+(f	PROPN
iajs-1071	330	11	-	-	PUNCT
iajs-1071	330	12	anna1i)+(fanna2i	anna1i)+(fanna2i	NOUN
iajs-1071	330	13	)	)	PUNCT
iajs-1071	330	14	then	then	ADV
iajs-1071	330	15	we	we	PRON
iajs-1071	330	16	have	have	VERB
iajs-1071	330	17	:	:	PUNCT
iajs-1071	330	18	a+(f	a+(f	NOUN
iajs-1071	330	19	-	-	PUNCT
iajs-1071	330	20	annxi)=b+(f	annxi)=b+(f	NOUN
iajs-1071	330	21	-	-	PUNCT
iajs-1071	330	22	annxi	annxi	NOUN
iajs-1071	330	23	)	)	PUNCT
iajs-1071	331	1	therefore	therefore	ADV
iajs-1071	331	2	x	x	X
iajs-1071	331	3	is	be	AUX
iajs-1071	331	4	q	q	NOUN
iajs-1071	331	5	-	-	PUNCT
iajs-1071	331	6	fcf(m	fcf(m	NOUN
iajs-1071	331	7	)	)	PUNCT
iajs-1071	331	8	.	.	PUNCT
iajs-1071	332	1	(	(	PUNCT
iajs-1071	332	2	)	)	PUNCT
iajs-1071	332	3	it	it	PRON
iajs-1071	332	4	is	be	AUX
iajs-1071	332	5	clear	clear	ADJ
iajs-1071	332	6	by	by	ADP
iajs-1071	332	7	used	used	ADJ
iajs-1071	332	8	remarks	remark	NOUN
iajs-1071	332	9	and	and	CCONJ
iajs-1071	332	10	examples	example	NOUN
iajs-1071	332	11	(	(	PUNCT
iajs-1071	332	12	(	(	PUNCT
iajs-1071	332	13	1.3	1.3	NUM
iajs-1071	332	14	)	)	PUNCT
iajs-1071	332	15	(	(	PUNCT
iajs-1071	332	16	4	4	NUM
iajs-1071	332	17	)	)	PUNCT
iajs-1071	332	18	)	)	PUNCT
iajs-1071	332	19	.	.	PUNCT
iajs-1071	333	1	we	we	PRON
iajs-1071	333	2	end	end	VERB
iajs-1071	333	3	this	this	DET
iajs-1071	333	4	section	section	NOUN
iajs-1071	333	5	by	by	ADP
iajs-1071	333	6	the	the	DET
iajs-1071	333	7	following	follow	VERB
iajs-1071	333	8	result	result	NOUN
iajs-1071	333	9	.	.	PUNCT
iajs-1071	334	1	proposition	proposition	NOUN
iajs-1071	334	2	3.3	3.3	NUM
iajs-1071	334	3	:	:	PUNCT
iajs-1071	334	4	let	let	VERB
iajs-1071	334	5	x	x	PRON
iajs-1071	334	6	be	be	AUX
iajs-1071	334	7	f(m	f(m	PROPN
iajs-1071	334	8	)	)	PUNCT
iajs-1071	334	9	and	and	CCONJ
iajs-1071	334	10	let	let	VERB
iajs-1071	334	11	x=	x=	PROPN
iajs-1071	334	12	a1	a1	PROPN
iajs-1071	334	13	a2	a2	PROPN
iajs-1071	334	14	where	where	SCONJ
iajs-1071	334	15	a1	a1	NOUN
iajs-1071	334	16	and	and	CCONJ
iajs-1071	334	17	a2	a2	PROPN
iajs-1071	334	18	are	be	AUX
iajs-1071	334	19	two	two	NUM
iajs-1071	334	20	fuzzy	fuzzy	ADJ
iajs-1071	334	21	submodules	submodule	NOUN
iajs-1071	334	22	of	of	ADP
iajs-1071	334	23	x	x	NOUN
iajs-1071	334	24	,	,	PUNCT
iajs-1071	334	25	such	such	ADJ
iajs-1071	334	26	that	that	SCONJ
iajs-1071	334	27	f	f	PROPN
iajs-1071	334	28	-	-	PUNCT
iajs-1071	334	29	anna1	anna1	ADJ
iajs-1071	334	30	+	+	CCONJ
iajs-1071	334	31	f	f	ADJ
iajs-1071	334	32	-	-	PUNCT
iajs-1071	334	33	anna2=	anna2=	NOUN
iajs-1071	334	34	r	r	NOUN
iajs-1071	334	35	where	where	SCONJ
iajs-1071	334	36	r(x)=1	r(x)=1	NOUN
iajs-1071	334	37	,	,	PUNCT
iajs-1071	334	38	x	x	PROPN
iajs-1071	334	39	r.	r.	PROPN
iajs-1071	334	40	then	then	ADV
iajs-1071	334	41	a1	a1	PROPN
iajs-1071	334	42	and	and	CCONJ
iajs-1071	334	43	a2	a2	PROPN
iajs-1071	334	44	are	be	AUX
iajs-1071	334	45	q	q	NOUN
iajs-1071	334	46	-	-	PUNCT
iajs-1071	334	47	mfcf(m)if	mfcf(m)if	NOUN
iajs-1071	334	48	and	and	CCONJ
iajs-1071	334	49	only	only	ADV
iajs-1071	334	50	if	if	SCONJ
iajs-1071	334	51	x	x	PRON
iajs-1071	334	52	is	be	AUX
iajs-1071	334	53	q	q	NOUN
iajs-1071	334	54	-	-	PUNCT
iajs-1071	334	55	mfcf(m	mfcf(m	NOUN
iajs-1071	334	56	)	)	PUNCT
iajs-1071	334	57	.	.	PUNCT
iajs-1071	335	1	proof	proof	NOUN
iajs-1071	335	2	:	:	PUNCT
iajs-1071	335	3	first	first	ADJ
iajs-1071	335	4	side	side	NOUN
iajs-1071	335	5	,	,	PUNCT
iajs-1071	335	6	let	let	VERB
iajs-1071	335	7	a	a	PRON
iajs-1071	335	8	and	and	CCONJ
iajs-1071	335	9	b	b	NOUN
iajs-1071	335	10	be	be	AUX
iajs-1071	335	11	two	two	NUM
iajs-1071	335	12	fuzzy	fuzzy	ADJ
iajs-1071	335	13	submodules	submodule	NOUN
iajs-1071	335	14	of	of	ADP
iajs-1071	335	15	x	x	PUNCT
iajs-1071	335	16	and	and	CCONJ
iajs-1071	335	17	let	let	VERB
iajs-1071	335	18	i	i	PRON
iajs-1071	335	19	be	be	AUX
iajs-1071	335	20	a	a	DET
iajs-1071	335	21	maximal	maximal	ADJ
iajs-1071	335	22	fuzzy	fuzzy	ADJ
iajs-1071	335	23	ideal	ideal	NOUN
iajs-1071	335	24	of	of	ADP
iajs-1071	335	25	r.	r.	PROPN
iajs-1071	335	26	since	since	SCONJ
iajs-1071	335	27	f	f	PROPN
iajs-1071	335	28	-	-	PUNCT
iajs-1071	335	29	anna1+f	anna1+f	NOUN
iajs-1071	335	30	-	-	PUNCT
iajs-1071	335	31	anna2=	anna2=	NOUN
iajs-1071	335	32	r	r	NOUN
iajs-1071	335	33	,	,	PUNCT
iajs-1071	335	34	where	where	SCONJ
iajs-1071	335	35	r(x)=1	r(x)=1	NOUN
iajs-1071	335	36	,	,	PUNCT
iajs-1071	335	37	x	x	SYM
iajs-1071	335	38	r.then	r.then	ADV
iajs-1071	335	39	by[4	by[4	ADJ
iajs-1071	335	40	,	,	PUNCT
iajs-1071	335	41	lemma	lemma	PROPN
iajs-1071	335	42	(	(	PUNCT
iajs-1071	335	43	1.5.5	1.5.5	NUM
iajs-1071	335	44	)	)	PUNCT
iajs-1071	335	45	]	]	PUNCT
iajs-1071	335	46	we	we	PRON
iajs-1071	335	47	get	get	VERB
iajs-1071	335	48	,	,	PUNCT
iajs-1071	335	49	a=	a=	ADV
iajs-1071	335	50	a1	a1	NOUN
iajs-1071	335	51	a2	a2	PROPN
iajs-1071	335	52	and	and	CCONJ
iajs-1071	335	53	b=	b=	NOUN
iajs-1071	335	54	b1	b1	PROPN
iajs-1071	335	55	b2	b2	NOUN
iajs-1071	335	56	,	,	PUNCT
iajs-1071	335	57	and	and	CCONJ
iajs-1071	335	58	by	by	ADP
iajs-1071	335	59	similar	similar	ADJ
iajs-1071	335	60	procedure	procedure	NOUN
iajs-1071	335	61	as	as	ADP
iajs-1071	335	62	in	in	ADP
iajs-1071	335	63	the	the	DET
iajs-1071	335	64	proposition	proposition	NOUN
iajs-1071	335	65	(	(	PUNCT
iajs-1071	335	66	3.2	3.2	NUM
iajs-1071	335	67	)	)	PUNCT
iajs-1071	335	68	.	.	PUNCT
iajs-1071	336	1	the	the	DET
iajs-1071	336	2	required	require	VERB
iajs-1071	336	3	result	result	NOUN
iajs-1071	336	4	can	can	AUX
iajs-1071	336	5	be	be	AUX
iajs-1071	336	6	obtained	obtain	VERB
iajs-1071	336	7	.	.	PUNCT
iajs-1071	337	1	another	another	DET
iajs-1071	337	2	side	side	NOUN
iajs-1071	337	3	,	,	PUNCT
iajs-1071	337	4	it	it	PRON
iajs-1071	337	5	is	be	AUX
iajs-1071	337	6	clear	clear	ADJ
iajs-1071	337	7	by	by	ADP
iajs-1071	337	8	remarks	remark	NOUN
iajs-1071	337	9	and	and	CCONJ
iajs-1071	337	10	examples	example	NOUN
iajs-1071	337	11	(	(	PUNCT
iajs-1071	337	12	(	(	PUNCT
iajs-1071	337	13	2.3)(5	2.3)(5	NUM
iajs-1071	337	14	)	)	PUNCT
iajs-1071	337	15	)	)	PUNCT
iajs-1071	337	16	.	.	PUNCT
iajs-1071	338	1	mathematics	mathematic	NOUN
iajs-1071	338	2	|	|	ADV
iajs-1071	338	3	206	206	NUM
iajs-1071	338	4	2012	2012	NUM
iajs-1071	338	5	(	(	PUNCT
iajs-1071	338	6	عام	عام	PROPN
iajs-1071	338	7	1	1	NUM
iajs-1071	338	8	)	)	PUNCT
iajs-1071	338	9	(	(	PUNCT
iajs-1071	338	10	العدد	العدد	PROPN
iajs-1071	338	11	30مجلة	30مجلة	NUM
iajs-1071	338	12	إبن	إبن	VERB
iajs-1071	338	13	الهيثم	الهيثم	ADJ
iajs-1071	338	14	للعلوم	للعلوم	NOUN
iajs-1071	338	15	الصرفة	الصرفة	NOUN
iajs-1071	339	1	و	و	PRON
iajs-1071	339	2	التطبيقية	التطبيقية	ADV
iajs-1071	339	3	المجلد	المجلد	ADV
iajs-1071	339	4	)	)	PUNCT
iajs-1071	340	1	ibn	ibn	PROPN
iajs-1071	340	2	al	al	PROPN
iajs-1071	340	3	-	-	PUNCT
iajs-1071	340	4	haitham	haitham	PROPN
iajs-1071	340	5	j.	j.	PROPN
iajs-1071	340	6	for	for	ADP
iajs-1071	340	7	pure	pure	PROPN
iajs-1071	340	8	&	&	CCONJ
iajs-1071	340	9	appl	appl	PROPN
iajs-1071	340	10	.	.	PUNCT
iajs-1071	341	1	sci	sci	PROPN
iajs-1071	341	2	.	.	PUNCT
iajs-1071	342	1	vol.30	vol.30	NOUN
iajs-1071	342	2	(	(	PUNCT
iajs-1071	342	3	1	1	NUM
iajs-1071	342	4	)	)	PUNCT
iajs-1071	342	5	2017	2017	NUM
iajs-1071	342	6	references	reference	NOUN
iajs-1071	342	7	1	1	NUM
iajs-1071	342	8	.	.	PUNCT
iajs-1071	342	9	inaam	inaam	PROPN
iajs-1071	342	10	,	,	PUNCT
iajs-1071	342	11	m.a.hadi	m.a.hadi	PROPN
iajs-1071	342	12	,	,	PUNCT
iajs-1071	342	13	alaa	alaa	PROPN
iajs-1071	342	14	,	,	PUNCT
iajs-1071	342	15	a.elewi	a.elewi	ADP
iajs-1071	342	16	(	(	PUNCT
iajs-1071	342	17	2014)"quasi	2014)"quasi	NOUN
iajs-1071	342	18	-	-	PUNCT
iajs-1071	342	19	fully	fully	ADV
iajs-1071	342	20	cancellation	cancellation	NOUN
iajs-1071	342	21	module	module	NOUN
iajs-1071	342	22	"	"	PUNCT
iajs-1071	342	23	iraqi	iraqi	ADJ
iajs-1071	342	24	journal	journal	NOUN
iajs-1071	342	25	of	of	ADP
iajs-1071	342	26	science	science	NOUN
iajs-1071	342	27	(	(	PUNCT
iajs-1071	342	28	2014	2014	NUM
iajs-1071	342	29	)	)	PUNCT
iajs-1071	342	30	,	,	PUNCT
iajs-1071	342	31	vol55,no.3a	vol55,no.3a	VERB
iajs-1071	342	32	pp(1080	pp(1080	NOUN
iajs-1071	342	33	-	-	PUNCT
iajs-1071	342	34	1085	1085	NUM
iajs-1071	342	35	)	)	PUNCT
iajs-1071	342	36	.	.	PUNCT
iajs-1071	343	1	2	2	X
iajs-1071	343	2	.	.	X
iajs-1071	343	3	gada	gada	PROPN
iajs-1071	343	4	,	,	PUNCT
iajs-1071	343	5	a.a	a.a	PROPN
iajs-1071	343	6	.	.	PROPN
iajs-1071	343	7	,	,	PUNCT
iajs-1071	343	8	(	(	PUNCT
iajs-1071	343	9	2000),"fuzzy	2000),"fuzzy	NUM
iajs-1071	343	10	spectrum	spectrum	NOUN
iajs-1071	343	11	of	of	ADP
iajs-1071	343	12	a	a	DET
iajs-1071	343	13	modules	module	NOUN
iajs-1071	343	14	over	over	ADP
iajs-1071	343	15	commutative	commutative	ADJ
iajs-1071	343	16	ring",m.sc.thesis	ring",m.sc.thesis	NOUN
iajs-1071	343	17	,	,	PUNCT
iajs-1071	343	18	university	university	NOUN
iajs-1071	343	19	of	of	ADP
iajs-1071	343	20	baghdad	baghdad	PROPN
iajs-1071	343	21	.	.	PUNCT
iajs-1071	344	1	3	3	X
iajs-1071	344	2	.	.	X
iajs-1071	344	3	inaam	inaam	PROPN
iajs-1071	344	4	,	,	PUNCT
iajs-1071	344	5	m.a.hadi	m.a.hadi	PROPN
iajs-1071	344	6	,	,	PUNCT
iajs-1071	344	7	alaa	alaa	PROPN
iajs-1071	344	8	,	,	PUNCT
iajs-1071	344	9	a.	a.	PROPN
iajs-1071	344	10	elewi	elewi	PROPN
iajs-1071	344	11	(	(	PUNCT
iajs-1071	344	12	2014	2014	NUM
iajs-1071	344	13	)	)	PUNCT
iajs-1071	344	14	,	,	PUNCT
iajs-1071	344	15	“	"	PUNCT
iajs-1071	344	16	fully	fully	ADV
iajs-1071	344	17	cancellation	cancellation	NOUN
iajs-1071	344	18	and	and	CCONJ
iajs-1071	344	19	naturally	naturally	ADV
iajs-1071	344	20	cancellation	cancellation	NOUN
iajs-1071	344	21	module	module	NOUN
iajs-1071	344	22	”	"	PUNCT
iajs-1071	344	23	journal	journal	NOUN
iajs-1071	344	24	of	of	ADP
iajs-1071	344	25	al	al	PROPN
iajs-1071	344	26	-	-	PUNCT
iajs-1071	344	27	nahrain	nahrain	PROPN
iajs-1071	344	28	university	university	NOUN
iajs-1071	344	29	,	,	PUNCT
iajs-1071	344	30	vol	vol	NOUN
iajs-1071	344	31	.	.	PUNCT
iajs-1071	344	32	17(3).sep	17(3).sep	NUM
iajs-1071	344	33	,	,	PUNCT
iajs-1071	344	34	pp.178	pp.178	PROPN
iajs-1071	344	35	-	-	PUNCT
iajs-1071	344	36	184	184	NUM
iajs-1071	344	37	.	.	NOUN
iajs-1071	345	1	4	4	NUM
iajs-1071	345	2	.	.	NUM
iajs-1071	345	3	.hatam	.hatam	NOUN
iajs-1071	345	4	,	,	PUNCT
iajs-1071	345	5	y.khalaf	y.khalaf	PROPN
iajs-1071	345	6	.	.	PROPN
iajs-1071	345	7	,	,	PUNCT
iajs-1071	345	8	and	and	CCONJ
iajs-1071	345	9	hadi	hadi	PROPN
iajs-1071	345	10	,	,	PUNCT
iajs-1071	345	11	g.rashed(2016),"fully	g.rashed(2016),"fully	ADV
iajs-1071	345	12	and	and	CCONJ
iajs-1071	345	13	naturally	naturally	ADV
iajs-1071	345	14	cancellation	cancellation	VERB
iajs-1071	345	15	fuzzy	fuzzy	ADJ
iajs-1071	345	16	modules"international	modules"international	PROPN
iajs-1071	345	17	journal	journal	NOUN
iajs-1071	345	18	of	of	ADP
iajs-1071	345	19	applied	apply	VERB
iajs-1071	345	20	mathematics	mathematic	NOUN
iajs-1071	345	21	statistical	statistical	ADJ
iajs-1071	345	22	sciences	science	NOUN
iajs-1071	345	23	(	(	PUNCT
iajs-1071	345	24	ijamss):vol.(5).pp.2319	ijamss):vol.(5).pp.2319	PROPN
iajs-1071	345	25	-	-	PUNCT
iajs-1071	345	26	3980	3980	NUM
iajs-1071	345	27	.	.	PUNCT
iajs-1071	346	1	5	5	X
iajs-1071	346	2	.	.	X
iajs-1071	346	3	inaam	inaam	PROPN
iajs-1071	346	4	,	,	PUNCT
iajs-1071	346	5	m.a.hadi	m.a.hadi	NOUN
iajs-1071	346	6	,	,	PUNCT
iajs-1071	346	7	maysoun	maysoun	NOUN
iajs-1071	346	8	,	,	PUNCT
iajs-1071	346	9	a.	a.	PROPN
iajs-1071	346	10	hamil	hamil	PROPN
iajs-1071	346	11	.	.	PUNCT
iajs-1071	347	1	(	(	PUNCT
iajs-1071	347	2	2011),”cancellation	2011),”cancellation	NUM
iajs-1071	347	3	and	and	CCONJ
iajs-1071	347	4	weakly	weakly	ADJ
iajs-1071	347	5	cancellation	cancellation	NOUN
iajs-1071	347	6	fuzzy	fuzzy	ADJ
iajs-1071	347	7	modules	module	NOUN
iajs-1071	347	8	”	"	PUNCT
iajs-1071	347	9	journal	journal	NOUN
iajs-1071	347	10	of	of	ADP
iajs-1071	347	11	basrah	basrah	PROPN
iajs-1071	347	12	reserchs((sciences	reserchs((science	NOUN
iajs-1071	347	13	)	)	PUNCT
iajs-1071	347	14	)	)	PUNCT
iajs-1071	347	15	vol.37	vol.37	VERB
iajs-1071	347	16	no.4.d	no.4.d	NOUN
iajs-1071	347	17	.	.	PUNCT
iajs-1071	348	1	6	6	X
iajs-1071	348	2	.	.	X
iajs-1071	349	1	bothaynah	bothaynah	ADJ
iajs-1071	349	2	,	,	PUNCT
iajs-1071	349	3	n.shihab	n.shihab	PROPN
iajs-1071	349	4	and	and	CCONJ
iajs-1071	349	5	heba	heba	PROPN
iajs-1071	349	6	,	,	PUNCT
iajs-1071	349	7	m.a	m.a	PROPN
iajs-1071	349	8	jude	jude	PROPN
iajs-1071	349	9	(	(	PUNCT
iajs-1071	349	10	2015	2015	NUM
iajs-1071	349	11	)	)	PUNCT
iajs-1071	349	12	”	"	PUNCT
iajs-1071	349	13	max	max	PROPN
iajs-1071	349	14	-	-	PUNCT
iajs-1071	349	15	fully	fully	ADV
iajs-1071	349	16	cancellation	cancellation	NOUN
iajs-1071	349	17	modules	module	NOUN
iajs-1071	349	18	”	"	PUNCT
iajs-1071	349	19	journal	journal	NOUN
iajs-1071	349	20	of	of	ADP
iajs-1071	349	21	advances	advance	NOUN
iajs-1071	349	22	in	in	ADP
iajs-1071	349	23	mathematics	mathematic	NOUN
iajs-1071	349	24	.	.	PUNCT
iajs-1071	350	1	vol.11no.7,p5462	vol.11no.7,p5462	PROPN
iajs-1071	350	2	-	-	PUNCT
iajs-1071	350	3	5475	5475	NUM
iajs-1071	350	4	7	7	NUM
iajs-1071	350	5	.	.	PUNCT
iajs-1071	351	1	layla	layla	PROPN
iajs-1071	351	2	,	,	PUNCT
iajs-1071	351	3	s.m.and	s.m.and	PROPN
iajs-1071	351	4	shrooq	shrooq	PROPN
iajs-1071	351	5	,	,	PUNCT
iajs-1071	351	6	b.s.(2003),"semi	b.s.(2003),"semi	PROPN
iajs-1071	351	7	-	-	ADJ
iajs-1071	351	8	primary	primary	ADJ
iajs-1071	351	9	fuzzy	fuzzy	ADJ
iajs-1071	351	10	submodules"sc.thesis	submodules"sc.thesis	NOUN
iajs-1071	351	11	.	.	PUNCT
iajs-1071	352	1	university	university	NOUN
iajs-1071	352	2	of	of	ADP
iajs-1071	352	3	baghdad	baghdad	PROPN
iajs-1071	352	4	.	.	PUNCT
iajs-1071	353	1	mathematics	mathematic	NOUN
iajs-1071	353	2	|	|	ADV
iajs-1071	353	3	207	207	NUM
iajs-1071	353	4	2012	2012	NUM
iajs-1071	353	5	(	(	PUNCT
iajs-1071	353	6	عام	عام	PROPN
iajs-1071	353	7	1	1	NUM
iajs-1071	353	8	)	)	PUNCT
iajs-1071	353	9	(	(	PUNCT
iajs-1071	353	10	العدد	العدد	PROPN
iajs-1071	353	11	30مجلة	30مجلة	NUM
iajs-1071	353	12	إبن	إبن	VERB
iajs-1071	353	13	الهيثم	الهيثم	ADJ
iajs-1071	353	14	للعلوم	للعلوم	NOUN
iajs-1071	353	15	الصرفة	الصرفة	NOUN
iajs-1071	354	1	و	و	PRON
iajs-1071	354	2	التطبيقية	التطبيقية	ADV
iajs-1071	354	3	المجلد	المجلد	ADV
iajs-1071	354	4	)	)	PUNCT
iajs-1071	355	1	ibn	ibn	PROPN
iajs-1071	355	2	al	al	PROPN
iajs-1071	355	3	-	-	PUNCT
iajs-1071	355	4	haitham	haitham	PROPN
iajs-1071	355	5	j.	j.	PROPN
iajs-1071	355	6	for	for	ADP
iajs-1071	355	7	pure	pure	PROPN
iajs-1071	355	8	&	&	CCONJ
iajs-1071	355	9	appl	appl	PROPN
iajs-1071	355	10	.	.	PUNCT
iajs-1071	356	1	sci	sci	PROPN
iajs-1071	356	2	.	.	PUNCT
iajs-1071	357	1	vol.30	vol.30	NOUN
iajs-1071	357	2	(	(	PUNCT
iajs-1071	357	3	1	1	NUM
iajs-1071	357	4	)	)	PUNCT
iajs-1071	357	5	2017	2017	NUM
iajs-1071	357	6	انمودٌوالت	انمودٌوالت	PROPN
iajs-1071	357	7	انحذف	انحذف	PROPN
iajs-1071	357	8	شبه	شبه	NOUN
iajs-1071	357	9	انتامة	انتامة	PROPN
iajs-1071	357	10	انضبابٍة	انضبابٍة	PROPN
iajs-1071	357	11	حاتم	حاتم	ADJ
iajs-1071	358	1	ٌحٍى	ٌحٍى	PROPN
iajs-1071	358	2	خهف	خهف	NOUN
iajs-1071	358	3	جاهعت	جاهعت	NOUN
iajs-1071	358	4	بغداد	بغداد	PROPN
iajs-1071	358	5	/للعلٌم	/للعلٌم	SYM
iajs-1071	358	6	الصزفت	الصزفت	NOUN
iajs-1071	358	7	)	)	PUNCT
iajs-1071	358	8	ابن	ابن	PROPN
iajs-1071	358	9	الييثن	الييثن	NOUN
iajs-1071	358	10	(	(	PUNCT
iajs-1071	358	11	كليت	كليت	ADJ
iajs-1071	358	12	الخزبيت	الخزبيت	PROPN
iajs-1071	358	13	/قسن	/قسن	PUNCT
iajs-1071	358	14	الزياضياث	الزياضياث	NOUN
iajs-1071	358	15	هادي	هادي	NOUN
iajs-1071	358	16	غانً	غانً	NUM
iajs-1071	358	17	راشذ	راشذ	ADJ
iajs-1071	358	18	ًسارة	ًسارة	NOUN
iajs-1071	358	19	الخزبيت	الخزبيت	PROPN
iajs-1071	358	20	/األًلىحزبيت	/األًلىحزبيت	PUNCT
iajs-1071	358	21	الزصافت	الزصافت	ADJ
iajs-1071	358	22	6102/	6102/	NUM
iajs-1071	358	23	االول	االول	NOUN
iajs-1071	358	24	/	/	SYM
iajs-1071	358	25	كانون	كانون	NOUN
iajs-1071	358	26	62قبم	62قبم	NOUN
iajs-1071	358	27	فً	فً	NUM
iajs-1071	358	28	:	:	PUNCT
iajs-1071	358	29	6102	6102	NUM
iajs-1071	358	30	/	/	SYM
iajs-1071	358	31	كانون	كانون	NOUN
iajs-1071	358	32	األول/5استهم	األول/5استهم	VERB
iajs-1071	358	33	فً	فً	PUNCT
iajs-1071	358	34	:	:	PUNCT
iajs-1071	358	35	انخالصة	انخالصة	PROPN
iajs-1071	358	36	q	q	PROPN
iajs-1071	358	37	-	-	PUNCT
iajs-1071	358	38	fcf(m	fcf(m	NOUN
iajs-1071	358	39	)	)	PUNCT
iajs-1071	358	40	.	.	PUNCT
iajs-1071	359	1	ـشبابيت	ـشبابيت	VERB
iajs-1071	359	2	.	.	PUNCT
iajs-1071	360	1	ًقد	ًقد	X
iajs-1071	360	2	حن	حن	ADP
iajs-1071	360	3	إعطائيا	إعطائيا	NOUN
iajs-1071	360	4	الزهفي	الزهفي	PROPN
iajs-1071	360	5	ىذا	ىذا	NOUN
iajs-1071	360	6	البحث	البحث	VERB
iajs-1071	360	7	حوج	حوج	NOUN
iajs-1071	361	1	دراست	دراست	PROPN
iajs-1071	361	2	فكزة	فكزة	PROPN
iajs-1071	361	3	الوٌديٌالث	الوٌديٌالث	PROPN
iajs-1071	361	4	الحذف	الحذف	PROPN
iajs-1071	361	5	شبو	شبو	PROPN
iajs-1071	361	6	الخاهت	الخاهت	AUX
iajs-1071	361	7	الض	الض	PROPN
iajs-1071	361	8	ًىي	ًىي	PUNCT
iajs-1071	361	9	اعوام	اعوام	PROPN
iajs-1071	361	10	لحالت	لحالت	ADJ
iajs-1071	361	11	الوٌديٌالث	الوٌديٌالث	PROPN
iajs-1071	361	12	الحذف	الحذف	PROPN
iajs-1071	361	13	شبو	شبو	PROPN
iajs-1071	361	14	الخاهت	الخاهت	VERB
iajs-1071	361	15	االعخياديت	االعخياديت	PRON
iajs-1071	361	16	ًقد	ًقد	NOUN
iajs-1071	361	17	حن	حن	ADP
iajs-1071	361	18	حعوين	حعوين	NOUN
iajs-1071	361	19	ىذه	ىذه	NOUN
iajs-1071	361	20	الفكزه	الفكزه	NOUN
iajs-1071	361	21	الى	الى	VERB
iajs-1071	362	1	هٌديٌالث	هٌديٌالث	PROPN
iajs-1071	362	2	شبو	شبو	VERB
iajs-1071	362	3	الخاهت	الخاهت	X
iajs-1071	362	4	العظوى	العظوى	PROPN
iajs-1071	362	5	.	.	PUNCT
iajs-1071	363	1	نخائج	نخائج	PROPN
iajs-1071	363	2	عديدة	عديدة	PROPN
iajs-1071	363	3	ًخٌاص	ًخٌاص	NOUN
iajs-1071	363	4	كثيزة	كثيزة	ADV
iajs-1071	363	5	حوج	حوج	NOUN
iajs-1071	363	6	دراسخيا	دراسخيا	NOUN
iajs-1071	363	7	في	في	ADP
iajs-1071	363	8	بحثنا	بحثنا	ADJ
iajs-1071	363	9	ىذا	ىذا	NOUN
iajs-1071	363	10	.	.	PUNCT
iajs-1071	364	1	q	q	X
iajs-1071	364	2	-	-	PUNCT
iajs-1071	364	3	mfcf(m)الضبابيت	mfcf(m)الضبابيت	PROPN
iajs-1071	364	4	ًقد	ًقد	X
iajs-1071	364	5	حن	حن	PROPN
iajs-1071	364	6	اعطائيا	اعطائيا	PROPN
iajs-1071	364	7	الزهش	الزهش	PROPN
iajs-1071	364	8	بابيت	بابيت	ADV
iajs-1071	364	9	,	,	PUNCT
iajs-1071	364	10	الوٌديٌالث	الوٌديٌالث	PROPN
iajs-1071	364	11	الحذف	الحذف	PROPN
iajs-1071	364	12	شبو	شبو	PROPN
iajs-1071	364	13	الخاهت	الخاهت	VERB
iajs-1071	364	14	االعخياديت	االعخياديت	NOUN
iajs-1071	364	15	,	,	PUNCT
iajs-1071	364	16	الوٌديٌالث	الوٌديٌالث	PROPN
iajs-1071	364	17	الوٌديٌالث	الوٌديٌالث	PROPN
iajs-1071	364	18	الحذف	الحذف	PROPN
iajs-1071	364	19	شبو	شبو	PROPN
iajs-1071	364	20	الخاهت	الخاهت	VERB
iajs-1071	364	21	الض	الض	NOUN
iajs-1071	364	22	انكهمات	انكهمات	VERB
iajs-1071	364	23	انمفتاحٍة	انمفتاحٍة	PROPN
iajs-1071	364	24	:	:	PUNCT
iajs-1071	364	25	الحذف	الحذف	PROPN
iajs-1071	364	26	شبو	شبو	PROPN
iajs-1071	364	27	الخاهت	الخاهت	PROPN
iajs-1071	364	28	لعظوى	لعظوى	PROPN
iajs-1071	364	29	الضبابيت	الضبابيت	PROPN
iajs-1071	364	30	.	.	PUNCT