id	sid	tid	token	lemma	pos
iajs-2149	1	1	111	111	NUM
iajs-2149	1	2	ibn	ibn	PROPN
iajs-2149	1	3	al	al	PROPN
iajs-2149	1	4	-	-	PUNCT
iajs-2149	1	5	haitham	haitham	PROPN
iajs-2149	1	6	jour	jour	X
iajs-2149	1	7	.	.	PROPN
iajs-2149	1	8	for	for	ADP
iajs-2149	1	9	pure	pure	ADJ
iajs-2149	1	10	&	&	CCONJ
iajs-2149	1	11	appl	appl	PROPN
iajs-2149	1	12	.	.	PUNCT
iajs-2149	2	1	sci	sci	PROPN
iajs-2149	2	2	.	.	PROPN
iajs-2149	2	3	32	32	NUM
iajs-2149	2	4	(	(	PUNCT
iajs-2149	2	5	2	2	NUM
iajs-2149	2	6	)	)	PUNCT
iajs-2149	2	7	2019	2019	NUM
iajs-2149	2	8	abstract	abstract	NOUN
iajs-2149	2	9	let	let	AUX
iajs-2149	2	10	be	be	AUX
iajs-2149	2	11	a	a	DET
iajs-2149	2	12	ring	ring	NOUN
iajs-2149	2	13	and	and	CCONJ
iajs-2149	2	14	let	let	VERB
iajs-2149	2	15	be	be	AUX
iajs-2149	2	16	a	a	DET
iajs-2149	2	17	unitary	unitary	ADJ
iajs-2149	2	18	left	left	ADJ
iajs-2149	2	19	-module	-module	NOUN
iajs-2149	2	20	.	.	PUNCT
iajs-2149	3	1	a	a	DET
iajs-2149	3	2	proper	proper	ADJ
iajs-2149	3	3	submodule	submodule	NOUN
iajs-2149	3	4	of	of	ADP
iajs-2149	3	5	an	an	DET
iajs-2149	3	6	module	module	NOUN
iajs-2149	3	7	is	be	AUX
iajs-2149	3	8	called	call	VERB
iajs-2149	3	9	2	2	NUM
iajs-2149	3	10	-	-	PUNCT
iajs-2149	3	11	absorbing	absorbing	ADJ
iajs-2149	3	12	,	,	PUNCT
iajs-2149	3	13	if	if	SCONJ
iajs-2149	3	14	,	,	PUNCT
iajs-2149	3	15	where	where	SCONJ
iajs-2149	3	16	implies	imply	VERB
iajs-2149	3	17	that	that	SCONJ
iajs-2149	3	18	either	either	CCONJ
iajs-2149	3	19	or	or	CCONJ
iajs-2149	3	20	or	or	CCONJ
iajs-2149	3	21	[	[	PUNCT
iajs-2149	3	22	]	]	X
iajs-2149	3	23	,	,	PUNCT
iajs-2149	3	24	and	and	CCONJ
iajs-2149	3	25	a	a	DET
iajs-2149	3	26	proper	proper	ADJ
iajs-2149	3	27	submodule	submodule	NOUN
iajs-2149	3	28	of	of	ADP
iajs-2149	3	29	an	an	DET
iajs-2149	3	30	-module	-module	NOUN
iajs-2149	3	31	is	be	AUX
iajs-2149	3	32	called	call	VERB
iajs-2149	3	33	quasi	quasi	ADJ
iajs-2149	3	34	-	-	NOUN
iajs-2149	3	35	prime	prime	ADJ
iajs-2149	3	36	,	,	PUNCT
iajs-2149	3	37	if	if	SCONJ
iajs-2149	3	38	,	,	PUNCT
iajs-2149	3	39	where	where	SCONJ
iajs-2149	3	40	implies	imply	VERB
iajs-2149	3	41	that	that	SCONJ
iajs-2149	3	42	either	either	ADV
iajs-2149	3	43	or	or	CCONJ
iajs-2149	3	44	.	.	PUNCT
iajs-2149	4	1	this	this	PRON
iajs-2149	4	2	led	lead	VERB
iajs-2149	4	3	us	we	PRON
iajs-2149	4	4	to	to	PART
iajs-2149	4	5	introduce	introduce	VERB
iajs-2149	4	6	the	the	DET
iajs-2149	4	7	concept	concept	NOUN
iajs-2149	4	8	pseudo	pseudo	NOUN
iajs-2149	4	9	quasi-2	quasi-2	NOUN
iajs-2149	4	10	-	-	PUNCT
iajs-2149	4	11	absorbing	absorbing	ADJ
iajs-2149	4	12	submodule	submodule	NOUN
iajs-2149	4	13	,	,	PUNCT
iajs-2149	4	14	as	as	ADP
iajs-2149	4	15	a	a	DET
iajs-2149	4	16	generalization	generalization	NOUN
iajs-2149	4	17	of	of	ADP
iajs-2149	4	18	both	both	DET
iajs-2149	4	19	concepts	concept	NOUN
iajs-2149	4	20	above	above	ADP
iajs-2149	4	21	,	,	PUNCT
iajs-2149	4	22	where	where	SCONJ
iajs-2149	4	23	a	a	DET
iajs-2149	4	24	proper	proper	ADJ
iajs-2149	4	25	submodule	submodule	NOUN
iajs-2149	4	26	of	of	ADP
iajs-2149	4	27	an	an	DET
iajs-2149	4	28	-module	-module	NOUN
iajs-2149	4	29	is	be	AUX
iajs-2149	4	30	called	call	VERB
iajs-2149	4	31	a	a	DET
iajs-2149	4	32	pseudo	pseudo	NOUN
iajs-2149	4	33	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	4	34	submodule	submodule	NOUN
iajs-2149	4	35	of	of	ADP
iajs-2149	4	36	,	,	PUNCT
iajs-2149	4	37	if	if	SCONJ
iajs-2149	4	38	whenever	whenever	ADV
iajs-2149	4	39	,	,	PUNCT
iajs-2149	4	40	where	where	SCONJ
iajs-2149	4	41	implies	imply	VERB
iajs-2149	4	42	that	that	SCONJ
iajs-2149	4	43	either	either	CCONJ
iajs-2149	4	44	or	or	CCONJ
iajs-2149	4	45	or	or	CCONJ
iajs-2149	4	46	,	,	PUNCT
iajs-2149	4	47	where	where	SCONJ
iajs-2149	4	48	is	be	AUX
iajs-2149	4	49	socal	socal	NOUN
iajs-2149	4	50	of	of	ADP
iajs-2149	4	51	an	an	DET
iajs-2149	4	52	-module	-module	NOUN
iajs-2149	4	53	.	.	PUNCT
iajs-2149	5	1	several	several	ADJ
iajs-2149	5	2	basic	basic	ADJ
iajs-2149	5	3	properties	property	NOUN
iajs-2149	5	4	,	,	PUNCT
iajs-2149	5	5	examples	example	NOUN
iajs-2149	5	6	and	and	CCONJ
iajs-2149	5	7	characterizations	characterization	NOUN
iajs-2149	5	8	of	of	ADP
iajs-2149	5	9	this	this	DET
iajs-2149	5	10	concept	concept	NOUN
iajs-2149	5	11	are	be	AUX
iajs-2149	5	12	given	give	VERB
iajs-2149	5	13	.	.	PUNCT
iajs-2149	6	1	moreover	moreover	ADV
iajs-2149	6	2	,	,	PUNCT
iajs-2149	6	3	we	we	PRON
iajs-2149	6	4	investigate	investigate	VERB
iajs-2149	6	5	relationships	relationship	NOUN
iajs-2149	6	6	between	between	ADP
iajs-2149	6	7	pseudo	pseudo	NOUN
iajs-2149	6	8	quasi-2	quasi-2	NOUN
iajs-2149	6	9	-	-	PUNCT
iajs-2149	6	10	absorbing	absorbing	ADJ
iajs-2149	6	11	submodule	submodule	NOUN
iajs-2149	6	12	and	and	CCONJ
iajs-2149	6	13	other	other	ADJ
iajs-2149	6	14	classes	class	NOUN
iajs-2149	6	15	of	of	ADP
iajs-2149	6	16	submodules	submodule	NOUN
iajs-2149	6	17	.	.	PUNCT
iajs-2149	7	1	keywords	keyword	NOUN
iajs-2149	7	2	:	:	PUNCT
iajs-2149	7	3	prime	prime	ADJ
iajs-2149	7	4	submodules	submodule	NOUN
iajs-2149	7	5	,	,	PUNCT
iajs-2149	7	6	quasi	quasi	ADJ
iajs-2149	7	7	-	-	ADJ
iajs-2149	7	8	prime	prime	ADJ
iajs-2149	7	9	submodules	submodule	NOUN
iajs-2149	7	10	,	,	PUNCT
iajs-2149	7	11	2	2	NUM
iajs-2149	7	12	-	-	PUNCT
iajs-2149	7	13	absorbing	absorbing	ADJ
iajs-2149	7	14	submodules	submodule	NOUN
iajs-2149	7	15	,	,	PUNCT
iajs-2149	7	16	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	7	17	submodules	submodule	NOUN
iajs-2149	7	18	,	,	PUNCT
iajs-2149	7	19	pseudo	pseudo	NOUN
iajs-2149	7	20	quasi-2	quasi-2	NOUN
iajs-2149	7	21	-	-	PUNCT
iajs-2149	7	22	absorbing	absorbing	ADJ
iajs-2149	7	23	submodules	submodule	NOUN
iajs-2149	7	24	.	.	PUNCT
iajs-2149	8	1	1	1	X
iajs-2149	8	2	.	.	X
iajs-2149	8	3	introduction	introduction	NOUN
iajs-2149	8	4	and	and	CCONJ
iajs-2149	8	5	preliminaries	preliminary	NOUN
iajs-2149	8	6	throughout	throughout	ADP
iajs-2149	8	7	this	this	DET
iajs-2149	8	8	dissertation	dissertation	NOUN
iajs-2149	8	9	all	all	DET
iajs-2149	8	10	ring	ring	NOUN
iajs-2149	8	11	is	be	AUX
iajs-2149	8	12	commutative	commutative	ADJ
iajs-2149	8	13	with	with	ADP
iajs-2149	8	14	identity	identity	NOUN
iajs-2149	8	15	and	and	CCONJ
iajs-2149	8	16	all	all	DET
iajs-2149	8	17	-modules	-module	NOUN
iajs-2149	8	18	are	be	AUX
iajs-2149	8	19	left	leave	VERB
iajs-2149	8	20	unitary	unitary	ADJ
iajs-2149	8	21	.	.	PUNCT
iajs-2149	9	1	a	a	DET
iajs-2149	9	2	proper	proper	ADJ
iajs-2149	9	3	submodule	submodule	NOUN
iajs-2149	9	4	of	of	ADP
iajs-2149	9	5	an	an	DET
iajs-2149	9	6	-module	-module	NOUN
iajs-2149	9	7	is	be	AUX
iajs-2149	9	8	called	call	VERB
iajs-2149	9	9	a	a	DET
iajs-2149	9	10	prime	prime	ADJ
iajs-2149	9	11	submodule	submodule	NOUN
iajs-2149	9	12	if	if	SCONJ
iajs-2149	9	13	whenever	whenever	SCONJ
iajs-2149	9	14	,	,	PUNCT
iajs-2149	9	15	with	with	ADP
iajs-2149	9	16	implies	implie	NOUN
iajs-2149	9	17	that	that	SCONJ
iajs-2149	9	18	either	either	CCONJ
iajs-2149	9	19	or	or	CCONJ
iajs-2149	9	20	[	[	PUNCT
iajs-2149	9	21	]	]	X
iajs-2149	9	22	[	[	PUNCT
iajs-2149	9	23	]	]	X
iajs-2149	9	24	.	.	PUNCT
iajs-2149	10	1	prime	prime	ADJ
iajs-2149	10	2	submodules	submodule	NOUN
iajs-2149	10	3	play	play	VERB
iajs-2149	10	4	an	an	DET
iajs-2149	10	5	important	important	ADJ
iajs-2149	10	6	role	role	NOUN
iajs-2149	10	7	in	in	ADP
iajs-2149	10	8	the	the	DET
iajs-2149	10	9	module	module	NOUN
iajs-2149	10	10	theory	theory	NOUN
iajs-2149	10	11	over	over	ADP
iajs-2149	10	12	a	a	DET
iajs-2149	10	13	commutative	commutative	ADJ
iajs-2149	10	14	ring	ring	NOUN
iajs-2149	10	15	.	.	PUNCT
iajs-2149	11	1	there	there	PRON
iajs-2149	11	2	are	be	VERB
iajs-2149	11	3	several	several	ADJ
iajs-2149	11	4	generalizations	generalization	NOUN
iajs-2149	11	5	of	of	ADP
iajs-2149	11	6	the	the	DET
iajs-2149	11	7	notion	notion	NOUN
iajs-2149	11	8	of	of	ADP
iajs-2149	11	9	prime	prime	ADJ
iajs-2149	11	10	submodules	submodule	NOUN
iajs-2149	11	11	such	such	ADJ
iajs-2149	11	12	as	as	ADP
iajs-2149	11	13	,	,	PUNCT
iajs-2149	11	14	quasi	quasi	ADJ
iajs-2149	11	15	prime	prime	PROPN
iajs-2149	11	16	submodule	submodule	NOUN
iajs-2149	11	17	,	,	PUNCT
iajs-2149	11	18	where	where	SCONJ
iajs-2149	11	19	a	a	DET
iajs-2149	11	20	proper	proper	ADJ
iajs-2149	11	21	submodule	submodule	NOUN
iajs-2149	11	22	of	of	ADP
iajs-2149	11	23	an	an	DET
iajs-2149	11	24	-module	-module	NOUN
iajs-2149	11	25	is	be	AUX
iajs-2149	11	26	called	call	VERB
iajs-2149	11	27	a	a	DET
iajs-2149	11	28	quasi	quasi	NOUN
iajs-2149	11	29	-	-	NOUN
iajs-2149	11	30	prime	prime	ADJ
iajs-2149	11	31	,	,	PUNCT
iajs-2149	11	32	if	if	SCONJ
iajs-2149	11	33	whenever	whenever	ADV
iajs-2149	11	34	,	,	PUNCT
iajs-2149	11	35	with	with	ADP
iajs-2149	11	36	,	,	PUNCT
iajs-2149	11	37	implies	imply	VERB
iajs-2149	11	38	that	that	SCONJ
iajs-2149	11	39	either	either	CCONJ
iajs-2149	11	40	or	or	CCONJ
iajs-2149	11	41	[	[	PUNCT
iajs-2149	11	42	]	]	X
iajs-2149	11	43	.	.	PUNCT
iajs-2149	12	1	we	we	PRON
iajs-2149	12	2	-	-	PUNCT
iajs-2149	12	3	prime	prime	NOUN
iajs-2149	12	4	submodules	submodule	NOUN
iajs-2149	12	5	and	and	CCONJ
iajs-2149	12	6	we	we	PRON
iajs-2149	12	7	-	-	PUNCT
iajs-2149	12	8	semi	semi	ADV
iajs-2149	12	9	prime	prime	ADJ
iajs-2149	12	10	submodules	submodule	NOUN
iajs-2149	12	11	which	which	PRON
iajs-2149	12	12	appear	appear	VERB
iajs-2149	12	13	in	in	ADP
iajs-2149	12	14	[	[	PUNCT
iajs-2149	12	15	]	]	X
iajs-2149	12	16	.	.	PUNCT
iajs-2149	13	1	the	the	DET
iajs-2149	13	2	concept	concept	NOUN
iajs-2149	13	3	of	of	ADP
iajs-2149	13	4	prime	prime	ADJ
iajs-2149	13	5	submodule	submodule	PROPN
iajs-2149	13	6	was	be	AUX
iajs-2149	13	7	generalized	generalize	VERB
iajs-2149	13	8	by	by	ADP
iajs-2149	13	9	darani	darani	PROPN
iajs-2149	13	10	and	and	CCONJ
iajs-2149	13	11	soheilnia	soheilnia	NOUN
iajs-2149	13	12	to	to	ADP
iajs-2149	13	13	2	2	NUM
iajs-2149	13	14	-	-	PUNCT
iajs-2149	13	15	absorbing	absorb	VERB
iajs-2149	13	16	submodule	submodule	NOUN
iajs-2149	13	17	,	,	PUNCT
iajs-2149	13	18	where	where	SCONJ
iajs-2149	13	19	a	a	DET
iajs-2149	13	20	proper	proper	ADJ
iajs-2149	13	21	submodule	submodule	NOUN
iajs-2149	13	22	of	of	ADP
iajs-2149	13	23	an	an	DET
iajs-2149	13	24	-module	-module	NOUN
iajs-2149	13	25	is	be	AUX
iajs-2149	13	26	called	call	VERB
iajs-2149	13	27	2	2	NUM
iajs-2149	13	28	-	-	PUNCT
iajs-2149	13	29	absorbing	absorbing	ADJ
iajs-2149	13	30	,	,	PUNCT
iajs-2149	13	31	if	if	SCONJ
iajs-2149	13	32	whenever	whenever	SCONJ
iajs-2149	13	33	,	,	PUNCT
iajs-2149	13	34	with	with	ADP
iajs-2149	13	35	implies	implie	NOUN
iajs-2149	13	36	that	that	SCONJ
iajs-2149	13	37	either	either	CCONJ
iajs-2149	13	38	or	or	CCONJ
iajs-2149	13	39	or	or	CCONJ
iajs-2149	13	40	[	[	PUNCT
iajs-2149	13	41	]	]	X
iajs-2149	13	42	[	[	PUNCT
iajs-2149	13	43	]	]	X
iajs-2149	13	44	.	.	PUNCT
iajs-2149	14	1	there	there	PRON
iajs-2149	14	2	are	be	VERB
iajs-2149	14	3	several	several	ADJ
iajs-2149	14	4	generalizations	generalization	NOUN
iajs-2149	14	5	of	of	ADP
iajs-2149	14	6	2absorbing	2absorbing	NUM
iajs-2149	14	7	submodules	submodule	NOUN
iajs-2149	14	8	such	such	ADJ
iajs-2149	14	9	as	as	ADP
iajs-2149	14	10	wn-2	wn-2	ADP
iajs-2149	14	11	-	-	ADJ
iajs-2149	14	12	absorbing	absorbing	ADJ
iajs-2149	14	13	submodules	submodule	NOUN
iajs-2149	14	14	and	and	CCONJ
iajs-2149	14	15	wns2	wns2	PROPN
iajs-2149	14	16	-	-	PUNCT
iajs-2149	14	17	absorbing	absorb	VERB
iajs-2149	14	18	submodules	submodule	NOUN
iajs-2149	14	19	which	which	PRON
iajs-2149	14	20	appear	appear	VERB
iajs-2149	14	21	in	in	ADP
iajs-2149	14	22	[	[	PUNCT
iajs-2149	14	23	]	]	X
iajs-2149	14	24	.	.	PUNCT
iajs-2149	15	1	the	the	DET
iajs-2149	15	2	concept	concept	NOUN
iajs-2149	15	3	of	of	ADP
iajs-2149	15	4	quasi-2	quasi-2	NOUN
iajs-2149	15	5	-	-	PUNCT
iajs-2149	15	6	absorbing	absorbing	ADJ
iajs-2149	15	7	submodule	submodule	NOUN
iajs-2149	15	8	,	,	PUNCT
iajs-2149	15	9	was	be	AUX
iajs-2149	15	10	pseudo	pseudo	VERB
iajs-2149	15	11	quasi-2	quasi-2	ADJ
iajs-2149	15	12	-	-	PUNCT
iajs-2149	15	13	absorbing	absorbing	ADJ
iajs-2149	15	14	submodules	submodule	NOUN
iajs-2149	15	15	and	and	CCONJ
iajs-2149	15	16	some	some	DET
iajs-2149	15	17	related	relate	VERB
iajs-2149	15	18	concepts	concept	NOUN
iajs-2149	15	19	omar.aldoori87@gmail.com	omar.aldoori87@gmail.com	X
iajs-2149	15	20	ibn	ibn	PROPN
iajs-2149	15	21	al	al	PROPN
iajs-2149	15	22	haitham	haitham	PROPN
iajs-2149	15	23	journal	journal	PROPN
iajs-2149	15	24	for	for	ADP
iajs-2149	15	25	pure	pure	ADJ
iajs-2149	15	26	and	and	CCONJ
iajs-2149	15	27	applied	apply	VERB
iajs-2149	15	28	science	science	NOUN
iajs-2149	15	29	journal	journal	PROPN
iajs-2149	15	30	homepage	homepage	NOUN
iajs-2149	15	31	:	:	PUNCT
iajs-2149	15	32	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2149	15	33	article	article	NOUN
iajs-2149	15	34	history	history	NOUN
iajs-2149	15	35	:	:	PUNCT
iajs-2149	15	36	received	receive	VERB
iajs-2149	15	37	27	27	NUM
iajs-2149	15	38	december	december	PROPN
iajs-2149	15	39	2018	2018	NUM
iajs-2149	15	40	,	,	PUNCT
iajs-2149	15	41	accepted	accept	VERB
iajs-2149	15	42	20	20	NUM
iajs-2149	15	43	january	january	PROPN
iajs-2149	15	44	2019	2019	NUM
iajs-2149	15	45	,	,	PUNCT
iajs-2149	15	46	publish	publish	VERB
iajs-2149	15	47	may	may	PROPN
iajs-2149	15	48	2019	2019	NUM
iajs-2149	15	49	omar	omar	PROPN
iajs-2149	15	50	a.	a.	PROPN
iajs-2149	15	51	abdulla	abdulla	PROPN
iajs-2149	15	52	doi	doi	PROPN
iajs-2149	15	53	:	:	PUNCT
iajs-2149	15	54	10.30526/32.2.2149	10.30526/32.2.2149	NUM
iajs-2149	15	55	department	department	NOUN
iajs-2149	15	56	of	of	ADP
iajs-2149	15	57	mathematics	mathematic	NOUN
iajs-2149	15	58	,	,	PUNCT
iajs-2149	15	59	college	college	NOUN
iajs-2149	15	60	of	of	ADP
iajs-2149	15	61	computer	computer	NOUN
iajs-2149	15	62	science	science	NOUN
iajs-2149	15	63	and	and	CCONJ
iajs-2149	15	64	mathematics	mathematic	NOUN
iajs-2149	15	65	,	,	PUNCT
iajs-2149	15	66	university	university	NOUN
iajs-2149	15	67	of	of	ADP
iajs-2149	15	68	tikrit	tikrit	NOUN
iajs-2149	15	69	,	,	PUNCT
iajs-2149	15	70	tikrit	tikrit	NOUN
iajs-2149	15	71	,	,	PUNCT
iajs-2149	15	72	iraq	iraq	PROPN
iajs-2149	15	73	.	.	PUNCT
iajs-2149	16	1	mohammadali2013@gmail.com	mohammadali2013@gmail.com	PROPN
iajs-2149	17	1	haibat	haibat	PROPN
iajs-2149	17	2	k.	k.	PROPN
iajs-2149	17	3	mohammadali	mohammadali	PROPN
iajs-2149	17	4	mailto:omar.aldoori87@gmail.com	mailto:omar.aldoori87@gmail.com	X
iajs-2149	17	5	mailto:omar.aldoori87@gmail.com	mailto:omar.aldoori87@gmail.com	X
iajs-2149	17	6	mailto:mohammadali2013@gmail.com	mailto:mohammadali2013@gmail.com	X
iajs-2149	18	1	mailto:mohammadali2013@gmail.com	mailto:mohammadali2013@gmail.com	PROPN
iajs-2149	18	2	111	111	PROPN
iajs-2149	18	3	ibn	ibn	PROPN
iajs-2149	18	4	al	al	PROPN
iajs-2149	18	5	-	-	PUNCT
iajs-2149	18	6	haitham	haitham	PROPN
iajs-2149	18	7	jour	jour	X
iajs-2149	18	8	.	.	PROPN
iajs-2149	19	1	for	for	ADP
iajs-2149	19	2	pure	pure	ADJ
iajs-2149	19	3	&	&	CCONJ
iajs-2149	19	4	appl	appl	PROPN
iajs-2149	19	5	.	.	PUNCT
iajs-2149	20	1	sci	sci	PROPN
iajs-2149	20	2	.	.	PROPN
iajs-2149	20	3	32	32	NUM
iajs-2149	20	4	(	(	PUNCT
iajs-2149	20	5	2	2	NUM
iajs-2149	20	6	)	)	PUNCT
iajs-2149	20	7	2019	2019	NUM
iajs-2149	20	8	introduced	introduce	VERB
iajs-2149	20	9	in	in	ADP
iajs-2149	20	10	2018	2018	NUM
iajs-2149	20	11	as	as	ADP
iajs-2149	20	12	a	a	DET
iajs-2149	20	13	generalization	generalization	NOUN
iajs-2149	20	14	of	of	ADP
iajs-2149	20	15	2	2	NUM
iajs-2149	20	16	-	-	PUNCT
iajs-2149	20	17	absorbing	absorb	VERB
iajs-2149	20	18	submodule	submodule	NOUN
iajs-2149	20	19	,	,	PUNCT
iajs-2149	20	20	where	where	SCONJ
iajs-2149	20	21	a	a	DET
iajs-2149	20	22	proper	proper	ADJ
iajs-2149	20	23	submodule	submodule	NOUN
iajs-2149	20	24	of	of	ADP
iajs-2149	20	25	an	an	DET
iajs-2149	20	26	-module	-module	NOUN
iajs-2149	20	27	is	be	AUX
iajs-2149	20	28	called	call	VERB
iajs-2149	20	29	a	a	DET
iajs-2149	20	30	quasi-2	quasi-2	ADV
iajs-2149	20	31	-	-	PUNCT
iajs-2149	20	32	absorbing	absorbing	ADJ
iajs-2149	20	33	,	,	PUNCT
iajs-2149	20	34	if	if	SCONJ
iajs-2149	20	35	whenever	whenever	SCONJ
iajs-2149	20	36	,	,	PUNCT
iajs-2149	20	37	with	with	ADP
iajs-2149	20	38	implies	implie	NOUN
iajs-2149	20	39	that	that	SCONJ
iajs-2149	20	40	either	either	CCONJ
iajs-2149	20	41	or	or	CCONJ
iajs-2149	20	42	or	or	CCONJ
iajs-2149	20	43	[	[	PUNCT
iajs-2149	20	44	]	]	X
iajs-2149	20	45	in	in	ADP
iajs-2149	20	46	this	this	DET
iajs-2149	20	47	paper	paper	NOUN
iajs-2149	20	48	we	we	PRON
iajs-2149	20	49	establish	establish	VERB
iajs-2149	20	50	new	new	ADJ
iajs-2149	20	51	concept	concept	NOUN
iajs-2149	20	52	called	call	VERB
iajs-2149	20	53	pseudo	pseudo	NOUN
iajs-2149	20	54	quasi-2	quasi-2	NOUN
iajs-2149	20	55	-	-	PUNCT
iajs-2149	20	56	absorbing	absorbing	ADJ
iajs-2149	20	57	submodule	submodule	NOUN
iajs-2149	20	58	as	as	ADP
iajs-2149	20	59	generalization	generalization	NOUN
iajs-2149	20	60	of	of	ADP
iajs-2149	20	61	(	(	PUNCT
iajs-2149	20	62	prime	prime	ADJ
iajs-2149	20	63	,	,	PUNCT
iajs-2149	20	64	quasiprime	quasiprime	ADJ
iajs-2149	20	65	,	,	PUNCT
iajs-2149	20	66	2	2	NUM
iajs-2149	20	67	-	-	PUNCT
iajs-2149	20	68	absorbing	absorbing	ADJ
iajs-2149	20	69	and	and	CCONJ
iajs-2149	20	70	quasi-2	quasi-2	ADV
iajs-2149	20	71	-	-	PUNCT
iajs-2149	20	72	absorbing	absorbing	ADJ
iajs-2149	20	73	)	)	PUNCT
iajs-2149	20	74	submodules	submodule	NOUN
iajs-2149	20	75	.	.	PUNCT
iajs-2149	21	1	several	several	ADJ
iajs-2149	21	2	basic	basic	ADJ
iajs-2149	21	3	properties	property	NOUN
iajs-2149	21	4	examples	example	NOUN
iajs-2149	21	5	,	,	PUNCT
iajs-2149	21	6	and	and	CCONJ
iajs-2149	21	7	relationships	relationship	NOUN
iajs-2149	21	8	of	of	ADP
iajs-2149	21	9	pseudo	pseudo	NOUN
iajs-2149	21	10	quasi-2	quasi-2	NOUN
iajs-2149	21	11	-	-	PUNCT
iajs-2149	21	12	absorbing	absorbing	ADJ
iajs-2149	21	13	submodules	submodule	NOUN
iajs-2149	21	14	,	,	PUNCT
iajs-2149	21	15	with	with	ADP
iajs-2149	21	16	other	other	ADJ
iajs-2149	21	17	classes	class	NOUN
iajs-2149	21	18	of	of	ADP
iajs-2149	21	19	submodules	submodule	NOUN
iajs-2149	21	20	are	be	AUX
iajs-2149	21	21	studied	study	VERB
iajs-2149	21	22	.	.	PUNCT
iajs-2149	22	1	socle	socle	NOUN
iajs-2149	22	2	of	of	ADP
iajs-2149	22	3	a	a	DET
iajs-2149	22	4	module	module	NOUN
iajs-2149	22	5	denoted	denote	VERB
iajs-2149	22	6	by	by	ADP
iajs-2149	22	7	defined	define	VERB
iajs-2149	22	8	to	to	PART
iajs-2149	22	9	be	be	AUX
iajs-2149	22	10	the	the	DET
iajs-2149	22	11	intersection	intersection	NOUN
iajs-2149	22	12	of	of	ADP
iajs-2149	22	13	all	all	DET
iajs-2149	22	14	essential	essential	ADJ
iajs-2149	22	15	submodules	submodule	NOUN
iajs-2149	22	16	of	of	ADP
iajs-2149	22	17	[	[	PUNCT
iajs-2149	22	18	]	]	X
iajs-2149	22	19	.	.	PUNCT
iajs-2149	23	1	where	where	SCONJ
iajs-2149	23	2	a	a	DET
iajs-2149	23	3	submodule	submodule	NOUN
iajs-2149	23	4	of	of	ADP
iajs-2149	23	5	an	an	DET
iajs-2149	23	6	-module	-module	NOUN
iajs-2149	23	7	is	be	AUX
iajs-2149	23	8	called	call	VERB
iajs-2149	23	9	essential	essential	ADJ
iajs-2149	23	10	,	,	PUNCT
iajs-2149	23	11	if	if	SCONJ
iajs-2149	23	12	has	have	VERB
iajs-2149	23	13	non	non	ADJ
iajs-2149	23	14	-	-	ADJ
iajs-2149	23	15	zero	zero	NUM
iajs-2149	23	16	intersection	intersection	NOUN
iajs-2149	23	17	with	with	ADP
iajs-2149	23	18	every	every	DET
iajs-2149	23	19	non	non	ADJ
iajs-2149	23	20	-	-	ADJ
iajs-2149	23	21	zero	zero	NUM
iajs-2149	23	22	submodule	submodule	NOUN
iajs-2149	23	23	of	of	ADP
iajs-2149	23	24	[	[	PUNCT
iajs-2149	23	25	]	]	X
iajs-2149	23	26	.	.	PUNCT
iajs-2149	23	27	recall	recall	VERB
iajs-2149	23	28	that	that	SCONJ
iajs-2149	23	29	a	a	DET
iajs-2149	23	30	non	non	ADJ
iajs-2149	23	31	-	-	ADJ
iajs-2149	23	32	zero	zero	ADJ
iajs-2149	23	33	proper	proper	ADJ
iajs-2149	23	34	ideal	ideal	NOUN
iajs-2149	23	35	of	of	ADP
iajs-2149	23	36	is	be	AUX
iajs-2149	23	37	called	call	VERB
iajs-2149	23	38	2	2	NUM
iajs-2149	23	39	-	-	PUNCT
iajs-2149	23	40	absorbing	absorbing	ADJ
iajs-2149	23	41	ideal	ideal	NOUN
iajs-2149	23	42	of	of	ADP
iajs-2149	23	43	,	,	PUNCT
iajs-2149	24	1	if	if	SCONJ
iajs-2149	24	2	whenever	whenever	ADV
iajs-2149	24	3	and	and	CCONJ
iajs-2149	24	4	,	,	PUNCT
iajs-2149	24	5	then	then	ADV
iajs-2149	24	6	or	or	CCONJ
iajs-2149	24	7	or	or	CCONJ
iajs-2149	24	8	[	[	PUNCT
iajs-2149	24	9	]	]	X
iajs-2149	24	10	.	.	PUNCT
iajs-2149	25	1	recall	recall	VERB
iajs-2149	25	2	that	that	SCONJ
iajs-2149	25	3	an	an	DET
iajs-2149	25	4	-module	-module	NOUN
iajs-2149	25	5	is	be	AUX
iajs-2149	25	6	multiplication	multiplication	NOUN
iajs-2149	25	7	if	if	SCONJ
iajs-2149	25	8	every	every	DET
iajs-2149	25	9	submodule	submodule	NOUN
iajs-2149	25	10	of	of	ADP
iajs-2149	25	11	is	be	AUX
iajs-2149	25	12	of	of	ADP
iajs-2149	25	13	the	the	DET
iajs-2149	25	14	form	form	NOUN
iajs-2149	25	15	for	for	ADP
iajs-2149	25	16	some	some	DET
iajs-2149	25	17	ideal	ideal	NOUN
iajs-2149	25	18	of	of	ADP
iajs-2149	25	19	[	[	PUNCT
iajs-2149	25	20	]	]	X
iajs-2149	25	21	.	.	X
iajs-2149	26	1	2	2	X
iajs-2149	26	2	.	.	X
iajs-2149	26	3	pseudo	pseudo	NOUN
iajs-2149	26	4	quasi-2	quasi-2	NOUN
iajs-2149	26	5	-	-	PUNCT
iajs-2149	26	6	absorbing	absorbing	ADJ
iajs-2149	26	7	submodules	submodule	NOUN
iajs-2149	26	8	in	in	ADP
iajs-2149	26	9	this	this	DET
iajs-2149	26	10	section	section	NOUN
iajs-2149	26	11	,	,	PUNCT
iajs-2149	26	12	we	we	PRON
iajs-2149	26	13	introduced	introduce	VERB
iajs-2149	26	14	the	the	DET
iajs-2149	26	15	definition	definition	NOUN
iajs-2149	26	16	of	of	ADP
iajs-2149	26	17	a	a	DET
iajs-2149	26	18	pseudo	pseudo	NOUN
iajs-2149	26	19	quasi-2	quasi-2	NOUN
iajs-2149	26	20	-	-	PUNCT
iajs-2149	26	21	absorbing	absorbing	ADJ
iajs-2149	26	22	submodule	submodule	NOUN
iajs-2149	26	23	definition	definition	NOUN
iajs-2149	26	24	(	(	PUNCT
iajs-2149	26	25	1	1	X
iajs-2149	26	26	)	)	PUNCT
iajs-2149	26	27	a	a	DET
iajs-2149	26	28	proper	proper	ADJ
iajs-2149	26	29	submodule	submodule	NOUN
iajs-2149	26	30	of	of	ADP
iajs-2149	26	31	an	an	DET
iajs-2149	26	32	-module	-module	NOUN
iajs-2149	26	33	is	be	AUX
iajs-2149	26	34	called	call	VERB
iajs-2149	26	35	a	a	DET
iajs-2149	26	36	pseudo	pseudo	NOUN
iajs-2149	26	37	quasi-2	quasi-2	NOUN
iajs-2149	26	38	-	-	PUNCT
iajs-2149	26	39	absorbing	absorbing	ADJ
iajs-2149	26	40	submodule	submodule	NOUN
iajs-2149	26	41	,	,	PUNCT
iajs-2149	26	42	if	if	SCONJ
iajs-2149	26	43	whenever	whenever	ADV
iajs-2149	26	44	,	,	PUNCT
iajs-2149	26	45	with	with	ADP
iajs-2149	26	46	,	,	PUNCT
iajs-2149	26	47	implies	imply	VERB
iajs-2149	26	48	that	that	SCONJ
iajs-2149	26	49	either	either	CCONJ
iajs-2149	26	50	or	or	CCONJ
iajs-2149	26	51	or	or	CCONJ
iajs-2149	26	52	.	.	PUNCT
iajs-2149	27	1	and	and	CCONJ
iajs-2149	27	2	a	a	DET
iajs-2149	27	3	proper	proper	ADJ
iajs-2149	27	4	ideal	ideal	NOUN
iajs-2149	27	5	of	of	ADP
iajs-2149	27	6	a	a	DET
iajs-2149	27	7	ring	ring	NOUN
iajs-2149	27	8	is	be	AUX
iajs-2149	27	9	called	call	VERB
iajs-2149	27	10	a	a	DET
iajs-2149	27	11	pseudo	pseudo	NOUN
iajs-2149	27	12	quasi-2	quasi-2	NOUN
iajs-2149	27	13	-	-	PUNCT
iajs-2149	27	14	absorbing	absorbing	ADJ
iajs-2149	27	15	,	,	PUNCT
iajs-2149	27	16	if	if	SCONJ
iajs-2149	27	17	is	be	AUX
iajs-2149	27	18	a	a	DET
iajs-2149	27	19	pseudo	pseudo	NOUN
iajs-2149	27	20	quasi-2	quasi-2	NOUN
iajs-2149	27	21	-	-	PUNCT
iajs-2149	27	22	absorbing	absorbing	ADJ
iajs-2149	27	23	submodule	submodule	NOUN
iajs-2149	27	24	of	of	ADP
iajs-2149	27	25	an	an	DET
iajs-2149	27	26	-module	-module	NOUN
iajs-2149	27	27	.	.	PUNCT
iajs-2149	28	1	the	the	DET
iajs-2149	28	2	following	follow	VERB
iajs-2149	28	3	proposition	proposition	NOUN
iajs-2149	28	4	gives	give	VERB
iajs-2149	28	5	characterization	characterization	NOUN
iajs-2149	28	6	of	of	ADP
iajs-2149	28	7	a	a	DET
iajs-2149	28	8	pseudo	pseudo	NOUN
iajs-2149	28	9	quasi-2	quasi-2	NOUN
iajs-2149	28	10	-	-	PUNCT
iajs-2149	28	11	absorbing	absorbing	ADJ
iajs-2149	28	12	submodules	submodule	NOUN
iajs-2149	28	13	.	.	PUNCT
iajs-2149	29	1	proposition	proposition	NOUN
iajs-2149	29	2	(	(	PUNCT
iajs-2149	29	3	2	2	X
iajs-2149	29	4	)	)	PUNCT
iajs-2149	29	5	let	let	AUX
iajs-2149	29	6	be	be	AUX
iajs-2149	29	7	an	an	DET
iajs-2149	29	8	-module	-module	NOUN
iajs-2149	29	9	,	,	PUNCT
iajs-2149	29	10	and	and	CCONJ
iajs-2149	29	11	is	be	AUX
iajs-2149	29	12	a	a	DET
iajs-2149	29	13	submodule	submodule	NOUN
iajs-2149	29	14	of	of	ADP
iajs-2149	29	15	.	.	PUNCT
iajs-2149	30	1	then	then	ADV
iajs-2149	30	2	is	be	AUX
iajs-2149	30	3	a	a	DET
iajs-2149	30	4	pseudo	pseudo	NOUN
iajs-2149	30	5	quasi-2	quasi-2	NOUN
iajs-2149	30	6	-	-	PUNCT
iajs-2149	30	7	absorbing	absorbing	ADJ
iajs-2149	30	8	submodule	submodule	NOUN
iajs-2149	30	9	of	of	ADP
iajs-2149	30	10	if	if	SCONJ
iajs-2149	30	11	and	and	CCONJ
iajs-2149	30	12	only	only	ADV
iajs-2149	30	13	if	if	SCONJ
iajs-2149	30	14	for	for	ADP
iajs-2149	30	15	every	every	DET
iajs-2149	30	16	ideals	ideal	NOUN
iajs-2149	30	17	of	of	ADP
iajs-2149	30	18	and	and	CCONJ
iajs-2149	30	19	submodule	submodule	NOUN
iajs-2149	30	20	of	of	ADP
iajs-2149	30	21	with	with	ADP
iajs-2149	30	22	,	,	PUNCT
iajs-2149	30	23	implies	imply	VERB
iajs-2149	30	24	that	that	SCONJ
iajs-2149	30	25	either	either	CCONJ
iajs-2149	30	26	or	or	CCONJ
iajs-2149	30	27	or	or	CCONJ
iajs-2149	30	28	.	.	PUNCT
iajs-2149	31	1	proof	proof	NOUN
iajs-2149	31	2	suppose	suppose	VERB
iajs-2149	31	3	that	that	SCONJ
iajs-2149	31	4	,	,	PUNCT
iajs-2149	31	5	where	where	SCONJ
iajs-2149	31	6	are	be	AUX
iajs-2149	31	7	ideals	ideal	NOUN
iajs-2149	31	8	of	of	ADP
iajs-2149	31	9	,	,	PUNCT
iajs-2149	31	10	and	and	CCONJ
iajs-2149	31	11	is	be	AUX
iajs-2149	31	12	a	a	DET
iajs-2149	31	13	submodule	submodule	NOUN
iajs-2149	31	14	of	of	ADP
iajs-2149	31	15	with	with	ADP
iajs-2149	31	16	and	and	CCONJ
iajs-2149	31	17	and	and	CCONJ
iajs-2149	31	18	.	.	PUNCT
iajs-2149	32	1	thus	thus	ADV
iajs-2149	32	2	,	,	PUNCT
iajs-2149	32	3	there	there	PRON
iajs-2149	32	4	exists	exist	VERB
iajs-2149	32	5	and	and	CCONJ
iajs-2149	32	6	and	and	CCONJ
iajs-2149	32	7	such	such	ADJ
iajs-2149	32	8	that	that	PRON
iajs-2149	32	9	and	and	CCONJ
iajs-2149	32	10	and	and	CCONJ
iajs-2149	32	11	.	.	PUNCT
iajs-2149	33	1	but	but	CCONJ
iajs-2149	33	2	,	,	PUNCT
iajs-2149	33	3	and	and	CCONJ
iajs-2149	33	4	k	k	PROPN
iajs-2149	33	5	is	be	AUX
iajs-2149	33	6	a	a	DET
iajs-2149	33	7	pseudo	pseudo	NOUN
iajs-2149	33	8	quasi2	quasi2	NOUN
iajs-2149	33	9	-	-	PUNCT
iajs-2149	33	10	absorbing	absorb	VERB
iajs-2149	33	11	submodule	submodule	NOUN
iajs-2149	33	12	of	of	ADP
iajs-2149	33	13	,	,	PUNCT
iajs-2149	33	14	with	with	ADP
iajs-2149	33	15	,	,	PUNCT
iajs-2149	33	16	then	then	ADV
iajs-2149	33	17	we	we	PRON
iajs-2149	33	18	have	have	VERB
iajs-2149	33	19	or	or	CCONJ
iajs-2149	33	20	.	.	PUNCT
iajs-2149	34	1	again	again	ADV
iajs-2149	34	2	and	and	CCONJ
iajs-2149	34	3	,	,	PUNCT
iajs-2149	34	4	implies	imply	VERB
iajs-2149	34	5	that	that	SCONJ
iajs-2149	34	6	either	either	CCONJ
iajs-2149	34	7	or	or	CCONJ
iajs-2149	34	8	.	.	PUNCT
iajs-2149	35	1	also	also	ADV
iajs-2149	35	2	,	,	PUNCT
iajs-2149	35	3	and	and	CCONJ
iajs-2149	35	4	,	,	PUNCT
iajs-2149	35	5	implies	imply	VERB
iajs-2149	35	6	that	that	SCONJ
iajs-2149	35	7	either	either	CCONJ
iajs-2149	35	8	or	or	CCONJ
iajs-2149	35	9	.	.	PUNCT
iajs-2149	36	1	thus	thus	ADV
iajs-2149	36	2	either	either	CCONJ
iajs-2149	36	3	or	or	CCONJ
iajs-2149	36	4	or	or	CCONJ
iajs-2149	36	5	.	.	PUNCT
iajs-2149	36	6	suppose	suppose	VERB
iajs-2149	36	7	that	that	SCONJ
iajs-2149	36	8	,	,	PUNCT
iajs-2149	36	9	where	where	SCONJ
iajs-2149	36	10	then	then	ADV
iajs-2149	36	11	,	,	PUNCT
iajs-2149	36	12	so	so	ADV
iajs-2149	36	13	by	by	ADP
iajs-2149	36	14	hypothesis	hypothesis	NOUN
iajs-2149	36	15	,	,	PUNCT
iajs-2149	36	16	either	either	ADV
iajs-2149	36	17	or	or	CCONJ
iajs-2149	36	18	or	or	CCONJ
iajs-2149	36	19	.	.	PUNCT
iajs-2149	37	1	thus	thus	ADV
iajs-2149	37	2	either	either	CCONJ
iajs-2149	37	3	or	or	CCONJ
iajs-2149	37	4	or	or	CCONJ
iajs-2149	37	5	.	.	PUNCT
iajs-2149	38	1	hence	hence	ADV
iajs-2149	38	2	is	be	AUX
iajs-2149	38	3	a	a	DET
iajs-2149	38	4	pseudo	pseudo	NOUN
iajs-2149	38	5	quasi-2	quasi-2	NOUN
iajs-2149	38	6	-	-	PUNCT
iajs-2149	38	7	absorbing	absorbing	ADJ
iajs-2149	38	8	submodule	submodule	NOUN
iajs-2149	38	9	of	of	ADP
iajs-2149	38	10	.	.	PUNCT
iajs-2149	39	1	as	as	ADP
iajs-2149	39	2	a	a	DET
iajs-2149	39	3	direct	direct	ADJ
iajs-2149	39	4	consequence	consequence	NOUN
iajs-2149	39	5	of	of	ADP
iajs-2149	39	6	proposition	proposition	NOUN
iajs-2149	39	7	(	(	PUNCT
iajs-2149	39	8	2	2	X
iajs-2149	39	9	)	)	PUNCT
iajs-2149	39	10	we	we	PRON
iajs-2149	39	11	get	get	VERB
iajs-2149	39	12	the	the	DET
iajs-2149	39	13	following	follow	VERB
iajs-2149	39	14	result	result	NOUN
iajs-2149	39	15	.	.	PUNCT
iajs-2149	40	1	111	111	NUM
iajs-2149	40	2	ibn	ibn	PROPN
iajs-2149	40	3	al	al	PROPN
iajs-2149	40	4	-	-	PUNCT
iajs-2149	40	5	haitham	haitham	PROPN
iajs-2149	40	6	jour	jour	X
iajs-2149	40	7	.	.	PROPN
iajs-2149	40	8	for	for	ADP
iajs-2149	40	9	pure	pure	ADJ
iajs-2149	40	10	&	&	CCONJ
iajs-2149	40	11	appl	appl	PROPN
iajs-2149	40	12	.	.	PUNCT
iajs-2149	41	1	sci	sci	PROPN
iajs-2149	41	2	.	.	PROPN
iajs-2149	41	3	32	32	NUM
iajs-2149	41	4	(	(	PUNCT
iajs-2149	41	5	2	2	NUM
iajs-2149	41	6	)	)	SYM
iajs-2149	41	7	2019	2019	NUM
iajs-2149	41	8	corollary	corollary	NOUN
iajs-2149	41	9	(	(	PUNCT
iajs-2149	41	10	3	3	X
iajs-2149	41	11	)	)	PUNCT
iajs-2149	41	12	let	let	AUX
iajs-2149	41	13	be	be	AUX
iajs-2149	41	14	an	an	DET
iajs-2149	41	15	-module	-module	NOUN
iajs-2149	41	16	,	,	PUNCT
iajs-2149	41	17	and	and	CCONJ
iajs-2149	41	18	is	be	AUX
iajs-2149	41	19	a	a	DET
iajs-2149	41	20	submodule	submodule	NOUN
iajs-2149	41	21	of	of	ADP
iajs-2149	41	22	.	.	PUNCT
iajs-2149	42	1	then	then	ADV
iajs-2149	42	2	is	be	AUX
iajs-2149	42	3	a	a	DET
iajs-2149	42	4	pseudo	pseudo	NOUN
iajs-2149	42	5	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	42	6	submodule	submodule	NOUN
iajs-2149	42	7	of	of	ADP
iajs-2149	42	8	if	if	SCONJ
iajs-2149	43	1	and	and	CCONJ
iajs-2149	43	2	only	only	ADV
iajs-2149	43	3	if	if	SCONJ
iajs-2149	43	4	for	for	ADP
iajs-2149	43	5	each	each	PRON
iajs-2149	43	6	and	and	CCONJ
iajs-2149	43	7	for	for	ADP
iajs-2149	43	8	each	each	DET
iajs-2149	43	9	submodule	submodule	NOUN
iajs-2149	43	10	of	of	ADP
iajs-2149	43	11	with	with	ADP
iajs-2149	43	12	,	,	PUNCT
iajs-2149	43	13	implies	imply	VERB
iajs-2149	43	14	that	that	SCONJ
iajs-2149	43	15	either	either	CCONJ
iajs-2149	43	16	or	or	CCONJ
iajs-2149	43	17	or	or	CCONJ
iajs-2149	43	18	.	.	PUNCT
iajs-2149	44	1	remarks	remark	NOUN
iajs-2149	44	2	and	and	CCONJ
iajs-2149	44	3	examples	example	NOUN
iajs-2149	44	4	(	(	PUNCT
iajs-2149	44	5	4	4	X
iajs-2149	44	6	)	)	PUNCT
iajs-2149	44	7	1it	1it	NOUN
iajs-2149	44	8	is	be	AUX
iajs-2149	44	9	clear	clear	ADJ
iajs-2149	44	10	that	that	SCONJ
iajs-2149	44	11	every	every	DET
iajs-2149	44	12	quasi	quasi	ADJ
iajs-2149	44	13	-	-	ADJ
iajs-2149	44	14	prime	prime	ADJ
iajs-2149	44	15	submodule	submodule	NOUN
iajs-2149	44	16	of	of	ADP
iajs-2149	44	17	an	an	DET
iajs-2149	44	18	-module	-module	NOUN
iajs-2149	44	19	is	be	AUX
iajs-2149	44	20	a	a	DET
iajs-2149	44	21	pseudo	pseudo	NOUN
iajs-2149	44	22	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	44	23	submodule	submodule	NOUN
iajs-2149	44	24	of	of	ADP
iajs-2149	44	25	,	,	PUNCT
iajs-2149	44	26	while	while	SCONJ
iajs-2149	44	27	the	the	DET
iajs-2149	44	28	converse	converse	NOUN
iajs-2149	44	29	is	be	AUX
iajs-2149	44	30	not	not	PART
iajs-2149	44	31	true	true	ADJ
iajs-2149	44	32	in	in	ADP
iajs-2149	44	33	general	general	ADJ
iajs-2149	44	34	.	.	PUNCT
iajs-2149	45	1	for	for	ADP
iajs-2149	45	2	the	the	DET
iajs-2149	45	3	converse	converse	NOUN
iajs-2149	45	4	consider	consider	VERB
iajs-2149	45	5	the	the	DET
iajs-2149	45	6	following	follow	VERB
iajs-2149	45	7	example	example	NOUN
iajs-2149	45	8	:	:	PUNCT
iajs-2149	45	9	in	in	ADP
iajs-2149	45	10	the	the	DET
iajs-2149	45	11	-module	-module	NOUN
iajs-2149	45	12	,	,	PUNCT
iajs-2149	45	13	the	the	DET
iajs-2149	45	14	submodule	submodule	NOUN
iajs-2149	45	15	〈	〈	PROPN
iajs-2149	45	16	̅	̅	NOUN
iajs-2149	45	17	〉	〉	NOUN
iajs-2149	45	18	is	be	AUX
iajs-2149	45	19	pseudo	pseudo	NOUN
iajs-2149	45	20	quasi-2	quasi-2	NOUN
iajs-2149	45	21	-	-	PUNCT
iajs-2149	45	22	absorbing	absorbing	ADJ
iajs-2149	45	23	,	,	PUNCT
iajs-2149	45	24	but	but	CCONJ
iajs-2149	45	25	not	not	PART
iajs-2149	45	26	quasiprime	quasiprime	ADJ
iajs-2149	45	27	since	since	SCONJ
iajs-2149	45	28	̅	̅	NOUN
iajs-2149	45	29	〈	〈	PRON
iajs-2149	45	30	̅	̅	NOUN
iajs-2149	45	31	〉	〉	NOUN
iajs-2149	45	32	,	,	PUNCT
iajs-2149	45	33	but	but	CCONJ
iajs-2149	45	34	̅	̅	NOUN
iajs-2149	45	35	〈	〈	PRON
iajs-2149	45	36	̅	̅	NOUN
iajs-2149	45	37	〉	〉	NOUN
iajs-2149	45	38	.	.	PUNCT
iajs-2149	46	1	since	since	SCONJ
iajs-2149	46	2	〈	〈	PROPN
iajs-2149	46	3	̅	̅	NOUN
iajs-2149	46	4	〉	〉	NOUN
iajs-2149	46	5	,	,	PUNCT
iajs-2149	46	6	it	it	PRON
iajs-2149	46	7	is	be	AUX
iajs-2149	46	8	clear	clear	ADJ
iajs-2149	46	9	that	that	SCONJ
iajs-2149	46	10	for	for	ADP
iajs-2149	46	11	each	each	PRON
iajs-2149	46	12	and	and	CCONJ
iajs-2149	46	13	,	,	PUNCT
iajs-2149	46	14	if	if	SCONJ
iajs-2149	46	15	〈	〈	PROPN
iajs-2149	46	16	̅	̅	NOUN
iajs-2149	46	17	〉	〉	NOUN
iajs-2149	46	18	,	,	PUNCT
iajs-2149	46	19	implies	imply	VERB
iajs-2149	46	20	that	that	SCONJ
iajs-2149	46	21	either	either	CCONJ
iajs-2149	46	22	〈	〈	PROPN
iajs-2149	46	23	̅	̅	NOUN
iajs-2149	46	24	〉	〉	NOUN
iajs-2149	46	25	or	or	CCONJ
iajs-2149	46	26	〈	〈	NOUN
iajs-2149	46	27	̅	̅	NOUN
iajs-2149	46	28	〉	〉	NOUN
iajs-2149	46	29	or	or	CCONJ
iajs-2149	46	30	[	[	X
iajs-2149	46	31	〈	〈	NOUN
iajs-2149	46	32	̅	̅	NOUN
iajs-2149	46	33	〉	〉	NOUN
iajs-2149	46	34	]	]	PUNCT
iajs-2149	46	35	.	.	PUNCT
iajs-2149	47	1	2it	2it	NOUN
iajs-2149	47	2	is	be	AUX
iajs-2149	47	3	clear	clear	ADJ
iajs-2149	47	4	that	that	SCONJ
iajs-2149	47	5	every	every	DET
iajs-2149	47	6	prime	prime	ADJ
iajs-2149	47	7	submodule	submodule	NOUN
iajs-2149	47	8	of	of	ADP
iajs-2149	47	9	an	an	DET
iajs-2149	47	10	-module	-module	NOUN
iajs-2149	47	11	is	be	AUX
iajs-2149	47	12	a	a	DET
iajs-2149	47	13	pseudo	pseudo	NOUN
iajs-2149	47	14	quasi-2	quasi-2	NOUN
iajs-2149	47	15	-	-	PUNCT
iajs-2149	47	16	absorbing	absorbing	ADJ
iajs-2149	47	17	submodule	submodule	NOUN
iajs-2149	47	18	of	of	ADP
iajs-2149	47	19	,	,	PUNCT
iajs-2149	47	20	while	while	SCONJ
iajs-2149	47	21	the	the	DET
iajs-2149	47	22	converse	converse	NOUN
iajs-2149	47	23	is	be	AUX
iajs-2149	47	24	not	not	PART
iajs-2149	47	25	true	true	ADJ
iajs-2149	47	26	in	in	ADP
iajs-2149	47	27	general	general	ADJ
iajs-2149	47	28	.	.	PUNCT
iajs-2149	48	1	for	for	ADP
iajs-2149	48	2	the	the	DET
iajs-2149	48	3	converse	converse	NOUN
iajs-2149	48	4	see	see	VERB
iajs-2149	48	5	the	the	DET
iajs-2149	48	6	following	follow	VERB
iajs-2149	48	7	example	example	NOUN
iajs-2149	48	8	:	:	PUNCT
iajs-2149	48	9	in	in	ADP
iajs-2149	48	10	the	the	DET
iajs-2149	48	11	-module	-module	NOUN
iajs-2149	48	12	,	,	PUNCT
iajs-2149	48	13	the	the	DET
iajs-2149	48	14	submodule	submodule	NOUN
iajs-2149	48	15	〈	〈	PROPN
iajs-2149	48	16	̅	̅	NOUN
iajs-2149	48	17	〉	〉	NOUN
iajs-2149	48	18	is	be	AUX
iajs-2149	48	19	pseudo	pseudo	NOUN
iajs-2149	48	20	quasi-2	quasi-2	NOUN
iajs-2149	48	21	-	-	PUNCT
iajs-2149	48	22	absorbing	absorbing	ADJ
iajs-2149	48	23	,	,	PUNCT
iajs-2149	48	24	but	but	CCONJ
iajs-2149	48	25	not	not	PART
iajs-2149	48	26	prime	prime	ADJ
iajs-2149	48	27	,	,	PUNCT
iajs-2149	48	28	since	since	SCONJ
iajs-2149	48	29	̅	̅	NOUN
iajs-2149	48	30	,	,	PUNCT
iajs-2149	48	31	but	but	CCONJ
iajs-2149	48	32	̅	̅	NOUN
iajs-2149	48	33	and	and	CCONJ
iajs-2149	48	34	[	[	PUNCT
iajs-2149	48	35	]	]	X
iajs-2149	48	36	.	.	PUNCT
iajs-2149	49	1	3it	3it	PROPN
iajs-2149	49	2	is	be	AUX
iajs-2149	49	3	clear	clear	ADJ
iajs-2149	49	4	that	that	SCONJ
iajs-2149	49	5	every	every	DET
iajs-2149	49	6	2	2	NUM
iajs-2149	49	7	-	-	PUNCT
iajs-2149	49	8	absorbing	absorb	VERB
iajs-2149	49	9	submodule	submodule	NOUN
iajs-2149	49	10	of	of	ADP
iajs-2149	49	11	an	an	DET
iajs-2149	49	12	-module	-module	NOUN
iajs-2149	49	13	is	be	AUX
iajs-2149	49	14	a	a	DET
iajs-2149	49	15	pseudo	pseudo	NOUN
iajs-2149	49	16	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	49	17	submodule	submodule	NOUN
iajs-2149	49	18	of	of	ADP
iajs-2149	49	19	,	,	PUNCT
iajs-2149	49	20	while	while	SCONJ
iajs-2149	49	21	the	the	DET
iajs-2149	49	22	converse	converse	NOUN
iajs-2149	49	23	is	be	AUX
iajs-2149	49	24	not	not	PART
iajs-2149	49	25	true	true	ADJ
iajs-2149	49	26	in	in	ADP
iajs-2149	49	27	general	general	ADJ
iajs-2149	49	28	.	.	PUNCT
iajs-2149	50	1	for	for	ADP
iajs-2149	50	2	the	the	DET
iajs-2149	50	3	converse	converse	NOUN
iajs-2149	50	4	see	see	VERB
iajs-2149	50	5	the	the	DET
iajs-2149	50	6	following	follow	VERB
iajs-2149	50	7	example	example	NOUN
iajs-2149	50	8	:	:	PUNCT
iajs-2149	50	9	in	in	ADP
iajs-2149	50	10	the	the	DET
iajs-2149	50	11	-module	-module	NOUN
iajs-2149	50	12	,	,	PUNCT
iajs-2149	50	13	the	the	DET
iajs-2149	50	14	submodule	submodule	NOUN
iajs-2149	50	15	〈	〈	PROPN
iajs-2149	50	16	̅	̅	NOUN
iajs-2149	50	17	〉	〉	NOUN
iajs-2149	50	18	is	be	AUX
iajs-2149	50	19	pseudo	pseudo	NOUN
iajs-2149	50	20	quasi-2	quasi-2	NOUN
iajs-2149	50	21	-	-	PUNCT
iajs-2149	50	22	absorbing	absorbing	ADJ
iajs-2149	50	23	,	,	PUNCT
iajs-2149	50	24	but	but	CCONJ
iajs-2149	50	25	not	not	PART
iajs-2149	50	26	2absorbing	2absorbing	NUM
iajs-2149	50	27	,	,	PUNCT
iajs-2149	50	28	since	since	SCONJ
iajs-2149	50	29	̅	̅	NOUN
iajs-2149	50	30	,	,	PUNCT
iajs-2149	50	31	but	but	CCONJ
iajs-2149	50	32	̅	̅	NOUN
iajs-2149	50	33	and	and	CCONJ
iajs-2149	50	34	̅	̅	NOUN
iajs-2149	50	35	and	and	CCONJ
iajs-2149	50	36	[	[	PUNCT
iajs-2149	50	37	]	]	X
iajs-2149	50	38	.	.	PUNCT
iajs-2149	51	1	since	since	SCONJ
iajs-2149	51	2	〈	〈	PROPN
iajs-2149	51	3	̅	̅	NOUN
iajs-2149	51	4	〉	〉	NOUN
iajs-2149	51	5	,	,	PUNCT
iajs-2149	51	6	it	it	PRON
iajs-2149	51	7	is	be	AUX
iajs-2149	51	8	clear	clear	ADJ
iajs-2149	51	9	that	that	SCONJ
iajs-2149	51	10	for	for	ADP
iajs-2149	51	11	all	all	PRON
iajs-2149	51	12	and	and	CCONJ
iajs-2149	51	13	,	,	PUNCT
iajs-2149	51	14	if	if	SCONJ
iajs-2149	51	15	〈	〈	PROPN
iajs-2149	51	16	̅	̅	NOUN
iajs-2149	51	17	〉	〉	NOUN
iajs-2149	51	18	,	,	PUNCT
iajs-2149	51	19	implies	imply	VERB
iajs-2149	51	20	that	that	SCONJ
iajs-2149	51	21	either	either	CCONJ
iajs-2149	51	22	〈	〈	PROPN
iajs-2149	51	23	̅	̅	NOUN
iajs-2149	51	24	〉	〉	NOUN
iajs-2149	51	25	or	or	CCONJ
iajs-2149	51	26	〈	〈	NOUN
iajs-2149	51	27	̅	̅	NOUN
iajs-2149	51	28	〉	〉	NOUN
iajs-2149	51	29	or	or	CCONJ
iajs-2149	51	30	〈	〈	NOUN
iajs-2149	51	31	̅	̅	NOUN
iajs-2149	51	32	〉	〉	NOUN
iajs-2149	51	33	.	.	PUNCT
iajs-2149	52	1	4it	4it	NOUN
iajs-2149	52	2	is	be	AUX
iajs-2149	52	3	clear	clear	ADJ
iajs-2149	52	4	that	that	SCONJ
iajs-2149	52	5	every	every	DET
iajs-2149	52	6	quasi-2	quasi-2	NUM
iajs-2149	52	7	-	-	PUNCT
iajs-2149	52	8	absorbing	absorbing	ADJ
iajs-2149	52	9	submodule	submodule	NOUN
iajs-2149	52	10	of	of	ADP
iajs-2149	52	11	an	an	DET
iajs-2149	52	12	-module	-module	NOUN
iajs-2149	52	13	is	be	AUX
iajs-2149	52	14	a	a	DET
iajs-2149	52	15	pseudo	pseudo	NOUN
iajs-2149	52	16	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	52	17	submodule	submodule	NOUN
iajs-2149	52	18	of	of	ADP
iajs-2149	52	19	,	,	PUNCT
iajs-2149	52	20	while	while	SCONJ
iajs-2149	52	21	the	the	DET
iajs-2149	52	22	converse	converse	NOUN
iajs-2149	52	23	is	be	AUX
iajs-2149	52	24	not	not	PART
iajs-2149	52	25	true	true	ADJ
iajs-2149	52	26	in	in	ADP
iajs-2149	52	27	general	general	ADJ
iajs-2149	52	28	.	.	PUNCT
iajs-2149	53	1	for	for	ADP
iajs-2149	53	2	the	the	DET
iajs-2149	53	3	converse	converse	NOUN
iajs-2149	53	4	see	see	VERB
iajs-2149	53	5	the	the	DET
iajs-2149	53	6	following	follow	VERB
iajs-2149	53	7	example	example	NOUN
iajs-2149	53	8	:	:	PUNCT
iajs-2149	53	9	in	in	ADP
iajs-2149	53	10	the	the	DET
iajs-2149	53	11	-module	-module	NOUN
iajs-2149	53	12	,	,	PUNCT
iajs-2149	53	13	the	the	DET
iajs-2149	53	14	submodule	submodule	NOUN
iajs-2149	53	15	〈	〈	PROPN
iajs-2149	53	16	̅	̅	NOUN
iajs-2149	53	17	〉	〉	NOUN
iajs-2149	53	18	is	be	AUX
iajs-2149	53	19	pseudo	pseudo	NOUN
iajs-2149	53	20	quasi-2	quasi-2	NOUN
iajs-2149	53	21	-	-	PUNCT
iajs-2149	53	22	absorbing	absorbing	ADJ
iajs-2149	53	23	,	,	PUNCT
iajs-2149	53	24	but	but	CCONJ
iajs-2149	53	25	not	not	PART
iajs-2149	53	26	quasi	quasi	VERB
iajs-2149	53	27	2	2	NUM
iajs-2149	53	28	-	-	ADJ
iajs-2149	53	29	absorbing	absorbing	ADJ
iajs-2149	53	30	,	,	PUNCT
iajs-2149	53	31	since	since	SCONJ
iajs-2149	53	32	̅	̅	NOUN
iajs-2149	53	33	,	,	PUNCT
iajs-2149	53	34	but	but	CCONJ
iajs-2149	53	35	̅	̅	NOUN
iajs-2149	53	36	and	and	CCONJ
iajs-2149	53	37	̅	̅	NOUN
iajs-2149	53	38	and	and	CCONJ
iajs-2149	53	39	̅	̅	NOUN
iajs-2149	53	40	.	.	PUNCT
iajs-2149	54	1	since	since	SCONJ
iajs-2149	54	2	〈	〈	PROPN
iajs-2149	54	3	̅	̅	NOUN
iajs-2149	54	4	〉	〉	NOUN
iajs-2149	54	5	,	,	PUNCT
iajs-2149	54	6	it	it	PRON
iajs-2149	54	7	is	be	AUX
iajs-2149	54	8	clear	clear	ADJ
iajs-2149	54	9	that	that	PRON
iajs-2149	54	10	is	be	AUX
iajs-2149	54	11	a	a	DET
iajs-2149	54	12	pseudo	pseudo	NOUN
iajs-2149	54	13	quasi-2	quasi-2	NOUN
iajs-2149	54	14	-	-	PUNCT
iajs-2149	54	15	absorbing	absorbing	ADJ
iajs-2149	54	16	submodule	submodule	NOUN
iajs-2149	54	17	of	of	ADP
iajs-2149	54	18	.	.	PUNCT
iajs-2149	55	1	proposition	proposition	NOUN
iajs-2149	55	2	(	(	PUNCT
iajs-2149	55	3	5	5	X
iajs-2149	55	4	)	)	PUNCT
iajs-2149	55	5	let	let	AUX
iajs-2149	55	6	be	be	AUX
iajs-2149	55	7	an	an	DET
iajs-2149	55	8	-module	-module	NOUN
iajs-2149	55	9	,	,	PUNCT
iajs-2149	55	10	and	and	CCONJ
iajs-2149	55	11	is	be	AUX
iajs-2149	55	12	a	a	DET
iajs-2149	55	13	proper	proper	ADJ
iajs-2149	55	14	submodule	submodule	NOUN
iajs-2149	55	15	of	of	ADP
iajs-2149	55	16	,	,	PUNCT
iajs-2149	55	17	with	with	SCONJ
iajs-2149	55	18	[	[	PUNCT
iajs-2149	55	19	]	]	X
iajs-2149	55	20	is	be	AUX
iajs-2149	55	21	2absorbing	2absorbing	NUM
iajs-2149	55	22	ideal	ideal	NOUN
iajs-2149	55	23	of	of	ADP
iajs-2149	55	24	for	for	ADP
iajs-2149	55	25	each	each	PRON
iajs-2149	55	26	.then	.then	PRON
iajs-2149	55	27	is	be	AUX
iajs-2149	55	28	a	a	DET
iajs-2149	55	29	pseudo	pseudo	NOUN
iajs-2149	55	30	quasi-2	quasi-2	NOUN
iajs-2149	55	31	-	-	PUNCT
iajs-2149	55	32	absorbing	absorbing	ADJ
iajs-2149	55	33	submodule	submodule	NOUN
iajs-2149	55	34	of	of	ADP
iajs-2149	55	35	.	.	PUNCT
iajs-2149	56	1	proof	proof	NOUN
iajs-2149	56	2	assume	assume	VERB
iajs-2149	56	3	that	that	SCONJ
iajs-2149	56	4	,	,	PUNCT
iajs-2149	56	5	where	where	SCONJ
iajs-2149	56	6	.	.	PUNCT
iajs-2149	57	1	since	since	SCONJ
iajs-2149	57	2	,	,	PUNCT
iajs-2149	57	3	implies	imply	VERB
iajs-2149	57	4	that	that	SCONJ
iajs-2149	57	5	[	[	X
iajs-2149	57	6	]	]	X
iajs-2149	57	7	.	.	PUNCT
iajs-2149	58	1	but	but	CCONJ
iajs-2149	58	2	[	[	PUNCT
iajs-2149	58	3	]	]	X
iajs-2149	58	4	is	be	AUX
iajs-2149	58	5	a	a	DET
iajs-2149	58	6	2	2	NUM
iajs-2149	58	7	-	-	PUNCT
iajs-2149	58	8	absorbing	absorbing	ADJ
iajs-2149	58	9	ideal	ideal	NOUN
iajs-2149	58	10	of	of	ADP
iajs-2149	58	11	,	,	PUNCT
iajs-2149	58	12	then	then	ADV
iajs-2149	58	13	either	either	CCONJ
iajs-2149	58	14	[	[	PUNCT
iajs-2149	58	15	]	]	X
iajs-2149	58	16	or	or	CCONJ
iajs-2149	58	17	[	[	PUNCT
iajs-2149	58	18	]	]	X
iajs-2149	58	19	or	or	CCONJ
iajs-2149	58	20	[	[	PUNCT
iajs-2149	58	21	]	]	X
iajs-2149	58	22	.	.	PUNCT
iajs-2149	59	1	that	that	PRON
iajs-2149	59	2	is	be	AUX
iajs-2149	59	3	either	either	PRON
iajs-2149	59	4	or	or	CCONJ
iajs-2149	59	5	or	or	CCONJ
iajs-2149	59	6	.	.	PUNCT
iajs-2149	60	1	hence	hence	ADV
iajs-2149	60	2	is	be	AUX
iajs-2149	60	3	a	a	DET
iajs-2149	60	4	pseudo	pseudo	NOUN
iajs-2149	60	5	quasi2	quasi2	NOUN
iajs-2149	60	6	-	-	PUNCT
iajs-2149	60	7	absorbing	absorb	VERB
iajs-2149	60	8	submodule	submodule	NOUN
iajs-2149	60	9	of	of	ADP
iajs-2149	60	10	.	.	PUNCT
iajs-2149	61	1	proposition	proposition	NOUN
iajs-2149	61	2	(	(	PUNCT
iajs-2149	61	3	6	6	X
iajs-2149	61	4	)	)	PUNCT
iajs-2149	61	5	let	let	AUX
iajs-2149	61	6	be	be	AUX
iajs-2149	61	7	an	an	DET
iajs-2149	61	8	-module	-module	NOUN
iajs-2149	61	9	and	and	CCONJ
iajs-2149	61	10	is	be	AUX
iajs-2149	61	11	a	a	DET
iajs-2149	61	12	pseudo	pseudo	NOUN
iajs-2149	61	13	quasi-2	quasi-2	NOUN
iajs-2149	61	14	-	-	PUNCT
iajs-2149	61	15	absorbing	absorbing	ADJ
iajs-2149	61	16	submodule	submodule	NOUN
iajs-2149	61	17	of	of	ADP
iajs-2149	61	18	,	,	PUNCT
iajs-2149	61	19	with	with	ADP
iajs-2149	61	20	.	.	PUNCT
iajs-2149	62	1	then	then	ADV
iajs-2149	62	2	[	[	PUNCT
iajs-2149	62	3	]	]	X
iajs-2149	62	4	is	be	AUX
iajs-2149	62	5	2	2	NUM
iajs-2149	62	6	-	-	PUNCT
iajs-2149	62	7	absorbing	absorbing	ADJ
iajs-2149	62	8	(	(	PUNCT
iajs-2149	62	9	hence	hence	ADV
iajs-2149	62	10	a	a	DET
iajs-2149	62	11	pseudo	pseudo	NOUN
iajs-2149	62	12	quasi-2	quasi-2	NOUN
iajs-2149	62	13	-	-	PUNCT
iajs-2149	62	14	absorbing	absorbing	ADJ
iajs-2149	62	15	)	)	PUNCT
iajs-2149	62	16	ideal	ideal	NOUN
iajs-2149	62	17	of	of	ADP
iajs-2149	62	18	.	.	PUNCT
iajs-2149	63	1	111	111	NUM
iajs-2149	63	2	ibn	ibn	PROPN
iajs-2149	63	3	al	al	PROPN
iajs-2149	63	4	-	-	PUNCT
iajs-2149	63	5	haitham	haitham	PROPN
iajs-2149	63	6	jour	jour	X
iajs-2149	63	7	.	.	PROPN
iajs-2149	63	8	for	for	ADP
iajs-2149	63	9	pure	pure	ADJ
iajs-2149	63	10	&	&	CCONJ
iajs-2149	63	11	appl	appl	PROPN
iajs-2149	63	12	.	.	PUNCT
iajs-2149	64	1	sci	sci	PROPN
iajs-2149	64	2	.	.	PROPN
iajs-2149	64	3	32	32	NUM
iajs-2149	64	4	(	(	PUNCT
iajs-2149	64	5	2	2	NUM
iajs-2149	64	6	)	)	PUNCT
iajs-2149	64	7	2019	2019	NUM
iajs-2149	64	8	proof	proof	NOUN
iajs-2149	64	9	let	let	VERB
iajs-2149	64	10	[	[	PUNCT
iajs-2149	64	11	]	]	X
iajs-2149	64	12	,	,	PUNCT
iajs-2149	64	13	where	where	SCONJ
iajs-2149	64	14	,	,	PUNCT
iajs-2149	64	15	then	then	ADV
iajs-2149	64	16	,	,	PUNCT
iajs-2149	64	17	it	it	PRON
iajs-2149	64	18	follows	follow	VERB
iajs-2149	64	19	that	that	SCONJ
iajs-2149	64	20	for	for	ADP
iajs-2149	64	21	all	all	PRON
iajs-2149	64	22	.	.	PUNCT
iajs-2149	65	1	but	but	CCONJ
iajs-2149	65	2	is	be	AUX
iajs-2149	65	3	a	a	DET
iajs-2149	65	4	pseudo	pseudo	NOUN
iajs-2149	65	5	quasi-2	quasi-2	NOUN
iajs-2149	65	6	-	-	PUNCT
iajs-2149	65	7	absorbing	absorbing	ADJ
iajs-2149	65	8	submodule	submodule	NOUN
iajs-2149	65	9	of	of	ADP
iajs-2149	65	10	,	,	PUNCT
iajs-2149	65	11	implies	imply	VERB
iajs-2149	65	12	that	that	SCONJ
iajs-2149	65	13	either	either	CCONJ
iajs-2149	65	14	or	or	CCONJ
iajs-2149	65	15	or	or	CCONJ
iajs-2149	65	16	.	.	PUNCT
iajs-2149	66	1	but	but	CCONJ
iajs-2149	66	2	,	,	PUNCT
iajs-2149	66	3	implies	imply	VERB
iajs-2149	66	4	that	that	PRON
iajs-2149	66	5	.	.	PUNCT
iajs-2149	67	1	that	that	PRON
iajs-2149	67	2	is	be	AUX
iajs-2149	67	3	either	either	PRON
iajs-2149	67	4	or	or	CCONJ
iajs-2149	67	5	or	or	CCONJ
iajs-2149	67	6	for	for	ADP
iajs-2149	67	7	all	all	PRON
iajs-2149	67	8	.	.	PUNCT
iajs-2149	68	1	hence	hence	ADV
iajs-2149	68	2	either	either	ADV
iajs-2149	68	3	or	or	CCONJ
iajs-2149	68	4	or	or	CCONJ
iajs-2149	68	5	.	.	PUNCT
iajs-2149	69	1	thus	thus	ADV
iajs-2149	69	2	either	either	CCONJ
iajs-2149	69	3	[	[	PUNCT
iajs-2149	69	4	]	]	X
iajs-2149	69	5	or	or	CCONJ
iajs-2149	69	6	[	[	PUNCT
iajs-2149	69	7	]	]	X
iajs-2149	69	8	or	or	CCONJ
iajs-2149	69	9	[	[	PUNCT
iajs-2149	69	10	]	]	X
iajs-2149	69	11	.	.	PUNCT
iajs-2149	70	1	that	that	PRON
iajs-2149	70	2	is	be	AUX
iajs-2149	70	3	[	[	PUNCT
iajs-2149	70	4	]	]	X
iajs-2149	70	5	is	be	AUX
iajs-2149	70	6	2	2	NUM
iajs-2149	70	7	-	-	PUNCT
iajs-2149	70	8	absorbing	absorbing	ADJ
iajs-2149	70	9	ideal	ideal	NOUN
iajs-2149	70	10	of	of	ADP
iajs-2149	70	11	,	,	PUNCT
iajs-2149	70	12	hence	hence	ADV
iajs-2149	70	13	is	be	AUX
iajs-2149	70	14	a	a	DET
iajs-2149	70	15	pseudo	pseudo	NOUN
iajs-2149	70	16	quasi-2	quasi-2	NOUN
iajs-2149	70	17	-	-	PUNCT
iajs-2149	70	18	absorbing	absorbing	ADJ
iajs-2149	70	19	ideal	ideal	NOUN
iajs-2149	70	20	of	of	ADP
iajs-2149	70	21	.	.	PUNCT
iajs-2149	71	1	recall	recall	VERB
iajs-2149	71	2	that	that	SCONJ
iajs-2149	71	3	an	an	DET
iajs-2149	71	4	-module	-module	NOUN
iajs-2149	71	5	is	be	AUX
iajs-2149	71	6	called	call	VERB
iajs-2149	71	7	faithful	faithful	ADJ
iajs-2149	71	8	if	if	SCONJ
iajs-2149	71	9	[	[	PUNCT
iajs-2149	71	10	]	]	X
iajs-2149	71	11	.	.	PUNCT
iajs-2149	72	1	before	before	SCONJ
iajs-2149	72	2	we	we	PRON
iajs-2149	72	3	give	give	VERB
iajs-2149	72	4	the	the	DET
iajs-2149	72	5	converse	converse	NOUN
iajs-2149	72	6	of	of	ADP
iajs-2149	72	7	proposition	proposition	NOUN
iajs-2149	72	8	(	(	PUNCT
iajs-2149	72	9	2.6	2.6	NUM
iajs-2149	72	10	)	)	PUNCT
iajs-2149	72	11	,	,	PUNCT
iajs-2149	72	12	we	we	PRON
iajs-2149	72	13	recalled	recall	VERB
iajs-2149	72	14	the	the	DET
iajs-2149	72	15	following	follow	VERB
iajs-2149	72	16	lemmas	lemmas	PROPN
iajs-2149	72	17	.	.	PUNCT
iajs-2149	73	1	lemma	lemma	PROPN
iajs-2149	73	2	(	(	PUNCT
iajs-2149	73	3	7	7	NUM
iajs-2149	73	4	)	)	PUNCT
iajs-2149	73	5	[	[	PUNCT
iajs-2149	73	6	]	]	X
iajs-2149	73	7	.	.	PUNCT
iajs-2149	74	1	let	let	AUX
iajs-2149	74	2	be	be	AUX
iajs-2149	74	3	faithful	faithful	ADJ
iajs-2149	74	4	multiplication	multiplication	NOUN
iajs-2149	74	5	-module	-module	NOUN
iajs-2149	74	6	,	,	PUNCT
iajs-2149	74	7	then	then	ADV
iajs-2149	74	8	.	.	PUNCT
iajs-2149	75	1	proposition	proposition	NOUN
iajs-2149	75	2	(	(	PUNCT
iajs-2149	75	3	8)	8)	NUM
iajs-2149	75	4	let	let	VERB
iajs-2149	75	5	be	be	AUX
iajs-2149	75	6	a	a	DET
iajs-2149	75	7	faithful	faithful	ADJ
iajs-2149	75	8	multiplication	multiplication	NOUN
iajs-2149	75	9	-module	-module	NOUN
iajs-2149	75	10	and	and	CCONJ
iajs-2149	75	11	is	be	AUX
iajs-2149	75	12	a	a	DET
iajs-2149	75	13	proper	proper	ADJ
iajs-2149	75	14	submodule	submodule	NOUN
iajs-2149	75	15	of	of	ADP
iajs-2149	75	16	.	.	PUNCT
iajs-2149	76	1	if	if	SCONJ
iajs-2149	76	2	[	[	PUNCT
iajs-2149	76	3	]	]	X
iajs-2149	76	4	is	be	AUX
iajs-2149	76	5	a	a	DET
iajs-2149	76	6	pseudo	pseudo	NOUN
iajs-2149	76	7	quasi-2	quasi-2	NOUN
iajs-2149	76	8	-	-	PUNCT
iajs-2149	76	9	absorbing	absorbing	ADJ
iajs-2149	76	10	ideal	ideal	NOUN
iajs-2149	76	11	of	of	ADP
iajs-2149	76	12	,	,	PUNCT
iajs-2149	76	13	then	then	ADV
iajs-2149	76	14	is	be	AUX
iajs-2149	76	15	a	a	DET
iajs-2149	76	16	pseudo	pseudo	NOUN
iajs-2149	76	17	quasi-2	quasi-2	NOUN
iajs-2149	76	18	-	-	PUNCT
iajs-2149	76	19	absorbing	absorbing	ADJ
iajs-2149	76	20	submodule	submodule	NOUN
iajs-2149	76	21	of	of	ADP
iajs-2149	76	22	proof	proof	NOUN
iajs-2149	76	23	let	let	VERB
iajs-2149	76	24	with	with	ADP
iajs-2149	76	25	,	,	PUNCT
iajs-2149	76	26	then	then	ADV
iajs-2149	76	27	.	.	PUNCT
iajs-2149	77	1	but	but	CCONJ
iajs-2149	77	2	is	be	AUX
iajs-2149	77	3	a	a	DET
iajs-2149	77	4	multiplication	multiplication	NOUN
iajs-2149	77	5	,	,	PUNCT
iajs-2149	77	6	so	so	SCONJ
iajs-2149	77	7	for	for	ADP
iajs-2149	77	8	some	some	DET
iajs-2149	77	9	ideal	ideal	NOUN
iajs-2149	77	10	of	of	ADP
iajs-2149	77	11	.	.	PUNCT
iajs-2149	78	1	thus	thus	ADV
iajs-2149	78	2	,	,	PUNCT
iajs-2149	78	3	it	it	PRON
iajs-2149	78	4	follows	follow	VERB
iajs-2149	78	5	that	that	SCONJ
iajs-2149	78	6	[	[	X
iajs-2149	78	7	]	]	X
iajs-2149	78	8	.	.	PUNCT
iajs-2149	79	1	but	but	CCONJ
iajs-2149	79	2	[	[	PUNCT
iajs-2149	79	3	]	]	X
iajs-2149	79	4	is	be	AUX
iajs-2149	79	5	a	a	DET
iajs-2149	79	6	pseudo	pseudo	NOUN
iajs-2149	79	7	quasi-2	quasi-2	NOUN
iajs-2149	79	8	-	-	PUNCT
iajs-2149	79	9	absorbing	absorbing	ADJ
iajs-2149	79	10	ideal	ideal	NOUN
iajs-2149	79	11	of	of	ADP
iajs-2149	79	12	,	,	PUNCT
iajs-2149	79	13	then	then	ADV
iajs-2149	79	14	by	by	ADP
iajs-2149	79	15	corollary	corollary	ADJ
iajs-2149	79	16	(	(	PUNCT
iajs-2149	79	17	3	3	NUM
iajs-2149	79	18	)	)	PUNCT
iajs-2149	79	19	either	either	CCONJ
iajs-2149	79	20	[	[	PUNCT
iajs-2149	79	21	]	]	X
iajs-2149	79	22	or	or	CCONJ
iajs-2149	79	23	[	[	PUNCT
iajs-2149	79	24	]	]	X
iajs-2149	79	25	or	or	CCONJ
iajs-2149	79	26	[	[	PUNCT
iajs-2149	79	27	]	]	X
iajs-2149	79	28	.	.	PUNCT
iajs-2149	80	1	hence	hence	ADV
iajs-2149	80	2	either	either	CCONJ
iajs-2149	80	3	[	[	PUNCT
iajs-2149	80	4	]	]	X
iajs-2149	80	5	or	or	CCONJ
iajs-2149	80	6	[	[	PUNCT
iajs-2149	80	7	]	]	X
iajs-2149	80	8	or	or	CCONJ
iajs-2149	80	9	[	[	PUNCT
iajs-2149	80	10	]	]	X
iajs-2149	80	11	.	.	PUNCT
iajs-2149	81	1	but	but	CCONJ
iajs-2149	81	2	[	[	PUNCT
iajs-2149	81	3	]	]	X
iajs-2149	81	4	and	and	CCONJ
iajs-2149	81	5	by	by	ADP
iajs-2149	81	6	lemma	lemma	PROPN
iajs-2149	81	7	(	(	PUNCT
iajs-2149	81	8	7	7	NUM
iajs-2149	81	9	)	)	PUNCT
iajs-2149	81	10	.	.	PUNCT
iajs-2149	82	1	thus	thus	ADV
iajs-2149	82	2	,	,	PUNCT
iajs-2149	82	3	either	either	ADV
iajs-2149	82	4	or	or	CCONJ
iajs-2149	82	5	or	or	CCONJ
iajs-2149	82	6	.	.	PUNCT
iajs-2149	83	1	therefore	therefore	ADV
iajs-2149	83	2	is	be	AUX
iajs-2149	83	3	a	a	DET
iajs-2149	83	4	pseudo	pseudo	NOUN
iajs-2149	83	5	quasi-2	quasi-2	NOUN
iajs-2149	83	6	-	-	PUNCT
iajs-2149	83	7	absorbing	absorbing	ADJ
iajs-2149	83	8	submodule	submodule	NOUN
iajs-2149	83	9	of	of	ADP
iajs-2149	83	10	.	.	PUNCT
iajs-2149	84	1	recall	recall	VERB
iajs-2149	84	2	that	that	SCONJ
iajs-2149	84	3	an	an	DET
iajs-2149	84	4	-module	-module	NOUN
iajs-2149	84	5	is	be	AUX
iajs-2149	84	6	called	call	VERB
iajs-2149	84	7	singular	singular	ADJ
iajs-2149	84	8	module	module	NOUN
iajs-2149	84	9	provided	provide	VERB
iajs-2149	84	10	.	.	PUNCT
iajs-2149	85	1	at	at	ADP
iajs-2149	85	2	the	the	DET
iajs-2149	85	3	other	other	ADJ
iajs-2149	85	4	extreme	extreme	NOUN
iajs-2149	85	5	,	,	PUNCT
iajs-2149	85	6	we	we	PRON
iajs-2149	85	7	say	say	VERB
iajs-2149	85	8	that	that	PRON
iajs-2149	85	9	is	be	AUX
iajs-2149	85	10	non	non	ADJ
iajs-2149	85	11	-	-	ADJ
iajs-2149	85	12	singular	singular	ADJ
iajs-2149	85	13	module	module	NOUN
iajs-2149	85	14	provided	provide	VERB
iajs-2149	85	15	,	,	PUNCT
iajs-2149	85	16	where	where	SCONJ
iajs-2149	85	17	{	{	PUNCT
iajs-2149	85	18	}	}	PUNCT
iajs-2149	85	19	,	,	PUNCT
iajs-2149	85	20	where	where	SCONJ
iajs-2149	85	21	is	be	AUX
iajs-2149	85	22	the	the	DET
iajs-2149	85	23	set	set	NOUN
iajs-2149	85	24	of	of	ADP
iajs-2149	85	25	all	all	DET
iajs-2149	85	26	essential	essential	ADJ
iajs-2149	85	27	right	right	ADJ
iajs-2149	85	28	ideals	ideal	NOUN
iajs-2149	85	29	of	of	ADP
iajs-2149	85	30	the	the	DET
iajs-2149	85	31	ring	ring	NOUN
iajs-2149	85	32	[	[	PUNCT
iajs-2149	85	33	]	]	X
iajs-2149	85	34	.	.	PUNCT
iajs-2149	86	1	lemma	lemma	PROPN
iajs-2149	86	2	(	(	PUNCT
iajs-2149	86	3	9	9	NUM
iajs-2149	86	4	)	)	PUNCT
iajs-2149	86	5	[	[	PUNCT
iajs-2149	86	6	]	]	X
iajs-2149	86	7	if	if	SCONJ
iajs-2149	86	8	is	be	AUX
iajs-2149	86	9	a	a	DET
iajs-2149	86	10	non	non	ADJ
iajs-2149	86	11	-	-	ADJ
iajs-2149	86	12	singular	singular	ADJ
iajs-2149	86	13	-module	-module	NOUN
iajs-2149	86	14	,	,	PUNCT
iajs-2149	86	15	then	then	ADV
iajs-2149	86	16	.	.	PUNCT
iajs-2149	87	1	proposition	proposition	NOUN
iajs-2149	87	2	(	(	PUNCT
iajs-2149	87	3	10	10	NUM
iajs-2149	87	4	)	)	PUNCT
iajs-2149	87	5	let	let	AUX
iajs-2149	87	6	be	be	AUX
iajs-2149	87	7	a	a	DET
iajs-2149	87	8	non	non	ADJ
iajs-2149	87	9	-	-	ADJ
iajs-2149	87	10	singular	singular	ADJ
iajs-2149	87	11	multiplication	multiplication	NOUN
iajs-2149	87	12	-module	-module	NOUN
iajs-2149	87	13	and	and	CCONJ
iajs-2149	87	14	is	be	AUX
iajs-2149	87	15	a	a	DET
iajs-2149	87	16	proper	proper	ADJ
iajs-2149	87	17	submodule	submodule	NOUN
iajs-2149	87	18	of	of	ADP
iajs-2149	87	19	.	.	PUNCT
iajs-2149	88	1	if	if	SCONJ
iajs-2149	88	2	[	[	PUNCT
iajs-2149	88	3	]	]	X
iajs-2149	88	4	is	be	AUX
iajs-2149	88	5	pseudo	pseudo	NOUN
iajs-2149	88	6	quasi-2	quasi-2	ADJ
iajs-2149	88	7	-	-	PUNCT
iajs-2149	88	8	absorbing	absorbing	ADJ
iajs-2149	88	9	ideal	ideal	NOUN
iajs-2149	88	10	of	of	ADP
iajs-2149	88	11	,	,	PUNCT
iajs-2149	88	12	then	then	ADV
iajs-2149	88	13	is	be	AUX
iajs-2149	88	14	a	a	DET
iajs-2149	88	15	pseudo	pseudo	NOUN
iajs-2149	88	16	quasi-2	quasi-2	NOUN
iajs-2149	88	17	-	-	PUNCT
iajs-2149	88	18	absorbing	absorbing	ADJ
iajs-2149	88	19	submodule	submodule	NOUN
iajs-2149	88	20	of	of	ADP
iajs-2149	88	21	.	.	PUNCT
iajs-2149	89	1	proof	proof	NOUN
iajs-2149	89	2	similarly	similarly	ADV
iajs-2149	89	3	,	,	PUNCT
iajs-2149	89	4	as	as	ADP
iajs-2149	89	5	in	in	ADP
iajs-2149	89	6	proposition	proposition	NOUN
iajs-2149	89	7	(	(	PUNCT
iajs-2149	89	8	6	6	NUM
iajs-2149	89	9	)	)	PUNCT
iajs-2149	89	10	,	,	PUNCT
iajs-2149	89	11	by	by	ADP
iajs-2149	89	12	using	use	VERB
iajs-2149	89	13	lemma	lemma	PROPN
iajs-2149	89	14	(	(	PUNCT
iajs-2149	89	15	9	9	NUM
iajs-2149	89	16	)	)	PUNCT
iajs-2149	89	17	.	.	PUNCT
iajs-2149	90	1	lemma	lemma	PROPN
iajs-2149	90	2	(	(	PUNCT
iajs-2149	90	3	11	11	NUM
iajs-2149	90	4	)	)	PUNCT
iajs-2149	90	5	[	[	PUNCT
iajs-2149	90	6	]	]	X
iajs-2149	90	7	.	.	PUNCT
iajs-2149	91	1	let	let	VERB
iajs-2149	91	2	and	and	CCONJ
iajs-2149	91	3	be	be	AUX
iajs-2149	91	4	ideals	ideal	NOUN
iajs-2149	91	5	of	of	ADP
iajs-2149	91	6	a	a	DET
iajs-2149	91	7	ring	ring	NOUN
iajs-2149	91	8	and	and	CCONJ
iajs-2149	91	9	is	be	AUX
iajs-2149	91	10	a	a	DET
iajs-2149	91	11	finitely	finitely	ADV
iajs-2149	91	12	generated	generate	VERB
iajs-2149	91	13	multiplication	multiplication	NOUN
iajs-2149	91	14	-module	-module	NOUN
iajs-2149	91	15	.	.	PUNCT
iajs-2149	92	1	then	then	ADV
iajs-2149	92	2	if	if	SCONJ
iajs-2149	92	3	and	and	CCONJ
iajs-2149	92	4	only	only	ADV
iajs-2149	92	5	if	if	SCONJ
iajs-2149	92	6	.	.	PUNCT
iajs-2149	93	1	proposition	proposition	NOUN
iajs-2149	93	2	(	(	PUNCT
iajs-2149	93	3	12	12	NUM
iajs-2149	93	4	)	)	PUNCT
iajs-2149	93	5	let	let	AUX
iajs-2149	93	6	be	be	AUX
iajs-2149	93	7	a	a	DET
iajs-2149	93	8	faithful	faithful	ADJ
iajs-2149	93	9	finitely	finitely	ADV
iajs-2149	93	10	generated	generate	VERB
iajs-2149	93	11	multiplication	multiplication	NOUN
iajs-2149	93	12	-module	-module	NOUN
iajs-2149	93	13	.	.	PUNCT
iajs-2149	94	1	if	if	SCONJ
iajs-2149	94	2	is	be	AUX
iajs-2149	94	3	a	a	DET
iajs-2149	94	4	pseudo	pseudo	NOUN
iajs-2149	94	5	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	94	6	ideal	ideal	NOUN
iajs-2149	94	7	of	of	ADP
iajs-2149	94	8	,	,	PUNCT
iajs-2149	94	9	then	then	ADV
iajs-2149	94	10	is	be	AUX
iajs-2149	94	11	a	a	DET
iajs-2149	94	12	pseudo	pseudo	NOUN
iajs-2149	94	13	quasi-2	quasi-2	NOUN
iajs-2149	94	14	-	-	PUNCT
iajs-2149	94	15	absorbing	absorbing	ADJ
iajs-2149	94	16	submodule	submodule	NOUN
iajs-2149	94	17	of	of	ADP
iajs-2149	94	18	.	.	PUNCT
iajs-2149	95	1	proof	proof	NOUN
iajs-2149	95	2	let	let	VERB
iajs-2149	95	3	,	,	PUNCT
iajs-2149	95	4	where	where	SCONJ
iajs-2149	95	5	,	,	PUNCT
iajs-2149	95	6	that	that	PRON
iajs-2149	95	7	is	be	AUX
iajs-2149	95	8	.	.	PUNCT
iajs-2149	96	1	but	but	CCONJ
iajs-2149	96	2	is	be	AUX
iajs-2149	96	3	a	a	DET
iajs-2149	96	4	multiplication	multiplication	NOUN
iajs-2149	96	5	,	,	PUNCT
iajs-2149	96	6	then	then	ADV
iajs-2149	96	7	for	for	ADP
iajs-2149	96	8	some	some	DET
iajs-2149	96	9	ideal	ideal	NOUN
iajs-2149	96	10	of	of	ADP
iajs-2149	96	11	.	.	PUNCT
iajs-2149	97	1	thus	thus	ADV
iajs-2149	97	2	,	,	PUNCT
iajs-2149	97	3	and	and	CCONJ
iajs-2149	97	4	so	so	ADV
iajs-2149	97	5	by	by	ADP
iajs-2149	97	6	lemma	lemma	PROPN
iajs-2149	97	7	(	(	PUNCT
iajs-2149	97	8	11	11	NUM
iajs-2149	97	9	)	)	PUNCT
iajs-2149	97	10	,	,	PUNCT
iajs-2149	97	11	,	,	PUNCT
iajs-2149	97	12	but	but	CCONJ
iajs-2149	97	13	is	be	AUX
iajs-2149	97	14	faithful	faithful	ADJ
iajs-2149	97	15	,	,	PUNCT
iajs-2149	97	16	then	then	ADV
iajs-2149	97	17	,	,	PUNCT
iajs-2149	97	18	hence	hence	ADV
iajs-2149	97	19	.	.	PUNCT
iajs-2149	98	1	but	but	CCONJ
iajs-2149	98	2	is	be	AUX
iajs-2149	98	3	a	a	DET
iajs-2149	98	4	pseudo	pseudo	NOUN
iajs-2149	98	5	quasi-2	quasi-2	NUM
iajs-2149	98	6	111	111	NUM
iajs-2149	98	7	ibn	ibn	PROPN
iajs-2149	98	8	al	al	PROPN
iajs-2149	98	9	-	-	PUNCT
iajs-2149	98	10	haitham	haitham	PROPN
iajs-2149	98	11	jour	jour	X
iajs-2149	98	12	.	.	PROPN
iajs-2149	99	1	for	for	ADP
iajs-2149	99	2	pure	pure	ADJ
iajs-2149	99	3	&	&	CCONJ
iajs-2149	99	4	appl	appl	PROPN
iajs-2149	99	5	.	.	PUNCT
iajs-2149	100	1	sci	sci	PROPN
iajs-2149	100	2	.	.	PROPN
iajs-2149	100	3	32	32	NUM
iajs-2149	100	4	(	(	PUNCT
iajs-2149	100	5	2	2	NUM
iajs-2149	100	6	)	)	PUNCT
iajs-2149	100	7	2019	2019	NUM
iajs-2149	100	8	absorbing	absorb	VERB
iajs-2149	100	9	ideal	ideal	NOUN
iajs-2149	100	10	of	of	ADP
iajs-2149	100	11	,	,	PUNCT
iajs-2149	100	12	then	then	ADV
iajs-2149	100	13	by	by	ADP
iajs-2149	100	14	corollary	corollary	ADJ
iajs-2149	100	15	(	(	PUNCT
iajs-2149	100	16	3	3	NUM
iajs-2149	100	17	)	)	PUNCT
iajs-2149	100	18	either	either	CCONJ
iajs-2149	100	19	or	or	CCONJ
iajs-2149	100	20	or	or	CCONJ
iajs-2149	100	21	.	.	PUNCT
iajs-2149	101	1	thus	thus	ADV
iajs-2149	101	2	either	either	CCONJ
iajs-2149	101	3	or	or	CCONJ
iajs-2149	101	4	or	or	CCONJ
iajs-2149	101	5	.	.	PUNCT
iajs-2149	102	1	but	but	CCONJ
iajs-2149	102	2	by	by	ADP
iajs-2149	102	3	lemma	lemma	PROPN
iajs-2149	102	4	(	(	PUNCT
iajs-2149	102	5	7	7	NUM
iajs-2149	102	6	)	)	PUNCT
iajs-2149	102	7	.	.	PUNCT
iajs-2149	103	1	hence	hence	ADV
iajs-2149	103	2	either	either	ADV
iajs-2149	103	3	or	or	CCONJ
iajs-2149	103	4	or	or	CCONJ
iajs-2149	103	5	,	,	PUNCT
iajs-2149	103	6	it	it	PRON
iajs-2149	103	7	follows	follow	VERB
iajs-2149	103	8	that	that	PRON
iajs-2149	103	9	or	or	CCONJ
iajs-2149	103	10	or	or	CCONJ
iajs-2149	103	11	.	.	PUNCT
iajs-2149	104	1	therefore	therefore	ADV
iajs-2149	104	2	is	be	AUX
iajs-2149	104	3	a	a	DET
iajs-2149	104	4	pseudo	pseudo	NOUN
iajs-2149	104	5	quasi-2	quasi-2	NOUN
iajs-2149	104	6	-	-	PUNCT
iajs-2149	104	7	absorbing	absorbing	ADJ
iajs-2149	104	8	submodule	submodule	NOUN
iajs-2149	104	9	of	of	ADP
iajs-2149	104	10	.	.	PUNCT
iajs-2149	105	1	by	by	ADP
iajs-2149	105	2	using	use	VERB
iajs-2149	105	3	lemma	lemma	PROPN
iajs-2149	105	4	(	(	PUNCT
iajs-2149	105	5	9	9	NUM
iajs-2149	105	6	)	)	PUNCT
iajs-2149	105	7	and	and	CCONJ
iajs-2149	105	8	lemma	lemma	PROPN
iajs-2149	105	9	(	(	PUNCT
iajs-2149	105	10	11	11	NUM
iajs-2149	105	11	)	)	PUNCT
iajs-2149	105	12	we	we	PRON
iajs-2149	105	13	get	get	VERB
iajs-2149	105	14	the	the	DET
iajs-2149	105	15	following	follow	VERB
iajs-2149	105	16	result	result	NOUN
iajs-2149	105	17	.	.	PUNCT
iajs-2149	106	1	proposition	proposition	NOUN
iajs-2149	106	2	(	(	PUNCT
iajs-2149	106	3	13	13	NUM
iajs-2149	106	4	)	)	PUNCT
iajs-2149	106	5	let	let	AUX
iajs-2149	106	6	be	be	AUX
iajs-2149	106	7	a	a	DET
iajs-2149	106	8	finitely	finitely	ADV
iajs-2149	106	9	generated	generate	VERB
iajs-2149	106	10	multiplication	multiplication	NOUN
iajs-2149	106	11	non	non	ADJ
iajs-2149	106	12	-	-	ADJ
iajs-2149	106	13	singular	singular	ADJ
iajs-2149	106	14	-module	-module	NOUN
iajs-2149	106	15	.	.	PUNCT
iajs-2149	107	1	if	if	SCONJ
iajs-2149	107	2	is	be	AUX
iajs-2149	107	3	a	a	DET
iajs-2149	107	4	pseudo	pseudo	NOUN
iajs-2149	107	5	quasi-2	quasi-2	NOUN
iajs-2149	107	6	-	-	PUNCT
iajs-2149	107	7	absorbing	absorbing	ADJ
iajs-2149	107	8	ideal	ideal	NOUN
iajs-2149	107	9	of	of	ADP
iajs-2149	107	10	with	with	ADP
iajs-2149	107	11	,	,	PUNCT
iajs-2149	107	12	then	then	ADV
iajs-2149	107	13	is	be	AUX
iajs-2149	107	14	a	a	DET
iajs-2149	107	15	pseudo	pseudo	NOUN
iajs-2149	107	16	quasi-2	quasi-2	NOUN
iajs-2149	107	17	-	-	PUNCT
iajs-2149	107	18	absorbing	absorbing	ADJ
iajs-2149	107	19	submodule	submodule	NOUN
iajs-2149	107	20	of	of	ADP
iajs-2149	107	21	.	.	PUNCT
iajs-2149	108	1	proof	proof	NOUN
iajs-2149	108	2	similar	similar	ADJ
iajs-2149	108	3	steps	step	NOUN
iajs-2149	108	4	of	of	ADP
iajs-2149	108	5	proposition	proposition	NOUN
iajs-2149	108	6	(	(	PUNCT
iajs-2149	108	7	12	12	NUM
iajs-2149	108	8	)	)	PUNCT
iajs-2149	108	9	.	.	PUNCT
iajs-2149	109	1	proposition	proposition	NOUN
iajs-2149	109	2	(	(	PUNCT
iajs-2149	109	3	14	14	NUM
iajs-2149	109	4	)	)	PUNCT
iajs-2149	109	5	let	let	AUX
iajs-2149	109	6	be	be	AUX
iajs-2149	109	7	an	an	DET
iajs-2149	109	8	-module	-module	NOUN
iajs-2149	109	9	and	and	CCONJ
iajs-2149	109	10	is	be	AUX
iajs-2149	109	11	a	a	DET
iajs-2149	109	12	proper	proper	ADJ
iajs-2149	109	13	submodule	submodule	NOUN
iajs-2149	109	14	of	of	ADP
iajs-2149	109	15	,	,	PUNCT
iajs-2149	109	16	with	with	ADP
iajs-2149	109	17	.then	.then	X
iajs-2149	109	18	is	be	AUX
iajs-2149	109	19	a	a	DET
iajs-2149	109	20	pseudo	pseudo	NOUN
iajs-2149	109	21	quasi-2	quasi-2	NOUN
iajs-2149	109	22	-	-	PUNCT
iajs-2149	109	23	absorbing	absorbing	ADJ
iajs-2149	109	24	submodule	submodule	NOUN
iajs-2149	109	25	of	of	ADP
iajs-2149	109	26	if	if	SCONJ
iajs-2149	109	27	and	and	CCONJ
iajs-2149	109	28	only	only	ADV
iajs-2149	109	29	if	if	SCONJ
iajs-2149	109	30	[	[	PUNCT
iajs-2149	109	31	]	]	X
iajs-2149	109	32	[	[	PUNCT
iajs-2149	109	33	]	]	X
iajs-2149	109	34	[	[	PUNCT
iajs-2149	109	35	]	]	X
iajs-2149	109	36	[	[	PUNCT
iajs-2149	109	37	]	]	X
iajs-2149	109	38	for	for	ADP
iajs-2149	109	39	all	all	PRON
iajs-2149	109	40	.	.	PUNCT
iajs-2149	110	1	proof	proof	NOUN
iajs-2149	110	2	let	let	VERB
iajs-2149	110	3	[	[	PUNCT
iajs-2149	110	4	]	]	X
iajs-2149	110	5	,	,	PUNCT
iajs-2149	110	6	implies	imply	VERB
iajs-2149	110	7	that	that	PRON
iajs-2149	110	8	.	.	PUNCT
iajs-2149	111	1	but	but	CCONJ
iajs-2149	111	2	is	be	AUX
iajs-2149	111	3	a	a	DET
iajs-2149	111	4	pseudo	pseudo	NOUN
iajs-2149	111	5	quasi-2	quasi-2	NOUN
iajs-2149	111	6	-	-	PUNCT
iajs-2149	111	7	absorbing	absorbing	ADJ
iajs-2149	111	8	submodule	submodule	NOUN
iajs-2149	111	9	of	of	ADP
iajs-2149	111	10	,	,	PUNCT
iajs-2149	111	11	then	then	ADV
iajs-2149	111	12	either	either	CCONJ
iajs-2149	111	13	or	or	CCONJ
iajs-2149	111	14	or	or	CCONJ
iajs-2149	111	15	.	.	PUNCT
iajs-2149	112	1	but	but	CCONJ
iajs-2149	112	2	,	,	PUNCT
iajs-2149	112	3	then	then	ADV
iajs-2149	112	4	,	,	PUNCT
iajs-2149	112	5	it	it	PRON
iajs-2149	112	6	follows	follow	VERB
iajs-2149	112	7	that	that	SCONJ
iajs-2149	112	8	either	either	CCONJ
iajs-2149	112	9	or	or	CCONJ
iajs-2149	112	10	or	or	CCONJ
iajs-2149	112	11	,	,	PUNCT
iajs-2149	112	12	implies	imply	VERB
iajs-2149	112	13	that	that	SCONJ
iajs-2149	112	14	either	either	CCONJ
iajs-2149	112	15	[	[	PUNCT
iajs-2149	112	16	]	]	X
iajs-2149	112	17	or	or	CCONJ
iajs-2149	112	18	[	[	PUNCT
iajs-2149	112	19	]	]	X
iajs-2149	112	20	or	or	CCONJ
iajs-2149	112	21	[	[	PUNCT
iajs-2149	112	22	]	]	X
iajs-2149	112	23	.	.	PUNCT
iajs-2149	113	1	that	that	PRON
iajs-2149	113	2	is	be	AUX
iajs-2149	113	3	[	[	PUNCT
iajs-2149	113	4	]	]	X
iajs-2149	113	5	[	[	PUNCT
iajs-2149	113	6	]	]	X
iajs-2149	113	7	[	[	PUNCT
iajs-2149	113	8	]	]	X
iajs-2149	113	9	.	.	PUNCT
iajs-2149	114	1	clearly	clearly	ADV
iajs-2149	114	2	that	that	SCONJ
iajs-2149	114	3	[	[	PUNCT
iajs-2149	114	4	]	]	X
iajs-2149	114	5	[	[	PUNCT
iajs-2149	114	6	]	]	X
iajs-2149	114	7	[	[	PUNCT
iajs-2149	114	8	]	]	X
iajs-2149	114	9	[	[	PUNCT
iajs-2149	114	10	]	]	X
iajs-2149	114	11	.	.	PUNCT
iajs-2149	115	1	thus	thus	ADV
iajs-2149	115	2	[	[	PUNCT
iajs-2149	115	3	]	]	X
iajs-2149	115	4	[	[	PUNCT
iajs-2149	115	5	]	]	X
iajs-2149	115	6	[	[	PUNCT
iajs-2149	115	7	]	]	X
iajs-2149	115	8	[	[	PUNCT
iajs-2149	115	9	]	]	X
iajs-2149	115	10	.	.	PUNCT
iajs-2149	115	11	suppose	suppose	VERB
iajs-2149	115	12	that	that	SCONJ
iajs-2149	115	13	with	with	ADP
iajs-2149	115	14	,	,	PUNCT
iajs-2149	115	15	implies	imply	VERB
iajs-2149	115	16	that	that	SCONJ
iajs-2149	115	17	[	[	X
iajs-2149	115	18	]	]	X
iajs-2149	115	19	[	[	PUNCT
iajs-2149	115	20	]	]	X
iajs-2149	115	21	[	[	PUNCT
iajs-2149	115	22	]	]	X
iajs-2149	115	23	[	[	PUNCT
iajs-2149	115	24	]	]	X
iajs-2149	115	25	,	,	PUNCT
iajs-2149	115	26	implies	imply	VERB
iajs-2149	115	27	that	that	SCONJ
iajs-2149	115	28	either	either	CCONJ
iajs-2149	115	29	[	[	PUNCT
iajs-2149	115	30	]	]	X
iajs-2149	115	31	or	or	CCONJ
iajs-2149	115	32	[	[	PUNCT
iajs-2149	115	33	]	]	X
iajs-2149	115	34	or	or	CCONJ
iajs-2149	115	35	[	[	PUNCT
iajs-2149	115	36	]	]	X
iajs-2149	115	37	.	.	PUNCT
iajs-2149	116	1	that	that	PRON
iajs-2149	116	2	is	be	AUX
iajs-2149	116	3	either	either	PRON
iajs-2149	116	4	or	or	CCONJ
iajs-2149	116	5	or	or	CCONJ
iajs-2149	116	6	.	.	PUNCT
iajs-2149	117	1	hence	hence	ADV
iajs-2149	117	2	is	be	AUX
iajs-2149	117	3	a	a	DET
iajs-2149	117	4	pseudo	pseudo	NOUN
iajs-2149	117	5	quasi-2	quasi-2	NOUN
iajs-2149	117	6	-	-	PUNCT
iajs-2149	117	7	absorbing	absorbing	ADJ
iajs-2149	117	8	submodule	submodule	NOUN
iajs-2149	117	9	of	of	ADP
iajs-2149	117	10	.	.	PUNCT
iajs-2149	118	1	proposition	proposition	NOUN
iajs-2149	118	2	(	(	PUNCT
iajs-2149	118	3	15	15	NUM
iajs-2149	118	4	)	)	PUNCT
iajs-2149	118	5	let	let	AUX
iajs-2149	118	6	be	be	AUX
iajs-2149	118	7	an	an	DET
iajs-2149	118	8	-module	-module	NOUN
iajs-2149	118	9	and	and	CCONJ
iajs-2149	118	10	is	be	AUX
iajs-2149	118	11	a	a	DET
iajs-2149	118	12	proper	proper	ADJ
iajs-2149	118	13	submodule	submodule	NOUN
iajs-2149	118	14	of	of	ADP
iajs-2149	118	15	,	,	PUNCT
iajs-2149	118	16	with	with	ADP
iajs-2149	118	17	.then	.then	X
iajs-2149	118	18	is	be	AUX
iajs-2149	118	19	a	a	DET
iajs-2149	118	20	pseudo	pseudo	NOUN
iajs-2149	118	21	quasi-2	quasi-2	NOUN
iajs-2149	118	22	-	-	PUNCT
iajs-2149	118	23	absorbing	absorbing	ADJ
iajs-2149	118	24	submodule	submodule	NOUN
iajs-2149	118	25	of	of	ADP
iajs-2149	118	26	if	if	SCONJ
iajs-2149	118	27	and	and	CCONJ
iajs-2149	118	28	only	only	ADV
iajs-2149	118	29	if	if	SCONJ
iajs-2149	118	30	[	[	PUNCT
iajs-2149	118	31	]	]	X
iajs-2149	118	32	[	[	PUNCT
iajs-2149	118	33	]	]	X
iajs-2149	118	34	[	[	PUNCT
iajs-2149	118	35	]	]	X
iajs-2149	118	36	for	for	ADP
iajs-2149	118	37	all	all	PRON
iajs-2149	118	38	.	.	PUNCT
iajs-2149	119	1	proof	proof	NOUN
iajs-2149	119	2	let	let	VERB
iajs-2149	119	3	[	[	PUNCT
iajs-2149	119	4	]	]	X
iajs-2149	119	5	,	,	PUNCT
iajs-2149	119	6	implies	imply	VERB
iajs-2149	119	7	that	that	PRON
iajs-2149	119	8	.	.	PUNCT
iajs-2149	120	1	but	but	CCONJ
iajs-2149	120	2	is	be	AUX
iajs-2149	120	3	a	a	DET
iajs-2149	120	4	pseudo	pseudo	NOUN
iajs-2149	120	5	quasi-2	quasi-2	NOUN
iajs-2149	120	6	-	-	PUNCT
iajs-2149	120	7	absorbing	absorbing	ADJ
iajs-2149	120	8	submodule	submodule	NOUN
iajs-2149	120	9	of	of	ADP
iajs-2149	120	10	,	,	PUNCT
iajs-2149	120	11	and	and	CCONJ
iajs-2149	120	12	let	let	VERB
iajs-2149	120	13	,	,	PUNCT
iajs-2149	120	14	then	then	ADV
iajs-2149	120	15	either	either	ADV
iajs-2149	120	16	or	or	CCONJ
iajs-2149	120	17	.	.	PUNCT
iajs-2149	121	1	but	but	CCONJ
iajs-2149	121	2	,	,	PUNCT
iajs-2149	121	3	then	then	ADV
iajs-2149	121	4	.	.	PUNCT
iajs-2149	122	1	hence	hence	ADV
iajs-2149	122	2	either	either	ADV
iajs-2149	122	3	or	or	CCONJ
iajs-2149	122	4	.	.	PUNCT
iajs-2149	123	1	thus	thus	ADV
iajs-2149	123	2	either	either	CCONJ
iajs-2149	123	3	[	[	PUNCT
iajs-2149	123	4	]	]	X
iajs-2149	123	5	or	or	CCONJ
iajs-2149	123	6	[	[	PUNCT
iajs-2149	123	7	]	]	X
iajs-2149	123	8	,	,	PUNCT
iajs-2149	123	9	it	it	PRON
iajs-2149	123	10	follows	follow	VERB
iajs-2149	123	11	that	that	SCONJ
iajs-2149	123	12	[	[	X
iajs-2149	123	13	]	]	X
iajs-2149	123	14	[	[	PUNCT
iajs-2149	123	15	]	]	X
iajs-2149	123	16	,	,	PUNCT
iajs-2149	123	17	hence	hence	ADV
iajs-2149	123	18	[	[	X
iajs-2149	123	19	]	]	X
iajs-2149	123	20	[	[	PUNCT
iajs-2149	123	21	]	]	X
iajs-2149	123	22	[	[	PUNCT
iajs-2149	123	23	]	]	X
iajs-2149	123	24	.	.	PUNCT
iajs-2149	124	1	consequently	consequently	ADV
iajs-2149	124	2	[	[	PUNCT
iajs-2149	124	3	]	]	X
iajs-2149	124	4	[	[	PUNCT
iajs-2149	124	5	]	]	X
iajs-2149	124	6	[	[	PUNCT
iajs-2149	124	7	]	]	X
iajs-2149	124	8	.	.	PUNCT
iajs-2149	124	9	suppose	suppose	VERB
iajs-2149	124	10	that	that	SCONJ
iajs-2149	124	11	with	with	ADP
iajs-2149	124	12	,	,	PUNCT
iajs-2149	124	13	with	with	ADP
iajs-2149	124	14	,	,	PUNCT
iajs-2149	124	15	then	then	ADV
iajs-2149	124	16	[	[	PUNCT
iajs-2149	124	17	]	]	X
iajs-2149	124	18	[	[	PUNCT
iajs-2149	124	19	]	]	X
iajs-2149	124	20	[	[	PUNCT
iajs-2149	124	21	]	]	X
iajs-2149	124	22	,	,	PUNCT
iajs-2149	124	23	implies	imply	VERB
iajs-2149	124	24	that	that	SCONJ
iajs-2149	124	25	either	either	CCONJ
iajs-2149	124	26	[	[	PUNCT
iajs-2149	124	27	]	]	X
iajs-2149	124	28	or	or	CCONJ
iajs-2149	124	29	[	[	PUNCT
iajs-2149	124	30	]	]	X
iajs-2149	124	31	,	,	PUNCT
iajs-2149	124	32	it	it	PRON
iajs-2149	124	33	follows	follow	VERB
iajs-2149	124	34	that	that	PRON
iajs-2149	124	35	or	or	CCONJ
iajs-2149	124	36	,	,	PUNCT
iajs-2149	124	37	hence	hence	ADV
iajs-2149	124	38	either	either	ADV
iajs-2149	124	39	or	or	CCONJ
iajs-2149	124	40	.	.	PUNCT
iajs-2149	125	1	therefore	therefore	ADV
iajs-2149	125	2	is	be	AUX
iajs-2149	125	3	a	a	DET
iajs-2149	125	4	pseudo	pseudo	NOUN
iajs-2149	125	5	quasi-2	quasi-2	NOUN
iajs-2149	125	6	-	-	PUNCT
iajs-2149	125	7	absorbing	absorbing	ADJ
iajs-2149	125	8	submodule	submodule	NOUN
iajs-2149	125	9	of	of	ADP
iajs-2149	125	10	.	.	PUNCT
iajs-2149	125	11	111	111	NUM
iajs-2149	125	12	ibn	ibn	PROPN
iajs-2149	125	13	al	al	PROPN
iajs-2149	125	14	-	-	PUNCT
iajs-2149	125	15	haitham	haitham	PROPN
iajs-2149	125	16	jour	jour	X
iajs-2149	125	17	.	.	PROPN
iajs-2149	125	18	for	for	ADP
iajs-2149	125	19	pure	pure	ADJ
iajs-2149	125	20	&	&	CCONJ
iajs-2149	125	21	appl	appl	PROPN
iajs-2149	125	22	.	.	PUNCT
iajs-2149	126	1	sci	sci	PROPN
iajs-2149	126	2	.	.	PROPN
iajs-2149	126	3	32	32	NUM
iajs-2149	126	4	(	(	PUNCT
iajs-2149	126	5	2	2	NUM
iajs-2149	126	6	)	)	SYM
iajs-2149	126	7	2019	2019	NUM
iajs-2149	126	8	proposition	proposition	NOUN
iajs-2149	126	9	(	(	PUNCT
iajs-2149	126	10	16	16	NUM
iajs-2149	126	11	)	)	PUNCT
iajs-2149	126	12	let	let	AUX
iajs-2149	126	13	be	be	AUX
iajs-2149	126	14	an	an	DET
iajs-2149	126	15	-module	-module	NOUN
iajs-2149	126	16	and	and	CCONJ
iajs-2149	126	17	is	be	AUX
iajs-2149	126	18	a	a	DET
iajs-2149	126	19	pseudo	pseudo	NOUN
iajs-2149	126	20	quasi-2	quasi-2	NOUN
iajs-2149	126	21	-	-	PUNCT
iajs-2149	126	22	absorbing	absorbing	ADJ
iajs-2149	126	23	submodule	submodule	NOUN
iajs-2149	126	24	of	of	ADP
iajs-2149	126	25	,	,	PUNCT
iajs-2149	126	26	with	with	ADP
iajs-2149	126	27	,	,	PUNCT
iajs-2149	126	28	then	then	ADV
iajs-2149	126	29	[	[	PUNCT
iajs-2149	126	30	]	]	X
iajs-2149	126	31	[	[	PUNCT
iajs-2149	126	32	]	]	X
iajs-2149	126	33	[	[	PUNCT
iajs-2149	126	34	]	]	X
iajs-2149	126	35	[	[	PUNCT
iajs-2149	126	36	]	]	X
iajs-2149	126	37	for	for	ADP
iajs-2149	126	38	all	all	PRON
iajs-2149	126	39	.	.	PUNCT
iajs-2149	127	1	proof	proof	NOUN
iajs-2149	127	2	let	let	VERB
iajs-2149	127	3	[	[	PUNCT
iajs-2149	127	4	]	]	X
iajs-2149	127	5	,	,	PUNCT
iajs-2149	127	6	implies	imply	VERB
iajs-2149	127	7	that	that	PRON
iajs-2149	127	8	.	.	PUNCT
iajs-2149	128	1	but	but	CCONJ
iajs-2149	128	2	is	be	AUX
iajs-2149	128	3	a	a	DET
iajs-2149	128	4	pseudo	pseudo	NOUN
iajs-2149	128	5	quasi-2	quasi-2	NOUN
iajs-2149	128	6	-	-	PUNCT
iajs-2149	128	7	absorbing	absorbing	ADJ
iajs-2149	128	8	submodule	submodule	NOUN
iajs-2149	128	9	of	of	ADP
iajs-2149	128	10	,	,	PUNCT
iajs-2149	128	11	then	then	ADV
iajs-2149	128	12	either	either	CCONJ
iajs-2149	128	13	or	or	CCONJ
iajs-2149	128	14	or	or	CCONJ
iajs-2149	128	15	.	.	PUNCT
iajs-2149	129	1	but	but	CCONJ
iajs-2149	129	2	,	,	PUNCT
iajs-2149	129	3	then	then	ADV
iajs-2149	129	4	,	,	PUNCT
iajs-2149	129	5	it	it	PRON
iajs-2149	129	6	follows	follow	VERB
iajs-2149	129	7	that	that	SCONJ
iajs-2149	129	8	either	either	CCONJ
iajs-2149	129	9	or	or	CCONJ
iajs-2149	129	10	or	or	CCONJ
iajs-2149	129	11	.	.	PUNCT
iajs-2149	130	1	hence	hence	ADV
iajs-2149	130	2	[	[	PUNCT
iajs-2149	130	3	]	]	X
iajs-2149	130	4	or	or	CCONJ
iajs-2149	130	5	[	[	PUNCT
iajs-2149	130	6	]	]	X
iajs-2149	130	7	or	or	CCONJ
iajs-2149	130	8	[	[	PUNCT
iajs-2149	130	9	]	]	X
iajs-2149	130	10	.	.	PUNCT
iajs-2149	131	1	therefore	therefore	ADV
iajs-2149	131	2	[	[	PUNCT
iajs-2149	131	3	]	]	X
iajs-2149	131	4	[	[	PUNCT
iajs-2149	131	5	]	]	X
iajs-2149	131	6	[	[	PUNCT
iajs-2149	131	7	]	]	X
iajs-2149	131	8	,	,	PUNCT
iajs-2149	131	9	hence	hence	ADV
iajs-2149	131	10	[	[	X
iajs-2149	131	11	]	]	X
iajs-2149	131	12	[	[	PUNCT
iajs-2149	131	13	]	]	X
iajs-2149	131	14	[	[	PUNCT
iajs-2149	131	15	]	]	X
iajs-2149	131	16	[	[	PUNCT
iajs-2149	131	17	]	]	X
iajs-2149	131	18	.	.	PUNCT
iajs-2149	132	1	consequently	consequently	ADV
iajs-2149	132	2	,	,	PUNCT
iajs-2149	132	3	the	the	DET
iajs-2149	132	4	equality	equality	NOUN
iajs-2149	132	5	holds	hold	VERB
iajs-2149	132	6	.	.	PUNCT
iajs-2149	133	1	proposition	proposition	NOUN
iajs-2149	133	2	(	(	PUNCT
iajs-2149	133	3	17	17	NUM
iajs-2149	133	4	)	)	PUNCT
iajs-2149	133	5	let	let	AUX
iajs-2149	133	6	be	be	AUX
iajs-2149	133	7	an	an	DET
iajs-2149	133	8	-module	-module	NOUN
iajs-2149	133	9	,	,	PUNCT
iajs-2149	133	10	and	and	CCONJ
iajs-2149	133	11	are	be	AUX
iajs-2149	133	12	submodules	submodule	NOUN
iajs-2149	133	13	of	of	ADP
iajs-2149	133	14	such	such	ADJ
iajs-2149	133	15	that	that	PRON
iajs-2149	133	16	and	and	CCONJ
iajs-2149	133	17	is	be	AUX
iajs-2149	133	18	an	an	DET
iajs-2149	133	19	essential	essential	ADJ
iajs-2149	133	20	submodule	submodule	NOUN
iajs-2149	133	21	of	of	ADP
iajs-2149	133	22	.	.	PUNCT
iajs-2149	134	1	if	if	SCONJ
iajs-2149	134	2	is	be	AUX
iajs-2149	134	3	a	a	DET
iajs-2149	134	4	pseudo	pseudo	NOUN
iajs-2149	134	5	quasi-2	quasi-2	NOUN
iajs-2149	134	6	-	-	PUNCT
iajs-2149	134	7	absorbing	absorbing	ADJ
iajs-2149	134	8	submodule	submodule	NOUN
iajs-2149	134	9	of	of	ADP
iajs-2149	134	10	,	,	PUNCT
iajs-2149	134	11	then	then	ADV
iajs-2149	134	12	is	be	AUX
iajs-2149	134	13	a	a	DET
iajs-2149	134	14	pseudo	pseudo	NOUN
iajs-2149	134	15	quasi-2	quasi-2	NOUN
iajs-2149	134	16	-	-	PUNCT
iajs-2149	134	17	absorbing	absorbing	ADJ
iajs-2149	134	18	submodule	submodule	NOUN
iajs-2149	134	19	of	of	ADP
iajs-2149	134	20	.	.	PUNCT
iajs-2149	135	1	proof	proof	NOUN
iajs-2149	135	2	let	let	VERB
iajs-2149	135	3	,	,	PUNCT
iajs-2149	135	4	with	with	ADP
iajs-2149	135	5	.	.	PUNCT
iajs-2149	136	1	since	since	SCONJ
iajs-2149	136	2	is	be	AUX
iajs-2149	136	3	a	a	DET
iajs-2149	136	4	pseudo	pseudo	NOUN
iajs-2149	136	5	quasi-2	quasi-2	NOUN
iajs-2149	136	6	-	-	PUNCT
iajs-2149	136	7	absorbing	absorbing	ADJ
iajs-2149	136	8	submodule	submodule	NOUN
iajs-2149	136	9	of	of	ADP
iajs-2149	136	10	,	,	PUNCT
iajs-2149	136	11	then	then	ADV
iajs-2149	136	12	either	either	CCONJ
iajs-2149	136	13	or	or	CCONJ
iajs-2149	136	14	or	or	CCONJ
iajs-2149	136	15	.	.	PUNCT
iajs-2149	137	1	but	but	CCONJ
iajs-2149	137	2	is	be	AUX
iajs-2149	137	3	essential	essential	ADJ
iajs-2149	137	4	submodule	submodule	NOUN
iajs-2149	137	5	of	of	ADP
iajs-2149	137	6	,	,	PUNCT
iajs-2149	137	7	then	then	ADV
iajs-2149	137	8	by	by	ADP
iajs-2149	137	9	[	[	PUNCT
iajs-2149	137	10	]	]	X
iajs-2149	137	11	.	.	PUNCT
iajs-2149	138	1	we	we	PRON
iajs-2149	138	2	have	have	VERB
iajs-2149	138	3	.	.	PUNCT
iajs-2149	139	1	hence	hence	ADV
iajs-2149	139	2	either	either	ADV
iajs-2149	139	3	or	or	CCONJ
iajs-2149	139	4	or	or	CCONJ
iajs-2149	139	5	.	.	PUNCT
iajs-2149	140	1	therefore	therefore	ADV
iajs-2149	140	2	is	be	AUX
iajs-2149	140	3	a	a	DET
iajs-2149	140	4	pseudo	pseudo	NOUN
iajs-2149	140	5	quasi-2	quasi-2	NOUN
iajs-2149	140	6	-	-	PUNCT
iajs-2149	140	7	absorbing	absorbing	ADJ
iajs-2149	140	8	submodule	submodule	NOUN
iajs-2149	140	9	in	in	ADP
iajs-2149	140	10	.	.	PUNCT
iajs-2149	141	1	proposition	proposition	NOUN
iajs-2149	141	2	(	(	PUNCT
iajs-2149	141	3	18	18	NUM
iajs-2149	141	4	)	)	PUNCT
iajs-2149	141	5	let	let	AUX
iajs-2149	141	6	be	be	AUX
iajs-2149	141	7	an	an	DET
iajs-2149	141	8	-module	-module	NOUN
iajs-2149	141	9	,	,	PUNCT
iajs-2149	141	10	and	and	CCONJ
iajs-2149	141	11	are	be	AUX
iajs-2149	141	12	submodules	submodule	NOUN
iajs-2149	141	13	of	of	ADP
iajs-2149	141	14	such	such	ADJ
iajs-2149	141	15	that	that	PRON
iajs-2149	141	16	and	and	CCONJ
iajs-2149	141	17	.	.	PUNCT
iajs-2149	142	1	if	if	SCONJ
iajs-2149	142	2	is	be	AUX
iajs-2149	142	3	a	a	DET
iajs-2149	142	4	pseudo	pseudo	NOUN
iajs-2149	142	5	quasi-2	quasi-2	NOUN
iajs-2149	142	6	-	-	PUNCT
iajs-2149	142	7	absorbing	absorbing	ADJ
iajs-2149	142	8	submodule	submodule	NOUN
iajs-2149	142	9	of	of	ADP
iajs-2149	142	10	,	,	PUNCT
iajs-2149	142	11	then	then	ADV
iajs-2149	142	12	is	be	AUX
iajs-2149	142	13	a	a	DET
iajs-2149	142	14	pseudo	pseudo	NOUN
iajs-2149	142	15	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	142	16	submodule	submodule	NOUN
iajs-2149	142	17	of	of	ADP
iajs-2149	142	18	.	.	PUNCT
iajs-2149	143	1	proof	proof	NOUN
iajs-2149	143	2	:	:	PUNCT
iajs-2149	143	3	similar	similar	ADJ
iajs-2149	143	4	steps	step	NOUN
iajs-2149	143	5	as	as	ADP
iajs-2149	143	6	proposition	proposition	NOUN
iajs-2149	143	7	(	(	PUNCT
iajs-2149	143	8	17	17	NUM
iajs-2149	143	9	)	)	PUNCT
iajs-2149	143	10	.	.	PUNCT
iajs-2149	144	1	remark	remark	NOUN
iajs-2149	144	2	(	(	PUNCT
iajs-2149	144	3	19	19	NUM
iajs-2149	144	4	)	)	PUNCT
iajs-2149	144	5	the	the	DET
iajs-2149	144	6	intersection	intersection	NOUN
iajs-2149	144	7	of	of	ADP
iajs-2149	144	8	two	two	NUM
iajs-2149	144	9	pseudo	pseudo	NOUN
iajs-2149	144	10	quasi-2	quasi-2	NOUN
iajs-2149	144	11	-	-	PUNCT
iajs-2149	144	12	absorbing	absorbing	ADJ
iajs-2149	144	13	submodules	submodule	NOUN
iajs-2149	144	14	of	of	ADP
iajs-2149	144	15	an	an	DET
iajs-2149	144	16	-module	-module	NOUN
iajs-2149	144	17	need	need	VERB
iajs-2149	144	18	not	not	PART
iajs-2149	144	19	to	to	PART
iajs-2149	144	20	be	be	AUX
iajs-2149	144	21	pseudo	pseudo	VERB
iajs-2149	144	22	quasi-2	quasi-2	ADJ
iajs-2149	144	23	-	-	PUNCT
iajs-2149	144	24	absorbing	absorbing	ADJ
iajs-2149	144	25	submodule	submodule	NOUN
iajs-2149	144	26	of	of	ADP
iajs-2149	144	27	,	,	PUNCT
iajs-2149	144	28	as	as	SCONJ
iajs-2149	144	29	the	the	DET
iajs-2149	144	30	following	following	ADJ
iajs-2149	144	31	example	example	NOUN
iajs-2149	144	32	explains	explain	VERB
iajs-2149	144	33	that	that	SCONJ
iajs-2149	144	34	:	:	PUNCT
iajs-2149	144	35	in	in	ADP
iajs-2149	144	36	the	the	DET
iajs-2149	144	37	-module	-module	NOUN
iajs-2149	144	38	,	,	PUNCT
iajs-2149	144	39	the	the	DET
iajs-2149	144	40	submodules	submodule	NOUN
iajs-2149	144	41	and	and	CCONJ
iajs-2149	144	42	are	be	AUX
iajs-2149	144	43	pseudo	pseudo	NOUN
iajs-2149	144	44	quasi-2	quasi-2	ADJ
iajs-2149	144	45	-	-	PUNCT
iajs-2149	144	46	absorbing	absorbing	ADJ
iajs-2149	144	47	submodules	submodule	NOUN
iajs-2149	144	48	of	of	ADP
iajs-2149	144	49	,	,	PUNCT
iajs-2149	144	50	but	but	CCONJ
iajs-2149	144	51	is	be	AUX
iajs-2149	144	52	not	not	PART
iajs-2149	144	53	a	a	DET
iajs-2149	144	54	pseudo	pseudo	NOUN
iajs-2149	144	55	quasi-2	quasi-2	NOUN
iajs-2149	144	56	-	-	PUNCT
iajs-2149	144	57	absorbing	absorbing	NOUN
iajs-2149	144	58	of	of	ADP
iajs-2149	144	59	,	,	PUNCT
iajs-2149	144	60	since	since	SCONJ
iajs-2149	144	61	,	,	PUNCT
iajs-2149	144	62	but	but	CCONJ
iajs-2149	144	63	and	and	CCONJ
iajs-2149	144	64	.	.	PUNCT
iajs-2149	145	1	proposition	proposition	NOUN
iajs-2149	145	2	(	(	PUNCT
iajs-2149	145	3	20	20	NUM
iajs-2149	145	4	)	)	PUNCT
iajs-2149	145	5	let	let	AUX
iajs-2149	145	6	be	be	AUX
iajs-2149	145	7	an	an	DET
iajs-2149	145	8	-module	-module	NOUN
iajs-2149	145	9	,	,	PUNCT
iajs-2149	145	10	and	and	CCONJ
iajs-2149	145	11	are	be	AUX
iajs-2149	145	12	pseudo	pseudo	NOUN
iajs-2149	145	13	quasi-2	quasi-2	ADJ
iajs-2149	145	14	-	-	PUNCT
iajs-2149	145	15	absorbing	absorbing	ADJ
iajs-2149	145	16	submodules	submodule	NOUN
iajs-2149	145	17	of	of	ADP
iajs-2149	145	18	,	,	PUNCT
iajs-2149	145	19	with	with	ADP
iajs-2149	145	20	and	and	CCONJ
iajs-2149	145	21	.	.	PUNCT
iajs-2149	146	1	then	then	ADV
iajs-2149	146	2	is	be	AUX
iajs-2149	146	3	a	a	DET
iajs-2149	146	4	pseudo	pseudo	NOUN
iajs-2149	146	5	quasi-2	quasi-2	NOUN
iajs-2149	146	6	-	-	PUNCT
iajs-2149	146	7	absorbing	absorbing	ADJ
iajs-2149	146	8	submodule	submodule	NOUN
iajs-2149	146	9	of	of	ADP
iajs-2149	146	10	.	.	PUNCT
iajs-2149	147	1	proof	proof	NOUN
iajs-2149	147	2	let	let	VERB
iajs-2149	147	3	,	,	PUNCT
iajs-2149	147	4	where	where	SCONJ
iajs-2149	147	5	,	,	PUNCT
iajs-2149	147	6	then	then	ADV
iajs-2149	147	7	and	and	CCONJ
iajs-2149	147	8	.	.	PUNCT
iajs-2149	148	1	but	but	CCONJ
iajs-2149	148	2	and	and	CCONJ
iajs-2149	148	3	are	be	AUX
iajs-2149	148	4	pseudo	pseudo	NOUN
iajs-2149	148	5	quasi-2	quasi-2	ADJ
iajs-2149	148	6	-	-	PUNCT
iajs-2149	148	7	absorbing	absorbing	ADJ
iajs-2149	148	8	submodules	submodule	NOUN
iajs-2149	148	9	of	of	ADP
iajs-2149	148	10	,	,	PUNCT
iajs-2149	148	11	so	so	ADV
iajs-2149	148	12	either	either	PRON
iajs-2149	148	13	or	or	CCONJ
iajs-2149	148	14	or	or	CCONJ
iajs-2149	148	15	and	and	CCONJ
iajs-2149	148	16	either	either	ADV
iajs-2149	148	17	or	or	CCONJ
iajs-2149	148	18	or	or	CCONJ
iajs-2149	148	19	.	.	PUNCT
iajs-2149	149	1	but	but	CCONJ
iajs-2149	149	2	and	and	CCONJ
iajs-2149	149	3	,	,	PUNCT
iajs-2149	149	4	implies	imply	VERB
iajs-2149	149	5	that	that	SCONJ
iajs-2149	149	6	,	,	PUNCT
iajs-2149	149	7	and	and	CCONJ
iajs-2149	149	8	hence	hence	ADV
iajs-2149	149	9	,	,	PUNCT
iajs-2149	149	10	and	and	CCONJ
iajs-2149	149	11	.	.	PUNCT
iajs-2149	150	1	thus	thus	ADV
iajs-2149	150	2	either	either	CCONJ
iajs-2149	150	3	or	or	CCONJ
iajs-2149	150	4	or	or	CCONJ
iajs-2149	150	5	.	.	PUNCT
iajs-2149	151	1	hence	hence	ADV
iajs-2149	151	2	is	be	AUX
iajs-2149	151	3	a	a	DET
iajs-2149	151	4	pseudo	pseudo	NOUN
iajs-2149	151	5	quasi-2	quasi-2	NOUN
iajs-2149	151	6	-	-	PUNCT
iajs-2149	151	7	absorbing	absorbing	ADJ
iajs-2149	151	8	submodule	submodule	NOUN
iajs-2149	151	9	of	of	ADP
iajs-2149	151	10	.	.	PUNCT
iajs-2149	152	1	121	121	NUM
iajs-2149	152	2	ibn	ibn	PROPN
iajs-2149	152	3	al	al	PROPN
iajs-2149	152	4	-	-	PUNCT
iajs-2149	152	5	haitham	haitham	PROPN
iajs-2149	152	6	jour	jour	X
iajs-2149	152	7	.	.	PROPN
iajs-2149	152	8	for	for	ADP
iajs-2149	152	9	pure	pure	ADJ
iajs-2149	152	10	&	&	CCONJ
iajs-2149	152	11	appl	appl	PROPN
iajs-2149	152	12	.	.	PUNCT
iajs-2149	153	1	sci	sci	PROPN
iajs-2149	153	2	.	.	PROPN
iajs-2149	153	3	32	32	NUM
iajs-2149	153	4	(	(	PUNCT
iajs-2149	153	5	2	2	NUM
iajs-2149	153	6	)	)	SYM
iajs-2149	153	7	2019	2019	NUM
iajs-2149	153	8	proposition	proposition	NOUN
iajs-2149	153	9	(	(	PUNCT
iajs-2149	153	10	21	21	NUM
iajs-2149	153	11	)	)	PUNCT
iajs-2149	153	12	let	let	AUX
iajs-2149	153	13	be	be	AUX
iajs-2149	153	14	an	an	DET
iajs-2149	153	15	-module	-module	NOUN
iajs-2149	153	16	and	and	CCONJ
iajs-2149	153	17	is	be	AUX
iajs-2149	153	18	a	a	DET
iajs-2149	153	19	pseudo	pseudo	NOUN
iajs-2149	153	20	quasi-2	quasi-2	NOUN
iajs-2149	153	21	-	-	PUNCT
iajs-2149	153	22	absorbing	absorbing	ADJ
iajs-2149	153	23	submodule	submodule	NOUN
iajs-2149	153	24	of	of	ADP
iajs-2149	153	25	and	and	CCONJ
iajs-2149	153	26	is	be	AUX
iajs-2149	153	27	a	a	DET
iajs-2149	153	28	submodule	submodule	NOUN
iajs-2149	153	29	of	of	ADP
iajs-2149	153	30	,	,	PUNCT
iajs-2149	153	31	with	with	ADP
iajs-2149	153	32	and	and	CCONJ
iajs-2149	153	33	is	be	AUX
iajs-2149	153	34	not	not	PART
iajs-2149	153	35	contained	contain	VERB
iajs-2149	153	36	in	in	ADP
iajs-2149	153	37	.	.	PUNCT
iajs-2149	154	1	then	then	ADV
iajs-2149	154	2	is	be	AUX
iajs-2149	154	3	a	a	DET
iajs-2149	154	4	pseudo	pseudo	NOUN
iajs-2149	154	5	quasi-2	quasi-2	NOUN
iajs-2149	154	6	-	-	PUNCT
iajs-2149	154	7	absorbing	absorbing	ADJ
iajs-2149	154	8	submodule	submodule	NOUN
iajs-2149	154	9	of	of	ADP
iajs-2149	154	10	.	.	PUNCT
iajs-2149	155	1	proof	proof	NOUN
iajs-2149	155	2	since	since	SCONJ
iajs-2149	155	3	is	be	AUX
iajs-2149	155	4	not	not	PART
iajs-2149	155	5	contained	contain	VERB
iajs-2149	155	6	in	in	ADP
iajs-2149	155	7	,	,	PUNCT
iajs-2149	155	8	then	then	ADV
iajs-2149	155	9	is	be	AUX
iajs-2149	155	10	a	a	DET
iajs-2149	155	11	proper	proper	ADJ
iajs-2149	155	12	submodule	submodule	NOUN
iajs-2149	155	13	of	of	ADP
iajs-2149	155	14	.	.	PUNCT
iajs-2149	156	1	let	let	VERB
iajs-2149	156	2	,	,	PUNCT
iajs-2149	156	3	where	where	SCONJ
iajs-2149	156	4	,	,	PUNCT
iajs-2149	156	5	then	then	ADV
iajs-2149	156	6	and	and	CCONJ
iajs-2149	156	7	.	.	PUNCT
iajs-2149	157	1	but	but	CCONJ
iajs-2149	157	2	is	be	AUX
iajs-2149	157	3	a	a	DET
iajs-2149	157	4	pseudo	pseudo	NOUN
iajs-2149	157	5	quasi2	quasi2	NOUN
iajs-2149	157	6	-	-	PUNCT
iajs-2149	157	7	absorbing	absorb	VERB
iajs-2149	157	8	submodule	submodule	NOUN
iajs-2149	157	9	of	of	ADP
iajs-2149	157	10	,	,	PUNCT
iajs-2149	157	11	then	then	ADV
iajs-2149	157	12	either	either	CCONJ
iajs-2149	157	13	or	or	CCONJ
iajs-2149	157	14	or	or	CCONJ
iajs-2149	157	15	.	.	PUNCT
iajs-2149	158	1	but	but	CCONJ
iajs-2149	158	2	,	,	PUNCT
iajs-2149	158	3	it	it	PRON
iajs-2149	158	4	follows	follow	VERB
iajs-2149	158	5	that	that	SCONJ
iajs-2149	158	6	either	either	CCONJ
iajs-2149	158	7	or	or	CCONJ
iajs-2149	158	8	or	or	CCONJ
iajs-2149	158	9	.	.	PUNCT
iajs-2149	159	1	by	by	ADP
iajs-2149	159	2	hypothesis	hypothesis	NOUN
iajs-2149	159	3	,	,	PUNCT
iajs-2149	159	4	then	then	ADV
iajs-2149	159	5	by	by	ADP
iajs-2149	159	6	[	[	PUNCT
iajs-2149	159	7	]	]	X
iajs-2149	159	8	we	we	PRON
iajs-2149	159	9	have	have	VERB
iajs-2149	159	10	either	either	CCONJ
iajs-2149	159	11	(	(	PUNCT
iajs-2149	159	12	or	or	CCONJ
iajs-2149	159	13	(	(	PUNCT
iajs-2149	159	14	or	or	CCONJ
iajs-2149	159	15	(	(	PUNCT
iajs-2149	159	16	.	.	PUNCT
iajs-2149	160	1	but	but	CCONJ
iajs-2149	160	2	by	by	ADP
iajs-2149	160	3	[	[	PUNCT
iajs-2149	160	4	]	]	X
iajs-2149	160	5	.	.	PUNCT
iajs-2149	161	1	hence	hence	ADV
iajs-2149	161	2	either	either	CCONJ
iajs-2149	161	3	or	or	CCONJ
iajs-2149	161	4	or	or	CCONJ
iajs-2149	161	5	.	.	PUNCT
iajs-2149	162	1	therefore	therefore	ADV
iajs-2149	162	2	is	be	AUX
iajs-2149	162	3	a	a	DET
iajs-2149	162	4	pseudo	pseudo	NOUN
iajs-2149	162	5	quasi-2	quasi-2	NOUN
iajs-2149	162	6	-	-	PUNCT
iajs-2149	162	7	absorbing	absorbing	ADJ
iajs-2149	162	8	submodule	submodule	NOUN
iajs-2149	162	9	of	of	ADP
iajs-2149	162	10	.	.	PUNCT
iajs-2149	163	1	proposition	proposition	NOUN
iajs-2149	163	2	(	(	PUNCT
iajs-2149	163	3	22	22	NUM
iajs-2149	163	4	)	)	PUNCT
iajs-2149	163	5	let	let	VERB
iajs-2149	163	6	́	́	PUNCT
iajs-2149	163	7	be	be	AUX
iajs-2149	163	8	an	an	DET
iajs-2149	163	9	-epimorphism	-epimorphism	NOUN
iajs-2149	163	10	and	and	CCONJ
iajs-2149	163	11	is	be	AUX
iajs-2149	163	12	a	a	DET
iajs-2149	163	13	pseudo	pseudo	NOUN
iajs-2149	163	14	quasi-2	quasi-2	NOUN
iajs-2149	163	15	-	-	PUNCT
iajs-2149	163	16	absorbing	absorbing	ADJ
iajs-2149	163	17	submodule	submodule	NOUN
iajs-2149	163	18	of	of	ADP
iajs-2149	163	19	́.	́.	PUNCT
iajs-2149	163	20	then	then	ADV
iajs-2149	163	21	is	be	AUX
iajs-2149	163	22	a	a	DET
iajs-2149	163	23	pseudo	pseudo	NOUN
iajs-2149	163	24	quasi-2	quasi-2	NOUN
iajs-2149	163	25	-	-	PUNCT
iajs-2149	163	26	absorbing	absorbing	ADJ
iajs-2149	163	27	submodule	submodule	NOUN
iajs-2149	163	28	of	of	ADP
iajs-2149	163	29	.	.	PUNCT
iajs-2149	164	1	proof	proof	NOUN
iajs-2149	164	2	it	it	PRON
iajs-2149	164	3	is	be	AUX
iajs-2149	164	4	clear	clear	ADJ
iajs-2149	164	5	that	that	PRON
iajs-2149	164	6	is	be	AUX
iajs-2149	164	7	a	a	DET
iajs-2149	164	8	proper	proper	ADJ
iajs-2149	164	9	submodule	submodule	NOUN
iajs-2149	164	10	of	of	ADP
iajs-2149	164	11	.	.	PUNCT
iajs-2149	165	1	let	let	VERB
iajs-2149	165	2	,	,	PUNCT
iajs-2149	165	3	where	where	SCONJ
iajs-2149	165	4	,	,	PUNCT
iajs-2149	165	5	then	then	ADV
iajs-2149	165	6	,	,	PUNCT
iajs-2149	165	7	as	as	SCONJ
iajs-2149	165	8	is	be	AUX
iajs-2149	165	9	a	a	DET
iajs-2149	165	10	pseudo	pseudo	NOUN
iajs-2149	165	11	quasi-2	quasi-2	NOUN
iajs-2149	165	12	-	-	PUNCT
iajs-2149	165	13	absorbing	absorbing	ADJ
iajs-2149	165	14	submodule	submodule	NOUN
iajs-2149	165	15	of	of	ADP
iajs-2149	165	16	́	́	NOUN
iajs-2149	165	17	,	,	PUNCT
iajs-2149	165	18	implies	imply	VERB
iajs-2149	165	19	that	that	SCONJ
iajs-2149	165	20	either	either	CCONJ
iajs-2149	165	21	́	́	PUNCT
iajs-2149	165	22	or	or	CCONJ
iajs-2149	165	23	́	́	PROPN
iajs-2149	165	24	or	or	CCONJ
iajs-2149	165	25	́	́	PROPN
iajs-2149	165	26	.	.	PUNCT
iajs-2149	166	1	that	that	PRON
iajs-2149	166	2	is	be	AUX
iajs-2149	166	3	either	either	CCONJ
iajs-2149	166	4	(	(	PUNCT
iajs-2149	166	5	(	(	PUNCT
iajs-2149	166	6	́	́	NOUN
iajs-2149	166	7	)	)	PUNCT
iajs-2149	166	8	)	)	PUNCT
iajs-2149	166	9	or	or	CCONJ
iajs-2149	166	10	(	(	PUNCT
iajs-2149	166	11	(	(	PUNCT
iajs-2149	166	12	́	́	NOUN
iajs-2149	166	13	)	)	PUNCT
iajs-2149	166	14	)	)	PUNCT
iajs-2149	166	15	or	or	CCONJ
iajs-2149	166	16	(	(	PUNCT
iajs-2149	166	17	(	(	PUNCT
iajs-2149	166	18	́	́	NOUN
iajs-2149	166	19	)	)	PUNCT
iajs-2149	166	20	)	)	PUNCT
iajs-2149	166	21	,	,	PUNCT
iajs-2149	166	22	it	it	PRON
iajs-2149	166	23	follows	follow	VERB
iajs-2149	166	24	that	that	SCONJ
iajs-2149	166	25	either	either	CCONJ
iajs-2149	166	26	or	or	CCONJ
iajs-2149	166	27	or	or	CCONJ
iajs-2149	166	28	.	.	PUNCT
iajs-2149	167	1	therefore	therefore	ADV
iajs-2149	167	2	is	be	AUX
iajs-2149	167	3	a	a	DET
iajs-2149	167	4	pseudo	pseudo	NOUN
iajs-2149	167	5	quasi-2	quasi-2	NOUN
iajs-2149	167	6	-	-	PUNCT
iajs-2149	167	7	absorbing	absorbing	ADJ
iajs-2149	167	8	submodule	submodule	NOUN
iajs-2149	167	9	of	of	ADP
iajs-2149	167	10	.	.	PUNCT
iajs-2149	168	1	proposition	proposition	NOUN
iajs-2149	168	2	(	(	PUNCT
iajs-2149	168	3	23	23	NUM
iajs-2149	168	4	)	)	PUNCT
iajs-2149	168	5	let	let	VERB
iajs-2149	168	6	́	́	PUNCT
iajs-2149	168	7	be	be	AUX
iajs-2149	168	8	an	an	DET
iajs-2149	168	9	-epimorphism	-epimorphism	NOUN
iajs-2149	168	10	and	and	CCONJ
iajs-2149	168	11	is	be	AUX
iajs-2149	168	12	a	a	DET
iajs-2149	168	13	pseudo	pseudo	NOUN
iajs-2149	168	14	quasi-2	quasi-2	NOUN
iajs-2149	168	15	-	-	PUNCT
iajs-2149	168	16	absorbing	absorbing	ADJ
iajs-2149	168	17	submodule	submodule	NOUN
iajs-2149	168	18	of	of	ADP
iajs-2149	168	19	,	,	PUNCT
iajs-2149	168	20	with	with	ADP
iajs-2149	168	21	.	.	PUNCT
iajs-2149	169	1	then	then	ADV
iajs-2149	169	2	is	be	AUX
iajs-2149	169	3	a	a	DET
iajs-2149	169	4	pseudo	pseudo	NOUN
iajs-2149	169	5	quasi-2	quasi-2	NOUN
iajs-2149	169	6	-	-	PUNCT
iajs-2149	169	7	absorbing	absorbing	ADJ
iajs-2149	169	8	submodule	submodule	NOUN
iajs-2149	169	9	of	of	ADP
iajs-2149	169	10	́.	́.	SYM
iajs-2149	169	11	proof	proof	NOUN
iajs-2149	169	12	is	be	AUX
iajs-2149	169	13	a	a	DET
iajs-2149	169	14	proper	proper	ADJ
iajs-2149	169	15	submodule	submodule	NOUN
iajs-2149	169	16	of	of	ADP
iajs-2149	169	17	́	́	PROPN
iajs-2149	169	18	,	,	PUNCT
iajs-2149	169	19	if	if	SCONJ
iajs-2149	169	20	not	not	PART
iajs-2149	169	21	that	that	PRON
iajs-2149	169	22	is	be	AUX
iajs-2149	169	23	́.	́.	PUNCT
iajs-2149	169	24	let	let	VERB
iajs-2149	169	25	then	then	ADV
iajs-2149	169	26	́	́	PUNCT
iajs-2149	169	27	,	,	PUNCT
iajs-2149	169	28	then	then	ADV
iajs-2149	169	29	for	for	ADP
iajs-2149	169	30	some	some	PRON
iajs-2149	169	31	,	,	PUNCT
iajs-2149	169	32	hence	hence	ADV
iajs-2149	169	33	,	,	PUNCT
iajs-2149	169	34	implies	imply	VERB
iajs-2149	169	35	that	that	SCONJ
iajs-2149	169	36	,	,	PUNCT
iajs-2149	169	37	it	it	PRON
iajs-2149	169	38	follows	follow	VERB
iajs-2149	169	39	that	that	SCONJ
iajs-2149	169	40	,	,	PUNCT
iajs-2149	169	41	hence	hence	ADV
iajs-2149	169	42	contradiction	contradiction	NOUN
iajs-2149	169	43	.	.	PUNCT
iajs-2149	170	1	let	let	VERB
iajs-2149	170	2	́	́	PROPN
iajs-2149	170	3	,	,	PUNCT
iajs-2149	170	4	where	where	SCONJ
iajs-2149	170	5	and	and	CCONJ
iajs-2149	170	6	́	́	PROPN
iajs-2149	170	7	́	́	NOUN
iajs-2149	170	8	,	,	PUNCT
iajs-2149	170	9	since	since	SCONJ
iajs-2149	170	10	is	be	AUX
iajs-2149	170	11	on	on	ADP
iajs-2149	170	12	to	to	ADP
iajs-2149	170	13	,	,	PUNCT
iajs-2149	170	14	then	then	ADV
iajs-2149	170	15	́	́	PUNCT
iajs-2149	170	16	for	for	ADP
iajs-2149	170	17	some	some	PRON
iajs-2149	170	18	,	,	PUNCT
iajs-2149	170	19	hence	hence	ADV
iajs-2149	170	20	,	,	PUNCT
iajs-2149	170	21	it	it	PRON
iajs-2149	170	22	follows	follow	VERB
iajs-2149	170	23	that	that	SCONJ
iajs-2149	170	24	for	for	ADP
iajs-2149	170	25	some	some	PRON
iajs-2149	170	26	,	,	PUNCT
iajs-2149	170	27	that	that	ADV
iajs-2149	170	28	is	is	ADV
iajs-2149	170	29	,	,	PUNCT
iajs-2149	170	30	implies	imply	VERB
iajs-2149	170	31	that	that	SCONJ
iajs-2149	170	32	,	,	PUNCT
iajs-2149	170	33	it	it	PRON
iajs-2149	170	34	follows	follow	VERB
iajs-2149	170	35	that	that	PRON
iajs-2149	170	36	.	.	PUNCT
iajs-2149	171	1	but	but	CCONJ
iajs-2149	171	2	is	be	AUX
iajs-2149	171	3	a	a	DET
iajs-2149	171	4	pseudo	pseudo	NOUN
iajs-2149	171	5	quasi-2	quasi-2	NOUN
iajs-2149	171	6	-	-	PUNCT
iajs-2149	171	7	absorbing	absorbing	ADJ
iajs-2149	171	8	submodule	submodule	NOUN
iajs-2149	171	9	of	of	ADP
iajs-2149	171	10	,	,	PUNCT
iajs-2149	171	11	then	then	ADV
iajs-2149	171	12	either	either	CCONJ
iajs-2149	171	13	or	or	CCONJ
iajs-2149	171	14	or	or	CCONJ
iajs-2149	171	15	.	.	PUNCT
iajs-2149	172	1	it	it	PRON
iajs-2149	172	2	follows	follow	VERB
iajs-2149	172	3	that	that	SCONJ
iajs-2149	172	4	either	either	CCONJ
iajs-2149	172	5	(	(	PUNCT
iajs-2149	172	6	)	)	PUNCT
iajs-2149	172	7	́	́	PROPN
iajs-2149	172	8	or	or	CCONJ
iajs-2149	172	9	(	(	PUNCT
iajs-2149	172	10	)	)	PUNCT
iajs-2149	172	11	́	́	PROPN
iajs-2149	172	12	or	or	CCONJ
iajs-2149	172	13	(	(	PUNCT
iajs-2149	172	14	)	)	PUNCT
iajs-2149	172	15	́	́	PROPN
iajs-2149	172	16	.	.	PUNCT
iajs-2149	173	1	that	that	PRON
iajs-2149	173	2	is	be	AUX
iajs-2149	173	3	either	either	PRON
iajs-2149	173	4	́	́	PUNCT
iajs-2149	173	5	́	́	PROPN
iajs-2149	173	6	or	or	CCONJ
iajs-2149	173	7	́	́	PROPN
iajs-2149	173	8	́	́	PROPN
iajs-2149	173	9	or	or	CCONJ
iajs-2149	173	10	́	́	PROPN
iajs-2149	173	11	́	́	PROPN
iajs-2149	173	12	.	.	PUNCT
iajs-2149	174	1	therefore	therefore	ADV
iajs-2149	174	2	is	be	AUX
iajs-2149	174	3	a	a	DET
iajs-2149	174	4	pseudo	pseudo	NOUN
iajs-2149	174	5	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	174	6	submodule	submodule	NOUN
iajs-2149	174	7	of	of	ADP
iajs-2149	174	8	́.	́.	SYM
iajs-2149	174	9	121	121	NUM
iajs-2149	174	10	ibn	ibn	PROPN
iajs-2149	174	11	al	al	PROPN
iajs-2149	174	12	-	-	PUNCT
iajs-2149	174	13	haitham	haitham	PROPN
iajs-2149	174	14	jour	jour	X
iajs-2149	174	15	.	.	PROPN
iajs-2149	174	16	for	for	ADP
iajs-2149	174	17	pure	pure	ADJ
iajs-2149	174	18	&	&	CCONJ
iajs-2149	174	19	appl	appl	PROPN
iajs-2149	174	20	.	.	PUNCT
iajs-2149	175	1	sci	sci	PROPN
iajs-2149	175	2	.	.	PROPN
iajs-2149	175	3	32	32	NUM
iajs-2149	175	4	(	(	PUNCT
iajs-2149	175	5	2	2	NUM
iajs-2149	175	6	)	)	SYM
iajs-2149	175	7	2019	2019	NUM
iajs-2149	175	8	proposition	proposition	NOUN
iajs-2149	175	9	(	(	PUNCT
iajs-2149	175	10	24	24	NUM
iajs-2149	175	11	)	)	PUNCT
iajs-2149	175	12	let	let	AUX
iajs-2149	175	13	be	be	AUX
iajs-2149	175	14	an	an	DET
iajs-2149	175	15	-module	-module	NOUN
iajs-2149	175	16	,	,	PUNCT
iajs-2149	175	17	where	where	SCONJ
iajs-2149	175	18	are	be	AUX
iajs-2149	175	19	-modules	-module	NOUN
iajs-2149	175	20	and	and	CCONJ
iajs-2149	175	21	be	be	AUX
iajs-2149	175	22	a	a	DET
iajs-2149	175	23	submodule	submodule	NOUN
iajs-2149	175	24	of	of	ADP
iajs-2149	175	25	,	,	PUNCT
iajs-2149	175	26	where	where	SCONJ
iajs-2149	175	27	are	be	AUX
iajs-2149	175	28	submodules	submodule	NOUN
iajs-2149	175	29	of	of	ADP
iajs-2149	175	30	respectively	respectively	ADV
iajs-2149	175	31	,	,	PUNCT
iajs-2149	175	32	with	with	ADP
iajs-2149	175	33	.	.	PUNCT
iajs-2149	176	1	if	if	SCONJ
iajs-2149	176	2	is	be	AUX
iajs-2149	176	3	a	a	DET
iajs-2149	176	4	pseudo	pseudo	NOUN
iajs-2149	176	5	quasi-2	quasi-2	NOUN
iajs-2149	176	6	-	-	PUNCT
iajs-2149	176	7	absorbing	absorbing	ADJ
iajs-2149	176	8	submodule	submodule	NOUN
iajs-2149	176	9	of	of	ADP
iajs-2149	176	10	,	,	PUNCT
iajs-2149	176	11	then	then	ADV
iajs-2149	176	12	and	and	CCONJ
iajs-2149	176	13	are	be	AUX
iajs-2149	176	14	pseudo	pseudo	NOUN
iajs-2149	176	15	quasi-2	quasi-2	ADJ
iajs-2149	176	16	-	-	PUNCT
iajs-2149	176	17	absorbing	absorbing	ADJ
iajs-2149	176	18	submodules	submodule	NOUN
iajs-2149	176	19	of	of	ADP
iajs-2149	176	20	respectively	respectively	ADV
iajs-2149	176	21	.	.	PUNCT
iajs-2149	177	1	proof	proof	NOUN
iajs-2149	177	2	let	let	VERB
iajs-2149	177	3	,	,	PUNCT
iajs-2149	177	4	where	where	SCONJ
iajs-2149	177	5	,	,	PUNCT
iajs-2149	177	6	then	then	ADV
iajs-2149	177	7	.	.	PUNCT
iajs-2149	178	1	but	but	CCONJ
iajs-2149	178	2	is	be	AUX
iajs-2149	178	3	a	a	DET
iajs-2149	178	4	pseudo	pseudo	NOUN
iajs-2149	178	5	quasi2	quasi2	NOUN
iajs-2149	178	6	-	-	PUNCT
iajs-2149	178	7	absorbing	absorb	VERB
iajs-2149	178	8	submodule	submodule	NOUN
iajs-2149	178	9	of	of	ADP
iajs-2149	178	10	,	,	PUNCT
iajs-2149	178	11	then	then	ADV
iajs-2149	178	12	either	either	CCONJ
iajs-2149	178	13	or	or	CCONJ
iajs-2149	178	14	or	or	CCONJ
iajs-2149	178	15	.	.	PUNCT
iajs-2149	179	1	but	but	CCONJ
iajs-2149	179	2	,	,	PUNCT
iajs-2149	179	3	implies	imply	VERB
iajs-2149	179	4	that	that	PRON
iajs-2149	179	5	and	and	CCONJ
iajs-2149	179	6	.	.	PUNCT
iajs-2149	180	1	if	if	SCONJ
iajs-2149	180	2	,	,	PUNCT
iajs-2149	180	3	implies	imply	VERB
iajs-2149	180	4	that	that	PRON
iajs-2149	180	5	.	.	PUNCT
iajs-2149	181	1	if	if	SCONJ
iajs-2149	181	2	,	,	PUNCT
iajs-2149	181	3	implies	imply	VERB
iajs-2149	181	4	that	that	SCONJ
iajs-2149	181	5	,	,	PUNCT
iajs-2149	181	6	also	also	ADV
iajs-2149	181	7	in	in	ADP
iajs-2149	181	8	similar	similar	ADJ
iajs-2149	181	9	way	way	NOUN
iajs-2149	181	10	we	we	PRON
iajs-2149	181	11	get	get	VERB
iajs-2149	181	12	.	.	PUNCT
iajs-2149	182	1	therefore	therefore	ADV
iajs-2149	182	2	is	be	AUX
iajs-2149	182	3	a	a	DET
iajs-2149	182	4	pseudo	pseudo	NOUN
iajs-2149	182	5	quasi-2	quasi-2	NOUN
iajs-2149	182	6	-	-	PUNCT
iajs-2149	182	7	absorbing	absorbing	ADJ
iajs-2149	182	8	submodule	submodule	NOUN
iajs-2149	182	9	of	of	ADP
iajs-2149	182	10	.	.	PUNCT
iajs-2149	183	1	similarly	similarly	ADV
iajs-2149	183	2	,	,	PUNCT
iajs-2149	183	3	is	be	AUX
iajs-2149	183	4	a	a	DET
iajs-2149	183	5	pseudo	pseudo	NOUN
iajs-2149	183	6	quasi-2	quasi-2	NOUN
iajs-2149	183	7	-	-	PUNCT
iajs-2149	183	8	absorbing	absorbing	ADJ
iajs-2149	183	9	submodule	submodule	NOUN
iajs-2149	183	10	of	of	ADP
iajs-2149	183	11	.	.	PUNCT
iajs-2149	184	1	proposition	proposition	NOUN
iajs-2149	184	2	(	(	PUNCT
iajs-2149	184	3	25	25	NUM
iajs-2149	184	4	)	)	PUNCT
iajs-2149	184	5	let	let	AUX
iajs-2149	184	6	be	be	AUX
iajs-2149	184	7	two	two	NUM
iajs-2149	184	8	-modules	-module	NOUN
iajs-2149	184	9	and	and	CCONJ
iajs-2149	184	10	.	.	PUNCT
iajs-2149	185	1	then	then	ADV
iajs-2149	185	2	a	a	X
iajs-2149	185	3	)	)	PUNCT
iajs-2149	185	4	is	be	AUX
iajs-2149	185	5	a	a	DET
iajs-2149	185	6	pseudo	pseudo	NOUN
iajs-2149	185	7	quasi-2	quasi-2	NOUN
iajs-2149	185	8	-	-	PUNCT
iajs-2149	185	9	absorbing	absorbing	ADJ
iajs-2149	185	10	submodule	submodule	NOUN
iajs-2149	185	11	of	of	ADP
iajs-2149	185	12	,	,	PUNCT
iajs-2149	185	13	with	with	ADP
iajs-2149	185	14	and	and	CCONJ
iajs-2149	185	15	is	be	AUX
iajs-2149	185	16	a	a	DET
iajs-2149	185	17	semi	semi	ADJ
iajs-2149	185	18	simple	simple	ADJ
iajs-2149	185	19	if	if	SCONJ
iajs-2149	185	20	and	and	CCONJ
iajs-2149	185	21	only	only	ADV
iajs-2149	185	22	if	if	SCONJ
iajs-2149	185	23	is	be	AUX
iajs-2149	185	24	a	a	DET
iajs-2149	185	25	pseudo	pseudo	NOUN
iajs-2149	185	26	quasi-2	quasi-2	NOUN
iajs-2149	185	27	-	-	PUNCT
iajs-2149	185	28	absorbing	absorbing	ADJ
iajs-2149	185	29	submodule	submodule	NOUN
iajs-2149	185	30	of	of	ADP
iajs-2149	185	31	.	.	PUNCT
iajs-2149	186	1	b	b	X
iajs-2149	186	2	)	)	PUNCT
iajs-2149	186	3	is	be	AUX
iajs-2149	186	4	a	a	DET
iajs-2149	186	5	pseudo	pseudo	NOUN
iajs-2149	186	6	quasi-2	quasi-2	NOUN
iajs-2149	186	7	-	-	PUNCT
iajs-2149	186	8	absorbing	absorbing	ADJ
iajs-2149	186	9	submodule	submodule	NOUN
iajs-2149	186	10	of	of	ADP
iajs-2149	186	11	,	,	PUNCT
iajs-2149	186	12	with	with	ADP
iajs-2149	186	13	and	and	CCONJ
iajs-2149	186	14	is	be	AUX
iajs-2149	186	15	a	a	DET
iajs-2149	186	16	semi	semi	ADJ
iajs-2149	186	17	simple	simple	ADJ
iajs-2149	186	18	if	if	SCONJ
iajs-2149	186	19	and	and	CCONJ
iajs-2149	186	20	only	only	ADV
iajs-2149	186	21	if	if	SCONJ
iajs-2149	186	22	is	be	AUX
iajs-2149	186	23	a	a	DET
iajs-2149	186	24	pseudo	pseudo	NOUN
iajs-2149	186	25	quasi-2	quasi-2	NOUN
iajs-2149	186	26	-	-	PUNCT
iajs-2149	186	27	absorbing	absorbing	ADJ
iajs-2149	186	28	submodule	submodule	NOUN
iajs-2149	186	29	of	of	ADP
iajs-2149	186	30	.	.	PUNCT
iajs-2149	187	1	proof	proof	NOUN
iajs-2149	187	2	a	a	X
iajs-2149	187	3	)	)	PUNCT
iajs-2149	187	4	let	let	VERB
iajs-2149	187	5	,	,	PUNCT
iajs-2149	187	6	where	where	SCONJ
iajs-2149	187	7	and	and	CCONJ
iajs-2149	187	8	,	,	PUNCT
iajs-2149	187	9	implies	imply	VERB
iajs-2149	187	10	that	that	PRON
iajs-2149	187	11	and	and	CCONJ
iajs-2149	187	12	.	.	PUNCT
iajs-2149	188	1	since	since	SCONJ
iajs-2149	188	2	is	be	AUX
iajs-2149	188	3	a	a	DET
iajs-2149	188	4	pseudo	pseudo	NOUN
iajs-2149	188	5	quasi-2	quasi-2	NOUN
iajs-2149	188	6	-	-	PUNCT
iajs-2149	188	7	absorbing	absorbing	ADJ
iajs-2149	188	8	submodule	submodule	NOUN
iajs-2149	188	9	of	of	ADP
iajs-2149	188	10	,	,	PUNCT
iajs-2149	188	11	and	and	CCONJ
iajs-2149	188	12	,	,	PUNCT
iajs-2149	188	13	then	then	ADV
iajs-2149	188	14	either	either	CCONJ
iajs-2149	188	15	or	or	CCONJ
iajs-2149	188	16	or	or	CCONJ
iajs-2149	188	17	.	.	PUNCT
iajs-2149	189	1	since	since	SCONJ
iajs-2149	189	2	is	be	AUX
iajs-2149	189	3	a	a	DET
iajs-2149	189	4	semi	semi	ADJ
iajs-2149	189	5	simple	simple	ADJ
iajs-2149	189	6	,	,	PUNCT
iajs-2149	189	7	then	then	ADV
iajs-2149	189	8	by	by	ADP
iajs-2149	189	9	[	[	PUNCT
iajs-2149	189	10	]	]	X
iajs-2149	189	11	,	,	PUNCT
iajs-2149	189	12	then	then	ADV
iajs-2149	189	13	.	.	PUNCT
iajs-2149	190	1	if	if	SCONJ
iajs-2149	190	2	.	.	PUNCT
iajs-2149	191	1	if	if	SCONJ
iajs-2149	191	2	.	.	PUNCT
iajs-2149	192	1	hence	hence	ADV
iajs-2149	192	2	is	be	AUX
iajs-2149	192	3	a	a	DET
iajs-2149	192	4	pseudo	pseudo	NOUN
iajs-2149	192	5	quasi-2	quasi-2	NOUN
iajs-2149	192	6	-	-	PUNCT
iajs-2149	192	7	absorbing	absorbing	ADJ
iajs-2149	192	8	submodule	submodule	NOUN
iajs-2149	192	9	of	of	ADP
iajs-2149	192	10	.	.	PUNCT
iajs-2149	193	1	let	let	VERB
iajs-2149	193	2	,	,	PUNCT
iajs-2149	193	3	where	where	SCONJ
iajs-2149	193	4	,	,	PUNCT
iajs-2149	193	5	then	then	ADV
iajs-2149	193	6	for	for	ADP
iajs-2149	193	7	each	each	PRON
iajs-2149	193	8	,	,	PUNCT
iajs-2149	193	9	.	.	PUNCT
iajs-2149	194	1	but	but	CCONJ
iajs-2149	194	2	is	be	AUX
iajs-2149	194	3	a	a	DET
iajs-2149	194	4	pseudo	pseudo	NOUN
iajs-2149	194	5	quasi-2	quasi-2	NOUN
iajs-2149	194	6	-	-	PUNCT
iajs-2149	194	7	absorbing	absorbing	ADJ
iajs-2149	194	8	submodule	submodule	NOUN
iajs-2149	194	9	of	of	ADP
iajs-2149	194	10	,	,	PUNCT
iajs-2149	194	11	so	so	ADV
iajs-2149	194	12	either	either	PRON
iajs-2149	194	13	or	or	CCONJ
iajs-2149	194	14	or	or	CCONJ
iajs-2149	194	15	.	.	PUNCT
iajs-2149	195	1	if	if	SCONJ
iajs-2149	195	2	(	(	PUNCT
iajs-2149	195	3	)	)	PUNCT
iajs-2149	195	4	.	.	PUNCT
iajs-2149	196	1	it	it	PRON
iajs-2149	196	2	follows	follow	VERB
iajs-2149	196	3	that	that	PRON
iajs-2149	196	4	.	.	PUNCT
iajs-2149	197	1	similarly	similarly	ADV
iajs-2149	197	2	,	,	PUNCT
iajs-2149	197	3	if	if	SCONJ
iajs-2149	197	4	,	,	PUNCT
iajs-2149	197	5	implies	imply	VERB
iajs-2149	197	6	that	that	SCONJ
iajs-2149	197	7	:	:	PUNCT
iajs-2149	197	8	,	,	PUNCT
iajs-2149	197	9	it	it	PRON
iajs-2149	197	10	follows	follow	VERB
iajs-2149	197	11	that	that	PRON
iajs-2149	197	12	.	.	PUNCT
iajs-2149	198	1	similarly	similarly	ADV
iajs-2149	198	2	,	,	PUNCT
iajs-2149	198	3	we	we	PRON
iajs-2149	198	4	get	get	VERB
iajs-2149	198	5	.	.	PUNCT
iajs-2149	199	1	therefore	therefore	ADV
iajs-2149	199	2	is	be	AUX
iajs-2149	199	3	a	a	DET
iajs-2149	199	4	pseudo	pseudo	NOUN
iajs-2149	199	5	quasi-2	quasi-2	NOUN
iajs-2149	199	6	-	-	PUNCT
iajs-2149	199	7	absorbing	absorbing	ADJ
iajs-2149	199	8	submodule	submodule	NOUN
iajs-2149	199	9	of	of	ADP
iajs-2149	199	10	.	.	PUNCT
iajs-2149	200	1	the	the	DET
iajs-2149	200	2	proof	proof	NOUN
iajs-2149	200	3	of	of	ADP
iajs-2149	200	4	(	(	PUNCT
iajs-2149	200	5	b	b	NOUN
iajs-2149	200	6	)	)	PUNCT
iajs-2149	200	7	is	be	AUX
iajs-2149	200	8	similarly	similarly	ADV
iajs-2149	200	9	.	.	PUNCT
iajs-2149	201	1	122	122	NUM
iajs-2149	201	2	ibn	ibn	PROPN
iajs-2149	201	3	al	al	PROPN
iajs-2149	201	4	-	-	PUNCT
iajs-2149	201	5	haitham	haitham	PROPN
iajs-2149	201	6	jour	jour	X
iajs-2149	201	7	.	.	PROPN
iajs-2149	201	8	for	for	ADP
iajs-2149	201	9	pure	pure	ADJ
iajs-2149	201	10	&	&	CCONJ
iajs-2149	201	11	appl	appl	PROPN
iajs-2149	201	12	.	.	PUNCT
iajs-2149	202	1	sci	sci	PROPN
iajs-2149	202	2	.	.	PROPN
iajs-2149	202	3	32	32	NUM
iajs-2149	202	4	(	(	PUNCT
iajs-2149	202	5	2	2	NUM
iajs-2149	202	6	)	)	PUNCT
iajs-2149	202	7	2019	2019	NUM
iajs-2149	202	8	3	3	NUM
iajs-2149	202	9	.	.	PUNCT
iajs-2149	202	10	conclusion	conclusion	NOUN
iajs-2149	202	11	in	in	ADP
iajs-2149	202	12	this	this	DET
iajs-2149	202	13	research	research	NOUN
iajs-2149	202	14	we	we	PRON
iajs-2149	202	15	introduce	introduce	VERB
iajs-2149	202	16	and	and	CCONJ
iajs-2149	202	17	study	study	VERB
iajs-2149	202	18	the	the	DET
iajs-2149	202	19	concept	concept	NOUN
iajs-2149	202	20	pseudo	pseudo	NOUN
iajs-2149	202	21	quasi-2	quasi-2	NOUN
iajs-2149	202	22	-	-	PUNCT
iajs-2149	202	23	absorbing	absorbing	ADJ
iajs-2149	202	24	submodules	submodule	NOUN
iajs-2149	202	25	as	as	ADP
iajs-2149	202	26	a	a	DET
iajs-2149	202	27	generalization	generalization	NOUN
iajs-2149	202	28	of	of	ADP
iajs-2149	202	29	quasi	quasi	ADJ
iajs-2149	202	30	-	-	ADJ
iajs-2149	202	31	prime	prime	ADJ
iajs-2149	202	32	and	and	CCONJ
iajs-2149	202	33	2	2	NUM
iajs-2149	202	34	-	-	PUNCT
iajs-2149	202	35	absorbing	absorbing	ADJ
iajs-2149	202	36	submodules	submodule	NOUN
iajs-2149	202	37	.	.	PUNCT
iajs-2149	203	1	the	the	DET
iajs-2149	203	2	main	main	ADJ
iajs-2149	203	3	results	result	NOUN
iajs-2149	203	4	of	of	ADP
iajs-2149	203	5	this	this	DET
iajs-2149	203	6	study	study	NOUN
iajs-2149	203	7	are	be	AUX
iajs-2149	203	8	the	the	DET
iajs-2149	203	9	following	follow	VERB
iajs-2149	203	10	:	:	PUNCT
iajs-2149	203	11	1a	1a	X
iajs-2149	203	12	proper	proper	ADJ
iajs-2149	203	13	submodule	submodule	NOUN
iajs-2149	203	14	of	of	ADP
iajs-2149	203	15	an	an	DET
iajs-2149	203	16	-module	-module	NOUN
iajs-2149	203	17	is	be	AUX
iajs-2149	203	18	a	a	DET
iajs-2149	203	19	pseudo	pseudo	NOUN
iajs-2149	203	20	quasi-2	quasi-2	NOUN
iajs-2149	203	21	-	-	PUNCT
iajs-2149	203	22	absorbing	absorbing	ADJ
iajs-2149	203	23	submodule	submodule	NOUN
iajs-2149	203	24	of	of	ADP
iajs-2149	203	25	if	if	SCONJ
iajs-2149	203	26	and	and	CCONJ
iajs-2149	203	27	only	only	ADV
iajs-2149	203	28	if	if	SCONJ
iajs-2149	203	29	for	for	ADP
iajs-2149	203	30	every	every	DET
iajs-2149	203	31	ideals	ideal	NOUN
iajs-2149	203	32	of	of	ADP
iajs-2149	203	33	and	and	CCONJ
iajs-2149	203	34	submodule	submodule	NOUN
iajs-2149	203	35	of	of	ADP
iajs-2149	203	36	with	with	ADP
iajs-2149	203	37	,	,	PUNCT
iajs-2149	203	38	implies	imply	VERB
iajs-2149	203	39	that	that	SCONJ
iajs-2149	203	40	either	either	CCONJ
iajs-2149	203	41	or	or	CCONJ
iajs-2149	203	42	or	or	CCONJ
iajs-2149	203	43	.	.	PUNCT
iajs-2149	204	1	2let	2let	NUM
iajs-2149	204	2	be	be	AUX
iajs-2149	204	3	a	a	DET
iajs-2149	204	4	faithful	faithful	ADJ
iajs-2149	204	5	finitely	finitely	ADV
iajs-2149	204	6	generated	generate	VERB
iajs-2149	204	7	multiplication	multiplication	NOUN
iajs-2149	204	8	-module	-module	NOUN
iajs-2149	204	9	and	and	CCONJ
iajs-2149	204	10	is	be	AUX
iajs-2149	204	11	a	a	DET
iajs-2149	204	12	pseudo	pseudo	NOUN
iajs-2149	204	13	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	204	14	ideal	ideal	NOUN
iajs-2149	204	15	of	of	ADP
iajs-2149	204	16	,	,	PUNCT
iajs-2149	204	17	then	then	ADV
iajs-2149	204	18	is	be	AUX
iajs-2149	204	19	a	a	DET
iajs-2149	204	20	pseudo	pseudo	NOUN
iajs-2149	204	21	quasi-2	quasi-2	NOUN
iajs-2149	204	22	-	-	PUNCT
iajs-2149	204	23	absorbing	absorbing	ADJ
iajs-2149	204	24	submodule	submodule	NOUN
iajs-2149	204	25	of	of	ADP
iajs-2149	204	26	.	.	PUNCT
iajs-2149	205	1	3a	3a	PROPN
iajs-2149	205	2	proper	proper	ADJ
iajs-2149	205	3	submodule	submodule	NOUN
iajs-2149	205	4	of	of	ADP
iajs-2149	205	5	an	an	DET
iajs-2149	205	6	-module	-module	NOUN
iajs-2149	205	7	,	,	PUNCT
iajs-2149	205	8	with	with	ADP
iajs-2149	205	9	is	be	AUX
iajs-2149	205	10	a	a	DET
iajs-2149	205	11	pseudo	pseudo	NOUN
iajs-2149	205	12	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	205	13	submodule	submodule	NOUN
iajs-2149	205	14	of	of	ADP
iajs-2149	205	15	if	if	SCONJ
iajs-2149	206	1	and	and	CCONJ
iajs-2149	206	2	only	only	ADV
iajs-2149	206	3	if	if	SCONJ
iajs-2149	206	4	[	[	PUNCT
iajs-2149	206	5	]	]	X
iajs-2149	206	6	[	[	PUNCT
iajs-2149	206	7	]	]	X
iajs-2149	206	8	[	[	PUNCT
iajs-2149	206	9	]	]	X
iajs-2149	206	10	[	[	PUNCT
iajs-2149	206	11	]	]	X
iajs-2149	206	12	for	for	ADP
iajs-2149	206	13	all	all	PRON
iajs-2149	206	14	.	.	PUNCT
iajs-2149	207	1	4a	4a	NUM
iajs-2149	207	2	proper	proper	ADJ
iajs-2149	207	3	submodule	submodule	NOUN
iajs-2149	207	4	of	of	ADP
iajs-2149	207	5	an	an	DET
iajs-2149	207	6	-module	-module	NOUN
iajs-2149	207	7	,	,	PUNCT
iajs-2149	207	8	with	with	ADP
iajs-2149	207	9	is	be	AUX
iajs-2149	207	10	a	a	DET
iajs-2149	207	11	pseudo	pseudo	NOUN
iajs-2149	207	12	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	207	13	submodule	submodule	NOUN
iajs-2149	207	14	of	of	ADP
iajs-2149	207	15	if	if	SCONJ
iajs-2149	208	1	and	and	CCONJ
iajs-2149	208	2	only	only	ADV
iajs-2149	208	3	if	if	SCONJ
iajs-2149	208	4	[	[	PUNCT
iajs-2149	208	5	]	]	X
iajs-2149	208	6	[	[	PUNCT
iajs-2149	208	7	]	]	X
iajs-2149	208	8	[	[	PUNCT
iajs-2149	208	9	]	]	X
iajs-2149	208	10	for	for	ADP
iajs-2149	208	11	all	all	PRON
iajs-2149	208	12	.	.	PUNCT
iajs-2149	209	1	5the	5the	DET
iajs-2149	209	2	intersection	intersection	NOUN
iajs-2149	209	3	of	of	ADP
iajs-2149	209	4	two	two	NUM
iajs-2149	209	5	pseudo	pseudo	NOUN
iajs-2149	209	6	quasi-2	quasi-2	NOUN
iajs-2149	209	7	-	-	PUNCT
iajs-2149	209	8	absorbing	absorbing	ADJ
iajs-2149	209	9	submodules	submodule	NOUN
iajs-2149	209	10	of	of	ADP
iajs-2149	209	11	an	an	DET
iajs-2149	209	12	-module	-module	NOUN
iajs-2149	209	13	need	need	VERB
iajs-2149	209	14	not	not	PART
iajs-2149	209	15	to	to	PART
iajs-2149	209	16	be	be	AUX
iajs-2149	209	17	pseudo	pseudo	VERB
iajs-2149	209	18	quasi-2	quasi-2	NOUN
iajs-2149	209	19	-	-	PUNCT
iajs-2149	209	20	absorbing	absorbing	NOUN
iajs-2149	209	21	.	.	PUNCT
iajs-2149	210	1	this	this	PRON
iajs-2149	210	2	explain	explain	VERB
iajs-2149	210	3	by	by	ADP
iajs-2149	210	4	example	example	NOUN
iajs-2149	210	5	see	see	NOUN
iajs-2149	210	6	remark	remark	NOUN
iajs-2149	210	7	(	(	PUNCT
iajs-2149	210	8	19	19	NUM
iajs-2149	210	9	)	)	PUNCT
iajs-2149	210	10	.	.	PUNCT
iajs-2149	211	1	but	but	CCONJ
iajs-2149	211	2	under	under	ADP
iajs-2149	211	3	certain	certain	ADJ
iajs-2149	211	4	conditions	condition	NOUN
iajs-2149	211	5	the	the	DET
iajs-2149	211	6	intersection	intersection	NOUN
iajs-2149	211	7	are	be	AUX
iajs-2149	211	8	satisfies	satisfie	NOUN
iajs-2149	211	9	see	see	VERB
iajs-2149	211	10	proposition	proposition	NOUN
iajs-2149	211	11	(	(	PUNCT
iajs-2149	211	12	20	20	NUM
iajs-2149	211	13	)	)	PUNCT
iajs-2149	211	14	.	.	PUNCT
iajs-2149	212	1	6the	6the	DET
iajs-2149	212	2	inverse	inverse	NOUN
iajs-2149	212	3	image	image	NOUN
iajs-2149	212	4	and	and	CCONJ
iajs-2149	212	5	homomorphism	homomorphism	NOUN
iajs-2149	212	6	image	image	NOUN
iajs-2149	212	7	of	of	ADP
iajs-2149	212	8	pseudo	pseudo	NOUN
iajs-2149	212	9	quasi-2	quasi-2	NOUN
iajs-2149	212	10	-	-	PUNCT
iajs-2149	212	11	absorbing	absorb	VERB
iajs-2149	212	12	submodule	submodule	NOUN
iajs-2149	212	13	is	be	AUX
iajs-2149	212	14	pseudo	pseudo	ADJ
iajs-2149	212	15	quasi-2	quasi-2	ADJ
iajs-2149	212	16	-	-	PUNCT
iajs-2149	212	17	absorbing	absorbing	ADJ
iajs-2149	212	18	see	see	NOUN
iajs-2149	212	19	proposition	proposition	NOUN
iajs-2149	212	20	(	(	PUNCT
iajs-2149	212	21	22	22	NUM
iajs-2149	212	22	)	)	PUNCT
iajs-2149	212	23	,	,	PUNCT
iajs-2149	212	24	(	(	PUNCT
iajs-2149	212	25	23	23	NUM
iajs-2149	212	26	)	)	PUNCT
iajs-2149	212	27	.	.	PUNCT
iajs-2149	213	1	7the	7the	NUM
iajs-2149	213	2	direct	direct	ADJ
iajs-2149	213	3	summand	summand	NOUN
iajs-2149	213	4	of	of	ADP
iajs-2149	213	5	pseudo	pseudo	NOUN
iajs-2149	213	6	quasi2	quasi2	NOUN
iajs-2149	213	7	-	-	PUNCT
iajs-2149	213	8	absorbing	absorb	VERB
iajs-2149	213	9	submodule	submodule	NOUN
iajs-2149	213	10	is	be	AUX
iajs-2149	213	11	a	a	DET
iajs-2149	213	12	pseudo	pseudo	NOUN
iajs-2149	213	13	quasi-2absorbing	quasi-2absorbe	VERB
iajs-2149	213	14	submodule	submodule	NOUN
iajs-2149	213	15	see	see	VERB
iajs-2149	213	16	proposition	proposition	NOUN
iajs-2149	213	17	(	(	PUNCT
iajs-2149	213	18	24	24	NUM
iajs-2149	213	19	)	)	PUNCT
iajs-2149	213	20	.	.	PUNCT
iajs-2149	214	1	references	reference	NOUN
iajs-2149	214	2	1	1	NUM
iajs-2149	214	3	.	.	X
iajs-2149	214	4	lu	lu	PROPN
iajs-2149	214	5	,	,	PUNCT
iajs-2149	214	6	c.p	c.p	PROPN
iajs-2149	214	7	.	.	PROPN
iajs-2149	214	8	prime	prime	ADJ
iajs-2149	214	9	submodules	submodule	NOUN
iajs-2149	214	10	of	of	ADP
iajs-2149	214	11	modules	module	NOUN
iajs-2149	214	12	.	.	PUNCT
iajs-2149	215	1	commutative	commutative	ADJ
iajs-2149	215	2	mathematics	mathematic	NOUN
iajs-2149	215	3	.	.	PUNCT
iajs-2149	216	1	university	university	NOUN
iajs-2149	216	2	spatula	spatula	NOUN
iajs-2149	216	3	.	.	PUNCT
iajs-2149	217	1	1981	1981	NUM
iajs-2149	217	2	,	,	PUNCT
iajs-2149	217	3	33	33	NUM
iajs-2149	217	4	,	,	PUNCT
iajs-2149	217	5	61	61	NUM
iajs-2149	217	6	-	-	SYM
iajs-2149	217	7	69	69	NUM
iajs-2149	217	8	.	.	PUNCT
iajs-2149	218	1	2	2	NUM
iajs-2149	218	2	.	.	X
iajs-2149	218	3	abdwl	abdwl	NOUN
iajs-2149	218	4	-	-	PUNCT
iajs-2149	218	5	razak	razak	PROPN
iajs-2149	218	6	,	,	PUNCT
iajs-2149	218	7	h.m	h.m	PROPN
iajs-2149	218	8	.	.	PROPN
iajs-2149	218	9	quasi	quasi	ADJ
iajs-2149	218	10	-	-	ADJ
iajs-2149	218	11	prime	prime	ADJ
iajs-2149	218	12	modules	module	NOUN
iajs-2149	218	13	and	and	CCONJ
iajs-2149	218	14	quasi	quasi	ADJ
iajs-2149	218	15	-	-	ADJ
iajs-2149	218	16	prime	prime	ADJ
iajs-2149	218	17	submodules	submodule	NOUN
iajs-2149	218	18	.	.	PUNCT
iajs-2149	219	1	m.sc	m.sc	NOUN
iajs-2149	219	2	.	.	PUNCT
iajs-2149	220	1	thesis	thesis	NOUN
iajs-2149	220	2	.	.	PUNCT
iajs-2149	221	1	university	university	NOUN
iajs-2149	221	2	of	of	ADP
iajs-2149	221	3	baghdad	baghdad	PROPN
iajs-2149	221	4	.	.	PUNCT
iajs-2149	222	1	1999	1999	NUM
iajs-2149	222	2	3	3	NUM
iajs-2149	222	3	.	.	PUNCT
iajs-2149	222	4	hussin	hussin	PROPN
iajs-2149	222	5	,	,	PUNCT
iajs-2149	222	6	s.a	s.a	PROPN
iajs-2149	222	7	.	.	PROPN
iajs-2149	222	8	;	;	PUNCT
iajs-2149	222	9	mohammad	mohammad	PROPN
iajs-2149	222	10	ali	ali	PROPN
iajs-2149	222	11	,	,	PUNCT
iajs-2149	222	12	h.k	h.k	PROPN
iajs-2149	222	13	.	.	PROPN
iajs-2149	223	1	we	we	PRON
iajs-2149	223	2	prime	prime	ADJ
iajs-2149	223	3	sub	sub	NOUN
iajs-2149	223	4	modules	module	NOUN
iajs-2149	223	5	and	and	CCONJ
iajs-2149	223	6	we	we	PRON
iajs-2149	223	7	–	–	PUNCT
iajs-2149	223	8	semi	semi	ADV
iajs-2149	223	9	prime	prime	ADJ
iajs-2149	223	10	sub	sub	NOUN
iajs-2149	223	11	modules	module	NOUN
iajs-2149	223	12	.	.	PUNCT
iajs-2149	224	1	ibn	ibn	PROPN
iajs-2149	224	2	-	-	PUNCT
iajs-2149	224	3	al	al	PROPN
iajs-2149	224	4	-	-	PUNCT
iajs-2149	224	5	haitham	haitham	PROPN
iajs-2149	224	6	jonral	jonral	PROPN
iajs-2149	224	7	for	for	ADP
iajs-2149	224	8	pure	pure	ADJ
iajs-2149	224	9	and	and	CCONJ
iajs-2149	224	10	appled	appled	ADJ
iajs-2149	224	11	science	science	NOUN
iajs-2149	224	12	.	.	PUNCT
iajs-2149	225	1	2018	2018	NUM
iajs-2149	225	2	,	,	PUNCT
iajs-2149	225	3	31	31	NUM
iajs-2149	225	4	,	,	PUNCT
iajs-2149	225	5	3	3	NUM
iajs-2149	225	6	,	,	PUNCT
iajs-2149	225	7	109	109	NUM
iajs-2149	225	8	-	-	SYM
iajs-2149	225	9	117	117	NUM
iajs-2149	225	10	.	.	NOUN
iajs-2149	226	1	4	4	NUM
iajs-2149	226	2	.	.	X
iajs-2149	226	3	darani	darani	PROPN
iajs-2149	226	4	,	,	PUNCT
iajs-2149	226	5	a.y	a.y	PROPN
iajs-2149	226	6	.	.	PROPN
iajs-2149	226	7	;	;	PUNCT
iajs-2149	226	8	soheilniai	soheilniai	PROPN
iajs-2149	226	9	,	,	PUNCT
iajs-2149	226	10	f.	f.	NOUN
iajs-2149	226	11	2	2	NUM
iajs-2149	226	12	-	-	PUNCT
iajs-2149	226	13	absorbing	absorbing	ADJ
iajs-2149	226	14	and	and	CCONJ
iajs-2149	226	15	weakly	weakly	ADJ
iajs-2149	226	16	2	2	NUM
iajs-2149	226	17	-	-	PUNCT
iajs-2149	226	18	absorbing	absorbing	ADJ
iajs-2149	226	19	submodules	submodule	NOUN
iajs-2149	226	20	.	.	PUNCT
iajs-2149	227	1	tahi	tahi	NOUN
iajs-2149	227	2	journal	journal	PROPN
iajs-2149	228	1	math.2011	math.2011	PROPN
iajs-2149	228	2	,	,	PUNCT
iajs-2149	228	3	9	9	NUM
iajs-2149	228	4	,	,	PUNCT
iajs-2149	228	5	577	577	NUM
iajs-2149	228	6	-	-	SYM
iajs-2149	228	7	584	584	NUM
iajs-2149	228	8	.	.	NOUN
iajs-2149	228	9	5	5	NUM
iajs-2149	228	10	.	.	X
iajs-2149	229	1	hussin	hussin	PROPN
iajs-2149	229	2	,	,	PUNCT
iajs-2149	229	3	w.a	w.a	PROPN
iajs-2149	229	4	.	.	PROPN
iajs-2149	229	5	;	;	PUNCT
iajs-2149	229	6	mohammad	mohammad	PROPN
iajs-2149	229	7	ali	ali	PROPN
iajs-2149	229	8	,	,	PUNCT
iajs-2149	229	9	h.k	h.k	PROPN
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iajs-2149	229	16	wes-2	wes-2	NOUN
iajs-2149	229	17	-	-	PUNCT
iajs-2149	229	18	absorbing	absorbing	ADJ
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iajs-2149	229	20	.	.	PUNCT
iajs-2149	230	1	ibn	ibn	PROPN
iajs-2149	230	2	-	-	PUNCT
iajs-2149	230	3	al	al	PROPN
iajs-2149	230	4	-	-	PUNCT
iajs-2149	230	5	haitham	haitham	PROPN
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iajs-2149	230	12	.	.	PUNCT
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iajs-2149	231	8	.	.	NOUN
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iajs-2149	232	2	.	.	X
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iajs-2149	232	5	h.k	h.k	PROPN
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iajs-2149	233	8	,	,	PUNCT
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iajs-2149	233	10	.	.	PUNCT
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iajs-2149	234	2	.	.	PUNCT
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iajs-2149	235	4	.	.	PUNCT
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iajs-2149	236	2	.	.	PUNCT
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iajs-2149	237	2	.	.	X
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iajs-2149	237	4	,	,	PUNCT
iajs-2149	237	5	k.r	k.r	PROPN
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iajs-2149	237	15	.	.	PUNCT
iajs-2149	238	1	marcel	marcel	PROPN
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iajs-2149	238	3	.	.	PUNCT
iajs-2149	239	1	inc	inc	PROPN
iajs-2149	239	2	.	.	PROPN
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iajs-2149	239	7	.	.	PUNCT
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iajs-2149	239	9	.	.	PUNCT
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iajs-2149	240	2	.	.	X
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iajs-2149	240	14	,	,	PUNCT
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iajs-2149	241	1	aus	aus	PROPN
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iajs-2149	241	3	.	.	PUNCT
iajs-2149	242	1	math	math	NOUN
iajs-2149	242	2	.	.	PUNCT
iajs-2149	243	1	soc	soc	PROPN
iajs-2149	243	2	.	.	PUNCT
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iajs-2149	244	2	,	,	PUNCT
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iajs-2149	244	8	.	.	NOUN
iajs-2149	245	1	9	9	NUM
iajs-2149	245	2	.	.	X
iajs-2149	246	1	el	el	NOUN
iajs-2149	246	2	-	-	PUNCT
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iajs-2149	246	5	z.a	z.a	PROPN
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iajs-2149	246	10	p.f	p.f	PROPN
iajs-2149	246	11	.	.	PROPN
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iajs-2149	246	14	.	.	PUNCT
iajs-2149	247	1	comm	comm	NOUN
iajs-2149	247	2	.	.	PUNCT
iajs-2149	248	1	in	in	ADP
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iajs-2149	248	3	,	,	PUNCT
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iajs-2149	248	7	,	,	PUNCT
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iajs-2149	248	9	-	-	SYM
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iajs-2149	248	12	.	.	PUNCT
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iajs-2149	249	2	,	,	PUNCT
iajs-2149	249	3	p.f	p.f	PROPN
iajs-2149	249	4	.	.	PUNCT
iajs-2149	250	1	some	some	DET
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iajs-2149	250	3	on	on	ADP
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iajs-2149	250	6	.	.	PUNCT
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iajs-2149	251	2	.	.	PUNCT
iajs-2149	252	1	math.1988	math.1988	PROPN
iajs-2149	252	2	,	,	PUNCT
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iajs-2149	252	4	,	,	PUNCT
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iajs-2149	252	6	-	-	SYM
iajs-2149	252	7	225	225	NUM
iajs-2149	252	8	.	.	PUNCT
iajs-2149	253	1	11	11	NUM
iajs-2149	253	2	.	.	PUNCT
iajs-2149	254	1	kasch	kasch	PROPN
iajs-2149	254	2	,	,	PUNCT
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iajs-2149	254	6	rings	ring	NOUN
iajs-2149	254	7	.	.	PUNCT
iajs-2149	255	1	london	london	PROPN
iajs-2149	255	2	mathematical	mathematical	ADJ
iajs-2149	255	3	society	society	NOUN
iajs-2149	255	4	monographs	monograph	NOUN
iajs-2149	255	5	.	.	PUNCT
iajs-2149	256	1	new	new	PROPN
iajs-2149	256	2	york	york	PROPN
iajs-2149	256	3	.	.	PUNCT
iajs-2149	257	1	academic	academic	ADJ
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iajs-2149	257	3	.	.	PUNCT
iajs-2149	258	1	1982	1982	NUM
iajs-2149	258	2	.	.	PUNCT
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iajs-2149	259	2	.	.	PUNCT
iajs-2149	260	1	anderson	anderson	PROPN
iajs-2149	260	2	,	,	PUNCT
iajs-2149	260	3	e.w	e.w	PROPN
iajs-2149	260	4	.	.	PROPN
iajs-2149	260	5	;	;	PUNCT
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iajs-2149	260	7	k.r	k.r	PROPN
iajs-2149	260	8	.	.	PROPN
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iajs-2149	260	10	and	and	CCONJ
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iajs-2149	260	13	modules	module	NOUN
iajs-2149	260	14	.	.	PUNCT
iajs-2149	261	1	springervelage	springervelage	PROPN
iajs-2149	261	2	new	new	PROPN
iajs-2149	261	3	york	york	PROPN
iajs-2149	261	4	.	.	PUNCT
iajs-2149	261	5	1992	1992	NUM