id	sid	tid	token	lemma	pos
iajs-2476	1	1	microsoft	microsoft	PROPN
iajs-2476	1	2	word	word	PROPN
iajs-2476	1	3	89	89	NUM
iajs-2476	1	4	-	-	SYM
iajs-2476	1	5	100	100	NUM
iajs-2476	1	6	  	  	SPACE
iajs-2476	1	7	89	89	NUM
iajs-2476	1	8	ibn	ibn	PROPN
iajs-2476	1	9	al	al	PROPN
iajs-2476	1	10	-	-	PUNCT
iajs-2476	1	11	haitham	haitham	PROPN
iajs-2476	1	12	jour	jour	X
iajs-2476	1	13	.	.	PROPN
iajs-2476	2	1	for	for	ADP
iajs-2476	2	2	pure	pure	ADJ
iajs-2476	2	3	&	&	CCONJ
iajs-2476	2	4	appl	appl	PROPN
iajs-2476	2	5	.	.	PUNCT
iajs-2476	3	1	sci	sci	PROPN
iajs-2476	3	2	.	.	PROPN
iajs-2476	4	1	33	33	NUM
iajs-2476	4	2	(	(	PUNCT
iajs-2476	4	3	3	3	NUM
iajs-2476	4	4	)	)	PUNCT
iajs-2476	4	5	2020	2020	NUM
iajs-2476	4	6	      	      	SPACE
iajs-2476	4	7	on	on	ADP
iajs-2476	4	8	the	the	DET
iajs-2476	4	9	space	space	NOUN
iajs-2476	4	10	of	of	ADP
iajs-2476	4	11	primary	primary	ADJ
iajs-2476	4	12	la	la	ADJ
iajs-2476	4	13	-	-	PUNCT
iajs-2476	4	14	submodules	submodules	PROPN
iajs-2476	4	15	eman	eman	NOUN
iajs-2476	4	16	yahea	yahea	PROPN
iajs-2476	4	17	habeeb	habeeb	PROPN
iajs-2476	4	18	department	department	PROPN
iajs-2476	4	19	of	of	ADP
iajs-2476	4	20	mathematics	mathematic	NOUN
iajs-2476	4	21	,	,	PUNCT
iajs-2476	4	22	faculty	faculty	NOUN
iajs-2476	4	23	of	of	ADP
iajs-2476	4	24	education	education	NOUN
iajs-2476	4	25	for	for	ADP
iajs-2476	4	26	girls	girl	NOUN
iajs-2476	4	27	,	,	PUNCT
iajs-2476	4	28	kufa	kufa	PROPN
iajs-2476	4	29	university	university	PROPN
iajs-2476	4	30	iman.habeeb@uokufa.edu.iq	iman.habeeb@uokufa.edu.iq	PROPN
iajs-2476	4	31	abstract	abstract	PROPN
iajs-2476	4	32	suppose	suppose	VERB
iajs-2476	4	33	that	that	SCONJ
iajs-2476	4	34	f	f	PROPN
iajs-2476	4	35	is	be	AUX
iajs-2476	4	36	a	a	DET
iajs-2476	4	37	reciprocal	reciprocal	ADJ
iajs-2476	4	38	ring	ring	NOUN
iajs-2476	4	39	which	which	PRON
iajs-2476	4	40	has	have	VERB
iajs-2476	4	41	a	a	DET
iajs-2476	4	42	unity	unity	NOUN
iajs-2476	4	43	and	and	CCONJ
iajs-2476	4	44	suppose	suppose	VERB
iajs-2476	4	45	that	that	SCONJ
iajs-2476	4	46	h	h	NOUN
iajs-2476	4	47	is	be	AUX
iajs-2476	4	48	an	an	DET
iajs-2476	4	49	f	f	NOUN
iajs-2476	4	50	-	-	PUNCT
iajs-2476	4	51	module	module	NOUN
iajs-2476	4	52	.	.	PUNCT
iajs-2476	5	1	we	we	PRON
iajs-2476	5	2	topologize	topologize	VERB
iajs-2476	5	3	la	la	ADJ
iajs-2476	5	4	-	-	PUNCT
iajs-2476	5	5	prim(h	prim(h	NOUN
iajs-2476	5	6	)	)	PUNCT
iajs-2476	5	7	,	,	PUNCT
iajs-2476	5	8	the	the	DET
iajs-2476	5	9	set	set	NOUN
iajs-2476	5	10	of	of	ADP
iajs-2476	5	11	all	all	DET
iajs-2476	5	12	primary	primary	ADJ
iajs-2476	5	13	la	la	ADJ
iajs-2476	5	14	-	-	PUNCT
iajs-2476	5	15	submodules	submodule	NOUN
iajs-2476	5	16	of	of	ADP
iajs-2476	5	17	h	h	NOUN
iajs-2476	5	18	,	,	PUNCT
iajs-2476	5	19	similar	similar	ADJ
iajs-2476	5	20	to	to	ADP
iajs-2476	5	21	that	that	PRON
iajs-2476	5	22	for	for	ADP
iajs-2476	5	23	fprim(f	fprim(f	NOUN
iajs-2476	5	24	)	)	PUNCT
iajs-2476	5	25	,	,	PUNCT
iajs-2476	5	26	the	the	DET
iajs-2476	5	27	spectrum	spectrum	NOUN
iajs-2476	5	28	of	of	ADP
iajs-2476	5	29	fuzzy	fuzzy	ADJ
iajs-2476	5	30	primary	primary	ADJ
iajs-2476	5	31	ideals	ideal	NOUN
iajs-2476	5	32	of	of	ADP
iajs-2476	5	33	f	f	NOUN
iajs-2476	5	34	,	,	PUNCT
iajs-2476	5	35	and	and	CCONJ
iajs-2476	5	36	examine	examine	VERB
iajs-2476	5	37	the	the	DET
iajs-2476	5	38	characteristics	characteristic	NOUN
iajs-2476	5	39	of	of	ADP
iajs-2476	5	40	this	this	DET
iajs-2476	5	41	topological	topological	ADJ
iajs-2476	5	42	space	space	NOUN
iajs-2476	5	43	.	.	PUNCT
iajs-2476	6	1	particularly	particularly	ADV
iajs-2476	6	2	,	,	PUNCT
iajs-2476	6	3	we	we	PRON
iajs-2476	6	4	will	will	AUX
iajs-2476	6	5	research	research	VERB
iajs-2476	6	6	the	the	DET
iajs-2476	6	7	relation	relation	NOUN
iajs-2476	6	8	between	between	ADP
iajs-2476	6	9	la	la	NOUN
iajs-2476	6	10	-	-	PUNCT
iajs-2476	6	11	prim(h	prim(h	NOUN
iajs-2476	6	12	)	)	PUNCT
iajs-2476	6	13	and	and	CCONJ
iajs-2476	6	14	laprim(f/	laprim(f/	NOUN
iajs-2476	6	15	ann(h	ann(h	PROPN
iajs-2476	6	16	)	)	PUNCT
iajs-2476	6	17	)	)	PUNCT
iajs-2476	6	18	and	and	CCONJ
iajs-2476	6	19	get	get	VERB
iajs-2476	6	20	some	some	DET
iajs-2476	6	21	results	result	NOUN
iajs-2476	6	22	.	.	PUNCT
iajs-2476	7	1	keywords	keyword	NOUN
iajs-2476	7	2	primary	primary	ADJ
iajs-2476	7	3	la	la	ADJ
iajs-2476	7	4	-	-	PUNCT
iajs-2476	7	5	submodules	submodules	NOUN
iajs-2476	7	6	,	,	PUNCT
iajs-2476	7	7	fuzzy	fuzzy	ADJ
iajs-2476	7	8	primary	primary	ADJ
iajs-2476	7	9	spectrum	spectrum	NOUN
iajs-2476	7	10	,	,	PUNCT
iajs-2476	7	11	la	la	ADJ
iajs-2476	7	12	-	-	PUNCT
iajs-2476	7	13	top	top	ADJ
iajs-2476	7	14	modules	module	NOUN
iajs-2476	7	15	.	.	PUNCT
iajs-2476	8	1	1	1	X
iajs-2476	8	2	.	.	X
iajs-2476	8	3	introduction	introduction	NOUN
iajs-2476	8	4	suppose	suppose	VERB
iajs-2476	8	5	that	that	SCONJ
iajs-2476	8	6	f	f	PROPN
iajs-2476	8	7	is	be	AUX
iajs-2476	8	8	a	a	DET
iajs-2476	8	9	reciprocal	reciprocal	ADJ
iajs-2476	8	10	ring	ring	NOUN
iajs-2476	8	11	with	with	ADP
iajs-2476	8	12	a	a	DET
iajs-2476	8	13	unity	unity	NOUN
iajs-2476	8	14	and	and	CCONJ
iajs-2476	8	15	h	h	NOUN
iajs-2476	8	16	is	be	AUX
iajs-2476	8	17	a	a	DET
iajs-2476	8	18	unitary	unitary	ADJ
iajs-2476	8	19	f	f	NOUN
iajs-2476	8	20	-	-	PUNCT
iajs-2476	8	21	module	module	NOUN
iajs-2476	8	22	.	.	PUNCT
iajs-2476	9	1	the	the	DET
iajs-2476	9	2	primary	primary	ADJ
iajs-2476	9	3	spectrum	spectrum	NOUN
iajs-2476	9	4	prim	prim	ADJ
iajs-2476	9	5	(	(	PUNCT
iajs-2476	9	6	f	f	X
iajs-2476	9	7	)	)	PUNCT
iajs-2476	9	8	and	and	CCONJ
iajs-2476	9	9	the	the	DET
iajs-2476	9	10	topological	topological	ADJ
iajs-2476	9	11	space	space	NOUN
iajs-2476	9	12	acquired	acquire	VERB
iajs-2476	9	13	by	by	ADP
iajs-2476	9	14	inserting	insert	VERB
iajs-2476	9	15	zariski	zariski	NOUN
iajs-2476	9	16	topology	topology	NOUN
iajs-2476	9	17	on	on	ADP
iajs-2476	9	18	the	the	DET
iajs-2476	9	19	collection	collection	NOUN
iajs-2476	9	20	of	of	ADP
iajs-2476	9	21	primary	primary	ADJ
iajs-2476	9	22	ideals	ideal	NOUN
iajs-2476	9	23	of	of	ADP
iajs-2476	9	24	a	a	DET
iajs-2476	9	25	reciprocal	reciprocal	ADJ
iajs-2476	9	26	ring	ring	NOUN
iajs-2476	9	27	with	with	ADP
iajs-2476	9	28	unity	unity	NOUN
iajs-2476	9	29	play	play	VERB
iajs-2476	9	30	an	an	DET
iajs-2476	9	31	significant	significant	ADJ
iajs-2476	9	32	role	role	NOUN
iajs-2476	9	33	in	in	ADP
iajs-2476	9	34	the	the	DET
iajs-2476	9	35	fields	field	NOUN
iajs-2476	9	36	of	of	ADP
iajs-2476	9	37	reciprocal	reciprocal	ADJ
iajs-2476	9	38	algebra	algebra	NOUN
iajs-2476	9	39	,	,	PUNCT
iajs-2476	9	40	algebraic	algebraic	ADJ
iajs-2476	9	41	geometry	geometry	NOUN
iajs-2476	9	42	and	and	CCONJ
iajs-2476	9	43	lattice	lattice	PROPN
iajs-2476	9	44	theory	theory	NOUN
iajs-2476	9	45	.	.	PUNCT
iajs-2476	10	1	as	as	ADV
iajs-2476	10	2	well	well	ADV
iajs-2476	10	3	,	,	PUNCT
iajs-2476	10	4	lately	lately	ADV
iajs-2476	10	5	the	the	DET
iajs-2476	10	6	concept	concept	NOUN
iajs-2476	10	7	of	of	ADP
iajs-2476	10	8	primary	primary	ADJ
iajs-2476	10	9	submodules	submodule	NOUN
iajs-2476	10	10	and	and	CCONJ
iajs-2476	10	11	zariski	zariski	NOUN
iajs-2476	10	12	topology	topology	NOUN
iajs-2476	10	13	on	on	ADP
iajs-2476	10	14	prim	prim	ADJ
iajs-2476	10	15	(	(	PUNCT
iajs-2476	10	16	h	h	NOUN
iajs-2476	10	17	)	)	PUNCT
iajs-2476	10	18	,	,	PUNCT
iajs-2476	10	19	the	the	DET
iajs-2476	10	20	collection	collection	NOUN
iajs-2476	10	21	of	of	ADP
iajs-2476	10	22	all	all	DET
iajs-2476	10	23	primary	primary	ADJ
iajs-2476	10	24	submodules	submodule	NOUN
iajs-2476	10	25	of	of	ADP
iajs-2476	10	26	a	a	DET
iajs-2476	10	27	module	module	NOUN
iajs-2476	10	28	h	h	NOUN
iajs-2476	10	29	on	on	ADP
iajs-2476	10	30	a	a	DET
iajs-2476	10	31	reciprocal	reciprocal	ADJ
iajs-2476	10	32	ring	ring	NOUN
iajs-2476	10	33	together	together	ADV
iajs-2476	10	34	identity	identity	NOUN
iajs-2476	10	35	f	f	NOUN
iajs-2476	10	36	,	,	PUNCT
iajs-2476	10	37	were	be	AUX
iajs-2476	10	38	studied	study	VERB
iajs-2476	10	39	in	in	ADP
iajs-2476	10	40	a	a	DET
iajs-2476	10	41	previous	previous	ADJ
iajs-2476	10	42	article	article	NOUN
iajs-2476	10	43	[	[	X
iajs-2476	10	44	1	1	NUM
iajs-2476	10	45	]	]	PUNCT
iajs-2476	10	46	.	.	PUNCT
iajs-2476	11	1	as	as	SCONJ
iajs-2476	11	2	it	it	PRON
iajs-2476	11	3	is	be	AUX
iajs-2476	11	4	famous	famous	ADJ
iajs-2476	11	5	[	[	X
iajs-2476	11	6	2	2	NUM
iajs-2476	11	7	]	]	PUNCT
iajs-2476	11	8	.	.	PUNCT
iajs-2476	12	1	inserted	insert	VERB
iajs-2476	12	2	the	the	DET
iajs-2476	12	3	concept	concept	NOUN
iajs-2476	12	4	of	of	ADP
iajs-2476	12	5	a	a	DET
iajs-2476	12	6	fuzzy	fuzzy	ADJ
iajs-2476	12	7	subset	subset	NOUN
iajs-2476	12	8	ϑ	ϑ	PROPN
iajs-2476	12	9	of	of	ADP
iajs-2476	12	10	a	a	DET
iajs-2476	12	11	nonempty	nonempty	ADJ
iajs-2476	12	12	collection	collection	NOUN
iajs-2476	12	13	l	l	NOUN
iajs-2476	12	14	as	as	ADP
iajs-2476	12	15	a	a	DET
iajs-2476	12	16	mapping	mapping	NOUN
iajs-2476	12	17	from	from	ADP
iajs-2476	12	18	l	l	NOUN
iajs-2476	12	19	to	to	ADP
iajs-2476	12	20	[	[	X
iajs-2476	12	21	0,1	0,1	NUM
iajs-2476	12	22	]	]	PUNCT
iajs-2476	12	23	.	.	PUNCT
iajs-2476	13	1	goguen	goguen	PROPN
iajs-2476	13	2	ja	ja	PROPN
iajs-2476	14	1	[	[	X
iajs-2476	14	2	3	3	NUM
iajs-2476	14	3	]	]	PUNCT
iajs-2476	14	4	.	.	PUNCT
iajs-2476	15	1	changed	change	VERB
iajs-2476	15	2	[	[	X
iajs-2476	15	3	0,1	0,1	NUM
iajs-2476	15	4	]	]	PUNCT
iajs-2476	15	5	by	by	ADP
iajs-2476	15	6	an	an	DET
iajs-2476	15	7	entire	entire	ADJ
iajs-2476	15	8	lattice	lattice	NOUN
iajs-2476	15	9	la	la	ADV
iajs-2476	15	10	in	in	ADP
iajs-2476	15	11	the	the	DET
iajs-2476	15	12	definition	definition	NOUN
iajs-2476	15	13	of	of	ADP
iajs-2476	15	14	fuzzy	fuzzy	ADJ
iajs-2476	15	15	collections	collection	NOUN
iajs-2476	15	16	while	while	SCONJ
iajs-2476	15	17	inserted	insert	VERB
iajs-2476	15	18	the	the	DET
iajs-2476	15	19	concept	concept	NOUN
iajs-2476	15	20	of	of	ADP
iajs-2476	15	21	la	la	ADJ
iajs-2476	15	22	-	-	PUNCT
iajs-2476	15	23	fuzzy	fuzzy	ADJ
iajs-2476	15	24	sets	set	NOUN
iajs-2476	15	25	.	.	PUNCT
iajs-2476	16	1	rosenfeld	rosenfeld	PROPN
iajs-2476	16	2	inserted	insert	VERB
iajs-2476	16	3	the	the	DET
iajs-2476	16	4	concept	concept	NOUN
iajs-2476	16	5	of	of	ADP
iajs-2476	16	6	fuzzy	fuzzy	ADJ
iajs-2476	16	7	groups	group	NOUN
iajs-2476	16	8	[	[	X
iajs-2476	16	9	4	4	NUM
iajs-2476	16	10	]	]	PUNCT
iajs-2476	16	11	.	.	PUNCT
iajs-2476	17	1	while	while	SCONJ
iajs-2476	17	2	fuzzy	fuzzy	ADJ
iajs-2476	17	3	submodules	submodule	NOUN
iajs-2476	17	4	of	of	ADP
iajs-2476	17	5	h	h	NOUN
iajs-2476	17	6	over	over	ADP
iajs-2476	17	7	f	f	PROPN
iajs-2476	17	8	were	be	AUX
iajs-2476	17	9	first	first	ADV
iajs-2476	17	10	inserted	insert	VERB
iajs-2476	17	11	by	by	ADP
iajs-2476	17	12	[	[	X
iajs-2476	17	13	5	5	NUM
iajs-2476	17	14	]	]	PUNCT
iajs-2476	17	15	.	.	PUNCT
iajs-2476	18	1	pan	pan	PROPN
iajs-2476	19	1	f	f	PROPN
iajs-2476	19	2	-	-	PROPN
iajs-2476	19	3	z	z	PROPN
iajs-2476	20	1	[	[	X
iajs-2476	20	2	6	6	NUM
iajs-2476	20	3	]	]	PUNCT
iajs-2476	20	4	.	.	PUNCT
iajs-2476	21	1	elaborate	elaborate	ADJ
iajs-2476	21	2	fuzzy	fuzzy	ADJ
iajs-2476	21	3	finitely	finitely	ADV
iajs-2476	21	4	created	create	VERB
iajs-2476	21	5	modules	module	NOUN
iajs-2476	21	6	while	while	SCONJ
iajs-2476	21	7	fuzzy	fuzzy	ADJ
iajs-2476	21	8	quotient	quotient	NOUN
iajs-2476	21	9	modules	module	NOUN
iajs-2476	21	10	(	(	PUNCT
iajs-2476	21	11	look	look	VERB
iajs-2476	21	12	at	at	ADP
iajs-2476	21	13	[	[	X
iajs-2476	21	14	7	7	NUM
iajs-2476	21	15	]	]	NUM
iajs-2476	21	16	)	)	PUNCT
iajs-2476	21	17	.	.	PUNCT
iajs-2476	22	1	in	in	ADP
iajs-2476	22	2	previous	previous	ADJ
iajs-2476	22	3	years	year	NOUN
iajs-2476	22	4	a	a	DET
iajs-2476	22	5	large	large	ADJ
iajs-2476	22	6	saucepan	saucepan	NOUN
iajs-2476	22	7	of	of	ADP
iajs-2476	22	8	labor	labor	NOUN
iajs-2476	22	9	has	have	AUX
iajs-2476	22	10	been	be	AUX
iajs-2476	22	11	completed	complete	VERB
iajs-2476	22	12	on	on	ADP
iajs-2476	22	13	fuzzy	fuzzy	ADJ
iajs-2476	22	14	ideals	ideal	NOUN
iajs-2476	22	15	in	in	ADP
iajs-2476	22	16	common	common	ADJ
iajs-2476	22	17	and	and	CCONJ
iajs-2476	22	18	primary	primary	ADJ
iajs-2476	22	19	fuzzy	fuzzy	ADJ
iajs-2476	22	20	ideals	ideal	NOUN
iajs-2476	22	21	in	in	ADP
iajs-2476	22	22	special	special	ADJ
iajs-2476	22	23	,	,	PUNCT
iajs-2476	22	24	while	while	SCONJ
iajs-2476	22	25	several	several	ADJ
iajs-2476	22	26	motivating	motivating	NOUN
iajs-2476	22	27	topological	topological	ADJ
iajs-2476	22	28	features	feature	NOUN
iajs-2476	22	29	of	of	ADP
iajs-2476	22	30	the	the	DET
iajs-2476	22	31	spectrum	spectrum	NOUN
iajs-2476	22	32	of	of	ADP
iajs-2476	22	33	fuzzy	fuzzy	ADJ
iajs-2476	22	34	primary	primary	ADJ
iajs-2476	22	35	ideals	ideal	NOUN
iajs-2476	22	36	of	of	ADP
iajs-2476	22	37	a	a	DET
iajs-2476	22	38	ring	ring	NOUN
iajs-2476	22	39	were	be	AUX
iajs-2476	22	40	acquired	acquire	VERB
iajs-2476	22	41	(	(	PUNCT
iajs-2476	22	42	look	look	VERB
iajs-2476	22	43	at	at	ADP
iajs-2476	22	44	[	[	X
iajs-2476	22	45	815	815	NUM
iajs-2476	22	46	]	]	PUNCT
iajs-2476	22	47	)	)	PUNCT
iajs-2476	22	48	.	.	PUNCT
iajs-2476	23	1	suppose	suppose	VERB
iajs-2476	23	2	that	that	SCONJ
iajs-2476	23	3	h	h	NOUN
iajs-2476	23	4	is	be	AUX
iajs-2476	23	5	an	an	DET
iajs-2476	23	6	f	f	NOUN
iajs-2476	23	7	-	-	PUNCT
iajs-2476	23	8	module	module	NOUN
iajs-2476	23	9	.	.	PUNCT
iajs-2476	24	1	by	by	ADP
iajs-2476	24	2	g	g	PROPN
iajs-2476	24	3	h	h	NOUN
iajs-2476	24	4	,	,	PUNCT
iajs-2476	24	5	we	we	PRON
iajs-2476	24	6	mean	mean	VERB
iajs-2476	24	7	that	that	SCONJ
iajs-2476	24	8	g	g	PROPN
iajs-2476	24	9	is	be	AUX
iajs-2476	24	10	a	a	DET
iajs-2476	24	11	submodule	submodule	NOUN
iajs-2476	24	12	of	of	ADP
iajs-2476	24	13	h.	h.	PROPN
iajs-2476	24	14	for	for	ADP
iajs-2476	24	15	any	any	DET
iajs-2476	24	16	g	g	PROPN
iajs-2476	24	17	h	h	NOUN
iajs-2476	24	18	,	,	PUNCT
iajs-2476	24	19	we	we	PRON
iajs-2476	24	20	indicate	indicate	VERB
iajs-2476	24	21	the	the	DET
iajs-2476	24	22	residual	residual	NOUN
iajs-2476	24	23	of	of	ADP
iajs-2476	24	24	g	g	NOUN
iajs-2476	24	25	by	by	ADP
iajs-2476	24	26	h	h	NOUN
iajs-2476	24	27	by	by	ADP
iajs-2476	24	28	[	[	X
iajs-2476	24	29	g	g	X
iajs-2476	24	30	:	:	PUNCT
iajs-2476	24	31	h	h	NOUN
iajs-2476	24	32	]	]	X
iajs-2476	24	33	,	,	PUNCT
iajs-2476	24	34	and	and	CCONJ
iajs-2476	24	35	define[g	define[g	NOUN
iajs-2476	24	36	:	:	PUNCT
iajs-2476	24	37	h	h	NOUN
iajs-2476	24	38	]	]	X
iajs-2476	24	39	=	=	X
iajs-2476	24	40	{	{	PUNCT
iajs-2476	24	41	r	r	NOUN
iajs-2476	24	42	́∈	́∈	X
iajs-2476	24	43	f	f	PROPN
iajs-2476	24	44	\	\	PROPN
iajs-2476	24	45	r	r	PROPN
iajs-2476	24	46	́h⊆g	́h⊆g	PROPN
iajs-2476	24	47	}	}	PUNCT
iajs-2476	24	48	.	.	PUNCT
iajs-2476	25	1	in	in	ADP
iajs-2476	25	2	special	special	ADJ
iajs-2476	25	3	,	,	PUNCT
iajs-2476	25	4	[	[	X
iajs-2476	25	5	(	(	PUNCT
iajs-2476	25	6	0	0	NUM
iajs-2476	25	7	)	)	PUNCT
iajs-2476	25	8	:	:	PUNCT
iajs-2476	25	9	h	h	X
iajs-2476	25	10	]	]	X
iajs-2476	25	11	is	be	AUX
iajs-2476	25	12	called	call	VERB
iajs-2476	25	13	the	the	DET
iajs-2476	25	14	annihilator	annihilator	NOUN
iajs-2476	25	15	of	of	ADP
iajs-2476	25	16	h	h	PROPN
iajs-2476	25	17	and	and	CCONJ
iajs-2476	25	18	is	be	AUX
iajs-2476	25	19	indicated	indicate	VERB
iajs-2476	25	20	by	by	ADP
iajs-2476	25	21	ann(h	ann(h	PROPN
iajs-2476	25	22	)	)	PUNCT
iajs-2476	25	23	,	,	PUNCT
iajs-2476	25	24	that	that	PRON
iajs-2476	25	25	is	be	AUX
iajs-2476	25	26	ibn	ibn	PROPN
iajs-2476	25	27	al	al	PROPN
iajs-2476	25	28	haitham	haitham	PROPN
iajs-2476	25	29	journal	journal	PROPN
iajs-2476	25	30	for	for	ADP
iajs-2476	25	31	pure	pure	ADJ
iajs-2476	25	32	and	and	CCONJ
iajs-2476	25	33	applied	apply	VERB
iajs-2476	25	34	science	science	NOUN
iajs-2476	25	35	journal	journal	PROPN
iajs-2476	25	36	homepage	homepage	NOUN
iajs-2476	25	37	:	:	PUNCT
iajs-2476	25	38	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2476	25	39	doi	doi	NOUN
iajs-2476	25	40	:	:	PUNCT
iajs-2476	25	41	10.30526/33.3.2476	10.30526/33.3.2476	PROPN
iajs-2476	25	42	article	article	NOUN
iajs-2476	25	43	history	history	NOUN
iajs-2476	25	44	:	:	PUNCT
iajs-2476	25	45	received	receive	VERB
iajs-2476	25	46	23	23	NUM
iajs-2476	25	47	july	july	PROPN
iajs-2476	25	48	2019	2019	NUM
iajs-2476	25	49	,	,	PUNCT
iajs-2476	25	50	accepted	accept	VERB
iajs-2476	25	51	22	22	NUM
iajs-2476	25	52	septamber	septamber	NOUN
iajs-2476	25	53	2019	2019	NUM
iajs-2476	25	54	,	,	PUNCT
iajs-2476	25	55	published	publish	VERB
iajs-2476	25	56	in	in	ADP
iajs-2476	25	57	july	july	PROPN
iajs-2476	25	58	2020	2020	NUM
iajs-2476	25	59	.	.	PUNCT
iajs-2476	25	60	  	  	SPACE
iajs-2476	26	1	90	90	NUM
iajs-2476	26	2	ibn	ibn	PROPN
iajs-2476	26	3	al	al	PROPN
iajs-2476	26	4	-	-	PUNCT
iajs-2476	26	5	haitham	haitham	PROPN
iajs-2476	26	6	jour	jour	X
iajs-2476	26	7	.	.	PROPN
iajs-2476	26	8	for	for	ADP
iajs-2476	26	9	pure	pure	ADJ
iajs-2476	26	10	&	&	CCONJ
iajs-2476	26	11	appl	appl	PROPN
iajs-2476	26	12	.	.	PUNCT
iajs-2476	27	1	sci	sci	PROPN
iajs-2476	27	2	.	.	PROPN
iajs-2476	28	1	33	33	NUM
iajs-2476	28	2	(	(	PUNCT
iajs-2476	28	3	3	3	NUM
iajs-2476	28	4	)	)	PUNCT
iajs-2476	28	5	2020	2020	NUM
iajs-2476	29	1	ann(h)={r	ann(h)={r	ADP
iajs-2476	29	2	́∈f	́∈f	NOUN
iajs-2476	29	3	\	\	PROPN
iajs-2476	29	4	r	r	NOUN
iajs-2476	29	5	́h=0	́h=0	NOUN
iajs-2476	29	6	}	}	PUNCT
iajs-2476	29	7	.	.	PUNCT
iajs-2476	30	1	a	a	DET
iajs-2476	30	2	primary	primary	ADJ
iajs-2476	30	3	submodule	submodule	NOUN
iajs-2476	30	4	(	(	PUNCT
iajs-2476	30	5	or	or	CCONJ
iajs-2476	30	6	a	a	DET
iajs-2476	30	7	q	q	ADJ
iajs-2476	30	8	-	-	PUNCT
iajs-2476	30	9	primary	primary	ADJ
iajs-2476	30	10	submodule	submodule	NOUN
iajs-2476	30	11	)	)	PUNCT
iajs-2476	30	12	of	of	ADP
iajs-2476	30	13	h	h	NOUN
iajs-2476	30	14	is	be	AUX
iajs-2476	30	15	a	a	DET
iajs-2476	30	16	proper	proper	ADJ
iajs-2476	30	17	submodule	submodule	NOUN
iajs-2476	30	18	q	q	NOUN
iajs-2476	30	19	with	with	ADP
iajs-2476	30	20	q	q	NOUN
iajs-2476	30	21	:	:	PUNCT
iajs-2476	30	22	h	h	NOUN
iajs-2476	30	23	=	=	NOUN
iajs-2476	30	24	q	q	NOUN
iajs-2476	30	25	,	,	PUNCT
iajs-2476	30	26	such	such	ADJ
iajs-2476	30	27	that	that	SCONJ
iajs-2476	30	28	r	r	NOUN
iajs-2476	30	29	́h	́h	PROPN
iajs-2476	30	30	∈	∈	PROPN
iajs-2476	30	31	q	q	NOUN
iajs-2476	30	32	for	for	ADP
iajs-2476	30	33	r	r	NOUN
iajs-2476	30	34	́∈	́∈	X
iajs-2476	30	35	f	f	PROPN
iajs-2476	30	36	and	and	CCONJ
iajs-2476	30	37	h	h	NOUN
iajs-2476	30	38	∈	∈	PROPN
iajs-2476	30	39	h	h	NOUN
iajs-2476	30	40	,	,	PUNCT
iajs-2476	30	41	either	either	CCONJ
iajs-2476	30	42	h	h	ADP
iajs-2476	30	43	∈	∈	PROPN
iajs-2476	30	44	q	q	NOUN
iajs-2476	30	45	or	or	CCONJ
iajs-2476	30	46	r	r	PROPN
iajs-2476	30	47	∈́	∈́	PROPN
iajs-2476	30	48	q.	q.	NOUN
iajs-2476	30	49	the	the	DET
iajs-2476	30	50	collection	collection	NOUN
iajs-2476	30	51	of	of	ADP
iajs-2476	30	52	all	all	DET
iajs-2476	30	53	primary	primary	ADJ
iajs-2476	30	54	submodules	submodule	NOUN
iajs-2476	30	55	of	of	ADP
iajs-2476	30	56	h	h	NOUN
iajs-2476	30	57	is	be	AUX
iajs-2476	30	58	called	call	VERB
iajs-2476	30	59	the	the	DET
iajs-2476	30	60	primary	primary	ADJ
iajs-2476	30	61	spectrum	spectrum	NOUN
iajs-2476	30	62	of	of	ADP
iajs-2476	30	63	h	h	NOUN
iajs-2476	30	64	or	or	CCONJ
iajs-2476	30	65	,	,	PUNCT
iajs-2476	30	66	artlessly	artlessly	ADV
iajs-2476	30	67	the	the	DET
iajs-2476	30	68	p	p	PROPN
iajs-2476	30	69	spectra	spectra	NOUN
iajs-2476	30	70	of	of	ADP
iajs-2476	30	71	h	h	NOUN
iajs-2476	30	72	and	and	CCONJ
iajs-2476	30	73	is	be	AUX
iajs-2476	30	74	indicated	indicate	VERB
iajs-2476	30	75	by	by	ADP
iajs-2476	30	76	prim(h	prim(h	NOUN
iajs-2476	30	77	)	)	PUNCT
iajs-2476	30	78	.	.	PUNCT
iajs-2476	31	1	note	note	VERB
iajs-2476	31	2	that	that	SCONJ
iajs-2476	31	3	the	the	DET
iajs-2476	31	4	prim(h	prim(h	NOUN
iajs-2476	31	5	)	)	PUNCT
iajs-2476	31	6	may	may	AUX
iajs-2476	31	7	be	be	AUX
iajs-2476	31	8	empty	empty	ADJ
iajs-2476	31	9	for	for	ADP
iajs-2476	31	10	some	some	DET
iajs-2476	31	11	module	module	NOUN
iajs-2476	31	12	h	h	NOUN
iajs-2476	31	13	.	.	PUNCT
iajs-2476	32	1	such	such	DET
iajs-2476	32	2	a	a	DET
iajs-2476	32	3	module	module	NOUN
iajs-2476	32	4	is	be	AUX
iajs-2476	32	5	said	say	VERB
iajs-2476	32	6	to	to	PART
iajs-2476	32	7	be	be	AUX
iajs-2476	32	8	primary	primary	ADJ
iajs-2476	32	9	less	less	ADV
iajs-2476	32	10	(	(	PUNCT
iajs-2476	32	11	cf	cf	NOUN
iajs-2476	32	12	.	.	PUNCT
iajs-2476	33	1	[	[	X
iajs-2476	33	2	1	1	NUM
iajs-2476	33	3	]	]	PUNCT
iajs-2476	33	4	)	)	PUNCT
iajs-2476	33	5	.	.	PUNCT
iajs-2476	34	1	clearly	clearly	ADV
iajs-2476	34	2	,	,	PUNCT
iajs-2476	34	3	zero	zero	NUM
iajs-2476	34	4	module	module	NOUN
iajs-2476	34	5	is	be	AUX
iajs-2476	34	6	primary	primary	ADJ
iajs-2476	34	7	less	less	ADV
iajs-2476	34	8	,	,	PUNCT
iajs-2476	34	9	but	but	CCONJ
iajs-2476	34	10	in	in	ADP
iajs-2476	34	11	[	[	X
iajs-2476	34	12	1	1	NUM
iajs-2476	34	13	]	]	PUNCT
iajs-2476	34	14	.	.	PUNCT
iajs-2476	35	1	some	some	DET
iajs-2476	35	2	nontrivial	nontrivial	ADJ
iajs-2476	35	3	examples	example	NOUN
iajs-2476	35	4	are	be	AUX
iajs-2476	35	5	shown	show	VERB
iajs-2476	35	6	.	.	PUNCT
iajs-2476	36	1	for	for	ADP
iajs-2476	36	2	example	example	NOUN
iajs-2476	36	3	,	,	PUNCT
iajs-2476	36	4	the	the	DET
iajs-2476	36	5	prüfer	prüfer	NOUN
iajs-2476	36	6	group	group	NOUN
iajs-2476	36	7	ℤ	ℤ	PROPN
iajs-2476	36	8	(	(	PUNCT
iajs-2476	36	9	p∞	p∞	PROPN
iajs-2476	36	10	)	)	PUNCT
iajs-2476	36	11	as	as	ADP
iajs-2476	36	12	a	a	DET
iajs-2476	36	13	ℤ-module	ℤ-module	PROPN
iajs-2476	36	14	has	have	VERB
iajs-2476	36	15	no	no	DET
iajs-2476	36	16	primary	primary	ADJ
iajs-2476	36	17	submodule	submodule	NOUN
iajs-2476	36	18	for	for	ADP
iajs-2476	36	19	any	any	DET
iajs-2476	36	20	prime	prime	ADJ
iajs-2476	36	21	integer	integer	NOUN
iajs-2476	36	22	p.	p.	NOUN
iajs-2476	36	23	when	when	SCONJ
iajs-2476	36	24	prim(h	prim(h	VERB
iajs-2476	36	25	)	)	PUNCT
iajs-2476	36	26	∅	∅	NOUN
iajs-2476	36	27	,	,	PUNCT
iajs-2476	36	28	the	the	DET
iajs-2476	36	29	map	map	NOUN
iajs-2476	36	30	φ	φ	NOUN
iajs-2476	36	31	:	:	PUNCT
iajs-2476	36	32	la	la	ADJ
iajs-2476	36	33	-	-	PUNCT
iajs-2476	36	34	prim(h)→	prim(h)→	VERB
iajs-2476	36	35	la	la	ADJ
iajs-2476	36	36	-	-	PUNCT
iajs-2476	36	37	prim(f/	prim(f/	NOUN
iajs-2476	36	38	ann(h	ann(h	PROPN
iajs-2476	36	39	)	)	PUNCT
iajs-2476	36	40	)	)	PUNCT
iajs-2476	36	41	defined	define	VERB
iajs-2476	36	42	by	by	ADP
iajs-2476	36	43	φ(ϑ)=	φ(ϑ)=	NOUN
iajs-2476	36	44	ϑ	ϑ	X
iajs-2476	36	45	:	:	PUNCT
iajs-2476	36	46	1h	1h	NUM
iajs-2476	36	47	for	for	ADP
iajs-2476	36	48	ϑ	ϑ	PROPN
iajs-2476	36	49	∈	∈	PROPN
iajs-2476	36	50	la	la	PROPN
iajs-2476	36	51	-	-	PUNCT
iajs-2476	36	52	prim(h	prim(h	NOUN
iajs-2476	36	53	)	)	PUNCT
iajs-2476	36	54	,	,	PUNCT
iajs-2476	36	55	φ	φ	PROPN
iajs-2476	36	56	will	will	AUX
iajs-2476	36	57	be	be	AUX
iajs-2476	36	58	called	call	VERB
iajs-2476	36	59	the	the	DET
iajs-2476	36	60	standard	standard	ADJ
iajs-2476	36	61	map	map	NOUN
iajs-2476	36	62	.	.	PUNCT
iajs-2476	37	1	in	in	ADP
iajs-2476	37	2	[	[	X
iajs-2476	37	3	1	1	NUM
iajs-2476	37	4	]	]	PUNCT
iajs-2476	37	5	.	.	PUNCT
iajs-2476	38	1	it	it	PRON
iajs-2476	38	2	is	be	AUX
iajs-2476	38	3	shown	show	VERB
iajs-2476	38	4	that	that	SCONJ
iajs-2476	38	5	for	for	ADP
iajs-2476	38	6	each	each	DET
iajs-2476	38	7	multiplication	multiplication	NOUN
iajs-2476	38	8	module	module	NOUN
iajs-2476	38	9	h,(an	h,(an	NOUN
iajs-2476	38	10	f	f	NOUN
iajs-2476	38	11	-	-	PUNCT
iajs-2476	38	12	module	module	NOUN
iajs-2476	38	13	h	h	NOUN
iajs-2476	38	14	is	be	AUX
iajs-2476	38	15	called	call	VERB
iajs-2476	38	16	a	a	DET
iajs-2476	38	17	multiplication	multiplication	NOUN
iajs-2476	38	18	module	module	NOUN
iajs-2476	38	19	if	if	SCONJ
iajs-2476	38	20	every	every	DET
iajs-2476	38	21	submodule	submodule	PROPN
iajs-2476	38	22	b	b	PROPN
iajs-2476	38	23	of	of	ADP
iajs-2476	38	24	h	h	NOUN
iajs-2476	38	25	is	be	AUX
iajs-2476	38	26	of	of	ADP
iajs-2476	38	27	the	the	DET
iajs-2476	38	28	form	form	NOUN
iajs-2476	38	29	ih	ih	NOUN
iajs-2476	38	30	for	for	ADP
iajs-2476	38	31	some	some	DET
iajs-2476	38	32	ideal	ideal	ADJ
iajs-2476	38	33	i	i	PRON
iajs-2476	38	34	of	of	ADP
iajs-2476	38	35	f	f	PROPN
iajs-2476	38	36	)	)	PUNCT
iajs-2476	38	37	the	the	DET
iajs-2476	38	38	prim(h	prim(h	NOUN
iajs-2476	38	39	)	)	PUNCT
iajs-2476	38	40	is	be	AUX
iajs-2476	38	41	non	non	ADJ
iajs-2476	38	42	-	-	ADJ
iajs-2476	38	43	empty	empty	ADJ
iajs-2476	38	44	.	.	PUNCT
iajs-2476	39	1	for	for	ADP
iajs-2476	39	2	any	any	DET
iajs-2476	39	3	submodule	submodule	NOUN
iajs-2476	39	4	g	g	PROPN
iajs-2476	39	5	of	of	ADP
iajs-2476	39	6	h	h	NOUN
iajs-2476	39	7	,	,	PUNCT
iajs-2476	39	8	v(g	v(g	ADJ
iajs-2476	39	9	)	)	PUNCT
iajs-2476	39	10	indicates	indicate	VERB
iajs-2476	39	11	the	the	DET
iajs-2476	39	12	collection	collection	NOUN
iajs-2476	39	13	of	of	ADP
iajs-2476	39	14	all	all	DET
iajs-2476	39	15	primary	primary	ADJ
iajs-2476	39	16	submodules	submodule	NOUN
iajs-2476	39	17	of	of	ADP
iajs-2476	39	18	h	h	NOUN
iajs-2476	39	19	including	include	VERB
iajs-2476	39	20	g.	g.	PROPN
iajs-2476	39	21	of	of	ADP
iajs-2476	39	22	course	course	NOUN
iajs-2476	39	23	v(h	v(h	NOUN
iajs-2476	39	24	)	)	PUNCT
iajs-2476	39	25	is	be	AUX
iajs-2476	39	26	just	just	ADV
iajs-2476	39	27	the	the	DET
iajs-2476	39	28	empty	empty	ADJ
iajs-2476	39	29	set	set	NOUN
iajs-2476	39	30	and	and	CCONJ
iajs-2476	39	31	v(0	v(0	NOUN
iajs-2476	39	32	)	)	PUNCT
iajs-2476	39	33	is	be	AUX
iajs-2476	39	34	prim(h	prim(h	ADJ
iajs-2476	39	35	)	)	PUNCT
iajs-2476	39	36	.	.	PUNCT
iajs-2476	40	1	for	for	ADP
iajs-2476	40	2	any	any	DET
iajs-2476	40	3	family	family	NOUN
iajs-2476	40	4	of	of	ADP
iajs-2476	40	5	submodules	submodule	NOUN
iajs-2476	40	6	gj(j	gj(j	NOUN
iajs-2476	40	7	∈	∈	PROPN
iajs-2476	40	8	j	j	PROPN
iajs-2476	40	9	)	)	PUNCT
iajs-2476	40	10	of	of	ADP
iajs-2476	40	11	h	h	PROPN
iajs-2476	40	12	,	,	PUNCT
iajs-2476	40	13	⋂	⋂	PROPN
iajs-2476	40	14	v	v	ADP
iajs-2476	40	15	g	g	PROPN
iajs-2476	40	16	v	v	NUM
iajs-2476	40	17	∑	∑	PROPN
iajs-2476	40	18	g∈∈	g∈∈	PROPN
iajs-2476	40	19	thus	thus	ADV
iajs-2476	40	20	if	if	SCONJ
iajs-2476	40	21	ω(h	ω(h	NUM
iajs-2476	40	22	)	)	PUNCT
iajs-2476	40	23	indicates	indicate	VERB
iajs-2476	40	24	the	the	DET
iajs-2476	40	25	set	set	NOUN
iajs-2476	40	26	of	of	ADP
iajs-2476	40	27	all	all	DET
iajs-2476	40	28	subsets	subset	NOUN
iajs-2476	40	29	v(g	v(g	ADJ
iajs-2476	40	30	)	)	PUNCT
iajs-2476	40	31	of	of	ADP
iajs-2476	40	32	prim(h	prim(h	PROPN
iajs-2476	40	33	)	)	PUNCT
iajs-2476	40	34	,	,	PUNCT
iajs-2476	40	35	then	then	ADV
iajs-2476	40	36	ω(h	ω(h	NUM
iajs-2476	40	37	)	)	PUNCT
iajs-2476	40	38	includes	include	VERB
iajs-2476	40	39	the	the	DET
iajs-2476	40	40	empty	empty	ADJ
iajs-2476	40	41	set	set	NOUN
iajs-2476	40	42	and	and	CCONJ
iajs-2476	40	43	prim(h	prim(h	VERB
iajs-2476	40	44	)	)	PUNCT
iajs-2476	40	45	and	and	CCONJ
iajs-2476	40	46	is	be	AUX
iajs-2476	40	47	closed	close	VERB
iajs-2476	40	48	beneath	beneath	ADP
iajs-2476	40	49	arbitrary	arbitrary	ADJ
iajs-2476	40	50	intersection	intersection	NOUN
iajs-2476	40	51	.	.	PUNCT
iajs-2476	41	1	if	if	SCONJ
iajs-2476	41	2	also	also	ADV
iajs-2476	41	3	ω(h	ω(h	NUM
iajs-2476	41	4	)	)	PUNCT
iajs-2476	41	5	is	be	AUX
iajs-2476	41	6	closed	close	VERB
iajs-2476	41	7	beneath	beneath	ADP
iajs-2476	41	8	finite	finite	PROPN
iajs-2476	41	9	union	union	PROPN
iajs-2476	41	10	,	,	PUNCT
iajs-2476	41	11	i.e.	i.e.	X
iajs-2476	41	12	for	for	ADP
iajs-2476	41	13	any	any	DET
iajs-2476	41	14	submodules	submodule	NOUN
iajs-2476	41	15	g	g	PROPN
iajs-2476	41	16	and	and	CCONJ
iajs-2476	41	17	k	k	PROPN
iajs-2476	41	18	of	of	ADP
iajs-2476	41	19	h	h	NOUN
iajs-2476	41	20	,	,	PUNCT
iajs-2476	41	21	there	there	PRON
iajs-2476	41	22	occurs	occur	VERB
iajs-2476	41	23	a	a	DET
iajs-2476	41	24	submodule	submodule	NOUN
iajs-2476	41	25	j	j	PROPN
iajs-2476	41	26	of	of	ADP
iajs-2476	41	27	h	h	PROPN
iajs-2476	41	28	such	such	ADJ
iajs-2476	41	29	that	that	DET
iajs-2476	41	30	v(g)⋃	v(g)⋃	PROPN
iajs-2476	41	31	v(k)=v	v(k)=v	ADP
iajs-2476	41	32	(	(	PUNCT
iajs-2476	41	33	j	j	NOUN
iajs-2476	41	34	)	)	PUNCT
iajs-2476	41	35	,	,	PUNCT
iajs-2476	41	36	for	for	ADP
iajs-2476	41	37	in	in	ADP
iajs-2476	41	38	this	this	DET
iajs-2476	41	39	state	state	NOUN
iajs-2476	41	40	ω(h	ω(h	NUM
iajs-2476	41	41	)	)	PUNCT
iajs-2476	42	1	satisfies	satisfy	VERB
iajs-2476	42	2	the	the	DET
iajs-2476	42	3	axioms	axiom	NOUN
iajs-2476	42	4	of	of	ADP
iajs-2476	42	5	closed	closed	ADJ
iajs-2476	42	6	subsets	subset	NOUN
iajs-2476	42	7	of	of	ADP
iajs-2476	42	8	a	a	DET
iajs-2476	42	9	topological	topological	ADJ
iajs-2476	42	10	spaces	space	NOUN
iajs-2476	42	11	,	,	PUNCT
iajs-2476	42	12	which	which	PRON
iajs-2476	42	13	is	be	AUX
iajs-2476	42	14	called	call	VERB
iajs-2476	42	15	zariski	zariski	ADJ
iajs-2476	42	16	topology	topology	NOUN
iajs-2476	42	17	.	.	PUNCT
iajs-2476	43	1	in	in	ADP
iajs-2476	43	2	[	[	X
iajs-2476	43	3	1	1	NUM
iajs-2476	43	4	]	]	PUNCT
iajs-2476	43	5	.	.	PUNCT
iajs-2476	44	1	a	a	DET
iajs-2476	44	2	module	module	NOUN
iajs-2476	44	3	with	with	ADP
iajs-2476	44	4	zariski	zariski	NOUN
iajs-2476	44	5	topology	topology	NOUN
iajs-2476	44	6	is	be	AUX
iajs-2476	44	7	called	call	VERB
iajs-2476	44	8	top	top	ADJ
iajs-2476	44	9	module	module	NOUN
iajs-2476	44	10	and	and	CCONJ
iajs-2476	44	11	it	it	PRON
iajs-2476	44	12	is	be	AUX
iajs-2476	44	13	shown	show	VERB
iajs-2476	44	14	that	that	SCONJ
iajs-2476	44	15	each	each	DET
iajs-2476	44	16	multiplication	multiplication	NOUN
iajs-2476	44	17	module	module	NOUN
iajs-2476	44	18	is	be	AUX
iajs-2476	44	19	a	a	DET
iajs-2476	44	20	top	top	ADJ
iajs-2476	44	21	module	module	NOUN
iajs-2476	44	22	[	[	X
iajs-2476	44	23	1	1	NUM
iajs-2476	44	24	]	]	PUNCT
iajs-2476	44	25	.	.	PUNCT
iajs-2476	45	1	in	in	ADP
iajs-2476	45	2	[	[	X
iajs-2476	45	3	16,17	16,17	NUM
iajs-2476	45	4	]	]	PUNCT
iajs-2476	45	5	.	.	PUNCT
iajs-2476	46	1	inserted	insert	VERB
iajs-2476	46	2	the	the	DET
iajs-2476	46	3	concept	concept	NOUN
iajs-2476	46	4	of	of	ADP
iajs-2476	46	5	primary	primary	ADJ
iajs-2476	46	6	la	la	ADJ
iajs-2476	46	7	-	-	PUNCT
iajs-2476	46	8	submodules	submodule	NOUN
iajs-2476	46	9	of	of	ADP
iajs-2476	46	10	a	a	DET
iajs-2476	46	11	module	module	NOUN
iajs-2476	46	12	h	h	NOUN
iajs-2476	46	13	on	on	ADP
iajs-2476	46	14	a	a	DET
iajs-2476	46	15	commutative	commutative	ADJ
iajs-2476	46	16	ring	ring	NOUN
iajs-2476	46	17	together	together	ADV
iajs-2476	46	18	unity	unity	NOUN
iajs-2476	46	19	f	f	NOUN
iajs-2476	46	20	,	,	PUNCT
iajs-2476	46	21	where	where	SCONJ
iajs-2476	46	22	la	la	PROPN
iajs-2476	46	23	is	be	AUX
iajs-2476	46	24	a	a	DET
iajs-2476	46	25	whole	whole	ADJ
iajs-2476	46	26	lattice	lattice	NOUN
iajs-2476	46	27	.	.	PUNCT
iajs-2476	47	1	the	the	DET
iajs-2476	47	2	collection	collection	NOUN
iajs-2476	47	3	of	of	ADP
iajs-2476	47	4	all	all	DET
iajs-2476	47	5	primary	primary	ADJ
iajs-2476	47	6	lasubmodules	lasubmodule	NOUN
iajs-2476	47	7	of	of	ADP
iajs-2476	47	8	h	h	NOUN
iajs-2476	47	9	is	be	AUX
iajs-2476	47	10	called	call	VERB
iajs-2476	47	11	the	the	DET
iajs-2476	47	12	primary	primary	ADJ
iajs-2476	47	13	la	la	PROPN
iajs-2476	47	14	-	-	NOUN
iajs-2476	47	15	spectrum	spectrum	NOUN
iajs-2476	47	16	of	of	ADP
iajs-2476	47	17	h	h	NOUN
iajs-2476	47	18	or	or	CCONJ
iajs-2476	47	19	,	,	PUNCT
iajs-2476	47	20	artlessly	artlessly	ADV
iajs-2476	47	21	the	the	DET
iajs-2476	47	22	p	p	NOUN
iajs-2476	47	23	-	-	PUNCT
iajs-2476	47	24	la	la	NOUN
iajs-2476	47	25	-	-	NOUN
iajs-2476	47	26	spectrum	spectrum	NOUN
iajs-2476	47	27	of	of	ADP
iajs-2476	47	28	h	h	NOUN
iajs-2476	47	29	while	while	SCONJ
iajs-2476	47	30	is	be	AUX
iajs-2476	47	31	indicated	indicate	VERB
iajs-2476	47	32	via	via	ADP
iajs-2476	47	33	la	la	NOUN
iajs-2476	47	34	-	-	PUNCT
iajs-2476	47	35	prim(h	prim(h	NOUN
iajs-2476	47	36	)	)	PUNCT
iajs-2476	47	37	.	.	PUNCT
iajs-2476	48	1	in	in	ADP
iajs-2476	48	2	this	this	DET
iajs-2476	48	3	work	work	NOUN
iajs-2476	48	4	,	,	PUNCT
iajs-2476	48	5	we	we	PRON
iajs-2476	48	6	follow	follow	VERB
iajs-2476	48	7	[	[	X
iajs-2476	48	8	18	18	NUM
iajs-2476	48	9	]	]	PUNCT
iajs-2476	48	10	.	.	PUNCT
iajs-2476	49	1	and	and	CCONJ
iajs-2476	49	2	topologize	topologize	VERB
iajs-2476	49	3	laprim(h	laprim(h	PROPN
iajs-2476	49	4	)	)	PUNCT
iajs-2476	49	5	,	,	PUNCT
iajs-2476	49	6	which	which	PRON
iajs-2476	49	7	its	its	PRON
iajs-2476	49	8	surname	surname	NOUN
iajs-2476	49	9	is	be	AUX
iajs-2476	49	10	zariski	zariski	ADJ
iajs-2476	49	11	topology	topology	NOUN
iajs-2476	49	12	while	while	SCONJ
iajs-2476	49	13	examine	examine	VERB
iajs-2476	49	14	the	the	DET
iajs-2476	49	15	characteristics	characteristic	NOUN
iajs-2476	49	16	of	of	ADP
iajs-2476	49	17	this	this	DET
iajs-2476	49	18	topological	topological	ADJ
iajs-2476	49	19	space	space	NOUN
iajs-2476	49	20	.	.	PUNCT
iajs-2476	50	1	thereafter	thereafter	ADV
iajs-2476	50	2	,	,	PUNCT
iajs-2476	50	3	we	we	PRON
iajs-2476	50	4	discussed	discuss	VERB
iajs-2476	50	5	the	the	DET
iajs-2476	50	6	relation	relation	NOUN
iajs-2476	50	7	between	between	ADP
iajs-2476	50	8	the	the	DET
iajs-2476	50	9	topological	topological	ADJ
iajs-2476	50	10	spaces	space	NOUN
iajs-2476	50	11	laprim(h	laprim(h	PROPN
iajs-2476	50	12	)	)	PUNCT
iajs-2476	50	13	and	and	CCONJ
iajs-2476	50	14	la	la	NOUN
iajs-2476	50	15	-	-	PUNCT
iajs-2476	50	16	prim(f	prim(f	NOUN
iajs-2476	50	17	/	/	SYM
iajs-2476	50	18	ann(h	ann(h	PROPN
iajs-2476	50	19	)	)	PUNCT
iajs-2476	50	20	)	)	PUNCT
iajs-2476	50	21	.	.	PUNCT
iajs-2476	51	1	finally	finally	ADV
iajs-2476	51	2	,	,	PUNCT
iajs-2476	51	3	we	we	PRON
iajs-2476	51	4	located	locate	VERB
iajs-2476	51	5	a	a	DET
iajs-2476	51	6	basis	basis	NOUN
iajs-2476	51	7	for	for	ADP
iajs-2476	51	8	the	the	DET
iajs-2476	51	9	zariski	zariski	ADJ
iajs-2476	51	10	topology	topology	NOUN
iajs-2476	51	11	on	on	ADP
iajs-2476	51	12	la	la	NOUN
iajs-2476	51	13	-	-	PUNCT
iajs-2476	51	14	prim(h	prim(h	NOUN
iajs-2476	51	15	)	)	PUNCT
iajs-2476	51	16	.	.	PUNCT
iajs-2476	52	1	2	2	X
iajs-2476	52	2	.	.	NUM
iajs-2476	52	3	basic	basic	ADJ
iajs-2476	52	4	concepts	concept	NOUN
iajs-2476	52	5	during	during	ADP
iajs-2476	52	6	this	this	DET
iajs-2476	52	7	article	article	NOUN
iajs-2476	52	8	via	via	ADP
iajs-2476	52	9	f	f	PROPN
iajs-2476	52	10	,	,	PUNCT
iajs-2476	52	11	we	we	PRON
iajs-2476	52	12	mean	mean	VERB
iajs-2476	52	13	a	a	DET
iajs-2476	52	14	reciprocal	reciprocal	ADJ
iajs-2476	52	15	ring	ring	NOUN
iajs-2476	52	16	together	together	ADV
iajs-2476	52	17	unity	unity	NOUN
iajs-2476	52	18	,	,	PUNCT
iajs-2476	52	19	and	and	CCONJ
iajs-2476	52	20	h	h	NOUN
iajs-2476	52	21	is	be	AUX
iajs-2476	52	22	a	a	DET
iajs-2476	52	23	unital	unital	ADJ
iajs-2476	52	24	fmodule	fmodule	NOUN
iajs-2476	52	25	and	and	CCONJ
iajs-2476	52	26	la	la	PROPN
iajs-2476	52	27	indicates	indicate	VERB
iajs-2476	52	28	a	a	DET
iajs-2476	52	29	whole	whole	ADJ
iajs-2476	52	30	lattice	lattice	NOUN
iajs-2476	52	31	.	.	PUNCT
iajs-2476	53	1	via	via	ADP
iajs-2476	53	2	an	an	DET
iajs-2476	53	3	la	la	NOUN
iajs-2476	53	4	-	-	PUNCT
iajs-2476	53	5	subset	subset	NOUN
iajs-2476	53	6	ϑ	ϑ	PROPN
iajs-2476	53	7	of	of	ADP
iajs-2476	53	8	y	y	PROPN
iajs-2476	53	9	∅	∅	NOUN
iajs-2476	53	10	,	,	PUNCT
iajs-2476	53	11	we	we	PRON
iajs-2476	53	12	mean	mean	VERB
iajs-2476	53	13	a	a	DET
iajs-2476	53	14	mapping	mapping	NOUN
iajs-2476	53	15	ϑ	ϑ	X
iajs-2476	53	16	from	from	ADP
iajs-2476	53	17	y	y	PRON
iajs-2476	53	18	to	to	PART
iajs-2476	53	19	la	la	VERB
iajs-2476	53	20	while	while	SCONJ
iajs-2476	53	21	if	if	SCONJ
iajs-2476	53	22	la=[0,1	la=[0,1	PROPN
iajs-2476	53	23	]	]	PUNCT
iajs-2476	53	24	,	,	PUNCT
iajs-2476	53	25	then	then	ADV
iajs-2476	53	26	ϑ	ϑ	X
iajs-2476	53	27	is	be	AUX
iajs-2476	53	28	a	a	DET
iajs-2476	53	29	surname	surname	NOUN
iajs-2476	53	30	of	of	ADP
iajs-2476	53	31	a	a	DET
iajs-2476	53	32	fuzzy	fuzzy	ADJ
iajs-2476	53	33	subset	subset	NOUN
iajs-2476	53	34	of	of	ADP
iajs-2476	53	35	y.	y.	PROPN
iajs-2476	53	36	lay	lay	PROPN
iajs-2476	53	37	indicates	indicate	VERB
iajs-2476	53	38	the	the	DET
iajs-2476	53	39	collection	collection	NOUN
iajs-2476	53	40	of	of	ADP
iajs-2476	53	41	each	each	DET
iajs-2476	53	42	la	la	NOUN
iajs-2476	53	43	-	-	PUNCT
iajs-2476	53	44	subsets	subset	NOUN
iajs-2476	53	45	of	of	ADP
iajs-2476	53	46	y	y	PROPN
iajs-2476	53	47	.	.	PUNCT
iajs-2476	54	1	suppose	suppose	VERB
iajs-2476	54	2	that	that	SCONJ
iajs-2476	54	3	c	c	PROPN
iajs-2476	54	4	is	be	AUX
iajs-2476	54	5	a	a	DET
iajs-2476	54	6	subset	subset	NOUN
iajs-2476	54	7	of	of	ADP
iajs-2476	54	8	y	y	PROPN
iajs-2476	54	9	and	and	CCONJ
iajs-2476	54	10	b	b	X
iajs-2476	54	11	∈	∈	PROPN
iajs-2476	54	12	la	la	PROPN
iajs-2476	54	13	.	.	PROPN
iajs-2476	54	14	define	define	VERB
iajs-2476	54	15	bc	bc	PROPN
iajs-2476	54	16	∈	∈	PROPN
iajs-2476	54	17	lay	lie	VERB
iajs-2476	54	18	as	as	SCONJ
iajs-2476	54	19	follows	follow	VERB
iajs-2476	54	20	:	:	PUNCT
iajs-2476	55	1	b	b	X
iajs-2476	55	2	y	y	PROPN
iajs-2476	55	3	b	b	PROPN
iajs-2476	56	1	if	if	SCONJ
iajs-2476	56	2	y	y	PROPN
iajs-2476	56	3	∈	∈	PROPN
iajs-2476	56	4	c	c	NOUN
iajs-2476	56	5	0	0	PUNCT
iajs-2476	56	6	otherwise	otherwise	ADV
iajs-2476	56	7	in	in	ADP
iajs-2476	56	8	particular	particular	ADJ
iajs-2476	56	9	case	case	NOUN
iajs-2476	56	10	if	if	SCONJ
iajs-2476	56	11	c={c	c={c	NOUN
iajs-2476	56	12	}	}	PUNCT
iajs-2476	56	13	we	we	PRON
iajs-2476	56	14	indicate	indicate	VERB
iajs-2476	56	15	b{c	b{c	PROPN
iajs-2476	56	16	}	}	PUNCT
iajs-2476	56	17	by	by	ADP
iajs-2476	56	18	bc	bc	PROPN
iajs-2476	56	19	,	,	PUNCT
iajs-2476	56	20	while	while	SCONJ
iajs-2476	56	21	its	its	PRON
iajs-2476	56	22	surname	surname	NOUN
iajs-2476	56	23	is	be	AUX
iajs-2476	56	24	an	an	DET
iajs-2476	56	25	la	la	ADJ
iajs-2476	56	26	-	-	PUNCT
iajs-2476	56	27	point	point	NOUN
iajs-2476	56	28	of	of	ADP
iajs-2476	56	29	y.	y.	NOUN
iajs-2476	56	30	for	for	ADP
iajs-2476	56	31	ϑ	ϑ	PROPN
iajs-2476	56	32	∈	∈	NOUN
iajs-2476	56	33	lay	lie	VERB
iajs-2476	56	34	while	while	SCONJ
iajs-2476	56	35	c	c	PROPN
iajs-2476	56	36	∈	∈	PROPN
iajs-2476	56	37	la	la	PROPN
iajs-2476	56	38	,	,	PUNCT
iajs-2476	56	39	locate	locate	ADJ
iajs-2476	56	40	ϑc	ϑc	NOUN
iajs-2476	56	41	as	as	SCONJ
iajs-2476	56	42	follows	follow	VERB
iajs-2476	56	43	:	:	PUNCT
iajs-2476	56	44	  	  	SPACE
iajs-2476	56	45	91	91	NUM
iajs-2476	56	46	ibn	ibn	PROPN
iajs-2476	56	47	al	al	PROPN
iajs-2476	56	48	-	-	PUNCT
iajs-2476	56	49	haitham	haitham	PROPN
iajs-2476	56	50	jour	jour	X
iajs-2476	56	51	.	.	PROPN
iajs-2476	57	1	for	for	ADP
iajs-2476	57	2	pure	pure	ADJ
iajs-2476	57	3	&	&	CCONJ
iajs-2476	57	4	appl	appl	PROPN
iajs-2476	57	5	.	.	PUNCT
iajs-2476	58	1	sci	sci	PROPN
iajs-2476	58	2	.	.	PROPN
iajs-2476	59	1	33	33	NUM
iajs-2476	59	2	(	(	PUNCT
iajs-2476	59	3	3	3	NUM
iajs-2476	59	4	)	)	PUNCT
iajs-2476	59	5	2020	2020	NUM
iajs-2476	59	6	ϑc	ϑc	NOUN
iajs-2476	59	7	=	=	SYM
iajs-2476	59	8	{	{	PUNCT
iajs-2476	59	9	y	y	PROPN
iajs-2476	59	10	∈	∈	PROPN
iajs-2476	59	11	y	y	PROPN
iajs-2476	59	12	|	|	NOUN
iajs-2476	59	13	ϑ(y	ϑ(y	PROPN
iajs-2476	59	14	)	)	PUNCT
iajs-2476	59	15	≥	≥	NOUN
iajs-2476	59	16	c	c	NOUN
iajs-2476	59	17	}	}	PUNCT
iajs-2476	59	18	,	,	PUNCT
iajs-2476	59	19	ϑc	ϑc	PROPN
iajs-2476	59	20	is	be	AUX
iajs-2476	59	21	called	call	VERB
iajs-2476	59	22	the	the	DET
iajs-2476	59	23	c	c	NOUN
iajs-2476	59	24	-	-	PUNCT
iajs-2476	59	25	level	level	NOUN
iajs-2476	59	26	subset	subset	NOUN
iajs-2476	59	27	of	of	ADP
iajs-2476	59	28	ϑ.	ϑ.	NOUN
iajs-2476	59	29	the	the	DET
iajs-2476	59	30	image	image	NOUN
iajs-2476	59	31	of	of	ADP
iajs-2476	59	32	ϑ	ϑ	PROPN
iajs-2476	59	33	is	be	AUX
iajs-2476	59	34	indicated	indicate	VERB
iajs-2476	59	35	via	via	ADP
iajs-2476	59	36	ima(ϑ	ima(ϑ	PROPN
iajs-2476	59	37	)	)	PUNCT
iajs-2476	59	38	or	or	CCONJ
iajs-2476	59	39	ϑ(y	ϑ(y	PROPN
iajs-2476	59	40	)	)	PUNCT
iajs-2476	59	41	.	.	PUNCT
iajs-2476	60	1	in	in	ADP
iajs-2476	60	2	[	[	X
iajs-2476	60	3	18	18	NUM
iajs-2476	60	4	]	]	PUNCT
iajs-2476	60	5	.	.	PUNCT
iajs-2476	61	1	it	it	PRON
iajs-2476	61	2	was	be	AUX
iajs-2476	61	3	proved	prove	VERB
iajs-2476	61	4	that	that	SCONJ
iajs-2476	61	5	ϑ	ϑ	X
iajs-2476	61	6	⋃	⋃	NOUN
iajs-2476	61	7	c∈	c∈	NOUN
iajs-2476	61	8	.	.	PUNCT
iajs-2476	62	1	for	for	ADP
iajs-2476	62	2	ϑ	ϑ	X
iajs-2476	62	3	,	,	PUNCT
iajs-2476	62	4	ϖ	ϖ	PROPN
iajs-2476	62	5	∈	∈	PROPN
iajs-2476	62	6	lay	lay	VERB
iajs-2476	62	7	we	we	PRON
iajs-2476	62	8	say	say	VERB
iajs-2476	62	9	that	that	SCONJ
iajs-2476	62	10	ϑ	ϑ	NOUN
iajs-2476	62	11	is	be	AUX
iajs-2476	62	12	included	include	VERB
iajs-2476	62	13	in	in	ADP
iajs-2476	62	14	ϖ	ϖ	NOUN
iajs-2476	62	15	while	while	SCONJ
iajs-2476	62	16	we	we	PRON
iajs-2476	62	17	write	write	VERB
iajs-2476	62	18	ϑ	ϑ	PRON
iajs-2476	62	19	⊆	⊆	NUM
iajs-2476	62	20	ϖ	ϖ	NOUN
iajs-2476	62	21	if	if	SCONJ
iajs-2476	62	22	for	for	ADP
iajs-2476	62	23	every	every	DET
iajs-2476	62	24	y	y	PROPN
iajs-2476	62	25	∈	∈	PROPN
iajs-2476	62	26	y	y	PROPN
iajs-2476	62	27	,	,	PUNCT
iajs-2476	62	28	ϑ	ϑ	X
iajs-2476	62	29	(	(	PUNCT
iajs-2476	62	30	y	y	NOUN
iajs-2476	62	31	)	)	PUNCT
iajs-2476	62	32	≤	≤	NOUN
iajs-2476	63	1	ϖ	ϖ	X
iajs-2476	63	2	(	(	PUNCT
iajs-2476	63	3	y	y	NOUN
iajs-2476	63	4	)	)	PUNCT
iajs-2476	63	5	.	.	PUNCT
iajs-2476	64	1	for	for	ADP
iajs-2476	64	2	ϑ	ϑ	X
iajs-2476	64	3	,	,	PUNCT
iajs-2476	64	4	ϖ	ϖ	PROPN
iajs-2476	64	5	∈	∈	PROPN
iajs-2476	64	6	la	la	X
iajs-2476	64	7	,	,	PUNCT
iajs-2476	64	8	ϑ	ϑ	X
iajs-2476	64	9	∪	∪	X
iajs-2476	64	10	ϖ	ϖ	NOUN
iajs-2476	64	11	,	,	PUNCT
iajs-2476	64	12	ϑ	ϑ	X
iajs-2476	64	13	∩	∩	NOUN
iajs-2476	64	14	ϖ	ϖ	X
iajs-2476	64	15	∈	∈	PROPN
iajs-2476	64	16	lay	lay	VERB
iajs-2476	64	17	,	,	PUNCT
iajs-2476	64	18	are	be	AUX
iajs-2476	64	19	defined	define	VERB
iajs-2476	64	20	via	via	ADP
iajs-2476	64	21	(	(	PUNCT
iajs-2476	64	22	ϑ	ϑ	X
iajs-2476	64	23	∪	∪	X
iajs-2476	64	24	ϖ	ϖ	NOUN
iajs-2476	64	25	)	)	PUNCT
iajs-2476	64	26	(	(	PUNCT
iajs-2476	64	27	y	y	NOUN
iajs-2476	64	28	)	)	PUNCT
iajs-2476	64	29	=	=	SYM
iajs-2476	64	30	ϑ(y	ϑ(y	PROPN
iajs-2476	64	31	)	)	PUNCT
iajs-2476	64	32	∨	∨	NUM
iajs-2476	64	33	ϖ	ϖ	PROPN
iajs-2476	64	34	(	(	PUNCT
iajs-2476	64	35	y	y	NOUN
iajs-2476	64	36	)	)	PUNCT
iajs-2476	64	37	and	and	CCONJ
iajs-2476	64	38	(	(	PUNCT
iajs-2476	64	39	ϑ	ϑ	X
iajs-2476	64	40	∩	∩	NOUN
iajs-2476	64	41	ϖ)(y	ϖ)(y	X
iajs-2476	64	42	)	)	PUNCT
iajs-2476	64	43	=	=	SYM
iajs-2476	64	44	ϑ(y	ϑ(y	PROPN
iajs-2476	64	45	)	)	PUNCT
iajs-2476	64	46	∧	∧	PROPN
iajs-2476	64	47	ϖ	ϖ	INTJ
iajs-2476	64	48	(	(	PUNCT
iajs-2476	64	49	y	y	NOUN
iajs-2476	64	50	)	)	PUNCT
iajs-2476	64	51	,	,	PUNCT
iajs-2476	64	52	for	for	ADP
iajs-2476	64	53	each	each	DET
iajs-2476	64	54	y	y	PROPN
iajs-2476	64	55	∈	∈	PROPN
iajs-2476	64	56	y	y	PROPN
iajs-2476	64	57	.	.	PUNCT
iajs-2476	65	1	if	if	SCONJ
iajs-2476	65	2	g	g	PROPN
iajs-2476	65	3	is	be	AUX
iajs-2476	65	4	a	a	DET
iajs-2476	65	5	function	function	NOUN
iajs-2476	65	6	from	from	ADP
iajs-2476	65	7	h	h	NOUN
iajs-2476	65	8	into	into	ADP
iajs-2476	65	9	g	g	PROPN
iajs-2476	65	10	,	,	PUNCT
iajs-2476	65	11	ϑ	ϑ	X
iajs-2476	65	12	∈	∈	PROPN
iajs-2476	65	13	la	la	NOUN
iajs-2476	65	14	and	and	CCONJ
iajs-2476	65	15	ϖ	ϖ	X
iajs-2476	65	16	∈	∈	PROPN
iajs-2476	65	17	la	la	NOUN
iajs-2476	65	18	,	,	PUNCT
iajs-2476	65	19	then	then	ADV
iajs-2476	65	20	the	the	DET
iajs-2476	65	21	la	la	ADJ
iajs-2476	65	22	-	-	PUNCT
iajs-2476	65	23	subsets	subset	NOUN
iajs-2476	65	24	g	g	PROPN
iajs-2476	65	25	(	(	PUNCT
iajs-2476	65	26	ϑ	ϑ	NOUN
iajs-2476	65	27	)	)	PUNCT
iajs-2476	65	28	∈	∈	PROPN
iajs-2476	65	29	lag	lag	NOUN
iajs-2476	65	30	and	and	CCONJ
iajs-2476	65	31	g	g	PROPN
iajs-2476	65	32	(	(	PUNCT
iajs-2476	65	33	ϖ	ϖ	NOUN
iajs-2476	65	34	)	)	PUNCT
iajs-2476	65	35	∈	∈	PROPN
iajs-2476	65	36	lah	lah	PROPN
iajs-2476	65	37	are	be	AUX
iajs-2476	65	38	defined	define	VERB
iajs-2476	65	39	as	as	SCONJ
iajs-2476	65	40	follows	follow	VERB
iajs-2476	65	41	:	:	PUNCT
iajs-2476	65	42	∀	∀	X
iajs-2476	65	43	d	d	X
iajs-2476	65	44	∈	∈	PROPN
iajs-2476	65	45	g	g	PROPN
iajs-2476	65	46	,	,	PUNCT
iajs-2476	65	47	g	g	PROPN
iajs-2476	65	48	(	(	PUNCT
iajs-2476	65	49	ϑ)(d)=	ϑ)(d)=	PROPN
iajs-2476	65	50	∨	∨	X
iajs-2476	65	51	ϑ	ϑ	X
iajs-2476	65	52	y	y	PROPN
iajs-2476	65	53	|y	|y	NOUN
iajs-2476	65	54	∈	∈	PROPN
iajs-2476	65	55	g	g	NOUN
iajs-2476	65	56	d	d	X
iajs-2476	65	57	g	g	PROPN
iajs-2476	65	58	d	d	NOUN
iajs-2476	65	59	∅	∅	NOUN
iajs-2476	65	60	;	;	PUNCT
iajs-2476	65	61	0	0	NUM
iajs-2476	65	62	otherwise	otherwise	ADV
iajs-2476	65	63	and	and	CCONJ
iajs-2476	65	64	g	g	PROPN
iajs-2476	65	65	(	(	PUNCT
iajs-2476	65	66	ϖ)(h)=ϖ	ϖ)(h)=ϖ	PROPN
iajs-2476	65	67	(	(	PUNCT
iajs-2476	65	68	g	g	PROPN
iajs-2476	65	69	(	(	PUNCT
iajs-2476	65	70	h	h	NOUN
iajs-2476	65	71	)	)	PUNCT
iajs-2476	65	72	)	)	PUNCT
iajs-2476	65	73	∀	∀	NUM
iajs-2476	66	1	h	h	NOUN
iajs-2476	66	2	∈	∈	PROPN
iajs-2476	66	3	h.	h.	PROPN
iajs-2476	66	4	suppose	suppose	VERB
iajs-2476	66	5	that	that	SCONJ
iajs-2476	66	6	h	h	NOUN
iajs-2476	66	7	,	,	PUNCT
iajs-2476	66	8	g	g	PROPN
iajs-2476	66	9	are	be	AUX
iajs-2476	66	10	two	two	NUM
iajs-2476	66	11	f	f	NOUN
iajs-2476	66	12	-	-	PUNCT
iajs-2476	66	13	modules	module	NOUN
iajs-2476	66	14	while	while	SCONJ
iajs-2476	66	15	g	g	NOUN
iajs-2476	66	16	:	:	PUNCT
iajs-2476	66	17	h→	h→	NOUN
iajs-2476	66	18	g	g	NOUN
iajs-2476	66	19	is	be	AUX
iajs-2476	66	20	an	an	DET
iajs-2476	66	21	f	f	NOUN
iajs-2476	66	22	-	-	PUNCT
iajs-2476	66	23	homomorphism	homomorphism	NOUN
iajs-2476	66	24	.	.	PUNCT
iajs-2476	67	1	then	then	ADV
iajs-2476	67	2	an	an	DET
iajs-2476	67	3	la	la	NOUN
iajs-2476	67	4	-	-	PUNCT
iajs-2476	67	5	subset	subset	NOUN
iajs-2476	67	6	ϑ	ϑ	PROPN
iajs-2476	67	7	of	of	ADP
iajs-2476	67	8	h	h	NOUN
iajs-2476	67	9	is	be	AUX
iajs-2476	67	10	surname	surname	NOUN
iajs-2476	67	11	g	g	NOUN
iajs-2476	67	12	-	-	PUNCT
iajs-2476	67	13	invariant	invariant	ADJ
iajs-2476	67	14	if	if	SCONJ
iajs-2476	67	15	g	g	PROPN
iajs-2476	67	16	(	(	PUNCT
iajs-2476	67	17	a)=	a)=	PROPN
iajs-2476	67	18	g(b	g(b	PROPN
iajs-2476	67	19	)	)	PUNCT
iajs-2476	67	20	then	then	ADV
iajs-2476	67	21	ϑ(a)=ϑ(b	ϑ(a)=ϑ(b	PROPN
iajs-2476	67	22	)	)	PUNCT
iajs-2476	67	23	for	for	ADP
iajs-2476	67	24	all	all	DET
iajs-2476	67	25	a	a	DET
iajs-2476	67	26	,	,	PUNCT
iajs-2476	67	27	b∈h	b∈h	NOUN
iajs-2476	67	28	.	.	PUNCT
iajs-2476	68	1	definition	definition	NOUN
iajs-2476	68	2	2.1	2.1	NUM
iajs-2476	68	3	suppose	suppose	VERB
iajs-2476	68	4	that	that	SCONJ
iajs-2476	68	5	ϑ	ϑ	X
iajs-2476	68	6	∈	∈	PROPN
iajs-2476	68	7	la	la	X
iajs-2476	68	8	.	.	PUNCT
iajs-2476	69	1	then	then	ADV
iajs-2476	69	2	ϑ	ϑ	PROPN
iajs-2476	69	3	is	be	AUX
iajs-2476	69	4	surname	surname	NOUN
iajs-2476	69	5	an	an	DET
iajs-2476	69	6	la	la	NOUN
iajs-2476	69	7	-	-	PUNCT
iajs-2476	69	8	ideal	ideal	NOUN
iajs-2476	69	9	of	of	ADP
iajs-2476	69	10	f	f	PROPN
iajs-2476	69	11	if	if	SCONJ
iajs-2476	69	12	for	for	ADP
iajs-2476	69	13	all	all	DET
iajs-2476	69	14	a	a	PRON
iajs-2476	69	15	,	,	PUNCT
iajs-2476	69	16	b	b	X
iajs-2476	69	17	∈	∈	PROPN
iajs-2476	69	18	f	f	X
iajs-2476	69	19	the	the	DET
iajs-2476	69	20	following	follow	VERB
iajs-2476	69	21	situations	situation	NOUN
iajs-2476	69	22	are	be	AUX
iajs-2476	69	23	satisfied	satisfied	ADJ
iajs-2476	69	24	:	:	PUNCT
iajs-2476	69	25	(	(	PUNCT
iajs-2476	69	26	1	1	X
iajs-2476	69	27	)	)	PUNCT
iajs-2476	69	28	ϑ(a	ϑ(a	VERB
iajs-2476	69	29	−	−	PROPN
iajs-2476	69	30	b	b	NOUN
iajs-2476	69	31	)	)	PUNCT
iajs-2476	69	32	≥	≥	NOUN
iajs-2476	69	33	ϑ(a	ϑ(a	VERB
iajs-2476	69	34	)	)	PUNCT
iajs-2476	69	35	∧	∧	NOUN
iajs-2476	69	36	ϑ(b	ϑ(b	VERB
iajs-2476	69	37	)	)	PUNCT
iajs-2476	69	38	;	;	PUNCT
iajs-2476	69	39	(	(	PUNCT
iajs-2476	69	40	2	2	X
iajs-2476	69	41	)	)	PUNCT
iajs-2476	69	42	ϑ(ab	ϑ(ab	PROPN
iajs-2476	69	43	)	)	PUNCT
iajs-2476	69	44	≥	≥	NOUN
iajs-2476	69	45	ϑ(a	ϑ(a	VERB
iajs-2476	69	46	)	)	PUNCT
iajs-2476	69	47	∨	∨	NUM
iajs-2476	69	48	ϑ(b	ϑ(b	PROPN
iajs-2476	69	49	)	)	PUNCT
iajs-2476	69	50	.	.	PUNCT
iajs-2476	70	1	the	the	DET
iajs-2476	70	2	collection	collection	NOUN
iajs-2476	70	3	of	of	ADP
iajs-2476	70	4	every	every	DET
iajs-2476	70	5	la	la	ADJ
iajs-2476	70	6	-	-	PUNCT
iajs-2476	70	7	ideals	ideal	NOUN
iajs-2476	70	8	of	of	ADP
iajs-2476	70	9	f	f	PROPN
iajs-2476	70	10	is	be	AUX
iajs-2476	70	11	indicated	indicate	VERB
iajs-2476	70	12	via	via	ADP
iajs-2476	70	13	lai	lai	PROPN
iajs-2476	70	14	(	(	PUNCT
iajs-2476	70	15	f	f	PROPN
iajs-2476	70	16	)	)	PUNCT
iajs-2476	70	17	.	.	PUNCT
iajs-2476	71	1	for	for	ADP
iajs-2476	71	2	ϑ	ϑ	X
iajs-2476	71	3	,	,	PUNCT
iajs-2476	71	4	ϖ	ϖ	PROPN
iajs-2476	71	5	∈	∈	PROPN
iajs-2476	71	6	lai	lai	NOUN
iajs-2476	71	7	(	(	PUNCT
iajs-2476	71	8	f	f	PROPN
iajs-2476	71	9	)	)	PUNCT
iajs-2476	71	10	,	,	PUNCT
iajs-2476	71	11	ϑ	ϑ	X
iajs-2476	71	12	ϖ	ϖ	X
iajs-2476	71	13	(	(	PUNCT
iajs-2476	71	14	a	a	NOUN
iajs-2476	71	15	)	)	PUNCT
iajs-2476	71	16	=	=	SYM
iajs-2476	71	17	∨{ϑ(b	∨{ϑ(b	ADJ
iajs-2476	71	18	)	)	PUNCT
iajs-2476	71	19	∧	∧	PROPN
iajs-2476	71	20	ϖ(c)|b	ϖ(c)|b	PROPN
iajs-2476	71	21	,	,	PUNCT
iajs-2476	72	1	c	c	PROPN
iajs-2476	72	2	∈	∈	PROPN
iajs-2476	73	1	f	f	PROPN
iajs-2476	73	2	,	,	PUNCT
iajs-2476	73	3	a	a	DET
iajs-2476	73	4	=	=	PUNCT
iajs-2476	73	5	bc	bc	ADJ
iajs-2476	73	6	}	}	PUNCT
iajs-2476	73	7	∀a	∀a	NOUN
iajs-2476	73	8	∈	∈	PROPN
iajs-2476	73	9	f	f	NOUN
iajs-2476	73	10	,	,	PUNCT
iajs-2476	73	11	and	and	CCONJ
iajs-2476	73	12	in	in	ADP
iajs-2476	73	13	[	[	X
iajs-2476	73	14	18	18	NUM
iajs-2476	73	15	]	]	PUNCT
iajs-2476	73	16	.	.	PUNCT
iajs-2476	74	1	it	it	PRON
iajs-2476	74	2	was	be	AUX
iajs-2476	74	3	confirmed	confirm	VERB
iajs-2476	74	4	that	that	SCONJ
iajs-2476	74	5	ϑ	ϑ	X
iajs-2476	74	6	ϖ	ϖ	X
iajs-2476	74	7	∈	∈	PROPN
iajs-2476	74	8	lai	lai	PROPN
iajs-2476	74	9	(	(	PUNCT
iajs-2476	74	10	f	f	PROPN
iajs-2476	74	11	)	)	PUNCT
iajs-2476	74	12	.	.	PUNCT
iajs-2476	75	1	if	if	SCONJ
iajs-2476	75	2	la=[0	la=[0	ADJ
iajs-2476	75	3	,	,	PUNCT
iajs-2476	75	4	1	1	NUM
iajs-2476	75	5	]	]	PUNCT
iajs-2476	75	6	,	,	PUNCT
iajs-2476	75	7	then	then	ADV
iajs-2476	75	8	an	an	DET
iajs-2476	75	9	la	la	ADJ
iajs-2476	75	10	-	-	PUNCT
iajs-2476	75	11	ideal	ideal	NOUN
iajs-2476	75	12	is	be	AUX
iajs-2476	75	13	surname	surname	NOUN
iajs-2476	75	14	a	a	DET
iajs-2476	75	15	fuzzy	fuzzy	ADJ
iajs-2476	75	16	ideal	ideal	NOUN
iajs-2476	75	17	while	while	SCONJ
iajs-2476	75	18	the	the	DET
iajs-2476	75	19	collection	collection	NOUN
iajs-2476	75	20	of	of	ADP
iajs-2476	75	21	every	every	DET
iajs-2476	75	22	fuzzy	fuzzy	ADJ
iajs-2476	75	23	ideals	ideal	NOUN
iajs-2476	75	24	of	of	ADP
iajs-2476	75	25	f	f	PROPN
iajs-2476	75	26	is	be	AUX
iajs-2476	75	27	indicated	indicate	VERB
iajs-2476	75	28	via	via	ADP
iajs-2476	75	29	fi	fi	NOUN
iajs-2476	75	30	(	(	PUNCT
iajs-2476	75	31	f	f	NOUN
iajs-2476	75	32	)	)	PUNCT
iajs-2476	75	33	.	.	PUNCT
iajs-2476	76	1	definition	definition	NOUN
iajs-2476	76	2	2.2	2.2	NUM
iajs-2476	77	1	[	[	X
iajs-2476	77	2	18	18	NUM
iajs-2476	77	3	]	]	PUNCT
iajs-2476	77	4	.	.	PUNCT
iajs-2476	78	1	suppose	suppose	VERB
iajs-2476	78	2	that	that	SCONJ
iajs-2476	78	3	ϑ	ϑ	PROPN
iajs-2476	78	4	is	be	AUX
iajs-2476	78	5	a	a	DET
iajs-2476	78	6	la	la	NOUN
iajs-2476	78	7	-	-	NOUN
iajs-2476	78	8	subset	subset	NOUN
iajs-2476	78	9	of	of	ADP
iajs-2476	78	10	f.	f.	PROPN
iajs-2476	78	11	the	the	DET
iajs-2476	78	12	radical	radical	NOUN
iajs-2476	78	13	of	of	ADP
iajs-2476	78	14	ϑ	ϑ	PROPN
iajs-2476	78	15	is	be	AUX
iajs-2476	78	16	indicated	indicate	VERB
iajs-2476	78	17	by	by	ADP
iajs-2476	78	18	(	(	PUNCT
iajs-2476	78	19	√ϑ	√ϑ	NOUN
iajs-2476	78	20	)	)	PUNCT
iajs-2476	78	21	and	and	CCONJ
iajs-2476	78	22	is	be	AUX
iajs-2476	78	23	defined	define	VERB
iajs-2476	78	24	by	by	ADP
iajs-2476	78	25	√ϑ	√ϑ	NOUN
iajs-2476	78	26	(	(	PUNCT
iajs-2476	78	27	y)=	y)=	ADP
iajs-2476	78	28	⋁	⋁	PROPN
iajs-2476	78	29	ϑ	ϑ	X
iajs-2476	78	30	y∈	y∈	NOUN
iajs-2476	78	31	for	for	ADP
iajs-2476	78	32	all	all	DET
iajs-2476	78	33	y	y	PROPN
iajs-2476	78	34	∈	∈	PROPN
iajs-2476	78	35	f	f	X
iajs-2476	78	36	.	.	PUNCT
iajs-2476	79	1	definition	definition	NOUN
iajs-2476	79	2	2.3	2.3	NUM
iajs-2476	79	3	η	η	PROPN
iajs-2476	79	4	∈	∈	PROPN
iajs-2476	79	5	lai	lai	PROPN
iajs-2476	79	6	(	(	PUNCT
iajs-2476	79	7	f	f	X
iajs-2476	79	8	)	)	PUNCT
iajs-2476	79	9	is	be	AUX
iajs-2476	79	10	surname	surname	NOUN
iajs-2476	79	11	a	a	DET
iajs-2476	79	12	primary	primary	ADJ
iajs-2476	79	13	la	la	NOUN
iajs-2476	79	14	-	-	PUNCT
iajs-2476	79	15	ideal	ideal	NOUN
iajs-2476	79	16	of	of	ADP
iajs-2476	79	17	f	f	PROPN
iajs-2476	79	18	if	if	SCONJ
iajs-2476	79	19	η	η	PROPN
iajs-2476	79	20	is	be	AUX
iajs-2476	79	21	non	non	ADJ
iajs-2476	79	22	-	-	ADJ
iajs-2476	79	23	fixed	fixed	ADJ
iajs-2476	79	24	and	and	CCONJ
iajs-2476	79	25	for	for	ADP
iajs-2476	79	26	all	all	DET
iajs-2476	79	27	ϑ	ϑ	X
iajs-2476	79	28	,	,	PUNCT
iajs-2476	79	29	ϖ	ϖ	PROPN
iajs-2476	79	30	∈	∈	PROPN
iajs-2476	79	31	lai(f	lai(f	PROPN
iajs-2476	79	32	)	)	PUNCT
iajs-2476	79	33	,	,	PUNCT
iajs-2476	79	34	if	if	SCONJ
iajs-2476	79	35	ϑ	ϑ	ADP
iajs-2476	79	36	ϖ	ϖ	PROPN
iajs-2476	79	37	⊆	⊆	NUM
iajs-2476	79	38	η	η	PROPN
iajs-2476	79	39	then	then	ADV
iajs-2476	79	40	ϑ	ϑ	PROPN
iajs-2476	79	41	⊆	⊆	NUM
iajs-2476	79	42	η	η	NOUN
iajs-2476	79	43	or	or	CCONJ
iajs-2476	79	44	ϖ	ϖ	PROPN
iajs-2476	79	45	⊆	⊆	NUM
iajs-2476	79	46	η	η	X
iajs-2476	79	47	.	.	PROPN
iajs-2476	79	48	via	via	ADP
iajs-2476	79	49	la	la	NOUN
iajs-2476	79	50	-	-	PUNCT
iajs-2476	79	51	prim(f	prim(f	NOUN
iajs-2476	79	52	)	)	PUNCT
iajs-2476	79	53	,	,	PUNCT
iajs-2476	79	54	we	we	PRON
iajs-2476	79	55	mean	mean	VERB
iajs-2476	79	56	the	the	DET
iajs-2476	79	57	collection	collection	NOUN
iajs-2476	79	58	of	of	ADP
iajs-2476	79	59	each	each	DET
iajs-2476	79	60	primary	primary	ADJ
iajs-2476	79	61	la	la	ADJ
iajs-2476	79	62	-	-	PUNCT
iajs-2476	79	63	ideals	ideal	NOUN
iajs-2476	79	64	of	of	ADP
iajs-2476	79	65	f.	f.	PROPN
iajs-2476	79	66	proposition	proposition	PROPN
iajs-2476	79	67	2.4	2.4	NUM
iajs-2476	79	68	[	[	SYM
iajs-2476	79	69	18	18	NUM
iajs-2476	79	70	]	]	PUNCT
iajs-2476	79	71	.	.	PUNCT
iajs-2476	79	72	suppose	suppose	VERB
iajs-2476	79	73	that	that	SCONJ
iajs-2476	79	74	f	f	PROPN
iajs-2476	79	75	and	and	CCONJ
iajs-2476	79	76	s	s	PART
iajs-2476	79	77	́	́	PROPN
iajs-2476	79	78	are	be	AUX
iajs-2476	79	79	two	two	NUM
iajs-2476	79	80	rings	ring	NOUN
iajs-2476	79	81	while	while	SCONJ
iajs-2476	79	82	g	g	NOUN
iajs-2476	79	83	:	:	PUNCT
iajs-2476	79	84	f	f	PROPN
iajs-2476	79	85	⟶	⟶	PROPN
iajs-2476	79	86	s	s	PART
iajs-2476	79	87	́	́	PROPN
iajs-2476	79	88	is	be	AUX
iajs-2476	79	89	an	an	DET
iajs-2476	79	90	epimorphism	epimorphism	NOUN
iajs-2476	79	91	.	.	PUNCT
iajs-2476	80	1	1	1	X
iajs-2476	80	2	)	)	PUNCT
iajs-2476	80	3	suppose	suppose	VERB
iajs-2476	80	4	that	that	SCONJ
iajs-2476	80	5	ϑ	ϑ	PROPN
iajs-2476	80	6	∈	∈	PROPN
iajs-2476	80	7	la	la	PROPN
iajs-2476	80	8	-	-	PUNCT
iajs-2476	80	9	prim(f	prim(f	NOUN
iajs-2476	80	10	)	)	PUNCT
iajs-2476	80	11	and	and	CCONJ
iajs-2476	80	12	g	g	NOUN
iajs-2476	80	13	-	-	PUNCT
iajs-2476	80	14	invariant	invariant	ADJ
iajs-2476	80	15	,	,	PUNCT
iajs-2476	80	16	then	then	ADV
iajs-2476	80	17	g(ϑ	g(ϑ	PROPN
iajs-2476	80	18	)	)	PUNCT
iajs-2476	80	19	∈	∈	PROPN
iajs-2476	80	20	la	la	NOUN
iajs-2476	80	21	-	-	PUNCT
iajs-2476	80	22	prim(s	prim(s	NOUN
iajs-2476	80	23	́	́	NOUN
iajs-2476	80	24	)	)	PUNCT
iajs-2476	80	25	.	.	PUNCT
iajs-2476	81	1	2	2	X
iajs-2476	81	2	)	)	PUNCT
iajs-2476	81	3	if	if	SCONJ
iajs-2476	81	4	ϖ	ϖ	X
iajs-2476	81	5	∈	∈	VERB
iajs-2476	81	6	la	la	NOUN
iajs-2476	81	7	-	-	PUNCT
iajs-2476	81	8	prim(s	prim(s	NOUN
iajs-2476	81	9	́	́	NOUN
iajs-2476	81	10	)	)	PUNCT
iajs-2476	81	11	,	,	PUNCT
iajs-2476	81	12	then	then	ADV
iajs-2476	81	13	g	g	PROPN
iajs-2476	81	14	(	(	PUNCT
iajs-2476	81	15	ϖ	ϖ	NOUN
iajs-2476	81	16	)	)	PUNCT
iajs-2476	81	17	∈	∈	PROPN
iajs-2476	81	18	la	la	NOUN
iajs-2476	81	19	-	-	PUNCT
iajs-2476	81	20	prim(f	prim(f	NOUN
iajs-2476	81	21	)	)	PUNCT
iajs-2476	81	22	.	.	PUNCT
iajs-2476	81	23	  	  	SPACE
iajs-2476	82	1	92	92	NUM
iajs-2476	82	2	ibn	ibn	PROPN
iajs-2476	82	3	al	al	PROPN
iajs-2476	82	4	-	-	PUNCT
iajs-2476	82	5	haitham	haitham	PROPN
iajs-2476	82	6	jour	jour	X
iajs-2476	82	7	.	.	PROPN
iajs-2476	82	8	for	for	ADP
iajs-2476	82	9	pure	pure	ADJ
iajs-2476	82	10	&	&	CCONJ
iajs-2476	82	11	appl	appl	PROPN
iajs-2476	82	12	.	.	PUNCT
iajs-2476	83	1	sci	sci	PROPN
iajs-2476	83	2	.	.	PROPN
iajs-2476	84	1	33	33	NUM
iajs-2476	84	2	(	(	PUNCT
iajs-2476	84	3	3	3	NUM
iajs-2476	84	4	)	)	PUNCT
iajs-2476	84	5	2020	2020	NUM
iajs-2476	85	1	for	for	ADP
iajs-2476	85	2	γ	γ	PROPN
iajs-2476	85	3	∈	∈	PROPN
iajs-2476	85	4	lai	lai	PROPN
iajs-2476	85	5	(	(	PUNCT
iajs-2476	85	6	f	f	PROPN
iajs-2476	85	7	)	)	PUNCT
iajs-2476	85	8	,	,	PUNCT
iajs-2476	85	9	v	v	X
iajs-2476	85	10	(	(	PUNCT
iajs-2476	85	11	γ	γ	NOUN
iajs-2476	85	12	)	)	PUNCT
iajs-2476	85	13	be	be	VERB
iajs-2476	85	14	the	the	DET
iajs-2476	85	15	collection	collection	NOUN
iajs-2476	85	16	of	of	ADP
iajs-2476	85	17	all	all	DET
iajs-2476	85	18	primary	primary	ADJ
iajs-2476	85	19	la	la	ADJ
iajs-2476	85	20	-	-	PUNCT
iajs-2476	85	21	ideals	ideal	NOUN
iajs-2476	85	22	of	of	ADP
iajs-2476	85	23	f	f	PROPN
iajs-2476	85	24	such	such	ADJ
iajs-2476	85	25	that	that	PRON
iajs-2476	85	26	includes	include	VERB
iajs-2476	85	27	γ	γ	PROPN
iajs-2476	85	28	,	,	PUNCT
iajs-2476	85	29	i.e	i.e	PROPN
iajs-2476	85	30	v	v	X
iajs-2476	85	31	(	(	PUNCT
iajs-2476	85	32	γ	γ	NOUN
iajs-2476	85	33	)	)	PUNCT
iajs-2476	85	34	=	=	NOUN
iajs-2476	85	35	{	{	PUNCT
iajs-2476	85	36	q	q	PUNCT
iajs-2476	85	37	∈	∈	PROPN
iajs-2476	85	38	la	la	PROPN
iajs-2476	85	39	-	-	PUNCT
iajs-2476	85	40	prim(f)|	prim(f)|	NOUN
iajs-2476	85	41	γ	γ	NOUN
iajs-2476	85	42	⊆	⊆	NUM
iajs-2476	85	43	q	q	NOUN
iajs-2476	85	44	}	}	PUNCT
iajs-2476	85	45	.	.	PUNCT
iajs-2476	86	1	collection	collection	PROPN
iajs-2476	86	2	x(γ	x(γ	PROPN
iajs-2476	86	3	)	)	PUNCT
iajs-2476	87	1	=	=	PUNCT
iajs-2476	87	2	la	la	PROPN
iajs-2476	87	3	-	-	PUNCT
iajs-2476	87	4	prim(f)\v	prim(f)\v	PROPN
iajs-2476	87	5	(	(	PUNCT
iajs-2476	87	6	γ	γ	PROPN
iajs-2476	87	7	)	)	PUNCT
iajs-2476	87	8	,	,	PUNCT
iajs-2476	87	9	the	the	DET
iajs-2476	87	10	la	la	NOUN
iajs-2476	87	11	-	-	PUNCT
iajs-2476	87	12	prim(f	prim(f	NOUN
iajs-2476	87	13	)	)	PUNCT
iajs-2476	87	14	together	together	ADV
iajs-2476	87	15	the	the	DET
iajs-2476	87	16	collection	collection	NOUN
iajs-2476	87	17	𝒯	𝒯	PROPN
iajs-2476	87	18	́=	́=	PROPN
iajs-2476	87	19	{	{	PUNCT
iajs-2476	87	20	x(γ)|	x(γ)|	PROPN
iajs-2476	87	21	γ	γ	PROPN
iajs-2476	87	22	∈	∈	PROPN
iajs-2476	87	23	lai	lai	PROPN
iajs-2476	87	24	(	(	PUNCT
iajs-2476	87	25	f	f	X
iajs-2476	87	26	)	)	PUNCT
iajs-2476	87	27	}	}	PUNCT
iajs-2476	87	28	is	be	AUX
iajs-2476	87	29	a	a	DET
iajs-2476	87	30	topological	topological	ADJ
iajs-2476	87	31	space	space	NOUN
iajs-2476	87	32	while	while	SCONJ
iajs-2476	87	33	the	the	DET
iajs-2476	87	34	collection	collection	NOUN
iajs-2476	87	35	ℬ	ℬ	NOUN
iajs-2476	87	36	́=	́=	PROPN
iajs-2476	87	37	{	{	PUNCT
iajs-2476	87	38	x(yα)|	x(yα)|	NOUN
iajs-2476	87	39	y	y	PROPN
iajs-2476	87	40	∈	∈	PROPN
iajs-2476	88	1	f	f	PROPN
iajs-2476	88	2	,	,	PUNCT
iajs-2476	88	3	α	α	PROPN
iajs-2476	88	4	∈	∈	PROPN
iajs-2476	88	5	(	(	PUNCT
iajs-2476	88	6	0	0	NUM
iajs-2476	88	7	,	,	PUNCT
iajs-2476	88	8	1	1	NUM
iajs-2476	88	9	]	]	PUNCT
iajs-2476	88	10	formation	formation	NOUN
iajs-2476	88	11	a	a	DET
iajs-2476	88	12	basis	basis	NOUN
iajs-2476	88	13	for	for	ADP
iajs-2476	88	14	𝒯	𝒯	PROPN
iajs-2476	88	15	́	́	PROPN
iajs-2476	88	16	.	.	PUNCT
iajs-2476	89	1	as	as	ADV
iajs-2476	89	2	well	well	ADV
iajs-2476	89	3	,	,	PUNCT
iajs-2476	89	4	it	it	PRON
iajs-2476	89	5	can	can	AUX
iajs-2476	89	6	be	be	AUX
iajs-2476	89	7	shown	show	VERB
iajs-2476	89	8	that	that	SCONJ
iajs-2476	89	9	for	for	ADP
iajs-2476	89	10	two	two	NUM
iajs-2476	89	11	elements	element	NOUN
iajs-2476	89	12	x(y	x(y	PUNCT
iajs-2476	89	13	)	)	PUNCT
iajs-2476	89	14	,	,	PUNCT
iajs-2476	89	15	x(x	x(x	PROPN
iajs-2476	89	16	́	́	PROPN
iajs-2476	89	17	)	)	PUNCT
iajs-2476	89	18	;	;	PUNCT
iajs-2476	89	19	x(y	x(y	X
iajs-2476	89	20	)	)	PUNCT
iajs-2476	89	21	∩	∩	PROPN
iajs-2476	89	22	x(x	x(x	PROPN
iajs-2476	89	23	́	́	PROPN
iajs-2476	89	24	)	)	PUNCT
iajs-2476	89	25	=	=	SYM
iajs-2476	90	1	x	x	X
iajs-2476	90	2	(	(	PUNCT
iajs-2476	90	3	yx	yx	PROPN
iajs-2476	90	4	∧	∧	PROPN
iajs-2476	90	5	́	́	PROPN
iajs-2476	90	6	,	,	PUNCT
iajs-2476	90	7	y	y	PROPN
iajs-2476	90	8	,	,	PUNCT
iajs-2476	90	9	x	x	PROPN
iajs-2476	90	10	∈	∈	PROPN
iajs-2476	90	11	f	f	PROPN
iajs-2476	90	12	,	,	PUNCT
iajs-2476	90	13	α	α	PROPN
iajs-2476	90	14	,	,	PUNCT
iajs-2476	90	15	α	α	PROPN
iajs-2476	90	16	́	́	PUNCT
iajs-2476	90	17	∈	∈	PROPN
iajs-2476	90	18	la	la	NOUN
iajs-2476	90	19	\{0	\{0	NOUN
iajs-2476	90	20	}	}	PUNCT
iajs-2476	90	21	.	.	PUNCT
iajs-2476	91	1	definition	definition	NOUN
iajs-2476	91	2	2.5	2.5	NUM
iajs-2476	91	3	an	an	DET
iajs-2476	91	4	element	element	NOUN
iajs-2476	91	5	z	z	PROPN
iajs-2476	91	6	∈	∈	PROPN
iajs-2476	91	7	la\{1	la\{1	PROPN
iajs-2476	91	8	}	}	PUNCT
iajs-2476	91	9	is	be	AUX
iajs-2476	91	10	surname	surname	NOUN
iajs-2476	91	11	a	a	DET
iajs-2476	91	12	prime	prime	ADJ
iajs-2476	91	13	element	element	NOUN
iajs-2476	91	14	of	of	ADP
iajs-2476	91	15	la	la	PROPN
iajs-2476	91	16	if	if	SCONJ
iajs-2476	91	17	for	for	ADP
iajs-2476	91	18	c	c	NOUN
iajs-2476	91	19	,	,	PUNCT
iajs-2476	91	20	d	d	PROPN
iajs-2476	91	21	∈	∈	PROPN
iajs-2476	91	22	la	la	PROPN
iajs-2476	91	23	,	,	PUNCT
iajs-2476	91	24	c	c	PROPN
iajs-2476	91	25	∧	∧	PROPN
iajs-2476	91	26	d	d	PROPN
iajs-2476	91	27	≤	≤	PROPN
iajs-2476	92	1	z	z	NOUN
iajs-2476	92	2	,	,	PUNCT
iajs-2476	92	3	then	then	ADV
iajs-2476	92	4	c	c	X
iajs-2476	92	5	≤	≤	ADJ
iajs-2476	92	6	z	z	NOUN
iajs-2476	92	7	or	or	CCONJ
iajs-2476	92	8	d≤	d≤	PROPN
iajs-2476	92	9	z.	z.	PROPN
iajs-2476	92	10	definition	definition	NOUN
iajs-2476	92	11	2.6	2.6	NUM
iajs-2476	92	12	suppose	suppose	VERB
iajs-2476	92	13	that	that	SCONJ
iajs-2476	92	14	ε	ε	PROPN
iajs-2476	92	15	∈	∈	PROPN
iajs-2476	92	16	la	la	PROPN
iajs-2476	92	17	and	and	CCONJ
iajs-2476	92	18	ϑ	ϑ	PROPN
iajs-2476	92	19	∈	∈	PROPN
iajs-2476	92	20	lah	lah	NOUN
iajs-2476	92	21	.	.	PUNCT
iajs-2476	93	1	define	define	VERB
iajs-2476	93	2	ε	ε	PROPN
iajs-2476	93	3	·	·	PUNCT
iajs-2476	93	4	ϑ	ϑ	X
iajs-2476	93	5	∈	∈	X
iajs-2476	93	6	lah	lah	NOUN
iajs-2476	93	7	as	as	SCONJ
iajs-2476	93	8	follows	follow	VERB
iajs-2476	93	9	:	:	PUNCT
iajs-2476	94	1	(	(	PUNCT
iajs-2476	94	2	ε	ε	PROPN
iajs-2476	94	3	.	.	PUNCT
iajs-2476	94	4	ϑ)(y)=∨	ϑ)(y)=∨	PROPN
iajs-2476	94	5	{	{	PUNCT
iajs-2476	94	6	ε(r	ε(r	PROPN
iajs-2476	94	7	́)∧	́)∧	ADJ
iajs-2476	94	8	ϑ(b)|	ϑ(b)|	ADJ
iajs-2476	94	9	r	r	NOUN
iajs-2476	94	10	́	́	PUNCT
iajs-2476	94	11	∈	∈	PROPN
iajs-2476	94	12	f	f	PROPN
iajs-2476	94	13	,	,	PUNCT
iajs-2476	94	14	b	b	PROPN
iajs-2476	94	15	∈	∈	PROPN
iajs-2476	94	16	h	h	NOUN
iajs-2476	94	17	,	,	PUNCT
iajs-2476	94	18	r	r	NOUN
iajs-2476	94	19	́b	́b	PROPN
iajs-2476	94	20	=	=	SYM
iajs-2476	94	21	y	y	NOUN
iajs-2476	94	22	}	}	PUNCT
iajs-2476	94	23	for	for	ADP
iajs-2476	94	24	all	all	DET
iajs-2476	94	25	y	y	PROPN
iajs-2476	94	26	∈	∈	PROPN
iajs-2476	94	27	h.	h.	NOUN
iajs-2476	94	28	definition	definition	NOUN
iajs-2476	94	29	2.7	2.7	NUM
iajs-2476	94	30	an	an	DET
iajs-2476	94	31	la	la	NOUN
iajs-2476	94	32	-	-	PUNCT
iajs-2476	94	33	subset	subset	NOUN
iajs-2476	94	34	ϑ	ϑ	PROPN
iajs-2476	94	35	∈lah	∈lah	PROPN
iajs-2476	94	36	is	be	AUX
iajs-2476	94	37	a	a	DET
iajs-2476	94	38	la	la	ADJ
iajs-2476	94	39	-	-	PUNCT
iajs-2476	94	40	submodule	submodule	NOUN
iajs-2476	94	41	of	of	ADP
iajs-2476	94	42	h	h	NOUN
iajs-2476	94	43	if	if	SCONJ
iajs-2476	94	44	:	:	PUNCT
iajs-2476	94	45	1	1	X
iajs-2476	94	46	)	)	PUNCT
iajs-2476	94	47	ϑ	ϑ	X
iajs-2476	94	48	(	(	PUNCT
iajs-2476	94	49	0	0	NUM
iajs-2476	94	50	)	)	PUNCT
iajs-2476	94	51	=	=	SYM
iajs-2476	94	52	1	1	NUM
iajs-2476	94	53	;	;	PUNCT
iajs-2476	94	54	2	2	X
iajs-2476	94	55	)	)	PUNCT
iajs-2476	94	56	ϑ	ϑ	X
iajs-2476	94	57	(	(	PUNCT
iajs-2476	94	58	r	r	NOUN
iajs-2476	94	59	́a	́a	PROPN
iajs-2476	94	60	)	)	PUNCT
iajs-2476	94	61	≥	≥	NOUN
iajs-2476	94	62	ϑ	ϑ	X
iajs-2476	94	63	(	(	PUNCT
iajs-2476	94	64	a	a	NOUN
iajs-2476	94	65	)	)	PUNCT
iajs-2476	94	66	for	for	ADP
iajs-2476	94	67	all	all	DET
iajs-2476	94	68	r	r	NOUN
iajs-2476	94	69	́	́	PUNCT
iajs-2476	94	70	∈	∈	PROPN
iajs-2476	94	71	f	f	PROPN
iajs-2476	94	72	and	and	CCONJ
iajs-2476	94	73	a	a	DET
iajs-2476	94	74	∈	∈	PROPN
iajs-2476	94	75	h	h	NOUN
iajs-2476	94	76	;	;	PUNCT
iajs-2476	94	77	3	3	X
iajs-2476	94	78	)	)	PUNCT
iajs-2476	94	79	ϑ	ϑ	X
iajs-2476	94	80	(	(	PUNCT
iajs-2476	94	81	a	a	DET
iajs-2476	94	82	+	+	NOUN
iajs-2476	94	83	b	b	NOUN
iajs-2476	94	84	)	)	PUNCT
iajs-2476	94	85	≥	≥	NOUN
iajs-2476	94	86	ϑ	ϑ	X
iajs-2476	94	87	(	(	PUNCT
iajs-2476	94	88	a	a	X
iajs-2476	94	89	)	)	PUNCT
iajs-2476	94	90	∧	∧	PROPN
iajs-2476	94	91	ϑ	ϑ	X
iajs-2476	94	92	(	(	PUNCT
iajs-2476	94	93	b	b	NOUN
iajs-2476	94	94	)	)	PUNCT
iajs-2476	94	95	for	for	ADP
iajs-2476	94	96	all	all	DET
iajs-2476	94	97	a	a	PRON
iajs-2476	94	98	,	,	PUNCT
iajs-2476	94	99	b	b	PROPN
iajs-2476	94	100	∈	∈	PROPN
iajs-2476	94	101	h.	h.	NOUN
iajs-2476	95	1	the	the	DET
iajs-2476	95	2	collection	collection	NOUN
iajs-2476	95	3	of	of	ADP
iajs-2476	95	4	all	all	DET
iajs-2476	95	5	la	la	ADJ
iajs-2476	95	6	-	-	PUNCT
iajs-2476	95	7	submodules	submodule	NOUN
iajs-2476	95	8	of	of	ADP
iajs-2476	95	9	h	h	NOUN
iajs-2476	95	10	is	be	AUX
iajs-2476	95	11	indicated	indicate	VERB
iajs-2476	95	12	by	by	ADP
iajs-2476	95	13	la(h	la(h	NOUN
iajs-2476	95	14	)	)	PUNCT
iajs-2476	95	15	.	.	PUNCT
iajs-2476	96	1	definition	definition	NOUN
iajs-2476	96	2	2.8	2.8	NUM
iajs-2476	96	3	[	[	X
iajs-2476	96	4	18	18	NUM
iajs-2476	96	5	]	]	PUNCT
iajs-2476	96	6	.	.	PUNCT
iajs-2476	96	7	suppose	suppose	VERB
iajs-2476	96	8	that	that	SCONJ
iajs-2476	96	9	{	{	PUNCT
iajs-2476	96	10	ϑ	ϑ	X
iajs-2476	96	11	j	j	PROPN
iajs-2476	96	12	|j	|j	PROPN
iajs-2476	96	13	∈	∈	PROPN
iajs-2476	96	14	j	j	PROPN
iajs-2476	96	15	}	}	PUNCT
iajs-2476	96	16	⊆la(h	⊆la(h	PROPN
iajs-2476	96	17	)	)	PUNCT
iajs-2476	96	18	.	.	PUNCT
iajs-2476	97	1	define	define	VERB
iajs-2476	97	2	the	the	DET
iajs-2476	97	3	la	la	ADJ
iajs-2476	97	4	-	-	PUNCT
iajs-2476	97	5	submodule	submodule	NOUN
iajs-2476	97	6	∑	∑	PUNCT
iajs-2476	97	7	ϑ	ϑ	X
iajs-2476	97	8	∈	∈	NOUN
iajs-2476	97	9	of	of	ADP
iajs-2476	97	10	h	h	NOUN
iajs-2476	97	11	by	by	ADP
iajs-2476	97	12	(	(	PUNCT
iajs-2476	97	13	∑	∑	PROPN
iajs-2476	97	14	ϑ	ϑ	X
iajs-2476	97	15	∈	∈	NOUN
iajs-2476	97	16	)	)	PUNCT
iajs-2476	97	17	(	(	PUNCT
iajs-2476	97	18	y	y	X
iajs-2476	97	19	)	)	PUNCT
iajs-2476	97	20	=	=	NOUN
iajs-2476	97	21	∨{⋀	∨{⋀	PROPN
iajs-2476	97	22	ϑ	ϑ	PROPN
iajs-2476	97	23	y∈	y∈	NOUN
iajs-2476	98	1	|	|	NOUN
iajs-2476	98	2	y=∑	y=∑	VERB
iajs-2476	98	3	y	y	PROPN
iajs-2476	98	4	∈	∈	PROPN
iajs-2476	98	5	,	,	PUNCT
iajs-2476	99	1	y	y	PROPN
iajs-2476	99	2	∈	∈	PROPN
iajs-2476	99	3	h	h	NOUN
iajs-2476	99	4	,	,	PUNCT
iajs-2476	99	5	∀j	∀j	PROPN
iajs-2476	99	6	∈	∈	PROPN
iajs-2476	99	7	j	j	PROPN
iajs-2476	99	8	}	}	SYM
iajs-2476	99	9	∀y	∀y	PROPN
iajs-2476	99	10	∈	∈	PROPN
iajs-2476	99	11	h.	h.	NOUN
iajs-2476	100	1	it	it	PRON
iajs-2476	100	2	is	be	AUX
iajs-2476	100	3	easy	easy	ADJ
iajs-2476	100	4	to	to	PART
iajs-2476	100	5	look	look	VERB
iajs-2476	100	6	that	that	SCONJ
iajs-2476	100	7	∑	∑	ADP
iajs-2476	100	8	ϑ	ϑ	X
iajs-2476	100	9	∈	∈	PROPN
iajs-2476	100	10	∈	∈	PROPN
iajs-2476	100	11	la(h	la(h	NUM
iajs-2476	100	12	)	)	PUNCT
iajs-2476	100	13	.	.	PUNCT
iajs-2476	101	1	for	for	ADP
iajs-2476	101	2	ϑ	ϑ	PRON
iajs-2476	101	3	,	,	PUNCT
iajs-2476	101	4	ϖ	ϖ	PROPN
iajs-2476	101	5	∈	∈	PROPN
iajs-2476	101	6	lah	lah	NOUN
iajs-2476	101	7	and	and	CCONJ
iajs-2476	101	8	ε	ε	PROPN
iajs-2476	101	9	∈	∈	PROPN
iajs-2476	101	10	laf	laf	PROPN
iajs-2476	101	11	,	,	PUNCT
iajs-2476	101	12	ϑ∶	ϑ∶	ADJ
iajs-2476	101	13	ϖ	ϖ	NOUN
iajs-2476	101	14	∈	∈	PROPN
iajs-2476	101	15	la	la	NOUN
iajs-2476	101	16	and	and	CCONJ
iajs-2476	101	17	ϑ∶	ϑ∶	ADJ
iajs-2476	101	18	ε	ε	PROPN
iajs-2476	101	19	∈	∈	PROPN
iajs-2476	101	20	lah	lah	PROPN
iajs-2476	101	21	are	be	AUX
iajs-2476	101	22	defined	define	VERB
iajs-2476	101	23	as	as	SCONJ
iajs-2476	101	24	follows	follow	VERB
iajs-2476	101	25	:	:	PUNCT
iajs-2476	101	26	ϑ∶	ϑ∶	ADJ
iajs-2476	101	27	ϖ	ϖ	NOUN
iajs-2476	101	28	=	=	PUNCT
iajs-2476	101	29	⋃	⋃	NOUN
iajs-2476	101	30	γ|γ	γ|γ	NOUN
iajs-2476	101	31	∈	∈	PROPN
iajs-2476	101	32	la	la	X
iajs-2476	101	33	,	,	PUNCT
iajs-2476	101	34	γ	γ	PROPN
iajs-2476	101	35	.	.	PUNCT
iajs-2476	101	36	ϖ	ϖ	PROPN
iajs-2476	101	37	⊆	⊆	NUM
iajs-2476	101	38	ϑ	ϑ	X
iajs-2476	101	39	.	.	PUNCT
iajs-2476	102	1	ϑ∶	ϑ∶	ADJ
iajs-2476	102	2	ε	ε	NOUN
iajs-2476	102	3	=	=	NOUN
iajs-2476	102	4	⋃	⋃	PROPN
iajs-2476	102	5	ϖ|ϖ	ϖ|ϖ	NOUN
iajs-2476	102	6	∈	∈	PROPN
iajs-2476	102	7	la	la	X
iajs-2476	102	8	,	,	PUNCT
iajs-2476	102	9	ε	ε	PROPN
iajs-2476	102	10	.	.	PUNCT
iajs-2476	103	1	ϖ	ϖ	PROPN
iajs-2476	103	2	⊆	⊆	NUM
iajs-2476	103	3	ϑ	ϑ	X
iajs-2476	103	4	.	.	PUNCT
iajs-2476	104	1	in	in	ADP
iajs-2476	104	2	[	[	X
iajs-2476	104	3	18	18	NUM
iajs-2476	104	4	]	]	PUNCT
iajs-2476	104	5	.	.	PUNCT
iajs-2476	105	1	it	it	PRON
iajs-2476	105	2	was	be	AUX
iajs-2476	105	3	proved	prove	VERB
iajs-2476	105	4	that	that	SCONJ
iajs-2476	105	5	if	if	SCONJ
iajs-2476	105	6	ϖ	ϖ	X
iajs-2476	105	7	∈	∈	NOUN
iajs-2476	105	8	la	la	X
iajs-2476	105	9	,	,	PUNCT
iajs-2476	105	10	ϑ	ϑ	PROPN
iajs-2476	105	11	∈	∈	PROPN
iajs-2476	105	12	la(h	la(h	NUM
iajs-2476	105	13	)	)	PUNCT
iajs-2476	105	14	,	,	PUNCT
iajs-2476	105	15	and	and	CCONJ
iajs-2476	105	16	ε	ε	PROPN
iajs-2476	105	17	∈	∈	PROPN
iajs-2476	105	18	lai	lai	PROPN
iajs-2476	105	19	f	f	PROPN
iajs-2476	105	20	,	,	PUNCT
iajs-2476	105	21	then	then	ADV
iajs-2476	105	22	ϑ∶	ϑ∶	ADJ
iajs-2476	105	23	ϖ	ϖ	NOUN
iajs-2476	105	24	=	=	PUNCT
iajs-2476	105	25	⋃	⋃	NOUN
iajs-2476	105	26	γ|γ	γ|γ	NOUN
iajs-2476	105	27	∈	∈	PROPN
iajs-2476	105	28	lai	lai	PROPN
iajs-2476	105	29	f	f	PROPN
iajs-2476	105	30	,	,	PUNCT
iajs-2476	105	31	γ	γ	PROPN
iajs-2476	105	32	.	.	PUNCT
iajs-2476	106	1	ϖ	ϖ	PROPN
iajs-2476	106	2	⊆	⊆	NUM
iajs-2476	106	3	ϑ	ϑ	X
iajs-2476	106	4	and	and	CCONJ
iajs-2476	106	5	ϑ∶	ϑ∶	ADJ
iajs-2476	106	6	ε	ε	NOUN
iajs-2476	106	7	=	=	NOUN
iajs-2476	106	8	⋃	⋃	PROPN
iajs-2476	106	9	ϖ|ϖ	ϖ|ϖ	NOUN
iajs-2476	106	10	∈	∈	PROPN
iajs-2476	106	11	la	la	PROPN
iajs-2476	106	12	h	h	PROPN
iajs-2476	106	13	,	,	PUNCT
iajs-2476	106	14	ε	ε	PROPN
iajs-2476	106	15	.	.	PUNCT
iajs-2476	107	1	ϖ	ϖ	PROPN
iajs-2476	107	2	⊆	⊆	NUM
iajs-2476	107	3	ϑ	ϑ	X
iajs-2476	107	4	.also	.also	PRON
iajs-2476	107	5	it	it	PRON
iajs-2476	107	6	was	be	AUX
iajs-2476	107	7	shown	show	VERB
iajs-2476	107	8	that	that	SCONJ
iajs-2476	107	9	if	if	SCONJ
iajs-2476	107	10	ϑ	ϑ	X
iajs-2476	107	11	∈	∈	NOUN
iajs-2476	107	12	la(h	la(h	NUM
iajs-2476	107	13	)	)	PUNCT
iajs-2476	107	14	,	,	PUNCT
iajs-2476	107	15	ϖ	ϖ	PROPN
iajs-2476	107	16	∈	∈	PROPN
iajs-2476	107	17	la	la	X
iajs-2476	107	18	,	,	PUNCT
iajs-2476	107	19	ε	ε	PROPN
iajs-2476	107	20	∈	∈	PROPN
iajs-2476	107	21	lai	lai	PROPN
iajs-2476	107	22	f	f	PROPN
iajs-2476	107	23	,	,	PUNCT
iajs-2476	107	24	then	then	ADV
iajs-2476	107	25	ϑ∶	ϑ∶	ADJ
iajs-2476	107	26	ϖ	ϖ	PROPN
iajs-2476	107	27	∈	∈	PROPN
iajs-2476	107	28	lai	lai	PROPN
iajs-2476	107	29	f	f	PROPN
iajs-2476	107	30	and	and	CCONJ
iajs-2476	107	31	ϑ	ϑ	PRON
iajs-2476	107	32	∶	∶	NOUN
iajs-2476	107	33	ε	ε	X
iajs-2476	107	34	∈	∈	PROPN
iajs-2476	107	35	la	la	PROPN
iajs-2476	107	36	h	h	PROPN
iajs-2476	107	37	.	.	PUNCT
iajs-2476	108	1	theorem	theorem	VERB
iajs-2476	108	2	2.9	2.9	NUM
iajs-2476	109	1	[	[	SYM
iajs-2476	109	2	18	18	NUM
iajs-2476	109	3	]	]	PUNCT
iajs-2476	109	4	.	.	PUNCT
iajs-2476	110	1	if	if	SCONJ
iajs-2476	110	2	b∈	b∈	PROPN
iajs-2476	110	3	la	la	PROPN
iajs-2476	110	4	and	and	CCONJ
iajs-2476	110	5	g	g	PROPN
iajs-2476	110	6	are	be	AUX
iajs-2476	110	7	a	a	DET
iajs-2476	110	8	submodule	submodule	NOUN
iajs-2476	110	9	of	of	ADP
iajs-2476	110	10	h	h	NOUN
iajs-2476	110	11	,	,	PUNCT
iajs-2476	110	12	then	then	ADV
iajs-2476	110	13	(	(	PUNCT
iajs-2476	110	14	1g⋃	1g⋃	NUM
iajs-2476	110	15	b	b	NOUN
iajs-2476	110	16	:	:	PUNCT
iajs-2476	110	17	1h=1[g	1h=1[g	NUM
iajs-2476	110	18	:	:	PUNCT
iajs-2476	110	19	h	h	NOUN
iajs-2476	110	20	]	]	X
iajs-2476	110	21	⋃	⋃	PROPN
iajs-2476	110	22	b	b	NOUN
iajs-2476	110	23	.	.	PUNCT
iajs-2476	111	1	definition	definition	NOUN
iajs-2476	111	2	2.10[16	2.10[16	NUM
iajs-2476	111	3	]	]	X
iajs-2476	111	4	.	.	PUNCT
iajs-2476	112	1	a	a	DET
iajs-2476	112	2	nonconstant	nonconstant	ADJ
iajs-2476	112	3	la	la	PROPN
iajs-2476	112	4	-	-	PUNCT
iajs-2476	112	5	submodule	submodule	NOUN
iajs-2476	112	6	ϑ	ϑ	PROPN
iajs-2476	112	7	of	of	ADP
iajs-2476	112	8	h	h	NOUN
iajs-2476	112	9	is	be	AUX
iajs-2476	112	10	called	call	VERB
iajs-2476	112	11	primary	primary	ADJ
iajs-2476	112	12	if	if	SCONJ
iajs-2476	112	13	for	for	ADP
iajs-2476	112	14	ε	ε	PROPN
iajs-2476	112	15	∈	∈	PROPN
iajs-2476	112	16	lai(f	lai(f	PROPN
iajs-2476	112	17	)	)	PUNCT
iajs-2476	112	18	and	and	CCONJ
iajs-2476	112	19	ϖ	ϖ	PROPN
iajs-2476	112	20	∈	∈	PROPN
iajs-2476	112	21	la(h	la(h	NUM
iajs-2476	112	22	)	)	PUNCT
iajs-2476	112	23	such	such	ADJ
iajs-2476	112	24	that	that	DET
iajs-2476	112	25	ε	ε	PROPN
iajs-2476	112	26	.	.	PUNCT
iajs-2476	113	1	ϖ	ϖ	PROPN
iajs-2476	113	2	⊆	⊆	NUM
iajs-2476	113	3	ϑ	ϑ	NOUN
iajs-2476	113	4	then	then	ADV
iajs-2476	113	5	either	either	CCONJ
iajs-2476	113	6	ϖ	ϖ	PROPN
iajs-2476	113	7	⊆	⊆	NUM
iajs-2476	113	8	ϑ	ϑ	X
iajs-2476	113	9	or	or	CCONJ
iajs-2476	113	10	ε	ε	PROPN
iajs-2476	113	11	⊆	⊆	NUM
iajs-2476	113	12	ϑ	ϑ	NOUN
iajs-2476	113	13	:	:	SYM
iajs-2476	113	14	1	1	NUM
iajs-2476	113	15	.	.	PUNCT
iajs-2476	114	1	in	in	ADP
iajs-2476	114	2	the	the	DET
iajs-2476	114	3	complement	complement	NOUN
iajs-2476	114	4	la	la	NOUN
iajs-2476	114	5	-	-	PUNCT
iajs-2476	114	6	prim(h	prim(h	NOUN
iajs-2476	114	7	)	)	PUNCT
iajs-2476	114	8	indicates	indicate	VERB
iajs-2476	114	9	the	the	DET
iajs-2476	114	10	collection	collection	NOUN
iajs-2476	114	11	of	of	ADP
iajs-2476	114	12	all	all	DET
iajs-2476	114	13	primary	primary	ADJ
iajs-2476	114	14	la	la	ADJ
iajs-2476	114	15	-	-	PUNCT
iajs-2476	114	16	submodules	submodules	NOUN
iajs-2476	114	17	of	of	ADP
iajs-2476	114	18	h.	h.	PROPN
iajs-2476	114	19	theorem	theorem	VERB
iajs-2476	114	20	2.11	2.11	NUM
iajs-2476	115	1	[	[	X
iajs-2476	115	2	16	16	NUM
iajs-2476	115	3	]	]	PUNCT
iajs-2476	115	4	.	.	PUNCT
iajs-2476	116	1	ϑ	ϑ	X
iajs-2476	116	2	∈	∈	PROPN
iajs-2476	116	3	la	la	PROPN
iajs-2476	116	4	-	-	PUNCT
iajs-2476	116	5	prim(h	prim(h	NOUN
iajs-2476	116	6	)	)	PUNCT
iajs-2476	116	7	if	if	SCONJ
iajs-2476	116	8	and	and	CCONJ
iajs-2476	116	9	only	only	ADV
iajs-2476	116	10	if	if	SCONJ
iajs-2476	116	11	ϑ=1ϑ∗	ϑ=1ϑ∗	PROPN
iajs-2476	116	12	∪	∪	VERB
iajs-2476	116	13	ch	ch	NOUN
iajs-2476	116	14	such	such	ADJ
iajs-2476	116	15	that	that	DET
iajs-2476	116	16	ϑ∗=	ϑ∗=	NOUN
iajs-2476	116	17	{	{	PUNCT
iajs-2476	116	18	h∈h|ϑ(h)=1	h∈h|ϑ(h)=1	PROPN
iajs-2476	116	19	}	}	PUNCT
iajs-2476	116	20	be	be	AUX
iajs-2476	116	21	a	a	DET
iajs-2476	116	22	primary	primary	ADJ
iajs-2476	116	23	submodule	submodule	NOUN
iajs-2476	116	24	of	of	ADP
iajs-2476	116	25	h	h	NOUN
iajs-2476	116	26	while	while	SCONJ
iajs-2476	116	27	z	z	NOUN
iajs-2476	116	28	is	be	AUX
iajs-2476	116	29	a	a	DET
iajs-2476	116	30	prime	prime	ADJ
iajs-2476	116	31	element	element	NOUN
iajs-2476	116	32	of	of	ADP
iajs-2476	116	33	la	la	PROPN
iajs-2476	116	34	.	.	PUNCT
iajs-2476	116	35	  	  	SPACE
iajs-2476	116	36	93	93	NUM
iajs-2476	116	37	ibn	ibn	PROPN
iajs-2476	116	38	al	al	PROPN
iajs-2476	116	39	-	-	PUNCT
iajs-2476	116	40	haitham	haitham	PROPN
iajs-2476	116	41	jour	jour	X
iajs-2476	116	42	.	.	PROPN
iajs-2476	117	1	for	for	ADP
iajs-2476	117	2	pure	pure	ADJ
iajs-2476	117	3	&	&	CCONJ
iajs-2476	117	4	appl	appl	PROPN
iajs-2476	117	5	.	.	PUNCT
iajs-2476	118	1	sci	sci	PROPN
iajs-2476	118	2	.	.	PROPN
iajs-2476	119	1	33	33	NUM
iajs-2476	119	2	(	(	PUNCT
iajs-2476	119	3	3	3	NUM
iajs-2476	119	4	)	)	PUNCT
iajs-2476	119	5	2020	2020	NUM
iajs-2476	119	6	theorem	theorem	VERB
iajs-2476	119	7	2.12	2.12	NUM
iajs-2476	119	8	[	[	X
iajs-2476	119	9	16	16	NUM
iajs-2476	119	10	]	]	PUNCT
iajs-2476	119	11	.	.	PUNCT
iajs-2476	120	1	if	if	SCONJ
iajs-2476	120	2	ϑ	ϑ	X
iajs-2476	120	3	∈	∈	PROPN
iajs-2476	120	4	la	la	NOUN
iajs-2476	120	5	-	-	PUNCT
iajs-2476	120	6	prim(h	prim(h	NOUN
iajs-2476	120	7	)	)	PUNCT
iajs-2476	120	8	,	,	PUNCT
iajs-2476	120	9	then	then	ADV
iajs-2476	120	10	ϑ	ϑ	X
iajs-2476	120	11	:	:	PUNCT
iajs-2476	120	12	1h	1h	NUM
iajs-2476	120	13	is	be	AUX
iajs-2476	120	14	a	a	DET
iajs-2476	120	15	primary	primary	ADJ
iajs-2476	120	16	la	la	NOUN
iajs-2476	120	17	-	-	PUNCT
iajs-2476	120	18	ideal	ideal	NOUN
iajs-2476	120	19	of	of	ADP
iajs-2476	120	20	f.	f.	PROPN
iajs-2476	120	21	3	3	NUM
iajs-2476	120	22	.	.	PUNCT
iajs-2476	120	23	topologies	topology	NOUN
iajs-2476	120	24	on	on	ADP
iajs-2476	120	25	la	la	NOUN
iajs-2476	120	26	-	-	PUNCT
iajs-2476	120	27	prim(h	prim(h	NOUN
iajs-2476	120	28	)	)	PUNCT
iajs-2476	120	29	in	in	ADP
iajs-2476	120	30	the	the	DET
iajs-2476	120	31	complement	complement	NOUN
iajs-2476	120	32	via	via	ADP
iajs-2476	120	33	h	h	NOUN
iajs-2476	120	34	we	we	PRON
iajs-2476	120	35	indicate	indicate	VERB
iajs-2476	120	36	a	a	DET
iajs-2476	120	37	unitary	unitary	ADJ
iajs-2476	120	38	module	module	NOUN
iajs-2476	120	39	on	on	ADP
iajs-2476	120	40	a	a	DET
iajs-2476	120	41	reciprocal	reciprocal	ADJ
iajs-2476	120	42	ring	ring	NOUN
iajs-2476	120	43	together	together	ADV
iajs-2476	120	44	unity	unity	NOUN
iajs-2476	120	45	f.	f.	NOUN
iajs-2476	120	46	for	for	ADP
iajs-2476	120	47	ϑ	ϑ	PROPN
iajs-2476	120	48	∈	∈	PROPN
iajs-2476	120	49	lah	lah	PROPN
iajs-2476	120	50	put	put	VERB
iajs-2476	120	51	v∗	v∗	PROPN
iajs-2476	120	52	(	(	PUNCT
iajs-2476	120	53	ϑ	ϑ	NOUN
iajs-2476	120	54	)	)	PUNCT
iajs-2476	120	55	=	=	NOUN
iajs-2476	120	56	{	{	PUNCT
iajs-2476	120	57	q	q	NOUN
iajs-2476	120	58	∈	∈	PROPN
iajs-2476	120	59	la	la	PROPN
iajs-2476	120	60	-	-	PUNCT
iajs-2476	120	61	prim(h)|	prim(h)|	PROPN
iajs-2476	120	62	ϑ	ϑ	X
iajs-2476	120	63	⊆	⊆	NUM
iajs-2476	120	64	q	q	NOUN
iajs-2476	120	65	}	}	PUNCT
iajs-2476	120	66	.	.	PUNCT
iajs-2476	121	1	proposition	proposition	NOUN
iajs-2476	121	2	3.1	3.1	NUM
iajs-2476	121	3	for	for	ADP
iajs-2476	121	4	family	family	NOUN
iajs-2476	121	5	{	{	PUNCT
iajs-2476	121	6	ϑ	ϑ	X
iajs-2476	121	7	j}j∈j	j}j∈j	X
iajs-2476	121	8	in	in	ADP
iajs-2476	121	9	la(h	la(h	NUM
iajs-2476	121	10	)	)	PUNCT
iajs-2476	121	11	,	,	PUNCT
iajs-2476	121	12	the	the	DET
iajs-2476	121	13	following	follow	VERB
iajs-2476	121	14	situations	situation	NOUN
iajs-2476	121	15	are	be	AUX
iajs-2476	121	16	satisfied	satisfied	ADJ
iajs-2476	121	17	:	:	PUNCT
iajs-2476	121	18	1v∗(1{0})=	1v∗(1{0})=	NUM
iajs-2476	121	19	la	la	PROPN
iajs-2476	121	20	-	-	PUNCT
iajs-2476	121	21	prim(h	prim(h	NOUN
iajs-2476	121	22	)	)	PUNCT
iajs-2476	121	23	,	,	PUNCT
iajs-2476	121	24	v∗(1h	v∗(1h	PROPN
iajs-2476	121	25	)	)	PUNCT
iajs-2476	121	26	=	=	SYM
iajs-2476	121	27	∅	∅	NOUN
iajs-2476	121	28	;	;	PUNCT
iajs-2476	121	29	2⋂	2⋂	NUM
iajs-2476	121	30	∈	∈	PROPN
iajs-2476	121	31	v∗	v∗	PROPN
iajs-2476	121	32	(	(	PUNCT
iajs-2476	121	33	ϑj)=v∗(∑	ϑj)=v∗(∑	NOUN
iajs-2476	121	34	ϑj∈	ϑj∈	PROPN
iajs-2476	121	35	)	)	PUNCT
iajs-2476	121	36	,	,	PUNCT
iajs-2476	121	37	for	for	ADP
iajs-2476	121	38	index	index	NOUN
iajs-2476	121	39	collection	collection	NOUN
iajs-2476	121	40	j	j	PROPN
iajs-2476	121	41	and	and	CCONJ
iajs-2476	121	42	ϑj	ϑj	NOUN
iajs-2476	121	43	∈	∈	PROPN
iajs-2476	121	44	la(h	la(h	NUM
iajs-2476	121	45	)	)	PUNCT
iajs-2476	121	46	;	;	PUNCT
iajs-2476	121	47	3v∗(ϑ	3v∗(ϑ	NUM
iajs-2476	121	48	)	)	PUNCT
iajs-2476	121	49	∪	∪	ADP
iajs-2476	121	50	v∗	v∗	PROPN
iajs-2476	121	51	(	(	PUNCT
iajs-2476	121	52	ϖ	ϖ	NOUN
iajs-2476	121	53	)	)	PUNCT
iajs-2476	121	54	⊆	⊆	NUM
iajs-2476	121	55	v∗	v∗	NOUN
iajs-2476	121	56	(	(	PUNCT
iajs-2476	121	57	ϑ	ϑ	X
iajs-2476	121	58	∩	∩	ADJ
iajs-2476	121	59	ϖ	ϖ	NOUN
iajs-2476	121	60	)	)	PUNCT
iajs-2476	121	61	,	,	PUNCT
iajs-2476	121	62	for	for	ADP
iajs-2476	121	63	ϑ	ϑ	PRON
iajs-2476	121	64	,	,	PUNCT
iajs-2476	121	65	ϖ	ϖ	PROPN
iajs-2476	121	66	∈	∈	PROPN
iajs-2476	121	67	la(h	la(h	NUM
iajs-2476	121	68	)	)	PUNCT
iajs-2476	121	69	.	.	PUNCT
iajs-2476	122	1	proof	proof	NOUN
iajs-2476	122	2	(	(	PUNCT
iajs-2476	122	3	1	1	X
iajs-2476	122	4	)	)	PUNCT
iajs-2476	122	5	clearly	clearly	ADV
iajs-2476	122	6	.	.	PUNCT
iajs-2476	123	1	(	(	PUNCT
iajs-2476	123	2	2	2	X
iajs-2476	123	3	)	)	PUNCT
iajs-2476	123	4	let	let	VERB
iajs-2476	123	5	q	q	NOUN
iajs-2476	123	6	∈	∈	PROPN
iajs-2476	123	7	⋂	⋂	PROPN
iajs-2476	123	8	∈	∈	PROPN
iajs-2476	123	9	v∗	v∗	PROPN
iajs-2476	123	10	(	(	PUNCT
iajs-2476	123	11	ϑj	ϑj	NOUN
iajs-2476	123	12	)	)	PUNCT
iajs-2476	123	13	,	,	PUNCT
iajs-2476	123	14	then	then	ADV
iajs-2476	123	15	q	q	PROPN
iajs-2476	123	16	∈	∈	PROPN
iajs-2476	123	17	v∗	v∗	PROPN
iajs-2476	123	18	(	(	PUNCT
iajs-2476	123	19	ϑj	ϑj	NOUN
iajs-2476	123	20	)	)	PUNCT
iajs-2476	123	21	,	,	PUNCT
iajs-2476	123	22	∀𝑗	∀𝑗	NOUN
iajs-2476	123	23	∈	∈	PROPN
iajs-2476	123	24	𝐽	𝐽	PROPN
iajs-2476	123	25	,	,	PUNCT
iajs-2476	123	26	and	and	CCONJ
iajs-2476	123	27	hence	hence	ADV
iajs-2476	123	28	q	q	NOUN
iajs-2476	123	29	⊆	⊆	NUM
iajs-2476	123	30	ϑj	ϑj	NOUN
iajs-2476	123	31	,	,	PUNCT
iajs-2476	123	32	∀𝑗	∀𝑗	NOUN
iajs-2476	123	33	∈	∈	PROPN
iajs-2476	123	34	𝐽.	𝐽.	PROPN
iajs-2476	123	35	moreover	moreover	ADV
iajs-2476	123	36	,	,	PUNCT
iajs-2476	123	37	we	we	PRON
iajs-2476	123	38	have	have	VERB
iajs-2476	123	39	(	(	PUNCT
iajs-2476	123	40	∑	∑	PROPN
iajs-2476	123	41	ϑ	ϑ	X
iajs-2476	123	42	∈	∈	NOUN
iajs-2476	123	43	)	)	PUNCT
iajs-2476	123	44	(	(	PUNCT
iajs-2476	123	45	y	y	X
iajs-2476	123	46	)	)	PUNCT
iajs-2476	123	47	=	=	NOUN
iajs-2476	124	1	∨{⋀	∨{⋀	PROPN
iajs-2476	124	2	ϑ	ϑ	PROPN
iajs-2476	124	3	y∈	y∈	NOUN
iajs-2476	124	4	|	|	NOUN
iajs-2476	124	5	y=∑	y=∑	VERB
iajs-2476	124	6	y	y	PROPN
iajs-2476	124	7	∈	∈	PROPN
iajs-2476	124	8	,	,	PUNCT
iajs-2476	124	9	y	y	PROPN
iajs-2476	124	10	∈	∈	PROPN
iajs-2476	124	11	h	h	NOUN
iajs-2476	124	12	,	,	PUNCT
iajs-2476	124	13	∀j	∀j	PROPN
iajs-2476	124	14	∈	∈	PROPN
iajs-2476	124	15	j	j	PROPN
iajs-2476	124	16	}	}	PUNCT
iajs-2476	124	17	=	=	SYM
iajs-2476	124	18	∨{⋀	∨{⋀	PROPN
iajs-2476	124	19	q	q	NOUN
iajs-2476	124	20	y∈	y∈	NOUN
iajs-2476	125	1	|	|	NOUN
iajs-2476	125	2	y=∑	y=∑	VERB
iajs-2476	125	3	y	y	PROPN
iajs-2476	125	4	∈	∈	PROPN
iajs-2476	125	5	,	,	PUNCT
iajs-2476	126	1	y	y	PROPN
iajs-2476	126	2	∈	∈	PROPN
iajs-2476	126	3	h	h	NOUN
iajs-2476	126	4	,	,	PUNCT
iajs-2476	126	5	∀j	∀j	PROPN
iajs-2476	126	6	∈	∈	PROPN
iajs-2476	126	7	j	j	PROPN
iajs-2476	126	8	}	}	PUNCT
iajs-2476	126	9	q	q	PROPN
iajs-2476	126	10	y	y	PROPN
iajs-2476	126	11	.	.	PUNCT
iajs-2476	127	1	then	then	ADV
iajs-2476	127	2	∑	∑	PUNCT
iajs-2476	127	3	ϑ	ϑ	X
iajs-2476	127	4	∈	∈	PROPN
iajs-2476	127	5	⊆	⊆	NUM
iajs-2476	127	6	q	q	NOUN
iajs-2476	127	7	implies	imply	VERB
iajs-2476	127	8	that	that	SCONJ
iajs-2476	127	9	q	q	PROPN
iajs-2476	127	10	∈	∈	PROPN
iajs-2476	127	11	v∗(∑	v∗(∑	PROPN
iajs-2476	127	12	ϑ	ϑ	X
iajs-2476	127	13	∈	∈	PROPN
iajs-2476	127	14	)	)	PUNCT
iajs-2476	127	15	,	,	PUNCT
iajs-2476	127	16	and	and	CCONJ
iajs-2476	127	17	hence	hence	ADV
iajs-2476	127	18	⋂	⋂	PROPN
iajs-2476	127	19	∈	∈	PROPN
iajs-2476	127	20	v∗	v∗	PROPN
iajs-2476	127	21	(	(	PUNCT
iajs-2476	127	22	ϑj	ϑj	NOUN
iajs-2476	127	23	)	)	PUNCT
iajs-2476	127	24	⊆	⊆	NUM
iajs-2476	127	25	v∗(∑	v∗(∑	PROPN
iajs-2476	127	26	ϑ	ϑ	X
iajs-2476	127	27	∈	∈	PROPN
iajs-2476	127	28	)	)	PUNCT
iajs-2476	127	29	(	(	PUNCT
iajs-2476	127	30	i	i	NOUN
iajs-2476	127	31	)	)	PUNCT
iajs-2476	127	32	.	.	PUNCT
iajs-2476	128	1	for	for	ADP
iajs-2476	128	2	the	the	DET
iajs-2476	128	3	converse	converse	NOUN
iajs-2476	128	4	,	,	PUNCT
iajs-2476	128	5	q	q	PROPN
iajs-2476	128	6	∈	∈	PROPN
iajs-2476	128	7	v∗(∑	v∗(∑	PROPN
iajs-2476	128	8	ϑ	ϑ	X
iajs-2476	128	9	∈	∈	PROPN
iajs-2476	128	10	)	)	PUNCT
iajs-2476	129	1	then	then	ADV
iajs-2476	129	2	∑	∑	PUNCT
iajs-2476	129	3	ϑ	ϑ	X
iajs-2476	129	4	∈	∈	PRON
iajs-2476	129	5	⊆	⊆	NUM
iajs-2476	129	6	q	q	NOUN
iajs-2476	129	7	,	,	PUNCT
iajs-2476	129	8	and	and	CCONJ
iajs-2476	129	9	so	so	ADV
iajs-2476	129	10	ϑj	ϑj	ADP
iajs-2476	129	11	⊆	⊆	NUM
iajs-2476	129	12	∑	∑	PUNCT
iajs-2476	129	13	ϑ	ϑ	X
iajs-2476	129	14	∈	∈	NOUN
iajs-2476	129	15	,	,	PUNCT
iajs-2476	130	1	∀j	∀j	PROPN
iajs-2476	130	2	∈	∈	PROPN
iajs-2476	130	3	j.	j.	PROPN
iajs-2476	130	4	so	so	ADV
iajs-2476	130	5	ϑj	ϑj	X
iajs-2476	130	6	⊆q	⊆q	NOUN
iajs-2476	130	7	,	,	PUNCT
iajs-2476	130	8	∀j	∀j	PROPN
iajs-2476	130	9	∈	∈	PROPN
iajs-2476	130	10	j.	j.	PROPN
iajs-2476	130	11	therefore	therefore	ADV
iajs-2476	130	12	,	,	PUNCT
iajs-2476	130	13	q	q	PROPN
iajs-2476	130	14	∈	∈	PROPN
iajs-2476	130	15	v∗	v∗	PROPN
iajs-2476	130	16	(	(	PUNCT
iajs-2476	130	17	ϑj	ϑj	NOUN
iajs-2476	130	18	)	)	PUNCT
iajs-2476	130	19	∀𝑗	∀𝑗	NOUN
iajs-2476	130	20	∈	∈	PROPN
iajs-2476	130	21	𝐽	𝐽	PROPN
iajs-2476	130	22	,	,	PUNCT
iajs-2476	130	23	and	and	CCONJ
iajs-2476	130	24	hence	hence	ADV
iajs-2476	130	25	q	q	X
iajs-2476	130	26	∈	∈	PROPN
iajs-2476	130	27	⋂	⋂	PROPN
iajs-2476	130	28	∈	∈	PROPN
iajs-2476	130	29	v∗	v∗	PROPN
iajs-2476	130	30	(	(	PUNCT
iajs-2476	130	31	ϑj	ϑj	NOUN
iajs-2476	130	32	)	)	PUNCT
iajs-2476	130	33	then	then	ADV
iajs-2476	130	34	v∗(∑	v∗(∑	PROPN
iajs-2476	130	35	ϑ	ϑ	X
iajs-2476	130	36	∈	∈	PROPN
iajs-2476	130	37	)	)	PUNCT
iajs-2476	131	1	⊆	⊆	NUM
iajs-2476	131	2	⋂	⋂	PROPN
iajs-2476	131	3	∈	∈	PROPN
iajs-2476	131	4	v∗	v∗	PROPN
iajs-2476	131	5	(	(	PUNCT
iajs-2476	131	6	ϑj	ϑj	NOUN
iajs-2476	131	7	)	)	PUNCT
iajs-2476	131	8	(	(	PUNCT
iajs-2476	131	9	ii	ii	NOUN
iajs-2476	131	10	)	)	PUNCT
iajs-2476	131	11	.	.	PUNCT
iajs-2476	132	1	now	now	ADV
iajs-2476	132	2	(	(	PUNCT
iajs-2476	132	3	2	2	X
iajs-2476	132	4	)	)	PUNCT
iajs-2476	132	5	instantly	instantly	ADV
iajs-2476	132	6	follows	follow	VERB
iajs-2476	132	7	from	from	ADP
iajs-2476	132	8	(	(	PUNCT
iajs-2476	132	9	i	i	NOUN
iajs-2476	132	10	)	)	PUNCT
iajs-2476	132	11	and	and	CCONJ
iajs-2476	132	12	(	(	PUNCT
iajs-2476	132	13	ii	ii	NOUN
iajs-2476	132	14	)	)	PUNCT
iajs-2476	132	15	.	.	PUNCT
iajs-2476	133	1	for	for	ADP
iajs-2476	133	2	(	(	PUNCT
iajs-2476	133	3	3	3	X
iajs-2476	133	4	)	)	PUNCT
iajs-2476	133	5	let	let	VERB
iajs-2476	133	6	ϑ	ϑ	X
iajs-2476	133	7	,	,	PUNCT
iajs-2476	133	8	ϖ	ϖ	PROPN
iajs-2476	133	9	∈	∈	PROPN
iajs-2476	133	10	la(h	la(h	NUM
iajs-2476	133	11	)	)	PUNCT
iajs-2476	133	12	and	and	CCONJ
iajs-2476	133	13	q	q	PROPN
iajs-2476	133	14	∈	∈	PROPN
iajs-2476	133	15	v∗	v∗	NOUN
iajs-2476	133	16	(	(	PUNCT
iajs-2476	133	17	ϑ	ϑ	NOUN
iajs-2476	133	18	)	)	PUNCT
iajs-2476	133	19	∪	∪	ADP
iajs-2476	133	20	v∗	v∗	PROPN
iajs-2476	133	21	(	(	PUNCT
iajs-2476	133	22	ϖ	ϖ	NOUN
iajs-2476	133	23	)	)	PUNCT
iajs-2476	133	24	.	.	PUNCT
iajs-2476	134	1	then	then	ADV
iajs-2476	134	2	ϑ	ϑ	X
iajs-2476	134	3	⊆	⊆	NUM
iajs-2476	134	4	q	q	NOUN
iajs-2476	134	5	,	,	PUNCT
iajs-2476	134	6	or	or	CCONJ
iajs-2476	134	7	ϖ	ϖ	INTJ
iajs-2476	134	8	⊆	⊆	NUM
iajs-2476	134	9	q	q	NOUN
iajs-2476	134	10	,	,	PUNCT
iajs-2476	134	11	and	and	CCONJ
iajs-2476	134	12	hence	hence	ADV
iajs-2476	134	13	ϑ	ϑ	X
iajs-2476	134	14	∩	∩	NOUN
iajs-2476	134	15	ϖ	ϖ	PROPN
iajs-2476	134	16	⊆	⊆	NUM
iajs-2476	134	17	q.	q.	NOUN
iajs-2476	134	18	thus	thus	ADV
iajs-2476	134	19	q	q	PROPN
iajs-2476	134	20	∈	∈	PROPN
iajs-2476	134	21	v∗	v∗	PROPN
iajs-2476	134	22	(	(	PUNCT
iajs-2476	134	23	ϑ	ϑ	X
iajs-2476	134	24	∩	∩	ADJ
iajs-2476	134	25	ϖ	ϖ	NOUN
iajs-2476	134	26	)	)	PUNCT
iajs-2476	134	27	,	,	PUNCT
iajs-2476	134	28	while	while	SCONJ
iajs-2476	134	29	so	so	ADV
iajs-2476	134	30	v∗	v∗	PROPN
iajs-2476	134	31	(	(	PUNCT
iajs-2476	134	32	ϑ	ϑ	NOUN
iajs-2476	134	33	)	)	PUNCT
iajs-2476	134	34	∪	∪	ADP
iajs-2476	134	35	v∗	v∗	PROPN
iajs-2476	134	36	(	(	PUNCT
iajs-2476	134	37	ϖ	ϖ	NOUN
iajs-2476	134	38	)	)	PUNCT
iajs-2476	134	39	⊆	⊆	NUM
iajs-2476	134	40	v∗	v∗	NOUN
iajs-2476	134	41	(	(	PUNCT
iajs-2476	134	42	ϑ	ϑ	X
iajs-2476	134	43	∩	∩	ADJ
iajs-2476	134	44	ϖ	ϖ	NOUN
iajs-2476	134	45	)	)	PUNCT
iajs-2476	134	46	.	.	PUNCT
iajs-2476	134	47	suppose	suppose	VERB
iajs-2476	134	48	that	that	SCONJ
iajs-2476	134	49	ϑ	ϑ	PROPN
iajs-2476	134	50	∈	∈	PROPN
iajs-2476	134	51	lah	lah	NOUN
iajs-2476	134	52	.	.	PUNCT
iajs-2476	135	1	the	the	DET
iajs-2476	135	2	la	la	PROPN
iajs-2476	135	3	-	-	PUNCT
iajs-2476	135	4	submodule	submodule	NOUN
iajs-2476	135	5	generated	generate	VERB
iajs-2476	135	6	by	by	ADP
iajs-2476	135	7	ϑ	ϑ	PRON
iajs-2476	135	8	,	,	PUNCT
iajs-2476	135	9	indicated	indicate	VERB
iajs-2476	135	10	via	via	ADP
iajs-2476	135	11	ϑ	ϑ	PROPN
iajs-2476	135	12	,	,	PUNCT
iajs-2476	135	13	is	be	AUX
iajs-2476	135	14	the	the	DET
iajs-2476	135	15	smallest	small	ADJ
iajs-2476	135	16	la	la	ADJ
iajs-2476	135	17	-	-	PUNCT
iajs-2476	135	18	submodule	submodule	NOUN
iajs-2476	135	19	of	of	ADP
iajs-2476	135	20	h	h	NOUN
iajs-2476	135	21	including	include	VERB
iajs-2476	135	22	ϑ.	ϑ.	NOUN
iajs-2476	135	23	in	in	ADP
iajs-2476	135	24	fact	fact	NOUN
iajs-2476	135	25	,	,	PUNCT
iajs-2476	135	26	ϑ	ϑ	X
iajs-2476	135	27	=	=	X
iajs-2476	135	28	∩{ϖ	∩{ϖ	NOUN
iajs-2476	135	29	∈	∈	NOUN
iajs-2476	135	30	la(h	la(h	NOUN
iajs-2476	135	31	)	)	PUNCT
iajs-2476	136	1	|	|	ADV
iajs-2476	136	2	ϑ	ϑ	X
iajs-2476	136	3	⊆	⊆	NUM
iajs-2476	136	4	ϖ	ϖ	NOUN
iajs-2476	136	5	}	}	PUNCT
iajs-2476	136	6	.	.	PUNCT
iajs-2476	137	1	for	for	ADP
iajs-2476	137	2	ϑ	ϑ	PROPN
iajs-2476	137	3	∈	∈	NOUN
iajs-2476	137	4	la(h	la(h	NUM
iajs-2476	137	5	)	)	PUNCT
iajs-2476	137	6	,	,	PUNCT
iajs-2476	137	7	put	put	VERB
iajs-2476	137	8	v	v	NOUN
iajs-2476	137	9	(	(	PUNCT
iajs-2476	137	10	ϑ)={q	ϑ)={q	PROPN
iajs-2476	137	11	∈	∈	PROPN
iajs-2476	137	12	la	la	NOUN
iajs-2476	137	13	-	-	PUNCT
iajs-2476	137	14	prim(h	prim(h	NOUN
iajs-2476	137	15	)	)	PUNCT
iajs-2476	137	16	|	|	ADV
iajs-2476	137	17	ϑ:1h⊆q	ϑ:1h⊆q	NUM
iajs-2476	137	18	:	:	PUNCT
iajs-2476	137	19	1h	1h	NUM
iajs-2476	137	20	}	}	PUNCT
iajs-2476	137	21	,	,	PUNCT
iajs-2476	137	22	while	while	SCONJ
iajs-2476	137	23	if	if	SCONJ
iajs-2476	137	24	ϖ	ϖ	PROPN
iajs-2476	137	25	∈	∈	PROPN
iajs-2476	137	26	lah	lah	NOUN
iajs-2476	137	27	,	,	PUNCT
iajs-2476	137	28	by	by	ADP
iajs-2476	137	29	v(ϖ	v(ϖ	PROPN
iajs-2476	137	30	)	)	PUNCT
iajs-2476	137	31	we	we	PRON
iajs-2476	137	32	mean	mean	VERB
iajs-2476	137	33	v	v	INTJ
iajs-2476	137	34	(	(	PUNCT
iajs-2476	137	35	ϖ	ϖ	NOUN
iajs-2476	137	36	)	)	PUNCT
iajs-2476	137	37	.	.	PUNCT
iajs-2476	138	1	then	then	ADV
iajs-2476	138	2	we	we	PRON
iajs-2476	138	3	have	have	VERB
iajs-2476	138	4	the	the	DET
iajs-2476	138	5	next	next	ADJ
iajs-2476	138	6	outcomes	outcome	NOUN
iajs-2476	138	7	.	.	PUNCT
iajs-2476	139	1	proposition	proposition	NOUN
iajs-2476	139	2	3.2	3.2	NUM
iajs-2476	139	3	.	.	PUNCT
iajs-2476	139	4	suppose	suppose	VERB
iajs-2476	139	5	that	that	SCONJ
iajs-2476	139	6	ϑj	ϑj	PROPN
iajs-2476	139	7	∈	∈	PROPN
iajs-2476	139	8	,	,	PUNCT
iajs-2476	139	9	ϑj	ϑj	X
iajs-2476	139	10	∈	∈	PROPN
iajs-2476	139	11	la(h	la(h	NUM
iajs-2476	139	12	)	)	PUNCT
iajs-2476	139	13	.	.	PUNCT
iajs-2476	140	1	then	then	ADV
iajs-2476	140	2	the	the	DET
iajs-2476	140	3	following	follow	VERB
iajs-2476	140	4	hold	hold	NOUN
iajs-2476	140	5	:	:	PUNCT
iajs-2476	140	6	)	)	PUNCT
iajs-2476	140	7	1	1	X
iajs-2476	140	8	(	(	PUNCT
iajs-2476	140	9	prim(h	prim(h	PROPN
iajs-2476	140	10	)	)	PUNCT
iajs-2476	140	11	;	;	PUNCT
iajs-2476	140	12	-)=	-)=	PROPN
iajs-2476	140	13	la{0}(1	la{0}(1	PROPN
iajs-2476	140	14	v	v	NOUN
iajs-2476	140	15	,	,	PUNCT
iajs-2476	140	16	∅)=	∅)=	PROPN
iajs-2476	140	17	h1	h1	PROPN
iajs-2476	140	18	(	(	PUNCT
iajs-2476	140	19	v	v	NOUN
iajs-2476	140	20	)	)	PUNCT
iajs-2476	140	21	2	2	NUM
iajs-2476	140	22	(	(	PUNCT
iajs-2476	140	23	;	;	PUNCT
iajs-2476	140	24	hla∈	hla∈	X
iajs-2476	140	25	ϑ	ϑ	NOUN
iajs-2476	140	26	)	)	PUNCT
iajs-2476	140	27	,	,	PUNCT
iajs-2476	140	28	for	for	ADP
iajs-2476	140	29	every	every	DET
iajs-2476	140	30	ϑ)=v(ϑv	ϑ)=v(ϑv	NUM
iajs-2476	140	31	(	(	PUNCT
iajs-2476	140	32	)	)	PUNCT
iajs-2476	140	33	3	3	NUM
iajs-2476	140	34	(	(	PUNCT
iajs-2476	140	35	⋂	⋂	PROPN
iajs-2476	140	36	∈	∈	PROPN
iajs-2476	140	37	)	)	PUNCT
iajs-2476	140	38	;	;	PUNCT
iajs-2476	140	39	∑	∑	ADP
iajs-2476	140	40	ϑ	ϑ	X
iajs-2476	140	41	:	:	PUNCT
iajs-2476	140	42	1	1	NUM
iajs-2476	140	43	∈	∈	NOUN
iajs-2476	140	44	.	.	PUNCT
iajs-2476	141	1	1v	1v	NUM
iajs-2476	141	2	(	(	PUNCT
iajs-2476	141	3	=	=	NOUN
iajs-2476	141	4	)	)	PUNCT
iajs-2476	141	5	jϑ	jϑ	PRON
iajs-2476	141	6	v	v	NOUN
iajs-2476	141	7	(	(	PUNCT
iajs-2476	141	8	)	)	PUNCT
iajs-2476	141	9	4	4	NUM
iajs-2476	141	10	(	(	PUNCT
iajs-2476	141	11	v(ϑ	v(ϑ	NOUN
iajs-2476	141	12	)	)	PUNCT
iajs-2476	141	13	∪	∪	ADP
iajs-2476	141	14	v(ϖ	v(ϖ	PROPN
iajs-2476	141	15	)	)	PUNCT
iajs-2476	141	16	=	=	SYM
iajs-2476	141	17	v(ϑ	v(ϑ	NOUN
iajs-2476	141	18	∩	∩	ADJ
iajs-2476	141	19	ϖ	ϖ	NOUN
iajs-2476	141	20	)	)	PUNCT
iajs-2476	141	21	,	,	PUNCT
iajs-2476	141	22	for	for	ADP
iajs-2476	141	23	ϑ	ϑ	X
iajs-2476	141	24	,	,	PUNCT
iajs-2476	141	25	ϖ	ϖ	PROPN
iajs-2476	141	26	∈	∈	PROPN
iajs-2476	141	27	la(h	la(h	NUM
iajs-2476	141	28	)	)	PUNCT
iajs-2476	141	29	.	.	PUNCT
iajs-2476	142	1	proof	proof	NOUN
iajs-2476	142	2	(	(	PUNCT
iajs-2476	142	3	1	1	NUM
iajs-2476	142	4	)	)	PUNCT
iajs-2476	142	5	instant	instant	NOUN
iajs-2476	142	6	.	.	PUNCT
iajs-2476	142	7	  	  	SPACE
iajs-2476	142	8	94	94	NUM
iajs-2476	142	9	ibn	ibn	PROPN
iajs-2476	142	10	al	al	PROPN
iajs-2476	142	11	-	-	PUNCT
iajs-2476	142	12	haitham	haitham	PROPN
iajs-2476	142	13	jour	jour	X
iajs-2476	142	14	.	.	PROPN
iajs-2476	143	1	for	for	ADP
iajs-2476	143	2	pure	pure	ADJ
iajs-2476	143	3	&	&	CCONJ
iajs-2476	143	4	appl	appl	PROPN
iajs-2476	143	5	.	.	PUNCT
iajs-2476	144	1	sci	sci	PROPN
iajs-2476	144	2	.	.	PROPN
iajs-2476	145	1	33	33	NUM
iajs-2476	145	2	(	(	PUNCT
iajs-2476	145	3	3	3	NUM
iajs-2476	145	4	)	)	PUNCT
iajs-2476	145	5	2020	2020	NUM
iajs-2476	145	6	(	(	PUNCT
iajs-2476	145	7	2	2	X
iajs-2476	145	8	)	)	PUNCT
iajs-2476	145	9	it	it	PRON
iajs-2476	145	10	is	be	AUX
iajs-2476	145	11	an	an	DET
iajs-2476	145	12	instant	instant	ADJ
iajs-2476	145	13	result	result	NOUN
iajs-2476	145	14	of	of	ADP
iajs-2476	145	15	definition	definition	NOUN
iajs-2476	145	16	of	of	ADP
iajs-2476	145	17	〈	〈	PROPN
iajs-2476	145	18	ϑ	ϑ	X
iajs-2476	145	19	〉	〉	NOUN
iajs-2476	145	20	.	.	PUNCT
iajs-2476	146	1	for	for	ADP
iajs-2476	146	2	(	(	PUNCT
iajs-2476	146	3	3	3	X
iajs-2476	146	4	)	)	PUNCT
iajs-2476	146	5	let	let	VERB
iajs-2476	146	6	q	q	NOUN
iajs-2476	146	7	∈	∈	PROPN
iajs-2476	146	8	⋂	⋂	PROPN
iajs-2476	146	9	∈	∈	PROPN
iajs-2476	146	10	v	v	ADP
iajs-2476	146	11	(	(	PUNCT
iajs-2476	146	12	ϑj	ϑj	NOUN
iajs-2476	146	13	)	)	PUNCT
iajs-2476	146	14	,	,	PUNCT
iajs-2476	146	15	then	then	ADV
iajs-2476	146	16	ϑj	ϑj	X
iajs-2476	146	17	:	:	PUNCT
iajs-2476	146	18	1	1	NUM
iajs-2476	146	19	⊆q	⊆q	NOUN
iajs-2476	146	20	:	:	PUNCT
iajs-2476	146	21	1	1	NUM
iajs-2476	146	22	,	,	PUNCT
iajs-2476	146	23	∀𝑗	∀𝑗	NOUN
iajs-2476	146	24	∈	∈	NOUN
iajs-2476	146	25	𝐽.	𝐽.	PROPN
iajs-2476	146	26	thus	thus	ADV
iajs-2476	146	27	for	for	ADP
iajs-2476	146	28	all	all	DET
iajs-2476	146	29	𝑗	𝑗	PROPN
iajs-2476	146	30	∈	∈	ADJ
iajs-2476	146	31	𝐽	𝐽	NOUN
iajs-2476	146	32	we	we	PRON
iajs-2476	146	33	have	have	VERB
iajs-2476	146	34	(	(	PUNCT
iajs-2476	146	35	ϑj	ϑj	X
iajs-2476	146	36	:	:	SYM
iajs-2476	146	37	1	1	NUM
iajs-2476	146	38	)	)	PUNCT
iajs-2476	146	39	.	.	PUNCT
iajs-2476	147	1	1	1	NUM
iajs-2476	147	2	⊆	⊆	X
iajs-2476	147	3	(	(	PUNCT
iajs-2476	147	4	q	q	NOUN
iajs-2476	147	5	:	:	PUNCT
iajs-2476	147	6	1	1	NUM
iajs-2476	147	7	)	)	PUNCT
iajs-2476	147	8	.	.	PUNCT
iajs-2476	148	1	1	1	NUM
iajs-2476	148	2	⊆q	⊆q	NOUN
iajs-2476	148	3	⟹	⟹	PUNCT
iajs-2476	148	4	∑	∑	ADP
iajs-2476	148	5	ϑj	ϑj	NOUN
iajs-2476	148	6	∶	∶	NOUN
iajs-2476	148	7	1	1	NUM
iajs-2476	148	8	∈	∈	NOUN
iajs-2476	148	9	.	.	PUNCT
iajs-2476	149	1	1	1	NUM
iajs-2476	149	2	⊆	⊆	NUM
iajs-2476	149	3	q	q	NOUN
iajs-2476	149	4	⟹	⟹	NUM
iajs-2476	149	5	∑	∑	ADP
iajs-2476	149	6	ϑj	ϑj	NOUN
iajs-2476	149	7	∶	∶	NOUN
iajs-2476	149	8	1	1	NUM
iajs-2476	149	9	∈	∈	NOUN
iajs-2476	149	10	.	.	PUNCT
iajs-2476	150	1	1	1	NUM
iajs-2476	150	2	:	:	SYM
iajs-2476	150	3	1	1	NUM
iajs-2476	150	4	⊆	⊆	NUM
iajs-2476	150	5	q	q	NOUN
iajs-2476	150	6	:	:	PUNCT
iajs-2476	150	7	1	1	NUM
iajs-2476	150	8	so	so	ADV
iajs-2476	150	9	q	q	X
iajs-2476	150	10	∈	∈	PROPN
iajs-2476	150	11	v	v	ADP
iajs-2476	150	12	∑	∑	PROPN
iajs-2476	150	13	ϑj	ϑj	NOUN
iajs-2476	150	14	∶	∶	NOUN
iajs-2476	150	15	1	1	NUM
iajs-2476	150	16	∈	∈	NOUN
iajs-2476	150	17	.	.	PUNCT
iajs-2476	151	1	1	1	NUM
iajs-2476	151	2	,	,	PUNCT
iajs-2476	151	3	and	and	CCONJ
iajs-2476	151	4	hence	hence	ADV
iajs-2476	151	5	⋂	⋂	PROPN
iajs-2476	151	6	∈	∈	PROPN
iajs-2476	151	7	v	v	ADP
iajs-2476	151	8	(	(	PUNCT
iajs-2476	151	9	ϑj	ϑj	NOUN
iajs-2476	151	10	)	)	PUNCT
iajs-2476	151	11	⊆	⊆	NUM
iajs-2476	151	12	v	v	NOUN
iajs-2476	151	13	∑	∑	ADP
iajs-2476	151	14	ϑj	ϑj	NOUN
iajs-2476	151	15	∶	∶	NOUN
iajs-2476	151	16	1	1	NUM
iajs-2476	151	17	∈	∈	NOUN
iajs-2476	151	18	.	.	PUNCT
iajs-2476	152	1	1	1	NUM
iajs-2476	152	2	(	(	PUNCT
iajs-2476	152	3	a	a	NOUN
iajs-2476	152	4	)	)	PUNCT
iajs-2476	152	5	reciprocally	reciprocally	ADV
iajs-2476	152	6	,	,	PUNCT
iajs-2476	152	7	let	let	VERB
iajs-2476	152	8	q	q	PROPN
iajs-2476	152	9	∈	∈	PROPN
iajs-2476	152	10	v	v	ADP
iajs-2476	152	11	∑	∑	PROPN
iajs-2476	152	12	ϑj	ϑj	NOUN
iajs-2476	152	13	∶	∶	NOUN
iajs-2476	152	14	1	1	NUM
iajs-2476	152	15	∈	∈	NOUN
iajs-2476	152	16	.	.	PUNCT
iajs-2476	153	1	1	1	NUM
iajs-2476	153	2	,	,	PUNCT
iajs-2476	153	3	then	then	ADV
iajs-2476	153	4	∑	∑	ADP
iajs-2476	153	5	ϑj	ϑj	PROPN
iajs-2476	154	1	∶	∶	NOUN
iajs-2476	154	2	1	1	NUM
iajs-2476	154	3	∈	∈	NOUN
iajs-2476	154	4	.	.	PUNCT
iajs-2476	155	1	1	1	NUM
iajs-2476	155	2	:	:	SYM
iajs-2476	155	3	1	1	NUM
iajs-2476	155	4	⊆	⊆	NUM
iajs-2476	155	5	q	q	NOUN
iajs-2476	155	6	:	:	PUNCT
iajs-2476	155	7	1	1	NUM
iajs-2476	155	8	.	.	PUNCT
iajs-2476	156	1	clearly	clearly	ADV
iajs-2476	156	2	,	,	PUNCT
iajs-2476	156	3	we	we	PRON
iajs-2476	156	4	have	have	VERB
iajs-2476	156	5	ϑj	ϑj	NOUN
iajs-2476	156	6	∶	∶	NOUN
iajs-2476	156	7	1	1	NUM
iajs-2476	156	8	.	.	PUNCT
iajs-2476	157	1	1	1	NUM
iajs-2476	157	2	:	:	SYM
iajs-2476	157	3	1	1	NUM
iajs-2476	157	4	=	=	SYM
iajs-2476	157	5	ϑj	ϑj	NOUN
iajs-2476	157	6	:	:	PUNCT
iajs-2476	157	7	1	1	NUM
iajs-2476	157	8	,	,	PUNCT
iajs-2476	157	9	∀𝑗	∀𝑗	NOUN
iajs-2476	157	10	∈	∈	PROPN
iajs-2476	157	11	𝐽.	𝐽.	PROPN
iajs-2476	157	12	also	also	ADV
iajs-2476	157	13	for	for	ADP
iajs-2476	157	14	each	each	DET
iajs-2476	157	15	𝑗	𝑗	PROPN
iajs-2476	157	16	∈	∈	PROPN
iajs-2476	157	17	𝐽	𝐽	PROPN
iajs-2476	157	18	,	,	PUNCT
iajs-2476	157	19	we	we	PRON
iajs-2476	157	20	get	get	VERB
iajs-2476	157	21	that	that	DET
iajs-2476	157	22	ϑj	ϑj	NOUN
iajs-2476	158	1	∶	∶	NOUN
iajs-2476	158	2	1	1	NUM
iajs-2476	158	3	.	.	PUNCT
iajs-2476	158	4	1	1	NUM
iajs-2476	158	5	:	:	SYM
iajs-2476	158	6	1	1	NUM
iajs-2476	158	7	⊆	⊆	NUM
iajs-2476	158	8	∑	∑	PUNCT
iajs-2476	158	9	ϑj	ϑj	NOUN
iajs-2476	158	10	∶	∶	NOUN
iajs-2476	158	11	1	1	NUM
iajs-2476	158	12	∈	∈	NOUN
iajs-2476	158	13	.	.	PUNCT
iajs-2476	159	1	1	1	NUM
iajs-2476	159	2	∶	∶	NOUN
iajs-2476	159	3	1	1	NUM
iajs-2476	159	4	⊆	⊆	NUM
iajs-2476	159	5	q	q	NOUN
iajs-2476	159	6	:	:	PUNCT
iajs-2476	159	7	1	1	NUM
iajs-2476	159	8	.	.	PUNCT
iajs-2476	160	1	thus	thus	ADV
iajs-2476	160	2	for	for	ADP
iajs-2476	160	3	any	any	DET
iajs-2476	160	4	𝑗	𝑗	PROPN
iajs-2476	160	5	∈	∈	PROPN
iajs-2476	160	6	𝐽	𝐽	NOUN
iajs-2476	160	7	it	it	PRON
iajs-2476	160	8	deduces	deduce	VERB
iajs-2476	160	9	that	that	DET
iajs-2476	160	10	ϑj	ϑj	ADP
iajs-2476	160	11	∶	∶	NOUN
iajs-2476	160	12	1	1	NUM
iajs-2476	160	13	⊆	⊆	NUM
iajs-2476	160	14	q	q	NOUN
iajs-2476	160	15	:	:	PUNCT
iajs-2476	160	16	1	1	NUM
iajs-2476	160	17	⟹	⟹	NOUN
iajs-2476	160	18	∀𝑗	∀𝑗	NOUN
iajs-2476	160	19	∈	∈	PROPN
iajs-2476	160	20	𝐽	𝐽	PROPN
iajs-2476	160	21	,	,	PUNCT
iajs-2476	160	22	q	q	PROPN
iajs-2476	160	23	∈	∈	PROPN
iajs-2476	160	24	v	v	ADP
iajs-2476	160	25	(	(	PUNCT
iajs-2476	160	26	ϑj	ϑj	NOUN
iajs-2476	160	27	)	)	PUNCT
iajs-2476	160	28	⟹	⟹	NUM
iajs-2476	161	1	q	q	PROPN
iajs-2476	161	2	∈	∈	PROPN
iajs-2476	161	3	⋂	⋂	PROPN
iajs-2476	161	4	∈	∈	PROPN
iajs-2476	161	5	v	v	ADP
iajs-2476	161	6	(	(	PUNCT
iajs-2476	161	7	ϑj	ϑj	NOUN
iajs-2476	161	8	)	)	PUNCT
iajs-2476	161	9	.	.	PUNCT
iajs-2476	162	1	thus	thus	ADV
iajs-2476	162	2	v	v	ADP
iajs-2476	162	3	∑	∑	ADP
iajs-2476	162	4	ϑj	ϑj	NOUN
iajs-2476	162	5	∶	∶	NOUN
iajs-2476	162	6	1	1	NUM
iajs-2476	162	7	∈	∈	NOUN
iajs-2476	162	8	.	.	PUNCT
iajs-2476	163	1	1	1	NUM
iajs-2476	163	2	⊆	⊆	NUM
iajs-2476	163	3	⋂	⋂	PROPN
iajs-2476	163	4	∈	∈	PROPN
iajs-2476	163	5	v	v	ADP
iajs-2476	163	6	(	(	PUNCT
iajs-2476	163	7	ϑj	ϑj	NOUN
iajs-2476	163	8	)	)	PUNCT
iajs-2476	163	9	(	(	PUNCT
iajs-2476	163	10	2	2	NUM
iajs-2476	163	11	)	)	PUNCT
iajs-2476	163	12	.	.	PUNCT
iajs-2476	164	1	now	now	ADV
iajs-2476	164	2	(	(	PUNCT
iajs-2476	164	3	3	3	X
iajs-2476	164	4	)	)	PUNCT
iajs-2476	164	5	follows	follow	VERB
iajs-2476	164	6	by	by	ADP
iajs-2476	164	7	(	(	PUNCT
iajs-2476	164	8	a	a	NOUN
iajs-2476	164	9	)	)	PUNCT
iajs-2476	164	10	and	and	CCONJ
iajs-2476	164	11	(	(	PUNCT
iajs-2476	164	12	b	b	NOUN
iajs-2476	164	13	)	)	PUNCT
iajs-2476	164	14	.	.	PUNCT
iajs-2476	165	1	for(4	for(4	PROPN
iajs-2476	165	2	)	)	PUNCT
iajs-2476	166	1	let	let	VERB
iajs-2476	166	2	ϑ	ϑ	X
iajs-2476	166	3	,	,	PUNCT
iajs-2476	166	4	ϖ	ϖ	PROPN
iajs-2476	166	5	∈	∈	PROPN
iajs-2476	166	6	la(h	la(h	NUM
iajs-2476	166	7	)	)	PUNCT
iajs-2476	166	8	and	and	CCONJ
iajs-2476	166	9	q	q	PROPN
iajs-2476	166	10	∈	∈	PROPN
iajs-2476	166	11	v	v	ADP
iajs-2476	166	12	(	(	PUNCT
iajs-2476	166	13	ϑ	ϑ	NOUN
iajs-2476	166	14	)	)	PUNCT
iajs-2476	166	15	∪	∪	ADP
iajs-2476	166	16	v	v	NOUN
iajs-2476	166	17	(	(	PUNCT
iajs-2476	166	18	ϖ	ϖ	NOUN
iajs-2476	166	19	)	)	PUNCT
iajs-2476	166	20	.	.	PUNCT
iajs-2476	167	1	then	then	ADV
iajs-2476	167	2	q	q	PROPN
iajs-2476	167	3	∈	∈	PROPN
iajs-2476	167	4	v	v	ADP
iajs-2476	167	5	(	(	PUNCT
iajs-2476	167	6	ϑ	ϑ	NOUN
iajs-2476	167	7	)	)	PUNCT
iajs-2476	167	8	or	or	CCONJ
iajs-2476	167	9	q	q	ADJ
iajs-2476	167	10	∈	∈	PROPN
iajs-2476	167	11	v(ϖ	v(ϖ	PROPN
iajs-2476	167	12	)	)	PUNCT
iajs-2476	167	13	.	.	PUNCT
iajs-2476	168	1	without	without	ADP
iajs-2476	168	2	loose	loose	ADJ
iajs-2476	168	3	of	of	ADP
iajs-2476	168	4	commonness	commonness	NOUN
iajs-2476	168	5	,	,	PUNCT
iajs-2476	168	6	let	let	VERB
iajs-2476	168	7	q	q	PROPN
iajs-2476	168	8	∈	∈	PROPN
iajs-2476	168	9	v	v	NOUN
iajs-2476	168	10	(	(	PUNCT
iajs-2476	168	11	ϑ	ϑ	X
iajs-2476	168	12	)	)	PUNCT
iajs-2476	168	13	we	we	PRON
iajs-2476	168	14	have	have	VERB
iajs-2476	168	15	ϑ	ϑ	X
iajs-2476	168	16	:	:	PUNCT
iajs-2476	168	17	1	1	NUM
iajs-2476	168	18	⊆	⊆	NUM
iajs-2476	168	19	q	q	NOUN
iajs-2476	168	20	:	:	PUNCT
iajs-2476	168	21	1	1	NUM
iajs-2476	168	22	⟹	⟹	NUM
iajs-2476	168	23	(	(	PUNCT
iajs-2476	168	24	ϑ	ϑ	X
iajs-2476	168	25	∩	∩	ADJ
iajs-2476	168	26	ϖ	ϖ	NOUN
iajs-2476	168	27	)	)	PUNCT
iajs-2476	168	28	:	:	PUNCT
iajs-2476	169	1	1	1	NUM
iajs-2476	169	2	⊆	⊆	NUM
iajs-2476	169	3	ϑ	ϑ	NOUN
iajs-2476	169	4	:	:	PUNCT
iajs-2476	169	5	1	1	NUM
iajs-2476	169	6	⊆	⊆	NUM
iajs-2476	169	7	q	q	NOUN
iajs-2476	169	8	:	:	PUNCT
iajs-2476	169	9	1	1	NUM
iajs-2476	169	10	⟹	⟹	NUM
iajs-2476	169	11	q	q	PROPN
iajs-2476	169	12	∈	∈	PROPN
iajs-2476	169	13	v(ϑ	v(ϑ	NOUN
iajs-2476	169	14	∩	∩	ADJ
iajs-2476	169	15	ϖ	ϖ	NOUN
iajs-2476	169	16	)	)	PUNCT
iajs-2476	169	17	.	.	PUNCT
iajs-2476	170	1	thus	thus	ADV
iajs-2476	170	2	v(ϑ	v(ϑ	NOUN
iajs-2476	170	3	)	)	PUNCT
iajs-2476	170	4	∪	∪	ADP
iajs-2476	170	5	v(ϖ	v(ϖ	PROPN
iajs-2476	170	6	)	)	PUNCT
iajs-2476	170	7	⊆	⊆	NUM
iajs-2476	170	8	v(ϑ	v(ϑ	NOUN
iajs-2476	170	9	∩	∩	ADJ
iajs-2476	170	10	ϖ	ϖ	NOUN
iajs-2476	170	11	)	)	PUNCT
iajs-2476	170	12	(	(	PUNCT
iajs-2476	170	13	c	c	X
iajs-2476	170	14	)	)	PUNCT
iajs-2476	170	15	for	for	ADP
iajs-2476	170	16	the	the	DET
iajs-2476	170	17	opposite	opposite	NOUN
iajs-2476	170	18	,	,	PUNCT
iajs-2476	170	19	let	let	VERB
iajs-2476	170	20	q	q	ADJ
iajs-2476	170	21	∈	∈	PROPN
iajs-2476	170	22	v(ϑ	v(ϑ	NOUN
iajs-2476	170	23	∩	∩	ADJ
iajs-2476	170	24	ϖ	ϖ	NOUN
iajs-2476	170	25	)	)	PUNCT
iajs-2476	170	26	then	then	ADV
iajs-2476	170	27	(	(	PUNCT
iajs-2476	170	28	ϑ	ϑ	X
iajs-2476	170	29	∩	∩	ADJ
iajs-2476	170	30	ϖ	ϖ	NOUN
iajs-2476	170	31	)	)	PUNCT
iajs-2476	170	32	:	:	PUNCT
iajs-2476	170	33	1	1	NUM
iajs-2476	170	34	⊆	⊆	NUM
iajs-2476	170	35	q	q	NOUN
iajs-2476	170	36	:	:	PUNCT
iajs-2476	170	37	1	1	NUM
iajs-2476	170	38	.	.	PUNCT
iajs-2476	171	1	but	but	CCONJ
iajs-2476	171	2	we	we	PRON
iajs-2476	171	3	have	have	VERB
iajs-2476	171	4	(	(	PUNCT
iajs-2476	171	5	ϑ	ϑ	X
iajs-2476	171	6	∩	∩	ADJ
iajs-2476	171	7	ϖ	ϖ	NOUN
iajs-2476	171	8	)	)	PUNCT
iajs-2476	171	9	:	:	PUNCT
iajs-2476	172	1	1	1	X
iajs-2476	172	2	=	=	SYM
iajs-2476	172	3	(	(	PUNCT
iajs-2476	172	4	ϑ	ϑ	NOUN
iajs-2476	172	5	:	:	SYM
iajs-2476	172	6	1	1	NUM
iajs-2476	172	7	)	)	PUNCT
iajs-2476	172	8	∩	∩	NOUN
iajs-2476	172	9	(	(	PUNCT
iajs-2476	172	10	ϖ	ϖ	NOUN
iajs-2476	172	11	:	:	SYM
iajs-2476	172	12	1	1	NUM
iajs-2476	172	13	)	)	PUNCT
iajs-2476	172	14	,	,	PUNCT
iajs-2476	172	15	and	and	CCONJ
iajs-2476	172	16	hence	hence	ADV
iajs-2476	172	17	(	(	PUNCT
iajs-2476	172	18	ϑ	ϑ	NOUN
iajs-2476	172	19	:	:	SYM
iajs-2476	172	20	1	1	NUM
iajs-2476	172	21	)	)	PUNCT
iajs-2476	172	22	(	(	PUNCT
iajs-2476	172	23	ϖ	ϖ	NOUN
iajs-2476	172	24	:	:	SYM
iajs-2476	172	25	1	1	NUM
iajs-2476	172	26	)	)	PUNCT
iajs-2476	172	27	⊆	⊆	NUM
iajs-2476	172	28	(	(	PUNCT
iajs-2476	172	29	ϑ	ϑ	NOUN
iajs-2476	172	30	:	:	SYM
iajs-2476	172	31	1	1	NUM
iajs-2476	172	32	)	)	PUNCT
iajs-2476	172	33	∩	∩	NOUN
iajs-2476	172	34	(	(	PUNCT
iajs-2476	172	35	ϖ	ϖ	NOUN
iajs-2476	172	36	:	:	SYM
iajs-2476	172	37	1	1	NUM
iajs-2476	172	38	)	)	PUNCT
iajs-2476	172	39	.	.	PUNCT
iajs-2476	173	1	thus	thus	ADV
iajs-2476	173	2	(	(	PUNCT
iajs-2476	173	3	ϑ	ϑ	NOUN
iajs-2476	173	4	:	:	SYM
iajs-2476	173	5	1	1	NUM
iajs-2476	173	6	)	)	PUNCT
iajs-2476	173	7	(	(	PUNCT
iajs-2476	173	8	ϖ	ϖ	NOUN
iajs-2476	173	9	:	:	SYM
iajs-2476	173	10	1	1	NUM
iajs-2476	173	11	)	)	PUNCT
iajs-2476	174	1	⊆	⊆	NUM
iajs-2476	174	2	q	q	NOUN
iajs-2476	174	3	:	:	PUNCT
iajs-2476	174	4	1	1	X
iajs-2476	174	5	.	.	PUNCT
iajs-2476	175	1	since	since	SCONJ
iajs-2476	175	2	q	q	PROPN
iajs-2476	175	3	∶	∶	NOUN
iajs-2476	175	4	1	1	NUM
iajs-2476	175	5	is	be	AUX
iajs-2476	175	6	a	a	DET
iajs-2476	175	7	primary	primary	ADJ
iajs-2476	175	8	la	la	ADJ
iajs-2476	175	9	-	-	PUNCT
iajs-2476	175	10	ideal	ideal	NOUN
iajs-2476	175	11	then	then	ADV
iajs-2476	175	12	ϑ	ϑ	X
iajs-2476	175	13	:	:	PUNCT
iajs-2476	175	14	1	1	NUM
iajs-2476	175	15	⊆	⊆	NUM
iajs-2476	175	16	q	q	NOUN
iajs-2476	175	17	:	:	PUNCT
iajs-2476	175	18	1	1	NUM
iajs-2476	175	19	or	or	CCONJ
iajs-2476	175	20	ϖ	ϖ	PRON
iajs-2476	175	21	:	:	PUNCT
iajs-2476	175	22	1	1	NUM
iajs-2476	175	23	⊆	⊆	NUM
iajs-2476	175	24	q	q	NOUN
iajs-2476	175	25	∶	∶	NOUN
iajs-2476	175	26	1	1	NUM
iajs-2476	175	27	,	,	PUNCT
iajs-2476	175	28	since	since	SCONJ
iajs-2476	175	29	q	q	NOUN
iajs-2476	175	30	is	be	AUX
iajs-2476	175	31	la	la	ADJ
iajs-2476	175	32	-	-	ADJ
iajs-2476	175	33	primary	primary	ADJ
iajs-2476	175	34	submodule	submodule	NOUN
iajs-2476	175	35	then	then	ADV
iajs-2476	175	36	q	q	PROPN
iajs-2476	175	37	∶	∶	NOUN
iajs-2476	175	38	1	1	NUM
iajs-2476	175	39	is	be	AUX
iajs-2476	175	40	prime	prime	ADJ
iajs-2476	175	41	thus	thus	ADV
iajs-2476	175	42	q	q	PROPN
iajs-2476	175	43	∶	∶	NOUN
iajs-2476	175	44	1	1	NUM
iajs-2476	175	45	q	q	NOUN
iajs-2476	175	46	∶	∶	NOUN
iajs-2476	175	47	1	1	NUM
iajs-2476	175	48	.	.	PUNCT
iajs-2476	176	1	thus	thus	ADV
iajs-2476	176	2	q	q	X
iajs-2476	176	3	∈	∈	ADJ
iajs-2476	176	4	v(ϑ	v(ϑ	NOUN
iajs-2476	176	5	or	or	CCONJ
iajs-2476	176	6	q	q	NOUN
iajs-2476	176	7	∈	∈	PROPN
iajs-2476	176	8	v(ϖ	v(ϖ	PROPN
iajs-2476	176	9	,	,	PUNCT
iajs-2476	176	10	so	so	CCONJ
iajs-2476	176	11	q	q	X
iajs-2476	176	12	∈	∈	PROPN
iajs-2476	176	13	v(ϑ	v(ϑ	NOUN
iajs-2476	176	14	∪	∪	ADP
iajs-2476	176	15	v(ϖ	v(ϖ	PROPN
iajs-2476	176	16	and	and	CCONJ
iajs-2476	176	17	hence	hence	ADV
iajs-2476	176	18	v(ϑ	v(ϑ	NOUN
iajs-2476	176	19	∩	∩	ADJ
iajs-2476	176	20	ϖ	ϖ	NOUN
iajs-2476	176	21	)	)	PUNCT
iajs-2476	176	22	⊆	⊆	NUM
iajs-2476	176	23	v(ϑ	v(ϑ	NOUN
iajs-2476	176	24	∪	∪	ADP
iajs-2476	176	25	v(ϖ	v(ϖ	PROPN
iajs-2476	176	26	.	.	PUNCT
iajs-2476	177	1	(	(	PUNCT
iajs-2476	177	2	d	d	X
iajs-2476	177	3	)	)	PUNCT
iajs-2476	177	4	subsequently	subsequently	ADV
iajs-2476	177	5	(	(	PUNCT
iajs-2476	177	6	2	2	X
iajs-2476	177	7	)	)	PUNCT
iajs-2476	177	8	follows	follow	VERB
iajs-2476	177	9	via	via	ADP
iajs-2476	177	10	(	(	PUNCT
iajs-2476	177	11	c	c	NOUN
iajs-2476	177	12	)	)	PUNCT
iajs-2476	177	13	and	and	CCONJ
iajs-2476	177	14	(	(	PUNCT
iajs-2476	177	15	d	d	NOUN
iajs-2476	177	16	)	)	PUNCT
iajs-2476	177	17	.	.	PUNCT
iajs-2476	178	1	now	now	ADV
iajs-2476	178	2	,	,	PUNCT
iajs-2476	178	3	we	we	PRON
iajs-2476	178	4	set	set	VERB
iajs-2476	178	5	laε∗(h	laε∗(h	PRON
iajs-2476	178	6	)	)	PUNCT
iajs-2476	178	7	=	=	PRON
iajs-2476	178	8	{	{	PUNCT
iajs-2476	178	9	v∗(ϑ	v∗(ϑ	PROPN
iajs-2476	178	10	|	|	CCONJ
iajs-2476	178	11	ϑ	ϑ	NOUN
iajs-2476	178	12	∈	∈	NOUN
iajs-2476	178	13	la(h	la(h	NUM
iajs-2476	178	14	)	)	PUNCT
iajs-2476	178	15	}	}	PUNCT
iajs-2476	178	16	;	;	PUNCT
iajs-2476	178	17	laε	laε	NOUN
iajs-2476	178	18	,	,	PUNCT
iajs-2476	178	19	(	(	PUNCT
iajs-2476	178	20	h	h	NOUN
iajs-2476	178	21	)	)	PUNCT
iajs-2476	178	22	=	=	PRON
iajs-2476	178	23	{	{	PUNCT
iajs-2476	178	24	v∗(𝛾.	v∗(𝛾.	NOUN
iajs-2476	178	25	1	1	NUM
iajs-2476	178	26	|	|	ADV
iajs-2476	178	27	𝛾	𝛾	ADP
iajs-2476	178	28	∈	∈	PROPN
iajs-2476	178	29	lai(f	lai(f	PROPN
iajs-2476	178	30	)	)	PUNCT
iajs-2476	178	31	}	}	PUNCT
iajs-2476	178	32	;	;	PUNCT
iajs-2476	178	33	laε	laε	PROPN
iajs-2476	178	34	(	(	PUNCT
iajs-2476	178	35	h	h	NOUN
iajs-2476	178	36	)	)	PUNCT
iajs-2476	178	37	=	=	PRON
iajs-2476	178	38	{	{	PUNCT
iajs-2476	178	39	v∗(ϑ	v∗(ϑ	PROPN
iajs-2476	178	40	|	|	CCONJ
iajs-2476	178	41	ϑ	ϑ	NOUN
iajs-2476	178	42	∈	∈	NOUN
iajs-2476	178	43	la(h	la(h	NUM
iajs-2476	178	44	)	)	PUNCT
iajs-2476	178	45	}	}	PUNCT
iajs-2476	178	46	.	.	PUNCT
iajs-2476	179	1	we	we	PRON
iajs-2476	179	2	consider	consider	VERB
iajs-2476	179	3	the	the	DET
iajs-2476	179	4	topologies	topology	NOUN
iajs-2476	179	5	of	of	ADP
iajs-2476	179	6	la	la	NOUN
iajs-2476	179	7	-	-	PUNCT
iajs-2476	179	8	prim(h	prim(h	NOUN
iajs-2476	179	9	)	)	PUNCT
iajs-2476	179	10	produced	produce	VERB
iajs-2476	179	11	,	,	PUNCT
iajs-2476	179	12	respectively	respectively	ADV
iajs-2476	179	13	,	,	PUNCT
iajs-2476	179	14	via	via	ADP
iajs-2476	179	15	these	these	DET
iajs-2476	179	16	three	three	NUM
iajs-2476	179	17	collections	collection	NOUN
iajs-2476	179	18	.	.	PUNCT
iajs-2476	180	1	from	from	ADP
iajs-2476	180	2	proposition	proposition	NOUN
iajs-2476	180	3	3.1	3.1	NUM
iajs-2476	180	4	,	,	PUNCT
iajs-2476	180	5	we	we	PRON
iajs-2476	180	6	can	can	AUX
iajs-2476	180	7	facilely	facilely	ADV
iajs-2476	180	8	look	look	VERB
iajs-2476	180	9	that	that	SCONJ
iajs-2476	180	10	there	there	PRON
iajs-2476	180	11	occurs	occur	VERB
iajs-2476	180	12	a	a	DET
iajs-2476	180	13	topology	topology	NOUN
iajs-2476	180	14	𝜏∗	𝜏∗	NOUN
iajs-2476	180	15	say	say	VERB
iajs-2476	180	16	,	,	PUNCT
iajs-2476	180	17	over	over	ADP
iajs-2476	180	18	la	la	NOUN
iajs-2476	180	19	-	-	PUNCT
iajs-2476	180	20	prim(h	prim(h	NOUN
iajs-2476	180	21	)	)	PUNCT
iajs-2476	180	22	having	have	VERB
iajs-2476	180	23	laε∗(h	laε∗(h	PROPN
iajs-2476	180	24	)	)	PUNCT
iajs-2476	180	25	as	as	ADP
iajs-2476	180	26	the	the	DET
iajs-2476	180	27	set	set	NOUN
iajs-2476	180	28	of	of	ADP
iajs-2476	180	29	every	every	DET
iajs-2476	180	30	closed	closed	ADJ
iajs-2476	180	31	collections	collection	NOUN
iajs-2476	180	32	if	if	SCONJ
iajs-2476	180	33	and	and	CCONJ
iajs-2476	180	34	only	only	ADV
iajs-2476	180	35	if	if	SCONJ
iajs-2476	180	36	laε∗(h	laε∗(h	NOUN
iajs-2476	180	37	)	)	PUNCT
iajs-2476	180	38	is	be	AUX
iajs-2476	180	39	closed	close	VERB
iajs-2476	180	40	beneath	beneath	ADP
iajs-2476	180	41	finite	finite	PROPN
iajs-2476	180	42	union	union	PROPN
iajs-2476	180	43	.	.	PUNCT
iajs-2476	181	1	in	in	ADP
iajs-2476	181	2	this	this	DET
iajs-2476	181	3	state	state	NOUN
iajs-2476	181	4	,	,	PUNCT
iajs-2476	181	5	we	we	PRON
iajs-2476	181	6	call	call	VERB
iajs-2476	181	7	the	the	DET
iajs-2476	181	8	topology	topology	NOUN
iajs-2476	181	9	𝜏∗	𝜏∗	NOUN
iajs-2476	181	10	the	the	DET
iajs-2476	181	11	near	near	ADJ
iajs-2476	181	12	-	-	PUNCT
iajs-2476	181	13	zariski	zariski	NOUN
iajs-2476	181	14	topology	topology	NOUN
iajs-2476	181	15	on	on	ADP
iajs-2476	181	16	la	la	NOUN
iajs-2476	181	17	-	-	PUNCT
iajs-2476	181	18	prim(h	prim(h	NOUN
iajs-2476	181	19	)	)	PUNCT
iajs-2476	181	20	.	.	PUNCT
iajs-2476	182	1	following	follow	VERB
iajs-2476	182	2	[	[	X
iajs-2476	182	3	17	17	NUM
iajs-2476	182	4	]	]	PUNCT
iajs-2476	182	5	.	.	PUNCT
iajs-2476	183	1	a	a	DET
iajs-2476	183	2	module	module	NOUN
iajs-2476	183	3	h	h	NOUN
iajs-2476	183	4	is	be	AUX
iajs-2476	183	5	surname	surname	NOUN
iajs-2476	183	6	an	an	DET
iajs-2476	183	7	la	la	PROPN
iajs-2476	183	8	-	-	ADJ
iajs-2476	183	9	p	p	ADJ
iajs-2476	183	10	top	top	ADJ
iajs-2476	183	11	module	module	NOUN
iajs-2476	183	12	,	,	PUNCT
iajs-2476	183	13	if	if	SCONJ
iajs-2476	183	14	laε∗(h	laε∗(h	NUM
iajs-2476	183	15	)	)	PUNCT
iajs-2476	183	16	result	result	VERB
iajs-2476	183	17	the	the	DET
iajs-2476	183	18	topology	topology	NOUN
iajs-2476	183	19	𝜏∗	𝜏∗	NOUN
iajs-2476	183	20	over	over	ADP
iajs-2476	183	21	laprim(h	laprim(h	PROPN
iajs-2476	183	22	)	)	PUNCT
iajs-2476	183	23	.	.	PUNCT
iajs-2476	184	1	in	in	ADP
iajs-2476	184	2	contrast	contrast	NOUN
iajs-2476	184	3	with	with	ADP
iajs-2476	184	4	laε∗(h	laε∗(h	PROPN
iajs-2476	184	5	)	)	PUNCT
iajs-2476	184	6	,	,	PUNCT
iajs-2476	184	7	laε	laε	NOUN
iajs-2476	184	8	,	,	PUNCT
iajs-2476	184	9	(	(	PUNCT
iajs-2476	184	10	h	h	NOUN
iajs-2476	184	11	)	)	PUNCT
iajs-2476	184	12	,	,	PUNCT
iajs-2476	184	13	permanently	permanently	ADV
iajs-2476	184	14	occurs	occur	VERB
iajs-2476	184	15	a	a	DET
iajs-2476	184	16	topology	topology	NOUN
iajs-2476	184	17	𝜏	𝜏	NOUN
iajs-2476	184	18	,	,	PUNCT
iajs-2476	184	19	on	on	ADP
iajs-2476	184	20	laprim(h	laprim(h	NOUN
iajs-2476	184	21	)	)	PUNCT
iajs-2476	184	22	,	,	PUNCT
iajs-2476	184	23	since	since	SCONJ
iajs-2476	184	24	v∗(𝛾	v∗(𝛾	X
iajs-2476	184	25	.	.	PUNCT
iajs-2476	184	26	1	1	NUM
iajs-2476	185	1	⋃	⋃	NOUN
iajs-2476	185	2	v∗(𝛾	v∗(𝛾	NOUN
iajs-2476	185	3	.	.	PUNCT
iajs-2476	186	1	1	1	NUM
iajs-2476	186	2	=	=	SYM
iajs-2476	186	3	v∗	v∗	PROPN
iajs-2476	186	4	(	(	PUNCT
iajs-2476	186	5	𝛾	𝛾	NOUN
iajs-2476	186	6	.	.	PUNCT
iajs-2476	187	1	𝛾	𝛾	ADP
iajs-2476	187	2	.1	.1	NUM
iajs-2476	187	3	.	.	PUNCT
iajs-2476	187	4	  	  	SPACE
iajs-2476	188	1	95	95	NUM
iajs-2476	188	2	ibn	ibn	PROPN
iajs-2476	188	3	al	al	PROPN
iajs-2476	188	4	-	-	PUNCT
iajs-2476	188	5	haitham	haitham	PROPN
iajs-2476	188	6	jour	jour	X
iajs-2476	188	7	.	.	PROPN
iajs-2476	188	8	for	for	ADP
iajs-2476	188	9	pure	pure	ADJ
iajs-2476	188	10	&	&	CCONJ
iajs-2476	188	11	appl	appl	PROPN
iajs-2476	188	12	.	.	PUNCT
iajs-2476	189	1	sci	sci	PROPN
iajs-2476	189	2	.	.	PROPN
iajs-2476	190	1	33	33	NUM
iajs-2476	190	2	(	(	PUNCT
iajs-2476	190	3	3	3	NUM
iajs-2476	190	4	)	)	PUNCT
iajs-2476	190	5	2020	2020	NUM
iajs-2476	191	1	also	also	ADV
iajs-2476	191	2	,	,	PUNCT
iajs-2476	191	3	laε	laε	VERB
iajs-2476	191	4	,	,	PUNCT
iajs-2476	191	5	(	(	PUNCT
iajs-2476	191	6	h	h	NOUN
iajs-2476	191	7	)	)	PUNCT
iajs-2476	191	8	is	be	AUX
iajs-2476	191	9	closed	close	VERB
iajs-2476	191	10	beneath	beneath	ADP
iajs-2476	191	11	finite	finite	PROPN
iajs-2476	191	12	union	union	PROPN
iajs-2476	191	13	.	.	PUNCT
iajs-2476	192	1	obviously	obviously	ADV
iajs-2476	192	2	,	,	PUNCT
iajs-2476	192	3	𝜏	𝜏	NOUN
iajs-2476	192	4	,	,	PUNCT
iajs-2476	192	5	is	be	AUX
iajs-2476	192	6	coarser	coarse	ADJ
iajs-2476	192	7	than	than	ADP
iajs-2476	192	8	the	the	DET
iajs-2476	192	9	near	near	ADJ
iajs-2476	192	10	-	-	PUNCT
iajs-2476	192	11	zariski	zariski	NOUN
iajs-2476	192	12	topology	topology	NOUN
iajs-2476	192	13	𝜏∗	𝜏∗	NOUN
iajs-2476	192	14	,	,	PUNCT
iajs-2476	192	15	when	when	SCONJ
iajs-2476	192	16	h	h	PRON
iajs-2476	192	17	be	be	VERB
iajs-2476	192	18	an	an	DET
iajs-2476	192	19	la	la	ADJ
iajs-2476	192	20	-	-	ADJ
iajs-2476	192	21	p	p	ADJ
iajs-2476	192	22	top	top	ADJ
iajs-2476	192	23	module	module	NOUN
iajs-2476	192	24	.	.	PUNCT
iajs-2476	193	1	for	for	ADP
iajs-2476	193	2	each	each	DET
iajs-2476	193	3	f	f	NOUN
iajs-2476	193	4	-	-	PUNCT
iajs-2476	193	5	module	module	NOUN
iajs-2476	193	6	h	h	NOUN
iajs-2476	193	7	while	while	SCONJ
iajs-2476	193	8	ϑ	ϑ	X
iajs-2476	193	9	,	,	PUNCT
iajs-2476	193	10	ϑ	ϑ	X
iajs-2476	193	11	∈	∈	NOUN
iajs-2476	193	12	la(h	la(h	PRON
iajs-2476	193	13	)	)	PUNCT
iajs-2476	193	14	we	we	PRON
iajs-2476	193	15	have	have	VERB
iajs-2476	193	16	the	the	DET
iajs-2476	193	17	next	next	ADJ
iajs-2476	193	18	outcome	outcome	NOUN
iajs-2476	193	19	.	.	PUNCT
iajs-2476	194	1	proposition	proposition	NOUN
iajs-2476	194	2	3.3	3.3	NUM
iajs-2476	194	3	if	if	SCONJ
iajs-2476	194	4	ϑ1	ϑ1	PROPN
iajs-2476	194	5	:	:	PUNCT
iajs-2476	194	6	1h	1h	NUM
iajs-2476	194	7	=	=	SYM
iajs-2476	194	8	ϑ2	ϑ2	PROPN
iajs-2476	194	9	:	:	PUNCT
iajs-2476	194	10	1h	1h	NUM
iajs-2476	194	11	,	,	PUNCT
iajs-2476	194	12	then	then	ADV
iajs-2476	194	13	v(ϑ1	v(ϑ1	NOUN
iajs-2476	194	14	)	)	PUNCT
iajs-2476	195	1	=	=	NOUN
iajs-2476	195	2	v(ϑ2	v(ϑ2	NOUN
iajs-2476	195	3	)	)	PUNCT
iajs-2476	195	4	.	.	PUNCT
iajs-2476	196	1	the	the	DET
iajs-2476	196	2	converse	converse	NOUN
iajs-2476	196	3	is	be	AUX
iajs-2476	196	4	true	true	ADJ
iajs-2476	196	5	if	if	SCONJ
iajs-2476	196	6	both	both	DET
iajs-2476	196	7	ϑ1	ϑ1	NOUN
iajs-2476	196	8	and	and	CCONJ
iajs-2476	196	9	ϑ2	ϑ2	PROPN
iajs-2476	196	10	are	be	AUX
iajs-2476	196	11	primary	primary	ADJ
iajs-2476	196	12	.	.	PUNCT
iajs-2476	197	1	proof	proof	NOUN
iajs-2476	197	2	first	first	ADV
iajs-2476	197	3	let	let	VERB
iajs-2476	197	4	ϑ1	ϑ1	PROPN
iajs-2476	197	5	:	:	PUNCT
iajs-2476	197	6	1h	1h	NUM
iajs-2476	197	7	=	=	SYM
iajs-2476	197	8	ϑ2	ϑ2	NOUN
iajs-2476	197	9	:	:	PUNCT
iajs-2476	197	10	1h	1h	NUM
iajs-2476	197	11	,	,	PUNCT
iajs-2476	197	12	and	and	CCONJ
iajs-2476	197	13	ϖ	ϖ	PRON
iajs-2476	197	14	∈	∈	PROPN
iajs-2476	197	15	v(ϑ1	v(ϑ1	NOUN
iajs-2476	197	16	)	)	PUNCT
iajs-2476	197	17	.	.	PUNCT
iajs-2476	198	1	then	then	ADV
iajs-2476	198	2	ϑ1	ϑ1	NOUN
iajs-2476	198	3	:	:	PUNCT
iajs-2476	198	4	1h	1h	NUM
iajs-2476	198	5	⊆	⊆	NUM
iajs-2476	198	6	ϖ	ϖ	X
iajs-2476	198	7	:	:	PUNCT
iajs-2476	198	8	1h	1h	NUM
iajs-2476	198	9	and	and	CCONJ
iajs-2476	198	10	hence	hence	ADV
iajs-2476	198	11	ϑ2	ϑ2	PROPN
iajs-2476	198	12	:	:	PUNCT
iajs-2476	198	13	1h	1h	NUM
iajs-2476	198	14	⊆	⊆	NUM
iajs-2476	198	15	ϖ	ϖ	X
iajs-2476	198	16	:	:	PUNCT
iajs-2476	198	17	1h	1h	NUM
iajs-2476	198	18	,	,	PUNCT
iajs-2476	198	19	that	that	PRON
iajs-2476	198	20	is	be	AUX
iajs-2476	198	21	ϖ	ϖ	PRON
iajs-2476	198	22	∈	∈	PROPN
iajs-2476	198	23	v(ϑ2	v(ϑ2	NOUN
iajs-2476	198	24	)	)	PUNCT
iajs-2476	198	25	.	.	PUNCT
iajs-2476	199	1	therefore	therefore	ADV
iajs-2476	199	2	v(ϑ1	v(ϑ1	VERB
iajs-2476	199	3	)	)	PUNCT
iajs-2476	199	4	⊆	⊆	NUM
iajs-2476	199	5	v(ϑ2	v(ϑ2	NOUN
iajs-2476	199	6	)	)	PUNCT
iajs-2476	199	7	.	.	PUNCT
iajs-2476	200	1	similarly	similarly	ADV
iajs-2476	200	2	we	we	PRON
iajs-2476	200	3	get	get	VERB
iajs-2476	200	4	that	that	DET
iajs-2476	200	5	v(ϑ2	v(ϑ2	NOUN
iajs-2476	200	6	)	)	PUNCT
iajs-2476	200	7	⊆	⊆	NUM
iajs-2476	200	8	v(ϑ1	v(ϑ1	NOUN
iajs-2476	200	9	)	)	PUNCT
iajs-2476	200	10	.	.	PUNCT
iajs-2476	201	1	therefore	therefore	ADV
iajs-2476	201	2	v(ϑ1	v(ϑ1	NOUN
iajs-2476	201	3	)	)	PUNCT
iajs-2476	201	4	=	=	SYM
iajs-2476	201	5	v(ϑ2	v(ϑ2	NOUN
iajs-2476	201	6	)	)	PUNCT
iajs-2476	201	7	.	.	PUNCT
iajs-2476	202	1	for	for	ADP
iajs-2476	202	2	the	the	DET
iajs-2476	202	3	opposite	opposite	NOUN
iajs-2476	202	4	,	,	PUNCT
iajs-2476	202	5	let	let	VERB
iajs-2476	202	6	ϑ1	ϑ1	NOUN
iajs-2476	202	7	,	,	PUNCT
iajs-2476	202	8	ϑ2	ϑ2	PROPN
iajs-2476	202	9	∈	∈	PROPN
iajs-2476	202	10	la(h	la(h	PRON
iajs-2476	202	11	)	)	PUNCT
iajs-2476	202	12	are	be	AUX
iajs-2476	202	13	primary	primary	ADJ
iajs-2476	202	14	while	while	SCONJ
iajs-2476	202	15	v(ϑ1	v(ϑ1	NOUN
iajs-2476	202	16	)	)	PUNCT
iajs-2476	202	17	=	=	VERB
iajs-2476	202	18	v(ϑ2	v(ϑ2	NOUN
iajs-2476	202	19	)	)	PUNCT
iajs-2476	202	20	.	.	PUNCT
iajs-2476	203	1	then	then	ADV
iajs-2476	203	2	ϑ1	ϑ1	NOUN
iajs-2476	203	3	⊆	⊆	NUM
iajs-2476	203	4	v(ϑ1	v(ϑ1	NOUN
iajs-2476	203	5	)	)	PUNCT
iajs-2476	203	6	=	=	SYM
iajs-2476	203	7	v(ϑ2	v(ϑ2	NOUN
iajs-2476	203	8	)	)	PUNCT
iajs-2476	203	9	⟹	⟹	NUM
iajs-2476	204	1	ϑ2	ϑ2	NOUN
iajs-2476	204	2	:	:	PUNCT
iajs-2476	204	3	1h	1h	NUM
iajs-2476	204	4	⊆	⊆	NUM
iajs-2476	204	5	ϑ1	ϑ1	NOUN
iajs-2476	204	6	:	:	PUNCT
iajs-2476	204	7	1h	1h	NUM
iajs-2476	204	8	(	(	PUNCT
iajs-2476	204	9	a	a	NOUN
iajs-2476	204	10	)	)	PUNCT
iajs-2476	204	11	and	and	CCONJ
iajs-2476	204	12	ϑ2	ϑ2	PROPN
iajs-2476	204	13	⊆	⊆	NUM
iajs-2476	204	14	v(ϑ2	v(ϑ2	NOUN
iajs-2476	204	15	)	)	PUNCT
iajs-2476	204	16	=	=	SYM
iajs-2476	204	17	v(ϑ1	v(ϑ1	NOUN
iajs-2476	204	18	)	)	PUNCT
iajs-2476	204	19	⟹	⟹	NUM
iajs-2476	205	1	ϑ1	ϑ1	NOUN
iajs-2476	205	2	:	:	PUNCT
iajs-2476	205	3	1h	1h	NUM
iajs-2476	205	4	⊆	⊆	NUM
iajs-2476	205	5	ϑ2	ϑ2	NOUN
iajs-2476	205	6	:	:	PUNCT
iajs-2476	205	7	1h	1h	NUM
iajs-2476	205	8	(	(	PUNCT
iajs-2476	205	9	b	b	NOUN
iajs-2476	205	10	)	)	PUNCT
iajs-2476	205	11	then	then	ADV
iajs-2476	205	12	by	by	ADP
iajs-2476	205	13	(	(	PUNCT
iajs-2476	205	14	a	a	X
iajs-2476	205	15	)	)	PUNCT
iajs-2476	205	16	and	and	CCONJ
iajs-2476	205	17	(	(	PUNCT
iajs-2476	205	18	b	b	X
iajs-2476	205	19	)	)	PUNCT
iajs-2476	205	20	we	we	PRON
iajs-2476	205	21	get	get	VERB
iajs-2476	205	22	that	that	DET
iajs-2476	205	23	ϑ1	ϑ1	NOUN
iajs-2476	205	24	:	:	PUNCT
iajs-2476	205	25	1h	1h	NUM
iajs-2476	205	26	=	=	SYM
iajs-2476	205	27	ϑ2	ϑ2	PROPN
iajs-2476	205	28	:	:	PUNCT
iajs-2476	205	29	1h	1h	NUM
iajs-2476	205	30	.	.	PUNCT
iajs-2476	206	1	for	for	ADP
iajs-2476	206	2	q	q	PROPN
iajs-2476	206	3	∈	∈	PROPN
iajs-2476	206	4	la	la	PROPN
iajs-2476	206	5	-	-	PUNCT
iajs-2476	206	6	prim(f	prim(f	NOUN
iajs-2476	206	7	)	)	PUNCT
iajs-2476	206	8	,	,	PUNCT
iajs-2476	206	9	by	by	ADP
iajs-2476	206	10	la	la	PROPN
iajs-2476	206	11	-	-	PUNCT
iajs-2476	206	12	primq(h	primq(h	NOUN
iajs-2476	206	13	)	)	PUNCT
iajs-2476	206	14	we	we	PRON
iajs-2476	206	15	mean	mean	VERB
iajs-2476	206	16	the	the	DET
iajs-2476	206	17	collection	collection	NOUN
iajs-2476	206	18	of	of	ADP
iajs-2476	206	19	all	all	PRON
iajs-2476	206	20	ϑ	ϑ	X
iajs-2476	206	21	∈	∈	NOUN
iajs-2476	206	22	la(h	la(h	NUM
iajs-2476	206	23	)	)	PUNCT
iajs-2476	206	24	such	such	ADJ
iajs-2476	206	25	that	that	SCONJ
iajs-2476	206	26	ϑ	ϑ	X
iajs-2476	206	27	:	:	PUNCT
iajs-2476	206	28	1h	1h	NUM
iajs-2476	206	29	=	=	SYM
iajs-2476	206	30	q	q	X
iajs-2476	206	31	.	.	PUNCT
iajs-2476	207	1	in	in	ADP
iajs-2476	207	2	other	other	ADJ
iajs-2476	207	3	words	word	NOUN
iajs-2476	207	4	la	la	PROPN
iajs-2476	207	5	-	-	NOUN
iajs-2476	207	6	primq(h)=	primq(h)=	NOUN
iajs-2476	207	7	{	{	PUNCT
iajs-2476	207	8	ϑ	ϑ	X
iajs-2476	207	9	∈	∈	PROPN
iajs-2476	207	10	la	la	PROPN
iajs-2476	207	11	-	-	PUNCT
iajs-2476	207	12	prim(h)|	prim(h)|	PROPN
iajs-2476	207	13	ϑ	ϑ	PROPN
iajs-2476	207	14	:	:	PUNCT
iajs-2476	207	15	1h	1h	NUM
iajs-2476	207	16	=	=	SYM
iajs-2476	207	17	q	q	NOUN
iajs-2476	207	18	}	}	PUNCT
iajs-2476	207	19	.	.	PUNCT
iajs-2476	208	1	proposition	proposition	NOUN
iajs-2476	208	2	3.4	3.4	NUM
iajs-2476	208	3	(	(	PUNCT
iajs-2476	208	4	a	a	X
iajs-2476	208	5	)	)	PUNCT
iajs-2476	208	6	v(ϑ	v(ϑ	NOUN
iajs-2476	208	7	)	)	PUNCT
iajs-2476	208	8	=	=	SYM
iajs-2476	209	1	⋃	⋃	SCONJ
iajs-2476	209	2	q∈v	q∈v	ADV
iajs-2476	209	3	ϑ	ϑ	NOUN
iajs-2476	209	4	:	:	PUNCT
iajs-2476	209	5	1h	1h	NUM
iajs-2476	209	6	)	)	PUNCT
iajs-2476	209	7	la	la	PROPN
iajs-2476	209	8	-	-	PUNCT
iajs-2476	209	9	primq(h	primq(h	NOUN
iajs-2476	209	10	)	)	PUNCT
iajs-2476	209	11	for	for	ADP
iajs-2476	209	12	ϑ	ϑ	PROPN
iajs-2476	209	13	∈	∈	NOUN
iajs-2476	209	14	la(h	la(h	NUM
iajs-2476	209	15	)	)	PUNCT
iajs-2476	209	16	(	(	PUNCT
iajs-2476	209	17	b	b	X
iajs-2476	209	18	)	)	PUNCT
iajs-2476	209	19	v(𝛾.	v(𝛾.	NOUN
iajs-2476	209	20	1	1	NUM
iajs-2476	209	21	=	=	SYM
iajs-2476	209	22	v∗(𝛾.	v∗(𝛾.	NOUN
iajs-2476	209	23	1	1	NUM
iajs-2476	209	24	for	for	ADP
iajs-2476	209	25	every	every	DET
iajs-2476	209	26	la	la	ADJ
iajs-2476	209	27	-	-	PUNCT
iajs-2476	209	28	ideal	ideal	ADJ
iajs-2476	209	29	𝛾	𝛾	PROPN
iajs-2476	209	30	of	of	ADP
iajs-2476	209	31	f.	f.	PROPN
iajs-2476	209	32	further	far	ADV
iajs-2476	209	33	,	,	PUNCT
iajs-2476	209	34	if	if	SCONJ
iajs-2476	209	35	ϑ	ϑ	X
iajs-2476	209	36	∈	∈	NOUN
iajs-2476	209	37	la(h	la(h	NUM
iajs-2476	209	38	)	)	PUNCT
iajs-2476	209	39	,	,	PUNCT
iajs-2476	209	40	then	then	ADV
iajs-2476	209	41	v(ϑ	v(ϑ	PROPN
iajs-2476	209	42	=	=	SYM
iajs-2476	209	43	v	v	NOUN
iajs-2476	209	44	(	(	PUNCT
iajs-2476	209	45	ϑ	ϑ	NOUN
iajs-2476	209	46	:	:	SYM
iajs-2476	209	47	1	1	NUM
iajs-2476	209	48	.	.	SYM
iajs-2476	209	49	1	1	NUM
iajs-2476	209	50	=	=	SYM
iajs-2476	209	51	v∗	v∗	PROPN
iajs-2476	209	52	(	(	PUNCT
iajs-2476	209	53	ϑ	ϑ	NOUN
iajs-2476	209	54	:	:	PUNCT
iajs-2476	209	55	1	1	NUM
iajs-2476	209	56	.	.	NUM
iajs-2476	209	57	1	1	NUM
iajs-2476	209	58	.	.	PUNCT
iajs-2476	210	1	proof	proof	NOUN
iajs-2476	210	2	(	(	PUNCT
iajs-2476	210	3	1	1	NUM
iajs-2476	210	4	)	)	PUNCT
iajs-2476	210	5	:	:	PUNCT
iajs-2476	210	6	suppose	suppose	VERB
iajs-2476	210	7	that	that	SCONJ
iajs-2476	210	8	ϖ	ϖ	PROPN
iajs-2476	210	9	∈	∈	PRON
iajs-2476	210	10	v(ϑ	v(ϑ	NOUN
iajs-2476	210	11	.	.	PUNCT
iajs-2476	211	1	then	then	ADV
iajs-2476	211	2	ϑ	ϑ	X
iajs-2476	211	3	:	:	PUNCT
iajs-2476	211	4	1	1	NUM
iajs-2476	211	5	⊆	⊆	NUM
iajs-2476	211	6	ϖ	ϖ	X
iajs-2476	211	7	:	:	PUNCT
iajs-2476	211	8	1	1	NUM
iajs-2476	211	9	=	=	SYM
iajs-2476	211	10	q	q	NOUN
iajs-2476	211	11	,	,	PUNCT
iajs-2476	211	12	and	and	CCONJ
iajs-2476	211	13	hence	hence	ADV
iajs-2476	211	14	q	q	X
iajs-2476	211	15	∈	∈	PROPN
iajs-2476	211	16	v(ϑ	v(ϑ	NOUN
iajs-2476	211	17	:	:	PUNCT
iajs-2476	211	18	1	1	NUM
iajs-2476	211	19	.	.	PUNCT
iajs-2476	212	1	also	also	ADV
iajs-2476	212	2	,	,	PUNCT
iajs-2476	212	3	ϖ	ϖ	PROPN
iajs-2476	212	4	∈	∈	PROPN
iajs-2476	212	5	la	la	PROPN
iajs-2476	212	6	-	-	PUNCT
iajs-2476	212	7	primq(h	primq(h	NOUN
iajs-2476	212	8	)	)	PUNCT
iajs-2476	212	9	⟹	⟹	PUNCT
iajs-2476	213	1	ϖ	ϖ	NOUN
iajs-2476	213	2	∈	∈	PROPN
iajs-2476	213	3	⋃	⋃	VERB
iajs-2476	213	4	q∈v	q∈v	ADJ
iajs-2476	213	5	ϑ	ϑ	NOUN
iajs-2476	213	6	:	:	PUNCT
iajs-2476	213	7	1h	1h	NUM
iajs-2476	213	8	)	)	PUNCT
iajs-2476	213	9	la	la	PROPN
iajs-2476	213	10	-	-	PUNCT
iajs-2476	213	11	primq(h	primq(h	NOUN
iajs-2476	213	12	)	)	PUNCT
iajs-2476	213	13	⟹	⟹	PUNCT
iajs-2476	213	14	v(ϑ	v(ϑ	NOUN
iajs-2476	213	15	⊆	⊆	NUM
iajs-2476	213	16	⋃	⋃	X
iajs-2476	213	17	q∈v	q∈v	ADJ
iajs-2476	213	18	ϑ	ϑ	NOUN
iajs-2476	213	19	:	:	PUNCT
iajs-2476	213	20	1h	1h	NUM
iajs-2476	213	21	)	)	PUNCT
iajs-2476	213	22	la	la	PROPN
iajs-2476	213	23	-	-	PUNCT
iajs-2476	213	24	primq(h	primq(h	NOUN
iajs-2476	213	25	)	)	PUNCT
iajs-2476	213	26	(	(	PUNCT
iajs-2476	213	27	a	a	X
iajs-2476	213	28	)	)	PUNCT
iajs-2476	213	29	now	now	ADV
iajs-2476	213	30	suppose	suppose	VERB
iajs-2476	213	31	that	that	SCONJ
iajs-2476	213	32	ϖ	ϖ	PROPN
iajs-2476	213	33	∈	∈	PROPN
iajs-2476	213	34	⋃	⋃	VERB
iajs-2476	213	35	q∈v	q∈v	ADJ
iajs-2476	213	36	ϑ	ϑ	NOUN
iajs-2476	213	37	:	:	PUNCT
iajs-2476	213	38	1h	1h	NUM
iajs-2476	213	39	)	)	PUNCT
iajs-2476	213	40	la	la	PROPN
iajs-2476	213	41	-	-	PUNCT
iajs-2476	213	42	primq(h	primq(h	NOUN
iajs-2476	213	43	)	)	PUNCT
iajs-2476	213	44	.	.	PUNCT
iajs-2476	214	1	then	then	ADV
iajs-2476	214	2	there	there	PRON
iajs-2476	214	3	occurs	occur	VERB
iajs-2476	214	4	q	q	PROPN
iajs-2476	214	5	∈	∈	PROPN
iajs-2476	214	6	la	la	PROPN
iajs-2476	214	7	-	-	PUNCT
iajs-2476	214	8	primq(h	primq(h	NOUN
iajs-2476	214	9	)	)	PUNCT
iajs-2476	214	10	such	such	ADJ
iajs-2476	214	11	that	that	SCONJ
iajs-2476	214	12	ϑ	ϑ	VERB
iajs-2476	214	13	:	:	PUNCT
iajs-2476	214	14	1	1	NUM
iajs-2476	214	15	⊆	⊆	NUM
iajs-2476	214	16	q	q	NOUN
iajs-2476	214	17	and	and	CCONJ
iajs-2476	214	18	ϖ	ϖ	X
iajs-2476	214	19	∈	∈	PROPN
iajs-2476	214	20	la	la	PROPN
iajs-2476	214	21	-	-	PUNCT
iajs-2476	214	22	primq(h	primq(h	NOUN
iajs-2476	214	23	)	)	PUNCT
iajs-2476	214	24	.	.	PUNCT
iajs-2476	215	1	thus	thus	ADV
iajs-2476	215	2	ϖ	ϖ	X
iajs-2476	215	3	:	:	SYM
iajs-2476	215	4	1	1	NUM
iajs-2476	215	5	=	=	SYM
iajs-2476	215	6	q	q	X
iajs-2476	215	7	⟹	⟹	X
iajs-2476	215	8	ϑ	ϑ	X
iajs-2476	215	9	:	:	PUNCT
iajs-2476	215	10	1	1	NUM
iajs-2476	215	11	⊆	⊆	NUM
iajs-2476	215	12	ϖ	ϖ	X
iajs-2476	215	13	:	:	PUNCT
iajs-2476	215	14	1	1	NUM
iajs-2476	215	15	⟹	⟹	NUM
iajs-2476	215	16	ϖ	ϖ	PROPN
iajs-2476	215	17	∈	∈	PROPN
iajs-2476	215	18	v(ϑ	v(ϑ	NOUN
iajs-2476	215	19	⟹	⟹	NUM
iajs-2476	215	20	⋃	⋃	VERB
iajs-2476	215	21	q∈v	q∈v	ADJ
iajs-2476	215	22	ϑ	ϑ	NOUN
iajs-2476	215	23	:	:	PUNCT
iajs-2476	215	24	1h	1h	NUM
iajs-2476	215	25	)	)	PUNCT
iajs-2476	215	26	la	la	PROPN
iajs-2476	215	27	-	-	PUNCT
iajs-2476	215	28	primq(h	primq(h	NOUN
iajs-2476	215	29	)	)	PUNCT
iajs-2476	215	30	⊆v(ϑ	⊆v(ϑ	NOUN
iajs-2476	215	31	(	(	PUNCT
iajs-2476	215	32	b	b	NOUN
iajs-2476	215	33	)	)	PUNCT
iajs-2476	215	34	now	now	ADV
iajs-2476	215	35	it	it	PRON
iajs-2476	215	36	follows	follow	VERB
iajs-2476	215	37	from	from	ADP
iajs-2476	215	38	(	(	PUNCT
iajs-2476	215	39	a	a	NOUN
iajs-2476	215	40	)	)	PUNCT
iajs-2476	215	41	and	and	CCONJ
iajs-2476	215	42	(	(	PUNCT
iajs-2476	215	43	b	b	NOUN
iajs-2476	215	44	)	)	PUNCT
iajs-2476	215	45	.	.	PUNCT
iajs-2476	216	1	(	(	PUNCT
iajs-2476	216	2	2	2	X
iajs-2476	216	3	)	)	PUNCT
iajs-2476	216	4	suppose	suppose	VERB
iajs-2476	216	5	that	that	SCONJ
iajs-2476	216	6	q	q	PROPN
iajs-2476	216	7	∈	∈	NOUN
iajs-2476	216	8	v∗(𝛾.	v∗(𝛾.	NOUN
iajs-2476	216	9	1	1	NUM
iajs-2476	216	10	.	.	PUNCT
iajs-2476	217	1	then	then	ADV
iajs-2476	217	2	we	we	PRON
iajs-2476	217	3	have	have	VERB
iajs-2476	217	4	𝛾.	𝛾.	NOUN
iajs-2476	217	5	1	1	NUM
iajs-2476	217	6	⊆	⊆	NUM
iajs-2476	217	7	q	q	NOUN
iajs-2476	217	8	⟹	⟹	X
iajs-2476	217	9	𝛾.	𝛾.	NOUN
iajs-2476	217	10	1	1	NUM
iajs-2476	217	11	:	:	SYM
iajs-2476	217	12	1	1	NUM
iajs-2476	217	13	⊆	⊆	NUM
iajs-2476	217	14	q	q	NOUN
iajs-2476	217	15	:	:	PUNCT
iajs-2476	217	16	1	1	NUM
iajs-2476	217	17	⟹	⟹	NUM
iajs-2476	217	18	q	q	PROPN
iajs-2476	217	19	∈	∈	PROPN
iajs-2476	217	20	v(𝛾.	v(𝛾.	NUM
iajs-2476	217	21	1	1	NUM
iajs-2476	217	22	⟹	⟹	NUM
iajs-2476	217	23	v∗(𝛾.	v∗(𝛾.	ADP
iajs-2476	217	24	1	1	NUM
iajs-2476	217	25	⊆	⊆	NUM
iajs-2476	217	26	v(𝛾.	v(𝛾.	NUM
iajs-2476	217	27	1	1	NUM
iajs-2476	217	28	(	(	PUNCT
iajs-2476	217	29	c	c	X
iajs-2476	217	30	)	)	PUNCT
iajs-2476	217	31	let	let	VERB
iajs-2476	217	32	q	q	PROPN
iajs-2476	217	33	∈	∈	NOUN
iajs-2476	217	34	v(𝛾.	v(𝛾.	X
iajs-2476	217	35	1	1	NUM
iajs-2476	217	36	,	,	PUNCT
iajs-2476	218	1	then	then	ADV
iajs-2476	218	2	𝛾.	𝛾.	ADV
iajs-2476	218	3	1	1	NUM
iajs-2476	218	4	:	:	SYM
iajs-2476	218	5	1	1	NUM
iajs-2476	218	6	⊆	⊆	NUM
iajs-2476	218	7	q	q	NOUN
iajs-2476	218	8	:	:	PUNCT
iajs-2476	218	9	1	1	NUM
iajs-2476	218	10	.	.	PUNCT
iajs-2476	219	1	clearly	clearly	ADV
iajs-2476	219	2	,	,	PUNCT
iajs-2476	219	3	𝛾	𝛾	VERB
iajs-2476	219	4	⊆	⊆	NUM
iajs-2476	219	5	𝛾.	𝛾.	ADV
iajs-2476	219	6	1	1	NUM
iajs-2476	219	7	.	.	PUNCT
iajs-2476	220	1	thus	thus	ADV
iajs-2476	220	2	𝛾	𝛾	ADP
iajs-2476	220	3	⊆	⊆	NUM
iajs-2476	220	4	q	q	NOUN
iajs-2476	220	5	:	:	PUNCT
iajs-2476	220	6	1	1	NUM
iajs-2476	220	7	⟹	⟹	X
iajs-2476	220	8	𝛾.	𝛾.	NOUN
iajs-2476	220	9	1	1	NUM
iajs-2476	220	10	⊆	⊆	NUM
iajs-2476	220	11	q	q	NOUN
iajs-2476	220	12	⟹	⟹	NUM
iajs-2476	220	13	q	q	NOUN
iajs-2476	220	14	∈	∈	PROPN
iajs-2476	220	15	v∗(𝛾.	v∗(𝛾.	NOUN
iajs-2476	220	16	1	1	NUM
iajs-2476	220	17	⟹	⟹	X
iajs-2476	220	18	v(𝛾.	v(𝛾.	NUM
iajs-2476	220	19	1	1	NUM
iajs-2476	220	20	⊆	⊆	NUM
iajs-2476	220	21	v∗(𝛾.	v∗(𝛾.	NOUN
iajs-2476	220	22	1	1	NUM
iajs-2476	220	23	(	(	PUNCT
iajs-2476	220	24	d	d	NOUN
iajs-2476	220	25	)	)	PUNCT
iajs-2476	220	26	then	then	ADV
iajs-2476	220	27	from	from	ADP
iajs-2476	220	28	(	(	PUNCT
iajs-2476	220	29	c	c	NOUN
iajs-2476	220	30	)	)	PUNCT
iajs-2476	220	31	,	,	PUNCT
iajs-2476	220	32	(	(	PUNCT
iajs-2476	220	33	d	d	X
iajs-2476	220	34	)	)	PUNCT
iajs-2476	220	35	the	the	DET
iajs-2476	220	36	outcome	outcome	NOUN
iajs-2476	220	37	 	 	SPACE
iajs-2476	220	38	satisfying	satisfying	ADJ
iajs-2476	220	39	.	.	PUNCT
iajs-2476	221	1	as	as	ADV
iajs-2476	221	2	well	well	ADV
iajs-2476	221	3	,	,	PUNCT
iajs-2476	221	4	via	via	ADP
iajs-2476	221	5	the	the	DET
iajs-2476	221	6	preceding	precede	VERB
iajs-2476	221	7	debate	debate	NOUN
iajs-2476	221	8	instantly	instantly	ADV
iajs-2476	221	9	we	we	PRON
iajs-2476	221	10	get	get	VERB
iajs-2476	221	11	that	that	PRON
iajs-2476	221	12	v	v	NOUN
iajs-2476	221	13	(	(	PUNCT
iajs-2476	221	14	ϑ	ϑ	NOUN
iajs-2476	221	15	:	:	SYM
iajs-2476	221	16	1	1	NUM
iajs-2476	221	17	.	.	SYM
iajs-2476	221	18	1	1	NUM
iajs-2476	221	19	=	=	SYM
iajs-2476	221	20	v∗	v∗	PROPN
iajs-2476	221	21	(	(	PUNCT
iajs-2476	221	22	ϑ	ϑ	NOUN
iajs-2476	221	23	:	:	SYM
iajs-2476	221	24	1	1	NUM
iajs-2476	221	25	.	.	NOUN
iajs-2476	221	26	1	1	NUM
iajs-2476	221	27	)	)	PUNCT
iajs-2476	221	28	.	.	PUNCT
iajs-2476	222	1	now	now	ADV
iajs-2476	222	2	for	for	ADP
iajs-2476	222	3	q	q	PROPN
iajs-2476	222	4	∈	∈	PROPN
iajs-2476	222	5	v(ϑ	v(ϑ	NOUN
iajs-2476	222	6	,	,	PUNCT
iajs-2476	222	7	it	it	PRON
iajs-2476	222	8	deduce	deduce	VERB
iajs-2476	222	9	that	that	SCONJ
iajs-2476	222	10	ϑ	ϑ	VERB
iajs-2476	222	11	:	:	PUNCT
iajs-2476	222	12	1	1	NUM
iajs-2476	222	13	⊆	⊆	NUM
iajs-2476	222	14	q	q	NOUN
iajs-2476	222	15	:	:	PUNCT
iajs-2476	222	16	1	1	X
iajs-2476	222	17	.	.	PUNCT
iajs-2476	223	1	then	then	ADV
iajs-2476	223	2	we	we	PRON
iajs-2476	223	3	get	get	VERB
iajs-2476	223	4	that	that	PRON
iajs-2476	223	5	ϑ	ϑ	VERB
iajs-2476	223	6	:	:	PUNCT
iajs-2476	223	7	1	1	NUM
iajs-2476	223	8	.	.	SYM
iajs-2476	223	9	1	1	NUM
iajs-2476	223	10	⊆	⊆	NUM
iajs-2476	223	11	ϑ	ϑ	NOUN
iajs-2476	223	12	,	,	PUNCT
iajs-2476	223	13	and	and	CCONJ
iajs-2476	223	14	so	so	ADV
iajs-2476	223	15	(	(	PUNCT
iajs-2476	223	16	ϑ	ϑ	NOUN
iajs-2476	223	17	:	:	SYM
iajs-2476	223	18	1	1	NUM
iajs-2476	223	19	.	.	X
iajs-2476	223	20	1	1	NUM
iajs-2476	223	21	:	:	SYM
iajs-2476	223	22	1	1	NUM
iajs-2476	223	23	⊆	⊆	NUM
iajs-2476	223	24	ϑ	ϑ	X
iajs-2476	223	25	:	:	PUNCT
iajs-2476	223	26	1	1	NUM
iajs-2476	223	27	⊆	⊆	NUM
iajs-2476	223	28	q	q	NOUN
iajs-2476	223	29	:	:	PUNCT
iajs-2476	223	30	1	1	NUM
iajs-2476	223	31	⟹	⟹	NUM
iajs-2476	223	32	q	q	PROPN
iajs-2476	223	33	∈	∈	PROPN
iajs-2476	223	34	v	v	NOUN
iajs-2476	223	35	(	(	PUNCT
iajs-2476	223	36	ϑ	ϑ	NOUN
iajs-2476	223	37	:	:	SYM
iajs-2476	223	38	1	1	NUM
iajs-2476	223	39	.	.	SYM
iajs-2476	223	40	1	1	NUM
iajs-2476	223	41	⟹	⟹	NUM
iajs-2476	223	42	v(ϑ	v(ϑ	NOUN
iajs-2476	223	43	⊆	⊆	NUM
iajs-2476	223	44	v	v	NOUN
iajs-2476	223	45	(	(	PUNCT
iajs-2476	223	46	ϑ	ϑ	NOUN
iajs-2476	223	47	:	:	SYM
iajs-2476	223	48	1	1	NUM
iajs-2476	223	49	.	.	SYM
iajs-2476	223	50	1	1	NUM
iajs-2476	223	51	(	(	PUNCT
iajs-2476	223	52	e	e	NOUN
iajs-2476	223	53	)	)	PUNCT
iajs-2476	223	54	let	let	VERB
iajs-2476	223	55	q	q	PROPN
iajs-2476	223	56	∈	∈	PROPN
iajs-2476	223	57	v∗	v∗	PROPN
iajs-2476	223	58	(	(	PUNCT
iajs-2476	223	59	ϑ	ϑ	NOUN
iajs-2476	223	60	:	:	SYM
iajs-2476	223	61	1	1	NUM
iajs-2476	223	62	.	.	NOUN
iajs-2476	223	63	1	1	NUM
iajs-2476	223	64	)	)	PUNCT
iajs-2476	223	65	.	.	PUNCT
iajs-2476	224	1	then	then	ADV
iajs-2476	224	2	ϑ	ϑ	X
iajs-2476	224	3	:	:	PUNCT
iajs-2476	224	4	1	1	NUM
iajs-2476	224	5	.	.	NOUN
iajs-2476	224	6	1	1	NUM
iajs-2476	224	7	)	)	PUNCT
iajs-2476	224	8	⊆	⊆	NUM
iajs-2476	224	9	q	q	NOUN
iajs-2476	224	10	,	,	PUNCT
iajs-2476	224	11	so	so	CCONJ
iajs-2476	224	12	ϑ	ϑ	ADP
iajs-2476	224	13	∶	∶	NOUN
iajs-2476	224	14	1	1	NUM
iajs-2476	224	15	⊆	⊆	NUM
iajs-2476	224	16	q	q	NOUN
iajs-2476	224	17	:	:	PUNCT
iajs-2476	224	18	1	1	NUM
iajs-2476	224	19	.	.	PUNCT
iajs-2476	225	1	thus	thus	ADV
iajs-2476	225	2	q	q	X
iajs-2476	225	3	∈	∈	ADJ
iajs-2476	225	4	v(ϑ	v(ϑ	NOUN
iajs-2476	225	5	and	and	CCONJ
iajs-2476	225	6	  	  	SPACE
iajs-2476	225	7	96	96	NUM
iajs-2476	225	8	ibn	ibn	PROPN
iajs-2476	225	9	al	al	PROPN
iajs-2476	225	10	-	-	PUNCT
iajs-2476	225	11	haitham	haitham	PROPN
iajs-2476	225	12	jour	jour	X
iajs-2476	225	13	.	.	PROPN
iajs-2476	226	1	for	for	ADP
iajs-2476	226	2	pure	pure	ADJ
iajs-2476	226	3	&	&	CCONJ
iajs-2476	226	4	appl	appl	PROPN
iajs-2476	226	5	.	.	PUNCT
iajs-2476	227	1	sci	sci	PROPN
iajs-2476	227	2	.	.	PROPN
iajs-2476	228	1	33	33	NUM
iajs-2476	228	2	(	(	PUNCT
iajs-2476	228	3	3	3	NUM
iajs-2476	228	4	)	)	PUNCT
iajs-2476	228	5	2020	2020	NUM
iajs-2476	228	6	hence	hence	ADV
iajs-2476	228	7	v∗	v∗	PROPN
iajs-2476	228	8	(	(	PUNCT
iajs-2476	228	9	ϑ	ϑ	NOUN
iajs-2476	228	10	:	:	SYM
iajs-2476	228	11	1	1	NUM
iajs-2476	228	12	.	.	NOUN
iajs-2476	228	13	1	1	NUM
iajs-2476	228	14	)	)	PUNCT
iajs-2476	229	1	⊆	⊆	NUM
iajs-2476	229	2	v(ϑ	v(ϑ	NOUN
iajs-2476	229	3	(	(	PUNCT
iajs-2476	229	4	f	f	X
iajs-2476	229	5	)	)	PUNCT
iajs-2476	229	6	consequently	consequently	ADV
iajs-2476	229	7	from	from	ADP
iajs-2476	229	8	(	(	PUNCT
iajs-2476	229	9	e	e	NOUN
iajs-2476	229	10	)	)	PUNCT
iajs-2476	229	11	and	and	CCONJ
iajs-2476	229	12	(	(	PUNCT
iajs-2476	229	13	f	f	X
iajs-2476	229	14	)	)	PUNCT
iajs-2476	229	15	,	,	PUNCT
iajs-2476	229	16	we	we	PRON
iajs-2476	229	17	get	get	VERB
iajs-2476	229	18	that	that	DET
iajs-2476	229	19	v∗	v∗	NOUN
iajs-2476	229	20	(	(	PUNCT
iajs-2476	229	21	ϑ	ϑ	NOUN
iajs-2476	229	22	:	:	SYM
iajs-2476	229	23	1	1	NUM
iajs-2476	229	24	.	.	NOUN
iajs-2476	229	25	1	1	NUM
iajs-2476	229	26	)	)	PUNCT
iajs-2476	229	27	⊆	⊆	NUM
iajs-2476	229	28	v(ϑ	v(ϑ	NOUN
iajs-2476	229	29	⊆	⊆	NUM
iajs-2476	229	30	v	v	NOUN
iajs-2476	229	31	(	(	PUNCT
iajs-2476	229	32	ϑ	ϑ	NOUN
iajs-2476	229	33	:	:	PUNCT
iajs-2476	229	34	1	1	NUM
iajs-2476	229	35	.	.	SYM
iajs-2476	229	36	1	1	NUM
iajs-2476	229	37	.	.	PUNCT
iajs-2476	230	1	thus	thus	ADV
iajs-2476	230	2	v(ϑ	v(ϑ	PROPN
iajs-2476	230	3	=	=	SYM
iajs-2476	230	4	v∗	v∗	PROPN
iajs-2476	230	5	(	(	PUNCT
iajs-2476	230	6	ϑ	ϑ	NOUN
iajs-2476	230	7	:	:	SYM
iajs-2476	230	8	1	1	NUM
iajs-2476	230	9	.	.	NOUN
iajs-2476	230	10	1	1	NUM
iajs-2476	230	11	)	)	PUNCT
iajs-2476	230	12	=	=	SYM
iajs-2476	230	13	v	v	NOUN
iajs-2476	230	14	(	(	PUNCT
iajs-2476	230	15	ϑ	ϑ	NOUN
iajs-2476	230	16	:	:	SYM
iajs-2476	230	17	1	1	NUM
iajs-2476	230	18	.	.	SYM
iajs-2476	230	19	1	1	NUM
iajs-2476	230	20	.	.	PUNCT
iajs-2476	230	21	note	note	VERB
iajs-2476	230	22	that	that	SCONJ
iajs-2476	230	23	from	from	ADP
iajs-2476	230	24	proposition	proposition	NOUN
iajs-2476	230	25	3.4	3.4	NUM
iajs-2476	230	26	we	we	PRON
iajs-2476	230	27	get	get	VERB
iajs-2476	230	28	that	that	PRON
iajs-2476	230	29	la-𝜀	la-𝜀	PROPN
iajs-2476	230	30	(	(	PUNCT
iajs-2476	230	31	h)=la	h)=la	NOUN
iajs-2476	230	32	-	-	PUNCT
iajs-2476	230	33	ε	ε	NOUN
iajs-2476	230	34	,	,	PUNCT
iajs-2476	230	35	(	(	PUNCT
iajs-2476	230	36	h	h	NOUN
iajs-2476	230	37	)	)	PUNCT
iajs-2476	230	38	⊆	⊆	NUM
iajs-2476	230	39	la	la	PROPN
iajs-2476	230	40	-	-	PUNCT
iajs-2476	230	41	ε∗(h	ε∗(h	PROPN
iajs-2476	230	42	)	)	PUNCT
iajs-2476	230	43	.	.	PUNCT
iajs-2476	231	1	example	example	NOUN
iajs-2476	231	2	3.5	3.5	NUM
iajs-2476	231	3	(	(	PUNCT
iajs-2476	231	4	1	1	NUM
iajs-2476	231	5	)	)	PUNCT
iajs-2476	231	6	let	let	VERB
iajs-2476	231	7	h	h	NOUN
iajs-2476	231	8	=	=	SYM
iajs-2476	231	9	ℤ	ℤ	PROPN
iajs-2476	231	10	as	as	ADP
iajs-2476	231	11	ℤ-module	ℤ-module	PROPN
iajs-2476	231	12	and	and	CCONJ
iajs-2476	231	13	suppose	suppose	VERB
iajs-2476	231	14	that	that	SCONJ
iajs-2476	231	15	la	la	PROPN
iajs-2476	231	16	is	be	AUX
iajs-2476	231	17	an	an	DET
iajs-2476	231	18	arbitrary	arbitrary	ADJ
iajs-2476	231	19	lattice	lattice	NOUN
iajs-2476	231	20	.	.	PUNCT
iajs-2476	232	1	let	let	VERB
iajs-2476	232	2	q	q	PROPN
iajs-2476	232	3	∈	∈	PROPN
iajs-2476	232	4	ℤ	ℤ	PROPN
iajs-2476	232	5	is	be	AUX
iajs-2476	232	6	prime	prime	ADJ
iajs-2476	232	7	.	.	PUNCT
iajs-2476	233	1	for	for	ADP
iajs-2476	233	2	each	each	DET
iajs-2476	233	3	prime	prime	ADJ
iajs-2476	233	4	element	element	NOUN
iajs-2476	233	5	s	s	PART
iajs-2476	233	6	∈	∈	PROPN
iajs-2476	233	7	la	la	NOUN
iajs-2476	233	8	,	,	PUNCT
iajs-2476	233	9	define	define	VERB
iajs-2476	233	10	t(s	t(s	PROPN
iajs-2476	233	11	)	)	PUNCT
iajs-2476	233	12	∈	∈	PROPN
iajs-2476	233	13	la(ℤ	la(ℤ	PROPN
iajs-2476	233	14	)	)	PUNCT
iajs-2476	233	15	by	by	ADP
iajs-2476	233	16	t(s)(y)=	t(s)(y)=	NOUN
iajs-2476	233	17	1	1	NUM
iajs-2476	233	18	𝑖𝑓	𝑖𝑓	ADP
iajs-2476	233	19	𝑦	𝑦	NUM
iajs-2476	233	20	∈	∈	PROPN
iajs-2476	233	21	〈	〈	PROPN
iajs-2476	233	22	q	q	NOUN
iajs-2476	233	23	〉	〉	NOUN
iajs-2476	233	24	;	;	PUNCT
iajs-2476	233	25	𝑠	𝑠	PROPN
iajs-2476	233	26	𝑖𝑓	𝑖𝑓	ADP
iajs-2476	233	27	𝑦	𝑦	NUM
iajs-2476	233	28	∈	∈	PROPN
iajs-2476	233	29	ℤ\〈q	ℤ\〈q	X
iajs-2476	233	30	〉	〉	NOUN
iajs-2476	233	31	then	then	ADV
iajs-2476	233	32	by	by	ADP
iajs-2476	233	33	theorem	theorem	ADJ
iajs-2476	233	34	2.10	2.10	NUM
iajs-2476	233	35	,	,	PUNCT
iajs-2476	233	36	t(s	t(s	PROPN
iajs-2476	233	37	)	)	PUNCT
iajs-2476	233	38	is	be	AUX
iajs-2476	233	39	a	a	DET
iajs-2476	233	40	primary	primary	ADJ
iajs-2476	233	41	la	la	NOUN
iajs-2476	233	42	-	-	PUNCT
iajs-2476	233	43	submodule	submodule	NOUN
iajs-2476	233	44	of	of	ADP
iajs-2476	233	45	h	h	PROPN
iajs-2476	233	46	.	.	PUNCT
iajs-2476	234	1	therefore	therefore	ADV
iajs-2476	234	2	laprim(h)={t(s)|s	laprim(h)={t(s)|s	PROPN
iajs-2476	234	3	is	be	AUX
iajs-2476	234	4	a	a	DET
iajs-2476	234	5	prime	prime	ADJ
iajs-2476	234	6	element	element	NOUN
iajs-2476	234	7	of	of	ADP
iajs-2476	234	8	la	la	NOUN
iajs-2476	234	9	while	while	SCONJ
iajs-2476	234	10	q	q	NOUN
iajs-2476	234	11	is	be	AUX
iajs-2476	234	12	prime	prime	ADJ
iajs-2476	234	13	element	element	NOUN
iajs-2476	234	14	of	of	ADP
iajs-2476	234	15	ℤ	ℤ	PROPN
iajs-2476	234	16	}	}	PUNCT
iajs-2476	234	17	,	,	PUNCT
iajs-2476	234	18	and	and	CCONJ
iajs-2476	234	19	for	for	ADP
iajs-2476	234	20	la	la	NOUN
iajs-2476	234	21	=	=	PUNCT
iajs-2476	235	1	[	[	X
iajs-2476	235	2	0	0	NUM
iajs-2476	235	3	,	,	PUNCT
iajs-2476	235	4	1	1	NUM
iajs-2476	235	5	]	]	PUNCT
iajs-2476	235	6	,	,	PUNCT
iajs-2476	235	7	then	then	ADV
iajs-2476	235	8	la	la	PROPN
iajs-2476	235	9	-	-	PUNCT
iajs-2476	235	10	prim(h	prim(h	NOUN
iajs-2476	235	11	)	)	PUNCT
iajs-2476	235	12	=	=	SYM
iajs-2476	235	13	{	{	PUNCT
iajs-2476	235	14	t(s)|s	t(s)|s	NOUN
iajs-2476	235	15	∈	∈	PROPN
iajs-2476	236	1	[	[	X
iajs-2476	236	2	0	0	NUM
iajs-2476	236	3	,	,	PUNCT
iajs-2476	236	4	1	1	NUM
iajs-2476	236	5	]	]	PUNCT
iajs-2476	236	6	while	while	SCONJ
iajs-2476	236	7	q	q	NOUN
iajs-2476	236	8	is	be	AUX
iajs-2476	236	9	prime	prime	ADJ
iajs-2476	236	10	element	element	NOUN
iajs-2476	236	11	of	of	ADP
iajs-2476	236	12	ℤ	ℤ	PROPN
iajs-2476	236	13	}	}	PUNCT
iajs-2476	236	14	.	.	PUNCT
iajs-2476	237	1	(	(	PUNCT
iajs-2476	237	2	2	2	X
iajs-2476	237	3	)	)	PUNCT
iajs-2476	237	4	let	let	VERB
iajs-2476	237	5	h	h	NOUN
iajs-2476	237	6	=	=	PUNCT
iajs-2476	237	7	ℝ[x	ℝ[x	X
iajs-2476	237	8	]	]	X
iajs-2476	237	9	as	as	ADP
iajs-2476	237	10	ℝ	ℝ	PROPN
iajs-2476	237	11	[	[	X
iajs-2476	237	12	x]−module	x]−module	PROPN
iajs-2476	237	13	,	,	PUNCT
iajs-2476	237	14	where	where	SCONJ
iajs-2476	237	15	ℝ	ℝ	PROPN
iajs-2476	237	16	is	be	AUX
iajs-2476	237	17	the	the	DET
iajs-2476	237	18	field	field	NOUN
iajs-2476	237	19	of	of	ADP
iajs-2476	237	20	real	real	ADJ
iajs-2476	237	21	numbers	number	NOUN
iajs-2476	237	22	.	.	PUNCT
iajs-2476	238	1	for	for	ADP
iajs-2476	238	2	each	each	DET
iajs-2476	238	3	t	t	NOUN
iajs-2476	238	4	∈	∈	NOUN
iajs-2476	238	5	ℝ	ℝ	PROPN
iajs-2476	238	6	[	[	X
iajs-2476	238	7	x	x	X
iajs-2476	238	8	]	]	X
iajs-2476	238	9	while	while	SCONJ
iajs-2476	238	10	each	each	DET
iajs-2476	238	11	s	s	PROPN
iajs-2476	238	12	∈	∈	PROPN
iajs-2476	238	13	la	la	NOUN
iajs-2476	238	14	,	,	PUNCT
iajs-2476	238	15	defined	define	VERB
iajs-2476	238	16	the	the	DET
iajs-2476	238	17	fuzzy	fuzzy	ADJ
iajs-2476	238	18	subset	subset	VERB
iajs-2476	238	19	t(s	t(s	PROPN
iajs-2476	238	20	)	)	PUNCT
iajs-2476	238	21	of	of	ADP
iajs-2476	238	22	ℝ	ℝ	PROPN
iajs-2476	238	23	[	[	X
iajs-2476	238	24	x	x	X
iajs-2476	238	25	]	]	X
iajs-2476	238	26	via	via	ADP
iajs-2476	238	27	t(s)(y)=	t(s)(y)=	NOUN
iajs-2476	238	28	1	1	NUM
iajs-2476	238	29	𝑦	𝑦	NUM
iajs-2476	238	30	∈	∈	NOUN
iajs-2476	238	31	〈	〈	NOUN
iajs-2476	238	32	q	q	NOUN
iajs-2476	238	33	〉	〉	NOUN
iajs-2476	238	34	;	;	PUNCT
iajs-2476	238	35	𝑠	𝑠	PROPN
iajs-2476	238	36	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	VERB
iajs-2476	238	37	then	then	ADV
iajs-2476	238	38	by	by	ADP
iajs-2476	238	39	theorem	theorem	NOUN
iajs-2476	238	40	2.10	2.10	NUM
iajs-2476	238	41	,	,	PUNCT
iajs-2476	238	42	t(s	t(s	PROPN
iajs-2476	238	43	)	)	PUNCT
iajs-2476	238	44	primary	primary	ADJ
iajs-2476	238	45	la	la	PROPN
iajs-2476	238	46	-	-	PUNCT
iajs-2476	238	47	submodule	submodule	NOUN
iajs-2476	238	48	of	of	ADP
iajs-2476	238	49	h	h	NOUN
iajs-2476	238	50	if	if	SCONJ
iajs-2476	238	51	and	and	CCONJ
iajs-2476	238	52	only	only	ADV
iajs-2476	238	53	if	if	SCONJ
iajs-2476	238	54	t	t	PROPN
iajs-2476	238	55	is	be	AUX
iajs-2476	238	56	irreducible	irreducible	ADJ
iajs-2476	238	57	and	and	CCONJ
iajs-2476	238	58	s	s	NOUN
iajs-2476	238	59	is	be	AUX
iajs-2476	238	60	a	a	DET
iajs-2476	238	61	prime	prime	ADJ
iajs-2476	238	62	element	element	NOUN
iajs-2476	238	63	of	of	ADP
iajs-2476	238	64	la	la	PROPN
iajs-2476	238	65	.	.	PUNCT
iajs-2476	238	66	further	far	ADV
iajs-2476	238	67	,	,	PUNCT
iajs-2476	238	68	for	for	ADP
iajs-2476	238	69	la=[0,1	la=[0,1	NOUN
iajs-2476	238	70	]	]	PUNCT
iajs-2476	238	71	,	,	PUNCT
iajs-2476	238	72	we	we	PRON
iajs-2476	238	73	have	have	VERB
iajs-2476	238	74	la	la	ADJ
iajs-2476	238	75	-	-	PUNCT
iajs-2476	238	76	prim(h)=	prim(h)=	NOUN
iajs-2476	238	77	{	{	PUNCT
iajs-2476	238	78	t(s)|q	t(s)|q	PROPN
iajs-2476	238	79	is	be	AUX
iajs-2476	238	80	irreducible	irreducible	ADJ
iajs-2476	238	81	in	in	ADP
iajs-2476	238	82	ℝ	ℝ	PROPN
iajs-2476	238	83	[	[	X
iajs-2476	238	84	y	y	X
iajs-2476	238	85	]	]	PUNCT
iajs-2476	238	86	,	,	PUNCT
iajs-2476	238	87	s	s	NOUN
iajs-2476	238	88	∈	∈	PROPN
iajs-2476	239	1	[	[	X
iajs-2476	239	2	0	0	NUM
iajs-2476	239	3	,	,	PUNCT
iajs-2476	239	4	1	1	NUM
iajs-2476	239	5	]	]	PUNCT
iajs-2476	239	6	}	}	PUNCT
iajs-2476	239	7	.	.	PUNCT
iajs-2476	240	1	(	(	PUNCT
iajs-2476	240	2	3	3	X
iajs-2476	240	3	)	)	PUNCT
iajs-2476	240	4	let	let	VERB
iajs-2476	240	5	h	h	NOUN
iajs-2476	240	6	be	be	AUX
iajs-2476	240	7	an	an	DET
iajs-2476	240	8	arbitrary	arbitrary	ADJ
iajs-2476	240	9	f	f	NOUN
iajs-2476	240	10	-	-	PUNCT
iajs-2476	240	11	module	module	NOUN
iajs-2476	240	12	and	and	CCONJ
iajs-2476	240	13	t	t	NOUN
iajs-2476	240	14	is	be	AUX
iajs-2476	240	15	a	a	DET
iajs-2476	240	16	prime	prime	ADJ
iajs-2476	240	17	submodule	submodule	NOUN
iajs-2476	240	18	of	of	ADP
iajs-2476	240	19	h	h	PROPN
iajs-2476	240	20	.	.	PUNCT
iajs-2476	241	1	for	for	ADP
iajs-2476	241	2	each	each	DET
iajs-2476	241	3	s	s	X
iajs-2476	241	4	∈	∈	PROPN
iajs-2476	241	5	la	la	NOUN
iajs-2476	241	6	,	,	PUNCT
iajs-2476	241	7	define	define	VERB
iajs-2476	241	8	t(s)(y)=	t(s)(y)=	NOUN
iajs-2476	241	9	1	1	NUM
iajs-2476	241	10	𝑦	𝑦	NOUN
iajs-2476	241	11	∈	∈	NOUN
iajs-2476	241	12	t	t	NOUN
iajs-2476	241	13	;	;	PUNCT
iajs-2476	241	14	𝑠	𝑠	PROPN
iajs-2476	241	15	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	VERB
iajs-2476	241	16	then	then	ADV
iajs-2476	241	17	via	via	ADP
iajs-2476	241	18	theorem	theorem	ADJ
iajs-2476	241	19	2.10	2.10	NUM
iajs-2476	241	20	,	,	PUNCT
iajs-2476	241	21	t(s	t(s	PROPN
iajs-2476	241	22	)	)	PUNCT
iajs-2476	241	23	is	be	AUX
iajs-2476	241	24	a	a	DET
iajs-2476	241	25	primary	primary	ADJ
iajs-2476	241	26	la	la	NOUN
iajs-2476	241	27	-	-	PUNCT
iajs-2476	241	28	submodule	submodule	NOUN
iajs-2476	241	29	of	of	ADP
iajs-2476	241	30	h	h	NOUN
iajs-2476	241	31	if	if	SCONJ
iajs-2476	242	1	and	and	CCONJ
iajs-2476	242	2	only	only	ADV
iajs-2476	242	3	if	if	SCONJ
iajs-2476	242	4	s	s	NOUN
iajs-2476	242	5	is	be	AUX
iajs-2476	242	6	a	a	DET
iajs-2476	242	7	prime	prime	ADJ
iajs-2476	242	8	element	element	NOUN
iajs-2476	242	9	of	of	ADP
iajs-2476	242	10	la	la	PROPN
iajs-2476	242	11	.	.	PUNCT
iajs-2476	243	1	if	if	SCONJ
iajs-2476	243	2	spec(la	spec(la	NOUN
iajs-2476	243	3	)	)	PUNCT
iajs-2476	243	4	indicate	indicate	VERB
iajs-2476	243	5	the	the	DET
iajs-2476	243	6	collection	collection	NOUN
iajs-2476	243	7	of	of	ADP
iajs-2476	243	8	all	all	DET
iajs-2476	243	9	prime	prime	ADJ
iajs-2476	243	10	elements	element	NOUN
iajs-2476	243	11	of	of	ADP
iajs-2476	243	12	la	la	X
iajs-2476	243	13	,	,	PUNCT
iajs-2476	243	14	then	then	ADV
iajs-2476	243	15	laprim(h)={t(s)|s	laprim(h)={t(s)|s	VERB
iajs-2476	243	16	∈	∈	PROPN
iajs-2476	243	17	spec(la	spec(la	NOUN
iajs-2476	243	18	)	)	PUNCT
iajs-2476	243	19	and	and	CCONJ
iajs-2476	243	20	t	t	PROPN
iajs-2476	243	21	be	be	AUX
iajs-2476	243	22	a	a	DET
iajs-2476	243	23	primary	primary	ADJ
iajs-2476	243	24	submodule	submodule	NOUN
iajs-2476	243	25	of	of	ADP
iajs-2476	243	26	h	h	NOUN
iajs-2476	243	27	}	}	PUNCT
iajs-2476	243	28	.	.	PUNCT
iajs-2476	244	1	(	(	PUNCT
iajs-2476	244	2	4	4	X
iajs-2476	244	3	)	)	PUNCT
iajs-2476	244	4	if	if	SCONJ
iajs-2476	244	5	we	we	PRON
iajs-2476	244	6	let	let	VERB
iajs-2476	244	7	h=	h=	PRON
iajs-2476	244	8	ℝ	ℝ	PROPN
iajs-2476	245	1	[	[	X
iajs-2476	245	2	y	y	X
iajs-2476	245	3	]	]	X
iajs-2476	245	4	as	as	ADP
iajs-2476	245	5	ℝ-module	ℝ-module	PROPN
iajs-2476	245	6	.	.	PUNCT
iajs-2476	246	1	then	then	ADV
iajs-2476	246	2	all	all	DET
iajs-2476	246	3	proper	proper	ADJ
iajs-2476	246	4	submodulest	submodulest	NOUN
iajs-2476	246	5	of	of	ADP
iajs-2476	246	6	h	h	NOUN
iajs-2476	246	7	,	,	PUNCT
iajs-2476	246	8	are	be	AUX
iajs-2476	246	9	indicated	indicate	VERB
iajs-2476	246	10	via	via	ADP
iajs-2476	246	11	t	t	PROPN
iajs-2476	246	12	<	<	X
iajs-2476	246	13	h	h	NOUN
iajs-2476	246	14	,	,	PUNCT
iajs-2476	246	15	is	be	AUX
iajs-2476	246	16	primary	primary	ADJ
iajs-2476	246	17	.	.	PUNCT
iajs-2476	247	1	then	then	ADV
iajs-2476	247	2	by	by	ADP
iajs-2476	247	3	part	part	NOUN
iajs-2476	247	4	(	(	PUNCT
iajs-2476	247	5	3	3	NUM
iajs-2476	247	6	)	)	PUNCT
iajs-2476	247	7	la	la	PROPN
iajs-2476	247	8	-	-	PUNCT
iajs-2476	247	9	prim(h)=	prim(h)=	NOUN
iajs-2476	247	10	{	{	PUNCT
iajs-2476	247	11	t(s)|	t(s)|	NOUN
iajs-2476	247	12	s	s	NOUN
iajs-2476	247	13	∈	∈	NOUN
iajs-2476	247	14	spec(la	spec(la	NOUN
iajs-2476	247	15	)	)	PUNCT
iajs-2476	247	16	and	and	CCONJ
iajs-2476	247	17	t	t	X
iajs-2476	247	18	<	<	X
iajs-2476	247	19	h	h	X
iajs-2476	247	20	}	}	PUNCT
iajs-2476	247	21	.	.	PUNCT
iajs-2476	248	1	(	(	PUNCT
iajs-2476	248	2	5	5	X
iajs-2476	248	3	)	)	PUNCT
iajs-2476	248	4	let	let	VERB
iajs-2476	248	5	la={0	la={0	PRON
iajs-2476	248	6	,	,	PUNCT
iajs-2476	248	7	x	x	X
iajs-2476	248	8	,	,	PUNCT
iajs-2476	248	9	y	y	PROPN
iajs-2476	248	10	,	,	PUNCT
iajs-2476	248	11	1	1	NUM
iajs-2476	248	12	}	}	PUNCT
iajs-2476	248	13	is	be	AUX
iajs-2476	248	14	a	a	DET
iajs-2476	248	15	lattice	lattice	NOUN
iajs-2476	248	16	which	which	PRON
iajs-2476	248	17	is	be	AUX
iajs-2476	248	18	not	not	PART
iajs-2476	248	19	a	a	DET
iajs-2476	248	20	chain	chain	NOUN
iajs-2476	248	21	,	,	PUNCT
iajs-2476	248	22	that	that	ADV
iajs-2476	248	23	is	is	ADV
iajs-2476	248	24	x	x	PUNCT
iajs-2476	248	25	and	and	CCONJ
iajs-2476	248	26	y	y	PROPN
iajs-2476	248	27	are	be	AUX
iajs-2476	248	28	not	not	PART
iajs-2476	248	29	similar	similar	ADJ
iajs-2476	248	30	.	.	PUNCT
iajs-2476	249	1	then	then	ADV
iajs-2476	249	2	la	la	PROPN
iajs-2476	249	3	-	-	PUNCT
iajs-2476	249	4	prim(h)=∅	prim(h)=∅	PROPN
iajs-2476	249	5	,	,	PUNCT
iajs-2476	249	6	for	for	ADP
iajs-2476	249	7	each	each	DET
iajs-2476	249	8	f	f	NOUN
iajs-2476	249	9	-	-	PUNCT
iajs-2476	249	10	module	module	NOUN
iajs-2476	249	11	h	h	NOUN
iajs-2476	249	12	,	,	PUNCT
iajs-2476	249	13	since	since	SCONJ
iajs-2476	249	14	la	la	NOUN
iajs-2476	249	15	has	have	VERB
iajs-2476	249	16	not	not	PART
iajs-2476	249	17	any	any	DET
iajs-2476	249	18	prime	prime	ADJ
iajs-2476	249	19	element	element	NOUN
iajs-2476	249	20	.	.	PUNCT
iajs-2476	250	1	this	this	DET
iajs-2476	250	2	example	example	NOUN
iajs-2476	250	3	display	display	NOUN
iajs-2476	250	4	that	that	SCONJ
iajs-2476	250	5	la	la	PROPN
iajs-2476	250	6	-	-	PUNCT
iajs-2476	250	7	prim(h)=∅	prim(h)=∅	PROPN
iajs-2476	250	8	,	,	PUNCT
iajs-2476	250	9	but	but	CCONJ
iajs-2476	250	10	prim(h	prim(h	ADP
iajs-2476	250	11	)	)	PUNCT
iajs-2476	250	12	may	may	AUX
iajs-2476	250	13	be	be	AUX
iajs-2476	250	14	non	non	ADJ
iajs-2476	250	15	-	-	ADJ
iajs-2476	250	16	empty	empty	ADJ
iajs-2476	250	17	.	.	PUNCT
iajs-2476	251	1	4	4	NUM
iajs-2476	251	2	.the	.the	NOUN
iajs-2476	251	3	relation	relation	PROPN
iajs-2476	251	4	b	b	X
iajs-2476	251	5	etween	etween	VERB
iajs-2476	251	6	la	la	NOUN
iajs-2476	251	7	-	-	PUNCT
iajs-2476	251	8	prim(h	prim(h	NOUN
iajs-2476	251	9	)	)	PUNCT
iajs-2476	251	10	and	and	CCONJ
iajs-2476	251	11	la	la	ADJ
iajs-2476	251	12	-	-	PUNCT
iajs-2476	251	13	prim(𝐅	prim(𝐅	PROPN
iajs-2476	251	14	/	/	SYM
iajs-2476	251	15	ann(h	ann(h	PROPN
iajs-2476	251	16	)	)	PUNCT
iajs-2476	251	17	)	)	PUNCT
iajs-2476	251	18	suppose	suppose	VERB
iajs-2476	251	19	that	that	SCONJ
iajs-2476	251	20	ϑ	ϑ	PROPN
iajs-2476	251	21	is	be	AUX
iajs-2476	251	22	a	a	DET
iajs-2476	251	23	primary	primary	ADJ
iajs-2476	251	24	la	la	NOUN
iajs-2476	251	25	-	-	PUNCT
iajs-2476	251	26	submodule	submodule	NOUN
iajs-2476	251	27	of	of	ADP
iajs-2476	251	28	h	h	PROPN
iajs-2476	251	29	.	.	PUNCT
iajs-2476	252	1	then	then	ADV
iajs-2476	252	2	by	by	ADP
iajs-2476	252	3	corollary	corollary	NOUN
iajs-2476	252	4	2.11	2.11	NUM
iajs-2476	252	5	we	we	PRON
iajs-2476	252	6	have	have	AUX
iajs-2476	252	7	(	(	PUNCT
iajs-2476	252	8	ϑ	ϑ	X
iajs-2476	252	9	:	:	PUNCT
iajs-2476	252	10	1h	1h	NUM
iajs-2476	252	11	)	)	PUNCT
iajs-2476	252	12	be	be	AUX
iajs-2476	252	13	a	a	DET
iajs-2476	252	14	primary	primary	ADJ
iajs-2476	252	15	la	la	NOUN
iajs-2476	252	16	-	-	PUNCT
iajs-2476	252	17	ideal	ideal	NOUN
iajs-2476	252	18	of	of	ADP
iajs-2476	252	19	f.	f.	PROPN
iajs-2476	252	20	let	let	VERB
iajs-2476	252	21	the	the	DET
iajs-2476	252	22	quotient	quotient	NOUN
iajs-2476	252	23	ring	ring	NOUN
iajs-2476	252	24	f/	f/	ADV
iajs-2476	252	25	ann(h	ann(h	PROPN
iajs-2476	252	26	)	)	PUNCT
iajs-2476	252	27	.	.	PUNCT
iajs-2476	253	1	we	we	PRON
iajs-2476	253	2	indicate	indicate	VERB
iajs-2476	253	3	a	a	DET
iajs-2476	253	4	typical	typical	ADJ
iajs-2476	253	5	element	element	NOUN
iajs-2476	253	6	of	of	ADP
iajs-2476	253	7	f/	f/	NUM
iajs-2476	253	8	ann(h	ann(h	PROPN
iajs-2476	253	9	)	)	PUNCT
iajs-2476	253	10	by	by	ADP
iajs-2476	253	11	[	[	X
iajs-2476	253	12	y	y	X
iajs-2476	253	13	]	]	X
iajs-2476	253	14	,	,	PUNCT
iajs-2476	253	15	where	where	SCONJ
iajs-2476	253	16	y	y	PROPN
iajs-2476	253	17	∈	∈	PROPN
iajs-2476	253	18	f.	f.	PROPN
iajs-2476	253	19	consider	consider	VERB
iajs-2476	253	20	the	the	DET
iajs-2476	253	21	quotient	quotient	NOUN
iajs-2476	253	22	map	map	VERB
iajs-2476	253	23	𝜌:f	𝜌:f	NOUN
iajs-2476	253	24	→	→	PUNCT
iajs-2476	253	25	f	f	PROPN
iajs-2476	253	26	/	/	SYM
iajs-2476	253	27	ann(h	ann(h	PROPN
iajs-2476	253	28	)	)	PUNCT
iajs-2476	253	29	,	,	PUNCT
iajs-2476	253	30	is	be	AUX
iajs-2476	253	31	defined	define	VERB
iajs-2476	253	32	via	via	ADP
iajs-2476	253	33	𝜌(y)=	𝜌(y)=	PROPN
iajs-2476	253	34	[	[	X
iajs-2476	253	35	y	y	X
iajs-2476	253	36	]	]	PUNCT
iajs-2476	253	37	,	,	PUNCT
iajs-2476	253	38	we	we	PRON
iajs-2476	253	39	indicate	indicate	VERB
iajs-2476	253	40	the	the	DET
iajs-2476	253	41	image	image	NOUN
iajs-2476	253	42	of	of	ADP
iajs-2476	253	43	ϑ	ϑ	X
iajs-2476	253	44	:	:	PUNCT
iajs-2476	253	45	1h	1h	NUM
iajs-2476	253	46	beneath	beneath	ADP
iajs-2476	253	47	𝜌	𝜌	PRON
iajs-2476	253	48	by	by	ADP
iajs-2476	253	49	(	(	PUNCT
iajs-2476	253	50	ϑ	ϑ	NOUN
iajs-2476	253	51	:	:	SYM
iajs-2476	253	52	1	1	NUM
iajs-2476	253	53	)	)	PUNCT
iajs-2476	253	54	.	.	PUNCT
iajs-2476	254	1	in	in	ADP
iajs-2476	254	2	fact	fact	NOUN
iajs-2476	254	3	,	,	PUNCT
iajs-2476	254	4	(	(	PUNCT
iajs-2476	254	5	ϑ	ϑ	X
iajs-2476	254	6	:	:	SYM
iajs-2476	254	7	1	1	NUM
iajs-2476	254	8	)	)	PUNCT
iajs-2476	254	9	(	(	PUNCT
iajs-2476	255	1	[	[	X
iajs-2476	255	2	y	y	X
iajs-2476	255	3	]	]	X
iajs-2476	255	4	)	)	PUNCT
iajs-2476	255	5	  	  	SPACE
iajs-2476	255	6	97	97	NUM
iajs-2476	255	7	ibn	ibn	PROPN
iajs-2476	255	8	al	al	PROPN
iajs-2476	255	9	-	-	PUNCT
iajs-2476	255	10	haitham	haitham	PROPN
iajs-2476	255	11	jour	jour	X
iajs-2476	255	12	.	.	PROPN
iajs-2476	256	1	for	for	ADP
iajs-2476	256	2	pure	pure	ADJ
iajs-2476	256	3	&	&	CCONJ
iajs-2476	256	4	appl	appl	PROPN
iajs-2476	256	5	.	.	PUNCT
iajs-2476	257	1	sci	sci	PROPN
iajs-2476	257	2	.	.	PROPN
iajs-2476	258	1	33	33	NUM
iajs-2476	258	2	(	(	PUNCT
iajs-2476	258	3	3	3	NUM
iajs-2476	258	4	)	)	PUNCT
iajs-2476	258	5	2020	2020	NUM
iajs-2476	259	1	=	=	SYM
iajs-2476	259	2	⋁	⋁	ADP
iajs-2476	259	3	ϑ	ϑ	VERB
iajs-2476	259	4	:	:	PUNCT
iajs-2476	259	5	1	1	NUM
iajs-2476	259	6	a	a	DET
iajs-2476	259	7	|a	|a	NOUN
iajs-2476	259	8	∈	∈	PROPN
iajs-2476	259	9	y	y	PROPN
iajs-2476	259	10	.	.	PUNCT
iajs-2476	260	1	proposition	proposition	NOUN
iajs-2476	260	2	4.1	4.1	NUM
iajs-2476	260	3	suppose	suppose	VERB
iajs-2476	260	4	that	that	SCONJ
iajs-2476	260	5	ϑ	ϑ	PROPN
iajs-2476	260	6	∈	∈	PROPN
iajs-2476	260	7	lah	lah	PROPN
iajs-2476	260	8	.	.	PUNCT
iajs-2476	261	1	then	then	ADV
iajs-2476	261	2	(	(	PUNCT
iajs-2476	261	3	ϑ	ϑ	NOUN
iajs-2476	261	4	:	:	SYM
iajs-2476	261	5	1	1	NUM
iajs-2476	261	6	)	)	PUNCT
iajs-2476	261	7	is	be	AUX
iajs-2476	261	8	a	a	DET
iajs-2476	261	9	primary	primary	ADJ
iajs-2476	261	10	la	la	NOUN
iajs-2476	261	11	-	-	PUNCT
iajs-2476	261	12	ideal	ideal	NOUN
iajs-2476	261	13	of	of	ADP
iajs-2476	261	14	f/	f/	NUM
iajs-2476	261	15	ann(h	ann(h	PROPN
iajs-2476	261	16	)	)	PUNCT
iajs-2476	261	17	.	.	PUNCT
iajs-2476	262	1	proof	proof	NOUN
iajs-2476	262	2	the	the	DET
iajs-2476	262	3	quotient	quotient	NOUN
iajs-2476	262	4	function	function	NOUN
iajs-2476	262	5	𝜌	𝜌	PROPN
iajs-2476	262	6	is	be	AUX
iajs-2476	262	7	epimorphism	epimorphism	NOUN
iajs-2476	262	8	,	,	PUNCT
iajs-2476	262	9	it	it	PRON
iajs-2476	262	10	is	be	AUX
iajs-2476	262	11	facile	facile	ADJ
iajs-2476	262	12	to	to	PART
iajs-2476	262	13	prove	prove	VERB
iajs-2476	262	14	that	that	SCONJ
iajs-2476	262	15	the	the	DET
iajs-2476	262	16	(	(	PUNCT
iajs-2476	262	17	ϑ	ϑ	X
iajs-2476	262	18	:	:	PUNCT
iajs-2476	262	19	1h	1h	NUM
iajs-2476	262	20	)	)	PUNCT
iajs-2476	262	21	is	be	AUX
iajs-2476	262	22	𝜌invariant	𝜌invariant	ADJ
iajs-2476	262	23	.	.	PUNCT
iajs-2476	263	1	then	then	ADV
iajs-2476	263	2	via	via	ADP
iajs-2476	263	3	proposition	proposition	NOUN
iajs-2476	263	4	2.3	2.3	NUM
iajs-2476	263	5	,	,	PUNCT
iajs-2476	263	6	(	(	PUNCT
iajs-2476	263	7	ϑ	ϑ	X
iajs-2476	263	8	:	:	SYM
iajs-2476	263	9	1	1	NUM
iajs-2476	263	10	)	)	PUNCT
iajs-2476	263	11	is	be	AUX
iajs-2476	263	12	primary	primary	ADJ
iajs-2476	263	13	la	la	ADJ
iajs-2476	263	14	-	-	PUNCT
iajs-2476	263	15	ideal	ideal	NOUN
iajs-2476	263	16	of	of	ADP
iajs-2476	263	17	f/	f/	NUM
iajs-2476	263	18	ann(h	ann(h	PROPN
iajs-2476	263	19	)	)	PUNCT
iajs-2476	263	20	.	.	PUNCT
iajs-2476	264	1	define	define	VERB
iajs-2476	264	2	the	the	DET
iajs-2476	264	3	function	function	NOUN
iajs-2476	264	4	𝜎	𝜎	NOUN
iajs-2476	264	5	:	:	PUNCT
iajs-2476	264	6	la	la	ADJ
iajs-2476	264	7	-	-	PUNCT
iajs-2476	264	8	prim(h)→	prim(h)→	VERB
iajs-2476	264	9	la	la	ADJ
iajs-2476	264	10	-	-	PUNCT
iajs-2476	264	11	prim(f/	prim(f/	NOUN
iajs-2476	264	12	ann(h	ann(h	PROPN
iajs-2476	264	13	)	)	PUNCT
iajs-2476	264	14	)	)	PUNCT
iajs-2476	264	15	by	by	ADP
iajs-2476	264	16	𝜎(ϑ	𝜎(ϑ	PROPN
iajs-2476	264	17	)	)	PUNCT
iajs-2476	264	18	=	=	PUNCT
iajs-2476	264	19	(	(	PUNCT
iajs-2476	264	20	ϑ	ϑ	NOUN
iajs-2476	264	21	:	:	SYM
iajs-2476	264	22	1	1	NUM
iajs-2476	264	23	)	)	PUNCT
iajs-2476	264	24	for	for	ADP
iajs-2476	264	25	ϑ	ϑ	PROPN
iajs-2476	264	26	∈	∈	PROPN
iajs-2476	264	27	laprim(h	laprim(h	NOUN
iajs-2476	264	28	)	)	PUNCT
iajs-2476	264	29	,	,	PUNCT
iajs-2476	264	30	𝜎	𝜎	PROPN
iajs-2476	264	31	is	be	AUX
iajs-2476	264	32	called	call	VERB
iajs-2476	264	33	the	the	DET
iajs-2476	264	34	standard	standard	ADJ
iajs-2476	264	35	function	function	NOUN
iajs-2476	264	36	.	.	PUNCT
iajs-2476	265	1	lemma	lemma	PROPN
iajs-2476	265	2	4.2	4.2	NUM
iajs-2476	265	3	suppose	suppose	VERB
iajs-2476	265	4	that	that	SCONJ
iajs-2476	265	5	b	b	PROPN
iajs-2476	265	6	is	be	AUX
iajs-2476	265	7	an	an	DET
iajs-2476	265	8	ideal	ideal	NOUN
iajs-2476	265	9	of	of	ADP
iajs-2476	265	10	f	f	NOUN
iajs-2476	265	11	while	while	SCONJ
iajs-2476	265	12	𝜚	𝜚	NOUN
iajs-2476	265	13	∈	∈	PROPN
iajs-2476	265	14	lai	lai	NOUN
iajs-2476	265	15	(	(	PUNCT
iajs-2476	265	16	f	f	X
iajs-2476	265	17	/	/	SYM
iajs-2476	265	18	b	b	NOUN
iajs-2476	265	19	)	)	PUNCT
iajs-2476	265	20	.	.	PUNCT
iajs-2476	266	1	there	there	ADV
iajs-2476	266	2	occur𝑠	occur𝑠	NOUN
iajs-2476	266	3	𝛾	𝛾	PROPN
iajs-2476	266	4	∈	∈	PROPN
iajs-2476	266	5	lai	lai	NOUN
iajs-2476	266	6	(	(	PUNCT
iajs-2476	266	7	f	f	X
iajs-2476	266	8	)	)	PUNCT
iajs-2476	266	9	such	such	ADJ
iajs-2476	266	10	that	that	DET
iajs-2476	266	11	𝜚=𝛾	𝜚=𝛾	PROPN
iajs-2476	266	12	.	.	PUNCT
iajs-2476	267	1	proof	proof	NOUN
iajs-2476	267	2	let	let	VERB
iajs-2476	267	3	the	the	DET
iajs-2476	267	4	quotient	quotient	NOUN
iajs-2476	267	5	function𝜌	function𝜌	NOUN
iajs-2476	267	6	:	:	PUNCT
iajs-2476	267	7	f	f	X
iajs-2476	267	8	→	→	SYM
iajs-2476	267	9	f	f	PROPN
iajs-2476	267	10	/	/	SYM
iajs-2476	267	11	b.	b.	PROPN
iajs-2476	268	1	then	then	ADV
iajs-2476	268	2	it	it	PRON
iajs-2476	268	3	is	be	AUX
iajs-2476	268	4	to	to	PART
iajs-2476	268	5	prove	prove	VERB
iajs-2476	268	6	that	that	SCONJ
iajs-2476	269	1	𝜚	𝜚	NOUN
iajs-2476	269	2	=	=	NOUN
iajs-2476	270	1	𝑜	𝑜	NOUN
iajs-2476	270	2	𝜌.	𝜌.	NOUN
iajs-2476	270	3	proposition	proposition	NOUN
iajs-2476	270	4	4.3	4.3	NUM
iajs-2476	270	5	the	the	DET
iajs-2476	270	6	standard	standard	PROPN
iajs-2476	270	7	function𝜎	function𝜎	NOUN
iajs-2476	270	8	be	be	AUX
iajs-2476	270	9	persistent	persistent	ADJ
iajs-2476	270	10	for	for	ADP
iajs-2476	270	11	the	the	DET
iajs-2476	270	12	topologies	topology	NOUN
iajs-2476	270	13	on	on	ADP
iajs-2476	270	14	laprim(h)while	laprim(h)while	NOUN
iajs-2476	270	15	la	la	ADJ
iajs-2476	270	16	-	-	ADJ
iajs-2476	270	17	prim	prim	ADJ
iajs-2476	270	18	(	(	PUNCT
iajs-2476	270	19	f	f	X
iajs-2476	270	20	/	/	SYM
iajs-2476	270	21	ann(h	ann(h	PROPN
iajs-2476	270	22	)	)	PUNCT
iajs-2476	270	23	)	)	PUNCT
iajs-2476	270	24	.	.	PUNCT
iajs-2476	271	1	proof	proof	NOUN
iajs-2476	271	2	suppose	suppose	VERB
iajs-2476	271	3	that	that	SCONJ
iajs-2476	271	4	𝛾	𝛾	PROPN
iajs-2476	271	5	∈	∈	PROPN
iajs-2476	271	6	lai	lai	PROPN
iajs-2476	271	7	(	(	PUNCT
iajs-2476	271	8	f/	f/	NOUN
iajs-2476	271	9	ann(h	ann(h	PROPN
iajs-2476	271	10	)	)	PUNCT
iajs-2476	271	11	)	)	PUNCT
iajs-2476	271	12	.	.	PUNCT
iajs-2476	272	1	we	we	PRON
iajs-2476	272	2	claim	claim	VERB
iajs-2476	272	3	that	that	SCONJ
iajs-2476	272	4	𝜎	𝜎	PROPN
iajs-2476	272	5	(	(	PUNCT
iajs-2476	272	6	v	v	NOUN
iajs-2476	272	7	(	(	PUNCT
iajs-2476	272	8	𝛾	𝛾	NOUN
iajs-2476	272	9	)	)	PUNCT
iajs-2476	272	10	)	)	PUNCT
iajs-2476	273	1	=	=	NOUN
iajs-2476	273	2	v	v	NOUN
iajs-2476	273	3	(	(	PUNCT
iajs-2476	273	4	𝛾.1h	𝛾.1h	PROPN
iajs-2476	273	5	)	)	PUNCT
iajs-2476	273	6	.	.	PUNCT
iajs-2476	274	1	for	for	ADP
iajs-2476	274	2	this	this	PRON
iajs-2476	274	3	let	let	VERB
iajs-2476	274	4	q	q	PROPN
iajs-2476	274	5	∈	∈	PROPN
iajs-2476	274	6	v	v	X
iajs-2476	274	7	(	(	PUNCT
iajs-2476	274	8	𝛾.1h	𝛾.1h	PROPN
iajs-2476	274	9	)	)	PUNCT
iajs-2476	274	10	.	.	PUNCT
iajs-2476	275	1	then	then	ADV
iajs-2476	275	2	𝛾.1h	𝛾.1h	VERB
iajs-2476	275	3	⊆	⊆	NUM
iajs-2476	275	4	q	q	NOUN
iajs-2476	275	5	and	and	CCONJ
iajs-2476	275	6	1h	1h	NUM
iajs-2476	275	7	⊈	⊈	PROPN
iajs-2476	275	8	q.	q.	NOUN
iajs-2476	275	9	thus	thus	ADV
iajs-2476	275	10	𝛾	𝛾	VERB
iajs-2476	275	11	⊆	⊆	NUM
iajs-2476	275	12	q:1h	q:1h	NOUN
iajs-2476	275	13	and	and	CCONJ
iajs-2476	275	14	hence	hence	ADV
iajs-2476	275	15	𝛾	𝛾	ADP
iajs-2476	275	16	⊆	⊆	NUM
iajs-2476	275	17	q	q	NOUN
iajs-2476	275	18	∶	∶	NOUN
iajs-2476	275	19	1	1	NUM
iajs-2476	275	20	.	.	PUNCT
iajs-2476	276	1	hence	hence	ADV
iajs-2476	276	2	q	q	PROPN
iajs-2476	276	3	∶	∶	NOUN
iajs-2476	276	4	1	1	NUM
iajs-2476	276	5	⊆	⊆	NUM
iajs-2476	276	6	v	v	NOUN
iajs-2476	276	7	(	(	PUNCT
iajs-2476	276	8	𝛾	𝛾	NOUN
iajs-2476	276	9	)	)	PUNCT
iajs-2476	276	10	and	and	CCONJ
iajs-2476	276	11	q	q	PROPN
iajs-2476	276	12	∶	∶	NOUN
iajs-2476	276	13	1	1	NUM
iajs-2476	276	14	=	=	SYM
iajs-2476	276	15	𝜎(q	𝜎(q	PROPN
iajs-2476	276	16	)	)	PUNCT
iajs-2476	276	17	,	,	PUNCT
iajs-2476	276	18	so	so	SCONJ
iajs-2476	276	19	q	q	PROPN
iajs-2476	276	20	∈	∈	PROPN
iajs-2476	276	21	𝜎	𝜎	X
iajs-2476	276	22	(	(	PUNCT
iajs-2476	276	23	v	v	NOUN
iajs-2476	276	24	(	(	PUNCT
iajs-2476	276	25	𝛾	𝛾	NOUN
iajs-2476	276	26	)	)	PUNCT
iajs-2476	276	27	)	)	PUNCT
iajs-2476	276	28	⟹	⟹	PROPN
iajs-2476	276	29	v	v	NOUN
iajs-2476	276	30	(	(	PUNCT
iajs-2476	276	31	𝛾.1h	𝛾.1h	PROPN
iajs-2476	276	32	)	)	PUNCT
iajs-2476	277	1	⊆	⊆	NUM
iajs-2476	277	2	𝜎	𝜎	PROPN
iajs-2476	277	3	(	(	PUNCT
iajs-2476	277	4	v	v	NOUN
iajs-2476	277	5	(	(	PUNCT
iajs-2476	277	6	𝛾	𝛾	NOUN
iajs-2476	277	7	)	)	PUNCT
iajs-2476	277	8	)	)	PUNCT
iajs-2476	277	9	.	.	PUNCT
iajs-2476	278	1	identically	identically	ADV
iajs-2476	278	2	we	we	PRON
iajs-2476	278	3	can	can	AUX
iajs-2476	278	4	prove	prove	VERB
iajs-2476	278	5	that	that	SCONJ
iajs-2476	279	1	𝜎	𝜎	PROPN
iajs-2476	279	2	(	(	PUNCT
iajs-2476	279	3	v	v	NOUN
iajs-2476	279	4	(	(	PUNCT
iajs-2476	279	5	𝛾	𝛾	NOUN
iajs-2476	279	6	)	)	PUNCT
iajs-2476	279	7	)	)	PUNCT
iajs-2476	280	1	⊆	⊆	NUM
iajs-2476	280	2	v	v	X
iajs-2476	280	3	(	(	PUNCT
iajs-2476	280	4	𝛾.1	𝛾.1	NOUN
iajs-2476	280	5	m	m	VERB
iajs-2476	280	6	)	)	PUNCT
iajs-2476	280	7	and	and	CCONJ
iajs-2476	280	8	hence	hence	ADV
iajs-2476	280	9	𝜎	𝜎	PROPN
iajs-2476	280	10	(	(	PUNCT
iajs-2476	280	11	v	v	NOUN
iajs-2476	280	12	(	(	PUNCT
iajs-2476	280	13	𝛾	𝛾	NOUN
iajs-2476	280	14	)	)	PUNCT
iajs-2476	280	15	)	)	PUNCT
iajs-2476	281	1	=	=	SYM
iajs-2476	281	2	v	v	X
iajs-2476	281	3	(	(	PUNCT
iajs-2476	281	4	𝛾.1h	𝛾.1h	PROPN
iajs-2476	281	5	)	)	PUNCT
iajs-2476	281	6	.	.	PUNCT
iajs-2476	282	1	thus	thus	ADV
iajs-2476	282	2	σ	σ	X
iajs-2476	282	3	is	be	AUX
iajs-2476	282	4	persistent	persistent	ADJ
iajs-2476	282	5	.	.	PUNCT
iajs-2476	283	1	proposition	proposition	NOUN
iajs-2476	283	2	4.4	4.4	NUM
iajs-2476	283	3	for	for	ADP
iajs-2476	283	4	each	each	DET
iajs-2476	283	5	f	f	NOUN
iajs-2476	283	6	-	-	PUNCT
iajs-2476	283	7	module	module	NOUN
iajs-2476	283	8	h	h	NOUN
iajs-2476	283	9	the	the	DET
iajs-2476	283	10	following	follow	VERB
iajs-2476	283	11	assertions	assertion	NOUN
iajs-2476	283	12	are	be	AUX
iajs-2476	283	13	equivalent	equivalent	ADJ
iajs-2476	283	14	:	:	PUNCT
iajs-2476	283	15	(	(	PUNCT
iajs-2476	283	16	1	1	X
iajs-2476	283	17	)	)	PUNCT
iajs-2476	283	18	𝜎	𝜎	NOUN
iajs-2476	283	19	be	be	AUX
iajs-2476	283	20	injective	injective	ADJ
iajs-2476	283	21	;	;	PUNCT
iajs-2476	283	22	(	(	PUNCT
iajs-2476	283	23	2	2	X
iajs-2476	283	24	)	)	PUNCT
iajs-2476	283	25	for	for	ADP
iajs-2476	283	26	ϑ	ϑ	X
iajs-2476	283	27	,	,	PUNCT
iajs-2476	283	28	ϖ	ϖ	PROPN
iajs-2476	283	29	∈	∈	PROPN
iajs-2476	283	30	la	la	PROPN
iajs-2476	283	31	-	-	PUNCT
iajs-2476	283	32	prim(h	prim(h	NOUN
iajs-2476	283	33	)	)	PUNCT
iajs-2476	283	34	,	,	PUNCT
iajs-2476	283	35	if	if	SCONJ
iajs-2476	283	36	v(ϑ)=v(ϖ	v(ϑ)=v(ϖ	NUM
iajs-2476	283	37	)	)	PUNCT
iajs-2476	283	38	,	,	PUNCT
iajs-2476	283	39	then	then	ADV
iajs-2476	283	40	ϑ=	ϑ=	VERB
iajs-2476	283	41	ϖ	ϖ	NOUN
iajs-2476	283	42	;	;	PUNCT
iajs-2476	283	43	(	(	PUNCT
iajs-2476	283	44	3	3	X
iajs-2476	283	45	)	)	PUNCT
iajs-2476	283	46	for	for	ADP
iajs-2476	283	47	every	every	DET
iajs-2476	283	48	q	q	PROPN
iajs-2476	283	49	∈	∈	PROPN
iajs-2476	283	50	la	la	PROPN
iajs-2476	283	51	-	-	PUNCT
iajs-2476	283	52	prim(f),|la	prim(f),|la	NOUN
iajs-2476	283	53	-	-	PUNCT
iajs-2476	283	54	primp(h)|≤	primp(h)|≤	NOUN
iajs-2476	283	55	1	1	NUM
iajs-2476	283	56	.	.	PUNCT
iajs-2476	284	1	proof	proof	NOUN
iajs-2476	284	2	(	(	PUNCT
iajs-2476	284	3	1	1	NUM
iajs-2476	284	4	)	)	PUNCT
iajs-2476	284	5	⟹	⟹	NOUN
iajs-2476	284	6	(	(	PUNCT
iajs-2476	284	7	2	2	NUM
iajs-2476	284	8	):	):	PUNCT
iajs-2476	284	9	suppose	suppose	VERB
iajs-2476	284	10	that	that	SCONJ
iajs-2476	284	11	ϑ	ϑ	X
iajs-2476	284	12	,	,	PUNCT
iajs-2476	284	13	ϖ	ϖ	PROPN
iajs-2476	284	14	∈	∈	PROPN
iajs-2476	284	15	la	la	PROPN
iajs-2476	284	16	-	-	PUNCT
iajs-2476	284	17	prim(h	prim(h	NOUN
iajs-2476	284	18	)	)	PUNCT
iajs-2476	284	19	.	.	PUNCT
iajs-2476	285	1	if	if	SCONJ
iajs-2476	285	2	v(ϑ)=v	v(ϑ)=v	INTJ
iajs-2476	285	3	(	(	PUNCT
iajs-2476	285	4	ϖ	ϖ	NOUN
iajs-2476	285	5	)	)	PUNCT
iajs-2476	285	6	then	then	ADV
iajs-2476	285	7	ϑ:1h=	ϑ:1h=	PROPN
iajs-2476	285	8	ϖ	ϖ	NOUN
iajs-2476	285	9	:	:	PUNCT
iajs-2476	285	10	1h	1h	NUM
iajs-2476	285	11	,	,	PUNCT
iajs-2476	285	12	by	by	ADP
iajs-2476	285	13	proposition	proposition	NOUN
iajs-2476	285	14	3.3	3.3	NUM
iajs-2476	285	15	and	and	CCONJ
iajs-2476	285	16	hence	hence	ADV
iajs-2476	285	17	ϑ	ϑ	PROPN
iajs-2476	285	18	∶	∶	NOUN
iajs-2476	285	19	1	1	NUM
iajs-2476	285	20	ϖ	ϖ	NOUN
iajs-2476	285	21	∶	∶	NOUN
iajs-2476	285	22	1	1	NUM
iajs-2476	285	23	which	which	PRON
iajs-2476	285	24	lead	lead	VERB
iajs-2476	285	25	to	to	ADP
iajs-2476	285	26	that	that	DET
iajs-2476	285	27	𝜎(ϑ)=𝜎(ϖ	𝜎(ϑ)=𝜎(ϖ	PROPN
iajs-2476	285	28	)	)	PUNCT
iajs-2476	285	29	.	.	PUNCT
iajs-2476	286	1	thus	thus	ADV
iajs-2476	286	2	ϑ	ϑ	X
iajs-2476	286	3	=	=	SYM
iajs-2476	286	4	ϖ	ϖ	NOUN
iajs-2476	286	5	,	,	PUNCT
iajs-2476	286	6	since	since	SCONJ
iajs-2476	286	7	σ	σ	PROPN
iajs-2476	286	8	is	be	AUX
iajs-2476	286	9	injective	injective	ADJ
iajs-2476	286	10	by(1	by(1	NOUN
iajs-2476	286	11	)	)	PUNCT
iajs-2476	286	12	.	.	PUNCT
iajs-2476	287	1	(	(	PUNCT
iajs-2476	287	2	2	2	X
iajs-2476	287	3	)	)	PUNCT
iajs-2476	287	4	⟹	⟹	NOUN
iajs-2476	287	5	(	(	PUNCT
iajs-2476	287	6	3	3	NUM
iajs-2476	287	7	):	):	PUNCT
iajs-2476	287	8	suppose	suppose	VERB
iajs-2476	287	9	that	that	SCONJ
iajs-2476	287	10	ϑ	ϑ	X
iajs-2476	287	11	,	,	PUNCT
iajs-2476	287	12	ϖ	ϖ	PROPN
iajs-2476	287	13	∈	∈	PROPN
iajs-2476	287	14	la	la	PROPN
iajs-2476	287	15	-	-	PUNCT
iajs-2476	287	16	primp(h	primp(h	NOUN
iajs-2476	287	17	)	)	PUNCT
iajs-2476	287	18	,	,	PUNCT
iajs-2476	287	19	then	then	ADV
iajs-2476	287	20	ϑ:1h	ϑ:1h	VERB
iajs-2476	287	21	=	=	PRON
iajs-2476	287	22	ϖ	ϖ	X
iajs-2476	287	23	:	:	PUNCT
iajs-2476	287	24	1h	1h	NUM
iajs-2476	287	25	=	=	SYM
iajs-2476	287	26	q.	q.	PROPN
iajs-2476	287	27	therefore	therefore	ADV
iajs-2476	287	28	v	v	NOUN
iajs-2476	287	29	(	(	PUNCT
iajs-2476	287	30	ϑ)=v	ϑ)=v	X
iajs-2476	287	31	(	(	PUNCT
iajs-2476	287	32	ϖ	ϖ	NOUN
iajs-2476	287	33	)	)	PUNCT
iajs-2476	287	34	via	via	ADP
iajs-2476	287	35	proposition	proposition	NOUN
iajs-2476	287	36	3.3	3.3	NUM
iajs-2476	287	37	.	.	PUNCT
iajs-2476	288	1	then	then	ADV
iajs-2476	288	2	by	by	ADP
iajs-2476	288	3	(	(	PUNCT
iajs-2476	288	4	2	2	X
iajs-2476	288	5	)	)	PUNCT
iajs-2476	288	6	we	we	PRON
iajs-2476	288	7	have	have	VERB
iajs-2476	288	8	ϑ	ϑ	X
iajs-2476	288	9	=	=	SYM
iajs-2476	288	10	ϖ	ϖ	NOUN
iajs-2476	288	11	,	,	PUNCT
iajs-2476	288	12	and	and	CCONJ
iajs-2476	288	13	hence	hence	ADV
iajs-2476	288	14	|la	|la	NUM
iajs-2476	288	15	-	-	PUNCT
iajs-2476	288	16	primp(h)|≤	primp(h)|≤	NOUN
iajs-2476	288	17	1	1	NUM
iajs-2476	288	18	.	.	PUNCT
iajs-2476	289	1	(	(	PUNCT
iajs-2476	289	2	3	3	NUM
iajs-2476	289	3	)	)	PUNCT
iajs-2476	289	4	⟹	⟹	NOUN
iajs-2476	289	5	(	(	PUNCT
iajs-2476	289	6	1	1	NUM
iajs-2476	289	7	):	):	PUNCT
iajs-2476	289	8	let	let	VERB
iajs-2476	289	9	ϑ	ϑ	X
iajs-2476	289	10	,	,	PUNCT
iajs-2476	289	11	ν	ν	PROPN
iajs-2476	289	12	∈	∈	PROPN
iajs-2476	289	13	la	la	PROPN
iajs-2476	289	14	-	-	PROPN
iajs-2476	289	15	prim(h)and	prim(h)and	PROPN
iajs-2476	289	16	𝜎(ϑ)=𝜎(ϖ	𝜎(ϑ)=𝜎(ϖ	PROPN
iajs-2476	289	17	)	)	PUNCT
iajs-2476	289	18	.	.	PUNCT
iajs-2476	290	1	then	then	ADV
iajs-2476	290	2	ϑ	ϑ	X
iajs-2476	290	3	∶	∶	NOUN
iajs-2476	290	4	1	1	NUM
iajs-2476	290	5	ϖ	ϖ	NOUN
iajs-2476	290	6	∶	∶	NOUN
iajs-2476	290	7	1	1	NUM
iajs-2476	290	8	⟹	⟹	NOUN
iajs-2476	290	9	ϑ	ϑ	PROPN
iajs-2476	290	10	∶	∶	NOUN
iajs-2476	290	11	1	1	NUM
iajs-2476	290	12	=	=	SYM
iajs-2476	290	13	ϖ	ϖ	NOUN
iajs-2476	290	14	∶	∶	NOUN
iajs-2476	290	15	1	1	NUM
iajs-2476	290	16	=	=	NOUN
iajs-2476	290	17	q	q	X
iajs-2476	290	18	⟹	⟹	NUM
iajs-2476	290	19	ϑ	ϑ	X
iajs-2476	290	20	,	,	PUNCT
iajs-2476	290	21	ϖ	ϖ	PROPN
iajs-2476	290	22	∈	∈	PROPN
iajs-2476	290	23	la	la	PROPN
iajs-2476	290	24	-	-	PUNCT
iajs-2476	290	25	primp(h	primp(h	NOUN
iajs-2476	290	26	)	)	PUNCT
iajs-2476	290	27	⟹	⟹	NUM
iajs-2476	290	28	𝜗	𝜗	VERB
iajs-2476	290	29	ϖ.	ϖ.	NOUN
iajs-2476	290	30	that	that	PRON
iajs-2476	290	31	is	be	AUX
iajs-2476	290	32	𝜎	𝜎	PROPN
iajs-2476	290	33	injective	injective	NOUN
iajs-2476	290	34	.	.	PUNCT
iajs-2476	291	1	in	in	ADP
iajs-2476	291	2	the	the	DET
iajs-2476	291	3	complements	complement	NOUN
iajs-2476	291	4	we	we	PRON
iajs-2476	291	5	put	put	VERB
iajs-2476	291	6	y=	y=	PRON
iajs-2476	291	7	la	la	NOUN
iajs-2476	291	8	-	-	PUNCT
iajs-2476	291	9	prim(h	prim(h	NOUN
iajs-2476	291	10	)	)	PUNCT
iajs-2476	291	11	and	and	CCONJ
iajs-2476	291	12	y	y	PROPN
iajs-2476	291	13	=	=	SYM
iajs-2476	291	14	la	la	PROPN
iajs-2476	291	15	-	-	PUNCT
iajs-2476	291	16	prim(f	prim(f	NOUN
iajs-2476	291	17	/	/	SYM
iajs-2476	291	18	ann(h	ann(h	PROPN
iajs-2476	291	19	)	)	PUNCT
iajs-2476	291	20	)	)	PUNCT
iajs-2476	291	21	.	.	PUNCT
iajs-2476	292	1	theorem	theorem	VERB
iajs-2476	292	2	4.5	4.5	NUM
iajs-2476	292	3	suppose	suppose	VERB
iajs-2476	292	4	that	that	SCONJ
iajs-2476	292	5	𝜎	𝜎	PROPN
iajs-2476	292	6	is	be	AUX
iajs-2476	292	7	the	the	DET
iajs-2476	292	8	natural	natural	ADJ
iajs-2476	292	9	map	map	NOUN
iajs-2476	292	10	.	.	PUNCT
iajs-2476	293	1	if	if	SCONJ
iajs-2476	293	2	σ	σ	PROPN
iajs-2476	293	3	is	be	AUX
iajs-2476	293	4	inclusive	inclusive	ADJ
iajs-2476	293	5	then	then	ADV
iajs-2476	293	6	σ	σ	PROPN
iajs-2476	293	7	is	be	AUX
iajs-2476	293	8	both	both	PRON
iajs-2476	293	9	closed	close	VERB
iajs-2476	293	10	while	while	SCONJ
iajs-2476	293	11	open	open	ADJ
iajs-2476	293	12	.	.	PUNCT
iajs-2476	294	1	proof	proof	NOUN
iajs-2476	294	2	let	let	VERB
iajs-2476	294	3	σ	σ	NOUN
iajs-2476	294	4	:	:	PUNCT
iajs-2476	294	5	y	y	PROPN
iajs-2476	294	6	→	→	SYM
iajs-2476	294	7	y	y	PROPN
iajs-2476	294	8	is	be	AUX
iajs-2476	294	9	the	the	DET
iajs-2476	294	10	standard	standard	ADJ
iajs-2476	294	11	function	function	NOUN
iajs-2476	294	12	and	and	CCONJ
iajs-2476	294	13	ϑ	ϑ	X
iajs-2476	294	14	∈	∈	PROPN
iajs-2476	294	15	y.	y.	NOUN
iajs-2476	294	16	then	then	ADV
iajs-2476	294	17	via	via	ADP
iajs-2476	294	18	the	the	DET
iajs-2476	294	19	proof	proof	NOUN
iajs-2476	294	20	of	of	ADP
iajs-2476	294	21	proposition	proposition	NOUN
iajs-2476	294	22	4.3	4.3	NUM
iajs-2476	294	23	,	,	PUNCT
iajs-2476	294	24	  	  	SPACE
iajs-2476	294	25	98	98	NUM
iajs-2476	294	26	ibn	ibn	PROPN
iajs-2476	294	27	al	al	PROPN
iajs-2476	294	28	-	-	PUNCT
iajs-2476	294	29	haitham	haitham	PROPN
iajs-2476	294	30	jour	jour	X
iajs-2476	294	31	.	.	PROPN
iajs-2476	295	1	for	for	ADP
iajs-2476	295	2	pure	pure	ADJ
iajs-2476	295	3	&	&	CCONJ
iajs-2476	295	4	appl	appl	PROPN
iajs-2476	295	5	.	.	PUNCT
iajs-2476	296	1	sci	sci	PROPN
iajs-2476	296	2	.	.	PROPN
iajs-2476	297	1	33	33	NUM
iajs-2476	297	2	(	(	PUNCT
iajs-2476	297	3	3	3	NUM
iajs-2476	297	4	)	)	PUNCT
iajs-2476	297	5	2020	2020	NUM
iajs-2476	297	6	𝜎	𝜎	PROPN
iajs-2476	297	7	(	(	PUNCT
iajs-2476	297	8	v	v	NOUN
iajs-2476	297	9	(	(	PUNCT
iajs-2476	297	10	ϑ	ϑ	X
iajs-2476	297	11	∶	∶	NOUN
iajs-2476	297	12	1	1	NUM
iajs-2476	297	13	)	)	PUNCT
iajs-2476	297	14	)	)	PUNCT
iajs-2476	298	1	=	=	SYM
iajs-2476	298	2	v	v	NOUN
iajs-2476	298	3	(	(	PUNCT
iajs-2476	298	4	ϑ	ϑ	X
iajs-2476	298	5	∶	∶	NOUN
iajs-2476	298	6	1	1	NUM
iajs-2476	298	7	.	.	PUNCT
iajs-2476	299	1	1	1	NUM
iajs-2476	299	2	=	=	SYM
iajs-2476	299	3	v	v	NUM
iajs-2476	299	4	ϑ	ϑ	NOUN
iajs-2476	299	5	)	)	PUNCT
iajs-2476	299	6	⟹	⟹	PROPN
iajs-2476	299	7	𝜎	𝜎	PROPN
iajs-2476	299	8	(	(	PUNCT
iajs-2476	299	9	v	v	NUM
iajs-2476	299	10	ϑ))=𝜎	ϑ))=𝜎	NOUN
iajs-2476	299	11	𝑜	𝑜	X
iajs-2476	299	12	𝜎	𝜎	PROPN
iajs-2476	299	13	(	(	PUNCT
iajs-2476	299	14	v	v	NOUN
iajs-2476	299	15	(	(	PUNCT
iajs-2476	299	16	ϑ	ϑ	X
iajs-2476	299	17	∶	∶	NOUN
iajs-2476	299	18	1	1	NUM
iajs-2476	299	19	)	)	PUNCT
iajs-2476	299	20	)	)	PUNCT
iajs-2476	299	21	=	=	SYM
iajs-2476	299	22	v	v	X
iajs-2476	299	23	(	(	PUNCT
iajs-2476	299	24	ϑ	ϑ	X
iajs-2476	299	25	∶	∶	NOUN
iajs-2476	299	26	1	1	NUM
iajs-2476	299	27	,	,	PUNCT
iajs-2476	299	28	that	that	ADV
iajs-2476	299	29	is	is	ADV
iajs-2476	299	30	σ	σ	NOUN
iajs-2476	299	31	is	be	AUX
iajs-2476	299	32	closed	closed	ADJ
iajs-2476	299	33	.	.	PUNCT
iajs-2476	300	1	also	also	ADV
iajs-2476	300	2	we	we	PRON
iajs-2476	300	3	have	have	VERB
iajs-2476	300	4	𝜎	𝜎	PROPN
iajs-2476	300	5	(	(	PUNCT
iajs-2476	300	6	y	y	PROPN
iajs-2476	300	7	-	-	PUNCT
iajs-2476	300	8	v	v	NOUN
iajs-2476	300	9	ϑ))=𝜎	ϑ))=𝜎	X
iajs-2476	300	10	𝜎	𝜎	PROPN
iajs-2476	300	11	(	(	PUNCT
iajs-2476	300	12	y	y	PROPN
iajs-2476	300	13	)	)	PUNCT
iajs-2476	300	14	𝜎	𝜎	NOUN
iajs-2476	300	15	v(ϑ	v(ϑ	NOUN
iajs-2476	300	16	∶	∶	NOUN
iajs-2476	300	17	1	1	NUM
iajs-2476	300	18	=	=	SYM
iajs-2476	301	1	𝜎	𝜎	PRON
iajs-2476	301	2	𝜎	𝜎	PROPN
iajs-2476	301	3	(	(	PUNCT
iajs-2476	301	4	y	y	PROPN
iajs-2476	301	5	v(ϑ	v(ϑ	PROPN
iajs-2476	301	6	∶	∶	ADV
iajs-2476	301	7	1	1	NUM
iajs-2476	301	8	=	=	SYM
iajs-2476	301	9	y	y	PROPN
iajs-2476	301	10	v(ϑ	v(ϑ	NOUN
iajs-2476	301	11	∶	∶	ADV
iajs-2476	301	12	1	1	NUM
iajs-2476	301	13	,	,	PUNCT
iajs-2476	301	14	that	that	PRON
iajs-2476	301	15	is	be	AUX
iajs-2476	301	16	𝜎	𝜎	PROPN
iajs-2476	301	17	be	be	AUX
iajs-2476	301	18	open	open	ADJ
iajs-2476	301	19	.	.	PUNCT
iajs-2476	302	1	proposition	proposition	NOUN
iajs-2476	302	2	4.6	4.6	NUM
iajs-2476	302	3	suppose	suppose	VERB
iajs-2476	302	4	that	that	SCONJ
iajs-2476	302	5	σ	σ	PROPN
iajs-2476	302	6	is	be	AUX
iajs-2476	302	7	the	the	DET
iajs-2476	302	8	standard	standard	ADJ
iajs-2476	302	9	function	function	NOUN
iajs-2476	302	10	from	from	ADP
iajs-2476	302	11	y	y	PROPN
iajs-2476	302	12	into	into	ADP
iajs-2476	302	13	y	y	PROPN
iajs-2476	302	14	and	and	CCONJ
iajs-2476	302	15	it	it	PRON
iajs-2476	302	16	is	be	AUX
iajs-2476	302	17	inclusive	inclusive	ADJ
iajs-2476	302	18	.	.	PUNCT
iajs-2476	303	1	then	then	ADV
iajs-2476	303	2	y	y	PROPN
iajs-2476	303	3	is	be	AUX
iajs-2476	303	4	linked	link	VERB
iajs-2476	303	5	if	if	SCONJ
iajs-2476	303	6	and	and	CCONJ
iajs-2476	303	7	only	only	ADV
iajs-2476	303	8	if	if	SCONJ
iajs-2476	303	9	y	y	PROPN
iajs-2476	303	10	is	be	AUX
iajs-2476	303	11	linked	link	VERB
iajs-2476	303	12	.	.	PUNCT
iajs-2476	304	1	proof	proof	NOUN
iajs-2476	304	2	suppose	suppose	VERB
iajs-2476	304	3	that	that	SCONJ
iajs-2476	304	4	y	y	PROPN
iajs-2476	304	5	is	be	AUX
iajs-2476	304	6	linked	link	VERB
iajs-2476	304	7	.	.	PUNCT
iajs-2476	305	1	then	then	ADV
iajs-2476	305	2	y	y	PROPN
iajs-2476	305	3	=	=	SYM
iajs-2476	305	4	σ(y	σ(y	PROPN
iajs-2476	305	5	)	)	PUNCT
iajs-2476	305	6	is	be	AUX
iajs-2476	305	7	linked	link	VERB
iajs-2476	305	8	,	,	PUNCT
iajs-2476	305	9	since	since	SCONJ
iajs-2476	305	10	σ	σ	PROPN
iajs-2476	305	11	be	be	AUX
iajs-2476	305	12	persistent	persistent	ADJ
iajs-2476	305	13	while	while	SCONJ
iajs-2476	305	14	inclusive	inclusive	ADJ
iajs-2476	305	15	.	.	PUNCT
iajs-2476	306	1	conversely	conversely	ADV
iajs-2476	306	2	,	,	PUNCT
iajs-2476	306	3	let	let	VERB
iajs-2476	306	4	y	y	PROPN
iajs-2476	306	5	is	be	AUX
iajs-2476	306	6	linked	link	VERB
iajs-2476	306	7	but	but	CCONJ
iajs-2476	306	8	y	y	PROPN
iajs-2476	306	9	is	be	AUX
iajs-2476	306	10	non	non	ADJ
iajs-2476	306	11	-	-	ADJ
iajs-2476	306	12	linked	link	VERB
iajs-2476	306	13	.	.	PUNCT
iajs-2476	307	1	then	then	ADV
iajs-2476	307	2	y	y	PROPN
iajs-2476	307	3	includes	include	VERB
iajs-2476	307	4	a	a	DET
iajs-2476	307	5	non	non	ADJ
iajs-2476	307	6	-	-	ADJ
iajs-2476	307	7	empty	empty	ADJ
iajs-2476	307	8	proper	proper	ADJ
iajs-2476	307	9	subset	subset	NOUN
iajs-2476	307	10	a	a	DET
iajs-2476	307	11	such	such	ADJ
iajs-2476	307	12	that	that	SCONJ
iajs-2476	307	13	it	it	PRON
iajs-2476	307	14	is	be	AUX
iajs-2476	307	15	both	both	CCONJ
iajs-2476	307	16	open	open	ADJ
iajs-2476	307	17	and	and	CCONJ
iajs-2476	307	18	closed	closed	ADJ
iajs-2476	307	19	.	.	PUNCT
iajs-2476	308	1	we	we	PRON
iajs-2476	308	2	prove	prove	VERB
iajs-2476	308	3	that	that	SCONJ
iajs-2476	308	4	σ(a	σ(a	PROPN
iajs-2476	308	5	)	)	PUNCT
iajs-2476	308	6	is	be	AUX
iajs-2476	308	7	a	a	DET
iajs-2476	308	8	non	non	ADJ
iajs-2476	308	9	-	-	ADJ
iajs-2476	308	10	empty	empty	ADJ
iajs-2476	308	11	proper	proper	ADJ
iajs-2476	308	12	subset	subset	NOUN
iajs-2476	308	13	of	of	ADP
iajs-2476	308	14	y	y	PROPN
iajs-2476	308	15	.	.	PUNCT
iajs-2476	309	1	since	since	SCONJ
iajs-2476	309	2	a	a	PRON
iajs-2476	309	3	is	be	AUX
iajs-2476	309	4	open	open	ADJ
iajs-2476	309	5	then	then	ADV
iajs-2476	309	6	there	there	ADV
iajs-2476	309	7	occur𝑠	occur𝑠	NOUN
iajs-2476	309	8	ϑ	ϑ	X
iajs-2476	309	9	∈	∈	PROPN
iajs-2476	309	10	la(h	la(h	PRON
iajs-2476	309	11	)	)	PUNCT
iajs-2476	309	12	such	such	ADJ
iajs-2476	309	13	that	that	SCONJ
iajs-2476	309	14	a	a	DET
iajs-2476	309	15	=	=	X
iajs-2476	309	16	y	y	PROPN
iajs-2476	309	17	\v	\v	X
iajs-2476	309	18	(	(	PUNCT
iajs-2476	309	19	ϑ	ϑ	NOUN
iajs-2476	309	20	)	)	PUNCT
iajs-2476	309	21	.	.	PUNCT
iajs-2476	310	1	thus	thus	ADV
iajs-2476	310	2	σ(a	σ(a	PROPN
iajs-2476	310	3	)	)	PUNCT
iajs-2476	310	4	=	=	SYM
iajs-2476	310	5	y	y	PROPN
iajs-2476	310	6	\v	\v	X
iajs-2476	310	7	(	(	PUNCT
iajs-2476	310	8	ϑ	ϑ	X
iajs-2476	310	9	∶	∶	NOUN
iajs-2476	310	10	1	1	NUM
iajs-2476	310	11	)	)	PUNCT
iajs-2476	310	12	,	,	PUNCT
iajs-2476	310	13	.	.	PUNCT
iajs-2476	311	1	if	if	SCONJ
iajs-2476	311	2	σ(a	σ(a	PROPN
iajs-2476	311	3	)	)	PUNCT
iajs-2476	312	1	=	=	SYM
iajs-2476	312	2	y	y	PROPN
iajs-2476	312	3	then	then	ADV
iajs-2476	312	4	v(ϑ	v(ϑ	PROPN
iajs-2476	312	5	∶	∶	ADV
iajs-2476	312	6	1	1	NUM
iajs-2476	312	7	)	)	PUNCT
iajs-2476	312	8	=	=	NOUN
iajs-2476	312	9	∅	∅	NOUN
iajs-2476	312	10	,	,	PUNCT
iajs-2476	312	11	and	and	CCONJ
iajs-2476	312	12	hence	hence	ADV
iajs-2476	312	13	(	(	PUNCT
iajs-2476	312	14	ϑ	ϑ	X
iajs-2476	312	15	∶	∶	NOUN
iajs-2476	312	16	1	1	NUM
iajs-2476	312	17	)	)	PUNCT
iajs-2476	312	18	=	=	SYM
iajs-2476	312	19	𝜒	𝜒	X
iajs-2476	312	20	f/	f/	NUM
iajs-2476	312	21	ann(h	ann(h	PROPN
iajs-2476	312	22	)	)	PUNCT
iajs-2476	312	23	⟹	⟹	X
iajs-2476	312	24	ϑ	ϑ	PROPN
iajs-2476	312	25	1	1	NUM
iajs-2476	312	26	⟹	⟹	NUM
iajs-2476	312	27	a	a	DET
iajs-2476	312	28	=	=	PROPN
iajs-2476	312	29	y	y	PROPN
iajs-2476	312	30	\	\	PROPN
iajs-2476	312	31	v	v	NOUN
iajs-2476	312	32	(	(	PUNCT
iajs-2476	312	33	ϑ	ϑ	X
iajs-2476	312	34	=	=	SYM
iajs-2476	312	35	y	y	PROPN
iajs-2476	312	36	\	\	PROPN
iajs-2476	312	37	v	v	NOUN
iajs-2476	312	38	(	(	PUNCT
iajs-2476	312	39	1	1	NUM
iajs-2476	312	40	=	=	PROPN
iajs-2476	312	41	y	y	PROPN
iajs-2476	312	42	,	,	PUNCT
iajs-2476	312	43	a	a	DET
iajs-2476	312	44	discrepancy	discrepancy	NOUN
iajs-2476	312	45	,	,	PUNCT
iajs-2476	312	46	if	if	SCONJ
iajs-2476	312	47	σ(a	σ(a	PROPN
iajs-2476	312	48	)	)	PUNCT
iajs-2476	312	49	=	=	NOUN
iajs-2476	312	50	∅	∅	NOUN
iajs-2476	312	51	,	,	PUNCT
iajs-2476	312	52	then	then	ADV
iajs-2476	312	53	we	we	PRON
iajs-2476	312	54	must	must	AUX
iajs-2476	312	55	have	have	VERB
iajs-2476	312	56	v	v	NOUN
iajs-2476	312	57	(	(	PUNCT
iajs-2476	312	58	ϑ	ϑ	X
iajs-2476	312	59	∶	∶	NOUN
iajs-2476	312	60	1	1	NUM
iajs-2476	312	61	)	)	PUNCT
iajs-2476	313	1	=	=	SYM
iajs-2476	313	2	y	y	PROPN
iajs-2476	313	3	,	,	PUNCT
iajs-2476	313	4	and	and	CCONJ
iajs-2476	313	5	hence	hence	ADV
iajs-2476	313	6	ϑ	ϑ	X
iajs-2476	313	7	∶	∶	NOUN
iajs-2476	313	8	1	1	NUM
iajs-2476	313	9	=	=	SYM
iajs-2476	313	10	χ	χ	X
iajs-2476	313	11	0	0	NUM
iajs-2476	313	12	⟹	⟹	NUM
iajs-2476	313	13	ϑ	ϑ	PROPN
iajs-2476	313	14	χ	χ	PROPN
iajs-2476	313	15	0	0	NUM
iajs-2476	313	16	⟹	⟹	NUM
iajs-2476	313	17	a	a	DET
iajs-2476	313	18	=	=	PROPN
iajs-2476	313	19	y	y	NOUN
iajs-2476	313	20	\	\	PUNCT
iajs-2476	313	21	v(χ	v(χ	ADP
iajs-2476	313	22	0	0	NUM
iajs-2476	313	23	)	)	PUNCT
iajs-2476	313	24	=	=	SYM
iajs-2476	313	25	y	y	PROPN
iajs-2476	313	26	\	\	PROPN
iajs-2476	313	27	y	y	PROPN
iajs-2476	313	28	=	=	PUNCT
iajs-2476	313	29	∅	∅	NOUN
iajs-2476	313	30	,	,	PUNCT
iajs-2476	313	31	which	which	PRON
iajs-2476	313	32	is	be	AUX
iajs-2476	313	33	a	a	DET
iajs-2476	313	34	discrepancy	discrepancy	NOUN
iajs-2476	313	35	.	.	PUNCT
iajs-2476	314	1	therefore	therefore	ADV
iajs-2476	314	2	σ(a	σ(a	PROPN
iajs-2476	314	3	)	)	PUNCT
iajs-2476	314	4	is	be	AUX
iajs-2476	314	5	a	a	DET
iajs-2476	314	6	proper	proper	ADJ
iajs-2476	314	7	non	non	ADJ
iajs-2476	314	8	-	-	ADJ
iajs-2476	314	9	empty	empty	ADJ
iajs-2476	314	10	subset	subset	NOUN
iajs-2476	314	11	of	of	ADP
iajs-2476	314	12	y	y	PRON
iajs-2476	314	13	such	such	ADJ
iajs-2476	314	14	that	that	SCONJ
iajs-2476	314	15	it	it	PRON
iajs-2476	314	16	is	be	AUX
iajs-2476	314	17	both	both	CCONJ
iajs-2476	314	18	open	open	ADJ
iajs-2476	314	19	and	and	CCONJ
iajs-2476	314	20	closed	closed	ADJ
iajs-2476	314	21	,	,	PUNCT
iajs-2476	314	22	a	a	DET
iajs-2476	314	23	discrepancy	discrepancy	NOUN
iajs-2476	314	24	.	.	PUNCT
iajs-2476	315	1	thus	thus	ADV
iajs-2476	315	2	y	y	PROPN
iajs-2476	315	3	is	be	AUX
iajs-2476	315	4	linked	link	VERB
iajs-2476	315	5	.	.	PUNCT
iajs-2476	316	1	proposition	proposition	NOUN
iajs-2476	316	2	4.7	4.7	NUM
iajs-2476	316	3	:	:	PUNCT
iajs-2476	316	4	suppose	suppose	VERB
iajs-2476	316	5	that	that	SCONJ
iajs-2476	316	6	h	h	NOUN
iajs-2476	316	7	while	while	SCONJ
iajs-2476	316	8	h	h	NOUN
iajs-2476	316	9	́	́	PROPN
iajs-2476	316	10	is	be	AUX
iajs-2476	316	11	f	f	X
iajs-2476	316	12	–	–	PUNCT
iajs-2476	316	13	modules	module	NOUN
iajs-2476	316	14	.	.	PUNCT
iajs-2476	317	1	if	if	SCONJ
iajs-2476	317	2	y	y	PROPN
iajs-2476	317	3	=	=	PROPN
iajs-2476	317	4	la	la	NOUN
iajs-2476	317	5	-	-	PUNCT
iajs-2476	317	6	prim(h	prim(h	NOUN
iajs-2476	317	7	)	)	PUNCT
iajs-2476	317	8	,	,	PUNCT
iajs-2476	317	9	y	y	PROPN
iajs-2476	317	10	=	=	SYM
iajs-2476	317	11	́	́	PROPN
iajs-2476	317	12	la	la	ADJ
iajs-2476	317	13	-	-	PUNCT
iajs-2476	317	14	prim(h	prim(h	NOUN
iajs-2476	317	15	́	́	NOUN
iajs-2476	317	16	)	)	PUNCT
iajs-2476	317	17	and	and	CCONJ
iajs-2476	317	18	f	f	PROPN
iajs-2476	317	19	∶	∶	NOUN
iajs-2476	317	20	h	h	NOUN
iajs-2476	317	21	→	→	SYM
iajs-2476	317	22	h	h	NOUN
iajs-2476	317	23	́	́	PROPN
iajs-2476	317	24	be	be	AUX
iajs-2476	317	25	an	an	DET
iajs-2476	317	26	epimorphism	epimorphism	NOUN
iajs-2476	317	27	,	,	PUNCT
iajs-2476	317	28	then	then	ADV
iajs-2476	317	29	the	the	DET
iajs-2476	317	30	function	function	NOUN
iajs-2476	317	31	g	g	NOUN
iajs-2476	317	32	:	:	PUNCT
iajs-2476	317	33	y	y	PROPN
iajs-2476	317	34	́	́	PROPN
iajs-2476	317	35	→y	→y	PROPN
iajs-2476	317	36	is	be	AUX
iajs-2476	317	37	defined	define	VERB
iajs-2476	317	38	via	via	ADP
iajs-2476	317	39	g(ϑ	g(ϑ	PROPN
iajs-2476	317	40	́	́	PUNCT
iajs-2476	318	1	=	=	SYM
iajs-2476	318	2	f	f	X
iajs-2476	318	3	(	(	PUNCT
iajs-2476	318	4	ϑ	ϑ	X
iajs-2476	318	5	́	́	PROPN
iajs-2476	318	6	)	)	PUNCT
iajs-2476	318	7	be	be	AUX
iajs-2476	318	8	persistent	persistent	ADJ
iajs-2476	318	9	.	.	PUNCT
iajs-2476	319	1	proof	proof	NOUN
iajs-2476	319	2	let	let	VERB
iajs-2476	319	3	ϑ	ϑ	X
iajs-2476	319	4	∈	∈	NOUN
iajs-2476	319	5	la(h	la(h	PRON
iajs-2476	319	6	)	)	PUNCT
iajs-2476	319	7	while	while	SCONJ
iajs-2476	319	8	v(ϑ	v(ϑ	NOUN
iajs-2476	319	9	)	)	PUNCT
iajs-2476	319	10	be	be	VERB
iajs-2476	319	11	a	a	DET
iajs-2476	319	12	closed	closed	ADJ
iajs-2476	319	13	set	set	NOUN
iajs-2476	319	14	in	in	ADP
iajs-2476	319	15	y.	y.	NOUN
iajs-2476	319	16	for	for	ADP
iajs-2476	319	17	q	q	PROPN
iajs-2476	319	18	∈	∈	PROPN
iajs-2476	319	19	g	g	PROPN
iajs-2476	319	20	(	(	PUNCT
iajs-2476	319	21	v(ϑ	v(ϑ	PROPN
iajs-2476	319	22	)	)	PUNCT
iajs-2476	319	23	)	)	PUNCT
iajs-2476	319	24	by	by	ADP
iajs-2476	319	25	proposition	proposition	NOUN
iajs-2476	319	26	3.4	3.4	NUM
iajs-2476	319	27	(	(	PUNCT
iajs-2476	319	28	b	b	NOUN
iajs-2476	319	29	)	)	PUNCT
iajs-2476	319	30	,	,	PUNCT
iajs-2476	319	31	we	we	PRON
iajs-2476	319	32	have	have	VERB
iajs-2476	319	33	v(ϑ	v(ϑ	NOUN
iajs-2476	319	34	)	)	PUNCT
iajs-2476	319	35	=	=	SYM
iajs-2476	320	1	v∗((ϑ	v∗((ϑ	NOUN
iajs-2476	320	2	:	:	PUNCT
iajs-2476	320	3	1	1	NUM
iajs-2476	320	4	)	)	PUNCT
iajs-2476	320	5	.	.	PUNCT
iajs-2476	321	1	1	1	X
iajs-2476	321	2	.	.	PUNCT
iajs-2476	322	1	thus	thus	ADV
iajs-2476	322	2	q	q	X
iajs-2476	322	3	∈	∈	PROPN
iajs-2476	322	4	g	g	PROPN
iajs-2476	322	5	(	(	PUNCT
iajs-2476	322	6	v∗((ϑ	v∗((ϑ	NOUN
iajs-2476	322	7	:	:	PUNCT
iajs-2476	322	8	1	1	NUM
iajs-2476	322	9	)	)	PUNCT
iajs-2476	322	10	.	.	PUNCT
iajs-2476	323	1	1	1	NUM
iajs-2476	323	2	⇔	⇔	PROPN
iajs-2476	323	3	g(q	g(q	PROPN
iajs-2476	323	4	́	́	PROPN
iajs-2476	323	5	)	)	PUNCT
iajs-2476	323	6	∈	∈	PROPN
iajs-2476	323	7	v∗((ϑ	v∗((ϑ	NOUN
iajs-2476	323	8	:	:	PUNCT
iajs-2476	323	9	1	1	NUM
iajs-2476	323	10	)	)	PUNCT
iajs-2476	323	11	.	.	PUNCT
iajs-2476	324	1	1	1	NUM
iajs-2476	324	2	⇔	⇔	X
iajs-2476	324	3	ϑ	ϑ	NOUN
iajs-2476	324	4	:	:	PUNCT
iajs-2476	324	5	1	1	NUM
iajs-2476	324	6	)	)	PUNCT
iajs-2476	324	7	.	.	PUNCT
iajs-2476	325	1	1	1	NUM
iajs-2476	325	2	⊆	⊆	NUM
iajs-2476	325	3	g(q	g(q	PROPN
iajs-2476	325	4	́	́	NOUN
iajs-2476	325	5	)	)	PUNCT
iajs-2476	325	6	=	=	SYM
iajs-2476	325	7	f	f	PROPN
iajs-2476	325	8	(	(	PUNCT
iajs-2476	325	9	q	q	PROPN
iajs-2476	325	10	́)⇔f((ϑ	́)⇔f((ϑ	PROPN
iajs-2476	325	11	:	:	PUNCT
iajs-2476	325	12	1	1	NUM
iajs-2476	325	13	)	)	PUNCT
iajs-2476	325	14	.	.	PUNCT
iajs-2476	326	1	1	1	NUM
iajs-2476	326	2	⊆	⊆	NUM
iajs-2476	326	3	q	q	PUNCT
iajs-2476	326	4	́	́	PROPN
iajs-2476	326	5	⇔	⇔	X
iajs-2476	326	6	(	(	PUNCT
iajs-2476	326	7	(	(	PUNCT
iajs-2476	326	8	ϑ	ϑ	X
iajs-2476	326	9	:	:	SYM
iajs-2476	326	10	1	1	NUM
iajs-2476	326	11	)	)	PUNCT
iajs-2476	326	12	.	.	PUNCT
iajs-2476	327	1	1	1	NUM
iajs-2476	327	2	́	́	NUM
iajs-2476	327	3	⊆	⊆	NUM
iajs-2476	327	4	q	q	SYM
iajs-2476	327	5	́	́	PROPN
iajs-2476	327	6	⇔	⇔	X
iajs-2476	327	7	q	q	X
iajs-2476	327	8	́	́	PROPN
iajs-2476	327	9	∈	∈	PROPN
iajs-2476	327	10	v∗((ϑ	v∗((ϑ	NOUN
iajs-2476	327	11	:	:	PUNCT
iajs-2476	327	12	1	1	NUM
iajs-2476	327	13	)	)	PUNCT
iajs-2476	327	14	.	.	PUNCT
iajs-2476	328	1	1	1	NUM
iajs-2476	328	2	́	́	PROPN
iajs-2476	328	3	=	=	PUNCT
iajs-2476	328	4	v((ϑ	v((ϑ	NOUN
iajs-2476	328	5	:	:	PUNCT
iajs-2476	328	6	1	1	NUM
iajs-2476	328	7	)	)	PUNCT
iajs-2476	328	8	.	.	PUNCT
iajs-2476	329	1	1	1	NUM
iajs-2476	329	2	́	́	PROPN
iajs-2476	329	3	.	.	PUNCT
iajs-2476	330	1	therefore	therefore	ADV
iajs-2476	330	2	g	g	PROPN
iajs-2476	330	3	(	(	PUNCT
iajs-2476	330	4	v(ϑ	v(ϑ	NOUN
iajs-2476	330	5	)	)	PUNCT
iajs-2476	330	6	)	)	PUNCT
iajs-2476	331	1	=	=	SYM
iajs-2476	331	2	v((ϑ	v((ϑ	NOUN
iajs-2476	331	3	:	:	PUNCT
iajs-2476	331	4	1	1	NUM
iajs-2476	331	5	)	)	PUNCT
iajs-2476	331	6	.	.	PUNCT
iajs-2476	332	1	1	1	NUM
iajs-2476	332	2	́	́	PROPN
iajs-2476	332	3	,	,	PUNCT
iajs-2476	332	4	and	and	CCONJ
iajs-2476	332	5	hence	hence	ADV
iajs-2476	332	6	g	g	PROPN
iajs-2476	332	7	is	be	AUX
iajs-2476	332	8	persistent	persistent	ADJ
iajs-2476	332	9	.	.	PUNCT
iajs-2476	333	1	5	5	NUM
iajs-2476	333	2	a	a	DET
iajs-2476	333	3	basis	basis	NOUN
iajs-2476	333	4	for	for	ADP
iajs-2476	333	5	the	the	DET
iajs-2476	333	6	zariski	zariski	NOUN
iajs-2476	333	7	topology	topology	NOUN
iajs-2476	333	8	over	over	ADP
iajs-2476	333	9	la	la	NOUN
iajs-2476	333	10	-	-	PUNCT
iajs-2476	333	11	prim(h	prim(h	NOUN
iajs-2476	333	12	)	)	PUNCT
iajs-2476	333	13	proposition	proposition	NOUN
iajs-2476	333	14	5.1	5.1	NUM
iajs-2476	333	15	[	[	X
iajs-2476	333	16	12	12	NUM
iajs-2476	333	17	]	]	X
iajs-2476	333	18	if	if	SCONJ
iajs-2476	333	19	g	g	PROPN
iajs-2476	333	20	is	be	AUX
iajs-2476	333	21	a	a	DET
iajs-2476	333	22	homomorphism	homomorphism	NOUN
iajs-2476	333	23	from	from	ADP
iajs-2476	333	24	𝐅	𝐅	PROPN
iajs-2476	333	25	onto	onto	ADP
iajs-2476	333	26	𝐅	𝐅	PROPN
iajs-2476	333	27	́	́	PROPN
iajs-2476	333	28	,	,	PUNCT
iajs-2476	333	29	then	then	ADV
iajs-2476	333	30	for	for	ADP
iajs-2476	333	31	each	each	DET
iajs-2476	333	32	y	y	PROPN
iajs-2476	333	33	∈	∈	PROPN
iajs-2476	333	34	𝐅	𝐅	PROPN
iajs-2476	333	35	and	and	CCONJ
iajs-2476	333	36	𝜶	𝜶	ADP
iajs-2476	333	37	∈	∈	NOUN
iajs-2476	333	38	la	la	PRON
iajs-2476	333	39	\	\	PROPN
iajs-2476	333	40	{	{	PUNCT
iajs-2476	333	41	0	0	NUM
iajs-2476	333	42	}	}	PUNCT
iajs-2476	333	43	;	;	PUNCT
iajs-2476	333	44	g(y	g(y	PROPN
iajs-2476	333	45	𝜶	𝜶	NOUN
iajs-2476	333	46	=	=	SYM
iajs-2476	333	47	(	(	PUNCT
iajs-2476	333	48	𝐠	𝐠	X
iajs-2476	333	49	𝐲	𝐲	ADP
iajs-2476	333	50	𝜶.	𝜶.	NOUN
iajs-2476	333	51	corollary	corollary	NOUN
iajs-2476	333	52	5.2	5.2	NUM
iajs-2476	333	53	suppose	suppose	VERB
iajs-2476	333	54	that	that	SCONJ
iajs-2476	333	55	y	y	PROPN
iajs-2476	333	56	∈	∈	PROPN
iajs-2476	333	57	𝐅	𝐅	PROPN
iajs-2476	333	58	,	,	PUNCT
iajs-2476	333	59	then	then	ADV
iajs-2476	333	60	for	for	ADP
iajs-2476	333	61	all	all	DET
iajs-2476	333	62	ideal	ideal	PROPN
iajs-2476	333	63	b	b	PROPN
iajs-2476	333	64	of	of	ADP
iajs-2476	333	65	𝐅	𝐅	PROPN
iajs-2476	333	66	,	,	PUNCT
iajs-2476	333	67	and	and	CCONJ
iajs-2476	333	68	for	for	ADP
iajs-2476	333	69	all	all	PRON
iajs-2476	333	70	𝜶	𝜶	PART
iajs-2476	333	71	∈	∈	NOUN
iajs-2476	333	72	la	la	PRON
iajs-2476	333	73	\	\	X
iajs-2476	333	74	{	{	PUNCT
iajs-2476	333	75	0	0	NUM
iajs-2476	333	76	}	}	PUNCT
iajs-2476	333	77	;	;	PUNCT
iajs-2476	333	78	𝒚𝜶	𝒚𝜶	ADP
iajs-2476	333	79	=	=	SYM
iajs-2476	333	80	𝒚𝜶	𝒚𝜶	NOUN
iajs-2476	333	81	)	)	PUNCT
iajs-2476	333	82	,	,	PUNCT
iajs-2476	333	83	where	where	SCONJ
iajs-2476	333	84	𝒚𝜶	𝒚𝜶	AUX
iajs-2476	333	85	be	be	AUX
iajs-2476	333	86	an	an	DET
iajs-2476	333	87	la	la	ADJ
iajs-2476	333	88	-	-	PUNCT
iajs-2476	333	89	point	point	NOUN
iajs-2476	333	90	of	of	ADP
iajs-2476	333	91	𝐅	𝐅	PROPN
iajs-2476	333	92	/	/	SYM
iajs-2476	333	93	b	b	PROPN
iajs-2476	333	94	for	for	ADP
iajs-2476	333	95	each	each	DET
iajs-2476	333	96	𝐅-module	𝐅-module	PROPN
iajs-2476	333	97	h	h	NOUN
iajs-2476	333	98	,	,	PUNCT
iajs-2476	333	99	we	we	PRON
iajs-2476	333	100	suppose	suppose	VERB
iajs-2476	333	101	the	the	DET
iajs-2476	333	102	collection	collection	NOUN
iajs-2476	333	103	c={d(𝒚𝜶.	c={d(𝒚𝜶.	NOUN
iajs-2476	333	104	𝟏𝐇	𝟏𝐇	NOUN
iajs-2476	333	105	|	|	INTJ
iajs-2476	333	106	y	y	PROPN
iajs-2476	333	107	∈	∈	PROPN
iajs-2476	333	108	𝐅	𝐅	PROPN
iajs-2476	333	109	,	,	PUNCT
iajs-2476	333	110	𝜶	𝜶	NOUN
iajs-2476	333	111	∈	∈	NOUN
iajs-2476	333	112	la	la	PRON
iajs-2476	333	113	\	\	PROPN
iajs-2476	333	114	{	{	PUNCT
iajs-2476	333	115	0	0	NUM
iajs-2476	333	116	}	}	PUNCT
iajs-2476	333	117	}	}	PUNCT
iajs-2476	333	118	such	such	ADJ
iajs-2476	333	119	that	that	DET
iajs-2476	333	120	d(𝒚𝜶.	d(𝒚𝜶.	NOUN
iajs-2476	333	121	𝟏𝐇	𝟏𝐇	NOUN
iajs-2476	333	122	=	=	NOUN
iajs-2476	333	123	y	y	NOUN
iajs-2476	333	124	\	\	PROPN
iajs-2476	333	125	𝐕	𝐕	PROPN
iajs-2476	333	126	𝒚𝜶.	𝒚𝜶.	NOUN
iajs-2476	333	127	𝟏𝐇	𝟏𝐇	NOUN
iajs-2476	333	128	.	.	PUNCT
iajs-2476	334	1	we	we	PRON
iajs-2476	334	2	assumption	assumption	VERB
iajs-2476	334	3	that	that	SCONJ
iajs-2476	334	4	if	if	SCONJ
iajs-2476	334	5	the	the	DET
iajs-2476	334	6	lattice	lattice	NOUN
iajs-2476	334	7	la	la	PROPN
iajs-2476	334	8	is	be	AUX
iajs-2476	334	9	a	a	DET
iajs-2476	334	10	chain	chain	NOUN
iajs-2476	334	11	then	then	ADV
iajs-2476	334	12	c	c	NOUN
iajs-2476	334	13	formation	formation	VERB
iajs-2476	334	14	a	a	DET
iajs-2476	334	15	basis	basis	NOUN
iajs-2476	334	16	for	for	ADP
iajs-2476	334	17	zarski	zarski	ADJ
iajs-2476	334	18	topology	topology	NOUN
iajs-2476	334	19	on	on	ADP
iajs-2476	334	20	y	y	PROPN
iajs-2476	334	21	=	=	PROPN
iajs-2476	334	22	la	la	NOUN
iajs-2476	334	23	-	-	PUNCT
iajs-2476	334	24	prim(h	prim(h	NOUN
iajs-2476	334	25	)	)	PUNCT
iajs-2476	334	26	.	.	PUNCT
iajs-2476	335	1	we	we	PRON
iajs-2476	335	2	suppose	suppose	VERB
iajs-2476	335	3	the	the	DET
iajs-2476	335	4	following	follow	VERB
iajs-2476	335	5	states	state	NOUN
iajs-2476	335	6	:	:	PUNCT
iajs-2476	335	7	(	(	PUNCT
iajs-2476	335	8	1	1	X
iajs-2476	335	9	)	)	PUNCT
iajs-2476	335	10	if	if	SCONJ
iajs-2476	335	11	𝜶=1	𝜶=1	ADP
iajs-2476	335	12	while	while	SCONJ
iajs-2476	335	13	y	y	PROPN
iajs-2476	335	14	=	=	SYM
iajs-2476	335	15	0	0	PROPN
iajs-2476	335	16	,	,	PUNCT
iajs-2476	335	17	d(01.1h	d(01.1h	NUM
iajs-2476	335	18	)	)	PUNCT
iajs-2476	335	19	=	=	SYM
iajs-2476	336	1	y	y	PROPN
iajs-2476	336	2	\v	\v	X
iajs-2476	336	3	(	(	PUNCT
iajs-2476	336	4	01.1h	01.1h	NUM
iajs-2476	336	5	)	)	PUNCT
iajs-2476	336	6	=	=	SYM
iajs-2476	336	7	y	y	PROPN
iajs-2476	336	8	\v	\v	X
iajs-2476	336	9	(	(	PUNCT
iajs-2476	336	10	0h	0h	PROPN
iajs-2476	336	11	)	)	PUNCT
iajs-2476	336	12	=	=	PUNCT
iajs-2476	336	13	∅.	∅.	X
iajs-2476	336	14	(	(	PUNCT
iajs-2476	336	15	2	2	NUM
iajs-2476	336	16	)	)	PUNCT
iajs-2476	336	17	if	if	SCONJ
iajs-2476	336	18	𝜶	𝜶	NUM
iajs-2476	336	19	=	=	SYM
iajs-2476	336	20	1	1	NUM
iajs-2476	336	21	while	while	SCONJ
iajs-2476	336	22	y	y	PROPN
iajs-2476	336	23	=	=	SYM
iajs-2476	336	24	1	1	NUM
iajs-2476	336	25	,	,	PUNCT
iajs-2476	336	26	d(11.1h	d(11.1h	NUM
iajs-2476	336	27	)	)	PUNCT
iajs-2476	337	1	=	=	SYM
iajs-2476	337	2	y	y	PROPN
iajs-2476	337	3	\v	\v	X
iajs-2476	337	4	(	(	PUNCT
iajs-2476	337	5	11.1h	11.1h	NUM
iajs-2476	337	6	)	)	PUNCT
iajs-2476	337	7	=	=	SYM
iajs-2476	337	8	y	y	PROPN
iajs-2476	337	9	\v	\v	X
iajs-2476	337	10	(	(	PUNCT
iajs-2476	337	11	1h	1h	NUM
iajs-2476	337	12	)	)	PUNCT
iajs-2476	337	13	=	=	PUNCT
iajs-2476	338	1	y.	y.	NOUN
iajs-2476	338	2	  	  	SPACE
iajs-2476	338	3	99	99	NUM
iajs-2476	338	4	ibn	ibn	PROPN
iajs-2476	338	5	al	al	PROPN
iajs-2476	338	6	-	-	PUNCT
iajs-2476	338	7	haitham	haitham	PROPN
iajs-2476	338	8	jour	jour	X
iajs-2476	338	9	.	.	PROPN
iajs-2476	339	1	for	for	ADP
iajs-2476	339	2	pure	pure	ADJ
iajs-2476	339	3	&	&	CCONJ
iajs-2476	339	4	appl	appl	PROPN
iajs-2476	339	5	.	.	PUNCT
iajs-2476	340	1	sci	sci	PROPN
iajs-2476	340	2	.	.	PROPN
iajs-2476	341	1	33	33	NUM
iajs-2476	341	2	(	(	PUNCT
iajs-2476	341	3	3	3	NUM
iajs-2476	341	4	)	)	PUNCT
iajs-2476	341	5	2020	2020	NUM
iajs-2476	341	6	notation	notation	NOUN
iajs-2476	341	7	in	in	ADP
iajs-2476	341	8	the	the	DET
iajs-2476	341	9	complement	complement	NOUN
iajs-2476	341	10	for	for	ADP
iajs-2476	341	11	𝛾	𝛾	PROPN
iajs-2476	341	12	∈	∈	PROPN
iajs-2476	341	13	lai	lai	NOUN
iajs-2476	341	14	(	(	PUNCT
iajs-2476	341	15	f	f	X
iajs-2476	341	16	)	)	PUNCT
iajs-2476	341	17	we	we	PRON
iajs-2476	341	18	put	put	VERB
iajs-2476	341	19	e(𝛾	e(𝛾	NOUN
iajs-2476	341	20	)	)	PUNCT
iajs-2476	342	1	=	=	SYM
iajs-2476	342	2	la	la	NOUN
iajs-2476	342	3	-	-	PUNCT
iajs-2476	342	4	prim(f	prim(f	NOUN
iajs-2476	342	5	)	)	PUNCT
iajs-2476	342	6	\	\	PUNCT
iajs-2476	343	1	v(𝛾	v(𝛾	NOUN
iajs-2476	343	2	)	)	PUNCT
iajs-2476	343	3	.	.	PUNCT
iajs-2476	344	1	proposition	proposition	NOUN
iajs-2476	344	2	5.3	5.3	NUM
iajs-2476	344	3	if	if	SCONJ
iajs-2476	344	4	σ	σ	NOUN
iajs-2476	344	5	:	:	PUNCT
iajs-2476	344	6	y	y	PROPN
iajs-2476	344	7	→	→	SYM
iajs-2476	344	8	y	y	PROPN
iajs-2476	344	9	is	be	AUX
iajs-2476	344	10	standard	standard	ADJ
iajs-2476	344	11	function	function	NOUN
iajs-2476	344	12	,	,	PUNCT
iajs-2476	344	13	then	then	ADV
iajs-2476	344	14	(	(	PUNCT
iajs-2476	344	15	a	a	X
iajs-2476	344	16	)	)	PUNCT
iajs-2476	344	17	σ−1(e(y	σ−1(e(y	X
iajs-2476	344	18	)	)	PUNCT
iajs-2476	344	19	)	)	PUNCT
iajs-2476	345	1	=	=	PUNCT
iajs-2476	345	2	d(y	d(y	NOUN
iajs-2476	345	3	.1h	.1h	PROPN
iajs-2476	345	4	)	)	PUNCT
iajs-2476	345	5	;	;	PUNCT
iajs-2476	345	6	(	(	PUNCT
iajs-2476	345	7	b	b	X
iajs-2476	345	8	)	)	PUNCT
iajs-2476	345	9	σ(d(y	σ(d(y	NOUN
iajs-2476	345	10	.1h	.1h	PROPN
iajs-2476	345	11	)	)	PUNCT
iajs-2476	345	12	)	)	PUNCT
iajs-2476	346	1	⊆	⊆	NUM
iajs-2476	346	2	e(y	e(y	ADJ
iajs-2476	346	3	)	)	PUNCT
iajs-2476	346	4	.	.	PUNCT
iajs-2476	347	1	further	far	ADV
iajs-2476	347	2	if	if	SCONJ
iajs-2476	347	3	σ	σ	PROPN
iajs-2476	347	4	is	be	AUX
iajs-2476	347	5	inclusive	inclusive	ADJ
iajs-2476	347	6	then	then	ADV
iajs-2476	347	7	the	the	DET
iajs-2476	347	8	parity	parity	NOUN
iajs-2476	347	9	satisfies	satisfie	NOUN
iajs-2476	347	10	.	.	PUNCT
iajs-2476	348	1	proof	proof	NOUN
iajs-2476	348	2	for	for	ADP
iajs-2476	348	3	(	(	PUNCT
iajs-2476	348	4	a	a	X
iajs-2476	348	5	)	)	PUNCT
iajs-2476	348	6	we	we	PRON
iajs-2476	348	7	have	have	AUX
iajs-2476	348	8	σ−1(e(y	σ−1(e(y	VERB
iajs-2476	348	9	)	)	PUNCT
iajs-2476	348	10	)	)	PUNCT
iajs-2476	349	1	=	=	SYM
iajs-2476	349	2	σ−1	σ−1	NUM
iajs-2476	349	3	y	y	NOUN
iajs-2476	349	4	\	\	PROPN
iajs-2476	349	5	v(y	v(y	PROPN
iajs-2476	349	6	)	)	PUNCT
iajs-2476	349	7	)	)	PUNCT
iajs-2476	350	1	=	=	SYM
iajs-2476	350	2	y	y	PROPN
iajs-2476	350	3	\	\	PROPN
iajs-2476	350	4	σ−1(v(y	σ−1(v(y	PROPN
iajs-2476	350	5	)	)	PUNCT
iajs-2476	350	6	)	)	PUNCT
iajs-2476	351	1	=	=	SYM
iajs-2476	351	2	y	y	NOUN
iajs-2476	351	3	\	\	PUNCT
iajs-2476	351	4	v(y	v(y	PROPN
iajs-2476	351	5	.	.	PUNCT
iajs-2476	352	1	1h	1h	NUM
iajs-2476	352	2	)	)	PUNCT
iajs-2476	353	1	=	=	SYM
iajs-2476	353	2	d	d	X
iajs-2476	353	3	(	(	PUNCT
iajs-2476	353	4	y	y	PROPN
iajs-2476	353	5	.	.	PUNCT
iajs-2476	353	6	1h	1h	NUM
iajs-2476	353	7	)	)	PUNCT
iajs-2476	353	8	.	.	PUNCT
iajs-2476	354	1	for	for	ADP
iajs-2476	354	2	(	(	PUNCT
iajs-2476	354	3	b	b	X
iajs-2476	354	4	)	)	PUNCT
iajs-2476	354	5	we	we	PRON
iajs-2476	354	6	have	have	VERB
iajs-2476	354	7	σ(σ−1(e(y	σ(σ−1(e(y	NOUN
iajs-2476	354	8	)	)	PUNCT
iajs-2476	354	9	)	)	PUNCT
iajs-2476	354	10	)	)	PUNCT
iajs-2476	355	1	=	=	PRON
iajs-2476	355	2	σ(d(y	σ(d(y	PROPN
iajs-2476	355	3	.1h	.1h	PROPN
iajs-2476	355	4	)	)	PUNCT
iajs-2476	355	5	)	)	PUNCT
iajs-2476	355	6	and	and	CCONJ
iajs-2476	355	7	σ(σ−1(e(y	σ(σ−1(e(y	NOUN
iajs-2476	355	8	)	)	PUNCT
iajs-2476	355	9	)	)	PUNCT
iajs-2476	355	10	)	)	PUNCT
iajs-2476	356	1	=	=	PUNCT
iajs-2476	356	2	⊆	⊆	NUM
iajs-2476	356	3	e(y	e(y	ADJ
iajs-2476	356	4	)	)	PUNCT
iajs-2476	356	5	.	.	PUNCT
iajs-2476	357	1	then	then	ADV
iajs-2476	357	2	σ(d(y	σ(d(y	VERB
iajs-2476	357	3	.1h	.1h	PROPN
iajs-2476	357	4	)	)	PUNCT
iajs-2476	357	5	)	)	PUNCT
iajs-2476	358	1	⊆	⊆	NUM
iajs-2476	358	2	e(y	e(y	ADJ
iajs-2476	358	3	)	)	PUNCT
iajs-2476	358	4	.	.	PUNCT
iajs-2476	359	1	so	so	ADV
iajs-2476	359	2	if	if	SCONJ
iajs-2476	359	3	σ	σ	PROPN
iajs-2476	359	4	is	be	AUX
iajs-2476	359	5	inclusive	inclusive	ADJ
iajs-2476	359	6	then	then	ADV
iajs-2476	359	7	we	we	PRON
iajs-2476	359	8	get	get	VERB
iajs-2476	359	9	that	that	DET
iajs-2476	359	10	σ(σ−1(e(y	σ(σ−1(e(y	NOUN
iajs-2476	359	11	)	)	PUNCT
iajs-2476	359	12	)	)	PUNCT
iajs-2476	359	13	)	)	PUNCT
iajs-2476	360	1	=	=	PUNCT
iajs-2476	360	2	e(y	e(y	ADJ
iajs-2476	360	3	)	)	PUNCT
iajs-2476	360	4	.	.	PUNCT
iajs-2476	361	1	thus	thus	ADV
iajs-2476	361	2	σ(d(y	σ(d(y	PROPN
iajs-2476	361	3	.1h)=e(y	.1h)=e(y	VERB
iajs-2476	361	4	)	)	PUNCT
iajs-2476	361	5	.	.	PUNCT
iajs-2476	362	1	proposition	proposition	NOUN
iajs-2476	362	2	5.4	5.4	NUM
iajs-2476	362	3	if	if	SCONJ
iajs-2476	362	4	a	a	PRON
iajs-2476	362	5	,	,	PUNCT
iajs-2476	362	6	b	b	PROPN
iajs-2476	362	7	∈	∈	PROPN
iajs-2476	362	8	f	f	PROPN
iajs-2476	362	9	and	and	CCONJ
iajs-2476	362	10	𝛼	𝛼	ADV
iajs-2476	362	11	,	,	PUNCT
iajs-2476	362	12	𝛼	𝛼	VERB
iajs-2476	362	13	◦	◦	NOUN
iajs-2476	362	14	∈	∈	NOUN
iajs-2476	362	15	la\{0	la\{0	NOUN
iajs-2476	362	16	}	}	PUNCT
iajs-2476	362	17	,	,	PUNCT
iajs-2476	362	18	then	then	ADV
iajs-2476	362	19	d(a	d(a	PROPN
iajs-2476	362	20	.1h	.1h	PROPN
iajs-2476	362	21	)	)	PUNCT
iajs-2476	362	22	∩	∩	NOUN
iajs-2476	362	23	d(𝑏	d(𝑏	PROPN
iajs-2476	362	24	◦	◦	NOUN
iajs-2476	362	25	.1h)=d	.1h)=d	PROPN
iajs-2476	362	26	(	(	PUNCT
iajs-2476	362	27	ab	ab	PROPN
iajs-2476	362	28	∧	∧	PROPN
iajs-2476	362	29	◦	◦	PROPN
iajs-2476	362	30	.1h	.1h	PROPN
iajs-2476	362	31	)	)	PUNCT
iajs-2476	362	32	.	.	PUNCT
iajs-2476	363	1	proof	proof	NOUN
iajs-2476	363	2	we	we	PRON
iajs-2476	363	3	have	have	VERB
iajs-2476	363	4	d(a	d(a	PROPN
iajs-2476	363	5	.	.	PUNCT
iajs-2476	364	1	1h	1h	NUM
iajs-2476	364	2	)	)	PUNCT
iajs-2476	364	3	∩	∩	PROPN
iajs-2476	364	4	d(𝑏	d(𝑏	PROPN
iajs-2476	364	5	◦	◦	NOUN
iajs-2476	364	6	.1h	.1h	NOUN
iajs-2476	364	7	)	)	PUNCT
iajs-2476	365	1	=	=	SYM
iajs-2476	365	2	σ−1(e(a	σ−1(e(a	NOUN
iajs-2476	365	3	)	)	PUNCT
iajs-2476	365	4	)	)	PUNCT
iajs-2476	365	5	∩	∩	NOUN
iajs-2476	365	6	σ−1(e(𝑏	σ−1(e(𝑏	VERB
iajs-2476	365	7	◦	◦	NOUN
iajs-2476	365	8	.	.	PUNCT
iajs-2476	365	9	)	)	PUNCT
iajs-2476	365	10	)	)	PUNCT
iajs-2476	366	1	=	=	SYM
iajs-2476	366	2	σ−1(e(a	σ−1(e(a	NOUN
iajs-2476	366	3	)	)	PUNCT
iajs-2476	366	4	∩	∩	NOUN
iajs-2476	366	5	e(𝑏	e(𝑏	PROPN
iajs-2476	366	6	◦	◦	NOUN
iajs-2476	366	7	.	.	PUNCT
iajs-2476	366	8	)	)	PUNCT
iajs-2476	366	9	)	)	PUNCT
iajs-2476	367	1	=	=	PUNCT
iajs-2476	367	2	σ−1(e	σ−1(e	PROPN
iajs-2476	367	3	(	(	PUNCT
iajs-2476	367	4	ab	ab	PROPN
iajs-2476	367	5	∧	∧	PROPN
iajs-2476	367	6	◦	◦	NOUN
iajs-2476	367	7	)	)	PUNCT
iajs-2476	367	8	=	=	PUNCT
iajs-2476	368	1	d	d	X
iajs-2476	368	2	(	(	PUNCT
iajs-2476	368	3	ab	ab	PROPN
iajs-2476	368	4	∧	∧	PROPN
iajs-2476	368	5	◦	◦	PROPN
iajs-2476	368	6	.1h	.1h	PROPN
iajs-2476	368	7	)	)	PUNCT
iajs-2476	368	8	.	.	PUNCT
iajs-2476	369	1	in	in	ADP
iajs-2476	369	2	the	the	DET
iajs-2476	369	3	complement	complement	NOUN
iajs-2476	369	4	,	,	PUNCT
iajs-2476	369	5	we	we	PRON
iajs-2476	369	6	suppose	suppose	VERB
iajs-2476	369	7	that	that	SCONJ
iajs-2476	369	8	the	the	DET
iajs-2476	369	9	lattice	lattice	NOUN
iajs-2476	369	10	la	la	PROPN
iajs-2476	369	11	is	be	AUX
iajs-2476	369	12	a	a	DET
iajs-2476	369	13	chain	chain	NOUN
iajs-2476	369	14	.	.	PUNCT
iajs-2476	370	1	theorem	theorem	VERB
iajs-2476	370	2	5.5	5.5	NUM
iajs-2476	370	3	for	for	ADP
iajs-2476	370	4	each	each	DET
iajs-2476	370	5	f	f	NOUN
iajs-2476	370	6	-	-	PUNCT
iajs-2476	370	7	module	module	NOUN
iajs-2476	370	8	h	h	NOUN
iajs-2476	370	9	,	,	PUNCT
iajs-2476	370	10	the	the	DET
iajs-2476	370	11	collection	collection	NOUN
iajs-2476	370	12	c={d(a	c={d(a	PROPN
iajs-2476	370	13	.1h	.1h	PROPN
iajs-2476	370	14	)	)	PUNCT
iajs-2476	370	15	|x	|x	NOUN
iajs-2476	370	16	∈	∈	PROPN
iajs-2476	370	17	f	f	PROPN
iajs-2476	370	18	,	,	PUNCT
iajs-2476	370	19	α	α	PROPN
iajs-2476	370	20	∈	∈	PROPN
iajs-2476	370	21	la\{0	la\{0	PRON
iajs-2476	370	22	}	}	PUNCT
iajs-2476	370	23	}	}	PUNCT
iajs-2476	370	24	formation	formation	VERB
iajs-2476	370	25	a	a	DET
iajs-2476	370	26	basis	basis	NOUN
iajs-2476	370	27	for	for	ADP
iajs-2476	370	28	zariski	zariski	ADJ
iajs-2476	370	29	topology	topology	NOUN
iajs-2476	370	30	over	over	ADP
iajs-2476	370	31	y	y	PROPN
iajs-2476	370	32	=	=	PROPN
iajs-2476	370	33	la	la	NOUN
iajs-2476	370	34	-	-	PUNCT
iajs-2476	370	35	prim(h	prim(h	NOUN
iajs-2476	370	36	)	)	PUNCT
iajs-2476	370	37	.	.	PUNCT
iajs-2476	371	1	proof	proof	NOUN
iajs-2476	371	2	let	let	VERB
iajs-2476	371	3	w	w	NOUN
iajs-2476	371	4	be	be	AUX
iajs-2476	371	5	an	an	DET
iajs-2476	371	6	arbitrary	arbitrary	ADJ
iajs-2476	371	7	open	open	ADJ
iajs-2476	371	8	set	set	NOUN
iajs-2476	371	9	in	in	ADP
iajs-2476	371	10	y.	y.	PROPN
iajs-2476	371	11	then	then	ADV
iajs-2476	371	12	w=	w=	PROPN
iajs-2476	371	13	d(ϑ)=y	d(ϑ)=y	PROPN
iajs-2476	371	14	\v	\v	X
iajs-2476	371	15	(	(	PUNCT
iajs-2476	371	16	ϑ	ϑ	NOUN
iajs-2476	371	17	)	)	PUNCT
iajs-2476	371	18	for	for	ADP
iajs-2476	371	19	several	several	ADJ
iajs-2476	371	20	ϑ	ϑ	X
iajs-2476	371	21	∈	∈	NOUN
iajs-2476	371	22	la(h	la(h	NUM
iajs-2476	371	23	)	)	PUNCT
iajs-2476	371	24	.	.	PUNCT
iajs-2476	372	1	via	via	ADP
iajs-2476	372	2	proposition	proposition	NOUN
iajs-2476	372	3	3.4	3.4	NUM
iajs-2476	372	4	,	,	PUNCT
iajs-2476	372	5	v(ϑ)=v((ϑ:1h	v(ϑ)=v((ϑ:1h	PUNCT
iajs-2476	372	6	)	)	PUNCT
iajs-2476	372	7	.1h	.1h	PROPN
iajs-2476	372	8	)	)	PUNCT
iajs-2476	372	9	.	.	PUNCT
iajs-2476	373	1	by	by	ADP
iajs-2476	373	2	considering	consider	VERB
iajs-2476	373	3	𝛾	𝛾	ADP
iajs-2476	373	4	ϑ:1h	ϑ:1h	NOUN
iajs-2476	373	5	,	,	PUNCT
iajs-2476	373	6	then	then	ADV
iajs-2476	373	7	v(ϑ)=v(𝛾.1h	v(ϑ)=v(𝛾.1h	PROPN
iajs-2476	373	8	)	)	PUNCT
iajs-2476	373	9	as	as	SCONJ
iajs-2476	373	10	we	we	PRON
iajs-2476	373	11	aforesaid	aforesaid	VERB
iajs-2476	373	12	in	in	ADP
iajs-2476	373	13	the	the	DET
iajs-2476	373	14	basic	basic	ADJ
iajs-2476	373	15	concepts	concept	NOUN
iajs-2476	373	16	,	,	PUNCT
iajs-2476	373	17	we	we	PRON
iajs-2476	373	18	can	can	AUX
iajs-2476	373	19	write	write	VERB
iajs-2476	373	20	𝛾=⋃	𝛾=⋃	NOUN
iajs-2476	373	21	𝑐𝛾∈	𝑐𝛾∈	PROPN
iajs-2476	373	22	.	.	PUNCT
iajs-2476	374	1	obviously	obviously	ADV
iajs-2476	374	2	we	we	PRON
iajs-2476	374	3	have	have	VERB
iajs-2476	374	4	𝑐𝛾	𝑐𝛾	ADP
iajs-2476	374	5	=	=	NOUN
iajs-2476	374	6	⋃	⋃	PROPN
iajs-2476	374	7	𝛾∈	𝛾∈	PROPN
iajs-2476	374	8	.	.	PUNCT
iajs-2476	375	1	thus	thus	ADV
iajs-2476	375	2	we	we	PRON
iajs-2476	375	3	get	get	VERB
iajs-2476	375	4	that	that	PRON
iajs-2476	375	5	v(𝛾.1h	v(𝛾.1h	NOUN
iajs-2476	375	6	)	)	PUNCT
iajs-2476	375	7	=	=	NOUN
iajs-2476	375	8	v	v	ADP
iajs-2476	375	9	⋃	⋃	NOUN
iajs-2476	375	10	⋃	⋃	NOUN
iajs-2476	375	11	𝑦	𝑦	NOUN
iajs-2476	375	12	.1∈∈	.1∈∈	PUNCT
iajs-2476	376	1	=	=	NOUN
iajs-2476	376	2	v	v	ADP
iajs-2476	376	3	⋃	⋃	PROPN
iajs-2476	376	4	𝑦	𝑦	NOUN
iajs-2476	376	5	.1∈	.1∈	X
iajs-2476	376	6	,	,	PUNCT
iajs-2476	376	7	∈	∈	PROPN
iajs-2476	376	8	=	=	SYM
iajs-2476	376	9	v	v	ADP
iajs-2476	376	10	⋃	⋃	PROPN
iajs-2476	376	11	𝑦	𝑦	NOUN
iajs-2476	376	12	.	.	PUNCT
iajs-2476	377	1	1∈	1∈	PROPN
iajs-2476	377	2	,	,	PUNCT
iajs-2476	377	3	∈	∈	PROPN
iajs-2476	377	4	(	(	PUNCT
iajs-2476	377	5	since	since	SCONJ
iajs-2476	377	6	la	la	X
iajs-2476	377	7	is	be	AUX
iajs-2476	377	8	a	a	DET
iajs-2476	377	9	chain	chain	NOUN
iajs-2476	377	10	)	)	PUNCT
iajs-2476	378	1	=	=	SYM
iajs-2476	379	1	⋂	⋂	PROPN
iajs-2476	379	2	v	v	NUM
iajs-2476	379	3	𝑦	𝑦	PROPN
iajs-2476	379	4	.	.	PUNCT
iajs-2476	380	1	1∈	1∈	PROPN
iajs-2476	380	2	,	,	PUNCT
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iajs-2476	380	6	\v(ϑ	\v(ϑ	NOUN
iajs-2476	380	7	)	)	PUNCT
iajs-2476	381	1	=	=	SYM
iajs-2476	381	2	y	y	PROPN
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iajs-2476	382	1	⋂	⋂	PROPN
iajs-2476	382	2	v	v	NUM
iajs-2476	382	3	𝑦	𝑦	PROPN
iajs-2476	382	4	.	.	PUNCT
iajs-2476	383	1	1∈	1∈	PROPN
iajs-2476	383	2	,	,	PUNCT
iajs-2476	383	3	∈	∈	PROPN
iajs-2476	384	1	=	=	PUNCT
iajs-2476	384	2	⋃	⋃	PROPN
iajs-2476	384	3	y	y	PROPN
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iajs-2476	384	5	𝑦	𝑦	PROPN
iajs-2476	384	6	.	.	PUNCT
iajs-2476	385	1	1∈	1∈	PROPN
iajs-2476	385	2	,	,	PUNCT
iajs-2476	385	3	∈	∈	PROPN
iajs-2476	385	4	)	)	PUNCT
iajs-2476	385	5	)	)	PUNCT
iajs-2476	386	1	=	=	SYM
iajs-2476	386	2	⋃	⋃	PROPN
iajs-2476	386	3	𝐷	𝐷	NOUN
iajs-2476	386	4	𝑦	𝑦	NOUN
iajs-2476	386	5	.	.	PUNCT
iajs-2476	387	1	1∈	1∈	PROPN
iajs-2476	387	2	,	,	PUNCT
iajs-2476	387	3	∈	∈	PROPN
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iajs-2476	387	7	c	c	PROPN
iajs-2476	387	8	is	be	AUX
iajs-2476	387	9	a	a	DET
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iajs-2476	387	12	the	the	DET
iajs-2476	387	13	zariski	zariski	NOUN
iajs-2476	387	14	topology	topology	NOUN
iajs-2476	387	15	over	over	ADP
iajs-2476	387	16	y	y	PROPN
iajs-2476	387	17	.	.	PUNCT
iajs-2476	388	1	proposition	proposition	NOUN
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iajs-2476	388	4	that	that	SCONJ
iajs-2476	388	5	h	h	NOUN
iajs-2476	388	6	is	be	AUX
iajs-2476	388	7	an	an	DET
iajs-2476	388	8	f	f	NOUN
iajs-2476	388	9	-	-	PUNCT
iajs-2476	388	10	module	module	NOUN
iajs-2476	388	11	.	.	PUNCT
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iajs-2476	389	4	function	function	NOUN
iajs-2476	389	5	σ	σ	PROPN
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iajs-2476	389	10	y	y	PROPN
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iajs-2476	389	13	-	-	PUNCT
iajs-2476	389	14	prim(h	prim(h	NOUN
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iajs-2476	389	18	.	.	PUNCT
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iajs-2476	390	2	:	:	PUNCT
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iajs-2476	390	4	that	that	SCONJ
iajs-2476	390	5	y=⋃	y=⋃	PROPN
iajs-2476	390	6	𝐷	𝐷	PROPN
iajs-2476	390	7	𝑦α	𝑦α	NOUN
iajs-2476	390	8	.	.	PROPN
iajs-2476	390	9	1	1	NUM
iajs-2476	390	10	|𝑦	|𝑦	PROPN
iajs-2476	390	11	∈	∈	PROPN
iajs-2476	390	12	f	f	PROPN
iajs-2476	390	13	,	,	PUNCT
iajs-2476	390	14	α	α	PROPN
iajs-2476	390	15	∈	∈	PROPN
iajs-2476	390	16	𝐿𝑎\	𝐿𝑎\	PROPN
iajs-2476	390	17	{	{	PUNCT
iajs-2476	390	18	0	0	NUM
iajs-2476	390	19	}	}	PUNCT
iajs-2476	390	20	}	}	PUNCT
iajs-2476	390	21	.	.	PUNCT
iajs-2476	391	1	then	then	ADV
iajs-2476	391	2	𝑌=	𝑌=	PROPN
iajs-2476	391	3	σ(y	σ(y	X
iajs-2476	391	4	)	)	PUNCT
iajs-2476	391	5	=	=	SYM
iajs-2476	392	1	σ(⋃	σ(⋃	PUNCT
iajs-2476	392	2	𝐷	𝐷	PROPN
iajs-2476	392	3	𝑦	𝑦	NOUN
iajs-2476	392	4	.	.	PROPN
iajs-2476	393	1	1	1	NUM
iajs-2476	393	2	|𝑦	|𝑦	PROPN
iajs-2476	393	3	∈	∈	PROPN
iajs-2476	393	4	f	f	PROPN
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iajs-2476	393	6	α	α	PROPN
iajs-2476	393	7	∈	∈	PROPN
iajs-2476	393	8	𝐿𝑎\	𝐿𝑎\	PROPN
iajs-2476	393	9	{	{	PUNCT
iajs-2476	393	10	0	0	NUM
iajs-2476	393	11	}	}	PUNCT
iajs-2476	393	12	}	}	PUNCT
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iajs-2476	394	1	=	=	NOUN
iajs-2476	394	2	⋃	⋃	PROPN
iajs-2476	394	3	σ	σ	PROPN
iajs-2476	394	4	𝐷	𝐷	PROPN
iajs-2476	394	5	𝑦	𝑦	NOUN
iajs-2476	394	6	.	.	PROPN
iajs-2476	394	7	1	1	NUM
iajs-2476	394	8	|𝑦	|𝑦	PROPN
iajs-2476	394	9	∈	∈	PROPN
iajs-2476	394	10	f	f	PROPN
iajs-2476	394	11	,	,	PUNCT
iajs-2476	394	12	α	α	PROPN
iajs-2476	394	13	∈	∈	PROPN
iajs-2476	394	14	𝐿𝑎\	𝐿𝑎\	PROPN
iajs-2476	394	15	{	{	PUNCT
iajs-2476	394	16	0	0	NUM
iajs-2476	394	17	}	}	PUNCT
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iajs-2476	394	19	=	=	PUNCT
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iajs-2476	394	21	𝑦	𝑦	X
iajs-2476	394	22	|𝑦	|𝑦	PROPN
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iajs-2476	394	24	f	f	PROPN
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iajs-2476	394	27	∈	∈	PROPN
iajs-2476	394	28	𝐿𝑎\	𝐿𝑎\	PROPN
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iajs-2476	394	35	σ	σ	PROPN
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iajs-2476	394	40	  	  	SPACE
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iajs-2476	395	12	.	.	PUNCT
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iajs-2476	397	2	(	(	PUNCT
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iajs-2476	398	3	since	since	SCONJ
iajs-2476	398	4	𝑌	𝑌	PROPN
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iajs-2476	398	7	,	,	PUNCT
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iajs-2476	398	9	can	can	AUX
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iajs-2476	398	11	𝑌=⋃	𝑌=⋃	NUM
iajs-2476	398	12	𝑦𝚥𝒏	𝑦𝚥𝒏	NOUN
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iajs-2476	398	14	𝟏	𝟏	NUM
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iajs-2476	398	19	)	)	PUNCT
iajs-2476	398	20	=	=	PUNCT
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iajs-2476	398	22	𝑦𝚥𝒏	𝑦𝚥𝒏	NOUN
iajs-2476	398	23	𝒋	𝒋	X
iajs-2476	398	24	𝟏	𝟏	NUM
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iajs-2476	398	26	.	.	PUNCT
iajs-2476	399	1	thus	thus	ADV
iajs-2476	399	2	y=⋃	y=⋃	PROPN
iajs-2476	399	3	σ	σ	PROPN
iajs-2476	399	4	𝑦𝚥𝒏	𝑦𝚥𝒏	PROPN
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iajs-2476	399	10	σ	σ	NOUN
iajs-2476	399	11	𝑦𝚥	𝑦𝚥	X
iajs-2476	399	12	=	=	PUNCT
iajs-2476	399	13	𝑦𝑗	𝑦𝑗	NOUN
iajs-2476	399	14	.	.	PUNCT
iajs-2476	400	1	1	1	X
iajs-2476	400	2	.	.	PUNCT
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iajs-2476	401	2	y	y	PROPN
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iajs-2476	401	5	.	.	PUNCT
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iajs-2476	403	13	a	a	DET
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iajs-2476	403	17	.	.	PUNCT
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iajs-2476	404	18	.	.	X
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iajs-2476	406	7	,	,	PUNCT
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iajs-2476	406	9	.	.	PUNCT
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iajs-2476	407	2	.	.	X
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iajs-2476	407	11	.	.	PUNCT
iajs-2476	408	1	j	j	PROPN
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iajs-2476	408	6	,	,	PUNCT
iajs-2476	408	7	1	1	NUM
iajs-2476	408	8	,	,	PUNCT
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iajs-2476	408	10	.	.	PUNCT
iajs-2476	409	1	4	4	X
iajs-2476	409	2	.	.	X
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iajs-2476	409	4	,	,	PUNCT
iajs-2476	409	5	r.	r.	PROPN
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iajs-2476	409	8	.	.	PUNCT
iajs-2476	410	1	j	j	PROPN
iajs-2476	410	2	math	math	PROPN
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iajs-2476	410	10	517	517	NUM
iajs-2476	410	11	.	.	NOUN
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iajs-2476	410	13	.	.	X
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iajs-2476	410	20	,	,	PUNCT
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iajs-2476	410	22	.	.	PROPN
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iajs-2476	410	28	,	,	PUNCT
iajs-2476	410	29	679	679	NUM
iajs-2476	410	30	.	.	NOUN
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iajs-2476	410	32	.	.	X
iajs-2476	411	1	pan	pan	PROPN
iajs-2476	411	2	,	,	PUNCT
iajs-2476	411	3	f	f	PROPN
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iajs-2476	411	5	z.	z.	PROPN
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iajs-2476	411	9	modules	module	NOUN
iajs-2476	411	10	.	.	PUNCT
iajs-2476	412	1	fuzzy	fuzzy	ADJ
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iajs-2476	412	4	,	,	PUNCT
iajs-2476	412	5	21	21	NUM
iajs-2476	412	6	,	,	PUNCT
iajs-2476	412	7	105–113	105–113	NUM
iajs-2476	412	8	.	.	PUNCT
iajs-2476	413	1	7	7	X
iajs-2476	413	2	.	.	X
iajs-2476	413	3	sidky	sidky	NOUN
iajs-2476	413	4	,	,	PUNCT
iajs-2476	413	5	fi	fi	NOUN
iajs-2476	413	6	.	.	NOUN
iajs-2476	414	1	on	on	ADP
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iajs-2476	414	5	submodules	submodule	NOUN
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iajs-2476	414	8	fuzzy	fuzzy	ADJ
iajs-2476	414	9	submodules	submodule	NOUN
iajs-2476	414	10	.	.	PUNCT
iajs-2476	415	1	fuzzy	fuzzy	ADJ
iajs-2476	415	2	sets	set	NOUN
iajs-2476	415	3	syst.2001	syst.2001	PROPN
iajs-2476	415	4	,	,	PUNCT
iajs-2476	415	5	119	119	NUM
iajs-2476	415	6	,	,	PUNCT
iajs-2476	415	7	419–425	419–425	NUM
iajs-2476	415	8	.	.	NOUN
iajs-2476	415	9	8	8	NUM
iajs-2476	415	10	.	.	PUNCT
iajs-2476	416	1	dixit	dixit	PROPN
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iajs-2476	416	3	v.n.l	v.n.l	PROPN
iajs-2476	416	4	.	.	PUNCT
iajs-2476	416	5	;	;	PUNCT
iajs-2476	416	6	kummar	kummar	PROPN
iajs-2476	416	7	,	,	PUNCT
iajs-2476	416	8	r.	r.	PROPN
iajs-2476	416	9	;	;	PUNCT
iajs-2476	416	10	ajmal	ajmal	ADJ
iajs-2476	416	11	,	,	PUNCT
iajs-2476	416	12	n.	n.	ADJ
iajs-2476	416	13	fuzzy	fuzzy	ADJ
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iajs-2476	416	15	and	and	CCONJ
iajs-2476	416	16	fuzzy	fuzzy	ADJ
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iajs-2476	417	6	,	,	PUNCT
iajs-2476	417	7	127	127	NUM
iajs-2476	417	8	-	-	SYM
iajs-2476	417	9	138	138	NUM
iajs-2476	417	10	.	.	NOUN
iajs-2476	418	1	9	9	NUM
iajs-2476	418	2	.	.	X
iajs-2476	418	3	mukherjee	mukherjee	PROPN
iajs-2476	418	4	,	,	PUNCT
iajs-2476	418	5	t.k	t.k	PROPN
iajs-2476	418	6	.	.	PROPN
iajs-2476	418	7	;	;	PUNCT
iajs-2476	418	8	sen	sen	PROPN
iajs-2476	418	9	,	,	PUNCT
iajs-2476	418	10	m.k	m.k	PROPN
iajs-2476	418	11	.	.	PUNCT
iajs-2476	419	1	on	on	ADP
iajs-2476	419	2	fuzzy	fuzzy	ADJ
iajs-2476	419	3	ideals	ideal	NOUN
iajs-2476	419	4	of	of	ADP
iajs-2476	419	5	a	a	DET
iajs-2476	419	6	ring	ring	NOUN
iajs-2476	419	7	i.	i.	NOUN
iajs-2476	419	8	fuzzy	fuzzy	PROPN
iajs-2476	419	9	sets	set	VERB
iajs-2476	419	10	syst.1987	syst.1987	PROPN
iajs-2476	419	11	,	,	PUNCT
iajs-2476	419	12	21	21	NUM
iajs-2476	419	13	,	,	PUNCT
iajs-2476	419	14	1	1	NUM
iajs-2476	419	15	,	,	PUNCT
iajs-2476	419	16	99	99	NUM
iajs-2476	419	17	–	–	PUNCT
iajs-2476	419	18	104	104	NUM
iajs-2476	419	19	.	.	PUNCT
iajs-2476	419	20	10	10	NUM
iajs-2476	419	21	.	.	PUNCT
iajs-2476	419	22	bhambri	bhambri	PROPN
iajs-2476	419	23	,	,	PUNCT
iajs-2476	419	24	s.k	s.k	PROPN
iajs-2476	419	25	.	.	PROPN
iajs-2476	419	26	;	;	PUNCT
iajs-2476	419	27	kumar	kumar	PROPN
iajs-2476	419	28	,	,	PUNCT
iajs-2476	419	29	r.	r.	PROPN
iajs-2476	419	30	;	;	PUNCT
iajs-2476	419	31	kumar	kumar	PROPN
iajs-2476	419	32	,	,	PUNCT
iajs-2476	419	33	p.	p.	NOUN
iajs-2476	419	34	fuzzy	fuzzy	ADJ
iajs-2476	419	35	prime	prime	ADJ
iajs-2476	419	36	submodules	submodule	NOUN
iajs-2476	419	37	and	and	CCONJ
iajs-2476	419	38	radical	radical	ADJ
iajs-2476	419	39	of	of	ADP
iajs-2476	419	40	a	a	DET
iajs-2476	419	41	fuzzy	fuzzy	ADJ
iajs-2476	419	42	submodules	submodule	NOUN
iajs-2476	419	43	.	.	PUNCT
iajs-2476	420	1	bull	bull	PROPN
iajs-2476	420	2	cal	cal	PROPN
iajs-2476	420	3	math	math	PROPN
iajs-2476	420	4	soc.1993	soc.1993	PROPN
iajs-2476	420	5	,	,	PUNCT
iajs-2476	420	6	87	87	NUM
iajs-2476	420	7	,	,	PUNCT
iajs-2476	420	8	163–168	163–168	NUM
iajs-2476	420	9	.	.	PUNCT
iajs-2476	420	10	11	11	NUM
iajs-2476	420	11	.	.	PUNCT
iajs-2476	421	1	hadji	hadji	PROPN
iajs-2476	421	2	-	-	PUNCT
iajs-2476	421	3	abadi	abadi	PROPN
iajs-2476	421	4	,	,	PUNCT
iajs-2476	421	5	h.	h.	PROPN
iajs-2476	421	6	;	;	PUNCT
iajs-2476	421	7	zahedi	zahedi	PROPN
iajs-2476	421	8	,	,	PUNCT
iajs-2476	421	9	m.m	m.m	PROPN
iajs-2476	421	10	.	.	PROPN
iajs-2476	421	11	some	some	DET
iajs-2476	421	12	results	result	NOUN
iajs-2476	421	13	on	on	ADP
iajs-2476	421	14	fuzzy	fuzzy	ADJ
iajs-2476	421	15	prime	prime	ADJ
iajs-2476	421	16	spectrum	spectrum	NOUN
iajs-2476	421	17	of	of	ADP
iajs-2476	421	18	a	a	DET
iajs-2476	421	19	ring	ring	NOUN
iajs-2476	421	20	.	.	PUNCT
iajs-2476	422	1	fuzzy	fuzzy	ADJ
iajs-2476	422	2	sets	set	NOUN
iajs-2476	422	3	syst.1996	syst.1996	PROPN
iajs-2476	422	4	,	,	PUNCT
iajs-2476	422	5	77	77	NUM
iajs-2476	422	6	,	,	PUNCT
iajs-2476	422	7	235–240	235–240	NUM
iajs-2476	422	8	.	.	PUNCT
iajs-2476	422	9	12	12	NUM
iajs-2476	422	10	.	.	PUNCT
iajs-2476	423	1	kumar	kumar	PROPN
iajs-2476	423	2	,	,	PUNCT
iajs-2476	423	3	r.	r.	PROPN
iajs-2476	423	4	fuzzy	fuzzy	ADJ
iajs-2476	423	5	prime	prime	ADJ
iajs-2476	423	6	spectrum	spectrum	NOUN
iajs-2476	423	7	of	of	ADP
iajs-2476	423	8	a	a	DET
iajs-2476	423	9	ring	ring	NOUN
iajs-2476	423	10	.	.	PUNCT
iajs-2476	424	1	fuzzy	fuzzy	ADJ
iajs-2476	424	2	sets	set	NOUN
iajs-2476	424	3	syst.1992	syst.1992	PROPN
iajs-2476	424	4	,	,	PUNCT
iajs-2476	424	5	46	46	NUM
iajs-2476	424	6	,	,	PUNCT
iajs-2476	424	7	147–154	147–154	NUM
iajs-2476	424	8	.	.	PUNCT
iajs-2476	424	9	13	13	NUM
iajs-2476	424	10	.	.	PUNCT
iajs-2476	425	1	kumar	kumar	PROPN
iajs-2476	425	2	,	,	PUNCT
iajs-2476	425	3	r.	r.	PROPN
iajs-2476	425	4	;	;	PUNCT
iajs-2476	425	5	kohli	kohli	PROPN
iajs-2476	425	6	,	,	PUNCT
iajs-2476	425	7	j.k	j.k	PROPN
iajs-2476	425	8	.	.	PROPN
iajs-2476	425	9	fuzzy	fuzzy	ADJ
iajs-2476	425	10	prime	prime	ADJ
iajs-2476	425	11	spectrum	spectrum	NOUN
iajs-2476	425	12	of	of	ADP
iajs-2476	425	13	a	a	DET
iajs-2476	425	14	ring	ring	NOUN
iajs-2476	425	15	ii	ii	PROPN
iajs-2476	425	16	.	.	PUNCT
iajs-2476	426	1	fuzzy	fuzzy	PROPN
iajs-2476	426	2	sets	set	VERB
iajs-2476	426	3	syst.1993	syst.1993	PRON
iajs-2476	426	4	,	,	PUNCT
iajs-2476	426	5	59	59	NUM
iajs-2476	426	6	,	,	PUNCT
iajs-2476	426	7	223–230	223–230	NUM
iajs-2476	426	8	.	.	PUNCT
iajs-2476	427	1	14	14	NUM
iajs-2476	427	2	.	.	PUNCT
iajs-2476	428	1	kumbhojkar	kumbhojkar	PROPN
iajs-2476	428	2	,	,	PUNCT
iajs-2476	428	3	h.v	h.v	PROPN
iajs-2476	428	4	.	.	PROPN
iajs-2476	428	5	spectrum	spectrum	NOUN
iajs-2476	428	6	of	of	ADP
iajs-2476	428	7	prime	prime	ADJ
iajs-2476	428	8	fuzzy	fuzzy	ADJ
iajs-2476	428	9	ideals	ideal	NOUN
iajs-2476	428	10	.	.	PUNCT
iajs-2476	429	1	fuzzy	fuzzy	ADJ
iajs-2476	429	2	sets	set	NOUN
iajs-2476	429	3	syst.1994	syst.1994	PROPN
iajs-2476	429	4	,	,	PUNCT
iajs-2476	429	5	62	62	NUM
iajs-2476	429	6	,	,	PUNCT
iajs-2476	429	7	101	101	NUM
iajs-2476	429	8	–	–	PUNCT
iajs-2476	429	9	109	109	NUM
iajs-2476	429	10	.	.	NOUN
iajs-2476	429	11	15	15	NUM
iajs-2476	429	12	.	.	PUNCT
iajs-2476	430	1	kumbhojkar	kumbhojkar	PROPN
iajs-2476	430	2	,	,	PUNCT
iajs-2476	430	3	h.v	h.v	PROPN
iajs-2476	430	4	.	.	PROPN
iajs-2476	431	1	some	some	DET
iajs-2476	431	2	comments	comment	NOUN
iajs-2476	431	3	on	on	ADP
iajs-2476	431	4	spectrum	spectrum	NOUN
iajs-2476	431	5	of	of	ADP
iajs-2476	431	6	prime	prime	ADJ
iajs-2476	431	7	fuzzy	fuzzy	ADJ
iajs-2476	431	8	ideals	ideal	NOUN
iajs-2476	431	9	of	of	ADP
iajs-2476	431	10	a	a	DET
iajs-2476	431	11	ring	ring	NOUN
iajs-2476	431	12	.	.	PUNCT
iajs-2476	432	1	fuzzy	fuzzy	ADJ
iajs-2476	432	2	sets	set	NOUN
iajs-2476	432	3	syst.1997	syst.1997	PROPN
iajs-2476	432	4	,	,	PUNCT
iajs-2476	432	5	85	85	NUM
iajs-2476	432	6	,	,	PUNCT
iajs-2476	432	7	109–114	109–114	NUM
iajs-2476	432	8	.	.	PUNCT
iajs-2476	433	1	16	16	NUM
iajs-2476	433	2	.	.	PUNCT
iajs-2476	434	1	ameri	ameri	PROPN
iajs-2476	434	2	,	,	PUNCT
iajs-2476	434	3	r.	r.	PROPN
iajs-2476	434	4	;	;	PUNCT
iajs-2476	434	5	mahjoob	mahjoob	PROPN
iajs-2476	434	6	,	,	PUNCT
iajs-2476	434	7	r.	r.	PROPN
iajs-2476	434	8	spectrum	spectrum	PROPN
iajs-2476	434	9	of	of	ADP
iajs-2476	434	10	prime	prime	ADJ
iajs-2476	434	11	l	l	NOUN
iajs-2476	434	12	-	-	NOUN
iajs-2476	434	13	submodules	submodules	NOUN
iajs-2476	434	14	.	.	PUNCT
iajs-2476	435	1	fuzzy	fuzzy	ADJ
iajs-2476	435	2	sets	set	NOUN
iajs-2476	435	3	and	and	CCONJ
iajs-2476	435	4	systems	system	NOUN
iajs-2476	435	5	.	.	PUNCT
iajs-2476	436	1	2008	2008	NUM
iajs-2476	436	2	,	,	PUNCT
iajs-2476	436	3	159	159	NUM
iajs-2476	436	4	,	,	PUNCT
iajs-2476	436	5	1107	1107	NUM
iajs-2476	436	6	-	-	SYM
iajs-2476	436	7	1115	1115	NUM
iajs-2476	436	8	.	.	PUNCT
iajs-2476	437	1	17	17	NUM
iajs-2476	437	2	.	.	X
iajs-2476	438	1	lu	lu	PROPN
iajs-2476	438	2	,	,	PUNCT
iajs-2476	438	3	c.p	c.p	PROPN
iajs-2476	438	4	.	.	PUNCT
iajs-2476	439	1	the	the	DET
iajs-2476	439	2	zariski	zariski	NOUN
iajs-2476	439	3	topology	topology	NOUN
iajs-2476	439	4	on	on	ADP
iajs-2476	439	5	the	the	DET
iajs-2476	439	6	spectrum	spectrum	NOUN
iajs-2476	439	7	of	of	ADP
iajs-2476	439	8	a	a	DET
iajs-2476	439	9	modules	module	NOUN
iajs-2476	439	10	.	.	PUNCT
iajs-2476	440	1	houst	houst	PROPN
iajs-2476	440	2	j	j	PROPN
iajs-2476	440	3	mat.1999	mat.1999	PROPN
iajs-2476	440	4	,	,	PUNCT
iajs-2476	440	5	25	25	NUM
iajs-2476	440	6	,	,	PUNCT
iajs-2476	440	7	3	3	NUM
iajs-2476	440	8	,	,	PUNCT
iajs-2476	440	9	417–432	417–432	NUM
iajs-2476	440	10	.	.	PROPN
iajs-2476	440	11	18	18	NUM
iajs-2476	440	12	.	.	X
iajs-2476	440	13	mordeson	mordeson	NOUN
iajs-2476	440	14	,	,	PUNCT
iajs-2476	440	15	j.n	j.n	PROPN
iajs-2476	440	16	.	.	PROPN
iajs-2476	440	17	;	;	PUNCT
iajs-2476	440	18	malik	malik	PROPN
iajs-2476	440	19	,	,	PUNCT
iajs-2476	440	20	d.s	d.s	PROPN
iajs-2476	440	21	.	.	PROPN
iajs-2476	440	22	fuzzy	fuzzy	ADJ
iajs-2476	440	23	commutative	commutative	ADJ
iajs-2476	440	24	algebra	algebra	NOUN
iajs-2476	440	25	.	.	PUNCT
iajs-2476	441	1	world	world	NOUN
iajs-2476	441	2	scientific	scientific	PROPN
iajs-2476	441	3	,	,	PUNCT
iajs-2476	441	4	ed.1	ed.1	NOUN
iajs-2476	441	5	,	,	PUNCT
iajs-2476	441	6	publishing	publishing	NOUN
iajs-2476	441	7	,	,	PUNCT
iajs-2476	441	8	singapore,1998	singapore,1998	NOUN
iajs-2476	441	9	.	.	PUNCT