id	sid	tid	token	lemma	pos
cana-1296	1	1	communications	communication	NOUN
cana-1296	1	2	on	on	ADP
cana-1296	1	3	applied	apply	VERB
cana-1296	1	4	nonlinear	nonlinear	ADJ
cana-1296	1	5	analysis	analysis	NOUN
cana-1296	1	6	issn	issn	NOUN
cana-1296	1	7	:	:	PUNCT
cana-1296	1	8	1074	1074	NUM
cana-1296	1	9	-	-	PUNCT
cana-1296	1	10	133x	133x	NUM
cana-1296	1	11	vol	vol	NOUN
cana-1296	1	12	31	31	NUM
cana-1296	1	13	no	no	NOUN
cana-1296	1	14	.	.	PUNCT
cana-1296	2	1	7s	7	NOUN
cana-1296	2	2	(	(	PUNCT
cana-1296	2	3	2024	2024	NUM
cana-1296	2	4	)	)	PUNCT
cana-1296	3	1	214	214	NUM
cana-1296	3	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	3	3	generalization	generalization	NOUN
cana-1296	3	4	of	of	ADP
cana-1296	3	5	biг	biг	NOUN
cana-1296	3	6	-	-	PUNCT
cana-1296	3	7	ideals	ideal	NOUN
cana-1296	3	8	in	in	ADP
cana-1296	3	9	ternary	ternary	ADJ
cana-1296	3	10	г	г	NOUN
cana-1296	3	11	-	-	PUNCT
cana-1296	3	12	semirings	semirings	PROPN
cana-1296	3	13	k.	k.	PROPN
cana-1296	3	14	maha	maha	PROPN
cana-1296	3	15	lakshmi,1,2	lakshmi,1,2	PROPN
cana-1296	3	16	,	,	PUNCT
cana-1296	3	17	p.	p.	PROPN
cana-1296	3	18	siva	siva	PROPN
cana-1296	3	19	prasad3,d.madhusudana	prasad3,d.madhusudana	PROPN
cana-1296	3	20	rao4	rao4	PROPN
cana-1296	3	21	,	,	PUNCT
cana-1296	3	22	1	1	NUM
cana-1296	3	23	research	research	NOUN
cana-1296	3	24	scholar	scholar	NOUN
cana-1296	3	25	,	,	PUNCT
cana-1296	3	26	department	department	NOUN
cana-1296	3	27	of	of	ADP
cana-1296	3	28	mathematics	mathematic	NOUN
cana-1296	3	29	,	,	PUNCT
cana-1296	3	30	vfstr	vfstr	NOUN
cana-1296	3	31	deemed	deem	VERB
cana-1296	3	32	to	to	PART
cana-1296	3	33	be	be	AUX
cana-1296	3	34	university	university	NOUN
cana-1296	3	35	,	,	PUNCT
cana-1296	3	36	vadlamudi	vadlamudi	NOUN
cana-1296	3	37	,	,	PUNCT
cana-1296	3	38	guntur	guntur	PROPN
cana-1296	3	39	,	,	PUNCT
cana-1296	3	40	andhra	andhra	PROPN
cana-1296	3	41	pradesh	pradesh	PROPN
cana-1296	3	42	,	,	PUNCT
cana-1296	3	43	india	india	PROPN
cana-1296	3	44	,	,	PUNCT
cana-1296	3	45	mailid	mailid	NOUN
cana-1296	3	46	:	:	PUNCT
cana-1296	4	1	mhlakahmi@gmail.com	mhlakahmi@gmail.com	X
cana-1296	4	2	.	.	PUNCT
cana-1296	5	1	2assistant	2assistant	NUM
cana-1296	5	2	professor	professor	NOUN
cana-1296	5	3	,	,	PUNCT
cana-1296	5	4	department	department	NOUN
cana-1296	5	5	of	of	ADP
cana-1296	5	6	mathematics	mathematic	NOUN
cana-1296	5	7	,	,	PUNCT
cana-1296	5	8	vignan	vignan	NOUN
cana-1296	5	9	nirulla	nirulla	NOUN
cana-1296	5	10	engineering	engineering	PROPN
cana-1296	5	11	college	college	PROPN
cana-1296	5	12	,	,	PUNCT
cana-1296	5	13	guntur	guntur	PROPN
cana-1296	5	14	,	,	PUNCT
cana-1296	5	15	andhra	andhra	PROPN
cana-1296	5	16	pradesh	pradesh	PROPN
cana-1296	5	17	,	,	PUNCT
cana-1296	5	18	india	india	PROPN
cana-1296	5	19	,	,	PUNCT
cana-1296	5	20	mailid	mailid	NOUN
cana-1296	5	21	:	:	PUNCT
cana-1296	5	22	mhlakahmi@gmail.com	mhlakahmi@gmail.com	X
cana-1296	5	23	.	.	PUNCT
cana-1296	6	1	3associate	3associate	NUM
cana-1296	6	2	professor	professor	NOUN
cana-1296	6	3	,	,	PUNCT
cana-1296	6	4	department	department	NOUN
cana-1296	6	5	of	of	ADP
cana-1296	6	6	computer	computer	NOUN
cana-1296	6	7	science	science	PROPN
cana-1296	6	8	&	&	CCONJ
cana-1296	6	9	engineering	engineering	PROPN
cana-1296	6	10	,	,	PUNCT
cana-1296	6	11	school	school	NOUN
cana-1296	6	12	of	of	ADP
cana-1296	6	13	computing	computing	PROPN
cana-1296	6	14	&	&	CCONJ
cana-1296	6	15	informatics	informatics	PROPN
cana-1296	6	16	,	,	PUNCT
cana-1296	6	17	vfstr	vfstr	NOUN
cana-1296	6	18	deemed	deem	VERB
cana-1296	6	19	to	to	ADP
cana-1296	6	20	university	university	NOUN
cana-1296	6	21	,	,	PUNCT
cana-1296	6	22	vadlamudi	vadlamudi	NOUN
cana-1296	6	23	,	,	PUNCT
cana-1296	6	24	guntur	guntur	PROPN
cana-1296	6	25	,	,	PUNCT
cana-1296	6	26	a.p	a.p	PROPN
cana-1296	6	27	,	,	PUNCT
cana-1296	6	28	india	india	PROPN
cana-1296	6	29	,	,	PUNCT
cana-1296	6	30	mailid:pusapatisivaprasad@gmail.com	mailid:pusapatisivaprasad@gmail.com	X
cana-1296	6	31	4professor	4professor	NUM
cana-1296	6	32	of	of	ADP
cana-1296	6	33	mathematics	mathematic	NOUN
cana-1296	6	34	,	,	PUNCT
cana-1296	6	35	government	government	NOUN
cana-1296	6	36	college	college	NOUN
cana-1296	6	37	for	for	ADP
cana-1296	6	38	women(a	women(a	PROPN
cana-1296	6	39	)	)	PUNCT
cana-1296	6	40	,	,	PUNCT
cana-1296	6	41	samba	samba	PROPN
cana-1296	6	42	siva	siva	PROPN
cana-1296	6	43	peta	peta	PROPN
cana-1296	6	44	rd	rd	PROPN
cana-1296	6	45	,	,	PUNCT
cana-1296	6	46	opp	opp	PROPN
cana-1296	6	47	:	:	PUNCT
cana-1296	6	48	ac	ac	PROPN
cana-1296	6	49	college	college	PROPN
cana-1296	6	50	,	,	PUNCT
cana-1296	6	51	samba	samba	PROPN
cana-1296	6	52	siva	siva	PROPN
cana-1296	6	53	pet	pet	PROPN
cana-1296	6	54	,	,	PUNCT
cana-1296	6	55	guntur	guntur	PROPN
cana-1296	6	56	,	,	PUNCT
cana-1296	6	57	andhra	andhra	PROPN
cana-1296	6	58	pradesh	pradesh	PROPN
cana-1296	6	59	,	,	PUNCT
cana-1296	6	60	india,mailid:dmrmaths@gmail.com	india,mailid:dmrmaths@gmail.com	X
cana-1296	6	61	article	article	NOUN
cana-1296	6	62	history	history	NOUN
cana-1296	6	63	:	:	PUNCT
cana-1296	6	64	received	receive	VERB
cana-1296	6	65	:	:	PUNCT
cana-1296	6	66	01	01	NUM
cana-1296	6	67	-	-	PUNCT
cana-1296	6	68	06	06	NUM
cana-1296	6	69	-	-	PUNCT
cana-1296	6	70	2024	2024	NUM
cana-1296	6	71	revised	revise	VERB
cana-1296	6	72	:	:	PUNCT
cana-1296	6	73	03	03	NUM
cana-1296	6	74	-	-	PUNCT
cana-1296	6	75	07	07	NUM
cana-1296	6	76	-	-	PUNCT
cana-1296	6	77	2024	2024	NUM
cana-1296	6	78	accepted	accept	VERB
cana-1296	6	79	:	:	PUNCT
cana-1296	6	80	29	29	NUM
cana-1296	6	81	-	-	SYM
cana-1296	6	82	07	07	NUM
cana-1296	6	83	-	-	PUNCT
cana-1296	6	84	2024	2024	NUM
cana-1296	6	85	abstract	abstract	NOUN
cana-1296	6	86	:	:	PUNCT
cana-1296	6	87	murali	murali	PROPN
cana-1296	6	88	krishna	krishna	PROPN
cana-1296	6	89	rao	rao	PROPN
cana-1296	6	90	was	be	AUX
cana-1296	6	91	presented	present	VERB
cana-1296	6	92	the	the	DET
cana-1296	6	93	idea	idea	NOUN
cana-1296	6	94	of	of	ADP
cana-1296	6	95	г	г	NOUN
cana-1296	6	96	-	-	PUNCT
cana-1296	6	97	semirings	semiring	NOUN
cana-1296	6	98	as	as	ADP
cana-1296	6	99	a	a	DET
cana-1296	6	100	speculation	speculation	NOUN
cana-1296	6	101	of	of	ADP
cana-1296	6	102	the	the	DET
cana-1296	6	103	thought	thought	NOUN
cana-1296	6	104	of	of	ADP
cana-1296	6	105	г	г	NOUN
cana-1296	6	106	-	-	PUNCT
cana-1296	6	107	rings	ring	NOUN
cana-1296	6	108	as	as	ADV
cana-1296	6	109	well	well	ADV
cana-1296	6	110	as	as	ADP
cana-1296	6	111	of	of	ADP
cana-1296	6	112	semirings	semiring	NOUN
cana-1296	6	113	.	.	PUNCT
cana-1296	7	1	we	we	PRON
cana-1296	7	2	have	have	AUX
cana-1296	7	3	realized	realize	VERB
cana-1296	7	4	that	that	SCONJ
cana-1296	7	5	the	the	DET
cana-1296	7	6	thought	thought	NOUN
cana-1296	7	7	of	of	ADP
cana-1296	7	8	г	г	NOUN
cana-1296	7	9	-	-	PUNCT
cana-1296	7	10	semirings	semiring	NOUN
cana-1296	7	11	is	be	AUX
cana-1296	7	12	a	a	DET
cana-1296	7	13	generality	generality	NOUN
cana-1296	7	14	of	of	ADP
cana-1296	7	15	the	the	DET
cana-1296	7	16	idea	idea	NOUN
cana-1296	7	17	of	of	ADP
cana-1296	7	18	semirings	semiring	NOUN
cana-1296	7	19	.	.	PUNCT
cana-1296	8	1	during	during	ADP
cana-1296	8	2	this	this	DET
cana-1296	8	3	paper	paper	NOUN
cana-1296	8	4	we	we	PRON
cana-1296	8	5	sum	sum	VERB
cana-1296	8	6	up	up	ADP
cana-1296	8	7	the	the	DET
cana-1296	8	8	thought	thought	NOUN
cana-1296	8	9	of	of	ADP
cana-1296	8	10	summed	sum	VERB
cana-1296	8	11	up	up	ADP
cana-1296	8	12	bi	bi	ADJ
cana-1296	8	13	-	-	ADJ
cana-1296	8	14	г	г	NOUN
cana-1296	8	15	-	-	PUNCT
cana-1296	8	16	ideals	ideal	NOUN
cana-1296	8	17	of	of	ADP
cana-1296	8	18	ternary	ternary	ADJ
cana-1296	8	19	г	г	NOUN
cana-1296	8	20	-	-	PUNCT
cana-1296	8	21	semirings	semiring	NOUN
cana-1296	8	22	and	and	CCONJ
cana-1296	8	23	examine	examine	VERB
cana-1296	8	24	a	a	DET
cana-1296	8	25	few	few	ADJ
cana-1296	8	26	related	relate	VERB
cana-1296	8	27	properties	property	NOUN
cana-1296	8	28	of	of	ADP
cana-1296	8	29	summed	sum	VERB
cana-1296	8	30	up	up	ADP
cana-1296	8	31	bi	bi	NOUN
cana-1296	8	32	-	-	NOUN
cana-1296	8	33	гideals	гideal	NOUN
cana-1296	8	34	.	.	PUNCT
cana-1296	9	1	keywords	keyword	NOUN
cana-1296	9	2	:	:	PUNCT
cana-1296	9	3	ternary	ternary	ADJ
cana-1296	9	4	г	г	NOUN
cana-1296	9	5	-	-	PUNCT
cana-1296	9	6	ideal	ideal	ADJ
cana-1296	9	7	,	,	PUNCT
cana-1296	9	8	generalized	generalized	ADJ
cana-1296	9	9	biternary	biternary	ADJ
cana-1296	9	10	г	г	NOUN
cana-1296	9	11	-	-	PUNCT
cana-1296	9	12	ideal	ideal	ADJ
cana-1296	9	13	,	,	PUNCT
cana-1296	9	14	biternary	biternary	ADJ
cana-1296	9	15	г	г	NOUN
cana-1296	9	16	-	-	PUNCT
cana-1296	9	17	ideal	ideal	ADJ
cana-1296	9	18	mathematics	mathematic	NOUN
cana-1296	9	19	subject	subject	ADJ
cana-1296	9	20	classification	classification	NOUN
cana-1296	9	21	.	.	PUNCT
cana-1296	10	1	16y30	16y30	NUM
cana-1296	10	2	,	,	PUNCT
cana-1296	10	3	16y99	16y99	NUM
cana-1296	10	4	1	1	NUM
cana-1296	10	5	.	.	PUNCT
cana-1296	10	6	introduction	introduction	NOUN
cana-1296	10	7	and	and	CCONJ
cana-1296	10	8	preliminaries	preliminary	NOUN
cana-1296	10	9	the	the	DET
cana-1296	10	10	possibility	possibility	NOUN
cana-1296	10	11	of	of	ADP
cana-1296	10	12	г	г	NOUN
cana-1296	10	13	-	-	PUNCT
cana-1296	10	14	semirings	semiring	NOUN
cana-1296	10	15	was	be	AUX
cana-1296	10	16	laid	lay	VERB
cana-1296	10	17	out	out	ADP
cana-1296	10	18	and	and	CCONJ
cana-1296	10	19	concentrated	concentrate	VERB
cana-1296	10	20	in	in	ADP
cana-1296	10	21	1995	1995	NUM
cana-1296	10	22	by	by	ADP
cana-1296	10	23	murali	murali	PROPN
cana-1296	10	24	krishna	krishna	PROPN
cana-1296	10	25	rao	rao	PROPN
cana-1296	11	1	[	[	X
cana-1296	11	2	10	10	NUM
cana-1296	11	3	]	]	PUNCT
cana-1296	11	4	as	as	ADP
cana-1296	11	5	a	a	DET
cana-1296	11	6	speculation	speculation	NOUN
cana-1296	11	7	of	of	ADP
cana-1296	11	8	the	the	DET
cana-1296	11	9	thought	thought	NOUN
cana-1296	11	10	of	of	ADP
cana-1296	11	11	г	г	NOUN
cana-1296	11	12	-	-	PUNCT
cana-1296	11	13	rings	ring	NOUN
cana-1296	11	14	as	as	ADV
cana-1296	11	15	well	well	ADV
cana-1296	11	16	as	as	ADP
cana-1296	11	17	of	of	ADP
cana-1296	11	18	semiring	semiring	NOUN
cana-1296	11	19	,	,	PUNCT
cana-1296	11	20	and	and	CCONJ
cana-1296	11	21	summed	sum	VERB
cana-1296	11	22	up	up	ADP
cana-1296	11	23	bi	bi	NOUN
cana-1296	11	24	-	-	NOUN
cana-1296	11	25	ideals	ideal	NOUN
cana-1296	11	26	was	be	AUX
cana-1296	11	27	first	first	ADV
cana-1296	11	28	presented	present	VERB
cana-1296	11	29	for	for	ADP
cana-1296	11	30	rings	ring	NOUN
cana-1296	11	31	in	in	ADP
cana-1296	11	32	1970	1970	NUM
cana-1296	11	33	by	by	ADP
cana-1296	11	34	szasz[12	szasz[12	PROPN
cana-1296	11	35	,	,	PUNCT
cana-1296	11	36	13	13	NUM
cana-1296	11	37	]	]	PUNCT
cana-1296	11	38	and	and	CCONJ
cana-1296	11	39	afterward	afterward	ADV
cana-1296	11	40	for	for	ADP
cana-1296	11	41	semigroups	semigroup	NOUN
cana-1296	11	42	by	by	ADP
cana-1296	11	43	lajos[8	lajos[8	PROPN
cana-1296	11	44	]	]	PUNCT
cana-1296	11	45	.	.	PUNCT
cana-1296	12	1	many	many	ADJ
cana-1296	12	2	sorts	sort	NOUN
cana-1296	12	3	of	of	ADP
cana-1296	12	4	ideals	ideal	NOUN
cana-1296	12	5	on	on	ADP
cana-1296	12	6	the	the	DET
cana-1296	12	7	mathematical	mathematical	ADJ
cana-1296	12	8	designs	design	NOUN
cana-1296	12	9	were	be	AUX
cana-1296	12	10	portrayed	portray	VERB
cana-1296	12	11	by	by	ADP
cana-1296	12	12	a	a	DET
cana-1296	12	13	few	few	ADJ
cana-1296	12	14	creators	creator	NOUN
cana-1296	12	15	,	,	PUNCT
cana-1296	12	16	for	for	ADP
cana-1296	12	17	example	example	NOUN
cana-1296	12	18	,	,	PUNCT
cana-1296	12	19	in	in	ADP
cana-1296	12	20	2000	2000	NUM
cana-1296	12	21	,	,	PUNCT
cana-1296	12	22	concentrated	concentrate	VERB
cana-1296	12	23	on	on	ADP
cana-1296	12	24	the	the	DET
cana-1296	12	25	portrayal	portrayal	NOUN
cana-1296	12	26	of	of	ADP
cana-1296	12	27	semiprime	semiprime	NOUN
cana-1296	12	28	ideals	ideal	NOUN
cana-1296	12	29	and	and	CCONJ
cana-1296	12	30	irreducible	irreducible	ADJ
cana-1296	12	31	ideals	ideal	NOUN
cana-1296	12	32	of	of	ADP
cana-1296	12	33	г	г	NOUN
cana-1296	12	34	-	-	PUNCT
cana-1296	12	35	semirings	semiring	NOUN
cana-1296	12	36	concentrated	concentrate	VERB
cana-1296	12	37	by	by	ADP
cana-1296	12	38	dutta	dutta	PROPN
cana-1296	12	39	and	and	CCONJ
cana-1296	12	40	sardar[3	sardar[3	NOUN
cana-1296	12	41	]	]	PUNCT
cana-1296	12	42	and	and	CCONJ
cana-1296	12	43	primitive	primitive	ADJ
cana-1296	12	44	ideals	ideal	NOUN
cana-1296	12	45	of	of	ADP
cana-1296	12	46	г	г	NOUN
cana-1296	12	47	-	-	PUNCT
cana-1296	12	48	semirings	semiring	NOUN
cana-1296	12	49	,	,	PUNCT
cana-1296	12	50	pianskool	pianskool	NOUN
cana-1296	12	51	,	,	PUNCT
cana-1296	12	52	sangwirotjanapat	sangwirotjanapat	PROPN
cana-1296	12	53	and	and	CCONJ
cana-1296	12	54	tipyota[9	tipyota[9	NOUN
cana-1296	12	55	]	]	PUNCT
cana-1296	12	56	presented	present	VERB
cana-1296	12	57	and	and	CCONJ
cana-1296	12	58	concentrated	concentrate	VERB
cana-1296	12	59	on	on	ADP
cana-1296	12	60	valuation	valuation	NOUN
cana-1296	12	61	of	of	ADP
cana-1296	12	62	г	г	PROPN
cana-1296	12	63	-	-	PUNCT
cana-1296	12	64	semirings	semiring	NOUN
cana-1296	12	65	and	and	CCONJ
cana-1296	12	66	valuation	valuation	NOUN
cana-1296	12	67	of	of	ADP
cana-1296	12	68	г	г	NOUN
cana-1296	12	69	-	-	PUNCT
cana-1296	12	70	ideals	ideal	NOUN
cana-1296	12	71	of	of	ADP
cana-1296	12	72	a	a	DET
cana-1296	12	73	гsemiring	гsemiring	NOUN
cana-1296	12	74	,	,	PUNCT
cana-1296	12	75	and	and	CCONJ
cana-1296	12	76	chinram[1	chinram[1	VERB
cana-1296	12	77	]	]	X
cana-1296	12	78	gave	give	VERB
cana-1296	12	79	a	a	DET
cana-1296	12	80	few	few	ADJ
cana-1296	12	81	properties	property	NOUN
cana-1296	12	82	of	of	ADP
cana-1296	12	83	quasi	quasi	NOUN
cana-1296	12	84	-	-	NOUN
cana-1296	12	85	ideals	ideal	NOUN
cana-1296	12	86	in	in	ADP
cana-1296	12	87	г	г	NOUN
cana-1296	12	88	-	-	PUNCT
cana-1296	12	89	semirings	semiring	NOUN
cana-1296	12	90	.	.	PUNCT
cana-1296	13	1	jagatap	jagatap	PROPN
cana-1296	13	2	and	and	CCONJ
cana-1296	13	3	pawar	pawar	PROPN
cana-1296	14	1	[	[	X
cana-1296	14	2	6	6	NUM
cana-1296	14	3	]	]	PUNCT
cana-1296	14	4	presented	present	VERB
cana-1296	14	5	the	the	DET
cana-1296	14	6	idea	idea	NOUN
cana-1296	14	7	of	of	ADP
cana-1296	14	8	minimal	minimal	ADJ
cana-1296	14	9	quasi	quasi	NOUN
cana-1296	14	10	-	-	NOUN
cana-1296	14	11	ideals	ideal	NOUN
cana-1296	14	12	in	in	ADP
cana-1296	14	13	г	г	NOUN
cana-1296	14	14	-	-	PUNCT
cana-1296	14	15	semirings	semiring	NOUN
cana-1296	14	16	in	in	ADP
cana-1296	14	17	2009	2009	NUM
cana-1296	14	18	.	.	PUNCT
cana-1296	15	1	a	a	DET
cana-1296	15	2	few	few	ADJ
cana-1296	15	3	properties	property	NOUN
cana-1296	15	4	of	of	ADP
cana-1296	15	5	minimal	minimal	ADJ
cana-1296	15	6	quasi	quasi	NOUN
cana-1296	15	7	-	-	NOUN
cana-1296	15	8	ideals	ideal	NOUN
cana-1296	15	9	in	in	ADP
cana-1296	15	10	г	г	NOUN
cana-1296	15	11	-	-	PUNCT
cana-1296	15	12	semirings	semiring	NOUN
cana-1296	15	13	are	be	AUX
cana-1296	15	14	given	give	VERB
cana-1296	15	15	.	.	PUNCT
cana-1296	16	1	in	in	ADP
cana-1296	16	2	2010	2010	NUM
cana-1296	16	3	,	,	PUNCT
cana-1296	16	4	ghosh	ghosh	PROPN
cana-1296	16	5	and	and	CCONJ
cana-1296	16	6	samanta[5	samanta[5	VERB
cana-1296	16	7	]	]	X
cana-1296	16	8	concentrated	concentrate	VERB
cana-1296	16	9	on	on	ADP
cana-1296	16	10	the	the	DET
cana-1296	16	11	connection	connection	NOUN
cana-1296	16	12	between	between	ADP
cana-1296	16	13	the	the	DET
cana-1296	16	14	fuzzy	fuzzy	ADJ
cana-1296	16	15	left	left	NOUN
cana-1296	16	16	(	(	PUNCT
cana-1296	16	17	separately	separately	ADV
cana-1296	16	18	,	,	PUNCT
cana-1296	16	19	right	right	ADJ
cana-1296	16	20	)	)	PUNCT
cana-1296	16	21	ideals	ideal	NOUN
cana-1296	16	22	of	of	ADP
cana-1296	16	23	г	г	NOUN
cana-1296	16	24	-	-	PUNCT
cana-1296	16	25	semirings	semiring	NOUN
cana-1296	16	26	and	and	CCONJ
cana-1296	16	27	that	that	PRON
cana-1296	16	28	of	of	ADP
cana-1296	16	29	operator	operator	NOUN
cana-1296	16	30	semiring	semiring	NOUN
cana-1296	16	31	.	.	PUNCT
cana-1296	17	1	in	in	ADP
cana-1296	17	2	2011	2011	NUM
cana-1296	17	3	,	,	PUNCT
cana-1296	17	4	dutta	dutta	PROPN
cana-1296	17	5	,	,	PUNCT
cana-1296	17	6	sardar	sardar	NOUN
cana-1296	17	7	and	and	CCONJ
cana-1296	17	8	goswami[4	goswami[4	PROPN
cana-1296	17	9	]	]	X
cana-1296	17	10	presented	present	VERB
cana-1296	17	11	various	various	ADJ
cana-1296	17	12	kinds	kind	NOUN
cana-1296	17	13	of	of	ADP
cana-1296	17	14	procedure	procedure	NOUN
cana-1296	17	15	on	on	ADP
cana-1296	17	16	fuzzy	fuzzy	ADJ
cana-1296	17	17	ideals	ideal	NOUN
cana-1296	17	18	of	of	ADP
cana-1296	17	19	г	г	NOUN
cana-1296	17	20	-	-	PUNCT
cana-1296	17	21	semirings	semiring	NOUN
cana-1296	17	22	and	and	CCONJ
cana-1296	17	23	demonstrated	demonstrate	VERB
cana-1296	17	24	consequently	consequently	ADV
cana-1296	17	25	that	that	SCONJ
cana-1296	17	26	these	these	DET
cana-1296	17	27	activities	activity	NOUN
cana-1296	17	28	bring	bring	VERB
cana-1296	17	29	about	about	ADP
cana-1296	17	30	various	various	ADJ
cana-1296	17	31	designs	design	NOUN
cana-1296	17	32	like	like	ADP
cana-1296	17	33	complete	complete	ADJ
cana-1296	17	34	lattice	lattice	NOUN
cana-1296	17	35	,	,	PUNCT
cana-1296	17	36	modular	modular	ADJ
cana-1296	17	37	lattice	lattice	NOUN
cana-1296	17	38	on	on	ADP
cana-1296	17	39	some	some	DET
cana-1296	17	40	limited	limited	ADJ
cana-1296	17	41	class	class	NOUN
cana-1296	17	42	of	of	ADP
cana-1296	17	43	fuzzy	fuzzy	ADJ
cana-1296	17	44	ideals	ideal	NOUN
cana-1296	17	45	of	of	ADP
cana-1296	17	46	г	г	NOUN
cana-1296	17	47	-	-	PUNCT
cana-1296	17	48	semirings	semiring	NOUN
cana-1296	17	49	.	.	PUNCT
cana-1296	18	1	in	in	ADP
cana-1296	18	2	2012	2012	NUM
cana-1296	18	3	,	,	PUNCT
cana-1296	18	4	bektas	bekta	NOUN
cana-1296	18	5	,	,	PUNCT
cana-1296	18	6	bayrak	bayrak	NOUN
cana-1296	18	7	and	and	CCONJ
cana-1296	18	8	ersoy[2	ersoy[2	PROPN
cana-1296	18	9	]	]	PUNCT
cana-1296	18	10	presented	present	VERB
cana-1296	18	11	and	and	CCONJ
cana-1296	18	12	concentrated	concentrate	VERB
cana-1296	18	13	on	on	ADP
cana-1296	18	14	the	the	DET
cana-1296	18	15	portrayal	portrayal	NOUN
cana-1296	18	16	of	of	ADP
cana-1296	18	17	soft	soft	ADJ
cana-1296	18	18	г	г	NOUN
cana-1296	18	19	-	-	PUNCT
cana-1296	18	20	semirings	semiring	NOUN
cana-1296	18	21	and	and	CCONJ
cana-1296	18	22	soft	soft	ADJ
cana-1296	18	23	sub	sub	ADJ
cana-1296	18	24	-	-	ADJ
cana-1296	18	25	г	г	NOUN
cana-1296	18	26	-	-	PUNCT
cana-1296	18	27	semiring	semiring	NOUN
cana-1296	18	28	.	.	PUNCT
cana-1296	19	1	the	the	DET
cana-1296	19	2	view	view	NOUN
cana-1296	19	3	of	of	ADP
cana-1296	19	4	ideals	ideal	NOUN
cana-1296	19	5	for	for	ADP
cana-1296	19	6	some	some	DET
cana-1296	19	7	kinds	kind	NOUN
cana-1296	19	8	of	of	ADP
cana-1296	19	9	г	г	NOUN
cana-1296	19	10	-	-	PUNCT
cana-1296	19	11	semirings	semiring	NOUN
cana-1296	19	12	is	be	AUX
cana-1296	19	13	the	the	DET
cana-1296	19	14	truly	truly	ADV
cana-1296	19	15	significant	significant	ADJ
cana-1296	19	16	and	and	CCONJ
cana-1296	19	17	intrigued	intrigue	VERB
cana-1296	19	18	thing	thing	NOUN
cana-1296	19	19	with	with	ADP
cana-1296	19	20	regards	regard	NOUN
cana-1296	19	21	to	to	ADP
cana-1296	19	22	г	г	NOUN
cana-1296	19	23	-	-	PUNCT
cana-1296	19	24	semirings	semiring	NOUN
cana-1296	19	25	.	.	PUNCT
cana-1296	20	1	hence	hence	ADV
cana-1296	20	2	,	,	PUNCT
cana-1296	20	3	we	we	PRON
cana-1296	20	4	will	will	AUX
cana-1296	20	5	start	start	VERB
cana-1296	20	6	and	and	CCONJ
cana-1296	20	7	concentrate	concentrate	VERB
cana-1296	20	8	on	on	ADP
cana-1296	20	9	summed	sum	VERB
cana-1296	20	10	up	up	ADP
cana-1296	20	11	bi	bi	NOUN
cana-1296	20	12	-	-	NOUN
cana-1296	20	13	ternay	ternay	ADJ
cana-1296	20	14	г	г	NOUN
cana-1296	20	15	-	-	PUNCT
cana-1296	20	16	ideals	ideal	NOUN
cana-1296	20	17	of	of	ADP
cana-1296	20	18	гcommunications	гcommunication	NOUN
cana-1296	20	19	on	on	ADP
cana-1296	20	20	applied	apply	VERB
cana-1296	20	21	nonlinear	nonlinear	ADJ
cana-1296	20	22	analysis	analysis	NOUN
cana-1296	20	23	issn	issn	NOUN
cana-1296	20	24	:	:	PUNCT
cana-1296	20	25	1074	1074	NUM
cana-1296	20	26	-	-	PUNCT
cana-1296	20	27	133x	133x	NUM
cana-1296	20	28	vol	vol	NOUN
cana-1296	20	29	31	31	NUM
cana-1296	20	30	no	no	NOUN
cana-1296	20	31	.	.	PUNCT
cana-1296	21	1	7s	7	NOUN
cana-1296	21	2	(	(	PUNCT
cana-1296	21	3	2024	2024	NUM
cana-1296	21	4	)	)	PUNCT
cana-1296	21	5	215	215	NUM
cana-1296	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	21	7	semirings	semiring	NOUN
cana-1296	21	8	similarly	similarly	ADV
cana-1296	21	9	as	as	ADP
cana-1296	21	10	of	of	ADP
cana-1296	21	11	bi	bi	ADJ
cana-1296	21	12	-	-	ADJ
cana-1296	21	13	г	г	NOUN
cana-1296	21	14	-	-	PUNCT
cana-1296	21	15	ideals	ideal	NOUN
cana-1296	21	16	of	of	ADP
cana-1296	21	17	ternary	ternary	ADJ
cana-1296	21	18	г	г	NOUN
cana-1296	21	19	-	-	PUNCT
cana-1296	21	20	semirings	semiring	NOUN
cana-1296	21	21	which	which	PRON
cana-1296	21	22	was	be	AUX
cana-1296	21	23	concentrated	concentrate	VERB
cana-1296	21	24	by	by	ADP
cana-1296	21	25	kaushik	kaushik	PROPN
cana-1296	21	26	,	,	PUNCT
cana-1296	21	27	moin	moin	PROPN
cana-1296	21	28	and	and	CCONJ
cana-1296	21	29	khan[7	khan[7	PROPN
cana-1296	21	30	]	]	PUNCT
cana-1296	21	31	.	.	PUNCT
cana-1296	22	1	“	"	PUNCT
cana-1296	22	2	throughout	throughout	ADP
cana-1296	22	3	this	this	DET
cana-1296	22	4	paper	paper	NOUN
cana-1296	22	5	generalized	generalize	VERB
cana-1296	22	6	biternary	biternary	ADJ
cana-1296	22	7	г	г	NOUN
cana-1296	22	8	-	-	PUNCT
cana-1296	22	9	idealgbtγi	idealgbtγi	NOUN
cana-1296	22	10	,	,	PUNCT
cana-1296	22	11	smallest	small	ADJ
cana-1296	22	12	generalized	generalize	VERB
cana-1296	22	13	biternary	biternary	ADJ
cana-1296	22	14	гidealsgbtγi	гidealsgbtγi	NOUN
cana-1296	22	15	,	,	PUNCT
cana-1296	22	16	ternary	ternary	ADJ
cana-1296	22	17	г	г	NOUN
cana-1296	22	18	-	-	PUNCT
cana-1296	22	19	semiringtгs	semiringtгs	NOUN
cana-1296	22	20	,	,	PUNCT
cana-1296	22	21	minimal	minimal	ADJ
cana-1296	22	22	generalized	generalized	ADJ
cana-1296	22	23	biγ	biγ	NOUN
cana-1296	22	24	-	-	PUNCT
cana-1296	22	25	idealmgbtγi	idealmgbtγi	NOUN
cana-1296	22	26	,	,	PUNCT
cana-1296	22	27	quasi	quasi	ADJ
cana-1296	22	28	ternary	ternary	ADJ
cana-1296	22	29	г	г	NOUN
cana-1296	22	30	-	-	PUNCT
cana-1296	22	31	ideal	ideal	ADJ
cana-1296	22	32	–	–	PUNCT
cana-1296	22	33	qtгi	qtгi	NOUN
cana-1296	22	34	,	,	PUNCT
cana-1296	22	35	partial	partial	ADJ
cana-1296	22	36	ternary	ternary	ADJ
cana-1296	22	37	γ	γ	NOUN
cana-1296	22	38	-	-	ADJ
cana-1296	22	39	idealptγi	idealptγi	ADJ
cana-1296	22	40	”	"	PUNCT
cana-1296	22	41	definition	definition	NOUN
cana-1296	22	42	1.1	1.1	NUM
cana-1296	22	43	:	:	PUNCT
cana-1296	22	44	let	let	VERB
cana-1296	22	45	u	u	NOUN
cana-1296	22	46	,	,	PUNCT
cana-1296	22	47			VERB
cana-1296	22	48	be	be	AUX
cana-1296	22	49	two	two	NUM
cana-1296	22	50	additive	additive	ADJ
cana-1296	22	51	commutative	commutative	ADJ
cana-1296	22	52	semigroups	semigroup	NOUN
cana-1296	22	53	.	.	PUNCT
cana-1296	23	1	then	then	ADV
cana-1296	23	2	u	u	PRON
cana-1296	23	3	is	be	AUX
cana-1296	23	4	entitled	entitle	VERB
cana-1296	23	5	a	a	DET
cana-1296	23	6	ternary	ternary	ADJ
cana-1296	23	7	gamma	gamma	NOUN
cana-1296	23	8	semiring	semiring	NOUN
cana-1296	23	9	presented	present	VERB
cana-1296	23	10			NUM
cana-1296	23	11	a	a	DET
cana-1296	23	12	mapping	mapping	NOUN
cana-1296	23	13	u	u	NOUN
cana-1296	23	14	u	u	X
cana-1296	23	15	u	u	NOUN
cana-1296	23	16	u	u	VERB
cana-1296	23	17			PROPN
cana-1296	23	18	→	→	PUNCT
cana-1296	23	19	suiting	suit	VERB
cana-1296	23	20	the	the	DET
cana-1296	23	21	next	next	ADJ
cana-1296	23	22	conditions	condition	NOUN
cana-1296	23	23	:	:	PUNCT
cana-1296	24	1	(	(	PUNCT
cana-1296	24	2	1	1	X
cana-1296	24	3	)	)	PUNCT
cana-1296	24	4	(	(	PUNCT
cana-1296	24	5	)	)	PUNCT
cana-1296	24	6	(	(	PUNCT
cana-1296	24	7	)	)	PUNCT
cana-1296	24	8	(	(	PUNCT
cana-1296	24	9	)	)	PUNCT
cana-1296	24	10	x	x	SYM
cana-1296	24	11	y	y	PROPN
cana-1296	24	12	z	z	PROPN
cana-1296	24	13	p	p	NOUN
cana-1296	25	1	q	q	X
cana-1296	25	2	x	x	X
cana-1296	25	3	y	y	NOUN
cana-1296	25	4	z	z	PROPN
cana-1296	25	5	p	p	NOUN
cana-1296	26	1	q	q	X
cana-1296	26	2	x	x	X
cana-1296	26	3	y	y	NOUN
cana-1296	26	4	z	z	PROPN
cana-1296	26	5	p	p	NOUN
cana-1296	26	6	q	q	X
cana-1296	27	1			PROPN
cana-1296	27	2			ADJ
cana-1296	27	3			NOUN
cana-1296	27	4			NUM
cana-1296	27	5			PROPN
cana-1296	27	6			ADJ
cana-1296	27	7			NOUN
cana-1296	27	8			NUM
cana-1296	27	9			PROPN
cana-1296	27	10			ADJ
cana-1296	27	11	=	=	PROPN
cana-1296	27	12	=	=	SYM
cana-1296	27	13	(	(	PUNCT
cana-1296	27	14	2	2	NUM
cana-1296	27	15	)	)	PUNCT
cana-1296	27	16	[	[	X
cana-1296	27	17	(	(	PUNCT
cana-1296	27	18	)	)	PUNCT
cana-1296	27	19	]	]	PUNCT
cana-1296	28	1	[	[	X
cana-1296	28	2	(	(	PUNCT
cana-1296	28	3	]	]	PUNCT
cana-1296	28	4	[	[	PUNCT
cana-1296	28	5	]	]	X
cana-1296	28	6	p	p	X
cana-1296	28	7	q	q	X
cana-1296	28	8	r	r	NOUN
cana-1296	28	9	s	s	X
cana-1296	28	10	p	p	NOUN
cana-1296	28	11	r	r	NOUN
cana-1296	28	12	s	s	PART
cana-1296	28	13	q	q	NOUN
cana-1296	28	14	r	r	NOUN
cana-1296	28	15	s	s	NOUN
cana-1296	28	16			PROPN
cana-1296	28	17			NUM
cana-1296	28	18			PROPN
cana-1296	28	19			NUM
cana-1296	28	20	+	+	NOUN
cana-1296	28	21	=	=	PUNCT
cana-1296	28	22	+	+	CCONJ
cana-1296	28	23	(	(	PUNCT
cana-1296	28	24	3	3	NUM
cana-1296	28	25	)	)	PUNCT
cana-1296	28	26	[	[	PUNCT
cana-1296	28	27	(	(	PUNCT
cana-1296	28	28	)	)	PUNCT
cana-1296	28	29	]	]	PUNCT
cana-1296	29	1	[	[	X
cana-1296	29	2	(	(	PUNCT
cana-1296	29	3	]	]	PUNCT
cana-1296	29	4	[	[	PUNCT
cana-1296	29	5	]	]	X
cana-1296	29	6	p	p	X
cana-1296	29	7	q	q	X
cana-1296	29	8	r	r	NOUN
cana-1296	29	9	s	s	X
cana-1296	29	10	p	p	NOUN
cana-1296	29	11	q	q	X
cana-1296	29	12	s	s	X
cana-1296	29	13	p	p	NOUN
cana-1296	29	14	r	r	NOUN
cana-1296	29	15	s	s	NOUN
cana-1296	29	16			PROPN
cana-1296	29	17			NUM
cana-1296	29	18			PROPN
cana-1296	29	19			NUM
cana-1296	29	20	+	+	NOUN
cana-1296	29	21	=	=	PUNCT
cana-1296	30	1	+	+	CCONJ
cana-1296	30	2	(	(	PUNCT
cana-1296	30	3	4	4	NUM
cana-1296	30	4	)	)	PUNCT
cana-1296	30	5	[	[	PUNCT
cana-1296	30	6	(	(	PUNCT
cana-1296	30	7	)	)	PUNCT
cana-1296	30	8	]	]	PUNCT
cana-1296	31	1	[	[	X
cana-1296	31	2	(	(	PUNCT
cana-1296	31	3	]	]	PUNCT
cana-1296	31	4	[	[	PUNCT
cana-1296	31	5	]	]	X
cana-1296	31	6	,	,	PUNCT
cana-1296	31	7	,	,	PUNCT
cana-1296	31	8	,	,	PUNCT
cana-1296	31	9	&	&	CCONJ
cana-1296	31	10	,	,	PUNCT
cana-1296	31	11	,	,	PUNCT
cana-1296	31	12	,	,	PUNCT
cana-1296	31	13	.p	.p	PROPN
cana-1296	31	14	q	q	X
cana-1296	31	15	r	r	NOUN
cana-1296	31	16	s	s	X
cana-1296	31	17	p	p	NOUN
cana-1296	31	18	q	q	NOUN
cana-1296	31	19	r	r	NOUN
cana-1296	31	20	p	p	NOUN
cana-1296	31	21	q	q	NOUN
cana-1296	31	22	s	s	X
cana-1296	31	23	p	p	X
cana-1296	31	24	q	q	NOUN
cana-1296	31	25	r	r	NOUN
cana-1296	31	26	s	s	PART
cana-1296	31	27	u	u	ADJ
cana-1296	31	28			PROPN
cana-1296	31	29			NUM
cana-1296	31	30			PROPN
cana-1296	31	31			NUM
cana-1296	31	32			PROPN
cana-1296	31	33			NUM
cana-1296	31	34			PROPN
cana-1296	31	35			NUM
cana-1296	31	36	+	+	PROPN
cana-1296	31	37	=	=	SYM
cana-1296	31	38	+	+	CCONJ
cana-1296	31	39			ADJ
cana-1296	31	40			NOUN
cana-1296	31	41			NOUN
cana-1296	31	42	example	example	NOUN
cana-1296	31	43	:	:	PUNCT
cana-1296	31	44	1.2	1.2	NUM
cana-1296	31	45	set	set	VERB
cana-1296	31	46	n	n	PROPN
cana-1296	31	47	of	of	ADP
cana-1296	31	48	natural	natural	ADJ
cana-1296	31	49	numbers	number	NOUN
cana-1296	31	50	&	&	CCONJ
cana-1296	31	51	=	=	X
cana-1296	31	52	{	{	PUNCT
cana-1296	31	53	1	1	NUM
cana-1296	31	54	,	,	PUNCT
cana-1296	31	55	2	2	NUM
cana-1296	31	56	,	,	PUNCT
cana-1296	31	57	3	3	NUM
cana-1296	31	58	}	}	PUNCT
cana-1296	31	59	.	.	PUNCT
cana-1296	32	1	then	then	ADV
cana-1296	32	2	(	(	PUNCT
cana-1296	32	3			PROPN
cana-1296	32	4	,	,	PUNCT
cana-1296	32	5	max	max	PROPN
cana-1296	32	6	)	)	PUNCT
cana-1296	32	7	&	&	CCONJ
cana-1296	32	8	(	(	PUNCT
cana-1296	32	9	n	n	CCONJ
cana-1296	32	10	,	,	PUNCT
cana-1296	32	11	max	max	PROPN
cana-1296	32	12	)	)	PUNCT
cana-1296	32	13	are	be	AUX
cana-1296	32	14	commutative	commutative	ADJ
cana-1296	32	15	semigroups	semigroup	NOUN
cana-1296	32	16	.	.	PUNCT
cana-1296	33	1	characterize	characterize	VERB
cana-1296	33	2	the	the	DET
cana-1296	33	3	mapping	mapping	NOUN
cana-1296	33	4	n	n	CCONJ
cana-1296	33	5	n	n	CCONJ
cana-1296	33	6	n	n	ADV
cana-1296	33	7	n	n	PROPN
cana-1296	33	8			PROPN
cana-1296	33	9	→	→	SYM
cana-1296	33	10	,	,	PUNCT
cana-1296	33	11	by	by	ADP
cana-1296	33	12	min	min	PROPN
cana-1296	33	13	{	{	PUNCT
cana-1296	33	14	,	,	PUNCT
cana-1296	33	15	,	,	PUNCT
cana-1296	33	16	,	,	PUNCT
cana-1296	33	17	,	,	PUNCT
cana-1296	33	18	}	}	PUNCT
cana-1296	33	19	,	,	PUNCT
cana-1296	33	20	,	,	PUNCT
cana-1296	33	21	&	&	CCONJ
cana-1296	33	22	,	,	PUNCT
cana-1296	33	23	.b	.b	PROPN
cana-1296	34	1	c	c	PROPN
cana-1296	34	2	d	d	X
cana-1296	34	3	b	b	X
cana-1296	34	4	c	c	PROPN
cana-1296	34	5	d	d	PROPN
cana-1296	34	6	b	b	PROPN
cana-1296	34	7	c	c	PROPN
cana-1296	34	8	d	d	NOUN
cana-1296	34	9	n	n	PROPN
cana-1296	34	10			PROPN
cana-1296	34	11			NUM
cana-1296	34	12			PROPN
cana-1296	34	13			NUM
cana-1296	34	14	=	=	PROPN
cana-1296	34	15			PROPN
cana-1296	34	16			NOUN
cana-1296	34	17			NOUN
cana-1296	34	18	next	next	ADJ
cana-1296	34	19	n	n	VERB
cana-1296	34	20	is	be	AUX
cana-1296	34	21	a	a	DET
cana-1296	34	22	tγs	tγs	PROPN
cana-1296	34	23	.	.	PUNCT
cana-1296	35	1	example	example	NOUN
cana-1296	35	2	:	:	PUNCT
cana-1296	36	1	1.3	1.3	NUM
cana-1296	36	2	rational	rational	ADJ
cana-1296	36	3	numbers	number	NOUN
cana-1296	36	4	set	set	VERB
cana-1296	36	5	(	(	PUNCT
cana-1296	36	6	q	q	NOUN
cana-1296	36	7	)	)	PUNCT
cana-1296	36	8	&	&	CCONJ
cana-1296	36	9	n=	n=	VERB
cana-1296	36	10	the	the	DET
cana-1296	36	11	set	set	NOUN
cana-1296	36	12	of	of	ADP
cana-1296	36	13	natural	natural	ADJ
cana-1296	36	14	numbers	number	NOUN
cana-1296	36	15	.	.	PUNCT
cana-1296	37	1	afterward	afterward	ADV
cana-1296	37	2	(	(	PUNCT
cana-1296	37	3	n	n	X
cana-1296	37	4	,	,	PUNCT
cana-1296	37	5	+	+	NOUN
cana-1296	37	6	)	)	PUNCT
cana-1296	37	7	,	,	PUNCT
cana-1296	37	8	(	(	PUNCT
cana-1296	37	9	q	q	X
cana-1296	37	10	,	,	PUNCT
cana-1296	37	11	+	+	ADJ
cana-1296	37	12	)	)	PUNCT
cana-1296	37	13	are	be	AUX
cana-1296	37	14	commutative	commutative	ADJ
cana-1296	37	15	semigroups	semigroup	NOUN
cana-1296	37	16	.	.	PUNCT
cana-1296	38	1	identify	identify	VERB
cana-1296	38	2	the	the	DET
cana-1296	38	3	mapping	mapping	NOUN
cana-1296	38	4	q	q	NOUN
cana-1296	38	5	q	q	X
cana-1296	38	6	q	q	X
cana-1296	38	7	q	q	PROPN
cana-1296	38	8			PROPN
cana-1296	38	9	→	→	PUNCT
cana-1296	38	10	by	by	ADP
cana-1296	38	11	b	b	PROPN
cana-1296	38	12	c	c	PROPN
cana-1296	38	13	d	d	NOUN
cana-1296	38	14			PROPN
cana-1296	38	15	usual	usual	ADJ
cana-1296	38	16	product	product	NOUN
cana-1296	38	17	,	,	PUNCT
cana-1296	38	18	,	,	PUNCT
cana-1296	38	19	,	,	PUNCT
cana-1296	38	20	,	,	PUNCT
cana-1296	38	21	,	,	PUNCT
cana-1296	38	22	,	,	PUNCT
cana-1296	38	23	&	&	CCONJ
cana-1296	38	24	,	,	PUNCT
cana-1296	38	25	.b	.b	PROPN
cana-1296	39	1	c	c	PROPN
cana-1296	39	2	d	d	X
cana-1296	39	3	b	b	PROPN
cana-1296	39	4	c	c	X
cana-1296	39	5	d	d	NOUN
cana-1296	39	6	q	q	X
cana-1296	39	7			PROPN
cana-1296	39	8			NUM
cana-1296	39	9			PROPN
cana-1296	39	10			PROPN
cana-1296	39	11			NOUN
cana-1296	39	12	followed	follow	VERB
cana-1296	39	13	by	by	ADP
cana-1296	39	14	q	q	NOUN
cana-1296	39	15	is	be	AUX
cana-1296	39	16	a	a	DET
cana-1296	39	17	tγs	tγs	PROPN
cana-1296	39	18	.	.	PUNCT
cana-1296	40	1	example	example	NOUN
cana-1296	40	2	:	:	PUNCT
cana-1296	41	1	1.4	1.4	NUM
cana-1296	41	2	rational	rational	ADJ
cana-1296	41	3	numbers	number	NOUN
cana-1296	41	4	set	set	VERB
cana-1296	41	5	(	(	PUNCT
cana-1296	41	6	q	q	NOUN
cana-1296	41	7	)	)	PUNCT
cana-1296	41	8	.	.	PUNCT
cana-1296	42	1	the	the	DET
cana-1296	42	2	commutative	commutative	ADJ
cana-1296	42	3	semigroup	semigroup	NOUN
cana-1296	42	4	(	(	PUNCT
cana-1296	42	5	s	s	X
cana-1296	42	6	,	,	PUNCT
cana-1296	42	7	+	+	NOUN
cana-1296	42	8	)	)	PUNCT
cana-1296	42	9	of	of	ADP
cana-1296	42	10	all	all	PRON
cana-1296	42	11	2	2	NUM
cana-1296	42	12	3	3	NUM
cana-1296	42	13	matrices	matrix	NOUN
cana-1296	42	14	over	over	ADP
cana-1296	42	15	q	q	PROPN
cana-1296	42	16	&	&	CCONJ
cana-1296	42	17	(	(	PUNCT
cana-1296	42	18			PROPN
cana-1296	42	19	,	,	PUNCT
cana-1296	42	20	+	+	ADJ
cana-1296	42	21	)	)	PUNCT
cana-1296	42	22	commutative	commutative	ADJ
cana-1296	42	23	semigroup	semigroup	NOUN
cana-1296	42	24	of	of	ADP
cana-1296	42	25	all	all	DET
cana-1296	42	26	3	3	NUM
cana-1296	42	27	2	2	NUM
cana-1296	42	28	matrices	matrix	NOUN
cana-1296	42	29	over	over	ADP
cana-1296	42	30	q.	q.	PROPN
cana-1296	42	31	classify	classify	VERB
cana-1296	42	32	w	w	PROPN
cana-1296	42	33	y	y	PROPN
cana-1296	42	34	x	x	PUNCT
cana-1296	43	1			PROPN
cana-1296	43	2	standard	standard	ADJ
cana-1296	43	3	matrix	matrix	NOUN
cana-1296	43	4	product	product	NOUN
cana-1296	43	5	of	of	ADP
cana-1296	43	6	,	,	PUNCT
cana-1296	43	7	,	,	PUNCT
cana-1296	43	8	,	,	PUNCT
cana-1296	43	9	,	,	PUNCT
cana-1296	43	10	,	,	PUNCT
cana-1296	43	11	,	,	PUNCT
cana-1296	43	12	&	&	CCONJ
cana-1296	43	13	,	,	PUNCT
cana-1296	43	14	.w	.w	PROPN
cana-1296	44	1	y	y	PROPN
cana-1296	44	2	x	x	PROPN
cana-1296	44	3	w	w	VERB
cana-1296	44	4	y	y	PROPN
cana-1296	44	5	x	x	NOUN
cana-1296	44	6	s	s	PROPN
cana-1296	44	7			PROPN
cana-1296	44	8			NUM
cana-1296	44	9			PROPN
cana-1296	44	10			PROPN
cana-1296	44	11			VERB
cana-1296	44	12			NOUN
cana-1296	44	13	afterward	afterward	ADV
cana-1296	44	14	s	s	VERB
cana-1296	44	15	is	be	AUX
cana-1296	44	16	not	not	PART
cana-1296	44	17	a	a	DET
cana-1296	44	18	semiring	semiring	NOUN
cana-1296	44	19	&	&	CCONJ
cana-1296	44	20	a	a	DET
cana-1296	44	21	ts	ts	NOUN
cana-1296	44	22	.	.	PUNCT
cana-1296	45	1	definition	definition	NOUN
cana-1296	45	2	1.5	1.5	NUM
cana-1296	45	3	:	:	PUNCT
cana-1296	45	4	a	a	DET
cana-1296	45	5	partial	partial	ADJ
cana-1296	45	6	ternary	ternary	ADJ
cana-1296	45	7			VERB
cana-1296	45	8	-semiring	-semiring	NOUN
cana-1296	45	9	known	know	VERB
cana-1296	45	10	to	to	PART
cana-1296	45	11	have	have	VERB
cana-1296	45	12	a	a	DET
cana-1296	45	13	l	l	NOUN
cana-1296	45	14	(	(	PUNCT
cana-1296	45	15	la	la	X
cana-1296	45	16	,	,	PUNCT
cana-1296	45	17	r	r	NOUN
cana-1296	45	18	)	)	PUNCT
cana-1296	45	19	unity	unity	NOUN
cana-1296	45	20	element	element	NOUN
cana-1296	45	21	afford	afford	NOUN
cana-1296	45	22	,	,	PUNCT
cana-1296	45	23	:	:	PUNCT
cana-1296	45	24	,	,	PUNCT
cana-1296	45	25	e	e	X
cana-1296	45	26	:	:	PUNCT
cana-1296	45	27	i	i	PRON
cana-1296	45	28	i	i	PRON
cana-1296	46	1	ii	ii	VERB
cana-1296	47	1	i	i	PRON
cana-1296	47	2	i	i	PRON
cana-1296	47	3	i	i	VERB
cana-1296	47	4			X
cana-1296	48	1			PROPN
cana-1296	48	2			NOUN
cana-1296	48	3	of	of	ADP
cana-1296	48	4	m	m	PROPN
cana-1296	48	5	&	&	CCONJ
cana-1296	48	6	of	of	ADP
cana-1296	48	7			PUNCT
cana-1296	48	8			PROPN
cana-1296	48	9	(	(	PUNCT
cana-1296	48	10	,	,	PUNCT
cana-1296	48	11	)	)	PUNCT
cana-1296	49	1	i	i	PRON
cana-1296	49	2	i	i	PRON
cana-1296	50	1	i	i	PRON
cana-1296	50	2	i	i	PRON
cana-1296	51	1	i	i	PRON
cana-1296	51	2	i	i	PRON
cana-1296	52	1	i	i	PRON
cana-1296	52	2	i	i	PRON
cana-1296	53	1	i	i	PRON
cana-1296	53	2	i	i	VERB
cana-1296	54	1	i	i	PRON
cana-1296	54	2	ie	ie	ADV
cana-1296	54	3	e	e	X
cana-1296	54	4	c	c	NOUN
cana-1296	54	5	c	c	NOUN
cana-1296	54	6	e	e	X
cana-1296	54	7	c	c	NOUN
cana-1296	54	8	e	e	X
cana-1296	54	9	c	c	NOUN
cana-1296	54	10	c	c	NOUN
cana-1296	54	11	e	e	X
cana-1296	54	12	e	e	NOUN
cana-1296	54	13	c	c	NOUN
cana-1296	54	14			PROPN
cana-1296	54	15			NUM
cana-1296	54	16			PROPN
cana-1296	54	17			NUM
cana-1296	54	18	=	=	PROPN
cana-1296	54	19	=	=	SYM
cana-1296	55	1	=	=	PRON
cana-1296	55	2			X
cana-1296	55	3			X
cana-1296	55	4			X
cana-1296	55	5	for	for	ADP
cana-1296	55	6	any	any	DET
cana-1296	55	7	cm	cm	PROPN
cana-1296	55	8	.	.	PUNCT
cana-1296	56	1	definition	definition	NOUN
cana-1296	56	2	1.6	1.6	NUM
cana-1296	56	3	:	:	PUNCT
cana-1296	56	4	let	let	VERB
cana-1296	56	5	m	m	PRON
cana-1296	56	6	be	be	AUX
cana-1296	56	7	a	a	DET
cana-1296	56	8	partial	partial	ADJ
cana-1296	56	9	ternary	ternary	ADJ
cana-1296	56	10	γ	γ	NOUN
cana-1296	56	11	-	-	PUNCT
cana-1296	56	12	semiring	semiring	NOUN
cana-1296	56	13	.	.	PUNCT
cana-1296	57	1	(	(	PUNCT
cana-1296	57	2	)	)	PUNCT
cana-1296	57	3	a	a	DET
cana-1296	57	4	m	m	PROPN
cana-1296	57	5			PROPN
cana-1296	57	6	is	be	AUX
cana-1296	57	7	known	know	VERB
cana-1296	57	8	to	to	PART
cana-1296	57	9	be	be	AUX
cana-1296	57	10	l	l	NOUN
cana-1296	57	11	(	(	PUNCT
cana-1296	57	12	la	la	X
cana-1296	57	13	,	,	PUNCT
cana-1296	57	14	r	r	NOUN
cana-1296	57	15	)	)	PUNCT
cana-1296	57	16	partial	partial	ADJ
cana-1296	57	17	ternary	ternary	ADJ
cana-1296	57	18	γ	γ	NOUN
cana-1296	57	19	-	-	NOUN
cana-1296	57	20	ideal	ideal	NOUN
cana-1296	57	21	of	of	ADP
cana-1296	57	22	m	m	VERB
cana-1296	57	23	afford	afford	ADJ
cana-1296	57	24	(	(	PUNCT
cana-1296	57	25	i	i	NOUN
cana-1296	57	26	)	)	PUNCT
cana-1296	57	27	(	(	PUNCT
cana-1296	57	28	:	:	PUNCT
cana-1296	57	29	)	)	PUNCT
cana-1296	57	30	iv	iv	X
cana-1296	57	31	i	i	PRON
cana-1296	57	32	i	i	VERB
cana-1296	57	33	is	be	AUX
cana-1296	57	34	a	a	DET
cana-1296	57	35	sum	sum	NOUN
cana-1296	57	36	able	able	ADJ
cana-1296	57	37	family	family	NOUN
cana-1296	57	38	&	&	CCONJ
cana-1296	57	39	vi∈	vi∈	PROPN
cana-1296	58	1	a	a	PRON
cana-1296	59	1	i	i	NOUN
cana-1296	59	2	ii	ii	VERB
cana-1296	60	1	i	i	PRON
cana-1296	60	2	v	v	VERB
cana-1296	60	3	a	a	PRON
cana-1296	61	1			PROPN
cana-1296	61	2			NOUN
cana-1296	61	3			PROPN
cana-1296	61	4	(	(	PUNCT
cana-1296	61	5	ii	ii	NOUN
cana-1296	61	6	)	)	PUNCT
cana-1296	61	7	,	,	PUNCT
cana-1296	61	8	&	&	CCONJ
cana-1296	61	9	a	a	PRON
cana-1296	61	10	(	(	PUNCT
cana-1296	61	11	a	a	PRON
cana-1296	61	12	,	,	PUNCT
cana-1296	61	13	a)u	a)u	NOUN
cana-1296	61	14	v	v	ADP
cana-1296	61	15	m	m	PROPN
cana-1296	61	16	q	q	NOUN
cana-1296	61	17	a	a	DET
cana-1296	61	18	q	q	X
cana-1296	61	19	u	u	NOUN
cana-1296	61	20	v	v	ADP
cana-1296	61	21	u	u	NOUN
cana-1296	61	22	q	q	PROPN
cana-1296	61	23	v	v	ADP
cana-1296	61	24	u	u	NOUN
cana-1296	61	25	v	v	NOUN
cana-1296	61	26	q	q	NOUN
cana-1296	62	1			PROPN
cana-1296	62	2			NUM
cana-1296	62	3			PROPN
cana-1296	62	4			NUM
cana-1296	62	5			PROPN
cana-1296	62	6			PROPN
cana-1296	62	7			PROPN
cana-1296	62	8			PROPN
cana-1296	63	1			PROPN
cana-1296	63	2			NOUN
cana-1296	63	3			NOUN
cana-1296	63	4	if	if	SCONJ
cana-1296	63	5	a	a	PRON
cana-1296	63	6	is	be	AUX
cana-1296	63	7	l	l	NOUN
cana-1296	63	8	(	(	PUNCT
cana-1296	63	9	la	la	X
cana-1296	63	10	,	,	PUNCT
cana-1296	63	11	r	r	NOUN
cana-1296	63	12	)	)	PUNCT
cana-1296	63	13	ptγi	ptγi	NOUN
cana-1296	63	14	of	of	ADP
cana-1296	63	15	m.	m.	NOUN
cana-1296	63	16	definition	definition	NOUN
cana-1296	63	17	1.7	1.7	NUM
cana-1296	63	18	:	:	PUNCT
cana-1296	63	19	let	let	VERB
cana-1296	63	20	m	m	PRON
cana-1296	63	21	be	be	AUX
cana-1296	63	22	a	a	DET
cana-1296	63	23	tγs	tγs	PROPN
cana-1296	63	24	.	.	PUNCT
cana-1296	64	1	(	(	PUNCT
cana-1296	64	2	)	)	PUNCT
cana-1296	64	3	a	a	DET
cana-1296	64	4	m	m	PROPN
cana-1296	64	5			PROPN
cana-1296	64	6	is	be	AUX
cana-1296	64	7	known	know	VERB
cana-1296	64	8	as	as	ADP
cana-1296	64	9	a	a	DET
cana-1296	64	10	l	l	NOUN
cana-1296	64	11	(	(	PUNCT
cana-1296	64	12	la	la	X
cana-1296	64	13	,	,	PUNCT
cana-1296	64	14	r	r	NOUN
cana-1296	64	15	)	)	PUNCT
cana-1296	64	16	tγi	tγi	NOUN
cana-1296	64	17	of	of	ADP
cana-1296	64	18	m	m	PROPN
cana-1296	64	19	,	,	PUNCT
cana-1296	64	20	if	if	SCONJ
cana-1296	64	21	it	it	PRON
cana-1296	64	22	satisfy	satisfy	VERB
cana-1296	64	23	the	the	DET
cana-1296	64	24	next	next	ADJ
cana-1296	64	25	:	:	PUNCT
cana-1296	64	26	(	(	PUNCT
cana-1296	64	27	i	i	NOUN
cana-1296	64	28	)	)	PUNCT
cana-1296	64	29	a	a	PRON
cana-1296	64	30	is	be	AUX
cana-1296	64	31	a	a	DET
cana-1296	64	32	l	l	NOUN
cana-1296	64	33	(	(	PUNCT
cana-1296	64	34	la	la	X
cana-1296	64	35	,	,	PUNCT
cana-1296	64	36	r	r	NOUN
cana-1296	64	37	)	)	PUNCT
cana-1296	64	38	ptγi	ptγi	NOUN
cana-1296	64	39	of	of	ADP
cana-1296	64	40	m.	m.	NOUN
cana-1296	64	41	(	(	PUNCT
cana-1296	64	42	ii	ii	NOUN
cana-1296	64	43	)	)	PUNCT
cana-1296	64	44	&	&	CCONJ
cana-1296	64	45	v	v	ADP
cana-1296	64	46	m	m	PROPN
cana-1296	64	47	w	w	ADP
cana-1296	64	48	a	a	DET
cana-1296	64	49	v	v	NOUN
cana-1296	64	50	w	w	NOUN
cana-1296	64	51			NOUN
cana-1296	64	52			NUM
cana-1296	64	53			NOUN
cana-1296	64	54	then	then	ADV
cana-1296	64	55	v∈	v∈	PROPN
cana-1296	64	56	a.	a.	NOUN
cana-1296	64	57	communications	communication	NOUN
cana-1296	64	58	on	on	ADP
cana-1296	64	59	applied	apply	VERB
cana-1296	64	60	nonlinear	nonlinear	ADJ
cana-1296	64	61	analysis	analysis	NOUN
cana-1296	64	62	issn	issn	NOUN
cana-1296	64	63	:	:	PUNCT
cana-1296	64	64	1074	1074	NUM
cana-1296	64	65	-	-	PUNCT
cana-1296	64	66	133x	133x	NUM
cana-1296	64	67	vol	vol	NOUN
cana-1296	64	68	31	31	NUM
cana-1296	64	69	no	no	NOUN
cana-1296	64	70	.	.	PUNCT
cana-1296	65	1	7s	7	NOUN
cana-1296	65	2	(	(	PUNCT
cana-1296	65	3	2024	2024	NUM
cana-1296	65	4	)	)	PUNCT
cana-1296	65	5	216	216	NUM
cana-1296	65	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	65	7	if	if	SCONJ
cana-1296	65	8	a	a	PRON
cana-1296	65	9	is	be	AUX
cana-1296	65	10	l	l	NOUN
cana-1296	65	11	(	(	PUNCT
cana-1296	65	12	la	la	X
cana-1296	65	13	,	,	PUNCT
cana-1296	65	14	r	r	NOUN
cana-1296	65	15	)	)	PUNCT
cana-1296	65	16	tγi	tγi	NOUN
cana-1296	65	17	of	of	ADP
cana-1296	65	18	m	m	PROPN
cana-1296	65	19	,	,	PUNCT
cana-1296	65	20	afterward	afterward	ADV
cana-1296	65	21	a	a	PRON
cana-1296	65	22	is	be	AUX
cana-1296	65	23	recognized	recognize	VERB
cana-1296	65	24	as	as	ADP
cana-1296	65	25	tγi	tγi	NOUN
cana-1296	65	26	of	of	ADP
cana-1296	65	27	m.	m.	NOUN
cana-1296	65	28	definition1.8	definition1.8	PROPN
cana-1296	65	29	:	:	PUNCT
cana-1296	65	30	a	a	DET
cana-1296	65	31	(	(	PUNCT
cana-1296	65	32	)	)	PUNCT
cana-1296	65	33	o	o	NOUN
cana-1296	66	1			PROPN
cana-1296	66	2			PROPN
cana-1296	66	3			NOUN
cana-1296	66	4	is	be	AUX
cana-1296	66	5	entitled	entitle	VERB
cana-1296	66	6	(	(	PUNCT
cana-1296	66	7	1	1	X
cana-1296	66	8	)	)	PUNCT
cana-1296	66	9	a	a	DET
cana-1296	66	10	btγi	btγi	NOUN
cana-1296	66	11	of	of	ADP
cana-1296	66	12	n	n	PRON
cana-1296	66	13	if	if	SCONJ
cana-1296	66	14	o	o	NOUN
cana-1296	66	15	is	be	AUX
cana-1296	66	16	a	a	DET
cana-1296	66	17	subγ	subγ	NOUN
cana-1296	66	18	-	-	PUNCT
cana-1296	66	19	semiring	semiring	NOUN
cana-1296	66	20	of	of	ADP
cana-1296	66	21	n	n	PROPN
cana-1296	66	22	&	&	CCONJ
cana-1296	66	23	.o	.o	PROPN
cana-1296	67	1	n	n	CCONJ
cana-1296	67	2	o	o	NOUN
cana-1296	67	3	n	n	X
cana-1296	67	4	o	o	NOUN
cana-1296	68	1	o	o	VERB
cana-1296	68	2			NOUN
cana-1296	68	3			VERB
cana-1296	68	4			VERB
cana-1296	68	5			NOUN
cana-1296	68	6	(	(	PUNCT
cana-1296	68	7	2	2	NUM
cana-1296	68	8	)	)	PUNCT
cana-1296	68	9	a	a	DET
cana-1296	68	10	gbtγi	gbtγi	NOUN
cana-1296	68	11	of	of	ADP
cana-1296	68	12	n	n	NOUN
cana-1296	68	13	if	if	SCONJ
cana-1296	68	14	.o	.o	PROPN
cana-1296	68	15	n	n	NUM
cana-1296	68	16	o	o	NOUN
cana-1296	68	17	n	n	X
cana-1296	68	18	o	o	NOUN
cana-1296	68	19	o	o	VERB
cana-1296	68	20			NOUN
cana-1296	68	21			VERB
cana-1296	68	22			VERB
cana-1296	68	23			NOUN
cana-1296	68	24	(	(	PUNCT
cana-1296	68	25	3	3	NUM
cana-1296	68	26	)	)	PUNCT
cana-1296	68	27	a	a	DET
cana-1296	68	28	qtγi	qtγi	NOUN
cana-1296	68	29	of	of	ADP
cana-1296	68	30	n	n	PRON
cana-1296	68	31	if	if	SCONJ
cana-1296	68	32	o	o	NOUN
cana-1296	68	33	is	be	AUX
cana-1296	68	34	a	a	DET
cana-1296	68	35	subγ	subγ	NOUN
cana-1296	68	36	-	-	PUNCT
cana-1296	68	37	semiring	semiring	NOUN
cana-1296	68	38	of	of	ADP
cana-1296	68	39	n	n	PROPN
cana-1296	68	40	&	&	CCONJ
cana-1296	68	41	(	(	PUNCT
cana-1296	68	42	)	)	PUNCT
cana-1296	68	43	(	(	PUNCT
cana-1296	68	44	)	)	PUNCT
cana-1296	68	45	(	(	PUNCT
cana-1296	68	46	)	)	PUNCT
cana-1296	68	47			NOUN
cana-1296	68	48	+	+	PROPN
cana-1296	68	49			ADJ
cana-1296	68	50			PROPN
cana-1296	68	51			PROPN
cana-1296	68	52	remark1.9	remark1.9	PRON
cana-1296	68	53	:	:	PUNCT
cana-1296	68	54	let	let	VERB
cana-1296	68	55	m	m	PRON
cana-1296	68	56	be	be	AUX
cana-1296	68	57	a	a	DET
cana-1296	68	58	tγs	tγs	PROPN
cana-1296	68	59	.	.	PUNCT
cana-1296	69	1	then	then	ADV
cana-1296	69	2	:	:	PUNCT
cana-1296	69	3	(	(	PUNCT
cana-1296	69	4	1)each	1)each	NUM
cana-1296	69	5	qtγi	qtγi	NOUN
cana-1296	69	6	of	of	ADP
cana-1296	69	7	m	m	PROPN
cana-1296	69	8	is	be	AUX
cana-1296	69	9	a	a	DET
cana-1296	69	10	btγi	btγi	NOUN
cana-1296	69	11	.	.	PUNCT
cana-1296	70	1	(	(	PUNCT
cana-1296	70	2	2)each	2)each	NUM
cana-1296	70	3	btγi	btγi	NOUN
cana-1296	70	4	of	of	ADP
cana-1296	70	5	m	m	PROPN
cana-1296	70	6	is	be	AUX
cana-1296	70	7	a	a	DET
cana-1296	70	8	gbtγi	gbtγi	NOUN
cana-1296	70	9	.	.	PUNCT
cana-1296	71	1	definition1.10	definition1.10	NOUN
cana-1296	71	2	:	:	PUNCT
cana-1296	71	3	a	a	DET
cana-1296	71	4	tγs	tγs	PROPN
cana-1296	71	5	is	be	AUX
cana-1296	71	6	named	name	VERB
cana-1296	71	7	a	a	DET
cana-1296	71	8	gb	gb	NOUN
cana-1296	71	9	-	-	PUNCT
cana-1296	71	10	simple	simple	ADJ
cana-1296	71	11	tγ	tγ	NOUN
cana-1296	71	12	-	-	PUNCT
cana-1296	71	13	semiring	semiring	NOUN
cana-1296	71	14	if	if	SCONJ
cana-1296	71	15	m	m	NOUN
cana-1296	71	16	is	be	AUX
cana-1296	71	17	the	the	DET
cana-1296	71	18	unique	unique	ADJ
cana-1296	71	19	gbtγi	gbtγi	NOUN
cana-1296	71	20	of	of	ADP
cana-1296	71	21	m.	m.	NOUN
cana-1296	71	22	2.properties	2.properties	NUM
cana-1296	71	23	of	of	ADP
cana-1296	71	24	gbtγi	gbtγi	NOUN
cana-1296	71	25	’s	’s	ADV
cana-1296	71	26	:	:	PUNCT
cana-1296	71	27	before	before	ADP
cana-1296	71	28	the	the	DET
cana-1296	71	29	portrayals	portrayal	NOUN
cana-1296	71	30	of	of	ADP
cana-1296	71	31	generalized	generalized	ADJ
cana-1296	71	32	bi	bi	ADJ
cana-1296	71	33	-	-	ADJ
cana-1296	71	34	γ	γ	NOUN
cana-1296	71	35	-	-	PUNCT
cana-1296	71	36	ideals	ideal	NOUN
cana-1296	71	37	of	of	ADP
cana-1296	71	38	γ	γ	NOUN
cana-1296	71	39	-	-	NOUN
cana-1296	71	40	semirings	semiring	NOUN
cana-1296	71	41	for	for	ADP
cana-1296	71	42	the	the	DET
cana-1296	71	43	primary	primary	ADJ
cana-1296	71	44	outcomes	outcome	NOUN
cana-1296	71	45	,	,	PUNCT
cana-1296	71	46	we	we	PRON
cana-1296	71	47	give	give	VERB
cana-1296	71	48	a	a	DET
cana-1296	71	49	few	few	ADJ
cana-1296	71	50	helper	helper	NOUN
cana-1296	71	51	results	result	NOUN
cana-1296	71	52	which	which	PRON
cana-1296	71	53	are	be	AUX
cana-1296	71	54	vital	vital	ADJ
cana-1296	71	55	in	in	ADP
cana-1296	71	56	what	what	PRON
cana-1296	71	57	follows	follow	VERB
cana-1296	71	58	.	.	PUNCT
cana-1296	72	1	lemma2.1	lemma2.1	NOUN
cana-1296	72	2	:	:	PUNCT
cana-1296	72	3	let	let	VERB
cana-1296	72	4	u	u	PRON
cana-1296	72	5	be	be	AUX
cana-1296	72	6	a	a	DET
cana-1296	72	7	tγs	tγs	PROPN
cana-1296	72	8	and	and	CCONJ
cana-1296	72	9	.l	.l	PROPN
cana-1296	72	10	u	u	PROPN
cana-1296	72	11	then	then	ADV
cana-1296	72	12	,	,	PUNCT
cana-1296	72	13	&	&	CCONJ
cana-1296	72	14	l	l	PROPN
cana-1296	72	15	l	l	X
cana-1296	72	16	u	u	X
cana-1296	72	17	l	l	NOUN
cana-1296	72	18	u	u	X
cana-1296	72	19	l	l	NOUN
cana-1296	72	20	u	u	NOUN
cana-1296	72	21	l	l	NOUN
cana-1296	72	22	l	l	ADP
cana-1296	72	23			VERB
cana-1296	72	24			VERB
cana-1296	72	25			VERB
cana-1296	72	26			VERB
cana-1296	72	27			NOUN
cana-1296	72	28	are	be	AUX
cana-1296	72	29	gbtγi	gbtγi	NOUN
cana-1296	72	30	’s	’s	ADV
cana-1296	72	31	of	of	ADP
cana-1296	72	32	u.	u.	PROPN
cana-1296	72	33	lemma2.2	lemma2.2	PROPN
cana-1296	72	34	:	:	PUNCT
cana-1296	72	35	let	let	VERB
cana-1296	72	36	m	m	PRON
cana-1296	72	37	be	be	AUX
cana-1296	72	38	a	a	DET
cana-1296	72	39	tγs	tγs	NOUN
cana-1296	72	40	,	,	PUNCT
cana-1296	72	41	{	{	PUNCT
cana-1296	72	42	/	/	SYM
cana-1296	72	43	}	}	PUNCT
cana-1296	72	44	i	i	NOUN
cana-1296	73	1	d	d	NOUN
cana-1296	74	1	i	i	PRON
cana-1296	74	2	i	i	VERB
cana-1296	74	3	a	a	DET
cana-1296	74	4	non	non	ADJ
cana-1296	74	5	-	-	ADJ
cana-1296	74	6	empty	empty	ADJ
cana-1296	74	7	family	family	NOUN
cana-1296	74	8	of	of	ADP
cana-1296	74	9	gbtγi	gbtγi	PROPN
cana-1296	74	10	’s	’s	ADV
cana-1296	74	11	of	of	ADP
cana-1296	74	12	m	m	VERB
cana-1296	74	13	with	with	ADP
cana-1296	74	14	.i	.i	PROPN
cana-1296	75	1	i	i	PRON
cana-1296	75	2	i	i	VERB
cana-1296	76	1	d	d	NOUN
cana-1296	76	2			NOUN
cana-1296	76	3			NOUN
cana-1296	76	4			NOUN
cana-1296	76	5	then	then	ADV
cana-1296	76	6	i	i	PRON
cana-1296	76	7	i	i	PRON
cana-1296	77	1	i	i	VERB
cana-1296	77	2	d	d	VERB
cana-1296	77	3			NOUN
cana-1296	77	4	is	be	AUX
cana-1296	77	5	a	a	DET
cana-1296	77	6	gbtγi	gbtγi	NOUN
cana-1296	77	7	of	of	ADP
cana-1296	77	8	m.	m.	NOUN
cana-1296	77	9	proof	proof	NOUN
cana-1296	77	10	:	:	PUNCT
cana-1296	77	11	i	i	PRON
cana-1296	77	12	i	i	VERB
cana-1296	77	13			NOUN
cana-1296	77	14	,	,	PUNCT
cana-1296	77	15	we	we	PRON
cana-1296	77	16	have	have	VERB
cana-1296	77	17	(	(	PUNCT
cana-1296	77	18	)	)	PUNCT
cana-1296	77	19	(	(	PUNCT
cana-1296	78	1	)	)	PUNCT
cana-1296	78	2	(	(	PUNCT
cana-1296	78	3	)	)	PUNCT
cana-1296	78	4	i	i	PRON
cana-1296	78	5	i	i	PRON
cana-1296	79	1	i	i	PRON
cana-1296	79	2	i	i	PRON
cana-1296	80	1	i	i	PRON
cana-1296	80	2	i	i	PRON
cana-1296	81	1	i	i	PRON
cana-1296	81	2	i	i	PRON
cana-1296	82	1	i	i	PRON
cana-1296	82	2	i	i	PRON
cana-1296	83	1	i	i	PRON
cana-1296	84	1	i	i	PRON
cana-1296	84	2	i	i	VERB
cana-1296	85	1	d	d	NOUN
cana-1296	85	2	m	m	VERB
cana-1296	85	3	d	d	NOUN
cana-1296	85	4	m	m	NOUN
cana-1296	85	5	d	d	X
cana-1296	86	1	d	d	NOUN
cana-1296	86	2	m	m	PROPN
cana-1296	86	3	d	d	NOUN
cana-1296	86	4	m	m	PROPN
cana-1296	86	5	d	d	PROPN
cana-1296	86	6	d	d	PROPN
cana-1296	86	7			PROPN
cana-1296	86	8			NOUN
cana-1296	86	9			NOUN
cana-1296	86	10			PUNCT
cana-1296	86	11			VERB
cana-1296	86	12			VERB
cana-1296	86	13			VERB
cana-1296	86	14			NOUN
cana-1296	86	15			VERB
cana-1296	86	16			VERB
cana-1296	86	17			VERB
cana-1296	86	18			VERB
cana-1296	86	19			PROPN
cana-1296	86	20	(	(	PUNCT
cana-1296	86	21	)	)	PUNCT
cana-1296	86	22	(	(	PUNCT
cana-1296	86	23	)	)	PUNCT
cana-1296	86	24	(	(	PUNCT
cana-1296	86	25	)	)	PUNCT
cana-1296	86	26	.i	.i	NOUN
cana-1296	87	1	i	i	PRON
cana-1296	87	2	i	i	PRON
cana-1296	88	1	i	i	PRON
cana-1296	88	2	i	i	PRON
cana-1296	89	1	i	i	PRON
cana-1296	89	2	i	i	PRON
cana-1296	90	1	i	i	PRON
cana-1296	90	2	i	i	PRON
cana-1296	91	1	i	i	PRON
cana-1296	91	2	i	i	PRON
cana-1296	92	1	i	i	PRON
cana-1296	92	2	thus	thus	ADV
cana-1296	93	1	d	d	X
cana-1296	93	2	m	m	VERB
cana-1296	93	3	d	d	NOUN
cana-1296	93	4	m	m	PROPN
cana-1296	93	5	d	d	PROPN
cana-1296	93	6	d	d	PROPN
cana-1296	93	7			PROPN
cana-1296	93	8			PROPN
cana-1296	93	9			PROPN
cana-1296	93	10			NOUN
cana-1296	93	11			PUNCT
cana-1296	93	12			VERB
cana-1296	93	13			VERB
cana-1296	93	14			ADJ
cana-1296	93	15			NOUN
cana-1296	94	1	hence	hence	ADV
cana-1296	94	2	i	i	PRON
cana-1296	95	1	i	i	PRON
cana-1296	95	2	i	i	VERB
cana-1296	96	1	d	d	VERB
cana-1296	96	2			NOUN
cana-1296	96	3	is	be	AUX
cana-1296	96	4	a	a	DET
cana-1296	96	5	gbtγi	gbtγi	NOUN
cana-1296	96	6	of	of	ADP
cana-1296	96	7	m.	m.	NOUN
cana-1296	96	8	lemma	lemma	PROPN
cana-1296	96	9	2.3	2.3	NUM
cana-1296	96	10	:	:	PUNCT
cana-1296	96	11	let	let	VERB
cana-1296	96	12	m	m	PRON
cana-1296	96	13	be	be	AUX
cana-1296	96	14	a	a	DET
cana-1296	96	15	tγs	tγs	PROPN
cana-1296	96	16	&	&	CCONJ
cana-1296	96	17	e	e	PROPN
cana-1296	96	18	s	s	PROPN
cana-1296	96	19			PROPN
cana-1296	96	20			PROPN
cana-1296	96	21	.	.	PUNCT
cana-1296	97	1	then	then	ADV
cana-1296	97	2	e	e	X
cana-1296	97	3	e	e	NOUN
cana-1296	97	4	s	s	PROPN
cana-1296	97	5	e	e	NOUN
cana-1296	97	6	s	s	PART
cana-1296	97	7	e	e	PROPN
cana-1296	97	8			VERB
cana-1296	97	9			VERB
cana-1296	97	10			NOUN
cana-1296	97	11	is	be	AUX
cana-1296	97	12	the	the	DET
cana-1296	97	13	sgbtγi	sgbtγi	NOUN
cana-1296	97	14	of	of	ADP
cana-1296	97	15	s	s	NOUN
cana-1296	97	16	containing	contain	VERB
cana-1296	97	17	e.	e.	PROPN
cana-1296	97	18	proof	proof	PROPN
cana-1296	97	19	:	:	PUNCT
cana-1296	97	20	let	let	VERB
cana-1296	97	21	d	d	X
cana-1296	97	22	e	e	X
cana-1296	97	23	e	e	NOUN
cana-1296	97	24	s	s	PROPN
cana-1296	97	25	e	e	NOUN
cana-1296	97	26	s	s	PART
cana-1296	97	27	e=	e=	X
cana-1296	97	28			VERB
cana-1296	97	29			VERB
cana-1296	97	30			VERB
cana-1296	97	31			NOUN
cana-1296	97	32	.	.	PUNCT
cana-1296	98	1	then	then	ADV
cana-1296	98	2	.e	.e	PUNCT
cana-1296	99	1	d	d	PROPN
cana-1296	99	2	therefore	therefore	ADV
cana-1296	99	3	(	(	PUNCT
cana-1296	99	4	)	)	PUNCT
cana-1296	99	5	(	(	PUNCT
cana-1296	99	6	)	)	PUNCT
cana-1296	99	7	(	(	PUNCT
cana-1296	99	8	)	)	PUNCT
cana-1296	100	1	[	[	PUNCT
cana-1296	100	2	(	(	PUNCT
cana-1296	100	3	)	)	PUNCT
cana-1296	100	4	(	(	PUNCT
cana-1296	100	5	(	(	PUNCT
cana-1296	100	6	)	)	PUNCT
cana-1296	100	7	)	)	PUNCT
cana-1296	100	8	]	]	PUNCT
cana-1296	101	1	[	[	PUNCT
cana-1296	101	2	(	(	PUNCT
cana-1296	101	3	)	)	PUNCT
cana-1296	101	4	(	(	PUNCT
cana-1296	101	5	)	)	PUNCT
cana-1296	101	6	]	]	PUNCT
cana-1296	101	7	.	.	PUNCT
cana-1296	102	1	d	d	X
cana-1296	102	2	s	s	X
cana-1296	102	3	d	d	X
cana-1296	102	4	s	s	PROPN
cana-1296	102	5	d	d	X
cana-1296	102	6	s	s	X
cana-1296	102	7	s	s	X
cana-1296	102	8	s	s	X
cana-1296	102	9	s	s	X
cana-1296	102	10	s	s	X
cana-1296	102	11	u	u	NOUN
cana-1296	102	12	s	s	NOUN
cana-1296	102	13	s	s	X
cana-1296	102	14	s	s	X
cana-1296	102	15	s	s	X
cana-1296	102	16	s	s	X
cana-1296	102	17	s	s	X
cana-1296	102	18	s	s	X
cana-1296	102	19	s	s	X
cana-1296	102	20	s	s	X
cana-1296	102	21	s	s	X
cana-1296	102	22	s	s	X
cana-1296	102	23	s	s	X
cana-1296	102	24	s	s	X
cana-1296	102	25	s	s	X
cana-1296	102	26	s	s	X
cana-1296	102	27	s	s	X
cana-1296	102	28	s	s	X
cana-1296	102	29	s	s	X
cana-1296	102	30	s	s	X
cana-1296	102	31	s	s	X
cana-1296	102	32	s	s	X
cana-1296	102	33	s	s	X
cana-1296	102	34	d	d	NOUN
cana-1296	102	35			VERB
cana-1296	102	36			VERB
cana-1296	102	37			VERB
cana-1296	102	38			VERB
cana-1296	102	39	=	=	PUNCT
cana-1296	102	40			ADJ
cana-1296	102	41			NOUN
cana-1296	102	42			PRON
cana-1296	102	43			PROPN
cana-1296	102	44			VERB
cana-1296	102	45			VERB
cana-1296	102	46			ADJ
cana-1296	102	47			NOUN
cana-1296	102	48			PRON
cana-1296	102	49			PROPN
cana-1296	102	50			VERB
cana-1296	102	51			VERB
cana-1296	102	52			ADJ
cana-1296	102	53			NOUN
cana-1296	102	54			PRON
cana-1296	102	55			PROPN
cana-1296	102	56			ADJ
cana-1296	102	57			ADJ
cana-1296	102	58			PUNCT
cana-1296	102	59			VERB
cana-1296	102	60			VERB
cana-1296	102	61			ADJ
cana-1296	102	62			ADJ
cana-1296	102	63			PUNCT
cana-1296	102	64			VERB
cana-1296	102	65			ADJ
cana-1296	102	66			NOUN
cana-1296	102	67			PRON
cana-1296	102	68			NOUN
cana-1296	102	69			VERB
cana-1296	102	70			PRON
cana-1296	102	71			PROPN
cana-1296	102	72			VERB
cana-1296	102	73			VERB
cana-1296	102	74			VERB
cana-1296	102	75			ADJ
cana-1296	102	76			NOUN
cana-1296	102	77			PRON
cana-1296	102	78			PROPN
cana-1296	102	79			VERB
cana-1296	102	80			VERB
cana-1296	102	81			ADJ
cana-1296	102	82			NOUN
cana-1296	102	83			NOUN
cana-1296	102	84			NOUN
cana-1296	102	85	=	=	SYM
cana-1296	102	86			NOUN
cana-1296	102	87			PRON
cana-1296	102	88			NOUN
cana-1296	102	89			ADJ
cana-1296	102	90			ADJ
cana-1296	102	91			NOUN
cana-1296	102	92			PRON
cana-1296	102	93			NOUN
cana-1296	102	94	=	=	SYM
cana-1296	102	95	communications	communication	NOUN
cana-1296	102	96	on	on	ADP
cana-1296	102	97	applied	apply	VERB
cana-1296	102	98	nonlinear	nonlinear	ADJ
cana-1296	102	99	analysis	analysis	NOUN
cana-1296	102	100	issn	issn	NOUN
cana-1296	102	101	:	:	PUNCT
cana-1296	102	102	1074	1074	NUM
cana-1296	102	103	-	-	PUNCT
cana-1296	102	104	133x	133x	NUM
cana-1296	102	105	vol	vol	NOUN
cana-1296	102	106	31	31	NUM
cana-1296	102	107	no	no	NOUN
cana-1296	102	108	.	.	PUNCT
cana-1296	103	1	7s	7	NOUN
cana-1296	103	2	(	(	PUNCT
cana-1296	103	3	2024	2024	NUM
cana-1296	103	4	)	)	PUNCT
cana-1296	103	5	217	217	NUM
cana-1296	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	104	1	thus	thus	ADV
cana-1296	104	2	d	d	X
cana-1296	104	3	s	s	PROPN
cana-1296	104	4	s=	s=	NOUN
cana-1296	104	5			NOUN
cana-1296	104	6			PRON
cana-1296	104	7			PROPN
cana-1296	104	8	is	be	AUX
cana-1296	104	9	a	a	DET
cana-1296	104	10	gbtγi	gbtγi	NOUN
cana-1296	104	11	of	of	ADP
cana-1296	104	12	s.	s.	PROPN
cana-1296	104	13	we	we	PRON
cana-1296	104	14	shall	shall	AUX
cana-1296	104	15	explain	explain	VERB
cana-1296	104	16	that	that	SCONJ
cana-1296	104	17	d	d	NOUN
cana-1296	104	18	is	be	AUX
cana-1296	104	19	the	the	DET
cana-1296	104	20	sgbtγi	sgbtγi	NOUN
cana-1296	104	21	of	of	ADP
cana-1296	104	22	s	s	NOUN
cana-1296	104	23	containing	contain	VERB
cana-1296	104	24	e.	e.	PROPN
cana-1296	104	25	let	let	VERB
cana-1296	104	26	c	c	PRON
cana-1296	104	27	be	be	AUX
cana-1296	104	28	a	a	DET
cana-1296	104	29	gbtγi	gbtγi	NOUN
cana-1296	104	30	of	of	ADP
cana-1296	104	31	s.	s.	PROPN
cana-1296	104	32	then	then	ADV
cana-1296	104	33	.s	.s	VERB
cana-1296	104	34	s	s	VERB
cana-1296	104	35	c	c	NOUN
cana-1296	104	36	s	s	ADP
cana-1296	104	37	c	c	NOUN
cana-1296	104	38	s	s	X
cana-1296	104	39	c	c	NOUN
cana-1296	104	40	c	c	PROPN
cana-1296	104	41			ADP
cana-1296	104	42			NUM
cana-1296	104	43			VERB
cana-1296	104	44			PROPN
cana-1296	104	45			VERB
cana-1296	104	46			ADJ
cana-1296	104	47			NOUN
cana-1296	104	48	thus	thus	ADV
cana-1296	104	49	.d	.d	PRON
cana-1296	104	50	s	s	PART
cana-1296	104	51	s	s	NOUN
cana-1296	104	52	c=	c=	NOUN
cana-1296	104	53			NOUN
cana-1296	104	54			NOUN
cana-1296	104	55			PROPN
cana-1296	104	56	hence	hence	ADV
cana-1296	104	57	d	d	PROPN
cana-1296	104	58	is	be	AUX
cana-1296	104	59	the	the	DET
cana-1296	104	60	sgbtγi	sgbtγi	NOUN
cana-1296	104	61	of	of	ADP
cana-1296	104	62	s	s	AUX
cana-1296	104	63	having	have	VERB
cana-1296	104	64	e.	e.	PROPN
cana-1296	104	65	(	(	PUNCT
cana-1296	104	66	)	)	PUNCT
cana-1296	104	67	s	s	PART
cana-1296	104	68	s	s	NOUN
cana-1296	104	69			ADJ
cana-1296	104	70	=	=	SYM
cana-1296	104	71			ADJ
cana-1296	104	72			NOUN
cana-1296	104	73			PRON
cana-1296	104	74			NOUN
cana-1296	104	75	it	it	PRON
cana-1296	104	76	is	be	AUX
cana-1296	104	77	also	also	ADV
cana-1296	104	78	denoted	denote	VERB
cana-1296	104	79	the	the	DET
cana-1296	104	80	sgbtγi	sgbtγi	NOUN
cana-1296	104	81	of	of	ADP
cana-1296	104	82	s	s	VERB
cana-1296	104	83	containing	contain	VERB
cana-1296	104	84	{	{	PUNCT
cana-1296	104	85	e	e	NOUN
cana-1296	104	86	}	}	PUNCT
cana-1296	104	87	as	as	ADP
cana-1296	104	88	(	(	PUNCT
cana-1296	104	89	e	e	NOUN
cana-1296	104	90	)	)	PUNCT
cana-1296	104	91	.	.	PUNCT
cana-1296	105	1	lemma	lemma	PROPN
cana-1296	105	2	2.4	2.4	NUM
cana-1296	105	3	:	:	PUNCT
cana-1296	105	4	let	let	VERB
cana-1296	105	5	t	t	NOUN
cana-1296	105	6	be	be	AUX
cana-1296	105	7	a	a	DET
cana-1296	105	8	sub	sub	NOUN
cana-1296	105	9	tγ	tγ	NOUN
cana-1296	105	10	-	-	PUNCT
cana-1296	105	11	semiring	semiring	NOUN
cana-1296	105	12	of	of	ADP
cana-1296	105	13	a	a	DET
cana-1296	105	14	tγs	tγs	PROPN
cana-1296	105	15	m	m	PROPN
cana-1296	105	16	,	,	PUNCT
cana-1296	105	17	a	a	DET
cana-1296	105	18	m	m	PROPN
cana-1296	105	19	&	&	CCONJ
cana-1296	105	20	(	(	PUNCT
cana-1296	105	21	)	)	PUNCT
cana-1296	105	22	a	a	DET
cana-1296	105	23	a	a	DET
cana-1296	105	24	a	a	DET
cana-1296	105	25			NOUN
cana-1296	105	26			PROPN
cana-1296	105	27			PROPN
cana-1296	105	28			NOUN
cana-1296	105	29	.	.	PUNCT
cana-1296	106	1	then	then	ADV
cana-1296	106	2	(	(	PUNCT
cana-1296	106	3	)	)	PUNCT
cana-1296	106	4	a	a	DET
cana-1296	106	5	a	a	DET
cana-1296	106	6	a	a	PRON
cana-1296	106	7			PROPN
cana-1296	106	8			NOUN
cana-1296	106	9	is	be	AUX
cana-1296	106	10	a	a	DET
cana-1296	106	11	gbtγi	gbtγi	NOUN
cana-1296	106	12	of	of	ADP
cana-1296	106	13	t.	t.	NOUN
cana-1296	106	14	proof	proof	NOUN
cana-1296	106	15	:	:	PUNCT
cana-1296	106	16	believe	believe	VERB
cana-1296	106	17	(	(	PUNCT
cana-1296	106	18	)	)	PUNCT
cana-1296	106	19	(	(	PUNCT
cana-1296	106	20	)	)	PUNCT
cana-1296	107	1	[	[	X
cana-1296	107	2	(	(	PUNCT
cana-1296	107	3	)	)	PUNCT
cana-1296	107	4	]	]	PUNCT
cana-1296	107	5	(	(	PUNCT
cana-1296	107	6	)	)	PUNCT
cana-1296	108	1	[	[	X
cana-1296	108	2	(	(	PUNCT
cana-1296	108	3	)	)	PUNCT
cana-1296	108	4	]	]	PUNCT
cana-1296	108	5	(	(	PUNCT
cana-1296	108	6	)	)	PUNCT
cana-1296	109	1	[	[	X
cana-1296	109	2	[	[	X
cana-1296	109	3	(	(	PUNCT
cana-1296	109	4	)	)	PUNCT
cana-1296	109	5	(	(	PUNCT
cana-1296	109	6	)	)	PUNCT
cana-1296	109	7	]	]	PUNCT
cana-1296	109	8	[	[	PUNCT
cana-1296	109	9	(	(	PUNCT
cana-1296	109	10	)	)	PUNCT
cana-1296	109	11	]	]	PUNCT
cana-1296	109	12	]	]	X
cana-1296	110	1	[	[	X
cana-1296	110	2	(	(	PUNCT
cana-1296	110	3	)	)	PUNCT
cana-1296	110	4	(	(	PUNCT
cana-1296	110	5	)	)	PUNCT
cana-1296	110	6	]	]	PUNCT
cana-1296	110	7	(	(	PUNCT
cana-1296	110	8	)	)	PUNCT
cana-1296	110	9	.	.	PUNCT
cana-1296	111	1	a	a	DET
cana-1296	111	2	a	a	DET
cana-1296	111	3	a	a	DET
cana-1296	111	4	a	a	DET
cana-1296	111	5	a	a	DET
cana-1296	111	6	a	a	DET
cana-1296	111	7	a	a	DET
cana-1296	111	8	a	a	DET
cana-1296	111	9	a	a	DET
cana-1296	111	10	a	a	DET
cana-1296	111	11	a	a	DET
cana-1296	111	12	a	a	DET
cana-1296	111	13	a	a	DET
cana-1296	111	14	a	a	DET
cana-1296	111	15	a	a	DET
cana-1296	111	16	a	a	DET
cana-1296	111	17	a	a	DET
cana-1296	111	18	a	a	DET
cana-1296	111	19	a	a	DET
cana-1296	111	20	a	a	DET
cana-1296	111	21	a	a	DET
cana-1296	111	22	a	a	DET
cana-1296	111	23	a	a	DET
cana-1296	111	24	a	a	DET
cana-1296	111	25	a	a	DET
cana-1296	111	26	a	a	DET
cana-1296	111	27	a	a	DET
cana-1296	111	28	a	a	DET
cana-1296	111	29	a	a	DET
cana-1296	111	30	a	a	DET
cana-1296	111	31	a	a	DET
cana-1296	111	32	a	a	DET
cana-1296	111	33	a	a	DET
cana-1296	111	34	a	a	DET
cana-1296	111	35	a	a	DET
cana-1296	111	36	a	a	DET
cana-1296	111	37			PROPN
cana-1296	111	38			PROPN
cana-1296	111	39			NOUN
cana-1296	111	40			PROPN
cana-1296	111	41			PROPN
cana-1296	111	42			PROPN
cana-1296	111	43			NOUN
cana-1296	111	44			ADJ
cana-1296	111	45			PROPN
cana-1296	111	46			PROPN
cana-1296	111	47			NOUN
cana-1296	111	48			NOUN
cana-1296	111	49			VERB
cana-1296	111	50			PROPN
cana-1296	111	51			PROPN
cana-1296	111	52			NOUN
cana-1296	111	53			ADJ
cana-1296	111	54			PROPN
cana-1296	111	55			PROPN
cana-1296	111	56			ADJ
cana-1296	111	57			NOUN
cana-1296	111	58			VERB
cana-1296	111	59			PROPN
cana-1296	111	60			PROPN
cana-1296	111	61			NOUN
cana-1296	111	62			ADJ
cana-1296	111	63			PROPN
cana-1296	111	64			PROPN
cana-1296	111	65			NOUN
cana-1296	111	66			VERB
cana-1296	111	67			PROPN
cana-1296	111	68			PROPN
cana-1296	111	69			VERB
cana-1296	111	70			PROPN
cana-1296	111	71			PROPN
cana-1296	111	72			NOUN
cana-1296	111	73			ADJ
cana-1296	111	74			PROPN
cana-1296	111	75			PROPN
cana-1296	111	76			VERB
cana-1296	111	77			PROPN
cana-1296	111	78			PROPN
cana-1296	111	79			NOUN
cana-1296	111	80			ADJ
cana-1296	111	81			PROPN
cana-1296	111	82			PROPN
cana-1296	111	83			NOUN
cana-1296	111	84	hence	hence	ADV
cana-1296	111	85	(	(	PUNCT
cana-1296	111	86	)	)	PUNCT
cana-1296	111	87	a	a	DET
cana-1296	111	88	a	a	DET
cana-1296	111	89	a	a	PRON
cana-1296	111	90			PROPN
cana-1296	111	91			NOUN
cana-1296	111	92	is	be	AUX
cana-1296	111	93	a	a	DET
cana-1296	111	94	generalized	generalized	ADJ
cana-1296	111	95	biγ	biγ	NOUN
cana-1296	111	96	-	-	PUNCT
cana-1296	111	97	ideal	ideal	NOUN
cana-1296	111	98	of	of	ADP
cana-1296	111	99	t.	t.	PROPN
cana-1296	111	100	lemma	lemma	PROPN
cana-1296	111	101	2.5	2.5	NUM
cana-1296	111	102	:	:	PUNCT
cana-1296	111	103	let	let	VERB
cana-1296	111	104	j	j	PROPN
cana-1296	111	105	be	be	AUX
cana-1296	111	106	a	a	DET
cana-1296	111	107	tγs	tγs	PROPN
cana-1296	111	108	&	&	CCONJ
cana-1296	111	109	j	j	PROPN
cana-1296	111	110	j	j	PROPN
cana-1296	111	111	.	.	PUNCT
cana-1296	112	1	then	then	ADV
cana-1296	112	2	j	j	PROPN
cana-1296	113	1	j	j	PROPN
cana-1296	113	2	j	j	PROPN
cana-1296	113	3	j	j	PROPN
cana-1296	114	1	j	j	PROPN
cana-1296	114	2	j	j	PROPN
cana-1296	114	3			VERB
cana-1296	114	4			PROPN
cana-1296	114	5			VERB
cana-1296	114	6			NOUN
cana-1296	114	7	is	be	AUX
cana-1296	114	8	a	a	DET
cana-1296	114	9	gbtγi	gbtγi	NOUN
cana-1296	114	10	of	of	ADP
cana-1296	114	11	j.	j.	PROPN
cana-1296	114	12	proof	proof	PROPN
cana-1296	114	13	:	:	PUNCT
cana-1296	114	14	consider	consider	VERB
cana-1296	114	15	(	(	PUNCT
cana-1296	114	16	)	)	PUNCT
cana-1296	114	17	(	(	PUNCT
cana-1296	114	18	)	)	PUNCT
cana-1296	114	19	(	(	PUNCT
cana-1296	114	20	)	)	PUNCT
cana-1296	114	21	(	(	PUNCT
cana-1296	114	22	)	)	PUNCT
cana-1296	115	1	j	j	PROPN
cana-1296	116	1	j	j	PROPN
cana-1296	116	2	j	j	PROPN
cana-1296	117	1	j	j	PROPN
cana-1296	117	2	j	j	PROPN
cana-1296	118	1	i	i	PRON
cana-1296	118	2	j	j	PROPN
cana-1296	119	1	j	j	PROPN
cana-1296	119	2	j	j	PROPN
cana-1296	120	1	j	j	PROPN
cana-1296	120	2	j	j	PROPN
cana-1296	120	3	j	j	PROPN
cana-1296	120	4	j	j	PROPN
cana-1296	120	5	j	j	PROPN
cana-1296	120	6	j	j	PROPN
cana-1296	120	7	j	j	PROPN
cana-1296	120	8	j	j	PROPN
cana-1296	120	9	j	j	PROPN
cana-1296	120	10	j	j	PROPN
cana-1296	120	11	j	j	PROPN
cana-1296	120	12	j	j	PROPN
cana-1296	120	13	j	j	PROPN
cana-1296	120	14	j	j	PROPN
cana-1296	120	15	j	j	PROPN
cana-1296	120	16	j	j	PROPN
cana-1296	120	17	j	j	PROPN
cana-1296	120	18	j	j	PROPN
cana-1296	120	19	j	j	PROPN
cana-1296	120	20	j	j	PROPN
cana-1296	120	21	j	j	PROPN
cana-1296	120	22	j	j	PROPN
cana-1296	120	23	j	j	PROPN
cana-1296	120	24	j	j	PROPN
cana-1296	121	1	j	j	PROPN
cana-1296	121	2	j	j	PROPN
cana-1296	122	1	j	j	PROPN
cana-1296	122	2	j	j	PROPN
cana-1296	122	3	j	j	PROPN
cana-1296	122	4			VERB
cana-1296	122	5			VERB
cana-1296	122	6			VERB
cana-1296	122	7			VERB
cana-1296	122	8			VERB
cana-1296	122	9			VERB
cana-1296	122	10			VERB
cana-1296	122	11			VERB
cana-1296	122	12			VERB
cana-1296	122	13			VERB
cana-1296	122	14			VERB
cana-1296	122	15			VERB
cana-1296	122	16			VERB
cana-1296	122	17			VERB
cana-1296	122	18			VERB
cana-1296	122	19			VERB
cana-1296	122	20	=	=	PUNCT
cana-1296	122	21			VERB
cana-1296	122	22			VERB
cana-1296	122	23			VERB
cana-1296	122	24			VERB
cana-1296	122	25			VERB
cana-1296	122	26			VERB
cana-1296	122	27			VERB
cana-1296	122	28			VERB
cana-1296	122	29			VERB
cana-1296	122	30			VERB
cana-1296	122	31			VERB
cana-1296	122	32			VERB
cana-1296	122	33			VERB
cana-1296	122	34			VERB
cana-1296	122	35			VERB
cana-1296	122	36			VERB
cana-1296	122	37			NOUN
cana-1296	122	38			VERB
cana-1296	122	39			NOUN
cana-1296	122	40			PROPN
cana-1296	122	41	hence	hence	ADV
cana-1296	122	42	j	j	PROPN
cana-1296	122	43	j	j	PROPN
cana-1296	122	44	j	j	PROPN
cana-1296	122	45	j	j	PROPN
cana-1296	123	1	j	j	PROPN
cana-1296	123	2			VERB
cana-1296	123	3			VERB
cana-1296	123	4			NOUN
cana-1296	123	5	is	be	AUX
cana-1296	123	6	a	a	DET
cana-1296	123	7	gbtγi	gbtγi	NOUN
cana-1296	123	8	of	of	ADP
cana-1296	123	9	j.	j.	PROPN
cana-1296	123	10	proposition2.6	proposition2.6	PROPN
cana-1296	123	11	:	:	PUNCT
cana-1296	123	12	let	let	VERB
cana-1296	123	13	m	m	PRON
cana-1296	123	14	be	be	AUX
cana-1296	123	15	a	a	DET
cana-1296	123	16	tγs	tγs	PROPN
cana-1296	123	17	&	&	CCONJ
cana-1296	123	18	t	t	PROPN
cana-1296	123	19	a	a	DET
cana-1296	123	20	sub	sub	NOUN
cana-1296	123	21	-	-	ADJ
cana-1296	123	22	tγs	tγs	NOUN
cana-1296	123	23	of	of	ADP
cana-1296	123	24	m.	m.	NOUN
cana-1296	123	25	then	then	ADV
cana-1296	123	26	each	each	DET
cana-1296	123	27	subset	subset	NOUN
cana-1296	123	28	of	of	ADP
cana-1296	123	29	t	t	PROPN
cana-1296	123	30	having	have	VERB
cana-1296	123	31	m	m	VERB
cana-1296	123	32	m	m	VERB
cana-1296	123	33	t	t	NOUN
cana-1296	123	34			VERB
cana-1296	123	35	is	be	AUX
cana-1296	123	36	a	a	DET
cana-1296	123	37	subtγs	subtγs	NOUN
cana-1296	123	38	of	of	ADP
cana-1296	123	39	m.	m.	NOUN
cana-1296	123	40	proof	proof	NOUN
cana-1296	123	41	:	:	PUNCT
cana-1296	123	42	let	let	VERB
cana-1296	123	43	.j	.j	PROPN
cana-1296	123	44	t	t	PROPN
cana-1296	123	45	t	t	PROPN
cana-1296	123	46	j	j	NOUN
cana-1296	123	47			PROPN
cana-1296	124	1			PROPN
cana-1296	124	2	.j	.j	PROPN
cana-1296	125	1	j	j	PROPN
cana-1296	125	2	j	j	PROPN
cana-1296	125	3	t	t	PROPN
cana-1296	125	4	j	j	PROPN
cana-1296	125	5			VERB
cana-1296	125	6			VERB
cana-1296	125	7			NOUN
cana-1296	125	8			PROPN
cana-1296	125	9	consequently	consequently	ADV
cana-1296	125	10	j	j	PROPN
cana-1296	125	11	is	be	AUX
cana-1296	125	12	a	a	DET
cana-1296	125	13	subtγs	subtγs	NOUN
cana-1296	125	14	of	of	ADP
cana-1296	125	15	m.	m.	NOUN
cana-1296	125	16	proposition	proposition	NOUN
cana-1296	125	17	2.7	2.7	NUM
cana-1296	125	18	:	:	PUNCT
cana-1296	125	19	let	let	VERB
cana-1296	125	20	z	z	PRON
cana-1296	125	21	be	be	AUX
cana-1296	125	22	a	a	DET
cana-1296	125	23	tγs	tγs	PROPN
cana-1296	125	24	&	&	CCONJ
cana-1296	125	25	t	t	PROPN
cana-1296	125	26	is	be	AUX
cana-1296	125	27	tγi	tγi	NOUN
cana-1296	125	28	of	of	ADP
cana-1296	125	29	m.	m.	NOUN
cana-1296	125	30	next	next	ADP
cana-1296	125	31	each	each	DET
cana-1296	125	32	subset	subset	NOUN
cana-1296	125	33	of	of	ADP
cana-1296	125	34	t	t	PROPN
cana-1296	125	35	including	include	VERB
cana-1296	125	36	t	t	PROPN
cana-1296	125	37	t	t	PROPN
cana-1296	125	38	t	t	PROPN
cana-1296	125	39			PROPN
cana-1296	125	40			PROPN
cana-1296	125	41			PROPN
cana-1296	125	42	is	be	AUX
cana-1296	125	43	a	a	DET
cana-1296	125	44	tγi	tγi	NOUN
cana-1296	125	45	of	of	ADP
cana-1296	125	46	m.	m.	NOUN
cana-1296	125	47	proof	proof	NOUN
cana-1296	125	48	:	:	PUNCT
cana-1296	125	49	let	let	VERB
cana-1296	125	50	.b	.b	PROPN
cana-1296	125	51	b	b	NOUN
cana-1296	125	52			NOUN
cana-1296	125	53			PROPN
cana-1296	125	54	then	then	ADV
cana-1296	125	55	b	b	PROPN
cana-1296	125	56	b	b	PROPN
cana-1296	125	57			X
cana-1296	125	58			PROPN
cana-1296	125	59			PROPN
cana-1296	125	60	b	b	PROPN
cana-1296	125	61	b	b	PROPN
cana-1296	125	62			NOUN
cana-1296	125	63			NOUN
cana-1296	125	64			ADP
cana-1296	125	65	communications	communication	NOUN
cana-1296	125	66	on	on	ADP
cana-1296	125	67	applied	apply	VERB
cana-1296	125	68	nonlinear	nonlinear	ADJ
cana-1296	125	69	analysis	analysis	NOUN
cana-1296	125	70	issn	issn	NOUN
cana-1296	125	71	:	:	PUNCT
cana-1296	125	72	1074	1074	NUM
cana-1296	125	73	-	-	PUNCT
cana-1296	125	74	133x	133x	NUM
cana-1296	125	75	vol	vol	NOUN
cana-1296	125	76	31	31	NUM
cana-1296	125	77	no	no	NOUN
cana-1296	125	78	.	.	PUNCT
cana-1296	126	1	7s	7	NOUN
cana-1296	126	2	(	(	PUNCT
cana-1296	126	3	2024	2024	NUM
cana-1296	126	4	)	)	PUNCT
cana-1296	126	5	218	218	NUM
cana-1296	127	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	127	2	b	b	PROPN
cana-1296	127	3	b	b	PROPN
cana-1296	127	4			NOUN
cana-1296	127	5			ADP
cana-1296	127	6	thus	thus	ADV
cana-1296	127	7	b	b	NOUN
cana-1296	127	8	is	be	AUX
cana-1296	127	9	a	a	DET
cana-1296	127	10	tγi	tγi	NOUN
cana-1296	127	11	of	of	ADP
cana-1296	127	12	z.	z.	PROPN
cana-1296	127	13	proposition	proposition	PROPN
cana-1296	127	14	2.8	2.8	NUM
cana-1296	127	15	:	:	PUNCT
cana-1296	127	16	let	let	VERB
cana-1296	127	17	l	l	NOUN
cana-1296	127	18	be	be	AUX
cana-1296	127	19	a	a	DET
cana-1296	127	20	tγs	tγs	PROPN
cana-1296	127	21	&	&	CCONJ
cana-1296	127	22	t	t	PROPN
cana-1296	127	23	is	be	AUX
cana-1296	127	24	tγi	tγi	PROPN
cana-1296	127	25	of	of	ADP
cana-1296	127	26	l.	l.	PROPN
cana-1296	127	27	afterward	afterward	ADV
cana-1296	127	28	each	each	DET
cana-1296	127	29	subset	subset	NOUN
cana-1296	127	30	of	of	ADP
cana-1296	127	31	t	t	PROPN
cana-1296	127	32	containing	contain	VERB
cana-1296	127	33	(	(	PUNCT
cana-1296	127	34	)	)	PUNCT
cana-1296	127	35	(	(	PUNCT
cana-1296	127	36	)	)	PUNCT
cana-1296	127	37	(	(	PUNCT
cana-1296	127	38	)	)	PUNCT
cana-1296	127	39	l	l	NOUN
cana-1296	128	1	l	l	NOUN
cana-1296	128	2	l	l	NOUN
cana-1296	128	3	l	l	NOUN
cana-1296	128	4	l	l	NOUN
cana-1296	128	5	l	l	NOUN
cana-1296	128	6	l	l	NOUN
cana-1296	128	7	l	l	NOUN
cana-1296	128	8	l	l	NOUN
cana-1296	128	9	l	l	NUM
cana-1296	128	10			ADJ
cana-1296	128	11			PROPN
cana-1296	128	12	+	+	CCONJ
cana-1296	128	13			VERB
cana-1296	128	14			PROPN
cana-1296	128	15			VERB
cana-1296	128	16			VERB
cana-1296	128	17			NOUN
cana-1296	128	18	is	be	AUX
cana-1296	128	19	a	a	DET
cana-1296	128	20	qtγi	qtγi	NOUN
cana-1296	128	21	of	of	ADP
cana-1296	128	22	l.	l.	PROPN
cana-1296	128	23	proof	proof	PROPN
cana-1296	128	24	:	:	PUNCT
cana-1296	128	25	allow	allow	VERB
cana-1296	128	26	(	(	PUNCT
cana-1296	128	27	)	)	PUNCT
cana-1296	128	28	(	(	PUNCT
cana-1296	128	29	)	)	PUNCT
cana-1296	128	30	(	(	PUNCT
cana-1296	128	31	)	)	PUNCT
cana-1296	128	32	.c	.c	VERB
cana-1296	129	1	v	v	PRON
cana-1296	129	2	v	v	NUM
cana-1296	129	3	v	v	NUM
cana-1296	129	4	v	v	NUM
cana-1296	129	5	v	v	NUM
cana-1296	129	6	v	v	NUM
cana-1296	129	7	v	v	NUM
cana-1296	129	8	v	v	NUM
cana-1296	129	9	v	v	NOUN
cana-1296	129	10	v	v	NOUN
cana-1296	129	11	c	c	NOUN
cana-1296	129	12			NOUN
cana-1296	129	13			PROPN
cana-1296	129	14			PROPN
cana-1296	129	15			NUM
cana-1296	129	16			PROPN
cana-1296	129	17	+	+	CCONJ
cana-1296	129	18			VERB
cana-1296	129	19			PROPN
cana-1296	129	20			VERB
cana-1296	129	21			VERB
cana-1296	129	22			ADJ
cana-1296	129	23			NOUN
cana-1296	129	24	then	then	ADV
cana-1296	129	25	(	(	PUNCT
cana-1296	129	26	)	)	PUNCT
cana-1296	129	27	(	(	PUNCT
cana-1296	129	28	)	)	PUNCT
cana-1296	129	29	(	(	PUNCT
cana-1296	129	30	)	)	PUNCT
cana-1296	129	31	c	c	NOUN
cana-1296	129	32	c	c	NOUN
cana-1296	129	33	c	c	NOUN
cana-1296	129	34	l	l	NOUN
cana-1296	129	35	l	l	X
cana-1296	129	36	l	l	X
cana-1296	129	37	l	l	NOUN
cana-1296	129	38	l	l	NOUN
cana-1296	129	39	l	l	NOUN
cana-1296	129	40	l	l	NOUN
cana-1296	129	41	l	l	X
cana-1296	129	42	l	l	X
cana-1296	129	43	l	l	NOUN
cana-1296	129	44	c	c	PROPN
cana-1296	129	45			VERB
cana-1296	129	46			PROPN
cana-1296	129	47			PROPN
cana-1296	129	48			NUM
cana-1296	129	49			PROPN
cana-1296	129	50	+	+	CCONJ
cana-1296	129	51			VERB
cana-1296	129	52			PROPN
cana-1296	129	53			VERB
cana-1296	129	54			VERB
cana-1296	129	55			ADJ
cana-1296	129	56			NOUN
cana-1296	129	57	and	and	CCONJ
cana-1296	129	58	(	(	PUNCT
cana-1296	129	59	)	)	PUNCT
cana-1296	129	60	(	(	PUNCT
cana-1296	129	61	)	)	PUNCT
cana-1296	129	62	(	(	PUNCT
cana-1296	129	63	)	)	PUNCT
cana-1296	129	64	(	(	PUNCT
cana-1296	129	65	)	)	PUNCT
cana-1296	129	66	(	(	PUNCT
cana-1296	129	67	)	)	PUNCT
cana-1296	129	68	(	(	PUNCT
cana-1296	129	69	)	)	PUNCT
cana-1296	129	70	.	.	PUNCT
cana-1296	130	1	c	c	NOUN
cana-1296	130	2	l	l	NOUN
cana-1296	130	3	l	l	X
cana-1296	130	4	l	l	X
cana-1296	130	5	c	c	NOUN
cana-1296	130	6	l	l	NOUN
cana-1296	130	7	l	l	X
cana-1296	130	8	l	l	X
cana-1296	130	9	c	c	NOUN
cana-1296	130	10	l	l	NOUN
cana-1296	130	11	l	l	X
cana-1296	130	12	l	l	X
cana-1296	130	13	l	l	NOUN
cana-1296	130	14	c	c	NOUN
cana-1296	130	15	t	t	NOUN
cana-1296	130	16	l	l	NOUN
cana-1296	130	17	l	l	X
cana-1296	130	18	l	l	NOUN
cana-1296	130	19	t	t	NOUN
cana-1296	130	20	l	l	NOUN
cana-1296	130	21	l	l	X
cana-1296	130	22	l	l	NOUN
cana-1296	130	23	t	t	NOUN
cana-1296	130	24	l	l	NOUN
cana-1296	130	25	l	l	X
cana-1296	130	26	l	l	X
cana-1296	130	27	l	l	NOUN
cana-1296	130	28	t	t	NOUN
cana-1296	130	29	c	c	NOUN
cana-1296	130	30			VERB
cana-1296	130	31			VERB
cana-1296	130	32			VERB
cana-1296	130	33			VERB
cana-1296	130	34	+	+	CCONJ
cana-1296	130	35			VERB
cana-1296	130	36			VERB
cana-1296	130	37			VERB
cana-1296	130	38			VERB
cana-1296	130	39			VERB
cana-1296	130	40			VERB
cana-1296	130	41			NOUN
cana-1296	130	42			VERB
cana-1296	130	43			VERB
cana-1296	130	44			VERB
cana-1296	130	45			VERB
cana-1296	130	46	+	+	CCONJ
cana-1296	130	47			VERB
cana-1296	130	48			VERB
cana-1296	130	49			VERB
cana-1296	130	50			VERB
cana-1296	130	51			VERB
cana-1296	130	52			ADJ
cana-1296	130	53			NOUN
cana-1296	130	54	so	so	SCONJ
cana-1296	130	55	c	c	PROPN
cana-1296	130	56	is	be	AUX
cana-1296	130	57	a	a	DET
cana-1296	130	58	qtγi	qtγi	NOUN
cana-1296	130	59	of	of	ADP
cana-1296	130	60	l.	l.	PROPN
cana-1296	130	61	proposition	proposition	PROPN
cana-1296	130	62	2.9	2.9	NUM
cana-1296	130	63	:	:	PUNCT
cana-1296	130	64	let	let	VERB
cana-1296	130	65	m	m	PRON
cana-1296	130	66	be	be	AUX
cana-1296	130	67	a	a	DET
cana-1296	130	68	tγs	tγs	PROPN
cana-1296	130	69	&	&	CCONJ
cana-1296	130	70	t	t	PROPN
cana-1296	130	71	be	be	AUX
cana-1296	130	72	btγi	btγi	NOUN
cana-1296	130	73	of	of	ADP
cana-1296	130	74	m.	m.	NOUN
cana-1296	130	75	afterward	afterward	ADV
cana-1296	130	76	each	each	DET
cana-1296	130	77	subset	subset	NOUN
cana-1296	130	78	of	of	ADP
cana-1296	130	79	t	t	PROPN
cana-1296	130	80	holding	hold	VERB
cana-1296	130	81	t	t	PROPN
cana-1296	130	82	t	t	PROPN
cana-1296	130	83	t	t	NOUN
cana-1296	130	84			NOUN
cana-1296	130	85	and	and	CCONJ
cana-1296	130	86	all	all	PRON
cana-1296	130	87	of	of	ADP
cana-1296	130	88	its	its	PRON
cana-1296	130	89	images	image	NOUN
cana-1296	130	90	is	be	AUX
cana-1296	130	91	a	a	DET
cana-1296	130	92	btγi	btγi	NOUN
cana-1296	130	93	of	of	ADP
cana-1296	130	94	m.	m.	NOUN
cana-1296	130	95	proof	proof	NOUN
cana-1296	130	96	:	:	PUNCT
cana-1296	130	97	permit	permit	NOUN
cana-1296	130	98	&	&	CCONJ
cana-1296	130	99	.t	.t	PROPN
cana-1296	131	1	t	t	PROPN
cana-1296	131	2	t	t	PROPN
cana-1296	131	3	t	t	PROPN
cana-1296	131	4			PROPN
cana-1296	131	5			NUM
cana-1296	131	6			ADJ
cana-1296	131	7			NOUN
cana-1296	131	8			NOUN
cana-1296	131	9			NOUN
cana-1296	131	10	.t	.t	VERB
cana-1296	131	11	t	t	PROPN
cana-1296	131	12	t	t	NUM
cana-1296	131	13			NOUN
cana-1296	131	14			NOUN
cana-1296	131	15			PROPN
cana-1296	131	16	consequently	consequently	ADV
cana-1296	131	17			VERB
cana-1296	131	18	is	be	AUX
cana-1296	131	19	a	a	DET
cana-1296	131	20	btγi	btγi	NOUN
cana-1296	131	21	of	of	ADP
cana-1296	131	22	m.	m.	NOUN
cana-1296	131	23	proposition	proposition	NOUN
cana-1296	131	24	2.10	2.10	NUM
cana-1296	131	25	.	.	PUNCT
cana-1296	132	1	let	let	VERB
cana-1296	132	2	m	m	PRON
cana-1296	132	3	be	be	AUX
cana-1296	132	4	a	a	DET
cana-1296	132	5	tγs	tγs	PROPN
cana-1296	132	6	&	&	CCONJ
cana-1296	132	7	t	t	PROPN
cana-1296	132	8	is	be	AUX
cana-1296	132	9	a	a	DET
cana-1296	132	10	gbtγi	gbtγi	NOUN
cana-1296	132	11	of	of	ADP
cana-1296	132	12	m.	m.	NOUN
cana-1296	132	13	then	then	ADV
cana-1296	132	14	each	each	DET
cana-1296	132	15	subset	subset	NOUN
cana-1296	132	16	of	of	ADP
cana-1296	132	17	t	t	PROPN
cana-1296	132	18	holding	hold	VERB
cana-1296	132	19	t	t	PROPN
cana-1296	132	20	m	m	VERB
cana-1296	132	21	t	t	PROPN
cana-1296	132	22	m	m	VERB
cana-1296	132	23	t	t	PROPN
cana-1296	133	1			VERB
cana-1296	133	2			VERB
cana-1296	133	3			NOUN
cana-1296	133	4	is	be	AUX
cana-1296	133	5	a	a	DET
cana-1296	133	6	gbtγi	gbtγi	NOUN
cana-1296	133	7	of	of	ADP
cana-1296	133	8	m.	m.	NOUN
cana-1296	133	9	proof	proof	NOUN
cana-1296	133	10	:	:	PUNCT
cana-1296	133	11	permit	permit	NOUN
cana-1296	133	12	.t	.t	PROPN
cana-1296	133	13	t	t	PROPN
cana-1296	133	14	t	t	PROPN
cana-1296	133	15	t	t	PRON
cana-1296	133	16			NUM
cana-1296	133	17			ADJ
cana-1296	133	18			NOUN
cana-1296	133	19			PROPN
cana-1296	133	20	then	then	ADV
cana-1296	133	21	.m	.m	PROPN
cana-1296	134	1	m	m	VERB
cana-1296	134	2	t	t	PROPN
cana-1296	134	3	t	t	PROPN
cana-1296	134	4	t	t	PROPN
cana-1296	134	5			NOUN
cana-1296	134	6			DET
cana-1296	134	7			NOUN
cana-1296	134	8			NOUN
cana-1296	134	9			PROPN
cana-1296	134	10	e	e	PROPN
cana-1296	134	11	is	be	AUX
cana-1296	134	12	a	a	DET
cana-1296	134	13	gbtγi	gbtγi	NOUN
cana-1296	134	14	of	of	ADP
cana-1296	134	15	m.	m.	NOUN
cana-1296	135	1	theorem2.11	theorem2.11	PROPN
cana-1296	135	2	.	.	PUNCT
cana-1296	136	1	let	let	VERB
cana-1296	136	2	m	m	PRON
cana-1296	136	3	be	be	AUX
cana-1296	136	4	a	a	DET
cana-1296	136	5	tγs	tγs	PROPN
cana-1296	136	6	.	.	PUNCT
cana-1296	137	1	then	then	ADV
cana-1296	137	2	the	the	DET
cana-1296	137	3	next	next	ADJ
cana-1296	137	4	declarations	declaration	NOUN
cana-1296	137	5	are	be	AUX
cana-1296	137	6	correspondent	correspondent	NOUN
cana-1296	137	7	.	.	PUNCT
cana-1296	138	1	(	(	PUNCT
cana-1296	138	2	1)m	1)m	PROPN
cana-1296	138	3	is	be	AUX
cana-1296	138	4	a	a	DET
cana-1296	138	5	gb	gb	NOUN
cana-1296	138	6	-	-	PUNCT
cana-1296	138	7	simple	simple	ADJ
cana-1296	138	8	γ	γ	X
cana-1296	138	9	-	-	PUNCT
cana-1296	138	10	semiring	semiring	NOUN
cana-1296	138	11	.	.	PUNCT
cana-1296	139	1	(	(	PUNCT
cana-1296	139	2	2	2	X
cana-1296	139	3	)	)	PUNCT
cana-1296	139	4	.h	.h	NOUN
cana-1296	140	1	h	h	NOUN
cana-1296	140	2	h	h	PROPN
cana-1296	140	3	h	h	ADJ
cana-1296	140	4			NOUN
cana-1296	140	5	=	=	NUM
cana-1296	140	6			NOUN
cana-1296	140	7			NOUN
cana-1296	140	8	(	(	PUNCT
cana-1296	140	9	3	3	NUM
cana-1296	140	10	)	)	PUNCT
cana-1296	140	11	(	(	PUNCT
cana-1296	140	12	)	)	PUNCT
cana-1296	140	13	.h	.h	NOUN
cana-1296	140	14	h=	h=	PROPN
cana-1296	140	15			NOUN
cana-1296	140	16			NOUN
cana-1296	140	17	proof	proof	NOUN
cana-1296	140	18	:	:	PUNCT
cana-1296	140	19	(	(	PUNCT
cana-1296	140	20	1	1	X
cana-1296	140	21	)	)	PUNCT
cana-1296	140	22	(	(	PUNCT
cana-1296	140	23	2)	2)	NOUN
cana-1296	140	24	believe	believe	VERB
cana-1296	140	25	that	that	SCONJ
cana-1296	140	26	m	m	PROPN
cana-1296	140	27	is	be	AUX
cana-1296	140	28	a	a	DET
cana-1296	140	29	gb	gb	ADV
cana-1296	140	30	-	-	PUNCT
cana-1296	140	31	simple	simple	ADJ
cana-1296	140	32	tγs	tγs	PROPN
cana-1296	140	33	&	&	CCONJ
cana-1296	140	34	.h	.h	PROPN
cana-1296	141	1	h	h	PROPN
cana-1296	141	2	h	h	PROPN
cana-1296	141	3	h	h	PROPN
cana-1296	141	4			NOUN
cana-1296	141	5	is	be	AUX
cana-1296	141	6	a	a	DET
cana-1296	141	7	gbtγi	gbtγi	NOUN
cana-1296	141	8	of	of	ADP
cana-1296	141	9	m	m	PRON
cana-1296	141	10	by	by	ADP
cana-1296	141	11	lemma	lemma	PROPN
cana-1296	141	12	2.5	2.5	NUM
cana-1296	141	13	,	,	PUNCT
cana-1296	141	14	m	m	VERB
cana-1296	141	15	is	be	AUX
cana-1296	141	16	a	a	DET
cana-1296	141	17	gb	gb	ADV
cana-1296	141	18	-	-	PUNCT
cana-1296	141	19	simple	simple	ADJ
cana-1296	141	20	tγ	tγ	NOUN
cana-1296	141	21	-	-	PUNCT
cana-1296	141	22	semiring	semiring	NOUN
cana-1296	141	23	,	,	PUNCT
cana-1296	141	24	.h	.h	PUNCT
cana-1296	141	25	h	h	NOUN
cana-1296	142	1	h=	h=	ADJ
cana-1296	142	2			NOUN
cana-1296	142	3			NOUN
cana-1296	142	4	(	(	PUNCT
cana-1296	142	5	2	2	NUM
cana-1296	142	6	)	)	PUNCT
cana-1296	142	7	(	(	PUNCT
cana-1296	142	8	3)	3)	PROPN
cana-1296	142	9	believe	believe	VERB
cana-1296	142	10	that	that	SCONJ
cana-1296	142	11	h	h	NOUN
cana-1296	142	12	h	h	NOUN
cana-1296	142	13	h	h	NOUN
cana-1296	142	14	h=	h=	ADJ
cana-1296	142	15			NOUN
cana-1296	142	16			NOUN
cana-1296	142	17			NOUN
cana-1296	142	18			PROPN
cana-1296	142	19	&	&	CCONJ
cana-1296	142	20	let	let	VERB
cana-1296	142	21	.h	.h	PUNCT
cana-1296	143	1	then	then	ADV
cana-1296	143	2	,	,	PUNCT
cana-1296	143	3	by	by	ADP
cana-1296	143	4	(	(	PUNCT
cana-1296	143	5	2.2	2.2	NUM
cana-1296	143	6	)	)	PUNCT
cana-1296	143	7	,	,	PUNCT
cana-1296	143	8	we	we	PRON
cana-1296	143	9	cover	cover	VERB
cana-1296	143	10	(	(	PUNCT
cana-1296	143	11	)	)	PUNCT
cana-1296	143	12	{	{	PUNCT
cana-1296	143	13	}	}	PUNCT
cana-1296	143	14	{	{	PUNCT
cana-1296	143	15	}	}	PUNCT
cana-1296	143	16	.h	.h	PUNCT
cana-1296	144	1	h	h	NOUN
cana-1296	144	2	h	h	NOUN
cana-1296	144	3	h	h	PROPN
cana-1296	144	4	h	h	PROPN
cana-1296	144	5	h=	h=	NOUN
cana-1296	144	6			PROPN
cana-1296	144	7			NOUN
cana-1296	144	8	=	=	SYM
cana-1296	144	9			PROPN
cana-1296	144	10	=	=	NOUN
cana-1296	144	11			VERB
cana-1296	144	12	(	(	PUNCT
cana-1296	144	13	3	3	NUM
cana-1296	144	14	)	)	PUNCT
cana-1296	144	15	(	(	PUNCT
cana-1296	144	16	1)	1)	NUM
cana-1296	144	17	assume	assume	VERB
cana-1296	144	18	that	that	SCONJ
cana-1296	144	19	(	(	PUNCT
cana-1296	144	20	h)=m	h)=m	NOUN
cana-1296	144	21	for	for	ADP
cana-1296	144	22	all	all	PRON
cana-1296	144	23	,	,	PUNCT
cana-1296	144	24	h	h	NOUN
cana-1296	144	25	and	and	CCONJ
cana-1296	144	26	let	let	VERB
cana-1296	144	27	h	h	NOUN
cana-1296	144	28	be	be	AUX
cana-1296	144	29	a	a	DET
cana-1296	144	30	gbtγi	gbtγi	NOUN
cana-1296	144	31	of	of	ADP
cana-1296	144	32	m	m	PROPN
cana-1296	144	33	&	&	CCONJ
cana-1296	144	34	.h	.h	PROPN
cana-1296	144	35	h	h	PROPN
cana-1296	144	36	(	(	PUNCT
cana-1296	144	37	)	)	PUNCT
cana-1296	144	38	.h	.h	PUNCT
cana-1296	145	1	h	h	NOUN
cana-1296	145	2			ADJ
cana-1296	145	3	with	with	ADP
cana-1296	145	4	statement	statement	NOUN
cana-1296	145	5	,	,	PUNCT
cana-1296	145	6	(	(	PUNCT
cana-1296	145	7	)	)	PUNCT
cana-1296	145	8	.h	.h	NOUN
cana-1296	145	9	h	h	X
cana-1296	146	1	=	=	PRON
cana-1296	146	2			ADJ
cana-1296	146	3			ADV
cana-1296	146	4	thus	thus	ADV
cana-1296	146	5	m	m	PROPN
cana-1296	146	6	=	=	PROPN
cana-1296	146	7	h.	h.	PROPN
cana-1296	146	8			PROPN
cana-1296	146	9	m	m	VERB
cana-1296	146	10	is	be	AUX
cana-1296	146	11	a	a	DET
cana-1296	146	12	gb	gb	ADV
cana-1296	146	13	-	-	PUNCT
cana-1296	146	14	simple	simple	ADJ
cana-1296	146	15	tγ	tγ	NOUN
cana-1296	146	16	-	-	PUNCT
cana-1296	146	17	semiring	semiring	NOUN
cana-1296	146	18	.	.	PUNCT
cana-1296	147	1	communications	communication	NOUN
cana-1296	147	2	on	on	ADP
cana-1296	147	3	applied	apply	VERB
cana-1296	147	4	nonlinear	nonlinear	ADJ
cana-1296	147	5	analysis	analysis	NOUN
cana-1296	147	6	issn	issn	NOUN
cana-1296	147	7	:	:	PUNCT
cana-1296	147	8	1074	1074	NUM
cana-1296	147	9	-	-	PUNCT
cana-1296	147	10	133x	133x	NUM
cana-1296	147	11	vol	vol	NOUN
cana-1296	147	12	31	31	NUM
cana-1296	147	13	no	no	NOUN
cana-1296	147	14	.	.	PUNCT
cana-1296	148	1	7s	7	NOUN
cana-1296	148	2	(	(	PUNCT
cana-1296	148	3	2024	2024	NUM
cana-1296	148	4	)	)	PUNCT
cana-1296	148	5	219	219	NUM
cana-1296	149	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	149	2	lemma	lemma	PROPN
cana-1296	149	3	2.12	2.12	NUM
cana-1296	149	4	:	:	PUNCT
cana-1296	149	5	let	let	VERB
cana-1296	149	6	b	b	X
cana-1296	149	7	be	be	AUX
cana-1296	149	8	a	a	DET
cana-1296	149	9	gbtγi	gbtγi	NOUN
cana-1296	149	10	of	of	ADP
cana-1296	149	11	a	a	DET
cana-1296	149	12	tγs	tγs	PROPN
cana-1296	149	13	m	m	PROPN
cana-1296	149	14	&	&	CCONJ
cana-1296	149	15	t	t	PROPN
cana-1296	149	16	a	a	DET
cana-1296	149	17	sub	sub	ADJ
cana-1296	149	18	-	-	ADJ
cana-1296	149	19	tγ	tγ	NOUN
cana-1296	149	20	-	-	PUNCT
cana-1296	149	21	semiring	semiring	NOUN
cana-1296	149	22	of	of	ADP
cana-1296	149	23	m.	m.	NOUN
cana-1296	149	24	if	if	SCONJ
cana-1296	149	25	t	t	PROPN
cana-1296	149	26	is	be	AUX
cana-1296	149	27	a	a	DET
cana-1296	149	28	gb	gb	ADV
cana-1296	149	29	-	-	PUNCT
cana-1296	149	30	simple	simple	ADJ
cana-1296	149	31	tγ	tγ	NOUN
cana-1296	149	32	-	-	PUNCT
cana-1296	149	33	semiring	semiring	NOUN
cana-1296	149	34	,	,	PUNCT
cana-1296	149	35	t	t	PROPN
cana-1296	149	36	b	b	PROPN
cana-1296	149	37			PROPN
cana-1296	149	38			PROPN
cana-1296	149	39	then	then	ADV
cana-1296	149	40	.t	.t	PROPN
cana-1296	149	41	b	b	PROPN
cana-1296	149	42	proof	proof	NOUN
cana-1296	149	43	:	:	PUNCT
cana-1296	149	44	presume	presume	VERB
cana-1296	149	45	t	t	PROPN
cana-1296	149	46	is	be	AUX
cana-1296	149	47	a	a	DET
cana-1296	149	48	gb	gb	ADV
cana-1296	149	49	-	-	PUNCT
cana-1296	149	50	simple	simple	ADJ
cana-1296	149	51	tγ	tγ	NOUN
cana-1296	149	52	-	-	PUNCT
cana-1296	149	53	semiring	semire	VERB
cana-1296	149	54	t	t	PROPN
cana-1296	149	55	b	b	PROPN
cana-1296	149	56			PROPN
cana-1296	149	57			PROPN
cana-1296	149	58	&	&	CCONJ
cana-1296	149	59	let	let	VERB
cana-1296	149	60	.h	.h	PROPN
cana-1296	149	61	t	t	PROPN
cana-1296	149	62			NOUN
cana-1296	149	63	via	via	ADP
cana-1296	149	64	lemma	lemma	PROPN
cana-1296	149	65	2.3	2.3	NUM
cana-1296	149	66	,	,	PUNCT
cana-1296	149	67	{	{	PUNCT
cana-1296	149	68	}	}	PUNCT
cana-1296	149	69	.t	.t	PROPN
cana-1296	150	1	h	h	PROPN
cana-1296	150	2	h	h	NOUN
cana-1296	150	3	t	t	PROPN
cana-1296	150	4	h	h	NOUN
cana-1296	150	5	t	t	PROPN
cana-1296	150	6	h	h	NOUN
cana-1296	150	7	m	m	AUX
cana-1296	150	8	m=	m=	X
cana-1296	150	9			VERB
cana-1296	150	10			VERB
cana-1296	150	11			VERB
cana-1296	150	12			ADJ
cana-1296	150	13			PROPN
cana-1296	150	14			NOUN
cana-1296	151	1			PROPN
cana-1296	151	2			PROPN
cana-1296	151	3			AUX
cana-1296	151	4			PROPN
cana-1296	151	5			PROPN
cana-1296	151	6			PROPN
cana-1296	151	7			PROPN
cana-1296	151	8			PROPN
cana-1296	151	9	hence	hence	ADV
cana-1296	151	10	.t	.t	PROPN
cana-1296	151	11			PROPN
cana-1296	151	12	theorem	theorem	VERB
cana-1296	151	13	2.13	2.13	NUM
cana-1296	151	14	:	:	PUNCT
cana-1296	151	15	let	let	VERB
cana-1296	151	16	v	v	PART
cana-1296	151	17	be	be	AUX
cana-1296	151	18	a	a	DET
cana-1296	151	19	tγs	tγs	PROPN
cana-1296	151	20	,	,	PUNCT
cana-1296	151	21	b	b	X
cana-1296	151	22	be	be	AUX
cana-1296	151	23	a	a	DET
cana-1296	151	24	gbtγi	gbtγi	NOUN
cana-1296	151	25	of	of	ADP
cana-1296	151	26	v	v	PROPN
cana-1296	151	27	&	&	CCONJ
cana-1296	151	28	(	(	PUNCT
cana-1296	151	29	)	)	PUNCT
cana-1296	151	30	g	g	PROPN
cana-1296	151	31	v	v	NOUN
cana-1296	151	32			PROPN
cana-1296	151	33	then	then	ADV
cana-1296	151	34	,	,	PUNCT
cana-1296	151	35	&	&	CCONJ
cana-1296	151	36	g	g	PROPN
cana-1296	151	37	g	g	PROPN
cana-1296	151	38	b	b	PROPN
cana-1296	151	39	g	g	PROPN
cana-1296	151	40	b	b	PROPN
cana-1296	151	41	g	g	PROPN
cana-1296	151	42	b	b	PROPN
cana-1296	151	43	g	g	PROPN
cana-1296	151	44	g	g	PROPN
cana-1296	151	45			VERB
cana-1296	151	46			VERB
cana-1296	151	47			VERB
cana-1296	151	48			VERB
cana-1296	151	49			NOUN
cana-1296	151	50	are	be	AUX
cana-1296	151	51	gbtγi	gbtγi	NOUN
cana-1296	151	52	of	of	ADP
cana-1296	151	53	v.	v.	ADP
cana-1296	151	54	proof	proof	NOUN
cana-1296	151	55	:	:	PUNCT
cana-1296	151	56	b	b	X
cana-1296	151	57	is	be	AUX
cana-1296	151	58	a	a	DET
cana-1296	151	59	gbtγi	gbtγi	NOUN
cana-1296	151	60	of	of	ADP
cana-1296	151	61	v	v	NOUN
cana-1296	151	62	,	,	PUNCT
cana-1296	151	63	(	(	PUNCT
cana-1296	151	64	)	)	PUNCT
cana-1296	151	65	(	(	PUNCT
cana-1296	151	66	)	)	PUNCT
cana-1296	151	67	(	(	PUNCT
cana-1296	151	68	(	(	PUNCT
cana-1296	151	69	)	)	PUNCT
cana-1296	151	70	)	)	PUNCT
cana-1296	152	1	b	b	X
cana-1296	153	1	g	g	NOUN
cana-1296	153	2	g	g	PROPN
cana-1296	153	3	v	v	NUM
cana-1296	153	4	b	b	NOUN
cana-1296	153	5	g	g	NOUN
cana-1296	153	6	g	g	PROPN
cana-1296	153	7	b	b	PROPN
cana-1296	153	8	g	g	PROPN
cana-1296	153	9	g	g	PROPN
cana-1296	153	10	v	v	NUM
cana-1296	153	11	b	b	NUM
cana-1296	153	12	g	g	PROPN
cana-1296	153	13	b	b	PROPN
cana-1296	153	14	g	g	ADP
cana-1296	153	15	g	g	PROPN
cana-1296	153	16			VERB
cana-1296	153	17			VERB
cana-1296	153	18			VERB
cana-1296	153	19			VERB
cana-1296	153	20			VERB
cana-1296	153	21			VERB
cana-1296	153	22	=	=	PUNCT
cana-1296	153	23			VERB
cana-1296	153	24			VERB
cana-1296	153	25			NOUN
cana-1296	153	26			VERB
cana-1296	153	27			VERB
cana-1296	153	28			NOUN
cana-1296	153	29			VERB
cana-1296	153	30			VERB
cana-1296	153	31	(	(	PUNCT
cana-1296	153	32	)	)	PUNCT
cana-1296	153	33	(	(	PUNCT
cana-1296	153	34	)	)	PUNCT
cana-1296	153	35	(	(	PUNCT
cana-1296	153	36	(	(	PUNCT
cana-1296	153	37	)	)	PUNCT
cana-1296	153	38	)	)	PUNCT
cana-1296	154	1	g	g	PROPN
cana-1296	154	2	b	b	PROPN
cana-1296	154	3	g	g	NOUN
cana-1296	154	4	v	v	NUM
cana-1296	154	5	g	g	PROPN
cana-1296	154	6	b	b	PROPN
cana-1296	154	7	g	g	PROPN
cana-1296	154	8	g	g	PROPN
cana-1296	154	9	b	b	PROPN
cana-1296	154	10	g	g	NOUN
cana-1296	154	11	v	v	NUM
cana-1296	154	12	g	g	PROPN
cana-1296	154	13	b	b	PROPN
cana-1296	154	14	g	g	PROPN
cana-1296	154	15	g	g	PROPN
cana-1296	154	16	b	b	PROPN
cana-1296	154	17	g	g	PROPN
cana-1296	154	18			VERB
cana-1296	154	19			VERB
cana-1296	154	20			VERB
cana-1296	154	21			VERB
cana-1296	154	22			VERB
cana-1296	154	23	=	=	PUNCT
cana-1296	154	24			VERB
cana-1296	154	25			VERB
cana-1296	154	26			VERB
cana-1296	154	27			VERB
cana-1296	154	28			VERB
cana-1296	154	29			VERB
cana-1296	154	30			NOUN
cana-1296	154	31			VERB
cana-1296	154	32			VERB
cana-1296	154	33	(	(	PUNCT
cana-1296	154	34	)	)	PUNCT
cana-1296	154	35	(	(	PUNCT
cana-1296	154	36	)	)	PUNCT
cana-1296	154	37	similarly	similarly	ADV
cana-1296	154	38	g	g	PROPN
cana-1296	154	39	g	g	PROPN
cana-1296	154	40	b	b	PROPN
cana-1296	154	41	v	v	NOUN
cana-1296	154	42	g	g	PROPN
cana-1296	154	43	g	g	PROPN
cana-1296	154	44	b	b	PROPN
cana-1296	154	45	g	g	PROPN
cana-1296	154	46	g	g	PROPN
cana-1296	154	47	b	b	PROPN
cana-1296	154	48			PUNCT
cana-1296	154	49			VERB
cana-1296	154	50			VERB
cana-1296	154	51			VERB
cana-1296	154	52			VERB
cana-1296	154	53			NOUN
cana-1296	154	54			PUNCT
cana-1296	154	55			NOUN
cana-1296	154	56	are	be	AUX
cana-1296	154	57	gbtγi	gbtγi	NOUN
cana-1296	154	58	of	of	ADP
cana-1296	154	59	v.	v.	PROPN
cana-1296	154	60	theorem2.14	theorem2.14	PROPN
cana-1296	154	61	:	:	PUNCT
cana-1296	154	62	let	let	VERB
cana-1296	154	63	m	m	PRON
cana-1296	154	64	be	be	AUX
cana-1296	154	65	a	a	DET
cana-1296	154	66	tγs	tγs	PROPN
cana-1296	154	67	.	.	PUNCT
cana-1296	155	1	subsequently	subsequently	ADV
cana-1296	155	2	i	i	PRON
cana-1296	155	3	i	i	PRON
cana-1296	156	1	i	i	PRON
cana-1296	156	2	i	i	VERB
cana-1296	156	3	=	=	PRON
cana-1296	157	1			NOUN
cana-1296	157	2			PROPN
cana-1296	157	3	iff	iff	PROPN
cana-1296	157	4	m	m	VERB
cana-1296	157	5	is	be	AUX
cana-1296	157	6	a	a	DET
cana-1296	157	7	gb	gb	ADV
cana-1296	157	8	-	-	PUNCT
cana-1296	157	9	simple	simple	ADJ
cana-1296	157	10	tγsemiring	tγsemiring	NOUN
cana-1296	157	11	.	.	PUNCT
cana-1296	158	1	proof	proof	NOUN
cana-1296	158	2	:	:	PUNCT
cana-1296	158	3	presume	presume	VERB
cana-1296	158	4	i	i	PRON
cana-1296	159	1	i	i	PRON
cana-1296	160	1	i	i	PRON
cana-1296	160	2	i	i	VERB
cana-1296	161	1	=	=	PRON
cana-1296	161	2			X
cana-1296	161	3			NOUN
cana-1296	162	1	&	&	CCONJ
cana-1296	163	1	let	let	VERB
cana-1296	163	2	b	b	NOUN
cana-1296	163	3	is	be	AUX
cana-1296	163	4	a	a	DET
cana-1296	163	5	gbtγi	gbtγi	NOUN
cana-1296	163	6	of	of	ADP
cana-1296	163	7	m	m	PROPN
cana-1296	163	8	&	&	CCONJ
cana-1296	163	9	.b	.b	PROPN
cana-1296	163	10	by	by	ADP
cana-1296	163	11	hypothesis	hypothesis	NOUN
cana-1296	163	12	,	,	PUNCT
cana-1296	163	13	.b	.b	PROPN
cana-1296	164	1	b	b	X
cana-1296	164	2	b=	b=	NUM
cana-1296	164	3			NOUN
cana-1296	164	4			NOUN
cana-1296	164	5			PROPN
cana-1296	164	6	hence	hence	NOUN
cana-1296	164	7	m	m	NOUN
cana-1296	164	8	=	=	PROPN
cana-1296	164	9	b	b	PROPN
cana-1296	164	10	,	,	PUNCT
cana-1296	164	11	so	so	ADV
cana-1296	164	12	m	m	VERB
cana-1296	164	13	is	be	AUX
cana-1296	164	14	a	a	DET
cana-1296	164	15	gbsimple	gbsimple	NOUN
cana-1296	164	16	tγ	tγ	NOUN
cana-1296	164	17	-	-	PUNCT
cana-1296	164	18	semiring	semiring	NOUN
cana-1296	164	19	.	.	PUNCT
cana-1296	165	1	on	on	ADP
cana-1296	165	2	the	the	DET
cana-1296	165	3	contrary	contrary	NOUN
cana-1296	165	4	,	,	PUNCT
cana-1296	165	5	assume	assume	VERB
cana-1296	165	6	that	that	SCONJ
cana-1296	165	7	m	m	PROPN
cana-1296	165	8	is	be	AUX
cana-1296	165	9	a	a	DET
cana-1296	165	10	gbsimple	gbsimple	NOUN
cana-1296	165	11	tγ	tγ	NOUN
cana-1296	165	12	-	-	PUNCT
cana-1296	165	13	semiring	semire	VERB
cana-1296	165	14	.i	.i	PUNCT
cana-1296	166	1	by	by	ADP
cana-1296	166	2	lemma	lemma	PROPN
cana-1296	166	3	2.1	2.1	NUM
cana-1296	166	4	and	and	CCONJ
cana-1296	166	5	theorem	theorem	VERB
cana-1296	166	6	2.13	2.13	NUM
cana-1296	166	7	,	,	PUNCT
cana-1296	166	8	we	we	PRON
cana-1296	166	9	have	have	VERB
cana-1296	166	10	i	i	PRON
cana-1296	166	11	i	i	PRON
cana-1296	166	12	i	i	VERB
cana-1296	166	13	is	be	AUX
cana-1296	166	14	a	a	DET
cana-1296	166	15	gbtγi	gbtγi	NOUN
cana-1296	166	16	of	of	ADP
cana-1296	166	17	m.	m.	NOUN
cana-1296	166	18	m	m	AUX
cana-1296	166	19	is	be	AUX
cana-1296	166	20	a	a	DET
cana-1296	166	21	gb	gb	ADV
cana-1296	166	22	-	-	PUNCT
cana-1296	166	23	simple	simple	ADJ
cana-1296	166	24	tγ	tγ	NOUN
cana-1296	166	25	-	-	PUNCT
cana-1296	166	26	semiring	semiring	NOUN
cana-1296	166	27	,	,	PUNCT
cana-1296	166	28	.i	.i	PROPN
cana-1296	167	1	i	i	PRON
cana-1296	167	2	i	i	VERB
cana-1296	167	3			NUM
cana-1296	167	4	=	=	VERB
cana-1296	167	5			NUM
cana-1296	167	6	theorem2.15	theorem2.15	NOUN
cana-1296	167	7	:	:	PUNCT
cana-1296	167	8	let	let	VERB
cana-1296	167	9	q	q	PART
cana-1296	167	10	be	be	AUX
cana-1296	167	11	a	a	DET
cana-1296	167	12	tγs	tγs	PROPN
cana-1296	167	13	&	&	CCONJ
cana-1296	167	14	d	d	PROPN
cana-1296	167	15	a	a	DET
cana-1296	167	16	btγi	btγi	NOUN
cana-1296	167	17	of	of	ADP
cana-1296	167	18	q.	q.	PROPN
cana-1296	168	1	then	then	ADV
cana-1296	168	2	d	d	PROPN
cana-1296	168	3	is	be	AUX
cana-1296	168	4	a	a	DET
cana-1296	168	5	mgbtγi	mgbtγi	NOUN
cana-1296	168	6	of	of	ADP
cana-1296	168	7	q	q	PROPN
cana-1296	168	8	iff	iff	PROPN
cana-1296	168	9	d	d	PROPN
cana-1296	168	10	is	be	AUX
cana-1296	168	11	a	a	DET
cana-1296	168	12	gbsimple	gbsimple	NOUN
cana-1296	168	13	tγ	tγ	NOUN
cana-1296	168	14	-	-	PUNCT
cana-1296	168	15	semiring	semiring	NOUN
cana-1296	168	16	.	.	PUNCT
cana-1296	169	1	proof	proof	NOUN
cana-1296	169	2	:	:	PUNCT
cana-1296	169	3	presume	presume	VERB
cana-1296	169	4	that	that	SCONJ
cana-1296	169	5	d	d	NOUN
cana-1296	169	6	is	be	AUX
cana-1296	169	7	a	a	DET
cana-1296	169	8	mgbtγi	mgbtγi	NOUN
cana-1296	169	9	of	of	ADP
cana-1296	169	10	q.	q.	PROPN
cana-1296	169	11	via	via	ADP
cana-1296	169	12	supposition	supposition	NOUN
cana-1296	169	13	,	,	PUNCT
cana-1296	169	14	d	d	PROPN
cana-1296	169	15	is	be	AUX
cana-1296	169	16	a	a	DET
cana-1296	169	17	tγs	tγs	PROPN
cana-1296	169	18	.	.	PUNCT
cana-1296	170	1	let	let	VERB
cana-1296	170	2	b	b	X
cana-1296	170	3	be	be	AUX
cana-1296	170	4	a	a	DET
cana-1296	170	5	gbtγi	gbtγi	NOUN
cana-1296	170	6	of	of	ADP
cana-1296	170	7	d.	d.	PROPN
cana-1296	170	8	next	next	ADV
cana-1296	170	9	.b	.b	PROPN
cana-1296	171	1	d	d	X
cana-1296	171	2	b	b	X
cana-1296	171	3	d	d	X
cana-1296	171	4	b	b	PROPN
cana-1296	171	5	b	b	PROPN
cana-1296	171	6	d	d	PROPN
cana-1296	171	7			PROPN
cana-1296	171	8			VERB
cana-1296	171	9			VERB
cana-1296	171	10			PROPN
cana-1296	171	11			PROPN
cana-1296	171	12	d	d	PROPN
cana-1296	171	13	is	be	AUX
cana-1296	171	14	a	a	DET
cana-1296	171	15	gbtγi	gbtγi	NOUN
cana-1296	171	16	of	of	ADP
cana-1296	171	17	q	q	PROPN
cana-1296	171	18	&	&	CCONJ
cana-1296	171	19	by	by	ADP
cana-1296	171	20	th	th	NUM
cana-1296	171	21	2.13	2.13	NUM
cana-1296	171	22	,	,	PUNCT
cana-1296	171	23	cover	cover	VERB
cana-1296	171	24	b	b	PROPN
cana-1296	171	25	d	d	X
cana-1296	171	26	b	b	PROPN
cana-1296	172	1	d	d	X
cana-1296	172	2	b	b	PROPN
cana-1296	172	3			PUNCT
cana-1296	172	4			VERB
cana-1296	172	5			NOUN
cana-1296	172	6	is	be	AUX
cana-1296	172	7	a	a	DET
cana-1296	172	8	gbtγi	gbtγi	NOUN
cana-1296	172	9	of	of	ADP
cana-1296	172	10	q.	q.	PROPN
cana-1296	172	11	as	as	SCONJ
cana-1296	172	12	d	d	PROPN
cana-1296	172	13	is	be	AUX
cana-1296	172	14	a	a	DET
cana-1296	172	15	mgbtγi	mgbtγi	NOUN
cana-1296	172	16	of	of	ADP
cana-1296	172	17	q	q	NOUN
cana-1296	172	18	,	,	PUNCT
cana-1296	172	19	we	we	PRON
cana-1296	172	20	get	get	VERB
cana-1296	172	21	.b	.b	PROPN
cana-1296	173	1	d	d	X
cana-1296	173	2	b	b	X
cana-1296	173	3	d	d	X
cana-1296	173	4	b	b	X
cana-1296	173	5	d	d	PROPN
cana-1296	173	6			PUNCT
cana-1296	173	7			VERB
cana-1296	173	8			VERB
cana-1296	173	9	=	=	PRON
cana-1296	173	10	via	via	ADP
cana-1296	173	11	(	(	PUNCT
cana-1296	173	12	2.3	2.3	NUM
cana-1296	173	13	)	)	PUNCT
cana-1296	173	14	,	,	PUNCT
cana-1296	174	1	d	d	X
cana-1296	174	2	=	=	X
cana-1296	174	3	b.	b.	PROPN
cana-1296	175	1	so	so	ADV
cana-1296	175	2	d	d	PROPN
cana-1296	175	3	is	be	AUX
cana-1296	175	4	gb	gb	ADV
cana-1296	175	5	-	-	PUNCT
cana-1296	175	6	simple	simple	ADJ
cana-1296	175	7	tγ	tγ	NOUN
cana-1296	175	8	-	-	PUNCT
cana-1296	175	9	semiring	semiring	NOUN
cana-1296	175	10	.	.	PUNCT
cana-1296	176	1	permit	permit	PROPN
cana-1296	176	2	b	b	NOUN
cana-1296	176	3	be	be	AUX
cana-1296	176	4	a	a	DET
cana-1296	176	5	gbtγi	gbtγi	NOUN
cana-1296	176	6	of	of	ADP
cana-1296	176	7	q	q	PROPN
cana-1296	176	8	.b	.b	PROPN
cana-1296	177	1	q	q	PROPN
cana-1296	177	2			PROPN
cana-1296	177	3	.b	.b	PROPN
cana-1296	178	1	d	d	X
cana-1296	178	2	b	b	X
cana-1296	178	3	d	d	X
cana-1296	178	4	b	b	PROPN
cana-1296	178	5	b	b	PROPN
cana-1296	178	6	q	q	X
cana-1296	178	7	b	b	PROPN
cana-1296	178	8	q	q	X
cana-1296	178	9	b	b	PROPN
cana-1296	178	10	b	b	NOUN
cana-1296	178	11			VERB
cana-1296	178	12			VERB
cana-1296	179	1			VERB
cana-1296	179	2			VERB
cana-1296	179	3			NOUN
cana-1296	179	4			VERB
cana-1296	179	5			VERB
cana-1296	179	6			VERB
cana-1296	179	7			VERB
cana-1296	179	8			NOUN
cana-1296	179	9	consequently	consequently	ADV
cana-1296	179	10	c	c	PROPN
cana-1296	179	11	is	be	AUX
cana-1296	179	12	a	a	DET
cana-1296	179	13	gbtγi	gbtγi	NOUN
cana-1296	179	14	.	.	PUNCT
cana-1296	180	1	d	d	X
cana-1296	180	2	is	be	AUX
cana-1296	180	3	a	a	DET
cana-1296	180	4	gb	gb	ADV
cana-1296	180	5	-	-	PUNCT
cana-1296	180	6	simple	simple	ADJ
cana-1296	180	7	tγ	tγ	NOUN
cana-1296	180	8	-	-	PUNCT
cana-1296	180	9	semiring	semiring	NOUN
cana-1296	180	10	,	,	PUNCT
cana-1296	180	11	enclose	enclose	VERB
cana-1296	180	12	d	d	PROPN
cana-1296	180	13	=	=	PROPN
cana-1296	180	14	b.	b.	X
cana-1296	180	15			PROPN
cana-1296	180	16	d	d	PROPN
cana-1296	180	17	is	be	AUX
cana-1296	180	18	a	a	DET
cana-1296	180	19	mgbtγi	mgbtγi	NOUN
cana-1296	180	20	of	of	ADP
cana-1296	180	21	q.	q.	PROPN
cana-1296	180	22	communications	communication	NOUN
cana-1296	180	23	on	on	ADP
cana-1296	180	24	applied	apply	VERB
cana-1296	180	25	nonlinear	nonlinear	ADJ
cana-1296	180	26	analysis	analysis	NOUN
cana-1296	180	27	issn	issn	NOUN
cana-1296	180	28	:	:	PUNCT
cana-1296	180	29	1074	1074	NUM
cana-1296	180	30	-	-	PUNCT
cana-1296	180	31	133x	133x	NUM
cana-1296	180	32	vol	vol	NOUN
cana-1296	180	33	31	31	NUM
cana-1296	180	34	no	no	NOUN
cana-1296	180	35	.	.	PUNCT
cana-1296	181	1	7s	7	NOUN
cana-1296	181	2	(	(	PUNCT
cana-1296	181	3	2024	2024	NUM
cana-1296	181	4	)	)	PUNCT
cana-1296	181	5	220	220	NUM
cana-1296	181	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1296	182	1	theorem2.16	theorem2.16	PROPN
cana-1296	182	2	:	:	PUNCT
cana-1296	182	3	let	let	VERB
cana-1296	182	4	m	m	PRON
cana-1296	182	5	be	be	AUX
cana-1296	182	6	a	a	DET
cana-1296	182	7	tγs	tγs	NOUN
cana-1296	182	8	having	have	VERB
cana-1296	182	9	a	a	DET
cana-1296	182	10	proper	proper	ADJ
cana-1296	182	11	gbtγi	gbtγi	NOUN
cana-1296	182	12	.	.	PUNCT
cana-1296	183	1	afterward	afterward	ADV
cana-1296	183	2	each	each	DET
cana-1296	183	3	proper	proper	ADJ
cana-1296	183	4	gbtγi	gbtγi	NOUN
cana-1296	183	5	of	of	ADP
cana-1296	183	6	m	m	PROPN
cana-1296	183	7	is	be	AUX
cana-1296	183	8	minimal	minimal	ADJ
cana-1296	183	9	iff	iff	VERB
cana-1296	183	10	the	the	DET
cana-1296	183	11	intersection	intersection	NOUN
cana-1296	183	12	of	of	ADP
cana-1296	183	13	any	any	DET
cana-1296	183	14	two	two	NUM
cana-1296	183	15	distinct	distinct	ADJ
cana-1296	183	16	proper	proper	ADJ
cana-1296	183	17	gbtγi	gbtγi	NOUN
cana-1296	183	18	’s	’s	PART
cana-1296	183	19	is	be	AUX
cana-1296	183	20	empty	empty	ADJ
cana-1296	183	21	.	.	PUNCT
cana-1296	184	1	proof	proof	NOUN
cana-1296	184	2	:	:	PUNCT
cana-1296	184	3	similar	similar	ADJ
cana-1296	184	4	to	to	ADP
cana-1296	184	5	the	the	DET
cana-1296	184	6	above	above	ADJ
cana-1296	184	7	theorem	theorem	ADJ
cana-1296	184	8	references	reference	NOUN
cana-1296	184	9	:	:	PUNCT
cana-1296	184	10	[	[	X
cana-1296	184	11	1	1	NUM
cana-1296	184	12	]	]	PUNCT
cana-1296	184	13	r.chinram	r.chinram	PROPN
cana-1296	184	14	,	,	PUNCT
cana-1296	184	15	a	a	DET
cana-1296	184	16	note	note	NOUN
cana-1296	184	17	on	on	ADP
cana-1296	184	18	quasi	quasi	NOUN
cana-1296	184	19	-	-	NOUN
cana-1296	184	20	ideals	ideal	NOUN
cana-1296	184	21	in	in	ADP
cana-1296	184	22	γ	γ	NOUN
cana-1296	184	23	-	-	PUNCT
cana-1296	184	24	semirings	semiring	NOUN
cana-1296	184	25	,	,	PUNCT
cana-1296	184	26	international	international	PROPN
cana-1296	184	27	mathematical	mathematical	ADJ
cana-1296	184	28	forum	forum	PROPN
cana-1296	184	29	26(2008	26(2008	NOUN
cana-1296	184	30	)	)	PUNCT
cana-1296	184	31	,	,	PUNCT
cana-1296	184	32	1253	1253	NUM
cana-1296	184	33	-	-	SYM
cana-1296	184	34	1259	1259	NUM
cana-1296	184	35	.	.	PUNCT
cana-1296	185	1	[	[	X
cana-1296	185	2	2	2	NUM
cana-1296	185	3	]	]	PUNCT
cana-1296	185	4	o.bektas	o.bekta	NOUN
cana-1296	185	5	,	,	PUNCT
cana-1296	185	6	n.bayrak	n.bayrak	NOUN
cana-1296	185	7	,	,	PUNCT
cana-1296	185	8	and	and	CCONJ
cana-1296	185	9	a.ersoy	a.ersoy	NOUN
cana-1296	185	10	,	,	PUNCT
cana-1296	185	11	soft	soft	ADJ
cana-1296	185	12	γ	γ	NOUN
cana-1296	185	13	-	-	PUNCT
cana-1296	185	14	semirings	semiring	NOUN
cana-1296	185	15	,	,	PUNCT
cana-1296	185	16	arxiv:1202.1496[math.ra	arxiv:1202.1496[math.ra	NOUN
cana-1296	185	17	]	]	PUNCT
cana-1296	185	18	,	,	PUNCT
cana-1296	185	19	7	7	NUM
cana-1296	185	20	feb	feb	NOUN
cana-1296	185	21	2012	2012	NUM
cana-1296	185	22	.	.	PUNCT
cana-1296	186	1	[	[	X
cana-1296	186	2	3	3	X
cana-1296	186	3	]	]	PUNCT
cana-1296	186	4	t.k.dutta	t.k.dutta	NOUN
cana-1296	186	5	and	and	CCONJ
cana-1296	186	6	s.k.sardar	s.k.sardar	NOUN
cana-1296	186	7	,	,	PUNCT
cana-1296	186	8	semiprime	semiprime	NOUN
cana-1296	186	9	ideals	ideal	NOUN
cana-1296	186	10	and	and	CCONJ
cana-1296	186	11	irreducible	irreducible	ADJ
cana-1296	186	12	ideals	ideal	NOUN
cana-1296	186	13	of	of	ADP
cana-1296	186	14	γ	γ	NOUN
cana-1296	186	15	-	-	PUNCT
cana-1296	186	16	semirings	semiring	NOUN
cana-1296	186	17	,	,	PUNCT
cana-1296	186	18	novi	novi	PROPN
cana-1296	186	19	sad	sad	PROPN
cana-1296	186	20	journal	journal	PROPN
cana-1296	186	21	of	of	ADP
cana-1296	186	22	mathematics	mathematic	NOUN
cana-1296	186	23	30(2000	30(2000	NUM
cana-1296	186	24	)	)	PUNCT
cana-1296	186	25	,	,	PUNCT
cana-1296	186	26	97	97	NUM
cana-1296	186	27	-	-	SYM
cana-1296	186	28	108	108	NUM
cana-1296	186	29	.	.	PUNCT
cana-1296	187	1	[	[	X
cana-1296	187	2	4	4	NUM
cana-1296	187	3	]	]	PUNCT
cana-1296	187	4	t.k.dutta	t.k.dutta	NOUN
cana-1296	187	5	,	,	PUNCT
cana-1296	187	6	s.k.sardar	s.k.sardar	NOUN
cana-1296	187	7	,	,	PUNCT
cana-1296	187	8	and	and	CCONJ
cana-1296	187	9	s.goswami	s.goswami	NOUN
cana-1296	187	10	,	,	PUNCT
cana-1296	187	11	operations	operation	NOUN
cana-1296	187	12	on	on	ADP
cana-1296	187	13	fuzzy	fuzzy	ADJ
cana-1296	187	14	ideals	ideal	NOUN
cana-1296	187	15	of	of	ADP
cana-1296	187	16	γ	γ	NOUN
cana-1296	187	17	-	-	PUNCT
cana-1296	187	18	semirings	semiring	NOUN
cana-1296	187	19	,	,	PUNCT
cana-1296	187	20	arxiv:1101.4791[math.ra	arxiv:1101.4791[math.ra	PROPN
cana-1296	187	21	]	]	X
cana-1296	187	22	,	,	PUNCT
cana-1296	187	23	25	25	NUM
cana-1296	187	24	jan2011	jan2011	NOUN
cana-1296	187	25	.	.	PUNCT
cana-1296	188	1	[	[	X
cana-1296	188	2	5	5	NUM
cana-1296	188	3	]	]	PUNCT
cana-1296	188	4	j.ghosh	j.ghosh	NOUN
cana-1296	188	5	and	and	CCONJ
cana-1296	188	6	t.k.samanta	t.k.samanta	VERB
cana-1296	188	7	fuzzy	fuzzy	ADJ
cana-1296	188	8	ideals	ideal	NOUN
cana-1296	188	9	in	in	ADP
cana-1296	188	10	γ	γ	NOUN
cana-1296	188	11	-	-	PUNCT
cana-1296	188	12	semirings	semiring	NOUN
cana-1296	188	13	,	,	PUNCT
cana-1296	188	14	arxiv:1010.2469[math.gm	arxiv:1010.2469[math.gm	NOUN
cana-1296	188	15	]	]	X
cana-1296	188	16	,	,	PUNCT
cana-1296	188	17	12	12	NUM
cana-1296	188	18	oct	oct	NOUN
cana-1296	188	19	2010	2010	NUM
cana-1296	188	20	.	.	PUNCT
cana-1296	189	1	[	[	X
cana-1296	189	2	6	6	NUM
cana-1296	189	3	]	]	X
cana-1296	189	4	r.d.jagatap	r.d.jagatap	NOUN
cana-1296	189	5	and	and	CCONJ
cana-1296	189	6	y.s.pawar	y.s.pawar	ADJ
cana-1296	189	7	,	,	PUNCT
cana-1296	189	8	quasi	quasi	NOUN
cana-1296	189	9	-	-	NOUN
cana-1296	189	10	ideals	ideal	NOUN
cana-1296	189	11	and	and	CCONJ
cana-1296	189	12	minimal	minimal	ADJ
cana-1296	189	13	quasi	quasi	NOUN
cana-1296	189	14	-	-	NOUN
cana-1296	189	15	ideals	ideal	NOUN
cana-1296	189	16	in	in	ADP
cana-1296	189	17	γ	γ	NOUN
cana-1296	189	18	-	-	PUNCT
cana-1296	189	19	semirings	semiring	NOUN
cana-1296	189	20	,	,	PUNCT
cana-1296	189	21	novi	novi	PROPN
cana-1296	189	22	sad	sad	PROPN
cana-1296	189	23	journal	journal	PROPN
cana-1296	189	24	of	of	ADP
cana-1296	189	25	mathematics	mathematics	PROPN
cana-1296	189	26	39(2009	39(2009	NUM
cana-1296	189	27	)	)	PUNCT
cana-1296	189	28	,	,	PUNCT
cana-1296	189	29	79	79	NUM
cana-1296	189	30	-	-	SYM
cana-1296	189	31	87	87	NUM
cana-1296	189	32	.	.	PUNCT
cana-1296	190	1	[	[	X
cana-1296	190	2	7	7	NUM
cana-1296	190	3	]	]	SYM
cana-1296	190	4	j.p.kaushik	j.p.kaushik	NOUN
cana-1296	190	5	,	,	PUNCT
cana-1296	190	6	m.a.ansari	m.a.ansari	PROPN
cana-1296	190	7	and	and	CCONJ
cana-1296	190	8	m.r.khan	m.r.khan	ADJ
cana-1296	190	9	,	,	PUNCT
cana-1296	190	10	on	on	ADP
cana-1296	190	11	biγ	biγ	NOUN
cana-1296	190	12	-	-	PUNCT
cana-1296	190	13	ideal	ideal	NOUN
cana-1296	190	14	in	in	ADP
cana-1296	190	15	γ	γ	NOUN
cana-1296	190	16	-	-	PUNCT
cana-1296	190	17	semirings	semiring	NOUN
cana-1296	190	18	,	,	PUNCT
cana-1296	190	19	international	international	ADJ
cana-1296	190	20	journal	journal	NOUN
cana-1296	190	21	of	of	ADP
cana-1296	190	22	contemporary	contemporary	PROPN
cana-1296	190	23	mathematical	mathematical	PROPN
cana-1296	190	24	sciences	sciences	PROPN
cana-1296	190	25	3(2008	3(2008	NUM
cana-1296	190	26	)	)	PUNCT
cana-1296	190	27	,	,	PUNCT
cana-1296	190	28	1255	1255	NUM
cana-1296	190	29	-	-	SYM
cana-1296	190	30	1260	1260	NUM
cana-1296	190	31	.	.	PUNCT
cana-1296	191	1	[	[	X
cana-1296	191	2	8	8	NUM
cana-1296	191	3	]	]	SYM
cana-1296	191	4	s.lajos	s.lajo	NOUN
cana-1296	191	5	,	,	PUNCT
cana-1296	191	6	notes	note	NOUN
cana-1296	191	7	on	on	ADP
cana-1296	191	8	generalized	generalized	ADJ
cana-1296	191	9	bi	bi	NOUN
cana-1296	191	10	-	-	NOUN
cana-1296	191	11	ideals	ideal	NOUN
cana-1296	191	12	in	in	ADP
cana-1296	191	13	semigroups	semigroup	NOUN
cana-1296	191	14	,	,	PUNCT
cana-1296	191	15	soochow	soochow	PROPN
cana-1296	191	16	journal	journal	NOUN
cana-1296	191	17	of	of	ADP
cana-1296	191	18	mathematics	mathematics	PROPN
cana-1296	191	19	10(1984	10(1984	NUM
cana-1296	191	20	)	)	PUNCT
cana-1296	191	21	,	,	PUNCT
cana-1296	191	22	55	55	NUM
cana-1296	191	23	-	-	SYM
cana-1296	191	24	59	59	NUM
cana-1296	191	25	.	.	PUNCT
cana-1296	192	1	[	[	X
cana-1296	192	2	9	9	NUM
cana-1296	192	3	]	]	SYM
cana-1296	192	4	s.pianskool	s.pianskool	NOUN
cana-1296	192	5	,	,	PUNCT
cana-1296	192	6	s.sangwirotjanapat	s.sangwirotjanapat	NOUN
cana-1296	192	7	,	,	PUNCT
cana-1296	192	8	and	and	CCONJ
cana-1296	192	9	s.tipyota	s.tipyota	NOUN
cana-1296	192	10	,	,	PUNCT
cana-1296	192	11	valuation	valuation	NOUN
cana-1296	192	12	γ	γ	PROPN
cana-1296	192	13	-	-	PUNCT
cana-1296	192	14	of	of	ADP
cana-1296	192	15	semirings	semiring	NOUN
cana-1296	192	16	and	and	CCONJ
cana-1296	192	17	valuation	valuation	NOUN
cana-1296	192	18	γ	γ	NOUN
cana-1296	192	19	-	-	NOUN
cana-1296	192	20	ideals	ideal	NOUN
cana-1296	192	21	,	,	PUNCT
cana-1296	192	22	tahi	tahi	NOUN
cana-1296	192	23	journal	journal	NOUN
cana-1296	192	24	of	of	ADP
cana-1296	192	25	mathematics	mathematics	PROPN
cana-1296	192	26	special	special	ADJ
cana-1296	192	27	issue	issue	NOUN
cana-1296	192	28	(	(	PUNCT
cana-1296	192	29	annual	annual	ADJ
cana-1296	192	30	meeting	meeting	NOUN
cana-1296	192	31	in	in	ADP
cana-1296	192	32	mathematics	mathematic	NOUN
cana-1296	192	33	)	)	PUNCT
cana-1296	192	34	(	(	PUNCT
cana-1296	192	35	2008	2008	NUM
cana-1296	192	36	)	)	PUNCT
cana-1296	192	37	,	,	PUNCT
cana-1296	192	38	93	93	NUM
cana-1296	192	39	-	-	SYM
cana-1296	192	40	102	102	NUM
cana-1296	192	41	.	.	PUNCT
cana-1296	193	1	[	[	X
cana-1296	193	2	10	10	NUM
cana-1296	193	3	]	]	SYM
cana-1296	193	4	m.murali	m.murali	PROPN
cana-1296	193	5	krishna	krishna	PROPN
cana-1296	193	6	rao	rao	PROPN
cana-1296	193	7	,	,	PUNCT
cana-1296	193	8	γ	γ	PROPN
cana-1296	193	9	-	-	PUNCT
cana-1296	193	10	semirings	semiring	NOUN
cana-1296	193	11	i	i	PRON
cana-1296	193	12	,	,	PUNCT
cana-1296	193	13	southeast	southeast	ADJ
cana-1296	193	14	asian	asian	ADJ
cana-1296	193	15	bulletin	bulletin	NOUN
cana-1296	193	16	of	of	ADP
cana-1296	193	17	mathematics19(1995	mathematics19(1995	PROPN
cana-1296	193	18	)	)	PUNCT
cana-1296	193	19	,	,	PUNCT
cana-1296	193	20	49	49	NUM
cana-1296	193	21	-	-	SYM
cana-1296	193	22	54	54	NUM
cana-1296	193	23	.	.	PUNCT
cana-1296	194	1	[	[	X
cana-1296	194	2	11	11	NUM
cana-1296	194	3	]	]	PUNCT
cana-1296	194	4	g.	g.	PROPN
cana-1296	194	5	srinivasa	srinivasa	PROPN
cana-1296	194	6	rao	rao	PROPN
cana-1296	194	7	p.siva	p.siva	PROPN
cana-1296	194	8	prasad	prasad	PROPN
cana-1296	194	9	,	,	PUNCT
cana-1296	194	10	m.	m.	NOUN
cana-1296	194	11	vasantha	vasantha	PROPN
cana-1296	194	12	,	,	PUNCT
cana-1296	194	13	dr	dr	PROPN
cana-1296	194	14	.	.	PROPN
cana-1296	194	15	d.	d.	PROPN
cana-1296	194	16	madhusudhana	madhusudhana	PROPN
cana-1296	194	17	rao	rao	PROPN
cana-1296	194	18	“	"	PUNCT
cana-1296	194	19	on	on	ADP
cana-1296	194	20	strongly	strongly	ADV
cana-1296	194	21	duo	duo	NOUN
cana-1296	194	22	and	and	CCONJ
cana-1296	194	23	duo	duo	NOUN
cana-1296	194	24	left	leave	VERB
cana-1296	194	25	γ	γ	PROPN
cana-1296	194	26	-	-	PUNCT
cana-1296	194	27	ts	ts	NOUN
cana-1296	194	28	-	-	PUNCT
cana-1296	194	29	acts	act	NOUN
cana-1296	194	30	over	over	ADP
cana-1296	194	31	ternary	ternary	NOUN
cana-1296	194	32	-	-	PUNCT
cana-1296	194	33	semigroups	semigroup	NOUN
cana-1296	194	34	”	"	PUNCT
cana-1296	194	35	,	,	PUNCT
cana-1296	194	36	international	international	ADJ
cana-1296	194	37	journal	journal	NOUN
cana-1296	194	38	of	of	ADP
cana-1296	194	39	pure	pure	ADJ
cana-1296	194	40	and	and	CCONJ
cana-1296	194	41	applied	applied	ADJ
cana-1296	194	42	mathematics	mathematic	NOUN
cana-1296	194	43	volume	volume	NOUN
cana-1296	194	44	113	113	NUM
cana-1296	194	45	no	no	NOUN
cana-1296	194	46	.	.	PROPN
cana-1296	194	47	6	6	NUM
cana-1296	194	48	2017	2017	NUM
cana-1296	194	49	,	,	PUNCT
cana-1296	194	50	65	65	NUM
cana-1296	194	51	–	–	SYM
cana-1296	194	52	73	73	NUM
cana-1296	194	53	,	,	PUNCT
cana-1296	194	54	issn	issn	NOUN
cana-1296	194	55	:	:	PUNCT
cana-1296	194	56	1311	1311	NUM
cana-1296	194	57	-	-	SYM
cana-1296	194	58	8080	8080	NUM
cana-1296	194	59	(	(	PUNCT
cana-1296	194	60	printed	print	VERB
cana-1296	194	61	version	version	NOUN
cana-1296	194	62	)	)	PUNCT
cana-1296	194	63	;	;	PUNCT
cana-1296	194	64	issn	issn	PROPN
cana-1296	194	65	:	:	PUNCT
cana-1296	194	66	1314	1314	NUM
cana-1296	194	67	-	-	SYM
cana-1296	194	68	3395	3395	NUM
cana-1296	194	69	(	(	PUNCT
cana-1296	194	70	on	on	ADP
cana-1296	194	71	-	-	PUNCT
cana-1296	194	72	line	line	NOUN
cana-1296	194	73	version	version	NOUN
cana-1296	194	74	)	)	PUNCT
cana-1296	194	75	pp	pp	ADP
cana-1296	194	76	67	67	NUM
cana-1296	194	77	-	-	SYM
cana-1296	194	78	73	73	NUM
cana-1296	194	79	.	.	PUNCT
cana-1296	195	1	[	[	X
cana-1296	195	2	12	12	NUM
cana-1296	195	3	]	]	X
cana-1296	195	4	ch	ch	NOUN
cana-1296	195	5	.	.	PUNCT
cana-1296	195	6	manikyarao	manikyarao	PROPN
cana-1296	195	7	p.siva	p.siva	PROPN
cana-1296	195	8	prasad	prasad	PROPN
cana-1296	195	9	,	,	PUNCT
cana-1296	195	10	d.	d.	PROPN
cana-1296	195	11	madhusudhana	madhusudhana	PROPN
cana-1296	195	12	rao	rao	PROPN
cana-1296	195	13	,	,	PUNCT
cana-1296	195	14	g.	g.	PROPN
cana-1296	196	1	srinivasarao,”maximal	srinivasarao,”maximal	PROPN
cana-1296	196	2	ideal	ideal	NOUN
cana-1296	196	3	of	of	ADP
cana-1296	196	4	compact	compact	ADJ
cana-1296	196	5	connected	connect	VERB
cana-1296	196	6	topological	topological	ADJ
cana-1296	196	7	ternary	ternary	ADJ
cana-1296	196	8	semigroups	semigroup	NOUN
cana-1296	196	9	”	"	PUNCT
cana-1296	196	10	international	international	ADJ
cana-1296	196	11	conference	conference	NOUN
cana-1296	196	12	on	on	ADP
cana-1296	196	13	mathematics	mathematics	PROPN
cana-1296	196	14	2015,at	2015,at	NOUN
cana-1296	196	15	:	:	PUNCT
cana-1296	196	16	kerela	kerela	PROPN
cana-1296	196	17	,	,	PUNCT
cana-1296	196	18	volume	volume	NOUN
cana-1296	196	19	:	:	PUNCT
cana-1296	196	20	volume	volume	NOUN
cana-1296	196	21	4	4	NUM
cana-1296	196	22	issue	issue	NOUN
cana-1296	196	23	2	2	NUM
cana-1296	196	24	[	[	SYM
cana-1296	196	25	13	13	NUM
cana-1296	196	26	]	]	PUNCT
cana-1296	196	27	p.	p.	NOUN
cana-1296	196	28	sivaprasad	sivaprasad	PROPN
cana-1296	196	29	,	,	PUNCT
cana-1296	196	30	dr	dr	PROPN
cana-1296	196	31	.	.	PROPN
cana-1296	196	32	d.	d.	PROPN
cana-1296	196	33	madhusudhana	madhusudhana	PROPN
cana-1296	196	34	rao	rao	PROPN
cana-1296	196	35	,	,	PUNCT
cana-1296	196	36	g.	g.	PROPN
cana-1296	196	37	srinivasa	srinivasa	PROPN
cana-1296	196	38	rao	rao	PROPN
cana-1296	196	39	,	,	PUNCT
cana-1296	196	40	”	"	PUNCT
cana-1296	196	41	a	a	DET
cana-1296	196	42	study	study	NOUN
cana-1296	196	43	on	on	ADP
cana-1296	196	44	structure	structure	NOUN
cana-1296	196	45	of	of	ADP
cana-1296	196	46	po	po	NOUN
cana-1296	196	47	-	-	ADJ
cana-1296	196	48	ternary	ternary	ADJ
cana-1296	196	49	semirings	semiring	NOUN
cana-1296	196	50	”	"	PUNCT
cana-1296	196	51	,	,	PUNCT
cana-1296	196	52	journal	journal	NOUN
cana-1296	196	53	of	of	ADP
cana-1296	196	54	advances	advance	NOUN
cana-1296	196	55	in	in	ADP
cana-1296	196	56	mathematics	mathematic	NOUN
cana-1296	196	57	,	,	PUNCT
cana-1296	196	58	vol	vol	NOUN
cana-1296	196	59	.10	.10	NUM
cana-1296	196	60	,	,	PUNCT
cana-1296	196	61	no.8,pp:3717	no.8,pp:3717	NOUN
cana-1296	196	62	-	-	PUNCT
cana-1296	196	63	3724	3724	NUM
cana-1296	196	64	.	.	PUNCT
cana-1296	197	1	[	[	X
cana-1296	197	2	14	14	NUM
cana-1296	197	3	]	]	PUNCT
cana-1296	197	4	p.	p.	NOUN
cana-1296	197	5	sivaprasad	sivaprasad	PROPN
cana-1296	197	6	,	,	PUNCT
cana-1296	197	7	dr	dr	PROPN
cana-1296	197	8	.	.	PROPN
cana-1296	197	9	d.	d.	PROPN
cana-1296	197	10	madhusudhana	madhusudhana	PROPN
cana-1296	197	11	rao	rao	PROPN
cana-1296	197	12	,	,	PUNCT
cana-1296	197	13	mamidipalli	mamidipalli	PROPN
cana-1296	197	14	.	.	PUNCT
cana-1296	198	1	vasantha	vasantha	PROPN
cana-1296	198	2	,	,	PUNCT
cana-1296	198	3	,	,	PUNCT
cana-1296	198	4	b.	b.	PROPN
cana-1296	198	5	srinivasa	srinivasa	PROPN
cana-1296	198	6	kumar	kumar	PROPN
cana-1296	198	7	,	,	PUNCT
cana-1296	198	8	”	"	PUNCT
cana-1296	198	9	on	on	ADP
cana-1296	198	10	γ	γ	PROPN
cana-1296	198	11	-	-	PUNCT
cana-1296	198	12	ts	ts	NOUN
cana-1296	198	13	-	-	PUNCT
cana-1296	198	14	acts	act	NOUN
cana-1296	198	15	over	over	ADP
cana-1296	198	16	ternary	ternary	ADJ
cana-1296	198	17	γ	γ	PROPN
cana-1296	198	18	-	-	PUNCT
cana-1296	198	19	semigroups	semigroup	NOUN
cana-1296	198	20	”	"	PUNCT
cana-1296	198	21	international	international	ADJ
cana-1296	198	22	journal	journal	NOUN
cana-1296	198	23	of	of	ADP
cana-1296	198	24	engineering	engineering	PROPN
cana-1296	198	25	&	&	CCONJ
cana-1296	198	26	technology	technology	PROPN
cana-1296	198	27	,	,	PUNCT
cana-1296	198	28	7	7	NUM
cana-1296	198	29	(	(	PUNCT
cana-1296	198	30	4.10	4.10	NUM
cana-1296	198	31	)	)	PUNCT
cana-1296	198	32	(	(	PUNCT
cana-1296	198	33	2018)pp:812	2018)pp:812	NUM
cana-1296	198	34	-	-	SYM
cana-1296	198	35	815	815	NUM
cana-1296	198	36	.	.	PUNCT
cana-1296	199	1	[	[	X
cana-1296	199	2	15	15	NUM
cana-1296	199	3	]	]	X
cana-1296	199	4	siva	siva	PROPN
cana-1296	199	5	prasad.p	prasad.p	PROPN
cana-1296	199	6	,	,	PUNCT
cana-1296	199	7	revathi.k	revathi.k	PROPN
cana-1296	199	8	,	,	PUNCT
cana-1296	199	9	2	2	NUM
cana-1296	199	10	,	,	PUNCT
cana-1296	199	11	sundarayya.p	sundarayya.p	NOUN
cana-1296	199	12	,	,	PUNCT
cana-1296	199	13	madhusudhana	madhusudhana	PROPN
cana-1296	199	14	rao.d	rao.d	PUNCT
cana-1296	199	15	,	,	PUNCT
cana-1296	199	16	“	"	PUNCT
cana-1296	199	17	compositions	composition	NOUN
cana-1296	199	18	of	of	ADP
cana-1296	199	19	fuzzy	fuzzy	ADJ
cana-1296	199	20	t	t	NOUN
cana-1296	199	21	-	-	PUNCT
cana-1296	199	22	ideals	ideal	NOUN
cana-1296	199	23	in	in	ADP
cana-1296	199	24	ternary	ternary	ADJ
cana-1296	199	25	semi	semi	ADJ
cana-1296	199	26	ring	ring	NOUN
cana-1296	199	27	”	"	PUNCT
cana-1296	199	28	,	,	PUNCT
cana-1296	199	29	international	international	ADJ
cana-1296	199	30	journal	journal	NOUN
cana-1296	199	31	of	of	ADP
cana-1296	199	32	advanced	advanced	ADJ
cana-1296	199	33	in	in	ADP
cana-1296	199	34	management	management	NOUN
cana-1296	199	35	,	,	PUNCT
cana-1296	199	36	technology	technology	NOUN
cana-1296	199	37	and	and	CCONJ
cana-1296	199	38	engineering	engineering	NOUN
cana-1296	199	39	sciences	science	NOUN
cana-1296	199	40	volume	volume	NOUN
cana-1296	199	41	7	7	NUM
cana-1296	199	42	,	,	PUNCT
cana-1296	199	43	issue	issue	NOUN
cana-1296	199	44	12	12	NUM
cana-1296	199	45	,	,	PUNCT
cana-1296	199	46	2017	2017	NUM
cana-1296	199	47	issn	issn	VERB
cana-1296	199	48	no	no	DET
cana-1296	199	49	:	:	PUNCT
cana-1296	199	50	2249	2249	NUM
cana-1296	199	51	-	-	PUNCT
cana-1296	199	52	7455,pp:135	7455,pp:135	NUM
cana-1296	199	53	-	-	NUM
cana-1296	199	54	145	145	NUM
cana-1296	199	55	.	.	PUNCT
cana-1296	200	1	[	[	X
cana-1296	200	2	16	16	NUM
cana-1296	200	3	]	]	PUNCT
cana-1296	200	4	p.	p.	PROPN
cana-1296	200	5	sivaprasad	sivaprasad	PROPN
cana-1296	200	6	,	,	PUNCT
cana-1296	200	7	c.	c.	PROPN
cana-1296	200	8	sreemannarayana	sreemannarayana	PROPN
cana-1296	200	9	,	,	PUNCT
cana-1296	200	10	d.	d.	PROPN
cana-1296	200	11	madhusudhana	madhusudhana	PROPN
cana-1296	200	12	rao	rao	PROPN
cana-1296	200	13	,	,	PUNCT
cana-1296	200	14	t.	t.	PROPN
cana-1296	200	15	nageswara	nageswara	PROPN
cana-1296	200	16	rao	rao	PROPN
cana-1296	200	17	,	,	PUNCT
cana-1296	200	18	k.	k.	PROPN
cana-1296	200	19	anuradha	anuradha	PROPN
cana-1296	200	20	,	,	PUNCT
cana-1296	200	21	”	"	PUNCT
cana-1296	200	22	on	on	ADP
cana-1296	200	23	leternary	leternary	ADJ
cana-1296	200	24	semi	semi	ADJ
cana-1296	200	25	groups	group	NOUN
cana-1296	200	26	-	-	PUNCT
cana-1296	200	27	i	i	PROPN
cana-1296	200	28	”	"	PUNCT
cana-1296	200	29	international	international	ADJ
cana-1296	200	30	journal	journal	NOUN
cana-1296	200	31	of	of	ADP
cana-1296	200	32	recent	recent	ADJ
cana-1296	200	33	technology	technology	NOUN
cana-1296	200	34	and	and	CCONJ
cana-1296	200	35	engineering	engineering	NOUN
cana-1296	200	36	(	(	PUNCT
cana-1296	200	37	ijrte	ijrte	NOUN
cana-1296	200	38	)	)	PUNCT
cana-1296	200	39	issn	issn	PROPN
cana-1296	200	40	:	:	PUNCT
cana-1296	200	41	2277	2277	NUM
cana-1296	200	42	-	-	SYM
cana-1296	200	43	3878	3878	NUM
cana-1296	200	44	,	,	PUNCT
cana-1296	200	45	volume-7	volume-7	ADJ
cana-1296	200	46	,	,	PUNCT
cana-1296	200	47	issueicetesm	issueicetesm	NOUN
cana-1296	200	48	,	,	PUNCT
cana-1296	200	49	march	march	PROPN
cana-1296	200	50	2019,pp:165	2019,pp:165	NUM
cana-1296	200	51	-	-	PUNCT
cana-1296	200	52	167	167	NUM
cana-1296	200	53	.	.	PUNCT
cana-1296	201	1	[	[	X
cana-1296	201	2	17	17	NUM
cana-1296	201	3	]	]	PUNCT
cana-1296	201	4	p.	p.	PROPN
cana-1296	201	5	sivaprasad	sivaprasad	PROPN
cana-1296	201	6	,	,	PUNCT
cana-1296	201	7	c.	c.	PROPN
cana-1296	201	8	sreemannarayana	sreemannarayana	PROPN
cana-1296	201	9	,	,	PUNCT
cana-1296	201	10	d.	d.	PROPN
cana-1296	201	11	madhusudhana	madhusudhana	PROPN
cana-1296	201	12	rao	rao	PROPN
cana-1296	201	13	,	,	PUNCT
cana-1296	201	14	t.	t.	PROPN
cana-1296	201	15	nageswara	nageswara	PROPN
cana-1296	201	16	rao	rao	PROPN
cana-1296	201	17	,	,	PUNCT
cana-1296	201	18	sajani	sajani	PROPN
cana-1296	201	19	lavanya	lavanya	NOUN
cana-1296	201	20	.	.	PUNCT
cana-1296	202	1	m	m	PROPN
cana-1296	202	2	,	,	PUNCT
cana-1296	202	3	”	"	PUNCT
cana-1296	202	4	on	on	ADP
cana-1296	202	5	leternary	leternary	ADJ
cana-1296	202	6	semi	semi	ADJ
cana-1296	202	7	groups	groups	PROPN
cana-1296	202	8	-	-	PUNCT
cana-1296	202	9	ii	ii	NOUN
cana-1296	202	10	”	"	PUNCT
cana-1296	202	11	international	international	ADJ
cana-1296	202	12	journal	journal	NOUN
cana-1296	202	13	of	of	ADP
cana-1296	202	14	recent	recent	ADJ
cana-1296	202	15	technology	technology	NOUN
cana-1296	202	16	and	and	CCONJ
cana-1296	202	17	engineering	engineering	NOUN
cana-1296	202	18	(	(	PUNCT
cana-1296	202	19	ijrte	ijrte	NOUN
cana-1296	202	20	)	)	PUNCT
cana-1296	202	21	issn	issn	PROPN
cana-1296	202	22	:	:	PUNCT
cana-1296	202	23	2277	2277	NUM
cana-1296	202	24	-	-	SYM
cana-1296	202	25	3878	3878	NUM
cana-1296	202	26	,	,	PUNCT
cana-1296	202	27	volume-7	volume-7	ADJ
cana-1296	202	28	,	,	PUNCT
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cana-1296	202	30	-	-	PUNCT
cana-1296	202	31	icetesm	icetesm	NOUN
cana-1296	202	32	,	,	PUNCT
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cana-1296	202	35	-	-	SYM
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cana-1296	202	37	.	.	PUNCT
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cana-1296	203	2	18	18	NUM
cana-1296	203	3	]	]	X
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cana-1296	203	5	and	and	CCONJ
cana-1296	203	6	u.dasgupta	u.dasgupta	NOUN
cana-1296	203	7	,	,	PUNCT
cana-1296	203	8	on	on	ADP
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cana-1296	203	10	γ	γ	NOUN
cana-1296	203	11	-	-	PUNCT
cana-1296	203	12	semirings	semiring	NOUN
cana-1296	203	13	,	,	PUNCT
cana-1296	203	14	novi	novi	PROPN
cana-1296	203	15	sad	sad	PROPN
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cana-1296	203	17	of	of	ADP
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cana-1296	203	20	)	)	PUNCT
cana-1296	203	21	,	,	PUNCT
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cana-1296	203	23	-	-	SYM
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cana-1296	203	25	.	.	PUNCT
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cana-1296	204	2	19	19	NUM
cana-1296	204	3	]	]	X
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cana-1296	204	5	,	,	PUNCT
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cana-1296	204	7	biideals	biideal	NOUN
cana-1296	204	8	of	of	ADP
cana-1296	204	9	rings	ring	NOUN
cana-1296	204	10	i	i	PRON
cana-1296	204	11	,	,	PUNCT
cana-1296	204	12	mathematische	mathematische	PROPN
cana-1296	204	13	nachrichten	nachrichten	PROPN
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cana-1296	204	15	)	)	PUNCT
cana-1296	204	16	,	,	PUNCT
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cana-1296	204	18	-	-	SYM
cana-1296	204	19	360	360	NUM
cana-1296	204	20	.	.	PUNCT
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cana-1296	205	2	20	20	NUM
cana-1296	205	3	]	]	X
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cana-1296	205	11	,	,	PUNCT
cana-1296	205	12	mathematische	mathematische	PROPN
cana-1296	205	13	nachrichten	nachrichten	PROPN
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cana-1296	205	15	)	)	PUNCT
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cana-1296	205	21	21	21	NUM
cana-1296	205	22	]	]	PUNCT
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cana-1296	205	25	,	,	PUNCT
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cana-1296	205	40	,	,	PUNCT
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cana-1296	205	42	)	)	PUNCT
cana-1296	205	43	,	,	PUNCT
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cana-1296	205	45	-	-	PUNCT
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cana-1296	206	2	22	22	NUM
cana-1296	206	3	]	]	PUNCT
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cana-1296	206	6	,	,	PUNCT
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cana-1296	206	21	,	,	PUNCT
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cana-1296	206	28	-	-	PUNCT
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cana-1296	206	30	.	.	PUNCT
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cana-1296	207	2	23	23	NUM
cana-1296	207	3	]	]	PUNCT
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cana-1296	208	2	24	24	NUM
cana-1296	208	3	]	]	PUNCT
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cana-1296	208	15	bi	bi	NOUN
cana-1296	208	16	-	-	NOUN
cana-1296	208	17	ideals	ideal	NOUN
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cana-1296	208	20	г	г	PROPN
cana-1296	208	21	-	-	PUNCT
cana-1296	208	22	so	so	ADV
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cana-1296	208	31	,	,	PUNCT
cana-1296	208	32	2375	2375	NUM
cana-1296	208	33	,	,	PUNCT
cana-1296	208	34	0066394	0066394	NUM
cana-1296	208	35	.	.	PUNCT
cana-1296	209	1	communications	communication	NOUN
cana-1296	209	2	on	on	ADP
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cana-1296	209	4	nonlinear	nonlinear	ADJ
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cana-1296	209	6	issn	issn	NOUN
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cana-1296	209	8	1074	1074	NUM
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cana-1296	211	2	25	25	NUM
cana-1296	211	3	]	]	SYM
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cana-1296	211	5	,	,	PUNCT
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cana-1296	211	9	-	-	NOUN
cana-1296	211	10	ideals	ideal	NOUN
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cana-1296	211	12	ternary	ternary	ADJ
cana-1296	211	13	г	г	PROPN
cana-1296	211	14	-	-	PUNCT
cana-1296	211	15	so	so	ADV
cana-1296	211	16	-	-	PUNCT
cana-1296	211	17	semirings	semiring	NOUN
cana-1296	211	18	,	,	PUNCT
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cana-1296	211	21	proceedings	proceeding	NOUN
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cana-1296	211	23	2021	2021	NUM
cana-1296	211	24	,	,	PUNCT
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cana-1296	212	3	]	]	PUNCT
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cana-1296	212	6	rao	rao	PROPN
cana-1296	212	7	,	,	PUNCT
cana-1296	212	8	d.	d.	PROPN
cana-1296	212	9	madhusudhanarao	madhusudhanarao	PROPN
cana-1296	212	10	and	and	CCONJ
cana-1296	212	11	p.	p.	PROPN
cana-1296	212	12	siva	siva	PROPN
cana-1296	212	13	prasad	prasad	PROPN
cana-1296	212	14	,	,	PUNCT
cana-1296	212	15	simple	simple	ADJ
cana-1296	212	16	ternary	ternary	ADJ
cana-1296	212	17	semi	semi	NOUN
cana-1296	212	18	-	-	NOUN
cana-1296	212	19	rings	ring	NOUN
cana-1296	212	20	,	,	PUNCT
cana-1296	212	21	the	the	DET
cana-1296	212	22	global	global	ADJ
cana-1296	212	23	journal	journal	NOUN
cana-1296	212	24	of	of	ADP
cana-1296	212	25	mathematics	mathematics	PROPN
cana-1296	212	26	&	&	CCONJ
cana-1296	212	27	mathematical	mathematical	PROPN
cana-1296	212	28	sciences	sciences	PROPN
cana-1296	212	29	,	,	PUNCT
cana-1296	212	30	9(2	9(2	NUM
cana-1296	212	31	)	)	PUNCT
cana-1296	212	32	(	(	PUNCT
cana-1296	212	33	2016	2016	NUM
cana-1296	212	34	)	)	PUNCT
cana-1296	212	35	,	,	PUNCT
cana-1296	212	36	185	185	NUM
cana-1296	212	37	-	-	SYM
cana-1296	212	38	196	196	NUM
cana-1296	212	39	.	.	PUNCT
cana-1296	213	1	[	[	X
cana-1296	213	2	27	27	NUM
cana-1296	213	3	]	]	X
cana-1296	213	4	d.	d.	PROPN
cana-1296	213	5	madhusudhana	madhusudhana	PROPN
cana-1296	213	6	rao	rao	PROPN
cana-1296	213	7	,	,	PUNCT
cana-1296	213	8	g.	g.	PROPN
cana-1296	213	9	srinivasa	srinivasa	PROPN
cana-1296	213	10	rao	rao	PROPN
cana-1296	213	11	,	,	PUNCT
cana-1296	213	12	special	special	ADJ
cana-1296	213	13	elements	element	NOUN
cana-1296	213	14	in	in	ADP
cana-1296	213	15	ternary	ternary	ADJ
cana-1296	213	16	semi	semi	ADJ
cana-1296	213	17	rings	ring	NOUN
cana-1296	213	18	,	,	PUNCT
cana-1296	213	19	international	international	ADJ
cana-1296	213	20	journal	journal	NOUN
cana-1296	213	21	of	of	ADP
cana-1296	213	22	engineering	engineering	NOUN
cana-1296	213	23	research	research	NOUN
cana-1296	213	24	and	and	CCONJ
cana-1296	213	25	applications	application	NOUN
cana-1296	213	26	,	,	PUNCT
cana-1296	213	27	4(11	4(11	NUM
cana-1296	213	28	)	)	PUNCT
cana-1296	213	29	(	(	PUNCT
cana-1296	213	30	2014	2014	NUM
cana-1296	213	31	)	)	PUNCT
cana-1296	213	32	,	,	PUNCT
cana-1296	213	33	123	123	NUM
cana-1296	213	34	-	-	SYM
cana-1296	213	35	130	130	NUM
cana-1296	213	36	.	.	PUNCT
cana-1296	214	1	[	[	X
cana-1296	214	2	28	28	NUM
cana-1296	214	3	]	]	X
cana-1296	214	4	g.	g.	PROPN
cana-1296	214	5	srinivasa	srinivasa	PROPN
cana-1296	214	6	rao	rao	PROPN
cana-1296	214	7	,	,	PUNCT
cana-1296	214	8	d.	d.	PROPN
cana-1296	214	9	madhusudhana	madhusudhana	PROPN
cana-1296	214	10	rao	rao	PROPN
cana-1296	214	11	,	,	PUNCT
cana-1296	214	12	structure	structure	NOUN
cana-1296	214	13	of	of	ADP
cana-1296	214	14	certain	certain	ADJ
cana-1296	214	15	ideals	ideal	NOUN
cana-1296	214	16	in	in	ADP
cana-1296	214	17	ternary	ternary	ADJ
cana-1296	214	18	semi	semi	ADJ
cana-1296	214	19	rings	ring	NOUN
cana-1296	214	20	,	,	PUNCT
cana-1296	214	21	int	int	NOUN
cana-1296	214	22	.	.	PUNCT
cana-1296	215	1	j.	j.	PROPN
cana-1296	215	2	of	of	ADP
cana-1296	215	3	innovative	innovative	ADJ
cana-1296	215	4	science	science	NOUN
cana-1296	215	5	and	and	CCONJ
cana-1296	215	6	modern	modern	ADJ
cana-1296	215	7	engg	engg	PROPN
cana-1296	215	8	.	.	PUNCT
cana-1296	215	9	,	,	PUNCT
cana-1296	215	10	3(3	3(3	NUM
cana-1296	215	11	)	)	PUNCT
cana-1296	215	12	(	(	PUNCT
cana-1296	215	13	2015	2015	NUM
cana-1296	215	14	)	)	PUNCT
cana-1296	215	15	,	,	PUNCT
cana-1296	215	16	49	49	NUM
cana-1296	215	17	-	-	SYM
cana-1296	215	18	56	56	NUM
cana-1296	215	19	.	.	PUNCT
cana-1296	216	1	[	[	X
cana-1296	216	2	29	29	NUM
cana-1296	216	3	]	]	X
cana-1296	216	4	g.	g.	PROPN
cana-1296	216	5	srinivasa	srinivasa	PROPN
cana-1296	216	6	rao	rao	PROPN
cana-1296	216	7	,	,	PUNCT
cana-1296	216	8	d.	d.	PROPN
cana-1296	216	9	madhusudhana	madhusudhana	PROPN
cana-1296	216	10	rao	rao	PROPN
cana-1296	216	11	,	,	PUNCT
cana-1296	216	12	a	a	DET
cana-1296	216	13	study	study	NOUN
cana-1296	216	14	on	on	ADP
cana-1296	216	15	ternary	ternary	ADJ
cana-1296	216	16	semi	semi	ADJ
cana-1296	216	17	rings	ring	NOUN
cana-1296	216	18	,	,	PUNCT
cana-1296	216	19	int	int	NOUN
cana-1296	216	20	.	.	PUNCT
cana-1296	217	1	j.	j.	PROPN
cana-1296	217	2	of	of	ADP
cana-1296	217	3	math	math	PROPN
cana-1296	217	4	.	.	PUNCT
cana-1296	218	1	archive	archive	NOUN
cana-1296	218	2	,	,	PUNCT
cana-1296	218	3	5(12	5(12	NUM
cana-1296	218	4	)	)	PUNCT
cana-1296	218	5	(	(	PUNCT
cana-1296	218	6	2014	2014	NUM
cana-1296	218	7	)	)	PUNCT
cana-1296	218	8	,	,	PUNCT
cana-1296	218	9	2430	2430	NUM
cana-1296	218	10	.	.	PUNCT
cana-1296	219	1	[	[	X
cana-1296	219	2	30	30	NUM
cana-1296	219	3	]	]	X
cana-1296	219	4	g.	g.	PROPN
cana-1296	219	5	srinivasa	srinivasa	PROPN
cana-1296	219	6	rao	rao	PROPN
cana-1296	219	7	,	,	PUNCT
cana-1296	219	8	d.	d.	PROPN
cana-1296	219	9	madhusudhana	madhusudhana	PROPN
cana-1296	219	10	rao	rao	PROPN
cana-1296	219	11	,	,	PUNCT
cana-1296	219	12	characteristics	characteristic	NOUN
cana-1296	219	13	of	of	ADP
cana-1296	219	14	ternary	ternary	ADJ
cana-1296	219	15	semi	semi	ADJ
cana-1296	219	16	rings	ring	NOUN
cana-1296	219	17	,	,	PUNCT
cana-1296	219	18	int.j	int.j	PROPN
cana-1296	219	19	.	.	PROPN
cana-1296	219	20	of	of	ADP
cana-1296	219	21	engg	engg	PROPN
cana-1296	219	22	.	.	PUNCT
cana-1296	220	1	res	re	NOUN
cana-1296	220	2	.	.	PUNCT
cana-1296	220	3	and	and	CCONJ
cana-1296	220	4	mgt	mgt	PROPN
cana-1296	220	5	.	.	PUNCT
cana-1296	220	6	,	,	PUNCT
cana-1296	220	7	2(1	2(1	NUM
cana-1296	220	8	)	)	PUNCT
cana-1296	220	9	(	(	PUNCT
cana-1296	220	10	2015	2015	NUM
cana-1296	220	11	)	)	PUNCT
cana-1296	220	12	,	,	PUNCT
cana-1296	220	13	3	3	NUM
cana-1296	220	14	-	-	SYM
cana-1296	220	15	6	6	NUM
cana-1296	220	16	.	.	PUNCT