id	sid	tid	token	lemma	pos
cana-2736	1	1	communications	communication	NOUN
cana-2736	1	2	on	on	ADP
cana-2736	1	3	applied	apply	VERB
cana-2736	1	4	nonlinear	nonlinear	ADJ
cana-2736	1	5	analysis	analysis	NOUN
cana-2736	1	6	issn	issn	NOUN
cana-2736	1	7	:	:	PUNCT
cana-2736	1	8	1074	1074	NUM
cana-2736	1	9	-	-	PUNCT
cana-2736	1	10	133x	133x	NUM
cana-2736	1	11	vol	vol	NOUN
cana-2736	1	12	32	32	NUM
cana-2736	1	13	no	no	NOUN
cana-2736	1	14	.	.	PUNCT
cana-2736	2	1	4s	4s	NUM
cana-2736	2	2	(	(	PUNCT
cana-2736	2	3	2025	2025	NUM
cana-2736	2	4	)	)	PUNCT
cana-2736	2	5	12	12	NUM
cana-2736	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-2736	2	7	endomorphisms	endomorphism	NOUN
cana-2736	2	8	and	and	CCONJ
cana-2736	2	9	their	their	PRON
cana-2736	2	10	role	role	NOUN
cana-2736	2	11	in	in	ADP
cana-2736	2	12	novel	novel	ADJ
cana-2736	2	13	derivations	derivation	NOUN
cana-2736	2	14	of	of	ADP
cana-2736	2	15	hilbert	hilbert	PROPN
cana-2736	2	16	algebras	algebras	PROPN
cana-2736	2	17	aiyared	aiyare	VERB
cana-2736	2	18	iampan1	iampan1	PROPN
cana-2736	2	19	,	,	PUNCT
cana-2736	2	20	*	*	PROPN
cana-2736	2	21	,	,	PUNCT
cana-2736	2	22	r.	r.	PROPN
cana-2736	2	23	vennila2	vennila2	PROPN
cana-2736	2	24	,	,	PUNCT
cana-2736	2	25	neelamegarajan	neelamegarajan	NOUN
cana-2736	2	26	rajesh3	rajesh3	PROPN
cana-2736	2	27	,	,	PUNCT
cana-2736	2	28	c.	c.	PROPN
cana-2736	2	29	arivazhagi4	arivazhagi4	PROPN
cana-2736	3	1	1department	1department	NUM
cana-2736	3	2	of	of	ADP
cana-2736	3	3	mathematics	mathematic	NOUN
cana-2736	3	4	,	,	PUNCT
cana-2736	3	5	school	school	NOUN
cana-2736	3	6	of	of	ADP
cana-2736	3	7	science	science	NOUN
cana-2736	3	8	,	,	PUNCT
cana-2736	3	9	university	university	NOUN
cana-2736	3	10	of	of	ADP
cana-2736	3	11	phayao	phayao	NOUN
cana-2736	3	12	,	,	PUNCT
cana-2736	3	13	mae	mae	PROPN
cana-2736	3	14	ka	ka	PROPN
cana-2736	3	15	,	,	PUNCT
cana-2736	3	16	mueang	mueang	PROPN
cana-2736	3	17	,	,	PUNCT
cana-2736	3	18	phayao	phayao	NOUN
cana-2736	3	19	56000	56000	NUM
cana-2736	3	20	,	,	PUNCT
cana-2736	3	21	thailand	thailand	PROPN
cana-2736	3	22	.	.	PUNCT
cana-2736	4	1	27405	27405	NUM
cana-2736	4	2	goreway	goreway	PROPN
cana-2736	4	3	drive	drive	NOUN
cana-2736	4	4	,	,	PUNCT
cana-2736	4	5	mississauga	mississauga	PROPN
cana-2736	4	6	l4t0a3	l4t0a3	PROPN
cana-2736	4	7	,	,	PUNCT
cana-2736	4	8	canada	canada	PROPN
cana-2736	4	9	.	.	PUNCT
cana-2736	5	1	3department	3department	NUM
cana-2736	5	2	of	of	ADP
cana-2736	5	3	mathematics	mathematic	NOUN
cana-2736	5	4	,	,	PUNCT
cana-2736	5	5	rajah	rajah	NOUN
cana-2736	5	6	serfoji	serfoji	ADJ
cana-2736	5	7	government	government	NOUN
cana-2736	5	8	college	college	NOUN
cana-2736	5	9	(	(	PUNCT
cana-2736	5	10	affiliated	affiliate	VERB
cana-2736	5	11	to	to	PART
cana-2736	5	12	bharathidasan	bharathidasan	VERB
cana-2736	5	13	university	university	NOUN
cana-2736	5	14	)	)	PUNCT
cana-2736	5	15	,	,	PUNCT
cana-2736	5	16	thanjavur613005	thanjavur613005	PROPN
cana-2736	5	17	,	,	PUNCT
cana-2736	5	18	tamilnadu	tamilnadu	NOUN
cana-2736	5	19	,	,	PUNCT
cana-2736	5	20	india	india	PROPN
cana-2736	5	21	.	.	PUNCT
cana-2736	6	1	4department	4department	NUM
cana-2736	6	2	of	of	ADP
cana-2736	6	3	mathematics	mathematic	NOUN
cana-2736	6	4	,	,	PUNCT
cana-2736	6	5	government	government	NOUN
cana-2736	6	6	arts	art	NOUN
cana-2736	6	7	and	and	CCONJ
cana-2736	6	8	science	science	PROPN
cana-2736	6	9	college	college	PROPN
cana-2736	6	10	,	,	PUNCT
cana-2736	6	11	peravurani-614804	peravurani-614804	NOUN
cana-2736	6	12	,	,	PUNCT
cana-2736	6	13	tamilnadu	tamilnadu	NOUN
cana-2736	6	14	,	,	PUNCT
cana-2736	6	15	india	india	PROPN
cana-2736	6	16	.	.	PUNCT
cana-2736	7	1	e	e	X
cana-2736	7	2	-	-	NOUN
cana-2736	7	3	mail	mail	NOUN
cana-2736	7	4	:	:	PUNCT
cana-2736	7	5	1aiyared.ia@up.ac.th	1aiyared.ia@up.ac.th	NUM
cana-2736	7	6	,	,	PUNCT
cana-2736	7	7	2vennilamaths@gmail.com	2vennilamaths@gmail.com	NUM
cana-2736	7	8	,	,	PUNCT
cana-2736	7	9	3nrajesh_topology@yahoo.co.in	3nrajesh_topology@yahoo.co.in	NUM
cana-2736	7	10	,	,	PUNCT
cana-2736	7	11	4arivuniralya@gmail.com	4arivuniralya@gmail.com	NOUN
cana-2736	7	12	*	*	PUNCT
cana-2736	7	13	corresponding	correspond	VERB
cana-2736	7	14	author	author	NOUN
cana-2736	7	15	:	:	PUNCT
cana-2736	7	16	aiyared	aiyare	VERB
cana-2736	7	17	iampan	iampan	PROPN
cana-2736	7	18	article	article	NOUN
cana-2736	7	19	history	history	NOUN
cana-2736	7	20	:	:	PUNCT
cana-2736	7	21	received	receive	VERB
cana-2736	7	22	:	:	PUNCT
cana-2736	7	23	10	10	NUM
cana-2736	7	24	-	-	SYM
cana-2736	7	25	09	09	NUM
cana-2736	7	26	-	-	PUNCT
cana-2736	7	27	2024	2024	NUM
cana-2736	7	28	revised	revise	VERB
cana-2736	7	29	:	:	PUNCT
cana-2736	7	30	16	16	NUM
cana-2736	7	31	-	-	SYM
cana-2736	7	32	11	11	NUM
cana-2736	7	33	-	-	PUNCT
cana-2736	7	34	2024	2024	NUM
cana-2736	7	35	accepted	accept	VERB
cana-2736	7	36	:	:	PUNCT
cana-2736	7	37	26	26	NUM
cana-2736	7	38	-	-	SYM
cana-2736	7	39	11	11	NUM
cana-2736	7	40	-	-	PUNCT
cana-2736	7	41	2024	2024	NUM
cana-2736	7	42	abstract	abstract	NOUN
cana-2736	7	43	:	:	PUNCT
cana-2736	7	44	this	this	DET
cana-2736	7	45	study	study	NOUN
cana-2736	7	46	introduces	introduce	NOUN
cana-2736	7	47	and	and	CCONJ
cana-2736	7	48	explores	explore	NOUN
cana-2736	7	49	leftf	leftf	VERB
cana-2736	7	50	-derivations	-derivation	NOUN
cana-2736	7	51	,	,	PUNCT
cana-2736	7	52	rightf	rightf	ADJ
cana-2736	7	53	-derivations	-derivation	NOUN
cana-2736	7	54	,	,	PUNCT
cana-2736	7	55	and	and	CCONJ
cana-2736	7	56	f	f	PROPN
cana-2736	7	57	derivations	derivation	NOUN
cana-2736	7	58	of	of	ADP
cana-2736	7	59	type	type	NOUN
cana-2736	7	60	i	i	PRON
cana-2736	7	61	and	and	CCONJ
cana-2736	7	62	type	type	NOUN
cana-2736	7	63	ii	ii	PROPN
cana-2736	7	64	within	within	ADP
cana-2736	7	65	the	the	DET
cana-2736	7	66	framework	framework	NOUN
cana-2736	7	67	of	of	ADP
cana-2736	7	68	hilbert	hilbert	PROPN
cana-2736	7	69	algebras	algebras	PROPN
cana-2736	7	70	,	,	PUNCT
cana-2736	7	71	focusing	focus	VERB
cana-2736	7	72	on	on	ADP
cana-2736	7	73	their	their	PRON
cana-2736	7	74	fundamental	fundamental	ADJ
cana-2736	7	75	properties	property	NOUN
cana-2736	7	76	and	and	CCONJ
cana-2736	7	77	structural	structural	ADJ
cana-2736	7	78	significance	significance	NOUN
cana-2736	7	79	.	.	PUNCT
cana-2736	8	1	we	we	PRON
cana-2736	8	2	show	show	VERB
cana-2736	8	3	that	that	SCONJ
cana-2736	8	4	the	the	DET
cana-2736	8	5	kernel	kernel	NOUN
cana-2736	8	6	of	of	ADP
cana-2736	8	7	an	an	DET
cana-2736	8	8	f	f	PROPN
cana-2736	8	9	-derivation	-derivation	PROPN
cana-2736	8	10	,	,	PUNCT
cana-2736	8	11	ker	ker	NOUN
cana-2736	8	12	(	(	PUNCT
cana-2736	8	13	)	)	PUNCT
cana-2736	8	14	d	d	X
cana-2736	8	15	a	a	PRON
cana-2736	8	16	,	,	PUNCT
cana-2736	8	17	forms	form	VERB
cana-2736	8	18	a	a	DET
cana-2736	8	19	near	near	ADJ
cana-2736	8	20	filter	filter	NOUN
cana-2736	8	21	and	and	CCONJ
cana-2736	8	22	operates	operate	VERB
cana-2736	8	23	as	as	ADP
cana-2736	8	24	a	a	DET
cana-2736	8	25	subalgebra	subalgebra	NOUN
cana-2736	8	26	of	of	ADP
cana-2736	8	27	the	the	DET
cana-2736	8	28	hilbert	hilbert	PROPN
cana-2736	8	29	algebra	algebra	PROPN
cana-2736	8	30	a	a	PRON
cana-2736	8	31	.	.	PUNCT
cana-2736	9	1	these	these	DET
cana-2736	9	2	findings	finding	NOUN
cana-2736	9	3	enhance	enhance	VERB
cana-2736	9	4	the	the	DET
cana-2736	9	5	understanding	understanding	NOUN
cana-2736	9	6	of	of	ADP
cana-2736	9	7	hilbert	hilbert	PROPN
cana-2736	9	8	algebras	algebras	PROPN
cana-2736	9	9	and	and	CCONJ
cana-2736	9	10	offer	offer	VERB
cana-2736	9	11	new	new	ADJ
cana-2736	9	12	perspectives	perspective	NOUN
cana-2736	9	13	on	on	ADP
cana-2736	9	14	the	the	DET
cana-2736	9	15	role	role	NOUN
cana-2736	9	16	of	of	ADP
cana-2736	9	17	derivations	derivation	NOUN
cana-2736	9	18	in	in	ADP
cana-2736	9	19	algebraic	algebraic	ADJ
cana-2736	9	20	logic	logic	NOUN
cana-2736	9	21	.	.	PUNCT
cana-2736	10	1	keywords	keyword	NOUN
cana-2736	10	2	:	:	PUNCT
cana-2736	10	3	hilbert	hilbert	PROPN
cana-2736	10	4	algebra	algebra	PROPN
cana-2736	10	5	,	,	PUNCT
cana-2736	10	6	near	near	ADP
cana-2736	10	7	filter	filter	NOUN
cana-2736	10	8	,	,	PUNCT
cana-2736	10	9	subalgebra	subalgebra	NOUN
cana-2736	10	10	,	,	PUNCT
cana-2736	10	11	leftf	leftf	ADJ
cana-2736	10	12	-derivation	-derivation	PROPN
cana-2736	10	13	,	,	PUNCT
cana-2736	10	14	rightf	rightf	PROPN
cana-2736	10	15	-derivation	-derivation	PROPN
cana-2736	10	16	.	.	PUNCT
cana-2736	11	1	1	1	X
cana-2736	11	2	.	.	X
cana-2736	11	3	introduction	introduction	NOUN
cana-2736	11	4	the	the	DET
cana-2736	11	5	concept	concept	NOUN
cana-2736	11	6	of	of	ADP
cana-2736	11	7	hilbert	hilbert	PROPN
cana-2736	11	8	algebras	algebras	PROPN
cana-2736	11	9	,	,	PUNCT
cana-2736	11	10	introduced	introduce	VERB
cana-2736	11	11	by	by	ADP
cana-2736	11	12	henkin	henkin	PROPN
cana-2736	11	13	in	in	ADP
cana-2736	11	14	the	the	DET
cana-2736	11	15	early	early	ADJ
cana-2736	11	16	1950s	1950s	NUM
cana-2736	11	17	,	,	PUNCT
cana-2736	11	18	emerged	emerge	VERB
cana-2736	11	19	as	as	ADP
cana-2736	11	20	a	a	DET
cana-2736	11	21	groundbreaking	groundbreake	VERB
cana-2736	11	22	algebraic	algebraic	ADJ
cana-2736	11	23	framework	framework	NOUN
cana-2736	11	24	aimed	aim	VERB
cana-2736	11	25	at	at	ADP
cana-2736	11	26	formalizing	formalizing	NOUN
cana-2736	11	27	implications	implication	NOUN
cana-2736	11	28	within	within	ADP
cana-2736	11	29	intuitionistic	intuitionistic	ADJ
cana-2736	11	30	and	and	CCONJ
cana-2736	11	31	other	other	ADJ
cana-2736	11	32	non	non	ADJ
cana-2736	11	33	-	-	ADJ
cana-2736	11	34	classical	classical	ADJ
cana-2736	11	35	logics	logic	NOUN
cana-2736	11	36	[	[	X
cana-2736	11	37	9	9	NUM
cana-2736	11	38	]	]	PUNCT
cana-2736	11	39	.	.	PUNCT
cana-2736	12	1	unlike	unlike	ADP
cana-2736	12	2	classical	classical	ADJ
cana-2736	12	3	logic	logic	NOUN
cana-2736	12	4	,	,	PUNCT
cana-2736	12	5	which	which	PRON
cana-2736	12	6	operates	operate	VERB
cana-2736	12	7	on	on	ADP
cana-2736	12	8	binary	binary	ADJ
cana-2736	12	9	truth	truth	NOUN
cana-2736	12	10	values	value	NOUN
cana-2736	12	11	,	,	PUNCT
cana-2736	12	12	non	non	ADJ
cana-2736	12	13	-	-	ADJ
cana-2736	12	14	classical	classical	ADJ
cana-2736	12	15	logic	logic	NOUN
cana-2736	12	16	,	,	PUNCT
cana-2736	12	17	including	include	VERB
cana-2736	12	18	intuitionistic	intuitionistic	ADJ
cana-2736	12	19	logic	logic	NOUN
cana-2736	12	20	,	,	PUNCT
cana-2736	12	21	requires	require	VERB
cana-2736	12	22	more	more	ADV
cana-2736	12	23	nuanced	nuanced	ADJ
cana-2736	12	24	structures	structure	NOUN
cana-2736	12	25	to	to	PART
cana-2736	12	26	capture	capture	VERB
cana-2736	12	27	their	their	PRON
cana-2736	12	28	subtleties	subtlety	NOUN
cana-2736	12	29	.	.	PUNCT
cana-2736	13	1	hilbert	hilbert	PROPN
cana-2736	13	2	algebras	algebras	PROPN
cana-2736	13	3	provided	provide	VERB
cana-2736	13	4	a	a	DET
cana-2736	13	5	sophisticated	sophisticated	ADJ
cana-2736	13	6	tool	tool	NOUN
cana-2736	13	7	for	for	ADP
cana-2736	13	8	this	this	DET
cana-2736	13	9	purpose	purpose	NOUN
cana-2736	13	10	,	,	PUNCT
cana-2736	13	11	offering	offer	VERB
cana-2736	13	12	an	an	DET
cana-2736	13	13	algebraic	algebraic	ADJ
cana-2736	13	14	lens	lens	NOUN
cana-2736	13	15	through	through	ADP
cana-2736	13	16	which	which	PRON
cana-2736	13	17	to	to	PART
cana-2736	13	18	analyze	analyze	VERB
cana-2736	13	19	and	and	CCONJ
cana-2736	13	20	comprehend	comprehend	VERB
cana-2736	13	21	the	the	DET
cana-2736	13	22	behaviour	behaviour	NOUN
cana-2736	13	23	of	of	ADP
cana-2736	13	24	implication	implication	NOUN
cana-2736	13	25	in	in	ADP
cana-2736	13	26	these	these	DET
cana-2736	13	27	alternative	alternative	ADJ
cana-2736	13	28	logical	logical	ADJ
cana-2736	13	29	systems	system	NOUN
cana-2736	13	30	.	.	PUNCT
cana-2736	14	1	by	by	ADP
cana-2736	14	2	the	the	DET
cana-2736	14	3	1960s	1960	NOUN
cana-2736	14	4	,	,	PUNCT
cana-2736	14	5	the	the	DET
cana-2736	14	6	fundamental	fundamental	ADJ
cana-2736	14	7	importance	importance	NOUN
cana-2736	14	8	of	of	ADP
cana-2736	14	9	hilbert	hilbert	PROPN
cana-2736	14	10	algebras	algebras	PROPN
cana-2736	14	11	was	be	AUX
cana-2736	14	12	further	far	ADV
cana-2736	14	13	solidified	solidify	VERB
cana-2736	14	14	through	through	ADP
cana-2736	14	15	diego	diego	NOUN
cana-2736	14	16	's	's	PART
cana-2736	14	17	seminal	seminal	ADJ
cana-2736	14	18	work	work	NOUN
cana-2736	14	19	,	,	PUNCT
cana-2736	14	20	demonstrating	demonstrate	VERB
cana-2736	14	21	that	that	SCONJ
cana-2736	14	22	hilbert	hilbert	PROPN
cana-2736	14	23	algebras	algebras	PROPN
cana-2736	14	24	constitute	constitute	VERB
cana-2736	14	25	a	a	DET
cana-2736	14	26	locally	locally	ADV
cana-2736	14	27	finite	finite	ADJ
cana-2736	14	28	variety	variety	NOUN
cana-2736	15	1	[	[	X
cana-2736	15	2	7	7	NUM
cana-2736	15	3	]	]	PUNCT
cana-2736	15	4	.	.	PUNCT
cana-2736	16	1	this	this	DET
cana-2736	16	2	revelation	revelation	NOUN
cana-2736	16	3	not	not	PART
cana-2736	16	4	only	only	ADV
cana-2736	16	5	underscored	underscore	VERB
cana-2736	16	6	the	the	DET
cana-2736	16	7	structural	structural	ADJ
cana-2736	16	8	richness	richness	NOUN
cana-2736	16	9	of	of	ADP
cana-2736	16	10	hilbert	hilbert	PROPN
cana-2736	16	11	algebras	algebras	PROPN
cana-2736	16	12	but	but	CCONJ
cana-2736	16	13	also	also	ADV
cana-2736	16	14	integrated	integrate	VERB
cana-2736	16	15	them	they	PRON
cana-2736	16	16	firmly	firmly	ADV
cana-2736	16	17	within	within	ADP
cana-2736	16	18	the	the	DET
cana-2736	16	19	broader	broad	ADJ
cana-2736	16	20	domain	domain	NOUN
cana-2736	16	21	of	of	ADP
cana-2736	16	22	algebraic	algebraic	ADJ
cana-2736	16	23	logic	logic	NOUN
cana-2736	16	24	.	.	PUNCT
cana-2736	17	1	diego	diego	PROPN
cana-2736	17	2	's	's	PART
cana-2736	17	3	results	result	NOUN
cana-2736	17	4	provided	provide	VERB
cana-2736	17	5	essential	essential	ADJ
cana-2736	17	6	insights	insight	NOUN
cana-2736	17	7	,	,	PUNCT
cana-2736	17	8	laying	lay	VERB
cana-2736	17	9	a	a	DET
cana-2736	17	10	rigorous	rigorous	ADJ
cana-2736	17	11	foundation	foundation	NOUN
cana-2736	17	12	for	for	ADP
cana-2736	17	13	further	further	ADJ
cana-2736	17	14	explorations	exploration	NOUN
cana-2736	17	15	into	into	ADP
cana-2736	17	16	their	their	PRON
cana-2736	17	17	properties	property	NOUN
cana-2736	17	18	and	and	CCONJ
cana-2736	17	19	applications	application	NOUN
cana-2736	17	20	.	.	PUNCT
cana-2736	18	1	as	as	ADP
cana-2736	18	2	a	a	DET
cana-2736	18	3	result	result	NOUN
cana-2736	18	4	,	,	PUNCT
cana-2736	18	5	hilbert	hilbert	PROPN
cana-2736	18	6	algebras	algebras	PROPN
cana-2736	18	7	have	have	AUX
cana-2736	18	8	become	become	VERB
cana-2736	18	9	an	an	DET
cana-2736	18	10	essential	essential	ADJ
cana-2736	18	11	structure	structure	NOUN
cana-2736	18	12	in	in	ADP
cana-2736	18	13	the	the	DET
cana-2736	18	14	study	study	NOUN
cana-2736	18	15	of	of	ADP
cana-2736	18	16	non	non	ADJ
cana-2736	18	17	-	-	ADJ
cana-2736	18	18	classical	classical	ADJ
cana-2736	18	19	logics	logic	NOUN
cana-2736	18	20	,	,	PUNCT
cana-2736	18	21	facilitating	facilitate	VERB
cana-2736	18	22	deeper	deep	ADJ
cana-2736	18	23	inquiries	inquiry	NOUN
cana-2736	18	24	into	into	ADP
cana-2736	18	25	the	the	DET
cana-2736	18	26	interplay	interplay	NOUN
cana-2736	18	27	between	between	ADP
cana-2736	18	28	algebra	algebra	NOUN
cana-2736	18	29	and	and	CCONJ
cana-2736	18	30	logic	logic	NOUN
cana-2736	18	31	.	.	PUNCT
cana-2736	19	1	building	build	VERB
cana-2736	19	2	upon	upon	SCONJ
cana-2736	19	3	these	these	DET
cana-2736	19	4	foundational	foundational	ADJ
cana-2736	19	5	developments	development	NOUN
cana-2736	19	6	,	,	PUNCT
cana-2736	19	7	subsequent	subsequent	ADJ
cana-2736	19	8	research	research	NOUN
cana-2736	19	9	delved	delve	VERB
cana-2736	19	10	deeper	deeply	ADV
cana-2736	19	11	into	into	ADP
cana-2736	19	12	both	both	CCONJ
cana-2736	19	13	the	the	DET
cana-2736	19	14	algebraic	algebraic	ADJ
cana-2736	19	15	and	and	CCONJ
cana-2736	19	16	logical	logical	ADJ
cana-2736	19	17	aspects	aspect	NOUN
cana-2736	19	18	of	of	ADP
cana-2736	19	19	hilbert	hilbert	PROPN
cana-2736	19	20	algebras	algebras	PROPN
cana-2736	19	21	,	,	PUNCT
cana-2736	19	22	further	far	ADV
cana-2736	19	23	expanding	expand	VERB
cana-2736	19	24	their	their	PRON
cana-2736	19	25	theoretical	theoretical	ADJ
cana-2736	19	26	and	and	CCONJ
cana-2736	19	27	practical	practical	ADJ
cana-2736	19	28	relevance	relevance	NOUN
cana-2736	19	29	.	.	PUNCT
cana-2736	20	1	notably	notably	ADV
cana-2736	20	2	,	,	PUNCT
cana-2736	20	3	busneag	busneag	NOUN
cana-2736	21	1	[	[	X
cana-2736	21	2	4,5	4,5	X
cana-2736	21	3	]	]	PUNCT
cana-2736	21	4	and	and	CCONJ
cana-2736	21	5	jun	jun	PROPN
cana-2736	21	6	[	[	X
cana-2736	21	7	15	15	NUM
cana-2736	21	8	]	]	PUNCT
cana-2736	21	9	explored	explore	VERB
cana-2736	21	10	the	the	DET
cana-2736	21	11	critical	critical	ADJ
cana-2736	21	12	role	role	NOUN
cana-2736	21	13	of	of	ADP
cana-2736	21	14	filters	filter	NOUN
cana-2736	21	15	within	within	ADP
cana-2736	21	16	hilbert	hilbert	PROPN
cana-2736	21	17	algebras	algebras	PROPN
cana-2736	21	18	,	,	PUNCT
cana-2736	21	19	establishing	establish	VERB
cana-2736	21	20	that	that	SCONJ
cana-2736	21	21	these	these	DET
cana-2736	21	22	filters	filter	NOUN
cana-2736	21	23	act	act	VERB
cana-2736	21	24	as	as	ADP
cana-2736	21	25	deductive	deductive	ADJ
cana-2736	21	26	systems	system	NOUN
cana-2736	21	27	fundamental	fundamental	ADJ
cana-2736	21	28	to	to	ADP
cana-2736	21	29	the	the	DET
cana-2736	21	30	underlying	underlie	VERB
cana-2736	21	31	logical	logical	ADJ
cana-2736	21	32	communications	communication	NOUN
cana-2736	21	33	on	on	ADP
cana-2736	21	34	applied	apply	VERB
cana-2736	21	35	nonlinear	nonlinear	ADJ
cana-2736	21	36	analysis	analysis	NOUN
cana-2736	21	37	issn	issn	NOUN
cana-2736	21	38	:	:	PUNCT
cana-2736	21	39	1074	1074	NUM
cana-2736	21	40	-	-	PUNCT
cana-2736	21	41	133x	133x	NUM
cana-2736	21	42	vol	vol	NOUN
cana-2736	21	43	32	32	NUM
cana-2736	21	44	no	no	NOUN
cana-2736	21	45	.	.	PUNCT
cana-2736	22	1	4s	4s	NUM
cana-2736	22	2	(	(	PUNCT
cana-2736	22	3	2025	2025	NUM
cana-2736	22	4	)	)	PUNCT
cana-2736	22	5	13	13	NUM
cana-2736	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	22	7	structure	structure	NOUN
cana-2736	22	8	.	.	PUNCT
cana-2736	23	1	their	their	PRON
cana-2736	23	2	work	work	NOUN
cana-2736	23	3	unveiled	unveil	VERB
cana-2736	23	4	profound	profound	ADJ
cana-2736	23	5	connections	connection	NOUN
cana-2736	23	6	between	between	ADP
cana-2736	23	7	the	the	DET
cana-2736	23	8	algebraic	algebraic	ADJ
cana-2736	23	9	properties	property	NOUN
cana-2736	23	10	of	of	ADP
cana-2736	23	11	hilbert	hilbert	PROPN
cana-2736	23	12	algebras	algebra	NOUN
cana-2736	23	13	and	and	CCONJ
cana-2736	23	14	their	their	PRON
cana-2736	23	15	logical	logical	ADJ
cana-2736	23	16	interpretations	interpretation	NOUN
cana-2736	23	17	,	,	PUNCT
cana-2736	23	18	offering	offer	VERB
cana-2736	23	19	a	a	DET
cana-2736	23	20	refined	refined	ADJ
cana-2736	23	21	understanding	understanding	NOUN
cana-2736	23	22	of	of	ADP
cana-2736	23	23	how	how	SCONJ
cana-2736	23	24	these	these	DET
cana-2736	23	25	systems	system	NOUN
cana-2736	23	26	model	model	VERB
cana-2736	23	27	non	non	ADJ
cana-2736	23	28	-	-	ADJ
cana-2736	23	29	classical	classical	ADJ
cana-2736	23	30	logic	logic	NOUN
cana-2736	23	31	.	.	PUNCT
cana-2736	24	1	additionally	additionally	ADV
cana-2736	24	2	,	,	PUNCT
cana-2736	24	3	dudek	dudek	PROPN
cana-2736	24	4	's	's	PART
cana-2736	24	5	contributions	contribution	NOUN
cana-2736	24	6	[	[	X
cana-2736	24	7	8	8	NUM
cana-2736	24	8	]	]	PUNCT
cana-2736	24	9	extended	extend	VERB
cana-2736	24	10	the	the	DET
cana-2736	24	11	versatility	versatility	NOUN
cana-2736	24	12	of	of	ADP
cana-2736	24	13	hilbert	hilbert	PROPN
cana-2736	24	14	algebras	algebras	PROPN
cana-2736	24	15	through	through	ADP
cana-2736	24	16	the	the	DET
cana-2736	24	17	concept	concept	NOUN
cana-2736	24	18	of	of	ADP
cana-2736	24	19	fuzzification	fuzzification	NOUN
cana-2736	24	20	,	,	PUNCT
cana-2736	24	21	where	where	SCONJ
cana-2736	24	22	the	the	DET
cana-2736	24	23	algebraic	algebraic	ADJ
cana-2736	24	24	framework	framework	NOUN
cana-2736	24	25	was	be	AUX
cana-2736	24	26	adapted	adapt	VERB
cana-2736	24	27	to	to	PART
cana-2736	24	28	accommodate	accommodate	VERB
cana-2736	24	29	fuzzy	fuzzy	ADJ
cana-2736	24	30	logic	logic	NOUN
cana-2736	24	31	,	,	PUNCT
cana-2736	24	32	characterized	characterize	VERB
cana-2736	24	33	by	by	ADP
cana-2736	24	34	truth	truth	NOUN
cana-2736	24	35	values	value	NOUN
cana-2736	24	36	that	that	PRON
cana-2736	24	37	exist	exist	VERB
cana-2736	24	38	on	on	ADP
cana-2736	24	39	a	a	DET
cana-2736	24	40	continuum	continuum	ADJ
cana-2736	24	41	rather	rather	ADV
cana-2736	24	42	than	than	ADP
cana-2736	24	43	binary	binary	ADJ
cana-2736	24	44	distinctions	distinction	NOUN
cana-2736	24	45	.	.	PUNCT
cana-2736	25	1	this	this	DET
cana-2736	25	2	innovation	innovation	NOUN
cana-2736	25	3	enriched	enrich	VERB
cana-2736	25	4	the	the	DET
cana-2736	25	5	study	study	NOUN
cana-2736	25	6	of	of	ADP
cana-2736	25	7	hilbert	hilbert	PROPN
cana-2736	25	8	algebras	algebras	PROPN
cana-2736	25	9	,	,	PUNCT
cana-2736	25	10	enabling	enable	VERB
cana-2736	25	11	their	their	PRON
cana-2736	25	12	application	application	NOUN
cana-2736	25	13	in	in	ADP
cana-2736	25	14	domains	domain	NOUN
cana-2736	25	15	that	that	PRON
cana-2736	25	16	address	address	VERB
cana-2736	25	17	uncertainty	uncertainty	NOUN
cana-2736	25	18	,	,	PUNCT
cana-2736	25	19	partial	partial	ADJ
cana-2736	25	20	truth	truth	NOUN
cana-2736	25	21	,	,	PUNCT
cana-2736	25	22	and	and	CCONJ
cana-2736	25	23	vagueness	vagueness	NOUN
cana-2736	25	24	—	—	PUNCT
cana-2736	25	25	critical	critical	ADJ
cana-2736	25	26	aspects	aspect	NOUN
cana-2736	25	27	of	of	ADP
cana-2736	25	28	real	real	ADJ
cana-2736	25	29	-	-	PUNCT
cana-2736	25	30	world	world	NOUN
cana-2736	25	31	reasoning	reasoning	NOUN
cana-2736	25	32	systems	system	NOUN
cana-2736	25	33	.	.	PUNCT
cana-2736	26	1	the	the	DET
cana-2736	26	2	inclusion	inclusion	NOUN
cana-2736	26	3	of	of	ADP
cana-2736	26	4	fuzzy	fuzzy	ADJ
cana-2736	26	5	subalgebras	subalgebra	NOUN
cana-2736	26	6	and	and	CCONJ
cana-2736	26	7	deductive	deductive	ADJ
cana-2736	26	8	systems	system	NOUN
cana-2736	26	9	demonstrated	demonstrate	VERB
cana-2736	26	10	the	the	DET
cana-2736	26	11	flexibility	flexibility	NOUN
cana-2736	26	12	of	of	ADP
cana-2736	26	13	hilbert	hilbert	PROPN
cana-2736	26	14	algebras	algebra	NOUN
cana-2736	26	15	and	and	CCONJ
cana-2736	26	16	further	far	ADV
cana-2736	26	17	reinforced	reinforce	VERB
cana-2736	26	18	their	their	PRON
cana-2736	26	19	importance	importance	NOUN
cana-2736	26	20	in	in	ADP
cana-2736	26	21	contemporary	contemporary	ADJ
cana-2736	26	22	logical	logical	ADJ
cana-2736	26	23	and	and	CCONJ
cana-2736	26	24	algebraic	algebraic	ADJ
cana-2736	26	25	research	research	NOUN
cana-2736	26	26	.	.	PUNCT
cana-2736	27	1	the	the	DET
cana-2736	27	2	study	study	NOUN
cana-2736	27	3	of	of	ADP
cana-2736	27	4	derivations	derivation	NOUN
cana-2736	27	5	has	have	AUX
cana-2736	27	6	seen	see	VERB
cana-2736	27	7	remarkable	remarkable	ADJ
cana-2736	27	8	progress	progress	NOUN
cana-2736	27	9	in	in	ADP
cana-2736	27	10	recent	recent	ADJ
cana-2736	27	11	years	year	NOUN
cana-2736	27	12	,	,	PUNCT
cana-2736	27	13	particularly	particularly	ADV
cana-2736	27	14	in	in	ADP
cana-2736	27	15	their	their	PRON
cana-2736	27	16	application	application	NOUN
cana-2736	27	17	to	to	PART
cana-2736	27	18	diverse	diverse	VERB
cana-2736	27	19	algebraic	algebraic	ADJ
cana-2736	27	20	structures	structure	NOUN
cana-2736	27	21	.	.	PUNCT
cana-2736	28	1	in	in	ADP
cana-2736	28	2	2021	2021	NUM
cana-2736	28	3	,	,	PUNCT
cana-2736	28	4	muangkarn	muangkarn	VERB
cana-2736	28	5	et	et	PROPN
cana-2736	28	6	al	al	PROPN
cana-2736	28	7	.	.	PUNCT
cana-2736	29	1	[	[	X
cana-2736	29	2	18	18	NUM
cana-2736	29	3	]	]	PUNCT
cana-2736	29	4	examined	examine	VERB
cana-2736	29	5	qf	qf	PROPN
cana-2736	29	6	-derivations	-derivation	NOUN
cana-2736	29	7	,	,	PUNCT
cana-2736	29	8	while	while	SCONJ
cana-2736	29	9	bantaojai	bantaojai	NOUN
cana-2736	29	10	et	et	PROPN
cana-2736	29	11	al	al	PROPN
cana-2736	29	12	.	.	PUNCT
cana-2736	30	1	[	[	X
cana-2736	30	2	3	3	NUM
cana-2736	30	3	]	]	PUNCT
cana-2736	30	4	explored	explore	VERB
cana-2736	30	5	derivations	derivation	NOUN
cana-2736	30	6	induced	induce	VERB
cana-2736	30	7	by	by	ADP
cana-2736	30	8	endomorphisms	endomorphism	NOUN
cana-2736	30	9	within	within	ADP
cana-2736	30	10	b	b	NOUN
cana-2736	30	11	-	-	PUNCT
cana-2736	30	12	algebras	algebras	X
cana-2736	30	13	.	.	PUNCT
cana-2736	31	1	this	this	DET
cana-2736	31	2	investigation	investigation	NOUN
cana-2736	31	3	revealed	reveal	VERB
cana-2736	31	4	new	new	ADJ
cana-2736	31	5	insights	insight	NOUN
cana-2736	31	6	into	into	ADP
cana-2736	31	7	the	the	DET
cana-2736	31	8	interplay	interplay	NOUN
cana-2736	31	9	between	between	ADP
cana-2736	31	10	derivations	derivation	NOUN
cana-2736	31	11	and	and	CCONJ
cana-2736	31	12	algebraic	algebraic	ADJ
cana-2736	31	13	morphisms	morphism	NOUN
cana-2736	31	14	,	,	PUNCT
cana-2736	31	15	broadening	broaden	VERB
cana-2736	31	16	the	the	DET
cana-2736	31	17	understanding	understanding	NOUN
cana-2736	31	18	of	of	ADP
cana-2736	31	19	structural	structural	ADJ
cana-2736	31	20	transformations	transformation	NOUN
cana-2736	31	21	in	in	ADP
cana-2736	31	22	these	these	DET
cana-2736	31	23	systems	system	NOUN
cana-2736	31	24	.	.	PUNCT
cana-2736	32	1	continuing	continue	VERB
cana-2736	32	2	this	this	DET
cana-2736	32	3	trajectory	trajectory	NOUN
cana-2736	32	4	,	,	PUNCT
cana-2736	32	5	bantaojai	bantaojai	NOUN
cana-2736	32	6	et	et	PROPN
cana-2736	32	7	al	al	PROPN
cana-2736	32	8	.	.	PUNCT
cana-2736	33	1	[	[	X
cana-2736	33	2	1,2	1,2	NUM
cana-2736	33	3	]	]	PUNCT
cana-2736	33	4	expanded	expand	VERB
cana-2736	33	5	their	their	PRON
cana-2736	33	6	research	research	NOUN
cana-2736	33	7	in	in	ADP
cana-2736	33	8	2022	2022	NUM
cana-2736	33	9	to	to	PART
cana-2736	33	10	encompass	encompass	VERB
cana-2736	33	11	derivations	derivation	NOUN
cana-2736	33	12	on	on	ADP
cana-2736	33	13	d	d	PROPN
cana-2736	33	14	-algebras	-algebras	PROPN
cana-2736	33	15	and	and	CCONJ
cana-2736	33	16	balgebras	balgebras	PROPN
cana-2736	33	17	,	,	PUNCT
cana-2736	33	18	further	far	ADV
cana-2736	33	19	enriching	enrich	VERB
cana-2736	33	20	the	the	DET
cana-2736	33	21	theoretical	theoretical	ADJ
cana-2736	33	22	framework	framework	NOUN
cana-2736	33	23	and	and	CCONJ
cana-2736	33	24	offering	offer	VERB
cana-2736	33	25	deeper	deep	ADJ
cana-2736	33	26	perspectives	perspective	NOUN
cana-2736	33	27	on	on	ADP
cana-2736	33	28	the	the	DET
cana-2736	33	29	behaviour	behaviour	NOUN
cana-2736	33	30	of	of	ADP
cana-2736	33	31	derivations	derivation	NOUN
cana-2736	33	32	in	in	ADP
cana-2736	33	33	more	more	ADV
cana-2736	33	34	complex	complex	ADJ
cana-2736	33	35	algebraic	algebraic	ADJ
cana-2736	33	36	systems	system	NOUN
cana-2736	33	37	.	.	PUNCT
cana-2736	34	1	simultaneously	simultaneously	ADV
cana-2736	34	2	,	,	PUNCT
cana-2736	34	3	muangkarn	muangkarn	VERB
cana-2736	34	4	et	et	PROPN
cana-2736	34	5	al	al	PROPN
cana-2736	34	6	.	.	PUNCT
cana-2736	35	1	[	[	X
cana-2736	35	2	17,19	17,19	X
cana-2736	35	3	]	]	PUNCT
cana-2736	35	4	focused	focus	VERB
cana-2736	35	5	on	on	ADP
cana-2736	35	6	the	the	DET
cana-2736	35	7	structural	structural	ADJ
cana-2736	35	8	implications	implication	NOUN
cana-2736	35	9	of	of	ADP
cana-2736	35	10	derivations	derivation	NOUN
cana-2736	35	11	induced	induce	VERB
cana-2736	35	12	by	by	ADP
cana-2736	35	13	endomorphisms	endomorphism	NOUN
cana-2736	35	14	in	in	ADP
cana-2736	35	15	bg	bg	PROPN
cana-2736	35	16	-	-	PUNCT
cana-2736	35	17	algebras	algebras	PROPN
cana-2736	35	18	and	and	CCONJ
cana-2736	35	19	d	d	PROPN
cana-2736	35	20	-algebras	-algebras	PROPN
cana-2736	35	21	,	,	PUNCT
cana-2736	35	22	shedding	shed	VERB
cana-2736	35	23	light	light	NOUN
cana-2736	35	24	on	on	ADP
cana-2736	35	25	the	the	DET
cana-2736	35	26	intricate	intricate	ADJ
cana-2736	35	27	relationships	relationship	NOUN
cana-2736	35	28	between	between	ADP
cana-2736	35	29	these	these	DET
cana-2736	35	30	operations	operation	NOUN
cana-2736	35	31	and	and	CCONJ
cana-2736	35	32	the	the	DET
cana-2736	35	33	underlying	underlying	ADJ
cana-2736	35	34	algebraic	algebraic	ADJ
cana-2736	35	35	properties	property	NOUN
cana-2736	35	36	.	.	PUNCT
cana-2736	36	1	additionally	additionally	ADV
cana-2736	36	2	,	,	PUNCT
cana-2736	36	3	iampan	iampan	NOUN
cana-2736	36	4	et	et	PROPN
cana-2736	36	5	al	al	PROPN
cana-2736	36	6	.	.	PUNCT
cana-2736	37	1	[	[	X
cana-2736	37	2	10,20,21	10,20,21	NUM
cana-2736	37	3	]	]	PUNCT
cana-2736	37	4	made	make	VERB
cana-2736	37	5	substantial	substantial	ADJ
cana-2736	37	6	contributions	contribution	NOUN
cana-2736	37	7	by	by	ADP
cana-2736	37	8	studying	study	VERB
cana-2736	37	9	derivations	derivation	NOUN
cana-2736	37	10	in	in	ADP
cana-2736	37	11	up	up	ADP
cana-2736	37	12	-	-	PUNCT
cana-2736	37	13	algebras	algebras	X
cana-2736	37	14	,	,	PUNCT
cana-2736	37	15	emphasizing	emphasize	VERB
cana-2736	37	16	the	the	DET
cana-2736	37	17	versatility	versatility	NOUN
cana-2736	37	18	and	and	CCONJ
cana-2736	37	19	broad	broad	ADJ
cana-2736	37	20	applicability	applicability	NOUN
cana-2736	37	21	of	of	ADP
cana-2736	37	22	derivation	derivation	NOUN
cana-2736	37	23	theory	theory	NOUN
cana-2736	37	24	across	across	ADP
cana-2736	37	25	various	various	ADJ
cana-2736	37	26	algebraic	algebraic	ADJ
cana-2736	37	27	frameworks	framework	NOUN
cana-2736	37	28	.	.	PUNCT
cana-2736	38	1	building	build	VERB
cana-2736	38	2	on	on	ADP
cana-2736	38	3	this	this	DET
cana-2736	38	4	rich	rich	ADJ
cana-2736	38	5	foundation	foundation	NOUN
cana-2736	38	6	,	,	PUNCT
cana-2736	38	7	iampan	iampan	NOUN
cana-2736	38	8	et	et	PROPN
cana-2736	38	9	al	al	PROPN
cana-2736	38	10	.	.	PUNCT
cana-2736	39	1	[	[	X
cana-2736	39	2	11,13	11,13	X
cana-2736	39	3	]	]	PUNCT
cana-2736	39	4	introduced	introduce	VERB
cana-2736	39	5	and	and	CCONJ
cana-2736	39	6	rigorously	rigorously	ADV
cana-2736	39	7	developed	develop	VERB
cana-2736	39	8	the	the	DET
cana-2736	39	9	concepts	concept	NOUN
cana-2736	39	10	of	of	ADP
cana-2736	39	11	(	(	PUNCT
cana-2736	39	12	,	,	PUNCT
cana-2736	39	13	)	)	PUNCT
cana-2736	39	14	l	l	NOUN
cana-2736	39	15	r	r	NOUN
cana-2736	39	16	-derivations	-derivation	NOUN
cana-2736	39	17	,	,	PUNCT
cana-2736	39	18	(	(	PUNCT
cana-2736	39	19	,	,	PUNCT
cana-2736	39	20	)	)	PUNCT
cana-2736	39	21	r	r	NOUN
cana-2736	39	22	l	l	NOUN
cana-2736	39	23	-derivations	-derivation	NOUN
cana-2736	39	24	,	,	PUNCT
cana-2736	39	25	and	and	CCONJ
cana-2736	39	26	general	general	ADJ
cana-2736	39	27	derivations	derivation	NOUN
cana-2736	39	28	within	within	ADP
cana-2736	39	29	the	the	DET
cana-2736	39	30	context	context	NOUN
cana-2736	39	31	of	of	ADP
cana-2736	39	32	hilbert	hilbert	PROPN
cana-2736	39	33	algebras	algebras	PROPN
cana-2736	39	34	.	.	PUNCT
cana-2736	40	1	their	their	PRON
cana-2736	40	2	work	work	NOUN
cana-2736	40	3	not	not	PART
cana-2736	40	4	only	only	ADV
cana-2736	40	5	advanced	advance	VERB
cana-2736	40	6	the	the	DET
cana-2736	40	7	understanding	understanding	NOUN
cana-2736	40	8	of	of	ADP
cana-2736	40	9	derivations	derivation	NOUN
cana-2736	40	10	in	in	ADP
cana-2736	40	11	these	these	DET
cana-2736	40	12	specific	specific	ADJ
cana-2736	40	13	algebraic	algebraic	ADJ
cana-2736	40	14	structures	structure	NOUN
cana-2736	40	15	but	but	CCONJ
cana-2736	40	16	also	also	ADV
cana-2736	40	17	illuminated	illuminate	VERB
cana-2736	40	18	their	their	PRON
cana-2736	40	19	logical	logical	ADJ
cana-2736	40	20	implications	implication	NOUN
cana-2736	40	21	.	.	PUNCT
cana-2736	41	1	subsequently	subsequently	ADV
cana-2736	41	2	,	,	PUNCT
cana-2736	41	3	their	their	PRON
cana-2736	41	4	investigation	investigation	NOUN
cana-2736	41	5	into	into	ADP
cana-2736	41	6	the	the	DET
cana-2736	41	7	relationship	relationship	NOUN
cana-2736	41	8	between	between	ADP
cana-2736	41	9	derivations	derivation	NOUN
cana-2736	41	10	and	and	CCONJ
cana-2736	41	11	endomorphisms	endomorphism	NOUN
cana-2736	41	12	opened	open	VERB
cana-2736	41	13	up	up	ADP
cana-2736	41	14	new	new	ADJ
cana-2736	41	15	pathways	pathway	NOUN
cana-2736	41	16	for	for	ADP
cana-2736	41	17	exploring	explore	VERB
cana-2736	41	18	the	the	DET
cana-2736	41	19	structural	structural	ADJ
cana-2736	41	20	properties	property	NOUN
cana-2736	41	21	of	of	ADP
cana-2736	41	22	hilbert	hilbert	PROPN
cana-2736	41	23	algebras	algebras	PROPN
cana-2736	41	24	.	.	PUNCT
cana-2736	42	1	this	this	DET
cana-2736	42	2	research	research	NOUN
cana-2736	42	3	has	have	AUX
cana-2736	42	4	significantly	significantly	ADV
cana-2736	42	5	enriched	enrich	VERB
cana-2736	42	6	the	the	DET
cana-2736	42	7	algebraic	algebraic	ADJ
cana-2736	42	8	theory	theory	NOUN
cana-2736	42	9	surrounding	surround	VERB
cana-2736	42	10	hilbert	hilbert	PROPN
cana-2736	42	11	algebras	algebra	NOUN
cana-2736	42	12	,	,	PUNCT
cana-2736	42	13	contributing	contribute	VERB
cana-2736	42	14	valuable	valuable	ADJ
cana-2736	42	15	insights	insight	NOUN
cana-2736	42	16	into	into	ADP
cana-2736	42	17	the	the	DET
cana-2736	42	18	role	role	NOUN
cana-2736	42	19	of	of	ADP
cana-2736	42	20	derivations	derivation	NOUN
cana-2736	42	21	in	in	ADP
cana-2736	42	22	both	both	CCONJ
cana-2736	42	23	classical	classical	ADJ
cana-2736	42	24	and	and	CCONJ
cana-2736	42	25	non	non	ADJ
cana-2736	42	26	-	-	ADJ
cana-2736	42	27	classical	classical	ADJ
cana-2736	42	28	logical	logical	ADJ
cana-2736	42	29	systems	system	NOUN
cana-2736	42	30	.	.	PUNCT
cana-2736	43	1	collectively	collectively	ADV
cana-2736	43	2	,	,	PUNCT
cana-2736	43	3	these	these	DET
cana-2736	43	4	studies	study	NOUN
cana-2736	43	5	have	have	AUX
cana-2736	43	6	deepened	deepen	VERB
cana-2736	43	7	our	our	PRON
cana-2736	43	8	comprehension	comprehension	NOUN
cana-2736	43	9	of	of	ADP
cana-2736	43	10	derivations	derivation	NOUN
cana-2736	43	11	across	across	ADP
cana-2736	43	12	a	a	DET
cana-2736	43	13	wide	wide	ADJ
cana-2736	43	14	array	array	NOUN
cana-2736	43	15	of	of	ADP
cana-2736	43	16	algebraic	algebraic	ADJ
cana-2736	43	17	structures	structure	NOUN
cana-2736	43	18	,	,	PUNCT
cana-2736	43	19	laying	lay	VERB
cana-2736	43	20	a	a	DET
cana-2736	43	21	robust	robust	ADJ
cana-2736	43	22	foundation	foundation	NOUN
cana-2736	43	23	for	for	ADP
cana-2736	43	24	future	future	ADJ
cana-2736	43	25	research	research	NOUN
cana-2736	43	26	in	in	ADP
cana-2736	43	27	this	this	DET
cana-2736	43	28	dynamic	dynamic	ADJ
cana-2736	43	29	area	area	NOUN
cana-2736	43	30	of	of	ADP
cana-2736	43	31	algebraic	algebraic	PROPN
cana-2736	43	32	theory	theory	NOUN
cana-2736	43	33	.	.	PUNCT
cana-2736	44	1	this	this	DET
cana-2736	44	2	paper	paper	NOUN
cana-2736	44	3	introduces	introduce	NOUN
cana-2736	44	4	and	and	CCONJ
cana-2736	44	5	investigates	investigate	VERB
cana-2736	44	6	leftf	leftf	ADJ
cana-2736	44	7	-derivations	-derivation	NOUN
cana-2736	44	8	,	,	PUNCT
cana-2736	44	9	rightf	rightf	ADJ
cana-2736	44	10	-derivations	-derivation	NOUN
cana-2736	44	11	,	,	PUNCT
cana-2736	44	12	and	and	CCONJ
cana-2736	44	13	f	f	PROPN
cana-2736	44	14	-derivations	-derivation	NOUN
cana-2736	44	15	of	of	ADP
cana-2736	44	16	type	type	NOUN
cana-2736	44	17	i	i	PRON
cana-2736	44	18	and	and	CCONJ
cana-2736	44	19	type	type	NOUN
cana-2736	44	20	ii	ii	PROPN
cana-2736	44	21	within	within	ADP
cana-2736	44	22	the	the	DET
cana-2736	44	23	framework	framework	NOUN
cana-2736	44	24	of	of	ADP
cana-2736	44	25	hilbert	hilbert	PROPN
cana-2736	44	26	algebras	algebras	PROPN
cana-2736	44	27	.	.	PUNCT
cana-2736	45	1	we	we	PRON
cana-2736	45	2	explore	explore	VERB
cana-2736	45	3	the	the	DET
cana-2736	45	4	fundamental	fundamental	ADJ
cana-2736	45	5	properties	property	NOUN
cana-2736	45	6	of	of	ADP
cana-2736	45	7	these	these	DET
cana-2736	45	8	derivations	derivation	NOUN
cana-2736	45	9	,	,	PUNCT
cana-2736	45	10	highlighting	highlight	VERB
cana-2736	45	11	their	their	PRON
cana-2736	45	12	structural	structural	ADJ
cana-2736	45	13	roles	role	NOUN
cana-2736	45	14	and	and	CCONJ
cana-2736	45	15	interactions	interaction	NOUN
cana-2736	45	16	.	.	PUNCT
cana-2736	46	1	notably	notably	ADV
cana-2736	46	2	,	,	PUNCT
cana-2736	46	3	we	we	PRON
cana-2736	46	4	establish	establish	VERB
cana-2736	46	5	that	that	SCONJ
cana-2736	46	6	the	the	DET
cana-2736	46	7	kernel	kernel	NOUN
cana-2736	46	8	of	of	ADP
cana-2736	46	9	an	an	DET
cana-2736	46	10	f	f	PROPN
cana-2736	46	11	-derivation	-derivation	PROPN
cana-2736	46	12	,	,	PUNCT
cana-2736	46	13	ker	ker	NOUN
cana-2736	46	14	(	(	PUNCT
cana-2736	46	15	)	)	PUNCT
cana-2736	46	16	d	d	X
cana-2736	46	17	a	a	PRON
cana-2736	46	18	,	,	PUNCT
cana-2736	46	19	forms	form	VERB
cana-2736	46	20	a	a	DET
cana-2736	46	21	near	near	ADJ
cana-2736	46	22	filter	filter	NOUN
cana-2736	46	23	and	and	CCONJ
cana-2736	46	24	functions	function	NOUN
cana-2736	46	25	as	as	ADP
cana-2736	46	26	a	a	DET
cana-2736	46	27	subalgebra	subalgebra	NOUN
cana-2736	46	28	of	of	ADP
cana-2736	46	29	the	the	DET
cana-2736	46	30	hilbert	hilbert	PROPN
cana-2736	46	31	algebra	algebra	PROPN
cana-2736	46	32	a	a	PRON
cana-2736	46	33	.	.	PUNCT
cana-2736	47	1	these	these	DET
cana-2736	47	2	results	result	NOUN
cana-2736	47	3	not	not	PART
cana-2736	47	4	only	only	ADV
cana-2736	47	5	deepen	deepen	VERB
cana-2736	47	6	our	our	PRON
cana-2736	47	7	understanding	understanding	NOUN
cana-2736	47	8	of	of	ADP
cana-2736	47	9	the	the	DET
cana-2736	47	10	algebraic	algebraic	ADJ
cana-2736	47	11	structure	structure	NOUN
cana-2736	47	12	of	of	ADP
cana-2736	47	13	hilbert	hilbert	PROPN
cana-2736	47	14	algebras	algebras	PROPN
cana-2736	47	15	but	but	CCONJ
cana-2736	47	16	also	also	ADV
cana-2736	47	17	pave	pave	VERB
cana-2736	47	18	the	the	DET
cana-2736	47	19	way	way	NOUN
cana-2736	47	20	for	for	ADP
cana-2736	47	21	future	future	ADJ
cana-2736	47	22	research	research	NOUN
cana-2736	47	23	into	into	ADP
cana-2736	47	24	the	the	DET
cana-2736	47	25	broader	broad	ADJ
cana-2736	47	26	implications	implication	NOUN
cana-2736	47	27	of	of	ADP
cana-2736	47	28	derivations	derivation	NOUN
cana-2736	47	29	in	in	ADP
cana-2736	47	30	algebraic	algebraic	ADJ
cana-2736	47	31	logic	logic	NOUN
cana-2736	47	32	and	and	CCONJ
cana-2736	47	33	their	their	PRON
cana-2736	47	34	potential	potential	ADJ
cana-2736	47	35	applications	application	NOUN
cana-2736	47	36	.	.	PUNCT
cana-2736	48	1	communications	communication	NOUN
cana-2736	48	2	on	on	ADP
cana-2736	48	3	applied	apply	VERB
cana-2736	48	4	nonlinear	nonlinear	ADJ
cana-2736	48	5	analysis	analysis	NOUN
cana-2736	48	6	issn	issn	NOUN
cana-2736	48	7	:	:	PUNCT
cana-2736	48	8	1074	1074	NUM
cana-2736	48	9	-	-	PUNCT
cana-2736	48	10	133x	133x	NUM
cana-2736	48	11	vol	vol	NOUN
cana-2736	48	12	32	32	NUM
cana-2736	48	13	no	no	NOUN
cana-2736	48	14	.	.	PUNCT
cana-2736	49	1	4s	4s	NUM
cana-2736	49	2	(	(	PUNCT
cana-2736	49	3	2025	2025	NUM
cana-2736	49	4	)	)	PUNCT
cana-2736	49	5	14	14	NUM
cana-2736	50	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	50	2	2	2	X
cana-2736	50	3	.	.	PUNCT
cana-2736	50	4	preliminaries	preliminary	NOUN
cana-2736	50	5	before	before	ADP
cana-2736	50	6	proceeding	proceed	VERB
cana-2736	50	7	,	,	PUNCT
cana-2736	50	8	it	it	PRON
cana-2736	50	9	's	be	AUX
cana-2736	50	10	important	important	ADJ
cana-2736	50	11	to	to	PART
cana-2736	50	12	revisit	revisit	VERB
cana-2736	50	13	the	the	DET
cana-2736	50	14	concept	concept	NOUN
cana-2736	50	15	of	of	ADP
cana-2736	50	16	hilbert	hilbert	PROPN
cana-2736	50	17	algebras	algebras	PROPN
cana-2736	50	18	,	,	PUNCT
cana-2736	50	19	introduced	introduce	VERB
cana-2736	50	20	by	by	ADP
cana-2736	50	21	diego	diego	NOUN
cana-2736	50	22	in	in	ADP
cana-2736	50	23	1966	1966	NUM
cana-2736	50	24	[	[	X
cana-2736	50	25	7	7	NUM
cana-2736	50	26	]	]	PUNCT
cana-2736	50	27	.	.	PUNCT
cana-2736	51	1	as	as	ADP
cana-2736	51	2	a	a	DET
cana-2736	51	3	key	key	ADJ
cana-2736	51	4	structure	structure	NOUN
cana-2736	51	5	in	in	ADP
cana-2736	51	6	algebraic	algebraic	ADJ
cana-2736	51	7	logic	logic	NOUN
cana-2736	51	8	,	,	PUNCT
cana-2736	51	9	they	they	PRON
cana-2736	51	10	capture	capture	VERB
cana-2736	51	11	the	the	DET
cana-2736	51	12	behaviour	behaviour	NOUN
cana-2736	51	13	of	of	ADP
cana-2736	51	14	implication	implication	NOUN
cana-2736	51	15	in	in	ADP
cana-2736	51	16	nonclassical	nonclassical	ADJ
cana-2736	51	17	systems	system	NOUN
cana-2736	51	18	,	,	PUNCT
cana-2736	51	19	making	make	VERB
cana-2736	51	20	them	they	PRON
cana-2736	51	21	central	central	ADJ
cana-2736	51	22	to	to	ADP
cana-2736	51	23	further	further	ADJ
cana-2736	51	24	studies	study	NOUN
cana-2736	51	25	of	of	ADP
cana-2736	51	26	derivations	derivation	NOUN
cana-2736	51	27	and	and	CCONJ
cana-2736	51	28	algebraic	algebraic	ADJ
cana-2736	51	29	operations	operation	NOUN
cana-2736	51	30	.	.	PUNCT
cana-2736	52	1	definition	definition	NOUN
cana-2736	52	2	2.1	2.1	NUM
cana-2736	52	3	.	.	PUNCT
cana-2736	53	1	[	[	X
cana-2736	53	2	7	7	X
cana-2736	53	3	]	]	X
cana-2736	53	4	a	a	DET
cana-2736	53	5	hilbert	hilbert	NOUN
cana-2736	53	6	algebra	algebra	NOUN
cana-2736	53	7	is	be	AUX
cana-2736	53	8	a	a	DET
cana-2736	53	9	triplet	triplet	NOUN
cana-2736	53	10	with	with	ADP
cana-2736	53	11	the	the	DET
cana-2736	53	12	formula	formula	NOUN
cana-2736	53	13	(	(	PUNCT
cana-2736	53	14	,	,	PUNCT
cana-2736	53	15	,	,	PUNCT
cana-2736	53	16	1)a	1)a	PRON
cana-2736	53	17	a=	a=	PROPN
cana-2736	53	18			PROPN
cana-2736	53	19	,	,	PUNCT
cana-2736	53	20	where	where	SCONJ
cana-2736	53	21	a	a	PRON
cana-2736	53	22	is	be	AUX
cana-2736	53	23	a	a	DET
cana-2736	53	24	nonempty	nonempty	ADJ
cana-2736	53	25	set	set	VERB
cana-2736	53	26	,	,	PUNCT
cana-2736	53	27			PROPN
cana-2736	53	28	is	be	AUX
cana-2736	53	29	a	a	DET
cana-2736	53	30	binary	binary	ADJ
cana-2736	53	31	operation	operation	NOUN
cana-2736	53	32	,	,	PUNCT
cana-2736	53	33	and	and	CCONJ
cana-2736	53	34	1	1	NUM
cana-2736	53	35	is	be	AUX
cana-2736	53	36	a	a	DET
cana-2736	53	37	fixed	fix	VERB
cana-2736	53	38	member	member	NOUN
cana-2736	53	39	of	of	ADP
cana-2736	53	40	a	a	PRON
cana-2736	53	41	that	that	PRON
cana-2736	53	42	is	be	AUX
cana-2736	53	43	true	true	ADJ
cana-2736	53	44	according	accord	VERB
cana-2736	53	45	to	to	ADP
cana-2736	53	46	the	the	DET
cana-2736	53	47	axioms	axiom	NOUN
cana-2736	53	48	stated	state	VERB
cana-2736	53	49	below	below	ADV
cana-2736	53	50	:	:	PUNCT
cana-2736	53	51	(	(	PUNCT
cana-2736	53	52	,	,	PUNCT
cana-2736	53	53	)	)	PUNCT
cana-2736	53	54	(	(	PUNCT
cana-2736	53	55	(	(	PUNCT
cana-2736	53	56	)	)	PUNCT
cana-2736	53	57	1)x	1)x	PROPN
cana-2736	53	58	y	y	PROPN
cana-2736	53	59	a	a	DET
cana-2736	53	60	x	x	X
cana-2736	53	61	y	y	PROPN
cana-2736	53	62	x	x	PROPN
cana-2736	53	63			NOUN
cana-2736	53	64			PROPN
cana-2736	53	65			PROPN
cana-2736	53	66	=	=	SYM
cana-2736	53	67	(	(	PUNCT
cana-2736	53	68	2.1	2.1	NUM
cana-2736	53	69	)	)	PUNCT
cana-2736	53	70	(	(	PUNCT
cana-2736	53	71	,	,	PUNCT
cana-2736	53	72	,	,	PUNCT
cana-2736	53	73	)	)	PUNCT
cana-2736	53	74	(	(	PUNCT
cana-2736	53	75	(	(	PUNCT
cana-2736	53	76	(	(	PUNCT
cana-2736	53	77	)	)	PUNCT
cana-2736	53	78	)	)	PUNCT
cana-2736	53	79	(	(	PUNCT
cana-2736	53	80	(	(	PUNCT
cana-2736	53	81	)	)	PUNCT
cana-2736	53	82	(	(	PUNCT
cana-2736	53	83	)	)	PUNCT
cana-2736	53	84	)	)	PUNCT
cana-2736	54	1	1)x	1)x	NUM
cana-2736	55	1	y	y	PROPN
cana-2736	55	2	z	z	VERB
cana-2736	55	3	a	a	X
cana-2736	55	4	x	x	X
cana-2736	55	5	y	y	NOUN
cana-2736	55	6	z	z	NOUN
cana-2736	55	7	x	x	SYM
cana-2736	55	8	y	y	PROPN
cana-2736	55	9	x	x	SYM
cana-2736	55	10	z	z	PART
cana-2736	55	11			NOUN
cana-2736	55	12			PROPN
cana-2736	55	13			PROPN
cana-2736	55	14			ADJ
cana-2736	55	15			ADJ
cana-2736	55	16			ADJ
cana-2736	55	17			PROPN
cana-2736	55	18	=	=	SYM
cana-2736	55	19	(	(	PUNCT
cana-2736	55	20	2.2	2.2	NUM
cana-2736	55	21	)	)	PUNCT
cana-2736	55	22	(	(	PUNCT
cana-2736	55	23	,	,	PUNCT
cana-2736	55	24	)	)	PUNCT
cana-2736	55	25	(	(	PUNCT
cana-2736	55	26	1	1	NUM
cana-2736	55	27	and	and	CCONJ
cana-2736	55	28	1	1	NUM
cana-2736	55	29	)	)	PUNCT
cana-2736	55	30	x	x	PROPN
cana-2736	56	1	y	y	PROPN
cana-2736	56	2	a	a	X
cana-2736	56	3	x	x	X
cana-2736	56	4	y	y	NOUN
cana-2736	56	5	y	y	PROPN
cana-2736	56	6	x	x	PUNCT
cana-2736	56	7	x	x	SYM
cana-2736	56	8	y	y	PROPN
cana-2736	56	9			NOUN
cana-2736	56	10			NUM
cana-2736	56	11	=	=	SYM
cana-2736	56	12			PROPN
cana-2736	56	13	=	=	SYM
cana-2736	56	14			NOUN
cana-2736	56	15	=	=	PUNCT
cana-2736	56	16	(	(	PUNCT
cana-2736	56	17	2.3	2.3	NUM
cana-2736	56	18	)	)	PUNCT
cana-2736	56	19	in	in	ADP
cana-2736	56	20	[	[	X
cana-2736	56	21	8	8	NUM
cana-2736	56	22	]	]	PUNCT
cana-2736	56	23	,	,	PUNCT
cana-2736	56	24	the	the	DET
cana-2736	56	25	following	follow	VERB
cana-2736	56	26	conclusion	conclusion	NOUN
cana-2736	56	27	was	be	AUX
cana-2736	56	28	established	establish	VERB
cana-2736	56	29	.	.	PUNCT
cana-2736	57	1	lemma	lemma	PROPN
cana-2736	57	2	2.2	2.2	NUM
cana-2736	57	3	.	.	PUNCT
cana-2736	58	1	let	let	AUX
cana-2736	58	2	(	(	PUNCT
cana-2736	58	3	,	,	PUNCT
cana-2736	58	4	,	,	PUNCT
cana-2736	58	5	1)a	1)a	PRON
cana-2736	58	6	a=	a=	ADJ
cana-2736	58	7			VERB
cana-2736	58	8	be	be	AUX
cana-2736	58	9	a	a	DET
cana-2736	58	10	hilbert	hilbert	NOUN
cana-2736	58	11	algebra	algebra	NOUN
cana-2736	58	12	.	.	PUNCT
cana-2736	59	1	then	then	ADV
cana-2736	59	2	(	(	PUNCT
cana-2736	59	3	1	1	X
cana-2736	59	4	)	)	PUNCT
cana-2736	59	5	(	(	PUNCT
cana-2736	59	6	)	)	PUNCT
cana-2736	59	7	(	(	PUNCT
cana-2736	59	8	1)x	1)x	NUM
cana-2736	59	9	a	a	DET
cana-2736	59	10	x	x	SYM
cana-2736	59	11	x	x	NOUN
cana-2736	59	12			NOUN
cana-2736	59	13			PROPN
cana-2736	59	14	=	=	SYM
cana-2736	59	15	,	,	PUNCT
cana-2736	59	16	(	(	PUNCT
cana-2736	59	17	2	2	NUM
cana-2736	59	18	)	)	PUNCT
cana-2736	59	19	(	(	PUNCT
cana-2736	59	20	)	)	PUNCT
cana-2736	59	21	(	(	PUNCT
cana-2736	59	22	1	1	X
cana-2736	59	23	)	)	PUNCT
cana-2736	59	24	x	x	NOUN
cana-2736	59	25	a	a	DET
cana-2736	59	26	x	x	SYM
cana-2736	59	27	x	x	NOUN
cana-2736	59	28			NOUN
cana-2736	59	29			PROPN
cana-2736	59	30	=	=	SYM
cana-2736	59	31	,	,	PUNCT
cana-2736	59	32	(	(	PUNCT
cana-2736	59	33	3	3	X
cana-2736	59	34	)	)	PUNCT
cana-2736	59	35	(	(	PUNCT
cana-2736	59	36	)	)	PUNCT
cana-2736	59	37	(	(	PUNCT
cana-2736	59	38	1	1	NUM
cana-2736	59	39	1)x	1)x	NUM
cana-2736	59	40	a	a	DET
cana-2736	59	41	x	x	NOUN
cana-2736	59	42			NOUN
cana-2736	59	43			PROPN
cana-2736	59	44	=	=	SYM
cana-2736	59	45	,	,	PUNCT
cana-2736	59	46	(	(	PUNCT
cana-2736	59	47	4	4	NUM
cana-2736	59	48	)	)	PUNCT
cana-2736	59	49	(	(	PUNCT
cana-2736	59	50	,	,	PUNCT
cana-2736	59	51	,	,	PUNCT
cana-2736	59	52	)	)	PUNCT
cana-2736	59	53	(	(	PUNCT
cana-2736	59	54	(	(	PUNCT
cana-2736	59	55	)	)	PUNCT
cana-2736	59	56	(	(	PUNCT
cana-2736	59	57	)	)	PUNCT
cana-2736	59	58	)	)	PUNCT
cana-2736	60	1	x	x	X
cana-2736	61	1	y	y	PROPN
cana-2736	61	2	z	z	PROPN
cana-2736	61	3	a	a	X
cana-2736	61	4	x	x	X
cana-2736	61	5	y	y	PROPN
cana-2736	61	6	z	z	PROPN
cana-2736	61	7	y	y	PROPN
cana-2736	61	8	x	x	SYM
cana-2736	61	9	z	z	PART
cana-2736	61	10			NOUN
cana-2736	61	11			PROPN
cana-2736	61	12			PROPN
cana-2736	61	13	=	=	SYM
cana-2736	61	14			PROPN
cana-2736	61	15			PROPN
cana-2736	61	16	,	,	PUNCT
cana-2736	61	17	(	(	PUNCT
cana-2736	61	18	5	5	NUM
cana-2736	61	19	)	)	PUNCT
cana-2736	61	20	(	(	PUNCT
cana-2736	61	21	,	,	PUNCT
cana-2736	61	22	,	,	PUNCT
cana-2736	61	23	)	)	PUNCT
cana-2736	61	24	(	(	PUNCT
cana-2736	61	25	(	(	PUNCT
cana-2736	61	26	)	)	PUNCT
cana-2736	61	27	(	(	PUNCT
cana-2736	61	28	(	(	PUNCT
cana-2736	61	29	)	)	PUNCT
cana-2736	61	30	(	(	PUNCT
cana-2736	61	31	)	)	PUNCT
cana-2736	61	32	)	)	PUNCT
cana-2736	61	33	1)x	1)x	NUM
cana-2736	62	1	y	y	PROPN
cana-2736	62	2	z	z	VERB
cana-2736	62	3	a	a	X
cana-2736	62	4	x	x	X
cana-2736	62	5	z	z	NOUN
cana-2736	62	6	z	z	NOUN
cana-2736	62	7	y	y	PROPN
cana-2736	62	8	x	x	SYM
cana-2736	62	9	y	y	PROPN
cana-2736	62	10			NOUN
cana-2736	62	11			NUM
cana-2736	62	12			PROPN
cana-2736	62	13			ADJ
cana-2736	62	14			ADJ
cana-2736	62	15			PROPN
cana-2736	62	16	=	=	SYM
cana-2736	62	17	.	.	PUNCT
cana-2736	63	1	in	in	ADP
cana-2736	63	2	a	a	DET
cana-2736	63	3	hilbert	hilbert	NOUN
cana-2736	63	4	algebra	algebra	NOUN
cana-2736	63	5	(	(	PUNCT
cana-2736	63	6	,	,	PUNCT
cana-2736	63	7	,	,	PUNCT
cana-2736	63	8	1)a	1)a	PRON
cana-2736	63	9	a=	a=	PROPN
cana-2736	63	10			PROPN
cana-2736	63	11	,	,	PUNCT
cana-2736	63	12	the	the	DET
cana-2736	63	13	binary	binary	PROPN
cana-2736	63	14	relation	relation	PROPN
cana-2736	63	15			PROPN
cana-2736	63	16	is	be	AUX
cana-2736	63	17	defined	define	VERB
cana-2736	63	18	by	by	ADP
cana-2736	63	19	(	(	PUNCT
cana-2736	63	20	,	,	PUNCT
cana-2736	63	21	)	)	PUNCT
cana-2736	63	22	(	(	PUNCT
cana-2736	63	23	1)x	1)x	NUM
cana-2736	63	24	y	y	NOUN
cana-2736	63	25	a	a	DET
cana-2736	63	26	x	x	X
cana-2736	63	27	y	y	PROPN
cana-2736	63	28	x	x	SYM
cana-2736	63	29	y	y	PROPN
cana-2736	63	30			NOUN
cana-2736	63	31			NOUN
cana-2736	63	32			ADP
cana-2736	63	33			PROPN
cana-2736	63	34	=	=	PUNCT
cana-2736	63	35	,	,	PUNCT
cana-2736	63	36	which	which	PRON
cana-2736	63	37	is	be	AUX
cana-2736	63	38	a	a	DET
cana-2736	63	39	partial	partial	ADJ
cana-2736	63	40	order	order	NOUN
cana-2736	63	41	on	on	ADP
cana-2736	63	42	a	a	DET
cana-2736	63	43	with	with	ADP
cana-2736	63	44	1	1	NUM
cana-2736	63	45	as	as	ADP
cana-2736	63	46	the	the	DET
cana-2736	63	47	largest	large	ADJ
cana-2736	63	48	element	element	NOUN
cana-2736	63	49	.	.	PUNCT
cana-2736	64	1	definition	definition	NOUN
cana-2736	64	2	2.3	2.3	NUM
cana-2736	64	3	.	.	PUNCT
cana-2736	65	1	[	[	X
cana-2736	65	2	16	16	NUM
cana-2736	65	3	]	]	PUNCT
cana-2736	65	4	a	a	DET
cana-2736	65	5	nonempty	nonempty	ADV
cana-2736	65	6	subset	subset	VERB
cana-2736	65	7	d	d	NOUN
cana-2736	65	8	of	of	ADP
cana-2736	65	9	a	a	DET
cana-2736	65	10	hilbert	hilbert	NOUN
cana-2736	65	11	algebra	algebra	NOUN
cana-2736	65	12	(	(	PUNCT
cana-2736	65	13	,	,	PUNCT
cana-2736	65	14	,	,	PUNCT
cana-2736	65	15	1)a	1)a	PRON
cana-2736	65	16	a=	a=	NOUN
cana-2736	65	17			PROPN
cana-2736	65	18	is	be	AUX
cana-2736	65	19	called	call	VERB
cana-2736	65	20	a	a	DET
cana-2736	65	21	subalgebra	subalgebra	NOUN
cana-2736	65	22	of	of	ADP
cana-2736	65	23	a	a	DET
cana-2736	65	24	if	if	NOUN
cana-2736	65	25	x	x	X
cana-2736	65	26	y	y	PROPN
cana-2736	65	27	d	d	PROPN
cana-2736	65	28			NOUN
cana-2736	65	29	for	for	ADP
cana-2736	65	30	all	all	PRON
cana-2736	65	31	,	,	PUNCT
cana-2736	65	32	x	x	PROPN
cana-2736	65	33	y	y	PROPN
cana-2736	65	34	d	d	PROPN
cana-2736	65	35	.	.	PUNCT
cana-2736	66	1	definition	definition	NOUN
cana-2736	66	2	2.4	2.4	NUM
cana-2736	66	3	.	.	PUNCT
cana-2736	67	1	[	[	X
cana-2736	67	2	6	6	NUM
cana-2736	67	3	]	]	PUNCT
cana-2736	67	4	a	a	DET
cana-2736	67	5	nonempty	nonempty	NOUN
cana-2736	67	6	subset	subset	VERB
cana-2736	67	7	d	d	NOUN
cana-2736	67	8	of	of	ADP
cana-2736	67	9	a	a	DET
cana-2736	67	10	hilbert	hilbert	NOUN
cana-2736	67	11	algebra	algebra	NOUN
cana-2736	67	12	(	(	PUNCT
cana-2736	67	13	,	,	PUNCT
cana-2736	67	14	,	,	PUNCT
cana-2736	67	15	1)a	1)a	PRON
cana-2736	67	16	a=	a=	NOUN
cana-2736	67	17			PROPN
cana-2736	67	18	is	be	AUX
cana-2736	67	19	called	call	VERB
cana-2736	67	20	an	an	DET
cana-2736	67	21	ideal	ideal	NOUN
cana-2736	67	22	of	of	ADP
cana-2736	67	23	a	a	PRON
cana-2736	67	24	if	if	SCONJ
cana-2736	67	25	the	the	DET
cana-2736	67	26	following	follow	VERB
cana-2736	67	27	conditions	condition	NOUN
cana-2736	67	28	hold	hold	VERB
cana-2736	67	29	:	:	PUNCT
cana-2736	67	30	(	(	PUNCT
cana-2736	67	31	1	1	X
cana-2736	67	32	)	)	PUNCT
cana-2736	67	33	1	1	NUM
cana-2736	67	34	d	d	ADJ
cana-2736	67	35	,	,	PUNCT
cana-2736	67	36	(	(	PUNCT
cana-2736	67	37	2	2	NUM
cana-2736	67	38	)	)	PUNCT
cana-2736	67	39	(	(	PUNCT
cana-2736	67	40	,	,	PUNCT
cana-2736	67	41	)	)	PUNCT
cana-2736	67	42	(	(	PUNCT
cana-2736	67	43	)	)	PUNCT
cana-2736	67	44	x	x	X
cana-2736	67	45	y	y	PROPN
cana-2736	67	46	a	a	DET
cana-2736	67	47	y	y	PROPN
cana-2736	67	48	d	d	X
cana-2736	67	49	x	x	SYM
cana-2736	67	50	y	y	PROPN
cana-2736	67	51	d	d	PROPN
cana-2736	67	52			PROPN
cana-2736	67	53			PROPN
cana-2736	67	54			NOUN
cana-2736	68	1			ADJ
cana-2736	68	2			NOUN
cana-2736	68	3	,	,	PUNCT
cana-2736	68	4	(	(	PUNCT
cana-2736	68	5	3	3	X
cana-2736	68	6	)	)	SYM
cana-2736	68	7	1	1	NUM
cana-2736	68	8	2	2	NUM
cana-2736	68	9	1	1	NUM
cana-2736	68	10	2	2	NUM
cana-2736	68	11	1	1	NUM
cana-2736	68	12	2	2	NUM
cana-2736	68	13	(	(	PUNCT
cana-2736	68	14	,	,	PUNCT
cana-2736	68	15	,	,	PUNCT
cana-2736	68	16	)	)	PUNCT
cana-2736	68	17	(	(	PUNCT
cana-2736	68	18	,	,	PUNCT
cana-2736	68	19	(	(	PUNCT
cana-2736	68	20	(	(	PUNCT
cana-2736	68	21	)	)	PUNCT
cana-2736	68	22	)	)	PUNCT
cana-2736	68	23	)	)	PUNCT
cana-2736	69	1	x	x	X
cana-2736	69	2	y	y	NOUN
cana-2736	69	3	y	y	PROPN
cana-2736	70	1	a	a	PRON
cana-2736	70	2	y	y	PROPN
cana-2736	70	3	y	y	PROPN
cana-2736	70	4	d	d	PROPN
cana-2736	70	5	y	y	PROPN
cana-2736	70	6	y	y	PROPN
cana-2736	70	7	x	x	PUNCT
cana-2736	70	8	x	x	PROPN
cana-2736	70	9	d	d	PROPN
cana-2736	70	10			PROPN
cana-2736	70	11			PROPN
cana-2736	70	12			NOUN
cana-2736	71	1			VERB
cana-2736	71	2			PROPN
cana-2736	71	3			PROPN
cana-2736	71	4			NOUN
cana-2736	71	5	.	.	PUNCT
cana-2736	72	1	definition	definition	NOUN
cana-2736	72	2	2.5	2.5	NUM
cana-2736	72	3	.	.	PUNCT
cana-2736	73	1	[	[	X
cana-2736	73	2	12	12	NUM
cana-2736	73	3	]	]	PUNCT
cana-2736	73	4	a	a	DET
cana-2736	73	5	nonempty	nonempty	NOUN
cana-2736	73	6	subset	subset	VERB
cana-2736	73	7	d	d	NOUN
cana-2736	73	8	of	of	ADP
cana-2736	73	9	a	a	DET
cana-2736	73	10	hilbert	hilbert	NOUN
cana-2736	73	11	algebra	algebra	NOUN
cana-2736	73	12	(	(	PUNCT
cana-2736	73	13	,	,	PUNCT
cana-2736	73	14	,	,	PUNCT
cana-2736	73	15	1)a	1)a	PRON
cana-2736	73	16	a=	a=	NOUN
cana-2736	73	17			PROPN
cana-2736	73	18	is	be	AUX
cana-2736	73	19	called	call	VERB
cana-2736	73	20	a	a	DET
cana-2736	73	21	near	near	ADJ
cana-2736	73	22	filter	filter	NOUN
cana-2736	73	23	of	of	ADP
cana-2736	73	24	a	a	PRON
cana-2736	73	25	if	if	SCONJ
cana-2736	73	26	the	the	DET
cana-2736	73	27	following	follow	VERB
cana-2736	73	28	conditions	condition	NOUN
cana-2736	73	29	hold	hold	VERB
cana-2736	73	30	:	:	PUNCT
cana-2736	73	31	(	(	PUNCT
cana-2736	73	32	1	1	X
cana-2736	73	33	)	)	PUNCT
cana-2736	73	34	1	1	NUM
cana-2736	73	35	d	d	ADJ
cana-2736	73	36	,	,	PUNCT
cana-2736	73	37	communications	communication	NOUN
cana-2736	73	38	on	on	ADP
cana-2736	73	39	applied	apply	VERB
cana-2736	73	40	nonlinear	nonlinear	ADJ
cana-2736	73	41	analysis	analysis	NOUN
cana-2736	73	42	issn	issn	NOUN
cana-2736	73	43	:	:	PUNCT
cana-2736	73	44	1074	1074	NUM
cana-2736	73	45	-	-	PUNCT
cana-2736	73	46	133x	133x	NUM
cana-2736	73	47	vol	vol	NOUN
cana-2736	73	48	32	32	NUM
cana-2736	74	1	no	no	NOUN
cana-2736	74	2	.	.	PUNCT
cana-2736	75	1	4s	4s	NUM
cana-2736	75	2	(	(	PUNCT
cana-2736	75	3	2025	2025	NUM
cana-2736	75	4	)	)	PUNCT
cana-2736	75	5	15	15	NUM
cana-2736	75	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	75	7	(	(	PUNCT
cana-2736	75	8	2	2	NUM
cana-2736	75	9	)	)	PUNCT
cana-2736	75	10	(	(	PUNCT
cana-2736	75	11	,	,	PUNCT
cana-2736	75	12	)	)	PUNCT
cana-2736	75	13	(	(	PUNCT
cana-2736	75	14	)	)	PUNCT
cana-2736	75	15	x	x	X
cana-2736	75	16	y	y	PROPN
cana-2736	75	17	a	a	DET
cana-2736	75	18	y	y	PROPN
cana-2736	75	19	d	d	X
cana-2736	75	20	x	x	SYM
cana-2736	75	21	y	y	PROPN
cana-2736	75	22	d	d	PROPN
cana-2736	75	23			PROPN
cana-2736	75	24			PROPN
cana-2736	75	25			NOUN
cana-2736	75	26			ADJ
cana-2736	75	27			NOUN
cana-2736	75	28	.	.	PUNCT
cana-2736	76	1	definition	definition	NOUN
cana-2736	76	2	2.6	2.6	NUM
cana-2736	76	3	.	.	PUNCT
cana-2736	77	1	[	[	X
cana-2736	77	2	12	12	NUM
cana-2736	77	3	]	]	PUNCT
cana-2736	77	4	a	a	DET
cana-2736	77	5	nonempty	nonempty	NOUN
cana-2736	77	6	subset	subset	VERB
cana-2736	77	7	d	d	NOUN
cana-2736	77	8	of	of	ADP
cana-2736	77	9	a	a	DET
cana-2736	77	10	hilbert	hilbert	NOUN
cana-2736	77	11	algebra	algebra	NOUN
cana-2736	77	12	(	(	PUNCT
cana-2736	77	13	,	,	PUNCT
cana-2736	77	14	,	,	PUNCT
cana-2736	77	15	1)a	1)a	PRON
cana-2736	77	16	a=	a=	NOUN
cana-2736	77	17			PROPN
cana-2736	77	18	is	be	AUX
cana-2736	77	19	called	call	VERB
cana-2736	77	20	a	a	DET
cana-2736	77	21	filter	filter	NOUN
cana-2736	77	22	of	of	ADP
cana-2736	77	23	a	a	PRON
cana-2736	77	24	if	if	SCONJ
cana-2736	77	25	the	the	DET
cana-2736	77	26	following	follow	VERB
cana-2736	77	27	conditions	condition	NOUN
cana-2736	77	28	hold	hold	VERB
cana-2736	77	29	:	:	PUNCT
cana-2736	77	30	(	(	PUNCT
cana-2736	77	31	1	1	X
cana-2736	77	32	)	)	PUNCT
cana-2736	77	33	1	1	NUM
cana-2736	77	34	d	d	ADJ
cana-2736	77	35	,	,	PUNCT
cana-2736	77	36	(	(	PUNCT
cana-2736	77	37	2	2	NUM
cana-2736	77	38	)	)	PUNCT
cana-2736	77	39	(	(	PUNCT
cana-2736	77	40	,	,	PUNCT
cana-2736	77	41	)	)	PUNCT
cana-2736	77	42	(	(	PUNCT
cana-2736	77	43	,	,	PUNCT
cana-2736	77	44	)	)	PUNCT
cana-2736	77	45	x	x	PROPN
cana-2736	78	1	y	y	PROPN
cana-2736	78	2	a	a	X
cana-2736	78	3	x	x	X
cana-2736	78	4	y	y	NOUN
cana-2736	78	5	x	x	PROPN
cana-2736	78	6	d	d	X
cana-2736	78	7	y	y	PROPN
cana-2736	78	8	d	d	PROPN
cana-2736	78	9			NOUN
cana-2736	78	10			PROPN
cana-2736	78	11			NOUN
cana-2736	78	12			NOUN
cana-2736	78	13			NOUN
cana-2736	78	14	.	.	PUNCT
cana-2736	79	1	definition	definition	NOUN
cana-2736	79	2	2.7	2.7	NUM
cana-2736	79	3	.	.	PUNCT
cana-2736	80	1	let	let	AUX
cana-2736	80	2	(	(	PUNCT
cana-2736	80	3	,	,	PUNCT
cana-2736	80	4	,	,	PUNCT
cana-2736	80	5	1	1	X
cana-2736	80	6	)	)	PUNCT
cana-2736	80	7	aa	aa	NOUN
cana-2736	80	8	a=	a=	VERB
cana-2736	80	9			ADJ
cana-2736	80	10	and	and	CCONJ
cana-2736	80	11	(	(	PUNCT
cana-2736	80	12	,	,	PUNCT
cana-2736	80	13	,	,	PUNCT
cana-2736	80	14	1	1	X
cana-2736	80	15	)	)	PUNCT
cana-2736	80	16	bb	bb	NUM
cana-2736	80	17	b=	b=	NOUN
cana-2736	80	18	å	å	PROPN
cana-2736	80	19	be	be	AUX
cana-2736	80	20	hilbert	hilbert	PROPN
cana-2736	80	21	algebras	algebras	PROPN
cana-2736	80	22	.	.	PUNCT
cana-2736	81	1	a	a	DET
cana-2736	81	2	function	function	NOUN
cana-2736	81	3	:	:	PUNCT
cana-2736	81	4	f	f	PROPN
cana-2736	81	5	a	a	DET
cana-2736	81	6	b→	b→	PROPN
cana-2736	81	7	is	be	AUX
cana-2736	81	8	called	call	VERB
cana-2736	81	9	a	a	DET
cana-2736	81	10	homomorphism	homomorphism	NOUN
cana-2736	81	11	if	if	SCONJ
cana-2736	81	12	(	(	PUNCT
cana-2736	81	13	)	)	PUNCT
cana-2736	81	14	(	(	PUNCT
cana-2736	81	15	)	)	PUNCT
cana-2736	81	16	(	(	PUNCT
cana-2736	81	17	)	)	PUNCT
cana-2736	81	18	f	f	X
cana-2736	82	1	x	x	PUNCT
cana-2736	82	2	y	y	NOUN
cana-2736	82	3	f	f	NOUN
cana-2736	82	4	x	x	X
cana-2736	82	5	f	f	X
cana-2736	82	6	y	y	NOUN
cana-2736	82	7	=	=	SYM
cana-2736	82	8	å	å	PROPN
cana-2736	82	9	for	for	ADP
cana-2736	82	10	all	all	PRON
cana-2736	82	11	,	,	PUNCT
cana-2736	82	12	x	x	PRON
cana-2736	82	13	y	y	NOUN
cana-2736	82	14	a	a	PROPN
cana-2736	82	15	.	.	PUNCT
cana-2736	83	1	now	now	ADV
cana-2736	83	2	,	,	PUNCT
cana-2736	83	3	(	(	PUNCT
cana-2736	83	4	1	1	X
cana-2736	83	5	)	)	PUNCT
cana-2736	83	6	(	(	PUNCT
cana-2736	83	7	1	1	NUM
cana-2736	83	8	1	1	NUM
cana-2736	83	9	)	)	PUNCT
cana-2736	83	10	(	(	PUNCT
cana-2736	83	11	1	1	X
cana-2736	83	12	)	)	PUNCT
cana-2736	83	13	(	(	PUNCT
cana-2736	83	14	1	1	X
cana-2736	83	15	)	)	PUNCT
cana-2736	83	16	1a	1a	NOUN
cana-2736	83	17	a	a	DET
cana-2736	83	18	a	a	DET
cana-2736	83	19	a	a	DET
cana-2736	83	20	a	a	DET
cana-2736	83	21	bf	bf	NOUN
cana-2736	83	22	f	f	PROPN
cana-2736	83	23	f	f	PROPN
cana-2736	83	24	f=	f=	VERB
cana-2736	83	25			PROPN
cana-2736	83	26	=	=	PUNCT
cana-2736	83	27	=	=	NUM
cana-2736	83	28	å	å	PROPN
cana-2736	83	29	.	.	PUNCT
cana-2736	84	1	a	a	DET
cana-2736	84	2	homomorphism	homomorphism	NOUN
cana-2736	84	3	:	:	PUNCT
cana-2736	84	4	f	f	X
cana-2736	84	5	a	a	DET
cana-2736	84	6	a→	a→	NUM
cana-2736	84	7	is	be	AUX
cana-2736	84	8	said	say	VERB
cana-2736	84	9	to	to	PART
cana-2736	84	10	be	be	AUX
cana-2736	84	11	an	an	DET
cana-2736	84	12	endomorphism	endomorphism	NOUN
cana-2736	84	13	.	.	PUNCT
cana-2736	85	1	for	for	ADP
cana-2736	85	2	any	any	PRON
cana-2736	85	3	,	,	PUNCT
cana-2736	85	4	x	x	PROPN
cana-2736	85	5	y	y	NOUN
cana-2736	85	6	in	in	ADP
cana-2736	85	7	a	a	DET
cana-2736	85	8	hilbert	hilbert	NOUN
cana-2736	85	9	algebra	algebra	NOUN
cana-2736	85	10	(	(	PUNCT
cana-2736	85	11	,	,	PUNCT
cana-2736	85	12	,	,	PUNCT
cana-2736	85	13	1)a	1)a	PRON
cana-2736	85	14	a=	a=	PROPN
cana-2736	85	15			NUM
cana-2736	85	16	,	,	PUNCT
cana-2736	85	17	we	we	PRON
cana-2736	85	18	define	define	VERB
cana-2736	85	19	x	x	PUNCT
cana-2736	85	20	y	y	NOUN
cana-2736	85	21	by	by	ADP
cana-2736	85	22	(	(	PUNCT
cana-2736	85	23	)	)	PUNCT
cana-2736	85	24	y	y	NOUN
cana-2736	85	25	x	x	PUNCT
cana-2736	85	26	x	x	PROPN
cana-2736	85	27			PROPN
cana-2736	85	28	.	.	PUNCT
cana-2736	86	1	by	by	ADP
cana-2736	86	2	lemma	lemma	PROPN
cana-2736	86	3	2.2	2.2	NUM
cana-2736	86	4	(	(	PUNCT
cana-2736	86	5	4	4	NUM
cana-2736	86	6	)	)	PUNCT
cana-2736	86	7	,	,	PUNCT
cana-2736	86	8	we	we	PRON
cana-2736	86	9	can	can	AUX
cana-2736	86	10	prove	prove	VERB
cana-2736	86	11	that	that	SCONJ
cana-2736	86	12	x	x	PRON
cana-2736	86	13	y	y	NOUN
cana-2736	86	14	is	be	AUX
cana-2736	86	15	an	an	DET
cana-2736	86	16	upper	upper	ADJ
cana-2736	86	17	bound	bind	VERB
cana-2736	86	18	of	of	ADP
cana-2736	86	19	x	x	PROPN
cana-2736	86	20	and	and	CCONJ
cana-2736	86	21	y	y	PROPN
cana-2736	86	22	.	.	PUNCT
cana-2736	87	1	that	that	PRON
cana-2736	87	2	is	is	ADV
cana-2736	87	3	,	,	PUNCT
cana-2736	87	4	(	(	PUNCT
cana-2736	87	5	,	,	PUNCT
cana-2736	87	6	)	)	PUNCT
cana-2736	87	7	(	(	PUNCT
cana-2736	87	8	(	(	PUNCT
cana-2736	87	9	)	)	PUNCT
cana-2736	87	10	1)x	1)x	PROPN
cana-2736	87	11	y	y	NOUN
cana-2736	87	12	x	x	SYM
cana-2736	87	13	x	x	PUNCT
cana-2736	87	14	x	x	SYM
cana-2736	87	15	y	y	PROPN
cana-2736	87	16			NOUN
cana-2736	87	17			NUM
cana-2736	87	18			NOUN
cana-2736	87	19	=	=	SYM
cana-2736	87	20	,	,	PUNCT
cana-2736	87	21	(	(	PUNCT
cana-2736	87	22	2.4	2.4	NUM
cana-2736	87	23	)	)	PUNCT
cana-2736	87	24	(	(	PUNCT
cana-2736	87	25	,	,	PUNCT
cana-2736	87	26	)	)	PUNCT
cana-2736	87	27	(	(	PUNCT
cana-2736	87	28	(	(	PUNCT
cana-2736	87	29	)	)	PUNCT
cana-2736	87	30	1)x	1)x	PROPN
cana-2736	87	31	y	y	NOUN
cana-2736	87	32	x	x	SYM
cana-2736	87	33	y	y	PROPN
cana-2736	87	34	x	x	SYM
cana-2736	87	35	y	y	PROPN
cana-2736	87	36			NOUN
cana-2736	87	37			NUM
cana-2736	87	38			NOUN
cana-2736	87	39	=	=	PUNCT
cana-2736	87	40	.	.	PUNCT
cana-2736	88	1	(	(	PUNCT
cana-2736	88	2	2.5	2.5	NUM
cana-2736	88	3	)	)	PUNCT
cana-2736	88	4	a	a	DET
cana-2736	88	5	hilbert	hilbert	NOUN
cana-2736	88	6	algebra	algebra	NOUN
cana-2736	88	7	(	(	PUNCT
cana-2736	88	8	,	,	PUNCT
cana-2736	88	9	,	,	PUNCT
cana-2736	88	10	1)a	1)a	PRON
cana-2736	88	11	a=	a=	NOUN
cana-2736	88	12			PROPN
cana-2736	88	13	is	be	AUX
cana-2736	88	14	said	say	VERB
cana-2736	88	15	to	to	PART
cana-2736	88	16	be	be	AUX
cana-2736	88	17			ADV
cana-2736	88	18	-commutative	-commutative	ADJ
cana-2736	88	19	[	[	X
cana-2736	88	20	14	14	NUM
cana-2736	88	21	]	]	X
cana-2736	88	22	if	if	SCONJ
cana-2736	88	23	for	for	ADP
cana-2736	88	24	all	all	PRON
cana-2736	88	25	,	,	PUNCT
cana-2736	88	26	,	,	PUNCT
cana-2736	88	27	(	(	PUNCT
cana-2736	88	28	)	)	PUNCT
cana-2736	88	29	(	(	PUNCT
cana-2736	88	30	)	)	PUNCT
cana-2736	88	31	x	x	X
cana-2736	88	32	y	y	PROPN
cana-2736	88	33	a	a	PRON
cana-2736	88	34	y	y	NOUN
cana-2736	88	35	x	x	PUNCT
cana-2736	88	36	x	x	PUNCT
cana-2736	88	37	x	x	SYM
cana-2736	88	38	y	y	PROPN
cana-2736	88	39	y	y	VERB
cana-2736	88	40			VERB
cana-2736	88	41			PROPN
cana-2736	88	42	=	=	SYM
cana-2736	88	43			PROPN
cana-2736	88	44			PROPN
cana-2736	88	45	,	,	PUNCT
cana-2736	88	46	that	that	ADV
cana-2736	88	47	is	is	ADV
cana-2736	88	48	,	,	PUNCT
cana-2736	88	49	x	x	PROPN
cana-2736	88	50	y	y	NOUN
cana-2736	88	51	y	y	PROPN
cana-2736	88	52	x	x	PUNCT
cana-2736	89	1	=	=	NOUN
cana-2736	89	2			NOUN
cana-2736	89	3	.	.	PUNCT
cana-2736	90	1	from	from	ADP
cana-2736	90	2	[	[	X
cana-2736	90	3	14	14	NUM
cana-2736	90	4	]	]	PUNCT
cana-2736	90	5	,	,	PUNCT
cana-2736	90	6	we	we	PRON
cana-2736	90	7	know	know	VERB
cana-2736	90	8	that	that	PRON
cana-2736	90	9	(	(	PUNCT
cana-2736	90	10	)	)	PUNCT
cana-2736	90	11	(	(	PUNCT
cana-2736	90	12	)	)	PUNCT
cana-2736	90	13	x	x	SYM
cana-2736	90	14	x	x	PUNCT
cana-2736	90	15	x	x	PUNCT
cana-2736	90	16	x	x	SYM
cana-2736	90	17	x	x	NOUN
cana-2736	90	18			NOUN
cana-2736	90	19			NOUN
cana-2736	90	20	=	=	SYM
cana-2736	90	21	,	,	PUNCT
cana-2736	90	22	(	(	PUNCT
cana-2736	90	23	2.6	2.6	NUM
cana-2736	90	24	)	)	PUNCT
cana-2736	90	25	(	(	PUNCT
cana-2736	90	26	)	)	PUNCT
cana-2736	90	27	(	(	PUNCT
cana-2736	90	28	1	1	NUM
cana-2736	90	29	1	1	NUM
cana-2736	90	30	1)x	1)x	NUM
cana-2736	90	31	x	x	SYM
cana-2736	90	32	x	x	SYM
cana-2736	90	33	x	x	NOUN
cana-2736	90	34			NOUN
cana-2736	90	35			ADV
cana-2736	90	36	=	=	NOUN
cana-2736	90	37			NOUN
cana-2736	90	38	=	=	PUNCT
cana-2736	90	39	.	.	PUNCT
cana-2736	91	1	(	(	PUNCT
cana-2736	91	2	2.7	2.7	NUM
cana-2736	91	3	)	)	PUNCT
cana-2736	91	4	3	3	NUM
cana-2736	91	5	.	.	PUNCT
cana-2736	91	6	left	leave	VERB
cana-2736	91	7	and	and	CCONJ
cana-2736	91	8	rightf	rightf	ADJ
cana-2736	91	9	-derivations	-derivation	NOUN
cana-2736	91	10	of	of	ADP
cana-2736	91	11	type	type	NOUN
cana-2736	91	12	i	i	PRON
cana-2736	91	13	in	in	ADP
cana-2736	91	14	this	this	DET
cana-2736	91	15	section	section	NOUN
cana-2736	91	16	,	,	PUNCT
cana-2736	91	17	we	we	PRON
cana-2736	91	18	introduce	introduce	VERB
cana-2736	91	19	the	the	DET
cana-2736	91	20	concepts	concept	NOUN
cana-2736	91	21	of	of	ADP
cana-2736	91	22	leftf	leftf	ADJ
cana-2736	91	23	-derivations	-derivation	NOUN
cana-2736	91	24	,	,	PUNCT
cana-2736	91	25	rightf	rightf	ADJ
cana-2736	91	26	-derivations	-derivation	NOUN
cana-2736	91	27	,	,	PUNCT
cana-2736	91	28	and	and	CCONJ
cana-2736	91	29	f	f	PROPN
cana-2736	91	30	derivations	derivation	NOUN
cana-2736	91	31	of	of	ADP
cana-2736	91	32	type	type	NOUN
cana-2736	91	33	i	i	PRON
cana-2736	91	34	in	in	ADP
cana-2736	91	35	hilbert	hilbert	PROPN
cana-2736	91	36	algebras	algebras	PROPN
cana-2736	91	37	,	,	PUNCT
cana-2736	91	38	examining	examine	VERB
cana-2736	91	39	their	their	PRON
cana-2736	91	40	fundamental	fundamental	ADJ
cana-2736	91	41	properties	property	NOUN
cana-2736	91	42	.	.	PUNCT
cana-2736	92	1	we	we	PRON
cana-2736	92	2	then	then	ADV
cana-2736	92	3	focus	focus	VERB
cana-2736	92	4	on	on	ADP
cana-2736	92	5	analyzing	analyze	VERB
cana-2736	92	6	the	the	DET
cana-2736	92	7	subset	subset	ADJ
cana-2736	92	8	ker	ker	NOUN
cana-2736	92	9	(	(	PUNCT
cana-2736	92	10	)	)	PUNCT
cana-2736	92	11	d	d	ADP
cana-2736	92	12	a	a	PRON
cana-2736	92	13	associated	associate	VERB
cana-2736	92	14	with	with	ADP
cana-2736	92	15	a	a	DET
cana-2736	92	16	left	left	ADJ
cana-2736	92	17	(	(	PUNCT
cana-2736	92	18	or	or	CCONJ
cana-2736	92	19	right	right	ADJ
cana-2736	92	20	)	)	PUNCT
cana-2736	92	21	f	f	PROPN
cana-2736	92	22	-derivation	-derivation	NOUN
cana-2736	92	23	of	of	ADP
cana-2736	92	24	type	type	NOUN
cana-2736	92	25	i	i	PRON
cana-2736	92	26	,	,	PUNCT
cana-2736	92	27	highlighting	highlight	VERB
cana-2736	92	28	its	its	PRON
cana-2736	92	29	structural	structural	ADJ
cana-2736	92	30	significance	significance	NOUN
cana-2736	92	31	within	within	ADP
cana-2736	92	32	the	the	DET
cana-2736	92	33	algebra	algebra	NOUN
cana-2736	92	34	.	.	PUNCT
cana-2736	93	1	definition	definition	NOUN
cana-2736	93	2	3.1	3.1	NUM
cana-2736	93	3	.	.	PUNCT
cana-2736	94	1	let	let	VERB
cana-2736	94	2	(	(	PUNCT
cana-2736	94	3	,	,	PUNCT
cana-2736	94	4	,	,	PUNCT
cana-2736	94	5	1)a	1)a	PRON
cana-2736	94	6	a=	a=	ADJ
cana-2736	94	7			VERB
cana-2736	94	8	be	be	AUX
cana-2736	94	9	a	a	DET
cana-2736	94	10	hilbert	hilbert	NOUN
cana-2736	94	11	algebra	algebra	NOUN
cana-2736	94	12	and	and	CCONJ
cana-2736	94	13	f	f	PROPN
cana-2736	94	14	be	be	AUX
cana-2736	94	15	an	an	DET
cana-2736	94	16	endomorphism	endomorphism	NOUN
cana-2736	94	17	of	of	ADP
cana-2736	94	18	a	a	PRON
cana-2736	94	19	.	.	PUNCT
cana-2736	95	1	a	a	DET
cana-2736	95	2	self	self	NOUN
cana-2736	95	3	-	-	PUNCT
cana-2736	95	4	map	map	NOUN
cana-2736	95	5	:	:	PUNCT
cana-2736	95	6	d	d	ADP
cana-2736	95	7	a	a	DET
cana-2736	95	8	a→	a→	PUNCT
cana-2736	95	9	is	be	AUX
cana-2736	95	10	called	call	VERB
cana-2736	95	11	a	a	DET
cana-2736	95	12	leftf	leftf	ADJ
cana-2736	95	13	-derivation	-derivation	NOUN
cana-2736	95	14	of	of	ADP
cana-2736	95	15	type	type	NOUN
cana-2736	95	16	i	i	PRON
cana-2736	95	17	of	of	ADP
cana-2736	95	18	a	a	PRON
cana-2736	95	19	if	if	SCONJ
cana-2736	95	20	it	it	PRON
cana-2736	95	21	satisfies	satisfy	VERB
cana-2736	95	22	the	the	DET
cana-2736	95	23	identity	identity	NOUN
cana-2736	95	24	(	(	PUNCT
cana-2736	95	25	)	)	PUNCT
cana-2736	95	26	(	(	PUNCT
cana-2736	95	27	(	(	PUNCT
cana-2736	95	28	)	)	PUNCT
cana-2736	95	29	(	(	PUNCT
cana-2736	95	30	)	)	PUNCT
cana-2736	95	31	)	)	PUNCT
cana-2736	96	1	(	(	PUNCT
cana-2736	96	2	)	)	PUNCT
cana-2736	96	3	d	d	X
cana-2736	96	4	x	x	PUNCT
cana-2736	96	5	y	y	NOUN
cana-2736	96	6	d	d	NOUN
cana-2736	96	7	x	x	X
cana-2736	96	8	f	f	PROPN
cana-2736	96	9	y	y	PROPN
cana-2736	96	10	x	x	SYM
cana-2736	96	11	y	y	NOUN
cana-2736	96	12	=	=	SYM
cana-2736	96	13			ADJ
cana-2736	96	14			NOUN
cana-2736	96	15			PROPN
cana-2736	96	16	for	for	ADP
cana-2736	96	17	all	all	PRON
cana-2736	96	18	,	,	PUNCT
cana-2736	96	19	x	x	PRON
cana-2736	96	20	y	y	PROPN
cana-2736	96	21	a	a	PROPN
cana-2736	96	22	.	.	PUNCT
cana-2736	97	1	similarly	similarly	ADV
cana-2736	97	2	,	,	PUNCT
cana-2736	97	3	a	a	DET
cana-2736	97	4	self	self	NOUN
cana-2736	97	5	-	-	PUNCT
cana-2736	97	6	map	map	NOUN
cana-2736	97	7	:	:	PUNCT
cana-2736	97	8	d	d	ADP
cana-2736	97	9	a	a	DET
cana-2736	97	10	a→	a→	PUNCT
cana-2736	97	11	is	be	AUX
cana-2736	97	12	called	call	VERB
cana-2736	97	13	a	a	DET
cana-2736	97	14	rightf	rightf	ADJ
cana-2736	97	15	-derivation	-derivation	NOUN
cana-2736	97	16	of	of	ADP
cana-2736	97	17	type	type	NOUN
cana-2736	97	18	i	i	PRON
cana-2736	97	19	of	of	ADP
cana-2736	97	20	a	a	PRON
cana-2736	97	21	if	if	SCONJ
cana-2736	97	22	it	it	PRON
cana-2736	97	23	satisfies	satisfy	VERB
cana-2736	97	24	the	the	DET
cana-2736	97	25	identity	identity	NOUN
cana-2736	97	26	(	(	PUNCT
cana-2736	97	27	)	)	PUNCT
cana-2736	97	28	(	(	PUNCT
cana-2736	97	29	(	(	PUNCT
cana-2736	97	30	)	)	PUNCT
cana-2736	97	31	(	(	PUNCT
cana-2736	97	32	)	)	PUNCT
cana-2736	97	33	)	)	PUNCT
cana-2736	98	1	(	(	PUNCT
cana-2736	98	2	)	)	PUNCT
cana-2736	98	3	d	d	X
cana-2736	98	4	x	x	PUNCT
cana-2736	98	5	y	y	NOUN
cana-2736	98	6	f	f	NOUN
cana-2736	98	7	x	x	PROPN
cana-2736	98	8	d	d	X
cana-2736	98	9	y	y	PROPN
cana-2736	98	10	x	x	SYM
cana-2736	98	11	y	y	NOUN
cana-2736	98	12	=	=	SYM
cana-2736	98	13			ADJ
cana-2736	98	14			NOUN
cana-2736	98	15			PROPN
cana-2736	98	16	for	for	ADP
cana-2736	98	17	all	all	PRON
cana-2736	98	18	,	,	PUNCT
cana-2736	98	19	x	x	PRON
cana-2736	98	20	y	y	NOUN
cana-2736	98	21	a	a	PROPN
cana-2736	98	22	.	.	PUNCT
cana-2736	99	1	moreover	moreover	ADV
cana-2736	99	2	,	,	PUNCT
cana-2736	99	3	if	if	SCONJ
cana-2736	99	4	d	d	NOUN
cana-2736	99	5	is	be	AUX
cana-2736	99	6	a	a	DET
cana-2736	99	7	leftf	leftf	ADJ
cana-2736	99	8	-derivation	-derivation	NOUN
cana-2736	99	9	of	of	ADP
cana-2736	99	10	type	type	NOUN
cana-2736	99	11	i	i	PROPN
cana-2736	99	12	and	and	CCONJ
cana-2736	99	13	a	a	DET
cana-2736	99	14	rightf	rightf	ADJ
cana-2736	99	15	-derivation	-derivation	NOUN
cana-2736	99	16	of	of	ADP
cana-2736	99	17	type	type	NOUN
cana-2736	99	18	i	i	PRON
cana-2736	99	19	of	of	ADP
cana-2736	99	20	a	a	PRON
cana-2736	99	21	,	,	PUNCT
cana-2736	99	22	it	it	PRON
cana-2736	99	23	is	be	AUX
cana-2736	99	24	called	call	VERB
cana-2736	99	25	an	an	DET
cana-2736	99	26	f	f	PROPN
cana-2736	99	27	-derivation	-derivation	NOUN
cana-2736	99	28	of	of	ADP
cana-2736	99	29	type	type	NOUN
cana-2736	99	30	i	i	PRON
cana-2736	99	31	of	of	ADP
cana-2736	99	32	a	a	PRON
cana-2736	99	33	.	.	PUNCT
cana-2736	100	1	communications	communication	NOUN
cana-2736	100	2	on	on	ADP
cana-2736	100	3	applied	apply	VERB
cana-2736	100	4	nonlinear	nonlinear	ADJ
cana-2736	100	5	analysis	analysis	NOUN
cana-2736	100	6	issn	issn	NOUN
cana-2736	100	7	:	:	PUNCT
cana-2736	100	8	1074	1074	NUM
cana-2736	100	9	-	-	PUNCT
cana-2736	100	10	133x	133x	NUM
cana-2736	100	11	vol	vol	NOUN
cana-2736	100	12	32	32	NUM
cana-2736	100	13	no	no	NOUN
cana-2736	100	14	.	.	PUNCT
cana-2736	101	1	4s	4s	NUM
cana-2736	101	2	(	(	PUNCT
cana-2736	101	3	2025	2025	NUM
cana-2736	101	4	)	)	PUNCT
cana-2736	101	5	16	16	NUM
cana-2736	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	101	7	example	example	NOUN
cana-2736	101	8	3.2	3.2	NUM
cana-2736	101	9	.	.	PUNCT
cana-2736	102	1	let	let	VERB
cana-2736	102	2	{	{	PUNCT
cana-2736	102	3	1	1	NUM
cana-2736	102	4	,	,	PUNCT
cana-2736	102	5	2,3	2,3	NUM
cana-2736	102	6	,	,	PUNCT
cana-2736	102	7	4}a	4}a	PRON
cana-2736	102	8	=	=	PUNCT
cana-2736	102	9	be	be	AUX
cana-2736	102	10	a	a	DET
cana-2736	102	11	hilbert	hilbert	NOUN
cana-2736	102	12	algebra	algebra	NOUN
cana-2736	102	13	with	with	ADP
cana-2736	102	14	a	a	DET
cana-2736	102	15	fixed	fix	VERB
cana-2736	102	16	element	element	NOUN
cana-2736	102	17	1	1	NUM
cana-2736	102	18	and	and	CCONJ
cana-2736	102	19	a	a	DET
cana-2736	102	20	binary	binary	ADJ
cana-2736	102	21	operation	operation	NOUN
cana-2736	102	22			PROPN
cana-2736	102	23	defined	define	VERB
cana-2736	102	24	by	by	ADP
cana-2736	102	25	the	the	DET
cana-2736	102	26	following	following	ADJ
cana-2736	102	27	cayley	cayley	ADJ
cana-2736	102	28	table	table	NOUN
cana-2736	102	29	:	:	PUNCT
cana-2736	102	30	1	1	NUM
cana-2736	102	31	2	2	NUM
cana-2736	102	32	3	3	NUM
cana-2736	102	33	4	4	NUM
cana-2736	102	34	1	1	NUM
cana-2736	102	35	1	1	NUM
cana-2736	102	36	2	2	NUM
cana-2736	102	37	3	3	NUM
cana-2736	102	38	4	4	NUM
cana-2736	102	39	2	2	NUM
cana-2736	102	40	1	1	NUM
cana-2736	102	41	1	1	NUM
cana-2736	102	42	3	3	NUM
cana-2736	102	43	4	4	NUM
cana-2736	102	44	3	3	NUM
cana-2736	102	45	1	1	NUM
cana-2736	102	46	1	1	NUM
cana-2736	102	47	1	1	NUM
cana-2736	102	48	4	4	NUM
cana-2736	102	49	4	4	NUM
cana-2736	102	50	1	1	NUM
cana-2736	102	51	1	1	NUM
cana-2736	102	52	3	3	NUM
cana-2736	102	53	1	1	NUM
cana-2736	102	54			NUM
cana-2736	102	55	then	then	ADV
cana-2736	102	56	(	(	PUNCT
cana-2736	102	57	,	,	PUNCT
cana-2736	102	58	,	,	PUNCT
cana-2736	102	59	1)a	1)a	PROPN
cana-2736	102	60			PROPN
cana-2736	102	61	is	be	AUX
cana-2736	102	62	a	a	DET
cana-2736	102	63	hilbert	hilbert	NOUN
cana-2736	102	64	algebra	algebra	NOUN
cana-2736	102	65	.	.	PUNCT
cana-2736	103	1	we	we	PRON
cana-2736	103	2	define	define	VERB
cana-2736	103	3	an	an	DET
cana-2736	103	4	endomorphism	endomorphism	PROPN
cana-2736	103	5	f	f	PROPN
cana-2736	103	6	on	on	ADP
cana-2736	103	7	a	a	PRON
cana-2736	103	8	as	as	SCONJ
cana-2736	103	9	follows	follow	VERB
cana-2736	103	10	:	:	PUNCT
cana-2736	103	11	1	1	NUM
cana-2736	103	12	2	2	NUM
cana-2736	103	13	3	3	NUM
cana-2736	103	14	4	4	NUM
cana-2736	103	15	1	1	NUM
cana-2736	103	16	1	1	NUM
cana-2736	103	17	3	3	NUM
cana-2736	103	18	4	4	NUM
cana-2736	103	19	f	f	NOUN
cana-2736	103	20			NOUN
cana-2736	103	21			PROPN
cana-2736	103	22	=	=	SYM
cana-2736	103	23			PROPN
cana-2736	104	1			PROPN
cana-2736	104	2			ADJ
cana-2736	104	3			NOUN
cana-2736	104	4	define	define	VERB
cana-2736	104	5	a	a	DET
cana-2736	104	6	self	self	NOUN
cana-2736	104	7	-	-	PUNCT
cana-2736	104	8	map	map	NOUN
cana-2736	104	9	1	1	NUM
cana-2736	104	10	:	:	PUNCT
cana-2736	104	11	d	d	ADP
cana-2736	104	12	a	a	DET
cana-2736	104	13	a→	a→	PUNCT
cana-2736	104	14	as	as	SCONJ
cana-2736	104	15	follows	follow	VERB
cana-2736	104	16	:	:	PUNCT
cana-2736	104	17	1	1	NUM
cana-2736	104	18	1	1	NUM
cana-2736	104	19	2	2	NUM
cana-2736	104	20	3	3	NUM
cana-2736	104	21	4	4	NUM
cana-2736	104	22	1	1	NUM
cana-2736	104	23	1	1	NUM
cana-2736	104	24	3	3	NUM
cana-2736	104	25	4	4	NUM
cana-2736	104	26	d	d	NOUN
cana-2736	104	27			NOUN
cana-2736	104	28			NOUN
cana-2736	104	29	=	=	SYM
cana-2736	104	30			PROPN
cana-2736	104	31			PROPN
cana-2736	105	1			ADJ
cana-2736	105	2			NOUN
cana-2736	105	3	hence	hence	ADV
cana-2736	105	4	,	,	PUNCT
cana-2736	105	5	1d	1d	NUM
cana-2736	105	6	is	be	AUX
cana-2736	105	7	a	a	DET
cana-2736	105	8	leftf	leftf	ADJ
cana-2736	105	9	-derivation	-derivation	NOUN
cana-2736	105	10	of	of	ADP
cana-2736	105	11	type	type	NOUN
cana-2736	105	12	i	i	PRON
cana-2736	105	13	of	of	ADP
cana-2736	105	14	a	a	PRON
cana-2736	105	15	.	.	PUNCT
cana-2736	106	1	define	define	VERB
cana-2736	106	2	a	a	DET
cana-2736	106	3	self	self	NOUN
cana-2736	106	4	-	-	PUNCT
cana-2736	106	5	map	map	NOUN
cana-2736	106	6	2	2	NUM
cana-2736	106	7	:	:	PUNCT
cana-2736	106	8	d	d	ADP
cana-2736	106	9	a	a	DET
cana-2736	106	10	a→	a→	PUNCT
cana-2736	106	11	as	as	SCONJ
cana-2736	106	12	follows	follow	VERB
cana-2736	106	13	:	:	PUNCT
cana-2736	106	14	2	2	NUM
cana-2736	106	15	1	1	NUM
cana-2736	106	16	2	2	NUM
cana-2736	106	17	3	3	NUM
cana-2736	106	18	4	4	NUM
cana-2736	106	19	1	1	NUM
cana-2736	106	20	2	2	NUM
cana-2736	106	21	1	1	NUM
cana-2736	106	22	1	1	NUM
cana-2736	106	23	d	d	NOUN
cana-2736	106	24			NOUN
cana-2736	106	25			NOUN
cana-2736	106	26	=	=	SYM
cana-2736	106	27			PROPN
cana-2736	107	1			PROPN
cana-2736	107	2			ADJ
cana-2736	107	3			NOUN
cana-2736	107	4	hence	hence	ADV
cana-2736	107	5	,	,	PUNCT
cana-2736	107	6	1d	1d	NUM
cana-2736	107	7	is	be	AUX
cana-2736	107	8	a	a	DET
cana-2736	107	9	rightf	rightf	ADJ
cana-2736	107	10	-derivation	-derivation	NOUN
cana-2736	107	11	of	of	ADP
cana-2736	107	12	type	type	NOUN
cana-2736	107	13	i	i	PRON
cana-2736	107	14	of	of	ADP
cana-2736	107	15	a	a	PRON
cana-2736	107	16	.	.	PUNCT
cana-2736	108	1	definition	definition	NOUN
cana-2736	108	2	3.3	3.3	NUM
cana-2736	108	3	.	.	PUNCT
cana-2736	109	1	a	a	DET
cana-2736	109	2	self	self	NOUN
cana-2736	109	3	-	-	PUNCT
cana-2736	109	4	map	map	NOUN
cana-2736	109	5	d	d	NOUN
cana-2736	109	6	of	of	ADP
cana-2736	109	7	a	a	DET
cana-2736	109	8	hilbert	hilbert	NOUN
cana-2736	109	9	algebra	algebra	NOUN
cana-2736	109	10	(	(	PUNCT
cana-2736	109	11	,	,	PUNCT
cana-2736	109	12	,	,	PUNCT
cana-2736	109	13	1)a	1)a	PRON
cana-2736	109	14	a=	a=	NOUN
cana-2736	109	15			PROPN
cana-2736	109	16	is	be	AUX
cana-2736	109	17	called	call	VERB
cana-2736	109	18	regular	regular	ADJ
cana-2736	109	19	if	if	SCONJ
cana-2736	109	20	(	(	PUNCT
cana-2736	109	21	1	1	NUM
cana-2736	109	22	)	)	PUNCT
cana-2736	109	23	1d	1d	NUM
cana-2736	109	24	=	=	SYM
cana-2736	109	25	.	.	PUNCT
cana-2736	110	1	theorem	theorem	VERB
cana-2736	110	2	3.4	3.4	NUM
cana-2736	110	3	.	.	PUNCT
cana-2736	111	1	in	in	ADP
cana-2736	111	2	a	a	DET
cana-2736	111	3	hilbert	hilbert	NOUN
cana-2736	111	4	algebra	algebra	NOUN
cana-2736	111	5	(	(	PUNCT
cana-2736	111	6	,	,	PUNCT
cana-2736	111	7	,	,	PUNCT
cana-2736	111	8	1)a	1)a	PRON
cana-2736	111	9	a=	a=	PROPN
cana-2736	111	10			PROPN
cana-2736	111	11	,	,	PUNCT
cana-2736	111	12	the	the	DET
cana-2736	111	13	following	follow	VERB
cana-2736	111	14	statements	statement	NOUN
cana-2736	111	15	hold	hold	VERB
cana-2736	111	16	:	:	PUNCT
cana-2736	111	17	(	(	PUNCT
cana-2736	111	18	1	1	X
cana-2736	111	19	)	)	PUNCT
cana-2736	111	20	every	every	DET
cana-2736	111	21	leftf	leftf	ADJ
cana-2736	111	22	-derivation	-derivation	NOUN
cana-2736	111	23	of	of	ADP
cana-2736	111	24	type	type	NOUN
cana-2736	111	25	i	i	PRON
cana-2736	111	26	of	of	ADP
cana-2736	111	27	a	a	PRON
cana-2736	111	28	is	be	AUX
cana-2736	111	29	regular	regular	ADJ
cana-2736	111	30	,	,	PUNCT
cana-2736	111	31	(	(	PUNCT
cana-2736	111	32	2	2	X
cana-2736	111	33	)	)	PUNCT
cana-2736	111	34	every	every	DET
cana-2736	111	35	rightf	rightf	ADJ
cana-2736	111	36	-derivation	-derivation	NOUN
cana-2736	111	37	of	of	ADP
cana-2736	111	38	type	type	NOUN
cana-2736	111	39	i	i	PRON
cana-2736	111	40	of	of	ADP
cana-2736	111	41	a	a	PRON
cana-2736	111	42	is	be	AUX
cana-2736	111	43	regular	regular	ADJ
cana-2736	111	44	.	.	PUNCT
cana-2736	112	1	proof	proof	NOUN
cana-2736	112	2	.	.	PUNCT
cana-2736	113	1	(	(	PUNCT
cana-2736	113	2	1	1	X
cana-2736	113	3	)	)	PUNCT
cana-2736	113	4	assume	assume	VERB
cana-2736	113	5	that	that	SCONJ
cana-2736	113	6	d	d	NOUN
cana-2736	113	7	is	be	AUX
cana-2736	113	8	a	a	DET
cana-2736	113	9	leftf	leftf	ADJ
cana-2736	113	10	-derivation	-derivation	NOUN
cana-2736	113	11	of	of	ADP
cana-2736	113	12	type	type	NOUN
cana-2736	113	13	i	i	PRON
cana-2736	113	14	of	of	ADP
cana-2736	113	15	a	a	PRON
cana-2736	113	16	.	.	PUNCT
cana-2736	114	1	then	then	ADV
cana-2736	114	2	(	(	PUNCT
cana-2736	114	3	1	1	X
cana-2736	114	4	)	)	PUNCT
cana-2736	114	5	(	(	PUNCT
cana-2736	114	6	1	1	NUM
cana-2736	114	7	1)d	1)d	NUM
cana-2736	114	8	d=	d=	NOUN
cana-2736	115	1			PROPN
cana-2736	115	2	[	[	X
cana-2736	115	3	lemma	lemma	PROPN
cana-2736	115	4	2.2	2.2	NUM
cana-2736	115	5	(	(	PUNCT
cana-2736	115	6	1	1	NUM
cana-2736	115	7	)	)	PUNCT
cana-2736	115	8	]	]	PUNCT
cana-2736	116	1	(	(	PUNCT
cana-2736	116	2	(	(	PUNCT
cana-2736	116	3	1	1	X
cana-2736	116	4	)	)	PUNCT
cana-2736	116	5	(	(	PUNCT
cana-2736	116	6	1	1	NUM
cana-2736	116	7	)	)	PUNCT
cana-2736	116	8	)	)	PUNCT
cana-2736	116	9	(	(	PUNCT
cana-2736	116	10	1	1	NUM
cana-2736	116	11	1)d	1)d	NUM
cana-2736	116	12	f=	f=	ADJ
cana-2736	116	13			ADJ
cana-2736	116	14			NOUN
cana-2736	116	15			NUM
cana-2736	116	16	(	(	PUNCT
cana-2736	116	17	(	(	PUNCT
cana-2736	116	18	1	1	NUM
cana-2736	116	19	)	)	PUNCT
cana-2736	116	20	1	1	NUM
cana-2736	116	21	)	)	PUNCT
cana-2736	116	22	1d=	1d=	NUM
cana-2736	117	1			ADJ
cana-2736	117	2			NOUN
cana-2736	117	3	[	[	X
cana-2736	117	4	lemma	lemma	PROPN
cana-2736	117	5	2.2	2.2	NUM
cana-2736	117	6	(	(	PUNCT
cana-2736	117	7	1	1	NUM
cana-2736	117	8	)	)	PUNCT
cana-2736	117	9	]	]	PUNCT
cana-2736	117	10	1=	1=	X
cana-2736	117	11	.	.	PUNCT
cana-2736	118	1	[	[	X
cana-2736	118	2	(	(	PUNCT
cana-2736	118	3	2.7	2.7	NUM
cana-2736	118	4	)	)	PUNCT
cana-2736	118	5	]	]	PUNCT
cana-2736	119	1	hence	hence	ADV
cana-2736	119	2	,	,	PUNCT
cana-2736	119	3	d	d	PROPN
cana-2736	119	4	is	be	AUX
cana-2736	119	5	regular	regular	ADJ
cana-2736	119	6	.	.	PUNCT
cana-2736	120	1	(	(	PUNCT
cana-2736	120	2	2	2	X
cana-2736	120	3	)	)	PUNCT
cana-2736	120	4	assume	assume	VERB
cana-2736	120	5	that	that	SCONJ
cana-2736	120	6	d	d	NOUN
cana-2736	120	7	is	be	AUX
cana-2736	120	8	a	a	DET
cana-2736	120	9	rightf	rightf	ADJ
cana-2736	120	10	-derivation	-derivation	NOUN
cana-2736	120	11	of	of	ADP
cana-2736	120	12	type	type	NOUN
cana-2736	120	13	i	i	PRON
cana-2736	120	14	of	of	ADP
cana-2736	120	15	a	a	PRON
cana-2736	120	16	.	.	PUNCT
cana-2736	121	1	then	then	ADV
cana-2736	121	2	(	(	PUNCT
cana-2736	121	3	1	1	X
cana-2736	121	4	)	)	PUNCT
cana-2736	121	5	(	(	PUNCT
cana-2736	121	6	1	1	NUM
cana-2736	121	7	1)d	1)d	NUM
cana-2736	121	8	d=	d=	NOUN
cana-2736	122	1			PROPN
cana-2736	122	2	[	[	X
cana-2736	122	3	lemma	lemma	PROPN
cana-2736	122	4	2.2	2.2	NUM
cana-2736	122	5	(	(	PUNCT
cana-2736	122	6	1	1	NUM
cana-2736	122	7	)	)	PUNCT
cana-2736	122	8	]	]	PUNCT
cana-2736	122	9	communications	communication	NOUN
cana-2736	122	10	on	on	ADP
cana-2736	122	11	applied	apply	VERB
cana-2736	122	12	nonlinear	nonlinear	ADJ
cana-2736	122	13	analysis	analysis	NOUN
cana-2736	122	14	issn	issn	NOUN
cana-2736	122	15	:	:	PUNCT
cana-2736	122	16	1074	1074	NUM
cana-2736	122	17	-	-	PUNCT
cana-2736	122	18	133x	133x	NUM
cana-2736	122	19	vol	vol	NOUN
cana-2736	122	20	32	32	NUM
cana-2736	122	21	no	no	NOUN
cana-2736	122	22	.	.	PUNCT
cana-2736	123	1	4s	4s	NUM
cana-2736	123	2	(	(	PUNCT
cana-2736	123	3	2025	2025	NUM
cana-2736	123	4	)	)	PUNCT
cana-2736	123	5	17	17	NUM
cana-2736	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	123	7	(	(	PUNCT
cana-2736	123	8	(	(	PUNCT
cana-2736	123	9	1	1	NUM
cana-2736	123	10	)	)	PUNCT
cana-2736	123	11	(	(	PUNCT
cana-2736	123	12	1	1	NUM
cana-2736	123	13	)	)	PUNCT
cana-2736	123	14	)	)	PUNCT
cana-2736	123	15	(	(	PUNCT
cana-2736	123	16	1	1	NUM
cana-2736	123	17	1)f	1)f	NUM
cana-2736	123	18	d=	d=	NOUN
cana-2736	123	19			ADJ
cana-2736	123	20			NOUN
cana-2736	123	21			NUM
cana-2736	123	22	(	(	PUNCT
cana-2736	123	23	1	1	NUM
cana-2736	123	24	(	(	PUNCT
cana-2736	123	25	1	1	NUM
cana-2736	123	26	)	)	PUNCT
cana-2736	123	27	)	)	PUNCT
cana-2736	123	28	1d=	1d=	NUM
cana-2736	124	1			ADJ
cana-2736	124	2			NOUN
cana-2736	124	3	[	[	X
cana-2736	124	4	lemma	lemma	PROPN
cana-2736	124	5	2.2	2.2	NUM
cana-2736	124	6	(	(	PUNCT
cana-2736	124	7	1	1	NUM
cana-2736	124	8	)	)	PUNCT
cana-2736	124	9	]	]	PUNCT
cana-2736	124	10	1=	1=	X
cana-2736	124	11	.	.	PUNCT
cana-2736	125	1	[	[	X
cana-2736	125	2	(	(	PUNCT
cana-2736	125	3	2.7	2.7	NUM
cana-2736	125	4	)	)	PUNCT
cana-2736	125	5	]	]	PUNCT
cana-2736	126	1	hence	hence	ADV
cana-2736	126	2	,	,	PUNCT
cana-2736	126	3	d	d	PROPN
cana-2736	126	4	is	be	AUX
cana-2736	126	5	regular	regular	ADJ
cana-2736	126	6	.	.	PUNCT
cana-2736	127	1	corollary	corollary	ADJ
cana-2736	127	2	3.5	3.5	NUM
cana-2736	127	3	.	.	PUNCT
cana-2736	128	1	every	every	DET
cana-2736	128	2	f	f	PROPN
cana-2736	128	3	-derivation	-derivation	NOUN
cana-2736	128	4	of	of	ADP
cana-2736	128	5	type	type	NOUN
cana-2736	128	6	i	i	PRON
cana-2736	128	7	of	of	ADP
cana-2736	128	8	a	a	DET
cana-2736	128	9	hilbert	hilbert	NOUN
cana-2736	128	10	algebra	algebra	NOUN
cana-2736	128	11	a	a	PRON
cana-2736	128	12	is	be	AUX
cana-2736	128	13	regular	regular	ADJ
cana-2736	128	14	.	.	PUNCT
cana-2736	129	1	theorem	theorem	VERB
cana-2736	129	2	3.6	3.6	NUM
cana-2736	129	3	.	.	PUNCT
cana-2736	130	1	in	in	ADP
cana-2736	130	2	a	a	DET
cana-2736	130	3	hilbert	hilbert	NOUN
cana-2736	130	4	algebra	algebra	NOUN
cana-2736	130	5	(	(	PUNCT
cana-2736	130	6	,	,	PUNCT
cana-2736	130	7	,	,	PUNCT
cana-2736	130	8	1)a	1)a	PRON
cana-2736	130	9	a=	a=	PROPN
cana-2736	130	10			PROPN
cana-2736	130	11	,	,	PUNCT
cana-2736	130	12	the	the	DET
cana-2736	130	13	following	follow	VERB
cana-2736	130	14	statements	statement	NOUN
cana-2736	130	15	hold	hold	VERB
cana-2736	130	16	:	:	PUNCT
cana-2736	130	17	(	(	PUNCT
cana-2736	130	18	1	1	X
cana-2736	130	19	)	)	PUNCT
cana-2736	130	20	if	if	SCONJ
cana-2736	130	21	d	d	NOUN
cana-2736	130	22	is	be	AUX
cana-2736	130	23	a	a	DET
cana-2736	130	24	leftf	leftf	ADJ
cana-2736	130	25	-derivation	-derivation	NOUN
cana-2736	130	26	of	of	ADP
cana-2736	130	27	type	type	NOUN
cana-2736	130	28	i	i	PRON
cana-2736	130	29	of	of	ADP
cana-2736	130	30	a	a	PRON
cana-2736	130	31	,	,	PUNCT
cana-2736	130	32	then	then	ADV
cana-2736	130	33	(	(	PUNCT
cana-2736	130	34	)	)	PUNCT
cana-2736	130	35	(	(	PUNCT
cana-2736	130	36	)	)	PUNCT
cana-2736	131	1	d	d	X
cana-2736	131	2	x	x	X
cana-2736	131	3	f	f	X
cana-2736	131	4	x	x	SYM
cana-2736	131	5	x=	x=	X
cana-2736	131	6			NOUN
cana-2736	131	7	for	for	ADP
cana-2736	131	8	all	all	PRON
cana-2736	131	9	x	x	SYM
cana-2736	131	10	a	a	PROPN
cana-2736	131	11	,	,	PUNCT
cana-2736	131	12	(	(	PUNCT
cana-2736	131	13	2	2	X
cana-2736	131	14	)	)	PUNCT
cana-2736	131	15	if	if	SCONJ
cana-2736	131	16	d	d	NOUN
cana-2736	131	17	is	be	AUX
cana-2736	131	18	a	a	DET
cana-2736	131	19	rightf	rightf	ADJ
cana-2736	131	20	-derivation	-derivation	NOUN
cana-2736	131	21	of	of	ADP
cana-2736	131	22	type	type	NOUN
cana-2736	131	23	i	i	PRON
cana-2736	131	24	of	of	ADP
cana-2736	131	25	a	a	PRON
cana-2736	131	26	,	,	PUNCT
cana-2736	131	27	then	then	ADV
cana-2736	131	28	(	(	PUNCT
cana-2736	131	29	)	)	PUNCT
cana-2736	131	30	(	(	PUNCT
cana-2736	131	31	)	)	PUNCT
cana-2736	131	32	d	d	X
cana-2736	131	33	x	x	PUNCT
cana-2736	131	34	d	d	NOUN
cana-2736	131	35	x	x	SYM
cana-2736	131	36	x=	x=	NOUN
cana-2736	131	37			NOUN
cana-2736	131	38	for	for	ADP
cana-2736	131	39	all	all	PRON
cana-2736	131	40	x	x	SYM
cana-2736	131	41	a	a	PROPN
cana-2736	131	42	.	.	PUNCT
cana-2736	132	1	proof	proof	NOUN
cana-2736	132	2	.	.	PUNCT
cana-2736	133	1	(	(	PUNCT
cana-2736	133	2	1	1	X
cana-2736	133	3	)	)	PUNCT
cana-2736	133	4	assume	assume	VERB
cana-2736	133	5	that	that	SCONJ
cana-2736	133	6	d	d	NOUN
cana-2736	133	7	is	be	AUX
cana-2736	133	8	a	a	DET
cana-2736	133	9	leftf	leftf	ADJ
cana-2736	133	10	-derivation	-derivation	NOUN
cana-2736	133	11	of	of	ADP
cana-2736	133	12	type	type	NOUN
cana-2736	133	13	i	i	PRON
cana-2736	133	14	of	of	ADP
cana-2736	133	15	a	a	PRON
cana-2736	133	16	.	.	PUNCT
cana-2736	134	1	then	then	ADV
cana-2736	134	2	,	,	PUNCT
cana-2736	134	3	for	for	ADP
cana-2736	134	4	all	all	PRON
cana-2736	134	5	x	x	SYM
cana-2736	134	6	a	a	PROPN
cana-2736	134	7	,	,	PUNCT
cana-2736	134	8	(	(	PUNCT
cana-2736	134	9	)	)	PUNCT
cana-2736	134	10	(	(	PUNCT
cana-2736	134	11	1	1	X
cana-2736	134	12	)	)	PUNCT
cana-2736	134	13	d	d	NOUN
cana-2736	134	14	x	x	SYM
cana-2736	134	15	d	d	NOUN
cana-2736	134	16	x=	x=	PUNCT
cana-2736	135	1			PROPN
cana-2736	135	2	[	[	X
cana-2736	135	3	lemma	lemma	PROPN
cana-2736	135	4	2.2	2.2	NUM
cana-2736	135	5	(	(	PUNCT
cana-2736	135	6	2	2	NUM
cana-2736	135	7	)	)	PUNCT
cana-2736	135	8	]	]	PUNCT
cana-2736	135	9	(	(	PUNCT
cana-2736	135	10	(	(	PUNCT
cana-2736	135	11	1	1	X
cana-2736	135	12	)	)	PUNCT
cana-2736	135	13	(	(	PUNCT
cana-2736	135	14	)	)	PUNCT
cana-2736	135	15	)	)	PUNCT
cana-2736	135	16	(	(	PUNCT
cana-2736	135	17	1	1	X
cana-2736	135	18	)	)	PUNCT
cana-2736	136	1	d	d	NOUN
cana-2736	136	2	f	f	PROPN
cana-2736	136	3	x	x	X
cana-2736	136	4	x=	x=	PUNCT
cana-2736	137	1			ADJ
cana-2736	137	2			NOUN
cana-2736	137	3			NUM
cana-2736	137	4	(	(	PUNCT
cana-2736	137	5	1	1	NUM
cana-2736	137	6	(	(	PUNCT
cana-2736	137	7	)	)	PUNCT
cana-2736	137	8	)	)	PUNCT
cana-2736	137	9	(	(	PUNCT
cana-2736	137	10	1	1	X
cana-2736	137	11	)	)	PUNCT
cana-2736	137	12	f	f	NOUN
cana-2736	137	13	x	x	PUNCT
cana-2736	137	14	x=	x=	PUNCT
cana-2736	137	15			ADJ
cana-2736	137	16			NOUN
cana-2736	137	17			PROPN
cana-2736	137	18	[	[	X
cana-2736	137	19	regular	regular	X
cana-2736	137	20	]	]	PUNCT
cana-2736	137	21	(	(	PUNCT
cana-2736	137	22	)	)	PUNCT
cana-2736	137	23	f	f	PROPN
cana-2736	137	24	x	x	SYM
cana-2736	137	25	x=	x=	NOUN
cana-2736	137	26			NOUN
cana-2736	137	27	.	.	PUNCT
cana-2736	138	1	[	[	X
cana-2736	138	2	lemma	lemma	X
cana-2736	138	3	2.2	2.2	NUM
cana-2736	138	4	(	(	PUNCT
cana-2736	138	5	2	2	NUM
cana-2736	138	6	)	)	PUNCT
cana-2736	138	7	]	]	PUNCT
cana-2736	138	8	(	(	PUNCT
cana-2736	138	9	2	2	X
cana-2736	138	10	)	)	PUNCT
cana-2736	138	11	assume	assume	VERB
cana-2736	138	12	that	that	SCONJ
cana-2736	138	13	d	d	NOUN
cana-2736	138	14	is	be	AUX
cana-2736	138	15	a	a	DET
cana-2736	138	16	rightf	rightf	ADJ
cana-2736	138	17	-derivation	-derivation	NOUN
cana-2736	138	18	of	of	ADP
cana-2736	138	19	type	type	NOUN
cana-2736	138	20	i	i	PRON
cana-2736	138	21	of	of	ADP
cana-2736	138	22	a	a	PRON
cana-2736	138	23	.	.	PUNCT
cana-2736	139	1	then	then	ADV
cana-2736	139	2	,	,	PUNCT
cana-2736	139	3	for	for	ADP
cana-2736	139	4	all	all	PRON
cana-2736	139	5	x	x	SYM
cana-2736	139	6	a	a	PROPN
cana-2736	139	7	,	,	PUNCT
cana-2736	139	8	(	(	PUNCT
cana-2736	139	9	)	)	PUNCT
cana-2736	139	10	(	(	PUNCT
cana-2736	139	11	1	1	X
cana-2736	139	12	)	)	PUNCT
cana-2736	139	13	d	d	NOUN
cana-2736	139	14	x	x	SYM
cana-2736	139	15	d	d	NOUN
cana-2736	139	16	x=	x=	PUNCT
cana-2736	140	1			PROPN
cana-2736	140	2	[	[	X
cana-2736	140	3	lemma	lemma	PROPN
cana-2736	140	4	2.2	2.2	NUM
cana-2736	140	5	(	(	PUNCT
cana-2736	140	6	2	2	NUM
cana-2736	140	7	)	)	PUNCT
cana-2736	140	8	]	]	PUNCT
cana-2736	140	9	(	(	PUNCT
cana-2736	140	10	(	(	PUNCT
cana-2736	140	11	1	1	X
cana-2736	140	12	)	)	PUNCT
cana-2736	140	13	(	(	PUNCT
cana-2736	140	14	)	)	PUNCT
cana-2736	140	15	)	)	PUNCT
cana-2736	140	16	(	(	PUNCT
cana-2736	140	17	1	1	X
cana-2736	140	18	)	)	PUNCT
cana-2736	140	19	f	f	NOUN
cana-2736	141	1	d	d	NOUN
cana-2736	141	2	x	x	X
cana-2736	141	3	x=	x=	PUNCT
cana-2736	142	1			ADJ
cana-2736	142	2			NOUN
cana-2736	142	3			NUM
cana-2736	142	4	(	(	PUNCT
cana-2736	142	5	1	1	NUM
cana-2736	142	6	(	(	PUNCT
cana-2736	142	7	)	)	PUNCT
cana-2736	142	8	)	)	PUNCT
cana-2736	142	9	(	(	PUNCT
cana-2736	142	10	1	1	X
cana-2736	142	11	)	)	PUNCT
cana-2736	142	12	d	d	NOUN
cana-2736	142	13	x	x	SYM
cana-2736	142	14	x=	x=	X
cana-2736	142	15			ADJ
cana-2736	142	16			NOUN
cana-2736	142	17			NUM
cana-2736	142	18	(	(	PUNCT
cana-2736	142	19	)	)	PUNCT
cana-2736	142	20	d	d	NOUN
cana-2736	142	21	x	x	SYM
cana-2736	142	22	x=	x=	NOUN
cana-2736	142	23			NOUN
cana-2736	142	24	.	.	PUNCT
cana-2736	143	1	[	[	X
cana-2736	143	2	lemma	lemma	X
cana-2736	143	3	2.2	2.2	NUM
cana-2736	143	4	(	(	PUNCT
cana-2736	143	5	2	2	NUM
cana-2736	143	6	)	)	PUNCT
cana-2736	143	7	]	]	PUNCT
cana-2736	143	8	corollary	corollary	ADJ
cana-2736	143	9	3.7	3.7	NUM
cana-2736	143	10	.	.	PUNCT
cana-2736	144	1	if	if	SCONJ
cana-2736	144	2	d	d	PROPN
cana-2736	144	3	is	be	AUX
cana-2736	144	4	an	an	DET
cana-2736	144	5	f	f	PROPN
cana-2736	144	6	-derivation	-derivation	NOUN
cana-2736	144	7	of	of	ADP
cana-2736	144	8	type	type	NOUN
cana-2736	144	9	i	i	PRON
cana-2736	144	10	of	of	ADP
cana-2736	144	11	a	a	PRON
cana-2736	144	12	,	,	PUNCT
cana-2736	144	13	then	then	ADV
cana-2736	144	14	(	(	PUNCT
cana-2736	144	15	)	)	PUNCT
cana-2736	144	16	(	(	PUNCT
cana-2736	144	17	)	)	PUNCT
cana-2736	144	18	(	(	PUNCT
cana-2736	144	19	)	)	PUNCT
cana-2736	144	20	d	d	X
cana-2736	144	21	x	x	X
cana-2736	144	22	f	f	NOUN
cana-2736	144	23	x	x	PUNCT
cana-2736	144	24	x	x	SYM
cana-2736	144	25	d	d	NOUN
cana-2736	144	26	x	x	SYM
cana-2736	144	27	x=	x=	NOUN
cana-2736	144	28			NOUN
cana-2736	144	29	=	=	NOUN
cana-2736	144	30			NOUN
cana-2736	144	31	for	for	ADP
cana-2736	144	32	all	all	PRON
cana-2736	144	33	x	x	PUNCT
cana-2736	144	34	a	a	PROPN
cana-2736	144	35	.	.	PUNCT
cana-2736	145	1	proposition	proposition	NOUN
cana-2736	145	2	3.8	3.8	NUM
cana-2736	145	3	.	.	PUNCT
cana-2736	146	1	let	let	VERB
cana-2736	146	2	d	d	PRON
cana-2736	146	3	be	be	AUX
cana-2736	146	4	a	a	DET
cana-2736	146	5	leftf	leftf	ADJ
cana-2736	146	6	-derivation	-derivation	NOUN
cana-2736	146	7	of	of	ADP
cana-2736	146	8	type	type	NOUN
cana-2736	146	9	i	i	PRON
cana-2736	146	10	of	of	ADP
cana-2736	146	11	a	a	DET
cana-2736	146	12	hilbert	hilbert	NOUN
cana-2736	146	13	algebra	algebra	NOUN
cana-2736	146	14	(	(	PUNCT
cana-2736	146	15	,	,	PUNCT
cana-2736	146	16	,	,	PUNCT
cana-2736	146	17	1)a	1)a	PRON
cana-2736	146	18	a=	a=	PROPN
cana-2736	146	19			PROPN
cana-2736	146	20	.	.	PUNCT
cana-2736	147	1	then	then	ADV
cana-2736	147	2	the	the	DET
cana-2736	147	3	following	follow	VERB
cana-2736	147	4	properties	property	NOUN
cana-2736	147	5	hold	hold	VERB
cana-2736	147	6	:	:	PUNCT
cana-2736	147	7	for	for	ADP
cana-2736	147	8	any	any	PRON
cana-2736	147	9	,	,	PUNCT
cana-2736	147	10	x	x	PROPN
cana-2736	147	11	y	y	NOUN
cana-2736	147	12	a	a	PROPN
cana-2736	147	13	,	,	PUNCT
cana-2736	147	14	(	(	PUNCT
cana-2736	147	15	1	1	X
cana-2736	147	16	)	)	PUNCT
cana-2736	147	17	(	(	PUNCT
cana-2736	147	18	)	)	PUNCT
cana-2736	147	19	(	(	PUNCT
cana-2736	147	20	)	)	PUNCT
cana-2736	147	21	f	f	X
cana-2736	148	1	x	x	PUNCT
cana-2736	148	2	d	d	X
cana-2736	148	3	x	x	PROPN
cana-2736	148	4	,	,	PUNCT
cana-2736	148	5	(	(	PUNCT
cana-2736	148	6	2	2	X
cana-2736	148	7	)	)	PUNCT
cana-2736	148	8	(	(	PUNCT
cana-2736	148	9	)	)	PUNCT
cana-2736	148	10	(	(	PUNCT
cana-2736	148	11	)	)	PUNCT
cana-2736	148	12	(	(	PUNCT
cana-2736	148	13	)	)	PUNCT
cana-2736	149	1	d	d	X
cana-2736	149	2	x	x	X
cana-2736	149	3	f	f	NOUN
cana-2736	149	4	y	y	PROPN
cana-2736	149	5	d	d	X
cana-2736	149	6	x	x	X
cana-2736	149	7	y	y	NOUN
cana-2736	149	8			NOUN
cana-2736	149	9			NUM
cana-2736	149	10	,	,	PUNCT
cana-2736	149	11	(	(	PUNCT
cana-2736	149	12	3	3	X
cana-2736	149	13	)	)	PUNCT
cana-2736	149	14	(	(	PUNCT
cana-2736	149	15	(	(	PUNCT
cana-2736	149	16	)	)	PUNCT
cana-2736	149	17	)	)	PUNCT
cana-2736	150	1	(	(	PUNCT
cana-2736	150	2	(	(	PUNCT
cana-2736	150	3	)	)	PUNCT
cana-2736	150	4	)	)	PUNCT
cana-2736	151	1	(	(	PUNCT
cana-2736	151	2	(	(	PUNCT
cana-2736	151	3	)	)	PUNCT
cana-2736	151	4	)	)	PUNCT
cana-2736	152	1	d	d	X
cana-2736	152	2	x	x	PUNCT
cana-2736	153	1	f	f	X
cana-2736	153	2	x	x	X
cana-2736	153	3	f	f	NOUN
cana-2736	153	4	f	f	NOUN
cana-2736	154	1	x	x	SYM
cana-2736	154	2	d	d	PROPN
cana-2736	154	3	d	d	X
cana-2736	154	4	x	x	X
cana-2736	154	5			ADJ
cana-2736	154	6			NOUN
cana-2736	154	7	,	,	PUNCT
cana-2736	154	8	(	(	PUNCT
cana-2736	154	9	4	4	NUM
cana-2736	154	10	)	)	PUNCT
cana-2736	154	11	(	(	PUNCT
cana-2736	154	12	)	)	PUNCT
cana-2736	154	13	(	(	PUNCT
cana-2736	154	14	)	)	PUNCT
cana-2736	154	15	(	(	PUNCT
cana-2736	154	16	)	)	PUNCT
cana-2736	155	1	d	d	NOUN
cana-2736	155	2	y	y	NOUN
cana-2736	155	3	x	x	X
cana-2736	155	4	f	f	NOUN
cana-2736	155	5	x	x	SYM
cana-2736	155	6	d	d	X
cana-2736	155	7	x	x	X
cana-2736	155	8	y	y	NOUN
cana-2736	155	9			VERB
cana-2736	155	10			NOUN
cana-2736	155	11			NOUN
cana-2736	155	12	,	,	PUNCT
cana-2736	155	13	(	(	PUNCT
cana-2736	155	14	5	5	NUM
cana-2736	155	15	)	)	PUNCT
cana-2736	155	16	(	(	PUNCT
cana-2736	155	17	)	)	PUNCT
cana-2736	155	18	(	(	PUNCT
cana-2736	155	19	)	)	PUNCT
cana-2736	155	20	(	(	PUNCT
cana-2736	155	21	)	)	PUNCT
cana-2736	156	1	d	d	X
cana-2736	156	2	x	x	PUNCT
cana-2736	156	3	d	d	NOUN
cana-2736	156	4	x	x	X
cana-2736	156	5	f	f	NOUN
cana-2736	156	6	x=	x=	X
cana-2736	156	7			NOUN
cana-2736	156	8	.	.	PUNCT
cana-2736	157	1	proof	proof	NOUN
cana-2736	157	2	.	.	PUNCT
cana-2736	158	1	(	(	PUNCT
cana-2736	158	2	1	1	X
cana-2736	158	3	)	)	PUNCT
cana-2736	158	4	for	for	ADP
cana-2736	158	5	all	all	PRON
cana-2736	158	6	x	x	SYM
cana-2736	158	7	a	a	PROPN
cana-2736	158	8	,	,	PUNCT
cana-2736	158	9	communications	communication	NOUN
cana-2736	158	10	on	on	ADP
cana-2736	158	11	applied	apply	VERB
cana-2736	158	12	nonlinear	nonlinear	ADJ
cana-2736	158	13	analysis	analysis	NOUN
cana-2736	158	14	issn	issn	NOUN
cana-2736	158	15	:	:	PUNCT
cana-2736	158	16	1074	1074	NUM
cana-2736	158	17	-	-	PUNCT
cana-2736	158	18	133x	133x	NUM
cana-2736	158	19	vol	vol	NOUN
cana-2736	158	20	32	32	NUM
cana-2736	158	21	no	no	NOUN
cana-2736	158	22	.	.	PUNCT
cana-2736	159	1	4s	4s	NUM
cana-2736	159	2	(	(	PUNCT
cana-2736	159	3	2025	2025	NUM
cana-2736	159	4	)	)	PUNCT
cana-2736	159	5	18	18	NUM
cana-2736	159	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	159	7	(	(	PUNCT
cana-2736	159	8	)	)	PUNCT
cana-2736	159	9	(	(	PUNCT
cana-2736	159	10	)	)	PUNCT
cana-2736	159	11	(	(	PUNCT
cana-2736	159	12	)	)	PUNCT
cana-2736	159	13	(	(	PUNCT
cana-2736	159	14	(	(	PUNCT
cana-2736	159	15	)	)	PUNCT
cana-2736	159	16	)	)	PUNCT
cana-2736	160	1	f	f	X
cana-2736	161	1	x	x	PUNCT
cana-2736	161	2	d	d	NOUN
cana-2736	161	3	x	x	X
cana-2736	161	4	f	f	NOUN
cana-2736	161	5	x	x	X
cana-2736	161	6	f	f	NOUN
cana-2736	161	7	x	x	X
cana-2736	161	8	x	x	PUNCT
cana-2736	161	9	=	=	SYM
cana-2736	161	10			ADJ
cana-2736	161	11			NOUN
cana-2736	161	12	[	[	PUNCT
cana-2736	161	13	theorem	theorem	ADJ
cana-2736	161	14	3.6	3.6	NUM
cana-2736	161	15	(	(	PUNCT
cana-2736	161	16	1	1	NUM
cana-2736	161	17	)	)	PUNCT
cana-2736	161	18	]	]	PUNCT
cana-2736	161	19	1=	1=	X
cana-2736	161	20	.	.	PUNCT
cana-2736	162	1	[	[	X
cana-2736	162	2	(	(	PUNCT
cana-2736	162	3	2.4	2.4	NUM
cana-2736	162	4	)	)	PUNCT
cana-2736	162	5	]	]	PUNCT
cana-2736	163	1	hence	hence	ADV
cana-2736	163	2	,	,	PUNCT
cana-2736	163	3	(	(	PUNCT
cana-2736	163	4	)	)	PUNCT
cana-2736	163	5	(	(	PUNCT
cana-2736	163	6	)	)	PUNCT
cana-2736	163	7	f	f	X
cana-2736	163	8	x	x	PUNCT
cana-2736	164	1	d	d	X
cana-2736	164	2	x	x	PROPN
cana-2736	164	3	for	for	ADP
cana-2736	164	4	all	all	PRON
cana-2736	164	5	x	x	SYM
cana-2736	164	6	a	a	PROPN
cana-2736	164	7	.	.	PUNCT
cana-2736	165	1	(	(	PUNCT
cana-2736	165	2	2	2	X
cana-2736	165	3	)	)	PUNCT
cana-2736	165	4	for	for	ADP
cana-2736	165	5	all	all	PRON
cana-2736	165	6	,	,	PUNCT
cana-2736	165	7	x	x	PRON
cana-2736	165	8	y	y	NOUN
cana-2736	165	9	a	a	PROPN
cana-2736	165	10	,	,	PUNCT
cana-2736	165	11	(	(	PUNCT
cana-2736	165	12	(	(	PUNCT
cana-2736	165	13	)	)	PUNCT
cana-2736	165	14	(	(	PUNCT
cana-2736	165	15	)	)	PUNCT
cana-2736	165	16	)	)	PUNCT
cana-2736	166	1	(	(	PUNCT
cana-2736	166	2	)	)	PUNCT
cana-2736	166	3	(	(	PUNCT
cana-2736	166	4	(	(	PUNCT
cana-2736	166	5	)	)	PUNCT
cana-2736	166	6	(	(	PUNCT
cana-2736	166	7	)	)	PUNCT
cana-2736	166	8	)	)	PUNCT
cana-2736	167	1	(	(	PUNCT
cana-2736	167	2	(	(	PUNCT
cana-2736	167	3	(	(	PUNCT
cana-2736	167	4	)	)	PUNCT
cana-2736	167	5	(	(	PUNCT
cana-2736	167	6	)	)	PUNCT
cana-2736	167	7	)	)	PUNCT
cana-2736	168	1	(	(	PUNCT
cana-2736	168	2	)	)	PUNCT
cana-2736	168	3	)	)	PUNCT
cana-2736	168	4	d	d	X
cana-2736	168	5	x	x	X
cana-2736	169	1	f	f	NOUN
cana-2736	169	2	y	y	PROPN
cana-2736	169	3	d	d	NOUN
cana-2736	169	4	x	x	PUNCT
cana-2736	169	5	y	y	PROPN
cana-2736	169	6	d	d	NOUN
cana-2736	169	7	x	x	X
cana-2736	170	1	f	f	PROPN
cana-2736	170	2	y	y	PROPN
cana-2736	170	3	d	d	NOUN
cana-2736	170	4	x	x	X
cana-2736	170	5	f	f	PROPN
cana-2736	170	6	y	y	PROPN
cana-2736	170	7	x	x	SYM
cana-2736	170	8	y	y	NOUN
cana-2736	170	9			VERB
cana-2736	170	10			PROPN
cana-2736	170	11	=	=	SYM
cana-2736	170	12			PROPN
cana-2736	170	13			ADJ
cana-2736	170	14			ADJ
cana-2736	170	15			NOUN
cana-2736	170	16			NUM
cana-2736	170	17	1=	1=	NOUN
cana-2736	170	18	.	.	PUNCT
cana-2736	171	1	[	[	X
cana-2736	171	2	(	(	PUNCT
cana-2736	171	3	2.4	2.4	NUM
cana-2736	171	4	)	)	PUNCT
cana-2736	171	5	]	]	PUNCT
cana-2736	172	1	hence	hence	ADV
cana-2736	172	2	,	,	PUNCT
cana-2736	172	3	(	(	PUNCT
cana-2736	172	4	)	)	PUNCT
cana-2736	172	5	(	(	PUNCT
cana-2736	172	6	)	)	PUNCT
cana-2736	172	7	(	(	PUNCT
cana-2736	172	8	)	)	PUNCT
cana-2736	172	9	d	d	X
cana-2736	172	10	x	x	X
cana-2736	172	11	f	f	NOUN
cana-2736	172	12	y	y	PROPN
cana-2736	172	13	d	d	X
cana-2736	172	14	x	x	X
cana-2736	172	15	y	y	NOUN
cana-2736	172	16			NUM
cana-2736	172	17			PROPN
cana-2736	172	18	for	for	ADP
cana-2736	172	19	all	all	PRON
cana-2736	172	20	,	,	PUNCT
cana-2736	172	21	x	x	PRON
cana-2736	172	22	y	y	NOUN
cana-2736	172	23	a	a	PROPN
cana-2736	172	24	.	.	PUNCT
cana-2736	173	1	(	(	PUNCT
cana-2736	173	2	3	3	X
cana-2736	173	3	)	)	PUNCT
cana-2736	173	4	for	for	ADP
cana-2736	173	5	all	all	PRON
cana-2736	173	6	x	x	SYM
cana-2736	173	7	a	a	PROPN
cana-2736	173	8	,	,	PUNCT
cana-2736	173	9	(	(	PUNCT
cana-2736	173	10	(	(	PUNCT
cana-2736	173	11	(	(	PUNCT
cana-2736	173	12	)	)	PUNCT
cana-2736	173	13	)	)	PUNCT
cana-2736	174	1	(	(	PUNCT
cana-2736	174	2	(	(	PUNCT
cana-2736	174	3	)	)	PUNCT
cana-2736	174	4	)	)	PUNCT
cana-2736	174	5	)	)	PUNCT
cana-2736	175	1	(	(	PUNCT
cana-2736	175	2	(	(	PUNCT
cana-2736	175	3	)	)	PUNCT
cana-2736	175	4	)	)	PUNCT
cana-2736	175	5	(	(	PUNCT
cana-2736	175	6	(	(	PUNCT
cana-2736	175	7	(	(	PUNCT
cana-2736	175	8	)	)	PUNCT
cana-2736	175	9	)	)	PUNCT
cana-2736	176	1	(	(	PUNCT
cana-2736	176	2	(	(	PUNCT
cana-2736	176	3	)	)	PUNCT
cana-2736	176	4	)	)	PUNCT
cana-2736	176	5	)	)	PUNCT
cana-2736	177	1	(	(	PUNCT
cana-2736	177	2	(	(	PUNCT
cana-2736	177	3	)	)	PUNCT
cana-2736	177	4	)	)	PUNCT
cana-2736	178	1	d	d	X
cana-2736	178	2	x	x	X
cana-2736	179	1	f	f	X
cana-2736	179	2	x	x	X
cana-2736	179	3	f	f	NOUN
cana-2736	179	4	f	f	NOUN
cana-2736	180	1	x	x	SYM
cana-2736	180	2	d	d	NOUN
cana-2736	180	3	d	d	X
cana-2736	180	4	x	x	X
cana-2736	180	5	d	d	NOUN
cana-2736	180	6	x	x	X
cana-2736	180	7	f	f	NOUN
cana-2736	180	8	x	x	X
cana-2736	181	1	f	f	NOUN
cana-2736	181	2	f	f	NOUN
cana-2736	182	1	x	x	SYM
cana-2736	182	2	d	d	NOUN
cana-2736	182	3	f	f	X
cana-2736	182	4	x	x	SYM
cana-2736	182	5	x	x	PUNCT
cana-2736	182	6			VERB
cana-2736	182	7			PROPN
cana-2736	182	8	=	=	SYM
cana-2736	182	9			PROPN
cana-2736	182	10			ADJ
cana-2736	182	11			ADJ
cana-2736	182	12			NOUN
cana-2736	182	13	[	[	PUNCT
cana-2736	182	14	theorem	theorem	ADJ
cana-2736	182	15	3.6	3.6	NUM
cana-2736	182	16	(	(	PUNCT
cana-2736	182	17	1	1	NUM
cana-2736	182	18	)	)	PUNCT
cana-2736	182	19	]	]	PUNCT
cana-2736	182	20	(	(	PUNCT
cana-2736	182	21	(	(	PUNCT
cana-2736	182	22	(	(	PUNCT
cana-2736	182	23	)	)	PUNCT
cana-2736	182	24	)	)	PUNCT
cana-2736	182	25	(	(	PUNCT
cana-2736	182	26	(	(	PUNCT
cana-2736	182	27	)	)	PUNCT
cana-2736	182	28	)	)	PUNCT
cana-2736	182	29	)	)	PUNCT
cana-2736	183	1	(	(	PUNCT
cana-2736	183	2	(	(	PUNCT
cana-2736	183	3	(	(	PUNCT
cana-2736	183	4	)	)	PUNCT
cana-2736	183	5	)	)	PUNCT
cana-2736	183	6	(	(	PUNCT
cana-2736	183	7	)	)	PUNCT
cana-2736	183	8	)	)	PUNCT
cana-2736	184	1	d	d	X
cana-2736	184	2	x	x	PUNCT
cana-2736	185	1	f	f	X
cana-2736	185	2	x	x	X
cana-2736	185	3	f	f	NOUN
cana-2736	185	4	f	f	NOUN
cana-2736	186	1	x	x	SYM
cana-2736	186	2	d	d	NOUN
cana-2736	186	3	x	x	X
cana-2736	186	4	f	f	NOUN
cana-2736	186	5	x	x	SYM
cana-2736	186	6	f	f	PROPN
cana-2736	186	7	x=	x=	PUNCT
cana-2736	187	1			PROPN
cana-2736	187	2			ADJ
cana-2736	187	3			ADJ
cana-2736	187	4			ADJ
cana-2736	187	5			NUM
cana-2736	187	6	1=	1=	NOUN
cana-2736	187	7	.	.	PUNCT
cana-2736	188	1	[	[	X
cana-2736	188	2	(	(	PUNCT
cana-2736	188	3	2	2	NUM
cana-2736	188	4	)	)	PUNCT
cana-2736	188	5	]	]	PUNCT
cana-2736	189	1	hence	hence	ADV
cana-2736	189	2	,	,	PUNCT
cana-2736	189	3	(	(	PUNCT
cana-2736	189	4	(	(	PUNCT
cana-2736	189	5	)	)	PUNCT
cana-2736	189	6	)	)	PUNCT
cana-2736	189	7	(	(	PUNCT
cana-2736	189	8	(	(	PUNCT
cana-2736	189	9	)	)	PUNCT
cana-2736	189	10	)	)	PUNCT
cana-2736	190	1	(	(	PUNCT
cana-2736	190	2	(	(	PUNCT
cana-2736	190	3	)	)	PUNCT
cana-2736	190	4	)	)	PUNCT
cana-2736	191	1	d	d	X
cana-2736	191	2	x	x	PUNCT
cana-2736	192	1	f	f	X
cana-2736	192	2	x	x	X
cana-2736	192	3	f	f	NOUN
cana-2736	192	4	f	f	NOUN
cana-2736	193	1	x	x	SYM
cana-2736	193	2	d	d	PROPN
cana-2736	193	3	d	d	X
cana-2736	193	4	x	x	X
cana-2736	193	5			VERB
cana-2736	193	6			NOUN
cana-2736	193	7	for	for	ADP
cana-2736	193	8	all	all	PRON
cana-2736	193	9	x	x	SYM
cana-2736	193	10	a	a	PROPN
cana-2736	193	11	.	.	PUNCT
cana-2736	194	1	(	(	PUNCT
cana-2736	194	2	4	4	X
cana-2736	194	3	)	)	PUNCT
cana-2736	194	4	for	for	ADP
cana-2736	194	5	all	all	PRON
cana-2736	194	6	,	,	PUNCT
cana-2736	194	7	x	x	PRON
cana-2736	194	8	y	y	NOUN
cana-2736	194	9	a	a	PROPN
cana-2736	194	10	,	,	PUNCT
cana-2736	194	11	(	(	PUNCT
cana-2736	194	12	(	(	PUNCT
cana-2736	194	13	)	)	PUNCT
cana-2736	194	14	(	(	PUNCT
cana-2736	194	15	)	)	PUNCT
cana-2736	194	16	)	)	PUNCT
cana-2736	195	1	(	(	PUNCT
cana-2736	195	2	)	)	PUNCT
cana-2736	195	3	(	(	PUNCT
cana-2736	195	4	(	(	PUNCT
cana-2736	195	5	)	)	PUNCT
cana-2736	195	6	(	(	PUNCT
cana-2736	195	7	)	)	PUNCT
cana-2736	195	8	)	)	PUNCT
cana-2736	196	1	(	(	PUNCT
cana-2736	196	2	(	(	PUNCT
cana-2736	196	3	)	)	PUNCT
cana-2736	196	4	)	)	PUNCT
cana-2736	197	1	d	d	NOUN
cana-2736	197	2	y	y	NOUN
cana-2736	197	3	x	x	X
cana-2736	197	4	f	f	NOUN
cana-2736	197	5	x	x	SYM
cana-2736	198	1	d	d	NOUN
cana-2736	198	2	x	x	X
cana-2736	198	3	y	y	PROPN
cana-2736	198	4	d	d	X
cana-2736	198	5	y	y	PROPN
cana-2736	198	6	x	x	X
cana-2736	198	7	f	f	NOUN
cana-2736	198	8	x	x	PUNCT
cana-2736	199	1	d	d	X
cana-2736	199	2	y	y	PROPN
cana-2736	199	3	x	x	PROPN
cana-2736	199	4	x	x	X
cana-2736	199	5			VERB
cana-2736	199	6			ADJ
cana-2736	199	7			NOUN
cana-2736	199	8	=	=	PUNCT
cana-2736	199	9			ADJ
cana-2736	199	10			ADJ
cana-2736	199	11			ADJ
cana-2736	199	12			ADJ
cana-2736	199	13			NUM
cana-2736	199	14	1=	1=	NOUN
cana-2736	199	15	.	.	PUNCT
cana-2736	200	1	[	[	X
cana-2736	200	2	(	(	PUNCT
cana-2736	200	3	2	2	NUM
cana-2736	200	4	)	)	PUNCT
cana-2736	200	5	]	]	PUNCT
cana-2736	200	6	hence	hence	ADV
cana-2736	200	7	,	,	PUNCT
cana-2736	200	8	(	(	PUNCT
cana-2736	200	9	)	)	PUNCT
cana-2736	200	10	(	(	PUNCT
cana-2736	200	11	)	)	PUNCT
cana-2736	200	12	(	(	PUNCT
cana-2736	200	13	)	)	PUNCT
cana-2736	201	1	d	d	NOUN
cana-2736	201	2	y	y	NOUN
cana-2736	201	3	x	x	X
cana-2736	201	4	f	f	NOUN
cana-2736	201	5	x	x	SYM
cana-2736	201	6	d	d	X
cana-2736	201	7	x	x	X
cana-2736	201	8	y	y	NOUN
cana-2736	201	9			VERB
cana-2736	201	10			NOUN
cana-2736	201	11			NOUN
cana-2736	201	12	for	for	ADP
cana-2736	201	13	all	all	PRON
cana-2736	201	14	,	,	PUNCT
cana-2736	201	15	x	x	PRON
cana-2736	201	16	y	y	NOUN
cana-2736	201	17	a	a	PROPN
cana-2736	201	18	.	.	PUNCT
cana-2736	202	1	(	(	PUNCT
cana-2736	202	2	5	5	NUM
cana-2736	202	3	)	)	PUNCT
cana-2736	202	4	for	for	ADP
cana-2736	202	5	all	all	PRON
cana-2736	202	6	x	x	SYM
cana-2736	202	7	a	a	PROPN
cana-2736	202	8	,	,	PUNCT
cana-2736	202	9	(	(	PUNCT
cana-2736	202	10	)	)	PUNCT
cana-2736	202	11	1	1	NUM
cana-2736	202	12	(	(	PUNCT
cana-2736	202	13	)	)	PUNCT
cana-2736	202	14	d	d	NOUN
cana-2736	203	1	x	x	SYM
cana-2736	203	2	d	d	NOUN
cana-2736	203	3	x=	x=	PUNCT
cana-2736	204	1			PROPN
cana-2736	204	2	[	[	X
cana-2736	204	3	lemma	lemma	PROPN
cana-2736	204	4	2.2	2.2	NUM
cana-2736	204	5	(	(	PUNCT
cana-2736	204	6	2	2	NUM
cana-2736	204	7	)	)	PUNCT
cana-2736	204	8	]	]	PUNCT
cana-2736	204	9	(	(	PUNCT
cana-2736	204	10	(	(	PUNCT
cana-2736	204	11	)	)	PUNCT
cana-2736	204	12	(	(	PUNCT
cana-2736	204	13	)	)	PUNCT
cana-2736	204	14	)	)	PUNCT
cana-2736	204	15	(	(	PUNCT
cana-2736	204	16	)	)	PUNCT
cana-2736	204	17	f	f	X
cana-2736	205	1	x	x	PUNCT
cana-2736	205	2	d	d	NOUN
cana-2736	205	3	x	x	X
cana-2736	205	4	d	d	NOUN
cana-2736	205	5	x=	x=	PUNCT
cana-2736	206	1			PROPN
cana-2736	206	2			PROPN
cana-2736	206	3	[	[	X
cana-2736	206	4	(	(	PUNCT
cana-2736	206	5	1	1	NUM
cana-2736	206	6	)	)	PUNCT
cana-2736	206	7	]	]	PUNCT
cana-2736	206	8	(	(	PUNCT
cana-2736	206	9	)	)	PUNCT
cana-2736	206	10	(	(	PUNCT
cana-2736	206	11	)	)	PUNCT
cana-2736	206	12	d	d	X
cana-2736	206	13	x	x	SYM
cana-2736	206	14	f	f	NOUN
cana-2736	206	15	x=	x=	X
cana-2736	206	16			NOUN
cana-2736	206	17	.	.	PUNCT
cana-2736	207	1	proposition	proposition	NOUN
cana-2736	207	2	3.9	3.9	NUM
cana-2736	207	3	.	.	PUNCT
cana-2736	208	1	let	let	VERB
cana-2736	208	2	d	d	PRON
cana-2736	208	3	be	be	AUX
cana-2736	208	4	a	a	DET
cana-2736	208	5	rightf	rightf	ADJ
cana-2736	208	6	-derivation	-derivation	NOUN
cana-2736	208	7	of	of	ADP
cana-2736	208	8	type	type	NOUN
cana-2736	208	9	i	i	PRON
cana-2736	208	10	of	of	ADP
cana-2736	208	11	a	a	DET
cana-2736	208	12	hilbert	hilbert	NOUN
cana-2736	208	13	algebra	algebra	NOUN
cana-2736	208	14	(	(	PUNCT
cana-2736	208	15	,	,	PUNCT
cana-2736	208	16	,	,	PUNCT
cana-2736	208	17	1)a	1)a	PRON
cana-2736	208	18	a=	a=	PROPN
cana-2736	208	19			PROPN
cana-2736	208	20	.	.	PUNCT
cana-2736	209	1	then	then	ADV
cana-2736	209	2	the	the	DET
cana-2736	209	3	following	follow	VERB
cana-2736	209	4	properties	property	NOUN
cana-2736	209	5	hold	hold	VERB
cana-2736	209	6	:	:	PUNCT
cana-2736	209	7	for	for	ADP
cana-2736	209	8	any	any	PRON
cana-2736	209	9	,	,	PUNCT
cana-2736	209	10	x	x	PROPN
cana-2736	209	11	y	y	NOUN
cana-2736	209	12	a	a	PROPN
cana-2736	209	13	,	,	PUNCT
cana-2736	209	14	(	(	PUNCT
cana-2736	209	15	1	1	X
cana-2736	209	16	)	)	PUNCT
cana-2736	209	17	(	(	PUNCT
cana-2736	209	18	)	)	PUNCT
cana-2736	209	19	x	x	SYM
cana-2736	210	1	d	d	NOUN
cana-2736	210	2	x	x	PROPN
cana-2736	210	3	,	,	PUNCT
cana-2736	210	4	(	(	PUNCT
cana-2736	210	5	2	2	X
cana-2736	210	6	)	)	PUNCT
cana-2736	210	7	(	(	PUNCT
cana-2736	210	8	)	)	PUNCT
cana-2736	210	9	(	(	PUNCT
cana-2736	210	10	)	)	PUNCT
cana-2736	210	11	(	(	PUNCT
cana-2736	210	12	)	)	PUNCT
cana-2736	210	13	f	f	X
cana-2736	210	14	x	x	PUNCT
cana-2736	210	15	d	d	X
cana-2736	210	16	y	y	PROPN
cana-2736	210	17	d	d	X
cana-2736	210	18	x	x	X
cana-2736	210	19	y	y	NOUN
cana-2736	210	20			NOUN
cana-2736	210	21			NUM
cana-2736	210	22	,	,	PUNCT
cana-2736	210	23	(	(	PUNCT
cana-2736	210	24	3	3	X
cana-2736	210	25	)	)	PUNCT
cana-2736	210	26	(	(	PUNCT
cana-2736	210	27	(	(	PUNCT
cana-2736	210	28	)	)	PUNCT
cana-2736	210	29	)	)	PUNCT
cana-2736	210	30	(	(	PUNCT
cana-2736	210	31	(	(	PUNCT
cana-2736	210	32	)	)	PUNCT
cana-2736	210	33	)	)	PUNCT
cana-2736	210	34	(	(	PUNCT
cana-2736	210	35	(	(	PUNCT
cana-2736	210	36	)	)	PUNCT
cana-2736	210	37	)	)	PUNCT
cana-2736	211	1	f	f	X
cana-2736	212	1	x	x	PUNCT
cana-2736	212	2	d	d	NOUN
cana-2736	212	3	x	x	PUNCT
cana-2736	213	1	d	d	NOUN
cana-2736	213	2	d	d	X
cana-2736	213	3	x	x	SYM
cana-2736	213	4	d	d	X
cana-2736	213	5	d	d	X
cana-2736	213	6	x	x	PUNCT
cana-2736	213	7			ADJ
cana-2736	213	8			NOUN
cana-2736	213	9	,	,	PUNCT
cana-2736	213	10	(	(	PUNCT
cana-2736	213	11	4	4	NUM
cana-2736	213	12	)	)	PUNCT
cana-2736	213	13	(	(	PUNCT
cana-2736	213	14	)	)	PUNCT
cana-2736	213	15	(	(	PUNCT
cana-2736	213	16	)	)	PUNCT
cana-2736	213	17	(	(	PUNCT
cana-2736	213	18	)	)	PUNCT
cana-2736	214	1	f	f	PROPN
cana-2736	214	2	y	y	NOUN
cana-2736	214	3	x	x	PUNCT
cana-2736	215	1	d	d	NOUN
cana-2736	215	2	x	x	X
cana-2736	215	3	d	d	X
cana-2736	215	4	x	x	X
cana-2736	215	5	y	y	NOUN
cana-2736	215	6			VERB
cana-2736	215	7			NOUN
cana-2736	215	8			NOUN
cana-2736	215	9	.	.	PUNCT
cana-2736	216	1	proof	proof	NOUN
cana-2736	216	2	.	.	PUNCT
cana-2736	217	1	(	(	PUNCT
cana-2736	217	2	1	1	X
cana-2736	217	3	)	)	PUNCT
cana-2736	217	4	for	for	ADP
cana-2736	217	5	all	all	PRON
cana-2736	217	6	x	x	SYM
cana-2736	217	7	a	a	PROPN
cana-2736	217	8	,	,	PUNCT
cana-2736	217	9	(	(	PUNCT
cana-2736	217	10	)	)	PUNCT
cana-2736	217	11	(	(	PUNCT
cana-2736	217	12	(	(	PUNCT
cana-2736	217	13	)	)	PUNCT
cana-2736	217	14	)	)	PUNCT
cana-2736	217	15	x	x	PUNCT
cana-2736	218	1	d	d	NOUN
cana-2736	218	2	x	x	PUNCT
cana-2736	218	3	x	x	SYM
cana-2736	218	4	d	d	NOUN
cana-2736	218	5	x	x	PUNCT
cana-2736	218	6	x	x	PUNCT
cana-2736	218	7	=	=	SYM
cana-2736	218	8			ADJ
cana-2736	218	9			NOUN
cana-2736	218	10	[	[	PUNCT
cana-2736	218	11	theorem	theorem	ADJ
cana-2736	218	12	3.6	3.6	NUM
cana-2736	218	13	(	(	PUNCT
cana-2736	218	14	2	2	NUM
cana-2736	218	15	)	)	PUNCT
cana-2736	218	16	]	]	PUNCT
cana-2736	218	17	communications	communication	NOUN
cana-2736	218	18	on	on	ADP
cana-2736	218	19	applied	apply	VERB
cana-2736	218	20	nonlinear	nonlinear	ADJ
cana-2736	218	21	analysis	analysis	NOUN
cana-2736	218	22	issn	issn	NOUN
cana-2736	218	23	:	:	PUNCT
cana-2736	218	24	1074	1074	NUM
cana-2736	218	25	-	-	PUNCT
cana-2736	218	26	133x	133x	NUM
cana-2736	218	27	vol	vol	NOUN
cana-2736	218	28	32	32	NUM
cana-2736	218	29	no	no	NOUN
cana-2736	218	30	.	.	PUNCT
cana-2736	219	1	4s	4s	NUM
cana-2736	219	2	(	(	PUNCT
cana-2736	219	3	2025	2025	NUM
cana-2736	219	4	)	)	PUNCT
cana-2736	219	5	19	19	NUM
cana-2736	219	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	219	7	1=	1=	X
cana-2736	219	8	.	.	PUNCT
cana-2736	220	1	[	[	X
cana-2736	220	2	(	(	PUNCT
cana-2736	220	3	2.5	2.5	NUM
cana-2736	220	4	)	)	PUNCT
cana-2736	220	5	]	]	PUNCT
cana-2736	221	1	hence	hence	ADV
cana-2736	221	2	,	,	PUNCT
cana-2736	221	3	(	(	PUNCT
cana-2736	221	4	)	)	PUNCT
cana-2736	221	5	x	x	SYM
cana-2736	221	6	d	d	X
cana-2736	221	7	x	x	PROPN
cana-2736	221	8	for	for	ADP
cana-2736	221	9	all	all	PRON
cana-2736	221	10	x	x	SYM
cana-2736	221	11	a	a	PROPN
cana-2736	221	12	.	.	PUNCT
cana-2736	222	1	(	(	PUNCT
cana-2736	222	2	2	2	X
cana-2736	222	3	)	)	PUNCT
cana-2736	222	4	for	for	ADP
cana-2736	222	5	all	all	PRON
cana-2736	222	6	,	,	PUNCT
cana-2736	222	7	x	x	PRON
cana-2736	222	8	y	y	NOUN
cana-2736	222	9	a	a	PROPN
cana-2736	222	10	,	,	PUNCT
cana-2736	222	11	(	(	PUNCT
cana-2736	222	12	(	(	PUNCT
cana-2736	222	13	)	)	PUNCT
cana-2736	222	14	(	(	PUNCT
cana-2736	222	15	)	)	PUNCT
cana-2736	222	16	)	)	PUNCT
cana-2736	223	1	(	(	PUNCT
cana-2736	223	2	)	)	PUNCT
cana-2736	223	3	(	(	PUNCT
cana-2736	223	4	(	(	PUNCT
cana-2736	223	5	)	)	PUNCT
cana-2736	223	6	(	(	PUNCT
cana-2736	223	7	)	)	PUNCT
cana-2736	223	8	)	)	PUNCT
cana-2736	224	1	(	(	PUNCT
cana-2736	224	2	(	(	PUNCT
cana-2736	224	3	(	(	PUNCT
cana-2736	224	4	)	)	PUNCT
cana-2736	224	5	(	(	PUNCT
cana-2736	224	6	)	)	PUNCT
cana-2736	224	7	)	)	PUNCT
cana-2736	225	1	(	(	PUNCT
cana-2736	225	2	)	)	PUNCT
cana-2736	225	3	)	)	PUNCT
cana-2736	225	4	f	f	X
cana-2736	226	1	x	x	PUNCT
cana-2736	226	2	d	d	X
cana-2736	226	3	y	y	PROPN
cana-2736	226	4	d	d	NOUN
cana-2736	226	5	x	x	X
cana-2736	227	1	y	y	NOUN
cana-2736	227	2	f	f	NOUN
cana-2736	227	3	x	x	PROPN
cana-2736	228	1	d	d	X
cana-2736	228	2	y	y	NOUN
cana-2736	228	3	f	f	NOUN
cana-2736	228	4	x	x	PROPN
cana-2736	228	5	d	d	X
cana-2736	228	6	y	y	PROPN
cana-2736	228	7	x	x	SYM
cana-2736	228	8	y	y	NOUN
cana-2736	228	9			VERB
cana-2736	228	10			PROPN
cana-2736	228	11	=	=	SYM
cana-2736	228	12			PROPN
cana-2736	228	13			ADJ
cana-2736	228	14			ADJ
cana-2736	228	15			NOUN
cana-2736	228	16			NUM
cana-2736	228	17	1=	1=	NOUN
cana-2736	228	18	.	.	PUNCT
cana-2736	229	1	[	[	X
cana-2736	229	2	(	(	PUNCT
cana-2736	229	3	2.4	2.4	NUM
cana-2736	229	4	)	)	PUNCT
cana-2736	229	5	]	]	PUNCT
cana-2736	230	1	hence	hence	ADV
cana-2736	230	2	,	,	PUNCT
cana-2736	230	3	(	(	PUNCT
cana-2736	230	4	)	)	PUNCT
cana-2736	230	5	(	(	PUNCT
cana-2736	230	6	)	)	PUNCT
cana-2736	230	7	(	(	PUNCT
cana-2736	230	8	)	)	PUNCT
cana-2736	230	9	f	f	X
cana-2736	230	10	x	x	PUNCT
cana-2736	230	11	d	d	X
cana-2736	230	12	y	y	PROPN
cana-2736	230	13	d	d	X
cana-2736	230	14	x	x	X
cana-2736	230	15	y	y	NOUN
cana-2736	230	16			NUM
cana-2736	230	17			PROPN
cana-2736	230	18	for	for	ADP
cana-2736	230	19	all	all	PRON
cana-2736	230	20	,	,	PUNCT
cana-2736	230	21	x	x	PRON
cana-2736	230	22	y	y	NOUN
cana-2736	230	23	a	a	PROPN
cana-2736	230	24	.	.	PUNCT
cana-2736	231	1	(	(	PUNCT
cana-2736	231	2	3	3	X
cana-2736	231	3	)	)	PUNCT
cana-2736	231	4	for	for	ADP
cana-2736	231	5	all	all	PRON
cana-2736	231	6	x	x	SYM
cana-2736	231	7	a	a	PROPN
cana-2736	231	8	,	,	PUNCT
cana-2736	231	9	(	(	PUNCT
cana-2736	231	10	(	(	PUNCT
cana-2736	231	11	(	(	PUNCT
cana-2736	231	12	)	)	PUNCT
cana-2736	231	13	)	)	PUNCT
cana-2736	232	1	(	(	PUNCT
cana-2736	232	2	(	(	PUNCT
cana-2736	232	3	)	)	PUNCT
cana-2736	232	4	)	)	PUNCT
cana-2736	232	5	)	)	PUNCT
cana-2736	233	1	(	(	PUNCT
cana-2736	233	2	(	(	PUNCT
cana-2736	233	3	)	)	PUNCT
cana-2736	233	4	)	)	PUNCT
cana-2736	233	5	(	(	PUNCT
cana-2736	233	6	(	(	PUNCT
cana-2736	233	7	(	(	PUNCT
cana-2736	233	8	)	)	PUNCT
cana-2736	233	9	)	)	PUNCT
cana-2736	234	1	(	(	PUNCT
cana-2736	234	2	(	(	PUNCT
cana-2736	234	3	)	)	PUNCT
cana-2736	234	4	)	)	PUNCT
cana-2736	234	5	)	)	PUNCT
cana-2736	235	1	(	(	PUNCT
cana-2736	235	2	(	(	PUNCT
cana-2736	235	3	)	)	PUNCT
cana-2736	235	4	)	)	PUNCT
cana-2736	235	5	f	f	X
cana-2736	236	1	x	x	PUNCT
cana-2736	236	2	d	d	NOUN
cana-2736	236	3	x	x	PUNCT
cana-2736	237	1	d	d	NOUN
cana-2736	237	2	d	d	X
cana-2736	237	3	x	x	X
cana-2736	238	1	d	d	NOUN
cana-2736	238	2	d	d	X
cana-2736	238	3	x	x	X
cana-2736	238	4	f	f	NOUN
cana-2736	239	1	x	x	SYM
cana-2736	239	2	d	d	NOUN
cana-2736	239	3	x	x	X
cana-2736	240	1	d	d	NOUN
cana-2736	240	2	d	d	X
cana-2736	240	3	x	x	X
cana-2736	240	4	d	d	NOUN
cana-2736	240	5	d	d	X
cana-2736	240	6	x	x	PUNCT
cana-2736	240	7	x	x	PUNCT
cana-2736	240	8			VERB
cana-2736	240	9			PROPN
cana-2736	240	10	=	=	SYM
cana-2736	240	11			PROPN
cana-2736	240	12			ADJ
cana-2736	240	13			ADJ
cana-2736	240	14			NOUN
cana-2736	240	15	[	[	PUNCT
cana-2736	240	16	theorem	theorem	ADJ
cana-2736	240	17	3.6	3.6	NUM
cana-2736	240	18	(	(	PUNCT
cana-2736	240	19	2	2	NUM
cana-2736	240	20	)	)	PUNCT
cana-2736	240	21	]	]	PUNCT
cana-2736	241	1	(	(	PUNCT
cana-2736	241	2	(	(	PUNCT
cana-2736	241	3	(	(	PUNCT
cana-2736	241	4	)	)	PUNCT
cana-2736	241	5	)	)	PUNCT
cana-2736	241	6	(	(	PUNCT
cana-2736	241	7	(	(	PUNCT
cana-2736	241	8	)	)	PUNCT
cana-2736	241	9	)	)	PUNCT
cana-2736	241	10	)	)	PUNCT
cana-2736	242	1	(	(	PUNCT
cana-2736	242	2	(	(	PUNCT
cana-2736	242	3	(	(	PUNCT
cana-2736	242	4	)	)	PUNCT
cana-2736	242	5	)	)	PUNCT
cana-2736	242	6	(	(	PUNCT
cana-2736	242	7	)	)	PUNCT
cana-2736	242	8	)	)	PUNCT
cana-2736	242	9	f	f	X
cana-2736	243	1	x	x	PUNCT
cana-2736	243	2	d	d	NOUN
cana-2736	243	3	x	x	PUNCT
cana-2736	244	1	d	d	NOUN
cana-2736	244	2	d	d	X
cana-2736	244	3	x	x	X
cana-2736	244	4	d	d	NOUN
cana-2736	244	5	x	x	X
cana-2736	244	6	d	d	NOUN
cana-2736	244	7	x	x	SYM
cana-2736	244	8	d	d	NOUN
cana-2736	244	9	x=	x=	PUNCT
cana-2736	245	1			ADJ
cana-2736	245	2			ADJ
cana-2736	245	3			ADJ
cana-2736	245	4			ADJ
cana-2736	245	5			NUM
cana-2736	245	6	1=	1=	NOUN
cana-2736	245	7	.	.	PUNCT
cana-2736	246	1	[	[	X
cana-2736	246	2	(	(	PUNCT
cana-2736	246	3	2	2	NUM
cana-2736	246	4	)	)	PUNCT
cana-2736	246	5	]	]	PUNCT
cana-2736	247	1	hence	hence	ADV
cana-2736	247	2	,	,	PUNCT
cana-2736	247	3	(	(	PUNCT
cana-2736	247	4	(	(	PUNCT
cana-2736	247	5	)	)	PUNCT
cana-2736	247	6	)	)	PUNCT
cana-2736	247	7	(	(	PUNCT
cana-2736	247	8	(	(	PUNCT
cana-2736	247	9	)	)	PUNCT
cana-2736	247	10	)	)	PUNCT
cana-2736	248	1	(	(	PUNCT
cana-2736	248	2	(	(	PUNCT
cana-2736	248	3	)	)	PUNCT
cana-2736	248	4	)	)	PUNCT
cana-2736	248	5	f	f	X
cana-2736	249	1	x	x	PUNCT
cana-2736	249	2	d	d	NOUN
cana-2736	249	3	x	x	PUNCT
cana-2736	250	1	d	d	NOUN
cana-2736	250	2	d	d	X
cana-2736	250	3	x	x	SYM
cana-2736	250	4	d	d	X
cana-2736	250	5	d	d	X
cana-2736	250	6	x	x	X
cana-2736	250	7			VERB
cana-2736	250	8			NOUN
cana-2736	250	9	for	for	ADP
cana-2736	250	10	all	all	PRON
cana-2736	250	11	x	x	SYM
cana-2736	250	12	a	a	PROPN
cana-2736	250	13	.	.	PUNCT
cana-2736	251	1	(	(	PUNCT
cana-2736	251	2	4	4	X
cana-2736	251	3	)	)	PUNCT
cana-2736	251	4	for	for	ADP
cana-2736	251	5	all	all	PRON
cana-2736	251	6	,	,	PUNCT
cana-2736	251	7	x	x	PRON
cana-2736	251	8	y	y	NOUN
cana-2736	251	9	a	a	PROPN
cana-2736	251	10	,	,	PUNCT
cana-2736	251	11	(	(	PUNCT
cana-2736	251	12	(	(	PUNCT
cana-2736	251	13	)	)	PUNCT
cana-2736	251	14	(	(	PUNCT
cana-2736	251	15	)	)	PUNCT
cana-2736	251	16	)	)	PUNCT
cana-2736	252	1	(	(	PUNCT
cana-2736	252	2	)	)	PUNCT
cana-2736	252	3	(	(	PUNCT
cana-2736	252	4	(	(	PUNCT
cana-2736	252	5	)	)	PUNCT
cana-2736	252	6	(	(	PUNCT
cana-2736	252	7	)	)	PUNCT
cana-2736	252	8	)	)	PUNCT
cana-2736	253	1	(	(	PUNCT
cana-2736	253	2	(	(	PUNCT
cana-2736	253	3	)	)	PUNCT
cana-2736	253	4	)	)	PUNCT
cana-2736	254	1	f	f	PROPN
cana-2736	255	1	y	y	NOUN
cana-2736	255	2	x	x	PUNCT
cana-2736	256	1	d	d	NOUN
cana-2736	256	2	x	x	X
cana-2736	256	3	d	d	NOUN
cana-2736	256	4	x	x	X
cana-2736	256	5	y	y	NOUN
cana-2736	256	6	f	f	PROPN
cana-2736	256	7	y	y	PROPN
cana-2736	256	8	x	x	SYM
cana-2736	257	1	d	d	NOUN
cana-2736	257	2	x	x	X
cana-2736	258	1	d	d	X
cana-2736	258	2	y	y	PROPN
cana-2736	258	3	x	x	PROPN
cana-2736	258	4	x	x	X
cana-2736	258	5			VERB
cana-2736	258	6			ADJ
cana-2736	258	7			NOUN
cana-2736	258	8	=	=	PUNCT
cana-2736	258	9			ADJ
cana-2736	258	10			ADJ
cana-2736	258	11			ADJ
cana-2736	258	12			ADJ
cana-2736	258	13			NUM
cana-2736	258	14	1=	1=	NOUN
cana-2736	258	15	.	.	PUNCT
cana-2736	259	1	[	[	X
cana-2736	259	2	(	(	PUNCT
cana-2736	259	3	2	2	NUM
cana-2736	259	4	)	)	PUNCT
cana-2736	259	5	]	]	PUNCT
cana-2736	259	6	hence	hence	ADV
cana-2736	259	7	,	,	PUNCT
cana-2736	259	8	(	(	PUNCT
cana-2736	259	9	)	)	PUNCT
cana-2736	259	10	(	(	PUNCT
cana-2736	259	11	)	)	PUNCT
cana-2736	259	12	(	(	PUNCT
cana-2736	259	13	)	)	PUNCT
cana-2736	259	14	f	f	PROPN
cana-2736	260	1	y	y	NOUN
cana-2736	260	2	x	x	PUNCT
cana-2736	261	1	d	d	NOUN
cana-2736	261	2	x	x	X
cana-2736	261	3	d	d	X
cana-2736	261	4	x	x	X
cana-2736	261	5	y	y	NOUN
cana-2736	261	6			VERB
cana-2736	261	7			NOUN
cana-2736	261	8			NOUN
cana-2736	261	9	for	for	ADP
cana-2736	261	10	all	all	PRON
cana-2736	261	11	,	,	PUNCT
cana-2736	261	12	x	x	PRON
cana-2736	261	13	y	y	PROPN
cana-2736	261	14	a	a	PROPN
cana-2736	261	15	.	.	PUNCT
cana-2736	262	1	definition	definition	NOUN
cana-2736	262	2	3.10	3.10	NUM
cana-2736	262	3	.	.	PUNCT
cana-2736	263	1	let	let	VERB
cana-2736	263	2	d	d	PRON
cana-2736	263	3	be	be	AUX
cana-2736	263	4	a	a	DET
cana-2736	263	5	self	self	NOUN
cana-2736	263	6	-	-	PUNCT
cana-2736	263	7	map	map	NOUN
cana-2736	263	8	of	of	ADP
cana-2736	263	9	a	a	DET
cana-2736	263	10	hilbert	hilbert	NOUN
cana-2736	263	11	algebra	algebra	NOUN
cana-2736	263	12	(	(	PUNCT
cana-2736	263	13	,	,	PUNCT
cana-2736	263	14	,	,	PUNCT
cana-2736	263	15	1)a	1)a	PRON
cana-2736	263	16	a=	a=	PROPN
cana-2736	263	17			NUM
cana-2736	263	18	.	.	PUNCT
cana-2736	264	1	we	we	PRON
cana-2736	264	2	define	define	VERB
cana-2736	264	3	the	the	DET
cana-2736	264	4	kernel	kernel	PROPN
cana-2736	264	5	ker	ker	PROPN
cana-2736	265	1	(	(	PUNCT
cana-2736	265	2	)	)	PUNCT
cana-2736	265	3	d	d	NOUN
cana-2736	265	4	a	a	PRON
cana-2736	265	5	of	of	ADP
cana-2736	265	6	a	a	PRON
cana-2736	265	7	as	as	SCONJ
cana-2736	265	8	follows	follow	VERB
cana-2736	265	9	:	:	PUNCT
cana-2736	265	10	ker	ker	NOUN
cana-2736	265	11	(	(	PUNCT
cana-2736	265	12	)	)	PUNCT
cana-2736	265	13	{	{	PUNCT
cana-2736	265	14	:	:	PUNCT
cana-2736	265	15	(	(	PUNCT
cana-2736	265	16	)	)	PUNCT
cana-2736	265	17	1}d	1}d	NUM
cana-2736	265	18	a	a	DET
cana-2736	265	19	x	x	SYM
cana-2736	265	20	a	a	DET
cana-2736	265	21	d	d	PROPN
cana-2736	265	22	x=	x=	PROPN
cana-2736	265	23			PROPN
cana-2736	265	24	=	=	PUNCT
cana-2736	265	25	theorem	theorem	VERB
cana-2736	265	26	3.11	3.11	NUM
cana-2736	265	27	.	.	PUNCT
cana-2736	266	1	if	if	SCONJ
cana-2736	266	2	d	d	PROPN
cana-2736	266	3	is	be	AUX
cana-2736	266	4	a	a	DET
cana-2736	266	5	rightf	rightf	ADJ
cana-2736	266	6	-derivation	-derivation	NOUN
cana-2736	266	7	of	of	ADP
cana-2736	266	8	type	type	NOUN
cana-2736	266	9	i	i	PRON
cana-2736	266	10	of	of	ADP
cana-2736	266	11	a	a	DET
cana-2736	266	12	hilbert	hilbert	NOUN
cana-2736	266	13	algebra	algebra	NOUN
cana-2736	266	14	(	(	PUNCT
cana-2736	266	15	,	,	PUNCT
cana-2736	266	16	,	,	PUNCT
cana-2736	266	17	1)a	1)a	PRON
cana-2736	266	18	a=	a=	PROPN
cana-2736	266	19			NUM
cana-2736	266	20	,	,	PUNCT
cana-2736	266	21	then	then	ADV
cana-2736	266	22	ker	ker	PROPN
cana-2736	266	23	(	(	PUNCT
cana-2736	266	24	)	)	PUNCT
cana-2736	266	25	dy	dy	NOUN
cana-2736	266	26	x	x	SYM
cana-2736	266	27	a	a	PROPN
cana-2736	266	28			NOUN
cana-2736	266	29	for	for	ADP
cana-2736	266	30	all	all	DET
cana-2736	266	31	ker	ker	NOUN
cana-2736	266	32	(	(	PUNCT
cana-2736	266	33	)	)	PUNCT
cana-2736	266	34	dy	dy	NOUN
cana-2736	266	35	a	a	PROPN
cana-2736	266	36	and	and	CCONJ
cana-2736	266	37	x	x	X
cana-2736	266	38	a	a	PROPN
cana-2736	266	39	.	.	PUNCT
cana-2736	267	1	proof	proof	NOUN
cana-2736	267	2	.	.	PUNCT
cana-2736	268	1	assume	assume	VERB
cana-2736	268	2	that	that	SCONJ
cana-2736	268	3	d	d	NOUN
cana-2736	268	4	is	be	AUX
cana-2736	268	5	a	a	DET
cana-2736	268	6	rightf	rightf	ADJ
cana-2736	268	7	-derivation	-derivation	NOUN
cana-2736	268	8	of	of	ADP
cana-2736	268	9	a	a	PRON
cana-2736	268	10	.	.	PUNCT
cana-2736	269	1	let	let	VERB
cana-2736	269	2	ker	ker	PROPN
cana-2736	269	3	(	(	PUNCT
cana-2736	269	4	)	)	PUNCT
cana-2736	269	5	dy	dy	NOUN
cana-2736	269	6	a	a	PROPN
cana-2736	269	7	and	and	CCONJ
cana-2736	269	8	x	x	PUNCT
cana-2736	269	9	a	a	PROPN
cana-2736	269	10	.	.	PUNCT
cana-2736	270	1	then	then	ADV
cana-2736	270	2	(	(	PUNCT
cana-2736	270	3	)	)	PUNCT
cana-2736	270	4	1d	1d	NUM
cana-2736	270	5	y	y	NOUN
cana-2736	270	6	=	=	PROPN
cana-2736	270	7	.	.	PUNCT
cana-2736	271	1	thus	thus	ADV
cana-2736	271	2	,	,	PUNCT
cana-2736	271	3	(	(	PUNCT
cana-2736	271	4	)	)	PUNCT
cana-2736	271	5	(	(	PUNCT
cana-2736	271	6	(	(	PUNCT
cana-2736	271	7	)	)	PUNCT
cana-2736	271	8	)	)	PUNCT
cana-2736	272	1	d	d	X
cana-2736	272	2	y	y	NOUN
cana-2736	273	1	x	x	PUNCT
cana-2736	273	2	d	d	NOUN
cana-2736	273	3	x	x	X
cana-2736	273	4	y	y	NOUN
cana-2736	273	5	y	y	NOUN
cana-2736	273	6	=	=	PUNCT
cana-2736	274	1			PROPN
cana-2736	274	2			PROPN
cana-2736	274	3	(	(	PUNCT
cana-2736	274	4	(	(	PUNCT
cana-2736	274	5	)	)	PUNCT
cana-2736	274	6	(	(	PUNCT
cana-2736	274	7	)	)	PUNCT
cana-2736	274	8	)	)	PUNCT
cana-2736	274	9	(	(	PUNCT
cana-2736	274	10	(	(	PUNCT
cana-2736	274	11	)	)	PUNCT
cana-2736	274	12	)	)	PUNCT
cana-2736	275	1	f	f	X
cana-2736	276	1	x	x	PUNCT
cana-2736	276	2	y	y	PROPN
cana-2736	276	3	d	d	X
cana-2736	276	4	y	y	PROPN
cana-2736	276	5	x	x	SYM
cana-2736	276	6	y	y	NOUN
cana-2736	276	7	y=	y=	PRON
cana-2736	276	8			ADJ
cana-2736	276	9			ADJ
cana-2736	276	10			NOUN
cana-2736	276	11			PROPN
cana-2736	276	12			NUM
cana-2736	276	13	(	(	PUNCT
cana-2736	276	14	(	(	PUNCT
cana-2736	276	15	)	)	PUNCT
cana-2736	276	16	1	1	NUM
cana-2736	276	17	)	)	PUNCT
cana-2736	276	18	(	(	PUNCT
cana-2736	276	19	(	(	PUNCT
cana-2736	276	20	)	)	PUNCT
cana-2736	276	21	)	)	PUNCT
cana-2736	277	1	f	f	X
cana-2736	277	2	x	x	PUNCT
cana-2736	277	3	y	y	NOUN
cana-2736	277	4	x	x	SYM
cana-2736	277	5	y	y	NOUN
cana-2736	277	6	y=	y=	PRON
cana-2736	277	7			ADJ
cana-2736	277	8			ADJ
cana-2736	277	9			NOUN
cana-2736	277	10			PROPN
cana-2736	277	11			NUM
cana-2736	277	12	1	1	NUM
cana-2736	277	13	(	(	PUNCT
cana-2736	277	14	(	(	PUNCT
cana-2736	277	15	)	)	PUNCT
cana-2736	277	16	)	)	PUNCT
cana-2736	278	1	x	x	X
cana-2736	278	2	y	y	NOUN
cana-2736	278	3	y=	y=	PRON
cana-2736	278	4			NOUN
cana-2736	278	5			PROPN
cana-2736	278	6			PROPN
cana-2736	278	7	[	[	X
cana-2736	278	8	lemma	lemma	PROPN
cana-2736	278	9	2.2	2.2	NUM
cana-2736	278	10	(	(	PUNCT
cana-2736	278	11	3	3	NUM
cana-2736	278	12	)	)	PUNCT
cana-2736	278	13	]	]	PUNCT
cana-2736	278	14	1=	1=	X
cana-2736	278	15	.	.	PUNCT
cana-2736	279	1	[	[	X
cana-2736	279	2	(	(	PUNCT
cana-2736	279	3	2.7	2.7	NUM
cana-2736	279	4	)	)	PUNCT
cana-2736	279	5	]	]	PUNCT
cana-2736	280	1	hence	hence	ADV
cana-2736	280	2	,	,	PUNCT
cana-2736	280	3	ker	ker	X
cana-2736	280	4	(	(	PUNCT
cana-2736	280	5	)	)	PUNCT
cana-2736	280	6	dy	dy	NOUN
cana-2736	280	7	x	x	SYM
cana-2736	280	8	a	a	PROPN
cana-2736	280	9			NOUN
cana-2736	280	10	.	.	PUNCT
cana-2736	281	1	communications	communication	NOUN
cana-2736	281	2	on	on	ADP
cana-2736	281	3	applied	apply	VERB
cana-2736	281	4	nonlinear	nonlinear	ADJ
cana-2736	281	5	analysis	analysis	NOUN
cana-2736	281	6	issn	issn	NOUN
cana-2736	281	7	:	:	PUNCT
cana-2736	281	8	1074	1074	NUM
cana-2736	281	9	-	-	PUNCT
cana-2736	281	10	133x	133x	NUM
cana-2736	281	11	vol	vol	NOUN
cana-2736	281	12	32	32	NUM
cana-2736	281	13	no	no	NOUN
cana-2736	281	14	.	.	PUNCT
cana-2736	282	1	4s	4s	NUM
cana-2736	282	2	(	(	PUNCT
cana-2736	282	3	2025	2025	NUM
cana-2736	282	4	)	)	PUNCT
cana-2736	282	5	20	20	NUM
cana-2736	282	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	282	7	theorem	theorem	VERB
cana-2736	282	8	3.12	3.12	NUM
cana-2736	282	9	.	.	PUNCT
cana-2736	283	1	if	if	SCONJ
cana-2736	283	2	d	d	PROPN
cana-2736	283	3	is	be	AUX
cana-2736	283	4	a	a	DET
cana-2736	283	5	rightf	rightf	ADJ
cana-2736	283	6	-derivation	-derivation	NOUN
cana-2736	283	7	of	of	ADP
cana-2736	283	8	type	type	NOUN
cana-2736	283	9	i	i	PRON
cana-2736	283	10	of	of	ADP
cana-2736	283	11	a	a	DET
cana-2736	283	12	commutative	commutative	ADJ
cana-2736	283	13	hilbert	hilbert	NOUN
cana-2736	283	14	algebra	algebra	PROPN
cana-2736	283	15	(	(	PUNCT
cana-2736	283	16	,	,	PUNCT
cana-2736	283	17	,	,	PUNCT
cana-2736	283	18	1)a	1)a	PRON
cana-2736	283	19	a=	a=	PROPN
cana-2736	283	20			PROPN
cana-2736	283	21	and	and	CCONJ
cana-2736	283	22	for	for	ADP
cana-2736	283	23	any	any	PRON
cana-2736	283	24	,	,	PUNCT
cana-2736	283	25	x	x	PRON
cana-2736	283	26	y	y	PROPN
cana-2736	283	27	a	a	PROPN
cana-2736	283	28	is	be	AUX
cana-2736	283	29	such	such	ADJ
cana-2736	283	30	that	that	SCONJ
cana-2736	283	31	y	y	PROPN
cana-2736	283	32	x	x	PROPN
cana-2736	283	33	and	and	CCONJ
cana-2736	283	34	ker	ker	PROPN
cana-2736	283	35	(	(	PUNCT
cana-2736	283	36	)	)	PUNCT
cana-2736	283	37	dy	dy	NOUN
cana-2736	283	38	a	a	PROPN
cana-2736	283	39	,	,	PUNCT
cana-2736	283	40	then	then	ADV
cana-2736	283	41	ker	ker	PROPN
cana-2736	283	42	(	(	PUNCT
cana-2736	283	43	)	)	PUNCT
cana-2736	283	44	dx	dx	PROPN
cana-2736	283	45	a	a	PROPN
cana-2736	283	46	.	.	PUNCT
cana-2736	284	1	proof	proof	NOUN
cana-2736	284	2	.	.	PUNCT
cana-2736	285	1	assume	assume	VERB
cana-2736	285	2	that	that	SCONJ
cana-2736	285	3	d	d	NOUN
cana-2736	285	4	is	be	AUX
cana-2736	285	5	a	a	DET
cana-2736	285	6	rightf	rightf	ADJ
cana-2736	285	7	-derivation	-derivation	NOUN
cana-2736	285	8	of	of	ADP
cana-2736	285	9	type	type	NOUN
cana-2736	285	10	i	i	PRON
cana-2736	285	11	of	of	ADP
cana-2736	285	12	a	a	PRON
cana-2736	285	13	.	.	PUNCT
cana-2736	286	1	let	let	VERB
cana-2736	286	2	,	,	PUNCT
cana-2736	286	3	x	x	SYM
cana-2736	286	4	y	y	PROPN
cana-2736	286	5	a	a	PROPN
cana-2736	286	6	be	be	AUX
cana-2736	286	7	such	such	ADJ
cana-2736	286	8	that	that	SCONJ
cana-2736	286	9	y	y	PROPN
cana-2736	286	10	x	x	PROPN
cana-2736	286	11	and	and	CCONJ
cana-2736	286	12	ker	ker	PROPN
cana-2736	286	13	(	(	PUNCT
cana-2736	286	14	)	)	PUNCT
cana-2736	286	15	dy	dy	NOUN
cana-2736	286	16	a	a	PROPN
cana-2736	286	17	.	.	PUNCT
cana-2736	287	1	then	then	ADV
cana-2736	287	2	1y	1y	NUM
cana-2736	287	3	x	x	SYM
cana-2736	288	1	=	=	SYM
cana-2736	288	2	and	and	CCONJ
cana-2736	288	3	(	(	PUNCT
cana-2736	288	4	)	)	PUNCT
cana-2736	288	5	1d	1d	NUM
cana-2736	289	1	y	y	NOUN
cana-2736	289	2	=	=	PROPN
cana-2736	289	3	.	.	PUNCT
cana-2736	290	1	thus	thus	ADV
cana-2736	290	2	,	,	PUNCT
cana-2736	290	3	(	(	PUNCT
cana-2736	290	4	)	)	PUNCT
cana-2736	290	5	(	(	PUNCT
cana-2736	290	6	1	1	X
cana-2736	290	7	)	)	PUNCT
cana-2736	290	8	d	d	NOUN
cana-2736	291	1	x	x	SYM
cana-2736	291	2	d	d	NOUN
cana-2736	291	3	x=	x=	PUNCT
cana-2736	292	1			PROPN
cana-2736	292	2	[	[	X
cana-2736	292	3	lemma	lemma	PROPN
cana-2736	292	4	2.2	2.2	NUM
cana-2736	292	5	(	(	PUNCT
cana-2736	292	6	2	2	NUM
cana-2736	292	7	)	)	PUNCT
cana-2736	292	8	]	]	PUNCT
cana-2736	292	9	(	(	PUNCT
cana-2736	292	10	(	(	PUNCT
cana-2736	292	11	)	)	PUNCT
cana-2736	292	12	)	)	PUNCT
cana-2736	293	1	d	d	X
cana-2736	293	2	y	y	PROPN
cana-2736	293	3	x	x	SYM
cana-2736	293	4	x=	x=	PROPN
cana-2736	294	1			PROPN
cana-2736	294	2			PROPN
cana-2736	294	3	(	(	PUNCT
cana-2736	294	4	(	(	PUNCT
cana-2736	294	5	)	)	PUNCT
cana-2736	294	6	)	)	PUNCT
cana-2736	295	1	d	d	X
cana-2736	295	2	x	x	PUNCT
cana-2736	295	3	y	y	NOUN
cana-2736	295	4	y=	y=	NOUN
cana-2736	295	5			PROPN
cana-2736	295	6			PROPN
cana-2736	296	1	[	[	X
cana-2736	296	2	commutative	commutative	ADJ
cana-2736	296	3	]	]	X
cana-2736	296	4	(	(	PUNCT
cana-2736	296	5	(	(	PUNCT
cana-2736	296	6	)	)	PUNCT
cana-2736	296	7	(	(	PUNCT
cana-2736	296	8	)	)	PUNCT
cana-2736	296	9	)	)	PUNCT
cana-2736	296	10	(	(	PUNCT
cana-2736	296	11	(	(	PUNCT
cana-2736	296	12	)	)	PUNCT
cana-2736	296	13	)	)	PUNCT
cana-2736	297	1	f	f	X
cana-2736	298	1	x	x	PUNCT
cana-2736	298	2	y	y	PROPN
cana-2736	298	3	d	d	X
cana-2736	298	4	y	y	PROPN
cana-2736	298	5	x	x	SYM
cana-2736	298	6	y	y	NOUN
cana-2736	298	7	y=	y=	PRON
cana-2736	298	8			ADJ
cana-2736	298	9			ADJ
cana-2736	298	10			NOUN
cana-2736	298	11			PROPN
cana-2736	298	12			NUM
cana-2736	298	13	(	(	PUNCT
cana-2736	298	14	(	(	PUNCT
cana-2736	298	15	)	)	PUNCT
cana-2736	298	16	1	1	NUM
cana-2736	298	17	)	)	PUNCT
cana-2736	298	18	(	(	PUNCT
cana-2736	298	19	(	(	PUNCT
cana-2736	298	20	)	)	PUNCT
cana-2736	298	21	)	)	PUNCT
cana-2736	299	1	f	f	X
cana-2736	299	2	x	x	PUNCT
cana-2736	299	3	y	y	NOUN
cana-2736	299	4	x	x	SYM
cana-2736	299	5	y	y	NOUN
cana-2736	299	6	y=	y=	PRON
cana-2736	299	7			ADJ
cana-2736	299	8			ADJ
cana-2736	299	9			NOUN
cana-2736	299	10			PROPN
cana-2736	299	11			NUM
cana-2736	299	12	1	1	NUM
cana-2736	299	13	(	(	PUNCT
cana-2736	299	14	(	(	PUNCT
cana-2736	299	15	)	)	PUNCT
cana-2736	299	16	)	)	PUNCT
cana-2736	300	1	x	x	X
cana-2736	300	2	y	y	NOUN
cana-2736	300	3	y=	y=	PRON
cana-2736	300	4			NOUN
cana-2736	300	5			PROPN
cana-2736	300	6			PROPN
cana-2736	300	7	[	[	X
cana-2736	300	8	lemma	lemma	PROPN
cana-2736	300	9	2.2	2.2	NUM
cana-2736	300	10	(	(	PUNCT
cana-2736	300	11	3	3	NUM
cana-2736	300	12	)	)	PUNCT
cana-2736	300	13	]	]	PUNCT
cana-2736	300	14	1=	1=	X
cana-2736	300	15	.	.	PUNCT
cana-2736	301	1	[	[	X
cana-2736	301	2	(	(	PUNCT
cana-2736	301	3	2.7	2.7	NUM
cana-2736	301	4	)	)	PUNCT
cana-2736	301	5	]	]	PUNCT
cana-2736	302	1	hence	hence	ADV
cana-2736	302	2	,	,	PUNCT
cana-2736	302	3	ker	ker	X
cana-2736	302	4	(	(	PUNCT
cana-2736	302	5	)	)	PUNCT
cana-2736	302	6	dx	dx	PROPN
cana-2736	302	7	a	a	PROPN
cana-2736	302	8	.	.	PUNCT
cana-2736	303	1	theorem	theorem	VERB
cana-2736	303	2	3.13	3.13	NUM
cana-2736	303	3	.	.	PUNCT
cana-2736	304	1	if	if	SCONJ
cana-2736	304	2	d	d	PROPN
cana-2736	304	3	is	be	AUX
cana-2736	304	4	a	a	DET
cana-2736	304	5	rightf	rightf	ADJ
cana-2736	304	6	-derivation	-derivation	NOUN
cana-2736	304	7	of	of	ADP
cana-2736	304	8	type	type	NOUN
cana-2736	304	9	i	i	PRON
cana-2736	304	10	of	of	ADP
cana-2736	304	11	a	a	DET
cana-2736	304	12	hilbert	hilbert	NOUN
cana-2736	304	13	algebra	algebra	NOUN
cana-2736	304	14	(	(	PUNCT
cana-2736	304	15	,	,	PUNCT
cana-2736	304	16	,	,	PUNCT
cana-2736	304	17	1)a	1)a	PRON
cana-2736	304	18	a=	a=	PROPN
cana-2736	304	19			NUM
cana-2736	304	20	,	,	PUNCT
cana-2736	304	21	then	then	ADV
cana-2736	304	22	ker	ker	INTJ
cana-2736	304	23	(	(	PUNCT
cana-2736	304	24	)	)	PUNCT
cana-2736	304	25	d	d	NOUN
cana-2736	304	26	a	a	PRON
cana-2736	304	27	is	be	AUX
cana-2736	304	28	a	a	DET
cana-2736	304	29	near	near	ADJ
cana-2736	304	30	filter	filter	NOUN
cana-2736	304	31	(	(	PUNCT
cana-2736	304	32	subalgebra	subalgebra	PROPN
cana-2736	304	33	)	)	PUNCT
cana-2736	304	34	of	of	ADP
cana-2736	304	35	a	a	PRON
cana-2736	304	36	.	.	PUNCT
cana-2736	305	1	proof	proof	NOUN
cana-2736	305	2	.	.	PUNCT
cana-2736	306	1	assume	assume	VERB
cana-2736	306	2	that	that	SCONJ
cana-2736	306	3	d	d	NOUN
cana-2736	306	4	is	be	AUX
cana-2736	306	5	a	a	DET
cana-2736	306	6	rightf	rightf	ADJ
cana-2736	306	7	-derivation	-derivation	NOUN
cana-2736	306	8	of	of	ADP
cana-2736	306	9	type	type	NOUN
cana-2736	306	10	i	i	PRON
cana-2736	306	11	of	of	ADP
cana-2736	306	12	a	a	PRON
cana-2736	306	13	.	.	PUNCT
cana-2736	307	1	by	by	ADP
cana-2736	307	2	theorem	theorem	ADJ
cana-2736	307	3	3.4	3.4	NUM
cana-2736	307	4	(	(	PUNCT
cana-2736	307	5	2	2	NUM
cana-2736	307	6	)	)	PUNCT
cana-2736	307	7	,	,	PUNCT
cana-2736	307	8	we	we	PRON
cana-2736	307	9	have	have	VERB
cana-2736	307	10	(	(	PUNCT
cana-2736	307	11	1	1	X
cana-2736	307	12	)	)	PUNCT
cana-2736	307	13	1d	1d	NUM
cana-2736	307	14	=	=	SYM
cana-2736	308	1	and	and	CCONJ
cana-2736	308	2	so	so	ADV
cana-2736	308	3	1	1	NUM
cana-2736	308	4	ker	ker	NOUN
cana-2736	308	5	(	(	PUNCT
cana-2736	308	6	)	)	PUNCT
cana-2736	308	7	d	d	NOUN
cana-2736	308	8	a	a	PROPN
cana-2736	308	9			VERB
cana-2736	308	10			ADJ
cana-2736	308	11	.	.	PUNCT
cana-2736	309	1	let	let	VERB
cana-2736	309	2	x	x	PRON
cana-2736	309	3	a	a	VERB
cana-2736	309	4	and	and	CCONJ
cana-2736	309	5	ker	ker	PROPN
cana-2736	309	6	(	(	PUNCT
cana-2736	309	7	)	)	PUNCT
cana-2736	309	8	dy	dy	NOUN
cana-2736	309	9	a	a	PROPN
cana-2736	309	10	.	.	PUNCT
cana-2736	310	1	then	then	ADV
cana-2736	310	2	(	(	PUNCT
cana-2736	310	3	)	)	PUNCT
cana-2736	310	4	1d	1d	NUM
cana-2736	310	5	y	y	NOUN
cana-2736	310	6	=	=	PROPN
cana-2736	310	7	.	.	PUNCT
cana-2736	311	1	thus	thus	ADV
cana-2736	311	2	,	,	PUNCT
cana-2736	311	3	(	(	PUNCT
cana-2736	311	4	)	)	PUNCT
cana-2736	311	5	(	(	PUNCT
cana-2736	311	6	(	(	PUNCT
cana-2736	311	7	)	)	PUNCT
cana-2736	311	8	(	(	PUNCT
cana-2736	311	9	)	)	PUNCT
cana-2736	311	10	)	)	PUNCT
cana-2736	311	11	(	(	PUNCT
cana-2736	311	12	)	)	PUNCT
cana-2736	311	13	d	d	X
cana-2736	311	14	x	x	PUNCT
cana-2736	311	15	y	y	NOUN
cana-2736	311	16	f	f	NOUN
cana-2736	311	17	x	x	PROPN
cana-2736	311	18	d	d	X
cana-2736	311	19	y	y	PROPN
cana-2736	311	20	x	x	SYM
cana-2736	311	21	y	y	NOUN
cana-2736	311	22	=	=	SYM
cana-2736	311	23			ADJ
cana-2736	311	24			NOUN
cana-2736	311	25			NUM
cana-2736	311	26	(	(	PUNCT
cana-2736	311	27	(	(	PUNCT
cana-2736	311	28	)	)	PUNCT
cana-2736	311	29	1	1	NUM
cana-2736	311	30	)	)	PUNCT
cana-2736	311	31	(	(	PUNCT
cana-2736	311	32	)	)	PUNCT
cana-2736	311	33	f	f	X
cana-2736	312	1	x	x	SYM
cana-2736	312	2	x	x	X
cana-2736	312	3	y=	y=	PRON
cana-2736	312	4			ADJ
cana-2736	312	5			NOUN
cana-2736	312	6			NUM
cana-2736	312	7	1	1	NUM
cana-2736	312	8	(	(	PUNCT
cana-2736	312	9	)	)	PUNCT
cana-2736	312	10	x	x	X
cana-2736	312	11	y=	y=	PRON
cana-2736	312	12			NOUN
cana-2736	312	13			PROPN
cana-2736	312	14	[	[	X
cana-2736	312	15	lemma	lemma	PROPN
cana-2736	312	16	2.2	2.2	NUM
cana-2736	312	17	(	(	PUNCT
cana-2736	312	18	3	3	NUM
cana-2736	312	19	)	)	PUNCT
cana-2736	312	20	]	]	PUNCT
cana-2736	312	21	1=	1=	X
cana-2736	312	22	.	.	PUNCT
cana-2736	313	1	[	[	X
cana-2736	313	2	(	(	PUNCT
cana-2736	313	3	2.7	2.7	NUM
cana-2736	313	4	)	)	PUNCT
cana-2736	313	5	]	]	PUNCT
cana-2736	314	1	hence	hence	ADV
cana-2736	314	2	,	,	PUNCT
cana-2736	314	3	ker	ker	X
cana-2736	314	4	(	(	PUNCT
cana-2736	314	5	)	)	PUNCT
cana-2736	314	6	dx	dx	PROPN
cana-2736	314	7	y	y	PROPN
cana-2736	314	8	a	a	VERB
cana-2736	314	9			NOUN
cana-2736	314	10	,	,	PUNCT
cana-2736	314	11	so	so	ADV
cana-2736	314	12	ker	ker	X
cana-2736	314	13	(	(	PUNCT
cana-2736	314	14	)	)	PUNCT
cana-2736	314	15	d	d	NOUN
cana-2736	314	16	a	a	PRON
cana-2736	314	17	is	be	AUX
cana-2736	314	18	a	a	DET
cana-2736	314	19	near	near	ADJ
cana-2736	314	20	filter	filter	NOUN
cana-2736	314	21	of	of	ADP
cana-2736	314	22	a	a	PRON
cana-2736	314	23	.	.	NOUN
cana-2736	315	1	4	4	X
cana-2736	315	2	.	.	X
cana-2736	315	3	left	leave	VERB
cana-2736	315	4	and	and	CCONJ
cana-2736	315	5	rightf	rightf	ADJ
cana-2736	315	6	-derivations	-derivation	NOUN
cana-2736	315	7	of	of	ADP
cana-2736	315	8	type	type	NOUN
cana-2736	315	9	ii	ii	PROPN
cana-2736	315	10	building	building	NOUN
cana-2736	315	11	on	on	ADP
cana-2736	315	12	the	the	DET
cana-2736	315	13	concepts	concept	NOUN
cana-2736	315	14	discussed	discuss	VERB
cana-2736	315	15	earlier	early	ADV
cana-2736	315	16	,	,	PUNCT
cana-2736	315	17	in	in	ADP
cana-2736	315	18	this	this	DET
cana-2736	315	19	section	section	NOUN
cana-2736	315	20	,	,	PUNCT
cana-2736	315	21	we	we	PRON
cana-2736	315	22	redefine	redefine	VERB
cana-2736	315	23	leftf	leftf	ADJ
cana-2736	315	24	-derivations	-derivation	NOUN
cana-2736	315	25	,	,	PUNCT
cana-2736	315	26	rightf	rightf	ADJ
cana-2736	315	27	derivations	derivation	NOUN
cana-2736	315	28	,	,	PUNCT
cana-2736	315	29	and	and	CCONJ
cana-2736	315	30	f	f	PROPN
cana-2736	315	31	-derivations	-derivation	NOUN
cana-2736	315	32	of	of	ADP
cana-2736	315	33	type	type	NOUN
cana-2736	315	34	ii	ii	PROPN
cana-2736	315	35	in	in	ADP
cana-2736	315	36	hilbert	hilbert	PROPN
cana-2736	315	37	algebras	algebras	PROPN
cana-2736	315	38	,	,	PUNCT
cana-2736	315	39	examining	examine	VERB
cana-2736	315	40	their	their	PRON
cana-2736	315	41	fundamental	fundamental	ADJ
cana-2736	315	42	properties	property	NOUN
cana-2736	315	43	.	.	PUNCT
cana-2736	316	1	we	we	PRON
cana-2736	316	2	then	then	ADV
cana-2736	316	3	analyze	analyze	VERB
cana-2736	316	4	the	the	DET
cana-2736	316	5	subset	subset	NOUN
cana-2736	316	6	ker	ker	NOUN
cana-2736	317	1	(	(	PUNCT
cana-2736	317	2	)	)	PUNCT
cana-2736	317	3	d	d	ADP
cana-2736	317	4	a	a	PRON
cana-2736	317	5	associated	associate	VERB
cana-2736	317	6	with	with	ADP
cana-2736	317	7	these	these	DET
cana-2736	317	8	derivations	derivation	NOUN
cana-2736	317	9	,	,	PUNCT
cana-2736	317	10	emphasizing	emphasize	VERB
cana-2736	317	11	its	its	PRON
cana-2736	317	12	structural	structural	ADJ
cana-2736	317	13	importance	importance	NOUN
cana-2736	317	14	within	within	ADP
cana-2736	317	15	the	the	DET
cana-2736	317	16	algebra	algebra	NOUN
cana-2736	317	17	.	.	PUNCT
cana-2736	318	1	definition	definition	NOUN
cana-2736	318	2	4.1	4.1	NUM
cana-2736	318	3	.	.	PUNCT
cana-2736	319	1	let	let	VERB
cana-2736	319	2	(	(	PUNCT
cana-2736	319	3	,	,	PUNCT
cana-2736	319	4	,	,	PUNCT
cana-2736	319	5	1)a	1)a	PRON
cana-2736	319	6	a=	a=	ADJ
cana-2736	319	7			VERB
cana-2736	319	8	be	be	AUX
cana-2736	319	9	a	a	DET
cana-2736	319	10	hilbert	hilbert	NOUN
cana-2736	319	11	algebra	algebra	NOUN
cana-2736	319	12	and	and	CCONJ
cana-2736	319	13	f	f	PROPN
cana-2736	319	14	be	be	AUX
cana-2736	319	15	an	an	DET
cana-2736	319	16	endomorphism	endomorphism	NOUN
cana-2736	319	17	of	of	ADP
cana-2736	319	18	a	a	PRON
cana-2736	319	19	.	.	PUNCT
cana-2736	320	1	a	a	DET
cana-2736	320	2	self	self	NOUN
cana-2736	320	3	-	-	PUNCT
cana-2736	320	4	map	map	NOUN
cana-2736	320	5	:	:	PUNCT
cana-2736	320	6	d	d	ADP
cana-2736	320	7	a	a	DET
cana-2736	320	8	a→	a→	PUNCT
cana-2736	320	9	is	be	AUX
cana-2736	320	10	called	call	VERB
cana-2736	320	11	a	a	DET
cana-2736	320	12	leftf	leftf	ADJ
cana-2736	320	13	-derivation	-derivation	NOUN
cana-2736	320	14	of	of	ADP
cana-2736	320	15	type	type	NOUN
cana-2736	320	16	ii	ii	PROPN
cana-2736	320	17	of	of	ADP
cana-2736	320	18	a	a	PRON
cana-2736	320	19	if	if	SCONJ
cana-2736	320	20	it	it	PRON
cana-2736	320	21	satisfies	satisfy	VERB
cana-2736	320	22	the	the	DET
cana-2736	320	23	identity	identity	NOUN
cana-2736	320	24	(	(	PUNCT
cana-2736	320	25	)	)	PUNCT
cana-2736	320	26	(	(	PUNCT
cana-2736	320	27	)	)	PUNCT
cana-2736	320	28	(	(	PUNCT
cana-2736	320	29	(	(	PUNCT
cana-2736	320	30	)	)	PUNCT
cana-2736	320	31	(	(	PUNCT
cana-2736	320	32	)	)	PUNCT
cana-2736	320	33	)	)	PUNCT
cana-2736	321	1	d	d	X
cana-2736	321	2	x	x	PUNCT
cana-2736	321	3	y	y	NOUN
cana-2736	321	4	x	x	PUNCT
cana-2736	321	5	y	y	PROPN
cana-2736	321	6	d	d	NOUN
cana-2736	321	7	x	x	X
cana-2736	321	8	f	f	X
cana-2736	321	9	y	y	NOUN
cana-2736	321	10	=	=	PUNCT
cana-2736	321	11			ADJ
cana-2736	321	12			NOUN
cana-2736	321	13			PROPN
cana-2736	321	14	for	for	ADP
cana-2736	321	15	all	all	PRON
cana-2736	321	16	,	,	PUNCT
cana-2736	321	17	x	x	PRON
cana-2736	321	18	y	y	NOUN
cana-2736	321	19	a	a	PROPN
cana-2736	321	20	.	.	PUNCT
cana-2736	322	1	communications	communication	NOUN
cana-2736	322	2	on	on	ADP
cana-2736	322	3	applied	apply	VERB
cana-2736	322	4	nonlinear	nonlinear	ADJ
cana-2736	322	5	analysis	analysis	NOUN
cana-2736	322	6	issn	issn	NOUN
cana-2736	322	7	:	:	PUNCT
cana-2736	322	8	1074	1074	NUM
cana-2736	322	9	-	-	PUNCT
cana-2736	322	10	133x	133x	NUM
cana-2736	322	11	vol	vol	NOUN
cana-2736	322	12	32	32	NUM
cana-2736	322	13	no	no	NOUN
cana-2736	322	14	.	.	PUNCT
cana-2736	323	1	4s	4s	NUM
cana-2736	323	2	(	(	PUNCT
cana-2736	323	3	2025	2025	NUM
cana-2736	323	4	)	)	PUNCT
cana-2736	323	5	21	21	NUM
cana-2736	323	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	323	7	similarly	similarly	ADV
cana-2736	323	8	,	,	PUNCT
cana-2736	323	9	a	a	DET
cana-2736	323	10	self	self	NOUN
cana-2736	323	11	-	-	PUNCT
cana-2736	323	12	map	map	NOUN
cana-2736	323	13	:	:	PUNCT
cana-2736	323	14	d	d	ADP
cana-2736	323	15	a	a	DET
cana-2736	323	16	a→	a→	PUNCT
cana-2736	323	17	is	be	AUX
cana-2736	323	18	called	call	VERB
cana-2736	323	19	a	a	DET
cana-2736	323	20	rightf	rightf	ADJ
cana-2736	323	21	-derivation	-derivation	NOUN
cana-2736	323	22	of	of	ADP
cana-2736	323	23	type	type	NOUN
cana-2736	323	24	ii	ii	PROPN
cana-2736	323	25	of	of	ADP
cana-2736	323	26	a	a	PRON
cana-2736	323	27	if	if	SCONJ
cana-2736	323	28	it	it	PRON
cana-2736	323	29	satisfies	satisfy	VERB
cana-2736	323	30	the	the	DET
cana-2736	323	31	identity	identity	NOUN
cana-2736	323	32	(	(	PUNCT
cana-2736	323	33	)	)	PUNCT
cana-2736	323	34	(	(	PUNCT
cana-2736	323	35	)	)	PUNCT
cana-2736	323	36	(	(	PUNCT
cana-2736	323	37	(	(	PUNCT
cana-2736	323	38	)	)	PUNCT
cana-2736	323	39	(	(	PUNCT
cana-2736	323	40	)	)	PUNCT
cana-2736	323	41	)	)	PUNCT
cana-2736	324	1	d	d	X
cana-2736	324	2	x	x	PUNCT
cana-2736	324	3	y	y	NOUN
cana-2736	324	4	x	x	X
cana-2736	324	5	y	y	NOUN
cana-2736	324	6	f	f	NOUN
cana-2736	324	7	x	x	PROPN
cana-2736	325	1	d	d	X
cana-2736	325	2	y	y	NOUN
cana-2736	325	3	=	=	PUNCT
cana-2736	325	4			ADJ
cana-2736	325	5			NOUN
cana-2736	325	6			PROPN
cana-2736	325	7	for	for	ADP
cana-2736	325	8	all	all	PRON
cana-2736	325	9	,	,	PUNCT
cana-2736	325	10	x	x	PRON
cana-2736	325	11	y	y	NOUN
cana-2736	325	12	a	a	PROPN
cana-2736	325	13	.	.	PUNCT
cana-2736	326	1	moreover	moreover	ADV
cana-2736	326	2	,	,	PUNCT
cana-2736	326	3	if	if	SCONJ
cana-2736	326	4	d	d	NOUN
cana-2736	326	5	is	be	AUX
cana-2736	326	6	a	a	DET
cana-2736	326	7	leftf	leftf	ADJ
cana-2736	326	8	-derivation	-derivation	NOUN
cana-2736	326	9	of	of	ADP
cana-2736	326	10	type	type	NOUN
cana-2736	326	11	ii	ii	PROPN
cana-2736	326	12	and	and	CCONJ
cana-2736	326	13	a	a	DET
cana-2736	326	14	rightf	rightf	ADJ
cana-2736	326	15	-derivation	-derivation	NOUN
cana-2736	326	16	of	of	ADP
cana-2736	326	17	type	type	NOUN
cana-2736	326	18	ii	ii	PROPN
cana-2736	326	19	of	of	ADP
cana-2736	326	20	a	a	PRON
cana-2736	326	21	,	,	PUNCT
cana-2736	326	22	it	it	PRON
cana-2736	326	23	is	be	AUX
cana-2736	326	24	called	call	VERB
cana-2736	326	25	an	an	DET
cana-2736	326	26	f	f	PROPN
cana-2736	326	27	-derivation	-derivation	NOUN
cana-2736	326	28	of	of	ADP
cana-2736	326	29	type	type	NOUN
cana-2736	326	30	ii	ii	PROPN
cana-2736	326	31	of	of	ADP
cana-2736	326	32	a	a	DET
cana-2736	326	33	.	.	PUNCT
cana-2736	326	34	example	example	NOUN
cana-2736	326	35	4.2	4.2	NUM
cana-2736	326	36	.	.	PUNCT
cana-2736	327	1	let	let	VERB
cana-2736	327	2	{	{	PUNCT
cana-2736	327	3	1	1	NUM
cana-2736	327	4	,	,	PUNCT
cana-2736	327	5	2,3	2,3	NUM
cana-2736	327	6	,	,	PUNCT
cana-2736	327	7	4}a	4}a	PRON
cana-2736	327	8	=	=	PUNCT
cana-2736	327	9	be	be	AUX
cana-2736	327	10	a	a	DET
cana-2736	327	11	hilbert	hilbert	NOUN
cana-2736	327	12	algebra	algebra	NOUN
cana-2736	327	13	with	with	ADP
cana-2736	327	14	a	a	DET
cana-2736	327	15	fixed	fix	VERB
cana-2736	327	16	element	element	NOUN
cana-2736	327	17	1	1	NUM
cana-2736	327	18	and	and	CCONJ
cana-2736	327	19	a	a	DET
cana-2736	327	20	binary	binary	ADJ
cana-2736	327	21	operation	operation	NOUN
cana-2736	327	22			PROPN
cana-2736	327	23	defined	define	VERB
cana-2736	327	24	by	by	ADP
cana-2736	327	25	the	the	DET
cana-2736	327	26	following	following	ADJ
cana-2736	327	27	cayley	cayley	ADJ
cana-2736	327	28	table	table	NOUN
cana-2736	327	29	:	:	PUNCT
cana-2736	327	30	1	1	NUM
cana-2736	327	31	2	2	NUM
cana-2736	327	32	3	3	NUM
cana-2736	327	33	4	4	NUM
cana-2736	327	34	1	1	NUM
cana-2736	327	35	1	1	NUM
cana-2736	327	36	2	2	NUM
cana-2736	327	37	3	3	NUM
cana-2736	327	38	4	4	NUM
cana-2736	327	39	2	2	NUM
cana-2736	327	40	1	1	NUM
cana-2736	327	41	1	1	NUM
cana-2736	327	42	3	3	NUM
cana-2736	327	43	4	4	NUM
cana-2736	327	44	3	3	NUM
cana-2736	327	45	1	1	NUM
cana-2736	327	46	2	2	NUM
cana-2736	327	47	1	1	NUM
cana-2736	327	48	4	4	NUM
cana-2736	327	49	4	4	NUM
cana-2736	327	50	1	1	NUM
cana-2736	327	51	1	1	NUM
cana-2736	327	52	1	1	NUM
cana-2736	327	53	1	1	NUM
cana-2736	327	54			NUM
cana-2736	327	55	then	then	ADV
cana-2736	327	56	(	(	PUNCT
cana-2736	327	57	,	,	PUNCT
cana-2736	327	58	,	,	PUNCT
cana-2736	327	59	1)a	1)a	PROPN
cana-2736	327	60			PROPN
cana-2736	327	61	is	be	AUX
cana-2736	327	62	a	a	DET
cana-2736	327	63	hilbert	hilbert	NOUN
cana-2736	327	64	algebra	algebra	NOUN
cana-2736	327	65	.	.	PUNCT
cana-2736	328	1	we	we	PRON
cana-2736	328	2	define	define	VERB
cana-2736	328	3	an	an	DET
cana-2736	328	4	endomorphism	endomorphism	PROPN
cana-2736	328	5	f	f	PROPN
cana-2736	328	6	on	on	ADP
cana-2736	328	7	a	a	PRON
cana-2736	328	8	as	as	SCONJ
cana-2736	328	9	follows	follow	VERB
cana-2736	328	10	:	:	PUNCT
cana-2736	328	11	1	1	NUM
cana-2736	328	12	2	2	NUM
cana-2736	328	13	3	3	NUM
cana-2736	328	14	4	4	NUM
cana-2736	328	15	1	1	NUM
cana-2736	328	16	3	3	NUM
cana-2736	328	17	2	2	NUM
cana-2736	328	18	4	4	NUM
cana-2736	328	19	f	f	NOUN
cana-2736	328	20			NOUN
cana-2736	328	21			PROPN
cana-2736	328	22	=	=	SYM
cana-2736	328	23			PROPN
cana-2736	329	1			PROPN
cana-2736	329	2			ADJ
cana-2736	329	3			NOUN
cana-2736	329	4	define	define	VERB
cana-2736	329	5	a	a	DET
cana-2736	329	6	self	self	NOUN
cana-2736	329	7	-	-	PUNCT
cana-2736	329	8	map	map	NOUN
cana-2736	329	9	3	3	NUM
cana-2736	329	10	:	:	PUNCT
cana-2736	329	11	d	d	ADP
cana-2736	329	12	a	a	DET
cana-2736	329	13	a→	a→	PUNCT
cana-2736	329	14	as	as	SCONJ
cana-2736	329	15	follows	follow	VERB
cana-2736	329	16	:	:	PUNCT
cana-2736	329	17	3	3	NUM
cana-2736	329	18	1	1	NUM
cana-2736	329	19	2	2	NUM
cana-2736	329	20	3	3	NUM
cana-2736	329	21	4	4	NUM
cana-2736	329	22	1	1	NUM
cana-2736	329	23	1	1	NUM
cana-2736	329	24	1	1	NUM
cana-2736	329	25	4	4	NUM
cana-2736	329	26	d	d	NOUN
cana-2736	329	27			NOUN
cana-2736	329	28			NOUN
cana-2736	329	29	=	=	SYM
cana-2736	329	30			PROPN
cana-2736	330	1			PROPN
cana-2736	330	2			ADJ
cana-2736	330	3			NOUN
cana-2736	330	4	hence	hence	ADV
cana-2736	330	5	,	,	PUNCT
cana-2736	330	6	3d	3d	PROPN
cana-2736	330	7	is	be	AUX
cana-2736	330	8	a	a	DET
cana-2736	330	9	leftf	leftf	ADJ
cana-2736	330	10	-derivation	-derivation	NOUN
cana-2736	330	11	of	of	ADP
cana-2736	330	12	type	type	NOUN
cana-2736	330	13	ii	ii	PROPN
cana-2736	330	14	and	and	CCONJ
cana-2736	330	15	a	a	DET
cana-2736	330	16	rightf	rightf	ADJ
cana-2736	330	17	-derivation	-derivation	NOUN
cana-2736	330	18	of	of	ADP
cana-2736	330	19	type	type	NOUN
cana-2736	330	20	ii	ii	PROPN
cana-2736	330	21	of	of	ADP
cana-2736	330	22	a	a	PRON
cana-2736	330	23	,	,	PUNCT
cana-2736	330	24	so	so	CCONJ
cana-2736	330	25	it	it	PRON
cana-2736	330	26	is	be	AUX
cana-2736	330	27	an	an	DET
cana-2736	330	28	f	f	PROPN
cana-2736	330	29	derivation	derivation	NOUN
cana-2736	330	30	of	of	ADP
cana-2736	330	31	type	type	NOUN
cana-2736	330	32	ii	ii	PROPN
cana-2736	330	33	of	of	ADP
cana-2736	330	34	a	a	PRON
cana-2736	330	35	.	.	PUNCT
cana-2736	331	1	theorem	theorem	VERB
cana-2736	331	2	4.3	4.3	NUM
cana-2736	331	3	.	.	PUNCT
cana-2736	332	1	in	in	ADP
cana-2736	332	2	a	a	DET
cana-2736	332	3	hilbert	hilbert	NOUN
cana-2736	332	4	algebra	algebra	NOUN
cana-2736	332	5	(	(	PUNCT
cana-2736	332	6	,	,	PUNCT
cana-2736	332	7	,	,	PUNCT
cana-2736	332	8	1)a	1)a	PRON
cana-2736	332	9	a=	a=	PROPN
cana-2736	332	10			PROPN
cana-2736	332	11	,	,	PUNCT
cana-2736	332	12	the	the	DET
cana-2736	332	13	following	follow	VERB
cana-2736	332	14	statements	statement	NOUN
cana-2736	332	15	hold	hold	VERB
cana-2736	332	16	:	:	PUNCT
cana-2736	332	17	(	(	PUNCT
cana-2736	332	18	1	1	X
cana-2736	332	19	)	)	PUNCT
cana-2736	332	20	every	every	DET
cana-2736	332	21	leftf	leftf	ADJ
cana-2736	332	22	-derivation	-derivation	NOUN
cana-2736	332	23	of	of	ADP
cana-2736	332	24	type	type	NOUN
cana-2736	332	25	ii	ii	PROPN
cana-2736	332	26	of	of	ADP
cana-2736	332	27	a	a	PRON
cana-2736	332	28	is	be	AUX
cana-2736	332	29	regular	regular	ADJ
cana-2736	332	30	,	,	PUNCT
cana-2736	332	31	(	(	PUNCT
cana-2736	332	32	2	2	X
cana-2736	332	33	)	)	PUNCT
cana-2736	332	34	every	every	DET
cana-2736	332	35	rightf	rightf	ADJ
cana-2736	332	36	-derivation	-derivation	NOUN
cana-2736	332	37	of	of	ADP
cana-2736	332	38	type	type	NOUN
cana-2736	332	39	ii	ii	PROPN
cana-2736	332	40	of	of	ADP
cana-2736	332	41	a	a	PRON
cana-2736	332	42	is	be	AUX
cana-2736	332	43	regular	regular	ADJ
cana-2736	332	44	.	.	PUNCT
cana-2736	333	1	proof	proof	NOUN
cana-2736	333	2	.	.	PUNCT
cana-2736	334	1	(	(	PUNCT
cana-2736	334	2	1	1	X
cana-2736	334	3	)	)	PUNCT
cana-2736	334	4	assume	assume	VERB
cana-2736	334	5	that	that	SCONJ
cana-2736	334	6	d	d	NOUN
cana-2736	334	7	is	be	AUX
cana-2736	334	8	a	a	DET
cana-2736	334	9	leftf	leftf	ADJ
cana-2736	334	10	-derivation	-derivation	NOUN
cana-2736	334	11	of	of	ADP
cana-2736	334	12	type	type	NOUN
cana-2736	334	13	ii	ii	PROPN
cana-2736	334	14	of	of	ADP
cana-2736	334	15	a	a	PRON
cana-2736	334	16	.	.	PUNCT
cana-2736	335	1	then	then	ADV
cana-2736	335	2	(	(	PUNCT
cana-2736	335	3	1	1	X
cana-2736	335	4	)	)	PUNCT
cana-2736	335	5	(	(	PUNCT
cana-2736	335	6	1	1	NUM
cana-2736	335	7	1)d	1)d	NUM
cana-2736	335	8	d=	d=	NOUN
cana-2736	336	1			PROPN
cana-2736	336	2	[	[	X
cana-2736	336	3	lemma	lemma	PROPN
cana-2736	336	4	2.2	2.2	NUM
cana-2736	336	5	(	(	PUNCT
cana-2736	336	6	1	1	NUM
cana-2736	336	7	)	)	PUNCT
cana-2736	336	8	]	]	PUNCT
cana-2736	337	1	(	(	PUNCT
cana-2736	337	2	1	1	NUM
cana-2736	337	3	1	1	NUM
cana-2736	337	4	)	)	PUNCT
cana-2736	337	5	(	(	PUNCT
cana-2736	337	6	(	(	PUNCT
cana-2736	337	7	1	1	X
cana-2736	337	8	)	)	PUNCT
cana-2736	337	9	(	(	PUNCT
cana-2736	337	10	1))d	1))d	NUM
cana-2736	337	11	f=	f=	ADJ
cana-2736	337	12			ADJ
cana-2736	337	13			NOUN
cana-2736	337	14			NUM
cana-2736	337	15	1	1	NUM
cana-2736	337	16	(	(	PUNCT
cana-2736	337	17	(	(	PUNCT
cana-2736	337	18	1	1	X
cana-2736	337	19	)	)	PUNCT
cana-2736	337	20	1)d=	1)d=	NUM
cana-2736	337	21			NOUN
cana-2736	337	22			PROPN
cana-2736	338	1	[	[	X
cana-2736	338	2	lemma	lemma	PROPN
cana-2736	338	3	2.2	2.2	NUM
cana-2736	338	4	(	(	PUNCT
cana-2736	338	5	1	1	NUM
cana-2736	338	6	)	)	PUNCT
cana-2736	338	7	]	]	PUNCT
cana-2736	338	8	1=	1=	X
cana-2736	338	9	.	.	PUNCT
cana-2736	339	1	[	[	X
cana-2736	339	2	(	(	PUNCT
cana-2736	339	3	2.7	2.7	NUM
cana-2736	339	4	)	)	PUNCT
cana-2736	339	5	]	]	PUNCT
cana-2736	340	1	hence	hence	ADV
cana-2736	340	2	,	,	PUNCT
cana-2736	340	3	d	d	PROPN
cana-2736	340	4	is	be	AUX
cana-2736	340	5	regular	regular	ADJ
cana-2736	340	6	.	.	PUNCT
cana-2736	341	1	(	(	PUNCT
cana-2736	341	2	2	2	X
cana-2736	341	3	)	)	PUNCT
cana-2736	341	4	assume	assume	VERB
cana-2736	341	5	that	that	SCONJ
cana-2736	341	6	d	d	NOUN
cana-2736	341	7	is	be	AUX
cana-2736	341	8	a	a	DET
cana-2736	341	9	rightf	rightf	ADJ
cana-2736	341	10	-derivation	-derivation	NOUN
cana-2736	341	11	of	of	ADP
cana-2736	341	12	type	type	NOUN
cana-2736	341	13	ii	ii	PROPN
cana-2736	341	14	of	of	ADP
cana-2736	341	15	a	a	PRON
cana-2736	341	16	.	.	PUNCT
cana-2736	342	1	then	then	ADV
cana-2736	342	2	(	(	PUNCT
cana-2736	342	3	1	1	X
cana-2736	342	4	)	)	PUNCT
cana-2736	342	5	(	(	PUNCT
cana-2736	342	6	1	1	NUM
cana-2736	342	7	1)d	1)d	NUM
cana-2736	342	8	d=	d=	NOUN
cana-2736	343	1			PROPN
cana-2736	343	2	[	[	X
cana-2736	343	3	lemma	lemma	PROPN
cana-2736	343	4	2.2	2.2	NUM
cana-2736	343	5	(	(	PUNCT
cana-2736	343	6	1	1	NUM
cana-2736	343	7	)	)	PUNCT
cana-2736	343	8	]	]	PUNCT
cana-2736	343	9	communications	communication	NOUN
cana-2736	343	10	on	on	ADP
cana-2736	343	11	applied	apply	VERB
cana-2736	343	12	nonlinear	nonlinear	ADJ
cana-2736	343	13	analysis	analysis	NOUN
cana-2736	343	14	issn	issn	NOUN
cana-2736	343	15	:	:	PUNCT
cana-2736	343	16	1074	1074	NUM
cana-2736	343	17	-	-	PUNCT
cana-2736	343	18	133x	133x	NUM
cana-2736	343	19	vol	vol	NOUN
cana-2736	343	20	32	32	NUM
cana-2736	343	21	no	no	NOUN
cana-2736	343	22	.	.	PUNCT
cana-2736	344	1	4s	4s	NUM
cana-2736	344	2	(	(	PUNCT
cana-2736	344	3	2025	2025	NUM
cana-2736	344	4	)	)	PUNCT
cana-2736	344	5	22	22	NUM
cana-2736	344	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	344	7	(	(	PUNCT
cana-2736	344	8	1	1	NUM
cana-2736	344	9	1	1	NUM
cana-2736	344	10	)	)	PUNCT
cana-2736	344	11	(	(	PUNCT
cana-2736	344	12	(	(	PUNCT
cana-2736	344	13	1	1	X
cana-2736	344	14	)	)	PUNCT
cana-2736	344	15	(	(	PUNCT
cana-2736	344	16	1))f	1))f	NUM
cana-2736	345	1	d=	d=	NOUN
cana-2736	345	2			ADJ
cana-2736	345	3			NOUN
cana-2736	345	4			NUM
cana-2736	345	5	1	1	NUM
cana-2736	345	6	(	(	PUNCT
cana-2736	345	7	1	1	NUM
cana-2736	345	8	(	(	PUNCT
cana-2736	345	9	1))d=	1))d=	NUM
cana-2736	345	10			NOUN
cana-2736	345	11			PROPN
cana-2736	345	12	[	[	X
cana-2736	345	13	lemma	lemma	PROPN
cana-2736	345	14	2.2	2.2	NUM
cana-2736	345	15	(	(	PUNCT
cana-2736	345	16	1	1	NUM
cana-2736	345	17	)	)	PUNCT
cana-2736	345	18	]	]	PUNCT
cana-2736	345	19	1=	1=	X
cana-2736	345	20	.	.	PUNCT
cana-2736	346	1	[	[	X
cana-2736	346	2	(	(	PUNCT
cana-2736	346	3	2.7	2.7	NUM
cana-2736	346	4	)	)	PUNCT
cana-2736	346	5	]	]	PUNCT
cana-2736	347	1	hence	hence	ADV
cana-2736	347	2	,	,	PUNCT
cana-2736	347	3	d	d	PROPN
cana-2736	347	4	is	be	AUX
cana-2736	347	5	regular	regular	ADJ
cana-2736	347	6	.	.	PUNCT
cana-2736	348	1	corollary	corollary	ADJ
cana-2736	348	2	4.4	4.4	NUM
cana-2736	348	3	.	.	PUNCT
cana-2736	349	1	every	every	DET
cana-2736	349	2	f	f	PROPN
cana-2736	349	3	-derivation	-derivation	NOUN
cana-2736	349	4	of	of	ADP
cana-2736	349	5	type	type	NOUN
cana-2736	349	6	ii	ii	PROPN
cana-2736	349	7	of	of	ADP
cana-2736	349	8	a	a	DET
cana-2736	349	9	hilbert	hilbert	NOUN
cana-2736	349	10	algebra	algebra	NOUN
cana-2736	349	11	a	a	PRON
cana-2736	349	12	is	be	AUX
cana-2736	349	13	regular	regular	ADJ
cana-2736	349	14	.	.	PUNCT
cana-2736	350	1	theorem	theorem	VERB
cana-2736	350	2	4.5	4.5	NUM
cana-2736	350	3	.	.	PUNCT
cana-2736	351	1	in	in	ADP
cana-2736	351	2	a	a	DET
cana-2736	351	3	hilbert	hilbert	NOUN
cana-2736	351	4	algebra	algebra	NOUN
cana-2736	351	5	(	(	PUNCT
cana-2736	351	6	,	,	PUNCT
cana-2736	351	7	,	,	PUNCT
cana-2736	351	8	1)a	1)a	PRON
cana-2736	351	9	a=	a=	PROPN
cana-2736	351	10			PROPN
cana-2736	351	11	,	,	PUNCT
cana-2736	351	12	the	the	DET
cana-2736	351	13	following	follow	VERB
cana-2736	351	14	statements	statement	NOUN
cana-2736	351	15	hold	hold	VERB
cana-2736	351	16	:	:	PUNCT
cana-2736	351	17	(	(	PUNCT
cana-2736	351	18	1	1	X
cana-2736	351	19	)	)	PUNCT
cana-2736	351	20	if	if	SCONJ
cana-2736	351	21	d	d	NOUN
cana-2736	351	22	is	be	AUX
cana-2736	351	23	a	a	DET
cana-2736	351	24	leftf	leftf	ADJ
cana-2736	351	25	-derivation	-derivation	NOUN
cana-2736	351	26	of	of	ADP
cana-2736	351	27	type	type	NOUN
cana-2736	351	28	ii	ii	PROPN
cana-2736	351	29	of	of	ADP
cana-2736	351	30	a	a	PRON
cana-2736	351	31	,	,	PUNCT
cana-2736	351	32	then	then	ADV
cana-2736	351	33	(	(	PUNCT
cana-2736	351	34	)	)	PUNCT
cana-2736	351	35	(	(	PUNCT
cana-2736	351	36	)	)	PUNCT
cana-2736	351	37	d	d	X
cana-2736	351	38	x	x	X
cana-2736	351	39	x	x	SYM
cana-2736	351	40	f	f	X
cana-2736	351	41	x=	x=	X
cana-2736	351	42			NOUN
cana-2736	351	43	for	for	ADP
cana-2736	351	44	all	all	PRON
cana-2736	351	45	x	x	SYM
cana-2736	351	46	a	a	PROPN
cana-2736	351	47	,	,	PUNCT
cana-2736	351	48	(	(	PUNCT
cana-2736	351	49	2	2	X
cana-2736	351	50	)	)	PUNCT
cana-2736	351	51	if	if	SCONJ
cana-2736	351	52	d	d	NOUN
cana-2736	351	53	is	be	AUX
cana-2736	351	54	a	a	DET
cana-2736	351	55	rightf	rightf	ADJ
cana-2736	351	56	-derivation	-derivation	NOUN
cana-2736	351	57	of	of	ADP
cana-2736	351	58	type	type	NOUN
cana-2736	351	59	ii	ii	PROPN
cana-2736	351	60	of	of	ADP
cana-2736	351	61	a	a	PRON
cana-2736	351	62	,	,	PUNCT
cana-2736	351	63	then	then	ADV
cana-2736	351	64	(	(	PUNCT
cana-2736	351	65	)	)	PUNCT
cana-2736	351	66	(	(	PUNCT
cana-2736	351	67	)	)	PUNCT
cana-2736	352	1	d	d	X
cana-2736	352	2	x	x	PUNCT
cana-2736	352	3	x	x	SYM
cana-2736	352	4	d	d	NOUN
cana-2736	352	5	x=	x=	X
cana-2736	352	6			NOUN
cana-2736	352	7	for	for	ADP
cana-2736	352	8	all	all	PRON
cana-2736	352	9	x	x	SYM
cana-2736	352	10	a	a	PROPN
cana-2736	352	11	.	.	PUNCT
cana-2736	353	1	proof	proof	NOUN
cana-2736	353	2	.	.	PUNCT
cana-2736	354	1	(	(	PUNCT
cana-2736	354	2	1	1	X
cana-2736	354	3	)	)	PUNCT
cana-2736	354	4	assume	assume	VERB
cana-2736	354	5	that	that	SCONJ
cana-2736	354	6	d	d	NOUN
cana-2736	354	7	is	be	AUX
cana-2736	354	8	a	a	DET
cana-2736	354	9	leftf	leftf	ADJ
cana-2736	354	10	-derivation	-derivation	NOUN
cana-2736	354	11	of	of	ADP
cana-2736	354	12	type	type	NOUN
cana-2736	354	13	ii	ii	PROPN
cana-2736	354	14	of	of	ADP
cana-2736	354	15	a	a	PRON
cana-2736	354	16	.	.	PUNCT
cana-2736	355	1	then	then	ADV
cana-2736	355	2	,	,	PUNCT
cana-2736	355	3	for	for	ADP
cana-2736	355	4	all	all	PRON
cana-2736	355	5	x	x	SYM
cana-2736	355	6	a	a	PROPN
cana-2736	355	7	,	,	PUNCT
cana-2736	355	8	(	(	PUNCT
cana-2736	355	9	)	)	PUNCT
cana-2736	355	10	(	(	PUNCT
cana-2736	355	11	1	1	X
cana-2736	355	12	)	)	PUNCT
cana-2736	355	13	d	d	NOUN
cana-2736	355	14	x	x	SYM
cana-2736	355	15	d	d	NOUN
cana-2736	355	16	x=	x=	PUNCT
cana-2736	356	1			PROPN
cana-2736	356	2	[	[	X
cana-2736	356	3	lemma	lemma	PROPN
cana-2736	356	4	2.2	2.2	NUM
cana-2736	356	5	(	(	PUNCT
cana-2736	356	6	2	2	NUM
cana-2736	356	7	)	)	PUNCT
cana-2736	356	8	]	]	PUNCT
cana-2736	356	9	(	(	PUNCT
cana-2736	356	10	1	1	X
cana-2736	356	11	)	)	PUNCT
cana-2736	356	12	(	(	PUNCT
cana-2736	356	13	(	(	PUNCT
cana-2736	356	14	1	1	X
cana-2736	356	15	)	)	PUNCT
cana-2736	356	16	(	(	PUNCT
cana-2736	356	17	)	)	PUNCT
cana-2736	356	18	)	)	PUNCT
cana-2736	356	19	x	x	PUNCT
cana-2736	357	1	d	d	X
cana-2736	357	2	f	f	PROPN
cana-2736	357	3	x=	x=	PUNCT
cana-2736	358	1			ADJ
cana-2736	358	2			NOUN
cana-2736	358	3			NUM
cana-2736	358	4	(	(	PUNCT
cana-2736	358	5	1	1	NUM
cana-2736	358	6	)	)	PUNCT
cana-2736	358	7	(	(	PUNCT
cana-2736	358	8	1	1	NUM
cana-2736	358	9	(	(	PUNCT
cana-2736	358	10	)	)	PUNCT
cana-2736	358	11	)	)	PUNCT
cana-2736	358	12	x	x	SYM
cana-2736	358	13	f	f	NOUN
cana-2736	358	14	x=	x=	PUNCT
cana-2736	358	15			ADJ
cana-2736	358	16			NOUN
cana-2736	358	17			PROPN
cana-2736	358	18	[	[	X
cana-2736	358	19	regular	regular	X
cana-2736	358	20	]	]	PUNCT
cana-2736	358	21	(	(	PUNCT
cana-2736	358	22	)	)	PUNCT
cana-2736	358	23	x	x	SYM
cana-2736	358	24	f	f	PROPN
cana-2736	358	25	x=	x=	X
cana-2736	358	26			NOUN
cana-2736	358	27	.	.	PUNCT
cana-2736	359	1	[	[	X
cana-2736	359	2	lemma	lemma	X
cana-2736	359	3	2.2	2.2	NUM
cana-2736	359	4	(	(	PUNCT
cana-2736	359	5	2	2	NUM
cana-2736	359	6	)	)	PUNCT
cana-2736	359	7	]	]	PUNCT
cana-2736	359	8	(	(	PUNCT
cana-2736	359	9	2	2	X
cana-2736	359	10	)	)	PUNCT
cana-2736	359	11	assume	assume	VERB
cana-2736	359	12	that	that	SCONJ
cana-2736	359	13	d	d	NOUN
cana-2736	359	14	is	be	AUX
cana-2736	359	15	a	a	DET
cana-2736	359	16	rightf	rightf	ADJ
cana-2736	359	17	-derivation	-derivation	NOUN
cana-2736	359	18	of	of	ADP
cana-2736	359	19	type	type	NOUN
cana-2736	359	20	ii	ii	PROPN
cana-2736	359	21	of	of	ADP
cana-2736	359	22	a	a	PRON
cana-2736	359	23	.	.	PUNCT
cana-2736	360	1	then	then	ADV
cana-2736	360	2	,	,	PUNCT
cana-2736	360	3	for	for	ADP
cana-2736	360	4	all	all	PRON
cana-2736	360	5	x	x	SYM
cana-2736	360	6	a	a	PROPN
cana-2736	360	7	,	,	PUNCT
cana-2736	360	8	(	(	PUNCT
cana-2736	360	9	)	)	PUNCT
cana-2736	360	10	(	(	PUNCT
cana-2736	360	11	1	1	X
cana-2736	360	12	)	)	PUNCT
cana-2736	360	13	d	d	NOUN
cana-2736	360	14	x	x	SYM
cana-2736	360	15	d	d	NOUN
cana-2736	360	16	x=	x=	PUNCT
cana-2736	361	1			PROPN
cana-2736	361	2	[	[	X
cana-2736	361	3	lemma	lemma	PROPN
cana-2736	361	4	2.2	2.2	NUM
cana-2736	361	5	(	(	PUNCT
cana-2736	361	6	2	2	NUM
cana-2736	361	7	)	)	PUNCT
cana-2736	361	8	]	]	PUNCT
cana-2736	361	9	(	(	PUNCT
cana-2736	361	10	1	1	X
cana-2736	361	11	)	)	PUNCT
cana-2736	361	12	(	(	PUNCT
cana-2736	361	13	(	(	PUNCT
cana-2736	361	14	1	1	X
cana-2736	361	15	)	)	PUNCT
cana-2736	361	16	(	(	PUNCT
cana-2736	361	17	)	)	PUNCT
cana-2736	361	18	)	)	PUNCT
cana-2736	361	19	x	x	X
cana-2736	361	20	f	f	PROPN
cana-2736	361	21	d	d	X
cana-2736	361	22	x=	x=	PUNCT
cana-2736	362	1			ADJ
cana-2736	362	2			NOUN
cana-2736	362	3			NUM
cana-2736	362	4	(	(	PUNCT
cana-2736	362	5	1	1	NUM
cana-2736	362	6	)	)	PUNCT
cana-2736	362	7	(	(	PUNCT
cana-2736	362	8	1	1	NUM
cana-2736	362	9	(	(	PUNCT
cana-2736	362	10	)	)	PUNCT
cana-2736	362	11	)	)	PUNCT
cana-2736	362	12	x	x	X
cana-2736	363	1	d	d	NOUN
cana-2736	363	2	x=	x=	PUNCT
cana-2736	363	3			ADJ
cana-2736	363	4			NOUN
cana-2736	363	5			NUM
cana-2736	363	6	(	(	PUNCT
cana-2736	363	7	)	)	PUNCT
cana-2736	363	8	x	x	SYM
cana-2736	363	9	d	d	NOUN
cana-2736	363	10	x=	x=	X
cana-2736	363	11			NOUN
cana-2736	363	12	.	.	PUNCT
cana-2736	364	1	[	[	X
cana-2736	364	2	lemma	lemma	X
cana-2736	364	3	2.2	2.2	NUM
cana-2736	364	4	(	(	PUNCT
cana-2736	364	5	2	2	NUM
cana-2736	364	6	)	)	PUNCT
cana-2736	364	7	]	]	PUNCT
cana-2736	364	8	corollary	corollary	ADJ
cana-2736	364	9	4.6	4.6	NUM
cana-2736	364	10	.	.	PUNCT
cana-2736	365	1	if	if	SCONJ
cana-2736	365	2	d	d	PROPN
cana-2736	365	3	is	be	AUX
cana-2736	365	4	an	an	DET
cana-2736	365	5	f	f	PROPN
cana-2736	365	6	-derivation	-derivation	NOUN
cana-2736	365	7	of	of	ADP
cana-2736	365	8	type	type	NOUN
cana-2736	365	9	ii	ii	PROPN
cana-2736	365	10	of	of	ADP
cana-2736	365	11	a	a	PRON
cana-2736	365	12	,	,	PUNCT
cana-2736	365	13	then	then	ADV
cana-2736	365	14	(	(	PUNCT
cana-2736	365	15	)	)	PUNCT
cana-2736	365	16	(	(	PUNCT
cana-2736	365	17	)	)	PUNCT
cana-2736	365	18	(	(	PUNCT
cana-2736	365	19	)	)	PUNCT
cana-2736	365	20	d	d	X
cana-2736	365	21	x	x	PUNCT
cana-2736	366	1	x	x	X
cana-2736	366	2	f	f	NOUN
cana-2736	366	3	x	x	PUNCT
cana-2736	366	4	x	x	SYM
cana-2736	366	5	d	d	NOUN
cana-2736	366	6	x=	x=	X
cana-2736	366	7			NOUN
cana-2736	366	8	=	=	NOUN
cana-2736	366	9			NOUN
cana-2736	366	10	for	for	ADP
cana-2736	366	11	all	all	PRON
cana-2736	366	12	x	x	PUNCT
cana-2736	366	13	a	a	PROPN
cana-2736	366	14	.	.	PUNCT
cana-2736	367	1	proposition	proposition	NOUN
cana-2736	367	2	4.7	4.7	NUM
cana-2736	367	3	.	.	PUNCT
cana-2736	368	1	let	let	VERB
cana-2736	368	2	d	d	PRON
cana-2736	368	3	be	be	AUX
cana-2736	368	4	a	a	DET
cana-2736	368	5	leftf	leftf	ADJ
cana-2736	368	6	-derivation	-derivation	NOUN
cana-2736	368	7	of	of	ADP
cana-2736	368	8	type	type	NOUN
cana-2736	368	9	ii	ii	PROPN
cana-2736	368	10	of	of	ADP
cana-2736	368	11	a	a	DET
cana-2736	368	12	hilbert	hilbert	NOUN
cana-2736	368	13	algebra	algebra	NOUN
cana-2736	368	14	(	(	PUNCT
cana-2736	368	15	,	,	PUNCT
cana-2736	368	16	,	,	PUNCT
cana-2736	368	17	1)a	1)a	PRON
cana-2736	368	18	a=	a=	PROPN
cana-2736	368	19			PROPN
cana-2736	368	20	.	.	PUNCT
cana-2736	369	1	then	then	ADV
cana-2736	369	2	the	the	DET
cana-2736	369	3	following	follow	VERB
cana-2736	369	4	properties	property	NOUN
cana-2736	369	5	hold	hold	VERB
cana-2736	369	6	:	:	PUNCT
cana-2736	369	7	for	for	ADP
cana-2736	369	8	any	any	DET
cana-2736	369	9	x	x	SYM
cana-2736	369	10	a	a	PROPN
cana-2736	369	11	,	,	PUNCT
cana-2736	369	12	(	(	PUNCT
cana-2736	369	13	1	1	X
cana-2736	369	14	)	)	PUNCT
cana-2736	369	15	(	(	PUNCT
cana-2736	369	16	)	)	PUNCT
cana-2736	369	17	,	,	PUNCT
cana-2736	369	18	x	x	PUNCT
cana-2736	370	1	d	d	X
cana-2736	370	2	x	x	PROPN
cana-2736	370	3	(	(	PUNCT
cana-2736	370	4	2	2	NUM
cana-2736	370	5	)	)	PUNCT
cana-2736	370	6	(	(	PUNCT
cana-2736	370	7	)	)	PUNCT
cana-2736	370	8	(	(	PUNCT
cana-2736	370	9	)	)	PUNCT
cana-2736	370	10	d	d	X
cana-2736	370	11	x	x	PUNCT
cana-2736	370	12	d	d	NOUN
cana-2736	370	13	x	x	X
cana-2736	370	14	x=	x=	NOUN
cana-2736	370	15			NOUN
cana-2736	370	16	.	.	PUNCT
cana-2736	371	1	proof	proof	NOUN
cana-2736	371	2	.	.	PUNCT
cana-2736	372	1	(	(	PUNCT
cana-2736	372	2	1	1	X
cana-2736	372	3	)	)	PUNCT
cana-2736	372	4	for	for	ADP
cana-2736	372	5	all	all	PRON
cana-2736	372	6	x	x	SYM
cana-2736	372	7	a	a	PROPN
cana-2736	372	8	,	,	PUNCT
cana-2736	372	9	(	(	PUNCT
cana-2736	372	10	)	)	PUNCT
cana-2736	372	11	(	(	PUNCT
cana-2736	372	12	(	(	PUNCT
cana-2736	372	13	)	)	PUNCT
cana-2736	372	14	)	)	PUNCT
cana-2736	372	15	x	x	PUNCT
cana-2736	373	1	d	d	NOUN
cana-2736	373	2	x	x	PUNCT
cana-2736	373	3	x	x	PUNCT
cana-2736	373	4	x	x	X
cana-2736	373	5	f	f	PROPN
cana-2736	373	6	x	x	PUNCT
cana-2736	373	7	=	=	SYM
cana-2736	373	8			ADJ
cana-2736	373	9			NOUN
cana-2736	373	10	[	[	PUNCT
cana-2736	373	11	theorem	theorem	VERB
cana-2736	373	12	4.5	4.5	NUM
cana-2736	373	13	(	(	PUNCT
cana-2736	373	14	1	1	NUM
cana-2736	373	15	)	)	PUNCT
cana-2736	373	16	]	]	PUNCT
cana-2736	373	17	1=	1=	X
cana-2736	373	18	.	.	PUNCT
cana-2736	374	1	[	[	X
cana-2736	374	2	(	(	PUNCT
cana-2736	374	3	2.4	2.4	NUM
cana-2736	374	4	)	)	PUNCT
cana-2736	374	5	]	]	PUNCT
cana-2736	375	1	hence	hence	ADV
cana-2736	375	2	,	,	PUNCT
cana-2736	375	3	(	(	PUNCT
cana-2736	375	4	)	)	PUNCT
cana-2736	375	5	x	x	SYM
cana-2736	375	6	d	d	X
cana-2736	375	7	x	x	PROPN
cana-2736	375	8	for	for	ADP
cana-2736	375	9	all	all	PRON
cana-2736	375	10	x	x	PUNCT
cana-2736	375	11	a	a	PROPN
cana-2736	375	12	.	.	PUNCT
cana-2736	376	1	communications	communication	NOUN
cana-2736	376	2	on	on	ADP
cana-2736	376	3	applied	apply	VERB
cana-2736	376	4	nonlinear	nonlinear	ADJ
cana-2736	376	5	analysis	analysis	NOUN
cana-2736	376	6	issn	issn	NOUN
cana-2736	376	7	:	:	PUNCT
cana-2736	376	8	1074	1074	NUM
cana-2736	376	9	-	-	PUNCT
cana-2736	376	10	133x	133x	NUM
cana-2736	376	11	vol	vol	NOUN
cana-2736	376	12	32	32	NUM
cana-2736	376	13	no	no	NOUN
cana-2736	376	14	.	.	PUNCT
cana-2736	377	1	4s	4s	NUM
cana-2736	377	2	(	(	PUNCT
cana-2736	377	3	2025	2025	NUM
cana-2736	377	4	)	)	PUNCT
cana-2736	377	5	23	23	NUM
cana-2736	377	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	377	7	(	(	PUNCT
cana-2736	377	8	2	2	NUM
cana-2736	377	9	)	)	PUNCT
cana-2736	377	10	for	for	ADP
cana-2736	377	11	all	all	PRON
cana-2736	377	12	x	x	SYM
cana-2736	377	13	a	a	PROPN
cana-2736	377	14	,	,	PUNCT
cana-2736	377	15	(	(	PUNCT
cana-2736	377	16	)	)	PUNCT
cana-2736	377	17	1	1	NUM
cana-2736	377	18	(	(	PUNCT
cana-2736	377	19	)	)	PUNCT
cana-2736	377	20	d	d	NOUN
cana-2736	378	1	x	x	SYM
cana-2736	378	2	d	d	NOUN
cana-2736	378	3	x=	x=	PUNCT
cana-2736	379	1			PROPN
cana-2736	379	2	[	[	X
cana-2736	379	3	lemma	lemma	PROPN
cana-2736	379	4	2.2	2.2	NUM
cana-2736	379	5	(	(	PUNCT
cana-2736	379	6	2	2	NUM
cana-2736	379	7	)	)	PUNCT
cana-2736	379	8	]	]	PUNCT
cana-2736	379	9	(	(	PUNCT
cana-2736	379	10	(	(	PUNCT
cana-2736	379	11	)	)	PUNCT
cana-2736	379	12	)	)	PUNCT
cana-2736	379	13	(	(	PUNCT
cana-2736	379	14	)	)	PUNCT
cana-2736	379	15	x	x	X
cana-2736	380	1	d	d	NOUN
cana-2736	380	2	x	x	SYM
cana-2736	380	3	d	d	NOUN
cana-2736	380	4	x=	x=	PUNCT
cana-2736	381	1			PROPN
cana-2736	381	2			PROPN
cana-2736	381	3	[	[	X
cana-2736	381	4	(	(	PUNCT
cana-2736	381	5	1	1	NUM
cana-2736	381	6	)	)	PUNCT
cana-2736	381	7	]	]	PUNCT
cana-2736	381	8	(	(	PUNCT
cana-2736	381	9	)	)	PUNCT
cana-2736	381	10	d	d	NOUN
cana-2736	381	11	x	x	SYM
cana-2736	381	12	x=	x=	NOUN
cana-2736	381	13			NOUN
cana-2736	381	14	.	.	PUNCT
cana-2736	382	1	proposition	proposition	NOUN
cana-2736	382	2	4.8	4.8	NUM
cana-2736	382	3	.	.	PUNCT
cana-2736	383	1	let	let	VERB
cana-2736	383	2	d	d	PRON
cana-2736	383	3	be	be	AUX
cana-2736	383	4	a	a	DET
cana-2736	383	5	rightf	rightf	ADJ
cana-2736	383	6	-derivation	-derivation	NOUN
cana-2736	383	7	of	of	ADP
cana-2736	383	8	type	type	NOUN
cana-2736	383	9	ii	ii	PROPN
cana-2736	383	10	of	of	ADP
cana-2736	383	11	a	a	DET
cana-2736	383	12	hilbert	hilbert	NOUN
cana-2736	383	13	algebra	algebra	NOUN
cana-2736	383	14	(	(	PUNCT
cana-2736	383	15	,	,	PUNCT
cana-2736	383	16	,	,	PUNCT
cana-2736	383	17	1)a	1)a	PRON
cana-2736	383	18	a=	a=	PROPN
cana-2736	383	19			PROPN
cana-2736	383	20	.	.	PUNCT
cana-2736	384	1	then	then	ADV
cana-2736	384	2	the	the	DET
cana-2736	384	3	following	follow	VERB
cana-2736	384	4	properties	property	NOUN
cana-2736	384	5	hold	hold	VERB
cana-2736	384	6	:	:	PUNCT
cana-2736	384	7	for	for	ADP
cana-2736	384	8	any	any	DET
cana-2736	384	9	x	x	SYM
cana-2736	384	10	a	a	PROPN
cana-2736	384	11	,	,	PUNCT
cana-2736	384	12	(	(	PUNCT
cana-2736	384	13	1	1	X
cana-2736	384	14	)	)	PUNCT
cana-2736	384	15	(	(	PUNCT
cana-2736	384	16	)	)	PUNCT
cana-2736	384	17	x	x	SYM
cana-2736	385	1	d	d	NOUN
cana-2736	385	2	x	x	PROPN
cana-2736	385	3	,	,	PUNCT
cana-2736	385	4	(	(	PUNCT
cana-2736	385	5	2	2	X
cana-2736	385	6	)	)	PUNCT
cana-2736	385	7	(	(	PUNCT
cana-2736	385	8	)	)	PUNCT
cana-2736	385	9	(	(	PUNCT
cana-2736	385	10	)	)	PUNCT
cana-2736	386	1	d	d	X
cana-2736	386	2	x	x	PUNCT
cana-2736	386	3	d	d	NOUN
cana-2736	386	4	x	x	X
cana-2736	386	5	x=	x=	NOUN
cana-2736	386	6			NOUN
cana-2736	386	7	.	.	PUNCT
cana-2736	387	1	proof	proof	NOUN
cana-2736	387	2	.	.	PUNCT
cana-2736	388	1	(	(	PUNCT
cana-2736	388	2	1	1	X
cana-2736	388	3	)	)	PUNCT
cana-2736	388	4	for	for	ADP
cana-2736	388	5	all	all	PRON
cana-2736	388	6	x	x	SYM
cana-2736	388	7	a	a	PROPN
cana-2736	388	8	,	,	PUNCT
cana-2736	388	9	(	(	PUNCT
cana-2736	388	10	)	)	PUNCT
cana-2736	388	11	(	(	PUNCT
cana-2736	388	12	(	(	PUNCT
cana-2736	388	13	)	)	PUNCT
cana-2736	388	14	)	)	PUNCT
cana-2736	388	15	x	x	PUNCT
cana-2736	389	1	d	d	NOUN
cana-2736	389	2	x	x	PUNCT
cana-2736	389	3	x	x	PUNCT
cana-2736	389	4	x	x	PUNCT
cana-2736	389	5	d	d	X
cana-2736	389	6	x	x	PUNCT
cana-2736	389	7	=	=	SYM
cana-2736	389	8			ADJ
cana-2736	389	9			NOUN
cana-2736	389	10	[	[	PUNCT
cana-2736	389	11	theorem	theorem	VERB
cana-2736	389	12	4.5	4.5	NUM
cana-2736	389	13	(	(	PUNCT
cana-2736	389	14	2	2	NUM
cana-2736	389	15	)	)	PUNCT
cana-2736	389	16	]	]	PUNCT
cana-2736	389	17	1=	1=	X
cana-2736	389	18	.	.	PUNCT
cana-2736	390	1	[	[	X
cana-2736	390	2	(	(	PUNCT
cana-2736	390	3	2.4	2.4	NUM
cana-2736	390	4	)	)	PUNCT
cana-2736	390	5	]	]	PUNCT
cana-2736	391	1	hence	hence	ADV
cana-2736	391	2	,	,	PUNCT
cana-2736	391	3	(	(	PUNCT
cana-2736	391	4	)	)	PUNCT
cana-2736	391	5	x	x	SYM
cana-2736	391	6	d	d	X
cana-2736	391	7	x	x	PROPN
cana-2736	391	8	for	for	ADP
cana-2736	391	9	all	all	PRON
cana-2736	391	10	x	x	SYM
cana-2736	391	11	a	a	PROPN
cana-2736	391	12	.	.	PUNCT
cana-2736	392	1	(	(	PUNCT
cana-2736	392	2	2	2	X
cana-2736	392	3	)	)	PUNCT
cana-2736	392	4	for	for	ADP
cana-2736	392	5	all	all	PRON
cana-2736	392	6	x	x	SYM
cana-2736	392	7	a	a	PROPN
cana-2736	392	8	,	,	PUNCT
cana-2736	392	9	(	(	PUNCT
cana-2736	392	10	)	)	PUNCT
cana-2736	392	11	1	1	NUM
cana-2736	392	12	(	(	PUNCT
cana-2736	392	13	)	)	PUNCT
cana-2736	392	14	d	d	NOUN
cana-2736	392	15	x	x	SYM
cana-2736	392	16	d	d	NOUN
cana-2736	392	17	x=	x=	PUNCT
cana-2736	393	1			PROPN
cana-2736	393	2	[	[	X
cana-2736	393	3	lemma	lemma	PROPN
cana-2736	393	4	2.2	2.2	NUM
cana-2736	393	5	(	(	PUNCT
cana-2736	393	6	2	2	NUM
cana-2736	393	7	)	)	PUNCT
cana-2736	393	8	]	]	PUNCT
cana-2736	393	9	(	(	PUNCT
cana-2736	393	10	(	(	PUNCT
cana-2736	393	11	)	)	PUNCT
cana-2736	393	12	)	)	PUNCT
cana-2736	393	13	(	(	PUNCT
cana-2736	393	14	)	)	PUNCT
cana-2736	393	15	x	x	X
cana-2736	394	1	d	d	NOUN
cana-2736	394	2	x	x	SYM
cana-2736	394	3	d	d	NOUN
cana-2736	394	4	x=	x=	PUNCT
cana-2736	395	1			PROPN
cana-2736	395	2			PROPN
cana-2736	395	3	[	[	X
cana-2736	395	4	(	(	PUNCT
cana-2736	395	5	1	1	NUM
cana-2736	395	6	)	)	PUNCT
cana-2736	395	7	]	]	PUNCT
cana-2736	395	8	(	(	PUNCT
cana-2736	395	9	)	)	PUNCT
cana-2736	395	10	d	d	NOUN
cana-2736	395	11	x	x	SYM
cana-2736	395	12	x=	x=	X
cana-2736	395	13			NOUN
cana-2736	395	14	.	.	PUNCT
cana-2736	396	1	theorem	theorem	VERB
cana-2736	396	2	4.9	4.9	NUM
cana-2736	396	3	.	.	PUNCT
cana-2736	397	1	if	if	SCONJ
cana-2736	397	2	d	d	PROPN
cana-2736	397	3	is	be	AUX
cana-2736	397	4	a	a	DET
cana-2736	397	5	rightf	rightf	ADJ
cana-2736	397	6	-derivation	-derivation	NOUN
cana-2736	397	7	of	of	ADP
cana-2736	397	8	type	type	NOUN
cana-2736	397	9	ii	ii	PROPN
cana-2736	397	10	of	of	ADP
cana-2736	397	11	a	a	DET
cana-2736	397	12	hilbert	hilbert	NOUN
cana-2736	397	13	algebra	algebra	NOUN
cana-2736	397	14	(	(	PUNCT
cana-2736	397	15	,	,	PUNCT
cana-2736	397	16	,	,	PUNCT
cana-2736	397	17	1)a	1)a	PRON
cana-2736	397	18	a=	a=	PROPN
cana-2736	397	19			NUM
cana-2736	397	20	,	,	PUNCT
cana-2736	397	21	then	then	ADV
cana-2736	397	22	ker	ker	PROPN
cana-2736	397	23	(	(	PUNCT
cana-2736	397	24	)	)	PUNCT
cana-2736	397	25	dy	dy	NOUN
cana-2736	397	26	x	x	SYM
cana-2736	397	27	a	a	PROPN
cana-2736	397	28			NOUN
cana-2736	397	29	for	for	ADP
cana-2736	397	30	all	all	DET
cana-2736	397	31	ker	ker	NOUN
cana-2736	397	32	(	(	PUNCT
cana-2736	397	33	)	)	PUNCT
cana-2736	397	34	dy	dy	NOUN
cana-2736	397	35	a	a	PROPN
cana-2736	397	36	and	and	CCONJ
cana-2736	397	37	x	x	X
cana-2736	397	38	a	a	PROPN
cana-2736	397	39	.	.	PUNCT
cana-2736	398	1	proof	proof	NOUN
cana-2736	398	2	.	.	PUNCT
cana-2736	399	1	let	let	VERB
cana-2736	399	2	ker	ker	PROPN
cana-2736	399	3	(	(	PUNCT
cana-2736	399	4	)	)	PUNCT
cana-2736	399	5	dy	dy	NOUN
cana-2736	399	6	a	a	PROPN
cana-2736	399	7	and	and	CCONJ
cana-2736	399	8	x	x	PUNCT
cana-2736	399	9	a	a	PROPN
cana-2736	399	10	.	.	PUNCT
cana-2736	400	1	then	then	ADV
cana-2736	400	2	(	(	PUNCT
cana-2736	400	3	)	)	PUNCT
cana-2736	400	4	1d	1d	NUM
cana-2736	400	5	y	y	NOUN
cana-2736	400	6	=	=	PROPN
cana-2736	400	7	.	.	PUNCT
cana-2736	401	1	thus	thus	ADV
cana-2736	401	2	,	,	PUNCT
cana-2736	401	3	(	(	PUNCT
cana-2736	401	4	)	)	PUNCT
cana-2736	401	5	(	(	PUNCT
cana-2736	401	6	(	(	PUNCT
cana-2736	401	7	)	)	PUNCT
cana-2736	401	8	)	)	PUNCT
cana-2736	402	1	d	d	X
cana-2736	402	2	y	y	NOUN
cana-2736	403	1	x	x	PUNCT
cana-2736	403	2	d	d	NOUN
cana-2736	403	3	x	x	X
cana-2736	403	4	y	y	NOUN
cana-2736	403	5	y	y	NOUN
cana-2736	403	6	=	=	PUNCT
cana-2736	404	1			PROPN
cana-2736	404	2			PROPN
cana-2736	404	3	(	(	PUNCT
cana-2736	404	4	(	(	PUNCT
cana-2736	404	5	)	)	PUNCT
cana-2736	404	6	)	)	PUNCT
cana-2736	405	1	(	(	PUNCT
cana-2736	405	2	(	(	PUNCT
cana-2736	405	3	)	)	PUNCT
cana-2736	405	4	(	(	PUNCT
cana-2736	405	5	)	)	PUNCT
cana-2736	405	6	)	)	PUNCT
cana-2736	405	7	x	x	X
cana-2736	405	8	y	y	NOUN
cana-2736	405	9	y	y	NOUN
cana-2736	405	10	f	f	PROPN
cana-2736	406	1	x	x	X
cana-2736	406	2	y	y	PROPN
cana-2736	406	3	d	d	NOUN
cana-2736	406	4	y=	y=	PRON
cana-2736	407	1			ADJ
cana-2736	407	2			ADJ
cana-2736	407	3			NOUN
cana-2736	407	4			PROPN
cana-2736	407	5			PROPN
cana-2736	407	6	(	(	PUNCT
cana-2736	407	7	)	)	PUNCT
cana-2736	407	8	(	(	PUNCT
cana-2736	407	9	(	(	PUNCT
cana-2736	407	10	)	)	PUNCT
cana-2736	407	11	1)y	1)y	NUM
cana-2736	408	1	x	x	SYM
cana-2736	408	2	f	f	X
cana-2736	408	3	x	x	SYM
cana-2736	408	4	y=	y=	PRON
cana-2736	408	5			NOUN
cana-2736	408	6			NOUN
cana-2736	408	7			PROPN
cana-2736	408	8			PROPN
cana-2736	408	9	(	(	PUNCT
cana-2736	408	10	)	)	PUNCT
cana-2736	408	11	1y	1y	NUM
cana-2736	408	12	x=	x=	X
cana-2736	408	13			NOUN
cana-2736	408	14			NOUN
cana-2736	408	15	[	[	X
cana-2736	408	16	lemma	lemma	PROPN
cana-2736	408	17	2.2	2.2	NUM
cana-2736	408	18	(	(	PUNCT
cana-2736	408	19	3	3	NUM
cana-2736	408	20	)	)	PUNCT
cana-2736	408	21	]	]	PUNCT
cana-2736	408	22	1=	1=	X
cana-2736	408	23	.	.	PUNCT
cana-2736	409	1	[	[	X
cana-2736	409	2	(	(	PUNCT
cana-2736	409	3	2.7	2.7	NUM
cana-2736	409	4	)	)	PUNCT
cana-2736	409	5	]	]	PUNCT
cana-2736	410	1	hence	hence	ADV
cana-2736	410	2	,	,	PUNCT
cana-2736	410	3	ker	ker	X
cana-2736	410	4	(	(	PUNCT
cana-2736	410	5	)	)	PUNCT
cana-2736	410	6	dy	dy	NOUN
cana-2736	410	7	x	x	SYM
cana-2736	410	8	a	a	PROPN
cana-2736	410	9			PROPN
cana-2736	410	10	.	.	PUNCT
cana-2736	410	11	theorem	theorem	VERB
cana-2736	410	12	4.10	4.10	NUM
cana-2736	410	13	.	.	PUNCT
cana-2736	411	1	if	if	SCONJ
cana-2736	411	2	d	d	PROPN
cana-2736	411	3	is	be	AUX
cana-2736	411	4	a	a	DET
cana-2736	411	5	rightf	rightf	ADJ
cana-2736	411	6	-derivation	-derivation	NOUN
cana-2736	411	7	of	of	ADP
cana-2736	411	8	type	type	NOUN
cana-2736	411	9	ii	ii	PROPN
cana-2736	411	10	of	of	ADP
cana-2736	411	11	a	a	DET
cana-2736	411	12	commutative	commutative	ADJ
cana-2736	411	13	hilbert	hilbert	NOUN
cana-2736	411	14	algebra	algebra	PROPN
cana-2736	411	15	(	(	PUNCT
cana-2736	411	16	,	,	PUNCT
cana-2736	411	17	,	,	PUNCT
cana-2736	411	18	1)a	1)a	PRON
cana-2736	411	19	a=	a=	PROPN
cana-2736	411	20			PROPN
cana-2736	411	21	and	and	CCONJ
cana-2736	411	22	for	for	ADP
cana-2736	411	23	any	any	PRON
cana-2736	411	24	,	,	PUNCT
cana-2736	411	25	x	x	PRON
cana-2736	411	26	y	y	PROPN
cana-2736	411	27	a	a	PROPN
cana-2736	411	28	is	be	AUX
cana-2736	411	29	such	such	ADJ
cana-2736	411	30	that	that	SCONJ
cana-2736	411	31	y	y	PROPN
cana-2736	411	32	x	x	PROPN
cana-2736	411	33	and	and	CCONJ
cana-2736	411	34	ker	ker	PROPN
cana-2736	411	35	(	(	PUNCT
cana-2736	411	36	)	)	PUNCT
cana-2736	411	37	dy	dy	NOUN
cana-2736	411	38	a	a	PROPN
cana-2736	411	39	,	,	PUNCT
cana-2736	411	40	then	then	ADV
cana-2736	411	41	ker	ker	PROPN
cana-2736	411	42	(	(	PUNCT
cana-2736	411	43	)	)	PUNCT
cana-2736	411	44	dx	dx	PROPN
cana-2736	411	45	a	a	PROPN
cana-2736	411	46	.	.	PUNCT
cana-2736	412	1	proof	proof	NOUN
cana-2736	412	2	.	.	PUNCT
cana-2736	413	1	let	let	VERB
cana-2736	413	2	,	,	PUNCT
cana-2736	413	3	x	x	SYM
cana-2736	413	4	y	y	PROPN
cana-2736	413	5	a	a	PROPN
cana-2736	413	6	be	be	AUX
cana-2736	413	7	such	such	ADJ
cana-2736	413	8	that	that	SCONJ
cana-2736	413	9	y	y	PROPN
cana-2736	413	10	x	x	PROPN
cana-2736	413	11	and	and	CCONJ
cana-2736	413	12	ker	ker	PROPN
cana-2736	413	13	(	(	PUNCT
cana-2736	413	14	)	)	PUNCT
cana-2736	413	15	dy	dy	NOUN
cana-2736	413	16	a	a	PROPN
cana-2736	413	17	.	.	PUNCT
cana-2736	414	1	then	then	ADV
cana-2736	414	2	1y	1y	NUM
cana-2736	414	3	x	x	SYM
cana-2736	415	1	=	=	SYM
cana-2736	415	2	and	and	CCONJ
cana-2736	415	3	(	(	PUNCT
cana-2736	415	4	)	)	PUNCT
cana-2736	415	5	1d	1d	NUM
cana-2736	416	1	y	y	NOUN
cana-2736	416	2	=	=	PROPN
cana-2736	416	3	.	.	PUNCT
cana-2736	417	1	thus	thus	ADV
cana-2736	417	2	,	,	PUNCT
cana-2736	417	3	communications	communication	NOUN
cana-2736	417	4	on	on	ADP
cana-2736	417	5	applied	apply	VERB
cana-2736	417	6	nonlinear	nonlinear	ADJ
cana-2736	417	7	analysis	analysis	NOUN
cana-2736	417	8	issn	issn	NOUN
cana-2736	417	9	:	:	PUNCT
cana-2736	417	10	1074	1074	NUM
cana-2736	417	11	-	-	PUNCT
cana-2736	417	12	133x	133x	NUM
cana-2736	417	13	vol	vol	NOUN
cana-2736	417	14	32	32	NUM
cana-2736	417	15	no	no	NOUN
cana-2736	417	16	.	.	PUNCT
cana-2736	418	1	4s	4s	NUM
cana-2736	418	2	(	(	PUNCT
cana-2736	418	3	2025	2025	NUM
cana-2736	418	4	)	)	PUNCT
cana-2736	418	5	24	24	NUM
cana-2736	418	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	418	7	(	(	PUNCT
cana-2736	418	8	)	)	PUNCT
cana-2736	418	9	(	(	PUNCT
cana-2736	418	10	1	1	X
cana-2736	418	11	)	)	PUNCT
cana-2736	419	1	d	d	NOUN
cana-2736	419	2	x	x	SYM
cana-2736	419	3	d	d	NOUN
cana-2736	419	4	x=	x=	PUNCT
cana-2736	420	1			PROPN
cana-2736	420	2	[	[	X
cana-2736	420	3	lemma	lemma	PROPN
cana-2736	420	4	2.2	2.2	NUM
cana-2736	420	5	(	(	PUNCT
cana-2736	420	6	2	2	NUM
cana-2736	420	7	)	)	PUNCT
cana-2736	420	8	]	]	PUNCT
cana-2736	420	9	(	(	PUNCT
cana-2736	420	10	(	(	PUNCT
cana-2736	420	11	)	)	PUNCT
cana-2736	420	12	)	)	PUNCT
cana-2736	421	1	d	d	X
cana-2736	421	2	y	y	PROPN
cana-2736	421	3	x	x	SYM
cana-2736	421	4	x=	x=	PROPN
cana-2736	422	1			PROPN
cana-2736	422	2			PROPN
cana-2736	422	3	(	(	PUNCT
cana-2736	422	4	(	(	PUNCT
cana-2736	422	5	)	)	PUNCT
cana-2736	422	6	)	)	PUNCT
cana-2736	423	1	d	d	X
cana-2736	423	2	x	x	PUNCT
cana-2736	423	3	y	y	NOUN
cana-2736	423	4	y=	y=	NOUN
cana-2736	423	5			PROPN
cana-2736	423	6			PROPN
cana-2736	423	7	[	[	X
cana-2736	423	8	commutative	commutative	ADJ
cana-2736	423	9	]	]	X
cana-2736	423	10	(	(	PUNCT
cana-2736	423	11	(	(	PUNCT
cana-2736	423	12	)	)	PUNCT
cana-2736	423	13	)	)	PUNCT
cana-2736	423	14	(	(	PUNCT
cana-2736	423	15	(	(	PUNCT
cana-2736	423	16	)	)	PUNCT
cana-2736	423	17	(	(	PUNCT
cana-2736	423	18	)	)	PUNCT
cana-2736	423	19	)	)	PUNCT
cana-2736	423	20	x	x	X
cana-2736	424	1	y	y	NOUN
cana-2736	424	2	y	y	NOUN
cana-2736	424	3	f	f	PROPN
cana-2736	424	4	x	x	X
cana-2736	424	5	y	y	PROPN
cana-2736	424	6	d	d	NOUN
cana-2736	424	7	y=	y=	PRON
cana-2736	425	1			ADJ
cana-2736	425	2			ADJ
cana-2736	425	3			NOUN
cana-2736	425	4			PROPN
cana-2736	425	5			PROPN
cana-2736	425	6	(	(	PUNCT
cana-2736	425	7	)	)	PUNCT
cana-2736	425	8	(	(	PUNCT
cana-2736	425	9	(	(	PUNCT
cana-2736	425	10	)	)	PUNCT
cana-2736	425	11	1)y	1)y	NUM
cana-2736	426	1	x	x	SYM
cana-2736	426	2	f	f	X
cana-2736	426	3	x	x	SYM
cana-2736	426	4	y=	y=	PRON
cana-2736	426	5			NOUN
cana-2736	426	6			NOUN
cana-2736	426	7			PROPN
cana-2736	426	8			PROPN
cana-2736	426	9	(	(	PUNCT
cana-2736	426	10	)	)	PUNCT
cana-2736	426	11	1y	1y	NUM
cana-2736	426	12	x=	x=	X
cana-2736	426	13			NOUN
cana-2736	426	14			NOUN
cana-2736	426	15	[	[	X
cana-2736	426	16	lemma	lemma	PROPN
cana-2736	426	17	2.2	2.2	NUM
cana-2736	426	18	(	(	PUNCT
cana-2736	426	19	3	3	NUM
cana-2736	426	20	)	)	PUNCT
cana-2736	426	21	]	]	PUNCT
cana-2736	426	22	1=	1=	X
cana-2736	426	23	.	.	PUNCT
cana-2736	427	1	[	[	X
cana-2736	427	2	(	(	PUNCT
cana-2736	427	3	2.7	2.7	NUM
cana-2736	427	4	)	)	PUNCT
cana-2736	427	5	]	]	PUNCT
cana-2736	428	1	hence	hence	ADV
cana-2736	428	2	,	,	PUNCT
cana-2736	428	3	ker	ker	X
cana-2736	428	4	(	(	PUNCT
cana-2736	428	5	)	)	PUNCT
cana-2736	428	6	dx	dx	PROPN
cana-2736	428	7	a	a	PROPN
cana-2736	428	8	.	.	PUNCT
cana-2736	429	1	theorem	theorem	VERB
cana-2736	429	2	4.11	4.11	NUM
cana-2736	429	3	.	.	PUNCT
cana-2736	430	1	if	if	SCONJ
cana-2736	430	2	d	d	PROPN
cana-2736	430	3	is	be	AUX
cana-2736	430	4	a	a	DET
cana-2736	430	5	rightf	rightf	ADJ
cana-2736	430	6	-derivation	-derivation	NOUN
cana-2736	430	7	of	of	ADP
cana-2736	430	8	type	type	NOUN
cana-2736	430	9	ii	ii	PROPN
cana-2736	430	10	of	of	ADP
cana-2736	430	11	a	a	DET
cana-2736	430	12	hilbert	hilbert	NOUN
cana-2736	430	13	algebra	algebra	NOUN
cana-2736	430	14	(	(	PUNCT
cana-2736	430	15	,	,	PUNCT
cana-2736	430	16	,	,	PUNCT
cana-2736	430	17	1)a	1)a	PRON
cana-2736	430	18	a=	a=	PROPN
cana-2736	430	19			NUM
cana-2736	430	20	,	,	PUNCT
cana-2736	430	21	then	then	ADV
cana-2736	430	22	ker	ker	INTJ
cana-2736	430	23	(	(	PUNCT
cana-2736	430	24	)	)	PUNCT
cana-2736	430	25	d	d	NOUN
cana-2736	430	26	a	a	PRON
cana-2736	430	27	is	be	AUX
cana-2736	430	28	a	a	DET
cana-2736	430	29	near	near	ADJ
cana-2736	430	30	filter	filter	NOUN
cana-2736	430	31	(	(	PUNCT
cana-2736	430	32	subalgebra	subalgebra	PROPN
cana-2736	430	33	)	)	PUNCT
cana-2736	430	34	of	of	ADP
cana-2736	430	35	a	a	PRON
cana-2736	430	36	.	.	PUNCT
cana-2736	431	1	proof	proof	NOUN
cana-2736	431	2	.	.	PUNCT
cana-2736	432	1	assume	assume	VERB
cana-2736	432	2	that	that	SCONJ
cana-2736	432	3	d	d	NOUN
cana-2736	432	4	is	be	AUX
cana-2736	432	5	a	a	DET
cana-2736	432	6	rightf	rightf	ADJ
cana-2736	432	7	-derivation	-derivation	NOUN
cana-2736	432	8	of	of	ADP
cana-2736	432	9	type	type	NOUN
cana-2736	432	10	ii	ii	PROPN
cana-2736	432	11	of	of	ADP
cana-2736	432	12	a	a	PRON
cana-2736	432	13	.	.	PUNCT
cana-2736	433	1	by	by	ADP
cana-2736	433	2	theorem	theorem	ADJ
cana-2736	433	3	4.3	4.3	NUM
cana-2736	433	4	(	(	PUNCT
cana-2736	433	5	2	2	NUM
cana-2736	433	6	)	)	PUNCT
cana-2736	433	7	,	,	PUNCT
cana-2736	433	8	we	we	PRON
cana-2736	433	9	have	have	VERB
cana-2736	433	10	(	(	PUNCT
cana-2736	433	11	1	1	X
cana-2736	433	12	)	)	PUNCT
cana-2736	433	13	1d	1d	NUM
cana-2736	433	14	=	=	SYM
cana-2736	434	1	and	and	CCONJ
cana-2736	434	2	so	so	ADV
cana-2736	434	3	1	1	NUM
cana-2736	434	4	ker	ker	NOUN
cana-2736	434	5	(	(	PUNCT
cana-2736	434	6	)	)	PUNCT
cana-2736	434	7	d	d	NOUN
cana-2736	434	8	a	a	PROPN
cana-2736	434	9			VERB
cana-2736	434	10			ADJ
cana-2736	434	11	.	.	PUNCT
cana-2736	435	1	let	let	VERB
cana-2736	435	2	x	x	PRON
cana-2736	435	3	a	a	VERB
cana-2736	435	4	and	and	CCONJ
cana-2736	435	5	ker	ker	PROPN
cana-2736	435	6	(	(	PUNCT
cana-2736	435	7	)	)	PUNCT
cana-2736	435	8	dy	dy	NOUN
cana-2736	435	9	a	a	PROPN
cana-2736	435	10	.	.	PUNCT
cana-2736	436	1	then	then	ADV
cana-2736	436	2	(	(	PUNCT
cana-2736	436	3	)	)	PUNCT
cana-2736	436	4	1d	1d	NUM
cana-2736	436	5	y	y	NOUN
cana-2736	436	6	=	=	PROPN
cana-2736	436	7	.	.	PUNCT
cana-2736	437	1	thus	thus	ADV
cana-2736	437	2	,	,	PUNCT
cana-2736	437	3	(	(	PUNCT
cana-2736	437	4	)	)	PUNCT
cana-2736	437	5	(	(	PUNCT
cana-2736	437	6	)	)	PUNCT
cana-2736	437	7	(	(	PUNCT
cana-2736	437	8	(	(	PUNCT
cana-2736	437	9	)	)	PUNCT
cana-2736	437	10	(	(	PUNCT
cana-2736	437	11	)	)	PUNCT
cana-2736	437	12	)	)	PUNCT
cana-2736	438	1	d	d	X
cana-2736	438	2	x	x	PUNCT
cana-2736	438	3	y	y	NOUN
cana-2736	438	4	x	x	X
cana-2736	438	5	y	y	NOUN
cana-2736	438	6	f	f	NOUN
cana-2736	438	7	x	x	PROPN
cana-2736	439	1	d	d	X
cana-2736	439	2	y	y	NOUN
cana-2736	439	3	=	=	PUNCT
cana-2736	439	4			ADJ
cana-2736	439	5			NOUN
cana-2736	439	6			NUM
cana-2736	439	7	(	(	PUNCT
cana-2736	439	8	)	)	PUNCT
cana-2736	439	9	(	(	PUNCT
cana-2736	439	10	(	(	PUNCT
cana-2736	439	11	)	)	PUNCT
cana-2736	439	12	1)x	1)x	NUM
cana-2736	439	13	y	y	PROPN
cana-2736	439	14	f	f	PROPN
cana-2736	439	15	x=	x=	PUNCT
cana-2736	440	1			ADJ
cana-2736	440	2			NOUN
cana-2736	440	3			NUM
cana-2736	440	4	(	(	PUNCT
cana-2736	440	5	)	)	PUNCT
cana-2736	440	6	1x	1x	NOUN
cana-2736	440	7	y=	y=	NUM
cana-2736	440	8			ADJ
cana-2736	440	9			NOUN
cana-2736	440	10	[	[	X
cana-2736	440	11	lemma	lemma	PROPN
cana-2736	440	12	2.2	2.2	NUM
cana-2736	440	13	(	(	PUNCT
cana-2736	440	14	3	3	NUM
cana-2736	440	15	)	)	PUNCT
cana-2736	440	16	]	]	PUNCT
cana-2736	440	17	1=	1=	X
cana-2736	440	18	.	.	PUNCT
cana-2736	441	1	[	[	X
cana-2736	441	2	(	(	PUNCT
cana-2736	441	3	2.7	2.7	NUM
cana-2736	441	4	)	)	PUNCT
cana-2736	441	5	]	]	PUNCT
cana-2736	442	1	hence	hence	ADV
cana-2736	442	2	,	,	PUNCT
cana-2736	442	3	ker	ker	X
cana-2736	442	4	(	(	PUNCT
cana-2736	442	5	)	)	PUNCT
cana-2736	442	6	dx	dx	PROPN
cana-2736	442	7	y	y	PROPN
cana-2736	442	8	a	a	VERB
cana-2736	442	9			NOUN
cana-2736	442	10	,	,	PUNCT
cana-2736	442	11	so	so	ADV
cana-2736	442	12	ker	ker	X
cana-2736	442	13	(	(	PUNCT
cana-2736	442	14	)	)	PUNCT
cana-2736	442	15	d	d	NOUN
cana-2736	442	16	a	a	PRON
cana-2736	442	17	is	be	AUX
cana-2736	442	18	a	a	DET
cana-2736	442	19	near	near	ADJ
cana-2736	442	20	filter	filter	NOUN
cana-2736	442	21	of	of	ADP
cana-2736	442	22	a	a	PRON
cana-2736	442	23	.	.	NOUN
cana-2736	443	1	5	5	X
cana-2736	443	2	.	.	X
cana-2736	443	3	conclusion	conclusion	NOUN
cana-2736	443	4	this	this	DET
cana-2736	443	5	study	study	NOUN
cana-2736	443	6	introduced	introduce	VERB
cana-2736	443	7	and	and	CCONJ
cana-2736	443	8	investigated	investigate	VERB
cana-2736	443	9	leftf	leftf	ADJ
cana-2736	443	10	-derivations	-derivation	NOUN
cana-2736	443	11	,	,	PUNCT
cana-2736	443	12	rightf	rightf	ADJ
cana-2736	443	13	-derivations	-derivation	NOUN
cana-2736	443	14	,	,	PUNCT
cana-2736	443	15	and	and	CCONJ
cana-2736	443	16	f	f	PROPN
cana-2736	443	17	-derivations	-derivation	NOUN
cana-2736	443	18	of	of	ADP
cana-2736	443	19	type	type	NOUN
cana-2736	443	20	i	i	PRON
cana-2736	443	21	and	and	CCONJ
cana-2736	443	22	type	type	NOUN
cana-2736	443	23	ii	ii	PROPN
cana-2736	443	24	within	within	ADP
cana-2736	443	25	the	the	DET
cana-2736	443	26	framework	framework	NOUN
cana-2736	443	27	of	of	ADP
cana-2736	443	28	hilbert	hilbert	PROPN
cana-2736	443	29	algebras	algebras	PROPN
cana-2736	443	30	,	,	PUNCT
cana-2736	443	31	focusing	focus	VERB
cana-2736	443	32	on	on	ADP
cana-2736	443	33	their	their	PRON
cana-2736	443	34	fundamental	fundamental	ADJ
cana-2736	443	35	properties	property	NOUN
cana-2736	443	36	and	and	CCONJ
cana-2736	443	37	structural	structural	ADJ
cana-2736	443	38	roles	role	NOUN
cana-2736	443	39	.	.	PUNCT
cana-2736	444	1	we	we	PRON
cana-2736	444	2	demonstrated	demonstrate	VERB
cana-2736	444	3	that	that	SCONJ
cana-2736	444	4	the	the	DET
cana-2736	444	5	kernel	kernel	NOUN
cana-2736	444	6	of	of	ADP
cana-2736	444	7	an	an	DET
cana-2736	444	8	f	f	PROPN
cana-2736	444	9	-derivation	-derivation	PROPN
cana-2736	444	10	,	,	PUNCT
cana-2736	444	11	ker	ker	NOUN
cana-2736	444	12	(	(	PUNCT
cana-2736	444	13	)	)	PUNCT
cana-2736	444	14	d	d	X
cana-2736	444	15	a	a	PRON
cana-2736	444	16	,	,	PUNCT
cana-2736	444	17	forms	form	VERB
cana-2736	444	18	a	a	DET
cana-2736	444	19	near	near	ADJ
cana-2736	444	20	filter	filter	NOUN
cana-2736	444	21	and	and	CCONJ
cana-2736	444	22	functions	function	NOUN
cana-2736	444	23	as	as	ADP
cana-2736	444	24	a	a	DET
cana-2736	444	25	subalgebra	subalgebra	NOUN
cana-2736	444	26	of	of	ADP
cana-2736	444	27	the	the	DET
cana-2736	444	28	hilbert	hilbert	PROPN
cana-2736	444	29	algebra	algebra	PROPN
cana-2736	444	30	a	a	PRON
cana-2736	444	31	.	.	PUNCT
cana-2736	445	1	these	these	DET
cana-2736	445	2	results	result	NOUN
cana-2736	445	3	deepened	deepen	VERB
cana-2736	445	4	the	the	DET
cana-2736	445	5	understanding	understanding	NOUN
cana-2736	445	6	of	of	ADP
cana-2736	445	7	the	the	DET
cana-2736	445	8	algebraic	algebraic	ADJ
cana-2736	445	9	structure	structure	NOUN
cana-2736	445	10	of	of	ADP
cana-2736	445	11	hilbert	hilbert	PROPN
cana-2736	445	12	algebras	algebras	PROPN
cana-2736	445	13	and	and	CCONJ
cana-2736	445	14	provided	provide	VERB
cana-2736	445	15	new	new	ADJ
cana-2736	445	16	insights	insight	NOUN
cana-2736	445	17	into	into	ADP
cana-2736	445	18	the	the	DET
cana-2736	445	19	broader	broad	ADJ
cana-2736	445	20	implications	implication	NOUN
cana-2736	445	21	of	of	ADP
cana-2736	445	22	derivations	derivation	NOUN
cana-2736	445	23	in	in	ADP
cana-2736	445	24	algebraic	algebraic	ADJ
cana-2736	445	25	logic	logic	NOUN
cana-2736	445	26	.	.	PUNCT
cana-2736	446	1	future	future	ADJ
cana-2736	446	2	research	research	NOUN
cana-2736	446	3	could	could	AUX
cana-2736	446	4	extend	extend	VERB
cana-2736	446	5	these	these	DET
cana-2736	446	6	concepts	concept	NOUN
cana-2736	446	7	to	to	ADP
cana-2736	446	8	other	other	ADJ
cana-2736	446	9	non	non	ADJ
cana-2736	446	10	-	-	ADJ
cana-2736	446	11	classical	classical	ADJ
cana-2736	446	12	algebraic	algebraic	ADJ
cana-2736	446	13	systems	system	NOUN
cana-2736	446	14	and	and	CCONJ
cana-2736	446	15	explore	explore	VERB
cana-2736	446	16	their	their	PRON
cana-2736	446	17	applications	application	NOUN
cana-2736	446	18	in	in	ADP
cana-2736	446	19	logical	logical	ADJ
cana-2736	446	20	frameworks	framework	NOUN
cana-2736	446	21	and	and	CCONJ
cana-2736	446	22	computational	computational	ADJ
cana-2736	446	23	logic	logic	NOUN
cana-2736	446	24	models	model	NOUN
cana-2736	446	25	.	.	PUNCT
cana-2736	447	1	acknowledgement	acknowledgement	NOUN
cana-2736	447	2	this	this	DET
cana-2736	447	3	research	research	NOUN
cana-2736	447	4	was	be	AUX
cana-2736	447	5	supported	support	VERB
cana-2736	447	6	by	by	ADP
cana-2736	447	7	university	university	NOUN
cana-2736	447	8	of	of	ADP
cana-2736	447	9	phayao	phayao	NOUN
cana-2736	447	10	and	and	CCONJ
cana-2736	447	11	thailand	thailand	PROPN
cana-2736	447	12	science	science	PROPN
cana-2736	447	13	research	research	PROPN
cana-2736	447	14	and	and	CCONJ
cana-2736	447	15	innovation	innovation	NOUN
cana-2736	447	16	fund	fund	NOUN
cana-2736	447	17	(	(	PUNCT
cana-2736	447	18	fundamental	fundamental	ADJ
cana-2736	447	19	fund	fund	NOUN
cana-2736	447	20	2025	2025	NUM
cana-2736	447	21	,	,	PUNCT
cana-2736	447	22	grant	grant	VERB
cana-2736	447	23	no	no	NOUN
cana-2736	447	24	.	.	PROPN
cana-2736	448	1	5027/2567	5027/2567	NUM
cana-2736	448	2	)	)	PUNCT
cana-2736	448	3	.	.	PUNCT
cana-2736	449	1	communications	communication	NOUN
cana-2736	449	2	on	on	ADP
cana-2736	449	3	applied	apply	VERB
cana-2736	449	4	nonlinear	nonlinear	ADJ
cana-2736	449	5	analysis	analysis	NOUN
cana-2736	449	6	issn	issn	NOUN
cana-2736	449	7	:	:	PUNCT
cana-2736	449	8	1074	1074	NUM
cana-2736	449	9	-	-	PUNCT
cana-2736	449	10	133x	133x	NUM
cana-2736	449	11	vol	vol	NOUN
cana-2736	449	12	32	32	NUM
cana-2736	449	13	no	no	NOUN
cana-2736	449	14	.	.	PUNCT
cana-2736	450	1	4s	4s	NUM
cana-2736	450	2	(	(	PUNCT
cana-2736	450	3	2025	2025	NUM
cana-2736	450	4	)	)	PUNCT
cana-2736	450	5	25	25	NUM
cana-2736	450	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2736	450	7	refrences	refrence	VERB
cana-2736	451	1	[	[	X
cana-2736	451	2	1	1	X
cana-2736	451	3	]	]	PUNCT
cana-2736	451	4	t.	t.	NOUN
cana-2736	451	5	bantaojai	bantaojai	NOUN
cana-2736	451	6	,	,	PUNCT
cana-2736	451	7	c.	c.	PROPN
cana-2736	451	8	suanoom	suanoom	PROPN
cana-2736	451	9	,	,	PUNCT
cana-2736	451	10	j.	j.	PROPN
cana-2736	451	11	phuto	phuto	PROPN
cana-2736	451	12	and	and	CCONJ
cana-2736	451	13	a.	a.	NOUN
cana-2736	451	14	iampan	iampan	PROPN
cana-2736	451	15	,	,	PUNCT
cana-2736	451	16	a	a	DET
cana-2736	451	17	bi	bi	NOUN
cana-2736	451	18	-	-	ADJ
cana-2736	451	19	endomorphism	endomorphism	NOUN
cana-2736	451	20	induces	induce	VERB
cana-2736	451	21	a	a	DET
cana-2736	451	22	new	new	ADJ
cana-2736	451	23	type	type	NOUN
cana-2736	451	24	of	of	ADP
cana-2736	451	25	derivations	derivation	NOUN
cana-2736	451	26	on	on	ADP
cana-2736	451	27	balgebras	balgebras	PROPN
cana-2736	451	28	,	,	PUNCT
cana-2736	451	29	ital	ital	PROPN
cana-2736	451	30	.	.	PUNCT
cana-2736	452	1	j.	j.	PROPN
cana-2736	452	2	pure	pure	PROPN
cana-2736	452	3	appl	appl	PROPN
cana-2736	452	4	.	.	PUNCT
cana-2736	452	5	math	math	PROPN
cana-2736	452	6	.	.	PUNCT
cana-2736	452	7	,	,	PUNCT
cana-2736	452	8	48	48	NUM
cana-2736	452	9	(	(	PUNCT
cana-2736	452	10	2022	2022	NUM
cana-2736	452	11	)	)	PUNCT
cana-2736	452	12	,	,	PUNCT
cana-2736	452	13	336	336	NUM
cana-2736	452	14	-	-	SYM
cana-2736	452	15	348	348	NUM
cana-2736	452	16	.	.	PUNCT
cana-2736	453	1	[	[	X
cana-2736	453	2	2	2	X
cana-2736	453	3	]	]	PUNCT
cana-2736	453	4	t.	t.	NOUN
cana-2736	453	5	bantaojai	bantaojai	NOUN
cana-2736	453	6	,	,	PUNCT
cana-2736	453	7	c.	c.	PROPN
cana-2736	453	8	suanoom	suanoom	PROPN
cana-2736	453	9	,	,	PUNCT
cana-2736	453	10	j.	j.	PROPN
cana-2736	453	11	phuto	phuto	PROPN
cana-2736	453	12	and	and	CCONJ
cana-2736	453	13	a.	a.	NOUN
cana-2736	453	14	iampan	iampan	PROPN
cana-2736	453	15	,	,	PUNCT
cana-2736	453	16	a	a	DET
cana-2736	453	17	novel	novel	ADJ
cana-2736	453	18	derivation	derivation	NOUN
cana-2736	453	19	induced	induce	VERB
cana-2736	453	20	by	by	ADP
cana-2736	453	21	some	some	DET
cana-2736	453	22	binary	binary	ADJ
cana-2736	453	23	operations	operation	NOUN
cana-2736	453	24	on	on	ADP
cana-2736	453	25	d	d	PROPN
cana-2736	453	26	algebras	algebra	NOUN
cana-2736	453	27	,	,	PUNCT
cana-2736	453	28	int	int	PROPN
cana-2736	453	29	.	.	PUNCT
cana-2736	454	1	j.	j.	PROPN
cana-2736	454	2	math	math	PROPN
cana-2736	454	3	.	.	PUNCT
cana-2736	455	1	comput	comput	NOUN
cana-2736	455	2	.	.	PUNCT
cana-2736	456	1	sci	sci	PROPN
cana-2736	456	2	.	.	PROPN
cana-2736	456	3	,	,	PUNCT
cana-2736	456	4	17	17	NUM
cana-2736	456	5	(	(	PUNCT
cana-2736	456	6	2022	2022	NUM
cana-2736	456	7	)	)	PUNCT
cana-2736	456	8	,	,	PUNCT
cana-2736	456	9	no	no	INTJ
cana-2736	456	10	.	.	NOUN
cana-2736	456	11	1	1	NUM
cana-2736	456	12	,	,	PUNCT
cana-2736	456	13	173	173	NUM
cana-2736	456	14	-	-	SYM
cana-2736	456	15	182	182	NUM
cana-2736	456	16	.	.	PUNCT
cana-2736	457	1	[	[	X
cana-2736	457	2	3	3	X
cana-2736	457	3	]	]	PUNCT
cana-2736	457	4	t.	t.	NOUN
cana-2736	457	5	bantaojai	bantaojai	NOUN
cana-2736	457	6	,	,	PUNCT
cana-2736	457	7	c.	c.	PROPN
cana-2736	457	8	suanoom	suanoom	PROPN
cana-2736	457	9	,	,	PUNCT
cana-2736	457	10	j.	j.	PROPN
cana-2736	457	11	phuto	phuto	PROPN
cana-2736	457	12	and	and	CCONJ
cana-2736	457	13	a.	a.	NOUN
cana-2736	457	14	iampan	iampan	PROPN
cana-2736	457	15	,	,	PUNCT
cana-2736	457	16	new	new	ADJ
cana-2736	457	17	derivations	derivation	NOUN
cana-2736	457	18	utilizing	utilize	VERB
cana-2736	457	19	bi	bi	NOUN
cana-2736	457	20	-	-	NOUN
cana-2736	457	21	endomorphisms	endomorphism	NOUN
cana-2736	457	22	on	on	ADP
cana-2736	457	23	b	b	NOUN
cana-2736	457	24	-	-	PUNCT
cana-2736	457	25	algebras	algebras	PROPN
cana-2736	457	26	,	,	PUNCT
cana-2736	457	27	j.	j.	PROPN
cana-2736	457	28	math	math	PROPN
cana-2736	457	29	.	.	PUNCT
cana-2736	458	1	comput	comput	NOUN
cana-2736	458	2	.	.	PUNCT
cana-2736	459	1	sci	sci	PROPN
cana-2736	459	2	.	.	PROPN
cana-2736	459	3	,	,	PUNCT
cana-2736	459	4	11	11	NUM
cana-2736	459	5	(	(	PUNCT
cana-2736	459	6	2021	2021	NUM
cana-2736	459	7	)	)	PUNCT
cana-2736	459	8	,	,	PUNCT
cana-2736	459	9	no	no	INTJ
cana-2736	459	10	.	.	NOUN
cana-2736	459	11	5	5	NUM
cana-2736	459	12	,	,	PUNCT
cana-2736	459	13	6420	6420	NUM
cana-2736	459	14	-	-	SYM
cana-2736	459	15	6432	6432	NUM
cana-2736	459	16	.	.	PUNCT
cana-2736	460	1	[	[	X
cana-2736	460	2	4	4	X
cana-2736	460	3	]	]	X
cana-2736	460	4	d.	d.	PROPN
cana-2736	460	5	busneag	busneag	PROPN
cana-2736	460	6	,	,	PUNCT
cana-2736	460	7	a	a	DET
cana-2736	460	8	note	note	NOUN
cana-2736	460	9	on	on	ADP
cana-2736	460	10	deductive	deductive	ADJ
cana-2736	460	11	systems	system	NOUN
cana-2736	460	12	of	of	ADP
cana-2736	460	13	a	a	DET
cana-2736	460	14	hilbert	hilbert	NOUN
cana-2736	460	15	algebra	algebra	NOUN
cana-2736	460	16	,	,	PUNCT
cana-2736	460	17	kobe	kobe	PROPN
cana-2736	460	18	j.	j.	PROPN
cana-2736	460	19	math	math	PROPN
cana-2736	460	20	.	.	PUNCT
cana-2736	460	21	,	,	PUNCT
cana-2736	460	22	2	2	NUM
cana-2736	460	23	(	(	PUNCT
cana-2736	460	24	1985	1985	NUM
cana-2736	460	25	)	)	PUNCT
cana-2736	460	26	,	,	PUNCT
cana-2736	460	27	29	29	NUM
cana-2736	460	28	-	-	SYM
cana-2736	460	29	35	35	NUM
cana-2736	460	30	.	.	PUNCT
cana-2736	461	1	[	[	X
cana-2736	461	2	5	5	X
cana-2736	461	3	]	]	X
cana-2736	461	4	d.	d.	PROPN
cana-2736	461	5	busneag	busneag	PROPN
cana-2736	461	6	,	,	PUNCT
cana-2736	461	7	hilbert	hilbert	PROPN
cana-2736	461	8	algebras	algebra	NOUN
cana-2736	461	9	of	of	ADP
cana-2736	461	10	fractions	fraction	NOUN
cana-2736	461	11	and	and	CCONJ
cana-2736	461	12	maximal	maximal	ADJ
cana-2736	461	13	hilbert	hilbert	NOUN
cana-2736	461	14	algebras	algebra	NOUN
cana-2736	461	15	of	of	ADP
cana-2736	461	16	quotients	quotient	NOUN
cana-2736	461	17	,	,	PUNCT
cana-2736	461	18	kobe	kobe	PROPN
cana-2736	461	19	j.	j.	PROPN
cana-2736	461	20	math	math	PROPN
cana-2736	461	21	.	.	PUNCT
cana-2736	461	22	,	,	PUNCT
cana-2736	461	23	5	5	NUM
cana-2736	461	24	(	(	PUNCT
cana-2736	461	25	1988	1988	NUM
cana-2736	461	26	)	)	PUNCT
cana-2736	461	27	,	,	PUNCT
cana-2736	461	28	161172	161172	NUM
cana-2736	461	29	.	.	PUNCT
cana-2736	462	1	[	[	X
cana-2736	462	2	6	6	NUM
cana-2736	462	3	]	]	PUNCT
cana-2736	462	4	i.	i.	NOUN
cana-2736	462	5	chajda	chajda	PROPN
cana-2736	462	6	and	and	CCONJ
cana-2736	462	7	r.	r.	PROPN
cana-2736	462	8	halaš	halaš	PROPN
cana-2736	462	9	,	,	PUNCT
cana-2736	462	10	congruences	congruence	NOUN
cana-2736	462	11	and	and	CCONJ
cana-2736	462	12	ideals	ideal	NOUN
cana-2736	462	13	in	in	ADP
cana-2736	462	14	hilbert	hilbert	PROPN
cana-2736	462	15	algebras	algebras	PROPN
cana-2736	462	16	,	,	PUNCT
cana-2736	462	17	kyungpook	kyungpook	PROPN
cana-2736	462	18	math	math	NOUN
cana-2736	462	19	.	.	PUNCT
cana-2736	463	1	j.	j.	PROPN
cana-2736	463	2	,	,	PUNCT
cana-2736	463	3	39	39	NUM
cana-2736	463	4	(	(	PUNCT
cana-2736	463	5	1999	1999	NUM
cana-2736	463	6	)	)	PUNCT
cana-2736	463	7	,	,	PUNCT
cana-2736	463	8	no	no	INTJ
cana-2736	463	9	.	.	NOUN
cana-2736	463	10	2	2	NUM
cana-2736	463	11	,	,	PUNCT
cana-2736	463	12	429	429	NUM
cana-2736	463	13	-	-	SYM
cana-2736	463	14	432	432	NUM
cana-2736	463	15	.	.	PUNCT
cana-2736	464	1	[	[	X
cana-2736	464	2	7	7	NUM
cana-2736	464	3	]	]	X
cana-2736	464	4	a.	a.	NOUN
cana-2736	464	5	diego	diego	PROPN
cana-2736	464	6	,	,	PUNCT
cana-2736	464	7	sur	sur	PROPN
cana-2736	464	8	les	les	PROPN
cana-2736	464	9	algébres	algébres	PROPN
cana-2736	464	10	de	de	X
cana-2736	464	11	hilbert	hilbert	PROPN
cana-2736	464	12	,	,	PUNCT
cana-2736	464	13	collection	collection	NOUN
cana-2736	464	14	de	de	X
cana-2736	464	15	logique	logique	X
cana-2736	464	16	math	math	PROPN
cana-2736	464	17	.	.	PUNCT
cana-2736	465	1	ser	ser	PROPN
cana-2736	465	2	.	.	PUNCT
cana-2736	466	1	a	a	DET
cana-2736	466	2	(	(	PUNCT
cana-2736	466	3	ed	ed	NOUN
cana-2736	466	4	.	.	PUNCT
cana-2736	466	5	hermann	hermann	PROPN
cana-2736	466	6	,	,	PUNCT
cana-2736	466	7	paris	paris	PROPN
cana-2736	466	8	)	)	PUNCT
cana-2736	466	9	,	,	PUNCT
cana-2736	466	10	21	21	NUM
cana-2736	466	11	(	(	PUNCT
cana-2736	466	12	1966	1966	NUM
cana-2736	466	13	)	)	PUNCT
cana-2736	466	14	,	,	PUNCT
cana-2736	466	15	1	1	NUM
cana-2736	466	16	-	-	SYM
cana-2736	466	17	52	52	NUM
cana-2736	466	18	.	.	PUNCT
cana-2736	467	1	[	[	X
cana-2736	467	2	8	8	NUM
cana-2736	467	3	]	]	X
cana-2736	467	4	w.	w.	PROPN
cana-2736	467	5	a.	a.	PROPN
cana-2736	467	6	dudek	dudek	PROPN
cana-2736	467	7	,	,	PUNCT
cana-2736	467	8	on	on	ADP
cana-2736	467	9	fuzzification	fuzzification	NOUN
cana-2736	467	10	in	in	ADP
cana-2736	467	11	hilbert	hilbert	PROPN
cana-2736	467	12	algebras	algebras	PROPN
cana-2736	467	13	,	,	PUNCT
cana-2736	467	14	contrib	contrib	PROPN
cana-2736	467	15	.	.	PUNCT
cana-2736	467	16	gen	gen	PROPN
cana-2736	467	17	.	.	PROPN
cana-2736	467	18	algebra	algebra	PROPN
cana-2736	467	19	,	,	PUNCT
cana-2736	467	20	11	11	NUM
cana-2736	467	21	(	(	PUNCT
cana-2736	467	22	1999	1999	NUM
cana-2736	467	23	)	)	PUNCT
cana-2736	467	24	,	,	PUNCT
cana-2736	467	25	77	77	NUM
cana-2736	467	26	-	-	SYM
cana-2736	467	27	83	83	NUM
cana-2736	467	28	.	.	PUNCT
cana-2736	468	1	[	[	X
cana-2736	468	2	9	9	NUM
cana-2736	468	3	]	]	X
cana-2736	468	4	l.	l.	PROPN
cana-2736	468	5	henkin	henkin	PROPN
cana-2736	468	6	,	,	PUNCT
cana-2736	468	7	an	an	DET
cana-2736	468	8	algebraic	algebraic	ADJ
cana-2736	468	9	characterization	characterization	NOUN
cana-2736	468	10	of	of	ADP
cana-2736	468	11	quantifiers	quantifier	NOUN
cana-2736	468	12	,	,	PUNCT
cana-2736	468	13	fund	fund	PROPN
cana-2736	468	14	.	.	PUNCT
cana-2736	468	15	math	math	NOUN
cana-2736	468	16	.	.	PUNCT
cana-2736	469	1	,	,	PUNCT
cana-2736	469	2	37	37	NUM
cana-2736	469	3	(	(	PUNCT
cana-2736	469	4	1950	1950	NUM
cana-2736	469	5	)	)	PUNCT
cana-2736	469	6	,	,	PUNCT
cana-2736	469	7	63	63	NUM
cana-2736	469	8	-	-	SYM
cana-2736	469	9	74	74	NUM
cana-2736	469	10	.	.	PUNCT
cana-2736	470	1	[	[	X
cana-2736	470	2	10	10	NUM
cana-2736	470	3	]	]	PUNCT
cana-2736	470	4	a.	a.	NOUN
cana-2736	470	5	iampan	iampan	PROPN
cana-2736	470	6	,	,	PUNCT
cana-2736	470	7	derivations	derivation	NOUN
cana-2736	470	8	of	of	ADP
cana-2736	470	9	up	up	ADV
cana-2736	470	10	-	-	PUNCT
cana-2736	470	11	algebras	algebra	VERB
cana-2736	470	12	by	by	ADP
cana-2736	470	13	means	mean	NOUN
cana-2736	470	14	of	of	ADP
cana-2736	470	15	up	up	ADP
cana-2736	470	16	-	-	PUNCT
cana-2736	470	17	endomorphisms	endomorphism	NOUN
cana-2736	470	18	,	,	PUNCT
cana-2736	470	19	algebr	algebr	NOUN
cana-2736	470	20	.	.	PUNCT
cana-2736	470	21	struct	struct	NOUN
cana-2736	470	22	.	.	PUNCT
cana-2736	471	1	appl	appl	PROPN
cana-2736	471	2	.	.	PROPN
cana-2736	471	3	,	,	PUNCT
cana-2736	471	4	3	3	NUM
cana-2736	471	5	(	(	PUNCT
cana-2736	471	6	2016	2016	NUM
cana-2736	471	7	)	)	PUNCT
cana-2736	471	8	,	,	PUNCT
cana-2736	471	9	no	no	INTJ
cana-2736	471	10	.	.	NOUN
cana-2736	471	11	2	2	NUM
cana-2736	471	12	,	,	PUNCT
cana-2736	471	13	1	1	NUM
cana-2736	471	14	-	-	SYM
cana-2736	471	15	20	20	NUM
cana-2736	471	16	.	.	PUNCT
cana-2736	472	1	[	[	X
cana-2736	472	2	11	11	NUM
cana-2736	472	3	]	]	PUNCT
cana-2736	472	4	a.	a.	NOUN
cana-2736	472	5	iampan	iampan	PROPN
cana-2736	472	6	,	,	PUNCT
cana-2736	472	7	r.	r.	PROPN
cana-2736	472	8	alayakkaniamuthu	alayakkaniamuthu	PROPN
cana-2736	472	9	,	,	PUNCT
cana-2736	472	10	p.	p.	NOUN
cana-2736	472	11	gomathi	gomathi	PROPN
cana-2736	472	12	sundari	sundari	PROPN
cana-2736	472	13	and	and	CCONJ
cana-2736	472	14	n.	n.	PROPN
cana-2736	472	15	rajesh	rajesh	PROPN
cana-2736	472	16	,	,	PUNCT
cana-2736	472	17	derivations	derivation	NOUN
cana-2736	472	18	of	of	ADP
cana-2736	472	19	hilbert	hilbert	PROPN
cana-2736	472	20	algebras	algebras	PROPN
cana-2736	472	21	,	,	PUNCT
cana-2736	472	22	int	int	PROPN
cana-2736	472	23	.	.	PUNCT
cana-2736	473	1	j.	j.	PROPN
cana-2736	473	2	anal	anal	PROPN
cana-2736	473	3	.	.	PUNCT
cana-2736	474	1	appl	appl	PROPN
cana-2736	474	2	.	.	PROPN
cana-2736	474	3	,	,	PUNCT
cana-2736	474	4	21	21	NUM
cana-2736	474	5	(	(	PUNCT
cana-2736	474	6	2023	2023	NUM
cana-2736	474	7	)	)	PUNCT
cana-2736	474	8	,	,	PUNCT
cana-2736	474	9	article	article	NOUN
cana-2736	474	10	i	i	PROPN
cana-2736	474	11	d	d	PROPN
cana-2736	474	12	39	39	NUM
cana-2736	474	13	.	.	PUNCT
cana-2736	475	1	[	[	X
cana-2736	475	2	12	12	NUM
cana-2736	475	3	]	]	PUNCT
cana-2736	475	4	a.	a.	NOUN
cana-2736	475	5	iampan	iampan	NOUN
cana-2736	475	6	and	and	CCONJ
cana-2736	475	7	n.	n.	PROPN
cana-2736	475	8	rajesh	rajesh	PROPN
cana-2736	475	9	,	,	PUNCT
cana-2736	475	10	on	on	ADP
cana-2736	475	11	multipliers	multiplier	NOUN
cana-2736	475	12	of	of	ADP
cana-2736	475	13	hilbert	hilbert	PROPN
cana-2736	475	14	algebras	algebras	PROPN
cana-2736	475	15	,	,	PUNCT
cana-2736	475	16	eur	eur	PROPN
cana-2736	475	17	.	.	PUNCT
cana-2736	476	1	j.	j.	PROPN
cana-2736	476	2	pure	pure	PROPN
cana-2736	476	3	appl	appl	PROPN
cana-2736	476	4	.	.	PUNCT
cana-2736	476	5	math	math	PROPN
cana-2736	476	6	.	.	PUNCT
cana-2736	476	7	,	,	PUNCT
cana-2736	476	8	17	17	NUM
cana-2736	476	9	(	(	PUNCT
cana-2736	476	10	2024	2024	NUM
cana-2736	476	11	)	)	PUNCT
cana-2736	476	12	,	,	PUNCT
cana-2736	476	13	no	no	INTJ
cana-2736	476	14	.	.	NOUN
cana-2736	476	15	4	4	NUM
cana-2736	476	16	,	,	PUNCT
cana-2736	476	17	2726	2726	NUM
cana-2736	476	18	-	-	SYM
cana-2736	476	19	2737	2737	NUM
cana-2736	476	20	.	.	PUNCT
cana-2736	477	1	[	[	X
cana-2736	477	2	13	13	NUM
cana-2736	477	3	]	]	PUNCT
cana-2736	477	4	a.	a.	NOUN
cana-2736	477	5	iampan	iampan	PROPN
cana-2736	477	6	,	,	PUNCT
cana-2736	477	7	n.	n.	PROPN
cana-2736	477	8	rajesh	rajesh	PROPN
cana-2736	477	9	,	,	PUNCT
cana-2736	477	10	c.	c.	PROPN
cana-2736	477	11	arivazhagi	arivazhagi	PROPN
cana-2736	477	12	and	and	CCONJ
cana-2736	477	13	r.	r.	PROPN
cana-2736	477	14	vennila	vennila	PROPN
cana-2736	477	15	,	,	PUNCT
cana-2736	477	16	structural	structural	ADJ
cana-2736	477	17	derivations	derivation	NOUN
cana-2736	477	18	in	in	ADP
cana-2736	477	19	hilbert	hilbert	PROPN
cana-2736	477	20	algebras	algebras	PROPN
cana-2736	477	21	by	by	ADP
cana-2736	477	22	endomorphisms	endomorphism	NOUN
cana-2736	477	23	,	,	PUNCT
cana-2736	477	24	int	int	NOUN
cana-2736	477	25	.	.	PUNCT
cana-2736	478	1	j.	j.	PROPN
cana-2736	478	2	anal	anal	PROPN
cana-2736	478	3	.	.	PUNCT
cana-2736	479	1	appl	appl	PROPN
cana-2736	479	2	.	.	PROPN
cana-2736	479	3	,	,	PUNCT
cana-2736	479	4	22	22	NUM
cana-2736	479	5	(	(	PUNCT
cana-2736	479	6	2024	2024	NUM
cana-2736	479	7	)	)	PUNCT
cana-2736	479	8	,	,	PUNCT
cana-2736	479	9	article	article	NOUN
cana-2736	479	10	i	i	PROPN
cana-2736	479	11	d	d	PROPN
cana-2736	479	12	213	213	NUM
cana-2736	479	13	.	.	PUNCT
cana-2736	480	1	[	[	X
cana-2736	480	2	14	14	NUM
cana-2736	480	3	]	]	X
cana-2736	480	4	y.	y.	PROPN
cana-2736	480	5	b.	b.	PROPN
cana-2736	480	6	jun	jun	PROPN
cana-2736	480	7	,	,	PUNCT
cana-2736	480	8	commutative	commutative	ADJ
cana-2736	480	9	hilbert	hilbert	PROPN
cana-2736	480	10	algebras	algebras	PROPN
cana-2736	480	11	,	,	PUNCT
cana-2736	480	12	soochow	soochow	PROPN
cana-2736	480	13	j.	j.	PROPN
cana-2736	480	14	math	math	PROPN
cana-2736	480	15	.	.	PUNCT
cana-2736	480	16	,	,	PUNCT
cana-2736	480	17	22	22	NUM
cana-2736	480	18	(	(	PUNCT
cana-2736	480	19	1996	1996	NUM
cana-2736	480	20	)	)	PUNCT
cana-2736	480	21	,	,	PUNCT
cana-2736	480	22	no	no	INTJ
cana-2736	480	23	.	.	NOUN
cana-2736	480	24	4	4	NUM
cana-2736	480	25	,	,	PUNCT
cana-2736	480	26	477	477	NUM
cana-2736	480	27	-	-	SYM
cana-2736	480	28	484	484	NUM
cana-2736	480	29	.	.	PUNCT
cana-2736	481	1	[	[	X
cana-2736	481	2	15	15	NUM
cana-2736	481	3	]	]	X
cana-2736	481	4	y.	y.	PROPN
cana-2736	481	5	b.	b.	PROPN
cana-2736	481	6	jun	jun	PROPN
cana-2736	481	7	,	,	PUNCT
cana-2736	481	8	deductive	deductive	ADJ
cana-2736	481	9	systems	system	NOUN
cana-2736	481	10	of	of	ADP
cana-2736	481	11	hilbert	hilbert	PROPN
cana-2736	481	12	algebras	algebras	PROPN
cana-2736	481	13	,	,	PUNCT
cana-2736	481	14	math	math	NOUN
cana-2736	481	15	.	.	PUNCT
cana-2736	482	1	japon	japon	PROPN
cana-2736	482	2	.	.	PROPN
cana-2736	482	3	,	,	PUNCT
cana-2736	482	4	43	43	NUM
cana-2736	482	5	(	(	PUNCT
cana-2736	482	6	1996	1996	NUM
cana-2736	482	7	)	)	PUNCT
cana-2736	482	8	,	,	PUNCT
cana-2736	482	9	51	51	NUM
cana-2736	482	10	-	-	SYM
cana-2736	482	11	54	54	NUM
cana-2736	482	12	.	.	PUNCT
cana-2736	483	1	[	[	X
cana-2736	483	2	16	16	NUM
cana-2736	483	3	]	]	X
cana-2736	483	4	y.	y.	PROPN
cana-2736	483	5	b.	b.	PROPN
cana-2736	483	6	jun	jun	PROPN
cana-2736	483	7	,	,	PUNCT
cana-2736	483	8	j.-w	j.-w	PROPN
cana-2736	483	9	.	.	PUNCT
cana-2736	484	1	nam	nam	PROPN
cana-2736	484	2	and	and	CCONJ
cana-2736	484	3	s.	s.	PROPN
cana-2736	484	4	m.	m.	PROPN
cana-2736	484	5	hong	hong	PROPN
cana-2736	484	6	,	,	PUNCT
cana-2736	484	7	a	a	DET
cana-2736	484	8	note	note	NOUN
cana-2736	484	9	on	on	ADP
cana-2736	484	10	hilbert	hilbert	PROPN
cana-2736	484	11	algebras	algebras	PROPN
cana-2736	484	12	,	,	PUNCT
cana-2736	484	13	east	east	ADJ
cana-2736	484	14	asian	asian	ADJ
cana-2736	484	15	math	math	PROPN
cana-2736	484	16	.	.	PUNCT
cana-2736	485	1	j.	j.	PROPN
cana-2736	485	2	,	,	PUNCT
cana-2736	485	3	10	10	NUM
cana-2736	485	4	(	(	PUNCT
cana-2736	485	5	1994	1994	NUM
cana-2736	485	6	)	)	PUNCT
cana-2736	485	7	,	,	PUNCT
cana-2736	485	8	no	no	INTJ
cana-2736	485	9	.	.	NOUN
cana-2736	485	10	2	2	NUM
cana-2736	485	11	,	,	PUNCT
cana-2736	485	12	279	279	NUM
cana-2736	485	13	-	-	SYM
cana-2736	485	14	285	285	NUM
cana-2736	485	15	.	.	PUNCT
cana-2736	486	1	[	[	X
cana-2736	486	2	17	17	NUM
cana-2736	486	3	]	]	X
cana-2736	486	4	p.	p.	NOUN
cana-2736	486	5	muangkarn	muangkarn	PROPN
cana-2736	486	6	,	,	PUNCT
cana-2736	486	7	c.	c.	NOUN
cana-2736	486	8	suanoom	suanoom	NOUN
cana-2736	486	9	and	and	CCONJ
cana-2736	486	10	a.	a.	NOUN
cana-2736	486	11	iampan	iampan	PROPN
cana-2736	486	12	,	,	PUNCT
cana-2736	486	13	new	new	ADJ
cana-2736	486	14	derivations	derivation	NOUN
cana-2736	486	15	of	of	ADP
cana-2736	486	16	d	d	PROPN
cana-2736	486	17	-algebras	-algebra	NOUN
cana-2736	486	18	based	base	VERB
cana-2736	486	19	on	on	ADP
cana-2736	486	20	endomorphisms	endomorphism	NOUN
cana-2736	486	21	,	,	PUNCT
cana-2736	486	22	int	int	NOUN
cana-2736	486	23	.	.	PUNCT
cana-2736	487	1	j.	j.	PROPN
cana-2736	487	2	math	math	PROPN
cana-2736	487	3	.	.	PUNCT
cana-2736	488	1	comput	comput	NOUN
cana-2736	488	2	.	.	PUNCT
cana-2736	489	1	sci	sci	PROPN
cana-2736	489	2	.	.	PROPN
cana-2736	489	3	,	,	PUNCT
cana-2736	489	4	17	17	NUM
cana-2736	489	5	(	(	PUNCT
cana-2736	489	6	2022	2022	NUM
cana-2736	489	7	)	)	PUNCT
cana-2736	489	8	,	,	PUNCT
cana-2736	489	9	no	no	INTJ
cana-2736	489	10	.	.	NOUN
cana-2736	489	11	3	3	NUM
cana-2736	489	12	,	,	PUNCT
cana-2736	489	13	1025	1025	NUM
cana-2736	489	14	-	-	SYM
cana-2736	489	15	1032	1032	NUM
cana-2736	489	16	.	.	PUNCT
cana-2736	490	1	[	[	X
cana-2736	490	2	18	18	NUM
cana-2736	490	3	]	]	PUNCT
cana-2736	490	4	p.	p.	NOUN
cana-2736	490	5	muangkarn	muangkarn	PROPN
cana-2736	490	6	,	,	PUNCT
cana-2736	490	7	c.	c.	PROPN
cana-2736	490	8	suanoom	suanoom	NOUN
cana-2736	490	9	,	,	PUNCT
cana-2736	490	10	p.	p.	PROPN
cana-2736	490	11	pengyim	pengyim	PROPN
cana-2736	490	12	and	and	CCONJ
cana-2736	490	13	a.	a.	NOUN
cana-2736	490	14	iampan	iampan	PROPN
cana-2736	490	15	,	,	PUNCT
cana-2736	490	16	qf	qf	PROPN
cana-2736	490	17	-derivations	-derivation	NOUN
cana-2736	490	18	of	of	ADP
cana-2736	490	19	b	b	NOUN
cana-2736	490	20	-	-	PUNCT
cana-2736	490	21	algebras	algebras	PROPN
cana-2736	490	22	,	,	PUNCT
cana-2736	490	23	j.	j.	PROPN
cana-2736	490	24	math	math	PROPN
cana-2736	490	25	.	.	PUNCT
cana-2736	491	1	comput	comput	NOUN
cana-2736	491	2	.	.	PUNCT
cana-2736	492	1	sci	sci	PROPN
cana-2736	492	2	.	.	PROPN
cana-2736	492	3	,	,	PUNCT
cana-2736	492	4	11	11	NUM
cana-2736	492	5	(	(	PUNCT
cana-2736	492	6	2021	2021	NUM
cana-2736	492	7	)	)	PUNCT
cana-2736	492	8	,	,	PUNCT
cana-2736	492	9	no	no	INTJ
cana-2736	492	10	.	.	NOUN
cana-2736	492	11	2	2	NUM
cana-2736	492	12	,	,	PUNCT
cana-2736	492	13	2047	2047	NUM
cana-2736	492	14	-	-	SYM
cana-2736	492	15	2057	2057	NUM
cana-2736	492	16	.	.	PUNCT
cana-2736	493	1	[	[	X
cana-2736	493	2	19	19	NUM
cana-2736	493	3	]	]	PUNCT
cana-2736	493	4	p.	p.	NOUN
cana-2736	493	5	muangkarn	muangkarn	PROPN
cana-2736	493	6	,	,	PUNCT
cana-2736	493	7	c.	c.	PROPN
cana-2736	493	8	suanoom	suanoom	PROPN
cana-2736	493	9	,	,	PUNCT
cana-2736	493	10	a.	a.	PROPN
cana-2736	493	11	yodkheeree	yodkheeree	NOUN
cana-2736	493	12	and	and	CCONJ
cana-2736	493	13	a.	a.	NOUN
cana-2736	493	14	iampan	iampan	PROPN
cana-2736	493	15	,	,	PUNCT
cana-2736	493	16	derivations	derivation	NOUN
cana-2736	493	17	induced	induce	VERB
cana-2736	493	18	by	by	ADP
cana-2736	493	19	an	an	DET
cana-2736	493	20	endomorphism	endomorphism	NOUN
cana-2736	493	21	of	of	ADP
cana-2736	493	22	bgalgebras	bgalgebras	PROPN
cana-2736	493	23	,	,	PUNCT
cana-2736	493	24	int	int	PROPN
cana-2736	493	25	.	.	PUNCT
cana-2736	494	1	j.	j.	PROPN
cana-2736	494	2	math	math	PROPN
cana-2736	494	3	.	.	PUNCT
cana-2736	495	1	comput	comput	NOUN
cana-2736	495	2	.	.	PUNCT
cana-2736	496	1	sci	sci	PROPN
cana-2736	496	2	.	.	PROPN
cana-2736	496	3	,	,	PUNCT
cana-2736	496	4	17	17	NUM
cana-2736	496	5	(	(	PUNCT
cana-2736	496	6	2022	2022	NUM
cana-2736	496	7	)	)	PUNCT
cana-2736	496	8	,	,	PUNCT
cana-2736	496	9	no	no	INTJ
cana-2736	496	10	.	.	NOUN
cana-2736	496	11	2	2	NUM
cana-2736	496	12	,	,	PUNCT
cana-2736	496	13	847	847	NUM
cana-2736	496	14	-	-	SYM
cana-2736	496	15	852	852	NUM
cana-2736	496	16	.	.	PUNCT
cana-2736	497	1	[	[	X
cana-2736	497	2	20	20	NUM
cana-2736	497	3	]	]	PUNCT
cana-2736	497	4	k.	k.	PROPN
cana-2736	497	5	sawika	sawika	PROPN
cana-2736	497	6	,	,	PUNCT
cana-2736	497	7	r.	r.	PROPN
cana-2736	497	8	intasan	intasan	PROPN
cana-2736	497	9	,	,	PUNCT
cana-2736	497	10	a.	a.	NOUN
cana-2736	497	11	kaewwasri	kaewwasri	PROPN
cana-2736	497	12	and	and	CCONJ
cana-2736	497	13	a.	a.	NOUN
cana-2736	497	14	iampan	iampan	PROPN
cana-2736	497	15	,	,	PUNCT
cana-2736	497	16	derivations	derivation	NOUN
cana-2736	497	17	of	of	ADP
cana-2736	497	18	up	up	ADP
cana-2736	497	19	-	-	PUNCT
cana-2736	497	20	algebras	algebra	NOUN
cana-2736	497	21	,	,	PUNCT
cana-2736	497	22	korean	korean	ADJ
cana-2736	497	23	j.	j.	PROPN
cana-2736	497	24	math	math	PROPN
cana-2736	497	25	.	.	PROPN
cana-2736	497	26	,	,	PUNCT
cana-2736	497	27	24	24	NUM
cana-2736	497	28	(	(	PUNCT
cana-2736	497	29	2016	2016	NUM
cana-2736	497	30	)	)	PUNCT
cana-2736	497	31	,	,	PUNCT
cana-2736	497	32	no	no	INTJ
cana-2736	497	33	.	.	NOUN
cana-2736	497	34	3	3	NUM
cana-2736	497	35	,	,	PUNCT
cana-2736	497	36	345	345	NUM
cana-2736	497	37	-	-	SYM
cana-2736	497	38	367	367	NUM
cana-2736	497	39	.	.	PUNCT
cana-2736	498	1	[	[	X
cana-2736	498	2	21	21	NUM
cana-2736	498	3	]	]	X
cana-2736	498	4	t.	t.	PROPN
cana-2736	498	5	tippanya	tippanya	PROPN
cana-2736	498	6	,	,	PUNCT
cana-2736	498	7	n.	n.	PROPN
cana-2736	498	8	iam	iam	PROPN
cana-2736	498	9	-	-	PUNCT
cana-2736	498	10	art	art	NOUN
cana-2736	498	11	,	,	PUNCT
cana-2736	498	12	p.	p.	NOUN
cana-2736	498	13	moonfong	moonfong	PROPN
cana-2736	498	14	and	and	CCONJ
cana-2736	498	15	a.	a.	NOUN
cana-2736	498	16	iampan	iampan	PROPN
cana-2736	498	17	,	,	PUNCT
cana-2736	498	18	a	a	DET
cana-2736	498	19	new	new	ADJ
cana-2736	498	20	derivation	derivation	NOUN
cana-2736	498	21	of	of	ADP
cana-2736	498	22	up	up	ADV
cana-2736	498	23	-	-	PUNCT
cana-2736	498	24	algebras	algebra	VERB
cana-2736	498	25	by	by	ADP
cana-2736	498	26	means	mean	NOUN
cana-2736	498	27	of	of	ADP
cana-2736	498	28	upendomorphisms	upendomorphism	NOUN
cana-2736	498	29	,	,	PUNCT
cana-2736	498	30	algebra	algebra	VERB
cana-2736	498	31	lett	lett	PROPN
cana-2736	498	32	.	.	PROPN
cana-2736	498	33	,	,	PUNCT
cana-2736	498	34	2017	2017	NUM
cana-2736	498	35	(	(	PUNCT
cana-2736	498	36	2017	2017	NUM
cana-2736	498	37	)	)	PUNCT
cana-2736	498	38	,	,	PUNCT
cana-2736	498	39	article	article	NOUN
cana-2736	498	40	i	i	PROPN
cana-2736	498	41	d	d	PROPN
cana-2736	498	42	4	4	X
cana-2736	498	43	.	.	PUNCT