id	sid	tid	token	lemma	pos
ejpam-5025	1	1	european	european	PROPN
ejpam-5025	1	2	journal	journal	PROPN
ejpam-5025	1	3	of	of	ADP
ejpam-5025	1	4	pure	pure	ADJ
ejpam-5025	1	5	and	and	CCONJ
ejpam-5025	1	6	applied	apply	VERB
ejpam-5025	1	7	mathematics	mathematic	NOUN
ejpam-5025	1	8	vol	vol	NOUN
ejpam-5025	1	9	.	.	PROPN
ejpam-5025	2	1	17	17	NUM
ejpam-5025	2	2	,	,	PUNCT
ejpam-5025	2	3	no	no	INTJ
ejpam-5025	2	4	.	.	NOUN
ejpam-5025	2	5	1	1	NUM
ejpam-5025	2	6	,	,	PUNCT
ejpam-5025	2	7	2024	2024	NUM
ejpam-5025	2	8	,	,	PUNCT
ejpam-5025	2	9	362	362	NUM
ejpam-5025	2	10	-	-	SYM
ejpam-5025	2	11	371	371	NUM
ejpam-5025	2	12	issn	issn	PROPN
ejpam-5025	2	13	1307	1307	NUM
ejpam-5025	2	14	-	-	SYM
ejpam-5025	2	15	5543	5543	NUM
ejpam-5025	2	16	–	–	PUNCT
ejpam-5025	2	17	ejpam.com	ejpam.com	X
ejpam-5025	2	18	published	publish	VERB
ejpam-5025	2	19	by	by	ADP
ejpam-5025	2	20	new	new	PROPN
ejpam-5025	2	21	york	york	PROPN
ejpam-5025	2	22	business	business	PROPN
ejpam-5025	2	23	global	global	ADJ
ejpam-5025	2	24	on	on	ADP
ejpam-5025	2	25	reverse	reverse	ADJ
ejpam-5025	2	26	derivations	derivation	NOUN
ejpam-5025	2	27	in	in	ADP
ejpam-5025	2	28	d	d	NOUN
ejpam-5025	2	29	-	-	PUNCT
ejpam-5025	2	30	algebras	algebras	PROPN
ejpam-5025	2	31	kholood	kholood	PROPN
ejpam-5025	2	32	alnefaie	alnefaie	PROPN
ejpam-5025	2	33	department	department	PROPN
ejpam-5025	2	34	of	of	ADP
ejpam-5025	2	35	mathematics	mathematics	PROPN
ejpam-5025	2	36	,	,	PUNCT
ejpam-5025	2	37	college	college	NOUN
ejpam-5025	2	38	of	of	ADP
ejpam-5025	2	39	science	science	PROPN
ejpam-5025	2	40	,	,	PUNCT
ejpam-5025	2	41	taibah	taibah	PROPN
ejpam-5025	2	42	university	university	PROPN
ejpam-5025	2	43	,	,	PUNCT
ejpam-5025	2	44	madinah	madinah	PROPN
ejpam-5025	2	45	,	,	PUNCT
ejpam-5025	2	46	saudi	saudi	PROPN
ejpam-5025	2	47	arabia	arabia	PROPN
ejpam-5025	2	48	abstract	abstract	NOUN
ejpam-5025	2	49	.	.	PUNCT
ejpam-5025	3	1	in	in	ADP
ejpam-5025	3	2	the	the	DET
ejpam-5025	3	3	present	present	ADJ
ejpam-5025	3	4	paper	paper	NOUN
ejpam-5025	3	5	,	,	PUNCT
ejpam-5025	3	6	we	we	PRON
ejpam-5025	3	7	apply	apply	VERB
ejpam-5025	3	8	the	the	DET
ejpam-5025	3	9	concept	concept	NOUN
ejpam-5025	3	10	of	of	ADP
ejpam-5025	3	11	reverse	reverse	ADJ
ejpam-5025	3	12	derivation	derivation	NOUN
ejpam-5025	3	13	in	in	ADP
ejpam-5025	3	14	rings	ring	NOUN
ejpam-5025	3	15	on	on	ADP
ejpam-5025	3	16	the	the	DET
ejpam-5025	3	17	concept	concept	NOUN
ejpam-5025	3	18	of	of	ADP
ejpam-5025	3	19	d	d	NOUN
ejpam-5025	3	20	−	−	PROPN
ejpam-5025	3	21	algebra	algebra	NOUN
ejpam-5025	3	22	to	to	PART
ejpam-5025	3	23	obtain	obtain	VERB
ejpam-5025	3	24	the	the	DET
ejpam-5025	3	25	concept	concept	NOUN
ejpam-5025	3	26	called	call	VERB
ejpam-5025	3	27	a	a	DET
ejpam-5025	3	28	left	left	ADJ
ejpam-5025	3	29	-	-	PUNCT
ejpam-5025	3	30	right	right	NOUN
ejpam-5025	3	31	(	(	PUNCT
ejpam-5025	3	32	resp	resp	NOUN
ejpam-5025	3	33	.	.	PUNCT
ejpam-5025	4	1	right	right	ADJ
ejpam-5025	4	2	-	-	PUNCT
ejpam-5025	4	3	left	left	ADJ
ejpam-5025	4	4	)	)	PUNCT
ejpam-5025	4	5	reverse	reverse	ADJ
ejpam-5025	4	6	derivations	derivation	NOUN
ejpam-5025	4	7	of	of	ADP
ejpam-5025	4	8	d−algebra	d−algebra	X
ejpam-5025	4	9	x	x	X
ejpam-5025	4	10	(	(	PUNCT
ejpam-5025	4	11	briefly	briefly	ADV
ejpam-5025	4	12	,	,	PUNCT
ejpam-5025	4	13	(	(	PUNCT
ejpam-5025	4	14	l	l	NOUN
ejpam-5025	4	15	,	,	PUNCT
ejpam-5025	4	16	r	r	NOUN
ejpam-5025	4	17	)	)	PUNCT
ejpam-5025	4	18	resp	resp	NOUN
ejpam-5025	4	19	.	.	PUNCT
ejpam-5025	5	1	(	(	PUNCT
ejpam-5025	5	2	r	r	X
ejpam-5025	5	3	,	,	PUNCT
ejpam-5025	5	4	l)−	l)−	PROPN
ejpam-5025	5	5	reverse	reverse	VERB
ejpam-5025	5	6	derivation	derivation	NOUN
ejpam-5025	5	7	of	of	ADP
ejpam-5025	5	8	d−algebra	d−algebra	NOUN
ejpam-5025	5	9	)	)	PUNCT
ejpam-5025	5	10	,	,	PUNCT
ejpam-5025	5	11	we	we	PRON
ejpam-5025	5	12	will	will	AUX
ejpam-5025	5	13	also	also	ADV
ejpam-5025	5	14	,	,	PUNCT
ejpam-5025	5	15	define	define	VERB
ejpam-5025	5	16	some	some	DET
ejpam-5025	5	17	concepts	concept	NOUN
ejpam-5025	5	18	such	such	ADJ
ejpam-5025	5	19	as	as	ADP
ejpam-5025	5	20	regular	regular	ADJ
ejpam-5025	5	21	map	map	NOUN
ejpam-5025	5	22	,	,	PUNCT
ejpam-5025	5	23	composition	composition	NOUN
ejpam-5025	5	24	two	two	NUM
ejpam-5025	5	25	maps	map	NOUN
ejpam-5025	5	26	and	and	CCONJ
ejpam-5025	5	27	study	study	VERB
ejpam-5025	5	28	the	the	DET
ejpam-5025	5	29	related	relate	VERB
ejpam-5025	5	30	properties	property	NOUN
ejpam-5025	5	31	.	.	PUNCT
ejpam-5025	6	1	moreover	moreover	ADV
ejpam-5025	6	2	,	,	PUNCT
ejpam-5025	6	3	the	the	DET
ejpam-5025	6	4	notions	notion	NOUN
ejpam-5025	6	5	of	of	ADP
ejpam-5025	6	6	partial	partial	ADJ
ejpam-5025	6	7	ordered	order	VERB
ejpam-5025	6	8	edge	edge	NOUN
ejpam-5025	6	9	d	d	NOUN
ejpam-5025	6	10	−	−	PROPN
ejpam-5025	6	11	algebra	algebra	NOUN
ejpam-5025	6	12	as	as	ADV
ejpam-5025	6	13	well	well	ADV
ejpam-5025	6	14	as	as	ADP
ejpam-5025	6	15	d	d	NOUN
ejpam-5025	6	16	−	−	NOUN
ejpam-5025	6	17	subalgebra	subalgebra	NOUN
ejpam-5025	6	18	and	and	CCONJ
ejpam-5025	6	19	their	their	PRON
ejpam-5025	6	20	relation	relation	NOUN
ejpam-5025	6	21	to	to	ADP
ejpam-5025	6	22	our	our	PRON
ejpam-5025	6	23	current	current	ADJ
ejpam-5025	6	24	study	study	NOUN
ejpam-5025	6	25	are	be	AUX
ejpam-5025	6	26	obtained	obtain	VERB
ejpam-5025	6	27	.	.	PUNCT
ejpam-5025	7	1	in	in	ADP
ejpam-5025	7	2	addition	addition	NOUN
ejpam-5025	7	3	,	,	PUNCT
ejpam-5025	7	4	some	some	DET
ejpam-5025	7	5	illustrative	illustrative	ADJ
ejpam-5025	7	6	examples	example	NOUN
ejpam-5025	7	7	and	and	CCONJ
ejpam-5025	7	8	counterexamples	counterexample	NOUN
ejpam-5025	7	9	are	be	AUX
ejpam-5025	7	10	discussed	discuss	VERB
ejpam-5025	7	11	.	.	PUNCT
ejpam-5025	8	1	2020	2020	NUM
ejpam-5025	8	2	mathematics	mathematic	NOUN
ejpam-5025	8	3	subject	subject	NOUN
ejpam-5025	8	4	classifications	classification	NOUN
ejpam-5025	8	5	:	:	PUNCT
ejpam-5025	8	6	03g25	03g25	NUM
ejpam-5025	8	7	,	,	PUNCT
ejpam-5025	8	8	06f35	06f35	NUM
ejpam-5025	8	9	key	key	ADJ
ejpam-5025	8	10	words	word	NOUN
ejpam-5025	8	11	and	and	CCONJ
ejpam-5025	8	12	phrases	phrase	NOUN
ejpam-5025	8	13	:	:	PUNCT
ejpam-5025	8	14	d−algebras	d−algebra	NOUN
ejpam-5025	8	15	,	,	PUNCT
ejpam-5025	8	16	bci−algebras	bci−algebra	NOUN
ejpam-5025	8	17	,	,	PUNCT
ejpam-5025	8	18	reverse	reverse	ADJ
ejpam-5025	8	19	derivations	derivation	NOUN
ejpam-5025	8	20	1	1	NUM
ejpam-5025	8	21	.	.	PUNCT
ejpam-5025	8	22	introduction	introduction	NOUN
ejpam-5025	8	23	in	in	ADP
ejpam-5025	8	24	the	the	DET
ejpam-5025	8	25	theory	theory	NOUN
ejpam-5025	8	26	of	of	ADP
ejpam-5025	8	27	rings	ring	NOUN
ejpam-5025	8	28	,	,	PUNCT
ejpam-5025	8	29	the	the	DET
ejpam-5025	8	30	study	study	NOUN
ejpam-5025	8	31	of	of	ADP
ejpam-5025	8	32	derivation	derivation	NOUN
ejpam-5025	8	33	plays	play	VERB
ejpam-5025	8	34	an	an	DET
ejpam-5025	8	35	important	important	ADJ
ejpam-5025	8	36	role	role	NOUN
ejpam-5025	8	37	in	in	ADP
ejpam-5025	8	38	the	the	DET
ejpam-5025	8	39	properties	property	NOUN
ejpam-5025	8	40	of	of	ADP
ejpam-5025	8	41	algebraic	algebraic	ADJ
ejpam-5025	8	42	systems	system	NOUN
ejpam-5025	8	43	,	,	PUNCT
ejpam-5025	8	44	analysis	analysis	NOUN
ejpam-5025	8	45	and	and	CCONJ
ejpam-5025	8	46	algebraic	algebraic	ADJ
ejpam-5025	8	47	geometry	geometry	NOUN
ejpam-5025	8	48	.	.	PUNCT
ejpam-5025	9	1	it	it	PRON
ejpam-5025	9	2	is	be	AUX
ejpam-5025	9	3	known	know	VERB
ejpam-5025	9	4	that	that	SCONJ
ejpam-5025	9	5	boolean	boolean	ADJ
ejpam-5025	9	6	algebra	algebra	NOUN
ejpam-5025	9	7	was	be	AUX
ejpam-5025	9	8	developed	develop	VERB
ejpam-5025	9	9	from	from	ADP
ejpam-5025	9	10	boolean	boolean	ADJ
ejpam-5025	9	11	logic	logic	NOUN
ejpam-5025	9	12	and	and	CCONJ
ejpam-5025	9	13	similarly	similarly	ADV
ejpam-5025	9	14	,	,	PUNCT
ejpam-5025	9	15	bci	bci	PROPN
ejpam-5025	9	16	−	−	PROPN
ejpam-5025	9	17	algebra	algebra	NOUN
ejpam-5025	9	18	was	be	AUX
ejpam-5025	9	19	developed	develop	VERB
ejpam-5025	9	20	from	from	ADP
ejpam-5025	9	21	bci	bci	PROPN
ejpam-5025	9	22	−	−	PROPN
ejpam-5025	9	23	logic	logic	NOUN
ejpam-5025	9	24	.	.	PUNCT
ejpam-5025	10	1	an	an	DET
ejpam-5025	10	2	algebric	algebric	ADJ
ejpam-5025	10	3	structures	structure	NOUN
ejpam-5025	10	4	bck	bck	VERB
ejpam-5025	10	5	−	−	PROPN
ejpam-5025	10	6	algebras	algebra	NOUN
ejpam-5025	10	7	and	and	CCONJ
ejpam-5025	10	8	bci	bci	PROPN
ejpam-5025	10	9	−	−	PROPN
ejpam-5025	10	10	algebras	algebras	PROPN
ejpam-5025	10	11	introduced	introduce	VERB
ejpam-5025	10	12	by	by	ADP
ejpam-5025	10	13	imai.y	imai.y	PROPN
ejpam-5025	10	14	and	and	CCONJ
ejpam-5025	10	15	iseki	iseki	PROPN
ejpam-5025	10	16	.	.	PUNCT
ejpam-5025	11	1	k	k	PROPN
ejpam-5025	11	2	(	(	PUNCT
ejpam-5025	11	3	see	see	VERB
ejpam-5025	11	4	[	[	X
ejpam-5025	11	5	12	12	NUM
ejpam-5025	11	6	]	]	PUNCT
ejpam-5025	11	7	,	,	PUNCT
ejpam-5025	11	8	[	[	X
ejpam-5025	11	9	11	11	NUM
ejpam-5025	11	10	]	]	PUNCT
ejpam-5025	11	11	)	)	PUNCT
ejpam-5025	11	12	and	and	CCONJ
ejpam-5025	11	13	have	have	AUX
ejpam-5025	11	14	been	be	AUX
ejpam-5025	11	15	extensively	extensively	ADV
ejpam-5025	11	16	investigated	investigate	VERB
ejpam-5025	11	17	by	by	ADP
ejpam-5025	11	18	many	many	ADJ
ejpam-5025	11	19	researchers	researcher	NOUN
ejpam-5025	11	20	.	.	PUNCT
ejpam-5025	12	1	it	it	PRON
ejpam-5025	12	2	is	be	AUX
ejpam-5025	12	3	shown	show	VERB
ejpam-5025	12	4	that	that	SCONJ
ejpam-5025	12	5	the	the	DET
ejpam-5025	12	6	notion	notion	NOUN
ejpam-5025	12	7	of	of	ADP
ejpam-5025	12	8	bck−algebra	bck−algebra	PROPN
ejpam-5025	12	9	is	be	AUX
ejpam-5025	12	10	a	a	DET
ejpam-5025	12	11	generalization	generalization	NOUN
ejpam-5025	12	12	of	of	ADP
ejpam-5025	12	13	bck−algebra	bck−algebra	PROPN
ejpam-5025	12	14	.	.	PUNCT
ejpam-5025	13	1	that	that	PRON
ejpam-5025	13	2	is	is	ADV
ejpam-5025	13	3	,	,	PUNCT
ejpam-5025	13	4	every	every	DET
ejpam-5025	13	5	bck	bck	NOUN
ejpam-5025	13	6	−	−	PROPN
ejpam-5025	13	7	algebra	algebra	NOUN
ejpam-5025	13	8	is	be	AUX
ejpam-5025	13	9	a	a	DET
ejpam-5025	13	10	bci	bci	NOUN
ejpam-5025	13	11	−	−	PROPN
ejpam-5025	13	12	algebra	algebra	NOUN
ejpam-5025	13	13	,	,	PUNCT
ejpam-5025	13	14	but	but	CCONJ
ejpam-5025	13	15	the	the	DET
ejpam-5025	13	16	converse	converse	NOUN
ejpam-5025	13	17	is	be	AUX
ejpam-5025	13	18	not	not	PART
ejpam-5025	13	19	true	true	ADJ
ejpam-5025	13	20	.	.	PUNCT
ejpam-5025	14	1	the	the	DET
ejpam-5025	14	2	concept	concept	NOUN
ejpam-5025	14	3	of	of	ADP
ejpam-5025	14	4	d	d	NOUN
ejpam-5025	14	5	−	−	PROPN
ejpam-5025	14	6	algebra	algebra	NOUN
ejpam-5025	14	7	introduced	introduce	VERB
ejpam-5025	14	8	in	in	ADP
ejpam-5025	14	9	[	[	X
ejpam-5025	14	10	20	20	NUM
ejpam-5025	14	11	]	]	PUNCT
ejpam-5025	14	12	,	,	PUNCT
ejpam-5025	14	13	[	[	X
ejpam-5025	14	14	19	19	NUM
ejpam-5025	14	15	]	]	PUNCT
ejpam-5025	14	16	which	which	PRON
ejpam-5025	14	17	is	be	AUX
ejpam-5025	14	18	one	one	NUM
ejpam-5025	14	19	of	of	ADP
ejpam-5025	14	20	the	the	DET
ejpam-5025	14	21	generalization	generalization	NOUN
ejpam-5025	14	22	of	of	ADP
ejpam-5025	14	23	bck−algebras	bck−algebras	PROPN
ejpam-5025	14	24	.	.	PUNCT
ejpam-5025	15	1	then	then	ADV
ejpam-5025	15	2	they	they	PRON
ejpam-5025	15	3	investigated	investigate	VERB
ejpam-5025	15	4	some	some	DET
ejpam-5025	15	5	interesting	interesting	ADJ
ejpam-5025	15	6	relations	relation	NOUN
ejpam-5025	15	7	between	between	ADP
ejpam-5025	15	8	bck	bck	PROPN
ejpam-5025	15	9	−	−	PROPN
ejpam-5025	15	10	algebras	algebra	NOUN
ejpam-5025	15	11	and	and	CCONJ
ejpam-5025	15	12	d−algebras	d−algebras	PROPN
ejpam-5025	15	13	,	,	PUNCT
ejpam-5025	15	14	they	they	PRON
ejpam-5025	15	15	also	also	ADV
ejpam-5025	15	16	studied	study	VERB
ejpam-5025	15	17	ideal	ideal	ADJ
ejpam-5025	15	18	theory	theory	NOUN
ejpam-5025	15	19	in	in	ADP
ejpam-5025	15	20	d−algebras	d−algebras	PUNCT
ejpam-5025	15	21	and	and	CCONJ
ejpam-5025	15	22	introduced	introduce	VERB
ejpam-5025	15	23	the	the	DET
ejpam-5025	15	24	notion	notion	NOUN
ejpam-5025	15	25	of	of	ADP
ejpam-5025	15	26	d−ideal	d−ideal	PROPN
ejpam-5025	15	27	and	and	CCONJ
ejpam-5025	15	28	investigated	investigate	VERB
ejpam-5025	15	29	some	some	DET
ejpam-5025	15	30	relations	relation	NOUN
ejpam-5025	15	31	among	among	ADP
ejpam-5025	15	32	them	they	PRON
ejpam-5025	15	33	.	.	PUNCT
ejpam-5025	16	1	the	the	DET
ejpam-5025	16	2	concept	concept	NOUN
ejpam-5025	16	3	of	of	ADP
ejpam-5025	16	4	derivation	derivation	NOUN
ejpam-5025	16	5	on	on	ADP
ejpam-5025	16	6	a	a	DET
ejpam-5025	16	7	ring	ring	NOUN
ejpam-5025	16	8	r	r	NOUN
ejpam-5025	16	9	is	be	AUX
ejpam-5025	16	10	defined	define	VERB
ejpam-5025	16	11	as	as	ADP
ejpam-5025	16	12	an	an	DET
ejpam-5025	16	13	additive	additive	ADJ
ejpam-5025	16	14	map	map	NOUN
ejpam-5025	17	1	d	d	NOUN
ejpam-5025	17	2	:	:	PUNCT
ejpam-5025	17	3	r	r	NOUN
ejpam-5025	17	4	−→	−→	NOUN
ejpam-5025	17	5	r	r	NOUN
ejpam-5025	17	6	satisfying	satisfy	VERB
ejpam-5025	17	7	the	the	DET
ejpam-5025	17	8	condition	condition	NOUN
ejpam-5025	17	9	d(ab	d(ab	NOUN
ejpam-5025	17	10	)	)	PUNCT
ejpam-5025	17	11	=	=	SYM
ejpam-5025	17	12	d(a)b+ad(b	d(a)b+ad(b	PROPN
ejpam-5025	17	13	)	)	PUNCT
ejpam-5025	17	14	∀	∀	NOUN
ejpam-5025	17	15	a	a	PRON
ejpam-5025	17	16	,	,	PUNCT
ejpam-5025	17	17	b	b	X
ejpam-5025	17	18	∈	∈	PROPN
ejpam-5025	17	19	r.	r.	NOUN
ejpam-5025	17	20	the	the	DET
ejpam-5025	17	21	notion	notion	NOUN
ejpam-5025	17	22	of	of	ADP
ejpam-5025	17	23	reverse	reverse	ADJ
ejpam-5025	17	24	derivations	derivation	NOUN
ejpam-5025	17	25	on	on	ADP
ejpam-5025	17	26	a	a	DET
ejpam-5025	17	27	ring	ring	NOUN
ejpam-5025	17	28	r	r	NOUN
ejpam-5025	17	29	introduced	introduce	VERB
ejpam-5025	17	30	in	in	ADP
ejpam-5025	17	31	a	a	DET
ejpam-5025	17	32	paper	paper	NOUN
ejpam-5025	17	33	[	[	X
ejpam-5025	17	34	8	8	NUM
ejpam-5025	17	35	]	]	PUNCT
ejpam-5025	17	36	of	of	ADP
ejpam-5025	17	37	herstein	herstein	NOUN
ejpam-5025	17	38	as	as	ADP
ejpam-5025	17	39	a	a	DET
ejpam-5025	17	40	map	map	NOUN
ejpam-5025	18	1	d	d	X
ejpam-5025	18	2	:	:	PUNCT
ejpam-5025	18	3	r	r	AUX
ejpam-5025	18	4	−→	−→	NOUN
ejpam-5025	18	5	r	r	NOUN
ejpam-5025	18	6	satisfying	satisfy	VERB
ejpam-5025	18	7	the	the	DET
ejpam-5025	18	8	condition	condition	NOUN
ejpam-5025	18	9	d(ab	d(ab	NOUN
ejpam-5025	18	10	)	)	PUNCT
ejpam-5025	18	11	=	=	SYM
ejpam-5025	18	12	d(b)a+	d(b)a+	NOUN
ejpam-5025	18	13	bd(a	bd(a	X
ejpam-5025	18	14	)	)	PUNCT
ejpam-5025	18	15	∀	∀	X
ejpam-5025	19	1	a	a	PRON
ejpam-5025	19	2	,	,	PUNCT
ejpam-5025	19	3	b	b	X
ejpam-5025	19	4	∈	∈	NOUN
ejpam-5025	19	5	r	r	NOUN
ejpam-5025	19	6	(	(	PUNCT
ejpam-5025	19	7	and	and	CCONJ
ejpam-5025	19	8	in	in	ADP
ejpam-5025	19	9	the	the	DET
ejpam-5025	19	10	case	case	NOUN
ejpam-5025	19	11	of	of	ADP
ejpam-5025	19	12	lie	lie	NOUN
ejpam-5025	19	13	algebras	algebras	PROPN
ejpam-5025	19	14	book	book	PROPN
ejpam-5025	19	15	of	of	ADP
ejpam-5025	19	16	jacobson	jacobson	PROPN
ejpam-5025	19	17	doi	doi	PROPN
ejpam-5025	19	18	:	:	PUNCT
ejpam-5025	19	19	https://doi.org/10.29020/nybg.ejpam.v17i1.5025	https://doi.org/10.29020/nybg.ejpam.v17i1.5025	ADJ
ejpam-5025	19	20	email	email	NOUN
ejpam-5025	19	21	address	address	NOUN
ejpam-5025	19	22	:	:	PUNCT
ejpam-5025	19	23	knefaie@taibahu.edu.sa	knefaie@taibahu.edu.sa	PROPN
ejpam-5025	19	24	(	(	PUNCT
ejpam-5025	19	25	k.	k.	PROPN
ejpam-5025	19	26	alnefaie	alnefaie	PROPN
ejpam-5025	19	27	)	)	PUNCT
ejpam-5025	19	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5025	20	1	362	362	NUM
ejpam-5025	20	2	©	©	ADP
ejpam-5025	20	3	2024	2024	NUM
ejpam-5025	20	4	ejpam	ejpam	NOUN
ejpam-5025	20	5	all	all	DET
ejpam-5025	20	6	rights	right	NOUN
ejpam-5025	20	7	reserved	reserve	VERB
ejpam-5025	20	8	.	.	PUNCT
ejpam-5025	21	1	k.	k.	PROPN
ejpam-5025	21	2	alnefaie	alnefaie	PROPN
ejpam-5025	21	3	/	/	SYM
ejpam-5025	21	4	eur	eur	PROPN
ejpam-5025	21	5	.	.	PUNCT
ejpam-5025	22	1	j.	j.	PROPN
ejpam-5025	22	2	pure	pure	PROPN
ejpam-5025	22	3	appl	appl	PROPN
ejpam-5025	22	4	.	.	PROPN
ejpam-5025	22	5	math	math	PROPN
ejpam-5025	22	6	,	,	PUNCT
ejpam-5025	22	7	17	17	NUM
ejpam-5025	22	8	(	(	PUNCT
ejpam-5025	22	9	1	1	NUM
ejpam-5025	22	10	)	)	PUNCT
ejpam-5025	22	11	(	(	PUNCT
ejpam-5025	22	12	2024	2024	NUM
ejpam-5025	22	13	)	)	PUNCT
ejpam-5025	22	14	,	,	PUNCT
ejpam-5025	22	15	362	362	NUM
ejpam-5025	22	16	-	-	SYM
ejpam-5025	22	17	371	371	NUM
ejpam-5025	22	18	363	363	NUM
ejpam-5025	22	19	[	[	SYM
ejpam-5025	22	20	13	13	NUM
ejpam-5025	22	21	]	]	NUM
ejpam-5025	22	22	)	)	PUNCT
ejpam-5025	22	23	.	.	PUNCT
ejpam-5025	23	1	the	the	DET
ejpam-5025	23	2	case	case	NOUN
ejpam-5025	23	3	of	of	ADP
ejpam-5025	23	4	lie	lie	NOUN
ejpam-5025	23	5	algebras	algebras	NOUN
ejpam-5025	23	6	is	be	AUX
ejpam-5025	23	7	very	very	ADV
ejpam-5025	23	8	important	important	ADJ
ejpam-5025	23	9	because	because	SCONJ
ejpam-5025	23	10	the	the	DET
ejpam-5025	23	11	definition	definition	NOUN
ejpam-5025	23	12	of	of	ADP
ejpam-5025	23	13	reverse	reverse	ADJ
ejpam-5025	23	14	derivations	derivation	NOUN
ejpam-5025	23	15	coincides	coincide	VERB
ejpam-5025	23	16	with	with	ADP
ejpam-5025	23	17	the	the	DET
ejpam-5025	23	18	notion	notion	NOUN
ejpam-5025	23	19	of	of	ADP
ejpam-5025	23	20	antiderivations	antiderivation	NOUN
ejpam-5025	23	21	(	(	PUNCT
ejpam-5025	23	22	about	about	ADP
ejpam-5025	23	23	reverse	reverse	ADJ
ejpam-5025	23	24	derivations	derivation	NOUN
ejpam-5025	23	25	of	of	ADP
ejpam-5025	23	26	algebras	algebra	NOUN
ejpam-5025	23	27	and	and	CCONJ
ejpam-5025	23	28	superalgebras	superalgebra	NOUN
ejpam-5025	23	29	see	see	VERB
ejpam-5025	23	30	,	,	PUNCT
ejpam-5025	23	31	[	[	X
ejpam-5025	23	32	7	7	NUM
ejpam-5025	23	33	]	]	PUNCT
ejpam-5025	23	34	,	,	PUNCT
ejpam-5025	23	35	[	[	X
ejpam-5025	23	36	9	9	NUM
ejpam-5025	23	37	]	]	PUNCT
ejpam-5025	23	38	and	and	CCONJ
ejpam-5025	23	39	[	[	X
ejpam-5025	23	40	15	15	NUM
ejpam-5025	23	41	]	]	NUM
ejpam-5025	23	42	)	)	PUNCT
ejpam-5025	23	43	,	,	PUNCT
ejpam-5025	23	44	also	also	ADV
ejpam-5025	23	45	we	we	PRON
ejpam-5025	23	46	can	can	AUX
ejpam-5025	23	47	see	see	VERB
ejpam-5025	23	48	that	that	SCONJ
ejpam-5025	23	49	the	the	DET
ejpam-5025	23	50	reverse	reverse	ADJ
ejpam-5025	23	51	derivations	derivation	NOUN
ejpam-5025	23	52	are	be	AUX
ejpam-5025	23	53	a	a	DET
ejpam-5025	23	54	particular	particular	ADJ
ejpam-5025	23	55	case	case	NOUN
ejpam-5025	23	56	of	of	ADP
ejpam-5025	23	57	jordan	jordan	PROPN
ejpam-5025	23	58	derivations	derivations	PROPN
ejpam-5025	23	59	.	.	PUNCT
ejpam-5025	24	1	in	in	ADP
ejpam-5025	24	2	the	the	DET
ejpam-5025	24	3	same	same	ADJ
ejpam-5025	24	4	way	way	NOUN
ejpam-5025	24	5	,	,	PUNCT
ejpam-5025	24	6	many	many	ADJ
ejpam-5025	24	7	researchers	researcher	NOUN
ejpam-5025	24	8	have	have	AUX
ejpam-5025	24	9	studied	study	VERB
ejpam-5025	24	10	the	the	DET
ejpam-5025	24	11	reverse	reverse	ADJ
ejpam-5025	24	12	derivation	derivation	NOUN
ejpam-5025	24	13	on	on	ADP
ejpam-5025	24	14	different	different	ADJ
ejpam-5025	24	15	types	type	NOUN
ejpam-5025	24	16	of	of	ADP
ejpam-5025	24	17	algebraic	algebraic	ADJ
ejpam-5025	24	18	structures	structure	NOUN
ejpam-5025	24	19	,	,	PUNCT
ejpam-5025	24	20	such	such	ADJ
ejpam-5025	24	21	as	as	ADP
ejpam-5025	24	22	the	the	DET
ejpam-5025	24	23	prime	prime	ADJ
ejpam-5025	24	24	ring	ring	NOUN
ejpam-5025	24	25	,	,	PUNCT
ejpam-5025	24	26	semiprime	semiprime	NOUN
ejpam-5025	24	27	rings	ring	NOUN
ejpam-5025	24	28	and	and	CCONJ
ejpam-5025	24	29	associative	associative	ADJ
ejpam-5025	24	30	algebras	algebra	NOUN
ejpam-5025	24	31	.	.	PUNCT
ejpam-5025	25	1	(	(	PUNCT
ejpam-5025	25	2	for	for	ADP
ejpam-5025	25	3	more	more	ADJ
ejpam-5025	25	4	details	detail	NOUN
ejpam-5025	25	5	,	,	PUNCT
ejpam-5025	25	6	see	see	VERB
ejpam-5025	25	7	[	[	X
ejpam-5025	25	8	1	1	NUM
ejpam-5025	25	9	]	]	PUNCT
ejpam-5025	25	10	,	,	PUNCT
ejpam-5025	25	11	[	[	X
ejpam-5025	25	12	10	10	NUM
ejpam-5025	25	13	]	]	PUNCT
ejpam-5025	25	14	,	,	PUNCT
ejpam-5025	25	15	[	[	X
ejpam-5025	25	16	5	5	NUM
ejpam-5025	25	17	]	]	PUNCT
ejpam-5025	25	18	,	,	PUNCT
ejpam-5025	25	19	[	[	X
ejpam-5025	25	20	21	21	NUM
ejpam-5025	25	21	]	]	PUNCT
ejpam-5025	25	22	and	and	CCONJ
ejpam-5025	25	23	[	[	X
ejpam-5025	25	24	16	16	NUM
ejpam-5025	25	25	]	]	PUNCT
ejpam-5025	25	26	)	)	PUNCT
ejpam-5025	25	27	in	in	ADP
ejpam-5025	25	28	[	[	X
ejpam-5025	25	29	14	14	NUM
ejpam-5025	25	30	]	]	PUNCT
ejpam-5025	25	31	,	,	PUNCT
ejpam-5025	25	32	the	the	DET
ejpam-5025	25	33	notion	notion	NOUN
ejpam-5025	25	34	of	of	ADP
ejpam-5025	25	35	derivation	derivation	NOUN
ejpam-5025	25	36	in	in	ADP
ejpam-5025	25	37	rings	ring	NOUN
ejpam-5025	25	38	and	and	CCONJ
ejpam-5025	25	39	near	near	ADJ
ejpam-5025	25	40	rings	ring	NOUN
ejpam-5025	25	41	theory	theory	NOUN
ejpam-5025	25	42	applied	apply	VERB
ejpam-5025	25	43	to	to	ADP
ejpam-5025	25	44	bci−	bci−	PROPN
ejpam-5025	25	45	algebras	algebras	PROPN
ejpam-5025	25	46	also	also	ADV
ejpam-5025	25	47	the	the	DET
ejpam-5025	25	48	notion	notion	NOUN
ejpam-5025	25	49	called	call	VERB
ejpam-5025	25	50	a	a	DET
ejpam-5025	25	51	regular	regular	ADJ
ejpam-5025	25	52	derivation	derivation	NOUN
ejpam-5025	25	53	in	in	ADP
ejpam-5025	25	54	bci−	bci−	PROPN
ejpam-5025	25	55	algebras	algebras	PROPN
ejpam-5025	25	56	introduced	introduce	VERB
ejpam-5025	25	57	by	by	ADP
ejpam-5025	25	58	them	they	PRON
ejpam-5025	25	59	,	,	PUNCT
ejpam-5025	25	60	and	and	CCONJ
ejpam-5025	25	61	discussed	discuss	VERB
ejpam-5025	25	62	some	some	PRON
ejpam-5025	25	63	of	of	ADP
ejpam-5025	25	64	its	its	PRON
ejpam-5025	25	65	properties	property	NOUN
ejpam-5025	25	66	,	,	PUNCT
ejpam-5025	25	67	defined	define	VERB
ejpam-5025	25	68	a	a	DET
ejpam-5025	25	69	d−	d−	PROPN
ejpam-5025	25	70	invariant	invariant	ADJ
ejpam-5025	25	71	ideal	ideal	NOUN
ejpam-5025	25	72	,	,	PUNCT
ejpam-5025	25	73	also	also	ADV
ejpam-5025	25	74	they	they	PRON
ejpam-5025	25	75	gave	give	VERB
ejpam-5025	25	76	conditions	condition	NOUN
ejpam-5025	25	77	for	for	ADP
ejpam-5025	25	78	an	an	DET
ejpam-5025	25	79	ideal	ideal	NOUN
ejpam-5025	25	80	to	to	PART
ejpam-5025	25	81	be	be	AUX
ejpam-5025	25	82	d−invariant	d−invariant	ADJ
ejpam-5025	25	83	.	.	PUNCT
ejpam-5025	26	1	the	the	DET
ejpam-5025	26	2	concept	concept	NOUN
ejpam-5025	26	3	of	of	ADP
ejpam-5025	26	4	derivations	derivation	NOUN
ejpam-5025	26	5	in	in	ADP
ejpam-5025	26	6	non	non	ADJ
ejpam-5025	26	7	-	-	ADJ
ejpam-5025	26	8	commutative	commutative	ADJ
ejpam-5025	26	9	rings	ring	NOUN
ejpam-5025	26	10	extended	extend	VERB
ejpam-5025	26	11	to	to	ADP
ejpam-5025	26	12	left	left	ADJ
ejpam-5025	26	13	derivations	derivation	NOUN
ejpam-5025	26	14	,	,	PUNCT
ejpam-5025	26	15	central	central	ADJ
ejpam-5025	26	16	derivations	derivation	NOUN
ejpam-5025	26	17	and	and	CCONJ
ejpam-5025	26	18	d−derivations	d−derivation	NOUN
ejpam-5025	26	19	.	.	PUNCT
ejpam-5025	27	1	several	several	ADJ
ejpam-5025	27	2	authors	author	NOUN
ejpam-5025	27	3	,	,	PUNCT
ejpam-5025	27	4	(	(	PUNCT
ejpam-5025	27	5	for	for	ADP
ejpam-5025	27	6	example	example	NOUN
ejpam-5025	27	7	,	,	PUNCT
ejpam-5025	27	8	you	you	PRON
ejpam-5025	27	9	can	can	AUX
ejpam-5025	27	10	refer	refer	VERB
ejpam-5025	27	11	to	to	ADP
ejpam-5025	27	12	[	[	X
ejpam-5025	27	13	6	6	NUM
ejpam-5025	27	14	]	]	PUNCT
ejpam-5025	27	15	,	,	PUNCT
ejpam-5025	27	16	[	[	X
ejpam-5025	27	17	18	18	NUM
ejpam-5025	27	18	]	]	PUNCT
ejpam-5025	27	19	and	and	CCONJ
ejpam-5025	27	20	[	[	X
ejpam-5025	27	21	17	17	NUM
ejpam-5025	27	22	]	]	PUNCT
ejpam-5025	27	23	)	)	PUNCT
ejpam-5025	27	24	have	have	AUX
ejpam-5025	27	25	studied	study	VERB
ejpam-5025	27	26	derivations	derivation	NOUN
ejpam-5025	27	27	in	in	ADP
ejpam-5025	27	28	d	d	PROPN
ejpam-5025	27	29	and	and	CCONJ
ejpam-5025	27	30	bci−algebras	bci−algebras	PROPN
ejpam-5025	27	31	.	.	PUNCT
ejpam-5025	28	1	recently	recently	ADV
ejpam-5025	28	2	,	,	PUNCT
ejpam-5025	28	3	al	al	PROPN
ejpam-5025	28	4	-	-	PUNCT
ejpam-5025	28	5	omary	omary	PROPN
ejpam-5025	28	6	rm	rm	NOUN
ejpam-5025	28	7	(	(	PUNCT
ejpam-5025	28	8	[	[	X
ejpam-5025	28	9	2	2	NUM
ejpam-5025	28	10	]	]	PUNCT
ejpam-5025	28	11	)	)	PUNCT
ejpam-5025	28	12	introduced	introduce	VERB
ejpam-5025	28	13	the	the	DET
ejpam-5025	28	14	notion	notion	NOUN
ejpam-5025	28	15	of	of	ADP
ejpam-5025	28	16	(	(	PUNCT
ejpam-5025	28	17	α	α	X
ejpam-5025	28	18	,	,	PUNCT
ejpam-5025	28	19	β)−derivations	β)−derivation	NOUN
ejpam-5025	28	20	of	of	ADP
ejpam-5025	28	21	d−algebras	d−algebras	PROPN
ejpam-5025	28	22	and	and	CCONJ
ejpam-5025	28	23	obtained	obtain	VERB
ejpam-5025	28	24	some	some	DET
ejpam-5025	28	25	properties	property	NOUN
ejpam-5025	28	26	.	.	PUNCT
ejpam-5025	29	1	very	very	ADV
ejpam-5025	29	2	recently	recently	ADV
ejpam-5025	29	3	,	,	PUNCT
ejpam-5025	29	4	aslıhan	aslıhan	PROPN
ejpam-5025	29	5	s	s	PROPN
ejpam-5025	29	6	,	,	PUNCT
ejpam-5025	29	7	damla	damla	NOUN
ejpam-5025	29	8	y	y	NOUN
ejpam-5025	29	9	(	(	PUNCT
ejpam-5025	30	1	[	[	X
ejpam-5025	30	2	4	4	NUM
ejpam-5025	30	3	]	]	PUNCT
ejpam-5025	30	4	)	)	PUNCT
ejpam-5025	30	5	discussed	discuss	VERB
ejpam-5025	30	6	the	the	DET
ejpam-5025	30	7	concept	concept	NOUN
ejpam-5025	30	8	of	of	ADP
ejpam-5025	30	9	generalized	generalized	ADJ
ejpam-5025	30	10	(	(	PUNCT
ejpam-5025	30	11	α	α	NOUN
ejpam-5025	30	12	,	,	PUNCT
ejpam-5025	30	13	β)−derivations	β)−derivation	NOUN
ejpam-5025	30	14	of	of	ADP
ejpam-5025	30	15	d−algebras	d−algebras	PROPN
ejpam-5025	30	16	and	and	CCONJ
ejpam-5025	30	17	studied	study	VERB
ejpam-5025	30	18	some	some	PRON
ejpam-5025	30	19	of	of	ADP
ejpam-5025	30	20	it	it	PRON
ejpam-5025	30	21	is	be	AUX
ejpam-5025	30	22	properties	property	NOUN
ejpam-5025	30	23	.	.	PUNCT
ejpam-5025	31	1	motivated	motivate	VERB
ejpam-5025	31	2	by	by	ADP
ejpam-5025	31	3	the	the	DET
ejpam-5025	31	4	previous	previous	ADJ
ejpam-5025	31	5	results	result	NOUN
ejpam-5025	31	6	,	,	PUNCT
ejpam-5025	31	7	it	it	PRON
ejpam-5025	31	8	is	be	AUX
ejpam-5025	31	9	natural	natural	ADJ
ejpam-5025	31	10	to	to	PART
ejpam-5025	31	11	ask	ask	VERB
ejpam-5025	31	12	whether	whether	SCONJ
ejpam-5025	31	13	it	it	PRON
ejpam-5025	31	14	is	be	AUX
ejpam-5025	31	15	possible	possible	ADJ
ejpam-5025	31	16	to	to	PART
ejpam-5025	31	17	define	define	VERB
ejpam-5025	31	18	a	a	DET
ejpam-5025	31	19	reverse	reverse	ADJ
ejpam-5025	31	20	derivation	derivation	NOUN
ejpam-5025	31	21	on	on	ADP
ejpam-5025	31	22	d−algebra	d−algebra	X
ejpam-5025	31	23	x	x	X
ejpam-5025	31	24	.	.	PUNCT
ejpam-5025	32	1	the	the	DET
ejpam-5025	32	2	aim	aim	NOUN
ejpam-5025	32	3	of	of	ADP
ejpam-5025	32	4	this	this	DET
ejpam-5025	32	5	paper	paper	NOUN
ejpam-5025	32	6	is	be	AUX
ejpam-5025	32	7	to	to	PART
ejpam-5025	32	8	introduce	introduce	VERB
ejpam-5025	32	9	the	the	DET
ejpam-5025	32	10	concept	concept	NOUN
ejpam-5025	32	11	of	of	ADP
ejpam-5025	32	12	left	left	ADJ
ejpam-5025	32	13	-	-	PUNCT
ejpam-5025	32	14	right	right	NOUN
ejpam-5025	32	15	(	(	PUNCT
ejpam-5025	32	16	resp	resp	NOUN
ejpam-5025	32	17	.	.	PUNCT
ejpam-5025	33	1	right	right	ADJ
ejpam-5025	33	2	-	-	PUNCT
ejpam-5025	33	3	left	left	ADJ
ejpam-5025	33	4	)	)	PUNCT
ejpam-5025	33	5	reverse	reverse	ADJ
ejpam-5025	33	6	derivations	derivation	NOUN
ejpam-5025	33	7	of	of	ADP
ejpam-5025	33	8	d−algebra	d−algebra	NOUN
ejpam-5025	33	9	x	x	INTJ
ejpam-5025	33	10	(	(	PUNCT
ejpam-5025	33	11	briefly	briefly	ADV
ejpam-5025	33	12	,	,	PUNCT
ejpam-5025	33	13	(	(	PUNCT
ejpam-5025	33	14	l	l	NOUN
ejpam-5025	33	15	,	,	PUNCT
ejpam-5025	33	16	r	r	NOUN
ejpam-5025	33	17	)	)	PUNCT
ejpam-5025	33	18	resp	resp	NOUN
ejpam-5025	33	19	.	.	PUNCT
ejpam-5025	34	1	(	(	PUNCT
ejpam-5025	34	2	r	r	X
ejpam-5025	34	3	,	,	PUNCT
ejpam-5025	34	4	l)−	l)−	PROPN
ejpam-5025	34	5	reverse	reverse	VERB
ejpam-5025	34	6	derivation	derivation	NOUN
ejpam-5025	34	7	of	of	ADP
ejpam-5025	34	8	d−algebra	d−algebra	NOUN
ejpam-5025	34	9	)	)	PUNCT
ejpam-5025	34	10	and	and	CCONJ
ejpam-5025	34	11	investigate	investigate	VERB
ejpam-5025	34	12	some	some	PRON
ejpam-5025	34	13	of	of	ADP
ejpam-5025	34	14	it	it	PRON
ejpam-5025	34	15	is	be	AUX
ejpam-5025	34	16	properties	property	NOUN
ejpam-5025	34	17	.	.	PUNCT
ejpam-5025	35	1	we	we	PRON
ejpam-5025	35	2	discuss	discuss	VERB
ejpam-5025	35	3	some	some	DET
ejpam-5025	35	4	properties	property	NOUN
ejpam-5025	35	5	regarding	regard	VERB
ejpam-5025	35	6	the	the	DET
ejpam-5025	35	7	regular	regular	ADJ
ejpam-5025	35	8	,	,	PUNCT
ejpam-5025	35	9	composition	composition	NOUN
ejpam-5025	35	10	of	of	ADP
ejpam-5025	35	11	two	two	NUM
ejpam-5025	35	12	maps	map	NOUN
ejpam-5025	35	13	,	,	PUNCT
ejpam-5025	35	14	edge	edge	NOUN
ejpam-5025	35	15	d	d	NOUN
ejpam-5025	35	16	−	−	NOUN
ejpam-5025	35	17	algebra	algebra	NOUN
ejpam-5025	35	18	and	and	CCONJ
ejpam-5025	35	19	reverse	reverse	ADJ
ejpam-5025	35	20	derivation	derivation	NOUN
ejpam-5025	35	21	on	on	ADP
ejpam-5025	35	22	d	d	NOUN
ejpam-5025	35	23	−	−	PROPN
ejpam-5025	35	24	algebra	algebra	NOUN
ejpam-5025	35	25	.	.	PUNCT
ejpam-5025	36	1	furthermore	furthermore	ADV
ejpam-5025	36	2	,	,	PUNCT
ejpam-5025	36	3	some	some	DET
ejpam-5025	36	4	illustrative	illustrative	ADJ
ejpam-5025	36	5	examples	example	NOUN
ejpam-5025	36	6	of	of	ADP
ejpam-5025	36	7	what	what	PRON
ejpam-5025	36	8	we	we	PRON
ejpam-5025	36	9	studied	study	VERB
ejpam-5025	36	10	were	be	AUX
ejpam-5025	36	11	given	give	VERB
ejpam-5025	36	12	.	.	PUNCT
ejpam-5025	37	1	2	2	X
ejpam-5025	37	2	.	.	X
ejpam-5025	37	3	elementaries	elementarie	NOUN
ejpam-5025	37	4	here	here	ADV
ejpam-5025	37	5	,	,	PUNCT
ejpam-5025	37	6	we	we	PRON
ejpam-5025	37	7	will	will	AUX
ejpam-5025	37	8	repeat	repeat	VERB
ejpam-5025	37	9	some	some	DET
ejpam-5025	37	10	basic	basic	ADJ
ejpam-5025	37	11	properties	property	NOUN
ejpam-5025	37	12	and	and	CCONJ
ejpam-5025	37	13	lemmas	lemma	VERB
ejpam-5025	37	14	in	in	ADP
ejpam-5025	37	15	d−algebra	d−algebra	NOUN
ejpam-5025	37	16	which	which	PRON
ejpam-5025	37	17	are	be	AUX
ejpam-5025	37	18	usefull	usefull	ADJ
ejpam-5025	37	19	for	for	ADP
ejpam-5025	37	20	developing	develop	VERB
ejpam-5025	37	21	the	the	DET
ejpam-5025	37	22	proof	proof	NOUN
ejpam-5025	37	23	of	of	ADP
ejpam-5025	37	24	our	our	PRON
ejpam-5025	37	25	results	result	NOUN
ejpam-5025	37	26	.	.	PUNCT
ejpam-5025	38	1	definitions	definition	NOUN
ejpam-5025	38	2	1	1	NUM
ejpam-5025	38	3	,	,	PUNCT
ejpam-5025	38	4	2	2	NUM
ejpam-5025	38	5	and	and	CCONJ
ejpam-5025	38	6	the	the	DET
ejpam-5025	38	7	proofs	proof	NOUN
ejpam-5025	38	8	of	of	ADP
ejpam-5025	38	9	lemmas	lemmas	PROPN
ejpam-5025	38	10	1	1	NUM
ejpam-5025	38	11	,	,	PUNCT
ejpam-5025	38	12	2	2	NUM
ejpam-5025	38	13	can	can	AUX
ejpam-5025	38	14	be	be	AUX
ejpam-5025	38	15	seen	see	VERB
ejpam-5025	38	16	in	in	ADP
ejpam-5025	38	17	[	[	X
ejpam-5025	38	18	20	20	NUM
ejpam-5025	38	19	]	]	PUNCT
ejpam-5025	38	20	.	.	PUNCT
ejpam-5025	39	1	definition	definition	NOUN
ejpam-5025	39	2	1	1	NUM
ejpam-5025	39	3	.	.	PUNCT
ejpam-5025	40	1	a	a	DET
ejpam-5025	40	2	set	set	VERB
ejpam-5025	40	3	∅	∅	NOUN
ejpam-5025	40	4	=	=	NOUN
ejpam-5025	40	5	̸	̸	VERB
ejpam-5025	40	6	x	x	PUNCT
ejpam-5025	40	7	with	with	ADP
ejpam-5025	40	8	a	a	DET
ejpam-5025	40	9	constant	constant	ADJ
ejpam-5025	40	10	0	0	NUM
ejpam-5025	40	11	and	and	CCONJ
ejpam-5025	40	12	a	a	DET
ejpam-5025	40	13	binary	binary	ADJ
ejpam-5025	40	14	operation	operation	NOUN
ejpam-5025	40	15	∗	∗	NOUN
ejpam-5025	40	16	is	be	AUX
ejpam-5025	40	17	called	call	VERB
ejpam-5025	40	18	a	a	DET
ejpam-5025	40	19	d−algebra	d−algebra	NOUN
ejpam-5025	40	20	if	if	SCONJ
ejpam-5025	40	21	∗	∗	NOUN
ejpam-5025	40	22	satisfying	satisfy	VERB
ejpam-5025	40	23	the	the	DET
ejpam-5025	40	24	following	follow	VERB
ejpam-5025	40	25	axioms	axiom	NOUN
ejpam-5025	40	26	:	:	PUNCT
ejpam-5025	40	27	∀	∀	PUNCT
ejpam-5025	40	28	x	x	X
ejpam-5025	40	29	,	,	PUNCT
ejpam-5025	40	30	y	y	PROPN
ejpam-5025	40	31	∈	∈	PROPN
ejpam-5025	40	32	x	x	X
ejpam-5025	40	33	,	,	PUNCT
ejpam-5025	40	34	(	(	PUNCT
ejpam-5025	40	35	i	i	NOUN
ejpam-5025	40	36	)	)	PUNCT
ejpam-5025	40	37	x	x	SYM
ejpam-5025	41	1	∗	∗	NOUN
ejpam-5025	41	2	x	x	SYM
ejpam-5025	41	3	=	=	SYM
ejpam-5025	41	4	0	0	NUM
ejpam-5025	41	5	,	,	PUNCT
ejpam-5025	41	6	(	(	PUNCT
ejpam-5025	41	7	ii	ii	NOUN
ejpam-5025	41	8	)	)	PUNCT
ejpam-5025	41	9	0	0	NUM
ejpam-5025	41	10	∗	∗	NOUN
ejpam-5025	41	11	x	x	X
ejpam-5025	41	12	=	=	SYM
ejpam-5025	41	13	0	0	NUM
ejpam-5025	41	14	,	,	PUNCT
ejpam-5025	41	15	(	(	PUNCT
ejpam-5025	41	16	iii	iii	X
ejpam-5025	41	17	)	)	PUNCT
ejpam-5025	41	18	if	if	SCONJ
ejpam-5025	41	19	x	x	PROPN
ejpam-5025	41	20	∗	∗	VERB
ejpam-5025	41	21	y	y	NOUN
ejpam-5025	41	22	=	=	SYM
ejpam-5025	41	23	0	0	PROPN
ejpam-5025	41	24	,	,	PUNCT
ejpam-5025	41	25	y	y	PROPN
ejpam-5025	41	26	∗	∗	NOUN
ejpam-5025	41	27	x	x	PUNCT
ejpam-5025	41	28	=	=	SYM
ejpam-5025	41	29	0	0	NUM
ejpam-5025	41	30	,	,	PUNCT
ejpam-5025	41	31	then	then	ADV
ejpam-5025	41	32	x	x	X
ejpam-5025	41	33	=	=	PUNCT
ejpam-5025	41	34	y.	y.	NOUN
ejpam-5025	41	35	definition	definition	NOUN
ejpam-5025	41	36	2	2	X
ejpam-5025	41	37	.	.	PUNCT
ejpam-5025	42	1	let	let	VERB
ejpam-5025	42	2	(	(	PUNCT
ejpam-5025	42	3	x	x	X
ejpam-5025	42	4	,	,	PUNCT
ejpam-5025	42	5	∗	∗	NOUN
ejpam-5025	42	6	,	,	PUNCT
ejpam-5025	42	7	0	0	NUM
ejpam-5025	42	8	)	)	PUNCT
ejpam-5025	42	9	be	be	AUX
ejpam-5025	42	10	a	a	DET
ejpam-5025	42	11	d−algebra	d−algebra	NOUN
ejpam-5025	42	12	,	,	PUNCT
ejpam-5025	42	13	define	define	NOUN
ejpam-5025	42	14	x	x	X
ejpam-5025	42	15	∗	∗	NOUN
ejpam-5025	42	16	x	x	X
ejpam-5025	42	17	=	=	PRON
ejpam-5025	42	18	{	{	PUNCT
ejpam-5025	42	19	x	x	SYM
ejpam-5025	42	20	∗	∗	NOUN
ejpam-5025	42	21	a	a	DET
ejpam-5025	42	22	|	|	NOUN
ejpam-5025	42	23	a	a	DET
ejpam-5025	42	24	∈	∈	NOUN
ejpam-5025	42	25	x	x	NOUN
ejpam-5025	42	26	}	}	PUNCT
ejpam-5025	42	27	.	.	PUNCT
ejpam-5025	43	1	then	then	ADV
ejpam-5025	43	2	x	x	X
ejpam-5025	43	3	is	be	AUX
ejpam-5025	43	4	said	say	VERB
ejpam-5025	43	5	to	to	PART
ejpam-5025	43	6	be	be	AUX
ejpam-5025	43	7	edge	edge	NOUN
ejpam-5025	43	8	d−algebra	d−algebra	NOUN
ejpam-5025	43	9	if	if	SCONJ
ejpam-5025	43	10	∀x	∀x	VERB
ejpam-5025	43	11	∈	∈	PROPN
ejpam-5025	43	12	x	x	X
ejpam-5025	43	13	,	,	PUNCT
ejpam-5025	43	14	x	x	X
ejpam-5025	43	15	∗	∗	NOUN
ejpam-5025	43	16	x	x	X
ejpam-5025	43	17	=	=	SYM
ejpam-5025	43	18	{	{	PUNCT
ejpam-5025	43	19	x	x	NOUN
ejpam-5025	43	20	,	,	PUNCT
ejpam-5025	43	21	0	0	NUM
ejpam-5025	43	22	}	}	PUNCT
ejpam-5025	43	23	.	.	PUNCT
ejpam-5025	44	1	k.	k.	PROPN
ejpam-5025	44	2	alnefaie	alnefaie	PROPN
ejpam-5025	44	3	/	/	SYM
ejpam-5025	44	4	eur	eur	PROPN
ejpam-5025	44	5	.	.	PUNCT
ejpam-5025	45	1	j.	j.	PROPN
ejpam-5025	45	2	pure	pure	PROPN
ejpam-5025	45	3	appl	appl	PROPN
ejpam-5025	45	4	.	.	PROPN
ejpam-5025	45	5	math	math	PROPN
ejpam-5025	45	6	,	,	PUNCT
ejpam-5025	45	7	17	17	NUM
ejpam-5025	45	8	(	(	PUNCT
ejpam-5025	45	9	1	1	NUM
ejpam-5025	45	10	)	)	PUNCT
ejpam-5025	45	11	(	(	PUNCT
ejpam-5025	45	12	2024	2024	NUM
ejpam-5025	45	13	)	)	PUNCT
ejpam-5025	45	14	,	,	PUNCT
ejpam-5025	45	15	362	362	NUM
ejpam-5025	45	16	-	-	SYM
ejpam-5025	45	17	371	371	NUM
ejpam-5025	45	18	364	364	NUM
ejpam-5025	45	19	lemma	lemma	PROPN
ejpam-5025	45	20	1	1	NUM
ejpam-5025	45	21	.	.	PUNCT
ejpam-5025	46	1	in	in	ADP
ejpam-5025	46	2	edge	edge	NOUN
ejpam-5025	46	3	d−algebra	d−algebra	NOUN
ejpam-5025	46	4	(	(	PUNCT
ejpam-5025	46	5	x	x	INTJ
ejpam-5025	46	6	,	,	PUNCT
ejpam-5025	46	7	∗	∗	NOUN
ejpam-5025	46	8	,	,	PUNCT
ejpam-5025	46	9	0	0	NUM
ejpam-5025	46	10	)	)	PUNCT
ejpam-5025	46	11	,	,	PUNCT
ejpam-5025	46	12	the	the	DET
ejpam-5025	46	13	identity	identity	NOUN
ejpam-5025	46	14	x	x	NOUN
ejpam-5025	46	15	∗	∗	NOUN
ejpam-5025	46	16	0	0	NUM
ejpam-5025	47	1	=	=	NOUN
ejpam-5025	47	2	x	x	NOUN
ejpam-5025	47	3	hold	hold	VERB
ejpam-5025	47	4	∀	∀	NOUN
ejpam-5025	47	5	x	x	X
ejpam-5025	47	6	∈	∈	NOUN
ejpam-5025	47	7	x	x	X
ejpam-5025	47	8	.	.	PUNCT
ejpam-5025	48	1	lemma	lemma	PROPN
ejpam-5025	49	1	2	2	X
ejpam-5025	49	2	.	.	PUNCT
ejpam-5025	50	1	if	if	SCONJ
ejpam-5025	50	2	x	x	PRON
ejpam-5025	50	3	is	be	AUX
ejpam-5025	50	4	an	an	DET
ejpam-5025	50	5	edge	edge	NOUN
ejpam-5025	50	6	d−algebra	d−algebra	NOUN
ejpam-5025	50	7	,	,	PUNCT
ejpam-5025	50	8	then	then	ADV
ejpam-5025	50	9	the	the	DET
ejpam-5025	50	10	identity	identity	NOUN
ejpam-5025	50	11	(	(	PUNCT
ejpam-5025	50	12	x∗(x∗y))∗y	x∗(x∗y))∗y	X
ejpam-5025	50	13	=	=	SYM
ejpam-5025	50	14	0	0	NUM
ejpam-5025	50	15	hold	hold	VERB
ejpam-5025	50	16	∀	∀	X
ejpam-5025	50	17	x	x	NOUN
ejpam-5025	50	18	,	,	PUNCT
ejpam-5025	50	19	y	y	PROPN
ejpam-5025	50	20	∈	∈	PROPN
ejpam-5025	50	21	x	x	X
ejpam-5025	50	22	.	.	PUNCT
ejpam-5025	51	1	3	3	X
ejpam-5025	51	2	.	.	X
ejpam-5025	51	3	main	main	ADJ
ejpam-5025	51	4	results	result	NOUN
ejpam-5025	51	5	in	in	ADP
ejpam-5025	51	6	the	the	DET
ejpam-5025	51	7	present	present	ADJ
ejpam-5025	51	8	section	section	NOUN
ejpam-5025	51	9	,	,	PUNCT
ejpam-5025	51	10	we	we	PRON
ejpam-5025	51	11	introduce	introduce	VERB
ejpam-5025	51	12	the	the	DET
ejpam-5025	51	13	concept	concept	NOUN
ejpam-5025	51	14	of	of	ADP
ejpam-5025	51	15	left	left	ADJ
ejpam-5025	51	16	-	-	PUNCT
ejpam-5025	51	17	right	right	NOUN
ejpam-5025	51	18	(	(	PUNCT
ejpam-5025	51	19	resp	resp	NOUN
ejpam-5025	51	20	.	.	PUNCT
ejpam-5025	52	1	right	right	ADJ
ejpam-5025	52	2	-	-	PUNCT
ejpam-5025	52	3	left	left	ADJ
ejpam-5025	52	4	)	)	PUNCT
ejpam-5025	52	5	reverse	reverse	ADJ
ejpam-5025	52	6	derivations	derivation	NOUN
ejpam-5025	52	7	of	of	ADP
ejpam-5025	52	8	d−algebra	d−algebra	X
ejpam-5025	52	9	x	x	X
ejpam-5025	52	10	(	(	PUNCT
ejpam-5025	52	11	briefly	briefly	ADV
ejpam-5025	52	12	,	,	PUNCT
ejpam-5025	52	13	(	(	PUNCT
ejpam-5025	52	14	l	l	NOUN
ejpam-5025	52	15	,	,	PUNCT
ejpam-5025	52	16	r	r	NOUN
ejpam-5025	52	17	)	)	PUNCT
ejpam-5025	52	18	resp	resp	NOUN
ejpam-5025	52	19	.	.	PUNCT
ejpam-5025	53	1	(	(	PUNCT
ejpam-5025	53	2	r	r	X
ejpam-5025	53	3	,	,	PUNCT
ejpam-5025	53	4	l)−	l)−	PROPN
ejpam-5025	53	5	reverse	reverse	VERB
ejpam-5025	53	6	derivation	derivation	NOUN
ejpam-5025	53	7	of	of	ADP
ejpam-5025	53	8	d−	d−	PROPN
ejpam-5025	53	9	algebra	algebra	PROPN
ejpam-5025	53	10	)	)	PUNCT
ejpam-5025	53	11	and	and	CCONJ
ejpam-5025	53	12	will	will	AUX
ejpam-5025	53	13	discuss	discuss	VERB
ejpam-5025	53	14	some	some	DET
ejpam-5025	53	15	consequenes	consequene	NOUN
ejpam-5025	53	16	,	,	PUNCT
ejpam-5025	53	17	also	also	ADV
ejpam-5025	53	18	we	we	PRON
ejpam-5025	53	19	will	will	AUX
ejpam-5025	53	20	give	give	VERB
ejpam-5025	53	21	some	some	DET
ejpam-5025	53	22	illustrative	illustrative	ADJ
ejpam-5025	53	23	examples	example	NOUN
ejpam-5025	53	24	and	and	CCONJ
ejpam-5025	53	25	counterexamples	counterexample	NOUN
ejpam-5025	53	26	.	.	PUNCT
ejpam-5025	54	1	throughout	throughout	ADP
ejpam-5025	54	2	this	this	DET
ejpam-5025	54	3	paper	paper	NOUN
ejpam-5025	54	4	unless	unless	SCONJ
ejpam-5025	54	5	we	we	PRON
ejpam-5025	54	6	mention	mention	VERB
ejpam-5025	54	7	otherwise	otherwise	ADV
ejpam-5025	54	8	,	,	PUNCT
ejpam-5025	54	9	x	x	PRON
ejpam-5025	54	10	denotes	denote	VERB
ejpam-5025	54	11	a	a	DET
ejpam-5025	54	12	d−algebra	d−algebra	X
ejpam-5025	54	13	(	(	PUNCT
ejpam-5025	54	14	x	x	NOUN
ejpam-5025	54	15	,	,	PUNCT
ejpam-5025	54	16	∗	∗	NOUN
ejpam-5025	54	17	,	,	PUNCT
ejpam-5025	54	18	0	0	NUM
ejpam-5025	54	19	)	)	PUNCT
ejpam-5025	54	20	and	and	CCONJ
ejpam-5025	55	1	∀	∀	X
ejpam-5025	55	2	x	x	NOUN
ejpam-5025	55	3	,	,	PUNCT
ejpam-5025	55	4	y	y	PROPN
ejpam-5025	55	5	∈	∈	PROPN
ejpam-5025	55	6	x	x	INTJ
ejpam-5025	55	7	we	we	PRON
ejpam-5025	55	8	write	write	VERB
ejpam-5025	55	9	x	x	PROPN
ejpam-5025	55	10	∗	∗	NOUN
ejpam-5025	55	11	y	y	PROPN
ejpam-5025	55	12	=	=	SYM
ejpam-5025	55	13	xy	xy	PROPN
ejpam-5025	55	14	,	,	PUNCT
ejpam-5025	55	15	also	also	ADV
ejpam-5025	55	16	x	x	X
ejpam-5025	55	17	∧	∧	NOUN
ejpam-5025	55	18	y	y	PROPN
ejpam-5025	55	19	=	=	SYM
ejpam-5025	55	20	y(yx	y(yx	PROPN
ejpam-5025	55	21	)	)	PUNCT
ejpam-5025	55	22	.	.	PUNCT
ejpam-5025	56	1	we	we	PRON
ejpam-5025	56	2	will	will	AUX
ejpam-5025	56	3	begin	begin	VERB
ejpam-5025	56	4	our	our	PRON
ejpam-5025	56	5	study	study	NOUN
ejpam-5025	56	6	with	with	ADP
ejpam-5025	56	7	the	the	DET
ejpam-5025	56	8	following	follow	VERB
ejpam-5025	56	9	definition	definition	NOUN
ejpam-5025	56	10	,	,	PUNCT
ejpam-5025	56	11	which	which	PRON
ejpam-5025	56	12	can	can	AUX
ejpam-5025	56	13	be	be	AUX
ejpam-5025	56	14	found	find	VERB
ejpam-5025	56	15	in	in	ADP
ejpam-5025	56	16	[	[	X
ejpam-5025	56	17	3	3	NUM
ejpam-5025	56	18	]	]	PUNCT
ejpam-5025	56	19	.	.	PUNCT
ejpam-5025	57	1	definition	definition	NOUN
ejpam-5025	57	2	3	3	NUM
ejpam-5025	57	3	.	.	PUNCT
ejpam-5025	57	4	suppose	suppose	VERB
ejpam-5025	57	5	that	that	SCONJ
ejpam-5025	57	6	x	x	PRON
ejpam-5025	57	7	be	be	AUX
ejpam-5025	57	8	a	a	DET
ejpam-5025	57	9	d−algebra	d−algebra	NOUN
ejpam-5025	57	10	,	,	PUNCT
ejpam-5025	57	11	then	then	ADV
ejpam-5025	57	12	x	x	PUNCT
ejpam-5025	57	13	is	be	AUX
ejpam-5025	57	14	called	call	VERB
ejpam-5025	57	15	a	a	DET
ejpam-5025	57	16	super	super	ADV
ejpam-5025	57	17	commutative	commutative	ADJ
ejpam-5025	57	18	if	if	SCONJ
ejpam-5025	57	19	x	x	PROPN
ejpam-5025	57	20	̸=	̸=	PROPN
ejpam-5025	57	21	y	y	PROPN
ejpam-5025	57	22	,	,	PUNCT
ejpam-5025	57	23	xy	xy	PROPN
ejpam-5025	58	1	=	=	SYM
ejpam-5025	58	2	yx	yx	PROPN
ejpam-5025	58	3	̸=	̸=	PROPN
ejpam-5025	58	4	0	0	NUM
ejpam-5025	58	5	for	for	ADP
ejpam-5025	58	6	any	any	DET
ejpam-5025	58	7	non	non	ADJ
ejpam-5025	58	8	-	-	ADJ
ejpam-5025	58	9	zero	zero	NUM
ejpam-5025	58	10	x	x	NOUN
ejpam-5025	58	11	,	,	PUNCT
ejpam-5025	58	12	y	y	PROPN
ejpam-5025	58	13	∈	∈	PROPN
ejpam-5025	58	14	x	x	X
ejpam-5025	58	15	.	.	PUNCT
ejpam-5025	59	1	remark	remark	NOUN
ejpam-5025	59	2	that	that	SCONJ
ejpam-5025	59	3	the	the	DET
ejpam-5025	59	4	commutativity	commutativity	NOUN
ejpam-5025	59	5	of	of	ADP
ejpam-5025	59	6	d−algebras	d−algebras	PROPN
ejpam-5025	59	7	x	x	SYM
ejpam-5025	59	8	,	,	PUNCT
ejpam-5025	59	9	defined	define	VERB
ejpam-5025	59	10	as	as	ADP
ejpam-5025	59	11	x(xy	x(xy	PROPN
ejpam-5025	59	12	)	)	PUNCT
ejpam-5025	59	13	=	=	SYM
ejpam-5025	59	14	y(yx	y(yx	PROPN
ejpam-5025	59	15	)	)	PUNCT
ejpam-5025	59	16	∀	∀	X
ejpam-5025	60	1	x	x	NOUN
ejpam-5025	60	2	,	,	PUNCT
ejpam-5025	60	3	y	y	PROPN
ejpam-5025	60	4	∈	∈	PROPN
ejpam-5025	60	5	x	x	INTJ
ejpam-5025	60	6	,	,	PUNCT
ejpam-5025	60	7	that	that	PRON
ejpam-5025	60	8	is	is	ADV
ejpam-5025	60	9	x	x	X
ejpam-5025	60	10	∧	∧	NOUN
ejpam-5025	60	11	y	y	PROPN
ejpam-5025	60	12	=	=	SYM
ejpam-5025	60	13	y	y	PROPN
ejpam-5025	60	14	∧	∧	PROPN
ejpam-5025	60	15	x.	x.	NOUN
ejpam-5025	60	16	in	in	ADP
ejpam-5025	60	17	the	the	DET
ejpam-5025	60	18	next	next	ADJ
ejpam-5025	60	19	example	example	NOUN
ejpam-5025	60	20	,	,	PUNCT
ejpam-5025	60	21	d−algebra	d−algebra	X
ejpam-5025	60	22	x	x	X
ejpam-5025	60	23	is	be	AUX
ejpam-5025	60	24	a	a	DET
ejpam-5025	60	25	commutative	commutative	ADJ
ejpam-5025	60	26	but	but	CCONJ
ejpam-5025	60	27	not	not	PART
ejpam-5025	60	28	super	super	ADV
ejpam-5025	60	29	commutative	commutative	ADJ
ejpam-5025	60	30	:	:	PUNCT
ejpam-5025	60	31	example	example	NOUN
ejpam-5025	60	32	1	1	X
ejpam-5025	60	33	.	.	X
ejpam-5025	60	34	define	define	VERB
ejpam-5025	60	35	a	a	DET
ejpam-5025	60	36	binary	binary	ADJ
ejpam-5025	60	37	operation	operation	NOUN
ejpam-5025	60	38	∗	∗	NOUN
ejpam-5025	60	39	on	on	ADP
ejpam-5025	60	40	x	x	X
ejpam-5025	60	41	=	=	SYM
ejpam-5025	60	42	{	{	PUNCT
ejpam-5025	60	43	0	0	NUM
ejpam-5025	60	44	,	,	PUNCT
ejpam-5025	60	45	a	a	DET
ejpam-5025	60	46	,	,	PUNCT
ejpam-5025	60	47	b	b	NOUN
ejpam-5025	60	48	}	}	PUNCT
ejpam-5025	60	49	as	as	SCONJ
ejpam-5025	60	50	follows	follow	VERB
ejpam-5025	60	51	:	:	PUNCT
ejpam-5025	60	52	∗	∗	NOUN
ejpam-5025	60	53	0	0	NUM
ejpam-5025	61	1	a	a	DET
ejpam-5025	61	2	b	b	NOUN
ejpam-5025	61	3	0	0	NUM
ejpam-5025	61	4	0	0	NUM
ejpam-5025	61	5	0	0	NUM
ejpam-5025	61	6	0	0	NUM
ejpam-5025	61	7	a	a	DET
ejpam-5025	61	8	a	a	DET
ejpam-5025	61	9	0	0	NUM
ejpam-5025	61	10	a	a	DET
ejpam-5025	61	11	b	b	PROPN
ejpam-5025	61	12	b	b	PROPN
ejpam-5025	61	13	b	b	PROPN
ejpam-5025	61	14	0	0	NUM
ejpam-5025	62	1	then	then	ADV
ejpam-5025	62	2	,	,	PUNCT
ejpam-5025	62	3	it	it	PRON
ejpam-5025	62	4	can	can	AUX
ejpam-5025	62	5	be	be	AUX
ejpam-5025	62	6	cheked	cheke	VERB
ejpam-5025	62	7	that	that	SCONJ
ejpam-5025	62	8	x	x	PRON
ejpam-5025	62	9	is	be	AUX
ejpam-5025	62	10	a	a	DET
ejpam-5025	62	11	commutative	commutative	ADJ
ejpam-5025	62	12	d−algebra	d−algebra	NOUN
ejpam-5025	62	13	,	,	PUNCT
ejpam-5025	62	14	but	but	CCONJ
ejpam-5025	62	15	not	not	PART
ejpam-5025	62	16	super	super	ADV
ejpam-5025	62	17	commutative	commutative	ADJ
ejpam-5025	62	18	,	,	PUNCT
ejpam-5025	62	19	(	(	PUNCT
ejpam-5025	62	20	clearly	clearly	ADV
ejpam-5025	62	21	,	,	PUNCT
ejpam-5025	62	22	for	for	ADP
ejpam-5025	62	23	two	two	NUM
ejpam-5025	62	24	elements	element	NOUN
ejpam-5025	62	25	a	a	PRON
ejpam-5025	62	26	,	,	PUNCT
ejpam-5025	62	27	b	b	X
ejpam-5025	62	28	∈	∈	NOUN
ejpam-5025	62	29	x	x	X
ejpam-5025	62	30	we	we	PRON
ejpam-5025	62	31	can	can	AUX
ejpam-5025	62	32	see	see	VERB
ejpam-5025	62	33	that	that	DET
ejpam-5025	62	34	b	b	NOUN
ejpam-5025	62	35	∗	∗	NOUN
ejpam-5025	62	36	a	a	DET
ejpam-5025	62	37	=	=	SYM
ejpam-5025	62	38	b	b	NOUN
ejpam-5025	62	39	,	,	PUNCT
ejpam-5025	62	40	while	while	SCONJ
ejpam-5025	62	41	a	a	DET
ejpam-5025	62	42	∗	∗	NOUN
ejpam-5025	62	43	b	b	NOUN
ejpam-5025	62	44	=	=	SYM
ejpam-5025	62	45	a	a	NOUN
ejpam-5025	62	46	,	,	PUNCT
ejpam-5025	62	47	therefore	therefore	ADV
ejpam-5025	62	48	,	,	PUNCT
ejpam-5025	62	49	b	b	PROPN
ejpam-5025	62	50	∗	∗	NOUN
ejpam-5025	62	51	a	a	DET
ejpam-5025	62	52	̸=	̸=	PROPN
ejpam-5025	62	53	a	a	DET
ejpam-5025	62	54	∗	∗	NOUN
ejpam-5025	62	55	b	b	NOUN
ejpam-5025	62	56	)	)	PUNCT
ejpam-5025	62	57	.	.	PUNCT
ejpam-5025	63	1	definition	definition	NOUN
ejpam-5025	63	2	4	4	NUM
ejpam-5025	63	3	.	.	PUNCT
ejpam-5025	64	1	a	a	DET
ejpam-5025	64	2	mapping	mapping	NOUN
ejpam-5025	64	3	ζ	ζ	NOUN
ejpam-5025	64	4	:	:	PUNCT
ejpam-5025	64	5	x	x	PUNCT
ejpam-5025	64	6	−→	−→	NOUN
ejpam-5025	64	7	x	x	VERB
ejpam-5025	64	8	is	be	AUX
ejpam-5025	64	9	called	call	VERB
ejpam-5025	64	10	a	a	DET
ejpam-5025	64	11	(	(	PUNCT
ejpam-5025	64	12	l	l	NOUN
ejpam-5025	64	13	,	,	PUNCT
ejpam-5025	64	14	r)−	r)−	PROPN
ejpam-5025	64	15	reverse	reverse	ADJ
ejpam-5025	64	16	derivation	derivation	NOUN
ejpam-5025	64	17	on	on	ADP
ejpam-5025	64	18	a	a	DET
ejpam-5025	64	19	d−algebra	d−algebra	NOUN
ejpam-5025	64	20	x	x	SYM
ejpam-5025	64	21	,	,	PUNCT
ejpam-5025	64	22	if	if	SCONJ
ejpam-5025	64	23	∀	∀	X
ejpam-5025	64	24	x	x	X
ejpam-5025	64	25	,	,	PUNCT
ejpam-5025	64	26	y	y	PROPN
ejpam-5025	64	27	∈	∈	PROPN
ejpam-5025	64	28	x	x	X
ejpam-5025	64	29	the	the	DET
ejpam-5025	64	30	identity	identity	NOUN
ejpam-5025	64	31	ζ(xy	ζ(xy	NOUN
ejpam-5025	64	32	)	)	PUNCT
ejpam-5025	64	33	=	=	PUNCT
ejpam-5025	64	34	ζ(y)x	ζ(y)x	X
ejpam-5025	64	35	∧	∧	PROPN
ejpam-5025	64	36	yζ(x	yζ(x	NOUN
ejpam-5025	64	37	)	)	PUNCT
ejpam-5025	64	38	holds	hold	VERB
ejpam-5025	64	39	.	.	PUNCT
ejpam-5025	65	1	similarly	similarly	ADV
ejpam-5025	65	2	,	,	PUNCT
ejpam-5025	65	3	the	the	DET
ejpam-5025	65	4	(	(	PUNCT
ejpam-5025	65	5	r	r	NOUN
ejpam-5025	65	6	,	,	PUNCT
ejpam-5025	65	7	l)−	l)−	PROPN
ejpam-5025	65	8	reverse	reverse	VERB
ejpam-5025	65	9	derivation	derivation	NOUN
ejpam-5025	65	10	ζ	ζ	NOUN
ejpam-5025	65	11	on	on	ADP
ejpam-5025	65	12	x	x	PUNCT
ejpam-5025	65	13	can	can	AUX
ejpam-5025	65	14	be	be	AUX
ejpam-5025	65	15	defined	define	VERB
ejpam-5025	65	16	as	as	ADP
ejpam-5025	65	17	ζ(xy	ζ(xy	NOUN
ejpam-5025	65	18	)	)	PUNCT
ejpam-5025	65	19	=	=	SYM
ejpam-5025	65	20	yζ(x)∧ζ(y)x	yζ(x)∧ζ(y)x	NOUN
ejpam-5025	65	21	∀	∀	X
ejpam-5025	66	1	x	x	X
ejpam-5025	66	2	,	,	PUNCT
ejpam-5025	66	3	y	y	PROPN
ejpam-5025	66	4	∈	∈	PROPN
ejpam-5025	66	5	x	x	X
ejpam-5025	66	6	.	.	PUNCT
ejpam-5025	67	1	furthermore	furthermore	ADV
ejpam-5025	67	2	,	,	PUNCT
ejpam-5025	67	3	ζ	ζ	PROPN
ejpam-5025	67	4	is	be	AUX
ejpam-5025	67	5	called	call	VERB
ejpam-5025	67	6	a	a	DET
ejpam-5025	67	7	reverse	reverse	ADJ
ejpam-5025	67	8	derivation	derivation	NOUN
ejpam-5025	67	9	of	of	ADP
ejpam-5025	67	10	x	x	INTJ
ejpam-5025	67	11	,	,	PUNCT
ejpam-5025	67	12	if	if	SCONJ
ejpam-5025	67	13	it	it	PRON
ejpam-5025	67	14	is	be	AUX
ejpam-5025	67	15	(	(	PUNCT
ejpam-5025	67	16	l	l	NOUN
ejpam-5025	67	17	,	,	PUNCT
ejpam-5025	67	18	r)−	r)−	PROPN
ejpam-5025	67	19	and	and	CCONJ
ejpam-5025	67	20	(	(	PUNCT
ejpam-5025	67	21	r	r	NOUN
ejpam-5025	67	22	,	,	PUNCT
ejpam-5025	67	23	l)−	l)−	PROPN
ejpam-5025	67	24	reverse	reverse	VERB
ejpam-5025	67	25	derivation	derivation	NOUN
ejpam-5025	67	26	at	at	ADP
ejpam-5025	67	27	the	the	DET
ejpam-5025	67	28	same	same	ADJ
ejpam-5025	67	29	time	time	NOUN
ejpam-5025	67	30	.	.	PUNCT
ejpam-5025	68	1	the	the	DET
ejpam-5025	68	2	existence	existence	NOUN
ejpam-5025	68	3	of	of	ADP
ejpam-5025	68	4	the	the	DET
ejpam-5025	68	5	(	(	PUNCT
ejpam-5025	68	6	(	(	PUNCT
ejpam-5025	68	7	l	l	NOUN
ejpam-5025	68	8	,	,	PUNCT
ejpam-5025	68	9	r	r	NOUN
ejpam-5025	68	10	)	)	PUNCT
ejpam-5025	68	11	resp	resp	NOUN
ejpam-5025	68	12	.	.	PUNCT
ejpam-5025	69	1	(	(	PUNCT
ejpam-5025	69	2	r	r	X
ejpam-5025	69	3	,	,	PUNCT
ejpam-5025	69	4	l)−	l)−	NOUN
ejpam-5025	69	5	reverse	reverse	ADJ
ejpam-5025	69	6	derivation	derivation	NOUN
ejpam-5025	69	7	)	)	PUNCT
ejpam-5025	69	8	of	of	ADP
ejpam-5025	69	9	d−	d−	PROPN
ejpam-5025	69	10	algebra	algebra	NOUN
ejpam-5025	69	11	x	x	PRON
ejpam-5025	69	12	,	,	PUNCT
ejpam-5025	69	13	and	and	CCONJ
ejpam-5025	69	14	thus	thus	ADV
ejpam-5025	69	15	the	the	DET
ejpam-5025	69	16	existence	existence	NOUN
ejpam-5025	69	17	of	of	ADP
ejpam-5025	69	18	the	the	DET
ejpam-5025	69	19	reverse	reverse	ADJ
ejpam-5025	69	20	derivation	derivation	NOUN
ejpam-5025	69	21	in	in	ADP
ejpam-5025	69	22	d−algebra	d−algebra	X
ejpam-5025	69	23	x	x	X
ejpam-5025	69	24	,	,	PUNCT
ejpam-5025	69	25	is	be	AUX
ejpam-5025	69	26	illustrated	illustrate	VERB
ejpam-5025	69	27	by	by	ADP
ejpam-5025	69	28	the	the	DET
ejpam-5025	69	29	following	follow	VERB
ejpam-5025	69	30	example	example	NOUN
ejpam-5025	69	31	:	:	PUNCT
ejpam-5025	69	32	example	example	NOUN
ejpam-5025	69	33	2	2	NUM
ejpam-5025	69	34	.	.	PUNCT
ejpam-5025	69	35	define	define	VERB
ejpam-5025	69	36	a	a	DET
ejpam-5025	69	37	binary	binary	ADJ
ejpam-5025	69	38	operation	operation	NOUN
ejpam-5025	69	39	∗	∗	NOUN
ejpam-5025	69	40	on	on	ADP
ejpam-5025	69	41	a	a	DET
ejpam-5025	69	42	set	set	NOUN
ejpam-5025	69	43	x	x	X
ejpam-5025	69	44	=	=	SYM
ejpam-5025	69	45	{	{	PUNCT
ejpam-5025	69	46	0	0	NUM
ejpam-5025	69	47	,	,	PUNCT
ejpam-5025	69	48	a	a	DET
ejpam-5025	69	49	,	,	PUNCT
ejpam-5025	69	50	b	b	NOUN
ejpam-5025	69	51	,	,	PUNCT
ejpam-5025	69	52	c	c	NOUN
ejpam-5025	69	53	}	}	PUNCT
ejpam-5025	69	54	as	as	SCONJ
ejpam-5025	69	55	follows	follow	VERB
ejpam-5025	69	56	:	:	PUNCT
ejpam-5025	69	57	k.	k.	PROPN
ejpam-5025	69	58	alnefaie	alnefaie	PROPN
ejpam-5025	69	59	/	/	SYM
ejpam-5025	69	60	eur	eur	PROPN
ejpam-5025	69	61	.	.	PUNCT
ejpam-5025	70	1	j.	j.	PROPN
ejpam-5025	70	2	pure	pure	PROPN
ejpam-5025	70	3	appl	appl	PROPN
ejpam-5025	70	4	.	.	PROPN
ejpam-5025	70	5	math	math	PROPN
ejpam-5025	70	6	,	,	PUNCT
ejpam-5025	70	7	17	17	NUM
ejpam-5025	70	8	(	(	PUNCT
ejpam-5025	70	9	1	1	NUM
ejpam-5025	70	10	)	)	PUNCT
ejpam-5025	70	11	(	(	PUNCT
ejpam-5025	70	12	2024	2024	NUM
ejpam-5025	70	13	)	)	PUNCT
ejpam-5025	70	14	,	,	PUNCT
ejpam-5025	70	15	362	362	NUM
ejpam-5025	70	16	-	-	SYM
ejpam-5025	70	17	371	371	NUM
ejpam-5025	70	18	365	365	NUM
ejpam-5025	70	19	∗	∗	NOUN
ejpam-5025	70	20	0	0	NUM
ejpam-5025	71	1	a	a	DET
ejpam-5025	71	2	b	b	NOUN
ejpam-5025	71	3	c	c	NOUN
ejpam-5025	71	4	0	0	NUM
ejpam-5025	71	5	0	0	NUM
ejpam-5025	71	6	0	0	NUM
ejpam-5025	71	7	0	0	NUM
ejpam-5025	71	8	0	0	NUM
ejpam-5025	71	9	a	a	DET
ejpam-5025	71	10	a	a	DET
ejpam-5025	71	11	0	0	NUM
ejpam-5025	71	12	a	a	DET
ejpam-5025	71	13	0	0	NUM
ejpam-5025	71	14	b	b	PROPN
ejpam-5025	71	15	b	b	PROPN
ejpam-5025	71	16	b	b	PROPN
ejpam-5025	71	17	0	0	NUM
ejpam-5025	71	18	0	0	NUM
ejpam-5025	71	19	c	c	PROPN
ejpam-5025	71	20	b	b	PROPN
ejpam-5025	71	21	b	b	PROPN
ejpam-5025	71	22	b	b	PROPN
ejpam-5025	71	23	0	0	NUM
ejpam-5025	71	24	let	let	VERB
ejpam-5025	71	25	ζ	ζ	NOUN
ejpam-5025	71	26	:	:	PUNCT
ejpam-5025	71	27	x	x	PUNCT
ejpam-5025	71	28	−→	−→	NOUN
ejpam-5025	71	29	x	x	VERB
ejpam-5025	71	30	be	be	AUX
ejpam-5025	71	31	a	a	DET
ejpam-5025	71	32	map	map	NOUN
ejpam-5025	71	33	defined	define	VERB
ejpam-5025	71	34	as	as	ADP
ejpam-5025	71	35	:	:	PUNCT
ejpam-5025	71	36	ζ(x	ζ(x	NOUN
ejpam-5025	71	37	)	)	PUNCT
ejpam-5025	71	38	=	=	PRON
ejpam-5025	71	39	{	{	PUNCT
ejpam-5025	71	40	0	0	NUM
ejpam-5025	71	41	if	if	SCONJ
ejpam-5025	71	42	x	x	X
ejpam-5025	71	43	=	=	SYM
ejpam-5025	71	44	0	0	NUM
ejpam-5025	71	45	,	,	PUNCT
ejpam-5025	71	46	a	a	PRON
ejpam-5025	71	47	,	,	PUNCT
ejpam-5025	71	48	b	b	NOUN
ejpam-5025	72	1	a	a	DET
ejpam-5025	72	2	if	if	NOUN
ejpam-5025	72	3	x	x	X
ejpam-5025	72	4	=	=	SYM
ejpam-5025	72	5	c	c	NOUN
ejpam-5025	72	6	then	then	ADV
ejpam-5025	72	7	it	it	PRON
ejpam-5025	72	8	is	be	AUX
ejpam-5025	72	9	easily	easily	ADV
ejpam-5025	72	10	checked	check	VERB
ejpam-5025	72	11	that	that	SCONJ
ejpam-5025	72	12	x	x	PRON
ejpam-5025	72	13	is	be	AUX
ejpam-5025	72	14	a	a	DET
ejpam-5025	72	15	d−algebra	d−algebra	NOUN
ejpam-5025	72	16	,	,	PUNCT
ejpam-5025	72	17	ζ	ζ	NOUN
ejpam-5025	72	18	is	be	AUX
ejpam-5025	72	19	both	both	PRON
ejpam-5025	72	20	a	a	DET
ejpam-5025	72	21	(	(	PUNCT
ejpam-5025	72	22	l	l	NOUN
ejpam-5025	72	23	,	,	PUNCT
ejpam-5025	72	24	r)−	r)−	PROPN
ejpam-5025	72	25	and	and	CCONJ
ejpam-5025	72	26	(	(	PUNCT
ejpam-5025	72	27	r	r	NOUN
ejpam-5025	72	28	,	,	PUNCT
ejpam-5025	72	29	l)−	l)−	NOUN
ejpam-5025	72	30	reverse	reverse	VERB
ejpam-5025	72	31	derivation	derivation	NOUN
ejpam-5025	72	32	on	on	ADP
ejpam-5025	72	33	x	x	X
ejpam-5025	72	34	.	.	PUNCT
ejpam-5025	73	1	hence	hence	ADV
ejpam-5025	73	2	ζ	ζ	NOUN
ejpam-5025	73	3	is	be	AUX
ejpam-5025	73	4	a	a	DET
ejpam-5025	73	5	reverse	reverse	ADJ
ejpam-5025	73	6	derivation	derivation	NOUN
ejpam-5025	73	7	on	on	ADP
ejpam-5025	73	8	x	x	X
ejpam-5025	73	9	.	.	PUNCT
ejpam-5025	73	10	remark	remark	PROPN
ejpam-5025	73	11	1	1	NUM
ejpam-5025	73	12	.	.	PUNCT
ejpam-5025	74	1	in	in	ADP
ejpam-5025	74	2	example	example	NOUN
ejpam-5025	74	3	2	2	NUM
ejpam-5025	74	4	,	,	PUNCT
ejpam-5025	74	5	we	we	PRON
ejpam-5025	74	6	can	can	AUX
ejpam-5025	74	7	remark	remark	VERB
ejpam-5025	74	8	that	that	SCONJ
ejpam-5025	74	9	x	x	PRON
ejpam-5025	74	10	is	be	AUX
ejpam-5025	74	11	a	a	DET
ejpam-5025	74	12	d−algebra	d−algebra	NOUN
ejpam-5025	74	13	but	but	CCONJ
ejpam-5025	74	14	not	not	PART
ejpam-5025	74	15	edge	edge	VERB
ejpam-5025	74	16	d−algebra	d−algebra	NOUN
ejpam-5025	74	17	(	(	PUNCT
ejpam-5025	74	18	because	because	SCONJ
ejpam-5025	74	19	c	c	PROPN
ejpam-5025	74	20	∗	∗	X
ejpam-5025	74	21	0	0	NUM
ejpam-5025	75	1	=	=	SYM
ejpam-5025	75	2	b	b	X
ejpam-5025	75	3	̸=	̸=	PROPN
ejpam-5025	75	4	c	c	PROPN
ejpam-5025	75	5	)	)	PUNCT
ejpam-5025	75	6	.	.	PUNCT
ejpam-5025	76	1	also	also	ADV
ejpam-5025	76	2	,	,	PUNCT
ejpam-5025	76	3	we	we	PRON
ejpam-5025	76	4	can	can	AUX
ejpam-5025	76	5	remark	remark	VERB
ejpam-5025	76	6	that	that	SCONJ
ejpam-5025	76	7	x	x	PUNCT
ejpam-5025	76	8	neither	neither	CCONJ
ejpam-5025	76	9	super	super	ADV
ejpam-5025	76	10	commutative	commutative	ADJ
ejpam-5025	76	11	(	(	PUNCT
ejpam-5025	76	12	because	because	SCONJ
ejpam-5025	76	13	for	for	ADP
ejpam-5025	76	14	a	a	PRON
ejpam-5025	76	15	,	,	PUNCT
ejpam-5025	76	16	c	c	PROPN
ejpam-5025	76	17	∈	∈	PROPN
ejpam-5025	76	18	x	x	PUNCT
ejpam-5025	76	19	,	,	PUNCT
ejpam-5025	76	20	we	we	PRON
ejpam-5025	76	21	have	have	VERB
ejpam-5025	76	22	c	c	NOUN
ejpam-5025	76	23	∗	∗	NOUN
ejpam-5025	76	24	a	a	DET
ejpam-5025	76	25	=	=	SYM
ejpam-5025	76	26	b	b	SYM
ejpam-5025	76	27	̸=	̸=	PROPN
ejpam-5025	76	28	a	a	DET
ejpam-5025	76	29	∗	∗	NOUN
ejpam-5025	76	30	c	c	NOUN
ejpam-5025	76	31	=	=	SYM
ejpam-5025	76	32	0	0	NUM
ejpam-5025	76	33	)	)	PUNCT
ejpam-5025	76	34	,	,	PUNCT
ejpam-5025	76	35	nor	nor	CCONJ
ejpam-5025	76	36	commutative	commutative	ADJ
ejpam-5025	76	37	(	(	PUNCT
ejpam-5025	76	38	note	note	VERB
ejpam-5025	76	39	that	that	SCONJ
ejpam-5025	76	40	for	for	ADP
ejpam-5025	76	41	a	a	PRON
ejpam-5025	76	42	,	,	PUNCT
ejpam-5025	76	43	c	c	PROPN
ejpam-5025	76	44	∈	∈	PROPN
ejpam-5025	76	45	x	x	X
ejpam-5025	76	46	,	,	PUNCT
ejpam-5025	76	47	we	we	PRON
ejpam-5025	76	48	have	have	VERB
ejpam-5025	76	49	a∧c	a∧c	NOUN
ejpam-5025	76	50	=	=	SYM
ejpam-5025	76	51	c	c	X
ejpam-5025	76	52	(	(	PUNCT
ejpam-5025	76	53	c	c	NOUN
ejpam-5025	76	54	a	a	X
ejpam-5025	76	55	)	)	PUNCT
ejpam-5025	76	56	=	=	SYM
ejpam-5025	76	57	c	c	NOUN
ejpam-5025	76	58	∗	∗	X
ejpam-5025	76	59	b	b	PROPN
ejpam-5025	76	60	=	=	PROPN
ejpam-5025	76	61	b.	b.	PROPN
ejpam-5025	76	62	on	on	ADP
ejpam-5025	76	63	the	the	DET
ejpam-5025	76	64	other	other	ADJ
ejpam-5025	76	65	hand	hand	NOUN
ejpam-5025	76	66	,	,	PUNCT
ejpam-5025	76	67	c∧a	c∧a	X
ejpam-5025	76	68	=	=	PUNCT
ejpam-5025	76	69	a	a	DET
ejpam-5025	76	70	(	(	PUNCT
ejpam-5025	76	71	a	a	DET
ejpam-5025	76	72	c	c	NOUN
ejpam-5025	76	73	)	)	PUNCT
ejpam-5025	76	74	=	=	PUNCT
ejpam-5025	76	75	a	a	DET
ejpam-5025	76	76	∗	∗	NOUN
ejpam-5025	76	77	0	0	NUM
ejpam-5025	77	1	=	=	SYM
ejpam-5025	77	2	a	a	NOUN
ejpam-5025	77	3	,	,	PUNCT
ejpam-5025	77	4	so	so	SCONJ
ejpam-5025	77	5	that	that	SCONJ
ejpam-5025	77	6	a	a	DET
ejpam-5025	77	7	∧	∧	PROPN
ejpam-5025	77	8	c	c	NOUN
ejpam-5025	77	9	̸=	̸=	PROPN
ejpam-5025	77	10	c	c	PROPN
ejpam-5025	77	11	∧	∧	PROPN
ejpam-5025	77	12	a	a	PRON
ejpam-5025	77	13	)	)	PUNCT
ejpam-5025	77	14	.	.	PUNCT
ejpam-5025	78	1	remark	remark	PROPN
ejpam-5025	78	2	2	2	NUM
ejpam-5025	78	3	.	.	PUNCT
ejpam-5025	79	1	some	some	DET
ejpam-5025	79	2	generalizations	generalization	NOUN
ejpam-5025	79	3	of	of	ADP
ejpam-5025	79	4	(	(	PUNCT
ejpam-5025	79	5	l	l	NOUN
ejpam-5025	79	6	,	,	PUNCT
ejpam-5025	79	7	r)−	r)−	PROPN
ejpam-5025	79	8	derivations	derivation	NOUN
ejpam-5025	79	9	on	on	ADP
ejpam-5025	79	10	x	x	PART
ejpam-5025	79	11	have	have	VERB
ejpam-5025	79	12	relations	relation	NOUN
ejpam-5025	79	13	with	with	ADP
ejpam-5025	79	14	the	the	DET
ejpam-5025	79	15	concept	concept	NOUN
ejpam-5025	79	16	of	of	ADP
ejpam-5025	79	17	(	(	PUNCT
ejpam-5025	79	18	r	r	NOUN
ejpam-5025	79	19	,	,	PUNCT
ejpam-5025	79	20	l)−	l)−	PROPN
ejpam-5025	79	21	reverse	reverse	ADJ
ejpam-5025	79	22	derivations	derivation	NOUN
ejpam-5025	79	23	on	on	ADP
ejpam-5025	79	24	x	x	X
ejpam-5025	79	25	.	.	PUNCT
ejpam-5025	80	1	also	also	ADV
ejpam-5025	80	2	we	we	PRON
ejpam-5025	80	3	can	can	AUX
ejpam-5025	80	4	observe	observe	VERB
ejpam-5025	80	5	that	that	SCONJ
ejpam-5025	80	6	,	,	PUNCT
ejpam-5025	80	7	both	both	PRON
ejpam-5025	80	8	of	of	ADP
ejpam-5025	80	9	(	(	PUNCT
ejpam-5025	80	10	r	r	NOUN
ejpam-5025	80	11	,	,	PUNCT
ejpam-5025	80	12	l)−reverse	l)−reverse	VERB
ejpam-5025	80	13	derivations	derivation	NOUN
ejpam-5025	80	14	and	and	CCONJ
ejpam-5025	80	15	(	(	PUNCT
ejpam-5025	80	16	l	l	NOUN
ejpam-5025	80	17	,	,	PUNCT
ejpam-5025	80	18	r)−	r)−	PROPN
ejpam-5025	80	19	derivations	derivation	NOUN
ejpam-5025	80	20	are	be	AUX
ejpam-5025	80	21	the	the	DET
ejpam-5025	80	22	same	same	ADJ
ejpam-5025	80	23	on	on	ADP
ejpam-5025	80	24	x	x	SYM
ejpam-5025	80	25	,	,	PUNCT
ejpam-5025	80	26	if	if	SCONJ
ejpam-5025	80	27	x	x	PRON
ejpam-5025	80	28	is	be	AUX
ejpam-5025	80	29	super	super	ADV
ejpam-5025	80	30	commutative	commutative	ADJ
ejpam-5025	80	31	,	,	PUNCT
ejpam-5025	80	32	but	but	CCONJ
ejpam-5025	80	33	in	in	ADP
ejpam-5025	80	34	general	general	ADJ
ejpam-5025	80	35	the	the	DET
ejpam-5025	80	36	converse	converse	NOUN
ejpam-5025	80	37	may	may	AUX
ejpam-5025	80	38	not	not	PART
ejpam-5025	80	39	be	be	AUX
ejpam-5025	80	40	true	true	ADJ
ejpam-5025	80	41	as	as	SCONJ
ejpam-5025	80	42	illustrated	illustrate	VERB
ejpam-5025	80	43	in	in	ADP
ejpam-5025	80	44	the	the	DET
ejpam-5025	80	45	following	follow	VERB
ejpam-5025	80	46	example	example	NOUN
ejpam-5025	80	47	.	.	PUNCT
ejpam-5025	81	1	example	example	NOUN
ejpam-5025	82	1	3	3	X
ejpam-5025	82	2	.	.	X
ejpam-5025	82	3	consider	consider	VERB
ejpam-5025	82	4	x	x	PUNCT
ejpam-5025	82	5	and	and	CCONJ
ejpam-5025	82	6	the	the	DET
ejpam-5025	82	7	(	(	PUNCT
ejpam-5025	82	8	r	r	NOUN
ejpam-5025	82	9	,	,	PUNCT
ejpam-5025	82	10	l)−	l)−	NOUN
ejpam-5025	82	11	reverse	reverse	VERB
ejpam-5025	82	12	derivation	derivation	NOUN
ejpam-5025	82	13	ζ(x	ζ(x	NOUN
ejpam-5025	82	14	)	)	PUNCT
ejpam-5025	82	15	as	as	ADP
ejpam-5025	82	16	in	in	ADP
ejpam-5025	82	17	example	example	NOUN
ejpam-5025	82	18	2	2	NUM
ejpam-5025	82	19	.	.	PUNCT
ejpam-5025	83	1	hence	hence	ADV
ejpam-5025	83	2	,	,	PUNCT
ejpam-5025	83	3	it	it	PRON
ejpam-5025	83	4	is	be	AUX
ejpam-5025	83	5	not	not	PART
ejpam-5025	83	6	difficult	difficult	ADJ
ejpam-5025	83	7	to	to	PART
ejpam-5025	83	8	see	see	VERB
ejpam-5025	83	9	that	that	SCONJ
ejpam-5025	83	10	ζ(x	ζ(x	NOUN
ejpam-5025	83	11	)	)	PUNCT
ejpam-5025	83	12	is	be	AUX
ejpam-5025	83	13	also	also	ADV
ejpam-5025	83	14	(	(	PUNCT
ejpam-5025	83	15	l	l	NOUN
ejpam-5025	83	16	,	,	PUNCT
ejpam-5025	83	17	r)−derivation	r)−derivation	NOUN
ejpam-5025	83	18	of	of	ADP
ejpam-5025	83	19	x	x	PRON
ejpam-5025	83	20	,	,	PUNCT
ejpam-5025	83	21	but	but	CCONJ
ejpam-5025	83	22	x	x	X
ejpam-5025	83	23	not	not	PART
ejpam-5025	83	24	super	super	ADV
ejpam-5025	83	25	commutative	commutative	ADJ
ejpam-5025	83	26	.	.	PUNCT
ejpam-5025	84	1	therefore	therefore	ADV
ejpam-5025	84	2	,	,	PUNCT
ejpam-5025	84	3	in	in	ADP
ejpam-5025	84	4	remark	remark	NOUN
ejpam-5025	84	5	2	2	NUM
ejpam-5025	84	6	the	the	DET
ejpam-5025	84	7	condition	condition	NOUN
ejpam-5025	84	8	of	of	ADP
ejpam-5025	84	9	super	super	ADJ
ejpam-5025	84	10	commutativity	commutativity	NOUN
ejpam-5025	84	11	can	can	AUX
ejpam-5025	84	12	not	not	PART
ejpam-5025	84	13	be	be	AUX
ejpam-5025	84	14	omitted	omit	VERB
ejpam-5025	84	15	.	.	PUNCT
ejpam-5025	85	1	definition	definition	NOUN
ejpam-5025	85	2	5	5	NUM
ejpam-5025	85	3	.	.	PUNCT
ejpam-5025	86	1	let	let	VERB
ejpam-5025	86	2	ζ	ζ	NOUN
ejpam-5025	86	3	:	:	PUNCT
ejpam-5025	86	4	x	x	PUNCT
ejpam-5025	86	5	−→	−→	NOUN
ejpam-5025	86	6	x	x	VERB
ejpam-5025	86	7	be	be	AUX
ejpam-5025	86	8	a	a	DET
ejpam-5025	86	9	self	self	NOUN
ejpam-5025	86	10	map	map	NOUN
ejpam-5025	86	11	of	of	ADP
ejpam-5025	86	12	a	a	DET
ejpam-5025	86	13	d	d	NOUN
ejpam-5025	86	14	−	−	PROPN
ejpam-5025	86	15	algebra	algebra	NOUN
ejpam-5025	86	16	x	x	X
ejpam-5025	86	17	.	.	PUNCT
ejpam-5025	87	1	if	if	SCONJ
ejpam-5025	87	2	ζ(0	ζ(0	NOUN
ejpam-5025	87	3	)	)	PUNCT
ejpam-5025	88	1	=	=	SYM
ejpam-5025	88	2	0	0	NUM
ejpam-5025	88	3	,	,	PUNCT
ejpam-5025	88	4	then	then	ADV
ejpam-5025	88	5	ζ	ζ	NOUN
ejpam-5025	88	6	is	be	AUX
ejpam-5025	88	7	called	call	VERB
ejpam-5025	88	8	a	a	DET
ejpam-5025	88	9	regular	regular	NOUN
ejpam-5025	88	10	.	.	PUNCT
ejpam-5025	89	1	example	example	NOUN
ejpam-5025	90	1	4	4	NUM
ejpam-5025	90	2	.	.	X
ejpam-5025	90	3	assume	assume	VERB
ejpam-5025	90	4	that	that	SCONJ
ejpam-5025	90	5	ζ	ζ	NOUN
ejpam-5025	90	6	is	be	AUX
ejpam-5025	90	7	a	a	DET
ejpam-5025	90	8	(	(	PUNCT
ejpam-5025	90	9	r	r	NOUN
ejpam-5025	90	10	,	,	PUNCT
ejpam-5025	90	11	l)−	l)−	PROPN
ejpam-5025	90	12	reverse	reverse	VERB
ejpam-5025	90	13	derivation	derivation	NOUN
ejpam-5025	90	14	on	on	ADP
ejpam-5025	90	15	the	the	DET
ejpam-5025	90	16	d	d	NOUN
ejpam-5025	90	17	−	−	PROPN
ejpam-5025	90	18	algebra	algebra	NOUN
ejpam-5025	90	19	x	x	PUNCT
ejpam-5025	90	20	as	as	ADP
ejpam-5025	90	21	in	in	ADP
ejpam-5025	90	22	example	example	NOUN
ejpam-5025	90	23	2	2	X
ejpam-5025	90	24	.	.	PUNCT
ejpam-5025	91	1	it	it	PRON
ejpam-5025	91	2	is	be	AUX
ejpam-5025	91	3	obvious	obvious	ADJ
ejpam-5025	91	4	from	from	ADP
ejpam-5025	91	5	the	the	DET
ejpam-5025	91	6	definition	definition	NOUN
ejpam-5025	91	7	of	of	ADP
ejpam-5025	91	8	ζ	ζ	NOUN
ejpam-5025	91	9	that	that	DET
ejpam-5025	91	10	ζ(0	ζ(0	NOUN
ejpam-5025	91	11	)	)	PUNCT
ejpam-5025	91	12	=	=	SYM
ejpam-5025	91	13	0	0	NUM
ejpam-5025	91	14	,	,	PUNCT
ejpam-5025	91	15	therefore	therefore	ADV
ejpam-5025	91	16	ζ(x	ζ(x	NOUN
ejpam-5025	91	17	)	)	PUNCT
ejpam-5025	91	18	is	be	AUX
ejpam-5025	91	19	regular	regular	ADJ
ejpam-5025	91	20	.	.	PUNCT
ejpam-5025	92	1	theorem	theorem	NOUN
ejpam-5025	92	2	1	1	NUM
ejpam-5025	92	3	.	.	PUNCT
ejpam-5025	93	1	if	if	SCONJ
ejpam-5025	93	2	ζ	ζ	PRON
ejpam-5025	93	3	:	:	PUNCT
ejpam-5025	93	4	x	x	PUNCT
ejpam-5025	93	5	−→	−→	NOUN
ejpam-5025	93	6	x	x	VERB
ejpam-5025	93	7	is	be	AUX
ejpam-5025	93	8	a	a	DET
ejpam-5025	93	9	(	(	PUNCT
ejpam-5025	93	10	r	r	NOUN
ejpam-5025	93	11	,	,	PUNCT
ejpam-5025	93	12	l	l	NOUN
ejpam-5025	93	13	)	)	PUNCT
ejpam-5025	93	14	−	−	ADP
ejpam-5025	93	15	reverse	reverse	ADJ
ejpam-5025	93	16	derivation	derivation	NOUN
ejpam-5025	93	17	on	on	ADP
ejpam-5025	93	18	an	an	DET
ejpam-5025	93	19	edge	edge	NOUN
ejpam-5025	94	1	d	d	PRON
ejpam-5025	94	2	−	−	PROPN
ejpam-5025	94	3	algebra	algebra	NOUN
ejpam-5025	94	4	x	x	SYM
ejpam-5025	94	5	,	,	PUNCT
ejpam-5025	94	6	then	then	ADV
ejpam-5025	94	7	ζ	ζ	NOUN
ejpam-5025	94	8	is	be	AUX
ejpam-5025	94	9	regular	regular	ADJ
ejpam-5025	94	10	.	.	PUNCT
ejpam-5025	95	1	proof	proof	NOUN
ejpam-5025	95	2	.	.	PUNCT
ejpam-5025	96	1	by	by	ADP
ejpam-5025	96	2	assumption	assumption	NOUN
ejpam-5025	96	3	ζ	ζ	NOUN
ejpam-5025	96	4	is	be	AUX
ejpam-5025	96	5	a	a	DET
ejpam-5025	96	6	(	(	PUNCT
ejpam-5025	96	7	r	r	NOUN
ejpam-5025	96	8	,	,	PUNCT
ejpam-5025	96	9	l)−reverse	l)−reverse	VERB
ejpam-5025	96	10	derivation	derivation	NOUN
ejpam-5025	96	11	of	of	ADP
ejpam-5025	96	12	x	x	PRON
ejpam-5025	96	13	,	,	PUNCT
ejpam-5025	96	14	then	then	ADV
ejpam-5025	96	15	we	we	PRON
ejpam-5025	96	16	have	have	VERB
ejpam-5025	96	17	ζ(xy	ζ(xy	PROPN
ejpam-5025	96	18	)	)	PUNCT
ejpam-5025	96	19	=	=	PUNCT
ejpam-5025	97	1	yζ(x)∧	yζ(x)∧	PROPN
ejpam-5025	97	2	ζ(y)x	ζ(y)x	NOUN
ejpam-5025	97	3	∀	∀	X
ejpam-5025	97	4	x	x	X
ejpam-5025	97	5	,	,	PUNCT
ejpam-5025	97	6	y	y	PROPN
ejpam-5025	97	7	∈	∈	PROPN
ejpam-5025	97	8	x	x	X
ejpam-5025	97	9	.	.	PUNCT
ejpam-5025	98	1	replace	replace	VERB
ejpam-5025	98	2	y	y	PROPN
ejpam-5025	98	3	by	by	ADP
ejpam-5025	98	4	x	x	PUNCT
ejpam-5025	98	5	in	in	ADP
ejpam-5025	98	6	the	the	DET
ejpam-5025	98	7	previous	previous	ADJ
ejpam-5025	98	8	equation	equation	NOUN
ejpam-5025	98	9	and	and	CCONJ
ejpam-5025	98	10	use	use	VERB
ejpam-5025	98	11	the	the	DET
ejpam-5025	98	12	axiom	axiom	NOUN
ejpam-5025	98	13	(	(	PUNCT
ejpam-5025	98	14	i	i	NOUN
ejpam-5025	98	15	)	)	PUNCT
ejpam-5025	98	16	in	in	ADP
ejpam-5025	98	17	definition	definition	NOUN
ejpam-5025	98	18	1	1	NUM
ejpam-5025	98	19	,	,	PUNCT
ejpam-5025	98	20	to	to	PART
ejpam-5025	98	21	get	get	VERB
ejpam-5025	98	22	ζ(0	ζ(0	NOUN
ejpam-5025	98	23	)	)	PUNCT
ejpam-5025	98	24	=	=	SYM
ejpam-5025	98	25	ζ(xx	ζ(xx	PROPN
ejpam-5025	98	26	)	)	PUNCT
ejpam-5025	98	27	=	=	SYM
ejpam-5025	98	28	xζ(x	xζ(x	X
ejpam-5025	98	29	)	)	PUNCT
ejpam-5025	98	30	∧	∧	NOUN
ejpam-5025	98	31	ζ(x)x	ζ(x)x	ADJ
ejpam-5025	98	32	for	for	ADP
ejpam-5025	98	33	any	any	DET
ejpam-5025	98	34	x	x	NOUN
ejpam-5025	98	35	,	,	PUNCT
ejpam-5025	98	36	y	y	PROPN
ejpam-5025	98	37	∈	∈	PROPN
ejpam-5025	98	38	x	x	X
ejpam-5025	98	39	.	.	PUNCT
ejpam-5025	99	1	k.	k.	PROPN
ejpam-5025	99	2	alnefaie	alnefaie	PROPN
ejpam-5025	99	3	/	/	SYM
ejpam-5025	99	4	eur	eur	PROPN
ejpam-5025	99	5	.	.	PUNCT
ejpam-5025	100	1	j.	j.	PROPN
ejpam-5025	100	2	pure	pure	PROPN
ejpam-5025	100	3	appl	appl	PROPN
ejpam-5025	100	4	.	.	PROPN
ejpam-5025	100	5	math	math	PROPN
ejpam-5025	100	6	,	,	PUNCT
ejpam-5025	100	7	17	17	NUM
ejpam-5025	100	8	(	(	PUNCT
ejpam-5025	100	9	1	1	NUM
ejpam-5025	100	10	)	)	PUNCT
ejpam-5025	100	11	(	(	PUNCT
ejpam-5025	100	12	2024	2024	NUM
ejpam-5025	100	13	)	)	PUNCT
ejpam-5025	100	14	,	,	PUNCT
ejpam-5025	100	15	362	362	NUM
ejpam-5025	100	16	-	-	SYM
ejpam-5025	100	17	371	371	NUM
ejpam-5025	100	18	366	366	NUM
ejpam-5025	100	19	now	now	ADV
ejpam-5025	100	20	,	,	PUNCT
ejpam-5025	100	21	put	put	VERB
ejpam-5025	100	22	x	x	X
ejpam-5025	100	23	=	=	SYM
ejpam-5025	100	24	0	0	NUM
ejpam-5025	100	25	in	in	ADP
ejpam-5025	100	26	the	the	DET
ejpam-5025	100	27	last	last	ADJ
ejpam-5025	100	28	equation	equation	NOUN
ejpam-5025	100	29	,	,	PUNCT
ejpam-5025	100	30	to	to	PART
ejpam-5025	100	31	get	get	VERB
ejpam-5025	100	32	ζ(0	ζ(0	NOUN
ejpam-5025	100	33	)	)	PUNCT
ejpam-5025	100	34	=	=	SYM
ejpam-5025	100	35	0ζ(0	0ζ(0	X
ejpam-5025	100	36	)	)	PUNCT
ejpam-5025	100	37	∧	∧	NOUN
ejpam-5025	100	38	ζ(0)0	ζ(0)0	NOUN
ejpam-5025	100	39	=	=	SYM
ejpam-5025	100	40	0	0	NUM
ejpam-5025	100	41	∧	∧	PROPN
ejpam-5025	100	42	ζ(0)0	ζ(0)0	NOUN
ejpam-5025	100	43	[	[	PUNCT
ejpam-5025	100	44	by	by	ADP
ejpam-5025	100	45	axiom	axiom	NOUN
ejpam-5025	100	46	(	(	PUNCT
ejpam-5025	100	47	ii	ii	NOUN
ejpam-5025	100	48	)	)	PUNCT
ejpam-5025	100	49	in	in	ADP
ejpam-5025	100	50	definition	definition	NOUN
ejpam-5025	100	51	1	1	NUM
ejpam-5025	100	52	]	]	PUNCT
ejpam-5025	100	53	=	=	SYM
ejpam-5025	100	54	ζ(0)(ζ(0)0	ζ(0)(ζ(0)0	PROPN
ejpam-5025	100	55	)	)	PUNCT
ejpam-5025	100	56	[	[	PUNCT
ejpam-5025	100	57	by	by	ADP
ejpam-5025	100	58	x	x	PUNCT
ejpam-5025	100	59	∧	∧	PROPN
ejpam-5025	100	60	y	y	PROPN
ejpam-5025	100	61	=	=	SYM
ejpam-5025	100	62	y(yx	y(yx	PROPN
ejpam-5025	100	63	)	)	PUNCT
ejpam-5025	100	64	]	]	PUNCT
ejpam-5025	101	1	=	=	SYM
ejpam-5025	101	2	ζ(0)ζ(0	ζ(0)ζ(0	NOUN
ejpam-5025	101	3	)	)	PUNCT
ejpam-5025	102	1	[	[	X
ejpam-5025	102	2	by	by	ADP
ejpam-5025	102	3	lemma	lemma	PROPN
ejpam-5025	102	4	1	1	NUM
ejpam-5025	102	5	]	]	X
ejpam-5025	102	6	=	=	SYM
ejpam-5025	102	7	0	0	X
ejpam-5025	102	8	.	.	PUNCT
ejpam-5025	102	9	[	[	PUNCT
ejpam-5025	102	10	by	by	ADP
ejpam-5025	102	11	axiom	axiom	NOUN
ejpam-5025	102	12	(	(	PUNCT
ejpam-5025	102	13	i	i	NOUN
ejpam-5025	102	14	)	)	PUNCT
ejpam-5025	102	15	in	in	ADP
ejpam-5025	102	16	definition	definition	NOUN
ejpam-5025	102	17	1	1	NUM
ejpam-5025	102	18	]	]	PUNCT
ejpam-5025	102	19	hence	hence	ADV
ejpam-5025	102	20	ζ	ζ	NOUN
ejpam-5025	102	21	is	be	AUX
ejpam-5025	102	22	regular	regular	ADJ
ejpam-5025	102	23	.	.	PUNCT
ejpam-5025	103	1	now	now	ADV
ejpam-5025	103	2	,	,	PUNCT
ejpam-5025	103	3	replace	replace	VERB
ejpam-5025	103	4	the	the	DET
ejpam-5025	103	5	condition	condition	NOUN
ejpam-5025	103	6	x	x	PUNCT
ejpam-5025	103	7	is	be	AUX
ejpam-5025	103	8	an	an	DET
ejpam-5025	103	9	edge	edge	NOUN
ejpam-5025	103	10	d−algebra	d−algebra	X
ejpam-5025	103	11	by	by	SCONJ
ejpam-5025	103	12	x	x	SYM
ejpam-5025	103	13	is	be	AUX
ejpam-5025	103	14	a	a	DET
ejpam-5025	103	15	d−algebra	d−algebra	NOUN
ejpam-5025	103	16	in	in	ADP
ejpam-5025	103	17	theorem	theorem	NOUN
ejpam-5025	103	18	1	1	NUM
ejpam-5025	103	19	,	,	PUNCT
ejpam-5025	103	20	to	to	PART
ejpam-5025	103	21	obtain	obtain	VERB
ejpam-5025	103	22	the	the	DET
ejpam-5025	103	23	same	same	ADJ
ejpam-5025	103	24	results	result	NOUN
ejpam-5025	103	25	for	for	ADP
ejpam-5025	103	26	(	(	PUNCT
ejpam-5025	103	27	l	l	NOUN
ejpam-5025	103	28	,	,	PUNCT
ejpam-5025	103	29	r)−	r)−	PROPN
ejpam-5025	103	30	reverse	reverse	VERB
ejpam-5025	103	31	derivation	derivation	NOUN
ejpam-5025	103	32	as	as	ADP
ejpam-5025	103	33	in	in	ADP
ejpam-5025	103	34	the	the	DET
ejpam-5025	103	35	next	next	ADJ
ejpam-5025	103	36	theorem	theorem	PROPN
ejpam-5025	103	37	.	.	PUNCT
ejpam-5025	103	38	theorem	theorem	NOUN
ejpam-5025	103	39	2	2	NUM
ejpam-5025	103	40	.	.	PUNCT
ejpam-5025	104	1	if	if	SCONJ
ejpam-5025	104	2	ζ	ζ	PRON
ejpam-5025	104	3	:	:	PUNCT
ejpam-5025	104	4	x	x	PUNCT
ejpam-5025	104	5	−→	−→	NOUN
ejpam-5025	104	6	x	x	VERB
ejpam-5025	104	7	is	be	AUX
ejpam-5025	104	8	a	a	DET
ejpam-5025	104	9	(	(	PUNCT
ejpam-5025	104	10	l	l	NOUN
ejpam-5025	104	11	,	,	PUNCT
ejpam-5025	104	12	r	r	NOUN
ejpam-5025	104	13	)	)	PUNCT
ejpam-5025	104	14	−	−	NOUN
ejpam-5025	104	15	reverse	reverse	ADJ
ejpam-5025	104	16	derivation	derivation	NOUN
ejpam-5025	104	17	on	on	ADP
ejpam-5025	104	18	a	a	DET
ejpam-5025	104	19	d	d	NOUN
ejpam-5025	104	20	−	−	PROPN
ejpam-5025	104	21	algebra	algebra	NOUN
ejpam-5025	104	22	x	x	SYM
ejpam-5025	104	23	,	,	PUNCT
ejpam-5025	104	24	then	then	ADV
ejpam-5025	104	25	ζ	ζ	NOUN
ejpam-5025	104	26	is	be	AUX
ejpam-5025	104	27	regular	regular	ADJ
ejpam-5025	104	28	.	.	PUNCT
ejpam-5025	105	1	proof	proof	NOUN
ejpam-5025	105	2	.	.	PUNCT
ejpam-5025	106	1	assume	assume	VERB
ejpam-5025	106	2	that	that	SCONJ
ejpam-5025	106	3	ζ	ζ	NOUN
ejpam-5025	106	4	is	be	AUX
ejpam-5025	106	5	a	a	DET
ejpam-5025	106	6	(	(	PUNCT
ejpam-5025	106	7	l	l	NOUN
ejpam-5025	106	8	,	,	PUNCT
ejpam-5025	106	9	r	r	NOUN
ejpam-5025	106	10	)	)	PUNCT
ejpam-5025	106	11	−	−	NOUN
ejpam-5025	106	12	reverse	reverse	ADJ
ejpam-5025	106	13	derivation	derivation	NOUN
ejpam-5025	106	14	of	of	ADP
ejpam-5025	106	15	a	a	DET
ejpam-5025	106	16	d	d	NOUN
ejpam-5025	106	17	−	−	PROPN
ejpam-5025	106	18	algebra	algebra	NOUN
ejpam-5025	106	19	x	x	X
ejpam-5025	106	20	.	.	PUNCT
ejpam-5025	107	1	then	then	ADV
ejpam-5025	107	2	by	by	ADP
ejpam-5025	107	3	definition	definition	NOUN
ejpam-5025	107	4	of	of	ADP
ejpam-5025	107	5	ζ	ζ	NOUN
ejpam-5025	107	6	we	we	PRON
ejpam-5025	107	7	have	have	VERB
ejpam-5025	107	8	,	,	PUNCT
ejpam-5025	107	9	ζ(xy	ζ(xy	PROPN
ejpam-5025	107	10	)	)	PUNCT
ejpam-5025	107	11	=	=	PUNCT
ejpam-5025	108	1	ζ(y)x	ζ(y)x	X
ejpam-5025	108	2	∧	∧	PROPN
ejpam-5025	108	3	yζ(x	yζ(x	NOUN
ejpam-5025	108	4	)	)	PUNCT
ejpam-5025	108	5	∀	∀	X
ejpam-5025	109	1	x	x	NOUN
ejpam-5025	109	2	,	,	PUNCT
ejpam-5025	109	3	y	y	PROPN
ejpam-5025	109	4	∈	∈	PROPN
ejpam-5025	109	5	x	x	X
ejpam-5025	109	6	.	.	PUNCT
ejpam-5025	110	1	now	now	ADV
ejpam-5025	110	2	,	,	PUNCT
ejpam-5025	110	3	in	in	ADP
ejpam-5025	110	4	the	the	DET
ejpam-5025	110	5	previous	previous	ADJ
ejpam-5025	110	6	equation	equation	NOUN
ejpam-5025	110	7	replace	replace	VERB
ejpam-5025	110	8	y	y	NOUN
ejpam-5025	110	9	by	by	ADP
ejpam-5025	110	10	x	x	PUNCT
ejpam-5025	110	11	and	and	CCONJ
ejpam-5025	110	12	use	use	VERB
ejpam-5025	110	13	the	the	DET
ejpam-5025	110	14	axiom	axiom	NOUN
ejpam-5025	110	15	(	(	PUNCT
ejpam-5025	110	16	i	i	NOUN
ejpam-5025	110	17	)	)	PUNCT
ejpam-5025	110	18	in	in	ADP
ejpam-5025	110	19	definition	definition	NOUN
ejpam-5025	110	20	1	1	NUM
ejpam-5025	110	21	,	,	PUNCT
ejpam-5025	110	22	to	to	PART
ejpam-5025	110	23	get	get	VERB
ejpam-5025	110	24	ζ(0	ζ(0	NOUN
ejpam-5025	110	25	)	)	PUNCT
ejpam-5025	110	26	=	=	SYM
ejpam-5025	110	27	ζ(xx	ζ(xx	PROPN
ejpam-5025	110	28	)	)	PUNCT
ejpam-5025	110	29	=	=	SYM
ejpam-5025	110	30	ζ(x)x∧xζ(x	ζ(x)x∧xζ(x	NOUN
ejpam-5025	110	31	)	)	PUNCT
ejpam-5025	110	32	,	,	PUNCT
ejpam-5025	110	33	∀	∀	PUNCT
ejpam-5025	110	34	x	x	SYM
ejpam-5025	110	35	∈	∈	NOUN
ejpam-5025	110	36	x	x	X
ejpam-5025	110	37	.	.	PUNCT
ejpam-5025	111	1	now	now	ADV
ejpam-5025	111	2	,	,	PUNCT
ejpam-5025	111	3	put	put	VERB
ejpam-5025	111	4	x	x	X
ejpam-5025	111	5	=	=	SYM
ejpam-5025	111	6	0	0	NUM
ejpam-5025	111	7	in	in	ADP
ejpam-5025	111	8	the	the	DET
ejpam-5025	111	9	previous	previous	ADJ
ejpam-5025	111	10	equation	equation	NOUN
ejpam-5025	111	11	,	,	PUNCT
ejpam-5025	111	12	to	to	PART
ejpam-5025	111	13	get	get	VERB
ejpam-5025	111	14	ζ(0	ζ(0	NOUN
ejpam-5025	111	15	)	)	PUNCT
ejpam-5025	112	1	=	=	SYM
ejpam-5025	112	2	ζ(0)0	ζ(0)0	NOUN
ejpam-5025	112	3	∧	∧	PROPN
ejpam-5025	112	4	0ζ(0	0ζ(0	NUM
ejpam-5025	112	5	)	)	PUNCT
ejpam-5025	112	6	=	=	SYM
ejpam-5025	113	1	ζ(0)0	ζ(0)0	NOUN
ejpam-5025	113	2	∧	∧	PROPN
ejpam-5025	113	3	0	0	PUNCT
ejpam-5025	114	1	[	[	X
ejpam-5025	114	2	using	use	VERB
ejpam-5025	114	3	axiom	axiom	NOUN
ejpam-5025	114	4	(	(	PUNCT
ejpam-5025	114	5	ii	ii	NOUN
ejpam-5025	114	6	)	)	PUNCT
ejpam-5025	114	7	in	in	ADP
ejpam-5025	114	8	definition	definition	NOUN
ejpam-5025	114	9	1	1	NUM
ejpam-5025	114	10	]	]	PUNCT
ejpam-5025	114	11	=	=	PUNCT
ejpam-5025	114	12	0(0ζ(0	0(0ζ(0	NOUN
ejpam-5025	114	13	)	)	PUNCT
ejpam-5025	114	14	)	)	PUNCT
ejpam-5025	115	1	[	[	X
ejpam-5025	115	2	by	by	ADP
ejpam-5025	115	3	x	x	PUNCT
ejpam-5025	115	4	∧	∧	PROPN
ejpam-5025	115	5	y	y	PROPN
ejpam-5025	115	6	=	=	SYM
ejpam-5025	115	7	y(yx	y(yx	PROPN
ejpam-5025	115	8	)	)	PUNCT
ejpam-5025	115	9	]	]	PUNCT
ejpam-5025	115	10	=	=	PUNCT
ejpam-5025	115	11	0	0	X
ejpam-5025	115	12	.	.	PUNCT
ejpam-5025	116	1	[	[	X
ejpam-5025	116	2	again	again	ADV
ejpam-5025	116	3	using	use	VERB
ejpam-5025	116	4	axiom	axiom	NOUN
ejpam-5025	116	5	(	(	PUNCT
ejpam-5025	116	6	ii	ii	NOUN
ejpam-5025	116	7	)	)	PUNCT
ejpam-5025	116	8	in	in	ADP
ejpam-5025	116	9	definition	definition	NOUN
ejpam-5025	116	10	1	1	NUM
ejpam-5025	116	11	]	]	PUNCT
ejpam-5025	116	12	hence	hence	ADV
ejpam-5025	116	13	ζ	ζ	NOUN
ejpam-5025	116	14	is	be	AUX
ejpam-5025	116	15	regular	regular	ADJ
ejpam-5025	116	16	.	.	PUNCT
ejpam-5025	117	1	theorem	theorem	NOUN
ejpam-5025	117	2	3	3	X
ejpam-5025	117	3	.	.	PUNCT
ejpam-5025	117	4	suppose	suppose	VERB
ejpam-5025	117	5	that	that	SCONJ
ejpam-5025	117	6	x	x	PRON
ejpam-5025	117	7	be	be	AUX
ejpam-5025	117	8	an	an	DET
ejpam-5025	117	9	edge	edge	NOUN
ejpam-5025	117	10	d−algebra	d−algebra	NOUN
ejpam-5025	117	11	and	and	CCONJ
ejpam-5025	117	12	ζ	ζ	NOUN
ejpam-5025	117	13	:	:	PUNCT
ejpam-5025	117	14	x	x	PUNCT
ejpam-5025	117	15	−→	−→	NOUN
ejpam-5025	117	16	x	x	VERB
ejpam-5025	117	17	is	be	AUX
ejpam-5025	117	18	a	a	DET
ejpam-5025	117	19	(	(	PUNCT
ejpam-5025	117	20	l	l	NOUN
ejpam-5025	117	21	,	,	PUNCT
ejpam-5025	117	22	r)−	r)−	PROPN
ejpam-5025	117	23	reverse	reverse	ADJ
ejpam-5025	117	24	derivation	derivation	NOUN
ejpam-5025	117	25	of	of	ADP
ejpam-5025	117	26	x	x	SYM
ejpam-5025	117	27	such	such	ADJ
ejpam-5025	117	28	that	that	SCONJ
ejpam-5025	117	29	ζ(x	ζ(x	NOUN
ejpam-5025	117	30	)	)	PUNCT
ejpam-5025	117	31	=	=	SYM
ejpam-5025	118	1	x	x	X
ejpam-5025	118	2	,	,	PUNCT
ejpam-5025	118	3	then	then	ADV
ejpam-5025	118	4	(	(	PUNCT
ejpam-5025	118	5	i	i	NOUN
ejpam-5025	118	6	)	)	PUNCT
ejpam-5025	118	7	ζ	ζ	PROPN
ejpam-5025	118	8	is	be	AUX
ejpam-5025	118	9	a	a	DET
ejpam-5025	118	10	reverse	reverse	ADJ
ejpam-5025	118	11	derivation	derivation	NOUN
ejpam-5025	118	12	on	on	ADP
ejpam-5025	118	13	x	x	X
ejpam-5025	118	14	.	.	PUNCT
ejpam-5025	119	1	(	(	PUNCT
ejpam-5025	119	2	ii	ii	NOUN
ejpam-5025	119	3	)	)	PUNCT
ejpam-5025	119	4	ζ(xy	ζ(xy	PROPN
ejpam-5025	119	5	)	)	PUNCT
ejpam-5025	119	6	=	=	SYM
ejpam-5025	119	7	ζ(y)ζ(x	ζ(y)ζ(x	NOUN
ejpam-5025	119	8	)	)	PUNCT
ejpam-5025	119	9	,	,	PUNCT
ejpam-5025	119	10	∀	∀	X
ejpam-5025	120	1	x	x	NOUN
ejpam-5025	120	2	,	,	PUNCT
ejpam-5025	120	3	y	y	PROPN
ejpam-5025	120	4	∈	∈	PROPN
ejpam-5025	120	5	x	x	X
ejpam-5025	120	6	.	.	PUNCT
ejpam-5025	121	1	proof	proof	NOUN
ejpam-5025	121	2	.	.	PUNCT
ejpam-5025	122	1	(	(	PUNCT
ejpam-5025	122	2	1	1	X
ejpam-5025	122	3	)	)	PUNCT
ejpam-5025	122	4	suppose	suppose	VERB
ejpam-5025	122	5	that	that	SCONJ
ejpam-5025	122	6	ζ	ζ	NOUN
ejpam-5025	122	7	be	be	AUX
ejpam-5025	122	8	a	a	DET
ejpam-5025	122	9	(	(	PUNCT
ejpam-5025	122	10	l	l	NOUN
ejpam-5025	122	11	,	,	PUNCT
ejpam-5025	122	12	r)−	r)−	PROPN
ejpam-5025	122	13	reverse	reverse	VERB
ejpam-5025	122	14	derivation	derivation	NOUN
ejpam-5025	122	15	on	on	ADP
ejpam-5025	122	16	edge	edge	NOUN
ejpam-5025	122	17	d−algebra	d−algebra	NOUN
ejpam-5025	122	18	x	x	X
ejpam-5025	122	19	where	where	SCONJ
ejpam-5025	122	20	ζ(x	ζ(x	NOUN
ejpam-5025	122	21	)	)	PUNCT
ejpam-5025	123	1	=	=	SYM
ejpam-5025	123	2	x	x	SYM
ejpam-5025	123	3	∀	∀	PUNCT
ejpam-5025	123	4	x	x	SYM
ejpam-5025	123	5	∈	∈	NOUN
ejpam-5025	123	6	x	x	X
ejpam-5025	123	7	,	,	PUNCT
ejpam-5025	123	8	therefore	therefore	ADV
ejpam-5025	123	9	,	,	PUNCT
ejpam-5025	123	10	to	to	PART
ejpam-5025	123	11	prove	prove	VERB
ejpam-5025	123	12	that	that	SCONJ
ejpam-5025	123	13	ζ	ζ	NOUN
ejpam-5025	123	14	is	be	AUX
ejpam-5025	123	15	a	a	DET
ejpam-5025	123	16	reverse	reverse	ADJ
ejpam-5025	123	17	derivation	derivation	NOUN
ejpam-5025	123	18	of	of	ADP
ejpam-5025	123	19	x	x	PRON
ejpam-5025	123	20	it	it	PRON
ejpam-5025	123	21	is	be	AUX
ejpam-5025	123	22	enough	enough	ADJ
ejpam-5025	123	23	to	to	PART
ejpam-5025	123	24	verify	verify	VERB
ejpam-5025	123	25	that	that	SCONJ
ejpam-5025	123	26	ζ	ζ	NOUN
ejpam-5025	123	27	is	be	AUX
ejpam-5025	123	28	a	a	DET
ejpam-5025	123	29	(	(	PUNCT
ejpam-5025	123	30	r	r	NOUN
ejpam-5025	123	31	,	,	PUNCT
ejpam-5025	123	32	l	l	NOUN
ejpam-5025	123	33	)	)	PUNCT
ejpam-5025	123	34	−	−	ADP
ejpam-5025	123	35	reverse	reverse	ADJ
ejpam-5025	123	36	derivation	derivation	NOUN
ejpam-5025	123	37	on	on	ADP
ejpam-5025	123	38	x	x	PUNCT
ejpam-5025	123	39	as	as	SCONJ
ejpam-5025	123	40	follows	follow	VERB
ejpam-5025	123	41	:	:	PUNCT
ejpam-5025	123	42	by	by	ADP
ejpam-5025	123	43	assumption	assumption	NOUN
ejpam-5025	123	44	ζ	ζ	NOUN
ejpam-5025	123	45	is	be	AUX
ejpam-5025	123	46	a	a	DET
ejpam-5025	123	47	(	(	PUNCT
ejpam-5025	123	48	l	l	NOUN
ejpam-5025	123	49	,	,	PUNCT
ejpam-5025	123	50	r)−	r)−	PROPN
ejpam-5025	123	51	reverse	reverse	ADJ
ejpam-5025	123	52	derivation	derivation	NOUN
ejpam-5025	123	53	of	of	ADP
ejpam-5025	123	54	x	x	INTJ
ejpam-5025	123	55	,	,	PUNCT
ejpam-5025	123	56	so	so	SCONJ
ejpam-5025	123	57	∀	∀	NOUN
ejpam-5025	123	58	x	x	NOUN
ejpam-5025	123	59	,	,	PUNCT
ejpam-5025	123	60	y	y	PROPN
ejpam-5025	123	61	∈	∈	PROPN
ejpam-5025	123	62	x	x	INTJ
ejpam-5025	123	63	we	we	PRON
ejpam-5025	123	64	get	get	VERB
ejpam-5025	123	65	ζ(xy	ζ(xy	NOUN
ejpam-5025	123	66	)	)	PUNCT
ejpam-5025	123	67	=	=	PUNCT
ejpam-5025	123	68	ζ(y)x	ζ(y)x	X
ejpam-5025	123	69	∧	∧	PROPN
ejpam-5025	123	70	yζ(x	yζ(x	NOUN
ejpam-5025	123	71	)	)	PUNCT
ejpam-5025	123	72	=	=	SYM
ejpam-5025	123	73	yζ(x	yζ(x	NOUN
ejpam-5025	123	74	)	)	PUNCT
ejpam-5025	123	75	∧	∧	PROPN
ejpam-5025	123	76	ζ(y)x	ζ(y)x	PROPN
ejpam-5025	123	77	.	.	PUNCT
ejpam-5025	124	1	[	[	X
ejpam-5025	124	2	using	use	VERB
ejpam-5025	124	3	the	the	DET
ejpam-5025	124	4	assumption	assumption	NOUN
ejpam-5025	124	5	that	that	SCONJ
ejpam-5025	124	6	ζ(y	ζ(y	PRON
ejpam-5025	124	7	)	)	PUNCT
ejpam-5025	124	8	=	=	SYM
ejpam-5025	124	9	y	y	PROPN
ejpam-5025	124	10	,	,	PUNCT
ejpam-5025	124	11	ζ(x	ζ(x	NOUN
ejpam-5025	124	12	)	)	PUNCT
ejpam-5025	124	13	=	=	SYM
ejpam-5025	124	14	x	x	X
ejpam-5025	124	15	]	]	X
ejpam-5025	124	16	thus	thus	ADV
ejpam-5025	124	17	,	,	PUNCT
ejpam-5025	124	18	ζ	ζ	NOUN
ejpam-5025	124	19	is	be	AUX
ejpam-5025	124	20	a	a	DET
ejpam-5025	124	21	(	(	PUNCT
ejpam-5025	124	22	r	r	NOUN
ejpam-5025	124	23	,	,	PUNCT
ejpam-5025	124	24	l)−	l)−	NOUN
ejpam-5025	124	25	reverse	reverse	VERB
ejpam-5025	124	26	derivation	derivation	NOUN
ejpam-5025	124	27	on	on	ADP
ejpam-5025	124	28	x	x	SYM
ejpam-5025	124	29	,	,	PUNCT
ejpam-5025	124	30	hence	hence	ADV
ejpam-5025	124	31	we	we	PRON
ejpam-5025	124	32	conclude	conclude	VERB
ejpam-5025	124	33	that	that	SCONJ
ejpam-5025	124	34	ζ	ζ	NOUN
ejpam-5025	124	35	is	be	AUX
ejpam-5025	124	36	a	a	DET
ejpam-5025	124	37	reverse	reverse	ADJ
ejpam-5025	124	38	derivation	derivation	NOUN
ejpam-5025	124	39	on	on	ADP
ejpam-5025	124	40	x	x	X
ejpam-5025	124	41	.	.	PUNCT
ejpam-5025	125	1	k.	k.	PROPN
ejpam-5025	125	2	alnefaie	alnefaie	PROPN
ejpam-5025	125	3	/	/	SYM
ejpam-5025	125	4	eur	eur	PROPN
ejpam-5025	125	5	.	.	PUNCT
ejpam-5025	126	1	j.	j.	PROPN
ejpam-5025	126	2	pure	pure	PROPN
ejpam-5025	126	3	appl	appl	PROPN
ejpam-5025	126	4	.	.	PROPN
ejpam-5025	126	5	math	math	PROPN
ejpam-5025	126	6	,	,	PUNCT
ejpam-5025	126	7	17	17	NUM
ejpam-5025	126	8	(	(	PUNCT
ejpam-5025	126	9	1	1	NUM
ejpam-5025	126	10	)	)	PUNCT
ejpam-5025	126	11	(	(	PUNCT
ejpam-5025	126	12	2024	2024	NUM
ejpam-5025	126	13	)	)	PUNCT
ejpam-5025	126	14	,	,	PUNCT
ejpam-5025	126	15	362	362	NUM
ejpam-5025	126	16	-	-	SYM
ejpam-5025	126	17	371	371	NUM
ejpam-5025	126	18	367	367	NUM
ejpam-5025	126	19	(	(	PUNCT
ejpam-5025	126	20	2	2	NUM
ejpam-5025	126	21	)	)	PUNCT
ejpam-5025	126	22	for	for	ADP
ejpam-5025	126	23	all	all	DET
ejpam-5025	126	24	x	x	NOUN
ejpam-5025	126	25	,	,	PUNCT
ejpam-5025	126	26	y	y	PROPN
ejpam-5025	126	27	∈	∈	PROPN
ejpam-5025	126	28	x	x	INTJ
ejpam-5025	126	29	,	,	PUNCT
ejpam-5025	126	30	we	we	PRON
ejpam-5025	126	31	have	have	AUX
ejpam-5025	126	32	ζ(xy	ζ(xy	PROPN
ejpam-5025	126	33	)	)	PUNCT
ejpam-5025	126	34	=	=	PUNCT
ejpam-5025	126	35	ζ(y)x	ζ(y)x	X
ejpam-5025	126	36	∧	∧	PROPN
ejpam-5025	126	37	yζ(x	yζ(x	NOUN
ejpam-5025	126	38	)	)	PUNCT
ejpam-5025	127	1	[	[	X
ejpam-5025	127	2	by	by	ADP
ejpam-5025	127	3	the	the	DET
ejpam-5025	127	4	definition	definition	NOUN
ejpam-5025	127	5	4	4	NUM
ejpam-5025	127	6	]	]	PUNCT
ejpam-5025	127	7	=	=	PUNCT
ejpam-5025	127	8	yx	yx	PROPN
ejpam-5025	127	9	∧	∧	PROPN
ejpam-5025	127	10	yx	yx	PROPN
ejpam-5025	128	1	[	[	X
ejpam-5025	128	2	by	by	ADP
ejpam-5025	128	3	assumption	assumption	NOUN
ejpam-5025	128	4	that	that	SCONJ
ejpam-5025	128	5	ζ(x	ζ(x	NOUN
ejpam-5025	128	6	)	)	PUNCT
ejpam-5025	128	7	=	=	SYM
ejpam-5025	129	1	x	x	X
ejpam-5025	129	2	]	]	X
ejpam-5025	129	3	=	=	X
ejpam-5025	129	4	yx[yx(yx	yx[yx(yx	NOUN
ejpam-5025	129	5	)	)	PUNCT
ejpam-5025	129	6	]	]	PUNCT
ejpam-5025	130	1	[	[	X
ejpam-5025	130	2	using	use	VERB
ejpam-5025	130	3	x	x	PUNCT
ejpam-5025	130	4	∧	∧	PROPN
ejpam-5025	130	5	y	y	PROPN
ejpam-5025	130	6	=	=	SYM
ejpam-5025	130	7	y(yx	y(yx	PROPN
ejpam-5025	130	8	)	)	PUNCT
ejpam-5025	130	9	]	]	PUNCT
ejpam-5025	130	10	=	=	PUNCT
ejpam-5025	131	1	(	(	PUNCT
ejpam-5025	131	2	yx)0	yx)0	NOUN
ejpam-5025	131	3	[	[	X
ejpam-5025	131	4	using	use	VERB
ejpam-5025	131	5	axiom	axiom	NOUN
ejpam-5025	131	6	(	(	PUNCT
ejpam-5025	131	7	i	i	NOUN
ejpam-5025	131	8	)	)	PUNCT
ejpam-5025	131	9	in	in	ADP
ejpam-5025	131	10	definition	definition	NOUN
ejpam-5025	131	11	1	1	NUM
ejpam-5025	131	12	]	]	PUNCT
ejpam-5025	132	1	=	=	PUNCT
ejpam-5025	132	2	yx	yx	X
ejpam-5025	133	1	[	[	X
ejpam-5025	133	2	by	by	ADP
ejpam-5025	133	3	lemma	lemma	PROPN
ejpam-5025	133	4	1	1	NUM
ejpam-5025	133	5	]	]	X
ejpam-5025	133	6	=	=	NOUN
ejpam-5025	133	7	ζ(y)ζ(x	ζ(y)ζ(x	NOUN
ejpam-5025	133	8	)	)	PUNCT
ejpam-5025	133	9	.	.	PUNCT
ejpam-5025	134	1	[	[	X
ejpam-5025	134	2	again	again	ADV
ejpam-5025	134	3	by	by	ADP
ejpam-5025	134	4	assumption	assumption	NOUN
ejpam-5025	134	5	that	that	SCONJ
ejpam-5025	134	6	ζ(x	ζ(x	NOUN
ejpam-5025	134	7	)	)	PUNCT
ejpam-5025	134	8	=	=	SYM
ejpam-5025	134	9	x	x	X
ejpam-5025	134	10	]	]	X
ejpam-5025	134	11	hence	hence	ADV
ejpam-5025	134	12	,	,	PUNCT
ejpam-5025	134	13	we	we	PRON
ejpam-5025	134	14	get	get	VERB
ejpam-5025	134	15	the	the	DET
ejpam-5025	134	16	required	require	VERB
ejpam-5025	134	17	result	result	NOUN
ejpam-5025	134	18	.	.	PUNCT
ejpam-5025	135	1	by	by	ADP
ejpam-5025	135	2	using	use	VERB
ejpam-5025	135	3	the	the	DET
ejpam-5025	135	4	similar	similar	ADJ
ejpam-5025	135	5	arguments	argument	NOUN
ejpam-5025	135	6	as	as	ADP
ejpam-5025	135	7	in	in	ADP
ejpam-5025	135	8	theorem	theorem	ADJ
ejpam-5025	135	9	3	3	NUM
ejpam-5025	135	10	(	(	PUNCT
ejpam-5025	135	11	2	2	NUM
ejpam-5025	135	12	)	)	PUNCT
ejpam-5025	135	13	,	,	PUNCT
ejpam-5025	135	14	it	it	PRON
ejpam-5025	135	15	is	be	AUX
ejpam-5025	135	16	easy	easy	ADJ
ejpam-5025	135	17	to	to	PART
ejpam-5025	135	18	show	show	VERB
ejpam-5025	135	19	that	that	SCONJ
ejpam-5025	135	20	,	,	PUNCT
ejpam-5025	135	21	if	if	SCONJ
ejpam-5025	135	22	ζ	ζ	NOUN
ejpam-5025	135	23	is	be	AUX
ejpam-5025	135	24	a	a	DET
ejpam-5025	135	25	(	(	PUNCT
ejpam-5025	135	26	r	r	NOUN
ejpam-5025	135	27	,	,	PUNCT
ejpam-5025	135	28	l)−reverse	l)−reverse	VERB
ejpam-5025	135	29	derivation	derivation	NOUN
ejpam-5025	135	30	of	of	ADP
ejpam-5025	135	31	edge	edge	NOUN
ejpam-5025	135	32	algebra	algebra	PROPN
ejpam-5025	135	33	x	x	PUNCT
ejpam-5025	135	34	,	,	PUNCT
ejpam-5025	135	35	then	then	ADV
ejpam-5025	135	36	also	also	ADV
ejpam-5025	135	37	we	we	PRON
ejpam-5025	135	38	get	get	VERB
ejpam-5025	135	39	ζ(xy	ζ(xy	NOUN
ejpam-5025	135	40	)	)	PUNCT
ejpam-5025	135	41	=	=	PUNCT
ejpam-5025	135	42	ζ(y)ζ(x	ζ(y)ζ(x	NOUN
ejpam-5025	135	43	)	)	PUNCT
ejpam-5025	135	44	∀	∀	PUNCT
ejpam-5025	136	1	x	x	NOUN
ejpam-5025	136	2	,	,	PUNCT
ejpam-5025	136	3	y	y	PROPN
ejpam-5025	136	4	∈	∈	PROPN
ejpam-5025	136	5	x	x	X
ejpam-5025	136	6	.	.	PUNCT
ejpam-5025	137	1	definition	definition	NOUN
ejpam-5025	137	2	6	6	NUM
ejpam-5025	137	3	.	.	PUNCT
ejpam-5025	138	1	if	if	SCONJ
ejpam-5025	138	2	ζ	ζ	NOUN
ejpam-5025	138	3	,	,	PUNCT
ejpam-5025	138	4	ζ	ζ	NOUN
ejpam-5025	138	5	′	′	NOUN
ejpam-5025	138	6	are	be	AUX
ejpam-5025	138	7	two	two	NUM
ejpam-5025	138	8	self	self	NOUN
ejpam-5025	138	9	maps	map	NOUN
ejpam-5025	138	10	on	on	ADP
ejpam-5025	138	11	a	a	DET
ejpam-5025	138	12	d−algebra	d−algebra	NOUN
ejpam-5025	138	13	x	x	SYM
ejpam-5025	138	14	,	,	PUNCT
ejpam-5025	138	15	then	then	ADV
ejpam-5025	138	16	the	the	DET
ejpam-5025	138	17	map	map	NOUN
ejpam-5025	138	18	ζ	ζ	NOUN
ejpam-5025	138	19	◦	◦	NOUN
ejpam-5025	138	20	ζ	ζ	NOUN
ejpam-5025	138	21	′	′	NOUN
ejpam-5025	138	22	:	:	PUNCT
ejpam-5025	139	1	x	x	PUNCT
ejpam-5025	139	2	−→	−→	NOUN
ejpam-5025	139	3	x	x	PUNCT
ejpam-5025	139	4	defined	define	VERB
ejpam-5025	139	5	as	as	ADP
ejpam-5025	139	6	ζ	ζ	NOUN
ejpam-5025	139	7	◦	◦	NOUN
ejpam-5025	139	8	ζ	ζ	NOUN
ejpam-5025	139	9	′	′	NOUN
ejpam-5025	139	10	(	(	PUNCT
ejpam-5025	139	11	x	x	X
ejpam-5025	139	12	)	)	PUNCT
ejpam-5025	139	13	=	=	SYM
ejpam-5025	139	14	ζ(ζ	ζ(ζ	PROPN
ejpam-5025	139	15	′	′	NUM
ejpam-5025	139	16	(	(	PUNCT
ejpam-5025	139	17	x	x	NOUN
ejpam-5025	139	18	)	)	PUNCT
ejpam-5025	139	19	)	)	PUNCT
ejpam-5025	139	20	,	,	PUNCT
ejpam-5025	139	21	∀	∀	PUNCT
ejpam-5025	139	22	x	x	SYM
ejpam-5025	139	23	∈	∈	NOUN
ejpam-5025	139	24	x	x	X
ejpam-5025	139	25	.	.	PUNCT
ejpam-5025	139	26	theorem	theorem	ADJ
ejpam-5025	139	27	4	4	NUM
ejpam-5025	139	28	.	.	PUNCT
ejpam-5025	139	29	suppose	suppose	VERB
ejpam-5025	139	30	that	that	SCONJ
ejpam-5025	139	31	ζ	ζ	NOUN
ejpam-5025	139	32	and	and	CCONJ
ejpam-5025	139	33	ζ	ζ	NOUN
ejpam-5025	139	34	′	′	NOUN
ejpam-5025	139	35	are	be	AUX
ejpam-5025	139	36	two	two	NUM
ejpam-5025	139	37	(	(	PUNCT
ejpam-5025	139	38	r	r	NOUN
ejpam-5025	139	39	,	,	PUNCT
ejpam-5025	139	40	l	l	NOUN
ejpam-5025	139	41	)	)	PUNCT
ejpam-5025	139	42	−	−	ADP
ejpam-5025	139	43	reverse	reverse	ADJ
ejpam-5025	139	44	derivations	derivation	NOUN
ejpam-5025	139	45	on	on	ADP
ejpam-5025	139	46	an	an	DET
ejpam-5025	139	47	edge	edge	NOUN
ejpam-5025	140	1	d	d	PRON
ejpam-5025	140	2	−	−	PROPN
ejpam-5025	140	3	algebra	algebra	NOUN
ejpam-5025	140	4	x	x	SYM
ejpam-5025	140	5	,	,	PUNCT
ejpam-5025	140	6	then	then	ADV
ejpam-5025	140	7	the	the	DET
ejpam-5025	140	8	map	map	NOUN
ejpam-5025	140	9	ζ	ζ	NOUN
ejpam-5025	140	10	◦	◦	NOUN
ejpam-5025	140	11	ζ	ζ	NOUN
ejpam-5025	140	12	′	′	NOUN
ejpam-5025	140	13	is	be	AUX
ejpam-5025	140	14	regular	regular	ADJ
ejpam-5025	140	15	.	.	PUNCT
ejpam-5025	141	1	proof	proof	NOUN
ejpam-5025	141	2	.	.	PUNCT
ejpam-5025	142	1	let	let	VERB
ejpam-5025	142	2	ζ	ζ	NOUN
ejpam-5025	142	3	,	,	PUNCT
ejpam-5025	142	4	ζ	ζ	NOUN
ejpam-5025	142	5	′	′	NOUN
ejpam-5025	142	6	are	be	AUX
ejpam-5025	142	7	two	two	NUM
ejpam-5025	142	8	(	(	PUNCT
ejpam-5025	142	9	r	r	NOUN
ejpam-5025	142	10	,	,	PUNCT
ejpam-5025	142	11	l	l	NOUN
ejpam-5025	142	12	)	)	PUNCT
ejpam-5025	142	13	−	−	ADP
ejpam-5025	142	14	reverse	reverse	ADJ
ejpam-5025	142	15	derivations	derivation	NOUN
ejpam-5025	142	16	on	on	ADP
ejpam-5025	142	17	x	x	X
ejpam-5025	142	18	.	.	PUNCT
ejpam-5025	143	1	then	then	ADV
ejpam-5025	143	2	by	by	ADP
ejpam-5025	143	3	definition	definition	NOUN
ejpam-5025	143	4	,	,	PUNCT
ejpam-5025	143	5	we	we	PRON
ejpam-5025	143	6	have	have	VERB
ejpam-5025	143	7	ζ	ζ	NOUN
ejpam-5025	143	8	◦	◦	NOUN
ejpam-5025	143	9	ζ	ζ	NOUN
ejpam-5025	143	10	′	′	NOUN
ejpam-5025	143	11	(	(	PUNCT
ejpam-5025	143	12	xy	xy	NOUN
ejpam-5025	143	13	)	)	PUNCT
ejpam-5025	143	14	=	=	SYM
ejpam-5025	144	1	y(ζ	y(ζ	PROPN
ejpam-5025	144	2	◦	◦	VERB
ejpam-5025	144	3	ζ	ζ	NOUN
ejpam-5025	144	4	′	′	NUM
ejpam-5025	144	5	)	)	PUNCT
ejpam-5025	144	6	(	(	PUNCT
ejpam-5025	144	7	x	x	X
ejpam-5025	144	8	)	)	PUNCT
ejpam-5025	144	9	∧	∧	NOUN
ejpam-5025	144	10	(	(	PUNCT
ejpam-5025	144	11	ζ	ζ	NOUN
ejpam-5025	144	12	◦	◦	VERB
ejpam-5025	144	13	ζ	ζ	NOUN
ejpam-5025	144	14	′	′	NUM
ejpam-5025	144	15	)	)	PUNCT
ejpam-5025	144	16	(	(	PUNCT
ejpam-5025	144	17	y)x	y)x	NOUN
ejpam-5025	144	18	,	,	PUNCT
ejpam-5025	144	19	∀	∀	X
ejpam-5025	144	20	x	x	NOUN
ejpam-5025	144	21	,	,	PUNCT
ejpam-5025	144	22	y	y	PROPN
ejpam-5025	144	23	∈	∈	PROPN
ejpam-5025	144	24	x	x	X
ejpam-5025	144	25	.	.	PUNCT
ejpam-5025	145	1	replacing	replace	VERB
ejpam-5025	145	2	y	y	PRON
ejpam-5025	145	3	by	by	ADP
ejpam-5025	145	4	x	x	PROPN
ejpam-5025	145	5	in	in	ADP
ejpam-5025	145	6	the	the	DET
ejpam-5025	145	7	last	last	ADJ
ejpam-5025	145	8	equation	equation	NOUN
ejpam-5025	145	9	and	and	CCONJ
ejpam-5025	145	10	using	use	VERB
ejpam-5025	145	11	axiom	axiom	NOUN
ejpam-5025	145	12	(	(	PUNCT
ejpam-5025	145	13	i	i	NOUN
ejpam-5025	145	14	)	)	PUNCT
ejpam-5025	145	15	in	in	ADP
ejpam-5025	145	16	the	the	DET
ejpam-5025	145	17	definition	definition	NOUN
ejpam-5025	145	18	1	1	NUM
ejpam-5025	145	19	,	,	PUNCT
ejpam-5025	145	20	we	we	PRON
ejpam-5025	145	21	get	get	VERB
ejpam-5025	145	22	(	(	PUNCT
ejpam-5025	145	23	ζ	ζ	NOUN
ejpam-5025	145	24	◦	◦	VERB
ejpam-5025	145	25	ζ	ζ	NOUN
ejpam-5025	145	26	′	′	NUM
ejpam-5025	145	27	)	)	PUNCT
ejpam-5025	145	28	(	(	PUNCT
ejpam-5025	145	29	0	0	NUM
ejpam-5025	145	30	)	)	PUNCT
ejpam-5025	145	31	=	=	SYM
ejpam-5025	146	1	(	(	PUNCT
ejpam-5025	146	2	ζ	ζ	NOUN
ejpam-5025	146	3	◦	◦	VERB
ejpam-5025	146	4	ζ	ζ	NOUN
ejpam-5025	146	5	′	′	NUM
ejpam-5025	146	6	)	)	PUNCT
ejpam-5025	146	7	(	(	PUNCT
ejpam-5025	146	8	xx	xx	X
ejpam-5025	146	9	)	)	PUNCT
ejpam-5025	146	10	=	=	SYM
ejpam-5025	147	1	x(ζ	x(ζ	PUNCT
ejpam-5025	147	2	◦	◦	VERB
ejpam-5025	147	3	ζ	ζ	NOUN
ejpam-5025	147	4	′	′	NUM
ejpam-5025	147	5	)	)	PUNCT
ejpam-5025	147	6	(	(	PUNCT
ejpam-5025	147	7	x	x	X
ejpam-5025	147	8	)	)	PUNCT
ejpam-5025	147	9	∧	∧	NOUN
ejpam-5025	147	10	(	(	PUNCT
ejpam-5025	147	11	ζ	ζ	NOUN
ejpam-5025	147	12	◦	◦	VERB
ejpam-5025	147	13	ζ	ζ	NOUN
ejpam-5025	147	14	′	′	NUM
ejpam-5025	147	15	)	)	PUNCT
ejpam-5025	147	16	(	(	PUNCT
ejpam-5025	147	17	x)x	x)x	X
ejpam-5025	147	18	,	,	PUNCT
ejpam-5025	147	19	∀	∀	X
ejpam-5025	148	1	x	x	SYM
ejpam-5025	148	2	∈	∈	NOUN
ejpam-5025	148	3	x	x	X
ejpam-5025	148	4	.	.	PUNCT
ejpam-5025	149	1	now	now	ADV
ejpam-5025	149	2	,	,	PUNCT
ejpam-5025	149	3	put	put	VERB
ejpam-5025	149	4	x	x	X
ejpam-5025	149	5	=	=	SYM
ejpam-5025	149	6	0	0	NUM
ejpam-5025	149	7	in	in	ADP
ejpam-5025	149	8	the	the	DET
ejpam-5025	149	9	last	last	ADJ
ejpam-5025	149	10	equation	equation	NOUN
ejpam-5025	149	11	,	,	PUNCT
ejpam-5025	149	12	to	to	PART
ejpam-5025	149	13	get	get	VERB
ejpam-5025	149	14	(	(	PUNCT
ejpam-5025	149	15	ζ	ζ	NOUN
ejpam-5025	149	16	◦	◦	VERB
ejpam-5025	149	17	ζ	ζ	NOUN
ejpam-5025	149	18	′	′	NUM
ejpam-5025	149	19	)	)	PUNCT
ejpam-5025	149	20	(	(	PUNCT
ejpam-5025	149	21	0	0	NUM
ejpam-5025	149	22	)	)	PUNCT
ejpam-5025	149	23	=	=	NOUN
ejpam-5025	149	24	0(ζ	0(ζ	NUM
ejpam-5025	149	25	◦	◦	VERB
ejpam-5025	149	26	ζ	ζ	NOUN
ejpam-5025	149	27	′	′	NUM
ejpam-5025	149	28	)	)	PUNCT
ejpam-5025	150	1	(	(	PUNCT
ejpam-5025	150	2	0	0	X
ejpam-5025	150	3	)	)	PUNCT
ejpam-5025	150	4	∧	∧	NOUN
ejpam-5025	150	5	(	(	PUNCT
ejpam-5025	150	6	ζ	ζ	NOUN
ejpam-5025	150	7	◦	◦	VERB
ejpam-5025	150	8	ζ	ζ	NOUN
ejpam-5025	150	9	′	′	NUM
ejpam-5025	150	10	)	)	PUNCT
ejpam-5025	151	1	(	(	PUNCT
ejpam-5025	151	2	0)0	0)0	NOUN
ejpam-5025	151	3	=	=	SYM
ejpam-5025	151	4	0	0	NUM
ejpam-5025	151	5	∧	∧	NOUN
ejpam-5025	151	6	(	(	PUNCT
ejpam-5025	151	7	ζ	ζ	NOUN
ejpam-5025	151	8	◦	◦	VERB
ejpam-5025	151	9	ζ	ζ	NOUN
ejpam-5025	151	10	′	′	NUM
ejpam-5025	151	11	)	)	PUNCT
ejpam-5025	151	12	(	(	PUNCT
ejpam-5025	151	13	0)0	0)0	SYM
ejpam-5025	152	1	[	[	X
ejpam-5025	152	2	by	by	ADP
ejpam-5025	152	3	axiom	axiom	NOUN
ejpam-5025	152	4	(	(	PUNCT
ejpam-5025	152	5	ii	ii	NOUN
ejpam-5025	152	6	)	)	PUNCT
ejpam-5025	152	7	in	in	ADP
ejpam-5025	152	8	definition	definition	NOUN
ejpam-5025	152	9	1	1	NUM
ejpam-5025	152	10	]	]	PUNCT
ejpam-5025	152	11	=	=	SYM
ejpam-5025	152	12	0	0	NUM
ejpam-5025	152	13	∧	∧	NOUN
ejpam-5025	152	14	(	(	PUNCT
ejpam-5025	152	15	ζ	ζ	NOUN
ejpam-5025	152	16	◦	◦	VERB
ejpam-5025	152	17	ζ	ζ	NOUN
ejpam-5025	152	18	′	′	NUM
ejpam-5025	152	19	)	)	PUNCT
ejpam-5025	152	20	(	(	PUNCT
ejpam-5025	152	21	0	0	NUM
ejpam-5025	152	22	)	)	PUNCT
ejpam-5025	153	1	[	[	X
ejpam-5025	153	2	by	by	ADP
ejpam-5025	153	3	lemma	lemma	PROPN
ejpam-5025	153	4	1	1	NUM
ejpam-5025	153	5	]	]	X
ejpam-5025	153	6	=	=	SYM
ejpam-5025	153	7	(	(	PUNCT
ejpam-5025	153	8	ζ	ζ	NOUN
ejpam-5025	153	9	◦	◦	VERB
ejpam-5025	153	10	ζ	ζ	NOUN
ejpam-5025	153	11	′	′	NUM
ejpam-5025	153	12	)	)	PUNCT
ejpam-5025	153	13	(	(	PUNCT
ejpam-5025	153	14	0)((ζ	0)((ζ	NOUN
ejpam-5025	153	15	◦	◦	NOUN
ejpam-5025	153	16	ζ	ζ	NOUN
ejpam-5025	153	17	′	′	NUM
ejpam-5025	153	18	)	)	PUNCT
ejpam-5025	153	19	(	(	PUNCT
ejpam-5025	153	20	0)0	0)0	NOUN
ejpam-5025	153	21	)	)	PUNCT
ejpam-5025	154	1	[	[	X
ejpam-5025	154	2	by	by	ADP
ejpam-5025	154	3	x	x	PUNCT
ejpam-5025	154	4	∧	∧	PROPN
ejpam-5025	154	5	y	y	PROPN
ejpam-5025	154	6	=	=	SYM
ejpam-5025	154	7	y(yx	y(yx	PROPN
ejpam-5025	154	8	)	)	PUNCT
ejpam-5025	154	9	]	]	PUNCT
ejpam-5025	155	1	=	=	PUNCT
ejpam-5025	155	2	(	(	PUNCT
ejpam-5025	155	3	ζ	ζ	NOUN
ejpam-5025	155	4	◦	◦	VERB
ejpam-5025	155	5	ζ	ζ	NOUN
ejpam-5025	155	6	′	′	NUM
ejpam-5025	155	7	)	)	PUNCT
ejpam-5025	155	8	(	(	PUNCT
ejpam-5025	155	9	0)(ζ	0)(ζ	NUM
ejpam-5025	155	10	◦	◦	VERB
ejpam-5025	155	11	ζ	ζ	NOUN
ejpam-5025	155	12	′	′	NUM
ejpam-5025	155	13	)	)	PUNCT
ejpam-5025	155	14	(	(	PUNCT
ejpam-5025	155	15	0	0	NUM
ejpam-5025	155	16	)	)	PUNCT
ejpam-5025	156	1	[	[	X
ejpam-5025	156	2	again	again	ADV
ejpam-5025	156	3	by	by	ADP
ejpam-5025	156	4	lemma	lemma	PROPN
ejpam-5025	156	5	1	1	NUM
ejpam-5025	156	6	]	]	X
ejpam-5025	156	7	=	=	SYM
ejpam-5025	156	8	0	0	X
ejpam-5025	156	9	.	.	PUNCT
ejpam-5025	157	1	[	[	X
ejpam-5025	157	2	by	by	ADP
ejpam-5025	157	3	axiom	axiom	NOUN
ejpam-5025	157	4	(	(	PUNCT
ejpam-5025	157	5	i	i	NOUN
ejpam-5025	157	6	)	)	PUNCT
ejpam-5025	157	7	in	in	ADP
ejpam-5025	157	8	definition	definition	NOUN
ejpam-5025	157	9	1	1	NUM
ejpam-5025	157	10	]	]	PUNCT
ejpam-5025	157	11	hence	hence	ADV
ejpam-5025	157	12	ζ	ζ	NOUN
ejpam-5025	157	13	◦	◦	NOUN
ejpam-5025	157	14	ζ	ζ	NOUN
ejpam-5025	157	15	′	′	NUM
ejpam-5025	157	16	(	(	PUNCT
ejpam-5025	157	17	0	0	NUM
ejpam-5025	157	18	)	)	PUNCT
ejpam-5025	157	19	=	=	SYM
ejpam-5025	157	20	0	0	NUM
ejpam-5025	157	21	,	,	PUNCT
ejpam-5025	157	22	and	and	CCONJ
ejpam-5025	157	23	so	so	ADV
ejpam-5025	157	24	ζ	ζ	NOUN
ejpam-5025	157	25	◦	◦	NOUN
ejpam-5025	157	26	ζ	ζ	NOUN
ejpam-5025	157	27	′	′	NOUN
ejpam-5025	157	28	is	be	AUX
ejpam-5025	157	29	regular	regular	ADJ
ejpam-5025	157	30	.	.	PUNCT
ejpam-5025	158	1	in	in	ADP
ejpam-5025	158	2	the	the	DET
ejpam-5025	158	3	following	following	NOUN
ejpam-5025	158	4	theorem	theorem	NOUN
ejpam-5025	158	5	,	,	PUNCT
ejpam-5025	158	6	the	the	DET
ejpam-5025	158	7	condition	condition	NOUN
ejpam-5025	158	8	x	x	PUNCT
ejpam-5025	158	9	is	be	AUX
ejpam-5025	158	10	an	an	DET
ejpam-5025	158	11	edge	edge	NOUN
ejpam-5025	158	12	algebra	algebra	NOUN
ejpam-5025	158	13	(	(	PUNCT
ejpam-5025	158	14	i.e.	i.e.	X
ejpam-5025	158	15	,	,	PUNCT
ejpam-5025	158	16	x	x	SYM
ejpam-5025	158	17	0	0	PUNCT
ejpam-5025	159	1	=	=	SYM
ejpam-5025	159	2	0	0	NUM
ejpam-5025	159	3	)	)	PUNCT
ejpam-5025	159	4	omitted	omit	VERB
ejpam-5025	159	5	and	and	CCONJ
ejpam-5025	159	6	attempt	attempt	VERB
ejpam-5025	159	7	to	to	PART
ejpam-5025	159	8	get	get	VERB
ejpam-5025	159	9	the	the	DET
ejpam-5025	159	10	same	same	ADJ
ejpam-5025	159	11	results	result	NOUN
ejpam-5025	159	12	in	in	ADP
ejpam-5025	159	13	theorem	theorem	NOUN
ejpam-5025	159	14	4	4	NUM
ejpam-5025	159	15	,	,	PUNCT
ejpam-5025	159	16	for	for	ADP
ejpam-5025	159	17	(	(	PUNCT
ejpam-5025	159	18	l	l	NOUN
ejpam-5025	159	19	,	,	PUNCT
ejpam-5025	159	20	r)−reverse	r)−reverse	VERB
ejpam-5025	159	21	derivation	derivation	NOUN
ejpam-5025	159	22	of	of	ADP
ejpam-5025	159	23	d−algebra	d−algebra	X
ejpam-5025	159	24	x	x	X
ejpam-5025	159	25	.	.	PUNCT
ejpam-5025	160	1	theorem	theorem	NOUN
ejpam-5025	160	2	5	5	NUM
ejpam-5025	160	3	.	.	PUNCT
ejpam-5025	160	4	suppose	suppose	VERB
ejpam-5025	160	5	that	that	SCONJ
ejpam-5025	160	6	ζ	ζ	NOUN
ejpam-5025	160	7	and	and	CCONJ
ejpam-5025	160	8	ζ	ζ	NOUN
ejpam-5025	160	9	′	′	NOUN
ejpam-5025	160	10	are	be	AUX
ejpam-5025	160	11	two	two	NUM
ejpam-5025	160	12	(	(	PUNCT
ejpam-5025	160	13	l	l	NOUN
ejpam-5025	160	14	,	,	PUNCT
ejpam-5025	160	15	r)−	r)−	PROPN
ejpam-5025	160	16	reverse	reverse	ADJ
ejpam-5025	160	17	derivations	derivation	NOUN
ejpam-5025	160	18	of	of	ADP
ejpam-5025	160	19	a	a	DET
ejpam-5025	160	20	d−	d−	PROPN
ejpam-5025	160	21	algebra	algebra	NOUN
ejpam-5025	160	22	x	x	SYM
ejpam-5025	160	23	,	,	PUNCT
ejpam-5025	160	24	then	then	ADV
ejpam-5025	160	25	ζ	ζ	NOUN
ejpam-5025	160	26	◦	◦	NOUN
ejpam-5025	160	27	ζ	ζ	NOUN
ejpam-5025	160	28	′	′	NOUN
ejpam-5025	160	29	is	be	AUX
ejpam-5025	160	30	regular	regular	ADJ
ejpam-5025	160	31	.	.	PUNCT
ejpam-5025	161	1	proof	proof	NOUN
ejpam-5025	161	2	.	.	PUNCT
ejpam-5025	162	1	by	by	ADP
ejpam-5025	162	2	assumption	assumption	NOUN
ejpam-5025	162	3	that	that	SCONJ
ejpam-5025	162	4	ζ	ζ	NOUN
ejpam-5025	162	5	and	and	CCONJ
ejpam-5025	162	6	ζ	ζ	NOUN
ejpam-5025	162	7	′	′	NOUN
ejpam-5025	162	8	are	be	AUX
ejpam-5025	162	9	two	two	NUM
ejpam-5025	162	10	(	(	PUNCT
ejpam-5025	162	11	l	l	NOUN
ejpam-5025	162	12	,	,	PUNCT
ejpam-5025	162	13	r)−reverse	r)−reverse	VERB
ejpam-5025	162	14	derivations	derivation	NOUN
ejpam-5025	162	15	on	on	ADP
ejpam-5025	162	16	x	x	SYM
ejpam-5025	162	17	,	,	PUNCT
ejpam-5025	162	18	then	then	ADV
ejpam-5025	162	19	∀	∀	X
ejpam-5025	162	20	x	x	NOUN
ejpam-5025	162	21	,	,	PUNCT
ejpam-5025	162	22	y	y	PROPN
ejpam-5025	162	23	∈	∈	PROPN
ejpam-5025	162	24	x	x	INTJ
ejpam-5025	162	25	,	,	PUNCT
ejpam-5025	162	26	we	we	PRON
ejpam-5025	162	27	have	have	VERB
ejpam-5025	162	28	ζ	ζ	NOUN
ejpam-5025	162	29	◦	◦	NOUN
ejpam-5025	162	30	ζ	ζ	NOUN
ejpam-5025	162	31	′	′	NOUN
ejpam-5025	163	1	(	(	PUNCT
ejpam-5025	163	2	xy	xy	NOUN
ejpam-5025	163	3	)	)	PUNCT
ejpam-5025	163	4	=	=	SYM
ejpam-5025	163	5	ζ	ζ	NOUN
ejpam-5025	163	6	◦	◦	NOUN
ejpam-5025	163	7	ζ	ζ	NOUN
ejpam-5025	163	8	′	′	NUM
ejpam-5025	163	9	(	(	PUNCT
ejpam-5025	163	10	y)x	y)x	X
ejpam-5025	163	11	∧	∧	PROPN
ejpam-5025	163	12	yζ	yζ	NOUN
ejpam-5025	163	13	◦	◦	VERB
ejpam-5025	163	14	ζ	ζ	NOUN
ejpam-5025	164	1	′	′	NUM
ejpam-5025	164	2	(	(	PUNCT
ejpam-5025	164	3	x	x	NOUN
ejpam-5025	164	4	)	)	PUNCT
ejpam-5025	164	5	.	.	PUNCT
ejpam-5025	165	1	replace	replace	VERB
ejpam-5025	165	2	y	y	PROPN
ejpam-5025	165	3	by	by	ADP
ejpam-5025	165	4	x	x	PUNCT
ejpam-5025	165	5	in	in	ADP
ejpam-5025	165	6	the	the	DET
ejpam-5025	165	7	previous	previous	ADJ
ejpam-5025	165	8	k.	k.	PROPN
ejpam-5025	165	9	alnefaie	alnefaie	PROPN
ejpam-5025	165	10	/	/	SYM
ejpam-5025	165	11	eur	eur	PROPN
ejpam-5025	165	12	.	.	PUNCT
ejpam-5025	166	1	j.	j.	PROPN
ejpam-5025	166	2	pure	pure	PROPN
ejpam-5025	166	3	appl	appl	PROPN
ejpam-5025	166	4	.	.	PROPN
ejpam-5025	166	5	math	math	PROPN
ejpam-5025	166	6	,	,	PUNCT
ejpam-5025	166	7	17	17	NUM
ejpam-5025	166	8	(	(	PUNCT
ejpam-5025	166	9	1	1	NUM
ejpam-5025	166	10	)	)	PUNCT
ejpam-5025	166	11	(	(	PUNCT
ejpam-5025	166	12	2024	2024	NUM
ejpam-5025	166	13	)	)	PUNCT
ejpam-5025	166	14	,	,	PUNCT
ejpam-5025	166	15	362	362	NUM
ejpam-5025	166	16	-	-	SYM
ejpam-5025	166	17	371	371	NUM
ejpam-5025	166	18	368	368	NUM
ejpam-5025	166	19	equation	equation	NOUN
ejpam-5025	166	20	,	,	PUNCT
ejpam-5025	166	21	to	to	PART
ejpam-5025	166	22	get	get	VERB
ejpam-5025	166	23	(	(	PUNCT
ejpam-5025	166	24	ζ	ζ	NOUN
ejpam-5025	166	25	◦	◦	VERB
ejpam-5025	166	26	ζ	ζ	NOUN
ejpam-5025	166	27	′	′	NUM
ejpam-5025	166	28	)	)	PUNCT
ejpam-5025	166	29	(	(	PUNCT
ejpam-5025	166	30	0	0	NUM
ejpam-5025	166	31	)	)	PUNCT
ejpam-5025	166	32	=	=	SYM
ejpam-5025	166	33	(	(	PUNCT
ejpam-5025	166	34	ζ	ζ	NOUN
ejpam-5025	166	35	◦	◦	VERB
ejpam-5025	166	36	ζ	ζ	NOUN
ejpam-5025	166	37	′	′	NUM
ejpam-5025	166	38	)	)	PUNCT
ejpam-5025	166	39	(	(	PUNCT
ejpam-5025	166	40	xx	xx	X
ejpam-5025	166	41	)	)	PUNCT
ejpam-5025	166	42	=	=	SYM
ejpam-5025	167	1	(	(	PUNCT
ejpam-5025	167	2	ζ	ζ	NOUN
ejpam-5025	167	3	◦	◦	VERB
ejpam-5025	167	4	ζ	ζ	NOUN
ejpam-5025	167	5	′	′	NUM
ejpam-5025	167	6	)	)	PUNCT
ejpam-5025	167	7	(	(	PUNCT
ejpam-5025	167	8	x)x	x)x	PUNCT
ejpam-5025	167	9	∧	∧	PROPN
ejpam-5025	167	10	x(ζ	x(ζ	PROPN
ejpam-5025	167	11	◦	◦	VERB
ejpam-5025	167	12	ζ	ζ	NOUN
ejpam-5025	167	13	′	′	NUM
ejpam-5025	167	14	)	)	PUNCT
ejpam-5025	167	15	(	(	PUNCT
ejpam-5025	167	16	x	x	X
ejpam-5025	167	17	)	)	PUNCT
ejpam-5025	167	18	,	,	PUNCT
ejpam-5025	167	19	∀	∀	PUNCT
ejpam-5025	168	1	x	x	SYM
ejpam-5025	168	2	∈	∈	NOUN
ejpam-5025	168	3	x	x	X
ejpam-5025	168	4	.	.	PUNCT
ejpam-5025	169	1	now	now	ADV
ejpam-5025	169	2	,	,	PUNCT
ejpam-5025	169	3	put	put	VERB
ejpam-5025	169	4	x	x	X
ejpam-5025	169	5	=	=	SYM
ejpam-5025	169	6	0	0	NUM
ejpam-5025	169	7	in	in	ADP
ejpam-5025	169	8	the	the	DET
ejpam-5025	169	9	last	last	ADJ
ejpam-5025	169	10	equation	equation	NOUN
ejpam-5025	169	11	,	,	PUNCT
ejpam-5025	169	12	to	to	PART
ejpam-5025	169	13	get	get	VERB
ejpam-5025	169	14	(	(	PUNCT
ejpam-5025	169	15	ζ	ζ	NOUN
ejpam-5025	169	16	◦	◦	VERB
ejpam-5025	169	17	ζ	ζ	NOUN
ejpam-5025	169	18	′	′	NUM
ejpam-5025	169	19	)	)	PUNCT
ejpam-5025	169	20	(	(	PUNCT
ejpam-5025	169	21	0	0	NUM
ejpam-5025	169	22	)	)	PUNCT
ejpam-5025	169	23	=	=	SYM
ejpam-5025	170	1	(	(	PUNCT
ejpam-5025	170	2	ζ	ζ	NOUN
ejpam-5025	170	3	◦	◦	VERB
ejpam-5025	170	4	ζ	ζ	NOUN
ejpam-5025	170	5	′	′	NUM
ejpam-5025	170	6	)	)	PUNCT
ejpam-5025	171	1	(	(	PUNCT
ejpam-5025	171	2	0)0	0)0	PROPN
ejpam-5025	171	3	∧	∧	PROPN
ejpam-5025	171	4	0(ζ	0(ζ	X
ejpam-5025	171	5	◦	◦	VERB
ejpam-5025	171	6	ζ	ζ	NOUN
ejpam-5025	171	7	′	′	NUM
ejpam-5025	171	8	)	)	PUNCT
ejpam-5025	171	9	(	(	PUNCT
ejpam-5025	171	10	0	0	NUM
ejpam-5025	171	11	)	)	PUNCT
ejpam-5025	171	12	=	=	SYM
ejpam-5025	172	1	(	(	PUNCT
ejpam-5025	172	2	ζ	ζ	NOUN
ejpam-5025	172	3	◦	◦	VERB
ejpam-5025	172	4	ζ	ζ	NOUN
ejpam-5025	172	5	′	′	NUM
ejpam-5025	172	6	)	)	PUNCT
ejpam-5025	173	1	(	(	PUNCT
ejpam-5025	173	2	0)0	0)0	PROPN
ejpam-5025	173	3	∧	∧	NOUN
ejpam-5025	173	4	0	0	PUNCT
ejpam-5025	174	1	[	[	X
ejpam-5025	174	2	using	use	VERB
ejpam-5025	174	3	axiom	axiom	NOUN
ejpam-5025	174	4	(	(	PUNCT
ejpam-5025	174	5	ii	ii	NOUN
ejpam-5025	174	6	)	)	PUNCT
ejpam-5025	174	7	in	in	ADP
ejpam-5025	174	8	definition	definition	NOUN
ejpam-5025	174	9	1	1	NUM
ejpam-5025	174	10	]	]	PUNCT
ejpam-5025	174	11	=	=	SYM
ejpam-5025	174	12	0(0(ζ	0(0(ζ	NOUN
ejpam-5025	174	13	◦	◦	VERB
ejpam-5025	174	14	ζ	ζ	NOUN
ejpam-5025	174	15	′	′	NUM
ejpam-5025	174	16	)	)	PUNCT
ejpam-5025	175	1	(	(	PUNCT
ejpam-5025	175	2	0)0	0)0	NOUN
ejpam-5025	175	3	)	)	PUNCT
ejpam-5025	176	1	[	[	X
ejpam-5025	176	2	by	by	ADP
ejpam-5025	176	3	x	x	PUNCT
ejpam-5025	176	4	∧	∧	PROPN
ejpam-5025	176	5	y	y	PROPN
ejpam-5025	176	6	=	=	SYM
ejpam-5025	176	7	y(yx	y(yx	PROPN
ejpam-5025	176	8	)	)	PUNCT
ejpam-5025	176	9	]	]	PUNCT
ejpam-5025	176	10	=	=	PUNCT
ejpam-5025	176	11	0	0	X
ejpam-5025	176	12	.	.	PUNCT
ejpam-5025	177	1	[	[	X
ejpam-5025	177	2	by	by	ADP
ejpam-5025	177	3	axiom	axiom	NOUN
ejpam-5025	177	4	(	(	PUNCT
ejpam-5025	177	5	ii	ii	NOUN
ejpam-5025	177	6	)	)	PUNCT
ejpam-5025	177	7	in	in	ADP
ejpam-5025	177	8	definition	definition	NOUN
ejpam-5025	177	9	1	1	NUM
ejpam-5025	177	10	]	]	PUNCT
ejpam-5025	177	11	hence	hence	ADV
ejpam-5025	177	12	ζ	ζ	NOUN
ejpam-5025	177	13	◦	◦	NOUN
ejpam-5025	177	14	ζ	ζ	NOUN
ejpam-5025	177	15	′	′	NUM
ejpam-5025	177	16	(	(	PUNCT
ejpam-5025	177	17	0	0	NUM
ejpam-5025	177	18	)	)	PUNCT
ejpam-5025	177	19	=	=	SYM
ejpam-5025	177	20	0	0	NUM
ejpam-5025	177	21	,	,	PUNCT
ejpam-5025	177	22	and	and	CCONJ
ejpam-5025	177	23	so	so	ADV
ejpam-5025	177	24	ζ	ζ	NOUN
ejpam-5025	177	25	◦	◦	NOUN
ejpam-5025	177	26	ζ	ζ	NOUN
ejpam-5025	177	27	′	′	NOUN
ejpam-5025	177	28	is	be	AUX
ejpam-5025	177	29	regular	regular	ADJ
ejpam-5025	177	30	.	.	PUNCT
ejpam-5025	178	1	theorem	theorem	VERB
ejpam-5025	178	2	6	6	NUM
ejpam-5025	178	3	.	.	PUNCT
ejpam-5025	179	1	if	if	SCONJ
ejpam-5025	179	2	ζ	ζ	PRON
ejpam-5025	179	3	:	:	PUNCT
ejpam-5025	179	4	x	x	PUNCT
ejpam-5025	179	5	−→	−→	NOUN
ejpam-5025	179	6	x	x	VERB
ejpam-5025	179	7	is	be	AUX
ejpam-5025	179	8	a	a	DET
ejpam-5025	179	9	(	(	PUNCT
ejpam-5025	179	10	l	l	NOUN
ejpam-5025	179	11	,	,	PUNCT
ejpam-5025	179	12	r	r	NOUN
ejpam-5025	179	13	)	)	PUNCT
ejpam-5025	179	14	−	−	NOUN
ejpam-5025	179	15	reverse	reverse	ADJ
ejpam-5025	179	16	derivation	derivation	NOUN
ejpam-5025	179	17	on	on	ADP
ejpam-5025	179	18	a	a	DET
ejpam-5025	179	19	d	d	NOUN
ejpam-5025	179	20	−	−	PROPN
ejpam-5025	179	21	algebra	algebra	NOUN
ejpam-5025	179	22	x	x	X
ejpam-5025	179	23	,	,	PUNCT
ejpam-5025	179	24	then	then	ADV
ejpam-5025	179	25	∀	∀	X
ejpam-5025	180	1	x	x	SYM
ejpam-5025	180	2	∈	∈	NOUN
ejpam-5025	180	3	x	x	SYM
ejpam-5025	180	4	ζ(xζ(x	ζ(xζ(x	NOUN
ejpam-5025	180	5	)	)	PUNCT
ejpam-5025	180	6	)	)	PUNCT
ejpam-5025	181	1	=	=	PUNCT
ejpam-5025	181	2	0	0	X
ejpam-5025	181	3	.	.	PUNCT
ejpam-5025	182	1	proof	proof	NOUN
ejpam-5025	182	2	.	.	PUNCT
ejpam-5025	183	1	by	by	ADP
ejpam-5025	183	2	assumption	assumption	NOUN
ejpam-5025	183	3	,	,	PUNCT
ejpam-5025	183	4	x	x	PRON
ejpam-5025	183	5	is	be	AUX
ejpam-5025	183	6	a	a	DET
ejpam-5025	183	7	d	d	NOUN
ejpam-5025	183	8	−	−	NOUN
ejpam-5025	183	9	algebra	algebra	NOUN
ejpam-5025	183	10	and	and	CCONJ
ejpam-5025	183	11	ζ	ζ	NOUN
ejpam-5025	183	12	is	be	AUX
ejpam-5025	183	13	a	a	DET
ejpam-5025	183	14	(	(	PUNCT
ejpam-5025	183	15	l	l	NOUN
ejpam-5025	183	16	,	,	PUNCT
ejpam-5025	183	17	r	r	NOUN
ejpam-5025	183	18	)	)	PUNCT
ejpam-5025	183	19	−	−	NOUN
ejpam-5025	183	20	reverse	reverse	ADJ
ejpam-5025	183	21	derivation	derivation	NOUN
ejpam-5025	183	22	such	such	ADJ
ejpam-5025	183	23	that	that	PRON
ejpam-5025	183	24	ζ(xζ(x	ζ(xζ(x	NOUN
ejpam-5025	183	25	)	)	PUNCT
ejpam-5025	183	26	)	)	PUNCT
ejpam-5025	184	1	=	=	SYM
ejpam-5025	184	2	0	0	NUM
ejpam-5025	184	3	∀	∀	NOUN
ejpam-5025	184	4	x	x	SYM
ejpam-5025	184	5	∈	∈	NOUN
ejpam-5025	184	6	x	x	INTJ
ejpam-5025	184	7	,	,	PUNCT
ejpam-5025	184	8	therefore	therefore	ADV
ejpam-5025	184	9	we	we	PRON
ejpam-5025	184	10	have	have	VERB
ejpam-5025	184	11	ζ(xζ(x	ζ(xζ(x	NOUN
ejpam-5025	184	12	)	)	PUNCT
ejpam-5025	184	13	)	)	PUNCT
ejpam-5025	185	1	=	=	PRON
ejpam-5025	185	2	(	(	PUNCT
ejpam-5025	185	3	ζ	ζ	NOUN
ejpam-5025	185	4	◦	◦	NOUN
ejpam-5025	185	5	ζ)(x)x	ζ)(x)x	PUNCT
ejpam-5025	185	6	∧	∧	NOUN
ejpam-5025	185	7	ζ(x)ζ(x	ζ(x)ζ(x	NOUN
ejpam-5025	185	8	)	)	PUNCT
ejpam-5025	186	1	[	[	X
ejpam-5025	186	2	by	by	ADP
ejpam-5025	186	3	the	the	DET
ejpam-5025	186	4	definitions	definition	NOUN
ejpam-5025	186	5	4	4	NUM
ejpam-5025	186	6	,	,	PUNCT
ejpam-5025	186	7	6	6	NUM
ejpam-5025	186	8	,	,	PUNCT
ejpam-5025	186	9	respectively	respectively	ADV
ejpam-5025	186	10	]	]	PUNCT
ejpam-5025	186	11	=	=	SYM
ejpam-5025	186	12	(	(	PUNCT
ejpam-5025	186	13	ζ	ζ	NOUN
ejpam-5025	186	14	◦	◦	NOUN
ejpam-5025	186	15	ζ)(x)x	ζ)(x)x	PUNCT
ejpam-5025	186	16	∧	∧	NOUN
ejpam-5025	186	17	0	0	PUNCT
ejpam-5025	187	1	[	[	X
ejpam-5025	187	2	by	by	ADP
ejpam-5025	187	3	axiom	axiom	NOUN
ejpam-5025	187	4	(	(	PUNCT
ejpam-5025	187	5	i	i	NOUN
ejpam-5025	187	6	)	)	PUNCT
ejpam-5025	187	7	in	in	ADP
ejpam-5025	187	8	definition	definition	NOUN
ejpam-5025	187	9	1	1	NUM
ejpam-5025	187	10	]	]	PUNCT
ejpam-5025	187	11	=	=	SYM
ejpam-5025	187	12	0(0(ζ	0(0(ζ	NOUN
ejpam-5025	187	13	◦	◦	NOUN
ejpam-5025	187	14	ζ)(x	ζ)(x	PROPN
ejpam-5025	187	15	)	)	PUNCT
ejpam-5025	187	16	)	)	PUNCT
ejpam-5025	188	1	[	[	X
ejpam-5025	188	2	by	by	ADP
ejpam-5025	188	3	x	x	PUNCT
ejpam-5025	188	4	∧	∧	PROPN
ejpam-5025	188	5	y	y	PROPN
ejpam-5025	188	6	=	=	SYM
ejpam-5025	188	7	y(yx	y(yx	PROPN
ejpam-5025	188	8	)	)	PUNCT
ejpam-5025	188	9	]	]	PUNCT
ejpam-5025	188	10	=	=	PUNCT
ejpam-5025	188	11	0	0	X
ejpam-5025	188	12	.	.	PUNCT
ejpam-5025	189	1	[	[	X
ejpam-5025	189	2	by	by	ADP
ejpam-5025	189	3	axiom	axiom	NOUN
ejpam-5025	189	4	(	(	PUNCT
ejpam-5025	189	5	ii	ii	NOUN
ejpam-5025	189	6	)	)	PUNCT
ejpam-5025	189	7	in	in	ADP
ejpam-5025	189	8	definition	definition	NOUN
ejpam-5025	189	9	1	1	NUM
ejpam-5025	189	10	]	]	PUNCT
ejpam-5025	189	11	thus	thus	ADV
ejpam-5025	189	12	,	,	PUNCT
ejpam-5025	189	13	∀	∀	X
ejpam-5025	189	14	x	x	SYM
ejpam-5025	189	15	∈	∈	NOUN
ejpam-5025	189	16	x	x	SYM
ejpam-5025	189	17	ζ(xζ(x	ζ(xζ(x	NOUN
ejpam-5025	189	18	)	)	PUNCT
ejpam-5025	189	19	)	)	PUNCT
ejpam-5025	190	1	=	=	SYM
ejpam-5025	190	2	0	0	PUNCT
ejpam-5025	190	3	as	as	SCONJ
ejpam-5025	190	4	required	require	VERB
ejpam-5025	190	5	.	.	PUNCT
ejpam-5025	191	1	theorem	theorem	VERB
ejpam-5025	191	2	7	7	NUM
ejpam-5025	191	3	.	.	PUNCT
ejpam-5025	192	1	if	if	SCONJ
ejpam-5025	192	2	ζ	ζ	PRON
ejpam-5025	192	3	:	:	PUNCT
ejpam-5025	192	4	x	x	PUNCT
ejpam-5025	192	5	−→	−→	NOUN
ejpam-5025	192	6	x	x	VERB
ejpam-5025	192	7	is	be	AUX
ejpam-5025	192	8	a	a	DET
ejpam-5025	192	9	(	(	PUNCT
ejpam-5025	192	10	l	l	NOUN
ejpam-5025	192	11	,	,	PUNCT
ejpam-5025	192	12	r	r	NOUN
ejpam-5025	192	13	)	)	PUNCT
ejpam-5025	192	14	−	−	NOUN
ejpam-5025	192	15	reverse	reverse	ADJ
ejpam-5025	192	16	derivation	derivation	NOUN
ejpam-5025	192	17	on	on	ADP
ejpam-5025	192	18	an	an	DET
ejpam-5025	192	19	edge	edge	NOUN
ejpam-5025	193	1	d	d	PRON
ejpam-5025	193	2	−	−	PROPN
ejpam-5025	193	3	algebra	algebra	NOUN
ejpam-5025	193	4	x	x	X
ejpam-5025	193	5	,	,	PUNCT
ejpam-5025	193	6	then	then	ADV
ejpam-5025	193	7	∀	∀	X
ejpam-5025	193	8	x	x	SYM
ejpam-5025	193	9	∈	∈	NOUN
ejpam-5025	193	10	x	x	X
ejpam-5025	193	11	ζ(ζ(x)x	ζ(ζ(x)x	ADV
ejpam-5025	193	12	)	)	PUNCT
ejpam-5025	193	13	=	=	SYM
ejpam-5025	193	14	0	0	X
ejpam-5025	193	15	.	.	PUNCT
ejpam-5025	193	16	proof	proof	NOUN
ejpam-5025	193	17	.	.	PUNCT
ejpam-5025	194	1	it	it	PRON
ejpam-5025	194	2	is	be	AUX
ejpam-5025	194	3	given	give	VERB
ejpam-5025	194	4	that	that	SCONJ
ejpam-5025	194	5	,	,	PUNCT
ejpam-5025	194	6	ζ	ζ	NOUN
ejpam-5025	194	7	is	be	AUX
ejpam-5025	194	8	a	a	DET
ejpam-5025	194	9	(	(	PUNCT
ejpam-5025	194	10	l	l	NOUN
ejpam-5025	194	11	,	,	PUNCT
ejpam-5025	194	12	r)−	r)−	PROPN
ejpam-5025	194	13	reverse	reverse	ADJ
ejpam-5025	194	14	derivation	derivation	NOUN
ejpam-5025	194	15	of	of	ADP
ejpam-5025	194	16	an	an	DET
ejpam-5025	194	17	edge	edge	NOUN
ejpam-5025	194	18	d−	d−	PROPN
ejpam-5025	194	19	algebra	algebra	NOUN
ejpam-5025	194	20	x	x	PRON
ejpam-5025	194	21	,	,	PUNCT
ejpam-5025	194	22	then	then	ADV
ejpam-5025	194	23	for	for	ADP
ejpam-5025	194	24	any	any	DET
ejpam-5025	194	25	x	x	SYM
ejpam-5025	194	26	∈	∈	PROPN
ejpam-5025	194	27	x	x	X
ejpam-5025	194	28	,	,	PUNCT
ejpam-5025	194	29	we	we	PRON
ejpam-5025	194	30	have	have	VERB
ejpam-5025	194	31	ζ(ζ(x)x	ζ(ζ(x)x	ADV
ejpam-5025	194	32	)	)	PUNCT
ejpam-5025	194	33	=	=	SYM
ejpam-5025	194	34	ζ(x)ζ(x	ζ(x)ζ(x	NOUN
ejpam-5025	194	35	)	)	PUNCT
ejpam-5025	194	36	∧	∧	PROPN
ejpam-5025	194	37	x(ζ	x(ζ	PROPN
ejpam-5025	194	38	◦	◦	PROPN
ejpam-5025	194	39	ζ)(x	ζ)(x	PROPN
ejpam-5025	194	40	)	)	PUNCT
ejpam-5025	195	1	[	[	X
ejpam-5025	195	2	by	by	ADP
ejpam-5025	195	3	the	the	DET
ejpam-5025	195	4	definitions	definition	NOUN
ejpam-5025	195	5	4	4	NUM
ejpam-5025	195	6	,	,	PUNCT
ejpam-5025	195	7	6	6	NUM
ejpam-5025	195	8	,	,	PUNCT
ejpam-5025	195	9	respectively	respectively	ADV
ejpam-5025	195	10	]	]	PUNCT
ejpam-5025	195	11	=	=	SYM
ejpam-5025	195	12	0	0	NUM
ejpam-5025	195	13	∧	∧	PROPN
ejpam-5025	195	14	x(ζ	x(ζ	PROPN
ejpam-5025	195	15	◦	◦	PROPN
ejpam-5025	195	16	ζ)(x	ζ)(x	PROPN
ejpam-5025	195	17	)	)	PUNCT
ejpam-5025	196	1	[	[	X
ejpam-5025	196	2	by	by	ADP
ejpam-5025	196	3	axiom	axiom	NOUN
ejpam-5025	196	4	(	(	PUNCT
ejpam-5025	196	5	i	i	NOUN
ejpam-5025	196	6	)	)	PUNCT
ejpam-5025	196	7	in	in	ADP
ejpam-5025	196	8	definition	definition	NOUN
ejpam-5025	196	9	1	1	NUM
ejpam-5025	196	10	]	]	PUNCT
ejpam-5025	196	11	=	=	SYM
ejpam-5025	196	12	x(ζ	x(ζ	PROPN
ejpam-5025	196	13	◦	◦	NOUN
ejpam-5025	196	14	ζ)(x)[(x(ζ	ζ)(x)[(x(ζ	ADJ
ejpam-5025	196	15	◦	◦	NOUN
ejpam-5025	196	16	ζ)(x))0	ζ)(x))0	PROPN
ejpam-5025	196	17	]	]	PUNCT
ejpam-5025	197	1	[	[	X
ejpam-5025	197	2	by	by	ADP
ejpam-5025	197	3	x	x	PUNCT
ejpam-5025	197	4	∧	∧	PROPN
ejpam-5025	197	5	y	y	PROPN
ejpam-5025	197	6	=	=	SYM
ejpam-5025	197	7	y(yx	y(yx	PROPN
ejpam-5025	197	8	)	)	PUNCT
ejpam-5025	197	9	]	]	PUNCT
ejpam-5025	198	1	=	=	PUNCT
ejpam-5025	199	1	x(ζ	x(ζ	PROPN
ejpam-5025	199	2	◦	◦	NOUN
ejpam-5025	199	3	ζ)(x)(x(ζ	ζ)(x)(x(ζ	ADJ
ejpam-5025	199	4	◦	◦	NOUN
ejpam-5025	199	5	ζ)(x	ζ)(x	PROPN
ejpam-5025	199	6	)	)	PUNCT
ejpam-5025	199	7	)	)	PUNCT
ejpam-5025	200	1	[	[	X
ejpam-5025	200	2	by	by	ADP
ejpam-5025	200	3	lemma	lemma	PROPN
ejpam-5025	200	4	1	1	NUM
ejpam-5025	200	5	]	]	X
ejpam-5025	200	6	=	=	SYM
ejpam-5025	200	7	0	0	X
ejpam-5025	200	8	.	.	PUNCT
ejpam-5025	201	1	[	[	X
ejpam-5025	201	2	by	by	ADP
ejpam-5025	201	3	axiom	axiom	NOUN
ejpam-5025	201	4	(	(	PUNCT
ejpam-5025	201	5	ii	ii	NOUN
ejpam-5025	201	6	)	)	PUNCT
ejpam-5025	201	7	in	in	ADP
ejpam-5025	201	8	definition	definition	NOUN
ejpam-5025	201	9	1	1	NUM
ejpam-5025	201	10	]	]	PUNCT
ejpam-5025	201	11	the	the	DET
ejpam-5025	201	12	proof	proof	NOUN
ejpam-5025	201	13	is	be	AUX
ejpam-5025	201	14	completed	complete	VERB
ejpam-5025	201	15	as	as	ADP
ejpam-5025	201	16	required	require	VERB
ejpam-5025	201	17	.	.	PUNCT
ejpam-5025	202	1	definition	definition	NOUN
ejpam-5025	202	2	7	7	NUM
ejpam-5025	202	3	.	.	PUNCT
ejpam-5025	202	4	define	define	VERB
ejpam-5025	202	5	a	a	DET
ejpam-5025	202	6	relation	relation	NOUN
ejpam-5025	202	7	”	"	PUNCT
ejpam-5025	202	8	≤	≤	NOUN
ejpam-5025	202	9	”	"	PUNCT
ejpam-5025	202	10	on	on	ADP
ejpam-5025	202	11	a	a	DET
ejpam-5025	202	12	d−	d−	PROPN
ejpam-5025	202	13	algebra	algebra	NOUN
ejpam-5025	202	14	x	x	PUNCT
ejpam-5025	202	15	by	by	ADP
ejpam-5025	202	16	x	x	PROPN
ejpam-5025	202	17	≤	≤	PROPN
ejpam-5025	202	18	y	y	PROPN
ejpam-5025	202	19	,	,	PUNCT
ejpam-5025	202	20	iff	iff	VERB
ejpam-5025	202	21	xy	xy	PROPN
ejpam-5025	202	22	=	=	NOUN
ejpam-5025	202	23	0	0	PROPN
ejpam-5025	203	1	for	for	ADP
ejpam-5025	203	2	any	any	DET
ejpam-5025	203	3	x	x	NOUN
ejpam-5025	203	4	,	,	PUNCT
ejpam-5025	203	5	y	y	PROPN
ejpam-5025	203	6	∈	∈	PROPN
ejpam-5025	203	7	x	x	X
ejpam-5025	203	8	.	.	PUNCT
ejpam-5025	204	1	thus	thus	ADV
ejpam-5025	204	2	,	,	PUNCT
ejpam-5025	204	3	x	x	PRON
ejpam-5025	204	4	becomes	becomes	AUX
ejpam-5025	204	5	a	a	DET
ejpam-5025	204	6	partially	partially	ADV
ejpam-5025	204	7	ordered	order	VERB
ejpam-5025	204	8	by	by	ADP
ejpam-5025	204	9	the	the	DET
ejpam-5025	204	10	relation	relation	NOUN
ejpam-5025	204	11	x	x	SYM
ejpam-5025	204	12	≤	≤	NOUN
ejpam-5025	204	13	y	y	NOUN
ejpam-5025	204	14	,	,	PUNCT
ejpam-5025	204	15	denoted	denote	VERB
ejpam-5025	204	16	it	it	PRON
ejpam-5025	204	17	by	by	ADP
ejpam-5025	204	18	(	(	PUNCT
ejpam-5025	204	19	x	x	INTJ
ejpam-5025	204	20	,	,	PUNCT
ejpam-5025	204	21	≤	≤	NUM
ejpam-5025	204	22	)	)	PUNCT
ejpam-5025	204	23	.	.	PUNCT
ejpam-5025	205	1	definition	definition	NOUN
ejpam-5025	205	2	8	8	NUM
ejpam-5025	205	3	.	.	PUNCT
ejpam-5025	206	1	[	[	X
ejpam-5025	206	2	20	20	NUM
ejpam-5025	206	3	]	]	SYM
ejpam-5025	206	4	a	a	PRON
ejpam-5025	206	5	d	d	NOUN
ejpam-5025	206	6	−	−	PROPN
ejpam-5025	206	7	subalgebra	subalgebra	NOUN
ejpam-5025	206	8	s	s	NOUN
ejpam-5025	206	9	of	of	ADP
ejpam-5025	206	10	a	a	DET
ejpam-5025	206	11	d	d	NOUN
ejpam-5025	206	12	−	−	PROPN
ejpam-5025	206	13	algebra	algebra	NOUN
ejpam-5025	206	14	x	x	PUNCT
ejpam-5025	206	15	is	be	AUX
ejpam-5025	206	16	a	a	DET
ejpam-5025	206	17	non	non	ADJ
ejpam-5025	206	18	-	-	ADJ
ejpam-5025	206	19	empty	empty	ADJ
ejpam-5025	206	20	subset	subset	NOUN
ejpam-5025	206	21	of	of	ADP
ejpam-5025	206	22	x	x	PUNCT
ejpam-5025	206	23	satisfing	satisfe	VERB
ejpam-5025	206	24	the	the	DET
ejpam-5025	206	25	condition	condition	NOUN
ejpam-5025	206	26	x	x	PUNCT
ejpam-5025	206	27	∗	∗	VERB
ejpam-5025	206	28	y	y	PROPN
ejpam-5025	206	29	∈	∈	PROPN
ejpam-5025	206	30	s	s	NOUN
ejpam-5025	206	31	,	,	PUNCT
ejpam-5025	206	32	whenever	whenever	SCONJ
ejpam-5025	206	33	x	x	X
ejpam-5025	206	34	,	,	PUNCT
ejpam-5025	206	35	y	y	PROPN
ejpam-5025	206	36	∈	∈	PROPN
ejpam-5025	206	37	s.	s.	PROPN
ejpam-5025	206	38	k.	k.	PROPN
ejpam-5025	206	39	alnefaie	alnefaie	PROPN
ejpam-5025	206	40	/	/	SYM
ejpam-5025	206	41	eur	eur	PROPN
ejpam-5025	206	42	.	.	PUNCT
ejpam-5025	207	1	j.	j.	PROPN
ejpam-5025	207	2	pure	pure	PROPN
ejpam-5025	207	3	appl	appl	PROPN
ejpam-5025	207	4	.	.	PROPN
ejpam-5025	207	5	math	math	PROPN
ejpam-5025	207	6	,	,	PUNCT
ejpam-5025	207	7	17	17	NUM
ejpam-5025	207	8	(	(	PUNCT
ejpam-5025	207	9	1	1	NUM
ejpam-5025	207	10	)	)	PUNCT
ejpam-5025	207	11	(	(	PUNCT
ejpam-5025	207	12	2024	2024	NUM
ejpam-5025	207	13	)	)	PUNCT
ejpam-5025	207	14	,	,	PUNCT
ejpam-5025	207	15	362	362	NUM
ejpam-5025	207	16	-	-	SYM
ejpam-5025	207	17	371	371	NUM
ejpam-5025	207	18	369	369	NUM
ejpam-5025	207	19	example	example	NOUN
ejpam-5025	207	20	5	5	NUM
ejpam-5025	207	21	.	.	PUNCT
ejpam-5025	208	1	let	let	VERB
ejpam-5025	208	2	s	s	VERB
ejpam-5025	208	3	=	=	X
ejpam-5025	208	4	{	{	PUNCT
ejpam-5025	208	5	0	0	NUM
ejpam-5025	208	6	,	,	PUNCT
ejpam-5025	208	7	a	a	DET
ejpam-5025	208	8	,	,	PUNCT
ejpam-5025	208	9	b	b	NOUN
ejpam-5025	208	10	}	}	PUNCT
ejpam-5025	208	11	and	and	CCONJ
ejpam-5025	208	12	h	h	NOUN
ejpam-5025	208	13	=	=	SYM
ejpam-5025	208	14	{	{	PUNCT
ejpam-5025	208	15	0	0	NUM
ejpam-5025	208	16	,	,	PUNCT
ejpam-5025	208	17	c	c	AUX
ejpam-5025	208	18	}	}	PUNCT
ejpam-5025	208	19	be	be	AUX
ejpam-5025	208	20	two	two	NUM
ejpam-5025	208	21	non	non	ADJ
ejpam-5025	208	22	-	-	ADJ
ejpam-5025	208	23	empty	empty	ADJ
ejpam-5025	208	24	sets	set	NOUN
ejpam-5025	208	25	of	of	ADP
ejpam-5025	208	26	the	the	DET
ejpam-5025	208	27	d−algebra	d−algebra	NOUN
ejpam-5025	208	28	x	x	PUNCT
ejpam-5025	208	29	shown	show	VERB
ejpam-5025	208	30	in	in	ADP
ejpam-5025	208	31	the	the	DET
ejpam-5025	208	32	example	example	NOUN
ejpam-5025	208	33	2	2	NUM
ejpam-5025	208	34	.	.	PUNCT
ejpam-5025	208	35	clearly	clearly	ADV
ejpam-5025	208	36	,	,	PUNCT
ejpam-5025	208	37	we	we	PRON
ejpam-5025	208	38	can	can	AUX
ejpam-5025	208	39	verify	verify	VERB
ejpam-5025	208	40	that	that	DET
ejpam-5025	208	41	s	s	VERB
ejpam-5025	208	42	=	=	X
ejpam-5025	208	43	{	{	PUNCT
ejpam-5025	208	44	0	0	NUM
ejpam-5025	208	45	,	,	PUNCT
ejpam-5025	208	46	a	a	DET
ejpam-5025	208	47	,	,	PUNCT
ejpam-5025	208	48	b	b	NOUN
ejpam-5025	208	49	}	}	PUNCT
ejpam-5025	208	50	is	be	AUX
ejpam-5025	208	51	a	a	DET
ejpam-5025	208	52	d−	d−	ADJ
ejpam-5025	208	53	subalgebra	subalgebra	NOUN
ejpam-5025	208	54	in	in	ADP
ejpam-5025	208	55	x	x	X
ejpam-5025	208	56	.	.	PUNCT
ejpam-5025	209	1	but	but	CCONJ
ejpam-5025	209	2	h	h	NOUN
ejpam-5025	209	3	=	=	SYM
ejpam-5025	209	4	{	{	PUNCT
ejpam-5025	209	5	0	0	NUM
ejpam-5025	209	6	,	,	PUNCT
ejpam-5025	209	7	c	c	NOUN
ejpam-5025	209	8	}	}	PUNCT
ejpam-5025	209	9	is	be	AUX
ejpam-5025	209	10	not	not	PART
ejpam-5025	209	11	a	a	DET
ejpam-5025	209	12	d−	d−	ADJ
ejpam-5025	209	13	subalgebra	subalgebra	NOUN
ejpam-5025	209	14	in	in	ADP
ejpam-5025	209	15	x	x	SYM
ejpam-5025	209	16	,	,	PUNCT
ejpam-5025	209	17	because	because	SCONJ
ejpam-5025	209	18	c	c	NOUN
ejpam-5025	209	19	∗	∗	X
ejpam-5025	209	20	0	0	NUM
ejpam-5025	210	1	=	=	SYM
ejpam-5025	210	2	b	b	NOUN
ejpam-5025	210	3	not	not	PART
ejpam-5025	210	4	in	in	ADP
ejpam-5025	210	5	h.	h.	NOUN
ejpam-5025	210	6	proposition	proposition	NOUN
ejpam-5025	210	7	1	1	X
ejpam-5025	210	8	.	.	PUNCT
ejpam-5025	210	9	assume	assume	VERB
ejpam-5025	210	10	that	that	SCONJ
ejpam-5025	210	11	ζ	ζ	X
ejpam-5025	210	12	:	:	PUNCT
ejpam-5025	210	13	x	x	PUNCT
ejpam-5025	210	14	−→	−→	NOUN
ejpam-5025	210	15	x	x	VERB
ejpam-5025	210	16	is	be	AUX
ejpam-5025	210	17	a	a	DET
ejpam-5025	210	18	(	(	PUNCT
ejpam-5025	210	19	l	l	NOUN
ejpam-5025	210	20	,	,	PUNCT
ejpam-5025	210	21	r)−	r)−	PROPN
ejpam-5025	210	22	reverse	reverse	VERB
ejpam-5025	210	23	derivation	derivation	NOUN
ejpam-5025	210	24	such	such	ADJ
ejpam-5025	210	25	that	that	SCONJ
ejpam-5025	210	26	x	x	PRON
ejpam-5025	210	27	is	be	AUX
ejpam-5025	210	28	an	an	DET
ejpam-5025	210	29	edge	edge	NOUN
ejpam-5025	210	30	d−	d−	PROPN
ejpam-5025	210	31	algebra	algebra	NOUN
ejpam-5025	210	32	with	with	ADP
ejpam-5025	210	33	partial	partial	ADJ
ejpam-5025	210	34	order	order	NOUN
ejpam-5025	210	35	≤.	≤.	NOUN
ejpam-5025	210	36	then	then	ADV
ejpam-5025	210	37	(	(	PUNCT
ejpam-5025	210	38	i	i	NOUN
ejpam-5025	210	39	)	)	PUNCT
ejpam-5025	210	40	ζ(xy	ζ(xy	PROPN
ejpam-5025	210	41	)	)	PUNCT
ejpam-5025	210	42	≤	≤	NOUN
ejpam-5025	210	43	ζ(y)x	ζ(y)x	NOUN
ejpam-5025	210	44	for	for	ADP
ejpam-5025	210	45	all	all	DET
ejpam-5025	210	46	x	x	NOUN
ejpam-5025	210	47	,	,	PUNCT
ejpam-5025	210	48	y	y	PROPN
ejpam-5025	210	49	∈	∈	PROPN
ejpam-5025	210	50	x	x	X
ejpam-5025	210	51	.	.	PUNCT
ejpam-5025	211	1	(	(	PUNCT
ejpam-5025	211	2	ii	ii	NOUN
ejpam-5025	211	3	)	)	PUNCT
ejpam-5025	211	4	if	if	SCONJ
ejpam-5025	211	5	ζ−1(0	ζ−1(0	NOUN
ejpam-5025	211	6	)	)	PUNCT
ejpam-5025	211	7	=	=	PRON
ejpam-5025	212	1	{	{	PUNCT
ejpam-5025	212	2	x	x	PUNCT
ejpam-5025	212	3	∈	∈	PROPN
ejpam-5025	212	4	x	x	X
ejpam-5025	212	5	|	|	NOUN
ejpam-5025	212	6	ζ(x	ζ(x	NOUN
ejpam-5025	212	7	)	)	PUNCT
ejpam-5025	212	8	=	=	SYM
ejpam-5025	212	9	0	0	X
ejpam-5025	212	10	}	}	PUNCT
ejpam-5025	212	11	∀	∀	X
ejpam-5025	212	12	x	x	SYM
ejpam-5025	212	13	∈	∈	NOUN
ejpam-5025	212	14	x	x	PUNCT
ejpam-5025	212	15	such	such	ADJ
ejpam-5025	212	16	that	that	SCONJ
ejpam-5025	212	17	ζ	ζ	NOUN
ejpam-5025	212	18	is	be	AUX
ejpam-5025	212	19	regular	regular	ADJ
ejpam-5025	212	20	,	,	PUNCT
ejpam-5025	212	21	then	then	ADV
ejpam-5025	212	22	ζ−1(0	ζ−1(0	NOUN
ejpam-5025	212	23	)	)	PUNCT
ejpam-5025	212	24	is	be	AUX
ejpam-5025	212	25	a	a	DET
ejpam-5025	212	26	d−subalgebra	d−subalgebra	PROPN
ejpam-5025	212	27	of	of	ADP
ejpam-5025	212	28	x	x	PROPN
ejpam-5025	212	29	.	.	PUNCT
ejpam-5025	213	1	(	(	PUNCT
ejpam-5025	213	2	iii	iii	X
ejpam-5025	213	3	)	)	PUNCT
ejpam-5025	213	4	if	if	SCONJ
ejpam-5025	213	5	x	x	X
ejpam-5025	213	6	,	,	PUNCT
ejpam-5025	213	7	y	y	PROPN
ejpam-5025	213	8	∈	∈	PROPN
ejpam-5025	213	9	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	213	10	)	)	PUNCT
ejpam-5025	213	11	,	,	PUNCT
ejpam-5025	213	12	then	then	ADV
ejpam-5025	213	13	x	x	PART
ejpam-5025	213	14	∧	∧	NOUN
ejpam-5025	213	15	y	y	PROPN
ejpam-5025	213	16	∈	∈	PROPN
ejpam-5025	213	17	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	213	18	)	)	PUNCT
ejpam-5025	213	19	.	.	PUNCT
ejpam-5025	214	1	proof	proof	NOUN
ejpam-5025	214	2	.	.	PUNCT
ejpam-5025	215	1	(	(	PUNCT
ejpam-5025	215	2	1	1	X
ejpam-5025	215	3	)	)	PUNCT
ejpam-5025	215	4	we	we	PRON
ejpam-5025	215	5	have	have	VERB
ejpam-5025	215	6	,	,	PUNCT
ejpam-5025	215	7	ζ	ζ	NOUN
ejpam-5025	215	8	is	be	AUX
ejpam-5025	215	9	a	a	DET
ejpam-5025	215	10	(	(	PUNCT
ejpam-5025	215	11	l	l	NOUN
ejpam-5025	215	12	,	,	PUNCT
ejpam-5025	215	13	r)−	r)−	PROPN
ejpam-5025	215	14	reverse	reverse	VERB
ejpam-5025	215	15	derivation	derivation	NOUN
ejpam-5025	215	16	on	on	ADP
ejpam-5025	215	17	edge	edge	NOUN
ejpam-5025	215	18	d	d	NOUN
ejpam-5025	215	19	−	−	PROPN
ejpam-5025	215	20	algebra	algebra	NOUN
ejpam-5025	215	21	x	x	X
ejpam-5025	215	22	,	,	PUNCT
ejpam-5025	215	23	then	then	ADV
ejpam-5025	215	24	for	for	ADP
ejpam-5025	215	25	any	any	DET
ejpam-5025	215	26	x	x	NOUN
ejpam-5025	215	27	,	,	PUNCT
ejpam-5025	215	28	y	y	PROPN
ejpam-5025	215	29	∈	∈	PROPN
ejpam-5025	215	30	x	x	INTJ
ejpam-5025	215	31	,	,	PUNCT
ejpam-5025	215	32	we	we	PRON
ejpam-5025	215	33	get	get	VERB
ejpam-5025	215	34	ζ(xy	ζ(xy	NOUN
ejpam-5025	215	35	)	)	PUNCT
ejpam-5025	215	36	=	=	PUNCT
ejpam-5025	215	37	ζ(y)x	ζ(y)x	X
ejpam-5025	215	38	∧	∧	PROPN
ejpam-5025	215	39	yζ(x	yζ(x	NOUN
ejpam-5025	215	40	)	)	PUNCT
ejpam-5025	216	1	[	[	X
ejpam-5025	216	2	using	use	VERB
ejpam-5025	216	3	the	the	DET
ejpam-5025	216	4	definition	definition	NOUN
ejpam-5025	216	5	4	4	NUM
ejpam-5025	216	6	]	]	PUNCT
ejpam-5025	216	7	=	=	PUNCT
ejpam-5025	216	8	yζ(x)[yζ(x)(ζ(y)x	yζ(x)[yζ(x)(ζ(y)x	NOUN
ejpam-5025	216	9	)	)	PUNCT
ejpam-5025	216	10	]	]	PUNCT
ejpam-5025	217	1	[	[	X
ejpam-5025	217	2	by	by	ADP
ejpam-5025	217	3	x	x	PUNCT
ejpam-5025	217	4	∧	∧	PROPN
ejpam-5025	217	5	y	y	PROPN
ejpam-5025	217	6	=	=	SYM
ejpam-5025	217	7	y(yx	y(yx	PROPN
ejpam-5025	217	8	)	)	PUNCT
ejpam-5025	217	9	]	]	PUNCT
ejpam-5025	217	10	.	.	PUNCT
ejpam-5025	217	11	now	now	ADV
ejpam-5025	217	12	,	,	PUNCT
ejpam-5025	217	13	multiplying	multiply	VERB
ejpam-5025	217	14	both	both	DET
ejpam-5025	217	15	sides	side	NOUN
ejpam-5025	217	16	by	by	ADP
ejpam-5025	217	17	ζ(y)x	ζ(y)x	NOUN
ejpam-5025	217	18	from	from	ADP
ejpam-5025	217	19	the	the	DET
ejpam-5025	217	20	right	right	ADJ
ejpam-5025	217	21	hand	hand	NOUN
ejpam-5025	217	22	,	,	PUNCT
ejpam-5025	217	23	we	we	PRON
ejpam-5025	217	24	get	get	VERB
ejpam-5025	217	25	ζ(xy)ζ(y)x	ζ(xy)ζ(y)x	NOUN
ejpam-5025	217	26	=	=	PUNCT
ejpam-5025	218	1	[	[	X
ejpam-5025	218	2	yζ(x)(yζ(x)ζ(y)x)]ζ(y)x	yζ(x)(yζ(x)ζ(y)x)]ζ(y)x	NOUN
ejpam-5025	218	3	=	=	PUNCT
ejpam-5025	218	4	0	0	PUNCT
ejpam-5025	219	1	[	[	X
ejpam-5025	219	2	by	by	ADP
ejpam-5025	219	3	lemma	lemma	PROPN
ejpam-5025	219	4	2	2	NUM
ejpam-5025	219	5	]	]	PUNCT
ejpam-5025	219	6	.	.	PUNCT
ejpam-5025	220	1	that	that	PRON
ejpam-5025	220	2	is	be	AUX
ejpam-5025	220	3	,	,	PUNCT
ejpam-5025	220	4	ζ(xy)ζ(y)x	ζ(xy)ζ(y)x	X
ejpam-5025	220	5	=	=	SYM
ejpam-5025	220	6	0	0	PROPN
ejpam-5025	220	7	for	for	ADP
ejpam-5025	220	8	all	all	DET
ejpam-5025	220	9	x	x	NOUN
ejpam-5025	220	10	,	,	PUNCT
ejpam-5025	220	11	y	y	PROPN
ejpam-5025	220	12	∈	∈	PROPN
ejpam-5025	220	13	x	x	X
ejpam-5025	220	14	.	.	PUNCT
ejpam-5025	221	1	now	now	ADV
ejpam-5025	221	2	,	,	PUNCT
ejpam-5025	221	3	using	use	VERB
ejpam-5025	221	4	definition	definition	NOUN
ejpam-5025	221	5	7	7	NUM
ejpam-5025	221	6	,	,	PUNCT
ejpam-5025	221	7	we	we	PRON
ejpam-5025	221	8	get	get	VERB
ejpam-5025	221	9	ζ(xy	ζ(xy	NOUN
ejpam-5025	221	10	)	)	PUNCT
ejpam-5025	221	11	≤	≤	NOUN
ejpam-5025	221	12	ζ(y)x	ζ(y)x	NOUN
ejpam-5025	221	13	for	for	ADP
ejpam-5025	221	14	all	all	DET
ejpam-5025	221	15	x	x	NOUN
ejpam-5025	221	16	,	,	PUNCT
ejpam-5025	221	17	y	y	PROPN
ejpam-5025	221	18	∈	∈	PROPN
ejpam-5025	221	19	x	x	INTJ
ejpam-5025	221	20	,	,	PUNCT
ejpam-5025	221	21	as	as	SCONJ
ejpam-5025	221	22	required	require	VERB
ejpam-5025	221	23	.	.	PUNCT
ejpam-5025	222	1	(	(	PUNCT
ejpam-5025	222	2	2	2	X
ejpam-5025	222	3	)	)	PUNCT
ejpam-5025	222	4	it	it	PRON
ejpam-5025	222	5	is	be	AUX
ejpam-5025	222	6	given	give	VERB
ejpam-5025	222	7	that	that	SCONJ
ejpam-5025	222	8	ζ	ζ	NOUN
ejpam-5025	222	9	is	be	AUX
ejpam-5025	222	10	regular	regular	ADJ
ejpam-5025	222	11	.	.	PUNCT
ejpam-5025	223	1	hence	hence	ADV
ejpam-5025	223	2	,	,	PUNCT
ejpam-5025	223	3	ζ−1(0	ζ−1(0	NOUN
ejpam-5025	223	4	)	)	PUNCT
ejpam-5025	223	5	̸=	̸=	PROPN
ejpam-5025	223	6	∅.	∅.	ADV
ejpam-5025	223	7	let	let	VERB
ejpam-5025	223	8	x	x	PRON
ejpam-5025	223	9	,	,	PUNCT
ejpam-5025	223	10	y	y	PROPN
ejpam-5025	223	11	∈	∈	PROPN
ejpam-5025	223	12	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	223	13	)	)	PUNCT
ejpam-5025	223	14	.	.	PUNCT
ejpam-5025	224	1	then	then	ADV
ejpam-5025	224	2	by	by	ADP
ejpam-5025	224	3	the	the	DET
ejpam-5025	224	4	part	part	NOUN
ejpam-5025	224	5	(	(	PUNCT
ejpam-5025	224	6	1	1	NUM
ejpam-5025	224	7	)	)	PUNCT
ejpam-5025	224	8	of	of	ADP
ejpam-5025	224	9	the	the	DET
ejpam-5025	224	10	present	present	ADJ
ejpam-5025	224	11	theorem	theorem	NOUN
ejpam-5025	224	12	,	,	PUNCT
ejpam-5025	224	13	we	we	PRON
ejpam-5025	224	14	get	get	VERB
ejpam-5025	224	15	ζ(xy	ζ(xy	NOUN
ejpam-5025	224	16	)	)	PUNCT
ejpam-5025	224	17	≤	≤	NOUN
ejpam-5025	224	18	ζ(y)x	ζ(y)x	NOUN
ejpam-5025	224	19	for	for	ADP
ejpam-5025	224	20	all	all	DET
ejpam-5025	224	21	x	x	NOUN
ejpam-5025	224	22	,	,	PUNCT
ejpam-5025	224	23	y	y	PROPN
ejpam-5025	224	24	∈	∈	PROPN
ejpam-5025	224	25	x	x	X
ejpam-5025	224	26	.	.	PUNCT
ejpam-5025	225	1	(	(	PUNCT
ejpam-5025	225	2	1	1	X
ejpam-5025	225	3	)	)	PUNCT
ejpam-5025	225	4	but	but	CCONJ
ejpam-5025	225	5	,	,	PUNCT
ejpam-5025	225	6	y	y	PROPN
ejpam-5025	225	7	∈	∈	PROPN
ejpam-5025	225	8	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	225	9	)	)	PUNCT
ejpam-5025	225	10	so	so	SCONJ
ejpam-5025	225	11	that	that	SCONJ
ejpam-5025	225	12	ζ(y	ζ(y	PRON
ejpam-5025	225	13	)	)	PUNCT
ejpam-5025	225	14	=	=	SYM
ejpam-5025	225	15	0	0	NUM
ejpam-5025	225	16	,	,	PUNCT
ejpam-5025	225	17	now	now	ADV
ejpam-5025	225	18	replacing	replace	VERB
ejpam-5025	225	19	ζ(y	ζ(y	PRON
ejpam-5025	225	20	)	)	PUNCT
ejpam-5025	225	21	by	by	ADP
ejpam-5025	225	22	0	0	NUM
ejpam-5025	225	23	in	in	ADP
ejpam-5025	225	24	equation	equation	NOUN
ejpam-5025	225	25	(	(	PUNCT
ejpam-5025	225	26	1	1	NUM
ejpam-5025	225	27	)	)	PUNCT
ejpam-5025	225	28	and	and	CCONJ
ejpam-5025	225	29	using	use	VERB
ejpam-5025	225	30	axiom	axiom	NOUN
ejpam-5025	225	31	(	(	PUNCT
ejpam-5025	225	32	ii	ii	NOUN
ejpam-5025	225	33	)	)	PUNCT
ejpam-5025	225	34	in	in	ADP
ejpam-5025	225	35	definition	definition	NOUN
ejpam-5025	225	36	1	1	NUM
ejpam-5025	225	37	respectively	respectively	ADV
ejpam-5025	225	38	,	,	PUNCT
ejpam-5025	225	39	we	we	PRON
ejpam-5025	225	40	get	get	VERB
ejpam-5025	225	41	ζ(xy	ζ(xy	NOUN
ejpam-5025	225	42	)	)	PUNCT
ejpam-5025	225	43	≤	≤	NOUN
ejpam-5025	225	44	0x	0x	NOUN
ejpam-5025	225	45	=	=	SYM
ejpam-5025	225	46	0	0	NUM
ejpam-5025	225	47	∀	∀	NOUN
ejpam-5025	225	48	x	x	NOUN
ejpam-5025	225	49	,	,	PUNCT
ejpam-5025	225	50	y	y	PROPN
ejpam-5025	225	51	∈	∈	PROPN
ejpam-5025	225	52	x	x	X
ejpam-5025	225	53	.	.	PUNCT
ejpam-5025	226	1	therefore	therefore	ADV
ejpam-5025	226	2	,	,	PUNCT
ejpam-5025	226	3	ζ(xy	ζ(xy	PROPN
ejpam-5025	226	4	)	)	PUNCT
ejpam-5025	226	5	=	=	SYM
ejpam-5025	227	1	0	0	NUM
ejpam-5025	227	2	∀	∀	NOUN
ejpam-5025	227	3	x	x	NOUN
ejpam-5025	227	4	,	,	PUNCT
ejpam-5025	227	5	y	y	PROPN
ejpam-5025	227	6	∈	∈	PROPN
ejpam-5025	227	7	x	x	INTJ
ejpam-5025	227	8	,	,	PUNCT
ejpam-5025	227	9	hence	hence	ADV
ejpam-5025	227	10	xy	xy	PROPN
ejpam-5025	227	11	∈	∈	PROPN
ejpam-5025	227	12	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	227	13	)	)	PUNCT
ejpam-5025	227	14	.	.	PUNCT
ejpam-5025	228	1	which	which	PRON
ejpam-5025	228	2	yields	yield	VERB
ejpam-5025	228	3	that	that	PRON
ejpam-5025	228	4	ζ−1(0	ζ−1(0	NOUN
ejpam-5025	228	5	)	)	PUNCT
ejpam-5025	228	6	is	be	AUX
ejpam-5025	228	7	a	a	DET
ejpam-5025	228	8	d−subalgebra	d−subalgebra	PROPN
ejpam-5025	228	9	of	of	ADP
ejpam-5025	228	10	x	x	PROPN
ejpam-5025	228	11	.	.	PUNCT
ejpam-5025	229	1	(	(	PUNCT
ejpam-5025	229	2	3	3	X
ejpam-5025	229	3	)	)	PUNCT
ejpam-5025	229	4	let	let	VERB
ejpam-5025	229	5	ζ	ζ	NOUN
ejpam-5025	229	6	be	be	AUX
ejpam-5025	229	7	a	a	DET
ejpam-5025	229	8	(	(	PUNCT
ejpam-5025	229	9	l	l	NOUN
ejpam-5025	229	10	,	,	PUNCT
ejpam-5025	229	11	r)−	r)−	PROPN
ejpam-5025	229	12	reverse	reverse	VERB
ejpam-5025	229	13	derivation	derivation	NOUN
ejpam-5025	229	14	on	on	ADP
ejpam-5025	229	15	x	x	X
ejpam-5025	229	16	.	.	PUNCT
ejpam-5025	230	1	then	then	ADV
ejpam-5025	230	2	we	we	PRON
ejpam-5025	230	3	get	get	VERB
ejpam-5025	230	4	,	,	PUNCT
ejpam-5025	230	5	ζ(x	ζ(x	PROPN
ejpam-5025	230	6	∧	∧	PROPN
ejpam-5025	230	7	y	y	NOUN
ejpam-5025	230	8	)	)	PUNCT
ejpam-5025	230	9	=	=	PUNCT
ejpam-5025	230	10	ζ(y(yx	ζ(y(yx	NOUN
ejpam-5025	230	11	)	)	PUNCT
ejpam-5025	230	12	)	)	PUNCT
ejpam-5025	231	1	[	[	X
ejpam-5025	231	2	by	by	ADP
ejpam-5025	231	3	x	x	PUNCT
ejpam-5025	231	4	∧	∧	PROPN
ejpam-5025	231	5	y	y	PROPN
ejpam-5025	231	6	=	=	SYM
ejpam-5025	231	7	y(yx	y(yx	PROPN
ejpam-5025	231	8	)	)	PUNCT
ejpam-5025	231	9	]	]	PUNCT
ejpam-5025	231	10	=	=	PUNCT
ejpam-5025	231	11	ζ(yx)y	ζ(yx)y	NUM
ejpam-5025	231	12	∧	∧	PROPN
ejpam-5025	231	13	(	(	PUNCT
ejpam-5025	231	14	yx)ζ(y	yx)ζ(y	X
ejpam-5025	231	15	)	)	PUNCT
ejpam-5025	232	1	[	[	X
ejpam-5025	232	2	by	by	ADP
ejpam-5025	232	3	definition	definition	NOUN
ejpam-5025	232	4	4	4	NUM
ejpam-5025	232	5	]	]	PUNCT
ejpam-5025	232	6	=	=	PUNCT
ejpam-5025	233	1	[	[	X
ejpam-5025	233	2	ζ(x)y	ζ(x)y	PROPN
ejpam-5025	233	3	∧	∧	PROPN
ejpam-5025	233	4	xζ(y)]y	xζ(y)]y	PROPN
ejpam-5025	233	5	∧	∧	PROPN
ejpam-5025	233	6	(	(	PUNCT
ejpam-5025	233	7	yx)ζ(y	yx)ζ(y	X
ejpam-5025	233	8	)	)	PUNCT
ejpam-5025	234	1	[	[	X
ejpam-5025	234	2	again	again	ADV
ejpam-5025	234	3	using	use	VERB
ejpam-5025	234	4	definition	definition	NOUN
ejpam-5025	234	5	4	4	NUM
ejpam-5025	234	6	]	]	X
ejpam-5025	234	7	=	=	SYM
ejpam-5025	234	8	(	(	PUNCT
ejpam-5025	234	9	0y	0y	X
ejpam-5025	234	10	∧	∧	PROPN
ejpam-5025	234	11	x0)y	x0)y	ADJ
ejpam-5025	234	12	∧	∧	PROPN
ejpam-5025	234	13	(	(	PUNCT
ejpam-5025	234	14	yx)0	yx)0	PROPN
ejpam-5025	234	15	[	[	PUNCT
ejpam-5025	234	16	by	by	ADP
ejpam-5025	234	17	assumption	assumption	NOUN
ejpam-5025	234	18	x	x	SYM
ejpam-5025	234	19	,	,	PUNCT
ejpam-5025	234	20	y	y	PROPN
ejpam-5025	234	21	∈	∈	PROPN
ejpam-5025	234	22	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	234	23	)	)	PUNCT
ejpam-5025	234	24	,	,	PUNCT
ejpam-5025	234	25	i.e.	i.e.	X
ejpam-5025	234	26	,	,	PUNCT
ejpam-5025	234	27	ζ(x	ζ(x	NOUN
ejpam-5025	234	28	)	)	PUNCT
ejpam-5025	234	29	=	=	SYM
ejpam-5025	234	30	ζ(y	ζ(y	X
ejpam-5025	234	31	)	)	PUNCT
ejpam-5025	234	32	=	=	PUNCT
ejpam-5025	235	1	0	0	X
ejpam-5025	235	2	]	]	X
ejpam-5025	235	3	=	=	SYM
ejpam-5025	235	4	(	(	PUNCT
ejpam-5025	235	5	0	0	NUM
ejpam-5025	235	6	∧	∧	PROPN
ejpam-5025	235	7	x)y	x)y	PUNCT
ejpam-5025	236	1	∧	∧	PROPN
ejpam-5025	236	2	yx	yx	X
ejpam-5025	236	3	[	[	X
ejpam-5025	236	4	by	by	ADP
ejpam-5025	236	5	(	(	PUNCT
ejpam-5025	236	6	ii	ii	NOUN
ejpam-5025	236	7	)	)	PUNCT
ejpam-5025	236	8	in	in	ADP
ejpam-5025	236	9	definition	definition	NOUN
ejpam-5025	236	10	1	1	NUM
ejpam-5025	236	11	and	and	CCONJ
ejpam-5025	236	12	lemma	lemma	PROPN
ejpam-5025	236	13	1	1	NUM
ejpam-5025	236	14	]	]	X
ejpam-5025	236	15	=	=	SYM
ejpam-5025	236	16	(	(	PUNCT
ejpam-5025	236	17	x(x0))y	x(x0))y	NOUN
ejpam-5025	236	18	∧	∧	PROPN
ejpam-5025	236	19	yx	yx	PROPN
ejpam-5025	237	1	[	[	X
ejpam-5025	237	2	by	by	ADP
ejpam-5025	237	3	x	x	PROPN
ejpam-5025	237	4	∧	∧	PROPN
ejpam-5025	237	5	y	y	PROPN
ejpam-5025	237	6	=	=	SYM
ejpam-5025	237	7	y(yx	y(yx	PROPN
ejpam-5025	237	8	)	)	PUNCT
ejpam-5025	237	9	]	]	PUNCT
ejpam-5025	238	1	=	=	SYM
ejpam-5025	238	2	0y	0y	NUM
ejpam-5025	238	3	∧	∧	PROPN
ejpam-5025	238	4	yx	yx	PROPN
ejpam-5025	239	1	[	[	X
ejpam-5025	239	2	by	by	ADP
ejpam-5025	239	3	lemma	lemma	PROPN
ejpam-5025	239	4	1	1	NUM
ejpam-5025	239	5	and	and	CCONJ
ejpam-5025	239	6	(	(	PUNCT
ejpam-5025	239	7	i	i	NOUN
ejpam-5025	239	8	)	)	PUNCT
ejpam-5025	239	9	in	in	ADP
ejpam-5025	239	10	definition	definition	NOUN
ejpam-5025	239	11	1	1	NUM
ejpam-5025	239	12	,	,	PUNCT
ejpam-5025	239	13	respectively	respectively	ADV
ejpam-5025	239	14	]	]	PUNCT
ejpam-5025	239	15	=	=	SYM
ejpam-5025	239	16	0	0	NUM
ejpam-5025	239	17	∧	∧	NOUN
ejpam-5025	239	18	yx	yx	PROPN
ejpam-5025	239	19	[	[	X
ejpam-5025	239	20	by	by	ADP
ejpam-5025	239	21	(	(	PUNCT
ejpam-5025	239	22	ii	ii	NOUN
ejpam-5025	239	23	)	)	PUNCT
ejpam-5025	239	24	in	in	ADP
ejpam-5025	239	25	definition	definition	NOUN
ejpam-5025	239	26	1	1	NUM
ejpam-5025	239	27	]	]	PUNCT
ejpam-5025	239	28	=	=	SYM
ejpam-5025	239	29	yx((yx)0	yx((yx)0	NOUN
ejpam-5025	239	30	)	)	PUNCT
ejpam-5025	240	1	[	[	X
ejpam-5025	240	2	by	by	ADP
ejpam-5025	240	3	x	x	PUNCT
ejpam-5025	240	4	∧	∧	PROPN
ejpam-5025	240	5	y	y	PROPN
ejpam-5025	240	6	=	=	SYM
ejpam-5025	240	7	y(yx	y(yx	PROPN
ejpam-5025	240	8	)	)	PUNCT
ejpam-5025	240	9	]	]	PUNCT
ejpam-5025	240	10	=	=	SYM
ejpam-5025	240	11	yx(yx	yx(yx	NOUN
ejpam-5025	240	12	)	)	PUNCT
ejpam-5025	241	1	[	[	X
ejpam-5025	241	2	again	again	ADV
ejpam-5025	241	3	by	by	ADP
ejpam-5025	241	4	lemma	lemma	PROPN
ejpam-5025	241	5	1	1	NUM
ejpam-5025	241	6	]	]	X
ejpam-5025	241	7	=	=	SYM
ejpam-5025	241	8	0	0	X
ejpam-5025	241	9	.	.	PUNCT
ejpam-5025	242	1	[	[	X
ejpam-5025	242	2	by	by	ADP
ejpam-5025	242	3	(	(	PUNCT
ejpam-5025	242	4	i	i	NOUN
ejpam-5025	242	5	)	)	PUNCT
ejpam-5025	242	6	in	in	ADP
ejpam-5025	242	7	definition	definition	NOUN
ejpam-5025	242	8	1	1	NUM
ejpam-5025	242	9	]	]	PUNCT
ejpam-5025	242	10	references	reference	NOUN
ejpam-5025	242	11	370	370	NUM
ejpam-5025	242	12	hence	hence	ADV
ejpam-5025	242	13	,	,	PUNCT
ejpam-5025	242	14	we	we	PRON
ejpam-5025	242	15	conclude	conclude	VERB
ejpam-5025	242	16	that	that	SCONJ
ejpam-5025	242	17	,	,	PUNCT
ejpam-5025	242	18	ζ(x	ζ(x	PROPN
ejpam-5025	242	19	∧	∧	PROPN
ejpam-5025	242	20	y	y	NOUN
ejpam-5025	242	21	)	)	PUNCT
ejpam-5025	242	22	=	=	SYM
ejpam-5025	242	23	0	0	NUM
ejpam-5025	242	24	for	for	ADP
ejpam-5025	242	25	any	any	DET
ejpam-5025	242	26	x	x	NOUN
ejpam-5025	242	27	,	,	PUNCT
ejpam-5025	242	28	y	y	PROPN
ejpam-5025	242	29	∈	∈	PROPN
ejpam-5025	242	30	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	242	31	)	)	PUNCT
ejpam-5025	242	32	which	which	PRON
ejpam-5025	242	33	means	mean	VERB
ejpam-5025	242	34	x	x	PUNCT
ejpam-5025	242	35	∧	∧	NOUN
ejpam-5025	242	36	y	y	PROPN
ejpam-5025	242	37	∈	∈	PROPN
ejpam-5025	242	38	ζ−1(0	ζ−1(0	PROPN
ejpam-5025	242	39	)	)	PUNCT
ejpam-5025	242	40	as	as	SCONJ
ejpam-5025	242	41	required	require	VERB
ejpam-5025	242	42	.	.	PUNCT
ejpam-5025	243	1	references	reference	NOUN
ejpam-5025	243	2	[	[	X
ejpam-5025	243	3	1	1	X
ejpam-5025	243	4	]	]	PUNCT
ejpam-5025	243	5	a	a	DET
ejpam-5025	243	6	aboubakr	aboubakr	NOUN
ejpam-5025	243	7	and	and	CCONJ
ejpam-5025	243	8	s	s	NOUN
ejpam-5025	243	9	gonzález	gonzález	PROPN
ejpam-5025	243	10	.	.	PUNCT
ejpam-5025	244	1	generalized	generalize	VERB
ejpam-5025	244	2	reverse	reverse	ADJ
ejpam-5025	244	3	derivations	derivation	NOUN
ejpam-5025	244	4	on	on	ADP
ejpam-5025	244	5	semiprime	semiprime	NOUN
ejpam-5025	244	6	rings	ring	NOUN
ejpam-5025	244	7	.	.	PUNCT
ejpam-5025	245	1	siberian	siberian	PROPN
ejpam-5025	245	2	mathematical	mathematical	PROPN
ejpam-5025	245	3	journal	journal	NOUN
ejpam-5025	245	4	,	,	PUNCT
ejpam-5025	245	5	56(2):199–205	56(2):199–205	PROPN
ejpam-5025	245	6	,	,	PUNCT
ejpam-5025	245	7	2015	2015	NUM
ejpam-5025	245	8	.	.	PUNCT
ejpam-5025	246	1	[	[	X
ejpam-5025	246	2	2	2	NUM
ejpam-5025	246	3	]	]	X
ejpam-5025	246	4	r	r	NOUN
ejpam-5025	246	5	al	al	PROPN
ejpam-5025	246	6	-	-	PUNCT
ejpam-5025	246	7	omary	omary	NOUN
ejpam-5025	246	8	.	.	PUNCT
ejpam-5025	247	1	on	on	ADP
ejpam-5025	247	2	(	(	PUNCT
ejpam-5025	247	3	α	α	X
ejpam-5025	247	4	,	,	PUNCT
ejpam-5025	247	5	β)-derivations	β)-derivation	NOUN
ejpam-5025	247	6	in	in	ADP
ejpam-5025	247	7	d	d	NOUN
ejpam-5025	247	8	-	-	PUNCT
ejpam-5025	247	9	algebras	algebras	X
ejpam-5025	247	10	.	.	PUNCT
ejpam-5025	248	1	bollettino	bollettino	PROPN
ejpam-5025	248	2	dell’unione	dell’unione	PROPN
ejpam-5025	248	3	matematica	matematica	PROPN
ejpam-5025	248	4	italiana	italiana	PROPN
ejpam-5025	248	5	,	,	PUNCT
ejpam-5025	248	6	12(4):549–556	12(4):549–556	NUM
ejpam-5025	248	7	,	,	PUNCT
ejpam-5025	248	8	2019	2019	NUM
ejpam-5025	248	9	.	.	PUNCT
ejpam-5025	249	1	[	[	X
ejpam-5025	249	2	3	3	X
ejpam-5025	249	3	]	]	X
ejpam-5025	249	4	p	p	X
ejpam-5025	249	5	allen	allen	PROPN
ejpam-5025	249	6	,	,	PUNCT
ejpam-5025	249	7	h	h	PROPN
ejpam-5025	249	8	kim	kim	PROPN
ejpam-5025	249	9	,	,	PUNCT
ejpam-5025	249	10	and	and	CCONJ
ejpam-5025	249	11	j	j	PROPN
ejpam-5025	249	12	neggers	negger	NOUN
ejpam-5025	249	13	.	.	PUNCT
ejpam-5025	250	1	super	super	ADV
ejpam-5025	250	2	commutative	commutative	ADJ
ejpam-5025	250	3	d−algebras	d−algebras	PROPN
ejpam-5025	250	4	and	and	CCONJ
ejpam-5025	250	5	bck−algebra	bck−algebra	PROPN
ejpam-5025	250	6	in	in	ADP
ejpam-5025	250	7	the	the	DET
ejpam-5025	250	8	smarandache	smarandache	NOUN
ejpam-5025	250	9	setting	setting	NOUN
ejpam-5025	250	10	.	.	PUNCT
ejpam-5025	251	1	scientiae	scientiae	PROPN
ejpam-5025	251	2	mathematicae	mathematicae	PROPN
ejpam-5025	251	3	japonicae	japonicae	PROPN
ejpam-5025	251	4	,	,	PUNCT
ejpam-5025	251	5	pages	page	NOUN
ejpam-5025	251	6	161–165	161–165	NUM
ejpam-5025	251	7	,	,	PUNCT
ejpam-5025	251	8	2005	2005	NUM
ejpam-5025	251	9	.	.	PUNCT
ejpam-5025	252	1	[	[	X
ejpam-5025	252	2	4	4	NUM
ejpam-5025	252	3	]	]	SYM
ejpam-5025	252	4	s	s	X
ejpam-5025	252	5	aslıhan	aslıhan	NOUN
ejpam-5025	252	6	and	and	CCONJ
ejpam-5025	252	7	y	y	PROPN
ejpam-5025	252	8	damla	damla	NOUN
ejpam-5025	252	9	.	.	PUNCT
ejpam-5025	253	1	generalized	generalize	VERB
ejpam-5025	253	2	(	(	PUNCT
ejpam-5025	253	3	α	α	X
ejpam-5025	253	4	,	,	PUNCT
ejpam-5025	253	5	β)-derivations	β)-derivation	NOUN
ejpam-5025	253	6	in	in	ADP
ejpam-5025	253	7	d	d	NOUN
ejpam-5025	253	8	-	-	PUNCT
ejpam-5025	253	9	algebras	algebras	X
ejpam-5025	253	10	.	.	PUNCT
ejpam-5025	254	1	bull	bull	PROPN
ejpam-5025	254	2	int	int	PROPN
ejpam-5025	254	3	math	math	PROPN
ejpam-5025	254	4	virtual	virtual	ADJ
ejpam-5025	254	5	inst	inst	NOUN
ejpam-5025	254	6	,	,	PUNCT
ejpam-5025	254	7	13(2):239–247	13(2):239–247	PROPN
ejpam-5025	254	8	,	,	PUNCT
ejpam-5025	254	9	2023	2023	NUM
ejpam-5025	254	10	.	.	PUNCT
ejpam-5025	255	1	[	[	X
ejpam-5025	255	2	5	5	NUM
ejpam-5025	255	3	]	]	PUNCT
ejpam-5025	255	4	m	m	VERB
ejpam-5025	255	5	brešar	brešar	ADJ
ejpam-5025	255	6	and	and	CCONJ
ejpam-5025	255	7	j	j	PROPN
ejpam-5025	255	8	vukman	vukman	NOUN
ejpam-5025	255	9	.	.	PUNCT
ejpam-5025	256	1	on	on	ADP
ejpam-5025	256	2	some	some	DET
ejpam-5025	256	3	additive	additive	ADJ
ejpam-5025	256	4	mappings	mapping	NOUN
ejpam-5025	256	5	in	in	ADP
ejpam-5025	256	6	rings	ring	NOUN
ejpam-5025	256	7	with	with	ADP
ejpam-5025	256	8	involution	involution	NOUN
ejpam-5025	256	9	.	.	PUNCT
ejpam-5025	257	1	aequationes	aequatione	NOUN
ejpam-5025	257	2	mathematicae	mathematicae	PROPN
ejpam-5025	257	3	,	,	PUNCT
ejpam-5025	257	4	38(2	38(2	NOUN
ejpam-5025	257	5	-	-	SYM
ejpam-5025	257	6	3):178–185	3):178–185	NUM
ejpam-5025	257	7	,	,	PUNCT
ejpam-5025	257	8	1989	1989	NUM
ejpam-5025	257	9	.	.	PUNCT
ejpam-5025	258	1	[	[	X
ejpam-5025	258	2	6	6	NUM
ejpam-5025	258	3	]	]	PUNCT
ejpam-5025	258	4	m	m	AUX
ejpam-5025	258	5	chandramouleeswaran	chandramouleeswaran	ADJ
ejpam-5025	258	6	and	and	CCONJ
ejpam-5025	258	7	n	n	PRON
ejpam-5025	258	8	kandaraj	kandaraj	ADJ
ejpam-5025	258	9	.	.	PUNCT
ejpam-5025	259	1	derivation	derivation	NOUN
ejpam-5025	259	2	on	on	ADP
ejpam-5025	259	3	d−algebra	d−algebra	NOUN
ejpam-5025	259	4	.	.	PUNCT
ejpam-5025	260	1	inter	inter	PROPN
ejpam-5025	260	2	j	j	PROPN
ejpam-5025	260	3	of	of	ADP
ejpam-5025	260	4	math	math	PROPN
ejpam-5025	260	5	sciences	sciences	PROPN
ejpam-5025	260	6	and	and	CCONJ
ejpam-5025	260	7	applications	application	NOUN
ejpam-5025	260	8	,	,	PUNCT
ejpam-5025	260	9	1(1):231–237	1(1):231–237	NUM
ejpam-5025	260	10	,	,	PUNCT
ejpam-5025	260	11	2011	2011	NUM
ejpam-5025	260	12	.	.	PUNCT
ejpam-5025	261	1	[	[	X
ejpam-5025	261	2	7	7	NUM
ejpam-5025	261	3	]	]	SYM
ejpam-5025	261	4	v	v	NOUN
ejpam-5025	261	5	filippov	filippov	NOUN
ejpam-5025	261	6	.	.	PUNCT
ejpam-5025	262	1	on	on	ADP
ejpam-5025	262	2	δ	δ	PROPN
ejpam-5025	262	3	-	-	PUNCT
ejpam-5025	262	4	derivations	derivation	NOUN
ejpam-5025	262	5	of	of	ADP
ejpam-5025	262	6	lie	lie	NOUN
ejpam-5025	262	7	algebras	algebra	NOUN
ejpam-5025	262	8	.	.	PUNCT
ejpam-5025	262	9	siberian	siberian	ADJ
ejpam-5025	262	10	math	math	PROPN
ejpam-5025	262	11	.	.	PUNCT
ejpam-5025	263	1	j.	j.	PROPN
ejpam-5025	263	2	,	,	PUNCT
ejpam-5025	263	3	39(6):1218–1230	39(6):1218–1230	NUM
ejpam-5025	263	4	,	,	PUNCT
ejpam-5025	263	5	1998	1998	NUM
ejpam-5025	263	6	.	.	PUNCT
ejpam-5025	264	1	[	[	X
ejpam-5025	264	2	8	8	NUM
ejpam-5025	264	3	]	]	X
ejpam-5025	264	4	i	i	PROPN
ejpam-5025	264	5	herstein	herstein	NOUN
ejpam-5025	264	6	.	.	PUNCT
ejpam-5025	265	1	jordan	jordan	PROPN
ejpam-5025	265	2	derivations	derivation	NOUN
ejpam-5025	265	3	of	of	ADP
ejpam-5025	265	4	prime	prime	ADJ
ejpam-5025	265	5	rings	ring	NOUN
ejpam-5025	265	6	.	.	PUNCT
ejpam-5025	266	1	proceedings	proceeding	NOUN
ejpam-5025	266	2	of	of	ADP
ejpam-5025	266	3	the	the	DET
ejpam-5025	266	4	american	american	PROPN
ejpam-5025	266	5	mathematical	mathematical	PROPN
ejpam-5025	266	6	society	society	NOUN
ejpam-5025	266	7	,	,	PUNCT
ejpam-5025	266	8	8(6):1104–1110	8(6):1104–1110	PROPN
ejpam-5025	266	9	,	,	PUNCT
ejpam-5025	266	10	1957	1957	NUM
ejpam-5025	266	11	.	.	PUNCT
ejpam-5025	267	1	[	[	X
ejpam-5025	267	2	9	9	NUM
ejpam-5025	267	3	]	]	PUNCT
ejpam-5025	267	4	n	n	DET
ejpam-5025	267	5	hopkins	hopkin	NOUN
ejpam-5025	267	6	.	.	PUNCT
ejpam-5025	268	1	generalized	generalized	ADJ
ejpam-5025	268	2	derivations	derivation	NOUN
ejpam-5025	268	3	of	of	ADP
ejpam-5025	268	4	nonassociative	nonassociative	ADJ
ejpam-5025	268	5	algebras	algebra	NOUN
ejpam-5025	268	6	.	.	PUNCT
ejpam-5025	269	1	nova	nova	PROPN
ejpam-5025	269	2	j	j	PROPN
ejpam-5025	269	3	math	math	PROPN
ejpam-5025	269	4	game	game	PROPN
ejpam-5025	269	5	theory	theory	NOUN
ejpam-5025	269	6	algebra	algebra	PROPN
ejpam-5025	269	7	,	,	PUNCT
ejpam-5025	269	8	5(3):215–224	5(3):215–224	NUM
ejpam-5025	269	9	,	,	PUNCT
ejpam-5025	269	10	1996	1996	NUM
ejpam-5025	269	11	.	.	PUNCT
ejpam-5025	270	1	[	[	X
ejpam-5025	270	2	10	10	NUM
ejpam-5025	270	3	]	]	X
ejpam-5025	270	4	s	s	PROPN
ejpam-5025	270	5	huang	huang	PROPN
ejpam-5025	270	6	.	.	PROPN
ejpam-5025	271	1	generalized	generalize	VERB
ejpam-5025	271	2	reverse	reverse	ADJ
ejpam-5025	271	3	derivations	derivation	NOUN
ejpam-5025	271	4	and	and	CCONJ
ejpam-5025	271	5	commutativity	commutativity	NOUN
ejpam-5025	271	6	of	of	ADP
ejpam-5025	271	7	prime	prime	ADJ
ejpam-5025	271	8	rings	ring	NOUN
ejpam-5025	271	9	.	.	PUNCT
ejpam-5025	272	1	communications	communication	NOUN
ejpam-5025	272	2	in	in	ADP
ejpam-5025	272	3	mathematics	mathematic	NOUN
ejpam-5025	272	4	,	,	PUNCT
ejpam-5025	272	5	27(1):43–50	27(1):43–50	NUM
ejpam-5025	272	6	,	,	PUNCT
ejpam-5025	272	7	2019	2019	NUM
ejpam-5025	272	8	.	.	PUNCT
ejpam-5025	273	1	[	[	X
ejpam-5025	273	2	11	11	NUM
ejpam-5025	273	3	]	]	X
ejpam-5025	273	4	y	y	PROPN
ejpam-5025	273	5	imai	imai	PROPN
ejpam-5025	273	6	and	and	CCONJ
ejpam-5025	273	7	k	k	PROPN
ejpam-5025	273	8	iséki	iséki	PROPN
ejpam-5025	273	9	.	.	PROPN
ejpam-5025	274	1	on	on	ADP
ejpam-5025	274	2	axiom	axiom	NOUN
ejpam-5025	274	3	systems	system	NOUN
ejpam-5025	274	4	of	of	ADP
ejpam-5025	274	5	propositional	propositional	ADJ
ejpam-5025	274	6	calculi	calculi	PROPN
ejpam-5025	274	7	,	,	PUNCT
ejpam-5025	274	8	xiv	xiv	PROPN
ejpam-5025	274	9	.	.	PUNCT
ejpam-5025	275	1	proceedings	proceeding	NOUN
ejpam-5025	275	2	of	of	ADP
ejpam-5025	275	3	the	the	DET
ejpam-5025	275	4	japan	japan	PROPN
ejpam-5025	275	5	academy	academy	PROPN
ejpam-5025	275	6	,	,	PUNCT
ejpam-5025	275	7	series	series	PROPN
ejpam-5025	275	8	a	a	PRON
ejpam-5025	275	9	,	,	PUNCT
ejpam-5025	275	10	mathematical	mathematical	ADJ
ejpam-5025	275	11	sciences	science	NOUN
ejpam-5025	275	12	,	,	PUNCT
ejpam-5025	275	13	42(1	42(1	NOUN
ejpam-5025	275	14	)	)	PUNCT
ejpam-5025	275	15	,	,	PUNCT
ejpam-5025	275	16	1966	1966	NUM
ejpam-5025	275	17	.	.	PUNCT
ejpam-5025	276	1	[	[	X
ejpam-5025	276	2	12	12	NUM
ejpam-5025	276	3	]	]	X
ejpam-5025	276	4	k	k	PROPN
ejpam-5025	276	5	iseki	iseki	PROPN
ejpam-5025	276	6	and	and	CCONJ
ejpam-5025	276	7	s	s	VERB
ejpam-5025	276	8	tanaka	tanaka	PROPN
ejpam-5025	276	9	.	.	PUNCT
ejpam-5025	277	1	an	an	DET
ejpam-5025	277	2	introduction	introduction	NOUN
ejpam-5025	277	3	to	to	ADP
ejpam-5025	277	4	theory	theory	NOUN
ejpam-5025	277	5	of	of	ADP
ejpam-5025	277	6	bck−algebras	bck−algebras	PROPN
ejpam-5025	277	7	.	.	PUNCT
ejpam-5025	277	8	math	math	PROPN
ejpam-5025	277	9	japo	japo	PROPN
ejpam-5025	277	10	.	.	PUNCT
ejpam-5025	277	11	,	,	PUNCT
ejpam-5025	277	12	23(1):1–26	23(1):1–26	NUM
ejpam-5025	277	13	,	,	PUNCT
ejpam-5025	277	14	1978	1978	NUM
ejpam-5025	277	15	.	.	PUNCT
ejpam-5025	278	1	[	[	X
ejpam-5025	278	2	13	13	NUM
ejpam-5025	278	3	]	]	PUNCT
ejpam-5025	278	4	n	n	PRON
ejpam-5025	278	5	jacobson	jacobson	PROPN
ejpam-5025	278	6	.	.	PROPN
ejpam-5025	279	1	lie	lie	PROPN
ejpam-5025	279	2	algebras	algebras	PROPN
ejpam-5025	279	3	.	.	PUNCT
ejpam-5025	280	1	10	10	NUM
ejpam-5025	280	2	.	.	X
ejpam-5025	281	1	interscience	interscience	NOUN
ejpam-5025	281	2	publisher	publisher	NOUN
ejpam-5025	281	3	,	,	PUNCT
ejpam-5025	281	4	1962	1962	NUM
ejpam-5025	281	5	.	.	PUNCT
ejpam-5025	282	1	[	[	X
ejpam-5025	282	2	14	14	NUM
ejpam-5025	282	3	]	]	X
ejpam-5025	282	4	y	y	PROPN
ejpam-5025	282	5	jun	jun	PROPN
ejpam-5025	282	6	and	and	CCONJ
ejpam-5025	282	7	x	x	NOUN
ejpam-5025	282	8	xin	xin	PROPN
ejpam-5025	282	9	.	.	PUNCT
ejpam-5025	283	1	on	on	ADP
ejpam-5025	283	2	derivations	derivation	NOUN
ejpam-5025	283	3	of	of	ADP
ejpam-5025	283	4	bci−algebras	bci−algebras	PROPN
ejpam-5025	283	5	.	.	PUNCT
ejpam-5025	283	6	information	information	NOUN
ejpam-5025	283	7	sciences	sciences	PROPN
ejpam-5025	283	8	,	,	PUNCT
ejpam-5025	283	9	159(34):167–176	159(34):167–176	NUM
ejpam-5025	283	10	,	,	PUNCT
ejpam-5025	283	11	2004	2004	NUM
ejpam-5025	283	12	.	.	PUNCT
ejpam-5025	284	1	[	[	X
ejpam-5025	284	2	15	15	NUM
ejpam-5025	284	3	]	]	X
ejpam-5025	284	4	i	i	PRON
ejpam-5025	284	5	kaygorodov	kaygorodov	PROPN
ejpam-5025	284	6	.	.	PUNCT
ejpam-5025	285	1	on	on	ADP
ejpam-5025	285	2	δ	δ	PROPN
ejpam-5025	285	3	-	-	PUNCT
ejpam-5025	285	4	derivations	derivation	NOUN
ejpam-5025	285	5	of	of	ADP
ejpam-5025	285	6	classical	classical	ADJ
ejpam-5025	285	7	lie	lie	NOUN
ejpam-5025	285	8	superalgebras	superalgebras	PROPN
ejpam-5025	285	9	.	.	PUNCT
ejpam-5025	286	1	siberian	siberian	PROPN
ejpam-5025	286	2	mathematical	mathematical	PROPN
ejpam-5025	286	3	journal	journal	PROPN
ejpam-5025	286	4	,	,	PUNCT
ejpam-5025	286	5	50(3):434–449	50(3):434–449	PROPN
ejpam-5025	286	6	,	,	PUNCT
ejpam-5025	286	7	2009	2009	NUM
ejpam-5025	286	8	.	.	PUNCT
ejpam-5025	287	1	references	reference	NOUN
ejpam-5025	287	2	371	371	NUM
ejpam-5025	288	1	[	[	X
ejpam-5025	288	2	16	16	NUM
ejpam-5025	288	3	]	]	X
ejpam-5025	288	4	i	i	PRON
ejpam-5025	288	5	kaygorodov	kaygorodov	PROPN
ejpam-5025	288	6	.	.	PUNCT
ejpam-5025	289	1	on	on	ADP
ejpam-5025	289	2	(	(	PUNCT
ejpam-5025	289	3	reverse	reverse	VERB
ejpam-5025	289	4	)	)	PUNCT
ejpam-5025	289	5	(	(	PUNCT
ejpam-5025	289	6	α	α	X
ejpam-5025	289	7	,	,	PUNCT
ejpam-5025	289	8	β	β	X
ejpam-5025	289	9	,	,	PUNCT
ejpam-5025	289	10	γ)-derivations	γ)-derivation	NOUN
ejpam-5025	289	11	of	of	ADP
ejpam-5025	289	12	associative	associative	ADJ
ejpam-5025	289	13	algebras	algebra	NOUN
ejpam-5025	289	14	.	.	PUNCT
ejpam-5025	289	15	boll	boll	PROPN
ejpam-5025	289	16	unione	unione	PROPN
ejpam-5025	289	17	mat	mat	PROPN
ejpam-5025	289	18	ital	ital	PROPN
ejpam-5025	289	19	.	.	PROPN
ejpam-5025	289	20	,	,	PUNCT
ejpam-5025	289	21	8(3):181–187	8(3):181–187	NUM
ejpam-5025	289	22	,	,	PUNCT
ejpam-5025	289	23	2015	2015	NUM
ejpam-5025	289	24	.	.	PUNCT
ejpam-5025	290	1	[	[	X
ejpam-5025	290	2	17	17	NUM
ejpam-5025	290	3	]	]	X
ejpam-5025	290	4	y	y	PROPN
ejpam-5025	290	5	kim	kim	PROPN
ejpam-5025	290	6	.	.	PUNCT
ejpam-5025	291	1	some	some	DET
ejpam-5025	291	2	derivations	derivation	NOUN
ejpam-5025	291	3	on	on	ADP
ejpam-5025	291	4	d−algebras	d−algebra	NOUN
ejpam-5025	291	5	.	.	PROPN
ejpam-5025	291	6	international	international	ADJ
ejpam-5025	291	7	journal	journal	PROPN
ejpam-5025	291	8	of	of	ADP
ejpam-5025	291	9	fuzzy	fuzzy	ADJ
ejpam-5025	291	10	logic	logic	NOUN
ejpam-5025	291	11	and	and	CCONJ
ejpam-5025	291	12	intelligent	intelligent	ADJ
ejpam-5025	291	13	systems	system	NOUN
ejpam-5025	291	14	,	,	PUNCT
ejpam-5025	291	15	18(4):298–302	18(4):298–302	PROPN
ejpam-5025	291	16	,	,	PUNCT
ejpam-5025	291	17	2018	2018	NUM
ejpam-5025	291	18	.	.	PUNCT
ejpam-5025	292	1	[	[	X
ejpam-5025	292	2	18	18	NUM
ejpam-5025	292	3	]	]	X
ejpam-5025	292	4	g	g	PROPN
ejpam-5025	292	5	muhiuddin	muhiuddin	NOUN
ejpam-5025	292	6	and	and	CCONJ
ejpam-5025	292	7	a	a	DET
ejpam-5025	292	8	al	al	PROPN
ejpam-5025	292	9	-	-	PUNCT
ejpam-5025	292	10	roqi	roqi	ADJ
ejpam-5025	292	11	.	.	PUNCT
ejpam-5025	293	1	on	on	ADP
ejpam-5025	293	2	generalized	generalized	ADJ
ejpam-5025	293	3	left	leave	VERB
ejpam-5025	293	4	derivations	derivation	NOUN
ejpam-5025	293	5	in	in	ADP
ejpam-5025	293	6	bci−algebras	bci−algebra	NOUN
ejpam-5025	293	7	.	.	NOUN
ejpam-5025	293	8	applied	apply	VERB
ejpam-5025	293	9	mathematics	mathematic	NOUN
ejpam-5025	293	10	and	and	CCONJ
ejpam-5025	293	11	information	information	NOUN
ejpam-5025	293	12	sciences	science	NOUN
ejpam-5025	293	13	,	,	PUNCT
ejpam-5025	293	14	8(3):1153–1158	8(3):1153–1158	NUM
ejpam-5025	293	15	,	,	PUNCT
ejpam-5025	293	16	2014	2014	NUM
ejpam-5025	293	17	.	.	PUNCT
ejpam-5025	294	1	[	[	X
ejpam-5025	294	2	19	19	NUM
ejpam-5025	294	3	]	]	X
ejpam-5025	294	4	j	j	PROPN
ejpam-5025	294	5	neggers	negger	NOUN
ejpam-5025	294	6	,	,	PUNCT
ejpam-5025	294	7	y	y	PROPN
ejpam-5025	294	8	jun	jun	PROPN
ejpam-5025	294	9	,	,	PUNCT
ejpam-5025	294	10	and	and	CCONJ
ejpam-5025	294	11	h	h	PROPN
ejpam-5025	294	12	kim	kim	PROPN
ejpam-5025	294	13	.	.	PUNCT
ejpam-5025	295	1	on	on	ADP
ejpam-5025	295	2	d−ideals	d−ideal	NOUN
ejpam-5025	295	3	in	in	ADP
ejpam-5025	295	4	d−algebras	d−algebras	PROPN
ejpam-5025	295	5	.	.	PROPN
ejpam-5025	295	6	mathematica	mathematica	PROPN
ejpam-5025	295	7	slovaca	slovaca	PROPN
ejpam-5025	295	8	,	,	PUNCT
ejpam-5025	295	9	49(3):243–251	49(3):243–251	PROPN
ejpam-5025	295	10	,	,	PUNCT
ejpam-5025	295	11	1999	1999	NUM
ejpam-5025	295	12	.	.	PUNCT
ejpam-5025	296	1	[	[	X
ejpam-5025	296	2	20	20	NUM
ejpam-5025	296	3	]	]	X
ejpam-5025	296	4	j	j	PROPN
ejpam-5025	296	5	neggers	negger	NOUN
ejpam-5025	296	6	and	and	CCONJ
ejpam-5025	296	7	h	h	PROPN
ejpam-5025	296	8	kim	kim	PROPN
ejpam-5025	296	9	.	.	PUNCT
ejpam-5025	297	1	on	on	ADP
ejpam-5025	297	2	d−algebras	d−algebras	PROPN
ejpam-5025	297	3	.	.	PROPN
ejpam-5025	297	4	math	math	PROPN
ejpam-5025	297	5	slovaca	slovaca	PROPN
ejpam-5025	297	6	co.	co.	PROPN
ejpam-5025	297	7	,	,	PUNCT
ejpam-5025	297	8	49(1):19–26	49(1):19–26	NUM
ejpam-5025	297	9	,	,	PUNCT
ejpam-5025	297	10	1999	1999	NUM
ejpam-5025	297	11	.	.	PUNCT
ejpam-5025	298	1	[	[	X
ejpam-5025	298	2	21	21	NUM
ejpam-5025	298	3	]	]	X
ejpam-5025	298	4	m	m	VERB
ejpam-5025	298	5	samman	samman	NOUN
ejpam-5025	298	6	and	and	CCONJ
ejpam-5025	298	7	n	n	PRON
ejpam-5025	298	8	alyamani	alyamani	NOUN
ejpam-5025	298	9	.	.	PUNCT
ejpam-5025	299	1	derivations	derivation	NOUN
ejpam-5025	299	2	and	and	CCONJ
ejpam-5025	299	3	reverse	reverse	ADJ
ejpam-5025	299	4	derivations	derivation	NOUN
ejpam-5025	299	5	in	in	ADP
ejpam-5025	299	6	semiprime	semiprime	NOUN
ejpam-5025	299	7	rings	ring	NOUN
ejpam-5025	299	8	.	.	PUNCT
ejpam-5025	300	1	international	international	PROPN
ejpam-5025	300	2	mathematical	mathematical	PROPN
ejpam-5025	300	3	forum	forum	PROPN
ejpam-5025	300	4	,	,	PUNCT
ejpam-5025	300	5	2:1895–1902	2:1895–1902	NUM
ejpam-5025	300	6	,	,	PUNCT
ejpam-5025	300	7	2007	2007	NUM
ejpam-5025	300	8	.	.	PUNCT