id	sid	tid	token	lemma	pos
ejpam-4924	1	1	european	european	PROPN
ejpam-4924	1	2	journal	journal	PROPN
ejpam-4924	1	3	of	of	ADP
ejpam-4924	1	4	pure	pure	ADJ
ejpam-4924	1	5	and	and	CCONJ
ejpam-4924	1	6	applied	apply	VERB
ejpam-4924	1	7	mathematics	mathematic	NOUN
ejpam-4924	1	8	vol	vol	NOUN
ejpam-4924	1	9	.	.	PUNCT
ejpam-4924	2	1	16	16	NUM
ejpam-4924	2	2	,	,	PUNCT
ejpam-4924	2	3	no	no	INTJ
ejpam-4924	2	4	.	.	NOUN
ejpam-4924	2	5	4	4	NUM
ejpam-4924	2	6	,	,	PUNCT
ejpam-4924	2	7	2023	2023	NUM
ejpam-4924	2	8	,	,	PUNCT
ejpam-4924	2	9	2145	2145	NUM
ejpam-4924	2	10	-	-	SYM
ejpam-4924	2	11	2155	2155	NUM
ejpam-4924	2	12	issn	issn	PROPN
ejpam-4924	2	13	1307	1307	NUM
ejpam-4924	2	14	-	-	SYM
ejpam-4924	2	15	5543	5543	NUM
ejpam-4924	2	16	–	–	PUNCT
ejpam-4924	3	1	ejpam.com	ejpam.com	X
ejpam-4924	3	2	published	publish	VERB
ejpam-4924	3	3	by	by	ADP
ejpam-4924	3	4	new	new	PROPN
ejpam-4924	3	5	york	york	PROPN
ejpam-4924	3	6	business	business	PROPN
ejpam-4924	3	7	global	global	ADJ
ejpam-4924	3	8	derivations	derivation	NOUN
ejpam-4924	3	9	and	and	CCONJ
ejpam-4924	3	10	representations	representation	NOUN
ejpam-4924	3	11	of	of	ADP
ejpam-4924	3	12	commutative	commutative	ADJ
ejpam-4924	3	13	algebras	algebra	NOUN
ejpam-4924	3	14	verifying	verify	VERB
ejpam-4924	3	15	a	a	DET
ejpam-4924	3	16	polynomial	polynomial	ADJ
ejpam-4924	3	17	identity	identity	NOUN
ejpam-4924	3	18	of	of	ADP
ejpam-4924	3	19	degree	degree	NOUN
ejpam-4924	3	20	five	five	NUM
ejpam-4924	3	21	hamed	hamed	ADJ
ejpam-4924	3	22	ouédraogo1	ouédraogo1	PROPN
ejpam-4924	3	23	,	,	PUNCT
ejpam-4924	3	24	abdoulaye	abdoulaye	VERB
ejpam-4924	3	25	dembega1	dembega1	PROPN
ejpam-4924	3	26	,	,	PUNCT
ejpam-4924	3	27	andré	andré	ADJ
ejpam-4924	3	28	conseibo1,∗	conseibo1,∗	NOUN
ejpam-4924	3	29	1	1	NUM
ejpam-4924	3	30	départment	départment	PROPN
ejpam-4924	3	31	de	de	X
ejpam-4924	3	32	mathematiques	mathematiques	PROPN
ejpam-4924	3	33	/	/	SYM
ejpam-4924	3	34	université	université	ADJ
ejpam-4924	3	35	norbert	norbert	PROPN
ejpam-4924	3	36	zongo	zongo	PROPN
ejpam-4924	3	37	,	,	PUNCT
ejpam-4924	3	38	koudougou	koudougou	PROPN
ejpam-4924	3	39	,	,	PUNCT
ejpam-4924	3	40	burkina	burkina	PROPN
ejpam-4924	3	41	faso	faso	PROPN
ejpam-4924	3	42	abstract	abstract	NOUN
ejpam-4924	3	43	.	.	PUNCT
ejpam-4924	4	1	in	in	ADP
ejpam-4924	4	2	this	this	DET
ejpam-4924	4	3	paper	paper	NOUN
ejpam-4924	4	4	we	we	PRON
ejpam-4924	4	5	study	study	VERB
ejpam-4924	4	6	a	a	DET
ejpam-4924	4	7	class	class	NOUN
ejpam-4924	4	8	of	of	ADP
ejpam-4924	4	9	commutative	commutative	ADJ
ejpam-4924	4	10	non	non	ADJ
ejpam-4924	4	11	associative	associative	NOUN
ejpam-4924	4	12	algebras	algebra	NOUN
ejpam-4924	4	13	satisfying	satisfy	VERB
ejpam-4924	4	14	a	a	DET
ejpam-4924	4	15	polynomial	polynomial	ADJ
ejpam-4924	4	16	identity	identity	NOUN
ejpam-4924	4	17	of	of	ADP
ejpam-4924	4	18	degree	degree	NOUN
ejpam-4924	4	19	five	five	NUM
ejpam-4924	4	20	.	.	PUNCT
ejpam-4924	5	1	we	we	PRON
ejpam-4924	5	2	show	show	VERB
ejpam-4924	5	3	that	that	SCONJ
ejpam-4924	5	4	under	under	ADP
ejpam-4924	5	5	the	the	DET
ejpam-4924	5	6	assumption	assumption	NOUN
ejpam-4924	5	7	of	of	ADP
ejpam-4924	5	8	the	the	DET
ejpam-4924	5	9	existence	existence	NOUN
ejpam-4924	5	10	of	of	ADP
ejpam-4924	5	11	a	a	DET
ejpam-4924	5	12	non	non	ADJ
ejpam-4924	5	13	-	-	ADJ
ejpam-4924	5	14	zero	zero	ADJ
ejpam-4924	5	15	idempotent	idempotent	NOUN
ejpam-4924	5	16	,	,	PUNCT
ejpam-4924	5	17	any	any	DET
ejpam-4924	5	18	commutative	commutative	ADJ
ejpam-4924	5	19	algebra	algebra	NOUN
ejpam-4924	5	20	verifying	verify	VERB
ejpam-4924	5	21	such	such	DET
ejpam-4924	5	22	an	an	DET
ejpam-4924	5	23	identity	identity	NOUN
ejpam-4924	5	24	admits	admit	VERB
ejpam-4924	5	25	a	a	DET
ejpam-4924	5	26	peirce	peirce	NOUN
ejpam-4924	5	27	decomposition	decomposition	NOUN
ejpam-4924	5	28	.	.	PUNCT
ejpam-4924	6	1	using	use	VERB
ejpam-4924	6	2	this	this	DET
ejpam-4924	6	3	decomposition	decomposition	NOUN
ejpam-4924	6	4	we	we	PRON
ejpam-4924	6	5	proceeded	proceed	VERB
ejpam-4924	6	6	to	to	ADP
ejpam-4924	6	7	the	the	DET
ejpam-4924	6	8	study	study	NOUN
ejpam-4924	6	9	of	of	ADP
ejpam-4924	6	10	the	the	DET
ejpam-4924	6	11	derivations	derivation	NOUN
ejpam-4924	6	12	and	and	CCONJ
ejpam-4924	6	13	representations	representation	NOUN
ejpam-4924	6	14	of	of	ADP
ejpam-4924	6	15	algebras	algebra	NOUN
ejpam-4924	6	16	of	of	ADP
ejpam-4924	6	17	this	this	DET
ejpam-4924	6	18	class	class	NOUN
ejpam-4924	6	19	.	.	PUNCT
ejpam-4924	7	1	2020	2020	NUM
ejpam-4924	7	2	mathematics	mathematic	NOUN
ejpam-4924	7	3	subject	subject	NOUN
ejpam-4924	7	4	classifications	classification	NOUN
ejpam-4924	7	5	:	:	PUNCT
ejpam-4924	7	6	17a30	17a30	NUM
ejpam-4924	7	7	,	,	PUNCT
ejpam-4924	7	8	17a36	17a36	NUM
ejpam-4924	7	9	key	key	ADJ
ejpam-4924	7	10	words	word	NOUN
ejpam-4924	7	11	and	and	CCONJ
ejpam-4924	7	12	phrases	phrase	NOUN
ejpam-4924	7	13	:	:	PUNCT
ejpam-4924	7	14	generalized	generalize	VERB
ejpam-4924	7	15	almost	almost	ADV
ejpam-4924	7	16	-	-	PUNCT
ejpam-4924	7	17	jordan	jordan	PROPN
ejpam-4924	7	18	algebra	algebra	PROPN
ejpam-4924	7	19	,	,	PUNCT
ejpam-4924	7	20	identity	identity	NOUN
ejpam-4924	7	21	of	of	ADP
ejpam-4924	7	22	degree	degree	NOUN
ejpam-4924	7	23	five	five	NUM
ejpam-4924	7	24	,	,	PUNCT
ejpam-4924	7	25	peirce	peirce	NOUN
ejpam-4924	7	26	decomposition	decomposition	NOUN
ejpam-4924	7	27	,	,	PUNCT
ejpam-4924	7	28	idempotent	idempotent	ADJ
ejpam-4924	7	29	,	,	PUNCT
ejpam-4924	7	30	derivation	derivation	NOUN
ejpam-4924	7	31	,	,	PUNCT
ejpam-4924	7	32	representation	representation	NOUN
ejpam-4924	7	33	1	1	NUM
ejpam-4924	7	34	.	.	PUNCT
ejpam-4924	8	1	introduction	introduction	NOUN
ejpam-4924	8	2	albert[1	albert[1	PROPN
ejpam-4924	8	3	]	]	PUNCT
ejpam-4924	8	4	was	be	AUX
ejpam-4924	8	5	one	one	NUM
ejpam-4924	8	6	of	of	ADP
ejpam-4924	8	7	the	the	DET
ejpam-4924	8	8	authors	author	NOUN
ejpam-4924	8	9	who	who	PRON
ejpam-4924	8	10	made	make	VERB
ejpam-4924	8	11	a	a	DET
ejpam-4924	8	12	major	major	ADJ
ejpam-4924	8	13	contribution	contribution	NOUN
ejpam-4924	8	14	to	to	ADP
ejpam-4924	8	15	the	the	DET
ejpam-4924	8	16	study	study	NOUN
ejpam-4924	8	17	of	of	ADP
ejpam-4924	8	18	jordan	jordan	PROPN
ejpam-4924	8	19	algebras	algebras	PROPN
ejpam-4924	8	20	in	in	ADP
ejpam-4924	8	21	the	the	DET
ejpam-4924	8	22	algebra	algebra	NOUN
ejpam-4924	8	23	theory	theory	NOUN
ejpam-4924	8	24	of	of	ADP
ejpam-4924	8	25	population	population	NOUN
ejpam-4924	8	26	genetics	genetic	NOUN
ejpam-4924	8	27	.	.	PUNCT
ejpam-4924	9	1	following	follow	VERB
ejpam-4924	9	2	him	he	PRON
ejpam-4924	9	3	,	,	PUNCT
ejpam-4924	9	4	several	several	ADJ
ejpam-4924	9	5	authors	author	NOUN
ejpam-4924	9	6	[	[	X
ejpam-4924	9	7	4	4	NUM
ejpam-4924	9	8	]	]	PUNCT
ejpam-4924	9	9	studied	study	VERB
ejpam-4924	9	10	algebras	algebra	NOUN
ejpam-4924	9	11	verifying	verify	VERB
ejpam-4924	9	12	more	more	ADJ
ejpam-4924	9	13	general	general	ADJ
ejpam-4924	9	14	polynomial	polynomial	ADJ
ejpam-4924	9	15	identities	identity	NOUN
ejpam-4924	9	16	,	,	PUNCT
ejpam-4924	9	17	such	such	ADJ
ejpam-4924	9	18	as	as	ADP
ejpam-4924	9	19	almost	almost	ADV
ejpam-4924	9	20	jordan	jordan	PROPN
ejpam-4924	9	21	algebras	algebras	PROPN
ejpam-4924	9	22	.	.	PUNCT
ejpam-4924	10	1	the	the	DET
ejpam-4924	10	2	irreducible	irreducible	ADJ
ejpam-4924	10	3	identities	identity	NOUN
ejpam-4924	10	4	of	of	ADP
ejpam-4924	10	5	degree	degree	NOUN
ejpam-4924	10	6	five	five	NUM
ejpam-4924	10	7	,	,	PUNCT
ejpam-4924	10	8	not	not	PART
ejpam-4924	10	9	a	a	DET
ejpam-4924	10	10	consequence	consequence	NOUN
ejpam-4924	10	11	of	of	ADP
ejpam-4924	10	12	commutativity	commutativity	NOUN
ejpam-4924	10	13	,	,	PUNCT
ejpam-4924	10	14	have	have	AUX
ejpam-4924	10	15	all	all	PRON
ejpam-4924	10	16	been	be	AUX
ejpam-4924	10	17	determined	determine	VERB
ejpam-4924	10	18	by	by	ADP
ejpam-4924	10	19	osborn	osborn	PROPN
ejpam-4924	10	20	in	in	ADP
ejpam-4924	10	21	[	[	X
ejpam-4924	10	22	8	8	NUM
ejpam-4924	10	23	]	]	PUNCT
ejpam-4924	10	24	,	,	PUNCT
ejpam-4924	10	25	in	in	ADP
ejpam-4924	10	26	characteristics	characteristic	NOUN
ejpam-4924	10	27	other	other	ADJ
ejpam-4924	10	28	than	than	ADP
ejpam-4924	10	29	2	2	NUM
ejpam-4924	10	30	,	,	PUNCT
ejpam-4924	10	31	3	3	NUM
ejpam-4924	10	32	,	,	PUNCT
ejpam-4924	10	33	and	and	CCONJ
ejpam-4924	11	1	5	5	NUM
ejpam-4924	11	2	.	.	X
ejpam-4924	12	1	in[7	in[7	PROPN
ejpam-4924	12	2	]	]	PUNCT
ejpam-4924	12	3	,	,	PUNCT
ejpam-4924	12	4	he	he	PRON
ejpam-4924	12	5	proceeds	proceed	VERB
ejpam-4924	12	6	to	to	PART
ejpam-4924	12	7	study	study	VERB
ejpam-4924	12	8	his	his	PRON
ejpam-4924	12	9	first	first	ADJ
ejpam-4924	12	10	identity	identity	NOUN
ejpam-4924	12	11	2((x2x)x)x−	2((x2x)x)x−	NOUN
ejpam-4924	12	12	3(x2x2)x+	3(x2x2)x+	PROPN
ejpam-4924	12	13	(	(	PUNCT
ejpam-4924	12	14	x2x)x2	x2x)x2	X
ejpam-4924	12	15	=	=	SYM
ejpam-4924	13	1	0	0	X
ejpam-4924	13	2	.	.	PUNCT
ejpam-4924	14	1	(	(	PUNCT
ejpam-4924	14	2	1	1	X
ejpam-4924	14	3	)	)	PUNCT
ejpam-4924	14	4	more	more	ADV
ejpam-4924	14	5	recently	recently	ADV
ejpam-4924	14	6	,	,	PUNCT
ejpam-4924	14	7	in	in	ADP
ejpam-4924	14	8	[	[	PUNCT
ejpam-4924	14	9	2	2	NUM
ejpam-4924	14	10	]	]	PUNCT
ejpam-4924	14	11	,	,	PUNCT
ejpam-4924	14	12	a.	a.	PROPN
ejpam-4924	14	13	dembega	dembega	PROPN
ejpam-4924	14	14	study	study	VERB
ejpam-4924	14	15	the	the	DET
ejpam-4924	14	16	second	second	ADJ
ejpam-4924	14	17	identity	identity	NOUN
ejpam-4924	14	18	under	under	ADP
ejpam-4924	14	19	certain	certain	ADJ
ejpam-4924	14	20	conditions	condition	NOUN
ejpam-4924	14	21	β1[yx	β1[yx	PROPN
ejpam-4924	14	22	4	4	NUM
ejpam-4924	14	23	−	−	NOUN
ejpam-4924	14	24	4(yx3)x+	4(yx3)x+	NUM
ejpam-4924	15	1	6((yx2)x)x−	6((yx2)x)x−	NUM
ejpam-4924	15	2	3(((yx)x)x)x]+	3(((yx)x)x)x]+	NUM
ejpam-4924	15	3	β2[−y(x2.x2	β2[−y(x2.x2	NOUN
ejpam-4924	15	4	)	)	PUNCT
ejpam-4924	16	1	+	+	CCONJ
ejpam-4924	16	2	5(yx3)x−	5(yx3)x−	NUM
ejpam-4924	16	3	9((yx2)x)x+	9((yx2)x)x+	NUM
ejpam-4924	16	4	4(((yx)x)x)x+	4(((yx)x)x)x+	NUM
ejpam-4924	16	5	(	(	PUNCT
ejpam-4924	16	6	(	(	PUNCT
ejpam-4924	16	7	yx)x2)x+	yx)x2)x+	NOUN
ejpam-4924	16	8	(	(	PUNCT
ejpam-4924	16	9	2	2	NUM
ejpam-4924	16	10	)	)	PUNCT
ejpam-4924	16	11	(	(	PUNCT
ejpam-4924	16	12	yx2)x2	yx2)x2	X
ejpam-4924	16	13	−	−	PROPN
ejpam-4924	16	14	(	(	PUNCT
ejpam-4924	16	15	yx)x3	yx)x3	NOUN
ejpam-4924	16	16	]	]	PUNCT
ejpam-4924	16	17	+	+	CCONJ
ejpam-4924	16	18	β3[((yx	β3[((yx	PROPN
ejpam-4924	16	19	2)x)x−	2)x)x−	NUM
ejpam-4924	16	20	(	(	PUNCT
ejpam-4924	16	21	(	(	PUNCT
ejpam-4924	16	22	(	(	PUNCT
ejpam-4924	16	23	yx)x)x)x−	yx)x)x)x−	NOUN
ejpam-4924	16	24	(	(	PUNCT
ejpam-4924	16	25	yx2)x2	yx2)x2	X
ejpam-4924	16	26	+	+	X
ejpam-4924	16	27	(	(	PUNCT
ejpam-4924	16	28	(	(	PUNCT
ejpam-4924	16	29	yx)x)x2	yx)x)x2	NOUN
ejpam-4924	16	30	]	]	X
ejpam-4924	16	31	=	=	SYM
ejpam-4924	16	32	0	0	NUM
ejpam-4924	16	33	∗corresponding	∗corresponde	VERB
ejpam-4924	16	34	author	author	NOUN
ejpam-4924	16	35	.	.	PUNCT
ejpam-4924	17	1	doi	doi	NOUN
ejpam-4924	17	2	:	:	PUNCT
ejpam-4924	17	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4924	https://doi.org/10.29020/nybg.ejpam.v16i4.4924	NOUN
ejpam-4924	17	4	email	email	NOUN
ejpam-4924	17	5	addresses	address	VERB
ejpam-4924	17	6	:	:	PUNCT
ejpam-4924	17	7	ouedraogohamed557@gmail.com	ouedraogohamed557@gmail.com	NUM
ejpam-4924	17	8	(	(	PUNCT
ejpam-4924	17	9	h.	h.	PROPN
ejpam-4924	17	10	ouédraogo	ouédraogo	PROPN
ejpam-4924	17	11	)	)	PUNCT
ejpam-4924	17	12	,	,	PUNCT
ejpam-4924	17	13	doulaydem@yahoo.fr	doulaydem@yahoo.fr	NOUN
ejpam-4924	17	14	(	(	PUNCT
ejpam-4924	17	15	a.	a.	NOUN
ejpam-4924	17	16	dembega	dembega	PROPN
ejpam-4924	17	17	)	)	PUNCT
ejpam-4924	17	18	,	,	PUNCT
ejpam-4924	17	19	andreconsebo@yahoo.fr	andreconsebo@yahoo.fr	PROPN
ejpam-4924	17	20	(	(	PUNCT
ejpam-4924	17	21	a.	a.	NOUN
ejpam-4924	17	22	conseibo	conseibo	PROPN
ejpam-4924	17	23	)	)	PUNCT
ejpam-4924	17	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4924	17	25	2145	2145	NUM
ejpam-4924	18	1	©	©	ADP
ejpam-4924	18	2	2023	2023	NUM
ejpam-4924	18	3	ejpam	ejpam	NOUN
ejpam-4924	18	4	all	all	DET
ejpam-4924	18	5	rights	right	NOUN
ejpam-4924	18	6	reserved	reserve	VERB
ejpam-4924	18	7	.	.	PUNCT
ejpam-4924	19	1	h.	h.	PROPN
ejpam-4924	19	2	ouédraogo	ouédraogo	PROPN
ejpam-4924	19	3	,	,	PUNCT
ejpam-4924	19	4	a.	a.	NOUN
ejpam-4924	19	5	dembega	dembega	PROPN
ejpam-4924	19	6	,	,	PUNCT
ejpam-4924	19	7	a.	a.	PROPN
ejpam-4924	19	8	conseibo	conseibo	PROPN
ejpam-4924	19	9	/	/	SYM
ejpam-4924	19	10	eur	eur	PROPN
ejpam-4924	19	11	.	.	PUNCT
ejpam-4924	20	1	j.	j.	PROPN
ejpam-4924	20	2	pure	pure	PROPN
ejpam-4924	20	3	appl	appl	PROPN
ejpam-4924	20	4	.	.	PROPN
ejpam-4924	20	5	math	math	PROPN
ejpam-4924	20	6	,	,	PUNCT
ejpam-4924	20	7	16	16	NUM
ejpam-4924	20	8	(	(	PUNCT
ejpam-4924	20	9	4	4	NUM
ejpam-4924	20	10	)	)	PUNCT
ejpam-4924	20	11	(	(	PUNCT
ejpam-4924	20	12	2023	2023	NUM
ejpam-4924	20	13	)	)	PUNCT
ejpam-4924	20	14	,	,	PUNCT
ejpam-4924	20	15	2145	2145	NUM
ejpam-4924	20	16	-	-	SYM
ejpam-4924	20	17	2155	2155	NUM
ejpam-4924	20	18	2146	2146	NUM
ejpam-4924	20	19	where	where	SCONJ
ejpam-4924	20	20	β1	β1	PROPN
ejpam-4924	20	21	,	,	PUNCT
ejpam-4924	20	22	β2	β2	NOUN
ejpam-4924	20	23	and	and	CCONJ
ejpam-4924	20	24	β3	β3	VERB
ejpam-4924	20	25	∈	∈	PROPN
ejpam-4924	20	26	k	k	NOUN
ejpam-4924	20	27	,	,	PUNCT
ejpam-4924	20	28	where	where	SCONJ
ejpam-4924	20	29	k	k	PROPN
ejpam-4924	20	30	is	be	AUX
ejpam-4924	20	31	a	a	DET
ejpam-4924	20	32	commutative	commutative	ADJ
ejpam-4924	20	33	field	field	NOUN
ejpam-4924	20	34	.	.	PUNCT
ejpam-4924	21	1	the	the	DET
ejpam-4924	21	2	aim	aim	NOUN
ejpam-4924	21	3	of	of	ADP
ejpam-4924	21	4	the	the	DET
ejpam-4924	21	5	this	this	DET
ejpam-4924	21	6	paper	paper	NOUN
ejpam-4924	21	7	is	be	AUX
ejpam-4924	21	8	to	to	PART
ejpam-4924	21	9	determine	determine	VERB
ejpam-4924	21	10	the	the	DET
ejpam-4924	21	11	representations	representation	NOUN
ejpam-4924	21	12	and	and	CCONJ
ejpam-4924	21	13	the	the	DET
ejpam-4924	21	14	derivations	derivation	NOUN
ejpam-4924	21	15	of	of	ADP
ejpam-4924	21	16	commutative	commutative	ADJ
ejpam-4924	21	17	algebras	algebra	NOUN
ejpam-4924	22	1	a	a	PRON
ejpam-4924	22	2	defined	define	VERB
ejpam-4924	22	3	by	by	ADP
ejpam-4924	22	4	yx4	yx4	PROPN
ejpam-4924	22	5	−	−	PROPN
ejpam-4924	22	6	4(yx3)x+	4(yx3)x+	NOUN
ejpam-4924	23	1	6((yx2)x)x−	6((yx2)x)x−	NOUN
ejpam-4924	23	2	3(((yx)x)x)x	3(((yx)x)x)x	NUM
ejpam-4924	23	3	=	=	SYM
ejpam-4924	23	4	0	0	NUM
ejpam-4924	23	5	,	,	PUNCT
ejpam-4924	23	6	(	(	PUNCT
ejpam-4924	23	7	3	3	X
ejpam-4924	23	8	)	)	PUNCT
ejpam-4924	23	9	corresponding	correspond	VERB
ejpam-4924	23	10	to	to	ADP
ejpam-4924	23	11	β1	β1	PROPN
ejpam-4924	23	12	=	=	SYM
ejpam-4924	23	13	1	1	NUM
ejpam-4924	23	14	,	,	PUNCT
ejpam-4924	23	15	β2	β2	NOUN
ejpam-4924	23	16	=	=	NOUN
ejpam-4924	23	17	β3	β3	PROPN
ejpam-4924	23	18	=	=	SYM
ejpam-4924	23	19	0	0	NUM
ejpam-4924	23	20	in	in	ADP
ejpam-4924	23	21	the	the	DET
ejpam-4924	23	22	identity	identity	NOUN
ejpam-4924	23	23	(	(	PUNCT
ejpam-4924	23	24	2	2	NUM
ejpam-4924	23	25	)	)	PUNCT
ejpam-4924	23	26	.	.	PUNCT
ejpam-4924	24	1	such	such	ADJ
ejpam-4924	24	2	algebras	algebra	NOUN
ejpam-4924	24	3	can	can	AUX
ejpam-4924	24	4	be	be	AUX
ejpam-4924	24	5	illustrated	illustrate	VERB
ejpam-4924	24	6	by	by	ADP
ejpam-4924	24	7	the	the	DET
ejpam-4924	24	8	following	follow	VERB
ejpam-4924	24	9	examples	example	NOUN
ejpam-4924	24	10	given	give	VERB
ejpam-4924	24	11	in	in	ADP
ejpam-4924	24	12	[	[	X
ejpam-4924	24	13	2	2	NUM
ejpam-4924	24	14	]	]	PUNCT
ejpam-4924	24	15	.	.	PUNCT
ejpam-4924	25	1	in	in	ADP
ejpam-4924	25	2	the	the	DET
ejpam-4924	25	3	rest	rest	NOUN
ejpam-4924	25	4	of	of	ADP
ejpam-4924	25	5	the	the	DET
ejpam-4924	25	6	paper	paper	NOUN
ejpam-4924	25	7	,	,	PUNCT
ejpam-4924	25	8	k	k	PROPN
ejpam-4924	25	9	refers	refer	VERB
ejpam-4924	25	10	to	to	ADP
ejpam-4924	25	11	the	the	DET
ejpam-4924	25	12	field	field	NOUN
ejpam-4924	25	13	c	c	PROPN
ejpam-4924	25	14	of	of	ADP
ejpam-4924	25	15	complex	complex	ADJ
ejpam-4924	25	16	numbers	number	NOUN
ejpam-4924	25	17	.	.	PUNCT
ejpam-4924	26	1	example	example	NOUN
ejpam-4924	26	2	1.1	1.1	NUM
ejpam-4924	26	3	.	.	PUNCT
ejpam-4924	27	1	let	let	VERB
ejpam-4924	27	2	a	a	PRON
ejpam-4924	27	3	be	be	AUX
ejpam-4924	27	4	the	the	DET
ejpam-4924	27	5	commutative	commutative	ADJ
ejpam-4924	27	6	five	five	NUM
ejpam-4924	27	7	-	-	PUNCT
ejpam-4924	27	8	dimensional	dimensional	ADJ
ejpam-4924	27	9	algebra	algebra	NOUN
ejpam-4924	27	10	whose	whose	DET
ejpam-4924	27	11	the	the	DET
ejpam-4924	27	12	multiplication	multiplication	NOUN
ejpam-4924	27	13	table	table	NOUN
ejpam-4924	27	14	in	in	ADP
ejpam-4924	27	15	the	the	DET
ejpam-4924	27	16	basis	basis	NOUN
ejpam-4924	27	17	{	{	PUNCT
ejpam-4924	27	18	e1	e1	PROPN
ejpam-4924	27	19	,	,	PUNCT
ejpam-4924	27	20	e2	e2	PROPN
ejpam-4924	27	21	,	,	PUNCT
ejpam-4924	27	22	e3	e3	NOUN
ejpam-4924	27	23	,	,	PUNCT
ejpam-4924	27	24	e4	e4	PROPN
ejpam-4924	27	25	,	,	PUNCT
ejpam-4924	27	26	e5	e5	PROPN
ejpam-4924	27	27	}	}	PUNCT
ejpam-4924	27	28	is	be	AUX
ejpam-4924	27	29	e21	e21	PROPN
ejpam-4924	27	30	=	=	SYM
ejpam-4924	27	31	e2	e2	PROPN
ejpam-4924	27	32	,	,	PUNCT
ejpam-4924	27	33	e1e2	e1e2	X
ejpam-4924	27	34	=	=	SYM
ejpam-4924	27	35	e3	e3	NOUN
ejpam-4924	27	36	,	,	PUNCT
ejpam-4924	27	37	e22	e22	PROPN
ejpam-4924	27	38	=	=	PROPN
ejpam-4924	27	39	e4	e4	PROPN
ejpam-4924	27	40	,	,	PUNCT
ejpam-4924	27	41	e1e3	e1e3	X
ejpam-4924	27	42	=	=	SYM
ejpam-4924	27	43	e5	e5	PROPN
ejpam-4924	27	44	,	,	PUNCT
ejpam-4924	27	45	the	the	DET
ejpam-4924	27	46	other	other	ADJ
ejpam-4924	27	47	products	product	NOUN
ejpam-4924	27	48	not	not	PART
ejpam-4924	27	49	mentioned	mention	VERB
ejpam-4924	27	50	being	be	AUX
ejpam-4924	27	51	zero	zero	NUM
ejpam-4924	27	52	.	.	PUNCT
ejpam-4924	28	1	this	this	DET
ejpam-4924	28	2	algebra	algebra	NOUN
ejpam-4924	28	3	verifies	verifie	NOUN
ejpam-4924	28	4	(	(	PUNCT
ejpam-4924	28	5	3	3	NUM
ejpam-4924	28	6	)	)	PUNCT
ejpam-4924	28	7	.	.	PUNCT
ejpam-4924	29	1	indeed	indeed	ADV
ejpam-4924	29	2	,	,	PUNCT
ejpam-4924	29	3	a2	a2	PROPN
ejpam-4924	29	4	=	=	PROPN
ejpam-4924	29	5	<	<	X
ejpam-4924	29	6	e2	e2	PROPN
ejpam-4924	29	7	,	,	PUNCT
ejpam-4924	29	8	e3	e3	NOUN
ejpam-4924	29	9	,	,	PUNCT
ejpam-4924	29	10	e4	e4	PROPN
ejpam-4924	29	11	,	,	PUNCT
ejpam-4924	29	12	e5	e5	PROPN
ejpam-4924	29	13	>	>	X
ejpam-4924	29	14	,	,	PUNCT
ejpam-4924	29	15	a3	a3	NOUN
ejpam-4924	29	16	=	=	NOUN
ejpam-4924	29	17	<	<	X
ejpam-4924	29	18	e3	e3	PROPN
ejpam-4924	29	19	,	,	PUNCT
ejpam-4924	29	20	e4	e4	PROPN
ejpam-4924	29	21	,	,	PUNCT
ejpam-4924	29	22	e5	e5	PROPN
ejpam-4924	29	23	>	>	X
ejpam-4924	29	24	,	,	PUNCT
ejpam-4924	29	25	a4	a4	NOUN
ejpam-4924	30	1	=	=	NOUN
ejpam-4924	30	2	<	<	X
ejpam-4924	30	3	e5	e5	PROPN
ejpam-4924	30	4	>	>	X
ejpam-4924	30	5	and	and	CCONJ
ejpam-4924	30	6	a5	a5	PROPN
ejpam-4924	30	7	=	=	PUNCT
ejpam-4924	30	8	0	0	X
ejpam-4924	30	9	.	.	NOUN
ejpam-4924	30	10	example	example	NOUN
ejpam-4924	31	1	1.2	1.2	NUM
ejpam-4924	31	2	.	.	PUNCT
ejpam-4924	31	3	let	let	VERB
ejpam-4924	31	4	a	a	PRON
ejpam-4924	31	5	be	be	AUX
ejpam-4924	31	6	the	the	DET
ejpam-4924	31	7	commutative	commutative	ADJ
ejpam-4924	31	8	5	5	NUM
ejpam-4924	31	9	-	-	PUNCT
ejpam-4924	31	10	dimensional	dimensional	ADJ
ejpam-4924	31	11	algebra	algebra	NOUN
ejpam-4924	31	12	whose	whose	DET
ejpam-4924	31	13	the	the	DET
ejpam-4924	31	14	multiplication	multiplication	NOUN
ejpam-4924	31	15	table	table	NOUN
ejpam-4924	31	16	in	in	ADP
ejpam-4924	31	17	the	the	DET
ejpam-4924	31	18	basis	basis	NOUN
ejpam-4924	31	19	{	{	PUNCT
ejpam-4924	31	20	e	e	NOUN
ejpam-4924	31	21	,	,	PUNCT
ejpam-4924	31	22	x0	x0	PROPN
ejpam-4924	31	23	,	,	PUNCT
ejpam-4924	31	24	y1	y1	PROPN
ejpam-4924	31	25	,	,	PUNCT
ejpam-4924	31	26	zλ1	zλ1	NOUN
ejpam-4924	31	27	,	,	PUNCT
ejpam-4924	31	28	wλ2	wλ2	PROPN
ejpam-4924	31	29	}	}	PUNCT
ejpam-4924	31	30	is	be	AUX
ejpam-4924	31	31	e2	e2	NOUN
ejpam-4924	31	32	=	=	SYM
ejpam-4924	31	33	e	e	NOUN
ejpam-4924	31	34	,	,	PUNCT
ejpam-4924	31	35	ey1	ey1	PROPN
ejpam-4924	31	36	=	=	SYM
ejpam-4924	31	37	y1	y1	PROPN
ejpam-4924	31	38	,	,	PUNCT
ejpam-4924	31	39	ezλ1	ezλ1	NOUN
ejpam-4924	31	40	=	=	SYM
ejpam-4924	31	41	λ1zλ1	λ1zλ1	PROPN
ejpam-4924	31	42	,	,	PUNCT
ejpam-4924	31	43	ewλ2	ewλ2	PROPN
ejpam-4924	31	44	=	=	SYM
ejpam-4924	31	45	λ2wλ2	λ2wλ2	NOUN
ejpam-4924	31	46	,	,	PUNCT
ejpam-4924	31	47	x0zλ1	x0zλ1	NOUN
ejpam-4924	31	48	=	=	SYM
ejpam-4924	31	49	zλ1	zλ1	PROPN
ejpam-4924	31	50	,	,	PUNCT
ejpam-4924	31	51	y1wλ2	y1wλ2	NOUN
ejpam-4924	31	52	=	=	SYM
ejpam-4924	31	53	wλ2	wλ2	VERB
ejpam-4924	31	54	with	with	ADP
ejpam-4924	31	55	λ1	λ1	PROPN
ejpam-4924	31	56	=	=	SYM
ejpam-4924	31	57	3+i	3+i	NUM
ejpam-4924	31	58	√	√	NUM
ejpam-4924	31	59	3	3	NUM
ejpam-4924	31	60	6	6	NUM
ejpam-4924	31	61	and	and	CCONJ
ejpam-4924	31	62	λ2	λ2	NOUN
ejpam-4924	31	63	=	=	SYM
ejpam-4924	31	64	3−i	3−i	NUM
ejpam-4924	31	65	√	√	NUM
ejpam-4924	31	66	3	3	NUM
ejpam-4924	31	67	6	6	NUM
ejpam-4924	31	68	,	,	PUNCT
ejpam-4924	31	69	all	all	DET
ejpam-4924	31	70	other	other	ADJ
ejpam-4924	31	71	products	product	NOUN
ejpam-4924	31	72	not	not	PART
ejpam-4924	31	73	mentioned	mention	VERB
ejpam-4924	31	74	being	be	AUX
ejpam-4924	31	75	zero	zero	NUM
ejpam-4924	31	76	.	.	PUNCT
ejpam-4924	32	1	2	2	NUM
ejpam-4924	32	2	.	.	X
ejpam-4924	32	3	peirce	peirce	NOUN
ejpam-4924	32	4	decomposition	decomposition	NOUN
ejpam-4924	32	5	in	in	ADP
ejpam-4924	32	6	the	the	DET
ejpam-4924	32	7	rest	rest	NOUN
ejpam-4924	32	8	of	of	ADP
ejpam-4924	32	9	the	the	DET
ejpam-4924	32	10	paper	paper	NOUN
ejpam-4924	32	11	we	we	PRON
ejpam-4924	32	12	study	study	VERB
ejpam-4924	32	13	commutative	commutative	ADJ
ejpam-4924	32	14	algebras	algebra	NOUN
ejpam-4924	32	15	verifying	verify	VERB
ejpam-4924	32	16	the	the	DET
ejpam-4924	32	17	identity	identity	NOUN
ejpam-4924	32	18	(	(	PUNCT
ejpam-4924	32	19	3	3	NUM
ejpam-4924	32	20	)	)	PUNCT
ejpam-4924	32	21	and	and	CCONJ
ejpam-4924	32	22	admitting	admit	VERB
ejpam-4924	32	23	a	a	DET
ejpam-4924	32	24	non	non	ADJ
ejpam-4924	32	25	-	-	ADJ
ejpam-4924	32	26	zero	zero	ADJ
ejpam-4924	32	27	idempotent	idempotent	NOUN
ejpam-4924	32	28	e.	e.	NOUN
ejpam-4924	32	29	by	by	ADP
ejpam-4924	32	30	setting	set	VERB
ejpam-4924	32	31	x	x	PUNCT
ejpam-4924	32	32	=	=	SYM
ejpam-4924	32	33	e	e	X
ejpam-4924	32	34	in	in	ADP
ejpam-4924	32	35	(	(	PUNCT
ejpam-4924	32	36	3	3	NUM
ejpam-4924	32	37	)	)	PUNCT
ejpam-4924	32	38	,	,	PUNCT
ejpam-4924	32	39	we	we	PRON
ejpam-4924	32	40	obtain	obtain	VERB
ejpam-4924	32	41	[	[	X
ejpam-4924	32	42	le(le	le(le	NOUN
ejpam-4924	32	43	−	−	ADP
ejpam-4924	32	44	ida)(3l	ida)(3l	ADJ
ejpam-4924	32	45	2	2	NUM
ejpam-4924	32	46	e	e	NOUN
ejpam-4924	32	47	−	−	NOUN
ejpam-4924	32	48	3le	3le	NOUN
ejpam-4924	32	49	+	+	CCONJ
ejpam-4924	32	50	i)](y	i)](y	NOUN
ejpam-4924	32	51	)	)	PUNCT
ejpam-4924	32	52	=	=	SYM
ejpam-4924	32	53	0	0	NUM
ejpam-4924	32	54	,	,	PUNCT
ejpam-4924	32	55	(	(	PUNCT
ejpam-4924	32	56	4	4	X
ejpam-4924	32	57	)	)	PUNCT
ejpam-4924	32	58	where	where	SCONJ
ejpam-4924	32	59	y	y	PROPN
ejpam-4924	32	60	∈	∈	PROPN
ejpam-4924	32	61	a	a	PROPN
ejpam-4924	32	62	,	,	PUNCT
ejpam-4924	32	63	ida	ida	PROPN
ejpam-4924	32	64	:	:	PUNCT
ejpam-4924	32	65	a	a	DET
ejpam-4924	32	66	→	→	SYM
ejpam-4924	32	67	a	a	NOUN
ejpam-4924	32	68	,	,	PUNCT
ejpam-4924	32	69	x	x	PROPN
ejpam-4924	32	70	7→	7→	NUM
ejpam-4924	32	71	x	x	PUNCT
ejpam-4924	32	72	and	and	CCONJ
ejpam-4924	32	73	le	le	X
ejpam-4924	32	74	:	:	PUNCT
ejpam-4924	32	75	a	a	DET
ejpam-4924	32	76	→	→	SYM
ejpam-4924	32	77	a	a	X
ejpam-4924	32	78	,	,	PUNCT
ejpam-4924	32	79	y	y	PROPN
ejpam-4924	32	80	7→	7→	PROPN
ejpam-4924	32	81	ey	ey	NOUN
ejpam-4924	32	82	is	be	AUX
ejpam-4924	32	83	the	the	DET
ejpam-4924	32	84	multiplication	multiplication	NOUN
ejpam-4924	32	85	by	by	ADP
ejpam-4924	32	86	e.	e.	PROPN
ejpam-4924	32	87	consider	consider	VERB
ejpam-4924	32	88	p(t	p(t	NOUN
ejpam-4924	32	89	)	)	PUNCT
ejpam-4924	32	90	=	=	PUNCT
ejpam-4924	33	1	−3t4	−3t4	PROPN
ejpam-4924	34	1	+	+	NUM
ejpam-4924	34	2	6t3	6t3	NUM
ejpam-4924	34	3	−	−	PROPN
ejpam-4924	34	4	4t2	4t2	NOUN
ejpam-4924	35	1	+	+	NUM
ejpam-4924	35	2	t	t	NOUN
ejpam-4924	35	3	which	which	PRON
ejpam-4924	35	4	factorises	factorise	VERB
ejpam-4924	35	5	to	to	ADP
ejpam-4924	35	6	p(t	p(t	VERB
ejpam-4924	35	7	)	)	PUNCT
ejpam-4924	35	8	=	=	SYM
ejpam-4924	35	9	−t(t	−t(t	NOUN
ejpam-4924	35	10	−	−	PROPN
ejpam-4924	35	11	1)(3t2	1)(3t2	NUM
ejpam-4924	35	12	−	−	PROPN
ejpam-4924	35	13	3	3	NUM
ejpam-4924	35	14	t	t	NOUN
ejpam-4924	35	15	+	+	NOUN
ejpam-4924	35	16	1	1	NUM
ejpam-4924	35	17	)	)	PUNCT
ejpam-4924	35	18	.	.	PUNCT
ejpam-4924	36	1	since	since	SCONJ
ejpam-4924	36	2	k	k	PROPN
ejpam-4924	36	3	is	be	AUX
ejpam-4924	36	4	algebraically	algebraically	ADV
ejpam-4924	36	5	closed	closed	ADJ
ejpam-4924	36	6	,	,	PUNCT
ejpam-4924	36	7	then	then	ADV
ejpam-4924	36	8	the	the	DET
ejpam-4924	36	9	polynomial	polynomial	ADJ
ejpam-4924	36	10	3t2	3t2	NUM
ejpam-4924	36	11	−	−	PROPN
ejpam-4924	36	12	3	3	NUM
ejpam-4924	36	13	t	t	NOUN
ejpam-4924	36	14	+	+	NOUN
ejpam-4924	36	15	1	1	NUM
ejpam-4924	36	16	has	have	VERB
ejpam-4924	36	17	two	two	NUM
ejpam-4924	36	18	roots	root	NOUN
ejpam-4924	36	19	λ1	λ1	ADJ
ejpam-4924	36	20	and	and	CCONJ
ejpam-4924	36	21	λ2	λ2	PROPN
ejpam-4924	36	22	,	,	PUNCT
ejpam-4924	36	23	i.e	i.e	PRON
ejpam-4924	36	24	p(t	p(t	NOUN
ejpam-4924	36	25	)	)	PUNCT
ejpam-4924	36	26	=	=	SYM
ejpam-4924	36	27	−t(t	−t(t	NOUN
ejpam-4924	37	1	−	−	NOUN
ejpam-4924	37	2	1)(t	1)(t	NUM
ejpam-4924	37	3	−	−	NOUN
ejpam-4924	37	4	λ1)(t	λ1)(t	SYM
ejpam-4924	38	1	−	−	NUM
ejpam-4924	38	2	λ2	λ2	NOUN
ejpam-4924	38	3	)	)	PUNCT
ejpam-4924	38	4	,	,	PUNCT
ejpam-4924	38	5	in	in	ADP
ejpam-4924	38	6	which	which	DET
ejpam-4924	38	7	case	case	NOUN
ejpam-4924	38	8	a	a	DET
ejpam-4924	38	9	=	=	SYM
ejpam-4924	38	10	a0	a0	PROPN
ejpam-4924	38	11	⊕	⊕	PROPN
ejpam-4924	38	12	a1	a1	PROPN
ejpam-4924	38	13	⊕	⊕	PROPN
ejpam-4924	38	14	aλ1	aλ1	PROPN
ejpam-4924	38	15	⊕	⊕	PROPN
ejpam-4924	38	16	aλ2	aλ2	PROPN
ejpam-4924	38	17	,	,	PUNCT
ejpam-4924	38	18	where	where	SCONJ
ejpam-4924	38	19	aµ	aµ	PROPN
ejpam-4924	38	20	=	=	PRON
ejpam-4924	38	21	{	{	PUNCT
ejpam-4924	38	22	x	x	PUNCT
ejpam-4924	38	23	∈	∈	PROPN
ejpam-4924	38	24	a|ex	a|ex	NUM
ejpam-4924	38	25	=	=	SYM
ejpam-4924	38	26	µx	µx	VERB
ejpam-4924	38	27	}	}	PUNCT
ejpam-4924	38	28	,	,	PUNCT
ejpam-4924	38	29	λ1	λ1	PROPN
ejpam-4924	38	30	=	=	SYM
ejpam-4924	38	31	3+i	3+i	NUM
ejpam-4924	38	32	√	√	NUM
ejpam-4924	38	33	3	3	NUM
ejpam-4924	38	34	6	6	NUM
ejpam-4924	38	35	and	and	CCONJ
ejpam-4924	38	36	λ2	λ2	NOUN
ejpam-4924	38	37	=	=	SYM
ejpam-4924	38	38	3−i	3−i	NUM
ejpam-4924	38	39	√	√	NUM
ejpam-4924	38	40	3	3	NUM
ejpam-4924	38	41	6	6	NUM
ejpam-4924	38	42	.	.	PUNCT
ejpam-4924	39	1	the	the	DET
ejpam-4924	39	2	products	product	NOUN
ejpam-4924	39	3	of	of	ADP
ejpam-4924	39	4	the	the	DET
ejpam-4924	39	5	components	component	NOUN
ejpam-4924	39	6	of	of	ADP
ejpam-4924	39	7	the	the	DET
ejpam-4924	39	8	peirce	peirce	NOUN
ejpam-4924	39	9	decomposition	decomposition	NOUN
ejpam-4924	39	10	are	be	AUX
ejpam-4924	39	11	given	give	VERB
ejpam-4924	39	12	by	by	ADP
ejpam-4924	39	13	the	the	DET
ejpam-4924	39	14	following	follow	VERB
ejpam-4924	39	15	theorem	theorem	PROPN
ejpam-4924	39	16	.	.	PUNCT
ejpam-4924	39	17	theorem	theorem	VERB
ejpam-4924	39	18	2.1	2.1	NUM
ejpam-4924	39	19	.	.	PUNCT
ejpam-4924	40	1	(	(	PUNCT
ejpam-4924	40	2	[	[	X
ejpam-4924	40	3	2],théorème	2],théorème	NUM
ejpam-4924	40	4	5.1.1	5.1.1	NUM
ejpam-4924	40	5	)	)	PUNCT
ejpam-4924	40	6	let	let	VERB
ejpam-4924	40	7	a	a	PRON
ejpam-4924	40	8	be	be	AUX
ejpam-4924	40	9	an	an	DET
ejpam-4924	40	10	algebra	algebra	NOUN
ejpam-4924	40	11	satisfying	satisfy	VERB
ejpam-4924	40	12	the	the	DET
ejpam-4924	40	13	identity	identity	NOUN
ejpam-4924	40	14	(	(	PUNCT
ejpam-4924	40	15	3	3	NUM
ejpam-4924	40	16	)	)	PUNCT
ejpam-4924	40	17	.	.	PUNCT
ejpam-4924	41	1	suppose	suppose	VERB
ejpam-4924	41	2	that	that	SCONJ
ejpam-4924	41	3	the	the	DET
ejpam-4924	41	4	polynomial	polynomial	ADJ
ejpam-4924	41	5	3t2	3t2	NUM
ejpam-4924	41	6	−	−	PROPN
ejpam-4924	41	7	3	3	NUM
ejpam-4924	41	8	t	t	NOUN
ejpam-4924	41	9	+	+	NOUN
ejpam-4924	41	10	1	1	NUM
ejpam-4924	41	11	=	=	SYM
ejpam-4924	41	12	3(t	3(t	NUM
ejpam-4924	41	13	−	−	NOUN
ejpam-4924	41	14	λ1)(t	λ1)(t	SYM
ejpam-4924	41	15	−	−	NUM
ejpam-4924	41	16	λ2	λ2	NOUN
ejpam-4924	41	17	)	)	PUNCT
ejpam-4924	41	18	in	in	ADP
ejpam-4924	41	19	k[t	k[t	PROPN
ejpam-4924	41	20	]	]	PUNCT
ejpam-4924	41	21	.	.	PUNCT
ejpam-4924	42	1	then	then	ADV
ejpam-4924	42	2	the	the	DET
ejpam-4924	42	3	peirce	peirce	NOUN
ejpam-4924	42	4	decomposition	decomposition	NOUN
ejpam-4924	42	5	of	of	ADP
ejpam-4924	42	6	a	a	PRON
ejpam-4924	42	7	is	be	AUX
ejpam-4924	42	8	a	a	DET
ejpam-4924	42	9	=	=	SYM
ejpam-4924	42	10	a0	a0	PROPN
ejpam-4924	42	11	⊕	⊕	PROPN
ejpam-4924	42	12	a1	a1	PROPN
ejpam-4924	42	13	⊕	⊕	PROPN
ejpam-4924	42	14	aλ1	aλ1	PROPN
ejpam-4924	42	15	⊕	⊕	PROPN
ejpam-4924	42	16	aλ2	aλ2	PROPN
ejpam-4924	42	17	,	,	PUNCT
ejpam-4924	42	18	where	where	SCONJ
ejpam-4924	42	19	λ1	λ1	PROPN
ejpam-4924	42	20	=	=	SYM
ejpam-4924	42	21	3+i	3+i	NUM
ejpam-4924	42	22	√	√	NUM
ejpam-4924	42	23	3	3	NUM
ejpam-4924	42	24	6	6	NUM
ejpam-4924	42	25	and	and	CCONJ
ejpam-4924	42	26	λ2	λ2	NOUN
ejpam-4924	42	27	=	=	SYM
ejpam-4924	42	28	3−i	3−i	NUM
ejpam-4924	42	29	√	√	NUM
ejpam-4924	42	30	3	3	NUM
ejpam-4924	42	31	6	6	NUM
ejpam-4924	42	32	.	.	PUNCT
ejpam-4924	43	1	we	we	PRON
ejpam-4924	43	2	have	have	VERB
ejpam-4924	43	3	:	:	PUNCT
ejpam-4924	43	4	i	i	NOUN
ejpam-4924	43	5	)	)	PUNCT
ejpam-4924	43	6	aiaλj	aiaλj	PROPN
ejpam-4924	43	7	⊆	⊆	NUM
ejpam-4924	43	8	aλj	aλj	PROPN
ejpam-4924	43	9	,	,	PUNCT
ejpam-4924	43	10	with	with	ADP
ejpam-4924	43	11	i	i	PRON
ejpam-4924	43	12	∈	∈	PROPN
ejpam-4924	43	13	{	{	PUNCT
ejpam-4924	43	14	0	0	NUM
ejpam-4924	43	15	,	,	PUNCT
ejpam-4924	43	16	1	1	NUM
ejpam-4924	43	17	}	}	PUNCT
ejpam-4924	43	18	and	and	CCONJ
ejpam-4924	43	19	j	j	PROPN
ejpam-4924	43	20	∈	∈	PROPN
ejpam-4924	43	21	{	{	PUNCT
ejpam-4924	43	22	1	1	NUM
ejpam-4924	43	23	;	;	PUNCT
ejpam-4924	43	24	2	2	NUM
ejpam-4924	43	25	}	}	PUNCT
ejpam-4924	43	26	;	;	PUNCT
ejpam-4924	43	27	ii	ii	X
ejpam-4924	43	28	)	)	PUNCT
ejpam-4924	43	29	aλi	aλi	PROPN
ejpam-4924	44	1	aλj	aλj	PROPN
ejpam-4924	45	1	=	=	PUNCT
ejpam-4924	46	1	{	{	PUNCT
ejpam-4924	46	2	0	0	NUM
ejpam-4924	46	3	}	}	PUNCT
ejpam-4924	46	4	,	,	PUNCT
ejpam-4924	46	5	with	with	ADP
ejpam-4924	46	6	i	i	PRON
ejpam-4924	46	7	,	,	PUNCT
ejpam-4924	46	8	j	j	PROPN
ejpam-4924	46	9	∈	∈	PROPN
ejpam-4924	46	10	{	{	PUNCT
ejpam-4924	46	11	1	1	NUM
ejpam-4924	46	12	;	;	PUNCT
ejpam-4924	46	13	2	2	NUM
ejpam-4924	46	14	}	}	PUNCT
ejpam-4924	46	15	;	;	PUNCT
ejpam-4924	46	16	h.	h.	PROPN
ejpam-4924	46	17	ouédraogo	ouédraogo	PROPN
ejpam-4924	46	18	,	,	PUNCT
ejpam-4924	46	19	a.	a.	NOUN
ejpam-4924	46	20	dembega	dembega	PROPN
ejpam-4924	46	21	,	,	PUNCT
ejpam-4924	46	22	a.	a.	PROPN
ejpam-4924	46	23	conseibo	conseibo	PROPN
ejpam-4924	46	24	/	/	SYM
ejpam-4924	46	25	eur	eur	PROPN
ejpam-4924	46	26	.	.	PUNCT
ejpam-4924	47	1	j.	j.	PROPN
ejpam-4924	47	2	pure	pure	PROPN
ejpam-4924	47	3	appl	appl	PROPN
ejpam-4924	47	4	.	.	PROPN
ejpam-4924	47	5	math	math	PROPN
ejpam-4924	47	6	,	,	PUNCT
ejpam-4924	47	7	16	16	NUM
ejpam-4924	47	8	(	(	PUNCT
ejpam-4924	47	9	4	4	NUM
ejpam-4924	47	10	)	)	PUNCT
ejpam-4924	47	11	(	(	PUNCT
ejpam-4924	47	12	2023	2023	NUM
ejpam-4924	47	13	)	)	PUNCT
ejpam-4924	47	14	,	,	PUNCT
ejpam-4924	47	15	2145	2145	NUM
ejpam-4924	47	16	-	-	SYM
ejpam-4924	47	17	2155	2155	NUM
ejpam-4924	47	18	2147	2147	NUM
ejpam-4924	47	19	iii	iii	NOUN
ejpam-4924	47	20	)	)	PUNCT
ejpam-4924	47	21	aiai	aiai	VERB
ejpam-4924	47	22	⊆	⊆	NUM
ejpam-4924	47	23	ai	ai	VERB
ejpam-4924	47	24	with	with	ADP
ejpam-4924	47	25	i	i	PRON
ejpam-4924	47	26	∈	∈	PROPN
ejpam-4924	47	27	{	{	PUNCT
ejpam-4924	47	28	0	0	NUM
ejpam-4924	47	29	;	;	PUNCT
ejpam-4924	47	30	1	1	NUM
ejpam-4924	47	31	}	}	PUNCT
ejpam-4924	47	32	;	;	PUNCT
ejpam-4924	47	33	iv	iv	X
ejpam-4924	47	34	)	)	PUNCT
ejpam-4924	47	35	a0a1	a0a1	X
ejpam-4924	48	1	=	=	PUNCT
ejpam-4924	48	2	{	{	PUNCT
ejpam-4924	48	3	0	0	NUM
ejpam-4924	48	4	}	}	PUNCT
ejpam-4924	48	5	.	.	PUNCT
ejpam-4924	49	1	the	the	DET
ejpam-4924	49	2	following	follow	VERB
ejpam-4924	49	3	theorem	theorem	NOUN
ejpam-4924	49	4	gives	give	VERB
ejpam-4924	49	5	us	we	PRON
ejpam-4924	49	6	the	the	DET
ejpam-4924	49	7	identities	identity	NOUN
ejpam-4924	49	8	used	use	VERB
ejpam-4924	49	9	in	in	ADP
ejpam-4924	49	10	the	the	DET
ejpam-4924	49	11	rest	rest	NOUN
ejpam-4924	49	12	of	of	ADP
ejpam-4924	49	13	the	the	DET
ejpam-4924	49	14	document	document	NOUN
ejpam-4924	49	15	.	.	PUNCT
ejpam-4924	50	1	theorem	theorem	VERB
ejpam-4924	50	2	2.2	2.2	NUM
ejpam-4924	50	3	.	.	PUNCT
ejpam-4924	51	1	(	(	PUNCT
ejpam-4924	51	2	[	[	X
ejpam-4924	51	3	2	2	NUM
ejpam-4924	51	4	]	]	PUNCT
ejpam-4924	51	5	,	,	PUNCT
ejpam-4924	51	6	théorème	théorème	PROPN
ejpam-4924	51	7	5.1.2	5.1.2	NUM
ejpam-4924	51	8	)	)	PUNCT
ejpam-4924	51	9	let	let	VERB
ejpam-4924	51	10	a	a	PRON
ejpam-4924	51	11	be	be	AUX
ejpam-4924	51	12	an	an	DET
ejpam-4924	51	13	algebra	algebra	NOUN
ejpam-4924	51	14	satisfying	satisfy	VERB
ejpam-4924	51	15	the	the	DET
ejpam-4924	51	16	identity	identity	NOUN
ejpam-4924	51	17	(	(	PUNCT
ejpam-4924	51	18	3	3	NUM
ejpam-4924	51	19	)	)	PUNCT
ejpam-4924	51	20	,	,	PUNCT
ejpam-4924	51	21	whose	whose	DET
ejpam-4924	51	22	peirce	peirce	NOUN
ejpam-4924	51	23	decomposition	decomposition	NOUN
ejpam-4924	51	24	of	of	ADP
ejpam-4924	51	25	a	a	PRON
ejpam-4924	51	26	is	be	AUX
ejpam-4924	51	27	written	write	VERB
ejpam-4924	51	28	a	a	DET
ejpam-4924	51	29	=	=	SYM
ejpam-4924	51	30	a0	a0	PROPN
ejpam-4924	51	31	⊕a1	⊕a1	PROPN
ejpam-4924	51	32	⊕aλ1	⊕aλ1	PRON
ejpam-4924	51	33	⊕aλ2	⊕aλ2	NOUN
ejpam-4924	51	34	,	,	PUNCT
ejpam-4924	51	35	then	then	ADV
ejpam-4924	51	36	i	i	PRON
ejpam-4924	51	37	)	)	PUNCT
ejpam-4924	51	38	x0(y0xλk	x0(y0xλk	PUNCT
ejpam-4924	51	39	)	)	PUNCT
ejpam-4924	52	1	+	+	CCONJ
ejpam-4924	52	2	y0(x0xλk	y0(x0xλk	X
ejpam-4924	52	3	)	)	PUNCT
ejpam-4924	53	1	=	=	SYM
ejpam-4924	53	2	2λkxλk	2λkxλk	NUM
ejpam-4924	53	3	(	(	PUNCT
ejpam-4924	53	4	x0y0	x0y0	NOUN
ejpam-4924	53	5	)	)	PUNCT
ejpam-4924	53	6	;	;	PUNCT
ejpam-4924	53	7	ii	ii	X
ejpam-4924	53	8	)	)	PUNCT
ejpam-4924	53	9	x1(y1xλk	x1(y1xλk	PROPN
ejpam-4924	53	10	)	)	PUNCT
ejpam-4924	54	1	+	+	NUM
ejpam-4924	54	2	y1(x1xλk	y1(x1xλk	X
ejpam-4924	54	3	)	)	PUNCT
ejpam-4924	54	4	=	=	SYM
ejpam-4924	54	5	(	(	PUNCT
ejpam-4924	54	6	1−	1−	NUM
ejpam-4924	54	7	3(λk	3(λk	NUM
ejpam-4924	54	8	)	)	PUNCT
ejpam-4924	54	9	3)xλk	3)xλk	NUM
ejpam-4924	54	10	(	(	PUNCT
ejpam-4924	54	11	x1y1	x1y1	X
ejpam-4924	54	12	)	)	PUNCT
ejpam-4924	54	13	;	;	PUNCT
ejpam-4924	54	14	iii	iii	X
ejpam-4924	54	15	)	)	PUNCT
ejpam-4924	54	16	x1(xλk	x1(xλk	NOUN
ejpam-4924	54	17	x0	x0	PROPN
ejpam-4924	54	18	)	)	PUNCT
ejpam-4924	54	19	=	=	SYM
ejpam-4924	54	20	x0(x1xλk	x0(x1xλk	PROPN
ejpam-4924	54	21	)	)	PUNCT
ejpam-4924	54	22	,	,	PUNCT
ejpam-4924	54	23	where	where	SCONJ
ejpam-4924	54	24	λk	λk	ADV
ejpam-4924	54	25	is	be	AUX
ejpam-4924	54	26	the	the	DET
ejpam-4924	54	27	conjugate	conjugate	NOUN
ejpam-4924	54	28	of	of	ADP
ejpam-4924	54	29	λk	λk	NOUN
ejpam-4924	54	30	,	,	PUNCT
ejpam-4924	54	31	and	and	CCONJ
ejpam-4924	54	32	xi	xi	PROPN
ejpam-4924	54	33	,	,	PUNCT
ejpam-4924	54	34	yi	yi	PROPN
ejpam-4924	54	35	∈	∈	PROPN
ejpam-4924	54	36	ai	ai	VERB
ejpam-4924	54	37	,	,	PUNCT
ejpam-4924	54	38	xλk	xλk	PROPN
ejpam-4924	54	39	∈	∈	PROPN
ejpam-4924	54	40	aλk	aλk	INTJ
ejpam-4924	54	41	for	for	ADP
ejpam-4924	54	42	i	i	PRON
ejpam-4924	54	43	∈	∈	PROPN
ejpam-4924	54	44	{	{	PUNCT
ejpam-4924	54	45	0	0	NUM
ejpam-4924	54	46	;	;	PUNCT
ejpam-4924	54	47	1	1	NUM
ejpam-4924	54	48	}	}	PUNCT
ejpam-4924	54	49	and	and	CCONJ
ejpam-4924	54	50	k	k	PROPN
ejpam-4924	54	51	∈	∈	PROPN
ejpam-4924	54	52	{	{	PUNCT
ejpam-4924	54	53	1	1	NUM
ejpam-4924	54	54	;	;	PUNCT
ejpam-4924	54	55	2	2	NUM
ejpam-4924	54	56	}	}	PUNCT
ejpam-4924	54	57	.	.	PUNCT
ejpam-4924	55	1	3	3	X
ejpam-4924	55	2	.	.	X
ejpam-4924	55	3	derivations	derivation	NOUN
ejpam-4924	55	4	let	let	VERB
ejpam-4924	55	5	a	a	PRON
ejpam-4924	55	6	be	be	AUX
ejpam-4924	55	7	ak	ak	NOUN
ejpam-4924	55	8	-	-	NOUN
ejpam-4924	55	9	algebra	algebra	NOUN
ejpam-4924	55	10	satisfying	satisfying	NOUN
ejpam-4924	55	11	(	(	PUNCT
ejpam-4924	55	12	3	3	NUM
ejpam-4924	55	13	)	)	PUNCT
ejpam-4924	55	14	.	.	PUNCT
ejpam-4924	56	1	we	we	PRON
ejpam-4924	56	2	say	say	VERB
ejpam-4924	56	3	that	that	SCONJ
ejpam-4924	56	4	an	an	DET
ejpam-4924	56	5	endomorphism	endomorphism	PROPN
ejpam-4924	56	6	d	d	NOUN
ejpam-4924	56	7	of	of	ADP
ejpam-4924	56	8	a	a	PRON
ejpam-4924	56	9	is	be	AUX
ejpam-4924	56	10	a	a	DET
ejpam-4924	56	11	derivation	derivation	NOUN
ejpam-4924	56	12	of	of	ADP
ejpam-4924	56	13	a	a	DET
ejpam-4924	56	14	if	if	NOUN
ejpam-4924	56	15	for	for	ADP
ejpam-4924	56	16	all	all	DET
ejpam-4924	56	17	x	x	NOUN
ejpam-4924	56	18	,	,	PUNCT
ejpam-4924	56	19	y	y	PROPN
ejpam-4924	56	20	∈	∈	PROPN
ejpam-4924	56	21	a	a	PRON
ejpam-4924	56	22	,	,	PUNCT
ejpam-4924	56	23	d(xy	d(xy	PROPN
ejpam-4924	56	24	)	)	PUNCT
ejpam-4924	56	25	=	=	SYM
ejpam-4924	56	26	d(x)y+xd(y	d(x)y+xd(y	PROPN
ejpam-4924	56	27	)	)	PUNCT
ejpam-4924	56	28	.	.	PUNCT
ejpam-4924	57	1	the	the	DET
ejpam-4924	57	2	set	set	NOUN
ejpam-4924	57	3	derk(a	derk(a	NOUN
ejpam-4924	57	4	)	)	PUNCT
ejpam-4924	57	5	of	of	ADP
ejpam-4924	57	6	all	all	DET
ejpam-4924	57	7	derivations	derivation	NOUN
ejpam-4924	57	8	of	of	ADP
ejpam-4924	57	9	a	a	PRON
ejpam-4924	57	10	with	with	ADP
ejpam-4924	57	11	the	the	DET
ejpam-4924	57	12	lie	lie	NOUN
ejpam-4924	57	13	bracket	bracket	NOUN
ejpam-4924	57	14	[	[	X
ejpam-4924	57	15	,	,	PUNCT
ejpam-4924	57	16	]	]	PUNCT
ejpam-4924	57	17	,	,	PUNCT
ejpam-4924	57	18	is	be	AUX
ejpam-4924	57	19	a	a	DET
ejpam-4924	57	20	lie	lie	NOUN
ejpam-4924	57	21	subalgebra	subalgebra	NOUN
ejpam-4924	57	22	of	of	ADP
ejpam-4924	57	23	endk(a)−	endk(a)−	PROPN
ejpam-4924	57	24	,	,	PUNCT
ejpam-4924	57	25	where	where	SCONJ
ejpam-4924	57	26	endk(a	endk(a	VERB
ejpam-4924	57	27	)	)	PUNCT
ejpam-4924	57	28	is	be	AUX
ejpam-4924	57	29	the	the	DET
ejpam-4924	57	30	associative	associative	ADJ
ejpam-4924	57	31	algebra	algebra	NOUN
ejpam-4924	57	32	of	of	ADP
ejpam-4924	57	33	endomorphisms	endomorphism	NOUN
ejpam-4924	57	34	of	of	ADP
ejpam-4924	57	35	a.	a.	NOUN
ejpam-4924	57	36	the	the	DET
ejpam-4924	57	37	lie	lie	NOUN
ejpam-4924	57	38	bracket	bracket	NOUN
ejpam-4924	57	39	is	be	AUX
ejpam-4924	57	40	defined	define	VERB
ejpam-4924	57	41	by	by	ADP
ejpam-4924	57	42	:	:	PUNCT
ejpam-4924	58	1	[	[	X
ejpam-4924	58	2	d	d	X
ejpam-4924	58	3	,	,	PUNCT
ejpam-4924	58	4	d′	d′	X
ejpam-4924	58	5	]	]	PUNCT
ejpam-4924	58	6	=	=	SYM
ejpam-4924	58	7	dd′−	dd′−	PROPN
ejpam-4924	58	8	d′d	d′d	NOUN
ejpam-4924	58	9	(	(	PUNCT
ejpam-4924	58	10	[	[	X
ejpam-4924	58	11	5	5	NUM
ejpam-4924	58	12	]	]	PUNCT
ejpam-4924	58	13	,	,	PUNCT
ejpam-4924	58	14	[	[	X
ejpam-4924	58	15	6	6	NUM
ejpam-4924	58	16	]	]	NUM
ejpam-4924	58	17	)	)	PUNCT
ejpam-4924	58	18	.	.	PUNCT
ejpam-4924	59	1	the	the	DET
ejpam-4924	59	2	following	follow	VERB
ejpam-4924	59	3	theorems	theorem	NOUN
ejpam-4924	59	4	characterise	characterise	VERB
ejpam-4924	59	5	the	the	DET
ejpam-4924	59	6	derivations	derivation	NOUN
ejpam-4924	59	7	of	of	ADP
ejpam-4924	59	8	an	an	DET
ejpam-4924	59	9	algebra	algebra	NOUN
ejpam-4924	59	10	satisfying	satisfy	VERB
ejpam-4924	59	11	(	(	PUNCT
ejpam-4924	59	12	3	3	NUM
ejpam-4924	59	13	)	)	PUNCT
ejpam-4924	59	14	.	.	PUNCT
ejpam-4924	60	1	theorem	theorem	VERB
ejpam-4924	60	2	3.1	3.1	NUM
ejpam-4924	60	3	.	.	PUNCT
ejpam-4924	61	1	let	let	VERB
ejpam-4924	61	2	a	a	DET
ejpam-4924	61	3	=	=	SYM
ejpam-4924	61	4	a0	a0	PROPN
ejpam-4924	61	5	⊕	⊕	PROPN
ejpam-4924	61	6	a1	a1	PROPN
ejpam-4924	61	7	⊕	⊕	PROPN
ejpam-4924	61	8	aλ1	aλ1	PROPN
ejpam-4924	62	1	⊕	⊕	PROPN
ejpam-4924	62	2	aλ2	aλ2	PROPN
ejpam-4924	62	3	be	be	AUX
ejpam-4924	62	4	the	the	DET
ejpam-4924	62	5	peirce	peirce	NOUN
ejpam-4924	62	6	decomposition	decomposition	NOUN
ejpam-4924	62	7	of	of	ADP
ejpam-4924	62	8	an	an	DET
ejpam-4924	62	9	algebra	algebra	NOUN
ejpam-4924	62	10	satisfying	satisfy	VERB
ejpam-4924	62	11	(	(	PUNCT
ejpam-4924	62	12	3	3	NUM
ejpam-4924	62	13	)	)	PUNCT
ejpam-4924	62	14	.	.	PUNCT
ejpam-4924	63	1	if	if	SCONJ
ejpam-4924	63	2	d	d	NOUN
ejpam-4924	63	3	is	be	AUX
ejpam-4924	63	4	a	a	DET
ejpam-4924	63	5	derivation	derivation	NOUN
ejpam-4924	63	6	of	of	ADP
ejpam-4924	63	7	a	a	PRON
ejpam-4924	63	8	,	,	PUNCT
ejpam-4924	63	9	then	then	ADV
ejpam-4924	63	10	d	d	X
ejpam-4924	63	11	satisfies	satisfy	VERB
ejpam-4924	63	12	the	the	DET
ejpam-4924	63	13	following	follow	VERB
ejpam-4924	63	14	properties	property	NOUN
ejpam-4924	63	15	,	,	PUNCT
ejpam-4924	63	16	for	for	ADP
ejpam-4924	63	17	i	i	PRON
ejpam-4924	63	18	∈	∈	PROPN
ejpam-4924	63	19	{	{	PUNCT
ejpam-4924	63	20	0	0	NUM
ejpam-4924	63	21	,	,	PUNCT
ejpam-4924	63	22	1	1	NUM
ejpam-4924	63	23	,	,	PUNCT
ejpam-4924	63	24	λ1	λ1	ADJ
ejpam-4924	63	25	,	,	PUNCT
ejpam-4924	63	26	λ2	λ2	PROPN
ejpam-4924	63	27	}	}	PUNCT
ejpam-4924	63	28	;	;	PUNCT
ejpam-4924	63	29	α	α	PROPN
ejpam-4924	63	30	∈	∈	PROPN
ejpam-4924	63	31	{	{	PUNCT
ejpam-4924	63	32	λ1	λ1	ADJ
ejpam-4924	63	33	,	,	PUNCT
ejpam-4924	63	34	λ2	λ2	PROPN
ejpam-4924	63	35	}	}	PUNCT
ejpam-4924	63	36	;	;	PUNCT
ejpam-4924	63	37	β	β	X
ejpam-4924	63	38	∈	∈	PROPN
ejpam-4924	63	39	{	{	PUNCT
ejpam-4924	63	40	0	0	NUM
ejpam-4924	63	41	,	,	PUNCT
ejpam-4924	63	42	1	1	NUM
ejpam-4924	63	43	}	}	PUNCT
ejpam-4924	63	44	:	:	PUNCT
ejpam-4924	63	45	i	i	X
ejpam-4924	63	46	)	)	PUNCT
ejpam-4924	63	47	d(e	d(e	PROPN
ejpam-4924	63	48	)	)	PUNCT
ejpam-4924	63	49	=	=	SYM
ejpam-4924	63	50	0	0	NUM
ejpam-4924	63	51	;	;	PUNCT
ejpam-4924	63	52	ii	ii	X
ejpam-4924	63	53	)	)	PUNCT
ejpam-4924	63	54	d(xi	d(xi	PROPN
ejpam-4924	63	55	)	)	PUNCT
ejpam-4924	63	56	∈	∈	PROPN
ejpam-4924	63	57	ai	ai	VERB
ejpam-4924	63	58	;	;	PUNCT
ejpam-4924	63	59	iii	iii	X
ejpam-4924	63	60	)	)	PUNCT
ejpam-4924	63	61	fi	fi	NOUN
ejpam-4924	64	1	=	=	PUNCT
ejpam-4924	64	2	d	d	X
ejpam-4924	64	3	/	/	SYM
ejpam-4924	64	4	ai	ai	NOUN
ejpam-4924	64	5	;	;	PUNCT
ejpam-4924	64	6	iv	iv	X
ejpam-4924	64	7	)	)	PUNCT
ejpam-4924	64	8	fα(xβyα	fα(xβyα	NOUN
ejpam-4924	64	9	)	)	PUNCT
ejpam-4924	64	10	=	=	SYM
ejpam-4924	64	11	xβfα(yα	xβfα(yα	PROPN
ejpam-4924	64	12	)	)	PUNCT
ejpam-4924	64	13	+	+	NUM
ejpam-4924	64	14	yαfβ(xβ	yαfβ(xβ	NOUN
ejpam-4924	64	15	)	)	PUNCT
ejpam-4924	64	16	.	.	PUNCT
ejpam-4924	65	1	proof	proof	NOUN
ejpam-4924	65	2	.	.	PUNCT
ejpam-4924	66	1	i	i	PRON
ejpam-4924	66	2	)	)	PUNCT
ejpam-4924	66	3	since	since	SCONJ
ejpam-4924	66	4	e	e	NOUN
ejpam-4924	66	5	is	be	AUX
ejpam-4924	66	6	an	an	DET
ejpam-4924	66	7	idempotent	idempotent	NOUN
ejpam-4924	66	8	of	of	ADP
ejpam-4924	66	9	a	a	DET
ejpam-4924	66	10	then	then	ADV
ejpam-4924	66	11	2ed(e	2ed(e	NUM
ejpam-4924	66	12	)	)	PUNCT
ejpam-4924	66	13	=	=	SYM
ejpam-4924	66	14	d(e	d(e	NOUN
ejpam-4924	66	15	)	)	PUNCT
ejpam-4924	66	16	.	.	PUNCT
ejpam-4924	67	1	by	by	ADP
ejpam-4924	67	2	setting	set	VERB
ejpam-4924	67	3	d(e	d(e	NOUN
ejpam-4924	67	4	)	)	PUNCT
ejpam-4924	67	5	=	=	PUNCT
ejpam-4924	67	6	x0+x1	x0+x1	PROPN
ejpam-4924	67	7	+	+	PROPN
ejpam-4924	67	8	xλ1	xλ1	NOUN
ejpam-4924	68	1	+	+	PROPN
ejpam-4924	68	2	xλ2	xλ2	PROPN
ejpam-4924	68	3	,	,	PUNCT
ejpam-4924	68	4	we	we	PRON
ejpam-4924	68	5	have	have	VERB
ejpam-4924	68	6	−x0+x1+(2λ1−1)xλ1	−x0+x1+(2λ1−1)xλ1	PRON
ejpam-4924	69	1	+	+	ADJ
ejpam-4924	69	2	(	(	PUNCT
ejpam-4924	69	3	2λ2−1)xλ2	2λ2−1)xλ2	NOUN
ejpam-4924	69	4	=	=	NOUN
ejpam-4924	69	5	0	0	NUM
ejpam-4924	70	1	i.e	i.e	PRON
ejpam-4924	70	2	x0	x0	NOUN
ejpam-4924	70	3	=	=	PUNCT
ejpam-4924	71	1	x1	x1	PROPN
ejpam-4924	71	2	=	=	PUNCT
ejpam-4924	71	3	xλ1	xλ1	X
ejpam-4924	72	1	=	=	PUNCT
ejpam-4924	72	2	xλ2	xλ2	PROPN
ejpam-4924	72	3	=	=	SYM
ejpam-4924	72	4	0	0	NUM
ejpam-4924	72	5	;	;	PUNCT
ejpam-4924	72	6	hence	hence	ADV
ejpam-4924	72	7	d(e	d(e	NOUN
ejpam-4924	72	8	)	)	PUNCT
ejpam-4924	72	9	=	=	SYM
ejpam-4924	72	10	0	0	X
ejpam-4924	72	11	.	.	X
ejpam-4924	72	12	ii	ii	PROPN
ejpam-4924	72	13	)	)	PUNCT
ejpam-4924	72	14	and	and	CCONJ
ejpam-4924	72	15	iii	iii	X
ejpam-4924	72	16	)	)	PUNCT
ejpam-4924	72	17	let	let	VERB
ejpam-4924	72	18	xi	xi	PROPN
ejpam-4924	72	19	∈	∈	PROPN
ejpam-4924	72	20	ai	ai	VERB
ejpam-4924	72	21	for	for	ADP
ejpam-4924	72	22	i	i	PRON
ejpam-4924	72	23	∈	∈	PROPN
ejpam-4924	72	24	{	{	PUNCT
ejpam-4924	72	25	0	0	NUM
ejpam-4924	72	26	,	,	PUNCT
ejpam-4924	72	27	1	1	NUM
ejpam-4924	72	28	,	,	PUNCT
ejpam-4924	72	29	λ1	λ1	ADJ
ejpam-4924	72	30	,	,	PUNCT
ejpam-4924	72	31	λ2	λ2	PROPN
ejpam-4924	72	32	}	}	PUNCT
ejpam-4924	72	33	;	;	PUNCT
ejpam-4924	72	34	then	then	ADV
ejpam-4924	72	35	exi	exi	PROPN
ejpam-4924	72	36	=	=	PROPN
ejpam-4924	72	37	ixi	ixi	PROPN
ejpam-4924	72	38	i.e	i.e	PROPN
ejpam-4924	72	39	ed(xi	ed(xi	PROPN
ejpam-4924	72	40	)	)	PUNCT
ejpam-4924	73	1	=	=	SYM
ejpam-4924	73	2	id(xi	id(xi	X
ejpam-4924	73	3	)	)	PUNCT
ejpam-4924	73	4	because	because	SCONJ
ejpam-4924	73	5	d(e	d(e	NOUN
ejpam-4924	73	6	)	)	PUNCT
ejpam-4924	73	7	=	=	SYM
ejpam-4924	74	1	0	0	X
ejpam-4924	74	2	.	.	PUNCT
ejpam-4924	75	1	so	so	ADV
ejpam-4924	75	2	we	we	PRON
ejpam-4924	75	3	have	have	VERB
ejpam-4924	75	4	d(xi	d(xi	NOUN
ejpam-4924	75	5	)	)	PUNCT
ejpam-4924	75	6	∈	∈	PROPN
ejpam-4924	75	7	ai	ai	VERB
ejpam-4924	75	8	,	,	PUNCT
ejpam-4924	75	9	and	and	CCONJ
ejpam-4924	76	1	fi	fi	NOUN
ejpam-4924	76	2	=	=	SYM
ejpam-4924	77	1	d	d	X
ejpam-4924	77	2	/	/	SYM
ejpam-4924	77	3	ai	ai	NOUN
ejpam-4924	77	4	.	.	PUNCT
ejpam-4924	78	1	iv	iv	X
ejpam-4924	78	2	)	)	PUNCT
ejpam-4924	78	3	we	we	PRON
ejpam-4924	78	4	have	have	VERB
ejpam-4924	78	5	xβyα	xβyα	PROPN
ejpam-4924	78	6	∈	∈	PROPN
ejpam-4924	78	7	aα	aα	NOUN
ejpam-4924	78	8	for	for	ADP
ejpam-4924	78	9	α	α	DET
ejpam-4924	78	10	∈	∈	PROPN
ejpam-4924	78	11	{	{	PUNCT
ejpam-4924	78	12	λ1	λ1	ADJ
ejpam-4924	78	13	,	,	PUNCT
ejpam-4924	78	14	λ2	λ2	NOUN
ejpam-4924	78	15	}	}	PUNCT
ejpam-4924	78	16	and	and	CCONJ
ejpam-4924	78	17	β	β	X
ejpam-4924	78	18	∈	∈	PROPN
ejpam-4924	78	19	{	{	PUNCT
ejpam-4924	78	20	0	0	NUM
ejpam-4924	78	21	,	,	PUNCT
ejpam-4924	78	22	1	1	NUM
ejpam-4924	78	23	}	}	PUNCT
ejpam-4924	78	24	according	accord	VERB
ejpam-4924	78	25	to	to	ADP
ejpam-4924	78	26	the	the	DET
ejpam-4924	78	27	products	product	NOUN
ejpam-4924	78	28	of	of	ADP
ejpam-4924	78	29	the	the	DET
ejpam-4924	78	30	peirce	peirce	NOUN
ejpam-4924	78	31	subspaces	subspace	NOUN
ejpam-4924	78	32	of	of	ADP
ejpam-4924	78	33	a	a	PRON
ejpam-4924	78	34	,	,	PUNCT
ejpam-4924	78	35	since	since	SCONJ
ejpam-4924	78	36	d(xβyα	d(xβyα	PROPN
ejpam-4924	78	37	)	)	PUNCT
ejpam-4924	79	1	=	=	SYM
ejpam-4924	79	2	xβd(yα)+	xβd(yα)+	PROPN
ejpam-4924	79	3	yαd(xβ	yαd(xβ	NUM
ejpam-4924	79	4	)	)	PUNCT
ejpam-4924	80	1	then	then	ADV
ejpam-4924	80	2	,	,	PUNCT
ejpam-4924	80	3	applying	apply	VERB
ejpam-4924	80	4	iii	iii	NOUN
ejpam-4924	80	5	)	)	PUNCT
ejpam-4924	80	6	,	,	PUNCT
ejpam-4924	80	7	we	we	PRON
ejpam-4924	80	8	have	have	VERB
ejpam-4924	80	9	fα(xβyα	fα(xβyα	NOUN
ejpam-4924	80	10	)	)	PUNCT
ejpam-4924	80	11	=	=	SYM
ejpam-4924	80	12	xβfβ(yα	xβfβ(yα	NOUN
ejpam-4924	80	13	)	)	PUNCT
ejpam-4924	81	1	+	+	X
ejpam-4924	81	2	yαfα(xβ	yαfα(xβ	NOUN
ejpam-4924	81	3	)	)	PUNCT
ejpam-4924	81	4	.	.	PUNCT
ejpam-4924	82	1	h.	h.	PROPN
ejpam-4924	82	2	ouédraogo	ouédraogo	PROPN
ejpam-4924	82	3	,	,	PUNCT
ejpam-4924	82	4	a.	a.	NOUN
ejpam-4924	82	5	dembega	dembega	PROPN
ejpam-4924	82	6	,	,	PUNCT
ejpam-4924	82	7	a.	a.	PROPN
ejpam-4924	82	8	conseibo	conseibo	PROPN
ejpam-4924	82	9	/	/	SYM
ejpam-4924	82	10	eur	eur	PROPN
ejpam-4924	82	11	.	.	PUNCT
ejpam-4924	83	1	j.	j.	PROPN
ejpam-4924	83	2	pure	pure	PROPN
ejpam-4924	83	3	appl	appl	PROPN
ejpam-4924	83	4	.	.	PROPN
ejpam-4924	83	5	math	math	PROPN
ejpam-4924	83	6	,	,	PUNCT
ejpam-4924	83	7	16	16	NUM
ejpam-4924	83	8	(	(	PUNCT
ejpam-4924	83	9	4	4	NUM
ejpam-4924	83	10	)	)	PUNCT
ejpam-4924	83	11	(	(	PUNCT
ejpam-4924	83	12	2023	2023	NUM
ejpam-4924	83	13	)	)	PUNCT
ejpam-4924	83	14	,	,	PUNCT
ejpam-4924	83	15	2145	2145	NUM
ejpam-4924	83	16	-	-	SYM
ejpam-4924	83	17	2155	2155	NUM
ejpam-4924	83	18	2148	2148	NUM
ejpam-4924	83	19	theorem	theorem	NOUN
ejpam-4924	83	20	3.2	3.2	NUM
ejpam-4924	83	21	.	.	PUNCT
ejpam-4924	84	1	let	let	VERB
ejpam-4924	84	2	a	a	DET
ejpam-4924	84	3	=	=	SYM
ejpam-4924	84	4	a0	a0	PROPN
ejpam-4924	84	5	⊕	⊕	PROPN
ejpam-4924	84	6	a1	a1	PROPN
ejpam-4924	84	7	⊕	⊕	PROPN
ejpam-4924	84	8	aλ1	aλ1	PROPN
ejpam-4924	85	1	⊕	⊕	PROPN
ejpam-4924	85	2	aλ2	aλ2	PROPN
ejpam-4924	85	3	be	be	AUX
ejpam-4924	85	4	the	the	DET
ejpam-4924	85	5	peirce	peirce	NOUN
ejpam-4924	85	6	decomposition	decomposition	NOUN
ejpam-4924	85	7	of	of	ADP
ejpam-4924	85	8	an	an	DET
ejpam-4924	85	9	algebra	algebra	NOUN
ejpam-4924	85	10	satisfying	satisfy	VERB
ejpam-4924	85	11	(	(	PUNCT
ejpam-4924	85	12	3	3	NUM
ejpam-4924	85	13	)	)	PUNCT
ejpam-4924	85	14	.	.	PUNCT
ejpam-4924	86	1	let	let	VERB
ejpam-4924	86	2	d	d	NOUN
ejpam-4924	86	3	and	and	CCONJ
ejpam-4924	86	4	d′	d′	PRON
ejpam-4924	86	5	be	be	AUX
ejpam-4924	86	6	derivations	derivation	NOUN
ejpam-4924	86	7	of	of	ADP
ejpam-4924	86	8	a	a	PRON
ejpam-4924	86	9	,	,	PUNCT
ejpam-4924	86	10	then	then	ADV
ejpam-4924	86	11	the	the	DET
ejpam-4924	86	12	derivation	derivation	NOUN
ejpam-4924	86	13	[	[	X
ejpam-4924	86	14	d	d	X
ejpam-4924	86	15	,	,	PUNCT
ejpam-4924	86	16	d′	d′	PRON
ejpam-4924	86	17	]	]	PUNCT
ejpam-4924	86	18	satisfies	satisfie	NOUN
ejpam-4924	86	19	for	for	ADP
ejpam-4924	86	20	i	i	PROPN
ejpam-4924	86	21	∈	∈	PROPN
ejpam-4924	86	22	{	{	PUNCT
ejpam-4924	86	23	0	0	NUM
ejpam-4924	86	24	;	;	PUNCT
ejpam-4924	86	25	1;λ1;λ2	1;λ1;λ2	NUM
ejpam-4924	86	26	}	}	PUNCT
ejpam-4924	86	27	;	;	PUNCT
ejpam-4924	86	28	α	α	PROPN
ejpam-4924	86	29	∈	∈	PROPN
ejpam-4924	86	30	{	{	PUNCT
ejpam-4924	86	31	λ1;λ2	λ1;λ2	NOUN
ejpam-4924	86	32	}	}	PUNCT
ejpam-4924	86	33	and	and	CCONJ
ejpam-4924	86	34	β	β	X
ejpam-4924	86	35	∈	∈	PROPN
ejpam-4924	86	36	{	{	PUNCT
ejpam-4924	86	37	0	0	NUM
ejpam-4924	86	38	;	;	PUNCT
ejpam-4924	86	39	1	1	NUM
ejpam-4924	86	40	}	}	PUNCT
ejpam-4924	86	41	the	the	DET
ejpam-4924	86	42	following	follow	VERB
ejpam-4924	86	43	conditions	condition	NOUN
ejpam-4924	86	44	:	:	PUNCT
ejpam-4924	86	45	i	i	X
ejpam-4924	86	46	)	)	PUNCT
ejpam-4924	87	1	[	[	X
ejpam-4924	87	2	d	d	X
ejpam-4924	87	3	,	,	PUNCT
ejpam-4924	87	4	d′](e	d′](e	PROPN
ejpam-4924	87	5	)	)	PUNCT
ejpam-4924	87	6	=	=	SYM
ejpam-4924	87	7	0	0	NUM
ejpam-4924	87	8	;	;	PUNCT
ejpam-4924	87	9	ii	ii	X
ejpam-4924	87	10	)	)	PUNCT
ejpam-4924	88	1	[	[	X
ejpam-4924	88	2	d	d	X
ejpam-4924	88	3	,	,	PUNCT
ejpam-4924	88	4	d′](xi	d′](xi	PROPN
ejpam-4924	88	5	)	)	PUNCT
ejpam-4924	88	6	∈	∈	PROPN
ejpam-4924	88	7	ai	ai	VERB
ejpam-4924	88	8	;	;	PUNCT
ejpam-4924	88	9	iii	iii	X
ejpam-4924	88	10	)	)	PUNCT
ejpam-4924	88	11	f[d	f[d	NOUN
ejpam-4924	88	12	,	,	PUNCT
ejpam-4924	88	13	d′](xi	d′](xi	PROPN
ejpam-4924	88	14	)	)	PUNCT
ejpam-4924	88	15	=	=	PUNCT
ejpam-4924	89	1	[	[	X
ejpam-4924	89	2	d	d	X
ejpam-4924	89	3	,	,	PUNCT
ejpam-4924	89	4	d′]/ai	d′]/ai	PROPN
ejpam-4924	89	5	=	=	SYM
ejpam-4924	89	6	fd(fd′(xi))−	fd(fd′(xi))−	PROPN
ejpam-4924	89	7	fd′(fd(xi	fd′(fd(xi	PROPN
ejpam-4924	89	8	)	)	PUNCT
ejpam-4924	89	9	)	)	PUNCT
ejpam-4924	89	10	.	.	PUNCT
ejpam-4924	90	1	proof	proof	NOUN
ejpam-4924	90	2	.	.	PUNCT
ejpam-4924	91	1	we	we	PRON
ejpam-4924	91	2	have	have	VERB
ejpam-4924	91	3	d(e	d(e	NOUN
ejpam-4924	91	4	)	)	PUNCT
ejpam-4924	92	1	=	=	SYM
ejpam-4924	92	2	0	0	NUM
ejpam-4924	92	3	by	by	ADP
ejpam-4924	92	4	the	the	DET
ejpam-4924	92	5	theorem(3.1	theorem(3.1	NOUN
ejpam-4924	92	6	)	)	PUNCT
ejpam-4924	92	7	,	,	PUNCT
ejpam-4924	93	1	so	so	CCONJ
ejpam-4924	93	2	[	[	X
ejpam-4924	93	3	d	d	X
ejpam-4924	93	4	,	,	PUNCT
ejpam-4924	93	5	d′](e	d′](e	PROPN
ejpam-4924	93	6	)	)	PUNCT
ejpam-4924	93	7	=	=	SYM
ejpam-4924	93	8	d(d′(e	d(d′(e	ADJ
ejpam-4924	93	9	)	)	PUNCT
ejpam-4924	93	10	)	)	PUNCT
ejpam-4924	94	1	−	−	PROPN
ejpam-4924	94	2	d′(d(e	d′(d(e	NOUN
ejpam-4924	94	3	)	)	PUNCT
ejpam-4924	94	4	)	)	PUNCT
ejpam-4924	95	1	=	=	PUNCT
ejpam-4924	95	2	0	0	X
ejpam-4924	95	3	.	.	PUNCT
ejpam-4924	96	1	hence	hence	ADV
ejpam-4924	96	2	i	i	NOUN
ejpam-4924	96	3	)	)	PUNCT
ejpam-4924	96	4	.	.	PUNCT
ejpam-4924	97	1	also	also	ADV
ejpam-4924	97	2	[	[	X
ejpam-4924	97	3	d	d	X
ejpam-4924	97	4	,	,	PUNCT
ejpam-4924	97	5	d′](xi	d′](xi	PROPN
ejpam-4924	97	6	)	)	PUNCT
ejpam-4924	97	7	=	=	PROPN
ejpam-4924	97	8	fd(fd′(xi))−	fd(fd′(xi))−	PROPN
ejpam-4924	97	9	fd′(fd(xi	fd′(fd(xi	PROPN
ejpam-4924	97	10	)	)	PUNCT
ejpam-4924	97	11	)	)	PUNCT
ejpam-4924	97	12	,	,	PUNCT
ejpam-4924	97	13	hence	hence	ADV
ejpam-4924	97	14	ii	ii	NOUN
ejpam-4924	97	15	)	)	PUNCT
ejpam-4924	97	16	and	and	CCONJ
ejpam-4924	97	17	iii	iii	NOUN
ejpam-4924	97	18	)	)	PUNCT
ejpam-4924	97	19	.	.	PUNCT
ejpam-4924	98	1	4	4	X
ejpam-4924	98	2	.	.	X
ejpam-4924	98	3	representations	representation	NOUN
ejpam-4924	98	4	we	we	PRON
ejpam-4924	98	5	are	be	AUX
ejpam-4924	98	6	interested	interested	ADJ
ejpam-4924	98	7	here	here	ADV
ejpam-4924	98	8	in	in	ADP
ejpam-4924	98	9	the	the	DET
ejpam-4924	98	10	representations	representation	NOUN
ejpam-4924	98	11	of	of	ADP
ejpam-4924	98	12	algebras	algebra	NOUN
ejpam-4924	98	13	defined	define	VERB
ejpam-4924	98	14	by	by	ADP
ejpam-4924	98	15	the	the	DET
ejpam-4924	98	16	identity	identity	NOUN
ejpam-4924	98	17	(	(	PUNCT
ejpam-4924	98	18	3	3	NUM
ejpam-4924	98	19	)	)	PUNCT
ejpam-4924	98	20	(	(	PUNCT
ejpam-4924	99	1	[	[	X
ejpam-4924	99	2	4	4	NUM
ejpam-4924	99	3	]	]	NUM
ejpam-4924	99	4	)	)	PUNCT
ejpam-4924	99	5	.	.	PUNCT
ejpam-4924	100	1	following	follow	VERB
ejpam-4924	100	2	eilenberg	eilenberg	NOUN
ejpam-4924	101	1	[	[	X
ejpam-4924	101	2	3	3	NUM
ejpam-4924	101	3	]	]	PUNCT
ejpam-4924	101	4	,	,	PUNCT
ejpam-4924	101	5	if	if	SCONJ
ejpam-4924	101	6	a	a	PRON
ejpam-4924	101	7	is	be	AUX
ejpam-4924	101	8	a	a	DET
ejpam-4924	101	9	commutative	commutative	ADJ
ejpam-4924	101	10	k	k	NOUN
ejpam-4924	101	11	-	-	NOUN
ejpam-4924	101	12	algebra	algebra	NOUN
ejpam-4924	101	13	belonging	belong	VERB
ejpam-4924	101	14	to	to	ADP
ejpam-4924	101	15	a	a	DET
ejpam-4924	101	16	class	class	NOUN
ejpam-4924	101	17	c	c	NOUN
ejpam-4924	101	18	and	and	CCONJ
ejpam-4924	101	19	m	m	PROPN
ejpam-4924	101	20	a	a	DET
ejpam-4924	101	21	vector	vector	NOUN
ejpam-4924	101	22	space	space	NOUN
ejpam-4924	101	23	on	on	ADP
ejpam-4924	101	24	k	k	PROPN
ejpam-4924	101	25	,	,	PUNCT
ejpam-4924	101	26	a	a	DET
ejpam-4924	101	27	linear	linear	ADJ
ejpam-4924	101	28	application	application	NOUN
ejpam-4924	101	29	ρ	ρ	NOUN
ejpam-4924	101	30	:	:	PUNCT
ejpam-4924	101	31	a	a	DET
ejpam-4924	101	32	−→	−→	NOUN
ejpam-4924	101	33	end(m	end(m	PROPN
ejpam-4924	101	34	)	)	PUNCT
ejpam-4924	101	35	is	be	AUX
ejpam-4924	101	36	a	a	DET
ejpam-4924	101	37	representation	representation	NOUN
ejpam-4924	101	38	of	of	ADP
ejpam-4924	101	39	a	a	PRON
ejpam-4924	101	40	in	in	ADP
ejpam-4924	101	41	the	the	DET
ejpam-4924	101	42	class	class	NOUN
ejpam-4924	101	43	c	c	NOUN
ejpam-4924	101	44	if	if	SCONJ
ejpam-4924	101	45	the	the	DET
ejpam-4924	101	46	extension	extension	NOUN
ejpam-4924	101	47	s	s	VERB
ejpam-4924	101	48	=	=	X
ejpam-4924	101	49	a	a	DET
ejpam-4924	101	50	⊕	⊕	PROPN
ejpam-4924	101	51	m	m	VERB
ejpam-4924	101	52	of	of	ADP
ejpam-4924	101	53	m	m	PROPN
ejpam-4924	101	54	with	with	ADP
ejpam-4924	101	55	multiplication	multiplication	NOUN
ejpam-4924	101	56	given	give	VERB
ejpam-4924	101	57	by	by	ADP
ejpam-4924	101	58	(	(	PUNCT
ejpam-4924	101	59	a+m)(b+	a+m)(b+	NOUN
ejpam-4924	101	60	n	n	CCONJ
ejpam-4924	101	61	)	)	PUNCT
ejpam-4924	101	62	=	=	SYM
ejpam-4924	101	63	ab+	ab+	NOUN
ejpam-4924	101	64	ρ(a)(n	ρ(a)(n	NUM
ejpam-4924	101	65	)	)	PUNCT
ejpam-4924	101	66	+	+	CCONJ
ejpam-4924	101	67	ρ(b)(m	ρ(b)(m	NUM
ejpam-4924	101	68	)	)	PUNCT
ejpam-4924	101	69	for	for	ADP
ejpam-4924	101	70	all	all	DET
ejpam-4924	101	71	a	a	PRON
ejpam-4924	101	72	,	,	PUNCT
ejpam-4924	101	73	b	b	X
ejpam-4924	101	74	∈	∈	PROPN
ejpam-4924	101	75	a	a	DET
ejpam-4924	101	76	,	,	PUNCT
ejpam-4924	101	77	m	m	PROPN
ejpam-4924	101	78	,	,	PUNCT
ejpam-4924	101	79	n	n	PROPN
ejpam-4924	101	80	∈	∈	NOUN
ejpam-4924	101	81	m	m	VERB
ejpam-4924	101	82	;	;	PUNCT
ejpam-4924	101	83	belong	belong	VERB
ejpam-4924	101	84	to	to	ADP
ejpam-4924	101	85	the	the	DET
ejpam-4924	101	86	class	class	NOUN
ejpam-4924	101	87	c.	c.	NOUN
ejpam-4924	101	88	in	in	ADP
ejpam-4924	101	89	the	the	DET
ejpam-4924	101	90	following	follow	VERB
ejpam-4924	101	91	section	section	NOUN
ejpam-4924	101	92	,	,	PUNCT
ejpam-4924	101	93	we	we	PRON
ejpam-4924	101	94	give	give	VERB
ejpam-4924	101	95	some	some	DET
ejpam-4924	101	96	results	result	NOUN
ejpam-4924	101	97	on	on	ADP
ejpam-4924	101	98	the	the	DET
ejpam-4924	101	99	representations	representation	NOUN
ejpam-4924	101	100	of	of	ADP
ejpam-4924	101	101	algebras	algebra	NOUN
ejpam-4924	101	102	verifying	verify	VERB
ejpam-4924	101	103	the	the	DET
ejpam-4924	101	104	identity	identity	NOUN
ejpam-4924	101	105	(	(	PUNCT
ejpam-4924	101	106	3	3	NUM
ejpam-4924	101	107	)	)	PUNCT
ejpam-4924	101	108	.	.	PUNCT
ejpam-4924	102	1	4.1	4.1	NUM
ejpam-4924	102	2	.	.	PUNCT
ejpam-4924	102	3	general	general	ADJ
ejpam-4924	102	4	results	result	NOUN
ejpam-4924	102	5	lemma	lemma	PROPN
ejpam-4924	102	6	4.1	4.1	NUM
ejpam-4924	102	7	.	.	PUNCT
ejpam-4924	103	1	let	let	VERB
ejpam-4924	103	2	a	a	DET
ejpam-4924	103	3	be	be	AUX
ejpam-4924	103	4	an	an	DET
ejpam-4924	103	5	algebra	algebra	NOUN
ejpam-4924	103	6	verifying	verify	VERB
ejpam-4924	103	7	the	the	DET
ejpam-4924	103	8	identity	identity	NOUN
ejpam-4924	103	9	(	(	PUNCT
ejpam-4924	103	10	3	3	NUM
ejpam-4924	103	11	)	)	PUNCT
ejpam-4924	103	12	and	and	CCONJ
ejpam-4924	103	13	ρ	ρ	NUM
ejpam-4924	103	14	:	:	PUNCT
ejpam-4924	103	15	a	a	DET
ejpam-4924	103	16	−→	−→	NOUN
ejpam-4924	103	17	end(m	end(m	PROPN
ejpam-4924	103	18	)	)	PUNCT
ejpam-4924	103	19	a	a	DET
ejpam-4924	103	20	linear	linear	ADJ
ejpam-4924	103	21	application	application	NOUN
ejpam-4924	103	22	.	.	PUNCT
ejpam-4924	104	1	the	the	DET
ejpam-4924	104	2	application	application	NOUN
ejpam-4924	104	3	ρ	ρ	NOUN
ejpam-4924	104	4	is	be	AUX
ejpam-4924	104	5	a	a	DET
ejpam-4924	104	6	representation	representation	NOUN
ejpam-4924	104	7	of	of	ADP
ejpam-4924	104	8	a	a	DET
ejpam-4924	104	9	if	if	NOUN
ejpam-4924	104	10	and	and	CCONJ
ejpam-4924	104	11	only	only	ADV
ejpam-4924	104	12	if	if	SCONJ
ejpam-4924	104	13	for	for	ADP
ejpam-4924	104	14	all	all	DET
ejpam-4924	104	15	a	a	PRON
ejpam-4924	104	16	,	,	PUNCT
ejpam-4924	104	17	b	b	X
ejpam-4924	104	18	∈	∈	PROPN
ejpam-4924	104	19	a	a	DET
ejpam-4924	104	20	the	the	DET
ejpam-4924	104	21	following	follow	VERB
ejpam-4924	104	22	identities	identity	NOUN
ejpam-4924	104	23	are	be	AUX
ejpam-4924	104	24	verified	verify	VERB
ejpam-4924	104	25	:	:	PUNCT
ejpam-4924	104	26	ρa4	ρa4	VERB
ejpam-4924	104	27	−	−	NUM
ejpam-4924	104	28	4ρaρa3	4ρaρa3	NUM
ejpam-4924	105	1	+	+	CCONJ
ejpam-4924	105	2	6ρ2aρa2	6ρ2aρa2	NUM
ejpam-4924	105	3	−	−	NOUN
ejpam-4924	105	4	3ρ4a	3ρ4a	NOUN
ejpam-4924	105	5	=	=	SYM
ejpam-4924	105	6	0	0	NUM
ejpam-4924	105	7	;	;	PUNCT
ejpam-4924	105	8	(	(	PUNCT
ejpam-4924	105	9	5	5	NUM
ejpam-4924	105	10	)	)	PUNCT
ejpam-4924	105	11	ρbρaρa2	ρbρaρa2	PUNCT
ejpam-4924	106	1	+	+	ADJ
ejpam-4924	106	2	2ρbρ	2ρbρ	NOUN
ejpam-4924	106	3	3	3	NUM
ejpam-4924	106	4	a+ρbρa3−4ρaρbρa2−8ρaρbρ	a+ρbρa3−4ρaρbρa2−8ρaρbρ	SYM
ejpam-4924	106	5	2	2	NUM
ejpam-4924	106	6	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	NOUN
ejpam-4924	106	7	−	−	PROPN
ejpam-4924	106	8	3ρ2aρab	3ρ2aρab	NOUN
ejpam-4924	106	9	−	−	PROPN
ejpam-4924	106	10	3ρaρa(ab	3ρaρa(ab	NUM
ejpam-4924	106	11	)	)	PUNCT
ejpam-4924	106	12	−	−	PROPN
ejpam-4924	106	13	3ρa(a(ab	3ρa(a(ab	NUM
ejpam-4924	106	14	)	)	PUNCT
ejpam-4924	106	15	)	)	PUNCT
ejpam-4924	107	1	=	=	SYM
ejpam-4924	107	2	0	0	PUNCT
ejpam-4924	107	3	(	(	PUNCT
ejpam-4924	107	4	6	6	NUM
ejpam-4924	107	5	)	)	PUNCT
ejpam-4924	107	6	where	where	SCONJ
ejpam-4924	107	7	ρa	ρa	ADP
ejpam-4924	107	8	:	:	PUNCT
ejpam-4924	107	9	=	=	SYM
ejpam-4924	107	10	ρ(a	ρ(a	PROPN
ejpam-4924	107	11	)	)	PUNCT
ejpam-4924	107	12	∈	∈	PROPN
ejpam-4924	108	1	end(m	end(m	PROPN
ejpam-4924	108	2	)	)	PUNCT
ejpam-4924	108	3	and	and	CCONJ
ejpam-4924	108	4	for	for	ADP
ejpam-4924	108	5	any	any	DET
ejpam-4924	108	6	a	a	DET
ejpam-4924	108	7	∈	∈	NOUN
ejpam-4924	108	8	a.	a.	NOUN
ejpam-4924	108	9	proof	proof	NOUN
ejpam-4924	108	10	.	.	PUNCT
ejpam-4924	109	1	the	the	DET
ejpam-4924	109	2	application	application	NOUN
ejpam-4924	109	3	ρ	ρ	NOUN
ejpam-4924	109	4	is	be	AUX
ejpam-4924	109	5	a	a	DET
ejpam-4924	109	6	representation	representation	NOUN
ejpam-4924	109	7	of	of	ADP
ejpam-4924	109	8	a	a	DET
ejpam-4924	109	9	if	if	NOUN
ejpam-4924	109	10	and	and	CCONJ
ejpam-4924	109	11	only	only	ADV
ejpam-4924	109	12	if	if	SCONJ
ejpam-4924	109	13	for	for	ADP
ejpam-4924	109	14	all	all	DET
ejpam-4924	109	15	x	x	NOUN
ejpam-4924	109	16	=	=	SYM
ejpam-4924	109	17	a+m	a+m	NUM
ejpam-4924	109	18	,	,	PUNCT
ejpam-4924	109	19	and	and	CCONJ
ejpam-4924	109	20	y	y	PROPN
ejpam-4924	109	21	=	=	PUNCT
ejpam-4924	109	22	b+	b+	X
ejpam-4924	109	23	n	n	X
ejpam-4924	109	24	∈	∈	PROPN
ejpam-4924	109	25	a⊕m	a⊕m	NOUN
ejpam-4924	109	26	,	,	PUNCT
ejpam-4924	109	27	the	the	DET
ejpam-4924	109	28	equality	equality	NOUN
ejpam-4924	109	29	(	(	PUNCT
ejpam-4924	109	30	3	3	NUM
ejpam-4924	109	31	)	)	PUNCT
ejpam-4924	109	32	is	be	AUX
ejpam-4924	109	33	satisfied	satisfied	ADJ
ejpam-4924	109	34	.	.	PUNCT
ejpam-4924	110	1	since	since	SCONJ
ejpam-4924	110	2	:	:	PUNCT
ejpam-4924	110	3	yx4	yx4	PROPN
ejpam-4924	110	4	=	=	PUNCT
ejpam-4924	110	5	a4b+	a4b+	PROPN
ejpam-4924	110	6	ρbρaρa2(m	ρbρaρa2(m	ADP
ejpam-4924	110	7	)	)	PUNCT
ejpam-4924	111	1	+	+	CCONJ
ejpam-4924	111	2	2ρbρ	2ρbρ	NUM
ejpam-4924	111	3	3	3	NUM
ejpam-4924	111	4	a(m	a(m	NOUN
ejpam-4924	111	5	)	)	PUNCT
ejpam-4924	112	1	+	+	CCONJ
ejpam-4924	112	2	ρa4(n	ρa4(n	NOUN
ejpam-4924	112	3	)	)	PUNCT
ejpam-4924	113	1	+	+	PUNCT
ejpam-4924	113	2	ρbρa3(m	ρbρa3(m	NOUN
ejpam-4924	113	3	)	)	PUNCT
ejpam-4924	113	4	;	;	PUNCT
ejpam-4924	113	5	x(yx3	x(yx3	PROPN
ejpam-4924	113	6	)	)	PUNCT
ejpam-4924	113	7	=	=	PUNCT
ejpam-4924	113	8	a(a3b	a(a3b	ADP
ejpam-4924	113	9	)	)	PUNCT
ejpam-4924	113	10	+	+	NUM
ejpam-4924	113	11	ρaρbρa2(m	ρaρbρa2(m	NOUN
ejpam-4924	113	12	)	)	PUNCT
ejpam-4924	113	13	+	+	CCONJ
ejpam-4924	113	14	2ρaρbρ	2ρaρbρ	NUM
ejpam-4924	113	15	2	2	NUM
ejpam-4924	113	16	a(m	a(m	NOUN
ejpam-4924	113	17	)	)	PUNCT
ejpam-4924	113	18	+	+	NUM
ejpam-4924	113	19	ρaρa3(n	ρaρa3(n	NOUN
ejpam-4924	113	20	)	)	PUNCT
ejpam-4924	113	21	+	+	CCONJ
ejpam-4924	113	22	ρa3b(m	ρa3b(m	NUM
ejpam-4924	113	23	)	)	PUNCT
ejpam-4924	113	24	;	;	PUNCT
ejpam-4924	113	25	x(x(yx2	x(x(yx2	PROPN
ejpam-4924	113	26	)	)	PUNCT
ejpam-4924	113	27	)	)	PUNCT
ejpam-4924	113	28	=	=	SYM
ejpam-4924	113	29	a(a(a2b	a(a(a2b	NOUN
ejpam-4924	113	30	)	)	PUNCT
ejpam-4924	113	31	)	)	PUNCT
ejpam-4924	114	1	+	+	CCONJ
ejpam-4924	114	2	2ρ2aρbρa(m	2ρ2aρbρa(m	NUM
ejpam-4924	114	3	)	)	PUNCT
ejpam-4924	115	1	+	+	NUM
ejpam-4924	115	2	ρ2aρa2(n	ρ2aρa2(n	NOUN
ejpam-4924	115	3	)	)	PUNCT
ejpam-4924	116	1	+	+	NUM
ejpam-4924	116	2	ρaρa2b(m	ρaρa2b(m	NUM
ejpam-4924	116	3	)	)	PUNCT
ejpam-4924	117	1	+	+	CCONJ
ejpam-4924	117	2	ρa(a2b)(m	ρa(a2b)(m	PROPN
ejpam-4924	117	3	)	)	PUNCT
ejpam-4924	117	4	;	;	PUNCT
ejpam-4924	117	5	h.	h.	PROPN
ejpam-4924	117	6	ouédraogo	ouédraogo	PROPN
ejpam-4924	117	7	,	,	PUNCT
ejpam-4924	117	8	a.	a.	NOUN
ejpam-4924	117	9	dembega	dembega	PROPN
ejpam-4924	117	10	,	,	PUNCT
ejpam-4924	117	11	a.	a.	PROPN
ejpam-4924	117	12	conseibo	conseibo	PROPN
ejpam-4924	117	13	/	/	SYM
ejpam-4924	117	14	eur	eur	PROPN
ejpam-4924	117	15	.	.	PUNCT
ejpam-4924	118	1	j.	j.	PROPN
ejpam-4924	118	2	pure	pure	PROPN
ejpam-4924	118	3	appl	appl	PROPN
ejpam-4924	118	4	.	.	PROPN
ejpam-4924	118	5	math	math	PROPN
ejpam-4924	118	6	,	,	PUNCT
ejpam-4924	118	7	16	16	NUM
ejpam-4924	118	8	(	(	PUNCT
ejpam-4924	118	9	4	4	NUM
ejpam-4924	118	10	)	)	PUNCT
ejpam-4924	118	11	(	(	PUNCT
ejpam-4924	118	12	2023	2023	NUM
ejpam-4924	118	13	)	)	PUNCT
ejpam-4924	118	14	,	,	PUNCT
ejpam-4924	118	15	2145	2145	NUM
ejpam-4924	118	16	-	-	SYM
ejpam-4924	118	17	2155	2155	NUM
ejpam-4924	118	18	2149	2149	NUM
ejpam-4924	118	19	x(x(x(yx	x(x(x(yx	NOUN
ejpam-4924	118	20	)	)	PUNCT
ejpam-4924	118	21	)	)	PUNCT
ejpam-4924	118	22	)	)	PUNCT
ejpam-4924	119	1	=	=	PUNCT
ejpam-4924	119	2	a(a(a(ab	a(a(a(ab	PROPN
ejpam-4924	119	3	)	)	PUNCT
ejpam-4924	119	4	)	)	PUNCT
ejpam-4924	119	5	)	)	PUNCT
ejpam-4924	120	1	+	+	CCONJ
ejpam-4924	120	2	ρ4a(n	ρ4a(n	NOUN
ejpam-4924	120	3	)	)	PUNCT
ejpam-4924	120	4	+	+	PUNCT
ejpam-4924	120	5	ρ3aρb(m	ρ3aρb(m	NUM
ejpam-4924	120	6	)	)	PUNCT
ejpam-4924	120	7	+	+	CCONJ
ejpam-4924	120	8	ρ2aρab(m	ρ2aρab(m	NUM
ejpam-4924	120	9	)	)	PUNCT
ejpam-4924	120	10	+	+	NUM
ejpam-4924	120	11	ρaρa(ab)(m	ρaρa(ab)(m	NUM
ejpam-4924	120	12	)	)	PUNCT
ejpam-4924	120	13	+	+	CCONJ
ejpam-4924	120	14	ρa(a(ab))(m	ρa(a(ab))(m	NUM
ejpam-4924	120	15	)	)	PUNCT
ejpam-4924	120	16	;	;	PUNCT
ejpam-4924	120	17	equality	equality	NOUN
ejpam-4924	120	18	(	(	PUNCT
ejpam-4924	120	19	3	3	X
ejpam-4924	120	20	)	)	PUNCT
ejpam-4924	120	21	becomes	become	VERB
ejpam-4924	120	22	:	:	PUNCT
ejpam-4924	121	1	[	[	X
ejpam-4924	121	2	a4b−4a(a3b)+6a(a(a2b))−3a(a(a(ab)))]+[ρbρaρa2	a4b−4a(a3b)+6a(a(a2b))−3a(a(a(ab)))]+[ρbρaρa2	PROPN
ejpam-4924	121	3	+	+	ADJ
ejpam-4924	121	4	2ρbρ	2ρbρ	NUM
ejpam-4924	121	5	3	3	NUM
ejpam-4924	121	6	a+ρbρa3−4ρaρbρa2−8ρaρbρ	a+ρbρa3−4ρaρbρa2−8ρaρbρ	X
ejpam-4924	121	7	2	2	NUM
ejpam-4924	121	8	a−4ρa3b	a−4ρa3b	X
ejpam-4924	121	9	+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb−3ρ2aρab−3ρaρa(ab)−3ρa(a(ab))](m)+	+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb−3ρ2aρab−3ρaρa(ab)−3ρa(a(ab))](m)+	ADJ
ejpam-4924	121	10	[	[	X
ejpam-4924	121	11	ρa4	ρa4	ADJ
ejpam-4924	121	12	−4ρaρa3	−4ρaρa3	NOUN
ejpam-4924	121	13	+	+	CCONJ
ejpam-4924	121	14	6ρ2aρa2	6ρ2aρa2	NUM
ejpam-4924	121	15	−	−	NOUN
ejpam-4924	121	16	3ρ4a](n	3ρ4a](n	NUM
ejpam-4924	121	17	)	)	PUNCT
ejpam-4924	121	18	=	=	SYM
ejpam-4924	121	19	0	0	X
ejpam-4924	121	20	.	.	PUNCT
ejpam-4924	122	1	(	(	PUNCT
ejpam-4924	122	2	7	7	NUM
ejpam-4924	122	3	)	)	PUNCT
ejpam-4924	122	4	since	since	SCONJ
ejpam-4924	122	5	a	a	PRON
ejpam-4924	122	6	and	and	CCONJ
ejpam-4924	122	7	b	b	NOUN
ejpam-4924	122	8	are	be	AUX
ejpam-4924	122	9	elements	element	NOUN
ejpam-4924	122	10	of	of	ADP
ejpam-4924	122	11	the	the	DET
ejpam-4924	122	12	algebra	algebra	NOUN
ejpam-4924	122	13	a	a	X
ejpam-4924	122	14	,	,	PUNCT
ejpam-4924	122	15	then	then	ADV
ejpam-4924	122	16	:	:	PUNCT
ejpam-4924	122	17	a4b−	a4b−	NOUN
ejpam-4924	122	18	4a(a3b	4a(a3b	NUM
ejpam-4924	122	19	)	)	PUNCT
ejpam-4924	123	1	+	+	CCONJ
ejpam-4924	123	2	6a(a(a2b))−	6a(a(a2b))−	NUM
ejpam-4924	123	3	3a(a(a(ab	3a(a(a(ab	NUM
ejpam-4924	123	4	)	)	PUNCT
ejpam-4924	123	5	)	)	PUNCT
ejpam-4924	123	6	)	)	PUNCT
ejpam-4924	124	1	=	=	PUNCT
ejpam-4924	124	2	0	0	X
ejpam-4924	124	3	.	.	PUNCT
ejpam-4924	125	1	we	we	PRON
ejpam-4924	125	2	then	then	ADV
ejpam-4924	125	3	obtain	obtain	VERB
ejpam-4924	125	4	,	,	PUNCT
ejpam-4924	125	5	[	[	X
ejpam-4924	125	6	ρbρaρa2	ρbρaρa2	X
ejpam-4924	125	7	+	+	ADJ
ejpam-4924	125	8	2ρbρ	2ρbρ	NOUN
ejpam-4924	125	9	3	3	NUM
ejpam-4924	125	10	a+ρbρa3−4ρaρbρa2−8ρaρbρ	a+ρbρa3−4ρaρbρa2−8ρaρbρ	SYM
ejpam-4924	125	11	2	2	NUM
ejpam-4924	125	12	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	NOUN
ejpam-4924	125	13	−	−	PROPN
ejpam-4924	125	14	3ρ2aρab	3ρ2aρab	NOUN
ejpam-4924	125	15	−	−	PROPN
ejpam-4924	125	16	3ρaρa(ab	3ρaρa(ab	NUM
ejpam-4924	125	17	)	)	PUNCT
ejpam-4924	125	18	−	−	PROPN
ejpam-4924	126	1	3ρa(a(ab))](m	3ρa(a(ab))](m	NUM
ejpam-4924	126	2	)	)	PUNCT
ejpam-4924	126	3	+	+	CCONJ
ejpam-4924	127	1	[	[	X
ejpam-4924	127	2	ρa4	ρa4	INTJ
ejpam-4924	127	3	−	−	NOUN
ejpam-4924	127	4	4ρaρa3	4ρaρa3	NUM
ejpam-4924	127	5	+	+	CCONJ
ejpam-4924	127	6	6ρ2aρa2	6ρ2aρa2	NUM
ejpam-4924	127	7	−	−	NOUN
ejpam-4924	127	8	3ρ4a](n	3ρ4a](n	NUM
ejpam-4924	127	9	)	)	PUNCT
ejpam-4924	127	10	=	=	SYM
ejpam-4924	127	11	0	0	X
ejpam-4924	127	12	.	.	PUNCT
ejpam-4924	128	1	(	(	PUNCT
ejpam-4924	128	2	8)	8)	NUM
ejpam-4924	128	3	then	then	ADV
ejpam-4924	128	4	finally	finally	ADV
ejpam-4924	128	5	:	:	PUNCT
ejpam-4924	128	6	ρa4	ρa4	VERB
ejpam-4924	128	7	−	−	NUM
ejpam-4924	128	8	4ρaρa3	4ρaρa3	NUM
ejpam-4924	129	1	+	+	CCONJ
ejpam-4924	129	2	6ρ2aρa2	6ρ2aρa2	NUM
ejpam-4924	129	3	−	−	NOUN
ejpam-4924	129	4	3ρ4a	3ρ4a	NOUN
ejpam-4924	129	5	=	=	SYM
ejpam-4924	129	6	0	0	NUM
ejpam-4924	130	1	;	;	PUNCT
ejpam-4924	130	2	ρbρaρa2	ρbρaρa2	PROPN
ejpam-4924	130	3	+	+	ADJ
ejpam-4924	130	4	2ρbρ	2ρbρ	NUM
ejpam-4924	130	5	3	3	NUM
ejpam-4924	130	6	a+ρbρa3−4ρaρbρa2−8ρaρbρ	a+ρbρa3−4ρaρbρa2−8ρaρbρ	SYM
ejpam-4924	130	7	2	2	NUM
ejpam-4924	130	8	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	a−4ρa3b+12ρ2aρbρa+6ρaρa2b+6ρa(a2b)−3ρ3aρb	NOUN
ejpam-4924	130	9	−	−	PROPN
ejpam-4924	130	10	3ρ2aρab	3ρ2aρab	NOUN
ejpam-4924	130	11	−	−	PROPN
ejpam-4924	130	12	3ρaρa(ab	3ρaρa(ab	NUM
ejpam-4924	130	13	)	)	PUNCT
ejpam-4924	130	14	−	−	PROPN
ejpam-4924	130	15	3ρa(a(ab	3ρa(a(ab	NUM
ejpam-4924	130	16	)	)	PUNCT
ejpam-4924	130	17	)	)	PUNCT
ejpam-4924	131	1	=	=	PUNCT
ejpam-4924	131	2	0	0	X
ejpam-4924	131	3	.	.	PUNCT
ejpam-4924	132	1	proposition	proposition	NOUN
ejpam-4924	132	2	4.2	4.2	NUM
ejpam-4924	132	3	.	.	PUNCT
ejpam-4924	133	1	let	let	VERB
ejpam-4924	133	2	a	a	DET
ejpam-4924	133	3	be	be	AUX
ejpam-4924	133	4	an	an	DET
ejpam-4924	133	5	algebra	algebra	NOUN
ejpam-4924	133	6	verifying	verify	VERB
ejpam-4924	133	7	the	the	DET
ejpam-4924	133	8	identity	identity	NOUN
ejpam-4924	133	9	(	(	PUNCT
ejpam-4924	133	10	3	3	NUM
ejpam-4924	133	11	)	)	PUNCT
ejpam-4924	133	12	.	.	PUNCT
ejpam-4924	134	1	suppose	suppose	VERB
ejpam-4924	134	2	that	that	SCONJ
ejpam-4924	134	3	a	a	PRON
ejpam-4924	134	4	has	have	VERB
ejpam-4924	134	5	an	an	DET
ejpam-4924	134	6	idempotent	idempotent	NOUN
ejpam-4924	134	7	e	e	NOUN
ejpam-4924	134	8	̸=	̸=	PROPN
ejpam-4924	134	9	0	0	NUM
ejpam-4924	134	10	.	.	PUNCT
ejpam-4924	135	1	let	let	VERB
ejpam-4924	135	2	ρ	ρ	NOUN
ejpam-4924	135	3	:	:	PUNCT
ejpam-4924	135	4	a	a	DET
ejpam-4924	135	5	−→	−→	NOUN
ejpam-4924	135	6	end(m	end(m	PROPN
ejpam-4924	135	7	)	)	PUNCT
ejpam-4924	135	8	be	be	VERB
ejpam-4924	135	9	a	a	DET
ejpam-4924	135	10	representation	representation	NOUN
ejpam-4924	135	11	of	of	ADP
ejpam-4924	135	12	a.	a.	NOUN
ejpam-4924	135	13	then	then	ADV
ejpam-4924	135	14	:	:	PUNCT
ejpam-4924	135	15	m	m	VERB
ejpam-4924	135	16	=	=	VERB
ejpam-4924	135	17	m0	m0	PROPN
ejpam-4924	135	18	⊕m1	⊕m1	PUNCT
ejpam-4924	135	19	⊕mλ1	⊕mλ1	NOUN
ejpam-4924	135	20	⊕mλ2	⊕mλ2	NOUN
ejpam-4924	135	21	,	,	PUNCT
ejpam-4924	135	22	with	with	ADP
ejpam-4924	135	23	mi	mi	PROPN
ejpam-4924	135	24	=	=	PUNCT
ejpam-4924	135	25	{	{	PUNCT
ejpam-4924	135	26	m	m	PROPN
ejpam-4924	135	27	∈	∈	PROPN
ejpam-4924	135	28	m	m	NOUN
ejpam-4924	135	29	,	,	PUNCT
ejpam-4924	135	30	ρe(m	ρe(m	NUM
ejpam-4924	135	31	)	)	PUNCT
ejpam-4924	136	1	=	=	PUNCT
ejpam-4924	136	2	i	i	PRON
ejpam-4924	136	3	m	m	VERB
ejpam-4924	136	4	}	}	PUNCT
ejpam-4924	136	5	for	for	ADP
ejpam-4924	136	6	i	i	PROPN
ejpam-4924	136	7	∈	∈	PROPN
ejpam-4924	136	8	{	{	PUNCT
ejpam-4924	136	9	0	0	NUM
ejpam-4924	136	10	,	,	PUNCT
ejpam-4924	136	11	1	1	NUM
ejpam-4924	136	12	,	,	PUNCT
ejpam-4924	136	13	λ1	λ1	ADJ
ejpam-4924	136	14	,	,	PUNCT
ejpam-4924	136	15	λ2	λ2	NOUN
ejpam-4924	136	16	}	}	PUNCT
ejpam-4924	136	17	where	where	SCONJ
ejpam-4924	136	18	λ1	λ1	PROPN
ejpam-4924	136	19	=	=	SYM
ejpam-4924	136	20	3+i	3+i	NUM
ejpam-4924	136	21	√	√	NUM
ejpam-4924	136	22	3	3	NUM
ejpam-4924	136	23	6	6	NUM
ejpam-4924	136	24	and	and	CCONJ
ejpam-4924	136	25	λ2	λ2	NOUN
ejpam-4924	136	26	=	=	SYM
ejpam-4924	136	27	3−i	3−i	NUM
ejpam-4924	136	28	√	√	NUM
ejpam-4924	136	29	3	3	NUM
ejpam-4924	136	30	6	6	NUM
ejpam-4924	136	31	are	be	AUX
ejpam-4924	136	32	roots	root	NOUN
ejpam-4924	136	33	of	of	ADP
ejpam-4924	136	34	the	the	DET
ejpam-4924	136	35	polynomial	polynomial	ADJ
ejpam-4924	136	36	3t2	3t2	NUM
ejpam-4924	136	37	−	−	NOUN
ejpam-4924	136	38	3t+	3t+	NUM
ejpam-4924	136	39	1	1	NUM
ejpam-4924	136	40	.	.	PUNCT
ejpam-4924	137	1	proof	proof	NOUN
ejpam-4924	137	2	.	.	PUNCT
ejpam-4924	138	1	putting	put	VERB
ejpam-4924	138	2	a	a	DET
ejpam-4924	138	3	=	=	X
ejpam-4924	138	4	e	e	NOUN
ejpam-4924	138	5	into	into	ADP
ejpam-4924	138	6	the	the	DET
ejpam-4924	138	7	identity	identity	NOUN
ejpam-4924	138	8	(	(	PUNCT
ejpam-4924	138	9	5	5	NUM
ejpam-4924	138	10	)	)	PUNCT
ejpam-4924	138	11	,	,	PUNCT
ejpam-4924	138	12	we	we	PRON
ejpam-4924	138	13	obtain	obtain	VERB
ejpam-4924	138	14	−ρe(ρe	−ρe(ρe	X
ejpam-4924	138	15	−	−	PROPN
ejpam-4924	138	16	i)(3ρ2e	i)(3ρ2e	ADV
ejpam-4924	138	17	−	−	NOUN
ejpam-4924	138	18	3ρe	3ρe	ADJ
ejpam-4924	139	1	+	+	PUNCT
ejpam-4924	139	2	i	i	NOUN
ejpam-4924	139	3	)	)	PUNCT
ejpam-4924	140	1	=	=	PUNCT
ejpam-4924	140	2	0	0	X
ejpam-4924	140	3	.	.	PUNCT
ejpam-4924	141	1	the	the	DET
ejpam-4924	141	2	kernel	kernel	PROPN
ejpam-4924	141	3	lemma	lemma	PROPN
ejpam-4924	141	4	gives	give	VERB
ejpam-4924	141	5	us	we	PRON
ejpam-4924	141	6	:	:	PUNCT
ejpam-4924	141	7	m	m	VERB
ejpam-4924	141	8	=	=	SYM
ejpam-4924	141	9	m0⊕m1⊕mλ1	m0⊕m1⊕mλ1	PROPN
ejpam-4924	141	10	⊕mλ2	⊕mλ2	ADV
ejpam-4924	141	11	,	,	PUNCT
ejpam-4924	141	12	with	with	ADP
ejpam-4924	141	13	mi	mi	PROPN
ejpam-4924	141	14	=	=	PUNCT
ejpam-4924	141	15	{	{	PUNCT
ejpam-4924	141	16	m	m	PROPN
ejpam-4924	141	17	∈	∈	PROPN
ejpam-4924	141	18	m	m	NOUN
ejpam-4924	141	19	|ρe(m	|ρe(m	NUM
ejpam-4924	141	20	)	)	PUNCT
ejpam-4924	142	1	=	=	PUNCT
ejpam-4924	143	1	i	i	PRON
ejpam-4924	143	2	m	m	VERB
ejpam-4924	143	3	}	}	PUNCT
ejpam-4924	143	4	for	for	ADP
ejpam-4924	143	5	i	i	PROPN
ejpam-4924	143	6	∈	∈	PROPN
ejpam-4924	143	7	{	{	PUNCT
ejpam-4924	143	8	0	0	NUM
ejpam-4924	143	9	,	,	PUNCT
ejpam-4924	143	10	1	1	NUM
ejpam-4924	143	11	,	,	PUNCT
ejpam-4924	143	12	λ1	λ1	ADJ
ejpam-4924	143	13	,	,	PUNCT
ejpam-4924	143	14	λ2	λ2	PROPN
ejpam-4924	143	15	}	}	PUNCT
ejpam-4924	143	16	.	.	PUNCT
ejpam-4924	144	1	let	let	VERB
ejpam-4924	144	2	’s	’s	PRON
ejpam-4924	144	3	study	study	VERB
ejpam-4924	144	4	the	the	DET
ejpam-4924	144	5	action	action	NOUN
ejpam-4924	144	6	of	of	ADP
ejpam-4924	144	7	a	a	PRON
ejpam-4924	144	8	on	on	ADP
ejpam-4924	144	9	m	m	PRON
ejpam-4924	144	10	.	.	PUNCT
ejpam-4924	145	1	in	in	ADP
ejpam-4924	145	2	this	this	DET
ejpam-4924	145	3	section	section	NOUN
ejpam-4924	145	4	,	,	PUNCT
ejpam-4924	145	5	we	we	PRON
ejpam-4924	145	6	’ll	’ll	AUX
ejpam-4924	145	7	focus	focus	VERB
ejpam-4924	145	8	on	on	ADP
ejpam-4924	145	9	the	the	DET
ejpam-4924	145	10	products	product	NOUN
ejpam-4924	145	11	of	of	ADP
ejpam-4924	145	12	ai.mj	ai.mj	PROPN
ejpam-4924	145	13	,	,	PUNCT
ejpam-4924	145	14	for	for	ADP
ejpam-4924	145	15	i	i	PRON
ejpam-4924	145	16	;	;	PUNCT
ejpam-4924	145	17	j	j	PROPN
ejpam-4924	145	18	∈	∈	PROPN
ejpam-4924	145	19	{	{	PUNCT
ejpam-4924	145	20	0	0	NUM
ejpam-4924	145	21	,	,	PUNCT
ejpam-4924	145	22	1	1	NUM
ejpam-4924	145	23	,	,	PUNCT
ejpam-4924	145	24	λ1	λ1	ADJ
ejpam-4924	145	25	,	,	PUNCT
ejpam-4924	145	26	λ2	λ2	PROPN
ejpam-4924	145	27	}	}	PUNCT
ejpam-4924	145	28	.	.	PUNCT
ejpam-4924	146	1	theorem	theorem	VERB
ejpam-4924	146	2	4.3	4.3	NUM
ejpam-4924	146	3	.	.	PUNCT
ejpam-4924	147	1	let	let	VERB
ejpam-4924	147	2	a	a	DET
ejpam-4924	147	3	be	be	AUX
ejpam-4924	147	4	an	an	DET
ejpam-4924	147	5	algebra	algebra	NOUN
ejpam-4924	147	6	verifying	verify	VERB
ejpam-4924	147	7	the	the	DET
ejpam-4924	147	8	identity	identity	NOUN
ejpam-4924	147	9	(	(	PUNCT
ejpam-4924	147	10	3	3	X
ejpam-4924	147	11	)	)	PUNCT
ejpam-4924	147	12	admitting	admit	VERB
ejpam-4924	147	13	an	an	DET
ejpam-4924	147	14	idempotent	idempotent	NOUN
ejpam-4924	147	15	e	e	VERB
ejpam-4924	147	16	̸=	̸=	PROPN
ejpam-4924	147	17	0	0	NUM
ejpam-4924	147	18	.	.	PUNCT
ejpam-4924	148	1	let	let	VERB
ejpam-4924	148	2	ρ	ρ	NOUN
ejpam-4924	148	3	:	:	PUNCT
ejpam-4924	148	4	a	a	DET
ejpam-4924	148	5	−→	−→	NOUN
ejpam-4924	148	6	end(m	end(m	PROPN
ejpam-4924	148	7	)	)	PUNCT
ejpam-4924	148	8	be	be	VERB
ejpam-4924	148	9	a	a	DET
ejpam-4924	148	10	representation	representation	NOUN
ejpam-4924	148	11	of	of	ADP
ejpam-4924	148	12	a.	a.	NOUN
ejpam-4924	148	13	then	then	ADV
ejpam-4924	148	14	the	the	DET
ejpam-4924	148	15	action	action	NOUN
ejpam-4924	148	16	of	of	ADP
ejpam-4924	148	17	a	a	PRON
ejpam-4924	148	18	on	on	ADP
ejpam-4924	148	19	m	m	PROPN
ejpam-4924	148	20	satisfies	satisfie	NOUN
ejpam-4924	148	21	the	the	DET
ejpam-4924	148	22	following	follow	VERB
ejpam-4924	148	23	relations	relation	NOUN
ejpam-4924	148	24	:	:	PUNCT
ejpam-4924	148	25	i	i	X
ejpam-4924	148	26	)	)	PUNCT
ejpam-4924	148	27	ai.mλj	ai.mλj	PROPN
ejpam-4924	148	28	⊆	⊆	NUM
ejpam-4924	148	29	mλj	mλj	NOUN
ejpam-4924	148	30	,	,	PUNCT
ejpam-4924	148	31	where	where	SCONJ
ejpam-4924	148	32	i	i	PRON
ejpam-4924	148	33	∈	∈	PROPN
ejpam-4924	148	34	{	{	PUNCT
ejpam-4924	148	35	0	0	NUM
ejpam-4924	148	36	;	;	PUNCT
ejpam-4924	148	37	1	1	NUM
ejpam-4924	148	38	}	}	PUNCT
ejpam-4924	148	39	and	and	CCONJ
ejpam-4924	148	40	j	j	PROPN
ejpam-4924	148	41	∈	∈	PROPN
ejpam-4924	148	42	{	{	PUNCT
ejpam-4924	148	43	1	1	NUM
ejpam-4924	148	44	;	;	PUNCT
ejpam-4924	148	45	2	2	NUM
ejpam-4924	148	46	}	}	PUNCT
ejpam-4924	148	47	;	;	PUNCT
ejpam-4924	148	48	ii	ii	X
ejpam-4924	148	49	)	)	PUNCT
ejpam-4924	148	50	aλj	aλj	PROPN
ejpam-4924	148	51	.mi	.mi	PROPN
ejpam-4924	149	1	⊆	⊆	NUM
ejpam-4924	149	2	mλj	mλj	NOUN
ejpam-4924	149	3	,	,	PUNCT
ejpam-4924	149	4	where	where	SCONJ
ejpam-4924	149	5	i	i	PRON
ejpam-4924	149	6	∈	∈	PROPN
ejpam-4924	149	7	{	{	PUNCT
ejpam-4924	149	8	0	0	NUM
ejpam-4924	149	9	,	,	PUNCT
ejpam-4924	149	10	1	1	NUM
ejpam-4924	149	11	}	}	PUNCT
ejpam-4924	149	12	and	and	CCONJ
ejpam-4924	149	13	j	j	PROPN
ejpam-4924	149	14	∈	∈	PROPN
ejpam-4924	149	15	{	{	PUNCT
ejpam-4924	149	16	1	1	NUM
ejpam-4924	149	17	,	,	PUNCT
ejpam-4924	149	18	2	2	NUM
ejpam-4924	149	19	}	}	PUNCT
ejpam-4924	149	20	;	;	PUNCT
ejpam-4924	149	21	h.	h.	PROPN
ejpam-4924	149	22	ouédraogo	ouédraogo	PROPN
ejpam-4924	149	23	,	,	PUNCT
ejpam-4924	149	24	a.	a.	NOUN
ejpam-4924	149	25	dembega	dembega	PROPN
ejpam-4924	149	26	,	,	PUNCT
ejpam-4924	149	27	a.	a.	PROPN
ejpam-4924	149	28	conseibo	conseibo	PROPN
ejpam-4924	149	29	/	/	SYM
ejpam-4924	149	30	eur	eur	PROPN
ejpam-4924	149	31	.	.	PUNCT
ejpam-4924	150	1	j.	j.	PROPN
ejpam-4924	150	2	pure	pure	PROPN
ejpam-4924	150	3	appl	appl	PROPN
ejpam-4924	150	4	.	.	PROPN
ejpam-4924	150	5	math	math	PROPN
ejpam-4924	150	6	,	,	PUNCT
ejpam-4924	150	7	16	16	NUM
ejpam-4924	150	8	(	(	PUNCT
ejpam-4924	150	9	4	4	NUM
ejpam-4924	150	10	)	)	PUNCT
ejpam-4924	150	11	(	(	PUNCT
ejpam-4924	150	12	2023	2023	NUM
ejpam-4924	150	13	)	)	PUNCT
ejpam-4924	150	14	,	,	PUNCT
ejpam-4924	150	15	2145	2145	NUM
ejpam-4924	150	16	-	-	SYM
ejpam-4924	150	17	2155	2155	NUM
ejpam-4924	150	18	2150	2150	NUM
ejpam-4924	150	19	iii	iii	NOUN
ejpam-4924	150	20	)	)	PUNCT
ejpam-4924	150	21	aλi	aλi	NOUN
ejpam-4924	150	22	.mλj	.mλj	PUNCT
ejpam-4924	151	1	=	=	PRON
ejpam-4924	151	2	{	{	PUNCT
ejpam-4924	151	3	0	0	NUM
ejpam-4924	151	4	}	}	PUNCT
ejpam-4924	151	5	,	,	PUNCT
ejpam-4924	151	6	with	with	ADP
ejpam-4924	151	7	i	i	PRON
ejpam-4924	151	8	,	,	PUNCT
ejpam-4924	151	9	j	j	PROPN
ejpam-4924	151	10	∈	∈	PROPN
ejpam-4924	151	11	{	{	PUNCT
ejpam-4924	151	12	1	1	NUM
ejpam-4924	151	13	,	,	PUNCT
ejpam-4924	151	14	2	2	NUM
ejpam-4924	151	15	}	}	PUNCT
ejpam-4924	151	16	;	;	PUNCT
ejpam-4924	151	17	iv	iv	X
ejpam-4924	151	18	)	)	PUNCT
ejpam-4924	151	19	ai.mi	ai.mi	PROPN
ejpam-4924	151	20	⊆	⊆	NUM
ejpam-4924	151	21	mi	mi	NOUN
ejpam-4924	151	22	with	with	ADP
ejpam-4924	151	23	i	i	PRON
ejpam-4924	151	24	∈	∈	PROPN
ejpam-4924	151	25	{	{	PUNCT
ejpam-4924	151	26	0	0	NUM
ejpam-4924	151	27	,	,	PUNCT
ejpam-4924	151	28	1	1	NUM
ejpam-4924	151	29	}	}	PUNCT
ejpam-4924	151	30	;	;	PUNCT
ejpam-4924	151	31	v	v	X
ejpam-4924	151	32	)	)	PUNCT
ejpam-4924	151	33	ai.mj	ai.mj	PROPN
ejpam-4924	151	34	=	=	SYM
ejpam-4924	151	35	{	{	PUNCT
ejpam-4924	151	36	0	0	NUM
ejpam-4924	151	37	}	}	PUNCT
ejpam-4924	151	38	with	with	ADP
ejpam-4924	151	39	i	i	PRON
ejpam-4924	151	40	,	,	PUNCT
ejpam-4924	151	41	j	j	PROPN
ejpam-4924	151	42	∈	∈	PROPN
ejpam-4924	151	43	{	{	PUNCT
ejpam-4924	151	44	0	0	NUM
ejpam-4924	151	45	,	,	PUNCT
ejpam-4924	151	46	1	1	NUM
ejpam-4924	151	47	}	}	PUNCT
ejpam-4924	151	48	,	,	PUNCT
ejpam-4924	151	49	i	i	PRON
ejpam-4924	151	50	̸=	̸=	PROPN
ejpam-4924	151	51	j.	j.	PROPN
ejpam-4924	151	52	let	let	VERB
ejpam-4924	151	53	a	a	DET
ejpam-4924	151	54	=	=	SYM
ejpam-4924	151	55	a0	a0	PROPN
ejpam-4924	151	56	⊕	⊕	PROPN
ejpam-4924	151	57	a1	a1	PROPN
ejpam-4924	151	58	⊕	⊕	PROPN
ejpam-4924	151	59	aλ1	aλ1	PROPN
ejpam-4924	151	60	⊕	⊕	PROPN
ejpam-4924	151	61	aλ2	aλ2	PROPN
ejpam-4924	151	62	be	be	AUX
ejpam-4924	151	63	the	the	DET
ejpam-4924	151	64	peirce	peirce	NOUN
ejpam-4924	151	65	decomposition	decomposition	NOUN
ejpam-4924	151	66	of	of	ADP
ejpam-4924	151	67	an	an	DET
ejpam-4924	151	68	algebra	algebra	NOUN
ejpam-4924	151	69	satisfying	satisfy	VERB
ejpam-4924	151	70	(	(	PUNCT
ejpam-4924	151	71	3	3	NUM
ejpam-4924	151	72	)	)	PUNCT
ejpam-4924	151	73	relative	relative	ADJ
ejpam-4924	151	74	to	to	ADP
ejpam-4924	151	75	an	an	DET
ejpam-4924	151	76	idempotent	idempotent	ADJ
ejpam-4924	151	77	e	e	NOUN
ejpam-4924	151	78	and	and	CCONJ
ejpam-4924	151	79	that	that	PRON
ejpam-4924	151	80	of	of	ADP
ejpam-4924	151	81	the	the	DET
ejpam-4924	151	82	modulus	modulus	ADJ
ejpam-4924	151	83	m	m	PROPN
ejpam-4924	151	84	=	=	SYM
ejpam-4924	151	85	m0	m0	PROPN
ejpam-4924	151	86	⊕	⊕	PROPN
ejpam-4924	151	87	m1	m1	PROPN
ejpam-4924	151	88	⊕	⊕	PROPN
ejpam-4924	151	89	mλ1	mλ1	NOUN
ejpam-4924	152	1	⊕	⊕	PROPN
ejpam-4924	152	2	mλ2	mλ2	PROPN
ejpam-4924	152	3	then	then	ADV
ejpam-4924	152	4	the	the	DET
ejpam-4924	152	5	peirce	peirce	NOUN
ejpam-4924	152	6	decomposition	decomposition	NOUN
ejpam-4924	152	7	of	of	ADP
ejpam-4924	152	8	the	the	DET
ejpam-4924	152	9	extension	extension	NOUN
ejpam-4924	152	10	s	s	VERB
ejpam-4924	152	11	is	be	AUX
ejpam-4924	152	12	s	s	PART
ejpam-4924	152	13	=	=	PROPN
ejpam-4924	152	14	s0	s0	PROPN
ejpam-4924	152	15	⊕	⊕	PROPN
ejpam-4924	152	16	s1	s1	PROPN
ejpam-4924	152	17	⊕	⊕	PROPN
ejpam-4924	152	18	sλ1	sλ1	PROPN
ejpam-4924	152	19	⊕	⊕	PROPN
ejpam-4924	153	1	sλ2	sλ2	NOUN
ejpam-4924	153	2	where	where	SCONJ
ejpam-4924	153	3	sk	sk	VERB
ejpam-4924	153	4	=	=	PUNCT
ejpam-4924	153	5	{	{	PUNCT
ejpam-4924	153	6	a	a	PROPN
ejpam-4924	153	7	+	+	NOUN
ejpam-4924	153	8	m	m	VERB
ejpam-4924	153	9	∈	∈	NOUN
ejpam-4924	153	10	s	s	NOUN
ejpam-4924	153	11	:	:	PUNCT
ejpam-4924	153	12	e(a	e(a	PROPN
ejpam-4924	153	13	+	+	CCONJ
ejpam-4924	153	14	m	m	X
ejpam-4924	153	15	)	)	PUNCT
ejpam-4924	154	1	=	=	SYM
ejpam-4924	154	2	k(a	k(a	NOUN
ejpam-4924	154	3	+	+	CCONJ
ejpam-4924	154	4	m	m	NOUN
ejpam-4924	154	5	)	)	PUNCT
ejpam-4924	154	6	}	}	PUNCT
ejpam-4924	154	7	and	and	CCONJ
ejpam-4924	154	8	k	k	PROPN
ejpam-4924	154	9	=	=	X
ejpam-4924	154	10	{	{	PUNCT
ejpam-4924	154	11	0	0	NUM
ejpam-4924	154	12	,	,	PUNCT
ejpam-4924	154	13	1	1	NUM
ejpam-4924	154	14	,	,	PUNCT
ejpam-4924	154	15	λ1	λ1	ADJ
ejpam-4924	154	16	,	,	PUNCT
ejpam-4924	154	17	λ2	λ2	NOUN
ejpam-4924	154	18	}	}	PUNCT
ejpam-4924	154	19	such	such	ADJ
ejpam-4924	154	20	that	that	SCONJ
ejpam-4924	154	21	the	the	DET
ejpam-4924	154	22	following	follow	VERB
ejpam-4924	154	23	result	result	NOUN
ejpam-4924	154	24	is	be	AUX
ejpam-4924	154	25	verified	verify	VERB
ejpam-4924	154	26	.	.	PUNCT
ejpam-4924	155	1	proposition	proposition	NOUN
ejpam-4924	155	2	4.4	4.4	NUM
ejpam-4924	155	3	.	.	PUNCT
ejpam-4924	156	1	the	the	DET
ejpam-4924	156	2	subspaces	subspace	NOUN
ejpam-4924	156	3	si	si	X
ejpam-4924	156	4	of	of	ADP
ejpam-4924	156	5	the	the	DET
ejpam-4924	156	6	extension	extension	NOUN
ejpam-4924	156	7	s	s	PART
ejpam-4924	156	8	satisfy	satisfy	NOUN
ejpam-4924	156	9	the	the	DET
ejpam-4924	156	10	relations	relation	NOUN
ejpam-4924	156	11	:	:	PUNCT
ejpam-4924	156	12	i	i	X
ejpam-4924	156	13	)	)	PUNCT
ejpam-4924	156	14	si.sλj	si.sλj	PROPN
ejpam-4924	156	15	⊆	⊆	NUM
ejpam-4924	156	16	sλj	sλj	NOUN
ejpam-4924	156	17	,	,	PUNCT
ejpam-4924	156	18	and	and	CCONJ
ejpam-4924	156	19	sλj	sλj	VERB
ejpam-4924	156	20	.si	.si	PUNCT
ejpam-4924	157	1	⊆	⊆	NUM
ejpam-4924	157	2	sλj	sλj	VERB
ejpam-4924	157	3	with	with	ADP
ejpam-4924	157	4	i	i	PROPN
ejpam-4924	157	5	∈	∈	PROPN
ejpam-4924	157	6	{	{	PUNCT
ejpam-4924	157	7	0	0	NUM
ejpam-4924	157	8	,	,	PUNCT
ejpam-4924	157	9	1	1	NUM
ejpam-4924	157	10	}	}	PUNCT
ejpam-4924	157	11	and	and	CCONJ
ejpam-4924	157	12	j	j	PROPN
ejpam-4924	157	13	∈	∈	PROPN
ejpam-4924	157	14	{	{	PUNCT
ejpam-4924	157	15	1	1	NUM
ejpam-4924	157	16	,	,	PUNCT
ejpam-4924	157	17	2	2	NUM
ejpam-4924	157	18	}	}	PUNCT
ejpam-4924	157	19	;	;	PUNCT
ejpam-4924	157	20	ii	ii	X
ejpam-4924	157	21	)	)	PUNCT
ejpam-4924	157	22	sλi	sλi	NOUN
ejpam-4924	157	23	.sλj	.sλj	PUNCT
ejpam-4924	157	24	=	=	PUNCT
ejpam-4924	157	25	{	{	PUNCT
ejpam-4924	157	26	0	0	NUM
ejpam-4924	157	27	}	}	PUNCT
ejpam-4924	157	28	,	,	PUNCT
ejpam-4924	157	29	with	with	ADP
ejpam-4924	157	30	i	i	PRON
ejpam-4924	157	31	,	,	PUNCT
ejpam-4924	157	32	j	j	PROPN
ejpam-4924	157	33	∈	∈	PROPN
ejpam-4924	157	34	{	{	PUNCT
ejpam-4924	157	35	1	1	NUM
ejpam-4924	157	36	,	,	PUNCT
ejpam-4924	157	37	2	2	NUM
ejpam-4924	157	38	}	}	PUNCT
ejpam-4924	157	39	;	;	PUNCT
ejpam-4924	157	40	iii	iii	X
ejpam-4924	157	41	)	)	PUNCT
ejpam-4924	157	42	si.si	si.si	NOUN
ejpam-4924	157	43	⊆	⊆	NUM
ejpam-4924	157	44	si	si	NOUN
ejpam-4924	157	45	with	with	ADP
ejpam-4924	157	46	i	i	PRON
ejpam-4924	157	47	∈	∈	PROPN
ejpam-4924	157	48	{	{	PUNCT
ejpam-4924	157	49	0	0	NUM
ejpam-4924	157	50	,	,	PUNCT
ejpam-4924	157	51	1	1	NUM
ejpam-4924	157	52	}	}	PUNCT
ejpam-4924	157	53	;	;	PUNCT
ejpam-4924	157	54	iv	iv	X
ejpam-4924	157	55	)	)	PUNCT
ejpam-4924	157	56	si.sj	si.sj	PROPN
ejpam-4924	157	57	=	=	SYM
ejpam-4924	157	58	{	{	PUNCT
ejpam-4924	157	59	0	0	NUM
ejpam-4924	157	60	}	}	PUNCT
ejpam-4924	157	61	with	with	ADP
ejpam-4924	157	62	i	i	PRON
ejpam-4924	157	63	,	,	PUNCT
ejpam-4924	157	64	j	j	PROPN
ejpam-4924	157	65	∈	∈	PROPN
ejpam-4924	157	66	{	{	PUNCT
ejpam-4924	157	67	0	0	NUM
ejpam-4924	157	68	,	,	PUNCT
ejpam-4924	157	69	1	1	NUM
ejpam-4924	157	70	}	}	PUNCT
ejpam-4924	157	71	,	,	PUNCT
ejpam-4924	157	72	i	i	PRON
ejpam-4924	157	73	̸=	̸=	PROPN
ejpam-4924	157	74	j.	j.	PROPN
ejpam-4924	157	75	proof	proof	PROPN
ejpam-4924	157	76	.	.	PUNCT
ejpam-4924	158	1	this	this	PRON
ejpam-4924	158	2	follows	follow	VERB
ejpam-4924	158	3	from	from	ADP
ejpam-4924	158	4	the	the	DET
ejpam-4924	158	5	fact	fact	NOUN
ejpam-4924	158	6	that	that	SCONJ
ejpam-4924	158	7	the	the	DET
ejpam-4924	158	8	algebra	algebra	NOUN
ejpam-4924	158	9	s	s	VERB
ejpam-4924	158	10	must	must	AUX
ejpam-4924	158	11	belong	belong	VERB
ejpam-4924	158	12	to	to	ADP
ejpam-4924	158	13	the	the	DET
ejpam-4924	158	14	same	same	ADJ
ejpam-4924	158	15	class	class	NOUN
ejpam-4924	158	16	as	as	ADP
ejpam-4924	158	17	a	a	PRON
ejpam-4924	158	18	,	,	PUNCT
ejpam-4924	158	19	i.e	i.e	CCONJ
ejpam-4924	158	20	it	it	PRON
ejpam-4924	158	21	must	must	AUX
ejpam-4924	158	22	verify	verify	VERB
ejpam-4924	158	23	the	the	DET
ejpam-4924	158	24	identity	identity	NOUN
ejpam-4924	158	25	(	(	PUNCT
ejpam-4924	158	26	3	3	NUM
ejpam-4924	158	27	)	)	PUNCT
ejpam-4924	158	28	.	.	PUNCT
ejpam-4924	159	1	consequently	consequently	ADV
ejpam-4924	159	2	,	,	PUNCT
ejpam-4924	159	3	its	its	PRON
ejpam-4924	159	4	subspaces	subspace	NOUN
ejpam-4924	159	5	verify	verify	VERB
ejpam-4924	159	6	the	the	DET
ejpam-4924	159	7	same	same	ADJ
ejpam-4924	159	8	properties	property	NOUN
ejpam-4924	159	9	as	as	ADP
ejpam-4924	159	10	those	those	PRON
ejpam-4924	159	11	of	of	ADP
ejpam-4924	159	12	a.	a.	NOUN
ejpam-4924	159	13	4.2	4.2	NUM
ejpam-4924	159	14	.	.	PUNCT
ejpam-4924	160	1	irreducible	irreducible	ADJ
ejpam-4924	160	2	representations	representation	NOUN
ejpam-4924	160	3	as	as	ADP
ejpam-4924	160	4	in	in	ADP
ejpam-4924	160	5	the	the	DET
ejpam-4924	160	6	case	case	NOUN
ejpam-4924	160	7	of	of	ADP
ejpam-4924	160	8	groups	group	NOUN
ejpam-4924	160	9	,	,	PUNCT
ejpam-4924	160	10	rings	ring	NOUN
ejpam-4924	160	11	or	or	CCONJ
ejpam-4924	160	12	vector	vector	NOUN
ejpam-4924	160	13	spaces	space	NOUN
ejpam-4924	160	14	,	,	PUNCT
ejpam-4924	160	15	a	a	DET
ejpam-4924	160	16	submodule	submodule	NOUN
ejpam-4924	160	17	is	be	AUX
ejpam-4924	160	18	a	a	DET
ejpam-4924	160	19	non	non	ADJ
ejpam-4924	160	20	-	-	ADJ
ejpam-4924	160	21	empty	empty	ADJ
ejpam-4924	160	22	part	part	NOUN
ejpam-4924	160	23	of	of	ADP
ejpam-4924	160	24	a	a	DET
ejpam-4924	160	25	module	module	NOUN
ejpam-4924	160	26	,	,	PUNCT
ejpam-4924	160	27	stable	stable	ADJ
ejpam-4924	160	28	for	for	ADP
ejpam-4924	160	29	the	the	DET
ejpam-4924	160	30	laws	law	NOUN
ejpam-4924	160	31	of	of	ADP
ejpam-4924	160	32	modules	module	NOUN
ejpam-4924	160	33	,	,	PUNCT
ejpam-4924	160	34	hence	hence	ADV
ejpam-4924	160	35	the	the	DET
ejpam-4924	160	36	following	follow	VERB
ejpam-4924	160	37	definition	definition	NOUN
ejpam-4924	160	38	:	:	PUNCT
ejpam-4924	160	39	definition	definition	NOUN
ejpam-4924	160	40	4.5	4.5	NUM
ejpam-4924	160	41	.	.	PUNCT
ejpam-4924	161	1	let	let	VERB
ejpam-4924	161	2	a	a	DET
ejpam-4924	161	3	be	be	AUX
ejpam-4924	161	4	a	a	DET
ejpam-4924	161	5	k	k	NOUN
ejpam-4924	161	6	-	-	NOUN
ejpam-4924	161	7	algebra	algebra	NOUN
ejpam-4924	161	8	and	and	CCONJ
ejpam-4924	161	9	ρ	ρ	NOUN
ejpam-4924	161	10	:	:	PUNCT
ejpam-4924	161	11	a	a	DET
ejpam-4924	161	12	−→	−→	NOUN
ejpam-4924	161	13	end(m	end(m	PROPN
ejpam-4924	161	14	)	)	PUNCT
ejpam-4924	161	15	a	a	DET
ejpam-4924	161	16	representation	representation	NOUN
ejpam-4924	161	17	of	of	ADP
ejpam-4924	161	18	a.	a.	NOUN
ejpam-4924	161	19	i	i	PROPN
ejpam-4924	161	20	)	)	PUNCT
ejpam-4924	161	21	let	let	VERB
ejpam-4924	161	22	n	n	PRON
ejpam-4924	161	23	be	be	AUX
ejpam-4924	161	24	a	a	DET
ejpam-4924	161	25	subspace	subspace	NOUN
ejpam-4924	161	26	of	of	ADP
ejpam-4924	161	27	m	m	PROPN
ejpam-4924	161	28	,	,	PUNCT
ejpam-4924	161	29	n	n	PRON
ejpam-4924	161	30	is	be	AUX
ejpam-4924	161	31	a	a	DET
ejpam-4924	161	32	submodule	submodule	NOUN
ejpam-4924	161	33	of	of	ADP
ejpam-4924	161	34	m	m	PROPN
ejpam-4924	161	35	if	if	SCONJ
ejpam-4924	162	1	and	and	CCONJ
ejpam-4924	162	2	only	only	ADV
ejpam-4924	162	3	if	if	SCONJ
ejpam-4924	162	4	a.n	a.n	PROPN
ejpam-4924	162	5	⊆	⊆	NUM
ejpam-4924	162	6	n	n	NOUN
ejpam-4924	162	7	.	.	PUNCT
ejpam-4924	163	1	ii	ii	X
ejpam-4924	163	2	)	)	PUNCT
ejpam-4924	163	3	m	m	VERB
ejpam-4924	163	4	is	be	AUX
ejpam-4924	163	5	an	an	DET
ejpam-4924	163	6	irreducible	irreducible	ADJ
ejpam-4924	163	7	module	module	NOUN
ejpam-4924	163	8	or	or	CCONJ
ejpam-4924	163	9	ρ	ρ	NOUN
ejpam-4924	163	10	is	be	AUX
ejpam-4924	163	11	an	an	DET
ejpam-4924	163	12	irreducible	irreducible	ADJ
ejpam-4924	163	13	representation	representation	NOUN
ejpam-4924	163	14	of	of	ADP
ejpam-4924	163	15	a	a	PRON
ejpam-4924	163	16	,	,	PUNCT
ejpam-4924	163	17	if	if	SCONJ
ejpam-4924	163	18	m	m	PRON
ejpam-4924	163	19	̸=	̸=	NOUN
ejpam-4924	163	20	0	0	NUM
ejpam-4924	163	21	and	and	CCONJ
ejpam-4924	163	22	the	the	DET
ejpam-4924	163	23	only	only	ADJ
ejpam-4924	163	24	submodules	submodule	NOUN
ejpam-4924	163	25	of	of	ADP
ejpam-4924	163	26	m	m	NOUN
ejpam-4924	163	27	are	be	AUX
ejpam-4924	163	28	its	its	PRON
ejpam-4924	163	29	trivial	trivial	ADJ
ejpam-4924	163	30	submodules	submodule	NOUN
ejpam-4924	163	31	.	.	PUNCT
ejpam-4924	164	1	iii	iii	X
ejpam-4924	164	2	)	)	PUNCT
ejpam-4924	164	3	an	an	DET
ejpam-4924	164	4	a	a	DET
ejpam-4924	164	5	-	-	PUNCT
ejpam-4924	164	6	module	module	NOUN
ejpam-4924	164	7	m	m	NOUN
ejpam-4924	164	8	is	be	AUX
ejpam-4924	164	9	said	say	VERB
ejpam-4924	164	10	to	to	PART
ejpam-4924	164	11	be	be	AUX
ejpam-4924	164	12	simple	simple	ADJ
ejpam-4924	164	13	or	or	CCONJ
ejpam-4924	164	14	irreducible	irreducible	ADJ
ejpam-4924	164	15	if	if	SCONJ
ejpam-4924	164	16	m	m	NOUN
ejpam-4924	164	17	is	be	AUX
ejpam-4924	164	18	not	not	PART
ejpam-4924	164	19	the	the	DET
ejpam-4924	164	20	null	null	ADJ
ejpam-4924	164	21	module	module	NOUN
ejpam-4924	164	22	and	and	CCONJ
ejpam-4924	164	23	there	there	PRON
ejpam-4924	164	24	are	be	VERB
ejpam-4924	164	25	no	no	DET
ejpam-4924	164	26	submodules	submodule	NOUN
ejpam-4924	164	27	outside	outside	ADV
ejpam-4924	164	28	{	{	PUNCT
ejpam-4924	164	29	0	0	NUM
ejpam-4924	164	30	}	}	PUNCT
ejpam-4924	164	31	and	and	CCONJ
ejpam-4924	164	32	m	m	PROPN
ejpam-4924	164	33	.	.	PUNCT
ejpam-4924	165	1	lemma	lemma	PROPN
ejpam-4924	165	2	4.6	4.6	NUM
ejpam-4924	165	3	.	.	PUNCT
ejpam-4924	166	1	let	let	VERB
ejpam-4924	166	2	a	a	DET
ejpam-4924	166	3	be	be	AUX
ejpam-4924	166	4	an	an	DET
ejpam-4924	166	5	algebra	algebra	NOUN
ejpam-4924	166	6	satisfying	satisfy	VERB
ejpam-4924	166	7	the	the	DET
ejpam-4924	166	8	identity	identity	NOUN
ejpam-4924	166	9	(	(	PUNCT
ejpam-4924	166	10	3	3	NUM
ejpam-4924	166	11	)	)	PUNCT
ejpam-4924	166	12	,	,	PUNCT
ejpam-4924	166	13	then	then	ADV
ejpam-4924	166	14	mλ1	mλ1	NOUN
ejpam-4924	166	15	and	and	CCONJ
ejpam-4924	166	16	mλ2	mλ2	NOUN
ejpam-4924	166	17	are	be	AUX
ejpam-4924	166	18	submodules	submodule	NOUN
ejpam-4924	166	19	of	of	ADP
ejpam-4924	166	20	m	m	PROPN
ejpam-4924	166	21	.	.	PUNCT
ejpam-4924	167	1	proof	proof	NOUN
ejpam-4924	167	2	.	.	PUNCT
ejpam-4924	168	1	using	use	VERB
ejpam-4924	168	2	theorem	theorem	NOUN
ejpam-4924	168	3	(	(	PUNCT
ejpam-4924	168	4	4.3	4.3	NUM
ejpam-4924	168	5	)	)	PUNCT
ejpam-4924	168	6	,	,	PUNCT
ejpam-4924	168	7	we	we	PRON
ejpam-4924	168	8	observe	observe	VERB
ejpam-4924	168	9	that	that	SCONJ
ejpam-4924	168	10	for	for	ADP
ejpam-4924	168	11	all	all	DET
ejpam-4924	168	12	a	a	DET
ejpam-4924	168	13	∈	∈	PROPN
ejpam-4924	168	14	a	a	DET
ejpam-4924	168	15	and	and	CCONJ
ejpam-4924	168	16	m	m	PROPN
ejpam-4924	168	17	∈	∈	NOUN
ejpam-4924	168	18	mλ	mλ	NOUN
ejpam-4924	168	19	,	,	PUNCT
ejpam-4924	168	20	we	we	PRON
ejpam-4924	168	21	have	have	VERB
ejpam-4924	168	22	a.m	a.m	PROPN
ejpam-4924	168	23	∈	∈	PROPN
ejpam-4924	168	24	mλ	mλ	NOUN
ejpam-4924	168	25	for	for	ADP
ejpam-4924	168	26	any	any	DET
ejpam-4924	168	27	λ	λ	PROPN
ejpam-4924	168	28	∈	∈	PROPN
ejpam-4924	168	29	{	{	PUNCT
ejpam-4924	168	30	λ1	λ1	ADJ
ejpam-4924	168	31	,	,	PUNCT
ejpam-4924	168	32	λ2	λ2	PROPN
ejpam-4924	168	33	}	}	PUNCT
ejpam-4924	168	34	.	.	PUNCT
ejpam-4924	169	1	h.	h.	PROPN
ejpam-4924	169	2	ouédraogo	ouédraogo	PROPN
ejpam-4924	169	3	,	,	PUNCT
ejpam-4924	169	4	a.	a.	NOUN
ejpam-4924	169	5	dembega	dembega	PROPN
ejpam-4924	169	6	,	,	PUNCT
ejpam-4924	169	7	a.	a.	PROPN
ejpam-4924	169	8	conseibo	conseibo	PROPN
ejpam-4924	169	9	/	/	SYM
ejpam-4924	169	10	eur	eur	PROPN
ejpam-4924	169	11	.	.	PUNCT
ejpam-4924	170	1	j.	j.	PROPN
ejpam-4924	170	2	pure	pure	PROPN
ejpam-4924	170	3	appl	appl	PROPN
ejpam-4924	170	4	.	.	PROPN
ejpam-4924	170	5	math	math	PROPN
ejpam-4924	170	6	,	,	PUNCT
ejpam-4924	170	7	16	16	NUM
ejpam-4924	170	8	(	(	PUNCT
ejpam-4924	170	9	4	4	NUM
ejpam-4924	170	10	)	)	PUNCT
ejpam-4924	170	11	(	(	PUNCT
ejpam-4924	170	12	2023	2023	NUM
ejpam-4924	170	13	)	)	PUNCT
ejpam-4924	170	14	,	,	PUNCT
ejpam-4924	170	15	2145	2145	NUM
ejpam-4924	170	16	-	-	SYM
ejpam-4924	170	17	2155	2155	NUM
ejpam-4924	170	18	2151	2151	NUM
ejpam-4924	170	19	proposition	proposition	NOUN
ejpam-4924	170	20	4.7	4.7	NUM
ejpam-4924	170	21	.	.	PUNCT
ejpam-4924	171	1	let	let	VERB
ejpam-4924	171	2	a	a	DET
ejpam-4924	171	3	be	be	AUX
ejpam-4924	171	4	an	an	DET
ejpam-4924	171	5	algebra	algebra	NOUN
ejpam-4924	171	6	satisfying	satisfy	VERB
ejpam-4924	171	7	the	the	DET
ejpam-4924	171	8	identity	identity	NOUN
ejpam-4924	171	9	(	(	PUNCT
ejpam-4924	171	10	3	3	X
ejpam-4924	171	11	)	)	PUNCT
ejpam-4924	171	12	admitting	admit	VERB
ejpam-4924	171	13	an	an	DET
ejpam-4924	171	14	idempotent	idempotent	NOUN
ejpam-4924	171	15	e	e	VERB
ejpam-4924	171	16	̸=	̸=	PROPN
ejpam-4924	171	17	0	0	NUM
ejpam-4924	171	18	and	and	CCONJ
ejpam-4924	171	19	ρ	ρ	NUM
ejpam-4924	171	20	:	:	PUNCT
ejpam-4924	171	21	a	a	DET
ejpam-4924	171	22	−→	−→	NOUN
ejpam-4924	171	23	end(m	end(m	PROPN
ejpam-4924	171	24	)	)	PUNCT
ejpam-4924	171	25	an	an	DET
ejpam-4924	171	26	irreducible	irreducible	ADJ
ejpam-4924	171	27	representation	representation	NOUN
ejpam-4924	171	28	of	of	ADP
ejpam-4924	171	29	a.	a.	NOUN
ejpam-4924	171	30	then	then	ADV
ejpam-4924	171	31	one	one	NUM
ejpam-4924	171	32	of	of	ADP
ejpam-4924	171	33	the	the	DET
ejpam-4924	171	34	conditions	condition	NOUN
ejpam-4924	171	35	below	below	ADP
ejpam-4924	171	36	holds	hold	VERB
ejpam-4924	171	37	:	:	PUNCT
ejpam-4924	172	1	i	i	PRON
ejpam-4924	172	2	)	)	PUNCT
ejpam-4924	172	3	m	m	VERB
ejpam-4924	172	4	=	=	VERB
ejpam-4924	172	5	m0	m0	PROPN
ejpam-4924	172	6	or	or	CCONJ
ejpam-4924	172	7	m	m	PROPN
ejpam-4924	172	8	=	=	NOUN
ejpam-4924	172	9	m1	m1	PROPN
ejpam-4924	172	10	;	;	PUNCT
ejpam-4924	172	11	ii	ii	X
ejpam-4924	172	12	)	)	PUNCT
ejpam-4924	172	13	m	m	PROPN
ejpam-4924	172	14	=	=	SYM
ejpam-4924	172	15	mλ1	mλ1	NOUN
ejpam-4924	172	16	;	;	PUNCT
ejpam-4924	172	17	iii	iii	X
ejpam-4924	172	18	)	)	PUNCT
ejpam-4924	172	19	m	m	PROPN
ejpam-4924	172	20	=	=	SYM
ejpam-4924	172	21	mλ2	mλ2	PROPN
ejpam-4924	172	22	.	.	PUNCT
ejpam-4924	173	1	proof	proof	NOUN
ejpam-4924	173	2	.	.	PUNCT
ejpam-4924	174	1	using	use	VERB
ejpam-4924	174	2	the	the	DET
ejpam-4924	174	3	lemma	lemma	PROPN
ejpam-4924	174	4	4.6	4.6	NUM
ejpam-4924	174	5	,	,	PUNCT
ejpam-4924	174	6	we	we	PRON
ejpam-4924	174	7	have	have	VERB
ejpam-4924	174	8	mλ1	mλ1	NOUN
ejpam-4924	174	9	and	and	CCONJ
ejpam-4924	174	10	mλ2	mλ2	NOUN
ejpam-4924	174	11	are	be	AUX
ejpam-4924	174	12	submodules	submodule	NOUN
ejpam-4924	174	13	of	of	ADP
ejpam-4924	174	14	m	m	PROPN
ejpam-4924	174	15	.	.	PUNCT
ejpam-4924	175	1	since	since	SCONJ
ejpam-4924	175	2	m	m	PROPN
ejpam-4924	175	3	is	be	AUX
ejpam-4924	175	4	irreducible	irreducible	ADJ
ejpam-4924	175	5	,	,	PUNCT
ejpam-4924	175	6	then	then	ADV
ejpam-4924	175	7	:	:	PUNCT
ejpam-4924	175	8	mλ1	mλ1	NOUN
ejpam-4924	175	9	=	=	VERB
ejpam-4924	175	10	m	m	VERB
ejpam-4924	175	11	or	or	CCONJ
ejpam-4924	175	12	mλ1	mλ1	NOUN
ejpam-4924	175	13	=	=	PUNCT
ejpam-4924	175	14	{	{	PUNCT
ejpam-4924	175	15	0	0	NUM
ejpam-4924	175	16	}	}	PUNCT
ejpam-4924	175	17	.	.	PUNCT
ejpam-4924	176	1	in	in	ADP
ejpam-4924	176	2	other	other	ADJ
ejpam-4924	176	3	words	word	NOUN
ejpam-4924	176	4	,	,	PUNCT
ejpam-4924	176	5	mλ2	mλ2	NOUN
ejpam-4924	176	6	=	=	PUNCT
ejpam-4924	176	7	m	m	ADJ
ejpam-4924	176	8	or	or	CCONJ
ejpam-4924	176	9	mλ2	mλ2	NOUN
ejpam-4924	176	10	=	=	PUNCT
ejpam-4924	176	11	{	{	PUNCT
ejpam-4924	176	12	0	0	NUM
ejpam-4924	176	13	}	}	PUNCT
ejpam-4924	176	14	.	.	PUNCT
ejpam-4924	177	1	theorem	theorem	NOUN
ejpam-4924	177	2	4.8	4.8	NUM
ejpam-4924	177	3	.	.	PUNCT
ejpam-4924	178	1	let	let	VERB
ejpam-4924	178	2	a	a	DET
ejpam-4924	178	3	be	be	AUX
ejpam-4924	178	4	an	an	DET
ejpam-4924	178	5	algebra	algebra	NOUN
ejpam-4924	178	6	verifying	verify	VERB
ejpam-4924	178	7	the	the	DET
ejpam-4924	178	8	identity	identity	NOUN
ejpam-4924	178	9	(	(	PUNCT
ejpam-4924	178	10	3	3	NUM
ejpam-4924	178	11	)	)	PUNCT
ejpam-4924	178	12	.	.	PUNCT
ejpam-4924	179	1	suppose	suppose	VERB
ejpam-4924	179	2	that	that	SCONJ
ejpam-4924	179	3	a	a	PRON
ejpam-4924	179	4	has	have	VERB
ejpam-4924	179	5	an	an	DET
ejpam-4924	179	6	idempotent	idempotent	NOUN
ejpam-4924	179	7	e	e	NOUN
ejpam-4924	179	8	̸=	̸=	PROPN
ejpam-4924	179	9	0	0	NUM
ejpam-4924	179	10	and	and	CCONJ
ejpam-4924	179	11	m	m	VERB
ejpam-4924	179	12	an	an	DET
ejpam-4924	179	13	irreducible	irreducible	ADJ
ejpam-4924	179	14	module	module	NOUN
ejpam-4924	179	15	.	.	PUNCT
ejpam-4924	180	1	if	if	SCONJ
ejpam-4924	180	2	m	m	PROPN
ejpam-4924	180	3	=	=	SYM
ejpam-4924	180	4	mi	mi	PROPN
ejpam-4924	180	5	,	,	PUNCT
ejpam-4924	180	6	with	with	ADP
ejpam-4924	180	7	i	i	PRON
ejpam-4924	180	8	∈	∈	PROPN
ejpam-4924	180	9	{	{	PUNCT
ejpam-4924	180	10	0	0	NUM
ejpam-4924	180	11	;	;	PUNCT
ejpam-4924	180	12	1	1	NUM
ejpam-4924	180	13	}	}	PUNCT
ejpam-4924	180	14	,	,	PUNCT
ejpam-4924	180	15	then∀a	then∀a	PROPN
ejpam-4924	180	16	,	,	PUNCT
ejpam-4924	180	17	b	b	X
ejpam-4924	180	18	∈	∈	PROPN
ejpam-4924	180	19	a;m	a;m	PROPN
ejpam-4924	180	20	∈	∈	PROPN
ejpam-4924	180	21	m	m	VERB
ejpam-4924	180	22	1	1	NUM
ejpam-4924	180	23	)	)	PUNCT
ejpam-4924	180	24	(	(	PUNCT
ejpam-4924	180	25	a	a	DET
ejpam-4924	180	26	,	,	PUNCT
ejpam-4924	180	27	b	b	NOUN
ejpam-4924	180	28	,	,	PUNCT
ejpam-4924	180	29	m	m	NOUN
ejpam-4924	180	30	)	)	PUNCT
ejpam-4924	181	1	=	=	PRON
ejpam-4924	181	2	(	(	PUNCT
ejpam-4924	181	3	ai	ai	PROPN
ejpam-4924	181	4	,	,	PUNCT
ejpam-4924	181	5	bi	bi	NOUN
ejpam-4924	181	6	,	,	PUNCT
ejpam-4924	181	7	mi	mi	PROPN
ejpam-4924	181	8	)	)	PUNCT
ejpam-4924	181	9	;	;	PUNCT
ejpam-4924	181	10	2	2	X
ejpam-4924	181	11	)	)	PUNCT
ejpam-4924	181	12	(	(	PUNCT
ejpam-4924	181	13	a	a	PRON
ejpam-4924	181	14	,	,	PUNCT
ejpam-4924	181	15	m	m	PROPN
ejpam-4924	181	16	,	,	PUNCT
ejpam-4924	181	17	b	b	NOUN
ejpam-4924	181	18	)	)	PUNCT
ejpam-4924	181	19	=	=	SYM
ejpam-4924	181	20	(	(	PUNCT
ejpam-4924	181	21	ai	ai	PROPN
ejpam-4924	181	22	,	,	PUNCT
ejpam-4924	181	23	mi	mi	NOUN
ejpam-4924	181	24	,	,	PUNCT
ejpam-4924	181	25	bi	bi	NOUN
ejpam-4924	181	26	)	)	PUNCT
ejpam-4924	181	27	.	.	PUNCT
ejpam-4924	182	1	proof	proof	NOUN
ejpam-4924	182	2	.	.	PUNCT
ejpam-4924	183	1	suppose	suppose	VERB
ejpam-4924	183	2	m	m	VERB
ejpam-4924	183	3	=	=	SYM
ejpam-4924	183	4	mi	mi	PROPN
ejpam-4924	183	5	,	,	PUNCT
ejpam-4924	183	6	i	i	PRON
ejpam-4924	183	7	∈	∈	PROPN
ejpam-4924	183	8	{	{	PUNCT
ejpam-4924	183	9	0	0	NUM
ejpam-4924	183	10	;	;	PUNCT
ejpam-4924	183	11	1	1	NUM
ejpam-4924	183	12	}	}	PUNCT
ejpam-4924	183	13	then	then	ADV
ejpam-4924	183	14	mλ1	mλ1	NOUN
ejpam-4924	183	15	=	=	PUNCT
ejpam-4924	183	16	mλ2	mλ2	PROPN
ejpam-4924	183	17	=	=	PUNCT
ejpam-4924	183	18	{	{	PUNCT
ejpam-4924	183	19	0	0	NUM
ejpam-4924	183	20	}	}	PUNCT
ejpam-4924	183	21	.	.	PUNCT
ejpam-4924	184	1	we	we	PRON
ejpam-4924	184	2	’ll	’ll	AUX
ejpam-4924	184	3	do	do	VERB
ejpam-4924	184	4	the	the	DET
ejpam-4924	184	5	proof	proof	NOUN
ejpam-4924	184	6	for	for	ADP
ejpam-4924	184	7	m	m	PROPN
ejpam-4924	184	8	=	=	SYM
ejpam-4924	184	9	m0	m0	NOUN
ejpam-4924	184	10	;	;	PUNCT
ejpam-4924	184	11	for	for	ADP
ejpam-4924	184	12	the	the	DET
ejpam-4924	184	13	case	case	NOUN
ejpam-4924	184	14	where	where	SCONJ
ejpam-4924	184	15	m	m	NOUN
ejpam-4924	184	16	=	=	SYM
ejpam-4924	184	17	m1	m1	PROPN
ejpam-4924	184	18	,	,	PUNCT
ejpam-4924	184	19	the	the	DET
ejpam-4924	184	20	proof	proof	NOUN
ejpam-4924	184	21	is	be	AUX
ejpam-4924	184	22	done	do	VERB
ejpam-4924	184	23	simply	simply	ADV
ejpam-4924	184	24	.	.	PUNCT
ejpam-4924	185	1	let	let	VERB
ejpam-4924	185	2	a	a	DET
ejpam-4924	185	3	,	,	PUNCT
ejpam-4924	185	4	b	b	X
ejpam-4924	185	5	∈	∈	PROPN
ejpam-4924	185	6	a	a	PRON
ejpam-4924	185	7	be	be	AUX
ejpam-4924	185	8	such	such	ADJ
ejpam-4924	185	9	that	that	SCONJ
ejpam-4924	185	10	a	a	DET
ejpam-4924	185	11	=	=	PUNCT
ejpam-4924	185	12	a0+a1+aλ1	a0+a1+aλ1	PROPN
ejpam-4924	186	1	+	+	NOUN
ejpam-4924	186	2	aλ2	aλ2	PROPN
ejpam-4924	186	3	and	and	CCONJ
ejpam-4924	186	4	b	b	NOUN
ejpam-4924	186	5	=	=	PUNCT
ejpam-4924	186	6	b0+b1+bλ1	b0+b1+bλ1	PROPN
ejpam-4924	186	7	+	+	PROPN
ejpam-4924	186	8	bλ2	bλ2	NOUN
ejpam-4924	186	9	,	,	PUNCT
ejpam-4924	186	10	where	where	SCONJ
ejpam-4924	186	11	al	al	PROPN
ejpam-4924	186	12	,	,	PUNCT
ejpam-4924	186	13	bl	bl	PROPN
ejpam-4924	186	14	∈	∈	PROPN
ejpam-4924	186	15	al	al	PROPN
ejpam-4924	186	16	,	,	PUNCT
ejpam-4924	186	17	l	l	PROPN
ejpam-4924	186	18	∈	∈	PROPN
ejpam-4924	186	19	{	{	PUNCT
ejpam-4924	186	20	0	0	NUM
ejpam-4924	186	21	;	;	PUNCT
ejpam-4924	186	22	1;λ1;λ2	1;λ1;λ2	NUM
ejpam-4924	186	23	}	}	PUNCT
ejpam-4924	186	24	.	.	PUNCT
ejpam-4924	187	1	take	take	VERB
ejpam-4924	187	2	m	m	NOUN
ejpam-4924	187	3	∈	∈	NOUN
ejpam-4924	187	4	m	m	NOUN
ejpam-4924	187	5	=	=	NOUN
ejpam-4924	187	6	m0	m0	PROPN
ejpam-4924	187	7	,	,	PUNCT
ejpam-4924	187	8	so	so	SCONJ
ejpam-4924	187	9	m	m	NOUN
ejpam-4924	187	10	=	=	SYM
ejpam-4924	187	11	m0	m0	PROPN
ejpam-4924	187	12	,	,	PUNCT
ejpam-4924	187	13	where	where	SCONJ
ejpam-4924	187	14	m0	m0	PROPN
ejpam-4924	187	15	∈	∈	PROPN
ejpam-4924	187	16	m0	m0	PROPN
ejpam-4924	187	17	,	,	PUNCT
ejpam-4924	187	18	i.e	i.e	PROPN
ejpam-4924	187	19	ρe(m0	ρe(m0	NUM
ejpam-4924	187	20	)	)	PUNCT
ejpam-4924	187	21	=	=	SYM
ejpam-4924	188	1	0	0	X
ejpam-4924	188	2	.	.	PUNCT
ejpam-4924	189	1	let	let	VERB
ejpam-4924	189	2	’s	’s	NOUN
ejpam-4924	189	3	calculate	calculate	NOUN
ejpam-4924	189	4	(	(	PUNCT
ejpam-4924	189	5	a	a	PRON
ejpam-4924	189	6	,	,	PUNCT
ejpam-4924	189	7	b	b	NOUN
ejpam-4924	189	8	,	,	PUNCT
ejpam-4924	189	9	m0	m0	NOUN
ejpam-4924	189	10	)	)	PUNCT
ejpam-4924	189	11	,	,	PUNCT
ejpam-4924	189	12	(	(	PUNCT
ejpam-4924	189	13	a	a	X
ejpam-4924	189	14	,	,	PUNCT
ejpam-4924	189	15	m0	m0	NOUN
ejpam-4924	189	16	,	,	PUNCT
ejpam-4924	189	17	b	b	NOUN
ejpam-4924	189	18	)	)	PUNCT
ejpam-4924	189	19	∀a	∀a	NOUN
ejpam-4924	189	20	,	,	PUNCT
ejpam-4924	190	1	b	b	X
ejpam-4924	190	2	∈	∈	PROPN
ejpam-4924	190	3	a	a	PRON
ejpam-4924	190	4	and	and	CCONJ
ejpam-4924	190	5	m	m	NOUN
ejpam-4924	190	6	∈	∈	NOUN
ejpam-4924	190	7	m	m	NOUN
ejpam-4924	190	8	.	.	PUNCT
ejpam-4924	191	1	we	we	PRON
ejpam-4924	191	2	have	have	VERB
ejpam-4924	191	3	:	:	PUNCT
ejpam-4924	191	4	(	(	PUNCT
ejpam-4924	191	5	a	a	PRON
ejpam-4924	191	6	,	,	PUNCT
ejpam-4924	191	7	b	b	NOUN
ejpam-4924	191	8	,	,	PUNCT
ejpam-4924	191	9	m	m	NOUN
ejpam-4924	191	10	)	)	PUNCT
ejpam-4924	191	11	=	=	SYM
ejpam-4924	191	12	(	(	PUNCT
ejpam-4924	191	13	a0	a0	NOUN
ejpam-4924	191	14	+	+	CCONJ
ejpam-4924	191	15	a1	a1	NOUN
ejpam-4924	191	16	+	+	CCONJ
ejpam-4924	191	17	aλ1	aλ1	NOUN
ejpam-4924	191	18	+	+	CCONJ
ejpam-4924	191	19	aλ2	aλ2	NOUN
ejpam-4924	191	20	,	,	PUNCT
ejpam-4924	191	21	b0	b0	NOUN
ejpam-4924	191	22	+	+	CCONJ
ejpam-4924	191	23	b1	b1	NOUN
ejpam-4924	191	24	+	+	CCONJ
ejpam-4924	191	25	bλ1	bλ1	NOUN
ejpam-4924	191	26	+	+	CCONJ
ejpam-4924	191	27	bλ2	bλ2	NOUN
ejpam-4924	191	28	,	,	PUNCT
ejpam-4924	191	29	m0	m0	PROPN
ejpam-4924	191	30	)	)	PUNCT
ejpam-4924	192	1	=	=	PUNCT
ejpam-4924	192	2	(	(	PUNCT
ejpam-4924	192	3	a0	a0	NOUN
ejpam-4924	192	4	,	,	PUNCT
ejpam-4924	192	5	b0,m0	b0,m0	PROPN
ejpam-4924	192	6	)	)	PUNCT
ejpam-4924	193	1	+	+	CCONJ
ejpam-4924	193	2	(	(	PUNCT
ejpam-4924	193	3	a0	a0	NOUN
ejpam-4924	193	4	,	,	PUNCT
ejpam-4924	193	5	b1,m0	b1,m0	PROPN
ejpam-4924	193	6	)	)	PUNCT
ejpam-4924	194	1	+	+	CCONJ
ejpam-4924	194	2	(	(	PUNCT
ejpam-4924	194	3	a0	a0	NOUN
ejpam-4924	194	4	,	,	PUNCT
ejpam-4924	194	5	bλ1	bλ1	NOUN
ejpam-4924	194	6	,	,	PUNCT
ejpam-4924	194	7	m0	m0	NOUN
ejpam-4924	194	8	)	)	PUNCT
ejpam-4924	194	9	+	+	CCONJ
ejpam-4924	194	10	(	(	PUNCT
ejpam-4924	194	11	a0	a0	PROPN
ejpam-4924	194	12	,	,	PUNCT
ejpam-4924	194	13	bλ2	bλ2	NOUN
ejpam-4924	194	14	,	,	PUNCT
ejpam-4924	194	15	m0	m0	PROPN
ejpam-4924	194	16	)	)	PUNCT
ejpam-4924	194	17	+	+	CCONJ
ejpam-4924	194	18	(	(	PUNCT
ejpam-4924	194	19	a1	a1	NOUN
ejpam-4924	194	20	,	,	PUNCT
ejpam-4924	194	21	b0,m0	b0,m0	PROPN
ejpam-4924	194	22	)	)	PUNCT
ejpam-4924	195	1	+	+	CCONJ
ejpam-4924	195	2	(	(	PUNCT
ejpam-4924	195	3	a1	a1	PROPN
ejpam-4924	195	4	,	,	PUNCT
ejpam-4924	195	5	b1,m0	b1,m0	PROPN
ejpam-4924	195	6	)	)	PUNCT
ejpam-4924	196	1	+	+	CCONJ
ejpam-4924	196	2	(	(	PUNCT
ejpam-4924	196	3	a1	a1	NOUN
ejpam-4924	196	4	,	,	PUNCT
ejpam-4924	196	5	bλ1	bλ1	NOUN
ejpam-4924	196	6	,	,	PUNCT
ejpam-4924	196	7	m0	m0	NOUN
ejpam-4924	196	8	)	)	PUNCT
ejpam-4924	196	9	+	+	CCONJ
ejpam-4924	196	10	(	(	PUNCT
ejpam-4924	196	11	a1	a1	PROPN
ejpam-4924	196	12	,	,	PUNCT
ejpam-4924	196	13	bλ2	bλ2	NOUN
ejpam-4924	196	14	,	,	PUNCT
ejpam-4924	196	15	m0	m0	PROPN
ejpam-4924	196	16	)	)	PUNCT
ejpam-4924	196	17	+	+	CCONJ
ejpam-4924	196	18	(	(	PUNCT
ejpam-4924	196	19	aλ1	aλ1	INTJ
ejpam-4924	196	20	,	,	PUNCT
ejpam-4924	196	21	b0,m0	b0,m0	PROPN
ejpam-4924	196	22	)	)	PUNCT
ejpam-4924	197	1	+	+	CCONJ
ejpam-4924	197	2	(	(	PUNCT
ejpam-4924	197	3	aλ1	aλ1	INTJ
ejpam-4924	197	4	,	,	PUNCT
ejpam-4924	197	5	b1,m0	b1,m0	PROPN
ejpam-4924	197	6	)	)	PUNCT
ejpam-4924	198	1	+	+	CCONJ
ejpam-4924	198	2	(	(	PUNCT
ejpam-4924	198	3	aλ1	aλ1	INTJ
ejpam-4924	198	4	,	,	PUNCT
ejpam-4924	198	5	bλ1	bλ1	NOUN
ejpam-4924	198	6	,	,	PUNCT
ejpam-4924	198	7	m0	m0	NOUN
ejpam-4924	198	8	)	)	PUNCT
ejpam-4924	198	9	+	+	CCONJ
ejpam-4924	198	10	(	(	PUNCT
ejpam-4924	198	11	aλ1	aλ1	INTJ
ejpam-4924	198	12	,	,	PUNCT
ejpam-4924	198	13	bλ2	bλ2	NOUN
ejpam-4924	198	14	,	,	PUNCT
ejpam-4924	198	15	m0	m0	PROPN
ejpam-4924	198	16	)	)	PUNCT
ejpam-4924	198	17	+	+	CCONJ
ejpam-4924	198	18	(	(	PUNCT
ejpam-4924	198	19	aλ2	aλ2	PROPN
ejpam-4924	198	20	,	,	PUNCT
ejpam-4924	198	21	b0,m0	b0,m0	PROPN
ejpam-4924	198	22	)	)	PUNCT
ejpam-4924	199	1	+	+	CCONJ
ejpam-4924	199	2	(	(	PUNCT
ejpam-4924	199	3	aλ2	aλ2	PROPN
ejpam-4924	199	4	,	,	PUNCT
ejpam-4924	199	5	b1,m0	b1,m0	PROPN
ejpam-4924	199	6	)	)	PUNCT
ejpam-4924	200	1	+	+	CCONJ
ejpam-4924	200	2	(	(	PUNCT
ejpam-4924	200	3	aλ2	aλ2	PROPN
ejpam-4924	200	4	,	,	PUNCT
ejpam-4924	200	5	bλ1	bλ1	NOUN
ejpam-4924	200	6	,	,	PUNCT
ejpam-4924	200	7	m0	m0	NOUN
ejpam-4924	200	8	)	)	PUNCT
ejpam-4924	200	9	+	+	CCONJ
ejpam-4924	200	10	(	(	PUNCT
ejpam-4924	200	11	aλ2	aλ2	PROPN
ejpam-4924	200	12	,	,	PUNCT
ejpam-4924	200	13	bλ2	bλ2	NOUN
ejpam-4924	200	14	,	,	PUNCT
ejpam-4924	200	15	m0	m0	PROPN
ejpam-4924	200	16	)	)	PUNCT
ejpam-4924	200	17	=	=	SYM
ejpam-4924	200	18	(	(	PUNCT
ejpam-4924	200	19	a0b0)m0	a0b0)m0	X
ejpam-4924	200	20	−	−	PROPN
ejpam-4924	200	21	a0(b0m0	a0(b0m0	PROPN
ejpam-4924	200	22	)	)	PUNCT
ejpam-4924	201	1	+	+	CCONJ
ejpam-4924	201	2	(	(	PUNCT
ejpam-4924	201	3	a0b1)m0	a0b1)m0	PROPN
ejpam-4924	201	4	−	−	PROPN
ejpam-4924	201	5	a0(b1m0	a0(b1m0	PROPN
ejpam-4924	201	6	)	)	PUNCT
ejpam-4924	202	1	+	+	CCONJ
ejpam-4924	202	2	(	(	PUNCT
ejpam-4924	202	3	a0bλ1)m0	a0bλ1)m0	NUM
ejpam-4924	202	4	−	−	PROPN
ejpam-4924	202	5	a0(bλ1m0	a0(bλ1m0	PROPN
ejpam-4924	202	6	)	)	PUNCT
ejpam-4924	203	1	+	+	CCONJ
ejpam-4924	203	2	(	(	PUNCT
ejpam-4924	203	3	a0bλ2)m0	a0bλ2)m0	PROPN
ejpam-4924	203	4	−	−	PROPN
ejpam-4924	203	5	a0(bλ2m0	a0(bλ2m0	PROPN
ejpam-4924	203	6	)	)	PUNCT
ejpam-4924	204	1	+	+	CCONJ
ejpam-4924	204	2	(	(	PUNCT
ejpam-4924	204	3	a1b0)m0	a1b0)m0	PROPN
ejpam-4924	204	4	−	−	PROPN
ejpam-4924	204	5	a1(b0m0	a1(b0m0	PROPN
ejpam-4924	204	6	)	)	PUNCT
ejpam-4924	204	7	+	+	CCONJ
ejpam-4924	204	8	(	(	PUNCT
ejpam-4924	204	9	a1b1)m0	a1b1)m0	NUM
ejpam-4924	204	10	−	−	PROPN
ejpam-4924	204	11	a1(b1m0	a1(b1m0	PROPN
ejpam-4924	204	12	)	)	PUNCT
ejpam-4924	204	13	+	+	CCONJ
ejpam-4924	204	14	(	(	PUNCT
ejpam-4924	204	15	a1bλ1)m0	a1bλ1)m0	PROPN
ejpam-4924	204	16	−	−	PROPN
ejpam-4924	204	17	a1(bλ1m0	a1(bλ1m0	PROPN
ejpam-4924	204	18	)	)	PUNCT
ejpam-4924	204	19	+	+	CCONJ
ejpam-4924	204	20	(	(	PUNCT
ejpam-4924	204	21	a1bλ2)m0	a1bλ2)m0	NOUN
ejpam-4924	204	22	−	−	ADP
ejpam-4924	204	23	a1(bλ2m0	a1(bλ2m0	NOUN
ejpam-4924	204	24	)	)	PUNCT
ejpam-4924	204	25	+	+	CCONJ
ejpam-4924	204	26	(	(	PUNCT
ejpam-4924	204	27	aλ1b0)m0	aλ1b0)m0	X
ejpam-4924	204	28	−	−	PROPN
ejpam-4924	204	29	aλ1(b0m0	aλ1(b0m0	PROPN
ejpam-4924	204	30	)	)	PUNCT
ejpam-4924	205	1	+	+	CCONJ
ejpam-4924	205	2	(	(	PUNCT
ejpam-4924	205	3	aλ1b1)m0	aλ1b1)m0	ADJ
ejpam-4924	205	4	−	−	PROPN
ejpam-4924	205	5	aλ1(b1m0	aλ1(b1m0	NUM
ejpam-4924	205	6	)	)	PUNCT
ejpam-4924	206	1	+	+	CCONJ
ejpam-4924	206	2	(	(	PUNCT
ejpam-4924	206	3	aλ1bλ1)m0	aλ1bλ1)m0	PROPN
ejpam-4924	206	4	−	−	PROPN
ejpam-4924	206	5	aλ1(bλ1m0	aλ1(bλ1m0	NOUN
ejpam-4924	206	6	)	)	PUNCT
ejpam-4924	206	7	+	+	CCONJ
ejpam-4924	206	8	(	(	PUNCT
ejpam-4924	206	9	aλ1bλ2)m0	aλ1bλ2)m0	PROPN
ejpam-4924	206	10	−	−	PROPN
ejpam-4924	206	11	aλ1(bλ2m0	aλ1(bλ2m0	NUM
ejpam-4924	206	12	)	)	PUNCT
ejpam-4924	207	1	+	+	CCONJ
ejpam-4924	207	2	(	(	PUNCT
ejpam-4924	207	3	aλ1b0)m0	aλ1b0)m0	X
ejpam-4924	207	4	−	−	PROPN
ejpam-4924	207	5	aλ2(b0m0	aλ2(b0m0	PROPN
ejpam-4924	207	6	)	)	PUNCT
ejpam-4924	208	1	+	+	CCONJ
ejpam-4924	208	2	(	(	PUNCT
ejpam-4924	208	3	aλ2b1)m0	aλ2b1)m0	PRON
ejpam-4924	208	4	−	−	ADP
ejpam-4924	208	5	aλ2(b1m0	aλ2(b1m0	NOUN
ejpam-4924	208	6	)	)	PUNCT
ejpam-4924	208	7	+	+	CCONJ
ejpam-4924	208	8	(	(	PUNCT
ejpam-4924	208	9	aλ2bλ1)m0	aλ2bλ1)m0	PROPN
ejpam-4924	208	10	−	−	PROPN
ejpam-4924	208	11	aλ2(bλ1m0	aλ2(bλ1m0	NOUN
ejpam-4924	208	12	)	)	PUNCT
ejpam-4924	208	13	+	+	CCONJ
ejpam-4924	208	14	(	(	PUNCT
ejpam-4924	208	15	aλ2bλ2)m0	aλ2bλ2)m0	PROPN
ejpam-4924	208	16	−	−	PROPN
ejpam-4924	208	17	aλ2(bλ2m0	aλ2(bλ2m0	ADV
ejpam-4924	208	18	)	)	PUNCT
ejpam-4924	208	19	=	=	SYM
ejpam-4924	208	20	(	(	PUNCT
ejpam-4924	208	21	a0	a0	NOUN
ejpam-4924	208	22	,	,	PUNCT
ejpam-4924	208	23	b0,m0	b0,m0	PROPN
ejpam-4924	208	24	)	)	PUNCT
ejpam-4924	208	25	this	this	DET
ejpam-4924	208	26	result	result	NOUN
ejpam-4924	208	27	is	be	AUX
ejpam-4924	208	28	found	find	VERB
ejpam-4924	208	29	by	by	ADP
ejpam-4924	208	30	using	use	VERB
ejpam-4924	208	31	the	the	DET
ejpam-4924	208	32	multiplication	multiplication	NOUN
ejpam-4924	208	33	table	table	NOUN
ejpam-4924	208	34	of	of	ADP
ejpam-4924	208	35	a	a	DET
ejpam-4924	208	36	(	(	PUNCT
ejpam-4924	208	37	see	see	NOUN
ejpam-4924	208	38	theorem	theorem	NOUN
ejpam-4924	208	39	(	(	PUNCT
ejpam-4924	208	40	2.1	2.1	NUM
ejpam-4924	208	41	)	)	PUNCT
ejpam-4924	208	42	)	)	PUNCT
ejpam-4924	208	43	and	and	CCONJ
ejpam-4924	208	44	the	the	DET
ejpam-4924	208	45	action	action	NOUN
ejpam-4924	208	46	of	of	ADP
ejpam-4924	208	47	a	a	PRON
ejpam-4924	208	48	on	on	ADP
ejpam-4924	208	49	m	m	PROPN
ejpam-4924	208	50	(	(	PUNCT
ejpam-4924	208	51	see	see	VERB
ejpam-4924	208	52	theorem	theorem	NOUN
ejpam-4924	208	53	(	(	PUNCT
ejpam-4924	208	54	4.3	4.3	NUM
ejpam-4924	208	55	)	)	PUNCT
ejpam-4924	208	56	)	)	PUNCT
ejpam-4924	208	57	,	,	PUNCT
ejpam-4924	208	58	for	for	ADP
ejpam-4924	208	59	all	all	DET
ejpam-4924	208	60	m	m	VERB
ejpam-4924	208	61	∈	∈	ADJ
ejpam-4924	208	62	m	m	NOUN
ejpam-4924	208	63	,	,	PUNCT
ejpam-4924	208	64	we	we	PRON
ejpam-4924	208	65	have	have	VERB
ejpam-4924	208	66	:	:	PUNCT
ejpam-4924	208	67	(	(	PUNCT
ejpam-4924	208	68	a	a	PRON
ejpam-4924	208	69	,	,	PUNCT
ejpam-4924	208	70	b	b	NOUN
ejpam-4924	208	71	,	,	PUNCT
ejpam-4924	208	72	m	m	NOUN
ejpam-4924	208	73	)	)	PUNCT
ejpam-4924	208	74	=	=	SYM
ejpam-4924	208	75	(	(	PUNCT
ejpam-4924	208	76	a0	a0	NOUN
ejpam-4924	208	77	,	,	PUNCT
ejpam-4924	208	78	b0,m0	b0,m0	PROPN
ejpam-4924	208	79	)	)	PUNCT
ejpam-4924	208	80	.	.	PUNCT
ejpam-4924	209	1	similarly	similarly	ADV
ejpam-4924	209	2	,	,	PUNCT
ejpam-4924	209	3	if	if	SCONJ
ejpam-4924	209	4	m	m	VERB
ejpam-4924	209	5	∈	∈	PROPN
ejpam-4924	209	6	m	m	NOUN
ejpam-4924	209	7	=	=	NOUN
ejpam-4924	209	8	m0	m0	PROPN
ejpam-4924	209	9	,	,	PUNCT
ejpam-4924	209	10	then	then	ADV
ejpam-4924	209	11	we	we	PRON
ejpam-4924	209	12	have	have	VERB
ejpam-4924	209	13	:	:	PUNCT
ejpam-4924	209	14	(	(	PUNCT
ejpam-4924	209	15	a	a	PRON
ejpam-4924	209	16	,	,	PUNCT
ejpam-4924	209	17	m	m	PROPN
ejpam-4924	209	18	,	,	PUNCT
ejpam-4924	209	19	b	b	NOUN
ejpam-4924	209	20	)	)	PUNCT
ejpam-4924	209	21	=	=	SYM
ejpam-4924	209	22	(	(	PUNCT
ejpam-4924	209	23	a0	a0	NOUN
ejpam-4924	209	24	+	+	CCONJ
ejpam-4924	209	25	a1	a1	NOUN
ejpam-4924	209	26	+	+	CCONJ
ejpam-4924	209	27	aλ1	aλ1	PROPN
ejpam-4924	209	28	+	+	CCONJ
ejpam-4924	209	29	aλ2	aλ2	PROPN
ejpam-4924	209	30	,	,	PUNCT
ejpam-4924	209	31	m0	m0	NOUN
ejpam-4924	209	32	,	,	PUNCT
ejpam-4924	209	33	b0	b0	NOUN
ejpam-4924	209	34	+	+	CCONJ
ejpam-4924	209	35	b1	b1	NOUN
ejpam-4924	209	36	+	+	CCONJ
ejpam-4924	209	37	bλ1	bλ1	NOUN
ejpam-4924	209	38	+	+	CCONJ
ejpam-4924	209	39	bλ2	bλ2	NOUN
ejpam-4924	209	40	)	)	PUNCT
ejpam-4924	210	1	=	=	PUNCT
ejpam-4924	210	2	(	(	PUNCT
ejpam-4924	210	3	a0,m0	a0,m0	PROPN
ejpam-4924	210	4	,	,	PUNCT
ejpam-4924	210	5	b0	b0	NOUN
ejpam-4924	210	6	)	)	PUNCT
ejpam-4924	210	7	+	+	CCONJ
ejpam-4924	210	8	(	(	PUNCT
ejpam-4924	210	9	a0,m0	a0,m0	PROPN
ejpam-4924	210	10	,	,	PUNCT
ejpam-4924	210	11	b1	b1	NOUN
ejpam-4924	210	12	)	)	PUNCT
ejpam-4924	210	13	+	+	CCONJ
ejpam-4924	210	14	(	(	PUNCT
ejpam-4924	210	15	a0,m0	a0,m0	NOUN
ejpam-4924	210	16	,	,	PUNCT
ejpam-4924	210	17	bλ1	bλ1	NOUN
ejpam-4924	210	18	)	)	PUNCT
ejpam-4924	210	19	+	+	CCONJ
ejpam-4924	210	20	(	(	PUNCT
ejpam-4924	210	21	a0,m0	a0,m0	PROPN
ejpam-4924	210	22	,	,	PUNCT
ejpam-4924	210	23	bλ2	bλ2	NOUN
ejpam-4924	210	24	)	)	PUNCT
ejpam-4924	211	1	+	+	CCONJ
ejpam-4924	211	2	(	(	PUNCT
ejpam-4924	211	3	a1,m0	a1,m0	PROPN
ejpam-4924	211	4	,	,	PUNCT
ejpam-4924	211	5	b0	b0	NOUN
ejpam-4924	211	6	)	)	PUNCT
ejpam-4924	212	1	+	+	CCONJ
ejpam-4924	212	2	(	(	PUNCT
ejpam-4924	212	3	a1,m0	a1,m0	PROPN
ejpam-4924	212	4	,	,	PUNCT
ejpam-4924	212	5	b1	b1	PROPN
ejpam-4924	212	6	)	)	PUNCT
ejpam-4924	212	7	h.	h.	PROPN
ejpam-4924	212	8	ouédraogo	ouédraogo	PROPN
ejpam-4924	212	9	,	,	PUNCT
ejpam-4924	212	10	a.	a.	NOUN
ejpam-4924	212	11	dembega	dembega	PROPN
ejpam-4924	212	12	,	,	PUNCT
ejpam-4924	212	13	a.	a.	PROPN
ejpam-4924	212	14	conseibo	conseibo	PROPN
ejpam-4924	212	15	/	/	SYM
ejpam-4924	212	16	eur	eur	PROPN
ejpam-4924	212	17	.	.	PUNCT
ejpam-4924	213	1	j.	j.	PROPN
ejpam-4924	213	2	pure	pure	PROPN
ejpam-4924	213	3	appl	appl	PROPN
ejpam-4924	213	4	.	.	PROPN
ejpam-4924	213	5	math	math	PROPN
ejpam-4924	213	6	,	,	PUNCT
ejpam-4924	213	7	16	16	NUM
ejpam-4924	213	8	(	(	PUNCT
ejpam-4924	213	9	4	4	NUM
ejpam-4924	213	10	)	)	PUNCT
ejpam-4924	213	11	(	(	PUNCT
ejpam-4924	213	12	2023	2023	NUM
ejpam-4924	213	13	)	)	PUNCT
ejpam-4924	213	14	,	,	PUNCT
ejpam-4924	213	15	2145	2145	NUM
ejpam-4924	213	16	-	-	SYM
ejpam-4924	213	17	2155	2155	NUM
ejpam-4924	213	18	2152	2152	NUM
ejpam-4924	213	19	+	+	CCONJ
ejpam-4924	213	20	(	(	PUNCT
ejpam-4924	213	21	a1,m0	a1,m0	PROPN
ejpam-4924	213	22	,	,	PUNCT
ejpam-4924	213	23	bλ1	bλ1	NOUN
ejpam-4924	213	24	)	)	PUNCT
ejpam-4924	213	25	+	+	CCONJ
ejpam-4924	213	26	(	(	PUNCT
ejpam-4924	213	27	a1,m0	a1,m0	PROPN
ejpam-4924	213	28	,	,	PUNCT
ejpam-4924	213	29	bλ2	bλ2	PROPN
ejpam-4924	213	30	)	)	PUNCT
ejpam-4924	214	1	+	+	CCONJ
ejpam-4924	214	2	(	(	PUNCT
ejpam-4924	214	3	aλ1	aλ1	INTJ
ejpam-4924	214	4	,	,	PUNCT
ejpam-4924	214	5	m0	m0	NOUN
ejpam-4924	214	6	,	,	PUNCT
ejpam-4924	214	7	b0	b0	NOUN
ejpam-4924	214	8	)	)	PUNCT
ejpam-4924	215	1	+	+	CCONJ
ejpam-4924	215	2	(	(	PUNCT
ejpam-4924	215	3	aλ1	aλ1	INTJ
ejpam-4924	215	4	,	,	PUNCT
ejpam-4924	215	5	m0	m0	NOUN
ejpam-4924	215	6	,	,	PUNCT
ejpam-4924	215	7	b1	b1	NOUN
ejpam-4924	215	8	)	)	PUNCT
ejpam-4924	215	9	+	+	CCONJ
ejpam-4924	215	10	(	(	PUNCT
ejpam-4924	215	11	aλ1	aλ1	INTJ
ejpam-4924	215	12	,	,	PUNCT
ejpam-4924	215	13	m0	m0	NOUN
ejpam-4924	215	14	,	,	PUNCT
ejpam-4924	215	15	bλ1	bλ1	NOUN
ejpam-4924	215	16	)	)	PUNCT
ejpam-4924	215	17	+	+	CCONJ
ejpam-4924	215	18	(	(	PUNCT
ejpam-4924	215	19	aλ1	aλ1	INTJ
ejpam-4924	215	20	,	,	PUNCT
ejpam-4924	215	21	m0	m0	NOUN
ejpam-4924	215	22	,	,	PUNCT
ejpam-4924	215	23	bλ2	bλ2	NOUN
ejpam-4924	215	24	)	)	PUNCT
ejpam-4924	216	1	+	+	CCONJ
ejpam-4924	216	2	(	(	PUNCT
ejpam-4924	216	3	aλ2	aλ2	PROPN
ejpam-4924	216	4	,	,	PUNCT
ejpam-4924	216	5	m0	m0	NOUN
ejpam-4924	216	6	,	,	PUNCT
ejpam-4924	216	7	b0	b0	NOUN
ejpam-4924	216	8	)	)	PUNCT
ejpam-4924	216	9	+	+	CCONJ
ejpam-4924	216	10	(	(	PUNCT
ejpam-4924	216	11	aλ2	aλ2	PROPN
ejpam-4924	216	12	,	,	PUNCT
ejpam-4924	216	13	m0	m0	NOUN
ejpam-4924	216	14	,	,	PUNCT
ejpam-4924	216	15	b1	b1	NOUN
ejpam-4924	216	16	)	)	PUNCT
ejpam-4924	216	17	+	+	CCONJ
ejpam-4924	216	18	(	(	PUNCT
ejpam-4924	216	19	aλ2	aλ2	PROPN
ejpam-4924	216	20	,	,	PUNCT
ejpam-4924	216	21	m0	m0	NOUN
ejpam-4924	216	22	,	,	PUNCT
ejpam-4924	216	23	bλ1	bλ1	NOUN
ejpam-4924	216	24	)	)	PUNCT
ejpam-4924	216	25	+	+	CCONJ
ejpam-4924	216	26	(	(	PUNCT
ejpam-4924	216	27	aλ2	aλ2	PROPN
ejpam-4924	216	28	,	,	PUNCT
ejpam-4924	216	29	m0	m0	PROPN
ejpam-4924	216	30	,	,	PUNCT
ejpam-4924	216	31	bλ2	bλ2	NOUN
ejpam-4924	216	32	)	)	PUNCT
ejpam-4924	216	33	=	=	PUNCT
ejpam-4924	217	1	(	(	PUNCT
ejpam-4924	217	2	a0m0)b0	a0m0)b0	NOUN
ejpam-4924	217	3	−	−	NOUN
ejpam-4924	217	4	a0(m0b0	a0(m0b0	PROPN
ejpam-4924	217	5	)	)	PUNCT
ejpam-4924	218	1	+	+	CCONJ
ejpam-4924	218	2	(	(	PUNCT
ejpam-4924	218	3	a0m0)b1	a0m0)b1	NUM
ejpam-4924	218	4	−	−	PROPN
ejpam-4924	218	5	a0(m0b1	a0(m0b1	PROPN
ejpam-4924	218	6	)	)	PUNCT
ejpam-4924	218	7	+	+	CCONJ
ejpam-4924	218	8	(	(	PUNCT
ejpam-4924	218	9	a0m0)bλ1	a0m0)bλ1	NOUN
ejpam-4924	218	10	−	−	PROPN
ejpam-4924	218	11	a0(m0bλ1	a0(m0bλ1	NOUN
ejpam-4924	218	12	)	)	PUNCT
ejpam-4924	218	13	+	+	CCONJ
ejpam-4924	218	14	(	(	PUNCT
ejpam-4924	218	15	a0m0)bλ2	a0m0)bλ2	ADV
ejpam-4924	218	16	−	−	PROPN
ejpam-4924	218	17	a0(m0bλ2	a0(m0bλ2	PROPN
ejpam-4924	218	18	)	)	PUNCT
ejpam-4924	219	1	+	+	CCONJ
ejpam-4924	219	2	(	(	PUNCT
ejpam-4924	219	3	a1m0)b0	a1m0)b0	AUX
ejpam-4924	219	4	−	−	PROPN
ejpam-4924	219	5	a1(m0b0	a1(m0b0	PROPN
ejpam-4924	219	6	)	)	PUNCT
ejpam-4924	220	1	+	+	CCONJ
ejpam-4924	220	2	(	(	PUNCT
ejpam-4924	220	3	a1m0)b1	a1m0)b1	VERB
ejpam-4924	220	4	−	−	PROPN
ejpam-4924	220	5	a1(m0b1	a1(m0b1	PROPN
ejpam-4924	220	6	)	)	PUNCT
ejpam-4924	220	7	+	+	CCONJ
ejpam-4924	220	8	(	(	PUNCT
ejpam-4924	220	9	a1m0)bλ1	a1m0)bλ1	PROPN
ejpam-4924	220	10	−	−	PROPN
ejpam-4924	220	11	a1(m0bλ1	a1(m0bλ1	NOUN
ejpam-4924	220	12	)	)	PUNCT
ejpam-4924	221	1	+	+	CCONJ
ejpam-4924	221	2	(	(	PUNCT
ejpam-4924	221	3	a1m0)bλ2	a1m0)bλ2	PRON
ejpam-4924	221	4	−	−	PROPN
ejpam-4924	221	5	a1(m0bλ2	a1(m0bλ2	PROPN
ejpam-4924	221	6	)	)	PUNCT
ejpam-4924	222	1	+	+	CCONJ
ejpam-4924	222	2	(	(	PUNCT
ejpam-4924	222	3	aλ1m0)b0	aλ1m0)b0	NOUN
ejpam-4924	222	4	−	−	PUNCT
ejpam-4924	222	5	aλ1(m0b0	aλ1(m0b0	PROPN
ejpam-4924	222	6	)	)	PUNCT
ejpam-4924	223	1	+	+	CCONJ
ejpam-4924	223	2	(	(	PUNCT
ejpam-4924	223	3	aλ1m0)b1	aλ1m0)b1	NOUN
ejpam-4924	223	4	−	−	X
ejpam-4924	223	5	aλ1(m0b1	aλ1(m0b1	PROPN
ejpam-4924	223	6	)	)	PUNCT
ejpam-4924	223	7	+	+	CCONJ
ejpam-4924	223	8	(	(	PUNCT
ejpam-4924	223	9	aλ1m0)bλ1	aλ1m0)bλ1	NOUN
ejpam-4924	223	10	−	−	NOUN
ejpam-4924	223	11	aλ1(m0bλ1	aλ1(m0bλ1	NOUN
ejpam-4924	223	12	)	)	PUNCT
ejpam-4924	224	1	+	+	CCONJ
ejpam-4924	224	2	(	(	PUNCT
ejpam-4924	224	3	aλ1m0)bλ2	aλ1m0)bλ2	PROPN
ejpam-4924	224	4	−	−	PROPN
ejpam-4924	224	5	aλ1(m0bλ2	aλ1(m0bλ2	NOUN
ejpam-4924	224	6	)	)	PUNCT
ejpam-4924	225	1	+	+	CCONJ
ejpam-4924	225	2	(	(	PUNCT
ejpam-4924	225	3	aλ2m0)b0	aλ2m0)b0	NOUN
ejpam-4924	225	4	−	−	X
ejpam-4924	225	5	aλ2(m0b0	aλ2(m0b0	NOUN
ejpam-4924	225	6	)	)	PUNCT
ejpam-4924	226	1	+	+	CCONJ
ejpam-4924	226	2	(	(	PUNCT
ejpam-4924	226	3	aλ2m0)b1	aλ2m0)b1	ADJ
ejpam-4924	226	4	−	−	PROPN
ejpam-4924	226	5	aλ2(m0b1	aλ2(m0b1	PROPN
ejpam-4924	226	6	)	)	PUNCT
ejpam-4924	226	7	+	+	CCONJ
ejpam-4924	226	8	(	(	PUNCT
ejpam-4924	226	9	aλ2m0)bλ1	aλ2m0)bλ1	NOUN
ejpam-4924	226	10	−	−	NOUN
ejpam-4924	226	11	aλ2(m0bλ1	aλ2(m0bλ1	NOUN
ejpam-4924	226	12	)	)	PUNCT
ejpam-4924	227	1	+	+	CCONJ
ejpam-4924	227	2	(	(	PUNCT
ejpam-4924	227	3	aλ2m0)bλ2	aλ2m0)bλ2	NUM
ejpam-4924	227	4	−	−	NOUN
ejpam-4924	227	5	aλ2(m0bλ2	aλ2(m0bλ2	NOUN
ejpam-4924	227	6	)	)	PUNCT
ejpam-4924	227	7	=	=	SYM
ejpam-4924	227	8	(	(	PUNCT
ejpam-4924	227	9	a0,m0	a0,m0	PROPN
ejpam-4924	227	10	,	,	PUNCT
ejpam-4924	227	11	b0	b0	NOUN
ejpam-4924	227	12	)	)	PUNCT
ejpam-4924	227	13	theorem	theorem	VERB
ejpam-4924	227	14	4.9	4.9	NUM
ejpam-4924	227	15	.	.	PUNCT
ejpam-4924	228	1	let	let	VERB
ejpam-4924	228	2	a	a	DET
ejpam-4924	228	3	be	be	AUX
ejpam-4924	228	4	an	an	DET
ejpam-4924	228	5	algebra	algebra	NOUN
ejpam-4924	228	6	verifying	verify	VERB
ejpam-4924	228	7	the	the	DET
ejpam-4924	228	8	identity	identity	NOUN
ejpam-4924	228	9	(	(	PUNCT
ejpam-4924	228	10	3	3	NUM
ejpam-4924	228	11	)	)	PUNCT
ejpam-4924	228	12	.	.	PUNCT
ejpam-4924	229	1	suppose	suppose	VERB
ejpam-4924	229	2	that	that	SCONJ
ejpam-4924	229	3	a	a	PRON
ejpam-4924	229	4	has	have	VERB
ejpam-4924	229	5	an	an	DET
ejpam-4924	229	6	idempotent	idempotent	NOUN
ejpam-4924	229	7	e	e	NOUN
ejpam-4924	229	8	̸=	̸=	PROPN
ejpam-4924	229	9	0	0	NUM
ejpam-4924	229	10	and	and	CCONJ
ejpam-4924	229	11	m	m	VERB
ejpam-4924	229	12	an	an	DET
ejpam-4924	229	13	irreducible	irreducible	ADJ
ejpam-4924	229	14	module	module	NOUN
ejpam-4924	229	15	.	.	PUNCT
ejpam-4924	230	1	if	if	SCONJ
ejpam-4924	230	2	m	m	VERB
ejpam-4924	230	3	=	=	VERB
ejpam-4924	230	4	mλ	mλ	NOUN
ejpam-4924	230	5	,	,	PUNCT
ejpam-4924	230	6	with	with	ADP
ejpam-4924	230	7	λ	λ	PROPN
ejpam-4924	230	8	∈	∈	PROPN
ejpam-4924	230	9	{	{	PUNCT
ejpam-4924	230	10	λ1	λ1	ADJ
ejpam-4924	230	11	,	,	PUNCT
ejpam-4924	230	12	λ2	λ2	PROPN
ejpam-4924	230	13	}	}	PUNCT
ejpam-4924	230	14	then	then	ADV
ejpam-4924	230	15	(	(	PUNCT
ejpam-4924	230	16	i)(a	i)(a	NOUN
ejpam-4924	230	17	,	,	PUNCT
ejpam-4924	230	18	b	b	NOUN
ejpam-4924	230	19	,	,	PUNCT
ejpam-4924	230	20	m	m	NOUN
ejpam-4924	230	21	)	)	PUNCT
ejpam-4924	230	22	=	=	SYM
ejpam-4924	230	23	0	0	NUM
ejpam-4924	230	24	,	,	PUNCT
ejpam-4924	230	25	∀a	∀a	NUM
ejpam-4924	230	26	,	,	PUNCT
ejpam-4924	230	27	b	b	X
ejpam-4924	230	28	∈	∈	PROPN
ejpam-4924	230	29	a;m	a;m	PROPN
ejpam-4924	230	30	∈	∈	NOUN
ejpam-4924	231	1	m	m	VERB
ejpam-4924	231	2	(	(	PUNCT
ejpam-4924	231	3	ii)ρbρc	ii)ρbρc	ADV
ejpam-4924	231	4	=	=	SYM
ejpam-4924	231	5	3λ2	3λ2	NUM
ejpam-4924	231	6	−	−	NUM
ejpam-4924	231	7	1	1	NUM
ejpam-4924	231	8	9λ3	9λ3	NUM
ejpam-4924	231	9	ρcb	ρcb	NOUN
ejpam-4924	231	10	,	,	PUNCT
ejpam-4924	231	11	∀a	∀a	X
ejpam-4924	231	12	,	,	PUNCT
ejpam-4924	231	13	b	b	X
ejpam-4924	231	14	∈	∈	PROPN
ejpam-4924	231	15	a;m	a;m	PROPN
ejpam-4924	231	16	∈	∈	NOUN
ejpam-4924	231	17	m	m	VERB
ejpam-4924	231	18	(	(	PUNCT
ejpam-4924	231	19	9	9	NUM
ejpam-4924	231	20	)	)	PUNCT
ejpam-4924	231	21	proof	proof	NOUN
ejpam-4924	231	22	.	.	PUNCT
ejpam-4924	232	1	suppose	suppose	VERB
ejpam-4924	232	2	m	m	VERB
ejpam-4924	232	3	=	=	ADJ
ejpam-4924	232	4	mλ	mλ	PROPN
ejpam-4924	232	5	,	,	PUNCT
ejpam-4924	232	6	λ	λ	PROPN
ejpam-4924	232	7	∈	∈	PROPN
ejpam-4924	232	8	{	{	PUNCT
ejpam-4924	232	9	λ1	λ1	ADJ
ejpam-4924	232	10	,	,	PUNCT
ejpam-4924	232	11	λ2	λ2	PROPN
ejpam-4924	232	12	}	}	PUNCT
ejpam-4924	232	13	then	then	ADV
ejpam-4924	232	14	m0	m0	PROPN
ejpam-4924	232	15	=	=	SYM
ejpam-4924	232	16	m1	m1	PROPN
ejpam-4924	232	17	=	=	PUNCT
ejpam-4924	232	18	{	{	PUNCT
ejpam-4924	232	19	0	0	NUM
ejpam-4924	232	20	}	}	PUNCT
ejpam-4924	232	21	.	.	PUNCT
ejpam-4924	233	1	let	let	VERB
ejpam-4924	233	2	a	a	DET
ejpam-4924	233	3	,	,	PUNCT
ejpam-4924	233	4	b	b	X
ejpam-4924	233	5	∈	∈	PROPN
ejpam-4924	233	6	a	a	PRON
ejpam-4924	233	7	be	be	AUX
ejpam-4924	233	8	such	such	ADJ
ejpam-4924	233	9	that	that	SCONJ
ejpam-4924	233	10	a	a	DET
ejpam-4924	233	11	=	=	PUNCT
ejpam-4924	233	12	a0+a1+aλ1	a0+a1+aλ1	PROPN
ejpam-4924	234	1	+	+	NOUN
ejpam-4924	234	2	aλ2	aλ2	PROPN
ejpam-4924	234	3	and	and	CCONJ
ejpam-4924	234	4	b	b	PROPN
ejpam-4924	234	5	=	=	SYM
ejpam-4924	234	6	b0	b0	PROPN
ejpam-4924	234	7	+	+	CCONJ
ejpam-4924	234	8	b1	b1	NOUN
ejpam-4924	234	9	+	+	CCONJ
ejpam-4924	234	10	bλ1	bλ1	NOUN
ejpam-4924	234	11	+	+	CCONJ
ejpam-4924	234	12	bλ2	bλ2	NOUN
ejpam-4924	234	13	,	,	PUNCT
ejpam-4924	234	14	where	where	SCONJ
ejpam-4924	234	15	ai	ai	VERB
ejpam-4924	234	16	,	,	PUNCT
ejpam-4924	234	17	bi	bi	PROPN
ejpam-4924	234	18	∈	∈	PROPN
ejpam-4924	234	19	ai	ai	VERB
ejpam-4924	234	20	,	,	PUNCT
ejpam-4924	234	21	i	i	PRON
ejpam-4924	234	22	∈	∈	PROPN
ejpam-4924	234	23	{	{	PUNCT
ejpam-4924	234	24	0	0	NUM
ejpam-4924	234	25	;	;	PUNCT
ejpam-4924	234	26	1;λ1;λ2	1;λ1;λ2	NUM
ejpam-4924	234	27	}	}	PUNCT
ejpam-4924	234	28	.	.	PUNCT
ejpam-4924	235	1	take	take	VERB
ejpam-4924	235	2	m	m	NOUN
ejpam-4924	235	3	∈	∈	NOUN
ejpam-4924	235	4	m	m	NOUN
ejpam-4924	235	5	=	=	ADJ
ejpam-4924	235	6	mλ	mλ	PROPN
ejpam-4924	235	7	,	,	PUNCT
ejpam-4924	236	1	so	so	ADV
ejpam-4924	236	2	m	m	NOUN
ejpam-4924	236	3	=	=	ADJ
ejpam-4924	236	4	mλ	mλ	NOUN
ejpam-4924	236	5	,	,	PUNCT
ejpam-4924	236	6	where	where	SCONJ
ejpam-4924	236	7	mλ	mλ	PROPN
ejpam-4924	236	8	∈	∈	PROPN
ejpam-4924	236	9	mλ	mλ	PROPN
ejpam-4924	236	10	,	,	PUNCT
ejpam-4924	236	11	i.e	i.e	PROPN
ejpam-4924	236	12	ρe(mλ	ρe(mλ	PROPN
ejpam-4924	236	13	)	)	PUNCT
ejpam-4924	237	1	=	=	SYM
ejpam-4924	237	2	λmλ	λmλ	PROPN
ejpam-4924	237	3	.	.	PUNCT
ejpam-4924	238	1	let	let	VERB
ejpam-4924	238	2	’s	’s	NOUN
ejpam-4924	238	3	calculate	calculate	NOUN
ejpam-4924	238	4	(	(	PUNCT
ejpam-4924	238	5	a	a	DET
ejpam-4924	238	6	,	,	PUNCT
ejpam-4924	238	7	b	b	NOUN
ejpam-4924	238	8	,	,	PUNCT
ejpam-4924	238	9	mλ	mλ	NOUN
ejpam-4924	238	10	)	)	PUNCT
ejpam-4924	238	11	,	,	PUNCT
ejpam-4924	238	12	(	(	PUNCT
ejpam-4924	238	13	a	a	PRON
ejpam-4924	238	14	,	,	PUNCT
ejpam-4924	238	15	mλ	mλ	INTJ
ejpam-4924	238	16	,	,	PUNCT
ejpam-4924	238	17	b	b	NOUN
ejpam-4924	238	18	)	)	PUNCT
ejpam-4924	238	19	∀a	∀a	NOUN
ejpam-4924	238	20	,	,	PUNCT
ejpam-4924	238	21	b	b	X
ejpam-4924	238	22	∈	∈	PROPN
ejpam-4924	238	23	a	a	PRON
ejpam-4924	238	24	and	and	CCONJ
ejpam-4924	238	25	m	m	NOUN
ejpam-4924	238	26	∈	∈	NOUN
ejpam-4924	238	27	m	m	NOUN
ejpam-4924	238	28	.	.	PUNCT
ejpam-4924	239	1	we	we	PRON
ejpam-4924	239	2	have	have	VERB
ejpam-4924	239	3	:	:	PUNCT
ejpam-4924	239	4	(	(	PUNCT
ejpam-4924	239	5	a	a	PRON
ejpam-4924	239	6	,	,	PUNCT
ejpam-4924	239	7	b	b	NOUN
ejpam-4924	239	8	,	,	PUNCT
ejpam-4924	239	9	m	m	NOUN
ejpam-4924	239	10	)	)	PUNCT
ejpam-4924	239	11	=	=	SYM
ejpam-4924	239	12	(	(	PUNCT
ejpam-4924	239	13	a0	a0	NOUN
ejpam-4924	239	14	+	+	CCONJ
ejpam-4924	239	15	a1	a1	NOUN
ejpam-4924	239	16	+	+	CCONJ
ejpam-4924	239	17	aλ1	aλ1	NOUN
ejpam-4924	239	18	+	+	CCONJ
ejpam-4924	239	19	aλ2	aλ2	NOUN
ejpam-4924	239	20	,	,	PUNCT
ejpam-4924	239	21	b0	b0	NOUN
ejpam-4924	239	22	+	+	CCONJ
ejpam-4924	239	23	b1	b1	NOUN
ejpam-4924	239	24	+	+	CCONJ
ejpam-4924	239	25	bλ1	bλ1	NOUN
ejpam-4924	239	26	+	+	CCONJ
ejpam-4924	239	27	bλ2	bλ2	NOUN
ejpam-4924	239	28	,	,	PUNCT
ejpam-4924	239	29	mλ	mλ	NOUN
ejpam-4924	239	30	)	)	PUNCT
ejpam-4924	239	31	=	=	SYM
ejpam-4924	239	32	(	(	PUNCT
ejpam-4924	239	33	a0	a0	PROPN
ejpam-4924	239	34	,	,	PUNCT
ejpam-4924	239	35	b0,mλ	b0,mλ	NUM
ejpam-4924	239	36	)	)	PUNCT
ejpam-4924	240	1	+	+	CCONJ
ejpam-4924	240	2	(	(	PUNCT
ejpam-4924	240	3	a0	a0	NOUN
ejpam-4924	240	4	,	,	PUNCT
ejpam-4924	240	5	b1,mλ	b1,mλ	X
ejpam-4924	240	6	)	)	PUNCT
ejpam-4924	241	1	+	+	CCONJ
ejpam-4924	241	2	(	(	PUNCT
ejpam-4924	241	3	a0	a0	NOUN
ejpam-4924	241	4	,	,	PUNCT
ejpam-4924	241	5	bλ1	bλ1	NOUN
ejpam-4924	241	6	,	,	PUNCT
ejpam-4924	241	7	mλ	mλ	NOUN
ejpam-4924	241	8	)	)	PUNCT
ejpam-4924	241	9	+	+	CCONJ
ejpam-4924	241	10	(	(	PUNCT
ejpam-4924	241	11	a0	a0	PROPN
ejpam-4924	241	12	,	,	PUNCT
ejpam-4924	241	13	bλ2	bλ2	NOUN
ejpam-4924	241	14	,	,	PUNCT
ejpam-4924	241	15	mλ	mλ	PROPN
ejpam-4924	241	16	)	)	PUNCT
ejpam-4924	242	1	+	+	CCONJ
ejpam-4924	242	2	(	(	PUNCT
ejpam-4924	242	3	a1	a1	PROPN
ejpam-4924	242	4	,	,	PUNCT
ejpam-4924	242	5	b0,mλ	b0,mλ	NUM
ejpam-4924	242	6	)	)	PUNCT
ejpam-4924	243	1	+	+	CCONJ
ejpam-4924	243	2	(	(	PUNCT
ejpam-4924	243	3	a1	a1	NOUN
ejpam-4924	243	4	,	,	PUNCT
ejpam-4924	243	5	b1,mλ	b1,mλ	NOUN
ejpam-4924	243	6	)	)	PUNCT
ejpam-4924	244	1	+	+	CCONJ
ejpam-4924	244	2	(	(	PUNCT
ejpam-4924	244	3	a1	a1	NOUN
ejpam-4924	244	4	,	,	PUNCT
ejpam-4924	244	5	bλ1	bλ1	NOUN
ejpam-4924	244	6	,	,	PUNCT
ejpam-4924	244	7	mλ	mλ	NOUN
ejpam-4924	244	8	)	)	PUNCT
ejpam-4924	244	9	+	+	CCONJ
ejpam-4924	244	10	(	(	PUNCT
ejpam-4924	244	11	a1	a1	PROPN
ejpam-4924	244	12	,	,	PUNCT
ejpam-4924	244	13	bλ2	bλ2	NOUN
ejpam-4924	244	14	,	,	PUNCT
ejpam-4924	244	15	mλ	mλ	PROPN
ejpam-4924	244	16	)	)	PUNCT
ejpam-4924	245	1	+	+	CCONJ
ejpam-4924	245	2	(	(	PUNCT
ejpam-4924	245	3	aλ1	aλ1	INTJ
ejpam-4924	245	4	,	,	PUNCT
ejpam-4924	245	5	b0,mλ	b0,mλ	NUM
ejpam-4924	245	6	)	)	PUNCT
ejpam-4924	246	1	+	+	CCONJ
ejpam-4924	246	2	(	(	PUNCT
ejpam-4924	246	3	aλ1	aλ1	INTJ
ejpam-4924	246	4	,	,	PUNCT
ejpam-4924	246	5	b1,mλ	b1,mλ	X
ejpam-4924	246	6	)	)	PUNCT
ejpam-4924	247	1	+	+	CCONJ
ejpam-4924	247	2	(	(	PUNCT
ejpam-4924	247	3	aλ1	aλ1	INTJ
ejpam-4924	247	4	,	,	PUNCT
ejpam-4924	247	5	bλ1	bλ1	NOUN
ejpam-4924	247	6	,	,	PUNCT
ejpam-4924	247	7	mλ	mλ	NOUN
ejpam-4924	247	8	)	)	PUNCT
ejpam-4924	248	1	+	+	CCONJ
ejpam-4924	248	2	(	(	PUNCT
ejpam-4924	248	3	aλ1	aλ1	INTJ
ejpam-4924	248	4	,	,	PUNCT
ejpam-4924	248	5	bλ2	bλ2	NOUN
ejpam-4924	248	6	,	,	PUNCT
ejpam-4924	248	7	mλ	mλ	PROPN
ejpam-4924	248	8	)	)	PUNCT
ejpam-4924	248	9	+	+	CCONJ
ejpam-4924	248	10	(	(	PUNCT
ejpam-4924	248	11	aλ2	aλ2	PROPN
ejpam-4924	248	12	,	,	PUNCT
ejpam-4924	248	13	b0,mλ	b0,mλ	NUM
ejpam-4924	248	14	)	)	PUNCT
ejpam-4924	248	15	+	+	CCONJ
ejpam-4924	248	16	(	(	PUNCT
ejpam-4924	248	17	aλ2	aλ2	PROPN
ejpam-4924	248	18	,	,	PUNCT
ejpam-4924	248	19	b1,mλ	b1,mλ	VERB
ejpam-4924	248	20	)	)	PUNCT
ejpam-4924	249	1	+	+	CCONJ
ejpam-4924	249	2	(	(	PUNCT
ejpam-4924	249	3	aλ2	aλ2	PROPN
ejpam-4924	249	4	,	,	PUNCT
ejpam-4924	249	5	bλ1	bλ1	NOUN
ejpam-4924	249	6	,	,	PUNCT
ejpam-4924	249	7	mλ	mλ	NOUN
ejpam-4924	249	8	)	)	PUNCT
ejpam-4924	250	1	+	+	CCONJ
ejpam-4924	250	2	(	(	PUNCT
ejpam-4924	250	3	aλ2	aλ2	PROPN
ejpam-4924	250	4	,	,	PUNCT
ejpam-4924	250	5	bλ2	bλ2	NOUN
ejpam-4924	250	6	,	,	PUNCT
ejpam-4924	250	7	mλ	mλ	NOUN
ejpam-4924	250	8	)	)	PUNCT
ejpam-4924	250	9	=	=	SYM
ejpam-4924	250	10	(	(	PUNCT
ejpam-4924	250	11	a0b0)mλ	a0b0)mλ	PROPN
ejpam-4924	250	12	−	−	PROPN
ejpam-4924	250	13	a0(b0mλ	a0(b0mλ	ADJ
ejpam-4924	250	14	)	)	PUNCT
ejpam-4924	250	15	+	+	CCONJ
ejpam-4924	250	16	(	(	PUNCT
ejpam-4924	250	17	a0b1)mλ	a0b1)mλ	PROPN
ejpam-4924	250	18	−	−	PROPN
ejpam-4924	250	19	a0(b1mλ	a0(b1mλ	VERB
ejpam-4924	250	20	)	)	PUNCT
ejpam-4924	251	1	+	+	CCONJ
ejpam-4924	251	2	(	(	PUNCT
ejpam-4924	251	3	a0bλ1)mλ	a0bλ1)mλ	NOUN
ejpam-4924	251	4	−	−	PROPN
ejpam-4924	251	5	a0(bλ1mλ	a0(bλ1mλ	PROPN
ejpam-4924	251	6	)	)	PUNCT
ejpam-4924	252	1	+	+	CCONJ
ejpam-4924	252	2	(	(	PUNCT
ejpam-4924	252	3	a0bλ2)mλ	a0bλ2)mλ	NOUN
ejpam-4924	252	4	−	−	PROPN
ejpam-4924	252	5	a0(bλ2mλ	a0(bλ2mλ	NOUN
ejpam-4924	252	6	)	)	PUNCT
ejpam-4924	253	1	+	+	CCONJ
ejpam-4924	253	2	(	(	PUNCT
ejpam-4924	253	3	a1b0)mλ	a1b0)mλ	ADV
ejpam-4924	253	4	−	−	PROPN
ejpam-4924	253	5	a1(b0mλ	a1(b0mλ	NOUN
ejpam-4924	253	6	)	)	PUNCT
ejpam-4924	254	1	+	+	CCONJ
ejpam-4924	254	2	(	(	PUNCT
ejpam-4924	254	3	a1b1)mλ	a1b1)mλ	ADP
ejpam-4924	254	4	−	−	PROPN
ejpam-4924	254	5	a1(b1mλ	a1(b1mλ	NOUN
ejpam-4924	254	6	)	)	PUNCT
ejpam-4924	255	1	+	+	CCONJ
ejpam-4924	255	2	(	(	PUNCT
ejpam-4924	255	3	a1bλ1)mλ	a1bλ1)mλ	PROPN
ejpam-4924	255	4	−	−	PROPN
ejpam-4924	255	5	a1(bλ1mλ	a1(bλ1mλ	ADJ
ejpam-4924	255	6	)	)	PUNCT
ejpam-4924	256	1	+	+	CCONJ
ejpam-4924	256	2	(	(	PUNCT
ejpam-4924	256	3	a1bλ2)mλ	a1bλ2)mλ	ADP
ejpam-4924	256	4	−	−	PROPN
ejpam-4924	256	5	a1(bλ2mλ	a1(bλ2mλ	ADV
ejpam-4924	256	6	)	)	PUNCT
ejpam-4924	257	1	+	+	CCONJ
ejpam-4924	257	2	(	(	PUNCT
ejpam-4924	257	3	aλ1b0)mλ	aλ1b0)mλ	PROPN
ejpam-4924	257	4	−	−	PROPN
ejpam-4924	257	5	aλ1(b0mλ	aλ1(b0mλ	NUM
ejpam-4924	257	6	)	)	PUNCT
ejpam-4924	258	1	+	+	CCONJ
ejpam-4924	258	2	(	(	PUNCT
ejpam-4924	258	3	aλ1b1)mλ	aλ1b1)mλ	PROPN
ejpam-4924	258	4	−	−	PROPN
ejpam-4924	258	5	aλ1(b1mλ	aλ1(b1mλ	PROPN
ejpam-4924	258	6	)	)	PUNCT
ejpam-4924	259	1	+	+	CCONJ
ejpam-4924	259	2	(	(	PUNCT
ejpam-4924	259	3	aλ1bλ1)mλ	aλ1bλ1)mλ	NOUN
ejpam-4924	259	4	−	−	ADP
ejpam-4924	259	5	aλ1(bλ1mλ	aλ1(bλ1mλ	NUM
ejpam-4924	259	6	)	)	PUNCT
ejpam-4924	260	1	+	+	CCONJ
ejpam-4924	260	2	(	(	PUNCT
ejpam-4924	260	3	aλ1bλ2)mλ	aλ1bλ2)mλ	NOUN
ejpam-4924	260	4	−	−	PROPN
ejpam-4924	260	5	aλ1(bλ2mλ	aλ1(bλ2mλ	NUM
ejpam-4924	260	6	)	)	PUNCT
ejpam-4924	261	1	+	+	CCONJ
ejpam-4924	261	2	(	(	PUNCT
ejpam-4924	261	3	aλ2b0)mλ	aλ2b0)mλ	PROPN
ejpam-4924	261	4	−	−	PROPN
ejpam-4924	261	5	aλ2(b0mλ	aλ2(b0mλ	NOUN
ejpam-4924	261	6	)	)	PUNCT
ejpam-4924	262	1	+	+	CCONJ
ejpam-4924	262	2	(	(	PUNCT
ejpam-4924	262	3	aλ2b1)mλ	aλ2b1)mλ	PROPN
ejpam-4924	262	4	−	−	PROPN
ejpam-4924	262	5	aλ2(b1mλ	aλ2(b1mλ	PROPN
ejpam-4924	262	6	)	)	PUNCT
ejpam-4924	263	1	+	+	CCONJ
ejpam-4924	263	2	(	(	PUNCT
ejpam-4924	263	3	aλ2bλ1)mλ	aλ2bλ1)mλ	NOUN
ejpam-4924	263	4	−	−	NOUN
ejpam-4924	263	5	aλ2(bλ1mλ	aλ2(bλ1mλ	NOUN
ejpam-4924	263	6	)	)	PUNCT
ejpam-4924	264	1	+	+	CCONJ
ejpam-4924	264	2	(	(	PUNCT
ejpam-4924	264	3	aλ2bλ2)mλ	aλ2bλ2)mλ	NUM
ejpam-4924	264	4	−	−	PROPN
ejpam-4924	264	5	aλ2(bλ2mλ	aλ2(bλ2mλ	ADJ
ejpam-4924	264	6	)	)	PUNCT
ejpam-4924	264	7	=	=	SYM
ejpam-4924	264	8	(	(	PUNCT
ejpam-4924	264	9	a0b0)mλ	a0b0)mλ	PROPN
ejpam-4924	264	10	−	−	PROPN
ejpam-4924	264	11	a0(b0mλ)−	a0(b0mλ)−	PROPN
ejpam-4924	264	12	a0(b1mλ)−	a0(b1mλ)−	NUM
ejpam-4924	264	13	a1(b0mλ	a1(b0mλ	NOUN
ejpam-4924	264	14	)	)	PUNCT
ejpam-4924	264	15	+	+	CCONJ
ejpam-4924	264	16	(	(	PUNCT
ejpam-4924	264	17	a1b1)mλ	a1b1)mλ	ADP
ejpam-4924	264	18	−	−	PROPN
ejpam-4924	264	19	a1(b1mλ	a1(b1mλ	NOUN
ejpam-4924	264	20	)	)	PUNCT
ejpam-4924	264	21	=	=	SYM
ejpam-4924	264	22	(	(	PUNCT
ejpam-4924	264	23	a0	a0	PROPN
ejpam-4924	264	24	,	,	PUNCT
ejpam-4924	264	25	b0,mλ	b0,mλ	NUM
ejpam-4924	264	26	)	)	PUNCT
ejpam-4924	265	1	+	+	CCONJ
ejpam-4924	265	2	(	(	PUNCT
ejpam-4924	265	3	a1	a1	PROPN
ejpam-4924	265	4	,	,	PUNCT
ejpam-4924	265	5	b1,mλ)−	b1,mλ)−	X
ejpam-4924	265	6	a0(b1mλ)−	a0(b1mλ)−	NUM
ejpam-4924	265	7	a1(b0mλ	a1(b0mλ	NOUN
ejpam-4924	265	8	)	)	PUNCT
ejpam-4924	265	9	similarly	similarly	ADV
ejpam-4924	265	10	,	,	PUNCT
ejpam-4924	265	11	if	if	SCONJ
ejpam-4924	265	12	∀m	∀m	PROPN
ejpam-4924	265	13	∈	∈	PROPN
ejpam-4924	265	14	m	m	NOUN
ejpam-4924	265	15	=	=	NOUN
ejpam-4924	265	16	mλ	mλ	NOUN
ejpam-4924	265	17	,	,	PUNCT
ejpam-4924	265	18	we	we	PRON
ejpam-4924	265	19	have	have	VERB
ejpam-4924	265	20	:	:	PUNCT
ejpam-4924	265	21	(	(	PUNCT
ejpam-4924	265	22	a	a	PRON
ejpam-4924	265	23	,	,	PUNCT
ejpam-4924	265	24	m	m	PROPN
ejpam-4924	265	25	,	,	PUNCT
ejpam-4924	265	26	b	b	NOUN
ejpam-4924	265	27	)	)	PUNCT
ejpam-4924	265	28	=	=	SYM
ejpam-4924	265	29	(	(	PUNCT
ejpam-4924	265	30	a0	a0	NOUN
ejpam-4924	265	31	+	+	CCONJ
ejpam-4924	265	32	a1	a1	NOUN
ejpam-4924	265	33	+	+	CCONJ
ejpam-4924	265	34	aλ1	aλ1	NOUN
ejpam-4924	265	35	+	+	CCONJ
ejpam-4924	265	36	aλ2	aλ2	PROPN
ejpam-4924	265	37	,	,	PUNCT
ejpam-4924	265	38	mλ	mλ	INTJ
ejpam-4924	265	39	,	,	PUNCT
ejpam-4924	265	40	b0	b0	NOUN
ejpam-4924	265	41	+	+	CCONJ
ejpam-4924	265	42	b1	b1	NOUN
ejpam-4924	265	43	+	+	CCONJ
ejpam-4924	265	44	bλ1	bλ1	NOUN
ejpam-4924	265	45	+	+	CCONJ
ejpam-4924	265	46	bλ2	bλ2	NOUN
ejpam-4924	265	47	)	)	PUNCT
ejpam-4924	266	1	=	=	PUNCT
ejpam-4924	266	2	(	(	PUNCT
ejpam-4924	266	3	a0,mλ	a0,mλ	PROPN
ejpam-4924	266	4	,	,	PUNCT
ejpam-4924	266	5	b0	b0	NOUN
ejpam-4924	266	6	)	)	PUNCT
ejpam-4924	266	7	+	+	CCONJ
ejpam-4924	266	8	(	(	PUNCT
ejpam-4924	266	9	a0,mλ	a0,mλ	ADJ
ejpam-4924	266	10	,	,	PUNCT
ejpam-4924	266	11	b1	b1	NOUN
ejpam-4924	266	12	)	)	PUNCT
ejpam-4924	266	13	+	+	CCONJ
ejpam-4924	266	14	(	(	PUNCT
ejpam-4924	266	15	a0,mλ	a0,mλ	ADJ
ejpam-4924	266	16	,	,	PUNCT
ejpam-4924	266	17	bλ1	bλ1	NOUN
ejpam-4924	266	18	)	)	PUNCT
ejpam-4924	266	19	+	+	CCONJ
ejpam-4924	266	20	(	(	PUNCT
ejpam-4924	266	21	a0,mλ	a0,mλ	PROPN
ejpam-4924	266	22	,	,	PUNCT
ejpam-4924	266	23	bλ2	bλ2	NOUN
ejpam-4924	266	24	)	)	PUNCT
ejpam-4924	267	1	+	+	CCONJ
ejpam-4924	267	2	(	(	PUNCT
ejpam-4924	267	3	a1,mλ	a1,mλ	PROPN
ejpam-4924	267	4	,	,	PUNCT
ejpam-4924	267	5	b0	b0	NOUN
ejpam-4924	267	6	)	)	PUNCT
ejpam-4924	267	7	+	+	CCONJ
ejpam-4924	267	8	(	(	PUNCT
ejpam-4924	267	9	a1,mλ	a1,mλ	PROPN
ejpam-4924	267	10	,	,	PUNCT
ejpam-4924	267	11	b1	b1	NOUN
ejpam-4924	267	12	)	)	PUNCT
ejpam-4924	267	13	h.	h.	PROPN
ejpam-4924	267	14	ouédraogo	ouédraogo	PROPN
ejpam-4924	267	15	,	,	PUNCT
ejpam-4924	267	16	a.	a.	NOUN
ejpam-4924	267	17	dembega	dembega	PROPN
ejpam-4924	267	18	,	,	PUNCT
ejpam-4924	267	19	a.	a.	PROPN
ejpam-4924	267	20	conseibo	conseibo	PROPN
ejpam-4924	267	21	/	/	SYM
ejpam-4924	267	22	eur	eur	PROPN
ejpam-4924	267	23	.	.	PUNCT
ejpam-4924	268	1	j.	j.	PROPN
ejpam-4924	268	2	pure	pure	PROPN
ejpam-4924	268	3	appl	appl	PROPN
ejpam-4924	268	4	.	.	PROPN
ejpam-4924	268	5	math	math	PROPN
ejpam-4924	268	6	,	,	PUNCT
ejpam-4924	268	7	16	16	NUM
ejpam-4924	268	8	(	(	PUNCT
ejpam-4924	268	9	4	4	NUM
ejpam-4924	268	10	)	)	PUNCT
ejpam-4924	268	11	(	(	PUNCT
ejpam-4924	268	12	2023	2023	NUM
ejpam-4924	268	13	)	)	PUNCT
ejpam-4924	268	14	,	,	PUNCT
ejpam-4924	268	15	2145	2145	NUM
ejpam-4924	268	16	-	-	SYM
ejpam-4924	268	17	2155	2155	NUM
ejpam-4924	268	18	2153	2153	NUM
ejpam-4924	268	19	+	+	CCONJ
ejpam-4924	268	20	(	(	PUNCT
ejpam-4924	268	21	a1,mλ	a1,mλ	ADJ
ejpam-4924	268	22	,	,	PUNCT
ejpam-4924	268	23	bλ1	bλ1	NOUN
ejpam-4924	268	24	)	)	PUNCT
ejpam-4924	268	25	+	+	CCONJ
ejpam-4924	268	26	(	(	PUNCT
ejpam-4924	268	27	a1,mλ	a1,mλ	PROPN
ejpam-4924	268	28	,	,	PUNCT
ejpam-4924	268	29	bλ2	bλ2	NOUN
ejpam-4924	268	30	)	)	PUNCT
ejpam-4924	269	1	+	+	CCONJ
ejpam-4924	269	2	(	(	PUNCT
ejpam-4924	269	3	aλ1	aλ1	INTJ
ejpam-4924	269	4	,	,	PUNCT
ejpam-4924	269	5	mλ	mλ	INTJ
ejpam-4924	269	6	,	,	PUNCT
ejpam-4924	269	7	b0	b0	NOUN
ejpam-4924	269	8	)	)	PUNCT
ejpam-4924	270	1	+	+	CCONJ
ejpam-4924	270	2	(	(	PUNCT
ejpam-4924	270	3	aλ1	aλ1	INTJ
ejpam-4924	270	4	,	,	PUNCT
ejpam-4924	270	5	mλ	mλ	INTJ
ejpam-4924	270	6	,	,	PUNCT
ejpam-4924	270	7	b1	b1	NOUN
ejpam-4924	270	8	)	)	PUNCT
ejpam-4924	271	1	+	+	CCONJ
ejpam-4924	271	2	(	(	PUNCT
ejpam-4924	271	3	aλ1	aλ1	INTJ
ejpam-4924	271	4	,	,	PUNCT
ejpam-4924	271	5	mλ	mλ	INTJ
ejpam-4924	271	6	,	,	PUNCT
ejpam-4924	271	7	bλ1	bλ1	NOUN
ejpam-4924	271	8	)	)	PUNCT
ejpam-4924	272	1	+	+	CCONJ
ejpam-4924	272	2	(	(	PUNCT
ejpam-4924	272	3	aλ1	aλ1	INTJ
ejpam-4924	272	4	,	,	PUNCT
ejpam-4924	272	5	mλ	mλ	INTJ
ejpam-4924	272	6	,	,	PUNCT
ejpam-4924	272	7	bλ2	bλ2	NOUN
ejpam-4924	272	8	)	)	PUNCT
ejpam-4924	273	1	+	+	CCONJ
ejpam-4924	273	2	(	(	PUNCT
ejpam-4924	273	3	aλ2	aλ2	PROPN
ejpam-4924	273	4	,	,	PUNCT
ejpam-4924	273	5	mλ	mλ	NOUN
ejpam-4924	273	6	,	,	PUNCT
ejpam-4924	273	7	b0	b0	NOUN
ejpam-4924	273	8	)	)	PUNCT
ejpam-4924	274	1	+	+	CCONJ
ejpam-4924	274	2	(	(	PUNCT
ejpam-4924	274	3	aλ2	aλ2	PROPN
ejpam-4924	274	4	,	,	PUNCT
ejpam-4924	274	5	mλ	mλ	NOUN
ejpam-4924	274	6	,	,	PUNCT
ejpam-4924	274	7	b1	b1	NOUN
ejpam-4924	274	8	)	)	PUNCT
ejpam-4924	275	1	+	+	CCONJ
ejpam-4924	275	2	(	(	PUNCT
ejpam-4924	275	3	aλ2	aλ2	PROPN
ejpam-4924	275	4	,	,	PUNCT
ejpam-4924	275	5	mλ	mλ	NOUN
ejpam-4924	275	6	,	,	PUNCT
ejpam-4924	275	7	bλ1	bλ1	NOUN
ejpam-4924	275	8	)	)	PUNCT
ejpam-4924	275	9	+	+	CCONJ
ejpam-4924	275	10	(	(	PUNCT
ejpam-4924	275	11	aλ2	aλ2	PROPN
ejpam-4924	275	12	,	,	PUNCT
ejpam-4924	275	13	mλ	mλ	INTJ
ejpam-4924	275	14	,	,	PUNCT
ejpam-4924	275	15	bλ2	bλ2	NOUN
ejpam-4924	275	16	)	)	PUNCT
ejpam-4924	275	17	=	=	SYM
ejpam-4924	276	1	(	(	PUNCT
ejpam-4924	276	2	a0mλ)b0	a0mλ)b0	PUNCT
ejpam-4924	276	3	−	−	PROPN
ejpam-4924	276	4	a0(mλb0	a0(mλb0	NOUN
ejpam-4924	276	5	)	)	PUNCT
ejpam-4924	277	1	+	+	CCONJ
ejpam-4924	277	2	(	(	PUNCT
ejpam-4924	277	3	a0mλ)b1	a0mλ)b1	PUNCT
ejpam-4924	277	4	−	−	PROPN
ejpam-4924	277	5	a0(mλb1	a0(mλb1	PROPN
ejpam-4924	277	6	)	)	PUNCT
ejpam-4924	277	7	+	+	CCONJ
ejpam-4924	277	8	(	(	PUNCT
ejpam-4924	277	9	a0mλ)bλ1	a0mλ)bλ1	NOUN
ejpam-4924	277	10	−	−	PROPN
ejpam-4924	277	11	a0(mλbλ1	a0(mλbλ1	NOUN
ejpam-4924	277	12	)	)	PUNCT
ejpam-4924	277	13	+	+	CCONJ
ejpam-4924	277	14	(	(	PUNCT
ejpam-4924	277	15	a0mλ)bλ2	a0mλ)bλ2	NOUN
ejpam-4924	277	16	−	−	PROPN
ejpam-4924	277	17	a0(mλbλ2	a0(mλbλ2	NOUN
ejpam-4924	277	18	)	)	PUNCT
ejpam-4924	277	19	+	+	CCONJ
ejpam-4924	277	20	(	(	PUNCT
ejpam-4924	277	21	a1mλ)b0	a1mλ)b0	NOUN
ejpam-4924	277	22	−	−	PUNCT
ejpam-4924	277	23	a1(mλb0	a1(mλb0	NOUN
ejpam-4924	277	24	)	)	PUNCT
ejpam-4924	277	25	+	+	CCONJ
ejpam-4924	277	26	(	(	PUNCT
ejpam-4924	277	27	a1mλ)b1	a1mλ)b1	X
ejpam-4924	277	28	−	−	PROPN
ejpam-4924	277	29	a1(mλb1	a1(mλb1	PROPN
ejpam-4924	277	30	)	)	PUNCT
ejpam-4924	277	31	+	+	CCONJ
ejpam-4924	277	32	(	(	PUNCT
ejpam-4924	277	33	a1mλ)bλ1	a1mλ)bλ1	NOUN
ejpam-4924	277	34	−	−	NOUN
ejpam-4924	277	35	a1(mλbλ1	a1(mλbλ1	NOUN
ejpam-4924	277	36	)	)	PUNCT
ejpam-4924	278	1	+	+	CCONJ
ejpam-4924	278	2	(	(	PUNCT
ejpam-4924	278	3	a1mλ)bλ2	a1mλ)bλ2	NOUN
ejpam-4924	278	4	−	−	PROPN
ejpam-4924	278	5	a1(mλbλ2	a1(mλbλ2	PROPN
ejpam-4924	278	6	)	)	PUNCT
ejpam-4924	279	1	+	+	CCONJ
ejpam-4924	279	2	(	(	PUNCT
ejpam-4924	279	3	aλ1mλ)b0	aλ1mλ)b0	ADJ
ejpam-4924	279	4	−	−	PROPN
ejpam-4924	279	5	aλ1(mλb0	aλ1(mλb0	NOUN
ejpam-4924	279	6	)	)	PUNCT
ejpam-4924	280	1	+	+	CCONJ
ejpam-4924	280	2	(	(	PUNCT
ejpam-4924	280	3	aλ1mλ)b1	aλ1mλ)b1	X
ejpam-4924	280	4	−	−	PROPN
ejpam-4924	280	5	aλ1(mλb1	aλ1(mλb1	PROPN
ejpam-4924	280	6	)	)	PUNCT
ejpam-4924	280	7	+	+	CCONJ
ejpam-4924	280	8	(	(	PUNCT
ejpam-4924	280	9	aλ1mλ)bλ1	aλ1mλ)bλ1	NOUN
ejpam-4924	280	10	−	−	PROPN
ejpam-4924	280	11	aλ1(mλbλ1	aλ1(mλbλ1	PROPN
ejpam-4924	280	12	)	)	PUNCT
ejpam-4924	281	1	+	+	CCONJ
ejpam-4924	281	2	(	(	PUNCT
ejpam-4924	281	3	aλ1mλ)bλ2	aλ1mλ)bλ2	NOUN
ejpam-4924	281	4	−	−	NOUN
ejpam-4924	281	5	aλ1(mλbλ2	aλ1(mλbλ2	NOUN
ejpam-4924	281	6	)	)	PUNCT
ejpam-4924	282	1	+	+	CCONJ
ejpam-4924	282	2	(	(	PUNCT
ejpam-4924	282	3	aλ2mλ)b0	aλ2mλ)b0	NOUN
ejpam-4924	282	4	−	−	NOUN
ejpam-4924	282	5	aλ2(mλb0	aλ2(mλb0	NOUN
ejpam-4924	282	6	)	)	PUNCT
ejpam-4924	283	1	+	+	CCONJ
ejpam-4924	283	2	(	(	PUNCT
ejpam-4924	283	3	aλ2mλ)b1	aλ2mλ)b1	NUM
ejpam-4924	283	4	−	−	PROPN
ejpam-4924	283	5	aλ2(mλb1	aλ2(mλb1	PROPN
ejpam-4924	283	6	)	)	PUNCT
ejpam-4924	283	7	+	+	CCONJ
ejpam-4924	283	8	(	(	PUNCT
ejpam-4924	283	9	aλ2mλ)bλ1	aλ2mλ)bλ1	NOUN
ejpam-4924	283	10	−	−	PROPN
ejpam-4924	283	11	aλ2(mλbλ1	aλ2(mλbλ1	NOUN
ejpam-4924	283	12	)	)	PUNCT
ejpam-4924	284	1	+	+	CCONJ
ejpam-4924	284	2	(	(	PUNCT
ejpam-4924	284	3	aλ2mλ)bλ2	aλ2mλ)bλ2	NOUN
ejpam-4924	284	4	−	−	PROPN
ejpam-4924	284	5	aλ2(mλbλ2	aλ2(mλbλ2	PROPN
ejpam-4924	284	6	)	)	PUNCT
ejpam-4924	284	7	=	=	PUNCT
ejpam-4924	285	1	(	(	PUNCT
ejpam-4924	285	2	a0mλ)b0	a0mλ)b0	PUNCT
ejpam-4924	285	3	−	−	PROPN
ejpam-4924	285	4	a0(mλb0	a0(mλb0	NOUN
ejpam-4924	285	5	)	)	PUNCT
ejpam-4924	286	1	+	+	CCONJ
ejpam-4924	286	2	(	(	PUNCT
ejpam-4924	286	3	a0mλ)b1	a0mλ)b1	PUNCT
ejpam-4924	286	4	−	−	PROPN
ejpam-4924	286	5	a0(mλb1	a0(mλb1	PROPN
ejpam-4924	286	6	)	)	PUNCT
ejpam-4924	286	7	+	+	CCONJ
ejpam-4924	286	8	(	(	PUNCT
ejpam-4924	286	9	a1mλ)b0	a1mλ)b0	NOUN
ejpam-4924	286	10	−	−	PUNCT
ejpam-4924	286	11	a1(mλb0	a1(mλb0	NOUN
ejpam-4924	286	12	)	)	PUNCT
ejpam-4924	286	13	+	+	CCONJ
ejpam-4924	286	14	(	(	PUNCT
ejpam-4924	286	15	a1mλ)b1	a1mλ)b1	X
ejpam-4924	286	16	−	−	PROPN
ejpam-4924	286	17	a1(mλb1	a1(mλb1	PROPN
ejpam-4924	286	18	)	)	PUNCT
ejpam-4924	286	19	=	=	PUNCT
ejpam-4924	286	20	(	(	PUNCT
ejpam-4924	286	21	a0,mλ	a0,mλ	PROPN
ejpam-4924	286	22	,	,	PUNCT
ejpam-4924	286	23	b0	b0	NOUN
ejpam-4924	286	24	)	)	PUNCT
ejpam-4924	287	1	+	+	CCONJ
ejpam-4924	287	2	(	(	PUNCT
ejpam-4924	287	3	a0,mλ	a0,mλ	ADJ
ejpam-4924	287	4	,	,	PUNCT
ejpam-4924	287	5	b1	b1	NOUN
ejpam-4924	287	6	)	)	PUNCT
ejpam-4924	287	7	+	+	CCONJ
ejpam-4924	287	8	(	(	PUNCT
ejpam-4924	287	9	a1,mλ	a1,mλ	PROPN
ejpam-4924	287	10	,	,	PUNCT
ejpam-4924	287	11	b0	b0	NOUN
ejpam-4924	287	12	)	)	PUNCT
ejpam-4924	288	1	+	+	CCONJ
ejpam-4924	288	2	(	(	PUNCT
ejpam-4924	288	3	a1,mλ	a1,mλ	PROPN
ejpam-4924	288	4	,	,	PUNCT
ejpam-4924	288	5	b1	b1	NOUN
ejpam-4924	288	6	)	)	PUNCT
ejpam-4924	288	7	partial	partial	ADJ
ejpam-4924	288	8	linearisation	linearisation	NOUN
ejpam-4924	288	9	of	of	ADP
ejpam-4924	288	10	the	the	DET
ejpam-4924	288	11	terms	term	NOUN
ejpam-4924	288	12	of	of	ADP
ejpam-4924	288	13	the	the	DET
ejpam-4924	288	14	identity	identity	NOUN
ejpam-4924	288	15	(	(	PUNCT
ejpam-4924	288	16	6	6	NUM
ejpam-4924	288	17	)	)	PUNCT
ejpam-4924	288	18	gives	give	VERB
ejpam-4924	288	19	us	we	PRON
ejpam-4924	288	20	:	:	PUNCT
ejpam-4924	288	21	ρbρaρa2	ρbρaρa2	X
ejpam-4924	289	1	=	=	PUNCT
ejpam-4924	289	2	ρbρcρa2	ρbρcρa2	NOUN
ejpam-4924	289	3	+	+	CCONJ
ejpam-4924	289	4	2ρbρaρac	2ρbρaρac	NUM
ejpam-4924	289	5	;	;	PUNCT
ejpam-4924	289	6	2ρbρ	2ρbρ	NUM
ejpam-4924	289	7	3	3	NUM
ejpam-4924	289	8	a	a	PRON
ejpam-4924	289	9	=	=	SYM
ejpam-4924	289	10	2(ρbρcρ	2(ρbρcρ	NUM
ejpam-4924	289	11	2	2	NUM
ejpam-4924	289	12	a	a	DET
ejpam-4924	289	13	+	+	NUM
ejpam-4924	289	14	ρbρaρcρa	ρbρaρcρa	NOUN
ejpam-4924	289	15	+	+	CCONJ
ejpam-4924	289	16	ρbρ	ρbρ	X
ejpam-4924	289	17	2	2	NUM
ejpam-4924	289	18	aρc	aρc	PROPN
ejpam-4924	289	19	)	)	PUNCT
ejpam-4924	289	20	;	;	PUNCT
ejpam-4924	290	1	ρbρa3	ρbρa3	NOUN
ejpam-4924	290	2	=	=	SYM
ejpam-4924	290	3	ρbρca2	ρbρca2	NOUN
ejpam-4924	290	4	+	+	CCONJ
ejpam-4924	290	5	2ρbρa(ac	2ρbρa(ac	NUM
ejpam-4924	290	6	)	)	PUNCT
ejpam-4924	290	7	;	;	PUNCT
ejpam-4924	290	8	4ρaρbρa2	4ρaρbρa2	X
ejpam-4924	291	1	=	=	SYM
ejpam-4924	291	2	4(ρcρbρa2	4(ρcρbρa2	PROPN
ejpam-4924	291	3	+	+	CCONJ
ejpam-4924	291	4	2ρaρbρac	2ρaρbρac	NUM
ejpam-4924	291	5	)	)	PUNCT
ejpam-4924	291	6	;	;	PUNCT
ejpam-4924	291	7	8ρaρbρ	8ρaρbρ	NUM
ejpam-4924	291	8	2	2	NUM
ejpam-4924	291	9	a	a	PRON
ejpam-4924	291	10	=	=	NOUN
ejpam-4924	291	11	8(ρcρbρ	8(ρcρbρ	ADJ
ejpam-4924	291	12	2	2	NUM
ejpam-4924	291	13	a	a	DET
ejpam-4924	291	14	+	+	CCONJ
ejpam-4924	291	15	ρaρbρcρa	ρaρbρcρa	ADJ
ejpam-4924	291	16	+	+	CCONJ
ejpam-4924	291	17	ρaρbρaρc	ρaρbρaρc	ADJ
ejpam-4924	291	18	)	)	PUNCT
ejpam-4924	291	19	;	;	PUNCT
ejpam-4924	291	20	4ρa3b	4ρa3b	NUM
ejpam-4924	291	21	=	=	SYM
ejpam-4924	291	22	4(ρ(ca2)b	4(ρ(ca2)b	PROPN
ejpam-4924	291	23	+	+	NOUN
ejpam-4924	291	24	2ρ(a(ac))b	2ρ(a(ac))b	NUM
ejpam-4924	291	25	)	)	PUNCT
ejpam-4924	291	26	;	;	PUNCT
ejpam-4924	291	27	12ρ2aρbρa	12ρ2aρbρa	NOUN
ejpam-4924	291	28	=	=	SYM
ejpam-4924	291	29	12(ρaρcρbρa	12(ρaρcρbρa	NUM
ejpam-4924	291	30	+	+	CCONJ
ejpam-4924	291	31	ρcρaρbρa	ρcρaρbρa	NOUN
ejpam-4924	291	32	+	+	CCONJ
ejpam-4924	291	33	ρ2aρbρc	ρ2aρbρc	NUM
ejpam-4924	291	34	)	)	PUNCT
ejpam-4924	291	35	;	;	PUNCT
ejpam-4924	292	1	6ρaρa2b	6ρaρa2b	NUM
ejpam-4924	292	2	=	=	SYM
ejpam-4924	292	3	6(ρcρa2b	6(ρcρa2b	NUM
ejpam-4924	292	4	+	+	CCONJ
ejpam-4924	292	5	2ρaρ(ca)b	2ρaρ(ca)b	NUM
ejpam-4924	292	6	)	)	PUNCT
ejpam-4924	292	7	;	;	PUNCT
ejpam-4924	292	8	6ρa(a2b	6ρa(a2b	NUM
ejpam-4924	292	9	)	)	PUNCT
ejpam-4924	292	10	=	=	SYM
ejpam-4924	292	11	6(ρc(a2b	6(ρc(a2b	NOUN
ejpam-4924	292	12	)	)	PUNCT
ejpam-4924	292	13	+	+	NUM
ejpam-4924	292	14	2ρa((ac)b	2ρa((ac)b	NUM
ejpam-4924	292	15	)	)	PUNCT
ejpam-4924	292	16	)	)	PUNCT
ejpam-4924	292	17	;	;	PUNCT
ejpam-4924	293	1	3ρ3aρb	3ρ3aρb	NUM
ejpam-4924	293	2	=	=	SYM
ejpam-4924	294	1	3(ρcρ	3(ρcρ	NUM
ejpam-4924	294	2	2	2	NUM
ejpam-4924	294	3	aρb	aρb	VERB
ejpam-4924	294	4	+	+	CCONJ
ejpam-4924	294	5	ρaρcρaρb	ρaρcρaρb	VERB
ejpam-4924	294	6	+	+	CCONJ
ejpam-4924	294	7	ρ2aρcρb	ρ2aρcρb	ADJ
ejpam-4924	294	8	)	)	PUNCT
ejpam-4924	294	9	;	;	PUNCT
ejpam-4924	295	1	3ρ2aρab	3ρ2aρab	NOUN
ejpam-4924	295	2	=	=	SYM
ejpam-4924	295	3	3(ρcρaρab	3(ρcρaρab	PROPN
ejpam-4924	295	4	+	+	CCONJ
ejpam-4924	295	5	ρaρcρab	ρaρcρab	NOUN
ejpam-4924	295	6	+	+	CCONJ
ejpam-4924	295	7	ρ2aρcb	ρ2aρcb	NOUN
ejpam-4924	295	8	)	)	PUNCT
ejpam-4924	295	9	;	;	PUNCT
ejpam-4924	295	10	3ρaρa(ab	3ρaρa(ab	NUM
ejpam-4924	295	11	)	)	PUNCT
ejpam-4924	295	12	=	=	SYM
ejpam-4924	295	13	3(ρcρa(ab	3(ρcρa(ab	NUM
ejpam-4924	295	14	)	)	PUNCT
ejpam-4924	295	15	+	+	CCONJ
ejpam-4924	295	16	ρaρc(ab	ρaρc(ab	NOUN
ejpam-4924	295	17	)	)	PUNCT
ejpam-4924	295	18	+	+	CCONJ
ejpam-4924	295	19	ρaρa(cb	ρaρa(cb	NOUN
ejpam-4924	295	20	)	)	PUNCT
ejpam-4924	295	21	)	)	PUNCT
ejpam-4924	295	22	;	;	PUNCT
ejpam-4924	295	23	3ρa(a(ab	3ρa(a(ab	NUM
ejpam-4924	295	24	)	)	PUNCT
ejpam-4924	295	25	)	)	PUNCT
ejpam-4924	296	1	=	=	SYM
ejpam-4924	296	2	3(ρc(a(ab	3(ρc(a(ab	NUM
ejpam-4924	296	3	)	)	PUNCT
ejpam-4924	296	4	)	)	PUNCT
ejpam-4924	297	1	+	+	NUM
ejpam-4924	297	2	ρa(c(ab	ρa(c(ab	NUM
ejpam-4924	297	3	)	)	PUNCT
ejpam-4924	297	4	)	)	PUNCT
ejpam-4924	298	1	+	+	PUNCT
ejpam-4924	298	2	ρa(a(cb	ρa(a(cb	NUM
ejpam-4924	298	3	)	)	PUNCT
ejpam-4924	298	4	)	)	PUNCT
ejpam-4924	298	5	)	)	PUNCT
ejpam-4924	298	6	.	.	PUNCT
ejpam-4924	299	1	putting	put	VERB
ejpam-4924	299	2	it	it	PRON
ejpam-4924	299	3	all	all	PRON
ejpam-4924	299	4	together	together	ADV
ejpam-4924	299	5	gives	give	VERB
ejpam-4924	299	6	:	:	PUNCT
ejpam-4924	299	7	[	[	X
ejpam-4924	299	8	ρbρcρa2	ρbρcρa2	NOUN
ejpam-4924	299	9	+	+	CCONJ
ejpam-4924	299	10	2ρbρaρac	2ρbρaρac	NUM
ejpam-4924	299	11	+	+	NUM
ejpam-4924	299	12	2ρbρcρ	2ρbρcρ	NUM
ejpam-4924	299	13	2	2	NUM
ejpam-4924	299	14	a	a	DET
ejpam-4924	299	15	+	+	NOUN
ejpam-4924	299	16	2ρbρaρcρa	2ρbρaρcρa	NUM
ejpam-4924	299	17	+	+	CCONJ
ejpam-4924	299	18	2ρbρ	2ρbρ	NUM
ejpam-4924	299	19	2	2	NUM
ejpam-4924	299	20	aρc	aρc	VERB
ejpam-4924	299	21	+	+	X
ejpam-4924	299	22	ρbρca2	ρbρca2	NOUN
ejpam-4924	299	23	+	+	CCONJ
ejpam-4924	299	24	2ρbρa(ac	2ρbρa(ac	NUM
ejpam-4924	299	25	)	)	PUNCT
ejpam-4924	299	26	−	−	NOUN
ejpam-4924	299	27	4ρcρbρa2	4ρcρbρa2	NUM
ejpam-4924	299	28	−8ρaρbρac−8ρcρbρ	−8ρaρbρac−8ρcρbρ	X
ejpam-4924	299	29	2	2	NUM
ejpam-4924	299	30	a−8ρaρbρcρa−8ρaρbρaρc−4ρ(ca2)b−8ρ(a(ac))b+12ρaρcρbρa+12ρcρaρbρa+12ρ2aρbρc	a−8ρaρbρcρa−8ρaρbρaρc−4ρ(ca2)b−8ρ(a(ac))b+12ρaρcρbρa+12ρcρaρbρa+12ρ2aρbρc	PROPN
ejpam-4924	299	31	+6ρcρa2b+12ρaρ(ca)b+6ρc(a2b)+12ρa((ac)b)−3ρcρ	+6ρcρa2b+12ρaρ(ca)b+6ρc(a2b)+12ρa((ac)b)−3ρcρ	NUM
ejpam-4924	299	32	2	2	NUM
ejpam-4924	299	33	aρb−3ρaρcρaρb−3ρ2aρcρb−3ρcρaρab−3ρaρcρab−3ρ2aρcb	aρb−3ρaρcρaρb−3ρ2aρcρb−3ρcρaρab−3ρaρcρab−3ρ2aρcb	NUM
ejpam-4924	299	34	−	−	PROPN
ejpam-4924	299	35	3ρcρa(ab	3ρcρa(ab	NUM
ejpam-4924	299	36	)	)	PUNCT
ejpam-4924	299	37	−	−	PROPN
ejpam-4924	299	38	3ρaρc(ab	3ρaρc(ab	NUM
ejpam-4924	299	39	)	)	PUNCT
ejpam-4924	299	40	−	−	PROPN
ejpam-4924	299	41	3ρaρa(cb	3ρaρa(cb	NUM
ejpam-4924	299	42	)	)	PUNCT
ejpam-4924	299	43	−	−	PROPN
ejpam-4924	300	1	3ρc(a(ab	3ρc(a(ab	NUM
ejpam-4924	300	2	)	)	PUNCT
ejpam-4924	300	3	)	)	PUNCT
ejpam-4924	301	1	−	−	ADP
ejpam-4924	301	2	3ρa(c(ab	3ρa(c(ab	NUM
ejpam-4924	301	3	)	)	PUNCT
ejpam-4924	301	4	)	)	PUNCT
ejpam-4924	302	1	−	−	PROPN
ejpam-4924	302	2	3ρa(a(cb))](m	3ρa(a(cb))](m	NUM
ejpam-4924	302	3	)	)	PUNCT
ejpam-4924	302	4	=	=	SYM
ejpam-4924	303	1	0	0	X
ejpam-4924	303	2	.	.	PUNCT
ejpam-4924	304	1	(	(	PUNCT
ejpam-4924	304	2	10	10	NUM
ejpam-4924	304	3	)	)	PUNCT
ejpam-4924	304	4	if	if	SCONJ
ejpam-4924	304	5	we	we	PRON
ejpam-4924	304	6	put	put	VERB
ejpam-4924	304	7	a	a	PRON
ejpam-4924	304	8	=	=	X
ejpam-4924	304	9	e	e	NOUN
ejpam-4924	304	10	in	in	ADP
ejpam-4924	304	11	(	(	PUNCT
ejpam-4924	304	12	10	10	NUM
ejpam-4924	304	13	)	)	PUNCT
ejpam-4924	304	14	then	then	ADV
ejpam-4924	305	1	[	[	X
ejpam-4924	305	2	ρbρcρe2	ρbρcρe2	X
ejpam-4924	305	3	+	+	CCONJ
ejpam-4924	305	4	2ρbρeρec	2ρbρeρec	NUM
ejpam-4924	305	5	+	+	CCONJ
ejpam-4924	305	6	2ρbρcρ	2ρbρcρ	NUM
ejpam-4924	305	7	2	2	NUM
ejpam-4924	305	8	e	e	NOUN
ejpam-4924	305	9	+	+	NOUN
ejpam-4924	305	10	2ρbρeρcρe	2ρbρeρcρe	NUM
ejpam-4924	305	11	+	+	CCONJ
ejpam-4924	305	12	2ρbρ	2ρbρ	NUM
ejpam-4924	305	13	2	2	NUM
ejpam-4924	305	14	eρc	eρc	NOUN
ejpam-4924	305	15	+	+	NOUN
ejpam-4924	305	16	ρbρce2	ρbρce2	NOUN
ejpam-4924	305	17	+	+	CCONJ
ejpam-4924	305	18	2ρbρe(ec	2ρbρe(ec	NUM
ejpam-4924	305	19	)	)	PUNCT
ejpam-4924	305	20	−	−	PROPN
ejpam-4924	305	21	4ρcρbρe2	4ρcρbρe2	NUM
ejpam-4924	305	22	h.	h.	PROPN
ejpam-4924	305	23	ouédraogo	ouédraogo	PROPN
ejpam-4924	305	24	,	,	PUNCT
ejpam-4924	305	25	a.	a.	NOUN
ejpam-4924	305	26	dembega	dembega	PROPN
ejpam-4924	305	27	,	,	PUNCT
ejpam-4924	305	28	a.	a.	PROPN
ejpam-4924	305	29	conseibo	conseibo	PROPN
ejpam-4924	305	30	/	/	SYM
ejpam-4924	305	31	eur	eur	PROPN
ejpam-4924	305	32	.	.	PUNCT
ejpam-4924	306	1	j.	j.	PROPN
ejpam-4924	306	2	pure	pure	PROPN
ejpam-4924	306	3	appl	appl	PROPN
ejpam-4924	306	4	.	.	PROPN
ejpam-4924	306	5	math	math	PROPN
ejpam-4924	306	6	,	,	PUNCT
ejpam-4924	306	7	16	16	NUM
ejpam-4924	306	8	(	(	PUNCT
ejpam-4924	306	9	4	4	NUM
ejpam-4924	306	10	)	)	PUNCT
ejpam-4924	306	11	(	(	PUNCT
ejpam-4924	306	12	2023	2023	NUM
ejpam-4924	306	13	)	)	PUNCT
ejpam-4924	306	14	,	,	PUNCT
ejpam-4924	306	15	2145	2145	NUM
ejpam-4924	306	16	-	-	SYM
ejpam-4924	306	17	2155	2155	NUM
ejpam-4924	306	18	2154	2154	NUM
ejpam-4924	306	19	−8ρeρbρec−8ρcρbρ	−8ρeρbρec−8ρcρbρ	X
ejpam-4924	306	20	2	2	NUM
ejpam-4924	306	21	e−8ρeρbρcρe−8ρeρbρeρc−4ρ(ce2)b−8ρ(e(ec))b+12ρeρcρbρe+12ρcρeρbρe+12ρ2eρbρc	e−8ρeρbρcρe−8ρeρbρeρc−4ρ(ce2)b−8ρ(e(ec))b+12ρeρcρbρe+12ρcρeρbρe+12ρ2eρbρc	VERB
ejpam-4924	306	22	+6ρcρe2b+12ρeρ(ce)b+6ρc(e2b)+12ρe((ec)b)−3ρcρ	+6ρcρe2b+12ρeρ(ce)b+6ρc(e2b)+12ρe((ec)b)−3ρcρ	NUM
ejpam-4924	306	23	2	2	NUM
ejpam-4924	306	24	eρb−3ρeρcρeρb−3ρ2eρcρb−3ρcρeρeb−3ρeρcρeb−3ρ2eρcb	eρb−3ρeρcρeρb−3ρ2eρcρb−3ρcρeρeb−3ρeρcρeb−3ρ2eρcb	NOUN
ejpam-4924	306	25	−	−	PROPN
ejpam-4924	306	26	3ρcρe(eb	3ρcρe(eb	NUM
ejpam-4924	306	27	)	)	PUNCT
ejpam-4924	306	28	−	−	PROPN
ejpam-4924	306	29	3ρeρc(eb	3ρeρc(eb	NUM
ejpam-4924	306	30	)	)	PUNCT
ejpam-4924	307	1	−	−	PROPN
ejpam-4924	307	2	3ρeρe(cb	3ρeρe(cb	NUM
ejpam-4924	307	3	)	)	PUNCT
ejpam-4924	307	4	−	−	PROPN
ejpam-4924	307	5	3ρc(e(eb	3ρc(e(eb	NUM
ejpam-4924	307	6	)	)	PUNCT
ejpam-4924	307	7	)	)	PUNCT
ejpam-4924	308	1	−	−	PROPN
ejpam-4924	308	2	3ρe(c(eb	3ρe(c(eb	NUM
ejpam-4924	308	3	)	)	PUNCT
ejpam-4924	308	4	)	)	PUNCT
ejpam-4924	309	1	−	−	PROPN
ejpam-4924	309	2	3ρe(e(cb))](m	3ρe(e(cb))](m	NUM
ejpam-4924	309	3	)	)	PUNCT
ejpam-4924	309	4	=	=	SYM
ejpam-4924	309	5	0	0	X
ejpam-4924	309	6	.	.	PUNCT
ejpam-4924	310	1	(	(	PUNCT
ejpam-4924	310	2	11	11	NUM
ejpam-4924	310	3	)	)	PUNCT
ejpam-4924	310	4	we	we	PRON
ejpam-4924	310	5	will	will	AUX
ejpam-4924	310	6	demonstrate	demonstrate	VERB
ejpam-4924	310	7	(	(	PUNCT
ejpam-4924	310	8	i	i	NOUN
ejpam-4924	310	9	)	)	PUNCT
ejpam-4924	310	10	and	and	CCONJ
ejpam-4924	310	11	(	(	PUNCT
ejpam-4924	310	12	ii	ii	NOUN
ejpam-4924	310	13	)	)	PUNCT
ejpam-4924	310	14	by	by	ADP
ejpam-4924	310	15	taking	take	VERB
ejpam-4924	310	16	a	a	DET
ejpam-4924	310	17	,	,	PUNCT
ejpam-4924	310	18	b	b	PROPN
ejpam-4924	310	19	∈	∈	NOUN
ejpam-4924	310	20	a1	a1	NOUN
ejpam-4924	310	21	and	and	CCONJ
ejpam-4924	310	22	m	m	PROPN
ejpam-4924	310	23	∈	∈	NOUN
ejpam-4924	310	24	mλ	mλ	NOUN
ejpam-4924	310	25	,	,	PUNCT
ejpam-4924	310	26	with	with	ADP
ejpam-4924	310	27	λ	λ	PROPN
ejpam-4924	310	28	∈	∈	PROPN
ejpam-4924	310	29	{	{	PUNCT
ejpam-4924	310	30	λ1	λ1	ADJ
ejpam-4924	310	31	,	,	PUNCT
ejpam-4924	310	32	λ2	λ2	PROPN
ejpam-4924	310	33	}	}	PUNCT
ejpam-4924	310	34	.	.	PUNCT
ejpam-4924	311	1	if	if	SCONJ
ejpam-4924	311	2	m	m	NOUN
ejpam-4924	311	3	=	=	VERB
ejpam-4924	311	4	mλi	mλi	NOUN
ejpam-4924	311	5	,	,	PUNCT
ejpam-4924	311	6	i	i	PRON
ejpam-4924	311	7	=	=	NOUN
ejpam-4924	311	8	1	1	NUM
ejpam-4924	311	9	,	,	PUNCT
ejpam-4924	311	10	2	2	NUM
ejpam-4924	311	11	,	,	PUNCT
ejpam-4924	311	12	we	we	PRON
ejpam-4924	311	13	have	have	VERB
ejpam-4924	311	14	ρe	ρe	NOUN
ejpam-4924	311	15	=	=	PUNCT
ejpam-4924	311	16	λiidm	λiidm	NOUN
ejpam-4924	311	17	.	.	PUNCT
ejpam-4924	312	1	by	by	ADP
ejpam-4924	312	2	replacing	replace	VERB
ejpam-4924	312	3	b	b	NUM
ejpam-4924	312	4	,	,	PUNCT
ejpam-4924	312	5	c	c	PROPN
ejpam-4924	312	6	∈	∈	PROPN
ejpam-4924	312	7	a1	a1	NOUN
ejpam-4924	312	8	and	and	CCONJ
ejpam-4924	312	9	m	m	PROPN
ejpam-4924	312	10	∈	∈	NOUN
ejpam-4924	312	11	m	m	VERB
ejpam-4924	312	12	in	in	ADP
ejpam-4924	312	13	(	(	PUNCT
ejpam-4924	312	14	11	11	NUM
ejpam-4924	312	15	)	)	PUNCT
ejpam-4924	312	16	we	we	PRON
ejpam-4924	312	17	obtain	obtain	VERB
ejpam-4924	312	18	:	:	PUNCT
ejpam-4924	313	1	[	[	X
ejpam-4924	313	2	λρbρc+2λρbρc+2λ2ρbρc+2λ2ρbρc+2λ2ρbρc+ρbρc+2ρbρc−4λρcρb−8λρbρc−8λ2ρcρb−8λ2ρbρc	λρbρc+2λρbρc+2λ2ρbρc+2λ2ρbρc+2λ2ρbρc+ρbρc+2ρbρc−4λρcρb−8λρbρc−8λ2ρcρb−8λ2ρbρc	NOUN
ejpam-4924	313	3	−	−	X
ejpam-4924	313	4	8λ2ρbρc	8λ2ρbρc	NUM
ejpam-4924	313	5	−	−	PROPN
ejpam-4924	313	6	4ρcb	4ρcb	NUM
ejpam-4924	313	7	−	−	PROPN
ejpam-4924	313	8	8ρcb	8ρcb	NUM
ejpam-4924	313	9	+	+	CCONJ
ejpam-4924	313	10	12λ2ρcρb	12λ2ρcρb	ADJ
ejpam-4924	313	11	+	+	CCONJ
ejpam-4924	313	12	12λ2ρcρb	12λ2ρcρb	NOUN
ejpam-4924	314	1	+	+	CCONJ
ejpam-4924	314	2	12λ2ρbρc	12λ2ρbρc	PROPN
ejpam-4924	314	3	+	+	CCONJ
ejpam-4924	314	4	6ρcρb	6ρcρb	NUM
ejpam-4924	315	1	+	+	NUM
ejpam-4924	315	2	12λρcb	12λρcb	NUM
ejpam-4924	316	1	+	+	CCONJ
ejpam-4924	316	2	6ρcb	6ρcb	NUM
ejpam-4924	316	3	+	+	NUM
ejpam-4924	316	4	12ρcb	12ρcb	NUM
ejpam-4924	316	5	−3λ2ρcρb−3λ2ρcρb−3λ2ρcρb−3λρcρb−3λρcρb−3λ2ρcb−3ρcρb−3λρcb−3λρcb−3ρcb−3ρcb−3ρcb](m	−3λ2ρcρb−3λ2ρcρb−3λ2ρcρb−3λρcρb−3λρcρb−3λ2ρcb−3ρcρb−3λρcb−3λρcb−3ρcb−3ρcb−3ρcb](m	NOUN
ejpam-4924	316	6	)	)	PUNCT
ejpam-4924	316	7	=	=	SYM
ejpam-4924	317	1	0	0	X
ejpam-4924	317	2	.	.	PUNCT
ejpam-4924	318	1	after	after	ADP
ejpam-4924	318	2	reduction	reduction	NOUN
ejpam-4924	318	3	we	we	PRON
ejpam-4924	318	4	have	have	VERB
ejpam-4924	318	5	:	:	PUNCT
ejpam-4924	318	6	(	(	PUNCT
ejpam-4924	318	7	2λ2	2λ2	NUM
ejpam-4924	318	8	−	−	NUM
ejpam-4924	318	9	5λ+	5λ+	NUM
ejpam-4924	318	10	3)ρbρc	3)ρbρc	NUM
ejpam-4924	318	11	+	+	CCONJ
ejpam-4924	318	12	(	(	PUNCT
ejpam-4924	318	13	7λ2	7λ2	NUM
ejpam-4924	318	14	−	−	NUM
ejpam-4924	318	15	10λ+	10λ+	NUM
ejpam-4924	318	16	3)ρcρb	3)ρcρb	NUM
ejpam-4924	318	17	+	+	CCONJ
ejpam-4924	318	18	(	(	PUNCT
ejpam-4924	318	19	−3λ2	−3λ2	PUNCT
ejpam-4924	318	20	+	+	CCONJ
ejpam-4924	318	21	6λ−	6λ−	NOUN
ejpam-4924	318	22	3)ρcb	3)ρcb	NUM
ejpam-4924	318	23	=	=	SYM
ejpam-4924	318	24	0	0	NUM
ejpam-4924	318	25	.	.	PUNCT
ejpam-4924	319	1	(	(	PUNCT
ejpam-4924	319	2	12	12	NUM
ejpam-4924	319	3	)	)	PUNCT
ejpam-4924	319	4	since	since	SCONJ
ejpam-4924	319	5	3λ2	3λ2	NUM
ejpam-4924	319	6	=	=	SYM
ejpam-4924	319	7	3λ−	3λ−	NUM
ejpam-4924	319	8	1	1	NUM
ejpam-4924	319	9	,	,	PUNCT
ejpam-4924	319	10	then	then	ADV
ejpam-4924	319	11	1	1	NUM
ejpam-4924	319	12	3	3	NUM
ejpam-4924	319	13	(	(	PUNCT
ejpam-4924	319	14	−9λ+	−9λ+	NUM
ejpam-4924	319	15	7)ρbρc	7)ρbρc	NUM
ejpam-4924	319	16	+	+	CCONJ
ejpam-4924	319	17	1	1	NUM
ejpam-4924	319	18	3	3	NUM
ejpam-4924	319	19	(	(	PUNCT
ejpam-4924	319	20	−9λ+	−9λ+	NUM
ejpam-4924	319	21	2)ρcρb	2)ρcρb	NUM
ejpam-4924	319	22	+	+	CCONJ
ejpam-4924	319	23	1	1	NUM
ejpam-4924	319	24	3	3	NUM
ejpam-4924	319	25	(	(	PUNCT
ejpam-4924	319	26	9λ−	9λ−	NOUN
ejpam-4924	319	27	6)ρcb	6)ρcb	NUM
ejpam-4924	319	28	=	=	NOUN
ejpam-4924	319	29	0	0	NUM
ejpam-4924	319	30	.	.	PUNCT
ejpam-4924	320	1	(	(	PUNCT
ejpam-4924	320	2	−9λ+	−9λ+	PROPN
ejpam-4924	320	3	7)ρbρc	7)ρbρc	NUM
ejpam-4924	320	4	+	+	CCONJ
ejpam-4924	320	5	(	(	PUNCT
ejpam-4924	320	6	−9λ+	−9λ+	X
ejpam-4924	320	7	2)ρcρb	2)ρcρb	NUM
ejpam-4924	320	8	+	+	CCONJ
ejpam-4924	320	9	(	(	PUNCT
ejpam-4924	320	10	9λ−	9λ−	NUM
ejpam-4924	320	11	6)ρcb	6)ρcb	NUM
ejpam-4924	320	12	=	=	SYM
ejpam-4924	320	13	0	0	PUNCT
ejpam-4924	320	14	(	(	PUNCT
ejpam-4924	320	15	13	13	NUM
ejpam-4924	320	16	)	)	PUNCT
ejpam-4924	320	17	by	by	ADP
ejpam-4924	320	18	interchanging	interchanging	PROPN
ejpam-4924	320	19	b	b	PROPN
ejpam-4924	320	20	and	and	CCONJ
ejpam-4924	320	21	c	c	PROPN
ejpam-4924	320	22	in	in	ADP
ejpam-4924	320	23	(	(	PUNCT
ejpam-4924	320	24	13	13	NUM
ejpam-4924	320	25	)	)	PUNCT
ejpam-4924	320	26	we	we	PRON
ejpam-4924	320	27	obtain	obtain	VERB
ejpam-4924	320	28	:	:	PUNCT
ejpam-4924	320	29	(	(	PUNCT
ejpam-4924	320	30	−9λ+	−9λ+	NUM
ejpam-4924	320	31	7)ρcρb	7)ρcρb	NUM
ejpam-4924	320	32	+	+	CCONJ
ejpam-4924	320	33	(	(	PUNCT
ejpam-4924	320	34	−9λ+	−9λ+	NUM
ejpam-4924	320	35	2)ρbρc	2)ρbρc	NUM
ejpam-4924	320	36	+	+	CCONJ
ejpam-4924	320	37	(	(	PUNCT
ejpam-4924	320	38	9λ−	9λ−	NUM
ejpam-4924	320	39	6)ρbc	6)ρbc	NUM
ejpam-4924	320	40	=	=	SYM
ejpam-4924	320	41	0	0	PUNCT
ejpam-4924	321	1	(	(	PUNCT
ejpam-4924	321	2	14	14	NUM
ejpam-4924	321	3	)	)	PUNCT
ejpam-4924	321	4	the	the	DET
ejpam-4924	321	5	difference	difference	NOUN
ejpam-4924	321	6	between	between	ADP
ejpam-4924	321	7	(	(	PUNCT
ejpam-4924	321	8	13	13	NUM
ejpam-4924	321	9	)	)	PUNCT
ejpam-4924	321	10	and	and	CCONJ
ejpam-4924	321	11	(	(	PUNCT
ejpam-4924	321	12	14	14	NUM
ejpam-4924	321	13	)	)	PUNCT
ejpam-4924	321	14	gives	give	VERB
ejpam-4924	321	15	:	:	PUNCT
ejpam-4924	321	16	5ρbρc	5ρbρc	NUM
ejpam-4924	321	17	−	−	PROPN
ejpam-4924	322	1	5ρcρb	5ρcρb	NUM
ejpam-4924	322	2	=	=	SYM
ejpam-4924	322	3	0	0	NUM
ejpam-4924	322	4	⇔	⇔	X
ejpam-4924	322	5	ρbρc	ρbρc	PROPN
ejpam-4924	322	6	=	=	SYM
ejpam-4924	322	7	ρcρb	ρcρb	ADJ
ejpam-4924	322	8	(	(	PUNCT
ejpam-4924	322	9	15	15	NUM
ejpam-4924	322	10	)	)	PUNCT
ejpam-4924	322	11	so	so	CCONJ
ejpam-4924	322	12	(	(	PUNCT
ejpam-4924	322	13	14	14	NUM
ejpam-4924	322	14	)	)	PUNCT
ejpam-4924	322	15	becomes	become	VERB
ejpam-4924	322	16	−3(2λ−	−3(2λ−	NUM
ejpam-4924	322	17	1)ρcρb	1)ρcρb	NUM
ejpam-4924	322	18	+	+	CCONJ
ejpam-4924	322	19	(	(	PUNCT
ejpam-4924	322	20	3λ−	3λ−	NUM
ejpam-4924	322	21	2)ρbc	2)ρbc	NUM
ejpam-4924	322	22	=	=	SYM
ejpam-4924	322	23	0	0	NUM
ejpam-4924	322	24	⇔	⇔	PROPN
ejpam-4924	322	25	−9λ3ρbρc	−9λ3ρbρc	PROPN
ejpam-4924	322	26	+	+	CCONJ
ejpam-4924	322	27	(	(	PUNCT
ejpam-4924	322	28	3λ2	3λ2	NUM
ejpam-4924	322	29	−	−	NUM
ejpam-4924	322	30	1)ρcb	1)ρcb	NUM
ejpam-4924	322	31	=	=	SYM
ejpam-4924	322	32	0	0	NUM
ejpam-4924	322	33	.	.	PUNCT
ejpam-4924	323	1	hence	hence	ADV
ejpam-4924	323	2	ρbρc	ρbρc	PROPN
ejpam-4924	323	3	=	=	PUNCT
ejpam-4924	324	1	3λ2	3λ2	NUM
ejpam-4924	324	2	−	−	NUM
ejpam-4924	324	3	1	1	NUM
ejpam-4924	324	4	9λ3	9λ3	NUM
ejpam-4924	324	5	ρcb	ρcb	NOUN
ejpam-4924	324	6	remark	remark	NOUN
ejpam-4924	324	7	4.10	4.10	NUM
ejpam-4924	324	8	.	.	PUNCT
ejpam-4924	325	1	taking	take	VERB
ejpam-4924	325	2	a	a	DET
ejpam-4924	325	3	,	,	PUNCT
ejpam-4924	325	4	b	b	PROPN
ejpam-4924	325	5	∈	∈	PROPN
ejpam-4924	325	6	a0	a0	NOUN
ejpam-4924	325	7	and	and	CCONJ
ejpam-4924	325	8	m	m	PROPN
ejpam-4924	325	9	∈	∈	PROPN
ejpam-4924	325	10	mλ	mλ	NOUN
ejpam-4924	325	11	,	,	PUNCT
ejpam-4924	325	12	then	then	ADV
ejpam-4924	325	13	replacing	replace	VERB
ejpam-4924	325	14	them	they	PRON
ejpam-4924	325	15	in	in	ADP
ejpam-4924	325	16	(	(	PUNCT
ejpam-4924	325	17	11	11	NUM
ejpam-4924	325	18	)	)	PUNCT
ejpam-4924	325	19	,	,	PUNCT
ejpam-4924	325	20	we	we	PRON
ejpam-4924	325	21	have	have	VERB
ejpam-4924	325	22	:	:	PUNCT
ejpam-4924	325	23	(	(	PUNCT
ejpam-4924	325	24	9λ−	9λ−	NOUN
ejpam-4924	325	25	2)ρbρc	2)ρbρc	NUM
ejpam-4924	325	26	+	+	CCONJ
ejpam-4924	325	27	(	(	PUNCT
ejpam-4924	325	28	9λ−	9λ−	NUM
ejpam-4924	325	29	7)ρcρb	7)ρcρb	NUM
ejpam-4924	325	30	−	−	PROPN
ejpam-4924	325	31	9λ2ρcb	9λ2ρcb	NUM
ejpam-4924	325	32	=	=	SYM
ejpam-4924	325	33	0	0	NUM
ejpam-4924	326	1	(	(	PUNCT
ejpam-4924	326	2	16	16	NUM
ejpam-4924	326	3	)	)	PUNCT
ejpam-4924	326	4	here	here	ADV
ejpam-4924	326	5	again	again	ADV
ejpam-4924	326	6	,	,	PUNCT
ejpam-4924	326	7	by	by	ADP
ejpam-4924	326	8	interchanging	interchanging	PROPN
ejpam-4924	326	9	b	b	PROPN
ejpam-4924	326	10	and	and	CCONJ
ejpam-4924	326	11	c	c	PROPN
ejpam-4924	327	1	and	and	CCONJ
ejpam-4924	327	2	then	then	ADV
ejpam-4924	327	3	subtracting	subtract	VERB
ejpam-4924	327	4	,	,	PUNCT
ejpam-4924	327	5	we	we	PRON
ejpam-4924	327	6	obtain	obtain	VERB
ejpam-4924	327	7	ρbρc	ρbρc	NOUN
ejpam-4924	327	8	=	=	SYM
ejpam-4924	327	9	ρcρb	ρcρb	ADJ
ejpam-4924	327	10	⇒	⇒	NOUN
ejpam-4924	327	11	(	(	PUNCT
ejpam-4924	327	12	a	a	DET
ejpam-4924	327	13	,	,	PUNCT
ejpam-4924	327	14	b	b	NOUN
ejpam-4924	327	15	,	,	PUNCT
ejpam-4924	327	16	m	m	NOUN
ejpam-4924	327	17	)	)	PUNCT
ejpam-4924	328	1	=	=	SYM
ejpam-4924	328	2	0	0	X
ejpam-4924	328	3	.	.	PUNCT
ejpam-4924	329	1	on	on	ADP
ejpam-4924	329	2	the	the	DET
ejpam-4924	329	3	other	other	ADJ
ejpam-4924	329	4	hand	hand	NOUN
ejpam-4924	329	5	,	,	PUNCT
ejpam-4924	329	6	here	here	ADV
ejpam-4924	329	7	we	we	PRON
ejpam-4924	329	8	have	have	VERB
ejpam-4924	329	9	:	:	PUNCT
ejpam-4924	329	10	ρbρc	ρbρc	ADJ
ejpam-4924	329	11	=	=	NOUN
ejpam-4924	329	12	1	1	NUM
ejpam-4924	329	13	3λρcb	3λρcb	NUM
ejpam-4924	329	14	.	.	PUNCT
ejpam-4924	330	1	references	reference	NOUN
ejpam-4924	330	2	2155	2155	NUM
ejpam-4924	330	3	acknowledgements	acknowledgement	NOUN
ejpam-4924	330	4	the	the	DET
ejpam-4924	330	5	authors	author	NOUN
ejpam-4924	330	6	would	would	AUX
ejpam-4924	330	7	like	like	VERB
ejpam-4924	330	8	to	to	PART
ejpam-4924	330	9	thank	thank	VERB
ejpam-4924	330	10	the	the	DET
ejpam-4924	330	11	referees	referee	NOUN
ejpam-4924	330	12	whose	whose	DET
ejpam-4924	330	13	suggestions	suggestion	NOUN
ejpam-4924	330	14	helped	help	VERB
ejpam-4924	330	15	to	to	PART
ejpam-4924	330	16	improve	improve	VERB
ejpam-4924	330	17	this	this	DET
ejpam-4924	330	18	paper	paper	NOUN
ejpam-4924	330	19	.	.	PUNCT
ejpam-4924	331	1	references	reference	NOUN
ejpam-4924	331	2	[	[	X
ejpam-4924	331	3	1	1	NUM
ejpam-4924	331	4	]	]	PUNCT
ejpam-4924	331	5	a.	a.	NOUN
ejpam-4924	331	6	a.	a.	PROPN
ejpam-4924	331	7	albert	albert	PROPN
ejpam-4924	331	8	.	.	PUNCT
ejpam-4924	332	1	a	a	DET
ejpam-4924	332	2	theory	theory	NOUN
ejpam-4924	332	3	of	of	ADP
ejpam-4924	332	4	power	power	NOUN
ejpam-4924	332	5	associative	associative	PROPN
ejpam-4924	332	6	commutative	commutative	ADJ
ejpam-4924	332	7	algebras	algebra	NOUN
ejpam-4924	332	8	.	.	PUNCT
ejpam-4924	333	1	trans	trans	PROPN
ejpam-4924	333	2	.	.	PROPN
ejpam-4924	334	1	amer	amer	PROPN
ejpam-4924	334	2	.	.	PUNCT
ejpam-4924	334	3	math	math	PROPN
ejpam-4924	334	4	.	.	PUNCT
ejpam-4924	335	1	soc	soc	PROPN
ejpam-4924	335	2	.	.	PUNCT
ejpam-4924	335	3	,	,	PUNCT
ejpam-4924	335	4	69:503–527	69:503–527	NUM
ejpam-4924	335	5	,	,	PUNCT
ejpam-4924	335	6	1950	1950	NUM
ejpam-4924	335	7	.	.	PUNCT
ejpam-4924	336	1	[	[	X
ejpam-4924	336	2	2	2	NUM
ejpam-4924	336	3	]	]	PUNCT
ejpam-4924	336	4	a.	a.	NOUN
ejpam-4924	336	5	dembega	dembega	PROPN
ejpam-4924	336	6	.	.	PUNCT
ejpam-4924	337	1	algèbres	algèbre	NOUN
ejpam-4924	337	2	preque	preque	ADJ
ejpam-4924	337	3	de	de	ADP
ejpam-4924	337	4	jordan	jordan	PROPN
ejpam-4924	337	5	et	et	PROPN
ejpam-4924	337	6	deux	deux	PROPN
ejpam-4924	337	7	classes	class	NOUN
ejpam-4924	337	8	d’algèbres	d’algèbre	VERB
ejpam-4924	337	9	commutatives	commutative	NOUN
ejpam-4924	337	10	de	de	X
ejpam-4924	337	11	degré	degré	ADJ
ejpam-4924	337	12	5	5	NUM
ejpam-4924	337	13	.	.	PUNCT
ejpam-4924	337	14	phd	phd	NOUN
ejpam-4924	337	15	thesis	thesis	NOUN
ejpam-4924	337	16	,	,	PUNCT
ejpam-4924	337	17	université	université	ADJ
ejpam-4924	337	18	joseph	joseph	PROPN
ejpam-4924	337	19	ki	ki	PROPN
ejpam-4924	337	20	-	-	PUNCT
ejpam-4924	337	21	zerbo	zerbo	PROPN
ejpam-4924	337	22	,	,	PUNCT
ejpam-4924	337	23	2019	2019	NUM
ejpam-4924	337	24	.	.	PUNCT
ejpam-4924	338	1	[	[	X
ejpam-4924	338	2	3	3	X
ejpam-4924	338	3	]	]	PUNCT
ejpam-4924	338	4	s.	s.	PROPN
ejpam-4924	338	5	eilenberg	eilenberg	PROPN
ejpam-4924	338	6	.	.	PUNCT
ejpam-4924	339	1	extensions	extension	NOUN
ejpam-4924	339	2	of	of	ADP
ejpam-4924	339	3	general	general	ADJ
ejpam-4924	339	4	algebras	algebra	NOUN
ejpam-4924	339	5	.	.	PUNCT
ejpam-4924	340	1	ann	ann	PROPN
ejpam-4924	340	2	.	.	PUNCT
ejpam-4924	340	3	soc	soc	PROPN
ejpam-4924	340	4	.	.	PUNCT
ejpam-4924	341	1	polon	polon	PROPN
ejpam-4924	341	2	.	.	PUNCT
ejpam-4924	342	1	math	math	NOUN
ejpam-4924	342	2	.	.	PUNCT
ejpam-4924	342	3	,	,	PUNCT
ejpam-4924	343	1	21:125–134	21:125–134	NUM
ejpam-4924	343	2	,	,	PUNCT
ejpam-4924	343	3	1948	1948	NUM
ejpam-4924	343	4	.	.	PUNCT
ejpam-4924	344	1	[	[	X
ejpam-4924	344	2	4	4	NUM
ejpam-4924	344	3	]	]	PUNCT
ejpam-4924	344	4	m.	m.	NOUN
ejpam-4924	344	5	flores	flore	NOUN
ejpam-4924	344	6	and	and	CCONJ
ejpam-4924	344	7	a.	a.	NOUN
ejpam-4924	344	8	labra	labra	PROPN
ejpam-4924	344	9	.	.	PUNCT
ejpam-4924	345	1	representations	representation	NOUN
ejpam-4924	345	2	of	of	ADP
ejpam-4924	345	3	generalized	generalized	ADJ
ejpam-4924	345	4	almost	almost	ADV
ejpam-4924	345	5	-	-	PUNCT
ejpam-4924	345	6	jordan	jordan	PROPN
ejpam-4924	345	7	algebras	algebras	PROPN
ejpam-4924	345	8	.	.	PUNCT
ejpam-4924	345	9	comm	comm	NOUN
ejpam-4924	345	10	.	.	PUNCT
ejpam-4924	346	1	in	in	ADP
ejpam-4924	346	2	algebra	algebra	PROPN
ejpam-4924	346	3	.	.	PUNCT
ejpam-4924	346	4	,	,	PUNCT
ejpam-4924	346	5	43(8):3373–3381	43(8):3373–3381	PROPN
ejpam-4924	346	6	,	,	PUNCT
ejpam-4924	346	7	2015	2015	NUM
ejpam-4924	346	8	.	.	PUNCT
ejpam-4924	347	1	[	[	X
ejpam-4924	347	2	5	5	NUM
ejpam-4924	347	3	]	]	PUNCT
ejpam-4924	347	4	a.	a.	NOUN
ejpam-4924	347	5	dembega	dembega	PROPN
ejpam-4924	347	6	;	;	PUNCT
ejpam-4924	347	7	a.	a.	NOUN
ejpam-4924	347	8	konkobo	konkobo	NOUN
ejpam-4924	347	9	and	and	CCONJ
ejpam-4924	347	10	m.	m.	NOUN
ejpam-4924	347	11	ouattara	ouattara	NOUN
ejpam-4924	347	12	.	.	PUNCT
ejpam-4924	348	1	derivations	derivation	NOUN
ejpam-4924	348	2	and	and	CCONJ
ejpam-4924	348	3	dimensionally	dimensionally	ADV
ejpam-4924	348	4	nilpotent	nilpotent	ADJ
ejpam-4924	348	5	derivations	derivation	NOUN
ejpam-4924	348	6	in	in	ADP
ejpam-4924	348	7	lie	lie	NOUN
ejpam-4924	348	8	triple	triple	DET
ejpam-4924	348	9	a	a	DET
ejpam-4924	348	10	algebras	algebra	NOUN
ejpam-4924	348	11	.	.	PUNCT
ejpam-4924	349	1	gulf	gulf	PROPN
ejpam-4924	349	2	journal	journal	PROPN
ejpam-4924	349	3	of	of	ADP
ejpam-4924	349	4	mathematics	mathematics	PROPN
ejpam-4924	349	5	.	.	PUNCT
ejpam-4924	349	6	,	,	PUNCT
ejpam-4924	349	7	7(2):71–84	7(2):71–84	NUM
ejpam-4924	349	8	,	,	PUNCT
ejpam-4924	349	9	2019	2019	NUM
ejpam-4924	349	10	.	.	PUNCT
ejpam-4924	350	1	[	[	X
ejpam-4924	350	2	6	6	X
ejpam-4924	350	3	]	]	PUNCT
ejpam-4924	350	4	j.	j.	PROPN
ejpam-4924	350	5	bayara	bayara	PROPN
ejpam-4924	350	6	;	;	PUNCT
ejpam-4924	350	7	a.	a.	NOUN
ejpam-4924	350	8	conseibo	conseibo	NOUN
ejpam-4924	350	9	;	;	PUNCT
ejpam-4924	350	10	a.	a.	NOUN
ejpam-4924	350	11	micali	micali	NOUN
ejpam-4924	350	12	and	and	CCONJ
ejpam-4924	350	13	m.	m.	NOUN
ejpam-4924	350	14	ouattara	ouattara	NOUN
ejpam-4924	350	15	.	.	PUNCT
ejpam-4924	351	1	derivations	derivation	NOUN
ejpam-4924	351	2	in	in	ADP
ejpam-4924	351	3	power	power	NOUN
ejpam-4924	351	4	-	-	PUNCT
ejpam-4924	351	5	associative	associative	NOUN
ejpam-4924	351	6	algebras	algebra	NOUN
ejpam-4924	351	7	.	.	PUNCT
ejpam-4924	351	8	discrete	discrete	ADJ
ejpam-4924	351	9	contin	contin	NOUN
ejpam-4924	351	10	.	.	PUNCT
ejpam-4924	352	1	syst	syst	PROPN
ejpam-4924	352	2	.	.	PUNCT
ejpam-4924	352	3	ser	ser	PROPN
ejpam-4924	352	4	.	.	PUNCT
ejpam-4924	353	1	s.	s.	PROPN
ejpam-4924	353	2	,	,	PUNCT
ejpam-4924	353	3	4(6):1359–1370	4(6):1359–1370	PROPN
ejpam-4924	353	4	,	,	PUNCT
ejpam-4924	353	5	2011	2011	NUM
ejpam-4924	353	6	.	.	PUNCT
ejpam-4924	354	1	[	[	X
ejpam-4924	354	2	7	7	X
ejpam-4924	354	3	]	]	X
ejpam-4924	354	4	j.	j.	PROPN
ejpam-4924	354	5	m.	m.	PROPN
ejpam-4924	354	6	osborn	osborn	PROPN
ejpam-4924	354	7	.	.	PUNCT
ejpam-4924	355	1	identities	identity	NOUN
ejpam-4924	355	2	of	of	ADP
ejpam-4924	355	3	non	non	ADJ
ejpam-4924	355	4	-	-	ADJ
ejpam-4924	355	5	associative	associative	ADJ
ejpam-4924	355	6	algebras	algebra	NOUN
ejpam-4924	355	7	.	.	PUNCT
ejpam-4924	356	1	can	can	AUX
ejpam-4924	356	2	.	.	PUNCT
ejpam-4924	357	1	j.	j.	PROPN
ejpam-4924	357	2	math	math	PROPN
ejpam-4924	357	3	.	.	PUNCT
ejpam-4924	357	4	,	,	PUNCT
ejpam-4924	357	5	17:78–92	17:78–92	NUM
ejpam-4924	357	6	,	,	PUNCT
ejpam-4924	357	7	1965	1965	NUM
ejpam-4924	357	8	.	.	PUNCT
ejpam-4924	358	1	[	[	X
ejpam-4924	358	2	8	8	X
ejpam-4924	358	3	]	]	X
ejpam-4924	358	4	j.	j.	PROPN
ejpam-4924	358	5	m.	m.	PROPN
ejpam-4924	358	6	osborn	osborn	PROPN
ejpam-4924	358	7	.	.	PROPN
ejpam-4924	358	8	commutative	commutative	PROPN
ejpam-4924	358	9	non	non	ADJ
ejpam-4924	358	10	-	-	ADJ
ejpam-4924	358	11	associative	associative	ADJ
ejpam-4924	358	12	algebras	algebra	NOUN
ejpam-4924	358	13	and	and	CCONJ
ejpam-4924	358	14	identities	identity	NOUN
ejpam-4924	358	15	of	of	ADP
ejpam-4924	358	16	degree	degree	NOUN
ejpam-4924	358	17	four	four	NUM
ejpam-4924	358	18	.	.	PUNCT
ejpam-4924	358	19	canadian	canadian	ADJ
ejpam-4924	358	20	journal	journal	PROPN
ejpam-4924	358	21	of	of	ADP
ejpam-4924	358	22	mathematics	mathematic	NOUN
ejpam-4924	358	23	,	,	PUNCT
ejpam-4924	358	24	20:769–794	20:769–794	PROPN
ejpam-4924	358	25	,	,	PUNCT
ejpam-4924	358	26	1968	1968	NUM
ejpam-4924	358	27	.	.	PUNCT