id	sid	tid	token	lemma	pos
ejpam-3979	1	1	european	european	PROPN
ejpam-3979	1	2	journal	journal	PROPN
ejpam-3979	1	3	of	of	ADP
ejpam-3979	1	4	pure	pure	ADJ
ejpam-3979	1	5	and	and	CCONJ
ejpam-3979	1	6	applied	apply	VERB
ejpam-3979	1	7	mathematics	mathematic	NOUN
ejpam-3979	1	8	vol	vol	NOUN
ejpam-3979	1	9	.	.	PUNCT
ejpam-3979	2	1	14	14	NUM
ejpam-3979	2	2	,	,	PUNCT
ejpam-3979	2	3	no	no	INTJ
ejpam-3979	2	4	.	.	NOUN
ejpam-3979	2	5	3	3	NUM
ejpam-3979	2	6	,	,	PUNCT
ejpam-3979	2	7	2021	2021	NUM
ejpam-3979	2	8	,	,	PUNCT
ejpam-3979	2	9	816	816	NUM
ejpam-3979	2	10	-	-	SYM
ejpam-3979	2	11	828	828	NUM
ejpam-3979	2	12	issn	issn	PROPN
ejpam-3979	2	13	1307	1307	NUM
ejpam-3979	2	14	-	-	SYM
ejpam-3979	2	15	5543	5543	NUM
ejpam-3979	2	16	–	–	PUNCT
ejpam-3979	3	1	ejpam.com	ejpam.com	X
ejpam-3979	3	2	published	publish	VERB
ejpam-3979	3	3	by	by	ADP
ejpam-3979	3	4	new	new	PROPN
ejpam-3979	3	5	york	york	PROPN
ejpam-3979	3	6	business	business	PROPN
ejpam-3979	3	7	global	global	PROPN
ejpam-3979	3	8	an	an	DET
ejpam-3979	3	9	application	application	NOUN
ejpam-3979	3	10	of	of	ADP
ejpam-3979	3	11	finite	finite	ADJ
ejpam-3979	3	12	groups	group	NOUN
ejpam-3979	3	13	to	to	ADP
ejpam-3979	3	14	hopf	hopf	PROPN
ejpam-3979	3	15	algebras	algebras	PROPN
ejpam-3979	3	16	tahani	tahani	PROPN
ejpam-3979	3	17	al	al	PROPN
ejpam-3979	3	18	-	-	PUNCT
ejpam-3979	3	19	mutairi1,2	mutairi1,2	PROPN
ejpam-3979	3	20	,	,	PUNCT
ejpam-3979	3	21	m.	m.	NOUN
ejpam-3979	3	22	m.	m.	PROPN
ejpam-3979	3	23	al	al	PROPN
ejpam-3979	3	24	-	-	PROPN
ejpam-3979	3	25	shomrani1,∗	shomrani1,∗	PROPN
ejpam-3979	3	26	1	1	NUM
ejpam-3979	3	27	department	department	NOUN
ejpam-3979	3	28	of	of	ADP
ejpam-3979	3	29	mathematics	mathematic	NOUN
ejpam-3979	3	30	,	,	PUNCT
ejpam-3979	3	31	faculty	faculty	NOUN
ejpam-3979	3	32	of	of	ADP
ejpam-3979	3	33	science	science	NOUN
ejpam-3979	3	34	,	,	PUNCT
ejpam-3979	3	35	king	king	PROPN
ejpam-3979	3	36	abdulaziz	abdulaziz	PROPN
ejpam-3979	3	37	university	university	PROPN
ejpam-3979	3	38	,	,	PUNCT
ejpam-3979	3	39	p.o.box	p.o.box	PROPN
ejpam-3979	3	40	80203	80203	NUM
ejpam-3979	3	41	,	,	PUNCT
ejpam-3979	3	42	jeddah	jeddah	PROPN
ejpam-3979	3	43	21589	21589	NUM
ejpam-3979	3	44	,	,	PUNCT
ejpam-3979	3	45	saudi	saudi	PROPN
ejpam-3979	3	46	arabia	arabia	PROPN
ejpam-3979	3	47	2	2	NUM
ejpam-3979	3	48	department	department	NOUN
ejpam-3979	3	49	of	of	ADP
ejpam-3979	3	50	mathematics	mathematic	NOUN
ejpam-3979	3	51	,	,	PUNCT
ejpam-3979	3	52	qassim	qassim	PROPN
ejpam-3979	3	53	university	university	PROPN
ejpam-3979	3	54	,	,	PUNCT
ejpam-3979	3	55	buraydah	buraydah	PROPN
ejpam-3979	3	56	,	,	PUNCT
ejpam-3979	3	57	saudi	saudi	PROPN
ejpam-3979	3	58	arabia	arabia	PROPN
ejpam-3979	3	59	abstract	abstract	NOUN
ejpam-3979	3	60	.	.	PUNCT
ejpam-3979	4	1	kaplansky	kaplansky	PROPN
ejpam-3979	4	2	’s	’s	PART
ejpam-3979	4	3	famous	famous	ADJ
ejpam-3979	4	4	conjectures	conjecture	NOUN
ejpam-3979	4	5	about	about	ADP
ejpam-3979	4	6	generalizing	generalize	VERB
ejpam-3979	4	7	results	result	NOUN
ejpam-3979	4	8	from	from	ADP
ejpam-3979	4	9	groups	group	NOUN
ejpam-3979	4	10	to	to	ADP
ejpam-3979	4	11	hopf	hopf	ADJ
ejpam-3979	4	12	algebras	algebras	PROPN
ejpam-3979	4	13	inspired	inspire	VERB
ejpam-3979	4	14	many	many	ADJ
ejpam-3979	4	15	mathematicians	mathematician	NOUN
ejpam-3979	4	16	to	to	PART
ejpam-3979	4	17	try	try	VERB
ejpam-3979	4	18	to	to	PART
ejpam-3979	4	19	find	find	VERB
ejpam-3979	4	20	solusions	solusion	NOUN
ejpam-3979	4	21	for	for	ADP
ejpam-3979	4	22	them	they	PRON
ejpam-3979	4	23	.	.	PUNCT
ejpam-3979	5	1	recently	recently	ADV
ejpam-3979	5	2	,	,	PUNCT
ejpam-3979	5	3	cohen	cohen	PROPN
ejpam-3979	5	4	and	and	CCONJ
ejpam-3979	5	5	westreich	westreich	PRON
ejpam-3979	5	6	in	in	ADP
ejpam-3979	5	7	[	[	X
ejpam-3979	5	8	8	8	NUM
ejpam-3979	5	9	]	]	PUNCT
ejpam-3979	5	10	and	and	CCONJ
ejpam-3979	5	11	[	[	X
ejpam-3979	5	12	10	10	NUM
ejpam-3979	5	13	]	]	PUNCT
ejpam-3979	5	14	have	have	AUX
ejpam-3979	5	15	generalized	generalize	VERB
ejpam-3979	5	16	the	the	DET
ejpam-3979	5	17	concepts	concept	NOUN
ejpam-3979	5	18	of	of	ADP
ejpam-3979	5	19	nilpotency	nilpotency	NOUN
ejpam-3979	5	20	and	and	CCONJ
ejpam-3979	5	21	solvability	solvability	NOUN
ejpam-3979	5	22	of	of	ADP
ejpam-3979	5	23	groups	group	NOUN
ejpam-3979	5	24	to	to	ADP
ejpam-3979	5	25	hopf	hopf	ADJ
ejpam-3979	5	26	algebras	algebra	NOUN
ejpam-3979	5	27	under	under	ADP
ejpam-3979	5	28	certain	certain	ADJ
ejpam-3979	5	29	conditions	condition	NOUN
ejpam-3979	5	30	and	and	CCONJ
ejpam-3979	5	31	proved	prove	VERB
ejpam-3979	5	32	interesting	interesting	ADJ
ejpam-3979	5	33	results	result	NOUN
ejpam-3979	5	34	.	.	PUNCT
ejpam-3979	6	1	in	in	ADP
ejpam-3979	6	2	this	this	DET
ejpam-3979	6	3	article	article	NOUN
ejpam-3979	6	4	,	,	PUNCT
ejpam-3979	6	5	we	we	PRON
ejpam-3979	6	6	follow	follow	VERB
ejpam-3979	6	7	their	their	PRON
ejpam-3979	6	8	work	work	NOUN
ejpam-3979	6	9	and	and	CCONJ
ejpam-3979	6	10	give	give	VERB
ejpam-3979	6	11	a	a	DET
ejpam-3979	6	12	detailed	detailed	ADJ
ejpam-3979	6	13	example	example	NOUN
ejpam-3979	6	14	by	by	ADP
ejpam-3979	6	15	considering	consider	VERB
ejpam-3979	6	16	a	a	DET
ejpam-3979	6	17	finite	finite	ADJ
ejpam-3979	6	18	group	group	NOUN
ejpam-3979	6	19	g	g	PROPN
ejpam-3979	6	20	and	and	CCONJ
ejpam-3979	6	21	an	an	DET
ejpam-3979	6	22	algebraically	algebraically	ADV
ejpam-3979	6	23	closed	close	VERB
ejpam-3979	6	24	field	field	NOUN
ejpam-3979	6	25	k.	k.	NOUN
ejpam-3979	6	26	in	in	ADP
ejpam-3979	6	27	more	more	ADJ
ejpam-3979	6	28	details	detail	NOUN
ejpam-3979	6	29	,	,	PUNCT
ejpam-3979	6	30	we	we	PRON
ejpam-3979	6	31	construct	construct	VERB
ejpam-3979	6	32	the	the	DET
ejpam-3979	6	33	group	group	NOUN
ejpam-3979	6	34	hopf	hopf	ADJ
ejpam-3979	6	35	algebra	algebra	NOUN
ejpam-3979	6	36	h	h	NOUN
ejpam-3979	7	1	=	=	SYM
ejpam-3979	7	2	kg	kg	NOUN
ejpam-3979	8	1	and	and	CCONJ
ejpam-3979	8	2	examine	examine	VERB
ejpam-3979	8	3	its	its	PRON
ejpam-3979	8	4	properties	property	NOUN
ejpam-3979	8	5	to	to	PART
ejpam-3979	8	6	see	see	VERB
ejpam-3979	8	7	what	what	PRON
ejpam-3979	8	8	of	of	ADP
ejpam-3979	8	9	the	the	DET
ejpam-3979	8	10	properties	property	NOUN
ejpam-3979	8	11	of	of	ADP
ejpam-3979	8	12	the	the	DET
ejpam-3979	8	13	original	original	ADJ
ejpam-3979	8	14	finite	finite	NOUN
ejpam-3979	8	15	group	group	NOUN
ejpam-3979	8	16	can	can	AUX
ejpam-3979	8	17	be	be	AUX
ejpam-3979	8	18	carried	carry	VERB
ejpam-3979	8	19	out	out	ADP
ejpam-3979	8	20	in	in	ADP
ejpam-3979	8	21	the	the	DET
ejpam-3979	8	22	case	case	NOUN
ejpam-3979	8	23	of	of	ADP
ejpam-3979	8	24	h.	h.	PROPN
ejpam-3979	8	25	2020	2020	NUM
ejpam-3979	8	26	mathematics	mathematics	PROPN
ejpam-3979	8	27	subject	subject	NOUN
ejpam-3979	8	28	classifications	classification	NOUN
ejpam-3979	8	29	:	:	PUNCT
ejpam-3979	8	30	20d10	20d10	NUM
ejpam-3979	8	31	,	,	PUNCT
ejpam-3979	8	32	20d15	20d15	NUM
ejpam-3979	8	33	,	,	PUNCT
ejpam-3979	8	34	16t20	16t20	NUM
ejpam-3979	8	35	,	,	PUNCT
ejpam-3979	8	36	17b37	17b37	NUM
ejpam-3979	8	37	,	,	PUNCT
ejpam-3979	8	38	81r50	81r50	NUM
ejpam-3979	8	39	,	,	PUNCT
ejpam-3979	8	40	81r12	81r12	NUM
ejpam-3979	8	41	key	key	ADJ
ejpam-3979	8	42	words	word	NOUN
ejpam-3979	8	43	and	and	CCONJ
ejpam-3979	8	44	phrases	phrase	NOUN
ejpam-3979	8	45	:	:	PUNCT
ejpam-3979	8	46	hopf	hopf	ADJ
ejpam-3979	8	47	algebras	algebra	NOUN
ejpam-3979	8	48	,	,	PUNCT
ejpam-3979	8	49	integral	integral	ADJ
ejpam-3979	8	50	elements	element	NOUN
ejpam-3979	8	51	,	,	PUNCT
ejpam-3979	8	52	semisimple	semisimple	NOUN
ejpam-3979	8	53	hopf	hopf	ADJ
ejpam-3979	8	54	algebra	algebra	NOUN
ejpam-3979	8	55	,	,	PUNCT
ejpam-3979	8	56	left	leave	VERB
ejpam-3979	8	57	coideal	coideal	NOUN
ejpam-3979	8	58	subalgebra	subalgebra	NOUN
ejpam-3979	8	59	,	,	PUNCT
ejpam-3979	8	60	solvability	solvability	NOUN
ejpam-3979	8	61	of	of	ADP
ejpam-3979	8	62	groups	group	NOUN
ejpam-3979	8	63	and	and	CCONJ
ejpam-3979	8	64	hopf	hopf	ADJ
ejpam-3979	8	65	algebras	algebra	NOUN
ejpam-3979	8	66	,	,	PUNCT
ejpam-3979	8	67	nilpotency	nilpotency	NOUN
ejpam-3979	8	68	of	of	ADP
ejpam-3979	8	69	groups	group	NOUN
ejpam-3979	8	70	and	and	CCONJ
ejpam-3979	8	71	hopf	hopf	ADJ
ejpam-3979	8	72	algebras	algebra	NOUN
ejpam-3979	8	73	.	.	PUNCT
ejpam-3979	9	1	1	1	X
ejpam-3979	9	2	.	.	X
ejpam-3979	9	3	introduction	introduction	NOUN
ejpam-3979	9	4	finite	finite	PROPN
ejpam-3979	9	5	group	group	PROPN
ejpam-3979	9	6	theory	theory	NOUN
ejpam-3979	9	7	has	have	AUX
ejpam-3979	9	8	been	be	AUX
ejpam-3979	9	9	remarkably	remarkably	ADV
ejpam-3979	9	10	enriched	enrich	VERB
ejpam-3979	9	11	in	in	ADP
ejpam-3979	9	12	the	the	DET
ejpam-3979	9	13	last	last	ADJ
ejpam-3979	9	14	few	few	ADJ
ejpam-3979	9	15	decades	decade	NOUN
ejpam-3979	9	16	by	by	ADP
ejpam-3979	9	17	putting	put	VERB
ejpam-3979	9	18	more	more	ADJ
ejpam-3979	9	19	attention	attention	NOUN
ejpam-3979	9	20	on	on	ADP
ejpam-3979	9	21	the	the	DET
ejpam-3979	9	22	classification	classification	NOUN
ejpam-3979	9	23	of	of	ADP
ejpam-3979	9	24	finite	finite	ADJ
ejpam-3979	9	25	simple	simple	ADJ
ejpam-3979	9	26	groups	group	NOUN
ejpam-3979	9	27	.	.	PUNCT
ejpam-3979	10	1	the	the	DET
ejpam-3979	10	2	most	most	ADV
ejpam-3979	10	3	important	important	ADJ
ejpam-3979	10	4	structure	structure	NOUN
ejpam-3979	10	5	theorem	theorem	NOUN
ejpam-3979	10	6	for	for	ADP
ejpam-3979	10	7	finite	finite	ADJ
ejpam-3979	10	8	groups	group	NOUN
ejpam-3979	10	9	is	be	AUX
ejpam-3979	10	10	the	the	DET
ejpam-3979	10	11	jordan	jordan	PROPN
ejpam-3979	10	12	–	–	PUNCT
ejpam-3979	10	13	holder	holder	NOUN
ejpam-3979	10	14	theorem	theorem	VERB
ejpam-3979	10	15	,	,	PUNCT
ejpam-3979	10	16	which	which	PRON
ejpam-3979	10	17	states	state	VERB
ejpam-3979	10	18	that	that	SCONJ
ejpam-3979	10	19	any	any	DET
ejpam-3979	10	20	finite	finite	ADJ
ejpam-3979	10	21	group	group	NOUN
ejpam-3979	10	22	is	be	AUX
ejpam-3979	10	23	built	build	VERB
ejpam-3979	10	24	up	up	ADP
ejpam-3979	10	25	from	from	ADP
ejpam-3979	10	26	finite	finite	ADJ
ejpam-3979	10	27	simple	simple	ADJ
ejpam-3979	10	28	groups	group	NOUN
ejpam-3979	10	29	.	.	PUNCT
ejpam-3979	11	1	the	the	DET
ejpam-3979	11	2	importance	importance	NOUN
ejpam-3979	11	3	of	of	ADP
ejpam-3979	11	4	this	this	DET
ejpam-3979	11	5	structure	structure	NOUN
ejpam-3979	11	6	is	be	AUX
ejpam-3979	11	7	that	that	SCONJ
ejpam-3979	11	8	the	the	DET
ejpam-3979	11	9	properties	property	NOUN
ejpam-3979	11	10	of	of	ADP
ejpam-3979	11	11	the	the	DET
ejpam-3979	11	12	subgroups	subgroup	NOUN
ejpam-3979	11	13	of	of	ADP
ejpam-3979	11	14	a	a	DET
ejpam-3979	11	15	given	give	VERB
ejpam-3979	11	16	finite	finite	ADJ
ejpam-3979	11	17	group	group	NOUN
ejpam-3979	11	18	g	g	PROPN
ejpam-3979	11	19	suggest	suggest	VERB
ejpam-3979	11	20	substantial	substantial	ADJ
ejpam-3979	11	21	information	information	NOUN
ejpam-3979	11	22	about	about	ADP
ejpam-3979	11	23	the	the	DET
ejpam-3979	11	24	group	group	NOUN
ejpam-3979	11	25	g	g	PROPN
ejpam-3979	11	26	itself	itself	PRON
ejpam-3979	11	27	such	such	ADJ
ejpam-3979	11	28	as	as	ADP
ejpam-3979	11	29	the	the	DET
ejpam-3979	11	30	nilpotence	nilpotence	NOUN
ejpam-3979	11	31	and	and	CCONJ
ejpam-3979	11	32	the	the	DET
ejpam-3979	11	33	solvability	solvability	NOUN
ejpam-3979	11	34	of	of	ADP
ejpam-3979	11	35	g	g	NOUN
ejpam-3979	11	36	,	,	PUNCT
ejpam-3979	11	37	see	see	VERB
ejpam-3979	11	38	[	[	X
ejpam-3979	11	39	3	3	NUM
ejpam-3979	11	40	]	]	PUNCT
ejpam-3979	11	41	,	,	PUNCT
ejpam-3979	12	1	[	[	X
ejpam-3979	12	2	1],[5],[4],[21],[16	1],[5],[4],[21],[16	X
ejpam-3979	12	3	]	]	X
ejpam-3979	12	4	and	and	CCONJ
ejpam-3979	12	5	[	[	X
ejpam-3979	12	6	15	15	NUM
ejpam-3979	12	7	]	]	PUNCT
ejpam-3979	12	8	.	.	PUNCT
ejpam-3979	13	1	in	in	ADP
ejpam-3979	13	2	particular	particular	ADJ
ejpam-3979	13	3	,	,	PUNCT
ejpam-3979	13	4	having	have	VERB
ejpam-3979	13	5	the	the	DET
ejpam-3979	13	6	property	property	NOUN
ejpam-3979	13	7	of	of	ADP
ejpam-3979	13	8	simplicity	simplicity	NOUN
ejpam-3979	13	9	of	of	ADP
ejpam-3979	13	10	the	the	DET
ejpam-3979	13	11	group	group	NOUN
ejpam-3979	13	12	g	g	PROPN
ejpam-3979	13	13	can	can	AUX
ejpam-3979	13	14	be	be	AUX
ejpam-3979	13	15	deduced	deduce	VERB
ejpam-3979	13	16	by	by	ADP
ejpam-3979	13	17	investigating	investigate	VERB
ejpam-3979	13	18	its	its	PRON
ejpam-3979	13	19	subgroups	subgroup	NOUN
ejpam-3979	13	20	.	.	PUNCT
ejpam-3979	14	1	finite	finite	PROPN
ejpam-3979	14	2	group	group	NOUN
ejpam-3979	14	3	properties	property	NOUN
ejpam-3979	14	4	such	such	ADJ
ejpam-3979	14	5	as	as	ADP
ejpam-3979	14	6	simplicity	simplicity	NOUN
ejpam-3979	14	7	,	,	PUNCT
ejpam-3979	14	8	solvability	solvability	NOUN
ejpam-3979	14	9	,	,	PUNCT
ejpam-3979	14	10	nilpotency	nilpotency	NOUN
ejpam-3979	14	11	,	,	PUNCT
ejpam-3979	14	12	supersolvability	supersolvability	NOUN
ejpam-3979	14	13	,	,	PUNCT
ejpam-3979	14	14	etc	etc	X
ejpam-3979	14	15	.	.	X
ejpam-3979	14	16	have	have	AUX
ejpam-3979	14	17	been	be	AUX
ejpam-3979	14	18	an	an	DET
ejpam-3979	14	19	active	active	ADJ
ejpam-3979	14	20	area	area	NOUN
ejpam-3979	14	21	of	of	ADP
ejpam-3979	14	22	reseach	reseach	PROPN
ejpam-3979	14	23	and	and	CCONJ
ejpam-3979	14	24	been	be	AUX
ejpam-3979	14	25	investigated	investigate	VERB
ejpam-3979	14	26	by	by	ADP
ejpam-3979	14	27	many	many	ADJ
ejpam-3979	14	28	mathematicians	mathematician	NOUN
ejpam-3979	14	29	as	as	ADP
ejpam-3979	14	30	idivisual	idivisual	ADJ
ejpam-3979	14	31	classes	class	NOUN
ejpam-3979	14	32	or	or	CCONJ
ejpam-3979	14	33	under	under	ADP
ejpam-3979	14	34	specific	specific	ADJ
ejpam-3979	14	35	formations	formation	NOUN
ejpam-3979	14	36	,	,	PUNCT
ejpam-3979	14	37	see	see	VERB
ejpam-3979	14	38	for	for	ADP
ejpam-3979	14	39	example	example	NOUN
ejpam-3979	14	40	[	[	X
ejpam-3979	14	41	14	14	NUM
ejpam-3979	14	42	]	]	PUNCT
ejpam-3979	14	43	and	and	CCONJ
ejpam-3979	14	44	[	[	X
ejpam-3979	14	45	26	26	NUM
ejpam-3979	14	46	]	]	PUNCT
ejpam-3979	14	47	.	.	PUNCT
ejpam-3979	15	1	∗corresponding	∗corresponde	VERB
ejpam-3979	15	2	author	author	NOUN
ejpam-3979	15	3	.	.	PUNCT
ejpam-3979	16	1	doi	doi	NOUN
ejpam-3979	16	2	:	:	PUNCT
ejpam-3979	16	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3979	https://doi.org/10.29020/nybg.ejpam.v14i3.3979	NOUN
ejpam-3979	16	4	email	email	NOUN
ejpam-3979	16	5	addresses	address	VERB
ejpam-3979	16	6	:	:	PUNCT
ejpam-3979	17	1	tahanialmutairi57@gmail.com	tahanialmutairi57@gmail.com	X
ejpam-3979	17	2	(	(	PUNCT
ejpam-3979	17	3	t.	t.	PROPN
ejpam-3979	17	4	al	al	PROPN
ejpam-3979	17	5	-	-	PUNCT
ejpam-3979	17	6	mutairi	mutairi	PROPN
ejpam-3979	17	7	)	)	PUNCT
ejpam-3979	17	8	,	,	PUNCT
ejpam-3979	17	9	malshomrani@hotmail.com	malshomrani@hotmail.com	X
ejpam-3979	17	10	(	(	PUNCT
ejpam-3979	17	11	m.	m.	NOUN
ejpam-3979	17	12	m.	m.	PROPN
ejpam-3979	17	13	al	al	PROPN
ejpam-3979	17	14	-	-	PUNCT
ejpam-3979	17	15	shomrani	shomrani	PROPN
ejpam-3979	17	16	)	)	PUNCT
ejpam-3979	17	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3979	18	1	816	816	NUM
ejpam-3979	19	1	©	©	NOUN
ejpam-3979	19	2	2021	2021	NUM
ejpam-3979	19	3	ejpam	ejpam	VERB
ejpam-3979	19	4	all	all	DET
ejpam-3979	19	5	rights	right	NOUN
ejpam-3979	19	6	reserved	reserve	VERB
ejpam-3979	19	7	.	.	PUNCT
ejpam-3979	20	1	t.	t.	PROPN
ejpam-3979	20	2	al	al	PROPN
ejpam-3979	20	3	-	-	PUNCT
ejpam-3979	20	4	mutairi	mutairi	PROPN
ejpam-3979	20	5	,	,	PUNCT
ejpam-3979	20	6	m.	m.	NOUN
ejpam-3979	20	7	m.	m.	PROPN
ejpam-3979	20	8	al	al	PROPN
ejpam-3979	20	9	-	-	PUNCT
ejpam-3979	20	10	shomrani	shomrani	PROPN
ejpam-3979	20	11	/	/	SYM
ejpam-3979	20	12	eur	eur	NOUN
ejpam-3979	20	13	.	.	PUNCT
ejpam-3979	21	1	j.	j.	PROPN
ejpam-3979	21	2	pure	pure	PROPN
ejpam-3979	21	3	appl	appl	PROPN
ejpam-3979	21	4	.	.	PROPN
ejpam-3979	21	5	math	math	PROPN
ejpam-3979	21	6	,	,	PUNCT
ejpam-3979	21	7	14	14	NUM
ejpam-3979	21	8	(	(	PUNCT
ejpam-3979	21	9	3	3	NUM
ejpam-3979	21	10	)	)	PUNCT
ejpam-3979	21	11	(	(	PUNCT
ejpam-3979	21	12	2021	2021	NUM
ejpam-3979	21	13	)	)	PUNCT
ejpam-3979	21	14	,	,	PUNCT
ejpam-3979	21	15	816	816	NUM
ejpam-3979	21	16	-	-	SYM
ejpam-3979	21	17	828	828	NUM
ejpam-3979	21	18	817	817	NUM
ejpam-3979	21	19	in	in	ADP
ejpam-3979	21	20	the	the	DET
ejpam-3979	21	21	present	present	ADJ
ejpam-3979	21	22	work	work	NOUN
ejpam-3979	21	23	we	we	PRON
ejpam-3979	21	24	limit	limit	VERB
ejpam-3979	21	25	our	our	PRON
ejpam-3979	21	26	attention	attention	NOUN
ejpam-3979	21	27	on	on	ADP
ejpam-3979	21	28	the	the	DET
ejpam-3979	21	29	concepts	concept	NOUN
ejpam-3979	21	30	of	of	ADP
ejpam-3979	21	31	solvability	solvability	NOUN
ejpam-3979	21	32	and	and	CCONJ
ejpam-3979	21	33	nilpotency	nilpotency	NOUN
ejpam-3979	21	34	of	of	ADP
ejpam-3979	21	35	finite	finite	ADJ
ejpam-3979	21	36	groups	group	NOUN
ejpam-3979	21	37	and	and	CCONJ
ejpam-3979	21	38	semisimple	semisimple	ADJ
ejpam-3979	21	39	hopf	hopf	PROPN
ejpam-3979	21	40	algebras	algebras	PROPN
ejpam-3979	21	41	.	.	PUNCT
ejpam-3979	22	1	recall	recall	VERB
ejpam-3979	22	2	that	that	SCONJ
ejpam-3979	22	3	a	a	DET
ejpam-3979	22	4	finite	finite	ADJ
ejpam-3979	22	5	group	group	NOUN
ejpam-3979	22	6	g	g	PROPN
ejpam-3979	22	7	is	be	AUX
ejpam-3979	22	8	said	say	VERB
ejpam-3979	22	9	to	to	PART
ejpam-3979	22	10	be	be	AUX
ejpam-3979	22	11	solvable	solvable	ADJ
ejpam-3979	22	12	if	if	SCONJ
ejpam-3979	22	13	it	it	PRON
ejpam-3979	22	14	has	have	VERB
ejpam-3979	22	15	a	a	DET
ejpam-3979	22	16	series	series	NOUN
ejpam-3979	22	17	of	of	ADP
ejpam-3979	22	18	normal	normal	ADJ
ejpam-3979	22	19	subgroups	subgroup	NOUN
ejpam-3979	22	20	{	{	PUNCT
ejpam-3979	22	21	e	e	NOUN
ejpam-3979	22	22	}	}	PUNCT
ejpam-3979	22	23	=	=	SYM
ejpam-3979	22	24	g0	g0	PROPN
ejpam-3979	22	25	c	c	PROPN
ejpam-3979	22	26	g1	g1	PROPN
ejpam-3979	22	27	c	c	PROPN
ejpam-3979	22	28	g2	g2	PROPN
ejpam-3979	22	29	c	c	PROPN
ejpam-3979	22	30	......	......	PUNCT
ejpam-3979	23	1	c	c	X
ejpam-3979	23	2	gn	gn	PROPN
ejpam-3979	24	1	=	=	PUNCT
ejpam-3979	24	2	g	g	PROPN
ejpam-3979	24	3	such	such	ADJ
ejpam-3979	24	4	that	that	PRON
ejpam-3979	24	5	gi	gi	PROPN
ejpam-3979	24	6	/	/	SYM
ejpam-3979	24	7	gi−1	gi−1	PROPN
ejpam-3979	24	8	is	be	AUX
ejpam-3979	24	9	abelian	abelian	ADJ
ejpam-3979	24	10	where	where	SCONJ
ejpam-3979	24	11	0	0	NUM
ejpam-3979	24	12	≤	≤	PUNCT
ejpam-3979	24	13	i	i	PRON
ejpam-3979	24	14	≤	≤	NOUN
ejpam-3979	24	15	n	n	CCONJ
ejpam-3979	24	16	,	,	PUNCT
ejpam-3979	24	17	(	(	PUNCT
ejpam-3979	24	18	see	see	VERB
ejpam-3979	24	19	[	[	X
ejpam-3979	24	20	23	23	NUM
ejpam-3979	24	21	]	]	PUNCT
ejpam-3979	24	22	)	)	PUNCT
ejpam-3979	24	23	.	.	PUNCT
ejpam-3979	25	1	in	in	ADP
ejpam-3979	25	2	[	[	X
ejpam-3979	25	3	26	26	NUM
ejpam-3979	25	4	]	]	PUNCT
ejpam-3979	25	5	,	,	PUNCT
ejpam-3979	25	6	wang	wang	PROPN
ejpam-3979	25	7	proved	prove	VERB
ejpam-3979	25	8	that	that	SCONJ
ejpam-3979	25	9	g	g	PROPN
ejpam-3979	25	10	is	be	AUX
ejpam-3979	25	11	solvable	solvable	ADJ
ejpam-3979	25	12	if	if	SCONJ
ejpam-3979	25	13	and	and	CCONJ
ejpam-3979	25	14	only	only	ADV
ejpam-3979	25	15	if	if	SCONJ
ejpam-3979	25	16	m	m	NOUN
ejpam-3979	25	17	is	be	AUX
ejpam-3979	25	18	c	c	NOUN
ejpam-3979	25	19	-	-	ADJ
ejpam-3979	25	20	normal	normal	ADJ
ejpam-3979	25	21	in	in	ADP
ejpam-3979	25	22	g	g	NOUN
ejpam-3979	25	23	for	for	ADP
ejpam-3979	25	24	every	every	DET
ejpam-3979	25	25	maximal	maximal	ADJ
ejpam-3979	25	26	subgroup	subgroup	NOUN
ejpam-3979	25	27	m	m	PROPN
ejpam-3979	25	28	of	of	ADP
ejpam-3979	25	29	g.	g.	PROPN
ejpam-3979	25	30	a	a	DET
ejpam-3979	25	31	group	group	NOUN
ejpam-3979	25	32	g	g	PROPN
ejpam-3979	25	33	is	be	AUX
ejpam-3979	25	34	called	call	VERB
ejpam-3979	25	35	σ	σ	NOUN
ejpam-3979	25	36	-	-	PUNCT
ejpam-3979	25	37	primary	primary	ADJ
ejpam-3979	25	38	if	if	SCONJ
ejpam-3979	25	39	|	|	ADV
ejpam-3979	25	40	g	g	PROPN
ejpam-3979	25	41	|	|	ADV
ejpam-3979	25	42	is	be	AUX
ejpam-3979	25	43	a	a	DET
ejpam-3979	25	44	σ	σ	NOUN
ejpam-3979	25	45	-	-	PUNCT
ejpam-3979	25	46	primary	primary	ADJ
ejpam-3979	25	47	number	number	NOUN
ejpam-3979	25	48	.	.	PUNCT
ejpam-3979	26	1	a	a	DET
ejpam-3979	26	2	group	group	NOUN
ejpam-3979	26	3	g	g	NOUN
ejpam-3979	26	4	is	be	AUX
ejpam-3979	26	5	said	say	VERB
ejpam-3979	26	6	to	to	PART
ejpam-3979	26	7	be	be	AUX
ejpam-3979	26	8	σ	σ	NOUN
ejpam-3979	26	9	-	-	PUNCT
ejpam-3979	26	10	solvable	solvable	ADJ
ejpam-3979	26	11	if	if	SCONJ
ejpam-3979	26	12	every	every	DET
ejpam-3979	26	13	chief	chief	ADJ
ejpam-3979	26	14	factor	factor	NOUN
ejpam-3979	26	15	of	of	ADP
ejpam-3979	26	16	g	g	PROPN
ejpam-3979	26	17	is	be	AUX
ejpam-3979	26	18	σ	σ	NOUN
ejpam-3979	26	19	-	-	NOUN
ejpam-3979	26	20	primary	primary	ADJ
ejpam-3979	27	1	[	[	X
ejpam-3979	27	2	2	2	NUM
ejpam-3979	27	3	]	]	PUNCT
ejpam-3979	27	4	.	.	PUNCT
ejpam-3979	28	1	in	in	ADP
ejpam-3979	28	2	1870	1870	NUM
ejpam-3979	28	3	,	,	PUNCT
ejpam-3979	28	4	benjamin	benjamin	PROPN
ejpam-3979	28	5	pierce	pierce	PROPN
ejpam-3979	28	6	was	be	AUX
ejpam-3979	28	7	the	the	DET
ejpam-3979	28	8	first	first	ADJ
ejpam-3979	28	9	who	who	PRON
ejpam-3979	28	10	introduced	introduce	VERB
ejpam-3979	28	11	the	the	DET
ejpam-3979	28	12	term	term	NOUN
ejpam-3979	28	13	nilpotent	nilpotent	NOUN
ejpam-3979	28	14	in	in	ADP
ejpam-3979	28	15	the	the	DET
ejpam-3979	28	16	context	context	NOUN
ejpam-3979	28	17	of	of	ADP
ejpam-3979	28	18	his	his	PRON
ejpam-3979	28	19	work	work	NOUN
ejpam-3979	28	20	on	on	ADP
ejpam-3979	28	21	the	the	DET
ejpam-3979	28	22	classification	classification	NOUN
ejpam-3979	28	23	of	of	ADP
ejpam-3979	28	24	algebras	algebras	PROPN
ejpam-3979	28	25	.	.	PUNCT
ejpam-3979	29	1	in	in	ADP
ejpam-3979	29	2	algebras	algebras	PROPN
ejpam-3979	29	3	,	,	PUNCT
ejpam-3979	29	4	an	an	DET
ejpam-3979	29	5	element	element	NOUN
ejpam-3979	29	6	x	x	PUNCT
ejpam-3979	29	7	of	of	ADP
ejpam-3979	29	8	a	a	DET
ejpam-3979	29	9	ring	ring	NOUN
ejpam-3979	29	10	r	r	NOUN
ejpam-3979	29	11	is	be	AUX
ejpam-3979	29	12	said	say	VERB
ejpam-3979	29	13	to	to	PART
ejpam-3979	29	14	be	be	AUX
ejpam-3979	29	15	nilpotent	nilpotent	ADJ
ejpam-3979	29	16	if	if	SCONJ
ejpam-3979	29	17	there	there	PRON
ejpam-3979	29	18	exists	exist	VERB
ejpam-3979	29	19	some	some	DET
ejpam-3979	29	20	positive	positive	ADJ
ejpam-3979	29	21	integer	integer	NOUN
ejpam-3979	29	22	n	n	CCONJ
ejpam-3979	29	23	such	such	ADJ
ejpam-3979	29	24	that	that	PRON
ejpam-3979	29	25	xn	xn	PUNCT
ejpam-3979	30	1	=	=	SYM
ejpam-3979	30	2	0	0	PROPN
ejpam-3979	30	3	.	.	PUNCT
ejpam-3979	31	1	in	in	ADP
ejpam-3979	31	2	group	group	NOUN
ejpam-3979	31	3	theory	theory	NOUN
ejpam-3979	31	4	,	,	PUNCT
ejpam-3979	31	5	a	a	DET
ejpam-3979	31	6	group	group	NOUN
ejpam-3979	31	7	g	g	NOUN
ejpam-3979	31	8	is	be	AUX
ejpam-3979	31	9	said	say	VERB
ejpam-3979	31	10	to	to	PART
ejpam-3979	31	11	be	be	AUX
ejpam-3979	31	12	nilpotent	nilpotent	ADJ
ejpam-3979	31	13	if	if	SCONJ
ejpam-3979	31	14	it	it	PRON
ejpam-3979	31	15	has	have	VERB
ejpam-3979	31	16	an	an	DET
ejpam-3979	31	17	invariant	invariant	ADJ
ejpam-3979	31	18	series	series	NOUN
ejpam-3979	31	19	{	{	PUNCT
ejpam-3979	31	20	e	e	NOUN
ejpam-3979	31	21	}	}	PUNCT
ejpam-3979	31	22	=	=	SYM
ejpam-3979	31	23	g0eg1eg2e	g0eg1eg2e	PROPN
ejpam-3979	31	24	....	....	X
ejpam-3979	31	25	egn	egn	PROPN
ejpam-3979	32	1	=	=	PUNCT
ejpam-3979	32	2	g	g	PROPN
ejpam-3979	32	3	such	such	ADJ
ejpam-3979	32	4	that	that	DET
ejpam-3979	32	5	gi+1	gi+1	NOUN
ejpam-3979	32	6	/	/	SYM
ejpam-3979	32	7	gi	gi	NOUN
ejpam-3979	32	8	6	6	NUM
ejpam-3979	32	9	z(g	z(g	NOUN
ejpam-3979	32	10	/	/	SYM
ejpam-3979	32	11	gi	gi	NOUN
ejpam-3979	32	12	)	)	PUNCT
ejpam-3979	32	13	,	,	PUNCT
ejpam-3979	32	14	(	(	PUNCT
ejpam-3979	32	15	see	see	VERB
ejpam-3979	32	16	[	[	X
ejpam-3979	32	17	23	23	NUM
ejpam-3979	32	18	]	]	PUNCT
ejpam-3979	32	19	)	)	PUNCT
ejpam-3979	32	20	.	.	PUNCT
ejpam-3979	33	1	generalizing	generalize	VERB
ejpam-3979	33	2	the	the	DET
ejpam-3979	33	3	notions	notion	NOUN
ejpam-3979	33	4	of	of	ADP
ejpam-3979	33	5	nilpotency	nilpotency	NOUN
ejpam-3979	33	6	and	and	CCONJ
ejpam-3979	33	7	solvability	solvability	NOUN
ejpam-3979	33	8	of	of	ADP
ejpam-3979	33	9	groups	group	NOUN
ejpam-3979	33	10	to	to	ADP
ejpam-3979	33	11	nilpotency	nilpotency	NOUN
ejpam-3979	33	12	and	and	CCONJ
ejpam-3979	33	13	solvability	solvability	NOUN
ejpam-3979	33	14	of	of	ADP
ejpam-3979	33	15	semisimple	semisimple	NOUN
ejpam-3979	33	16	hopf	hopf	ADJ
ejpam-3979	33	17	algebras	algebras	PROPN
ejpam-3979	33	18	was	be	AUX
ejpam-3979	33	19	shown	show	VERB
ejpam-3979	33	20	to	to	PART
ejpam-3979	33	21	be	be	AUX
ejpam-3979	33	22	available	available	ADJ
ejpam-3979	33	23	by	by	ADP
ejpam-3979	33	24	giving	give	VERB
ejpam-3979	33	25	several	several	ADJ
ejpam-3979	33	26	criteria	criterion	NOUN
ejpam-3979	33	27	for	for	ADP
ejpam-3979	33	28	hopf	hopf	ADJ
ejpam-3979	33	29	algebras	algebra	NOUN
ejpam-3979	33	30	to	to	PART
ejpam-3979	33	31	be	be	AUX
ejpam-3979	33	32	so	so	ADV
ejpam-3979	33	33	,	,	PUNCT
ejpam-3979	33	34	see	see	VERB
ejpam-3979	33	35	[	[	X
ejpam-3979	33	36	7],[8],[9],[10	7],[8],[9],[10	NUM
ejpam-3979	33	37	]	]	PUNCT
ejpam-3979	33	38	.	.	PUNCT
ejpam-3979	34	1	it	it	PRON
ejpam-3979	34	2	was	be	AUX
ejpam-3979	34	3	noticed	notice	VERB
ejpam-3979	34	4	that	that	SCONJ
ejpam-3979	34	5	chains	chain	NOUN
ejpam-3979	34	6	of	of	ADP
ejpam-3979	34	7	normal	normal	ADJ
ejpam-3979	34	8	left	left	ADJ
ejpam-3979	34	9	coideal	coideal	NOUN
ejpam-3979	34	10	subalgebras	subalgebra	NOUN
ejpam-3979	34	11	of	of	ADP
ejpam-3979	34	12	a	a	DET
ejpam-3979	34	13	hopf	hopf	ADJ
ejpam-3979	34	14	algebra	algebra	NOUN
ejpam-3979	34	15	h	h	NOUN
ejpam-3979	34	16	play	play	VERB
ejpam-3979	34	17	a	a	DET
ejpam-3979	34	18	similar	similar	ADJ
ejpam-3979	34	19	role	role	NOUN
ejpam-3979	34	20	to	to	ADP
ejpam-3979	34	21	chains	chain	NOUN
ejpam-3979	34	22	of	of	ADP
ejpam-3979	34	23	normal	normal	ADJ
ejpam-3979	34	24	subgroups	subgroup	NOUN
ejpam-3979	34	25	of	of	ADP
ejpam-3979	34	26	a	a	DET
ejpam-3979	34	27	group	group	NOUN
ejpam-3979	34	28	.	.	PUNCT
ejpam-3979	35	1	consecuently	consecuently	ADV
ejpam-3979	35	2	,	,	PUNCT
ejpam-3979	35	3	replacing	replace	VERB
ejpam-3979	35	4	normal	normal	ADJ
ejpam-3979	35	5	subgroups	subgroup	NOUN
ejpam-3979	35	6	with	with	ADP
ejpam-3979	35	7	normal	normal	ADJ
ejpam-3979	35	8	left	left	ADJ
ejpam-3979	35	9	coideal	coideal	NOUN
ejpam-3979	35	10	subalgebras	subalgebra	NOUN
ejpam-3979	35	11	can	can	AUX
ejpam-3979	35	12	give	give	VERB
ejpam-3979	35	13	a	a	DET
ejpam-3979	35	14	satisfactory	satisfactory	ADJ
ejpam-3979	35	15	intrinsic	intrinsic	ADJ
ejpam-3979	35	16	definition	definition	NOUN
ejpam-3979	35	17	of	of	ADP
ejpam-3979	35	18	nilpotent	nilpotent	ADJ
ejpam-3979	35	19	hopf	hopf	PROPN
ejpam-3979	35	20	algebras	algebra	NOUN
ejpam-3979	35	21	.	.	PUNCT
ejpam-3979	36	1	generalizing	generalize	VERB
ejpam-3979	36	2	solvability	solvability	NOUN
ejpam-3979	36	3	is	be	AUX
ejpam-3979	36	4	more	more	ADV
ejpam-3979	36	5	difficult	difficult	ADJ
ejpam-3979	36	6	as	as	SCONJ
ejpam-3979	36	7	there	there	PRON
ejpam-3979	36	8	is	be	VERB
ejpam-3979	36	9	no	no	DET
ejpam-3979	36	10	obvious	obvious	ADJ
ejpam-3979	36	11	analogue	analogue	NOUN
ejpam-3979	36	12	of	of	ADP
ejpam-3979	36	13	hopf	hopf	ADJ
ejpam-3979	36	14	quotients	quotient	NOUN
ejpam-3979	36	15	of	of	ADP
ejpam-3979	36	16	left	left	ADJ
ejpam-3979	36	17	coideal	coideal	NOUN
ejpam-3979	36	18	subalgebras	subalgebras	PROPN
ejpam-3979	36	19	l	l	PROPN
ejpam-3979	36	20	over	over	ADP
ejpam-3979	36	21	n	n	CCONJ
ejpam-3979	36	22	where	where	SCONJ
ejpam-3979	36	23	n	n	X
ejpam-3979	36	24	⊂	⊂	PROPN
ejpam-3979	36	25	l	l	NOUN
ejpam-3979	36	26	is	be	AUX
ejpam-3979	36	27	a	a	DET
ejpam-3979	36	28	left	left	ADJ
ejpam-3979	36	29	coideal	coideal	NOUN
ejpam-3979	36	30	subalgebra	subalgebra	NOUN
ejpam-3979	36	31	normal	normal	ADJ
ejpam-3979	36	32	in	in	ADP
ejpam-3979	36	33	l	l	PROPN
ejpam-3979	36	34	but	but	CCONJ
ejpam-3979	36	35	not	not	PART
ejpam-3979	36	36	necessarily	necessarily	ADV
ejpam-3979	36	37	in	in	ADP
ejpam-3979	36	38	h.	h.	PROPN
ejpam-3979	36	39	whatsoever	whatsoever	ADV
ejpam-3979	36	40	,	,	PUNCT
ejpam-3979	36	41	this	this	DET
ejpam-3979	36	42	definition	definition	NOUN
ejpam-3979	36	43	is	be	AUX
ejpam-3979	36	44	undesirable	undesirable	ADJ
ejpam-3979	36	45	as	as	SCONJ
ejpam-3979	36	46	it	it	PRON
ejpam-3979	36	47	conflicts	conflict	VERB
ejpam-3979	36	48	with	with	ADP
ejpam-3979	36	49	what	what	PRON
ejpam-3979	36	50	is	be	AUX
ejpam-3979	36	51	expected	expect	VERB
ejpam-3979	36	52	from	from	ADP
ejpam-3979	36	53	group	group	NOUN
ejpam-3979	36	54	theory	theory	NOUN
ejpam-3979	36	55	.	.	PUNCT
ejpam-3979	37	1	commutative	commutative	ADJ
ejpam-3979	37	2	or	or	CCONJ
ejpam-3979	37	3	nilpotent	nilpotent	ADJ
ejpam-3979	37	4	hopf	hopf	ADJ
ejpam-3979	37	5	algebras	algebra	NOUN
ejpam-3979	37	6	are	be	AUX
ejpam-3979	37	7	not	not	PART
ejpam-3979	37	8	always	always	ADV
ejpam-3979	37	9	solvable	solvable	ADJ
ejpam-3979	37	10	in	in	ADP
ejpam-3979	37	11	that	that	DET
ejpam-3979	37	12	sense	sense	NOUN
ejpam-3979	37	13	[	[	X
ejpam-3979	37	14	11	11	NUM
ejpam-3979	37	15	]	]	PUNCT
ejpam-3979	37	16	.	.	PUNCT
ejpam-3979	38	1	in	in	ADP
ejpam-3979	38	2	[	[	X
ejpam-3979	38	3	10	10	NUM
ejpam-3979	38	4	]	]	PUNCT
ejpam-3979	38	5	,	,	PUNCT
ejpam-3979	38	6	it	it	PRON
ejpam-3979	38	7	was	be	AUX
ejpam-3979	38	8	suggested	suggest	VERB
ejpam-3979	38	9	a	a	DET
ejpam-3979	38	10	concrete	concrete	ADJ
ejpam-3979	38	11	definition	definition	NOUN
ejpam-3979	38	12	for	for	ADP
ejpam-3979	38	13	solvability	solvability	NOUN
ejpam-3979	38	14	of	of	ADP
ejpam-3979	38	15	semisimple	semisimple	NOUN
ejpam-3979	38	16	hopf	hopf	PROPN
ejpam-3979	38	17	algebras	algebras	PROPN
ejpam-3979	38	18	named	name	VERB
ejpam-3979	38	19	hopf	hopf	ADJ
ejpam-3979	38	20	solvability	solvability	NOUN
ejpam-3979	38	21	.	.	PUNCT
ejpam-3979	39	1	when	when	SCONJ
ejpam-3979	39	2	h	h	NOUN
ejpam-3979	39	3	=	=	SYM
ejpam-3979	39	4	kg	kg	PROPN
ejpam-3979	39	5	,	,	PUNCT
ejpam-3979	39	6	then	then	ADV
ejpam-3979	39	7	hopf	hopf	ADJ
ejpam-3979	39	8	solvability	solvability	NOUN
ejpam-3979	39	9	is	be	AUX
ejpam-3979	39	10	equivalent	equivalent	ADJ
ejpam-3979	39	11	to	to	ADP
ejpam-3979	39	12	g	g	PROPN
ejpam-3979	39	13	being	be	AUX
ejpam-3979	39	14	a	a	DET
ejpam-3979	39	15	solvable	solvable	ADJ
ejpam-3979	39	16	group	group	NOUN
ejpam-3979	39	17	.	.	PUNCT
ejpam-3979	40	1	it	it	PRON
ejpam-3979	40	2	was	be	AUX
ejpam-3979	40	3	proved	prove	VERB
ejpam-3979	40	4	that	that	SCONJ
ejpam-3979	40	5	commutative	commutative	ADJ
ejpam-3979	40	6	or	or	CCONJ
ejpam-3979	40	7	nilpotent	nilpotent	ADJ
ejpam-3979	40	8	semisimple	semisimple	NOUN
ejpam-3979	40	9	hopf	hopf	PROPN
ejpam-3979	40	10	algebras	algebra	NOUN
ejpam-3979	40	11	are	be	AUX
ejpam-3979	40	12	always	always	ADV
ejpam-3979	40	13	solvable	solvable	ADJ
ejpam-3979	40	14	hopf	hopf	ADJ
ejpam-3979	40	15	algebras	algebra	NOUN
ejpam-3979	40	16	.	.	PUNCT
ejpam-3979	41	1	in	in	ADP
ejpam-3979	41	2	[	[	X
ejpam-3979	41	3	8	8	NUM
ejpam-3979	41	4	]	]	PUNCT
ejpam-3979	41	5	and	and	CCONJ
ejpam-3979	41	6	[	[	X
ejpam-3979	41	7	10	10	NUM
ejpam-3979	41	8	]	]	X
ejpam-3979	41	9	cohen	cohen	NOUN
ejpam-3979	41	10	and	and	CCONJ
ejpam-3979	41	11	westreich	westreich	PRON
ejpam-3979	41	12	introduced	introduce	VERB
ejpam-3979	41	13	the	the	DET
ejpam-3979	41	14	concepts	concept	NOUN
ejpam-3979	41	15	of	of	ADP
ejpam-3979	41	16	nilpotent	nilpotent	ADJ
ejpam-3979	41	17	and	and	CCONJ
ejpam-3979	41	18	solvable	solvable	ADJ
ejpam-3979	41	19	hopf	hopf	ADJ
ejpam-3979	41	20	algebras	algebra	NOUN
ejpam-3979	41	21	under	under	ADP
ejpam-3979	41	22	certain	certain	ADJ
ejpam-3979	41	23	conditions	condition	NOUN
ejpam-3979	41	24	and	and	CCONJ
ejpam-3979	41	25	they	they	PRON
ejpam-3979	41	26	proved	prove	VERB
ejpam-3979	41	27	many	many	ADJ
ejpam-3979	41	28	interesting	interesting	ADJ
ejpam-3979	41	29	related	related	ADJ
ejpam-3979	41	30	results	result	NOUN
ejpam-3979	41	31	.	.	PUNCT
ejpam-3979	42	1	in	in	ADP
ejpam-3979	42	2	this	this	DET
ejpam-3979	42	3	article	article	NOUN
ejpam-3979	42	4	,	,	PUNCT
ejpam-3979	42	5	we	we	PRON
ejpam-3979	42	6	construct	construct	VERB
ejpam-3979	42	7	the	the	DET
ejpam-3979	42	8	group	group	NOUN
ejpam-3979	42	9	hopf	hopf	ADJ
ejpam-3979	42	10	algebra	algebra	NOUN
ejpam-3979	42	11	h	h	NOUN
ejpam-3979	42	12	=	=	SYM
ejpam-3979	42	13	kg	kg	PROPN
ejpam-3979	42	14	,	,	PUNCT
ejpam-3979	42	15	for	for	ADP
ejpam-3979	42	16	a	a	DET
ejpam-3979	42	17	finite	finite	ADJ
ejpam-3979	42	18	group	group	NOUN
ejpam-3979	42	19	g	g	PROPN
ejpam-3979	42	20	and	and	CCONJ
ejpam-3979	42	21	an	an	DET
ejpam-3979	42	22	algebraically	algebraically	ADV
ejpam-3979	42	23	closed	close	VERB
ejpam-3979	42	24	field	field	NOUN
ejpam-3979	42	25	k	k	NOUN
ejpam-3979	42	26	,	,	PUNCT
ejpam-3979	42	27	and	and	CCONJ
ejpam-3979	42	28	examine	examine	VERB
ejpam-3979	42	29	its	its	PRON
ejpam-3979	42	30	properties	property	NOUN
ejpam-3979	42	31	to	to	PART
ejpam-3979	42	32	see	see	VERB
ejpam-3979	42	33	what	what	PRON
ejpam-3979	42	34	of	of	ADP
ejpam-3979	42	35	the	the	DET
ejpam-3979	42	36	properties	property	NOUN
ejpam-3979	42	37	of	of	ADP
ejpam-3979	42	38	the	the	DET
ejpam-3979	42	39	original	original	ADJ
ejpam-3979	42	40	finite	finite	NOUN
ejpam-3979	42	41	group	group	NOUN
ejpam-3979	42	42	can	can	AUX
ejpam-3979	42	43	be	be	AUX
ejpam-3979	42	44	carried	carry	VERB
ejpam-3979	42	45	out	out	ADP
ejpam-3979	42	46	in	in	ADP
ejpam-3979	42	47	the	the	DET
ejpam-3979	42	48	case	case	NOUN
ejpam-3979	42	49	of	of	ADP
ejpam-3979	42	50	h.	h.	PROPN
ejpam-3979	42	51	t.	t.	PROPN
ejpam-3979	42	52	al	al	PROPN
ejpam-3979	42	53	-	-	PUNCT
ejpam-3979	42	54	mutairi	mutairi	PROPN
ejpam-3979	42	55	,	,	PUNCT
ejpam-3979	42	56	m.	m.	NOUN
ejpam-3979	42	57	m.	m.	PROPN
ejpam-3979	42	58	al	al	PROPN
ejpam-3979	42	59	-	-	PUNCT
ejpam-3979	42	60	shomrani	shomrani	PROPN
ejpam-3979	42	61	/	/	SYM
ejpam-3979	42	62	eur	eur	NOUN
ejpam-3979	42	63	.	.	PUNCT
ejpam-3979	43	1	j.	j.	PROPN
ejpam-3979	43	2	pure	pure	PROPN
ejpam-3979	43	3	appl	appl	PROPN
ejpam-3979	43	4	.	.	PROPN
ejpam-3979	43	5	math	math	PROPN
ejpam-3979	43	6	,	,	PUNCT
ejpam-3979	43	7	14	14	NUM
ejpam-3979	43	8	(	(	PUNCT
ejpam-3979	43	9	3	3	NUM
ejpam-3979	43	10	)	)	PUNCT
ejpam-3979	43	11	(	(	PUNCT
ejpam-3979	43	12	2021	2021	NUM
ejpam-3979	43	13	)	)	PUNCT
ejpam-3979	43	14	,	,	PUNCT
ejpam-3979	43	15	816	816	NUM
ejpam-3979	43	16	-	-	SYM
ejpam-3979	43	17	828	828	NUM
ejpam-3979	43	18	818	818	NUM
ejpam-3979	43	19	2	2	NUM
ejpam-3979	43	20	.	.	PUNCT
ejpam-3979	44	1	preliminaries	preliminary	NOUN
ejpam-3979	44	2	recall	recall	VERB
ejpam-3979	44	3	that	that	SCONJ
ejpam-3979	44	4	if	if	SCONJ
ejpam-3979	44	5	h	h	NOUN
ejpam-3979	44	6	is	be	AUX
ejpam-3979	44	7	a	a	DET
ejpam-3979	44	8	bialgebra	bialgebra	NOUN
ejpam-3979	44	9	.	.	PUNCT
ejpam-3979	45	1	a	a	DET
ejpam-3979	45	2	subset	subset	NOUN
ejpam-3979	45	3	n	n	PRON
ejpam-3979	45	4	⊆	⊆	NUM
ejpam-3979	45	5	h	h	NOUN
ejpam-3979	45	6	is	be	AUX
ejpam-3979	45	7	a	a	DET
ejpam-3979	45	8	sub	sub	NOUN
ejpam-3979	45	9	-	-	NOUN
ejpam-3979	45	10	bialgebra	bialgebra	NOUN
ejpam-3979	45	11	of	of	ADP
ejpam-3979	45	12	h	h	NOUN
ejpam-3979	45	13	if	if	SCONJ
ejpam-3979	45	14	n	n	PRON
ejpam-3979	45	15	is	be	AUX
ejpam-3979	45	16	a	a	DET
ejpam-3979	45	17	sub	sub	NOUN
ejpam-3979	45	18	-	-	NOUN
ejpam-3979	45	19	algebra	algebra	ADJ
ejpam-3979	45	20	i.e	i.e	PRON
ejpam-3979	45	21	(	(	PUNCT
ejpam-3979	45	22	1h	1h	NUM
ejpam-3979	45	23	∈	∈	PROPN
ejpam-3979	45	24	n	n	NOUN
ejpam-3979	45	25	and	and	CCONJ
ejpam-3979	45	26	for	for	ADP
ejpam-3979	45	27	all	all	DET
ejpam-3979	45	28	a	a	PRON
ejpam-3979	45	29	,	,	PUNCT
ejpam-3979	45	30	b	b	X
ejpam-3979	45	31	∈	∈	PROPN
ejpam-3979	45	32	n	n	CCONJ
ejpam-3979	45	33	we	we	PRON
ejpam-3979	45	34	have	have	VERB
ejpam-3979	45	35	ab	ab	PROPN
ejpam-3979	45	36	∈	∈	PROPN
ejpam-3979	45	37	n	n	CCONJ
ejpam-3979	45	38	)	)	PUNCT
ejpam-3979	45	39	and	and	CCONJ
ejpam-3979	45	40	n	n	PRON
ejpam-3979	45	41	is	be	AUX
ejpam-3979	45	42	a	a	DET
ejpam-3979	45	43	sub	sub	NOUN
ejpam-3979	45	44	-	-	NOUN
ejpam-3979	45	45	coalgebra	coalgebra	ADJ
ejpam-3979	45	46	i.e	i.e	PRON
ejpam-3979	45	47	(	(	PUNCT
ejpam-3979	45	48	∆(n	∆(n	NOUN
ejpam-3979	45	49	)	)	PUNCT
ejpam-3979	45	50	⊂	⊂	PROPN
ejpam-3979	45	51	n	n	DET
ejpam-3979	45	52	⊗n	⊗n	NOUN
ejpam-3979	45	53	)	)	PUNCT
ejpam-3979	45	54	.	.	PUNCT
ejpam-3979	46	1	if	if	SCONJ
ejpam-3979	46	2	h	h	NOUN
ejpam-3979	46	3	is	be	AUX
ejpam-3979	46	4	hopf	hopf	ADJ
ejpam-3979	46	5	algebra	algebra	NOUN
ejpam-3979	46	6	with	with	ADP
ejpam-3979	46	7	antipode	antipode	NOUN
ejpam-3979	46	8	s	s	X
ejpam-3979	46	9	and	and	CCONJ
ejpam-3979	46	10	s(n	s(n	PROPN
ejpam-3979	46	11	)	)	PUNCT
ejpam-3979	46	12	⊆	⊆	NUM
ejpam-3979	46	13	n	n	NOUN
ejpam-3979	46	14	then	then	ADV
ejpam-3979	46	15	n	n	ADV
ejpam-3979	46	16	is	be	AUX
ejpam-3979	46	17	said	say	VERB
ejpam-3979	46	18	to	to	PART
ejpam-3979	46	19	be	be	AUX
ejpam-3979	46	20	a	a	DET
ejpam-3979	46	21	hopf	hopf	ADJ
ejpam-3979	46	22	subalgebra	subalgebra	NOUN
ejpam-3979	46	23	.	.	PUNCT
ejpam-3979	47	1	also	also	ADV
ejpam-3979	47	2	,	,	PUNCT
ejpam-3979	47	3	it	it	PRON
ejpam-3979	47	4	is	be	AUX
ejpam-3979	47	5	called	call	VERB
ejpam-3979	47	6	a	a	DET
ejpam-3979	47	7	left	left	ADJ
ejpam-3979	47	8	coideal	coideal	NOUN
ejpam-3979	47	9	subalgebras	subalgebras	PROPN
ejpam-3979	47	10	if	if	SCONJ
ejpam-3979	47	11	it	it	PRON
ejpam-3979	47	12	is	be	AUX
ejpam-3979	47	13	subalgebras	subalgebras	PROPN
ejpam-3979	47	14	and	and	CCONJ
ejpam-3979	47	15	∆(n	∆(n	NOUN
ejpam-3979	47	16	)	)	PUNCT
ejpam-3979	47	17	⊆	⊆	NUM
ejpam-3979	47	18	h	h	NOUN
ejpam-3979	47	19	⊗n	⊗n	PROPN
ejpam-3979	47	20	(	(	PUNCT
ejpam-3979	47	21	see[17	see[17	PROPN
ejpam-3979	47	22	]	]	PUNCT
ejpam-3979	47	23	and	and	CCONJ
ejpam-3979	48	1	[	[	X
ejpam-3979	48	2	22	22	NUM
ejpam-3979	48	3	]	]	PUNCT
ejpam-3979	48	4	)	)	PUNCT
ejpam-3979	48	5	.	.	PUNCT
ejpam-3979	49	1	the	the	DET
ejpam-3979	49	2	following	follow	VERB
ejpam-3979	49	3	definitions	definition	NOUN
ejpam-3979	49	4	and	and	CCONJ
ejpam-3979	49	5	results	result	NOUN
ejpam-3979	49	6	are	be	AUX
ejpam-3979	49	7	needed	need	VERB
ejpam-3979	49	8	for	for	ADP
ejpam-3979	49	9	our	our	PRON
ejpam-3979	49	10	work	work	NOUN
ejpam-3979	49	11	.	.	PUNCT
ejpam-3979	50	1	definition	definition	NOUN
ejpam-3979	50	2	1	1	NUM
ejpam-3979	50	3	.	.	PUNCT
ejpam-3979	51	1	[	[	X
ejpam-3979	51	2	17	17	NUM
ejpam-3979	51	3	]	]	PUNCT
ejpam-3979	51	4	the	the	DET
ejpam-3979	51	5	center	center	NOUN
ejpam-3979	51	6	of	of	ADP
ejpam-3979	51	7	an	an	DET
ejpam-3979	51	8	algebra	algebra	NOUN
ejpam-3979	51	9	h	h	NOUN
ejpam-3979	51	10	is	be	AUX
ejpam-3979	51	11	the	the	DET
ejpam-3979	51	12	set	set	NOUN
ejpam-3979	51	13	z	z	PROPN
ejpam-3979	51	14	⊆	⊆	NUM
ejpam-3979	51	15	h	h	NOUN
ejpam-3979	51	16	of	of	ADP
ejpam-3979	51	17	elements	element	NOUN
ejpam-3979	51	18	that	that	PRON
ejpam-3979	51	19	commute	commute	VERB
ejpam-3979	51	20	with	with	ADP
ejpam-3979	51	21	the	the	DET
ejpam-3979	51	22	whole	whole	ADJ
ejpam-3979	51	23	algebra	algebra	NOUN
ejpam-3979	51	24	,	,	PUNCT
ejpam-3979	51	25	i.e	i.e	PROPN
ejpam-3979	51	26	z	z	NOUN
ejpam-3979	51	27	=	=	SYM
ejpam-3979	51	28	{	{	PUNCT
ejpam-3979	51	29	z	z	NOUN
ejpam-3979	51	30	∈	∈	PROPN
ejpam-3979	51	31	h|	h|	NOUN
ejpam-3979	51	32	zh	zh	NOUN
ejpam-3979	52	1	=	=	PUNCT
ejpam-3979	52	2	hz	hz	VERB
ejpam-3979	52	3	∀	∀	PUNCT
ejpam-3979	52	4	h	h	NOUN
ejpam-3979	52	5	∈	∈	PROPN
ejpam-3979	52	6	h	h	NOUN
ejpam-3979	52	7	}	}	PUNCT
ejpam-3979	52	8	.	.	PUNCT
ejpam-3979	53	1	definition	definition	NOUN
ejpam-3979	53	2	2	2	NUM
ejpam-3979	53	3	.	.	PUNCT
ejpam-3979	54	1	[	[	X
ejpam-3979	54	2	22	22	NUM
ejpam-3979	54	3	]	]	PUNCT
ejpam-3979	54	4	let	let	VERB
ejpam-3979	54	5	h	h	NOUN
ejpam-3979	54	6	be	be	AUX
ejpam-3979	54	7	any	any	DET
ejpam-3979	54	8	hopf	hopf	ADJ
ejpam-3979	54	9	algebra	algebra	NOUN
ejpam-3979	54	10	.	.	PUNCT
ejpam-3979	55	1	the	the	DET
ejpam-3979	55	2	left	left	ADJ
ejpam-3979	55	3	adjoint	adjoint	PROPN
ejpam-3979	55	4	action	action	NOUN
ejpam-3979	55	5	of	of	ADP
ejpam-3979	55	6	h	h	NOUN
ejpam-3979	55	7	on	on	ADP
ejpam-3979	55	8	itself	itself	PRON
ejpam-3979	55	9	is	be	AUX
ejpam-3979	55	10	given	give	VERB
ejpam-3979	55	11	by	by	ADP
ejpam-3979	55	12	(	(	PUNCT
ejpam-3979	55	13	adlh)(g	adlh)(g	NOUN
ejpam-3979	55	14	)	)	PUNCT
ejpam-3979	56	1	=	=	PUNCT
ejpam-3979	56	2	∑	∑	PUNCT
ejpam-3979	56	3	h1gs(h2	h1gs(h2	PROPN
ejpam-3979	56	4	)	)	PUNCT
ejpam-3979	56	5	,	,	PUNCT
ejpam-3979	56	6	∀	∀	NOUN
ejpam-3979	56	7	h	h	NOUN
ejpam-3979	56	8	,	,	PUNCT
ejpam-3979	56	9	g	g	PROPN
ejpam-3979	56	10	∈	∈	PROPN
ejpam-3979	56	11	h	h	NOUN
ejpam-3979	57	1	the	the	DET
ejpam-3979	57	2	right	right	PROPN
ejpam-3979	57	3	adjoint	adjoint	NOUN
ejpam-3979	57	4	action	action	NOUN
ejpam-3979	57	5	of	of	ADP
ejpam-3979	57	6	h	h	NOUN
ejpam-3979	57	7	on	on	ADP
ejpam-3979	57	8	itself	itself	PRON
ejpam-3979	57	9	is	be	AUX
ejpam-3979	57	10	given	give	VERB
ejpam-3979	57	11	by	by	ADP
ejpam-3979	57	12	(	(	PUNCT
ejpam-3979	57	13	adrh)(g	adrh)(g	NOUN
ejpam-3979	57	14	)	)	PUNCT
ejpam-3979	57	15	=	=	SYM
ejpam-3979	57	16	∑	∑	PUNCT
ejpam-3979	57	17	s(h1)gh2	s(h1)gh2	PROPN
ejpam-3979	57	18	,	,	PUNCT
ejpam-3979	57	19	∀	∀	NOUN
ejpam-3979	57	20	h	h	NOUN
ejpam-3979	57	21	,	,	PUNCT
ejpam-3979	57	22	g	g	PROPN
ejpam-3979	57	23	∈	∈	PROPN
ejpam-3979	57	24	h	h	NOUN
ejpam-3979	57	25	a	a	DET
ejpam-3979	57	26	hopf	hopf	ADJ
ejpam-3979	57	27	subalgebra	subalgebra	NOUN
ejpam-3979	57	28	n	n	PRON
ejpam-3979	57	29	of	of	ADP
ejpam-3979	57	30	h	h	NOUN
ejpam-3979	57	31	is	be	AUX
ejpam-3979	57	32	said	say	VERB
ejpam-3979	57	33	to	to	PART
ejpam-3979	57	34	be	be	AUX
ejpam-3979	57	35	normal	normal	ADJ
ejpam-3979	57	36	if	if	SCONJ
ejpam-3979	57	37	(	(	PUNCT
ejpam-3979	57	38	adlh)(n	adlh)(n	PROPN
ejpam-3979	57	39	)	)	PUNCT
ejpam-3979	57	40	⊆	⊆	NUM
ejpam-3979	57	41	n	n	PROPN
ejpam-3979	57	42	and	and	CCONJ
ejpam-3979	57	43	(	(	PUNCT
ejpam-3979	57	44	adrh)(n	adrh)(n	PROPN
ejpam-3979	57	45	)	)	PUNCT
ejpam-3979	57	46	⊆	⊆	NUM
ejpam-3979	57	47	n	n	NOUN
ejpam-3979	57	48	.	.	PUNCT
ejpam-3979	58	1	definition	definition	NOUN
ejpam-3979	58	2	3	3	NUM
ejpam-3979	58	3	.	.	PUNCT
ejpam-3979	59	1	[	[	X
ejpam-3979	59	2	6	6	NUM
ejpam-3979	59	3	]	]	PUNCT
ejpam-3979	59	4	a	a	DET
ejpam-3979	59	5	left	left	ADJ
ejpam-3979	59	6	coideal	coideal	NOUN
ejpam-3979	59	7	subalgebra	subalgebra	NOUN
ejpam-3979	59	8	of	of	ADP
ejpam-3979	59	9	h	h	NOUN
ejpam-3979	59	10	is	be	AUX
ejpam-3979	59	11	called	call	VERB
ejpam-3979	59	12	normal	normal	ADJ
ejpam-3979	59	13	if	if	SCONJ
ejpam-3979	59	14	n	n	PRON
ejpam-3979	59	15	is	be	AUX
ejpam-3979	59	16	closed	close	VERB
ejpam-3979	59	17	under	under	ADP
ejpam-3979	59	18	the	the	DET
ejpam-3979	59	19	left	left	ADJ
ejpam-3979	59	20	adjoint	adjoint	NOUN
ejpam-3979	59	21	action	action	NOUN
ejpam-3979	59	22	of	of	ADP
ejpam-3979	59	23	h	h	NOUN
ejpam-3979	59	24	on	on	ADP
ejpam-3979	59	25	itself	itself	PRON
ejpam-3979	59	26	.	.	PUNCT
ejpam-3979	60	1	similarly	similarly	ADV
ejpam-3979	60	2	,	,	PUNCT
ejpam-3979	60	3	a	a	DET
ejpam-3979	60	4	right	right	ADJ
ejpam-3979	60	5	coideal	coideal	NOUN
ejpam-3979	60	6	subalgebra	subalgebra	NOUN
ejpam-3979	60	7	of	of	ADP
ejpam-3979	60	8	h	h	NOUN
ejpam-3979	60	9	is	be	AUX
ejpam-3979	60	10	called	call	VERB
ejpam-3979	60	11	normal	normal	ADJ
ejpam-3979	60	12	if	if	SCONJ
ejpam-3979	60	13	n	n	PRON
ejpam-3979	60	14	is	be	AUX
ejpam-3979	60	15	closed	close	VERB
ejpam-3979	60	16	under	under	ADP
ejpam-3979	60	17	the	the	DET
ejpam-3979	60	18	right	right	ADJ
ejpam-3979	60	19	adjoint	adjoint	NOUN
ejpam-3979	60	20	action	action	NOUN
ejpam-3979	60	21	of	of	ADP
ejpam-3979	60	22	h	h	NOUN
ejpam-3979	60	23	on	on	ADP
ejpam-3979	60	24	itself	itself	PRON
ejpam-3979	60	25	.	.	PUNCT
ejpam-3979	61	1	h	h	PROPN
ejpam-3979	61	2	is	be	AUX
ejpam-3979	61	3	called	call	VERB
ejpam-3979	61	4	simple	simple	ADJ
ejpam-3979	61	5	if	if	SCONJ
ejpam-3979	61	6	it	it	PRON
ejpam-3979	61	7	contains	contain	VERB
ejpam-3979	61	8	no	no	DET
ejpam-3979	61	9	proper	proper	ADJ
ejpam-3979	61	10	normal	normal	ADJ
ejpam-3979	61	11	hopf	hopf	ADJ
ejpam-3979	61	12	subalgebras	subalgebra	NOUN
ejpam-3979	62	1	[	[	X
ejpam-3979	62	2	13	13	NUM
ejpam-3979	62	3	]	]	PUNCT
ejpam-3979	62	4	.	.	PUNCT
ejpam-3979	63	1	theorem	theorem	NOUN
ejpam-3979	63	2	1	1	NUM
ejpam-3979	63	3	.	.	PUNCT
ejpam-3979	64	1	[	[	X
ejpam-3979	64	2	20	20	NUM
ejpam-3979	64	3	]	]	PUNCT
ejpam-3979	64	4	a	a	DET
ejpam-3979	64	5	group	group	NOUN
ejpam-3979	64	6	algebra	algebra	NOUN
ejpam-3979	64	7	kg	kg	X
ejpam-3979	64	8	of	of	ADP
ejpam-3979	64	9	an	an	DET
ejpam-3979	64	10	arbitrary	arbitrary	ADJ
ejpam-3979	64	11	group	group	NOUN
ejpam-3979	64	12	g	g	NOUN
ejpam-3979	64	13	over	over	ADP
ejpam-3979	64	14	a	a	DET
ejpam-3979	64	15	filed	file	VERB
ejpam-3979	64	16	k	k	PROPN
ejpam-3979	64	17	is	be	AUX
ejpam-3979	64	18	simple	simple	ADJ
ejpam-3979	64	19	if	if	SCONJ
ejpam-3979	64	20	and	and	CCONJ
ejpam-3979	64	21	only	only	ADV
ejpam-3979	64	22	if	if	SCONJ
ejpam-3979	64	23	g	g	PROPN
ejpam-3979	64	24	has	have	VERB
ejpam-3979	64	25	no	no	DET
ejpam-3979	64	26	non	non	ADJ
ejpam-3979	64	27	-	-	ADJ
ejpam-3979	64	28	trivial	trivial	ADJ
ejpam-3979	64	29	finite	finite	ADJ
ejpam-3979	64	30	normal	normal	ADJ
ejpam-3979	64	31	subgroup	subgroup	NOUN
ejpam-3979	64	32	.	.	PUNCT
ejpam-3979	65	1	definition	definition	NOUN
ejpam-3979	65	2	4	4	NUM
ejpam-3979	65	3	.	.	PUNCT
ejpam-3979	66	1	[	[	X
ejpam-3979	66	2	22	22	NUM
ejpam-3979	66	3	]	]	PUNCT
ejpam-3979	66	4	let	let	VERB
ejpam-3979	66	5	h	h	PRON
ejpam-3979	66	6	be	be	AUX
ejpam-3979	66	7	a	a	DET
ejpam-3979	66	8	hopf	hopf	ADJ
ejpam-3979	66	9	algebra	algebra	NOUN
ejpam-3979	66	10	.	.	PUNCT
ejpam-3979	67	1	a	a	DET
ejpam-3979	67	2	left	left	ADJ
ejpam-3979	67	3	integral	integral	ADJ
ejpam-3979	67	4	in	in	ADP
ejpam-3979	67	5	h	h	PROPN
ejpam-3979	67	6	is	be	AUX
ejpam-3979	67	7	an	an	DET
ejpam-3979	67	8	element	element	NOUN
ejpam-3979	67	9	λ	λ	PROPN
ejpam-3979	67	10	∈	∈	NOUN
ejpam-3979	67	11	h	h	NOUN
ejpam-3979	67	12	such	such	ADJ
ejpam-3979	67	13	that	that	PRON
ejpam-3979	67	14	hλ	hλ	ADP
ejpam-3979	67	15	=	=	SYM
ejpam-3979	67	16	ε(h)λ	ε(h)λ	PROPN
ejpam-3979	67	17	,	,	PUNCT
ejpam-3979	67	18	for	for	ADP
ejpam-3979	67	19	all	all	DET
ejpam-3979	67	20	h	h	NOUN
ejpam-3979	67	21	∈	∈	PROPN
ejpam-3979	67	22	h	h	NOUN
ejpam-3979	67	23	;	;	PUNCT
ejpam-3979	67	24	similarly	similarly	ADV
ejpam-3979	67	25	,	,	PUNCT
ejpam-3979	67	26	a	a	DET
ejpam-3979	67	27	right	right	ADJ
ejpam-3979	67	28	integral	integral	ADJ
ejpam-3979	67	29	in	in	ADP
ejpam-3979	67	30	h	h	PROPN
ejpam-3979	67	31	is	be	AUX
ejpam-3979	67	32	an	an	DET
ejpam-3979	67	33	element	element	NOUN
ejpam-3979	67	34	λ	λ	PROPN
ejpam-3979	67	35	∈	∈	NOUN
ejpam-3979	67	36	h	h	NOUN
ejpam-3979	67	37	such	such	ADJ
ejpam-3979	67	38	that	that	SCONJ
ejpam-3979	67	39	λh	λh	ADP
ejpam-3979	67	40	=	=	PROPN
ejpam-3979	67	41	ε(h)λ	ε(h)λ	PROPN
ejpam-3979	67	42	,	,	PUNCT
ejpam-3979	67	43	for	for	ADP
ejpam-3979	67	44	all	all	DET
ejpam-3979	67	45	h	h	NOUN
ejpam-3979	67	46	∈	∈	PROPN
ejpam-3979	67	47	h.	h.	NOUN
ejpam-3979	67	48	definition	definition	NOUN
ejpam-3979	67	49	5	5	NUM
ejpam-3979	67	50	.	.	PUNCT
ejpam-3979	68	1	[	[	X
ejpam-3979	68	2	19	19	NUM
ejpam-3979	68	3	]	]	X
ejpam-3979	68	4	an	an	DET
ejpam-3979	68	5	element	element	NOUN
ejpam-3979	68	6	h	h	NOUN
ejpam-3979	68	7	∈	∈	PROPN
ejpam-3979	68	8	h	h	NOUN
ejpam-3979	68	9	is	be	AUX
ejpam-3979	68	10	said	say	VERB
ejpam-3979	68	11	to	to	PART
ejpam-3979	68	12	be	be	AUX
ejpam-3979	68	13	cocommutative	cocommutative	ADJ
ejpam-3979	68	14	if	if	SCONJ
ejpam-3979	68	15	∑	∑	PART
ejpam-3979	68	16	h1	h1	VERB
ejpam-3979	68	17	⊗	⊗	PROPN
ejpam-3979	68	18	h2	h2	PROPN
ejpam-3979	68	19	=	=	NOUN
ejpam-3979	68	20	∑	∑	PROPN
ejpam-3979	68	21	h2	h2	PROPN
ejpam-3979	68	22	⊗	⊗	PROPN
ejpam-3979	68	23	h1	h1	PROPN
ejpam-3979	68	24	.	.	PUNCT
ejpam-3979	69	1	lemma	lemma	PROPN
ejpam-3979	69	2	1	1	NUM
ejpam-3979	69	3	.	.	PUNCT
ejpam-3979	70	1	[	[	X
ejpam-3979	70	2	10	10	NUM
ejpam-3979	70	3	]	]	PUNCT
ejpam-3979	70	4	let	let	VERB
ejpam-3979	70	5	n	n	PRON
ejpam-3979	70	6	be	be	AUX
ejpam-3979	70	7	a	a	DET
ejpam-3979	70	8	left	left	ADJ
ejpam-3979	70	9	coideal	coideal	NOUN
ejpam-3979	70	10	subalgebra	subalgebra	NOUN
ejpam-3979	70	11	of	of	ADP
ejpam-3979	70	12	h	h	NOUN
ejpam-3979	70	13	with	with	ADP
ejpam-3979	70	14	an	an	DET
ejpam-3979	70	15	integral	integral	ADJ
ejpam-3979	70	16	λn	λn	NOUN
ejpam-3979	70	17	.	.	PUNCT
ejpam-3979	71	1	then	then	ADV
ejpam-3979	71	2	:	:	PUNCT
ejpam-3979	71	3	(	(	PUNCT
ejpam-3979	71	4	i	i	NOUN
ejpam-3979	71	5	)	)	PUNCT
ejpam-3979	72	1	n	n	PRON
ejpam-3979	72	2	is	be	AUX
ejpam-3979	72	3	a	a	DET
ejpam-3979	72	4	hopf	hopf	ADJ
ejpam-3979	72	5	subalgebra	subalgebra	NOUN
ejpam-3979	72	6	if	if	SCONJ
ejpam-3979	72	7	and	and	CCONJ
ejpam-3979	72	8	only	only	ADV
ejpam-3979	72	9	if	if	SCONJ
ejpam-3979	72	10	λn	λn	NOUN
ejpam-3979	72	11	is	be	AUX
ejpam-3979	72	12	cocommutative	cocommutative	ADJ
ejpam-3979	72	13	.	.	PUNCT
ejpam-3979	73	1	(	(	PUNCT
ejpam-3979	73	2	ii	ii	NOUN
ejpam-3979	73	3	)	)	PUNCT
ejpam-3979	73	4	n	n	PRON
ejpam-3979	73	5	is	be	AUX
ejpam-3979	73	6	normal	normal	ADJ
ejpam-3979	73	7	in	in	ADP
ejpam-3979	73	8	h	h	NOUN
ejpam-3979	73	9	if	if	SCONJ
ejpam-3979	74	1	and	and	CCONJ
ejpam-3979	74	2	only	only	ADV
ejpam-3979	74	3	if	if	SCONJ
ejpam-3979	74	4	λn	λn	PROPN
ejpam-3979	74	5	∈	∈	PROPN
ejpam-3979	74	6	z(h	z(h	PROPN
ejpam-3979	74	7	)	)	PUNCT
ejpam-3979	74	8	.	.	PUNCT
ejpam-3979	75	1	t.	t.	PROPN
ejpam-3979	75	2	al	al	PROPN
ejpam-3979	75	3	-	-	PUNCT
ejpam-3979	75	4	mutairi	mutairi	PROPN
ejpam-3979	75	5	,	,	PUNCT
ejpam-3979	75	6	m.	m.	NOUN
ejpam-3979	75	7	m.	m.	PROPN
ejpam-3979	75	8	al	al	PROPN
ejpam-3979	75	9	-	-	PUNCT
ejpam-3979	75	10	shomrani	shomrani	PROPN
ejpam-3979	75	11	/	/	SYM
ejpam-3979	75	12	eur	eur	NOUN
ejpam-3979	75	13	.	.	PUNCT
ejpam-3979	76	1	j.	j.	PROPN
ejpam-3979	76	2	pure	pure	PROPN
ejpam-3979	76	3	appl	appl	PROPN
ejpam-3979	76	4	.	.	PROPN
ejpam-3979	76	5	math	math	PROPN
ejpam-3979	76	6	,	,	PUNCT
ejpam-3979	76	7	14	14	NUM
ejpam-3979	76	8	(	(	PUNCT
ejpam-3979	76	9	3	3	NUM
ejpam-3979	76	10	)	)	PUNCT
ejpam-3979	76	11	(	(	PUNCT
ejpam-3979	76	12	2021	2021	NUM
ejpam-3979	76	13	)	)	PUNCT
ejpam-3979	76	14	,	,	PUNCT
ejpam-3979	76	15	816	816	NUM
ejpam-3979	76	16	-	-	SYM
ejpam-3979	76	17	828	828	NUM
ejpam-3979	76	18	819	819	NUM
ejpam-3979	76	19	in	in	ADP
ejpam-3979	76	20	the	the	DET
ejpam-3979	76	21	next	next	ADJ
ejpam-3979	76	22	two	two	NUM
ejpam-3979	76	23	theorems	theorem	NOUN
ejpam-3979	76	24	we	we	PRON
ejpam-3979	76	25	present	present	VERB
ejpam-3979	76	26	maschke	maschke	ADV
ejpam-3979	76	27	’s	’s	PART
ejpam-3979	76	28	theorem	theorem	NOUN
ejpam-3979	76	29	in	in	ADP
ejpam-3979	76	30	the	the	DET
ejpam-3979	76	31	group	group	NOUN
ejpam-3979	76	32	algebras	algebras	PROPN
ejpam-3979	76	33	case	case	NOUN
ejpam-3979	76	34	and	and	CCONJ
ejpam-3979	76	35	in	in	ADP
ejpam-3979	76	36	the	the	DET
ejpam-3979	76	37	general	general	ADJ
ejpam-3979	76	38	finite	finite	ADJ
ejpam-3979	76	39	dimensional	dimensional	ADJ
ejpam-3979	76	40	hopf	hopf	ADJ
ejpam-3979	76	41	algebras	algebras	PROPN
ejpam-3979	76	42	case	case	NOUN
ejpam-3979	76	43	.	.	PUNCT
ejpam-3979	77	1	theorem	theorem	NOUN
ejpam-3979	77	2	2	2	NUM
ejpam-3979	77	3	.	.	PUNCT
ejpam-3979	78	1	[	[	X
ejpam-3979	78	2	18	18	NUM
ejpam-3979	78	3	]	]	PUNCT
ejpam-3979	78	4	a	a	DET
ejpam-3979	78	5	group	group	NOUN
ejpam-3979	78	6	algebra	algebra	NOUN
ejpam-3979	78	7	of	of	ADP
ejpam-3979	78	8	a	a	DET
ejpam-3979	78	9	finite	finite	ADJ
ejpam-3979	78	10	group	group	NOUN
ejpam-3979	78	11	is	be	AUX
ejpam-3979	78	12	semisimple	semisimple	ADJ
ejpam-3979	78	13	if	if	SCONJ
ejpam-3979	78	14	and	and	CCONJ
ejpam-3979	78	15	only	only	ADV
ejpam-3979	78	16	if	if	SCONJ
ejpam-3979	78	17	the	the	DET
ejpam-3979	78	18	characteristic	characteristic	NOUN
ejpam-3979	78	19	of	of	ADP
ejpam-3979	78	20	the	the	DET
ejpam-3979	78	21	field	field	NOUN
ejpam-3979	78	22	does	do	AUX
ejpam-3979	78	23	not	not	PART
ejpam-3979	78	24	divide	divide	VERB
ejpam-3979	78	25	the	the	DET
ejpam-3979	78	26	order	order	NOUN
ejpam-3979	78	27	of	of	ADP
ejpam-3979	78	28	the	the	DET
ejpam-3979	78	29	group	group	NOUN
ejpam-3979	78	30	.	.	PUNCT
ejpam-3979	79	1	theorem	theorem	VERB
ejpam-3979	79	2	3	3	NUM
ejpam-3979	79	3	.	.	PUNCT
ejpam-3979	80	1	[	[	X
ejpam-3979	80	2	24	24	NUM
ejpam-3979	80	3	]	]	PUNCT
ejpam-3979	80	4	a	a	DET
ejpam-3979	80	5	finite	finite	ADJ
ejpam-3979	80	6	dimensional	dimensional	ADJ
ejpam-3979	80	7	hopf	hopf	ADJ
ejpam-3979	80	8	algebra	algebra	NOUN
ejpam-3979	80	9	h	h	NOUN
ejpam-3979	80	10	is	be	AUX
ejpam-3979	80	11	semisimple	semisimple	ADJ
ejpam-3979	80	12	as	as	ADP
ejpam-3979	80	13	an	an	DET
ejpam-3979	80	14	algebra	algebra	NOUN
ejpam-3979	80	15	if	if	SCONJ
ejpam-3979	80	16	and	and	CCONJ
ejpam-3979	80	17	only	only	ADV
ejpam-3979	80	18	if	if	SCONJ
ejpam-3979	80	19	ε(λ	ε(λ	NOUN
ejpam-3979	80	20	)	)	PUNCT
ejpam-3979	80	21	6=	6=	ADP
ejpam-3979	80	22	0	0	X
ejpam-3979	80	23	.	.	PUNCT
ejpam-3979	81	1	in	in	ADP
ejpam-3979	81	2	[	[	X
ejpam-3979	81	3	11	11	NUM
ejpam-3979	81	4	]	]	PUNCT
ejpam-3979	81	5	,	,	PUNCT
ejpam-3979	81	6	the	the	DET
ejpam-3979	81	7	left	left	ADJ
ejpam-3979	81	8	adjoint	adjoint	NOUN
ejpam-3979	81	9	action	action	NOUN
ejpam-3979	81	10	of	of	ADP
ejpam-3979	81	11	h	h	NOUN
ejpam-3979	81	12	on	on	ADP
ejpam-3979	81	13	itself	itself	PRON
ejpam-3979	81	14	was	be	AUX
ejpam-3979	81	15	denoted	denote	VERB
ejpam-3979	81	16	by	by	ADP
ejpam-3979	81	17	.	.	PUNCT
ejpam-3979	82	1	ad	ad	NOUN
ejpam-3979	82	2	that	that	PRON
ejpam-3979	82	3	is	be	AUX
ejpam-3979	82	4	,	,	PUNCT
ejpam-3979	82	5	for	for	ADP
ejpam-3979	82	6	all	all	DET
ejpam-3979	82	7	a	a	PRON
ejpam-3979	82	8	,	,	PUNCT
ejpam-3979	82	9	h	h	NOUN
ejpam-3979	82	10	∈	∈	PROPN
ejpam-3979	82	11	h	h	NOUN
ejpam-3979	82	12	,	,	PUNCT
ejpam-3979	82	13	h	h	NOUN
ejpam-3979	82	14	.	.	PUNCT
ejpam-3979	83	1	ad	ad	NOUN
ejpam-3979	83	2	a	a	X
ejpam-3979	83	3	=	=	SYM
ejpam-3979	83	4	∑	∑	NOUN
ejpam-3979	83	5	h1as(h2	h1as(h2	PROPN
ejpam-3979	83	6	)	)	PUNCT
ejpam-3979	83	7	definition	definition	NOUN
ejpam-3979	83	8	6	6	NUM
ejpam-3979	83	9	.	.	PUNCT
ejpam-3979	84	1	[	[	X
ejpam-3979	84	2	10	10	NUM
ejpam-3979	84	3	]	]	PUNCT
ejpam-3979	84	4	let	let	VERB
ejpam-3979	84	5	h	h	PRON
ejpam-3979	84	6	be	be	AUX
ejpam-3979	84	7	a	a	DET
ejpam-3979	84	8	semisimple	semisimple	NOUN
ejpam-3979	84	9	hopf	hopf	ADJ
ejpam-3979	84	10	algebra	algebra	NOUN
ejpam-3979	84	11	.	.	PUNCT
ejpam-3979	85	1	a	a	DET
ejpam-3979	85	2	chain	chain	NOUN
ejpam-3979	85	3	of	of	ADP
ejpam-3979	85	4	left	left	ADJ
ejpam-3979	85	5	coideal	coideal	NOUN
ejpam-3979	85	6	subalgebras	subalgebra	NOUN
ejpam-3979	85	7	of	of	ADP
ejpam-3979	85	8	h	h	PROPN
ejpam-3979	85	9	,	,	PUNCT
ejpam-3979	85	10	n0	n0	PROPN
ejpam-3979	85	11	⊂	⊂	PROPN
ejpam-3979	85	12	n1	n1	PROPN
ejpam-3979	85	13	⊂	⊂	PROPN
ejpam-3979	85	14	.	.	PUNCT
ejpam-3979	85	15	.	.	PUNCT
ejpam-3979	85	16	.	.	PUNCT
ejpam-3979	86	1	⊂	⊂	PROPN
ejpam-3979	86	2	nt	not	PART
ejpam-3979	86	3	is	be	AUX
ejpam-3979	86	4	a	a	DET
ejpam-3979	86	5	solvable	solvable	ADJ
ejpam-3979	86	6	series	series	NOUN
ejpam-3979	86	7	if	if	SCONJ
ejpam-3979	86	8	,	,	PUNCT
ejpam-3979	86	9	for	for	SCONJ
ejpam-3979	86	10	all	all	PRON
ejpam-3979	86	11	0	0	NUM
ejpam-3979	86	12	≤	≤	NUM
ejpam-3979	87	1	i	i	PRON
ejpam-3979	87	2	≤	≤	NOUN
ejpam-3979	88	1	t−	t−	PROPN
ejpam-3979	88	2	1	1	NUM
ejpam-3979	88	3	,	,	PUNCT
ejpam-3979	88	4	(	(	PUNCT
ejpam-3979	88	5	i	i	NOUN
ejpam-3979	88	6	)	)	PUNCT
ejpam-3979	88	7	λni	λni	PROPN
ejpam-3979	88	8	∈	∈	PROPN
ejpam-3979	88	9	z(ni+1	z(ni+1	PROPN
ejpam-3979	88	10	)	)	PUNCT
ejpam-3979	88	11	,	,	PUNCT
ejpam-3979	88	12	the	the	DET
ejpam-3979	88	13	center	center	NOUN
ejpam-3979	88	14	of	of	ADP
ejpam-3979	88	15	ni+1	ni+1	ADP
ejpam-3979	88	16	,	,	PUNCT
ejpam-3979	88	17	where	where	SCONJ
ejpam-3979	88	18	λni	λni	PROPN
ejpam-3979	88	19	is	be	AUX
ejpam-3979	88	20	the	the	DET
ejpam-3979	88	21	integral	integral	ADJ
ejpam-3979	88	22	of	of	ADP
ejpam-3979	88	23	ni	ni	PROPN
ejpam-3979	88	24	.	.	PROPN
ejpam-3979	88	25	(	(	PUNCT
ejpam-3979	88	26	ii	ii	NOUN
ejpam-3979	88	27	)	)	PUNCT
ejpam-3979	88	28	for	for	ADP
ejpam-3979	88	29	all	all	DET
ejpam-3979	88	30	a	a	PRON
ejpam-3979	88	31	,	,	PUNCT
ejpam-3979	88	32	b	b	X
ejpam-3979	88	33	∈	∈	PROPN
ejpam-3979	88	34	ni+1	ni+1	ADP
ejpam-3979	88	35	,	,	PUNCT
ejpam-3979	88	36	(	(	PUNCT
ejpam-3979	88	37	a	a	X
ejpam-3979	88	38	.	.	PUNCT
ejpam-3979	89	1	ad	ad	NOUN
ejpam-3979	89	2	b)λni	b)λni	PROPN
ejpam-3979	89	3	=	=	SYM
ejpam-3979	89	4	〈	〈	PROPN
ejpam-3979	89	5	ε	ε	PROPN
ejpam-3979	89	6	,	,	PUNCT
ejpam-3979	89	7	a	a	DET
ejpam-3979	89	8	〉	〉	NOUN
ejpam-3979	89	9	bλni	bλni	NOUN
ejpam-3979	89	10	.	.	PUNCT
ejpam-3979	90	1	the	the	DET
ejpam-3979	90	2	hopf	hopf	ADJ
ejpam-3979	90	3	algebra	algebra	NOUN
ejpam-3979	90	4	h	h	NOUN
ejpam-3979	90	5	is	be	AUX
ejpam-3979	90	6	said	say	VERB
ejpam-3979	90	7	to	to	PART
ejpam-3979	90	8	be	be	AUX
ejpam-3979	90	9	solvable	solvable	ADJ
ejpam-3979	90	10	if	if	SCONJ
ejpam-3979	90	11	it	it	PRON
ejpam-3979	90	12	has	have	VERB
ejpam-3979	90	13	a	a	DET
ejpam-3979	90	14	solvable	solvable	ADJ
ejpam-3979	90	15	series	series	NOUN
ejpam-3979	90	16	so	so	SCONJ
ejpam-3979	90	17	that	that	SCONJ
ejpam-3979	90	18	n0	n0	X
ejpam-3979	90	19	=	=	SYM
ejpam-3979	90	20	k	k	PROPN
ejpam-3979	90	21	and	and	CCONJ
ejpam-3979	90	22	nt	not	PART
ejpam-3979	90	23	=	=	PROPN
ejpam-3979	90	24	h.	h.	PROPN
ejpam-3979	90	25	remark	remark	NOUN
ejpam-3979	90	26	1	1	NUM
ejpam-3979	90	27	.	.	PUNCT
ejpam-3979	91	1	[	[	X
ejpam-3979	91	2	10	10	NUM
ejpam-3979	91	3	]	]	X
ejpam-3979	91	4	commutative	commutative	ADJ
ejpam-3979	91	5	hopf	hopf	ADJ
ejpam-3979	91	6	algebras	algebra	NOUN
ejpam-3979	91	7	are	be	AUX
ejpam-3979	91	8	solvable	solvable	ADJ
ejpam-3979	91	9	by	by	ADP
ejpam-3979	91	10	the	the	DET
ejpam-3979	91	11	definition	definition	NOUN
ejpam-3979	91	12	with	with	ADP
ejpam-3979	91	13	k	k	PROPN
ejpam-3979	91	14	⊂	⊂	PROPN
ejpam-3979	91	15	h	h	PROPN
ejpam-3979	91	16	as	as	ADP
ejpam-3979	91	17	a	a	DET
ejpam-3979	91	18	solvable	solvable	ADJ
ejpam-3979	91	19	series	series	NOUN
ejpam-3979	91	20	.	.	PUNCT
ejpam-3979	92	1	lemma	lemma	PROPN
ejpam-3979	92	2	2	2	NUM
ejpam-3979	92	3	.	.	PUNCT
ejpam-3979	93	1	[	[	X
ejpam-3979	93	2	10	10	NUM
ejpam-3979	93	3	]	]	X
ejpam-3979	93	4	if	if	SCONJ
ejpam-3979	93	5	n	n	PRON
ejpam-3979	93	6	is	be	AUX
ejpam-3979	93	7	a	a	DET
ejpam-3979	93	8	left	left	ADJ
ejpam-3979	93	9	coideal	coideal	NOUN
ejpam-3979	93	10	subalgebra	subalgebra	NOUN
ejpam-3979	93	11	of	of	ADP
ejpam-3979	93	12	h	h	NOUN
ejpam-3979	93	13	,	,	PUNCT
ejpam-3979	93	14	then	then	ADV
ejpam-3979	93	15	the	the	DET
ejpam-3979	93	16	following	follow	VERB
ejpam-3979	93	17	hold	hold	NOUN
ejpam-3979	93	18	:	:	PUNCT
ejpam-3979	93	19	(	(	PUNCT
ejpam-3979	93	20	i	i	NOUN
ejpam-3979	93	21	)	)	PUNCT
ejpam-3979	93	22	hλn	hλn	VERB
ejpam-3979	93	23	∼=	∼=	PROPN
ejpam-3979	93	24	h	h	NOUN
ejpam-3979	93	25	�	�	NOUN
ejpam-3979	93	26	hn+	hn+	VERB
ejpam-3979	93	27	as	as	ADP
ejpam-3979	93	28	left	leave	VERB
ejpam-3979	93	29	h	h	NOUN
ejpam-3979	93	30	-	-	PUNCT
ejpam-3979	93	31	modules	module	NOUN
ejpam-3979	93	32	via	via	ADP
ejpam-3979	93	33	π|hλn	π|hλn	ADJ
ejpam-3979	93	34	,	,	PUNCT
ejpam-3979	93	35	where	where	SCONJ
ejpam-3979	93	36	π	π	PROPN
ejpam-3979	93	37	is	be	AUX
ejpam-3979	93	38	the	the	DET
ejpam-3979	93	39	natural	natural	ADJ
ejpam-3979	93	40	h	h	NOUN
ejpam-3979	93	41	-	-	PUNCT
ejpam-3979	93	42	module	module	NOUN
ejpam-3979	93	43	projection	projection	NOUN
ejpam-3979	93	44	from	from	ADP
ejpam-3979	93	45	h	h	NOUN
ejpam-3979	93	46	to	to	ADP
ejpam-3979	93	47	h	h	PROPN
ejpam-3979	93	48	�	�	PROPN
ejpam-3979	93	49	hn+	hn+	PROPN
ejpam-3979	93	50	,	,	PUNCT
ejpam-3979	93	51	where	where	SCONJ
ejpam-3979	93	52	n+	n+	ADP
ejpam-3979	93	53	=	=	SYM
ejpam-3979	93	54	n	n	X
ejpam-3979	93	55	∩	∩	X
ejpam-3979	93	56	ker(ε	ker(ε	PROPN
ejpam-3979	93	57	)	)	PUNCT
ejpam-3979	93	58	.	.	PUNCT
ejpam-3979	94	1	(	(	PUNCT
ejpam-3979	94	2	ii	ii	NOUN
ejpam-3979	94	3	)	)	PUNCT
ejpam-3979	94	4	hλn	hλn	NOUN
ejpam-3979	94	5	∼=	∼=	PROPN
ejpam-3979	94	6	h	h	NOUN
ejpam-3979	94	7	�	�	NOUN
ejpam-3979	94	8	hn+	hn+	VERB
ejpam-3979	94	9	as	as	ADP
ejpam-3979	94	10	right	right	ADJ
ejpam-3979	94	11	h	h	NOUN
ejpam-3979	94	12	-	-	PUNCT
ejpam-3979	94	13	modules	module	NOUN
ejpam-3979	94	14	and	and	CCONJ
ejpam-3979	94	15	(	(	PUNCT
ejpam-3979	94	16	iii	iii	NOUN
ejpam-3979	94	17	)	)	PUNCT
ejpam-3979	94	18	if	if	SCONJ
ejpam-3979	94	19	n	n	PRON
ejpam-3979	94	20	is	be	AUX
ejpam-3979	94	21	also	also	ADV
ejpam-3979	94	22	normal	normal	ADJ
ejpam-3979	94	23	in	in	ADP
ejpam-3979	94	24	h	h	NOUN
ejpam-3979	94	25	,	,	PUNCT
ejpam-3979	94	26	then	then	ADV
ejpam-3979	94	27	π|hλn	π|hλn	ADJ
ejpam-3979	94	28	is	be	AUX
ejpam-3979	94	29	an	an	DET
ejpam-3979	94	30	algebra	algebra	NOUN
ejpam-3979	94	31	isomorphism	isomorphism	NOUN
ejpam-3979	94	32	as	as	ADV
ejpam-3979	94	33	well	well	ADV
ejpam-3979	94	34	.	.	PUNCT
ejpam-3979	95	1	definition	definition	NOUN
ejpam-3979	95	2	7	7	NUM
ejpam-3979	95	3	.	.	PUNCT
ejpam-3979	96	1	[	[	X
ejpam-3979	96	2	8	8	X
ejpam-3979	96	3	]	]	PUNCT
ejpam-3979	96	4	a	a	DET
ejpam-3979	96	5	semisimple	semisimple	NOUN
ejpam-3979	96	6	hopf	hopf	ADJ
ejpam-3979	96	7	algebra	algebra	NOUN
ejpam-3979	96	8	h	h	NOUN
ejpam-3979	96	9	is	be	AUX
ejpam-3979	96	10	nilpotent	nilpotent	ADJ
ejpam-3979	96	11	if	if	SCONJ
ejpam-3979	96	12	the	the	DET
ejpam-3979	96	13	ascending	ascend	VERB
ejpam-3979	96	14	central	central	ADJ
ejpam-3979	96	15	series	series	NOUN
ejpam-3979	96	16	k	k	PROPN
ejpam-3979	96	17	⊆	⊆	NUM
ejpam-3979	96	18	z1	z1	PROPN
ejpam-3979	96	19	⊆	⊆	NUM
ejpam-3979	96	20	z2	z2	PROPN
ejpam-3979	96	21	⊆	⊆	NUM
ejpam-3979	96	22	....	....	PUNCT
ejpam-3979	96	23	satisfies	satisfy	VERB
ejpam-3979	96	24	zm	zm	PROPN
ejpam-3979	96	25	=	=	PROPN
ejpam-3979	96	26	h	h	PROPN
ejpam-3979	96	27	for	for	ADP
ejpam-3979	96	28	some	some	DET
ejpam-3979	96	29	m	m	NOUN
ejpam-3979	96	30	>	>	X
ejpam-3979	96	31	1	1	NUM
ejpam-3979	96	32	.	.	PUNCT
ejpam-3979	97	1	the	the	DET
ejpam-3979	97	2	smallest	small	ADJ
ejpam-3979	97	3	such	such	ADJ
ejpam-3979	97	4	m	m	VERB
ejpam-3979	97	5	is	be	AUX
ejpam-3979	97	6	called	call	VERB
ejpam-3979	97	7	the	the	DET
ejpam-3979	97	8	index	index	NOUN
ejpam-3979	97	9	of	of	ADP
ejpam-3979	97	10	nilpotency	nilpotency	NOUN
ejpam-3979	97	11	of	of	ADP
ejpam-3979	97	12	h.	h.	PROPN
ejpam-3979	97	13	remark	remark	PROPN
ejpam-3979	97	14	2	2	NUM
ejpam-3979	97	15	.	.	PUNCT
ejpam-3979	98	1	[	[	X
ejpam-3979	98	2	8	8	NUM
ejpam-3979	98	3	]	]	PUNCT
ejpam-3979	98	4	let	let	NOUN
ejpam-3979	98	5	h	h	NOUN
ejpam-3979	98	6	=	=	SYM
ejpam-3979	98	7	kg	kg	PROPN
ejpam-3979	98	8	,	,	PUNCT
ejpam-3979	98	9	g	g	PROPN
ejpam-3979	98	10	be	be	AUX
ejpam-3979	98	11	finite	finite	ADJ
ejpam-3979	98	12	group	group	NOUN
ejpam-3979	98	13	.	.	PUNCT
ejpam-3979	99	1	then	then	ADV
ejpam-3979	99	2	z̃(h	z̃(h	ADV
ejpam-3979	99	3	)	)	PUNCT
ejpam-3979	100	1	=	=	PUNCT
ejpam-3979	100	2	kzg	kzg	NOUN
ejpam-3979	100	3	,	,	PUNCT
ejpam-3979	100	4	where	where	SCONJ
ejpam-3979	100	5	zg	zg	PROPN
ejpam-3979	100	6	is	be	AUX
ejpam-3979	100	7	the	the	DET
ejpam-3979	100	8	center	center	NOUN
ejpam-3979	100	9	of	of	ADP
ejpam-3979	100	10	the	the	DET
ejpam-3979	100	11	group	group	NOUN
ejpam-3979	100	12	g	g	NOUN
ejpam-3979	100	13	and	and	CCONJ
ejpam-3979	100	14	z̃(h	z̃(h	PROPN
ejpam-3979	100	15	)	)	PUNCT
ejpam-3979	100	16	=	=	PRON
ejpam-3979	100	17	{	{	PUNCT
ejpam-3979	100	18	h	h	NOUN
ejpam-3979	100	19	∈	∈	PROPN
ejpam-3979	100	20	h	h	NOUN
ejpam-3979	100	21	;	;	PUNCT
ejpam-3979	100	22	∑	∑	PUNCT
ejpam-3979	100	23	h1⊗h2xsh3	h1⊗h2xsh3	NOUN
ejpam-3979	100	24	=	=	PUNCT
ejpam-3979	100	25	h⊗x	h⊗x	VERB
ejpam-3979	100	26	for	for	ADP
ejpam-3979	100	27	all	all	PRON
ejpam-3979	100	28	x	x	SYM
ejpam-3979	100	29	∈	∈	PROPN
ejpam-3979	100	30	h	h	NOUN
ejpam-3979	100	31	}	}	PUNCT
ejpam-3979	100	32	is	be	AUX
ejpam-3979	100	33	the	the	DET
ejpam-3979	100	34	hopf	hopf	ADJ
ejpam-3979	100	35	center	center	NOUN
ejpam-3979	100	36	of	of	ADP
ejpam-3979	100	37	h.	h.	PROPN
ejpam-3979	100	38	t.	t.	PROPN
ejpam-3979	100	39	al	al	PROPN
ejpam-3979	100	40	-	-	PUNCT
ejpam-3979	100	41	mutairi	mutairi	PROPN
ejpam-3979	100	42	,	,	PUNCT
ejpam-3979	100	43	m.	m.	NOUN
ejpam-3979	100	44	m.	m.	PROPN
ejpam-3979	100	45	al	al	PROPN
ejpam-3979	100	46	-	-	PUNCT
ejpam-3979	100	47	shomrani	shomrani	PROPN
ejpam-3979	100	48	/	/	SYM
ejpam-3979	100	49	eur	eur	NOUN
ejpam-3979	100	50	.	.	PUNCT
ejpam-3979	101	1	j.	j.	PROPN
ejpam-3979	101	2	pure	pure	PROPN
ejpam-3979	101	3	appl	appl	PROPN
ejpam-3979	101	4	.	.	PROPN
ejpam-3979	101	5	math	math	PROPN
ejpam-3979	101	6	,	,	PUNCT
ejpam-3979	101	7	14	14	NUM
ejpam-3979	101	8	(	(	PUNCT
ejpam-3979	101	9	3	3	NUM
ejpam-3979	101	10	)	)	PUNCT
ejpam-3979	101	11	(	(	PUNCT
ejpam-3979	101	12	2021	2021	NUM
ejpam-3979	101	13	)	)	PUNCT
ejpam-3979	101	14	,	,	PUNCT
ejpam-3979	101	15	816	816	NUM
ejpam-3979	101	16	-	-	SYM
ejpam-3979	101	17	828	828	NUM
ejpam-3979	101	18	820	820	NUM
ejpam-3979	101	19	proposition	proposition	NOUN
ejpam-3979	101	20	1	1	NUM
ejpam-3979	101	21	.	.	PUNCT
ejpam-3979	102	1	[	[	X
ejpam-3979	102	2	10	10	NUM
ejpam-3979	102	3	]	]	X
ejpam-3979	102	4	a	a	DET
ejpam-3979	102	5	semisimple	semisimple	NOUN
ejpam-3979	102	6	hopf	hopf	ADJ
ejpam-3979	102	7	algebra	algebra	NOUN
ejpam-3979	102	8	h	h	NOUN
ejpam-3979	102	9	is	be	AUX
ejpam-3979	102	10	nilpotent	nilpotent	ADJ
ejpam-3979	102	11	if	if	SCONJ
ejpam-3979	102	12	and	and	CCONJ
ejpam-3979	102	13	only	only	ADV
ejpam-3979	102	14	if	if	SCONJ
ejpam-3979	102	15	it	it	PRON
ejpam-3979	102	16	has	have	VERB
ejpam-3979	102	17	a	a	DET
ejpam-3979	102	18	series	series	NOUN
ejpam-3979	102	19	of	of	ADP
ejpam-3979	102	20	normal	normal	ADJ
ejpam-3979	102	21	left	left	ADJ
ejpam-3979	102	22	coideal	coideal	NOUN
ejpam-3979	103	1	subalgebras	subalgebras	PROPN
ejpam-3979	103	2	k	k	PROPN
ejpam-3979	103	3	=	=	PROPN
ejpam-3979	103	4	n0	n0	PROPN
ejpam-3979	103	5	⊂	⊂	PROPN
ejpam-3979	103	6	n1	n1	PROPN
ejpam-3979	103	7	⊂	⊂	PROPN
ejpam-3979	103	8	.	.	PUNCT
ejpam-3979	103	9	.	.	PUNCT
ejpam-3979	103	10	.	.	PUNCT
ejpam-3979	104	1	⊂	⊂	PROPN
ejpam-3979	104	2	nt	not	PART
ejpam-3979	105	1	=	=	PUNCT
ejpam-3979	105	2	h	h	PROPN
ejpam-3979	105	3	such	such	ADJ
ejpam-3979	105	4	that	that	SCONJ
ejpam-3979	105	5	ni+1λni	ni+1λni	PROPN
ejpam-3979	105	6	⊂	⊂	PROPN
ejpam-3979	105	7	z(hλni	z(hλni	PROPN
ejpam-3979	105	8	)	)	PUNCT
ejpam-3979	105	9	,	,	PUNCT
ejpam-3979	105	10	for	for	ADP
ejpam-3979	105	11	all	all	DET
ejpam-3979	105	12	1	1	NUM
ejpam-3979	105	13	≤	≤	NUM
ejpam-3979	105	14	i	i	NOUN
ejpam-3979	105	15	≤	≤	PROPN
ejpam-3979	105	16	t	t	PROPN
ejpam-3979	105	17	,	,	PUNCT
ejpam-3979	105	18	where	where	SCONJ
ejpam-3979	105	19	z(hλni	z(hλni	NOUN
ejpam-3979	105	20	)	)	PUNCT
ejpam-3979	105	21	is	be	AUX
ejpam-3979	105	22	the	the	DET
ejpam-3979	105	23	center	center	NOUN
ejpam-3979	105	24	of	of	ADP
ejpam-3979	105	25	hλni	hλni	ADJ
ejpam-3979	105	26	.	.	PUNCT
ejpam-3979	106	1	proof	proof	NOUN
ejpam-3979	106	2	.	.	PUNCT
ejpam-3979	107	1	we	we	PRON
ejpam-3979	107	2	assume	assume	VERB
ejpam-3979	107	3	that	that	SCONJ
ejpam-3979	107	4	h	h	NOUN
ejpam-3979	107	5	is	be	AUX
ejpam-3979	107	6	nilpotent	nilpotent	ADJ
ejpam-3979	107	7	with	with	ADP
ejpam-3979	107	8	k	k	PROPN
ejpam-3979	107	9	=	=	PUNCT
ejpam-3979	107	10	z0	z0	PROPN
ejpam-3979	107	11	⊂	⊂	PROPN
ejpam-3979	107	12	z1	z1	PROPN
ejpam-3979	107	13	⊂	⊂	PROPN
ejpam-3979	107	14	.	.	PUNCT
ejpam-3979	107	15	.	.	PUNCT
ejpam-3979	107	16	.	.	PUNCT
ejpam-3979	108	1	⊂	⊂	PROPN
ejpam-3979	108	2	zt	zt	PROPN
ejpam-3979	108	3	=	=	PROPN
ejpam-3979	108	4	h.	h.	PROPN
ejpam-3979	108	5	let	let	VERB
ejpam-3979	108	6	λzi	λzi	NOUN
ejpam-3979	108	7	be	be	AUX
ejpam-3979	108	8	the	the	DET
ejpam-3979	108	9	integral	integral	ADJ
ejpam-3979	108	10	of	of	ADP
ejpam-3979	108	11	zi	zi	NOUN
ejpam-3979	108	12	.	.	PUNCT
ejpam-3979	109	1	by	by	ADP
ejpam-3979	109	2	lemma	lemma	PROPN
ejpam-3979	109	3	1.4	1.4	NUM
ejpam-3979	109	4	,	,	PUNCT
ejpam-3979	109	5	πi	πi	ADV
ejpam-3979	109	6	is	be	AUX
ejpam-3979	109	7	an	an	DET
ejpam-3979	109	8	algebra	algebra	NOUN
ejpam-3979	109	9	isomorphism	isomorphism	NOUN
ejpam-3979	109	10	between	between	ADP
ejpam-3979	109	11	hλzi	hλzi	NOUN
ejpam-3979	109	12	and	and	CCONJ
ejpam-3979	109	13	hi	hi	INTJ
ejpam-3979	109	14	.	.	PROPN
ejpam-3979	110	1	as	as	ADP
ejpam-3979	110	2	πi(zi+1	πi(zi+1	NOUN
ejpam-3979	110	3	)	)	PUNCT
ejpam-3979	110	4	⊂	⊂	PROPN
ejpam-3979	110	5	z̃(hi	z̃(hi	PROPN
ejpam-3979	110	6	)	)	PUNCT
ejpam-3979	110	7	⊂	⊂	PROPN
ejpam-3979	110	8	z(hi	z(hi	PROPN
ejpam-3979	110	9	)	)	PUNCT
ejpam-3979	110	10	,	,	PUNCT
ejpam-3979	110	11	we	we	PRON
ejpam-3979	110	12	get	get	VERB
ejpam-3979	110	13	zi+1λzi	zi+1λzi	PUNCT
ejpam-3979	110	14	is	be	AUX
ejpam-3979	110	15	central	central	ADJ
ejpam-3979	110	16	in	in	ADP
ejpam-3979	110	17	hλzi	hλzi	NOUN
ejpam-3979	110	18	.	.	PUNCT
ejpam-3979	111	1	conversely	conversely	ADV
ejpam-3979	111	2	,	,	PUNCT
ejpam-3979	111	3	we	we	PRON
ejpam-3979	111	4	assume	assume	VERB
ejpam-3979	111	5	that	that	SCONJ
ejpam-3979	111	6	k	k	PROPN
ejpam-3979	111	7	=	=	PROPN
ejpam-3979	111	8	n0	n0	PROPN
ejpam-3979	111	9	⊂	⊂	PROPN
ejpam-3979	111	10	n1	n1	PROPN
ejpam-3979	111	11	⊂	⊂	PROPN
ejpam-3979	111	12	.	.	PUNCT
ejpam-3979	111	13	.	.	PUNCT
ejpam-3979	111	14	.	.	PUNCT
ejpam-3979	112	1	⊂	⊂	PROPN
ejpam-3979	112	2	nt	not	PART
ejpam-3979	113	1	=	=	SYM
ejpam-3979	113	2	h	h	NOUN
ejpam-3979	113	3	satisfies	satisfy	VERB
ejpam-3979	113	4	the	the	DET
ejpam-3979	113	5	condition	condition	NOUN
ejpam-3979	113	6	in	in	ADP
ejpam-3979	113	7	definition	definition	NOUN
ejpam-3979	113	8	1	1	NUM
ejpam-3979	113	9	.	.	PUNCT
ejpam-3979	114	1	let	let	VERB
ejpam-3979	114	2	k	k	PROPN
ejpam-3979	114	3	⊆	⊆	NUM
ejpam-3979	114	4	z1	z1	PROPN
ejpam-3979	114	5	⊆	⊆	NUM
ejpam-3979	114	6	...	...	PUNCT
ejpam-3979	114	7	be	be	AUX
ejpam-3979	114	8	an	an	DET
ejpam-3979	114	9	ascending	ascend	VERB
ejpam-3979	114	10	central	central	ADJ
ejpam-3979	114	11	series	series	NOUN
ejpam-3979	114	12	for	for	ADP
ejpam-3979	114	13	h.	h.	PROPN
ejpam-3979	114	14	then	then	ADV
ejpam-3979	114	15	by	by	ADP
ejpam-3979	114	16	the	the	DET
ejpam-3979	114	17	assumption	assumption	NOUN
ejpam-3979	114	18	we	we	PRON
ejpam-3979	114	19	get	get	VERB
ejpam-3979	114	20	n1	n1	PROPN
ejpam-3979	114	21	⊂	⊂	ADJ
ejpam-3979	114	22	z(h	z(h	PROPN
ejpam-3979	114	23	)	)	PUNCT
ejpam-3979	114	24	.	.	PUNCT
ejpam-3979	115	1	as	as	SCONJ
ejpam-3979	115	2	n1	n1	PROPN
ejpam-3979	115	3	is	be	AUX
ejpam-3979	115	4	a	a	DET
ejpam-3979	115	5	normal	normal	ADJ
ejpam-3979	115	6	left	left	ADJ
ejpam-3979	115	7	coideal	coideal	NOUN
ejpam-3979	115	8	subagebra	subagebra	NOUN
ejpam-3979	115	9	of	of	ADP
ejpam-3979	115	10	h	h	NOUN
ejpam-3979	115	11	,	,	PUNCT
ejpam-3979	115	12	we	we	PRON
ejpam-3979	115	13	have	have	VERB
ejpam-3979	115	14	n1	n1	PROPN
ejpam-3979	115	15	⊂	⊂	ADJ
ejpam-3979	115	16	z̃(h	z̃(h	PROPN
ejpam-3979	115	17	)	)	PUNCT
ejpam-3979	116	1	=	=	SYM
ejpam-3979	116	2	z1	z1	PROPN
ejpam-3979	116	3	.	.	PUNCT
ejpam-3979	117	1	if	if	SCONJ
ejpam-3979	117	2	ni	ni	PROPN
ejpam-3979	117	3	⊂	⊂	PROPN
ejpam-3979	117	4	zi	zi	PROPN
ejpam-3979	117	5	,	,	PUNCT
ejpam-3979	117	6	then	then	ADV
ejpam-3979	117	7	by	by	ADP
ejpam-3979	117	8	induction	induction	NOUN
ejpam-3979	117	9	we	we	PRON
ejpam-3979	117	10	show	show	VERB
ejpam-3979	117	11	that	that	SCONJ
ejpam-3979	117	12	ni+1	ni+1	PROPN
ejpam-3979	117	13	⊂	⊂	NOUN
ejpam-3979	117	14	zi+1	zi+1	NUM
ejpam-3979	117	15	.	.	PUNCT
ejpam-3979	118	1	by	by	ADP
ejpam-3979	118	2	the	the	DET
ejpam-3979	118	3	definition	definition	NOUN
ejpam-3979	118	4	of	of	ADP
ejpam-3979	118	5	zi	zi	NOUN
ejpam-3979	118	6	,	,	PUNCT
ejpam-3979	118	7	we	we	PRON
ejpam-3979	118	8	have	have	VERB
ejpam-3979	118	9	πi(ni	πi(ni	PROPN
ejpam-3979	118	10	)	)	PUNCT
ejpam-3979	118	11	⊆	⊆	NUM
ejpam-3979	118	12	πi(zi	πi(zi	NOUN
ejpam-3979	118	13	)	)	PUNCT
ejpam-3979	118	14	=	=	SYM
ejpam-3979	118	15	k.	k.	PROPN
ejpam-3979	118	16	as	as	ADP
ejpam-3979	118	17	by	by	ADP
ejpam-3979	118	18	the	the	DET
ejpam-3979	118	19	assumption	assumption	NOUN
ejpam-3979	118	20	ni+1λni	ni+1λni	PROPN
ejpam-3979	118	21	⊂	⊂	PROPN
ejpam-3979	118	22	z(hλi	z(hλi	PROPN
ejpam-3979	118	23	)	)	PUNCT
ejpam-3979	118	24	and	and	CCONJ
ejpam-3979	118	25	as	as	ADP
ejpam-3979	118	26	πi(λni	πi(λni	PROPN
ejpam-3979	118	27	)	)	PUNCT
ejpam-3979	118	28	=	=	SYM
ejpam-3979	118	29	1	1	NUM
ejpam-3979	118	30	,	,	PUNCT
ejpam-3979	118	31	we	we	PRON
ejpam-3979	118	32	get	get	VERB
ejpam-3979	118	33	πi(ni+1	πi(ni+1	NOUN
ejpam-3979	118	34	)	)	PUNCT
ejpam-3979	118	35	=	=	SYM
ejpam-3979	119	1	πi(ni+1λni	πi(ni+1λni	X
ejpam-3979	119	2	)	)	PUNCT
ejpam-3979	119	3	⊂	⊂	PROPN
ejpam-3979	119	4	πi(z(hλni	πi(z(hλni	PROPN
ejpam-3979	119	5	)	)	PUNCT
ejpam-3979	119	6	)	)	PUNCT
ejpam-3979	120	1	=	=	PUNCT
ejpam-3979	120	2	z(πi(h	z(πi(h	NOUN
ejpam-3979	120	3	)	)	PUNCT
ejpam-3979	120	4	)	)	PUNCT
ejpam-3979	121	1	=	=	SYM
ejpam-3979	121	2	z(hi	z(hi	NUM
ejpam-3979	121	3	)	)	PUNCT
ejpam-3979	121	4	.	.	PUNCT
ejpam-3979	122	1	but	but	CCONJ
ejpam-3979	122	2	πi(ni+1	πi(ni+1	NOUN
ejpam-3979	122	3	)	)	PUNCT
ejpam-3979	122	4	is	be	AUX
ejpam-3979	122	5	a	a	DET
ejpam-3979	122	6	normal	normal	ADJ
ejpam-3979	122	7	left	left	ADJ
ejpam-3979	122	8	coideal	coideal	NOUN
ejpam-3979	122	9	subalgebra	subalgebra	NOUN
ejpam-3979	122	10	of	of	ADP
ejpam-3979	122	11	hi	hi	INTJ
ejpam-3979	122	12	contained	contain	VERB
ejpam-3979	122	13	in	in	ADP
ejpam-3979	122	14	its	its	PRON
ejpam-3979	122	15	center	center	NOUN
ejpam-3979	122	16	,	,	PUNCT
ejpam-3979	122	17	hence	hence	ADV
ejpam-3979	122	18	πi(ni+1	πi(ni+1	NOUN
ejpam-3979	122	19	)	)	PUNCT
ejpam-3979	122	20	⊂	⊂	PROPN
ejpam-3979	122	21	z̃(hi	z̃(hi	NOUN
ejpam-3979	122	22	)	)	PUNCT
ejpam-3979	122	23	.	.	PUNCT
ejpam-3979	123	1	this	this	PRON
ejpam-3979	123	2	leads	lead	VERB
ejpam-3979	123	3	to	to	ADP
ejpam-3979	123	4	πi+1(ni+1	πi+1(ni+1	NOUN
ejpam-3979	123	5	)	)	PUNCT
ejpam-3979	124	1	=	=	SYM
ejpam-3979	124	2	k	k	PROPN
ejpam-3979	124	3	and	and	CCONJ
ejpam-3979	124	4	thus	thus	ADV
ejpam-3979	124	5	ni+1	ni+1	CCONJ
ejpam-3979	124	6	⊆	⊆	NUM
ejpam-3979	124	7	zi+1	zi+1	NOUN
ejpam-3979	124	8	.	.	PUNCT
ejpam-3979	125	1	as	as	ADP
ejpam-3979	125	2	nt	not	PART
ejpam-3979	125	3	=	=	NOUN
ejpam-3979	125	4	h	h	NOUN
ejpam-3979	125	5	we	we	PRON
ejpam-3979	125	6	get	get	VERB
ejpam-3979	125	7	zt	zt	PROPN
ejpam-3979	125	8	=	=	PROPN
ejpam-3979	125	9	h.	h.	PROPN
ejpam-3979	125	10	therefore	therefore	ADV
ejpam-3979	125	11	,	,	PUNCT
ejpam-3979	125	12	h	h	NOUN
ejpam-3979	125	13	is	be	AUX
ejpam-3979	125	14	nilpotent	nilpotent	ADJ
ejpam-3979	125	15	.	.	PUNCT
ejpam-3979	126	1	corollary	corollary	ADJ
ejpam-3979	126	2	1	1	NUM
ejpam-3979	126	3	.	.	PUNCT
ejpam-3979	127	1	[	[	X
ejpam-3979	127	2	10	10	NUM
ejpam-3979	127	3	]	]	X
ejpam-3979	127	4	semisimple	semisimple	ADJ
ejpam-3979	127	5	nilpotent	nilpotent	NOUN
ejpam-3979	127	6	hopf	hopf	PROPN
ejpam-3979	127	7	algebras	algebra	NOUN
ejpam-3979	127	8	are	be	AUX
ejpam-3979	127	9	solvable	solvable	ADJ
ejpam-3979	127	10	.	.	PUNCT
ejpam-3979	128	1	proof	proof	NOUN
ejpam-3979	128	2	.	.	PUNCT
ejpam-3979	129	1	we	we	PRON
ejpam-3979	129	2	assume	assume	VERB
ejpam-3979	129	3	that	that	SCONJ
ejpam-3979	129	4	h	h	NOUN
ejpam-3979	129	5	has	have	VERB
ejpam-3979	129	6	a	a	DET
ejpam-3979	129	7	series	series	NOUN
ejpam-3979	129	8	as	as	ADP
ejpam-3979	129	9	in	in	ADP
ejpam-3979	129	10	definition	definition	NOUN
ejpam-3979	129	11	1	1	NUM
ejpam-3979	129	12	.	.	PUNCT
ejpam-3979	130	1	as	as	SCONJ
ejpam-3979	130	2	each	each	DET
ejpam-3979	130	3	ni	ni	PROPN
ejpam-3979	130	4	is	be	AUX
ejpam-3979	130	5	normal	normal	ADJ
ejpam-3979	130	6	in	in	ADP
ejpam-3979	130	7	h	h	NOUN
ejpam-3979	130	8	,	,	PUNCT
ejpam-3979	130	9	we	we	PRON
ejpam-3979	130	10	obtain	obtain	VERB
ejpam-3979	130	11	λni	λni	ADJ
ejpam-3979	130	12	∈	∈	NOUN
ejpam-3979	130	13	z(h	z(h	NUM
ejpam-3979	130	14	)	)	PUNCT
ejpam-3979	130	15	,	,	PUNCT
ejpam-3979	130	16	which	which	PRON
ejpam-3979	130	17	satisfies	satisfy	VERB
ejpam-3979	130	18	(	(	PUNCT
ejpam-3979	130	19	i	i	NOUN
ejpam-3979	130	20	)	)	PUNCT
ejpam-3979	130	21	in	in	ADP
ejpam-3979	130	22	definition	definition	NOUN
ejpam-3979	130	23	6	6	NUM
ejpam-3979	130	24	of	of	ADP
ejpam-3979	130	25	solvability	solvability	NOUN
ejpam-3979	130	26	.	.	PUNCT
ejpam-3979	131	1	next	next	ADV
ejpam-3979	131	2	,	,	PUNCT
ejpam-3979	131	3	as	as	SCONJ
ejpam-3979	131	4	λni	λni	PROPN
ejpam-3979	131	5	is	be	AUX
ejpam-3979	131	6	a	a	DET
ejpam-3979	131	7	central	central	ADJ
ejpam-3979	131	8	idemoptent	idemoptent	NOUN
ejpam-3979	131	9	of	of	ADP
ejpam-3979	131	10	h	h	NOUN
ejpam-3979	131	11	,	,	PUNCT
ejpam-3979	131	12	it	it	PRON
ejpam-3979	131	13	follows	follow	VERB
ejpam-3979	131	14	by	by	ADP
ejpam-3979	131	15	assumption	assumption	NOUN
ejpam-3979	131	16	that	that	SCONJ
ejpam-3979	131	17	∑	∑	PUNCT
ejpam-3979	131	18	a1b(sa2)λni	a1b(sa2)λni	PROPN
ejpam-3979	131	19	=	=	SYM
ejpam-3979	131	20	〈	〈	PROPN
ejpam-3979	131	21	ε	ε	PROPN
ejpam-3979	131	22	,	,	PUNCT
ejpam-3979	131	23	a〉bλni	a〉bλni	ADJ
ejpam-3979	131	24	for	for	ADP
ejpam-3979	131	25	all	all	DET
ejpam-3979	131	26	a	a	DET
ejpam-3979	131	27	∈	∈	PROPN
ejpam-3979	131	28	h	h	NOUN
ejpam-3979	131	29	,	,	PUNCT
ejpam-3979	131	30	b	b	PROPN
ejpam-3979	131	31	∈	∈	PROPN
ejpam-3979	131	32	ni+11	ni+11	PROPN
ejpam-3979	131	33	.	.	PUNCT
ejpam-3979	132	1	this	this	PRON
ejpam-3979	132	2	leads	lead	VERB
ejpam-3979	132	3	to	to	ADP
ejpam-3979	132	4	(	(	PUNCT
ejpam-3979	132	5	ii	ii	NOUN
ejpam-3979	132	6	)	)	PUNCT
ejpam-3979	132	7	of	of	ADP
ejpam-3979	132	8	the	the	DET
ejpam-3979	132	9	definition	definition	NOUN
ejpam-3979	132	10	of	of	ADP
ejpam-3979	132	11	solvability	solvability	NOUN
ejpam-3979	132	12	.	.	PUNCT
ejpam-3979	133	1	3	3	X
ejpam-3979	133	2	.	.	X
ejpam-3979	133	3	from	from	ADP
ejpam-3979	133	4	finite	finite	ADJ
ejpam-3979	133	5	groups	group	NOUN
ejpam-3979	133	6	to	to	ADP
ejpam-3979	133	7	hopf	hopf	ADV
ejpam-3979	133	8	algebras	algebras	PROPN
ejpam-3979	133	9	3.1	3.1	NUM
ejpam-3979	133	10	.	.	PUNCT
ejpam-3979	134	1	the	the	DET
ejpam-3979	134	2	finite	finite	PROPN
ejpam-3979	134	3	group	group	NOUN
ejpam-3979	134	4	c3	c3	PROPN
ejpam-3979	134	5	we	we	PRON
ejpam-3979	134	6	first	first	ADV
ejpam-3979	134	7	consider	consider	VERB
ejpam-3979	134	8	the	the	DET
ejpam-3979	134	9	finite	finite	ADJ
ejpam-3979	134	10	group	group	NOUN
ejpam-3979	134	11	g	g	PROPN
ejpam-3979	134	12	=	=	PROPN
ejpam-3979	134	13	c3	c3	PROPN
ejpam-3979	134	14	=	=	PUNCT
ejpam-3979	134	15	〈	〈	PROPN
ejpam-3979	134	16	x|x3	x|x3	PROPN
ejpam-3979	134	17	=	=	NOUN
ejpam-3979	134	18	1	1	NUM
ejpam-3979	134	19	〉	〉	NUM
ejpam-3979	134	20	=	=	SYM
ejpam-3979	134	21	{	{	PUNCT
ejpam-3979	134	22	1	1	NUM
ejpam-3979	134	23	,	,	PUNCT
ejpam-3979	134	24	x	x	NOUN
ejpam-3979	134	25	,	,	PUNCT
ejpam-3979	134	26	x2	x2	PROPN
ejpam-3979	134	27	}	}	PUNCT
ejpam-3979	134	28	and	and	CCONJ
ejpam-3979	134	29	recall	recall	VERB
ejpam-3979	134	30	some	some	PRON
ejpam-3979	134	31	of	of	ADP
ejpam-3979	134	32	its	its	PRON
ejpam-3979	134	33	properties	property	NOUN
ejpam-3979	134	34	.	.	PUNCT
ejpam-3979	135	1	this	this	DET
ejpam-3979	135	2	group	group	NOUN
ejpam-3979	135	3	has	have	VERB
ejpam-3979	135	4	no	no	DET
ejpam-3979	135	5	proper	proper	ADJ
ejpam-3979	135	6	subgroup	subgroup	NOUN
ejpam-3979	135	7	in	in	ADP
ejpam-3979	135	8	particular	particular	ADJ
ejpam-3979	135	9	it	it	PRON
ejpam-3979	135	10	has	have	VERB
ejpam-3979	135	11	no	no	DET
ejpam-3979	135	12	proper	proper	ADJ
ejpam-3979	135	13	normal	normal	ADJ
ejpam-3979	135	14	subgroup	subgroup	NOUN
ejpam-3979	135	15	.	.	PUNCT
ejpam-3979	136	1	so	so	ADV
ejpam-3979	136	2	it	it	PRON
ejpam-3979	136	3	is	be	AUX
ejpam-3979	136	4	a	a	DET
ejpam-3979	136	5	simple	simple	ADJ
ejpam-3979	136	6	group	group	NOUN
ejpam-3979	136	7	.	.	PUNCT
ejpam-3979	137	1	furthermore	furthermore	ADV
ejpam-3979	137	2	,	,	PUNCT
ejpam-3979	137	3	since	since	SCONJ
ejpam-3979	137	4	|	|	ADV
ejpam-3979	137	5	c3	c3	NOUN
ejpam-3979	137	6	|=	|=	PUNCT
ejpam-3979	137	7	3	3	NUM
ejpam-3979	137	8	,	,	PUNCT
ejpam-3979	137	9	it	it	PRON
ejpam-3979	137	10	is	be	AUX
ejpam-3979	137	11	a	a	DET
ejpam-3979	137	12	cyclic	cyclic	ADJ
ejpam-3979	137	13	group	group	NOUN
ejpam-3979	137	14	,	,	PUNCT
ejpam-3979	137	15	hence	hence	ADV
ejpam-3979	137	16	it	it	PRON
ejpam-3979	137	17	is	be	AUX
ejpam-3979	137	18	abelian	abelian	ADJ
ejpam-3979	137	19	and	and	CCONJ
ejpam-3979	137	20	consequently	consequently	ADV
ejpam-3979	137	21	solvable	solvable	ADJ
ejpam-3979	137	22	and	and	CCONJ
ejpam-3979	137	23	nilpotent	nilpotent	ADJ
ejpam-3979	137	24	.	.	PUNCT
ejpam-3979	138	1	3.2	3.2	NUM
ejpam-3979	138	2	.	.	PUNCT
ejpam-3979	139	1	the	the	DET
ejpam-3979	139	2	group	group	NOUN
ejpam-3979	139	3	algebra	algebra	NOUN
ejpam-3979	139	4	h	h	NOUN
ejpam-3979	139	5	=	=	SYM
ejpam-3979	139	6	rc3	rc3	PROPN
ejpam-3979	139	7	the	the	DET
ejpam-3979	139	8	group	group	NOUN
ejpam-3979	139	9	algebra	algebra	NOUN
ejpam-3979	139	10	.	.	PUNCT
ejpam-3979	140	1	let	let	VERB
ejpam-3979	140	2	g	g	PRON
ejpam-3979	140	3	be	be	AUX
ejpam-3979	140	4	a	a	DET
ejpam-3979	140	5	(	(	PUNCT
ejpam-3979	140	6	multiplicative	multiplicative	ADJ
ejpam-3979	140	7	)	)	PUNCT
ejpam-3979	140	8	group	group	NOUN
ejpam-3979	140	9	,	,	PUNCT
ejpam-3979	140	10	and	and	CCONJ
ejpam-3979	140	11	kg	kg	VERB
ejpam-3979	140	12	the	the	DET
ejpam-3979	140	13	associated	associated	ADJ
ejpam-3979	140	14	group	group	NOUN
ejpam-3979	140	15	algebra	algebra	NOUN
ejpam-3979	140	16	.	.	PUNCT
ejpam-3979	141	1	this	this	PRON
ejpam-3979	141	2	is	be	AUX
ejpam-3979	141	3	a	a	DET
ejpam-3979	141	4	k	k	ADJ
ejpam-3979	141	5	-	-	ADJ
ejpam-3979	141	6	vector	vector	NOUN
ejpam-3979	141	7	space	space	NOUN
ejpam-3979	141	8	with	with	ADP
ejpam-3979	141	9	basis	basis	NOUN
ejpam-3979	141	10	{	{	PUNCT
ejpam-3979	141	11	g|g	g|g	NOUN
ejpam-3979	141	12	∈	∈	PROPN
ejpam-3979	141	13	g	g	NOUN
ejpam-3979	141	14	}	}	PUNCT
ejpam-3979	141	15	.	.	PUNCT
ejpam-3979	142	1	so	so	ADV
ejpam-3979	142	2	its	its	PRON
ejpam-3979	142	3	elements	element	NOUN
ejpam-3979	142	4	are	be	AUX
ejpam-3979	142	5	of	of	ADP
ejpam-3979	142	6	the	the	DET
ejpam-3979	142	7	form∑	form∑	PROPN
ejpam-3979	142	8	g∈g	g∈g	PROPN
ejpam-3979	142	9	rg	rg	PROPN
ejpam-3979	142	10	g	g	PROPN
ejpam-3979	142	11	where	where	SCONJ
ejpam-3979	142	12	(	(	PUNCT
ejpam-3979	142	13	rg)g∈g	rg)g∈g	NOUN
ejpam-3979	142	14	a	a	DET
ejpam-3979	142	15	family	family	NOUN
ejpam-3979	142	16	of	of	ADP
ejpam-3979	142	17	elements	element	NOUN
ejpam-3979	142	18	from	from	ADP
ejpam-3979	142	19	k	k	PROPN
ejpam-3979	143	1	[	[	X
ejpam-3979	143	2	12	12	NUM
ejpam-3979	143	3	]	]	PUNCT
ejpam-3979	143	4	.	.	PUNCT
ejpam-3979	144	1	t.	t.	PROPN
ejpam-3979	144	2	al	al	PROPN
ejpam-3979	144	3	-	-	PUNCT
ejpam-3979	144	4	mutairi	mutairi	PROPN
ejpam-3979	144	5	,	,	PUNCT
ejpam-3979	144	6	m.	m.	NOUN
ejpam-3979	144	7	m.	m.	PROPN
ejpam-3979	144	8	al	al	PROPN
ejpam-3979	144	9	-	-	PUNCT
ejpam-3979	144	10	shomrani	shomrani	PROPN
ejpam-3979	144	11	/	/	SYM
ejpam-3979	144	12	eur	eur	NOUN
ejpam-3979	144	13	.	.	PUNCT
ejpam-3979	145	1	j.	j.	PROPN
ejpam-3979	145	2	pure	pure	PROPN
ejpam-3979	145	3	appl	appl	PROPN
ejpam-3979	145	4	.	.	PROPN
ejpam-3979	145	5	math	math	PROPN
ejpam-3979	145	6	,	,	PUNCT
ejpam-3979	145	7	14	14	NUM
ejpam-3979	145	8	(	(	PUNCT
ejpam-3979	145	9	3	3	NUM
ejpam-3979	145	10	)	)	PUNCT
ejpam-3979	145	11	(	(	PUNCT
ejpam-3979	145	12	2021	2021	NUM
ejpam-3979	145	13	)	)	PUNCT
ejpam-3979	145	14	,	,	PUNCT
ejpam-3979	145	15	816	816	NUM
ejpam-3979	145	16	-	-	SYM
ejpam-3979	145	17	828	828	NUM
ejpam-3979	145	18	821	821	NUM
ejpam-3979	145	19	kg	kg	NOUN
ejpam-3979	145	20	is	be	AUX
ejpam-3979	145	21	an	an	DET
ejpam-3979	145	22	algebra	algebra	NOUN
ejpam-3979	145	23	with	with	ADP
ejpam-3979	145	24	multiplication	multiplication	NOUN
ejpam-3979	145	25	given	give	VERB
ejpam-3979	145	26	by	by	ADP
ejpam-3979	145	27	µ(g	µ(g	ADP
ejpam-3979	145	28	⊗	⊗	PROPN
ejpam-3979	145	29	h	h	NOUN
ejpam-3979	145	30	)	)	PUNCT
ejpam-3979	145	31	=	=	SYM
ejpam-3979	145	32	gh	gh	PROPN
ejpam-3979	145	33	and	and	CCONJ
ejpam-3979	145	34	a	a	DET
ejpam-3979	145	35	unit	unit	NOUN
ejpam-3979	145	36	map	map	NOUN
ejpam-3979	145	37	given	give	VERB
ejpam-3979	145	38	by	by	ADP
ejpam-3979	145	39	λ(r	λ(r	NOUN
ejpam-3979	145	40	)	)	PUNCT
ejpam-3979	146	1	=	=	SYM
ejpam-3979	146	2	r1	r1	PROPN
ejpam-3979	146	3	for	for	ADP
ejpam-3979	146	4	all	all	DET
ejpam-3979	146	5	g	g	NOUN
ejpam-3979	146	6	,	,	PUNCT
ejpam-3979	146	7	h	h	NOUN
ejpam-3979	146	8	∈	∈	PROPN
ejpam-3979	146	9	g	g	PROPN
ejpam-3979	146	10	and	and	CCONJ
ejpam-3979	146	11	r	r	NOUN
ejpam-3979	146	12	∈	∈	PROPN
ejpam-3979	146	13	k	k	PROPN
ejpam-3979	147	1	[	[	X
ejpam-3979	147	2	25	25	NUM
ejpam-3979	147	3	]	]	PUNCT
ejpam-3979	147	4	.	.	PUNCT
ejpam-3979	148	1	kg	kg	PROPN
ejpam-3979	148	2	is	be	AUX
ejpam-3979	148	3	a	a	DET
ejpam-3979	148	4	coalgebra	coalgebra	NOUN
ejpam-3979	148	5	with	with	ADP
ejpam-3979	148	6	comultiplication	comultiplication	NOUN
ejpam-3979	148	7	given	give	VERB
ejpam-3979	148	8	by	by	ADP
ejpam-3979	148	9	∆(g	∆(g	NOUN
ejpam-3979	148	10	)	)	PUNCT
ejpam-3979	148	11	=	=	PUNCT
ejpam-3979	149	1	g	g	PROPN
ejpam-3979	149	2	⊗	⊗	PROPN
ejpam-3979	149	3	g	g	PROPN
ejpam-3979	149	4	and	and	CCONJ
ejpam-3979	149	5	a	a	DET
ejpam-3979	149	6	counit	counit	VERB
ejpam-3979	149	7	map	map	NOUN
ejpam-3979	149	8	given	give	VERB
ejpam-3979	149	9	by	by	ADP
ejpam-3979	149	10	ε(g	ε(g	NOUN
ejpam-3979	149	11	)	)	PUNCT
ejpam-3979	149	12	=	=	SYM
ejpam-3979	149	13	1	1	NUM
ejpam-3979	149	14	for	for	ADP
ejpam-3979	149	15	all	all	DET
ejpam-3979	149	16	g	g	PROPN
ejpam-3979	149	17	∈	∈	PROPN
ejpam-3979	149	18	g.	g.	NOUN
ejpam-3979	149	19	moreover	moreover	ADV
ejpam-3979	149	20	,	,	PUNCT
ejpam-3979	149	21	kg	kg	PROPN
ejpam-3979	149	22	is	be	AUX
ejpam-3979	149	23	a	a	DET
ejpam-3979	149	24	hopf	hopf	ADJ
ejpam-3979	149	25	algebra	algebra	NOUN
ejpam-3979	149	26	with	with	ADP
ejpam-3979	149	27	an	an	DET
ejpam-3979	149	28	antipode	antipode	NOUN
ejpam-3979	149	29	map	map	NOUN
ejpam-3979	149	30	given	give	VERB
ejpam-3979	149	31	by	by	ADP
ejpam-3979	149	32	s(g	s(g	PROPN
ejpam-3979	149	33	)	)	PUNCT
ejpam-3979	149	34	=	=	PUNCT
ejpam-3979	150	1	g−1	g−1	PROPN
ejpam-3979	150	2	for	for	ADP
ejpam-3979	150	3	all	all	PRON
ejpam-3979	150	4	g	g	NOUN
ejpam-3979	150	5	∈	∈	PRON
ejpam-3979	150	6	g	g	NOUN
ejpam-3979	151	1	[	[	X
ejpam-3979	151	2	9	9	NUM
ejpam-3979	151	3	]	]	PUNCT
ejpam-3979	151	4	.	.	PUNCT
ejpam-3979	152	1	we	we	PRON
ejpam-3979	152	2	now	now	ADV
ejpam-3979	152	3	construct	construct	VERB
ejpam-3979	152	4	a	a	DET
ejpam-3979	152	5	group	group	NOUN
ejpam-3979	152	6	algebra	algebra	NOUN
ejpam-3979	152	7	h	h	NOUN
ejpam-3979	152	8	=	=	SYM
ejpam-3979	152	9	rc3	rc3	PROPN
ejpam-3979	152	10	considering	consider	VERB
ejpam-3979	152	11	the	the	DET
ejpam-3979	152	12	finite	finite	ADJ
ejpam-3979	152	13	group	group	NOUN
ejpam-3979	152	14	c3	c3	PROPN
ejpam-3979	152	15	with	with	ADP
ejpam-3979	152	16	basis	basis	NOUN
ejpam-3979	152	17	{	{	PUNCT
ejpam-3979	152	18	1	1	NUM
ejpam-3979	152	19	,	,	PUNCT
ejpam-3979	152	20	x	x	NOUN
ejpam-3979	152	21	,	,	PUNCT
ejpam-3979	152	22	x2	x2	PROPN
ejpam-3979	152	23	}	}	PUNCT
ejpam-3979	152	24	where	where	SCONJ
ejpam-3979	152	25	r	r	NOUN
ejpam-3979	152	26	is	be	AUX
ejpam-3979	152	27	the	the	DET
ejpam-3979	152	28	field	field	NOUN
ejpam-3979	152	29	of	of	ADP
ejpam-3979	152	30	real	real	ADJ
ejpam-3979	152	31	numbers	number	NOUN
ejpam-3979	152	32	.	.	PUNCT
ejpam-3979	153	1	in	in	ADP
ejpam-3979	153	2	the	the	DET
ejpam-3979	153	3	following	follow	VERB
ejpam-3979	153	4	table	table	NOUN
ejpam-3979	153	5	the	the	DET
ejpam-3979	153	6	product	product	NOUN
ejpam-3979	153	7	map	map	NOUN
ejpam-3979	153	8	µ	µ	X
ejpam-3979	153	9	:	:	PUNCT
ejpam-3979	153	10	h	h	NOUN
ejpam-3979	153	11	⊗h	⊗h	VERB
ejpam-3979	153	12	7−→	7−→	NOUN
ejpam-3979	153	13	h	h	NOUN
ejpam-3979	153	14	which	which	PRON
ejpam-3979	153	15	is	be	AUX
ejpam-3979	153	16	defined	define	VERB
ejpam-3979	153	17	by	by	ADP
ejpam-3979	153	18	µ(g1	µ(g1	NOUN
ejpam-3979	153	19	⊗	⊗	PROPN
ejpam-3979	153	20	g2	g2	PROPN
ejpam-3979	153	21	)	)	PUNCT
ejpam-3979	154	1	=	=	PUNCT
ejpam-3979	155	1	g1g2	g1g2	NOUN
ejpam-3979	155	2	is	be	AUX
ejpam-3979	155	3	applied	apply	VERB
ejpam-3979	155	4	and	and	CCONJ
ejpam-3979	155	5	calculated	calculate	VERB
ejpam-3979	155	6	for	for	ADP
ejpam-3979	155	7	all	all	DET
ejpam-3979	155	8	g1	g1	NOUN
ejpam-3979	155	9	,	,	PUNCT
ejpam-3979	155	10	g2	g2	PROPN
ejpam-3979	155	11	∈	∈	PROPN
ejpam-3979	156	1	g	g	NOUN
ejpam-3979	156	2	:	:	PUNCT
ejpam-3979	156	3	µ(g1	µ(g1	VERB
ejpam-3979	156	4	⊗	⊗	PROPN
ejpam-3979	156	5	g2	g2	PROPN
ejpam-3979	156	6	)	)	PUNCT
ejpam-3979	157	1	1	1	NUM
ejpam-3979	157	2	x	x	SYM
ejpam-3979	157	3	x2	x2	NOUN
ejpam-3979	157	4	1	1	NUM
ejpam-3979	157	5	1	1	NUM
ejpam-3979	157	6	x	x	SYM
ejpam-3979	157	7	x2	x2	NOUN
ejpam-3979	157	8	x	x	PUNCT
ejpam-3979	157	9	x	x	SYM
ejpam-3979	157	10	x2	x2	NOUN
ejpam-3979	157	11	1	1	NUM
ejpam-3979	157	12	x2	x2	NOUN
ejpam-3979	157	13	x2	x2	NOUN
ejpam-3979	157	14	1	1	NUM
ejpam-3979	157	15	x	x	NOUN
ejpam-3979	157	16	table	table	NOUN
ejpam-3979	157	17	1	1	NUM
ejpam-3979	157	18	:	:	PUNCT
ejpam-3979	157	19	µ(g1	µ(g1	VERB
ejpam-3979	157	20	⊗	⊗	PROPN
ejpam-3979	157	21	g2	g2	PROPN
ejpam-3979	157	22	)	)	PUNCT
ejpam-3979	157	23	.	.	PUNCT
ejpam-3979	158	1	the	the	DET
ejpam-3979	158	2	unit	unit	NOUN
ejpam-3979	158	3	map	map	NOUN
ejpam-3979	158	4	λ	λ	X
ejpam-3979	158	5	:	:	PUNCT
ejpam-3979	158	6	r	r	NOUN
ejpam-3979	158	7	7−→	7−→	NOUN
ejpam-3979	158	8	h	h	NOUN
ejpam-3979	158	9	is	be	AUX
ejpam-3979	158	10	defined	define	VERB
ejpam-3979	158	11	by	by	ADP
ejpam-3979	158	12	λ(r	λ(r	NOUN
ejpam-3979	158	13	)	)	PUNCT
ejpam-3979	158	14	=	=	SYM
ejpam-3979	159	1	1	1	X
ejpam-3979	159	2	.	.	PUNCT
ejpam-3979	160	1	the	the	DET
ejpam-3979	160	2	maps	map	NOUN
ejpam-3979	160	3	µ	µ	PROPN
ejpam-3979	160	4	and	and	CCONJ
ejpam-3979	160	5	λ	λ	PROPN
ejpam-3979	160	6	satisfy	satisfy	VERB
ejpam-3979	160	7	the	the	DET
ejpam-3979	160	8	required	require	VERB
ejpam-3979	160	9	conditions	condition	NOUN
ejpam-3979	160	10	that	that	PRON
ejpam-3979	160	11	are	be	AUX
ejpam-3979	160	12	:	:	PUNCT
ejpam-3979	160	13	(	(	PUNCT
ejpam-3979	160	14	i	i	NOUN
ejpam-3979	160	15	)	)	PUNCT
ejpam-3979	160	16	the	the	DET
ejpam-3979	160	17	associative	associative	ADJ
ejpam-3979	160	18	property	property	NOUN
ejpam-3979	160	19	:	:	PUNCT
ejpam-3979	160	20	µ(i	µ(i	PROPN
ejpam-3979	160	21	⊗	⊗	PROPN
ejpam-3979	160	22	µ)(g	µ)(g	PUNCT
ejpam-3979	160	23	⊗	⊗	PROPN
ejpam-3979	160	24	(	(	PUNCT
ejpam-3979	160	25	g1	g1	PROPN
ejpam-3979	160	26	⊗	⊗	PROPN
ejpam-3979	160	27	g2	g2	PROPN
ejpam-3979	160	28	)	)	PUNCT
ejpam-3979	160	29	)	)	PUNCT
ejpam-3979	161	1	=	=	PUNCT
ejpam-3979	161	2	µ(µ⊗	µ(µ⊗	PROPN
ejpam-3979	161	3	i)((g	i)((g	PROPN
ejpam-3979	161	4	⊗	⊗	PROPN
ejpam-3979	161	5	g1)⊗	g1)⊗	PROPN
ejpam-3979	161	6	g2	g2	PROPN
ejpam-3979	161	7	)	)	PUNCT
ejpam-3979	161	8	,	,	PUNCT
ejpam-3979	161	9	for	for	ADP
ejpam-3979	161	10	all	all	DET
ejpam-3979	161	11	g	g	NOUN
ejpam-3979	161	12	,	,	PUNCT
ejpam-3979	161	13	g1	g1	PROPN
ejpam-3979	161	14	,	,	PUNCT
ejpam-3979	161	15	g2	g2	PROPN
ejpam-3979	161	16	∈	∈	PROPN
ejpam-3979	161	17	g.	g.	NOUN
ejpam-3979	161	18	for	for	ADP
ejpam-3979	161	19	example	example	NOUN
ejpam-3979	161	20	,	,	PUNCT
ejpam-3979	161	21	if	if	SCONJ
ejpam-3979	161	22	g	g	PROPN
ejpam-3979	161	23	=	=	SYM
ejpam-3979	161	24	x	x	PROPN
ejpam-3979	161	25	,	,	PUNCT
ejpam-3979	161	26	g1	g1	X
ejpam-3979	161	27	=	=	PUNCT
ejpam-3979	161	28	x	x	PROPN
ejpam-3979	161	29	and	and	CCONJ
ejpam-3979	161	30	g2	g2	PROPN
ejpam-3979	161	31	=	=	SYM
ejpam-3979	162	1	x	x	X
ejpam-3979	162	2	,	,	PUNCT
ejpam-3979	162	3	then	then	ADV
ejpam-3979	162	4	µ(i	µ(i	PROPN
ejpam-3979	162	5	⊗	⊗	PROPN
ejpam-3979	162	6	µ)(g	µ)(g	PUNCT
ejpam-3979	162	7	⊗	⊗	PROPN
ejpam-3979	162	8	(	(	PUNCT
ejpam-3979	162	9	g1	g1	PROPN
ejpam-3979	162	10	⊗	⊗	PROPN
ejpam-3979	162	11	g2	g2	PROPN
ejpam-3979	162	12	)	)	PUNCT
ejpam-3979	162	13	)	)	PUNCT
ejpam-3979	163	1	=	=	PUNCT
ejpam-3979	163	2	µ(x	µ(x	VERB
ejpam-3979	163	3	⊗	⊗	NUM
ejpam-3979	163	4	x2	x2	NOUN
ejpam-3979	163	5	)	)	PUNCT
ejpam-3979	163	6	=	=	SYM
ejpam-3979	164	1	1	1	X
ejpam-3979	164	2	.	.	PUNCT
ejpam-3979	165	1	on	on	ADP
ejpam-3979	165	2	the	the	DET
ejpam-3979	165	3	other	other	ADJ
ejpam-3979	165	4	hand	hand	NOUN
ejpam-3979	165	5	,	,	PUNCT
ejpam-3979	165	6	µ(µ⊗	µ(µ⊗	PROPN
ejpam-3979	165	7	i)((g	i)((g	PROPN
ejpam-3979	165	8	⊗	⊗	PROPN
ejpam-3979	165	9	g1)⊗	g1)⊗	PROPN
ejpam-3979	165	10	g2	g2	PROPN
ejpam-3979	165	11	)	)	PUNCT
ejpam-3979	166	1	=	=	SYM
ejpam-3979	166	2	µ(x2	µ(x2	NOUN
ejpam-3979	166	3	⊗	⊗	NUM
ejpam-3979	166	4	x	x	NOUN
ejpam-3979	166	5	)	)	PUNCT
ejpam-3979	166	6	=	=	SYM
ejpam-3979	166	7	1	1	X
ejpam-3979	166	8	.	.	PUNCT
ejpam-3979	167	1	also	also	ADV
ejpam-3979	167	2	,	,	PUNCT
ejpam-3979	167	3	if	if	SCONJ
ejpam-3979	167	4	g	g	PROPN
ejpam-3979	167	5	=	=	SYM
ejpam-3979	167	6	x	x	PROPN
ejpam-3979	167	7	,	,	PUNCT
ejpam-3979	167	8	g1	g1	X
ejpam-3979	167	9	=	=	PUNCT
ejpam-3979	167	10	x	x	PROPN
ejpam-3979	167	11	and	and	CCONJ
ejpam-3979	167	12	g2	g2	PROPN
ejpam-3979	167	13	=	=	SYM
ejpam-3979	167	14	x2	x2	PROPN
ejpam-3979	167	15	,	,	PUNCT
ejpam-3979	167	16	then	then	ADV
ejpam-3979	167	17	µ(i	µ(i	PROPN
ejpam-3979	167	18	⊗	⊗	PROPN
ejpam-3979	167	19	µ)(g	µ)(g	PUNCT
ejpam-3979	167	20	⊗	⊗	PROPN
ejpam-3979	167	21	(	(	PUNCT
ejpam-3979	167	22	g1	g1	PROPN
ejpam-3979	167	23	⊗	⊗	PROPN
ejpam-3979	167	24	g2	g2	PROPN
ejpam-3979	167	25	)	)	PUNCT
ejpam-3979	167	26	)	)	PUNCT
ejpam-3979	168	1	=	=	SYM
ejpam-3979	168	2	µ(x⊗	µ(x⊗	NOUN
ejpam-3979	168	3	1	1	NUM
ejpam-3979	168	4	)	)	PUNCT
ejpam-3979	168	5	=	=	PUNCT
ejpam-3979	168	6	x.	x.	NOUN
ejpam-3979	168	7	on	on	ADP
ejpam-3979	168	8	the	the	DET
ejpam-3979	168	9	other	other	ADJ
ejpam-3979	168	10	hand	hand	NOUN
ejpam-3979	168	11	,	,	PUNCT
ejpam-3979	168	12	µ(µ⊗	µ(µ⊗	PROPN
ejpam-3979	168	13	i)((g	i)((g	PROPN
ejpam-3979	168	14	⊗	⊗	PROPN
ejpam-3979	168	15	g1)⊗	g1)⊗	PROPN
ejpam-3979	168	16	g2	g2	PROPN
ejpam-3979	168	17	)	)	PUNCT
ejpam-3979	169	1	=	=	SYM
ejpam-3979	169	2	µ(x2	µ(x2	NOUN
ejpam-3979	169	3	⊗	⊗	PROPN
ejpam-3979	169	4	x2	x2	PROPN
ejpam-3979	169	5	)	)	PUNCT
ejpam-3979	169	6	=	=	PUNCT
ejpam-3979	169	7	x.	x.	NOUN
ejpam-3979	169	8	by	by	ADP
ejpam-3979	169	9	using	use	VERB
ejpam-3979	169	10	the	the	DET
ejpam-3979	169	11	same	same	ADJ
ejpam-3979	169	12	way	way	NOUN
ejpam-3979	169	13	,	,	PUNCT
ejpam-3979	169	14	all	all	DET
ejpam-3979	169	15	the	the	DET
ejpam-3979	169	16	different	different	ADJ
ejpam-3979	169	17	choices	choice	NOUN
ejpam-3979	169	18	of	of	ADP
ejpam-3979	169	19	elements	element	NOUN
ejpam-3979	169	20	were	be	AUX
ejpam-3979	169	21	checked	check	VERB
ejpam-3979	169	22	and	and	CCONJ
ejpam-3979	169	23	we	we	PRON
ejpam-3979	169	24	present	present	VERB
ejpam-3979	169	25	all	all	PRON
ejpam-3979	169	26	of	of	ADP
ejpam-3979	169	27	them	they	PRON
ejpam-3979	169	28	in	in	ADP
ejpam-3979	169	29	the	the	DET
ejpam-3979	169	30	following	follow	VERB
ejpam-3979	169	31	table	table	NOUN
ejpam-3979	169	32	:	:	PUNCT
ejpam-3979	169	33	t.	t.	PROPN
ejpam-3979	169	34	al	al	PROPN
ejpam-3979	169	35	-	-	PUNCT
ejpam-3979	169	36	mutairi	mutairi	PROPN
ejpam-3979	169	37	,	,	PUNCT
ejpam-3979	169	38	m.	m.	NOUN
ejpam-3979	169	39	m.	m.	PROPN
ejpam-3979	169	40	al	al	PROPN
ejpam-3979	169	41	-	-	PUNCT
ejpam-3979	169	42	shomrani	shomrani	PROPN
ejpam-3979	169	43	/	/	SYM
ejpam-3979	169	44	eur	eur	NOUN
ejpam-3979	169	45	.	.	PUNCT
ejpam-3979	170	1	j.	j.	PROPN
ejpam-3979	170	2	pure	pure	PROPN
ejpam-3979	170	3	appl	appl	PROPN
ejpam-3979	170	4	.	.	PROPN
ejpam-3979	170	5	math	math	PROPN
ejpam-3979	170	6	,	,	PUNCT
ejpam-3979	170	7	14	14	NUM
ejpam-3979	170	8	(	(	PUNCT
ejpam-3979	170	9	3	3	NUM
ejpam-3979	170	10	)	)	PUNCT
ejpam-3979	170	11	(	(	PUNCT
ejpam-3979	170	12	2021	2021	NUM
ejpam-3979	170	13	)	)	PUNCT
ejpam-3979	170	14	,	,	PUNCT
ejpam-3979	170	15	816	816	NUM
ejpam-3979	170	16	-	-	SYM
ejpam-3979	170	17	828	828	NUM
ejpam-3979	170	18	822	822	NUM
ejpam-3979	170	19	g	g	PROPN
ejpam-3979	170	20	g1	g1	PROPN
ejpam-3979	170	21	g1	g1	PROPN
ejpam-3979	170	22	µ	µ	X
ejpam-3979	170	23	(	(	PUNCT
ejpam-3979	170	24	(	(	PUNCT
ejpam-3979	170	25	i⊗µ)g⊗(g1⊗g2	i⊗µ)g⊗(g1⊗g2	ADJ
ejpam-3979	170	26	)	)	PUNCT
ejpam-3979	170	27	)	)	PUNCT
ejpam-3979	170	28	µ	µ	X
ejpam-3979	170	29	(	(	PUNCT
ejpam-3979	170	30	(	(	PUNCT
ejpam-3979	170	31	µ⊗i)(g⊗g1)⊗g2	µ⊗i)(g⊗g1)⊗g2	X
ejpam-3979	170	32	)	)	PUNCT
ejpam-3979	170	33	1	1	NUM
ejpam-3979	170	34	1	1	NUM
ejpam-3979	170	35	1	1	NUM
ejpam-3979	170	36	1	1	NUM
ejpam-3979	170	37	1	1	NUM
ejpam-3979	170	38	1	1	NUM
ejpam-3979	170	39	1	1	NUM
ejpam-3979	170	40	x	x	SYM
ejpam-3979	170	41	x	x	SYM
ejpam-3979	170	42	x	x	SYM
ejpam-3979	170	43	1	1	NUM
ejpam-3979	170	44	1	1	NUM
ejpam-3979	170	45	x2	x2	NOUN
ejpam-3979	170	46	x2	x2	NOUN
ejpam-3979	171	1	x2	x2	NOUN
ejpam-3979	172	1	1	1	NUM
ejpam-3979	172	2	x	x	SYM
ejpam-3979	172	3	1	1	NUM
ejpam-3979	172	4	x	x	SYM
ejpam-3979	172	5	x	x	SYM
ejpam-3979	172	6	1	1	NUM
ejpam-3979	172	7	x2	x2	NOUN
ejpam-3979	172	8	1	1	NUM
ejpam-3979	172	9	x2	x2	NOUN
ejpam-3979	172	10	x2	x2	NOUN
ejpam-3979	173	1	x2	x2	NOUN
ejpam-3979	173	2	x2	x2	NOUN
ejpam-3979	174	1	1	1	NUM
ejpam-3979	174	2	x	x	SYM
ejpam-3979	174	3	x	x	SYM
ejpam-3979	174	4	x2	x2	NOUN
ejpam-3979	175	1	x2	x2	NOUN
ejpam-3979	175	2	x	x	PUNCT
ejpam-3979	176	1	x2	x2	NOUN
ejpam-3979	176	2	x2	x2	NOUN
ejpam-3979	177	1	x2	x2	INTJ
ejpam-3979	177	2	x2	x2	NOUN
ejpam-3979	178	1	x2	x2	NOUN
ejpam-3979	178	2	1	1	NUM
ejpam-3979	178	3	1	1	NUM
ejpam-3979	178	4	x2	x2	NOUN
ejpam-3979	178	5	1	1	NUM
ejpam-3979	179	1	x2	x2	NOUN
ejpam-3979	180	1	x2	x2	NOUN
ejpam-3979	181	1	x2	x2	INTJ
ejpam-3979	182	1	x2	x2	INTJ
ejpam-3979	182	2	x	x	PUNCT
ejpam-3979	183	1	x2	x2	NOUN
ejpam-3979	183	2	x2	x2	NOUN
ejpam-3979	184	1	x2	x2	NOUN
ejpam-3979	184	2	x	x	PUNCT
ejpam-3979	185	1	x	x	X
ejpam-3979	185	2	1	1	NUM
ejpam-3979	185	3	x2	x2	NOUN
ejpam-3979	185	4	x2	x2	NOUN
ejpam-3979	186	1	x	x	PUNCT
ejpam-3979	186	2	x	x	SYM
ejpam-3979	186	3	x	x	SYM
ejpam-3979	186	4	1	1	NUM
ejpam-3979	186	5	1	1	NUM
ejpam-3979	186	6	x	x	SYM
ejpam-3979	186	7	x	x	SYM
ejpam-3979	187	1	x2	x2	NOUN
ejpam-3979	187	2	x	x	PUNCT
ejpam-3979	187	3	x	x	PUNCT
ejpam-3979	187	4	x	x	SYM
ejpam-3979	187	5	1	1	NUM
ejpam-3979	187	6	x	x	SYM
ejpam-3979	187	7	x2	x2	NOUN
ejpam-3979	187	8	x2	x2	NOUN
ejpam-3979	187	9	x	x	PUNCT
ejpam-3979	188	1	x2	x2	NOUN
ejpam-3979	188	2	x	x	PUNCT
ejpam-3979	188	3	x	x	PUNCT
ejpam-3979	188	4	x	x	PUNCT
ejpam-3979	188	5	table	table	NOUN
ejpam-3979	188	6	2	2	NUM
ejpam-3979	188	7	:	:	PUNCT
ejpam-3979	188	8	the	the	DET
ejpam-3979	188	9	associative	associative	ADJ
ejpam-3979	188	10	property	property	NOUN
ejpam-3979	188	11	(	(	PUNCT
ejpam-3979	188	12	ii	ii	NOUN
ejpam-3979	188	13	)	)	PUNCT
ejpam-3979	188	14	the	the	DET
ejpam-3979	188	15	unit	unit	NOUN
ejpam-3979	188	16	property	property	NOUN
ejpam-3979	188	17	:	:	PUNCT
ejpam-3979	188	18	µ(i	µ(i	PROPN
ejpam-3979	188	19	⊗	⊗	PROPN
ejpam-3979	188	20	λ)(g	λ)(g	PROPN
ejpam-3979	188	21	⊗	⊗	PROPN
ejpam-3979	188	22	r	r	NOUN
ejpam-3979	188	23	)	)	PUNCT
ejpam-3979	188	24	=	=	PRON
ejpam-3979	188	25	µ(λ⊗	µ(λ⊗	VERB
ejpam-3979	188	26	i)(r	i)(r	NOUN
ejpam-3979	188	27	⊗	⊗	PROPN
ejpam-3979	188	28	g	g	NOUN
ejpam-3979	188	29	)	)	PUNCT
ejpam-3979	188	30	,	,	PUNCT
ejpam-3979	188	31	for	for	ADP
ejpam-3979	188	32	all	all	PRON
ejpam-3979	188	33	g	g	PROPN
ejpam-3979	188	34	∈	∈	PROPN
ejpam-3979	188	35	g	g	NOUN
ejpam-3979	188	36	and	and	CCONJ
ejpam-3979	188	37	r	r	NOUN
ejpam-3979	188	38	∈	∈	NOUN
ejpam-3979	188	39	r	r	NOUN
ejpam-3979	188	40	which	which	PRON
ejpam-3979	188	41	we	we	PRON
ejpam-3979	188	42	do	do	VERB
ejpam-3979	188	43	as	as	SCONJ
ejpam-3979	188	44	follows	follow	VERB
ejpam-3979	188	45	knowing	know	VERB
ejpam-3979	188	46	λ(r	λ(r	X
ejpam-3979	188	47	)	)	PUNCT
ejpam-3979	188	48	=	=	SYM
ejpam-3979	189	1	1	1	NUM
ejpam-3979	189	2	:	:	PUNCT
ejpam-3979	189	3	if	if	SCONJ
ejpam-3979	189	4	g	g	PROPN
ejpam-3979	189	5	=	=	SYM
ejpam-3979	189	6	1	1	NUM
ejpam-3979	189	7	,	,	PUNCT
ejpam-3979	189	8	then	then	ADV
ejpam-3979	189	9	µ(i	µ(i	PROPN
ejpam-3979	189	10	⊗	⊗	PROPN
ejpam-3979	189	11	λ)(1⊗	λ)(1⊗	NUM
ejpam-3979	189	12	r	r	X
ejpam-3979	189	13	)	)	PUNCT
ejpam-3979	189	14	=	=	NOUN
ejpam-3979	189	15	µ(1⊗	µ(1⊗	DET
ejpam-3979	189	16	1	1	NUM
ejpam-3979	189	17	)	)	PUNCT
ejpam-3979	189	18	=	=	SYM
ejpam-3979	189	19	1	1	X
ejpam-3979	189	20	.	.	PUNCT
ejpam-3979	190	1	on	on	ADP
ejpam-3979	190	2	the	the	DET
ejpam-3979	190	3	other	other	ADJ
ejpam-3979	190	4	hand	hand	NOUN
ejpam-3979	190	5	,	,	PUNCT
ejpam-3979	190	6	µ(λ⊗	µ(λ⊗	VERB
ejpam-3979	190	7	i)(r	i)(r	NOUN
ejpam-3979	190	8	⊗	⊗	PROPN
ejpam-3979	190	9	1	1	NUM
ejpam-3979	190	10	)	)	PUNCT
ejpam-3979	190	11	=	=	PUNCT
ejpam-3979	191	1	µ(1⊗	µ(1⊗	DET
ejpam-3979	191	2	1	1	NUM
ejpam-3979	191	3	)	)	PUNCT
ejpam-3979	191	4	=	=	SYM
ejpam-3979	191	5	1	1	X
ejpam-3979	191	6	.	.	PUNCT
ejpam-3979	192	1	if	if	SCONJ
ejpam-3979	192	2	g	g	PROPN
ejpam-3979	192	3	=	=	SYM
ejpam-3979	192	4	x	x	NOUN
ejpam-3979	192	5	,	,	PUNCT
ejpam-3979	192	6	then	then	ADV
ejpam-3979	192	7	µ(i	µ(i	PROPN
ejpam-3979	192	8	⊗λ)(x⊗	⊗λ)(x⊗	PROPN
ejpam-3979	192	9	r	r	X
ejpam-3979	192	10	)	)	PUNCT
ejpam-3979	192	11	=	=	SYM
ejpam-3979	192	12	µ(x⊗	µ(x⊗	NOUN
ejpam-3979	192	13	1	1	NUM
ejpam-3979	192	14	)	)	PUNCT
ejpam-3979	192	15	=	=	PUNCT
ejpam-3979	193	1	x.	x.	NOUN
ejpam-3979	193	2	on	on	ADP
ejpam-3979	193	3	the	the	DET
ejpam-3979	193	4	other	other	ADJ
ejpam-3979	193	5	hand	hand	NOUN
ejpam-3979	193	6	,	,	PUNCT
ejpam-3979	193	7	µ(λ⊗	µ(λ⊗	VERB
ejpam-3979	193	8	i)(r⊗x	i)(r⊗x	PROPN
ejpam-3979	193	9	)	)	PUNCT
ejpam-3979	193	10	=	=	PUNCT
ejpam-3979	194	1	µ(1⊗x	µ(1⊗x	PROPN
ejpam-3979	194	2	)	)	PUNCT
ejpam-3979	194	3	=	=	PUNCT
ejpam-3979	195	1	x.	x.	NOUN
ejpam-3979	195	2	if	if	SCONJ
ejpam-3979	195	3	g	g	PROPN
ejpam-3979	195	4	=	=	SYM
ejpam-3979	195	5	x2	x2	PROPN
ejpam-3979	195	6	,	,	PUNCT
ejpam-3979	195	7	then	then	ADV
ejpam-3979	195	8	µ(i	µ(i	PROPN
ejpam-3979	195	9	⊗λ)(x2⊗	⊗λ)(x2⊗	NOUN
ejpam-3979	195	10	r	r	NOUN
ejpam-3979	195	11	)	)	PUNCT
ejpam-3979	195	12	=	=	PUNCT
ejpam-3979	195	13	µ(x2⊗	µ(x2⊗	NUM
ejpam-3979	195	14	1	1	NUM
ejpam-3979	195	15	)	)	PUNCT
ejpam-3979	195	16	=	=	SYM
ejpam-3979	195	17	x2	x2	PROPN
ejpam-3979	195	18	.	.	PUNCT
ejpam-3979	196	1	on	on	ADP
ejpam-3979	196	2	the	the	DET
ejpam-3979	196	3	other	other	ADJ
ejpam-3979	196	4	hand	hand	NOUN
ejpam-3979	196	5	,	,	PUNCT
ejpam-3979	196	6	µ(λ⊗	µ(λ⊗	VERB
ejpam-3979	196	7	i)(r	i)(r	NOUN
ejpam-3979	196	8	⊗	⊗	PROPN
ejpam-3979	196	9	x2	x2	PROPN
ejpam-3979	196	10	)	)	PUNCT
ejpam-3979	197	1	=	=	SYM
ejpam-3979	197	2	µ(1⊗	µ(1⊗	DET
ejpam-3979	197	3	x2	x2	PROPN
ejpam-3979	197	4	)	)	PUNCT
ejpam-3979	197	5	=	=	SYM
ejpam-3979	197	6	x2	x2	PROPN
ejpam-3979	197	7	.	.	PUNCT
ejpam-3979	198	1	thus	thus	ADV
ejpam-3979	198	2	,	,	PUNCT
ejpam-3979	198	3	(	(	PUNCT
ejpam-3979	198	4	h	h	NOUN
ejpam-3979	198	5	,	,	PUNCT
ejpam-3979	198	6	µ	µ	NOUN
ejpam-3979	198	7	,	,	PUNCT
ejpam-3979	198	8	λ	λ	NOUN
ejpam-3979	198	9	)	)	PUNCT
ejpam-3979	198	10	is	be	AUX
ejpam-3979	198	11	an	an	DET
ejpam-3979	198	12	r	r	NOUN
ejpam-3979	198	13	-	-	PUNCT
ejpam-3979	198	14	algebra	algebra	NOUN
ejpam-3979	198	15	.	.	PUNCT
ejpam-3979	199	1	next	next	ADV
ejpam-3979	199	2	,	,	PUNCT
ejpam-3979	199	3	to	to	PART
ejpam-3979	199	4	show	show	VERB
ejpam-3979	199	5	that	that	SCONJ
ejpam-3979	199	6	(	(	PUNCT
ejpam-3979	199	7	h,∆	h,∆	X
ejpam-3979	199	8	,	,	PUNCT
ejpam-3979	199	9	ε	ε	PROPN
ejpam-3979	199	10	)	)	PUNCT
ejpam-3979	199	11	is	be	AUX
ejpam-3979	199	12	an	an	DET
ejpam-3979	199	13	r	r	NOUN
ejpam-3979	199	14	-	-	PUNCT
ejpam-3979	199	15	coalgebra	coalgebra	NOUN
ejpam-3979	199	16	,	,	PUNCT
ejpam-3979	199	17	we	we	PRON
ejpam-3979	199	18	define	define	VERB
ejpam-3979	199	19	the	the	DET
ejpam-3979	199	20	coproduct	coproduct	NOUN
ejpam-3979	199	21	map	map	NOUN
ejpam-3979	199	22	∆	∆	PROPN
ejpam-3979	199	23	:	:	PUNCT
ejpam-3979	199	24	h	h	NOUN
ejpam-3979	199	25	7−→	7−→	NOUN
ejpam-3979	199	26	h⊗h	h⊗h	NOUN
ejpam-3979	199	27	by	by	ADP
ejpam-3979	199	28	∆(g	∆(g	PROPN
ejpam-3979	199	29	)	)	PUNCT
ejpam-3979	199	30	=	=	SYM
ejpam-3979	199	31	g⊗	g⊗	PROPN
ejpam-3979	199	32	g	g	NOUN
ejpam-3979	199	33	and	and	CCONJ
ejpam-3979	199	34	the	the	DET
ejpam-3979	199	35	counit	counit	VERB
ejpam-3979	199	36	map	map	NOUN
ejpam-3979	199	37	ε	ε	PROPN
ejpam-3979	199	38	:	:	PUNCT
ejpam-3979	199	39	h	h	NOUN
ejpam-3979	200	1	7−→	7−→	NOUN
ejpam-3979	200	2	r	r	NOUN
ejpam-3979	200	3	by	by	ADP
ejpam-3979	200	4	ε(g	ε(g	NOUN
ejpam-3979	200	5	)	)	PUNCT
ejpam-3979	200	6	=	=	SYM
ejpam-3979	200	7	1	1	NUM
ejpam-3979	200	8	,	,	PUNCT
ejpam-3979	200	9	for	for	ADP
ejpam-3979	200	10	all	all	DET
ejpam-3979	200	11	g	g	PROPN
ejpam-3979	200	12	∈	∈	PROPN
ejpam-3979	200	13	g.	g.	NOUN
ejpam-3979	200	14	∆	∆	PROPN
ejpam-3979	200	15	and	and	CCONJ
ejpam-3979	200	16	ε	ε	PROPN
ejpam-3979	200	17	that	that	PRON
ejpam-3979	200	18	satisfy	satisfy	VERB
ejpam-3979	200	19	the	the	DET
ejpam-3979	200	20	following	follow	VERB
ejpam-3979	200	21	required	require	VERB
ejpam-3979	200	22	conditions	condition	NOUN
ejpam-3979	200	23	:	:	PUNCT
ejpam-3979	200	24	(	(	PUNCT
ejpam-3979	200	25	i	i	NOUN
ejpam-3979	200	26	)	)	PUNCT
ejpam-3979	200	27	the	the	DET
ejpam-3979	200	28	coassociative	coassociative	ADJ
ejpam-3979	200	29	property	property	NOUN
ejpam-3979	200	30	:	:	PUNCT
ejpam-3979	200	31	(	(	PUNCT
ejpam-3979	200	32	i	i	PROPN
ejpam-3979	200	33	⊗	⊗	PROPN
ejpam-3979	200	34	∆)∆(g	∆)∆(g	PROPN
ejpam-3979	200	35	)	)	PUNCT
ejpam-3979	200	36	=	=	PUNCT
ejpam-3979	200	37	(	(	PUNCT
ejpam-3979	200	38	∆	∆	PROPN
ejpam-3979	200	39	⊗	⊗	PROPN
ejpam-3979	200	40	i)∆(g	i)∆(g	PROPN
ejpam-3979	200	41	)	)	PUNCT
ejpam-3979	200	42	for	for	ADP
ejpam-3979	200	43	all	all	DET
ejpam-3979	200	44	g	g	PROPN
ejpam-3979	200	45	∈	∈	PROPN
ejpam-3979	200	46	g.	g.	NOUN
ejpam-3979	201	1	indeed	indeed	ADV
ejpam-3979	201	2	if	if	SCONJ
ejpam-3979	201	3	g	g	PROPN
ejpam-3979	201	4	=	=	SYM
ejpam-3979	201	5	1	1	NUM
ejpam-3979	201	6	,	,	PUNCT
ejpam-3979	201	7	then	then	ADV
ejpam-3979	201	8	(	(	PUNCT
ejpam-3979	201	9	i	i	PRON
ejpam-3979	201	10	⊗	⊗	PROPN
ejpam-3979	201	11	∆)∆(1	∆)∆(1	NUM
ejpam-3979	201	12	)	)	PUNCT
ejpam-3979	201	13	=	=	SYM
ejpam-3979	201	14	(	(	PUNCT
ejpam-3979	201	15	i	i	PRON
ejpam-3979	201	16	⊗	⊗	VERB
ejpam-3979	201	17	∆)(1	∆)(1	ADV
ejpam-3979	202	1	⊗	⊗	NUM
ejpam-3979	202	2	1	1	NUM
ejpam-3979	202	3	)	)	PUNCT
ejpam-3979	202	4	=	=	SYM
ejpam-3979	202	5	1	1	NUM
ejpam-3979	202	6	⊗	⊗	PROPN
ejpam-3979	202	7	1	1	NUM
ejpam-3979	202	8	⊗	⊗	NUM
ejpam-3979	202	9	1	1	NUM
ejpam-3979	202	10	.	.	PUNCT
ejpam-3979	203	1	also	also	ADV
ejpam-3979	203	2	,	,	PUNCT
ejpam-3979	203	3	(	(	PUNCT
ejpam-3979	203	4	∆	∆	X
ejpam-3979	203	5	⊗	⊗	ADJ
ejpam-3979	203	6	i)∆(1	i)∆(1	NOUN
ejpam-3979	203	7	)	)	PUNCT
ejpam-3979	203	8	=	=	SYM
ejpam-3979	203	9	(	(	PUNCT
ejpam-3979	203	10	∆⊗	∆⊗	PROPN
ejpam-3979	203	11	i)(1⊗	i)(1⊗	NOUN
ejpam-3979	203	12	1	1	NUM
ejpam-3979	203	13	)	)	PUNCT
ejpam-3979	203	14	=	=	PUNCT
ejpam-3979	204	1	1⊗	1⊗	NUM
ejpam-3979	204	2	1⊗	1⊗	NUM
ejpam-3979	204	3	1	1	NUM
ejpam-3979	204	4	.	.	PUNCT
ejpam-3979	205	1	if	if	SCONJ
ejpam-3979	205	2	g	g	PROPN
ejpam-3979	205	3	=	=	SYM
ejpam-3979	205	4	x	x	NOUN
ejpam-3979	205	5	,	,	PUNCT
ejpam-3979	205	6	then	then	ADV
ejpam-3979	205	7	(	(	PUNCT
ejpam-3979	205	8	i	i	PROPN
ejpam-3979	205	9	⊗∆)∆(x	⊗∆)∆(x	PROPN
ejpam-3979	205	10	)	)	PUNCT
ejpam-3979	206	1	=	=	PRON
ejpam-3979	206	2	(	(	PUNCT
ejpam-3979	206	3	i	i	PRON
ejpam-3979	206	4	⊗∆)(x⊗x	⊗∆)(x⊗x	PRON
ejpam-3979	206	5	)	)	PUNCT
ejpam-3979	206	6	=	=	PUNCT
ejpam-3979	207	1	x⊗x⊗x	x⊗x⊗x	PROPN
ejpam-3979	207	2	.	.	PUNCT
ejpam-3979	208	1	also	also	ADV
ejpam-3979	208	2	,	,	PUNCT
ejpam-3979	208	3	(	(	PUNCT
ejpam-3979	208	4	∆	∆	PROPN
ejpam-3979	208	5	⊗	⊗	PROPN
ejpam-3979	208	6	i)∆(x	i)∆(x	PROPN
ejpam-3979	208	7	)	)	PUNCT
ejpam-3979	208	8	=	=	PUNCT
ejpam-3979	208	9	(	(	PUNCT
ejpam-3979	208	10	∆	∆	PROPN
ejpam-3979	208	11	⊗	⊗	PROPN
ejpam-3979	208	12	i)(x	i)(x	PROPN
ejpam-3979	208	13	⊗	⊗	PROPN
ejpam-3979	208	14	x	x	NOUN
ejpam-3979	208	15	)	)	PUNCT
ejpam-3979	208	16	=	=	PUNCT
ejpam-3979	209	1	x	x	SYM
ejpam-3979	209	2	⊗	⊗	PROPN
ejpam-3979	209	3	x	x	PUNCT
ejpam-3979	210	1	⊗	⊗	PROPN
ejpam-3979	210	2	x.	x.	NOUN
ejpam-3979	211	1	if	if	SCONJ
ejpam-3979	211	2	g	g	PROPN
ejpam-3979	211	3	=	=	SYM
ejpam-3979	211	4	x2	x2	PROPN
ejpam-3979	211	5	,	,	PUNCT
ejpam-3979	211	6	then	then	ADV
ejpam-3979	211	7	(	(	PUNCT
ejpam-3979	211	8	i	i	NOUN
ejpam-3979	211	9	⊗∆)∆(x2	⊗∆)∆(x2	VERB
ejpam-3979	211	10	)	)	PUNCT
ejpam-3979	211	11	=	=	SYM
ejpam-3979	211	12	(	(	PUNCT
ejpam-3979	211	13	i⊗∆)(x2⊗x2	i⊗∆)(x2⊗x2	NOUN
ejpam-3979	211	14	)	)	PUNCT
ejpam-3979	211	15	=	=	PUNCT
ejpam-3979	212	1	x2⊗x2⊗x2	x2⊗x2⊗x2	PROPN
ejpam-3979	212	2	.	.	PUNCT
ejpam-3979	213	1	also	also	ADV
ejpam-3979	213	2	,	,	PUNCT
ejpam-3979	213	3	(	(	PUNCT
ejpam-3979	213	4	∆⊗i)∆(x2	∆⊗i)∆(x2	NOUN
ejpam-3979	213	5	)	)	PUNCT
ejpam-3979	213	6	=	=	PUNCT
ejpam-3979	213	7	(	(	PUNCT
ejpam-3979	213	8	∆⊗i)(x2⊗x2	∆⊗i)(x2⊗x2	NOUN
ejpam-3979	213	9	)	)	PUNCT
ejpam-3979	214	1	=	=	SYM
ejpam-3979	214	2	x2⊗x2⊗x2	x2⊗x2⊗x2	PROPN
ejpam-3979	214	3	.	.	PUNCT
ejpam-3979	215	1	(	(	PUNCT
ejpam-3979	215	2	ii	ii	X
ejpam-3979	215	3	)	)	PUNCT
ejpam-3979	215	4	the	the	DET
ejpam-3979	215	5	counit	counit	VERB
ejpam-3979	215	6	property	property	NOUN
ejpam-3979	215	7	:(	:(	PROPN
ejpam-3979	215	8	ε	ε	PROPN
ejpam-3979	215	9	⊗	⊗	PROPN
ejpam-3979	215	10	i)∆(g	i)∆(g	PROPN
ejpam-3979	215	11	)	)	PUNCT
ejpam-3979	215	12	=	=	PUNCT
ejpam-3979	215	13	1	1	NUM
ejpam-3979	215	14	⊗	⊗	NUM
ejpam-3979	215	15	g	g	PROPN
ejpam-3979	215	16	and	and	CCONJ
ejpam-3979	215	17	(	(	PUNCT
ejpam-3979	215	18	i	i	PROPN
ejpam-3979	215	19	⊗	⊗	PROPN
ejpam-3979	215	20	ε)∆(g	ε)∆(g	PROPN
ejpam-3979	215	21	)	)	PUNCT
ejpam-3979	216	1	=	=	SYM
ejpam-3979	216	2	g	g	PROPN
ejpam-3979	216	3	⊗	⊗	PROPN
ejpam-3979	216	4	1	1	NUM
ejpam-3979	216	5	for	for	ADP
ejpam-3979	216	6	all	all	DET
ejpam-3979	216	7	g	g	PROPN
ejpam-3979	216	8	∈	∈	PROPN
ejpam-3979	216	9	g.	g.	NOUN
ejpam-3979	216	10	indeed	indeed	ADV
ejpam-3979	216	11	,	,	PUNCT
ejpam-3979	216	12	if	if	SCONJ
ejpam-3979	216	13	g	g	PROPN
ejpam-3979	216	14	=	=	SYM
ejpam-3979	216	15	1	1	NUM
ejpam-3979	216	16	,	,	PUNCT
ejpam-3979	216	17	then	then	ADV
ejpam-3979	216	18	(	(	PUNCT
ejpam-3979	216	19	ε	ε	PROPN
ejpam-3979	216	20	⊗	⊗	PROPN
ejpam-3979	216	21	i)∆(1	i)∆(1	NOUN
ejpam-3979	216	22	)	)	PUNCT
ejpam-3979	216	23	=	=	SYM
ejpam-3979	216	24	(	(	PUNCT
ejpam-3979	216	25	ε	ε	PROPN
ejpam-3979	216	26	⊗	⊗	PROPN
ejpam-3979	216	27	i)(1	i)(1	X
ejpam-3979	217	1	⊗	⊗	PROPN
ejpam-3979	217	2	1	1	NUM
ejpam-3979	217	3	)	)	PUNCT
ejpam-3979	217	4	=	=	SYM
ejpam-3979	217	5	1	1	NUM
ejpam-3979	217	6	⊗	⊗	NUM
ejpam-3979	217	7	1	1	NUM
ejpam-3979	218	1	and	and	CCONJ
ejpam-3979	218	2	(	(	PUNCT
ejpam-3979	218	3	i	i	PROPN
ejpam-3979	218	4	⊗	⊗	PROPN
ejpam-3979	218	5	ε)∆(1	ε)∆(1	NOUN
ejpam-3979	218	6	)	)	PUNCT
ejpam-3979	219	1	=	=	PUNCT
ejpam-3979	219	2	(	(	PUNCT
ejpam-3979	219	3	i	i	PRON
ejpam-3979	219	4	⊗	⊗	PROPN
ejpam-3979	219	5	ε)(1	ε)(1	PROPN
ejpam-3979	220	1	⊗	⊗	NUM
ejpam-3979	220	2	1	1	NUM
ejpam-3979	220	3	)	)	PUNCT
ejpam-3979	220	4	=	=	SYM
ejpam-3979	220	5	1	1	NUM
ejpam-3979	220	6	⊗	⊗	NUM
ejpam-3979	220	7	1	1	NUM
ejpam-3979	220	8	.	.	PUNCT
ejpam-3979	221	1	if	if	SCONJ
ejpam-3979	221	2	g	g	PROPN
ejpam-3979	221	3	=	=	SYM
ejpam-3979	221	4	x	x	NOUN
ejpam-3979	221	5	,	,	PUNCT
ejpam-3979	221	6	then	then	ADV
ejpam-3979	221	7	(	(	PUNCT
ejpam-3979	221	8	ε	ε	PROPN
ejpam-3979	221	9	⊗	⊗	PROPN
ejpam-3979	221	10	i)∆(x	i)∆(x	PROPN
ejpam-3979	221	11	)	)	PUNCT
ejpam-3979	221	12	=	=	PUNCT
ejpam-3979	221	13	(	(	PUNCT
ejpam-3979	221	14	ε	ε	PROPN
ejpam-3979	221	15	⊗	⊗	PROPN
ejpam-3979	221	16	i)(x	i)(x	PROPN
ejpam-3979	221	17	⊗	⊗	PROPN
ejpam-3979	221	18	x	x	NOUN
ejpam-3979	221	19	)	)	PUNCT
ejpam-3979	221	20	=	=	SYM
ejpam-3979	221	21	1	1	NUM
ejpam-3979	221	22	⊗	⊗	NOUN
ejpam-3979	221	23	x	x	PUNCT
ejpam-3979	221	24	and	and	CCONJ
ejpam-3979	221	25	(	(	PUNCT
ejpam-3979	221	26	i⊗ε)∆(x	i⊗ε)∆(x	NUM
ejpam-3979	221	27	)	)	PUNCT
ejpam-3979	221	28	=	=	SYM
ejpam-3979	221	29	(	(	PUNCT
ejpam-3979	221	30	i⊗ε)(x⊗x	i⊗ε)(x⊗x	PROPN
ejpam-3979	221	31	)	)	PUNCT
ejpam-3979	221	32	=	=	SYM
ejpam-3979	221	33	x⊗1	x⊗1	NOUN
ejpam-3979	221	34	.	.	PUNCT
ejpam-3979	222	1	if	if	SCONJ
ejpam-3979	222	2	g	g	PROPN
ejpam-3979	222	3	=	=	SYM
ejpam-3979	222	4	x2	x2	PROPN
ejpam-3979	222	5	,	,	PUNCT
ejpam-3979	222	6	then	then	ADV
ejpam-3979	222	7	(	(	PUNCT
ejpam-3979	222	8	ε⊗i)∆(x2	ε⊗i)∆(x2	PROPN
ejpam-3979	222	9	)	)	PUNCT
ejpam-3979	222	10	=	=	SYM
ejpam-3979	222	11	(	(	PUNCT
ejpam-3979	222	12	ε⊗i)(x2⊗x2	ε⊗i)(x2⊗x2	PROPN
ejpam-3979	222	13	)	)	PUNCT
ejpam-3979	222	14	=	=	PUNCT
ejpam-3979	223	1	1⊗	1⊗	NUM
ejpam-3979	223	2	x2	x2	NOUN
ejpam-3979	224	1	and	and	CCONJ
ejpam-3979	224	2	(	(	PUNCT
ejpam-3979	224	3	i	i	NOUN
ejpam-3979	224	4	⊗	⊗	PROPN
ejpam-3979	224	5	ε)∆(x2	ε)∆(x2	NOUN
ejpam-3979	224	6	)	)	PUNCT
ejpam-3979	224	7	=	=	PUNCT
ejpam-3979	225	1	(	(	PUNCT
ejpam-3979	225	2	i	i	PRON
ejpam-3979	225	3	⊗	⊗	PROPN
ejpam-3979	225	4	ε)(x2	ε)(x2	PROPN
ejpam-3979	225	5	⊗	⊗	PROPN
ejpam-3979	225	6	x2	x2	PROPN
ejpam-3979	225	7	)	)	PUNCT
ejpam-3979	226	1	=	=	SYM
ejpam-3979	227	1	x2	x2	PROPN
ejpam-3979	227	2	⊗	⊗	NUM
ejpam-3979	227	3	1	1	NUM
ejpam-3979	227	4	.	.	PUNCT
ejpam-3979	228	1	t.	t.	PROPN
ejpam-3979	228	2	al	al	PROPN
ejpam-3979	228	3	-	-	PUNCT
ejpam-3979	228	4	mutairi	mutairi	PROPN
ejpam-3979	228	5	,	,	PUNCT
ejpam-3979	228	6	m.	m.	NOUN
ejpam-3979	228	7	m.	m.	PROPN
ejpam-3979	228	8	al	al	PROPN
ejpam-3979	228	9	-	-	PUNCT
ejpam-3979	228	10	shomrani	shomrani	PROPN
ejpam-3979	228	11	/	/	SYM
ejpam-3979	228	12	eur	eur	NOUN
ejpam-3979	228	13	.	.	PUNCT
ejpam-3979	229	1	j.	j.	PROPN
ejpam-3979	229	2	pure	pure	PROPN
ejpam-3979	229	3	appl	appl	PROPN
ejpam-3979	229	4	.	.	PROPN
ejpam-3979	229	5	math	math	PROPN
ejpam-3979	229	6	,	,	PUNCT
ejpam-3979	229	7	14	14	NUM
ejpam-3979	229	8	(	(	PUNCT
ejpam-3979	229	9	3	3	NUM
ejpam-3979	229	10	)	)	PUNCT
ejpam-3979	229	11	(	(	PUNCT
ejpam-3979	229	12	2021	2021	NUM
ejpam-3979	229	13	)	)	PUNCT
ejpam-3979	229	14	,	,	PUNCT
ejpam-3979	229	15	816	816	NUM
ejpam-3979	229	16	-	-	SYM
ejpam-3979	229	17	828	828	NUM
ejpam-3979	229	18	823	823	NUM
ejpam-3979	229	19	so	so	ADV
ejpam-3979	229	20	,	,	PUNCT
ejpam-3979	229	21	(	(	PUNCT
ejpam-3979	229	22	h,∆	h,∆	X
ejpam-3979	229	23	,	,	PUNCT
ejpam-3979	229	24	ε	ε	PROPN
ejpam-3979	229	25	)	)	PUNCT
ejpam-3979	229	26	is	be	AUX
ejpam-3979	229	27	an	an	DET
ejpam-3979	229	28	r	r	NOUN
ejpam-3979	229	29	-	-	PUNCT
ejpam-3979	229	30	coalgebra	coalgebra	NOUN
ejpam-3979	229	31	.	.	PUNCT
ejpam-3979	230	1	now	now	ADV
ejpam-3979	230	2	,	,	PUNCT
ejpam-3979	230	3	to	to	PART
ejpam-3979	230	4	show	show	VERB
ejpam-3979	230	5	that	that	SCONJ
ejpam-3979	230	6	(	(	PUNCT
ejpam-3979	230	7	h	h	NOUN
ejpam-3979	230	8	,	,	PUNCT
ejpam-3979	230	9	µ	µ	NOUN
ejpam-3979	230	10	,	,	PUNCT
ejpam-3979	230	11	λ,∆	λ,∆	NUM
ejpam-3979	230	12	,	,	PUNCT
ejpam-3979	230	13	ε	ε	PROPN
ejpam-3979	230	14	)	)	PUNCT
ejpam-3979	230	15	is	be	AUX
ejpam-3979	230	16	an	an	DET
ejpam-3979	230	17	r	r	NOUN
ejpam-3979	230	18	-	-	PUNCT
ejpam-3979	230	19	bialgebra	bialgebra	NOUN
ejpam-3979	230	20	,	,	PUNCT
ejpam-3979	230	21	as	as	SCONJ
ejpam-3979	230	22	we	we	PRON
ejpam-3979	230	23	have	have	AUX
ejpam-3979	230	24	already	already	ADV
ejpam-3979	230	25	shown	show	VERB
ejpam-3979	230	26	that	that	SCONJ
ejpam-3979	230	27	(	(	PUNCT
ejpam-3979	230	28	h	h	NOUN
ejpam-3979	230	29	,	,	PUNCT
ejpam-3979	230	30	µ	µ	NOUN
ejpam-3979	230	31	,	,	PUNCT
ejpam-3979	230	32	λ	λ	NOUN
ejpam-3979	230	33	)	)	PUNCT
ejpam-3979	230	34	is	be	AUX
ejpam-3979	230	35	an	an	DET
ejpam-3979	230	36	r	r	NOUN
ejpam-3979	230	37	-	-	PUNCT
ejpam-3979	230	38	algebra	algebra	NOUN
ejpam-3979	230	39	and	and	CCONJ
ejpam-3979	230	40	(	(	PUNCT
ejpam-3979	230	41	h,∆	h,∆	X
ejpam-3979	230	42	,	,	PUNCT
ejpam-3979	230	43	ε	ε	PROPN
ejpam-3979	230	44	)	)	PUNCT
ejpam-3979	230	45	is	be	AUX
ejpam-3979	230	46	an	an	DET
ejpam-3979	230	47	r	r	NOUN
ejpam-3979	230	48	-	-	PUNCT
ejpam-3979	230	49	coalgebra	coalgebra	NOUN
ejpam-3979	230	50	,	,	PUNCT
ejpam-3979	230	51	we	we	PRON
ejpam-3979	230	52	only	only	ADV
ejpam-3979	230	53	need	need	VERB
ejpam-3979	230	54	to	to	PART
ejpam-3979	230	55	show	show	VERB
ejpam-3979	230	56	that	that	SCONJ
ejpam-3979	230	57	∆	∆	PROPN
ejpam-3979	230	58	and	and	CCONJ
ejpam-3979	230	59	ε	ε	PROPN
ejpam-3979	230	60	are	be	AUX
ejpam-3979	230	61	algebra	algebra	NOUN
ejpam-3979	230	62	morphisms	morphism	NOUN
ejpam-3979	230	63	,	,	PUNCT
ejpam-3979	230	64	that	that	PRON
ejpam-3979	230	65	is	be	AUX
ejpam-3979	230	66	for	for	ADP
ejpam-3979	230	67	g	g	NOUN
ejpam-3979	230	68	,	,	PUNCT
ejpam-3979	230	69	g1	g1	PROPN
ejpam-3979	230	70	∈	∈	PROPN
ejpam-3979	230	71	g	g	NOUN
ejpam-3979	230	72	we	we	PRON
ejpam-3979	230	73	have	have	AUX
ejpam-3979	230	74	∆(µ(g	∆(µ(g	PROPN
ejpam-3979	230	75	⊗	⊗	PROPN
ejpam-3979	230	76	g1	g1	PROPN
ejpam-3979	230	77	)	)	PUNCT
ejpam-3979	231	1	=	=	SYM
ejpam-3979	231	2	∆(g	∆(g	PROPN
ejpam-3979	231	3	)	)	PUNCT
ejpam-3979	231	4	·	·	PUNCT
ejpam-3979	231	5	∆(g1	∆(g1	NOUN
ejpam-3979	231	6	)	)	PUNCT
ejpam-3979	231	7	,	,	PUNCT
ejpam-3979	231	8	and	and	CCONJ
ejpam-3979	231	9	ε(µ(g	ε(µ(g	PROPN
ejpam-3979	231	10	⊗	⊗	PROPN
ejpam-3979	231	11	g1	g1	PROPN
ejpam-3979	231	12	)	)	PUNCT
ejpam-3979	231	13	)	)	PUNCT
ejpam-3979	232	1	=	=	PUNCT
ejpam-3979	232	2	ε(g)ε(g1	ε(g)ε(g1	NOUN
ejpam-3979	232	3	)	)	PUNCT
ejpam-3979	232	4	,	,	PUNCT
ejpam-3979	232	5	where	where	SCONJ
ejpam-3979	232	6	the	the	DET
ejpam-3979	232	7	multiplication	multiplication	NOUN
ejpam-3979	232	8	·	·	PUNCT
ejpam-3979	232	9	on	on	ADP
ejpam-3979	232	10	h⊗h	h⊗h	PRON
ejpam-3979	232	11	is	be	AUX
ejpam-3979	232	12	just	just	ADV
ejpam-3979	232	13	the	the	DET
ejpam-3979	232	14	usual	usual	ADJ
ejpam-3979	232	15	multiplication	multiplication	NOUN
ejpam-3979	232	16	on	on	ADP
ejpam-3979	232	17	the	the	DET
ejpam-3979	232	18	tensor	tensor	NOUN
ejpam-3979	232	19	products	product	NOUN
ejpam-3979	232	20	(	(	PUNCT
ejpam-3979	232	21	g	g	PROPN
ejpam-3979	232	22	⊗	⊗	PROPN
ejpam-3979	232	23	g1	g1	PROPN
ejpam-3979	232	24	)	)	PUNCT
ejpam-3979	232	25	·	·	PUNCT
ejpam-3979	232	26	(	(	PUNCT
ejpam-3979	232	27	g′	g′	NOUN
ejpam-3979	232	28	⊗	⊗	PROPN
ejpam-3979	232	29	g′1	g′1	PROPN
ejpam-3979	232	30	)	)	PUNCT
ejpam-3979	233	1	=	=	SYM
ejpam-3979	234	1	µ(g	µ(g	ADP
ejpam-3979	234	2	⊗	⊗	PROPN
ejpam-3979	234	3	g′)⊗	g′)⊗	PROPN
ejpam-3979	234	4	µ(g1	µ(g1	VERB
ejpam-3979	234	5	⊗	⊗	PROPN
ejpam-3979	234	6	g	g	NOUN
ejpam-3979	234	7	′	′	NUM
ejpam-3979	234	8	1	1	NUM
ejpam-3979	234	9	)	)	PUNCT
ejpam-3979	234	10	.	.	PUNCT
ejpam-3979	235	1	we	we	PRON
ejpam-3979	235	2	check	check	VERB
ejpam-3979	235	3	this	this	DET
ejpam-3979	235	4	properties	property	NOUN
ejpam-3979	235	5	as	as	SCONJ
ejpam-3979	235	6	follows	follow	VERB
ejpam-3979	235	7	:	:	PUNCT
ejpam-3979	235	8	if	if	SCONJ
ejpam-3979	235	9	g	g	PROPN
ejpam-3979	235	10	=	=	SYM
ejpam-3979	235	11	x	x	X
ejpam-3979	235	12	and	and	CCONJ
ejpam-3979	235	13	g1	g1	PROPN
ejpam-3979	235	14	=	=	SYM
ejpam-3979	235	15	1	1	NUM
ejpam-3979	235	16	,	,	PUNCT
ejpam-3979	235	17	then	then	ADV
ejpam-3979	235	18	∆(µ(x⊗	∆(µ(x⊗	PROPN
ejpam-3979	235	19	1	1	NUM
ejpam-3979	235	20	)	)	PUNCT
ejpam-3979	235	21	)	)	PUNCT
ejpam-3979	236	1	=	=	SYM
ejpam-3979	236	2	∆(x	∆(x	NOUN
ejpam-3979	236	3	)	)	PUNCT
ejpam-3979	236	4	=	=	PRON
ejpam-3979	236	5	x⊗	x⊗	PROPN
ejpam-3979	236	6	x.	x.	NOUN
ejpam-3979	236	7	on	on	ADP
ejpam-3979	236	8	the	the	DET
ejpam-3979	236	9	other	other	ADJ
ejpam-3979	236	10	hand	hand	NOUN
ejpam-3979	236	11	,	,	PUNCT
ejpam-3979	236	12	∆(x	∆(x	PROPN
ejpam-3979	236	13	)	)	PUNCT
ejpam-3979	236	14	·	·	PUNCT
ejpam-3979	236	15	∆(1	∆(1	NOUN
ejpam-3979	236	16	)	)	PUNCT
ejpam-3979	236	17	=	=	SYM
ejpam-3979	236	18	(	(	PUNCT
ejpam-3979	236	19	x⊗	x⊗	NOUN
ejpam-3979	236	20	x	x	X
ejpam-3979	236	21	)	)	PUNCT
ejpam-3979	236	22	·	·	PUNCT
ejpam-3979	237	1	(	(	PUNCT
ejpam-3979	237	2	1⊗	1⊗	NUM
ejpam-3979	237	3	1	1	NUM
ejpam-3979	237	4	)	)	PUNCT
ejpam-3979	237	5	=	=	X
ejpam-3979	237	6	x⊗	x⊗	PROPN
ejpam-3979	237	7	x.	x.	PUNCT
ejpam-3979	238	1	so	so	ADV
ejpam-3979	238	2	,	,	PUNCT
ejpam-3979	238	3	∆(µ(x⊗	∆(µ(x⊗	NOUN
ejpam-3979	238	4	1	1	NUM
ejpam-3979	238	5	)	)	PUNCT
ejpam-3979	238	6	)	)	PUNCT
ejpam-3979	238	7	=	=	SYM
ejpam-3979	238	8	∆(x	∆(x	NOUN
ejpam-3979	238	9	)	)	PUNCT
ejpam-3979	238	10	·	·	PUNCT
ejpam-3979	238	11	∆(1	∆(1	NOUN
ejpam-3979	238	12	)	)	PUNCT
ejpam-3979	238	13	.	.	PUNCT
ejpam-3979	239	1	also	also	ADV
ejpam-3979	239	2	,	,	PUNCT
ejpam-3979	239	3	ε(µ(x⊗	ε(µ(x⊗	DET
ejpam-3979	239	4	1	1	NUM
ejpam-3979	239	5	)	)	PUNCT
ejpam-3979	239	6	)	)	PUNCT
ejpam-3979	240	1	=	=	SYM
ejpam-3979	240	2	ε(x	ε(x	X
ejpam-3979	240	3	)	)	PUNCT
ejpam-3979	240	4	=	=	SYM
ejpam-3979	240	5	1	1	X
ejpam-3979	240	6	.	.	PUNCT
ejpam-3979	241	1	on	on	ADP
ejpam-3979	241	2	the	the	DET
ejpam-3979	241	3	other	other	ADJ
ejpam-3979	241	4	hand	hand	NOUN
ejpam-3979	241	5	,	,	PUNCT
ejpam-3979	241	6	ε(x)ε(1	ε(x)ε(1	NOUN
ejpam-3979	241	7	)	)	PUNCT
ejpam-3979	241	8	=	=	PUNCT
ejpam-3979	241	9	(	(	PUNCT
ejpam-3979	241	10	1	1	NUM
ejpam-3979	241	11	)	)	PUNCT
ejpam-3979	241	12	(	(	PUNCT
ejpam-3979	241	13	1	1	X
ejpam-3979	241	14	)	)	PUNCT
ejpam-3979	242	1	=	=	SYM
ejpam-3979	242	2	1	1	X
ejpam-3979	242	3	.	.	PUNCT
ejpam-3979	243	1	so	so	ADV
ejpam-3979	243	2	,	,	PUNCT
ejpam-3979	243	3	ε(µ(x⊗	ε(µ(x⊗	PRON
ejpam-3979	243	4	1	1	NUM
ejpam-3979	243	5	)	)	PUNCT
ejpam-3979	243	6	)	)	PUNCT
ejpam-3979	244	1	=	=	SYM
ejpam-3979	244	2	ε(x)ε(1	ε(x)ε(1	NOUN
ejpam-3979	244	3	)	)	PUNCT
ejpam-3979	244	4	.	.	PUNCT
ejpam-3979	245	1	if	if	SCONJ
ejpam-3979	245	2	g	g	NOUN
ejpam-3979	245	3	=	=	SYM
ejpam-3979	245	4	x	x	X
ejpam-3979	245	5	and	and	CCONJ
ejpam-3979	245	6	g1	g1	PROPN
ejpam-3979	245	7	=	=	SYM
ejpam-3979	246	1	x	x	X
ejpam-3979	246	2	,	,	PUNCT
ejpam-3979	246	3	then	then	ADV
ejpam-3979	246	4	∆(µ(x⊗	∆(µ(x⊗	PROPN
ejpam-3979	246	5	x	x	PROPN
ejpam-3979	246	6	)	)	PUNCT
ejpam-3979	246	7	)	)	PUNCT
ejpam-3979	246	8	=	=	SYM
ejpam-3979	246	9	∆(x2	∆(x2	NUM
ejpam-3979	246	10	)	)	PUNCT
ejpam-3979	246	11	=	=	SYM
ejpam-3979	247	1	x2	x2	PROPN
ejpam-3979	247	2	⊗	⊗	NUM
ejpam-3979	247	3	x2	x2	PROPN
ejpam-3979	247	4	.	.	PUNCT
ejpam-3979	248	1	on	on	ADP
ejpam-3979	248	2	the	the	DET
ejpam-3979	248	3	other	other	ADJ
ejpam-3979	248	4	hand	hand	NOUN
ejpam-3979	248	5	,	,	PUNCT
ejpam-3979	248	6	∆(x	∆(x	PROPN
ejpam-3979	248	7	)	)	PUNCT
ejpam-3979	248	8	·	·	PUNCT
ejpam-3979	248	9	∆(x	∆(x	NOUN
ejpam-3979	248	10	)	)	PUNCT
ejpam-3979	248	11	=	=	SYM
ejpam-3979	248	12	(	(	PUNCT
ejpam-3979	248	13	x⊗	x⊗	NOUN
ejpam-3979	248	14	x	x	X
ejpam-3979	248	15	)	)	PUNCT
ejpam-3979	248	16	·	·	PUNCT
ejpam-3979	248	17	(	(	PUNCT
ejpam-3979	248	18	x⊗	x⊗	NOUN
ejpam-3979	248	19	x	x	X
ejpam-3979	248	20	)	)	PUNCT
ejpam-3979	249	1	=	=	SYM
ejpam-3979	249	2	x2	x2	PROPN
ejpam-3979	250	1	⊗	⊗	NUM
ejpam-3979	250	2	x2	x2	PROPN
ejpam-3979	250	3	.	.	PUNCT
ejpam-3979	251	1	so	so	ADV
ejpam-3979	251	2	,	,	PUNCT
ejpam-3979	251	3	∆(µ(x⊗	∆(µ(x⊗	PROPN
ejpam-3979	251	4	x	x	NOUN
ejpam-3979	251	5	)	)	PUNCT
ejpam-3979	251	6	)	)	PUNCT
ejpam-3979	251	7	=	=	SYM
ejpam-3979	251	8	∆(x	∆(x	NOUN
ejpam-3979	251	9	)	)	PUNCT
ejpam-3979	251	10	·	·	PUNCT
ejpam-3979	251	11	∆(x	∆(x	NOUN
ejpam-3979	251	12	)	)	PUNCT
ejpam-3979	251	13	.	.	PUNCT
ejpam-3979	252	1	also	also	ADV
ejpam-3979	252	2	,	,	PUNCT
ejpam-3979	252	3	ε(µ(x⊗	ε(µ(x⊗	NOUN
ejpam-3979	252	4	x	x	X
ejpam-3979	252	5	)	)	PUNCT
ejpam-3979	252	6	)	)	PUNCT
ejpam-3979	252	7	=	=	SYM
ejpam-3979	252	8	ε(x2	ε(x2	NOUN
ejpam-3979	252	9	)	)	PUNCT
ejpam-3979	252	10	=	=	SYM
ejpam-3979	253	1	1	1	X
ejpam-3979	253	2	.	.	PUNCT
ejpam-3979	254	1	on	on	ADP
ejpam-3979	254	2	the	the	DET
ejpam-3979	254	3	other	other	ADJ
ejpam-3979	254	4	hand	hand	NOUN
ejpam-3979	254	5	,	,	PUNCT
ejpam-3979	254	6	ε(x)ε(x	ε(x)ε(x	NOUN
ejpam-3979	254	7	)	)	PUNCT
ejpam-3979	254	8	=	=	PUNCT
ejpam-3979	254	9	(	(	PUNCT
ejpam-3979	254	10	1	1	NUM
ejpam-3979	254	11	)	)	PUNCT
ejpam-3979	254	12	(	(	PUNCT
ejpam-3979	254	13	1	1	X
ejpam-3979	254	14	)	)	PUNCT
ejpam-3979	254	15	=	=	SYM
ejpam-3979	255	1	1	1	X
ejpam-3979	255	2	.	.	PUNCT
ejpam-3979	256	1	so	so	ADV
ejpam-3979	256	2	,	,	PUNCT
ejpam-3979	257	1	ε(µ(x⊗	ε(µ(x⊗	NOUN
ejpam-3979	257	2	x	x	X
ejpam-3979	257	3	)	)	PUNCT
ejpam-3979	257	4	)	)	PUNCT
ejpam-3979	258	1	=	=	SYM
ejpam-3979	258	2	ε(x)ε(x	ε(x)ε(x	NOUN
ejpam-3979	258	3	)	)	PUNCT
ejpam-3979	258	4	.	.	PUNCT
ejpam-3979	259	1	if	if	SCONJ
ejpam-3979	259	2	g	g	NOUN
ejpam-3979	259	3	=	=	SYM
ejpam-3979	259	4	x	x	X
ejpam-3979	259	5	and	and	CCONJ
ejpam-3979	259	6	g1	g1	PROPN
ejpam-3979	259	7	=	=	SYM
ejpam-3979	259	8	x2	x2	PROPN
ejpam-3979	259	9	,	,	PUNCT
ejpam-3979	259	10	then	then	ADV
ejpam-3979	259	11	∆(µ(x⊗	∆(µ(x⊗	PROPN
ejpam-3979	259	12	x2	x2	PROPN
ejpam-3979	259	13	)	)	PUNCT
ejpam-3979	259	14	)	)	PUNCT
ejpam-3979	259	15	=	=	SYM
ejpam-3979	259	16	∆(1	∆(1	NOUN
ejpam-3979	259	17	)	)	PUNCT
ejpam-3979	259	18	=	=	PUNCT
ejpam-3979	260	1	1⊗	1⊗	NUM
ejpam-3979	260	2	1	1	NUM
ejpam-3979	260	3	.	.	PUNCT
ejpam-3979	261	1	t.	t.	PROPN
ejpam-3979	261	2	al	al	PROPN
ejpam-3979	261	3	-	-	PUNCT
ejpam-3979	261	4	mutairi	mutairi	PROPN
ejpam-3979	261	5	,	,	PUNCT
ejpam-3979	261	6	m.	m.	NOUN
ejpam-3979	261	7	m.	m.	PROPN
ejpam-3979	261	8	al	al	PROPN
ejpam-3979	261	9	-	-	PUNCT
ejpam-3979	261	10	shomrani	shomrani	PROPN
ejpam-3979	261	11	/	/	SYM
ejpam-3979	261	12	eur	eur	NOUN
ejpam-3979	261	13	.	.	PUNCT
ejpam-3979	262	1	j.	j.	PROPN
ejpam-3979	262	2	pure	pure	PROPN
ejpam-3979	262	3	appl	appl	PROPN
ejpam-3979	262	4	.	.	PROPN
ejpam-3979	262	5	math	math	PROPN
ejpam-3979	262	6	,	,	PUNCT
ejpam-3979	262	7	14	14	NUM
ejpam-3979	262	8	(	(	PUNCT
ejpam-3979	262	9	3	3	NUM
ejpam-3979	262	10	)	)	PUNCT
ejpam-3979	262	11	(	(	PUNCT
ejpam-3979	262	12	2021	2021	NUM
ejpam-3979	262	13	)	)	PUNCT
ejpam-3979	262	14	,	,	PUNCT
ejpam-3979	262	15	816	816	NUM
ejpam-3979	262	16	-	-	SYM
ejpam-3979	262	17	828	828	NUM
ejpam-3979	262	18	824	824	NUM
ejpam-3979	262	19	on	on	ADP
ejpam-3979	262	20	the	the	DET
ejpam-3979	262	21	other	other	ADJ
ejpam-3979	262	22	hand	hand	NOUN
ejpam-3979	262	23	,	,	PUNCT
ejpam-3979	262	24	∆(x	∆(x	PROPN
ejpam-3979	262	25	)	)	PUNCT
ejpam-3979	262	26	·	·	PUNCT
ejpam-3979	262	27	∆(x2	∆(x2	NUM
ejpam-3979	262	28	)	)	PUNCT
ejpam-3979	262	29	=	=	PUNCT
ejpam-3979	262	30	(	(	PUNCT
ejpam-3979	262	31	x⊗	x⊗	NOUN
ejpam-3979	262	32	x	x	X
ejpam-3979	262	33	)	)	PUNCT
ejpam-3979	262	34	·	·	PUNCT
ejpam-3979	263	1	(	(	PUNCT
ejpam-3979	263	2	x2	x2	PROPN
ejpam-3979	263	3	⊗	⊗	PROPN
ejpam-3979	263	4	x2	x2	PROPN
ejpam-3979	263	5	)	)	PUNCT
ejpam-3979	263	6	=	=	PUNCT
ejpam-3979	264	1	1⊗	1⊗	NUM
ejpam-3979	264	2	1	1	NUM
ejpam-3979	264	3	.	.	PUNCT
ejpam-3979	265	1	so	so	ADV
ejpam-3979	265	2	,	,	PUNCT
ejpam-3979	265	3	∆(µ(x⊗	∆(µ(x⊗	PROPN
ejpam-3979	265	4	x2	x2	PROPN
ejpam-3979	265	5	)	)	PUNCT
ejpam-3979	265	6	)	)	PUNCT
ejpam-3979	266	1	=	=	SYM
ejpam-3979	266	2	∆(x	∆(x	NOUN
ejpam-3979	266	3	)	)	PUNCT
ejpam-3979	266	4	·	·	PUNCT
ejpam-3979	266	5	∆(x2	∆(x2	NUM
ejpam-3979	266	6	)	)	PUNCT
ejpam-3979	266	7	.	.	PUNCT
ejpam-3979	267	1	also	also	ADV
ejpam-3979	267	2	,	,	PUNCT
ejpam-3979	267	3	ε(µ(x⊗	ε(µ(x⊗	PROPN
ejpam-3979	267	4	x2	x2	PROPN
ejpam-3979	267	5	)	)	PUNCT
ejpam-3979	267	6	)	)	PUNCT
ejpam-3979	268	1	=	=	SYM
ejpam-3979	268	2	ε(1	ε(1	NOUN
ejpam-3979	268	3	)	)	PUNCT
ejpam-3979	268	4	=	=	SYM
ejpam-3979	269	1	1	1	X
ejpam-3979	269	2	.	.	PUNCT
ejpam-3979	270	1	on	on	ADP
ejpam-3979	270	2	the	the	DET
ejpam-3979	270	3	other	other	ADJ
ejpam-3979	270	4	hand	hand	NOUN
ejpam-3979	270	5	,	,	PUNCT
ejpam-3979	270	6	ε(x)ε(x2	ε(x)ε(x2	NOUN
ejpam-3979	270	7	)	)	PUNCT
ejpam-3979	270	8	=	=	PUNCT
ejpam-3979	271	1	(	(	PUNCT
ejpam-3979	271	2	1	1	NUM
ejpam-3979	271	3	)	)	PUNCT
ejpam-3979	271	4	(	(	PUNCT
ejpam-3979	271	5	1	1	X
ejpam-3979	271	6	)	)	PUNCT
ejpam-3979	272	1	=	=	SYM
ejpam-3979	272	2	1	1	X
ejpam-3979	272	3	.	.	PUNCT
ejpam-3979	273	1	so	so	ADV
ejpam-3979	273	2	,	,	PUNCT
ejpam-3979	273	3	ε(µ(x⊗	ε(µ(x⊗	PROPN
ejpam-3979	273	4	x2	x2	PROPN
ejpam-3979	273	5	)	)	PUNCT
ejpam-3979	273	6	)	)	PUNCT
ejpam-3979	274	1	=	=	SYM
ejpam-3979	274	2	ε(x)ε(x2	ε(x)ε(x2	NOUN
ejpam-3979	274	3	)	)	PUNCT
ejpam-3979	274	4	.	.	PUNCT
ejpam-3979	275	1	if	if	SCONJ
ejpam-3979	275	2	g	g	NOUN
ejpam-3979	275	3	=	=	SYM
ejpam-3979	275	4	1	1	NUM
ejpam-3979	275	5	and	and	CCONJ
ejpam-3979	275	6	g1	g1	PROPN
ejpam-3979	275	7	=	=	SYM
ejpam-3979	275	8	1	1	NUM
ejpam-3979	275	9	,	,	PUNCT
ejpam-3979	275	10	then	then	ADV
ejpam-3979	275	11	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	275	12	1	1	NUM
ejpam-3979	275	13	)	)	PUNCT
ejpam-3979	275	14	)	)	PUNCT
ejpam-3979	275	15	=	=	SYM
ejpam-3979	275	16	∆(1	∆(1	NOUN
ejpam-3979	275	17	)	)	PUNCT
ejpam-3979	275	18	=	=	PUNCT
ejpam-3979	276	1	1⊗	1⊗	NUM
ejpam-3979	276	2	1	1	NUM
ejpam-3979	276	3	.	.	PUNCT
ejpam-3979	277	1	on	on	ADP
ejpam-3979	277	2	the	the	DET
ejpam-3979	277	3	other	other	ADJ
ejpam-3979	277	4	hand	hand	NOUN
ejpam-3979	277	5	,	,	PUNCT
ejpam-3979	277	6	∆(1	∆(1	NOUN
ejpam-3979	277	7	)	)	PUNCT
ejpam-3979	277	8	·	·	PUNCT
ejpam-3979	277	9	∆(1	∆(1	NOUN
ejpam-3979	277	10	)	)	PUNCT
ejpam-3979	277	11	=	=	SYM
ejpam-3979	277	12	(	(	PUNCT
ejpam-3979	277	13	1⊗	1⊗	NUM
ejpam-3979	277	14	1	1	NUM
ejpam-3979	277	15	)	)	PUNCT
ejpam-3979	277	16	·	·	PUNCT
ejpam-3979	277	17	(	(	PUNCT
ejpam-3979	277	18	1⊗	1⊗	NUM
ejpam-3979	277	19	1	1	NUM
ejpam-3979	277	20	)	)	PUNCT
ejpam-3979	277	21	=	=	PUNCT
ejpam-3979	278	1	1⊗	1⊗	NUM
ejpam-3979	278	2	1	1	NUM
ejpam-3979	278	3	.	.	PUNCT
ejpam-3979	279	1	so	so	ADV
ejpam-3979	279	2	,	,	PUNCT
ejpam-3979	279	3	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	279	4	1	1	NUM
ejpam-3979	279	5	)	)	PUNCT
ejpam-3979	279	6	)	)	PUNCT
ejpam-3979	279	7	=	=	SYM
ejpam-3979	279	8	∆(1	∆(1	NOUN
ejpam-3979	279	9	)	)	PUNCT
ejpam-3979	279	10	·	·	PUNCT
ejpam-3979	279	11	∆(1	∆(1	NOUN
ejpam-3979	279	12	)	)	PUNCT
ejpam-3979	279	13	.	.	PUNCT
ejpam-3979	280	1	also	also	ADV
ejpam-3979	280	2	,	,	PUNCT
ejpam-3979	280	3	ε(µ(1⊗	ε(µ(1⊗	PROPN
ejpam-3979	280	4	1	1	NUM
ejpam-3979	280	5	)	)	PUNCT
ejpam-3979	280	6	)	)	PUNCT
ejpam-3979	281	1	=	=	SYM
ejpam-3979	281	2	ε(1	ε(1	NOUN
ejpam-3979	281	3	)	)	PUNCT
ejpam-3979	281	4	=	=	SYM
ejpam-3979	282	1	1	1	X
ejpam-3979	282	2	.	.	PUNCT
ejpam-3979	283	1	on	on	ADP
ejpam-3979	283	2	the	the	DET
ejpam-3979	283	3	other	other	ADJ
ejpam-3979	283	4	hand	hand	NOUN
ejpam-3979	283	5	,	,	PUNCT
ejpam-3979	283	6	ε(1)ε(1	ε(1)ε(1	NOUN
ejpam-3979	283	7	)	)	PUNCT
ejpam-3979	283	8	=	=	PUNCT
ejpam-3979	284	1	(	(	PUNCT
ejpam-3979	284	2	1	1	NUM
ejpam-3979	284	3	)	)	PUNCT
ejpam-3979	284	4	(	(	PUNCT
ejpam-3979	284	5	1	1	X
ejpam-3979	284	6	)	)	PUNCT
ejpam-3979	284	7	=	=	SYM
ejpam-3979	285	1	1	1	X
ejpam-3979	285	2	.	.	PUNCT
ejpam-3979	286	1	so	so	ADV
ejpam-3979	286	2	,	,	PUNCT
ejpam-3979	286	3	ε(µ(1⊗	ε(µ(1⊗	PROPN
ejpam-3979	286	4	1	1	NUM
ejpam-3979	286	5	)	)	PUNCT
ejpam-3979	286	6	)	)	PUNCT
ejpam-3979	286	7	=	=	SYM
ejpam-3979	286	8	ε(1)ε(1	ε(1)ε(1	NOUN
ejpam-3979	286	9	)	)	PUNCT
ejpam-3979	286	10	.	.	PUNCT
ejpam-3979	287	1	if	if	SCONJ
ejpam-3979	287	2	g	g	NOUN
ejpam-3979	287	3	=	=	SYM
ejpam-3979	287	4	1	1	NUM
ejpam-3979	287	5	and	and	CCONJ
ejpam-3979	287	6	g1	g1	PROPN
ejpam-3979	287	7	=	=	SYM
ejpam-3979	288	1	x	x	X
ejpam-3979	288	2	,	,	PUNCT
ejpam-3979	288	3	then	then	ADV
ejpam-3979	288	4	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	288	5	x	x	NOUN
ejpam-3979	288	6	)	)	PUNCT
ejpam-3979	288	7	)	)	PUNCT
ejpam-3979	289	1	=	=	SYM
ejpam-3979	289	2	∆(x	∆(x	NOUN
ejpam-3979	289	3	)	)	PUNCT
ejpam-3979	289	4	=	=	PRON
ejpam-3979	289	5	x⊗	x⊗	PROPN
ejpam-3979	289	6	x.	x.	NOUN
ejpam-3979	289	7	on	on	ADP
ejpam-3979	289	8	the	the	DET
ejpam-3979	289	9	other	other	ADJ
ejpam-3979	289	10	hand	hand	NOUN
ejpam-3979	289	11	,	,	PUNCT
ejpam-3979	289	12	∆(1	∆(1	NOUN
ejpam-3979	289	13	)	)	PUNCT
ejpam-3979	289	14	·	·	PUNCT
ejpam-3979	289	15	∆(x	∆(x	NOUN
ejpam-3979	289	16	)	)	PUNCT
ejpam-3979	289	17	=	=	SYM
ejpam-3979	290	1	(	(	PUNCT
ejpam-3979	290	2	1⊗	1⊗	NUM
ejpam-3979	290	3	1	1	NUM
ejpam-3979	290	4	)	)	PUNCT
ejpam-3979	290	5	·	·	PUNCT
ejpam-3979	290	6	(	(	PUNCT
ejpam-3979	290	7	x⊗	x⊗	NOUN
ejpam-3979	290	8	x	x	X
ejpam-3979	290	9	)	)	PUNCT
ejpam-3979	290	10	=	=	PUNCT
ejpam-3979	291	1	x⊗	x⊗	PROPN
ejpam-3979	291	2	x.	x.	NOUN
ejpam-3979	292	1	so	so	ADV
ejpam-3979	292	2	,	,	PUNCT
ejpam-3979	292	3	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	292	4	x	x	NOUN
ejpam-3979	292	5	)	)	PUNCT
ejpam-3979	292	6	)	)	PUNCT
ejpam-3979	292	7	=	=	SYM
ejpam-3979	292	8	∆(1	∆(1	NOUN
ejpam-3979	292	9	)	)	PUNCT
ejpam-3979	292	10	·	·	PUNCT
ejpam-3979	292	11	∆(x	∆(x	NOUN
ejpam-3979	292	12	)	)	PUNCT
ejpam-3979	292	13	.	.	PUNCT
ejpam-3979	293	1	also	also	ADV
ejpam-3979	293	2	,	,	PUNCT
ejpam-3979	293	3	ε(µ(1⊗	ε(µ(1⊗	ADJ
ejpam-3979	293	4	x	x	X
ejpam-3979	293	5	)	)	PUNCT
ejpam-3979	293	6	)	)	PUNCT
ejpam-3979	293	7	=	=	SYM
ejpam-3979	293	8	ε(x	ε(x	X
ejpam-3979	293	9	)	)	PUNCT
ejpam-3979	293	10	=	=	SYM
ejpam-3979	293	11	1	1	X
ejpam-3979	293	12	.	.	PUNCT
ejpam-3979	294	1	on	on	ADP
ejpam-3979	294	2	the	the	DET
ejpam-3979	294	3	other	other	ADJ
ejpam-3979	294	4	hand	hand	NOUN
ejpam-3979	294	5	,	,	PUNCT
ejpam-3979	294	6	ε(1)ε(x	ε(1)ε(x	NOUN
ejpam-3979	294	7	)	)	PUNCT
ejpam-3979	295	1	=	=	SYM
ejpam-3979	295	2	(	(	PUNCT
ejpam-3979	295	3	1	1	NUM
ejpam-3979	295	4	)	)	PUNCT
ejpam-3979	295	5	(	(	PUNCT
ejpam-3979	295	6	1	1	X
ejpam-3979	295	7	)	)	PUNCT
ejpam-3979	295	8	=	=	SYM
ejpam-3979	295	9	1	1	X
ejpam-3979	295	10	.	.	PUNCT
ejpam-3979	296	1	so	so	ADV
ejpam-3979	296	2	,	,	PUNCT
ejpam-3979	296	3	ε(µ(1⊗	ε(µ(1⊗	PUNCT
ejpam-3979	296	4	x	x	X
ejpam-3979	296	5	)	)	PUNCT
ejpam-3979	296	6	=	=	PUNCT
ejpam-3979	296	7	ε(1)ε(x	ε(1)ε(x	NOUN
ejpam-3979	296	8	)	)	PUNCT
ejpam-3979	296	9	if	if	SCONJ
ejpam-3979	296	10	g	g	NOUN
ejpam-3979	296	11	=	=	SYM
ejpam-3979	296	12	1	1	NUM
ejpam-3979	296	13	and	and	CCONJ
ejpam-3979	296	14	g1	g1	PROPN
ejpam-3979	296	15	=	=	SYM
ejpam-3979	296	16	x2	x2	PROPN
ejpam-3979	296	17	,	,	PUNCT
ejpam-3979	296	18	then	then	ADV
ejpam-3979	296	19	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	296	20	x2	x2	NOUN
ejpam-3979	296	21	)	)	PUNCT
ejpam-3979	296	22	)	)	PUNCT
ejpam-3979	296	23	=	=	SYM
ejpam-3979	296	24	∆(x2	∆(x2	NUM
ejpam-3979	296	25	)	)	PUNCT
ejpam-3979	296	26	=	=	SYM
ejpam-3979	297	1	x2	x2	PROPN
ejpam-3979	297	2	⊗	⊗	NUM
ejpam-3979	297	3	x2	x2	PROPN
ejpam-3979	297	4	.	.	PUNCT
ejpam-3979	298	1	on	on	ADP
ejpam-3979	298	2	the	the	DET
ejpam-3979	298	3	other	other	ADJ
ejpam-3979	298	4	hand	hand	NOUN
ejpam-3979	298	5	,	,	PUNCT
ejpam-3979	298	6	∆(1	∆(1	NOUN
ejpam-3979	298	7	)	)	PUNCT
ejpam-3979	298	8	·	·	PUNCT
ejpam-3979	298	9	∆(x2	∆(x2	NUM
ejpam-3979	298	10	)	)	PUNCT
ejpam-3979	298	11	=	=	SYM
ejpam-3979	298	12	(	(	PUNCT
ejpam-3979	298	13	1⊗	1⊗	NUM
ejpam-3979	298	14	1	1	NUM
ejpam-3979	298	15	)	)	PUNCT
ejpam-3979	298	16	·	·	PUNCT
ejpam-3979	299	1	(	(	PUNCT
ejpam-3979	299	2	x2	x2	PROPN
ejpam-3979	299	3	⊗	⊗	PROPN
ejpam-3979	299	4	x2	x2	PROPN
ejpam-3979	299	5	)	)	PUNCT
ejpam-3979	300	1	=	=	SYM
ejpam-3979	300	2	x2	x2	PROPN
ejpam-3979	301	1	⊗	⊗	NUM
ejpam-3979	301	2	x2	x2	PROPN
ejpam-3979	301	3	.	.	PUNCT
ejpam-3979	302	1	so	so	ADV
ejpam-3979	302	2	,	,	PUNCT
ejpam-3979	302	3	∆(µ(1⊗	∆(µ(1⊗	PROPN
ejpam-3979	302	4	x2	x2	NOUN
ejpam-3979	302	5	)	)	PUNCT
ejpam-3979	302	6	)	)	PUNCT
ejpam-3979	303	1	=	=	SYM
ejpam-3979	303	2	∆(1	∆(1	NOUN
ejpam-3979	303	3	)	)	PUNCT
ejpam-3979	303	4	·	·	PUNCT
ejpam-3979	303	5	∆(x2	∆(x2	NUM
ejpam-3979	303	6	)	)	PUNCT
ejpam-3979	303	7	.	.	PUNCT
ejpam-3979	304	1	also	also	ADV
ejpam-3979	304	2	,	,	PUNCT
ejpam-3979	304	3	ε(µ(1⊗	ε(µ(1⊗	PROPN
ejpam-3979	304	4	x2	x2	PROPN
ejpam-3979	304	5	)	)	PUNCT
ejpam-3979	304	6	)	)	PUNCT
ejpam-3979	305	1	=	=	SYM
ejpam-3979	305	2	ε(x2	ε(x2	NOUN
ejpam-3979	305	3	)	)	PUNCT
ejpam-3979	305	4	=	=	SYM
ejpam-3979	306	1	1	1	X
ejpam-3979	306	2	.	.	PUNCT
ejpam-3979	306	3	t.	t.	PROPN
ejpam-3979	306	4	al	al	PROPN
ejpam-3979	306	5	-	-	PUNCT
ejpam-3979	306	6	mutairi	mutairi	PROPN
ejpam-3979	306	7	,	,	PUNCT
ejpam-3979	306	8	m.	m.	NOUN
ejpam-3979	306	9	m.	m.	PROPN
ejpam-3979	306	10	al	al	PROPN
ejpam-3979	306	11	-	-	PUNCT
ejpam-3979	306	12	shomrani	shomrani	PROPN
ejpam-3979	306	13	/	/	SYM
ejpam-3979	306	14	eur	eur	NOUN
ejpam-3979	306	15	.	.	PUNCT
ejpam-3979	307	1	j.	j.	PROPN
ejpam-3979	307	2	pure	pure	PROPN
ejpam-3979	307	3	appl	appl	PROPN
ejpam-3979	307	4	.	.	PROPN
ejpam-3979	307	5	math	math	PROPN
ejpam-3979	307	6	,	,	PUNCT
ejpam-3979	307	7	14	14	NUM
ejpam-3979	307	8	(	(	PUNCT
ejpam-3979	307	9	3	3	NUM
ejpam-3979	307	10	)	)	PUNCT
ejpam-3979	307	11	(	(	PUNCT
ejpam-3979	307	12	2021	2021	NUM
ejpam-3979	307	13	)	)	PUNCT
ejpam-3979	307	14	,	,	PUNCT
ejpam-3979	307	15	816	816	NUM
ejpam-3979	307	16	-	-	SYM
ejpam-3979	307	17	828	828	NUM
ejpam-3979	307	18	825	825	NUM
ejpam-3979	307	19	on	on	ADP
ejpam-3979	307	20	the	the	DET
ejpam-3979	307	21	other	other	ADJ
ejpam-3979	307	22	hand	hand	NOUN
ejpam-3979	307	23	,	,	PUNCT
ejpam-3979	307	24	ε(1)ε(x2	ε(1)ε(x2	NOUN
ejpam-3979	307	25	)	)	PUNCT
ejpam-3979	307	26	=	=	PUNCT
ejpam-3979	307	27	(	(	PUNCT
ejpam-3979	307	28	1	1	NUM
ejpam-3979	307	29	)	)	PUNCT
ejpam-3979	307	30	(	(	PUNCT
ejpam-3979	307	31	1	1	X
ejpam-3979	307	32	)	)	PUNCT
ejpam-3979	307	33	=	=	SYM
ejpam-3979	308	1	1	1	X
ejpam-3979	308	2	.	.	PUNCT
ejpam-3979	309	1	so	so	ADV
ejpam-3979	309	2	,	,	PUNCT
ejpam-3979	309	3	ε(µ(1⊗	ε(µ(1⊗	PROPN
ejpam-3979	309	4	x2	x2	ADJ
ejpam-3979	309	5	)	)	PUNCT
ejpam-3979	309	6	=	=	SYM
ejpam-3979	309	7	ε(1)ε(x2	ε(1)ε(x2	PROPN
ejpam-3979	309	8	)	)	PUNCT
ejpam-3979	309	9	.	.	PUNCT
ejpam-3979	310	1	if	if	SCONJ
ejpam-3979	310	2	g	g	PROPN
ejpam-3979	310	3	=	=	SYM
ejpam-3979	310	4	x2	x2	PROPN
ejpam-3979	310	5	and	and	CCONJ
ejpam-3979	310	6	g1	g1	PROPN
ejpam-3979	310	7	=	=	SYM
ejpam-3979	310	8	1	1	NUM
ejpam-3979	310	9	,	,	PUNCT
ejpam-3979	310	10	then	then	ADV
ejpam-3979	310	11	∆(µ(x2	∆(µ(x2	PROPN
ejpam-3979	310	12	⊗	⊗	PROPN
ejpam-3979	310	13	1	1	NUM
ejpam-3979	310	14	)	)	PUNCT
ejpam-3979	310	15	)	)	PUNCT
ejpam-3979	310	16	=	=	SYM
ejpam-3979	310	17	∆(x2	∆(x2	NUM
ejpam-3979	310	18	)	)	PUNCT
ejpam-3979	310	19	=	=	SYM
ejpam-3979	311	1	x2	x2	PROPN
ejpam-3979	311	2	⊗	⊗	NUM
ejpam-3979	311	3	x2	x2	PROPN
ejpam-3979	311	4	.	.	PUNCT
ejpam-3979	312	1	on	on	ADP
ejpam-3979	312	2	the	the	DET
ejpam-3979	312	3	other	other	ADJ
ejpam-3979	312	4	hand	hand	NOUN
ejpam-3979	312	5	,	,	PUNCT
ejpam-3979	312	6	∆(x2	∆(x2	NUM
ejpam-3979	312	7	)	)	PUNCT
ejpam-3979	312	8	·	·	PUNCT
ejpam-3979	312	9	∆(1	∆(1	NOUN
ejpam-3979	312	10	)	)	PUNCT
ejpam-3979	312	11	=	=	SYM
ejpam-3979	313	1	(	(	PUNCT
ejpam-3979	313	2	x2	x2	PROPN
ejpam-3979	313	3	⊗	⊗	PROPN
ejpam-3979	313	4	x2	x2	PROPN
ejpam-3979	313	5	)	)	PUNCT
ejpam-3979	313	6	·	·	PUNCT
ejpam-3979	314	1	(	(	PUNCT
ejpam-3979	314	2	1⊗	1⊗	NUM
ejpam-3979	314	3	1	1	NUM
ejpam-3979	314	4	)	)	PUNCT
ejpam-3979	314	5	=	=	SYM
ejpam-3979	315	1	x2	x2	PROPN
ejpam-3979	315	2	⊗	⊗	NUM
ejpam-3979	315	3	x2	x2	PROPN
ejpam-3979	315	4	.	.	PUNCT
ejpam-3979	316	1	so	so	ADV
ejpam-3979	316	2	,	,	PUNCT
ejpam-3979	316	3	∆(µ(x2	∆(µ(x2	PROPN
ejpam-3979	316	4	⊗	⊗	PROPN
ejpam-3979	316	5	1	1	NUM
ejpam-3979	316	6	)	)	PUNCT
ejpam-3979	316	7	)	)	PUNCT
ejpam-3979	317	1	=	=	SYM
ejpam-3979	317	2	∆(x2	∆(x2	NUM
ejpam-3979	317	3	)	)	PUNCT
ejpam-3979	317	4	·	·	PUNCT
ejpam-3979	317	5	∆(1	∆(1	NOUN
ejpam-3979	317	6	)	)	PUNCT
ejpam-3979	317	7	.	.	PUNCT
ejpam-3979	318	1	also	also	ADV
ejpam-3979	318	2	,	,	PUNCT
ejpam-3979	318	3	ε(µ(x2	ε(µ(x2	VERB
ejpam-3979	318	4	⊗	⊗	PROPN
ejpam-3979	318	5	1	1	NUM
ejpam-3979	318	6	)	)	PUNCT
ejpam-3979	318	7	)	)	PUNCT
ejpam-3979	319	1	=	=	SYM
ejpam-3979	319	2	ε(x2	ε(x2	NOUN
ejpam-3979	319	3	)	)	PUNCT
ejpam-3979	319	4	=	=	SYM
ejpam-3979	320	1	1	1	X
ejpam-3979	320	2	.	.	PUNCT
ejpam-3979	321	1	on	on	ADP
ejpam-3979	321	2	the	the	DET
ejpam-3979	321	3	other	other	ADJ
ejpam-3979	321	4	hand	hand	NOUN
ejpam-3979	321	5	,	,	PUNCT
ejpam-3979	321	6	ε(x2)ε(1	ε(x2)ε(1	PROPN
ejpam-3979	321	7	)	)	PUNCT
ejpam-3979	321	8	=	=	PUNCT
ejpam-3979	322	1	(	(	PUNCT
ejpam-3979	322	2	1	1	NUM
ejpam-3979	322	3	)	)	PUNCT
ejpam-3979	322	4	(	(	PUNCT
ejpam-3979	322	5	1	1	X
ejpam-3979	322	6	)	)	PUNCT
ejpam-3979	322	7	=	=	SYM
ejpam-3979	323	1	1	1	X
ejpam-3979	323	2	.	.	PUNCT
ejpam-3979	324	1	so	so	ADV
ejpam-3979	324	2	,	,	PUNCT
ejpam-3979	324	3	ε(µ(x2	ε(µ(x2	VERB
ejpam-3979	324	4	⊗	⊗	PROPN
ejpam-3979	324	5	1	1	NUM
ejpam-3979	324	6	)	)	PUNCT
ejpam-3979	324	7	=	=	PUNCT
ejpam-3979	325	1	ε(x2)ε(1	ε(x2)ε(1	PROPN
ejpam-3979	325	2	)	)	PUNCT
ejpam-3979	325	3	.	.	PUNCT
ejpam-3979	326	1	if	if	SCONJ
ejpam-3979	326	2	g	g	PROPN
ejpam-3979	326	3	=	=	SYM
ejpam-3979	326	4	x2	x2	PROPN
ejpam-3979	326	5	and	and	CCONJ
ejpam-3979	326	6	g1	g1	PROPN
ejpam-3979	326	7	=	=	SYM
ejpam-3979	327	1	x	x	NOUN
ejpam-3979	327	2	,	,	PUNCT
ejpam-3979	327	3	then	then	ADV
ejpam-3979	327	4	∆(µ(x2	∆(µ(x2	NOUN
ejpam-3979	327	5	⊗	⊗	PROPN
ejpam-3979	327	6	x	x	NOUN
ejpam-3979	327	7	)	)	PUNCT
ejpam-3979	327	8	)	)	PUNCT
ejpam-3979	327	9	=	=	SYM
ejpam-3979	327	10	∆(1	∆(1	NOUN
ejpam-3979	327	11	)	)	PUNCT
ejpam-3979	327	12	=	=	PUNCT
ejpam-3979	328	1	1⊗	1⊗	NUM
ejpam-3979	328	2	1	1	NUM
ejpam-3979	328	3	.	.	PUNCT
ejpam-3979	329	1	on	on	ADP
ejpam-3979	329	2	the	the	DET
ejpam-3979	329	3	other	other	ADJ
ejpam-3979	329	4	hand	hand	NOUN
ejpam-3979	329	5	,	,	PUNCT
ejpam-3979	329	6	∆(x2	∆(x2	NUM
ejpam-3979	329	7	)	)	PUNCT
ejpam-3979	329	8	·	·	PUNCT
ejpam-3979	329	9	∆(x	∆(x	NOUN
ejpam-3979	329	10	)	)	PUNCT
ejpam-3979	329	11	=	=	SYM
ejpam-3979	330	1	(	(	PUNCT
ejpam-3979	330	2	x2	x2	PROPN
ejpam-3979	330	3	⊗	⊗	PROPN
ejpam-3979	330	4	x2	x2	PROPN
ejpam-3979	330	5	)	)	PUNCT
ejpam-3979	330	6	·	·	PUNCT
ejpam-3979	330	7	(	(	PUNCT
ejpam-3979	330	8	x⊗	x⊗	NOUN
ejpam-3979	330	9	x	x	X
ejpam-3979	330	10	)	)	PUNCT
ejpam-3979	330	11	=	=	PUNCT
ejpam-3979	331	1	1⊗	1⊗	NUM
ejpam-3979	331	2	1	1	NUM
ejpam-3979	331	3	.	.	PUNCT
ejpam-3979	332	1	so	so	ADV
ejpam-3979	332	2	,	,	PUNCT
ejpam-3979	332	3	∆(µ(x2	∆(µ(x2	PROPN
ejpam-3979	332	4	⊗	⊗	PROPN
ejpam-3979	332	5	x	x	NOUN
ejpam-3979	332	6	)	)	PUNCT
ejpam-3979	332	7	)	)	PUNCT
ejpam-3979	332	8	=	=	SYM
ejpam-3979	332	9	∆(x2	∆(x2	NUM
ejpam-3979	332	10	)	)	PUNCT
ejpam-3979	332	11	·	·	PUNCT
ejpam-3979	332	12	∆(x	∆(x	NOUN
ejpam-3979	332	13	)	)	PUNCT
ejpam-3979	332	14	.	.	PUNCT
ejpam-3979	333	1	also	also	ADV
ejpam-3979	333	2	,	,	PUNCT
ejpam-3979	333	3	ε(µ(x2	ε(µ(x2	VERB
ejpam-3979	333	4	⊗	⊗	PROPN
ejpam-3979	333	5	x	x	X
ejpam-3979	333	6	)	)	PUNCT
ejpam-3979	333	7	)	)	PUNCT
ejpam-3979	334	1	=	=	SYM
ejpam-3979	334	2	ε(1	ε(1	NOUN
ejpam-3979	334	3	)	)	PUNCT
ejpam-3979	334	4	=	=	SYM
ejpam-3979	335	1	1	1	X
ejpam-3979	335	2	.	.	PUNCT
ejpam-3979	336	1	on	on	ADP
ejpam-3979	336	2	the	the	DET
ejpam-3979	336	3	other	other	ADJ
ejpam-3979	336	4	hand	hand	NOUN
ejpam-3979	336	5	,	,	PUNCT
ejpam-3979	336	6	ε(x2)ε(x	ε(x2)ε(x	NOUN
ejpam-3979	336	7	)	)	PUNCT
ejpam-3979	336	8	=	=	SYM
ejpam-3979	336	9	(	(	PUNCT
ejpam-3979	336	10	1	1	NUM
ejpam-3979	336	11	)	)	PUNCT
ejpam-3979	336	12	(	(	PUNCT
ejpam-3979	336	13	1	1	X
ejpam-3979	336	14	)	)	PUNCT
ejpam-3979	336	15	=	=	SYM
ejpam-3979	337	1	1	1	X
ejpam-3979	337	2	.	.	PUNCT
ejpam-3979	338	1	so	so	ADV
ejpam-3979	338	2	,	,	PUNCT
ejpam-3979	338	3	ε(µ(x2	ε(µ(x2	VERB
ejpam-3979	338	4	⊗	⊗	PROPN
ejpam-3979	338	5	x	x	NOUN
ejpam-3979	338	6	)	)	PUNCT
ejpam-3979	338	7	=	=	SYM
ejpam-3979	338	8	ε(x2)ε(x	ε(x2)ε(x	NOUN
ejpam-3979	338	9	)	)	PUNCT
ejpam-3979	338	10	.	.	PUNCT
ejpam-3979	339	1	if	if	SCONJ
ejpam-3979	339	2	g	g	PROPN
ejpam-3979	339	3	=	=	SYM
ejpam-3979	339	4	x2	x2	PROPN
ejpam-3979	339	5	and	and	CCONJ
ejpam-3979	339	6	g1	g1	PROPN
ejpam-3979	339	7	=	=	SYM
ejpam-3979	339	8	x2	x2	PROPN
ejpam-3979	339	9	,	,	PUNCT
ejpam-3979	339	10	then	then	ADV
ejpam-3979	339	11	∆(µ(x2	∆(µ(x2	NOUN
ejpam-3979	339	12	⊗	⊗	PROPN
ejpam-3979	339	13	x2	x2	PROPN
ejpam-3979	339	14	)	)	PUNCT
ejpam-3979	339	15	)	)	PUNCT
ejpam-3979	340	1	=	=	SYM
ejpam-3979	340	2	∆(x	∆(x	NOUN
ejpam-3979	340	3	)	)	PUNCT
ejpam-3979	340	4	=	=	PRON
ejpam-3979	340	5	x⊗	x⊗	PROPN
ejpam-3979	340	6	x.	x.	NOUN
ejpam-3979	340	7	on	on	ADP
ejpam-3979	340	8	the	the	DET
ejpam-3979	340	9	other	other	ADJ
ejpam-3979	340	10	hand	hand	NOUN
ejpam-3979	340	11	,	,	PUNCT
ejpam-3979	340	12	∆(x2	∆(x2	NUM
ejpam-3979	340	13	)	)	PUNCT
ejpam-3979	340	14	·	·	PUNCT
ejpam-3979	340	15	∆(x2	∆(x2	NUM
ejpam-3979	340	16	)	)	PUNCT
ejpam-3979	340	17	=	=	PUNCT
ejpam-3979	341	1	(	(	PUNCT
ejpam-3979	341	2	x2	x2	PROPN
ejpam-3979	341	3	⊗	⊗	PROPN
ejpam-3979	341	4	x2	x2	PROPN
ejpam-3979	341	5	)	)	PUNCT
ejpam-3979	341	6	·	·	PUNCT
ejpam-3979	342	1	(	(	PUNCT
ejpam-3979	342	2	x2	x2	PROPN
ejpam-3979	342	3	⊗	⊗	PROPN
ejpam-3979	342	4	x2	x2	PROPN
ejpam-3979	342	5	)	)	PUNCT
ejpam-3979	343	1	=	=	PUNCT
ejpam-3979	343	2	x⊗	x⊗	PROPN
ejpam-3979	343	3	x.	x.	PUNCT
ejpam-3979	344	1	so	so	ADV
ejpam-3979	344	2	,	,	PUNCT
ejpam-3979	344	3	∆(µ(x2	∆(µ(x2	PROPN
ejpam-3979	344	4	⊗	⊗	PROPN
ejpam-3979	344	5	x2	x2	PROPN
ejpam-3979	344	6	)	)	PUNCT
ejpam-3979	344	7	)	)	PUNCT
ejpam-3979	345	1	=	=	SYM
ejpam-3979	345	2	∆(x2	∆(x2	NUM
ejpam-3979	345	3	)	)	PUNCT
ejpam-3979	345	4	·	·	PUNCT
ejpam-3979	345	5	∆(x2	∆(x2	NUM
ejpam-3979	345	6	)	)	PUNCT
ejpam-3979	345	7	.	.	PUNCT
ejpam-3979	346	1	also	also	ADV
ejpam-3979	346	2	,	,	PUNCT
ejpam-3979	346	3	ε(µ(x2	ε(µ(x2	PROPN
ejpam-3979	346	4	⊗	⊗	PROPN
ejpam-3979	346	5	x2	x2	PROPN
ejpam-3979	346	6	)	)	PUNCT
ejpam-3979	346	7	)	)	PUNCT
ejpam-3979	347	1	=	=	SYM
ejpam-3979	347	2	ε(x	ε(x	X
ejpam-3979	347	3	)	)	PUNCT
ejpam-3979	347	4	=	=	SYM
ejpam-3979	347	5	1	1	X
ejpam-3979	347	6	.	.	PUNCT
ejpam-3979	348	1	on	on	ADP
ejpam-3979	348	2	the	the	DET
ejpam-3979	348	3	other	other	ADJ
ejpam-3979	348	4	hand	hand	NOUN
ejpam-3979	348	5	,	,	PUNCT
ejpam-3979	348	6	ε(x2)ε(x2	ε(x2)ε(x2	NOUN
ejpam-3979	348	7	)	)	PUNCT
ejpam-3979	348	8	=	=	PUNCT
ejpam-3979	349	1	(	(	PUNCT
ejpam-3979	349	2	1	1	NUM
ejpam-3979	349	3	)	)	PUNCT
ejpam-3979	349	4	(	(	PUNCT
ejpam-3979	349	5	1	1	X
ejpam-3979	349	6	)	)	PUNCT
ejpam-3979	349	7	=	=	SYM
ejpam-3979	350	1	1	1	X
ejpam-3979	350	2	.	.	PUNCT
ejpam-3979	351	1	so	so	ADV
ejpam-3979	351	2	,	,	PUNCT
ejpam-3979	351	3	ε(µ(x2	ε(µ(x2	PROPN
ejpam-3979	351	4	⊗	⊗	PROPN
ejpam-3979	351	5	x2	x2	PROPN
ejpam-3979	351	6	)	)	PUNCT
ejpam-3979	351	7	=	=	SYM
ejpam-3979	351	8	ε(x2)ε(x2	ε(x2)ε(x2	PROPN
ejpam-3979	351	9	)	)	PUNCT
ejpam-3979	351	10	.	.	PUNCT
ejpam-3979	352	1	thus	thus	ADV
ejpam-3979	352	2	,	,	PUNCT
ejpam-3979	352	3	(	(	PUNCT
ejpam-3979	352	4	h	h	NOUN
ejpam-3979	352	5	,	,	PUNCT
ejpam-3979	352	6	µ	µ	NOUN
ejpam-3979	352	7	,	,	PUNCT
ejpam-3979	352	8	λ,∆	λ,∆	NUM
ejpam-3979	352	9	,	,	PUNCT
ejpam-3979	352	10	ε	ε	PROPN
ejpam-3979	352	11	)	)	PUNCT
ejpam-3979	352	12	is	be	AUX
ejpam-3979	352	13	an	an	DET
ejpam-3979	352	14	r	r	NOUN
ejpam-3979	352	15	-	-	PUNCT
ejpam-3979	352	16	bialgebra	bialgebra	NOUN
ejpam-3979	352	17	.	.	PUNCT
ejpam-3979	353	1	t.	t.	PROPN
ejpam-3979	353	2	al	al	PROPN
ejpam-3979	353	3	-	-	PUNCT
ejpam-3979	353	4	mutairi	mutairi	PROPN
ejpam-3979	353	5	,	,	PUNCT
ejpam-3979	353	6	m.	m.	NOUN
ejpam-3979	353	7	m.	m.	PROPN
ejpam-3979	353	8	al	al	PROPN
ejpam-3979	353	9	-	-	PUNCT
ejpam-3979	353	10	shomrani	shomrani	PROPN
ejpam-3979	353	11	/	/	SYM
ejpam-3979	353	12	eur	eur	NOUN
ejpam-3979	353	13	.	.	PUNCT
ejpam-3979	354	1	j.	j.	PROPN
ejpam-3979	354	2	pure	pure	PROPN
ejpam-3979	354	3	appl	appl	PROPN
ejpam-3979	354	4	.	.	PROPN
ejpam-3979	354	5	math	math	PROPN
ejpam-3979	354	6	,	,	PUNCT
ejpam-3979	354	7	14	14	NUM
ejpam-3979	354	8	(	(	PUNCT
ejpam-3979	354	9	3	3	NUM
ejpam-3979	354	10	)	)	PUNCT
ejpam-3979	354	11	(	(	PUNCT
ejpam-3979	354	12	2021	2021	NUM
ejpam-3979	354	13	)	)	PUNCT
ejpam-3979	354	14	,	,	PUNCT
ejpam-3979	354	15	816	816	NUM
ejpam-3979	354	16	-	-	SYM
ejpam-3979	354	17	828	828	NUM
ejpam-3979	354	18	826	826	NUM
ejpam-3979	354	19	finally	finally	ADV
ejpam-3979	354	20	,	,	PUNCT
ejpam-3979	354	21	to	to	PART
ejpam-3979	354	22	show	show	VERB
ejpam-3979	354	23	that	that	SCONJ
ejpam-3979	354	24	(	(	PUNCT
ejpam-3979	354	25	h	h	NOUN
ejpam-3979	354	26	,	,	PUNCT
ejpam-3979	354	27	µ	µ	NOUN
ejpam-3979	354	28	,	,	PUNCT
ejpam-3979	354	29	λ,∆	λ,∆	NUM
ejpam-3979	354	30	,	,	PUNCT
ejpam-3979	354	31	ε	ε	PROPN
ejpam-3979	354	32	,	,	PUNCT
ejpam-3979	354	33	s	s	PART
ejpam-3979	354	34	)	)	PUNCT
ejpam-3979	354	35	is	be	AUX
ejpam-3979	354	36	an	an	DET
ejpam-3979	354	37	r	r	NOUN
ejpam-3979	354	38	-	-	PUNCT
ejpam-3979	354	39	hopf	hopf	ADJ
ejpam-3979	354	40	algebra	algebra	NOUN
ejpam-3979	354	41	,	,	PUNCT
ejpam-3979	354	42	we	we	PRON
ejpam-3979	354	43	define	define	VERB
ejpam-3979	354	44	the	the	DET
ejpam-3979	354	45	antipode	antipode	NOUN
ejpam-3979	354	46	map	map	NOUN
ejpam-3979	354	47	s	s	PART
ejpam-3979	354	48	:	:	PUNCT
ejpam-3979	354	49	h	h	NOUN
ejpam-3979	354	50	7−→	7−→	NOUN
ejpam-3979	354	51	h	h	NOUN
ejpam-3979	354	52	,	,	PUNCT
ejpam-3979	354	53	for	for	ADP
ejpam-3979	354	54	all	all	PRON
ejpam-3979	354	55	g	g	PROPN
ejpam-3979	354	56	∈	∈	PROPN
ejpam-3979	354	57	g	g	NOUN
ejpam-3979	354	58	,	,	PUNCT
ejpam-3979	354	59	by	by	ADP
ejpam-3979	354	60	s(g	s(g	PROPN
ejpam-3979	354	61	)	)	PUNCT
ejpam-3979	354	62	=	=	VERB
ejpam-3979	355	1	g−1	g−1	PROPN
ejpam-3979	355	2	and	and	CCONJ
ejpam-3979	355	3	we	we	PRON
ejpam-3979	355	4	check	check	VERB
ejpam-3979	355	5	that	that	SCONJ
ejpam-3979	355	6	s	s	AUX
ejpam-3979	355	7	satisfies	satisfie	NOUN
ejpam-3979	355	8	the	the	DET
ejpam-3979	355	9	antipode	antipode	NOUN
ejpam-3979	355	10	property	property	NOUN
ejpam-3979	355	11	,	,	PUNCT
ejpam-3979	355	12	i.e.	i.e.	X
ejpam-3979	355	13	µ(i	µ(i	PROPN
ejpam-3979	355	14	⊗	⊗	PROPN
ejpam-3979	355	15	s)∆(g	s)∆(g	PROPN
ejpam-3979	355	16	)	)	PUNCT
ejpam-3979	355	17	=	=	SYM
ejpam-3979	355	18	µ(s	µ(s	PROPN
ejpam-3979	355	19	⊗	⊗	PROPN
ejpam-3979	355	20	i)∆(g	i)∆(g	PROPN
ejpam-3979	355	21	)	)	PUNCT
ejpam-3979	355	22	for	for	SCONJ
ejpam-3979	355	23	all	all	PRON
ejpam-3979	355	24	g	g	PROPN
ejpam-3979	355	25	∈	∈	PROPN
ejpam-3979	355	26	g	g	PROPN
ejpam-3979	355	27	which	which	PRON
ejpam-3979	355	28	we	we	PRON
ejpam-3979	355	29	do	do	VERB
ejpam-3979	355	30	as	as	SCONJ
ejpam-3979	355	31	follows	follow	VERB
ejpam-3979	355	32	:	:	PUNCT
ejpam-3979	355	33	if	if	SCONJ
ejpam-3979	355	34	g	g	PROPN
ejpam-3979	355	35	=	=	SYM
ejpam-3979	355	36	1	1	NUM
ejpam-3979	355	37	,	,	PUNCT
ejpam-3979	355	38	then	then	ADV
ejpam-3979	355	39	µ(i	µ(i	PROPN
ejpam-3979	355	40	⊗	⊗	PROPN
ejpam-3979	355	41	s)∆(1	s)∆(1	NOUN
ejpam-3979	355	42	)	)	PUNCT
ejpam-3979	355	43	=	=	PUNCT
ejpam-3979	355	44	µ(i	µ(i	PROPN
ejpam-3979	355	45	⊗	⊗	PROPN
ejpam-3979	355	46	s)(1	s)(1	NUM
ejpam-3979	355	47	⊗	⊗	NUM
ejpam-3979	355	48	1	1	NUM
ejpam-3979	355	49	)	)	PUNCT
ejpam-3979	355	50	=	=	SYM
ejpam-3979	356	1	1	1	X
ejpam-3979	356	2	.	.	PUNCT
ejpam-3979	357	1	on	on	ADP
ejpam-3979	357	2	the	the	DET
ejpam-3979	357	3	other	other	ADJ
ejpam-3979	357	4	hand	hand	NOUN
ejpam-3979	357	5	,	,	PUNCT
ejpam-3979	357	6	µ(s	µ(s	X
ejpam-3979	357	7	⊗	⊗	NOUN
ejpam-3979	357	8	i)∆(1	i)∆(1	NOUN
ejpam-3979	357	9	)	)	PUNCT
ejpam-3979	357	10	=	=	SYM
ejpam-3979	357	11	µ(s	µ(s	ADV
ejpam-3979	357	12	⊗	⊗	X
ejpam-3979	357	13	i)(1	i)(1	X
ejpam-3979	358	1	⊗	⊗	PROPN
ejpam-3979	358	2	1	1	NUM
ejpam-3979	358	3	)	)	PUNCT
ejpam-3979	358	4	=	=	SYM
ejpam-3979	359	1	1	1	X
ejpam-3979	359	2	.	.	PUNCT
ejpam-3979	360	1	if	if	SCONJ
ejpam-3979	360	2	g	g	PROPN
ejpam-3979	360	3	=	=	SYM
ejpam-3979	360	4	x	x	NOUN
ejpam-3979	360	5	,	,	PUNCT
ejpam-3979	360	6	then	then	ADV
ejpam-3979	360	7	µ(i	µ(i	PROPN
ejpam-3979	360	8	⊗	⊗	PROPN
ejpam-3979	360	9	s)∆(x	s)∆(x	PROPN
ejpam-3979	360	10	)	)	PUNCT
ejpam-3979	360	11	=	=	PUNCT
ejpam-3979	361	1	µ(i	µ(i	PROPN
ejpam-3979	361	2	⊗	⊗	PROPN
ejpam-3979	361	3	s)(x	s)(x	PROPN
ejpam-3979	361	4	⊗	⊗	PROPN
ejpam-3979	361	5	x	x	SYM
ejpam-3979	361	6	)	)	PUNCT
ejpam-3979	361	7	=	=	VERB
ejpam-3979	361	8	µ(x	µ(x	VERB
ejpam-3979	361	9	⊗	⊗	NUM
ejpam-3979	361	10	x2	x2	NOUN
ejpam-3979	361	11	)	)	PUNCT
ejpam-3979	361	12	=	=	SYM
ejpam-3979	362	1	1	1	X
ejpam-3979	362	2	.	.	PUNCT
ejpam-3979	363	1	on	on	ADP
ejpam-3979	363	2	the	the	DET
ejpam-3979	363	3	other	other	ADJ
ejpam-3979	363	4	hand	hand	NOUN
ejpam-3979	363	5	,	,	PUNCT
ejpam-3979	363	6	µ(s	µ(s	PUNCT
ejpam-3979	363	7	⊗	⊗	PROPN
ejpam-3979	363	8	i)∆(x	i)∆(x	PROPN
ejpam-3979	363	9	)	)	PUNCT
ejpam-3979	363	10	=	=	PUNCT
ejpam-3979	363	11	µ(s	µ(s	X
ejpam-3979	363	12	⊗	⊗	NUM
ejpam-3979	363	13	i)(x	i)(x	NOUN
ejpam-3979	363	14	⊗	⊗	PROPN
ejpam-3979	363	15	x	x	NOUN
ejpam-3979	363	16	)	)	PUNCT
ejpam-3979	363	17	=	=	SYM
ejpam-3979	363	18	µ(x2	µ(x2	NOUN
ejpam-3979	363	19	⊗	⊗	NUM
ejpam-3979	363	20	x	x	NOUN
ejpam-3979	363	21	)	)	PUNCT
ejpam-3979	363	22	=	=	SYM
ejpam-3979	364	1	1	1	X
ejpam-3979	364	2	.	.	PUNCT
ejpam-3979	365	1	if	if	SCONJ
ejpam-3979	365	2	g	g	PROPN
ejpam-3979	365	3	=	=	SYM
ejpam-3979	365	4	x2	x2	PROPN
ejpam-3979	365	5	,	,	PUNCT
ejpam-3979	365	6	then	then	ADV
ejpam-3979	365	7	µ(i	µ(i	PROPN
ejpam-3979	365	8	⊗	⊗	PROPN
ejpam-3979	365	9	s)∆(x	s)∆(x	PROPN
ejpam-3979	365	10	)	)	PUNCT
ejpam-3979	365	11	=	=	PUNCT
ejpam-3979	365	12	µ(i	µ(i	PROPN
ejpam-3979	365	13	⊗	⊗	PROPN
ejpam-3979	365	14	s)(x2	s)(x2	PROPN
ejpam-3979	365	15	⊗	⊗	PROPN
ejpam-3979	365	16	x2	x2	PROPN
ejpam-3979	365	17	)	)	PUNCT
ejpam-3979	365	18	=	=	SYM
ejpam-3979	365	19	µ(x2	µ(x2	NOUN
ejpam-3979	365	20	⊗	⊗	NUM
ejpam-3979	365	21	x	x	NOUN
ejpam-3979	365	22	)	)	PUNCT
ejpam-3979	365	23	=	=	SYM
ejpam-3979	365	24	1	1	X
ejpam-3979	365	25	.	.	PUNCT
ejpam-3979	366	1	on	on	ADP
ejpam-3979	366	2	the	the	DET
ejpam-3979	366	3	other	other	ADJ
ejpam-3979	366	4	hand	hand	NOUN
ejpam-3979	366	5	,	,	PUNCT
ejpam-3979	366	6	µ(s	µ(s	X
ejpam-3979	366	7	⊗	⊗	NOUN
ejpam-3979	366	8	i)∆(x2	i)∆(x2	NOUN
ejpam-3979	366	9	)	)	PUNCT
ejpam-3979	366	10	=	=	SYM
ejpam-3979	366	11	µ(s	µ(s	ADJ
ejpam-3979	366	12	⊗	⊗	PROPN
ejpam-3979	366	13	i)(x2	i)(x2	PROPN
ejpam-3979	366	14	⊗	⊗	PROPN
ejpam-3979	366	15	x2	x2	PROPN
ejpam-3979	366	16	)	)	PUNCT
ejpam-3979	366	17	=	=	SYM
ejpam-3979	366	18	µ(x⊗	µ(x⊗	NOUN
ejpam-3979	366	19	x2	x2	PROPN
ejpam-3979	366	20	)	)	PUNCT
ejpam-3979	366	21	=	=	SYM
ejpam-3979	367	1	1	1	X
ejpam-3979	367	2	.	.	PUNCT
ejpam-3979	367	3	therefore	therefore	ADV
ejpam-3979	367	4	,	,	PUNCT
ejpam-3979	367	5	(	(	PUNCT
ejpam-3979	367	6	h	h	NOUN
ejpam-3979	367	7	,	,	PUNCT
ejpam-3979	367	8	µ	µ	NOUN
ejpam-3979	367	9	,	,	PUNCT
ejpam-3979	367	10	λ,∆	λ,∆	NUM
ejpam-3979	367	11	,	,	PUNCT
ejpam-3979	367	12	ε	ε	PROPN
ejpam-3979	367	13	,	,	PUNCT
ejpam-3979	367	14	s	s	PART
ejpam-3979	367	15	)	)	PUNCT
ejpam-3979	367	16	is	be	AUX
ejpam-3979	367	17	an	an	DET
ejpam-3979	367	18	r	r	NOUN
ejpam-3979	367	19	-	-	PUNCT
ejpam-3979	367	20	hopf	hopf	ADJ
ejpam-3979	367	21	algebra	algebra	NOUN
ejpam-3979	367	22	.	.	PUNCT
ejpam-3979	368	1	3.3	3.3	NUM
ejpam-3979	368	2	.	.	PUNCT
ejpam-3979	369	1	commutativity	commutativity	NOUN
ejpam-3979	369	2	and	and	CCONJ
ejpam-3979	369	3	cocommutativity	cocommutativity	NOUN
ejpam-3979	369	4	of	of	ADP
ejpam-3979	369	5	the	the	DET
ejpam-3979	369	6	hopf	hopf	ADJ
ejpam-3979	369	7	algebra	algebra	NOUN
ejpam-3979	369	8	h	h	NOUN
ejpam-3979	369	9	it	it	PRON
ejpam-3979	369	10	is	be	AUX
ejpam-3979	369	11	easy	easy	ADJ
ejpam-3979	369	12	to	to	PART
ejpam-3979	369	13	verify	verify	VERB
ejpam-3979	369	14	that	that	SCONJ
ejpam-3979	369	15	each	each	DET
ejpam-3979	369	16	element	element	NOUN
ejpam-3979	369	17	in	in	ADP
ejpam-3979	369	18	h	h	NOUN
ejpam-3979	369	19	commutes	commute	NOUN
ejpam-3979	369	20	with	with	ADP
ejpam-3979	369	21	all	all	DET
ejpam-3979	369	22	the	the	DET
ejpam-3979	369	23	other	other	ADJ
ejpam-3979	369	24	element	element	NOUN
ejpam-3979	369	25	of	of	ADP
ejpam-3979	369	26	h.	h.	PROPN
ejpam-3979	369	27	so	so	ADV
ejpam-3979	369	28	h	h	PROPN
ejpam-3979	369	29	is	be	AUX
ejpam-3979	369	30	commutative	commutative	ADJ
ejpam-3979	369	31	as	as	ADP
ejpam-3979	369	32	an	an	DET
ejpam-3979	369	33	algebra	algebra	NOUN
ejpam-3979	369	34	.	.	PUNCT
ejpam-3979	370	1	thus	thus	ADV
ejpam-3979	370	2	,	,	PUNCT
ejpam-3979	370	3	h	h	NOUN
ejpam-3979	370	4	is	be	AUX
ejpam-3979	370	5	a	a	DET
ejpam-3979	370	6	commutative	commutative	ADJ
ejpam-3979	370	7	hopf	hopf	ADJ
ejpam-3979	370	8	algebra	algebra	NOUN
ejpam-3979	370	9	.	.	PUNCT
ejpam-3979	371	1	now	now	ADV
ejpam-3979	371	2	,	,	PUNCT
ejpam-3979	371	3	to	to	PART
ejpam-3979	371	4	check	check	VERB
ejpam-3979	371	5	the	the	DET
ejpam-3979	371	6	cocommutativity	cocommutativity	NOUN
ejpam-3979	371	7	of	of	ADP
ejpam-3979	371	8	h	h	NOUN
ejpam-3979	371	9	we	we	PRON
ejpam-3979	371	10	need	need	VERB
ejpam-3979	371	11	to	to	PART
ejpam-3979	371	12	show	show	VERB
ejpam-3979	371	13	that	that	SCONJ
ejpam-3979	371	14	it	it	PRON
ejpam-3979	371	15	is	be	AUX
ejpam-3979	371	16	cocommutative	cocommutative	ADJ
ejpam-3979	371	17	as	as	ADP
ejpam-3979	371	18	a	a	DET
ejpam-3979	371	19	coalgebra	coalgebra	NOUN
ejpam-3979	371	20	,	,	PUNCT
ejpam-3979	371	21	i.e.	i.e.	X
ejpam-3979	371	22	τ(∆(g	τ(∆(g	X
ejpam-3979	371	23	)	)	PUNCT
ejpam-3979	371	24	)	)	PUNCT
ejpam-3979	372	1	=	=	SYM
ejpam-3979	372	2	∆(g	∆(g	PROPN
ejpam-3979	372	3	)	)	PUNCT
ejpam-3979	372	4	for	for	ADP
ejpam-3979	372	5	all	all	PRON
ejpam-3979	372	6	g	g	PROPN
ejpam-3979	372	7	∈	∈	PROPN
ejpam-3979	372	8	c3	c3	NOUN
ejpam-3979	372	9	which	which	PRON
ejpam-3979	372	10	we	we	PRON
ejpam-3979	372	11	do	do	VERB
ejpam-3979	372	12	as	as	SCONJ
ejpam-3979	372	13	follows	follow	VERB
ejpam-3979	372	14	:	:	PUNCT
ejpam-3979	372	15	if	if	SCONJ
ejpam-3979	372	16	g	g	PROPN
ejpam-3979	372	17	=	=	SYM
ejpam-3979	372	18	1	1	NUM
ejpam-3979	372	19	,	,	PUNCT
ejpam-3979	372	20	then	then	ADV
ejpam-3979	372	21	τ(∆(1	τ(∆(1	NOUN
ejpam-3979	372	22	)	)	PUNCT
ejpam-3979	372	23	)	)	PUNCT
ejpam-3979	373	1	=	=	SYM
ejpam-3979	373	2	τ(1⊗	τ(1⊗	PROPN
ejpam-3979	373	3	1	1	NUM
ejpam-3979	373	4	)	)	PUNCT
ejpam-3979	373	5	=	=	SYM
ejpam-3979	373	6	1⊗	1⊗	NUM
ejpam-3979	373	7	1	1	NUM
ejpam-3979	373	8	=	=	NOUN
ejpam-3979	373	9	∆(1	∆(1	NOUN
ejpam-3979	373	10	)	)	PUNCT
ejpam-3979	373	11	.	.	PUNCT
ejpam-3979	374	1	if	if	SCONJ
ejpam-3979	374	2	g	g	PROPN
ejpam-3979	374	3	=	=	SYM
ejpam-3979	374	4	x	x	NOUN
ejpam-3979	374	5	,	,	PUNCT
ejpam-3979	374	6	then	then	ADV
ejpam-3979	374	7	τ(∆(x	τ(∆(x	ADV
ejpam-3979	374	8	)	)	PUNCT
ejpam-3979	374	9	)	)	PUNCT
ejpam-3979	375	1	=	=	PUNCT
ejpam-3979	375	2	τ(x⊗	τ(x⊗	PROPN
ejpam-3979	375	3	x	x	X
ejpam-3979	375	4	)	)	PUNCT
ejpam-3979	375	5	=	=	PUNCT
ejpam-3979	375	6	x⊗	x⊗	NOUN
ejpam-3979	375	7	x	x	PUNCT
ejpam-3979	375	8	=	=	PUNCT
ejpam-3979	375	9	∆(x	∆(x	NOUN
ejpam-3979	375	10	)	)	PUNCT
ejpam-3979	375	11	.	.	PUNCT
ejpam-3979	376	1	if	if	SCONJ
ejpam-3979	376	2	g	g	PROPN
ejpam-3979	376	3	=	=	SYM
ejpam-3979	376	4	x2	x2	PROPN
ejpam-3979	376	5	,	,	PUNCT
ejpam-3979	376	6	then	then	ADV
ejpam-3979	376	7	τ(∆(x2	τ(∆(x2	ADP
ejpam-3979	376	8	)	)	PUNCT
ejpam-3979	376	9	)	)	PUNCT
ejpam-3979	377	1	=	=	SYM
ejpam-3979	377	2	τ(x2	τ(x2	PROPN
ejpam-3979	378	1	⊗	⊗	PROPN
ejpam-3979	378	2	x2	x2	PROPN
ejpam-3979	378	3	)	)	PUNCT
ejpam-3979	379	1	=	=	SYM
ejpam-3979	380	1	x2	x2	PROPN
ejpam-3979	381	1	⊗	⊗	NUM
ejpam-3979	381	2	x2	x2	PROPN
ejpam-3979	381	3	=	=	NOUN
ejpam-3979	381	4	∆(x2	∆(x2	NUM
ejpam-3979	381	5	)	)	PUNCT
ejpam-3979	381	6	.	.	PUNCT
ejpam-3979	382	1	therefore	therefore	ADV
ejpam-3979	382	2	,	,	PUNCT
ejpam-3979	382	3	h	h	NOUN
ejpam-3979	382	4	is	be	AUX
ejpam-3979	382	5	a	a	DET
ejpam-3979	382	6	cocommutative	cocommutative	ADJ
ejpam-3979	382	7	hopf	hopf	ADJ
ejpam-3979	382	8	algebra	algebra	NOUN
ejpam-3979	382	9	.	.	PUNCT
ejpam-3979	383	1	3.4	3.4	NUM
ejpam-3979	383	2	.	.	PUNCT
ejpam-3979	384	1	the	the	DET
ejpam-3979	384	2	normal	normal	ADJ
ejpam-3979	384	3	hopf	hopf	ADJ
ejpam-3979	384	4	subalgebras	subalgebras	PROPN
ejpam-3979	384	5	of	of	ADP
ejpam-3979	384	6	h	h	PROPN
ejpam-3979	384	7	since	since	SCONJ
ejpam-3979	384	8	c3	c3	PROPN
ejpam-3979	384	9	is	be	AUX
ejpam-3979	384	10	simple	simple	ADJ
ejpam-3979	384	11	,	,	PUNCT
ejpam-3979	384	12	it	it	PRON
ejpam-3979	384	13	follows	follow	VERB
ejpam-3979	384	14	that	that	SCONJ
ejpam-3979	384	15	h	h	NOUN
ejpam-3979	384	16	has	have	VERB
ejpam-3979	384	17	no	no	DET
ejpam-3979	384	18	proper	proper	ADJ
ejpam-3979	384	19	subalgebras	subalgebra	NOUN
ejpam-3979	384	20	.	.	PUNCT
ejpam-3979	385	1	moreover	moreover	ADV
ejpam-3979	385	2	,	,	PUNCT
ejpam-3979	385	3	since	since	SCONJ
ejpam-3979	385	4	the	the	DET
ejpam-3979	385	5	only	only	ADJ
ejpam-3979	385	6	hopf	hopf	ADJ
ejpam-3979	385	7	subalgebras	subalgebras	PROPN
ejpam-3979	385	8	of	of	ADP
ejpam-3979	385	9	h	h	PROPN
ejpam-3979	385	10	are	be	AUX
ejpam-3979	385	11	the	the	DET
ejpam-3979	385	12	trivial	trivial	ADJ
ejpam-3979	385	13	ones	one	NOUN
ejpam-3979	385	14	,	,	PUNCT
ejpam-3979	385	15	thus	thus	ADV
ejpam-3979	385	16	h	h	NOUN
ejpam-3979	385	17	has	have	VERB
ejpam-3979	385	18	no	no	DET
ejpam-3979	385	19	proper	proper	ADJ
ejpam-3979	385	20	normal	normal	ADJ
ejpam-3979	385	21	hopf	hopf	ADJ
ejpam-3979	385	22	subalgebra	subalgebra	NOUN
ejpam-3979	385	23	.	.	PUNCT
ejpam-3979	386	1	therefore	therefore	ADV
ejpam-3979	386	2	,	,	PUNCT
ejpam-3979	386	3	h	h	NOUN
ejpam-3979	386	4	is	be	AUX
ejpam-3979	386	5	simple	simple	ADJ
ejpam-3979	386	6	.	.	PUNCT
ejpam-3979	387	1	3.5	3.5	NUM
ejpam-3979	387	2	.	.	PUNCT
ejpam-3979	388	1	semi	semi	ADJ
ejpam-3979	388	2	-	-	NOUN
ejpam-3979	388	3	simplicity	simplicity	NOUN
ejpam-3979	388	4	of	of	ADP
ejpam-3979	388	5	the	the	DET
ejpam-3979	388	6	hopf	hopf	ADJ
ejpam-3979	388	7	algebra	algebra	NOUN
ejpam-3979	388	8	h	h	NOUN
ejpam-3979	388	9	to	to	PART
ejpam-3979	388	10	check	check	VERB
ejpam-3979	388	11	the	the	DET
ejpam-3979	388	12	semi	semi	ADJ
ejpam-3979	388	13	-	-	NOUN
ejpam-3979	388	14	simplicity	simplicity	NOUN
ejpam-3979	388	15	of	of	ADP
ejpam-3979	388	16	the	the	DET
ejpam-3979	388	17	hopf	hopf	ADJ
ejpam-3979	388	18	algebra	algebra	NOUN
ejpam-3979	388	19	h	h	NOUN
ejpam-3979	388	20	we	we	PRON
ejpam-3979	388	21	need	need	VERB
ejpam-3979	388	22	first	first	ADV
ejpam-3979	388	23	to	to	PART
ejpam-3979	388	24	recall	recall	VERB
ejpam-3979	388	25	that	that	SCONJ
ejpam-3979	388	26	the	the	DET
ejpam-3979	388	27	center	center	NOUN
ejpam-3979	388	28	of	of	ADP
ejpam-3979	388	29	a	a	DET
ejpam-3979	388	30	hopf	hopf	ADJ
ejpam-3979	388	31	algebra	algebra	NOUN
ejpam-3979	388	32	h	h	NOUN
ejpam-3979	388	33	is	be	AUX
ejpam-3979	388	34	defined	define	VERB
ejpam-3979	388	35	by	by	ADP
ejpam-3979	388	36	z(h	z(h	NOUN
ejpam-3979	388	37	)	)	PUNCT
ejpam-3979	389	1	=	=	PRON
ejpam-3979	389	2	{	{	PUNCT
ejpam-3979	389	3	h	h	NOUN
ejpam-3979	389	4	∈	∈	PROPN
ejpam-3979	389	5	h;hh1	h;hh1	PROPN
ejpam-3979	389	6	=	=	SYM
ejpam-3979	389	7	h1h	h1h	PROPN
ejpam-3979	389	8	for	for	ADP
ejpam-3979	389	9	all	all	DET
ejpam-3979	389	10	h1	h1	PROPN
ejpam-3979	389	11	∈	∈	PROPN
ejpam-3979	389	12	h	h	NOUN
ejpam-3979	389	13	}	}	PUNCT
ejpam-3979	389	14	.	.	PUNCT
ejpam-3979	390	1	in	in	ADP
ejpam-3979	390	2	our	our	PRON
ejpam-3979	390	3	example	example	NOUN
ejpam-3979	390	4	,	,	PUNCT
ejpam-3979	390	5	since	since	SCONJ
ejpam-3979	390	6	each	each	DET
ejpam-3979	390	7	element	element	NOUN
ejpam-3979	390	8	in	in	ADP
ejpam-3979	390	9	h	h	NOUN
ejpam-3979	390	10	commutes	commute	NOUN
ejpam-3979	390	11	with	with	ADP
ejpam-3979	390	12	all	all	DET
ejpam-3979	390	13	the	the	DET
ejpam-3979	390	14	element	element	NOUN
ejpam-3979	390	15	of	of	ADP
ejpam-3979	390	16	h	h	NOUN
ejpam-3979	390	17	,	,	PUNCT
ejpam-3979	390	18	then	then	ADV
ejpam-3979	390	19	z(h	z(h	NUM
ejpam-3979	390	20	)	)	PUNCT
ejpam-3979	390	21	=	=	SYM
ejpam-3979	390	22	h.	h.	PROPN
ejpam-3979	390	23	in	in	ADP
ejpam-3979	390	24	our	our	PRON
ejpam-3979	390	25	example	example	NOUN
ejpam-3979	390	26	|c3|	|c3|	NOUN
ejpam-3979	390	27	=	=	NOUN
ejpam-3979	390	28	3	3	NUM
ejpam-3979	390	29	is	be	AUX
ejpam-3979	390	30	not	not	PART
ejpam-3979	390	31	divisible	divisible	ADJ
ejpam-3979	390	32	by	by	ADP
ejpam-3979	390	33	the	the	DET
ejpam-3979	390	34	characteristic	characteristic	NOUN
ejpam-3979	390	35	of	of	ADP
ejpam-3979	390	36	the	the	DET
ejpam-3979	390	37	field	field	NOUN
ejpam-3979	390	38	r	r	NOUN
ejpam-3979	390	39	which	which	PRON
ejpam-3979	390	40	is	be	AUX
ejpam-3979	390	41	zero	zero	NUM
ejpam-3979	390	42	.	.	PUNCT
ejpam-3979	391	1	so	so	ADV
ejpam-3979	391	2	,	,	PUNCT
ejpam-3979	391	3	by	by	ADP
ejpam-3979	391	4	theorem	theorem	NOUN
ejpam-3979	391	5	2	2	NUM
ejpam-3979	391	6	,	,	PUNCT
ejpam-3979	391	7	h	h	NOUN
ejpam-3979	391	8	is	be	AUX
ejpam-3979	391	9	semisimple	semisimple	ADJ
ejpam-3979	391	10	hopf	hopf	ADJ
ejpam-3979	391	11	algebra	algebra	NOUN
ejpam-3979	391	12	.	.	PUNCT
ejpam-3979	392	1	references	reference	NOUN
ejpam-3979	392	2	827	827	NUM
ejpam-3979	392	3	3.6	3.6	NUM
ejpam-3979	392	4	.	.	PUNCT
ejpam-3979	393	1	nilpotency	nilpotency	NOUN
ejpam-3979	393	2	and	and	CCONJ
ejpam-3979	393	3	solvability	solvability	NOUN
ejpam-3979	393	4	of	of	ADP
ejpam-3979	393	5	the	the	DET
ejpam-3979	393	6	hopf	hopf	ADJ
ejpam-3979	393	7	algebra	algebra	NOUN
ejpam-3979	393	8	h	h	NOUN
ejpam-3979	393	9	in	in	ADP
ejpam-3979	393	10	this	this	DET
ejpam-3979	393	11	subsection	subsection	NOUN
ejpam-3979	393	12	we	we	PRON
ejpam-3979	393	13	discuss	discuss	VERB
ejpam-3979	393	14	whether	whether	SCONJ
ejpam-3979	393	15	h	h	NOUN
ejpam-3979	393	16	is	be	AUX
ejpam-3979	393	17	a	a	DET
ejpam-3979	393	18	nilpotent	nilpotent	NOUN
ejpam-3979	393	19	or	or	CCONJ
ejpam-3979	393	20	a	a	DET
ejpam-3979	393	21	solvable	solvable	ADJ
ejpam-3979	393	22	hopf	hopf	ADJ
ejpam-3979	393	23	algebra	algebra	NOUN
ejpam-3979	393	24	.	.	PUNCT
ejpam-3979	394	1	since	since	SCONJ
ejpam-3979	394	2	h	h	NOUN
ejpam-3979	394	3	is	be	AUX
ejpam-3979	394	4	commutative	commutative	ADJ
ejpam-3979	394	5	hopf	hopf	ADJ
ejpam-3979	394	6	algebra	algebra	NOUN
ejpam-3979	394	7	with	with	ADP
ejpam-3979	394	8	r	r	PROPN
ejpam-3979	394	9	⊂	⊂	PUNCT
ejpam-3979	394	10	h	h	NOUN
ejpam-3979	394	11	as	as	ADP
ejpam-3979	394	12	a	a	DET
ejpam-3979	394	13	solvable	solvable	ADJ
ejpam-3979	394	14	series	series	NOUN
ejpam-3979	394	15	,	,	PUNCT
ejpam-3979	394	16	it	it	PRON
ejpam-3979	394	17	follows	follow	VERB
ejpam-3979	394	18	that	that	SCONJ
ejpam-3979	394	19	h	h	NOUN
ejpam-3979	394	20	is	be	AUX
ejpam-3979	394	21	solvable	solvable	ADJ
ejpam-3979	394	22	by	by	ADP
ejpam-3979	394	23	using	use	VERB
ejpam-3979	394	24	remark	remark	NOUN
ejpam-3979	394	25	1	1	NUM
ejpam-3979	394	26	.	.	PUNCT
ejpam-3979	395	1	furthermore	furthermore	ADV
ejpam-3979	395	2	,	,	PUNCT
ejpam-3979	395	3	since	since	SCONJ
ejpam-3979	395	4	h	h	NOUN
ejpam-3979	395	5	has	have	VERB
ejpam-3979	395	6	central	central	ADJ
ejpam-3979	395	7	series	series	NOUN
ejpam-3979	395	8	r	r	NOUN
ejpam-3979	395	9	⊆	⊆	NUM
ejpam-3979	395	10	z1	z1	NOUN
ejpam-3979	395	11	,	,	PUNCT
ejpam-3979	395	12	where	where	SCONJ
ejpam-3979	395	13	z1	z1	PROPN
ejpam-3979	395	14	=	=	SYM
ejpam-3979	395	15	z̃(h	z̃(h	PROPN
ejpam-3979	395	16	)	)	PUNCT
ejpam-3979	395	17	,	,	PUNCT
ejpam-3979	395	18	hence	hence	ADV
ejpam-3979	395	19	by	by	ADP
ejpam-3979	395	20	using	use	VERB
ejpam-3979	395	21	remark	remark	NOUN
ejpam-3979	395	22	2	2	NUM
ejpam-3979	395	23	we	we	PRON
ejpam-3979	395	24	get	get	VERB
ejpam-3979	395	25	z̃(h	z̃(h	ADV
ejpam-3979	395	26	)	)	PUNCT
ejpam-3979	396	1	=	=	SYM
ejpam-3979	396	2	rzc3	rzc3	NOUN
ejpam-3979	396	3	=	=	SYM
ejpam-3979	396	4	rc3	rc3	PROPN
ejpam-3979	396	5	.	.	PUNCT
ejpam-3979	397	1	thus	thus	ADV
ejpam-3979	397	2	,	,	PUNCT
ejpam-3979	397	3	z1	z1	PROPN
ejpam-3979	397	4	=	=	SYM
ejpam-3979	397	5	rc3	rc3	PROPN
ejpam-3979	397	6	.	.	PUNCT
ejpam-3979	398	1	therefore	therefore	ADV
ejpam-3979	398	2	,	,	PUNCT
ejpam-3979	398	3	by	by	ADP
ejpam-3979	398	4	definition	definition	NOUN
ejpam-3979	398	5	7	7	NUM
ejpam-3979	398	6	,	,	PUNCT
ejpam-3979	398	7	h	h	NOUN
ejpam-3979	398	8	is	be	AUX
ejpam-3979	398	9	nilpotent	nilpotent	ADJ
ejpam-3979	398	10	.	.	PUNCT
ejpam-3979	399	1	4	4	X
ejpam-3979	399	2	.	.	X
ejpam-3979	399	3	conclusion	conclusion	NOUN
ejpam-3979	399	4	we	we	PRON
ejpam-3979	399	5	noticed	notice	VERB
ejpam-3979	399	6	from	from	ADP
ejpam-3979	399	7	our	our	PRON
ejpam-3979	399	8	example	example	NOUN
ejpam-3979	399	9	that	that	SCONJ
ejpam-3979	399	10	all	all	DET
ejpam-3979	399	11	the	the	DET
ejpam-3979	399	12	properties	property	NOUN
ejpam-3979	399	13	of	of	ADP
ejpam-3979	399	14	the	the	DET
ejpam-3979	399	15	original	original	ADJ
ejpam-3979	399	16	finite	finite	PROPN
ejpam-3979	399	17	group	group	NOUN
ejpam-3979	399	18	c3	c3	PROPN
ejpam-3979	399	19	have	have	AUX
ejpam-3979	399	20	been	be	AUX
ejpam-3979	399	21	carried	carry	VERB
ejpam-3979	399	22	out	out	ADP
ejpam-3979	399	23	in	in	ADP
ejpam-3979	399	24	the	the	DET
ejpam-3979	399	25	case	case	NOUN
ejpam-3979	399	26	of	of	ADP
ejpam-3979	399	27	its	its	PRON
ejpam-3979	399	28	group	group	NOUN
ejpam-3979	400	1	hopf	hopf	ADJ
ejpam-3979	400	2	algebra	algebra	NOUN
ejpam-3979	400	3	h	h	NOUN
ejpam-3979	400	4	=	=	NOUN
ejpam-3979	400	5	rc3	rc3	PROPN
ejpam-3979	400	6	such	such	ADJ
ejpam-3979	400	7	as	as	ADP
ejpam-3979	400	8	commutativity	commutativity	NOUN
ejpam-3979	400	9	,	,	PUNCT
ejpam-3979	400	10	simplicity	simplicity	NOUN
ejpam-3979	400	11	,	,	PUNCT
ejpam-3979	400	12	nilpotency	nilpotency	NOUN
ejpam-3979	400	13	and	and	CCONJ
ejpam-3979	400	14	solvability	solvability	NOUN
ejpam-3979	400	15	.	.	PUNCT
ejpam-3979	401	1	in	in	ADP
ejpam-3979	401	2	general	general	ADJ
ejpam-3979	401	3	,	,	PUNCT
ejpam-3979	401	4	for	for	ADP
ejpam-3979	401	5	a	a	DET
ejpam-3979	401	6	finite	finite	ADJ
ejpam-3979	401	7	group	group	NOUN
ejpam-3979	401	8	g	g	PROPN
ejpam-3979	401	9	,	,	PUNCT
ejpam-3979	401	10	the	the	DET
ejpam-3979	401	11	normal	normal	ADJ
ejpam-3979	401	12	hopf	hopf	ADJ
ejpam-3979	401	13	subalgebras	subalgebras	PROPN
ejpam-3979	401	14	of	of	ADP
ejpam-3979	401	15	kg	kg	NOUN
ejpam-3979	401	16	are	be	AUX
ejpam-3979	401	17	of	of	ADP
ejpam-3979	401	18	the	the	DET
ejpam-3979	401	19	form	form	NOUN
ejpam-3979	401	20	kgi	kgi	INTJ
ejpam-3979	401	21	where	where	SCONJ
ejpam-3979	401	22	gi	gi	PRON
ejpam-3979	401	23	is	be	AUX
ejpam-3979	401	24	a	a	DET
ejpam-3979	401	25	normal	normal	ADJ
ejpam-3979	401	26	subgroup	subgroup	NOUN
ejpam-3979	401	27	of	of	ADP
ejpam-3979	401	28	g	g	PROPN
ejpam-3979	401	29	and	and	CCONJ
ejpam-3979	401	30	k	k	PROPN
ejpam-3979	401	31	is	be	AUX
ejpam-3979	401	32	an	an	DET
ejpam-3979	401	33	algebraically	algebraically	ADV
ejpam-3979	401	34	closed	closed	ADJ
ejpam-3979	401	35	field	field	NOUN
ejpam-3979	401	36	of	of	ADP
ejpam-3979	401	37	characteristic	characteristic	ADJ
ejpam-3979	401	38	zero	zero	NUM
ejpam-3979	401	39	.	.	PUNCT
ejpam-3979	402	1	in	in	ADP
ejpam-3979	402	2	particular	particular	ADJ
ejpam-3979	402	3	,	,	PUNCT
ejpam-3979	402	4	kg	kg	PROPN
ejpam-3979	402	5	is	be	AUX
ejpam-3979	402	6	simple	simple	ADJ
ejpam-3979	402	7	as	as	ADP
ejpam-3979	402	8	a	a	DET
ejpam-3979	402	9	hopf	hopf	ADJ
ejpam-3979	402	10	algebra	algebra	NOUN
ejpam-3979	402	11	if	if	SCONJ
ejpam-3979	402	12	and	and	CCONJ
ejpam-3979	402	13	only	only	ADV
ejpam-3979	402	14	if	if	SCONJ
ejpam-3979	402	15	g	g	PROPN
ejpam-3979	402	16	is	be	AUX
ejpam-3979	402	17	a	a	DET
ejpam-3979	402	18	simple	simple	ADJ
ejpam-3979	402	19	group	group	NOUN
ejpam-3979	402	20	.	.	PUNCT
ejpam-3979	403	1	furthermore	furthermore	ADV
ejpam-3979	403	2	,	,	PUNCT
ejpam-3979	403	3	if	if	SCONJ
ejpam-3979	403	4	kg	kg	PROPN
ejpam-3979	403	5	is	be	AUX
ejpam-3979	403	6	simple	simple	ADJ
ejpam-3979	403	7	,	,	PUNCT
ejpam-3979	403	8	then	then	ADV
ejpam-3979	403	9	it	it	PRON
ejpam-3979	403	10	has	have	VERB
ejpam-3979	403	11	no	no	DET
ejpam-3979	403	12	a	a	DET
ejpam-3979	403	13	proper	proper	ADJ
ejpam-3979	403	14	quotient	quotient	NOUN
ejpam-3979	403	15	hopf	hopf	ADJ
ejpam-3979	403	16	algebra	algebra	NOUN
ejpam-3979	403	17	[	[	X
ejpam-3979	403	18	13	13	NUM
ejpam-3979	403	19	]	]	PUNCT
ejpam-3979	403	20	.	.	PUNCT
ejpam-3979	404	1	references	reference	NOUN
ejpam-3979	404	2	[	[	X
ejpam-3979	404	3	1	1	NUM
ejpam-3979	404	4	]	]	PUNCT
ejpam-3979	404	5	m.	m.	NOUN
ejpam-3979	404	6	m.	m.	PROPN
ejpam-3979	404	7	al	al	PROPN
ejpam-3979	404	8	-	-	PUNCT
ejpam-3979	404	9	shomrani	shomrani	PROPN
ejpam-3979	404	10	and	and	CCONJ
ejpam-3979	404	11	a.	a.	NOUN
ejpam-3979	404	12	a.	a.	NOUN
ejpam-3979	404	13	heliel	heliel	PROPN
ejpam-3979	404	14	.	.	PUNCT
ejpam-3979	405	1	the	the	DET
ejpam-3979	405	2	influence	influence	NOUN
ejpam-3979	405	3	of	of	ADP
ejpam-3979	405	4	c	c	PROPN
ejpam-3979	405	5	-	-	PUNCT
ejpam-3979	405	6	z	z	ADJ
ejpam-3979	405	7	-	-	PUNCT
ejpam-3979	405	8	permutable	permutable	ADJ
ejpam-3979	405	9	subgroups	subgroup	NOUN
ejpam-3979	405	10	on	on	ADP
ejpam-3979	405	11	the	the	DET
ejpam-3979	405	12	structure	structure	NOUN
ejpam-3979	405	13	of	of	ADP
ejpam-3979	405	14	finite	finite	ADJ
ejpam-3979	405	15	groups	group	NOUN
ejpam-3979	405	16	.	.	PUNCT
ejpam-3979	406	1	european	european	ADJ
ejpam-3979	406	2	journal	journal	PROPN
ejpam-3979	406	3	of	of	ADP
ejpam-3979	406	4	pure	pure	ADJ
ejpam-3979	406	5	and	and	CCONJ
ejpam-3979	406	6	applied	applied	ADJ
ejpam-3979	406	7	mathematics	mathematic	NOUN
ejpam-3979	406	8	,	,	PUNCT
ejpam-3979	406	9	11(1):160–168	11(1):160–168	PROPN
ejpam-3979	406	10	,	,	PUNCT
ejpam-3979	406	11	2018	2018	NUM
ejpam-3979	406	12	.	.	PUNCT
ejpam-3979	407	1	[	[	X
ejpam-3979	407	2	2	2	NUM
ejpam-3979	407	3	]	]	PUNCT
ejpam-3979	407	4	m.	m.	NOUN
ejpam-3979	407	5	m.	m.	PROPN
ejpam-3979	407	6	al	al	PROPN
ejpam-3979	407	7	-	-	PUNCT
ejpam-3979	407	8	shomrani	shomrani	PROPN
ejpam-3979	407	9	,	,	PUNCT
ejpam-3979	407	10	a.	a.	NOUN
ejpam-3979	407	11	a.	a.	NOUN
ejpam-3979	407	12	heliel	heliel	PROPN
ejpam-3979	407	13	,	,	PUNCT
ejpam-3979	407	14	and	and	CCONJ
ejpam-3979	407	15	adolfo	adolfo	PROPN
ejpam-3979	407	16	ballester	ballester	PROPN
ejpam-3979	407	17	-	-	PUNCT
ejpam-3979	407	18	bolinches	bolinche	NOUN
ejpam-3979	407	19	.	.	PUNCT
ejpam-3979	408	1	on	on	ADP
ejpam-3979	408	2	σ	σ	PROPN
ejpam-3979	408	3	-	-	ADJ
ejpam-3979	408	4	subnormal	subnormal	ADJ
ejpam-3979	408	5	closure	closure	NOUN
ejpam-3979	408	6	.	.	PUNCT
ejpam-3979	409	1	communications	communication	NOUN
ejpam-3979	409	2	in	in	ADP
ejpam-3979	409	3	algebra	algebra	NOUN
ejpam-3979	409	4	,	,	PUNCT
ejpam-3979	409	5	12(2	12(2	NUM
ejpam-3979	409	6	)	)	PUNCT
ejpam-3979	409	7	,	,	PUNCT
ejpam-3979	409	8	2020	2020	NUM
ejpam-3979	409	9	.	.	PUNCT
ejpam-3979	410	1	[	[	X
ejpam-3979	410	2	3	3	NUM
ejpam-3979	410	3	]	]	X
ejpam-3979	410	4	m.	m.	NOUN
ejpam-3979	410	5	m.	m.	PROPN
ejpam-3979	410	6	al	al	PROPN
ejpam-3979	410	7	-	-	PROPN
ejpam-3979	410	8	mosa	mosa	PROPN
ejpam-3979	410	9	al	al	PROPN
ejpam-3979	410	10	-	-	PUNCT
ejpam-3979	410	11	shomrani	shomrani	PROPN
ejpam-3979	410	12	,	,	PUNCT
ejpam-3979	410	13	m.	m.	NOUN
ejpam-3979	410	14	ramadan	ramadan	PROPN
ejpam-3979	410	15	,	,	PUNCT
ejpam-3979	410	16	and	and	CCONJ
ejpam-3979	410	17	a.	a.	NOUN
ejpam-3979	410	18	a.	a.	NOUN
ejpam-3979	410	19	heliel	heliel	PROPN
ejpam-3979	410	20	.	.	PUNCT
ejpam-3979	411	1	finite	finite	ADJ
ejpam-3979	411	2	groups	group	NOUN
ejpam-3979	411	3	whose	whose	DET
ejpam-3979	411	4	minimal	minimal	ADJ
ejpam-3979	411	5	subgroups	subgroup	NOUN
ejpam-3979	411	6	are	be	AUX
ejpam-3979	411	7	weakly	weakly	ADJ
ejpam-3979	411	8	-	-	PUNCT
ejpam-3979	411	9	subgroups	subgroup	NOUN
ejpam-3979	411	10	.	.	PUNCT
ejpam-3979	412	1	acta	acta	PROPN
ejpam-3979	412	2	mathematica	mathematica	PROPN
ejpam-3979	412	3	scientia	scientia	PROPN
ejpam-3979	412	4	,	,	PUNCT
ejpam-3979	412	5	32(6):2295	32(6):2295	NUM
ejpam-3979	412	6	–	–	PUNCT
ejpam-3979	412	7	2301	2301	NUM
ejpam-3979	412	8	,	,	PUNCT
ejpam-3979	412	9	2012	2012	NUM
ejpam-3979	412	10	.	.	PUNCT
ejpam-3979	413	1	[	[	X
ejpam-3979	413	2	4	4	X
ejpam-3979	413	3	]	]	PUNCT
ejpam-3979	413	4	m.	m.	NOUN
ejpam-3979	413	5	asaad	asaad	NOUN
ejpam-3979	413	6	,	,	PUNCT
ejpam-3979	413	7	m.	m.	NOUN
ejpam-3979	413	8	al	al	PROPN
ejpam-3979	413	9	-	-	PUNCT
ejpam-3979	413	10	shomrani	shomrani	PROPN
ejpam-3979	413	11	,	,	PUNCT
ejpam-3979	413	12	and	and	CCONJ
ejpam-3979	413	13	a.	a.	NOUN
ejpam-3979	413	14	heliel	heliel	PROPN
ejpam-3979	413	15	.	.	PUNCT
ejpam-3979	414	1	the	the	DET
ejpam-3979	414	2	influence	influence	NOUN
ejpam-3979	414	3	of	of	ADP
ejpam-3979	414	4	weakly	weakly	ADJ
ejpam-3979	414	5	-	-	PUNCT
ejpam-3979	414	6	subgroups	subgroup	NOUN
ejpam-3979	414	7	on	on	ADP
ejpam-3979	414	8	the	the	DET
ejpam-3979	414	9	structure	structure	NOUN
ejpam-3979	414	10	of	of	ADP
ejpam-3979	414	11	finite	finite	ADJ
ejpam-3979	414	12	groups	group	NOUN
ejpam-3979	414	13	.	.	PUNCT
ejpam-3979	415	1	studia	studia	PROPN
ejpam-3979	415	2	scientiarum	scientiarum	PROPN
ejpam-3979	415	3	mathematicarum	mathematicarum	PROPN
ejpam-3979	415	4	hungarica	hungarica	PROPN
ejpam-3979	415	5	,	,	PUNCT
ejpam-3979	415	6	51(1):27	51(1):27	NUM
ejpam-3979	415	7	–	–	SYM
ejpam-3979	415	8	40	40	NUM
ejpam-3979	415	9	,	,	PUNCT
ejpam-3979	415	10	2014	2014	NUM
ejpam-3979	415	11	.	.	PUNCT
ejpam-3979	416	1	[	[	X
ejpam-3979	416	2	5	5	NUM
ejpam-3979	416	3	]	]	PUNCT
ejpam-3979	416	4	m.	m.	NOUN
ejpam-3979	416	5	asaad	asaad	PROPN
ejpam-3979	416	6	,	,	PUNCT
ejpam-3979	416	7	a.	a.	NOUN
ejpam-3979	416	8	a.	a.	NOUN
ejpam-3979	416	9	heliel	heliel	PROPN
ejpam-3979	416	10	,	,	PUNCT
ejpam-3979	416	11	and	and	CCONJ
ejpam-3979	416	12	m.	m.	NOUN
ejpam-3979	416	13	m.	m.	PROPN
ejpam-3979	416	14	al	al	PROPN
ejpam-3979	416	15	-	-	PROPN
ejpam-3979	416	16	mosa	mosa	PROPN
ejpam-3979	416	17	al	al	PROPN
ejpam-3979	416	18	-	-	PUNCT
ejpam-3979	416	19	shomrani	shomrani	PROPN
ejpam-3979	416	20	.	.	PUNCT
ejpam-3979	417	1	on	on	ADP
ejpam-3979	417	2	weakly	weakly	ADJ
ejpam-3979	417	3	h	h	NOUN
ejpam-3979	417	4	-	-	PUNCT
ejpam-3979	417	5	subgroups	subgroup	NOUN
ejpam-3979	417	6	of	of	ADP
ejpam-3979	417	7	finite	finite	ADJ
ejpam-3979	417	8	groups	group	NOUN
ejpam-3979	417	9	.	.	PUNCT
ejpam-3979	418	1	communications	communication	NOUN
ejpam-3979	418	2	in	in	ADP
ejpam-3979	418	3	algebra	algebra	NOUN
ejpam-3979	418	4	,	,	PUNCT
ejpam-3979	418	5	40(9):3540–3550	40(9):3540–3550	NUM
ejpam-3979	418	6	,	,	PUNCT
ejpam-3979	418	7	2012	2012	NUM
ejpam-3979	418	8	.	.	PUNCT
ejpam-3979	419	1	[	[	X
ejpam-3979	419	2	6	6	NUM
ejpam-3979	419	3	]	]	PUNCT
ejpam-3979	419	4	s.	s.	PROPN
ejpam-3979	419	5	burciu	burciu	PROPN
ejpam-3979	419	6	.	.	PUNCT
ejpam-3979	420	1	normal	normal	ADJ
ejpam-3979	420	2	coideal	coideal	NOUN
ejpam-3979	420	3	subalgebras	subalgebra	NOUN
ejpam-3979	420	4	of	of	ADP
ejpam-3979	420	5	semisimple	semisimple	PROPN
ejpam-3979	420	6	hopf	hopf	PROPN
ejpam-3979	420	7	algebras	algebras	X
ejpam-3979	420	8	.	.	PUNCT
ejpam-3979	421	1	in	in	ADP
ejpam-3979	421	2	journal	journal	PROPN
ejpam-3979	421	3	of	of	ADP
ejpam-3979	421	4	physics	physics	PROPN
ejpam-3979	421	5	:	:	PUNCT
ejpam-3979	421	6	conference	conference	NOUN
ejpam-3979	421	7	series	series	NOUN
ejpam-3979	421	8	,	,	PUNCT
ejpam-3979	421	9	volume	volume	NOUN
ejpam-3979	421	10	346	346	NUM
ejpam-3979	421	11	,	,	PUNCT
ejpam-3979	421	12	page	page	NOUN
ejpam-3979	421	13	012004	012004	NUM
ejpam-3979	421	14	.	.	PUNCT
ejpam-3979	422	1	iop	iop	PROPN
ejpam-3979	422	2	publishing	publishing	NOUN
ejpam-3979	422	3	,	,	PUNCT
ejpam-3979	422	4	2012	2012	NUM
ejpam-3979	422	5	.	.	PUNCT
ejpam-3979	423	1	[	[	X
ejpam-3979	423	2	7	7	X
ejpam-3979	423	3	]	]	X
ejpam-3979	423	4	m.	m.	NOUN
ejpam-3979	423	5	cohen	cohen	PROPN
ejpam-3979	423	6	and	and	CCONJ
ejpam-3979	423	7	s.	s.	PROPN
ejpam-3979	423	8	westreich	westreich	PROPN
ejpam-3979	423	9	.	.	PUNCT
ejpam-3979	424	1	are	be	AUX
ejpam-3979	424	2	we	we	PRON
ejpam-3979	424	3	counting	count	VERB
ejpam-3979	424	4	or	or	CCONJ
ejpam-3979	424	5	measuring	measure	VERB
ejpam-3979	424	6	something	something	PRON
ejpam-3979	424	7	?	?	PUNCT
ejpam-3979	425	1	journal	journal	NOUN
ejpam-3979	425	2	of	of	ADP
ejpam-3979	425	3	algebra	algebra	PROPN
ejpam-3979	425	4	,	,	PUNCT
ejpam-3979	425	5	398:111–130	398:111–130	NUM
ejpam-3979	425	6	,	,	PUNCT
ejpam-3979	425	7	2014	2014	NUM
ejpam-3979	425	8	.	.	PUNCT
ejpam-3979	426	1	[	[	X
ejpam-3979	426	2	8	8	NUM
ejpam-3979	426	3	]	]	PUNCT
ejpam-3979	426	4	m.	m.	NOUN
ejpam-3979	426	5	cohen	cohen	PROPN
ejpam-3979	426	6	and	and	CCONJ
ejpam-3979	426	7	s.	s.	PROPN
ejpam-3979	426	8	westreich	westreich	PROPN
ejpam-3979	426	9	.	.	PUNCT
ejpam-3979	427	1	probabilistically	probabilistically	ADV
ejpam-3979	427	2	nilpotent	nilpotent	ADJ
ejpam-3979	427	3	hopf	hopf	PROPN
ejpam-3979	427	4	algebras	algebra	NOUN
ejpam-3979	427	5	.	.	PUNCT
ejpam-3979	428	1	transactions	transaction	NOUN
ejpam-3979	428	2	of	of	ADP
ejpam-3979	428	3	the	the	DET
ejpam-3979	428	4	american	american	PROPN
ejpam-3979	428	5	mathematical	mathematical	PROPN
ejpam-3979	428	6	society	society	NOUN
ejpam-3979	428	7	,	,	PUNCT
ejpam-3979	428	8	368(6):4295–4314	368(6):4295–4314	NOUN
ejpam-3979	428	9	,	,	PUNCT
ejpam-3979	428	10	2016	2016	NUM
ejpam-3979	428	11	.	.	PUNCT
ejpam-3979	429	1	references	reference	NOUN
ejpam-3979	429	2	828	828	NUM
ejpam-3979	429	3	[	[	X
ejpam-3979	429	4	9	9	NUM
ejpam-3979	429	5	]	]	PUNCT
ejpam-3979	429	6	m.	m.	NOUN
ejpam-3979	429	7	cohen	cohen	PROPN
ejpam-3979	429	8	and	and	CCONJ
ejpam-3979	429	9	s.	s.	PROPN
ejpam-3979	429	10	westreich	westreich	PROPN
ejpam-3979	429	11	.	.	PUNCT
ejpam-3979	430	1	from	from	ADP
ejpam-3979	430	2	finite	finite	ADJ
ejpam-3979	430	3	groups	group	NOUN
ejpam-3979	430	4	to	to	PART
ejpam-3979	430	5	finite	finite	VERB
ejpam-3979	430	6	-	-	ADJ
ejpam-3979	430	7	dimensional	dimensional	ADJ
ejpam-3979	430	8	hopf	hopf	ADJ
ejpam-3979	430	9	algebras	algebra	NOUN
ejpam-3979	430	10	.	.	PUNCT
ejpam-3979	431	1	bulletin	bulletin	NOUN
ejpam-3979	431	2	of	of	ADP
ejpam-3979	431	3	the	the	DET
ejpam-3979	431	4	belgian	belgian	ADJ
ejpam-3979	431	5	mathematical	mathematical	ADJ
ejpam-3979	431	6	society	society	NOUN
ejpam-3979	431	7	-	-	PUNCT
ejpam-3979	431	8	simon	simon	PROPN
ejpam-3979	431	9	stevin	stevin	NOUN
ejpam-3979	431	10	,	,	PUNCT
ejpam-3979	431	11	24(1):1–15	24(1):1–15	NUM
ejpam-3979	431	12	,	,	PUNCT
ejpam-3979	431	13	2017	2017	NUM
ejpam-3979	431	14	.	.	PUNCT
ejpam-3979	432	1	[	[	X
ejpam-3979	432	2	10	10	NUM
ejpam-3979	432	3	]	]	PUNCT
ejpam-3979	432	4	m.	m.	NOUN
ejpam-3979	432	5	cohen	cohen	PROPN
ejpam-3979	432	6	and	and	CCONJ
ejpam-3979	432	7	s.	s.	PROPN
ejpam-3979	432	8	westreich	westreich	PROPN
ejpam-3979	432	9	.	.	PUNCT
ejpam-3979	433	1	solvability	solvability	NOUN
ejpam-3979	433	2	for	for	ADP
ejpam-3979	433	3	semisimple	semisimple	ADJ
ejpam-3979	433	4	hopf	hopf	ADJ
ejpam-3979	433	5	algebras	algebras	PROPN
ejpam-3979	433	6	via	via	ADP
ejpam-3979	433	7	integrals	integral	NOUN
ejpam-3979	433	8	.	.	PUNCT
ejpam-3979	434	1	journal	journal	NOUN
ejpam-3979	434	2	of	of	ADP
ejpam-3979	434	3	algebra	algebra	PROPN
ejpam-3979	434	4	,	,	PUNCT
ejpam-3979	434	5	472:67–94	472:67–94	NUM
ejpam-3979	434	6	,	,	PUNCT
ejpam-3979	434	7	2017	2017	NUM
ejpam-3979	434	8	.	.	PUNCT
ejpam-3979	435	1	[	[	X
ejpam-3979	435	2	11	11	NUM
ejpam-3979	435	3	]	]	PUNCT
ejpam-3979	435	4	m.	m.	NOUN
ejpam-3979	435	5	cohen	cohen	PROPN
ejpam-3979	435	6	and	and	CCONJ
ejpam-3979	435	7	s.	s.	PROPN
ejpam-3979	435	8	westreich	westreich	PROPN
ejpam-3979	435	9	.	.	PUNCT
ejpam-3979	436	1	solvable	solvable	ADJ
ejpam-3979	436	2	hopf	hopf	ADJ
ejpam-3979	436	3	algebras	algebra	NOUN
ejpam-3979	436	4	and	and	CCONJ
ejpam-3979	436	5	their	their	PRON
ejpam-3979	436	6	twists	twist	NOUN
ejpam-3979	436	7	.	.	PUNCT
ejpam-3979	437	1	journal	journal	NOUN
ejpam-3979	437	2	of	of	ADP
ejpam-3979	437	3	algebra	algebra	PROPN
ejpam-3979	437	4	,	,	PUNCT
ejpam-3979	437	5	549:165–176	549:165–176	NUM
ejpam-3979	437	6	,	,	PUNCT
ejpam-3979	437	7	2020	2020	NUM
ejpam-3979	437	8	.	.	PUNCT
ejpam-3979	438	1	[	[	X
ejpam-3979	438	2	12	12	NUM
ejpam-3979	438	3	]	]	PUNCT
ejpam-3979	438	4	s.	s.	PROPN
ejpam-3979	438	5	dascalescu	dascalescu	PROPN
ejpam-3979	438	6	,	,	PUNCT
ejpam-3979	438	7	c.	c.	PROPN
ejpam-3979	438	8	nastasescu	nastasescu	PROPN
ejpam-3979	438	9	,	,	PUNCT
ejpam-3979	438	10	and	and	CCONJ
ejpam-3979	438	11	s.	s.	PROPN
ejpam-3979	438	12	raianu	raianu	PROPN
ejpam-3979	438	13	.	.	PUNCT
ejpam-3979	439	1	hopf	hopf	ADJ
ejpam-3979	439	2	algebra	algebra	NOUN
ejpam-3979	439	3	:	:	PUNCT
ejpam-3979	439	4	an	an	DET
ejpam-3979	439	5	introduction	introduction	NOUN
ejpam-3979	439	6	.	.	PUNCT
ejpam-3979	440	1	2000	2000	NUM
ejpam-3979	440	2	.	.	PUNCT
ejpam-3979	441	1	[	[	X
ejpam-3979	441	2	13	13	NUM
ejpam-3979	441	3	]	]	X
ejpam-3979	441	4	c.	c.	PROPN
ejpam-3979	441	5	n.	n.	PROPN
ejpam-3979	441	6	galindo	galindo	PROPN
ejpam-3979	441	7	and	and	CCONJ
ejpam-3979	441	8	s.	s.	PROPN
ejpam-3979	441	9	natale	natale	PROPN
ejpam-3979	441	10	.	.	PUNCT
ejpam-3979	442	1	simple	simple	ADJ
ejpam-3979	442	2	hopf	hopf	ADJ
ejpam-3979	442	3	algebras	algebra	NOUN
ejpam-3979	442	4	and	and	CCONJ
ejpam-3979	442	5	deformations	deformation	NOUN
ejpam-3979	442	6	of	of	ADP
ejpam-3979	442	7	finite	finite	ADJ
ejpam-3979	442	8	groups	group	NOUN
ejpam-3979	442	9	.	.	PUNCT
ejpam-3979	443	1	mathematical	mathematical	ADJ
ejpam-3979	443	2	research	research	NOUN
ejpam-3979	443	3	letters	letter	NOUN
ejpam-3979	443	4	,	,	PUNCT
ejpam-3979	443	5	14(6):943–954	14(6):943–954	NUM
ejpam-3979	443	6	,	,	PUNCT
ejpam-3979	443	7	2007	2007	NUM
ejpam-3979	443	8	.	.	PUNCT
ejpam-3979	444	1	[	[	X
ejpam-3979	444	2	14	14	NUM
ejpam-3979	444	3	]	]	PUNCT
ejpam-3979	444	4	a.	a.	NOUN
ejpam-3979	444	5	heliel	heliel	PROPN
ejpam-3979	444	6	,	,	PUNCT
ejpam-3979	444	7	m.	m.	NOUN
ejpam-3979	444	8	al	al	PROPN
ejpam-3979	444	9	-	-	PUNCT
ejpam-3979	444	10	shomrani	shomrani	PROPN
ejpam-3979	444	11	,	,	PUNCT
ejpam-3979	444	12	and	and	CCONJ
ejpam-3979	444	13	adolfo	adolfo	PROPN
ejpam-3979	444	14	ballester	ballester	PROPN
ejpam-3979	444	15	-	-	PUNCT
ejpam-3979	444	16	bolinches	bolinche	NOUN
ejpam-3979	444	17	.	.	PUNCT
ejpam-3979	445	1	on	on	ADP
ejpam-3979	445	2	the	the	DET
ejpam-3979	445	3	σ	σ	NOUN
ejpam-3979	445	4	-	-	PUNCT
ejpam-3979	445	5	length	length	NOUN
ejpam-3979	445	6	of	of	ADP
ejpam-3979	445	7	maximal	maximal	ADJ
ejpam-3979	445	8	subgroups	subgroup	NOUN
ejpam-3979	445	9	of	of	ADP
ejpam-3979	445	10	finite	finite	ADJ
ejpam-3979	445	11	σ	σ	PROPN
ejpam-3979	445	12	-	-	PUNCT
ejpam-3979	445	13	soluble	soluble	ADJ
ejpam-3979	445	14	groups	group	NOUN
ejpam-3979	445	15	.	.	PUNCT
ejpam-3979	446	1	mathematics	mathematic	NOUN
ejpam-3979	446	2	,	,	PUNCT
ejpam-3979	446	3	8(12):2165	8(12):2165	NUM
ejpam-3979	446	4	,	,	PUNCT
ejpam-3979	446	5	2020	2020	NUM
ejpam-3979	446	6	.	.	PUNCT
ejpam-3979	447	1	[	[	X
ejpam-3979	447	2	15	15	NUM
ejpam-3979	447	3	]	]	X
ejpam-3979	447	4	a.	a.	NOUN
ejpam-3979	447	5	a.	a.	NOUN
ejpam-3979	447	6	heliel	heliel	PROPN
ejpam-3979	447	7	,	,	PUNCT
ejpam-3979	447	8	m.	m.	NOUN
ejpam-3979	447	9	m.	m.	PROPN
ejpam-3979	447	10	al	al	PROPN
ejpam-3979	447	11	-	-	PUNCT
ejpam-3979	447	12	shomrani	shomrani	PROPN
ejpam-3979	447	13	,	,	PUNCT
ejpam-3979	447	14	and	and	CCONJ
ejpam-3979	447	15	t.	t.	PROPN
ejpam-3979	447	16	m.	m.	PROPN
ejpam-3979	447	17	al	al	PROPN
ejpam-3979	447	18	-	-	PUNCT
ejpam-3979	447	19	gafri	gafri	PROPN
ejpam-3979	447	20	.	.	PUNCT
ejpam-3979	448	1	on	on	ADP
ejpam-3979	448	2	weakly	weakly	ADJ
ejpam-3979	448	3	3	3	NUM
ejpam-3979	448	4	-	-	PUNCT
ejpam-3979	448	5	permutable	permutable	ADJ
ejpam-3979	448	6	subgroups	subgroup	NOUN
ejpam-3979	448	7	of	of	ADP
ejpam-3979	448	8	finite	finite	ADJ
ejpam-3979	448	9	groups	group	NOUN
ejpam-3979	448	10	.	.	PUNCT
ejpam-3979	449	1	journal	journal	NOUN
ejpam-3979	449	2	of	of	ADP
ejpam-3979	449	3	algebra	algebra	PROPN
ejpam-3979	449	4	and	and	CCONJ
ejpam-3979	449	5	its	its	PRON
ejpam-3979	449	6	applications	application	NOUN
ejpam-3979	449	7	,	,	PUNCT
ejpam-3979	449	8	14(05	14(05	NUM
ejpam-3979	449	9	)	)	PUNCT
ejpam-3979	449	10	,	,	PUNCT
ejpam-3979	449	11	2015	2015	NUM
ejpam-3979	449	12	.	.	PUNCT
ejpam-3979	450	1	[	[	X
ejpam-3979	450	2	16	16	NUM
ejpam-3979	450	3	]	]	PUNCT
ejpam-3979	450	4	a.	a.	NOUN
ejpam-3979	450	5	a.	a.	NOUN
ejpam-3979	450	6	heliel	heliel	PROPN
ejpam-3979	450	7	,	,	PUNCT
ejpam-3979	450	8	m.	m.	NOUN
ejpam-3979	450	9	m.	m.	PROPN
ejpam-3979	450	10	al	al	PROPN
ejpam-3979	450	11	-	-	PUNCT
ejpam-3979	450	12	shomrani	shomrani	PROPN
ejpam-3979	450	13	,	,	PUNCT
ejpam-3979	450	14	and	and	CCONJ
ejpam-3979	450	15	t.	t.	PROPN
ejpam-3979	450	16	m.	m.	PROPN
ejpam-3979	450	17	al	al	PROPN
ejpam-3979	450	18	-	-	PUNCT
ejpam-3979	450	19	gafri	gafri	PROPN
ejpam-3979	450	20	.	.	PUNCT
ejpam-3979	451	1	on	on	ADP
ejpam-3979	451	2	weakly	weakly	ADJ
ejpam-3979	451	3	3	3	NUM
ejpam-3979	451	4	-	-	PUNCT
ejpam-3979	451	5	permutable	permutable	ADJ
ejpam-3979	451	6	subgroups	subgroup	NOUN
ejpam-3979	451	7	of	of	ADP
ejpam-3979	451	8	finite	finite	PROPN
ejpam-3979	451	9	groups	groups	PROPN
ejpam-3979	451	10	ii	ii	PROPN
ejpam-3979	451	11	.	.	PUNCT
ejpam-3979	452	1	arabian	arabian	PROPN
ejpam-3979	452	2	journal	journal	PROPN
ejpam-3979	452	3	of	of	ADP
ejpam-3979	452	4	mathematics	mathematic	NOUN
ejpam-3979	452	5	,	,	PUNCT
ejpam-3979	452	6	5(1):63–68	5(1):63–68	NUM
ejpam-3979	452	7	,	,	PUNCT
ejpam-3979	452	8	2016	2016	NUM
ejpam-3979	452	9	.	.	PUNCT
ejpam-3979	453	1	[	[	X
ejpam-3979	453	2	17	17	NUM
ejpam-3979	453	3	]	]	PUNCT
ejpam-3979	453	4	k.	k.	PROPN
ejpam-3979	453	5	kytola	kytola	PROPN
ejpam-3979	453	6	.	.	PUNCT
ejpam-3979	454	1	introduction	introduction	NOUN
ejpam-3979	454	2	to	to	ADP
ejpam-3979	454	3	hopf	hopf	ADJ
ejpam-3979	454	4	algebras	algebra	NOUN
ejpam-3979	454	5	and	and	CCONJ
ejpam-3979	454	6	representations	representation	NOUN
ejpam-3979	454	7	.	.	PUNCT
ejpam-3979	455	1	notes	notes	PROPN
ejpam-3979	455	2	de	de	X
ejpam-3979	455	3	cours	cours	PROPN
ejpam-3979	455	4	,	,	PUNCT
ejpam-3979	455	5	2011	2011	NUM
ejpam-3979	455	6	.	.	PUNCT
ejpam-3979	456	1	[	[	X
ejpam-3979	456	2	18	18	NUM
ejpam-3979	456	3	]	]	PUNCT
ejpam-3979	456	4	r.	r.	PROPN
ejpam-3979	456	5	g.	g.	PROPN
ejpam-3979	456	6	larson	larson	PROPN
ejpam-3979	456	7	.	.	PUNCT
ejpam-3979	457	1	characters	character	NOUN
ejpam-3979	457	2	of	of	ADP
ejpam-3979	457	3	hopf	hopf	ADJ
ejpam-3979	457	4	algebras	algebras	PROPN
ejpam-3979	457	5	.	.	PUNCT
ejpam-3979	457	6	journal	journal	PROPN
ejpam-3979	457	7	of	of	ADP
ejpam-3979	457	8	algebra	algebra	PROPN
ejpam-3979	457	9	,	,	PUNCT
ejpam-3979	457	10	17(3):352–368	17(3):352–368	PROPN
ejpam-3979	457	11	,	,	PUNCT
ejpam-3979	457	12	1971	1971	NUM
ejpam-3979	457	13	.	.	PUNCT
ejpam-3979	458	1	[	[	X
ejpam-3979	458	2	19	19	NUM
ejpam-3979	458	3	]	]	PUNCT
ejpam-3979	458	4	r.	r.	PROPN
ejpam-3979	458	5	g.	g.	PROPN
ejpam-3979	458	6	larson	larson	PROPN
ejpam-3979	458	7	and	and	CCONJ
ejpam-3979	458	8	d.	d.	PROPN
ejpam-3979	458	9	e.	e.	PROPN
ejpam-3979	458	10	radford	radford	PROPN
ejpam-3979	458	11	.	.	PUNCT
ejpam-3979	459	1	semisimple	semisimple	PROPN
ejpam-3979	459	2	cosemisimple	cosemisimple	PROPN
ejpam-3979	459	3	hopf	hopf	PROPN
ejpam-3979	459	4	algebras	algebras	PROPN
ejpam-3979	459	5	.	.	PUNCT
ejpam-3979	460	1	american	american	PROPN
ejpam-3979	460	2	journal	journal	PROPN
ejpam-3979	460	3	of	of	ADP
ejpam-3979	460	4	mathematics	mathematic	NOUN
ejpam-3979	460	5	,	,	PUNCT
ejpam-3979	460	6	110(1):187–195	110(1):187–195	NUM
ejpam-3979	460	7	,	,	PUNCT
ejpam-3979	460	8	1988	1988	NUM
ejpam-3979	460	9	.	.	PUNCT
ejpam-3979	461	1	[	[	X
ejpam-3979	461	2	20	20	NUM
ejpam-3979	461	3	]	]	SYM
ejpam-3979	461	4	c	c	NOUN
ejpam-3979	461	5	.	.	PUNCT
ejpam-3979	462	1	p	p	NOUN
ejpam-3979	462	2	.milies	.milie	NOUN
ejpam-3979	462	3	and	and	CCONJ
ejpam-3979	462	4	s.	s.	PROPN
ejpam-3979	462	5	k.	k.	PROPN
ejpam-3979	462	6	sehgal	sehgal	PROPN
ejpam-3979	462	7	.	.	PUNCT
ejpam-3979	463	1	an	an	DET
ejpam-3979	463	2	introduction	introduction	NOUN
ejpam-3979	463	3	to	to	ADP
ejpam-3979	463	4	group	group	NOUN
ejpam-3979	463	5	ring	ring	NOUN
ejpam-3979	463	6	.	.	PUNCT
ejpam-3979	464	1	series	series	NOUN
ejpam-3979	464	2	:	:	PUNCT
ejpam-3979	464	3	algebra	algebra	NOUN
ejpam-3979	464	4	and	and	CCONJ
ejpam-3979	464	5	applications	application	NOUN
ejpam-3979	464	6	.	.	PUNCT
ejpam-3979	465	1	periodica	periodica	PROPN
ejpam-3979	465	2	mathematica	mathematica	PROPN
ejpam-3979	465	3	hungarica	hungarica	PROPN
ejpam-3979	465	4	,	,	PUNCT
ejpam-3979	465	5	1	1	NUM
ejpam-3979	465	6	,	,	PUNCT
ejpam-3979	465	7	2002	2002	NUM
ejpam-3979	465	8	.	.	PUNCT
ejpam-3979	466	1	[	[	X
ejpam-3979	466	2	21	21	NUM
ejpam-3979	466	3	]	]	PUNCT
ejpam-3979	466	4	m.	m.	PROPN
ejpam-3979	466	5	e.	e.	PROPN
ejpam-3979	466	6	mohamed	mohamed	PROPN
ejpam-3979	466	7	,	,	PUNCT
ejpam-3979	466	8	m.	m.	NOUN
ejpam-3979	466	9	m.	m.	PROPN
ejpam-3979	466	10	al	al	PROPN
ejpam-3979	466	11	-	-	PUNCT
ejpam-3979	466	12	shomrani	shomrani	PROPN
ejpam-3979	466	13	,	,	PUNCT
ejpam-3979	466	14	and	and	CCONJ
ejpam-3979	466	15	m.	m.	NOUN
ejpam-3979	466	16	elashiry	elashiry	NOUN
ejpam-3979	466	17	.	.	PUNCT
ejpam-3979	467	1	on	on	ADP
ejpam-3979	467	2	sh(q)-supplemented	sh(q)-supplemente	VERB
ejpam-3979	467	3	subgroups	subgroup	NOUN
ejpam-3979	467	4	of	of	ADP
ejpam-3979	467	5	a	a	DET
ejpam-3979	467	6	finite	finite	ADJ
ejpam-3979	467	7	group	group	NOUN
ejpam-3979	467	8	.	.	PUNCT
ejpam-3979	468	1	periodica	periodica	PROPN
ejpam-3979	468	2	mathematica	mathematica	PROPN
ejpam-3979	468	3	hungarica	hungarica	PROPN
ejpam-3979	468	4	,	,	PUNCT
ejpam-3979	468	5	76(2):27–265	76(2):27–265	NUM
ejpam-3979	468	6	,	,	PUNCT
ejpam-3979	468	7	2018	2018	NUM
ejpam-3979	468	8	.	.	PUNCT
ejpam-3979	469	1	[	[	X
ejpam-3979	469	2	22	22	NUM
ejpam-3979	469	3	]	]	X
ejpam-3979	469	4	d.	d.	PROPN
ejpam-3979	469	5	r.	r.	PROPN
ejpam-3979	469	6	pansera	pansera	PROPN
ejpam-3979	469	7	.	.	PUNCT
ejpam-3979	470	1	on	on	ADP
ejpam-3979	470	2	semisimple	semisimple	ADJ
ejpam-3979	470	3	hopf	hopf	ADJ
ejpam-3979	470	4	actions	action	NOUN
ejpam-3979	470	5	.	.	PUNCT
ejpam-3979	470	6	2017	2017	NUM
ejpam-3979	470	7	.	.	PUNCT
ejpam-3979	471	1	[	[	X
ejpam-3979	471	2	23	23	NUM
ejpam-3979	471	3	]	]	PUNCT
ejpam-3979	471	4	j.	j.	PROPN
ejpam-3979	471	5	s.	s.	PROPN
ejpam-3979	471	6	rose	rise	VERB
ejpam-3979	471	7	.	.	PUNCT
ejpam-3979	472	1	a	a	DET
ejpam-3979	472	2	course	course	NOUN
ejpam-3979	472	3	on	on	ADP
ejpam-3979	472	4	group	group	NOUN
ejpam-3979	472	5	theory	theory	NOUN
ejpam-3979	472	6	.	.	PUNCT
ejpam-3979	473	1	cambridge	cambridge	PROPN
ejpam-3979	473	2	uk	uk	PROPN
ejpam-3979	473	3	,	,	PUNCT
ejpam-3979	473	4	1978	1978	NUM
ejpam-3979	473	5	.	.	PUNCT
ejpam-3979	474	1	[	[	X
ejpam-3979	474	2	24	24	NUM
ejpam-3979	474	3	]	]	PUNCT
ejpam-3979	474	4	m.	m.	PROPN
ejpam-3979	474	5	e.	e.	PROPN
ejpam-3979	474	6	sweedler	sweedler	PROPN
ejpam-3979	474	7	.	.	PUNCT
ejpam-3979	475	1	hopf	hopf	PROPN
ejpam-3979	475	2	algebras	algebras	PROPN
ejpam-3979	475	3	.	.	PUNCT
ejpam-3979	476	1	new	new	PROPN
ejpam-3979	476	2	york	york	PROPN
ejpam-3979	476	3	,	,	PUNCT
ejpam-3979	476	4	1969	1969	NUM
ejpam-3979	476	5	.	.	PUNCT
ejpam-3979	477	1	[	[	X
ejpam-3979	477	2	25	25	NUM
ejpam-3979	477	3	]	]	PUNCT
ejpam-3979	477	4	r.	r.	PROPN
ejpam-3979	477	5	g.	g.	PROPN
ejpam-3979	477	6	underwood	underwood	PROPN
ejpam-3979	477	7	.	.	PUNCT
ejpam-3979	478	1	fundamentals	fundamental	NOUN
ejpam-3979	478	2	of	of	ADP
ejpam-3979	478	3	hopf	hopf	ADJ
ejpam-3979	478	4	algebras	algebra	NOUN
ejpam-3979	478	5	.	.	PUNCT
ejpam-3979	478	6	2010	2010	NUM
ejpam-3979	478	7	.	.	PUNCT
ejpam-3979	479	1	[	[	X
ejpam-3979	479	2	26	26	NUM
ejpam-3979	479	3	]	]	X
ejpam-3979	479	4	y.	y.	PROPN
ejpam-3979	479	5	wang	wang	PROPN
ejpam-3979	479	6	.	.	PUNCT
ejpam-3979	480	1	c	c	X
ejpam-3979	480	2	-	-	PUNCT
ejpam-3979	480	3	normality	normality	NOUN
ejpam-3979	480	4	of	of	ADP
ejpam-3979	480	5	groups	group	NOUN
ejpam-3979	480	6	and	and	CCONJ
ejpam-3979	480	7	its	its	PRON
ejpam-3979	480	8	properties	property	NOUN
ejpam-3979	480	9	.	.	PUNCT
ejpam-3979	481	1	journal	journal	NOUN
ejpam-3979	481	2	of	of	ADP
ejpam-3979	481	3	algebra	algebra	PROPN
ejpam-3979	481	4	,	,	PUNCT
ejpam-3979	481	5	180(3):954	180(3):954	NOUN
ejpam-3979	481	6	–	–	PUNCT
ejpam-3979	481	7	965	965	NUM
ejpam-3979	481	8	,	,	PUNCT
ejpam-3979	481	9	1996	1996	NUM
ejpam-3979	481	10	.	.	PUNCT