id	sid	tid	token	lemma	pos
ejpam-3285	1	1	european	european	PROPN
ejpam-3285	1	2	journal	journal	PROPN
ejpam-3285	1	3	of	of	ADP
ejpam-3285	1	4	pure	pure	ADJ
ejpam-3285	1	5	and	and	CCONJ
ejpam-3285	1	6	applied	apply	VERB
ejpam-3285	1	7	mathematics	mathematic	NOUN
ejpam-3285	1	8	vol	vol	NOUN
ejpam-3285	1	9	.	.	PUNCT
ejpam-3285	2	1	11	11	NUM
ejpam-3285	2	2	,	,	PUNCT
ejpam-3285	2	3	no	no	INTJ
ejpam-3285	2	4	.	.	NOUN
ejpam-3285	2	5	3	3	NUM
ejpam-3285	2	6	,	,	PUNCT
ejpam-3285	2	7	2018	2018	NUM
ejpam-3285	2	8	,	,	PUNCT
ejpam-3285	2	9	751	751	NUM
ejpam-3285	2	10	-	-	SYM
ejpam-3285	2	11	761	761	NUM
ejpam-3285	2	12	issn	issn	PROPN
ejpam-3285	2	13	1307	1307	NUM
ejpam-3285	2	14	-	-	SYM
ejpam-3285	2	15	5543	5543	NUM
ejpam-3285	2	16	–	–	PUNCT
ejpam-3285	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3285	2	18	published	publish	VERB
ejpam-3285	2	19	by	by	ADP
ejpam-3285	2	20	new	new	PROPN
ejpam-3285	2	21	york	york	PROPN
ejpam-3285	2	22	business	business	PROPN
ejpam-3285	2	23	global	global	ADJ
ejpam-3285	2	24	generalization	generalization	NOUN
ejpam-3285	2	25	of	of	ADP
ejpam-3285	2	26	schur	schur	PROPN
ejpam-3285	2	27	’s	’s	PART
ejpam-3285	2	28	lemma	lemma	PROPN
ejpam-3285	2	29	in	in	ADP
ejpam-3285	2	30	ring	ring	NOUN
ejpam-3285	2	31	representations	representation	NOUN
ejpam-3285	2	32	on	on	ADP
ejpam-3285	2	33	modules	module	NOUN
ejpam-3285	2	34	over	over	ADP
ejpam-3285	2	35	a	a	DET
ejpam-3285	2	36	commutative	commutative	ADJ
ejpam-3285	2	37	ring	ring	NOUN
ejpam-3285	2	38	na’imah	na’imah	NOUN
ejpam-3285	2	39	hijriati1,2,∗	hijriati1,2,∗	PROPN
ejpam-3285	2	40	,	,	PUNCT
ejpam-3285	2	41	sri	sri	PROPN
ejpam-3285	2	42	wahyuni1	wahyuni1	PROPN
ejpam-3285	2	43	,	,	PUNCT
ejpam-3285	2	44	indah	indah	PROPN
ejpam-3285	2	45	emilia	emilia	PROPN
ejpam-3285	2	46	wijayanti1	wijayanti1	PROPN
ejpam-3285	2	47	1	1	NUM
ejpam-3285	2	48	department	department	NOUN
ejpam-3285	2	49	of	of	ADP
ejpam-3285	2	50	mathematics	mathematic	NOUN
ejpam-3285	2	51	,	,	PUNCT
ejpam-3285	2	52	faculty	faculty	NOUN
ejpam-3285	2	53	of	of	ADP
ejpam-3285	2	54	mathematics	mathematic	NOUN
ejpam-3285	2	55	and	and	CCONJ
ejpam-3285	2	56	natural	natural	ADJ
ejpam-3285	2	57	sciences	science	NOUN
ejpam-3285	2	58	,	,	PUNCT
ejpam-3285	2	59	universitas	universita	NOUN
ejpam-3285	2	60	gadjah	gadjah	PROPN
ejpam-3285	2	61	mada	mada	PROPN
ejpam-3285	2	62	,	,	PUNCT
ejpam-3285	2	63	yogyakarta	yogyakarta	PROPN
ejpam-3285	2	64	,	,	PUNCT
ejpam-3285	2	65	indonesia	indonesia	PROPN
ejpam-3285	2	66	2	2	NUM
ejpam-3285	2	67	department	department	NOUN
ejpam-3285	2	68	of	of	ADP
ejpam-3285	2	69	mathematics	mathematic	NOUN
ejpam-3285	2	70	,	,	PUNCT
ejpam-3285	2	71	faculty	faculty	NOUN
ejpam-3285	2	72	of	of	ADP
ejpam-3285	2	73	mathematics	mathematic	NOUN
ejpam-3285	2	74	and	and	CCONJ
ejpam-3285	2	75	natural	natural	ADJ
ejpam-3285	2	76	sciences	science	NOUN
ejpam-3285	2	77	,	,	PUNCT
ejpam-3285	2	78	universitas	universita	NOUN
ejpam-3285	2	79	lambung	lambung	PROPN
ejpam-3285	2	80	mangkurat	mangkurat	PROPN
ejpam-3285	2	81	,	,	PUNCT
ejpam-3285	2	82	banjarmasin	banjarmasin	PROPN
ejpam-3285	2	83	,	,	PUNCT
ejpam-3285	2	84	indonesia	indonesia	PROPN
ejpam-3285	2	85	abstract	abstract	NOUN
ejpam-3285	2	86	.	.	PUNCT
ejpam-3285	3	1	let	let	VERB
ejpam-3285	3	2	r	r	NOUN
ejpam-3285	3	3	,	,	PUNCT
ejpam-3285	3	4	s	s	AUX
ejpam-3285	3	5	be	be	AUX
ejpam-3285	3	6	rings	ring	NOUN
ejpam-3285	3	7	with	with	ADP
ejpam-3285	3	8	unity	unity	NOUN
ejpam-3285	3	9	,	,	PUNCT
ejpam-3285	3	10	m	m	VERB
ejpam-3285	3	11	a	a	DET
ejpam-3285	3	12	module	module	NOUN
ejpam-3285	3	13	over	over	ADP
ejpam-3285	3	14	s	s	PROPN
ejpam-3285	3	15	,	,	PUNCT
ejpam-3285	3	16	where	where	SCONJ
ejpam-3285	3	17	s	s	VERB
ejpam-3285	3	18	a	a	DET
ejpam-3285	3	19	commutative	commutative	ADJ
ejpam-3285	3	20	ring	ring	NOUN
ejpam-3285	3	21	,	,	PUNCT
ejpam-3285	3	22	and	and	CCONJ
ejpam-3285	3	23	f	f	X
ejpam-3285	3	24	:	:	PUNCT
ejpam-3285	3	25	r→	r→	PROPN
ejpam-3285	3	26	s	s	VERB
ejpam-3285	3	27	a	a	DET
ejpam-3285	3	28	ring	ring	NOUN
ejpam-3285	3	29	homomorphism	homomorphism	NOUN
ejpam-3285	3	30	.	.	PUNCT
ejpam-3285	4	1	a	a	DET
ejpam-3285	4	2	ring	ring	NOUN
ejpam-3285	4	3	representation	representation	NOUN
ejpam-3285	4	4	of	of	ADP
ejpam-3285	4	5	r	r	NOUN
ejpam-3285	4	6	on	on	ADP
ejpam-3285	4	7	m	m	NOUN
ejpam-3285	4	8	via	via	ADP
ejpam-3285	4	9	f	f	PROPN
ejpam-3285	4	10	is	be	AUX
ejpam-3285	4	11	a	a	DET
ejpam-3285	4	12	ring	ring	NOUN
ejpam-3285	4	13	homomorphism	homomorphism	PROPN
ejpam-3285	4	14	µ	µ	X
ejpam-3285	4	15	:	:	PUNCT
ejpam-3285	4	16	r	r	NOUN
ejpam-3285	4	17	→	→	SYM
ejpam-3285	4	18	ends(m	ends(m	PROPN
ejpam-3285	4	19	)	)	PUNCT
ejpam-3285	4	20	,	,	PUNCT
ejpam-3285	4	21	where	where	SCONJ
ejpam-3285	4	22	ends(m	ends(m	PROPN
ejpam-3285	4	23	)	)	PUNCT
ejpam-3285	4	24	is	be	AUX
ejpam-3285	4	25	a	a	DET
ejpam-3285	4	26	ring	ring	NOUN
ejpam-3285	4	27	of	of	ADP
ejpam-3285	4	28	all	all	DET
ejpam-3285	4	29	s	s	NOUN
ejpam-3285	4	30	-	-	PUNCT
ejpam-3285	4	31	module	module	NOUN
ejpam-3285	4	32	homomorphisms	homomorphism	NOUN
ejpam-3285	4	33	on	on	ADP
ejpam-3285	4	34	m	m	PROPN
ejpam-3285	4	35	.	.	PUNCT
ejpam-3285	5	1	one	one	NUM
ejpam-3285	5	2	of	of	ADP
ejpam-3285	5	3	the	the	DET
ejpam-3285	5	4	important	important	ADJ
ejpam-3285	5	5	properties	property	NOUN
ejpam-3285	5	6	in	in	ADP
ejpam-3285	5	7	representation	representation	NOUN
ejpam-3285	5	8	of	of	ADP
ejpam-3285	5	9	ring	ring	NOUN
ejpam-3285	5	10	is	be	AUX
ejpam-3285	5	11	the	the	DET
ejpam-3285	5	12	schur	schur	PROPN
ejpam-3285	5	13	’s	’s	PART
ejpam-3285	5	14	lemma	lemma	PROPN
ejpam-3285	5	15	.	.	PUNCT
ejpam-3285	6	1	the	the	DET
ejpam-3285	6	2	main	main	ADJ
ejpam-3285	6	3	result	result	NOUN
ejpam-3285	6	4	of	of	ADP
ejpam-3285	6	5	this	this	DET
ejpam-3285	6	6	paper	paper	NOUN
ejpam-3285	6	7	is	be	AUX
ejpam-3285	6	8	partly	partly	ADV
ejpam-3285	6	9	the	the	DET
ejpam-3285	6	10	generalization	generalization	NOUN
ejpam-3285	6	11	of	of	ADP
ejpam-3285	6	12	schur	schur	PROPN
ejpam-3285	6	13	’s	’s	PART
ejpam-3285	6	14	lemma	lemma	PROPN
ejpam-3285	6	15	in	in	ADP
ejpam-3285	6	16	representations	representation	NOUN
ejpam-3285	6	17	of	of	ADP
ejpam-3285	6	18	ring	ring	NOUN
ejpam-3285	6	19	on	on	ADP
ejpam-3285	6	20	modules	module	NOUN
ejpam-3285	6	21	over	over	ADP
ejpam-3285	6	22	a	a	DET
ejpam-3285	6	23	commutative	commutative	ADJ
ejpam-3285	6	24	ring	ring	NOUN
ejpam-3285	6	25	2010	2010	NUM
ejpam-3285	6	26	mathematics	mathematic	NOUN
ejpam-3285	6	27	subject	subject	NOUN
ejpam-3285	6	28	classifications	classification	NOUN
ejpam-3285	6	29	:	:	PUNCT
ejpam-3285	6	30	16g10	16g10	NUM
ejpam-3285	6	31	,	,	PUNCT
ejpam-3285	6	32	16w20	16w20	NUM
ejpam-3285	6	33	,	,	PUNCT
ejpam-3285	6	34	12e15	12e15	NUM
ejpam-3285	6	35	key	key	ADJ
ejpam-3285	6	36	words	word	NOUN
ejpam-3285	6	37	and	and	CCONJ
ejpam-3285	6	38	phrases	phrase	NOUN
ejpam-3285	6	39	:	:	PUNCT
ejpam-3285	6	40	representation	representation	NOUN
ejpam-3285	6	41	of	of	ADP
ejpam-3285	6	42	ring	ring	NOUN
ejpam-3285	6	43	on	on	ADP
ejpam-3285	6	44	module	module	NOUN
ejpam-3285	6	45	,	,	PUNCT
ejpam-3285	6	46	generalized	generalize	VERB
ejpam-3285	6	47	schur	schur	PROPN
ejpam-3285	6	48	’s	’s	PART
ejpam-3285	6	49	lemma	lemma	PROPN
ejpam-3285	6	50	,	,	PUNCT
ejpam-3285	6	51	ring	re	VERB
ejpam-3285	6	52	homomorphism	homomorphism	NOUN
ejpam-3285	6	53	1	1	X
ejpam-3285	6	54	.	.	X
ejpam-3285	6	55	introduction	introduction	NOUN
ejpam-3285	6	56	in	in	ADP
ejpam-3285	6	57	[	[	X
ejpam-3285	6	58	2	2	NUM
ejpam-3285	6	59	]	]	PUNCT
ejpam-3285	6	60	,	,	PUNCT
ejpam-3285	6	61	an	an	DET
ejpam-3285	6	62	abelian	abelian	ADJ
ejpam-3285	6	63	group	group	NOUN
ejpam-3285	6	64	m	m	PROPN
ejpam-3285	6	65	is	be	AUX
ejpam-3285	6	66	called	call	VERB
ejpam-3285	6	67	an	an	DET
ejpam-3285	6	68	r	r	NOUN
ejpam-3285	6	69	-	-	PUNCT
ejpam-3285	6	70	module	module	NOUN
ejpam-3285	6	71	if	if	SCONJ
ejpam-3285	6	72	there	there	PRON
ejpam-3285	6	73	is	be	VERB
ejpam-3285	6	74	a	a	DET
ejpam-3285	6	75	ring	ring	NOUN
ejpam-3285	6	76	homomorphism	homomorphism	NOUN
ejpam-3285	6	77	ϕ	ϕ	X
ejpam-3285	6	78	:	:	PUNCT
ejpam-3285	6	79	r	r	NOUN
ejpam-3285	6	80	→	→	SYM
ejpam-3285	6	81	endz(m	endz(m	PROPN
ejpam-3285	6	82	)	)	PUNCT
ejpam-3285	6	83	where	where	SCONJ
ejpam-3285	6	84	endz(m	endz(m	PROPN
ejpam-3285	6	85	)	)	PUNCT
ejpam-3285	6	86	is	be	AUX
ejpam-3285	6	87	a	a	DET
ejpam-3285	6	88	ring	ring	NOUN
ejpam-3285	6	89	of	of	ADP
ejpam-3285	6	90	all	all	DET
ejpam-3285	6	91	group	group	NOUN
ejpam-3285	6	92	endomorphism	endomorphism	NOUN
ejpam-3285	6	93	of	of	ADP
ejpam-3285	6	94	m	m	PROPN
ejpam-3285	6	95	.	.	PUNCT
ejpam-3285	7	1	we	we	PRON
ejpam-3285	7	2	know	know	VERB
ejpam-3285	7	3	that	that	SCONJ
ejpam-3285	7	4	if	if	SCONJ
ejpam-3285	7	5	there	there	PRON
ejpam-3285	7	6	is	be	VERB
ejpam-3285	7	7	a	a	DET
ejpam-3285	7	8	ring	ring	NOUN
ejpam-3285	7	9	homomorphism	homomorphism	NOUN
ejpam-3285	7	10	f	f	X
ejpam-3285	7	11	:	:	PUNCT
ejpam-3285	7	12	r	r	NOUN
ejpam-3285	7	13	→	→	SYM
ejpam-3285	7	14	s	s	PROPN
ejpam-3285	7	15	,	,	PUNCT
ejpam-3285	7	16	then	then	ADV
ejpam-3285	7	17	every	every	DET
ejpam-3285	7	18	s	s	NOUN
ejpam-3285	7	19	-	-	PUNCT
ejpam-3285	7	20	module	module	NOUN
ejpam-3285	7	21	is	be	AUX
ejpam-3285	7	22	also	also	ADV
ejpam-3285	7	23	r	r	NOUN
ejpam-3285	7	24	-	-	PUNCT
ejpam-3285	7	25	module	module	NOUN
ejpam-3285	7	26	,	,	PUNCT
ejpam-3285	7	27	where	where	SCONJ
ejpam-3285	7	28	the	the	DET
ejpam-3285	7	29	scalar	scalar	ADJ
ejpam-3285	7	30	multiplication	multiplication	NOUN
ejpam-3285	7	31	on	on	ADP
ejpam-3285	7	32	r	r	NOUN
ejpam-3285	7	33	defined	define	VERB
ejpam-3285	7	34	by	by	ADP
ejpam-3285	7	35	rm	rm	NOUN
ejpam-3285	7	36	=	=	PUNCT
ejpam-3285	7	37	f(r)m	f(r)m	NOUN
ejpam-3285	7	38	[	[	X
ejpam-3285	7	39	2	2	NUM
ejpam-3285	7	40	]	]	PUNCT
ejpam-3285	7	41	.	.	PUNCT
ejpam-3285	8	1	we	we	PRON
ejpam-3285	8	2	generalize	generalize	VERB
ejpam-3285	8	3	the	the	DET
ejpam-3285	8	4	codomain	codomain	NOUN
ejpam-3285	8	5	of	of	ADP
ejpam-3285	8	6	the	the	DET
ejpam-3285	8	7	ring	ring	NOUN
ejpam-3285	8	8	homomorphism	homomorphism	PROPN
ejpam-3285	8	9	ϕ	ϕ	NOUN
ejpam-3285	8	10	to	to	ADP
ejpam-3285	8	11	the	the	DET
ejpam-3285	8	12	ring	ring	NOUN
ejpam-3285	8	13	of	of	ADP
ejpam-3285	8	14	endomorphisms	endomorphism	NOUN
ejpam-3285	8	15	of	of	ADP
ejpam-3285	8	16	a	a	DET
ejpam-3285	8	17	module	module	NOUN
ejpam-3285	8	18	over	over	ADP
ejpam-3285	8	19	any	any	DET
ejpam-3285	8	20	ring	ring	NOUN
ejpam-3285	8	21	s.	s.	PROPN
ejpam-3285	8	22	due	due	ADP
ejpam-3285	8	23	to	to	ADP
ejpam-3285	8	24	this	this	DET
ejpam-3285	8	25	aim	aim	NOUN
ejpam-3285	8	26	,	,	PUNCT
ejpam-3285	8	27	we	we	PRON
ejpam-3285	8	28	need	need	VERB
ejpam-3285	8	29	a	a	DET
ejpam-3285	8	30	connection	connection	NOUN
ejpam-3285	8	31	between	between	ADP
ejpam-3285	8	32	the	the	DET
ejpam-3285	8	33	ring	ring	NOUN
ejpam-3285	8	34	r	r	NOUN
ejpam-3285	8	35	and	and	CCONJ
ejpam-3285	8	36	the	the	DET
ejpam-3285	8	37	s	s	NOUN
ejpam-3285	8	38	-	-	PUNCT
ejpam-3285	8	39	module	module	NOUN
ejpam-3285	8	40	m	m	NOUN
ejpam-3285	8	41	.	.	PUNCT
ejpam-3285	9	1	moreover	moreover	ADV
ejpam-3285	9	2	,	,	PUNCT
ejpam-3285	9	3	we	we	PRON
ejpam-3285	9	4	need	need	VERB
ejpam-3285	9	5	the	the	DET
ejpam-3285	9	6	commutativity	commutativity	NOUN
ejpam-3285	9	7	of	of	ADP
ejpam-3285	9	8	s	s	PRON
ejpam-3285	9	9	to	to	PART
ejpam-3285	9	10	guarantee	guarantee	VERB
ejpam-3285	9	11	µ(r	µ(r	NUM
ejpam-3285	9	12	)	)	PUNCT
ejpam-3285	9	13	∈	∈	PROPN
ejpam-3285	9	14	ends(m	ends(m	PROPN
ejpam-3285	9	15	)	)	PUNCT
ejpam-3285	9	16	,	,	PUNCT
ejpam-3285	9	17	where	where	SCONJ
ejpam-3285	9	18	µ(r	µ(r	NOUN
ejpam-3285	9	19	)	)	PUNCT
ejpam-3285	9	20	:	:	PUNCT
ejpam-3285	10	1	=	=	PUNCT
ejpam-3285	10	2	µr	µr	ADP
ejpam-3285	10	3	:	:	PUNCT
ejpam-3285	10	4	m	m	VERB
ejpam-3285	10	5	→m	→m	X
ejpam-3285	10	6	,	,	PUNCT
ejpam-3285	10	7	m	m	PROPN
ejpam-3285	10	8	7→	7→	NUM
ejpam-3285	10	9	f(r)m	f(r)m	NOUN
ejpam-3285	10	10	.	.	PUNCT
ejpam-3285	11	1	recall	recall	VERB
ejpam-3285	11	2	the	the	DET
ejpam-3285	11	3	definition	definition	NOUN
ejpam-3285	11	4	of	of	ADP
ejpam-3285	11	5	a	a	DET
ejpam-3285	11	6	representation	representation	NOUN
ejpam-3285	11	7	of	of	ADP
ejpam-3285	11	8	a	a	DET
ejpam-3285	11	9	ring	ring	NOUN
ejpam-3285	11	10	r	r	NOUN
ejpam-3285	11	11	on	on	ADP
ejpam-3285	11	12	a	a	DET
ejpam-3285	11	13	vector	vector	NOUN
ejpam-3285	11	14	space	space	NOUN
ejpam-3285	11	15	v	v	NOUN
ejpam-3285	11	16	over	over	ADP
ejpam-3285	11	17	a	a	DET
ejpam-3285	11	18	field	field	NOUN
ejpam-3285	11	19	f	f	PROPN
ejpam-3285	12	1	i.e	i.e	PRON
ejpam-3285	12	2	a	a	DET
ejpam-3285	12	3	ring	ring	NOUN
ejpam-3285	12	4	homomorphism	homomorphism	PROPN
ejpam-3285	12	5	ρ	ρ	X
ejpam-3285	12	6	:	:	PUNCT
ejpam-3285	12	7	r	r	NOUN
ejpam-3285	12	8	→	→	SYM
ejpam-3285	12	9	endf	endf	NOUN
ejpam-3285	12	10	(	(	PUNCT
ejpam-3285	12	11	v	v	NOUN
ejpam-3285	12	12	)	)	PUNCT
ejpam-3285	12	13	,	,	PUNCT
ejpam-3285	12	14	where	where	SCONJ
ejpam-3285	12	15	endf	endf	NOUN
ejpam-3285	12	16	(	(	PUNCT
ejpam-3285	12	17	v	v	NOUN
ejpam-3285	12	18	)	)	PUNCT
ejpam-3285	12	19	is	be	AUX
ejpam-3285	12	20	a	a	DET
ejpam-3285	12	21	ring	ring	NOUN
ejpam-3285	12	22	of	of	ADP
ejpam-3285	12	23	all	all	DET
ejpam-3285	12	24	linear	linear	ADJ
ejpam-3285	12	25	transformations	transformation	NOUN
ejpam-3285	12	26	of	of	ADP
ejpam-3285	12	27	v	v	NOUN
ejpam-3285	12	28	[	[	X
ejpam-3285	12	29	7	7	NUM
ejpam-3285	12	30	]	]	PUNCT
ejpam-3285	12	31	.	.	PUNCT
ejpam-3285	13	1	analog	analog	NOUN
ejpam-3285	13	2	to	to	ADP
ejpam-3285	13	3	the	the	DET
ejpam-3285	13	4	definition	definition	NOUN
ejpam-3285	13	5	of	of	ADP
ejpam-3285	13	6	representations	representation	NOUN
ejpam-3285	13	7	of	of	ADP
ejpam-3285	13	8	rings	ring	NOUN
ejpam-3285	13	9	on	on	ADP
ejpam-3285	13	10	vector	vector	NOUN
ejpam-3285	13	11	spaces	space	NOUN
ejpam-3285	13	12	,	,	PUNCT
ejpam-3285	13	13	we	we	PRON
ejpam-3285	13	14	define	define	VERB
ejpam-3285	13	15	representations	representation	NOUN
ejpam-3285	13	16	of	of	ADP
ejpam-3285	13	17	rings	ring	NOUN
ejpam-3285	13	18	on	on	ADP
ejpam-3285	13	19	modules	module	NOUN
ejpam-3285	13	20	over	over	ADP
ejpam-3285	13	21	a	a	DET
ejpam-3285	13	22	commutative	commutative	ADJ
ejpam-3285	13	23	ring	ring	NOUN
ejpam-3285	13	24	as	as	SCONJ
ejpam-3285	13	25	follow	follow	VERB
ejpam-3285	13	26	:	:	PUNCT
ejpam-3285	13	27	∗corresponding	∗corresponde	VERB
ejpam-3285	13	28	author	author	NOUN
ejpam-3285	13	29	.	.	PUNCT
ejpam-3285	14	1	doi	doi	NOUN
ejpam-3285	14	2	:	:	PUNCT
ejpam-3285	14	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3285	https://doi.org/10.29020/nybg.ejpam.v11i3.3285	PROPN
ejpam-3285	14	4	email	email	NOUN
ejpam-3285	14	5	addresses	address	NOUN
ejpam-3285	14	6	:	:	PUNCT
ejpam-3285	14	7	naimah.hijriati@mail.ugm.ac.id	naimah.hijriati@mail.ugm.ac.id	PROPN
ejpam-3285	14	8	(	(	PUNCT
ejpam-3285	14	9	n.	n.	PROPN
ejpam-3285	14	10	hijriati	hijriati	PROPN
ejpam-3285	14	11	)	)	PUNCT
ejpam-3285	14	12	,	,	PUNCT
ejpam-3285	14	13	swahyuni@ugm.ac.id	swahyuni@ugm.ac.id	PROPN
ejpam-3285	14	14	(	(	PUNCT
ejpam-3285	14	15	s.	s.	PROPN
ejpam-3285	14	16	wahyuni	wahyuni	PROPN
ejpam-3285	14	17	)	)	PUNCT
ejpam-3285	14	18	,	,	PUNCT
ejpam-3285	14	19	ind	ind	NOUN
ejpam-3285	14	20	wijayanti@ugm.ac.id	wijayanti@ugm.ac.id	PROPN
ejpam-3285	14	21	(	(	PUNCT
ejpam-3285	14	22	i.e	i.e	X
ejpam-3285	14	23	wijayanti	wijayanti	NOUN
ejpam-3285	14	24	)	)	PUNCT
ejpam-3285	14	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3285	15	1	751	751	NUM
ejpam-3285	15	2	c	c	NOUN
ejpam-3285	15	3	©	©	PROPN
ejpam-3285	15	4	2018	2018	NUM
ejpam-3285	15	5	ejpam	ejpam	VERB
ejpam-3285	15	6	all	all	DET
ejpam-3285	15	7	rights	right	NOUN
ejpam-3285	15	8	reserved	reserve	VERB
ejpam-3285	15	9	.	.	PUNCT
ejpam-3285	16	1	n.	n.	PROPN
ejpam-3285	16	2	hijriati	hijriati	PROPN
ejpam-3285	16	3	,	,	PUNCT
ejpam-3285	16	4	s.	s.	PROPN
ejpam-3285	16	5	wahyuni	wahyuni	PROPN
ejpam-3285	16	6	,	,	PUNCT
ejpam-3285	16	7	i.e.	i.e.	X
ejpam-3285	16	8	wijayanti	wijayanti	X
ejpam-3285	16	9	/	/	SYM
ejpam-3285	16	10	eur	eur	PROPN
ejpam-3285	16	11	.	.	PUNCT
ejpam-3285	17	1	j.	j.	PROPN
ejpam-3285	17	2	pure	pure	PROPN
ejpam-3285	17	3	appl	appl	PROPN
ejpam-3285	17	4	.	.	PROPN
ejpam-3285	17	5	math	math	PROPN
ejpam-3285	17	6	,	,	PUNCT
ejpam-3285	17	7	11	11	NUM
ejpam-3285	17	8	(	(	PUNCT
ejpam-3285	17	9	3	3	NUM
ejpam-3285	17	10	)	)	PUNCT
ejpam-3285	17	11	(	(	PUNCT
ejpam-3285	17	12	2018	2018	NUM
ejpam-3285	17	13	)	)	PUNCT
ejpam-3285	17	14	,	,	PUNCT
ejpam-3285	17	15	751	751	NUM
ejpam-3285	17	16	-	-	SYM
ejpam-3285	17	17	761	761	NUM
ejpam-3285	17	18	752	752	NUM
ejpam-3285	17	19	definition	definition	NOUN
ejpam-3285	17	20	1	1	NUM
ejpam-3285	17	21	.	.	PUNCT
ejpam-3285	18	1	let	let	VERB
ejpam-3285	18	2	r	r	PRON
ejpam-3285	18	3	be	be	AUX
ejpam-3285	18	4	a	a	DET
ejpam-3285	18	5	ring	ring	NOUN
ejpam-3285	18	6	with	with	ADP
ejpam-3285	18	7	unity	unity	NOUN
ejpam-3285	18	8	,	,	PUNCT
ejpam-3285	18	9	s	s	VERB
ejpam-3285	18	10	a	a	DET
ejpam-3285	18	11	commutative	commutative	ADJ
ejpam-3285	18	12	ring	ring	NOUN
ejpam-3285	18	13	with	with	ADP
ejpam-3285	18	14	unity	unity	NOUN
ejpam-3285	18	15	and	and	CCONJ
ejpam-3285	18	16	f	f	NOUN
ejpam-3285	18	17	:	:	PUNCT
ejpam-3285	18	18	r	r	X
ejpam-3285	18	19	→	→	SYM
ejpam-3285	18	20	s	s	VERB
ejpam-3285	18	21	a	a	DET
ejpam-3285	18	22	ring	ring	NOUN
ejpam-3285	18	23	homomorphism	homomorphism	NOUN
ejpam-3285	18	24	.	.	PUNCT
ejpam-3285	19	1	a	a	DET
ejpam-3285	19	2	representation	representation	NOUN
ejpam-3285	19	3	of	of	ADP
ejpam-3285	19	4	a	a	DET
ejpam-3285	19	5	ring	ring	NOUN
ejpam-3285	19	6	r	r	NOUN
ejpam-3285	19	7	on	on	ADP
ejpam-3285	19	8	an	an	DET
ejpam-3285	19	9	s	s	NOUN
ejpam-3285	19	10	-	-	PUNCT
ejpam-3285	19	11	module	module	NOUN
ejpam-3285	19	12	m	m	NOUN
ejpam-3285	19	13	is	be	AUX
ejpam-3285	19	14	a	a	DET
ejpam-3285	19	15	ring	ring	NOUN
ejpam-3285	19	16	homomorphism	homomorphism	NOUN
ejpam-3285	19	17	µ	µ	X
ejpam-3285	19	18	:	:	PUNCT
ejpam-3285	19	19	r→	r→	PROPN
ejpam-3285	19	20	ends(m	ends(m	PROPN
ejpam-3285	19	21	)	)	PUNCT
ejpam-3285	19	22	,	,	PUNCT
ejpam-3285	19	23	r	r	NOUN
ejpam-3285	19	24	7→	7→	NUM
ejpam-3285	19	25	µr	µr	ADP
ejpam-3285	19	26	,	,	PUNCT
ejpam-3285	19	27	(	(	PUNCT
ejpam-3285	19	28	1	1	X
ejpam-3285	19	29	)	)	PUNCT
ejpam-3285	19	30	where	where	SCONJ
ejpam-3285	19	31	µr	µr	ADP
ejpam-3285	19	32	∈	∈	PROPN
ejpam-3285	19	33	ends(m	ends(m	PROPN
ejpam-3285	19	34	)	)	PUNCT
ejpam-3285	19	35	is	be	AUX
ejpam-3285	19	36	defined	define	VERB
ejpam-3285	19	37	by	by	ADP
ejpam-3285	19	38	µr(m	µr(m	NOUN
ejpam-3285	19	39	)	)	PUNCT
ejpam-3285	19	40	=	=	SYM
ejpam-3285	19	41	f(r)m	f(r)m	NOUN
ejpam-3285	19	42	for	for	ADP
ejpam-3285	19	43	every	every	DET
ejpam-3285	19	44	r	r	NOUN
ejpam-3285	19	45	∈	∈	NOUN
ejpam-3285	19	46	r	r	NOUN
ejpam-3285	19	47	and	and	CCONJ
ejpam-3285	19	48	m	m	NOUN
ejpam-3285	19	49	∈m	∈m	NOUN
ejpam-3285	19	50	.	.	PUNCT
ejpam-3285	20	1	furthermore	furthermore	ADV
ejpam-3285	20	2	,	,	PUNCT
ejpam-3285	20	3	this	this	DET
ejpam-3285	20	4	representation	representation	NOUN
ejpam-3285	20	5	µ	µ	X
ejpam-3285	20	6	of	of	ADP
ejpam-3285	20	7	ring	ring	NOUN
ejpam-3285	20	8	r	r	NOUN
ejpam-3285	20	9	on	on	ADP
ejpam-3285	20	10	module	module	NOUN
ejpam-3285	20	11	m	m	NOUN
ejpam-3285	20	12	is	be	AUX
ejpam-3285	20	13	called	call	VERB
ejpam-3285	20	14	an	an	DET
ejpam-3285	20	15	f	f	PROPN
ejpam-3285	20	16	-representation	-representation	NOUN
ejpam-3285	20	17	of	of	ADP
ejpam-3285	20	18	r	r	NOUN
ejpam-3285	20	19	and	and	CCONJ
ejpam-3285	20	20	m	m	PROPN
ejpam-3285	20	21	is	be	AUX
ejpam-3285	20	22	called	call	VERB
ejpam-3285	20	23	an	an	DET
ejpam-3285	20	24	f	f	PROPN
ejpam-3285	20	25	-representation	-representation	PROPN
ejpam-3285	20	26	module	module	NOUN
ejpam-3285	20	27	of	of	ADP
ejpam-3285	20	28	r.	r.	PROPN
ejpam-3285	20	29	note	note	PROPN
ejpam-3285	20	30	that	that	PRON
ejpam-3285	20	31	prefix	prefix	NOUN
ejpam-3285	20	32	f	f	PROPN
ejpam-3285	20	33	in	in	ADP
ejpam-3285	20	34	”	"	PUNCT
ejpam-3285	20	35	f	f	PROPN
ejpam-3285	20	36	-representation	-representation	PROPN
ejpam-3285	20	37	”	"	PUNCT
ejpam-3285	20	38	depends	depend	VERB
ejpam-3285	20	39	on	on	ADP
ejpam-3285	20	40	a	a	DET
ejpam-3285	20	41	ring	ring	NOUN
ejpam-3285	21	1	homomorphism	homomorphism	PROPN
ejpam-3285	21	2	f	f	X
ejpam-3285	21	3	:	:	PUNCT
ejpam-3285	21	4	r→	r→	PROPN
ejpam-3285	21	5	s	s	VERB
ejpam-3285	21	6	we	we	PRON
ejpam-3285	21	7	choose	choose	VERB
ejpam-3285	21	8	.	.	PUNCT
ejpam-3285	22	1	these	these	PRON
ejpam-3285	22	2	are	be	AUX
ejpam-3285	22	3	some	some	DET
ejpam-3285	22	4	examples	example	NOUN
ejpam-3285	22	5	of	of	ADP
ejpam-3285	22	6	representation	representation	NOUN
ejpam-3285	22	7	of	of	ADP
ejpam-3285	22	8	ring	ring	NOUN
ejpam-3285	22	9	.	.	PUNCT
ejpam-3285	22	10	example	example	NOUN
ejpam-3285	23	1	1	1	NUM
ejpam-3285	23	2	.	.	PUNCT
ejpam-3285	24	1	every	every	DET
ejpam-3285	24	2	ring	ring	NOUN
ejpam-3285	24	3	commutative	commutative	ADJ
ejpam-3285	24	4	r	r	NOUN
ejpam-3285	24	5	has	have	VERB
ejpam-3285	24	6	a	a	DET
ejpam-3285	24	7	1d	1d	NUM
ejpam-3285	24	8	-	-	PUNCT
ejpam-3285	24	9	representation	representation	NOUN
ejpam-3285	24	10	on	on	ADP
ejpam-3285	24	11	r	r	NOUN
ejpam-3285	24	12	-	-	PUNCT
ejpam-3285	24	13	module	module	NOUN
ejpam-3285	24	14	m	m	NOUN
ejpam-3285	24	15	,	,	PUNCT
ejpam-3285	24	16	since	since	SCONJ
ejpam-3285	24	17	there	there	PRON
ejpam-3285	24	18	exists	exist	VERB
ejpam-3285	24	19	the	the	DET
ejpam-3285	24	20	identity	identity	NOUN
ejpam-3285	24	21	ring	ring	NOUN
ejpam-3285	24	22	homomorphism	homomorphism	NOUN
ejpam-3285	24	23	1d	1d	NUM
ejpam-3285	24	24	:	:	PUNCT
ejpam-3285	24	25	r→	r→	PROPN
ejpam-3285	24	26	r.	r.	PROPN
ejpam-3285	24	27	example	example	NOUN
ejpam-3285	24	28	2	2	NUM
ejpam-3285	24	29	.	.	PUNCT
ejpam-3285	25	1	let	let	VERB
ejpam-3285	25	2	r[g	r[g	PROPN
ejpam-3285	25	3	]	]	PUNCT
ejpam-3285	25	4	be	be	AUX
ejpam-3285	25	5	a	a	DET
ejpam-3285	25	6	group	group	NOUN
ejpam-3285	25	7	ring	ring	NOUN
ejpam-3285	25	8	,	,	PUNCT
ejpam-3285	25	9	where	where	SCONJ
ejpam-3285	25	10	r	r	NOUN
ejpam-3285	25	11	is	be	AUX
ejpam-3285	25	12	a	a	DET
ejpam-3285	25	13	commutative	commutative	ADJ
ejpam-3285	25	14	ring	ring	NOUN
ejpam-3285	25	15	and	and	CCONJ
ejpam-3285	25	16	g	g	NOUN
ejpam-3285	25	17	is	be	AUX
ejpam-3285	25	18	a	a	DET
ejpam-3285	25	19	finite	finite	ADJ
ejpam-3285	25	20	group	group	NOUN
ejpam-3285	25	21	.	.	PUNCT
ejpam-3285	26	1	since	since	SCONJ
ejpam-3285	26	2	there	there	PRON
ejpam-3285	26	3	is	be	VERB
ejpam-3285	26	4	a	a	DET
ejpam-3285	26	5	ring	ring	NOUN
ejpam-3285	26	6	homomorphism	homomorphism	NOUN
ejpam-3285	26	7	h	h	NOUN
ejpam-3285	26	8	:	:	PUNCT
ejpam-3285	26	9	r[g]→	r[g]→	PROPN
ejpam-3285	26	10	r	r	PROPN
ejpam-3285	26	11	,	,	PUNCT
ejpam-3285	26	12	h	h	NOUN
ejpam-3285	26	13	(	(	PUNCT
ejpam-3285	26	14	∑	∑	PROPN
ejpam-3285	26	15	g∈g	g∈g	PROPN
ejpam-3285	26	16	agg	agg	PROPN
ejpam-3285	26	17	)	)	PUNCT
ejpam-3285	26	18	=	=	PUNCT
ejpam-3285	27	1	∑	∑	PROPN
ejpam-3285	27	2	g∈g	g∈g	PROPN
ejpam-3285	27	3	ag	ag	PROPN
ejpam-3285	27	4	,	,	PUNCT
ejpam-3285	27	5	(	(	PUNCT
ejpam-3285	27	6	2	2	X
ejpam-3285	27	7	)	)	PUNCT
ejpam-3285	27	8	a	a	DET
ejpam-3285	27	9	ring	ring	NOUN
ejpam-3285	27	10	homomorphism	homomorphism	PROPN
ejpam-3285	27	11	µ	µ	X
ejpam-3285	27	12	:	:	PUNCT
ejpam-3285	27	13	r[g]→	r[g]→	PROPN
ejpam-3285	27	14	endr(m	endr(m	PROPN
ejpam-3285	27	15	)	)	PUNCT
ejpam-3285	27	16	defined	define	VERB
ejpam-3285	27	17	by	by	ADP
ejpam-3285	27	18	µ	µ	PROPN
ejpam-3285	27	19	(	(	PUNCT
ejpam-3285	27	20	∑	∑	PROPN
ejpam-3285	27	21	g∈g	g∈g	PROPN
ejpam-3285	27	22	agg	agg	PROPN
ejpam-3285	27	23	)	)	PUNCT
ejpam-3285	28	1	=	=	SYM
ejpam-3285	28	2	µ∑	µ∑	PROPN
ejpam-3285	28	3	g∈g	g∈g	PROPN
ejpam-3285	28	4	agg	agg	PROPN
ejpam-3285	28	5	∈	∈	PROPN
ejpam-3285	28	6	endr(m	endr(m	PROPN
ejpam-3285	28	7	)	)	PUNCT
ejpam-3285	28	8	(	(	PUNCT
ejpam-3285	28	9	3	3	X
ejpam-3285	28	10	)	)	PUNCT
ejpam-3285	28	11	where	where	SCONJ
ejpam-3285	28	12	µ∑	µ∑	ADP
ejpam-3285	28	13	g∈g	g∈g	NOUN
ejpam-3285	28	14	agg(m	agg(m	PROPN
ejpam-3285	28	15	)	)	PUNCT
ejpam-3285	28	16	=	=	SYM
ejpam-3285	29	1	h	h	NOUN
ejpam-3285	29	2	(	(	PUNCT
ejpam-3285	29	3	∑	∑	INTJ
ejpam-3285	29	4	g∈g	g∈g	NOUN
ejpam-3285	29	5	agg)m	agg)m	PROPN
ejpam-3285	29	6	=	=	PUNCT
ejpam-3285	29	7	∑	∑	PROPN
ejpam-3285	29	8	g∈g	g∈g	PROPN
ejpam-3285	29	9	agm	agm	PROPN
ejpam-3285	29	10	(	(	PUNCT
ejpam-3285	29	11	4	4	NUM
ejpam-3285	29	12	)	)	PUNCT
ejpam-3285	29	13	is	be	AUX
ejpam-3285	29	14	an	an	DET
ejpam-3285	29	15	h	h	NOUN
ejpam-3285	29	16	-	-	PUNCT
ejpam-3285	29	17	representation	representation	NOUN
ejpam-3285	29	18	of	of	ADP
ejpam-3285	29	19	r[g	r[g	PROPN
ejpam-3285	29	20	]	]	PUNCT
ejpam-3285	29	21	.	.	PUNCT
ejpam-3285	30	1	example	example	NOUN
ejpam-3285	31	1	3	3	X
ejpam-3285	31	2	.	.	PUNCT
ejpam-3285	31	3	let	let	AUX
ejpam-3285	31	4	m	m	PRON
ejpam-3285	31	5	′2(z	′2(z	NUM
ejpam-3285	31	6	)	)	PUNCT
ejpam-3285	31	7	be	be	VERB
ejpam-3285	31	8	a	a	DET
ejpam-3285	31	9	ring	ring	NOUN
ejpam-3285	31	10	of	of	ADP
ejpam-3285	31	11	all	all	DET
ejpam-3285	31	12	2	2	NUM
ejpam-3285	31	13	×	×	NOUN
ejpam-3285	31	14	2	2	NUM
ejpam-3285	31	15	lower	low	ADJ
ejpam-3285	31	16	triangle	triangle	NOUN
ejpam-3285	31	17	matrices	matrix	NOUN
ejpam-3285	31	18	and	and	CCONJ
ejpam-3285	31	19	let	let	VERB
ejpam-3285	31	20	z2	z2	PROPN
ejpam-3285	31	21	be	be	AUX
ejpam-3285	31	22	a	a	DET
ejpam-3285	31	23	module	module	NOUN
ejpam-3285	31	24	over	over	ADP
ejpam-3285	31	25	itself	itself	PRON
ejpam-3285	31	26	,	,	PUNCT
ejpam-3285	31	27	where	where	SCONJ
ejpam-3285	31	28	the	the	DET
ejpam-3285	31	29	scalar	scalar	ADJ
ejpam-3285	31	30	multiplication	multiplication	NOUN
ejpam-3285	31	31	defined	define	VERB
ejpam-3285	31	32	by	by	ADP
ejpam-3285	31	33	(	(	PUNCT
ejpam-3285	31	34	a	a	PRON
ejpam-3285	31	35	,	,	PUNCT
ejpam-3285	31	36	b)(x	b)(x	PROPN
ejpam-3285	31	37	,	,	PUNCT
ejpam-3285	31	38	y	y	PROPN
ejpam-3285	31	39	)	)	PUNCT
ejpam-3285	32	1	=	=	SYM
ejpam-3285	32	2	(	(	PUNCT
ejpam-3285	32	3	ax	ax	NOUN
ejpam-3285	32	4	,	,	PUNCT
ejpam-3285	32	5	by	by	ADP
ejpam-3285	32	6	)	)	PUNCT
ejpam-3285	32	7	for	for	ADP
ejpam-3285	32	8	every	every	DET
ejpam-3285	32	9	(	(	PUNCT
ejpam-3285	32	10	a	a	PRON
ejpam-3285	32	11	,	,	PUNCT
ejpam-3285	32	12	b	b	NOUN
ejpam-3285	32	13	)	)	PUNCT
ejpam-3285	32	14	∈	∈	PROPN
ejpam-3285	32	15	z2	z2	PROPN
ejpam-3285	32	16	and	and	CCONJ
ejpam-3285	32	17	(	(	PUNCT
ejpam-3285	32	18	x	x	NOUN
ejpam-3285	32	19	,	,	PUNCT
ejpam-3285	32	20	y	y	NOUN
ejpam-3285	32	21	)	)	PUNCT
ejpam-3285	32	22	∈	∈	PROPN
ejpam-3285	32	23	z2	z2	PROPN
ejpam-3285	32	24	.	.	PUNCT
ejpam-3285	33	1	the	the	DET
ejpam-3285	33	2	function	function	NOUN
ejpam-3285	33	3	θ	θ	NOUN
ejpam-3285	33	4	:	:	PUNCT
ejpam-3285	33	5	m	m	VERB
ejpam-3285	33	6	′2(z)→	′2(z)→	PROPN
ejpam-3285	33	7	endz2(z2	endz2(z2	NOUN
ejpam-3285	33	8	)	)	PUNCT
ejpam-3285	33	9	defined	define	VERB
ejpam-3285	33	10	by	by	ADP
ejpam-3285	33	11	θr(m	θr(m	NOUN
ejpam-3285	33	12	)	)	PUNCT
ejpam-3285	33	13	=	=	SYM
ejpam-3285	33	14	f(r)m	f(r)m	NOUN
ejpam-3285	33	15	is	be	AUX
ejpam-3285	33	16	an	an	DET
ejpam-3285	33	17	f	f	PROPN
ejpam-3285	33	18	-representation	-representation	NOUN
ejpam-3285	33	19	of	of	ADP
ejpam-3285	33	20	ring	ring	NOUN
ejpam-3285	33	21	m	m	NOUN
ejpam-3285	33	22	′2(z	′2(z	NUM
ejpam-3285	33	23	)	)	PUNCT
ejpam-3285	33	24	by	by	ADP
ejpam-3285	33	25	a	a	DET
ejpam-3285	33	26	ring	ring	NOUN
ejpam-3285	33	27	homomorphism	homomorphism	PROPN
ejpam-3285	33	28	f	f	X
ejpam-3285	33	29	:	:	PUNCT
ejpam-3285	33	30	m	m	NOUN
ejpam-3285	33	31	′2(z	′2(z	NUM
ejpam-3285	33	32	)	)	PUNCT
ejpam-3285	33	33	→	→	SYM
ejpam-3285	33	34	z2	z2	PROPN
ejpam-3285	33	35	defined	define	VERB
ejpam-3285	33	36	by	by	ADP
ejpam-3285	33	37	f	f	PROPN
ejpam-3285	33	38	(	(	PUNCT
ejpam-3285	33	39	[	[	PUNCT
ejpam-3285	33	40	a	a	PRON
ejpam-3285	33	41	0	0	NUM
ejpam-3285	33	42	c	c	NOUN
ejpam-3285	33	43	b	b	NOUN
ejpam-3285	33	44	]	]	PUNCT
ejpam-3285	33	45	)	)	PUNCT
ejpam-3285	34	1	=	=	SYM
ejpam-3285	34	2	(	(	PUNCT
ejpam-3285	34	3	a	a	DET
ejpam-3285	34	4	,	,	PUNCT
ejpam-3285	34	5	b	b	NOUN
ejpam-3285	34	6	)	)	PUNCT
ejpam-3285	34	7	.	.	PUNCT
ejpam-3285	35	1	example	example	NOUN
ejpam-3285	36	1	4	4	X
ejpam-3285	36	2	.	.	PUNCT
ejpam-3285	36	3	let	let	AUX
ejpam-3285	36	4	m2(z	m2(z	PRON
ejpam-3285	36	5	)	)	PUNCT
ejpam-3285	36	6	be	be	AUX
ejpam-3285	36	7	an	an	DET
ejpam-3285	36	8	additive	additive	ADJ
ejpam-3285	36	9	group	group	NOUN
ejpam-3285	36	10	of	of	ADP
ejpam-3285	36	11	all	all	DET
ejpam-3285	36	12	2	2	NUM
ejpam-3285	36	13	×	×	NOUN
ejpam-3285	36	14	2	2	NUM
ejpam-3285	36	15	matrices	matrix	NOUN
ejpam-3285	36	16	,	,	PUNCT
ejpam-3285	36	17	where	where	SCONJ
ejpam-3285	36	18	entries	entry	NOUN
ejpam-3285	36	19	in	in	ADP
ejpam-3285	36	20	z.	z.	PROPN
ejpam-3285	36	21	we	we	PRON
ejpam-3285	36	22	define	define	VERB
ejpam-3285	36	23	the	the	DET
ejpam-3285	36	24	scalar	scalar	ADJ
ejpam-3285	36	25	multiplication	multiplication	NOUN
ejpam-3285	36	26	in	in	ADP
ejpam-3285	36	27	m2(z	m2(z	NOUN
ejpam-3285	36	28	)	)	PUNCT
ejpam-3285	36	29	over	over	ADP
ejpam-3285	36	30	z2	z2	PROPN
ejpam-3285	36	31	as	as	ADP
ejpam-3285	36	32	(	(	PUNCT
ejpam-3285	36	33	a	a	DET
ejpam-3285	36	34	,	,	PUNCT
ejpam-3285	36	35	b	b	NOUN
ejpam-3285	36	36	)	)	PUNCT
ejpam-3285	36	37	[	[	PUNCT
ejpam-3285	36	38	u	u	NOUN
ejpam-3285	36	39	r	r	NOUN
ejpam-3285	36	40	s	s	PROPN
ejpam-3285	36	41	t	t	X
ejpam-3285	36	42	]	]	PUNCT
ejpam-3285	36	43	:	:	PUNCT
ejpam-3285	36	44	=	=	PUNCT
ejpam-3285	36	45	[	[	PUNCT
ejpam-3285	36	46	au	au	X
ejpam-3285	36	47	br	br	NOUN
ejpam-3285	36	48	bs	bs	NOUN
ejpam-3285	36	49	at	at	ADP
ejpam-3285	36	50	]	]	PUNCT
ejpam-3285	36	51	.	.	PUNCT
ejpam-3285	37	1	hence	hence	ADV
ejpam-3285	37	2	m2(z	m2(z	NUM
ejpam-3285	37	3	)	)	PUNCT
ejpam-3285	37	4	is	be	AUX
ejpam-3285	37	5	a	a	DET
ejpam-3285	37	6	z2	z2	NOUN
ejpam-3285	37	7	-	-	PUNCT
ejpam-3285	37	8	module	module	NOUN
ejpam-3285	37	9	.	.	PUNCT
ejpam-3285	38	1	since	since	SCONJ
ejpam-3285	38	2	g	g	NOUN
ejpam-3285	38	3	:	:	PUNCT
ejpam-3285	38	4	m	m	NOUN
ejpam-3285	38	5	′2(z	′2(z	NUM
ejpam-3285	38	6	)	)	PUNCT
ejpam-3285	38	7	→	→	SYM
ejpam-3285	38	8	z2	z2	PROPN
ejpam-3285	38	9	defined	define	VERB
ejpam-3285	38	10	by	by	ADP
ejpam-3285	38	11	g	g	PROPN
ejpam-3285	38	12	(	(	PUNCT
ejpam-3285	38	13	[	[	PUNCT
ejpam-3285	38	14	a	a	PRON
ejpam-3285	38	15	0	0	NUM
ejpam-3285	38	16	c	c	NOUN
ejpam-3285	38	17	b	b	NOUN
ejpam-3285	38	18	]	]	PUNCT
ejpam-3285	38	19	)	)	PUNCT
ejpam-3285	39	1	=	=	SYM
ejpam-3285	39	2	(	(	PUNCT
ejpam-3285	39	3	a	a	PRON
ejpam-3285	39	4	,	,	PUNCT
ejpam-3285	39	5	0	0	NUM
ejpam-3285	39	6	)	)	PUNCT
ejpam-3285	39	7	is	be	AUX
ejpam-3285	39	8	a	a	DET
ejpam-3285	39	9	ring	ring	NOUN
ejpam-3285	39	10	homomorphism	homomorphism	NOUN
ejpam-3285	39	11	,	,	PUNCT
ejpam-3285	39	12	ϕ	ϕ	NOUN
ejpam-3285	39	13	:	:	PUNCT
ejpam-3285	39	14	m	m	NOUN
ejpam-3285	39	15	′2(z	′2(z	NUM
ejpam-3285	39	16	)	)	PUNCT
ejpam-3285	39	17	→	→	SYM
ejpam-3285	39	18	endz2(m2(z	endz2(m2(z	NOUN
ejpam-3285	39	19	)	)	PUNCT
ejpam-3285	39	20	)	)	PUNCT
ejpam-3285	39	21	defined	define	VERB
ejpam-3285	39	22	by	by	ADP
ejpam-3285	39	23	ϕ(r)(m	ϕ(r)(m	PRON
ejpam-3285	39	24	)	)	PUNCT
ejpam-3285	39	25	=	=	NOUN
ejpam-3285	40	1	g(r)m	g(r)m	NOUN
ejpam-3285	40	2	is	be	AUX
ejpam-3285	40	3	a	a	DET
ejpam-3285	40	4	g	g	NOUN
ejpam-3285	40	5	-	-	PUNCT
ejpam-3285	40	6	representation	representation	NOUN
ejpam-3285	40	7	of	of	ADP
ejpam-3285	40	8	ring	ring	NOUN
ejpam-3285	40	9	m	m	NOUN
ejpam-3285	40	10	′2(z	′2(z	NUM
ejpam-3285	40	11	)	)	PUNCT
ejpam-3285	40	12	.	.	PUNCT
ejpam-3285	41	1	n.	n.	PROPN
ejpam-3285	41	2	hijriati	hijriati	PROPN
ejpam-3285	41	3	,	,	PUNCT
ejpam-3285	41	4	s.	s.	PROPN
ejpam-3285	41	5	wahyuni	wahyuni	PROPN
ejpam-3285	41	6	,	,	PUNCT
ejpam-3285	41	7	i.e.	i.e.	X
ejpam-3285	41	8	wijayanti	wijayanti	X
ejpam-3285	41	9	/	/	SYM
ejpam-3285	41	10	eur	eur	PROPN
ejpam-3285	41	11	.	.	PUNCT
ejpam-3285	42	1	j.	j.	PROPN
ejpam-3285	42	2	pure	pure	PROPN
ejpam-3285	42	3	appl	appl	PROPN
ejpam-3285	42	4	.	.	PROPN
ejpam-3285	42	5	math	math	PROPN
ejpam-3285	42	6	,	,	PUNCT
ejpam-3285	42	7	11	11	NUM
ejpam-3285	42	8	(	(	PUNCT
ejpam-3285	42	9	3	3	NUM
ejpam-3285	42	10	)	)	PUNCT
ejpam-3285	42	11	(	(	PUNCT
ejpam-3285	42	12	2018	2018	NUM
ejpam-3285	42	13	)	)	PUNCT
ejpam-3285	42	14	,	,	PUNCT
ejpam-3285	42	15	751	751	NUM
ejpam-3285	42	16	-	-	SYM
ejpam-3285	42	17	761	761	NUM
ejpam-3285	42	18	753	753	NUM
ejpam-3285	42	19	example	example	NOUN
ejpam-3285	42	20	5	5	NUM
ejpam-3285	42	21	.	.	PUNCT
ejpam-3285	43	1	let	let	AUX
ejpam-3285	43	2	m2(z	m2(z	PRON
ejpam-3285	43	3	)	)	PUNCT
ejpam-3285	43	4	be	be	AUX
ejpam-3285	43	5	a	a	DET
ejpam-3285	43	6	z2	z2	NOUN
ejpam-3285	43	7	-	-	PUNCT
ejpam-3285	43	8	module	module	NOUN
ejpam-3285	43	9	defined	define	VERB
ejpam-3285	43	10	as	as	ADP
ejpam-3285	43	11	example	example	NOUN
ejpam-3285	43	12	4	4	NUM
ejpam-3285	43	13	.	.	PUNCT
ejpam-3285	44	1	if	if	SCONJ
ejpam-3285	44	2	f	f	PROPN
ejpam-3285	44	3	,	,	PUNCT
ejpam-3285	44	4	g	g	NOUN
ejpam-3285	44	5	:	:	PUNCT
ejpam-3285	44	6	z3	z3	PROPN
ejpam-3285	44	7	→	→	SYM
ejpam-3285	44	8	z2	z2	PROPN
ejpam-3285	44	9	are	be	AUX
ejpam-3285	44	10	ring	ring	NOUN
ejpam-3285	44	11	homomorphisms	homomorphism	NOUN
ejpam-3285	44	12	defined	define	VERB
ejpam-3285	44	13	by	by	ADP
ejpam-3285	44	14	f(a	f(a	PROPN
ejpam-3285	44	15	,	,	PUNCT
ejpam-3285	44	16	b	b	NOUN
ejpam-3285	44	17	,	,	PUNCT
ejpam-3285	44	18	c	c	NOUN
ejpam-3285	44	19	)	)	PUNCT
ejpam-3285	44	20	=	=	SYM
ejpam-3285	44	21	(	(	PUNCT
ejpam-3285	44	22	a	a	DET
ejpam-3285	44	23	,	,	PUNCT
ejpam-3285	44	24	b	b	NOUN
ejpam-3285	44	25	)	)	PUNCT
ejpam-3285	44	26	and	and	CCONJ
ejpam-3285	44	27	g(a	g(a	PROPN
ejpam-3285	44	28	,	,	PUNCT
ejpam-3285	44	29	b	b	PROPN
ejpam-3285	44	30	,	,	PUNCT
ejpam-3285	44	31	c	c	NOUN
ejpam-3285	44	32	)	)	PUNCT
ejpam-3285	45	1	=	=	SYM
ejpam-3285	45	2	(	(	PUNCT
ejpam-3285	45	3	0	0	NUM
ejpam-3285	45	4	,	,	PUNCT
ejpam-3285	45	5	c	c	NOUN
ejpam-3285	45	6	)	)	PUNCT
ejpam-3285	45	7	respectively	respectively	ADV
ejpam-3285	45	8	,	,	PUNCT
ejpam-3285	45	9	then	then	ADV
ejpam-3285	45	10	we	we	PRON
ejpam-3285	45	11	have	have	VERB
ejpam-3285	45	12	an	an	DET
ejpam-3285	45	13	f	f	PROPN
ejpam-3285	45	14	-representation	-representation	PROPN
ejpam-3285	45	15	µ	µ	X
ejpam-3285	45	16	:	:	PUNCT
ejpam-3285	45	17	z3	z3	PROPN
ejpam-3285	45	18	→	→	SYM
ejpam-3285	45	19	endz2(m2(z	endz2(m2(z	NOUN
ejpam-3285	45	20	)	)	PUNCT
ejpam-3285	45	21	)	)	PUNCT
ejpam-3285	45	22	of	of	ADP
ejpam-3285	45	23	z3	z3	PROPN
ejpam-3285	45	24	and	and	CCONJ
ejpam-3285	45	25	a	a	DET
ejpam-3285	45	26	g	g	NOUN
ejpam-3285	45	27	-	-	PUNCT
ejpam-3285	45	28	representation	representation	NOUN
ejpam-3285	45	29	ϕ	ϕ	NOUN
ejpam-3285	45	30	:	:	PUNCT
ejpam-3285	45	31	z3	z3	PROPN
ejpam-3285	45	32	→	→	SYM
ejpam-3285	45	33	endz2(m2(z	endz2(m2(z	NOUN
ejpam-3285	45	34	)	)	PUNCT
ejpam-3285	45	35	)	)	PUNCT
ejpam-3285	45	36	of	of	ADP
ejpam-3285	45	37	z3	z3	PROPN
ejpam-3285	45	38	where	where	SCONJ
ejpam-3285	45	39	µr(m	µr(m	PUNCT
ejpam-3285	45	40	)	)	PUNCT
ejpam-3285	45	41	=	=	SYM
ejpam-3285	45	42	f(r)m	f(r)m	NOUN
ejpam-3285	45	43	and	and	CCONJ
ejpam-3285	45	44	ϕr(m	ϕr(m	PUNCT
ejpam-3285	45	45	)	)	PUNCT
ejpam-3285	46	1	=	=	PUNCT
ejpam-3285	46	2	g(r)m	g(r)m	NOUN
ejpam-3285	46	3	for	for	ADP
ejpam-3285	46	4	all	all	DET
ejpam-3285	46	5	r	r	NOUN
ejpam-3285	46	6	∈	∈	NOUN
ejpam-3285	46	7	r	r	NOUN
ejpam-3285	46	8	,	,	PUNCT
ejpam-3285	46	9	and	and	CCONJ
ejpam-3285	46	10	m	m	PRON
ejpam-3285	46	11	∈m	∈m	NOUN
ejpam-3285	46	12	.	.	PUNCT
ejpam-3285	46	13	example	example	NOUN
ejpam-3285	46	14	3	3	NUM
ejpam-3285	46	15	,	,	PUNCT
ejpam-3285	46	16	example	example	NOUN
ejpam-3285	46	17	4	4	NUM
ejpam-3285	46	18	,	,	PUNCT
ejpam-3285	46	19	and	and	CCONJ
ejpam-3285	46	20	example	example	NOUN
ejpam-3285	46	21	5	5	NUM
ejpam-3285	46	22	can	can	AUX
ejpam-3285	46	23	be	be	AUX
ejpam-3285	46	24	generalized	generalize	VERB
ejpam-3285	46	25	to	to	ADP
ejpam-3285	46	26	any	any	DET
ejpam-3285	46	27	commutative	commutative	ADJ
ejpam-3285	46	28	ring	ring	NOUN
ejpam-3285	46	29	r.	r.	PROPN
ejpam-3285	46	30	furthermore	furthermore	ADV
ejpam-3285	46	31	,	,	PUNCT
ejpam-3285	46	32	since	since	SCONJ
ejpam-3285	46	33	µ	µ	NOUN
ejpam-3285	46	34	is	be	AUX
ejpam-3285	46	35	a	a	DET
ejpam-3285	46	36	ring	ring	NOUN
ejpam-3285	46	37	homomorphism	homomorphism	NOUN
ejpam-3285	46	38	,	,	PUNCT
ejpam-3285	46	39	so	so	SCONJ
ejpam-3285	46	40	we	we	PRON
ejpam-3285	46	41	can	can	AUX
ejpam-3285	46	42	find	find	VERB
ejpam-3285	46	43	the	the	DET
ejpam-3285	46	44	kernel	kernel	NOUN
ejpam-3285	46	45	of	of	ADP
ejpam-3285	46	46	µ	µ	NOUN
ejpam-3285	46	47	,	,	PUNCT
ejpam-3285	46	48	i.e.	i.e.	X
ejpam-3285	46	49	ker(µ	ker(µ	PROPN
ejpam-3285	46	50	)	)	PUNCT
ejpam-3285	46	51	=	=	PRON
ejpam-3285	47	1	{	{	PUNCT
ejpam-3285	47	2	r	r	NOUN
ejpam-3285	47	3	∈	∈	NOUN
ejpam-3285	47	4	r	r	NOUN
ejpam-3285	47	5	|	|	ADV
ejpam-3285	47	6	f(r	f(r	NOUN
ejpam-3285	47	7	)	)	PUNCT
ejpam-3285	47	8	∈	∈	PROPN
ejpam-3285	47	9	ann(m	ann(m	PROPN
ejpam-3285	47	10	)	)	PUNCT
ejpam-3285	47	11	}	}	PUNCT
ejpam-3285	47	12	.	.	PUNCT
ejpam-3285	48	1	(	(	PUNCT
ejpam-3285	48	2	5	5	X
ejpam-3285	48	3	)	)	PUNCT
ejpam-3285	48	4	we	we	PRON
ejpam-3285	48	5	know	know	VERB
ejpam-3285	48	6	that	that	SCONJ
ejpam-3285	48	7	the	the	DET
ejpam-3285	48	8	element	element	NOUN
ejpam-3285	48	9	of	of	ADP
ejpam-3285	48	10	ker(µ	ker(µ	PROPN
ejpam-3285	48	11	)	)	PUNCT
ejpam-3285	48	12	depend	depend	VERB
ejpam-3285	48	13	on	on	ADP
ejpam-3285	48	14	the	the	DET
ejpam-3285	48	15	properties	property	NOUN
ejpam-3285	48	16	of	of	ADP
ejpam-3285	48	17	f	f	PROPN
ejpam-3285	48	18	and	and	CCONJ
ejpam-3285	48	19	ann(m	ann(m	PROPN
ejpam-3285	48	20	)	)	PUNCT
ejpam-3285	48	21	.	.	PUNCT
ejpam-3285	49	1	so	so	ADV
ejpam-3285	49	2	we	we	PRON
ejpam-3285	49	3	have	have	VERB
ejpam-3285	49	4	the	the	DET
ejpam-3285	49	5	following	follow	VERB
ejpam-3285	49	6	properties	property	NOUN
ejpam-3285	49	7	:	:	PUNCT
ejpam-3285	49	8	proposition	proposition	NOUN
ejpam-3285	49	9	1	1	NUM
ejpam-3285	49	10	.	.	PUNCT
ejpam-3285	50	1	let	let	VERB
ejpam-3285	50	2	µ	µ	NOUN
ejpam-3285	50	3	:	:	PUNCT
ejpam-3285	50	4	r→	r→	PROPN
ejpam-3285	50	5	ends(m	ends(m	PROPN
ejpam-3285	50	6	)	)	PUNCT
ejpam-3285	50	7	is	be	AUX
ejpam-3285	50	8	an	an	DET
ejpam-3285	50	9	f	f	PROPN
ejpam-3285	50	10	-representation	-representation	NOUN
ejpam-3285	50	11	of	of	ADP
ejpam-3285	50	12	ring	ring	PROPN
ejpam-3285	50	13	r.	r.	PROPN
ejpam-3285	50	14	if	if	SCONJ
ejpam-3285	50	15	f	f	PROPN
ejpam-3285	50	16	is	be	AUX
ejpam-3285	50	17	injective	injective	ADJ
ejpam-3285	50	18	and	and	CCONJ
ejpam-3285	50	19	m	m	VERB
ejpam-3285	50	20	is	be	AUX
ejpam-3285	50	21	faithful	faithful	ADJ
ejpam-3285	50	22	(	(	PUNCT
ejpam-3285	50	23	ann(m	ann(m	PROPN
ejpam-3285	50	24	)	)	PUNCT
ejpam-3285	50	25	=	=	PUNCT
ejpam-3285	50	26	{	{	PUNCT
ejpam-3285	50	27	0s	0s	NOUN
ejpam-3285	50	28	}	}	PUNCT
ejpam-3285	50	29	)	)	PUNCT
ejpam-3285	50	30	,	,	PUNCT
ejpam-3285	50	31	then	then	ADV
ejpam-3285	50	32	µ	µ	NOUN
ejpam-3285	50	33	is	be	AUX
ejpam-3285	50	34	injective	injective	ADJ
ejpam-3285	50	35	.	.	PUNCT
ejpam-3285	51	1	proof	proof	NOUN
ejpam-3285	51	2	.	.	PUNCT
ejpam-3285	52	1	let	let	VERB
ejpam-3285	52	2	r	r	NOUN
ejpam-3285	52	3	be	be	AUX
ejpam-3285	52	4	any	any	DET
ejpam-3285	52	5	element	element	NOUN
ejpam-3285	52	6	of	of	ADP
ejpam-3285	52	7	ker(µ	ker(µ	PROPN
ejpam-3285	52	8	)	)	PUNCT
ejpam-3285	52	9	.	.	PUNCT
ejpam-3285	53	1	then	then	ADV
ejpam-3285	53	2	µr	µr	ADP
ejpam-3285	53	3	=	=	PUNCT
ejpam-3285	53	4	o	o	X
ejpam-3285	53	5	∈	∈	PROPN
ejpam-3285	53	6	ends(m	ends(m	PROPN
ejpam-3285	53	7	)	)	PUNCT
ejpam-3285	53	8	.	.	PUNCT
ejpam-3285	54	1	for	for	ADP
ejpam-3285	54	2	any	any	DET
ejpam-3285	54	3	m	m	NOUN
ejpam-3285	54	4	∈	∈	NOUN
ejpam-3285	54	5	m	m	NOUN
ejpam-3285	54	6	,	,	PUNCT
ejpam-3285	54	7	we	we	PRON
ejpam-3285	54	8	have	have	VERB
ejpam-3285	54	9	µr(m	µr(m	PUNCT
ejpam-3285	54	10	)	)	PUNCT
ejpam-3285	55	1	=	=	SYM
ejpam-3285	55	2	o(m	o(m	PROPN
ejpam-3285	55	3	)	)	PUNCT
ejpam-3285	55	4	=	=	SYM
ejpam-3285	55	5	0	0	PUNCT
ejpam-3285	56	1	if	if	SCONJ
ejpam-3285	56	2	and	and	CCONJ
ejpam-3285	56	3	only	only	ADV
ejpam-3285	56	4	if	if	SCONJ
ejpam-3285	56	5	f(r)m	f(r)m	NOUN
ejpam-3285	56	6	=	=	SYM
ejpam-3285	56	7	0	0	X
ejpam-3285	56	8	.	.	PUNCT
ejpam-3285	57	1	so	so	ADV
ejpam-3285	57	2	we	we	PRON
ejpam-3285	57	3	have	have	VERB
ejpam-3285	57	4	f(r	f(r	NOUN
ejpam-3285	57	5	)	)	PUNCT
ejpam-3285	57	6	∈	∈	PROPN
ejpam-3285	57	7	ann(m	ann(m	PROPN
ejpam-3285	57	8	)	)	PUNCT
ejpam-3285	57	9	.	.	PUNCT
ejpam-3285	58	1	since	since	SCONJ
ejpam-3285	58	2	ann(m	ann(m	PROPN
ejpam-3285	58	3	)	)	PUNCT
ejpam-3285	58	4	=	=	PUNCT
ejpam-3285	58	5	{	{	PUNCT
ejpam-3285	58	6	0	0	NUM
ejpam-3285	58	7	}	}	PUNCT
ejpam-3285	58	8	,	,	PUNCT
ejpam-3285	58	9	f(r	f(r	NOUN
ejpam-3285	58	10	)	)	PUNCT
ejpam-3285	58	11	=	=	SYM
ejpam-3285	58	12	0	0	NUM
ejpam-3285	58	13	and	and	CCONJ
ejpam-3285	58	14	r	r	PROPN
ejpam-3285	58	15	∈	∈	PROPN
ejpam-3285	58	16	ker(f	ker(f	PROPN
ejpam-3285	58	17	)	)	PUNCT
ejpam-3285	58	18	.	.	PUNCT
ejpam-3285	59	1	furthermore	furthermore	ADV
ejpam-3285	59	2	since	since	SCONJ
ejpam-3285	59	3	f	f	PROPN
ejpam-3285	59	4	is	be	AUX
ejpam-3285	59	5	injective	injective	ADJ
ejpam-3285	59	6	,	,	PUNCT
ejpam-3285	59	7	r	r	NOUN
ejpam-3285	59	8	=	=	SYM
ejpam-3285	59	9	0	0	NUM
ejpam-3285	59	10	.	.	PUNCT
ejpam-3285	60	1	thus	thus	ADV
ejpam-3285	60	2	µ	µ	X
ejpam-3285	60	3	is	be	AUX
ejpam-3285	60	4	injective	injective	ADJ
ejpam-3285	60	5	.	.	PUNCT
ejpam-3285	61	1	the	the	DET
ejpam-3285	61	2	converse	converse	NOUN
ejpam-3285	61	3	of	of	ADP
ejpam-3285	61	4	proposition	proposition	NOUN
ejpam-3285	61	5	1	1	NUM
ejpam-3285	61	6	is	be	AUX
ejpam-3285	61	7	not	not	PART
ejpam-3285	61	8	always	always	ADV
ejpam-3285	61	9	true	true	ADJ
ejpam-3285	61	10	.	.	PUNCT
ejpam-3285	62	1	this	this	PRON
ejpam-3285	62	2	is	be	AUX
ejpam-3285	62	3	the	the	DET
ejpam-3285	62	4	counterexample	counterexample	PROPN
ejpam-3285	62	5	.	.	PUNCT
ejpam-3285	62	6	example	example	NOUN
ejpam-3285	63	1	6	6	NUM
ejpam-3285	63	2	.	.	PUNCT
ejpam-3285	64	1	let	let	VERB
ejpam-3285	64	2	f	f	PROPN
ejpam-3285	64	3	:	:	PUNCT
ejpam-3285	64	4	z→	z→	PROPN
ejpam-3285	64	5	z2	z2	PROPN
ejpam-3285	64	6	,	,	PUNCT
ejpam-3285	64	7	a	a	DET
ejpam-3285	64	8	7→	7→	NUM
ejpam-3285	64	9	(	(	PUNCT
ejpam-3285	64	10	a	a	PRON
ejpam-3285	64	11	,	,	PUNCT
ejpam-3285	64	12	0	0	NUM
ejpam-3285	64	13	)	)	PUNCT
ejpam-3285	64	14	(	(	PUNCT
ejpam-3285	64	15	6	6	X
ejpam-3285	64	16	)	)	PUNCT
ejpam-3285	64	17	be	be	AUX
ejpam-3285	64	18	a	a	DET
ejpam-3285	64	19	ring	ring	NOUN
ejpam-3285	64	20	homomorphism	homomorphism	NOUN
ejpam-3285	64	21	and	and	CCONJ
ejpam-3285	64	22	m2(z	m2(z	NOUN
ejpam-3285	64	23	)	)	PUNCT
ejpam-3285	64	24	a	a	DET
ejpam-3285	64	25	module	module	NOUN
ejpam-3285	64	26	over	over	ADP
ejpam-3285	64	27	z2	z2	PROPN
ejpam-3285	64	28	.	.	PUNCT
ejpam-3285	65	1	the	the	DET
ejpam-3285	65	2	scalar	scalar	ADJ
ejpam-3285	65	3	multiplication	multiplication	NOUN
ejpam-3285	65	4	is	be	AUX
ejpam-3285	65	5	defined	define	VERB
ejpam-3285	65	6	by	by	ADP
ejpam-3285	65	7	(	(	PUNCT
ejpam-3285	65	8	a	a	DET
ejpam-3285	65	9	,	,	PUNCT
ejpam-3285	65	10	b	b	NOUN
ejpam-3285	65	11	)	)	PUNCT
ejpam-3285	66	1	[	[	PUNCT
ejpam-3285	66	2	u	u	NOUN
ejpam-3285	66	3	v	v	NOUN
ejpam-3285	66	4	w	w	NOUN
ejpam-3285	66	5	x	x	X
ejpam-3285	66	6	]	]	X
ejpam-3285	66	7	=	=	PUNCT
ejpam-3285	67	1	[	[	PUNCT
ejpam-3285	67	2	au	au	X
ejpam-3285	67	3	av	av	NOUN
ejpam-3285	67	4	aw	aw	INTJ
ejpam-3285	67	5	ax	ax	X
ejpam-3285	67	6	]	]	PUNCT
ejpam-3285	67	7	(	(	PUNCT
ejpam-3285	67	8	7	7	X
ejpam-3285	67	9	)	)	PUNCT
ejpam-3285	67	10	the	the	DET
ejpam-3285	67	11	f	f	PROPN
ejpam-3285	67	12	-representation	-representation	PROPN
ejpam-3285	67	13	µ	µ	PROPN
ejpam-3285	67	14	:	:	PUNCT
ejpam-3285	67	15	z→	z→	NUM
ejpam-3285	67	16	endz2(m2(z	endz2(m2(z	NOUN
ejpam-3285	67	17	)	)	PUNCT
ejpam-3285	67	18	)	)	PUNCT
ejpam-3285	67	19	is	be	AUX
ejpam-3285	67	20	injective	injective	ADJ
ejpam-3285	67	21	,	,	PUNCT
ejpam-3285	67	22	since	since	SCONJ
ejpam-3285	67	23	ker(µ	ker(µ	PROPN
ejpam-3285	67	24	)	)	PUNCT
ejpam-3285	67	25	=	=	PRON
ejpam-3285	67	26	{	{	PUNCT
ejpam-3285	67	27	0	0	NUM
ejpam-3285	67	28	}	}	PUNCT
ejpam-3285	67	29	.	.	PUNCT
ejpam-3285	68	1	but	but	CCONJ
ejpam-3285	68	2	m2(z	m2(z	X
ejpam-3285	68	3	)	)	PUNCT
ejpam-3285	68	4	is	be	AUX
ejpam-3285	68	5	not	not	PART
ejpam-3285	68	6	faithful	faithful	ADJ
ejpam-3285	68	7	,	,	PUNCT
ejpam-3285	68	8	since	since	SCONJ
ejpam-3285	68	9	ann(m	ann(m	PROPN
ejpam-3285	68	10	)	)	PUNCT
ejpam-3285	68	11	=	=	PRON
ejpam-3285	68	12	{	{	PUNCT
ejpam-3285	68	13	(	(	PUNCT
ejpam-3285	68	14	0	0	NUM
ejpam-3285	68	15	,	,	PUNCT
ejpam-3285	68	16	b	b	NOUN
ejpam-3285	68	17	)	)	PUNCT
ejpam-3285	69	1	|	|	ADV
ejpam-3285	69	2	b	b	X
ejpam-3285	69	3	∈	∈	PROPN
ejpam-3285	69	4	z	z	NOUN
ejpam-3285	69	5	}	}	PUNCT
ejpam-3285	69	6	.	.	PUNCT
ejpam-3285	70	1	remark	remark	NOUN
ejpam-3285	70	2	1	1	NUM
ejpam-3285	70	3	.	.	PUNCT
ejpam-3285	71	1	if	if	SCONJ
ejpam-3285	71	2	s	s	PROPN
ejpam-3285	71	3	is	be	AUX
ejpam-3285	71	4	an	an	DET
ejpam-3285	71	5	integral	integral	ADJ
ejpam-3285	71	6	domain	domain	NOUN
ejpam-3285	71	7	and	and	CCONJ
ejpam-3285	71	8	m	m	NOUN
ejpam-3285	71	9	is	be	AUX
ejpam-3285	71	10	a	a	DET
ejpam-3285	71	11	free	free	ADJ
ejpam-3285	71	12	torsian	torsian	NOUN
ejpam-3285	71	13	s	s	NOUN
ejpam-3285	71	14	-	-	NOUN
ejpam-3285	71	15	module	module	NOUN
ejpam-3285	71	16	,	,	PUNCT
ejpam-3285	71	17	then	then	ADV
ejpam-3285	71	18	an	an	DET
ejpam-3285	71	19	f	f	PROPN
ejpam-3285	71	20	representation	representation	PROPN
ejpam-3285	71	21	µ	µ	PROPN
ejpam-3285	71	22	of	of	ADP
ejpam-3285	71	23	a	a	DET
ejpam-3285	71	24	ring	ring	NOUN
ejpam-3285	71	25	r	r	NOUN
ejpam-3285	71	26	on	on	ADP
ejpam-3285	71	27	a	a	DET
ejpam-3285	71	28	module	module	NOUN
ejpam-3285	71	29	m	m	NOUN
ejpam-3285	71	30	is	be	AUX
ejpam-3285	71	31	injective	injective	ADJ
ejpam-3285	71	32	if	if	SCONJ
ejpam-3285	71	33	and	and	CCONJ
ejpam-3285	71	34	only	only	ADV
ejpam-3285	71	35	if	if	SCONJ
ejpam-3285	71	36	f	f	PROPN
ejpam-3285	71	37	is	be	AUX
ejpam-3285	71	38	injective	injective	ADJ
ejpam-3285	71	39	.	.	PUNCT
ejpam-3285	72	1	there	there	PRON
ejpam-3285	72	2	is	be	VERB
ejpam-3285	72	3	an	an	DET
ejpam-3285	72	4	important	important	ADJ
ejpam-3285	72	5	result	result	NOUN
ejpam-3285	72	6	in	in	ADP
ejpam-3285	72	7	representation	representation	NOUN
ejpam-3285	72	8	of	of	ADP
ejpam-3285	72	9	rings	ring	NOUN
ejpam-3285	72	10	on	on	ADP
ejpam-3285	72	11	vector	vector	NOUN
ejpam-3285	72	12	spaces	space	NOUN
ejpam-3285	72	13	i.e	i.e	PROPN
ejpam-3285	72	14	schur	schur	PROPN
ejpam-3285	72	15	’s	’s	PART
ejpam-3285	72	16	lemma	lemma	PROPN
ejpam-3285	72	17	.	.	PUNCT
ejpam-3285	73	1	schur	schur	PROPN
ejpam-3285	73	2	’s	’s	PROPN
ejpam-3285	73	3	lemma	lemma	PROPN
ejpam-3285	73	4	showed	show	VERB
ejpam-3285	73	5	that	that	SCONJ
ejpam-3285	73	6	the	the	DET
ejpam-3285	73	7	set	set	NOUN
ejpam-3285	73	8	all	all	DET
ejpam-3285	73	9	morphism	morphism	NOUN
ejpam-3285	73	10	of	of	ADP
ejpam-3285	73	11	an	an	DET
ejpam-3285	73	12	irreducible	irreducible	ADJ
ejpam-3285	73	13	representation	representation	NOUN
ejpam-3285	73	14	ρ	ρ	NOUN
ejpam-3285	73	15	of	of	ADP
ejpam-3285	73	16	a	a	DET
ejpam-3285	73	17	ring	ring	NOUN
ejpam-3285	73	18	r	r	NOUN
ejpam-3285	73	19	(	(	PUNCT
ejpam-3285	73	20	homr(ρ	homr(ρ	NOUN
ejpam-3285	73	21	,	,	PUNCT
ejpam-3285	73	22	ρ	ρ	NOUN
ejpam-3285	73	23	)	)	PUNCT
ejpam-3285	73	24	)	)	PUNCT
ejpam-3285	73	25	on	on	ADP
ejpam-3285	73	26	a	a	DET
ejpam-3285	73	27	vector	vector	NOUN
ejpam-3285	73	28	space	space	NOUN
ejpam-3285	73	29	v	v	NOUN
ejpam-3285	73	30	over	over	ADP
ejpam-3285	73	31	a	a	DET
ejpam-3285	73	32	field	field	NOUN
ejpam-3285	73	33	f	f	X
ejpam-3285	73	34	is	be	AUX
ejpam-3285	73	35	a	a	DET
ejpam-3285	73	36	skew	skew	ADJ
ejpam-3285	73	37	field	field	NOUN
ejpam-3285	73	38	,	,	PUNCT
ejpam-3285	73	39	and	and	CCONJ
ejpam-3285	73	40	the	the	DET
ejpam-3285	73	41	necessary	necessary	ADJ
ejpam-3285	73	42	condition	condition	NOUN
ejpam-3285	73	43	when	when	SCONJ
ejpam-3285	73	44	ρ	ρ	PROPN
ejpam-3285	73	45	is	be	AUX
ejpam-3285	73	46	irreducible([7],[8	irreducible([7],[8	NOUN
ejpam-3285	73	47	]	]	PUNCT
ejpam-3285	73	48	)	)	PUNCT
ejpam-3285	73	49	.	.	PUNCT
ejpam-3285	74	1	in	in	ADP
ejpam-3285	74	2	linear	linear	PROPN
ejpam-3285	74	3	algebra	algebra	PROPN
ejpam-3285	74	4	,	,	PUNCT
ejpam-3285	74	5	the	the	DET
ejpam-3285	74	6	ring	ring	NOUN
ejpam-3285	74	7	end(v	end(v	PROPN
ejpam-3285	74	8	)	)	PUNCT
ejpam-3285	74	9	,	,	PUNCT
ejpam-3285	74	10	where	where	SCONJ
ejpam-3285	74	11	v	v	NOUN
ejpam-3285	74	12	is	be	AUX
ejpam-3285	74	13	a	a	DET
ejpam-3285	74	14	finite	finite	ADJ
ejpam-3285	74	15	dimension	dimension	NOUN
ejpam-3285	74	16	vector	vector	NOUN
ejpam-3285	74	17	space	space	NOUN
ejpam-3285	74	18	over	over	ADP
ejpam-3285	74	19	f	f	PROPN
ejpam-3285	74	20	(	(	PUNCT
ejpam-3285	74	21	dim(v	dim(v	PROPN
ejpam-3285	74	22	)	)	PUNCT
ejpam-3285	74	23	=	=	SYM
ejpam-3285	74	24	n	n	CCONJ
ejpam-3285	74	25	)	)	PUNCT
ejpam-3285	74	26	,	,	PUNCT
ejpam-3285	74	27	is	be	AUX
ejpam-3285	74	28	isomorphic	isomorphic	ADJ
ejpam-3285	74	29	to	to	ADP
ejpam-3285	74	30	the	the	DET
ejpam-3285	74	31	ring	ring	NOUN
ejpam-3285	74	32	of	of	ADP
ejpam-3285	74	33	all	all	DET
ejpam-3285	74	34	n	n	PRON
ejpam-3285	74	35	×	×	NOUN
ejpam-3285	74	36	n	n	PRON
ejpam-3285	74	37	matrices	matrix	NOUN
ejpam-3285	74	38	mn(f	mn(f	PUNCT
ejpam-3285	74	39	)	)	PUNCT
ejpam-3285	75	1	[	[	X
ejpam-3285	75	2	1	1	NUM
ejpam-3285	75	3	]	]	PUNCT
ejpam-3285	75	4	.	.	PUNCT
ejpam-3285	76	1	so	so	ADV
ejpam-3285	76	2	the	the	DET
ejpam-3285	76	3	definition	definition	NOUN
ejpam-3285	76	4	of	of	ADP
ejpam-3285	76	5	the	the	DET
ejpam-3285	76	6	representation	representation	NOUN
ejpam-3285	76	7	of	of	ADP
ejpam-3285	76	8	a	a	DET
ejpam-3285	76	9	ring	ring	NOUN
ejpam-3285	76	10	r	r	NOUN
ejpam-3285	76	11	on	on	ADP
ejpam-3285	76	12	a	a	DET
ejpam-3285	76	13	vector	vector	NOUN
ejpam-3285	76	14	spaces	space	NOUN
ejpam-3285	76	15	v	v	NOUN
ejpam-3285	76	16	over	over	ADP
ejpam-3285	76	17	f	f	PROPN
ejpam-3285	76	18	can	can	AUX
ejpam-3285	76	19	be	be	AUX
ejpam-3285	76	20	denoted	denote	VERB
ejpam-3285	76	21	as	as	ADP
ejpam-3285	76	22	a	a	DET
ejpam-3285	76	23	ring	ring	NOUN
ejpam-3285	76	24	homomorphism	homomorphism	NOUN
ejpam-3285	76	25	from	from	ADP
ejpam-3285	76	26	ρ	ρ	PROPN
ejpam-3285	76	27	:	:	PUNCT
ejpam-3285	76	28	r	r	NOUN
ejpam-3285	76	29	→	→	SYM
ejpam-3285	76	30	mn(f	mn(f	NUM
ejpam-3285	76	31	)	)	PUNCT
ejpam-3285	76	32	.	.	PUNCT
ejpam-3285	77	1	if	if	SCONJ
ejpam-3285	77	2	we	we	PRON
ejpam-3285	77	3	generalize	generalize	VERB
ejpam-3285	77	4	the	the	DET
ejpam-3285	77	5	ring	ring	NOUN
ejpam-3285	77	6	of	of	ADP
ejpam-3285	77	7	all	all	DET
ejpam-3285	77	8	n	n	PRON
ejpam-3285	77	9	×	×	NOUN
ejpam-3285	77	10	n	n	PRON
ejpam-3285	77	11	matrices	matrix	NOUN
ejpam-3285	77	12	to	to	ADP
ejpam-3285	77	13	the	the	DET
ejpam-3285	77	14	ring	ring	NOUN
ejpam-3285	77	15	of	of	ADP
ejpam-3285	77	16	all	all	DET
ejpam-3285	77	17	m	m	NOUN
ejpam-3285	77	18	×	×	NOUN
ejpam-3285	77	19	n	n	PRON
ejpam-3285	77	20	matrices	matrix	NOUN
ejpam-3285	77	21	,	,	PUNCT
ejpam-3285	77	22	schur	schur	PROPN
ejpam-3285	77	23	’s	’s	PROPN
ejpam-3285	77	24	lemma	lemma	PROPN
ejpam-3285	77	25	still	still	ADV
ejpam-3285	77	26	considered	consider	VERB
ejpam-3285	77	27	[	[	X
ejpam-3285	77	28	12	12	NUM
ejpam-3285	77	29	]	]	PUNCT
ejpam-3285	77	30	.	.	PUNCT
ejpam-3285	78	1	n.	n.	PROPN
ejpam-3285	78	2	hijriati	hijriati	PROPN
ejpam-3285	78	3	,	,	PUNCT
ejpam-3285	78	4	s.	s.	PROPN
ejpam-3285	78	5	wahyuni	wahyuni	PROPN
ejpam-3285	78	6	,	,	PUNCT
ejpam-3285	78	7	i.e.	i.e.	X
ejpam-3285	78	8	wijayanti	wijayanti	X
ejpam-3285	78	9	/	/	SYM
ejpam-3285	78	10	eur	eur	PROPN
ejpam-3285	78	11	.	.	PUNCT
ejpam-3285	79	1	j.	j.	PROPN
ejpam-3285	79	2	pure	pure	PROPN
ejpam-3285	79	3	appl	appl	PROPN
ejpam-3285	79	4	.	.	PROPN
ejpam-3285	79	5	math	math	PROPN
ejpam-3285	79	6	,	,	PUNCT
ejpam-3285	79	7	11	11	NUM
ejpam-3285	79	8	(	(	PUNCT
ejpam-3285	79	9	3	3	NUM
ejpam-3285	79	10	)	)	PUNCT
ejpam-3285	79	11	(	(	PUNCT
ejpam-3285	79	12	2018	2018	NUM
ejpam-3285	79	13	)	)	PUNCT
ejpam-3285	79	14	,	,	PUNCT
ejpam-3285	79	15	751	751	NUM
ejpam-3285	79	16	-	-	SYM
ejpam-3285	79	17	761	761	NUM
ejpam-3285	79	18	754	754	NUM
ejpam-3285	79	19	let	let	VERB
ejpam-3285	79	20	s	s	PRON
ejpam-3285	79	21	be	be	AUX
ejpam-3285	79	22	an	an	DET
ejpam-3285	79	23	r	r	NOUN
ejpam-3285	79	24	-	-	PUNCT
ejpam-3285	79	25	algebra	algebra	NOUN
ejpam-3285	79	26	.	.	PUNCT
ejpam-3285	80	1	then	then	ADV
ejpam-3285	80	2	there	there	PRON
ejpam-3285	80	3	is	be	VERB
ejpam-3285	80	4	a	a	DET
ejpam-3285	80	5	ring	ring	NOUN
ejpam-3285	80	6	homomorphism	homomorphism	NOUN
ejpam-3285	80	7	g	g	NOUN
ejpam-3285	80	8	:	:	PUNCT
ejpam-3285	80	9	r	r	NOUN
ejpam-3285	80	10	→	→	SYM
ejpam-3285	80	11	s	s	VERB
ejpam-3285	80	12	such	such	ADJ
ejpam-3285	80	13	that	that	DET
ejpam-3285	80	14	sg(r	sg(r	NUM
ejpam-3285	80	15	)	)	PUNCT
ejpam-3285	80	16	=	=	PUNCT
ejpam-3285	81	1	g(r)s	g(r)s	PROPN
ejpam-3285	81	2	for	for	ADP
ejpam-3285	81	3	all	all	DET
ejpam-3285	81	4	r	r	NOUN
ejpam-3285	81	5	∈	∈	NOUN
ejpam-3285	81	6	r	r	NOUN
ejpam-3285	81	7	,	,	PUNCT
ejpam-3285	81	8	and	and	CCONJ
ejpam-3285	81	9	s	s	VERB
ejpam-3285	81	10	∈	∈	NOUN
ejpam-3285	81	11	s	s	X
ejpam-3285	81	12	(	(	PUNCT
ejpam-3285	81	13	g(r	g(r	NOUN
ejpam-3285	81	14	)	)	PUNCT
ejpam-3285	81	15	∈	∈	PROPN
ejpam-3285	81	16	z(s	z(s	PROPN
ejpam-3285	81	17	)	)	PUNCT
ejpam-3285	81	18	,	,	PUNCT
ejpam-3285	81	19	for	for	ADP
ejpam-3285	81	20	all	all	DET
ejpam-3285	81	21	r	r	NOUN
ejpam-3285	81	22	∈	∈	NOUN
ejpam-3285	81	23	r	r	NOUN
ejpam-3285	81	24	)	)	PUNCT
ejpam-3285	81	25	.	.	PUNCT
ejpam-3285	82	1	if	if	SCONJ
ejpam-3285	82	2	m	m	NOUN
ejpam-3285	82	3	is	be	AUX
ejpam-3285	82	4	an	an	DET
ejpam-3285	82	5	s	s	NOUN
ejpam-3285	82	6	-	-	NOUN
ejpam-3285	82	7	module	module	NOUN
ejpam-3285	82	8	,	,	PUNCT
ejpam-3285	82	9	then	then	ADV
ejpam-3285	82	10	m	m	NOUN
ejpam-3285	82	11	is	be	AUX
ejpam-3285	82	12	an	an	DET
ejpam-3285	82	13	r	r	NOUN
ejpam-3285	82	14	-	-	PUNCT
ejpam-3285	82	15	module	module	NOUN
ejpam-3285	82	16	with	with	ADP
ejpam-3285	82	17	scalar	scalar	ADJ
ejpam-3285	82	18	multiplication	multiplication	NOUN
ejpam-3285	82	19	defined	define	VERB
ejpam-3285	82	20	by	by	ADP
ejpam-3285	82	21	r.m	r.m	PROPN
ejpam-3285	82	22	=	=	PROPN
ejpam-3285	82	23	g(r)m	g(r)m	NOUN
ejpam-3285	82	24	for	for	ADP
ejpam-3285	82	25	every	every	DET
ejpam-3285	82	26	r	r	NOUN
ejpam-3285	82	27	∈	∈	NOUN
ejpam-3285	82	28	r	r	NOUN
ejpam-3285	82	29	and	and	CCONJ
ejpam-3285	82	30	m	m	NOUN
ejpam-3285	82	31	∈m	∈m	NOUN
ejpam-3285	82	32	,	,	PUNCT
ejpam-3285	82	33	such	such	ADJ
ejpam-3285	82	34	that	that	SCONJ
ejpam-3285	82	35	we	we	PRON
ejpam-3285	82	36	can	can	AUX
ejpam-3285	82	37	defined	define	VERB
ejpam-3285	82	38	a	a	DET
ejpam-3285	82	39	ring	ring	NOUN
ejpam-3285	82	40	homomorphism	homomorphism	NOUN
ejpam-3285	82	41	ϕ	ϕ	NOUN
ejpam-3285	82	42	:	:	PUNCT
ejpam-3285	82	43	r→	r→	PROPN
ejpam-3285	82	44	ends(m	ends(m	PROPN
ejpam-3285	82	45	)	)	PUNCT
ejpam-3285	82	46	,	,	PUNCT
ejpam-3285	82	47	r	r	NOUN
ejpam-3285	82	48	7→	7→	NUM
ejpam-3285	82	49	ϕr	ϕr	NOUN
ejpam-3285	82	50	(	(	PUNCT
ejpam-3285	82	51	8)	8)	NUM
ejpam-3285	82	52	where	where	SCONJ
ejpam-3285	82	53	ϕr	ϕr	X
ejpam-3285	82	54	:	:	PUNCT
ejpam-3285	82	55	m	m	PROPN
ejpam-3285	82	56	→	→	SYM
ejpam-3285	82	57	m	m	PROPN
ejpam-3285	82	58	,	,	PUNCT
ejpam-3285	82	59	m	m	VERB
ejpam-3285	82	60	7→	7→	NUM
ejpam-3285	82	61	r.m	r.m	NOUN
ejpam-3285	83	1	[	[	X
ejpam-3285	83	2	8	8	NUM
ejpam-3285	83	3	]	]	PUNCT
ejpam-3285	83	4	.	.	PUNCT
ejpam-3285	84	1	since	since	SCONJ
ejpam-3285	84	2	ring	ring	NOUN
ejpam-3285	84	3	s	s	PRON
ejpam-3285	84	4	in	in	ADP
ejpam-3285	84	5	definition	definition	NOUN
ejpam-3285	84	6	1	1	NUM
ejpam-3285	84	7	is	be	AUX
ejpam-3285	84	8	a	a	DET
ejpam-3285	84	9	commutative	commutative	ADJ
ejpam-3285	84	10	ring	ring	NOUN
ejpam-3285	84	11	then	then	ADV
ejpam-3285	84	12	z(s	z(s	PROPN
ejpam-3285	84	13	)	)	PUNCT
ejpam-3285	84	14	=	=	SYM
ejpam-3285	84	15	s	s	PROPN
ejpam-3285	84	16	and	and	CCONJ
ejpam-3285	84	17	s	s	VERB
ejpam-3285	84	18	is	be	AUX
ejpam-3285	84	19	an	an	DET
ejpam-3285	84	20	r	r	NOUN
ejpam-3285	84	21	-	-	PUNCT
ejpam-3285	84	22	algebra	algebra	NOUN
ejpam-3285	84	23	and	and	CCONJ
ejpam-3285	84	24	a	a	DET
ejpam-3285	84	25	representation	representation	NOUN
ejpam-3285	84	26	module	module	NOUN
ejpam-3285	84	27	m	m	NOUN
ejpam-3285	84	28	is	be	AUX
ejpam-3285	84	29	a	a	DET
ejpam-3285	84	30	module	module	NOUN
ejpam-3285	84	31	over	over	ADP
ejpam-3285	84	32	r	r	NOUN
ejpam-3285	84	33	-	-	PUNCT
ejpam-3285	84	34	algebra	algebra	NOUN
ejpam-3285	84	35	s.	s.	PROPN
ejpam-3285	84	36	auslander	auslander	PROPN
ejpam-3285	84	37	introduces	introduce	VERB
ejpam-3285	84	38	the	the	DET
ejpam-3285	84	39	concept	concept	NOUN
ejpam-3285	84	40	of	of	ADP
ejpam-3285	84	41	modules	module	NOUN
ejpam-3285	84	42	over	over	ADP
ejpam-3285	84	43	an	an	DET
ejpam-3285	84	44	r	r	NOUN
ejpam-3285	84	45	-	-	PUNCT
ejpam-3285	84	46	algebra	algebra	NOUN
ejpam-3285	84	47	,	,	PUNCT
ejpam-3285	84	48	where	where	SCONJ
ejpam-3285	84	49	the	the	DET
ejpam-3285	84	50	ring	ring	NOUN
ejpam-3285	84	51	r	r	NOUN
ejpam-3285	84	52	is	be	AUX
ejpam-3285	84	53	artinian	artinian	ADJ
ejpam-3285	84	54	by	by	ADP
ejpam-3285	84	55	using	use	VERB
ejpam-3285	84	56	categorical	categorical	ADJ
ejpam-3285	84	57	approach	approach	NOUN
ejpam-3285	84	58	[	[	X
ejpam-3285	84	59	3],[4	3],[4	NUM
ejpam-3285	84	60	]	]	PUNCT
ejpam-3285	84	61	,	,	PUNCT
ejpam-3285	84	62	and	and	CCONJ
ejpam-3285	84	63	used	use	VERB
ejpam-3285	84	64	the	the	DET
ejpam-3285	84	65	result	result	NOUN
ejpam-3285	84	66	to	to	PART
ejpam-3285	84	67	study	study	VERB
ejpam-3285	84	68	the	the	DET
ejpam-3285	84	69	representation	representation	NOUN
ejpam-3285	84	70	of	of	ADP
ejpam-3285	84	71	finite	finite	ADJ
ejpam-3285	84	72	dimension	dimension	NOUN
ejpam-3285	84	73	of	of	ADP
ejpam-3285	84	74	algebra	algebra	NOUN
ejpam-3285	84	75	[	[	X
ejpam-3285	84	76	5	5	NUM
ejpam-3285	84	77	]	]	PUNCT
ejpam-3285	84	78	.	.	PUNCT
ejpam-3285	85	1	this	this	DET
ejpam-3285	85	2	concept	concept	NOUN
ejpam-3285	85	3	is	be	AUX
ejpam-3285	85	4	used	use	VERB
ejpam-3285	85	5	in	in	ADP
ejpam-3285	85	6	the	the	DET
ejpam-3285	85	7	representation	representation	NOUN
ejpam-3285	85	8	theory	theory	NOUN
ejpam-3285	85	9	of	of	ADP
ejpam-3285	85	10	finite	finite	PROPN
ejpam-3285	85	11	f	f	PROPN
ejpam-3285	85	12	-algebras	-algebras	PROPN
ejpam-3285	85	13	on	on	ADP
ejpam-3285	85	14	vector	vector	NOUN
ejpam-3285	85	15	spaces	space	NOUN
ejpam-3285	85	16	over	over	ADP
ejpam-3285	85	17	a	a	DET
ejpam-3285	85	18	field	field	NOUN
ejpam-3285	85	19	f	f	NOUN
ejpam-3285	85	20	,	,	PUNCT
ejpam-3285	85	21	such	such	ADJ
ejpam-3285	85	22	as	as	ADP
ejpam-3285	85	23	the	the	DET
ejpam-3285	85	24	representation	representation	NOUN
ejpam-3285	85	25	theory	theory	NOUN
ejpam-3285	85	26	of	of	ADP
ejpam-3285	85	27	quiver	quiver	NOUN
ejpam-3285	85	28	[	[	X
ejpam-3285	85	29	15	15	NUM
ejpam-3285	85	30	]	]	PUNCT
ejpam-3285	85	31	,	,	PUNCT
ejpam-3285	85	32	and	and	CCONJ
ejpam-3285	85	33	the	the	DET
ejpam-3285	85	34	representation	representation	NOUN
ejpam-3285	85	35	theory	theory	NOUN
ejpam-3285	85	36	of	of	ADP
ejpam-3285	85	37	a	a	DET
ejpam-3285	85	38	group	group	NOUN
ejpam-3285	85	39	ring	ring	NOUN
ejpam-3285	85	40	f	f	PROPN
ejpam-3285	86	1	[	[	X
ejpam-3285	86	2	g	g	X
ejpam-3285	86	3	]	]	PUNCT
ejpam-3285	86	4	where	where	SCONJ
ejpam-3285	86	5	g	g	PROPN
ejpam-3285	86	6	is	be	AUX
ejpam-3285	86	7	a	a	DET
ejpam-3285	86	8	finite	finite	NOUN
ejpam-3285	86	9	group([6	group([6	NOUN
ejpam-3285	86	10	]	]	PUNCT
ejpam-3285	86	11	.	.	PUNCT
ejpam-3285	87	1	there	there	PRON
ejpam-3285	87	2	are	be	VERB
ejpam-3285	87	3	many	many	ADJ
ejpam-3285	87	4	mathematicians	mathematician	NOUN
ejpam-3285	87	5	is	be	AUX
ejpam-3285	87	6	developed	develop	VERB
ejpam-3285	87	7	the	the	DET
ejpam-3285	87	8	concept	concept	NOUN
ejpam-3285	87	9	that	that	PRON
ejpam-3285	87	10	auslander	auslander	NOUN
ejpam-3285	87	11	given	give	VERB
ejpam-3285	87	12	,	,	PUNCT
ejpam-3285	87	13	such	such	ADJ
ejpam-3285	87	14	as	as	ADP
ejpam-3285	87	15	iyama	iyama	NOUN
ejpam-3285	87	16	[	[	X
ejpam-3285	87	17	10],[11	10],[11	NUM
ejpam-3285	87	18	]	]	PUNCT
ejpam-3285	87	19	,	,	PUNCT
ejpam-3285	87	20	and	and	CCONJ
ejpam-3285	87	21	oppermann	oppermann	PROPN
ejpam-3285	87	22	[	[	X
ejpam-3285	87	23	14	14	NUM
ejpam-3285	87	24	]	]	PUNCT
ejpam-3285	87	25	.	.	PUNCT
ejpam-3285	88	1	from	from	ADP
ejpam-3285	88	2	the	the	DET
ejpam-3285	88	3	previous	previous	ADJ
ejpam-3285	88	4	paragraph	paragraph	NOUN
ejpam-3285	88	5	,	,	PUNCT
ejpam-3285	88	6	we	we	PRON
ejpam-3285	88	7	have	have	AUX
ejpam-3285	88	8	been	be	AUX
ejpam-3285	88	9	knowing	know	VERB
ejpam-3285	88	10	that	that	SCONJ
ejpam-3285	88	11	the	the	DET
ejpam-3285	88	12	f	f	PROPN
ejpam-3285	88	13	-representation	-representation	PROPN
ejpam-3285	88	14	module	module	NOUN
ejpam-3285	88	15	of	of	ADP
ejpam-3285	88	16	ring	ring	NOUN
ejpam-3285	88	17	r	r	NOUN
ejpam-3285	88	18	is	be	AUX
ejpam-3285	88	19	a	a	DET
ejpam-3285	88	20	module	module	NOUN
ejpam-3285	88	21	over	over	ADP
ejpam-3285	88	22	r	r	NOUN
ejpam-3285	88	23	-	-	PUNCT
ejpam-3285	88	24	algebra	algebra	NOUN
ejpam-3285	88	25	s.	s.	PROPN
ejpam-3285	88	26	however	however	ADV
ejpam-3285	88	27	,	,	PUNCT
ejpam-3285	88	28	base	base	NOUN
ejpam-3285	88	29	on	on	ADP
ejpam-3285	88	30	example	example	NOUN
ejpam-3285	88	31	5	5	NUM
ejpam-3285	88	32	and	and	CCONJ
ejpam-3285	88	33	proposition	proposition	NOUN
ejpam-3285	88	34	1	1	NUM
ejpam-3285	88	35	,	,	PUNCT
ejpam-3285	88	36	the	the	DET
ejpam-3285	88	37	properties	property	NOUN
ejpam-3285	88	38	of	of	ADP
ejpam-3285	88	39	the	the	DET
ejpam-3285	88	40	f	f	PROPN
ejpam-3285	88	41	-representation	-representation	PROPN
ejpam-3285	88	42	do	do	AUX
ejpam-3285	88	43	not	not	PART
ejpam-3285	88	44	only	only	ADV
ejpam-3285	88	45	depend	depend	VERB
ejpam-3285	88	46	on	on	ADP
ejpam-3285	88	47	f	f	PROPN
ejpam-3285	88	48	-representation	-representation	PROPN
ejpam-3285	88	49	module	module	NOUN
ejpam-3285	88	50	of	of	ADP
ejpam-3285	88	51	r	r	NOUN
ejpam-3285	88	52	but	but	CCONJ
ejpam-3285	88	53	also	also	ADV
ejpam-3285	88	54	on	on	ADP
ejpam-3285	88	55	the	the	DET
ejpam-3285	88	56	properties	property	NOUN
ejpam-3285	88	57	of	of	ADP
ejpam-3285	88	58	a	a	DET
ejpam-3285	88	59	ring	ring	NOUN
ejpam-3285	88	60	homomorphism	homomorphism	PROPN
ejpam-3285	88	61	f	f	X
ejpam-3285	88	62	.	.	PUNCT
ejpam-3285	89	1	in	in	ADP
ejpam-3285	89	2	the	the	DET
ejpam-3285	89	3	case	case	NOUN
ejpam-3285	89	4	of	of	ADP
ejpam-3285	89	5	the	the	DET
ejpam-3285	89	6	representation	representation	NOUN
ejpam-3285	89	7	of	of	ADP
ejpam-3285	89	8	ring	ring	NOUN
ejpam-3285	89	9	on	on	ADP
ejpam-3285	89	10	the	the	DET
ejpam-3285	89	11	module	module	NOUN
ejpam-3285	89	12	over	over	ADP
ejpam-3285	89	13	a	a	DET
ejpam-3285	89	14	commutative	commutative	ADJ
ejpam-3285	89	15	ring	ring	NOUN
ejpam-3285	89	16	,	,	PUNCT
ejpam-3285	89	17	the	the	DET
ejpam-3285	89	18	generalization	generalization	NOUN
ejpam-3285	89	19	of	of	ADP
ejpam-3285	89	20	schur	schur	PROPN
ejpam-3285	89	21	’s	’s	PART
ejpam-3285	89	22	lemma	lemma	PROPN
ejpam-3285	89	23	is	be	AUX
ejpam-3285	89	24	considered	consider	VERB
ejpam-3285	89	25	.	.	PUNCT
ejpam-3285	90	1	in	in	ADP
ejpam-3285	90	2	this	this	DET
ejpam-3285	90	3	paper	paper	NOUN
ejpam-3285	90	4	,	,	PUNCT
ejpam-3285	90	5	we	we	PRON
ejpam-3285	90	6	investigate	investigate	VERB
ejpam-3285	90	7	how	how	SCONJ
ejpam-3285	90	8	to	to	PART
ejpam-3285	90	9	generalize	generalize	VERB
ejpam-3285	90	10	schur	schur	PROPN
ejpam-3285	90	11	’s	’s	PART
ejpam-3285	90	12	lemma	lemma	PROPN
ejpam-3285	90	13	in	in	ADP
ejpam-3285	90	14	representations	representation	NOUN
ejpam-3285	90	15	of	of	ADP
ejpam-3285	90	16	rings	ring	NOUN
ejpam-3285	90	17	on	on	ADP
ejpam-3285	90	18	modules	module	NOUN
ejpam-3285	90	19	over	over	ADP
ejpam-3285	90	20	a	a	DET
ejpam-3285	90	21	commutative	commutative	ADJ
ejpam-3285	90	22	ring	ring	NOUN
ejpam-3285	90	23	.	.	PUNCT
ejpam-3285	91	1	the	the	DET
ejpam-3285	91	2	proof	proof	NOUN
ejpam-3285	91	3	of	of	ADP
ejpam-3285	91	4	generalization	generalization	NOUN
ejpam-3285	91	5	of	of	ADP
ejpam-3285	91	6	schur	schur	PROPN
ejpam-3285	91	7	’s	’s	PART
ejpam-3285	91	8	lemma	lemma	PROPN
ejpam-3285	91	9	in	in	ADP
ejpam-3285	91	10	this	this	DET
ejpam-3285	91	11	paper	paper	NOUN
ejpam-3285	91	12	is	be	AUX
ejpam-3285	91	13	analog	analog	NOUN
ejpam-3285	91	14	with	with	ADP
ejpam-3285	91	15	the	the	DET
ejpam-3285	91	16	proof	proof	NOUN
ejpam-3285	91	17	of	of	ADP
ejpam-3285	91	18	schur	schur	PROPN
ejpam-3285	91	19	’s	’s	PART
ejpam-3285	91	20	lemma	lemma	PROPN
ejpam-3285	91	21	in	in	ADP
ejpam-3285	91	22	module	module	NOUN
ejpam-3285	91	23	theory	theory	NOUN
ejpam-3285	91	24	.	.	PUNCT
ejpam-3285	92	1	however	however	ADV
ejpam-3285	92	2	,	,	PUNCT
ejpam-3285	92	3	the	the	DET
ejpam-3285	92	4	properties	property	NOUN
ejpam-3285	92	5	of	of	ADP
ejpam-3285	92	6	the	the	DET
ejpam-3285	92	7	representation	representation	NOUN
ejpam-3285	92	8	module	module	NOUN
ejpam-3285	92	9	m	m	PROPN
ejpam-3285	92	10	(	(	PUNCT
ejpam-3285	92	11	m	m	PROPN
ejpam-3285	92	12	is	be	AUX
ejpam-3285	92	13	an	an	DET
ejpam-3285	92	14	s	s	NOUN
ejpam-3285	92	15	-	-	NOUN
ejpam-3285	92	16	module	module	NOUN
ejpam-3285	92	17	)	)	PUNCT
ejpam-3285	92	18	of	of	ADP
ejpam-3285	92	19	a	a	DET
ejpam-3285	92	20	ring	ring	NOUN
ejpam-3285	92	21	r	r	NOUN
ejpam-3285	92	22	depend	depend	VERB
ejpam-3285	92	23	on	on	ADP
ejpam-3285	92	24	the	the	DET
ejpam-3285	92	25	properties	property	NOUN
ejpam-3285	92	26	of	of	ADP
ejpam-3285	92	27	a	a	DET
ejpam-3285	92	28	ring	ring	NOUN
ejpam-3285	92	29	s	s	NOUN
ejpam-3285	92	30	and	and	CCONJ
ejpam-3285	92	31	m	m	PROPN
ejpam-3285	92	32	as	as	ADP
ejpam-3285	92	33	s	s	NOUN
ejpam-3285	92	34	-	-	NOUN
ejpam-3285	92	35	module	module	NOUN
ejpam-3285	92	36	.	.	PUNCT
ejpam-3285	93	1	2	2	X
ejpam-3285	93	2	.	.	X
ejpam-3285	93	3	the	the	DET
ejpam-3285	93	4	main	main	ADJ
ejpam-3285	93	5	result	result	NOUN
ejpam-3285	93	6	to	to	PART
ejpam-3285	93	7	generalize	generalize	VERB
ejpam-3285	93	8	schur	schur	PROPN
ejpam-3285	93	9	’s	’s	PART
ejpam-3285	93	10	lemma	lemma	PROPN
ejpam-3285	93	11	,	,	PUNCT
ejpam-3285	93	12	we	we	PRON
ejpam-3285	93	13	need	need	VERB
ejpam-3285	93	14	to	to	PART
ejpam-3285	93	15	see	see	VERB
ejpam-3285	93	16	some	some	DET
ejpam-3285	93	17	properties	property	NOUN
ejpam-3285	93	18	of	of	ADP
ejpam-3285	93	19	representation	representation	NOUN
ejpam-3285	93	20	of	of	ADP
ejpam-3285	93	21	ring	ring	NOUN
ejpam-3285	93	22	on	on	ADP
ejpam-3285	93	23	module	module	NOUN
ejpam-3285	93	24	over	over	ADP
ejpam-3285	93	25	commutative	commutative	ADJ
ejpam-3285	93	26	ring	ring	NOUN
ejpam-3285	93	27	such	such	ADJ
ejpam-3285	93	28	as	as	ADP
ejpam-3285	93	29	equivalence	equivalence	NOUN
ejpam-3285	93	30	of	of	ADP
ejpam-3285	93	31	two	two	NUM
ejpam-3285	93	32	representations	representation	NOUN
ejpam-3285	93	33	,	,	PUNCT
ejpam-3285	93	34	and	and	CCONJ
ejpam-3285	93	35	morphism	morphism	NOUN
ejpam-3285	93	36	between	between	ADP
ejpam-3285	93	37	two	two	NUM
ejpam-3285	93	38	representations	representation	NOUN
ejpam-3285	93	39	.	.	PUNCT
ejpam-3285	94	1	let	let	VERB
ejpam-3285	94	2	µ	µ	X
ejpam-3285	94	3	be	be	AUX
ejpam-3285	94	4	a	a	DET
ejpam-3285	94	5	representation	representation	NOUN
ejpam-3285	94	6	of	of	ADP
ejpam-3285	94	7	ring	ring	NOUN
ejpam-3285	94	8	r	r	NOUN
ejpam-3285	94	9	on	on	ADP
ejpam-3285	94	10	an	an	DET
ejpam-3285	94	11	s	s	NOUN
ejpam-3285	94	12	-	-	PUNCT
ejpam-3285	94	13	module	module	NOUN
ejpam-3285	94	14	m	m	NOUN
ejpam-3285	94	15	.	.	PUNCT
ejpam-3285	95	1	a	a	DET
ejpam-3285	95	2	submodule	submodule	NOUN
ejpam-3285	95	3	u	u	NOUN
ejpam-3285	95	4	of	of	ADP
ejpam-3285	95	5	a	a	DET
ejpam-3285	95	6	representation	representation	NOUN
ejpam-3285	95	7	module	module	NOUN
ejpam-3285	95	8	m	m	NOUN
ejpam-3285	95	9	is	be	AUX
ejpam-3285	95	10	called	call	VERB
ejpam-3285	95	11	r	r	NOUN
ejpam-3285	95	12	-	-	PUNCT
ejpam-3285	95	13	invariant	invariant	ADJ
ejpam-3285	95	14	if	if	SCONJ
ejpam-3285	95	15	for	for	ADP
ejpam-3285	95	16	any	any	DET
ejpam-3285	95	17	r	r	NOUN
ejpam-3285	95	18	∈	∈	NOUN
ejpam-3285	95	19	r	r	NOUN
ejpam-3285	95	20	,	,	PUNCT
ejpam-3285	95	21	µr(u	µr(u	NOUN
ejpam-3285	95	22	)	)	PUNCT
ejpam-3285	95	23	⊆	⊆	NUM
ejpam-3285	95	24	u	u	NOUN
ejpam-3285	95	25	.	.	PUNCT
ejpam-3285	96	1	since	since	SCONJ
ejpam-3285	96	2	every	every	DET
ejpam-3285	96	3	f	f	PROPN
ejpam-3285	96	4	-representation	-representation	PROPN
ejpam-3285	96	5	module	module	NOUN
ejpam-3285	96	6	m	m	NOUN
ejpam-3285	96	7	is	be	AUX
ejpam-3285	96	8	an	an	DET
ejpam-3285	96	9	r	r	NOUN
ejpam-3285	96	10	-	-	PUNCT
ejpam-3285	96	11	module	module	NOUN
ejpam-3285	96	12	,	,	PUNCT
ejpam-3285	96	13	every	every	DET
ejpam-3285	96	14	submodule	submodule	NOUN
ejpam-3285	96	15	of	of	ADP
ejpam-3285	96	16	m	m	PROPN
ejpam-3285	96	17	is	be	AUX
ejpam-3285	96	18	an	an	DET
ejpam-3285	96	19	r	r	NOUN
ejpam-3285	96	20	-	-	PUNCT
ejpam-3285	96	21	invariant	invariant	ADJ
ejpam-3285	96	22	.	.	PUNCT
ejpam-3285	97	1	so	so	ADV
ejpam-3285	97	2	we	we	PRON
ejpam-3285	97	3	have	have	VERB
ejpam-3285	97	4	this	this	DET
ejpam-3285	97	5	properties	property	NOUN
ejpam-3285	97	6	.	.	PUNCT
ejpam-3285	98	1	remark	remark	PROPN
ejpam-3285	98	2	2	2	NUM
ejpam-3285	98	3	.	.	PUNCT
ejpam-3285	99	1	(	(	PUNCT
ejpam-3285	99	2	i	i	NOUN
ejpam-3285	99	3	)	)	PUNCT
ejpam-3285	99	4	if	if	SCONJ
ejpam-3285	99	5	an	an	DET
ejpam-3285	99	6	s	s	NOUN
ejpam-3285	99	7	-	-	PUNCT
ejpam-3285	99	8	module	module	NOUN
ejpam-3285	99	9	m	m	NOUN
ejpam-3285	99	10	is	be	AUX
ejpam-3285	99	11	an	an	DET
ejpam-3285	99	12	f	f	PROPN
ejpam-3285	99	13	-representation	-representation	PROPN
ejpam-3285	99	14	module	module	NOUN
ejpam-3285	99	15	of	of	ADP
ejpam-3285	99	16	an	an	DET
ejpam-3285	99	17	f	f	PROPN
ejpam-3285	99	18	-representation	-representation	PROPN
ejpam-3285	99	19	µ	µ	X
ejpam-3285	99	20	of	of	ADP
ejpam-3285	99	21	ring	ring	NOUN
ejpam-3285	99	22	r	r	NOUN
ejpam-3285	99	23	,	,	PUNCT
ejpam-3285	99	24	then	then	ADV
ejpam-3285	99	25	every	every	DET
ejpam-3285	99	26	submodule	submodule	NOUN
ejpam-3285	99	27	of	of	ADP
ejpam-3285	99	28	m	m	PROPN
ejpam-3285	99	29	is	be	AUX
ejpam-3285	99	30	r	r	NOUN
ejpam-3285	99	31	-	-	PUNCT
ejpam-3285	99	32	invariant	invariant	ADJ
ejpam-3285	99	33	.	.	PUNCT
ejpam-3285	100	1	(	(	PUNCT
ejpam-3285	100	2	ii	ii	NOUN
ejpam-3285	100	3	)	)	PUNCT
ejpam-3285	100	4	if	if	SCONJ
ejpam-3285	100	5	u	u	NOUN
ejpam-3285	100	6	is	be	AUX
ejpam-3285	100	7	an	an	DET
ejpam-3285	100	8	r	r	NOUN
ejpam-3285	100	9	-	-	PUNCT
ejpam-3285	100	10	invariant	invariant	ADJ
ejpam-3285	100	11	submodule	submodule	NOUN
ejpam-3285	100	12	,	,	PUNCT
ejpam-3285	100	13	then	then	ADV
ejpam-3285	100	14	we	we	PRON
ejpam-3285	100	15	can	can	AUX
ejpam-3285	100	16	construct	construct	VERB
ejpam-3285	100	17	a	a	DET
ejpam-3285	100	18	new	new	ADJ
ejpam-3285	100	19	f	f	PROPN
ejpam-3285	100	20	-representa	-representa	PROPN
ejpam-3285	100	21	-	-	PUNCT
ejpam-3285	100	22	tion	tion	NOUN
ejpam-3285	100	23	of	of	ADP
ejpam-3285	100	24	r	r	NOUN
ejpam-3285	100	25	,	,	PUNCT
ejpam-3285	100	26	that	that	PRON
ejpam-3285	100	27	is	be	AUX
ejpam-3285	100	28	a	a	DET
ejpam-3285	100	29	ring	ring	NOUN
ejpam-3285	100	30	homomorphism	homomorphism	NOUN
ejpam-3285	100	31	µ′	µ′	NOUN
ejpam-3285	100	32	:	:	PUNCT
ejpam-3285	100	33	r→	r→	PROPN
ejpam-3285	100	34	ends(u	ends(u	PROPN
ejpam-3285	100	35	)	)	PUNCT
ejpam-3285	100	36	defined	define	VERB
ejpam-3285	100	37	by	by	ADP
ejpam-3285	100	38	µ′r(a	µ′r(a	NOUN
ejpam-3285	100	39	)	)	PUNCT
ejpam-3285	100	40	=	=	PUNCT
ejpam-3285	100	41	µr(a	µr(a	X
ejpam-3285	100	42	)	)	PUNCT
ejpam-3285	100	43	=	=	SYM
ejpam-3285	100	44	f(r)a	f(r)a	PROPN
ejpam-3285	100	45	for	for	ADP
ejpam-3285	100	46	any	any	DET
ejpam-3285	100	47	r	r	NOUN
ejpam-3285	100	48	∈	∈	NOUN
ejpam-3285	100	49	r	r	NOUN
ejpam-3285	100	50	and	and	CCONJ
ejpam-3285	100	51	a	a	DET
ejpam-3285	100	52	∈	∈	PROPN
ejpam-3285	100	53	u	u	NOUN
ejpam-3285	100	54	.	.	PUNCT
ejpam-3285	101	1	n.	n.	PROPN
ejpam-3285	101	2	hijriati	hijriati	PROPN
ejpam-3285	101	3	,	,	PUNCT
ejpam-3285	101	4	s.	s.	PROPN
ejpam-3285	101	5	wahyuni	wahyuni	PROPN
ejpam-3285	101	6	,	,	PUNCT
ejpam-3285	101	7	i.e.	i.e.	X
ejpam-3285	101	8	wijayanti	wijayanti	X
ejpam-3285	101	9	/	/	SYM
ejpam-3285	101	10	eur	eur	PROPN
ejpam-3285	101	11	.	.	PUNCT
ejpam-3285	102	1	j.	j.	PROPN
ejpam-3285	102	2	pure	pure	PROPN
ejpam-3285	102	3	appl	appl	PROPN
ejpam-3285	102	4	.	.	PROPN
ejpam-3285	102	5	math	math	PROPN
ejpam-3285	102	6	,	,	PUNCT
ejpam-3285	102	7	11	11	NUM
ejpam-3285	102	8	(	(	PUNCT
ejpam-3285	102	9	3	3	NUM
ejpam-3285	102	10	)	)	PUNCT
ejpam-3285	102	11	(	(	PUNCT
ejpam-3285	102	12	2018	2018	NUM
ejpam-3285	102	13	)	)	PUNCT
ejpam-3285	102	14	,	,	PUNCT
ejpam-3285	102	15	751	751	NUM
ejpam-3285	102	16	-	-	SYM
ejpam-3285	102	17	761	761	NUM
ejpam-3285	102	18	755	755	NUM
ejpam-3285	102	19	a	a	DET
ejpam-3285	102	20	non	non	ADJ
ejpam-3285	102	21	zero	zero	NUM
ejpam-3285	102	22	r	r	NOUN
ejpam-3285	102	23	-	-	PUNCT
ejpam-3285	102	24	module	module	NOUN
ejpam-3285	102	25	m	m	NOUN
ejpam-3285	102	26	is	be	AUX
ejpam-3285	102	27	called	call	VERB
ejpam-3285	102	28	irreducible	irreducible	ADJ
ejpam-3285	102	29	if	if	SCONJ
ejpam-3285	102	30	it	it	PRON
ejpam-3285	102	31	has	have	VERB
ejpam-3285	102	32	only	only	ADV
ejpam-3285	102	33	trivial	trivial	ADJ
ejpam-3285	102	34	submodule	submodule	NOUN
ejpam-3285	102	35	.	.	PUNCT
ejpam-3285	103	1	the	the	DET
ejpam-3285	103	2	definition	definition	NOUN
ejpam-3285	103	3	of	of	ADP
ejpam-3285	103	4	an	an	DET
ejpam-3285	103	5	irreducible	irreducible	ADJ
ejpam-3285	103	6	representation	representation	NOUN
ejpam-3285	103	7	depend	depend	VERB
ejpam-3285	103	8	on	on	ADP
ejpam-3285	103	9	properties	property	NOUN
ejpam-3285	103	10	of	of	ADP
ejpam-3285	103	11	a	a	DET
ejpam-3285	103	12	representation	representation	NOUN
ejpam-3285	103	13	module	module	NOUN
ejpam-3285	103	14	that	that	PRON
ejpam-3285	103	15	we	we	PRON
ejpam-3285	103	16	give	give	VERB
ejpam-3285	103	17	as	as	ADP
ejpam-3285	103	18	the	the	DET
ejpam-3285	103	19	following	follow	VERB
ejpam-3285	103	20	:	:	PUNCT
ejpam-3285	103	21	definition	definition	NOUN
ejpam-3285	103	22	2	2	NUM
ejpam-3285	103	23	.	.	PUNCT
ejpam-3285	103	24	a	a	DET
ejpam-3285	103	25	non	non	ADJ
ejpam-3285	103	26	-	-	ADJ
ejpam-3285	103	27	zero	zero	NUM
ejpam-3285	103	28	f	f	PROPN
ejpam-3285	103	29	-representation	-representation	PROPN
ejpam-3285	103	30	µ	µ	NOUN
ejpam-3285	103	31	:	:	PUNCT
ejpam-3285	103	32	r	r	NOUN
ejpam-3285	103	33	→	→	SYM
ejpam-3285	103	34	ends(m	ends(m	PROPN
ejpam-3285	103	35	)	)	PUNCT
ejpam-3285	103	36	of	of	ADP
ejpam-3285	103	37	a	a	DET
ejpam-3285	103	38	ring	ring	NOUN
ejpam-3285	103	39	r	r	NOUN
ejpam-3285	103	40	is	be	AUX
ejpam-3285	103	41	said	say	VERB
ejpam-3285	103	42	to	to	PART
ejpam-3285	103	43	be	be	AUX
ejpam-3285	103	44	irreducible	irreducible	ADJ
ejpam-3285	103	45	if	if	SCONJ
ejpam-3285	103	46	the	the	DET
ejpam-3285	103	47	only	only	ADJ
ejpam-3285	103	48	r	r	NOUN
ejpam-3285	103	49	-	-	PUNCT
ejpam-3285	103	50	invariant	invariant	ADJ
ejpam-3285	103	51	submodules	submodule	NOUN
ejpam-3285	103	52	of	of	ADP
ejpam-3285	103	53	m	m	PROPN
ejpam-3285	103	54	are	be	AUX
ejpam-3285	103	55	zero	zero	NUM
ejpam-3285	103	56	and	and	CCONJ
ejpam-3285	103	57	m	m	PROPN
ejpam-3285	103	58	.	.	PUNCT
ejpam-3285	104	1	let	let	VERB
ejpam-3285	104	2	µ	µ	X
ejpam-3285	104	3	be	be	AUX
ejpam-3285	104	4	an	an	DET
ejpam-3285	104	5	f	f	PROPN
ejpam-3285	104	6	-representation	-representation	NOUN
ejpam-3285	104	7	of	of	ADP
ejpam-3285	104	8	r	r	NOUN
ejpam-3285	104	9	on	on	ADP
ejpam-3285	104	10	an	an	DET
ejpam-3285	104	11	s	s	NOUN
ejpam-3285	104	12	-	-	PUNCT
ejpam-3285	104	13	module	module	NOUN
ejpam-3285	104	14	m	m	NOUN
ejpam-3285	104	15	and	and	CCONJ
ejpam-3285	104	16	ϕ	ϕ	ADP
ejpam-3285	104	17	a	a	DET
ejpam-3285	104	18	g	g	NOUN
ejpam-3285	104	19	-	-	PUNCT
ejpam-3285	104	20	representation	representation	NOUN
ejpam-3285	104	21	of	of	ADP
ejpam-3285	104	22	r	r	NOUN
ejpam-3285	104	23	on	on	ADP
ejpam-3285	104	24	s	s	NOUN
ejpam-3285	104	25	-	-	PUNCT
ejpam-3285	104	26	module	module	NOUN
ejpam-3285	104	27	n	n	NOUN
ejpam-3285	104	28	.	.	PUNCT
ejpam-3285	105	1	if	if	SCONJ
ejpam-3285	105	2	there	there	PRON
ejpam-3285	105	3	is	be	VERB
ejpam-3285	105	4	a	a	DET
ejpam-3285	105	5	module	module	NOUN
ejpam-3285	105	6	homomorphism	homomorphism	NOUN
ejpam-3285	105	7	t	t	NOUN
ejpam-3285	105	8	:	:	PUNCT
ejpam-3285	105	9	m	m	VERB
ejpam-3285	105	10	→	→	SYM
ejpam-3285	105	11	n	n	CCONJ
ejpam-3285	105	12	,	,	PUNCT
ejpam-3285	105	13	then	then	ADV
ejpam-3285	105	14	we	we	PRON
ejpam-3285	105	15	obtain	obtain	VERB
ejpam-3285	105	16	tµr	tµr	NOUN
ejpam-3285	105	17	:	:	PUNCT
ejpam-3285	105	18	m	m	VERB
ejpam-3285	105	19	→	→	SYM
ejpam-3285	105	20	n	n	PROPN
ejpam-3285	105	21	and	and	CCONJ
ejpam-3285	105	22	ϕrt	ϕrt	ADJ
ejpam-3285	105	23	:	:	PUNCT
ejpam-3285	105	24	m	m	VERB
ejpam-3285	105	25	→	→	SYM
ejpam-3285	105	26	n	n	CCONJ
ejpam-3285	105	27	for	for	ADP
ejpam-3285	105	28	every	every	DET
ejpam-3285	105	29	r	r	NOUN
ejpam-3285	105	30	∈	∈	PROPN
ejpam-3285	105	31	r.	r.	NOUN
ejpam-3285	105	32	but	but	CCONJ
ejpam-3285	105	33	it	it	PRON
ejpam-3285	105	34	is	be	AUX
ejpam-3285	105	35	not	not	PART
ejpam-3285	105	36	necessary	necessary	ADJ
ejpam-3285	105	37	tµr	tµr	NOUN
ejpam-3285	105	38	=	=	SYM
ejpam-3285	105	39	ϕrt	ϕrt	PROPN
ejpam-3285	105	40	.	.	PUNCT
ejpam-3285	106	1	we	we	PRON
ejpam-3285	106	2	give	give	VERB
ejpam-3285	106	3	an	an	DET
ejpam-3285	106	4	example	example	NOUN
ejpam-3285	106	5	to	to	PART
ejpam-3285	106	6	show	show	VERB
ejpam-3285	106	7	this	this	DET
ejpam-3285	106	8	fact	fact	NOUN
ejpam-3285	106	9	.	.	PUNCT
ejpam-3285	107	1	example	example	NOUN
ejpam-3285	108	1	7	7	NUM
ejpam-3285	108	2	.	.	X
ejpam-3285	108	3	we	we	PRON
ejpam-3285	108	4	consider	consider	VERB
ejpam-3285	108	5	example	example	NOUN
ejpam-3285	108	6	3	3	NUM
ejpam-3285	108	7	and	and	CCONJ
ejpam-3285	108	8	example	example	NOUN
ejpam-3285	109	1	4	4	X
ejpam-3285	109	2	.	.	PUNCT
ejpam-3285	110	1	let	let	VERB
ejpam-3285	110	2	t	t	NOUN
ejpam-3285	110	3	:	:	PUNCT
ejpam-3285	110	4	z2	z2	PROPN
ejpam-3285	110	5	→	→	SYM
ejpam-3285	110	6	m2(z	m2(z	VERB
ejpam-3285	110	7	)	)	PUNCT
ejpam-3285	110	8	be	be	VERB
ejpam-3285	110	9	a	a	DET
ejpam-3285	110	10	z2module	z2module	PROPN
ejpam-3285	110	11	homomorphism	homomorphism	NOUN
ejpam-3285	110	12	defined	define	VERB
ejpam-3285	110	13	by	by	ADP
ejpam-3285	110	14	t	t	PROPN
ejpam-3285	110	15	(	(	PUNCT
ejpam-3285	110	16	a	a	DET
ejpam-3285	110	17	,	,	PUNCT
ejpam-3285	110	18	b	b	NOUN
ejpam-3285	110	19	)	)	PUNCT
ejpam-3285	111	1	=	=	NOUN
ejpam-3285	111	2	[	[	PUNCT
ejpam-3285	111	3	a	a	PRON
ejpam-3285	111	4	b	b	PROPN
ejpam-3285	111	5	b	b	PROPN
ejpam-3285	111	6	a	a	NOUN
ejpam-3285	111	7	]	]	PUNCT
ejpam-3285	111	8	.	.	PUNCT
ejpam-3285	112	1	since	since	SCONJ
ejpam-3285	112	2	for	for	ADP
ejpam-3285	112	3	any	any	DET
ejpam-3285	112	4	a	a	DET
ejpam-3285	112	5	=	=	SYM
ejpam-3285	112	6	[	[	PUNCT
ejpam-3285	112	7	u	u	NOUN
ejpam-3285	112	8	0	0	PROPN
ejpam-3285	112	9	w	w	NOUN
ejpam-3285	112	10	v	v	X
ejpam-3285	112	11	]	]	PUNCT
ejpam-3285	112	12	∈	∈	PROPN
ejpam-3285	112	13	m	m	NOUN
ejpam-3285	112	14	′2(z	′2(z	NUM
ejpam-3285	112	15	)	)	PUNCT
ejpam-3285	112	16	and	and	CCONJ
ejpam-3285	112	17	(	(	PUNCT
ejpam-3285	112	18	a	a	DET
ejpam-3285	112	19	,	,	PUNCT
ejpam-3285	112	20	b	b	NOUN
ejpam-3285	112	21	)	)	PUNCT
ejpam-3285	112	22	∈	∈	PROPN
ejpam-3285	112	23	z2	z2	NOUN
ejpam-3285	112	24	we	we	PRON
ejpam-3285	112	25	have	have	VERB
ejpam-3285	112	26	tµa(a	tµa(a	PROPN
ejpam-3285	112	27	,	,	PUNCT
ejpam-3285	112	28	b	b	NOUN
ejpam-3285	112	29	)	)	PUNCT
ejpam-3285	112	30	=	=	NOUN
ejpam-3285	113	1	[	[	PUNCT
ejpam-3285	113	2	ua	ua	PROPN
ejpam-3285	113	3	bv	bv	PROPN
ejpam-3285	113	4	bv	bv	PROPN
ejpam-3285	113	5	ua	ua	PROPN
ejpam-3285	113	6	]	]	PUNCT
ejpam-3285	113	7	,	,	PUNCT
ejpam-3285	113	8	ϕat	ϕat	PROPN
ejpam-3285	113	9	(	(	PUNCT
ejpam-3285	113	10	a	a	DET
ejpam-3285	113	11	,	,	PUNCT
ejpam-3285	113	12	b	b	NOUN
ejpam-3285	113	13	)	)	PUNCT
ejpam-3285	113	14	=	=	PUNCT
ejpam-3285	113	15	[	[	PUNCT
ejpam-3285	113	16	ua	ua	NOUN
ejpam-3285	113	17	0	0	NUM
ejpam-3285	113	18	0	0	NUM
ejpam-3285	113	19	av	av	PROPN
ejpam-3285	113	20	]	]	PUNCT
ejpam-3285	113	21	.	.	PUNCT
ejpam-3285	114	1	we	we	PRON
ejpam-3285	114	2	conclude	conclude	VERB
ejpam-3285	114	3	tµa	tµa	NOUN
ejpam-3285	114	4	6=	6=	PROPN
ejpam-3285	114	5	ϕat	ϕat	PROPN
ejpam-3285	114	6	.	.	PUNCT
ejpam-3285	115	1	furthermore	furthermore	ADV
ejpam-3285	115	2	,	,	PUNCT
ejpam-3285	115	3	if	if	SCONJ
ejpam-3285	115	4	there	there	PRON
ejpam-3285	115	5	is	be	VERB
ejpam-3285	115	6	a	a	DET
ejpam-3285	115	7	module	module	NOUN
ejpam-3285	115	8	isomorphism	isomorphism	NOUN
ejpam-3285	115	9	t	t	NOUN
ejpam-3285	115	10	:	:	PUNCT
ejpam-3285	115	11	m	m	VERB
ejpam-3285	115	12	→	→	SYM
ejpam-3285	115	13	n	n	X
ejpam-3285	115	14	such	such	ADJ
ejpam-3285	115	15	that	that	DET
ejpam-3285	115	16	tµr	tµr	NOUN
ejpam-3285	115	17	=	=	NOUN
ejpam-3285	115	18	ϕrt	ϕrt	NOUN
ejpam-3285	115	19	for	for	ADP
ejpam-3285	115	20	all	all	DET
ejpam-3285	115	21	r	r	NOUN
ejpam-3285	115	22	∈	∈	NOUN
ejpam-3285	115	23	r	r	NOUN
ejpam-3285	115	24	,	,	PUNCT
ejpam-3285	115	25	then	then	ADV
ejpam-3285	115	26	µ	µ	PROPN
ejpam-3285	115	27	and	and	CCONJ
ejpam-3285	115	28	ϕ	ϕ	PROPN
ejpam-3285	115	29	are	be	AUX
ejpam-3285	115	30	called	call	VERB
ejpam-3285	115	31	equivalent	equivalent	ADJ
ejpam-3285	115	32	.	.	PUNCT
ejpam-3285	116	1	the	the	DET
ejpam-3285	116	2	definition	definition	NOUN
ejpam-3285	116	3	of	of	ADP
ejpam-3285	116	4	the	the	DET
ejpam-3285	116	5	equivalent	equivalent	NOUN
ejpam-3285	116	6	of	of	ADP
ejpam-3285	116	7	two	two	NUM
ejpam-3285	116	8	representations	representation	NOUN
ejpam-3285	116	9	is	be	AUX
ejpam-3285	116	10	given	give	VERB
ejpam-3285	116	11	in	in	ADP
ejpam-3285	116	12	the	the	DET
ejpam-3285	116	13	following	follow	VERB
ejpam-3285	116	14	definition	definition	NOUN
ejpam-3285	116	15	.	.	PUNCT
ejpam-3285	117	1	definition	definition	NOUN
ejpam-3285	117	2	3	3	X
ejpam-3285	117	3	.	.	PUNCT
ejpam-3285	118	1	let	let	VERB
ejpam-3285	118	2	µ	µ	PRON
ejpam-3285	118	3	:	:	PUNCT
ejpam-3285	118	4	r	r	NOUN
ejpam-3285	118	5	→	→	SYM
ejpam-3285	118	6	ends(m	ends(m	PROPN
ejpam-3285	118	7	)	)	PUNCT
ejpam-3285	118	8	be	be	VERB
ejpam-3285	118	9	an	an	DET
ejpam-3285	118	10	f	f	PROPN
ejpam-3285	118	11	-representation	-representation	NOUN
ejpam-3285	118	12	of	of	ADP
ejpam-3285	118	13	r	r	NOUN
ejpam-3285	118	14	and	and	CCONJ
ejpam-3285	118	15	let	let	VERB
ejpam-3285	118	16	ϕ	ϕ	NOUN
ejpam-3285	118	17	:	:	PUNCT
ejpam-3285	118	18	r	r	NOUN
ejpam-3285	118	19	→	→	SYM
ejpam-3285	118	20	ends(n	ends(n	NOUN
ejpam-3285	118	21	)	)	PUNCT
ejpam-3285	118	22	be	be	VERB
ejpam-3285	118	23	a	a	DET
ejpam-3285	118	24	g	g	NOUN
ejpam-3285	118	25	-	-	PUNCT
ejpam-3285	118	26	representations	representation	NOUN
ejpam-3285	118	27	of	of	ADP
ejpam-3285	118	28	r.	r.	PROPN
ejpam-3285	118	29	representations	representations	PROPN
ejpam-3285	118	30	µ	µ	PROPN
ejpam-3285	118	31	and	and	CCONJ
ejpam-3285	118	32	ϕ	ϕ	NOUN
ejpam-3285	118	33	are	be	AUX
ejpam-3285	118	34	called	call	VERB
ejpam-3285	118	35	equivalent	equivalent	ADJ
ejpam-3285	118	36	if	if	SCONJ
ejpam-3285	118	37	there	there	PRON
ejpam-3285	118	38	is	be	VERB
ejpam-3285	118	39	an	an	DET
ejpam-3285	118	40	s	s	NOUN
ejpam-3285	118	41	-	-	PUNCT
ejpam-3285	118	42	module	module	NOUN
ejpam-3285	118	43	isomorphism	isomorphism	NOUN
ejpam-3285	118	44	t	t	NOUN
ejpam-3285	118	45	:	:	PUNCT
ejpam-3285	118	46	m	m	VERB
ejpam-3285	118	47	→	→	SYM
ejpam-3285	118	48	n	n	CCONJ
ejpam-3285	118	49	,	,	PUNCT
ejpam-3285	118	50	such	such	ADJ
ejpam-3285	118	51	that	that	DET
ejpam-3285	118	52	tµr	tµr	NOUN
ejpam-3285	118	53	=	=	NOUN
ejpam-3285	118	54	ϕrt	ϕrt	NOUN
ejpam-3285	118	55	for	for	ADP
ejpam-3285	118	56	any	any	DET
ejpam-3285	118	57	r	r	NOUN
ejpam-3285	118	58	∈	∈	PROPN
ejpam-3285	118	59	r.	r.	NOUN
ejpam-3285	118	60	furthermore	furthermore	ADV
ejpam-3285	118	61	µ	µ	X
ejpam-3285	118	62	equivalent	equivalent	ADJ
ejpam-3285	118	63	to	to	ADP
ejpam-3285	118	64	ϕ	ϕ	NOUN
ejpam-3285	118	65	denoted	denote	VERB
ejpam-3285	118	66	by	by	ADP
ejpam-3285	118	67	µ	µ	NUM
ejpam-3285	118	68	∼	∼	NOUN
ejpam-3285	118	69	ϕ.	ϕ.	NOUN
ejpam-3285	118	70	from	from	ADP
ejpam-3285	118	71	definition	definition	NOUN
ejpam-3285	118	72	3	3	NUM
ejpam-3285	118	73	,	,	PUNCT
ejpam-3285	118	74	we	we	PRON
ejpam-3285	118	75	know	know	VERB
ejpam-3285	118	76	that	that	SCONJ
ejpam-3285	118	77	two	two	NUM
ejpam-3285	118	78	representations	representation	NOUN
ejpam-3285	118	79	µ	µ	NOUN
ejpam-3285	118	80	and	and	CCONJ
ejpam-3285	118	81	ϕ	ϕ	NOUN
ejpam-3285	118	82	of	of	ADP
ejpam-3285	118	83	a	a	DET
ejpam-3285	118	84	ring	ring	NOUN
ejpam-3285	118	85	r	r	NOUN
ejpam-3285	118	86	are	be	AUX
ejpam-3285	118	87	equivalent	equivalent	ADJ
ejpam-3285	118	88	if	if	SCONJ
ejpam-3285	118	89	there	there	PRON
ejpam-3285	118	90	is	be	VERB
ejpam-3285	118	91	an	an	DET
ejpam-3285	118	92	s	s	NOUN
ejpam-3285	118	93	-	-	PUNCT
ejpam-3285	118	94	module	module	NOUN
ejpam-3285	118	95	isomorphism	isomorphism	NOUN
ejpam-3285	118	96	t	t	NOUN
ejpam-3285	118	97	:	:	PUNCT
ejpam-3285	118	98	m	m	VERB
ejpam-3285	118	99	→	→	SYM
ejpam-3285	118	100	n	n	CCONJ
ejpam-3285	118	101	,	,	PUNCT
ejpam-3285	118	102	such	such	ADJ
ejpam-3285	118	103	that	that	SCONJ
ejpam-3285	118	104	the	the	DET
ejpam-3285	118	105	diagram	diagram	NOUN
ejpam-3285	118	106	m	m	VERB
ejpam-3285	118	107	m	m	VERB
ejpam-3285	118	108	n	n	ADP
ejpam-3285	118	109	n	n	PRON
ejpam-3285	118	110	t	t	NOUN
ejpam-3285	118	111	µr	µr	ADP
ejpam-3285	118	112	ϕr	ϕr	NOUN
ejpam-3285	118	113	t	t	NOUN
ejpam-3285	118	114	commutes	commute	NOUN
ejpam-3285	118	115	.	.	PUNCT
ejpam-3285	119	1	the	the	DET
ejpam-3285	119	2	following	follow	VERB
ejpam-3285	119	3	proposition	proposition	NOUN
ejpam-3285	119	4	is	be	AUX
ejpam-3285	119	5	the	the	DET
ejpam-3285	119	6	sufficient	sufficient	ADJ
ejpam-3285	119	7	condition	condition	NOUN
ejpam-3285	119	8	two	two	NUM
ejpam-3285	119	9	representations	representation	NOUN
ejpam-3285	119	10	of	of	ADP
ejpam-3285	119	11	a	a	DET
ejpam-3285	119	12	ring	ring	NOUN
ejpam-3285	119	13	on	on	ADP
ejpam-3285	119	14	modules	module	NOUN
ejpam-3285	119	15	over	over	ADP
ejpam-3285	119	16	a	a	DET
ejpam-3285	119	17	commutative	commutative	ADJ
ejpam-3285	119	18	ring	ring	NOUN
ejpam-3285	119	19	are	be	AUX
ejpam-3285	119	20	equivalent	equivalent	ADJ
ejpam-3285	119	21	.	.	PUNCT
ejpam-3285	120	1	n.	n.	PROPN
ejpam-3285	120	2	hijriati	hijriati	PROPN
ejpam-3285	120	3	,	,	PUNCT
ejpam-3285	120	4	s.	s.	PROPN
ejpam-3285	120	5	wahyuni	wahyuni	PROPN
ejpam-3285	120	6	,	,	PUNCT
ejpam-3285	120	7	i.e.	i.e.	X
ejpam-3285	120	8	wijayanti	wijayanti	X
ejpam-3285	120	9	/	/	SYM
ejpam-3285	120	10	eur	eur	PROPN
ejpam-3285	120	11	.	.	PUNCT
ejpam-3285	121	1	j.	j.	PROPN
ejpam-3285	121	2	pure	pure	PROPN
ejpam-3285	121	3	appl	appl	PROPN
ejpam-3285	121	4	.	.	PROPN
ejpam-3285	121	5	math	math	PROPN
ejpam-3285	121	6	,	,	PUNCT
ejpam-3285	121	7	11	11	NUM
ejpam-3285	121	8	(	(	PUNCT
ejpam-3285	121	9	3	3	NUM
ejpam-3285	121	10	)	)	PUNCT
ejpam-3285	121	11	(	(	PUNCT
ejpam-3285	121	12	2018	2018	NUM
ejpam-3285	121	13	)	)	PUNCT
ejpam-3285	121	14	,	,	PUNCT
ejpam-3285	121	15	751	751	NUM
ejpam-3285	121	16	-	-	SYM
ejpam-3285	121	17	761	761	NUM
ejpam-3285	121	18	756	756	NUM
ejpam-3285	121	19	proposition	proposition	NOUN
ejpam-3285	121	20	2	2	NUM
ejpam-3285	121	21	.	.	PUNCT
ejpam-3285	122	1	let	let	VERB
ejpam-3285	122	2	µ	µ	PRON
ejpam-3285	122	3	:	:	PUNCT
ejpam-3285	122	4	r	r	NOUN
ejpam-3285	122	5	→	→	SYM
ejpam-3285	122	6	ends(m	ends(m	PROPN
ejpam-3285	122	7	)	)	PUNCT
ejpam-3285	122	8	be	be	VERB
ejpam-3285	122	9	an	an	DET
ejpam-3285	122	10	f	f	PROPN
ejpam-3285	122	11	-representation	-representation	NOUN
ejpam-3285	122	12	of	of	ADP
ejpam-3285	122	13	ring	ring	NOUN
ejpam-3285	122	14	r	r	NOUN
ejpam-3285	122	15	and	and	CCONJ
ejpam-3285	122	16	ϕ	ϕ	NOUN
ejpam-3285	122	17	:	:	PUNCT
ejpam-3285	122	18	r	r	NOUN
ejpam-3285	122	19	→	→	SYM
ejpam-3285	122	20	ends(n	ends(n	PROPN
ejpam-3285	122	21	)	)	PUNCT
ejpam-3285	122	22	a	a	DET
ejpam-3285	122	23	g	g	NOUN
ejpam-3285	122	24	-	-	PUNCT
ejpam-3285	122	25	representation	representation	NOUN
ejpam-3285	122	26	of	of	ADP
ejpam-3285	122	27	ring	ring	PROPN
ejpam-3285	122	28	r.	r.	PROPN
ejpam-3285	122	29	representation	representation	PROPN
ejpam-3285	122	30	µ	µ	PROPN
ejpam-3285	122	31	and	and	CCONJ
ejpam-3285	122	32	ϕ	ϕ	PROPN
ejpam-3285	122	33	are	be	AUX
ejpam-3285	122	34	equivalent	equivalent	ADJ
ejpam-3285	122	35	(	(	PUNCT
ejpam-3285	122	36	µ	µ	X
ejpam-3285	122	37	∼	∼	X
ejpam-3285	122	38	ϕ	ϕ	NOUN
ejpam-3285	122	39	)	)	PUNCT
ejpam-3285	122	40	if	if	SCONJ
ejpam-3285	122	41	and	and	CCONJ
ejpam-3285	122	42	only	only	ADV
ejpam-3285	122	43	if	if	SCONJ
ejpam-3285	122	44	there	there	PRON
ejpam-3285	122	45	is	be	VERB
ejpam-3285	122	46	an	an	DET
ejpam-3285	122	47	s	s	NOUN
ejpam-3285	122	48	-	-	PUNCT
ejpam-3285	122	49	module	module	NOUN
ejpam-3285	122	50	isomorphism	isomorphism	NOUN
ejpam-3285	122	51	t	t	NOUN
ejpam-3285	122	52	:	:	PUNCT
ejpam-3285	122	53	m	m	VERB
ejpam-3285	122	54	→	→	SYM
ejpam-3285	122	55	n	n	CCONJ
ejpam-3285	122	56	and	and	CCONJ
ejpam-3285	122	57	satisfy	satisfy	VERB
ejpam-3285	122	58	f(r)−g(r	f(r)−g(r	NOUN
ejpam-3285	122	59	)	)	PUNCT
ejpam-3285	122	60	∈	∈	PROPN
ejpam-3285	122	61	ann(n	ann(n	PROPN
ejpam-3285	122	62	)	)	PUNCT
ejpam-3285	122	63	for	for	ADP
ejpam-3285	122	64	any	any	DET
ejpam-3285	122	65	r	r	NOUN
ejpam-3285	122	66	∈	∈	PROPN
ejpam-3285	122	67	r.	r.	NOUN
ejpam-3285	122	68	proof	proof	NOUN
ejpam-3285	122	69	.	.	PUNCT
ejpam-3285	123	1	suppose	suppose	VERB
ejpam-3285	123	2	that	that	SCONJ
ejpam-3285	123	3	t	t	NOUN
ejpam-3285	123	4	:	:	PUNCT
ejpam-3285	123	5	m	m	VERB
ejpam-3285	123	6	→	→	SYM
ejpam-3285	123	7	n	n	X
ejpam-3285	123	8	is	be	AUX
ejpam-3285	123	9	an	an	DET
ejpam-3285	123	10	s	s	NOUN
ejpam-3285	123	11	-	-	PUNCT
ejpam-3285	123	12	module	module	NOUN
ejpam-3285	123	13	isomorphism	isomorphism	NOUN
ejpam-3285	123	14	and	and	CCONJ
ejpam-3285	123	15	f(r	f(r	NOUN
ejpam-3285	123	16	)	)	PUNCT
ejpam-3285	123	17	−	−	PROPN
ejpam-3285	123	18	g(r	g(r	SYM
ejpam-3285	123	19	)	)	PUNCT
ejpam-3285	123	20	∈	∈	PROPN
ejpam-3285	123	21	ann(n	ann(n	PROPN
ejpam-3285	123	22	)	)	PUNCT
ejpam-3285	123	23	.	.	PUNCT
ejpam-3285	124	1	then	then	ADV
ejpam-3285	124	2	im(t	im(t	ADV
ejpam-3285	124	3	)	)	PUNCT
ejpam-3285	125	1	=	=	SYM
ejpam-3285	125	2	n	n	CCONJ
ejpam-3285	125	3	,	,	PUNCT
ejpam-3285	125	4	and	and	CCONJ
ejpam-3285	125	5	for	for	ADP
ejpam-3285	125	6	any	any	DET
ejpam-3285	125	7	r	r	NOUN
ejpam-3285	125	8	∈	∈	NOUN
ejpam-3285	125	9	r	r	NOUN
ejpam-3285	125	10	,	,	PUNCT
ejpam-3285	125	11	n	n	NOUN
ejpam-3285	125	12	∈	∈	NOUN
ejpam-3285	125	13	n	n	CCONJ
ejpam-3285	125	14	(	(	PUNCT
ejpam-3285	125	15	f(r)−	f(r)−	NOUN
ejpam-3285	125	16	g(r))n	g(r))n	PROPN
ejpam-3285	125	17	=	=	PROPN
ejpam-3285	125	18	0n	0n	PROPN
ejpam-3285	125	19	⇔	⇔	PROPN
ejpam-3285	125	20	f(r)n−	f(r)n−	PROPN
ejpam-3285	125	21	g(r)n	g(r)n	PROPN
ejpam-3285	125	22	=	=	SYM
ejpam-3285	126	1	0n	0n	PROPN
ejpam-3285	126	2	⇔	⇔	PROPN
ejpam-3285	126	3	f(r)n	f(r)n	PROPN
ejpam-3285	126	4	=	=	PROPN
ejpam-3285	126	5	g(r)n	g(r)n	PROPN
ejpam-3285	126	6	(	(	PUNCT
ejpam-3285	126	7	9	9	NUM
ejpam-3285	126	8	)	)	PUNCT
ejpam-3285	127	1	so	so	ADV
ejpam-3285	127	2	for	for	ADP
ejpam-3285	127	3	any	any	DET
ejpam-3285	127	4	m	m	NOUN
ejpam-3285	127	5	∈m	∈m	NOUN
ejpam-3285	127	6	(	(	PUNCT
ejpam-3285	127	7	tµr)(m	tµr)(m	NOUN
ejpam-3285	127	8	)	)	PUNCT
ejpam-3285	127	9	=	=	SYM
ejpam-3285	127	10	tµr(m	tµr(m	X
ejpam-3285	127	11	)	)	PUNCT
ejpam-3285	127	12	=	=	SYM
ejpam-3285	127	13	t	t	PROPN
ejpam-3285	127	14	(	(	PUNCT
ejpam-3285	127	15	f(r)m	f(r)m	NOUN
ejpam-3285	127	16	)	)	PUNCT
ejpam-3285	127	17	=	=	SYM
ejpam-3285	127	18	f(r)t	f(r)t	X
ejpam-3285	127	19	(	(	PUNCT
ejpam-3285	127	20	m	m	NOUN
ejpam-3285	127	21	)	)	PUNCT
ejpam-3285	127	22	=	=	VERB
ejpam-3285	127	23	g(r)t	g(r)t	X
ejpam-3285	127	24	(	(	PUNCT
ejpam-3285	127	25	m	m	NOUN
ejpam-3285	127	26	)	)	PUNCT
ejpam-3285	127	27	=	=	SYM
ejpam-3285	127	28	ϕr(t	ϕr(t	NUM
ejpam-3285	127	29	(	(	PUNCT
ejpam-3285	127	30	m	m	NOUN
ejpam-3285	127	31	)	)	PUNCT
ejpam-3285	127	32	)	)	PUNCT
ejpam-3285	128	1	=	=	PRON
ejpam-3285	128	2	(	(	PUNCT
ejpam-3285	128	3	ϕrt	ϕrt	NOUN
ejpam-3285	128	4	)	)	PUNCT
ejpam-3285	128	5	(	(	PUNCT
ejpam-3285	128	6	m	m	NOUN
ejpam-3285	128	7	)	)	PUNCT
ejpam-3285	128	8	.	.	PUNCT
ejpam-3285	129	1	(	(	PUNCT
ejpam-3285	129	2	10	10	NUM
ejpam-3285	129	3	)	)	PUNCT
ejpam-3285	129	4	thus	thus	ADV
ejpam-3285	129	5	µ	µ	X
ejpam-3285	129	6	and	and	CCONJ
ejpam-3285	129	7	ϕ	ϕ	NOUN
ejpam-3285	129	8	are	be	AUX
ejpam-3285	129	9	equivalent	equivalent	ADJ
ejpam-3285	129	10	.	.	PUNCT
ejpam-3285	130	1	conversely	conversely	ADV
ejpam-3285	130	2	,	,	PUNCT
ejpam-3285	130	3	if	if	SCONJ
ejpam-3285	130	4	µ	µ	NOUN
ejpam-3285	130	5	is	be	AUX
ejpam-3285	130	6	equivalent	equivalent	ADJ
ejpam-3285	130	7	to	to	ADP
ejpam-3285	130	8	ϕ	ϕ	NOUN
ejpam-3285	130	9	,	,	PUNCT
ejpam-3285	130	10	then	then	ADV
ejpam-3285	130	11	there	there	PRON
ejpam-3285	130	12	is	be	VERB
ejpam-3285	130	13	an	an	DET
ejpam-3285	130	14	s	s	NOUN
ejpam-3285	130	15	-	-	PUNCT
ejpam-3285	130	16	module	module	NOUN
ejpam-3285	130	17	isomorphism	isomorphism	NOUN
ejpam-3285	130	18	t	t	NOUN
ejpam-3285	130	19	:	:	PUNCT
ejpam-3285	130	20	m	m	VERB
ejpam-3285	130	21	→	→	SYM
ejpam-3285	130	22	n	n	CCONJ
ejpam-3285	130	23	,	,	PUNCT
ejpam-3285	130	24	such	such	ADJ
ejpam-3285	130	25	that	that	DET
ejpam-3285	130	26	tµr	tµr	NOUN
ejpam-3285	130	27	=	=	NOUN
ejpam-3285	130	28	ϕrt	ϕrt	NOUN
ejpam-3285	130	29	for	for	ADP
ejpam-3285	130	30	any	any	DET
ejpam-3285	130	31	r	r	NOUN
ejpam-3285	130	32	∈	∈	PROPN
ejpam-3285	130	33	r.	r.	NOUN
ejpam-3285	130	34	then	then	ADV
ejpam-3285	130	35	we	we	PRON
ejpam-3285	130	36	have	have	VERB
ejpam-3285	130	37	for	for	ADP
ejpam-3285	130	38	any	any	DET
ejpam-3285	130	39	n	n	PRON
ejpam-3285	130	40	∈	∈	NOUN
ejpam-3285	130	41	n	n	CCONJ
ejpam-3285	130	42	there	there	PRON
ejpam-3285	130	43	is	be	VERB
ejpam-3285	130	44	m	m	PROPN
ejpam-3285	130	45	∈	∈	NOUN
ejpam-3285	130	46	m	m	NOUN
ejpam-3285	130	47	such	such	ADJ
ejpam-3285	130	48	that	that	SCONJ
ejpam-3285	130	49	t	t	PROPN
ejpam-3285	130	50	(	(	PUNCT
ejpam-3285	130	51	m	m	NOUN
ejpam-3285	130	52	)	)	PUNCT
ejpam-3285	131	1	=	=	VERB
ejpam-3285	131	2	n.	n.	NOUN
ejpam-3285	131	3	so	so	ADV
ejpam-3285	131	4	for	for	ADP
ejpam-3285	131	5	any	any	DET
ejpam-3285	131	6	r	r	NOUN
ejpam-3285	131	7	∈	∈	NOUN
ejpam-3285	131	8	r	r	NOUN
ejpam-3285	131	9	,	,	PUNCT
ejpam-3285	131	10	g(r)t	g(r)t	X
ejpam-3285	131	11	(	(	PUNCT
ejpam-3285	131	12	m	m	NOUN
ejpam-3285	131	13	)	)	PUNCT
ejpam-3285	131	14	=	=	SYM
ejpam-3285	131	15	ϕr(t	ϕr(t	NUM
ejpam-3285	131	16	(	(	PUNCT
ejpam-3285	131	17	m	m	NOUN
ejpam-3285	131	18	)	)	PUNCT
ejpam-3285	131	19	)	)	PUNCT
ejpam-3285	132	1	=	=	PRON
ejpam-3285	132	2	(	(	PUNCT
ejpam-3285	132	3	ϕrt	ϕrt	NOUN
ejpam-3285	132	4	)	)	PUNCT
ejpam-3285	132	5	(	(	PUNCT
ejpam-3285	132	6	m	m	NOUN
ejpam-3285	132	7	)	)	PUNCT
ejpam-3285	132	8	=	=	SYM
ejpam-3285	132	9	(	(	PUNCT
ejpam-3285	132	10	tµr)(m	tµr)(m	NOUN
ejpam-3285	132	11	)	)	PUNCT
ejpam-3285	132	12	=	=	SYM
ejpam-3285	132	13	t	t	PROPN
ejpam-3285	132	14	(	(	PUNCT
ejpam-3285	132	15	µr(m	µr(m	ADJ
ejpam-3285	132	16	)	)	PUNCT
ejpam-3285	132	17	)	)	PUNCT
ejpam-3285	133	1	=	=	SYM
ejpam-3285	133	2	t	t	PROPN
ejpam-3285	133	3	(	(	PUNCT
ejpam-3285	133	4	f(r)m	f(r)m	NOUN
ejpam-3285	133	5	)	)	PUNCT
ejpam-3285	133	6	=	=	SYM
ejpam-3285	133	7	f(r)t	f(r)t	X
ejpam-3285	133	8	(	(	PUNCT
ejpam-3285	133	9	m	m	NOUN
ejpam-3285	133	10	)	)	PUNCT
ejpam-3285	133	11	.	.	PUNCT
ejpam-3285	134	1	(	(	PUNCT
ejpam-3285	134	2	11	11	NUM
ejpam-3285	134	3	)	)	PUNCT
ejpam-3285	134	4	hence	hence	ADV
ejpam-3285	134	5	we	we	PRON
ejpam-3285	134	6	have	have	VERB
ejpam-3285	134	7	g(r)t	g(r)t	X
ejpam-3285	134	8	(	(	PUNCT
ejpam-3285	134	9	m	m	NOUN
ejpam-3285	134	10	)	)	PUNCT
ejpam-3285	134	11	=	=	SYM
ejpam-3285	134	12	f(r)t	f(r)t	PROPN
ejpam-3285	134	13	(	(	PUNCT
ejpam-3285	134	14	m)⇔	m)⇔	PROPN
ejpam-3285	134	15	(	(	PUNCT
ejpam-3285	134	16	f(r)−g(r))t	f(r)−g(r))t	PROPN
ejpam-3285	134	17	(	(	PUNCT
ejpam-3285	134	18	m	m	NOUN
ejpam-3285	134	19	)	)	PUNCT
ejpam-3285	134	20	=	=	SYM
ejpam-3285	135	1	0	0	X
ejpam-3285	135	2	.	.	PUNCT
ejpam-3285	136	1	since	since	SCONJ
ejpam-3285	136	2	t	t	PROPN
ejpam-3285	136	3	6=	6=	PROPN
ejpam-3285	136	4	0	0	NUM
ejpam-3285	136	5	,	,	PUNCT
ejpam-3285	136	6	f(r)−g(r	f(r)−g(r	NOUN
ejpam-3285	136	7	)	)	PUNCT
ejpam-3285	136	8	∈	∈	NOUN
ejpam-3285	137	1	ann(t	ann(t	X
ejpam-3285	137	2	(	(	PUNCT
ejpam-3285	137	3	m	m	NOUN
ejpam-3285	137	4	)	)	PUNCT
ejpam-3285	137	5	)	)	PUNCT
ejpam-3285	138	1	=	=	SYM
ejpam-3285	138	2	ann(n	ann(n	PROPN
ejpam-3285	138	3	)	)	PUNCT
ejpam-3285	138	4	for	for	ADP
ejpam-3285	138	5	any	any	DET
ejpam-3285	138	6	n	n	ADP
ejpam-3285	138	7	∈	∈	PROPN
ejpam-3285	138	8	n	n	NOUN
ejpam-3285	138	9	.	.	PUNCT
ejpam-3285	139	1	thus	thus	ADV
ejpam-3285	139	2	f(r)−	f(r)−	PROPN
ejpam-3285	139	3	g(r	g(r	PROPN
ejpam-3285	139	4	)	)	PUNCT
ejpam-3285	139	5	∈	∈	PROPN
ejpam-3285	139	6	ann(n	ann(n	PROPN
ejpam-3285	139	7	)	)	PUNCT
ejpam-3285	139	8	.	.	PUNCT
ejpam-3285	140	1	example	example	NOUN
ejpam-3285	141	1	8	8	NUM
ejpam-3285	141	2	.	.	PUNCT
ejpam-3285	142	1	let	let	VERB
ejpam-3285	142	2	µ	µ	X
ejpam-3285	142	3	be	be	AUX
ejpam-3285	142	4	an	an	DET
ejpam-3285	142	5	f	f	PROPN
ejpam-3285	142	6	-representation	-representation	NOUN
ejpam-3285	142	7	of	of	ADP
ejpam-3285	142	8	m	m	PROPN
ejpam-3285	142	9	′2(z	′2(z	NUM
ejpam-3285	142	10	)	)	PUNCT
ejpam-3285	142	11	defined	define	VERB
ejpam-3285	142	12	in	in	ADP
ejpam-3285	142	13	example	example	NOUN
ejpam-3285	142	14	3	3	X
ejpam-3285	142	15	.	.	PUNCT
ejpam-3285	143	1	let	let	VERB
ejpam-3285	143	2	m∗2	m∗2	NOUN
ejpam-3285	143	3	(	(	PUNCT
ejpam-3285	143	4	z	z	NOUN
ejpam-3285	143	5	)	)	PUNCT
ejpam-3285	143	6	be	be	AUX
ejpam-3285	143	7	an	an	DET
ejpam-3285	143	8	abelian	abelian	ADJ
ejpam-3285	143	9	group	group	NOUN
ejpam-3285	143	10	of	of	ADP
ejpam-3285	143	11	all	all	DET
ejpam-3285	143	12	2	2	NUM
ejpam-3285	143	13	×	×	NOUN
ejpam-3285	143	14	2	2	NUM
ejpam-3285	143	15	diagonal	diagonal	ADJ
ejpam-3285	143	16	matrices	matrix	NOUN
ejpam-3285	143	17	and	and	CCONJ
ejpam-3285	143	18	it	it	PRON
ejpam-3285	143	19	also	also	ADV
ejpam-3285	143	20	a	a	DET
ejpam-3285	143	21	z2	z2	NOUN
ejpam-3285	143	22	-	-	PUNCT
ejpam-3285	143	23	module	module	NOUN
ejpam-3285	143	24	,	,	PUNCT
ejpam-3285	143	25	where	where	SCONJ
ejpam-3285	143	26	scalar	scalar	ADJ
ejpam-3285	143	27	multiplication	multiplication	NOUN
ejpam-3285	143	28	defined	define	VERB
ejpam-3285	143	29	as	as	ADP
ejpam-3285	143	30	example	example	NOUN
ejpam-3285	143	31	4	4	NUM
ejpam-3285	143	32	.	.	PUNCT
ejpam-3285	144	1	we	we	PRON
ejpam-3285	144	2	define	define	VERB
ejpam-3285	144	3	ϕ	ϕ	NOUN
ejpam-3285	144	4	:	:	PUNCT
ejpam-3285	144	5	m	m	VERB
ejpam-3285	144	6	′2(z)→	′2(z)→	NOUN
ejpam-3285	144	7	endz2(m∗2	endz2(m∗2	X
ejpam-3285	144	8	(	(	PUNCT
ejpam-3285	144	9	z	z	NOUN
ejpam-3285	144	10	)	)	PUNCT
ejpam-3285	144	11	)	)	PUNCT
ejpam-3285	144	12	(	(	PUNCT
ejpam-3285	144	13	12	12	NUM
ejpam-3285	144	14	)	)	PUNCT
ejpam-3285	144	15	as	as	ADP
ejpam-3285	144	16	a	a	DET
ejpam-3285	144	17	g	g	NOUN
ejpam-3285	144	18	-	-	PUNCT
ejpam-3285	144	19	representation	representation	NOUN
ejpam-3285	144	20	of	of	ADP
ejpam-3285	144	21	m	m	NOUN
ejpam-3285	144	22	′2(z	′2(z	NOUN
ejpam-3285	144	23	)	)	PUNCT
ejpam-3285	144	24	where	where	SCONJ
ejpam-3285	144	25	g	g	PROPN
ejpam-3285	144	26	is	be	AUX
ejpam-3285	144	27	a	a	DET
ejpam-3285	144	28	ring	ring	NOUN
ejpam-3285	144	29	homomorphism	homomorphism	NOUN
ejpam-3285	144	30	in	in	ADP
ejpam-3285	144	31	example	example	NOUN
ejpam-3285	144	32	4	4	NUM
ejpam-3285	144	33	.	.	X
ejpam-3285	145	1	for	for	ADP
ejpam-3285	145	2	any	any	DET
ejpam-3285	145	3	a	a	DET
ejpam-3285	145	4	=	=	SYM
ejpam-3285	145	5	[	[	PUNCT
ejpam-3285	145	6	u	u	NOUN
ejpam-3285	145	7	0	0	PROPN
ejpam-3285	145	8	w	w	NOUN
ejpam-3285	145	9	v	v	X
ejpam-3285	145	10	]	]	PUNCT
ejpam-3285	145	11	∈	∈	PROPN
ejpam-3285	145	12	m	m	NOUN
ejpam-3285	145	13	′2(z	′2(z	NUM
ejpam-3285	145	14	)	)	PUNCT
ejpam-3285	145	15	,	,	PUNCT
ejpam-3285	145	16	we	we	PRON
ejpam-3285	145	17	have	have	VERB
ejpam-3285	145	18	f(a	f(a	NOUN
ejpam-3285	145	19	)	)	PUNCT
ejpam-3285	146	1	−	−	PROPN
ejpam-3285	146	2	g(a	g(a	PROPN
ejpam-3285	146	3	)	)	PUNCT
ejpam-3285	147	1	=	=	PUNCT
ejpam-3285	147	2	(	(	PUNCT
ejpam-3285	147	3	0	0	NUM
ejpam-3285	147	4	,	,	PUNCT
ejpam-3285	147	5	v	v	NOUN
ejpam-3285	147	6	)	)	PUNCT
ejpam-3285	147	7	∈	∈	PROPN
ejpam-3285	147	8	ann(m∗2	ann(m∗2	NOUN
ejpam-3285	147	9	(	(	PUNCT
ejpam-3285	147	10	z	z	NOUN
ejpam-3285	147	11	)	)	PUNCT
ejpam-3285	147	12	)	)	PUNCT
ejpam-3285	148	1	and	and	CCONJ
ejpam-3285	148	2	there	there	PRON
ejpam-3285	148	3	is	be	VERB
ejpam-3285	148	4	a	a	DET
ejpam-3285	148	5	z2	z2	NUM
ejpam-3285	148	6	-	-	PUNCT
ejpam-3285	148	7	module	module	NOUN
ejpam-3285	148	8	isomorphism	isomorphism	NOUN
ejpam-3285	148	9	t	t	NOUN
ejpam-3285	148	10	:	:	PUNCT
ejpam-3285	148	11	z2	z2	PROPN
ejpam-3285	148	12	→m∗2	→m∗2	X
ejpam-3285	148	13	(	(	PUNCT
ejpam-3285	148	14	z	z	NOUN
ejpam-3285	148	15	)	)	PUNCT
ejpam-3285	148	16	,	,	PUNCT
ejpam-3285	148	17	(	(	PUNCT
ejpam-3285	148	18	a	a	DET
ejpam-3285	148	19	,	,	PUNCT
ejpam-3285	148	20	b	b	NOUN
ejpam-3285	148	21	)	)	PUNCT
ejpam-3285	148	22	7→	7→	NOUN
ejpam-3285	148	23	[	[	PUNCT
ejpam-3285	148	24	a	a	DET
ejpam-3285	148	25	0	0	NUM
ejpam-3285	148	26	0	0	NUM
ejpam-3285	148	27	b	b	NOUN
ejpam-3285	148	28	]	]	PUNCT
ejpam-3285	148	29	.	.	PUNCT
ejpam-3285	149	1	(	(	PUNCT
ejpam-3285	149	2	13	13	NUM
ejpam-3285	149	3	)	)	PUNCT
ejpam-3285	149	4	so	so	SCONJ
ejpam-3285	149	5	we	we	PRON
ejpam-3285	149	6	conclude	conclude	VERB
ejpam-3285	149	7	µ	µ	PRON
ejpam-3285	149	8	∼	∼	NOUN
ejpam-3285	149	9	ϕ.	ϕ.	PROPN
ejpam-3285	149	10	n.	n.	PROPN
ejpam-3285	149	11	hijriati	hijriati	PROPN
ejpam-3285	149	12	,	,	PUNCT
ejpam-3285	149	13	s.	s.	PROPN
ejpam-3285	149	14	wahyuni	wahyuni	PROPN
ejpam-3285	149	15	,	,	PUNCT
ejpam-3285	149	16	i.e.	i.e.	X
ejpam-3285	149	17	wijayanti	wijayanti	X
ejpam-3285	149	18	/	/	SYM
ejpam-3285	149	19	eur	eur	PROPN
ejpam-3285	149	20	.	.	PUNCT
ejpam-3285	150	1	j.	j.	PROPN
ejpam-3285	150	2	pure	pure	PROPN
ejpam-3285	150	3	appl	appl	PROPN
ejpam-3285	150	4	.	.	PROPN
ejpam-3285	150	5	math	math	PROPN
ejpam-3285	150	6	,	,	PUNCT
ejpam-3285	150	7	11	11	NUM
ejpam-3285	150	8	(	(	PUNCT
ejpam-3285	150	9	3	3	NUM
ejpam-3285	150	10	)	)	PUNCT
ejpam-3285	150	11	(	(	PUNCT
ejpam-3285	150	12	2018	2018	NUM
ejpam-3285	150	13	)	)	PUNCT
ejpam-3285	150	14	,	,	PUNCT
ejpam-3285	150	15	751	751	NUM
ejpam-3285	150	16	-	-	SYM
ejpam-3285	150	17	761	761	NUM
ejpam-3285	150	18	757	757	NUM
ejpam-3285	150	19	from	from	ADP
ejpam-3285	150	20	definition	definition	NOUN
ejpam-3285	150	21	3	3	NUM
ejpam-3285	150	22	,	,	PUNCT
ejpam-3285	150	23	if	if	SCONJ
ejpam-3285	150	24	f	f	PROPN
ejpam-3285	150	25	=	=	SYM
ejpam-3285	150	26	g	g	PROPN
ejpam-3285	150	27	,	,	PUNCT
ejpam-3285	150	28	then	then	ADV
ejpam-3285	150	29	for	for	ADP
ejpam-3285	150	30	any	any	DET
ejpam-3285	150	31	m	m	NOUN
ejpam-3285	150	32	∈	∈	NOUN
ejpam-3285	150	33	m	m	NOUN
ejpam-3285	150	34	and	and	CCONJ
ejpam-3285	150	35	r	r	NOUN
ejpam-3285	150	36	∈	∈	NOUN
ejpam-3285	150	37	r	r	NOUN
ejpam-3285	150	38	we	we	PRON
ejpam-3285	150	39	always	always	ADV
ejpam-3285	150	40	have	have	VERB
ejpam-3285	150	41	tµr(m	tµr(m	NOUN
ejpam-3285	150	42	)	)	PUNCT
ejpam-3285	150	43	=	=	SYM
ejpam-3285	150	44	t	t	PROPN
ejpam-3285	150	45	(	(	PUNCT
ejpam-3285	150	46	f(r)m	f(r)m	NOUN
ejpam-3285	150	47	)	)	PUNCT
ejpam-3285	150	48	=	=	SYM
ejpam-3285	150	49	f(r)t	f(r)t	X
ejpam-3285	150	50	(	(	PUNCT
ejpam-3285	150	51	m	m	NOUN
ejpam-3285	150	52	)	)	PUNCT
ejpam-3285	150	53	=	=	SYM
ejpam-3285	150	54	ϕrt	ϕrt	PROPN
ejpam-3285	150	55	(	(	PUNCT
ejpam-3285	150	56	m	m	NOUN
ejpam-3285	150	57	)	)	PUNCT
ejpam-3285	150	58	.	.	PUNCT
ejpam-3285	151	1	furthermore	furthermore	ADV
ejpam-3285	151	2	,	,	PUNCT
ejpam-3285	151	3	if	if	SCONJ
ejpam-3285	151	4	n	n	PRON
ejpam-3285	151	5	is	be	AUX
ejpam-3285	151	6	a	a	DET
ejpam-3285	151	7	torsian	torsian	ADJ
ejpam-3285	151	8	s	s	NOUN
ejpam-3285	151	9	-	-	NOUN
ejpam-3285	151	10	module	module	NOUN
ejpam-3285	151	11	,	,	PUNCT
ejpam-3285	151	12	then	then	ADV
ejpam-3285	151	13	ann(n	ann(n	PROPN
ejpam-3285	151	14	)	)	PUNCT
ejpam-3285	152	1	=	=	SYM
ejpam-3285	152	2	0	0	X
ejpam-3285	152	3	.	.	PUNCT
ejpam-3285	153	1	based	base	VERB
ejpam-3285	153	2	on	on	ADP
ejpam-3285	153	3	this	this	DET
ejpam-3285	153	4	facts	fact	NOUN
ejpam-3285	153	5	we	we	PRON
ejpam-3285	153	6	have	have	VERB
ejpam-3285	153	7	this	this	DET
ejpam-3285	153	8	following	follow	VERB
ejpam-3285	153	9	:	:	PUNCT
ejpam-3285	153	10	corollary	corollary	ADJ
ejpam-3285	153	11	1	1	X
ejpam-3285	153	12	.	.	PUNCT
ejpam-3285	153	13	let	let	VERB
ejpam-3285	153	14	µ	µ	PRON
ejpam-3285	153	15	:	:	PUNCT
ejpam-3285	153	16	r	r	NOUN
ejpam-3285	153	17	→	→	SYM
ejpam-3285	153	18	ends(m	ends(m	PROPN
ejpam-3285	153	19	)	)	PUNCT
ejpam-3285	153	20	be	be	VERB
ejpam-3285	153	21	an	an	DET
ejpam-3285	153	22	f	f	PROPN
ejpam-3285	153	23	-representation	-representation	NOUN
ejpam-3285	153	24	of	of	ADP
ejpam-3285	153	25	r	r	NOUN
ejpam-3285	153	26	and	and	CCONJ
ejpam-3285	153	27	ϕ	ϕ	NOUN
ejpam-3285	153	28	:	:	PUNCT
ejpam-3285	153	29	r	r	NOUN
ejpam-3285	153	30	→	→	SYM
ejpam-3285	153	31	ends(n	ends(n	PROPN
ejpam-3285	153	32	)	)	PUNCT
ejpam-3285	153	33	a	a	DET
ejpam-3285	153	34	g	g	NOUN
ejpam-3285	153	35	-	-	PUNCT
ejpam-3285	153	36	representation	representation	NOUN
ejpam-3285	153	37	of	of	ADP
ejpam-3285	153	38	r.	r.	PROPN
ejpam-3285	153	39	(	(	PUNCT
ejpam-3285	153	40	i	i	NOUN
ejpam-3285	153	41	)	)	PUNCT
ejpam-3285	153	42	if	if	SCONJ
ejpam-3285	153	43	f	f	PROPN
ejpam-3285	153	44	=	=	SYM
ejpam-3285	153	45	g	g	PROPN
ejpam-3285	153	46	,	,	PUNCT
ejpam-3285	153	47	then	then	ADV
ejpam-3285	153	48	µ	µ	X
ejpam-3285	153	49	∼	∼	NOUN
ejpam-3285	153	50	ϕ	ϕ	NOUN
ejpam-3285	153	51	if	if	SCONJ
ejpam-3285	154	1	and	and	CCONJ
ejpam-3285	154	2	only	only	ADV
ejpam-3285	154	3	if	if	SCONJ
ejpam-3285	154	4	there	there	PRON
ejpam-3285	154	5	is	be	VERB
ejpam-3285	154	6	an	an	DET
ejpam-3285	154	7	s	s	NOUN
ejpam-3285	154	8	-	-	PUNCT
ejpam-3285	154	9	module	module	NOUN
ejpam-3285	154	10	isomorphism	isomorphism	NOUN
ejpam-3285	154	11	t	t	NOUN
ejpam-3285	154	12	:	:	PUNCT
ejpam-3285	154	13	m	m	VERB
ejpam-3285	154	14	→	→	SYM
ejpam-3285	154	15	n	n	X
ejpam-3285	154	16	.	.	PUNCT
ejpam-3285	155	1	(	(	PUNCT
ejpam-3285	155	2	ii	ii	NOUN
ejpam-3285	155	3	)	)	PUNCT
ejpam-3285	155	4	if	if	SCONJ
ejpam-3285	155	5	n	n	PRON
ejpam-3285	155	6	is	be	AUX
ejpam-3285	155	7	a	a	DET
ejpam-3285	155	8	free	free	ADJ
ejpam-3285	155	9	torsian	torsian	NOUN
ejpam-3285	155	10	s	s	NOUN
ejpam-3285	155	11	-	-	NOUN
ejpam-3285	155	12	module	module	NOUN
ejpam-3285	155	13	,	,	PUNCT
ejpam-3285	155	14	then	then	ADV
ejpam-3285	155	15	µ	µ	X
ejpam-3285	155	16	∼	∼	NOUN
ejpam-3285	155	17	ϕ	ϕ	NOUN
ejpam-3285	155	18	if	if	SCONJ
ejpam-3285	155	19	and	and	CCONJ
ejpam-3285	155	20	only	only	ADV
ejpam-3285	155	21	if	if	SCONJ
ejpam-3285	155	22	there	there	PRON
ejpam-3285	155	23	is	be	VERB
ejpam-3285	155	24	a	a	DET
ejpam-3285	155	25	ring	ring	NOUN
ejpam-3285	155	26	isomorphism	isomorphism	NOUN
ejpam-3285	155	27	from	from	ADP
ejpam-3285	155	28	m	m	PROPN
ejpam-3285	155	29	to	to	ADP
ejpam-3285	155	30	n	n	PROPN
ejpam-3285	155	31	and	and	CCONJ
ejpam-3285	156	1	f	f	PROPN
ejpam-3285	156	2	=	=	SYM
ejpam-3285	156	3	g.	g.	PROPN
ejpam-3285	156	4	proof	proof	NOUN
ejpam-3285	156	5	.	.	PUNCT
ejpam-3285	157	1	(	(	PUNCT
ejpam-3285	157	2	i	i	NOUN
ejpam-3285	157	3	)	)	PUNCT
ejpam-3285	157	4	if	if	SCONJ
ejpam-3285	157	5	f	f	PROPN
ejpam-3285	157	6	=	=	SYM
ejpam-3285	157	7	g	g	PROPN
ejpam-3285	157	8	,	,	PUNCT
ejpam-3285	157	9	then	then	ADV
ejpam-3285	157	10	f(r)−	f(r)−	PROPN
ejpam-3285	157	11	g(r	g(r	PROPN
ejpam-3285	157	12	)	)	PUNCT
ejpam-3285	157	13	=	=	SYM
ejpam-3285	157	14	0	0	NUM
ejpam-3285	157	15	for	for	ADP
ejpam-3285	157	16	any	any	DET
ejpam-3285	157	17	r	r	NOUN
ejpam-3285	157	18	∈	∈	PROPN
ejpam-3285	157	19	r.	r.	NOUN
ejpam-3285	157	20	hence	hence	ADV
ejpam-3285	157	21	by	by	ADP
ejpam-3285	157	22	proposition	proposition	NOUN
ejpam-3285	157	23	2	2	NUM
ejpam-3285	157	24	µ	µ	X
ejpam-3285	157	25	∼	∼	NOUN
ejpam-3285	157	26	ϕ	ϕ	NOUN
ejpam-3285	157	27	if	if	SCONJ
ejpam-3285	158	1	and	and	CCONJ
ejpam-3285	158	2	only	only	ADV
ejpam-3285	158	3	if	if	SCONJ
ejpam-3285	158	4	there	there	PRON
ejpam-3285	158	5	is	be	VERB
ejpam-3285	158	6	an	an	DET
ejpam-3285	158	7	s	s	NOUN
ejpam-3285	158	8	-	-	PUNCT
ejpam-3285	158	9	module	module	NOUN
ejpam-3285	158	10	isomorphism	isomorphism	NOUN
ejpam-3285	158	11	t	t	NOUN
ejpam-3285	158	12	:	:	PUNCT
ejpam-3285	158	13	m	m	VERB
ejpam-3285	158	14	→	→	SYM
ejpam-3285	158	15	n	n	X
ejpam-3285	158	16	.	.	PUNCT
ejpam-3285	159	1	(	(	PUNCT
ejpam-3285	159	2	ii	ii	NOUN
ejpam-3285	159	3	)	)	PUNCT
ejpam-3285	159	4	if	if	SCONJ
ejpam-3285	159	5	n	n	PRON
ejpam-3285	159	6	is	be	AUX
ejpam-3285	159	7	a	a	DET
ejpam-3285	159	8	free	free	ADJ
ejpam-3285	159	9	module	module	NOUN
ejpam-3285	159	10	,	,	PUNCT
ejpam-3285	159	11	then	then	ADV
ejpam-3285	159	12	ann(n	ann(n	PROPN
ejpam-3285	159	13	)	)	PUNCT
ejpam-3285	160	1	=	=	PRON
ejpam-3285	160	2	{	{	PUNCT
ejpam-3285	160	3	0	0	NUM
ejpam-3285	160	4	}	}	PUNCT
ejpam-3285	160	5	.	.	PUNCT
ejpam-3285	161	1	so	so	ADV
ejpam-3285	161	2	by	by	ADP
ejpam-3285	161	3	proposition	proposition	NOUN
ejpam-3285	161	4	2	2	NUM
ejpam-3285	161	5	,	,	PUNCT
ejpam-3285	161	6	µ	µ	X
ejpam-3285	161	7	∼	∼	NOUN
ejpam-3285	161	8	ϕ	ϕ	NOUN
ejpam-3285	161	9	if	if	SCONJ
ejpam-3285	162	1	and	and	CCONJ
ejpam-3285	162	2	only	only	ADV
ejpam-3285	162	3	if	if	SCONJ
ejpam-3285	162	4	there	there	PRON
ejpam-3285	162	5	is	be	VERB
ejpam-3285	162	6	a	a	DET
ejpam-3285	162	7	ring	ring	NOUN
ejpam-3285	162	8	isomorphism	isomorphism	NOUN
ejpam-3285	162	9	from	from	ADP
ejpam-3285	162	10	m	m	PROPN
ejpam-3285	162	11	to	to	ADP
ejpam-3285	162	12	n	n	PROPN
ejpam-3285	162	13	and	and	CCONJ
ejpam-3285	162	14	f(r	f(r	NOUN
ejpam-3285	162	15	)	)	PUNCT
ejpam-3285	162	16	−	−	PROPN
ejpam-3285	162	17	g(r	g(r	SYM
ejpam-3285	162	18	)	)	PUNCT
ejpam-3285	162	19	∈	∈	PROPN
ejpam-3285	162	20	ann(n	ann(n	PROPN
ejpam-3285	162	21	)	)	PUNCT
ejpam-3285	163	1	=	=	PRON
ejpam-3285	163	2	{	{	PUNCT
ejpam-3285	163	3	0	0	NUM
ejpam-3285	163	4	}	}	PUNCT
ejpam-3285	163	5	⇔	⇔	X
ejpam-3285	163	6	f(r	f(r	X
ejpam-3285	163	7	)	)	PUNCT
ejpam-3285	164	1	=	=	SYM
ejpam-3285	164	2	g(r	g(r	NOUN
ejpam-3285	164	3	)	)	PUNCT
ejpam-3285	164	4	for	for	ADP
ejpam-3285	164	5	any	any	DET
ejpam-3285	164	6	r	r	NOUN
ejpam-3285	164	7	∈	∈	NOUN
ejpam-3285	164	8	r	r	NOUN
ejpam-3285	164	9	i.e	i.e	PROPN
ejpam-3285	164	10	f	f	PROPN
ejpam-3285	164	11	=	=	PROPN
ejpam-3285	164	12	g.	g.	PROPN
ejpam-3285	164	13	in	in	ADP
ejpam-3285	164	14	the	the	DET
ejpam-3285	164	15	paragraph	paragraph	NOUN
ejpam-3285	164	16	before	before	ADV
ejpam-3285	164	17	,	,	PUNCT
ejpam-3285	164	18	we	we	PRON
ejpam-3285	164	19	have	have	AUX
ejpam-3285	164	20	explained	explain	VERB
ejpam-3285	164	21	that	that	SCONJ
ejpam-3285	164	22	not	not	PART
ejpam-3285	164	23	every	every	DET
ejpam-3285	164	24	s	s	NOUN
ejpam-3285	164	25	-	-	PUNCT
ejpam-3285	164	26	module	module	NOUN
ejpam-3285	164	27	homomorphism	homomorphism	NOUN
ejpam-3285	164	28	t	t	NOUN
ejpam-3285	164	29	:	:	PUNCT
ejpam-3285	164	30	m	m	VERB
ejpam-3285	164	31	→	→	SYM
ejpam-3285	164	32	n	n	CCONJ
ejpam-3285	164	33	satisfy	satisfy	VERB
ejpam-3285	164	34	tµr	tµr	PROPN
ejpam-3285	164	35	=	=	SYM
ejpam-3285	164	36	ϕrt	ϕrt	PROPN
ejpam-3285	164	37	where	where	SCONJ
ejpam-3285	164	38	µ	µ	NOUN
ejpam-3285	164	39	is	be	AUX
ejpam-3285	164	40	an	an	DET
ejpam-3285	164	41	f	f	PROPN
ejpam-3285	164	42	-representation	-representation	NOUN
ejpam-3285	164	43	of	of	ADP
ejpam-3285	164	44	r	r	NOUN
ejpam-3285	164	45	on	on	ADP
ejpam-3285	164	46	s	s	NOUN
ejpam-3285	164	47	-	-	PUNCT
ejpam-3285	164	48	module	module	NOUN
ejpam-3285	164	49	m	m	NOUN
ejpam-3285	164	50	and	and	CCONJ
ejpam-3285	164	51	ϕ	ϕ	PROPN
ejpam-3285	164	52	is	be	AUX
ejpam-3285	164	53	a	a	DET
ejpam-3285	164	54	g	g	NOUN
ejpam-3285	164	55	-	-	PUNCT
ejpam-3285	164	56	representation	representation	NOUN
ejpam-3285	164	57	of	of	ADP
ejpam-3285	164	58	r	r	NOUN
ejpam-3285	164	59	on	on	ADP
ejpam-3285	164	60	s	s	NOUN
ejpam-3285	164	61	-	-	PUNCT
ejpam-3285	164	62	module	module	NOUN
ejpam-3285	164	63	n	n	NOUN
ejpam-3285	164	64	.	.	PUNCT
ejpam-3285	165	1	if	if	SCONJ
ejpam-3285	165	2	t	t	PROPN
ejpam-3285	165	3	satisfy	satisfy	VERB
ejpam-3285	165	4	tµr	tµr	PROPN
ejpam-3285	165	5	=	=	NOUN
ejpam-3285	165	6	ϕrt	ϕrt	PROPN
ejpam-3285	165	7	for	for	ADP
ejpam-3285	165	8	all	all	DET
ejpam-3285	165	9	r	r	NOUN
ejpam-3285	165	10	∈	∈	NOUN
ejpam-3285	165	11	r	r	NOUN
ejpam-3285	165	12	,	,	PUNCT
ejpam-3285	165	13	then	then	ADV
ejpam-3285	165	14	t	t	PROPN
ejpam-3285	165	15	is	be	AUX
ejpam-3285	165	16	called	call	VERB
ejpam-3285	165	17	a	a	DET
ejpam-3285	165	18	morphism	morphism	NOUN
ejpam-3285	165	19	from	from	ADP
ejpam-3285	165	20	µ	µ	NUM
ejpam-3285	165	21	to	to	ADP
ejpam-3285	165	22	ϕ.	ϕ.	ADJ
ejpam-3285	165	23	definition	definition	NOUN
ejpam-3285	165	24	4	4	X
ejpam-3285	165	25	.	.	PUNCT
ejpam-3285	166	1	let	let	VERB
ejpam-3285	166	2	µ	µ	NOUN
ejpam-3285	166	3	:	:	PUNCT
ejpam-3285	166	4	r→	r→	PROPN
ejpam-3285	166	5	ends(m	ends(m	PROPN
ejpam-3285	166	6	)	)	PUNCT
ejpam-3285	166	7	be	be	AUX
ejpam-3285	166	8	an	an	DET
ejpam-3285	166	9	f	f	PROPN
ejpam-3285	166	10	-representation	-representation	NOUN
ejpam-3285	166	11	of	of	ADP
ejpam-3285	166	12	r	r	NOUN
ejpam-3285	166	13	and	and	CCONJ
ejpam-3285	166	14	ϕ	ϕ	NOUN
ejpam-3285	166	15	:	:	PUNCT
ejpam-3285	166	16	r→	r→	PROPN
ejpam-3285	166	17	ends(n	ends(n	PROPN
ejpam-3285	166	18	)	)	PUNCT
ejpam-3285	166	19	a	a	DET
ejpam-3285	166	20	g	g	NOUN
ejpam-3285	166	21	-	-	PUNCT
ejpam-3285	166	22	representation	representation	NOUN
ejpam-3285	166	23	of	of	ADP
ejpam-3285	166	24	ring	ring	PROPN
ejpam-3285	166	25	r.	r.	PROPN
ejpam-3285	166	26	a	a	DET
ejpam-3285	166	27	morphism	morphism	NOUN
ejpam-3285	166	28	from	from	ADP
ejpam-3285	166	29	µ	µ	PRON
ejpam-3285	166	30	to	to	ADP
ejpam-3285	166	31	ϕ	ϕ	NOUN
ejpam-3285	166	32	is	be	AUX
ejpam-3285	166	33	an	an	DET
ejpam-3285	166	34	s	s	NOUN
ejpam-3285	166	35	-	-	PUNCT
ejpam-3285	166	36	module	module	NOUN
ejpam-3285	166	37	homomorphism	homomorphism	NOUN
ejpam-3285	166	38	t	t	NOUN
ejpam-3285	166	39	:	:	PUNCT
ejpam-3285	166	40	m	m	VERB
ejpam-3285	166	41	→	→	SYM
ejpam-3285	166	42	n	n	CCONJ
ejpam-3285	166	43	,	,	PUNCT
ejpam-3285	166	44	such	such	ADJ
ejpam-3285	166	45	that	that	DET
ejpam-3285	166	46	tµr	tµr	NOUN
ejpam-3285	166	47	=	=	NOUN
ejpam-3285	166	48	ϕrt	ϕrt	NOUN
ejpam-3285	166	49	for	for	ADP
ejpam-3285	166	50	all	all	DET
ejpam-3285	166	51	r	r	NOUN
ejpam-3285	166	52	∈	∈	PROPN
ejpam-3285	166	53	r.	r.	NOUN
ejpam-3285	166	54	proposition	proposition	NOUN
ejpam-3285	166	55	3	3	X
ejpam-3285	166	56	.	.	PUNCT
ejpam-3285	167	1	let	let	VERB
ejpam-3285	167	2	µ	µ	NOUN
ejpam-3285	167	3	:	:	PUNCT
ejpam-3285	167	4	r→	r→	PROPN
ejpam-3285	167	5	ends(m	ends(m	PROPN
ejpam-3285	167	6	)	)	PUNCT
ejpam-3285	167	7	be	be	AUX
ejpam-3285	167	8	an	an	DET
ejpam-3285	167	9	f	f	PROPN
ejpam-3285	167	10	-representation	-representation	NOUN
ejpam-3285	167	11	of	of	ADP
ejpam-3285	167	12	r	r	NOUN
ejpam-3285	167	13	and	and	CCONJ
ejpam-3285	167	14	ϕ	ϕ	NOUN
ejpam-3285	167	15	:	:	PUNCT
ejpam-3285	167	16	r→	r→	PROPN
ejpam-3285	167	17	ends(n	ends(n	PROPN
ejpam-3285	167	18	)	)	PUNCT
ejpam-3285	167	19	a	a	DET
ejpam-3285	167	20	g	g	NOUN
ejpam-3285	167	21	-	-	PUNCT
ejpam-3285	167	22	representation	representation	NOUN
ejpam-3285	167	23	of	of	ADP
ejpam-3285	167	24	ring	ring	PROPN
ejpam-3285	167	25	r.	r.	PROPN
ejpam-3285	167	26	an	an	DET
ejpam-3285	167	27	s	s	NOUN
ejpam-3285	167	28	-	-	PUNCT
ejpam-3285	167	29	module	module	NOUN
ejpam-3285	167	30	homomorphism	homomorphism	NOUN
ejpam-3285	167	31	t	t	NOUN
ejpam-3285	167	32	:	:	PUNCT
ejpam-3285	167	33	m	m	VERB
ejpam-3285	167	34	→	→	SYM
ejpam-3285	167	35	n	n	X
ejpam-3285	167	36	is	be	AUX
ejpam-3285	167	37	a	a	DET
ejpam-3285	167	38	morphism	morphism	NOUN
ejpam-3285	167	39	from	from	ADP
ejpam-3285	167	40	µ	µ	PRON
ejpam-3285	167	41	to	to	ADP
ejpam-3285	167	42	ϕ	ϕ	NOUN
ejpam-3285	167	43	if	if	SCONJ
ejpam-3285	167	44	f(r)−	f(r)−	PROPN
ejpam-3285	167	45	g(r	g(r	PROPN
ejpam-3285	167	46	)	)	PUNCT
ejpam-3285	167	47	∈	∈	PROPN
ejpam-3285	167	48	ann(im(t	ann(im(t	NOUN
ejpam-3285	167	49	)	)	PUNCT
ejpam-3285	167	50	)	)	PUNCT
ejpam-3285	167	51	.	.	PUNCT
ejpam-3285	168	1	proof	proof	NOUN
ejpam-3285	168	2	.	.	PUNCT
ejpam-3285	169	1	suppose	suppose	VERB
ejpam-3285	169	2	f(r	f(r	NOUN
ejpam-3285	169	3	)	)	PUNCT
ejpam-3285	169	4	−	−	PROPN
ejpam-3285	169	5	g(r	g(r	SYM
ejpam-3285	169	6	)	)	PUNCT
ejpam-3285	169	7	∈	∈	PROPN
ejpam-3285	169	8	ann(im(t	ann(im(t	NOUN
ejpam-3285	169	9	)	)	PUNCT
ejpam-3285	169	10	)	)	PUNCT
ejpam-3285	169	11	.	.	PUNCT
ejpam-3285	170	1	then	then	ADV
ejpam-3285	170	2	for	for	ADP
ejpam-3285	170	3	any	any	DET
ejpam-3285	170	4	n	n	PRON
ejpam-3285	170	5	∈	∈	NOUN
ejpam-3285	170	6	im(t	im(t	NOUN
ejpam-3285	170	7	)	)	PUNCT
ejpam-3285	170	8	there	there	PRON
ejpam-3285	170	9	is	be	VERB
ejpam-3285	170	10	m	m	PROPN
ejpam-3285	170	11	∈	∈	NOUN
ejpam-3285	170	12	m	m	NOUN
ejpam-3285	170	13	such	such	ADJ
ejpam-3285	170	14	that	that	SCONJ
ejpam-3285	170	15	t	t	PROPN
ejpam-3285	170	16	(	(	PUNCT
ejpam-3285	170	17	m	m	NOUN
ejpam-3285	170	18	)	)	PUNCT
ejpam-3285	170	19	=	=	SYM
ejpam-3285	170	20	n	n	CCONJ
ejpam-3285	170	21	,	,	PUNCT
ejpam-3285	170	22	and	and	CCONJ
ejpam-3285	170	23	(	(	PUNCT
ejpam-3285	170	24	f(r)−	f(r)−	NOUN
ejpam-3285	170	25	g(r))n	g(r))n	PROPN
ejpam-3285	170	26	=	=	PUNCT
ejpam-3285	170	27	0⇔	0⇔	NOUN
ejpam-3285	170	28	f(r)n	f(r)n	PROPN
ejpam-3285	171	1	=	=	PUNCT
ejpam-3285	172	1	g(r)n	g(r)n	PROPN
ejpam-3285	172	2	.	.	PUNCT
ejpam-3285	173	1	so	so	ADV
ejpam-3285	173	2	for	for	ADP
ejpam-3285	173	3	any	any	DET
ejpam-3285	173	4	m	m	NOUN
ejpam-3285	173	5	∈m	∈m	NOUN
ejpam-3285	173	6	(	(	PUNCT
ejpam-3285	173	7	tµr)(m	tµr)(m	NOUN
ejpam-3285	173	8	)	)	PUNCT
ejpam-3285	173	9	=	=	SYM
ejpam-3285	173	10	t	t	PROPN
ejpam-3285	173	11	(	(	PUNCT
ejpam-3285	173	12	µr(m	µr(m	ADJ
ejpam-3285	173	13	)	)	PUNCT
ejpam-3285	173	14	)	)	PUNCT
ejpam-3285	174	1	=	=	SYM
ejpam-3285	174	2	t	t	PROPN
ejpam-3285	174	3	(	(	PUNCT
ejpam-3285	174	4	f(r)m	f(r)m	NOUN
ejpam-3285	174	5	)	)	PUNCT
ejpam-3285	174	6	=	=	SYM
ejpam-3285	174	7	f(r)t	f(r)t	X
ejpam-3285	174	8	(	(	PUNCT
ejpam-3285	174	9	m	m	NOUN
ejpam-3285	174	10	)	)	PUNCT
ejpam-3285	174	11	=	=	VERB
ejpam-3285	174	12	g(r)t	g(r)t	X
ejpam-3285	174	13	(	(	PUNCT
ejpam-3285	174	14	m	m	NOUN
ejpam-3285	174	15	)	)	PUNCT
ejpam-3285	174	16	=	=	SYM
ejpam-3285	174	17	ϕr(t	ϕr(t	NUM
ejpam-3285	174	18	(	(	PUNCT
ejpam-3285	174	19	m	m	NOUN
ejpam-3285	174	20	)	)	PUNCT
ejpam-3285	174	21	)	)	PUNCT
ejpam-3285	175	1	=	=	PRON
ejpam-3285	175	2	(	(	PUNCT
ejpam-3285	175	3	ϕrt	ϕrt	NOUN
ejpam-3285	175	4	)	)	PUNCT
ejpam-3285	175	5	(	(	PUNCT
ejpam-3285	175	6	m	m	NOUN
ejpam-3285	175	7	)	)	PUNCT
ejpam-3285	175	8	.	.	PUNCT
ejpam-3285	176	1	(	(	PUNCT
ejpam-3285	176	2	14	14	NUM
ejpam-3285	176	3	)	)	PUNCT
ejpam-3285	176	4	hence	hence	ADV
ejpam-3285	176	5	t	t	PROPN
ejpam-3285	176	6	is	be	AUX
ejpam-3285	176	7	a	a	DET
ejpam-3285	176	8	morphism	morphism	NOUN
ejpam-3285	176	9	from	from	ADP
ejpam-3285	176	10	µ	µ	NUM
ejpam-3285	176	11	to	to	ADP
ejpam-3285	176	12	ϕ.	ϕ.	PROPN
ejpam-3285	176	13	example	example	NOUN
ejpam-3285	177	1	9	9	X
ejpam-3285	177	2	.	.	PUNCT
ejpam-3285	178	1	let	let	VERB
ejpam-3285	178	2	µ	µ	X
ejpam-3285	178	3	be	be	AUX
ejpam-3285	178	4	an	an	DET
ejpam-3285	178	5	f	f	PROPN
ejpam-3285	178	6	-representation	-representation	NOUN
ejpam-3285	178	7	of	of	ADP
ejpam-3285	178	8	m	m	PROPN
ejpam-3285	178	9	′2(z	′2(z	NUM
ejpam-3285	178	10	)	)	PUNCT
ejpam-3285	178	11	defined	define	VERB
ejpam-3285	178	12	in	in	ADP
ejpam-3285	178	13	example	example	NOUN
ejpam-3285	178	14	3	3	NUM
ejpam-3285	178	15	and	and	CCONJ
ejpam-3285	178	16	ϕ	ϕ	X
ejpam-3285	178	17	a	a	DET
ejpam-3285	178	18	grepresentation	grepresentation	NOUN
ejpam-3285	178	19	of	of	ADP
ejpam-3285	178	20	m	m	NOUN
ejpam-3285	178	21	′2(z	′2(z	NUM
ejpam-3285	178	22	)	)	PUNCT
ejpam-3285	178	23	defined	define	VERB
ejpam-3285	178	24	in	in	ADP
ejpam-3285	178	25	example	example	NOUN
ejpam-3285	178	26	4	4	NUM
ejpam-3285	178	27	.	.	X
ejpam-3285	179	1	for	for	ADP
ejpam-3285	179	2	any	any	DET
ejpam-3285	179	3	[	[	PUNCT
ejpam-3285	179	4	a	a	PRON
ejpam-3285	179	5	0	0	NUM
ejpam-3285	179	6	c	c	NOUN
ejpam-3285	179	7	b	b	X
ejpam-3285	179	8	]	]	PUNCT
ejpam-3285	179	9	∈m	∈m	NOUN
ejpam-3285	179	10	′2(z	′2(z	NUM
ejpam-3285	179	11	)	)	PUNCT
ejpam-3285	179	12	we	we	PRON
ejpam-3285	179	13	have	have	VERB
ejpam-3285	179	14	f	f	X
ejpam-3285	179	15	(	(	PUNCT
ejpam-3285	179	16	[	[	PUNCT
ejpam-3285	179	17	a	a	PRON
ejpam-3285	179	18	0	0	NUM
ejpam-3285	179	19	c	c	NOUN
ejpam-3285	179	20	b	b	NOUN
ejpam-3285	179	21	]	]	PUNCT
ejpam-3285	179	22	)	)	PUNCT
ejpam-3285	179	23	−	−	PROPN
ejpam-3285	180	1	g	g	NOUN
ejpam-3285	180	2	(	(	PUNCT
ejpam-3285	180	3	[	[	PUNCT
ejpam-3285	180	4	a	a	PRON
ejpam-3285	180	5	0	0	NUM
ejpam-3285	180	6	c	c	NOUN
ejpam-3285	180	7	b	b	NOUN
ejpam-3285	180	8	]	]	PUNCT
ejpam-3285	180	9	)	)	PUNCT
ejpam-3285	180	10	=	=	SYM
ejpam-3285	180	11	(	(	PUNCT
ejpam-3285	180	12	0	0	NUM
ejpam-3285	180	13	,	,	PUNCT
ejpam-3285	180	14	b	b	NOUN
ejpam-3285	180	15	)	)	PUNCT
ejpam-3285	180	16	(	(	PUNCT
ejpam-3285	180	17	15	15	X
ejpam-3285	180	18	)	)	PUNCT
ejpam-3285	180	19	n.	n.	NOUN
ejpam-3285	180	20	hijriati	hijriati	PROPN
ejpam-3285	180	21	,	,	PUNCT
ejpam-3285	180	22	s.	s.	PROPN
ejpam-3285	180	23	wahyuni	wahyuni	PROPN
ejpam-3285	180	24	,	,	PUNCT
ejpam-3285	180	25	i.e.	i.e.	X
ejpam-3285	180	26	wijayanti	wijayanti	X
ejpam-3285	180	27	/	/	SYM
ejpam-3285	180	28	eur	eur	PROPN
ejpam-3285	180	29	.	.	PUNCT
ejpam-3285	181	1	j.	j.	PROPN
ejpam-3285	181	2	pure	pure	PROPN
ejpam-3285	181	3	appl	appl	PROPN
ejpam-3285	181	4	.	.	PROPN
ejpam-3285	181	5	math	math	PROPN
ejpam-3285	181	6	,	,	PUNCT
ejpam-3285	181	7	11	11	NUM
ejpam-3285	181	8	(	(	PUNCT
ejpam-3285	181	9	3	3	NUM
ejpam-3285	181	10	)	)	PUNCT
ejpam-3285	181	11	(	(	PUNCT
ejpam-3285	181	12	2018	2018	NUM
ejpam-3285	181	13	)	)	PUNCT
ejpam-3285	181	14	,	,	PUNCT
ejpam-3285	181	15	751	751	NUM
ejpam-3285	181	16	-	-	SYM
ejpam-3285	181	17	761	761	NUM
ejpam-3285	181	18	758	758	NUM
ejpam-3285	181	19	(	(	PUNCT
ejpam-3285	181	20	i	i	NOUN
ejpam-3285	181	21	)	)	PUNCT
ejpam-3285	181	22	let	let	VERB
ejpam-3285	181	23	t	t	NOUN
ejpam-3285	181	24	:	:	PUNCT
ejpam-3285	181	25	r2	r2	PROPN
ejpam-3285	181	26	→	→	SYM
ejpam-3285	181	27	m2(r	m2(r	PROPN
ejpam-3285	181	28	)	)	PUNCT
ejpam-3285	181	29	defined	define	VERB
ejpam-3285	181	30	by	by	ADP
ejpam-3285	181	31	t	t	PROPN
ejpam-3285	181	32	(	(	PUNCT
ejpam-3285	181	33	a	a	DET
ejpam-3285	181	34	,	,	PUNCT
ejpam-3285	181	35	b	b	NOUN
ejpam-3285	181	36	)	)	PUNCT
ejpam-3285	181	37	=	=	NOUN
ejpam-3285	182	1	[	[	PUNCT
ejpam-3285	182	2	a	a	PRON
ejpam-3285	182	3	0	0	NUM
ejpam-3285	182	4	0	0	NUM
ejpam-3285	182	5	a	a	PRON
ejpam-3285	182	6	]	]	PUNCT
ejpam-3285	182	7	be	be	AUX
ejpam-3285	182	8	an	an	DET
ejpam-3285	182	9	s	s	NOUN
ejpam-3285	182	10	-	-	PUNCT
ejpam-3285	182	11	module	module	NOUN
ejpam-3285	182	12	homomorphism	homomorphism	NOUN
ejpam-3285	182	13	.	.	PUNCT
ejpam-3285	183	1	since	since	SCONJ
ejpam-3285	183	2	an	an	DET
ejpam-3285	183	3	annihilator	annihilator	NOUN
ejpam-3285	183	4	of	of	ADP
ejpam-3285	183	5	s	s	NOUN
ejpam-3285	183	6	-	-	PUNCT
ejpam-3285	183	7	module	module	NOUN
ejpam-3285	183	8	homomorphism	homomorphism	NOUN
ejpam-3285	183	9	is	be	AUX
ejpam-3285	183	10	a	a	DET
ejpam-3285	183	11	set	set	NOUN
ejpam-3285	183	12	{	{	PUNCT
ejpam-3285	183	13	(	(	PUNCT
ejpam-3285	183	14	0	0	NUM
ejpam-3285	183	15	,	,	PUNCT
ejpam-3285	183	16	x	x	X
ejpam-3285	183	17	)	)	PUNCT
ejpam-3285	183	18	∈	∈	PROPN
ejpam-3285	183	19	z2	z2	NOUN
ejpam-3285	184	1	|	|	ADV
ejpam-3285	184	2	x	x	SYM
ejpam-3285	184	3	∈	∈	PROPN
ejpam-3285	184	4	z	z	PROPN
ejpam-3285	184	5	}	}	PUNCT
ejpam-3285	184	6	,	,	PUNCT
ejpam-3285	184	7	then	then	ADV
ejpam-3285	184	8	t	t	PROPN
ejpam-3285	184	9	is	be	AUX
ejpam-3285	184	10	a	a	DET
ejpam-3285	184	11	morphism	morphism	NOUN
ejpam-3285	184	12	from	from	ADP
ejpam-3285	184	13	µ	µ	NUM
ejpam-3285	184	14	to	to	ADP
ejpam-3285	184	15	ϕ.	ϕ.	PROPN
ejpam-3285	184	16	(	(	PUNCT
ejpam-3285	184	17	ii	ii	PROPN
ejpam-3285	184	18	)	)	PUNCT
ejpam-3285	184	19	let	let	VERB
ejpam-3285	184	20	t	t	NOUN
ejpam-3285	184	21	′	′	NUM
ejpam-3285	184	22	:	:	PUNCT
ejpam-3285	184	23	r2	r2	PROPN
ejpam-3285	184	24	→	→	SYM
ejpam-3285	184	25	m2(r	m2(r	PROPN
ejpam-3285	184	26	)	)	PUNCT
ejpam-3285	184	27	defined	define	VERB
ejpam-3285	184	28	by	by	ADP
ejpam-3285	184	29	t	t	PROPN
ejpam-3285	184	30	′(a	′(a	ADV
ejpam-3285	184	31	,	,	PUNCT
ejpam-3285	184	32	b	b	X
ejpam-3285	184	33	)	)	PUNCT
ejpam-3285	184	34	=	=	NOUN
ejpam-3285	185	1	[	[	PUNCT
ejpam-3285	185	2	a	a	PRON
ejpam-3285	185	3	b	b	PROPN
ejpam-3285	185	4	b	b	PROPN
ejpam-3285	185	5	a	a	PRON
ejpam-3285	185	6	]	]	PUNCT
ejpam-3285	185	7	is	be	AUX
ejpam-3285	185	8	an	an	DET
ejpam-3285	185	9	s	s	NOUN
ejpam-3285	185	10	-	-	PUNCT
ejpam-3285	185	11	module	module	NOUN
ejpam-3285	185	12	homomorphism	homomorphism	NOUN
ejpam-3285	185	13	.	.	PUNCT
ejpam-3285	186	1	because	because	SCONJ
ejpam-3285	186	2	an	an	DET
ejpam-3285	186	3	annihilator	annihilator	NOUN
ejpam-3285	186	4	of	of	ADP
ejpam-3285	186	5	t	t	PROPN
ejpam-3285	186	6	′	′	NUM
ejpam-3285	186	7	is	be	AUX
ejpam-3285	186	8	only	only	ADV
ejpam-3285	186	9	(	(	PUNCT
ejpam-3285	186	10	0	0	NUM
ejpam-3285	186	11	,	,	PUNCT
ejpam-3285	186	12	0	0	NUM
ejpam-3285	186	13	)	)	PUNCT
ejpam-3285	186	14	and	and	CCONJ
ejpam-3285	186	15	there	there	PRON
ejpam-3285	186	16	is	be	VERB
ejpam-3285	186	17	[	[	PUNCT
ejpam-3285	186	18	0	0	NUM
ejpam-3285	186	19	0	0	NUM
ejpam-3285	186	20	0	0	NUM
ejpam-3285	186	21	b	b	NOUN
ejpam-3285	186	22	]	]	PUNCT
ejpam-3285	186	23	∈m	∈m	NOUN
ejpam-3285	186	24	′2(z	′2(z	NUM
ejpam-3285	186	25	)	)	PUNCT
ejpam-3285	186	26	,	,	PUNCT
ejpam-3285	186	27	where	where	SCONJ
ejpam-3285	186	28	b	b	X
ejpam-3285	186	29	6=	6=	NUM
ejpam-3285	186	30	0	0	NUM
ejpam-3285	186	31	such	such	ADJ
ejpam-3285	186	32	that	that	SCONJ
ejpam-3285	186	33	f	f	X
ejpam-3285	186	34	(	(	PUNCT
ejpam-3285	186	35	[	[	PUNCT
ejpam-3285	186	36	0	0	NUM
ejpam-3285	186	37	0	0	NUM
ejpam-3285	186	38	0	0	NUM
ejpam-3285	186	39	b	b	NOUN
ejpam-3285	186	40	]	]	PUNCT
ejpam-3285	186	41	)	)	PUNCT
ejpam-3285	187	1	−	−	PROPN
ejpam-3285	187	2	g	g	NOUN
ejpam-3285	187	3	(	(	PUNCT
ejpam-3285	187	4	[	[	PUNCT
ejpam-3285	187	5	0	0	NUM
ejpam-3285	187	6	0	0	NUM
ejpam-3285	187	7	0	0	NUM
ejpam-3285	187	8	b	b	NOUN
ejpam-3285	187	9	,	,	PUNCT
ejpam-3285	187	10	]	]	PUNCT
ejpam-3285	187	11	)	)	PUNCT
ejpam-3285	187	12	=	=	SYM
ejpam-3285	187	13	(	(	PUNCT
ejpam-3285	187	14	0	0	NUM
ejpam-3285	187	15	,	,	PUNCT
ejpam-3285	187	16	b	b	NOUN
ejpam-3285	187	17	)	)	PUNCT
ejpam-3285	187	18	6=	6=	ADP
ejpam-3285	187	19	(	(	PUNCT
ejpam-3285	187	20	0	0	NUM
ejpam-3285	187	21	,	,	PUNCT
ejpam-3285	187	22	0	0	NUM
ejpam-3285	187	23	)	)	PUNCT
ejpam-3285	187	24	(	(	PUNCT
ejpam-3285	187	25	16	16	NUM
ejpam-3285	187	26	)	)	PUNCT
ejpam-3285	187	27	then	then	ADV
ejpam-3285	187	28	t	t	PROPN
ejpam-3285	187	29	′	′	NUM
ejpam-3285	187	30	is	be	AUX
ejpam-3285	187	31	not	not	PART
ejpam-3285	187	32	a	a	DET
ejpam-3285	187	33	morphism	morphism	NOUN
ejpam-3285	187	34	from	from	ADP
ejpam-3285	187	35	µ	µ	NUM
ejpam-3285	187	36	to	to	ADP
ejpam-3285	187	37	ϕ.	ϕ.	PROPN
ejpam-3285	187	38	let	let	VERB
ejpam-3285	187	39	µ	µ	X
ejpam-3285	187	40	:	:	PUNCT
ejpam-3285	187	41	r	r	NOUN
ejpam-3285	187	42	→	→	SYM
ejpam-3285	187	43	ends(m	ends(m	PROPN
ejpam-3285	187	44	)	)	PUNCT
ejpam-3285	187	45	be	be	VERB
ejpam-3285	187	46	an	an	DET
ejpam-3285	187	47	f	f	PROPN
ejpam-3285	187	48	-representation	-representation	NOUN
ejpam-3285	187	49	of	of	ADP
ejpam-3285	187	50	r	r	NOUN
ejpam-3285	187	51	and	and	CCONJ
ejpam-3285	187	52	let	let	VERB
ejpam-3285	187	53	ϕ	ϕ	NOUN
ejpam-3285	187	54	:	:	PUNCT
ejpam-3285	187	55	r	r	NOUN
ejpam-3285	187	56	→	→	SYM
ejpam-3285	187	57	ends(n	ends(n	NOUN
ejpam-3285	187	58	)	)	PUNCT
ejpam-3285	187	59	be	be	VERB
ejpam-3285	187	60	a	a	DET
ejpam-3285	187	61	g	g	NOUN
ejpam-3285	187	62	-	-	PUNCT
ejpam-3285	187	63	representation	representation	NOUN
ejpam-3285	187	64	of	of	ADP
ejpam-3285	187	65	r.	r.	PROPN
ejpam-3285	187	66	the	the	DET
ejpam-3285	187	67	set	set	NOUN
ejpam-3285	187	68	of	of	ADP
ejpam-3285	187	69	all	all	DET
ejpam-3285	187	70	morphism	morphism	NOUN
ejpam-3285	187	71	from	from	ADP
ejpam-3285	187	72	µ	µ	PRON
ejpam-3285	187	73	to	to	ADP
ejpam-3285	187	74	ϕ	ϕ	NOUN
ejpam-3285	187	75	is	be	AUX
ejpam-3285	187	76	denoted	denote	VERB
ejpam-3285	187	77	homr(µ	homr(µ	PROPN
ejpam-3285	187	78	,	,	PUNCT
ejpam-3285	187	79	ϕ	ϕ	NOUN
ejpam-3285	187	80	)	)	PUNCT
ejpam-3285	187	81	.	.	PUNCT
ejpam-3285	188	1	from	from	ADP
ejpam-3285	188	2	definition	definition	NOUN
ejpam-3285	188	3	4	4	NUM
ejpam-3285	188	4	,	,	PUNCT
ejpam-3285	188	5	we	we	PRON
ejpam-3285	188	6	know	know	VERB
ejpam-3285	188	7	that	that	SCONJ
ejpam-3285	188	8	every	every	DET
ejpam-3285	188	9	t	t	PROPN
ejpam-3285	188	10	∈	∈	PROPN
ejpam-3285	188	11	homr(µ	homr(µ	PROPN
ejpam-3285	188	12	,	,	PUNCT
ejpam-3285	188	13	ϕ	ϕ	NOUN
ejpam-3285	188	14	)	)	PUNCT
ejpam-3285	188	15	is	be	AUX
ejpam-3285	188	16	an	an	DET
ejpam-3285	188	17	element	element	NOUN
ejpam-3285	188	18	in	in	ADP
ejpam-3285	188	19	homs(m	homs(m	PROPN
ejpam-3285	188	20	,	,	PUNCT
ejpam-3285	188	21	n	n	CCONJ
ejpam-3285	188	22	)	)	PUNCT
ejpam-3285	188	23	.	.	PUNCT
ejpam-3285	189	1	remark	remark	PROPN
ejpam-3285	189	2	3	3	NUM
ejpam-3285	189	3	.	.	PUNCT
ejpam-3285	190	1	let	let	VERB
ejpam-3285	190	2	µ	µ	NOUN
ejpam-3285	190	3	:	:	PUNCT
ejpam-3285	190	4	r→	r→	PROPN
ejpam-3285	190	5	ends(m	ends(m	PROPN
ejpam-3285	190	6	)	)	PUNCT
ejpam-3285	190	7	be	be	AUX
ejpam-3285	190	8	an	an	DET
ejpam-3285	190	9	f	f	PROPN
ejpam-3285	190	10	-representation	-representation	NOUN
ejpam-3285	190	11	of	of	ADP
ejpam-3285	190	12	r	r	NOUN
ejpam-3285	190	13	and	and	CCONJ
ejpam-3285	190	14	ϕ	ϕ	NOUN
ejpam-3285	190	15	:	:	PUNCT
ejpam-3285	190	16	r→	r→	PROPN
ejpam-3285	190	17	ends(n	ends(n	PROPN
ejpam-3285	190	18	)	)	PUNCT
ejpam-3285	190	19	a	a	DET
ejpam-3285	190	20	g	g	NOUN
ejpam-3285	190	21	-	-	PUNCT
ejpam-3285	190	22	representation	representation	NOUN
ejpam-3285	190	23	of	of	ADP
ejpam-3285	190	24	r.	r.	PROPN
ejpam-3285	190	25	(	(	PUNCT
ejpam-3285	190	26	i	i	NOUN
ejpam-3285	190	27	)	)	PUNCT
ejpam-3285	190	28	if	if	SCONJ
ejpam-3285	190	29	f	f	PROPN
ejpam-3285	190	30	=	=	SYM
ejpam-3285	190	31	g	g	PROPN
ejpam-3285	190	32	,	,	PUNCT
ejpam-3285	190	33	then	then	ADV
ejpam-3285	190	34	every	every	DET
ejpam-3285	190	35	s	s	NOUN
ejpam-3285	190	36	-	-	PUNCT
ejpam-3285	190	37	module	module	NOUN
ejpam-3285	190	38	homomorphism	homomorphism	NOUN
ejpam-3285	190	39	t	t	NOUN
ejpam-3285	190	40	:	:	PUNCT
ejpam-3285	190	41	m	m	VERB
ejpam-3285	190	42	→	→	SYM
ejpam-3285	190	43	n	n	X
ejpam-3285	190	44	is	be	AUX
ejpam-3285	190	45	morphism	morphism	ADJ
ejpam-3285	190	46	from	from	ADP
ejpam-3285	190	47	µ	µ	NUM
ejpam-3285	190	48	to	to	ADP
ejpam-3285	190	49	ϕ	ϕ	PROPN
ejpam-3285	190	50	(	(	PUNCT
ejpam-3285	190	51	ii	ii	NOUN
ejpam-3285	190	52	)	)	PUNCT
ejpam-3285	190	53	if	if	SCONJ
ejpam-3285	190	54	t	t	PROPN
ejpam-3285	190	55	∈	∈	PROPN
ejpam-3285	190	56	homr(µ	homr(µ	PROPN
ejpam-3285	190	57	,	,	PUNCT
ejpam-3285	190	58	ϕ	ϕ	NOUN
ejpam-3285	190	59	)	)	PUNCT
ejpam-3285	190	60	is	be	AUX
ejpam-3285	190	61	an	an	DET
ejpam-3285	190	62	s	s	NOUN
ejpam-3285	190	63	-	-	PUNCT
ejpam-3285	190	64	module	module	NOUN
ejpam-3285	190	65	isomorphism	isomorphism	NOUN
ejpam-3285	190	66	,	,	PUNCT
ejpam-3285	190	67	then	then	ADV
ejpam-3285	190	68	µ	µ	X
ejpam-3285	190	69	∼	∼	NOUN
ejpam-3285	190	70	ϕ.	ϕ.	PROPN
ejpam-3285	190	71	(	(	PUNCT
ejpam-3285	190	72	iii	iii	PROPN
ejpam-3285	190	73	)	)	PUNCT
ejpam-3285	190	74	the	the	DET
ejpam-3285	190	75	identity	identity	NOUN
ejpam-3285	190	76	map	map	NOUN
ejpam-3285	190	77	i	i	NOUN
ejpam-3285	190	78	d	d	PROPN
ejpam-3285	190	79	:	:	PUNCT
ejpam-3285	191	1	m	m	PROPN
ejpam-3285	191	2	→m	→m	PUNCT
ejpam-3285	191	3	is	be	AUX
ejpam-3285	191	4	always	always	ADV
ejpam-3285	191	5	an	an	DET
ejpam-3285	191	6	element	element	NOUN
ejpam-3285	191	7	in	in	ADP
ejpam-3285	191	8	homr(µ	homr(µ	PROPN
ejpam-3285	191	9	,	,	PUNCT
ejpam-3285	191	10	µ	µ	NOUN
ejpam-3285	191	11	)	)	PUNCT
ejpam-3285	191	12	.	.	PUNCT
ejpam-3285	192	1	proposition	proposition	NOUN
ejpam-3285	192	2	4	4	NUM
ejpam-3285	192	3	.	.	PUNCT
ejpam-3285	193	1	let	let	VERB
ejpam-3285	193	2	µ	µ	NOUN
ejpam-3285	193	3	:	:	PUNCT
ejpam-3285	193	4	r→	r→	PROPN
ejpam-3285	193	5	ends(m	ends(m	PROPN
ejpam-3285	193	6	)	)	PUNCT
ejpam-3285	193	7	be	be	VERB
ejpam-3285	193	8	f	f	PROPN
ejpam-3285	193	9	-representation	-representation	NOUN
ejpam-3285	193	10	of	of	ADP
ejpam-3285	193	11	r	r	NOUN
ejpam-3285	193	12	and	and	CCONJ
ejpam-3285	193	13	ϕ	ϕ	NOUN
ejpam-3285	193	14	:	:	PUNCT
ejpam-3285	193	15	r→	r→	PROPN
ejpam-3285	193	16	ends(n	ends(n	PROPN
ejpam-3285	193	17	)	)	PUNCT
ejpam-3285	193	18	a	a	DET
ejpam-3285	193	19	g	g	NOUN
ejpam-3285	193	20	-	-	PUNCT
ejpam-3285	193	21	representation	representation	NOUN
ejpam-3285	193	22	of	of	ADP
ejpam-3285	193	23	ring	ring	PROPN
ejpam-3285	193	24	r.	r.	PROPN
ejpam-3285	193	25	then	then	ADV
ejpam-3285	193	26	homr(µ	homr(µ	PROPN
ejpam-3285	193	27	,	,	PUNCT
ejpam-3285	193	28	ϕ	ϕ	NOUN
ejpam-3285	193	29	)	)	PUNCT
ejpam-3285	193	30	is	be	AUX
ejpam-3285	193	31	a	a	DET
ejpam-3285	193	32	module	module	NOUN
ejpam-3285	193	33	over	over	ADP
ejpam-3285	193	34	s	s	PROPN
ejpam-3285	193	35	,	,	PUNCT
ejpam-3285	193	36	and	and	CCONJ
ejpam-3285	193	37	it	it	PRON
ejpam-3285	193	38	is	be	AUX
ejpam-3285	193	39	a	a	DET
ejpam-3285	193	40	submodule	submodule	NOUN
ejpam-3285	193	41	of	of	ADP
ejpam-3285	193	42	homs(m	homs(m	PROPN
ejpam-3285	193	43	,	,	PUNCT
ejpam-3285	193	44	n	n	CCONJ
ejpam-3285	193	45	)	)	PUNCT
ejpam-3285	193	46	.	.	PUNCT
ejpam-3285	194	1	proof	proof	NOUN
ejpam-3285	194	2	.	.	PUNCT
ejpam-3285	195	1	to	to	PART
ejpam-3285	195	2	prove	prove	VERB
ejpam-3285	195	3	homr(µ	homr(µ	PROPN
ejpam-3285	195	4	,	,	PUNCT
ejpam-3285	195	5	ϕ	ϕ	NOUN
ejpam-3285	195	6	)	)	PUNCT
ejpam-3285	195	7	is	be	AUX
ejpam-3285	195	8	an	an	DET
ejpam-3285	195	9	s	s	NOUN
ejpam-3285	195	10	-	-	NOUN
ejpam-3285	195	11	module	module	NOUN
ejpam-3285	195	12	,	,	PUNCT
ejpam-3285	195	13	we	we	PRON
ejpam-3285	195	14	must	must	AUX
ejpam-3285	195	15	show	show	VERB
ejpam-3285	195	16	homr(µ	homr(µ	PROPN
ejpam-3285	195	17	,	,	PUNCT
ejpam-3285	195	18	ϕ	ϕ	NOUN
ejpam-3285	195	19	)	)	PUNCT
ejpam-3285	195	20	is	be	AUX
ejpam-3285	195	21	an	an	DET
ejpam-3285	195	22	abelian	abelian	ADJ
ejpam-3285	195	23	additive	additive	NOUN
ejpam-3285	195	24	group	group	NOUN
ejpam-3285	195	25	and	and	CCONJ
ejpam-3285	195	26	it	it	PRON
ejpam-3285	195	27	is	be	AUX
ejpam-3285	195	28	closed	close	VERB
ejpam-3285	195	29	under	under	ADP
ejpam-3285	195	30	scalar	scalar	ADJ
ejpam-3285	195	31	multiplication	multiplication	NOUN
ejpam-3285	195	32	over	over	ADP
ejpam-3285	195	33	s.	s.	PROPN
ejpam-3285	195	34	let	let	VERB
ejpam-3285	195	35	t	t	PROPN
ejpam-3285	195	36	,	,	PUNCT
ejpam-3285	195	37	t1	t1	NOUN
ejpam-3285	195	38	and	and	CCONJ
ejpam-3285	195	39	t2	t2	NOUN
ejpam-3285	195	40	be	be	VERB
ejpam-3285	195	41	any	any	DET
ejpam-3285	195	42	elements	element	NOUN
ejpam-3285	195	43	of	of	ADP
ejpam-3285	195	44	homr(µ	homr(µ	PROPN
ejpam-3285	195	45	,	,	PUNCT
ejpam-3285	195	46	ϕ	ϕ	NOUN
ejpam-3285	195	47	)	)	PUNCT
ejpam-3285	195	48	,	,	PUNCT
ejpam-3285	195	49	and	and	CCONJ
ejpam-3285	195	50	let	let	VERB
ejpam-3285	195	51	s	s	PRON
ejpam-3285	195	52	be	be	AUX
ejpam-3285	195	53	any	any	DET
ejpam-3285	195	54	element	element	NOUN
ejpam-3285	195	55	of	of	ADP
ejpam-3285	195	56	s	s	PROPN
ejpam-3285	195	57	,	,	PUNCT
ejpam-3285	195	58	then	then	ADV
ejpam-3285	195	59	we	we	PRON
ejpam-3285	195	60	have	have	VERB
ejpam-3285	195	61	t	t	PROPN
ejpam-3285	195	62	,	,	PUNCT
ejpam-3285	195	63	t1	t1	PROPN
ejpam-3285	195	64	,	,	PUNCT
ejpam-3285	195	65	t2	t2	PROPN
ejpam-3285	195	66	∈	∈	PROPN
ejpam-3285	195	67	homs(m	homs(m	PROPN
ejpam-3285	195	68	,	,	PUNCT
ejpam-3285	195	69	n	n	CCONJ
ejpam-3285	195	70	)	)	PUNCT
ejpam-3285	195	71	,	,	PUNCT
ejpam-3285	195	72	and	and	CCONJ
ejpam-3285	195	73	from	from	ADP
ejpam-3285	195	74	[	[	X
ejpam-3285	195	75	1	1	NUM
ejpam-3285	195	76	]	]	X
ejpam-3285	195	77	st	st	PROPN
ejpam-3285	195	78	,	,	PUNCT
ejpam-3285	195	79	t1	t1	PROPN
ejpam-3285	195	80	+	+	CCONJ
ejpam-3285	195	81	t2	t2	PROPN
ejpam-3285	195	82	∈	∈	PROPN
ejpam-3285	195	83	homs(m	homs(m	PROPN
ejpam-3285	195	84	,	,	PUNCT
ejpam-3285	195	85	n	n	CCONJ
ejpam-3285	195	86	)	)	PUNCT
ejpam-3285	195	87	.	.	PUNCT
ejpam-3285	196	1	so	so	ADV
ejpam-3285	196	2	by	by	ADP
ejpam-3285	196	3	proposition	proposition	NOUN
ejpam-3285	196	4	3	3	NUM
ejpam-3285	196	5	to	to	PART
ejpam-3285	196	6	prove	prove	VERB
ejpam-3285	196	7	homr(µ	homr(µ	PROPN
ejpam-3285	196	8	,	,	PUNCT
ejpam-3285	196	9	ϕ	ϕ	NOUN
ejpam-3285	196	10	)	)	PUNCT
ejpam-3285	196	11	is	be	AUX
ejpam-3285	196	12	an	an	DET
ejpam-3285	196	13	s	s	NOUN
ejpam-3285	196	14	-	-	NOUN
ejpam-3285	196	15	module	module	NOUN
ejpam-3285	196	16	,	,	PUNCT
ejpam-3285	196	17	it	it	PRON
ejpam-3285	196	18	is	be	AUX
ejpam-3285	196	19	enough	enough	ADJ
ejpam-3285	196	20	to	to	PART
ejpam-3285	196	21	prove	prove	VERB
ejpam-3285	196	22	f(r	f(r	NOUN
ejpam-3285	196	23	)	)	PUNCT
ejpam-3285	196	24	−	−	PROPN
ejpam-3285	196	25	g(r	g(r	PROPN
ejpam-3285	196	26	)	)	PUNCT
ejpam-3285	196	27	∈	∈	PROPN
ejpam-3285	196	28	ann(im(t1	ann(im(t1	PROPN
ejpam-3285	196	29	+	+	CCONJ
ejpam-3285	196	30	t2	t2	NOUN
ejpam-3285	196	31	)	)	PUNCT
ejpam-3285	196	32	)	)	PUNCT
ejpam-3285	196	33	and	and	CCONJ
ejpam-3285	196	34	f(r)−	f(r)−	PROPN
ejpam-3285	196	35	g(r	g(r	PROPN
ejpam-3285	196	36	)	)	PUNCT
ejpam-3285	196	37	∈	∈	PROPN
ejpam-3285	196	38	ann(im(st	ann(im(st	PROPN
ejpam-3285	196	39	)	)	PUNCT
ejpam-3285	196	40	)	)	PUNCT
ejpam-3285	196	41	for	for	ADP
ejpam-3285	196	42	any	any	DET
ejpam-3285	196	43	r	r	NOUN
ejpam-3285	196	44	∈	∈	PROPN
ejpam-3285	196	45	r.	r.	NOUN
ejpam-3285	196	46	(	(	PUNCT
ejpam-3285	196	47	i	i	NOUN
ejpam-3285	196	48	)	)	PUNCT
ejpam-3285	196	49	since	since	SCONJ
ejpam-3285	196	50	t1	t1	NOUN
ejpam-3285	196	51	,	,	PUNCT
ejpam-3285	196	52	t2	t2	PROPN
ejpam-3285	196	53	∈	∈	PROPN
ejpam-3285	196	54	homr(µ	homr(µ	PROPN
ejpam-3285	196	55	,	,	PUNCT
ejpam-3285	196	56	ϕ	ϕ	NOUN
ejpam-3285	196	57	)	)	PUNCT
ejpam-3285	196	58	,	,	PUNCT
ejpam-3285	196	59	then	then	ADV
ejpam-3285	196	60	by	by	ADP
ejpam-3285	196	61	proposition	proposition	NOUN
ejpam-3285	196	62	3	3	NUM
ejpam-3285	196	63	we	we	PRON
ejpam-3285	196	64	have	have	VERB
ejpam-3285	196	65	f(r)−g(r	f(r)−g(r	NOUN
ejpam-3285	196	66	)	)	PUNCT
ejpam-3285	196	67	∈	∈	PROPN
ejpam-3285	196	68	ann(im(ti	ann(im(ti	NOUN
ejpam-3285	196	69	)	)	PUNCT
ejpam-3285	196	70	)	)	PUNCT
ejpam-3285	197	1	i.e	i.e	PROPN
ejpam-3285	197	2	(	(	PUNCT
ejpam-3285	197	3	f(r)−	f(r)−	PROPN
ejpam-3285	197	4	g(r))ti(m	g(r))ti(m	NOUN
ejpam-3285	197	5	)	)	PUNCT
ejpam-3285	197	6	=	=	SYM
ejpam-3285	197	7	0	0	NUM
ejpam-3285	197	8	for	for	ADP
ejpam-3285	197	9	any	any	DET
ejpam-3285	197	10	m	m	NOUN
ejpam-3285	197	11	∈m	∈m	NOUN
ejpam-3285	197	12	,	,	PUNCT
ejpam-3285	197	13	i	i	PRON
ejpam-3285	197	14	=	=	NOUN
ejpam-3285	197	15	1	1	NUM
ejpam-3285	197	16	,	,	PUNCT
ejpam-3285	197	17	2	2	NUM
ejpam-3285	197	18	.	.	X
ejpam-3285	198	1	let	let	VERB
ejpam-3285	198	2	n	n	PRON
ejpam-3285	198	3	be	be	AUX
ejpam-3285	198	4	any	any	DET
ejpam-3285	198	5	element	element	NOUN
ejpam-3285	198	6	in	in	ADP
ejpam-3285	198	7	im(t1+t2	im(t1+t2	NOUN
ejpam-3285	198	8	)	)	PUNCT
ejpam-3285	198	9	,	,	PUNCT
ejpam-3285	198	10	then	then	ADV
ejpam-3285	198	11	there	there	PRON
ejpam-3285	198	12	is	be	VERB
ejpam-3285	198	13	m	m	NOUN
ejpam-3285	198	14	∈m	∈m	NOUN
ejpam-3285	198	15	such	such	ADJ
ejpam-3285	198	16	that	that	SCONJ
ejpam-3285	198	17	(	(	PUNCT
ejpam-3285	198	18	t1+t2)(m	t1+t2)(m	PROPN
ejpam-3285	198	19	)	)	PUNCT
ejpam-3285	198	20	=	=	SYM
ejpam-3285	199	1	n	n	NOUN
ejpam-3285	199	2	if	if	SCONJ
ejpam-3285	199	3	and	and	CCONJ
ejpam-3285	199	4	only	only	ADV
ejpam-3285	199	5	if	if	SCONJ
ejpam-3285	199	6	t1(m	t1(m	PROPN
ejpam-3285	199	7	)	)	PUNCT
ejpam-3285	199	8	+	+	PUNCT
ejpam-3285	199	9	t2(m	t2(m	X
ejpam-3285	199	10	)	)	PUNCT
ejpam-3285	199	11	=	=	VERB
ejpam-3285	199	12	n.	n.	NOUN
ejpam-3285	199	13	hence	hence	ADV
ejpam-3285	199	14	we	we	PRON
ejpam-3285	199	15	have	have	VERB
ejpam-3285	199	16	(	(	PUNCT
ejpam-3285	199	17	f(r)−	f(r)−	NOUN
ejpam-3285	199	18	g(r))n	g(r))n	PROPN
ejpam-3285	199	19	=	=	PUNCT
ejpam-3285	199	20	(	(	PUNCT
ejpam-3285	199	21	f(r)−	f(r)−	PROPN
ejpam-3285	199	22	g(r))(t1(m	g(r))(t1(m	PROPN
ejpam-3285	199	23	)	)	PUNCT
ejpam-3285	200	1	+	+	PUNCT
ejpam-3285	201	1	t2(m	t2(m	X
ejpam-3285	201	2	)	)	PUNCT
ejpam-3285	201	3	)	)	PUNCT
ejpam-3285	202	1	=	=	SYM
ejpam-3285	202	2	(	(	PUNCT
ejpam-3285	202	3	f(r)−	f(r)−	PROPN
ejpam-3285	202	4	g(r))t1(m	g(r))t1(m	PROPN
ejpam-3285	202	5	)	)	PUNCT
ejpam-3285	203	1	+	+	CCONJ
ejpam-3285	203	2	(	(	PUNCT
ejpam-3285	203	3	f(r)−	f(r)−	PROPN
ejpam-3285	203	4	g(r))t2(m	g(r))t2(m	PROPN
ejpam-3285	203	5	)	)	PUNCT
ejpam-3285	203	6	=	=	SYM
ejpam-3285	203	7	0	0	NUM
ejpam-3285	203	8	(	(	PUNCT
ejpam-3285	203	9	17	17	NUM
ejpam-3285	203	10	)	)	PUNCT
ejpam-3285	203	11	n.	n.	NOUN
ejpam-3285	203	12	hijriati	hijriati	PROPN
ejpam-3285	203	13	,	,	PUNCT
ejpam-3285	203	14	s.	s.	PROPN
ejpam-3285	203	15	wahyuni	wahyuni	PROPN
ejpam-3285	203	16	,	,	PUNCT
ejpam-3285	203	17	i.e.	i.e.	X
ejpam-3285	203	18	wijayanti	wijayanti	X
ejpam-3285	203	19	/	/	SYM
ejpam-3285	203	20	eur	eur	PROPN
ejpam-3285	203	21	.	.	PUNCT
ejpam-3285	204	1	j.	j.	PROPN
ejpam-3285	204	2	pure	pure	PROPN
ejpam-3285	204	3	appl	appl	PROPN
ejpam-3285	204	4	.	.	PROPN
ejpam-3285	204	5	math	math	PROPN
ejpam-3285	204	6	,	,	PUNCT
ejpam-3285	204	7	11	11	NUM
ejpam-3285	204	8	(	(	PUNCT
ejpam-3285	204	9	3	3	NUM
ejpam-3285	204	10	)	)	PUNCT
ejpam-3285	204	11	(	(	PUNCT
ejpam-3285	204	12	2018	2018	NUM
ejpam-3285	204	13	)	)	PUNCT
ejpam-3285	204	14	,	,	PUNCT
ejpam-3285	204	15	751	751	NUM
ejpam-3285	204	16	-	-	SYM
ejpam-3285	204	17	761	761	NUM
ejpam-3285	204	18	759	759	NUM
ejpam-3285	204	19	(	(	PUNCT
ejpam-3285	204	20	ii	ii	NOUN
ejpam-3285	204	21	)	)	PUNCT
ejpam-3285	204	22	analog	analog	NOUN
ejpam-3285	204	23	to	to	ADP
ejpam-3285	204	24	(	(	PUNCT
ejpam-3285	204	25	1	1	NUM
ejpam-3285	204	26	)	)	PUNCT
ejpam-3285	204	27	,	,	PUNCT
ejpam-3285	204	28	if	if	SCONJ
ejpam-3285	204	29	t	t	PROPN
ejpam-3285	204	30	∈	∈	PROPN
ejpam-3285	204	31	homr(µ	homr(µ	PROPN
ejpam-3285	204	32	,	,	PUNCT
ejpam-3285	204	33	ϕ	ϕ	NOUN
ejpam-3285	204	34	)	)	PUNCT
ejpam-3285	204	35	,	,	PUNCT
ejpam-3285	204	36	then	then	ADV
ejpam-3285	204	37	for	for	ADP
ejpam-3285	204	38	any	any	DET
ejpam-3285	204	39	m	m	NOUN
ejpam-3285	204	40	∈m	∈m	NOUN
ejpam-3285	204	41	f(r)−	f(r)−	PROPN
ejpam-3285	204	42	g(r)t	g(r)t	X
ejpam-3285	204	43	(	(	PUNCT
ejpam-3285	204	44	m	m	NOUN
ejpam-3285	204	45	)	)	PUNCT
ejpam-3285	204	46	=	=	SYM
ejpam-3285	205	1	0	0	X
ejpam-3285	205	2	.	.	PUNCT
ejpam-3285	206	1	so	so	ADV
ejpam-3285	206	2	we	we	PRON
ejpam-3285	206	3	have	have	VERB
ejpam-3285	206	4	for	for	ADP
ejpam-3285	206	5	any	any	DET
ejpam-3285	206	6	n	n	PRON
ejpam-3285	206	7	∈	∈	NOUN
ejpam-3285	206	8	im(st	im(st	NOUN
ejpam-3285	206	9	)	)	PUNCT
ejpam-3285	206	10	,	,	PUNCT
ejpam-3285	206	11	there	there	PRON
ejpam-3285	206	12	is	be	VERB
ejpam-3285	206	13	m	m	PROPN
ejpam-3285	206	14	∈	∈	NOUN
ejpam-3285	206	15	m	m	NOUN
ejpam-3285	206	16	such	such	ADJ
ejpam-3285	206	17	that	that	SCONJ
ejpam-3285	206	18	(	(	PUNCT
ejpam-3285	206	19	st	st	PROPN
ejpam-3285	206	20	)	)	PUNCT
ejpam-3285	206	21	(	(	PUNCT
ejpam-3285	206	22	m	m	NOUN
ejpam-3285	206	23	)	)	PUNCT
ejpam-3285	206	24	=	=	SYM
ejpam-3285	206	25	st	st	PROPN
ejpam-3285	206	26	(	(	PUNCT
ejpam-3285	206	27	m	m	NOUN
ejpam-3285	206	28	)	)	PUNCT
ejpam-3285	206	29	=	=	SYM
ejpam-3285	206	30	n	n	CCONJ
ejpam-3285	207	1	and	and	CCONJ
ejpam-3285	207	2	we	we	PRON
ejpam-3285	207	3	have	have	VERB
ejpam-3285	207	4	(	(	PUNCT
ejpam-3285	207	5	f(r)−	f(r)−	PROPN
ejpam-3285	207	6	g(r))st	g(r))st	PROPN
ejpam-3285	207	7	(	(	PUNCT
ejpam-3285	207	8	m	m	NOUN
ejpam-3285	207	9	)	)	PUNCT
ejpam-3285	208	1	=	=	PUNCT
ejpam-3285	209	1	s(f(r)−	s(f(r)−	PROPN
ejpam-3285	209	2	g(r))t	g(r))t	PROPN
ejpam-3285	209	3	(	(	PUNCT
ejpam-3285	209	4	m	m	NOUN
ejpam-3285	209	5	)	)	PUNCT
ejpam-3285	209	6	=	=	SYM
ejpam-3285	209	7	0	0	NUM
ejpam-3285	209	8	(	(	PUNCT
ejpam-3285	209	9	18	18	NUM
ejpam-3285	209	10	)	)	PUNCT
ejpam-3285	209	11	from	from	ADP
ejpam-3285	209	12	(	(	PUNCT
ejpam-3285	209	13	1	1	NUM
ejpam-3285	209	14	)	)	PUNCT
ejpam-3285	209	15	and	and	CCONJ
ejpam-3285	209	16	(	(	PUNCT
ejpam-3285	209	17	2	2	X
ejpam-3285	209	18	)	)	PUNCT
ejpam-3285	209	19	so	so	SCONJ
ejpam-3285	209	20	we	we	PRON
ejpam-3285	209	21	have	have	VERB
ejpam-3285	209	22	f(r)−g(r	f(r)−g(r	NOUN
ejpam-3285	209	23	)	)	PUNCT
ejpam-3285	209	24	∈	∈	PROPN
ejpam-3285	209	25	ann(im(t1+t2	ann(im(t1+t2	PROPN
ejpam-3285	209	26	)	)	PUNCT
ejpam-3285	209	27	)	)	PUNCT
ejpam-3285	209	28	and	and	CCONJ
ejpam-3285	209	29	f(r)−g(r	f(r)−g(r	X
ejpam-3285	209	30	)	)	PUNCT
ejpam-3285	209	31	∈	∈	PROPN
ejpam-3285	209	32	ann(im(st	ann(im(st	PROPN
ejpam-3285	209	33	)	)	PUNCT
ejpam-3285	209	34	)	)	PUNCT
ejpam-3285	209	35	.	.	PUNCT
ejpam-3285	210	1	in	in	ADP
ejpam-3285	210	2	other	other	ADJ
ejpam-3285	210	3	words	word	NOUN
ejpam-3285	210	4	homr(µ	homr(µ	PROPN
ejpam-3285	210	5	,	,	PUNCT
ejpam-3285	210	6	ϕ	ϕ	NOUN
ejpam-3285	210	7	)	)	PUNCT
ejpam-3285	210	8	is	be	AUX
ejpam-3285	210	9	an	an	DET
ejpam-3285	210	10	s	s	NOUN
ejpam-3285	210	11	-	-	NOUN
ejpam-3285	210	12	module	module	NOUN
ejpam-3285	210	13	.	.	PUNCT
ejpam-3285	211	1	furthermore	furthermore	ADV
ejpam-3285	211	2	,	,	PUNCT
ejpam-3285	211	3	since	since	SCONJ
ejpam-3285	211	4	homr(µ	homr(µ	PROPN
ejpam-3285	211	5	,	,	PUNCT
ejpam-3285	211	6	ϕ	ϕ	NOUN
ejpam-3285	211	7	)	)	PUNCT
ejpam-3285	211	8	⊆	⊆	NUM
ejpam-3285	211	9	homs(m	homs(m	NOUN
ejpam-3285	211	10	,	,	PUNCT
ejpam-3285	211	11	n	n	CCONJ
ejpam-3285	211	12	)	)	PUNCT
ejpam-3285	211	13	,	,	PUNCT
ejpam-3285	211	14	then	then	ADV
ejpam-3285	211	15	homr(µ	homr(µ	PROPN
ejpam-3285	211	16	,	,	PUNCT
ejpam-3285	211	17	ϕ	ϕ	NOUN
ejpam-3285	211	18	)	)	PUNCT
ejpam-3285	211	19	is	be	AUX
ejpam-3285	211	20	an	an	DET
ejpam-3285	211	21	s	s	NOUN
ejpam-3285	211	22	-	-	NOUN
ejpam-3285	211	23	submodule	submodule	NOUN
ejpam-3285	211	24	of	of	ADP
ejpam-3285	211	25	homs(m	homs(m	PROPN
ejpam-3285	211	26	,	,	PUNCT
ejpam-3285	211	27	n	n	CCONJ
ejpam-3285	211	28	)	)	PUNCT
ejpam-3285	211	29	.	.	PUNCT
ejpam-3285	212	1	now	now	ADV
ejpam-3285	212	2	we	we	PRON
ejpam-3285	212	3	give	give	VERB
ejpam-3285	212	4	the	the	DET
ejpam-3285	212	5	generalization	generalization	NOUN
ejpam-3285	212	6	of	of	ADP
ejpam-3285	212	7	schur	schur	PROPN
ejpam-3285	212	8	’s	’s	PART
ejpam-3285	212	9	theorem	theorem	NOUN
ejpam-3285	212	10	which	which	PRON
ejpam-3285	212	11	is	be	AUX
ejpam-3285	212	12	the	the	DET
ejpam-3285	212	13	main	main	ADJ
ejpam-3285	212	14	result	result	NOUN
ejpam-3285	212	15	of	of	ADP
ejpam-3285	212	16	this	this	DET
ejpam-3285	212	17	paper	paper	NOUN
ejpam-3285	212	18	as	as	SCONJ
ejpam-3285	212	19	follows	follow	VERB
ejpam-3285	212	20	proposition	proposition	NOUN
ejpam-3285	212	21	5	5	NUM
ejpam-3285	212	22	.	.	PUNCT
ejpam-3285	213	1	let	let	VERB
ejpam-3285	213	2	µ	µ	PRON
ejpam-3285	213	3	:	:	PUNCT
ejpam-3285	213	4	r	r	NOUN
ejpam-3285	213	5	→	→	SYM
ejpam-3285	213	6	ends(m	ends(m	PROPN
ejpam-3285	213	7	)	)	PUNCT
ejpam-3285	213	8	be	be	VERB
ejpam-3285	213	9	an	an	DET
ejpam-3285	213	10	irreducible	irreducible	ADJ
ejpam-3285	213	11	f	f	NOUN
ejpam-3285	213	12	-representation	-representation	NOUN
ejpam-3285	213	13	of	of	ADP
ejpam-3285	213	14	r	r	NOUN
ejpam-3285	213	15	and	and	CCONJ
ejpam-3285	213	16	ϕ	ϕ	NOUN
ejpam-3285	213	17	:	:	PUNCT
ejpam-3285	213	18	r→	r→	PROPN
ejpam-3285	213	19	ends(n	ends(n	PROPN
ejpam-3285	213	20	)	)	PUNCT
ejpam-3285	213	21	an	an	DET
ejpam-3285	213	22	irreducible	irreducible	ADJ
ejpam-3285	213	23	g	g	NOUN
ejpam-3285	213	24	-	-	PUNCT
ejpam-3285	213	25	representation	representation	NOUN
ejpam-3285	213	26	of	of	ADP
ejpam-3285	213	27	ring	ring	PROPN
ejpam-3285	213	28	r.	r.	PROPN
ejpam-3285	213	29	we	we	PRON
ejpam-3285	213	30	have	have	VERB
ejpam-3285	213	31	the	the	DET
ejpam-3285	213	32	following	follow	VERB
ejpam-3285	213	33	:	:	PUNCT
ejpam-3285	213	34	(	(	PUNCT
ejpam-3285	213	35	i	i	NOUN
ejpam-3285	213	36	)	)	PUNCT
ejpam-3285	213	37	if	if	SCONJ
ejpam-3285	213	38	µ	µ	PRON
ejpam-3285	213	39	�	�	PROPN
ejpam-3285	213	40	ϕ	ϕ	PROPN
ejpam-3285	213	41	,	,	PUNCT
ejpam-3285	213	42	then	then	ADV
ejpam-3285	213	43	homr(µ	homr(µ	PROPN
ejpam-3285	213	44	,	,	PUNCT
ejpam-3285	213	45	ϕ	ϕ	NOUN
ejpam-3285	213	46	)	)	PUNCT
ejpam-3285	213	47	=	=	SYM
ejpam-3285	213	48	0	0	X
ejpam-3285	213	49	.	.	PUNCT
ejpam-3285	213	50	(	(	PUNCT
ejpam-3285	213	51	ii	ii	NOUN
ejpam-3285	213	52	)	)	PUNCT
ejpam-3285	213	53	if	if	SCONJ
ejpam-3285	213	54	µ	µ	X
ejpam-3285	213	55	=	=	SYM
ejpam-3285	213	56	ϕ	ϕ	NOUN
ejpam-3285	213	57	,	,	PUNCT
ejpam-3285	213	58	then	then	ADV
ejpam-3285	213	59	homr(µ	homr(µ	PROPN
ejpam-3285	213	60	,	,	PUNCT
ejpam-3285	213	61	µ	µ	NOUN
ejpam-3285	213	62	)	)	PUNCT
ejpam-3285	213	63	is	be	AUX
ejpam-3285	213	64	a	a	DET
ejpam-3285	213	65	skew	skew	ADJ
ejpam-3285	213	66	field	field	NOUN
ejpam-3285	213	67	.	.	PUNCT
ejpam-3285	214	1	furthermore	furthermore	ADV
ejpam-3285	214	2	,	,	PUNCT
ejpam-3285	214	3	if	if	SCONJ
ejpam-3285	214	4	s	s	VERB
ejpam-3285	214	5	is	be	AUX
ejpam-3285	214	6	a	a	DET
ejpam-3285	214	7	principle	principle	ADJ
ejpam-3285	214	8	ideal	ideal	ADJ
ejpam-3285	214	9	domain	domain	NOUN
ejpam-3285	214	10	(	(	PUNCT
ejpam-3285	214	11	pid	pid	NOUN
ejpam-3285	214	12	)	)	PUNCT
ejpam-3285	214	13	,	,	PUNCT
ejpam-3285	214	14	where	where	SCONJ
ejpam-3285	214	15	k	k	PROPN
ejpam-3285	214	16	is	be	AUX
ejpam-3285	214	17	a	a	DET
ejpam-3285	214	18	fractional	fractional	ADJ
ejpam-3285	214	19	field	field	NOUN
ejpam-3285	214	20	of	of	ADP
ejpam-3285	214	21	s	s	PRON
ejpam-3285	214	22	and	and	CCONJ
ejpam-3285	214	23	k	k	PROPN
ejpam-3285	214	24	′	′	NOUN
ejpam-3285	214	25	is	be	AUX
ejpam-3285	214	26	an	an	DET
ejpam-3285	214	27	extension	extension	NOUN
ejpam-3285	214	28	field	field	NOUN
ejpam-3285	214	29	of	of	ADP
ejpam-3285	214	30	k	k	NOUN
ejpam-3285	214	31	,	,	PUNCT
ejpam-3285	214	32	and	and	CCONJ
ejpam-3285	214	33	m	m	PROPN
ejpam-3285	214	34	is	be	AUX
ejpam-3285	214	35	a	a	DET
ejpam-3285	214	36	free	free	ADJ
ejpam-3285	214	37	s	s	NOUN
ejpam-3285	214	38	-	-	NOUN
ejpam-3285	214	39	module	module	NOUN
ejpam-3285	214	40	with	with	ADP
ejpam-3285	214	41	finite	finite	ADJ
ejpam-3285	214	42	dimension	dimension	NOUN
ejpam-3285	214	43	,	,	PUNCT
ejpam-3285	214	44	then	then	ADV
ejpam-3285	214	45	there	there	PRON
ejpam-3285	214	46	is	be	VERB
ejpam-3285	214	47	scalar	scalar	ADJ
ejpam-3285	214	48	α	α	PRON
ejpam-3285	214	49	∈	∈	PROPN
ejpam-3285	214	50	k	k	PROPN
ejpam-3285	214	51	′	′	PROPN
ejpam-3285	214	52	,	,	PUNCT
ejpam-3285	214	53	such	such	ADJ
ejpam-3285	214	54	that	that	SCONJ
ejpam-3285	214	55	µ	µ	NOUN
ejpam-3285	214	56	=	=	SYM
ejpam-3285	214	57	αi	αi	NOUN
ejpam-3285	214	58	.	.	PUNCT
ejpam-3285	215	1	proof	proof	NOUN
ejpam-3285	215	2	.	.	PUNCT
ejpam-3285	216	1	(	(	PUNCT
ejpam-3285	216	2	i	i	NOUN
ejpam-3285	216	3	)	)	PUNCT
ejpam-3285	216	4	suppose	suppose	VERB
ejpam-3285	216	5	that	that	SCONJ
ejpam-3285	216	6	homr(µ	homr(µ	PROPN
ejpam-3285	216	7	,	,	PUNCT
ejpam-3285	216	8	ϕ	ϕ	NOUN
ejpam-3285	216	9	)	)	PUNCT
ejpam-3285	216	10	6=	6=	ADP
ejpam-3285	216	11	0	0	NUM
ejpam-3285	216	12	.	.	PUNCT
ejpam-3285	217	1	then	then	ADV
ejpam-3285	217	2	there	there	PRON
ejpam-3285	217	3	is	be	VERB
ejpam-3285	217	4	t	t	PROPN
ejpam-3285	217	5	6=	6=	ADP
ejpam-3285	217	6	0	0	NUM
ejpam-3285	217	7	in	in	ADP
ejpam-3285	217	8	homr(µ	homr(µ	PROPN
ejpam-3285	217	9	,	,	PUNCT
ejpam-3285	217	10	ϕ	ϕ	NOUN
ejpam-3285	217	11	)	)	PUNCT
ejpam-3285	217	12	.	.	PUNCT
ejpam-3285	218	1	since	since	SCONJ
ejpam-3285	218	2	kert	kert	PROPN
ejpam-3285	218	3	is	be	AUX
ejpam-3285	218	4	a	a	DET
ejpam-3285	218	5	submodule	submodule	NOUN
ejpam-3285	218	6	of	of	ADP
ejpam-3285	218	7	m	m	PRON
ejpam-3285	218	8	,	,	PUNCT
ejpam-3285	218	9	by	by	ADP
ejpam-3285	218	10	remarks	remark	NOUN
ejpam-3285	218	11	2	2	NUM
ejpam-3285	218	12	ker(t	ker(t	NOUN
ejpam-3285	218	13	)	)	PUNCT
ejpam-3285	218	14	is	be	AUX
ejpam-3285	218	15	an	an	DET
ejpam-3285	218	16	r	r	NOUN
ejpam-3285	218	17	-	-	PUNCT
ejpam-3285	218	18	invariant	invariant	ADJ
ejpam-3285	218	19	submodule	submodule	NOUN
ejpam-3285	218	20	of	of	ADP
ejpam-3285	218	21	m	m	PRON
ejpam-3285	218	22	and	and	CCONJ
ejpam-3285	218	23	hence	hence	ADV
ejpam-3285	218	24	either	either	CCONJ
ejpam-3285	218	25	ker(t	ker(t	NOUN
ejpam-3285	218	26	)	)	PUNCT
ejpam-3285	219	1	=	=	SYM
ejpam-3285	219	2	m	m	NOUN
ejpam-3285	219	3	or	or	CCONJ
ejpam-3285	219	4	ker(t	ker(t	NOUN
ejpam-3285	219	5	)	)	PUNCT
ejpam-3285	220	1	=	=	SYM
ejpam-3285	220	2	0	0	X
ejpam-3285	220	3	.	.	PUNCT
ejpam-3285	221	1	because	because	SCONJ
ejpam-3285	221	2	µ	µ	NOUN
ejpam-3285	221	3	is	be	AUX
ejpam-3285	221	4	irreducible	irreducible	ADJ
ejpam-3285	221	5	and	and	CCONJ
ejpam-3285	221	6	t	t	PROPN
ejpam-3285	221	7	6=	6=	NUM
ejpam-3285	221	8	0	0	NUM
ejpam-3285	221	9	,	,	PUNCT
ejpam-3285	221	10	then	then	ADV
ejpam-3285	221	11	kert	kert	PROPN
ejpam-3285	221	12	=	=	PROPN
ejpam-3285	221	13	0	0	PROPN
ejpam-3285	221	14	.	.	PUNCT
ejpam-3285	222	1	so	so	ADV
ejpam-3285	222	2	t	t	PROPN
ejpam-3285	222	3	is	be	AUX
ejpam-3285	222	4	injective	injective	ADJ
ejpam-3285	222	5	.	.	PUNCT
ejpam-3285	223	1	furthermore	furthermore	ADV
ejpam-3285	223	2	,	,	PUNCT
ejpam-3285	223	3	since	since	SCONJ
ejpam-3285	223	4	im(t	im(t	VERB
ejpam-3285	223	5	)	)	PUNCT
ejpam-3285	223	6	is	be	AUX
ejpam-3285	223	7	also	also	ADV
ejpam-3285	223	8	submodule	submodule	NOUN
ejpam-3285	223	9	of	of	ADP
ejpam-3285	223	10	n	n	PROPN
ejpam-3285	223	11	,	,	PUNCT
ejpam-3285	223	12	by	by	ADP
ejpam-3285	223	13	remarks	remark	NOUN
ejpam-3285	223	14	2	2	NUM
ejpam-3285	223	15	im(t	im(t	NOUN
ejpam-3285	223	16	)	)	PUNCT
ejpam-3285	223	17	is	be	AUX
ejpam-3285	223	18	an	an	DET
ejpam-3285	223	19	r	r	NOUN
ejpam-3285	223	20	-	-	PUNCT
ejpam-3285	223	21	invariant	invariant	ADJ
ejpam-3285	223	22	submodule	submodule	NOUN
ejpam-3285	223	23	of	of	ADP
ejpam-3285	223	24	n	n	PROPN
ejpam-3285	223	25	,	,	PUNCT
ejpam-3285	223	26	so	so	ADV
ejpam-3285	223	27	im(t	im(t	VERB
ejpam-3285	223	28	)	)	PUNCT
ejpam-3285	224	1	=	=	SYM
ejpam-3285	224	2	0	0	NUM
ejpam-3285	224	3	or	or	CCONJ
ejpam-3285	224	4	im(t	im(t	ADJ
ejpam-3285	224	5	)	)	PUNCT
ejpam-3285	225	1	=	=	SYM
ejpam-3285	225	2	n	n	NOUN
ejpam-3285	225	3	.	.	PUNCT
ejpam-3285	226	1	if	if	SCONJ
ejpam-3285	226	2	im(t	im(t	VERB
ejpam-3285	226	3	)	)	PUNCT
ejpam-3285	226	4	=	=	SYM
ejpam-3285	226	5	0	0	NUM
ejpam-3285	226	6	,	,	PUNCT
ejpam-3285	226	7	then	then	ADV
ejpam-3285	226	8	t	t	PROPN
ejpam-3285	226	9	=	=	SYM
ejpam-3285	226	10	0	0	X
ejpam-3285	226	11	.	.	PUNCT
ejpam-3285	227	1	so	so	ADV
ejpam-3285	227	2	it	it	PRON
ejpam-3285	227	3	must	must	AUX
ejpam-3285	227	4	be	be	AUX
ejpam-3285	227	5	im(t	im(t	VERB
ejpam-3285	227	6	)	)	PUNCT
ejpam-3285	228	1	=	=	SYM
ejpam-3285	228	2	n	n	X
ejpam-3285	228	3	,	,	PUNCT
ejpam-3285	228	4	i.e	i.e	PRON
ejpam-3285	228	5	t	t	PROPN
ejpam-3285	228	6	is	be	AUX
ejpam-3285	228	7	surjective	surjective	ADJ
ejpam-3285	228	8	.	.	PUNCT
ejpam-3285	229	1	thus	thus	ADV
ejpam-3285	229	2	t	t	PROPN
ejpam-3285	229	3	is	be	AUX
ejpam-3285	229	4	invertible	invertible	ADJ
ejpam-3285	229	5	.	.	PUNCT
ejpam-3285	230	1	hence	hence	ADV
ejpam-3285	230	2	by	by	ADP
ejpam-3285	230	3	corollary	corollary	ADJ
ejpam-3285	230	4	1	1	NUM
ejpam-3285	230	5	µ	µ	NOUN
ejpam-3285	230	6	∼	∼	NOUN
ejpam-3285	230	7	ϕ.	ϕ.	NOUN
ejpam-3285	230	8	this	this	PRON
ejpam-3285	230	9	is	be	AUX
ejpam-3285	230	10	the	the	DET
ejpam-3285	230	11	contrapositive	contrapositive	NOUN
ejpam-3285	230	12	of	of	ADP
ejpam-3285	230	13	what	what	PRON
ejpam-3285	230	14	we	we	PRON
ejpam-3285	230	15	want	want	VERB
ejpam-3285	230	16	to	to	PART
ejpam-3285	230	17	prove	prove	VERB
ejpam-3285	230	18	.	.	PUNCT
ejpam-3285	231	1	(	(	PUNCT
ejpam-3285	231	2	ii	ii	NOUN
ejpam-3285	231	3	)	)	PUNCT
ejpam-3285	231	4	by	by	ADP
ejpam-3285	231	5	using	use	VERB
ejpam-3285	231	6	proposition	proposition	NOUN
ejpam-3285	231	7	4	4	NUM
ejpam-3285	231	8	and	and	CCONJ
ejpam-3285	231	9	schur	schur	PROPN
ejpam-3285	231	10	’s	’s	PART
ejpam-3285	231	11	lemma	lemma	PROPN
ejpam-3285	231	12	in	in	ADP
ejpam-3285	231	13	[	[	X
ejpam-3285	231	14	13	13	NUM
ejpam-3285	231	15	]	]	PUNCT
ejpam-3285	231	16	,	,	PUNCT
ejpam-3285	231	17	then	then	ADV
ejpam-3285	231	18	homr(µ	homr(µ	PROPN
ejpam-3285	231	19	,	,	PUNCT
ejpam-3285	231	20	µ	µ	NOUN
ejpam-3285	231	21	)	)	PUNCT
ejpam-3285	231	22	is	be	AUX
ejpam-3285	231	23	a	a	DET
ejpam-3285	231	24	skew	skew	ADJ
ejpam-3285	231	25	field	field	NOUN
ejpam-3285	231	26	.	.	PUNCT
ejpam-3285	232	1	let	let	VERB
ejpam-3285	232	2	t	t	PROPN
ejpam-3285	232	3	∈	∈	PROPN
ejpam-3285	232	4	homr(µ.µ	homr(µ.µ	PROPN
ejpam-3285	232	5	)	)	PUNCT
ejpam-3285	232	6	and	and	CCONJ
ejpam-3285	232	7	t	t	PROPN
ejpam-3285	232	8	6=	6=	PROPN
ejpam-3285	232	9	0	0	X
ejpam-3285	232	10	.	.	PUNCT
ejpam-3285	233	1	if	if	SCONJ
ejpam-3285	233	2	m	m	NOUN
ejpam-3285	233	3	is	be	AUX
ejpam-3285	233	4	a	a	DET
ejpam-3285	233	5	free	free	ADJ
ejpam-3285	233	6	s	s	NOUN
ejpam-3285	233	7	-	-	NOUN
ejpam-3285	233	8	module	module	NOUN
ejpam-3285	233	9	with	with	ADP
ejpam-3285	233	10	finite	finite	ADJ
ejpam-3285	233	11	dimension	dimension	NOUN
ejpam-3285	233	12	,	,	PUNCT
ejpam-3285	233	13	then	then	ADV
ejpam-3285	233	14	there	there	PRON
ejpam-3285	233	15	is	be	VERB
ejpam-3285	233	16	α	α	PRON
ejpam-3285	233	17	∈	∈	PROPN
ejpam-3285	234	1	k	k	NOUN
ejpam-3285	235	1	′	′	NUM
ejpam-3285	236	1	which	which	PRON
ejpam-3285	236	2	is	be	AUX
ejpam-3285	236	3	eigenvalue	eigenvalue	NOUN
ejpam-3285	236	4	of	of	ADP
ejpam-3285	236	5	t	t	PROPN
ejpam-3285	236	6	.	.	PUNCT
ejpam-3285	237	1	since	since	SCONJ
ejpam-3285	237	2	s	s	PROPN
ejpam-3285	237	3	is	be	AUX
ejpam-3285	237	4	a	a	DET
ejpam-3285	237	5	principle	principle	ADJ
ejpam-3285	237	6	ideal	ideal	ADJ
ejpam-3285	237	7	domain	domain	NOUN
ejpam-3285	237	8	,	,	PUNCT
ejpam-3285	237	9	s	s	PART
ejpam-3285	237	10	is	be	AUX
ejpam-3285	237	11	dedekind	dedekind	ADJ
ejpam-3285	237	12	domain	domain	NOUN
ejpam-3285	237	13	and	and	CCONJ
ejpam-3285	237	14	by	by	ADP
ejpam-3285	237	15	proposition	proposition	NOUN
ejpam-3285	237	16	16.3.14	16.3.14	NUM
ejpam-3285	237	17	in	in	ADP
ejpam-3285	237	18	[	[	X
ejpam-3285	237	19	9	9	NUM
ejpam-3285	237	20	]	]	PUNCT
ejpam-3285	237	21	,	,	PUNCT
ejpam-3285	237	22	s	s	VERB
ejpam-3285	237	23	is	be	AUX
ejpam-3285	237	24	integrally	integrally	ADV
ejpam-3285	237	25	closed	close	VERB
ejpam-3285	237	26	.	.	PUNCT
ejpam-3285	238	1	hence	hence	ADV
ejpam-3285	238	2	,	,	PUNCT
ejpam-3285	238	3	if	if	SCONJ
ejpam-3285	238	4	α	α	PRON
ejpam-3285	238	5	∈	∈	PROPN
ejpam-3285	238	6	k	k	NOUN
ejpam-3285	238	7	,	,	PUNCT
ejpam-3285	238	8	then	then	ADV
ejpam-3285	238	9	α	α	PROPN
ejpam-3285	238	10	∈	∈	PROPN
ejpam-3285	238	11	r.	r.	PROPN
ejpam-3285	238	12	by	by	ADP
ejpam-3285	238	13	definition	definition	NOUN
ejpam-3285	238	14	eigenvalue	eigenvalue	PROPN
ejpam-3285	238	15	αi	αi	PRON
ejpam-3285	238	16	−	−	PROPN
ejpam-3285	238	17	t	t	PROPN
ejpam-3285	238	18	is	be	AUX
ejpam-3285	238	19	not	not	PART
ejpam-3285	238	20	invertible	invertible	ADJ
ejpam-3285	238	21	.	.	PUNCT
ejpam-3285	239	1	consider	consider	VERB
ejpam-3285	239	2	that	that	SCONJ
ejpam-3285	239	3	i	i	PRON
ejpam-3285	239	4	∈	∈	PROPN
ejpam-3285	239	5	homr(µ	homr(µ	PROPN
ejpam-3285	239	6	,	,	PUNCT
ejpam-3285	239	7	µ	µ	NOUN
ejpam-3285	239	8	)	)	PUNCT
ejpam-3285	239	9	,	,	PUNCT
ejpam-3285	239	10	then	then	ADV
ejpam-3285	239	11	by	by	ADP
ejpam-3285	239	12	proposition	proposition	NOUN
ejpam-3285	239	13	4	4	NUM
ejpam-3285	239	14	αi	αi	ADV
ejpam-3285	239	15	−	−	PROPN
ejpam-3285	239	16	t	t	PROPN
ejpam-3285	239	17	∈	∈	PROPN
ejpam-3285	239	18	homr(µ	homr(µ	PROPN
ejpam-3285	239	19	,	,	PUNCT
ejpam-3285	239	20	µ	µ	NOUN
ejpam-3285	239	21	)	)	PUNCT
ejpam-3285	239	22	.	.	PUNCT
ejpam-3285	240	1	we	we	PRON
ejpam-3285	240	2	have	have	VERB
ejpam-3285	240	3	that	that	DET
ejpam-3285	240	4	homr(µ	homr(µ	PROPN
ejpam-3285	240	5	,	,	PUNCT
ejpam-3285	240	6	µ	µ	NOUN
ejpam-3285	240	7	)	)	PUNCT
ejpam-3285	240	8	is	be	AUX
ejpam-3285	240	9	a	a	DET
ejpam-3285	240	10	skew	skew	ADJ
ejpam-3285	240	11	field	field	NOUN
ejpam-3285	240	12	,	,	PUNCT
ejpam-3285	240	13	then	then	ADV
ejpam-3285	240	14	αi	αi	VERB
ejpam-3285	240	15	−	−	PROPN
ejpam-3285	240	16	t	t	PROPN
ejpam-3285	240	17	=	=	SYM
ejpam-3285	240	18	0	0	PROPN
ejpam-3285	240	19	⇔	⇔	PROPN
ejpam-3285	240	20	t	t	PROPN
ejpam-3285	240	21	=	=	SYM
ejpam-3285	240	22	αi	αi	PROPN
ejpam-3285	240	23	.	.	PUNCT
ejpam-3285	241	1	furthermore	furthermore	ADV
ejpam-3285	241	2	,	,	PUNCT
ejpam-3285	241	3	if	if	SCONJ
ejpam-3285	241	4	α	α	PRON
ejpam-3285	241	5	/∈	/∈	PUNCT
ejpam-3285	242	1	k	k	NOUN
ejpam-3285	242	2	then	then	ADV
ejpam-3285	242	3	t	t	PROPN
ejpam-3285	242	4	=	=	PUNCT
ejpam-3285	242	5	αi	αi	NOUN
ejpam-3285	242	6	with	with	ADP
ejpam-3285	242	7	α	α	PROPN
ejpam-3285	242	8	∈	∈	PROPN
ejpam-3285	242	9	k	k	PROPN
ejpam-3285	242	10	′.	′.	PROPN
ejpam-3285	242	11	references	reference	NOUN
ejpam-3285	242	12	760	760	NUM
ejpam-3285	242	13	acknowledgements	acknowledgement	NOUN
ejpam-3285	242	14	this	this	DET
ejpam-3285	242	15	paper	paper	NOUN
ejpam-3285	242	16	is	be	AUX
ejpam-3285	242	17	one	one	NUM
ejpam-3285	242	18	of	of	ADP
ejpam-3285	242	19	the	the	DET
ejpam-3285	242	20	result	result	NOUN
ejpam-3285	242	21	of	of	ADP
ejpam-3285	242	22	the	the	DET
ejpam-3285	242	23	graduate	graduate	NOUN
ejpam-3285	242	24	research	research	NOUN
ejpam-3285	242	25	grant	grant	NOUN
ejpam-3285	242	26	(	(	PUNCT
ejpam-3285	242	27	hibah	hibah	PROPN
ejpam-3285	242	28	penelitian	penelitian	PROPN
ejpam-3285	242	29	pascasarjana	pascasarjana	PROPN
ejpam-3285	242	30	)	)	PUNCT
ejpam-3285	242	31	from	from	ADP
ejpam-3285	242	32	the	the	DET
ejpam-3285	242	33	ministry	ministry	PROPN
ejpam-3285	242	34	of	of	ADP
ejpam-3285	242	35	research	research	PROPN
ejpam-3285	242	36	and	and	CCONJ
ejpam-3285	242	37	higher	high	ADJ
ejpam-3285	242	38	education	education	NOUN
ejpam-3285	242	39	by	by	ADP
ejpam-3285	242	40	contract	contract	NOUN
ejpam-3285	242	41	no	no	NOUN
ejpam-3285	242	42	.	.	NOUN
ejpam-3285	243	1	7167	7167	NUM
ejpam-3285	243	2	/	/	SYM
ejpam-3285	243	3	un1.p.iii	un1.p.iii	SYM
ejpam-3285	243	4	/	/	SYM
ejpam-3285	243	5	dit	dit	ADJ
ejpam-3285	243	6	-	-	PUNCT
ejpam-3285	243	7	lit	light	VERB
ejpam-3285	243	8	/	/	SYM
ejpam-3285	243	9	lt/2017	lt/2017	PROPN
ejpam-3285	243	10	.	.	NOUN
ejpam-3285	243	11	references	reference	NOUN
ejpam-3285	244	1	[	[	X
ejpam-3285	244	2	1	1	NUM
ejpam-3285	244	3	]	]	X
ejpam-3285	244	4	w	w	ADP
ejpam-3285	244	5	a	a	DET
ejpam-3285	244	6	adkins	adkin	NOUN
ejpam-3285	244	7	and	and	CCONJ
ejpam-3285	244	8	s	s	PROPN
ejpam-3285	244	9	h	h	PROPN
ejpam-3285	244	10	weintraub	weintraub	PROPN
ejpam-3285	244	11	.	.	PUNCT
ejpam-3285	245	1	algebra	algebra	NOUN
ejpam-3285	245	2	:	:	PUNCT
ejpam-3285	245	3	an	an	DET
ejpam-3285	245	4	approach	approach	NOUN
ejpam-3285	245	5	via	via	ADP
ejpam-3285	245	6	module	module	NOUN
ejpam-3285	245	7	theory	theory	NOUN
ejpam-3285	245	8	.	.	PUNCT
ejpam-3285	246	1	springer	springer	NOUN
ejpam-3285	246	2	-	-	PUNCT
ejpam-3285	246	3	verlag	verlag	PROPN
ejpam-3285	246	4	,	,	PUNCT
ejpam-3285	246	5	new	new	PROPN
ejpam-3285	246	6	york	york	PROPN
ejpam-3285	246	7	,	,	PUNCT
ejpam-3285	246	8	1992	1992	NUM
ejpam-3285	246	9	.	.	PUNCT
ejpam-3285	247	1	[	[	X
ejpam-3285	247	2	2	2	NUM
ejpam-3285	247	3	]	]	X
ejpam-3285	247	4	f	f	PROPN
ejpam-3285	247	5	w	w	PROPN
ejpam-3285	247	6	anderson	anderson	PROPN
ejpam-3285	247	7	and	and	CCONJ
ejpam-3285	247	8	f	f	PROPN
ejpam-3285	247	9	k	k	PROPN
ejpam-3285	247	10	fuller	fuller	X
ejpam-3285	247	11	.	.	PUNCT
ejpam-3285	248	1	rings	ring	NOUN
ejpam-3285	248	2	and	and	CCONJ
ejpam-3285	248	3	categories	category	NOUN
ejpam-3285	248	4	of	of	ADP
ejpam-3285	248	5	modules	module	NOUN
ejpam-3285	248	6	.	.	PUNCT
ejpam-3285	249	1	springer	springer	NOUN
ejpam-3285	249	2	-	-	PUNCT
ejpam-3285	249	3	verlag	verlag	PROPN
ejpam-3285	249	4	,	,	PUNCT
ejpam-3285	249	5	new	new	PROPN
ejpam-3285	249	6	york	york	PROPN
ejpam-3285	249	7	,	,	PUNCT
ejpam-3285	249	8	2nd	2nd	PROPN
ejpam-3285	249	9	ed	ed	NOUN
ejpam-3285	249	10	.	.	PUNCT
ejpam-3285	249	11	edition	edition	PROPN
ejpam-3285	249	12	,	,	PUNCT
ejpam-3285	249	13	1992	1992	NUM
ejpam-3285	249	14	.	.	PUNCT
ejpam-3285	250	1	[	[	X
ejpam-3285	250	2	3	3	NUM
ejpam-3285	250	3	]	]	X
ejpam-3285	250	4	m	m	VERB
ejpam-3285	250	5	auslander	auslander	ADJ
ejpam-3285	250	6	.	.	PUNCT
ejpam-3285	251	1	representation	representation	NOUN
ejpam-3285	251	2	theory	theory	NOUN
ejpam-3285	251	3	of	of	ADP
ejpam-3285	251	4	artin	artin	PROPN
ejpam-3285	251	5	algebras	algebras	PROPN
ejpam-3285	251	6	i.	i.	PROPN
ejpam-3285	251	7	communications	communication	NOUN
ejpam-3285	251	8	in	in	ADP
ejpam-3285	251	9	algebra	algebra	NOUN
ejpam-3285	251	10	,	,	PUNCT
ejpam-3285	251	11	1(3):177–268	1(3):177–268	NUM
ejpam-3285	251	12	,	,	PUNCT
ejpam-3285	251	13	1974a	1974a	NUM
ejpam-3285	251	14	.	.	PUNCT
ejpam-3285	252	1	[	[	X
ejpam-3285	252	2	4	4	NUM
ejpam-3285	252	3	]	]	PUNCT
ejpam-3285	252	4	m	m	VERB
ejpam-3285	252	5	auslander	auslander	ADJ
ejpam-3285	252	6	.	.	PUNCT
ejpam-3285	253	1	representation	representation	NOUN
ejpam-3285	253	2	theory	theory	NOUN
ejpam-3285	253	3	of	of	ADP
ejpam-3285	253	4	artin	artin	PROPN
ejpam-3285	253	5	algebras	algebras	PROPN
ejpam-3285	253	6	ii	ii	PROPN
ejpam-3285	253	7	.	.	PUNCT
ejpam-3285	253	8	communications	communication	NOUN
ejpam-3285	253	9	in	in	ADP
ejpam-3285	253	10	algebra	algebra	NOUN
ejpam-3285	253	11	,	,	PUNCT
ejpam-3285	253	12	1(4):269–310	1(4):269–310	NUM
ejpam-3285	253	13	,	,	PUNCT
ejpam-3285	253	14	1974b	1974b	NUM
ejpam-3285	253	15	.	.	PUNCT
ejpam-3285	254	1	[	[	X
ejpam-3285	254	2	5	5	NUM
ejpam-3285	254	3	]	]	PUNCT
ejpam-3285	254	4	m	m	NOUN
ejpam-3285	254	5	auslander	auslander	ADJ
ejpam-3285	254	6	.	.	PUNCT
ejpam-3285	255	1	a	a	DET
ejpam-3285	255	2	functorial	functorial	NOUN
ejpam-3285	255	3	approach	approach	NOUN
ejpam-3285	255	4	to	to	ADP
ejpam-3285	255	5	representation	representation	NOUN
ejpam-3285	255	6	theory	theory	NOUN
ejpam-3285	255	7	,	,	PUNCT
ejpam-3285	255	8	volume	volume	NOUN
ejpam-3285	255	9	944	944	NUM
ejpam-3285	255	10	of	of	ADP
ejpam-3285	255	11	lecture	lecture	NOUN
ejpam-3285	255	12	notes	note	NOUN
ejpam-3285	255	13	in	in	ADP
ejpam-3285	255	14	mathematics	mathematic	NOUN
ejpam-3285	255	15	,	,	PUNCT
ejpam-3285	255	16	pages	page	NOUN
ejpam-3285	255	17	105–179	105–179	NUM
ejpam-3285	255	18	.	.	PUNCT
ejpam-3285	255	19	springer	springer	NOUN
ejpam-3285	255	20	-	-	PUNCT
ejpam-3285	255	21	verlag	verlag	PROPN
ejpam-3285	255	22	,	,	PUNCT
ejpam-3285	255	23	new	new	PROPN
ejpam-3285	255	24	york	york	PROPN
ejpam-3285	255	25	,	,	PUNCT
ejpam-3285	255	26	1982	1982	NUM
ejpam-3285	255	27	.	.	PUNCT
ejpam-3285	256	1	[	[	X
ejpam-3285	256	2	6	6	NUM
ejpam-3285	256	3	]	]	PUNCT
ejpam-3285	256	4	m	m	VERB
ejpam-3285	256	5	auslander	auslander	ADJ
ejpam-3285	256	6	,	,	PUNCT
ejpam-3285	256	7	i	i	PRON
ejpam-3285	256	8	reiten	reiten	VERB
ejpam-3285	256	9	,	,	PUNCT
ejpam-3285	256	10	and	and	CCONJ
ejpam-3285	256	11	s	s	VERB
ejpam-3285	256	12	o	o	NOUN
ejpam-3285	256	13	smalo	smalo	NOUN
ejpam-3285	256	14	.	.	PUNCT
ejpam-3285	257	1	representation	representation	NOUN
ejpam-3285	257	2	theory	theory	NOUN
ejpam-3285	257	3	of	of	ADP
ejpam-3285	257	4	artin	artin	PROPN
ejpam-3285	257	5	algebras	algebras	PROPN
ejpam-3285	257	6	.	.	PUNCT
ejpam-3285	258	1	cambridge	cambridge	PROPN
ejpam-3285	258	2	university	university	PROPN
ejpam-3285	258	3	press	press	PROPN
ejpam-3285	258	4	,	,	PUNCT
ejpam-3285	258	5	united	united	ADJ
ejpam-3285	258	6	kingdom	kingdom	PROPN
ejpam-3285	258	7	,	,	PUNCT
ejpam-3285	258	8	1st	1st	ADJ
ejpam-3285	258	9	ed	ed	PROPN
ejpam-3285	258	10	edition	edition	NOUN
ejpam-3285	258	11	,	,	PUNCT
ejpam-3285	258	12	1997	1997	NUM
ejpam-3285	258	13	.	.	PUNCT
ejpam-3285	259	1	[	[	X
ejpam-3285	259	2	7	7	NUM
ejpam-3285	259	3	]	]	PUNCT
ejpam-3285	259	4	m	m	NOUN
ejpam-3285	259	5	burrow	burrow	NOUN
ejpam-3285	259	6	.	.	PUNCT
ejpam-3285	260	1	representation	representation	NOUN
ejpam-3285	260	2	theory	theory	NOUN
ejpam-3285	260	3	of	of	ADP
ejpam-3285	260	4	finite	finite	PROPN
ejpam-3285	260	5	.	.	PUNCT
ejpam-3285	261	1	academic	academic	ADJ
ejpam-3285	261	2	press	press	NOUN
ejpam-3285	261	3	,	,	PUNCT
ejpam-3285	261	4	new	new	PROPN
ejpam-3285	261	5	york	york	PROPN
ejpam-3285	261	6	,	,	PUNCT
ejpam-3285	261	7	1st	1st	PROPN
ejpam-3285	261	8	ed	ed	NOUN
ejpam-3285	261	9	.	.	PUNCT
ejpam-3285	261	10	edition	edition	PROPN
ejpam-3285	261	11	,	,	PUNCT
ejpam-3285	261	12	1965	1965	NUM
ejpam-3285	261	13	.	.	PUNCT
ejpam-3285	262	1	[	[	X
ejpam-3285	262	2	8	8	NUM
ejpam-3285	262	3	]	]	X
ejpam-3285	262	4	c	c	PROPN
ejpam-3285	262	5	w	w	PROPN
ejpam-3285	262	6	curtis	curtis	PROPN
ejpam-3285	262	7	and	and	CCONJ
ejpam-3285	262	8	i	i	PROPN
ejpam-3285	262	9	reiner	reiner	NOUN
ejpam-3285	262	10	.	.	PUNCT
ejpam-3285	263	1	representation	representation	NOUN
ejpam-3285	263	2	theory	theory	NOUN
ejpam-3285	263	3	of	of	ADP
ejpam-3285	263	4	finite	finite	ADJ
ejpam-3285	263	5	groups	group	NOUN
ejpam-3285	263	6	and	and	CCONJ
ejpam-3285	263	7	associative	associative	ADJ
ejpam-3285	263	8	algebras	algebra	NOUN
ejpam-3285	263	9	.	.	PUNCT
ejpam-3285	264	1	john	john	PROPN
ejpam-3285	264	2	wiley	wiley	PROPN
ejpam-3285	264	3	and	and	CCONJ
ejpam-3285	264	4	sons.inc	sons.inc	PROPN
ejpam-3285	264	5	,	,	PUNCT
ejpam-3285	264	6	new	new	PROPN
ejpam-3285	264	7	york	york	PROPN
ejpam-3285	264	8	,	,	PUNCT
ejpam-3285	264	9	1962	1962	NUM
ejpam-3285	264	10	.	.	PUNCT
ejpam-3285	265	1	[	[	X
ejpam-3285	265	2	9	9	NUM
ejpam-3285	265	3	]	]	X
ejpam-3285	265	4	d	d	X
ejpam-3285	265	5	s	s	X
ejpam-3285	265	6	dummit	dummit	NOUN
ejpam-3285	265	7	and	and	CCONJ
ejpam-3285	265	8	r	r	NOUN
ejpam-3285	265	9	m	m	NOUN
ejpam-3285	265	10	foote	foote	NOUN
ejpam-3285	265	11	.	.	PUNCT
ejpam-3285	266	1	abstract	abstract	ADJ
ejpam-3285	266	2	algebra	algebra	PROPN
ejpam-3285	266	3	.	.	PUNCT
ejpam-3285	267	1	john	john	PROPN
ejpam-3285	267	2	wiley	wiley	PROPN
ejpam-3285	267	3	and	and	CCONJ
ejpam-3285	267	4	sons	sons	PROPN
ejpam-3285	267	5	inc	inc	PROPN
ejpam-3285	267	6	,	,	PUNCT
ejpam-3285	267	7	new	new	PROPN
ejpam-3285	267	8	york	york	PROPN
ejpam-3285	267	9	,	,	PUNCT
ejpam-3285	267	10	third	third	ADJ
ejpam-3285	267	11	edition	edition	NOUN
ejpam-3285	267	12	,	,	PUNCT
ejpam-3285	267	13	2004	2004	NUM
ejpam-3285	267	14	.	.	PUNCT
ejpam-3285	268	1	[	[	X
ejpam-3285	268	2	10	10	NUM
ejpam-3285	268	3	]	]	X
ejpam-3285	268	4	o	o	X
ejpam-3285	268	5	iyama	iyama	NOUN
ejpam-3285	268	6	.	.	PUNCT
ejpam-3285	269	1	finiteness	finiteness	NOUN
ejpam-3285	269	2	of	of	ADP
ejpam-3285	269	3	representation	representation	NOUN
ejpam-3285	269	4	dimension	dimension	NOUN
ejpam-3285	269	5	.	.	PUNCT
ejpam-3285	270	1	in	in	ADP
ejpam-3285	270	2	proceeding	proceeding	NOUN
ejpam-3285	270	3	of	of	ADP
ejpam-3285	270	4	the	the	DET
ejpam-3285	270	5	american	american	PROPN
ejpam-3285	270	6	mathematics	mathematics	PROPN
ejpam-3285	270	7	society	society	NOUN
ejpam-3285	270	8	,	,	PUNCT
ejpam-3285	270	9	volume	volume	NOUN
ejpam-3285	270	10	131	131	NUM
ejpam-3285	270	11	,	,	PUNCT
ejpam-3285	270	12	pages	page	NOUN
ejpam-3285	270	13	1011–1014	1011–1014	NUM
ejpam-3285	270	14	,	,	PUNCT
ejpam-3285	270	15	2002	2002	NUM
ejpam-3285	270	16	.	.	PUNCT
ejpam-3285	271	1	[	[	X
ejpam-3285	271	2	11	11	NUM
ejpam-3285	271	3	]	]	X
ejpam-3285	271	4	o	o	X
ejpam-3285	271	5	iyama	iyama	NOUN
ejpam-3285	271	6	.	.	PUNCT
ejpam-3285	272	1	auslander	auslander	NOUN
ejpam-3285	272	2	-	-	PUNCT
ejpam-3285	272	3	reiten	reiten	VERB
ejpam-3285	272	4	theory	theory	NOUN
ejpam-3285	272	5	revisited	revisit	VERB
ejpam-3285	272	6	.	.	PUNCT
ejpam-3285	273	1	pages	page	NOUN
ejpam-3285	273	2	1–47	1–47	PROPN
ejpam-3285	273	3	,	,	PUNCT
ejpam-3285	273	4	2008	2008	NUM
ejpam-3285	273	5	.	.	PUNCT
ejpam-3285	274	1	arxiv:0803.2841v2	arxiv:0803.2841v2	NOUN
ejpam-3285	274	2	.	.	PUNCT
ejpam-3285	275	1	[	[	X
ejpam-3285	275	2	12	12	NUM
ejpam-3285	275	3	]	]	X
ejpam-3285	275	4	d	d	X
ejpam-3285	275	5	lahat	lahat	PROPN
ejpam-3285	275	6	and	and	CCONJ
ejpam-3285	275	7	c	c	PROPN
ejpam-3285	275	8	jutten	jutten	PROPN
ejpam-3285	275	9	.	.	PUNCT
ejpam-3285	276	1	a	a	DET
ejpam-3285	276	2	generalization	generalization	NOUN
ejpam-3285	276	3	to	to	PART
ejpam-3285	276	4	schurs	schurs	VERB
ejpam-3285	276	5	lemma	lemma	PROPN
ejpam-3285	276	6	with	with	ADP
ejpam-3285	276	7	an	an	DET
ejpam-3285	276	8	application	application	NOUN
ejpam-3285	276	9	to	to	ADP
ejpam-3285	276	10	joint	joint	ADJ
ejpam-3285	276	11	independent	independent	ADJ
ejpam-3285	276	12	subspace	subspace	NOUN
ejpam-3285	276	13	analysis	analysis	NOUN
ejpam-3285	276	14	.	.	PUNCT
ejpam-3285	277	1	hal	hal	PROPN
ejpam-3285	277	2	i	i	PROPN
ejpam-3285	277	3	d	d	PROPN
ejpam-3285	277	4	:	:	PUNCT
ejpam-3285	277	5	hal-01247899	hal-01247899	NOUN
ejpam-3285	277	6	,	,	PUNCT
ejpam-3285	277	7	https://hal.archivesouvertes.fr/hal-01247899v2	https://hal.archivesouvertes.fr/hal-01247899v2	PROPN
ejpam-3285	277	8	,	,	PUNCT
ejpam-3285	277	9	2016	2016	NUM
ejpam-3285	277	10	.	.	PUNCT
ejpam-3285	278	1	[	[	X
ejpam-3285	278	2	13	13	NUM
ejpam-3285	278	3	]	]	PUNCT
ejpam-3285	278	4	t	t	PROPN
ejpam-3285	278	5	y	y	PROPN
ejpam-3285	278	6	lam	lam	PROPN
ejpam-3285	278	7	.	.	PUNCT
ejpam-3285	279	1	a	a	DET
ejpam-3285	279	2	first	first	ADJ
ejpam-3285	279	3	course	course	NOUN
ejpam-3285	279	4	in	in	ADP
ejpam-3285	279	5	noncommutative	noncommutative	ADJ
ejpam-3285	279	6	rings	ring	NOUN
ejpam-3285	279	7	.	.	PUNCT
ejpam-3285	280	1	springer	springer	NOUN
ejpam-3285	280	2	-	-	PUNCT
ejpam-3285	280	3	verlag	verlag	PROPN
ejpam-3285	280	4	,	,	PUNCT
ejpam-3285	280	5	new	new	PROPN
ejpam-3285	280	6	york	york	PROPN
ejpam-3285	280	7	,	,	PUNCT
ejpam-3285	280	8	1991	1991	NUM
ejpam-3285	280	9	.	.	PUNCT
ejpam-3285	281	1	references	reference	NOUN
ejpam-3285	281	2	761	761	NUM
ejpam-3285	282	1	[	[	X
ejpam-3285	282	2	14	14	NUM
ejpam-3285	282	3	]	]	PUNCT
ejpam-3285	282	4	s	s	PART
ejpam-3285	283	1	oppermann	oppermann	NOUN
ejpam-3285	283	2	.	.	PUNCT
ejpam-3285	283	3	representation	representation	NOUN
ejpam-3285	283	4	dimension	dimension	NOUN
ejpam-3285	283	5	of	of	ADP
ejpam-3285	283	6	artin	artin	PROPN
ejpam-3285	283	7	algebras	algebras	PROPN
ejpam-3285	283	8	.	.	PUNCT
ejpam-3285	284	1	são	são	PROPN
ejpam-3285	284	2	paulo	paulo	PROPN
ejpam-3285	284	3	journal	journal	PROPN
ejpam-3285	284	4	of	of	ADP
ejpam-3285	284	5	mathematics	mathematics	PROPN
ejpam-3285	284	6	science	science	NOUN
ejpam-3285	284	7	,	,	PUNCT
ejpam-3285	284	8	3:479–498	3:479–498	NUM
ejpam-3285	284	9	,	,	PUNCT
ejpam-3285	284	10	2010	2010	NUM
ejpam-3285	284	11	.	.	PUNCT
ejpam-3285	285	1	[	[	X
ejpam-3285	285	2	15	15	NUM
ejpam-3285	285	3	]	]	X
ejpam-3285	285	4	c	c	NOUN
ejpam-3285	285	5	m	m	NOUN
ejpam-3285	285	6	ringel	ringel	NOUN
ejpam-3285	285	7	.	.	PUNCT
ejpam-3285	285	8	representation	representation	NOUN
ejpam-3285	285	9	theory	theory	NOUN
ejpam-3285	285	10	of	of	ADP
ejpam-3285	285	11	finite	finite	ADJ
ejpam-3285	285	12	dimensional	dimensional	ADJ
ejpam-3285	285	13	algebras	algebra	NOUN
ejpam-3285	285	14	.	.	PUNCT
ejpam-3285	286	1	in	in	ADP
ejpam-3285	286	2	representations	representation	NOUN
ejpam-3285	286	3	of	of	ADP
ejpam-3285	286	4	algebras	algebra	NOUN
ejpam-3285	286	5	:	:	PUNCT
ejpam-3285	286	6	proceedings	proceeding	NOUN
ejpam-3285	286	7	of	of	ADP
ejpam-3285	286	8	the	the	DET
ejpam-3285	286	9	durham	durham	PROPN
ejpam-3285	286	10	symposium	symposium	NOUN
ejpam-3285	286	11	1985	1985	NUM
ejpam-3285	286	12	,	,	PUNCT
ejpam-3285	286	13	volume	volume	NOUN
ejpam-3285	286	14	116	116	NUM
ejpam-3285	286	15	of	of	ADP
ejpam-3285	286	16	london	london	PROPN
ejpam-3285	286	17	mathematical	mathematical	ADJ
ejpam-3285	286	18	society	society	NOUN
ejpam-3285	286	19	lecture	lecture	NOUN
ejpam-3285	286	20	note	note	NOUN
ejpam-3285	286	21	series	series	NOUN
ejpam-3285	286	22	,	,	PUNCT
ejpam-3285	286	23	pages	page	NOUN
ejpam-3285	286	24	7–79	7–79	ADV
ejpam-3285	286	25	.	.	PUNCT
ejpam-3285	287	1	cambridge	cambridge	NOUN
ejpam-3285	287	2	:	:	PUNCT
ejpam-3285	287	3	univ	univ	PROPN
ejpam-3285	287	4	,	,	PUNCT
ejpam-3285	287	5	1985	1985	NUM
ejpam-3285	287	6	.	.	PUNCT