id	sid	tid	token	lemma	pos
ejpam-5032	1	1	european	european	PROPN
ejpam-5032	1	2	journal	journal	PROPN
ejpam-5032	1	3	of	of	ADP
ejpam-5032	1	4	pure	pure	ADJ
ejpam-5032	1	5	and	and	CCONJ
ejpam-5032	1	6	applied	apply	VERB
ejpam-5032	1	7	mathematics	mathematic	NOUN
ejpam-5032	1	8	vol	vol	NOUN
ejpam-5032	1	9	.	.	PROPN
ejpam-5032	2	1	17	17	NUM
ejpam-5032	2	2	,	,	PUNCT
ejpam-5032	2	3	no	no	INTJ
ejpam-5032	2	4	.	.	NOUN
ejpam-5032	2	5	2	2	NUM
ejpam-5032	2	6	,	,	PUNCT
ejpam-5032	2	7	2024	2024	NUM
ejpam-5032	2	8	,	,	PUNCT
ejpam-5032	2	9	1206	1206	NUM
ejpam-5032	2	10	-	-	SYM
ejpam-5032	2	11	1212	1212	NUM
ejpam-5032	2	12	issn	issn	PROPN
ejpam-5032	2	13	1307	1307	NUM
ejpam-5032	2	14	-	-	SYM
ejpam-5032	2	15	5543	5543	NUM
ejpam-5032	2	16	–	–	PUNCT
ejpam-5032	3	1	ejpam.com	ejpam.com	X
ejpam-5032	3	2	published	publish	VERB
ejpam-5032	3	3	by	by	ADP
ejpam-5032	3	4	new	new	PROPN
ejpam-5032	3	5	york	york	PROPN
ejpam-5032	3	6	business	business	PROPN
ejpam-5032	3	7	global	global	PROPN
ejpam-5032	3	8	on	on	ADP
ejpam-5032	3	9	the	the	DET
ejpam-5032	3	10	prime	prime	ADJ
ejpam-5032	3	11	radical	radical	NOUN
ejpam-5032	3	12	of	of	ADP
ejpam-5032	3	13	nearrings	nearring	NOUN
ejpam-5032	3	14	which	which	PRON
ejpam-5032	3	15	is	be	AUX
ejpam-5032	3	16	kurosh	kurosh	ADV
ejpam-5032	3	17	-	-	PUNCT
ejpam-5032	3	18	amitsur	amitsur	PROPN
ejpam-5032	3	19	kilaru	kilaru	PROPN
ejpam-5032	3	20	j.	j.	PROPN
ejpam-5032	3	21	lakshminarayana1,∗	lakshminarayana1,∗	PROPN
ejpam-5032	3	22	,	,	PUNCT
ejpam-5032	3	23	v.b.v.n	v.b.v.n	PROPN
ejpam-5032	3	24	.	.	PROPN
ejpam-5032	3	25	prasad1	prasad1	PROPN
ejpam-5032	3	26	,	,	PUNCT
ejpam-5032	3	27	srinivasa	srinivasa	PROPN
ejpam-5032	3	28	rao	rao	PROPN
ejpam-5032	3	29	ravi2	ravi2	PROPN
ejpam-5032	3	30	,	,	PUNCT
ejpam-5032	3	31	a.v	a.v	PROPN
ejpam-5032	3	32	.	.	PUNCT
ejpam-5032	3	33	ramakrishna3	ramakrishna3	NOUN
ejpam-5032	3	34	1	1	NUM
ejpam-5032	3	35	department	department	NOUN
ejpam-5032	3	36	of	of	ADP
ejpam-5032	3	37	engineering	engineering	NOUN
ejpam-5032	3	38	mathematics	mathematics	PROPN
ejpam-5032	3	39	koneru	koneru	PROPN
ejpam-5032	3	40	lakshmaiah	lakshmaiah	PROPN
ejpam-5032	3	41	education	education	PROPN
ejpam-5032	3	42	foundation	foundation	PROPN
ejpam-5032	3	43	,	,	PUNCT
ejpam-5032	3	44	vaddeswaram-522502	vaddeswaram-522502	PROPN
ejpam-5032	3	45	guntur	guntur	PROPN
ejpam-5032	3	46	(	(	PUNCT
ejpam-5032	3	47	dist	dist	NOUN
ejpam-5032	3	48	.	.	PUNCT
ejpam-5032	3	49	)	)	PUNCT
ejpam-5032	3	50	,	,	PUNCT
ejpam-5032	3	51	andhra	andhra	PROPN
ejpam-5032	3	52	pradesh	pradesh	PROPN
ejpam-5032	3	53	,	,	PUNCT
ejpam-5032	3	54	india	india	PROPN
ejpam-5032	3	55	2	2	NUM
ejpam-5032	3	56	department	department	NOUN
ejpam-5032	3	57	of	of	ADP
ejpam-5032	3	58	mathematics	mathematics	PROPN
ejpam-5032	3	59	,	,	PUNCT
ejpam-5032	3	60	university	university	NOUN
ejpam-5032	3	61	college	college	NOUN
ejpam-5032	3	62	of	of	ADP
ejpam-5032	3	63	sciences	sciences	PROPN
ejpam-5032	3	64	,	,	PUNCT
ejpam-5032	3	65	acharya	acharya	PROPN
ejpam-5032	3	66	nagarjuna	nagarjuna	PROPN
ejpam-5032	3	67	university	university	PROPN
ejpam-5032	3	68	,	,	PUNCT
ejpam-5032	3	69	nagarjuna	nagarjuna	PROPN
ejpam-5032	3	70	nagar-522510	nagar-522510	PROPN
ejpam-5032	3	71	guntur	guntur	PROPN
ejpam-5032	3	72	(	(	PUNCT
ejpam-5032	3	73	dist	dist	NOUN
ejpam-5032	3	74	.	.	PUNCT
ejpam-5032	3	75	)	)	PUNCT
ejpam-5032	3	76	,	,	PUNCT
ejpam-5032	3	77	andhra	andhra	PROPN
ejpam-5032	3	78	pradesh	pradesh	PROPN
ejpam-5032	3	79	,	,	PUNCT
ejpam-5032	3	80	india	india	PROPN
ejpam-5032	3	81	3	3	PROPN
ejpam-5032	3	82	department	department	PROPN
ejpam-5032	3	83	of	of	ADP
ejpam-5032	3	84	mathematics	mathematic	NOUN
ejpam-5032	3	85	,	,	PUNCT
ejpam-5032	3	86	r.v.r	r.v.r	NOUN
ejpam-5032	3	87	and	and	CCONJ
ejpam-5032	3	88	j.c	j.c	PROPN
ejpam-5032	3	89	college	college	PROPN
ejpam-5032	3	90	of	of	ADP
ejpam-5032	3	91	engineering	engineering	NOUN
ejpam-5032	3	92	chowdavaram-522019	chowdavaram-522019	NOUN
ejpam-5032	3	93	guntur	guntur	PROPN
ejpam-5032	3	94	(	(	PUNCT
ejpam-5032	3	95	dist	dist	NOUN
ejpam-5032	3	96	.	.	PUNCT
ejpam-5032	3	97	)	)	PUNCT
ejpam-5032	3	98	,	,	PUNCT
ejpam-5032	3	99	andhra	andhra	PROPN
ejpam-5032	3	100	pradesh	pradesh	PROPN
ejpam-5032	3	101	,	,	PUNCT
ejpam-5032	3	102	india	india	PROPN
ejpam-5032	3	103	abstract	abstract	PROPN
ejpam-5032	3	104	.	.	PUNCT
ejpam-5032	4	1	a	a	DET
ejpam-5032	4	2	prime	prime	ADJ
ejpam-5032	4	3	radical	radical	NOUN
ejpam-5032	4	4	of	of	ADP
ejpam-5032	4	5	near	near	ADJ
ejpam-5032	4	6	-	-	PUNCT
ejpam-5032	4	7	rings	ring	NOUN
ejpam-5032	4	8	is	be	AUX
ejpam-5032	4	9	introduced	introduce	VERB
ejpam-5032	4	10	by	by	ADP
ejpam-5032	4	11	defining	define	VERB
ejpam-5032	4	12	a	a	DET
ejpam-5032	4	13	new	new	ADJ
ejpam-5032	4	14	class	class	NOUN
ejpam-5032	4	15	of	of	ADP
ejpam-5032	4	16	prime	prime	ADJ
ejpam-5032	4	17	modules	module	NOUN
ejpam-5032	4	18	of	of	ADP
ejpam-5032	4	19	near	near	ADJ
ejpam-5032	4	20	-	-	PUNCT
ejpam-5032	4	21	rings	ring	NOUN
ejpam-5032	4	22	.	.	PUNCT
ejpam-5032	5	1	it	it	PRON
ejpam-5032	5	2	is	be	AUX
ejpam-5032	5	3	a	a	DET
ejpam-5032	5	4	generalization	generalization	NOUN
ejpam-5032	5	5	of	of	ADP
ejpam-5032	5	6	the	the	DET
ejpam-5032	5	7	prime	prime	ADJ
ejpam-5032	5	8	radical	radical	NOUN
ejpam-5032	5	9	of	of	ADP
ejpam-5032	5	10	rings	ring	NOUN
ejpam-5032	5	11	.	.	PUNCT
ejpam-5032	6	1	properties	property	NOUN
ejpam-5032	6	2	of	of	ADP
ejpam-5032	6	3	the	the	DET
ejpam-5032	6	4	radical	radical	ADJ
ejpam-5032	6	5	are	be	AUX
ejpam-5032	6	6	studied	study	VERB
ejpam-5032	6	7	.	.	PUNCT
ejpam-5032	7	1	it	it	PRON
ejpam-5032	7	2	is	be	AUX
ejpam-5032	7	3	established	establish	VERB
ejpam-5032	7	4	that	that	SCONJ
ejpam-5032	7	5	this	this	DET
ejpam-5032	7	6	radical	radical	NOUN
ejpam-5032	7	7	is	be	AUX
ejpam-5032	7	8	a	a	DET
ejpam-5032	7	9	kurosh	kurosh	ADV
ejpam-5032	7	10	-	-	PUNCT
ejpam-5032	7	11	amitsur	amitsur	NOUN
ejpam-5032	7	12	radical	radical	NOUN
ejpam-5032	7	13	of	of	ADP
ejpam-5032	7	14	near	near	ADJ
ejpam-5032	7	15	-	-	PUNCT
ejpam-5032	7	16	rings	ring	NOUN
ejpam-5032	7	17	.	.	PUNCT
ejpam-5032	8	1	2020	2020	NUM
ejpam-5032	8	2	mathematics	mathematics	PROPN
ejpam-5032	8	3	subject	subject	NOUN
ejpam-5032	8	4	classifications	classification	NOUN
ejpam-5032	8	5	:	:	PUNCT
ejpam-5032	8	6	16y30	16y30	NUM
ejpam-5032	8	7	key	key	ADJ
ejpam-5032	8	8	words	word	NOUN
ejpam-5032	8	9	and	and	CCONJ
ejpam-5032	8	10	phrases	phrase	NOUN
ejpam-5032	8	11	:	:	PUNCT
ejpam-5032	8	12	near	near	ADJ
ejpam-5032	8	13	-	-	PUNCT
ejpam-5032	8	14	ring	ring	NOUN
ejpam-5032	8	15	,	,	PUNCT
ejpam-5032	8	16	n	n	CCONJ
ejpam-5032	8	17	-group	-group	NOUN
ejpam-5032	8	18	,	,	PUNCT
ejpam-5032	8	19	primen	priman	NOUN
ejpam-5032	8	20	-groups	-group	NOUN
ejpam-5032	8	21	of	of	ADP
ejpam-5032	8	22	type	type	NOUN
ejpam-5032	8	23	2	2	NUM
ejpam-5032	8	24	,	,	PUNCT
ejpam-5032	8	25	prime	prime	ADJ
ejpam-5032	8	26	radical	radical	NOUN
ejpam-5032	8	27	of	of	ADP
ejpam-5032	8	28	type	type	NOUN
ejpam-5032	8	29	2	2	NUM
ejpam-5032	8	30	1	1	NUM
ejpam-5032	8	31	.	.	PUNCT
ejpam-5032	9	1	introduction	introduction	NOUN
ejpam-5032	9	2	n	n	NOUN
ejpam-5032	9	3	is	be	AUX
ejpam-5032	9	4	a	a	DET
ejpam-5032	9	5	near	near	ADJ
ejpam-5032	9	6	-	-	PUNCT
ejpam-5032	9	7	ring	ring	NOUN
ejpam-5032	9	8	and	and	CCONJ
ejpam-5032	9	9	all	all	DET
ejpam-5032	9	10	near	near	ADJ
ejpam-5032	9	11	-	-	PUNCT
ejpam-5032	9	12	rings	ring	NOUN
ejpam-5032	9	13	are	be	AUX
ejpam-5032	9	14	zero	zero	NUM
ejpam-5032	9	15	-	-	PUNCT
ejpam-5032	9	16	symmetric	symmetric	ADJ
ejpam-5032	9	17	.	.	PUNCT
ejpam-5032	10	1	one	one	PRON
ejpam-5032	10	2	may	may	AUX
ejpam-5032	10	3	look	look	VERB
ejpam-5032	10	4	for	for	ADP
ejpam-5032	10	5	more	more	ADJ
ejpam-5032	10	6	definitions	definition	NOUN
ejpam-5032	10	7	and	and	CCONJ
ejpam-5032	10	8	results	result	NOUN
ejpam-5032	10	9	of	of	ADP
ejpam-5032	10	10	near	near	NOUN
ejpam-5032	10	11	-	-	PUNCT
ejpam-5032	10	12	rings	ring	NOUN
ejpam-5032	10	13	in	in	ADP
ejpam-5032	10	14	pliz	pliz	NOUN
ejpam-5032	10	15	[	[	X
ejpam-5032	10	16	4	4	NUM
ejpam-5032	10	17	]	]	PUNCT
ejpam-5032	10	18	.	.	PUNCT
ejpam-5032	11	1	an	an	DET
ejpam-5032	11	2	additive	additive	ADJ
ejpam-5032	11	3	group	group	NOUN
ejpam-5032	11	4	h	h	NOUN
ejpam-5032	11	5	is	be	AUX
ejpam-5032	11	6	a	a	DET
ejpam-5032	11	7	right	right	ADJ
ejpam-5032	11	8	n	n	ADP
ejpam-5032	11	9	-group	-group	NOUN
ejpam-5032	11	10	if	if	SCONJ
ejpam-5032	11	11	there	there	PRON
ejpam-5032	11	12	is	be	VERB
ejpam-5032	11	13	a	a	DET
ejpam-5032	11	14	mapping	mapping	NOUN
ejpam-5032	11	15	(	(	PUNCT
ejpam-5032	11	16	h	h	NOUN
ejpam-5032	11	17	,	,	PUNCT
ejpam-5032	11	18	x	x	NOUN
ejpam-5032	11	19	)	)	PUNCT
ejpam-5032	11	20	→	→	SYM
ejpam-5032	11	21	hx	hx	PROPN
ejpam-5032	11	22	of	of	ADP
ejpam-5032	11	23	h	h	PROPN
ejpam-5032	11	24	×n	×n	PRON
ejpam-5032	11	25	into	into	ADP
ejpam-5032	11	26	h	h	PRON
ejpam-5032	11	27	such	such	ADJ
ejpam-5032	11	28	that	that	PRON
ejpam-5032	11	29	:	:	PUNCT
ejpam-5032	11	30	(	(	PUNCT
ejpam-5032	11	31	i	i	NOUN
ejpam-5032	11	32	)	)	PUNCT
ejpam-5032	11	33	h(xy	h(xy	PROPN
ejpam-5032	11	34	)	)	PUNCT
ejpam-5032	12	1	=	=	PUNCT
ejpam-5032	12	2	(	(	PUNCT
ejpam-5032	12	3	hx)y	hx)y	PROPN
ejpam-5032	12	4	;	;	PUNCT
ejpam-5032	12	5	(	(	PUNCT
ejpam-5032	12	6	ii	ii	NOUN
ejpam-5032	12	7	)	)	PUNCT
ejpam-5032	13	1	h(x+	h(x+	PROPN
ejpam-5032	13	2	y	y	X
ejpam-5032	13	3	)	)	PUNCT
ejpam-5032	13	4	=	=	VERB
ejpam-5032	13	5	hx+	hx+	PROPN
ejpam-5032	13	6	hy	hy	PROPN
ejpam-5032	13	7	for	for	ADP
ejpam-5032	13	8	all	all	DET
ejpam-5032	13	9	h	h	NOUN
ejpam-5032	13	10	∈	∈	PROPN
ejpam-5032	13	11	h	h	NOUN
ejpam-5032	13	12	,	,	PUNCT
ejpam-5032	13	13	x	x	PRON
ejpam-5032	13	14	,	,	PUNCT
ejpam-5032	13	15	y	y	PROPN
ejpam-5032	13	16	∈	∈	PROPN
ejpam-5032	13	17	n	n	ADV
ejpam-5032	13	18	.	.	PUNCT
ejpam-5032	14	1	if	if	SCONJ
ejpam-5032	14	2	k	k	PROPN
ejpam-5032	14	3	is	be	AUX
ejpam-5032	14	4	a	a	DET
ejpam-5032	14	5	right	right	ADJ
ejpam-5032	14	6	ideal	ideal	NOUN
ejpam-5032	14	7	of	of	ADP
ejpam-5032	14	8	n	n	PROPN
ejpam-5032	14	9	then	then	ADV
ejpam-5032	14	10	k	k	PROPN
ejpam-5032	14	11	is	be	AUX
ejpam-5032	14	12	a	a	DET
ejpam-5032	14	13	right	right	NOUN
ejpam-5032	14	14	n	n	ADP
ejpam-5032	14	15	-group	-group	NOUN
ejpam-5032	14	16	under	under	ADP
ejpam-5032	14	17	the	the	DET
ejpam-5032	14	18	multiplication	multiplication	NOUN
ejpam-5032	14	19	in	in	ADP
ejpam-5032	14	20	n	n	PROPN
ejpam-5032	14	21	.	.	PUNCT
ejpam-5032	15	1	also	also	ADV
ejpam-5032	15	2	the	the	DET
ejpam-5032	15	3	quotient	quotient	NOUN
ejpam-5032	15	4	group	group	NOUN
ejpam-5032	15	5	n	n	CCONJ
ejpam-5032	15	6	/	/	SYM
ejpam-5032	15	7	k	k	PROPN
ejpam-5032	15	8	is	be	AUX
ejpam-5032	15	9	a	a	DET
ejpam-5032	15	10	right	right	NOUN
ejpam-5032	15	11	n	n	ADP
ejpam-5032	15	12	-group	-group	NOUN
ejpam-5032	15	13	under	under	ADP
ejpam-5032	15	14	the	the	DET
ejpam-5032	15	15	operation	operation	NOUN
ejpam-5032	15	16	(	(	PUNCT
ejpam-5032	15	17	x	x	X
ejpam-5032	16	1	+	+	NOUN
ejpam-5032	16	2	k)y	k)y	NOUN
ejpam-5032	16	3	=	=	PUNCT
ejpam-5032	16	4	xy	xy	PROPN
ejpam-5032	17	1	+	+	PROPN
ejpam-5032	17	2	k	k	PROPN
ejpam-5032	17	3	for	for	ADP
ejpam-5032	17	4	all	all	DET
ejpam-5032	17	5	x	x	NOUN
ejpam-5032	17	6	,	,	PUNCT
ejpam-5032	17	7	y	y	PROPN
ejpam-5032	17	8	∈	∈	PROPN
ejpam-5032	17	9	n	n	ADV
ejpam-5032	17	10	.	.	PUNCT
ejpam-5032	18	1	a	a	DET
ejpam-5032	18	2	subgroup	subgroup	NOUN
ejpam-5032	18	3	(	(	PUNCT
ejpam-5032	18	4	normal	normal	ADJ
ejpam-5032	18	5	subgroup	subgroup	NOUN
ejpam-5032	18	6	)	)	PUNCT
ejpam-5032	18	7	c	c	PROPN
ejpam-5032	18	8	of	of	ADP
ejpam-5032	18	9	the	the	DET
ejpam-5032	18	10	right	right	ADJ
ejpam-5032	18	11	n	n	CCONJ
ejpam-5032	18	12	-group	-group	NOUN
ejpam-5032	18	13	h	h	NOUN
ejpam-5032	18	14	is	be	AUX
ejpam-5032	18	15	a	a	DET
ejpam-5032	18	16	right	right	NOUN
ejpam-5032	18	17	n	n	PRON
ejpam-5032	18	18	-subgroup	-subgroup	NOUN
ejpam-5032	18	19	(	(	PUNCT
ejpam-5032	18	20	ideal	ideal	NOUN
ejpam-5032	18	21	)	)	PUNCT
ejpam-5032	18	22	of	of	ADP
ejpam-5032	18	23	h	h	NOUN
ejpam-5032	18	24	if	if	SCONJ
ejpam-5032	18	25	cx	cx	PROPN
ejpam-5032	18	26	∈	∈	PROPN
ejpam-5032	18	27	c	c	PROPN
ejpam-5032	18	28	for	for	ADP
ejpam-5032	18	29	all	all	DET
ejpam-5032	18	30	c	c	NOUN
ejpam-5032	18	31	∈	∈	PROPN
ejpam-5032	18	32	c	c	NOUN
ejpam-5032	18	33	,	,	PUNCT
ejpam-5032	18	34	x	x	SYM
ejpam-5032	18	35	∈	∈	NOUN
ejpam-5032	18	36	n	n	X
ejpam-5032	18	37	.	.	PUNCT
ejpam-5032	19	1	∗corresponding	∗corresponde	VERB
ejpam-5032	19	2	author	author	NOUN
ejpam-5032	19	3	.	.	PUNCT
ejpam-5032	20	1	doi	doi	NOUN
ejpam-5032	20	2	:	:	PUNCT
ejpam-5032	20	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5032	https://doi.org/10.29020/nybg.ejpam.v17i2.5032	DET
ejpam-5032	20	4	email	email	NOUN
ejpam-5032	20	5	addresses	address	NOUN
ejpam-5032	20	6	:	:	PUNCT
ejpam-5032	20	7	2002511005@kluniversity.in	2002511005@kluniversity.in	NUM
ejpam-5032	20	8	(	(	PUNCT
ejpam-5032	20	9	k.	k.	PROPN
ejpam-5032	20	10	j.	j.	PROPN
ejpam-5032	20	11	lakshminarayana	lakshminarayana	PROPN
ejpam-5032	20	12	)	)	PUNCT
ejpam-5032	20	13	,	,	PUNCT
ejpam-5032	20	14	vbvnprasad@kluniversity.in	vbvnprasad@kluniversity.in	ADV
ejpam-5032	20	15	(	(	PUNCT
ejpam-5032	20	16	v.b.v	v.b.v	NOUN
ejpam-5032	20	17	.	.	PUNCT
ejpam-5032	20	18	n.	n.	PROPN
ejpam-5032	20	19	prasad	prasad	PROPN
ejpam-5032	20	20	)	)	PUNCT
ejpam-5032	20	21	,	,	PUNCT
ejpam-5032	20	22	dr	dr	PROPN
ejpam-5032	20	23	rsrao@yahoo.com	rsrao@yahoo.com	PROPN
ejpam-5032	20	24	(	(	PUNCT
ejpam-5032	20	25	s.	s.	PROPN
ejpam-5032	20	26	rao	rao	PROPN
ejpam-5032	20	27	ravi	ravi	PROPN
ejpam-5032	20	28	)	)	PUNCT
ejpam-5032	20	29	,	,	PUNCT
ejpam-5032	20	30	amathi7@gmail.com	amathi7@gmail.com	X
ejpam-5032	20	31	(	(	PUNCT
ejpam-5032	20	32	a.	a.	PROPN
ejpam-5032	20	33	v.	v.	PROPN
ejpam-5032	20	34	ramakrishna	ramakrishna	PROPN
ejpam-5032	20	35	)	)	PUNCT
ejpam-5032	20	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5032	20	37	1206	1206	NUM
ejpam-5032	21	1	©	©	PROPN
ejpam-5032	21	2	2024	2024	NUM
ejpam-5032	21	3	ejpam	ejpam	NOUN
ejpam-5032	21	4	all	all	DET
ejpam-5032	21	5	rights	right	NOUN
ejpam-5032	21	6	reserved	reserve	VERB
ejpam-5032	21	7	.	.	PUNCT
ejpam-5032	22	1	k.	k.	PROPN
ejpam-5032	23	1	j.	j.	PROPN
ejpam-5032	23	2	lakshminarayana	lakshminarayana	PROPN
ejpam-5032	23	3	et	et	PROPN
ejpam-5032	24	1	al	al	PROPN
ejpam-5032	24	2	.	.	PUNCT
ejpam-5032	24	3	/	/	SYM
ejpam-5032	24	4	eur	eur	PROPN
ejpam-5032	24	5	.	.	PUNCT
ejpam-5032	25	1	j.	j.	PROPN
ejpam-5032	25	2	pure	pure	PROPN
ejpam-5032	25	3	appl	appl	PROPN
ejpam-5032	25	4	.	.	PROPN
ejpam-5032	25	5	math	math	PROPN
ejpam-5032	25	6	,	,	PUNCT
ejpam-5032	25	7	17	17	NUM
ejpam-5032	25	8	(	(	PUNCT
ejpam-5032	25	9	2	2	NUM
ejpam-5032	25	10	)	)	PUNCT
ejpam-5032	25	11	(	(	PUNCT
ejpam-5032	25	12	2024	2024	NUM
ejpam-5032	25	13	)	)	PUNCT
ejpam-5032	25	14	,	,	PUNCT
ejpam-5032	25	15	1206	1206	NUM
ejpam-5032	25	16	-	-	SYM
ejpam-5032	25	17	1212	1212	NUM
ejpam-5032	25	18	1207	1207	NUM
ejpam-5032	25	19	an	an	DET
ejpam-5032	25	20	element	element	NOUN
ejpam-5032	25	21	h0	h0	NOUN
ejpam-5032	25	22	∈	∈	PROPN
ejpam-5032	25	23	h	h	NOUN
ejpam-5032	25	24	is	be	AUX
ejpam-5032	25	25	a	a	DET
ejpam-5032	25	26	distributive	distributive	ADJ
ejpam-5032	25	27	element	element	NOUN
ejpam-5032	25	28	if	if	SCONJ
ejpam-5032	25	29	h0(x+	h0(x+	PROPN
ejpam-5032	25	30	y	y	PROPN
ejpam-5032	25	31	)	)	PUNCT
ejpam-5032	26	1	=	=	VERB
ejpam-5032	26	2	h0x+	h0x+	PROPN
ejpam-5032	26	3	h0y	h0y	PROPN
ejpam-5032	26	4	for	for	ADP
ejpam-5032	26	5	all	all	DET
ejpam-5032	26	6	x	x	NOUN
ejpam-5032	26	7	,	,	PUNCT
ejpam-5032	26	8	y	y	PROPN
ejpam-5032	26	9	∈	∈	PROPN
ejpam-5032	26	10	n	n	ADV
ejpam-5032	26	11	.	.	PUNCT
ejpam-5032	27	1	since	since	SCONJ
ejpam-5032	27	2	only	only	ADV
ejpam-5032	27	3	right	right	NOUN
ejpam-5032	27	4	n	n	PRON
ejpam-5032	27	5	-groups	-group	NOUN
ejpam-5032	27	6	are	be	AUX
ejpam-5032	27	7	considered	consider	VERB
ejpam-5032	27	8	,	,	PUNCT
ejpam-5032	27	9	hereon	hereon	NOUN
ejpam-5032	27	10	we	we	PRON
ejpam-5032	27	11	call	call	VERB
ejpam-5032	27	12	a	a	DET
ejpam-5032	27	13	right	right	NOUN
ejpam-5032	27	14	n	n	ADP
ejpam-5032	27	15	-group	-group	NOUN
ejpam-5032	27	16	just	just	ADV
ejpam-5032	27	17	an	an	DET
ejpam-5032	27	18	n	n	NUM
ejpam-5032	27	19	-group	-group	NOUN
ejpam-5032	27	20	and	and	CCONJ
ejpam-5032	27	21	a	a	DET
ejpam-5032	27	22	right	right	NOUN
ejpam-5032	28	1	n	n	PRON
ejpam-5032	28	2	-subgroup	-subgroup	NOUN
ejpam-5032	28	3	just	just	ADV
ejpam-5032	28	4	an	an	DET
ejpam-5032	28	5	n	n	ADV
ejpam-5032	28	6	-subgroup	-subgroup	NOUN
ejpam-5032	28	7	.	.	PUNCT
ejpam-5032	29	1	unlike	unlike	ADP
ejpam-5032	29	2	in	in	ADP
ejpam-5032	29	3	rings	ring	NOUN
ejpam-5032	29	4	the	the	DET
ejpam-5032	29	5	prime	prime	ADJ
ejpam-5032	29	6	radical	radical	NOUN
ejpam-5032	29	7	of	of	ADP
ejpam-5032	29	8	near	near	ADJ
ejpam-5032	29	9	-	-	PUNCT
ejpam-5032	29	10	rings	ring	NOUN
ejpam-5032	29	11	is	be	AUX
ejpam-5032	29	12	not	not	PART
ejpam-5032	29	13	a	a	DET
ejpam-5032	29	14	kurosh	kurosh	ADV
ejpam-5032	29	15	-	-	PUNCT
ejpam-5032	29	16	amitsur	amitsur	NOUN
ejpam-5032	29	17	radical	radical	ADJ
ejpam-5032	30	1	[	[	X
ejpam-5032	30	2	1	1	NUM
ejpam-5032	30	3	]	]	PUNCT
ejpam-5032	30	4	.	.	PUNCT
ejpam-5032	31	1	in	in	ADP
ejpam-5032	31	2	1990	1990	NUM
ejpam-5032	31	3	,	,	PUNCT
ejpam-5032	31	4	near	near	ADP
ejpam-5032	31	5	-	-	PUNCT
ejpam-5032	31	6	ringers	ringer	NOUN
ejpam-5032	31	7	could	could	AUX
ejpam-5032	31	8	introduce	introduce	VERB
ejpam-5032	31	9	a	a	DET
ejpam-5032	31	10	kurosh	kurosh	ADV
ejpam-5032	31	11	-	-	PUNCT
ejpam-5032	31	12	amitsur	amitsur	ADJ
ejpam-5032	31	13	prime	prime	ADJ
ejpam-5032	31	14	radical	radical	NOUN
ejpam-5032	31	15	of	of	ADP
ejpam-5032	31	16	near	near	ADJ
ejpam-5032	31	17	-	-	PUNCT
ejpam-5032	31	18	rings	ring	NOUN
ejpam-5032	31	19	[	[	X
ejpam-5032	31	20	2	2	NUM
ejpam-5032	31	21	]	]	PUNCT
ejpam-5032	31	22	,	,	PUNCT
ejpam-5032	31	23	called	call	VERB
ejpam-5032	31	24	the	the	DET
ejpam-5032	31	25	equiprime	equiprime	NOUN
ejpam-5032	31	26	radical	radical	ADJ
ejpam-5032	31	27	.	.	PUNCT
ejpam-5032	32	1	a	a	DET
ejpam-5032	32	2	characterization	characterization	NOUN
ejpam-5032	32	3	of	of	ADP
ejpam-5032	32	4	the	the	DET
ejpam-5032	32	5	prime	prime	ADJ
ejpam-5032	32	6	radical	radical	NOUN
ejpam-5032	32	7	of	of	ADP
ejpam-5032	32	8	near	near	ADJ
ejpam-5032	32	9	-	-	PUNCT
ejpam-5032	32	10	rings	ring	NOUN
ejpam-5032	32	11	was	be	AUX
ejpam-5032	32	12	given	give	VERB
ejpam-5032	32	13	in	in	ADP
ejpam-5032	32	14	[	[	X
ejpam-5032	32	15	5	5	NUM
ejpam-5032	32	16	]	]	PUNCT
ejpam-5032	32	17	using	use	VERB
ejpam-5032	32	18	right	right	ADJ
ejpam-5032	32	19	modules	module	NOUN
ejpam-5032	32	20	of	of	ADP
ejpam-5032	32	21	near	near	ADJ
ejpam-5032	32	22	-	-	PUNCT
ejpam-5032	32	23	rings	ring	NOUN
ejpam-5032	32	24	.	.	PUNCT
ejpam-5032	33	1	with	with	ADP
ejpam-5032	33	2	this	this	DET
ejpam-5032	33	3	motivation	motivation	NOUN
ejpam-5032	33	4	right	right	ADJ
ejpam-5032	33	5	representation	representation	NOUN
ejpam-5032	33	6	of	of	ADP
ejpam-5032	33	7	radicals	radical	NOUN
ejpam-5032	33	8	of	of	ADP
ejpam-5032	33	9	right	right	ADJ
ejpam-5032	33	10	near	near	NOUN
ejpam-5032	33	11	-	-	PUNCT
ejpam-5032	33	12	ring	ring	NOUN
ejpam-5032	33	13	was	be	AUX
ejpam-5032	33	14	presented	present	VERB
ejpam-5032	33	15	in	in	ADP
ejpam-5032	33	16	[	[	X
ejpam-5032	33	17	7	7	NUM
ejpam-5032	33	18	]	]	PUNCT
ejpam-5032	33	19	and	and	CCONJ
ejpam-5032	33	20	a	a	DET
ejpam-5032	33	21	prime	prime	ADJ
ejpam-5032	33	22	radical	radical	NOUN
ejpam-5032	33	23	for	for	ADP
ejpam-5032	33	24	near	near	ADJ
ejpam-5032	33	25	-	-	PUNCT
ejpam-5032	33	26	rings	ring	NOUN
ejpam-5032	33	27	,	,	PUNCT
ejpam-5032	33	28	the	the	DET
ejpam-5032	33	29	right	right	ADJ
ejpam-5032	33	30	prime	prime	ADJ
ejpam-5032	33	31	radical	radical	NOUN
ejpam-5032	33	32	of	of	ADP
ejpam-5032	33	33	type	type	NOUN
ejpam-5032	33	34	1	1	NUM
ejpam-5032	33	35	,	,	PUNCT
ejpam-5032	33	36	was	be	AUX
ejpam-5032	33	37	defined	define	VERB
ejpam-5032	33	38	and	and	CCONJ
ejpam-5032	33	39	studied	study	VERB
ejpam-5032	33	40	in	in	ADP
ejpam-5032	33	41	[	[	X
ejpam-5032	33	42	6	6	NUM
ejpam-5032	33	43	]	]	PUNCT
ejpam-5032	33	44	which	which	PRON
ejpam-5032	33	45	is	be	AUX
ejpam-5032	33	46	a	a	DET
ejpam-5032	33	47	non	non	ADJ
ejpam-5032	33	48	-	-	ADJ
ejpam-5032	33	49	ideal	ideal	ADJ
ejpam-5032	33	50	hereditary	hereditary	ADJ
ejpam-5032	33	51	kuroshamitsur	kuroshamitsur	NOUN
ejpam-5032	33	52	radical	radical	ADJ
ejpam-5032	33	53	.	.	PUNCT
ejpam-5032	34	1	this	this	PRON
ejpam-5032	34	2	is	be	AUX
ejpam-5032	34	3	the	the	DET
ejpam-5032	34	4	second	second	ADV
ejpam-5032	34	5	known	know	VERB
ejpam-5032	34	6	kurosh	kurosh	PROPN
ejpam-5032	34	7	-	-	PUNCT
ejpam-5032	34	8	amitsur	amitsur	ADJ
ejpam-5032	34	9	prime	prime	PROPN
ejpam-5032	34	10	radical	radical	NOUN
ejpam-5032	34	11	of	of	ADP
ejpam-5032	34	12	near	near	ADJ
ejpam-5032	34	13	-	-	PUNCT
ejpam-5032	34	14	rings	ring	NOUN
ejpam-5032	34	15	.	.	PUNCT
ejpam-5032	35	1	in	in	ADP
ejpam-5032	35	2	this	this	DET
ejpam-5032	35	3	paper	paper	NOUN
ejpam-5032	35	4	,	,	PUNCT
ejpam-5032	35	5	using	use	VERB
ejpam-5032	35	6	right	right	ADJ
ejpam-5032	35	7	modules	module	NOUN
ejpam-5032	35	8	,	,	PUNCT
ejpam-5032	35	9	another	another	DET
ejpam-5032	35	10	prime	prime	ADJ
ejpam-5032	35	11	radical	radical	NOUN
ejpam-5032	35	12	is	be	AUX
ejpam-5032	35	13	introduced	introduce	VERB
ejpam-5032	35	14	for	for	ADP
ejpam-5032	35	15	near	near	NOUN
ejpam-5032	35	16	-	-	PUNCT
ejpam-5032	35	17	rings	ring	NOUN
ejpam-5032	35	18	which	which	PRON
ejpam-5032	35	19	is	be	AUX
ejpam-5032	35	20	a	a	DET
ejpam-5032	35	21	kurosh	kurosh	ADV
ejpam-5032	35	22	-	-	PUNCT
ejpam-5032	35	23	amitsur	amitsur	NOUN
ejpam-5032	35	24	radical	radical	NOUN
ejpam-5032	35	25	.	.	PUNCT
ejpam-5032	36	1	2	2	X
ejpam-5032	36	2	.	.	X
ejpam-5032	36	3	prime	prime	ADJ
ejpam-5032	36	4	n	n	CCONJ
ejpam-5032	36	5	-	-	PUNCT
ejpam-5032	36	6	groups	group	NOUN
ejpam-5032	36	7	of	of	ADP
ejpam-5032	36	8	type	type	NOUN
ejpam-5032	36	9	2	2	NUM
ejpam-5032	36	10	let	let	VERB
ejpam-5032	36	11	h	h	NOUN
ejpam-5032	36	12	be	be	AUX
ejpam-5032	36	13	an	an	DET
ejpam-5032	36	14	n	n	NUM
ejpam-5032	36	15	-group	-group	NOUN
ejpam-5032	36	16	.	.	PUNCT
ejpam-5032	37	1	the	the	DET
ejpam-5032	37	2	annihilator	annihilator	NOUN
ejpam-5032	37	3	of	of	ADP
ejpam-5032	37	4	h	h	PROPN
ejpam-5032	37	5	in	in	ADP
ejpam-5032	37	6	n	n	NUM
ejpam-5032	37	7	will	will	AUX
ejpam-5032	37	8	be	be	AUX
ejpam-5032	37	9	denoted	denote	VERB
ejpam-5032	37	10	by	by	ADP
ejpam-5032	37	11	an(h	an(h	NOUN
ejpam-5032	37	12	)	)	PUNCT
ejpam-5032	37	13	:	:	PUNCT
ejpam-5032	38	1	=	=	SYM
ejpam-5032	38	2	{	{	PUNCT
ejpam-5032	38	3	x	x	SYM
ejpam-5032	38	4	∈	∈	PROPN
ejpam-5032	38	5	n	n	CCONJ
ejpam-5032	38	6	|	|	ADV
ejpam-5032	38	7	hx	hx	PROPN
ejpam-5032	39	1	=	=	NOUN
ejpam-5032	39	2	0	0	NUM
ejpam-5032	39	3	for	for	ADP
ejpam-5032	39	4	all	all	DET
ejpam-5032	39	5	h	h	NOUN
ejpam-5032	39	6	∈	∈	PROPN
ejpam-5032	39	7	h	h	NOUN
ejpam-5032	39	8	}	}	PUNCT
ejpam-5032	39	9	.	.	PUNCT
ejpam-5032	40	1	the	the	DET
ejpam-5032	40	2	largest	large	ADJ
ejpam-5032	40	3	ideal	ideal	NOUN
ejpam-5032	40	4	of	of	ADP
ejpam-5032	40	5	n	n	NUM
ejpam-5032	40	6	contained	contain	VERB
ejpam-5032	40	7	in	in	ADP
ejpam-5032	40	8	an(h	an(h	NUM
ejpam-5032	40	9	)	)	PUNCT
ejpam-5032	40	10	,	,	PUNCT
ejpam-5032	40	11	if	if	SCONJ
ejpam-5032	40	12	it	it	PRON
ejpam-5032	40	13	exists	exist	VERB
ejpam-5032	40	14	,	,	PUNCT
ejpam-5032	40	15	will	will	AUX
ejpam-5032	40	16	be	be	AUX
ejpam-5032	40	17	denoted	denote	VERB
ejpam-5032	40	18	by	by	ADP
ejpam-5032	40	19	(	(	PUNCT
ejpam-5032	40	20	h	h	NOUN
ejpam-5032	40	21	:	:	PUNCT
ejpam-5032	40	22	0	0	NUM
ejpam-5032	40	23	)	)	PUNCT
ejpam-5032	40	24	.	.	PUNCT
ejpam-5032	41	1	definition	definition	NOUN
ejpam-5032	41	2	1	1	NUM
ejpam-5032	41	3	.	.	PUNCT
ejpam-5032	42	1	let	let	VERB
ejpam-5032	42	2	n	n	PRON
ejpam-5032	42	3	be	be	AUX
ejpam-5032	42	4	a	a	DET
ejpam-5032	42	5	near	near	ADJ
ejpam-5032	42	6	-	-	PUNCT
ejpam-5032	42	7	ring	ring	NOUN
ejpam-5032	42	8	and	and	CCONJ
ejpam-5032	42	9	h	h	NOUN
ejpam-5032	42	10	be	be	AUX
ejpam-5032	42	11	an	an	DET
ejpam-5032	42	12	n	n	NUM
ejpam-5032	42	13	-group	-group	NOUN
ejpam-5032	42	14	.	.	PUNCT
ejpam-5032	43	1	h	h	PROPN
ejpam-5032	43	2	is	be	AUX
ejpam-5032	43	3	a	a	DET
ejpam-5032	43	4	prime	prime	ADJ
ejpam-5032	43	5	n	n	ADP
ejpam-5032	43	6	-group	-group	NOUN
ejpam-5032	43	7	of	of	ADP
ejpam-5032	43	8	type	type	NOUN
ejpam-5032	43	9	2	2	NUM
ejpam-5032	43	10	if	if	SCONJ
ejpam-5032	43	11	:	:	PUNCT
ejpam-5032	43	12	(	(	PUNCT
ejpam-5032	43	13	i	i	NOUN
ejpam-5032	43	14	)	)	PUNCT
ejpam-5032	43	15	hn	hn	PROPN
ejpam-5032	43	16	̸=	̸=	PROPN
ejpam-5032	43	17	{	{	PUNCT
ejpam-5032	43	18	0	0	NUM
ejpam-5032	43	19	}	}	PUNCT
ejpam-5032	43	20	;	;	PUNCT
ejpam-5032	43	21	(	(	PUNCT
ejpam-5032	43	22	ii	ii	NOUN
ejpam-5032	43	23	)	)	PUNCT
ejpam-5032	43	24	for	for	ADP
ejpam-5032	43	25	each	each	DET
ejpam-5032	43	26	0	0	NUM
ejpam-5032	43	27	̸=	̸=	PROPN
ejpam-5032	43	28	h	h	NOUN
ejpam-5032	43	29	∈	∈	PROPN
ejpam-5032	43	30	h	h	NOUN
ejpam-5032	43	31	,	,	PUNCT
ejpam-5032	43	32	hn	hn	PROPN
ejpam-5032	43	33	has	have	VERB
ejpam-5032	43	34	a	a	DET
ejpam-5032	43	35	distributive	distributive	ADJ
ejpam-5032	43	36	element	element	NOUN
ejpam-5032	43	37	h0(̸=	h0(̸=	PROPN
ejpam-5032	43	38	0	0	NUM
ejpam-5032	43	39	)	)	PUNCT
ejpam-5032	43	40	;	;	PUNCT
ejpam-5032	43	41	(	(	PUNCT
ejpam-5032	43	42	iii	iii	X
ejpam-5032	43	43	)	)	PUNCT
ejpam-5032	43	44	for	for	ADP
ejpam-5032	43	45	each	each	DET
ejpam-5032	43	46	0	0	NUM
ejpam-5032	43	47	̸=	̸=	PROPN
ejpam-5032	43	48	h	h	NOUN
ejpam-5032	43	49	∈	∈	PROPN
ejpam-5032	43	50	h	h	NOUN
ejpam-5032	43	51	,	,	PUNCT
ejpam-5032	43	52	an(hn	an(hn	PROPN
ejpam-5032	43	53	)	)	PUNCT
ejpam-5032	43	54	=	=	SYM
ejpam-5032	43	55	an	an	DET
ejpam-5032	43	56	(	(	PUNCT
ejpam-5032	43	57	h	h	NOUN
ejpam-5032	43	58	)	)	PUNCT
ejpam-5032	43	59	.	.	PUNCT
ejpam-5032	44	1	if	if	SCONJ
ejpam-5032	44	2	the	the	DET
ejpam-5032	44	3	near	near	NOUN
ejpam-5032	44	4	-	-	PUNCT
ejpam-5032	44	5	ring	ring	NOUN
ejpam-5032	44	6	n	n	NOUN
ejpam-5032	44	7	is	be	AUX
ejpam-5032	44	8	a	a	DET
ejpam-5032	44	9	ring	ring	NOUN
ejpam-5032	44	10	then	then	ADV
ejpam-5032	44	11	from	from	ADP
ejpam-5032	44	12	the	the	DET
ejpam-5032	44	13	conditions	condition	NOUN
ejpam-5032	44	14	(	(	PUNCT
ejpam-5032	44	15	i	i	NOUN
ejpam-5032	44	16	)	)	PUNCT
ejpam-5032	44	17	and	and	CCONJ
ejpam-5032	44	18	(	(	PUNCT
ejpam-5032	44	19	iii	iii	NOUN
ejpam-5032	44	20	)	)	PUNCT
ejpam-5032	44	21	of	of	ADP
ejpam-5032	44	22	the	the	DET
ejpam-5032	44	23	prime	prime	ADJ
ejpam-5032	44	24	n	n	ADP
ejpam-5032	44	25	-group	-group	NOUN
ejpam-5032	44	26	of	of	ADP
ejpam-5032	44	27	type	type	NOUN
ejpam-5032	44	28	2	2	NUM
ejpam-5032	44	29	it	it	PRON
ejpam-5032	44	30	follows	follow	VERB
ejpam-5032	44	31	that	that	SCONJ
ejpam-5032	44	32	it	it	PRON
ejpam-5032	44	33	is	be	AUX
ejpam-5032	44	34	a	a	DET
ejpam-5032	44	35	prime	prime	ADJ
ejpam-5032	44	36	module	module	NOUN
ejpam-5032	44	37	[	[	X
ejpam-5032	44	38	3	3	NUM
ejpam-5032	44	39	]	]	PUNCT
ejpam-5032	44	40	.	.	PUNCT
ejpam-5032	45	1	it	it	PRON
ejpam-5032	45	2	is	be	AUX
ejpam-5032	45	3	clear	clear	ADJ
ejpam-5032	45	4	that	that	SCONJ
ejpam-5032	45	5	a	a	DET
ejpam-5032	45	6	non	non	ADJ
ejpam-5032	45	7	-	-	ADJ
ejpam-5032	45	8	zeron	zeron	ADJ
ejpam-5032	45	9	-subgroup	-subgroup	PROPN
ejpam-5032	45	10	of	of	ADP
ejpam-5032	45	11	a	a	DET
ejpam-5032	45	12	primen	priman	NOUN
ejpam-5032	45	13	-group	-group	NOUN
ejpam-5032	45	14	of	of	ADP
ejpam-5032	45	15	type	type	NOUN
ejpam-5032	45	16	2	2	NUM
ejpam-5032	45	17	is	be	AUX
ejpam-5032	45	18	also	also	ADV
ejpam-5032	45	19	a	a	DET
ejpam-5032	45	20	primen	priman	NOUN
ejpam-5032	45	21	-group	-group	NOUN
ejpam-5032	45	22	of	of	ADP
ejpam-5032	45	23	type	type	NOUN
ejpam-5032	45	24	2	2	NUM
ejpam-5032	45	25	.	.	NOUN
ejpam-5032	45	26	example	example	NOUN
ejpam-5032	46	1	1	1	NUM
ejpam-5032	46	2	.	.	PUNCT
ejpam-5032	47	1	we	we	PRON
ejpam-5032	47	2	give	give	VERB
ejpam-5032	47	3	an	an	DET
ejpam-5032	47	4	example	example	NOUN
ejpam-5032	47	5	of	of	ADP
ejpam-5032	47	6	a	a	DET
ejpam-5032	47	7	prime	prime	ADJ
ejpam-5032	47	8	n	n	ADP
ejpam-5032	47	9	-group	-group	NOUN
ejpam-5032	47	10	of	of	ADP
ejpam-5032	47	11	type	type	NOUN
ejpam-5032	47	12	2	2	NUM
ejpam-5032	47	13	.	.	PUNCT
ejpam-5032	48	1	let	let	AUX
ejpam-5032	48	2	h	h	NOUN
ejpam-5032	48	3	:	:	PUNCT
ejpam-5032	48	4	=	=	SYM
ejpam-5032	48	5	{	{	PUNCT
ejpam-5032	48	6	0	0	NUM
ejpam-5032	48	7	,	,	PUNCT
ejpam-5032	48	8	a	a	DET
ejpam-5032	48	9	,	,	PUNCT
ejpam-5032	48	10	b	b	NOUN
ejpam-5032	48	11	,	,	PUNCT
ejpam-5032	48	12	c	c	AUX
ejpam-5032	48	13	}	}	PUNCT
ejpam-5032	48	14	be	be	AUX
ejpam-5032	48	15	the	the	DET
ejpam-5032	48	16	additive	additive	ADJ
ejpam-5032	48	17	non	non	ADJ
ejpam-5032	48	18	-	-	ADJ
ejpam-5032	48	19	cyclic	cyclic	ADJ
ejpam-5032	48	20	group	group	NOUN
ejpam-5032	48	21	of	of	ADP
ejpam-5032	48	22	order	order	NOUN
ejpam-5032	48	23	4	4	NUM
ejpam-5032	48	24	.	.	PUNCT
ejpam-5032	48	25	consider	consider	VERB
ejpam-5032	48	26	the	the	DET
ejpam-5032	48	27	near	near	NOUN
ejpam-5032	48	28	-	-	PUNCT
ejpam-5032	48	29	ring	ring	NOUN
ejpam-5032	48	30	m0(h	m0(h	NOUN
ejpam-5032	48	31	)	)	PUNCT
ejpam-5032	48	32	of	of	ADP
ejpam-5032	48	33	mappings	mapping	NOUN
ejpam-5032	48	34	of	of	ADP
ejpam-5032	48	35	h	h	NOUN
ejpam-5032	48	36	into	into	ADP
ejpam-5032	48	37	h	h	NOUN
ejpam-5032	48	38	fixing	fix	VERB
ejpam-5032	48	39	0	0	NUM
ejpam-5032	48	40	.	.	PUNCT
ejpam-5032	49	1	we	we	PRON
ejpam-5032	49	2	claim	claim	VERB
ejpam-5032	49	3	that	that	SCONJ
ejpam-5032	49	4	the	the	DET
ejpam-5032	49	5	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	49	6	m0(h	m0(h	PROPN
ejpam-5032	49	7	)	)	PUNCT
ejpam-5032	49	8	is	be	AUX
ejpam-5032	49	9	a	a	DET
ejpam-5032	49	10	prime	prime	ADJ
ejpam-5032	49	11	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	49	12	of	of	ADP
ejpam-5032	49	13	type	type	NOUN
ejpam-5032	49	14	2	2	NUM
ejpam-5032	49	15	.	.	PUNCT
ejpam-5032	50	1	it	it	PRON
ejpam-5032	50	2	is	be	AUX
ejpam-5032	50	3	clear	clear	ADJ
ejpam-5032	50	4	that	that	SCONJ
ejpam-5032	50	5	the	the	DET
ejpam-5032	50	6	distributive	distributive	ADJ
ejpam-5032	50	7	elements	element	NOUN
ejpam-5032	50	8	of	of	ADP
ejpam-5032	50	9	the	the	DET
ejpam-5032	50	10	near	near	ADV
ejpam-5032	50	11	-	-	PUNCT
ejpam-5032	50	12	ring	ring	NOUN
ejpam-5032	50	13	m0(h	m0(h	X
ejpam-5032	50	14	)	)	PUNCT
ejpam-5032	50	15	are	be	AUX
ejpam-5032	50	16	precisely	precisely	ADV
ejpam-5032	50	17	the	the	DET
ejpam-5032	50	18	endomorphisms	endomorphism	NOUN
ejpam-5032	50	19	of	of	ADP
ejpam-5032	50	20	group	group	NOUN
ejpam-5032	50	21	h	h	NOUN
ejpam-5032	50	22	and	and	CCONJ
ejpam-5032	50	23	are	be	AUX
ejpam-5032	50	24	also	also	ADV
ejpam-5032	50	25	the	the	DET
ejpam-5032	50	26	distributive	distributive	ADJ
ejpam-5032	50	27	elements	element	NOUN
ejpam-5032	50	28	of	of	ADP
ejpam-5032	50	29	the	the	DET
ejpam-5032	50	30	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	50	31	m0(h	m0(h	PROPN
ejpam-5032	50	32	)	)	PUNCT
ejpam-5032	50	33	.	.	PUNCT
ejpam-5032	51	1	(	(	PUNCT
ejpam-5032	51	2	i	i	NOUN
ejpam-5032	51	3	)	)	PUNCT
ejpam-5032	51	4	we	we	PRON
ejpam-5032	51	5	have	have	VERB
ejpam-5032	51	6	m0(h)m0(h	m0(h)m0(h	ADJ
ejpam-5032	51	7	)	)	PUNCT
ejpam-5032	51	8	̸=	̸=	PROPN
ejpam-5032	51	9	{	{	PUNCT
ejpam-5032	51	10	0	0	NUM
ejpam-5032	51	11	}	}	PUNCT
ejpam-5032	51	12	;	;	PUNCT
ejpam-5032	51	13	(	(	PUNCT
ejpam-5032	51	14	ii	ii	NOUN
ejpam-5032	51	15	)	)	PUNCT
ejpam-5032	51	16	let	let	VERB
ejpam-5032	51	17	0	0	NUM
ejpam-5032	51	18	̸=	̸=	PROPN
ejpam-5032	51	19	f	f	PROPN
ejpam-5032	51	20	∈	∈	PROPN
ejpam-5032	51	21	m0(h	m0(h	PROPN
ejpam-5032	51	22	)	)	PUNCT
ejpam-5032	51	23	.	.	PUNCT
ejpam-5032	52	1	we	we	PRON
ejpam-5032	52	2	suppose	suppose	VERB
ejpam-5032	52	3	without	without	ADP
ejpam-5032	52	4	loss	loss	NOUN
ejpam-5032	52	5	of	of	ADP
ejpam-5032	52	6	generality	generality	NOUN
ejpam-5032	52	7	that	that	PRON
ejpam-5032	52	8	f(a	f(a	NOUN
ejpam-5032	52	9	)	)	PUNCT
ejpam-5032	52	10	̸=	̸=	NOUN
ejpam-5032	52	11	0	0	NUM
ejpam-5032	52	12	and	and	CCONJ
ejpam-5032	52	13	f(a	f(a	NOUN
ejpam-5032	52	14	)	)	PUNCT
ejpam-5032	53	1	=	=	SYM
ejpam-5032	53	2	x	x	X
ejpam-5032	53	3	,	,	PUNCT
ejpam-5032	53	4	x	x	SYM
ejpam-5032	53	5	∈	∈	PROPN
ejpam-5032	53	6	{	{	PUNCT
ejpam-5032	53	7	a	a	PROPN
ejpam-5032	53	8	,	,	PUNCT
ejpam-5032	53	9	b	b	NOUN
ejpam-5032	53	10	,	,	PUNCT
ejpam-5032	53	11	c	c	NOUN
ejpam-5032	53	12	}	}	PUNCT
ejpam-5032	53	13	.	.	PUNCT
ejpam-5032	54	1	we	we	PRON
ejpam-5032	54	2	choose	choose	VERB
ejpam-5032	54	3	g	g	PROPN
ejpam-5032	54	4	∈	∈	PROPN
ejpam-5032	54	5	m0(h	m0(h	PROPN
ejpam-5032	54	6	)	)	PUNCT
ejpam-5032	54	7	such	such	ADJ
ejpam-5032	54	8	that	that	DET
ejpam-5032	54	9	g(a	g(a	PROPN
ejpam-5032	54	10	)	)	PUNCT
ejpam-5032	55	1	=	=	PUNCT
ejpam-5032	55	2	a	a	DET
ejpam-5032	55	3	=	=	SYM
ejpam-5032	55	4	g(c	g(c	NOUN
ejpam-5032	55	5	)	)	PUNCT
ejpam-5032	55	6	,	,	PUNCT
ejpam-5032	55	7	g(b	g(b	X
ejpam-5032	55	8	)	)	PUNCT
ejpam-5032	55	9	=	=	SYM
ejpam-5032	56	1	0	0	X
ejpam-5032	56	2	.	.	PUNCT
ejpam-5032	57	1	now	now	ADV
ejpam-5032	57	2	fg	fg	PROPN
ejpam-5032	57	3	is	be	AUX
ejpam-5032	57	4	an	an	DET
ejpam-5032	57	5	endomorphism	endomorphism	NOUN
ejpam-5032	57	6	of	of	ADP
ejpam-5032	57	7	h	h	NOUN
ejpam-5032	57	8	and	and	CCONJ
ejpam-5032	57	9	hence	hence	ADV
ejpam-5032	57	10	a	a	DET
ejpam-5032	57	11	distributive	distributive	ADJ
ejpam-5032	57	12	element	element	NOUN
ejpam-5032	57	13	in	in	ADP
ejpam-5032	57	14	fm0(h	fm0(h	PROPN
ejpam-5032	57	15	)	)	PUNCT
ejpam-5032	57	16	;	;	PUNCT
ejpam-5032	57	17	(	(	PUNCT
ejpam-5032	57	18	iii	iii	X
ejpam-5032	57	19	)	)	PUNCT
ejpam-5032	57	20	let	let	VERB
ejpam-5032	57	21	0	0	NUM
ejpam-5032	58	1	̸=	̸=	PROPN
ejpam-5032	58	2	f	f	PROPN
ejpam-5032	58	3	∈	∈	PROPN
ejpam-5032	58	4	m0(h	m0(h	PROPN
ejpam-5032	58	5	)	)	PUNCT
ejpam-5032	58	6	.	.	PUNCT
ejpam-5032	59	1	it	it	PRON
ejpam-5032	59	2	is	be	AUX
ejpam-5032	59	3	clear	clear	ADJ
ejpam-5032	59	4	that	that	SCONJ
ejpam-5032	59	5	an(fm0(h	an(fm0(h	PROPN
ejpam-5032	59	6	)	)	PUNCT
ejpam-5032	59	7	)	)	PUNCT
ejpam-5032	60	1	=	=	PRON
ejpam-5032	60	2	{	{	PUNCT
ejpam-5032	60	3	0	0	NUM
ejpam-5032	60	4	}	}	PUNCT
ejpam-5032	60	5	=	=	SYM
ejpam-5032	60	6	an(m0(h	an(m0(h	NOUN
ejpam-5032	60	7	)	)	PUNCT
ejpam-5032	60	8	)	)	PUNCT
ejpam-5032	60	9	.	.	PUNCT
ejpam-5032	61	1	therefore	therefore	ADV
ejpam-5032	61	2	m0(h	m0(h	X
ejpam-5032	61	3	)	)	PUNCT
ejpam-5032	61	4	is	be	AUX
ejpam-5032	61	5	a	a	DET
ejpam-5032	61	6	prime	prime	ADJ
ejpam-5032	61	7	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	61	8	of	of	ADP
ejpam-5032	61	9	type	type	NOUN
ejpam-5032	61	10	2	2	NUM
ejpam-5032	61	11	.	.	PUNCT
ejpam-5032	62	1	k.	k.	PROPN
ejpam-5032	63	1	j.	j.	PROPN
ejpam-5032	63	2	lakshminarayana	lakshminarayana	PROPN
ejpam-5032	63	3	et	et	PROPN
ejpam-5032	64	1	al	al	PROPN
ejpam-5032	64	2	.	.	PUNCT
ejpam-5032	64	3	/	/	SYM
ejpam-5032	64	4	eur	eur	PROPN
ejpam-5032	64	5	.	.	PUNCT
ejpam-5032	65	1	j.	j.	PROPN
ejpam-5032	65	2	pure	pure	PROPN
ejpam-5032	65	3	appl	appl	PROPN
ejpam-5032	65	4	.	.	PROPN
ejpam-5032	65	5	math	math	PROPN
ejpam-5032	65	6	,	,	PUNCT
ejpam-5032	65	7	17	17	NUM
ejpam-5032	65	8	(	(	PUNCT
ejpam-5032	65	9	2	2	NUM
ejpam-5032	65	10	)	)	PUNCT
ejpam-5032	65	11	(	(	PUNCT
ejpam-5032	65	12	2024	2024	NUM
ejpam-5032	65	13	)	)	PUNCT
ejpam-5032	65	14	,	,	PUNCT
ejpam-5032	65	15	1206	1206	NUM
ejpam-5032	65	16	-	-	SYM
ejpam-5032	65	17	1212	1212	NUM
ejpam-5032	65	18	1208	1208	NUM
ejpam-5032	65	19	we	we	PRON
ejpam-5032	65	20	give	give	VERB
ejpam-5032	65	21	an	an	DET
ejpam-5032	65	22	example	example	NOUN
ejpam-5032	65	23	of	of	ADP
ejpam-5032	65	24	a	a	DET
ejpam-5032	65	25	prime	prime	ADJ
ejpam-5032	65	26	n	n	ADP
ejpam-5032	65	27	-group	-group	NOUN
ejpam-5032	65	28	of	of	ADP
ejpam-5032	65	29	type	type	NOUN
ejpam-5032	65	30	1	1	NUM
ejpam-5032	66	1	[	[	X
ejpam-5032	66	2	6	6	NUM
ejpam-5032	66	3	]	]	PUNCT
ejpam-5032	66	4	which	which	PRON
ejpam-5032	66	5	is	be	AUX
ejpam-5032	66	6	not	not	PART
ejpam-5032	66	7	of	of	ADP
ejpam-5032	66	8	type	type	NOUN
ejpam-5032	66	9	2	2	NUM
ejpam-5032	66	10	.	.	PUNCT
ejpam-5032	66	11	definition	definition	NOUN
ejpam-5032	66	12	2	2	NUM
ejpam-5032	66	13	.	.	PUNCT
ejpam-5032	67	1	let	let	VERB
ejpam-5032	67	2	h	h	PRON
ejpam-5032	67	3	be	be	AUX
ejpam-5032	67	4	an	an	DET
ejpam-5032	67	5	n	n	NUM
ejpam-5032	67	6	-group	-group	NOUN
ejpam-5032	67	7	with	with	ADP
ejpam-5032	67	8	hn	hn	PROPN
ejpam-5032	67	9	̸=	̸=	PROPN
ejpam-5032	67	10	{	{	PUNCT
ejpam-5032	67	11	0	0	NUM
ejpam-5032	67	12	}	}	PUNCT
ejpam-5032	67	13	.	.	PUNCT
ejpam-5032	68	1	then	then	ADV
ejpam-5032	68	2	h	h	PROPN
ejpam-5032	68	3	is	be	AUX
ejpam-5032	68	4	a	a	DET
ejpam-5032	68	5	prime	prime	ADJ
ejpam-5032	68	6	n	n	ADP
ejpam-5032	68	7	-group	-group	NOUN
ejpam-5032	68	8	of	of	ADP
ejpam-5032	68	9	type	type	NOUN
ejpam-5032	68	10	1	1	NUM
ejpam-5032	68	11	if	if	SCONJ
ejpam-5032	68	12	:	:	PUNCT
ejpam-5032	68	13	(	(	PUNCT
ejpam-5032	68	14	i	i	NOUN
ejpam-5032	68	15	)	)	PUNCT
ejpam-5032	68	16	every	every	DET
ejpam-5032	68	17	non	non	ADJ
ejpam-5032	68	18	-	-	ADJ
ejpam-5032	68	19	zero	zero	NUM
ejpam-5032	68	20	n	n	DET
ejpam-5032	68	21	-subgroup	-subgroup	NOUN
ejpam-5032	68	22	of	of	ADP
ejpam-5032	68	23	h	h	PROPN
ejpam-5032	68	24	has	have	VERB
ejpam-5032	68	25	a	a	DET
ejpam-5032	68	26	non	non	ADJ
ejpam-5032	68	27	-	-	ADJ
ejpam-5032	68	28	zero	zero	NUM
ejpam-5032	68	29	distributive	distributive	ADJ
ejpam-5032	68	30	element	element	NOUN
ejpam-5032	68	31	;	;	PUNCT
ejpam-5032	68	32	(	(	PUNCT
ejpam-5032	68	33	ii	ii	NOUN
ejpam-5032	68	34	)	)	PUNCT
ejpam-5032	68	35	hnx	hnx	NOUN
ejpam-5032	68	36	=	=	SYM
ejpam-5032	68	37	{	{	PUNCT
ejpam-5032	68	38	0	0	NUM
ejpam-5032	68	39	}	}	PUNCT
ejpam-5032	68	40	,	,	PUNCT
ejpam-5032	68	41	0	0	NUM
ejpam-5032	68	42	̸=	̸=	PROPN
ejpam-5032	68	43	h	h	NOUN
ejpam-5032	68	44	∈	∈	PROPN
ejpam-5032	68	45	h	h	NOUN
ejpam-5032	68	46	,	,	PUNCT
ejpam-5032	68	47	x	x	SYM
ejpam-5032	68	48	∈	∈	PROPN
ejpam-5032	68	49	n	n	PRON
ejpam-5032	68	50	implies	imply	VERB
ejpam-5032	68	51	hx	hx	X
ejpam-5032	68	52	=	=	PUNCT
ejpam-5032	68	53	{	{	PUNCT
ejpam-5032	68	54	0	0	NUM
ejpam-5032	68	55	}	}	PUNCT
ejpam-5032	68	56	.	.	PUNCT
ejpam-5032	69	1	example	example	NOUN
ejpam-5032	70	1	2	2	NUM
ejpam-5032	70	2	.	.	PUNCT
ejpam-5032	70	3	let	let	VERB
ejpam-5032	70	4	h	h	PRON
ejpam-5032	70	5	be	be	AUX
ejpam-5032	70	6	a	a	DET
ejpam-5032	70	7	cyclic	cyclic	ADJ
ejpam-5032	70	8	group	group	NOUN
ejpam-5032	70	9	of	of	ADP
ejpam-5032	70	10	order	order	NOUN
ejpam-5032	70	11	p	p	X
ejpam-5032	70	12	,	,	PUNCT
ejpam-5032	70	13	where	where	SCONJ
ejpam-5032	70	14	p	p	NOUN
ejpam-5032	70	15	is	be	AUX
ejpam-5032	70	16	a	a	DET
ejpam-5032	70	17	prime	prime	ADJ
ejpam-5032	70	18	number	number	NOUN
ejpam-5032	70	19	greater	great	ADJ
ejpam-5032	70	20	than	than	ADP
ejpam-5032	70	21	2	2	NUM
ejpam-5032	70	22	.	.	PUNCT
ejpam-5032	70	23	clearly	clearly	ADV
ejpam-5032	70	24	m0(h	m0(h	X
ejpam-5032	70	25	)	)	PUNCT
ejpam-5032	70	26	is	be	AUX
ejpam-5032	70	27	a	a	DET
ejpam-5032	70	28	m0(h)-group	m0(h)-group	PROPN
ejpam-5032	70	29	.	.	PUNCT
ejpam-5032	71	1	since	since	SCONJ
ejpam-5032	71	2	h	h	NOUN
ejpam-5032	71	3	has	have	VERB
ejpam-5032	71	4	exactly	exactly	ADV
ejpam-5032	71	5	two	two	NUM
ejpam-5032	71	6	subgroups	subgroup	NOUN
ejpam-5032	71	7	,	,	PUNCT
ejpam-5032	71	8	{	{	PUNCT
ejpam-5032	71	9	0	0	NUM
ejpam-5032	71	10	}	}	PUNCT
ejpam-5032	71	11	and	and	CCONJ
ejpam-5032	71	12	m0(h	m0(h	NUM
ejpam-5032	71	13	)	)	PUNCT
ejpam-5032	71	14	are	be	AUX
ejpam-5032	71	15	the	the	DET
ejpam-5032	71	16	only	only	ADJ
ejpam-5032	71	17	m0(h)-subgroups	m0(h)-subgroup	NOUN
ejpam-5032	71	18	of	of	ADP
ejpam-5032	71	19	m0(h	m0(h	NUM
ejpam-5032	71	20	)	)	PUNCT
ejpam-5032	71	21	.	.	PUNCT
ejpam-5032	72	1	therefore	therefore	ADV
ejpam-5032	72	2	m0(h	m0(h	X
ejpam-5032	72	3	)	)	PUNCT
ejpam-5032	72	4	is	be	AUX
ejpam-5032	72	5	a	a	DET
ejpam-5032	72	6	prime	prime	ADJ
ejpam-5032	72	7	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	72	8	of	of	ADP
ejpam-5032	72	9	type	type	NOUN
ejpam-5032	72	10	1	1	NUM
ejpam-5032	72	11	.	.	PUNCT
ejpam-5032	72	12	note	note	VERB
ejpam-5032	72	13	that	that	SCONJ
ejpam-5032	72	14	any	any	DET
ejpam-5032	72	15	non	non	ADJ
ejpam-5032	72	16	-	-	ADJ
ejpam-5032	72	17	zero	zero	ADJ
ejpam-5032	72	18	endomorphism	endomorphism	NOUN
ejpam-5032	72	19	of	of	ADP
ejpam-5032	72	20	h	h	NOUN
ejpam-5032	72	21	is	be	AUX
ejpam-5032	72	22	an	an	DET
ejpam-5032	72	23	automorphism	automorphism	NOUN
ejpam-5032	72	24	of	of	ADP
ejpam-5032	72	25	h.	h.	PROPN
ejpam-5032	72	26	choose	choose	VERB
ejpam-5032	72	27	a	a	DET
ejpam-5032	72	28	non	non	ADJ
ejpam-5032	72	29	-	-	ADJ
ejpam-5032	72	30	zero	zero	NUM
ejpam-5032	72	31	function	function	NOUN
ejpam-5032	72	32	f	f	PROPN
ejpam-5032	72	33	∈	∈	PROPN
ejpam-5032	72	34	m0(h	m0(h	PROPN
ejpam-5032	72	35	)	)	PUNCT
ejpam-5032	72	36	such	such	ADJ
ejpam-5032	72	37	that	that	SCONJ
ejpam-5032	72	38	the	the	DET
ejpam-5032	72	39	image	image	NOUN
ejpam-5032	72	40	of	of	ADP
ejpam-5032	72	41	f	f	PROPN
ejpam-5032	72	42	is	be	AUX
ejpam-5032	72	43	not	not	PART
ejpam-5032	72	44	equal	equal	ADJ
ejpam-5032	72	45	to	to	ADP
ejpam-5032	72	46	h.	h.	PROPN
ejpam-5032	72	47	we	we	PRON
ejpam-5032	72	48	have	have	VERB
ejpam-5032	72	49	no	no	DET
ejpam-5032	72	50	g	g	PROPN
ejpam-5032	72	51	∈	∈	PROPN
ejpam-5032	72	52	m0(h	m0(h	PROPN
ejpam-5032	72	53	)	)	PUNCT
ejpam-5032	72	54	such	such	ADJ
ejpam-5032	72	55	that	that	SCONJ
ejpam-5032	72	56	fg	fg	PROPN
ejpam-5032	72	57	is	be	AUX
ejpam-5032	72	58	an	an	DET
ejpam-5032	72	59	automorphism	automorphism	NOUN
ejpam-5032	72	60	of	of	ADP
ejpam-5032	72	61	h	h	NOUN
ejpam-5032	72	62	,	,	PUNCT
ejpam-5032	72	63	that	that	ADV
ejpam-5032	72	64	is	is	ADV
ejpam-5032	72	65	,	,	PUNCT
ejpam-5032	72	66	a	a	DET
ejpam-5032	72	67	non	non	ADJ
ejpam-5032	72	68	-	-	ADJ
ejpam-5032	72	69	zero	zero	ADJ
ejpam-5032	72	70	endomorphism	endomorphism	NOUN
ejpam-5032	72	71	of	of	ADP
ejpam-5032	72	72	h	h	NOUN
ejpam-5032	72	73	,	,	PUNCT
ejpam-5032	72	74	that	that	ADV
ejpam-5032	72	75	is	is	ADV
ejpam-5032	72	76	,	,	PUNCT
ejpam-5032	72	77	a	a	DET
ejpam-5032	72	78	non	non	ADJ
ejpam-5032	72	79	-	-	ADJ
ejpam-5032	72	80	zero	zero	NUM
ejpam-5032	72	81	distributive	distributive	ADJ
ejpam-5032	72	82	element	element	NOUN
ejpam-5032	72	83	of	of	ADP
ejpam-5032	72	84	m0(h	m0(h	PROPN
ejpam-5032	72	85	)	)	PUNCT
ejpam-5032	72	86	.	.	PUNCT
ejpam-5032	73	1	this	this	PRON
ejpam-5032	73	2	shows	show	VERB
ejpam-5032	73	3	that	that	SCONJ
ejpam-5032	73	4	fm0(h	fm0(h	PROPN
ejpam-5032	73	5	)	)	PUNCT
ejpam-5032	73	6	has	have	VERB
ejpam-5032	73	7	no	no	DET
ejpam-5032	73	8	non	non	ADJ
ejpam-5032	73	9	-	-	ADJ
ejpam-5032	73	10	zero	zero	NUM
ejpam-5032	73	11	distributive	distributive	ADJ
ejpam-5032	73	12	element	element	NOUN
ejpam-5032	73	13	.	.	PUNCT
ejpam-5032	74	1	therefore	therefore	ADV
ejpam-5032	74	2	m0(h	m0(h	X
ejpam-5032	74	3	)	)	PUNCT
ejpam-5032	74	4	is	be	AUX
ejpam-5032	74	5	not	not	PART
ejpam-5032	74	6	a	a	DET
ejpam-5032	74	7	prime	prime	ADJ
ejpam-5032	74	8	m0(h)-group	m0(h)-group	NOUN
ejpam-5032	74	9	of	of	ADP
ejpam-5032	74	10	type	type	NOUN
ejpam-5032	74	11	2	2	NUM
ejpam-5032	74	12	.	.	PUNCT
ejpam-5032	75	1	now	now	ADV
ejpam-5032	75	2	we	we	PRON
ejpam-5032	75	3	study	study	VERB
ejpam-5032	75	4	some	some	DET
ejpam-5032	75	5	properties	property	NOUN
ejpam-5032	75	6	of	of	ADP
ejpam-5032	75	7	prime	prime	ADJ
ejpam-5032	75	8	n	n	PROPN
ejpam-5032	75	9	-groups	-group	NOUN
ejpam-5032	75	10	of	of	ADP
ejpam-5032	75	11	type	type	NOUN
ejpam-5032	75	12	2	2	NUM
ejpam-5032	75	13	.	.	PUNCT
ejpam-5032	75	14	proposition	proposition	NOUN
ejpam-5032	75	15	1	1	NUM
ejpam-5032	75	16	.	.	PUNCT
ejpam-5032	76	1	let	let	VERB
ejpam-5032	76	2	h	h	PRON
ejpam-5032	76	3	be	be	AUX
ejpam-5032	76	4	a	a	DET
ejpam-5032	76	5	prime	prime	ADJ
ejpam-5032	76	6	n	n	ADP
ejpam-5032	76	7	-group	-group	NOUN
ejpam-5032	76	8	of	of	ADP
ejpam-5032	76	9	type	type	NOUN
ejpam-5032	76	10	2	2	NUM
ejpam-5032	76	11	.	.	PUNCT
ejpam-5032	77	1	then	then	ADV
ejpam-5032	77	2	(	(	PUNCT
ejpam-5032	77	3	h	h	NOUN
ejpam-5032	77	4	:	:	PUNCT
ejpam-5032	77	5	0)n	0)n	NOUN
ejpam-5032	77	6	exists	exist	VERB
ejpam-5032	77	7	.	.	PUNCT
ejpam-5032	78	1	proof	proof	NOUN
ejpam-5032	78	2	.	.	PUNCT
ejpam-5032	79	1	suppose	suppose	VERB
ejpam-5032	79	2	that	that	SCONJ
ejpam-5032	79	3	h	h	NOUN
ejpam-5032	79	4	is	be	AUX
ejpam-5032	79	5	a	a	DET
ejpam-5032	79	6	prime	prime	ADJ
ejpam-5032	79	7	n	n	ADP
ejpam-5032	79	8	-group	-group	NOUN
ejpam-5032	79	9	of	of	ADP
ejpam-5032	79	10	type	type	NOUN
ejpam-5032	79	11	2	2	NUM
ejpam-5032	79	12	.	.	PUNCT
ejpam-5032	80	1	now	now	ADV
ejpam-5032	80	2	h	h	NOUN
ejpam-5032	80	3	has	have	VERB
ejpam-5032	80	4	a	a	DET
ejpam-5032	80	5	distributive	distributive	ADJ
ejpam-5032	80	6	element	element	NOUN
ejpam-5032	80	7	0	0	NUM
ejpam-5032	81	1	̸=	̸=	PROPN
ejpam-5032	81	2	h0	h0	PROPN
ejpam-5032	81	3	.	.	PUNCT
ejpam-5032	82	1	it	it	PRON
ejpam-5032	82	2	is	be	AUX
ejpam-5032	82	3	clear	clear	ADJ
ejpam-5032	82	4	that	that	SCONJ
ejpam-5032	82	5	{	{	PUNCT
ejpam-5032	82	6	0	0	X
ejpam-5032	82	7	}	}	PUNCT
ejpam-5032	82	8	̸=	̸=	PROPN
ejpam-5032	82	9	h0n	h0n	NOUN
ejpam-5032	82	10	is	be	AUX
ejpam-5032	82	11	an	an	DET
ejpam-5032	82	12	n	n	NUM
ejpam-5032	82	13	-subgroup	-subgroup	NOUN
ejpam-5032	82	14	of	of	ADP
ejpam-5032	82	15	h.	h.	PROPN
ejpam-5032	82	16	we	we	PRON
ejpam-5032	82	17	have	have	VERB
ejpam-5032	82	18	(	(	PUNCT
ejpam-5032	82	19	h0x)0	h0x)0	PROPN
ejpam-5032	82	20	=	=	SYM
ejpam-5032	82	21	h0(x0	h0(x0	ADJ
ejpam-5032	82	22	)	)	PUNCT
ejpam-5032	83	1	=	=	VERB
ejpam-5032	83	2	h00	h00	NOUN
ejpam-5032	83	3	=	=	NOUN
ejpam-5032	83	4	0	0	NUM
ejpam-5032	83	5	for	for	ADP
ejpam-5032	83	6	all	all	DET
ejpam-5032	83	7	x	x	SYM
ejpam-5032	83	8	∈	∈	PROPN
ejpam-5032	83	9	n	n	NOUN
ejpam-5032	83	10	,	,	PUNCT
ejpam-5032	83	11	that	that	ADV
ejpam-5032	83	12	is	is	ADV
ejpam-5032	83	13	,	,	PUNCT
ejpam-5032	83	14	(	(	PUNCT
ejpam-5032	83	15	h0n)0	h0n)0	PROPN
ejpam-5032	83	16	=	=	PUNCT
ejpam-5032	83	17	{	{	PUNCT
ejpam-5032	83	18	0	0	NUM
ejpam-5032	83	19	}	}	PUNCT
ejpam-5032	83	20	.	.	PUNCT
ejpam-5032	84	1	so	so	ADV
ejpam-5032	84	2	h0	h0	PROPN
ejpam-5032	84	3	=	=	PROPN
ejpam-5032	84	4	{	{	PUNCT
ejpam-5032	84	5	0	0	NUM
ejpam-5032	84	6	}	}	PUNCT
ejpam-5032	84	7	.	.	PUNCT
ejpam-5032	85	1	let	let	VERB
ejpam-5032	85	2	k	k	X
ejpam-5032	85	3	,	,	PUNCT
ejpam-5032	85	4	l	l	NOUN
ejpam-5032	85	5	be	be	VERB
ejpam-5032	85	6	ideals	ideal	NOUN
ejpam-5032	85	7	of	of	ADP
ejpam-5032	85	8	n	n	NUM
ejpam-5032	85	9	contained	contain	VERB
ejpam-5032	85	10	in	in	ADP
ejpam-5032	85	11	an	an	DET
ejpam-5032	85	12	(	(	PUNCT
ejpam-5032	85	13	h	h	NOUN
ejpam-5032	85	14	)	)	PUNCT
ejpam-5032	85	15	.	.	PUNCT
ejpam-5032	86	1	we	we	PRON
ejpam-5032	86	2	have	have	VERB
ejpam-5032	86	3	(	(	PUNCT
ejpam-5032	86	4	h0x)(k	h0x)(k	PROPN
ejpam-5032	86	5	+	+	NUM
ejpam-5032	86	6	l	l	NOUN
ejpam-5032	86	7	)	)	PUNCT
ejpam-5032	87	1	=	=	PUNCT
ejpam-5032	87	2	h0(x((k	h0(x((k	NOUN
ejpam-5032	87	3	+	+	CCONJ
ejpam-5032	87	4	l	l	NOUN
ejpam-5032	87	5	)	)	PUNCT
ejpam-5032	87	6	−	−	PROPN
ejpam-5032	87	7	xk	xk	PROPN
ejpam-5032	88	1	+	+	CCONJ
ejpam-5032	88	2	xk	xk	PROPN
ejpam-5032	88	3	)	)	PUNCT
ejpam-5032	88	4	=	=	PUNCT
ejpam-5032	88	5	h0(x((k	h0(x((k	PROPN
ejpam-5032	88	6	+	+	CCONJ
ejpam-5032	88	7	l	l	NOUN
ejpam-5032	88	8	)	)	PUNCT
ejpam-5032	88	9	−	−	NOUN
ejpam-5032	88	10	xk	xk	NOUN
ejpam-5032	88	11	)	)	PUNCT
ejpam-5032	88	12	+	+	PUNCT
ejpam-5032	88	13	h0(xk	h0(xk	X
ejpam-5032	88	14	)	)	PUNCT
ejpam-5032	88	15	=	=	SYM
ejpam-5032	88	16	0	0	PUNCT
ejpam-5032	89	1	+	+	CCONJ
ejpam-5032	89	2	0	0	NUM
ejpam-5032	89	3	=	=	SYM
ejpam-5032	89	4	0	0	NUM
ejpam-5032	89	5	for	for	ADP
ejpam-5032	89	6	all	all	DET
ejpam-5032	89	7	x	x	SYM
ejpam-5032	89	8	∈	∈	PROPN
ejpam-5032	89	9	n	n	CCONJ
ejpam-5032	89	10	,	,	PUNCT
ejpam-5032	89	11	k	k	PROPN
ejpam-5032	89	12	∈	∈	PROPN
ejpam-5032	89	13	k	k	PROPN
ejpam-5032	89	14	,	,	PUNCT
ejpam-5032	89	15	l	l	PROPN
ejpam-5032	89	16	∈	∈	PROPN
ejpam-5032	89	17	l.	l.	NOUN
ejpam-5032	90	1	therefore	therefore	ADV
ejpam-5032	90	2	(	(	PUNCT
ejpam-5032	90	3	h0n)(k	h0n)(k	PROPN
ejpam-5032	90	4	+	+	NUM
ejpam-5032	90	5	l	l	NOUN
ejpam-5032	90	6	)	)	PUNCT
ejpam-5032	90	7	=	=	PRON
ejpam-5032	90	8	{	{	PUNCT
ejpam-5032	90	9	0	0	NUM
ejpam-5032	90	10	}	}	PUNCT
ejpam-5032	90	11	.	.	PUNCT
ejpam-5032	91	1	since	since	SCONJ
ejpam-5032	91	2	{	{	PUNCT
ejpam-5032	91	3	0	0	NUM
ejpam-5032	91	4	}	}	PUNCT
ejpam-5032	91	5	=	=	NOUN
ejpam-5032	91	6	̸	̸	NUM
ejpam-5032	91	7	h0n	h0n	VERB
ejpam-5032	91	8	is	be	AUX
ejpam-5032	91	9	an	an	DET
ejpam-5032	91	10	n	n	PRON
ejpam-5032	91	11	-subgroup	-subgroup	NOUN
ejpam-5032	91	12	of	of	ADP
ejpam-5032	91	13	h	h	NOUN
ejpam-5032	91	14	,	,	PUNCT
ejpam-5032	91	15	h(k	h(k	PROPN
ejpam-5032	91	16	+	+	NUM
ejpam-5032	91	17	l	l	NOUN
ejpam-5032	91	18	)	)	PUNCT
ejpam-5032	91	19	=	=	PRON
ejpam-5032	91	20	{	{	PUNCT
ejpam-5032	91	21	0	0	NUM
ejpam-5032	91	22	}	}	PUNCT
ejpam-5032	91	23	.	.	PUNCT
ejpam-5032	92	1	hence	hence	ADV
ejpam-5032	92	2	there	there	PRON
ejpam-5032	92	3	is	be	VERB
ejpam-5032	92	4	a	a	DET
ejpam-5032	92	5	largest	large	ADJ
ejpam-5032	92	6	ideal	ideal	NOUN
ejpam-5032	92	7	of	of	ADP
ejpam-5032	92	8	n	n	NUM
ejpam-5032	92	9	contained	contain	VERB
ejpam-5032	92	10	in	in	ADP
ejpam-5032	92	11	an	an	DET
ejpam-5032	92	12	(	(	PUNCT
ejpam-5032	92	13	h	h	NOUN
ejpam-5032	92	14	)	)	PUNCT
ejpam-5032	92	15	,	,	PUNCT
ejpam-5032	92	16	that	that	ADV
ejpam-5032	92	17	is	is	ADV
ejpam-5032	92	18	,	,	PUNCT
ejpam-5032	92	19	(	(	PUNCT
ejpam-5032	92	20	h	h	NOUN
ejpam-5032	92	21	:	:	PUNCT
ejpam-5032	92	22	0)n	0)n	NOUN
ejpam-5032	92	23	exists	exist	VERB
ejpam-5032	92	24	.	.	PUNCT
ejpam-5032	93	1	proposition	proposition	NOUN
ejpam-5032	93	2	2	2	NUM
ejpam-5032	93	3	.	.	PUNCT
ejpam-5032	94	1	let	let	VERB
ejpam-5032	94	2	h	h	PRON
ejpam-5032	94	3	be	be	AUX
ejpam-5032	94	4	a	a	DET
ejpam-5032	94	5	prime	prime	ADJ
ejpam-5032	94	6	n	n	ADP
ejpam-5032	94	7	-group	-group	NOUN
ejpam-5032	94	8	of	of	ADP
ejpam-5032	94	9	type	type	NOUN
ejpam-5032	94	10	2	2	NUM
ejpam-5032	94	11	and	and	CCONJ
ejpam-5032	94	12	k	k	PROPN
ejpam-5032	94	13	be	be	AUX
ejpam-5032	94	14	an	an	DET
ejpam-5032	94	15	ideal	ideal	NOUN
ejpam-5032	94	16	of	of	ADP
ejpam-5032	94	17	n	n	PROPN
ejpam-5032	94	18	and	and	CCONJ
ejpam-5032	94	19	hk	hk	PROPN
ejpam-5032	94	20	=	=	PUNCT
ejpam-5032	94	21	{	{	PUNCT
ejpam-5032	94	22	0	0	NUM
ejpam-5032	94	23	}	}	PUNCT
ejpam-5032	94	24	.	.	PUNCT
ejpam-5032	95	1	then	then	ADV
ejpam-5032	95	2	h0n	h0n	VERB
ejpam-5032	95	3	is	be	AUX
ejpam-5032	95	4	a	a	DET
ejpam-5032	95	5	prime	prime	ADJ
ejpam-5032	95	6	n	n	CCONJ
ejpam-5032	95	7	/	/	SYM
ejpam-5032	95	8	k	k	NOUN
ejpam-5032	95	9	-	-	NOUN
ejpam-5032	95	10	group	group	NOUN
ejpam-5032	95	11	of	of	ADP
ejpam-5032	95	12	type	type	NOUN
ejpam-5032	95	13	2	2	NUM
ejpam-5032	95	14	for	for	ADP
ejpam-5032	95	15	any	any	DET
ejpam-5032	95	16	distributive	distributive	ADJ
ejpam-5032	95	17	element	element	NOUN
ejpam-5032	95	18	0	0	NUM
ejpam-5032	96	1	̸=	̸=	PROPN
ejpam-5032	96	2	h0	h0	PROPN
ejpam-5032	96	3	∈	∈	PROPN
ejpam-5032	96	4	h.	h.	NOUN
ejpam-5032	97	1	moreover	moreover	ADV
ejpam-5032	97	2	(	(	PUNCT
ejpam-5032	97	3	h0n	h0n	NOUN
ejpam-5032	97	4	:	:	PUNCT
ejpam-5032	97	5	0)n	0)n	PROPN
ejpam-5032	97	6	/	/	SYM
ejpam-5032	97	7	k	k	PROPN
ejpam-5032	98	1	=	=	PUNCT
ejpam-5032	99	1	(	(	PUNCT
ejpam-5032	99	2	h	h	NOUN
ejpam-5032	99	3	:	:	PUNCT
ejpam-5032	99	4	0)n	0)n	PROPN
ejpam-5032	99	5	/	/	SYM
ejpam-5032	99	6	k.	k.	PROPN
ejpam-5032	100	1	proof	proof	NOUN
ejpam-5032	100	2	.	.	PUNCT
ejpam-5032	101	1	k	k	PROPN
ejpam-5032	101	2	is	be	AUX
ejpam-5032	101	3	an	an	DET
ejpam-5032	101	4	ideal	ideal	NOUN
ejpam-5032	101	5	of	of	ADP
ejpam-5032	101	6	n	n	NUM
ejpam-5032	101	7	and	and	CCONJ
ejpam-5032	101	8	h	h	NOUN
ejpam-5032	101	9	is	be	AUX
ejpam-5032	101	10	a	a	DET
ejpam-5032	101	11	prime	prime	ADJ
ejpam-5032	101	12	n	n	ADP
ejpam-5032	101	13	-group	-group	NOUN
ejpam-5032	101	14	of	of	ADP
ejpam-5032	101	15	type	type	NOUN
ejpam-5032	101	16	2	2	NUM
ejpam-5032	101	17	and	and	CCONJ
ejpam-5032	101	18	hk	hk	NOUN
ejpam-5032	101	19	=	=	PUNCT
ejpam-5032	101	20	{	{	PUNCT
ejpam-5032	101	21	0	0	NUM
ejpam-5032	101	22	}	}	PUNCT
ejpam-5032	101	23	.	.	PUNCT
ejpam-5032	102	1	let	let	VERB
ejpam-5032	102	2	0	0	NUM
ejpam-5032	102	3	̸=	̸=	PROPN
ejpam-5032	102	4	h0	h0	NOUN
ejpam-5032	102	5	∈	∈	PROPN
ejpam-5032	102	6	h	h	NOUN
ejpam-5032	102	7	be	be	AUX
ejpam-5032	102	8	a	a	DET
ejpam-5032	102	9	distributive	distributive	ADJ
ejpam-5032	102	10	element	element	NOUN
ejpam-5032	102	11	.	.	PUNCT
ejpam-5032	103	1	clearly	clearly	ADV
ejpam-5032	103	2	h0n	h0n	VERB
ejpam-5032	103	3	=	=	SYM
ejpam-5032	103	4	{	{	PUNCT
ejpam-5032	103	5	h0x	h0x	NOUN
ejpam-5032	103	6	|	|	ADV
ejpam-5032	103	7	x	x	SYM
ejpam-5032	103	8	∈	∈	PROPN
ejpam-5032	103	9	n	n	CCONJ
ejpam-5032	103	10	}	}	PUNCT
ejpam-5032	103	11	is	be	AUX
ejpam-5032	103	12	a	a	DET
ejpam-5032	103	13	subgroup	subgroup	NOUN
ejpam-5032	103	14	of	of	ADP
ejpam-5032	103	15	(	(	PUNCT
ejpam-5032	103	16	h,+	h,+	PROPN
ejpam-5032	103	17	)	)	PUNCT
ejpam-5032	103	18	and	and	CCONJ
ejpam-5032	103	19	is	be	AUX
ejpam-5032	103	20	an	an	DET
ejpam-5032	103	21	n	n	ADV
ejpam-5032	103	22	-subgroup	-subgroup	NOUN
ejpam-5032	103	23	of	of	ADP
ejpam-5032	103	24	h.	h.	PROPN
ejpam-5032	103	25	let	let	VERB
ejpam-5032	103	26	h0x	h0x	PROPN
ejpam-5032	103	27	∈	∈	PROPN
ejpam-5032	103	28	h0n	h0n	PROPN
ejpam-5032	103	29	,	,	PUNCT
ejpam-5032	103	30	x	x	X
ejpam-5032	103	31	,	,	PUNCT
ejpam-5032	103	32	y	y	PROPN
ejpam-5032	103	33	,	,	PUNCT
ejpam-5032	103	34	z	z	PROPN
ejpam-5032	103	35	∈	∈	PROPN
ejpam-5032	103	36	n	n	X
ejpam-5032	103	37	.	.	PUNCT
ejpam-5032	104	1	define	define	VERB
ejpam-5032	104	2	(	(	PUNCT
ejpam-5032	104	3	h0x)(y	h0x)(y	PROPN
ejpam-5032	104	4	+	+	NOUN
ejpam-5032	104	5	n	n	CCONJ
ejpam-5032	104	6	)	)	PUNCT
ejpam-5032	104	7	:	:	PUNCT
ejpam-5032	105	1	=	=	SYM
ejpam-5032	105	2	(	(	PUNCT
ejpam-5032	105	3	h0x)y	h0x)y	PROPN
ejpam-5032	105	4	.	.	PUNCT
ejpam-5032	106	1	this	this	DET
ejpam-5032	106	2	operation	operation	NOUN
ejpam-5032	106	3	is	be	AUX
ejpam-5032	106	4	well	well	ADV
ejpam-5032	106	5	-	-	PUNCT
ejpam-5032	106	6	defined	define	VERB
ejpam-5032	106	7	.	.	PUNCT
ejpam-5032	107	1	for	for	ADP
ejpam-5032	107	2	this	this	PRON
ejpam-5032	107	3	suppose	suppose	VERB
ejpam-5032	107	4	that	that	SCONJ
ejpam-5032	107	5	let	let	VERB
ejpam-5032	107	6	y+k	y+k	PRON
ejpam-5032	107	7	=	=	SYM
ejpam-5032	107	8	z+k	z+k	NUM
ejpam-5032	107	9	.	.	PUNCT
ejpam-5032	108	1	now	now	ADV
ejpam-5032	108	2	−z+y	−z+y	NOUN
ejpam-5032	108	3	∈	∈	PROPN
ejpam-5032	108	4	k.	k.	NOUN
ejpam-5032	108	5	we	we	PRON
ejpam-5032	108	6	have	have	VERB
ejpam-5032	108	7	(	(	PUNCT
ejpam-5032	108	8	h0x)y	h0x)y	X
ejpam-5032	108	9	=	=	PUNCT
ejpam-5032	108	10	(	(	PUNCT
ejpam-5032	108	11	h0x)[z+(−z+y)]−(h0xz)+(h0xz	h0x)[z+(−z+y)]−(h0xz)+(h0xz	NOUN
ejpam-5032	108	12	)	)	PUNCT
ejpam-5032	108	13	=	=	SYM
ejpam-5032	108	14	h0[(x(z+(−z+y))−xz]+(h0xz	h0[(x(z+(−z+y))−xz]+(h0xz	PROPN
ejpam-5032	108	15	)	)	PUNCT
ejpam-5032	108	16	=	=	SYM
ejpam-5032	108	17	0+(h0xz	0+(h0xz	NOUN
ejpam-5032	108	18	)	)	PUNCT
ejpam-5032	108	19	=	=	SYM
ejpam-5032	109	1	(	(	PUNCT
ejpam-5032	109	2	h0x)z	h0x)z	X
ejpam-5032	109	3	.	.	PUNCT
ejpam-5032	110	1	therefore	therefore	ADV
ejpam-5032	110	2	the	the	DET
ejpam-5032	110	3	above	above	ADJ
ejpam-5032	110	4	operation	operation	NOUN
ejpam-5032	110	5	is	be	AUX
ejpam-5032	110	6	well	well	ADV
ejpam-5032	110	7	defined	define	VERB
ejpam-5032	110	8	.	.	PUNCT
ejpam-5032	111	1	it	it	PRON
ejpam-5032	111	2	can	can	AUX
ejpam-5032	111	3	be	be	AUX
ejpam-5032	111	4	easily	easily	ADV
ejpam-5032	111	5	verified	verify	VERB
ejpam-5032	111	6	that	that	SCONJ
ejpam-5032	111	7	with	with	ADP
ejpam-5032	111	8	this	this	DET
ejpam-5032	111	9	operation	operation	NOUN
ejpam-5032	111	10	h0n	h0n	NOUN
ejpam-5032	111	11	is	be	AUX
ejpam-5032	111	12	ann	ann	PROPN
ejpam-5032	111	13	/	/	SYM
ejpam-5032	111	14	k	k	NOUN
ejpam-5032	111	15	-	-	NOUN
ejpam-5032	111	16	group	group	NOUN
ejpam-5032	111	17	.	.	PUNCT
ejpam-5032	112	1	moreover	moreover	ADV
ejpam-5032	112	2	h0n	h0n	NOUN
ejpam-5032	112	3	is	be	AUX
ejpam-5032	112	4	a	a	DET
ejpam-5032	112	5	primen	priman	NOUN
ejpam-5032	112	6	-group	-group	NOUN
ejpam-5032	112	7	of	of	ADP
ejpam-5032	112	8	type	type	NOUN
ejpam-5032	112	9	2	2	NUM
ejpam-5032	112	10	beingn	beingn	NOUN
ejpam-5032	112	11	-subgroup	-subgroup	PROPN
ejpam-5032	112	12	ofh	ofh	PROPN
ejpam-5032	112	13	.	.	PROPN
ejpam-5032	112	14	from	from	ADP
ejpam-5032	112	15	this	this	PRON
ejpam-5032	112	16	it	it	PRON
ejpam-5032	112	17	follows	follow	VERB
ejpam-5032	112	18	that	that	PRON
ejpam-5032	112	19	h0n	h0n	NOUN
ejpam-5032	112	20	is	be	AUX
ejpam-5032	112	21	a	a	DET
ejpam-5032	112	22	primen	priman	NOUN
ejpam-5032	112	23	/	/	SYM
ejpam-5032	112	24	k	k	NOUN
ejpam-5032	112	25	-	-	NOUN
ejpam-5032	112	26	group	group	NOUN
ejpam-5032	112	27	of	of	ADP
ejpam-5032	112	28	type	type	NOUN
ejpam-5032	112	29	2	2	NUM
ejpam-5032	112	30	.	.	PUNCT
ejpam-5032	113	1	let	let	VERB
ejpam-5032	113	2	m	m	PRON
ejpam-5032	113	3	be	be	AUX
ejpam-5032	113	4	the	the	DET
ejpam-5032	113	5	largest	large	ADJ
ejpam-5032	113	6	ideal	ideal	NOUN
ejpam-5032	113	7	of	of	ADP
ejpam-5032	113	8	n	n	NUM
ejpam-5032	113	9	contained	contain	VERB
ejpam-5032	113	10	in	in	ADP
ejpam-5032	113	11	an	an	DET
ejpam-5032	113	12	(	(	PUNCT
ejpam-5032	113	13	h	h	NOUN
ejpam-5032	113	14	)	)	PUNCT
ejpam-5032	113	15	,	,	PUNCT
ejpam-5032	113	16	that	that	ADV
ejpam-5032	113	17	is	is	ADV
ejpam-5032	113	18	,	,	PUNCT
ejpam-5032	113	19	(	(	PUNCT
ejpam-5032	113	20	h	h	NOUN
ejpam-5032	113	21	:	:	PUNCT
ejpam-5032	113	22	0)n	0)n	X
ejpam-5032	114	1	=	=	PUNCT
ejpam-5032	114	2	m	m	VERB
ejpam-5032	114	3	.	.	PUNCT
ejpam-5032	115	1	clearly	clearly	ADV
ejpam-5032	115	2	k	k	PROPN
ejpam-5032	115	3	⊆	⊆	NUM
ejpam-5032	115	4	m	m	NOUN
ejpam-5032	115	5	.	.	PUNCT
ejpam-5032	116	1	since	since	SCONJ
ejpam-5032	116	2	hm	hm	INTJ
ejpam-5032	116	3	=	=	X
ejpam-5032	116	4	{	{	PUNCT
ejpam-5032	116	5	0	0	NUM
ejpam-5032	116	6	}	}	PUNCT
ejpam-5032	116	7	,	,	PUNCT
ejpam-5032	116	8	(	(	PUNCT
ejpam-5032	116	9	h0n)m	h0n)m	X
ejpam-5032	116	10	=	=	PUNCT
ejpam-5032	116	11	{	{	PUNCT
ejpam-5032	116	12	0	0	NUM
ejpam-5032	116	13	}	}	PUNCT
ejpam-5032	116	14	.	.	PUNCT
ejpam-5032	117	1	so	so	ADV
ejpam-5032	117	2	(	(	PUNCT
ejpam-5032	117	3	h0n)(m	h0n)(m	PROPN
ejpam-5032	117	4	/	/	SYM
ejpam-5032	117	5	k	k	NOUN
ejpam-5032	117	6	)	)	PUNCT
ejpam-5032	117	7	=	=	PUNCT
ejpam-5032	117	8	{	{	PUNCT
ejpam-5032	117	9	0	0	NUM
ejpam-5032	117	10	}	}	PUNCT
ejpam-5032	117	11	,	,	PUNCT
ejpam-5032	117	12	that	that	ADV
ejpam-5032	117	13	is	be	AUX
ejpam-5032	117	14	,	,	PUNCT
ejpam-5032	117	15	m	m	PROPN
ejpam-5032	117	16	/	/	SYM
ejpam-5032	117	17	k	k	NOUN
ejpam-5032	117	18	⊆	⊆	NUM
ejpam-5032	117	19	(	(	PUNCT
ejpam-5032	117	20	h0n	h0n	NOUN
ejpam-5032	117	21	:	:	PUNCT
ejpam-5032	117	22	0)n	0)n	PROPN
ejpam-5032	117	23	/	/	SYM
ejpam-5032	118	1	k	k	PROPN
ejpam-5032	118	2	,	,	PUNCT
ejpam-5032	118	3	that	that	ADV
ejpam-5032	118	4	is	is	ADV
ejpam-5032	118	5	,	,	PUNCT
ejpam-5032	118	6	(	(	PUNCT
ejpam-5032	118	7	h	h	NOUN
ejpam-5032	118	8	:	:	PUNCT
ejpam-5032	118	9	0)n	0)n	PROPN
ejpam-5032	118	10	/	/	SYM
ejpam-5032	119	1	k	k	PROPN
ejpam-5032	119	2	⊆	⊆	NUM
ejpam-5032	119	3	(	(	PUNCT
ejpam-5032	119	4	h0n	h0n	NOUN
ejpam-5032	119	5	:	:	PUNCT
ejpam-5032	119	6	0)n	0)n	PROPN
ejpam-5032	119	7	/	/	SYM
ejpam-5032	119	8	k	k	X
ejpam-5032	119	9	.	.	PUNCT
ejpam-5032	120	1	similarly	similarly	ADV
ejpam-5032	120	2	if	if	SCONJ
ejpam-5032	120	3	(	(	PUNCT
ejpam-5032	120	4	h0n	h0n	NOUN
ejpam-5032	120	5	:	:	PUNCT
ejpam-5032	120	6	0)n	0)n	PROPN
ejpam-5032	120	7	/	/	SYM
ejpam-5032	120	8	k	k	PROPN
ejpam-5032	120	9	=	=	SYM
ejpam-5032	120	10	t	t	PROPN
ejpam-5032	120	11	/	/	SYM
ejpam-5032	120	12	k	k	PROPN
ejpam-5032	120	13	,	,	PUNCT
ejpam-5032	120	14	then	then	ADV
ejpam-5032	120	15	the	the	DET
ejpam-5032	120	16	ideal	ideal	ADJ
ejpam-5032	120	17	t	t	PROPN
ejpam-5032	120	18	of	of	ADP
ejpam-5032	120	19	n	n	PROPN
ejpam-5032	120	20	is	be	AUX
ejpam-5032	120	21	contained	contain	VERB
ejpam-5032	120	22	in	in	ADP
ejpam-5032	120	23	(	(	PUNCT
ejpam-5032	120	24	h	h	NOUN
ejpam-5032	120	25	:	:	PUNCT
ejpam-5032	120	26	0)n	0)n	NOUN
ejpam-5032	120	27	and	and	CCONJ
ejpam-5032	120	28	hence	hence	ADV
ejpam-5032	120	29	(	(	PUNCT
ejpam-5032	120	30	h0n	h0n	NOUN
ejpam-5032	120	31	:	:	PUNCT
ejpam-5032	120	32	0)n	0)n	PROPN
ejpam-5032	120	33	/	/	SYM
ejpam-5032	121	1	k	k	PROPN
ejpam-5032	121	2	⊆	⊆	NUM
ejpam-5032	121	3	(	(	PUNCT
ejpam-5032	121	4	h	h	NOUN
ejpam-5032	121	5	:	:	PUNCT
ejpam-5032	121	6	0)n	0)n	PROPN
ejpam-5032	121	7	/	/	SYM
ejpam-5032	121	8	k.	k.	PROPN
ejpam-5032	121	9	therefore	therefore	ADV
ejpam-5032	121	10	(	(	PUNCT
ejpam-5032	121	11	h0n	h0n	NOUN
ejpam-5032	121	12	:	:	PUNCT
ejpam-5032	122	1	0)n	0)n	PROPN
ejpam-5032	122	2	/	/	SYM
ejpam-5032	122	3	k	k	PROPN
ejpam-5032	123	1	=	=	PUNCT
ejpam-5032	123	2	(	(	PUNCT
ejpam-5032	123	3	h	h	NOUN
ejpam-5032	123	4	:	:	PUNCT
ejpam-5032	123	5	0)n	0)n	PROPN
ejpam-5032	123	6	/	/	SYM
ejpam-5032	123	7	k.	k.	PROPN
ejpam-5032	123	8	k.	k.	PROPN
ejpam-5032	124	1	j.	j.	PROPN
ejpam-5032	124	2	lakshminarayana	lakshminarayana	PROPN
ejpam-5032	124	3	et	et	PROPN
ejpam-5032	125	1	al	al	PROPN
ejpam-5032	125	2	.	.	PUNCT
ejpam-5032	125	3	/	/	SYM
ejpam-5032	125	4	eur	eur	PROPN
ejpam-5032	125	5	.	.	PUNCT
ejpam-5032	126	1	j.	j.	PROPN
ejpam-5032	126	2	pure	pure	PROPN
ejpam-5032	126	3	appl	appl	PROPN
ejpam-5032	126	4	.	.	PROPN
ejpam-5032	126	5	math	math	PROPN
ejpam-5032	126	6	,	,	PUNCT
ejpam-5032	126	7	17	17	NUM
ejpam-5032	126	8	(	(	PUNCT
ejpam-5032	126	9	2	2	NUM
ejpam-5032	126	10	)	)	PUNCT
ejpam-5032	126	11	(	(	PUNCT
ejpam-5032	126	12	2024	2024	NUM
ejpam-5032	126	13	)	)	PUNCT
ejpam-5032	126	14	,	,	PUNCT
ejpam-5032	126	15	1206	1206	NUM
ejpam-5032	126	16	-	-	SYM
ejpam-5032	126	17	1212	1212	NUM
ejpam-5032	126	18	1209	1209	NUM
ejpam-5032	126	19	proposition	proposition	NOUN
ejpam-5032	126	20	3	3	X
ejpam-5032	126	21	.	.	PUNCT
ejpam-5032	127	1	let	let	VERB
ejpam-5032	127	2	h	h	PRON
ejpam-5032	127	3	be	be	AUX
ejpam-5032	127	4	a	a	DET
ejpam-5032	127	5	prime	prime	ADJ
ejpam-5032	127	6	n	n	CCONJ
ejpam-5032	127	7	/	/	SYM
ejpam-5032	127	8	k	k	NOUN
ejpam-5032	127	9	-	-	NOUN
ejpam-5032	127	10	group	group	NOUN
ejpam-5032	127	11	of	of	ADP
ejpam-5032	127	12	type	type	NOUN
ejpam-5032	127	13	2	2	NUM
ejpam-5032	127	14	,	,	PUNCT
ejpam-5032	127	15	k	k	PROPN
ejpam-5032	127	16	an	an	DET
ejpam-5032	127	17	ideal	ideal	NOUN
ejpam-5032	127	18	of	of	ADP
ejpam-5032	127	19	n	n	PROPN
ejpam-5032	127	20	.	.	PUNCT
ejpam-5032	128	1	then	then	ADV
ejpam-5032	128	2	h	h	PROPN
ejpam-5032	128	3	is	be	AUX
ejpam-5032	128	4	a	a	DET
ejpam-5032	128	5	prime	prime	ADJ
ejpam-5032	128	6	n	n	ADP
ejpam-5032	128	7	-group	-group	NOUN
ejpam-5032	128	8	of	of	ADP
ejpam-5032	128	9	type	type	NOUN
ejpam-5032	128	10	2	2	NUM
ejpam-5032	128	11	and	and	CCONJ
ejpam-5032	128	12	(	(	PUNCT
ejpam-5032	128	13	h	h	NOUN
ejpam-5032	128	14	:	:	PUNCT
ejpam-5032	128	15	0)n	0)n	PROPN
ejpam-5032	128	16	/	/	SYM
ejpam-5032	128	17	k	k	PROPN
ejpam-5032	129	1	=	=	PUNCT
ejpam-5032	129	2	(	(	PUNCT
ejpam-5032	129	3	h	h	NOUN
ejpam-5032	129	4	:	:	PUNCT
ejpam-5032	129	5	0)n	0)n	PROPN
ejpam-5032	129	6	/	/	SYM
ejpam-5032	129	7	k	k	PROPN
ejpam-5032	129	8	.	.	PUNCT
ejpam-5032	130	1	proof	proof	NOUN
ejpam-5032	130	2	.	.	PUNCT
ejpam-5032	131	1	suppose	suppose	VERB
ejpam-5032	131	2	that	that	SCONJ
ejpam-5032	131	3	h	h	NOUN
ejpam-5032	131	4	is	be	AUX
ejpam-5032	131	5	a	a	DET
ejpam-5032	131	6	prime	prime	ADJ
ejpam-5032	131	7	n	n	CCONJ
ejpam-5032	131	8	/	/	SYM
ejpam-5032	131	9	k	k	NOUN
ejpam-5032	131	10	-	-	NOUN
ejpam-5032	131	11	group	group	NOUN
ejpam-5032	131	12	of	of	ADP
ejpam-5032	131	13	type	type	NOUN
ejpam-5032	131	14	2	2	NUM
ejpam-5032	131	15	,	,	PUNCT
ejpam-5032	131	16	k	k	X
ejpam-5032	131	17	is	be	AUX
ejpam-5032	131	18	an	an	DET
ejpam-5032	131	19	ideal	ideal	NOUN
ejpam-5032	131	20	of	of	ADP
ejpam-5032	131	21	n	n	PROPN
ejpam-5032	131	22	.	.	PUNCT
ejpam-5032	132	1	for	for	ADP
ejpam-5032	132	2	h	h	PROPN
ejpam-5032	132	3	∈	∈	PROPN
ejpam-5032	132	4	h	h	NOUN
ejpam-5032	132	5	,	,	PUNCT
ejpam-5032	132	6	x	x	SYM
ejpam-5032	132	7	∈	∈	NOUN
ejpam-5032	132	8	n	n	PRON
ejpam-5032	132	9	define	define	VERB
ejpam-5032	132	10	hx	hx	INTJ
ejpam-5032	132	11	:	:	PUNCT
ejpam-5032	132	12	=	=	PUNCT
ejpam-5032	132	13	h(x+k	h(x+k	NOUN
ejpam-5032	132	14	)	)	PUNCT
ejpam-5032	132	15	.	.	PUNCT
ejpam-5032	133	1	note	note	VERB
ejpam-5032	133	2	thathk	thathk	NOUN
ejpam-5032	133	3	=	=	SYM
ejpam-5032	133	4	{	{	PUNCT
ejpam-5032	133	5	0	0	NUM
ejpam-5032	133	6	}	}	PUNCT
ejpam-5032	133	7	.	.	PUNCT
ejpam-5032	134	1	clearlyh	clearlyh	PROPN
ejpam-5032	134	2	is	be	AUX
ejpam-5032	134	3	ann	ann	PROPN
ejpam-5032	134	4	-group	-group	PROPN
ejpam-5032	134	5	under	under	ADP
ejpam-5032	134	6	the	the	DET
ejpam-5032	134	7	above	above	ADJ
ejpam-5032	134	8	operation	operation	NOUN
ejpam-5032	134	9	.	.	PUNCT
ejpam-5032	135	1	it	it	PRON
ejpam-5032	135	2	is	be	AUX
ejpam-5032	135	3	an	an	DET
ejpam-5032	135	4	easy	easy	ADJ
ejpam-5032	135	5	observation	observation	NOUN
ejpam-5032	135	6	that	that	SCONJ
ejpam-5032	135	7	this	this	DET
ejpam-5032	135	8	operation	operation	NOUN
ejpam-5032	135	9	also	also	ADV
ejpam-5032	135	10	satisfies	satisfy	VERB
ejpam-5032	135	11	all	all	DET
ejpam-5032	135	12	the	the	DET
ejpam-5032	135	13	three	three	NUM
ejpam-5032	135	14	conditions	condition	NOUN
ejpam-5032	135	15	of	of	ADP
ejpam-5032	135	16	a	a	DET
ejpam-5032	135	17	prime	prime	ADJ
ejpam-5032	135	18	n	n	ADP
ejpam-5032	135	19	-group	-group	NOUN
ejpam-5032	135	20	of	of	ADP
ejpam-5032	135	21	type	type	NOUN
ejpam-5032	135	22	2	2	NUM
ejpam-5032	135	23	.	.	PUNCT
ejpam-5032	136	1	so	so	ADV
ejpam-5032	136	2	h	h	NOUN
ejpam-5032	136	3	is	be	AUX
ejpam-5032	136	4	a	a	DET
ejpam-5032	136	5	prime	prime	ADJ
ejpam-5032	136	6	n	n	ADP
ejpam-5032	136	7	-group	-group	NOUN
ejpam-5032	136	8	of	of	ADP
ejpam-5032	136	9	type	type	NOUN
ejpam-5032	136	10	2	2	NUM
ejpam-5032	136	11	.	.	PUNCT
ejpam-5032	137	1	let	let	VERB
ejpam-5032	137	2	m	m	PRON
ejpam-5032	137	3	/	/	SYM
ejpam-5032	137	4	k	k	PROPN
ejpam-5032	137	5	be	be	AUX
ejpam-5032	137	6	the	the	DET
ejpam-5032	137	7	largest	large	ADJ
ejpam-5032	137	8	ideal	ideal	NOUN
ejpam-5032	137	9	of	of	ADP
ejpam-5032	137	10	n	n	CCONJ
ejpam-5032	137	11	/	/	SYM
ejpam-5032	137	12	k	k	PROPN
ejpam-5032	137	13	contained	contain	VERB
ejpam-5032	137	14	in	in	ADP
ejpam-5032	137	15	an	an	DET
ejpam-5032	137	16	n	n	CCONJ
ejpam-5032	137	17	/	/	SYM
ejpam-5032	137	18	k(h	k(h	PROPN
ejpam-5032	137	19	)	)	PUNCT
ejpam-5032	137	20	,	,	PUNCT
ejpam-5032	137	21	that	that	ADV
ejpam-5032	137	22	is	is	ADV
ejpam-5032	137	23	,	,	PUNCT
ejpam-5032	137	24	(	(	PUNCT
ejpam-5032	137	25	h	h	NOUN
ejpam-5032	137	26	:	:	PUNCT
ejpam-5032	138	1	0)n	0)n	PROPN
ejpam-5032	138	2	/	/	SYM
ejpam-5032	138	3	k	k	PROPN
ejpam-5032	138	4	=	=	PUNCT
ejpam-5032	138	5	m	m	PROPN
ejpam-5032	138	6	/	/	SYM
ejpam-5032	138	7	k.	k.	PROPN
ejpam-5032	138	8	since	since	SCONJ
ejpam-5032	138	9	h(m	h(m	PROPN
ejpam-5032	138	10	/	/	SYM
ejpam-5032	138	11	k	k	NOUN
ejpam-5032	138	12	)	)	PUNCT
ejpam-5032	138	13	=	=	PUNCT
ejpam-5032	138	14	{	{	PUNCT
ejpam-5032	138	15	0	0	NUM
ejpam-5032	138	16	}	}	PUNCT
ejpam-5032	138	17	,	,	PUNCT
ejpam-5032	138	18	we	we	PRON
ejpam-5032	138	19	have	have	VERB
ejpam-5032	138	20	hm	hm	VERB
ejpam-5032	138	21	=	=	X
ejpam-5032	138	22	{	{	PUNCT
ejpam-5032	138	23	0	0	NUM
ejpam-5032	138	24	}	}	PUNCT
ejpam-5032	138	25	.	.	PUNCT
ejpam-5032	139	1	so	so	ADV
ejpam-5032	139	2	(	(	PUNCT
ejpam-5032	139	3	h	h	NOUN
ejpam-5032	139	4	:	:	PUNCT
ejpam-5032	139	5	0)n	0)n	PROPN
ejpam-5032	139	6	/	/	SYM
ejpam-5032	139	7	k	k	PROPN
ejpam-5032	140	1	⊆	⊆	NUM
ejpam-5032	140	2	(	(	PUNCT
ejpam-5032	140	3	h	h	NOUN
ejpam-5032	140	4	:	:	PUNCT
ejpam-5032	140	5	0)n	0)n	PROPN
ejpam-5032	140	6	/	/	SYM
ejpam-5032	140	7	k.	k.	PROPN
ejpam-5032	140	8	let	let	VERB
ejpam-5032	140	9	t	t	PROPN
ejpam-5032	140	10	be	be	AUX
ejpam-5032	140	11	the	the	DET
ejpam-5032	140	12	largest	large	ADJ
ejpam-5032	140	13	ideal	ideal	NOUN
ejpam-5032	140	14	of	of	ADP
ejpam-5032	140	15	n	n	NUM
ejpam-5032	140	16	contained	contain	VERB
ejpam-5032	140	17	in	in	ADP
ejpam-5032	140	18	an	an	DET
ejpam-5032	140	19	n	n	NOUN
ejpam-5032	140	20	(	(	PUNCT
ejpam-5032	140	21	h	h	NOUN
ejpam-5032	140	22	)	)	PUNCT
ejpam-5032	140	23	,	,	PUNCT
ejpam-5032	140	24	that	that	ADV
ejpam-5032	140	25	is	is	ADV
ejpam-5032	140	26	(	(	PUNCT
ejpam-5032	140	27	h	h	NOUN
ejpam-5032	140	28	:	:	PUNCT
ejpam-5032	140	29	0)n	0)n	X
ejpam-5032	141	1	=	=	PUNCT
ejpam-5032	141	2	t	t	PROPN
ejpam-5032	141	3	.	.	PUNCT
ejpam-5032	142	1	now	now	ADV
ejpam-5032	142	2	k	k	PROPN
ejpam-5032	142	3	⊆	⊆	NUM
ejpam-5032	142	4	t	t	NOUN
ejpam-5032	142	5	and	and	CCONJ
ejpam-5032	142	6	h(t	h(t	PROPN
ejpam-5032	142	7	/	/	SYM
ejpam-5032	142	8	k	k	NOUN
ejpam-5032	142	9	)	)	PUNCT
ejpam-5032	142	10	=	=	SYM
ejpam-5032	142	11	{	{	PUNCT
ejpam-5032	142	12	0	0	NUM
ejpam-5032	142	13	}	}	PUNCT
ejpam-5032	142	14	as	as	ADP
ejpam-5032	142	15	ht	ht	PROPN
ejpam-5032	142	16	=	=	PUNCT
ejpam-5032	142	17	{	{	PUNCT
ejpam-5032	142	18	0	0	NUM
ejpam-5032	142	19	}	}	PUNCT
ejpam-5032	142	20	.	.	PUNCT
ejpam-5032	143	1	so	so	ADV
ejpam-5032	143	2	(	(	PUNCT
ejpam-5032	143	3	h	h	NOUN
ejpam-5032	143	4	:	:	PUNCT
ejpam-5032	143	5	0)n	0)n	PROPN
ejpam-5032	143	6	/	/	SYM
ejpam-5032	143	7	k	k	PROPN
ejpam-5032	144	1	⊆	⊆	NUM
ejpam-5032	144	2	(	(	PUNCT
ejpam-5032	144	3	h	h	NOUN
ejpam-5032	144	4	:	:	PUNCT
ejpam-5032	144	5	0)n	0)n	PROPN
ejpam-5032	144	6	/	/	SYM
ejpam-5032	145	1	k	k	PROPN
ejpam-5032	145	2	.	.	PUNCT
ejpam-5032	146	1	therefore	therefore	ADV
ejpam-5032	146	2	(	(	PUNCT
ejpam-5032	146	3	h	h	NOUN
ejpam-5032	146	4	:	:	PUNCT
ejpam-5032	146	5	0)n	0)n	PROPN
ejpam-5032	146	6	/	/	SYM
ejpam-5032	146	7	k	k	PROPN
ejpam-5032	147	1	=	=	PUNCT
ejpam-5032	147	2	(	(	PUNCT
ejpam-5032	147	3	h	h	NOUN
ejpam-5032	147	4	:	:	PUNCT
ejpam-5032	147	5	0)n	0)n	PROPN
ejpam-5032	147	6	/	/	SYM
ejpam-5032	148	1	k	k	PROPN
ejpam-5032	148	2	.	.	PUNCT
ejpam-5032	149	1	3	3	X
ejpam-5032	149	2	.	.	X
ejpam-5032	149	3	the	the	DET
ejpam-5032	149	4	right	right	ADJ
ejpam-5032	149	5	prime	prime	ADJ
ejpam-5032	149	6	radical	radical	NOUN
ejpam-5032	149	7	of	of	ADP
ejpam-5032	149	8	type	type	NOUN
ejpam-5032	149	9	2	2	NUM
ejpam-5032	149	10	n	n	NOUN
ejpam-5032	149	11	denotes	denote	VERB
ejpam-5032	149	12	the	the	DET
ejpam-5032	149	13	class	class	NOUN
ejpam-5032	149	14	of	of	ADP
ejpam-5032	149	15	zero	zero	NUM
ejpam-5032	149	16	-	-	PUNCT
ejpam-5032	149	17	symmetric	symmetric	ADJ
ejpam-5032	149	18	near	near	ADJ
ejpam-5032	149	19	-	-	PUNCT
ejpam-5032	149	20	rings	ring	NOUN
ejpam-5032	149	21	.	.	PUNCT
ejpam-5032	150	1	an	an	DET
ejpam-5032	150	2	ideal	ideal	ADJ
ejpam-5032	150	3	-	-	PUNCT
ejpam-5032	150	4	mapping	mapping	NOUN
ejpam-5032	150	5	onn	onn	NOUN
ejpam-5032	150	6	is	be	AUX
ejpam-5032	150	7	a	a	DET
ejpam-5032	150	8	mapping	mapping	NOUN
ejpam-5032	150	9	r	r	NOUN
ejpam-5032	150	10	from	from	ADP
ejpam-5032	150	11	n	n	NOUN
ejpam-5032	150	12	into	into	ADP
ejpam-5032	150	13	itself	itself	PRON
ejpam-5032	150	14	such	such	ADJ
ejpam-5032	150	15	that	that	SCONJ
ejpam-5032	150	16	r(n	r(n	PROPN
ejpam-5032	150	17	)	)	PUNCT
ejpam-5032	150	18	is	be	AUX
ejpam-5032	150	19	an	an	DET
ejpam-5032	150	20	ideal	ideal	NOUN
ejpam-5032	150	21	of	of	ADP
ejpam-5032	150	22	n	n	PROPN
ejpam-5032	150	23	for	for	ADP
ejpam-5032	150	24	all	all	PRON
ejpam-5032	150	25	n	n	PRON
ejpam-5032	150	26	∈	∈	PROPN
ejpam-5032	150	27	n	n	NOUN
ejpam-5032	150	28	.	.	PUNCT
ejpam-5032	151	1	an	an	DET
ejpam-5032	151	2	ideal	ideal	ADJ
ejpam-5032	151	3	-	-	PUNCT
ejpam-5032	151	4	mapping	mapping	NOUN
ejpam-5032	151	5	is	be	AUX
ejpam-5032	151	6	a	a	DET
ejpam-5032	151	7	hoehnke	hoehnke	ADJ
ejpam-5032	151	8	radical	radical	ADJ
ejpam-5032	151	9	or	or	CCONJ
ejpam-5032	151	10	h	h	NOUN
ejpam-5032	151	11	-	-	PUNCT
ejpam-5032	151	12	radical	radical	ADJ
ejpam-5032	151	13	if	if	SCONJ
ejpam-5032	151	14	:	:	PUNCT
ejpam-5032	151	15	(	(	PUNCT
ejpam-5032	151	16	i	i	NOUN
ejpam-5032	151	17	)	)	PUNCT
ejpam-5032	151	18	t(r(n	t(r(n	NOUN
ejpam-5032	151	19	)	)	PUNCT
ejpam-5032	151	20	)	)	PUNCT
ejpam-5032	152	1	⊆	⊆	NUM
ejpam-5032	152	2	r(t(n	r(t(n	NUM
ejpam-5032	152	3	)	)	PUNCT
ejpam-5032	152	4	)	)	PUNCT
ejpam-5032	152	5	for	for	ADP
ejpam-5032	152	6	all	all	DET
ejpam-5032	152	7	homomorphisms	homomorphisms	PROPN
ejpam-5032	152	8	t	t	PROPN
ejpam-5032	152	9	of	of	ADP
ejpam-5032	152	10	n	n	PROPN
ejpam-5032	152	11	in	in	ADP
ejpam-5032	152	12	n	n	PROPN
ejpam-5032	152	13	;	;	PUNCT
ejpam-5032	152	14	(	(	PUNCT
ejpam-5032	152	15	ii	ii	NOUN
ejpam-5032	152	16	)	)	PUNCT
ejpam-5032	152	17	r(n	r(n	PROPN
ejpam-5032	152	18	/	/	SYM
ejpam-5032	152	19	r(n	r(n	PROPN
ejpam-5032	152	20	)	)	PUNCT
ejpam-5032	152	21	)	)	PUNCT
ejpam-5032	153	1	=	=	PRON
ejpam-5032	154	1	{	{	PUNCT
ejpam-5032	154	2	0	0	NUM
ejpam-5032	154	3	}	}	PUNCT
ejpam-5032	154	4	for	for	ADP
ejpam-5032	154	5	all	all	DET
ejpam-5032	154	6	n	n	NOUN
ejpam-5032	154	7	in	in	ADP
ejpam-5032	154	8	n	n	PROPN
ejpam-5032	154	9	.	.	PUNCT
ejpam-5032	155	1	for	for	ADP
ejpam-5032	155	2	a	a	DET
ejpam-5032	155	3	class	class	NOUN
ejpam-5032	155	4	of	of	ADP
ejpam-5032	155	5	near	near	ADJ
ejpam-5032	155	6	-	-	PUNCT
ejpam-5032	155	7	rings	ring	NOUN
ejpam-5032	155	8	m	m	NOUN
ejpam-5032	155	9	⊆	⊆	NUM
ejpam-5032	155	10	n	n	NOUN
ejpam-5032	155	11	and	and	CCONJ
ejpam-5032	155	12	for	for	ADP
ejpam-5032	155	13	n	n	PRON
ejpam-5032	155	14	in	in	ADP
ejpam-5032	155	15	n	n	PROPN
ejpam-5032	155	16	,	,	PUNCT
ejpam-5032	155	17	we	we	PRON
ejpam-5032	155	18	have	have	VERB
ejpam-5032	155	19	(	(	PUNCT
ejpam-5032	155	20	n)m	n)m	PUNCT
ejpam-5032	155	21	:	:	PUNCT
ejpam-5032	156	1	=	=	X
ejpam-5032	156	2	∩(j	∩(j	PROPN
ejpam-5032	157	1	|	|	ADV
ejpam-5032	157	2	j	j	PROPN
ejpam-5032	157	3	is	be	AUX
ejpam-5032	157	4	an	an	DET
ejpam-5032	157	5	ideal	ideal	NOUN
ejpam-5032	157	6	of	of	ADP
ejpam-5032	157	7	n	n	PROPN
ejpam-5032	157	8	and	and	CCONJ
ejpam-5032	157	9	n	n	CCONJ
ejpam-5032	157	10	/	/	SYM
ejpam-5032	157	11	j	j	PROPN
ejpam-5032	157	12	∈	∈	PROPN
ejpam-5032	157	13	m	m	PROPN
ejpam-5032	157	14	)	)	PUNCT
ejpam-5032	157	15	.	.	PUNCT
ejpam-5032	158	1	corresponding	correspond	VERB
ejpam-5032	158	2	to	to	ADP
ejpam-5032	158	3	any	any	DET
ejpam-5032	158	4	class	class	NOUN
ejpam-5032	158	5	of	of	ADP
ejpam-5032	158	6	near	near	ADJ
ejpam-5032	158	7	-	-	PUNCT
ejpam-5032	158	8	rings	ring	NOUN
ejpam-5032	158	9	m	m	NOUN
ejpam-5032	158	10	⊆	⊆	NUM
ejpam-5032	158	11	n	n	NOUN
ejpam-5032	158	12	,	,	PUNCT
ejpam-5032	158	13	we	we	PRON
ejpam-5032	158	14	have	have	VERB
ejpam-5032	158	15	an	an	DET
ejpam-5032	158	16	ideal	ideal	ADJ
ejpam-5032	158	17	-	-	PUNCT
ejpam-5032	158	18	mapping	mapping	NOUN
ejpam-5032	158	19	r	r	NOUN
ejpam-5032	158	20	defined	define	VERB
ejpam-5032	158	21	by	by	ADP
ejpam-5032	158	22	r(n	r(n	PROPN
ejpam-5032	158	23	)	)	PUNCT
ejpam-5032	158	24	:	:	PUNCT
ejpam-5032	159	1	=	=	SYM
ejpam-5032	159	2	(	(	PUNCT
ejpam-5032	159	3	n)m	n)m	PUNCT
ejpam-5032	159	4	and	and	CCONJ
ejpam-5032	159	5	it	it	PRON
ejpam-5032	159	6	is	be	AUX
ejpam-5032	159	7	well	well	ADV
ejpam-5032	159	8	known	know	VERB
ejpam-5032	159	9	that	that	SCONJ
ejpam-5032	159	10	this	this	DET
ejpam-5032	159	11	ideal	ideal	ADJ
ejpam-5032	159	12	-	-	PUNCT
ejpam-5032	159	13	mapping	mapping	NOUN
ejpam-5032	159	14	r	r	NOUN
ejpam-5032	159	15	is	be	AUX
ejpam-5032	159	16	a	a	DET
ejpam-5032	159	17	h	h	NOUN
ejpam-5032	159	18	-	-	PUNCT
ejpam-5032	159	19	radical	radical	ADJ
ejpam-5032	159	20	.	.	PUNCT
ejpam-5032	160	1	definition	definition	NOUN
ejpam-5032	160	2	3	3	NUM
ejpam-5032	160	3	.	.	PUNCT
ejpam-5032	161	1	an	an	DET
ejpam-5032	161	2	ideal	ideal	ADJ
ejpam-5032	161	3	p	p	NOUN
ejpam-5032	161	4	of	of	ADP
ejpam-5032	161	5	a	a	DET
ejpam-5032	161	6	near	near	ADJ
ejpam-5032	161	7	-	-	PUNCT
ejpam-5032	161	8	ring	ring	NOUN
ejpam-5032	161	9	n	n	NOUN
ejpam-5032	161	10	is	be	AUX
ejpam-5032	161	11	a	a	DET
ejpam-5032	161	12	right	right	ADJ
ejpam-5032	161	13	prime	prime	ADJ
ejpam-5032	161	14	ideal	ideal	NOUN
ejpam-5032	161	15	of	of	ADP
ejpam-5032	161	16	type	type	NOUN
ejpam-5032	161	17	2	2	NUM
ejpam-5032	161	18	if	if	SCONJ
ejpam-5032	161	19	p	p	NOUN
ejpam-5032	161	20	=	=	PUNCT
ejpam-5032	161	21	(	(	PUNCT
ejpam-5032	161	22	h	h	NOUN
ejpam-5032	161	23	:	:	PUNCT
ejpam-5032	161	24	0	0	NUM
ejpam-5032	161	25	)	)	PUNCT
ejpam-5032	161	26	for	for	ADP
ejpam-5032	161	27	a	a	DET
ejpam-5032	161	28	prime	prime	ADJ
ejpam-5032	161	29	n	n	CCONJ
ejpam-5032	161	30	-group	-group	NOUN
ejpam-5032	161	31	h	h	NOUN
ejpam-5032	161	32	of	of	ADP
ejpam-5032	161	33	type	type	NOUN
ejpam-5032	161	34	2	2	NUM
ejpam-5032	161	35	.	.	PUNCT
ejpam-5032	162	1	it	it	PRON
ejpam-5032	162	2	can	can	AUX
ejpam-5032	162	3	be	be	AUX
ejpam-5032	162	4	observed	observe	VERB
ejpam-5032	162	5	that	that	SCONJ
ejpam-5032	162	6	a	a	DET
ejpam-5032	162	7	right	right	ADJ
ejpam-5032	162	8	prime	prime	ADJ
ejpam-5032	162	9	ideal	ideal	NOUN
ejpam-5032	162	10	of	of	ADP
ejpam-5032	162	11	n	n	PROPN
ejpam-5032	162	12	of	of	ADP
ejpam-5032	162	13	type	type	NOUN
ejpam-5032	162	14	2	2	NUM
ejpam-5032	162	15	is	be	AUX
ejpam-5032	162	16	a	a	DET
ejpam-5032	162	17	prime	prime	ADJ
ejpam-5032	162	18	ideal	ideal	NOUN
ejpam-5032	162	19	of	of	ADP
ejpam-5032	162	20	n	n	PROPN
ejpam-5032	162	21	[	[	X
ejpam-5032	162	22	4	4	NUM
ejpam-5032	162	23	]	]	PUNCT
ejpam-5032	162	24	.	.	PUNCT
ejpam-5032	163	1	if	if	SCONJ
ejpam-5032	163	2	n	n	PRON
ejpam-5032	163	3	is	be	AUX
ejpam-5032	163	4	a	a	DET
ejpam-5032	163	5	ring	ring	NOUN
ejpam-5032	163	6	then	then	ADV
ejpam-5032	163	7	a	a	DET
ejpam-5032	163	8	right	right	ADJ
ejpam-5032	163	9	prime	prime	ADJ
ejpam-5032	163	10	ideal	ideal	NOUN
ejpam-5032	163	11	of	of	ADP
ejpam-5032	163	12	n	n	PROPN
ejpam-5032	163	13	of	of	ADP
ejpam-5032	163	14	type	type	NOUN
ejpam-5032	163	15	2	2	NUM
ejpam-5032	163	16	is	be	AUX
ejpam-5032	163	17	a	a	DET
ejpam-5032	163	18	prime	prime	ADJ
ejpam-5032	163	19	ideal	ideal	NOUN
ejpam-5032	163	20	of	of	ADP
ejpam-5032	163	21	the	the	DET
ejpam-5032	163	22	ring	ring	NOUN
ejpam-5032	163	23	n	n	NOUN
ejpam-5032	163	24	.	.	PUNCT
ejpam-5032	164	1	definition	definition	NOUN
ejpam-5032	164	2	4	4	NUM
ejpam-5032	164	3	.	.	PUNCT
ejpam-5032	165	1	a	a	DET
ejpam-5032	165	2	near	near	ADV
ejpam-5032	165	3	-	-	PUNCT
ejpam-5032	165	4	ring	ring	NOUN
ejpam-5032	165	5	is	be	AUX
ejpam-5032	165	6	a	a	DET
ejpam-5032	165	7	right	right	ADJ
ejpam-5032	165	8	prime	prime	ADJ
ejpam-5032	165	9	near	near	ADP
ejpam-5032	165	10	-	-	PUNCT
ejpam-5032	165	11	ring	ring	NOUN
ejpam-5032	165	12	of	of	ADP
ejpam-5032	165	13	type	type	NOUN
ejpam-5032	165	14	2	2	NUM
ejpam-5032	165	15	if	if	SCONJ
ejpam-5032	165	16	the	the	DET
ejpam-5032	165	17	zero	zero	NUM
ejpam-5032	165	18	ideal	ideal	NOUN
ejpam-5032	165	19	of	of	ADP
ejpam-5032	165	20	n	n	PROPN
ejpam-5032	165	21	is	be	AUX
ejpam-5032	165	22	a	a	DET
ejpam-5032	165	23	right	right	ADJ
ejpam-5032	165	24	prime	prime	ADJ
ejpam-5032	165	25	ideal	ideal	NOUN
ejpam-5032	165	26	of	of	ADP
ejpam-5032	165	27	type	type	NOUN
ejpam-5032	165	28	2	2	NUM
ejpam-5032	165	29	.	.	PUNCT
ejpam-5032	165	30	definition	definition	NOUN
ejpam-5032	165	31	5	5	NUM
ejpam-5032	165	32	.	.	PUNCT
ejpam-5032	166	1	the	the	DET
ejpam-5032	166	2	right	right	ADJ
ejpam-5032	166	3	prime	prime	ADJ
ejpam-5032	166	4	radical	radical	NOUN
ejpam-5032	166	5	of	of	ADP
ejpam-5032	166	6	n	n	PROPN
ejpam-5032	166	7	of	of	ADP
ejpam-5032	166	8	type	type	NOUN
ejpam-5032	166	9	2	2	NUM
ejpam-5032	166	10	is	be	AUX
ejpam-5032	166	11	the	the	DET
ejpam-5032	166	12	intersection	intersection	NOUN
ejpam-5032	166	13	of	of	ADP
ejpam-5032	166	14	all	all	DET
ejpam-5032	166	15	right	right	ADJ
ejpam-5032	166	16	prime	prime	ADJ
ejpam-5032	166	17	ideals	ideal	NOUN
ejpam-5032	166	18	of	of	ADP
ejpam-5032	166	19	n	n	NOUN
ejpam-5032	166	20	of	of	ADP
ejpam-5032	166	21	type	type	NOUN
ejpam-5032	166	22	2	2	NUM
ejpam-5032	166	23	and	and	CCONJ
ejpam-5032	166	24	it	it	PRON
ejpam-5032	166	25	will	will	AUX
ejpam-5032	166	26	be	be	AUX
ejpam-5032	166	27	denoted	denote	VERB
ejpam-5032	166	28	by	by	ADP
ejpam-5032	166	29	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	166	30	)	)	PUNCT
ejpam-5032	166	31	.	.	PUNCT
ejpam-5032	167	1	now	now	ADV
ejpam-5032	167	2	it	it	PRON
ejpam-5032	167	3	will	will	AUX
ejpam-5032	167	4	be	be	AUX
ejpam-5032	167	5	proved	prove	VERB
ejpam-5032	167	6	that	that	SCONJ
ejpam-5032	167	7	p2(r	p2(r	NOUN
ejpam-5032	167	8	)	)	PUNCT
ejpam-5032	167	9	is	be	AUX
ejpam-5032	167	10	a	a	DET
ejpam-5032	167	11	h	h	NOUN
ejpam-5032	167	12	-	-	PUNCT
ejpam-5032	167	13	radical	radical	ADJ
ejpam-5032	167	14	.	.	PUNCT
ejpam-5032	168	1	theorem	theorem	NOUN
ejpam-5032	168	2	1	1	NUM
ejpam-5032	168	3	.	.	X
ejpam-5032	169	1	p2(r	p2(r	NOUN
ejpam-5032	169	2	)	)	PUNCT
ejpam-5032	169	3	is	be	AUX
ejpam-5032	169	4	a	a	DET
ejpam-5032	169	5	h	h	NOUN
ejpam-5032	169	6	-	-	PUNCT
ejpam-5032	169	7	radical	radical	ADJ
ejpam-5032	169	8	.	.	PUNCT
ejpam-5032	170	1	proof	proof	NOUN
ejpam-5032	170	2	.	.	PUNCT
ejpam-5032	171	1	let	let	VERB
ejpam-5032	171	2	a	a	PRON
ejpam-5032	171	3	be	be	AUX
ejpam-5032	171	4	the	the	DET
ejpam-5032	171	5	h	h	ADJ
ejpam-5032	171	6	-	-	PUNCT
ejpam-5032	171	7	radical	radical	ADJ
ejpam-5032	171	8	determined	determine	VERB
ejpam-5032	171	9	by	by	ADP
ejpam-5032	171	10	the	the	DET
ejpam-5032	171	11	class	class	NOUN
ejpam-5032	171	12	of	of	ADP
ejpam-5032	171	13	right	right	ADJ
ejpam-5032	171	14	prime	prime	ADJ
ejpam-5032	171	15	near	near	ADP
ejpam-5032	171	16	-	-	PUNCT
ejpam-5032	171	17	ring	ring	NOUN
ejpam-5032	171	18	of	of	ADP
ejpam-5032	171	19	type	type	NOUN
ejpam-5032	171	20	2	2	NUM
ejpam-5032	171	21	.	.	PUNCT
ejpam-5032	172	1	let	let	VERB
ejpam-5032	172	2	q	q	PART
ejpam-5032	172	3	be	be	AUX
ejpam-5032	172	4	a	a	DET
ejpam-5032	172	5	right	right	ADJ
ejpam-5032	172	6	prime	prime	ADJ
ejpam-5032	172	7	ideal	ideal	NOUN
ejpam-5032	172	8	of	of	ADP
ejpam-5032	172	9	n	n	PROPN
ejpam-5032	172	10	of	of	ADP
ejpam-5032	172	11	type	type	NOUN
ejpam-5032	172	12	2	2	NUM
ejpam-5032	172	13	.	.	PUNCT
ejpam-5032	173	1	we	we	PRON
ejpam-5032	173	2	get	get	VERB
ejpam-5032	173	3	a	a	DET
ejpam-5032	173	4	prime	prime	ADJ
ejpam-5032	173	5	n	n	CCONJ
ejpam-5032	173	6	-group	-group	NOUN
ejpam-5032	173	7	h	h	NOUN
ejpam-5032	173	8	of	of	ADP
ejpam-5032	173	9	type	type	NOUN
ejpam-5032	173	10	2	2	NUM
ejpam-5032	173	11	such	such	ADJ
ejpam-5032	173	12	that	that	DET
ejpam-5032	173	13	q	q	NOUN
ejpam-5032	174	1	=	=	PUNCT
ejpam-5032	174	2	(	(	PUNCT
ejpam-5032	174	3	h	h	NOUN
ejpam-5032	174	4	:	:	PUNCT
ejpam-5032	174	5	0	0	NUM
ejpam-5032	174	6	)	)	PUNCT
ejpam-5032	174	7	.	.	PUNCT
ejpam-5032	175	1	by	by	ADP
ejpam-5032	175	2	proposition	proposition	NOUN
ejpam-5032	175	3	2	2	NUM
ejpam-5032	175	4	,	,	PUNCT
ejpam-5032	175	5	there	there	PRON
ejpam-5032	175	6	is	be	VERB
ejpam-5032	175	7	a	a	DET
ejpam-5032	175	8	prime	prime	ADJ
ejpam-5032	175	9	n	n	CCONJ
ejpam-5032	175	10	/	/	SYM
ejpam-5032	175	11	q	q	NOUN
ejpam-5032	175	12	-	-	PUNCT
ejpam-5032	175	13	group	group	NOUN
ejpam-5032	175	14	b	b	PROPN
ejpam-5032	175	15	of	of	ADP
ejpam-5032	175	16	type	type	NOUN
ejpam-5032	175	17	2	2	NUM
ejpam-5032	175	18	such	such	ADJ
ejpam-5032	175	19	that	that	SCONJ
ejpam-5032	175	20	(	(	PUNCT
ejpam-5032	175	21	b	b	X
ejpam-5032	175	22	:	:	PUNCT
ejpam-5032	175	23	0)n	0)n	PROPN
ejpam-5032	175	24	/	/	SYM
ejpam-5032	175	25	q	q	NOUN
ejpam-5032	176	1	=	=	PUNCT
ejpam-5032	176	2	(	(	PUNCT
ejpam-5032	176	3	h	h	NOUN
ejpam-5032	176	4	:	:	PUNCT
ejpam-5032	176	5	0)n	0)n	X
ejpam-5032	176	6	/	/	SYM
ejpam-5032	176	7	q	q	NOUN
ejpam-5032	176	8	=	=	NOUN
ejpam-5032	176	9	q	q	NOUN
ejpam-5032	176	10	/	/	SYM
ejpam-5032	176	11	q	q	NOUN
ejpam-5032	176	12	=	=	PUNCT
ejpam-5032	176	13	{	{	PUNCT
ejpam-5032	176	14	0	0	NUM
ejpam-5032	176	15	}	}	PUNCT
ejpam-5032	176	16	.	.	PUNCT
ejpam-5032	177	1	so	so	ADV
ejpam-5032	177	2	n	n	CCONJ
ejpam-5032	177	3	/	/	SYM
ejpam-5032	177	4	q	q	NOUN
ejpam-5032	177	5	is	be	AUX
ejpam-5032	177	6	right	right	ADJ
ejpam-5032	177	7	prime	prime	ADJ
ejpam-5032	177	8	near	near	ADP
ejpam-5032	177	9	-	-	PUNCT
ejpam-5032	177	10	ring	ring	NOUN
ejpam-5032	177	11	of	of	ADP
ejpam-5032	177	12	type	type	NOUN
ejpam-5032	177	13	2	2	NUM
ejpam-5032	177	14	.	.	PUNCT
ejpam-5032	177	15	therefore	therefore	ADV
ejpam-5032	177	16	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	177	17	)	)	PUNCT
ejpam-5032	177	18	⊇	⊇	NOUN
ejpam-5032	177	19	a(n	a(n	NOUN
ejpam-5032	177	20	)	)	PUNCT
ejpam-5032	177	21	.	.	PUNCT
ejpam-5032	178	1	on	on	ADP
ejpam-5032	178	2	the	the	DET
ejpam-5032	178	3	other	other	ADJ
ejpam-5032	178	4	hand	hand	NOUN
ejpam-5032	178	5	suppose	suppose	VERB
ejpam-5032	178	6	that	that	SCONJ
ejpam-5032	178	7	p	p	PROPN
ejpam-5032	178	8	is	be	AUX
ejpam-5032	178	9	an	an	DET
ejpam-5032	178	10	ideal	ideal	NOUN
ejpam-5032	178	11	of	of	ADP
ejpam-5032	178	12	n	n	PROPN
ejpam-5032	178	13	and	and	CCONJ
ejpam-5032	178	14	n	n	CCONJ
ejpam-5032	178	15	/	/	SYM
ejpam-5032	178	16	p	p	NOUN
ejpam-5032	178	17	is	be	AUX
ejpam-5032	178	18	right	right	ADJ
ejpam-5032	178	19	prime	prime	ADJ
ejpam-5032	178	20	near	near	ADP
ejpam-5032	178	21	-	-	PUNCT
ejpam-5032	178	22	ring	ring	NOUN
ejpam-5032	178	23	of	of	ADP
ejpam-5032	178	24	type	type	NOUN
ejpam-5032	178	25	2	2	NUM
ejpam-5032	178	26	.	.	PUNCT
ejpam-5032	179	1	we	we	PRON
ejpam-5032	179	2	get	get	VERB
ejpam-5032	179	3	a	a	DET
ejpam-5032	179	4	prime	prime	NOUN
ejpam-5032	179	5	n	n	CCONJ
ejpam-5032	179	6	/	/	SYM
ejpam-5032	179	7	p	p	NOUN
ejpam-5032	179	8	-group	-group	NOUN
ejpam-5032	179	9	a	a	PRON
ejpam-5032	179	10	of	of	ADP
ejpam-5032	179	11	type	type	NOUN
ejpam-5032	180	1	k.	k.	PROPN
ejpam-5032	180	2	j.	j.	PROPN
ejpam-5032	180	3	lakshminarayana	lakshminarayana	PROPN
ejpam-5032	180	4	et	et	PROPN
ejpam-5032	180	5	al	al	PROPN
ejpam-5032	180	6	.	.	PUNCT
ejpam-5032	180	7	/	/	SYM
ejpam-5032	180	8	eur	eur	PROPN
ejpam-5032	180	9	.	.	PUNCT
ejpam-5032	181	1	j.	j.	PROPN
ejpam-5032	181	2	pure	pure	PROPN
ejpam-5032	181	3	appl	appl	PROPN
ejpam-5032	181	4	.	.	PROPN
ejpam-5032	181	5	math	math	PROPN
ejpam-5032	181	6	,	,	PUNCT
ejpam-5032	181	7	17	17	NUM
ejpam-5032	181	8	(	(	PUNCT
ejpam-5032	181	9	2	2	NUM
ejpam-5032	181	10	)	)	PUNCT
ejpam-5032	181	11	(	(	PUNCT
ejpam-5032	181	12	2024	2024	NUM
ejpam-5032	181	13	)	)	PUNCT
ejpam-5032	181	14	,	,	PUNCT
ejpam-5032	181	15	1206	1206	NUM
ejpam-5032	181	16	-	-	SYM
ejpam-5032	181	17	1212	1212	NUM
ejpam-5032	181	18	1210	1210	NUM
ejpam-5032	181	19	2	2	NUM
ejpam-5032	181	20	such	such	ADJ
ejpam-5032	181	21	that	that	SCONJ
ejpam-5032	181	22	(	(	PUNCT
ejpam-5032	181	23	a	a	PRON
ejpam-5032	181	24	:	:	PUNCT
ejpam-5032	181	25	0)n	0)n	NOUN
ejpam-5032	181	26	/	/	SYM
ejpam-5032	181	27	p	p	NOUN
ejpam-5032	181	28	=	=	X
ejpam-5032	181	29	{	{	PUNCT
ejpam-5032	181	30	0	0	NUM
ejpam-5032	181	31	}	}	PUNCT
ejpam-5032	181	32	.	.	PUNCT
ejpam-5032	182	1	by	by	ADP
ejpam-5032	182	2	proposition	proposition	NOUN
ejpam-5032	182	3	3	3	NUM
ejpam-5032	182	4	,	,	PUNCT
ejpam-5032	182	5	a	a	PRON
ejpam-5032	182	6	is	be	AUX
ejpam-5032	182	7	a	a	DET
ejpam-5032	182	8	prime	prime	ADJ
ejpam-5032	182	9	n	n	ADP
ejpam-5032	182	10	-group	-group	NOUN
ejpam-5032	182	11	of	of	ADP
ejpam-5032	182	12	type	type	NOUN
ejpam-5032	182	13	2	2	NUM
ejpam-5032	182	14	and	and	CCONJ
ejpam-5032	183	1	(	(	PUNCT
ejpam-5032	183	2	a	a	PRON
ejpam-5032	183	3	:	:	PUNCT
ejpam-5032	183	4	0)n	0)n	NOUN
ejpam-5032	183	5	/	/	SYM
ejpam-5032	183	6	p	p	NOUN
ejpam-5032	183	7	=	=	X
ejpam-5032	183	8	(	(	PUNCT
ejpam-5032	183	9	a	a	PRON
ejpam-5032	183	10	:	:	PUNCT
ejpam-5032	183	11	0)n	0)n	NOUN
ejpam-5032	183	12	/	/	SYM
ejpam-5032	183	13	p	p	NOUN
ejpam-5032	183	14	=	=	X
ejpam-5032	183	15	{	{	PUNCT
ejpam-5032	183	16	0	0	NUM
ejpam-5032	183	17	}	}	PUNCT
ejpam-5032	183	18	.	.	PUNCT
ejpam-5032	184	1	so	so	ADV
ejpam-5032	184	2	(	(	PUNCT
ejpam-5032	184	3	a	a	X
ejpam-5032	184	4	:	:	PUNCT
ejpam-5032	184	5	0)n	0)n	X
ejpam-5032	184	6	=	=	PUNCT
ejpam-5032	184	7	p	p	X
ejpam-5032	184	8	.	.	PUNCT
ejpam-5032	185	1	therefore	therefore	ADV
ejpam-5032	185	2	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	185	3	)	)	PUNCT
ejpam-5032	185	4	⊆	⊆	NUM
ejpam-5032	185	5	a(n	a(n	NOUN
ejpam-5032	185	6	)	)	PUNCT
ejpam-5032	185	7	.	.	PUNCT
ejpam-5032	186	1	hence	hence	ADV
ejpam-5032	186	2	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	186	3	)	)	PUNCT
ejpam-5032	186	4	=	=	PUNCT
ejpam-5032	186	5	a(n	a(n	NOUN
ejpam-5032	186	6	)	)	PUNCT
ejpam-5032	186	7	.	.	PUNCT
ejpam-5032	187	1	since	since	SCONJ
ejpam-5032	187	2	a	a	PRON
ejpam-5032	187	3	is	be	AUX
ejpam-5032	187	4	a	a	DET
ejpam-5032	187	5	h	h	NOUN
ejpam-5032	187	6	-	-	PUNCT
ejpam-5032	187	7	radical	radical	ADJ
ejpam-5032	187	8	,	,	PUNCT
ejpam-5032	187	9	p2(r	p2(r	PROPN
ejpam-5032	187	10	)	)	PUNCT
ejpam-5032	187	11	is	be	AUX
ejpam-5032	187	12	also	also	ADV
ejpam-5032	187	13	a	a	DET
ejpam-5032	187	14	h	h	ADJ
ejpam-5032	187	15	-	-	PUNCT
ejpam-5032	187	16	radical	radical	ADJ
ejpam-5032	187	17	.	.	PUNCT
ejpam-5032	188	1	theorem	theorem	NOUN
ejpam-5032	188	2	2	2	NUM
ejpam-5032	188	3	.	.	PUNCT
ejpam-5032	189	1	let	let	VERB
ejpam-5032	189	2	h	h	PRON
ejpam-5032	189	3	be	be	AUX
ejpam-5032	189	4	a	a	DET
ejpam-5032	189	5	prime	prime	ADJ
ejpam-5032	189	6	n	n	ADP
ejpam-5032	189	7	-group	-group	NOUN
ejpam-5032	189	8	of	of	ADP
ejpam-5032	189	9	type	type	NOUN
ejpam-5032	189	10	2	2	NUM
ejpam-5032	189	11	.	.	PUNCT
ejpam-5032	190	1	if	if	SCONJ
ejpam-5032	190	2	k	k	PROPN
ejpam-5032	190	3	is	be	AUX
ejpam-5032	190	4	an	an	DET
ejpam-5032	190	5	ideal	ideal	NOUN
ejpam-5032	190	6	of	of	ADP
ejpam-5032	190	7	n	n	PROPN
ejpam-5032	190	8	and	and	CCONJ
ejpam-5032	190	9	k	k	PROPN
ejpam-5032	190	10	̸⊆	̸⊆	X
ejpam-5032	190	11	(	(	PUNCT
ejpam-5032	190	12	h	h	NOUN
ejpam-5032	190	13	:	:	PUNCT
ejpam-5032	190	14	0	0	X
ejpam-5032	190	15	)	)	PUNCT
ejpam-5032	190	16	then	then	ADV
ejpam-5032	190	17	h	h	PROPN
ejpam-5032	190	18	is	be	AUX
ejpam-5032	190	19	a	a	DET
ejpam-5032	190	20	prime	prime	ADJ
ejpam-5032	190	21	k	k	NOUN
ejpam-5032	190	22	-	-	NOUN
ejpam-5032	190	23	group	group	NOUN
ejpam-5032	190	24	of	of	ADP
ejpam-5032	190	25	type	type	NOUN
ejpam-5032	190	26	2	2	NUM
ejpam-5032	190	27	and	and	CCONJ
ejpam-5032	190	28	(	(	PUNCT
ejpam-5032	190	29	h	h	NOUN
ejpam-5032	190	30	:	:	PUNCT
ejpam-5032	190	31	0)k	0)k	NOUN
ejpam-5032	190	32	⊇	⊇	PROPN
ejpam-5032	190	33	k	k	PROPN
ejpam-5032	190	34	∩	∩	PROPN
ejpam-5032	190	35	(	(	PUNCT
ejpam-5032	190	36	h	h	NOUN
ejpam-5032	190	37	:	:	PUNCT
ejpam-5032	190	38	0)n	0)n	X
ejpam-5032	190	39	.	.	PUNCT
ejpam-5032	191	1	proof	proof	NOUN
ejpam-5032	191	2	.	.	PUNCT
ejpam-5032	192	1	suppose	suppose	VERB
ejpam-5032	192	2	that	that	SCONJ
ejpam-5032	192	3	h	h	NOUN
ejpam-5032	192	4	is	be	AUX
ejpam-5032	192	5	a	a	DET
ejpam-5032	192	6	prime	prime	ADJ
ejpam-5032	192	7	n	n	ADP
ejpam-5032	192	8	-group	-group	NOUN
ejpam-5032	192	9	of	of	ADP
ejpam-5032	192	10	type	type	NOUN
ejpam-5032	192	11	2	2	NUM
ejpam-5032	192	12	and	and	CCONJ
ejpam-5032	192	13	k	k	PROPN
ejpam-5032	192	14	is	be	AUX
ejpam-5032	192	15	an	an	DET
ejpam-5032	192	16	ideal	ideal	NOUN
ejpam-5032	192	17	of	of	ADP
ejpam-5032	192	18	n	n	PRON
ejpam-5032	192	19	and	and	CCONJ
ejpam-5032	192	20	hk	hk	PROPN
ejpam-5032	192	21	̸=	̸=	PROPN
ejpam-5032	192	22	{	{	PUNCT
ejpam-5032	192	23	0	0	NUM
ejpam-5032	192	24	}	}	PUNCT
ejpam-5032	192	25	.	.	PUNCT
ejpam-5032	193	1	we	we	PRON
ejpam-5032	193	2	claim	claim	VERB
ejpam-5032	193	3	that	that	SCONJ
ejpam-5032	193	4	h	h	NOUN
ejpam-5032	193	5	is	be	AUX
ejpam-5032	193	6	a	a	DET
ejpam-5032	193	7	prime	prime	ADJ
ejpam-5032	193	8	k	k	NOUN
ejpam-5032	193	9	-	-	NOUN
ejpam-5032	193	10	group	group	NOUN
ejpam-5032	193	11	of	of	ADP
ejpam-5032	193	12	type	type	NOUN
ejpam-5032	193	13	2	2	NUM
ejpam-5032	193	14	.	.	PUNCT
ejpam-5032	194	1	under	under	ADP
ejpam-5032	194	2	restriction	restriction	NOUN
ejpam-5032	194	3	,	,	PUNCT
ejpam-5032	194	4	clearly	clearly	ADV
ejpam-5032	194	5	h	h	NOUN
ejpam-5032	194	6	is	be	AUX
ejpam-5032	194	7	a	a	DET
ejpam-5032	194	8	k	k	NOUN
ejpam-5032	194	9	-	-	NOUN
ejpam-5032	194	10	group	group	NOUN
ejpam-5032	194	11	.	.	PUNCT
ejpam-5032	195	1	let	let	VERB
ejpam-5032	195	2	0	0	NUM
ejpam-5032	195	3	̸=	̸=	PROPN
ejpam-5032	195	4	h	h	NOUN
ejpam-5032	195	5	∈	∈	PROPN
ejpam-5032	195	6	h.	h.	PROPN
ejpam-5032	195	7	assume	assume	VERB
ejpam-5032	195	8	that	that	SCONJ
ejpam-5032	195	9	hk	hk	PROPN
ejpam-5032	195	10	=	=	PUNCT
ejpam-5032	195	11	{	{	PUNCT
ejpam-5032	195	12	0	0	NUM
ejpam-5032	195	13	}	}	PUNCT
ejpam-5032	195	14	.	.	PUNCT
ejpam-5032	196	1	now	now	ADV
ejpam-5032	196	2	(	(	PUNCT
ejpam-5032	196	3	hr)k	hr)k	PROPN
ejpam-5032	196	4	=	=	SYM
ejpam-5032	196	5	h(rk	h(rk	PROPN
ejpam-5032	196	6	)	)	PUNCT
ejpam-5032	196	7	⊆	⊆	NUM
ejpam-5032	196	8	hk	hk	NOUN
ejpam-5032	196	9	=	=	PUNCT
ejpam-5032	196	10	{	{	PUNCT
ejpam-5032	196	11	0	0	NUM
ejpam-5032	196	12	}	}	PUNCT
ejpam-5032	196	13	and	and	CCONJ
ejpam-5032	196	14	hence	hence	ADV
ejpam-5032	196	15	ak	ak	PROPN
ejpam-5032	196	16	=	=	PUNCT
ejpam-5032	196	17	{	{	PUNCT
ejpam-5032	196	18	0	0	NUM
ejpam-5032	196	19	}	}	PUNCT
ejpam-5032	196	20	,	,	PUNCT
ejpam-5032	196	21	where	where	SCONJ
ejpam-5032	196	22	a	a	PRON
ejpam-5032	196	23	is	be	AUX
ejpam-5032	196	24	the	the	DET
ejpam-5032	196	25	n	n	PRON
ejpam-5032	196	26	-subgroup	-subgroup	NOUN
ejpam-5032	196	27	of	of	ADP
ejpam-5032	196	28	h	h	PROPN
ejpam-5032	196	29	generated	generate	VERB
ejpam-5032	196	30	by	by	ADP
ejpam-5032	196	31	hk	hk	PROPN
ejpam-5032	196	32	.	.	PUNCT
ejpam-5032	197	1	so	so	ADV
ejpam-5032	197	2	hk	hk	PROPN
ejpam-5032	197	3	=	=	PUNCT
ejpam-5032	197	4	{	{	PUNCT
ejpam-5032	197	5	0	0	NUM
ejpam-5032	197	6	}	}	PUNCT
ejpam-5032	197	7	,	,	PUNCT
ejpam-5032	197	8	a	a	DET
ejpam-5032	197	9	contradiction	contradiction	NOUN
ejpam-5032	197	10	.	.	PUNCT
ejpam-5032	198	1	therefore	therefore	ADV
ejpam-5032	198	2	hk	hk	PROPN
ejpam-5032	198	3	̸=	̸=	PROPN
ejpam-5032	198	4	{	{	PUNCT
ejpam-5032	198	5	0	0	NUM
ejpam-5032	198	6	}	}	PUNCT
ejpam-5032	198	7	.	.	PUNCT
ejpam-5032	199	1	let	let	VERB
ejpam-5032	199	2	0	0	NUM
ejpam-5032	200	1	̸=	̸=	PROPN
ejpam-5032	200	2	hk	hk	PROPN
ejpam-5032	200	3	∈	∈	PROPN
ejpam-5032	200	4	hk	hk	PROPN
ejpam-5032	200	5	,	,	PUNCT
ejpam-5032	200	6	k	k	PROPN
ejpam-5032	200	7	∈	∈	PROPN
ejpam-5032	201	1	k.	k.	NOUN
ejpam-5032	202	1	we	we	PRON
ejpam-5032	202	2	have	have	VERB
ejpam-5032	202	3	that	that	PRON
ejpam-5032	202	4	(	(	PUNCT
ejpam-5032	202	5	hk)n	hk)n	PROPN
ejpam-5032	202	6	contains	contain	VERB
ejpam-5032	202	7	a	a	DET
ejpam-5032	202	8	non	non	ADJ
ejpam-5032	202	9	-	-	ADJ
ejpam-5032	202	10	zero	zero	NUM
ejpam-5032	202	11	distributive	distributive	ADJ
ejpam-5032	202	12	element	element	NOUN
ejpam-5032	202	13	(	(	PUNCT
ejpam-5032	202	14	hk)x	hk)x	PROPN
ejpam-5032	202	15	,	,	PUNCT
ejpam-5032	202	16	x	x	SYM
ejpam-5032	202	17	∈	∈	PROPN
ejpam-5032	202	18	n	n	ADV
ejpam-5032	202	19	.	.	PUNCT
ejpam-5032	203	1	clearly	clearly	ADV
ejpam-5032	203	2	(	(	PUNCT
ejpam-5032	203	3	hk)x	hk)x	PROPN
ejpam-5032	203	4	=	=	SYM
ejpam-5032	203	5	h(kx	h(kx	X
ejpam-5032	203	6	)	)	PUNCT
ejpam-5032	203	7	∈	∈	PROPN
ejpam-5032	203	8	hk	hk	PROPN
ejpam-5032	203	9	as	as	SCONJ
ejpam-5032	203	10	required	require	VERB
ejpam-5032	203	11	.	.	PUNCT
ejpam-5032	204	1	finally	finally	ADV
ejpam-5032	204	2	we	we	PRON
ejpam-5032	204	3	prove	prove	VERB
ejpam-5032	204	4	that	that	SCONJ
ejpam-5032	204	5	ank(hk	ank(hk	NOUN
ejpam-5032	204	6	)	)	PUNCT
ejpam-5032	204	7	=	=	SYM
ejpam-5032	204	8	ank(h	ank(h	PROPN
ejpam-5032	204	9	)	)	PUNCT
ejpam-5032	204	10	.	.	PUNCT
ejpam-5032	205	1	as	as	SCONJ
ejpam-5032	205	2	seen	see	VERB
ejpam-5032	205	3	above	above	ADV
ejpam-5032	205	4	,	,	PUNCT
ejpam-5032	205	5	we	we	PRON
ejpam-5032	205	6	have	have	VERB
ejpam-5032	205	7	0	0	NUM
ejpam-5032	205	8	̸=	̸=	PROPN
ejpam-5032	205	9	hk	hk	PROPN
ejpam-5032	205	10	∈	∈	PROPN
ejpam-5032	205	11	hk	hk	PROPN
ejpam-5032	205	12	,	,	PUNCT
ejpam-5032	205	13	k	k	PROPN
ejpam-5032	205	14	∈	∈	PROPN
ejpam-5032	205	15	k.	k.	PROPN
ejpam-5032	205	16	note	note	VERB
ejpam-5032	206	1	that	that	SCONJ
ejpam-5032	206	2	ann	ann	PROPN
ejpam-5032	206	3	(	(	PUNCT
ejpam-5032	206	4	(	(	PUNCT
ejpam-5032	206	5	hk)n	hk)n	PROPN
ejpam-5032	206	6	)	)	PUNCT
ejpam-5032	206	7	=	=	SYM
ejpam-5032	206	8	ann	ann	PROPN
ejpam-5032	206	9	(	(	PUNCT
ejpam-5032	206	10	h	h	NOUN
ejpam-5032	206	11	)	)	PUNCT
ejpam-5032	206	12	.	.	PUNCT
ejpam-5032	207	1	since	since	SCONJ
ejpam-5032	207	2	(	(	PUNCT
ejpam-5032	207	3	hk)n	hk)n	PROPN
ejpam-5032	207	4	=	=	SYM
ejpam-5032	207	5	h(kn	h(kn	PROPN
ejpam-5032	207	6	)	)	PUNCT
ejpam-5032	207	7	⊆	⊆	NUM
ejpam-5032	207	8	hk	hk	NOUN
ejpam-5032	207	9	⊆	⊆	NUM
ejpam-5032	207	10	h	h	NOUN
ejpam-5032	207	11	we	we	PRON
ejpam-5032	207	12	have	have	VERB
ejpam-5032	207	13	ann	ann	PROPN
ejpam-5032	207	14	(	(	PUNCT
ejpam-5032	207	15	h	h	NOUN
ejpam-5032	207	16	)	)	PUNCT
ejpam-5032	207	17	⊆	⊆	NUM
ejpam-5032	207	18	ann	ann	X
ejpam-5032	207	19	(	(	PUNCT
ejpam-5032	207	20	hk	hk	PROPN
ejpam-5032	207	21	)	)	PUNCT
ejpam-5032	207	22	⊆	⊆	NUM
ejpam-5032	207	23	ann	ann	X
ejpam-5032	207	24	(	(	PUNCT
ejpam-5032	207	25	(	(	PUNCT
ejpam-5032	207	26	hk)n	hk)n	PROPN
ejpam-5032	207	27	)	)	PUNCT
ejpam-5032	207	28	.	.	PUNCT
ejpam-5032	208	1	therefore	therefore	ADV
ejpam-5032	208	2	,	,	PUNCT
ejpam-5032	208	3	ann	ann	PROPN
ejpam-5032	208	4	(	(	PUNCT
ejpam-5032	208	5	h	h	NOUN
ejpam-5032	208	6	)	)	PUNCT
ejpam-5032	208	7	=	=	SYM
ejpam-5032	208	8	ann	ann	PROPN
ejpam-5032	208	9	(	(	PUNCT
ejpam-5032	208	10	hk	hk	PROPN
ejpam-5032	208	11	)	)	PUNCT
ejpam-5032	208	12	=	=	SYM
ejpam-5032	208	13	ann	ann	PROPN
ejpam-5032	208	14	(	(	PUNCT
ejpam-5032	208	15	(	(	PUNCT
ejpam-5032	208	16	hk)n	hk)n	PROPN
ejpam-5032	208	17	)	)	PUNCT
ejpam-5032	208	18	.	.	PUNCT
ejpam-5032	209	1	so	so	ADV
ejpam-5032	209	2	ank(h	ank(h	ADV
ejpam-5032	209	3	)	)	PUNCT
ejpam-5032	209	4	=	=	SYM
ejpam-5032	210	1	k∩	k∩	PROPN
ejpam-5032	210	2	ann	ann	PROPN
ejpam-5032	210	3	(	(	PUNCT
ejpam-5032	210	4	h	h	NOUN
ejpam-5032	210	5	)	)	PUNCT
ejpam-5032	210	6	=	=	SYM
ejpam-5032	210	7	k∩	k∩	PROPN
ejpam-5032	210	8	ann	ann	PROPN
ejpam-5032	210	9	(	(	PUNCT
ejpam-5032	210	10	hk	hk	PROPN
ejpam-5032	210	11	)	)	PUNCT
ejpam-5032	210	12	=	=	SYM
ejpam-5032	210	13	ank(hk	ank(hk	NOUN
ejpam-5032	210	14	)	)	PUNCT
ejpam-5032	210	15	.	.	PUNCT
ejpam-5032	211	1	now	now	ADV
ejpam-5032	211	2	it	it	PRON
ejpam-5032	211	3	is	be	AUX
ejpam-5032	211	4	also	also	ADV
ejpam-5032	211	5	clear	clear	ADJ
ejpam-5032	211	6	that	that	SCONJ
ejpam-5032	211	7	k	k	PROPN
ejpam-5032	211	8	∩	∩	X
ejpam-5032	211	9	(	(	PUNCT
ejpam-5032	211	10	h	h	NOUN
ejpam-5032	211	11	:	:	PUNCT
ejpam-5032	211	12	0)n	0)n	NUM
ejpam-5032	211	13	⊆	⊆	X
ejpam-5032	211	14	(	(	PUNCT
ejpam-5032	211	15	h	h	NOUN
ejpam-5032	211	16	:	:	PUNCT
ejpam-5032	211	17	0)k	0)k	NOUN
ejpam-5032	211	18	.	.	PUNCT
ejpam-5032	212	1	a	a	DET
ejpam-5032	212	2	h	h	NOUN
ejpam-5032	212	3	-	-	PUNCT
ejpam-5032	212	4	radical	radical	ADJ
ejpam-5032	212	5	r	r	NOUN
ejpam-5032	212	6	is	be	AUX
ejpam-5032	212	7	complete	complete	ADJ
ejpam-5032	212	8	if	if	SCONJ
ejpam-5032	212	9	k	k	PROPN
ejpam-5032	212	10	⊆	⊆	NUM
ejpam-5032	212	11	r(n	r(n	PROPN
ejpam-5032	212	12	)	)	PUNCT
ejpam-5032	212	13	for	for	ADP
ejpam-5032	212	14	all	all	DET
ejpam-5032	212	15	ideals	ideal	NOUN
ejpam-5032	212	16	k	k	PROPN
ejpam-5032	212	17	of	of	ADP
ejpam-5032	212	18	n	n	PRON
ejpam-5032	212	19	for	for	ADP
ejpam-5032	212	20	which	which	PRON
ejpam-5032	212	21	r(k	r(k	PROPN
ejpam-5032	212	22	)	)	PUNCT
ejpam-5032	212	23	=	=	SYM
ejpam-5032	212	24	k.	k.	PROPN
ejpam-5032	212	25	theorem	theorem	VERB
ejpam-5032	212	26	3	3	NUM
ejpam-5032	212	27	.	.	PUNCT
ejpam-5032	213	1	the	the	DET
ejpam-5032	213	2	h	h	NOUN
ejpam-5032	213	3	-	-	PUNCT
ejpam-5032	213	4	radical	radical	ADJ
ejpam-5032	213	5	p2(r	p2(r	NOUN
ejpam-5032	213	6	)	)	PUNCT
ejpam-5032	213	7	is	be	AUX
ejpam-5032	213	8	complete	complete	ADJ
ejpam-5032	213	9	.	.	PUNCT
ejpam-5032	214	1	proof	proof	NOUN
ejpam-5032	214	2	.	.	PUNCT
ejpam-5032	215	1	let	let	VERB
ejpam-5032	215	2	k	k	PRON
ejpam-5032	215	3	be	be	AUX
ejpam-5032	215	4	an	an	DET
ejpam-5032	215	5	ideal	ideal	ADJ
ejpam-5032	215	6	n	n	NOUN
ejpam-5032	215	7	and	and	CCONJ
ejpam-5032	215	8	p2(r)(k	p2(r)(k	NOUN
ejpam-5032	215	9	)	)	PUNCT
ejpam-5032	216	1	=	=	PUNCT
ejpam-5032	216	2	k.	k.	PROPN
ejpam-5032	216	3	suppose	suppose	VERB
ejpam-5032	216	4	that	that	SCONJ
ejpam-5032	216	5	k	k	PROPN
ejpam-5032	216	6	̸⊆	̸⊆	PROPN
ejpam-5032	216	7	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	216	8	)	)	PUNCT
ejpam-5032	216	9	.	.	PUNCT
ejpam-5032	217	1	so	so	ADV
ejpam-5032	217	2	there	there	PRON
ejpam-5032	217	3	is	be	VERB
ejpam-5032	217	4	a	a	DET
ejpam-5032	217	5	prime	prime	ADJ
ejpam-5032	217	6	n	n	CCONJ
ejpam-5032	217	7	-group	-group	NOUN
ejpam-5032	217	8	h	h	NOUN
ejpam-5032	217	9	of	of	ADP
ejpam-5032	217	10	type	type	NOUN
ejpam-5032	217	11	2	2	NUM
ejpam-5032	217	12	such	such	ADJ
ejpam-5032	217	13	that	that	SCONJ
ejpam-5032	217	14	k	k	PROPN
ejpam-5032	217	15	̸⊆	̸⊆	PROPN
ejpam-5032	218	1	(	(	PUNCT
ejpam-5032	218	2	h	h	NOUN
ejpam-5032	218	3	:	:	PUNCT
ejpam-5032	218	4	0)n	0)n	X
ejpam-5032	218	5	.	.	PUNCT
ejpam-5032	219	1	by	by	ADP
ejpam-5032	219	2	theorem	theorem	NOUN
ejpam-5032	219	3	2	2	NUM
ejpam-5032	219	4	,	,	PUNCT
ejpam-5032	219	5	h	h	NOUN
ejpam-5032	219	6	is	be	AUX
ejpam-5032	219	7	a	a	DET
ejpam-5032	219	8	prime	prime	ADJ
ejpam-5032	219	9	k	k	NOUN
ejpam-5032	219	10	-	-	NOUN
ejpam-5032	219	11	group	group	NOUN
ejpam-5032	219	12	of	of	ADP
ejpam-5032	219	13	type	type	NOUN
ejpam-5032	219	14	2	2	NUM
ejpam-5032	219	15	.	.	PUNCT
ejpam-5032	220	1	this	this	PRON
ejpam-5032	220	2	contradicts	contradict	VERB
ejpam-5032	220	3	p2(r)(k	p2(r)(k	NOUN
ejpam-5032	220	4	)	)	PUNCT
ejpam-5032	221	1	=	=	VERB
ejpam-5032	221	2	k.	k.	PROPN
ejpam-5032	221	3	therefore	therefore	ADV
ejpam-5032	221	4	k	k	PROPN
ejpam-5032	221	5	⊆	⊆	NUM
ejpam-5032	221	6	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	221	7	)	)	PUNCT
ejpam-5032	221	8	.	.	PUNCT
ejpam-5032	222	1	hence	hence	ADV
ejpam-5032	222	2	p2(r	p2(r	CCONJ
ejpam-5032	222	3	)	)	PUNCT
ejpam-5032	222	4	is	be	AUX
ejpam-5032	222	5	complete	complete	ADJ
ejpam-5032	222	6	.	.	PUNCT
ejpam-5032	223	1	theorem	theorem	ADJ
ejpam-5032	223	2	4	4	NUM
ejpam-5032	223	3	.	.	PUNCT
ejpam-5032	224	1	let	let	VERB
ejpam-5032	224	2	h	h	PRON
ejpam-5032	224	3	be	be	AUX
ejpam-5032	224	4	prime	prime	ADJ
ejpam-5032	224	5	k	k	NOUN
ejpam-5032	224	6	-	-	NOUN
ejpam-5032	224	7	group	group	NOUN
ejpam-5032	224	8	of	of	ADP
ejpam-5032	224	9	type	type	NOUN
ejpam-5032	224	10	2	2	NUM
ejpam-5032	224	11	and	and	CCONJ
ejpam-5032	224	12	k	k	PROPN
ejpam-5032	224	13	be	be	AUX
ejpam-5032	224	14	an	an	DET
ejpam-5032	224	15	ideal	ideal	NOUN
ejpam-5032	224	16	of	of	ADP
ejpam-5032	224	17	n	n	PROPN
ejpam-5032	224	18	.	.	PUNCT
ejpam-5032	225	1	then	then	ADV
ejpam-5032	225	2	there	there	PRON
ejpam-5032	225	3	is	be	VERB
ejpam-5032	225	4	a	a	DET
ejpam-5032	225	5	k	k	NOUN
ejpam-5032	225	6	-	-	NOUN
ejpam-5032	225	7	subgroup	subgroup	NOUN
ejpam-5032	225	8	c	c	PROPN
ejpam-5032	225	9	of	of	ADP
ejpam-5032	225	10	h	h	PRON
ejpam-5032	225	11	which	which	PRON
ejpam-5032	225	12	is	be	AUX
ejpam-5032	225	13	a	a	DET
ejpam-5032	225	14	prime	prime	ADJ
ejpam-5032	225	15	n	n	ADP
ejpam-5032	225	16	-group	-group	NOUN
ejpam-5032	225	17	of	of	ADP
ejpam-5032	225	18	type	type	NOUN
ejpam-5032	225	19	2	2	NUM
ejpam-5032	225	20	and	and	CCONJ
ejpam-5032	225	21	(	(	PUNCT
ejpam-5032	225	22	c	c	NOUN
ejpam-5032	225	23	:	:	PUNCT
ejpam-5032	225	24	0)n	0)n	X
ejpam-5032	225	25	∩k	∩k	VERB
ejpam-5032	225	26	⊆	⊆	NUM
ejpam-5032	225	27	(	(	PUNCT
ejpam-5032	225	28	h	h	NOUN
ejpam-5032	225	29	:	:	PUNCT
ejpam-5032	225	30	0)k	0)k	NOUN
ejpam-5032	225	31	.	.	PUNCT
ejpam-5032	226	1	proof	proof	NOUN
ejpam-5032	226	2	.	.	PUNCT
ejpam-5032	227	1	suppose	suppose	VERB
ejpam-5032	227	2	that	that	SCONJ
ejpam-5032	227	3	k	k	PROPN
ejpam-5032	227	4	is	be	AUX
ejpam-5032	227	5	an	an	DET
ejpam-5032	227	6	ideal	ideal	NOUN
ejpam-5032	227	7	of	of	ADP
ejpam-5032	227	8	n	n	NUM
ejpam-5032	227	9	and	and	CCONJ
ejpam-5032	227	10	h	h	NOUN
ejpam-5032	227	11	is	be	AUX
ejpam-5032	227	12	a	a	DET
ejpam-5032	227	13	prime	prime	ADJ
ejpam-5032	227	14	k	k	NOUN
ejpam-5032	227	15	-	-	NOUN
ejpam-5032	227	16	group	group	NOUN
ejpam-5032	227	17	of	of	ADP
ejpam-5032	227	18	type	type	NOUN
ejpam-5032	227	19	2	2	NUM
ejpam-5032	227	20	.	.	PUNCT
ejpam-5032	228	1	we	we	PRON
ejpam-5032	228	2	have	have	VERB
ejpam-5032	228	3	a	a	DET
ejpam-5032	228	4	distributive	distributive	ADJ
ejpam-5032	228	5	element	element	NOUN
ejpam-5032	228	6	h0	h0	PROPN
ejpam-5032	228	7	∈	∈	PROPN
ejpam-5032	228	8	h.	h.	NOUN
ejpam-5032	229	1	so	so	ADV
ejpam-5032	229	2	h0(y	h0(y	PROPN
ejpam-5032	230	1	+	+	PROPN
ejpam-5032	230	2	z	z	X
ejpam-5032	230	3	)	)	PUNCT
ejpam-5032	230	4	=	=	SYM
ejpam-5032	230	5	h0y	h0y	NOUN
ejpam-5032	230	6	+	+	CCONJ
ejpam-5032	230	7	h0z	h0z	NOUN
ejpam-5032	230	8	for	for	ADP
ejpam-5032	230	9	all	all	DET
ejpam-5032	230	10	y	y	PROPN
ejpam-5032	230	11	,	,	PUNCT
ejpam-5032	230	12	z	z	PROPN
ejpam-5032	230	13	∈	∈	PROPN
ejpam-5032	230	14	k.	k.	PROPN
ejpam-5032	231	1	clearly	clearly	ADV
ejpam-5032	231	2	h0k	h0k	VERB
ejpam-5032	231	3	:	:	PUNCT
ejpam-5032	231	4	=	=	SYM
ejpam-5032	231	5	{	{	PUNCT
ejpam-5032	231	6	h0k	h0k	PROPN
ejpam-5032	231	7	|	|	ADP
ejpam-5032	231	8	k	k	PROPN
ejpam-5032	231	9	∈	∈	PROPN
ejpam-5032	231	10	k	k	AUX
ejpam-5032	231	11	}	}	PUNCT
ejpam-5032	231	12	is	be	AUX
ejpam-5032	231	13	a	a	DET
ejpam-5032	231	14	non	non	ADJ
ejpam-5032	231	15	-	-	ADJ
ejpam-5032	231	16	zero	zero	ADJ
ejpam-5032	231	17	k	k	NOUN
ejpam-5032	231	18	-	-	NOUN
ejpam-5032	231	19	subgroup	subgroup	NOUN
ejpam-5032	231	20	of	of	ADP
ejpam-5032	231	21	h.	h.	PROPN
ejpam-5032	231	22	the	the	DET
ejpam-5032	231	23	claim	claim	NOUN
ejpam-5032	231	24	now	now	ADV
ejpam-5032	231	25	is	be	AUX
ejpam-5032	231	26	h0k	h0k	PROPN
ejpam-5032	231	27	is	be	AUX
ejpam-5032	231	28	an	an	DET
ejpam-5032	231	29	n	n	NUM
ejpam-5032	231	30	-group	-group	NOUN
ejpam-5032	231	31	.	.	PUNCT
ejpam-5032	232	1	for	for	ADP
ejpam-5032	232	2	this	this	PRON
ejpam-5032	232	3	,	,	PUNCT
ejpam-5032	232	4	define	define	VERB
ejpam-5032	232	5	(	(	PUNCT
ejpam-5032	232	6	h0k)x	h0k)x	ADJ
ejpam-5032	232	7	:	:	PUNCT
ejpam-5032	232	8	=	=	SYM
ejpam-5032	232	9	h0(kx	h0(kx	PROPN
ejpam-5032	232	10	)	)	PUNCT
ejpam-5032	232	11	for	for	ADP
ejpam-5032	232	12	all	all	DET
ejpam-5032	232	13	h0k	h0k	PROPN
ejpam-5032	232	14	∈	∈	PROPN
ejpam-5032	232	15	k	k	PROPN
ejpam-5032	232	16	,	,	PUNCT
ejpam-5032	232	17	x	x	PROPN
ejpam-5032	232	18	∈	∈	PROPN
ejpam-5032	232	19	n	n	NOUN
ejpam-5032	232	20	,	,	PUNCT
ejpam-5032	232	21	where	where	SCONJ
ejpam-5032	232	22	k	k	PROPN
ejpam-5032	232	23	∈	∈	PROPN
ejpam-5032	232	24	k.	k.	PROPN
ejpam-5032	232	25	to	to	PART
ejpam-5032	232	26	show	show	VERB
ejpam-5032	232	27	that	that	SCONJ
ejpam-5032	232	28	this	this	DET
ejpam-5032	232	29	operation	operation	NOUN
ejpam-5032	232	30	is	be	AUX
ejpam-5032	232	31	well	well	ADV
ejpam-5032	232	32	defined	define	VERB
ejpam-5032	232	33	,	,	PUNCT
ejpam-5032	232	34	suppose	suppose	VERB
ejpam-5032	232	35	that	that	SCONJ
ejpam-5032	232	36	h0y	h0y	PROPN
ejpam-5032	232	37	=	=	SYM
ejpam-5032	232	38	h0z	h0z	PROPN
ejpam-5032	232	39	,	,	PUNCT
ejpam-5032	232	40	y	y	PROPN
ejpam-5032	232	41	,	,	PUNCT
ejpam-5032	232	42	z	z	PROPN
ejpam-5032	232	43	∈	∈	PROPN
ejpam-5032	232	44	k.	k.	NOUN
ejpam-5032	232	45	let	let	VERB
ejpam-5032	232	46	x	x	SYM
ejpam-5032	232	47	∈	∈	PROPN
ejpam-5032	232	48	n	n	ADV
ejpam-5032	232	49	.	.	PUNCT
ejpam-5032	233	1	now	now	ADV
ejpam-5032	233	2	(	(	PUNCT
ejpam-5032	233	3	h0(yx	h0(yx	PROPN
ejpam-5032	233	4	)	)	PUNCT
ejpam-5032	233	5	−	−	PROPN
ejpam-5032	234	1	h0(zx))k	h0(zx))k	NOUN
ejpam-5032	234	2	=	=	X
ejpam-5032	234	3	(	(	PUNCT
ejpam-5032	234	4	h0(yx))k	h0(yx))k	PROPN
ejpam-5032	234	5	−	−	PROPN
ejpam-5032	234	6	(	(	PUNCT
ejpam-5032	234	7	h0(zx))k	h0(zx))k	NOUN
ejpam-5032	234	8	=	=	NOUN
ejpam-5032	234	9	h0((yx)k	h0((yx)k	NOUN
ejpam-5032	234	10	)	)	PUNCT
ejpam-5032	234	11	−	−	NOUN
ejpam-5032	234	12	h0((zx)k	h0((zx)k	NOUN
ejpam-5032	234	13	)	)	PUNCT
ejpam-5032	234	14	=	=	PUNCT
ejpam-5032	234	15	h0(y(xk))−	h0(y(xk))−	NOUN
ejpam-5032	234	16	h0(z(xk	h0(z(xk	PUNCT
ejpam-5032	234	17	)	)	PUNCT
ejpam-5032	234	18	)	)	PUNCT
ejpam-5032	235	1	=	=	SYM
ejpam-5032	235	2	(	(	PUNCT
ejpam-5032	235	3	h0y)(xk	h0y)(xk	X
ejpam-5032	235	4	)	)	PUNCT
ejpam-5032	235	5	=	=	SYM
ejpam-5032	235	6	(	(	PUNCT
ejpam-5032	235	7	h0z)(xk	h0z)(xk	X
ejpam-5032	235	8	)	)	PUNCT
ejpam-5032	235	9	=	=	SYM
ejpam-5032	235	10	(	(	PUNCT
ejpam-5032	235	11	(	(	PUNCT
ejpam-5032	235	12	h0y)−	h0y)−	X
ejpam-5032	235	13	(	(	PUNCT
ejpam-5032	235	14	h0z))(xk	h0z))(xk	ADJ
ejpam-5032	235	15	)	)	PUNCT
ejpam-5032	235	16	=	=	SYM
ejpam-5032	235	17	0(xk	0(xk	NOUN
ejpam-5032	235	18	)	)	PUNCT
ejpam-5032	235	19	=	=	SYM
ejpam-5032	235	20	0	0	NUM
ejpam-5032	235	21	for	for	ADP
ejpam-5032	235	22	all	all	DET
ejpam-5032	235	23	k	k	PROPN
ejpam-5032	235	24	∈	∈	PROPN
ejpam-5032	235	25	k.	k.	PROPN
ejpam-5032	235	26	therefore	therefore	ADV
ejpam-5032	235	27	h0(yx	h0(yx	PROPN
ejpam-5032	235	28	)	)	PUNCT
ejpam-5032	235	29	=	=	SYM
ejpam-5032	235	30	h0(zx	h0(zx	PROPN
ejpam-5032	235	31	)	)	PUNCT
ejpam-5032	236	1	and	and	CCONJ
ejpam-5032	236	2	that	that	SCONJ
ejpam-5032	236	3	the	the	DET
ejpam-5032	236	4	operation	operation	NOUN
ejpam-5032	236	5	is	be	AUX
ejpam-5032	236	6	well	well	ADV
ejpam-5032	236	7	defined	define	VERB
ejpam-5032	236	8	.	.	PUNCT
ejpam-5032	237	1	it	it	PRON
ejpam-5032	237	2	can	can	AUX
ejpam-5032	237	3	be	be	AUX
ejpam-5032	237	4	easily	easily	ADV
ejpam-5032	237	5	verified	verify	VERB
ejpam-5032	237	6	that	that	SCONJ
ejpam-5032	237	7	h0k	h0k	PROPN
ejpam-5032	237	8	is	be	AUX
ejpam-5032	237	9	an	an	DET
ejpam-5032	237	10	n	n	NUM
ejpam-5032	237	11	-group	-group	NOUN
ejpam-5032	237	12	.	.	PUNCT
ejpam-5032	238	1	we	we	PRON
ejpam-5032	238	2	see	see	VERB
ejpam-5032	238	3	now	now	ADV
ejpam-5032	238	4	that	that	SCONJ
ejpam-5032	238	5	h0k	h0k	PROPN
ejpam-5032	238	6	is	be	AUX
ejpam-5032	238	7	a	a	DET
ejpam-5032	238	8	prime	prime	ADJ
ejpam-5032	238	9	n	n	ADP
ejpam-5032	238	10	-group	-group	NOUN
ejpam-5032	238	11	of	of	ADP
ejpam-5032	238	12	type	type	NOUN
ejpam-5032	238	13	2	2	NUM
ejpam-5032	238	14	.	.	PUNCT
ejpam-5032	239	1	let	let	VERB
ejpam-5032	239	2	0	0	NUM
ejpam-5032	239	3	̸=	̸=	PROPN
ejpam-5032	239	4	h0	h0	PROPN
ejpam-5032	239	5	t	t	PROPN
ejpam-5032	239	6	∈	∈	PROPN
ejpam-5032	239	7	h0k	h0k	PROPN
ejpam-5032	239	8	,	,	PUNCT
ejpam-5032	239	9	t	t	PROPN
ejpam-5032	239	10	∈	∈	PROPN
ejpam-5032	240	1	k.	k.	PROPN
ejpam-5032	241	1	since	since	SCONJ
ejpam-5032	241	2	h	h	PROPN
ejpam-5032	241	3	is	be	AUX
ejpam-5032	241	4	a	a	DET
ejpam-5032	241	5	prime	prime	ADJ
ejpam-5032	241	6	k	k	NOUN
ejpam-5032	241	7	-	-	NOUN
ejpam-5032	241	8	group	group	NOUN
ejpam-5032	241	9	of	of	ADP
ejpam-5032	241	10	type	type	NOUN
ejpam-5032	241	11	2	2	NUM
ejpam-5032	241	12	,	,	PUNCT
ejpam-5032	241	13	we	we	PRON
ejpam-5032	241	14	get	get	VERB
ejpam-5032	241	15	a	a	DET
ejpam-5032	241	16	distributive	distributive	ADJ
ejpam-5032	241	17	element	element	NOUN
ejpam-5032	241	18	0	0	PUNCT
ejpam-5032	242	1	̸=	̸=	PROPN
ejpam-5032	242	2	h0y	h0y	PROPN
ejpam-5032	242	3	∈	∈	PROPN
ejpam-5032	242	4	(	(	PUNCT
ejpam-5032	242	5	h0t)k	h0t)k	X
ejpam-5032	242	6	(	(	PUNCT
ejpam-5032	242	7	⊆	⊆	NUM
ejpam-5032	242	8	(	(	PUNCT
ejpam-5032	242	9	h0t)n	h0t)n	NOUN
ejpam-5032	242	10	)	)	PUNCT
ejpam-5032	242	11	,	,	PUNCT
ejpam-5032	242	12	y	y	PROPN
ejpam-5032	242	13	∈	∈	PROPN
ejpam-5032	242	14	k.	k.	PROPN
ejpam-5032	242	15	also	also	ADV
ejpam-5032	242	16	,	,	PUNCT
ejpam-5032	242	17	for	for	ADP
ejpam-5032	242	18	a	a	DET
ejpam-5032	242	19	,	,	PUNCT
ejpam-5032	242	20	b	b	PROPN
ejpam-5032	242	21	∈	∈	PROPN
ejpam-5032	242	22	n	n	NOUN
ejpam-5032	242	23	,	,	PUNCT
ejpam-5032	243	1	[	[	X
ejpam-5032	243	2	(	(	PUNCT
ejpam-5032	243	3	h0y)(a+	h0y)(a+	NOUN
ejpam-5032	243	4	b)−	b)−	PROPN
ejpam-5032	243	5	(	(	PUNCT
ejpam-5032	243	6	(	(	PUNCT
ejpam-5032	243	7	h0y)a+	h0y)a+	PROPN
ejpam-5032	243	8	(	(	PUNCT
ejpam-5032	243	9	h0y)b)]k	h0y)b)]k	NOUN
ejpam-5032	243	10	=	=	X
ejpam-5032	243	11	(	(	PUNCT
ejpam-5032	243	12	h0y)(ak+	h0y)(ak+	X
ejpam-5032	243	13	bk)−	bk)−	NOUN
ejpam-5032	243	14	(	(	PUNCT
ejpam-5032	243	15	(	(	PUNCT
ejpam-5032	243	16	h0y)ak	h0y)ak	PROPN
ejpam-5032	243	17	+	+	CCONJ
ejpam-5032	243	18	(	(	PUNCT
ejpam-5032	243	19	h0y)bk	h0y)bk	NOUN
ejpam-5032	243	20	)	)	PUNCT
ejpam-5032	243	21	=	=	PUNCT
ejpam-5032	243	22	(	(	PUNCT
ejpam-5032	243	23	(	(	PUNCT
ejpam-5032	243	24	h0y)ak	h0y)ak	PROPN
ejpam-5032	243	25	+	+	CCONJ
ejpam-5032	243	26	(	(	PUNCT
ejpam-5032	243	27	h0y)bk	h0y)bk	NOUN
ejpam-5032	243	28	)	)	PUNCT
ejpam-5032	243	29	−	−	PROPN
ejpam-5032	243	30	(	(	PUNCT
ejpam-5032	243	31	(	(	PUNCT
ejpam-5032	243	32	h0y))ak	h0y))ak	NOUN
ejpam-5032	243	33	+	+	CCONJ
ejpam-5032	243	34	(	(	PUNCT
ejpam-5032	243	35	h0y))bk	h0y))bk	NUM
ejpam-5032	243	36	)	)	PUNCT
ejpam-5032	243	37	=	=	NOUN
ejpam-5032	243	38	0	0	NUM
ejpam-5032	244	1	for	for	ADP
ejpam-5032	244	2	all	all	DET
ejpam-5032	244	3	k	k	PROPN
ejpam-5032	244	4	∈	∈	PROPN
ejpam-5032	244	5	k.	k.	PROPN
ejpam-5032	245	1	therefore	therefore	ADV
ejpam-5032	245	2	(	(	PUNCT
ejpam-5032	245	3	h0y)(a+	h0y)(a+	NOUN
ejpam-5032	245	4	b	b	NOUN
ejpam-5032	245	5	)	)	PUNCT
ejpam-5032	245	6	=	=	SYM
ejpam-5032	245	7	(	(	PUNCT
ejpam-5032	245	8	h0y)a+	h0y)a+	PROPN
ejpam-5032	245	9	(	(	PUNCT
ejpam-5032	245	10	h0y)b	h0y)b	INTJ
ejpam-5032	245	11	and	and	CCONJ
ejpam-5032	245	12	that	that	SCONJ
ejpam-5032	245	13	h0y	h0y	PROPN
ejpam-5032	245	14	is	be	AUX
ejpam-5032	245	15	distributive	distributive	ADJ
ejpam-5032	245	16	over	over	ADP
ejpam-5032	245	17	n	n	NOUN
ejpam-5032	245	18	as	as	SCONJ
ejpam-5032	245	19	required	require	VERB
ejpam-5032	245	20	.	.	PUNCT
ejpam-5032	246	1	references	reference	NOUN
ejpam-5032	246	2	1211	1211	NUM
ejpam-5032	246	3	we	we	PRON
ejpam-5032	246	4	see	see	VERB
ejpam-5032	246	5	now	now	ADV
ejpam-5032	246	6	that	that	SCONJ
ejpam-5032	246	7	ann	ann	PROPN
ejpam-5032	246	8	(	(	PUNCT
ejpam-5032	246	9	(	(	PUNCT
ejpam-5032	246	10	h0t)n	h0t)n	NOUN
ejpam-5032	246	11	)	)	PUNCT
ejpam-5032	246	12	=	=	SYM
ejpam-5032	246	13	ann	ann	PROPN
ejpam-5032	246	14	(	(	PUNCT
ejpam-5032	246	15	h0k	h0k	PROPN
ejpam-5032	246	16	)	)	PUNCT
ejpam-5032	246	17	.	.	PUNCT
ejpam-5032	247	1	obviously	obviously	ADV
ejpam-5032	247	2	ann	ann	PROPN
ejpam-5032	247	3	(	(	PUNCT
ejpam-5032	247	4	h0k	h0k	PROPN
ejpam-5032	247	5	)	)	PUNCT
ejpam-5032	247	6	⊆	⊆	NUM
ejpam-5032	247	7	ann	ann	X
ejpam-5032	247	8	(	(	PUNCT
ejpam-5032	247	9	(	(	PUNCT
ejpam-5032	247	10	h0t)n	h0t)n	NOUN
ejpam-5032	247	11	)	)	PUNCT
ejpam-5032	247	12	as	as	ADP
ejpam-5032	247	13	(	(	PUNCT
ejpam-5032	247	14	h0t)n	h0t)n	PROPN
ejpam-5032	247	15	⊆	⊆	NUM
ejpam-5032	247	16	h0k	h0k	NOUN
ejpam-5032	247	17	.	.	PUNCT
ejpam-5032	248	1	since	since	SCONJ
ejpam-5032	248	2	h	h	NOUN
ejpam-5032	248	3	is	be	AUX
ejpam-5032	248	4	a	a	DET
ejpam-5032	248	5	prime	prime	ADJ
ejpam-5032	248	6	k	k	NOUN
ejpam-5032	248	7	-	-	NOUN
ejpam-5032	248	8	group	group	NOUN
ejpam-5032	248	9	of	of	ADP
ejpam-5032	248	10	type	type	NOUN
ejpam-5032	248	11	2	2	NUM
ejpam-5032	248	12	,	,	PUNCT
ejpam-5032	248	13	ank((h0t)k	ank((h0t)k	NUM
ejpam-5032	248	14	)	)	PUNCT
ejpam-5032	249	1	=	=	SYM
ejpam-5032	249	2	ank(h	ank(h	PROPN
ejpam-5032	249	3	)	)	PUNCT
ejpam-5032	249	4	.	.	PUNCT
ejpam-5032	250	1	we	we	PRON
ejpam-5032	250	2	have	have	VERB
ejpam-5032	250	3	(	(	PUNCT
ejpam-5032	250	4	(	(	PUNCT
ejpam-5032	250	5	h0t)k)k	h0t)k)k	NOUN
ejpam-5032	250	6	=	=	PUNCT
ejpam-5032	250	7	(	(	PUNCT
ejpam-5032	250	8	h0t)kk	h0t)kk	PROPN
ejpam-5032	250	9	⊆	⊆	NUM
ejpam-5032	250	10	(	(	PUNCT
ejpam-5032	250	11	h0t)k	h0t)k	ADP
ejpam-5032	250	12	⊆	⊆	NUM
ejpam-5032	250	13	(	(	PUNCT
ejpam-5032	250	14	h0t)n	h0t)n	X
ejpam-5032	250	15	.	.	PUNCT
ejpam-5032	251	1	let	let	VERB
ejpam-5032	251	2	x	x	SYM
ejpam-5032	251	3	∈	∈	PROPN
ejpam-5032	251	4	ann	ann	PROPN
ejpam-5032	251	5	(	(	PUNCT
ejpam-5032	251	6	(	(	PUNCT
ejpam-5032	251	7	h0t)n	h0t)n	NOUN
ejpam-5032	251	8	)	)	PUNCT
ejpam-5032	251	9	.	.	PUNCT
ejpam-5032	252	1	now	now	ADV
ejpam-5032	252	2	(	(	PUNCT
ejpam-5032	252	3	(	(	PUNCT
ejpam-5032	252	4	h0t)k)kx	h0t)k)kx	X
ejpam-5032	252	5	=	=	SYM
ejpam-5032	252	6	{	{	PUNCT
ejpam-5032	252	7	0	0	NUM
ejpam-5032	252	8	}	}	PUNCT
ejpam-5032	252	9	.	.	PUNCT
ejpam-5032	253	1	so	so	ADV
ejpam-5032	253	2	kx	kx	PROPN
ejpam-5032	253	3	⊆	⊆	NUM
ejpam-5032	253	4	ank((h0t)k	ank((h0t)k	NUM
ejpam-5032	253	5	)	)	PUNCT
ejpam-5032	254	1	=	=	SYM
ejpam-5032	254	2	ank(h	ank(h	X
ejpam-5032	254	3	)	)	PUNCT
ejpam-5032	254	4	and	and	CCONJ
ejpam-5032	254	5	hence	hence	ADV
ejpam-5032	254	6	h0kx	h0kx	PUNCT
ejpam-5032	254	7	=	=	PRON
ejpam-5032	254	8	{	{	PUNCT
ejpam-5032	254	9	0	0	NUM
ejpam-5032	254	10	}	}	PUNCT
ejpam-5032	254	11	,	,	PUNCT
ejpam-5032	254	12	that	that	PRON
ejpam-5032	254	13	is	is	ADV
ejpam-5032	254	14	x	x	X
ejpam-5032	254	15	∈	∈	PROPN
ejpam-5032	254	16	ann	ann	X
ejpam-5032	254	17	(	(	PUNCT
ejpam-5032	254	18	h0k	h0k	PROPN
ejpam-5032	254	19	)	)	PUNCT
ejpam-5032	254	20	.	.	PUNCT
ejpam-5032	255	1	therefore	therefore	ADV
ejpam-5032	255	2	ann	ann	PROPN
ejpam-5032	255	3	(	(	PUNCT
ejpam-5032	255	4	(	(	PUNCT
ejpam-5032	255	5	h0t)n	h0t)n	NOUN
ejpam-5032	255	6	)	)	PUNCT
ejpam-5032	255	7	⊆	⊆	NUM
ejpam-5032	255	8	ann	ann	X
ejpam-5032	255	9	(	(	PUNCT
ejpam-5032	255	10	h0k	h0k	PROPN
ejpam-5032	255	11	)	)	PUNCT
ejpam-5032	255	12	.	.	PUNCT
ejpam-5032	256	1	this	this	PRON
ejpam-5032	256	2	gives	give	VERB
ejpam-5032	256	3	the	the	DET
ejpam-5032	256	4	required	require	VERB
ejpam-5032	256	5	ann	ann	PROPN
ejpam-5032	256	6	(	(	PUNCT
ejpam-5032	256	7	(	(	PUNCT
ejpam-5032	256	8	h0t)n	h0t)n	NOUN
ejpam-5032	256	9	)	)	PUNCT
ejpam-5032	256	10	=	=	SYM
ejpam-5032	256	11	ann	ann	PROPN
ejpam-5032	256	12	(	(	PUNCT
ejpam-5032	256	13	h0k	h0k	PROPN
ejpam-5032	256	14	)	)	PUNCT
ejpam-5032	256	15	.	.	PUNCT
ejpam-5032	257	1	hence	hence	ADV
ejpam-5032	257	2	c	c	NOUN
ejpam-5032	257	3	:	:	PUNCT
ejpam-5032	257	4	=	=	NOUN
ejpam-5032	257	5	h0k	h0k	PROPN
ejpam-5032	257	6	is	be	AUX
ejpam-5032	257	7	a	a	DET
ejpam-5032	257	8	prime	prime	ADJ
ejpam-5032	257	9	n	n	ADP
ejpam-5032	257	10	-group	-group	NOUN
ejpam-5032	257	11	of	of	ADP
ejpam-5032	257	12	type	type	NOUN
ejpam-5032	257	13	2	2	NUM
ejpam-5032	257	14	.	.	PUNCT
ejpam-5032	258	1	finally	finally	ADV
ejpam-5032	258	2	,	,	PUNCT
ejpam-5032	258	3	let	let	VERB
ejpam-5032	258	4	t	t	NOUN
ejpam-5032	258	5	:	:	PUNCT
ejpam-5032	258	6	=	=	SYM
ejpam-5032	258	7	(	(	PUNCT
ejpam-5032	258	8	c	c	NOUN
ejpam-5032	258	9	:	:	PUNCT
ejpam-5032	258	10	0)n	0)n	X
ejpam-5032	258	11	.	.	PUNCT
ejpam-5032	259	1	now	now	ADV
ejpam-5032	259	2	t	t	PROPN
ejpam-5032	259	3	∩	∩	NOUN
ejpam-5032	259	4	k	k	PROPN
ejpam-5032	259	5	is	be	AUX
ejpam-5032	259	6	an	an	DET
ejpam-5032	259	7	ideal	ideal	NOUN
ejpam-5032	259	8	of	of	ADP
ejpam-5032	259	9	k.	k.	PROPN
ejpam-5032	259	10	also	also	ADV
ejpam-5032	259	11	t	t	PROPN
ejpam-5032	259	12	∩	∩	NOUN
ejpam-5032	259	13	k	k	PROPN
ejpam-5032	259	14	⊆	⊆	NUM
ejpam-5032	259	15	ank(h0k	ank(h0k	NUM
ejpam-5032	259	16	)	)	PUNCT
ejpam-5032	259	17	=	=	SYM
ejpam-5032	259	18	ank(h	ank(h	PROPN
ejpam-5032	259	19	)	)	PUNCT
ejpam-5032	259	20	.	.	PUNCT
ejpam-5032	260	1	therefore	therefore	ADV
ejpam-5032	260	2	t	t	PROPN
ejpam-5032	260	3	∩k	∩k	NOUN
ejpam-5032	260	4	⊆	⊆	NUM
ejpam-5032	260	5	(	(	PUNCT
ejpam-5032	260	6	h	h	NOUN
ejpam-5032	260	7	:	:	PUNCT
ejpam-5032	260	8	0)k	0)k	NOUN
ejpam-5032	260	9	,	,	PUNCT
ejpam-5032	260	10	that	that	ADV
ejpam-5032	260	11	is	is	ADV
ejpam-5032	260	12	,	,	PUNCT
ejpam-5032	260	13	(	(	PUNCT
ejpam-5032	260	14	c	c	NOUN
ejpam-5032	260	15	:	:	PUNCT
ejpam-5032	260	16	0)n	0)n	X
ejpam-5032	260	17	∩k	∩k	VERB
ejpam-5032	260	18	⊆	⊆	NUM
ejpam-5032	260	19	(	(	PUNCT
ejpam-5032	260	20	h	h	NOUN
ejpam-5032	260	21	:	:	PUNCT
ejpam-5032	260	22	0)k	0)k	NOUN
ejpam-5032	260	23	.	.	PUNCT
ejpam-5032	261	1	a	a	DET
ejpam-5032	261	2	h	h	NOUN
ejpam-5032	261	3	-	-	PUNCT
ejpam-5032	261	4	radical	radical	ADJ
ejpam-5032	261	5	r	r	NOUN
ejpam-5032	261	6	is	be	AUX
ejpam-5032	261	7	idempotent	idempotent	ADJ
ejpam-5032	261	8	if	if	SCONJ
ejpam-5032	261	9	r(n	r(n	VERB
ejpam-5032	261	10	)	)	PUNCT
ejpam-5032	261	11	=	=	SYM
ejpam-5032	261	12	r(r(n	r(r(n	PROPN
ejpam-5032	261	13	)	)	PUNCT
ejpam-5032	261	14	)	)	PUNCT
ejpam-5032	261	15	for	for	ADP
ejpam-5032	261	16	all	all	DET
ejpam-5032	261	17	n	n	NOUN
ejpam-5032	261	18	.	.	PUNCT
ejpam-5032	262	1	theorem	theorem	NOUN
ejpam-5032	262	2	5	5	NUM
ejpam-5032	262	3	.	.	PUNCT
ejpam-5032	263	1	the	the	DET
ejpam-5032	263	2	h	h	NOUN
ejpam-5032	263	3	-	-	PUNCT
ejpam-5032	263	4	radical	radical	ADJ
ejpam-5032	263	5	p2(r	p2(r	NOUN
ejpam-5032	263	6	)	)	PUNCT
ejpam-5032	263	7	is	be	AUX
ejpam-5032	263	8	idempotent	idempotent	ADJ
ejpam-5032	263	9	.	.	PUNCT
ejpam-5032	264	1	proof	proof	NOUN
ejpam-5032	264	2	.	.	PUNCT
ejpam-5032	265	1	let	let	VERB
ejpam-5032	265	2	k	k	PRON
ejpam-5032	265	3	be	be	AUX
ejpam-5032	265	4	an	an	DET
ejpam-5032	265	5	ideal	ideal	NOUN
ejpam-5032	265	6	of	of	ADP
ejpam-5032	265	7	n	n	PROPN
ejpam-5032	265	8	.	.	PUNCT
ejpam-5032	266	1	we	we	PRON
ejpam-5032	266	2	claim	claim	VERB
ejpam-5032	266	3	that	that	SCONJ
ejpam-5032	266	4	p2(r)(k	p2(r)(k	NOUN
ejpam-5032	266	5	)	)	PUNCT
ejpam-5032	266	6	⊇	⊇	PROPN
ejpam-5032	266	7	k	k	PROPN
ejpam-5032	266	8	∩	∩	PROPN
ejpam-5032	266	9	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	266	10	)	)	PUNCT
ejpam-5032	266	11	.	.	PUNCT
ejpam-5032	267	1	let	let	VERB
ejpam-5032	267	2	p	p	PRON
ejpam-5032	267	3	be	be	AUX
ejpam-5032	267	4	a	a	DET
ejpam-5032	267	5	right	right	ADJ
ejpam-5032	267	6	prime	prime	ADJ
ejpam-5032	267	7	ideal	ideal	NOUN
ejpam-5032	267	8	of	of	ADP
ejpam-5032	267	9	k	k	PROPN
ejpam-5032	267	10	of	of	ADP
ejpam-5032	267	11	type	type	NOUN
ejpam-5032	267	12	2	2	NUM
ejpam-5032	267	13	.	.	PUNCT
ejpam-5032	268	1	there	there	PRON
ejpam-5032	268	2	is	be	VERB
ejpam-5032	268	3	k	k	NOUN
ejpam-5032	268	4	-	-	ADJ
ejpam-5032	268	5	group	group	NOUN
ejpam-5032	268	6	h	h	NOUN
ejpam-5032	268	7	of	of	ADP
ejpam-5032	268	8	type	type	NOUN
ejpam-5032	268	9	2	2	NUM
ejpam-5032	268	10	with	with	ADP
ejpam-5032	268	11	p	p	NOUN
ejpam-5032	268	12	=	=	PUNCT
ejpam-5032	268	13	(	(	PUNCT
ejpam-5032	268	14	h	h	NOUN
ejpam-5032	268	15	:	:	PUNCT
ejpam-5032	268	16	0	0	NUM
ejpam-5032	268	17	)	)	PUNCT
ejpam-5032	268	18	.	.	PUNCT
ejpam-5032	269	1	by	by	ADP
ejpam-5032	269	2	theorem	theorem	NOUN
ejpam-5032	269	3	4	4	NUM
ejpam-5032	269	4	,	,	PUNCT
ejpam-5032	269	5	there	there	PRON
ejpam-5032	269	6	is	be	VERB
ejpam-5032	269	7	a	a	DET
ejpam-5032	269	8	k	k	NOUN
ejpam-5032	269	9	-	-	NOUN
ejpam-5032	269	10	subgroup	subgroup	NOUN
ejpam-5032	269	11	c	c	PROPN
ejpam-5032	269	12	of	of	ADP
ejpam-5032	269	13	the	the	DET
ejpam-5032	269	14	k	k	PROPN
ejpam-5032	269	15	-	-	PROPN
ejpam-5032	269	16	group	group	NOUN
ejpam-5032	269	17	h	h	NOUN
ejpam-5032	269	18	which	which	PRON
ejpam-5032	269	19	is	be	AUX
ejpam-5032	269	20	a	a	DET
ejpam-5032	269	21	prime	prime	ADJ
ejpam-5032	269	22	n	n	ADP
ejpam-5032	269	23	-group	-group	NOUN
ejpam-5032	269	24	of	of	ADP
ejpam-5032	269	25	type	type	NOUN
ejpam-5032	269	26	2	2	NUM
ejpam-5032	269	27	and	and	CCONJ
ejpam-5032	269	28	(	(	PUNCT
ejpam-5032	269	29	c	c	NOUN
ejpam-5032	269	30	:	:	PUNCT
ejpam-5032	269	31	0)n	0)n	PROPN
ejpam-5032	269	32	∩	∩	PROPN
ejpam-5032	269	33	k	k	PROPN
ejpam-5032	269	34	⊆	⊆	X
ejpam-5032	269	35	(	(	PUNCT
ejpam-5032	269	36	h	h	NOUN
ejpam-5032	269	37	:	:	PUNCT
ejpam-5032	269	38	0)k	0)k	NOUN
ejpam-5032	269	39	.	.	PUNCT
ejpam-5032	270	1	moreover	moreover	ADV
ejpam-5032	270	2	q	q	X
ejpam-5032	270	3	:	:	PUNCT
ejpam-5032	270	4	=	=	SYM
ejpam-5032	270	5	(	(	PUNCT
ejpam-5032	270	6	c	c	X
ejpam-5032	270	7	:	:	PUNCT
ejpam-5032	270	8	0)n	0)n	NUM
ejpam-5032	270	9	is	be	AUX
ejpam-5032	270	10	a	a	DET
ejpam-5032	270	11	right	right	ADJ
ejpam-5032	270	12	prime	prime	ADJ
ejpam-5032	270	13	ideal	ideal	NOUN
ejpam-5032	270	14	of	of	ADP
ejpam-5032	270	15	n	n	PRON
ejpam-5032	270	16	type	type	NOUN
ejpam-5032	270	17	2	2	NUM
ejpam-5032	270	18	and	and	CCONJ
ejpam-5032	270	19	p	p	PROPN
ejpam-5032	270	20	⊇	⊇	PROPN
ejpam-5032	270	21	k	k	PROPN
ejpam-5032	270	22	∩	∩	PROPN
ejpam-5032	270	23	q.	q.	PROPN
ejpam-5032	270	24	therefore	therefore	ADV
ejpam-5032	270	25	p2(r)(k	p2(r)(k	PROPN
ejpam-5032	270	26	)	)	PUNCT
ejpam-5032	270	27	⊇	⊇	PROPN
ejpam-5032	270	28	k	k	PROPN
ejpam-5032	270	29	∩	∩	PROPN
ejpam-5032	270	30	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	270	31	)	)	PUNCT
ejpam-5032	270	32	.	.	PUNCT
ejpam-5032	271	1	now	now	ADV
ejpam-5032	271	2	take	take	VERB
ejpam-5032	271	3	k	k	PROPN
ejpam-5032	271	4	=	=	SYM
ejpam-5032	271	5	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	271	6	)	)	PUNCT
ejpam-5032	271	7	.	.	PUNCT
ejpam-5032	272	1	this	this	PRON
ejpam-5032	272	2	gives	give	VERB
ejpam-5032	272	3	p2(r)(n)∩p2(r)(n	p2(r)(n)∩p2(r)(n	NOUN
ejpam-5032	272	4	)	)	PUNCT
ejpam-5032	272	5	⊆	⊆	NUM
ejpam-5032	272	6	p2(r)(p2(r)(n	p2(r)(p2(r)(n	NOUN
ejpam-5032	272	7	)	)	PUNCT
ejpam-5032	272	8	)	)	PUNCT
ejpam-5032	272	9	,	,	PUNCT
ejpam-5032	272	10	that	that	ADV
ejpam-5032	272	11	is	is	ADV
ejpam-5032	272	12	,	,	PUNCT
ejpam-5032	272	13	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	272	14	)	)	PUNCT
ejpam-5032	272	15	⊆	⊆	NUM
ejpam-5032	272	16	p2(r)(p2(r)(n	p2(r)(p2(r)(n	NOUN
ejpam-5032	272	17	)	)	PUNCT
ejpam-5032	272	18	)	)	PUNCT
ejpam-5032	272	19	.	.	PUNCT
ejpam-5032	273	1	the	the	DET
ejpam-5032	273	2	other	other	ADJ
ejpam-5032	273	3	inclusion	inclusion	NOUN
ejpam-5032	273	4	is	be	AUX
ejpam-5032	273	5	obvious	obvious	ADJ
ejpam-5032	273	6	and	and	CCONJ
ejpam-5032	273	7	hence	hence	ADV
ejpam-5032	273	8	p2(r)(n	p2(r)(n	PROPN
ejpam-5032	273	9	)	)	PUNCT
ejpam-5032	273	10	=	=	SYM
ejpam-5032	273	11	p2(r)(p2(r)(n	p2(r)(p2(r)(n	PROPN
ejpam-5032	273	12	)	)	PUNCT
ejpam-5032	273	13	)	)	PUNCT
ejpam-5032	273	14	.	.	PUNCT
ejpam-5032	274	1	so	so	ADV
ejpam-5032	274	2	the	the	DET
ejpam-5032	274	3	h	h	ADJ
ejpam-5032	274	4	-	-	PUNCT
ejpam-5032	274	5	radical	radical	ADJ
ejpam-5032	274	6	p2(r	p2(r	NOUN
ejpam-5032	274	7	)	)	PUNCT
ejpam-5032	274	8	is	be	AUX
ejpam-5032	274	9	idempotent	idempotent	ADJ
ejpam-5032	274	10	.	.	PUNCT
ejpam-5032	275	1	a	a	DET
ejpam-5032	275	2	h	h	NOUN
ejpam-5032	275	3	-	-	PUNCT
ejpam-5032	275	4	radical	radical	ADJ
ejpam-5032	275	5	r	r	NOUN
ejpam-5032	275	6	which	which	PRON
ejpam-5032	275	7	is	be	AUX
ejpam-5032	275	8	idempotent	idempotent	ADJ
ejpam-5032	275	9	and	and	CCONJ
ejpam-5032	275	10	complete	complete	ADJ
ejpam-5032	275	11	is	be	AUX
ejpam-5032	275	12	a	a	DET
ejpam-5032	275	13	kurosh	kurosh	ADV
ejpam-5032	275	14	-	-	PUNCT
ejpam-5032	275	15	amitsur	amitsur	NOUN
ejpam-5032	275	16	radical	radical	ADJ
ejpam-5032	275	17	or	or	CCONJ
ejpam-5032	275	18	ka	ka	NOUN
ejpam-5032	275	19	-	-	ADJ
ejpam-5032	275	20	radical	radical	ADJ
ejpam-5032	275	21	.	.	PUNCT
ejpam-5032	276	1	from	from	ADP
ejpam-5032	276	2	theorems	theorems	PROPN
ejpam-5032	276	3	3	3	NUM
ejpam-5032	276	4	and	and	CCONJ
ejpam-5032	276	5	5	5	NUM
ejpam-5032	276	6	we	we	PRON
ejpam-5032	276	7	have	have	AUX
ejpam-5032	276	8	:	:	PUNCT
ejpam-5032	276	9	theorem	theorem	VERB
ejpam-5032	276	10	6	6	NUM
ejpam-5032	276	11	.	.	PUNCT
ejpam-5032	277	1	the	the	DET
ejpam-5032	277	2	h	h	NOUN
ejpam-5032	277	3	-	-	PUNCT
ejpam-5032	277	4	radical	radical	ADJ
ejpam-5032	277	5	p2(r	p2(r	NOUN
ejpam-5032	277	6	)	)	PUNCT
ejpam-5032	277	7	is	be	AUX
ejpam-5032	277	8	a	a	DET
ejpam-5032	277	9	ka	ka	NOUN
ejpam-5032	277	10	-	-	ADJ
ejpam-5032	277	11	radical	radical	ADJ
ejpam-5032	277	12	.	.	PUNCT
ejpam-5032	278	1	references	reference	NOUN
ejpam-5032	278	2	[	[	X
ejpam-5032	278	3	1	1	X
ejpam-5032	278	4	]	]	PUNCT
ejpam-5032	278	5	j.	j.	PROPN
ejpam-5032	278	6	daunsr	daunsr	PROPN
ejpam-5032	278	7	.	.	PUNCT
ejpam-5032	279	1	prime	prime	ADJ
ejpam-5032	279	2	modules	module	NOUN
ejpam-5032	279	3	.	.	PUNCT
ejpam-5032	280	1	tartu	tartu	PROPN
ejpam-5032	280	2	rikkl	rikkl	PROPN
ejpam-5032	280	3	.	.	PUNCT
ejpam-5032	281	1	ul	ul	INTJ
ejpam-5032	281	2	.	.	PROPN
ejpam-5032	281	3	toitmetised	toitmetise	VERB
ejpam-5032	281	4	.	.	PUNCT
ejpam-5032	281	5	,	,	PUNCT
ejpam-5032	282	1	764:23–29	764:23–29	NUM
ejpam-5032	282	2	,	,	PUNCT
ejpam-5032	282	3	1987	1987	NUM
ejpam-5032	282	4	.	.	PUNCT
ejpam-5032	283	1	[	[	X
ejpam-5032	283	2	2	2	NUM
ejpam-5032	283	3	]	]	X
ejpam-5032	283	4	n.	n.	NOUN
ejpam-5032	283	5	j.	j.	PROPN
ejpam-5032	283	6	groenewald	groenewald	PROPN
ejpam-5032	283	7	g.	g.	PROPN
ejpam-5032	283	8	l.	l.	PROPN
ejpam-5032	283	9	booth	booth	PROPN
ejpam-5032	283	10	and	and	CCONJ
ejpam-5032	283	11	s.	s.	PROPN
ejpam-5032	283	12	veldsman	veldsman	PROPN
ejpam-5032	283	13	.	.	PUNCT
ejpam-5032	284	1	a	a	DET
ejpam-5032	284	2	kurosh	kurosh	ADV
ejpam-5032	284	3	-	-	PUNCT
ejpam-5032	284	4	amitsur	amitsur	ADJ
ejpam-5032	284	5	prime	prime	PROPN
ejpam-5032	284	6	radical	radical	NOUN
ejpam-5032	284	7	for	for	ADP
ejpam-5032	284	8	near	near	ADJ
ejpam-5032	284	9	-	-	PUNCT
ejpam-5032	284	10	rings	ring	NOUN
ejpam-5032	284	11	.	.	PUNCT
ejpam-5032	285	1	comm	comm	NOUN
ejpam-5032	285	2	.	.	PUNCT
ejpam-5032	286	1	algebra	algebra	NOUN
ejpam-5032	286	2	,	,	PUNCT
ejpam-5032	286	3	18(9):3111–3122	18(9):3111–3122	NUM
ejpam-5032	286	4	,	,	PUNCT
ejpam-5032	286	5	1990	1990	NUM
ejpam-5032	286	6	.	.	PUNCT
ejpam-5032	287	1	[	[	X
ejpam-5032	287	2	3	3	X
ejpam-5032	287	3	]	]	PUNCT
ejpam-5032	287	4	k.	k.	PROPN
ejpam-5032	287	5	kaarli	kaarli	PROPN
ejpam-5032	287	6	and	and	CCONJ
ejpam-5032	287	7	t.	t.	PROPN
ejpam-5032	287	8	kriis	kriis	PROPN
ejpam-5032	287	9	.	.	PUNCT
ejpam-5032	288	1	prime	prime	ADJ
ejpam-5032	288	2	ideals	ideal	NOUN
ejpam-5032	288	3	ofnear	ofnear	ADJ
ejpam-5032	288	4	-	-	PUNCT
ejpam-5032	288	5	rings	ring	NOUN
ejpam-5032	288	6	.	.	PUNCT
ejpam-5032	289	1	reine	reine	PROPN
ejpam-5032	289	2	angew.math	angew.math	PROPN
ejpam-5032	289	3	.	.	PROPN
ejpam-5032	289	4	,	,	PUNCT
ejpam-5032	289	5	298:156–181	298:156–181	NUM
ejpam-5032	289	6	,	,	PUNCT
ejpam-5032	289	7	1978	1978	NUM
ejpam-5032	289	8	.	.	PUNCT
ejpam-5032	290	1	[	[	X
ejpam-5032	290	2	4	4	X
ejpam-5032	290	3	]	]	X
ejpam-5032	290	4	g.	g.	PROPN
ejpam-5032	290	5	pilz	pilz	PROPN
ejpam-5032	290	6	.	.	PUNCT
ejpam-5032	291	1	near	near	ADP
ejpam-5032	291	2	-	-	PUNCT
ejpam-5032	291	3	rings	ring	NOUN
ejpam-5032	291	4	.	.	PUNCT
ejpam-5032	292	1	north	north	NOUN
ejpam-5032	292	2	-	-	PUNCT
ejpam-5032	292	3	holland	holland	PROPN
ejpam-5032	292	4	mathematical	mathematical	PROPN
ejpam-5032	292	5	studies	study	NOUN
ejpam-5032	292	6	,	,	PUNCT
ejpam-5032	292	7	amsterdam	amsterdam	PROPN
ejpam-5032	292	8	,	,	PUNCT
ejpam-5032	292	9	1983	1983	NUM
ejpam-5032	292	10	.	.	PUNCT
ejpam-5032	293	1	[	[	X
ejpam-5032	293	2	5	5	X
ejpam-5032	293	3	]	]	PUNCT
ejpam-5032	293	4	k.	k.	PROPN
ejpam-5032	293	5	naga	naga	PROPN
ejpam-5032	293	6	koteswara	koteswara	PROPN
ejpam-5032	293	7	rao	rao	PROPN
ejpam-5032	293	8	r.	r.	PROPN
ejpam-5032	293	9	srinivasa	srinivasa	PROPN
ejpam-5032	293	10	rao	rao	PROPN
ejpam-5032	293	11	and	and	CCONJ
ejpam-5032	293	12	k.	k.	PROPN
ejpam-5032	293	13	siva	siva	PROPN
ejpam-5032	293	14	prasad	prasad	PROPN
ejpam-5032	293	15	.	.	PUNCT
ejpam-5032	294	1	a	a	DET
ejpam-5032	294	2	module	module	NOUN
ejpam-5032	294	3	theoretic	theoretic	ADJ
ejpam-5032	294	4	characterization	characterization	NOUN
ejpam-5032	294	5	of	of	ADP
ejpam-5032	294	6	the	the	DET
ejpam-5032	294	7	prime	prime	ADJ
ejpam-5032	294	8	radical	radical	NOUN
ejpam-5032	294	9	of	of	ADP
ejpam-5032	294	10	near	near	ADJ
ejpam-5032	294	11	-	-	PUNCT
ejpam-5032	294	12	rings	ring	NOUN
ejpam-5032	294	13	.	.	PUNCT
ejpam-5032	295	1	beitr.algebra	beitr.algebra	PROPN
ejpam-5032	295	2	geom	geom	PROPN
ejpam-5032	295	3	.	.	PUNCT
ejpam-5032	295	4	,	,	PUNCT
ejpam-5032	295	5	59(1):51–60	59(1):51–60	NUM
ejpam-5032	295	6	,	,	PUNCT
ejpam-5032	295	7	2018	2018	NUM
ejpam-5032	295	8	.	.	PUNCT
ejpam-5032	296	1	[	[	X
ejpam-5032	296	2	6	6	NUM
ejpam-5032	296	3	]	]	PUNCT
ejpam-5032	296	4	k.	k.	PROPN
ejpam-5032	296	5	siva	siva	PROPN
ejpam-5032	296	6	prasad	prasad	PROPN
ejpam-5032	296	7	r.	r.	PROPN
ejpam-5032	296	8	srinivasa	srinivasa	PROPN
ejpam-5032	296	9	rao	rao	PROPN
ejpam-5032	296	10	,	,	PUNCT
ejpam-5032	296	11	k.	k.	PROPN
ejpam-5032	296	12	naga	naga	PROPN
ejpam-5032	296	13	koteswara	koteswara	PROPN
ejpam-5032	296	14	rao	rao	PROPN
ejpam-5032	296	15	and	and	CCONJ
ejpam-5032	296	16	k.	k.	PROPN
ejpam-5032	296	17	jaya	jaya	PROPN
ejpam-5032	296	18	lakshmi	lakshmi	PROPN
ejpam-5032	296	19	narayana	narayana	PROPN
ejpam-5032	296	20	.	.	PUNCT
ejpam-5032	297	1	a	a	DET
ejpam-5032	297	2	non	non	ADJ
ejpam-5032	297	3	-	-	ADJ
ejpam-5032	297	4	ideal	ideal	ADJ
ejpam-5032	297	5	hereditary	hereditary	ADJ
ejpam-5032	297	6	kurosh	kurosh	PROPN
ejpam-5032	297	7	-	-	PUNCT
ejpam-5032	297	8	amitsur	amitsur	ADJ
ejpam-5032	297	9	prime	prime	PROPN
ejpam-5032	297	10	radical	radical	NOUN
ejpam-5032	297	11	for	for	ADP
ejpam-5032	297	12	right	right	ADJ
ejpam-5032	297	13	nearrings	nearring	NOUN
ejpam-5032	297	14	.	.	PUNCT
ejpam-5032	298	1	afrika	afrika	PROPN
ejpam-5032	298	2	matematika	matematika	PROPN
ejpam-5032	298	3	.	.	PROPN
ejpam-5032	298	4	,	,	PUNCT
ejpam-5032	298	5	32:1333–1339	32:1333–1339	NUM
ejpam-5032	298	6	,	,	PUNCT
ejpam-5032	298	7	2021	2021	NUM
ejpam-5032	298	8	.	.	PUNCT
ejpam-5032	299	1	references	reference	NOUN
ejpam-5032	299	2	1212	1212	NUM
ejpam-5032	299	3	[	[	X
ejpam-5032	299	4	7	7	NUM
ejpam-5032	299	5	]	]	PUNCT
ejpam-5032	299	6	r.	r.	PROPN
ejpam-5032	299	7	srinivasa	srinivasa	PROPN
ejpam-5032	299	8	rao	rao	PROPN
ejpam-5032	299	9	and	and	CCONJ
ejpam-5032	299	10	s.	s.	PROPN
ejpam-5032	299	11	veldsman	veldsman	PROPN
ejpam-5032	299	12	.	.	PUNCT
ejpam-5032	300	1	right	right	ADJ
ejpam-5032	300	2	representations	representation	NOUN
ejpam-5032	300	3	of	of	ADP
ejpam-5032	300	4	right	right	ADJ
ejpam-5032	300	5	near	near	ADJ
ejpam-5032	300	6	-	-	PUNCT
ejpam-5032	300	7	ring	ring	NOUN
ejpam-5032	300	8	radicals	radical	NOUN
ejpam-5032	300	9	.	.	PUNCT
ejpam-5032	301	1	afrika	afrika	PROPN
ejpam-5032	301	2	matematika	matematika	PROPN
ejpam-5032	301	3	.	.	PROPN
ejpam-5032	301	4	,	,	PUNCT
ejpam-5032	301	5	30(1	30(1	NUM
ejpam-5032	301	6	-	-	SYM
ejpam-5032	301	7	2):37–52	2):37–52	NUM
ejpam-5032	301	8	,	,	PUNCT
ejpam-5032	301	9	2019	2019	NUM
ejpam-5032	301	10	.	.	PUNCT