id	sid	eid	entity	type
ejpam-2291	1	1	european journal	ORG
ejpam-2291	2	1	7	CARDINAL
ejpam-2291	2	2	4, 2014	DATE
ejpam-2291	2	3	429	CARDINAL
ejpam-2291	2	4	naser zamani	PERSON
ejpam-2291	2	5	university of	ORG
ejpam-2291	2	6	ardabili	PERSON
ejpam-2291	2	7	ardabil	ORG
ejpam-2291	2	8	iran	GPE
ejpam-2291	5	1	2010	DATE
ejpam-2291	5	2	13a99	CARDINAL
ejpam-2291	5	3	13d45	CARDINAL
ejpam-2291	5	4	1	CARDINAL
ejpam-2291	7	1	t. the end of l	DATE
ejpam-2291	7	2	end(l	ORG
ejpam-2291	7	3	6=	DATE
ejpam-2291	10	1	zero	CARDINAL
ejpam-2291	10	2	1	CARDINAL
ejpam-2291	10	3	chapter 15	LAW
ejpam-2291	11	1	3	CARDINAL
ejpam-2291	14	1	reg(l	GPE
ejpam-2291	20	1	r(b	PERSON
ejpam-2291	20	2	g(b	GPE
ejpam-2291	21	1	2	CARDINAL
ejpam-2291	21	2	4.6.4	CARDINAL
ejpam-2291	21	3	⊆	CARDINAL
ejpam-2291	23	1	429	CARDINAL
ejpam-2291	24	1	2014	DATE
ejpam-2291	25	1	n. zamani	PERSON
ejpam-2291	26	1	j. pure	PERSON
ejpam-2291	26	2	7 (2014	DATE
ejpam-2291	26	3	429	CARDINAL
ejpam-2291	28	1	3	CARDINAL
ejpam-2291	29	1	section 2	LAW
ejpam-2291	29	2	1	CARDINAL
ejpam-2291	29	3	reg(l	GPE
ejpam-2291	29	4	1	CARDINAL
ejpam-2291	29	5	section 3	LAW
ejpam-2291	29	6	5	CARDINAL
ejpam-2291	31	1	4	CARDINAL
ejpam-2291	31	2	2	CARDINAL
ejpam-2291	34	1	fh	ORG
ejpam-2291	34	2	f1	PERSON
ejpam-2291	36	1	fh	ORG
ejpam-2291	36	2	1	CARDINAL
ejpam-2291	38	1	f1	PERSON
ejpam-2291	40	1	e(f	PERSON
ejpam-2291	40	2	f1	PERSON
ejpam-2291	41	1	fi−1)l	PERSON
ejpam-2291	41	2	f1	PERSON
ejpam-2291	42	1	fi−1)l	PERSON
ejpam-2291	43	1	1	CARDINAL
ejpam-2291	45	1	1	CARDINAL
ejpam-2291	45	2	f1	PERSON
ejpam-2291	46	1	fh	ORG
ejpam-2291	47	1	e(f	PERSON
ejpam-2291	49	1	1	CARDINAL
ejpam-2291	49	2	6	CARDINAL
ejpam-2291	49	3	2.3	CARDINAL
ejpam-2291	51	1	1≤	ORDINAL
ejpam-2291	51	2	+ 1	DATE
ejpam-2291	53	1	0	CARDINAL
ejpam-2291	54	1	0	CARDINAL
ejpam-2291	55	1	0	CARDINAL
ejpam-2291	57	1	1	CARDINAL
ejpam-2291	59	1	1	CARDINAL
ejpam-2291	61	1	f −→ l(1	PRODUCT
ejpam-2291	63	1	l)n→	PERSON
ejpam-2291	64	1	n. zamani	PERSON
ejpam-2291	65	1	j. pure	PERSON
ejpam-2291	65	2	7 (2014	DATE
ejpam-2291	65	3	429	CARDINAL
ejpam-2291	65	4	2	CARDINAL
ejpam-2291	68	1	fh	ORG
ejpam-2291	68	2	1	CARDINAL
ejpam-2291	68	3	e(f	PERSON
ejpam-2291	70	1	1	CARDINAL
ejpam-2291	70	2	0≤	CARDINAL
ejpam-2291	70	3	t ≤ h	DATE
ejpam-2291	70	4	max{ai(l)+i	PERSON
ejpam-2291	71	1	f1	PERSON
ejpam-2291	73	1	ft)l	PERSON
ejpam-2291	79	1	h≥ 1	DATE
ejpam-2291	81	1	⊆	CARDINAL
ejpam-2291	81	2	⊆	CARDINAL
ejpam-2291	81	3	f1	PERSON
ejpam-2291	81	4	1	CARDINAL
ejpam-2291	83	1	1	CARDINAL
ejpam-2291	87	1	1	CARDINAL
ejpam-2291	88	1	1	CARDINAL
ejpam-2291	89	1	1	CARDINAL
ejpam-2291	92	1	2	CARDINAL
ejpam-2291	94	1	1	CARDINAL
ejpam-2291	95	1	e(f	PERSON
ejpam-2291	95	2	f1	PERSON
ejpam-2291	96	1	1	CARDINAL
ejpam-2291	97	1	f1	PERSON
ejpam-2291	98	1	j(l	PERSON
ejpam-2291	101	1	t ≤ h	DATE
ejpam-2291	102	1	t}=max{a0(l/	PERSON
ejpam-2291	102	2	f1	PERSON
ejpam-2291	106	1	f1	PERSON
ejpam-2291	109	1	f1	PERSON
ejpam-2291	111	1	⋃	PERSON
ejpam-2291	111	2	f1	PERSON
ejpam-2291	114	1	f1	PERSON
ejpam-2291	115	1	fi)l)a	ORG
ejpam-2291	115	2	f1	PERSON
ejpam-2291	118	1	⊆	CARDINAL
ejpam-2291	118	2	f1	PERSON
ejpam-2291	120	1	f1	PERSON
ejpam-2291	125	1	5	CARDINAL
ejpam-2291	125	2	2.3	CARDINAL
ejpam-2291	130	1	−1	DATE
ejpam-2291	131	1	n. zamani	PERSON
ejpam-2291	132	1	j. pure	PERSON
ejpam-2291	132	2	7 (2014	DATE
ejpam-2291	132	3	429	CARDINAL
ejpam-2291	135	1	2	CARDINAL
ejpam-2291	138	1	f1	PERSON
ejpam-2291	140	1	f1	PERSON
ejpam-2291	142	1	1	CARDINAL
ejpam-2291	144	1	2(ii	CARDINAL
ejpam-2291	144	2	j(l)+ j	PERSON
ejpam-2291	144	3	1	CARDINAL
ejpam-2291	149	1	1	CARDINAL
ejpam-2291	153	1	f1	PERSON
ejpam-2291	160	1	grade(s̄+	PERSON
ejpam-2291	160	2	1	CARDINAL
ejpam-2291	161	1	−1	DATE
ejpam-2291	162	1	1	CARDINAL
ejpam-2291	165	1	fh	PERSON
ejpam-2291	167	1	fh	ORG
ejpam-2291	167	2	reg(l	GPE
ejpam-2291	170	1	2	CARDINAL
ejpam-2291	170	2	e(f	PERSON
ejpam-2291	170	3	f1	PERSON
ejpam-2291	174	1	1	CARDINAL
ejpam-2291	175	1	end(l/bl	ORG
ejpam-2291	175	2	f1	PERSON
ejpam-2291	178	1	f1	PERSON
ejpam-2291	186	1	reg(l	GPE
ejpam-2291	189	1	0	CARDINAL
ejpam-2291	191	1	1	CARDINAL
ejpam-2291	193	1	1	CARDINAL
ejpam-2291	193	2	ai(l/ f1 l	PERSON
ejpam-2291	193	3	1	CARDINAL
ejpam-2291	193	4	lemma 1	ORG
ejpam-2291	196	1	3	CARDINAL
ejpam-2291	196	2	5	CARDINAL
ejpam-2291	198	1	4	CARDINAL
ejpam-2291	198	2	5	CARDINAL
ejpam-2291	198	3	3.1	CARDINAL
ejpam-2291	199	1	g(e	PERSON
ejpam-2291	199	2	g(b)+	ORG
ejpam-2291	200	1	n. zamani	PERSON
ejpam-2291	201	1	j. pure	PERSON
ejpam-2291	201	2	7 (2014	DATE
ejpam-2291	201	3	429	CARDINAL
ejpam-2291	201	4	436 433	CARDINAL
ejpam-2291	201	5	2	CARDINAL
ejpam-2291	206	1	6= 1	DATE
ejpam-2291	207	1	6=	CARDINAL
ejpam-2291	208	1	⊆	CARDINAL
ejpam-2291	208	2	0	CARDINAL
ejpam-2291	208	3	1	CARDINAL
ejpam-2291	209	1	6⊆	CARDINAL
ejpam-2291	209	2	0	CARDINAL
ejpam-2291	210	1	−1	DATE
ejpam-2291	212	1	0	CARDINAL
ejpam-2291	213	1	1	CARDINAL
ejpam-2291	213	2	zero	CARDINAL
ejpam-2291	216	1	1	CARDINAL
ejpam-2291	216	2	1	CARDINAL
ejpam-2291	217	1	2	CARDINAL
ejpam-2291	217	2	0	CARDINAL
ejpam-2291	218	1	h i g+ (g(e	ORG
ejpam-2291	221	1	g(e	PERSON
ejpam-2291	221	2	0 −→ r(e)+(1) −→	QUANTITY
ejpam-2291	221	3	2	CARDINAL
ejpam-2291	225	1	3	CARDINAL
ejpam-2291	228	1	g(e	PERSON
ejpam-2291	229	1	0	CARDINAL
ejpam-2291	233	1	+ 1	DATE
ejpam-2291	233	2	2	CARDINAL
ejpam-2291	235	1	n ≥ max{0	ORG
ejpam-2291	236	1	0	CARDINAL
ejpam-2291	236	2	1	DATE
ejpam-2291	237	1	+ 1	DATE
ejpam-2291	237	2	2	CARDINAL
ejpam-2291	238	1	2	CARDINAL
ejpam-2291	239	1	two	CARDINAL
ejpam-2291	240	1	g(e	PERSON
ejpam-2291	241	1	0	CARDINAL
ejpam-2291	242	1	4	CARDINAL
ejpam-2291	244	1	0	CARDINAL
ejpam-2291	247	1	g(e	PERSON
ejpam-2291	250	1	+ 1	DATE
ejpam-2291	250	2	4	CARDINAL
ejpam-2291	252	1	g(e	PERSON
ejpam-2291	253	1	0	CARDINAL
ejpam-2291	253	2	1(iii	CARDINAL
ejpam-2291	254	1	4	CARDINAL
ejpam-2291	255	1	⊆	CARDINAL
ejpam-2291	255	2	0	CARDINAL
ejpam-2291	258	1	g(e	PERSON
ejpam-2291	260	1	1	CARDINAL
ejpam-2291	262	1	first	ORDINAL
ejpam-2291	263	1	n. zamani	PERSON
ejpam-2291	264	1	j. pure	PERSON
ejpam-2291	264	2	7 (2014	DATE
ejpam-2291	264	3	429-436 434	QUANTITY
ejpam-2291	264	4	second	ORDINAL
ejpam-2291	267	1	6=	CARDINAL
ejpam-2291	269	1	4	CARDINAL
ejpam-2291	270	1	1	CARDINAL
ejpam-2291	275	1	0	CARDINAL
ejpam-2291	276	1	3	CARDINAL
ejpam-2291	278	1	g(e))n	GPE
ejpam-2291	279	1	0	CARDINAL
ejpam-2291	282	1	g(e	PERSON
ejpam-2291	283	1	0	CARDINAL
ejpam-2291	286	1	4	CARDINAL
ejpam-2291	289	1	0	CARDINAL
ejpam-2291	289	2	2	CARDINAL
ejpam-2291	289	3	0	CARDINAL
ejpam-2291	290	1	1	CARDINAL
ejpam-2291	291	1	0	CARDINAL
ejpam-2291	293	1	6⊆	CARDINAL
ejpam-2291	293	2	0	CARDINAL
ejpam-2291	294	1	−1	DATE
ejpam-2291	296	1	2	CARDINAL
ejpam-2291	298	1	6=	DATE
ejpam-2291	300	1	⊆	CARDINAL
ejpam-2291	300	2	0	CARDINAL
ejpam-2291	302	1	6=	DATE
ejpam-2291	307	1	1	CARDINAL
ejpam-2291	307	2	2(ii	CARDINAL
ejpam-2291	309	1	1	CARDINAL
ejpam-2291	312	1	1	CARDINAL
ejpam-2291	312	2	⊆	CARDINAL
ejpam-2291	312	3	0	CARDINAL
ejpam-2291	313	1	2(iii	CARDINAL
ejpam-2291	314	1	3	CARDINAL
ejpam-2291	317	1	2(i	CARDINAL
ejpam-2291	319	1	1	CARDINAL
ejpam-2291	319	2	2(iii	CARDINAL
ejpam-2291	320	1	+ 1≤ a1(g(e	DATE
ejpam-2291	321	1	+ 1 or a1(r(e	DATE
ejpam-2291	330	1	+ i.	PERSON
ejpam-2291	332	1	6=	CARDINAL
ejpam-2291	333	1	2(ii),(iii	CARDINAL
ejpam-2291	338	1	r(b	PERSON
ejpam-2291	339	1	435	CARDINAL
ejpam-2291	340	1	f1	PERSON
ejpam-2291	342	1	fh	ORG
ejpam-2291	344	1	fh	ORG
ejpam-2291	345	1	1	CARDINAL
ejpam-2291	345	2	f1	PERSON
ejpam-2291	347	1	f1	PERSON
ejpam-2291	349	1	fi−1)b	PERSON
ejpam-2291	350	1	1	CARDINAL
ejpam-2291	352	1	h.	PERSON
ejpam-2291	352	2	4	CARDINAL
ejpam-2291	352	3	e(f	PERSON
ejpam-2291	352	4	4	CARDINAL
ejpam-2291	352	5	+ 1	DATE
ejpam-2291	354	1	fh	ORG
ejpam-2291	358	1	1	CARDINAL
ejpam-2291	360	1	h.	PERSON
ejpam-2291	360	2	first	ORDINAL
ejpam-2291	360	3	f1	PERSON
ejpam-2291	362	1	∩ bne	PERSON
ejpam-2291	362	2	second	ORDINAL
ejpam-2291	362	3	f1	PERSON
ejpam-2291	366	1	e(f	PERSON
ejpam-2291	370	1	+ 1	DATE
ejpam-2291	373	1	fh	ORG
ejpam-2291	373	2	e.	PERSON
ejpam-2291	375	1	fh	ORG
ejpam-2291	378	1	4	CARDINAL
ejpam-2291	382	1	fh	ORG
ejpam-2291	386	1	1	CARDINAL
ejpam-2291	388	1	1	CARDINAL
ejpam-2291	388	2	1	CARDINAL
ejpam-2291	389	1	∈	ORG
ejpam-2291	389	2	g(b	GPE
ejpam-2291	390	1	2	CARDINAL
ejpam-2291	390	2	f1	PERSON
ejpam-2291	392	1	fh	ORG
ejpam-2291	395	1	f1	PERSON
ejpam-2291	396	1	f1	PERSON
ejpam-2291	398	1	fi−1)b	PERSON
ejpam-2291	399	1	1	CARDINAL
ejpam-2291	400	1	s.	PERSON
ejpam-2291	400	2	g(e	PERSON
ejpam-2291	400	3	+ 1	DATE
ejpam-2291	400	4	1	CARDINAL
ejpam-2291	402	1	cambridge university press	ORG
ejpam-2291	402	2	cambridge	GPE
ejpam-2291	402	3	1998	DATE
ejpam-2291	403	1	2	CARDINAL
ejpam-2291	403	2	j herzog	PERSON
ejpam-2291	403	3	cohen-macaulay rings	PERSON
ejpam-2291	404	1	cambridge university press	ORG
ejpam-2291	404	2	cambridge	GPE
ejpam-2291	404	3	1993	DATE
ejpam-2291	405	1	436	CARDINAL
ejpam-2291	406	1	3	CARDINAL
ejpam-2291	406	2	k watanabe	PERSON
ejpam-2291	407	1	rings i. journal	ORG
ejpam-2291	407	2	japan	GPE
ejpam-2291	407	3	213	CARDINAL
ejpam-2291	407	4	1978	DATE
ejpam-2291	408	1	4	CARDINAL
ejpam-2291	410	1	hiroshima mathematical journal	ORG
ejpam-2291	411	1	17:47	CARDINAL
ejpam-2291	412	1	5	CARDINAL
ejpam-2291	414	1	american	NORP
ejpam-2291	414	2	350	CARDINAL
ejpam-2291	414	3	2813-2832	CARDINAL
ejpam-2291	414	4	1998	DATE
ejpam-2291	415	1	6	CARDINAL
ejpam-2291	416	1	american	NORP
ejpam-2291	417	1	101:229-236	CARDINAL
ejpam-2291	417	2	1987	DATE