id	sid	eid	entity	type
ejpam-492	1	1	3_xxx_jayaram.dvi european journal	ORG
ejpam-492	2	1	2	CARDINAL
ejpam-492	2	2	4, 2009	DATE
ejpam-492	2	3	508-519	CARDINAL
ejpam-492	2	4	1307-5543	CARDINAL
ejpam-492	2	5	c. jayaram	PERSON
ejpam-492	2	6	p.o.	ORG
ejpam-492	2	7	64	DATE
ejpam-492	2	8	bridgetown	GPE
ejpam-492	2	9	barbados	GPE
ejpam-492	6	1	2000	CARDINAL
ejpam-492	6	2	15a15	DATE
ejpam-492	6	3	secondary	ORDINAL
ejpam-492	6	4	05a15	CARDINAL
ejpam-492	7	1	1	CARDINAL
ejpam-492	8	1	l(r	PERSON
ejpam-492	8	2	r.	NORP
ejpam-492	11	1	section 3	LAW
ejpam-492	12	1	jayaram	PERSON
ejpam-492	12	2	508	CARDINAL
ejpam-492	12	3	2009	DATE
ejpam-492	13	1	c. jayaram	PERSON
ejpam-492	14	1	j. pure	PERSON
ejpam-492	14	2	2	CARDINAL
ejpam-492	14	3	2009	DATE
ejpam-492	14	4	508-519	CARDINAL
ejpam-492	14	5	509	CARDINAL
ejpam-492	14	6	one	CARDINAL
ejpam-492	14	7	1	CARDINAL
ejpam-492	15	1	2	CARDINAL
ejpam-492	16	1	2.	CARDINAL
ejpam-492	16	2	∈	ORG
ejpam-492	17	1	j ⊆	PERSON
ejpam-492	18	1	2	CARDINAL
ejpam-492	18	2	5	CARDINAL
ejpam-492	18	3	6	CARDINAL
ejpam-492	19	1	16	CARDINAL
ejpam-492	19	2	10	CARDINAL
ejpam-492	19	3	147	CARDINAL
ejpam-492	19	4	l(r	PERSON
ejpam-492	20	1	19	CARDINAL
ejpam-492	20	2	i)+b	PRODUCT
ejpam-492	20	3	l(r	PERSON
ejpam-492	23	1	8	CARDINAL
ejpam-492	23	2	3	CARDINAL
ejpam-492	24	1	r.	NORP
ejpam-492	24	2	r. π-rings	PERSON
ejpam-492	24	3	13	CARDINAL
ejpam-492	24	4	15	CARDINAL
ejpam-492	24	5	17	CARDINAL
ejpam-492	25	1	one	CARDINAL
ejpam-492	25	2	6=	CARDINAL
ejpam-492	25	3	0	CARDINAL
ejpam-492	26	1	6=	CARDINAL
ejpam-492	27	1	two	CARDINAL
ejpam-492	27	2	∈	ORG
ejpam-492	27	3	ak ⊆ n	PRODUCT
ejpam-492	29	1	zero	CARDINAL
ejpam-492	29	2	r.	NORP
ejpam-492	30	1	9	CARDINAL
ejpam-492	31	1	r.	NORP
ejpam-492	32	1	r.	NORP
ejpam-492	32	2	c. jayaram	PERSON
ejpam-492	33	1	j. pure	PERSON
ejpam-492	33	2	2	CARDINAL
ejpam-492	33	3	2009	DATE
ejpam-492	33	4	508-519	CARDINAL
ejpam-492	33	5	510	CARDINAL
ejpam-492	34	1	∈	ORG
ejpam-492	34	2	∈	ORG
ejpam-492	34	3	∈	ORG
ejpam-492	34	4	∈	ORG
ejpam-492	34	5	∈	ORG
ejpam-492	35	1	∈	ORG
ejpam-492	35	2	∈	ORG
ejpam-492	35	3	∈	ORG
ejpam-492	35	4	∈ n	PERSON
ejpam-492	36	1	zero	CARDINAL
ejpam-492	37	1	11	CARDINAL
ejpam-492	38	1	6=	DATE
ejpam-492	38	2	11	CARDINAL
ejpam-492	38	3	2.11	CARDINAL
ejpam-492	39	1	11	CARDINAL
ejpam-492	39	2	3.l	CARDINAL
ejpam-492	41	1	r.	NORP
ejpam-492	41	2	multiplicative	NORP
ejpam-492	42	1	ab α	ORG
ejpam-492	43	1	1	CARDINAL
ejpam-492	43	2	multiplicative	NORP
ejpam-492	43	3	1	CARDINAL
ejpam-492	44	1	multiplicative	NORP
ejpam-492	46	1	1	CARDINAL
ejpam-492	47	1	l(r	PERSON
ejpam-492	48	1	l(r	PERSON
ejpam-492	49	1	16	CARDINAL
ejpam-492	49	2	20	CARDINAL
ejpam-492	50	1	c. jayaram	PERSON
ejpam-492	51	1	j. pure	PERSON
ejpam-492	51	2	2	CARDINAL
ejpam-492	51	3	2009	DATE
ejpam-492	51	4	508-519	CARDINAL
ejpam-492	51	5	511 3	DATE
ejpam-492	55	1	1	CARDINAL
ejpam-492	56	1	r.	NORP
ejpam-492	56	2	2	CARDINAL
ejpam-492	60	1	1	CARDINAL
ejpam-492	63	1	11	CARDINAL
ejpam-492	63	2	1.1	CARDINAL
ejpam-492	64	1	2	CARDINAL
ejpam-492	65	1	r. (ii	EVENT
ejpam-492	69	1	zero	CARDINAL
ejpam-492	71	1	lemma 1	ORG
ejpam-492	72	1	r.	NORP
ejpam-492	74	1	11	CARDINAL
ejpam-492	74	2	3.7	CARDINAL
ejpam-492	75	1	c. jayaram	PERSON
ejpam-492	76	1	j. pure	PERSON
ejpam-492	76	2	2	CARDINAL
ejpam-492	76	3	2009	DATE
ejpam-492	76	4	508-519	CARDINAL
ejpam-492	76	5	512	CARDINAL
ejpam-492	76	6	3	CARDINAL
ejpam-492	79	1	∈	ORG
ejpam-492	80	1	r.	NORP
ejpam-492	81	1	1	CARDINAL
ejpam-492	81	2	lemma 2	ORG
ejpam-492	82	1	r.	NORP
ejpam-492	82	2	11	CARDINAL
ejpam-492	82	3	3.1	CARDINAL
ejpam-492	82	4	⊆	CARDINAL
ejpam-492	82	5	⊆	CARDINAL
ejpam-492	82	6	⊆ pm	TIME
ejpam-492	86	1	4	CARDINAL
ejpam-492	90	1	14	CARDINAL
ejpam-492	90	2	6	CARDINAL
ejpam-492	90	3	11	CARDINAL
ejpam-492	90	4	3.1	CARDINAL
ejpam-492	91	1	5	CARDINAL
ejpam-492	94	1	r.	NORP
ejpam-492	96	1	lemma 4	ORG
ejpam-492	99	1	6	CARDINAL
ejpam-492	102	1	c. jayaram	PERSON
ejpam-492	103	1	j. pure	PERSON
ejpam-492	103	2	2	CARDINAL
ejpam-492	103	3	2009	DATE
ejpam-492	103	4	508-519	CARDINAL
ejpam-492	103	5	513	CARDINAL
ejpam-492	104	1	1	CARDINAL
ejpam-492	104	2	lemma 2	ORG
ejpam-492	106	1	r.	NORP
ejpam-492	106	2	⊆	CARDINAL
ejpam-492	106	3	∈	ORG
ejpam-492	107	1	r.	NORP
ejpam-492	107	2	⊆	CARDINAL
ejpam-492	107	3	11	CARDINAL
ejpam-492	107	4	3.1	CARDINAL
ejpam-492	107	5	⊆	CARDINAL
ejpam-492	107	6	i.	PERSON
ejpam-492	110	1	7	CARDINAL
ejpam-492	112	1	1	CARDINAL
ejpam-492	116	1	r.	NORP
ejpam-492	118	1	r.	NORP
ejpam-492	119	1	18	CARDINAL
ejpam-492	119	2	1.4	CARDINAL
ejpam-492	119	3	r.	NORP
ejpam-492	119	4	5	CARDINAL
ejpam-492	120	1	12	CARDINAL
ejpam-492	120	2	46.8	CARDINAL
ejpam-492	120	3	46.10	CARDINAL
ejpam-492	120	4	576	CARDINAL
ejpam-492	121	1	15	CARDINAL
ejpam-492	121	2	4.2	CARDINAL
ejpam-492	121	3	4.3	CARDINAL
ejpam-492	122	1	1	CARDINAL
ejpam-492	123	1	12	CARDINAL
ejpam-492	123	2	46.9	CARDINAL
ejpam-492	123	3	577	CARDINAL
ejpam-492	129	1	⊆	CARDINAL
ejpam-492	129	2	∈	ORG
ejpam-492	130	1	r.	NORP
ejpam-492	130	2	⊆	CARDINAL
ejpam-492	130	3	⊆	CARDINAL
ejpam-492	130	4	i.	PERSON
ejpam-492	134	1	c. jayaram	PERSON
ejpam-492	135	1	j. pure	PERSON
ejpam-492	135	2	2	CARDINAL
ejpam-492	135	3	2009	DATE
ejpam-492	135	4	508-519	CARDINAL
ejpam-492	135	5	514	CARDINAL
ejpam-492	137	1	1	CARDINAL
ejpam-492	137	2	11	CARDINAL
ejpam-492	137	3	3.1	CARDINAL
ejpam-492	137	4	1	CARDINAL
ejpam-492	139	1	8	CARDINAL
ejpam-492	144	1	3	CARDINAL
ejpam-492	145	1	r.	NORP
ejpam-492	145	2	1	CARDINAL
ejpam-492	145	3	2	DATE
ejpam-492	147	1	i.	PERSON
ejpam-492	147	2	12	CARDINAL
ejpam-492	147	3	46.10	CARDINAL
ejpam-492	147	4	577	CARDINAL
ejpam-492	148	1	6	CARDINAL
ejpam-492	148	2	lemma 7	ORG
ejpam-492	148	3	1	CARDINAL
ejpam-492	148	4	2	DATE
ejpam-492	148	5	11	CARDINAL
ejpam-492	148	6	3.1	CARDINAL
ejpam-492	148	7	18	CARDINAL
ejpam-492	148	8	1.4	CARDINAL
ejpam-492	149	1	one	CARDINAL
ejpam-492	150	1	one	CARDINAL
ejpam-492	150	2	5	CARDINAL
ejpam-492	150	3	3	CARDINAL
ejpam-492	151	1	3	CARDINAL
ejpam-492	151	2	2.2	CARDINAL
ejpam-492	151	3	1	CARDINAL
ejpam-492	151	4	2	DATE
ejpam-492	151	5	⊆	CARDINAL
ejpam-492	153	1	6⊆	DATE
ejpam-492	159	1	5	CARDINAL
ejpam-492	159	2	6	CARDINAL
ejpam-492	159	3	1	CARDINAL
ejpam-492	159	4	1 ≤	QUANTITY
ejpam-492	160	1	1	CARDINAL
ejpam-492	160	2	∩ pns s ∩	PERSON
ejpam-492	160	3	s+t+1	GPE
ejpam-492	163	1	r.	NORP
ejpam-492	163	2	pj ⊆	PERSON
ejpam-492	163	3	+ 1	DATE
ejpam-492	164	1	0q	CARDINAL
ejpam-492	165	1	c. jayaram	PERSON
ejpam-492	166	1	j. pure	PERSON
ejpam-492	166	2	2	CARDINAL
ejpam-492	166	3	2009	DATE
ejpam-492	166	4	508-519	CARDINAL
ejpam-492	166	5	515	CARDINAL
ejpam-492	166	6	1 ≤	QUANTITY
ejpam-492	166	7	pj 6⊆q	PERSON
ejpam-492	167	1	zero	CARDINAL
ejpam-492	168	1	15	CARDINAL
ejpam-492	168	2	4.2	CARDINAL
ejpam-492	168	3	4.3	CARDINAL
ejpam-492	168	4	one	CARDINAL
ejpam-492	169	1	3	CARDINAL
ejpam-492	169	2	7	CARDINAL
ejpam-492	169	3	∩	PERSON
ejpam-492	169	4	q.	PERSON
ejpam-492	171	1	pj ⊆q	PERSON
ejpam-492	171	2	= jq	PERSON
ejpam-492	173	1	6⊆	DATE
ejpam-492	176	1	j	PERSON
ejpam-492	176	2	11	CARDINAL
ejpam-492	176	3	1.6	CARDINAL
ejpam-492	176	4	21	CARDINAL
ejpam-492	176	5	1	CARDINAL
ejpam-492	178	1	1	CARDINAL
ejpam-492	182	1	one	CARDINAL
ejpam-492	187	1	lemma 5	ORG
ejpam-492	188	1	13	CARDINAL
ejpam-492	188	2	6	CARDINAL
ejpam-492	189	1	14	CARDINAL
ejpam-492	189	2	7	CARDINAL
ejpam-492	189	3	6	CARDINAL
ejpam-492	189	4	8, pm	TIME
ejpam-492	190	1	18	CARDINAL
ejpam-492	190	2	1.4	CARDINAL
ejpam-492	191	1	one	CARDINAL
ejpam-492	193	1	14	CARDINAL
ejpam-492	193	2	6	CARDINAL
ejpam-492	193	3	14	CARDINAL
ejpam-492	193	4	8, pm	TIME
ejpam-492	193	5	c. jayaram	PERSON
ejpam-492	194	1	j. pure	PERSON
ejpam-492	194	2	2	CARDINAL
ejpam-492	194	3	2009	DATE
ejpam-492	194	4	508-519	CARDINAL
ejpam-492	194	5	516	CARDINAL
ejpam-492	199	1	∈	ORG
ejpam-492	200	1	m)m	TIME
ejpam-492	202	1	11	CARDINAL
ejpam-492	202	2	3.7	CARDINAL
ejpam-492	203	1	18	CARDINAL
ejpam-492	203	2	1.4	CARDINAL
ejpam-492	204	1	l(r	PERSON
ejpam-492	204	2	4	CARDINAL
ejpam-492	204	3	2	CARDINAL
ejpam-492	205	1	iii)⇒(i	ORG
ejpam-492	206	1	2	CARDINAL
ejpam-492	217	1	18	CARDINAL
ejpam-492	217	2	1.4	CARDINAL
ejpam-492	217	3	l(r	PERSON
ejpam-492	218	1	c. jayaram	PERSON
ejpam-492	219	1	j. pure	PERSON
ejpam-492	219	2	2	CARDINAL
ejpam-492	219	3	2009	DATE
ejpam-492	219	4	508-519	CARDINAL
ejpam-492	219	5	517	CARDINAL
ejpam-492	219	6	1	CARDINAL
ejpam-492	219	7	13	CARDINAL
ejpam-492	219	8	6	CARDINAL
ejpam-492	219	9	11	CARDINAL
ejpam-492	219	10	1.6	CARDINAL
ejpam-492	219	11	21	CARDINAL
ejpam-492	219	12	1	CARDINAL
ejpam-492	223	1	1	CARDINAL
ejpam-492	224	1	14	CARDINAL
ejpam-492	227	1	1	CARDINAL
ejpam-492	232	1	9	CARDINAL
ejpam-492	232	2	5	CARDINAL
ejpam-492	233	1	5	CARDINAL
ejpam-492	234	1	11	CARDINAL
ejpam-492	234	2	3.1	CARDINAL
ejpam-492	235	1	13	CARDINAL
ejpam-492	235	2	6	CARDINAL
ejpam-492	236	1	18	CARDINAL
ejpam-492	236	2	1.4	CARDINAL
ejpam-492	236	3	11	CARDINAL
ejpam-492	236	4	3.1	CARDINAL
ejpam-492	240	1	10	CARDINAL
ejpam-492	240	2	2	CARDINAL
ejpam-492	241	1	11	CARDINAL
ejpam-492	241	2	3.1	CARDINAL
ejpam-492	241	3	18	CARDINAL
ejpam-492	241	4	1.4	CARDINAL
ejpam-492	242	1	1	CARDINAL
ejpam-492	242	2	13	CARDINAL
ejpam-492	242	3	6	CARDINAL
ejpam-492	243	1	518	CARDINAL
ejpam-492	244	1	anderson	PERSON
ejpam-492	244	2	6	CARDINAL
ejpam-492	244	3	131	CARDINAL
ejpam-492	244	4	1976	DATE
ejpam-492	245	1	2	CARDINAL
ejpam-492	245	2	anderson	PERSON
ejpam-492	245	3	r(x	PRODUCT
ejpam-492	245	4	canad	ORG
ejpam-492	246	1	jour	PERSON
ejpam-492	247	1	28	CARDINAL
ejpam-492	247	2	760-768	MONEY
ejpam-492	247	3	1976	DATE
ejpam-492	248	1	3	CARDINAL
ejpam-492	248	2	anderson	PERSON
ejpam-492	248	3	j. matijevic	PERSON
ejpam-492	248	4	w. nichols	PERSON
ejpam-492	248	5	krull	PERSON
ejpam-492	248	6	theorem ii	PERSON
ejpam-492	248	7	pacific journal	ORG
ejpam-492	248	8	66	CARDINAL
ejpam-492	248	9	15-22	CARDINAL
ejpam-492	248	10	1976	DATE
ejpam-492	249	1	4	CARDINAL
ejpam-492	249	2	anderson	PERSON
ejpam-492	249	3	8	CARDINAL
ejpam-492	249	4	330-335	CARDINAL
ejpam-492	249	5	1978	DATE
ejpam-492	250	1	5	CARDINAL
ejpam-492	250	2	anderson	PERSON
ejpam-492	251	1	japon	GPE
ejpam-492	252	1	25	CARDINAL
ejpam-492	252	2	463-469	CARDINAL
ejpam-492	252	3	1980	DATE
ejpam-492	253	1	6	CARDINAL
ejpam-492	253	2	anderson	PERSON
ejpam-492	253	3	canad	GPE
ejpam-492	255	1	bull	PERSON
ejpam-492	256	1	23(4	CARDINAL
ejpam-492	256	2	457	CARDINAL
ejpam-492	256	3	1980	DATE
ejpam-492	257	1	anderson	PERSON
ejpam-492	257	2	l.a	GPE
ejpam-492	257	3	mahaney	PERSON
ejpam-492	257	4	54	CARDINAL
ejpam-492	257	5	141-154	CARDINAL
ejpam-492	257	6	1988	DATE
ejpam-492	258	1	8	CARDINAL
ejpam-492	258	2	anderson	PERSON
ejpam-492	258	3	e.w. johnson	PERSON
ejpam-492	258	4	dilworth	GPE
ejpam-492	258	5	36	CARDINAL
ejpam-492	258	6	99-109	CARDINAL
ejpam-492	259	1	9	CARDINAL
ejpam-492	259	2	a. barnard	PERSON
ejpam-492	259	3	71	CARDINAL
ejpam-492	259	4	174	CARDINAL
ejpam-492	259	5	1981	DATE
ejpam-492	260	1	10	CARDINAL
ejpam-492	260	2	h. koohy	PERSON
ejpam-492	261	1	sci.	ORG
ejpam-492	262	1	6	CARDINAL
ejpam-492	262	2	83-88 (	PERCENT
ejpam-492	263	1	11	CARDINAL
ejpam-492	263	2	z. el-bast	PERSON
ejpam-492	263	3	16(4	DATE
ejpam-492	263	4	755	CARDINAL
ejpam-492	263	5	1988	DATE
ejpam-492	264	1	12	CARDINAL
ejpam-492	264	2	gilmer	GPE
ejpam-492	264	3	multiplicative	NORP
ejpam-492	264	4	marcel decker	PERSON
ejpam-492	264	5	1972	DATE
ejpam-492	265	1	13	CARDINAL
ejpam-492	265	2	c. jayaram	PERSON
ejpam-492	265	3	czechoslovak mathematical journal	ORG
ejpam-492	265	4	54(129	CARDINAL
ejpam-492	265	5	119-130	CARDINAL
ejpam-492	265	6	2004	DATE
ejpam-492	266	1	519	CARDINAL
ejpam-492	266	2	14	CARDINAL
ejpam-492	266	3	c. jayaram	PERSON
ejpam-492	266	4	turkish	NORP
ejpam-492	266	5	33	CARDINAL
ejpam-492	266	6	215-225	CARDINAL
ejpam-492	266	7	2009	DATE
ejpam-492	267	1	15	CARDINAL
ejpam-492	267	2	kang	PERSON
ejpam-492	267	3	krull	PERSON
ejpam-492	267	4	124	CARDINAL
ejpam-492	267	5	284	CARDINAL
ejpam-492	267	6	1989	DATE
ejpam-492	268	1	16	CARDINAL
ejpam-492	268	2	larsen	PERSON
ejpam-492	268	3	mccarthy	PERSON
ejpam-492	268	4	multiplicative	ORG
ejpam-492	268	5	new york	GPE
ejpam-492	268	6	1971	DATE
ejpam-492	269	1	17	CARDINAL
ejpam-492	269	2	levitz	ORG
ejpam-492	270	1	amer	PERSON
ejpam-492	272	1	32	CARDINAL
ejpam-492	272	2	376-380	CARDINAL
ejpam-492	272	3	1972	DATE
ejpam-492	273	1	18	CARDINAL
ejpam-492	273	2	g.m	PERSON
ejpam-492	273	3	18(12	CARDINAL
ejpam-492	273	4	4353-4375	DATE
ejpam-492	273	5	1990	DATE
ejpam-492	274	1	19	CARDINAL
ejpam-492	274	2	mccarthy	PERSON
ejpam-492	275	1	amer	PERSON
ejpam-492	277	1	30	CARDINAL
ejpam-492	277	2	43-45	CARDINAL
ejpam-492	277	3	1971	DATE
ejpam-492	278	1	20	CARDINAL
ejpam-492	278	2	d.g. northcott	PERSON
ejpam-492	278	3	multiplicities	ORG
ejpam-492	278	4	cambridge university press	ORG
ejpam-492	278	5	london	GPE
ejpam-492	278	6	1968	DATE
ejpam-492	279	1	21	CARDINAL
ejpam-492	279	2	shahabaddin ebrahimi atani	PERSON
ejpam-492	279	3	1	CARDINAL
ejpam-492	279	4	381-384	CARDINAL
ejpam-492	279	5	2007	DATE