id	sid	eid	entity	type
ejpam-1767	1	1	european journal	ORG
ejpam-1767	2	1	6	CARDINAL
ejpam-1767	2	2	2, 2013	DATE
ejpam-1767	2	3	119	CARDINAL
ejpam-1767	2	4	1307-5543	DATE
ejpam-1767	3	1	zhu zhanmin department of mathematics	ORG
ejpam-1767	3	2	jiaxing university	ORG
ejpam-1767	3	3	jiaxing	GPE
ejpam-1767	3	4	zhejiang province	GPE
ejpam-1767	3	5	314001	DATE
ejpam-1767	6	1	goldie dimensions	PERSON
ejpam-1767	7	1	2010	DATE
ejpam-1767	7	2	16d50	CARDINAL
ejpam-1767	7	3	16l30	CARDINAL
ejpam-1767	7	4	kasch modules	ORG
ejpam-1767	7	5	1	CARDINAL
ejpam-1767	8	1	⊆	CARDINAL
ejpam-1767	8	2	⊆	CARDINAL
ejpam-1767	8	3	⊆	CARDINAL
ejpam-1767	9	1	∈	ORG
ejpam-1767	9	2	∈	ORG
ejpam-1767	9	3	∈	ORG
ejpam-1767	9	4	∈	ORG
ejpam-1767	10	1	5	CARDINAL
ejpam-1767	10	2	w	PERSON
ejpam-1767	11	1	first	ORDINAL
ejpam-1767	14	1	2	CARDINAL
ejpam-1767	14	2	3	DATE
ejpam-1767	17	1	k ⊆⊕	ORG
ejpam-1767	17	2	0	CARDINAL
ejpam-1767	17	3	n ⊕ k ⊆⊕	FAC
ejpam-1767	19	1	c3	PERSON
ejpam-1767	22	1	119	CARDINAL
ejpam-1767	22	2	2013	DATE
ejpam-1767	23	1	z. zhanmin / eur	PERSON
ejpam-1767	24	1	j. pure	PERSON
ejpam-1767	24	2	6	CARDINAL
ejpam-1767	24	3	2013	DATE
ejpam-1767	24	4	119	CARDINAL
ejpam-1767	25	1	1	CARDINAL
ejpam-1767	26	1	goldie dimensions	PERSON
ejpam-1767	27	1	2	CARDINAL
ejpam-1767	28	1	1	CARDINAL
ejpam-1767	28	2	10	CARDINAL
ejpam-1767	28	3	1.2	CARDINAL
ejpam-1767	29	1	1	CARDINAL
ejpam-1767	29	2	fq-injective	PERSON
ejpam-1767	29	3	2	CARDINAL
ejpam-1767	31	1	0	CARDINAL
ejpam-1767	31	2	r. lemma	PERSON
ejpam-1767	31	3	2	CARDINAL
ejpam-1767	31	4	10	CARDINAL
ejpam-1767	31	5	2.1	CARDINAL
ejpam-1767	31	6	2.2	CARDINAL
ejpam-1767	33	1	1) ls(kerα	TIME
ejpam-1767	34	1	2	CARDINAL
ejpam-1767	35	1	3	CARDINAL
ejpam-1767	35	2	10	CARDINAL
ejpam-1767	35	3	2.3	CARDINAL
ejpam-1767	38	1	4	CARDINAL
ejpam-1767	43	1	∈ s.	PERSON
ejpam-1767	44	1	2(1	CARDINAL
ejpam-1767	44	2	sse	ORG
ejpam-1767	45	1	set)2	ORG
ejpam-1767	47	1	5	CARDINAL
ejpam-1767	49	1	s/w	ORG
ejpam-1767	51	1	s2− s ∈w	PERSON
ejpam-1767	51	2	ker(s2−	GPE
ejpam-1767	52	1	1− s)x ∈	TIME
ejpam-1767	52	2	sx ∈ ker(1− s	PERSON
ejpam-1767	53	1	1−	ORDINAL
ejpam-1767	55	1	⊆	CARDINAL
ejpam-1767	56	1	ker(1− s	PERSON
ejpam-1767	57	1	0	CARDINAL
ejpam-1767	61	1	1−e)m	ORG
ejpam-1767	62	1	1−	ORDINAL
ejpam-1767	63	1	1−	CARDINAL
ejpam-1767	63	2	0	CARDINAL
ejpam-1767	63	3	⊆	CARDINAL
ejpam-1767	63	4	− s	ORG
ejpam-1767	64	1	modulo w	ORG
ejpam-1767	65	1	z. zhanmin / eur	PERSON
ejpam-1767	66	1	j. pure	PERSON
ejpam-1767	66	2	6	CARDINAL
ejpam-1767	66	3	2013	DATE
ejpam-1767	66	4	119	CARDINAL
ejpam-1767	66	5	1	CARDINAL
ejpam-1767	70	1	lemma 4	ORG
ejpam-1767	72	1	5	CARDINAL
ejpam-1767	72	2	2(2	CARDINAL
ejpam-1767	73	1	11	CARDINAL
ejpam-1767	74	1	11	CARDINAL
ejpam-1767	74	2	0 6=	CARDINAL
ejpam-1767	74	3	∈	ORG
ejpam-1767	74	4	anr	ORG
ejpam-1767	74	5	6	CARDINAL
ejpam-1767	74	6	∈	ORG
ejpam-1767	75	1	xa	ORG
ejpam-1767	75	2	0 6=	CARDINAL
ejpam-1767	75	3	∈	ORG
ejpam-1767	75	4	6=	DATE
ejpam-1767	76	1	⊕ xan	PERSON
ejpam-1767	78	1	11	CARDINAL
ejpam-1767	78	2	2.7	CARDINAL
ejpam-1767	79	1	11	CARDINAL
ejpam-1767	79	2	3.4	CARDINAL
ejpam-1767	80	1	9	CARDINAL
ejpam-1767	80	2	3.4	CARDINAL
ejpam-1767	81	1	6	CARDINAL
ejpam-1767	81	2	2.3	CARDINAL
ejpam-1767	82	1	5	CARDINAL
ejpam-1767	83	1	2	CARDINAL
ejpam-1767	89	1	1 ≤	QUANTITY
ejpam-1767	89	2	ia	GPE
ejpam-1767	90	1	goldie dimension	PERSON
ejpam-1767	91	1	4	CARDINAL
ejpam-1767	91	2	goldie dimension	ORG
ejpam-1767	92	1	6	CARDINAL
ejpam-1767	92	2	4	CARDINAL
ejpam-1767	92	3	2.43	CARDINAL
ejpam-1767	93	1	goldie dimension	PERSON
ejpam-1767	93	2	goldie dimension	PERSON
ejpam-1767	94	1	1	CARDINAL
ejpam-1767	96	1	1	CARDINAL
ejpam-1767	97	1	2	CARDINAL
ejpam-1767	98	1	3	CARDINAL
ejpam-1767	100	1	1	CARDINAL
ejpam-1767	100	2	2	CARDINAL
ejpam-1767	103	1	∈	ORG
ejpam-1767	103	2	1,2	CARDINAL
ejpam-1767	103	3	3	CARDINAL
ejpam-1767	103	4	i=1 x ir	PERSON
ejpam-1767	104	1	fq-injective	PERSON
ejpam-1767	104	2	1	CARDINAL
ejpam-1767	104	3	n \m	PERSON
ejpam-1767	104	4	∑	PERSON
ejpam-1767	104	5	x ir	PERSON
ejpam-1767	104	6	= ls(xm	PERSON
ejpam-1767	105	1	= ls(xm	PERSON
ejpam-1767	107	1	z. zhanmin / eur	PERSON
ejpam-1767	108	1	j. pure	PERSON
ejpam-1767	108	2	6	CARDINAL
ejpam-1767	108	3	2013	DATE
ejpam-1767	108	4	119	CARDINAL
ejpam-1767	108	5	125 122	CARDINAL
ejpam-1767	108	6	1	CARDINAL
ejpam-1767	108	7	2,3	CARDINAL
ejpam-1767	109	1	6	CARDINAL
ejpam-1767	110	1	2)⇒	CARDINAL
ejpam-1767	110	2	1	CARDINAL
ejpam-1767	111	1	3	CARDINAL
ejpam-1767	112	1	lemma 4	ORG
ejpam-1767	112	2	w	GPE
ejpam-1767	112	3	2(2	CARDINAL
ejpam-1767	112	4	1)⇔ (	CARDINAL
ejpam-1767	112	5	3	CARDINAL
ejpam-1767	112	6	5	CARDINAL
ejpam-1767	113	1	1	CARDINAL
ejpam-1767	113	2	2	CARDINAL
ejpam-1767	113	3	3	CARDINAL
ejpam-1767	113	4	8	CARDINAL
ejpam-1767	113	5	4.5	CARDINAL
ejpam-1767	114	1	3	CARDINAL
ejpam-1767	116	1	1	CARDINAL
ejpam-1767	117	1	2	CARDINAL
ejpam-1767	118	1	3	CARDINAL
ejpam-1767	119	1	2	CARDINAL
ejpam-1767	120	1	1	CARDINAL
ejpam-1767	121	1	submodule kr	ORG
ejpam-1767	121	2	2	CARDINAL
ejpam-1767	124	1	3	CARDINAL
ejpam-1767	124	2	j(r))ãs m. moreover	PERSON
ejpam-1767	124	3	4	CARDINAL
ejpam-1767	124	4	m.	PERSON
ejpam-1767	124	5	5	CARDINAL
ejpam-1767	124	6	ls(rad(m))ãs s. proof	PERSON
ejpam-1767	125	1	1	CARDINAL
ejpam-1767	126	1	k ⊆	PERSON
ejpam-1767	127	1	∈	ORG
ejpam-1767	128	1	− k	PERSON
ejpam-1767	129	1	k ⊆ t ⊆max	ORG
ejpam-1767	129	2	+ k	PERSON
ejpam-1767	130	1	the kasch hypothesis	ORG
ejpam-1767	130	2	mr+ k)/t	ORG
ejpam-1767	130	3	mr+ k → m	FAC
ejpam-1767	131	1	fq-injective	PERSON
ejpam-1767	133	1	0	CARDINAL
ejpam-1767	134	1	∈	ORG
ejpam-1767	135	1	t ) 6=	DATE
ejpam-1767	139	1	2	CARDINAL
ejpam-1767	141	1	0 6=	CARDINAL
ejpam-1767	141	2	mr→ smr	PERSON
ejpam-1767	142	1	γ	GPE
ejpam-1767	143	1	m= γ−1(sm	PERSON
ejpam-1767	143	2	α(sm	CARDINAL
ejpam-1767	143	3	∈	ORG
ejpam-1767	145	1	1	CARDINAL
ejpam-1767	145	2	∈	ORG
ejpam-1767	145	3	∈	ORG
ejpam-1767	145	4	r.	NORP
ejpam-1767	146	1	r.	NORP
ejpam-1767	146	2	mab ∈	PERSON
ejpam-1767	148	1	3	CARDINAL
ejpam-1767	150	1	∈	ORG
ejpam-1767	151	1	the kasch hypothesis	ORG
ejpam-1767	153	1	fq-injective	PERSON
ejpam-1767	153	2	t ) 6=	DATE
ejpam-1767	153	3	0	CARDINAL
ejpam-1767	154	1	z. zhanmin / eur	PERSON
ejpam-1767	155	1	j. pure	PERSON
ejpam-1767	155	2	6	CARDINAL
ejpam-1767	155	3	2013	DATE
ejpam-1767	155	4	119	CARDINAL
ejpam-1767	156	1	m)j(r	ORG
ejpam-1767	156	2	t )j(r	DATE
ejpam-1767	158	1	0	CARDINAL
ejpam-1767	160	1	4	CARDINAL
ejpam-1767	161	1	kasch	PERSON
ejpam-1767	162	1	7→ ϕ(x +	DATE
ejpam-1767	163	1	0 6=	CARDINAL
ejpam-1767	163	2	∈	ORG
ejpam-1767	163	3	0	CARDINAL
ejpam-1767	164	1	0	CARDINAL
ejpam-1767	165	1	0 6=	CARDINAL
ejpam-1767	165	2	6=	CARDINAL
ejpam-1767	168	1	2(1	CARDINAL
ejpam-1767	169	1	s.	ORG
ejpam-1767	169	2	5	CARDINAL
ejpam-1767	170	1	0 6=	CARDINAL
ejpam-1767	170	2	∈	ORG
ejpam-1767	174	1	∈	ORG
ejpam-1767	176	1	0	CARDINAL
ejpam-1767	177	1	a(rad(m	PERSON
ejpam-1767	180	1	a(rad(m	PERSON
ejpam-1767	182	1	a(rad(m	PERSON
ejpam-1767	183	1	⊆	CARDINAL
ejpam-1767	184	1	0	CARDINAL
ejpam-1767	185	1	ls(rad(m))ãs s. lemma 7	PERSON
ejpam-1767	189	1	kasch	PERSON
ejpam-1767	190	1	7→ ϕ(x +	DATE
ejpam-1767	191	1	0 6=	CARDINAL
ejpam-1767	191	2	∈	ORG
ejpam-1767	191	3	0	CARDINAL
ejpam-1767	191	4	0	CARDINAL
ejpam-1767	193	1	k = ls(x	ORG
ejpam-1767	193	2	⊆	CARDINAL
ejpam-1767	194	1	6=	CARDINAL
ejpam-1767	194	2	⊆	CARDINAL
ejpam-1767	194	3	⊆	CARDINAL
ejpam-1767	194	4	6=	CARDINAL
ejpam-1767	197	1	ω	CARDINAL
ejpam-1767	197	2	i=1 ii	PERSON
ejpam-1767	197	3	ω	CARDINAL
ejpam-1767	198	1	1	CARDINAL
ejpam-1767	198	2	⊆	CARDINAL
ejpam-1767	198	3	rm ls(ti	PERSON
ejpam-1767	199	1	rm ls(ti	GPE
ejpam-1767	201	1	ω	DATE
ejpam-1767	202	1	0 6=	CARDINAL
ejpam-1767	202	2	∈	ORG
ejpam-1767	203	1	rm ls(ti	PERSON
ejpam-1767	205	1	2	CARDINAL
ejpam-1767	207	1	⊆	CARDINAL
ejpam-1767	208	1	0	CARDINAL
ejpam-1767	211	1	ii)⊆	GPE
ejpam-1767	212	1	1	CARDINAL
ejpam-1767	213	1	m+ radm 7→	MONEY
ejpam-1767	214	1	2	CARDINAL
ejpam-1767	215	1	3	CARDINAL
ejpam-1767	217	1	124	CARDINAL
ejpam-1767	217	2	1	CARDINAL
ejpam-1767	218	1	2	CARDINAL
ejpam-1767	219	1	3	CARDINAL
ejpam-1767	223	1	1	CARDINAL
ejpam-1767	223	2	2	CARDINAL
ejpam-1767	228	1	2(4	CARDINAL
ejpam-1767	228	2	s mr)∼= shomr(⊕n i=1m/ti	ORG
ejpam-1767	229	1	2(5	CARDINAL
ejpam-1767	229	2	g(ss	ORG
ejpam-1767	230	1	2)⇒	CARDINAL
ejpam-1767	230	2	3	CARDINAL
ejpam-1767	232	1	1	CARDINAL
ejpam-1767	233	1	lemma 7.	ORG
ejpam-1767	234	1	kasch ring	ORG
ejpam-1767	235	1	1	CARDINAL
ejpam-1767	236	1	2	CARDINAL
ejpam-1767	237	1	3	CARDINAL
ejpam-1767	238	1	= lr(j(r	PERSON
ejpam-1767	240	1	1	CARDINAL
ejpam-1767	240	2	r. wisbauer	PERSON
ejpam-1767	241	1	kasch modules	ORG
ejpam-1767	242	1	s. k. jain	PERSON
ejpam-1767	242	2	s. t. rizvi	PERSON
ejpam-1767	242	3	1–16, 1997	DATE
ejpam-1767	243	1	2	CARDINAL
ejpam-1767	243	2	j. l. chen	PERSON
ejpam-1767	243	3	n. q. ding	PERSON
ejpam-1767	243	4	y. l. li	PERSON
ejpam-1767	243	5	q. zhou	PERSON
ejpam-1767	245	1	29:5589–5603, 2001	DATE
ejpam-1767	246	1	3	CARDINAL
ejpam-1767	246	2	j. l. chen	PERSON
ejpam-1767	246	3	n. q. ding	PERSON
ejpam-1767	246	4	m. f. yousif	PERSON
ejpam-1767	248	1	32:521–533	CARDINAL
ejpam-1767	248	2	2004	DATE
ejpam-1767	249	1	4	CARDINAL
ejpam-1767	249	2	a. facchini	PERSON
ejpam-1767	250	1	birkhäuser verlag	PERSON
ejpam-1767	250	2	basel	GPE
ejpam-1767	250	3	1998	DATE
ejpam-1767	251	1	5	CARDINAL
ejpam-1767	251	2	w. k. nicholson	PERSON
ejpam-1767	251	3	j. k. park	PERSON
ejpam-1767	251	4	m. f. yousif	PERSON
ejpam-1767	253	1	27:1683–1693	CARDINAL
ejpam-1767	253	2	1999	DATE
ejpam-1767	254	1	6	CARDINAL
ejpam-1767	254	2	y. q. zhou	PERSON
ejpam-1767	256	1	206:706–721, 1998	DATE
ejpam-1767	257	1	125	CARDINAL
ejpam-1767	257	2	7	CARDINAL
ejpam-1767	257	3	v. s. ramamurthi	PERSON
ejpam-1767	257	4	k. m. rangaswamy	PERSON
ejpam-1767	259	1	australian	NORP
ejpam-1767	259	2	16:239–248, 1973	DATE
ejpam-1767	260	1	8	CARDINAL
ejpam-1767	260	2	j. l. chen	PERSON
ejpam-1767	262	1	35:3018–3025	CARDINAL
ejpam-1767	262	2	2007	DATE
ejpam-1767	263	1	9	CARDINAL
ejpam-1767	263	2	g. s. xiao	PERSON
ejpam-1767	263	3	x. b. yin	PERSON
ejpam-1767	263	4	w. t. tong	PERSON
ejpam-1767	265	1	mathematical research & exposition	ORG
ejpam-1767	265	2	35:211–216	CARDINAL
ejpam-1767	265	3	2003	DATE
ejpam-1767	266	1	10	CARDINAL
ejpam-1767	267	1	z. m. zhu	PERSON
ejpam-1767	269	1	journal of shandong university	ORG
ejpam-1767	269	2	nat	ORG
ejpam-1767	270	1	sci.	ORG
ejpam-1767	270	2	2010	DATE
ejpam-1767	271	1	11	CARDINAL
ejpam-1767	271	2	z. m. zhu	PERSON
ejpam-1767	273	1	indian	NORP
ejpam-1767	273	2	pure & applied	ORG
ejpam-1767	273	3	41:627–645	CARDINAL
ejpam-1767	273	4	2010	DATE