id	sid	eid	entity	type
ejpam-1097	1	1	2_talebi.dvi european journal	ORG
ejpam-1097	2	1	5	CARDINAL
ejpam-1097	2	2	2, 2012	DATE
ejpam-1097	2	3	108	CARDINAL
ejpam-1097	2	4	amouzegar1	PERSON
ejpam-1097	2	5	yahya talebi	PERSON
ejpam-1097	2	6	2,∗ 1	CARDINAL
ejpam-1097	2	7	quchan institute of engineering	ORG
ejpam-1097	2	8	iran	GPE
ejpam-1097	2	9	2	CARDINAL
ejpam-1097	2	10	iran	GPE
ejpam-1097	6	1	2010	DATE
ejpam-1097	6	2	16d90	CARDINAL
ejpam-1097	6	3	16d99	CARDINAL
ejpam-1097	6	4	1	CARDINAL
ejpam-1097	7	1	6=	CARDINAL
ejpam-1097	10	1	k	PERSON
ejpam-1097	10	2	= k	PERSON
ejpam-1097	12	1	= k	PERSON
ejpam-1097	13	1	k ∩ n	ORG
ejpam-1097	15	1	9	CARDINAL
ejpam-1097	16	1	6	CARDINAL
ejpam-1097	17	1	4	CARDINAL
ejpam-1097	19	1	5	CARDINAL
ejpam-1097	20	1	∃y ≤ x	QUANTITY
ejpam-1097	24	1	om	PERSON
ejpam-1097	25	1	108	CARDINAL
ejpam-1097	25	2	2012	DATE
ejpam-1097	26	1	t. amouzegar	GPE
ejpam-1097	27	1	j. pure	PERSON
ejpam-1097	27	2	5	CARDINAL
ejpam-1097	27	3	2012	DATE
ejpam-1097	27	4	108	CARDINAL
ejpam-1097	29	1	7	CARDINAL
ejpam-1097	29	2	a+ p. equivalently	PERSON
ejpam-1097	29	3	a+ p	PERSON
ejpam-1097	29	4	n ∈ b(m	ORG
ejpam-1097	30	1	n ∈ b(m	ORG
ejpam-1097	32	1	section 2	LAW
ejpam-1097	33	1	section 3	LAW
ejpam-1097	37	1	section 4	LAW
ejpam-1097	37	2	two	CARDINAL
ejpam-1097	37	3	goldie dimension	PERSON
ejpam-1097	37	4	one	CARDINAL
ejpam-1097	37	5	n ∈ b(m	ORG
ejpam-1097	38	1	2	CARDINAL
ejpam-1097	44	1	k∩a	ORG
ejpam-1097	44	2	0	CARDINAL
ejpam-1097	44	3	two	CARDINAL
ejpam-1097	45	1	= k⊕	PERSON
ejpam-1097	47	1	∈ endr(m),φ(n	PRODUCT
ejpam-1097	47	2	⊆	CARDINAL
ejpam-1097	48	1	1	CARDINAL
ejpam-1097	50	1	1	CARDINAL
ejpam-1097	50	2	∈b(m	PERSON
ejpam-1097	51	1	2	CARDINAL
ejpam-1097	51	2	ker h≤ a.	PERSON
ejpam-1097	51	3	h(a	ORG
ejpam-1097	52	1	∈b(n	GPE
ejpam-1097	54	1	3	CARDINAL
ejpam-1097	54	2	a≤ m. then a∈ b(m	WORK_OF_ART
ejpam-1097	54	3	∈b(m	PERSON
ejpam-1097	55	1	4	CARDINAL
ejpam-1097	57	1	∈b(n	GPE
ejpam-1097	58	1	t. amouzegar	GPE
ejpam-1097	59	1	j. pure	PERSON
ejpam-1097	59	2	5	CARDINAL
ejpam-1097	59	3	2012	DATE
ejpam-1097	59	4	108	CARDINAL
ejpam-1097	60	1	5	CARDINAL
ejpam-1097	60	2	2.2	CARDINAL
ejpam-1097	61	1	2	CARDINAL
ejpam-1097	63	1	1	CARDINAL
ejpam-1097	63	2	a+ b.	PERSON
ejpam-1097	64	1	∈ b(m	ORG
ejpam-1097	65	1	2	CARDINAL
ejpam-1097	65	2	⊕	PERSON
ejpam-1097	67	1	ni ∈b(m	PERSON
ejpam-1097	68	1	3	CARDINAL
ejpam-1097	69	1	∈ b(m	ORG
ejpam-1097	69	2	1,2	CARDINAL
ejpam-1097	71	1	1	CARDINAL
ejpam-1097	79	1	∈b(m	DATE
ejpam-1097	80	1	2	CARDINAL
ejpam-1097	80	2	mi/ni	PERSON
ejpam-1097	82	1	⊕i∈i	ORG
ejpam-1097	83	1	3	CARDINAL
ejpam-1097	83	2	1	CARDINAL
ejpam-1097	83	3	5	CARDINAL
ejpam-1097	83	4	3.5	CARDINAL
ejpam-1097	84	1	3.	CARDINAL
ejpam-1097	85	1	n ∈ b(m	ORG
ejpam-1097	88	1	1	CARDINAL
ejpam-1097	89	1	m.	PERSON
ejpam-1097	89	2	1	CARDINAL
ejpam-1097	90	1	2	CARDINAL
ejpam-1097	90	2	submodule h of m with	ORG
ejpam-1097	90	3	h ∈ b(m	ORG
ejpam-1097	90	4	m. (3) for any submodule	ORG
ejpam-1097	90	5	∈b(m	DATE
ejpam-1097	90	6	k ∈b(m	PERSON
ejpam-1097	90	7	4	CARDINAL
ejpam-1097	90	8	h ∈ b(m	ORG
ejpam-1097	90	9	k ∈b(m	PERSON
ejpam-1097	93	1	m. proof	PERSON
ejpam-1097	94	1	1)⇔ (	CARDINAL
ejpam-1097	94	2	3	CARDINAL
ejpam-1097	94	3	2)⇔	CARDINAL
ejpam-1097	94	4	4	CARDINAL
ejpam-1097	94	5	1)⇒	CARDINAL
ejpam-1097	94	6	2	CARDINAL
ejpam-1097	94	7	4	CARDINAL
ejpam-1097	95	1	4	CARDINAL
ejpam-1097	95	2	1	CARDINAL
ejpam-1097	96	1	1	CARDINAL
ejpam-1097	97	1	k ∈ b(m	ORG
ejpam-1097	99	1	a+ k	PERSON
ejpam-1097	101	1	6=	DATE
ejpam-1097	102	1	6=	CARDINAL
ejpam-1097	103	1	k ′	ORG
ejpam-1097	105	1	t. amouzegar	GPE
ejpam-1097	106	1	j. pure	PERSON
ejpam-1097	106	2	5	CARDINAL
ejpam-1097	106	3	2012	DATE
ejpam-1097	106	4	108	CARDINAL
ejpam-1097	106	5	111	CARDINAL
ejpam-1097	106	6	1	CARDINAL
ejpam-1097	110	1	n ∈ b(m	ORG
ejpam-1097	112	1	= m2 ⊕	PERSON
ejpam-1097	113	1	n +m2 ∈b(m	QUANTITY
ejpam-1097	113	2	2	CARDINAL
ejpam-1097	113	3	7	CARDINAL
ejpam-1097	113	4	3.1	CARDINAL
ejpam-1097	115	1	lemma 2	ORG
ejpam-1097	115	2	7	CARDINAL
ejpam-1097	115	3	3.1	CARDINAL
ejpam-1097	115	4	∈	ORG
ejpam-1097	117	1	k ∈ b(m	ORG
ejpam-1097	117	2	2	CARDINAL
ejpam-1097	118	1	m1 ≤ n + m2 + k1 and m2 ≤ n + k1 + k2	PRODUCT
ejpam-1097	120	1	n ∩	ORG
ejpam-1097	120	2	n ∩	ORG
ejpam-1097	122	1	1	CARDINAL
ejpam-1097	124	1	3	CARDINAL
ejpam-1097	126	1	k ∩	PERSON
ejpam-1097	126	2	′)≪ k	PERSON
ejpam-1097	126	3	k + n ′)≪ n ∩	FAC
ejpam-1097	128	1	n ⊕ n ′ → n	FAC
ejpam-1097	129	1	k ∩	ORG
ejpam-1097	130	1	= k ∩	PERSON
ejpam-1097	130	2	π(k)∩a≪	ORG
ejpam-1097	132	1	a∩(k+n	DATE
ejpam-1097	133	1	5	CARDINAL
ejpam-1097	133	2	φ	PERSON
ejpam-1097	134	1	two	CARDINAL
ejpam-1097	135	1	2	CARDINAL
ejpam-1097	138	1	1	CARDINAL
ejpam-1097	140	1	∈	PRODUCT
ejpam-1097	141	1	lemma 1	ORG
ejpam-1097	144	1	lemma 2, m2 +	ORG
ejpam-1097	144	2	∈b(m	DATE
ejpam-1097	145	1	5	CARDINAL
ejpam-1097	145	2	2.5	CARDINAL
ejpam-1097	145	3	t ≤ m2	FAC
ejpam-1097	147	1	m1 ∩	PRODUCT
ejpam-1097	147	2	t .	GPE
ejpam-1097	148	1	3	CARDINAL
ejpam-1097	148	2	m1 ∩	PRODUCT
ejpam-1097	152	1	7	CARDINAL
ejpam-1097	152	2	3.1	CARDINAL
ejpam-1097	152	3	1	CARDINAL
ejpam-1097	153	1	2	CARDINAL
ejpam-1097	155	1	t. amouzegar	GPE
ejpam-1097	156	1	j. pure	PERSON
ejpam-1097	156	2	5	CARDINAL
ejpam-1097	156	3	2012	DATE
ejpam-1097	156	4	108	CARDINAL
ejpam-1097	158	1	lemma 1	ORG
ejpam-1097	158	2	∈ b(m	ORG
ejpam-1097	159	1	∩	PERSON
ejpam-1097	166	1	2	CARDINAL
ejpam-1097	167	1	invariant submodule	ORG
ejpam-1097	169	1	2	CARDINAL
ejpam-1097	170	1	3	CARDINAL
ejpam-1097	173	1	2	CARDINAL
ejpam-1097	173	2	1	CARDINAL
ejpam-1097	174	1	= k ⊕	PERSON
ejpam-1097	174	2	⊕i∈i	ORG
ejpam-1097	176	1	3	CARDINAL
ejpam-1097	183	1	lemma 1	ORG
ejpam-1097	184	1	k ∈ b(m	ORG
ejpam-1097	185	1	= k	PERSON
ejpam-1097	186	1	′)∩k	ORG
ejpam-1097	187	1	⊆	MONEY
ejpam-1097	187	2	n ′1 ⊆ n	ORG
ejpam-1097	187	3	k ⊕ n ′1	ORG
ejpam-1097	188	1	lemma 2	ORG
ejpam-1097	188	2	7	CARDINAL
ejpam-1097	188	3	3.1	CARDINAL
ejpam-1097	188	4	n ∩	ORG
ejpam-1097	188	5	k ⊕ n ′1	ORG
ejpam-1097	189	1	k ⊕ n ′1	ORG
ejpam-1097	190	1	′)∩k	ORG
ejpam-1097	190	2	3	CARDINAL
ejpam-1097	190	3	′)≪ n	PERSON
ejpam-1097	192	1	n ∩	ORG
ejpam-1097	192	2	k ⊕ n ′1)≤ ⊕ m	ORG
ejpam-1097	192	3	k ⊕ n ′1)≪ n ∩	ORG
ejpam-1097	192	4	k ⊕ n ′1	ORG
ejpam-1097	195	1	4	CARDINAL
ejpam-1097	198	1	t. amouzegar	PERSON
ejpam-1097	199	1	j. pure	PERSON
ejpam-1097	199	2	5	CARDINAL
ejpam-1097	199	3	2012	DATE
ejpam-1097	199	4	108	CARDINAL
ejpam-1097	201	1	∈b(m	DATE
ejpam-1097	203	1	5	CARDINAL
ejpam-1097	204	1	3	CARDINAL
ejpam-1097	208	1	n ∈ b(m	ORG
ejpam-1097	212	1	1(4	CARDINAL
ejpam-1097	213	1	∈b(m	DATE
ejpam-1097	214	1	n + n ′	PRODUCT
ejpam-1097	214	2	2	CARDINAL
ejpam-1097	215	1	∈b(m	PERSON
ejpam-1097	215	2	a∩b≪ b.	PERSON
ejpam-1097	216	1	lemma 2	ORG
ejpam-1097	219	1	7	CARDINAL
ejpam-1097	219	2	3.1	CARDINAL
ejpam-1097	221	1	n ∈ b(m	ORG
ejpam-1097	221	2	k ∈ b(n	PERSON
ejpam-1097	221	3	k ′ of n with k ′	FAC
ejpam-1097	221	4	k ⊕ k	PERSON
ejpam-1097	222	1	4	CARDINAL
ejpam-1097	223	1	n ∩ rad(m	PRODUCT
ejpam-1097	226	1	k/rad(m	FAC
ejpam-1097	226	2	k/rad(m	FAC
ejpam-1097	227	1	k/rad(m	FAC
ejpam-1097	228	1	lemma 1	ORG
ejpam-1097	228	2	k ∈ b(m	ORG
ejpam-1097	230	1	= k	PERSON
ejpam-1097	231	1	k ∩	ORG
ejpam-1097	232	1	k/rad(m	PRODUCT
ejpam-1097	232	2	k/rad(m	FAC
ejpam-1097	235	1	4	CARDINAL
ejpam-1097	237	1	n ∩ rad(m	PRODUCT
ejpam-1097	238	1	n ∈ b(m	ORG
ejpam-1097	239	1	m1 ⊕ m2	PERSON
ejpam-1097	243	1	m1 ∩ m2	PRODUCT
ejpam-1097	243	2	t. amouzegar	GPE
ejpam-1097	244	1	j. pure	PERSON
ejpam-1097	244	2	5	CARDINAL
ejpam-1097	244	3	2012	DATE
ejpam-1097	244	4	108	CARDINAL
ejpam-1097	245	1	lemma 4	ORG
ejpam-1097	246	1	nonzero submodules.	ORG
ejpam-1097	247	1	4	CARDINAL
ejpam-1097	248	1	goldie dimension	PERSON
ejpam-1097	250	1	goldie dimension	PERSON
ejpam-1097	250	2	m2	PERSON
ejpam-1097	251	1	n ∩ rad(mi	ORG
ejpam-1097	253	1	⊕	PERSON
ejpam-1097	253	2	mi	PERSON
ejpam-1097	253	3	mi	PERSON
ejpam-1097	261	1	goldie dimension	PERSON
ejpam-1097	261	2	3	CARDINAL
ejpam-1097	261	3	3.20	CARDINAL
ejpam-1097	262	1	j ∈ j	PERSON
ejpam-1097	265	1	first	ORDINAL
ejpam-1097	265	2	rad(h	ORG
ejpam-1097	265	3	6=	DATE
ejpam-1097	266	1	1	CARDINAL
ejpam-1097	266	2	17.14	CARDINAL
ejpam-1097	267	1	goldie dimension 1	ORG
ejpam-1097	268	1	k ∈ b(h	ORG
ejpam-1097	268	2	xr+ k	PERSON
ejpam-1097	269	1	k ⊕ k1	PERSON
ejpam-1097	270	1	0	CARDINAL
ejpam-1097	271	1	0	CARDINAL
ejpam-1097	275	1	1	CARDINAL
ejpam-1097	275	2	goldie dimension k	PERSON
ejpam-1097	277	1	j ∈ j	PERSON
ejpam-1097	278	1	goldie dimension n.	PERSON
ejpam-1097	279	1	6=	CARDINAL
ejpam-1097	280	1	submodules k	PERSON
ejpam-1097	280	2	k ∈ b(h	ORG
ejpam-1097	285	1	6=	CARDINAL
ejpam-1097	285	2	0	CARDINAL
ejpam-1097	286	1	0	CARDINAL
ejpam-1097	288	1	3	CARDINAL
ejpam-1097	293	1	5	CARDINAL
ejpam-1097	299	1	n ∈ b(m	ORG
ejpam-1097	301	1	n = n ∩	PERSON
ejpam-1097	303	1	n ∈ b(m	ORG
ejpam-1097	304	1	∈ b(m	ORG
ejpam-1097	305	1	115	CARDINAL
ejpam-1097	305	2	5	CARDINAL
ejpam-1097	306	1	⊕	PERSON
ejpam-1097	310	1	5	CARDINAL
ejpam-1097	311	1	k ∈ b(m	ORG
ejpam-1097	313	1	6=	CARDINAL
ejpam-1097	314	1	1	CARDINAL
ejpam-1097	314	2	12.7	CARDINAL
ejpam-1097	315	1	k	PERSON
ejpam-1097	316	1	5	CARDINAL
ejpam-1097	317	1	goldie dimension	PERSON
ejpam-1097	318	1	n ∈ b(m	ORG
ejpam-1097	321	1	1	CARDINAL
ejpam-1097	321	2	n ∈ b(m	ORG
ejpam-1097	322	1	goldie dimension	PERSON
ejpam-1097	322	2	⊕	GPE
ejpam-1097	324	1	⊕	PERSON
ejpam-1097	325	1	li	PERSON
ejpam-1097	325	2	1≤ i ≤	QUANTITY
ejpam-1097	326	1	li	PERSON
ejpam-1097	327	1	5	CARDINAL
ejpam-1097	328	1	1	CARDINAL
ejpam-1097	330	1	new york	GPE
ejpam-1097	330	2	1992	DATE
ejpam-1097	331	1	2	CARDINAL
ejpam-1097	333	1	bull	ORG
ejpam-1097	334	1	korean	NORP
ejpam-1097	335	1	45(1):5966, 2008	DATE
ejpam-1097	336	1	3	CARDINAL
ejpam-1097	337	1	marcel dekker	PERSON
ejpam-1097	337	2	inc.	ORG
ejpam-1097	337	3	new york	GPE
ejpam-1097	337	4	basel	GPE
ejpam-1097	337	5	1976	DATE
ejpam-1097	338	1	4	CARDINAL
ejpam-1097	341	1	hungar	PERSON
ejpam-1097	341	2	169, 1999	DATE
ejpam-1097	342	1	5	CARDINAL
ejpam-1097	344	1	colloq	PERSON
ejpam-1097	344	2	11(3):361-370	CARDINAL
ejpam-1097	345	1	6	CARDINAL
ejpam-1097	347	1	london	GPE
ejpam-1097	349	1	147	CARDINAL
ejpam-1097	349	2	cambridge	GPE
ejpam-1097	349	3	university press	ORG
ejpam-1097	349	4	1990	DATE
ejpam-1097	351	1	ofb(m	ORG
ejpam-1097	351	2	j. mathematics	PERSON
ejpam-1097	351	3	6:647-660, 2005	DATE
ejpam-1097	352	1	8	CARDINAL
ejpam-1097	354	1	sci.	ORG
ejpam-1097	354	2	302	CARDINAL
ejpam-1097	354	3	singapore	GPE
ejpam-1097	354	4	1993	DATE
ejpam-1097	355	1	9	CARDINAL
ejpam-1097	357	1	gordon	PERSON
ejpam-1097	357	2	1991	DATE