id	sid	eid	entity	type
ejpam-4215	1	1	european journal	ORG
ejpam-4215	2	1	15	CARDINAL
ejpam-4215	2	2	1	CARDINAL
ejpam-4215	2	3	2022	CARDINAL
ejpam-4215	2	4	224	CARDINAL
ejpam-4215	2	5	1307-5543	DATE
ejpam-4215	2	6	new york	GPE
ejpam-4215	2	7	submodule hiba	ORG
ejpam-4215	2	8	r. baanoon1,∗	PERSON
ejpam-4215	2	9	2	CARDINAL
ejpam-4215	2	10	university of baghdad	ORG
ejpam-4215	2	11	baghdad	GPE
ejpam-4215	2	12	iraq	GPE
ejpam-4215	5	1	noetherian	NORP
ejpam-4215	6	1	e∗-closed	CARDINAL
ejpam-4215	6	2	2020	DATE
ejpam-4215	6	3	16d90, 16d99	DATE
ejpam-4215	6	4	16p40	CARDINAL
ejpam-4215	6	5	e∗-essential submodule	PERSON
ejpam-4215	6	6	submodule	ORG
ejpam-4215	6	7	noetherian	NORP
ejpam-4215	6	8	1	CARDINAL
ejpam-4215	7	1	e(m	DATE
ejpam-4215	8	1	5	CARDINAL
ejpam-4215	9	1	leonard defines	PERSON
ejpam-4215	9	2	1	CARDINAL
ejpam-4215	10	1	5	CARDINAL
ejpam-4215	10	2	3	CARDINAL
ejpam-4215	10	3	4	CARDINAL
ejpam-4215	11	1	2	CARDINAL
ejpam-4215	11	2	z∗(m	PERSON
ejpam-4215	12	1	∈	ORG
ejpam-4215	13	1	z∗(m	PERSON
ejpam-4215	16	1	6	CARDINAL
ejpam-4215	18	1	hibabaanoon@uomisan.edu.iq	TIME
ejpam-4215	18	2	baanoon	PERSON
ejpam-4215	18	3	w. khalid	PERSON
ejpam-4215	19	1	224	CARDINAL
ejpam-4215	19	2	2022	CARDINAL
ejpam-4215	20	1	baanoon	PERSON
ejpam-4215	20	2	w. khalid	PERSON
ejpam-4215	21	1	j. pure	PERSON
ejpam-4215	21	2	15	CARDINAL
ejpam-4215	21	3	1	CARDINAL
ejpam-4215	21	4	2022	CARDINAL
ejpam-4215	21	5	224	CARDINAL
ejpam-4215	21	6	2	CARDINAL
ejpam-4215	22	1	1	CARDINAL
ejpam-4215	22	2	cosingular submodule b	ORG
ejpam-4215	25	1	1.	CARDINAL
ejpam-4215	28	1	2	CARDINAL
ejpam-4215	31	1	1	CARDINAL
ejpam-4215	31	2	1	CARDINAL
ejpam-4215	33	1	z6	GPE
ejpam-4215	33	2	z6	ORG
ejpam-4215	33	3	z6	ORG
ejpam-4215	33	4	0	CARDINAL
ejpam-4215	34	1	k ∩	PERSON
ejpam-4215	34	2	0	CARDINAL
ejpam-4215	34	3	0	CARDINAL
ejpam-4215	35	1	0	CARDINAL
ejpam-4215	35	2	2	DATE
ejpam-4215	35	3	4	CARDINAL
ejpam-4215	35	4	z6	GPE
ejpam-4215	35	5	z6	ORG
ejpam-4215	35	6	0	CARDINAL
ejpam-4215	35	7	3	CARDINAL
ejpam-4215	35	8	0	CARDINAL
ejpam-4215	35	9	2	DATE
ejpam-4215	35	10	4	CARDINAL
ejpam-4215	35	11	0	CARDINAL
ejpam-4215	35	12	3	CARDINAL
ejpam-4215	35	13	0	CARDINAL
ejpam-4215	36	1	2	CARDINAL
ejpam-4215	37	1	3	CARDINAL
ejpam-4215	38	1	2	CARDINAL
ejpam-4215	41	1	4	CARDINAL
ejpam-4215	41	2	z6	GPE
ejpam-4215	41	3	2	CARDINAL
ejpam-4215	41	4	0	CARDINAL
ejpam-4215	41	5	2	DATE
ejpam-4215	41	6	4	CARDINAL
ejpam-4215	41	7	0	CARDINAL
ejpam-4215	41	8	2	DATE
ejpam-4215	41	9	4	CARDINAL
ejpam-4215	41	10	0	CARDINAL
ejpam-4215	41	11	3	CARDINAL
ejpam-4215	42	1	0	CARDINAL
ejpam-4215	43	1	0	CARDINAL
ejpam-4215	43	2	3	CARDINAL
ejpam-4215	43	3	cosingular submodule	ORG
ejpam-4215	44	1	5	CARDINAL
ejpam-4215	45	1	f(x	ORG
ejpam-4215	46	1	0	CARDINAL
ejpam-4215	46	2	1	CARDINAL
ejpam-4215	46	3	0	CARDINAL
ejpam-4215	47	1	2z	CARDINAL
ejpam-4215	47	2	0	CARDINAL
ejpam-4215	47	3	z2	ORG
ejpam-4215	48	1	6	CARDINAL
ejpam-4215	49	1	2zz	ORG
ejpam-4215	49	2	2z 2z	CARDINAL
ejpam-4215	49	3	0	CARDINAL
ejpam-4215	50	1	baanoon	PERSON
ejpam-4215	50	2	w. khalid	PERSON
ejpam-4215	51	1	j. pure	PERSON
ejpam-4215	51	2	15	CARDINAL
ejpam-4215	51	3	1	CARDINAL
ejpam-4215	51	4	2022	CARDINAL
ejpam-4215	51	5	224	CARDINAL
ejpam-4215	51	6	1	CARDINAL
ejpam-4215	52	1	a. proof	PERSON
ejpam-4215	53	1	2.2	CARDINAL
ejpam-4215	53	2	2	CARDINAL
ejpam-4215	53	3	k∩(b∩z∗(a	PERSON
ejpam-4215	54	1	k. hence	PERSON
ejpam-4215	54	2	k ≤ z∗(a	FAC
ejpam-4215	55	1	= k ∩ z∗(a	PERSON
ejpam-4215	56	1	a.	GPE
ejpam-4215	63	1	2.2	CARDINAL
ejpam-4215	63	2	2	CARDINAL
ejpam-4215	68	1	1	CARDINAL
ejpam-4215	72	1	lemma 1	ORG
ejpam-4215	73	1	a1 ≤ a2	PRODUCT
ejpam-4215	75	1	2	CARDINAL
ejpam-4215	79	1	cosingular submodule b	ORG
ejpam-4215	79	2	0	CARDINAL
ejpam-4215	80	1	ker(f	GPE
ejpam-4215	80	2	0	CARDINAL
ejpam-4215	81	1	f(b	GPE
ejpam-4215	82	1	f(b	GPE
ejpam-4215	82	2	0	CARDINAL
ejpam-4215	83	1	f(b	GPE
ejpam-4215	85	1	lemma 2.6	ORG
ejpam-4215	85	2	2	CARDINAL
ejpam-4215	85	3	f(b	GPE
ejpam-4215	86	1	f(b	GPE
ejpam-4215	86	2	0	CARDINAL
ejpam-4215	88	1	3	CARDINAL
ejpam-4215	89	1	′ ≤	CARDINAL
ejpam-4215	94	1	1 k	QUANTITY
ejpam-4215	97	1	k. hence	PERSON
ejpam-4215	99	1	∩	WORK_OF_ART
ejpam-4215	101	1	2	CARDINAL
ejpam-4215	104	1	i=1 ≤e∗	PERSON
ejpam-4215	105	1	4	CARDINAL
ejpam-4215	105	2	w. khalid	PERSON
ejpam-4215	106	1	j. pure	PERSON
ejpam-4215	106	2	15	CARDINAL
ejpam-4215	106	3	1	CARDINAL
ejpam-4215	106	4	2022	CARDINAL
ejpam-4215	106	5	224	CARDINAL
ejpam-4215	107	1	m1 ⊕ m2 → m2	PERSON
ejpam-4215	109	1	2	CARDINAL
ejpam-4215	109	2	⊕ m2 ≤e∗	PERSON
ejpam-4215	109	3	m1 ⊕ m2	PERSON
ejpam-4215	109	4	ρ−1	ORG
ejpam-4215	110	1	3 k1	QUANTITY
ejpam-4215	110	2	0,m2	CARDINAL
ejpam-4215	111	1	2	CARDINAL
ejpam-4215	111	2	1	CARDINAL
ejpam-4215	111	3	≤e∗	PERSON
ejpam-4215	111	4	2	CARDINAL
ejpam-4215	111	5	≤e∗ m2	PERSON
ejpam-4215	113	1	5	CARDINAL
ejpam-4215	121	1	n ∩ xr ̸= 0	PRODUCT
ejpam-4215	122	1	n ∩k ̸= 0	ORG
ejpam-4215	124	1	e∗-essentialr	CARDINAL
ejpam-4215	125	1	6	CARDINAL
ejpam-4215	131	1	0	CARDINAL
ejpam-4215	132	1	kerg = g−1(0	PERSON
ejpam-4215	134	1	∩ g−1(l	PERSON
ejpam-4215	134	2	∩ g−1(l	PERSON
ejpam-4215	136	1	c. hence g−1(l	GPE
ejpam-4215	137	1	0	CARDINAL
ejpam-4215	139	1	0	CARDINAL
ejpam-4215	141	1	noetherian	NORP
ejpam-4215	148	1	3	CARDINAL
ejpam-4215	150	1	228 3	DATE
ejpam-4215	151	1	2	CARDINAL
ejpam-4215	151	2	e∗-closed	DATE
ejpam-4215	151	3	2	CARDINAL
ejpam-4215	151	4	1	CARDINAL
ejpam-4215	154	1	2	CARDINAL
ejpam-4215	154	2	z6	GPE
ejpam-4215	154	3	z6	ORG
ejpam-4215	154	4	0	CARDINAL
ejpam-4215	154	5	2	DATE
ejpam-4215	154	6	4	CARDINAL
ejpam-4215	154	7	0	CARDINAL
ejpam-4215	154	8	2	DATE
ejpam-4215	154	9	4	CARDINAL
ejpam-4215	154	10	z6	GPE
ejpam-4215	159	1	k b ∩ l	PERSON
ejpam-4215	159	2	0	CARDINAL
ejpam-4215	160	1	k ∩ l	PERSON
ejpam-4215	160	2	k ≤e∗	PERSON
ejpam-4215	161	1	k ∩ l ≤e∗	ORG
ejpam-4215	163	1	0	CARDINAL
ejpam-4215	166	1	1	CARDINAL
ejpam-4215	166	2	f. auslander	PERSON
ejpam-4215	166	3	k. fuller	PERSON
ejpam-4215	167	1	1974	DATE
ejpam-4215	168	1	2	CARDINAL
ejpam-4215	168	2	a. ç. özcan	PERSON
ejpam-4215	170	1	2002	DATE
ejpam-4215	171	1	3	CARDINAL
ejpam-4215	171	2	k. goodearl	PERSON
ejpam-4215	171	3	33	CARDINAL
ejpam-4215	172	1	crc press	ORG
ejpam-4215	172	2	1976	DATE
ejpam-4215	173	1	4	CARDINAL
ejpam-4215	173	2	m. hazewinkel	PERSON
ejpam-4215	173	3	n. gubareni	PERSON
ejpam-4215	173	4	vladimir v. kirichenko	PERSON
ejpam-4215	174	1	algebras	PERSON
ejpam-4215	174	2	1	CARDINAL
ejpam-4215	174	3	springer science & business media	ORG
ejpam-4215	174	4	2004	DATE
ejpam-4215	175	1	5	CARDINAL
ejpam-4215	175	2	f. kasch	PERSON
ejpam-4215	175	3	17	CARDINAL
ejpam-4215	176	1	1982	DATE
ejpam-4215	177	1	6	CARDINAL
ejpam-4215	177	2	zhou	PERSON
ejpam-4215	179	1	southeast asian	NORP
ejpam-4215	179	2	2011	DATE