id	sid	eid	entity	type
ejpam-4301	1	1	european journal	ORG
ejpam-4301	2	1	15	CARDINAL
ejpam-4301	2	2	2	CARDINAL
ejpam-4301	2	3	2022	CARDINAL
ejpam-4301	2	4	478	CARDINAL
ejpam-4301	2	5	new york	GPE
ejpam-4301	2	6	hiba r. baanoon1,2,∗	PERSON
ejpam-4301	2	7	khalid2 1	ORG
ejpam-4301	2	8	iraq	GPE
ejpam-4301	2	9	2	CARDINAL
ejpam-4301	2	10	university of baghdad	ORG
ejpam-4301	2	11	iraq	GPE
ejpam-4301	5	1	2020	DATE
ejpam-4301	5	2	16d10,	DATE
ejpam-4301	5	3	16d90	DATE
ejpam-4301	5	4	16d99	DATE
ejpam-4301	5	5	16s90	CARDINAL
ejpam-4301	5	6	1	CARDINAL
ejpam-4301	9	1	6	CARDINAL
ejpam-4301	9	2	6	CARDINAL
ejpam-4301	9	3	4	CARDINAL
ejpam-4301	9	4	5	CARDINAL
ejpam-4301	10	1	2	CARDINAL
ejpam-4301	10	2	z∗(m	PERSON
ejpam-4301	11	1	∈	ORG
ejpam-4301	12	1	z∗(m	PERSON
ejpam-4301	15	1	baanoon	PERSON
ejpam-4301	15	2	1	CARDINAL
ejpam-4301	16	1	cosingular submodule b	ORG
ejpam-4301	18	1	1	CARDINAL
ejpam-4301	22	1	hibabaanoon@uomisan.edu.iq	TIME
ejpam-4301	22	2	baanoon	PERSON
ejpam-4301	22	3	w. khalid	PERSON
ejpam-4301	23	1	478	CARDINAL
ejpam-4301	24	1	2022	CARDINAL
ejpam-4301	25	1	baanoon	PERSON
ejpam-4301	25	2	w. khalid	PERSON
ejpam-4301	26	1	j. pure	PERSON
ejpam-4301	26	2	15	CARDINAL
ejpam-4301	26	3	2	CARDINAL
ejpam-4301	26	4	2022	CARDINAL
ejpam-4301	26	5	478-485 479 2	QUANTITY
ejpam-4301	28	1	cosingular submodule b	ORG
ejpam-4301	29	1	1	CARDINAL
ejpam-4301	31	1	1	CARDINAL
ejpam-4301	32	1	1	CARDINAL
ejpam-4301	33	1	1.	CARDINAL
ejpam-4301	34	1	2	CARDINAL
ejpam-4301	37	1	3	CARDINAL
ejpam-4301	37	2	′ ≤	CARDINAL
ejpam-4301	38	1	1	CARDINAL
ejpam-4301	39	1	e∗	GPE
ejpam-4301	39	2	1	CARDINAL
ejpam-4301	39	3	1	CARDINAL
ejpam-4301	41	1	z6	GPE
ejpam-4301	42	1	1	CARDINAL
ejpam-4301	44	1	2〉	CARDINAL
ejpam-4301	44	2	2〉+	CARDINAL
ejpam-4301	44	3	3〉	CARDINAL
ejpam-4301	44	4	3〉	CARDINAL
ejpam-4301	45	1	2	CARDINAL
ejpam-4301	45	2	z4	PERSON
ejpam-4301	45	3	2〉	CARDINAL
ejpam-4301	45	4	2〉	CARDINAL
ejpam-4301	46	1	3	CARDINAL
ejpam-4301	46	2	z6	ORG
ejpam-4301	47	1	1	CARDINAL
ejpam-4301	47	2	2〉	MONEY
ejpam-4301	47	3	3〉	CARDINAL
ejpam-4301	47	4	3〉	CARDINAL
ejpam-4301	48	1	2〉	CARDINAL
ejpam-4301	50	1	4	CARDINAL
ejpam-4301	50	2	•	CARDINAL
ejpam-4301	51	1	•	CARDINAL
ejpam-4301	51	2	e∗	GPE
ejpam-4301	56	1	n �e∗	GPE
ejpam-4301	56	2	e∗	GPE
ejpam-4301	56	3	e∗	GPE
ejpam-4301	57	1	2	CARDINAL
ejpam-4301	57	2	k �e∗ n	PERSON
ejpam-4301	57	3	e∗	GPE
ejpam-4301	59	1	baanoon	PERSON
ejpam-4301	59	2	w. khalid	PERSON
ejpam-4301	60	1	j. pure	PERSON
ejpam-4301	60	2	15	CARDINAL
ejpam-4301	60	3	2	CARDINAL
ejpam-4301	60	4	2022	CARDINAL
ejpam-4301	60	5	478	CARDINAL
ejpam-4301	61	1	k + l	ORG
ejpam-4301	62	1	k ≤ n	FAC
ejpam-4301	63	1	k �e∗	PERSON
ejpam-4301	64	1	e∗	GPE
ejpam-4301	65	1	1	CARDINAL
ejpam-4301	65	2	n �e∗	GPE
ejpam-4301	67	1	e∗	GPE
ejpam-4301	68	1	2	CARDINAL
ejpam-4301	69	1	1	CARDINAL
ejpam-4301	70	1	l∩n = n	PERSON
ejpam-4301	71	1	k ≤ l. hence	PERSON
ejpam-4301	73	1	k �e∗	PERSON
ejpam-4301	74	1	2	CARDINAL
ejpam-4301	75	1	k ≤ n	FAC
ejpam-4301	76	1	e∗	GPE
ejpam-4301	78	1	k + l = n	ORG
ejpam-4301	79	1	k + l) ⊕ n	ORG
ejpam-4301	83	1	1	CARDINAL
ejpam-4301	86	1	k �e∗ n	PERSON
ejpam-4301	88	1	n ∈ n	ORG
ejpam-4301	88	2	l ∈ l	ORG
ejpam-4301	90	1	n = l + n ′, so n − l = n ′ ∈ n ∩ n ′	ORG
ejpam-4301	90	2	k �e∗	ORG
ejpam-4301	91	1	3	CARDINAL
ejpam-4301	92	1	e∗	GPE
ejpam-4301	92	2	e∗	GPE
ejpam-4301	95	1	1	CARDINAL
ejpam-4301	96	1	∈	ORG
ejpam-4301	96	2	k ∈ k	PERSON
ejpam-4301	97	1	− k	PERSON
ejpam-4301	98	1	− k ∈	PERSON
ejpam-4301	101	1	e∗	GPE
ejpam-4301	104	1	⊆	CARDINAL
ejpam-4301	104	2	⊆	CARDINAL
ejpam-4301	109	1	n + l �	LOC
ejpam-4301	109	2	e∗	GPE
ejpam-4301	113	1	k +n + l	ORG
ejpam-4301	118	1	1	CARDINAL
ejpam-4301	119	1	e∗	GPE
ejpam-4301	120	1	n + l �e∗ m	PRODUCT
ejpam-4301	121	1	3	CARDINAL
ejpam-4301	121	2	4	CARDINAL
ejpam-4301	122	1	ki	PERSON
ejpam-4301	122	2	1	CARDINAL
ejpam-4301	122	3	2	CARDINAL
ejpam-4301	123	1	ki	PERSON
ejpam-4301	123	2	e∗	GPE
ejpam-4301	123	3	1	CARDINAL
ejpam-4301	123	4	2	CARDINAL
ejpam-4301	123	5	e∗	ORG
ejpam-4301	124	1	baanoon	PERSON
ejpam-4301	124	2	w. khalid	PERSON
ejpam-4301	125	1	j. pure	PERSON
ejpam-4301	125	2	15	CARDINAL
ejpam-4301	125	3	2	CARDINAL
ejpam-4301	125	4	2022	CARDINAL
ejpam-4301	125	5	478-485 481 3	QUANTITY
ejpam-4301	127	1	6	CARDINAL
ejpam-4301	128	1	2	CARDINAL
ejpam-4301	130	1	rad(m) e∗	ORG
ejpam-4301	131	1	e∗	GPE
ejpam-4301	134	1	5	CARDINAL
ejpam-4301	135	1	∈	ORG
ejpam-4301	135	2	〉	CARDINAL
ejpam-4301	141	1	〉	CARDINAL
ejpam-4301	141	2	≤e∗	PERSON
ejpam-4301	143	1	6=	CARDINAL
ejpam-4301	143	2	6=	CARDINAL
ejpam-4301	144	1	γ	GPE
ejpam-4301	144	2	≤e∗	PERSON
ejpam-4301	145	1	zorn	ORG
ejpam-4301	145	2	lemma	ORG
ejpam-4301	145	3	γ	GPE
ejpam-4301	147	1	6	CARDINAL
ejpam-4301	147	2	〉 ≤	MONEY
ejpam-4301	149	1	6=	CARDINAL
ejpam-4301	149	2	∈	ORG
ejpam-4301	152	1	〉 ⊆ b0	MONEY
ejpam-4301	152	2	〉 +	MONEY
ejpam-4301	153	1	〉	CARDINAL
ejpam-4301	155	1	e∗	GPE
ejpam-4301	156	1	〉	CARDINAL
ejpam-4301	157	1	2	CARDINAL
ejpam-4301	157	2	1	CARDINAL
ejpam-4301	158	1	e∗	GPE
ejpam-4301	160	1	z6	PERSON
ejpam-4301	160	2	0	CARDINAL
ejpam-4301	161	1	e∗	ORG
ejpam-4301	161	2	2〉	CARDINAL
ejpam-4301	161	3	3〉	CARDINAL
ejpam-4301	162	1	1	CARDINAL
ejpam-4301	163	1	2	CARDINAL
ejpam-4301	163	2	z4	GPE
ejpam-4301	163	3	e∗	GPE
ejpam-4301	163	4	0	CARDINAL
ejpam-4301	163	5	2	CARDINAL
ejpam-4301	164	1	0	CARDINAL
ejpam-4301	164	2	0	CARDINAL
ejpam-4301	164	3	2	CARDINAL
ejpam-4301	164	4	z4	GPE
ejpam-4301	165	1	0	CARDINAL
ejpam-4301	165	2	2	CARDINAL
ejpam-4301	165	3	z4	GPE
ejpam-4301	166	1	0	CARDINAL
ejpam-4301	166	2	2	CARDINAL
ejpam-4301	167	1	baanoon	PERSON
ejpam-4301	167	2	w. khalid	PERSON
ejpam-4301	168	1	j. pure	PERSON
ejpam-4301	168	2	15	CARDINAL
ejpam-4301	168	3	2	CARDINAL
ejpam-4301	168	4	2022	CARDINAL
ejpam-4301	168	5	478-485 482	QUANTITY
ejpam-4301	168	6	1	CARDINAL
ejpam-4301	169	1	e∗	GPE
ejpam-4301	172	1	e∗	GPE
ejpam-4301	174	1	〉	CARDINAL
ejpam-4301	175	1	e∗	GPE
ejpam-4301	176	1	∑ {n	PERSON
ejpam-4301	176	2	e∗	GPE
ejpam-4301	176	3	⊆	CARDINAL
ejpam-4301	176	4	e∗	GPE
ejpam-4301	177	1	e∗	GPE
ejpam-4301	177	2	e∗	GPE
ejpam-4301	178	1	〉	CARDINAL
ejpam-4301	180	1	e∗	GPE
ejpam-4301	180	2	e∗	GPE
ejpam-4301	180	3	e∗	GPE
ejpam-4301	180	4	e∗	GPE
ejpam-4301	181	1	6	CARDINAL
ejpam-4301	182	1	≤	CARDINAL
ejpam-4301	183	1	e∗	GPE
ejpam-4301	184	1	e∗	GPE
ejpam-4301	186	1	1	CARDINAL
ejpam-4301	186	2	e∗	GPE
ejpam-4301	186	3	∑ k k�e∗m	PERSON
ejpam-4301	187	1	e∗	GPE
ejpam-4301	189	1	e∗	GPE
ejpam-4301	189	2	e∗	GPE
ejpam-4301	189	3	∑ f(k	PERSON
ejpam-4301	189	4	e∗	GPE
ejpam-4301	189	5	e∗	ORG
ejpam-4301	190	1	e∗	GPE
ejpam-4301	191	1	2	CARDINAL
ejpam-4301	192	1	1	CARDINAL
ejpam-4301	192	2	e∗ ≤ rad(m	FAC
ejpam-4301	192	3	e∗	GPE
ejpam-4301	193	1	2.	CARDINAL
ejpam-4301	193	2	e∗	GPE
ejpam-4301	194	1	4	CARDINAL
ejpam-4301	194	2	3	CARDINAL
ejpam-4301	196	1	3	CARDINAL
ejpam-4301	196	2	zero	CARDINAL
ejpam-4301	197	1	3	CARDINAL
ejpam-4301	197	2	1	CARDINAL
ejpam-4301	200	1	z6	ORG
ejpam-4301	200	2	2〉	CARDINAL
ejpam-4301	201	1	baanoon	PERSON
ejpam-4301	201	2	w. khalid	PERSON
ejpam-4301	202	1	j. pure	PERSON
ejpam-4301	202	2	15	CARDINAL
ejpam-4301	202	3	2	CARDINAL
ejpam-4301	202	4	2022	CARDINAL
ejpam-4301	202	5	478-485 483 2	QUANTITY
ejpam-4301	202	6	z6	ORG
ejpam-4301	203	1	2〉	CARDINAL
ejpam-4301	204	1	z6	ORG
ejpam-4301	205	1	3	CARDINAL
ejpam-4301	205	2	two	CARDINAL
ejpam-4301	206	1	z4	PERSON
ejpam-4301	206	2	2〉	CARDINAL
ejpam-4301	210	1	2〉	CARDINAL
ejpam-4301	210	2	3〉+	CARDINAL
ejpam-4301	210	3	2〉	MONEY
ejpam-4301	211	1	4	CARDINAL
ejpam-4301	220	1	3	CARDINAL
ejpam-4301	221	1	3	CARDINAL
ejpam-4301	223	1	1	CARDINAL
ejpam-4301	226	1	0〉	CARDINAL
ejpam-4301	226	2	2〉	CARDINAL
ejpam-4301	226	3	4〉	CARDINAL
ejpam-4301	227	1	3〉+	CARDINAL
ejpam-4301	227	2	2〉	MONEY
ejpam-4301	227	3	3〉	CARDINAL
ejpam-4301	228	1	4〉	CARDINAL
ejpam-4301	228	2	4〉	CARDINAL
ejpam-4301	229	1	3	CARDINAL
ejpam-4301	230	1	e∗-closed	DATE
ejpam-4301	231	1	1	CARDINAL
ejpam-4301	232	1	2	CARDINAL
ejpam-4301	233	1	1	CARDINAL
ejpam-4301	233	2	e∗-closed	DATE
ejpam-4301	236	1	e∗-closed	DATE
ejpam-4301	240	1	n + k+n n	WORK_OF_ART
ejpam-4301	240	2	6=	CARDINAL
ejpam-4301	242	1	6=	CARDINAL
ejpam-4301	243	1	1	CARDINAL
ejpam-4301	243	2	k +n	FAC
ejpam-4301	243	3	lemma 2, k+n n	ORG
ejpam-4301	245	1	= k	PERSON
ejpam-4301	248	1	baanoon	PERSON
ejpam-4301	248	2	w. khalid	PERSON
ejpam-4301	249	1	j. pure	PERSON
ejpam-4301	249	2	15	CARDINAL
ejpam-4301	249	3	2	CARDINAL
ejpam-4301	249	4	2022	CARDINAL
ejpam-4301	249	5	478	CARDINAL
ejpam-4301	249	6	9	CARDINAL
ejpam-4301	254	1	〉	CARDINAL
ejpam-4301	255	1	∈	ORG
ejpam-4301	262	1	∈	ORG
ejpam-4301	265	1	n ∈ n	ORG
ejpam-4301	269	1	e∗	GPE
ejpam-4301	271	1	〉	CARDINAL
ejpam-4301	273	1	10	CARDINAL
ejpam-4301	277	1	6=	CARDINAL
ejpam-4301	281	1	4	CARDINAL
ejpam-4301	283	1	e∗	GPE
ejpam-4301	285	1	11	CARDINAL
ejpam-4301	287	1	1	CARDINAL
ejpam-4301	288	1	2	CARDINAL
ejpam-4301	290	1	1	CARDINAL
ejpam-4301	290	2	1	CARDINAL
ejpam-4301	293	1	≤e∗	PERSON
ejpam-4301	300	1	2	CARDINAL
ejpam-4301	301	1	3	CARDINAL
ejpam-4301	306	1	485	CARDINAL
ejpam-4301	307	1	1	CARDINAL
ejpam-4301	307	2	h. baanoon	PERSON
ejpam-4301	307	3	w. khalid	PERSON
ejpam-4301	308	1	e*-essential submodule	PERSON
ejpam-4301	309	1	european journal	ORG
ejpam-4301	309	2	15(1):224–228	CARDINAL
ejpam-4301	309	3	2022	CARDINAL
ejpam-4301	310	1	2	CARDINAL
ejpam-4301	312	1	2002	DATE
ejpam-4301	313	1	3	CARDINAL
ejpam-4301	313	2	patrick	PERSON
ejpam-4301	313	3	fleury	PRODUCT
ejpam-4301	315	1	pacific journal	ORG
ejpam-4301	315	2	53(2):379–385	CARDINAL
ejpam-4301	315	3	1974	DATE
ejpam-4301	316	1	4	CARDINAL
ejpam-4301	316	2	kenneth goodearl	PERSON
ejpam-4301	316	3	33	CARDINAL
ejpam-4301	317	1	crc press	ORG
ejpam-4301	317	2	1976	DATE
ejpam-4301	318	1	5	CARDINAL
ejpam-4301	318	2	michiel hazewinkel	PERSON
ejpam-4301	318	3	nadiya gubareni	PERSON
ejpam-4301	318	4	vladimir v kirichenko	PERSON
ejpam-4301	319	1	algebras	PERSON
ejpam-4301	319	2	1	CARDINAL
ejpam-4301	319	3	springer science & business media	ORG
ejpam-4301	319	4	2004	DATE
ejpam-4301	320	1	6	CARDINAL
ejpam-4301	320	2	friedrich kasch	PERSON
ejpam-4301	320	3	17	CARDINAL
ejpam-4301	321	1	1982	DATE
ejpam-4301	322	1	7	CARDINAL
ejpam-4301	322	2	dx zhou	PERSON
ejpam-4301	322	3	xr zhang	PERSON
ejpam-4301	324	1	southeast asian	NORP
ejpam-4301	324	2	2011	DATE