id	sid	eid	entity	type
iajs-2802	1	1	ibn al-haitham jour	PERSON
iajs-2802	2	1	sci	ORG
iajs-2802	3	1	53 (1)2022 84	DATE
iajs-2802	3	2	4.0	CARDINAL
iajs-2802	7	1	submodule	ORG
iajs-2802	8	1	1.introduction	CARDINAL
iajs-2802	10	1	1][12	CARDINAL
iajs-2802	11	1	z	ORG
iajs-2802	12	1	sm-submodule	ORG
iajs-2802	13	1	9	CARDINAL
iajs-2802	13	2	2	CARDINAL
iajs-2802	14	1	three	CARDINAL
iajs-2802	16	1	section three	LAW
iajs-2802	18	1	al haitham	ORG
iajs-2802	18	2	10.30526/35.1.2802	CARDINAL
iajs-2802	18	3	24	CARDINAL
iajs-2802	18	4	august	DATE
iajs-2802	18	5	2021	CARDINAL
iajs-2802	18	6	26, september	DATE
iajs-2802	18	7	2021	DATE
iajs-2802	18	8	january 2022	DATE
iajs-2802	19	1	fatima m. mohialdeen	PERSON
iajs-2802	19	2	al-haitham	ORG
iajs-2802	19	3	university of baghdad	ORG
iajs-2802	19	4	iraq	GPE
iajs-2802	19	5	fatima.mohy.fm@gmail.com	ORG
iajs-2802	19	6	buthyna n. shihab	PERSON
iajs-2802	19	7	al-haitham	ORG
iajs-2802	19	8	university of baghdad	ORG
iajs-2802	19	9	iraq	GPE
iajs-2802	19	10	ibn al-haitham jour	PERSON
iajs-2802	21	1	sci	ORG
iajs-2802	22	1	53 (1)2022 85	DATE
iajs-2802	23	1	2.basic	CARDINAL
iajs-2802	24	1	2.1	CARDINAL
iajs-2802	24	2	2	CARDINAL
iajs-2802	25	1	2.2	CARDINAL
iajs-2802	25	2	4	CARDINAL
iajs-2802	26	1	2.3	CARDINAL
iajs-2802	27	1	4	CARDINAL
iajs-2802	28	1	1	CARDINAL
iajs-2802	29	1	2.4	CARDINAL
iajs-2802	29	2	tx	ORG
iajs-2802	29	3	∈	PRODUCT
iajs-2802	29	4	t ∈ s	ORG
iajs-2802	31	1	∈	ORG
iajs-2802	32	1	5	CARDINAL
iajs-2802	33	1	2.5	CARDINAL
iajs-2802	33	2	3	CARDINAL
iajs-2802	33	3	2.1.1),p32	CARDINAL
iajs-2802	34	1	2.6	CARDINAL
iajs-2802	35	1	b:(x	PERSON
iajs-2802	37	1	⊆	CARDINAL
iajs-2802	38	1	7	CARDINAL
iajs-2802	39	1	sm-submodule	ORG
iajs-2802	41	1	3.1	CARDINAL
iajs-2802	41	2	submodule of a.	ORG
iajs-2802	41	3	sm-submodule	ORG
iajs-2802	43	1	3.2	CARDINAL
iajs-2802	43	2	al-haitham jour	ORG
iajs-2802	45	1	sci	ORG
iajs-2802	46	1	53 (1)2022 86 1	DATE
iajs-2802	51	1	2	CARDINAL
iajs-2802	55	1	3	CARDINAL
iajs-2802	55	2	zp∞	CARDINAL
iajs-2802	57	1	0	CARDINAL
iajs-2802	57	2	1	CARDINAL
iajs-2802	57	3	2	CARDINAL
iajs-2802	58	1	z.	PERSON
iajs-2802	58	2	1	CARDINAL
iajs-2802	60	1	zp∞.	ORG
iajs-2802	60	2	zp∞	GPE
iajs-2802	61	1	z8	DATE
iajs-2802	61	2	2	CARDINAL
iajs-2802	61	3	4	CARDINAL
iajs-2802	61	4	z8	DATE
iajs-2802	62	1	4	CARDINAL
iajs-2802	65	1	1	CARDINAL
iajs-2802	66	1	≅z3	CARDINAL
iajs-2802	67	1	2	CARDINAL
iajs-2802	68	1	≅z6	CARDINAL
iajs-2802	69	1	z6/	GPE
iajs-2802	69	2	2	CARDINAL
iajs-2802	70	1	≅	CARDINAL
iajs-2802	71	1	z6	GPE
iajs-2802	72	1	sm-submodules	ORG
iajs-2802	73	1	5	CARDINAL
iajs-2802	74	1	5	CARDINAL
iajs-2802	75	1	1	CARDINAL
iajs-2802	75	2	2	CARDINAL
iajs-2802	75	3	10	CARDINAL
iajs-2802	75	4	4	CARDINAL
iajs-2802	75	5	5	CARDINAL
iajs-2802	77	1	6	CARDINAL
iajs-2802	77	2	z4	PERSON
iajs-2802	78	1	2	CARDINAL
iajs-2802	78	2	z4	GPE
iajs-2802	79	1	z4	GPE
iajs-2802	79	2	z.	PERSON
iajs-2802	79	3	4	CARDINAL
iajs-2802	80	1	2	CARDINAL
iajs-2802	80	2	≅ z4	PERSON
iajs-2802	81	1	7	CARDINAL
iajs-2802	82	1	2	CARDINAL
iajs-2802	83	1	2	CARDINAL
iajs-2802	83	2	z4	GPE
iajs-2802	83	3	2	CARDINAL
iajs-2802	84	1	ibn al-haitham jour	PERSON
iajs-2802	85	1	sci	ORG
iajs-2802	86	1	53 (1)2022 87 8	DATE
iajs-2802	87	1	2	CARDINAL
iajs-2802	88	1	z10/	CARDINAL
iajs-2802	88	2	2b	CARDINAL
iajs-2802	88	3	≅	CARDINAL
iajs-2802	88	4	2	CARDINAL
iajs-2802	89	1	9	CARDINAL
iajs-2802	89	2	1	CARDINAL
iajs-2802	89	3	2	CARDINAL
iajs-2802	90	1	4	CARDINAL
iajs-2802	90	2	6	CARDINAL
iajs-2802	92	1	10	CARDINAL
iajs-2802	94	1	3>⊕<2	CARDINAL
iajs-2802	95	1	2	CARDINAL
iajs-2802	95	2	z. 11	ORG
iajs-2802	96	1	2	CARDINAL
iajs-2802	96	2	z4	GPE
iajs-2802	97	1	12	CARDINAL
iajs-2802	98	1	2	CARDINAL
iajs-2802	98	2	sm-submodule	ORG
iajs-2802	99	1	2	CARDINAL
iajs-2802	100	1	13	CARDINAL
iajs-2802	101	1	two	CARDINAL
iajs-2802	101	2	sm-submodule	ORG
iajs-2802	101	3	two	CARDINAL
iajs-2802	101	4	2	CARDINAL
iajs-2802	101	5	2	CARDINAL
iajs-2802	102	1	14	CARDINAL
iajs-2802	105	1	15	CARDINAL
iajs-2802	106	1	two	CARDINAL
iajs-2802	106	2	2	CARDINAL
iajs-2802	106	3	two	CARDINAL
iajs-2802	106	4	2>⊕<3>=z6	CARDINAL
iajs-2802	107	1	16	CARDINAL
iajs-2802	108	1	3	CARDINAL
iajs-2802	108	2	2.1.2	CARDINAL
iajs-2802	108	3	no.(11	GPE
iajs-2802	108	4	6z	CARDINAL
iajs-2802	109	1	6z	CARDINAL
iajs-2802	109	2	z.	PERSON
iajs-2802	109	3	6z =2z∩5z	QUANTITY
iajs-2802	109	4	2z	CARDINAL
iajs-2802	109	5	5z	DATE
iajs-2802	109	6	z.	PERSON
iajs-2802	109	7	6z	CARDINAL
iajs-2802	109	8	z.	PERSON
iajs-2802	110	1	3.3	CARDINAL
iajs-2802	110	2	two	CARDINAL
iajs-2802	110	3	b⊆d	NORP
iajs-2802	111	1	sm-submodule	ORG
iajs-2802	111	2	sm-submodule	ORG
iajs-2802	111	3	a. proof	PERSON
iajs-2802	111	4	sm-submodule	ORG
iajs-2802	112	1	⊆	CARDINAL
iajs-2802	112	2	⊆	CARDINAL
iajs-2802	112	3	2.1	CARDINAL
iajs-2802	113	1	sm-submodule	ORG
iajs-2802	113	2	d. ibn al-haitham jour	PERSON
iajs-2802	115	1	sci	ORG
iajs-2802	116	1	53 (1)2022 88	DATE
iajs-2802	116	2	3.3	CARDINAL
iajs-2802	116	3	3.4	CARDINAL
iajs-2802	117	1	a. proof	PERSON
iajs-2802	118	1	⊆	CARDINAL
iajs-2802	118	2	3.3	CARDINAL
iajs-2802	118	3	sm-submodule	ORG
iajs-2802	118	4	a.	GPE
iajs-2802	119	1	3.5	CARDINAL
iajs-2802	120	1	x∈a	PERSON
iajs-2802	121	1	x∈a	PERSON
iajs-2802	121	2	2.2	CARDINAL
iajs-2802	124	1	first	ORDINAL
iajs-2802	126	1	0a	CARDINAL
iajs-2802	126	2	≅a	DATE
iajs-2802	128	1	3.2	CARDINAL
iajs-2802	129	1	2	CARDINAL
iajs-2802	130	1	3.5	CARDINAL
iajs-2802	130	2	3.6	CARDINAL
iajs-2802	133	1	m1 and m2	PRODUCT
iajs-2802	133	2	m1 ≠ m2	PERSON
iajs-2802	133	3	m2≅	PERSON
iajs-2802	133	4	2.3	CARDINAL
iajs-2802	134	1	anns(m1	ORG
iajs-2802	136	1	m1 = m2	PERSON
iajs-2802	137	1	3.5	CARDINAL
iajs-2802	138	1	3.6	CARDINAL
iajs-2802	139	1	3.7	CARDINAL
iajs-2802	139	2	ibn al-haitham jour	PERSON
iajs-2802	141	1	sci	ORG
iajs-2802	142	1	53 (1)2022 89	DATE
iajs-2802	143	1	2.5	CARDINAL
iajs-2802	144	1	3	CARDINAL
iajs-2802	144	2	1.1.51	CARDINAL
iajs-2802	144	3	3.6	CARDINAL
iajs-2802	146	1	w	ORG
iajs-2802	146	2	two	CARDINAL
iajs-2802	147	1	1	CARDINAL
iajs-2802	148	1	∈	ORG
iajs-2802	149	1	2	CARDINAL
iajs-2802	152	1	w	ORG
iajs-2802	152	2	∈s	ORG
iajs-2802	152	3	w ∈w	NORP
iajs-2802	152	4	∈a	PERSON
iajs-2802	152	5	w ∈w	NORP
iajs-2802	153	1	m1, m2∈	PRODUCT
iajs-2802	153	2	w1,w2∈ w	GPE
iajs-2802	153	3	∃	ORG
iajs-2802	153	4	0	CARDINAL
iajs-2802	154	1	m1/w1+m2	PRODUCT
iajs-2802	154	2	∈	ORG
iajs-2802	154	3	ae	ORG
iajs-2802	155	1	only one	CARDINAL
iajs-2802	156	1	ae	ORG
iajs-2802	156	2	∈	ORG
iajs-2802	157	1	w	ORG
iajs-2802	157	2	n/w	ORG
iajs-2802	157	3	n ∈b	ORG
iajs-2802	157	4	8	CARDINAL
iajs-2802	159	1	lemma	ORG
iajs-2802	160	1	4.1	CARDINAL
iajs-2802	161	1	10	CARDINAL
iajs-2802	161	2	two	CARDINAL
iajs-2802	162	1	4.2	CARDINAL
iajs-2802	162	2	submodule of a.	ORG
iajs-2802	163	1	sm-submodule	ORG
iajs-2802	163	2	a. proof	PERSON
iajs-2802	163	3	ibn al-haitham jour	PERSON
iajs-2802	165	1	sci	ORG
iajs-2802	166	1	53 (1)2022 90	DATE
iajs-2802	168	1	i(l	GPE
iajs-2802	168	2	s. now	ORG
iajs-2802	168	3	⊆	CARDINAL
iajs-2802	170	1	i=1 i(li+e2b	PERSON
iajs-2802	171	1	i=1	NORP
iajs-2802	171	2	∈	ORG
iajs-2802	171	3	2bp	ORDINAL
iajs-2802	171	4	2bp	ORDINAL
iajs-2802	172	1	2bp	ORDINAL
iajs-2802	172	2	2bp	ORDINAL
iajs-2802	173	1	2bp	ORDINAL
iajs-2802	173	2	10	CARDINAL
iajs-2802	174	1	ia+e2b)/(e2b))⋂(l/(e2b)))p	NORP
iajs-2802	175	1	∈	ORG
iajs-2802	175	2	∈	ORG
iajs-2802	175	3	⊆	CARDINAL
iajs-2802	176	1	i(l	GPE
iajs-2802	178	1	2bp	ORDINAL
iajs-2802	179	1	2bp	ORDINAL
iajs-2802	179	2	⊆	CARDINAL
iajs-2802	179	3	2bp	ORDINAL
iajs-2802	180	1	2bp	ORDINAL
iajs-2802	181	1	⊆	CARDINAL
iajs-2802	181	2	2bp	ORDINAL
iajs-2802	182	1	x/1 ∈	PERSON
iajs-2802	182	2	2bp	ORDINAL
iajs-2802	183	1	2bp 2	ORG
iajs-2802	184	1	ci=siti .	PERSON
iajs-2802	187	1	k∉	PERSON
iajs-2802	187	2	13,theorem	CARDINAL
iajs-2802	187	3	2.6	CARDINAL
iajs-2802	188	1	xa+	GPE
iajs-2802	189	1	2bp)∈(ip(ap	CARDINAL
iajs-2802	189	2	2bp	ORDINAL
iajs-2802	190	1	2bp	ORDINAL
iajs-2802	191	1	⊆	CARDINAL
iajs-2802	191	2	2bp	ORDINAL
iajs-2802	191	3	2bp	ORDINAL
iajs-2802	192	1	4.3	CARDINAL
iajs-2802	192	2	two	CARDINAL
iajs-2802	192	3	two	CARDINAL
iajs-2802	192	4	10,p24	DATE
iajs-2802	193	1	lp⋂bp = lp	PERSON
iajs-2802	193	2	lp⋂bp	PERSON
iajs-2802	193	3	lp⋂bp	PERSON
iajs-2802	193	4	lp⋂bp	PERSON
iajs-2802	193	5	l⋂b)p	ORG
iajs-2802	194	1	l⋂b)p	ORG
iajs-2802	194	2	4.4	CARDINAL
iajs-2802	194	3	two	CARDINAL
iajs-2802	195	1	ibn al-haitham jour	PERSON
iajs-2802	196	1	sci	ORG
iajs-2802	197	1	53 (1)2022 91	DATE
iajs-2802	197	2	two	CARDINAL
iajs-2802	197	3	10	CARDINAL
iajs-2802	198	1	1	CARDINAL
iajs-2802	200	1	⊆	CARDINAL
iajs-2802	200	2	⊆	CARDINAL
iajs-2802	201	1	5.conclusion	CARDINAL
iajs-2802	203	1	1	CARDINAL
iajs-2802	203	2	burton	PERSON
iajs-2802	203	3	d. m. 1970	PERSON
iajs-2802	204	1	first	ORDINAL
iajs-2802	205	1	addison-wesley	ORG
iajs-2802	206	1	2	CARDINAL
iajs-2802	206	2	scince college	ORG
iajs-2802	206	3	baghdad	GPE
iajs-2802	206	4	1993	DATE
iajs-2802	207	1	3	CARDINAL
iajs-2802	208	1	khalaf	PERSON
iajs-2802	208	2	h.y. semimaximal submodules ph.d.thesis	PERSON
iajs-2802	208	3	baghdad	GPE
iajs-2802	208	4	2007	DATE
iajs-2802	209	1	4	CARDINAL
iajs-2802	209	2	frank w.	PERSON
iajs-2802	209	3	anderson k.	PERSON
iajs-2802	210	1	r.	NORP
iajs-2802	210	2	berlin	GPE
iajs-2802	210	3	heidelberg	GPE
iajs-2802	210	4	new york	GPE
iajs-2802	210	5	1974	DATE
iajs-2802	211	1	5	CARDINAL
iajs-2802	211	2	lu.c.p	PERSON
iajs-2802	213	1	japon.	GPE
iajs-2802	213	2	34 1989	DATE
iajs-2802	213	3	211	CARDINAL
iajs-2802	213	4	6	CARDINAL
iajs-2802	213	5	kazem	PERSON
iajs-2802	213	6	a.d.	PERSON
iajs-2802	215	1	7	CARDINAL
iajs-2802	215	2	goldie	PERSON
iajs-2802	215	3	k.r.	GPE
iajs-2802	215	4	j.algebra,1,268-287, 1964	EVENT
iajs-2802	216	1	8	CARDINAL
iajs-2802	217	1	larson m.d.	PERSON
iajs-2802	217	2	mc carthy p.j.	PERSON
iajs-2802	217	3	1971	DATE
iajs-2802	217	4	new york	GPE
iajs-2802	217	5	london	GPE
iajs-2802	218	1	9	CARDINAL
iajs-2802	218	2	fieldhouse	ORG
iajs-2802	218	3	d.j.	GPE
iajs-2802	218	4	math.ann.	GPE
iajs-2802	218	5	184,1	CARDINAL
iajs-2802	219	1	10	CARDINAL
iajs-2802	221	1	baghdad university	ORG
iajs-2802	221	2	1992	DATE
iajs-2802	222	1	11	CARDINAL
iajs-2802	222	2	faris	PERSON
iajs-2802	222	3	h. i.	PERSON
iajs-2802	222	4	jasim	GPE
iajs-2802	222	5	r. h., & mohammed	ORG
iajs-2802	222	6	n. j. 2021	PERSON
iajs-2802	224	1	1818	DATE
iajs-2802	224	2	1	CARDINAL
iajs-2802	224	3	012055	DATE
iajs-2802	225	1	iop publishing	ORG
iajs-2802	226	1	12	CARDINAL
iajs-2802	227	1	mohammed	PERSON
iajs-2802	227	2	a. s.	PERSON
iajs-2802	227	3	m. d. 2017	PERSON
iajs-2802	228	1	2	CARDINAL
iajs-2802	229	1	journal of university of anbar	ORG
iajs-2802	229	2	11(3	CARDINAL
iajs-2802	230	1	13	CARDINAL
iajs-2802	231	1	jud h.m.	PERSON
iajs-2802	231	2	baghdad	GPE