id	sid	eid	entity	type
iajs-3028	1	1	ihjpas	PERSON
iajs-3028	2	1	36(2)2023 383	CARDINAL
iajs-3028	2	2	4.0	CARDINAL
iajs-3028	6	1	the jacobsen radical	PERSON
iajs-3028	7	1	2017	DATE
iajs-3028	7	2	2022	CARDINAL
iajs-3028	7	3	3.14	CARDINAL
iajs-3028	9	1	jacobson radical	PERSON
iajs-3028	10	1	1.introduction	CARDINAL
iajs-3028	11	1	baer hypermodule	WORK_OF_ART
iajs-3028	12	1	1	CARDINAL
iajs-3028	12	2	2017	DATE
iajs-3028	12	3	irina cristea	ORG
iajs-3028	12	4	2022	CARDINAL
iajs-3028	13	1	2	CARDINAL
iajs-3028	15	1	french	NORP
iajs-3028	15	2	marty	PERSON
iajs-3028	15	3	1937	DATE
iajs-3028	17	1	3	CARDINAL
iajs-3028	17	2	p*(𝒢	ORG
iajs-3028	17	3	algebraic hyperstructure	PERSON
iajs-3028	18	1	3	CARDINAL
iajs-3028	21	1	𝑈𝑣∈𝓅⊚𝒹	MONEY
iajs-3028	23	1	3	CARDINAL
iajs-3028	23	2	1	CARDINAL
iajs-3028	25	1	3	CARDINAL
iajs-3028	26	1	21	CARDINAL
iajs-3028	26	2	2022	CARDINAL
iajs-3028	26	3	21	CARDINAL
iajs-3028	26	4	november 2022	DATE
iajs-3028	26	5	april 2023	DATE
iajs-3028	27	1	ibn al-haitham	PERSON
iajs-3028	27	2	applied sciences journal	ORG
iajs-3028	27	3	fadel abood department	ORG
iajs-3028	27	4	university of baghdad	ORG
iajs-3028	27	5	baghdad	GPE
iajs-3028	27	6	iraq	GPE
iajs-3028	28	1	arif ibrahiem department of	ORG
iajs-3028	28	2	university of baghdad	ORG
iajs-3028	28	3	baghdad	GPE
iajs-3028	28	4	iraq	GPE
iajs-3028	29	1	mailto:tamadherai_math@csw.uobaghdad.edu.iq ihjpas	PERSON
iajs-3028	30	1	36(2)2023 384	CARDINAL
iajs-3028	30	2	3	CARDINAL
iajs-3028	31	1	1956	DATE
iajs-3028	31	2	krasner hypermodule	PERSON
iajs-3028	33	1	1	CARDINAL
iajs-3028	34	1	ℛ-hypermodule	ORG
iajs-3028	34	2	ℳ. 2	ORG
iajs-3028	35	1	2.1	CARDINAL
iajs-3028	36	1	4	CARDINAL
iajs-3028	37	1	1	CARDINAL
iajs-3028	38	1	2	CARDINAL
iajs-3028	40	1	3	CARDINAL
iajs-3028	40	2	4	CARDINAL
iajs-3028	40	3	∈	ORG
iajs-3028	40	4	𝒹 ⊚𝓆	GPE
iajs-3028	42	1	5	CARDINAL
iajs-3028	42	2	2.2	CARDINAL
iajs-3028	42	3	4	CARDINAL
iajs-3028	43	1	1.	CARDINAL
iajs-3028	43	2	2	CARDINAL
iajs-3028	43	3	0	CARDINAL
iajs-3028	43	4	∈	ORG
iajs-3028	43	5	3	CARDINAL
iajs-3028	43	6	𝛼⨀𝛽 ⊚ 𝛼⨀𝛾	WORK_OF_ART
iajs-3028	43	7	ℛ,⨀	ORG
iajs-3028	44	1	2.3	CARDINAL
iajs-3028	45	1	5	CARDINAL
iajs-3028	47	1	2.4	CARDINAL
iajs-3028	47	2	5	CARDINAL
iajs-3028	48	1	ℛ,∔,⋅	PERSON
iajs-3028	48	2	∔ 𝐼	ORG
iajs-3028	48	3	∔ 𝐼	ORG
iajs-3028	48	4	∔ 𝐼	ORG
iajs-3028	49	1	∔	GPE
iajs-3028	49	2	∔ 𝐼	ORG
iajs-3028	49	3	∔ 𝐼)(𝑡 ∔ 𝐼	ORG
iajs-3028	49	4	∔ 𝐼.	PERSON
iajs-3028	51	1	2.5	CARDINAL
iajs-3028	52	1	1	CARDINAL
iajs-3028	55	1	1	CARDINAL
iajs-3028	55	2	𝒹	ORDINAL
iajs-3028	55	3	2	CARDINAL
iajs-3028	59	1	2.6	CARDINAL
iajs-3028	60	1	4	CARDINAL
iajs-3028	61	1	j ⊆ ℛ	PERSON
iajs-3028	61	2	j = ℛ. definition	PERSON
iajs-3028	61	3	2.7	CARDINAL
iajs-3028	61	4	1	CARDINAL
iajs-3028	62	1	ℛ,⊚,⨀	PERSON
iajs-3028	62	2	1	CARDINAL
iajs-3028	62	3	ℛ ×ℳ	ORG
iajs-3028	62	4	∈	ORG
iajs-3028	62	5	∈	ORG
iajs-3028	62	6	∈	ORG
iajs-3028	62	7	∈	ORG
iajs-3028	62	8	1	CARDINAL
iajs-3028	62	9	ihjpas	PERSON
iajs-3028	63	1	36(2)2023	CARDINAL
iajs-3028	64	1	𝓀(𝑚⨁𝑚ˋ)=𝓀𝓂⊕𝓀𝑚ˋ 3	CARDINAL
iajs-3028	64	2	4	CARDINAL
iajs-3028	65	1	0ℳ	CARDINAL
iajs-3028	65	2	0ℛ	CARDINAL
iajs-3028	65	3	zero	CARDINAL
iajs-3028	65	4	0ℳ	CARDINAL
iajs-3028	66	1	ℛhypermodule	ORG
iajs-3028	66	2	1.𝓂	CARDINAL
iajs-3028	66	3	1	CARDINAL
iajs-3028	66	4	2.8	CARDINAL
iajs-3028	66	5	6	CARDINAL
iajs-3028	67	1	≠ 𝒩	PERSON
iajs-3028	67	2	⊆	CARDINAL
iajs-3028	67	3	∈ 𝒩	PERSON
iajs-3028	67	4	2.9	CARDINAL
iajs-3028	67	5	2	CARDINAL
iajs-3028	67	6	ℛ,⊚,⨀	PERSON
iajs-3028	68	1	∈ ℛ	ORG
iajs-3028	72	1	0	CARDINAL
iajs-3028	73	1	zero	CARDINAL
iajs-3028	73	2	zero	CARDINAL
iajs-3028	74	1	2.10	CARDINAL
iajs-3028	74	2	2	CARDINAL
iajs-3028	74	3	∈	ORG
iajs-3028	74	4	∈	ORG
iajs-3028	75	1	2.11	CARDINAL
iajs-3028	75	2	4	CARDINAL
iajs-3028	76	1	jacobson	PERSON
iajs-3028	77	1	2.12	CARDINAL
iajs-3028	78	1	7	CARDINAL
iajs-3028	80	1	𝑟.	GPE
iajs-3028	80	2	𝑟.	GPE
iajs-3028	81	1	1	CARDINAL
iajs-3028	81	2	salasi	PERSON
iajs-3028	81	3	4	CARDINAL
iajs-3028	81	4	1 → 2	CARDINAL
iajs-3028	83	1	2.13	CARDINAL
iajs-3028	84	1	1	CARDINAL
iajs-3028	84	2	∈	ORG
iajs-3028	84	3	2	CARDINAL
iajs-3028	84	4	𝒹	CARDINAL
iajs-3028	84	5	1-𝓅𝒹 ⊆	CARDINAL
iajs-3028	84	6	3	CARDINAL
iajs-3028	84	7	⊆	CARDINAL
iajs-3028	86	1	1	CARDINAL
iajs-3028	86	2	4	CARDINAL
iajs-3028	86	3	2.14	CARDINAL
iajs-3028	88	1	∈	ORG
iajs-3028	88	2	1𝓅𝒹𝓆	CARDINAL
iajs-3028	88	3	⊆	CARDINAL
iajs-3028	89	1	ℛ𝓈 ≠ ℛ	PERSON
iajs-3028	89	2	ℛ𝓈 ⊆ 𝐼	ORG
iajs-3028	89	3	4	CARDINAL
iajs-3028	89	4	prop.2.12	ORG
iajs-3028	89	5	one	CARDINAL
iajs-3028	89	6	1∈	CARDINAL
iajs-3028	89	7	⊆	CARDINAL
iajs-3028	89	8	⊆	CARDINAL
iajs-3028	89	9	2.1	CARDINAL
iajs-3028	89	10	1∈	CARDINAL
iajs-3028	90	1	1-𝓅𝒹𝓆 ⊆	CARDINAL
iajs-3028	91	1	∈	ORG
iajs-3028	91	2	∃ 𝐼	PERSON
iajs-3028	91	3	≠ 𝐼	PERSON
iajs-3028	91	4	1	CARDINAL
iajs-3028	92	1	36(2)2023 386	CARDINAL
iajs-3028	92	2	1∈	CARDINAL
iajs-3028	93	1	⊆	CARDINAL
iajs-3028	93	2	1	CARDINAL
iajs-3028	93	3	∈	ORG
iajs-3028	93	4	3	CARDINAL
iajs-3028	94	1	3.1	CARDINAL
iajs-3028	96	1	∈ ℳ|	ORG
iajs-3028	96	2	𝑅𝑂	ORG
iajs-3028	96	3	∈	ORG
iajs-3028	97	1	3.2	CARDINAL
iajs-3028	102	1	∈	ORG
iajs-3028	103	1	∈	ORG
iajs-3028	103	2	∈	ORG
iajs-3028	104	1	∈	ORG
iajs-3028	104	2	∈	ORG
iajs-3028	104	3	∈	ORG
iajs-3028	106	1	3.3	CARDINAL
iajs-3028	107	1	1	CARDINAL
iajs-3028	107	2	ℛ-subhypermodule	PRODUCT
iajs-3028	107	3	ℛ-hypermodule	PRODUCT
iajs-3028	107	4	2	CARDINAL
iajs-3028	110	1	1	CARDINAL
iajs-3028	110	2	∈	ORG
iajs-3028	110	3	𝑅𝑂	ORG
iajs-3028	111	1	∈	ORG
iajs-3028	112	1	∈	ORG
iajs-3028	112	2	0 ≠	PERSON
iajs-3028	112	3	r∈ 𝑅𝑂	GPE
iajs-3028	112	4	𝑟𝑥.	TIME
iajs-3028	112	5	𝑎𝑟)𝑥	FAC
iajs-3028	114	1	2.	CARDINAL
iajs-3028	116	1	∈ 𝑅𝑂	ORG
iajs-3028	116	2	∃	ORG
iajs-3028	117	1	∈	ORG
iajs-3028	119	1	0	CARDINAL
iajs-3028	119	2	3.4	CARDINAL
iajs-3028	121	1	∈ 𝑅𝑂	ORG
iajs-3028	123	1	3.5	CARDINAL
iajs-3028	125	1	∈	ORG
iajs-3028	125	2	∈	ORG
iajs-3028	125	3	3.6	CARDINAL
iajs-3028	125	4	3	CARDINAL
iajs-3028	126	1	1	CARDINAL
iajs-3028	126	2	3.7	CARDINAL
iajs-3028	129	1	∈	ORG
iajs-3028	129	2	∃	ORG
iajs-3028	129	3	∈	ORG
iajs-3028	130	1	3.8	CARDINAL
iajs-3028	131	1	𝑅𝑂	ORG
iajs-3028	131	2	≠ ∅	PERSON
iajs-3028	131	3	d(ℛ)= ∩	PERSON
iajs-3028	134	1	⊆	CARDINAL
iajs-3028	134	2	d(ℛ	NORP
iajs-3028	135	1	𝑅ˆ ∩ 𝑅𝑂 ≠ ∅	PRODUCT
iajs-3028	137	1	⊆	CARDINAL
iajs-3028	137	2	𝑅ˆ	ORG
iajs-3028	138	1	ihjpas	PERSON
iajs-3028	139	1	36(2)2023 387	CARDINAL
iajs-3028	139	2	3.9	CARDINAL
iajs-3028	140	1	𝑅𝑂	ORG
iajs-3028	140	2	≠ ∅	PERSON
iajs-3028	140	3	1+d(ℛ	CARDINAL
iajs-3028	140	4	⊆	CARDINAL
iajs-3028	142	1	∈	ORG
iajs-3028	142	2	prop.2.13-3	CARDINAL
iajs-3028	142	3	1+𝑟	CARDINAL
iajs-3028	142	4	1 +	DATE
iajs-3028	142	5	1	CARDINAL
iajs-3028	142	6	1	CARDINAL
iajs-3028	142	7	∈	ORG
iajs-3028	142	8	1 + 𝑑(ℛ	DATE
iajs-3028	142	9	⊆	CARDINAL
iajs-3028	143	1	3.10	CARDINAL
iajs-3028	144	1	𝑅𝑂	ORG
iajs-3028	145	1	∃	ORG
iajs-3028	146	1	1	CARDINAL
iajs-3028	146	2	∈	ORG
iajs-3028	146	3	1	CARDINAL
iajs-3028	146	4	1	CARDINAL
iajs-3028	146	5	0	CARDINAL
iajs-3028	147	1	𝑅𝑂	ORG
iajs-3028	147	2	1	CARDINAL
iajs-3028	147	3	∈	ORG
iajs-3028	147	4	2	CARDINAL
iajs-3028	147	5	1	CARDINAL
iajs-3028	147	6	2	CARDINAL
iajs-3028	147	7	∈	ORG
iajs-3028	148	1	∈	ORG
iajs-3028	148	2	3.11	DATE
iajs-3028	150	1	3.11	CARDINAL
iajs-3028	150	2	3.4	CARDINAL
iajs-3028	150	3	3.12	CARDINAL
iajs-3028	152	1	3.13	CARDINAL
iajs-3028	153	1	• 𝑑(ℛ	TIME
iajs-3028	154	1	0 •	CARDINAL
iajs-3028	154	2	𝐼𝑗}𝑗∈𝐽	ORG
iajs-3028	154	3	𝑑(𝑅	PERSON
iajs-3028	154	4	∩ 𝐼𝑗 ∩ 𝑅 𝑂 ≠ ∅	PERSON
iajs-3028	154	5	3.14	CARDINAL
iajs-3028	157	1	𝐼𝑗 ≠ ℛ	PERSON
iajs-3028	158	1	ℛ	ORG
iajs-3028	158	2	3.13	CARDINAL
iajs-3028	159	1	𝐼𝑗}𝑗∈𝐽	ORG
iajs-3028	159	2	𝑑(𝑅	PERSON
iajs-3028	159	3	∩ 𝐼𝑗 ∩ 𝑅 𝑂 ≠	PERSON
iajs-3028	159	4	ℛ	ORG
iajs-3028	159	5	𝑅0	CARDINAL
iajs-3028	160	1	3.15	CARDINAL
iajs-3028	161	1	𝑅𝑂	ORG
iajs-3028	164	1	∈	ORG
iajs-3028	164	2	⊆ xℛ.	PERCENT
iajs-3028	165	1	36(2)2023 388	CARDINAL
iajs-3028	165	2	two	CARDINAL
iajs-3028	165	3	8	CARDINAL
iajs-3028	165	4	1	CARDINAL
iajs-3028	165	5	two	CARDINAL
iajs-3028	165	6	3.16	DATE
iajs-3028	166	1	two	CARDINAL
iajs-3028	166	2	∈	ORG
iajs-3028	166	3	∈ 𝒯	ORG
iajs-3028	166	4	3.17	CARDINAL
iajs-3028	169	1	∈	ORG
iajs-3028	169	2	𝑅𝑂	ORG
iajs-3028	169	3	∃𝓈 ∈ 𝒮	ORG
iajs-3028	169	4	∈	ORG
iajs-3028	169	5	∈	ORG
iajs-3028	171	1	3.18	CARDINAL
iajs-3028	171	2	2	CARDINAL
iajs-3028	172	1	1ℛ	CARDINAL
iajs-3028	172	2	1𝒮	CARDINAL
iajs-3028	172	3	1	CARDINAL
iajs-3028	173	1	ℓ(𝓀	PERSON
iajs-3028	173	2	∔ˈ ℓ(𝒷	PERSON
iajs-3028	173	3	2	DATE
iajs-3028	173	4	ℓ(𝓀⊙𝒷)= ℓ(𝓀	PERSON
iajs-3028	173	5	ℓ(𝒷) 3	ORG
iajs-3028	174	1	3.19	CARDINAL
iajs-3028	175	1	3.20	CARDINAL
iajs-3028	176	1	ℛ 𝒮	ORG
iajs-3028	177	1	ℛ 𝒮	ORG
iajs-3028	177	2	∈	ORG
iajs-3028	177	3	∈	ORG
iajs-3028	177	4	𝑟(𝑎ˊ	CARDINAL
iajs-3028	177	5	ℛ 𝒮	ORG
iajs-3028	178	1	3.21	CARDINAL
iajs-3028	180	1	3.22	CARDINAL
iajs-3028	181	1	2	CARDINAL
iajs-3028	182	1	1 and 2	CARDINAL
iajs-3028	182	2	0	CARDINAL
iajs-3028	182	3	1	DATE
iajs-3028	183	1	1	CARDINAL
iajs-3028	183	2	1	CARDINAL
iajs-3028	183	3	0	CARDINAL
iajs-3028	183	4	1	CARDINAL
iajs-3028	183	5	1,𝓅,𝒹	CARDINAL
iajs-3028	183	6	1,𝓅,𝒹	CARDINAL
iajs-3028	184	1	36(2)2023 389	CARDINAL
iajs-3028	184	2	2	CARDINAL
iajs-3028	184	3	ℛ	ORG
iajs-3028	189	1	1	CARDINAL
iajs-3028	189	2	s.	PERSON
iajs-3028	189	3	s.	PERSON
iajs-3028	189	4	baer hypermodules	PERSON
iajs-3028	192	1	2	CARDINAL
iajs-3028	192	2	1	CARDINAL
iajs-3028	192	3	bordbar	GPE
iajs-3028	192	4	cristea i.	PERSON
iajs-3028	193	1	univ	NORP
iajs-3028	193	2	constanta ser	PERSON
iajs-3028	193	3	2022	CARDINAL
iajs-3028	193	4	30	DATE
iajs-3028	193	5	1	CARDINAL
iajs-3028	193	6	57	CARDINAL
iajs-3028	194	1	3	CARDINAL
iajs-3028	195	1	anvariyeh	GPE
iajs-3028	195	2	sm.	GPE
iajs-3028	197	1	2019	DATE
iajs-3028	197	2	13	DATE
iajs-3028	197	3	2	DATE
iajs-3028	197	4	93–110	DATE
iajs-3028	198	1	4	CARDINAL
iajs-3028	198	2	davvaz	ORG
iajs-3028	198	3	b.	PERSON
iajs-3028	198	4	salasi, a.	PERSON
iajs-3028	199	1	2006	DATE
iajs-3028	199	2	34,12	CARDINAL
iajs-3028	199	3	4389–400	CARDINAL
iajs-3028	200	1	5	CARDINAL
iajs-3028	200	2	abumghaiseeb	ORG
iajs-3028	200	3	a. on 𝜹-primary hyperideals	ORG
iajs-3028	200	4	turkey	GPE
iajs-3028	200	5	yildiz technical university graduate school	ORG
iajs-3028	200	6	2018	DATE
iajs-3028	200	7	phd thesis	PERSON
iajs-3028	201	1	6.	PERCENT
iajs-3028	201	2	bordbar	GPE
iajs-3028	201	3	m.; cristea	PERSON
iajs-3028	201	4	i.	PERSON
iajs-3028	203	1	2020	DATE
iajs-3028	203	2	2050019	DATE
iajs-3028	204	1	7	CARDINAL
iajs-3028	207	1	13	CARDINAL
iajs-3028	207	2	oct 2021	DATE
iajs-3028	207	3	d.	NORP
iajs-3028	207	4	davvaz	ORG
iajs-3028	207	5	b.	PERSON
iajs-3028	207	6	quotients	ORG
iajs-3028	208	1	ital	ORG
iajs-3028	210	1	2020	DATE
iajs-3028	210	2	44	DATE
iajs-3028	210	3	938–951	CARDINAL
iajs-3028	211	1	1	CARDINAL
iajs-3028	211	2	1	CARDINAL
iajs-3028	211	3	0	CARDINAL
iajs-3028	211	4	1	CARDINAL