id	sid	eid	entity	type
ejpam-4432	1	1	european journal	ORG
ejpam-4432	2	1	15	CARDINAL
ejpam-4432	2	2	3	CARDINAL
ejpam-4432	2	3	2022	CARDINAL
ejpam-4432	2	4	1402	CARDINAL
ejpam-4432	2	5	new york	GPE
ejpam-4432	2	6	global annihilator	ORG
ejpam-4432	2	7	hani abughazalah2,∗ 1 department	ORG
ejpam-4432	2	8	science	ORG
ejpam-4432	2	9	tanta university	ORG
ejpam-4432	2	10	egypt 1,2	ORG
ejpam-4432	2	11	mathematical sciences department	ORG
ejpam-4432	2	12	bint abdulrahman university	ORG
ejpam-4432	2	13	84428	DATE
ejpam-4432	3	1	saudi arabia	GPE
ejpam-4432	9	1	2020	DATE
ejpam-4432	9	2	06b75	CARDINAL
ejpam-4432	9	3	06f99	DATE
ejpam-4432	9	4	08a05	CARDINAL
ejpam-4432	9	5	m. konstantinidou	PERSON
ejpam-4432	9	6	j. mittas	PERSON
ejpam-4432	9	7	1977	DATE
ejpam-4432	10	1	12	CARDINAL
ejpam-4432	11	1	m. konstantinidou	PERSON
ejpam-4432	11	2	10	CARDINAL
ejpam-4432	11	3	9	CARDINAL
ejpam-4432	12	1	15	CARDINAL
ejpam-4432	13	1	m. amiri bideshki	PERSON
ejpam-4432	13	2	11	CARDINAL
ejpam-4432	15	1	19	CARDINAL
ejpam-4432	15	2	8	CARDINAL
ejpam-4432	16	1	zero	CARDINAL
ejpam-4432	17	1	1970	DATE
ejpam-4432	17	2	13	CARDINAL
ejpam-4432	20	1	w. h. cornish	PERSON
ejpam-4432	20	2	the annihilator ∗corresponding	ORG
ejpam-4432	21	1	eman.rezk@science.tanta.edu.eg	PERSON
ejpam-4432	21	2	n.h. abughazalah	GPE
ejpam-4432	21	3	1402	CARDINAL
ejpam-4432	22	1	2022	CARDINAL
ejpam-4432	23	1	rezk	GPE
ejpam-4432	23	2	n.h.	GPE
ejpam-4432	24	1	j. pure	PERSON
ejpam-4432	24	2	15	CARDINAL
ejpam-4432	24	3	3	CARDINAL
ejpam-4432	24	4	2022	CARDINAL
ejpam-4432	24	5	1402-1416 1403	DATE
ejpam-4432	24	6	18	CARDINAL
ejpam-4432	25	1	zero	CARDINAL
ejpam-4432	26	1	cornish	NORP
ejpam-4432	26	2	two	CARDINAL
ejpam-4432	26	3	zero	CARDINAL
ejpam-4432	27	1	two	CARDINAL
ejpam-4432	28	1	1	CARDINAL
ejpam-4432	28	2	b. a. davey	PERSON
ejpam-4432	28	3	nieminen	PERSON
ejpam-4432	31	1	6	CARDINAL
ejpam-4432	32	1	4	CARDINAL
ejpam-4432	33	1	17	CARDINAL
ejpam-4432	34	1	7	CARDINAL
ejpam-4432	35	1	14	CARDINAL
ejpam-4432	37	1	section 2	LAW
ejpam-4432	38	1	section 3	DATE
ejpam-4432	39	1	section 4	LAW
ejpam-4432	41	1	section 5	LAW
ejpam-4432	42	1	2	CARDINAL
ejpam-4432	44	1	2	CARDINAL
ejpam-4432	44	2	5	CARDINAL
ejpam-4432	45	1	1	CARDINAL
ejpam-4432	46	1	11	CARDINAL
ejpam-4432	46	2	l, ∧̄ :	DATE
ejpam-4432	46	3	l × l	ORG
ejpam-4432	48	1	∈	ORG
ejpam-4432	48	2	ia	GPE
ejpam-4432	49	1	ia ∨ ibi = ib ∨	PERSON
ejpam-4432	49	2	h4	ORG
ejpam-4432	49	3	∈	ORG
ejpam-4432	49	4	ai∧̄i(a	ORG
ejpam-4432	49	5	∩ i(a	ORG
ejpam-4432	49	6	∈	ORG
ejpam-4432	49	7	two	CARDINAL
ejpam-4432	49	8	0	CARDINAL
ejpam-4432	49	9	1	CARDINAL
ejpam-4432	49	10	0 ≤	MONEY
ejpam-4432	49	11	∈	ORG
ejpam-4432	49	12	rezk	GPE
ejpam-4432	49	13	n.h.	GPE
ejpam-4432	50	1	j. pure	PERSON
ejpam-4432	50	2	15	CARDINAL
ejpam-4432	50	3	3	CARDINAL
ejpam-4432	50	4	2022	CARDINAL
ejpam-4432	50	5	1402-1416 1404	DATE
ejpam-4432	50	6	⊆	CARDINAL
ejpam-4432	51	1	ia ∈	PERSON
ejpam-4432	51	2	ia ∈	PERSON
ejpam-4432	52	1	1	CARDINAL
ejpam-4432	53	1	11	CARDINAL
ejpam-4432	56	1	1	CARDINAL
ejpam-4432	56	2	ia	GPE
ejpam-4432	56	3	∈	ORG
ejpam-4432	57	1	∨ i(bi∧̄ic	PERSON
ejpam-4432	58	1	∨ ic	PERSON
ejpam-4432	58	2	ai∧̄ib)i ∨ i(ai∧̄ic	ORG
ejpam-4432	59	1	2	CARDINAL
ejpam-4432	60	1	11	CARDINAL
ejpam-4432	62	1	∈	ORG
ejpam-4432	63	1	∩	PERSON
ejpam-4432	63	2	ai ∨ ib	PERSON
ejpam-4432	63	3	∈	ORG
ejpam-4432	64	1	1	CARDINAL
ejpam-4432	65	1	11	CARDINAL
ejpam-4432	65	2	0	DATE
ejpam-4432	66	1	3	CARDINAL
ejpam-4432	67	1	11	CARDINAL
ejpam-4432	67	2	⊆	CARDINAL
ejpam-4432	67	3	∈	ORG
ejpam-4432	67	4	annihilator hyperideal	PERSON
ejpam-4432	69	1	2	CARDINAL
ejpam-4432	70	1	11	CARDINAL
ejpam-4432	71	1	0r	CARDINAL
ejpam-4432	72	1	⊆	CARDINAL
ejpam-4432	72	2	rezk	GPE
ejpam-4432	72	3	n.h.	GPE
ejpam-4432	73	1	j. pure	PERSON
ejpam-4432	73	2	15	CARDINAL
ejpam-4432	73	3	3	CARDINAL
ejpam-4432	73	4	2022	CARDINAL
ejpam-4432	73	5	1402-1416 1405	DATE
ejpam-4432	74	1	⊆	CARDINAL
ejpam-4432	74	2	⊆	CARDINAL
ejpam-4432	74	3	⊆	CARDINAL
ejpam-4432	75	1	0	CARDINAL
ejpam-4432	75	2	1	CARDINAL
ejpam-4432	76	1	3	CARDINAL
ejpam-4432	78	1	2	CARDINAL
ejpam-4432	80	1	⊆	CARDINAL
ejpam-4432	81	1	⊆	CARDINAL
ejpam-4432	81	2	ir ∨ jr)r	ORG
ejpam-4432	81	3	ir ∩ jr	PERSON
ejpam-4432	82	1	∨	ORG
ejpam-4432	82	2	⊆	CARDINAL
ejpam-4432	82	3	∩ jrr	PERSON
ejpam-4432	82	4	1r	CARDINAL
ejpam-4432	82	5	⊆	PRODUCT
ejpam-4432	82	6	⊆	CARDINAL
ejpam-4432	82	7	ir ∩	PERSON
ejpam-4432	82	8	1r	CARDINAL
ejpam-4432	82	9	⊆	CARDINAL
ejpam-4432	82	10	1r	CARDINAL
ejpam-4432	82	11	1rr	CARDINAL
ejpam-4432	82	12	l. proof	PERSON
ejpam-4432	84	1	i.	PERSON
ejpam-4432	84	2	⊆	CARDINAL
ejpam-4432	85	1	⊆	CARDINAL
ejpam-4432	85	2	ir ⊆	ORG
ejpam-4432	86	1	⊆	CARDINAL
ejpam-4432	86	2	2	CARDINAL
ejpam-4432	88	1	rezk	GPE
ejpam-4432	88	2	n.h.	GPE
ejpam-4432	89	1	j. pure	PERSON
ejpam-4432	89	2	15	CARDINAL
ejpam-4432	89	3	3	CARDINAL
ejpam-4432	89	4	2022	CARDINAL
ejpam-4432	89	5	1402-1416 1406	DATE
ejpam-4432	89	6	ir ∨ jr.	PERSON
ejpam-4432	91	1	j ∈ jr	PERSON
ejpam-4432	92	1	⊆	CARDINAL
ejpam-4432	92	2	∨ j	ORG
ejpam-4432	92	3	x∧̄i	ORG
ejpam-4432	93	1	x∧̄i	ORG
ejpam-4432	93	2	0 ∈	CARDINAL
ejpam-4432	95	1	2	CARDINAL
ejpam-4432	95	2	0 ∈	CARDINAL
ejpam-4432	96	1	∈	ORG
ejpam-4432	96	2	ir ∨ jr)r	PERSON
ejpam-4432	96	3	⊆	CARDINAL
ejpam-4432	98	1	⊆	CARDINAL
ejpam-4432	98	2	ir ∩ jr.	PERSON
ejpam-4432	98	3	ir ∩ jr	PERSON
ejpam-4432	98	4	0 ∈	CARDINAL
ejpam-4432	98	5	∨ j	PERSON
ejpam-4432	99	1	⊆	CARDINAL
ejpam-4432	104	1	ir ∩ jr ⊆	ORG
ejpam-4432	105	1	⊆	CARDINAL
ejpam-4432	106	1	⊆	CARDINAL
ejpam-4432	107	1	vi	PERSON
ejpam-4432	107	2	∈	ORG
ejpam-4432	107	3	1r	CARDINAL
ejpam-4432	109	1	2	CARDINAL
ejpam-4432	109	2	0 ∈ x∧̄y	CARDINAL
ejpam-4432	110	1	2	CARDINAL
ejpam-4432	110	2	ir ∩	PERSON
ejpam-4432	111	1	∈	ORG
ejpam-4432	111	2	1r	CARDINAL
ejpam-4432	111	3	⊆	PRODUCT
ejpam-4432	112	1	1r	CARDINAL
ejpam-4432	112	2	∈	ORG
ejpam-4432	113	1	1r	CARDINAL
ejpam-4432	113	2	⊆	MONEY
ejpam-4432	113	3	i∪ir)r = ir∩irr	ORG
ejpam-4432	114	1	ir ∩	PERSON
ejpam-4432	114	2	1r	CARDINAL
ejpam-4432	115	1	⊆	CARDINAL
ejpam-4432	115	2	jrr	ORG
ejpam-4432	115	3	i ∩ jrr ⊆ jr ∩ jrr	ORG
ejpam-4432	115	4	1r	CARDINAL
ejpam-4432	116	1	1r	CARDINAL
ejpam-4432	117	1	1rr	ORDINAL
ejpam-4432	117	2	0	CARDINAL
ejpam-4432	118	1	4	CARDINAL
ejpam-4432	121	1	rezk	GPE
ejpam-4432	121	2	n.h.	GPE
ejpam-4432	122	1	j. pure	PERSON
ejpam-4432	122	2	15	CARDINAL
ejpam-4432	122	3	3	CARDINAL
ejpam-4432	122	4	2022	CARDINAL
ejpam-4432	122	5	1402-1416 1407	DATE
ejpam-4432	122	6	1	CARDINAL
ejpam-4432	124	1	jand k	PERSON
ejpam-4432	125	1	ir ∨	PERSON
ejpam-4432	125	2	∩ jrr	PERSON
ejpam-4432	125	3	1r	CARDINAL
ejpam-4432	125	4	⊆	CARDINAL
ejpam-4432	125	5	k ∩	PERSON
ejpam-4432	125	6	ir ∩ jr)r ⊆	ORG
ejpam-4432	125	7	ir ∩	ORG
ejpam-4432	125	8	j ∩k)r	PERSON
ejpam-4432	127	1	jr ⊆	PERSON
ejpam-4432	127	2	ir ∨ jr then	PERSON
ejpam-4432	127	3	2	CARDINAL
ejpam-4432	127	4	ir ∨ jr)r ⊆	ORG
ejpam-4432	128	1	ir ∨ jr)r	ORG
ejpam-4432	128	2	⊆	CARDINAL
ejpam-4432	128	3	ir ∨ jr)r ⊆	ORG
ejpam-4432	128	4	2	CARDINAL
ejpam-4432	130	1	2	CARDINAL
ejpam-4432	131	1	1r	CARDINAL
ejpam-4432	132	1	2	CARDINAL
ejpam-4432	133	1	k ∩ ir ∩	PERSON
ejpam-4432	133	2	j ∩k)r ⊆	PERSON
ejpam-4432	133	3	1	CARDINAL
ejpam-4432	133	4	j ∩k ∩	PERSON
ejpam-4432	133	5	ir ∩	PERSON
ejpam-4432	133	6	j ∩k)r	PERSON
ejpam-4432	134	1	j ∩k	PERSON
ejpam-4432	134	2	jrr ∩krr	ORG
ejpam-4432	134	3	j ∩k)rr ∩	WORK_OF_ART
ejpam-4432	135	1	1r	CARDINAL
ejpam-4432	135	2	2	CARDINAL
ejpam-4432	136	1	1r	CARDINAL
ejpam-4432	136	2	k ∩ ir ∩	PERSON
ejpam-4432	136	3	j ∩k)r ⊆	PERSON
ejpam-4432	136	4	2	CARDINAL
ejpam-4432	136	5	1	CARDINAL
ejpam-4432	136	6	2	CARDINAL
ejpam-4432	136	7	k ∩ ir ∩	ORG
ejpam-4432	136	8	j ∩k)r ⊆	PERSON
ejpam-4432	137	1	k ∩ ir ∩	PERSON
ejpam-4432	137	2	j ∩k)r	PERSON
ejpam-4432	137	3	ir ∩ jr)r	PERSON
ejpam-4432	137	4	1r	CARDINAL
ejpam-4432	137	5	rezk	GPE
ejpam-4432	137	6	n.h.	GPE
ejpam-4432	138	1	j. pure	PERSON
ejpam-4432	138	2	15	CARDINAL
ejpam-4432	138	3	3	CARDINAL
ejpam-4432	138	4	2022	CARDINAL
ejpam-4432	138	5	1402-1416 1408	DATE
ejpam-4432	138	6	ir ∩	PERSON
ejpam-4432	138	7	j ∩k)r ∩	PERSON
ejpam-4432	138	8	k ∩	PERSON
ejpam-4432	138	9	ir ∩ jr)r	PERSON
ejpam-4432	139	1	1r	CARDINAL
ejpam-4432	140	1	k ∩	PERSON
ejpam-4432	140	2	ir ∩ jr)r ⊆	ORG
ejpam-4432	140	3	ir ∩	ORG
ejpam-4432	140	4	j ∩k)r	PERSON
ejpam-4432	141	1	two	CARDINAL
ejpam-4432	144	1	ir ∩jr)r	PERSON
ejpam-4432	146	1	ir ∩ jr)r	ORG
ejpam-4432	147	1	3	CARDINAL
ejpam-4432	149	1	1r	CARDINAL
ejpam-4432	154	1	iri ∩	ORG
ejpam-4432	155	1	iri ∩	ORG
ejpam-4432	155	2	i(ji	PERSON
ejpam-4432	156	1	second	ORDINAL
ejpam-4432	157	1	j ∩k	PERSON
ejpam-4432	159	1	ir ⊆	ORG
ejpam-4432	159	2	ir ∩	PERSON
ejpam-4432	159	3	i.	PERSON
ejpam-4432	159	4	ir ∩ jr ⊆ ir	PERSON
ejpam-4432	160	1	⊆	CARDINAL
ejpam-4432	160	2	ir ∩ jr	PERSON
ejpam-4432	162	1	ir ∩ jr)r	PERSON
ejpam-4432	162	2	⊆	CARDINAL
ejpam-4432	162	3	0r	MONEY
ejpam-4432	162	4	∈	ORG
ejpam-4432	163	1	1r	CARDINAL
ejpam-4432	163	2	1rr	ORDINAL
ejpam-4432	163	3	1	CARDINAL
ejpam-4432	163	4	k ∩	PERSON
ejpam-4432	163	5	⊆	CARDINAL
ejpam-4432	163	6	j ∩k	PERSON
ejpam-4432	163	7	3	CARDINAL
ejpam-4432	163	8	3	CARDINAL
ejpam-4432	163	9	rezk	GPE
ejpam-4432	163	10	n.h.	GPE
ejpam-4432	164	1	j. pure	PERSON
ejpam-4432	164	2	15	CARDINAL
ejpam-4432	164	3	3	CARDINAL
ejpam-4432	164	4	2022	CARDINAL
ejpam-4432	164	5	1402-1416 1409	DATE
ejpam-4432	166	1	⊆	CARDINAL
ejpam-4432	167	1	i(k ∩	PERSON
ejpam-4432	167	2	3	CARDINAL
ejpam-4432	167	3	i(k ∩ j	PERSON
ejpam-4432	168	1	j ∩ k ⊆	PERSON
ejpam-4432	168	2	⊆	CARDINAL
ejpam-4432	168	3	ik	PERSON
ejpam-4432	168	4	ii	PERSON
ejpam-4432	168	5	i(j ∩k	PRODUCT
ejpam-4432	169	1	⊆	CARDINAL
ejpam-4432	170	1	4	CARDINAL
ejpam-4432	170	2	i(j ∩k	PERSON
ejpam-4432	170	3	3	CARDINAL
ejpam-4432	170	4	4	CARDINAL
ejpam-4432	172	1	1	CARDINAL
ejpam-4432	172	2	1	CARDINAL
ejpam-4432	172	3	2	CARDINAL
ejpam-4432	172	4	meethyberlattice l	ORG
ejpam-4432	172	5	0	CARDINAL
ejpam-4432	172	6	γ	GPE
ejpam-4432	172	7	1	CARDINAL
ejpam-4432	173	1	1	CARDINAL
ejpam-4432	173	2	l.	GPE
ejpam-4432	174	1	1	CARDINAL
ejpam-4432	174	2	0	CARDINAL
ejpam-4432	174	3	0	CARDINAL
ejpam-4432	174	4	0	CARDINAL
ejpam-4432	174	5	0	CARDINAL
ejpam-4432	174	6	0	CARDINAL
ejpam-4432	174	7	0	CARDINAL
ejpam-4432	174	8	0	CARDINAL
ejpam-4432	174	9	0	CARDINAL
ejpam-4432	174	10	0	CARDINAL
ejpam-4432	174	11	0	CARDINAL
ejpam-4432	174	12	0	CARDINAL
ejpam-4432	174	13	0	CARDINAL
ejpam-4432	174	14	0	CARDINAL
ejpam-4432	174	15	0	CARDINAL
ejpam-4432	174	16	0	CARDINAL
ejpam-4432	174	17	0	CARDINAL
ejpam-4432	174	18	0	CARDINAL
ejpam-4432	174	19	0	CARDINAL
ejpam-4432	174	20	0	CARDINAL
ejpam-4432	174	21	0	CARDINAL
ejpam-4432	174	22	0	CARDINAL
ejpam-4432	174	23	1	CARDINAL
ejpam-4432	174	24	0	CARDINAL
ejpam-4432	174	25	0	CARDINAL
ejpam-4432	174	26	1	CARDINAL
ejpam-4432	175	1	1	CARDINAL
ejpam-4432	176	1	γ γ δ 1	FAC
ejpam-4432	176	2	1 1	CARDINAL
ejpam-4432	176	3	0 1 1 δ	QUANTITY
ejpam-4432	176	4	1	CARDINAL
ejpam-4432	176	5	2	CARDINAL
ejpam-4432	176	6	0	CARDINAL
ejpam-4432	176	7	0	CARDINAL
ejpam-4432	176	8	1r	CARDINAL
ejpam-4432	176	9	0	CARDINAL
ejpam-4432	176	10	1r	CARDINAL
ejpam-4432	177	1	4	CARDINAL
ejpam-4432	177	2	annihilator hyperideal	PERSON
ejpam-4432	180	1	5	CARDINAL
ejpam-4432	181	1	two	CARDINAL
ejpam-4432	182	1	ϕ(a ∨	PERSON
ejpam-4432	183	1	rezk	GPE
ejpam-4432	183	2	n.h.	GPE
ejpam-4432	184	1	j. pure	PERSON
ejpam-4432	184	2	15	CARDINAL
ejpam-4432	184	3	3	CARDINAL
ejpam-4432	184	4	2022	CARDINAL
ejpam-4432	184	5	1402-1416 1410	DATE
ejpam-4432	186	1	0′	CARDINAL
ejpam-4432	186	2	0	CARDINAL
ejpam-4432	186	3	0′	CARDINAL
ejpam-4432	186	4	zero	CARDINAL
ejpam-4432	188	1	0′	CARDINAL
ejpam-4432	190	1	one	CARDINAL
ejpam-4432	190	2	2	CARDINAL
ejpam-4432	190	3	3	CARDINAL
ejpam-4432	190	4	4	CARDINAL
ejpam-4432	190	5	meethyberlattice	ORG
ejpam-4432	190	6	0′	CARDINAL
ejpam-4432	191	1	∧̄	ORDINAL
ejpam-4432	192	1	1′ 0′	DATE
ejpam-4432	192	2	0′	CARDINAL
ejpam-4432	192	3	0′	CARDINAL
ejpam-4432	192	4	0′	CARDINAL
ejpam-4432	192	5	0′	CARDINAL
ejpam-4432	192	6	0′	CARDINAL
ejpam-4432	192	7	0′	CARDINAL
ejpam-4432	192	8	0′	CARDINAL
ejpam-4432	192	9	0′	CARDINAL
ejpam-4432	192	10	0′	CARDINAL
ejpam-4432	192	11	0′	CARDINAL
ejpam-4432	192	12	0′	CARDINAL
ejpam-4432	192	13	1′	CARDINAL
ejpam-4432	193	1	1′	ORDINAL
ejpam-4432	195	1	1′ 1′ 1′ 1′ 1′ 1′ 1′	DATE
ejpam-4432	195	2	3	CARDINAL
ejpam-4432	195	3	4	CARDINAL
ejpam-4432	195	4	1	CARDINAL
ejpam-4432	196	1	f(0	PERSON
ejpam-4432	196	2	0′	CARDINAL
ejpam-4432	197	1	f(δ	PERSON
ejpam-4432	198	1	1′.	CARDINAL
ejpam-4432	200	1	ϕ(i	EVENT
ejpam-4432	200	2	l′	PERSON
ejpam-4432	200	3	⊆	CARDINAL
ejpam-4432	200	4	ϕ(a))r	ORG
ejpam-4432	201	1	y ∈ ϕ(i	PERSON
ejpam-4432	202	1	ϕ(a ∨	GPE
ejpam-4432	203	1	⊆	CARDINAL
ejpam-4432	205	1	∈ ϕ(a)∧̄ϕ(b	ORG
ejpam-4432	206	1	∈	ORG
ejpam-4432	206	2	∈	ORG
ejpam-4432	208	1	ϕ(i	WORK_OF_ART
ejpam-4432	210	1	∈	ORG
ejpam-4432	215	1	ϕ(a ∨	PERSON
ejpam-4432	217	1	∨	CARDINAL
ejpam-4432	220	1	∈	ORG
ejpam-4432	221	1	∈	ORG
ejpam-4432	223	1	ϕ(y	ORG
ejpam-4432	223	2	∨ ϕ(a	PERSON
ejpam-4432	224	1	ϕ(y	ORG
ejpam-4432	226	1	ϕ(y	ORG
ejpam-4432	228	1	0′	CARDINAL
ejpam-4432	228	2	∈	ORG
ejpam-4432	228	3	ϕ−1(0′	PERSON
ejpam-4432	228	4	⊆	CARDINAL
ejpam-4432	229	1	rezk	GPE
ejpam-4432	229	2	n.h.	GPE
ejpam-4432	230	1	j. pure	PERSON
ejpam-4432	230	2	15	CARDINAL
ejpam-4432	230	3	3	CARDINAL
ejpam-4432	230	4	2022	CARDINAL
ejpam-4432	230	5	1402-1416 1411	DATE
ejpam-4432	230	6	ϕ(x	LOC
ejpam-4432	230	7	0′	CARDINAL
ejpam-4432	231	1	∈ ϕ(x ∧	ORG
ejpam-4432	231	2	ϕ(a	CARDINAL
ejpam-4432	231	3	ϕ(a	PRODUCT
ejpam-4432	233	1	⊆	CARDINAL
ejpam-4432	235	1	6	CARDINAL
ejpam-4432	237	1	annihilator hyperideal	PERSON
ejpam-4432	239	1	2	CARDINAL
ejpam-4432	241	1	3	CARDINAL
ejpam-4432	241	2	5	CARDINAL
ejpam-4432	241	3	6	CARDINAL
ejpam-4432	241	4	0	CARDINAL
ejpam-4432	241	5	γ	GPE
ejpam-4432	241	6	1	CARDINAL
ejpam-4432	243	1	1	CARDINAL
ejpam-4432	243	2	0	CARDINAL
ejpam-4432	243	3	0	CARDINAL
ejpam-4432	243	4	0	CARDINAL
ejpam-4432	243	5	0	CARDINAL
ejpam-4432	243	6	0	CARDINAL
ejpam-4432	243	7	0	CARDINAL
ejpam-4432	243	8	0	CARDINAL
ejpam-4432	243	9	0	CARDINAL
ejpam-4432	243	10	0	CARDINAL
ejpam-4432	243	11	0	CARDINAL
ejpam-4432	243	12	0	CARDINAL
ejpam-4432	243	13	0	CARDINAL
ejpam-4432	243	14	1	CARDINAL
ejpam-4432	243	15	0	CARDINAL
ejpam-4432	243	16	1	CARDINAL
ejpam-4432	244	1	1	CARDINAL
ejpam-4432	245	1	γ γ δ 1	FAC
ejpam-4432	245	2	1 1	CARDINAL
ejpam-4432	245	3	0 1 1 δ	QUANTITY
ejpam-4432	245	4	5	CARDINAL
ejpam-4432	245	5	6	CARDINAL
ejpam-4432	245	6	0′	CARDINAL
ejpam-4432	245	7	g(γ	ORG
ejpam-4432	247	1	2	CARDINAL
ejpam-4432	248	1	4	CARDINAL
ejpam-4432	249	1	two	CARDINAL
ejpam-4432	249	2	0	CARDINAL
ejpam-4432	250	1	annihilator hyperideal	PERSON
ejpam-4432	251	1	annihilator hyperideal	PERSON
ejpam-4432	253	1	⊆	CARDINAL
ejpam-4432	254	1	3	CARDINAL
ejpam-4432	256	1	⊆	CARDINAL
ejpam-4432	258	1	ϕ(a)]r ⊆	ORG
ejpam-4432	258	2	∈	ORG
ejpam-4432	259	1	0′	CARDINAL
ejpam-4432	259	2	0	CARDINAL
ejpam-4432	259	3	∈	ORG
ejpam-4432	259	4	∈	ORG
ejpam-4432	260	1	rezk	GPE
ejpam-4432	260	2	n.h.	GPE
ejpam-4432	261	1	j. pure	PERSON
ejpam-4432	261	2	15	CARDINAL
ejpam-4432	261	3	3	CARDINAL
ejpam-4432	261	4	2022	CARDINAL
ejpam-4432	261	5	1402-1416 1412	DATE
ejpam-4432	267	1	0 ∈	CARDINAL
ejpam-4432	268	1	0′	CARDINAL
ejpam-4432	270	1	ϕ(x	ORG
ejpam-4432	272	1	0′	CARDINAL
ejpam-4432	274	1	∈	ORG
ejpam-4432	274	2	∈	ORG
ejpam-4432	274	3	⊆	CARDINAL
ejpam-4432	275	1	⊆	CARDINAL
ejpam-4432	275	2	ϕ−1(b	MONEY
ejpam-4432	278	1	0′	CARDINAL
ejpam-4432	279	1	ϕ(x	LOC
ejpam-4432	279	2	ϕ−1(br	PERSON
ejpam-4432	280	1	ϕ−1(br	PERSON
ejpam-4432	281	1	ϕ−1(br	PERSON
ejpam-4432	281	2	ϕ−1(b	MONEY
ejpam-4432	282	1	ϕ(x	LOC
ejpam-4432	284	1	0′	CARDINAL
ejpam-4432	286	1	ϕ−1(b	MONEY
ejpam-4432	288	1	ϕ−1(br	PERSON
ejpam-4432	289	1	⊆	CARDINAL
ejpam-4432	289	2	5	CARDINAL
ejpam-4432	290	1	two	CARDINAL
ejpam-4432	290	2	0	CARDINAL
ejpam-4432	291	1	annihilator hyperideal	PERSON
ejpam-4432	291	2	ϕ(i	WORK_OF_ART
ejpam-4432	291	3	annihilator hyperideal	PERSON
ejpam-4432	291	4	annihilator hyperideal	PERSON
ejpam-4432	291	5	preimage	ORG
ejpam-4432	291	6	annihilator hyperideal j	PERSON
ejpam-4432	291	7	annihilator hyperideal	PERSON
ejpam-4432	292	1	3,	DATE
ejpam-4432	293	1	annihilator hyperideal	PERSON
ejpam-4432	293	2	ϕ(i	WORK_OF_ART
ejpam-4432	294	1	ϕ(i	EVENT
ejpam-4432	294	2	3	CARDINAL
ejpam-4432	294	3	ϕ−1(i	PERSON
ejpam-4432	295	1	annihilator hyperideal	PERSON
ejpam-4432	297	1	ϕ−1(i	PERSON
ejpam-4432	298	1	ϕ−1(i	PERSON
ejpam-4432	298	2	0′	CARDINAL
ejpam-4432	298	3	1r	CARDINAL
ejpam-4432	298	4	annihilator hyperideal	PERSON
ejpam-4432	299	1	annihilator hyperideal	PERSON
ejpam-4432	300	1	rezk	GPE
ejpam-4432	300	2	n.h.	GPE
ejpam-4432	301	1	j. pure	PERSON
ejpam-4432	301	2	15	CARDINAL
ejpam-4432	301	3	3	CARDINAL
ejpam-4432	301	4	2022	CARDINAL
ejpam-4432	301	5	1402	CARDINAL
ejpam-4432	301	6	1	CARDINAL
ejpam-4432	302	1	two	CARDINAL
ejpam-4432	306	1	4	CARDINAL
ejpam-4432	307	1	3	CARDINAL
ejpam-4432	307	2	2	CARDINAL
ejpam-4432	308	1	3	CARDINAL
ejpam-4432	308	2	2	CARDINAL
ejpam-4432	308	3	0	CARDINAL
ejpam-4432	308	4	0	CARDINAL
ejpam-4432	308	5	1r	CARDINAL
ejpam-4432	308	6	1r	CARDINAL
ejpam-4432	308	7	l′′	GPE
ejpam-4432	308	8	0	CARDINAL
ejpam-4432	308	9	0	CARDINAL
ejpam-4432	308	10	0′	CARDINAL
ejpam-4432	308	11	1r	CARDINAL
ejpam-4432	309	1	5	CARDINAL
ejpam-4432	310	1	7	CARDINAL
ejpam-4432	311	1	⊆	CARDINAL
ejpam-4432	311	2	meet-hyperlattice l	ORG
ejpam-4432	312	1	6	CARDINAL
ejpam-4432	313	1	s. proof	PERSON
ejpam-4432	315	1	∈	ORG
ejpam-4432	315	2	k ∩	ORG
ejpam-4432	316	1	rezk	GPE
ejpam-4432	316	2	n.h.	GPE
ejpam-4432	317	1	j. pure	PERSON
ejpam-4432	317	2	15	CARDINAL
ejpam-4432	317	3	3	CARDINAL
ejpam-4432	317	4	2022	CARDINAL
ejpam-4432	317	5	1402	CARDINAL
ejpam-4432	317	6	1416 1414	CARDINAL
ejpam-4432	317	7	2	CARDINAL
ejpam-4432	318	1	s. example	ORG
ejpam-4432	319	1	5	CARDINAL
ejpam-4432	319	2	7	CARDINAL
ejpam-4432	319	3	8	CARDINAL
ejpam-4432	319	4	meet-hyperlattice l	ORG
ejpam-4432	319	5	1	CARDINAL
ejpam-4432	319	6	4	CARDINAL
ejpam-4432	319	7	h(s	PERSON
ejpam-4432	319	8	s.	GPE
ejpam-4432	320	1	0	CARDINAL
ejpam-4432	320	2	0	CARDINAL
ejpam-4432	320	3	0	CARDINAL
ejpam-4432	320	4	0	CARDINAL
ejpam-4432	320	5	0	CARDINAL
ejpam-4432	320	6	0	CARDINAL
ejpam-4432	320	7	0	CARDINAL
ejpam-4432	320	8	0	CARDINAL
ejpam-4432	320	9	0	CARDINAL
ejpam-4432	320	10	0	CARDINAL
ejpam-4432	320	11	0	CARDINAL
ejpam-4432	320	12	γ γ	ORG
ejpam-4432	320	13	7	CARDINAL
ejpam-4432	320	14	8	CARDINAL
ejpam-4432	320	15	1r	CARDINAL
ejpam-4432	320	16	0	CARDINAL
ejpam-4432	320	17	figure4	PERSON
ejpam-4432	320	18	1r	CARDINAL
ejpam-4432	320	19	8	CARDINAL
ejpam-4432	321	1	01	DATE
ejpam-4432	321	2	11	CARDINAL
ejpam-4432	321	3	12	CARDINAL
ejpam-4432	321	4	two	CARDINAL
ejpam-4432	322	1	a′	ORG
ejpam-4432	323	1	a′	ORG
ejpam-4432	323	2	zero	CARDINAL
ejpam-4432	323	3	0	CARDINAL
ejpam-4432	324	1	01, 02	DATE
ejpam-4432	324	2	one	CARDINAL
ejpam-4432	324	3	11	CARDINAL
ejpam-4432	324	4	12	CARDINAL
ejpam-4432	326	1	7	CARDINAL
ejpam-4432	326	2	two	CARDINAL
ejpam-4432	326	3	two	CARDINAL
ejpam-4432	327	1	i1	ORG
ejpam-4432	327	2	i2	ORG
ejpam-4432	329	1	i1	ORG
ejpam-4432	330	1	some two	CARDINAL
ejpam-4432	330	2	⊆	MONEY
ejpam-4432	331	1	0i	CARDINAL
ejpam-4432	331	2	∈	ORG
ejpam-4432	331	3	1	CARDINAL
ejpam-4432	331	4	2	CARDINAL
ejpam-4432	331	5	01, 02	DATE
ejpam-4432	331	6	x2)∧̄(a1	PERSON
ejpam-4432	332	1	i1 × i2	ORG
ejpam-4432	333	1	1415	CARDINAL
ejpam-4432	334	1	k ⊆ l1 ×	ORG
ejpam-4432	335	1	li	PERSON
ejpam-4432	335	2	1	CARDINAL
ejpam-4432	335	3	2	CARDINAL
ejpam-4432	338	1	1	CARDINAL
ejpam-4432	338	2	2	CARDINAL
ejpam-4432	339	1	01, 02	DATE
ejpam-4432	339	2	x2)∧̄(a1	PERSON
ejpam-4432	340	1	∈	ORG
ejpam-4432	340	2	0i	CARDINAL
ejpam-4432	340	3	∈	ORG
ejpam-4432	341	1	π1(i)×	PERSON
ejpam-4432	342	1	3	CARDINAL
ejpam-4432	343	1	two	CARDINAL
ejpam-4432	343	2	two	CARDINAL
ejpam-4432	344	1	i1×i2	ORG
ejpam-4432	345	1	6.	CARDINAL
ejpam-4432	349	1	homomorphisms	ORG
ejpam-4432	352	1	two	CARDINAL
ejpam-4432	352	2	one	CARDINAL
ejpam-4432	352	3	boolean algebras	ORG
ejpam-4432	355	1	1	CARDINAL
ejpam-4432	355	2	j nieminen	PERSON
ejpam-4432	357	1	22(2-3):154–158	CARDINAL
ejpam-4432	357	2	1986	DATE
ejpam-4432	358	1	2	CARDINAL
ejpam-4432	360	1	univ. of press	ORG
ejpam-4432	360	2	columbia	GPE
ejpam-4432	360	3	1974	DATE
ejpam-4432	361	1	3	CARDINAL
ejpam-4432	363	1	4:733–746, 2009	DATE
ejpam-4432	364	1	4	CARDINAL
ejpam-4432	365	1	0	CARDINAL
ejpam-4432	369	1	11(1):1–13	CARDINAL
ejpam-4432	369	2	2021	CARDINAL
ejpam-4432	370	1	5	CARDINAL
ejpam-4432	372	1	springer basel	PERSON
ejpam-4432	372	2	2011	DATE
ejpam-4432	373	1	1416	CARDINAL
ejpam-4432	373	2	6	CARDINAL
ejpam-4432	375	1	czechoslovak mathematical journal	ORG
ejpam-4432	375	2	45:127–134, 1995	DATE
ejpam-4432	377	1	annihilators inbck-algebras	PERSON
ejpam-4432	378	1	czechoslovak mathematical journal	ORG
ejpam-4432	378	2	53(128):1001–1007	CARDINAL
ejpam-4432	378	3	2003	DATE
ejpam-4432	379	1	8	CARDINAL
ejpam-4432	379	2	j keller	PERSON
ejpam-4432	381	1	pacific journal of mathematics	ORG
ejpam-4432	381	2	83(2	CARDINAL
ejpam-4432	381	3	1979	DATE
ejpam-4432	382	1	9	CARDINAL
ejpam-4432	383	1	γ	GPE
ejpam-4432	383	2	53:202–218	CARDINAL
ejpam-4432	383	3	1978	DATE
ejpam-4432	384	1	10	CARDINAL
ejpam-4432	386	1	56:339–360	CARDINAL
ejpam-4432	386	2	1981	DATE
ejpam-4432	387	1	11	CARDINAL
ejpam-4432	387	2	ameri	ORG
ejpam-4432	389	1	european	NORP
ejpam-4432	389	2	11(1):169	CARDINAL
ejpam-4432	389	3	188	CARDINAL
ejpam-4432	389	4	2018	DATE
ejpam-4432	390	1	12	CARDINAL
ejpam-4432	390	2	j mittas	PERSON
ejpam-4432	393	1	balcanica	PERSON
ejpam-4432	393	2	1977	DATE
ejpam-4432	394	1	13	CARDINAL
ejpam-4432	397	1	37:377–386	CARDINAL
ejpam-4432	397	2	1970	DATE
ejpam-4432	398	1	14	CARDINAL
ejpam-4432	399	1	congruences	ORG
ejpam-4432	400	1	central european journal of mathematics	ORG
ejpam-4432	400	2	3:83–97, 2005	DATE
ejpam-4432	401	1	15	CARDINAL
ejpam-4432	404	1	j. pure	PERSON
ejpam-4432	404	2	10:75–78, 2001	DATE
ejpam-4432	405	1	16	CARDINAL
ejpam-4432	407	1	asian	NORP
ejpam-4432	408	1	6(1	CARDINAL
ejpam-4432	408	2	2013	DATE
ejpam-4432	409	1	17	CARDINAL
ejpam-4432	409	2	e. g. rezk	PERSON
ejpam-4432	411	1	j.	PERSON
ejpam-4432	411	2	15(2):486–495	CARDINAL
ejpam-4432	411	3	2022	CARDINAL
ejpam-4432	412	1	18	CARDINAL
ejpam-4432	414	1	14:200–215	CARDINAL
ejpam-4432	414	2	1972	DATE
ejpam-4432	415	1	19	CARDINAL
ejpam-4432	417	1	american	NORP
ejpam-4432	417	2	19(6):1346–1348, 1968	DATE