id	sid	eid	entity	type
ejpam-6690	1	1	european journal	ORG
ejpam-6690	1	2	2025	DATE
ejpam-6690	1	3	18	CARDINAL
ejpam-6690	1	4	4	CARDINAL
ejpam-6690	1	5	6690	CARDINAL
ejpam-6690	1	6	1307-5543	DATE
ejpam-6690	1	7	new york	GPE
ejpam-6690	1	8	behnam afshar1	PERSON
ejpam-6690	1	9	reza ameri1,∗	PERSON
ejpam-6690	1	10	madeleine al-tahan2	PERSON
ejpam-6690	1	11	1	CARDINAL
ejpam-6690	1	12	university of tehran	ORG
ejpam-6690	1	13	tehran	GPE
ejpam-6690	1	14	iran	GPE
ejpam-6690	1	15	2	CARDINAL
ejpam-6690	1	16	abu dhabi university	ORG
ejpam-6690	1	17	abu dhabi	GPE
ejpam-6690	1	18	united arab	GPE
ejpam-6690	1	19	emirates	GPE
ejpam-6690	2	1	commutative krasner	ORG
ejpam-6690	7	1	2020	DATE
ejpam-6690	7	2	20n20	CARDINAL
ejpam-6690	7	3	16y99	CARDINAL
ejpam-6690	7	4	1	CARDINAL
ejpam-6690	7	5	algebraic hyperstructures	PERSON
ejpam-6690	7	6	f. marty	PERSON
ejpam-6690	7	7	1934	DATE
ejpam-6690	8	1	1	CARDINAL
ejpam-6690	9	1	algebraic geometry	PERSON
ejpam-6690	9	2	a. connes	PERSON
ejpam-6690	9	3	c. consani	PERSON
ejpam-6690	10	1	2–4	CARDINAL
ejpam-6690	11	1	2–4	CARDINAL
ejpam-6690	12	1	one	CARDINAL
ejpam-6690	13	1	behnamafshar@ut.ac.ir	PRODUCT
ejpam-6690	13	2	rameri@ut.ac.ir	PRODUCT
ejpam-6690	13	3	r. ameri	PERSON
ejpam-6690	13	4	m. al-tahan	PERSON
ejpam-6690	14	1	1	CARDINAL
ejpam-6690	14	2	2025	CARDINAL
ejpam-6690	15	1	r. ameri	PERSON
ejpam-6690	15	2	m. al-tahan	PERSON
ejpam-6690	16	1	j. pure	PERSON
ejpam-6690	16	2	18	CARDINAL
ejpam-6690	16	3	4	CARDINAL
ejpam-6690	16	4	2025	CARDINAL
ejpam-6690	16	5	6690 2	DATE
ejpam-6690	16	6	19	CARDINAL
ejpam-6690	17	1	1956	DATE
ejpam-6690	17	2	m. krasner	PERSON
ejpam-6690	17	3	5	CARDINAL
ejpam-6690	19	1	zero	CARDINAL
ejpam-6690	20	1	6	CARDINAL
ejpam-6690	21	1	one	CARDINAL
ejpam-6690	21	2	algebraic hyperstructures	PERSON
ejpam-6690	21	3	algebraic hyperstructures	PERSON
ejpam-6690	22	1	hypergroups	GPE
ejpam-6690	24	1	6	CARDINAL
ejpam-6690	25	1	8	CARDINAL
ejpam-6690	26	1	9	CARDINAL
ejpam-6690	27	1	γ∗	ORG
ejpam-6690	27	2	h/γ∗	ORG
ejpam-6690	27	3	abelian	NORP
ejpam-6690	28	1	t. vogiouklis	ORG
ejpam-6690	28	2	9	CARDINAL
ejpam-6690	28	3	10	CARDINAL
ejpam-6690	28	4	γ∗	ORG
ejpam-6690	28	5	γ∗	ORG
ejpam-6690	28	6	∗ β∗	PERCENT
ejpam-6690	29	1	11	CARDINAL
ejpam-6690	29	2	one	CARDINAL
ejpam-6690	30	1	12	CARDINAL
ejpam-6690	30	2	13	CARDINAL
ejpam-6690	31	1	algebraic hyperstructures	ORG
ejpam-6690	32	1	14	CARDINAL
ejpam-6690	34	1	section 2	LAW
ejpam-6690	34	2	krasner hyperrings	ORG
ejpam-6690	35	1	section 3	LAW
ejpam-6690	36	1	section 4	LAW
ejpam-6690	37	1	section 5	LAW
ejpam-6690	37	2	section 6	LAW
ejpam-6690	38	1	hyperalgebraic	GPE
ejpam-6690	39	1	γ∗	ORG
ejpam-6690	40	1	one	CARDINAL
ejpam-6690	42	1	b. afshar	PERSON
ejpam-6690	42	2	r. ameri	PERSON
ejpam-6690	42	3	m. al-tahan	PERSON
ejpam-6690	43	1	j. pure	PERSON
ejpam-6690	43	2	18	CARDINAL
ejpam-6690	43	3	4	CARDINAL
ejpam-6690	43	4	2025	CARDINAL
ejpam-6690	43	5	6690 3	DATE
ejpam-6690	44	1	15	CARDINAL
ejpam-6690	44	2	16	CARDINAL
ejpam-6690	45	1	•	CARDINAL
ejpam-6690	45	2	∈	ORG
ejpam-6690	48	1	•	CARDINAL
ejpam-6690	49	1	•	CARDINAL
ejpam-6690	51	1	•	CARDINAL
ejpam-6690	51	2	∈	ORG
ejpam-6690	51	3	x′	CARDINAL
ejpam-6690	51	4	x′	DATE
ejpam-6690	52	1	x′	DATE
ejpam-6690	52	2	•	CARDINAL
ejpam-6690	56	1	•	CARDINAL
ejpam-6690	56	2	∈	ORG
ejpam-6690	57	1	0	CARDINAL
ejpam-6690	57	2	0	CARDINAL
ejpam-6690	57	3	•	CARDINAL
ejpam-6690	59	1	0	CARDINAL
ejpam-6690	59	2	0	CARDINAL
ejpam-6690	59	3	∈	ORG
ejpam-6690	61	1	1	CARDINAL
ejpam-6690	62	1	15	CARDINAL
ejpam-6690	62	2	⊆	CARDINAL
ejpam-6690	63	1	∈	ORG
ejpam-6690	63	2	∈	ORG
ejpam-6690	65	1	∈	ORG
ejpam-6690	65	2	two	CARDINAL
ejpam-6690	65	3	r.	NORP
ejpam-6690	66	1	⊆	CARDINAL
ejpam-6690	66	2	⊆	CARDINAL
ejpam-6690	66	3	⊆	CARDINAL
ejpam-6690	66	4	⊆	CARDINAL
ejpam-6690	67	1	1	CARDINAL
ejpam-6690	68	1	15	CARDINAL
ejpam-6690	68	2	a−	ORG
ejpam-6690	68	3	⊆	CARDINAL
ejpam-6690	68	4	∈	ORG
ejpam-6690	68	5	∈	ORG
ejpam-6690	68	6	∈	ORG
ejpam-6690	68	7	r. b. afshar	PERSON
ejpam-6690	68	8	r. ameri	PERSON
ejpam-6690	68	9	m. al-tahan	PERSON
ejpam-6690	69	1	j. pure	PERSON
ejpam-6690	69	2	18	CARDINAL
ejpam-6690	69	3	4	CARDINAL
ejpam-6690	69	4	2025	CARDINAL
ejpam-6690	69	5	6690 4 of 19	DATE
ejpam-6690	69	6	ac	ORG
ejpam-6690	69	7	1	CARDINAL
ejpam-6690	70	1	ac	ORG
ejpam-6690	70	2	2	CARDINAL
ejpam-6690	70	3	r.	NORP
ejpam-6690	70	4	2	CARDINAL
ejpam-6690	71	1	15	CARDINAL
ejpam-6690	72	1	∈	ORG
ejpam-6690	73	1	f(b	GPE
ejpam-6690	73	2	f(0	PERSON
ejpam-6690	75	1	r.	NORP
ejpam-6690	76	1	ab ∈ p	ORG
ejpam-6690	76	2	∈	ORG
ejpam-6690	76	3	∈	ORG
ejpam-6690	76	4	r. proposition 1	WORK_OF_ART
ejpam-6690	77	1	15	CARDINAL
ejpam-6690	77	2	r.	NORP
ejpam-6690	82	1	hyperfield	GPE
ejpam-6690	83	1	n(sβ	ORG
ejpam-6690	83	2	φ	PERSON
ejpam-6690	83	3	sr(h	PERSON
ejpam-6690	83	4	n(sβ	ORG
ejpam-6690	83	5	ρ 7→	CARDINAL
ejpam-6690	83	6	3	CARDINAL
ejpam-6690	83	7	∈	ORG
ejpam-6690	83	8	ρ(x	PERSON
ejpam-6690	83	9	11	CARDINAL
ejpam-6690	84	1	3	CARDINAL
ejpam-6690	85	1	16	CARDINAL
ejpam-6690	86	1	•	CARDINAL
ejpam-6690	86	2	two	CARDINAL
ejpam-6690	87	1	•	CARDINAL
ejpam-6690	88	1	•	CARDINAL
ejpam-6690	88	2	∈	ORG
ejpam-6690	89	1	•	CARDINAL
ejpam-6690	89	2	∈	ORG
ejpam-6690	89	3	⊆	CARDINAL
ejpam-6690	89	4	∈	ORG
ejpam-6690	89	5	•	CARDINAL
ejpam-6690	89	6	∈	ORG
ejpam-6690	89	7	⊆	CARDINAL
ejpam-6690	89	8	∈	ORG
ejpam-6690	89	9	b. afshar	PERSON
ejpam-6690	89	10	r. ameri	PERSON
ejpam-6690	89	11	m. al-tahan	PERSON
ejpam-6690	90	1	j. pure	PERSON
ejpam-6690	90	2	18	CARDINAL
ejpam-6690	90	3	4	CARDINAL
ejpam-6690	90	4	2025	CARDINAL
ejpam-6690	90	5	6690 5	DATE
ejpam-6690	90	6	19	CARDINAL
ejpam-6690	90	7	1	CARDINAL
ejpam-6690	91	1	16	CARDINAL
ejpam-6690	94	1	t .	DATE
ejpam-6690	95	1	3	CARDINAL
ejpam-6690	98	1	r.	NORP
ejpam-6690	99	1	k(x	PERSON
ejpam-6690	100	1	∈	ORG
ejpam-6690	100	2	k(x	PERSON
ejpam-6690	101	1	1+p	CARDINAL
ejpam-6690	101	2	1	CARDINAL
ejpam-6690	102	1	⊆	CARDINAL
ejpam-6690	103	1	hyperfield	GPE
ejpam-6690	104	1	4	CARDINAL
ejpam-6690	105	1	⊆	CARDINAL
ejpam-6690	107	1	f(x	ORG
ejpam-6690	107	2	0	CARDINAL
ejpam-6690	107	3	⊆	CARDINAL
ejpam-6690	107	4	vm(s	PERSON
ejpam-6690	108	1	∈	ORG
ejpam-6690	108	2	f(x	ORG
ejpam-6690	109	1	0	CARDINAL
ejpam-6690	109	2	∈	ORG
ejpam-6690	109	3	⊆	CARDINAL
ejpam-6690	110	1	2	CARDINAL
ejpam-6690	112	1	⊆	CARDINAL
ejpam-6690	112	2	⊆	CARDINAL
ejpam-6690	113	1	1 ∈	CARDINAL
ejpam-6690	115	1	∈	ORG
ejpam-6690	118	1	2	CARDINAL
ejpam-6690	123	1	ij)}j∈j	PERSON
ejpam-6690	124	1	⊆	CARDINAL
ejpam-6690	126	1	∈	ORG
ejpam-6690	126	2	⊆	CARDINAL
ejpam-6690	127	1	⊆	CARDINAL
ejpam-6690	128	1	⊆	CARDINAL
ejpam-6690	130	1	⊆	CARDINAL
ejpam-6690	130	2	⊆	CARDINAL
ejpam-6690	130	3	j ⊆ p	ORG
ejpam-6690	132	1	⊆	CARDINAL
ejpam-6690	132	2	j ⊆ p	ORG
ejpam-6690	132	3	⊆	CARDINAL
ejpam-6690	135	1	b. afshar	PERSON
ejpam-6690	135	2	r. ameri	PERSON
ejpam-6690	135	3	m. al-tahan	PERSON
ejpam-6690	136	1	j. pure	PERSON
ejpam-6690	136	2	18	CARDINAL
ejpam-6690	136	3	4	CARDINAL
ejpam-6690	136	4	2025	CARDINAL
ejpam-6690	136	5	6690 6	DATE
ejpam-6690	137	1	2	CARDINAL
ejpam-6690	138	1	r.	NORP
ejpam-6690	138	2	i(sj	ORG
ejpam-6690	138	3	4	CARDINAL
ejpam-6690	138	4	lemma 2	ORG
ejpam-6690	139	1	i(sj	ORG
ejpam-6690	140	1	i(sj	ORG
ejpam-6690	140	2	i(si	ORG
ejpam-6690	140	3	i(sj	ORG
ejpam-6690	142	1	lemma 2	ORG
ejpam-6690	142	2	⊆	CARDINAL
ejpam-6690	142	3	i ∩ j	WORK_OF_ART
ejpam-6690	143	1	i ∩ j	WORK_OF_ART
ejpam-6690	149	1	xy ∈	ORG
ejpam-6690	151	1	xy ∈ p	ORG
ejpam-6690	152	1	i ∩ j	WORK_OF_ART
ejpam-6690	153	1	2	CARDINAL
ejpam-6690	156	1	⊆	CARDINAL
ejpam-6690	156	2	i. proof	PERSON
ejpam-6690	159	1	∈	ORG
ejpam-6690	161	1	3	CARDINAL
ejpam-6690	167	1	⊆	CARDINAL
ejpam-6690	167	2	f(i	GPE
ejpam-6690	167	3	⊆	CARDINAL
ejpam-6690	167	4	f(i	PERSON
ejpam-6690	169	1	4	CARDINAL
ejpam-6690	171	1	r.	NORP
ejpam-6690	174	1	subspace	ORG
ejpam-6690	180	1	⊆	CARDINAL
ejpam-6690	181	1	b. afshar	PERSON
ejpam-6690	181	2	r. ameri	PERSON
ejpam-6690	181	3	m. al-tahan	PERSON
ejpam-6690	182	1	j. pure	PERSON
ejpam-6690	182	2	18	CARDINAL
ejpam-6690	182	3	4	CARDINAL
ejpam-6690	182	4	2025	CARDINAL
ejpam-6690	182	5	6690 7	DATE
ejpam-6690	182	6	19	CARDINAL
ejpam-6690	183	1	3	CARDINAL
ejpam-6690	183	2	−1	DATE
ejpam-6690	183	3	−1	DATE
ejpam-6690	185	1	∈	ORG
ejpam-6690	186	1	1	CARDINAL
ejpam-6690	189	1	4	CARDINAL
ejpam-6690	190	1	nil(r	ORG
ejpam-6690	190	2	⊆	CARDINAL
ejpam-6690	192	1	5	CARDINAL
ejpam-6690	194	1	5	CARDINAL
ejpam-6690	196	1	r1 × r2	ORG
ejpam-6690	197	1	r1/p1 × r2	ORG
ejpam-6690	198	1	p1 ∈ spec(r1	ORG
ejpam-6690	199	1	5	CARDINAL
ejpam-6690	200	1	17	CARDINAL
ejpam-6690	201	1	chinese	NORP
ejpam-6690	202	1	+ ik	PERSON
ejpam-6690	202	2	∩ ik	PERSON
ejpam-6690	203	1	j ∈	PERSON
ejpam-6690	203	2	1	CARDINAL
ejpam-6690	203	3	2	DATE
ejpam-6690	203	4	∩ i2 ∩	PERSON
ejpam-6690	203	5	∩ ik	PERSON
ejpam-6690	204	1	6	CARDINAL
ejpam-6690	205	1	φ(r	PERSON
ejpam-6690	207	1	φ	ORG
ejpam-6690	210	1	1	CARDINAL
ejpam-6690	210	2	1	CARDINAL
ejpam-6690	210	3	⊆	CARDINAL
ejpam-6690	210	4	⊆	CARDINAL
ejpam-6690	210	5	1	CARDINAL
ejpam-6690	210	6	1 + j	DATE
ejpam-6690	211	1	1 + i. so φ(x	CARDINAL
ejpam-6690	212	1	1 + j	DATE
ejpam-6690	212	2	0r	CARDINAL
ejpam-6690	212	3	1r	CARDINAL
ejpam-6690	212	4	φ(y	ORG
ejpam-6690	213	1	0r	CARDINAL
ejpam-6690	217	1	0	CARDINAL
ejpam-6690	217	2	0	CARDINAL
ejpam-6690	217	3	1	CARDINAL
ejpam-6690	222	1	⊆	CARDINAL
ejpam-6690	223	1	two	CARDINAL
ejpam-6690	223	2	j =	PERSON
ejpam-6690	223	3	b. afshar	PERSON
ejpam-6690	223	4	r. ameri	PERSON
ejpam-6690	223	5	m. al-tahan	PERSON
ejpam-6690	224	1	j. pure	PERSON
ejpam-6690	224	2	18	CARDINAL
ejpam-6690	224	3	4	CARDINAL
ejpam-6690	224	4	2025	CARDINAL
ejpam-6690	224	5	6690 8	DATE
ejpam-6690	224	6	19	CARDINAL
ejpam-6690	224	7	2	CARDINAL
ejpam-6690	227	1	r.	NORP
ejpam-6690	230	1	chinese	NORP
ejpam-6690	231	1	1	CARDINAL
ejpam-6690	231	2	1	CARDINAL
ejpam-6690	233	1	3	CARDINAL
ejpam-6690	237	1	x2+nil(r	GPE
ejpam-6690	241	1	⊆	CARDINAL
ejpam-6690	244	1	0	CARDINAL
ejpam-6690	246	1	chinese	NORP
ejpam-6690	246	2	φ	PERSON
ejpam-6690	248	1	0	CARDINAL
ejpam-6690	248	2	1	CARDINAL
ejpam-6690	249	1	1	CARDINAL
ejpam-6690	251	1	7	CARDINAL
ejpam-6690	259	1	lemma 2	ORG
ejpam-6690	259	2	chinese	NORP
ejpam-6690	260	1	0	CARDINAL
ejpam-6690	261	1	4	CARDINAL
ejpam-6690	266	1	2	CARDINAL
ejpam-6690	267	1	3	CARDINAL
ejpam-6690	267	2	2	CARDINAL
ejpam-6690	268	1	3	CARDINAL
ejpam-6690	269	1	w	PERSON
ejpam-6690	271	1	w	GPE
ejpam-6690	271	2	0	CARDINAL
ejpam-6690	271	3	w	ORG
ejpam-6690	271	4	1	CARDINAL
ejpam-6690	271	5	⋃	DATE
ejpam-6690	271	6	f∈e w	ORG
ejpam-6690	271	7	⊆	CARDINAL
ejpam-6690	271	8	r.	NORP
ejpam-6690	271	9	∈	ORG
ejpam-6690	271	10	w	GPE
ejpam-6690	271	11	fg	ORG
ejpam-6690	272	1	w	ORG
ejpam-6690	273	1	∈	ORG
ejpam-6690	273	2	∈	ORG
ejpam-6690	274	1	∈	ORG
ejpam-6690	275	1	17	CARDINAL
ejpam-6690	277	1	∈	ORG
ejpam-6690	277	2	∈	ORG
ejpam-6690	278	1	8	CARDINAL
ejpam-6690	281	1	b. afshar	PERSON
ejpam-6690	281	2	r. ameri	PERSON
ejpam-6690	281	3	m. al-tahan	PERSON
ejpam-6690	282	1	j. pure	PERSON
ejpam-6690	282	2	18	CARDINAL
ejpam-6690	282	3	4	CARDINAL
ejpam-6690	282	4	2025	CARDINAL
ejpam-6690	282	5	6690 9	DATE
ejpam-6690	283	1	two	CARDINAL
ejpam-6690	284	1	∩ w	PERSON
ejpam-6690	285	1	∈	ORG
ejpam-6690	285	2	g /∈	PERSON
ejpam-6690	287	1	nil(r	ORG
ejpam-6690	287	2	r.	NORP
ejpam-6690	287	3	8	CARDINAL
ejpam-6690	288	1	3	CARDINAL
ejpam-6690	290	1	r.	NORP
ejpam-6690	290	2	√	PERSON
ejpam-6690	292	1	8	CARDINAL
ejpam-6690	292	2	√	PERSON
ejpam-6690	294	1	4	CARDINAL
ejpam-6690	295	1	∈	PRODUCT
ejpam-6690	296	1	⊆	CARDINAL
ejpam-6690	299	1	⊊ p1 ⊊ ...	ORG
ejpam-6690	300	1	dim(r	GPE
ejpam-6690	300	2	dim(r	GPE
ejpam-6690	302	1	hyperfield	GPE
ejpam-6690	302	2	dim(r	GPE
ejpam-6690	303	1	0	CARDINAL
ejpam-6690	304	1	dim(r	GPE
ejpam-6690	305	1	0	CARDINAL
ejpam-6690	306	1	dim(r	GPE
ejpam-6690	306	2	p1 ⊊	ORG
ejpam-6690	308	1	dim(r	GPE
ejpam-6690	311	1	⊆	CARDINAL
ejpam-6690	311	2	⊆	CARDINAL
ejpam-6690	315	1	9	CARDINAL
ejpam-6690	316	1	dim(r	GPE
ejpam-6690	323	1	1	CARDINAL
ejpam-6690	324	1	1	CARDINAL
ejpam-6690	324	2	0rp	ORDINAL
ejpam-6690	325	1	0	CARDINAL
ejpam-6690	327	1	∈	ORG
ejpam-6690	330	1	w	ORG
ejpam-6690	341	1	b. afshar	PERSON
ejpam-6690	341	2	r. ameri	PERSON
ejpam-6690	341	3	m. al-tahan	PERSON
ejpam-6690	342	1	j. pure	PERSON
ejpam-6690	342	2	18	CARDINAL
ejpam-6690	342	3	4	CARDINAL
ejpam-6690	342	4	2025	CARDINAL
ejpam-6690	342	5	6690 10	DATE
ejpam-6690	342	6	19	CARDINAL
ejpam-6690	342	7	4	CARDINAL
ejpam-6690	343	1	3	CARDINAL
ejpam-6690	345	1	ij)}j∈j	PERSON
ejpam-6690	345	2	⋃	DATE
ejpam-6690	345	3	j ∈ j	PERSON
ejpam-6690	346	1	⋃ j∈j(spec(r	PERSON
ejpam-6690	349	1	= r.	PERSON
ejpam-6690	351	1	∑ k∈k ik =	PERSON
ejpam-6690	351	2	∑ k∈k ik	PERSON
ejpam-6690	351	3	⋃	DATE
ejpam-6690	353	1	w	GPE
ejpam-6690	355	1	∈	ORG
ejpam-6690	356	1	w	PERSON
ejpam-6690	356	2	⋃	PERSON
ejpam-6690	360	1	∑ i∈i(xi	PERSON
ejpam-6690	361	1	k ⊆ p	ORG
ejpam-6690	363	1	xm ∈	ORG
ejpam-6690	364	1	ri ∈ r(1	ORG
ejpam-6690	365	1	xm	ORG
ejpam-6690	366	1	i=1 rixi	PERSON
ejpam-6690	367	1	⊆	CARDINAL
ejpam-6690	367	2	xm ∈	ORG
ejpam-6690	369	1	∈	ORG
ejpam-6690	373	1	1	CARDINAL
ejpam-6690	373	2	2	DATE
ejpam-6690	374	1	⋃n	PERSON
ejpam-6690	375	1	⋃	PERSON
ejpam-6690	376	1	⋃n	PERSON
ejpam-6690	378	1	⋃n	PERSON
ejpam-6690	379	1	5	CARDINAL
ejpam-6690	380	1	17	CARDINAL
ejpam-6690	381	1	dim(r	GPE
ejpam-6690	382	1	0	CARDINAL
ejpam-6690	383	1	2	CARDINAL
ejpam-6690	390	1	1 ⇒ 2	CARDINAL
ejpam-6690	390	2	5	CARDINAL
ejpam-6690	392	1	3	CARDINAL
ejpam-6690	393	1	lemma 2	ORG
ejpam-6690	394	1	dim(r	GPE
ejpam-6690	395	1	0	CARDINAL
ejpam-6690	395	2	5	CARDINAL
ejpam-6690	396	1	b. afshar	PERSON
ejpam-6690	396	2	r. ameri	PERSON
ejpam-6690	396	3	m. al-tahan	PERSON
ejpam-6690	397	1	j. pure	PERSON
ejpam-6690	397	2	18	CARDINAL
ejpam-6690	397	3	4	CARDINAL
ejpam-6690	397	4	2025	CARDINAL
ejpam-6690	397	5	6690 11	DATE
ejpam-6690	397	6	19	CARDINAL
ejpam-6690	399	1	r.	NORP
ejpam-6690	400	1	1	CARDINAL
ejpam-6690	400	2	3	CARDINAL
ejpam-6690	401	1	⊆	CARDINAL
ejpam-6690	401	2	⊆	CARDINAL
ejpam-6690	403	1	√ i. theorem	PERSON
ejpam-6690	403	2	10	CARDINAL
ejpam-6690	406	1	∈	ORG
ejpam-6690	406	2	r.	NORP
ejpam-6690	408	1	∈	ORG
ejpam-6690	409	1	6	CARDINAL
ejpam-6690	410	1	6	CARDINAL
ejpam-6690	410	2	r.	NORP
ejpam-6690	411	1	one	CARDINAL
ejpam-6690	411	2	∈	ORG
ejpam-6690	411	3	7→	CARDINAL
ejpam-6690	413	1	r.	NORP
ejpam-6690	413	2	nil(r	ORG
ejpam-6690	415	1	8	DATE
ejpam-6690	415	2	nil(r	ORG
ejpam-6690	415	3	nil(s−1r	LANGUAGE
ejpam-6690	415	4	∈	ORG
ejpam-6690	416	1	nil(s−1r	LANGUAGE
ejpam-6690	416	2	∈	ORG
ejpam-6690	417	1	nil(r	ORG
ejpam-6690	420	1	s−1(r1 × r2	ORG
ejpam-6690	420	2	s−1r1	CARDINAL
ejpam-6690	420	3	5	CARDINAL
ejpam-6690	420	4	7	CARDINAL
ejpam-6690	421	1	1	CARDINAL
ejpam-6690	423	1	0	CARDINAL
ejpam-6690	424	1	r.	NORP
ejpam-6690	424	2	1	CARDINAL
ejpam-6690	424	3	∈	ORG
ejpam-6690	425	1	tg	ORG
ejpam-6690	425	2	∈	ORG
ejpam-6690	425	3	rg⊙sg	GPE
ejpam-6690	427	1	0	CARDINAL
ejpam-6690	427	2	1r̄	CARDINAL
ejpam-6690	429	1	r.	NORP
ejpam-6690	429	2	⊙	NORP
ejpam-6690	430	1	rsg ∈ p/g	ORG
ejpam-6690	430	2	∈	ORG
ejpam-6690	431	1	∈	ORG
ejpam-6690	433	1	∈	ORG
ejpam-6690	434	1	∈	ORG
ejpam-6690	435	1	2	CARDINAL
ejpam-6690	436	1	∈	ORG
ejpam-6690	439	1	⊙	ORG
ejpam-6690	443	1	1r̄	CARDINAL
ejpam-6690	443	2	1 + i.	CARDINAL
ejpam-6690	444	1	∈	ORG
ejpam-6690	445	1	3	CARDINAL
ejpam-6690	445	2	∈	ORG
ejpam-6690	445	3	∈	ORG
ejpam-6690	446	1	∈	ORG
ejpam-6690	447	1	b. afshar	PERSON
ejpam-6690	447	2	r. ameri	PERSON
ejpam-6690	447	3	m. al-tahan	PERSON
ejpam-6690	448	1	j. pure	PERSON
ejpam-6690	448	2	18	CARDINAL
ejpam-6690	448	3	4	CARDINAL
ejpam-6690	448	4	2025	CARDINAL
ejpam-6690	448	5	6690 12	DATE
ejpam-6690	448	6	19	CARDINAL
ejpam-6690	448	7	5	CARDINAL
ejpam-6690	452	1	1r	CARDINAL
ejpam-6690	452	2	∈	PRODUCT
ejpam-6690	452	3	0	CARDINAL
ejpam-6690	452	4	0	CARDINAL
ejpam-6690	452	5	∈	ORG
ejpam-6690	454	1	nil(r	ORG
ejpam-6690	455	1	∈ spec(r̄	PERSON
ejpam-6690	456	1	8	CARDINAL
ejpam-6690	458	1	2	CARDINAL
ejpam-6690	458	2	±1	PERSON
ejpam-6690	460	1	k ∈ n	ORG
ejpam-6690	460	2	0	CARDINAL
ejpam-6690	463	1	3	CARDINAL
ejpam-6690	464	1	2	CARDINAL
ejpam-6690	466	1	f(x	ORG
ejpam-6690	469	1	4	CARDINAL
ejpam-6690	470	1	γ∗	ORG
ejpam-6690	471	1	6	CARDINAL
ejpam-6690	472	1	18	CARDINAL
ejpam-6690	472	2	r.	NORP
ejpam-6690	472	3	∈ γ∗	ORG
ejpam-6690	472	4	∈	ORG
ejpam-6690	472	5	un	ORG
ejpam-6690	472	6	∈	PRODUCT
ejpam-6690	472	7	⊆	CARDINAL
ejpam-6690	472	8	1	CARDINAL
ejpam-6690	472	9	2	DATE
ejpam-6690	473	1	γ∗	ORG
ejpam-6690	474	1	15	CARDINAL
ejpam-6690	475	1	9	CARDINAL
ejpam-6690	476	1	∈	ORG
ejpam-6690	476	2	ρ(x	PERSON
ejpam-6690	476	3	r.	NORP
ejpam-6690	477	1	ρ(x	PERSON
ejpam-6690	477	2	− ρ(y	PERSON
ejpam-6690	478	1	⊆	CARDINAL
ejpam-6690	479	1	∈	ORG
ejpam-6690	480	1	∈	ORG
ejpam-6690	481	1	γ∗	ORG
ejpam-6690	481	2	⊆	PRODUCT
ejpam-6690	481	3	⊆	CARDINAL
ejpam-6690	481	4	⊆	CARDINAL
ejpam-6690	481	5	⊆	CARDINAL
ejpam-6690	482	1	ρ(0	PERSON
ejpam-6690	485	1	4	CARDINAL
ejpam-6690	486	1	ρ ∈	PERSON
ejpam-6690	486	2	ρ(x	PERSON
ejpam-6690	487	1	x+ ρ(0	PERSON
ejpam-6690	487	2	r. proof	PERSON
ejpam-6690	488	1	⊆	PRODUCT
ejpam-6690	488	2	⊆	CARDINAL
ejpam-6690	489	1	ρ(x	PERSON
ejpam-6690	490	1	⊆	CARDINAL
ejpam-6690	493	1	ρ(x	PERSON
ejpam-6690	494	1	⊆	CARDINAL
ejpam-6690	494	2	ρ(x	PERSON
ejpam-6690	495	1	b. afshar	PERSON
ejpam-6690	495	2	r. ameri	PERSON
ejpam-6690	495	3	m. al-tahan	PERSON
ejpam-6690	496	1	j. pure	PERSON
ejpam-6690	496	2	18	CARDINAL
ejpam-6690	496	3	4	CARDINAL
ejpam-6690	496	4	2025	CARDINAL
ejpam-6690	496	5	6690 13	DATE
ejpam-6690	496	6	19	CARDINAL
ejpam-6690	496	7	5	CARDINAL
ejpam-6690	497	1	∈	ORG
ejpam-6690	499	1	∈	ORG
ejpam-6690	502	1	∈	ORG
ejpam-6690	503	1	i. hence	PERSON
ejpam-6690	505	1	ρ ∨	ORG
ejpam-6690	505	2	n(sβ	ORG
ejpam-6690	505	3	sβ ⊆ h ◁ r	ORG
ejpam-6690	505	4	11	CARDINAL
ejpam-6690	506	1	11	CARDINAL
ejpam-6690	509	1	⊆	CARDINAL
ejpam-6690	509	2	⊆	CARDINAL
ejpam-6690	509	3	∈	PRODUCT
ejpam-6690	510	1	ρ ∈	PERSON
ejpam-6690	510	2	ρ∈sr(r	GPE
ejpam-6690	510	3	γ∗	ORG
ejpam-6690	510	4	∈	ORG
ejpam-6690	512	1	ρ 7→ ρ(0	QUANTITY
ejpam-6690	512	2	7→	CARDINAL
ejpam-6690	513	1	lemmas 4 and	ORG
ejpam-6690	513	2	5	DATE
ejpam-6690	514	1	∈	ORG
ejpam-6690	517	1	∈	ORG
ejpam-6690	519	1	∈	ORG
ejpam-6690	519	2	⊆	CARDINAL
ejpam-6690	519	3	i.	PERSON
ejpam-6690	520	1	ρ(x	PERSON
ejpam-6690	520	2	ρ ⊆ σ	ORG
ejpam-6690	521	1	⊆	CARDINAL
ejpam-6690	521	2	σ(0	PERSON
ejpam-6690	524	1	f−1(i	GPE
ejpam-6690	524	2	⊆	CARDINAL
ejpam-6690	525	1	6	CARDINAL
ejpam-6690	526	1	ρ ∈	PERSON
ejpam-6690	528	1	∈	ORG
ejpam-6690	530	1	ρ(x	PERSON
ejpam-6690	530	2	7→	CARDINAL
ejpam-6690	538	1	+ ϕ(ρ(y	PERSON
ejpam-6690	540	1	xy	ORG
ejpam-6690	541	1	+ ρ(0	PERSON
ejpam-6690	543	1	ρ ∨ σ)(0	PERSON
ejpam-6690	543	2	∩ σ(0	PERSON
ejpam-6690	545	1	∈	ORG
ejpam-6690	545	2	18	CARDINAL
ejpam-6690	546	1	18	CARDINAL
ejpam-6690	547	1	b. afshar	PERSON
ejpam-6690	547	2	r. ameri	PERSON
ejpam-6690	547	3	m. al-tahan	PERSON
ejpam-6690	548	1	j. pure	PERSON
ejpam-6690	548	2	18	CARDINAL
ejpam-6690	548	3	4	CARDINAL
ejpam-6690	548	4	2025	CARDINAL
ejpam-6690	548	5	6690 14	DATE
ejpam-6690	548	6	19	CARDINAL
ejpam-6690	549	1	krasner hyperring r.	PERSON
ejpam-6690	549	2	γ∗(0	ORG
ejpam-6690	549	3	⊆	CARDINAL
ejpam-6690	549	4	i.	PERSON
ejpam-6690	550	1	⊆	CARDINAL
ejpam-6690	550	2	r.	NORP
ejpam-6690	550	3	y ∈ γ∗(0	PERSON
ejpam-6690	550	4	n ∈ n	ORG
ejpam-6690	551	1	0	CARDINAL
ejpam-6690	557	1	⊆	CARDINAL
ejpam-6690	557	2	γ∗(0	ORG
ejpam-6690	557	3	⊆	CARDINAL
ejpam-6690	557	4	i.	PERSON
ejpam-6690	557	5	⊆	CARDINAL
ejpam-6690	557	6	∈	ORG
ejpam-6690	558	1	∈	ORG
ejpam-6690	559	1	7	CARDINAL
ejpam-6690	559	2	xy	ORG
ejpam-6690	560	1	7	CARDINAL
ejpam-6690	560	2	xy	ORG
ejpam-6690	561	1	n s.t.	PERSON
ejpam-6690	561	2	yn	ORG
ejpam-6690	562	1	8)	CARDINAL
ejpam-6690	563	1	ρ(x	PERSON
ejpam-6690	566	1	r.	NORP
ejpam-6690	566	2	r.	NORP
ejpam-6690	567	1	4	CARDINAL
ejpam-6690	567	2	1,f	CARDINAL
ejpam-6690	569	1	1,f	CARDINAL
ejpam-6690	569	2	1	CARDINAL
ejpam-6690	569	3	0	CARDINAL
ejpam-6690	569	4	1,f	CARDINAL
ejpam-6690	570	1	0 1	CARDINAL
ejpam-6690	572	1	0 1	CARDINAL
ejpam-6690	573	1	0	CARDINAL
ejpam-6690	578	1	0	CARDINAL
ejpam-6690	584	1	r. ameri	PERSON
ejpam-6690	584	2	m. al-tahan	PERSON
ejpam-6690	585	1	j. pure	PERSON
ejpam-6690	585	2	18	CARDINAL
ejpam-6690	585	3	4	CARDINAL
ejpam-6690	585	4	2025	CARDINAL
ejpam-6690	585	5	6690 15 of 19	DATE
ejpam-6690	585	6	γ∗	ORG
ejpam-6690	585	7	1	CARDINAL
ejpam-6690	585	8	1	CARDINAL
ejpam-6690	585	9	0	CARDINAL
ejpam-6690	586	1	γ∗(0	ORG
ejpam-6690	586	2	0	CARDINAL
ejpam-6690	587	1	0	CARDINAL
ejpam-6690	587	2	1	CARDINAL
ejpam-6690	588	1	0	CARDINAL
ejpam-6690	588	2	0	CARDINAL
ejpam-6690	588	3	0	CARDINAL
ejpam-6690	588	4	γ∗(0	ORG
ejpam-6690	588	5	√ γ∗(0	PERSON
ejpam-6690	588	6	√ γ∗(0	PERSON
ejpam-6690	588	7	0	CARDINAL
ejpam-6690	588	8	1	CARDINAL
ejpam-6690	589	1	0	CARDINAL
ejpam-6690	589	2	0	CARDINAL
ejpam-6690	595	1	√ γ∗(0	PERSON
ejpam-6690	596	1	12	CARDINAL
ejpam-6690	598	1	γ∗	ORG
ejpam-6690	601	1	∈	ORG
ejpam-6690	604	1	k ∈	PERSON
ejpam-6690	606	1	⊆	CARDINAL
ejpam-6690	606	2	∈	ORG
ejpam-6690	607	1	γ∗(r)γ∗(k	ORG
ejpam-6690	608	1	γ∗(k	PERSON
ejpam-6690	609	1	∈	ORG
ejpam-6690	609	2	k ∈ p	ORG
ejpam-6690	610	1	6	CARDINAL
ejpam-6690	615	1	⊂	GPE
ejpam-6690	618	1	2	CARDINAL
ejpam-6690	618	2	i. theorem 13	PERSON
ejpam-6690	622	1	∈	ORG
ejpam-6690	622	2	−1	DATE
ejpam-6690	622	3	w	ORG
ejpam-6690	625	1	jc	PERSON
ejpam-6690	626	1	ker(f	GPE
ejpam-6690	630	1	ker(f	GPE
ejpam-6690	630	2	⊂	GPE
ejpam-6690	632	1	vi	PERSON
ejpam-6690	633	1	f̄	DATE
ejpam-6690	634	1	3	CARDINAL
ejpam-6690	635	1	f(i	PERSON
ejpam-6690	635	2	f(i	PERSON
ejpam-6690	636	1	lemma 2	ORG
ejpam-6690	636	2	f(i	PERSON
ejpam-6690	638	1	w	ORG
ejpam-6690	640	1	⊂	GPE
ejpam-6690	642	1	⊂	GPE
ejpam-6690	642	2	f(x	ORG
ejpam-6690	644	1	6	CARDINAL
ejpam-6690	647	1	j⊂q f−1(q	PERSON
ejpam-6690	650	1	b. afshar	PERSON
ejpam-6690	650	2	r. ameri	PERSON
ejpam-6690	650	3	m. al-tahan	PERSON
ejpam-6690	651	1	j. pure	PERSON
ejpam-6690	651	2	18	CARDINAL
ejpam-6690	651	3	4	CARDINAL
ejpam-6690	651	4	2025	CARDINAL
ejpam-6690	651	5	6690 16 of 19	DATE
ejpam-6690	651	6	2	CARDINAL
ejpam-6690	654	1	one	CARDINAL
ejpam-6690	654	2	one	CARDINAL
ejpam-6690	654	3	ker(f	GPE
ejpam-6690	655	1	ker(f	GPE
ejpam-6690	655	2	f̄(i/ker(f	ORG
ejpam-6690	657	1	i/ker(f	ORG
ejpam-6690	661	1	3	CARDINAL
ejpam-6690	662	1	ker(f	GPE
ejpam-6690	665	1	ker(f	GPE
ejpam-6690	666	1	ker(f	GPE
ejpam-6690	666	2	⊂	GPE
ejpam-6690	668	1	vi	PERSON
ejpam-6690	668	2	g ◦ f(p	ORG
ejpam-6690	673	1	ztop.hrg	CARDINAL
ejpam-6690	673	2	hom(x	ORG
ejpam-6690	675	1	14	DATE
ejpam-6690	676	1	7→	CARDINAL
ejpam-6690	676	2	γ∗	ORG
ejpam-6690	677	1	7→	CARDINAL
ejpam-6690	678	1	γ∗	ORG
ejpam-6690	680	1	γ∗	ORG
ejpam-6690	682	1	spec(s/γ∗	ORG
ejpam-6690	683	1	j/γ∗	ORG
ejpam-6690	683	2	j/γ∗	ORG
ejpam-6690	684	1	p/γ∗ ∈	ORG
ejpam-6690	684	2	∈	ORG
ejpam-6690	685	1	−1	DATE
ejpam-6690	685	2	j/γ∗	ORG
ejpam-6690	686	1	∈	ORG
ejpam-6690	689	1	−1	DATE
ejpam-6690	689	2	j/γ∗	ORG
ejpam-6690	693	1	= h∗ ◦ g∗.	PERSON
ejpam-6690	694	1	/γ∗	ORG
ejpam-6690	696	1	15	CARDINAL
ejpam-6690	698	1	7→	CARDINAL
ejpam-6690	698	2	7→	ORDINAL
ejpam-6690	699	1	3	CARDINAL
ejpam-6690	699	2	13	CARDINAL
ejpam-6690	699	3	f̄	DATE
ejpam-6690	699	4	r. ameri	PERSON
ejpam-6690	699	5	m. al-tahan	PERSON
ejpam-6690	700	1	j. pure	PERSON
ejpam-6690	700	2	18	CARDINAL
ejpam-6690	700	3	4	CARDINAL
ejpam-6690	700	4	2025	CARDINAL
ejpam-6690	700	5	6690 17	DATE
ejpam-6690	700	6	19	CARDINAL
ejpam-6690	700	7	16	DATE
ejpam-6690	701	1	γ∗	ORG
ejpam-6690	705	1	7→	CARDINAL
ejpam-6690	705	2	s/γ∗	ORG
ejpam-6690	705	3	7→	CARDINAL
ejpam-6690	706	1	p/γ∗	ORG
ejpam-6690	707	1	/γ∗	ORG
ejpam-6690	708	1	f∗−1	WORK_OF_ART
ejpam-6690	708	2	p/γ∗	ORG
ejpam-6690	709	1	∗(p/γ∗	ORG
ejpam-6690	710	1	5	CARDINAL
ejpam-6690	711	1	n̄;n ∈ z	DATE
ejpam-6690	711	2	n+m	DATE
ejpam-6690	713	1	z̄	PERSON
ejpam-6690	714	1	∈	ORG
ejpam-6690	714	2	z̄	GPE
ejpam-6690	717	1	γ∗(0̄	ORG
ejpam-6690	717	2	z̄	TIME
ejpam-6690	717	3	γ∗	ORG
ejpam-6690	718	1	commutative krasner	ORG
ejpam-6690	721	1	γ∗	ORG
ejpam-6690	721	2	hyperalgebraic lenses	ORG
ejpam-6690	723	1	the spec(−) functor	ORG
ejpam-6690	724	1	γ∗	ORG
ejpam-6690	726	1	b. afshar	PERSON
ejpam-6690	726	2	r. ameri	PERSON
ejpam-6690	726	3	m. al-tahan	PERSON
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ejpam-6690	727	5	6690 18 of 19	DATE
ejpam-6690	729	1	algebraic	PERSON
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ejpam-6690	730	2	commutative krasner	ORG
ejpam-6690	736	1	hyperalgebraic geometry	ORG
ejpam-6690	738	1	abu dhabi university	ORG
ejpam-6690	738	2	19300884	DATE
ejpam-6690	739	1	1	CARDINAL
ejpam-6690	740	1	sur une generalization de la	ORG
ejpam-6690	741	1	8th	ORDINAL
ejpam-6690	741	2	congress	ORG
ejpam-6690	742	1	1934	DATE
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ejpam-6690	744	3	4	CARDINAL
ejpam-6690	744	4	2025	CARDINAL
ejpam-6690	744	5	6690 19	DATE
ejpam-6690	745	1	2	CARDINAL
ejpam-6690	746	1	monoids	GPE
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ejpam-6690	746	5	147–198, 2010	DATE
ejpam-6690	747	1	3	CARDINAL
ejpam-6690	749	1	131(2):159–194, 2011	DATE
ejpam-6690	750	1	4	CARDINAL
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ejpam-6690	752	3	11–74,	DATE
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ejpam-6690	753	1	5	CARDINAL
ejpam-6690	755	1	6(2):307–311	CARDINAL
ejpam-6690	755	2	1983	DATE
ejpam-6690	756	1	6	CARDINAL
ejpam-6690	758	1	aviani editore	PERSON
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ejpam-6690	760	1	groupoides	PERSON
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ejpam-6690	763	1	8	CARDINAL
ejpam-6690	765	1	30(8):3977–3989, 2002	DATE
ejpam-6690	766	1	9	CARDINAL
ejpam-6690	768	1	hyperfield	GPE
ejpam-6690	770	1	fourth	ORDINAL
ejpam-6690	771	1	congress	ORG
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ejpam-6690	773	1	10	CARDINAL
ejpam-6690	775	1	algebraic hyperstructures	PERSON
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ejpam-6690	775	3	4(2):123–130	ORG
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ejpam-6690	776	1	11	CARDINAL
ejpam-6690	778	1	14(1):73–83	CARDINAL
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ejpam-6690	779	1	12	CARDINAL
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ejpam-6690	781	2	32(1):5–18	DATE
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ejpam-6690	784	2	2022	CARDINAL
ejpam-6690	785	1	14	CARDINAL
ejpam-6690	786	1	multiplicative	NORP
ejpam-6690	787	1	italian	NORP
ejpam-6690	787	2	2015	DATE
ejpam-6690	788	1	15	CARDINAL
ejpam-6690	790	1	usa	GPE
ejpam-6690	790	2	2007	DATE
ejpam-6690	791	1	16	CARDINAL
ejpam-6690	794	1	prentice hall	ORG
ejpam-6690	794	2	812:813	DATE
ejpam-6690	794	3	2000	DATE
ejpam-6690	795	1	17	CARDINAL
ejpam-6690	795	2	w jonsson	PERSON
ejpam-6690	796	1	cambridge university press	ORG
ejpam-6690	796	2	canadian	NORP
ejpam-6690	796	3	1970	DATE
ejpam-6690	797	1	18	CARDINAL
ejpam-6690	798	1	krasner hyperring	PERSON
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