id	sid	eid	entity	type
ejpam-5889	1	1	european journal	ORG
ejpam-5889	1	2	2025	DATE
ejpam-5889	1	3	18	CARDINAL
ejpam-5889	1	4	2	CARDINAL
ejpam-5889	1	5	5889	CARDINAL
ejpam-5889	1	6	1307-5543	DATE
ejpam-5889	1	7	new york	GPE
ejpam-5889	1	8	jordan-hölder	PERSON
ejpam-5889	1	9	paul augustine ejegwa1	PERSON
ejpam-5889	1	10	kausar2	ORG
ejpam-5889	1	11	1	CARDINAL
ejpam-5889	1	12	joseph sarwuan tarka university	PERSON
ejpam-5889	1	13	2373	CARDINAL
ejpam-5889	1	14	2	CARDINAL
ejpam-5889	1	15	balikesir university	ORG
ejpam-5889	1	16	10145	DATE
ejpam-5889	1	17	3	CARDINAL
ejpam-5889	1	18	kogi state	GPE
ejpam-5889	1	19	nigeria 4 college of business administration	ORG
ejpam-5889	1	20	american university of the middle east	ORG
ejpam-5889	1	21	kuwait	GPE
ejpam-5889	3	1	jordan	GPE
ejpam-5889	3	2	multiset	ORG
ejpam-5889	5	1	jordan	GPE
ejpam-5889	7	1	at least two	CARDINAL
ejpam-5889	8	1	2020	DATE
ejpam-5889	8	2	03e72	CARDINAL
ejpam-5889	8	3	11e57	CARDINAL
ejpam-5889	8	4	19a22	CARDINAL
ejpam-5889	8	5	multiset	ORG
ejpam-5889	8	6	one	CARDINAL
ejpam-5889	9	1	multiset	ORG
ejpam-5889	9	2	1	CARDINAL
ejpam-5889	10	1	2	CARDINAL
ejpam-5889	10	2	multiset	ORG
ejpam-5889	10	3	d. e. knuth	PERSON
ejpam-5889	10	4	n. g. de bruijn	PERSON
ejpam-5889	11	1	multiset	ORG
ejpam-5889	11	2	3–9	CARDINAL
ejpam-5889	12	1	zadeh	ORG
ejpam-5889	13	1	10	CARDINAL
ejpam-5889	13	2	11	CARDINAL
ejpam-5889	15	1	nazmul et al	PERSON
ejpam-5889	16	1	17	CARDINAL
ejpam-5889	18	1	n. kausar	PERSON
ejpam-5889	18	2	m. a. ibrahim	PERSON
ejpam-5889	19	1	1	CARDINAL
ejpam-5889	19	2	2025	CARDINAL
ejpam-5889	20	1	p. a. ejegwa et al	PERSON
ejpam-5889	21	1	j. pure	PERSON
ejpam-5889	21	2	18	CARDINAL
ejpam-5889	21	3	2	CARDINAL
ejpam-5889	21	4	2025	CARDINAL
ejpam-5889	21	5	5889 2	DATE
ejpam-5889	21	6	13	CARDINAL
ejpam-5889	21	7	18	CARDINAL
ejpam-5889	21	8	19	CARDINAL
ejpam-5889	21	9	20	CARDINAL
ejpam-5889	22	1	characteristic submultigroups	ORG
ejpam-5889	22	2	21	CARDINAL
ejpam-5889	22	3	24	CARDINAL
ejpam-5889	23	1	25–28	CARDINAL
ejpam-5889	24	1	29–34	CARDINAL
ejpam-5889	25	1	algebraic	PERSON
ejpam-5889	25	2	35–38	CARDINAL
ejpam-5889	26	1	39	CARDINAL
ejpam-5889	27	1	multiset	ORG
ejpam-5889	27	2	jordan	GPE
ejpam-5889	27	3	multiset	ORG
ejpam-5889	28	1	jordan	GPE
ejpam-5889	29	1	jordan	GPE
ejpam-5889	30	1	section 2	LAW
ejpam-5889	30	2	section 3	LAW
ejpam-5889	30	3	section 4	LAW
ejpam-5889	31	1	1	CARDINAL
ejpam-5889	32	1	1	CARDINAL
ejpam-5889	32	2	10	CARDINAL
ejpam-5889	33	1	1	CARDINAL
ejpam-5889	33	2	0	CARDINAL
ejpam-5889	33	3	1	CARDINAL
ejpam-5889	33	4	2	CARDINAL
ejpam-5889	33	5	11	CARDINAL
ejpam-5889	35	1	∈	ORG
ejpam-5889	36	1	3	CARDINAL
ejpam-5889	36	2	6	CARDINAL
ejpam-5889	37	1	1	CARDINAL
ejpam-5889	37	2	2	DATE
ejpam-5889	37	3	2	CARDINAL
ejpam-5889	37	4	d(s	PERSON
ejpam-5889	37	5	0	CARDINAL
ejpam-5889	38	1	d.	NORP
ejpam-5889	39	1	s /∈	ORG
ejpam-5889	40	1	s. p. a. ejegwa et al	PERSON
ejpam-5889	41	1	j. pure	PERSON
ejpam-5889	41	2	18	CARDINAL
ejpam-5889	41	3	2	CARDINAL
ejpam-5889	41	4	2025	CARDINAL
ejpam-5889	41	5	5889 3	DATE
ejpam-5889	41	6	4	CARDINAL
ejpam-5889	41	7	8	CARDINAL
ejpam-5889	46	1	⊆	CARDINAL
ejpam-5889	48	1	d⊕	DATE
ejpam-5889	48	2	⇒ cd⊕e(s	PERSON
ejpam-5889	51	1	5	CARDINAL
ejpam-5889	51	2	17	CARDINAL
ejpam-5889	53	1	∈	ORG
ejpam-5889	54	1	∈	ORG
ejpam-5889	54	2	−1	DATE
ejpam-5889	54	3	∈	PRODUCT
ejpam-5889	54	4	d∗	DATE
ejpam-5889	54	5	d∗	DATE
ejpam-5889	54	6	6	CARDINAL
ejpam-5889	54	7	26	CARDINAL
ejpam-5889	57	1	3	CARDINAL
ejpam-5889	57	2	7	CARDINAL
ejpam-5889	57	3	31	CARDINAL
ejpam-5889	61	1	8	CARDINAL
ejpam-5889	61	2	31	CARDINAL
ejpam-5889	62	1	⊆	CARDINAL
ejpam-5889	62	2	22	CARDINAL
ejpam-5889	66	1	10	CARDINAL
ejpam-5889	66	2	28	CARDINAL
ejpam-5889	68	1	d.	NORP
ejpam-5889	68	2	cdy(x	ORG
ejpam-5889	68	3	−1	CARDINAL
ejpam-5889	69	1	11	CARDINAL
ejpam-5889	69	2	18	CARDINAL
ejpam-5889	70	1	min{cd(y	PERSON
ejpam-5889	70	2	ce(z	ORG
ejpam-5889	70	3	∃ y	PERSON
ejpam-5889	71	1	4	CARDINAL
ejpam-5889	71	2	12	CARDINAL
ejpam-5889	71	3	28	CARDINAL
ejpam-5889	73	1	d. p. a. ejegwa et al	PERSON
ejpam-5889	74	1	j. pure	PERSON
ejpam-5889	74	2	18	CARDINAL
ejpam-5889	74	3	2	CARDINAL
ejpam-5889	74	4	2025	CARDINAL
ejpam-5889	74	5	5889 4	DATE
ejpam-5889	74	6	13 2	CARDINAL
ejpam-5889	74	7	jordan-hölder	PERSON
ejpam-5889	74	8	first	ORDINAL
ejpam-5889	74	9	39	CARDINAL
ejpam-5889	74	10	13	CARDINAL
ejpam-5889	75	1	⊆	CARDINAL
ejpam-5889	76	1	⊆	CARDINAL
ejpam-5889	76	2	5	CARDINAL
ejpam-5889	77	1	dn)∗	NORP
ejpam-5889	77	2	cd0(x	PERSON
ejpam-5889	78	1	∈	PRODUCT
ejpam-5889	78	2	6	CARDINAL
ejpam-5889	78	3	dn)∗	NORP
ejpam-5889	78	4	14	DATE
ejpam-5889	79	1	d0 ⊆	ORG
ejpam-5889	79	2	⊆	CARDINAL
ejpam-5889	80	1	⊆	CARDINAL
ejpam-5889	80	2	dn)∗	NORP
ejpam-5889	80	3	d∗	DATE
ejpam-5889	80	4	di−1 ◁di	PERSON
ejpam-5889	80	5	di/di−1	ORG
ejpam-5889	80	6	1 ≤	QUANTITY
ejpam-5889	81	1	d0 ◁d1 ◁	ORG
ejpam-5889	82	1	9	CARDINAL
ejpam-5889	82	2	15	CARDINAL
ejpam-5889	84	1	d. (ii	ORG
ejpam-5889	85	1	1	CARDINAL
ejpam-5889	86	1	d. p. a. ejegwa et al	PERSON
ejpam-5889	87	1	j. pure	PERSON
ejpam-5889	87	2	18	CARDINAL
ejpam-5889	87	3	2	CARDINAL
ejpam-5889	87	4	2025	CARDINAL
ejpam-5889	87	5	5889 5	DATE
ejpam-5889	87	6	13	CARDINAL
ejpam-5889	87	7	1	CARDINAL
ejpam-5889	87	8	1	CARDINAL
ejpam-5889	87	9	1	CARDINAL
ejpam-5889	87	10	d.	NORP
ejpam-5889	88	1	1	CARDINAL
ejpam-5889	88	2	1	DATE
ejpam-5889	88	3	1	CARDINAL
ejpam-5889	88	4	1	DATE
ejpam-5889	90	1	d∗	DATE
ejpam-5889	91	1	1},d1	CARDINAL
ejpam-5889	91	2	1	CARDINAL
ejpam-5889	91	3	d∗	DATE
ejpam-5889	91	4	1	CARDINAL
ejpam-5889	93	1	1	CARDINAL
ejpam-5889	93	2	1	CARDINAL
ejpam-5889	94	1	1	CARDINAL
ejpam-5889	95	1	1	CARDINAL
ejpam-5889	95	2	1	CARDINAL
ejpam-5889	95	3	submultigroups	PERSON
ejpam-5889	95	4	1	CARDINAL
ejpam-5889	95	5	1	CARDINAL
ejpam-5889	95	6	1	DATE
ejpam-5889	95	7	1	CARDINAL
ejpam-5889	95	8	1	DATE
ejpam-5889	95	9	1	CARDINAL
ejpam-5889	95	10	1	DATE
ejpam-5889	95	11	1	DATE
ejpam-5889	95	12	1	CARDINAL
ejpam-5889	95	13	1	DATE
ejpam-5889	95	14	1	DATE
ejpam-5889	96	1	1	CARDINAL
ejpam-5889	96	2	1	DATE
ejpam-5889	96	3	1	DATE
ejpam-5889	96	4	1	CARDINAL
ejpam-5889	96	5	1	DATE
ejpam-5889	96	6	1	CARDINAL
ejpam-5889	96	7	1	DATE
ejpam-5889	96	8	1	CARDINAL
ejpam-5889	96	9	1	DATE
ejpam-5889	96	10	1	CARDINAL
ejpam-5889	96	11	1	DATE
ejpam-5889	97	1	1	CARDINAL
ejpam-5889	97	2	1	DATE
ejpam-5889	97	3	1	CARDINAL
ejpam-5889	97	4	1	DATE
ejpam-5889	97	5	d∗	DATE
ejpam-5889	97	6	d.	NORP
ejpam-5889	98	1	2	CARDINAL
ejpam-5889	98	2	p. a. ejegwa et al	PERSON
ejpam-5889	99	1	j. pure	PERSON
ejpam-5889	99	2	18	CARDINAL
ejpam-5889	99	3	2	CARDINAL
ejpam-5889	99	4	2025	CARDINAL
ejpam-5889	99	5	5889 6	DATE
ejpam-5889	99	6	13	CARDINAL
ejpam-5889	99	7	2	CARDINAL
ejpam-5889	99	8	1	CARDINAL
ejpam-5889	99	9	1	CARDINAL
ejpam-5889	99	10	1	CARDINAL
ejpam-5889	99	11	1	CARDINAL
ejpam-5889	99	12	1	DATE
ejpam-5889	99	13	1	CARDINAL
ejpam-5889	99	14	1	DATE
ejpam-5889	99	15	1	CARDINAL
ejpam-5889	99	16	1	DATE
ejpam-5889	99	17	1	DATE
ejpam-5889	99	18	1	CARDINAL
ejpam-5889	99	19	1	DATE
ejpam-5889	99	20	1	DATE
ejpam-5889	99	21	1	CARDINAL
ejpam-5889	99	22	1	DATE
ejpam-5889	99	23	1	DATE
ejpam-5889	99	24	1	CARDINAL
ejpam-5889	99	25	1	DATE
ejpam-5889	99	26	1	CARDINAL
ejpam-5889	99	27	1	DATE
ejpam-5889	99	28	1	CARDINAL
ejpam-5889	99	29	1	DATE
ejpam-5889	99	30	1	CARDINAL
ejpam-5889	99	31	1	DATE
ejpam-5889	100	1	1	CARDINAL
ejpam-5889	100	2	1	DATE
ejpam-5889	100	3	1	CARDINAL
ejpam-5889	100	4	1	DATE
ejpam-5889	100	5	1	CARDINAL
ejpam-5889	100	6	1	CARDINAL
ejpam-5889	100	7	ḋ2	PERSON
ejpam-5889	100	8	1	CARDINAL
ejpam-5889	100	9	1	DATE
ejpam-5889	100	10	1	CARDINAL
ejpam-5889	100	11	ḋ3	GPE
ejpam-5889	100	12	1	CARDINAL
ejpam-5889	100	13	1	DATE
ejpam-5889	100	14	1	CARDINAL
ejpam-5889	100	15	1	CARDINAL
ejpam-5889	100	16	1	CARDINAL
ejpam-5889	100	17	1	DATE
ejpam-5889	100	18	1	CARDINAL
ejpam-5889	100	19	1	DATE
ejpam-5889	100	20	ḋ6	ORG
ejpam-5889	100	21	1	CARDINAL
ejpam-5889	100	22	1	DATE
ejpam-5889	100	23	1	DATE
ejpam-5889	100	24	1	CARDINAL
ejpam-5889	100	25	1	DATE
ejpam-5889	100	26	1	DATE
ejpam-5889	100	27	1	CARDINAL
ejpam-5889	100	28	1	DATE
ejpam-5889	100	29	1	DATE
ejpam-5889	100	30	1	CARDINAL
ejpam-5889	100	31	1	DATE
ejpam-5889	100	32	1	CARDINAL
ejpam-5889	100	33	1	DATE
ejpam-5889	100	34	ḋ10	ORG
ejpam-5889	100	35	1	CARDINAL
ejpam-5889	100	36	1	DATE
ejpam-5889	100	37	1	CARDINAL
ejpam-5889	100	38	1	DATE
ejpam-5889	100	39	ḋ11	ORG
ejpam-5889	100	40	1	CARDINAL
ejpam-5889	100	41	1	DATE
ejpam-5889	100	42	1	CARDINAL
ejpam-5889	100	43	1	DATE
ejpam-5889	100	44	ḋ3	GPE
ejpam-5889	100	45	d. submultigroups d̂2	PERSON
ejpam-5889	100	46	ḋ4	GPE
ejpam-5889	100	47	ofd	PRODUCT
ejpam-5889	103	1	2	CARDINAL
ejpam-5889	103	2	sn	ORG
ejpam-5889	103	3	1	CARDINAL
ejpam-5889	103	4	2	DATE
ejpam-5889	103	5	3	CARDINAL
ejpam-5889	103	6	⊆	CARDINAL
ejpam-5889	103	7	ρ−1	ORG
ejpam-5889	103	8	1	CARDINAL
ejpam-5889	103	9	ρ−1	ORG
ejpam-5889	103	10	2	CARDINAL
ejpam-5889	107	1	= e∗	PERSON
ejpam-5889	109	1	3	CARDINAL
ejpam-5889	109	2	3	CARDINAL
ejpam-5889	109	3	submultigroups	PERSON
ejpam-5889	114	1	4	CARDINAL
ejpam-5889	114	2	p. a. ejegwa et al	PERSON
ejpam-5889	115	1	j. pure	PERSON
ejpam-5889	115	2	18	CARDINAL
ejpam-5889	115	3	2	CARDINAL
ejpam-5889	115	4	2025	CARDINAL
ejpam-5889	115	5	5889 7	DATE
ejpam-5889	115	6	13	CARDINAL
ejpam-5889	115	7	4	CARDINAL
ejpam-5889	121	1	3	CARDINAL
ejpam-5889	121	2	1	CARDINAL
ejpam-5889	121	3	ab	ORG
ejpam-5889	121	4	8	CARDINAL
ejpam-5889	121	5	two	CARDINAL
ejpam-5889	121	6	1	CARDINAL
ejpam-5889	121	7	a−1b	ORG
ejpam-5889	121	8	d4	ORG
ejpam-5889	122	1	1	CARDINAL
ejpam-5889	123	1	a3)−1 =	PERSON
ejpam-5889	123	2	a2)−1	CARDINAL
ejpam-5889	124	1	non-abelian	NORP
ejpam-5889	125	1	1	CARDINAL
ejpam-5889	125	2	1	DATE
ejpam-5889	125	3	1	DATE
ejpam-5889	125	4	a2	ORG
ejpam-5889	125	5	a2	ORG
ejpam-5889	125	6	ab	GPE
ejpam-5889	125	7	ab	GPE
ejpam-5889	125	8	a2b	GPE
ejpam-5889	126	1	5	CARDINAL
ejpam-5889	126	2	5	CARDINAL
ejpam-5889	126	3	1	CARDINAL
ejpam-5889	126	4	1	CARDINAL
ejpam-5889	126	5	1	CARDINAL
ejpam-5889	126	6	1	CARDINAL
ejpam-5889	126	7	1	DATE
ejpam-5889	126	8	1	CARDINAL
ejpam-5889	126	9	1	CARDINAL
ejpam-5889	126	10	f4	CARDINAL
ejpam-5889	126	11	1	CARDINAL
ejpam-5889	126	12	1	DATE
ejpam-5889	126	13	1	CARDINAL
ejpam-5889	126	14	1	DATE
ejpam-5889	126	15	a2	ORG
ejpam-5889	126	16	1	CARDINAL
ejpam-5889	126	17	1	DATE
ejpam-5889	126	18	1	DATE
ejpam-5889	126	19	1	CARDINAL
ejpam-5889	126	20	1	DATE
ejpam-5889	126	21	1	DATE
ejpam-5889	126	22	a2	ORG
ejpam-5889	126	23	1	CARDINAL
ejpam-5889	126	24	1	DATE
ejpam-5889	126	25	1	DATE
ejpam-5889	126	26	a2	ORG
ejpam-5889	126	27	a2	ORG
ejpam-5889	126	28	f9	ORG
ejpam-5889	126	29	1	CARDINAL
ejpam-5889	126	30	1	CARDINAL
ejpam-5889	126	31	1	DATE
ejpam-5889	126	32	1	CARDINAL
ejpam-5889	126	33	1	DATE
ejpam-5889	126	34	1	CARDINAL
ejpam-5889	126	35	1	CARDINAL
ejpam-5889	126	36	1	CARDINAL
ejpam-5889	126	37	1	DATE
ejpam-5889	126	38	1	CARDINAL
ejpam-5889	126	39	1	CARDINAL
ejpam-5889	126	40	1	CARDINAL
ejpam-5889	126	41	1	DATE
ejpam-5889	126	42	1	CARDINAL
ejpam-5889	126	43	1	CARDINAL
ejpam-5889	126	44	ab	ORG
ejpam-5889	126	45	1	CARDINAL
ejpam-5889	126	46	1	DATE
ejpam-5889	126	47	ab	ORG
ejpam-5889	126	48	1	CARDINAL
ejpam-5889	126	49	1	DATE
ejpam-5889	126	50	a2	ORG
ejpam-5889	126	51	ab	GPE
ejpam-5889	126	52	ab	GPE
ejpam-5889	126	53	a2b	GPE
ejpam-5889	126	54	1	CARDINAL
ejpam-5889	126	55	1	DATE
ejpam-5889	126	56	1	DATE
ejpam-5889	126	57	ab	ORG
ejpam-5889	126	58	1	CARDINAL
ejpam-5889	126	59	1	DATE
ejpam-5889	126	60	1	DATE
ejpam-5889	126	61	a2	ORG
ejpam-5889	126	62	ab	GPE
ejpam-5889	126	63	ab	GPE
ejpam-5889	126	64	a2b	GPE
ejpam-5889	126	65	1	CARDINAL
ejpam-5889	126	66	1	DATE
ejpam-5889	126	67	1	DATE
ejpam-5889	126	68	a2	ORG
ejpam-5889	126	69	a2	ORG
ejpam-5889	126	70	ab	GPE
ejpam-5889	126	71	ab	GPE
ejpam-5889	126	72	a2b	GPE
ejpam-5889	127	1	j. pure	PERSON
ejpam-5889	127	2	18	CARDINAL
ejpam-5889	127	3	2	CARDINAL
ejpam-5889	127	4	2025	CARDINAL
ejpam-5889	127	5	5889 8 of 13	DATE
ejpam-5889	127	6	f9	ORG
ejpam-5889	128	1	f4	CARDINAL
ejpam-5889	128	2	f. hence	PERSON
ejpam-5889	130	1	2	CARDINAL
ejpam-5889	131	1	submultigroups	ORG
ejpam-5889	135	1	16	DATE
ejpam-5889	137	1	cd0(x	PERSON
ejpam-5889	138	1	9	CARDINAL
ejpam-5889	138	2	dn)∗	NORP
ejpam-5889	138	3	d∗	DATE
ejpam-5889	138	4	di	ORG
ejpam-5889	138	5	0 ≤	QUANTITY
ejpam-5889	139	1	1	CARDINAL
ejpam-5889	139	2	4	CARDINAL
ejpam-5889	139	3	1	CARDINAL
ejpam-5889	140	1	⊆	CARDINAL
ejpam-5889	140	2	⊆	CARDINAL
ejpam-5889	140	3	⊆	CARDINAL
ejpam-5889	140	4	⊆	CARDINAL
ejpam-5889	141	1	⊆	CARDINAL
ejpam-5889	141	2	⊆	CARDINAL
ejpam-5889	141	3	⊆	CARDINAL
ejpam-5889	141	4	⊆	CARDINAL
ejpam-5889	141	5	⊆	CARDINAL
ejpam-5889	142	1	⊆	CARDINAL
ejpam-5889	142	2	⊆	CARDINAL
ejpam-5889	142	3	⊆ d̂6	MONEY
ejpam-5889	142	4	⊆	CARDINAL
ejpam-5889	142	5	⊆	CARDINAL
ejpam-5889	142	6	d̂i ◁	PERSON
ejpam-5889	142	7	0 ≤	QUANTITY
ejpam-5889	143	1	1	CARDINAL
ejpam-5889	143	2	5	CARDINAL
ejpam-5889	144	1	2	CARDINAL
ejpam-5889	144	2	⊆	CARDINAL
ejpam-5889	144	3	⊆	CARDINAL
ejpam-5889	144	4	⊆	CARDINAL
ejpam-5889	144	5	⊆	CARDINAL
ejpam-5889	145	1	êi ◁	ORG
ejpam-5889	145	2	0 ≤	QUANTITY
ejpam-5889	146	1	1	CARDINAL
ejpam-5889	148	1	p. a. ejegwa et al	PERSON
ejpam-5889	149	1	j. pure	PERSON
ejpam-5889	149	2	18	CARDINAL
ejpam-5889	149	3	2	CARDINAL
ejpam-5889	149	4	2025	CARDINAL
ejpam-5889	149	5	5889 9	DATE
ejpam-5889	149	6	13	CARDINAL
ejpam-5889	149	7	17	DATE
ejpam-5889	152	1	10	CARDINAL
ejpam-5889	152	2	dn)∗	NORP
ejpam-5889	152	3	d∗	DATE
ejpam-5889	152	4	0 ≤	QUANTITY
ejpam-5889	153	1	1	CARDINAL
ejpam-5889	153	2	0 ≤	QUANTITY
ejpam-5889	154	1	1	CARDINAL
ejpam-5889	155	1	example 1	DATE
ejpam-5889	155	2	⊆	CARDINAL
ejpam-5889	155	3	⊆	CARDINAL
ejpam-5889	155	4	⊆	CARDINAL
ejpam-5889	155	5	⊆	CARDINAL
ejpam-5889	156	1	⊆	CARDINAL
ejpam-5889	156	2	⊆	CARDINAL
ejpam-5889	156	3	⊆	CARDINAL
ejpam-5889	156	4	⊆	CARDINAL
ejpam-5889	156	5	⊆	CARDINAL
ejpam-5889	157	1	⊆	CARDINAL
ejpam-5889	157	2	⊆	CARDINAL
ejpam-5889	157	3	⊆ d̂6	MONEY
ejpam-5889	157	4	⊆	CARDINAL
ejpam-5889	157	5	⊆	CARDINAL
ejpam-5889	157	6	d̂i ◁	PERSON
ejpam-5889	157	7	0 ≤	QUANTITY
ejpam-5889	158	1	1 and d̂i+1	QUANTITY
ejpam-5889	158	2	0 ≤	QUANTITY
ejpam-5889	159	1	1	CARDINAL
ejpam-5889	160	1	2	CARDINAL
ejpam-5889	160	2	⊆	CARDINAL
ejpam-5889	160	3	⊆	CARDINAL
ejpam-5889	160	4	⊆	CARDINAL
ejpam-5889	160	5	⊆	CARDINAL
ejpam-5889	160	6	1	CARDINAL
ejpam-5889	160	7	2	DATE
ejpam-5889	160	8	3	DATE
ejpam-5889	160	9	4	DATE
ejpam-5889	160	10	5	DATE
ejpam-5889	160	11	êi ◁	ORG
ejpam-5889	160	12	0 ≤	QUANTITY
ejpam-5889	161	1	0 ≤	QUANTITY
ejpam-5889	162	1	1	CARDINAL
ejpam-5889	162	2	6	CARDINAL
ejpam-5889	162	3	0	CARDINAL
ejpam-5889	162	4	0	DATE
ejpam-5889	162	5	0	CARDINAL
ejpam-5889	162	6	1	CARDINAL
ejpam-5889	162	7	1	CARDINAL
ejpam-5889	162	8	2	DATE
ejpam-5889	162	9	2	DATE
ejpam-5889	162	10	3	DATE
ejpam-5889	162	11	3	DATE
ejpam-5889	162	12	4	DATE
ejpam-5889	162	13	4	DATE
ejpam-5889	162	14	5	DATE
ejpam-5889	162	15	5	CARDINAL
ejpam-5889	163	1	0	CARDINAL
ejpam-5889	163	2	1	DATE
ejpam-5889	163	3	2	DATE
ejpam-5889	163	4	3	DATE
ejpam-5889	163	5	4	DATE
ejpam-5889	163	6	5	CARDINAL
ejpam-5889	163	7	0	CARDINAL
ejpam-5889	163	8	0	DATE
ejpam-5889	163	9	1	CARDINAL
ejpam-5889	163	10	2	DATE
ejpam-5889	163	11	3	DATE
ejpam-5889	163	12	4	DATE
ejpam-5889	163	13	5	CARDINAL
ejpam-5889	163	14	0	CARDINAL
ejpam-5889	163	15	0	DATE
ejpam-5889	163	16	1	CARDINAL
ejpam-5889	163	17	1	CARDINAL
ejpam-5889	163	18	2	DATE
ejpam-5889	163	19	2	DATE
ejpam-5889	163	20	3	DATE
ejpam-5889	163	21	3	DATE
ejpam-5889	163	22	4	DATE
ejpam-5889	163	23	4	DATE
ejpam-5889	163	24	5	DATE
ejpam-5889	163	25	5	CARDINAL
ejpam-5889	163	26	0	CARDINAL
ejpam-5889	163	27	0	DATE
ejpam-5889	163	28	0	CARDINAL
ejpam-5889	163	29	1	CARDINAL
ejpam-5889	163	30	2	DATE
ejpam-5889	163	31	3	DATE
ejpam-5889	163	32	4	DATE
ejpam-5889	163	33	5	CARDINAL
ejpam-5889	163	34	0	CARDINAL
ejpam-5889	163	35	0	DATE
ejpam-5889	163	36	0	CARDINAL
ejpam-5889	163	37	1	CARDINAL
ejpam-5889	163	38	1	CARDINAL
ejpam-5889	163	39	2	DATE
ejpam-5889	163	40	2	DATE
ejpam-5889	163	41	3	DATE
ejpam-5889	163	42	3	DATE
ejpam-5889	163	43	4	DATE
ejpam-5889	163	44	4	DATE
ejpam-5889	163	45	5	DATE
ejpam-5889	163	46	5	CARDINAL
ejpam-5889	163	47	⊆	CARDINAL
ejpam-5889	163	48	⊆	CARDINAL
ejpam-5889	163	49	⊆	CARDINAL
ejpam-5889	163	50	⊆	CARDINAL
ejpam-5889	163	51	⊆	CARDINAL
ejpam-5889	163	52	⊆	CARDINAL
ejpam-5889	164	1	1	CARDINAL
ejpam-5889	164	2	2	DATE
ejpam-5889	164	3	3	DATE
ejpam-5889	164	4	4	DATE
ejpam-5889	164	5	ĉi ◁ ĉi+1	ORG
ejpam-5889	164	6	0 ≤	QUANTITY
ejpam-5889	164	7	1	CARDINAL
ejpam-5889	164	8	0 ≤	QUANTITY
ejpam-5889	165	1	1	CARDINAL
ejpam-5889	166	1	1	CARDINAL
ejpam-5889	168	1	p. a. ejegwa et al	PERSON
ejpam-5889	169	1	j. pure	PERSON
ejpam-5889	169	2	18	CARDINAL
ejpam-5889	169	3	2	CARDINAL
ejpam-5889	169	4	2025	CARDINAL
ejpam-5889	169	5	5889 10	DATE
ejpam-5889	169	6	13	CARDINAL
ejpam-5889	175	1	|b|	ORG
ejpam-5889	175	2	cb0(x	PERSON
ejpam-5889	176	1	∈	PRODUCT
ejpam-5889	177	1	cb0(x	PERSON
ejpam-5889	178	1	∈	PRODUCT
ejpam-5889	178	2	2	CARDINAL
ejpam-5889	178	3	jordan	GPE
ejpam-5889	179	1	at least two	CARDINAL
ejpam-5889	181	1	two	CARDINAL
ejpam-5889	182	1	∈	PRODUCT
ejpam-5889	182	2	cb0(x	PERSON
ejpam-5889	182	3	∈	PRODUCT
ejpam-5889	182	4	0 ≤	QUANTITY
ejpam-5889	183	1	1	CARDINAL
ejpam-5889	183	2	0 ≤ j ≤ m−1	QUANTITY
ejpam-5889	184	1	dn	PERSON
ejpam-5889	184	2	bm/bm−1	ORG
ejpam-5889	186	1	1	CARDINAL
ejpam-5889	189	1	φ = dn−1	PERSON
ejpam-5889	189	2	ω	CARDINAL
ejpam-5889	189	3	ω	ORG
ejpam-5889	189	4	bm−1	GPE
ejpam-5889	190	1	ω	ORG
ejpam-5889	190	2	cω1(x	PERSON
ejpam-5889	191	1	∈	PRODUCT
ejpam-5889	191	2	cd0(x	ORG
ejpam-5889	191	3	∈	PRODUCT
ejpam-5889	191	4	cω1(x	PERSON
ejpam-5889	192	1	∈	PRODUCT
ejpam-5889	192	2	φ	ORG
ejpam-5889	193	1	1	CARDINAL
ejpam-5889	193	2	1	CARDINAL
ejpam-5889	193	3	2	CARDINAL
ejpam-5889	194	1	11	CARDINAL
ejpam-5889	194	2	cb0(x	PERSON
ejpam-5889	195	1	cω1(x	PERSON
ejpam-5889	197	1	j. pure	PERSON
ejpam-5889	197	2	18	CARDINAL
ejpam-5889	197	3	2	CARDINAL
ejpam-5889	197	4	2025	CARDINAL
ejpam-5889	197	5	5889 11	DATE
ejpam-5889	197	6	13	CARDINAL
ejpam-5889	198	1	m−	PERSON
ejpam-5889	198	2	1	CARDINAL
ejpam-5889	198	3	1	CARDINAL
ejpam-5889	198	4	2	CARDINAL
ejpam-5889	198	5	bm−1/bm−2	ORG
ejpam-5889	199	1	12	CARDINAL
ejpam-5889	199	2	1	CARDINAL
ejpam-5889	199	3	+ 1	DATE
ejpam-5889	199	4	11	CARDINAL
ejpam-5889	200	1	13	CARDINAL
ejpam-5889	200	2	12	CARDINAL
ejpam-5889	200	3	bm−1	PERSON
ejpam-5889	202	1	14	CARDINAL
ejpam-5889	202	2	13	CARDINAL
ejpam-5889	202	3	14	CARDINAL
ejpam-5889	202	4	φ/ω	ORG
ejpam-5889	203	1	φ/ω	ORG
ejpam-5889	203	2	dn	PERSON
ejpam-5889	203	3	bm/bm−1	ORG
ejpam-5889	204	1	3.	CARDINAL
ejpam-5889	204	2	multiset	ORG
ejpam-5889	206	1	jordan	GPE
ejpam-5889	206	2	multiset	ORG
ejpam-5889	206	3	at least two	CARDINAL
ejpam-5889	210	1	1	CARDINAL
ejpam-5889	212	1	second	ORDINAL
ejpam-5889	212	2	2	CARDINAL
ejpam-5889	212	3	addison-wesley	ORG
ejpam-5889	212	4	massachusetts	GPE
ejpam-5889	212	5	1981	DATE
ejpam-5889	213	1	2	CARDINAL
ejpam-5889	216	1	6:25–33	CARDINAL
ejpam-5889	216	2	1983	DATE
ejpam-5889	217	1	p. a. ejegwa et al	PERSON
ejpam-5889	218	1	j. pure	PERSON
ejpam-5889	218	2	18	CARDINAL
ejpam-5889	218	3	2	CARDINAL
ejpam-5889	218	4	2025	CARDINAL
ejpam-5889	218	5	5889 12	DATE
ejpam-5889	218	6	13	CARDINAL
ejpam-5889	218	7	3	CARDINAL
ejpam-5889	219	1	multiset	ORG
ejpam-5889	220	1	notre	ORG
ejpam-5889	220	2	j. logic	PERSON
ejpam-5889	220	3	31:36–65, 1989	DATE
ejpam-5889	221	1	4	CARDINAL
ejpam-5889	222	1	multiset	ORG
ejpam-5889	223	1	1(4):319–352	CARDINAL
ejpam-5889	223	2	1991	DATE
ejpam-5889	224	1	5	CARDINAL
ejpam-5889	224	2	k p girish	PERSON
ejpam-5889	225	1	multiset	ORG
ejpam-5889	227	1	sci.	ORG
ejpam-5889	227	2	179:758–768	CARDINAL
ejpam-5889	227	3	2009	DATE
ejpam-5889	228	1	6	CARDINAL
ejpam-5889	231	1	sci.	ORG
ejpam-5889	231	2	132:241–254, 2001	DATE
ejpam-5889	232	1	7	CARDINAL
ejpam-5889	232	2	singh	GPE
ejpam-5889	232	3	ibrahim	PERSON
ejpam-5889	232	4	t yohanna	PERSON
ejpam-5889	232	5	j n	PERSON
ejpam-5889	232	6	singh	GPE
ejpam-5889	234	1	novi	PERSON
ejpam-5889	234	2	j. math	PERSON
ejpam-5889	234	3	37(2):73–92	CARDINAL
ejpam-5889	234	4	2007	DATE
ejpam-5889	235	1	8	CARDINAL
ejpam-5889	237	1	berlin	GPE
ejpam-5889	237	2	heidelberg	GPE
ejpam-5889	237	3	347358, 2001	DATE
ejpam-5889	238	1	9	CARDINAL
ejpam-5889	238	2	william-west	PERSON
ejpam-5889	240	1	commun	PERSON
ejpam-5889	241	1	4(3):284–292	DATE
ejpam-5889	241	2	2021	CARDINAL
ejpam-5889	242	1	10	CARDINAL
ejpam-5889	243	1	contr.	PERSON
ejpam-5889	243	2	8(3):338–353, 1965	DATE
ejpam-5889	244	1	11	CARDINAL
ejpam-5889	244	2	rosenfeld	PERSON
ejpam-5889	246	1	j. math	PERSON
ejpam-5889	249	1	35(3):512–517	DATE
ejpam-5889	249	2	1971	DATE
ejpam-5889	250	1	12	CARDINAL
ejpam-5889	252	1	syst	ORG
ejpam-5889	252	2	7:297–305, 1982	DATE
ejpam-5889	253	1	13	CARDINAL
ejpam-5889	255	1	j. uni	PERSON
ejpam-5889	255	2	2(2):175–182	DATE
ejpam-5889	255	3	2019	DATE
ejpam-5889	256	1	14	CARDINAL
ejpam-5889	256	2	p preeti	PERSON
ejpam-5889	256	3	k sharma	PERSON
ejpam-5889	257	1	abelian	NORP
ejpam-5889	258	1	aip conf.	ORG
ejpam-5889	259	1	2142:170025	CARDINAL
ejpam-5889	259	2	2019	DATE
ejpam-5889	260	1	15	CARDINAL
ejpam-5889	260	2	j manjeet	PERSON
ejpam-5889	261	1	abelian p	GPE
ejpam-5889	261	2	three	CARDINAL
ejpam-5889	262	1	adv	ORG
ejpam-5889	262	2	2017	DATE
ejpam-5889	263	1	16	CARDINAL
ejpam-5889	263	2	k sharma	PERSON
ejpam-5889	266	1	j.	PERSON
ejpam-5889	267	1	8(1):51–57	CARDINAL
ejpam-5889	267	2	2015	DATE
ejpam-5889	268	1	17	CARDINAL
ejpam-5889	268	2	s k samanta	PERSON
ejpam-5889	270	1	ann	PERSON
ejpam-5889	271	1	6(3):643–656	CARDINAL
ejpam-5889	271	2	2013	DATE
ejpam-5889	272	1	18	CARDINAL
ejpam-5889	273	1	multiset	ORG
ejpam-5889	274	1	phd thesis	PERSON
ejpam-5889	274	2	ahmadu bello university	ORG
ejpam-5889	274	3	zaria	GPE
ejpam-5889	274	4	nigeria	GPE
ejpam-5889	274	5	2018	DATE
ejpam-5889	275	1	19	CARDINAL
ejpam-5889	275	2	ibrahim	PERSON
ejpam-5889	277	1	syst	LOC
ejpam-5889	277	2	24(2):169–177	DATE
ejpam-5889	277	3	2016	DATE
ejpam-5889	278	1	20	CARDINAL
ejpam-5889	278	2	ibrahim	PERSON
ejpam-5889	280	1	bul	PERSON
ejpam-5889	284	1	2017	DATE
ejpam-5889	285	1	21	CARDINAL
ejpam-5889	286	1	invariant submultigroups	ORG
ejpam-5889	288	1	sci.	ORG
ejpam-5889	288	2	10(2):96–103	DATE
ejpam-5889	288	3	2020	DATE
ejpam-5889	289	1	22	CARDINAL
ejpam-5889	289	2	ibrahim	PERSON
ejpam-5889	291	1	syst	LOC
ejpam-5889	291	2	25(2):231–244	CARDINAL
ejpam-5889	291	3	2017	DATE
ejpam-5889	292	1	23	CARDINAL
ejpam-5889	292	2	ibrahim	PERSON
ejpam-5889	294	1	5(4):1–8, 2017.	PERCENT
ejpam-5889	295	1	24	CARDINAL
ejpam-5889	297	1	mathematica	PERSON
ejpam-5889	297	2	39:147–163	CARDINAL
ejpam-5889	297	3	2020	DATE
ejpam-5889	298	1	25	CARDINAL
ejpam-5889	299	1	multiset	ORG
ejpam-5889	300	1	south east	LOC
ejpam-5889	300	2	j. math	PERSON
ejpam-5889	301	1	sci.	ORG
ejpam-5889	301	2	15(3):1–10	CARDINAL
ejpam-5889	301	3	2019	DATE
ejpam-5889	302	1	p. a. ejegwa et al	PERSON
ejpam-5889	303	1	j. pure	PERSON
ejpam-5889	303	2	18	CARDINAL
ejpam-5889	303	3	2	CARDINAL
ejpam-5889	303	4	2025	CARDINAL
ejpam-5889	303	5	5889 13	DATE
ejpam-5889	303	6	13	CARDINAL
ejpam-5889	303	7	26	CARDINAL
ejpam-5889	305	1	mathematica	PERSON
ejpam-5889	305	2	2019	DATE
ejpam-5889	306	1	27	CARDINAL
ejpam-5889	308	1	syst	LOC
ejpam-5889	308	2	25(1):21–26	DATE
ejpam-5889	308	3	2017	DATE
ejpam-5889	309	1	28	CARDINAL
ejpam-5889	309	2	ibrahim	PERSON
ejpam-5889	312	1	sci.	ORG
ejpam-5889	312	2	7(2):124–140	CARDINAL
ejpam-5889	312	3	2017	DATE
ejpam-5889	313	1	29	CARDINAL
ejpam-5889	313	2	ibrahim	PERSON
ejpam-5889	316	1	j. math	PERSON
ejpam-5889	317	1	combin	PERSON
ejpam-5889	317	2	2017	DATE
ejpam-5889	318	1	30	CARDINAL
ejpam-5889	318	2	ibrahim	PERSON
ejpam-5889	320	1	ann	PERSON
ejpam-5889	321	1	17(3):231–245	DATE
ejpam-5889	321	2	2019	DATE
ejpam-5889	322	1	31	CARDINAL
ejpam-5889	322	2	ibrahim	PERSON
ejpam-5889	324	1	palestine	GPE
ejpam-5889	324	2	9(1):31–47	CARDINAL
ejpam-5889	324	3	2020	DATE
ejpam-5889	325	1	32	CARDINAL
ejpam-5889	325	2	ibrahim	PERSON
ejpam-5889	326	1	multiset	ORG
ejpam-5889	327	1	ann	PERSON
ejpam-5889	328	1	14(5):515–526	CARDINAL
ejpam-5889	328	2	2017	DATE
ejpam-5889	329	1	33	CARDINAL
ejpam-5889	329	2	j m	PERSON
ejpam-5889	330	1	multigroup	GPE
ejpam-5889	331	1	ramanujan soc.	ORG
ejpam-5889	333	1	mathemat	PERSON
ejpam-5889	334	1	sci.	ORG
ejpam-5889	334	2	7(2):67–82	CARDINAL
ejpam-5889	334	3	2020	DATE
ejpam-5889	335	1	34	CARDINAL
ejpam-5889	335	2	ibrahim	PERSON
ejpam-5889	337	1	j. math	ORG
ejpam-5889	338	1	sci.	ORG
ejpam-5889	338	2	4:377–385	CARDINAL
ejpam-5889	338	3	2020	DATE
ejpam-5889	339	1	35	CARDINAL
ejpam-5889	340	1	multiset	ORG
ejpam-5889	341	1	sci.	ORG
ejpam-5889	341	2	21:84–90	DATE
ejpam-5889	341	3	2019	DATE
ejpam-5889	342	1	36	CARDINAL
ejpam-5889	344	1	j. math	PERSON
ejpam-5889	345	1	sci.	ORG
ejpam-5889	345	2	4(1):83–97	CARDINAL
ejpam-5889	345	3	2020	DATE
ejpam-5889	346	1	37	CARDINAL
ejpam-5889	347	1	multiset	ORG
ejpam-5889	347	2	algebraic structures	ORG
ejpam-5889	347	3	jana	PERSON
ejpam-5889	347	4	c.	PERSON
ejpam-5889	347	5	senapati	GPE
ejpam-5889	347	6	t. pal	GPE
ejpam-5889	348	1	hershey	ORG
ejpam-5889	348	2	pennsylvania	GPE
ejpam-5889	348	3	17033-1240	DATE
ejpam-5889	348	4	78-90, 2020	DATE
ejpam-5889	349	1	38	CARDINAL
ejpam-5889	350	1	multiset	ORG
ejpam-5889	351	1	j. math	PERSON
ejpam-5889	351	2	37(3):479–489	DATE
ejpam-5889	351	3	2018	DATE
ejpam-5889	352	1	39	CARDINAL
ejpam-5889	352	2	j m agbetayo	PERSON
ejpam-5889	357	1	13(2):375–381	CARDINAL
ejpam-5889	357	2	2023	CARDINAL