id	sid	eid	entity	type
ejpam-4793	1	1	european journal	ORG
ejpam-4793	2	1	16	CARDINAL
ejpam-4793	2	2	3	CARDINAL
ejpam-4793	2	3	2023	CARDINAL
ejpam-4793	2	4	1772-1793	DATE
ejpam-4793	2	5	1307-5543	CARDINAL
ejpam-4793	2	6	new york	GPE
ejpam-4793	2	7	γ-submonoids	GPE
ejpam-4793	2	8	γ-submonoids	ORG
ejpam-4793	2	9	t. sarapuddin1,∗	PERSON
ejpam-4793	2	10	jocelyn p. vilela1	PERSON
ejpam-4793	3	1	1	CARDINAL
ejpam-4793	3	2	msu-iligan institute of technology	ORG
ejpam-4793	3	3	9200	CARDINAL
ejpam-4793	3	4	iligan city	GPE
ejpam-4793	3	5	philippines	GPE
ejpam-4793	4	1	γ-submonoids	GPE
ejpam-4793	5	1	γ-submonoids	ORG
ejpam-4793	6	1	2020	DATE
ejpam-4793	6	2	20m32	CARDINAL
ejpam-4793	6	3	1	CARDINAL
ejpam-4793	6	4	te	ORG
ejpam-4793	9	1	∑ e∈s−1(v	PERSON
ejpam-4793	10	1	+ 1	DATE
ejpam-4793	12	1	3	CARDINAL
ejpam-4793	13	1	monoid automorphisms	ORG
ejpam-4793	13	2	li	PERSON
ejpam-4793	14	1	1	CARDINAL
ejpam-4793	17	1	5	CARDINAL
ejpam-4793	18	1	γ-submonoids	GPE
ejpam-4793	21	1	hulsen.sarapuddin@g.msuiit.edu.ph	ORG
ejpam-4793	21	2	h. t. sarapuddin	PERSON
ejpam-4793	21	3	jocelyn.vilela@g.msuiit.edu.ph	GPE
ejpam-4793	21	4	j. p. vilela	ORG
ejpam-4793	21	5	1772	DATE
ejpam-4793	22	1	2023	CARDINAL
ejpam-4793	23	1	h. sarapuddin	PERSON
ejpam-4793	23	2	j. vilela	PERSON
ejpam-4793	24	1	j. pure	PERSON
ejpam-4793	24	2	16	CARDINAL
ejpam-4793	24	3	3	CARDINAL
ejpam-4793	24	4	2023	CARDINAL
ejpam-4793	24	5	1772-1793	DATE
ejpam-4793	26	1	1	CARDINAL
ejpam-4793	27	1	2	CARDINAL
ejpam-4793	27	2	∈	ORG
ejpam-4793	27	3	∗	CARDINAL
ejpam-4793	27	4	∗	CARDINAL
ejpam-4793	27	5	∗	CARDINAL
ejpam-4793	27	6	2	CARDINAL
ejpam-4793	28	1	2	CARDINAL
ejpam-4793	28	2	1	CARDINAL
ejpam-4793	28	3	∈	ORG
ejpam-4793	28	4	1	CARDINAL
ejpam-4793	28	5	∗ 1	DATE
ejpam-4793	28	6	∈	ORG
ejpam-4793	29	1	∈	ORG
ejpam-4793	29	2	y ∗ x.	PERSON
ejpam-4793	30	1	1	CARDINAL
ejpam-4793	31	1	3	CARDINAL
ejpam-4793	32	1	6	CARDINAL
ejpam-4793	33	1	1	CARDINAL
ejpam-4793	34	1	4	CARDINAL
ejpam-4793	35	1	6	CARDINAL
ejpam-4793	36	1	φ(a	ORG
ejpam-4793	36	2	∗	CARDINAL
ejpam-4793	37	1	φ(1	ORG
ejpam-4793	38	1	1n	CARDINAL
ejpam-4793	38	2	∈	ORG
ejpam-4793	38	3	1m	QUANTITY
ejpam-4793	38	4	1n	CARDINAL
ejpam-4793	39	1	1	CARDINAL
ejpam-4793	39	2	n,+	PERSON
ejpam-4793	39	3	0	CARDINAL
ejpam-4793	40	1	∈	ORG
ejpam-4793	41	1	φ(y	ORG
ejpam-4793	41	2	1	CARDINAL
ejpam-4793	41	3	φ	ORG
ejpam-4793	42	1	5	CARDINAL
ejpam-4793	43	1	6	CARDINAL
ejpam-4793	43	2	∈	ORG
ejpam-4793	44	1	1	CARDINAL
ejpam-4793	45	1	6	CARDINAL
ejpam-4793	46	1	ρ(x	PERSON
ejpam-4793	47	1	∈	ORG
ejpam-4793	48	1	6	CARDINAL
ejpam-4793	49	1	4	CARDINAL
ejpam-4793	50	1	xρhy	ORG
ejpam-4793	50	2	1	CARDINAL
ejpam-4793	51	1	4	CARDINAL
ejpam-4793	52	1	7	CARDINAL
ejpam-4793	53	1	2	CARDINAL
ejpam-4793	53	2	∈	ORG
ejpam-4793	53	3	g1	ORG
ejpam-4793	57	1	s.	PERSON
ejpam-4793	57	2	2	CARDINAL
ejpam-4793	58	1	2gx	ORDINAL
ejpam-4793	63	1	2gx	ORDINAL
ejpam-4793	64	1	g1	ORG
ejpam-4793	65	1	20x	CARDINAL
ejpam-4793	66	1	2g1+g2x	CARDINAL
ejpam-4793	66	2	2g12g2x	CARDINAL
ejpam-4793	68	1	h. sarapuddin	PERSON
ejpam-4793	68	2	j. vilela	PERSON
ejpam-4793	69	1	j. pure	PERSON
ejpam-4793	69	2	16	CARDINAL
ejpam-4793	69	3	3	CARDINAL
ejpam-4793	69	4	2023	CARDINAL
ejpam-4793	69	5	1772-1793	DATE
ejpam-4793	69	6	8	CARDINAL
ejpam-4793	70	1	3	CARDINAL
ejpam-4793	71	1	∈	ORG
ejpam-4793	71	2	∈	ORG
ejpam-4793	72	1	∗	CARDINAL
ejpam-4793	73	1	∈	ORG
ejpam-4793	74	1	3	CARDINAL
ejpam-4793	75	1	0	CARDINAL
ejpam-4793	77	1	2αx	ORDINAL
ejpam-4793	77	2	2	CARDINAL
ejpam-4793	77	3	∈	ORG
ejpam-4793	81	1	2α(x	CARDINAL
ejpam-4793	82	1	2αx	ORDINAL
ejpam-4793	86	1	4	CARDINAL
ejpam-4793	87	1	γ ×	ORG
ejpam-4793	88	1	7→	CARDINAL
ejpam-4793	88	2	2αa	ORDINAL
ejpam-4793	88	3	2αb	ORDINAL
ejpam-4793	88	4	2αc	ORDINAL
ejpam-4793	91	1	γ×	ORG
ejpam-4793	95	1	2αa	ORDINAL
ejpam-4793	95	2	2αb	ORDINAL
ejpam-4793	95	3	2αc	ORDINAL
ejpam-4793	95	4	2βf 2βg 2βh	DATE
ejpam-4793	96	1	∈	ORG
ejpam-4793	96	2	0	CARDINAL
ejpam-4793	97	1	20a 20b 20c	DATE
ejpam-4793	98	1	2α+βa 2α+βb 2α+βc 2α+βd	DATE
ejpam-4793	98	2	2α2βa 2α3βb 2α4βc	CARDINAL
ejpam-4793	99	1	2βa	ORDINAL
ejpam-4793	99	2	2βb	ORDINAL
ejpam-4793	99	3	2βc	ORDINAL
ejpam-4793	101	1	φ	PERSON
ejpam-4793	108	1	2α(a+	CARDINAL
ejpam-4793	108	2	2α(b+	CARDINAL
ejpam-4793	108	3	2α(c+	CARDINAL
ejpam-4793	109	1	h. sarapuddin	PERSON
ejpam-4793	109	2	j. vilela	PERSON
ejpam-4793	110	1	j. pure	PERSON
ejpam-4793	110	2	16	CARDINAL
ejpam-4793	110	3	3	CARDINAL
ejpam-4793	110	4	2023	CARDINAL
ejpam-4793	110	5	1772-1793 1775	DATE
ejpam-4793	110	6	2αa+	CARDINAL
ejpam-4793	110	7	2αe 2αb+	WORK_OF_ART
ejpam-4793	110	8	2αg	ORDINAL
ejpam-4793	110	9	2αd+ 2αh	TIME
ejpam-4793	111	1	2αa	ORDINAL
ejpam-4793	111	2	2αb	ORDINAL
ejpam-4793	111	3	2αc	ORDINAL
ejpam-4793	112	1	2αe	ORDINAL
ejpam-4793	112	2	2αf	ORDINAL
ejpam-4793	112	3	2αg	ORDINAL
ejpam-4793	112	4	2αh	ORDINAL
ejpam-4793	116	1	5	CARDINAL
ejpam-4793	116	2	1	CARDINAL
ejpam-4793	116	3	∗ 1	DATE
ejpam-4793	118	1	∈	ORG
ejpam-4793	120	1	1	CARDINAL
ejpam-4793	122	1	9	CARDINAL
ejpam-4793	123	1	1	CARDINAL
ejpam-4793	123	2	m1 and m2	PRODUCT
ejpam-4793	126	1	2	CARDINAL
ejpam-4793	127	1	1	CARDINAL
ejpam-4793	127	2	γ	GPE
ejpam-4793	127	3	6	CARDINAL
ejpam-4793	128	1	n,+	PERSON
ejpam-4793	128	2	∈	ORG
ejpam-4793	132	1	∈	ORG
ejpam-4793	132	2	n ∈ n	ORG
ejpam-4793	133	1	∈	ORG
ejpam-4793	143	1	φ	PERSON
ejpam-4793	144	1	0	CARDINAL
ejpam-4793	144	2	example 1	DATE
ejpam-4793	144	3	∈	ORG
ejpam-4793	144	4	∈	ORG
ejpam-4793	145	1	9(ii	CARDINAL
ejpam-4793	145	2	φ	ORG
ejpam-4793	146	1	7	CARDINAL
ejpam-4793	146	2	3	CARDINAL
ejpam-4793	146	3	example 4	DATE
ejpam-4793	146	4	h. sarapuddin	PERSON
ejpam-4793	146	5	j. vilela	PERSON
ejpam-4793	147	1	j. pure	PERSON
ejpam-4793	147	2	16	CARDINAL
ejpam-4793	147	3	3	CARDINAL
ejpam-4793	147	4	2023	CARDINAL
ejpam-4793	147	5	1772-1793 1776	DATE
ejpam-4793	149	1	2(a	CARDINAL
ejpam-4793	153	1	2(a	CARDINAL
ejpam-4793	158	1	2(0	CARDINAL
ejpam-4793	160	1	2(0	CARDINAL
ejpam-4793	160	2	0	CARDINAL
ejpam-4793	164	1	2((a+	CARDINAL
ejpam-4793	169	1	2((a+	CARDINAL
ejpam-4793	171	1	2(a+	CARDINAL
ejpam-4793	175	1	∈	ORG
ejpam-4793	176	1	2αa	ORDINAL
ejpam-4793	176	2	2αb	ORDINAL
ejpam-4793	176	3	2αc	ORDINAL
ejpam-4793	177	1	2(2αa+ 2αb+ 2αc+	QUANTITY
ejpam-4793	177	2	2αd	ORDINAL
ejpam-4793	178	1	2α2(a+	CARDINAL
ejpam-4793	180	1	1	CARDINAL
ejpam-4793	181	1	4	CARDINAL
ejpam-4793	181	2	monoids	NORP
ejpam-4793	181	3	m1 −→ m2	PERSON
ejpam-4793	182	1	φ	PERSON
ejpam-4793	184	1	m1 m2 m1/ ker f rker f f φ	PERSON
ejpam-4793	184	2	φ	GPE
ejpam-4793	185	1	φ	ORG
ejpam-4793	186	1	φ	ORG
ejpam-4793	187	1	h. sarapuddin	PERSON
ejpam-4793	187	2	j. vilela	PERSON
ejpam-4793	188	1	j. pure	PERSON
ejpam-4793	188	2	16	CARDINAL
ejpam-4793	188	3	3	CARDINAL
ejpam-4793	188	4	2023	CARDINAL
ejpam-4793	188	5	1772-1793 1777 3	DATE
ejpam-4793	190	1	∈	ORG
ejpam-4793	191	1	8	DATE
ejpam-4793	191	2	∈	ORG
ejpam-4793	191	3	∗ α1	QUANTITY
ejpam-4793	191	4	1	CARDINAL
ejpam-4793	191	5	α(1	GPE
ejpam-4793	191	6	∗ x	PERSON
ejpam-4793	191	7	1	CARDINAL
ejpam-4793	191	8	3	CARDINAL
ejpam-4793	192	1	1	CARDINAL
ejpam-4793	193	1	10	CARDINAL
ejpam-4793	195	1	∈	ORG
ejpam-4793	196	1	∈	ORG
ejpam-4793	197	1	∈	ORG
ejpam-4793	197	2	∈	ORG
ejpam-4793	199	1	∗ α1	QUANTITY
ejpam-4793	199	2	∈ a.	PERSON
ejpam-4793	200	1	4	CARDINAL
ejpam-4793	203	1	∈	ORG
ejpam-4793	203	2	∈	ORG
ejpam-4793	203	3	a. lemma	PERSON
ejpam-4793	204	1	1	CARDINAL
ejpam-4793	209	1	⊆	CARDINAL
ejpam-4793	210	1	∈	ORG
ejpam-4793	211	1	∗	CARDINAL
ejpam-4793	211	2	∈	ORG
ejpam-4793	212	1	∗	CARDINAL
ejpam-4793	212	2	10	CARDINAL
ejpam-4793	216	1	8	CARDINAL
ejpam-4793	217	1	1	CARDINAL
ejpam-4793	217	2	∗ 1	DATE
ejpam-4793	221	1	1 ∗ 1	QUANTITY
ejpam-4793	221	2	1	CARDINAL
ejpam-4793	221	3	1 ∗	QUANTITY
ejpam-4793	221	4	1 ∗	CARDINAL
ejpam-4793	221	5	1 ∗	QUANTITY
ejpam-4793	221	6	1	CARDINAL
ejpam-4793	223	1	7→	CARDINAL
ejpam-4793	223	2	∈	ORG
ejpam-4793	224	1	0a	CARDINAL
ejpam-4793	226	1	ϕ((β	ORG
ejpam-4793	227	1	h. sarapuddin	PERSON
ejpam-4793	227	2	j. vilela	PERSON
ejpam-4793	228	1	j. pure	PERSON
ejpam-4793	228	2	16	CARDINAL
ejpam-4793	228	3	3	CARDINAL
ejpam-4793	228	4	2023	CARDINAL
ejpam-4793	228	5	1772-1793 1778	DATE
ejpam-4793	229	1	∈	ORG
ejpam-4793	230	1	∗	CARDINAL
ejpam-4793	231	1	∗	CARDINAL
ejpam-4793	232	1	∗	CARDINAL
ejpam-4793	232	2	∗	CARDINAL
ejpam-4793	234	1	n, h	ORG
ejpam-4793	235	1	∈	ORG
ejpam-4793	235	2	∈	ORG
ejpam-4793	236	1	n ∗ 1	WORK_OF_ART
ejpam-4793	241	1	∗	CARDINAL
ejpam-4793	241	2	1	CARDINAL
ejpam-4793	242	1	∗	CARDINAL
ejpam-4793	243	1	∗	CARDINAL
ejpam-4793	248	1	∗	CARDINAL
ejpam-4793	250	1	∗	CARDINAL
ejpam-4793	252	1	∗	CARDINAL
ejpam-4793	253	1	∗	CARDINAL
ejpam-4793	254	1	∗	CARDINAL
ejpam-4793	256	1	∗	CARDINAL
ejpam-4793	259	1	∗	CARDINAL
ejpam-4793	259	2	∈	ORG
ejpam-4793	259	3	10	CARDINAL
ejpam-4793	260	1	1	CARDINAL
ejpam-4793	262	1	9	CARDINAL
ejpam-4793	262	2	1	CARDINAL
ejpam-4793	262	3	example 8	DATE
ejpam-4793	263	1	1	CARDINAL
ejpam-4793	264	1	∈	ORG
ejpam-4793	264	2	three	CARDINAL
ejpam-4793	265	1	1	CARDINAL
ejpam-4793	266	1	∗	CARDINAL
ejpam-4793	266	2	1	CARDINAL
ejpam-4793	267	1	1	CARDINAL
ejpam-4793	267	2	1	CARDINAL
ejpam-4793	267	3	2	CARDINAL
ejpam-4793	268	1	∗	CARDINAL
ejpam-4793	269	1	1 ∗ n = n ∗ 1	QUANTITY
ejpam-4793	269	2	3	CARDINAL
ejpam-4793	269	3	∗	CARDINAL
ejpam-4793	269	4	1 ∗	CARDINAL
ejpam-4793	270	1	1	CARDINAL
ejpam-4793	270	2	1 ∗ 1	QUANTITY
ejpam-4793	270	3	1 ∈	CARDINAL
ejpam-4793	271	1	1 ∗ n = n ∈	QUANTITY
ejpam-4793	271	2	1 ∗	CARDINAL
ejpam-4793	276	1	∗	CARDINAL
ejpam-4793	277	1	∗	CARDINAL
ejpam-4793	279	1	n ∈	ORG
ejpam-4793	279	2	αn∗βs	PRODUCT
ejpam-4793	279	3	10	CARDINAL
ejpam-4793	280	1	5	CARDINAL
ejpam-4793	283	1	2	CARDINAL
ejpam-4793	285	1	1	CARDINAL
ejpam-4793	285	2	∈	ORG
ejpam-4793	288	1	1	CARDINAL
ejpam-4793	288	2	∈	ORG
ejpam-4793	289	1	0	CARDINAL
ejpam-4793	289	2	01	CARDINAL
ejpam-4793	289	3	1	CARDINAL
ejpam-4793	289	4	∈ i.	PERSON
ejpam-4793	289	5	⊆	CARDINAL
ejpam-4793	289	6	i.	PERSON
ejpam-4793	291	1	1	CARDINAL
ejpam-4793	291	2	∈ i. h. sarapuddin	ORG
ejpam-4793	291	3	j. vilela	PERSON
ejpam-4793	292	1	j. pure	PERSON
ejpam-4793	292	2	16	CARDINAL
ejpam-4793	292	3	3	CARDINAL
ejpam-4793	292	4	2023	CARDINAL
ejpam-4793	292	5	1772-1793	DATE
ejpam-4793	292	6	2	CARDINAL
ejpam-4793	292	7	3	CARDINAL
ejpam-4793	293	1	2	CARDINAL
ejpam-4793	300	1	1	CARDINAL
ejpam-4793	300	2	∈ i.	PERSON
ejpam-4793	300	3	lemma 2	ORG
ejpam-4793	303	1	3	CARDINAL
ejpam-4793	309	1	1	CARDINAL
ejpam-4793	310	1	lemma 2	ORG
ejpam-4793	312	1	4(i	CARDINAL
ejpam-4793	313	1	3	CARDINAL
ejpam-4793	318	1	∈	ORG
ejpam-4793	319	1	∈	ORG
ejpam-4793	319	2	∈	ORG
ejpam-4793	319	3	∈	ORG
ejpam-4793	321	1	∈	ORG
ejpam-4793	321	2	∈	ORG
ejpam-4793	323	1	∈	ORG
ejpam-4793	323	2	∈	ORG
ejpam-4793	323	3	∈	ORG
ejpam-4793	324	1	a∪b	PRODUCT
ejpam-4793	325	1	4	CARDINAL
ejpam-4793	327	1	j ∩	PERSON
ejpam-4793	327	2	j ∩	PERSON
ejpam-4793	327	3	i. (ii	ORG
ejpam-4793	330	1	∈	ORG
ejpam-4793	330	2	∈	ORG
ejpam-4793	330	3	j	PERSON
ejpam-4793	330	4	∗	CARDINAL
ejpam-4793	330	5	∈	ORG
ejpam-4793	331	1	∗	CARDINAL
ejpam-4793	331	2	∈	ORG
ejpam-4793	331	3	∗	CARDINAL
ejpam-4793	331	4	∈	ORG
ejpam-4793	331	5	j ∩ i.	PERSON
ejpam-4793	331	6	j ∩	PERSON
ejpam-4793	331	7	i. (ii	ORG
ejpam-4793	331	8	∈	ORG
ejpam-4793	332	1	∈	ORG
ejpam-4793	332	2	⊆	CARDINAL
ejpam-4793	332	3	i.	PERSON
ejpam-4793	332	4	∈	ORG
ejpam-4793	332	5	i.	PERSON
ejpam-4793	333	1	1	CARDINAL
ejpam-4793	334	1	∈	ORG
ejpam-4793	334	2	∈	ORG
ejpam-4793	335	1	⊆	CARDINAL
ejpam-4793	335	2	i.	PERSON
ejpam-4793	335	3	2	CARDINAL
ejpam-4793	336	1	∈	ORG
ejpam-4793	336	2	∈	ORG
ejpam-4793	338	1	∗	CARDINAL
ejpam-4793	339	1	∈	ORG
ejpam-4793	339	2	i. h. sarapuddin	PERSON
ejpam-4793	339	3	j. vilela	PERSON
ejpam-4793	340	1	j. pure	PERSON
ejpam-4793	340	2	16	CARDINAL
ejpam-4793	340	3	3	CARDINAL
ejpam-4793	340	4	2023	CARDINAL
ejpam-4793	340	5	1772-1793 1780	DATE
ejpam-4793	340	6	3	CARDINAL
ejpam-4793	340	7	∈	ORG
ejpam-4793	341	1	∈	ORG
ejpam-4793	342	1	i.	PERSON
ejpam-4793	342	2	4	CARDINAL
ejpam-4793	342	3	∈	ORG
ejpam-4793	344	1	∈	ORG
ejpam-4793	344	2	i.	PERSON
ejpam-4793	345	1	11	DATE
ejpam-4793	346	1	φ	ORG
ejpam-4793	347	1	φ	ORG
ejpam-4793	347	2	∈	ORG
ejpam-4793	347	3	1n	CARDINAL
ejpam-4793	348	1	2	CARDINAL
ejpam-4793	349	1	φ	ORG
ejpam-4793	350	1	φ	ORG
ejpam-4793	358	1	φ	ORG
ejpam-4793	358	2	y ∈ i.	PERSON
ejpam-4793	361	1	∈	ORG
ejpam-4793	363	1	∗	CARDINAL
ejpam-4793	364	1	φ(i	PERSON
ejpam-4793	365	1	∈	ORG
ejpam-4793	366	1	φ(y	ORG
ejpam-4793	367	1	φ(βm	ORG
ejpam-4793	369	1	∈	ORG
ejpam-4793	371	1	10	CARDINAL
ejpam-4793	372	1	φ	PERSON
ejpam-4793	373	1	6	CARDINAL
ejpam-4793	373	2	∈	ORG
ejpam-4793	374	1	1	CARDINAL
ejpam-4793	374	2	∈	ORG
ejpam-4793	374	3	1	CARDINAL
ejpam-4793	374	4	∈	ORG
ejpam-4793	374	5	1 or	CARDINAL
ejpam-4793	375	1	∈	ORG
ejpam-4793	375	2	2 ∈	CARDINAL
ejpam-4793	375	3	2	CARDINAL
ejpam-4793	378	1	+ 2	DATE
ejpam-4793	378	2	φ(2	DATE
ejpam-4793	380	1	22	CARDINAL
ejpam-4793	382	1	10	CARDINAL
ejpam-4793	383	1	6	CARDINAL
ejpam-4793	384	1	φ	PERSON
ejpam-4793	385	1	3	CARDINAL
ejpam-4793	386	1	φ	ORG
ejpam-4793	388	1	kerφ = m. h. sarapuddin	PERSON
ejpam-4793	388	2	j. vilela	PERSON
ejpam-4793	389	1	j. pure	PERSON
ejpam-4793	389	2	16	CARDINAL
ejpam-4793	389	3	3	CARDINAL
ejpam-4793	389	4	2023	CARDINAL
ejpam-4793	389	5	1772-1793	DATE
ejpam-4793	391	1	1	CARDINAL
ejpam-4793	391	2	∈	ORG
ejpam-4793	393	1	lemma 2	ORG
ejpam-4793	396	1	4(i	CARDINAL
ejpam-4793	398	1	φ	ORG
ejpam-4793	398	2	zero	CARDINAL
ejpam-4793	400	1	4	CARDINAL
ejpam-4793	400	2	γ-submonoids	GPE
ejpam-4793	400	3	γ-submonoids	GPE
ejpam-4793	401	1	12	CARDINAL
ejpam-4793	403	1	γ-submonoid	GPE
ejpam-4793	403	2	1	CARDINAL
ejpam-4793	403	3	∈	ORG
ejpam-4793	404	1	∈	ORG
ejpam-4793	404	2	γ-submonoid	GPE
ejpam-4793	405	1	1	CARDINAL
ejpam-4793	405	2	∈	ORG
ejpam-4793	406	1	0	CARDINAL
ejpam-4793	407	1	∗	CARDINAL
ejpam-4793	409	1	0s ∗	QUANTITY
ejpam-4793	410	1	7	CARDINAL
ejpam-4793	411	1	γ-submonoid	GPE
ejpam-4793	413	1	∈	ORG
ejpam-4793	413	2	αs	CARDINAL
ejpam-4793	413	3	∈	ORG
ejpam-4793	413	4	γ-submonoid	GPE
ejpam-4793	414	1	γ-submonoid	GPE
ejpam-4793	415	1	7	CARDINAL
ejpam-4793	416	1	monoid	ORG
ejpam-4793	416	2	8	CARDINAL
ejpam-4793	417	1	γ-submonoid	GPE
ejpam-4793	418	1	11	CARDINAL
ejpam-4793	419	1	0	CARDINAL
ejpam-4793	419	2	1	DATE
ejpam-4793	419	3	0	CARDINAL
ejpam-4793	419	4	1 1 1 1	CARDINAL
ejpam-4793	419	5	1 1 s s	QUANTITY
ejpam-4793	420	1	h. sarapuddin	PERSON
ejpam-4793	420	2	j. vilela	PERSON
ejpam-4793	421	1	j. pure	PERSON
ejpam-4793	421	2	16	CARDINAL
ejpam-4793	421	3	3	CARDINAL
ejpam-4793	421	4	2023	CARDINAL
ejpam-4793	421	5	1772-1793 1782	DATE
ejpam-4793	421	6	5	CARDINAL
ejpam-4793	421	7	0	CARDINAL
ejpam-4793	422	1	0	CARDINAL
ejpam-4793	422	2	0	CARDINAL
ejpam-4793	422	3	1	DATE
ejpam-4793	422	4	0	CARDINAL
ejpam-4793	422	5	1	DATE
ejpam-4793	422	6	0	CARDINAL
ejpam-4793	423	1	w	LANGUAGE
ejpam-4793	426	1	0	CARDINAL
ejpam-4793	429	1	0y	CARDINAL
ejpam-4793	430	1	y ∈ s	PERSON
ejpam-4793	430	2	0y	CARDINAL
ejpam-4793	430	3	∈	ORG
ejpam-4793	430	4	00	CARDINAL
ejpam-4793	431	1	00	CARDINAL
ejpam-4793	431	2	0	CARDINAL
ejpam-4793	432	1	∈	ORG
ejpam-4793	432	2	0y	CARDINAL
ejpam-4793	432	3	0s	MONEY
ejpam-4793	433	1	0b	CARDINAL
ejpam-4793	433	2	12	DATE
ejpam-4793	433	3	γ-submonoid	GPE
ejpam-4793	434	1	w	GPE
ejpam-4793	434	2	γ-submonoids	GPE
ejpam-4793	435	1	γ-submonoid	GPE
ejpam-4793	435	2	0	CARDINAL
ejpam-4793	436	1	0	CARDINAL
ejpam-4793	437	1	0 ∗	QUANTITY
ejpam-4793	440	1	9	CARDINAL
ejpam-4793	442	1	γ-submonoid	GPE
ejpam-4793	443	1	5	CARDINAL
ejpam-4793	443	2	6	CARDINAL
ejpam-4793	444	1	5	CARDINAL
ejpam-4793	445	1	γ-submonoid	GPE
ejpam-4793	449	1	γ-submonoid	GPE
ejpam-4793	451	1	γ-submonoid	GPE
ejpam-4793	451	2	1	CARDINAL
ejpam-4793	451	3	∈	ORG
ejpam-4793	451	4	lemma 2	ORG
ejpam-4793	453	1	4(i	CARDINAL
ejpam-4793	454	1	6	CARDINAL
ejpam-4793	456	1	γ-submonoid	GPE
ejpam-4793	460	1	γ-submonoid	GPE
ejpam-4793	461	1	1	CARDINAL
ejpam-4793	464	1	γ-submonoid	GPE
ejpam-4793	465	1	12	CARDINAL
ejpam-4793	466	1	γ-submonoid	GPE
ejpam-4793	466	2	0	CARDINAL
ejpam-4793	466	3	example 11	DATE
ejpam-4793	469	1	2	CARDINAL
ejpam-4793	469	2	1	CARDINAL
ejpam-4793	469	3	∈ s.	PERSON
ejpam-4793	470	1	∈	ORG
ejpam-4793	470	2	γ-submonoid	GPE
ejpam-4793	471	1	10	CARDINAL
ejpam-4793	472	1	γ-submonoid	GPE
ejpam-4793	473	1	γ-submonoid	GPE
ejpam-4793	474	1	γ-submonoid	GPE
ejpam-4793	475	1	h. sarapuddin	PERSON
ejpam-4793	475	2	j. vilela	PERSON
ejpam-4793	476	1	j. pure	PERSON
ejpam-4793	476	2	16	CARDINAL
ejpam-4793	476	3	3	CARDINAL
ejpam-4793	476	4	2023	CARDINAL
ejpam-4793	476	5	1772-1793 1783	DATE
ejpam-4793	476	6	13	CARDINAL
ejpam-4793	476	7	γ-submonoid	GPE
ejpam-4793	476	8	0	CARDINAL
ejpam-4793	476	9	1	DATE
ejpam-4793	476	10	example 11	DATE
ejpam-4793	477	1	∈	ORG
ejpam-4793	477	2	y ∗ z	PERSON
ejpam-4793	480	1	11	CARDINAL
ejpam-4793	481	1	γ-submonoid	GPE
ejpam-4793	488	1	10	CARDINAL
ejpam-4793	488	2	γ-submonoid	GPE
ejpam-4793	488	3	0	CARDINAL
ejpam-4793	489	1	γ-	GPE
ejpam-4793	489	2	y ∈ s	PERSON
ejpam-4793	490	1	∈ s.	PERSON
ejpam-4793	491	1	0	CARDINAL
ejpam-4793	493	1	4	CARDINAL
ejpam-4793	495	1	γ-submonoid	GPE
ejpam-4793	496	1	γ-submonoid	GPE
ejpam-4793	499	1	γ-submonoids	GPE
ejpam-4793	499	2	1	CARDINAL
ejpam-4793	499	3	∈	ORG
ejpam-4793	499	4	1	CARDINAL
ejpam-4793	500	1	1	CARDINAL
ejpam-4793	500	2	∈ a∩b	PERSON
ejpam-4793	502	1	γ-submonoids	GPE
ejpam-4793	502	2	∈	ORG
ejpam-4793	503	1	∈	ORG
ejpam-4793	504	1	γ-submonoid	GPE
ejpam-4793	505	1	γ-submonoid	GPE
ejpam-4793	507	1	γ-submonoid	GPE
ejpam-4793	508	1	14	CARDINAL
ejpam-4793	509	1	γ-submonoids	GPE
ejpam-4793	509	2	0	CARDINAL
ejpam-4793	509	3	1	DATE
ejpam-4793	509	4	0	CARDINAL
ejpam-4793	509	5	example 11	DATE
ejpam-4793	510	1	∪w	CARDINAL
ejpam-4793	510	2	0	CARDINAL
ejpam-4793	510	3	1	DATE
ejpam-4793	511	1	∪w	CARDINAL
ejpam-4793	511	2	∪w	CARDINAL
ejpam-4793	512	1	∪w	CARDINAL
ejpam-4793	512	2	γ-submonoid	GPE
ejpam-4793	513	1	12	CARDINAL
ejpam-4793	514	1	two	CARDINAL
ejpam-4793	515	1	8	CARDINAL
ejpam-4793	516	1	φ	ORG
ejpam-4793	517	1	γ-submonoid	GPE
ejpam-4793	517	2	φ(s	GPE
ejpam-4793	517	3	γ-submonoid	GPE
ejpam-4793	518	1	γ-submonoid	GPE
ejpam-4793	519	1	h. sarapuddin	PERSON
ejpam-4793	519	2	j. vilela	PERSON
ejpam-4793	520	1	j. pure	PERSON
ejpam-4793	520	2	16	CARDINAL
ejpam-4793	520	3	3	CARDINAL
ejpam-4793	520	4	2023	CARDINAL
ejpam-4793	520	5	1772-1793 1784	DATE
ejpam-4793	520	6	γ-submonoid	GPE
ejpam-4793	520	7	γ-submonoid	GPE
ejpam-4793	521	1	γ-submonoid	GPE
ejpam-4793	525	1	γ-submonoid	GPE
ejpam-4793	526	1	1	CARDINAL
ejpam-4793	526	2	1n	CARDINAL
ejpam-4793	526	3	φ(s	GPE
ejpam-4793	527	1	φ(s	GPE
ejpam-4793	528	1	∈ s.	PERSON
ejpam-4793	529	1	∗	CARDINAL
ejpam-4793	529	2	∈	ORG
ejpam-4793	529	3	φ(s	GPE
ejpam-4793	530	1	φ(s	GPE
ejpam-4793	530	2	γ-submonoid	GPE
ejpam-4793	531	1	γ-submonoid	GPE
ejpam-4793	533	1	1n	CARDINAL
ejpam-4793	533	2	1	CARDINAL
ejpam-4793	535	1	φ(y	ORG
ejpam-4793	536	1	∗	CARDINAL
ejpam-4793	536	2	γ-submonoid	GPE
ejpam-4793	537	1	∗	CARDINAL
ejpam-4793	538	1	γ-submonoid	GPE
ejpam-4793	539	1	φ	ORG
ejpam-4793	539	2	φ(1	ORG
ejpam-4793	540	1	1n	CARDINAL
ejpam-4793	541	1	1	CARDINAL
ejpam-4793	541	2	∈	ORG
ejpam-4793	542	1	∈	ORG
ejpam-4793	543	1	1n	CARDINAL
ejpam-4793	543	2	φ(y	ORG
ejpam-4793	543	3	1n	CARDINAL
ejpam-4793	544	1	3	CARDINAL
ejpam-4793	544	2	∗	CARDINAL
ejpam-4793	546	1	1n	CARDINAL
ejpam-4793	546	2	1n	CARDINAL
ejpam-4793	546	3	1n	CARDINAL
ejpam-4793	548	1	∈	ORG
ejpam-4793	549	1	γ-submonoid	GPE
ejpam-4793	550	1	∗	CARDINAL
ejpam-4793	551	1	1n	CARDINAL
ejpam-4793	552	1	1n	CARDINAL
ejpam-4793	553	1	φ(y	ORG
ejpam-4793	554	1	1n	CARDINAL
ejpam-4793	556	1	1n	CARDINAL
ejpam-4793	557	1	∈	ORG
ejpam-4793	557	2	kerφ	PERSON
ejpam-4793	558	1	9	CARDINAL
ejpam-4793	559	1	γ-submonoid	GPE
ejpam-4793	559	2	j ∩ s ̸=	LAW
ejpam-4793	559	3	j ∩ s	PERSON
ejpam-4793	559	4	γ-submonoid	GPE
ejpam-4793	561	1	γ-submonoid	GPE
ejpam-4793	561	2	j ∩ s ̸=	LAW
ejpam-4793	561	3	∈	ORG
ejpam-4793	561	4	∈	ORG
ejpam-4793	562	1	∈	ORG
ejpam-4793	564	1	γ-submonoid	GPE
ejpam-4793	564	2	∈	ORG
ejpam-4793	564	3	∈	ORG
ejpam-4793	564	4	j ∩ s	PERSON
ejpam-4793	564	5	j ∩ s	PERSON
ejpam-4793	564	6	s. (ii	ORG
ejpam-4793	564	7	∈	ORG
ejpam-4793	564	8	s.	PERSON
ejpam-4793	565	1	1	CARDINAL
ejpam-4793	566	1	∈	ORG
ejpam-4793	567	1	j	PERSON
ejpam-4793	567	2	∗	CARDINAL
ejpam-4793	568	1	∈	ORG
ejpam-4793	568	2	s.	PERSON
ejpam-4793	568	3	2	CARDINAL
ejpam-4793	568	4	∈	ORG
ejpam-4793	568	5	∗	CARDINAL
ejpam-4793	569	1	∈	ORG
ejpam-4793	569	2	s.	PERSON
ejpam-4793	569	3	3	CARDINAL
ejpam-4793	569	4	γ-submonoid	GPE
ejpam-4793	569	5	∗	CARDINAL
ejpam-4793	570	1	∈	ORG
ejpam-4793	570	2	⊆	CARDINAL
ejpam-4793	570	3	s.	PERSON
ejpam-4793	570	4	4	CARDINAL
ejpam-4793	570	5	∗	CARDINAL
ejpam-4793	571	1	∈	ORG
ejpam-4793	571	2	s. h. sarapuddin	PERSON
ejpam-4793	571	3	j. vilela	PERSON
ejpam-4793	572	1	j. pure	PERSON
ejpam-4793	572	2	16	CARDINAL
ejpam-4793	572	3	3	CARDINAL
ejpam-4793	572	4	2023	CARDINAL
ejpam-4793	572	5	1772-1793 1785	DATE
ejpam-4793	572	6	γ-submonoid	GPE
ejpam-4793	572	7	1	CARDINAL
ejpam-4793	572	8	∈	ORG
ejpam-4793	572	9	⊆	CARDINAL
ejpam-4793	573	1	j ∪s	PERSON
ejpam-4793	573	2	γ-submonoid	GPE
ejpam-4793	574	1	13	CARDINAL
ejpam-4793	575	1	4(i	CARDINAL
ejpam-4793	577	1	5	CARDINAL
ejpam-4793	579	1	∗	CARDINAL
ejpam-4793	579	2	γ-submonoid	GPE
ejpam-4793	581	1	y ∈	PERSON
ejpam-4793	582	1	γ-submonoids	GPE
ejpam-4793	582	2	αa1 ∗	PERSON
ejpam-4793	582	3	∈	ORG
ejpam-4793	582	4	1m	QUANTITY
ejpam-4793	582	5	1m ∗ 1m	QUANTITY
ejpam-4793	582	6	∈	ORG
ejpam-4793	584	1	αa1 ∗ αb1	ORG
ejpam-4793	585	1	αa1 ∗ βa2	PERSON
ejpam-4793	585	2	∗	CARDINAL
ejpam-4793	586	1	∗	CARDINAL
ejpam-4793	587	1	γ-submonoid	GPE
ejpam-4793	588	1	6	CARDINAL
ejpam-4793	595	1	y ∈ a.	PERSON
ejpam-4793	599	1	1m ∗ 1m	QUANTITY
ejpam-4793	601	1	∈	ORG
ejpam-4793	601	2	∗ α1	QUANTITY
ejpam-4793	601	3	1	CARDINAL
ejpam-4793	603	1	5	CARDINAL
ejpam-4793	603	2	5	CARDINAL
ejpam-4793	603	3	6	CARDINAL
ejpam-4793	603	4	γ-monoidm	ORG
ejpam-4793	603	5	ofm	DATE
ejpam-4793	604	1	third	ORDINAL
ejpam-4793	607	1	13	DATE
ejpam-4793	609	1	γ-submonoid	GPE
ejpam-4793	609	2	∈	ORG
ejpam-4793	609	3	∈	ORG
ejpam-4793	610	1	γ-submonoid	GPE
ejpam-4793	611	1	h. sarapuddin	PERSON
ejpam-4793	611	2	j. vilela	PERSON
ejpam-4793	612	1	j. pure	PERSON
ejpam-4793	612	2	16	CARDINAL
ejpam-4793	612	3	3	CARDINAL
ejpam-4793	612	4	2023	CARDINAL
ejpam-4793	612	5	1772-1793 1786	DATE
ejpam-4793	612	6	15	CARDINAL
ejpam-4793	612	7	1	CARDINAL
ejpam-4793	612	8	example 5	DATE
ejpam-4793	612	9	∗ 1	DATE
ejpam-4793	613	1	1	CARDINAL
ejpam-4793	614	1	γ-submonoid	GPE
ejpam-4793	616	1	∈	ORG
ejpam-4793	616	2	1∗s	CARDINAL
ejpam-4793	616	3	1	CARDINAL
ejpam-4793	616	4	∗	CARDINAL
ejpam-4793	617	1	∗ s)∩	ORG
ejpam-4793	617	2	α1 ∗ s	QUANTITY
ejpam-4793	617	3	aρs1	ORG
ejpam-4793	618	1	α1 ∗ s	QUANTITY
ejpam-4793	618	2	1ρsb	CARDINAL
ejpam-4793	620	1	γ-submonoid s	ORG
ejpam-4793	622	1	10	CARDINAL
ejpam-4793	623	1	γ-submonoid	ORG
ejpam-4793	627	1	γ-submonoid	ORG
ejpam-4793	628	1	γ-submonoid	GPE
ejpam-4793	630	1	∗ s ̸=	ORG
ejpam-4793	630	2	1	CARDINAL
ejpam-4793	630	3	∗ s.	ORG
ejpam-4793	630	4	xρsx	ORG
ejpam-4793	632	1	∈	ORG
ejpam-4793	632	2	∗ s	ORG
ejpam-4793	632	3	∗ s	ORG
ejpam-4793	632	4	∗ s	ORG
ejpam-4793	632	5	∗ s	ORG
ejpam-4793	632	6	∗ s	ORG
ejpam-4793	632	7	∗ s	ORG
ejpam-4793	633	1	yρsz	PERSON
ejpam-4793	634	1	∗ s	ORG
ejpam-4793	634	2	∗ s	ORG
ejpam-4793	634	3	∗ s	ORG
ejpam-4793	634	4	∗ s2	ORG
ejpam-4793	634	5	∗	CARDINAL
ejpam-4793	634	6	∈	ORG
ejpam-4793	634	7	∗ s2 ∗ s3 =	ORG
ejpam-4793	634	8	∗ s2 ∗ s4 and	ORG
ejpam-4793	634	9	∗	CARDINAL
ejpam-4793	634	10	γ-submonoid	GPE
ejpam-4793	638	1	γ-monoid	ORG
ejpam-4793	638	2	∈	ORG
ejpam-4793	639	1	∗ s	ORG
ejpam-4793	639	2	∗ s	ORG
ejpam-4793	639	3	∗	CARDINAL
ejpam-4793	639	4	∗	CARDINAL
ejpam-4793	640	1	∈	ORG
ejpam-4793	642	1	h. sarapuddin	PERSON
ejpam-4793	642	2	j. vilela	PERSON
ejpam-4793	643	1	j. pure	PERSON
ejpam-4793	643	2	16	CARDINAL
ejpam-4793	643	3	3	CARDINAL
ejpam-4793	643	4	2023	CARDINAL
ejpam-4793	643	5	1772-1793 1787	DATE
ejpam-4793	643	6	14	DATE
ejpam-4793	644	1	γ-submonoid	ORG
ejpam-4793	645	1	∈	ORG
ejpam-4793	646	1	∈	ORG
ejpam-4793	647	1	γ-submonoid	ORG
ejpam-4793	647	2	∈	ORG
ejpam-4793	648	1	∈	ORG
ejpam-4793	648	2	∗ s	ORG
ejpam-4793	648	3	∗ s	ORG
ejpam-4793	648	4	∗ s ̸=	ORG
ejpam-4793	649	1	∈	ORG
ejpam-4793	649	2	∗ s.	PERSON
ejpam-4793	649	3	∈	ORG
ejpam-4793	651	1	14	CARDINAL
ejpam-4793	652	1	γ-submonoid	ORG
ejpam-4793	653	1	∈	ORG
ejpam-4793	653	2	∈	ORG
ejpam-4793	656	1	αm2 ∗ s	QUANTITY
ejpam-4793	656	2	∈	ORG
ejpam-4793	657	1	6	DATE
ejpam-4793	657	2	13	DATE
ejpam-4793	657	3	γ-submonoid	GPE
ejpam-4793	659	1	16	CARDINAL
ejpam-4793	660	1	0	CARDINAL
ejpam-4793	660	2	1	DATE
ejpam-4793	660	3	2	DATE
ejpam-4793	660	4	3	DATE
ejpam-4793	660	5	4	DATE
ejpam-4793	660	6	5	DATE
ejpam-4793	660	7	6	DATE
ejpam-4793	660	8	7	CARDINAL
ejpam-4793	660	9	8	CARDINAL
ejpam-4793	661	1	0	CARDINAL
ejpam-4793	663	1	7αm	ORDINAL
ejpam-4793	665	1	7βy	ORDINAL
ejpam-4793	666	1	∈	ORG
ejpam-4793	669	1	70	CARDINAL
ejpam-4793	670	1	ϕ((β	ORG
ejpam-4793	672	1	∈	ORG
ejpam-4793	673	1	x+8 y	PERSON
ejpam-4793	674	1	x+8 y	PERSON
ejpam-4793	677	1	7αy	ORDINAL
ejpam-4793	680	1	0	CARDINAL
ejpam-4793	680	2	4	CARDINAL
ejpam-4793	682	1	0	CARDINAL
ejpam-4793	683	1	0	CARDINAL
ejpam-4793	683	2	0	CARDINAL
ejpam-4793	684	1	4	CARDINAL
ejpam-4793	685	1	4	CARDINAL
ejpam-4793	685	2	4	CARDINAL
ejpam-4793	685	3	∈	ORG
ejpam-4793	687	1	0	CARDINAL
ejpam-4793	687	2	4	CARDINAL
ejpam-4793	687	3	0	CARDINAL
ejpam-4793	687	4	4	CARDINAL
ejpam-4793	687	5	4 +8	QUANTITY
ejpam-4793	687	6	4 +8	TIME
ejpam-4793	687	7	0	CARDINAL
ejpam-4793	687	8	4	CARDINAL
ejpam-4793	687	9	0	CARDINAL
ejpam-4793	687	10	4	CARDINAL
ejpam-4793	687	11	1 +8 s	QUANTITY
ejpam-4793	687	12	1 +8	QUANTITY
ejpam-4793	687	13	0	CARDINAL
ejpam-4793	687	14	4	CARDINAL
ejpam-4793	687	15	1	CARDINAL
ejpam-4793	687	16	5	CARDINAL
ejpam-4793	687	17	5 +8	QUANTITY
ejpam-4793	687	18	5	CARDINAL
ejpam-4793	687	19	0	CARDINAL
ejpam-4793	687	20	4	CARDINAL
ejpam-4793	687	21	1	CARDINAL
ejpam-4793	687	22	5	CARDINAL
ejpam-4793	687	23	2 +8 s	QUANTITY
ejpam-4793	687	24	2 +8	CARDINAL
ejpam-4793	687	25	0	CARDINAL
ejpam-4793	687	26	4	CARDINAL
ejpam-4793	687	27	2	CARDINAL
ejpam-4793	687	28	6	CARDINAL
ejpam-4793	687	29	6 +8	QUANTITY
ejpam-4793	687	30	6 +8	QUANTITY
ejpam-4793	687	31	0	CARDINAL
ejpam-4793	687	32	4	CARDINAL
ejpam-4793	687	33	2	CARDINAL
ejpam-4793	687	34	6	CARDINAL
ejpam-4793	687	35	4 +8 s	QUANTITY
ejpam-4793	687	36	4 +8	TIME
ejpam-4793	687	37	0	CARDINAL
ejpam-4793	687	38	4	CARDINAL
ejpam-4793	687	39	0	CARDINAL
ejpam-4793	687	40	4	CARDINAL
ejpam-4793	687	41	7 +8 s	QUANTITY
ejpam-4793	687	42	0	CARDINAL
ejpam-4793	687	43	4	CARDINAL
ejpam-4793	687	44	3	CARDINAL
ejpam-4793	688	1	0	CARDINAL
ejpam-4793	688	2	4	CARDINAL
ejpam-4793	688	3	1	CARDINAL
ejpam-4793	688	4	5	CARDINAL
ejpam-4793	688	5	2	CARDINAL
ejpam-4793	688	6	6	CARDINAL
ejpam-4793	688	7	ρs(3	CARDINAL
ejpam-4793	688	8	3	CARDINAL
ejpam-4793	688	9	0	CARDINAL
ejpam-4793	688	10	4	CARDINAL
ejpam-4793	688	11	1	CARDINAL
ejpam-4793	688	12	5	CARDINAL
ejpam-4793	688	13	2	CARDINAL
ejpam-4793	688	14	6	CARDINAL
ejpam-4793	688	15	3	CARDINAL
ejpam-4793	689	1	ρs(3	CARDINAL
ejpam-4793	689	2	6	CARDINAL
ejpam-4793	690	1	∈	ORG
ejpam-4793	690	2	7α	CARDINAL
ejpam-4793	690	3	1	CARDINAL
ejpam-4793	690	4	7α	CARDINAL
ejpam-4793	690	5	7	CARDINAL
ejpam-4793	694	1	h. sarapuddin	PERSON
ejpam-4793	694	2	j. vilela	PERSON
ejpam-4793	695	1	j. pure	PERSON
ejpam-4793	695	2	16	CARDINAL
ejpam-4793	695	3	3	CARDINAL
ejpam-4793	695	4	2023	CARDINAL
ejpam-4793	695	5	1772-1793 1788	DATE
ejpam-4793	698	1	4	CARDINAL
ejpam-4793	699	1	7α4 +8 7β4	DATE
ejpam-4793	700	1	0	CARDINAL
ejpam-4793	700	2	4	CARDINAL
ejpam-4793	700	3	∈	ORG
ejpam-4793	700	4	γ-submonoid	GPE
ejpam-4793	701	1	∈	ORG
ejpam-4793	702	1	0	CARDINAL
ejpam-4793	702	2	4	CARDINAL
ejpam-4793	702	3	0	CARDINAL
ejpam-4793	702	4	4	CARDINAL
ejpam-4793	702	5	0	CARDINAL
ejpam-4793	702	6	4	CARDINAL
ejpam-4793	702	7	α1 +8 s	QUANTITY
ejpam-4793	702	8	0	CARDINAL
ejpam-4793	702	9	4	CARDINAL
ejpam-4793	702	10	7α1	CARDINAL
ejpam-4793	702	11	0	CARDINAL
ejpam-4793	702	12	4	CARDINAL
ejpam-4793	702	13	1	CARDINAL
ejpam-4793	702	14	5	CARDINAL
ejpam-4793	702	15	3	CARDINAL
ejpam-4793	702	16	0	CARDINAL
ejpam-4793	702	17	4	CARDINAL
ejpam-4793	702	18	7α2	CARDINAL
ejpam-4793	703	1	0	CARDINAL
ejpam-4793	703	2	4	CARDINAL
ejpam-4793	703	3	2	CARDINAL
ejpam-4793	703	4	6	CARDINAL
ejpam-4793	703	5	0	CARDINAL
ejpam-4793	703	6	4	CARDINAL
ejpam-4793	703	7	0	CARDINAL
ejpam-4793	703	8	4	CARDINAL
ejpam-4793	703	9	1	CARDINAL
ejpam-4793	703	10	5	CARDINAL
ejpam-4793	703	11	3	CARDINAL
ejpam-4793	703	12	α4 +8 s	PERSON
ejpam-4793	703	13	0	CARDINAL
ejpam-4793	703	14	4	CARDINAL
ejpam-4793	703	15	0	CARDINAL
ejpam-4793	703	16	4	CARDINAL
ejpam-4793	703	17	0	CARDINAL
ejpam-4793	703	18	4	CARDINAL
ejpam-4793	703	19	0	CARDINAL
ejpam-4793	703	20	4	CARDINAL
ejpam-4793	703	21	0	CARDINAL
ejpam-4793	703	22	4	CARDINAL
ejpam-4793	703	23	1	CARDINAL
ejpam-4793	703	24	5	CARDINAL
ejpam-4793	703	25	3	CARDINAL
ejpam-4793	703	26	α6 +8 s	QUANTITY
ejpam-4793	703	27	0	CARDINAL
ejpam-4793	703	28	4	CARDINAL
ejpam-4793	703	29	7α6 +8	PRODUCT
ejpam-4793	703	30	0	CARDINAL
ejpam-4793	703	31	4	CARDINAL
ejpam-4793	703	32	2	CARDINAL
ejpam-4793	703	33	6	CARDINAL
ejpam-4793	703	34	0	CARDINAL
ejpam-4793	703	35	4	CARDINAL
ejpam-4793	704	1	7α7	CARDINAL
ejpam-4793	704	2	0	CARDINAL
ejpam-4793	704	3	4	CARDINAL
ejpam-4793	704	4	1	CARDINAL
ejpam-4793	704	5	5	CARDINAL
ejpam-4793	704	6	3	CARDINAL
ejpam-4793	705	1	0	CARDINAL
ejpam-4793	705	2	4	CARDINAL
ejpam-4793	705	3	2	CARDINAL
ejpam-4793	706	1	1	CARDINAL
ejpam-4793	706	2	3	DATE
ejpam-4793	706	3	5	DATE
ejpam-4793	706	4	7	CARDINAL
ejpam-4793	707	1	13	CARDINAL
ejpam-4793	710	1	γ-submonoid	ORG
ejpam-4793	711	1	11	CARDINAL
ejpam-4793	712	1	γ-monoid	ORG
ejpam-4793	712	2	γ-submonoid	GPE
ejpam-4793	714	1	γ-monoid	ORG
ejpam-4793	714	2	γ-submonoid	GPE
ejpam-4793	715	1	ρs(x	CARDINAL
ejpam-4793	716	1	ρs(x	CARDINAL
ejpam-4793	717	1	7→	CARDINAL
ejpam-4793	718	1	∈	ORG
ejpam-4793	718	2	∈	ORG
ejpam-4793	723	1	14(ii	CARDINAL
ejpam-4793	723	2	y ∗ s	PERSON
ejpam-4793	723	3	y ∗ s2	PERSON
ejpam-4793	726	1	y ∗ s2	PERSON
ejpam-4793	729	1	γ-submonoid	GPE
ejpam-4793	729	2	y ∗ s	PERSON
ejpam-4793	729	3	ϕ(α	ORG
ejpam-4793	735	1	ϕ((β	ORG
ejpam-4793	737	1	∈	ORG
ejpam-4793	741	1	h. sarapuddin	PERSON
ejpam-4793	741	2	j. vilela	PERSON
ejpam-4793	742	1	j. pure	PERSON
ejpam-4793	742	2	16	CARDINAL
ejpam-4793	742	3	3	CARDINAL
ejpam-4793	742	4	2023	CARDINAL
ejpam-4793	742	5	1772-1793 1789	DATE
ejpam-4793	744	1	αρs(y	GPE
ejpam-4793	745	1	ρs(y	PERSON
ejpam-4793	748	1	γ-submonoid	GPE
ejpam-4793	751	1	∈	ORG
ejpam-4793	752	1	∈	ORG
ejpam-4793	753	1	∈	ORG
ejpam-4793	753	2	∈	ORG
ejpam-4793	753	3	∗	CARDINAL
ejpam-4793	753	4	γ-submonoid	GPE
ejpam-4793	753	5	∗	CARDINAL
ejpam-4793	753	6	∈	ORG
ejpam-4793	753	7	∈	ORG
ejpam-4793	753	8	∈	ORG
ejpam-4793	753	9	∈	ORG
ejpam-4793	753	10	xρs1	PERSON
ejpam-4793	754	1	⊆	CARDINAL
ejpam-4793	755	1	∈	ORG
ejpam-4793	756	1	∗ s	ORG
ejpam-4793	756	2	∈	ORG
ejpam-4793	757	1	∈	ORG
ejpam-4793	757	2	∈	ORG
ejpam-4793	757	3	∗	CARDINAL
ejpam-4793	757	4	γ-submonoid	GPE
ejpam-4793	757	5	∈	ORG
ejpam-4793	757	6	∈	ORG
ejpam-4793	757	7	αh∗1	PRODUCT
ejpam-4793	757	8	∈	ORG
ejpam-4793	757	9	γ-submonoid	GPE
ejpam-4793	758	1	∗ s	ORG
ejpam-4793	758	2	∗ s	ORG
ejpam-4793	759	1	⊆ ρs(h	QUANTITY
ejpam-4793	763	1	14(ii	CARDINAL
ejpam-4793	763	2	∗ s	ORG
ejpam-4793	763	3	∈	ORG
ejpam-4793	763	4	∈	ORG
ejpam-4793	764	1	∗	CARDINAL
ejpam-4793	764	2	∈	ORG
ejpam-4793	765	1	γ-submonoid	GPE
ejpam-4793	765	2	∗	CARDINAL
ejpam-4793	765	3	∈	ORG
ejpam-4793	765	4	∈	ORG
ejpam-4793	765	5	∈	ORG
ejpam-4793	765	6	5	CARDINAL
ejpam-4793	766	1	γ-submonoid	GPE
ejpam-4793	771	1	= s.	PERSON
ejpam-4793	772	1	∈	ORG
ejpam-4793	773	1	1m	QUANTITY
ejpam-4793	775	1	1	CARDINAL
ejpam-4793	777	1	∈	ORG
ejpam-4793	780	1	⊆	CARDINAL
ejpam-4793	780	2	= s. proposition	PERSON
ejpam-4793	780	3	6	CARDINAL
ejpam-4793	781	1	γ-submonoid	GPE
ejpam-4793	782	1	γ-submonoid	GPE
ejpam-4793	782	2	γ-submonoid	GPE
ejpam-4793	782	3	s. proof	PERSON
ejpam-4793	783	1	γ-submonoid	GPE
ejpam-4793	783	2	m/s.	ORG
ejpam-4793	783	3	⊆	CARDINAL
ejpam-4793	784	1	∈	ORG
ejpam-4793	784	2	∈	ORG
ejpam-4793	785	1	γ-submonoid	GPE
ejpam-4793	786	1	∈	ORG
ejpam-4793	786	2	1	CARDINAL
ejpam-4793	786	3	∈ r.	PERSON
ejpam-4793	786	4	∈	ORG
ejpam-4793	786	5	γ-submonoid	GPE
ejpam-4793	789	1	∗	CARDINAL
ejpam-4793	790	1	∈	ORG
ejpam-4793	790	2	γ-submonoid	GPE
ejpam-4793	791	1	r.	NORP
ejpam-4793	793	1	γ-submonoid	GPE
ejpam-4793	795	1	∈	ORG
ejpam-4793	795	2	r. therefore	PERSON
ejpam-4793	795	3	⊆	CARDINAL
ejpam-4793	795	4	r. h. sarapuddin	PERSON
ejpam-4793	795	5	j. vilela	PERSON
ejpam-4793	796	1	j. pure	PERSON
ejpam-4793	796	2	16	CARDINAL
ejpam-4793	796	3	3	CARDINAL
ejpam-4793	796	4	2023	CARDINAL
ejpam-4793	796	5	1772-1793 1790	DATE
ejpam-4793	796	6	12	CARDINAL
ejpam-4793	797	1	γ-monoid	ORG
ejpam-4793	797	2	γ-submonoid	GPE
ejpam-4793	799	1	kernel s. proof	PERSON
ejpam-4793	800	1	∈	ORG
ejpam-4793	803	1	∈	ORG
ejpam-4793	807	1	4	DATE
ejpam-4793	809	1	∈	ORG
ejpam-4793	809	2	ρs(a	ORG
ejpam-4793	809	3	∈	ORG
ejpam-4793	810	1	ρs(a	ORG
ejpam-4793	813	1	4	CARDINAL
ejpam-4793	813	2	∈	ORG
ejpam-4793	815	1	∈	ORG
ejpam-4793	816	1	∈	ORG
ejpam-4793	817	1	12	CARDINAL
ejpam-4793	820	1	⊆	CARDINAL
ejpam-4793	820	2	γ-submonoid	ORG
ejpam-4793	821	1	⋃	DATE
ejpam-4793	821	2	x∈a	PERSON
ejpam-4793	823	1	y ∈ π−1	PERSON
ejpam-4793	829	1	∗ s	ORG
ejpam-4793	829	2	∗ s	ORG
ejpam-4793	829	3	∈	ORG
ejpam-4793	830	1	x∈a	PERSON
ejpam-4793	831	1	x∈a	PERSON
ejpam-4793	832	1	x∈a	PERSON
ejpam-4793	833	1	∗ s	ORG
ejpam-4793	833	2	∗ s	ORG
ejpam-4793	833	3	∈	ORG
ejpam-4793	833	4	14(ii	CARDINAL
ejpam-4793	834	1	πs(y	PERSON
ejpam-4793	837	1	⊆	CARDINAL
ejpam-4793	838	1	π−1	PERSON
ejpam-4793	839	1	⋃	DATE
ejpam-4793	839	2	x∈a	PERSON
ejpam-4793	839	3	ρs(x	CARDINAL
ejpam-4793	840	1	6	CARDINAL
ejpam-4793	841	1	5	CARDINAL
ejpam-4793	842	1	γ-submonoids	ORG
ejpam-4793	843	1	16	CARDINAL
ejpam-4793	843	2	5	CARDINAL
ejpam-4793	844	1	13	CARDINAL
ejpam-4793	846	1	φ	PERSON
ejpam-4793	848	1	h. sarapuddin	PERSON
ejpam-4793	848	2	j. vilela	PERSON
ejpam-4793	849	1	j. pure	PERSON
ejpam-4793	849	2	16	CARDINAL
ejpam-4793	849	3	3	CARDINAL
ejpam-4793	849	4	2023	CARDINAL
ejpam-4793	849	5	1772-1793 1791	DATE
ejpam-4793	851	1	φ	ORG
ejpam-4793	852	1	φ	ORG
ejpam-4793	855	1	monoids	GPE
ejpam-4793	855	2	γ-monoid	ORG
ejpam-4793	855	3	1	CARDINAL
ejpam-4793	855	4	φ	PERSON
ejpam-4793	860	1	φ	ORG
ejpam-4793	861	1	φ	ORG
ejpam-4793	862	1	φ	ORG
ejpam-4793	865	1	∈	ORG
ejpam-4793	866	1	φ(αρker	CARDINAL
ejpam-4793	870	1	φ	PERSON
ejpam-4793	871	1	1	CARDINAL
ejpam-4793	877	1	13	CARDINAL
ejpam-4793	877	2	φ	PERSON
ejpam-4793	879	1	n = imf	ORG
ejpam-4793	881	1	1n	CARDINAL
ejpam-4793	886	1	1	CARDINAL
ejpam-4793	886	2	1	CARDINAL
ejpam-4793	886	3	φ	ORG
ejpam-4793	888	1	2	CARDINAL
ejpam-4793	890	1	k/(k ∩ l	FAC
ejpam-4793	890	2	k ∗ l)/l	PERSON
ejpam-4793	893	1	k → k ∗ l	ORG
ejpam-4793	894	1	k ∗ l	PERSON
ejpam-4793	894	2	πl(k∗l	PRODUCT
ejpam-4793	894	3	ρl(k∗l	DATE
ejpam-4793	897	1	k ∗ l)/l	PERSON
ejpam-4793	898	1	k ∈ k	PERSON
ejpam-4793	902	1	φ	PERSON
ejpam-4793	903	1	k ∈ k :	PERSON
ejpam-4793	905	1	k ∈	PERSON
ejpam-4793	906	1	k ∈ l	PERSON
ejpam-4793	906	2	k ∩ l.	PERSON
ejpam-4793	906	3	k/ kerφ	PERSON
ejpam-4793	906	4	k ∗ l)/l	PERSON
ejpam-4793	907	1	third	ORDINAL
ejpam-4793	907	2	γ-submonoids	ORG
ejpam-4793	908	1	h. sarapuddin	PERSON
ejpam-4793	908	2	j. vilela	PERSON
ejpam-4793	909	1	j. pure	PERSON
ejpam-4793	909	2	16	CARDINAL
ejpam-4793	909	3	3	CARDINAL
ejpam-4793	909	4	2023	CARDINAL
ejpam-4793	909	5	1772-1793 1792	DATE
ejpam-4793	909	6	14	DATE
ejpam-4793	910	1	γ-submonoids	GPE
ejpam-4793	910	2	⊆	CARDINAL
ejpam-4793	913	1	f(ρs(h	ORG
ejpam-4793	914	1	∈	ORG
ejpam-4793	915	1	∈	ORG
ejpam-4793	916	1	∈	ORG
ejpam-4793	916	2	⊆	CARDINAL
ejpam-4793	917	1	αh2 ∗	QUANTITY
ejpam-4793	917	2	∈	ORG
ejpam-4793	917	3	14(ii	CARDINAL
ejpam-4793	921	1	∈	ORG
ejpam-4793	930	1	f(ρs(h	ORG
ejpam-4793	931	1	1	CARDINAL
ejpam-4793	932	1	1	CARDINAL
ejpam-4793	933	1	4	CARDINAL
ejpam-4793	933	2	∈	ORG
ejpam-4793	934	1	⊆	CARDINAL
ejpam-4793	935	1	∈	ORG
ejpam-4793	936	1	4	CARDINAL
ejpam-4793	936	2	1	CARDINAL
ejpam-4793	937	1	f(ρs(h	ORG
ejpam-4793	939	1	1	CARDINAL
ejpam-4793	946	1	∈	ORG
ejpam-4793	951	1	∈	ORG
ejpam-4793	954	1	αρs(w	ORG
ejpam-4793	957	1	f(αρs(z	PERSON
ejpam-4793	959	1	1	CARDINAL
ejpam-4793	961	1	f(αρs(w	ORG
ejpam-4793	963	1	1	CARDINAL
ejpam-4793	967	1	f(αρs(z	PERSON
ejpam-4793	969	1	∈	ORG
ejpam-4793	970	1	ρker	PERSON
ejpam-4793	970	2	⊆	CARDINAL
ejpam-4793	971	1	∈	ORG
ejpam-4793	972	1	∈	ORG
ejpam-4793	972	2	f(αρs(z	PERSON
ejpam-4793	975	1	∗	CARDINAL
ejpam-4793	975	2	∗	CARDINAL
ejpam-4793	975	3	∈	ORG
ejpam-4793	978	1	∗	CARDINAL
ejpam-4793	979	1	∈	ORG
ejpam-4793	980	1	αρs(w	ORG
ejpam-4793	984	1	⊆	CARDINAL
ejpam-4793	987	1	13	CARDINAL
ejpam-4793	989	1	γ-submonoids	GPE
ejpam-4793	990	1	φ	PERSON
ejpam-4793	991	1	γ-submonoid	GPE
ejpam-4793	992	1	γ-submonoid	GPE
ejpam-4793	992	2	commutative γ-monoid	ORG
ejpam-4793	994	1	1793	DATE
ejpam-4793	994	2	msu-iligan institute of technology	ORG
ejpam-4793	995	1	1	CARDINAL
ejpam-4793	995	2	h. li	PERSON
ejpam-4793	996	1	leavitt	PERSON
ejpam-4793	997	1	547	CARDINAL
ejpam-4793	997	2	430–455, 2020	DATE
ejpam-4793	998	1	2	CARDINAL
ejpam-4793	998	2	t. w. hungerford	PERSON
ejpam-4793	1000	1	1980	DATE
ejpam-4793	1001	1	3	CARDINAL
ejpam-4793	1001	2	d.	NORP
ejpam-4793	1001	3	l. g. cordeiro	PERSON
ejpam-4793	1001	4	r. hazrat	PERSON
ejpam-4793	1002	1	rev	PERSON
ejpam-4793	1002	2	38:223–256	CARDINAL
ejpam-4793	1002	3	2022	CARDINAL
ejpam-4793	1003	1	4	CARDINAL
ejpam-4793	1005	1	1963	DATE
ejpam-4793	1006	1	5	CARDINAL
ejpam-4793	1006	2	j. vilela	PERSON
ejpam-4793	1007	1	jordan	GPE
ejpam-4793	1008	1	22(4):1–18	CARDINAL
ejpam-4793	1008	2	2023	CARDINAL
ejpam-4793	1009	1	6	CARDINAL
ejpam-4793	1009	2	b. steinberg.	PERSON
ejpam-4793	1010	1	2016	DATE