id	sid	eid	entity	type
ejpam-6327	1	1	european journal	ORG
ejpam-6327	1	2	2025	DATE
ejpam-6327	1	3	18	CARDINAL
ejpam-6327	1	4	3	CARDINAL
ejpam-6327	1	5	1307-5543	DATE
ejpam-6327	1	6	new york	GPE
ejpam-6327	1	7	ks	GPE
ejpam-6327	1	8	t. sarapuddin1,∗	PERSON
ejpam-6327	1	9	jocelyn p. vilela1	PERSON
ejpam-6327	2	1	1	CARDINAL
ejpam-6327	2	2	msu-iligan institute of technology	ORG
ejpam-6327	2	3	9200	CARDINAL
ejpam-6327	2	4	iligan city	GPE
ejpam-6327	2	5	philippines	GPE
ejpam-6327	4	1	quotient ks-semigroups	GPE
ejpam-6327	4	2	ks	GPE
ejpam-6327	6	1	2020	DATE
ejpam-6327	6	2	08a30	CARDINAL
ejpam-6327	6	3	08a72	CARDINAL
ejpam-6327	6	4	ks	GPE
ejpam-6327	6	5	ks	GPE
ejpam-6327	6	6	ks	GPE
ejpam-6327	7	1	imai	ORG
ejpam-6327	8	1	1	CARDINAL
ejpam-6327	8	2	1966	DATE
ejpam-6327	11	1	1905	DATE
ejpam-6327	11	2	dickson	PERSON
ejpam-6327	12	1	1928	DATE
ejpam-6327	12	2	2	CARDINAL
ejpam-6327	14	1	semigroups	ORG
ejpam-6327	14	2	3	CARDINAL
ejpam-6327	16	1	https://doi.org/10.29020/nybg.ejpam.v18i3.6327	PERSON
ejpam-6327	16	2	h. t. sarapuddin	PERSON
ejpam-6327	16	3	jocelyn.vilela@g.msuiit.edu.ph	GPE
ejpam-6327	16	4	j. p. vilela	ORG
ejpam-6327	17	1	1	CARDINAL
ejpam-6327	17	2	2025	CARDINAL
ejpam-6327	18	1	h. sarapuddin	PERSON
ejpam-6327	18	2	j. vilela	PERSON
ejpam-6327	19	1	j. pure	PERSON
ejpam-6327	19	2	18	CARDINAL
ejpam-6327	19	3	3	CARDINAL
ejpam-6327	19	4	2025	CARDINAL
ejpam-6327	19	5	6327	DATE
ejpam-6327	19	6	2	CARDINAL
ejpam-6327	19	7	23	CARDINAL
ejpam-6327	19	8	4	CARDINAL
ejpam-6327	19	9	1965	DATE
ejpam-6327	22	1	two	CARDINAL
ejpam-6327	23	1	rosenfeld	PERSON
ejpam-6327	23	2	1971	DATE
ejpam-6327	24	1	2006	DATE
ejpam-6327	24	2	kim	PERSON
ejpam-6327	24	3	5	CARDINAL
ejpam-6327	25	1	2009	DATE
ejpam-6327	26	1	6	CARDINAL
ejpam-6327	27	1	2007	DATE
ejpam-6327	27	2	prince williams	PERSON
ejpam-6327	29	1	2011	DATE
ejpam-6327	29	2	bautista	PERSON
ejpam-6327	30	1	8	CARDINAL
ejpam-6327	30	2	ks	GPE
ejpam-6327	30	3	ks	GPE
ejpam-6327	32	1	9	CARDINAL
ejpam-6327	32	2	ks	GPE
ejpam-6327	32	3	ks	GPE
ejpam-6327	32	4	10	CARDINAL
ejpam-6327	33	1	11	CARDINAL
ejpam-6327	35	1	ks	GPE
ejpam-6327	36	1	ks	GPE
ejpam-6327	37	1	2	CARDINAL
ejpam-6327	38	1	1	CARDINAL
ejpam-6327	39	1	5	CARDINAL
ejpam-6327	39	2	∗	CARDINAL
ejpam-6327	39	3	∗	CARDINAL
ejpam-6327	40	1	0 ∗	QUANTITY
ejpam-6327	44	1	0	CARDINAL
ejpam-6327	44	2	2	CARDINAL
ejpam-6327	45	1	5	CARDINAL
ejpam-6327	46	1	x.	GPE
ejpam-6327	46	2	1	CARDINAL
ejpam-6327	47	1	5	CARDINAL
ejpam-6327	49	1	y ∗ z	PERSON
ejpam-6327	49	2	h. sarapuddin	PERSON
ejpam-6327	49	3	j. vilela	PERSON
ejpam-6327	50	1	j. pure	PERSON
ejpam-6327	50	2	18	CARDINAL
ejpam-6327	50	3	3	CARDINAL
ejpam-6327	50	4	2025	CARDINAL
ejpam-6327	50	5	6327 3	CARDINAL
ejpam-6327	51	1	∗	CARDINAL
ejpam-6327	51	2	∗	CARDINAL
ejpam-6327	51	3	1	CARDINAL
ejpam-6327	52	1	12	CARDINAL
ejpam-6327	52	2	∗	CARDINAL
ejpam-6327	52	3	∗	CARDINAL
ejpam-6327	53	1	∗	CARDINAL
ejpam-6327	54	1	∗	CARDINAL
ejpam-6327	55	1	3	CARDINAL
ejpam-6327	56	1	13	CARDINAL
ejpam-6327	58	1	xy	ORG
ejpam-6327	59	1	4	CARDINAL
ejpam-6327	60	1	5	CARDINAL
ejpam-6327	60	2	∗	CARDINAL
ejpam-6327	60	3	0	DATE
ejpam-6327	60	4	ks	GPE
ejpam-6327	60	5	∗	CARDINAL
ejpam-6327	60	6	y ∗ z	PERSON
ejpam-6327	65	1	1	CARDINAL
ejpam-6327	66	1	5	CARDINAL
ejpam-6327	66	2	0	CARDINAL
ejpam-6327	68	1	0	CARDINAL
ejpam-6327	68	2	0	CARDINAL
ejpam-6327	69	1	0	CARDINAL
ejpam-6327	69	2	0	DATE
ejpam-6327	70	1	0	CARDINAL
ejpam-6327	70	2	0	CARDINAL
ejpam-6327	70	3	0	CARDINAL
ejpam-6327	70	4	0	CARDINAL
ejpam-6327	70	5	0	CARDINAL
ejpam-6327	71	1	ks	GPE
ejpam-6327	72	1	5	CARDINAL
ejpam-6327	73	1	5	CARDINAL
ejpam-6327	74	1	∗	CARDINAL
ejpam-6327	75	1	2	CARDINAL
ejpam-6327	76	1	5	CARDINAL
ejpam-6327	76	2	y ∗	PERSON
ejpam-6327	77	1	6	CARDINAL
ejpam-6327	78	1	5	CARDINAL
ejpam-6327	79	1	xa ∈	PERSON
ejpam-6327	80	1	∈	ORG
ejpam-6327	80	2	∈	ORG
ejpam-6327	80	3	two	CARDINAL
ejpam-6327	81	1	h. sarapuddin	PERSON
ejpam-6327	81	2	j. vilela	PERSON
ejpam-6327	82	1	j. pure	PERSON
ejpam-6327	82	2	18	CARDINAL
ejpam-6327	82	3	3	CARDINAL
ejpam-6327	82	4	2025	CARDINAL
ejpam-6327	82	5	6327	DATE
ejpam-6327	82	6	4	CARDINAL
ejpam-6327	82	7	23	CARDINAL
ejpam-6327	82	8	7	DATE
ejpam-6327	83	1	5	CARDINAL
ejpam-6327	83	2	ks	GPE
ejpam-6327	86	1	two	CARDINAL
ejpam-6327	87	1	2	CARDINAL
ejpam-6327	88	1	5	CARDINAL
ejpam-6327	88	2	ks	GPE
ejpam-6327	89	1	x.	EVENT
ejpam-6327	90	1	8	DATE
ejpam-6327	91	1	5	CARDINAL
ejpam-6327	91	2	ks	GPE
ejpam-6327	91	3	x.	GPE
ejpam-6327	92	1	y ∗ z	PERSON
ejpam-6327	94	1	∗	CARDINAL
ejpam-6327	94	2	y ∗ v and	PERSON
ejpam-6327	94	3	xu ∼ yv	PERSON
ejpam-6327	94	4	∈	ORG
ejpam-6327	95	1	1	CARDINAL
ejpam-6327	96	1	5	CARDINAL
ejpam-6327	96	2	ks	GPE
ejpam-6327	99	1	0	CARDINAL
ejpam-6327	99	2	1	CARDINAL
ejpam-6327	101	1	9	CARDINAL
ejpam-6327	102	1	7	CARDINAL
ejpam-6327	102	2	ks	GPE
ejpam-6327	103	1	ks	GPE
ejpam-6327	103	2	∈	ORG
ejpam-6327	103	3	f1	PERSON
ejpam-6327	104	1	µ(y	PERSON
ejpam-6327	104	2	µ(a	PERSON
ejpam-6327	105	1	µ(a	PERSON
ejpam-6327	106	1	ks	GPE
ejpam-6327	106	2	ks	GPE
ejpam-6327	106	3	x.	EVENT
ejpam-6327	106	4	10	CARDINAL
ejpam-6327	107	1	ks	GPE
ejpam-6327	109	1	f1	PERSON
ejpam-6327	110	1	µ(y ∗ z	PERSON
ejpam-6327	110	2	ks	GPE
ejpam-6327	110	3	ks	GPE
ejpam-6327	110	4	x.	GPE
ejpam-6327	110	5	2	CARDINAL
ejpam-6327	111	1	ks	GPE
ejpam-6327	112	1	x.	EVENT
ejpam-6327	113	1	h. sarapuddin	PERSON
ejpam-6327	113	2	j. vilela	PERSON
ejpam-6327	114	1	j. pure	PERSON
ejpam-6327	114	2	18	CARDINAL
ejpam-6327	114	3	3	CARDINAL
ejpam-6327	114	4	2025	CARDINAL
ejpam-6327	114	5	6327 5	DATE
ejpam-6327	115	1	ks	GPE
ejpam-6327	117	1	lemma	ORG
ejpam-6327	118	1	1	CARDINAL
ejpam-6327	119	1	ks	GPE
ejpam-6327	119	2	µ(y	PERSON
ejpam-6327	120	1	µ(z	PERSON
ejpam-6327	122	1	ks	GPE
ejpam-6327	123	1	f2	ORG
ejpam-6327	123	2	µ(y	PERSON
ejpam-6327	123	3	0	CARDINAL
ejpam-6327	124	1	µ(y	PERSON
ejpam-6327	124	2	µ(y	PERSON
ejpam-6327	124	3	µ(y	PERSON
ejpam-6327	125	1	µ(z	PERSON
ejpam-6327	126	1	f2	ORG
ejpam-6327	126	2	µ(y	PERSON
ejpam-6327	126	3	µ(y	PERSON
ejpam-6327	127	1	2	CARDINAL
ejpam-6327	129	1	3	CARDINAL
ejpam-6327	130	1	ks	GPE
ejpam-6327	130	2	µ(x ∗	PRODUCT
ejpam-6327	131	1	∗ y	PERSON
ejpam-6327	132	1	ks	GPE
ejpam-6327	132	2	2	CARDINAL
ejpam-6327	133	1	f4	CARDINAL
ejpam-6327	133	2	f1	PERSON
ejpam-6327	133	3	1	CARDINAL
ejpam-6327	133	4	µ(x ∗	PRODUCT
ejpam-6327	133	5	µ(y ∗ y	PERSON
ejpam-6327	135	1	∗ y	PERSON
ejpam-6327	136	1	1(i	CARDINAL
ejpam-6327	136	2	∗ y	PERSON
ejpam-6327	138	1	∗ y	PERSON
ejpam-6327	138	2	µ(x ∗	PRODUCT
ejpam-6327	139	1	∗ y	PERSON
ejpam-6327	139	2	1(i	CARDINAL
ejpam-6327	139	3	∗	CARDINAL
ejpam-6327	139	4	∗ z.	PERSON
ejpam-6327	140	1	µ(x ∗ z	PRODUCT
ejpam-6327	140	2	∗ z	ORG
ejpam-6327	140	3	∗	CARDINAL
ejpam-6327	140	4	µ(y ∗ z	PERSON
ejpam-6327	141	1	x.	EVENT
ejpam-6327	141	2	ks	GPE
ejpam-6327	142	1	h. sarapuddin	PERSON
ejpam-6327	142	2	j. vilela	PERSON
ejpam-6327	143	1	j. pure	PERSON
ejpam-6327	143	2	18	CARDINAL
ejpam-6327	143	3	3	CARDINAL
ejpam-6327	143	4	2025	CARDINAL
ejpam-6327	143	5	6	CARDINAL
ejpam-6327	143	6	23	CARDINAL
ejpam-6327	143	7	11	DATE
ejpam-6327	144	1	ks	GPE
ejpam-6327	146	1	ks	GPE
ejpam-6327	146	2	f1	PERSON
ejpam-6327	147	1	µ(z	PERSON
ejpam-6327	148	1	ks	GPE
ejpam-6327	148	2	ks	GPE
ejpam-6327	148	3	ks	GPE
ejpam-6327	148	4	x.	ORG
ejpam-6327	149	1	2	CARDINAL
ejpam-6327	149	2	0	CARDINAL
ejpam-6327	152	1	0	CARDINAL
ejpam-6327	152	2	0	CARDINAL
ejpam-6327	152	3	0	CARDINAL
ejpam-6327	152	4	0	DATE
ejpam-6327	153	1	0	CARDINAL
ejpam-6327	153	2	0	CARDINAL
ejpam-6327	153	3	0	CARDINAL
ejpam-6327	155	1	ks	GPE
ejpam-6327	157	1	0	CARDINAL
ejpam-6327	157	2	1	CARDINAL
ejpam-6327	159	1	µ(a	PERSON
ejpam-6327	160	1	µ(b	PERSON
ejpam-6327	160	2	µ(c	PERSON
ejpam-6327	161	1	ks	GPE
ejpam-6327	161	2	x.	GPE
ejpam-6327	161	3	ks	GPE
ejpam-6327	162	1	4	CARDINAL
ejpam-6327	163	1	ks	GPE
ejpam-6327	164	1	ks	GPE
ejpam-6327	164	2	x.	GPE
ejpam-6327	165	1	ks	GPE
ejpam-6327	165	2	1(i	CARDINAL
ejpam-6327	165	3	1	CARDINAL
ejpam-6327	167	1	0 ∗	CARDINAL
ejpam-6327	167	2	0 ∗ x	QUANTITY
ejpam-6327	167	3	∗	CARDINAL
ejpam-6327	167	4	µ(y	PERSON
ejpam-6327	168	1	µ(y	PERSON
ejpam-6327	169	1	x.	GPE
ejpam-6327	169	2	ks	GPE
ejpam-6327	169	3	ks	GPE
ejpam-6327	169	4	ks	GPE
ejpam-6327	171	1	3	CARDINAL
ejpam-6327	171	2	0	CARDINAL
ejpam-6327	171	3	1	DATE
ejpam-6327	171	4	2	DATE
ejpam-6327	171	5	3	DATE
ejpam-6327	171	6	4	CARDINAL
ejpam-6327	174	1	1	CARDINAL
ejpam-6327	174	2	0 3 3 3 3	TIME
ejpam-6327	174	3	0	CARDINAL
ejpam-6327	174	4	3	CARDINAL
ejpam-6327	174	5	h. sarapuddin	PERSON
ejpam-6327	174	6	j. vilela	PERSON
ejpam-6327	175	1	j. pure	PERSON
ejpam-6327	175	2	18	CARDINAL
ejpam-6327	175	3	3	CARDINAL
ejpam-6327	175	4	2025	CARDINAL
ejpam-6327	175	5	7	CARDINAL
ejpam-6327	175	6	ks	GPE
ejpam-6327	177	1	0	CARDINAL
ejpam-6327	177	2	1	CARDINAL
ejpam-6327	181	1	x.	EVENT
ejpam-6327	181	2	ks	GPE
ejpam-6327	181	3	∗	DATE
ejpam-6327	181	4	3 ∗	CARDINAL
ejpam-6327	181	5	3	CARDINAL
ejpam-6327	183	1	ks	GPE
ejpam-6327	184	1	5	CARDINAL
ejpam-6327	185	1	ks	GPE
ejpam-6327	185	2	ks	GPE
ejpam-6327	185	3	µ(x ∗	PRODUCT
ejpam-6327	187	1	ks	GPE
ejpam-6327	187	2	ks	GPE
ejpam-6327	187	3	4	CARDINAL
ejpam-6327	191	1	1(iv	CARDINAL
ejpam-6327	192	1	1(i	CARDINAL
ejpam-6327	193	1	µ(x ∗	PRODUCT
ejpam-6327	195	1	µ(x ∗	PRODUCT
ejpam-6327	196	1	f2	ORG
ejpam-6327	197	1	µ(z	PERSON
ejpam-6327	197	2	ks	GPE
ejpam-6327	197	3	x.	GPE
ejpam-6327	197	4	ks	GPE
ejpam-6327	198	1	6	CARDINAL
ejpam-6327	200	1	ks	GPE
ejpam-6327	204	1	1	CARDINAL
ejpam-6327	205	1	∗	CARDINAL
ejpam-6327	205	2	∗	CARDINAL
ejpam-6327	207	1	0	CARDINAL
ejpam-6327	208	1	2	CARDINAL
ejpam-6327	208	2	∗	CARDINAL
ejpam-6327	208	3	z.	PERSON
ejpam-6327	209	1	µ(z	PERSON
ejpam-6327	210	1	h. sarapuddin	PERSON
ejpam-6327	210	2	j. vilela	PERSON
ejpam-6327	211	1	j. pure	PERSON
ejpam-6327	211	2	18	CARDINAL
ejpam-6327	211	3	3	CARDINAL
ejpam-6327	211	4	2025	CARDINAL
ejpam-6327	211	5	6327 8	DATE
ejpam-6327	211	6	23	CARDINAL
ejpam-6327	212	1	ks	GPE
ejpam-6327	212	2	x.	ORG
ejpam-6327	212	3	12	CARDINAL
ejpam-6327	213	1	ks	GPE
ejpam-6327	215	1	ks	GPE
ejpam-6327	215	2	f1	PERSON
ejpam-6327	216	1	∗	CARDINAL
ejpam-6327	216	2	µ(z	PERSON
ejpam-6327	216	3	ks	GPE
ejpam-6327	216	4	ks	GPE
ejpam-6327	216	5	ks	GPE
ejpam-6327	216	6	x.	ORG
ejpam-6327	216	7	4	CARDINAL
ejpam-6327	217	1	0	CARDINAL
ejpam-6327	217	2	1	DATE
ejpam-6327	217	3	2	DATE
ejpam-6327	217	4	3	DATE
ejpam-6327	217	5	4	CARDINAL
ejpam-6327	220	1	1	CARDINAL
ejpam-6327	220	2	0 3 3 3 3	TIME
ejpam-6327	220	3	0	CARDINAL
ejpam-6327	220	4	3	CARDINAL
ejpam-6327	220	5	0	CARDINAL
ejpam-6327	220	6	ks	GPE
ejpam-6327	222	1	0	CARDINAL
ejpam-6327	222	2	1	CARDINAL
ejpam-6327	223	1	µ(3	GPE
ejpam-6327	224	1	ks	GPE
ejpam-6327	224	2	x.	GPE
ejpam-6327	224	3	ks	GPE
ejpam-6327	225	1	7	CARDINAL
ejpam-6327	226	1	ks	GPE
ejpam-6327	227	1	ks	GPE
ejpam-6327	227	2	x.	GPE
ejpam-6327	228	1	ks	GPE
ejpam-6327	228	2	ks	GPE
ejpam-6327	228	3	µ(y	PERSON
ejpam-6327	229	1	∗	CARDINAL
ejpam-6327	229	2	µ(y	PERSON
ejpam-6327	230	1	µ(y	PERSON
ejpam-6327	231	1	x.	GPE
ejpam-6327	231	2	7	DATE
ejpam-6327	232	1	5	CARDINAL
ejpam-6327	233	1	ks	GPE
ejpam-6327	233	2	example 4	DATE
ejpam-6327	233	3	0.8	CARDINAL
ejpam-6327	233	4	0.5	CARDINAL
ejpam-6327	233	5	x.	EVENT
ejpam-6327	233	6	ks	GPE
ejpam-6327	234	1	0.5	CARDINAL
ejpam-6327	234	2	0.8	CARDINAL
ejpam-6327	234	3	min{µ((1	PERSON
ejpam-6327	234	4	3 ∗ 1	CARDINAL
ejpam-6327	234	5	2	CARDINAL
ejpam-6327	235	1	ks	GPE
ejpam-6327	236	1	h. sarapuddin	PERSON
ejpam-6327	236	2	j. vilela	PERSON
ejpam-6327	237	1	j. pure	PERSON
ejpam-6327	237	2	18	CARDINAL
ejpam-6327	237	3	3	CARDINAL
ejpam-6327	237	4	2025	CARDINAL
ejpam-6327	237	5	6327 9	DATE
ejpam-6327	237	6	23	CARDINAL
ejpam-6327	238	1	ks	GPE
ejpam-6327	238	2	ks	GPE
ejpam-6327	239	1	ks	GPE
ejpam-6327	239	2	ks	GPE
ejpam-6327	239	3	7	DATE
ejpam-6327	239	4	x.	EVENT
ejpam-6327	242	1	1(i	CARDINAL
ejpam-6327	244	1	f2	ORG
ejpam-6327	245	1	µ(z	PERSON
ejpam-6327	245	2	ks	GPE
ejpam-6327	245	3	x.	GPE
ejpam-6327	245	4	ks	GPE
ejpam-6327	246	1	9	CARDINAL
ejpam-6327	247	1	ks	GPE
ejpam-6327	249	1	∗	CARDINAL
ejpam-6327	249	2	f2	ORG
ejpam-6327	250	1	µ(z	PERSON
ejpam-6327	251	1	∗	CARDINAL
ejpam-6327	251	2	µ(z	PERSON
ejpam-6327	252	1	ks	GPE
ejpam-6327	252	2	x.	GPE
ejpam-6327	252	3	10	CARDINAL
ejpam-6327	253	1	ks	GPE
ejpam-6327	253	2	ks	GPE
ejpam-6327	253	3	ks	GPE
ejpam-6327	255	1	ks	GPE
ejpam-6327	255	2	ks	GPE
ejpam-6327	255	3	x.	GPE
ejpam-6327	255	4	8	CARDINAL
ejpam-6327	255	5	1	CARDINAL
ejpam-6327	255	6	µ(x ∗ z	PRODUCT
ejpam-6327	255	7	∗ z	ORG
ejpam-6327	255	8	∗	CARDINAL
ejpam-6327	256	1	∗ z	ORG
ejpam-6327	256	2	∗	CARDINAL
ejpam-6327	256	3	µ(y ∗ z	PERSON
ejpam-6327	259	1	1(i	CARDINAL
ejpam-6327	259	2	8	CARDINAL
ejpam-6327	259	3	∗	CARDINAL
ejpam-6327	260	1	∗	CARDINAL
ejpam-6327	261	1	1	CARDINAL
ejpam-6327	263	1	1(i	CARDINAL
ejpam-6327	263	2	µ(x∗y	PRODUCT
ejpam-6327	264	1	µ(x∗y	PERSON
ejpam-6327	266	1	5	CARDINAL
ejpam-6327	266	2	ks	GPE
ejpam-6327	266	3	x.	GPE
ejpam-6327	266	4	ks	GPE
ejpam-6327	266	5	x.	EVENT
ejpam-6327	266	6	1(i	CARDINAL
ejpam-6327	266	7	1(i	CARDINAL
ejpam-6327	269	1	1	CARDINAL
ejpam-6327	269	2	h. sarapuddin	PERSON
ejpam-6327	269	3	j. vilela	PERSON
ejpam-6327	270	1	j. pure	PERSON
ejpam-6327	270	2	18	CARDINAL
ejpam-6327	270	3	3	CARDINAL
ejpam-6327	270	4	2025	CARDINAL
ejpam-6327	270	5	6327 10 of 23	DATE
ejpam-6327	270	6	1	CARDINAL
ejpam-6327	271	1	1(i	CARDINAL
ejpam-6327	272	1	ks	GPE
ejpam-6327	272	2	5	CARDINAL
ejpam-6327	275	1	2	CARDINAL
ejpam-6327	275	2	∗	CARDINAL
ejpam-6327	278	1	µ(y ∗	PERSON
ejpam-6327	279	1	1	CARDINAL
ejpam-6327	279	2	2	CARDINAL
ejpam-6327	280	1	µ(y ∗	PERSON
ejpam-6327	281	1	1(i	CARDINAL
ejpam-6327	282	1	8	CARDINAL
ejpam-6327	282	2	ks	GPE
ejpam-6327	282	3	x. 4	DATE
ejpam-6327	283	1	ks	GPE
ejpam-6327	283	2	5	CARDINAL
ejpam-6327	283	3	ks	GPE
ejpam-6327	286	1	ks	GPE
ejpam-6327	287	1	quotient ks-semigroups	GPE
ejpam-6327	288	1	13	DATE
ejpam-6327	289	1	ks	GPE
ejpam-6327	289	2	ks	GPE
ejpam-6327	290	1	µ(x ∗	PRODUCT
ejpam-6327	290	2	µ(y ∗ x	PERSON
ejpam-6327	291	1	0	CARDINAL
ejpam-6327	292	1	∼µ	DATE
ejpam-6327	292	2	ks	GPE
ejpam-6327	292	3	3	CARDINAL
ejpam-6327	293	1	ks	GPE
ejpam-6327	294	1	ks	GPE
ejpam-6327	294	2	ks	GPE
ejpam-6327	296	1	µ(z	ORG
ejpam-6327	296	2	µ(z	PERSON
ejpam-6327	296	3	0	CARDINAL
ejpam-6327	297	1	f1	PERSON
ejpam-6327	298	1	0	CARDINAL
ejpam-6327	298	2	1	CARDINAL
ejpam-6327	298	3	0	CARDINAL
ejpam-6327	299	1	∼µ	DATE
ejpam-6327	301	1	µ(x ∗	PRODUCT
ejpam-6327	302	1	µ(y ∗ x	PERSON
ejpam-6327	302	2	0	CARDINAL
ejpam-6327	302	3	µ(y ∗ x	PERSON
ejpam-6327	302	4	0	CARDINAL
ejpam-6327	303	1	µ(x ∗	PRODUCT
ejpam-6327	304	1	0	CARDINAL
ejpam-6327	305	1	∼µ	DATE
ejpam-6327	306	1	∼µ	DATE
ejpam-6327	306	2	y ∼µ z.	PERSON
ejpam-6327	307	1	µ(x ∗	PRODUCT
ejpam-6327	308	1	0	CARDINAL
ejpam-6327	308	2	µ(y ∗ x	PERSON
ejpam-6327	308	3	0	CARDINAL
ejpam-6327	308	4	µ(y ∗ z	PERSON
ejpam-6327	308	5	µ(z ∗ y	PERSON
ejpam-6327	309	1	0	CARDINAL
ejpam-6327	310	1	ks	GPE
ejpam-6327	310	2	∗	CARDINAL
ejpam-6327	311	1	y ∗ z	PERSON
ejpam-6327	311	2	∗	CARDINAL
ejpam-6327	312	1	y ∗ x	PERSON
ejpam-6327	312	2	µ(x ∗ z	PRODUCT
ejpam-6327	314	1	µ(y ∗ z	PERSON
ejpam-6327	314	2	0	CARDINAL
ejpam-6327	314	3	µ(z ∗ x	PERSON
ejpam-6327	314	4	µ(z ∗ y	PERSON
ejpam-6327	315	1	0	CARDINAL
ejpam-6327	316	1	z. hence	PERSON
ejpam-6327	316	2	∼µ	DATE
ejpam-6327	317	1	∼µ	DATE
ejpam-6327	317	2	x.	GPE
ejpam-6327	317	3	ks	GPE
ejpam-6327	317	4	ks	GPE
ejpam-6327	317	5	∼µ	DATE
ejpam-6327	318	1	h. sarapuddin	PERSON
ejpam-6327	318	2	j. vilela	PERSON
ejpam-6327	319	1	j. pure	PERSON
ejpam-6327	319	2	18	CARDINAL
ejpam-6327	319	3	3	CARDINAL
ejpam-6327	319	4	2025	CARDINAL
ejpam-6327	319	5	6327 11	DATE
ejpam-6327	319	6	23	CARDINAL
ejpam-6327	319	7	ks	GPE
ejpam-6327	319	8	0	CARDINAL
ejpam-6327	319	9	example 1	DATE
ejpam-6327	319	10	µ(a	PERSON
ejpam-6327	319	11	= µ(b	PERSON
ejpam-6327	319	12	0.8	CARDINAL
ejpam-6327	319	13	µ(c	PERSON
ejpam-6327	320	1	0	CARDINAL
ejpam-6327	321	1	x.	ORG
ejpam-6327	321	2	µ(c	PERSON
ejpam-6327	321	3	µ(a	PERSON
ejpam-6327	321	4	µ(a	PERSON
ejpam-6327	323	1	µ(a ∗	PERSON
ejpam-6327	323	2	µ(a	PERSON
ejpam-6327	323	3	0.8	CARDINAL
ejpam-6327	323	4	0	CARDINAL
ejpam-6327	323	5	µ(b ∗	PERSON
ejpam-6327	323	6	0.8	CARDINAL
ejpam-6327	323	7	0	CARDINAL
ejpam-6327	324	1	∼µ	DATE
ejpam-6327	324	2	µ(c	PERSON
ejpam-6327	324	3	µ(c	PERSON
ejpam-6327	325	1	ks	GPE
ejpam-6327	325	2	ks	GPE
ejpam-6327	326	1	∼µ	DATE
ejpam-6327	328	1	ks	GPE
ejpam-6327	328	2	ks	GPE
ejpam-6327	329	1	µ(x∗y	ORG
ejpam-6327	329	2	0	CARDINAL
ejpam-6327	330	1	µ(y	PERSON
ejpam-6327	331	1	0	CARDINAL
ejpam-6327	332	1	∗	CARDINAL
ejpam-6327	332	2	y ∗ x	PERSON
ejpam-6327	332	3	∗	CARDINAL
ejpam-6327	332	4	0	CARDINAL
ejpam-6327	333	1	0	CARDINAL
ejpam-6327	333	2	1(i	CARDINAL
ejpam-6327	338	1	0	CARDINAL
ejpam-6327	339	1	0	CARDINAL
ejpam-6327	341	1	∼µ	DATE
ejpam-6327	342	1	∗	CARDINAL
ejpam-6327	342	2	y ∗ z	PERSON
ejpam-6327	342	3	∗	CARDINAL
ejpam-6327	342	4	y ∗ x	PERSON
ejpam-6327	342	5	∗ z	ORG
ejpam-6327	342	6	∗	CARDINAL
ejpam-6327	342	7	0	CARDINAL
ejpam-6327	342	8	∗ z	PRODUCT
ejpam-6327	342	9	∗	CARDINAL
ejpam-6327	343	1	µ(y ∗ x	PERSON
ejpam-6327	343	2	0	CARDINAL
ejpam-6327	344	1	1(i	CARDINAL
ejpam-6327	345	1	y ∗ z.	PERSON
ejpam-6327	348	1	∗	CARDINAL
ejpam-6327	349	1	∗	CARDINAL
ejpam-6327	350	1	0	CARDINAL
ejpam-6327	352	1	0	CARDINAL
ejpam-6327	354	1	∼µ	DATE
ejpam-6327	355	1	3	CARDINAL
ejpam-6327	355	2	1	CARDINAL
ejpam-6327	356	1	ks	GPE
ejpam-6327	356	2	ks	GPE
ejpam-6327	357	1	∼µ	DATE
ejpam-6327	357	2	ks	GPE
ejpam-6327	357	3	ks	GPE
ejpam-6327	358	1	∼µ	WORK_OF_ART
ejpam-6327	360	1	3	CARDINAL
ejpam-6327	361	1	11	CARDINAL
ejpam-6327	362	1	ks	GPE
ejpam-6327	362	2	ks	GPE
ejpam-6327	363	1	ks	GPE
ejpam-6327	363	2	⊙	ORG
ejpam-6327	363	3	∈	ORG
ejpam-6327	364	1	ks	GPE
ejpam-6327	364	2	ks	GPE
ejpam-6327	365	1	1	CARDINAL
ejpam-6327	365	2	⊙	ORG
ejpam-6327	366	1	∈	ORG
ejpam-6327	366	2	h. sarapuddin	PERSON
ejpam-6327	366	3	j. vilela	PERSON
ejpam-6327	367	1	j. pure	PERSON
ejpam-6327	367	2	18	CARDINAL
ejpam-6327	367	3	3	CARDINAL
ejpam-6327	367	4	2025	CARDINAL
ejpam-6327	367	5	6327 12	DATE
ejpam-6327	367	6	23	CARDINAL
ejpam-6327	367	7	= µ((x∗y)∗(x∗z))∗(z∗y	PERSON
ejpam-6327	375	1	∗ y	PERSON
ejpam-6327	375	2	µ(y ∗ x	PERSON
ejpam-6327	375	3	∗ x	PERSON
ejpam-6327	375	4	0	CARDINAL
ejpam-6327	377	1	⊙	ORG
ejpam-6327	377	2	⊙	NORP
ejpam-6327	377	3	µ(xy)z	CARDINAL
ejpam-6327	377	4	⊙	FAC
ejpam-6327	378	1	⊙	ORG
ejpam-6327	378	2	⊙	NORP
ejpam-6327	379	1	x/µ,⊙	GPE
ejpam-6327	380	1	⊙	ORG
ejpam-6327	380	2	⊙	LAW
ejpam-6327	381	1	⊙ µy)⊛	ORG
ejpam-6327	381	2	⊙	NORP
ejpam-6327	381	3	⊙	NORP
ejpam-6327	381	4	⊙	FAC
ejpam-6327	381	5	⊙	NORP
ejpam-6327	382	1	ks	GPE
ejpam-6327	383	1	ks	GPE
ejpam-6327	383	2	ks-semigroup	ORG
ejpam-6327	384	1	12	CARDINAL
ejpam-6327	385	1	ks	GPE
ejpam-6327	387	1	ks	GPE
ejpam-6327	388	1	∈	ORG
ejpam-6327	390	1	1	CARDINAL
ejpam-6327	390	2	xa ∈ i.	ORG
ejpam-6327	393	1	1	CARDINAL
ejpam-6327	393	2	1	CARDINAL
ejpam-6327	394	1	1	CARDINAL
ejpam-6327	394	2	i.	PERSON
ejpam-6327	394	3	2(ii	CARDINAL
ejpam-6327	394	4	∈	ORG
ejpam-6327	394	5	1	CARDINAL
ejpam-6327	396	1	1	CARDINAL
ejpam-6327	397	1	i.	PERSON
ejpam-6327	397	2	1	CARDINAL
ejpam-6327	398	1	h. sarapuddin	PERSON
ejpam-6327	398	2	j. vilela	PERSON
ejpam-6327	399	1	j. pure	PERSON
ejpam-6327	399	2	18	CARDINAL
ejpam-6327	399	3	3	CARDINAL
ejpam-6327	399	4	2025	CARDINAL
ejpam-6327	399	5	6327 13	DATE
ejpam-6327	399	6	23	CARDINAL
ejpam-6327	399	7	2	CARDINAL
ejpam-6327	400	1	y /∈ i.	PERSON
ejpam-6327	400	2	0	CARDINAL
ejpam-6327	400	3	0	CARDINAL
ejpam-6327	401	1	3	CARDINAL
ejpam-6327	403	1	0	CARDINAL
ejpam-6327	403	2	0	CARDINAL
ejpam-6327	404	1	4	CARDINAL
ejpam-6327	405	1	y /∈ i.	PERSON
ejpam-6327	406	1	0	CARDINAL
ejpam-6327	406	2	0	CARDINAL
ejpam-6327	409	1	1	CARDINAL
ejpam-6327	409	2	∈	ORG
ejpam-6327	409	3	xa	PERSON
ejpam-6327	409	4	∈	ORG
ejpam-6327	409	5	1	CARDINAL
ejpam-6327	409	6	1	CARDINAL
ejpam-6327	410	1	2	CARDINAL
ejpam-6327	412	1	xa ∈	PERSON
ejpam-6327	412	2	1	CARDINAL
ejpam-6327	412	3	1	CARDINAL
ejpam-6327	413	1	xa	PERSON
ejpam-6327	416	1	0	CARDINAL
ejpam-6327	416	2	0	CARDINAL
ejpam-6327	419	1	1	CARDINAL
ejpam-6327	419	2	2	CARDINAL
ejpam-6327	420	1	ks	GPE
ejpam-6327	420	2	∼i	PERSON
ejpam-6327	420	3	x.	EVENT
ejpam-6327	420	4	5	CARDINAL
ejpam-6327	421	1	ks	GPE
ejpam-6327	423	1	ks	GPE
ejpam-6327	424	1	⇔	ORG
ejpam-6327	424	2	1 and χi(y ∗	QUANTITY
ejpam-6327	424	3	1 ⇔	CARDINAL
ejpam-6327	424	4	0	CARDINAL
ejpam-6327	425	1	ks	GPE
ejpam-6327	427	1	ks	GPE
ejpam-6327	427	2	ks	GPE
ejpam-6327	427	3	ks	GPE
ejpam-6327	427	4	i. theorem 13	PERSON
ejpam-6327	428	1	ks	GPE
ejpam-6327	428	2	ks	GPE
ejpam-6327	429	1	j	PERSON
ejpam-6327	429	2	j ∈ j	PERSON
ejpam-6327	429	3	x/µ. h. sarapuddin	PERSON
ejpam-6327	429	4	j. vilela	PERSON
ejpam-6327	430	1	j. pure	PERSON
ejpam-6327	430	2	18	CARDINAL
ejpam-6327	430	3	3	CARDINAL
ejpam-6327	430	4	2025	CARDINAL
ejpam-6327	430	5	14	CARDINAL
ejpam-6327	430	6	23	CARDINAL
ejpam-6327	431	1	ks	GPE
ejpam-6327	431	2	ks	GPE
ejpam-6327	431	3	x.	ORG
ejpam-6327	431	4	j/µ ⊆	ORG
ejpam-6327	432	1	∈	ORG
ejpam-6327	432	2	∈	ORG
ejpam-6327	433	1	∈	ORG
ejpam-6327	433	2	∈	ORG
ejpam-6327	434	1	∈	ORG
ejpam-6327	434	2	∈	PRODUCT
ejpam-6327	434	3	∈	ORG
ejpam-6327	436	1	∈	ORG
ejpam-6327	437	1	∈	ORG
ejpam-6327	437	2	14	DATE
ejpam-6327	438	1	ks	GPE
ejpam-6327	438	2	ks	GPE
ejpam-6327	439	1	j∗	ORG
ejpam-6327	439	2	j = ⋃	PERSON
ejpam-6327	439	3	14	DATE
ejpam-6327	440	1	5	CARDINAL
ejpam-6327	441	1	ks	GPE
ejpam-6327	441	2	f(x ∗ y	PERSON
ejpam-6327	442	1	one	CARDINAL
ejpam-6327	446	1	15	CARDINAL
ejpam-6327	447	1	ks	GPE
ejpam-6327	447	2	ks	GPE
ejpam-6327	448	1	j	PERSON
ejpam-6327	450	1	ks	GPE
ejpam-6327	450	2	ks	GPE
ejpam-6327	451	1	13	CARDINAL
ejpam-6327	451	2	j/µ	ORG
ejpam-6327	452	1	∈	ORG
ejpam-6327	454	1	φ((j/µ)µx	DATE
ejpam-6327	456	1	j/µ)µy ∈	ORG
ejpam-6327	457	1	j/µ)µy	PERSON
ejpam-6327	458	1	∼j/µ	DATE
ejpam-6327	460	1	∈	ORG
ejpam-6327	461	1	jx = jy.	PERSON
ejpam-6327	464	1	φ	PERSON
ejpam-6327	465	1	j/µ)µy ∈	ORG
ejpam-6327	468	1	φ((j/µ)µx ∗	QUANTITY
ejpam-6327	469	1	jx ∗ jy =	PERSON
ejpam-6327	469	2	∗	CARDINAL
ejpam-6327	469	3	h. sarapuddin	PERSON
ejpam-6327	469	4	j. vilela	PERSON
ejpam-6327	470	1	j. pure	PERSON
ejpam-6327	470	2	18	CARDINAL
ejpam-6327	470	3	3	CARDINAL
ejpam-6327	470	4	2025	CARDINAL
ejpam-6327	470	5	6327 15	CARDINAL
ejpam-6327	470	6	23	CARDINAL
ejpam-6327	473	1	φ	ORG
ejpam-6327	473	2	ks	GPE
ejpam-6327	475	1	φ	ORG
ejpam-6327	477	1	jx = jy.	PERSON
ejpam-6327	478	1	∈	ORG
ejpam-6327	480	1	∈	ORG
ejpam-6327	480	2	α∗x	CARDINAL
ejpam-6327	480	3	∈	ORG
ejpam-6327	480	4	j/µ)µy	ORG
ejpam-6327	481	1	j/µ)µx ⊆	ORG
ejpam-6327	481	2	j/µ)µy	ORG
ejpam-6327	482	1	j/µ)µy ⊆	ORG
ejpam-6327	484	1	φ	ORG
ejpam-6327	484	2	one	CARDINAL
ejpam-6327	485	1	φ	ORG
ejpam-6327	486	1	ks-ideals	ORG
ejpam-6327	486	2	ks	GPE
ejpam-6327	486	3	ks	GPE
ejpam-6327	487	1	16	CARDINAL
ejpam-6327	488	1	ks	GPE
ejpam-6327	488	2	ks	GPE
ejpam-6327	491	1	ks	GPE
ejpam-6327	491	2	ks	GPE
ejpam-6327	494	1	0	CARDINAL
ejpam-6327	494	2	5	CARDINAL
ejpam-6327	494	3	0	CARDINAL
ejpam-6327	495	1	∗	CARDINAL
ejpam-6327	495	2	∗	CARDINAL
ejpam-6327	495	3	∗	CARDINAL
ejpam-6327	495	4	0	CARDINAL
ejpam-6327	496	1	y ∗	PERSON
ejpam-6327	496	2	∗	CARDINAL
ejpam-6327	498	1	2	CARDINAL
ejpam-6327	499	1	17	CARDINAL
ejpam-6327	500	1	ks-p	ORG
ejpam-6327	500	2	ks	GPE
ejpam-6327	501	1	ks	GPE
ejpam-6327	503	1	ks-p	ORG
ejpam-6327	503	2	ks	GPE
ejpam-6327	504	1	∗	CARDINAL
ejpam-6327	505	1	0	CARDINAL
ejpam-6327	506	1	0	CARDINAL
ejpam-6327	507	1	3	CARDINAL
ejpam-6327	507	2	µ(u∗y	GPE
ejpam-6327	507	3	0	CARDINAL
ejpam-6327	508	1	∗ y	PERSON
ejpam-6327	509	1	µ(u ∗ y	PERSON
ejpam-6327	510	1	0	CARDINAL
ejpam-6327	511	1	µ(((x ∗ y	PERSON
ejpam-6327	513	1	0	CARDINAL
ejpam-6327	515	1	ks	GPE
ejpam-6327	516	1	h. sarapuddin	PERSON
ejpam-6327	516	2	j. vilela	PERSON
ejpam-6327	517	1	j. pure	PERSON
ejpam-6327	517	2	18	CARDINAL
ejpam-6327	517	3	3	CARDINAL
ejpam-6327	517	4	2025	CARDINAL
ejpam-6327	517	5	6327 16	QUANTITY
ejpam-6327	517	6	23	CARDINAL
ejpam-6327	517	7	18	CARDINAL
ejpam-6327	518	1	ks	GPE
ejpam-6327	518	2	ks	GPE
ejpam-6327	521	1	ks	GPE
ejpam-6327	521	2	ks	GPE
ejpam-6327	522	1	10	CARDINAL
ejpam-6327	522	2	ks	GPE
ejpam-6327	523	1	16	CARDINAL
ejpam-6327	523	2	17	DATE
ejpam-6327	523	3	ks	GPE
ejpam-6327	525	1	5	CARDINAL
ejpam-6327	525	2	ks-ideals	ORG
ejpam-6327	525	3	ks-semigroup	ORG
ejpam-6327	526	1	2	CARDINAL
ejpam-6327	527	1	ks	GPE
ejpam-6327	527	2	ks	GPE
ejpam-6327	530	1	ks	GPE
ejpam-6327	530	2	ks	GPE
ejpam-6327	531	1	∈	ORG
ejpam-6327	531	2	µ(a	PERSON
ejpam-6327	532	1	0	CARDINAL
ejpam-6327	534	1	0	CARDINAL
ejpam-6327	536	1	0	CARDINAL
ejpam-6327	537	1	xa	ORG
ejpam-6327	537	2	∈	ORG
ejpam-6327	538	1	µ(x ∗	PRODUCT
ejpam-6327	539	1	0	CARDINAL
ejpam-6327	540	1	µ(y	PERSON
ejpam-6327	540	2	0	CARDINAL
ejpam-6327	541	1	x.	EVENT
ejpam-6327	541	2	15	CARDINAL
ejpam-6327	542	1	5	CARDINAL
ejpam-6327	542	2	ks-semigroup	ORG
ejpam-6327	546	1	19	CARDINAL
ejpam-6327	547	1	ks	GPE
ejpam-6327	547	2	ks	GPE
ejpam-6327	548	1	γ(x	PERSON
ejpam-6327	549	1	ks	GPE
ejpam-6327	549	2	ν	NORP
ejpam-6327	550	1	ν	NORP
ejpam-6327	551	1	ν	NORP
ejpam-6327	551	2	x.	EVENT
ejpam-6327	552	1	3	CARDINAL
ejpam-6327	553	1	ks	GPE
ejpam-6327	554	1	ks	GPE
ejpam-6327	554	2	ks	GPE
ejpam-6327	556	1	ks	GPE
ejpam-6327	557	1	x.	EVENT
ejpam-6327	557	2	y ∈	PERSON
ejpam-6327	558	1	h. sarapuddin	PERSON
ejpam-6327	558	2	j. vilela	PERSON
ejpam-6327	559	1	j. pure	PERSON
ejpam-6327	559	2	18	CARDINAL
ejpam-6327	559	3	3	CARDINAL
ejpam-6327	559	4	2025	CARDINAL
ejpam-6327	559	5	6327 17	DATE
ejpam-6327	559	6	23	DATE
ejpam-6327	562	1	20	CARDINAL
ejpam-6327	563	1	ks	GPE
ejpam-6327	565	1	ks	GPE
ejpam-6327	566	1	3	CARDINAL
ejpam-6327	566	2	ks	GPE
ejpam-6327	567	1	11	CARDINAL
ejpam-6327	567	2	ks	GPE
ejpam-6327	578	1	φ	PERSON
ejpam-6327	581	1	φ(µfx ∗	PRODUCT
ejpam-6327	582	1	∗	CARDINAL
ejpam-6327	582	2	φ(µfxµ	ORG
ejpam-6327	584	1	14(i	CARDINAL
ejpam-6327	584	2	φ	ORG
ejpam-6327	588	1	φ	PERSON
ejpam-6327	595	1	µ(f(y ∗ x	PERSON
ejpam-6327	600	1	φ	ORG
ejpam-6327	600	2	one	CARDINAL
ejpam-6327	601	1	φ	PERSON
ejpam-6327	602	1	6	CARDINAL
ejpam-6327	603	1	ks-ideals	ORG
ejpam-6327	604	1	ks	GPE
ejpam-6327	605	1	h. sarapuddin	PERSON
ejpam-6327	605	2	j. vilela	PERSON
ejpam-6327	606	1	j. pure	PERSON
ejpam-6327	606	2	18	CARDINAL
ejpam-6327	606	3	3	CARDINAL
ejpam-6327	606	4	2025	CARDINAL
ejpam-6327	606	5	6327 18	DATE
ejpam-6327	606	6	23	CARDINAL
ejpam-6327	606	7	16	DATE
ejpam-6327	607	1	0y	CARDINAL
ejpam-6327	610	1	∗	CARDINAL
ejpam-6327	610	2	0	DATE
ejpam-6327	610	3	0	CARDINAL
ejpam-6327	610	4	0x	CARDINAL
ejpam-6327	610	5	0y	CARDINAL
ejpam-6327	611	1	17	CARDINAL
ejpam-6327	612	1	4	CARDINAL
ejpam-6327	613	1	cartesian	NORP
ejpam-6327	613	2	0	CARDINAL
ejpam-6327	613	3	1	CARDINAL
ejpam-6327	613	4	µ × ν(x	ORG
ejpam-6327	614	1	ν(y	PERSON
ejpam-6327	615	1	ks	GPE
ejpam-6327	615	2	ks	GPE
ejpam-6327	617	1	6	CARDINAL
ejpam-6327	618	1	ks	GPE
ejpam-6327	621	1	ks	GPE
ejpam-6327	622	1	ν(0x	PERSON
ejpam-6327	622	2	0y	CARDINAL
ejpam-6327	622	3	µ(y	PERSON
ejpam-6327	623	1	ν(x	PERSON
ejpam-6327	626	1	µ(y1)},min{ν(x2	GPE
ejpam-6327	626	2	y2)},min{µ(y1	GPE
ejpam-6327	626	3	min{µ×	DATE
ejpam-6327	626	4	ν(y1	PRODUCT
ejpam-6327	626	5	min{µ×	DATE
ejpam-6327	626	6	ν(y1	PRODUCT
ejpam-6327	629	1	x2)(y1	PERSON
ejpam-6327	630	1	ν(x1	PERSON
ejpam-6327	631	1	ν(x2	ORG
ejpam-6327	631	2	µ(y1)},min{ν(x2	GPE
ejpam-6327	631	3	ν(x2)},min{µ(y1	GPE
ejpam-6327	632	1	min{µ×	DATE
ejpam-6327	632	2	ν(y1	PRODUCT
ejpam-6327	634	1	h. sarapuddin	PERSON
ejpam-6327	634	2	j. vilela	PERSON
ejpam-6327	635	1	j. pure	PERSON
ejpam-6327	635	2	18	CARDINAL
ejpam-6327	635	3	3	CARDINAL
ejpam-6327	635	4	2025	CARDINAL
ejpam-6327	635	5	6327 19	DATE
ejpam-6327	635	6	23	CARDINAL
ejpam-6327	635	7	2	CARDINAL
ejpam-6327	636	1	ks-ideals	ORG
ejpam-6327	637	1	ks	GPE
ejpam-6327	639	1	ks-ideals	ORG
ejpam-6327	640	1	ν(y	PERSON
ejpam-6327	641	1	× ν(x	PERSON
ejpam-6327	641	2	ν(y	PERSON
ejpam-6327	645	1	ν	NORP
ejpam-6327	645	2	x2)(y1	PERSON
ejpam-6327	646	1	ν(x1	PERSON
ejpam-6327	647	1	ν(x2	ORG
ejpam-6327	648	1	x2)(y1	PERSON
ejpam-6327	649	1	ν(x1	PERSON
ejpam-6327	650	1	ν(x2	ORG
ejpam-6327	651	1	ν(y1	PRODUCT
ejpam-6327	653	1	theorems 16,	ORG
ejpam-6327	653	2	17	DATE
ejpam-6327	653	3	18	CARDINAL
ejpam-6327	654	1	3	CARDINAL
ejpam-6327	655	1	ks	GPE
ejpam-6327	656	1	ks	GPE
ejpam-6327	657	1	ks-p	ORG
ejpam-6327	657	2	ks-semigroup	ORG
ejpam-6327	658	1	ks	GPE
ejpam-6327	659	1	5	CARDINAL
ejpam-6327	659	2	ks-semigroup	ORG
ejpam-6327	660	1	21	DATE
ejpam-6327	661	1	ks-ideals	ORG
ejpam-6327	663	1	ks-ideals	ORG
ejpam-6327	664	1	h. sarapuddin	PERSON
ejpam-6327	664	2	j. vilela	PERSON
ejpam-6327	665	1	j. pure	PERSON
ejpam-6327	665	2	18	CARDINAL
ejpam-6327	665	3	3	CARDINAL
ejpam-6327	665	4	2025	CARDINAL
ejpam-6327	665	5	6327 20 of 23 ψ(x	DATE
ejpam-6327	671	1	µx2	GPE
ejpam-6327	671	2	νy2	PERSON
ejpam-6327	676	1	µx1∗xx2	NORP
ejpam-6327	676	2	νy1∗y	GPE
ejpam-6327	676	3	µx2	GPE
ejpam-6327	677	1	µx2	GPE
ejpam-6327	677	2	νy2	PERSON
ejpam-6327	678	1	νy1·y	PERSON
ejpam-6327	678	2	µx2	GPE
ejpam-6327	678	3	νy1	ORG
ejpam-6327	678	4	y νy2	PERSON
ejpam-6327	678	5	νy1)(µx2	GPE
ejpam-6327	678	6	νy2	PERSON
ejpam-6327	680	1	∈	ORG
ejpam-6327	682	1	ψ(x	ORG
ejpam-6327	684	1	first	ORDINAL
ejpam-6327	685	1	k = kerψ.	PERSON
ejpam-6327	688	1	k(x	PERSON
ejpam-6327	689	1	ν(x	PERSON
ejpam-6327	690	1	k(x	PERSON
ejpam-6327	691	1	∈ k(x	ORG
ejpam-6327	691	2	∈ k(x	ORG
ejpam-6327	691	3	⇔	PERSON
ejpam-6327	691	4	∼k	ORG
ejpam-6327	691	5	⇔	PERSON
ejpam-6327	691	6	k ⇔	PERSON
ejpam-6327	692	1	⇔ ψ(α ∗ x	PERSON
ejpam-6327	692	2	νβ∗y	GPE
ejpam-6327	692	3	h. sarapuddin	PERSON
ejpam-6327	692	4	j. vilela	PERSON
ejpam-6327	693	1	j. pure	PERSON
ejpam-6327	693	2	18	CARDINAL
ejpam-6327	693	3	3	CARDINAL
ejpam-6327	693	4	2025	CARDINAL
ejpam-6327	693	5	6327 21	DATE
ejpam-6327	693	6	23	CARDINAL
ejpam-6327	694	1	⇔	PERSON
ejpam-6327	696	1	ν(α ∗ x	PERSON
ejpam-6327	697	1	ν(x ∗ α	PERSON
ejpam-6327	697	2	0	CARDINAL
ejpam-6327	697	3	ν(y ∗	PERSON
ejpam-6327	698	1	0	CARDINAL
ejpam-6327	698	2	µ(x ∗ α	PRODUCT
ejpam-6327	698	3	0	CARDINAL
ejpam-6327	698	4	ν(y ∗	PERSON
ejpam-6327	698	5	0	CARDINAL
ejpam-6327	698	6	µ(x ∗ α	PRODUCT
ejpam-6327	698	7	0	CARDINAL
ejpam-6327	698	8	ν(y ∗	PERSON
ejpam-6327	700	1	∈ k(x	ORG
ejpam-6327	700	2	⇔	PERSON
ejpam-6327	703	1	4	CARDINAL
ejpam-6327	706	1	j × i ∼= x	WORK_OF_ART
ejpam-6327	706	2	j × y/i. proof	WORK_OF_ART
ejpam-6327	708	1	∈	ORG
ejpam-6327	709	1	j × i.	PERSON
ejpam-6327	709	2	j	PERSON
ejpam-6327	709	3	∈	ORG
ejpam-6327	710	1	j × i.	PERSON
ejpam-6327	711	1	j × i.	PERSON
ejpam-6327	713	1	∈	ORG
ejpam-6327	714	1	j × i.	PERSON
ejpam-6327	714	2	j	PERSON
ejpam-6327	715	1	j × i.	PERSON
ejpam-6327	716	1	φ	PERSON
ejpam-6327	716	2	jx	PERSON
ejpam-6327	720	1	jx2	PERSON
ejpam-6327	721	1	jx2	PERSON
ejpam-6327	722	1	φ	ORG
ejpam-6327	726	1	jx1∗xx2	GPE
ejpam-6327	726	2	j jx2	PERSON
ejpam-6327	726	3	jx2	PERSON
ejpam-6327	726	4	∗	CARDINAL
ejpam-6327	727	1	h. sarapuddin	PERSON
ejpam-6327	727	2	j. vilela	PERSON
ejpam-6327	728	1	j. pure	PERSON
ejpam-6327	728	2	18	CARDINAL
ejpam-6327	728	3	3	CARDINAL
ejpam-6327	728	4	2025	CARDINAL
ejpam-6327	728	5	22	CARDINAL
ejpam-6327	728	6	23	CARDINAL
ejpam-6327	729	1	j jx2	PERSON
ejpam-6327	730	1	jx2	PERSON
ejpam-6327	731	1	φ	ORG
ejpam-6327	732	1	j × y	WORK_OF_ART
ejpam-6327	733	1	jx	PERSON
ejpam-6327	734	1	φ	ORG
ejpam-6327	735	1	i0	GPE
ejpam-6327	735	2	jx	PERSON
ejpam-6327	735	3	i0	GPE
ejpam-6327	737	1	j × i.	PERSON
ejpam-6327	737	2	first	ORDINAL
ejpam-6327	738	1	j × y/i. theorem 22	WORK_OF_ART
ejpam-6327	739	1	ks-ideals	ORG
ejpam-6327	740	1	j	PERSON
ejpam-6327	740	2	j ×	PERSON
ejpam-6327	740	3	j × y/i. proof	WORK_OF_ART
ejpam-6327	741	1	ks-ideals	ORG
ejpam-6327	743	1	lemma 4	ORG
ejpam-6327	744	1	6	CARDINAL
ejpam-6327	744	2	j × i.	ORG
ejpam-6327	744	3	21	DATE
ejpam-6327	745	1	15	CARDINAL
ejpam-6327	745	2	lemma 4	ORG
ejpam-6327	745	3	j × i/µ×	PERSON
ejpam-6327	746	1	j/µ ×	ORG
ejpam-6327	746	2	j × y/i. 7	WORK_OF_ART
ejpam-6327	746	3	ks	GPE
ejpam-6327	747	1	ks-ideals h. sarapuddin	ORG
ejpam-6327	747	2	j. vilela	PERSON
ejpam-6327	748	1	j. pure	PERSON
ejpam-6327	748	2	18	CARDINAL
ejpam-6327	748	3	3	CARDINAL
ejpam-6327	748	4	2025	CARDINAL
ejpam-6327	748	5	6327 23	CARDINAL
ejpam-6327	748	6	23	DATE
ejpam-6327	749	1	ks	GPE
ejpam-6327	749	2	ks	GPE
ejpam-6327	750	1	ks	GPE
ejpam-6327	751	1	ks	GPE
ejpam-6327	751	2	ks	GPE
ejpam-6327	753	1	msu-iligan institute of technology	ORG
ejpam-6327	754	1	1	CARDINAL
ejpam-6327	754	2	k. iseki	PERSON
ejpam-6327	757	1	japan	GPE
ejpam-6327	757	2	42:19–22, 1966	DATE
ejpam-6327	758	1	2	CARDINAL
ejpam-6327	758	2	a. suschkewitsch	PERSON
ejpam-6327	759	1	ohne das gesetz der eindeutigen umkehrbarkeit	PERSON
ejpam-6327	761	1	ann.	PERSON
ejpam-6327	761	2	99:30–50	DATE
ejpam-6327	761	3	1928	DATE
ejpam-6327	762	1	3	CARDINAL
ejpam-6327	762	2	a. h. clifford	PERSON
ejpam-6327	762	3	g. b. preston	PERSON
ejpam-6327	764	1	1961	DATE
ejpam-6327	765	1	4	CARDINAL
ejpam-6327	765	2	l. a. zadeh	PERSON
ejpam-6327	766	1	8:338–353, 1965	DATE
ejpam-6327	767	1	5	CARDINAL
ejpam-6327	767	2	k. h. kim	PERSON
ejpam-6327	769	1	4(2):67–76, 2006	DATE
ejpam-6327	770	1	6	CARDINAL
ejpam-6327	770	2	j. p. vilela	PERSON
ejpam-6327	770	3	m. cawi	PERSON
ejpam-6327	771	1	ks	GPE
ejpam-6327	772	1	4(23):1129–1138	GPE
ejpam-6327	772	2	2009	DATE
ejpam-6327	773	1	7	CARDINAL
ejpam-6327	773	2	d. r. prince williams	PERSON
ejpam-6327	773	3	s. husain	PERSON
ejpam-6327	775	1	2(32):1577–1586, 2007	DATE
ejpam-6327	776	1	8	CARDINAL
ejpam-6327	776	2	l. r. bautista	PERSON
ejpam-6327	776	3	j. p. vilela	PERSON
ejpam-6327	778	1	6(39):1921–1932, 2011	DATE
ejpam-6327	779	1	9	CARDINAL
ejpam-6327	779	2	m. al tahan	PERSON
ejpam-6327	779	3	s. hoskova-mayerova	PERSON
ejpam-6327	779	4	s. al-kaseasbeh	PERSON
ejpam-6327	782	1	j. pure	PERSON
ejpam-6327	782	2	18(1	CARDINAL
ejpam-6327	782	3	2025	DATE
ejpam-6327	783	1	10	CARDINAL
ejpam-6327	783	2	s. mohammed	PERSON
ejpam-6327	783	3	s. jaber	PERSON
ejpam-6327	785	1	4(14):57–68	CARDINAL
ejpam-6327	785	2	2014	DATE
ejpam-6327	786	1	11	CARDINAL
ejpam-6327	786	2	h. k. kim	PERSON
ejpam-6327	786	3	d. h. hong	PERSON
ejpam-6327	786	4	j. y. kim	PERSON
ejpam-6327	788	1	kyungpook	PERSON
ejpam-6327	789	1	j.	PERSON
ejpam-6327	789	2	35:105–112, 1995	DATE
ejpam-6327	790	1	12	CARDINAL
ejpam-6327	790	2	j. meng	PERSON
ejpam-6327	792	1	japon.	GPE
ejpam-6327	792	2	40:143–154	CARDINAL
ejpam-6327	792	3	1994	DATE
ejpam-6327	793	1	13	CARDINAL
ejpam-6327	793	2	j. f. fraleigh	PERSON
ejpam-6327	794	1	first	ORDINAL
ejpam-6327	794	2	fifth	ORDINAL
ejpam-6327	795	1	1994	DATE