id	sid	eid	entity	type
ejpam-4788	1	1	european journal	ORG
ejpam-4788	2	1	16	CARDINAL
ejpam-4788	2	2	3	CARDINAL
ejpam-4788	2	3	2023	CARDINAL
ejpam-4788	2	4	1592-1607	DATE
ejpam-4788	3	1	1307-5543	DATE
ejpam-4788	3	2	new york	GPE
ejpam-4788	3	3	khamrot1	GPE
ejpam-4788	3	4	t.	GPE
ejpam-4788	3	5	1	CARDINAL
ejpam-4788	3	6	rajamangala university of technology lanna	ORG
ejpam-4788	3	7	phitsanulok	GPE
ejpam-4788	3	8	phitsanulok	GPE
ejpam-4788	3	9	thailand 2	ORG
ejpam-4788	3	10	algebras	ORG
ejpam-4788	3	11	university of phayao	ORG
ejpam-4788	3	12	56000	CARDINAL
ejpam-4788	3	13	thailand	GPE
ejpam-4788	7	1	2020	DATE
ejpam-4788	7	2	20m12	CARDINAL
ejpam-4788	7	3	1	CARDINAL
ejpam-4788	8	1	zadeh	ORG
ejpam-4788	8	2	1965	DATE
ejpam-4788	9	1	12	CARDINAL
ejpam-4788	11	1	1994	DATE
ejpam-4788	12	1	13	CARDINAL
ejpam-4788	13	1	2000	DATE
ejpam-4788	13	2	lee	PERSON
ejpam-4788	14	1	−1	DATE
ejpam-4788	14	2	0	CARDINAL
ejpam-4788	14	3	0	CARDINAL
ejpam-4788	14	4	1	CARDINAL
ejpam-4788	17	1	2012	DATE
ejpam-4788	18	1	9	CARDINAL
ejpam-4788	20	1	chinram et al	ORG
ejpam-4788	21	1	1	CARDINAL
ejpam-4788	21	2	m. k. r. marapureddy	PERSON
ejpam-4788	21	3	prv s. r.	PERSON
ejpam-4788	22	1	m. mandal	PERSON
ejpam-4788	23	1	4	CARDINAL
ejpam-4788	24	1	https://doi.org/10.29020/nybg.ejpam.v16i3.4788	DATE
ejpam-4788	24	2	thiti.ga@up.ac.th	DATE
ejpam-4788	24	3	t. gaketem	PERSON
ejpam-4788	24	4	1592	DATE
ejpam-4788	25	1	2023	CARDINAL
ejpam-4788	26	1	p. khamrot	PERSON
ejpam-4788	26	2	t. gaketem	PERSON
ejpam-4788	27	1	j. pure	PERSON
ejpam-4788	27	2	16	CARDINAL
ejpam-4788	27	3	3	CARDINAL
ejpam-4788	27	4	2023	CARDINAL
ejpam-4788	27	5	1592-1607	DATE
ejpam-4788	27	6	1593	DATE
ejpam-4788	28	1	2021	CARDINAL
ejpam-4788	28	2	t. gaketem	PERSON
ejpam-4788	29	1	2	CARDINAL
ejpam-4788	30	1	the same year	DATE
ejpam-4788	30	2	11	CARDINAL
ejpam-4788	30	3	a. simuen et al	PERSON
ejpam-4788	31	1	2022	CARDINAL
ejpam-4788	32	1	3	CARDINAL
ejpam-4788	32	2	5	DATE
ejpam-4788	32	3	6	CARDINAL
ejpam-4788	35	1	2	CARDINAL
ejpam-4788	37	1	kγk ⊆ k.	ORG
ejpam-4788	38	1	kγs ∩ sγk ⊆ k.	ORG
ejpam-4788	38	2	k.	PERSON
ejpam-4788	38	3	1	CARDINAL
ejpam-4788	39	1	11	CARDINAL
ejpam-4788	42	1	∩k ̸=	ORG
ejpam-4788	42	2	⊆	CARDINAL
ejpam-4788	43	1	0	CARDINAL
ejpam-4788	43	2	1	CARDINAL
ejpam-4788	45	1	0	CARDINAL
ejpam-4788	45	2	1	CARDINAL
ejpam-4788	46	1	p. khamrot	PERSON
ejpam-4788	46	2	t. gaketem	PERSON
ejpam-4788	47	1	j. pure	PERSON
ejpam-4788	47	2	16	CARDINAL
ejpam-4788	47	3	3	CARDINAL
ejpam-4788	47	4	2023	CARDINAL
ejpam-4788	47	5	1592-1607 1594	DATE
ejpam-4788	47	6	2	CARDINAL
ejpam-4788	48	1	12	CARDINAL
ejpam-4788	49	1	0	CARDINAL
ejpam-4788	49	2	1	CARDINAL
ejpam-4788	50	1	two	CARDINAL
ejpam-4788	50	2	⇔ ξ(k	NORP
ejpam-4788	50	3	ς(k	ORG
ejpam-4788	50	4	ξ(k)∧ς(k	PERSON
ejpam-4788	50	5	ς(k	ORG
ejpam-4788	50	6	ξ(k)∨ς(k	DATE
ejpam-4788	52	1	two	CARDINAL
ejpam-4788	52	2	k ∈	PERSON
ejpam-4788	52	3	ξ(k	NORP
ejpam-4788	52	4	⊆	CARDINAL
ejpam-4788	52	5	ξ(k	NORP
ejpam-4788	52	6	ς(k	ORG
ejpam-4788	52	7	ς(k	ORG
ejpam-4788	55	1	two	CARDINAL
ejpam-4788	56	1	0	CARDINAL
ejpam-4788	56	2	3	CARDINAL
ejpam-4788	57	1	0	CARDINAL
ejpam-4788	57	2	1	CARDINAL
ejpam-4788	58	1	1	CARDINAL
ejpam-4788	61	1	4	CARDINAL
ejpam-4788	62	1	11	CARDINAL
ejpam-4788	62	2	s ∈ s	ORG
ejpam-4788	63	1	∩ ξ ̸= 0	WORK_OF_ART
ejpam-4788	63	2	∩ ξ ̸= 0	WORK_OF_ART
ejpam-4788	64	1	1	CARDINAL
ejpam-4788	65	1	10	CARDINAL
ejpam-4788	66	1	5	CARDINAL
ejpam-4788	67	1	10	CARDINAL
ejpam-4788	68	1	∈ s	ORG
ejpam-4788	68	2	γ ∈	ORG
ejpam-4788	69	1	p. khamrot	PERSON
ejpam-4788	69	2	t. gaketem	PERSON
ejpam-4788	70	1	j. pure	PERSON
ejpam-4788	70	2	16	CARDINAL
ejpam-4788	70	3	3	CARDINAL
ejpam-4788	70	4	2023	CARDINAL
ejpam-4788	70	5	1592	CARDINAL
ejpam-4788	70	6	∈ s	ORG
ejpam-4788	70	7	γ ∈	ORG
ejpam-4788	70	8	s. (iv	ORG
ejpam-4788	70	9	w ∈ s	ORG
ejpam-4788	72	1	6	CARDINAL
ejpam-4788	73	1	8	CARDINAL
ejpam-4788	75	1	k ∈ s	ORG
ejpam-4788	75	2	0	CARDINAL
ejpam-4788	75	3	1	CARDINAL
ejpam-4788	75	4	−1	DATE
ejpam-4788	76	1	1	CARDINAL
ejpam-4788	78	1	k ∈ s	ORG
ejpam-4788	80	1	1	CARDINAL
ejpam-4788	81	1	21	CARDINAL
ejpam-4788	81	2	22	DATE
ejpam-4788	81	3	23	CARDINAL
ejpam-4788	82	1	0	CARDINAL
ejpam-4788	82	2	1	CARDINAL
ejpam-4788	83	1	0	CARDINAL
ejpam-4788	83	2	1	CARDINAL
ejpam-4788	83	3	−1	DATE
ejpam-4788	83	4	−1	CARDINAL
ejpam-4788	83	5	0	CARDINAL
ejpam-4788	86	1	ςp)(k	NORP
ejpam-4788	89	1	ςn)(k	GPE
ejpam-4788	92	1	p. khamrot	PERSON
ejpam-4788	92	2	t. gaketem	PERSON
ejpam-4788	93	1	j. pure	PERSON
ejpam-4788	93	2	16	CARDINAL
ejpam-4788	93	3	3	CARDINAL
ejpam-4788	93	4	2023	CARDINAL
ejpam-4788	93	5	1592	CARDINAL
ejpam-4788	94	1	0	CARDINAL
ejpam-4788	94	2	1	CARDINAL
ejpam-4788	95	1	1	CARDINAL
ejpam-4788	98	1	−1	DATE
ejpam-4788	98	2	0	CARDINAL
ejpam-4788	101	1	2	CARDINAL
ejpam-4788	103	1	k ∈	PERSON
ejpam-4788	104	1	u ∈ s	ORG
ejpam-4788	105	1	0	CARDINAL
ejpam-4788	105	2	1]×	CARDINAL
ejpam-4788	105	3	−1	CARDINAL
ejpam-4788	105	4	x(t	PERSON
ejpam-4788	105	5	xpt	PERSON
ejpam-4788	105	6	0	CARDINAL
ejpam-4788	106	1	0	CARDINAL
ejpam-4788	107	1	∩	PERSON
ejpam-4788	107	2	∩	PERSON
ejpam-4788	108	1	∩	PERSON
ejpam-4788	108	2	k ∈ s.	PERSON
ejpam-4788	108	3	8	DATE
ejpam-4788	110	1	9	CARDINAL
ejpam-4788	110	2	ξp(uαv	PERSON
ejpam-4788	111	1	∈	ORG
ejpam-4788	114	1	2	CARDINAL
ejpam-4788	117	1	1	CARDINAL
ejpam-4788	117	2	1	CARDINAL
ejpam-4788	119	1	0 1	CARDINAL
ejpam-4788	119	2	s.	PERSON
ejpam-4788	119	3	9	DATE
ejpam-4788	120	1	9	CARDINAL
ejpam-4788	120	2	ξp(uαv	PERSON
ejpam-4788	120	3	ξp(uαv	PERSON
ejpam-4788	120	4	∈	ORG
ejpam-4788	120	5	∈	ORG
ejpam-4788	121	1	p. khamrot	PERSON
ejpam-4788	121	2	t. gaketem	PERSON
ejpam-4788	122	1	j. pure	PERSON
ejpam-4788	122	2	16	CARDINAL
ejpam-4788	122	3	3	CARDINAL
ejpam-4788	122	4	2023	CARDINAL
ejpam-4788	122	5	1592	CARDINAL
ejpam-4788	122	6	1597 3	DATE
ejpam-4788	124	1	10	CARDINAL
ejpam-4788	126	1	ξp(uαv	PERSON
ejpam-4788	128	1	s. theorem 2.	ORG
ejpam-4788	131	1	s;λp k	PERSON
ejpam-4788	131	2	s. proof	ORG
ejpam-4788	133	1	uαv ∈ k.	PERSON
ejpam-4788	135	1	1	CARDINAL
ejpam-4788	136	1	−1	DATE
ejpam-4788	137	1	k(v	GPE
ejpam-4788	139	1	uαv ∈ k.	PERSON
ejpam-4788	142	1	1	CARDINAL
ejpam-4788	142	2	−1	DATE
ejpam-4788	143	1	k(v	GPE
ejpam-4788	144	1	s;λp k	PERSON
ejpam-4788	144	2	s;λp k	PERSON
ejpam-4788	144	3	∈	ORG
ejpam-4788	147	1	1	CARDINAL
ejpam-4788	147	2	−1	DATE
ejpam-4788	148	1	k(v	GPE
ejpam-4788	148	2	uαv ∈ k. hence	PERSON
ejpam-4788	148	3	s. theorem 3	ORG
ejpam-4788	149	1	two	CARDINAL
ejpam-4788	149	2	s. proof	PERSON
ejpam-4788	150	1	ξp(uαv	PERSON
ejpam-4788	150	2	∩ ςp)(v	ORG
ejpam-4788	150	3	∩	WORK_OF_ART
ejpam-4788	150	4	∩	WORK_OF_ART
ejpam-4788	151	1	ξp(uαv	PERSON
ejpam-4788	151	2	∩	WORK_OF_ART
ejpam-4788	152	1	s. p. khamrot	PERSON
ejpam-4788	152	2	t. gaketem	PERSON
ejpam-4788	153	1	j. pure	PERSON
ejpam-4788	153	2	16	CARDINAL
ejpam-4788	153	3	3	CARDINAL
ejpam-4788	153	4	2023	CARDINAL
ejpam-4788	153	5	1592	CARDINAL
ejpam-4788	153	6	1598	CARDINAL
ejpam-4788	153	7	4	CARDINAL
ejpam-4788	154	1	ξ(l	NORP
ejpam-4788	155	1	∈	ORG
ejpam-4788	157	1	ξ(l	NORP
ejpam-4788	157	2	ξ(l	NORP
ejpam-4788	157	3	0	CARDINAL
ejpam-4788	157	4	1]×	CARDINAL
ejpam-4788	157	5	−1	DATE
ejpam-4788	157	6	0	CARDINAL
ejpam-4788	159	1	s.	GPE
ejpam-4788	159	2	0	CARDINAL
ejpam-4788	159	3	1	CARDINAL
ejpam-4788	160	1	−1	DATE
ejpam-4788	160	2	0	CARDINAL
ejpam-4788	160	3	ξ(l	NORP
ejpam-4788	160	4	∈ s.	PERSON
ejpam-4788	161	1	m.	PERSON
ejpam-4788	161	2	ξ(l	NORP
ejpam-4788	162	1	ξ(l	NORP
ejpam-4788	162	2	ξ(l	NORP
ejpam-4788	162	3	0	CARDINAL
ejpam-4788	162	4	1	CARDINAL
ejpam-4788	163	1	−1	DATE
ejpam-4788	163	2	0	CARDINAL
ejpam-4788	163	3	ξ(l	NORP
ejpam-4788	163	4	∈	ORG
ejpam-4788	164	1	ξ(l	NORP
ejpam-4788	165	1	ξ(l	NORP
ejpam-4788	165	2	ξ(l	NORP
ejpam-4788	166	1	ξp(uαv	PERSON
ejpam-4788	167	1	s. next	ORG
ejpam-4788	168	1	z)∈fuα	ORG
ejpam-4788	171	1	z)∈fuα	ORG
ejpam-4788	174	1	11	DATE
ejpam-4788	176	1	s;λp s	ORG
ejpam-4788	176	2	−1	CARDINAL
ejpam-4788	176	3	1	CARDINAL
ejpam-4788	177	1	5	CARDINAL
ejpam-4788	179	1	s;λp k	PERSON
ejpam-4788	179	2	s. proof	ORG
ejpam-4788	180	1	kαsβk	PERSON
ejpam-4788	180	2	k.	PERSON
ejpam-4788	180	3	∈ kαsβk	PERSON
ejpam-4788	180	4	1	CARDINAL
ejpam-4788	181	1	−1	DATE
ejpam-4788	182	1	/∈ kαsβk	PERSON
ejpam-4788	185	1	0	CARDINAL
ejpam-4788	187	1	t. gaketem	PERSON
ejpam-4788	188	1	j. pure	PERSON
ejpam-4788	188	2	16	CARDINAL
ejpam-4788	188	3	3	CARDINAL
ejpam-4788	188	4	2023	CARDINAL
ejpam-4788	188	5	1592	CARDINAL
ejpam-4788	188	6	1599	CARDINAL
ejpam-4788	188	7	s;λp k	PERSON
ejpam-4788	188	8	s;λp k	PERSON
ejpam-4788	189	1	1	CARDINAL
ejpam-4788	189	2	−1	DATE
ejpam-4788	191	1	∈ k. hence	PERSON
ejpam-4788	191	2	s. theorem 6	ORG
ejpam-4788	192	1	two	CARDINAL
ejpam-4788	192	2	s. proof	ORG
ejpam-4788	193	1	∩	PERSON
ejpam-4788	193	2	∩ ςp))(u	WORK_OF_ART
ejpam-4788	193	3	∩ ςp)(u	WORK_OF_ART
ejpam-4788	193	4	∩	PERSON
ejpam-4788	193	5	∩	WORK_OF_ART
ejpam-4788	193	6	∩	WORK_OF_ART
ejpam-4788	194	1	s. theorem 7	ORG
ejpam-4788	195	1	ξ(l	NORP
ejpam-4788	196	1	∈	ORG
ejpam-4788	198	1	ξ(l	NORP
ejpam-4788	198	2	ξ(l	NORP
ejpam-4788	198	3	0	CARDINAL
ejpam-4788	198	4	1]×	CARDINAL
ejpam-4788	198	5	−1	DATE
ejpam-4788	198	6	0	CARDINAL
ejpam-4788	200	1	w ∈ s.	PERSON
ejpam-4788	200	2	0	CARDINAL
ejpam-4788	200	3	1]×[−1	DATE
ejpam-4788	200	4	0	CARDINAL
ejpam-4788	200	5	ξ(l	NORP
ejpam-4788	200	6	w ∈ ξ(l	PERSON
ejpam-4788	201	1	m.	PERSON
ejpam-4788	201	2	∨	CARDINAL
ejpam-4788	202	1	ξ(l	NORP
ejpam-4788	202	2	ξ(l	NORP
ejpam-4788	202	3	0	CARDINAL
ejpam-4788	202	4	1]×	CARDINAL
ejpam-4788	203	1	−1	DATE
ejpam-4788	203	2	0	CARDINAL
ejpam-4788	203	3	ξ(l	NORP
ejpam-4788	203	4	w ∈ s	PERSON
ejpam-4788	204	1	ξp(u)∧ξp(w	PERSON
ejpam-4788	204	2	m.	PERSON
ejpam-4788	204	3	w ∈ ξ(l	PERSON
ejpam-4788	205	1	s. since u	ORG
ejpam-4788	205	2	w ∈ ξ(l	PERSON
ejpam-4788	205	3	∈	ORG
ejpam-4788	207	1	s. next	ORG
ejpam-4788	208	1	12	CARDINAL
ejpam-4788	211	1	8	CARDINAL
ejpam-4788	215	1	s. p. khamrot	PERSON
ejpam-4788	215	2	t. gaketem	PERSON
ejpam-4788	216	1	j. pure	PERSON
ejpam-4788	216	2	16	CARDINAL
ejpam-4788	216	3	3	CARDINAL
ejpam-4788	216	4	2023	CARDINAL
ejpam-4788	216	5	1592	CARDINAL
ejpam-4788	220	1	⊆	CARDINAL
ejpam-4788	220	2	⊆	CARDINAL
ejpam-4788	220	3	⊆	CARDINAL
ejpam-4788	220	4	⊆	CARDINAL
ejpam-4788	221	1	⊆	CARDINAL
ejpam-4788	221	2	∩	ORG
ejpam-4788	222	1	∩	PERSON
ejpam-4788	222	2	∩	PERSON
ejpam-4788	222	3	∩	PERSON
ejpam-4788	222	4	∩	PERSON
ejpam-4788	222	5	∩	ORG
ejpam-4788	223	1	∩	PERSON
ejpam-4788	223	2	∩	PERSON
ejpam-4788	224	1	s. hence	ORG
ejpam-4788	225	1	s. theorem 9	ORG
ejpam-4788	227	1	s.	ORG
ejpam-4788	233	1	⊆	CARDINAL
ejpam-4788	236	1	⊆	CARDINAL
ejpam-4788	238	1	s. now	ORG
ejpam-4788	238	2	⊆	CARDINAL
ejpam-4788	239	1	∩	PERSON
ejpam-4788	240	1	∩	PERSON
ejpam-4788	241	1	⊆	CARDINAL
ejpam-4788	242	1	∩	PERSON
ejpam-4788	243	1	∩	PERSON
ejpam-4788	244	1	10	CARDINAL
ejpam-4788	247	1	s;λp k	PERSON
ejpam-4788	247	2	s. proof	ORG
ejpam-4788	248	1	∈	ORG
ejpam-4788	248	2	∩	PERSON
ejpam-4788	248	3	1	CARDINAL
ejpam-4788	248	4	−1	DATE
ejpam-4788	249	1	k(u	GPE
ejpam-4788	249	2	∩	PERSON
ejpam-4788	251	1	k(u	GPE
ejpam-4788	252	1	s;λp k	PERSON
ejpam-4788	252	2	s. p. khamrot	PERSON
ejpam-4788	252	3	t. gaketem	PERSON
ejpam-4788	253	1	j. pure	PERSON
ejpam-4788	253	2	16	CARDINAL
ejpam-4788	253	3	3	CARDINAL
ejpam-4788	253	4	2023	CARDINAL
ejpam-4788	253	5	1592-1607 1601	DATE
ejpam-4788	253	6	s;λp k	PERSON
ejpam-4788	253	7	∈	ORG
ejpam-4788	253	8	∩	PERSON
ejpam-4788	254	1	1	CARDINAL
ejpam-4788	254	2	−1	DATE
ejpam-4788	255	1	k ◦αλn s)∪(λn s ◦	ORG
ejpam-4788	255	2	k(u	GPE
ejpam-4788	256	1	∈ k. hence	PERSON
ejpam-4788	256	2	s. 4	ORG
ejpam-4788	257	1	13	DATE
ejpam-4788	263	1	s. theorem 11	ORG
ejpam-4788	264	1	⊆	CARDINAL
ejpam-4788	264	2	s. proof	ORG
ejpam-4788	265	1	⊆	CARDINAL
ejpam-4788	268	1	⊆	CARDINAL
ejpam-4788	269	1	⊆	CARDINAL
ejpam-4788	270	1	s. theorem 12	ORG
ejpam-4788	272	1	k	GPE
ejpam-4788	272	2	s;λp k	PERSON
ejpam-4788	272	3	s. proof	ORG
ejpam-4788	273	1	s.	ORG
ejpam-4788	273	2	∩k ̸=	ORG
ejpam-4788	273	3	∈	ORG
ejpam-4788	275	1	1	CARDINAL
ejpam-4788	276	1	−1	DATE
ejpam-4788	277	1	k ̸= 0	ORG
ejpam-4788	278	1	s;λp k	PERSON
ejpam-4788	278	2	s;λp k	PERSON
ejpam-4788	280	1	k ̸= 0	ORG
ejpam-4788	281	1	∈	ORG
ejpam-4788	283	1	∈	ORG
ejpam-4788	283	2	∩ k	PERSON
ejpam-4788	283	3	∩k ̸=	ORG
ejpam-4788	283	4	k	PERSON
ejpam-4788	283	5	s. next	ORG
ejpam-4788	284	1	s.	PERSON
ejpam-4788	284	2	∈ s. p. khamrot	PERSON
ejpam-4788	284	3	t. gaketem	PERSON
ejpam-4788	285	1	j. pure	PERSON
ejpam-4788	285	2	16	CARDINAL
ejpam-4788	285	3	3	CARDINAL
ejpam-4788	285	4	2023	CARDINAL
ejpam-4788	285	5	1592-1607	DATE
ejpam-4788	285	6	1602	CARDINAL
ejpam-4788	285	7	13	CARDINAL
ejpam-4788	287	1	s. proof	PERSON
ejpam-4788	290	1	∈	ORG
ejpam-4788	292	1	k ∈ s	PERSON
ejpam-4788	292	2	xpt	PERSON
ejpam-4788	293	1	k ∈	ORG
ejpam-4788	297	1	s.	PERSON
ejpam-4788	297	2	12	CARDINAL
ejpam-4788	298	1	∈	ORG
ejpam-4788	302	1	k ∈ s	PERSON
ejpam-4788	302	2	xpt	PERSON
ejpam-4788	305	1	14	DATE
ejpam-4788	306	1	j of s	WORK_OF_ART
ejpam-4788	306	2	j = i.	PERSON
ejpam-4788	306	3	15	DATE
ejpam-4788	308	1	⊆	CARDINAL
ejpam-4788	309	1	14	DATE
ejpam-4788	311	1	s;λp k	PERSON
ejpam-4788	311	2	s. proof	ORG
ejpam-4788	312	1	12	CARDINAL
ejpam-4788	312	2	s;λp k	PERSON
ejpam-4788	312	3	⊆	CARDINAL
ejpam-4788	313	1	13	CARDINAL
ejpam-4788	313	2	s.	ORG
ejpam-4788	313	3	⊆	CARDINAL
ejpam-4788	313	4	= k.	PERSON
ejpam-4788	315	1	s;λp k	PERSON
ejpam-4788	315	2	s;λp k	PERSON
ejpam-4788	315	3	s.	PERSON
ejpam-4788	315	4	12	CARDINAL
ejpam-4788	315	5	s. let j	ORG
ejpam-4788	316	1	j ⊆ k.	LAW
ejpam-4788	316	2	12	CARDINAL
ejpam-4788	316	3	⊆	CARDINAL
ejpam-4788	317	1	j = supp(λj	PERSON
ejpam-4788	318	1	s. corollary 1	ORG
ejpam-4788	322	1	s. p. khamrot	PERSON
ejpam-4788	322	2	t. gaketem	PERSON
ejpam-4788	323	1	j. pure	PERSON
ejpam-4788	323	2	16	CARDINAL
ejpam-4788	323	3	3	CARDINAL
ejpam-4788	323	4	2023	CARDINAL
ejpam-4788	323	5	1592	CARDINAL
ejpam-4788	324	1	16	DATE
ejpam-4788	325	1	x(t	PERSON
ejpam-4788	325	2	x(t	PERSON
ejpam-4788	326	1	15	CARDINAL
ejpam-4788	327	1	⊆	CARDINAL
ejpam-4788	327	2	s. proof	ORG
ejpam-4788	328	1	⊆	CARDINAL
ejpam-4788	333	1	⊆	CARDINAL
ejpam-4788	333	2	xpt ◦	ORG
ejpam-4788	334	1	⊆	CARDINAL
ejpam-4788	335	1	s. theorem 16	ORG
ejpam-4788	337	1	k	GPE
ejpam-4788	337	2	s;λp k	PERSON
ejpam-4788	337	3	s. proof	ORG
ejpam-4788	338	1	s.	ORG
ejpam-4788	338	2	∩ k ̸=	PERSON
ejpam-4788	338	3	∈	ORG
ejpam-4788	342	1	x(t	PERSON
ejpam-4788	342	2	x(t	PERSON
ejpam-4788	343	1	s;λp k	PERSON
ejpam-4788	343	2	s;λp k	PERSON
ejpam-4788	344	1	x(t	PERSON
ejpam-4788	344	2	x(t	PERSON
ejpam-4788	345	1	∈	ORG
ejpam-4788	348	1	∈	ORG
ejpam-4788	348	2	∩ k	PERSON
ejpam-4788	348	3	∩ k ̸=	PERSON
ejpam-4788	348	4	k	PERSON
ejpam-4788	348	5	s. next	ORG
ejpam-4788	349	1	17	CARDINAL
ejpam-4788	350	1	s. proof	ORG
ejpam-4788	351	1	s))∩(x(t	ORG
ejpam-4788	352	1	∈	ORG
ejpam-4788	356	1	xpt	PERSON
ejpam-4788	361	1	α xpt	PERSON
ejpam-4788	363	1	s. p. khamrot	PERSON
ejpam-4788	363	2	t. gaketem	PERSON
ejpam-4788	364	1	j. pure	PERSON
ejpam-4788	364	2	16	CARDINAL
ejpam-4788	364	3	3	CARDINAL
ejpam-4788	364	4	2023	CARDINAL
ejpam-4788	364	5	1592-1607 1604	DATE
ejpam-4788	365	1	s.	PERSON
ejpam-4788	365	2	16	CARDINAL
ejpam-4788	368	1	∈	ORG
ejpam-4788	374	1	x(t	PERSON
ejpam-4788	374	2	x(t	PERSON
ejpam-4788	375	1	17	DATE
ejpam-4788	378	1	⊆	CARDINAL
ejpam-4788	379	1	18	CARDINAL
ejpam-4788	381	1	s;λp k	PERSON
ejpam-4788	381	2	s. proof	ORG
ejpam-4788	382	1	s. thenk	PERSON
ejpam-4788	382	2	16	CARDINAL
ejpam-4788	382	3	s;λp k	PERSON
ejpam-4788	382	4	⊆	CARDINAL
ejpam-4788	383	1	15	CARDINAL
ejpam-4788	383	2	s.	ORG
ejpam-4788	383	3	⊆	CARDINAL
ejpam-4788	383	4	= k.	PERSON
ejpam-4788	385	1	s;λp k	PERSON
ejpam-4788	385	2	s;λp k	PERSON
ejpam-4788	385	3	s.	PERSON
ejpam-4788	385	4	17	DATE
ejpam-4788	385	5	s. let j	ORG
ejpam-4788	385	6	j ⊆ k.	LAW
ejpam-4788	385	7	17	CARDINAL
ejpam-4788	385	8	⊆	CARDINAL
ejpam-4788	386	1	j = supp(λj	PERSON
ejpam-4788	387	1	s. corollary 2.	ORG
ejpam-4788	393	1	18	DATE
ejpam-4788	395	1	19	CARDINAL
ejpam-4788	396	1	⊆	CARDINAL
ejpam-4788	396	2	s. proof	ORG
ejpam-4788	397	1	⊆	CARDINAL
ejpam-4788	398	1	α xpt ◦	PERSON
ejpam-4788	399	1	⊆	CARDINAL
ejpam-4788	399	2	⊆	CARDINAL
ejpam-4788	400	1	s. p. khamrot	PERSON
ejpam-4788	400	2	t. gaketem	PERSON
ejpam-4788	401	1	j. pure	PERSON
ejpam-4788	401	2	16	CARDINAL
ejpam-4788	401	3	3	CARDINAL
ejpam-4788	401	4	2023	CARDINAL
ejpam-4788	401	5	1592-1607	DATE
ejpam-4788	401	6	1605	CARDINAL
ejpam-4788	401	7	20	CARDINAL
ejpam-4788	403	1	k	GPE
ejpam-4788	403	2	s;λp k	PERSON
ejpam-4788	403	3	s. proof	ORG
ejpam-4788	404	1	s.	ORG
ejpam-4788	404	2	∈	ORG
ejpam-4788	407	1	1	CARDINAL
ejpam-4788	408	1	−1	DATE
ejpam-4788	410	1	k ̸= 0	ORG
ejpam-4788	411	1	s;λp k	PERSON
ejpam-4788	411	2	s;λp k	PERSON
ejpam-4788	413	1	∈	ORG
ejpam-4788	414	1	∈	ORG
ejpam-4788	414	2	k	PERSON
ejpam-4788	414	3	s. next	ORG
ejpam-4788	415	1	21	CARDINAL
ejpam-4788	417	1	s. proof	ORG
ejpam-4788	418	1	α xpt	PERSON
ejpam-4788	420	1	∈	ORG
ejpam-4788	420	2	α xpt ◦	PERSON
ejpam-4788	420	3	ξn)∨	LOC
ejpam-4788	423	1	α xpt	PERSON
ejpam-4788	425	1	α xpt	PERSON
ejpam-4788	428	1	s.	PERSON
ejpam-4788	428	2	20	CARDINAL
ejpam-4788	428	3	α xpt	PERSON
ejpam-4788	431	1	∈	ORG
ejpam-4788	432	1	α xpt	PERSON
ejpam-4788	435	1	α xpt ◦	PERSON
ejpam-4788	435	2	ξn)∨	LOC
ejpam-4788	435	3	̸= 0	ORG
ejpam-4788	436	1	s. definition 19.	ORG
ejpam-4788	437	1	⊆	CARDINAL
ejpam-4788	438	1	1606	CARDINAL
ejpam-4788	438	2	22	DATE
ejpam-4788	440	1	s;λp k	PERSON
ejpam-4788	440	2	s. proof.	ORG
ejpam-4788	441	1	20	CARDINAL
ejpam-4788	441	2	s;λp k	PERSON
ejpam-4788	441	3	⊆	CARDINAL
ejpam-4788	442	1	21	DATE
ejpam-4788	442	2	s.	ORG
ejpam-4788	442	3	⊆	CARDINAL
ejpam-4788	442	4	= k.	PERSON
ejpam-4788	444	1	s;λp k	PERSON
ejpam-4788	444	2	s;λp k	PERSON
ejpam-4788	444	3	s.	PERSON
ejpam-4788	444	4	20	DATE
ejpam-4788	444	5	s. let j	ORG
ejpam-4788	444	6	j ⊆ k.	LAW
ejpam-4788	444	7	20	CARDINAL
ejpam-4788	444	8	⊆	CARDINAL
ejpam-4788	445	1	j = supp(λj	PERSON
ejpam-4788	446	1	s. corollary 3	ORG
ejpam-4788	448	1	s. 5	PERSON
ejpam-4788	451	1	algebraic systems	ORG
ejpam-4788	452	1	the thailand science research	ORG
ejpam-4788	452	2	the university of phayao	ORG
ejpam-4788	453	1	algebras	ORG
ejpam-4788	453	2	university of phayao	ORG
ejpam-4788	453	3	56000	CARDINAL
ejpam-4788	453	4	thailand	GPE
ejpam-4788	454	1	1	CARDINAL
ejpam-4788	454	2	r. chinram	PERSON
ejpam-4788	456	1	asia	LOC
ejpam-4788	456	2	32:351–353	CARDINAL
ejpam-4788	456	3	2016	DATE
ejpam-4788	457	1	2	CARDINAL
ejpam-4788	457	2	p. khamrot	PERSON
ejpam-4788	459	1	iaeng international journal of computer science	ORG
ejpam-4788	459	2	48(2):250–256	CARDINAL
ejpam-4788	459	3	2021	DATE
ejpam-4788	460	1	3	CARDINAL
ejpam-4788	460	2	p. khamrot	PERSON
ejpam-4788	462	1	22(2):135–143	CARDINAL
ejpam-4788	462	2	2022	CARDINAL
ejpam-4788	463	1	1607	DATE
ejpam-4788	463	2	4	CARDINAL
ejpam-4788	463	3	a. iampan	PERSON
ejpam-4788	465	1	3(4):181–188	CARDINAL
ejpam-4788	465	2	2009	DATE
ejpam-4788	466	1	5	CARDINAL
ejpam-4788	466	2	t. gaketem	PERSON
ejpam-4788	468	1	20:1–15	CARDINAL
ejpam-4788	468	2	2012	DATE
ejpam-4788	469	1	6	CARDINAL
ejpam-4788	469	2	t. gaketem	PERSON
ejpam-4788	471	1	iaeng international journal of computer sciences	ORG
ejpam-4788	471	2	2023	CARDINAL
ejpam-4788	472	1	7	CARDINAL
ejpam-4788	472	2	t. changphas	PERSON
ejpam-4788	474	1	thai journal of mathematics	ORG
ejpam-4788	474	2	2017	DATE
ejpam-4788	475	1	8	CARDINAL
ejpam-4788	475	2	k. lee	PERSON
ejpam-4788	477	1	bangkok	GPE
ejpam-4788	477	2	thailand	GPE
ejpam-4788	477	3	307–312, 2000	DATE
ejpam-4788	478	1	9	CARDINAL
ejpam-4788	480	1	mathematica aeterna	PERSON
ejpam-4788	480	2	2(3):203–213, 2013	DATE
ejpam-4788	481	1	10	CARDINAL
ejpam-4788	481	2	mordeson	GPE
ejpam-4788	481	3	d. s. malik	PERSON
ejpam-4788	481	4	n. kuroki	PERSON
ejpam-4788	483	1	2003	DATE
ejpam-4788	484	1	11	CARDINAL
ejpam-4788	484	2	a. simuen, a. iampan	PERSON
ejpam-4788	484	3	r. chinram	PERSON
ejpam-4788	486	1	1–14	CARDINAL
ejpam-4788	486	2	2021	DATE
ejpam-4788	487	1	12	CARDINAL
ejpam-4788	488	1	8:338–353, 1965	DATE
ejpam-4788	489	1	13	CARDINAL
ejpam-4788	489	2	w. zhang	PERSON
ejpam-4788	491	1	305–309	CARDINAL
ejpam-4788	491	2	1994	DATE