id	sid	eid	entity	type
ejpam-3291	1	1	european journal	ORG
ejpam-3291	2	1	11	CARDINAL
ejpam-3291	2	2	3, 2018	DATE
ejpam-3291	2	3	815	CARDINAL
ejpam-3291	2	4	new york	GPE
ejpam-3291	2	5	nguyen dang hoa nghiem1	PERSON
ejpam-3291	2	6	janmuang1	GPE
ejpam-3291	2	7	1	CARDINAL
ejpam-3291	2	8	bangkok	GPE
ejpam-3291	2	9	10330	DATE
ejpam-3291	2	10	thailand 2	ORG
ejpam-3291	2	11	90110	DATE
ejpam-3291	2	12	thailand 3 centre of	ORG
ejpam-3291	2	13	si ayuthaya road	ORG
ejpam-3291	2	14	bangkok 10400	ORG
ejpam-3291	2	15	thailand	GPE
ejpam-3291	5	1	2010	DATE
ejpam-3291	5	2	16d50	CARDINAL
ejpam-3291	5	3	16d70	CARDINAL
ejpam-3291	5	4	16d80	CARDINAL
ejpam-3291	6	1	1	CARDINAL
ejpam-3291	11	1	jacobson	PERSON
ejpam-3291	11	2	j(r	PERSON
ejpam-3291	13	1	baer	PERSON
ejpam-3291	14	1	1989	DATE
ejpam-3291	14	2	camillo	PERSON
ejpam-3291	14	3	3	CARDINAL
ejpam-3291	16	1	nghiemndh@gmail.com	CARDINAL
ejpam-3291	16	2	n. d. h. nghiem	PERSON
ejpam-3291	17	1	janmuang	GPE
ejpam-3291	17	2	samruam.b@chula.ac.th	GPE
ejpam-3291	17	3	s. baupradist	PERSON
ejpam-3291	17	4	r. chinram	PERSON
ejpam-3291	18	1	2018	DATE
ejpam-3291	19	1	n. d. h. nghiem et al	PERSON
ejpam-3291	20	1	j. pure	PERSON
ejpam-3291	20	2	11	CARDINAL
ejpam-3291	20	3	3	CARDINAL
ejpam-3291	20	4	2018	DATE
ejpam-3291	20	5	815	CARDINAL
ejpam-3291	21	1	1999	DATE
ejpam-3291	21	2	sanh	PRODUCT
ejpam-3291	23	1	one	CARDINAL
ejpam-3291	24	1	9	CARDINAL
ejpam-3291	25	1	2006	DATE
ejpam-3291	25	2	10	CARDINAL
ejpam-3291	27	1	singh	GPE
ejpam-3291	27	2	8	CARDINAL
ejpam-3291	30	1	2	CARDINAL
ejpam-3291	32	1	baer	PERSON
ejpam-3291	35	1	1	CARDINAL
ejpam-3291	35	2	5	DATE
ejpam-3291	35	3	6	CARDINAL
ejpam-3291	36	1	2	CARDINAL
ejpam-3291	36	2	r.	NORP
ejpam-3291	38	1	1	CARDINAL
ejpam-3291	39	1	2	CARDINAL
ejpam-3291	40	1	s(m) ↪→ a.	ORG
ejpam-3291	41	1	2	CARDINAL
ejpam-3291	45	1	n. d. h. nghiem et al	PERSON
ejpam-3291	46	1	j. pure	PERSON
ejpam-3291	46	2	11	CARDINAL
ejpam-3291	46	3	3	CARDINAL
ejpam-3291	46	4	2018	DATE
ejpam-3291	46	5	815	CARDINAL
ejpam-3291	46	6	1	CARDINAL
ejpam-3291	47	1	1	CARDINAL
ejpam-3291	48	1	2	CARDINAL
ejpam-3291	48	2	5	CARDINAL
ejpam-3291	48	3	p.361	ORG
ejpam-3291	49	1	∈	ORG
ejpam-3291	51	1	∈	ORG
ejpam-3291	51	2	0	CARDINAL
ejpam-3291	51	3	∈	ORG
ejpam-3291	55	1	0	CARDINAL
ejpam-3291	55	2	f4	CARDINAL
ejpam-3291	55	3	f1	PERSON
ejpam-3291	55	4	f2	ORG
ejpam-3291	55	5	f4	CARDINAL
ejpam-3291	56	1	∈	ORG
ejpam-3291	62	1	1	CARDINAL
ejpam-3291	67	1	ia	GPE
ejpam-3291	67	2	ia	GPE
ejpam-3291	67	3	ia	GPE
ejpam-3291	67	4	a.	PERSON
ejpam-3291	69	1	2	CARDINAL
ejpam-3291	71	1	ker(g	GPE
ejpam-3291	71	2	⊆	CARDINAL
ejpam-3291	71	3	ker(f	GPE
ejpam-3291	74	1	ker(g	GPE
ejpam-3291	74	2	⊆	CARDINAL
ejpam-3291	74	3	ker(f	GPE
ejpam-3291	75	1	g′	PERSON
ejpam-3291	78	1	3	CARDINAL
ejpam-3291	86	1	n. d. h. nghiem et al	PERSON
ejpam-3291	87	1	j. pure	PERSON
ejpam-3291	87	2	11	CARDINAL
ejpam-3291	87	3	3	CARDINAL
ejpam-3291	87	4	2018	DATE
ejpam-3291	87	5	815	CARDINAL
ejpam-3291	88	1	f(n	ORG
ejpam-3291	88	2	αif(n	GPE
ejpam-3291	98	1	a′ ↪	PERSON
ejpam-3291	98	2	⊕	GPE
ejpam-3291	98	3	ia	GPE
ejpam-3291	101	1	ᾱ	CARDINAL
ejpam-3291	102	1	ᾱib	GPE
ejpam-3291	104	1	ia	GPE
ejpam-3291	105	1	5	CARDINAL
ejpam-3291	106	1	ifm	ORG
ejpam-3291	106	2	m. proof	PERSON
ejpam-3291	107	1	4	CARDINAL
ejpam-3291	109	1	3	CARDINAL
ejpam-3291	111	1	6	CARDINAL
ejpam-3291	113	1	k ⊂⊕	ORG
ejpam-3291	114	1	2	CARDINAL
ejpam-3291	114	2	k ⊂⊕	ORG
ejpam-3291	116	1	1	CARDINAL
ejpam-3291	116	2	k ⊂⊕	ORG
ejpam-3291	116	3	0 6=	CARDINAL
ejpam-3291	118	1	s(m) ↪	ORG
ejpam-3291	118	2	∈	ORG
ejpam-3291	119	1	ᾱ	CARDINAL
ejpam-3291	120	1	ia	GPE
ejpam-3291	120	2	a→m	ORG
ejpam-3291	122	1	k → n	ORG
ejpam-3291	124	1	2	CARDINAL
ejpam-3291	124	2	k ⊂⊕	ORG
ejpam-3291	125	1	1	CARDINAL
ejpam-3291	126	1	4	CARDINAL
ejpam-3291	128	1	n. d. h. nghiem et al	PERSON
ejpam-3291	129	1	j. pure	PERSON
ejpam-3291	129	2	11	CARDINAL
ejpam-3291	129	3	3	CARDINAL
ejpam-3291	129	4	2018	DATE
ejpam-3291	129	5	815	CARDINAL
ejpam-3291	130	1	12	CARDINAL
ejpam-3291	131	1	1	CARDINAL
ejpam-3291	133	1	a von neumann	PERSON
ejpam-3291	140	1	∈	ORG
ejpam-3291	141	1	s′→ s(m	ORG
ejpam-3291	141	2	0	CARDINAL
ejpam-3291	141	3	ker(s′	PERSON
ejpam-3291	141	4	ker(s′	PERSON
ejpam-3291	142	1	ker(s	PERSON
ejpam-3291	143	1	37.7(1	DATE
ejpam-3291	143	2	11	CARDINAL
ejpam-3291	143	3	∈	ORG
ejpam-3291	143	4	sgs	ORG
ejpam-3291	144	1	a von neumann	PERSON
ejpam-3291	145	1	2	CARDINAL
ejpam-3291	147	1	1	CARDINAL
ejpam-3291	148	1	2	CARDINAL
ejpam-3291	148	2	⊆	CARDINAL
ejpam-3291	148	3	⊆	CARDINAL
ejpam-3291	148	4	3	CARDINAL
ejpam-3291	148	5	ls(im(t	PERSON
ejpam-3291	150	1	1	CARDINAL
ejpam-3291	152	1	∈	ORG
ejpam-3291	154	1	⊆	CARDINAL
ejpam-3291	155	1	ᾱ	CARDINAL
ejpam-3291	157	1	∈	ORG
ejpam-3291	159	1	⊆	CARDINAL
ejpam-3291	162	1	2	CARDINAL
ejpam-3291	163	1	⊆	CARDINAL
ejpam-3291	164	1	2	CARDINAL
ejpam-3291	164	2	∈	PRODUCT
ejpam-3291	164	3	ss ⊆	ORG
ejpam-3291	165	1	3	CARDINAL
ejpam-3291	166	1	∈	ORG
ejpam-3291	169	1	ker(st	PERSON
ejpam-3291	169	2	⊆	CARDINAL
ejpam-3291	170	1	g′	PERSON
ejpam-3291	170	2	sincem	PERSON
ejpam-3291	172	1	− gs ∈ ls(im(t	PERSON
ejpam-3291	175	1	ls(im(t	PERSON
ejpam-3291	175	2	⊆	CARDINAL
ejpam-3291	175	3	ls(im(t	PERSON
ejpam-3291	177	1	ls(im(t	PERSON
ejpam-3291	179	1	ls(im(t	PERSON
ejpam-3291	180	1	ls(im(t	PERSON
ejpam-3291	181	1	s. n. d. h. nghiem et al	PERSON
ejpam-3291	182	1	j. pure	PERSON
ejpam-3291	182	2	11	CARDINAL
ejpam-3291	182	3	3	CARDINAL
ejpam-3291	182	4	2018	DATE
ejpam-3291	182	5	815	CARDINAL
ejpam-3291	182	6	3	CARDINAL
ejpam-3291	187	1	∈	ORG
ejpam-3291	188	1	ker(s	PERSON
ejpam-3291	189	1	0	CARDINAL
ejpam-3291	190	1	0	CARDINAL
ejpam-3291	191	1	= s.	PERSON
ejpam-3291	191	2	2(2	CARDINAL
ejpam-3291	193	1	s(1 − s	PRODUCT
ejpam-3291	194	1	1	CARDINAL
ejpam-3291	194	2	s.	GPE
ejpam-3291	194	3	9.3.1	CARDINAL
ejpam-3291	194	4	5	CARDINAL
ejpam-3291	194	5	⊆	CARDINAL
ejpam-3291	195	1	s ∈ j(s	ORG
ejpam-3291	196	1	ker(s	PERSON
ejpam-3291	197	1	first	ORDINAL
ejpam-3291	198	1	∈	ORG
ejpam-3291	199	1	∈	ORG
ejpam-3291	200	1	2(3	CARDINAL
ejpam-3291	202	1	= s.	PERSON
ejpam-3291	202	2	s ∈ j(s	ORG
ejpam-3291	202	3	ls(im(t	PERSON
ejpam-3291	204	1	0	CARDINAL
ejpam-3291	208	1	2.14	CARDINAL
ejpam-3291	208	2	2	CARDINAL
ejpam-3291	208	3	t(m	GPE
ejpam-3291	208	4	⊆	CARDINAL
ejpam-3291	208	5	t(m	GPE
ejpam-3291	209	1	0	CARDINAL
ejpam-3291	209	2	t(m	GPE
ejpam-3291	210	1	t(m	ORG
ejpam-3291	213	1	⊆	CARDINAL
ejpam-3291	215	1	4	CARDINAL
ejpam-3291	216	1	∈	ORG
ejpam-3291	217	1	t(m	CARDINAL
ejpam-3291	218	1	t(m	CARDINAL
ejpam-3291	219	1	s(m	ORG
ejpam-3291	219	2	t(m	GPE
ejpam-3291	220	1	s(m	ORG
ejpam-3291	223	1	t(m	ORG
ejpam-3291	224	1	β(ut	GPE
ejpam-3291	227	1	∈	ORG
ejpam-3291	227	2	∈	ORG
ejpam-3291	229	1	t(m	ORG
ejpam-3291	230	1	β(ϕt	ORG
ejpam-3291	236	1	ss ∼= st. theorem 5	ORG
ejpam-3291	239	1	sn ∈	PERSON
ejpam-3291	242	1	⊆	CARDINAL
ejpam-3291	243	1	n. d. h. nghiem et al	PERSON
ejpam-3291	244	1	j. pure	PERSON
ejpam-3291	244	2	11	CARDINAL
ejpam-3291	244	3	3	CARDINAL
ejpam-3291	244	4	2018	DATE
ejpam-3291	244	5	815	CARDINAL
ejpam-3291	244	6	6	CARDINAL
ejpam-3291	247	1	sn ∈	PERSON
ejpam-3291	249	1	sn(m	PERSON
ejpam-3291	249	2	1 ≤ k ≤ n.	QUANTITY
ejpam-3291	254	1	∈	ORG
ejpam-3291	255	1	theorem 5	DATE
ejpam-3291	255	2	→m	ORG
ejpam-3291	255	3	→m	ORG
ejpam-3291	256	1	ϕ(b	PERSON
ejpam-3291	258	1	∈	ORG
ejpam-3291	258	2	u− ϕ ∈	ORG
ejpam-3291	259	1	u− ϕ) + ϕ	ORG
ejpam-3291	259	2	∈	PRODUCT
ejpam-3291	260	1	7	CARDINAL
ejpam-3291	262	1	1	CARDINAL
ejpam-3291	262	2	2	DATE
ejpam-3291	264	1	⊕ni=1mi	ORG
ejpam-3291	268	1	jth	PRODUCT
ejpam-3291	268	2	ia	GPE
ejpam-3291	269	1	ᾱ	CARDINAL
ejpam-3291	280	1	j ∈	PERSON
ejpam-3291	282	1	→m	ORG
ejpam-3291	282	2	ᾱ	CARDINAL
ejpam-3291	282	3	ia	GPE
ejpam-3291	283	1	jth	PRODUCT
ejpam-3291	295	1	0	CARDINAL
ejpam-3291	296	1	0 6=	CARDINAL
ejpam-3291	299	1	ia	GPE
ejpam-3291	299	2	ia	GPE
ejpam-3291	299	3	a→m	ORG
ejpam-3291	299	4	ia	GPE
ejpam-3291	299	5	a.	PERSON
ejpam-3291	299	6	0	CARDINAL
ejpam-3291	299	7	0	CARDINAL
ejpam-3291	302	1	822	CARDINAL
ejpam-3291	302	2	first	ORDINAL
ejpam-3291	304	1	new york	GPE
ejpam-3291	304	2	1974	DATE
ejpam-3291	305	1	2	CARDINAL
ejpam-3291	305	2	janmuang	GPE
ejpam-3291	306	1	3	CARDINAL
ejpam-3291	306	2	portugaliae mathematica	PERSON
ejpam-3291	306	3	46:33-37, 1989	DATE
ejpam-3291	307	1	4	CARDINAL
ejpam-3291	307	2	thai journal of mathematics	ORG
ejpam-3291	307	3	10:137-145	CARDINAL
ejpam-3291	307	4	2012	DATE
ejpam-3291	308	1	5	CARDINAL
ejpam-3291	308	2	london	GPE
ejpam-3291	308	3	17(c.u.p	CARDINAL
ejpam-3291	308	4	1982	DATE
ejpam-3291	309	1	6	CARDINAL
ejpam-3291	309	2	serre	PERSON
ejpam-3291	309	3	berlin/heidelberg	ORG
ejpam-3291	309	4	2006	DATE
ejpam-3291	310	1	k p shum	ORG
ejpam-3291	310	2	6:269-276	CARDINAL
ejpam-3291	310	3	1999	DATE
ejpam-3291	311	1	8	CARDINAL
ejpam-3291	311	2	asian-european journal of mathematics	ORG
ejpam-3291	311	3	5	CARDINAL
ejpam-3291	311	4	1250028,	DATE
ejpam-3291	311	5	2012	DATE
ejpam-3291	312	1	9	CARDINAL
ejpam-3291	312	2	197:305-321, 2005	DATE
ejpam-3291	313	1	10	CARDINAL
ejpam-3291	313	2	304:812-831	CARDINAL
ejpam-3291	313	3	2006	DATE
ejpam-3291	314	1	11	CARDINAL
ejpam-3291	314	2	philadelphia	GPE
ejpam-3291	314	3	pa, usa: gordon	ORG
ejpam-3291	314	4	1991	DATE
ejpam-3291	315	1	12	CARDINAL
ejpam-3291	315	2	1993	DATE