id	sid	eid	entity	type
ejpam-3966	1	1	european journal	ORG
ejpam-3966	2	1	14	DATE
ejpam-3966	2	2	2	CARDINAL
ejpam-3966	2	3	2021	DATE
ejpam-3966	2	4	423	CARDINAL
ejpam-3966	2	5	1307-5543	CARDINAL
ejpam-3966	3	1	new york	GPE
ejpam-3966	3	2	jimboy r. albaracin1,∗	PERSON
ejpam-3966	3	3	jocelyn p. vilela2	PERSON
ejpam-3966	3	4	1	CARDINAL
ejpam-3966	3	5	6000	CARDINAL
ejpam-3966	3	6	cebu city	GPE
ejpam-3966	3	7	philippines 2 department	ORG
ejpam-3966	3	8	mindanao state university-iligan institute of technology	ORG
ejpam-3966	3	9	9200	CARDINAL
ejpam-3966	3	10	iligan city	GPE
ejpam-3966	3	11	philippines	GPE
ejpam-3966	6	1	2020	DATE
ejpam-3966	6	2	06f35	CARDINAL
ejpam-3966	6	3	03g25	CARDINAL
ejpam-3966	6	4	1	CARDINAL
ejpam-3966	7	1	bck-algebras	ORG
ejpam-3966	7	2	y. imai	PERSON
ejpam-3966	7	3	k. iséki	PERSON
ejpam-3966	8	1	1	CARDINAL
ejpam-3966	8	2	1966	DATE
ejpam-3966	9	1	3	CARDINAL
ejpam-3966	9	2	k. h. kim	PERSON
ejpam-3966	9	3	y. h. yon	PERSON
ejpam-3966	10	1	h. s. kim	PERSON
ejpam-3966	10	2	y. h. kim	PERSON
ejpam-3966	11	1	2	CARDINAL
ejpam-3966	12	1	today	DATE
ejpam-3966	17	1	∗	CARDINAL
ejpam-3966	17	2	1x	CARDINAL
ejpam-3966	18	1	1x	CARDINAL
ejpam-3966	19	1	1x	CARDINAL
ejpam-3966	19	2	be3	ORG
ejpam-3966	19	3	1x	CARDINAL
ejpam-3966	21	1	y ∗ (x∗z	PERSON
ejpam-3966	23	1	1x	CARDINAL
ejpam-3966	24	1	∗	CARDINAL
ejpam-3966	24	2	1x	CARDINAL
ejpam-3966	26	1	jralbaracin@up.edu.ph	PERSON
ejpam-3966	26	2	j. albaracin	PERSON
ejpam-3966	26	3	jocelyn.vilela@g.msuiit.edu.ph	GPE
ejpam-3966	26	4	j. vilela	PERSON
ejpam-3966	27	1	423	CARDINAL
ejpam-3966	27	2	2021	CARDINAL
ejpam-3966	28	1	j. albaracin	PERSON
ejpam-3966	28	2	j. vilela	PERSON
ejpam-3966	29	1	j. pure	PERSON
ejpam-3966	29	2	14	CARDINAL
ejpam-3966	29	3	2	CARDINAL
ejpam-3966	29	4	2021	CARDINAL
ejpam-3966	29	5	423	CARDINAL
ejpam-3966	29	6	f1	PERSON
ejpam-3966	29	7	1x	CARDINAL
ejpam-3966	30	1	∈	ORG
ejpam-3966	33	1	∗	CARDINAL
ejpam-3966	35	1	x∗(y∗z	CARDINAL
ejpam-3966	36	1	x∗y)∗(x∗z	GPE
ejpam-3966	36	2	y∗x)∗x	PERSON
ejpam-3966	37	1	y∗z ≤	FAC
ejpam-3966	37	2	x∗y)∗(x∗z	GPE
ejpam-3966	40	1	f(x∗y	PRODUCT
ejpam-3966	41	1	4	CARDINAL
ejpam-3966	42	1	1	CARDINAL
ejpam-3966	43	1	4	CARDINAL
ejpam-3966	44	1	1y	CARDINAL
ejpam-3966	45	1	2	CARDINAL
ejpam-3966	46	1	4	CARDINAL
ejpam-3966	47	1	1	CARDINAL
ejpam-3966	48	1	6	CARDINAL
ejpam-3966	49	1	3	CARDINAL
ejpam-3966	50	1	6	CARDINAL
ejpam-3966	51	1	x.	EVENT
ejpam-3966	51	2	1	CARDINAL
ejpam-3966	52	1	5	CARDINAL
ejpam-3966	52	2	i.	PERSON
ejpam-3966	57	1	k ∈	PERSON
ejpam-3966	60	1	j ≤ k. definition	PERSON
ejpam-3966	60	2	2	CARDINAL
ejpam-3966	69	1	3	CARDINAL
ejpam-3966	70	1	∈	ORG
ejpam-3966	70	2	j ≤ i.	LAW
ejpam-3966	70	3	4	DATE
ejpam-3966	71	1	i.	PERSON
ejpam-3966	75	1	j. albaracin	PERSON
ejpam-3966	75	2	j. vilela	PERSON
ejpam-3966	76	1	j. pure	PERSON
ejpam-3966	76	2	14	CARDINAL
ejpam-3966	76	3	2	CARDINAL
ejpam-3966	76	4	2021	CARDINAL
ejpam-3966	76	5	423	CARDINAL
ejpam-3966	77	1	4	CARDINAL
ejpam-3966	78	1	i.	PERSON
ejpam-3966	82	1	ϕij(xi ∗ yi	PERSON
ejpam-3966	82	2	∗ ϕij(yi	DATE
ejpam-3966	85	1	ϕijϕi((xi	GPE
ejpam-3966	87	1	= ϕj((xi	PERSON
ejpam-3966	91	1	ψ(y	PERSON
ejpam-3966	97	1	ϕiψ(y	GPE
ejpam-3966	98	1	φ	PERSON
ejpam-3966	98	2	∈	ORG
ejpam-3966	98	3	ψ(y	PERSON
ejpam-3966	101	1	6=	CARDINAL
ejpam-3966	103	1	ψ(y	PERSON
ejpam-3966	108	1	∈	ORG
ejpam-3966	111	1	1	CARDINAL
ejpam-3966	115	1	5	CARDINAL
ejpam-3966	116	1	i.	PERSON
ejpam-3966	116	2	two	CARDINAL
ejpam-3966	117	1	∈	ORG
ejpam-3966	117	2	two	CARDINAL
ejpam-3966	118	1	∈	ORG
ejpam-3966	119	1	1	CARDINAL
ejpam-3966	119	2	= idy	PERSON
ejpam-3966	122	1	j. albaracin	PERSON
ejpam-3966	122	2	j. vilela	PERSON
ejpam-3966	123	1	j. pure	PERSON
ejpam-3966	123	2	14	CARDINAL
ejpam-3966	123	3	2	CARDINAL
ejpam-3966	123	4	2021	CARDINAL
ejpam-3966	123	5	423	CARDINAL
ejpam-3966	123	6	y ∗ z	PERSON
ejpam-3966	125	1	4	CARDINAL
ejpam-3966	127	1	2	CARDINAL
ejpam-3966	130	1	commutative	ORG
ejpam-3966	132	1	commutative	ORG
ejpam-3966	132	2	3	CARDINAL
ejpam-3966	134	1	i0 ∈	ORG
ejpam-3966	135	1	i0	GPE
ejpam-3966	138	1	⊆	CARDINAL
ejpam-3966	138	2	0	CARDINAL
ejpam-3966	138	3	1	CARDINAL
ejpam-3966	139	1	6	CARDINAL
ejpam-3966	140	1	6	CARDINAL
ejpam-3966	142	1	6	CARDINAL
ejpam-3966	143	1	6	CARDINAL
ejpam-3966	144	1	xi0 ∈	GPE
ejpam-3966	144	2	ai0	GPE
ejpam-3966	145	1	j ≤ i0	ORG
ejpam-3966	146	1	i0	GPE
ejpam-3966	148	1	1	CARDINAL
ejpam-3966	150	1	⊆	CARDINAL
ejpam-3966	150	2	1	CARDINAL
ejpam-3966	151	1	xik ∈	PERSON
ejpam-3966	153	1	1	CARDINAL
ejpam-3966	154	1	6	CARDINAL
ejpam-3966	157	1	6	CARDINAL
ejpam-3966	161	1	6	CARDINAL
ejpam-3966	161	2	1xi0	CARDINAL
ejpam-3966	162	1	6	CARDINAL
ejpam-3966	163	1	1xit	DATE
ejpam-3966	163	2	i0	GPE
ejpam-3966	166	1	i0	GPE
ejpam-3966	168	1	1	CARDINAL
ejpam-3966	169	1	1	CARDINAL
ejpam-3966	170	1	1	CARDINAL
ejpam-3966	173	1	i0	GPE
ejpam-3966	175	1	1	CARDINAL
ejpam-3966	176	1	3	CARDINAL
ejpam-3966	177	1	6	CARDINAL
ejpam-3966	179	1	6	CARDINAL
ejpam-3966	180	1	j. albaracin	PERSON
ejpam-3966	180	2	j. vilela	PERSON
ejpam-3966	181	1	j. pure	PERSON
ejpam-3966	181	2	14	CARDINAL
ejpam-3966	181	3	2	CARDINAL
ejpam-3966	181	4	2021	CARDINAL
ejpam-3966	181	5	423	CARDINAL
ejpam-3966	186	1	1xj	ORDINAL
ejpam-3966	186	2	xj	ORG
ejpam-3966	186	3	1xj	ORDINAL
ejpam-3966	187	1	∩ ∏	PERSON
ejpam-3966	187	2	6	CARDINAL
ejpam-3966	187	3	1xj	ORDINAL
ejpam-3966	188	1	3	CARDINAL
ejpam-3966	188	2	4	CARDINAL
ejpam-3966	189	1	x.	GPE
ejpam-3966	189	2	θ ≤ φ	ORG
ejpam-3966	189	3	φ ⊆ θ	ORG
ejpam-3966	189	4	φ ∈ i. theorem 7	ORG
ejpam-3966	191	1	θ ≤ φ	ORG
ejpam-3966	192	1	φ ⊆ θ	ORG
ejpam-3966	196	1	4	CARDINAL
ejpam-3966	202	1	x]λ	PERSON
ejpam-3966	207	1	8	CARDINAL
ejpam-3966	208	1	x.	GPE
ejpam-3966	210	1	φ	ORG
ejpam-3966	210	2	φ ≥ θ	ORG
ejpam-3966	211	1	x]θ	DATE
ejpam-3966	213	1	4	CARDINAL
ejpam-3966	213	2	x̂ of theorem 8	ORG
ejpam-3966	214	1	1	CARDINAL
ejpam-3966	219	1	x]θ	CARDINAL
ejpam-3966	220	1	9	CARDINAL
ejpam-3966	224	1	j. albaracin	PERSON
ejpam-3966	224	2	j. vilela	PERSON
ejpam-3966	225	1	j. pure	PERSON
ejpam-3966	225	2	14	CARDINAL
ejpam-3966	225	3	2	CARDINAL
ejpam-3966	225	4	2021	CARDINAL
ejpam-3966	225	5	423	CARDINAL
ejpam-3966	226	1	lemma 1	ORG
ejpam-3966	228	1	4	CARDINAL
ejpam-3966	228	2	4	CARDINAL
ejpam-3966	229	1	10	CARDINAL
ejpam-3966	241	1	∈	ORG
ejpam-3966	243	1	⊆	CARDINAL
ejpam-3966	244	1	∈	ORG
ejpam-3966	254	1	x]θ ⊆	ORG
ejpam-3966	256	1	3	CARDINAL
ejpam-3966	256	2	one	CARDINAL
ejpam-3966	257	1	x.	GPE
ejpam-3966	257	2	11	DATE
ejpam-3966	259	1	⊆	CARDINAL
ejpam-3966	259	2	fj	NORP
ejpam-3966	260	1	kerγ	PERSON
ejpam-3966	264	1	kerγ	PERSON
ejpam-3966	265	1	1x	CARDINAL
ejpam-3966	265	2	x]fi	GPE
ejpam-3966	265	3	1x	CARDINAL
ejpam-3966	266	1	1x	CARDINAL
ejpam-3966	267	1	2	CARDINAL
ejpam-3966	269	1	12	CARDINAL
ejpam-3966	270	1	g ∈ i.	PERSON
ejpam-3966	271	1	x]g	ORG
ejpam-3966	272	1	⊆	CARDINAL
ejpam-3966	272	2	g. j. albaracin	PERSON
ejpam-3966	272	3	j. vilela	PERSON
ejpam-3966	273	1	j. pure	PERSON
ejpam-3966	273	2	14	CARDINAL
ejpam-3966	273	3	2	CARDINAL
ejpam-3966	273	4	2021	CARDINAL
ejpam-3966	273	5	423	CARDINAL
ejpam-3966	275	1	⊆	CARDINAL
ejpam-3966	276	1	⊆	CARDINAL
ejpam-3966	276	2	⊆	CARDINAL
ejpam-3966	276	3	⊆	CARDINAL
ejpam-3966	276	4	⊆	CARDINAL
ejpam-3966	278	1	⊆	CARDINAL
ejpam-3966	278	2	⊆	CARDINAL
ejpam-3966	280	1	i.	PERSON
ejpam-3966	281	1	g ≤ h. therefore	PERSON
ejpam-3966	285	1	ϕgh([x]g	ORDINAL
ejpam-3966	289	1	x]f	GPE
ejpam-3966	293	1	x.	ORG
ejpam-3966	293	2	1	CARDINAL
ejpam-3966	294	1	1	CARDINAL
ejpam-3966	295	1	1 1	CARDINAL
ejpam-3966	295	2	1 1	CARDINAL
ejpam-3966	295	3	1	CARDINAL
ejpam-3966	295	4	1	CARDINAL
ejpam-3966	295	5	1	CARDINAL
ejpam-3966	295	6	1	CARDINAL
ejpam-3966	295	7	3	CARDINAL
ejpam-3966	295	8	x.	ORG
ejpam-3966	295	9	1	CARDINAL
ejpam-3966	295	10	1	CARDINAL
ejpam-3966	295	11	1	CARDINAL
ejpam-3966	295	12	f4	CARDINAL
ejpam-3966	295	13	1	CARDINAL
ejpam-3966	295	14	1	CARDINAL
ejpam-3966	295	15	1	CARDINAL
ejpam-3966	295	16	1	CARDINAL
ejpam-3966	296	1	2	CARDINAL
ejpam-3966	298	1	1	CARDINAL
ejpam-3966	300	1	8	CARDINAL
ejpam-3966	301	1	1	CARDINAL
ejpam-3966	302	1	8	CARDINAL
ejpam-3966	303	1	∈	ORG
ejpam-3966	305	1	1]f1	CARDINAL
ejpam-3966	306	1	1]f1	CARDINAL
ejpam-3966	306	2	1	CARDINAL
ejpam-3966	306	3	1]f2	CARDINAL
ejpam-3966	306	4	1]f2	CARDINAL
ejpam-3966	307	1	1]f3	CARDINAL
ejpam-3966	307	2	1]f3	CARDINAL
ejpam-3966	307	3	1]f4	CARDINAL
ejpam-3966	307	4	1]f4	CARDINAL
ejpam-3966	307	5	f4	CARDINAL
ejpam-3966	308	1	1]f5	CARDINAL
ejpam-3966	308	2	1]f5	CARDINAL
ejpam-3966	309	1	1]f6	CARDINAL
ejpam-3966	309	2	1]f7	CARDINAL
ejpam-3966	309	3	1]f7 = f7	QUANTITY
ejpam-3966	309	4	430 x	QUANTITY
ejpam-3966	309	5	1]f8	CARDINAL
ejpam-3966	309	6	1]f8	CARDINAL
ejpam-3966	309	7	ϕfifj	PERSON
ejpam-3966	310	1	x.	ORG
ejpam-3966	310	2	2	CARDINAL
ejpam-3966	311	1	1	CARDINAL
ejpam-3966	311	2	x]fi	GPE
ejpam-3966	312	1	fj	NORP
ejpam-3966	312	2	ϕfifj	PERSON
ejpam-3966	312	3	x]fi	GPE
ejpam-3966	314	1	1]f1	CARDINAL
ejpam-3966	314	2	1]f2	CARDINAL
ejpam-3966	314	3	1]f4	CARDINAL
ejpam-3966	314	4	1]f5	CARDINAL
ejpam-3966	314	5	1]f7	CARDINAL
ejpam-3966	314	6	1]f8	CARDINAL
ejpam-3966	314	7	1]f2	CARDINAL
ejpam-3966	314	8	1]f5	CARDINAL
ejpam-3966	314	9	1]f8	CARDINAL
ejpam-3966	315	1	1]f5	CARDINAL
ejpam-3966	315	2	1]f7	CARDINAL
ejpam-3966	315	3	1]f8	CARDINAL
ejpam-3966	315	4	1]f4	CARDINAL
ejpam-3966	315	5	1]f7	CARDINAL
ejpam-3966	315	6	1]f8	CARDINAL
ejpam-3966	316	1	α1, α2	CARDINAL
ejpam-3966	317	1	1	CARDINAL
ejpam-3966	317	2	k. iséki	PERSON
ejpam-3966	319	1	the japan academy	ORG
ejpam-3966	319	2	42:19–22, 1996	DATE
ejpam-3966	320	1	2	CARDINAL
ejpam-3966	320	2	kim	PERSON
ejpam-3966	320	3	kim	PERSON
ejpam-3966	322	1	scientiae mathematicae japonicae online	PERSON
ejpam-3966	322	2	1299–1302, 2004	DATE
ejpam-3966	323	1	3	CARDINAL
ejpam-3966	323	2	kim	PERSON
ejpam-3966	325	1	393–399, 2007	DATE
ejpam-3966	326	1	4	CARDINAL
ejpam-3966	326	2	mukkamala	PERSON
ejpam-3966	328	1	springer nature singapore pte ltd.	ORG
ejpam-3966	328	2	singapore	GPE
ejpam-3966	328	3	2018	DATE
ejpam-3966	329	1	5	CARDINAL
ejpam-3966	331	1	berlin	GPE
ejpam-3966	331	2	heidelberg	GPE
ejpam-3966	331	3	2010	DATE
ejpam-3966	332	1	6	CARDINAL
ejpam-3966	332	2	a. walendziak	PERSON
ejpam-3966	334	1	commentationes mathematicae	PERSON
ejpam-3966	334	2	52:199–205	CARDINAL
ejpam-3966	334	3	2012	DATE