id	sid	eid	entity	type
ejpam-3781	1	1	european journal	ORG
ejpam-3781	2	1	14	DATE
ejpam-3781	2	2	1	CARDINAL
ejpam-3781	2	3	2021	DATE
ejpam-3781	2	4	126	CARDINAL
ejpam-3781	2	5	1307-5543	CARDINAL
ejpam-3781	3	1	new york	GPE
ejpam-3781	3	2	a. v. ramakrishna1,∗	PERSON
ejpam-3781	4	1	prasanna2	PERSON
ejpam-3781	4	2	j.c college	ORG
ejpam-3781	4	3	india 2	ORG
ejpam-3781	4	4	bs&h	GPE
ejpam-3781	4	5	vignan	GPE
ejpam-3781	4	6	nirula institute of technology& science	ORG
ejpam-3781	4	7	andhra pradesh	ORG
ejpam-3781	4	8	india	GPE
ejpam-3781	4	9	3	CARDINAL
ejpam-3781	4	10	andhra pradesh	ORG
ejpam-3781	4	11	india	GPE
ejpam-3781	6	1	2020	DATE
ejpam-3781	6	2	16y30	CARDINAL
ejpam-3781	6	3	1	CARDINAL
ejpam-3781	6	4	c.j.maxson	PERSON
ejpam-3781	6	5	m.johnson	GPE
ejpam-3781	7	1	j.r.	PERSON
ejpam-3781	7	2	1992	DATE
ejpam-3781	8	1	6	CARDINAL
ejpam-3781	9	1	k.d.	PERSON
ejpam-3781	9	2	magill, jr.	PERSON
ejpam-3781	9	3	1995	DATE
ejpam-3781	10	1	4	CARDINAL
ejpam-3781	11	1	2	CARDINAL
ejpam-3781	11	2	3	CARDINAL
ejpam-3781	12	1	1	CARDINAL
ejpam-3781	13	1	5]is	CARDINAL
ejpam-3781	13	2	n,+	PERSON
ejpam-3781	13	3	n,+	PERSON
ejpam-3781	13	4	abelian	NORP
ejpam-3781	14	1	bc	ORG
ejpam-3781	14	2	∈	ORG
ejpam-3781	16	1	n,+	PERSON
ejpam-3781	17	1	6	CARDINAL
ejpam-3781	18	1	a. v. ramakrishna	PERSON
ejpam-3781	18	2	prasanna	PERSON
ejpam-3781	18	3	d.v. lakshmi	ORG
ejpam-3781	19	1	126	CARDINAL
ejpam-3781	19	2	2021	CARDINAL
ejpam-3781	20	1	a.v. ramakrishna	PERSON
ejpam-3781	21	1	prasanna	PERSON
ejpam-3781	21	2	d.v. lakshmi / eur	ORG
ejpam-3781	22	1	j. pure	PERSON
ejpam-3781	22	2	14	CARDINAL
ejpam-3781	22	3	1	CARDINAL
ejpam-3781	22	4	2021	CARDINAL
ejpam-3781	22	5	126	CARDINAL
ejpam-3781	23	1	1	CARDINAL
ejpam-3781	24	1	n2 ∈ n	PRODUCT
ejpam-3781	24	2	n2 ∈ n	PRODUCT
ejpam-3781	25	1	1	CARDINAL
ejpam-3781	26	1	pilz.	ORG
ejpam-3781	27	1	2	CARDINAL
ejpam-3781	30	1	n2 ∈ n	PRODUCT
ejpam-3781	31	1	3	CARDINAL
ejpam-3781	32	1	n2 ∈ n	PRODUCT
ejpam-3781	35	1	n ∈ n	ORG
ejpam-3781	35	2	n2 ∈ n	PRODUCT
ejpam-3781	36	1	2	CARDINAL
ejpam-3781	37	1	abelian	NORP
ejpam-3781	37	2	1	CARDINAL
ejpam-3781	40	1	m(g	PERSON
ejpam-3781	40	2	∈m(g	CARDINAL
ejpam-3781	43	1	gx	GPE
ejpam-3781	43	2	6=	CARDINAL
ejpam-3781	44	1	g,+	GPE
ejpam-3781	45	1	2	CARDINAL
ejpam-3781	46	1	ab = a. let m	ORG
ejpam-3781	46	2	n,+	PERSON
ejpam-3781	49	1	n2 ∈ n	PRODUCT
ejpam-3781	49	2	m1,m2 ∈m	ORG
ejpam-3781	49	3	1	CARDINAL
ejpam-3781	49	4	2	CARDINAL
ejpam-3781	51	1	a.v. ramakrishna	PERSON
ejpam-3781	52	1	prasanna	PERSON
ejpam-3781	52	2	d.v. lakshmi / eur	ORG
ejpam-3781	53	1	j. pure	PERSON
ejpam-3781	53	2	14	CARDINAL
ejpam-3781	53	3	1	CARDINAL
ejpam-3781	53	4	2021	CARDINAL
ejpam-3781	53	5	126	CARDINAL
ejpam-3781	53	6	128	CARDINAL
ejpam-3781	53	7	3	CARDINAL
ejpam-3781	55	1	φ	PERSON
ejpam-3781	55	2	φ(r	PERSON
ejpam-3781	56	1	∈ r.	PERSON
ejpam-3781	58	1	1	CARDINAL
ejpam-3781	60	1	2	CARDINAL
ejpam-3781	60	2	1 + 1	DATE
ejpam-3781	60	3	2	CARDINAL
ejpam-3781	60	4	2	CARDINAL
ejpam-3781	60	5	2	CARDINAL
ejpam-3781	60	6	222	CARDINAL
ejpam-3781	60	7	8	CARDINAL
ejpam-3781	60	8	1	CARDINAL
ejpam-3781	60	9	2	CARDINAL
ejpam-3781	60	10	122	CARDINAL
ejpam-3781	61	1	2	CARDINAL
ejpam-3781	61	2	4	CARDINAL
ejpam-3781	61	3	1	CARDINAL
ejpam-3781	62	1	1	CARDINAL
ejpam-3781	63	1	1 φ(r2	PERSON
ejpam-3781	63	2	r2 ∈ r.	PERSON
ejpam-3781	64	1	1	CARDINAL
ejpam-3781	64	2	1	CARDINAL
ejpam-3781	64	3	∈	ORG
ejpam-3781	68	1	m⊕	PERSON
ejpam-3781	69	1	1	CARDINAL
ejpam-3781	69	2	m1,m2 ∈m	ORG
ejpam-3781	70	1	r2 ∈	PERSON
ejpam-3781	70	2	m1,m2 ∈m	ORG
ejpam-3781	70	3	1	CARDINAL
ejpam-3781	70	4	1	CARDINAL
ejpam-3781	70	5	1	CARDINAL
ejpam-3781	73	1	2	CARDINAL
ejpam-3781	73	2	= φ(r	PERSON
ejpam-3781	74	1	1 m2	QUANTITY
ejpam-3781	76	1	4	CARDINAL
ejpam-3781	78	1	n(m+ i)−	ORG
ejpam-3781	78	2	∈	ORG
ejpam-3781	80	1	5	CARDINAL
ejpam-3781	81	1	m1,+1	PERSON
ejpam-3781	81	2	1	CARDINAL
ejpam-3781	81	3	2	CARDINAL
ejpam-3781	82	1	φ(n	PERSON
ejpam-3781	82	2	1 m	QUANTITY
ejpam-3781	83	1	2	CARDINAL
ejpam-3781	83	2	n ∈ n	ORG
ejpam-3781	84	1	5	CARDINAL
ejpam-3781	85	1	a.v. ramakrishna	PERSON
ejpam-3781	86	1	prasanna	PERSON
ejpam-3781	86	2	d.v. lakshmi / eur	ORG
ejpam-3781	87	1	j. pure	PERSON
ejpam-3781	87	2	14	CARDINAL
ejpam-3781	87	3	1	CARDINAL
ejpam-3781	87	4	2021	CARDINAL
ejpam-3781	87	5	126	CARDINAL
ejpam-3781	87	6	129	CARDINAL
ejpam-3781	87	7	2	CARDINAL
ejpam-3781	89	1	m1 and m1 kerφ '	PRODUCT
ejpam-3781	90	1	3	CARDINAL
ejpam-3781	95	1	mi	NORP
ejpam-3781	95	2	⊕	GPE
ejpam-3781	95	3	⊕	PERSON
ejpam-3781	97	1	∈	ORG
ejpam-3781	97	2	n ∈ n	ORG
ejpam-3781	98	1	i. 3	PERSON
ejpam-3781	100	1	6	CARDINAL
ejpam-3781	103	1	4	CARDINAL
ejpam-3781	104	1	n,+	PERSON
ejpam-3781	109	1	f(f(m3)m2)m1	CARDINAL
ejpam-3781	113	1	m1 + m2	PRODUCT
ejpam-3781	113	2	+ m2	PERSON
ejpam-3781	113	3	f(m3)m1	ORG
ejpam-3781	113	4	+ m2	QUANTITY
ejpam-3781	115	1	3.3	CARDINAL
ejpam-3781	115	2	3.7	CARDINAL
ejpam-3781	116	1	4	CARDINAL
ejpam-3781	117	1	end(r,+),+	NORP
ejpam-3781	118	1	n,+	GPE
ejpam-3781	119	1	α(f	ORG
ejpam-3781	121	1	0	CARDINAL
ejpam-3781	122	1	f(x	ORG
ejpam-3781	123	1	0	CARDINAL
ejpam-3781	123	2	r.	NORP
ejpam-3781	124	1	a.v. ramakrishna	PERSON
ejpam-3781	125	1	prasanna	PERSON
ejpam-3781	125	2	d.v. lakshmi / eur	ORG
ejpam-3781	126	1	j. pure	PERSON
ejpam-3781	126	2	14	CARDINAL
ejpam-3781	126	3	1	CARDINAL
ejpam-3781	126	4	2021	CARDINAL
ejpam-3781	126	5	126	CARDINAL
ejpam-3781	126	6	g ∈m	PERSON
ejpam-3781	126	7	r. case(i	PERSON
ejpam-3781	126	8	6=	DATE
ejpam-3781	126	9	0	CARDINAL
ejpam-3781	133	1	α(f	ORG
ejpam-3781	133	2	α(α(f	CARDINAL
ejpam-3781	133	3	α(g	PERSON
ejpam-3781	134	1	case(ii	PERSON
ejpam-3781	134	2	0	CARDINAL
ejpam-3781	135	1	α(α(f	DATE
ejpam-3781	137	1	0	CARDINAL
ejpam-3781	138	1	α(f	ORG
ejpam-3781	139	1	′(g′(0	ORG
ejpam-3781	141	1	0	CARDINAL
ejpam-3781	142	1	α(g	PERSON
ejpam-3781	146	1	∗	CARDINAL
ejpam-3781	150	1	5	CARDINAL
ejpam-3781	151	1	abelian	NORP
ejpam-3781	152	1	k.	PERSON
ejpam-3781	153	1	max{|λi||λi	PERSON
ejpam-3781	155	1	α(a)α(b	ORDINAL
ejpam-3781	156	1	6	CARDINAL
ejpam-3781	157	1	abelian	NORP
ejpam-3781	162	1	la	GPE
ejpam-3781	163	1	7	CARDINAL
ejpam-3781	165	1	c→	ORG
ejpam-3781	166	1	1 2	CARDINAL
ejpam-3781	166	2	∈	ORG
ejpam-3781	167	1	2 + y1 2	QUANTITY
ejpam-3781	167	2	1 2	CARDINAL
ejpam-3781	168	1	2 + y1 2	QUANTITY
ejpam-3781	168	2	1	CARDINAL
ejpam-3781	168	3	2 + y1 2	QUANTITY
ejpam-3781	168	4	1 2 y2	QUANTITY
ejpam-3781	169	1	1 2x2	CARDINAL
ejpam-3781	169	2	2 +	DATE
ejpam-3781	169	3	1 2 y2	QUANTITY
ejpam-3781	169	4	2	CARDINAL
ejpam-3781	169	5	1 2	CARDINAL
ejpam-3781	169	6	1 2	CARDINAL
ejpam-3781	169	7	1 2	CARDINAL
ejpam-3781	170	1	∗	CARDINAL
ejpam-3781	171	1	1 2	CARDINAL
ejpam-3781	172	1	a.v. ramakrishna	PERSON
ejpam-3781	173	1	prasanna	PERSON
ejpam-3781	173	2	d.v. lakshmi / eur	ORG
ejpam-3781	174	1	j. pure	PERSON
ejpam-3781	174	2	14	CARDINAL
ejpam-3781	174	3	1	CARDINAL
ejpam-3781	174	4	2021	CARDINAL
ejpam-3781	174	5	126	CARDINAL
ejpam-3781	174	6	c→	ORG
ejpam-3781	176	1	∈	ORG
ejpam-3781	181	1	∗	CARDINAL
ejpam-3781	184	1	8	CARDINAL
ejpam-3781	187	1	f(a+	GPE
ejpam-3781	191	1	2 +	MONEY
ejpam-3781	194	1	∗	CARDINAL
ejpam-3781	195	1	2 +	DATE
ejpam-3781	195	2	2 +	DATE
ejpam-3781	195	3	2 + d2	QUANTITY
ejpam-3781	197	1	9	CARDINAL
ejpam-3781	201	1	1≤i	CARDINAL
ejpam-3781	201	2	2	CARDINAL
ejpam-3781	202	1	5	CARDINAL
ejpam-3781	204	1	n ∈ n	ORG
ejpam-3781	205	1	nf	ORG
ejpam-3781	208	1	n ∈ n	ORG
ejpam-3781	208	2	+m2	QUANTITY
ejpam-3781	209	1	f(n)m1 +	DATE
ejpam-3781	210	1	n2 ∈ n	PRODUCT
ejpam-3781	213	1	6	CARDINAL
ejpam-3781	217	1	a.v. ramakrishna	PERSON
ejpam-3781	218	1	prasanna	PERSON
ejpam-3781	218	2	d.v. lakshmi / eur	ORG
ejpam-3781	219	1	j. pure	PERSON
ejpam-3781	219	2	14	CARDINAL
ejpam-3781	219	3	1	CARDINAL
ejpam-3781	219	4	2021	CARDINAL
ejpam-3781	219	5	126	CARDINAL
ejpam-3781	221	1	any m2,m2 ′	TIME
ejpam-3781	221	2	g((f(φ(m2))(m2 ′	DATE
ejpam-3781	230	1	3	CARDINAL
ejpam-3781	230	2	n,+	PERSON
ejpam-3781	235	1	10	CARDINAL
ejpam-3781	236	1	y =	PERSON
ejpam-3781	236	2	2xy	ORDINAL
ejpam-3781	236	3	y ∈ r.	PERSON
ejpam-3781	236	4	r.	NORP
ejpam-3781	237	1	2	CARDINAL
ejpam-3781	237	2	∈	ORG
ejpam-3781	239	1	f(b	GPE
ejpam-3781	239	2	8ab	ORDINAL
ejpam-3781	241	1	2f(m2)m1	CARDINAL
ejpam-3781	241	2	2(2m2)m1	CARDINAL
ejpam-3781	241	3	4m2m1	CARDINAL
ejpam-3781	243	1	m4	ORG
ejpam-3781	243	2	m1 and m2	PERSON
ejpam-3781	243	3	m4 = α	PERSON
ejpam-3781	244	1	2αm1	CARDINAL
ejpam-3781	244	2	2m2m4	CARDINAL
ejpam-3781	244	3	2αm2	CARDINAL
ejpam-3781	245	1	1,m2	CARDINAL
ejpam-3781	245	2	2	CARDINAL
ejpam-3781	245	3	2	CARDINAL
ejpam-3781	245	4	2α	CARDINAL
ejpam-3781	245	5	8	CARDINAL
ejpam-3781	245	6	4α	CARDINAL
ejpam-3781	245	7	2	CARDINAL
ejpam-3781	246	1	7	CARDINAL
ejpam-3781	248	1	one-one	CARDINAL
ejpam-3781	250	1	0	CARDINAL
ejpam-3781	252	1	a.v. ramakrishna	PERSON
ejpam-3781	253	1	prasanna	PERSON
ejpam-3781	253	2	d.v. lakshmi / eur	ORG
ejpam-3781	254	1	j. pure	PERSON
ejpam-3781	254	2	14	CARDINAL
ejpam-3781	254	3	1	CARDINAL
ejpam-3781	254	4	2021	CARDINAL
ejpam-3781	254	5	126	CARDINAL
ejpam-3781	255	1	1	CARDINAL
ejpam-3781	255	2	f(m1)m2	ORG
ejpam-3781	259	1	one-one	CARDINAL
ejpam-3781	261	1	2	CARDINAL
ejpam-3781	262	1	f(m1)m2	ORG
ejpam-3781	262	2	m1 and m2	PRODUCT
ejpam-3781	263	1	1	CARDINAL
ejpam-3781	263	2	k=1	PERSON
ejpam-3781	263	3	m2 ∗ m1 =	PERSON
ejpam-3781	263	4	f(m1)m2	ORDINAL
ejpam-3781	263	5	f(m1)m2	ORG
ejpam-3781	264	1	1	CARDINAL
ejpam-3781	269	1	m1 ∗	LAW
ejpam-3781	270	1	+m3)m1	CARDINAL
ejpam-3781	273	1	∈	ORG
ejpam-3781	274	1	λm1	PERSON
ejpam-3781	275	1	1	CARDINAL
ejpam-3781	277	1	1	CARDINAL
ejpam-3781	277	2	ψ(m	ORG
ejpam-3781	279	1	0	CARDINAL
ejpam-3781	282	1	134	CARDINAL
ejpam-3781	282	2	1	CARDINAL
ejpam-3781	282	3	a. equiprime	PERSON
ejpam-3781	282	4	monogenic n	PERSON
ejpam-3781	283	1	hacettepe	PERSON
ejpam-3781	283	2	40:375–382, 2011	DATE
ejpam-3781	284	1	2	CARDINAL
ejpam-3781	286	1	2017	CARDINAL
ejpam-3781	287	1	3	CARDINAL
ejpam-3781	287	2	prasanna	PERSON
ejpam-3781	287	3	a.v. ramakrishna i.r.b	PERSON
ejpam-3781	288	1	sarma	PERSON
ejpam-3781	288	2	sudan rao	GPE
ejpam-3781	290	1	southeast asian	NORP
ejpam-3781	290	2	38:543–554	CARDINAL
ejpam-3781	290	3	2014	DATE
ejpam-3781	291	1	4	CARDINAL
ejpam-3781	291	2	magill, jr.	PERSON
ejpam-3781	292	1	mathematik	PERSON
ejpam-3781	292	2	119:281–301, 1995	DATE
ejpam-3781	293	1	5	CARDINAL
ejpam-3781	293	2	g. pilz	PERSON
ejpam-3781	295	1	north-	NORP
ejpam-3781	295	2	amsterdam	GPE
ejpam-3781	295	3	1983	DATE
ejpam-3781	296	1	6	CARDINAL
ejpam-3781	297	1	genesis	ORG
ejpam-3781	298	1	oxford science	ORG
ejpam-3781	298	2	new york	GPE
ejpam-3781	298	3	1992	DATE