id	sid	eid	entity	type
ejpam-3206	1	1	european journal	ORG
ejpam-3206	2	1	11	CARDINAL
ejpam-3206	2	2	1, 2018	DATE
ejpam-3206	2	3	244	CARDINAL
ejpam-3206	2	4	1307-5543	DATE
ejpam-3206	2	5	new york	GPE
ejpam-3206	2	6	hurwitz series mohamed a. farahat1,2,∗	ORG
ejpam-3206	2	7	t. al-bogamy1 1	PERSON
ejpam-3206	2	8	taif university	ORG
ejpam-3206	2	9	taif	GPE
ejpam-3206	2	10	el-haweiah	GPE
ejpam-3206	2	11	kingdom	GPE
ejpam-3206	2	12	saudi arabia	GPE
ejpam-3206	2	13	2	CARDINAL
ejpam-3206	2	14	al-azhar university	ORG
ejpam-3206	2	15	cairo	GPE
ejpam-3206	2	16	egypt	GPE
ejpam-3206	5	1	hurwitz series	PERSON
ejpam-3206	5	2	σ	PERSON
ejpam-3206	5	3	nil(r	ORG
ejpam-3206	6	1	σ	PERSON
ejpam-3206	7	1	2010	DATE
ejpam-3206	7	2	16w60	DATE
ejpam-3206	7	3	16d25	DATE
ejpam-3206	7	4	16p60	CARDINAL
ejpam-3206	7	5	hurwitz series rings 1	ORG
ejpam-3206	9	1	r(x	WORK_OF_ART
ejpam-3206	9	2	r.	NORP
ejpam-3206	9	3	r.	NORP
ejpam-3206	9	4	jacobson	PERSON
ejpam-3206	9	5	two	CARDINAL
ejpam-3206	10	1	0	CARDINAL
ejpam-3206	11	1	nicholson	PERSON
ejpam-3206	11	2	watters	PERSON
ejpam-3206	11	3	15	CARDINAL
ejpam-3206	11	4	1988	DATE
ejpam-3206	16	1	gordon	PERSON
ejpam-3206	16	2	6	CARDINAL
ejpam-3206	16	3	1969	DATE
ejpam-3206	18	1	11	CARDINAL
ejpam-3206	20	1	mohamed a. farahat	PERSON
ejpam-3206	20	2	s. t. al-bogamy	PERSON
ejpam-3206	21	1	244	CARDINAL
ejpam-3206	22	1	2018	DATE
ejpam-3206	23	1	m. a. farahat	PERSON
ejpam-3206	23	2	s. t. al-bogamy	PERSON
ejpam-3206	24	1	j. pure	PERSON
ejpam-3206	24	2	11	CARDINAL
ejpam-3206	24	3	1	CARDINAL
ejpam-3206	24	4	2018	DATE
ejpam-3206	24	5	244	CARDINAL
ejpam-3206	24	6	259 245	CARDINAL
ejpam-3206	24	7	15	CARDINAL
ejpam-3206	30	1	0	CARDINAL
ejpam-3206	31	1	r.	NORP
ejpam-3206	31	2	22	CARDINAL
ejpam-3206	31	3	1992	DATE
ejpam-3206	32	1	1	CARDINAL
ejpam-3206	32	2	22	CARDINAL
ejpam-3206	33	1	1	CARDINAL
ejpam-3206	33	2	rm	PERSON
ejpam-3206	34	1	2	CARDINAL
ejpam-3206	35	1	3	CARDINAL
ejpam-3206	35	2	0	CARDINAL
ejpam-3206	36	1	2	CARDINAL
ejpam-3206	36	2	15	CARDINAL
ejpam-3206	38	1	baer ring	PERSON
ejpam-3206	42	1	0	CARDINAL
ejpam-3206	42	2	⊆	CARDINAL
ejpam-3206	42	3	⊆	CARDINAL
ejpam-3206	43	1	0	CARDINAL
ejpam-3206	43	2	0	CARDINAL
ejpam-3206	44	1	15	CARDINAL
ejpam-3206	46	1	3	CARDINAL
ejpam-3206	46	2	15	CARDINAL
ejpam-3206	46	3	3.2	CARDINAL
ejpam-3206	48	1	nicholson	PERSON
ejpam-3206	48	2	watters	PERSON
ejpam-3206	48	3	15	CARDINAL
ejpam-3206	49	1	14	CARDINAL
ejpam-3206	49	2	1998	DATE
ejpam-3206	50	1	salem	GPE
ejpam-3206	50	2	20	CARDINAL
ejpam-3206	50	3	2015	DATE
ejpam-3206	51	1	al-harthy	PERSON
ejpam-3206	51	2	3	CARDINAL
ejpam-3206	51	3	2017	DATE
ejpam-3206	52	1	18	CARDINAL
ejpam-3206	52	2	2017	DATE
ejpam-3206	53	1	ouyang	PERSON
ejpam-3206	53	2	16	CARDINAL
ejpam-3206	53	3	2009	DATE
ejpam-3206	53	4	m. a. farahat	PERSON
ejpam-3206	53	5	s. t. al-bogamy	PERSON
ejpam-3206	54	1	j. pure	PERSON
ejpam-3206	54	2	11	CARDINAL
ejpam-3206	54	3	1	CARDINAL
ejpam-3206	54	4	2018	DATE
ejpam-3206	54	5	244	CARDINAL
ejpam-3206	54	6	∈	ORG
ejpam-3206	54	7	∈	ORG
ejpam-3206	55	1	ab ∈	ORG
ejpam-3206	55	2	r)⇔ ba	MONEY
ejpam-3206	55	3	∈	ORG
ejpam-3206	56	1	⊆	CARDINAL
ejpam-3206	59	1	0	CARDINAL
ejpam-3206	59	2	0	CARDINAL
ejpam-3206	61	1	0	CARDINAL
ejpam-3206	61	2	two	CARDINAL
ejpam-3206	64	1	r.	NORP
ejpam-3206	65	1	0	CARDINAL
ejpam-3206	66	1	0	CARDINAL
ejpam-3206	70	1	1	CARDINAL
ejpam-3206	70	2	16	CARDINAL
ejpam-3206	72	1	1	CARDINAL
ejpam-3206	72	2	⊆	CARDINAL
ejpam-3206	72	3	⊂	GPE
ejpam-3206	72	4	⊆	CARDINAL
ejpam-3206	72	5	2	CARDINAL
ejpam-3206	73	1	⊆	CARDINAL
ejpam-3206	73	2	nr(nr(x	TIME
ejpam-3206	73	3	3	CARDINAL
ejpam-3206	73	4	nr(nr(nr(x	ORG
ejpam-3206	74	1	4	CARDINAL
ejpam-3206	74	2	⊆	CARDINAL
ejpam-3206	74	3	∩ s. lemma	PERSON
ejpam-3206	75	1	1	CARDINAL
ejpam-3206	77	1	ab ∈	ORG
ejpam-3206	77	2	∈	ORG
ejpam-3206	78	1	∈	ORG
ejpam-3206	78	2	ab ∈	ORG
ejpam-3206	80	1	∈	ORG
ejpam-3206	80	2	∈	ORG
ejpam-3206	80	3	1	CARDINAL
ejpam-3206	81	1	r.	NORP
ejpam-3206	81	2	∈	ORG
ejpam-3206	81	3	hurwitz series	PERSON
ejpam-3206	81	4	σ	ORG
ejpam-3206	82	1	m. a. farahat	PERSON
ejpam-3206	82	2	s. t. al-bogamy	PERSON
ejpam-3206	83	1	j. pure	PERSON
ejpam-3206	83	2	11	CARDINAL
ejpam-3206	83	3	1	CARDINAL
ejpam-3206	83	4	2018	DATE
ejpam-3206	83	5	244	CARDINAL
ejpam-3206	83	6	1	CARDINAL
ejpam-3206	84	1	⊆	CARDINAL
ejpam-3206	84	2	∈	ORG
ejpam-3206	87	1	2	CARDINAL
ejpam-3206	87	2	1	CARDINAL
ejpam-3206	87	3	one	CARDINAL
ejpam-3206	87	4	two	CARDINAL
ejpam-3206	88	1	0	CARDINAL
ejpam-3206	89	1	2	CARDINAL
ejpam-3206	90	1	4	CARDINAL
ejpam-3206	91	1	zero	CARDINAL
ejpam-3206	92	1	zero	CARDINAL
ejpam-3206	93	1	zero	CARDINAL
ejpam-3206	93	2	1	CARDINAL
ejpam-3206	93	3	f. example	PERSON
ejpam-3206	94	1	5	CARDINAL
ejpam-3206	95	1	1	CARDINAL
ejpam-3206	95	2	2	CARDINAL
ejpam-3206	95	3	1〉	CARDINAL
ejpam-3206	95	4	1	CARDINAL
ejpam-3206	96	1	3	CARDINAL
ejpam-3206	96	2	〉	CARDINAL
ejpam-3206	98	1	〉	CARDINAL
ejpam-3206	100	1	6	CARDINAL
ejpam-3206	100	2	0	CARDINAL
ejpam-3206	101	1	two	CARDINAL
ejpam-3206	101	2	0	CARDINAL
ejpam-3206	101	3	2	DATE
ejpam-3206	101	4	4	CARDINAL
ejpam-3206	101	5	0	CARDINAL
ejpam-3206	101	6	3	CARDINAL
ejpam-3206	102	1	0	CARDINAL
ejpam-3206	102	2	1	DATE
ejpam-3206	102	3	3	DATE
ejpam-3206	102	4	4	CARDINAL
ejpam-3206	103	1	0	CARDINAL
ejpam-3206	103	2	3	CARDINAL
ejpam-3206	103	3	3	CARDINAL
ejpam-3206	104	1	0	CARDINAL
ejpam-3206	104	2	2	DATE
ejpam-3206	104	3	4	CARDINAL
ejpam-3206	104	4	4 〉	QUANTITY
ejpam-3206	105	1	z6	ORG
ejpam-3206	106	1	7	CARDINAL
ejpam-3206	106	2	nil(r	ORG
ejpam-3206	106	3	0	CARDINAL
ejpam-3206	106	4	0	CARDINAL
ejpam-3206	106	5	5	DATE
ejpam-3206	106	6	6	CARDINAL
ejpam-3206	107	1	two	CARDINAL
ejpam-3206	107	2	0	CARDINAL
ejpam-3206	107	3	2	DATE
ejpam-3206	107	4	4	DATE
ejpam-3206	107	5	6	DATE
ejpam-3206	107	6	8	CARDINAL
ejpam-3206	107	7	0	CARDINAL
ejpam-3206	107	8	5	CARDINAL
ejpam-3206	108	1	two	CARDINAL
ejpam-3206	108	2	0	CARDINAL
ejpam-3206	108	3	5	CARDINAL
ejpam-3206	108	4	5	CARDINAL
ejpam-3206	108	5	m. a. farahat	PERSON
ejpam-3206	108	6	s. t. al-bogamy	PERSON
ejpam-3206	109	1	j. pure	PERSON
ejpam-3206	109	2	11	CARDINAL
ejpam-3206	109	3	1	CARDINAL
ejpam-3206	109	4	2018	DATE
ejpam-3206	109	5	244	CARDINAL
ejpam-3206	109	6	0	CARDINAL
ejpam-3206	109	7	2	DATE
ejpam-3206	109	8	4	DATE
ejpam-3206	109	9	6	DATE
ejpam-3206	109	10	8	CARDINAL
ejpam-3206	109	11	6 〉	QUANTITY
ejpam-3206	110	1	8	CARDINAL
ejpam-3206	111	1	0	CARDINAL
ejpam-3206	111	2	6	CARDINAL
ejpam-3206	112	1	0	CARDINAL
ejpam-3206	112	2	1	DATE
ejpam-3206	112	3	9	CARDINAL
ejpam-3206	113	1	two	CARDINAL
ejpam-3206	113	2	0	CARDINAL
ejpam-3206	113	3	2	DATE
ejpam-3206	113	4	4	DATE
ejpam-3206	113	5	6	DATE
ejpam-3206	113	6	8	DATE
ejpam-3206	113	7	10	CARDINAL
ejpam-3206	113	8	0	CARDINAL
ejpam-3206	113	9	3	DATE
ejpam-3206	113	10	6	DATE
ejpam-3206	113	11	9	CARDINAL
ejpam-3206	114	1	two	CARDINAL
ejpam-3206	114	2	0	CARDINAL
ejpam-3206	114	3	3	DATE
ejpam-3206	114	4	6	DATE
ejpam-3206	114	5	9	CARDINAL
ejpam-3206	114	6	9	CARDINAL
ejpam-3206	114	7	0	CARDINAL
ejpam-3206	114	8	2	DATE
ejpam-3206	114	9	4	DATE
ejpam-3206	114	10	6	DATE
ejpam-3206	114	11	8	DATE
ejpam-3206	114	12	10	CARDINAL
ejpam-3206	114	13	2 〉	QUANTITY
ejpam-3206	114	14	10	CARDINAL
ejpam-3206	115	1	r.	NORP
ejpam-3206	116	1	two	CARDINAL
ejpam-3206	117	1	0	CARDINAL
ejpam-3206	117	2	6	CARDINAL
ejpam-3206	119	1	0	CARDINAL
ejpam-3206	121	1	9	CARDINAL
ejpam-3206	124	1	0	CARDINAL
ejpam-3206	124	2	r. nil	PERSON
ejpam-3206	124	3	0	CARDINAL
ejpam-3206	124	4	0	CARDINAL
ejpam-3206	124	5	r.	NORP
ejpam-3206	125	1	1	CARDINAL
ejpam-3206	125	2	2	CARDINAL
ejpam-3206	125	3	1	CARDINAL
ejpam-3206	127	1	m. a. farahat	PERSON
ejpam-3206	127	2	s. t. al-bogamy	PERSON
ejpam-3206	128	1	j. pure	PERSON
ejpam-3206	128	2	11	CARDINAL
ejpam-3206	128	3	1	CARDINAL
ejpam-3206	128	4	2018	DATE
ejpam-3206	128	5	244	CARDINAL
ejpam-3206	129	1	0	CARDINAL
ejpam-3206	129	2	4	CARDINAL
ejpam-3206	129	3	= kr	PERSON
ejpam-3206	129	4	k =	PERSON
ejpam-3206	129	5	1 1	CARDINAL
ejpam-3206	132	1	10	CARDINAL
ejpam-3206	136	1	∈	ORG
ejpam-3206	137	1	0	CARDINAL
ejpam-3206	137	2	0	CARDINAL
ejpam-3206	138	1	0	CARDINAL
ejpam-3206	138	2	two	CARDINAL
ejpam-3206	139	1	two	CARDINAL
ejpam-3206	140	1	0	CARDINAL
ejpam-3206	143	1	11	CARDINAL
ejpam-3206	145	1	αa+	PERSON
ejpam-3206	145	2	0	CARDINAL
ejpam-3206	146	1	0	CARDINAL
ejpam-3206	146	2	0	CARDINAL
ejpam-3206	147	1	1	CARDINAL
ejpam-3206	147	2	0	CARDINAL
ejpam-3206	147	3	2	CARDINAL
ejpam-3206	148	1	0	CARDINAL
ejpam-3206	148	2	3	CARDINAL
ejpam-3206	149	1	0	CARDINAL
ejpam-3206	149	2	2	CARDINAL
ejpam-3206	149	3	4	CARDINAL
ejpam-3206	149	4	nv	ORG
ejpam-3206	150	1	nv	ORG
ejpam-3206	151	1	nv	GPE
ejpam-3206	154	1	0	CARDINAL
ejpam-3206	154	2	nv	GPE
ejpam-3206	156	1	rv	PERSON
ejpam-3206	157	1	rv	GPE
ejpam-3206	158	1	rv	GPE
ejpam-3206	161	1	m. a. farahat	PERSON
ejpam-3206	161	2	s. t. al-bogamy	PERSON
ejpam-3206	162	1	j. pure	PERSON
ejpam-3206	162	2	11	CARDINAL
ejpam-3206	162	3	1	CARDINAL
ejpam-3206	162	4	2018	DATE
ejpam-3206	162	5	244	CARDINAL
ejpam-3206	162	6	2	CARDINAL
ejpam-3206	164	1	1	CARDINAL
ejpam-3206	164	2	2	CARDINAL
ejpam-3206	165	1	3	CARDINAL
ejpam-3206	167	1	1	CARDINAL
ejpam-3206	167	2	0 6=	CARDINAL
ejpam-3206	169	1	l+	EVENT
ejpam-3206	169	2	1	CARDINAL
ejpam-3206	169	3	∈	ORG
ejpam-3206	169	4	j(r	GPE
ejpam-3206	169	5	1−	CARDINAL
ejpam-3206	169	6	r. 2	PERSON
ejpam-3206	170	1	l ⊂	ORG
ejpam-3206	173	1	2	CARDINAL
ejpam-3206	176	1	r.	NORP
ejpam-3206	176	2	lemma 2	ORG
ejpam-3206	177	1	r.	NORP
ejpam-3206	177	2	⊆	CARDINAL
ejpam-3206	178	1	1	CARDINAL
ejpam-3206	178	2	first	ORDINAL
ejpam-3206	178	3	⊆	CARDINAL
ejpam-3206	179	1	∈	ORG
ejpam-3206	181	1	al ⊆	ORG
ejpam-3206	182	1	∈	ORG
ejpam-3206	182	2	⊆	CARDINAL
ejpam-3206	183	1	0	CARDINAL
ejpam-3206	185	1	2	CARDINAL
ejpam-3206	186	1	∈	ORG
ejpam-3206	188	1	al ⊆	ORG
ejpam-3206	189	1	∈	ORG
ejpam-3206	189	2	∈	ORG
ejpam-3206	191	1	12	CARDINAL
ejpam-3206	192	1	8	CARDINAL
ejpam-3206	193	1	6	CARDINAL
ejpam-3206	194	1	2	CARDINAL
ejpam-3206	195	1	13	CARDINAL
ejpam-3206	196	1	11	CARDINAL
ejpam-3206	197	1	⊕	PERSON
ejpam-3206	199	1	⊕	PERSON
ejpam-3206	199	2	0	CARDINAL
ejpam-3206	199	3	0	DATE
ejpam-3206	199	4	0	CARDINAL
ejpam-3206	199	5	0	CARDINAL
ejpam-3206	200	1	⊕	GPE
ejpam-3206	201	1	0	CARDINAL
ejpam-3206	201	2	0	DATE
ejpam-3206	201	3	0	CARDINAL
ejpam-3206	201	4	0	CARDINAL
ejpam-3206	201	5	0	CARDINAL
ejpam-3206	202	1	two	CARDINAL
ejpam-3206	202	2	k ⊕	PERSON
ejpam-3206	202	3	0	CARDINAL
ejpam-3206	202	4	0	DATE
ejpam-3206	202	5	0	CARDINAL
ejpam-3206	202	6	0	CARDINAL
ejpam-3206	202	7	0	CARDINAL
ejpam-3206	203	1	m. a. farahat	PERSON
ejpam-3206	203	2	s. t. al-bogamy	PERSON
ejpam-3206	204	1	j. pure	PERSON
ejpam-3206	204	2	11	CARDINAL
ejpam-3206	204	3	1	CARDINAL
ejpam-3206	204	4	2018	DATE
ejpam-3206	204	5	244	CARDINAL
ejpam-3206	204	6	k ⊕	PERSON
ejpam-3206	204	7	0	CARDINAL
ejpam-3206	204	8	0	DATE
ejpam-3206	204	9	0	CARDINAL
ejpam-3206	204	10	0	CARDINAL
ejpam-3206	204	11	0	CARDINAL
ejpam-3206	204	12	0	CARDINAL
ejpam-3206	205	1	k ⊕	PERSON
ejpam-3206	205	2	a.	PERSON
ejpam-3206	205	3	⊕	PERSON
ejpam-3206	206	1	r.	NORP
ejpam-3206	206	2	sr	ORG
ejpam-3206	206	3	∈	ORG
ejpam-3206	208	1	∈	ORG
ejpam-3206	210	1	sr	ORG
ejpam-3206	212	1	∈	ORG
ejpam-3206	213	1	2	CARDINAL
ejpam-3206	215	1	0	CARDINAL
ejpam-3206	216	1	14	CARDINAL
ejpam-3206	216	2	1	CARDINAL
ejpam-3206	216	3	example 5	DATE
ejpam-3206	217	1	sr	ORG
ejpam-3206	217	2	0	CARDINAL
ejpam-3206	217	3	2	CARDINAL
ejpam-3206	218	1	2	CARDINAL
ejpam-3206	218	2	6	CARDINAL
ejpam-3206	219	1	3	CARDINAL
ejpam-3206	219	2	7	CARDINAL
ejpam-3206	220	1	4	CARDINAL
ejpam-3206	220	2	8	CARDINAL
ejpam-3206	220	3	0	CARDINAL
ejpam-3206	220	4	6	CARDINAL
ejpam-3206	221	1	sr	ORG
ejpam-3206	221	2	0	CARDINAL
ejpam-3206	221	3	6	CARDINAL
ejpam-3206	222	1	5	CARDINAL
ejpam-3206	222	2	example 11	DATE
ejpam-3206	222	3	0	CARDINAL
ejpam-3206	224	1	0	CARDINAL
ejpam-3206	225	1	3	CARDINAL
ejpam-3206	226	1	sr	ORG
ejpam-3206	226	2	⊆	CARDINAL
ejpam-3206	227	1	m. a. farahat	PERSON
ejpam-3206	227	2	s. t. al-bogamy	PERSON
ejpam-3206	228	1	j. pure	PERSON
ejpam-3206	228	2	11	CARDINAL
ejpam-3206	228	3	1	CARDINAL
ejpam-3206	228	4	2018	DATE
ejpam-3206	228	5	244	CARDINAL
ejpam-3206	229	1	∈	ORG
ejpam-3206	230	1	⊆	CARDINAL
ejpam-3206	231	1	∈	ORG
ejpam-3206	232	1	sr	ORG
ejpam-3206	232	2	⊆	CARDINAL
ejpam-3206	233	1	1. 1	CARDINAL
ejpam-3206	234	1	2	CARDINAL
ejpam-3206	235	1	3	CARDINAL
ejpam-3206	236	1	1	CARDINAL
ejpam-3206	236	2	14	CARDINAL
ejpam-3206	236	3	1	CARDINAL
ejpam-3206	238	1	2	CARDINAL
ejpam-3206	238	2	14	CARDINAL
ejpam-3206	238	3	5	CARDINAL
ejpam-3206	240	1	2	CARDINAL
ejpam-3206	244	1	3	CARDINAL
ejpam-3206	250	1	4	CARDINAL
ejpam-3206	251	1	example 9	DATE
ejpam-3206	253	1	15	CARDINAL
ejpam-3206	254	1	example 11	DATE
ejpam-3206	256	1	r1,m1	ORG
ejpam-3206	256	2	r2 ∈	PERSON
ejpam-3206	256	3	m1,m2 ∈m	ORG
ejpam-3206	257	1	∈	ORG
ejpam-3206	257	2	∈	ORG
ejpam-3206	258	1	2	CARDINAL
ejpam-3206	259	1	rege	ORG
ejpam-3206	259	2	19	CARDINAL
ejpam-3206	259	3	1997	DATE
ejpam-3206	259	4	first	ORDINAL
ejpam-3206	260	1	2	CARDINAL
ejpam-3206	265	1	0	CARDINAL
ejpam-3206	265	2	0 0	DATE
ejpam-3206	266	1	m. a. farahat	PERSON
ejpam-3206	266	2	s. t. al-bogamy	PERSON
ejpam-3206	267	1	j. pure	PERSON
ejpam-3206	267	2	11	CARDINAL
ejpam-3206	267	3	1	CARDINAL
ejpam-3206	267	4	2018	DATE
ejpam-3206	267	5	244	CARDINAL
ejpam-3206	270	1	3	CARDINAL
ejpam-3206	273	1	3	CARDINAL
ejpam-3206	273	2	hurwitz series	PERSON
ejpam-3206	273	3	one	CARDINAL
ejpam-3206	274	1	10	CARDINAL
ejpam-3206	274	2	hurwitz series	ORG
ejpam-3206	275	1	11	CARDINAL
ejpam-3206	275	2	12	CARDINAL
ejpam-3206	275	3	hurwitz series	ORG
ejpam-3206	276	1	5	CARDINAL
ejpam-3206	277	1	21	CARDINAL
ejpam-3206	278	1	hurwitz series rings	ORG
ejpam-3206	278	2	10	CARDINAL
ejpam-3206	278	3	11	DATE
ejpam-3206	278	4	12	DATE
ejpam-3206	278	5	7	DATE
ejpam-3206	278	6	8	DATE
ejpam-3206	278	7	4	CARDINAL
ejpam-3206	279	1	hurwitz series rings over	ORG
ejpam-3206	280	1	∞∑ i=0	PERSON
ejpam-3206	280	2	∈	ORG
ejpam-3206	281	1	two	CARDINAL
ejpam-3206	284	1	j=0	GPE
ejpam-3206	284	2	j ∈	PERSON
ejpam-3206	285	1		GPE
ejpam-3206	285	2	j=0	GPE
ejpam-3206	286	1	∞∑ n=0	PERSON
ejpam-3206	295	1	i+ j j	PERSON
ejpam-3206	296	1	1r	CARDINAL
ejpam-3206	296	2	r.	NORP
ejpam-3206	298	1	m. a. farahat	PERSON
ejpam-3206	298	2	s. t. al-bogamy	PERSON
ejpam-3206	299	1	j. pure	PERSON
ejpam-3206	299	2	11	CARDINAL
ejpam-3206	299	3	1	CARDINAL
ejpam-3206	299	4	2018	DATE
ejpam-3206	299	5	244	CARDINAL
ejpam-3206	299	6	〈 x	PERSON
ejpam-3206	299	7	x3	PERSON
ejpam-3206	299	8	〉	CARDINAL
ejpam-3206	299	9	〈 x	PERSON
ejpam-3206	299	10	x3	PERSON
ejpam-3206	302	1	〉	CARDINAL
ejpam-3206	303	1	〈 x	PERSON
ejpam-3206	303	2	x3	PERSON
ejpam-3206	303	3	〉	CARDINAL
ejpam-3206	305	1	1	CARDINAL
ejpam-3206	306	1	σ	PERSON
ejpam-3206	306	2	hurwitz series	PERSON
ejpam-3206	306	3	∞∑ i=0	WORK_OF_ART
ejpam-3206	306	4	∈	ORG
ejpam-3206	306	5	two	CARDINAL
ejpam-3206	310	1	j=0	GPE
ejpam-3206	310	2	j ∈	PERSON
ejpam-3206	310	3	σ	PERSON
ejpam-3206	311	1		GPE
ejpam-3206	311	2	j=0	GPE
ejpam-3206	312	1	∞∑ n=0	PERSON
ejpam-3206	312	2	aiσ	PERSON
ejpam-3206	316	1	aiσ i(bj)x	PERSON
ejpam-3206	317	1	σ	PERSON
ejpam-3206	317	2	hurwitz	ORG
ejpam-3206	317	3	hurwitz ring	ORG
ejpam-3206	318	1	two	CARDINAL
ejpam-3206	320	1	v∑ i=0	PERSON
ejpam-3206	320	2	aix	PRODUCT
ejpam-3206	321	1	j ∈ p	PERSON
ejpam-3206	322	1		GPE
ejpam-3206	322	2	n=0	PERSON
ejpam-3206	322	3	aiσ	PERSON
ejpam-3206	324	1	annin	PERSON
ejpam-3206	324	2	1	CARDINAL
ejpam-3206	325	1	3	CARDINAL
ejpam-3206	325	2	1	CARDINAL
ejpam-3206	326	1	0	CARDINAL
ejpam-3206	326	2	r.	NORP
ejpam-3206	327	1	4	CARDINAL
ejpam-3206	327	2	1	CARDINAL
ejpam-3206	328	1	1	CARDINAL
ejpam-3206	329	1	1	CARDINAL
ejpam-3206	329	2	2	CARDINAL
ejpam-3206	329	3	3	CARDINAL
ejpam-3206	329	4	r. lemma 5	PERSON
ejpam-3206	329	5	1	CARDINAL
ejpam-3206	332	1	13	CARDINAL
ejpam-3206	332	2	m. a. farahat	PERSON
ejpam-3206	332	3	s. t. al-bogamy	PERSON
ejpam-3206	333	1	j. pure	PERSON
ejpam-3206	333	2	11	CARDINAL
ejpam-3206	333	3	1	CARDINAL
ejpam-3206	333	4	2018	DATE
ejpam-3206	333	5	244	CARDINAL
ejpam-3206	333	6	4	CARDINAL
ejpam-3206	333	7	13	CARDINAL
ejpam-3206	335	1	0	CARDINAL
ejpam-3206	335	2	∈	ORG
ejpam-3206	337	1	6	CARDINAL
ejpam-3206	337	2	9	CARDINAL
ejpam-3206	338	1	1	CARDINAL
ejpam-3206	338	2	2	CARDINAL
ejpam-3206	340	1	7	CARDINAL
ejpam-3206	340	2	9	CARDINAL
ejpam-3206	342	1	hong	GPE
ejpam-3206	343	1	al.	PERSON
ejpam-3206	343	2	9	CARDINAL
ejpam-3206	343	3	5	CARDINAL
ejpam-3206	345	1	hurwitz series	ORG
ejpam-3206	347	1	8	CARDINAL
ejpam-3206	347	2	2.5	CARDINAL
ejpam-3206	348	1	17	CARDINAL
ejpam-3206	349	1	nil(r	ORG
ejpam-3206	351	1	1	CARDINAL
ejpam-3206	351	2	σ	ORG
ejpam-3206	352	1	2	CARDINAL
ejpam-3206	353	1	∈	ORG
ejpam-3206	354	1	∈	ORG
ejpam-3206	354	2	0	CARDINAL
ejpam-3206	355	1	3	CARDINAL
ejpam-3206	357	1	j=0	GPE
ejpam-3206	357	2	j ∈	PERSON
ejpam-3206	357	3	∈	ORG
ejpam-3206	359	1	9	CARDINAL
ejpam-3206	360	1	nil(r	ORG
ejpam-3206	362	1	1	CARDINAL
ejpam-3206	362	2	σ	ORG
ejpam-3206	363	1	2	CARDINAL
ejpam-3206	364	1	aix	PRODUCT
ejpam-3206	364	2	∈	ORG
ejpam-3206	365	1	∈	ORG
ejpam-3206	365	2	0	CARDINAL
ejpam-3206	366	1	3	CARDINAL
ejpam-3206	366	2	aix	PRODUCT
ejpam-3206	366	3	j ∈	PERSON
ejpam-3206	367	1	∈	ORG
ejpam-3206	367	2	0 ≤ j ≤ n.	QUANTITY
ejpam-3206	367	3	4	CARDINAL
ejpam-3206	368	1	nil(r	ORG
ejpam-3206	370	1	σ	PERSON
ejpam-3206	371	1	m. a. farahat	PERSON
ejpam-3206	371	2	s. t. al-bogamy	PERSON
ejpam-3206	372	1	j. pure	PERSON
ejpam-3206	372	2	11	CARDINAL
ejpam-3206	372	3	1	CARDINAL
ejpam-3206	372	4	2018	DATE
ejpam-3206	372	5	244	CARDINAL
ejpam-3206	373	1	σ	ORG
ejpam-3206	374	1	∈	ORG
ejpam-3206	376	1	j = 〈	PERSON
ejpam-3206	377	1	j = r	PERSON
ejpam-3206	377	2	1	CARDINAL
ejpam-3206	378	1	ϕ(x	LOC
ejpam-3206	379	1	∞∑ i=0 bix	WORK_OF_ART
ejpam-3206	380	1	j ∈ l	PERSON
ejpam-3206	382	1	∞∑ i=0 bix	ORG
ejpam-3206	382	2		GPE
ejpam-3206	382	3	j=0	GPE
ejpam-3206	383	1	nil(r	ORG
ejpam-3206	383	2	8	CARDINAL
ejpam-3206	383	3	∈	ORG
ejpam-3206	383	4	0 ≤	MONEY
ejpam-3206	383	5	0 ≤	QUANTITY
ejpam-3206	383	6	j. consequently	PERSON
ejpam-3206	383	7	bia ∈ nil(r	PERSON
ejpam-3206	383	8	0 ≤	MONEY
ejpam-3206	383	9	i. hence	PERSON
ejpam-3206	384	1	∈	ORG
ejpam-3206	384	2	0 ≤	MONEY
ejpam-3206	384	3	ϕ(x	LOC
ejpam-3206	386	1	r.	NORP
ejpam-3206	386	2	∈	ORG
ejpam-3206	387	1	∈	ORG
ejpam-3206	388	1	∈	ORG
ejpam-3206	389	1	/∈ l.	PERSON
ejpam-3206	389	2	l+	EVENT
ejpam-3206	390	1	f(x	ORG
ejpam-3206	394	1	j=0	GPE
ejpam-3206	394	2	j ∈	PERSON
ejpam-3206	394	3	1	CARDINAL
ejpam-3206	394	4	+ rb0	PERSON
ejpam-3206	395	1	0	CARDINAL
ejpam-3206	395	2	1	CARDINAL
ejpam-3206	396	1	0	CARDINAL
ejpam-3206	398	1	j	PERSON
ejpam-3206	398	2	r.	NORP
ejpam-3206	398	3	⊆	CARDINAL
ejpam-3206	398	4	∈	ORG
ejpam-3206	399	1	1	CARDINAL
ejpam-3206	399	2	⊆	CARDINAL
ejpam-3206	403	1	j ∈ l	PERSON
ejpam-3206	404	1	∞∑ i=0 bix	ORG
ejpam-3206	404	2		GPE
ejpam-3206	404	3	j=0	GPE
ejpam-3206	405	1	nil(r	ORG
ejpam-3206	405	2	8	CARDINAL
ejpam-3206	405	3	∈	ORG
ejpam-3206	405	4	0 ≤	MONEY
ejpam-3206	405	5	0 ≤	QUANTITY
ejpam-3206	405	6	j. consequently	PERSON
ejpam-3206	405	7	bia ∈ nil(r	PERSON
ejpam-3206	405	8	m. a. farahat	PERSON
ejpam-3206	405	9	s. t. al-bogamy	PERSON
ejpam-3206	406	1	j. pure	PERSON
ejpam-3206	406	2	11	CARDINAL
ejpam-3206	406	3	1	CARDINAL
ejpam-3206	406	4	2018	DATE
ejpam-3206	406	5	244	CARDINAL
ejpam-3206	406	6	0 ≤	MONEY
ejpam-3206	407	1	∈	ORG
ejpam-3206	407	2	0 ≤	MONEY
ejpam-3206	407	3	ϕ(x	LOC
ejpam-3206	408	1	2	CARDINAL
ejpam-3206	408	2	∈	ORG
ejpam-3206	409	1	∈	ORG
ejpam-3206	410	1	ϕ(x	LOC
ejpam-3206	411	1	∞∑ i=0 bix	WORK_OF_ART
ejpam-3206	411	2	ϕ(x	LOC
ejpam-3206	412	1	j ∈ l	PERSON
ejpam-3206	414	1	∞∑ i=0 bix	ORG
ejpam-3206	414	2		GPE
ejpam-3206	414	3	j=0	GPE
ejpam-3206	415	1	nil(r	ORG
ejpam-3206	415	2	8	CARDINAL
ejpam-3206	415	3	∈	ORG
ejpam-3206	415	4	0 ≤	MONEY
ejpam-3206	415	5	0 ≤	QUANTITY
ejpam-3206	415	6	j. consequently	PERSON
ejpam-3206	415	7	bia ∈ nil(r	PERSON
ejpam-3206	415	8	0 ≤	MONEY
ejpam-3206	415	9	∈	ORG
ejpam-3206	415	10	bia2	ORG
ejpam-3206	417	1	bian	NORP
ejpam-3206	417	2	0 ≤	MONEY
ejpam-3206	418	1	∈	ORG
ejpam-3206	418	2	0 ≤	MONEY
ejpam-3206	418	3	i.	PERSON
ejpam-3206	418	4	0 ≤	MONEY
ejpam-3206	420	1	∞∑ i=0 bix	WORK_OF_ART
ejpam-3206	420	2	∈	ORG
ejpam-3206	423	1	nil(r	ORG
ejpam-3206	425	1	σ	PERSON
ejpam-3206	426	1	5	CARDINAL
ejpam-3206	427	1	nil(r	ORG
ejpam-3206	428	1	σ	PERSON
ejpam-3206	430	1	4	CARDINAL
ejpam-3206	431	1	σ	PERSON
ejpam-3206	431	2	2	CARDINAL
ejpam-3206	431	3	∈	ORG
ejpam-3206	432	1	0 ≤	MONEY
ejpam-3206	432	2	i.	PERSON
ejpam-3206	432	3	0 ≤	MONEY
ejpam-3206	432	4	i. so ϕ(x	PERSON
ejpam-3206	434	1	∞∑ i=0 bix	WORK_OF_ART
ejpam-3206	434	2	∈	ORG
ejpam-3206	436	1	258	CARDINAL
ejpam-3206	436	2	5	CARDINAL
ejpam-3206	437	1	nil(r	ORG
ejpam-3206	438	1	σ	PERSON
ejpam-3206	439	1	σ	ORG
ejpam-3206	439	2	hurwitz series	ORG
ejpam-3206	439	3	σ	PERSON
ejpam-3206	439	4	hurwitz series ring over	ORG
ejpam-3206	439	5	hurwitz polynomial ring p	ORG
ejpam-3206	439	6	σ	PERSON
ejpam-3206	439	7	hurwitz polynomial ring over	ORG
ejpam-3206	439	8	6	CARDINAL
ejpam-3206	440	1	nil(r	ORG
ejpam-3206	441	1	hurwitz series ring over hr	ORG
ejpam-3206	443	1	nil(r	ORG
ejpam-3206	444	1	hurwitz polynomial ring over hr	ORG
ejpam-3206	446	1	1	CARDINAL
ejpam-3206	446	2	s. annin	PERSON
ejpam-3206	448	1	j. algebr	PERSON
ejpam-3206	449	1	3:193–205, 2004	DATE
ejpam-3206	450	1	2	CARDINAL
ejpam-3206	451	1	baer	PERSON
ejpam-3206	452	1	j. aust	PERSON
ejpam-3206	454	1	18:470–473, 1974	DATE
ejpam-3206	455	1	3	CARDINAL
ejpam-3206	455	2	n. al-harthy	PERSON
ejpam-3206	457	1	hacettepe journal	PERSON
ejpam-3206	457	2	46(5):1–6	DATE
ejpam-3206	457	3	2017	DATE
ejpam-3206	458	1	4	CARDINAL
ejpam-3206	458	2	s. al-nafaie	PERSON
ejpam-3206	459	1	hurwitz series rings.	ORG
ejpam-3206	460	1	far east journal of mathematical sciences	ORG
ejpam-3206	460	2	101(12):2767–2784	CARDINAL
ejpam-3206	460	3	2017	DATE
ejpam-3206	461	1	5	CARDINAL
ejpam-3206	463	1	bull	PERSON
ejpam-3206	466	1	fr	PERSON
ejpam-3206	467	1	102:181–191,	DATE
ejpam-3206	467	2	1974	DATE
ejpam-3206	468	1	6	CARDINAL
ejpam-3206	468	2	r. gordon	PERSON
ejpam-3206	469	1	pac	PERSON
ejpam-3206	470	1	j. math	PERSON
ejpam-3206	470	2	692	CARDINAL
ejpam-3206	470	3	1969	DATE
ejpam-3206	471	1	7	CARDINAL
ejpam-3206	472	1	baer	PERSON
ejpam-3206	473	1	bull	ORG
ejpam-3206	474	1	iranian	NORP
ejpam-3206	475	1	37(1):1–13, 2011	DATE
ejpam-3206	476	1	8	CARDINAL
ejpam-3206	476	2	a. hassanein	PERSON
ejpam-3206	476	3	m. farahat	PERSON
ejpam-3206	477	1	hurwitz series	PERSON
ejpam-3206	478	1	lxix(i):169–178	GPE
ejpam-3206	478	2	2014	DATE
ejpam-3206	479	1	259	CARDINAL
ejpam-3206	479	2	9	CARDINAL
ejpam-3206	479	3	c. hong	PERSON
ejpam-3206	479	4	n. kim	PERSON
ejpam-3206	479	5	t. kwak	PERSON
ejpam-3206	480	1	baer	ORG
ejpam-3206	481	1	j. pure	PERSON
ejpam-3206	481	2	2000	DATE
ejpam-3206	482	1	10	CARDINAL
ejpam-3206	482	2	w. keigher	PERSON
ejpam-3206	483	1	adjunctions	PERSON
ejpam-3206	485	1	j. math	PERSON
ejpam-3206	485	2	248:99–112	CARDINAL
ejpam-3206	485	3	1975	DATE
ejpam-3206	486	1	11	CARDINAL
ejpam-3206	486	2	w. keigher	PERSON
ejpam-3206	487	1	hurwitz series	ORG
ejpam-3206	489	1	25(6):1845–1859, 1997	DATE
ejpam-3206	490	1	12	CARDINAL
ejpam-3206	490	2	w. keigher	PERSON
ejpam-3206	490	3	f. pritchard	PERSON
ejpam-3206	491	1	hurwitz series	PERSON
ejpam-3206	492	1	j. pure	PERSON
ejpam-3206	493	1	146:291–304, 2000	DATE
ejpam-3206	494	1	13	CARDINAL
ejpam-3206	494	2	j. krempa	PERSON
ejpam-3206	496	1	colloq	PERSON
ejpam-3206	496	2	3:289–300, 1996	DATE
ejpam-3206	497	1	14	CARDINAL
ejpam-3206	497	2	z. liu	PERSON
ejpam-3206	497	3	f. li	PERSON
ejpam-3206	497	4	generalized power series	ORG
ejpam-3206	499	1	26:2283–2291	CARDINAL
ejpam-3206	499	2	1998	DATE
ejpam-3206	500	1	15	CARDINAL
ejpam-3206	500	2	w. nicholson	PERSON
ejpam-3206	500	3	j. watters	PERSON
ejpam-3206	503	1	amer	PERSON
ejpam-3206	504	1	102:443–450, 1988	DATE
ejpam-3206	505	1	16	CARDINAL
ejpam-3206	505	2	l. ouyang	PERSON
ejpam-3206	505	3	glasg	PERSON
ejpam-3206	507	1	j.	PERSON
ejpam-3206	507	2	51:525–537	DATE
ejpam-3206	507	3	2009	DATE
ejpam-3206	508	1	17	CARDINAL
ejpam-3206	510	1	hurwitz series rings	ORG
ejpam-3206	512	1	circ	PERSON
ejpam-3206	513	1	palermo.	PERSON
ejpam-3206	513	2	2016	DATE
ejpam-3206	514	1	18	CARDINAL
ejpam-3206	517	1	czec	GPE
ejpam-3206	519	1	j.	PERSON
ejpam-3206	519	2	67(142):389–398	DATE
ejpam-3206	519	3	2017	DATE
ejpam-3206	520	1	19	CARDINAL
ejpam-3206	520	2	m. rege	PERSON
ejpam-3206	520	3	s. chhawchharia	PERSON
ejpam-3206	523	1	japan	GPE
ejpam-3206	524	1	ser	PERSON
ejpam-3206	526	1	sci.	ORG
ejpam-3206	526	2	73:14–17, 1997	DATE
ejpam-3206	527	1	20	CARDINAL
ejpam-3206	527	2	r. salem	GPE
ejpam-3206	527	3	m. farahat	PERSON
ejpam-3206	527	4	h. abd-elmalk	PERSON
ejpam-3206	530	1	j. math	PERSON
ejpam-3206	532	1	sci.	ORG
ejpam-3206	532	2	2015	DATE
ejpam-3206	533	1	21	CARDINAL
ejpam-3206	533	2	e. taft	PERSON
ejpam-3206	534	1	hurwitz invertibility	PERSON
ejpam-3206	536	1	numerantium	PERSON
ejpam-3206	536	2	73:37–40, 1990	DATE
ejpam-3206	537	1	22	CARDINAL
ejpam-3206	539	1	riv	PERSON
ejpam-3206	540	1	univ	NORP
ejpam-3206	541	1	parma	PERSON
ejpam-3206	541	2	n.s.	GPE
ejpam-3206	541	3	1(5):311	CARDINAL
ejpam-3206	541	4	315, 1992	DATE