id	sid	eid	entity	type
ejpam-4753	1	1	european journal	ORG
ejpam-4753	2	1	16	CARDINAL
ejpam-4753	2	2	3	CARDINAL
ejpam-4753	2	3	2023, 1913-1939	DATE
ejpam-4753	2	4	1307-5543	DATE
ejpam-4753	2	5	new york	GPE
ejpam-4753	2	6	ahmed ould chbih1,∗	PERSON
ejpam-4753	2	7	mohamed ben faraj ben maaouia2	PERSON
ejpam-4753	2	8	sanghare3 1	FAC
ejpam-4753	2	9	nouakchott	DATE
ejpam-4753	2	10	mauritanie 2	ORG
ejpam-4753	2	11	gaston berger	PERSON
ejpam-4753	2	12	saint-louis	GPE
ejpam-4753	2	13	anta diop	PERSON
ejpam-4753	2	14	dakar	PERSON
ejpam-4753	2	15	ucad	GPE
ejpam-4753	3	1	−1	DATE
ejpam-4753	3	2	−1	DATE
ejpam-4753	3	3	−1	DATE
ejpam-4753	5	1	−1	DATE
ejpam-4753	6	1	−1	DATE
ejpam-4753	6	2	−1	DATE
ejpam-4753	7	1	−1	DATE
ejpam-4753	15	1	2020	DATE
ejpam-4753	15	2	13a02	CARDINAL
ejpam-4753	15	3	16w50	CARDINAL
ejpam-4753	15	4	18c40	CARDINAL
ejpam-4753	15	5	18g35	CARDINAL
ejpam-4753	15	6	13d45	CARDINAL
ejpam-4753	16	1	a. o. chbih	PERSON
ejpam-4753	16	2	m. b. maaouia	PERSON
ejpam-4753	16	3	mamadou.sanghare@ucad.edu.sn	DATE
ejpam-4753	16	4	1913	DATE
ejpam-4753	17	1	2023	CARDINAL
ejpam-4753	18	1	a. o. chbih	PERSON
ejpam-4753	18	2	m. b. maaouia	PERSON
ejpam-4753	18	3	m. sanghare	PERSON
ejpam-4753	19	1	j. pure	PERSON
ejpam-4753	19	2	16	CARDINAL
ejpam-4753	19	3	3	CARDINAL
ejpam-4753	19	4	2023	CARDINAL
ejpam-4753	19	5	1913-1939 1914 1	DATE
ejpam-4753	21	1	gr(a − mod	PERSON
ejpam-4753	23	1	8	CARDINAL
ejpam-4753	23	2	2	CARDINAL
ejpam-4753	23	3	1	CARDINAL
ejpam-4753	24	1	second	ORDINAL
ejpam-4753	24	2	10	CARDINAL
ejpam-4753	25	1	11],[4	CARDINAL
ejpam-4753	25	2	9	CARDINAL
ejpam-4753	26	1	section 3	LAW
ejpam-4753	29	1	degree k ∈ z	PERSON
ejpam-4753	29	2	−1	DATE
ejpam-4753	29	3	−1	DATE
ejpam-4753	29	4	degree k ∈ z	PERSON
ejpam-4753	30	1	−1	DATE
ejpam-4753	31	1	degree k ∈ z	PERSON
ejpam-4753	33	1	m. b. maaouia	PERSON
ejpam-4753	33	2	m. sanghare	PERSON
ejpam-4753	34	1	j. pure	PERSON
ejpam-4753	34	2	16	CARDINAL
ejpam-4753	34	3	3	CARDINAL
ejpam-4753	34	4	2023	CARDINAL
ejpam-4753	34	5	1913-1939 1915	DATE
ejpam-4753	34	6	−1	CARDINAL
ejpam-4753	35	1	−1	DATE
ejpam-4753	36	1	−1	DATE
ejpam-4753	36	2	m(n−1	ORG
ejpam-4753	37	1	m(n	PERSON
ejpam-4753	37	2	1	CARDINAL
ejpam-4753	38	1	1	CARDINAL
ejpam-4753	38	2	−1	CARDINAL
ejpam-4753	39	1	//	PERSON
ejpam-4753	39	2	−1	DATE
ejpam-4753	40	1	−1	DATE
ejpam-4753	40	2	dn)//	FAC
ejpam-4753	40	3	1	CARDINAL
ejpam-4753	42	1	//	PERSON
ejpam-4753	42	2	−1	CARDINAL
ejpam-4753	42	3	d′n+1+k)//	ORG
ejpam-4753	42	4	−1	DATE
ejpam-4753	42	5	n(n	NORP
ejpam-4753	43	1	−1	DATE
ejpam-4753	43	2	1	CARDINAL
ejpam-4753	43	3	−1	DATE
ejpam-4753	43	4	−1	DATE
ejpam-4753	44	1	−1	DATE
ejpam-4753	45	1	−1	DATE
ejpam-4753	45	2	−1	DATE
ejpam-4753	46	1	−1	DATE
ejpam-4753	52	1	gr(a − mod	PERSON
ejpam-4753	53	1	gr(a − mod	PERSON
ejpam-4753	53	2	gr(a − mod	PERSON
ejpam-4753	54	1	vi	PERSON
ejpam-4753	57	1	a. o. chbih	PERSON
ejpam-4753	57	2	m. b. maaouia	PERSON
ejpam-4753	57	3	m. sanghare	PERSON
ejpam-4753	58	1	j. pure	PERSON
ejpam-4753	58	2	16	CARDINAL
ejpam-4753	58	3	3	CARDINAL
ejpam-4753	58	4	2023	CARDINAL
ejpam-4753	58	5	1913-1939	DATE
ejpam-4753	58	6	1	CARDINAL
ejpam-4753	59	1	⊂ an+m	PERSON
ejpam-4753	59	2	∀ n	ORG
ejpam-4753	59	3	∈ z.	PERSON
ejpam-4753	63	1	3	CARDINAL
ejpam-4753	64	1	mn	GPE
ejpam-4753	64	2	md ⊂ mn+d	PERSON
ejpam-4753	64	3	∀ n	ORG
ejpam-4753	64	4	4	DATE
ejpam-4753	66	1	mn	GPE
ejpam-4753	66	2	∀x	ORG
ejpam-4753	67	1	mn	GPE
ejpam-4753	67	2	m(n	PERSON
ejpam-4753	68	1	⊕ k≥n	PERSON
ejpam-4753	68	2	2	CARDINAL
ejpam-4753	69	1	1	CARDINAL
ejpam-4753	69	2	⊂	GPE
ejpam-4753	70	1	proof	PERSON
ejpam-4753	71	1	m(n	PERSON
ejpam-4753	71	2	⊕ k≥n	PERSON
ejpam-4753	71	3	mn+k	GPE
ejpam-4753	72	1	m(n	GPE
ejpam-4753	72	2	⊕ k≥n	PERSON
ejpam-4753	74	1	2	CARDINAL
ejpam-4753	74	2	1	CARDINAL
ejpam-4753	75	1	⊂	GPE
ejpam-4753	75	2	a. o. chbih	PERSON
ejpam-4753	75	3	m. b. maaouia	PERSON
ejpam-4753	75	4	m. sanghare	PERSON
ejpam-4753	76	1	j. pure	PERSON
ejpam-4753	76	2	16	CARDINAL
ejpam-4753	76	3	3	CARDINAL
ejpam-4753	76	4	2023	CARDINAL
ejpam-4753	76	5	1913-1939 1917	DATE
ejpam-4753	76	6	5	DATE
ejpam-4753	77	1	mn	GPE
ejpam-4753	77	2	n = ⊕	GPE
ejpam-4753	77	3	two	CARDINAL
ejpam-4753	78	1	degree k ∈ z	PERSON
ejpam-4753	79	1	∈	ORG
ejpam-4753	79	2	1	CARDINAL
ejpam-4753	80	1	k ∈ z.	PERSON
ejpam-4753	82	1	3	CARDINAL
ejpam-4753	82	2	6	CARDINAL
ejpam-4753	84	1	dn→ cn−1 dn−1→	GPE
ejpam-4753	84	2	a−	ORG
ejpam-4753	84	3	0	CARDINAL
ejpam-4753	84	4	7	DATE
ejpam-4753	85	1	d′	PERSON
ejpam-4753	91	1	d′	PERSON
ejpam-4753	94	1	d′n+1 //	ORG
ejpam-4753	98	1	n−1 //	ORG
ejpam-4753	99	1	∈	ORG
ejpam-4753	102	1	3	CARDINAL
ejpam-4753	102	2	3	CARDINAL
ejpam-4753	104	1	= ker dn	PERSON
ejpam-4753	104	2	d′	PERSON
ejpam-4753	106	1	d′	PERSON
ejpam-4753	107	1	a. o. chbih	PERSON
ejpam-4753	107	2	m. b. maaouia	PERSON
ejpam-4753	107	3	m. sanghare	PERSON
ejpam-4753	108	1	j. pure	PERSON
ejpam-4753	108	2	16	CARDINAL
ejpam-4753	108	3	3	CARDINAL
ejpam-4753	108	4	2023	CARDINAL
ejpam-4753	108	5	1913-1939	DATE
ejpam-4753	109	1	3	CARDINAL
ejpam-4753	109	2	2	CARDINAL
ejpam-4753	111	1	f−→	CARDINAL
ejpam-4753	111	2	′′	ORG
ejpam-4753	113	1	′′	ORG
ejpam-4753	116	1	3	CARDINAL
ejpam-4753	116	2	8	CARDINAL
ejpam-4753	117	1	two	CARDINAL
ejpam-4753	117	2	two	CARDINAL
ejpam-4753	120	1	6	CARDINAL
ejpam-4753	123	1	6	CARDINAL
ejpam-4753	124	1	6	CARDINAL
ejpam-4753	126	1	s.	PERSON
ejpam-4753	126	2	9	DATE
ejpam-4753	127	1	s. proposition 7	ORG
ejpam-4753	129	1	a. o. chbih	PERSON
ejpam-4753	129	2	m. b. maaouia	PERSON
ejpam-4753	129	3	m. sanghare	PERSON
ejpam-4753	130	1	j. pure	PERSON
ejpam-4753	130	2	16	CARDINAL
ejpam-4753	130	3	3	CARDINAL
ejpam-4753	130	4	2023	CARDINAL
ejpam-4753	130	5	1913-1939	DATE
ejpam-4753	132	1	si ∈ s	PERSON
ejpam-4753	133	1	1	CARDINAL
ejpam-4753	137	1	sph ⊂	ORG
ejpam-4753	139	1	5	CARDINAL
ejpam-4753	139	2	sph ⊂	ORG
ejpam-4753	140	1	2	CARDINAL
ejpam-4753	143	1	3	CARDINAL
ejpam-4753	144	1	3	CARDINAL
ejpam-4753	145	1	mn	GPE
ejpam-4753	145	2	n = ⊕	GPE
ejpam-4753	146	1	two	CARDINAL
ejpam-4753	146	2	degree k ∈ z	PERSON
ejpam-4753	147	1	7−→	CARDINAL
ejpam-4753	147	2	degree k ∈ z	PERSON
ejpam-4753	149	1	1	CARDINAL
ejpam-4753	151	1	∈	ORG
ejpam-4753	151	2	s−1	NORP
ejpam-4753	151	3	deg(m)− deg(s	PERSON
ejpam-4753	151	4	a. o. chbih	PERSON
ejpam-4753	151	5	m. b. maaouia	PERSON
ejpam-4753	151	6	m. sanghare	PERSON
ejpam-4753	152	1	j. pure	PERSON
ejpam-4753	152	2	16	CARDINAL
ejpam-4753	152	3	3	CARDINAL
ejpam-4753	152	4	2023	CARDINAL
ejpam-4753	152	5	1913-1939 1920	DATE
ejpam-4753	152	6	deg(m	ORG
ejpam-4753	152	7	+ k)− deg(s	PERSON
ejpam-4753	153	1	degree k ∈ z	PERSON
ejpam-4753	155	1	mn	GPE
ejpam-4753	155	2	n = ⊕	GPE
ejpam-4753	156	1	two	CARDINAL
ejpam-4753	156	2	degree k ∈ z	PERSON
ejpam-4753	156	3	degree k ∈ z	PERSON
ejpam-4753	156	4	−1	DATE
ejpam-4753	157	1	6	CARDINAL
ejpam-4753	157	2	9	CARDINAL
ejpam-4753	157	3	−1	DATE
ejpam-4753	157	4	10	CARDINAL
ejpam-4753	158	1	mn	GPE
ejpam-4753	158	2	n = ⊕	GPE
ejpam-4753	159	1	nn	GPE
ejpam-4753	159	2	l =⊕	PERSON
ejpam-4753	159	3	three	CARDINAL
ejpam-4753	159	4	degree k ∈ z	PERSON
ejpam-4753	159	5	0 −→ m	QUANTITY
ejpam-4753	159	6	degree k ∈ z	PERSON
ejpam-4753	162	1	3.4	CARDINAL
ejpam-4753	162	2	8	CARDINAL
ejpam-4753	163	1	m. b. maaouia	PERSON
ejpam-4753	163	2	m. sanghare	PERSON
ejpam-4753	164	1	j. pure	PERSON
ejpam-4753	164	2	16	CARDINAL
ejpam-4753	164	3	3	CARDINAL
ejpam-4753	164	4	2023	CARDINAL
ejpam-4753	164	5	1913-1939 1921	DATE
ejpam-4753	164	6	degree k ∈ z	PERSON
ejpam-4753	165	1	3	CARDINAL
ejpam-4753	166	1	mn	GPE
ejpam-4753	166	2	n = ⊕	GPE
ejpam-4753	166	3	nn	GPE
ejpam-4753	167	1	l = ⊕	PERSON
ejpam-4753	167	2	three	CARDINAL
ejpam-4753	167	3	degree k ∈ z	PERSON
ejpam-4753	167	4	0 −→ m	QUANTITY
ejpam-4753	169	1	degree k ∈ z	PERSON
ejpam-4753	171	1	6	CARDINAL
ejpam-4753	172	1	mn	GPE
ejpam-4753	172	2	n = ⊕	GPE
ejpam-4753	172	3	nn	GPE
ejpam-4753	173	1	l = ⊕	PERSON
ejpam-4753	173	2	three	CARDINAL
ejpam-4753	173	3	degree k ∈ z	PERSON
ejpam-4753	173	4	0 −→ m	QUANTITY
ejpam-4753	174	1	degree k ∈ z	PERSON
ejpam-4753	177	1	3	CARDINAL
ejpam-4753	177	2	a. o. chbih	PERSON
ejpam-4753	177	3	m. b. maaouia	PERSON
ejpam-4753	177	4	m. sanghare	PERSON
ejpam-4753	178	1	j. pure	PERSON
ejpam-4753	178	2	16	CARDINAL
ejpam-4753	178	3	3	CARDINAL
ejpam-4753	178	4	2023	CARDINAL
ejpam-4753	178	5	1913-1939 1922	DATE
ejpam-4753	178	6	4	DATE
ejpam-4753	180	1	gr(a − mod	PERSON
ejpam-4753	180	2	degree k ∈ z	PERSON
ejpam-4753	182	1	degree k ∈ z	PERSON
ejpam-4753	184	1	s−1	NORP
ejpam-4753	187	1	s−1	NORP
ejpam-4753	189	1	s−1(1m	PERSON
ejpam-4753	191	1	1s−1	CARDINAL
ejpam-4753	192	1	s−1	NORP
ejpam-4753	192	2	s−1(1m	PERSON
ejpam-4753	193	1	1s−1	CARDINAL
ejpam-4753	193	2	a. o. chbih	PERSON
ejpam-4753	193	3	m. b. maaouia	PERSON
ejpam-4753	193	4	m. sanghare	PERSON
ejpam-4753	194	1	j. pure	PERSON
ejpam-4753	194	2	16	CARDINAL
ejpam-4753	194	3	3	CARDINAL
ejpam-4753	194	4	2023	CARDINAL
ejpam-4753	194	5	1913-1939	DATE
ejpam-4753	197	1	deg(m	ORG
ejpam-4753	197	2	+ k)− deg(s	PERSON
ejpam-4753	198	1	11	CARDINAL
ejpam-4753	199	1	gr(a − mod	PERSON
ejpam-4753	199	2	−1	DATE
ejpam-4753	199	3	degree k ∈ z	PERSON
ejpam-4753	200	1	−1	DATE
ejpam-4753	201	1	4	CARDINAL
ejpam-4753	202	1	degree k ∈ z	PERSON
ejpam-4753	203	1	s−1	NORP
ejpam-4753	206	1	11	CARDINAL
ejpam-4753	207	1	12	CARDINAL
ejpam-4753	208	1	degree k ∈ z	PERSON
ejpam-4753	210	1	8 sph	QUANTITY
ejpam-4753	210	2	gr(a − mod	PERSON
ejpam-4753	211	1	two	CARDINAL
ejpam-4753	213	1	m. b. maaouia	PERSON
ejpam-4753	213	2	m. sanghare	PERSON
ejpam-4753	214	1	j. pure	PERSON
ejpam-4753	214	2	16	CARDINAL
ejpam-4753	214	3	3	CARDINAL
ejpam-4753	214	4	2023	CARDINAL
ejpam-4753	214	5	1913-1939	DATE
ejpam-4753	214	6	1924	DATE
ejpam-4753	215	1	−1	DATE
ejpam-4753	216	1	deg(m)− deg(s	PERSON
ejpam-4753	217	1	deg(m	ORG
ejpam-4753	217	2	+ k)− deg(s	PERSON
ejpam-4753	218	1	+ k.	PERSON
ejpam-4753	219	1	10	CARDINAL
ejpam-4753	221	1	mn	GPE
ejpam-4753	222	1	aph	PRODUCT
ejpam-4753	223	1	mph	CARDINAL
ejpam-4753	224	1	6	CARDINAL
ejpam-4753	226	1	degree k ∈ z	PERSON
ejpam-4753	230	1	2	CARDINAL
ejpam-4753	230	2	4.	CARDINAL
ejpam-4753	230	3	13	CARDINAL
ejpam-4753	231	1	mn	GPE
ejpam-4753	231	2	n = ⊕	GPE
ejpam-4753	231	3	two	CARDINAL
ejpam-4753	232	1	degree k ∈ z	PERSON
ejpam-4753	233	1	m(n	PERSON
ejpam-4753	233	2	m. b. maaouia	PERSON
ejpam-4753	233	3	m. sanghare	PERSON
ejpam-4753	234	1	j. pure	PERSON
ejpam-4753	234	2	16	CARDINAL
ejpam-4753	234	3	3	CARDINAL
ejpam-4753	234	4	2023	CARDINAL
ejpam-4753	234	5	1913-1939	DATE
ejpam-4753	234	6	1925	DATE
ejpam-4753	235	1	degree k ∈ z	PERSON
ejpam-4753	237	1	degree k ∈ z	PERSON
ejpam-4753	237	2	m(n	PERSON
ejpam-4753	237	3	∈ m(n	PERSON
ejpam-4753	238	1	degree k ∈ z	PERSON
ejpam-4753	240	1	mn	GPE
ejpam-4753	240	2	n = ⊕	GPE
ejpam-4753	240	3	two	CARDINAL
ejpam-4753	241	1	degree k ∈ z	PERSON
ejpam-4753	241	2	−→ n(k	PERSON
ejpam-4753	243	1	degree k ∈ z	PERSON
ejpam-4753	243	2	n(k	PERSON
ejpam-4753	243	3	∈	ORG
ejpam-4753	243	4	∑ i∈z mi =⇒	PERSON
ejpam-4753	244	1	∑ i∈z mi	PERSON
ejpam-4753	246	1	5	CARDINAL
ejpam-4753	247	1	gr(a − mod	PERSON
ejpam-4753	248	1	m(n	PERSON
ejpam-4753	248	2	degree k ∈ z	PERSON
ejpam-4753	250	1	degree k ∈ z	PERSON
ejpam-4753	250	2	m(n	GPE
ejpam-4753	250	3	n(n	GPE
ejpam-4753	251	1	m(n	PERSON
ejpam-4753	251	2	m(n	GPE
ejpam-4753	251	3	n(n	GPE
ejpam-4753	251	4	m(n	GPE
ejpam-4753	251	5	n(n	ORG
ejpam-4753	253	1	m(n	PERSON
ejpam-4753	254	1	degree k ∈ z	PERSON
ejpam-4753	255	1	m(n	PERSON
ejpam-4753	255	2	m(n	PERSON
ejpam-4753	258	1	a. o. chbih	PERSON
ejpam-4753	258	2	m. b. maaouia	PERSON
ejpam-4753	258	3	m. sanghare	PERSON
ejpam-4753	259	1	j. pure	PERSON
ejpam-4753	259	2	16	CARDINAL
ejpam-4753	259	3	3	CARDINAL
ejpam-4753	259	4	2023	CARDINAL
ejpam-4753	259	5	1913-1939 1926	DATE
ejpam-4753	262	1	∈ m(n	PERSON
ejpam-4753	265	1	m(n	PERSON
ejpam-4753	265	2	1	CARDINAL
ejpam-4753	265	3	m(n	PERSON
ejpam-4753	265	4	7→ 1m(n)(n)(m	DATE
ejpam-4753	265	5	1m(n)(m	CARDINAL
ejpam-4753	266	1	1(−)(n)(m)(m	CARDINAL
ejpam-4753	269	1	∈	ORG
ejpam-4753	272	1	k ∈ z. proposition	PERSON
ejpam-4753	272	2	14	DATE
ejpam-4753	273	1	mn	GPE
ejpam-4753	274	1	mn	GPE
ejpam-4753	276	1	1	CARDINAL
ejpam-4753	276	2	m(n	PERSON
ejpam-4753	277	1	m(n	PERSON
ejpam-4753	277	2	1	CARDINAL
ejpam-4753	278	1	1	CARDINAL
ejpam-4753	280	1	m(n	PERSON
ejpam-4753	281	1	mn+k	DATE
ejpam-4753	281	2	⊕ k≥n	PERSON
ejpam-4753	281	3	1	CARDINAL
ejpam-4753	281	4	⊕ m(n	PERSON
ejpam-4753	282	1	⊕ mn	GPE
ejpam-4753	284	1	1	CARDINAL
ejpam-4753	284	2	+ z.	PERSON
ejpam-4753	284	3	m(n	PERSON
ejpam-4753	284	4	1	CARDINAL
ejpam-4753	285	1	a. o. chbih	PERSON
ejpam-4753	285	2	m. b. maaouia	PERSON
ejpam-4753	285	3	m. sanghare	PERSON
ejpam-4753	286	1	j. pure	PERSON
ejpam-4753	286	2	16	CARDINAL
ejpam-4753	286	3	3	CARDINAL
ejpam-4753	286	4	2023	CARDINAL
ejpam-4753	286	5	1913-1939	DATE
ejpam-4753	286	6	im(dn	CARDINAL
ejpam-4753	286	7	1	CARDINAL
ejpam-4753	287	1	2	CARDINAL
ejpam-4753	288	1	7−→	CARDINAL
ejpam-4753	288	2	∈	ORG
ejpam-4753	288	3	m(n	PERSON
ejpam-4753	291	1	1	CARDINAL
ejpam-4753	292	1	15	CARDINAL
ejpam-4753	293	1	mn	GPE
ejpam-4753	293	2	n = ⊕	GPE
ejpam-4753	293	3	two	CARDINAL
ejpam-4753	296	1	nn	ORG
ejpam-4753	296	2	degree k ∈ z	PERSON
ejpam-4753	299	1	//	PERSON
ejpam-4753	299	2	dn //	PERSON
ejpam-4753	299	3	1	CARDINAL
ejpam-4753	300	1	n∗	ORG
ejpam-4753	301	1	d′n+1+k // n(n	PERSON
ejpam-4753	302	1	1	CARDINAL
ejpam-4753	303	1	proof	PERSON
ejpam-4753	304	1	1	CARDINAL
ejpam-4753	305	1	∈	ORG
ejpam-4753	313	1	′ n+1+k[f k(n + 1)(x	DATE
ejpam-4753	319	1	+ f(z	DATE
ejpam-4753	322	1	1))(x	CARDINAL
ejpam-4753	322	2	1	CARDINAL
ejpam-4753	323	1	a. o. chbih	PERSON
ejpam-4753	323	2	m. b. maaouia	PERSON
ejpam-4753	323	3	m. sanghare	PERSON
ejpam-4753	324	1	j. pure	PERSON
ejpam-4753	324	2	16	CARDINAL
ejpam-4753	324	3	3	CARDINAL
ejpam-4753	324	4	2023	CARDINAL
ejpam-4753	324	5	1913-1939	DATE
ejpam-4753	324	6	6	DATE
ejpam-4753	328	1	two	CARDINAL
ejpam-4753	328	2	comp	ORG
ejpam-4753	328	3	gr(a−mod))(m∗	ORG
ejpam-4753	328	4	m∗ to n∗	MONEY
ejpam-4753	329	1	∈	ORG
ejpam-4753	329	2	gr(a−mod))(m∗	ORG
ejpam-4753	329	3	∀	ORG
ejpam-4753	329	4	∈	ORG
ejpam-4753	329	5	∈	ORG
ejpam-4753	330	1	//	PERSON
ejpam-4753	330	2	1	CARDINAL
ejpam-4753	331	1	n∗	ORG
ejpam-4753	331	2	� //	PERSON
ejpam-4753	331	3	n+1+k // n(n	PERSON
ejpam-4753	331	4	n+k //	PERSON
ejpam-4753	332	1	hs ∗ �� //	PERSON
ejpam-4753	332	2	1	CARDINAL
ejpam-4753	332	3	′′	NORP
ejpam-4753	332	4	′′	ORG
ejpam-4753	334	1	// q(n+ 1	LAW
ejpam-4753	335	1	1m∗	DATE
ejpam-4753	336	1	1m∗	DATE
ejpam-4753	336	2	1	CARDINAL
ejpam-4753	336	3	1(n+1	CARDINAL
ejpam-4753	336	4	1(n	CARDINAL
ejpam-4753	339	1	1	CARDINAL
ejpam-4753	340	1	dn //	PERSON
ejpam-4753	342	1	1m∗	DATE
ejpam-4753	342	2	1m∗	DATE
ejpam-4753	342	3	∈	ORG
ejpam-4753	342	4	gr(a−mod))(m∗	ORG
ejpam-4753	342	5	n∗	ORG
ejpam-4753	343	1	1m∗	DATE
ejpam-4753	343	2	∈	ORG
ejpam-4753	344	1	a. o. chbih	PERSON
ejpam-4753	344	2	m. b. maaouia	PERSON
ejpam-4753	344	3	m. sanghare	PERSON
ejpam-4753	345	1	j. pure	PERSON
ejpam-4753	345	2	16	CARDINAL
ejpam-4753	345	3	3	CARDINAL
ejpam-4753	345	4	2023	CARDINAL
ejpam-4753	345	5	1913-1939 1929	DATE
ejpam-4753	346	1	16	CARDINAL
ejpam-4753	347	1	mn	GPE
ejpam-4753	347	2	n = ⊕	GPE
ejpam-4753	347	3	two	CARDINAL
ejpam-4753	349	1	1	CARDINAL
ejpam-4753	350	1	1	CARDINAL
ejpam-4753	352	1	1	CARDINAL
ejpam-4753	353	1	1	CARDINAL
ejpam-4753	354	1	s−1(n∗	PERSON
ejpam-4753	354	2	1	CARDINAL
ejpam-4753	354	3	1	CARDINAL
ejpam-4753	356	1	n∗	ORG
ejpam-4753	356	2	two	CARDINAL
ejpam-4753	356	3	two	CARDINAL
ejpam-4753	358	1	′ n+1+k	GPE
ejpam-4753	358	2	1	CARDINAL
ejpam-4753	361	1	(s−1d ′	DATE
ejpam-4753	362	1	1	CARDINAL
ejpam-4753	368	1	m. b. maaouia	PERSON
ejpam-4753	368	2	m. sanghare	PERSON
ejpam-4753	369	1	j. pure	PERSON
ejpam-4753	369	2	16	CARDINAL
ejpam-4753	369	3	3	CARDINAL
ejpam-4753	369	4	2023	CARDINAL
ejpam-4753	369	5	1913-1939 1930	DATE
ejpam-4753	370	1	∈	ORG
ejpam-4753	370	2	2 + k	QUANTITY
ejpam-4753	371	1	s−1fk(n)	NORP
ejpam-4753	372	1	(s−1d ′	DATE
ejpam-4753	373	1	s−1(fk ∗	PERSON
ejpam-4753	375	1	mn	GPE
ejpam-4753	375	2	n = ⊕	GPE
ejpam-4753	375	3	two	CARDINAL
ejpam-4753	377	1	−1	CARDINAL
ejpam-4753	378	1	−1	DATE
ejpam-4753	379	1	−1	DATE
ejpam-4753	379	2	m(n−1	ORG
ejpam-4753	380	1	−1	CARDINAL
ejpam-4753	381	1	//	PERSON
ejpam-4753	381	2	−1	DATE
ejpam-4753	382	1	−1	DATE
ejpam-4753	382	2	dn)//	FAC
ejpam-4753	382	3	1	CARDINAL
ejpam-4753	384	1	//	PERSON
ejpam-4753	384	2	−1	CARDINAL
ejpam-4753	384	3	d′n+1+k)//	ORG
ejpam-4753	384	4	−1	DATE
ejpam-4753	384	5	n(n	NORP
ejpam-4753	385	1	−1	DATE
ejpam-4753	385	2	1	CARDINAL
ejpam-4753	387	1	6	CARDINAL
ejpam-4753	387	2	16	CARDINAL
ejpam-4753	388	1	17	CARDINAL
ejpam-4753	389	1	mn	GPE
ejpam-4753	389	2	n = ⊕	GPE
ejpam-4753	389	3	two	CARDINAL
ejpam-4753	389	4	degree k ∈ z	PERSON
ejpam-4753	390	1	−→ s−1a⊗	PERSON
ejpam-4753	390	2	m(n	GPE
ejpam-4753	390	3	s−1a⊗	CARDINAL
ejpam-4753	390	4	1	CARDINAL
ejpam-4753	392	1	� // s−1a⊗	ORG
ejpam-4753	392	2	m(n	GPE
ejpam-4753	392	3	s−1a⊗(fk(n	PERSON
ejpam-4753	392	4	1	CARDINAL
ejpam-4753	393	1	d∗	PERSON
ejpam-4753	394	1	// s−1a⊗	PERSON
ejpam-4753	396	1	s−1a⊗	CARDINAL
ejpam-4753	396	2	1	CARDINAL
ejpam-4753	396	3	a. o. chbih	PERSON
ejpam-4753	396	4	m. b. maaouia	PERSON
ejpam-4753	396	5	m. sanghare	PERSON
ejpam-4753	397	1	j. pure	PERSON
ejpam-4753	397	2	16	CARDINAL
ejpam-4753	397	3	3	CARDINAL
ejpam-4753	397	4	2023	CARDINAL
ejpam-4753	397	5	1913-1939 1931	DATE
ejpam-4753	397	6	b∗	ORG
ejpam-4753	397	7	s−1a⊗	ORG
ejpam-4753	397	8	d∗	DATE
ejpam-4753	397	9	⊗ a(n∗	PERSON
ejpam-4753	400	1	⊗	ORG
ejpam-4753	402	1	// γ	PERSON
ejpam-4753	402	2	⊗ m(n+ 1	PRODUCT
ejpam-4753	402	3	⊗ m(n	PERSON
ejpam-4753	403	1	s−1fk ∗ �� //	PERSON
ejpam-4753	403	2	1	CARDINAL
ejpam-4753	404	1	1	CARDINAL
ejpam-4753	406	1	d∗	PERSON
ejpam-4753	407	1	//	PERSON
ejpam-4753	408	1	1	CARDINAL
ejpam-4753	408	2	⊗ n(n	PERSON
ejpam-4753	412	1	⊗ d′n+1+k	PERSON
ejpam-4753	413	1	⊗ fk(n	PERSON
ejpam-4753	414	1	1	CARDINAL
ejpam-4753	414	2	∈	PRODUCT
ejpam-4753	416	1	⊗	CARDINAL
ejpam-4753	417	1	s−1fk(n)◦	GPE
ejpam-4753	417	2	1	CARDINAL
ejpam-4753	418	1	s−1fk(n)◦	GPE
ejpam-4753	418	2	1 s	CARDINAL
ejpam-4753	420	1	1	CARDINAL
ejpam-4753	420	2	⊗ fk(n	PERSON
ejpam-4753	420	3	1	CARDINAL
ejpam-4753	420	4	1	CARDINAL
ejpam-4753	422	1	⊗ d′n+1+k	PERSON
ejpam-4753	422	2	1	CARDINAL
ejpam-4753	423	1	⊗ d′n+1+k	PERSON
ejpam-4753	423	2	1	CARDINAL
ejpam-4753	424	1	⊗ d′n+1+k	PERSON
ejpam-4753	425	1	1	CARDINAL
ejpam-4753	426	1	1	CARDINAL
ejpam-4753	426	2	s−1a⊗	ORG
ejpam-4753	428	1	mn	GPE
ejpam-4753	428	2	n = ⊕	GPE
ejpam-4753	428	3	two	CARDINAL
ejpam-4753	429	1	a. o. chbih	PERSON
ejpam-4753	429	2	m. b. maaouia	PERSON
ejpam-4753	429	3	m. sanghare	PERSON
ejpam-4753	430	1	j. pure	PERSON
ejpam-4753	430	2	16	CARDINAL
ejpam-4753	430	3	3	CARDINAL
ejpam-4753	430	4	2023	CARDINAL
ejpam-4753	430	5	1913-1939 1932	DATE
ejpam-4753	432	1	m(n	GPE
ejpam-4753	433	1	−1	DATE
ejpam-4753	433	2	1	CARDINAL
ejpam-4753	435	1	//	PERSON
ejpam-4753	435	2	∗	CARDINAL
ejpam-4753	436	1	−1	CARDINAL
ejpam-4753	437	1	m(n	GPE
ejpam-4753	438	1	−1	CARDINAL
ejpam-4753	438	2	a⊗(dn)//	ORG
ejpam-4753	438	3	1	CARDINAL
ejpam-4753	440	1	d∗	PERSON
ejpam-4753	441	1	//	PERSON
ejpam-4753	443	1	n+1+k)//	ORG
ejpam-4753	444	1	n+k)//	ORG
ejpam-4753	444	2	1	CARDINAL
ejpam-4753	445	1	b∗	ORG
ejpam-4753	445	2	−1	DATE
ejpam-4753	445	3	d∗	DATE
ejpam-4753	445	4	−1	CARDINAL
ejpam-4753	447	1	10	CARDINAL
ejpam-4753	448	1	mn	GPE
ejpam-4753	448	2	n = ⊕	GPE
ejpam-4753	448	3	two	CARDINAL
ejpam-4753	451	1	s−1a⊗(m(n	PERSON
ejpam-4753	453	1	s−1	NORP
ejpam-4753	454	1	m(n	GPE
ejpam-4753	455	1	a⊗(dn)//	ORG
ejpam-4753	455	2	1	CARDINAL
ejpam-4753	457	1	d∗	PERSON
ejpam-4753	457	2	//	PERSON
ejpam-4753	459	1	a⊗(d′n+1+k)//	GPE
ejpam-4753	460	1	a⊗(d′n+k)//	ORG
ejpam-4753	460	2	1	CARDINAL
ejpam-4753	461	1	b∗	ORG
ejpam-4753	461	2	d∗	DATE
ejpam-4753	466	1	gr(a − mod	PERSON
ejpam-4753	466	2	a. o. chbih	PERSON
ejpam-4753	466	3	m. b. maaouia	PERSON
ejpam-4753	466	4	m. sanghare	PERSON
ejpam-4753	467	1	j. pure	PERSON
ejpam-4753	467	2	16	CARDINAL
ejpam-4753	467	3	3	CARDINAL
ejpam-4753	467	4	2023	CARDINAL
ejpam-4753	467	5	1913-1939 1933	DATE
ejpam-4753	467	6	mn	GPE
ejpam-4753	474	1	two	CARDINAL
ejpam-4753	475	1	c(n	ORG
ejpam-4753	475	2	⊕	GPE
ejpam-4753	475	3	mn	GPE
ejpam-4753	475	4	∈	ORG
ejpam-4753	476	1	−→ n∗	ORG
ejpam-4753	479	1	mn	GPE
ejpam-4753	479	2	∈	ORG
ejpam-4753	481	1	−→ n∗	ORG
ejpam-4753	486	1	1c(m	DATE
ejpam-4753	487	1	a. o. chbih	PERSON
ejpam-4753	487	2	m. b. maaouia	PERSON
ejpam-4753	487	3	m. sanghare	PERSON
ejpam-4753	488	1	j. pure	PERSON
ejpam-4753	488	2	16	CARDINAL
ejpam-4753	488	3	3	CARDINAL
ejpam-4753	488	4	2023	CARDINAL
ejpam-4753	488	5	1913-1939	DATE
ejpam-4753	490	1	//	PERSON
ejpam-4753	490	2	1	CARDINAL
ejpam-4753	491	1	n∗	ORG
ejpam-4753	491	2	� //	PERSON
ejpam-4753	491	3	n+1+k // n(n	PERSON
ejpam-4753	491	4	n+k //	PERSON
ejpam-4753	492	1	l∗	PERSON
ejpam-4753	492	2	1	CARDINAL
ejpam-4753	492	3	′′	NORP
ejpam-4753	492	4	′′	ORG
ejpam-4753	499	1	8	CARDINAL
ejpam-4753	501	1	s−1	NORP
ejpam-4753	501	2	s−1	NORP
ejpam-4753	501	3	s−1	NORP
ejpam-4753	505	1	7	CARDINAL
ejpam-4753	505	2	9	CARDINAL
ejpam-4753	506	1	−1	DATE
ejpam-4753	508	1	−1	DATE
ejpam-4753	509	1	−1	DATE
ejpam-4753	509	2	−1	DATE
ejpam-4753	509	3	a. o. chbih	PERSON
ejpam-4753	509	4	m. b. maaouia	PERSON
ejpam-4753	509	5	m. sanghare	PERSON
ejpam-4753	510	1	j. pure	PERSON
ejpam-4753	510	2	16	CARDINAL
ejpam-4753	510	3	3	CARDINAL
ejpam-4753	510	4	2023	CARDINAL
ejpam-4753	510	5	1913-1939	DATE
ejpam-4753	511	1	7	CARDINAL
ejpam-4753	511	2	10	CARDINAL
ejpam-4753	517	1	7	CARDINAL
ejpam-4753	517	2	11	DATE
ejpam-4753	524	1	precedent7	PERSON
ejpam-4753	524	2	1	CARDINAL
ejpam-4753	524	3	mn	GPE
ejpam-4753	527	1	1	CARDINAL
ejpam-4753	528	1	ker(dn	GPE
ejpam-4753	528	2	1	CARDINAL
ejpam-4753	528	3	im(dn	CARDINAL
ejpam-4753	530	1	12	CARDINAL
ejpam-4753	531	1	gr(a − mod	PERSON
ejpam-4753	533	1	mn	GPE
ejpam-4753	536	1	mn −→ n = ⊕	PERSON
ejpam-4753	537	1	2	CARDINAL
ejpam-4753	537	2	a. o. chbih	PERSON
ejpam-4753	537	3	m. b. maaouia	PERSON
ejpam-4753	537	4	m. sanghare	PERSON
ejpam-4753	538	1	j. pure	PERSON
ejpam-4753	538	2	16	CARDINAL
ejpam-4753	538	3	3	CARDINAL
ejpam-4753	538	4	2023	CARDINAL
ejpam-4753	538	5	1913-1939 1936	DATE
ejpam-4753	538	6	13	CARDINAL
ejpam-4753	539	1	degree k ∈	PERSON
ejpam-4753	541	1	k ∈ z.	PERSON
ejpam-4753	542	1	2	CARDINAL
ejpam-4753	542	2	2	CARDINAL
ejpam-4753	542	3	2	CARDINAL
ejpam-4753	542	4	1	CARDINAL
ejpam-4753	544	1	12	CARDINAL
ejpam-4753	547	1	2	CARDINAL
ejpam-4753	547	2	2	CARDINAL
ejpam-4753	547	3	2	CARDINAL
ejpam-4753	547	4	1	CARDINAL
ejpam-4753	547	5	a. o. chbih	PERSON
ejpam-4753	547	6	m. b. maaouia	PERSON
ejpam-4753	547	7	m. sanghare	PERSON
ejpam-4753	548	1	j. pure	PERSON
ejpam-4753	548	2	16	CARDINAL
ejpam-4753	548	3	3	CARDINAL
ejpam-4753	548	4	2023	CARDINAL
ejpam-4753	548	5	1913-1939	DATE
ejpam-4753	548	6	18	CARDINAL
ejpam-4753	549	1	degree k ∈	PERSON
ejpam-4753	551	1	k ∈ z.	PERSON
ejpam-4753	552	1	2	CARDINAL
ejpam-4753	552	2	2	CARDINAL
ejpam-4753	552	3	2	CARDINAL
ejpam-4753	552	4	1	CARDINAL
ejpam-4753	553	1	11	CARDINAL
ejpam-4753	556	1	s−1 h m(n+ 2	PERSON
ejpam-4753	557	1	2	CARDINAL
ejpam-4753	557	2	2	CARDINAL
ejpam-4753	558	1	s−1	PERSON
ejpam-4753	561	1	18	CARDINAL
ejpam-4753	561	2	1938	DATE
ejpam-4753	561	3	19	DATE
ejpam-4753	562	1	mn	GPE
ejpam-4753	568	1	−1	DATE
ejpam-4753	570	1	−1	DATE
ejpam-4753	571	1	m(n + 2	DATE
ejpam-4753	572	1	−1	DATE
ejpam-4753	572	2	−1	DATE
ejpam-4753	574	1	12	CARDINAL
ejpam-4753	575	1	mn	GPE
ejpam-4753	582	1	5	CARDINAL
ejpam-4753	585	1	1	CARDINAL
ejpam-4753	586	1	sur des	ORG
ejpam-4753	586	2	anneaux	GPE
ejpam-4753	587	1	phd thesis	PERSON
ejpam-4753	587	2	2016	DATE
ejpam-4753	588	1	2	CARDINAL
ejpam-4753	590	1	10:457–474	CARDINAL
ejpam-4753	590	2	2015	DATE
ejpam-4753	591	1	1939	DATE
ejpam-4753	592	1	3	CARDINAL
ejpam-4753	592	2	dade	GPE
ejpam-4753	594	1	z.	PERSON
ejpam-4753	594	2	241–262	CARDINAL
ejpam-4753	594	3	1980	DATE
ejpam-4753	595	1	4	CARDINAL
ejpam-4753	597	1	switzerland	GPE
ejpam-4753	597	2	160:183–191	GPE
ejpam-4753	597	3	2016	DATE
ejpam-4753	598	1	5	CARDINAL
ejpam-4753	599	1	dans un	NORP
ejpam-4753	600	1	phd thesis	PERSON
ejpam-4753	600	2	2003	DATE
ejpam-4753	601	1	6	CARDINAL
ejpam-4753	602	1	les anneaux et modules de fractions	PERSON
ejpam-4753	602	2	enveloppe et couverture plate	ORG
ejpam-4753	602	3	dans un	NORP
ejpam-4753	603	1	phd thesis	PERSON
ejpam-4753	603	2	ucad	GPE
ejpam-4753	603	3	2011	DATE
ejpam-4753	605	1	dans les duo-anneaux	PERSON
ejpam-4753	606	1	20:163–179	CARDINAL
ejpam-4753	606	2	2009	DATE
ejpam-4753	607	1	8	CARDINAL
ejpam-4753	609	1	6, 2012	DATE
ejpam-4753	610	1	9	CARDINAL
ejpam-4753	610	2	mendelson	PERSON
ejpam-4753	610	3	algebras	ORG
ejpam-4753	610	4	1970	DATE
ejpam-4753	611	1	10	CARDINAL
ejpam-4753	614	1	10:1033–1071, 1981	DATE
ejpam-4753	615	1	11	CARDINAL
ejpam-4753	617	1	28	CARDINAL
ejpam-4753	617	2	north holland	GPE
ejpam-4753	617	3	amesterdam	GPE
ejpam-4753	617	4	1982	DATE