id	sid	eid	entity	type
cana-3972	1	1	1074	CARDINAL
cana-3972	1	2	32	CARDINAL
cana-3972	2	1	9s	CARDINAL
cana-3972	2	2	2025	CARDINAL
cana-3972	2	3	675	CARDINAL
cana-3972	3	1	diop 1	PERSON
cana-3972	3	2	de mathématiques	PERSON
cana-3972	3	3	ufr sciences et technologies	ORG
cana-3972	3	4	université iba der thiam de thiès	PERSON
cana-3972	3	5	14-11-2024	CARDINAL
cana-3972	3	6	22	CARDINAL
cana-3972	3	7	17-01-2025	CARDINAL
cana-3972	5	1	f ∶ n → k	ORG
cana-3972	5	2	ker(𝑓	ORG
cana-3972	9	1	2010	DATE
cana-3972	9	2	16d10,	DATE
cana-3972	9	3	16d40	DATE
cana-3972	9	4	16d60	DATE
cana-3972	9	5	16l30	CARDINAL
cana-3972	11	1	1	CARDINAL
cana-3972	17	1	⊆	CARDINAL
cana-3972	18	1	m1 ≤ n	PRODUCT
cana-3972	18	2	n ∩ m2	PRODUCT
cana-3972	20	1	m1 ∩ m2	PRODUCT
cana-3972	21	1	ker(𝑓	ORG
cana-3972	25	1	16	CARDINAL
cana-3972	25	2	w.k. nicholson	ORG
cana-3972	25	3	15	CARDINAL
cana-3972	25	4	2	CARDINAL
cana-3972	26	1	mailto:cheikh.diop@univ-thies.sn mailto:modou.seye@univ-thies.sn mailto:cheikh.diop@univ-thies.sn	PERSON
cana-3972	26	2	1074	CARDINAL
cana-3972	26	3	32	CARDINAL
cana-3972	27	1	9s	CARDINAL
cana-3972	27	2	2025	CARDINAL
cana-3972	27	3	676	CARDINAL
cana-3972	27	4	2016	DATE
cana-3972	27	5	n. ding	PERSON
cana-3972	27	6	y. ibrahim	PERSON
cana-3972	27	7	m. yousif	PERSON
cana-3972	28	1	6	CARDINAL
cana-3972	28	2	𝑓 ∶ 𝐴 → 𝐵	ORG
cana-3972	28	3	ker(𝑓	ORG
cana-3972	28	4	𝐵. d4-modules	PERSON
cana-3972	28	5	2017	CARDINAL
cana-3972	29	1	4	CARDINAL
cana-3972	30	1	4	CARDINAL
cana-3972	30	2	6	CARDINAL
cana-3972	30	3	3	CARDINAL
cana-3972	31	1	ker(𝑓	ORG
cana-3972	32	1	section 3	LAW
cana-3972	34	1	⊕ m	PERSON
cana-3972	37	1	hopfian	NORP
cana-3972	37	2	section 4	LAW
cana-3972	39	1	2	CARDINAL
cana-3972	39	2	2.1	CARDINAL
cana-3972	40	1	lemma	ORG
cana-3972	41	1	20	CARDINAL
cana-3972	41	2	2.1	CARDINAL
cana-3972	46	1	𝑍(∏𝑖∈𝐼𝑀𝑖	ORG
cana-3972	48	1	0	CARDINAL
cana-3972	48	2	2.2	CARDINAL
cana-3972	49	1	20	CARDINAL
cana-3972	49	2	corol lary 2.2	PERSON
cana-3972	50	1	2.3	CARDINAL
cana-3972	51	1	5	CARDINAL
cana-3972	51	2	2.1	CARDINAL
cana-3972	54	1	two	CARDINAL
cana-3972	55	1	1	CARDINAL
cana-3972	55	2	𝑁. 2	ORG
cana-3972	55	3	3	CARDINAL
cana-3972	55	4	5	CARDINAL
cana-3972	55	5	≅	CARDINAL
cana-3972	55	6	1074	CARDINAL
cana-3972	55	7	32	CARDINAL
cana-3972	56	1	9s	CARDINAL
cana-3972	56	2	2025	CARDINAL
cana-3972	56	3	677	CARDINAL
cana-3972	58	1	6	CARDINAL
cana-3972	58	2	≅	CARDINAL
cana-3972	60	1	5	CARDINAL
cana-3972	60	2	2.2	CARDINAL
cana-3972	61	1	3	CARDINAL
cana-3972	63	1	3.1	CARDINAL
cana-3972	65	1	𝑘𝑒𝑟(𝑓	CARDINAL
cana-3972	66	1	d41	DATE
cana-3972	67	1	3.2	CARDINAL
cana-3972	67	2	1	CARDINAL
cana-3972	69	1	2	CARDINAL
cana-3972	70	1	3	CARDINAL
cana-3972	71	1	4	CARDINAL
cana-3972	72	1	3.3	CARDINAL
cana-3972	73	1	ℚ	PERSON
cana-3972	73	2	ℤ	ORG
cana-3972	73	3	ℤ	ORG
cana-3972	73	4	ℤ	ORG
cana-3972	74	1	⊕ ℤ. ℤ	PERSON
cana-3972	74	2	ℤ	ORG
cana-3972	75	1	𝑓 ∶ ℚ → ℤ.	ORG
cana-3972	75	2	q.	PERSON
cana-3972	75	3	ℚ = ℚ ⊕	PERSON
cana-3972	75	4	0	CARDINAL
cana-3972	77	1	𝐷4	CARDINAL
cana-3972	78	1	𝐷4	CARDINAL
cana-3972	81	1	d4	ORG
cana-3972	82	1	3.4	CARDINAL
cana-3972	85	1	n ≤ ⊕ m	ORG
cana-3972	86	1	1074	CARDINAL
cana-3972	86	2	32	CARDINAL
cana-3972	87	1	9s	CARDINAL
cana-3972	87	2	2025	CARDINAL
cana-3972	87	3	678	CARDINAL
cana-3972	88	1	⊕	GPE
cana-3972	88	2	⊕	GPE
cana-3972	88	3	𝜋 ∶ 𝐾	PERSON
cana-3972	89	1	∘	DATE
cana-3972	89	2	𝜋 ∶ 𝐾 ⊕ 𝑁′ → 𝐾′	PRODUCT
cana-3972	89	3	𝑘𝑒𝑟(𝑓 ∘ 𝜋	DATE
cana-3972	89	4	𝑘𝑒𝑟𝑓 ⊕ 𝑁′.	PERSON
cana-3972	89	5	⊕	GPE
cana-3972	89	6	𝑘𝑒𝑟𝑓 ⊕ 𝑁′ ≤⊕	PERSON
cana-3972	89	7	⊕	GPE
cana-3972	89	8	𝐷41	ORG
cana-3972	90	1	3.5	CARDINAL
cana-3972	91	1	𝑀 ⊕ 𝑀	ORG
cana-3972	94	1	𝑀 ⊕	ORG
cana-3972	94	2	⊕ 𝐿.	PERSON
cana-3972	94	3	𝑀 ⊕	GPE
cana-3972	95	1	k ≤ ⊕	PERSON
cana-3972	96	1	3.6	CARDINAL
cana-3972	97	1	m1 ⊕ m2	PERSON
cana-3972	97	2	𝑀2	PRODUCT
cana-3972	98	1	𝑀1 ⊕ 𝑀2	DATE
cana-3972	98	2	𝑓 ∶ 𝑀1 →	ORG
cana-3972	98	3	𝑀2	PRODUCT
cana-3972	99	1	m1 as m1 = n ⊕ ker f	PRODUCT
cana-3972	100	1	𝑁 ≅	ORG
cana-3972	100	2	≅	CARDINAL
cana-3972	100	3	𝑀2	PRODUCT
cana-3972	101	1	𝑀2 ⊕	FAC
cana-3972	101	2	≤ ⊕	GPE
cana-3972	101	3	m1 ⊕ m2	LAW
cana-3972	102	1	m2 ⊕ m2	PERSON
cana-3972	102	2	𝐷41	ORG
cana-3972	102	3	3.4	CARDINAL
cana-3972	102	4	3.5	CARDINAL
cana-3972	103	1	two	CARDINAL
cana-3972	104	1	3.7	CARDINAL
cana-3972	105	1	9	CARDINAL
cana-3972	105	2	1.2	CARDINAL
cana-3972	106	1	⊕	GPE
cana-3972	106	2	3.8	CARDINAL
cana-3972	107	1	m. 1	PERSON
cana-3972	108	1	2	CARDINAL
cana-3972	108	2	n ⊕ n	ORG
cana-3972	109	1	⊕ k	PERSON
cana-3972	109	2	3.9	CARDINAL
cana-3972	111	1	∶ 𝑁 → 𝐾.	ORG
cana-3972	111	2	𝑁 ⊕	GPE
cana-3972	112	1	𝑁 ⊕	PERSON
cana-3972	115	1	3.7	CARDINAL
cana-3972	116	1	3.10	CARDINAL
cana-3972	118	1	∶ 𝐾 → 𝐾	ORG
cana-3972	124	1	1074	CARDINAL
cana-3972	124	2	32	CARDINAL
cana-3972	125	1	9s	CARDINAL
cana-3972	125	2	2025	CARDINAL
cana-3972	125	3	679	CARDINAL
cana-3972	126	1	3.11	CARDINAL
cana-3972	127	1	morita equivalence	ORG
cana-3972	127	2	epimorphisms	ORG
cana-3972	127	3	𝑀𝑅	ORG
cana-3972	129	1	ϕ(mr)s	ORG
cana-3972	130	1	3.12	CARDINAL
cana-3972	131	1	⊕	GPE
cana-3972	132	1	a von neumann	PERSON
cana-3972	133	1	⊕	PERSON
cana-3972	136	1	≅	CARDINAL
cana-3972	136	2	⊕	GPE
cana-3972	138	1	⊕	GPE
cana-3972	138	2	≅	CARDINAL
cana-3972	138	3	⊕ 𝐾.	PERSON
cana-3972	138	4	⊕ m	PERSON
cana-3972	138	5	𝑀 ⊕	ORG
cana-3972	138	6	∶ 𝑀	ORG
cana-3972	139	1	𝑘𝑒𝑟(𝑓	CARDINAL
cana-3972	140	1	a von neumann	PERSON
cana-3972	141	1	3.13	CARDINAL
cana-3972	142	1	1	CARDINAL
cana-3972	142	2	2	CARDINAL
cana-3972	142	3	3	CARDINAL
cana-3972	142	4	4	CARDINAL
cana-3972	143	1	1	CARDINAL
cana-3972	144	1	12	CARDINAL
cana-3972	144	2	2.16	CARDINAL
cana-3972	145	1	2	CARDINAL
cana-3972	148	1	⊕ n	PERSON
cana-3972	149	1	∩ n	PERSON
cana-3972	149	2	⊕ n	PERSON
cana-3972	149	3	n ≤ ⊕ m .	ORG
cana-3972	150	1	3	CARDINAL
cana-3972	153	1	n ∩ k ≤ ⊕ m	ORG
cana-3972	155	1	4	CARDINAL
cana-3972	157	1	𝑘𝑒𝑟(𝑓	CARDINAL
cana-3972	159	1	two	CARDINAL
cana-3972	160	1	3.14	CARDINAL
cana-3972	167	1	3.4	CARDINAL
cana-3972	168	1	≅	CARDINAL
cana-3972	169	1	1074	CARDINAL
cana-3972	169	2	32	CARDINAL
cana-3972	170	1	9s	CARDINAL
cana-3972	170	2	2025	CARDINAL
cana-3972	172	1	n ∩ k ≤ ⊕ k	ORG
cana-3972	174	1	3.15	CARDINAL
cana-3972	177	1	𝑀 𝑁 ≅	ORG
cana-3972	179	1	≅	CARDINAL
cana-3972	180	1	𝑀 𝑁 ≅	ORG
cana-3972	182	1	≅	CARDINAL
cana-3972	183	1	3.17	CARDINAL
cana-3972	184	1	3.16	DATE
cana-3972	185	1	m1 and m2	PRODUCT
cana-3972	188	1	0	CARDINAL
cana-3972	190	1	≅	CARDINAL
cana-3972	190	2	𝑀2	PRODUCT
cana-3972	191	1	3.15	CARDINAL
cana-3972	192	1	3.17	CARDINAL
cana-3972	195	1	≅	CARDINAL
cana-3972	195	2	l ≤	FAC
cana-3972	198	1	second	ORDINAL
cana-3972	198	2	≅	CARDINAL
cana-3972	203	1	3.18	CARDINAL
cana-3972	204	1	𝑘𝑒𝑟(𝑓	CARDINAL
cana-3972	205	1	1	CARDINAL
cana-3972	205	2	2	CARDINAL
cana-3972	205	3	1	CARDINAL
cana-3972	206	1	l ≤ ⊕ n	FAC
cana-3972	210	1	l ⊕ k	FAC
cana-3972	212	1	𝜋 ∘ ℎ	PERSON
cana-3972	212	2	∶ 𝐾 → 𝐿	ORG
cana-3972	212	3	lemma 2.4	ORG
cana-3972	213	1	⊕	PERSON
cana-3972	214	1	∘	DATE
cana-3972	214	2	𝑘𝑒𝑟(𝜋 ∘	MONEY
cana-3972	214	3	0	CARDINAL
cana-3972	215	1	𝑘𝑒𝑟(𝜋 ∘ ℎ	PERSON
cana-3972	215	2	𝑁 ≅	ORG
cana-3972	215	3	1074	CARDINAL
cana-3972	215	4	32	CARDINAL
cana-3972	216	1	9s	CARDINAL
cana-3972	216	2	2025	CARDINAL
cana-3972	217	1	681	CARDINAL
cana-3972	217	2	2	CARDINAL
cana-3972	219	1	𝜋 ∘	PERSON
cana-3972	219	2	∶ 𝐾 → 𝑘𝑒𝑟𝑓	ORG
cana-3972	221	1	lemma 2.4	ORG
cana-3972	221	2	𝜋 ∘	PERSON
cana-3972	221	3	⊕	PERSON
cana-3972	221	4	𝑘𝑒𝑟𝑓 ≅ 𝑄.	PERSON
cana-3972	222	1	∘	DATE
cana-3972	222	2	lemma 2.4	ORG
cana-3972	223	1	⊕	GPE
cana-3972	223	2	≅	CARDINAL
cana-3972	224	1	𝑘𝑒𝑟𝑓 ⊕	PERSON
cana-3972	224	2	⊕	GPE
cana-3972	224	3	≅	CARDINAL
cana-3972	225	1	≅	CARDINAL
cana-3972	225	2	𝑁 ≅	ORG
cana-3972	225	3	two	CARDINAL
cana-3972	225	4	13	CARDINAL
cana-3972	226	1	k ⊕ l	ORG
cana-3972	227	1	3.19	CARDINAL
cana-3972	228	1	1	CARDINAL
cana-3972	229	1	2	CARDINAL
cana-3972	230	1	m. 3	PERSON
cana-3972	231	1	m. proof:	PERSON
cana-3972	231	2	1	CARDINAL
cana-3972	233	1	𝜋 ∶ 𝑀	PRODUCT
cana-3972	234	1	≤ ⊕ n	ORG
cana-3972	235	1	n ∩ k ≤ ⊕ m .	ORG
cana-3972	236	1	2	CARDINAL
cana-3972	236	2	n + k ≤ ⊕ m	FAC
cana-3972	240	1	n + k = n ⊕	FAC
cana-3972	241	1	n ⊕ p	ORG
cana-3972	241	2	k ⊕ p	ORG
cana-3972	241	3	n ⊕ p	ORG
cana-3972	242	1	k ⊕ p	ORG
cana-3972	245	1	n ⊕ p	ORG
cana-3972	245	2	∩	PERSON
cana-3972	245	3	k ⊕ p	ORG
cana-3972	246	1	n ∩ k ≤ ⊕ m .	ORG
cana-3972	247	1	3	CARDINAL
cana-3972	248	1	𝑎 ∈ 𝐴	ORG
cana-3972	249	1	+ k	PERSON
cana-3972	249	2	g ∩ k = 0	PERSON
cana-3972	250	1	⊕ k	PERSON
cana-3972	256	1	3.20	CARDINAL
cana-3972	257	1	1	CARDINAL
cana-3972	258	1	2	CARDINAL
cana-3972	261	1	⊆	CARDINAL
cana-3972	263	1	1074	CARDINAL
cana-3972	263	2	32	CARDINAL
cana-3972	264	1	9s	CARDINAL
cana-3972	264	2	2025	CARDINAL
cana-3972	265	1	682	CARDINAL
cana-3972	265	2	1	CARDINAL
cana-3972	266	1	3.19	CARDINAL
cana-3972	266	2	submodule l.	PERSON
cana-3972	267	1	2	CARDINAL
cana-3972	268	1	⊆	CARDINAL
cana-3972	274	1	6	CARDINAL
cana-3972	278	1	4	CARDINAL
cana-3972	280	1	3.21	CARDINAL
cana-3972	281	1	1	CARDINAL
cana-3972	282	1	2	CARDINAL
cana-3972	283	1	1	CARDINAL
cana-3972	283	2	6	CARDINAL
cana-3972	285	1	two	CARDINAL
cana-3972	287	1	n ∩ k ≤ ⊕ m	ORG
cana-3972	288	1	n ∩ l	ORG
cana-3972	288	2	k ∩ l	ORG
cana-3972	289	1	n ∩ l ≅ n/(n	ORG
cana-3972	289	2	∩ k	PERSON
cana-3972	290	1	≅	CARDINAL
cana-3972	291	1	∩ k	PERSON
cana-3972	292	1	n ∩ l	ORG
cana-3972	292	2	k ∩ l	ORG
cana-3972	292	3	n ∩ l	ORG
cana-3972	292	4	k ∩ l	ORG
cana-3972	293	1	n ∩ l = k ∩ l = 0.	ORG
cana-3972	295	1	2	CARDINAL
cana-3972	295	2	4	CARDINAL
cana-3972	297	1	zero	CARDINAL
cana-3972	297	2	n ≅ k	ORG
cana-3972	297	3	0	CARDINAL
cana-3972	298	1	n ⊕ k ≤ ⊕	FAC
cana-3972	300	1	m/(n ⊕ l	DATE
cana-3972	301	1	≅	CARDINAL
cana-3972	305	1	3.22	CARDINAL
cana-3972	310	1	𝑀𝑖	GPE
cana-3972	310	2	1074	CARDINAL
cana-3972	310	3	32	CARDINAL
cana-3972	311	1	9s	CARDINAL
cana-3972	311	2	2025	CARDINAL
cana-3972	311	3	683	CARDINAL
cana-3972	313	1	k ⊕ l	ORG
cana-3972	316	1	k ⊕ l	ORG
cana-3972	319	1	⊕	PERSON
cana-3972	320	1	k ∩ mi	PERSON
cana-3972	320	2	⊕	PERSON
cana-3972	324	1	k ∩ mi	PERSON
cana-3972	325	1	k ∩ mi	PERSON
cana-3972	325	2	k ∩ mi	PERSON
cana-3972	325	3	∩	PERSON
cana-3972	325	4	k ∩ mi	PERSON
cana-3972	328	1	∩	PERSON
cana-3972	328	2	k ∩ mi	PERSON
cana-3972	329	1	3.4	CARDINAL
cana-3972	331	1	3.23	CARDINAL
cana-3972	332	1	𝜉 ∶ 𝑀 → 𝑀	ORG
cana-3972	333	1	3.24	CARDINAL
cana-3972	334	1	hopfian	ORG
cana-3972	337	1	first	ORDINAL
cana-3972	338	1	second	ORDINAL
cana-3972	339	1	𝑘𝑒𝑟(𝑓	CARDINAL
cana-3972	339	2	3.25	CARDINAL
cana-3972	340	1	hopfian d41-module	ORG
cana-3972	342	1	3.26	CARDINAL
cana-3972	343	1	1	CARDINAL
cana-3972	343	2	2	CARDINAL
cana-3972	343	3	3	CARDINAL
cana-3972	344	1	1	CARDINAL
cana-3972	344	2	8	CARDINAL
cana-3972	344	3	1.4	CARDINAL
cana-3972	345	1	⊕ m	PERSON
cana-3972	346	1	3	CARDINAL
cana-3972	346	2	⊕ m	PERSON
cana-3972	347	1	𝑓 ∶ 𝑀 → 𝑀	ORG
cana-3972	347	2	1	CARDINAL
cana-3972	347	3	1	CARDINAL
cana-3972	350	1	a. r. m. hamzekolaee	PERSON
cana-3972	350	2	2013	DATE
cana-3972	350	3	17	CARDINAL
cana-3972	351	1	1074	CARDINAL
cana-3972	351	2	32	CARDINAL
cana-3972	352	1	9s	CARDINAL
cana-3972	352	2	2025	CARDINAL
cana-3972	352	3	684	CARDINAL
cana-3972	354	1	0	CARDINAL
cana-3972	355	1	𝑇𝑆	ORG
cana-3972	358	1	→ l	DATE
cana-3972	359	1	3.27	CARDINAL
cana-3972	362	1	3.28	CARDINAL
cana-3972	363	1	17	CARDINAL
cana-3972	363	2	1	CARDINAL
cana-3972	363	3	⊆	CARDINAL
cana-3972	365	1	3.29	CARDINAL
cana-3972	367	1	n ≤ ⊕ m	ORG
cana-3972	368	1	k ′	ORG
cana-3972	370	1	⊕	GPE
cana-3972	370	2	⊕	GPE
cana-3972	370	3	𝜋 ∶ 𝐾	PERSON
cana-3972	371	1	∘	DATE
cana-3972	371	2	𝜋 ∶ 𝐾 ⊕ 𝑁′ → 𝐾′	PRODUCT
cana-3972	371	3	𝑘𝑒𝑟(𝑓 ∘ 𝜋	DATE
cana-3972	371	4	𝑘𝑒𝑟𝑓 ⊕ 𝑁′.	PERSON
cana-3972	372	1	⊕	GPE
cana-3972	377	1	3.30	CARDINAL
cana-3972	384	1	≅	CARDINAL
cana-3972	385	1	second	ORDINAL
cana-3972	386	1	≅ l.	PERSON
cana-3972	387	1	k = p /n	ORG
cana-3972	389	1	n / k	ORG
cana-3972	389	2	19	CARDINAL
cana-3972	389	3	n / k	ORG
cana-3972	390	1	n / k	ORG
cana-3972	391	1	n / k	ORG
cana-3972	391	2	m /k	DATE
cana-3972	392	1	3.31	CARDINAL
cana-3972	393	1	1074	CARDINAL
cana-3972	393	2	32	CARDINAL
cana-3972	394	1	9s	CARDINAL
cana-3972	394	2	2025	CARDINAL
cana-3972	394	3	685	CARDINAL
cana-3972	395	1	3.32	CARDINAL
cana-3972	396	1	1	CARDINAL
cana-3972	396	2	2	CARDINAL
cana-3972	396	3	m1 ≤ n	PRODUCT
cana-3972	396	4	n ∩ m2	PRODUCT
cana-3972	397	1	3	CARDINAL
cana-3972	398	1	1	CARDINAL
cana-3972	399	1	m1 ≤ n and n/m1	PRODUCT
cana-3972	400	1	n ∩ m2	PRODUCT
cana-3972	400	2	n ∩ m2 ≅ n/m1	PRODUCT
cana-3972	400	3	n ∩ m2	PRODUCT
cana-3972	401	1	2	CARDINAL
cana-3972	401	2	m1 ≤ n	PRODUCT
cana-3972	402	1	n ∩m2	ORG
cana-3972	404	1	3	CARDINAL
cana-3972	406	1	𝑁/𝑁1 ≅ 𝑁2	QUANTITY
cana-3972	408	1	3.33	CARDINAL
cana-3972	409	1	1	CARDINAL
cana-3972	409	2	2	CARDINAL
cana-3972	409	3	3	CARDINAL
cana-3972	411	1	1	CARDINAL
cana-3972	412	1	2	CARDINAL
cana-3972	412	2	3.32	CARDINAL
cana-3972	413	1	3	CARDINAL
cana-3972	413	2	3.32	CARDINAL
cana-3972	414	1	3.34	CARDINAL
cana-3972	415	1	m1 ⊕ m2	PERSON
cana-3972	415	2	m1 ⊕ m2	PERSON
cana-3972	417	1	n ∩ m1	PRODUCT
cana-3972	418	1	′ ≤ m1	QUANTITY
cana-3972	419	1	⊕	GPE
cana-3972	419	2	n ∩ m1) ⊕	PRODUCT
cana-3972	420	1	1074	CARDINAL
cana-3972	420	2	32	CARDINAL
cana-3972	421	1	9s	CARDINAL
cana-3972	421	2	2025	CARDINAL
cana-3972	421	3	686	CARDINAL
cana-3972	427	1	k	PERSON
cana-3972	428	1	′ ⊕	PERSON
cana-3972	428	2	k ∩	ORG
cana-3972	428	3	k ∩	PERSON
cana-3972	429	1	⊕	PERSON
cana-3972	429	2	k ∩	ORG
cana-3972	430	1	k ∩ a))≅	ORG
cana-3972	430	2	≅	CARDINAL
cana-3972	433	1	3.35	CARDINAL
cana-3972	436	1	4	CARDINAL
cana-3972	438	1	18	CARDINAL
cana-3972	438	2	3	CARDINAL
cana-3972	439	1	4.1	CARDINAL
cana-3972	440	1	1	CARDINAL
cana-3972	440	2	2	CARDINAL
cana-3972	440	3	1	CARDINAL
cana-3972	441	1	2	CARDINAL
cana-3972	444	1	4.2	CARDINAL
cana-3972	446	1	4.1	CARDINAL
cana-3972	447	1	4.3	CARDINAL
cana-3972	448	1	1	CARDINAL
cana-3972	449	1	2	CARDINAL
cana-3972	450	1	3	CARDINAL
cana-3972	451	1	4	CARDINAL
cana-3972	452	1	5	CARDINAL
cana-3972	453	1	6	CARDINAL
cana-3972	454	1	7	CARDINAL
cana-3972	454	2	two	CARDINAL
cana-3972	455	1	1	CARDINAL
cana-3972	456	1	6	CARDINAL
cana-3972	456	2	𝑓 ∶ 𝑅 → 𝑉	ORG
cana-3972	457	1	2.4	CARDINAL
cana-3972	459	1	1074	CARDINAL
cana-3972	459	2	32	CARDINAL
cana-3972	460	1	9s	CARDINAL
cana-3972	460	2	2025	CARDINAL
cana-3972	460	3	687	CARDINAL
cana-3972	461	1	21	CARDINAL
cana-3972	461	2	67	CARDINAL
cana-3972	462	1	11	CARDINAL
cana-3972	463	1	von neumann	PERSON
cana-3972	464	1	4.4	CARDINAL
cana-3972	465	1	1	CARDINAL
cana-3972	465	2	2	CARDINAL
cana-3972	465	3	3	CARDINAL
cana-3972	465	4	4	CARDINAL
cana-3972	465	5	5	CARDINAL
cana-3972	465	6	a von neumann	PERSON
cana-3972	467	1	4.5	CARDINAL
cana-3972	468	1	iso-morphisms	PERSON
cana-3972	469	1	1	CARDINAL
cana-3972	469	2	𝐴 ∈ 𝐴	ORG
cana-3972	470	1	2	CARDINAL
cana-3972	471	1	3	CARDINAL
cana-3972	472	1	4	CARDINAL
cana-3972	472	2	5	CARDINAL
cana-3972	473	1	1	CARDINAL
cana-3972	474	1	5	CARDINAL
cana-3972	474	2	14	CARDINAL
cana-3972	474	3	3.6	CARDINAL
cana-3972	475	1	r(i	PERSON
cana-3972	477	1	r(i	PERSON
cana-3972	479	1	14	CARDINAL
cana-3972	479	2	2.6	CARDINAL
cana-3972	479	3	r(i	PERSON
cana-3972	481	1	⊗ x	PERSON
cana-3972	484	1	4.6	CARDINAL
cana-3972	485	1	1	CARDINAL
cana-3972	486	1	2	CARDINAL
cana-3972	487	1	3	CARDINAL
cana-3972	487	2	two	CARDINAL
cana-3972	488	1	4	CARDINAL
cana-3972	488	2	2	CARDINAL
cana-3972	489	1	1074	CARDINAL
cana-3972	489	2	32	CARDINAL
cana-3972	490	1	9s	CARDINAL
cana-3972	490	2	2025	CARDINAL
cana-3972	490	3	688	CARDINAL
cana-3972	491	1	6	CARDINAL
cana-3972	491	2	a von neumann	PERSON
cana-3972	492	1	7	CARDINAL
cana-3972	493	1	1	CARDINAL
cana-3972	493	2	2	CARDINAL
cana-3972	494	1	7	DATE
cana-3972	495	1	2	CARDINAL
cana-3972	495	2	4	CARDINAL
cana-3972	496	1	3	CARDINAL
cana-3972	496	2	lemma 2.4	ORG
cana-3972	498	1	5	CARDINAL
cana-3972	498	2	⊕	GPE
cana-3972	499	1	5	CARDINAL
cana-3972	500	1	lemma 2.4	ORG
cana-3972	500	2	r.	NORP
cana-3972	501	1	6 ⟹ 1	DATE
cana-3972	502	1	1	CARDINAL
cana-3972	502	2	2	DATE
cana-3972	503	1	7	CARDINAL
cana-3972	503	2	38.1	CARDINAL
cana-3972	503	3	42.2	CARDINAL
cana-3972	504	1	von neumann	PERSON
cana-3972	504	2	22	CARDINAL
cana-3972	504	3	37.6	CARDINAL
cana-3972	505	1	6	CARDINAL
cana-3972	508	1	𝑖=1	PERSON
cana-3972	511	1	𝑖=1	PERSON
cana-3972	513	1	2	CARDINAL
cana-3972	513	2	1	CARDINAL
cana-3972	513	3	2	DATE
cana-3972	515	1	7	CARDINAL
cana-3972	515	2	38.1	CARDINAL
cana-3972	515	3	42.2	CARDINAL
cana-3972	515	4	7	CARDINAL
cana-3972	518	1	𝑖=1	PERSON
cana-3972	521	1	𝑖=1	PERSON
cana-3972	522	1	22	CARDINAL
cana-3972	522	2	53.7	CARDINAL
cana-3972	522	3	7	CARDINAL
cana-3972	523	1	10	CARDINAL
cana-3972	523	2	23.18	CARDINAL
cana-3972	525	1	15	CARDINAL
cana-3972	525	2	2.9	CARDINAL
cana-3972	526	1	4.7	CARDINAL
cana-3972	527	1	1	CARDINAL
cana-3972	528	1	2	CARDINAL
cana-3972	529	1	1	CARDINAL
cana-3972	530	1	1	CARDINAL
cana-3972	531	1	2	CARDINAL
cana-3972	531	2	4	CARDINAL
cana-3972	531	3	3.2	CARDINAL
cana-3972	533	1	4.8	CARDINAL
cana-3972	534	1	1	CARDINAL
cana-3972	534	2	2	CARDINAL
cana-3972	534	3	1074	CARDINAL
cana-3972	534	4	32	CARDINAL
cana-3972	535	1	9s	CARDINAL
cana-3972	535	2	2025	CARDINAL
cana-3972	535	3	689	CARDINAL
cana-3972	535	4	4	CARDINAL
cana-3972	536	1	5	CARDINAL
cana-3972	537	1	1	CARDINAL
cana-3972	537	2	1	CARDINAL
cana-3972	538	1	3	CARDINAL
cana-3972	540	1	⊕ n	PERSON
cana-3972	541	1	24	CARDINAL
cana-3972	541	2	10	CARDINAL
cana-3972	542	1	5	CARDINAL
cana-3972	543	1	4	CARDINAL
cana-3972	543	2	3.4	CARDINAL
cana-3972	544	1	1	CARDINAL
cana-3972	545	1	4.9	CARDINAL
cana-3972	547	1	d41	DATE
cana-3972	548	1	d41	DATE
cana-3972	548	2	mn	ORG
cana-3972	548	3	4.10	CARDINAL
cana-3972	549	1	1	CARDINAL
cana-3972	549	2	2	CARDINAL
cana-3972	549	3	3	CARDINAL
cana-3972	549	4	4	CARDINAL
cana-3972	549	5	2	CARDINAL
cana-3972	549	6	5	CARDINAL
cana-3972	549	7	6	CARDINAL
cana-3972	550	1	1	CARDINAL
cana-3972	550	2	⇔ 5	CARDINAL
cana-3972	550	3	23	CARDINAL
cana-3972	550	4	9	CARDINAL
cana-3972	551	1	6	CARDINAL
cana-3972	551	2	3	DATE
cana-3972	551	3	1	CARDINAL
cana-3972	552	1	6	CARDINAL
cana-3972	555	1	j of r.	PERSON
cana-3972	556	1	3.5	CARDINAL
cana-3972	558	1	4	CARDINAL
cana-3972	558	2	2	CARDINAL
cana-3972	558	3	6	CARDINAL
cana-3972	559	1	4.11	CARDINAL
cana-3972	560	1	1	CARDINAL
cana-3972	561	1	2	CARDINAL
cana-3972	562	1	3	CARDINAL
cana-3972	562	2	2	CARDINAL
cana-3972	563	1	4	CARDINAL
cana-3972	564	1	5	CARDINAL
cana-3972	564	2	2	CARDINAL
cana-3972	565	1	1	CARDINAL
cana-3972	565	2	1	CARDINAL
cana-3972	566	1	3	CARDINAL
cana-3972	568	1	3	CARDINAL
cana-3972	568	2	∶ 𝐶 → 𝑀	ORG
cana-3972	569	1	1074	CARDINAL
cana-3972	569	2	32	CARDINAL
cana-3972	571	1	9s	CARDINAL
cana-3972	571	2	2025	CARDINAL
cana-3972	571	3	690	CARDINAL
cana-3972	572	1	1	CARDINAL
cana-3972	572	2	2	CARDINAL
cana-3972	572	3	⊕ γ2	GPE
cana-3972	574	1	24	CARDINAL
cana-3972	574	2	4	CARDINAL
cana-3972	576	1	5	CARDINAL
cana-3972	578	1	5	CARDINAL
cana-3972	579	1	𝑓1 ∶ 𝐾 →	ORG
cana-3972	579	2	∶ 𝑀 → 𝑆	ORG
cana-3972	579	3	∶ 𝑀 → 𝑅	ORG
cana-3972	580	1	∶ 𝐾 → 𝑀	ORG
cana-3972	580	2	1	CARDINAL
cana-3972	580	3	2	CARDINAL
cana-3972	585	1	4.12	CARDINAL
cana-3972	586	1	1	CARDINAL
cana-3972	587	1	2	CARDINAL
cana-3972	588	1	3	CARDINAL
cana-3972	589	1	1	CARDINAL
cana-3972	589	2	1	CARDINAL
cana-3972	590	1	2	CARDINAL
cana-3972	592	1	∶ 𝐹	ORG
cana-3972	592	2	f ⊕ k	FAC
cana-3972	592	3	f ⊕ m	ORG
cana-3972	592	4	f ⊕ k	PERSON
cana-3972	593	1	∶ 𝐹 → 𝐾 →	ORG
cana-3972	593	2	0	CARDINAL
cana-3972	594	1	k	PERSON
cana-3972	595	1	4.13	CARDINAL
cana-3972	596	1	1	CARDINAL
cana-3972	597	1	2	CARDINAL
cana-3972	598	1	3	CARDINAL
cana-3972	599	1	4	CARDINAL
cana-3972	600	1	5	CARDINAL
cana-3972	601	1	1	CARDINAL
cana-3972	603	1	22	CARDINAL
cana-3972	603	2	20.7	CARDINAL
cana-3972	604	1	2	CARDINAL
cana-3972	605	1	4	CARDINAL
cana-3972	607	1	1	CARDINAL
cana-3972	607	2	22	CARDINAL
cana-3972	607	3	20.7	CARDINAL
cana-3972	608	1	1074	CARDINAL
cana-3972	608	2	32	CARDINAL
cana-3972	609	1	9s	CARDINAL
cana-3972	609	2	2025	CARDINAL
cana-3972	610	1	691	CARDINAL
cana-3972	610	2	1	CARDINAL
cana-3972	610	3	k. oshiro	PERSON
cana-3972	612	1	pte. ltd.	ORG
cana-3972	612	2	london	GPE
cana-3972	612	3	2009	DATE
cana-3972	613	1	2	CARDINAL
cana-3972	613	2	j. clark	PERSON
cana-3972	613	3	c. lomp	PERSON
cana-3972	613	4	n. vanaja	PERSON
cana-3972	613	5	r. wisbauer	PERSON
cana-3972	616	1	berlin	GPE
cana-3972	616	2	2000	DATE
cana-3972	617	1	3	CARDINAL
cana-3972	617	2	a. d. diallo	PERSON
cana-3972	617	3	c. diop	PERSON
cana-3972	617	4	f. kourki	PERSON
cana-3972	617	5	r. tribak	PERSON
cana-3972	620	1	2023	CARDINAL
cana-3972	621	1	mathematics & statistics	ORG
cana-3972	621	2	474	CARDINAL
cana-3972	621	3	387–404	CARDINAL
cana-3972	621	4	2025	DATE
cana-3972	622	1	4	CARDINAL
cana-3972	622	2	y. ibrahim	PERSON
cana-3972	622	3	m. yousif	PERSON
cana-3972	622	4	y. zhou	PERSON
cana-3972	622	5	1750166	DATE
cana-3972	622	6	25	CARDINAL
cana-3972	622	7	2017	DATE
cana-3972	623	1	5	CARDINAL
cana-3972	623	2	y. ibrahim	PERSON
cana-3972	623	3	m. yousif	PERSON
cana-3972	623	4	y. zhou	PERSON
cana-3972	625	1	25, 2017	DATE
cana-3972	626	1	6	CARDINAL
cana-3972	626	2	yasser ibrahim	PERSON
cana-3972	626	3	mohamed yousif	PERSON
cana-3972	626	4	yiqiang zhou	PERSON
cana-3972	628	1	45	CARDINAL
cana-3972	628	2	1727–1740	CARDINAL
cana-3972	628	3	2016	DATE
cana-3972	629	1	7	CARDINAL
cana-3972	630	1	abelian	NORP
cana-3972	630	2	1	CARDINAL
cana-3972	634	1	monogr	ORG
cana-3972	634	2	new york	GPE
cana-3972	634	3	san francisco	GPE
cana-3972	634	4	london	GPE
cana-3972	634	5	1970	DATE
cana-3972	635	1	8	CARDINAL
cana-3972	635	2	a. ghorbani	PERSON
cana-3972	635	3	a. haghany	PERSON
cana-3972	636	1	generalized hopfian	PERSON
cana-3972	637	1	324–341, 2002	DATE
cana-3972	638	1	9	CARDINAL
cana-3972	638	2	c. w. han	PERSON
cana-3972	638	3	b. y. lee	PERSON
cana-3972	638	4	s. j. choi	PERSON
cana-3972	640	1	pusan kyongnam	PERSON
cana-3972	640	2	3, 1994	DATE
cana-3972	641	1	10	CARDINAL
cana-3972	642	1	first	ORDINAL
cana-3972	643	1	1991	DATE
cana-3972	644	1	11	CARDINAL
cana-3972	644	2	gangyong lee	PERSON
cana-3972	644	3	s. tariq rizvi	PERSON
cana-3972	644	4	cosmin s roman	PERSON
cana-3972	646	1	4036	CARDINAL
cana-3972	646	2	4058, 2011	DATE
cana-3972	647	1	12	CARDINAL
cana-3972	647	2	gangyong lee	PERSON
cana-3972	647	3	s. tariq rizvi	PERSON
cana-3972	647	4	cosmin s roman	PERSON
cana-3972	648	1	rickart modules.	ORG
cana-3972	649	1	25, 2011	DATE
cana-3972	650	1	13	CARDINAL
cana-3972	650	2	a. ö. meltem	PERSON
cana-3972	650	3	i. yasser	PERSON
cana-3972	650	4	a. ç	PERSON
cana-3972	650	5	m. yousif	PERSON
cana-3972	650	6	d4	ORG
cana-3972	651	1	22, 2010	DATE
cana-3972	652	1	14	CARDINAL
cana-3972	652	2	a. a. nailevich	PERSON
cana-3972	652	3	t. c. quynh	GPE
cana-3972	652	4	t. h. n. nhan	PERSON
cana-3972	653	1	c3	ORG
cana-3972	653	2	d3	ORG
cana-3972	654	1	hacettepe journal	ORG
cana-3972	654	2	47	CARDINAL
cana-3972	654	3	2	CARDINAL
cana-3972	654	4	317	CARDINAL
cana-3972	654	5	329	CARDINAL
cana-3972	654	6	2018	DATE
cana-3972	655	1	15	CARDINAL
cana-3972	655	2	w. k. nicholson	PERSON
cana-3972	656	1	semiregular modules	ORG
cana-3972	658	1	j. math	PERSON
cana-3972	658	2	16, 1976	DATE
cana-3972	659	1	16	CARDINAL
cana-3972	659	2	k. oshiro	PERSON
cana-3972	661	1	310–338	CARDINAL
cana-3972	661	2	1984	DATE
cana-3972	662	1	17	CARDINAL
cana-3972	662	2	a. r. m. hamzekolaee	PERSON
cana-3972	664	1	6, 2013	DATE
cana-3972	665	1	18	CARDINAL
cana-3972	665	2	a. r. m. hamzekolaee	PERSON
cana-3972	665	3	m. hosseinpour	PERSON
cana-3972	665	4	a. harmanci	PERSON
cana-3972	667	1	hacettepe journal of mathematics & statistics	ORG
cana-3972	667	2	48	CARDINAL
cana-3972	667	3	4	CARDINAL
cana-3972	667	4	973–984	CARDINAL
cana-3972	667	5	2019	DATE
cana-3972	668	1	19	CARDINAL
cana-3972	668	2	m. j. nematollahi	PERSON
cana-3972	670	1	taiwanese	NORP
cana-3972	670	2	13	CARDINAL
cana-3972	670	3	5	CARDINAL
cana-3972	670	4	1451–1456, 2009	DATE
cana-3972	671	1	20	CARDINAL
cana-3972	671	2	n. vanaja	PERSON
cana-3972	673	1	1449–1460, 2002	DATE
cana-3972	674	1	21	CARDINAL
cana-3972	674	2	a. tuganbaev	PERSON
cana-3972	676	1	b.v.	GPE
cana-3972	676	2	russie	GPE
cana-3972	676	3	m. hazewinkel	PERSON
cana-3972	676	4	amsterdam	GPE
cana-3972	676	5	netherlands	GPE
cana-3972	677	1	22	CARDINAL
cana-3972	677	2	r. wisbauer	PERSON
cana-3972	679	1	gordon	PERSON
cana-3972	679	2	1991	DATE
cana-3972	680	1	23	CARDINAL
cana-3972	680	2	w. xue	PERSON
cana-3972	682	1	99–104, 1993	DATE
cana-3972	683	1	24	CARDINAL
cana-3972	683	2	m. yousif	PERSON
cana-3972	683	3	i. amin	PERSON
cana-3972	683	4	ibrahim	PERSON
cana-3972	685	1	578–592, 2013	DATE