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Sur les modules tels que toute suite croissante de sous-modules engendres par n générateurs soit stationnaire. (French) Zbl 0419.13010


MSC:

13E15 Commutative rings and modules of finite generation or presentation; number of generators
13E05 Commutative Noetherian rings and modules
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References:

[1] Baumslag, B.; Baumslag, G., On ascending chain conditions, (Proc. London Math. Soc. (3), 22 (1971)), 681-704 · Zbl 0226.20023
[2] Bourbaki, N., Algèbre (1962), Hermann: Hermann Paris · Zbl 0142.00102
[3] Bourbaki, N., Algèbre commutative (1965), Hermann: Hermann Paris · Zbl 0141.03501
[4] Cohen, I. S., Commutative rings with restricted minimum conditions, Duke Math. J., 17, 27-42 (1950) · Zbl 0041.36408
[5] Cohn, P. M., Free rings and Their Relations (1971), Academic Press: Academic Press New York · Zbl 0232.16003
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[8] Matlis, E., Torsion Free Modules, (Chicago Lectures in Mathematics Series (1972), Univ. of Chicago Press: Univ. of Chicago Press Chicago) · Zbl 0184.06602
[9] Nicolas, A. M., Extensions factorielles et modules factorables, Bull. Sc. Math. (2), 98, 117-143 (1974) · Zbl 0302.13006
[10] Nicolas, A. M., Sur certaines conditions de chaînes ascendantes dans les groupes abéliens et les modules sans torsion, Comm. Algebra, 5, 2, 171-191 (1977) · Zbl 0366.13005
[11] Pontryagin, L., Topological Groups (1966), Gordon & Breach: Gordon & Breach New York · Zbl 0022.17104
[12] Renault, G., Sur des conditions de chaînes ascendantes dans des modules libres, J. Algebra, 47, 268-275 (1977) · Zbl 0365.16011
[13] Renault, G., Algèbre non commutative (1965), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0307.16001
[14] Sabbach, G.; Eklof, P., Definability problems for modules and rings, J. Symbolic Logic, 36, No 4, 623-649 (December 1971)
[15] Soublin, J. P., Anneaux et modules cohérents, J. Algebra, 15, 455-472 (1970) · Zbl 0198.35803
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