Endomorphisms of finitely presented modules
HTML articles powered by AMS MathViewer
- by Gabriel Sabbagh PDF
- Proc. Amer. Math. Soc. 30 (1971), 75-78 Request permission
Abstract:
It is proved that every surjective or injective endomorphism of a finitely presented left module over a right perfect ring is an isomorphism.References
- Gorô Azumaya, Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt’s theorem, Nagoya Math. J. 1 (1950), 117–124. MR 37832
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- Jan-Erik Björk, Rings satisfying a minimum condition on principal ideals, J. Reine Angew. Math. 236 (1969), 112–119. MR 248165, DOI 10.1515/crll.1969.236.112 N. Bourbaki, Algébre commutative. Chaps. 1, 2, Actualités Sci. Indust., no. 1290, Hermann, Paris, 1961. MR 36 #146.
- P. M. Cohn, Hereditary local rings, Nagoya Math. J. 27 (1966), 223–230. MR 197498
- Samuel Eilenberg, Homological dimension and syzygies, Ann. of Math. (2) 64 (1956), 328–336. MR 82489, DOI 10.2307/1969977
- Irving Kaplansky, Projective modules, Ann. of Math (2) 68 (1958), 372–377. MR 0100017, DOI 10.2307/1970252
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- Jan R. Strooker, Lifting projectives, Nagoya Math. J. 27 (1966), 747–751. MR 197514
- Wolmer V. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505–512. MR 238839, DOI 10.1090/S0002-9947-1969-0238839-5
- Wolmer V. Vasconcelos, Injective endormorphisms of finitely generated modules, Proc. Amer. Math. Soc. 25 (1970), 900–901. MR 258814, DOI 10.1090/S0002-9939-1970-0258814-8
- R. B. Warfield Jr., A Krull-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969), 460–465. MR 242886, DOI 10.1090/S0002-9939-1969-0242886-2
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 75-78
- MSC: Primary 16.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283015-8
- MathSciNet review: 0283015