Injective endormorphisms of finitely generated modules
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- by Wolmer V. Vasconcelos
- Proc. Amer. Math. Soc. 25 (1970), 900-901
- DOI: https://doi.org/10.1090/S0002-9939-1970-0258814-8
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Abstract:
Let $R$ be a commutative ring. Then any infective endomorphism of a finitely generated $R$-module is always an isomorphism if and only if $R$ is $0$-dimensional, that is, if every prime ideal is maximal.References
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- A. Grothendieck, Groupes diagonalisables, Schémas en Groupes (Sém. Géométrie Algébrique, Inst. Hautes Études Sci., 1963/64) Inst. Hautes Études Sci., Paris, 1964, pp. Fasc. 3, Exposé 8, 36 (French). MR 0212024
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- 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
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 900-901
- MSC: Primary 13.40
- DOI: https://doi.org/10.1090/S0002-9939-1970-0258814-8
- MathSciNet review: 0258814