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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Injective endormorphisms of finitely generated modules

Author: Wolmer V. Vasconcelos
Journal: Proc. Amer. Math. Soc. 25 (1970), 900-901
MSC: Primary 13.40
MathSciNet review: 0258814
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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.

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PII: S 0002-9939(1970)0258814-8
Keywords: Injective endomorphism, finitely generated module, Krull dimension zero
Article copyright: © Copyright 1970 American Mathematical Society