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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Embedding of modules over Gorenstein rings


Author: Hans-Bjørn Foxby
Journal: Proc. Amer. Math. Soc. 36 (1972), 336-340
MSC: Primary 13H10; Secondary 13C99
DOI: https://doi.org/10.1090/S0002-9939-1972-0309930-5
MathSciNet review: 0309930
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Abstract: Let A be a noetherian commutative ring which is a homomorphic image of a Gorenstein ring. The first result in this note is that A is a Cohen-Macaulay ring if and only if every finitely generated A-module can be embedded in a finitely generated A-module T which is pointwise of finite injective dimension (i.e. all localizations of T are of finite injective dimension). The second result is that if A is Cohen-Macaulay, then every finitely generated A-module can be embedded in a finitely generated A-module of finite projective dimension if and only if A is Gorenstein.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0309930-5
Keywords: Cohen-Macaulay rings, Gorenstein rings, G-dimension
Article copyright: © Copyright 1972 American Mathematical Society