A Note on a Question of Bass

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1985Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 290, page 691 (issn: 0002-9947,

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Authors: Dutta, Sankar P.;

doi: 10.2307/2000307 , 10.1090/s0002-9947-1985-0792820-5

A Note on a Question of Bass

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Abstract

In this paper we study the following question raised by Bass: Is a local ring with a finitely generated module of finite injective dimension Cohen-Macaulay? We prove that the answer is in the affirmative when a certain local cohomology of the ring is either decomposible or cyclic. We also study the above question in some special cases and some of its implications.

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University of Pennsylvania
United States

Keywords

Homological dimension and commutative rings, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Cohen-Macaulayness, local ring, finite injective dimension

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