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2008 Direct summands of syzygy modules of the residue class field
Ryo Takahashi
Nagoya Math. J. 189: 1-25 (2008).

Abstract

Let $R$ be a commutative Noetherian local ring. This paper deals with the problem asking whether $R$ is Gorenstein if the $n$th syzygy module of the residue class field of $R$ has a non-trivial direct summand of finite G-dimension for some $n$. It is proved that if $n$ is at most two then it is true, and moreover, the structure of the ring $R$ is determined essentially uniquely.

Citation

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Ryo Takahashi. "Direct summands of syzygy modules of the residue class field." Nagoya Math. J. 189 1 - 25, 2008.

Information

Published: 2008
First available in Project Euclid: 10 March 2008

zbMATH: 1132.13305
MathSciNet: MR2396581

Subjects:
Primary: 13D02
Secondary: 13D05 , 13H10

Keywords: direct summand , G-dimension , Gorenstein ring , syzygy module

Rights: Copyright © 2008 Editorial Board, Nagoya Mathematical Journal

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