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Direct Summands of Syzygy Modules of the Residue Class Field

Published online by Cambridge University Press:  11 January 2016

Ryo Takahashi
Ryo Takahashi*
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, takahasi@math.meiji.ac.jp
*
Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan, takahasi@math.shinshu-u.ac.jp
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Abstract

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Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth 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.

Keywords

13D0213D0513H10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 189 , 2008 , pp. 1 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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