Direct summands of syzygy modules of the residue class field
Commutative Algebra
2007-05-23 v1
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 of the residue field of R has a nontrivial 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
Cite
@article{arxiv.math/0703186,
title = {Direct summands of syzygy modules of the residue class field},
author = {Ryo Takahashi},
journal= {arXiv preprint arXiv:math/0703186},
year = {2007}
}
Comments
18 pages, to appear in Nagoya Mathematical Journal