English

Quasi-socle ideals in a Gorenstein local ring

Commutative Algebra 2007-07-28 v2

Abstract

This paper explores the structure of quasi-socle ideals I=Q:m^2 in a Gorenstein local ring A, where Q is a parameter ideal and m is the maximal ideal in A. The purpose is to answer the problem of when Q is a reduction of I and when the associated graded ring G(I) = \bigoplus_{n \geq 0}I^n/I^{n+1} is Cohen-Macaulay. Wild examples are explored.

Keywords

Cite

@article{arxiv.math/0612333,
  title  = {Quasi-socle ideals in a Gorenstein local ring},
  author = {Shiro Goto and Naoyuki Matsuoka and Ryo Takahashi},
  journal= {arXiv preprint arXiv:math/0612333},
  year   = {2007}
}

Comments

20 pages, minor changes, to appear in J. Pure Appl. Algebra

R2 v1 2026-07-22T17:47:44.080Z