Quasi-socle ideals in a Gorenstein local ring
Shiro Goto, Naoyuki Matsuoka, Ryo Takahashi
Abstract
This paper explores the structure of quasi-socle ideals I=Q:m2 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) = n ≥ 0In/In+1 is Cohen-Macaulay. Wild examples are explored.
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