Quasi-socle ideals in a Gorenstein local ring

Details Quasi-socle ideals in a Gorenstein local ring Quasi-socle ideals in a Gorenstein local ring

2006-12-13

arxiv.org/abs/math/0612333v2

Mathematics

Commutative Algebra

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

Scientific paper

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.

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