Quasi-socle ideals in a Gorenstein local ring

2006/12/13 by Shirô Gotô, Goto, Shiro, Naoyuki Matsuoka +3 · 1 citation
Mathematics · #13A30 #13B22 #13H10 #13H15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0612333

openalex publication_date 2006/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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) = \bigoplus_{n ≥ 0}Iⁿ/Iⁿ⁺¹ is Cohen-Macaulay. Wild examples are explored.

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• The Goto numbers of parameter ideals

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