Quasi-socle ideals in Gorenstein numerical semigroup rings

2007/10/06 by Shirô Gotô, Goto, Shiro, Satoru Kimura +3
Computer Science · Mathematics · #13A30 #13B22 #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0710.1386

openalex publication_date 2007/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quasi-socle ideals, that is the ideals I of the form I= Q : \mathfrakm^q in Gorenstein numerical semigroup rings over fields are explored, where Q is a parameter ideal, and \mathfrakm is the maximal ideal in the base local ring, and q ≥ 1 is an integer. The problems of when I is integral over Q and of when the associated graded ring G(I) = \bigoplus_{n ≥ 0}Iⁿ/Iⁿ⁺¹ of I is Cohen-Macaulay are studied. The problems are rather wild; examples are given.

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