The reduction number of stretched ideals

2021/09/27 by Kazuho Ozeki, Ozeki, Kazuho
Computer Science · Mathematics · #13D40 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary:13A30 #Secondary: 13H10

paper · pdf · doi:10.48550/arxiv.2109.12918

openalex publication_date 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched \mathfrakm-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring (A,\mathfrakm). As an application, we present complete descriptions of the associated graded ring of stretched \mathfrakm-primary ideals with small reduction number.

Related

• The first Hilbert coefficient of stretched ideals
• Generalized stretched ideals and Sally Conjecture
• Generalized stretched ideals and Sally's Conjecture
• The depth of the associated graded ring of ideals with any reduction number
• The reduction number of canonical ideals