The reduction number of canonical ideals

2020/07/01 by Shinya Kumashiro, Kumashiro, Shinya · 3 citations
Mathematics · #13D40 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary: 13H10 #Rings, Modules, and Algebras #Secondary: 13B02

paper · pdf · doi:10.48550/arxiv.2007.00377

openalex publication_date 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce an invariant of Cohen-Macaulay local rings in terms of the reduction number of canonical ideals. The invariant can be defined in arbitrary Cohen-Macaulay rings and it measures how close to being Gorenstein. First, we clarify the relation between almost Gorenstein rings and nearly Gorenstein rings by using the invariant in dimension one. We next characterize the idealization of trace ideals over Gorenstein rings in terms of the invariant. It provides better prospects for a result of the almost Gorenstein property of idealization.

Cited by

• Characterization of almost Gorenstein rings in terms of the trace ideal
• Annihilation of cohomology over one dimensional almost Gorenstein rings
• When is the canonical conductor minimal?

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