The set of trace ideals of curve singularities

2022/03/09 by Toshinori Kobayashi, Kobayashi, Toshinori, Shinya Kumashiro +1 · 2 citations
Computer Science · Mathematics · #13A15 #13C05 #16S36 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2203.04469

openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed ideals. We also explore properties of such rings related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.

Cited by

• Optimal Parametrizations and Valuations
• Some classes of one-dimensional rings characterized by their reflexive ideals

Related

• When are trace ideals finite?
• On the set of trace ideals of a Noetherian ring
• Trace ideals, normalization chains, and endomorphism rings
• Rings whose ideals are isomorphic to trace ideals
• Reflexive modules over the endomorphism algebras of reflexive trace ideals