Canonical trace ideal and residue for numerical semigroup rings
type: Item
instance of: scholarly article
title: Canonical trace ideal and residue for numerical semigroup rings
zbMATH Open document ID: 1494.13003
author: Takayuki Hibi
author: Jürgen Herzog
author: Dumitru I. Stamate
published in: Semigroup Forum
publication date: 2021-09-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/2008.01428
review text: In this paper, the authors study numerical semigroup rings. They prove that for a numerical semigroup, \(H\), with three generators and a field, \(K\), the residue of \(K[H]\) is upper bounded by \(g(H)-n(H)\), where \(g(H)\) is the genus of \(H\) and \(n(H)\) is the cardinality of set \(\{x\in H\mid x\leq F(H)\}\) with \(F(H)\) being the Frobenius number of \(H\). Also, for the case of a numerical generators with embedding dimension three, they give a characterization for when the trace of \(H\) is \(H\setminus\{0\}\). Finally, they extend the definition of residue to finitely generated subsemigroups of \(\mathbb{N}\) and give conditions for computing it for shifted numerical semigroups.
reviewed by: Daniel Marín Aragon
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M13
Mathematics Subject Classification ID: 20M25
zbMATH DE Number: 7395083
zbMATH Keywords: numerical semigroup
zbMATH Keywords: residue
zbMATH Keywords: canonical module
zbMATH Keywords: trace ideal
zbMATH Keywords: nearly Gorenstein
zbMATH Keywords: conductor
zbMATH Keywords: shifted family
describes a project that uses: SINGULAR
describes a project that uses: numericalsgps
describes a project that uses: GAP
MaRDI profile type: Publication
OpenAlex ID: W3047608830
arXiv ID: 2008.01428
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DOI: 10.1007/S00233-021-10205-X
description: scientific article