Canonical trace ideal and residue for numerical semigroup rings

DOI10.1007/s00233-021-10205-xzbMath1494.13003arXiv2008.01428OpenAlexW3047608830MaRDI QIDQ1982581

Takayuki Hibi, Jürgen Herzog, Dumitru Ioan Stamate

Publication date: 14 September 2021

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.01428

zbMATH Keywords

conductorcanonical modulenumerical semigroupresiduetrace idealnearly Gorensteinshifted family

Mathematics Subject Classification ID

Commutative semigroups (20M14) Ideals and multiplicative ideal theory in commutative rings (13A15) Semigroup rings, multiplicative semigroups of rings (20M25) Arithmetic theory of semigroups (20M13)

Related Items (10)

The trace property in preenveloping classes ⋮ RINGS OF TETER TYPE ⋮ Upper bound on the colength of the trace of the canonical module in dimension one ⋮ When are trace ideals finite? ⋮ The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one ⋮ Nearly Gorenstein polytopes ⋮ Levelness versus nearly Gorensteinness of homogeneous rings ⋮ On the set of trace ideals of a Noetherian ring ⋮ Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein ⋮ Stable set rings which are Gorenstein on the punctured spectrum

Uses Software

• GAP
• numericalsgps
• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic properties in the shifted family of a numerical semigroup with few generators
• Almost Gorenstein rings
• On the defining equations of the tangent cone of a numerical semigroup ring
• Periodicity of Betti numbers of monomial curves
• Trace ideals and centers of endomorphism rings of modules over commutative rings
• Numerical semigroups.
• One-dimensional almost Gorenstein rings
• Betti numbers for numerical semigroup rings
• Apéry sets of shifted numerical monoids
• Genus of numerical semigroups generated by three elements.
• Symmetries on almost symmetric numerical semigroups.
• Nearly Gorenstein vs almost Gorenstein affine monomial curves
• The trace of the canonical module
• Almost symmetric numerical semigroups
• Minimal graded free resolutions for monomial curves defined by arithmetic sequences
• Generators and relations of abelian semigroups and semigroup rings
• Pseudo-symmetric numerical semigroups with three generators.
• Periodic occurrence of complete intersection monomial curves
• Minimal presentations of shifted numerical monoids
• Minimal set of generators for the derivation module of certain monomial curves
• numericalsgps, a GAP package for numerical semigroups
• The Value-Semigroup of a One-Dimensional Gorenstein Ring
• On numerical semigroups

This page was built for publication: Canonical trace ideal and residue for numerical semigroup rings