Almost Gorenstein simplicial semigroup rings
Kazufumi Eto, Naoyuki Matsuoka, Takahiro Numata, and Kei-ichi Watanabe
TL;DR
This paper establishes a criterion for identifying almost Gorenstein properties in simplicial semigroup rings, extending previous theorems to higher dimensions and characterizing certain 2D rings with special elements.
Contribution
It introduces a new criterion for almost Gorenstein simplicial semigroup rings and generalizes Nari's theorem to higher-rank semigroups.
Findings
Criterion for almost Gorenstein property in simplicial semigroup rings
Extension of Nari's theorem to higher-rank semigroups
Classification of 2D normal semigroup rings with Ulrich elements
Abstract
We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determine -dimensional normal semigroup rings which have ``Ulrich elements'' defined in [Herzog-Jafari-Stamate].
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras