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Almost Gorenstein simplicial semigroup rings

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arxiv 2406.05781 v1 pith:NWYQHGTZ submitted 2024-06-09 math.AC

Kazufumi Eto , Naoyuki Matsuoka , Takahiro Numata , Kei-ichi Watanabe This is my paper · ORCID
classification math.AC
keywords almostringssemigroupsemigroupssimplicialcriteriongorensteinassociated
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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 $2$-dimensional normal semigroup rings which have ``Ulrich elements'' defined in [Herzog-Jafari-Stamate].

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  1. On nearly Gorenstein affine semigroups

    math.AC 2024-11 conditional novelty 7.0 of 10

    Nearly Gorenstein affine semigroup rings of codimension three have Cohen-Macaulay type at most three (and at least the dimension when not Gorenstein), with both bounds sharp.

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