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.
Almost Gorenstein simplicial semigroup rings
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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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2024 1verdicts
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On nearly Gorenstein affine semigroups
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.