The short resolution of a semigroup algebra
Ignacio Ojeda, Alberto Vigneron-Tenorio
TL;DR
This paper extends the concept of short resolutions to all affine semigroups, provides a new characterization of Apéry sets, and offers a simple method to compute Frobenius numbers and Cohen-Macaulay properties.
Contribution
It generalizes short resolutions to any affine semigroup and introduces new characterizations for Apéry sets and Cohen-Macaulayness.
Findings
Generalized short resolution for affine semigroups
Characterization of Apéry sets enabling easier computation
New criteria for Cohen-Macaulay property in simplicial affine semigroups
Abstract
This work generalizes the short resolution given in Proc. Amer. Math. Soc. \textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a characterization of Ap\'{e}ry sets is given. This characterization lets compute Ap\'{e}ry sets of affine semigroups and the Frobenius number of a numerical semigroup in a simple way. We also exhibit a new characterization of the Cohen-Macaulay property for simplicial affine semigroups.
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