The short resolution of a semigroup algebra

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 Apéry sets is given. This characterization lets compute Apéry 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.

arXiv comment12 pages. In this new version, some proofs have been detailed, the references on the computatation of the Frobenius number of a numerical semigroup have been updated and some typpos have been corrected