A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings

Abstract

We provide algorithmic methods to check the Cohen--Macaulayness, Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are constructed from the dilation of bounded convex polyhedrons of ${\mathbb{R}}_{\ge }^3$. Some families of semigroup rings are given satifying these properties.