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

In this work, several properties of the convex polyhedron semigroups are studied. These semigroups are constructed from the dilation of bounded convex polyhedrons of R->=(3). For them, the Cohen-Macaulayness and Buchsbaumness properties are characterized in the simplicial case and algorithmic methods to check these properties are given. Another property, the Gorensteiness, is also studied and a family of semigroups fulfilling it is provided. (C) 2018 Elsevier B.V. All rights reserved.