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A characterization of some families of Cohen-Macaulay, Gorenstein and/or Buchsbaum rings. (English) Zbl 1422.13021
The organization of this paper as follows: in Section 1, the concept of convex polytope/polyhedron semigroup is defined and some basic notions and results used in the rest of the work are given. In Section 2, the set $$L_{\mathbb{R}\geq}(P)\setminus \bigcup_{j\in\mathbb{N}}jP$$ is completely described by using geometric tools. In Section 3, the Cohen-Macaulay property is studied and an algorithm that checks for this property in affine simplicial convex polyhedron semigroups is given. A family of Gorenstein affine semigroups is given in Section 4. Lastly, in Section 5, Buchsbaum affine simplicial convex polyhedron semigroups are characterized and a family of such semigroups is obtained.
##### MSC:
 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
##### Software:
Macaulay2; Normaliz; Python
Full Text:
##### References:
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