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...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-06, Vol.263, p.166-176
Main Authors: García-García, J.I., Marín-Aragón, D., Vigneron-Tenorio, A.
Format: Article
Language:English
Subjects:
Affine semigroup
Buchsbaum ring
Cohen–Macaulay ring
Gorenstein ring
Polyhedra
Properties (attributes)
Rings (mathematics)
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.03.021