Semigroup Forum

, Volume 97, Issue 2, pp 278–306 | Cite as

Homogeneous numerical semigroups

  • Raheleh Jafari
  • Santiago Zarzuela Armengou
Research Article


We introduce the concept of homogeneous numerical semigroups and show that all homogeneous numerical semigroups with Cohen–Macaulay tangent cones are of homogeneous type. In embedding dimension three, we classify all numerical semigroups of homogeneous type into numerical semigroups with complete intersection tangent cones and the homogeneous ones which are not symmetric with Cohen–Macaulay tangent cones. We also study the behavior of the homogeneous property by gluing and shiftings to construct large families of homogeneous numerical semigroups with Cohen–Macaulay tangent cones. In particular we show that these properties fulfill asymptotically in the shifting classes. Several explicit examples are provided along the paper to illustrate the property.


Numerical semigroup rings Tangent cones Betti numbers 


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Authors and Affiliations

  1. 1.Mosaheb Institute of MathematicsKharazmi UniverstityTehranIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.Departament de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain

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