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Paper   IPM / M / 16552
School of Mathematics
  Title:   Ulrich elements in normal simplicial affine semigroups
  Author(s):  Raheleh Jafari (Joint with J. Herzog and D. I. Stamate)
  Status:   Published
  Journal: Pacific J. Math.
  Vol.:  309
  Year:  2020
  Pages:   353-380
  Supported by:  IPM
Let H ⊆ \NNd be a normal affine semigroup, R=K[H] its semigroup ring over the field K and ωR its canonical module. The Ulrich elements for H are those h in H such that for the multiplication map by \xbh from R into ωR, the cokernel is an Ulrich module. We say that the ring R is almost Gorenstein if Ulrich elements exist in H. For the class of slim semigroups that we introduce, we provide an algebraic criterion for testing the Ulrich propery. When d=2, all normal affine semigroups are slim. Here we have a simpler combinatorial description of the Ulrich property. We improve this result for testing the elements in H which are closest to zero. In particular, we give a simple arithmetic criterion for when is (1,1) an Ulrich element in H.

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