“School of Mathematics”
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Paper IPM / M / 16552  


Abstract:  
Let H ⊆ \NN^{d} be a normal
affine semigroup, R=K[H] its semigroup ring over the field K and ω_{R} its canonical module.
The Ulrich elements for H are those h in H such that for the multiplication map by \xb^{h} from R into ω_{R}, 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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