We study the almost Gorenstein property in the sense of Goto et al for the class of normal semigroup rings. The graded version is related to the existence of what we call Ulrich elements for the semigroup. We provide an algebraic criterion for testing the Ulrich property for the class of slim semigroups that we introduce. Affine semigroups of small rank are slim, and in this setup, we obtain more precise results and the Ulrich property becomes easier to check.
This talk is based on joint work with J. Herzog and R. Jafari.