Almost Gorenstein simplicial semigroup rings

We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari’s theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determine $2$-dimensional normal semigroup rings which have ``Ulrich elements’’ defined in [Herzog-Jafari-Stamate].