\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
Let $H\subseteq \NN^d$ be a normal
affine semigroup, $R=K[H]$ its semigroup ring over the field $K$ and $\omega_R$ 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 $\omega_R$, 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 $H$.
\end{document}