Good ideals and $p_g$-ideals in two-dimensional normal singularities
  In this paper, we introduce the notion of $p_g$-ideals and $p_g$-cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we prove an existence of good ideals for two-dimensional Gorenstein normal local rings. Moreover, we classify all Ulrich ideals for two-dimensional simple elliptic singularities with small degree. 
Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida
math.AC math.AG