Pseudo-Gorenstein and level Hibi rings
  We introduce pseudo-Gorenstein rings and characterize those Hibi rings attached to a finite distributive lattice L which are pseudo-Gorenstein. The characterization is given in terms of the poset of join-irreducible elements of L. We also present a necessary condition for Hibi rings to be level. Special attention is given to planar and hyper-planar lattices. Finally the pseudo-Goresntein and level property of Hibi rings and generalized Hibi rings is compared with each other. 
Viviana Ene, J\"urgen Herzog, Takayuki Hibi, Sara Saeedi Madani
math.AC math.CO