  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.
