Pseudo-Gorenstein and level Hibi rings

2014/05/27 by Ene, Viviana, Herzog, Jürgen, Hibi, Takayuki +1 · 3 citations
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1405.6963

Abstract

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.

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• Bounded powers of edge ideals: Pseudo-Gorenstein and Level polytopes
• Higher-dimensional Teter rings via the canonical trace
• Extremal Betti numbers of certain two-dimensional monomial ideals

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