Pseudo-Gorenstein and level Hibi rings
Viviana Ene, J\"urgen Herzog, Takayuki Hibi, Sara Saeedi Madani
TL;DR
This paper introduces pseudo-Gorenstein rings, characterizes pseudo-Gorenstein Hibi rings via poset structures, and explores conditions for Hibi rings to be level, with focus on planar lattices.
Contribution
It provides a new classification of pseudo-Gorenstein Hibi rings based on poset properties and offers a necessary condition for Hibi rings to be level.
Findings
Characterization of pseudo-Gorenstein Hibi rings in terms of poset of join-irreducible elements
Necessary condition for Hibi rings to be level
Comparison of pseudo-Gorenstein and level properties in Hibi and generalized Hibi rings
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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