Monomial ideals and toric rings of Hibi type arising from a finite poset

TL;DR

This paper explores monomial ideals from posets, introduces generalized Hibi rings, and examines their algebraic and homological properties using Groebner bases, sortability, and weakly polymatroidal ideals.

Contribution

It introduces generalized Hibi rings associated with posets and analyzes their algebraic and homological features with new theoretical tools.

Findings

Characterization of generalized Hibi rings

Application of Groebner basis theory to these rings

Identification of properties using weakly polymatroidal ideals

Abstract

In this paper we study monomial ideals attached to posets, introduce generalized Hibi rings and investigate their algebraic and homological properties. The main tools to study these objects are Groebner basis theory, the concept of sortability due to Sturmfels and the theory of weakly polymatroidal ideals.