On the generators of the canonical module of a Hibi ring: a criterion of level property and the degrees of generators

TL;DR

This paper investigates the minimal generators of the canonical module in Hibi rings, providing criteria for levelness and type 2 classification, and showing the degrees of generators form consecutive integers.

Contribution

It offers new characterizations for Hibi rings being level or of type 2, and describes the structure of the degrees of generators of the canonical module.

Findings

Characterization of level Hibi rings

Criterion for Hibi rings to be of type 2

Degrees of generators form consecutive integers

Abstract

In this paper, we study the minimal generating system of the canonical module of a Hibi ring. Using the results, we state a characterization of a Hibi ring to be level. We also give a characterization of a Hibi ring to be of type 2. Further, we show that the degrees of the elements of the minimal generating system of the canonical module of a Hibi ring form a set of consecutive integers.