# Almost Gorenstein Hibi rings

## TL;DR

This paper provides criteria for identifying when Hibi rings and ladder determinantal rings are almost Gorenstein, based on their structural properties, extending understanding of their algebraic and combinatorial characteristics.

## Contribution

It introduces new criteria linking the almost Gorenstein property of these rings to their defining poset or ladder shape, advancing classification methods.

## Key findings

- Criteria for Hibi rings to be level, non-Gorenstein, and almost Gorenstein.
- Criteria for Hibi rings to be non-level and almost Gorenstein.
- Criteria for ladder determinantal rings to be non-Gorenstein and almost Gorenstein.

## Abstract

In this paper, we state criteria of a Hibi ring to be level, non-Gorenstein and almost Gorenstein and to be non-level and almost Gorenstein in terms of the structure of the partially ordered set defining the Hibi ring. We also state a criterion of a ladder determinantal ring defined by 2-minors to be non-Gorenstein and almost Gorenstein in terms of the shape of the ladder.