# Compatible algebras with straightening laws on distributive lattices

## TL;DR

This paper characterizes finite distributive lattices that admit a unique compatible algebra with straightening laws, providing a clear understanding of their algebraic structure.

## Contribution

It introduces a characterization of finite distributive lattices with a unique compatible algebra with straightening laws, advancing the theoretical understanding of these algebraic structures.

## Key findings

- Identifies conditions for the existence of a unique compatible algebra with straightening laws.
- Provides a classification of finite distributive lattices based on their algebraic compatibility.
- Enhances the theoretical framework connecting distributive lattices and straightening laws.

## Abstract

We characterize the finite distributive lattices on which there exists a unique compatible algebra with straightening laws.