# Another characterization of congruence distributive varieties

## TL;DR

This paper offers a new Maltsev-based characterization of congruence distributive varieties, establishing an equivalence with a specific congruence identity involving a finite number of factors.

## Contribution

It introduces a novel Maltsev characterization of congruence distributive varieties through a specific congruence identity involving a finite number of factors.

## Key findings

- Characterizes congruence distributive varieties via a congruence identity.
- Establishes equivalence between Maltsev conditions and the identity.
- Provides a new criterion for identifying such varieties.

## Abstract

We provide a Maltsev characterization of congruence distributive varieties by showing that a variety $\mathcal {V}$ is congruence distributive if and only if the congruence identity $\alpha \cap (\beta \circ \gamma \circ \beta ) \subseteq \alpha \beta \circ \gamma \circ \alpha \beta \circ \gamma \dots $ ($k$ factors) holds in $\mathcal {V}$, for some natural number $k$.