Maltsev conditions for general congruence meet-semidistributive algebras

TL;DR

This paper introduces a new Maltsev condition that characterizes meet-semidistributive varieties in universal algebra, addressing a longstanding open problem in the field.

Contribution

It proposes a simple Maltsev condition for meet-semidistributive varieties and suggests a candidate for a strong Maltsev condition, advancing the understanding of algebraic classifications.

Findings

New Maltsev condition characterizes meet-semidistributive varieties

Candidate for a strong Maltsev condition is proposed

Progress towards classifying algebraic varieties by Maltsev conditions

Abstract

Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev condition. We present a new, relatively simple Maltsev condition characterizing the meet-semidistributive varieties, and provide a candidate for a strong Maltsev condition.