Classification of limit varieties of J-trivial monoids

TL;DR

This paper classifies all seven limit varieties of J-trivial monoids, which are algebraic structures that are non-finitely based but have finitely based proper subvarieties, expanding the understanding of their structural properties.

Contribution

The paper introduces a new pair of limit varieties of monoids and completes the classification of all limit varieties of J-trivial monoids.

Findings

Identified a new pair of limit varieties of monoids.

Established that there are exactly seven limit varieties of J-trivial monoids.

Extended previous classifications by Jackson, Zhang, Luo, and the first author.

Abstract

A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show that together with the five limit varieties of monoids previously discovered by Jackson, Zhang and Luo and the first-named author, there are exactly seven limit varieties of J-trivial monoids.