Limit varieties of aperiodic monoids with commuting idempotents

TL;DR

This paper classifies all limit varieties of aperiodic monoids with commuting idempotents, expanding understanding of their algebraic structure and the boundaries of finite basis properties.

Contribution

It provides a complete classification of limit varieties within a specific class of aperiodic monoids with commuting idempotents, a previously unresolved problem.

Findings

Identified all limit varieties of the specified monoids.

Established criteria for a variety to be limit in this context.

Enhanced understanding of the structure of aperiodic monoids with commuting idempotents.

Abstract

A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. A monoid is aperiodic if all its subgroups are trivial. We classify all limit varieties of aperiodic monoids with commuting idempotents.