Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive

TL;DR

This paper provides a complete classification of aperiodic monoid varieties with central idempotents that have a distributive subvariety lattice, advancing the understanding of their algebraic structure.

Contribution

It offers the first comprehensive classification of such monoid varieties with distributive subvariety lattices.

Findings

Complete classification of the varieties

Identification of structural properties leading to distributivity

Clarification of the relationship between idempotents and lattice structure

Abstract

We completely classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive.