Limit varieties generated by finite non-J-trivial aperiodic monoids

TL;DR

This paper investigates specific finite monoids that generate complex algebraic structures called limit varieties, expanding understanding of the lattice of subvarieties within a particular hereditarily finitely based variety.

Contribution

It identifies syntactic monoids generating finitely generated subvarieties of a known limit variety and introduces a new limit variety generated by specific finite monoids.

Findings

Identification of syntactic monoids generating finitely generated subvarieties

Construction of a new limit variety from finite monoids

Analysis of the lattice of subvarieties within the studied variety

Abstract

Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety $\mathbb E^1$ whose lattice of subvarieties contains an infinite ascending chain. We identify syntactic monoids which generate finitely generated subvarieties of $\mathbb E^1$ and show that one of these finite monoids together with certain seven-element monoid generates a new limit variety.