Chains and anti-chains in the lattice of epigroup varieties

Abstract

Let ${\mathcal{E}}_n$ be the variety of all epigroups of index $\le n$. We prove that, for an arbitrary natural number $n$, the interval $[{\mathcal{E}}_n,{\mathcal{E}}_{n+1}]$ of the lattice of epigroup varieties contains a chain isomorphic to the chain of real numbers with the usual order and an anti-chain of the cardinality continuum.

arXiv comment5 pages, 2 figures