Cross varieties of aperiodic monoids

Abstract

A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.

17 pages, 2 figures

References in corpus (8)

• Chain varieties of monoids
• A new example of a limit variety of monoids
• Classification of limit varieties of J-trivial monoids
• Limit varieties of aperiodic monoids with commuting idempotents
• Limit varieties of monoids satisfying a certain identity
• Cross varieties of aperiodic monoids with commuting idempotents
• Varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive
• Characterization of Cross varieties of $J$-trivial monoids