A characterization of strong semilattices of periodic groups and rectangular bands by disjunctions of identities

Abstract

Each completely regular semigroup is a semilattice of completely simple semigroups. The more specific concept of a strong semilattice provides the concrete product between two arbitrary elements. We characterize strong semilattices of rectangular groups by so-called disjunctions of identities. Disjunctions of identities generalize the classical concept of an identity and of a variety, respectively. The rectangular groups will be on the one hand left zero semigroups and right zero semigroups and on the other hand groups of exponent [Formula: see text], where [Formula: see text] is any set of pairwise coprime natural numbers.