On the Lattice of Varieties of Involution Semigroups

Abstract

In this paper, we investigate the lattice \smallbf L( \cal S ^\ast) of varieties of involution semigroups (semigroups endowed with an involutorial antiautomorphism ^\ast as a fundamental operation). There are two kinds of atoms in \smallbf L( \cal S ^\ast) : four nongroup ones and two countably infinite families of varieties of groups with involution. We exhibit the sublattices of \smallbf L( \cal S ^\ast) generated by both of these two collections of its atoms.