On the Lattice of Varieties of Involution Semigroups

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. September 9, 1999