The Lattice of Equational Classes of Idempotent Semigroups

Abstract

The lattice of equational classes of idempotent semigroups is completely described. It is shown that every equational class of idempotent semigroups is determined by a single equation (in addition to the associative and idempotent equations). A method is presented for finding which class a given equation determines, and when the class determined by one equation is contained in the class determined by a second equation.