Complete Semigroups of Binary Relations Defined by Semilattices of the Class Z−elementary X−semilattice of Unions

Abstract

In this paper we investigate idempotents of complete semigroups of binary relations defined by semilattices of the class Z−elementary X−semilattice of unions. For the case where X is a finite set we derive formulas by calculating the numbers of idempotents of the respective semigroup.