In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class Σ1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.

How to cite this paper: Tsinaridze, N. and Makharadze, S. (2015)

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.

The paper gives description of regular elements of the semigroup BX(D) which are defined by semilattices of the class Σ2(X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup BX(D) which is defined by semilattices of the class Σ2(X, 8).