Idempotent Elements of the Semigroups Bx(D) Defined by Semilattices of the Class ∑3(x,8) When Z7‡Ø

In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.

Generated Sets of the Complete Semigroup Binary Relations Defined by Semilattices of the Class Σ₈(<em>X</em>, <em>n</em>+ <em>k</em>+ 1)

In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.

Regular Elements and Right Units of Semigroup <i>B_x</i>(<i>D</i>) Defined Semilattice <i>D</i>for Which <i>V</i>(<i>D</i>,а)=Q ∈ &sum;₃(<i>X</i>,8)

In this paper we take subsemilattice of X-semilattice of unions D which satisfies the following conditions: We will investigate the properties of regular elements of the complete semigroup of binary relations Bx(D) satisfying V(D,а)=Q. For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of regular elements and right units of the respective semigroup.