Complete Semigroups of Binary Relations Defined by Semilattices of the Class ∑<sub>1</sub>(<i>X</i>,10)

Abstract

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.

Regular Elements of <i>B<sub>x</sup></i>(D) Defined by the Class ∑<sub>1</sub>(X,10)-<i>I</i>

“…For any map f from X to D, we define a binary relation. All notations, symbol and required definitions used in this work can be found in [7]. Recall…”