Regular Elements of the Semigroup <i>B</i><sub> X </sub> (<i>D</i>) Defined by Semilattices of the Class Σ<sub>2</sub> (<i>X</i>, 8) and Their Calculation Formulas

Abstract

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).