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The paper gives description of regular elements of the semigroup  B x (D)  which are defined by semilattices of the class Σ 2 ( X ,8), for which intersection the minimal elements is 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 B x (D) which is defined by semilattices of the class Σ 2 (X,8).

international journal of pure mathematical sciences

Regular Elements of the Semigroup B&lt;sub&gt;x&lt;/sub&gt;(D) Defined by Semilattices of the Class Σ&lt;sub&gt;2&lt;/sub&gt;(X,8), when Ζ&lt;sub&gt;7 &lt;/sub&gt;∩ Z&lt;sub&gt;6 &lt;/sub&gt;=Ø and their Calculation Formulas