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In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (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.

applied mathematics

Complete Semigroups of Binary Relations Defined by Semilattices of the Class &amp;amp;sum;&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;(&amp;lt;i&amp;gt;X&amp;lt;/i&amp;gt;,10)