%0 Journal Article %T Regular Elements of the Complete Semigroups <i>B<sub>X</sub>(D)</i> of Binary Relations of the Class &sum;<sub>2</sub>(<i>X</i>,8) %A Nino Tsinaridze %A Shota Makharadze %J Applied Mathematics %P 447-455 %@ 2152-7393 %D 2015 %I Scientific Research Publishing %R 10.4236/am.2015.63042 %X As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q¡Ê¡Æ2(X,8) . Because the semilattice Q of the class ¡Æ2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q . %K Semilattice %K Semigroup %K Binary Relation %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=54371