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Diasamidze, Ya. and Makharadze, Sh. (2010) Complete Semigroups of Binary Relations. Monograph. M., Sputnik+, 657 p. (In Russian)

has been cited by the following article:

• TITLE: Regular Elements of the Complete Semigroups BX(D) of Binary Relations of the Class ∑2(X,8)

  AUTHORS: Nino Tsinaridze, Shota Makharadze

  KEYWORDS: Semilattice, Semigroup, Binary Relation

  JOURNAL NAME: Applied Mathematics, Vol.6 No.3, March 3, 2015

  ABSTRACT: 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∈∑2(X,8) . Because the semilattice Q of the class ∑2(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 .