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

Shota  Makharadze; Nino  Tsinaridze

doi:10.4236/am.2015.63042

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AM Vol.6 No.3 , March 2015

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

Nino Tsinaridze, Shota Makharadze

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 .

Keywords: Semilattice, Semigroup, Binary Relation

Cite this paper: Tsinaridze, N. and Makharadze, S. (2015) Regular Elements of the Complete Semigroups B_X(D) of Binary Relations of the Class ∑₂(X,8). Applied Mathematics, 6, 447-455. doi: 10.4236/am.2015.63042.

References

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