Complete Semigroups of Binary Relations Defined by Semilattices of the Class ∑₁(X,10)

Shota Makharadze¹, Neşet Aydın², Ali Erdoğan³

¹Shota Rustavelli University, Batum, Georgia.
²Çanakkale Onsekiz Mart University, Çanakkale, Turkey.
³Hacettepe University, Ankara, Turkey.

DOI: 10.4236/am.2015.62026                

Abstract

In this paper we give a full description of idempotent elements of the semigroup B_X (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.

Keywords

Semilattice, Semigroup, Binary Relation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Diasamidze, Ya. and Makharadze, Sh. (2013) Complete Semigroups of Binary Relations. Monograph. Kriter, Turkey, 620 p.
[2]	Diasamidze, Ya. and Makharadze, Sh. (2010) Complete Semigroups of Binary Relations. Monograph. M., Sputnik+, 657 p. (In Russian)
[3]	Diasamidze, Ya., Makharadze, Sh. and Diasamidze, Il. (2008) Idempotents and Regular Elements of Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, Plenum Publ. Cor., New York, 153, 481-499.
[4]	Diasamidze, Ya. and Bakuridze, Al. (to appear) On Some Properties of Regular Elements of Complete Semigroups Defined by Semilattices of the Class .