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

Shota Makharadze; Neşet Aydın; Ali Erdoğan

doi:10.4236/am.2015.62026

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Applied Mathematics > Vol.6 No.2, February 2015

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.
²&CCEDIL;anakkale Onsekiz Mart University, &CCEDIL;anakkale, Turkey.
³Hacettepe University, Ankara, Turkey.

DOI: 10.4236/am.2015.62026 PDF HTML XML 3,288 Downloads 3,655 Views Citations

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

Share and Cite:

Makharadze, S. , Aydın, N. and Erdoğan, A. (2015) Complete Semigroups of Binary Relations Defined by Semilattices of the Class ∑₁(X,10). Applied Mathematics, 6, 274-294. doi: 10.4236/am.2015.62026.

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 .