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

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DOI: 10.4236/am.2015.62026    3,023 Downloads   3,327 Views   Citations

ABSTRACT

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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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 .

  
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