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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    3,116 Downloads   3,482 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.

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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 .

  
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