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
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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.
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
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Diasamidze, Ya. and Makharadze, Sh. (2013) Complete Semigroups of Binary Relations. Monograph. Kriter, Turkey, 620 p.
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[2]
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Diasamidze, Ya. and Makharadze, Sh. (2010) Complete Semigroups of Binary Relations. Monograph. M., Sputnik+, 657 p. (In Russian)
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[3]
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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.
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[4]
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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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