AM  Vol.6 No.14 , December 2015
Regular Elements of the Semigroup B X (D) Defined by Semilattices of the Class Σ2 (X, 8) and Their Calculation Formulas
Author(s) Nino Tsinaridze, Shota Makharadze, Guladi Fartenadze
Affiliation(s)
Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia.
Abstract
The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B X (D) which is defined by semilattices of the class Σ2 (X, 8).
Keywords
Semilattice, Semigroup, Binary Relation, Regular Element

Cite this paper
Tsinaridze, N. , Makharadze, S. and Fartenadze, G. (2015) Regular Elements of the Semigroup B X (D) Defined by Semilattices of the Class Σ2 (X, 8) and Their Calculation Formulas. Applied Mathematics, 6, 2257-2278. doi: 10.4236/am.2015.614199.
References

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

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[4]   Tsinaridze, N. and Makharadze, Sh. (2015) Regular Elements of the Complete Semigroups of Binary Relations of the Class Applied Mathematics, 6, 447-455.

[5]   Diasamidze, Ya., Makharadze, Sh. and Diasamidze, Il. (2008) Idempotents and Regular Elements of Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, 153, 481-499.
http://dx.doi.org/10.1007/s10958-008-9132-1

[6]   Diasamidze, Ya. and Bakuridze, Al. (2015) On Some Properties of Regular Elements of Complete Semigroups Defined by Semilaices of the Class Σ4(x,8) International Journal of Engineering Science and Innovative Technology (IJESIT), 4, 8-15.

 
 
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