Regular Elements of the Semigroup *B*_{ X } (*D*) Defined by Semilattices of the Class Σ_{2} (*X*, 8) and Their Calculation Formulas

Abstract

The paper gives description of regular elements of the semigroup*B*_{ X }* (**D**) *which are defined by semilattices of the class Σ_{2}* (**X**, 8), **f*or 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.* I*n 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 *Σ*_{2}* (**X**, 8).*

The paper gives description of regular elements of the semigroup

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 Σ_{2} (*X*, 8) and Their Calculation Formulas. *Applied Mathematics*, **6**, 2257-2278. doi: 10.4236/am.2015.614199.

Tsinaridze, N. , Makharadze, S. and Fartenadze, G. (2015) Regular Elements of the Semigroup

References

[1] Diasamidze, Ya. and Makharadze, Sh. (2013) Complete Semigroups of Binary Relations. Monograph, Kriter, Turkey, 1-520 p.

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

[3] Diasamidze, Ya. (2009) The Properties of Right Units of Semigroups Belonging to Some Classes of Complete Semigroups of Binary Relations. Proceedings of A. Razmadze Mathematical Institute, 150, 51-70.

[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 Σ_{4}(x,8) International Journal of Engineering Science and Innovative Technology (IJESIT), 4, 8-15.