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), for which intersection the minimal elements is 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 Σ_{2}(X,8).

Periodical:

International Journal of Pure Mathematical Sciences (Volume 16)

Pages:

1-23

Citation:

Y. Diasamidze and N. Tsinaridze, "Regular Elements of the Semigroup B_{x}(D) Defined by Semilattices of the Class Σ_{2}(X,8), when Ζ_{7 }∩ Z_{6 }=Ø and their Calculation Formulas", International Journal of Pure Mathematical Sciences, Vol. 16, pp. 1-23, 2016

Online since:

Mar 2016

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

[1] Ya. Diasamidze, Sh. Makharadze. Complete Semigroups of binary relations. Monograph. Kriter, Turkey, 2013, 1-520 pp.

[2] Ya. Diasamidze, Sh. Makharadze. Complete Semigroups of binary relations. Monograph. M., Sputnik+, 2010, 657 p. (Russian).

[3] Ya. Diasamidze. The properties of right units of semigroups belonging to some classes of complete semigroups of binary relations. Proc. of A. Razmadze Math. Inst. 150, 2009, 51-70.

[4] Ya. Diasamidze, Sh. Makharadze, Il. Diasamidze. Idempotents and regular elements of complete semigroups of binary relations. Journal of Mathematical Sciences, Plenum Publ. Cor., New York, 153, № 4, 2008, 481-499.

DOI: https://doi.org/10.1007/s10958-008-9132-1[5] N. Tsinaridze, Sh. Makharadze. Regular Elements of the Complete Semigroups of Binary Relations of the Class. Applied Mathematics, 2015, 6, 447-455.

[6] N. Tsinaridze, Sh. Makharadze, G. Fartenadze. Regular Elements of the Semigroup Defined by Semilattices Of the Class and their calculation Formulas. Applied Mathematics (to appear).

[7] N. Tsinaridze, Ya. Diasamidze. Maximal Subgroups of the Semigroup Defined by Semilattices of The Class. International Journal of Engineering Science and Innovative Technology (IJESIT) (to appear).