Regular Elements of the Semigroup B X (D) Defined by Semilattices of the Class Σ2 (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 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).
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).
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.
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
[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 Σ4(x,8) International Journal of Engineering Science and Innovative Technology (IJESIT), 4, 8-15.
[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 Σ4(x,8) International Journal of Engineering Science and Innovative Technology (IJESIT), 4, 8-15.