Regular Elements and Right Units of Semigroup *B*_{x}(*D*) Defined Semilattice *D* for Which *V*(*D*,а)=Q ∈ ∑_{3}(*X*,8)

ABSTRACT

In this paper we take subsemilattice of*X*-semilattice of unions *D* which satisfies the following conditions:

We will investigate the properties of regular elements of the complete semigroup of binary relations*B*_{x}(*D*) satisfying *V*(*D*,а)=*Q*. For the case where *X* is a finite set we derive formulas by means of which we can calculate the numbers of regular elements and right units of the respective semigroup.

In this paper we take subsemilattice of

We will investigate the properties of regular elements of the complete semigroup of binary relations

Cite this paper

Tavdgiridze, G. and Diasamidze, Y. (2015) Regular Elements and Right Units of Semigroup*B*_{x}(*D*) Defined Semilattice *D* for Which *V*(*D*,а)=Q ∈ ∑_{3}(*X*,8). *Applied Mathematics*, **6**, 373-381. doi: 10.4236/am.2015.62035.

Tavdgiridze, G. and Diasamidze, Y. (2015) Regular Elements and Right Units of Semigroup

References

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

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

[3] Lyapin, E.S. (1960) Semigroups. Fizmatgiz, Moscow. (In Russian)

[4] Diasamidze, Ya.I. (2003) Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, 117, 4271-4319.

[5] Diasamidze, Ya.I., Makharadze, Sh.I. and Diasamidze, I.Ya. (2008) Idempotents and Regular Elements of Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, 153, 481-499.

[6] Diasamidze, Ya., Makharadze, Sh. and Rokva, N. (2008) On XI-Semilattices of Union. Bull. Georg. Nation. Acad. Sci., 2, 16-24.

[7] Diassamidze, Ya., Erdogan, A. and Aydm, N. (2014) Some Regular Elements, Idempotents and Right Units of Complete Semigroups of Binary Relations Defined by Semilattices of the Class Lower Incomplete Nets. International Journal of Pure and Applied Mathematics, 93, 549-566.

http://dx.doi.org/10.12732/ijpam.v93i4.6

[8] Diasamidze, Ya. (2009) The Properties of Right Units of Semigroups Belonging to Some Classes of Complete Semigroups of Binary Relations. Proc. of A. Razmadze Math. Inst., 150, 51-70.

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

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

[3] Lyapin, E.S. (1960) Semigroups. Fizmatgiz, Moscow. (In Russian)

[4] Diasamidze, Ya.I. (2003) Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, 117, 4271-4319.

[5] Diasamidze, Ya.I., Makharadze, Sh.I. and Diasamidze, I.Ya. (2008) Idempotents and Regular Elements of Complete Semigroups of Binary Relations. Journal of Mathematical Sciences, 153, 481-499.

[6] Diasamidze, Ya., Makharadze, Sh. and Rokva, N. (2008) On XI-Semilattices of Union. Bull. Georg. Nation. Acad. Sci., 2, 16-24.

[7] Diassamidze, Ya., Erdogan, A. and Aydm, N. (2014) Some Regular Elements, Idempotents and Right Units of Complete Semigroups of Binary Relations Defined by Semilattices of the Class Lower Incomplete Nets. International Journal of Pure and Applied Mathematics, 93, 549-566.

http://dx.doi.org/10.12732/ijpam.v93i4.6

[8] Diasamidze, Ya. (2009) The Properties of Right Units of Semigroups Belonging to Some Classes of Complete Semigroups of Binary Relations. Proc. of A. Razmadze Math. Inst., 150, 51-70.