Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class ∑_{3}(*X*,9)

Abstract

In this paper, we take*Q*_{16} subsemilattice of *D* and we will calculate the number of right unit, idempotent and regular elements *α* of *B*_{X} (*Q*_{16}) satisfied that *V* (*D*, *α*) = *Q*_{16} for a finite set *X*. Also we will give a formula for calculate idempotent and regular elements of *B*_{X} (*Q*) defined by an *X*-semilattice of unions *D*.

In this paper, we take

Cite this paper

Albayrak, B. and Aydın, N. (2015) Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class ∑_{3}(*X*,9). *Applied Mathematics*, **6**, 312-318. doi: 10.4236/am.2015.62029.

Albayrak, B. and Aydın, N. (2015) Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class ∑

References

[1] Diasamidze, Ya. and Makharadze, Sh. (2013) Complete Semigroups of Binary Relations. Kriter Yay1nevi, Istanbul, 524 p.

[2] Albayrak, B., Aydin, N. and Diasamidze, Ya. (2013) Reguler Elements of the Complete Semigroups of Binary Relations of the Class ∑_{7}(*X*,8). International Journal of Pure and Applied Mathematics, 86, 199-216.

http://dx.doi.org/10.12732/ijpam.v86i1.13

[3] Yesil Sungur, D. and Aydin, N. (2014) Reguler Elements of the Complete Semigroups of Binary Relations of the Class ∑_{8}(*X*,7). General Mathematics Notes, 21, 27-42.

[4] Albayrak, B., Aydin, N. and Yesil Sungur, D. (2014) Regular Elements of Semigroups Defined by the Generalized X-Semilattice. General Mathematics Notes, 23, 96-107.