Complete Semigroups of Binary Relations Defined by Semilattices of the Class $Z$−Elementary $X$−Semilattice of Unions

Yasha Diasamidze; Shota Makharadze; Ne¸set Aydın; Ali Erdo˘gan

doi:10.5644/SJM.11.1.02

Authors

Yasha Diasamidze Shota Rustaveli State University 35, Batumi, Georgia
Shota Makharadze Shota Rustaveli State University 35, Batumi, Georgia
Ne¸set Aydın Canakkale Onsekiz Mart University, Department of Mathematics, Canakkale, Turkey
Ali Erdo˘gan Hacettepe University, Department of Mathematics, Ankara, Turkey

DOI:

https://doi.org/10.5644/SJM.11.1.02

Keywords:

Semilattice, semigroup, binary relation

Abstract

In this paper we investigate idempotents of complete semigroups of binary relations deﬁned by semilattices of the class $Z$−elementary $X$−semilattice of unions. For the case where $X$ is a ﬁnite set we derive formulas by calculating the numbers of idempotents of the respective semigroup.

Statistics

Abstract: 42 / PDF: 3

References

[1] Ya. Diasamidze and Sh. Makharadze, Complete Semigroups of Binary Relations, Istanbul, Kriter Yayınevi, ISBN: 978-605-4613, 2013, 524p.

[2] Ya. I. Diasamidze, Complete Semigroups of Binary Relations, J. Math. Sci., Plenum Publishing Corporation, New York, 117 (4) (2003), 4271–4319.

[3] Ya. Diasamidze, Sh. Makharadze, G. Partenadze and O. Givradze, On ﬁnite X−semilattices of unions, J. Math. Sci., Plenum Publishing Corporation, New York, 141(4) (2007), 1134–1181.

[4] Ya. Diasamidze and Sh. Makharadze, Maximal subgroups of complete semigroups of binary relations, Proc. A. Razmadze Math. Inst., 131 (2003), 21–38.

[5] Ya. Diasamidze, Sh. Makharadze and Il. Diasamidze, Idempotents and regular elements of complete semigroups of binary relations, J. Math. Sci., Plenum Publshing Corporation, New York, 153 (4) (2008), 481–499.

[6] Ya. Diasamidze, Sh. Makharadze and N. Rokva, On XI −semilattices of union, Bull. Georg. Nation. Acad. Sci., 2 (1) (2008), 16–24.