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Regular Elements and Right Units of Semigroup <i>B<sub>x</sub></i>(<i>D</i>) Defined Semilattice <i>D</i> for Which <i>V</i>(<i>D</i>,а)=Q ∈ ∑<sub>3</sub>(<i>X</i>,8)
Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
- 1 Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
- 2 Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
Applied Mathematics·Volume 06 (2015)·Pages 373–381·Published 3 February 2015·DOI10.4236/am.2015.62035
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Abstract
In this paper we take subsemilattice of X -semilattice of unions D which satisfies the following conditions:<br/> 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.
KeywordsSemilatticeSemigroupRegular ElementRight UnitBinary Relation
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