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Regular Elements of the Complete Semigroups <i>B<sub>X</sub>(D)</i> of Binary Relations of the Class ∑<sub>2</sub>(<i>X</i>,8)
Department of Mathematics, Faculty of Mathematics, Physics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
Department of Mathematics, Faculty of Mathematics, Physics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
- 1 Department of Mathematics, Faculty of Mathematics, Physics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
- 2 Department of Mathematics, Faculty of Mathematics, Physics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
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Abstract
As we know if D is a complete X -semilattice of unions then semigroup Bx ( D) possesses a right unit iff D is an XI -semilattice of unions. The investigation of those a -idempotent and regular elements of semigroups B x ( D ) requires an investigation of XI -subsemilattices of semilattice D for which V ( D , a )= Q ∈ ∑ 2 ( X ,8) . Because the semilattice Q of the class ∑ 2 ( X ,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V ( D , a )= Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V ( D , a )= Q .
KeywordsSemilatticeSemigroupBinary Relation
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