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Regular Elements of the Semigroup <i>B</i><sub> X </sub> (<i>D</i>) Defined by Semilattices of the Class Σ<sub>2</sub> (<i>X</i>, 8) and Their Calculation Formulas
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
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
- 3 Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia
Applied Mathematics·Volume 06 (2015)·Pages 2257–2278·Published 21 December 2015·DOI10.4236/am.2015.614199
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Abstract
The paper gives description of regular elements of the semigroup B X ( D ) which are defined by semilattices of the class Σ 2 ( X , 8), f or which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. I n this case the set of all regular elements is a subsemigroup of the semigroup B X ( D ) which is defined by semilattices of the class Σ 2 ( X , 8).
KeywordsSemilatticeSemigroupBinary RelationRegular Element
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