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Idempotent Elements of the Semigroups <i>B</i><sub>x</sub>(<i>D</i>) Defined by Semilattices of the Class ∑<sub>3</sub>(<i>x</i>,8) When <i>Z</i><sub>7</sub>‡ Ø
Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
- 1 Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
- 2 Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
- 3 Faculty of Physics, Mathematics and Computer Sciences, Department of Mathematics, Shota Rustaveli Batumi State University, Batumi, Georgia
Applied Mathematics·Volume 07 (2016)·Pages 193–218·Published 24 February 2016·DOI10.4236/am.2016.73019
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Abstract
In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
KeywordsSemilatticeSemigroupBinary RelationIdempotent Element
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