Regularity on Variants of Transformation Semigroups that Preserve an Equivalence Relation

Authors

  • Piyaporn Tantong Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University
  • Nares Sawatraksa

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4596

Keywords:

Transformation semigroup, Equivalence relation, Left regular, Right regular, Completely regular

Abstract

The variant of a semigroup $ S $ with respect to an element $ a\in S $, is the semigroup with underlying set $ S $ and a new binary operation $ \ast $ defined by $ x\ast y=xay $ for $ x, y\in S $. Let $ T(X) $ be the full transformation semigroup on a nonempty set $ X $. For an arbitrary equivalence $ E $ on $ X $, let \[T_{E}(X)=\{\alpha\in T(X) : \forall a, b\in X, (a, b)\in E \Rightarrow (a\alpha, b\alpha\in E)\}.\]
Then $ T_{E}(X) $ is a subsemigroup of $ T(X) $. In this paper, we investigate regular, left regular and right regular elements for the variant of some subsemigroups of the semigroup $ T_{E}(X) $.

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How to Cite

Tantong, P., & Sawatraksa, N. . (2022). Regularity on Variants of Transformation Semigroups that Preserve an Equivalence Relation. European Journal of Pure and Applied Mathematics, 15(4), 2116–2126. https://doi.org/10.29020/nybg.ejpam.v15i4.4596