Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(3): 705-710

Online first article March 16, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170254

Copyright © The Korean Mathematical Society.

Remarks on isomorphisms of transformation semigroups restricted by an equivalence relation

Chaiwat Namnak, Nares Sawatraksa

Naresuan University, Naresuan University

Abstract

Let $T(X)$ be the full transformation semigroup on a set $X$ and $\sigma$ be an equivalence relation on $X$. Denote \[ E(X, \sigma) = \{\alpha \in T(X) : \forall x, y \in X, (x, y) \in \sigma \mbox{ implies } x\alpha = y\alpha \}. \] Then $E(X, \sigma)$ is a subsemigroup of $T(X)$. In this paper, we characterize two semigroups of type $E(X, \sigma)$ when they are isomorphic.

Keywords: transformation semigroup, isomorphism theorem, equivalence

MSC numbers: 20M20

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