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.
Chaiwat Namnak, Nares Sawatraksa
Naresuan University, Naresuan University
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
2019; 34(4): 1049-1067
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