# REMARKS ON ISOMORPHISMS OF TRANSFORMATION SEMIGROUPS RESTRICTED BY AN EQUIVALENCE RELATION

• Namnak, Chaiwat (Department of Mathematics Faculty of Science Naresuan University) ;
• Sawatraksa, Nares (Department of Mathematics Faculty of Science Naresuan University)
• Accepted : 2017.12.28
• Published : 2018.07.31
• 254 6

#### Abstract

Let T(X) be the full transformation semigroup on a set X and ${\sigma}$ be an equivalence relation on X. Denote $$E(X,{\sigma})=\{{\alpha}{\in}T(X):{\forall}x,\;y{\in}X,\;(x,y){\in}{\sigma}\;\text{implies}\;x{\alpha}=y{\alpha}\}.$$. 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

#### Acknowledgement

Supported by : Naresuan University

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