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A NOTE ON NATURALLY ORDERED SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET

Part of: Semigroups

Published online by Cambridge University Press:  26 November 2014

LEI SUN*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Henan, Jiaozuo, 454003, PR China email [email protected]
JUNLING SUN
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Henan, Jiaozuo, 454003, PR China
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Abstract

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In this short note, we describe all the elements in the semigroup

$$\begin{eqnarray}S(X,Y)=\{f\in {\mathcal{T}}_{X}:f(Y)\subseteq Y\}\end{eqnarray}$$
which are left compatible with respect to the so-called natural partial order. This result corrects an error in a paper by Sun and Wang [‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc.87 (2013), 94–107].

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Mitsch, H., ‘A natural partial order for semigroups’, Proc. Amer. Math. Soc. 97 (1986), 384388.Google Scholar
Sun, L. and Wang, L. M., ‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc. 87 (2013), 94107.CrossRefGoogle Scholar