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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  and
JUNLING SUN
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
*
✉[email protected]
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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].

Keywords

transformation semigroupsnatural partial order(strictly) left compatibility

MSC classification

Primary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 264 - 267
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Mitsch, H., ‘A natural partial order for semigroups’, Proc. Amer. Math. Soc. 97 (1986), 384–388.Google Scholar
Sun, L. and Wang, L. M., ‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc. 87 (2013), 94–107.CrossRefGoogle Scholar