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A NOTE ON MAXIMAL ELEMENTS IN NATURALLY ORDERED SEMIGROUPS OF TRANSFORMATIONS WITH AN INVARIANT SET

Part of: Semigroups

Published online by Cambridge University Press:  28 April 2025

AZIZAH BAKA Open the ORCID record for AZIZAH BAKA [Opens in a new window]  and
YANISA CHAIYA Open the ORCID record for YANISA CHAIYA [Opens in a new window]
AZIZAH BAKA
Affiliation:
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand e-mail: [email protected]
YANISA CHAIYA*
Affiliation:
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
*
e-mail: [email protected]
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Abstract

In this paper, we characterise all maximal elements in the semigroup $S(X,Y)=\{f\in T(X) : f(Y)\subseteq Y\}$ with respect to the natural partial order. Our results correct an error in the work of Sun and Wang [‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc. 87(1) (2013), 94–107].

Keywords

maximal elementtransformation semigroupnatural partial orderinvariant set

MSC classification

Primary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 5
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

This research was supported by Thammasat University Research Unit in Algebra and Its Applications.

References

Magill, K. D. Jr, ‘Subsemigroups of S(X)’, Math. Jpn. 11 (1966), 109–115.Google Scholar
Sun, L. and Sun, J., ‘A note on naturally ordered semigroups of transformations with invariant set’, Bull. Aust. Math. Soc. 91(2) (2015), 264–267.CrossRefGoogle Scholar
Sun, L. and Wang, L., ‘Natural partial order in semigroups of transformations with invariant set’, Bull. Aust. Math. Soc. 87(1) (2013), 94–107.CrossRefGoogle Scholar