Abstract
Let Y be a nonempty subset of X and T(X, Y) the set of all functions from X into Y. Then T(X, Y) with composition is a subsemigroup of the full transformation semigroup T(X). Let E be a nontrivial equivalence on X. Define a subsemigroup \(T_E(X,Y)\) of T(X, Y) by
We study \(T_E(X,Y)\) with the natural partial order and determine when two elements are related under this order. We also give a characterization of compatibility on \(T_E(X,Y)\) and then describe the maximal and minimal elements.
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Acknowledgements
This research was supported by the Thailand Research Fund under grant No. TRG5880113 and Chiang Mai University.
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Communicated by Marcel Jackson.
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Part of this work was presented in the Arbeitstagung Allgemeine Algebra conference (AAA96), Darmstadt, Germany, June 1–3, 2018
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Sangkhanan, K., Sanwong, J. The natural partial order on semigroups of transformations with restricted range that preserve an equivalence. Semigroup Forum 108, 438–456 (2024). https://doi.org/10.1007/s00233-024-10422-0
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DOI: https://doi.org/10.1007/s00233-024-10422-0