Natural Partial Order on Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section with Fixed Sets

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Published: May 25, 2023
Keywords:
transformation semigroup natural partial order compatibility equivalence relation cross-section

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Chollawat Pookpienlert
Department of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Chiang Mai, Thailand
Rattanakarn Khomson
Department of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Chiang Mai, Thailand

Abstract

Let gif.latex?\small&space;T(X,\rho,R) be the semigroup consisting of all total transformations preserving an equivalence relation gif.latex?\small&space;\rho and a cross-section gif.latex?R. The subsemigroup gif.latex?T_{Y}(X,\rho,R)  of gif.latex?T(X,\rho,R) is defined as follows:   


              gif.latex?\small&space;T_Y(X,\rho,R)=\{\alpha\in&space;T(X,\rho,R)&space;:&space;x\alpha=x~\text{for&space;all}~x\in&space;X~\text{in&space;which}~x\rho\cap&space;Y\neq\emptyset\}.


In this paper, we characterize the natural partial order and find elements which are left compatible, right compatible and compatible.     

Article Details

Issue
Vol. 15 No. 21 (2023): JANUARY 2023 - JUNE 2023
Section
บทความวิจัย
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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