An Observation on the Natural Partial Order of Transformation Semigroups Restricted by an Equivalence Relation

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Nares Sawatraksa
Piyaporn Tantong

Abstract

Let  gif.latex?T(X) be the full transformation semigroup of a set gif.latex?X . We consider the subsemigroup of  gif.latex?T(X) defined by gif.latex?E(X,\sigma)=\{\alpha\in&space;T(X):&space;\forall&space;x,y\in&space;X,&space;(x,y)\in\sigma&space;\;\text{implies}\;&space;x\alpha=y\alpha\}  for an arbitrary equivalence relation gif.latex?\sigma  on gif.latex?X . The natural partial order on the largest regular subsemigroup of gif.latex?E(X,\sigma)  is discussed in this paper, and we characterize when two regular elements of  gif.latex?E(X,\sigma) are related under this order. Also, their maximal, minimal and covering elements are described.

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How to Cite
1.
Sawatraksa N, Tantong P. An Observation on the Natural Partial Order of Transformation Semigroups Restricted by an Equivalence Relation. Prog Appl Sci Tech. [Internet]. 2022 Apr. 28 [cited 2022 Aug. 19];12(1):17-22. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/246019
Section
Mathematics and Applied Statistics

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