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Research articles

ScienceAsia 49 (2023):ID 678-684 |doi: 10.2306/scienceasia1513-1874.2023.024


On magnifying elements in semigroups of transformations restricted by an equivalence relation with a restricted range


Thananya Kaewnoi, Phoschanun Ratanaburee, Ronnason Chinram, Montakarn Petapirak*

 
ABSTRACT:     An element a of a semigroup S is called a right (left) magnifying element if S contains a proper subset M such that M a = S (aM = S). Let Y be a nonempty subset of a set X and ? be an equivalence relation on X. Denote the semigroup of transformations restricted by an equivalence relation with a restricted range by E(X, Y,?). In this paper, we investigate magnifying elements in E(X, Y,?) and give the necessary and sufficient conditions for elements in E(X, Y,?) to be a right or a left magnifying element.

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a Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110 Thailand

* Corresponding author, E-mail: montakarn.p@psu.ac.th

Received 10 May 2022, Accepted 14 Dec 2022