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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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
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