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Mathematics 2018, 6(9), 160; https://doi.org/10.3390/math6090160

On Magnifying Elements in E-Preserving Partial Transformation Semigroups

1
Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
2
Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
3
Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Received: 15 August 2018 / Revised: 3 September 2018 / Accepted: 4 September 2018 / Published: 6 September 2018
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Abstract

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X , E ) consisting of all E-preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X , E ) to be right or left magnifying. View Full-Text
Keywords: magnifying elements; transformation semigroups; equivalence relations magnifying elements; transformation semigroups; equivalence relations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kaewnoi, T.; Petapirak, M.; Chinram, R. On Magnifying Elements in E-Preserving Partial Transformation Semigroups. Mathematics 2018, 6, 160.

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