Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i3.3260

Keywords:

functions, transformation semigroups, partitions, left magnifying elements, right magnifying elements

Abstract

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let X be a nonempty set and T(X) be the semigroup of all transformation from X into itself under the composition of functions. For a partition P = {X_α | α ∈ I} of the set X, let T(X,P) = {f ∈ T(X) | (X_α)f ⊆ X_α for all α ∈ I}. Then T(X,P) is a subsemigroup of T(X) and if P = {X}, T(X,P) = T(X). Our aim in this paper is to give necessary and sufficient conditions for elements in T(X,P) to be left or right magnifying. Moreover, we apply those conditions to give necessary and sufficient conditions for elements in some generalized linear transformation semigroups.

Author Biographies

  • Ronnason Chinram, Prince of Songkla Unversity
    Department of Mathematics and Statistics
  • Pattarawan Petchkaew, Songkhla Rajabhat University
    Mathematics and Statistics Program
  • Samruam Baupradist, Chulalongkorn University

    Department of Mathematics and Computer Science

Downloads

Published

2018-07-31

Issue

Vol. 11 No. 3: (July 2018)

Section

Algebraic Geometry

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set. (2018). European Journal of Pure and Applied Mathematics, 11(3), 580-588. https://doi.org/10.29020/nybg.ejpam.v11i3.3260