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

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Published

2018-07-31

Issue

Section

Algebraic Geometry

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

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