Abstract
Let X be a nonempty set and Ο be an equivalence relation on X . For a nonempty subset S of X , we denote the semigroup of transformations restricted by an equivalence relation Ο fixing S pointwise by E F S X , Ο . In this paper, magnifying elements in E F S X , Ο will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in E F S X , Ο to be right or left magnifying elements.
Highlights
IntroductionHe established a characterization of semigroups in which all the left magnifying elements are very good
Journal of Mathematicshe established a characterization of semigroups in which all the left magnifying elements are very good
Luangchaisri et al [12] generalized Magillβs results in partial transformation semigroups, and Prakitsri [13] investigated magnifying elements in linear transformation semigroups with infinite nullity and in those with infinite co-rank. He showed that linear transformation semigroups with infinite nullity have no right magnifying elements
Summary
He established a characterization of semigroups in which all the left magnifying elements are very good. Luangchaisri et al [12] generalized Magillβs results in partial transformation semigroups, and Prakitsri [13] investigated magnifying elements in linear transformation semigroups with infinite nullity and in those with infinite co-rank. He showed that linear transformation semigroups with infinite nullity have no right magnifying elements. Efforts have been made to extend the results obtained in [14] by showing the necessary and sufficient conditions for elements in the semigroup of transformations restricted by an equivalence relation with a fixed point set to be right or left magnifying elements
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