Left (right) magnifying elements of a partial transformation semigroup

Luangchaisri, Panuwat; Changphas, Thawhat; Phanlert, Chalida

doi:10.1142/s1793557120500163

Cited by 4 publications

(2 citation statements)

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“…Recently, some researchers have paid attention to magnifying elements in various transformation semigroups. For instance, Luangchaisri et al [12] generalized Magill's 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.…”

Section: Introductionmentioning

confidence: 99%

Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Kaewnoi

Chinram

Petapirak

2021

Journal of Mathematics

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Let X be a nonempty set and ρ be an equivalence relation on X . For a nonempty subset S of X , we denote the semigroup of transformations restricted by an equivalence relation ρ fixing S pointwise by E F S X , ρ . In this paper, magnifying elements in E F S X , ρ will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in E F S X , ρ to be right or left magnifying elements.

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Section: Introductionmentioning

confidence: 99%

Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Kaewnoi

Chinram

Petapirak

2021

Journal of Mathematics

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“…For instance, Chinram, Petchkaew, and Buapradist investigated the magnifiers of T(X) determined by a partition of a set X in [6]. Left and right magnifiers in the partial transformation semigroups were characterized by Luangchaisri, Changphas, and Phanlert in [7].…”

Section: Introductionmentioning

confidence: 99%

Magnifiers in Some Generalization of the Full Transformation Semigroups

2020

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An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i ∣ i ∈ Λ } be a partition, and ρ be an equivalence relation on the set X. In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f ∈ T ( X ) ∣ ∀ ( x , y ) ∈ ρ , ( x f , y f ) ∈ ρ and X i f ⊆ X i for all i ∈ Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers.

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Magnifiers in various semigroups of transformations that preserve a partition

Khirabdhi

Singh

2023

Asian-European J. Math.

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Let [Formula: see text] be an arbitrary infinite set, and let [Formula: see text] be a partition of [Formula: see text] indexed by [Formula: see text]. Denote by [Formula: see text] the full transformation semigroup on [Formula: see text], and let [Formula: see text]. The character map of an element [Formula: see text] of [Formula: see text] is the self-map [Formula: see text] defined as [Formula: see text] whenever [Formula: see text]. In this paper, we describe magnifiers in [Formula: see text] in terms of their character and restriction maps. We further describe magnifiers in the subsemigroups [Formula: see text], [Formula: see text], and [Formula: see text] of [Formula: see text] that consist of all transformations whose character maps are injective, surjective, and bijective, respectively.

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Left (right) magnifying elements of a partial transformation semigroup

Cited by 4 publications

References 4 publications

Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Magnifiers in Some Generalization of the Full Transformation Semigroups

Magnifiers in various semigroups of transformations that preserve a partition

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