Infinite injective transformations whose centralizers have simple structure

• Autorzy: Janusz Konieczny
• Języki publikacji: EN

Abstrakty

EN

For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = {β ∈ g/g(X): αβ = βα} be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green's relations in C(α) coincide, characterize α ∈ Γ(X) such that the $$ \mathcal{J} $$-classes of C(α) form a chain, and describe Green's relations in C(α) for α with so-called finite ray-cycle decomposition. If α is a permutation, we also find the structure of C(α) in terms of direct and wreath products of familiar semigroups.

Słowa kluczowe

EN

Infinite injective transformations; Centralizers; Green's relations

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 23-35

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Janusz Konieczny

• University of Mary Washington

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0086-4