Centralizers in the full transformation semigroup

Araújo, João; Konieczny, Janusz

http://hdl.handle.net/10400.2/3795

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Authors

Araújo, João

Konieczny, Janusz

Abstract(s)

For an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations on X. For α ∈ T (X), let C(α) = {β ∈ T (X) : αβ = βα} be the centralizer of α in T (X). The aim of this paper is to characterize the elements of C(α). The characterization is obtained by decomposing α as a join of connected partial transformations on X and analyzing the homomorphisms of the directed graphs representing the connected transformations. The paper closes with a number of open problems and suggestions of future investigations.

Keywords

Full transformations Centralizers Digraph homomorphisms

URI

http://hdl.handle.net/10400.2/3795

Citation

Araújo, João; Konieczny, Janusz - Centralizers in the full transformation semigroup. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 86, nº 1 (2013), p. 1-32