Centralizers in the Full Transformation Semigroup
Araújo, João; Konieczny, Janusz
Semigroup forum, 86(1) (2013), 1-31
http://dx.doi.org/10.1007/s00233-012-9424-0
For an arbitrary set X (?nite or in?nite), denote by T (X) the semigroup of full transforma-
tions on X. For ? ? T (X), let C(?) = {? ? T (X) : ?? = ??} be the centralizer of ? in
T (X). The aim of this paper is to characterize the elements of C(?). The characterization is
obtained by decomposing ? 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.
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