caa a22 4500 445344997 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00233-010-9274-6 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9274-6 Regular centralizers of idempotent transformations [Elektronische Daten] [Jorge André, João Araújo, Janusz Konieczny] Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(idX)=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(idX) contains all non-invertible transformations in C(idX). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation. Springer Science+Business Media, LLC, 2010 Idempotent transformations nationallicence Regular centralizers nationallicence Generators nationallicence André Jorge Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut Araújo João Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut Konieczny Janusz Department of Mathematics, University of Mary Washington, 22401, Fredericksburg, VA, USA aut Semigroup Forum Springer-Verlag 82/2(2011-04-01), 307-318 0037-1912 82:2<307 2011 82 233 https://doi.org/10.1007/s00233-010-9274-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9274-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- André Jorge Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut NATIONALLICENCE 700 1- Araújo João Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut NATIONALLICENCE 700 1- Konieczny Janusz Department of Mathematics, University of Mary Washington, 22401, Fredericksburg, VA, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/2(2011-04-01), 307-318 0037-1912 82:2<307 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer