a1 Centro de Matemática, Universidade do Minho, 4710 Braga, Portugal (email: email@example.com)
a2 School of Mathematics and Statistics, University of Western Australia, Nedlands, 6009, Australia (email: firstname.lastname@example.org)
Let Y be a fixed nonempty subset of a set X and let T(X,Y ) denote the semigroup of all total transformations from X into Y. In 1975, Symons described the automorphisms of T(X,Y ). Three decades later, Nenthein, Youngkhong and Kemprasit determined its regular elements, and more recently Sanwong, Singha and Sullivan characterized all maximal and minimal congruences on T(X,Y ). In 2008, Sanwong and Sommanee determined the largest regular subsemigroup of T(X,Y ) when |Y |≠1 and Y ≠ X; and using this, they described the Green’s relations on T(X,Y ) . Here, we use their work to describe the ideal structure of T(X,Y ) . We also correct the proof of the corresponding result for a linear analogue of T(X,Y ) .
(Received June 16 2010)
(Online publication December 09 2010)
2010 Mathematics subject classification
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The authors acknowledge the support of the Portuguese ‘Fundação para a Ciência e a Tecnologia’ through its Multi-Year Funding Program for ‘Centro de Matemática’ at the University of Minho, Braga, Portugal.