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SEMIGROUPS OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE

Part of: Semigroups

Published online by Cambridge University Press:  01 June 2008

R. P. SULLIVAN
R. P. SULLIVAN*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Nedlands, 6009, Australia (email: [email protected])
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Abstract

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In 1975, Symons described the automorphisms of the semigroup T(X,Y ) consisting of all total transformations from a set X into a fixed subset Y of X. Recently Sanwong, Singha and Sullivan determined all maximal (and all minimal) congruences on T(X,Y ), and Sommanee studied Green’s relations in T(X,Y ). Here, we describe Green’s relations and ideals for the semigroup T(V,W) consisting of all linear transformations from a vector space V into a fixed subspace W of V.

Keywords

linear transformationGreen’s relationsideals

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 441 - 453
Copyright
Copyright © 2008 Australian Mathematical Society

References

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