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Regularity and products of idempotents in endomorphism monoids of projective acts

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

Sydney Bulman-Fleming
Sydney Bulman-Fleming
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada.
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Extract

That the monoid of all transformations of any set and the monoid of all endomorphisms of any vector space over a division ring are regular (in the sense of von Neumann) has been known for many years (see [6] and [16], respectively). A common generalization of these results to the endomorphism monoid of an independence algebra can be found in [13]. It also follows from [13] that the endomorphism monoid of a free G-act is regular, where G is any group. In the present paper we use a version of the wreath product construction of [8], [9] to determine the projective right S-acts (S any monoid) whose endomorphism monoid is regular.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 354 - 367
Copyright
Copyright © University College London 1995

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