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The ideal structure of idempotent-generated transformation semigroups

Published online by Cambridge University Press:  20 January 2009

M. A. Reynolds  and
R. P. Sullivan
M. A. Reynolds
Affiliation:
Mathematics Department, University of Western Australia, Nedlands, 6009, Western Australia
R. P. Sullivan
Affiliation:
Mathematics Department, University of Western Australia, Nedlands, 6009, Western Australia
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Let X be a set and the semigroup (under composition) of all total transformations from X into itself. In ([6], Theorem 3) Howie characterised those elements of that can be written as a product of idempotents in different from the identity. We gather from review articles that his work was later extended by Evseev and Podran [3, 4] (and independently for finite X by Sullivan [15]) to the semigroup of all partial transformations of X into itself. Howie's result was generalized in a different direction by Kim [8], and it has also been considered in both a topological and a totally ordered setting (see [11] and [14] for brief summaries of this latter work). In addition, Magill [10] investigated the corresponding idea for endomorphisms of a Boolean ring, while J. A. Erdos [2] resolved the analogous problem for linear transformations of a finite–dimensional vector space.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 3 , October 1985 , pp. 319 - 331
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

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