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Free generators in relatively free completely regular semigroups

Published online by Cambridge University Press:  14 November 2011

P.G. Trotter
P.G. Trotter
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Tasmania 7001, Australia
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Synopsis

A subset Y of a free completely regular semigroup FCRx freely generates a free completely regular subsemigroup if and only if (i) each -class of FCRx contains at most one element of Y, (ii) {Dy;y ∊ Y} freely generates a free subsemilattice of the free semilattice FCRx/), and (iii) Y consists of non-idempotents. A similar description applies in free objects of some subvarieties of the variety of all completely regular semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 329 - 339
Copyright
Copyright © Royal Society of Edinburgh 1988

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