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Relatively free algebras with weak exchange properties

Part of: Varieties Algebraic structures

Published online by Cambridge University Press:  09 April 2009

John Fountain  and
Victoria Gould
John Fountain
Affiliation:
Department of Mathematics, University of York Heslington York, YO10 5DD, UK, e-mail: jbfl@york.ac.uk, varg1@york.ac.uk
Victoria Gould
Affiliation:
Department of Mathematics, University of York Heslington York, YO10 5DD, UK, e-mail: jbfl@york.ac.uk, varg1@york.ac.uk
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Abstract

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We consider algebras for which the operation PC of pure closure of subsets satisfies the exchange property. Subsets that are independent with respect to PC are directly independent. We investigate algebras in which PC satisfies the exchange property and which are relatively free on a directly independent generating subset. Examples of such algebras include independence algebras and dinitely generated free modules over principal ideal domains.

Keywords

free generators(direct) independenceexchange property

MSC classification

Secondary: 08B20: Free algebras 08A05: Structure theory 08A60: Unary algebras 08A62: Finitary algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 355 - 384
Copyright
Copyright © Australian Mathematical Society 2003

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