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Relatively free algebras with weak exchange properties

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

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