J. Aust. Math. Soc.
75 (2003), 355-384
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Relatively free algebras with weak exchange properties
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John Fountain
Department of Mathematics
University of York
Heslington
York YO10 5DD
UK
jbf1@york.ac.uk
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Victoria Gould
Department of Mathematics
University of York
Heslington
York YO10 5DD
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 finitely generated free modules over
principal ideal domains.
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