Relatively free algebras with weak exchange properties
John Fountain, Victoria A. R. Gould · Journal of the Australian Mathematical Society · 2003
Abstract We consider algebras for which the operationPCof pure closure of subsets satisfies the exchange property. Subsets that are independent with respect to PC aredirectly 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.