Relatively Free Algebras with Weak Exchange Properties
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification primary 08B20, 08A05; secondary 08A60, 08A62.
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