Relatively free algebras with weak exchange properties

John Fountain; Victoria Gould

Relatively free algebras with weak exchange properties

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	355-384
Number of pages	30
Journal	Journal of the australian mathematical society
Volume	75
Publication status	Published - Dec 2003

Keywords

free generators
(direct) independence
exchange property
INDEPENDENCE ALGEBRAS

Access to Document

http://www-users.york.ac.uk/~jbf1/weakexchange.pdf

Cite this

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title = "Relatively free algebras with weak exchange properties",

abstract = "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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author = "John Fountain and Victoria Gould",

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AU - Gould, Victoria

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AB - 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.

KW - free generators

KW - (direct) independence

KW - exchange property

KW - INDEPENDENCE ALGEBRAS

M3 - Article

SN - 1446-7887

VL - 75

SP - 355

EP - 384

JO - Journal of the australian mathematical society

JF - Journal of the australian mathematical society

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