Independence algebras

Peter J. Cameron, Csaba Szabó

Research output: Contribution to journalArticlepeer-review

Abstract

An independence algebra is an algebra A in which the subalgebras satisfy the exchange axiom, and any map from a basis of A into A extends to an endomorphism. Independence algebras fall into two classes; the first is specified by a set X, a group G, and a G-space C. The second is much more restricted; it is shown that the subalgebra lattice is a projective or affine geometry, and a complete classification of the finite algebras is given.

Original languageEnglish
Pages (from-to)321-334
Number of pages14
JournalJournal of the London Mathematical Society
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Jan 2000

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