Independence algebras

Peter J. Cameron; Csaba Szabó

doi:10.1112/S0024610799008546

Independence algebras

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	321-334
Number of pages	14
Journal	Journal of the London Mathematical Society
Volume	61
Issue number	2
DOIs	https://doi.org/10.1112/S0024610799008546
Publication status	Published - 1 Jan 2000

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title = "Independence algebras",

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.",

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AB - 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.

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Independence algebras

Abstract

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