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INDEPENDENCE ALGEBRAS

Published online by Cambridge University Press:  01 April 2000

PETER J. CAMERON  and
CSABA SZABÓ
PETER J. CAMERON
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS
CSABA SZABÓ
Affiliation:
Department of Algebra and Number Theory, Eőtvős L. University, Muzeum krt. 6–8, H-1088 Budapest, Hungary
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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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 321 - 334
Copyright
The London Mathematical Society 2000

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