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Independence Algebras
Author(s) -
Cameron Peter J.,
Szabó Csaba
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008546
Subject(s) - mathematics , subalgebra , independence (probability theory) , pure mathematics , axiom , endomorphism , algebra over a field , lattice (music) , affine transformation , physics , geometry , statistics , acoustics
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.