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 |
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Pages (from-to) | 321-334 |
Number of pages | 14 |
Journal | Journal of the London Mathematical Society |
Volume | 61 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2000 |