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Lattice isomorphisms of associative algebras

Published online by Cambridge University Press:  09 April 2009

D. W. Barnes
D. W. Barnes
Affiliation:
University of Sydney
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Let A be an associative algebra over the field F. We denote by ℒ(A) the lattice of all subalgebras of A. By an ℒ-isomorphism (lattice isomorphism) of the algebra A onto an algebra B over the same field, we mean an isomorphism of ℒ(A) onto ℒ(B). We investigate the extent to which the algebra B is determined by the assumption that it is ℒ-isomorphic to a given algebra A. In this paper, we are mainly concerned with the case in which A is a finite- dimensional semi-simple algebra.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1966 , pp. 106 - 121
Copyright
Copyright © Australian Mathematical Society 1966

References

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