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Separability in an Algebra with Semi-Linear Homomorphism

Published online by Cambridge University Press:  20 November 2018

David J. Winter
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The purpose of this paper is to outline a simple theory of separability for a non-associative algebra A with semi-linear homomorphism σ. Taking A to be a finite dimensional abelian Lie p-algebra L and σ to be the pth power operation in L, this separability is the separability of [2]. Taking A to be an algebraic field extension K over k and σ to be the Frobenius (pth power) homomorphism in K, this separability is the usual separability of K over k. The theory also applies to any unital non-associative algebra A over a field k and any unital homomorphism σ from A to A such that σ(ke) ⊂ ke, e being the identity element of A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 668 - 671
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Nathan, Jacobson, Lectures in abstract algebra, Vol. III , Theory of Fields and Galois Theory (Van Nostrand, New York, 1964).Google Scholar
2. George, Seligman, Modular lie algebras (Springer, New York, 1966).Google Scholar