Separability in an Algebra with Semi-Linear Homomorphism
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 668-671
Voir la notice de l'article provenant de la source Cambridge University Press
The purpose of this paper is to outline a simple theory of separability for a non-associative algebra A with semi-linear homomorphismσ. Taking A to be a finite dimensional abelian Lie p-algebra L and σ to be thepth 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 overk. The theory also applies to any unital non-associative algebraA over a field k and any unital homomorphismσ from A to A such that σ(ke) ⊂ke, e being the identity element of A.
Separability in an Algebra with Semi-Linear Homomorphism. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 668-671. doi: 10.4153/CJM-1972-062-3
@misc{10_4153_CJM_1972_062_3,
title = {Separability in an {Algebra} with {Semi-Linear} {Homomorphism}},
journal = {Canadian journal of mathematics},
pages = {668--671},
year = {1972},
volume = {24},
number = {4},
doi = {10.4153/CJM-1972-062-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-062-3/}
}
[1] 1. Nathan, Jacobson, Lectures in abstract algebra, Vol. III , Theory of Fields and Galois Theory (Van Nostrand, New York, 1964). Google Scholar
[2] 2. George, Seligman, Modular lie algebras (Springer, New York, 1966). Google Scholar
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