A nonassociative method for associative algebras
Saunders MacLane · Bulletin of the American Mathematical Society · 1948
This note exhibits a nonassociative proof for a strictly associative theorem concerned with the "Galois theory" of associative crossed product algebras.The theorem in question has also been established by somewhat more elaborate associative computations : it is perhaps of interest that the nonassociative proof to be given here appears to be both shorter and more conceptual than the associative proof.Practically no technical facts about nonassociative algebras are required for our proof.Let KZ)NZ)P be fields such that both K and N are finite, separable, and normal extensions of the base field P. The Galois group of K over P, or briefly Ç(K/P), will be designated as G, and similarly,