The Wedderburn principal theorem for generalized alternative algebras. I

Smith, Harry F.

doi:10.1090/S0002-9947-1975-0376796-4

The Wedderburn principal theorem for generalized alternative algebras. I
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by Harry F. Smith

Trans. Amer. Math. Soc. 212 (1975), 139-148

DOI: https://doi.org/10.1090/S0002-9947-1975-0376796-4

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Abstract:

A generalized alternative ring I is a nonassociative ring R in which the identities $(wx,y,z) + (w,x,(y,z)) - w(x,y,z) - (w,y,z)x;((w,x),y,z) + (w,x,yz) - y(w,x,z) - (w,x,y)z$; and $(x,x,x)$ are identically zero. Let A be a finite-dimensional algebra of this type over a field F of characteristic $\ne 2,3$. Then it is established that (1) A cannot be a nodal algebra, and (2) the standard Wedderburn principal theorem is valid for A.

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