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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Wedderburn principal theorem for generalized alternative algebras. I


Author: Harry F. Smith
Journal: Trans. Amer. Math. Soc. 212 (1975), 139-148
MSC: Primary 17D05
MathSciNet review: 0376796
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0376796-4
PII: S 0002-9947(1975)0376796-4
Keywords: Generalized alternative ring I, Jordan algebra, nodal algebra, Penico solvable, semisimple, Wedderburn principal theorem
Article copyright: © Copyright 1975 American Mathematical Society