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A Wedderburn decomposition for certain generalized right alternative algebras

Author: Harry F. Smith
Journal: Proc. Amer. Math. Soc. 58 (1976), 1-7
MSC: Primary 17A30
MathSciNet review: 0419540
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Abstract: Finite-dimensional nonassociative algebras are considered which satisfy certain subsets of the following identities: (1) $ (x,x,x) = 0$, (2) $ (wx,y,z) + (w,x,[y,z]) = w(x,y,z) + (w,y,z)x$, (3) $ (w,x \cdot y,z) = x \cdot (w,y,z) + y \cdot (w,x,z)$, (4) $ (x,y,z) + (y,z,x) + (z,x,y) = 0$. It is first observed that nil algebras satisfying (1) and (2) are solvable. The standard Wedderburn principal theorem is then established both for algebras satisfying (1), (2) and (3) and for algebras which satisfy (2) and (4). Throughout it is assumed that the base fields have characteristic different from 2 and 3.

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Keywords: Generalized right alternative algebra, solvable, generalized alternative algebra, generalized $ ( - 1,1)$ algebra, Wedderburn decomposition
Article copyright: © Copyright 1976 American Mathematical Society

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