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- W4234579477 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. It is here demonstrated that if $A$ is a finite-dimensional algebra of this type over a field $F$ of characteristic # 2, 3, then $A$ a nilalgebra implies $A$ is nilpotent. A generalized alternative ring II is a nonassociative ring $R$ in which the identities $(wx,y,z) + (w,x,[y,z]) - w(x,y,z) - (w,y,z)x$ and $(x,y,x)$ are identically zero. Let $A$ be a finite-dimensional algebra of this type over a field $F$ of characteristic # 2. Then it is here established that (1) $A$ a nilalgebra implies $A$ is nilpotent; (2) $A$ simple with no nonzero idempotent other than 1 and $F$ algebraically closed imply $A$ itself is a field; and (3) the standard Wedderburn principal theorem is valid for $A$." @default.
- W4234579477 created "2022-05-12" @default.
- W4234579477 creator A5073667857 @default.
- W4234579477 date "1974-10-01" @default.
- W4234579477 modified "2023-10-14" @default.
- W4234579477 title "The Wedderburn Principal Theorem for a Generalization of Alternative Algebras" @default.
- W4234579477 doi "https://doi.org/10.2307/1996751" @default.
- W4234579477 hasPublicationYear "1974" @default.
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