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

 

On the Wedderburn principal theorem for nearly $ (1,\,1)$ algebras


Author: T. J. Miles
Journal: Trans. Amer. Math. Soc. 161 (1971), 101-110
MSC: Primary 17A05
MathSciNet review: 0306278
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Abstract: A nearly $ (1,1)$ algebra is a finite dimensional strictly power-associative algebra satisfying the identity $ (x,x,y) = (x,y,x)$ where the associator $ (x,y,z) = (xy)z - x(yz)$. An algebra A has a Wedderburn decomposition in case A has a subalgebra $ S \cong A - N$ with $ A = S + N$ (vector space direct sum) where N denotes the radical (maximal nil ideal) of A.

D. J. Rodabaugh has shown that certain classes of nearly $ (1,1)$ algebras have Wedderburn decompositions. The object of this paper is to expand these classes. The main result is that a nearly $ (1,1)$ algebra A containing 1 over a splitting field of characteristic not 2 or 3 such that A has no nodal subalgebras has a Wedderburn decomposition.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0306278-3
PII: S 0002-9947(1971)0306278-3
Keywords: Wedderburn principal theorem, nearly $ (1,1)$ algebra, associator dependent algebra, $ (\gamma ,\delta )$ algebra, split Cayley algebra, nodal subalgebra
Article copyright: © Copyright 1971 American Mathematical Society