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

 

Alternators of a right alternative algebra


Author: Irvin Roy Hentzel
Journal: Trans. Amer. Math. Soc. 242 (1978), 141-156
MSC: Primary 17A30
MathSciNet review: 496800
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Abstract: We show that in any right alternative algebra, the additive span of the alternators is nearly an ideal. We give an easy test to use to determine if a given set of additional identities will imply that the span of the alternators is an ideal. We apply our technique to the class of right alternative algebras satisfying the condition $ (a,a,b) = \lambda [a,[a,b]]$. We show that any semiprime algebra over a field of characteristic $ \ne 2$, $ \ne 3$ which satisfies the right alternative law and the above identity with $ \lambda \ne 0$ is a subdirect sum of (associative and commutative) integral domains.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0496800-5
PII: S 0002-9947(1978)0496800-5
Keywords: Right alternative, alternator ideal
Article copyright: © Copyright 1978 American Mathematical Society