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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Derivation alternator rings with idempotent

Authors: Irvin R. Hentzel and Harry F. Smith
Journal: Trans. Amer. Math. Soc. 258 (1980), 245-256
MSC: Primary 17A30; Secondary 17D05
MathSciNet review: 554331
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Abstract: A nonassociative ring is called a derivation alternator ring if it satisfies the identities $ (yz,\,x,\,x)\, = \,y(z,\,x,\,x)\, + \,(y,\,x,\,x)z,\,(x,\,x,\,yz)\, = \,y(x,\,x,\,z)\, + \,(x,\,x,\,y)z$ and $ (x,\,x,\,x)\, = 0$. Let R be a prime derivation alternator ring with idempotent $ e \ne 1$ and characteristic $ \ne 2$. If R is without nonzero nil ideals of index 2, then R is alternative.

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Keywords: Derivation alternator ring, alternative ring, flexible ring, power-associative, idempotent, Albert decomposition, semiprime, flexible nucleus, alternative nucleus, Peirce decomposition, prime, simple
Article copyright: © Copyright 1980 American Mathematical Society