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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Goldie's theorem for alternative rings


Authors: H. Essannouni and A. Kaidi
Journal: Proc. Amer. Math. Soc. 121 (1994), 39-45
MSC: Primary 17D05
MathSciNet review: 1181162
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Abstract: It is known that the socle of a semiprime Goldie ring is generated by a central idempotent and that a prime Goldie ring with a nonzero socle is a simple artinian ring. We prove the extension of these results to alternative rings. We also give an analogue of Goldie's theorem for alternative rings. A Goldie-like theorem was obtained earlier by the authors for noetherian alternative rings by a quite different method.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1181162-5
PII: S 0002-9939(1994)1181162-5
Keywords: Nonassociative ring, alternative ring, nucleus, center, socle, Goldie ring, semiprime alternative ring, prime alternative ring, essential right ideal, regular element
Article copyright: © Copyright 1994 American Mathematical Society