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 | References | Similar Articles | Additional Information

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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DOI:
https://doi.org/10.1090/S0002-9939-1994-1181162-5

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