
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.
socle, alternative rings, nucleus, semiprime alternative ring, Goldie's theorem, Alternative rings, regular element, center, Chain conditions on annihilators and summands: Goldie-type conditions, essential right ideal, prime alternative ring
socle, alternative rings, nucleus, semiprime alternative ring, Goldie's theorem, Alternative rings, regular element, center, Chain conditions on annihilators and summands: Goldie-type conditions, essential right ideal, prime alternative ring
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