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

 

On semiprime rings of bounded index


Author: Efraim P. Armendariz
Journal: Proc. Amer. Math. Soc. 85 (1982), 146-148
MSC: Primary 16A12; Secondary 16A48
MathSciNet review: 652429
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Abstract: A ring $ R$ is of bounded index (of nilpotency) if there is an integer $ n \geqslant 1$ such that $ {x^n} = 0$ whenever $ x \in R$ is nilpotent. The least such positive integer is the index of $ R$. We show that a semiprime ring $ R$ has index $ \leqslant n$ if and only if $ R$ is a subdirect product of prime rings of index $ \leqslant n$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0652429-3
PII: S 0002-9939(1982)0652429-3
Keywords: Bounded index, semiprime ring, prime rings, subdirect product
Article copyright: © Copyright 1982 American Mathematical Society