On semiprime rings of bounded index
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- by Efraim P. Armendariz PDF
- Proc. Amer. Math. Soc. 85 (1982), 146-148 Request permission
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 $\leqslant n$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 146-148
- MSC: Primary 16A12; Secondary 16A48
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652429-3
- MathSciNet review: 652429