On semiprime rings of bounded index-Reference-Cited by-同舟云学术

On semiprime rings of bounded index

Published:1982 Issue:2 Volume:85 Page:146-148
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Armendariz Efraim P.

Abstract

A ring R R is of bounded index (of nilpotency) if there is an integer n ⩾ 1 n \geqslant 1 such that x n = 0 {x^n} = 0 whenever x ∈ R x \in R is nilpotent. The least such positive integer is the index of R R . We show that a semiprime ring R R has index ⩽ n \leqslant n if and only if R R is a subdirect product of prime rings of index ⩽ n \leqslant n .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1982-085-02/S0002-9939-1982-0652429-3/S0002-9939-1982-0652429-3.pdf

Reference6 articles.

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3. Strongly semiprime rings;Handelman, D.;Pacific J. Math.,1975

4. J. Hannah, Semiprime rings with bounded index of nilpotence, Math. Res. Rep. No. 7, University of Melbourne, Melbourne, Australia, 1980.

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