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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A theorem for prime rings


Author: Anthony Richoux
Journal: Proc. Amer. Math. Soc. 77 (1979), 27-31
MSC: Primary 16A12
DOI: https://doi.org/10.1090/S0002-9939-1979-0539624-9
MathSciNet review: 539624
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Abstract: Let n be a positive integer and let R be a prime ring either of characteristic zero or of characteristic $ \geqslant n$. Then for any $ {a_1},{a_2}, \ldots ,{a_{n + 1}} \in R$, if $ {a_1}x{a_2}x \cdots {a_n}x{a_{n + 1}} = 0$ for all $ x \in R$. Then $ {a_i} = 0$ for some $ 1 \leqslant i \leqslant n + 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0539624-9
Article copyright: © Copyright 1979 American Mathematical Society