A theorem for prime rings
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- by Anthony Richoux PDF
- Proc. Amer. Math. Soc. 77 (1979), 27-31 Request permission
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 $1 \leqslant i \leqslant n + 1$.References
- Edward C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 95863, DOI 10.1090/S0002-9939-1957-0095863-0
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
Additional Information
- © Copyright 1979 American Mathematical Society
- 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