Derivations in prime rings
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- by B. Felzenszwalb
- Proc. Amer. Math. Soc. 84 (1982), 16-20
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633268-6
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Abstract:
Let $R$ be a ring and $d \ne 0$ a derivation of $R$ such that $d({x^n}) = 0$, $n = n(x) \geqslant 1$, for all $x \in R$. It is shown that if $R$ is primitive then $R$ is an infinite field of characteristic $p > 0$ and $p|n(x)$ if $d(x) \ne 0$. Moreover, if $R$ is prime and the set of integers $n(x)$ is bounded, the same conclusion holds.References
- I. N. Herstein, On the hypercenter of a ring, J. Algebra 36 (1975), no. 1, 151–157. MR 371962, DOI 10.1016/0021-8693(75)90161-1
- I. N. Herstein, On a result of Faith, Canad. Math. Bull. 18 (1975), no. 4, 609. MR 393136, DOI 10.4153/CMB-1975-109-9
- I. N. Herstein, Rings with involution, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1976. MR 0442017
- Wallace S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. MR 238897, DOI 10.1016/0021-8693(69)90029-5
- Martha Smith, Rings with an integral element whose centralizer satisfies a polynomial identity, Duke Math. J. 42 (1975), 137–149. MR 399156
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 16-20
- MSC: Primary 16A72; Secondary 16A12
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633268-6
- MathSciNet review: 633268