Lie and Jordan structure in prime rings with derivations
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- Proc. Amer. Math. Soc. 41 (1973), 67-74 Request permission
Abstract:
In this paper Lie ideals and Jordan ideals of a prime ring $R$ together with derivations on $R$ are studied. The following results are proved: Let $R$ be a prime ring, $U$ be a Lie ideal or a Jordan ideal of $R$ and $d$ be a nonzero derivation of $R$ such that $ud(u) - d(u)u$ is central in $R$ for all $u$ in $U$. (i) If the characteristic of $R$ is different from 2 and 3, then $U$ is central in $R$. (ii) If $R$ has characteristic 3 and $U$ is a Jordan ideal then $U$ is central in $R$; further, if $U$ is a Lie ideal with ${u^2} \in U$ for all $u$ in $U$, then $U$ is central in $R$. The case when $R$ has characteristic 2 is also studied. These results extend some due to Posner [2].References
- I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
- 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
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 67-74
- MSC: Primary 16A68
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318233-5
- MathSciNet review: 0318233