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Proceedings of the American Mathematical Society

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



Lie and Jordan structure in prime rings with derivations

Author: Ram Awtar
Journal: Proc. Amer. Math. Soc. 41 (1973), 67-74
MSC: Primary 16A68
MathSciNet review: 0318233
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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 [Enhancements On Off] (What's this?)

  • [1] I. N. Herstein, Topics in ring theory, Univ. of Chicago Press, Chicago, Ill., 1969. MR 42 #6018. MR 0271135 (42:6018)
  • [2] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. MR 20 #2361. MR 0095863 (20:2361)

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Keywords: Prime rings, Lie ideal, Jordan ideal, derivation and inner derivation
Article copyright: © Copyright 1973 American Mathematical Society

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