Lie and Jordan structure in prime rings with derivations
Abstract: In this paper Lie ideals and Jordan ideals of a prime ring together with derivations on are studied. The following results are proved: Let be a prime ring, be a Lie ideal or a Jordan ideal of and be a nonzero derivation of such that is central in for all in . (i) If the characteristic of is different from 2 and 3, then is central in . (ii) If has characteristic 3 and is a Jordan ideal then is central in ; further, if is a Lie ideal with for all in , then is central in . The case when has characteristic 2 is also studied. These results extend some due to Posner .
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Keywords: Prime rings, Lie ideal, Jordan ideal, derivation and inner derivation
Article copyright: © Copyright 1973 American Mathematical Society