Lie and Jordan ideals in prime rings with derivations
Abstract: In this paper derivations on Lie and Jordan ideals of a prime ring are studied. The following results are proved. (i) Let be a prime ring of characteristic not , and let be a Lie or Jordan ideal of . If is a derivation defined on , and if is an element of the subring , generated by , or is an element of , according as is a Lie or Jordan ideal of , such that , for all , then either or . (ii) Let be derivations defined for all , and also for and if is a Lie ideal of , such that the iterate is also a derivation, satisfying the same conditions as . Let , whether is a Lie or Jordan ideal of . Then, at least, one of and is zero, for all .
Keywords: Prime rings, Lie and Jordan ideals, derivation
Article copyright: © Copyright 1976 American Mathematical Society