J Austral Math Soc Ser A 54 pp133--141, 1993.

On Certain Subrings of Prime Rings with Derivations

M. Bresar and J. Vukman

Abstract

Let D be a nonzero derivation of a noncommutative prime ring R, and let U be the subring of R generated by all [D(x), x], x Î R. A classical theorem of Posner asserts that U is not contained in the center of R. Under the additional assumption that the characteristic of R as well as a nonzero right ideal if R.

1991 AMS Subject Classification: 16W25, 16N60

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Authors

M. Bresar

J. Vukman

University of Maribor, PF, Koroska, 160, 62000 Maribor, Slovenia.