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Derivations on a Lie Ideal
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.
If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.
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- Copyright © Canadian Mathematical Society 1988
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