Vol. 69, No. 2, 1977

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Lie ideals and derivations in rings with involution

Charles Philip Lanski

Vol. 69 (1977), No. 2, 449–460

Let R be a prime ring with involution and L a Lie ideal of R. It is known that if the commutator of an element of R with L is in the center of R, then either the element or L is in the center, unless R is an order in a simple algebra at most four dimensional over its center. This result is shown to hold if L is replaced by its (skew-) symmetric part. More generally, if a derivation of R sends the (skew-) symmetric part of L into the center of R, then one of the three possibilities mentioned above must hold. The same conclusion follows if one assumes that the image of L under the derivation is contained in the set of (skew-) symmetric elements of R.

Mathematical Subject Classification
Primary: 16A28, 16A28
Secondary: 16A68
Received: 30 August 1976
Published: 1 April 1977
Charles Philip Lanski