Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings

Brešar, Matej

doi:10.1090/S0002-9947-1993-1069746-X

Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings
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Trans. Amer. Math. Soc. 335 (1993), 525-546 Request permission

Abstract:

Biadditive mappings $B: R \times R \to R$ where $R$ is a prime ring with certain additional properties, satisfying $B(x,x)x = xB(x,x)$ for all $x \in R$, are characterized. As an application we determine the structures of commutativity-preserving mappings, Lie isomorphisms, and Lie derivations of certain prime rings.

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