Commuting maps on lie ideals |
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Authors: | Matej Brešar C Robert Miers |
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Institution: | 1. University of Maribor , Maribor, PF, 62000, Slovenia;2. University of Victoria , Victoria, British Columbia, V8W 3P4, Canada |
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Abstract: | Let R be a ring and let A be a subset of R. A map f : A→ R is commuting on A if f(x),x]= 0 for all xεA where x,y] = xy — yx. Suppose that R is a prime ring of characteristic ≠2 with extended centroid C. If L is a noncommutative Lie ideal of R and f:L→R an additive commuting map, then there is λε C and an additive map ∈: L→ C such that f(v) = λ(v)=λv+∈((v) for all vεL. |
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