m-Power Commuting MAPS on Semiprime Rings |
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Authors: | Hülya G Inceboz Tsiu-Kwen Lee |
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Institution: | 1. Department of Mathematics Science and Art Faculty , Adnan Menderes University , Aydin , Turkey;2. Department of Mathematics , National Taiwan University , Taipei , Taiwan |
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Abstract: | Let R be a semiprime ring with center Z(R), extended centroid C, U the maximal right ring of quotients of R, and m a positive integer. Let f: R → U be an additive m-power commuting map. Suppose that f is Z(R)-linear. It is proved that there exists an idempotent e ∈ C such that ef(x) = λx + μ(x) for all x ∈ R, where λ ∈C and μ: R → C. Moreover, (1 ? e)U ? M2(E), where E is a complete Boolean ring. As consequences of the theorem, it is proved that every additive, 2-power commuting map or centralizing map from R to U is commuting. |
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Keywords: | (Commuting) Centralizing map Derivation Faithful g-free ring Maximal right ring of quotients m-Power commuting map Orthogonally complete Semiprime ring |
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