Let R be a prime ring of characteristic different from 2, f : R → R a non-zero additive mapping on R, such that f(xy) = f(x)y + f(y)x. We prove that if [f(x), f(y)] = 0 for all x, y ∈ R, then R must be commutative.
A Note on Additive Mappings and Commutative Conditions for Prime Rings
RANIA F
2013-01-01
Abstract
Let R be a prime ring of characteristic different from 2, f : R → R a non-zero additive mapping on R, such that f(xy) = f(x)y + f(y)x. We prove that if [f(x), f(y)] = 0 for all x, y ∈ R, then R must be commutative.File in questo prodotto:
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