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Some theorems of commutativity on semiprime rings with mappings

Let R be a semiprime ring and F : R → R a mapping such that F (xy) = F (y)x + yd(x) for all x, y ∈ R, where d is any map on R. In this paper, we investigate the commutativity of semiprime rings with a mapping F on R. Several theorems of commutativity of semiprime rings are obtained.