Abstract
Let R be a semiprime ring with extended centroid C, right Utumi quotient ring U and σ an endomorphism of R. A map ƒ : S → U, where S is a subset of R, is called σ-commuting if [ƒ(s), σ(s)] = 0 for all s ∈ S. In this paper we give a characterization of maps σ-commuting on certain subrings of R. As an application we prove the semiprime case of Posner's theorem for σ-commuting (σ,τ)-derivations.
ACKNOWLEDGMENT
The author would like to thank the referee for his useful suggestions and for pointing out the two papers Citation[1] and Citation[7].