On strong commutativity-preserving maps. (Q2570936)

Summary: We identify some strong commutativity-preserving maps on semiprime rings. Among other results, we prove the following: (i) A centralizing homomorphism \(f\) of a semiprime ring \(R\) onto itself is strong commutativity preserving. (ii) A centralizing antihomomorphism \(f\) of a 2-torsion-free semiprime ring \(R\) onto itself is strong commutativity preserving.