On Jordan generalized \(k\)-derivations of semiprime \(\Gamma_N\)-rings. (Q537059)

The authors study generalized \(k\)-derivations and Jordan generalized \(k\)-derivations of \(\Gamma\)-rings. These notions are defined for \(\Gamma\)-rings as is to be expected from the corresponding definitions for rings. Every generalized \(k\)-derivation is a Jordan generalized \(k\)-derivation, but the converse is not true in general. The main result is to show that for a \(2\)-torsion free semiprime Nobusawa \(\Gamma\)-ring, a suitable ``commutativity'' requirement on the Jordan generalized \(k\)-derivation will ensure that it is also a generalized \(k\)-derivation.