On left \((\theta,\varphi)\)-derivations of prime rings. (English) Zbl 1114.16031

Ashraf, Mohammad

Arch. Math., Brno 41, No. 2, 157-166 (2005).

The author proves that every Jordan left \((\theta,\theta)\)-derivation on a 2-torsion free ring is a left \((\theta,\theta)\)-derivation. A consequence is that every left \((\theta,\varphi)\)-derivation acting on a nonzero ideal of a prime ring as a homomorphism is trivial.

Reviewer: David Kruml (Brno)

MSC:

16W25	Derivations, actions of Lie algebras
16N60	Prime and semiprime associative rings

Keywords:

Lie ideals; Jordan left derivations