Print ISSN: 1681-6900

Online ISSN: 2412-0758

Author : B. Yass, a


Commutativity Results on Prime Rings With Generalized Derivations

A. H. Majeed; Shaima; a B. Yass

Engineering and Technology Journal, 2016, Volume 34, Issue 2, Pages 328-333

Let R be a prime ring. For nonzero generalized derivations F and G associated with the same derivation d, we prove that if d≠0, then R is commutative, if any one of the following conditions hold: (1) [F(x), G(y)]  0, (2) F(x)oG(y)  0, (3) F(x)oG(y)  xoy, (4) [F(x), G(y)]  [x, y], (5) [F(x), G(y)]  xoy, (6) F(x)oG(y)  [x, y], for all x, y  R, where F will always denote onto map.