On Prime and Semiprime Near-Rings with Generalized Derivation


Golbasi O.

QUAESTIONES MATHEMATICAE, vol.33, no.3, pp.387-390, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.2989/16073606.2010.507328
  • Title of Journal : QUAESTIONES MATHEMATICAE
  • Page Numbers: pp.387-390

Abstract

Let N be a left near-ring and S be a nonempty subset of N. A mapping F from N to N is called commuting on S if [F(x),x] = 0 for all x S. The mapping F is called strong commutativity preserving (SCP) on S if [F(x),F(y)] = [x,y] for all x, y S. In the present paper, firstly we generalize the well known result of Posner which is commuting derivations on prime rings to generalized derivations of semiprime near-rings. Secondly, we investigate SCP-generalized derivations of prime near-rings.