ON COMMUTATIVITY OF SEMIPRIME RINGS WITH GENERALIZED DERIVATIONS


Golbasi O.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, cilt.40, ss.191-199, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 40 Konu: 3
  • Basım Tarihi: 2009
  • Dergi Adı: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Sayfa Sayıları: ss.191-199

Özet

Let R be an associative ring. An additive mapping f : R -> R is called a generalized derivation if there exists a derivation d : R -> R such that f (xy) f (x)y + xd(y), for all x, y E R. In this paper, we explore the commutativity of semiprime rings admitting generalized derivations f and g such that one of the following holds for all x, y is an element of R. Let (f, d) and (g, h) be two generalized derivations of R. (i) f (x)y = xg(y), (ii) f [(x, y])=-/+[x, y], (iii)f(xoy)=-/+ xoy for all x, y is an element of R.