b-GENERALIZED DERIVATIONS OF SEMIPRIME RINGS HAVING NILPOTENT VALUES


Kosan M. T. , Lee T.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.96, no.3, pp.326-337, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1017/s1446788713000670
  • Title of Journal : JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.326-337

Abstract

Let R be a semiprime ring with extended centroid C and with maximal right ring of quotients Q(mr)(R). Let d: R -> Q(mr)(R) be an additive map and b is an element of Q(mr)(R). An additive map delta: R -> Q(mr)(R) is called a (left) b-generalized derivation with associated map d if delta(xy) = delta(x)y + bxd(y) for all x, y is an element of R. This gives a unified viewpoint of derivations, generalized derivations and generalized sigma-derivations with an X-inner automorphism sigma. We give a complete characterization of b-generalized derivations of R having nilpotent values of bounded index. This extends several known results in the literature.