b-GENERALIZED DERIVATIONS OF SEMIPRIME RINGS HAVING NILPOTENT VALUES

Kosan M. T., Lee T.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.96, sa.3, ss.326-337, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 96 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1017/s1446788713000670
  • Dergi Adı: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.326-337
  • Anahtar Kelimeler: prime ring, semiprime ring, GPI, (generalized) sigma-derivation, b-generalized derivation, orthogonal completion, SKEW DERIVATIONS
  • Gazi Üniversitesi Adresli: Hayır

Özet

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.