Identities with Engel conditions on derivations

Kosan M. T., Lee T., Zhou Y.

MONATSHEFTE FUR MATHEMATIK, cilt.165, ss.543-556, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 165
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1007/s00605-010-0252-6
  • Dergi Adı: MONATSHEFTE FUR MATHEMATIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.543-556
  • Anahtar Kelimeler: Derivation, Prime ring, Engel condition, Differential identity, Faithful S-2n-ring, Orthogonally complete, CENTRALIZING MAPPINGS, PRIME, RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

Let R be a semiprime ring with a derivation D. The focus is on the two identities with Engel condition on D : [x(m), D(x(n1)),..., D(x(ns))](s) = 0 for all x. R and [x(m), D(x)(n1),..., D(x)(ns)](s) = 0 for all x. R, where s, m, n(1),..., n(s) are fixed positive integers. Our results are natural generalizations of Posner's theorem on centralizing derivations, Herstein's theorem on derivations with power-central values and a recent result by A. Fosner, M. Fosner and Vukman.