VANISHING DERIVATIONS AND CO-CENTRALIZING GENERALIZED DERIVATIONS ON MULTILINEAR POLYNOMIALS IN PRIME RINGS


DHARA B., ARGAÇ N. , ALBAŞ E.

COMMUNICATIONS IN ALGEBRA, cilt.44, ss.1905-1923, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 44 Konu: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00927872.2015.1027393
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Sayfa Sayıları: ss.1905-1923

Özet

Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x(1),...,x(n)) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) - f(r)G(f(r))) = 0 for all r = (r(1),...,r(n)) is an element of R-n, then one of the following holds: