Generalized derivations of prime rings on multilinear polynomials with annihilator conditions


ARGAÇ N. , DEMİR Ç.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.2, pp.231-243, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1106-46
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.231-243
  • Keywords: Prime ring, derivation, generalized derivation, right Utumi quotient ring, differential identity, generalized polynomial identity, ENGEL CONDITION, POWER VALUES, IDEALS, IDENTITIES

Abstract

Let K be a commutative ring with unity, R be a prime K-algebra with characteristic not 2, U be the right Utumi quotient ring of R, C the extended centroid of R, I a nonzero right ideal of R and a a fixed element of R. Let g be a generalized derivation of R and f(X-1,..., X-n) a multilinear polynomial over K. If ag(f(x(1),...,x(n)))f(x(1),...,x(n)) = 0 for all x1,..., x(n) is an element of I, then one of the following holds: