A NOTE ON CERTAIN CENTRAL DIFFERENTIAL IDENTITIES WITH GENERALIZED DERIVATIONS


ARGAÇ N. , De Filippis V.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.41, no.6, pp.847-852, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2012
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.847-852

Abstract

Let R be a noncommutatiye prime ring of characteristic different from 2 with right Utumi quotient ring U and extended centroid C, I a nonzero right ideal of R. Let f(x(1), . . ., x(n)) be a non-central multilinear polynomial over C, m >= 1 a fixed integer, a a fixed element of R, G a non-zero generalized derivation of R. If aG(f(r(1), . . ., r(n)))(m) is an element of Z(R) for all r(1), . . ., r(n) is an element of I, then one of the following holds: