On Identities with Composition of Generalized Derivations

EROĞLU M. P., ARGAÇ N.

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, vol.60, no.4, pp.721-735, 2017 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.4153/cmb-2017-072-4
  • Journal Name: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.721-735
  • Keywords: prime ring, generalized derivation, composition, extended centroid, multilinear polynomial, maximal right ring of quotients, PRIME-RINGS, POLYNOMIALS
  • Dokuz Eylül University Affiliated: Yes

Abstract

Let R be a prime ring with extended centroid C, Q maximal right ring of quotients of R, RC central closure of R such that dim(C) (RC) > 4, f(X-1,...,X-n) a multilinear polynomial over C that is not central-valued on R, and f (R) the set of all evaluations of the multilinear polynomial f(X-1,...,X-n) in R. Suppose that G is a nonzero generalized derivation of R such that G(2) (u) u is an element of C for all u is an element of f (R). Then one of the following conditions holds: