On Lie ideals with generalized derivations

Goelbasi O., Kaya K.

SIBERIAN MATHEMATICAL JOURNAL, vol.47, no.5, pp.862-866, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 5
  • Publication Date: 2006
  • Doi Number: 10.1007/s11202-006-0094-6
  • Journal Name: SIBERIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.862-866
  • Çanakkale Onsekiz Mart University Affiliated: No

Abstract

Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a is an element of R and [a, f (U)] = 0 then a is an element of Z or d(a) = 0 or U subset of Z; (ii) If f(2)(U) = 0 then U subset of Z; (iii) If u(2) is an element of U for all u is an element of U and f acts as a homomorphism or antihomomorphism on U then either d = 0 or U subset of Z.