ON A LIE RING OF GENERALIZED INNER DERIVATIONS


Aydın N. , Türkmen S.

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, vol.32, no.4, pp.827-833, 2017 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.4134/ckms.c170019
  • Title of Journal : COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.827-833

Abstract

In this paper, we define a set including of all f(a) with a is an element of R generalized derivations of R and is denoted by f(R). It is proved that (i) the mapping g : L (R) -> f(R) given by g (a) = f(-a) for all a is an element of R is a Lie epimorphism with kernel N-sigma,N-tau; (ii) if R is a semiprime ring and sigma is an epimorphism of R, the mapping h : f(R) -> I (R) given by h(f(a)) = i(sigma)(-a) is a Lie epimorphism with kernel 1 (f(R)); (iii) if f(R) is a prime Lie ring and A, B are Lie ideals of R, then [f(A), f(B)] = (0) implies that either f(A) = (0) or f(B) = (0).