ON A LIE RING OF GENERALIZED INNER DERIVATIONS


AYDIN N. , TÜRKMEN S.

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, cilt.32, ss.827-833, 2017 (ESCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 32 Konu: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.4134/ckms.c170019
  • Dergi Adı: COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.827-833

Özet

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).