ON MULTIPLICATIVE (GENERALIZED)-DERIVATIONS IN SEMIPRIME RINGS


KARALARLIOĞLU CAMCI D. , AYDIN N.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.66, no.1, pp.153-164, 2017 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1501/commual_0000000784
  • Title of Journal : COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Page Numbers: pp.153-164

Abstract

In this paper, we study commutativity of a prime or semiprime ring using a map F : R -> R, multiplicative (generalized) -derivation and a map H : R -> R, multiplicative left centralizer, under the following conditions: For all x,y is an element of R, i) F(xy) +/- H(xy) = 0, ii) F(xy) +/- H(yx) = 0, iii) F(x)F(y) +/- H(xy) = 0, iv) F(xy) +/- H(xy) is an element of Z, v) F(xy) +/- H(yx) is an element of Z, vi) F(x)F(y) +/- H(xy) is an element of Z.