Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Generalized Derivations on ∗-prime Rings

  • Received : 2015.12.30
  • Accepted : 2018.08.20
  • Published : 2018.09.23
Download PDF
⟨ Previous Next ⟩

Abstract

Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

Keywords

References

  1. E. Albas and N. Argac, Generalized derivations of prime rings, Algebra Colloq., 11(3)(2004), 399-410.
  2. N. Argac, On prime and semiprime rings with derivations, Algebra Colloq., 13(3)(2006), 371-380. https://doi.org/10.1142/S1005386706000320
  3. H. E. Bell and W. S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull., 30(1)(1987), 92-101. https://doi.org/10.4153/CMB-1987-014-x
  4. N. H. McCoy, The theory of rings, Macmillian, New York and Londan, 1964.
  5. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8(1957), 1093-1100.