On symmetric Jordan and Jordan left bi-derivations of prime rings

ÇEVEN Y. , Ciloglu Z.

AFRIKA MATEMATIKA, vol.29, pp.689-698, 2018 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29
  • Publication Date: 2018
  • Doi Number: 10.1007/s13370-018-0570-8
  • Title of Journal : AFRIKA MATEMATIKA
  • Page Numbers: pp.689-698

Abstract

In this paper, we investigated some properties of symmetric Jordan bi-derivation and symmetric Jordan left bi-derivation for associative rings. We showed that for an associative prime ring with char R not equal 2 if D is a symmetric Jordan bi-derivation then D is symmetric bi-derivation. And also we showed that for a 2-torsion free and 3-torsion free prime ring, if there exists a nonzero symmetric Jordan left bi-derivation D then R is commutative.