A Characterization of Jordan Automorphisms on Jordan Ideals of Prime Gamma Rings

Abstract

We study and develop the concepts of homomorphism and anti-homomorphism to derive some important results in the theory of gamma rings. This article attempts to analyze some of the results of Ali et al. [1] in case of classical rings for extending those in the context of gamma rings. We establish a number of results related to automorphism, antiautomorphism and Jordan automorphism on Jordan ideal of prime gamma rings to obtain a new characterizing result. If M is a 2-torsion free prime gamma ring fulfilling a suitable condition, J is a non-zero Jordan ideal as well as a subring of M and Φ:M → M is a Jordan automorphism, then we prove that  Φ is an automorphism or Φ is an anti-automorphism.

GANIT J. Bangladesh Math. Soc. 44.1 (2024) 92–98