Generalized Jordan Triple (σ,τ)-Higher Homomorphisms on Prime Rings

  • Neshtiman N. Sulaiman Department of Mathematics, College of Education, Salahaddin University, Erbil, Kurdistan Region, Iraq
  • Salah M. Salih Department of Mathematics, College of Education, Al-Mustansirya University, Baghdad, Iraq
Keywords: Generalized Jordan higher homomorphism, Prime ring, Jordan homomorphism, Homomorphisms, Higher homomorphisms

Abstract

Herstein proved that any Jordan homomorphism onto a prime ring of characteristic of different from 2 and 3 is either a homomorphism or an anti-homomorphism. In this paper the concept of Generalized Jordan triple ( )–Higher Homomorphisms (GJT( )-HH) where and are two commuting homomorphisms are introduced as follows:

A family of additive mappings  of  into  is said to be a Generalized Triple -Higher Homomorphism (GT( )-HH) if there exist a triple -higher homomorphism (T ( ) – HH)  such that for each  and for all , we have:

 

and is said to be the relating triple -HH.

We will primarily extend the result of Herstein on it. It should be proved that every GJT()-HH of ring  into prime ring  is either GT( )-HH or triple ( ) higher anti-homomorphism (T( )-HAH).

Published
2020-09-26
How to Cite
N. Sulaiman, N., & M. Salih, S. (2020). Generalized Jordan Triple (σ,τ)-Higher Homomorphisms on Prime Rings. Al-Nahrain Journal of Science, 23(3), 76-82. Retrieved from https://anjs.edu.iq/index.php/anjs/article/view/2248
Section
Articles