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