Generalized Jordan Right Derivations on Prime and Semiprime 𝚪-Rings

admin August 28, 2019

Authors:

Omar Faruk,Md. Mizanor Rahman,

DOI NO:

https://doi.org/10.26782/jmcms.2019.08.00022

Keywords:

Γ-Rings,Prime Γ-Rings,Semiprime Γ-Rings,Generalized Derivation,Generalized right derivation,Generalized Jordan Right Derivation,

Abstract

In this paper, we analyzed the basic properties and related theorems of generalized Jordan right derivations on prime and semiprime 𝛤-rings with their mathematical simulation. We mainly focused on the characterizations of 2 free prime and semiprime 𝛤-rings by using Jordan Right Derivations. Important propositions and theorems related to generalized Jordan right derivation on prime and semiprime 𝛤-ring have been derived here with sufficient calculations. Our main objective is to prove the theorem that if 𝑀 be a 2-torsion free 𝛤-ring having a commutator right non-Zero divisor which satisfies the condition 𝑎𝛼𝑏𝛽𝑐 = 𝑎𝛽𝑏𝛼𝑐 for all 𝑎, 𝑏, 𝑐 ∈ 𝑀 and 𝛼, 𝛽 ∈ 𝛤and if𝐷: 𝑀 → 𝑀 be a generalized Jordan right derivation and 𝑑: 𝑀 → 𝑀 be its associated Jordan right derivation then 𝐷 is a generalized right derivation on 𝑀.

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