Generalized Jordan Right Derivations on Prime and Semiprime πšͺ-Rings


Omar Faruk,Md. Mizanor Rahman,



Ξ“-Rings,Prime Ξ“-Rings,Semiprime Ξ“-Rings,Generalized Derivation,Generalized right derivation,Generalized Jordan Right Derivation,


In this paper, we analyzed the basic properties and related theorems of generalized Jordan right derivations on prime and semiprime 𝛀-rings with their mathematical simulation. We mainly focused on the characterizations of 2 free prime and semiprime 𝛀-rings by using Jordan Right Derivations. Important propositions and theorems related to generalized Jordan right derivation on prime and semiprime 𝛀-ring have been derived here with sufficient calculations. Our main objective is to prove the theorem that if 𝑀 be a 2-torsion free 𝛀-ring having a commutator right non-Zero divisor which satisfies the condition π‘Žπ›Όπ‘π›½π‘ = π‘Žπ›½π‘π›Όπ‘ for all π‘Ž, 𝑏, 𝑐 ∈ 𝑀 and 𝛼, 𝛽 ∈ 𝛀and if𝐷: 𝑀 β†’ 𝑀 be a generalized Jordan right derivation and 𝑑: 𝑀 β†’ 𝑀 be its associated Jordan right derivation then 𝐷 is a generalized right derivation on 𝑀.


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