Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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COMMUTATIVITY OF MULTIPLICATIVE b-GENERALIZED DERIVATIONS OF PRIME RINGS

  • Muzibur Rahman Mozumder (Faculty of Science, Department of Mathematics, Aligarh Muslim University) ;
  • Wasim Ahmed (Faculty of Science, Department of Mathematics, Aligarh Muslim University) ;
  • Mohd Arif Raza (Faculty of Science & Arts-Rabigh, Department of Mathematics, King Abdulaziz University) ;
  • Adnan Abbasi (Department of Mathematics, Madanapalle Institute of Technology and Science)
  • Received : 2022.08.10
  • Accepted : 2023.03.19
  • Published : 2023.03.30
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Abstract

Consider ℛ to be an associative prime ring and 𝒦 to be a nonzero dense ideal of ℛ. A mapping (need not be additive) ℱ : ℛ → 𝒬mr associated with derivation d : ℛ → ℛ is called a multiplicative b-generalized derivation if ℱ(αδ) = ℱ(α)δ +bαd(δ) holds for all α, δ ∈ ℛ and for any fixed (0 ≠)b ∈ 𝒬s ⊆ 𝒬mr. In this manuscript, we study the commutativity of prime rings when the map b-generalized derivation satisfies the strong commutativity preserving condition and moreover, we investigate the commutativity of prime rings that admit multiplicative b-generalized derivation, which improves many results in the literature.

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Acknowledgement

The authors are indebted to the referee/s for his/her careful reading the manuscript.

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