On generalized derivations in semiprime rings involving anticommutator

  • Mohammad AshrafEmail author
  • Sajad Ahmad Pary
  • Mohd Arif Raza
Original Paper


Let \(\mathfrak {R}\) be a prime ring with characteristic different from 2 and mnk be fixed positive integers. In this paper we study the case when \(\mathfrak {R}\) admits a generalized derivation \(\mathscr {F}\) with associated derivation \(\mathfrak {D}\) such that \((i)~(\mathscr {F}(x)\circ \mathscr {F}(y))^k=\mathscr {F}(x\circ _ky)~(ii)~ \mathscr {F}(x)\circ _m \mathscr {F}(y) =(\mathscr {F}(x\circ y))^n~(iii)~(\mathscr {F}\left( x\right) \circ \mathscr {F}\left( y\right) )^m =(\mathscr {F}(x\circ y))^n,\) for all \(x,y \in \mathscr {I}\), where \( \mathscr {I}\) is a non-zero ideal of \(\mathfrak {R}\). Moreover, we also examine the case when \(\mathfrak {R}\) is a semiprime ring.


(Semi)-prime ring Derivation Martindale ring of quotient Extended centroid 

Mathematics Subject Classification

16W25 16N20 16N60 



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© The Managing Editors 2019

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics, Faculty of Science and Arts-RabighKing Abdulaziz UniversityJeddahKingdom of Saudi Arabia

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