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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1805–1819 | Cite as

On Semi(prime) Rings and Algebras with Automorphisms and Generalized Derivations

  • Shakir AliEmail author
  • Basudeb Dhara
  • Brahim Fahid
  • Mohd Arif Raza
Original Paper
  • 26 Downloads

Abstract

Let R be a ring. An additive mapping \(F : R\rightarrow R\) is called a generalized derivation if there exists a derivation \(d : R\rightarrow R \) such that \( F(x y) = F(x)y + xd(y)\) for all \( x, y \in R\). In this paper, first we describe the structure of prime rings involving automorphisms and then characterized generalized derivations on semiprime rings which satisfy certain differential identities. As applications, and apart from proving the other results, many known theorems can be either generalized or deduced. Moreover, we apply our results to functional analysis, and to study the analogous conditions for continuous linear generalized derivations on Banach algebras.

Keywords

(Semi)prime ring Banach algebra Automorphism Derivation Generalized derivation 

Mathematics Subject Classification

16W25 16N60 16U80 46J45 

Notes

Acknowledgements

The authors are grateful to the learned referee(s) for his/her carefully reading the manuscript. The valuable suggestions and comments have simplified and clarified the paper immensely.

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  • Shakir Ali
    • 1
    Email author
  • Basudeb Dhara
    • 2
  • Brahim Fahid
    • 3
  • Mohd Arif Raza
    • 4
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of MathematicsBelda CollegePaschim MedinipurIndia
  3. 3.Centre de Recherche de Mathématiques et Applications de Rabat (CeReMAR), Faculty of SciencesMohammed V University in RabatRabatMorocco
  4. 4.Department of Mathematics, Faculty of Science and Arts-RabighKing Abdulaziz UniversityJeddahSaudi Arabia

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