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Proceedings - Mathematical Sciences

, Volume 126, Issue 3, pp 389–398 | Cite as

On prime and semiprime rings with generalized derivations and non-commutative Banach algebras

  • MOHD ARIF RAZA
  • NADEEM UR REHMAN
Article
  • 178 Downloads

Abstract

Let R be a prime ring of characteristic different from 2 and m a fixed positive integer. If R admits a generalized derivation associated with a nonzero deviation d such that [F(x),d(y)] m =[x,y] for all x,y in some appropriate subset of R, then R is commutative. Moreover, we also examine the case R is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer–Werner theorem.

Keywords

Banach algebras generalized derivations martindale ring of quotients prime and semiprime rings radical 

2010 Mathematics Subject Classification

46J10 16N20 16N60 16W25 

Notes

Acknowledgements

The authors wish to thank the referee for his/her valuable comments and suggestions.

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Copyright information

© Indian Academy of Sciences 2016

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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