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ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 63, Issue 2, pp 391–402 | Cite as

Skew n-derivation on prime and semi prime rings

  • V. K. Yadav
  • R. K. Sharma
Article

Abstract

Let \(n \ge 2\) be a fixed integer, R be a noncommutative n!-torsion free ring and I be any non zero ideal of R. In this paper we have proved the following results; (i) If R is a prime ring and there exists a symmetric skew n-derivation \(D: R^n \rightarrow R\) associated with the automorphism \(\sigma \) on R,  such that the trace function \(\delta : R \rightarrow R \) of D satisfies \([\delta (x), \sigma (x)] =0\), for all \(x\in I,\) then \(D=0;\,\)(ii) If R is a semi prime ring and the trace function \(\delta ,\) commuting on I,  satisfies \([\delta (x), \sigma (x)]\in Z\), for all \(x \in I,\) then \([\delta (x), \sigma (x)] = 0 \), for all \(x \in I.\) Moreover, we have proved some annihilating conditions for algebraic identity involving multiplicative(generalized) derivation.

Keywords

Commuting map Multiplicative (generalized) derivation Skew n-derivation Trace function 

Mathematics Subject Classification

16W25 16N60 16R50 

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Copyright information

© Università degli Studi di Ferrara 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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