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Vietnam Journal of Mathematics

, Volume 43, Issue 4, pp 819–828 | Cite as

On Additive Mappings in a ∗-Ring with an Identity Element

  • Nadeem ur RehmanEmail author
  • Abu Zaid Ansari
Article
  • 100 Downloads

Abstract

Let R be a semiprime ring with involution ∗ and let F, D : RR be additive mappings satisfying the conditions (i) F(x 2) = F(x)x +x D(x) and D(x 2) = D(x)x +x D(x); (ii) F(x n + 1) = F(x)(x ) n +x D(x)(x ) n − 1+(x )2 D(x)(x ) n − 2+⋯+(x ) n D(x) for all xR. Then, F(x y) = F(y)x +y D(x) and D(x y) = D(y)x +y D(x) for all x, yR.

Keywords

Additive mappings Semiprime rings and involution 

Mathematics Subject Classification (2010)

16W25 16N60 16R50 

Notes

Acknowledgments

The authors are greatly indebted to the referee for his/her several useful suggestions and valuable comments to improve the presentation of this paper.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics, Faculty of ScienceIslamic University in MadinahMadinahKingdom of Saudi Arabia

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