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Results in Mathematics

, Volume 42, Issue 1–2, pp 3–8 | Cite as

On Commutativity of Rings With Derivations

  • Mohammad Ashraf
  • Nadeem-ur Rehman
Article

Abstract

Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R.

Keywords and Phrases

prime rings derivations ideals Lie ideals and commutativity 

1991 Mathematics Subject Classification

16W25 16N60 16U80 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • Mohammad Ashraf
    • 1
  • Nadeem-ur Rehman
    • 2
  1. 1.Department of Mathematics Faculty of scienceKing Abdul Aziz UniversityJeddahSaudi-Arabia
  2. 2.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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