Afrika Matematika

, Volume 24, Issue 4, pp 503–510 | Cite as

Lie ideals and generalized (α, β)-derivations of *-prime rings

  • Nadeem ur Rehman
  • Radwan Mohammed AL-Omary
  • Shuliang Huang
Article

Abstract

Let (R, *) be a 2-torsion free *-prime ring with involution *, L ≠ 0 be a square closed *-Lie ideal of R and α, β automorphisms of R commuting with *. An additive mapping F: RR is called a generalized (α, β)-derivation on R if there exists an (α, β)-derivation d such that F(xy) = F(x)α(y) + β(x)d(y) holds for all \({x, y \in R}\). In the present paper, we shall show that \({L\subseteq Z(R)}\) such that R is a *-prime ring admits a generalized (α, β)-derivation satisfying several conditions, but associated with an (α, β)-derivation commuting with *.

Keywords

*-ideals *-prime rings Derivations and generalized (α, β)-derivations 

Mathematics Subject Classification

16D90 16W25 16N60 16U80 

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Copyright information

© African Mathematical Union and Springer-Verlag 2012

Authors and Affiliations

  • Nadeem ur Rehman
    • 1
  • Radwan Mohammed AL-Omary
    • 2
  • Shuliang Huang
    • 3
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics, Al-Naderah FacultyIbb UniversityIbbYemen
  3. 3.Department of MathematicsChuzhou UniversityChuzhouPeople’s Republic of China

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