Afrika Matematika

, Volume 24, Issue 4, pp 503–510

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

Authors

    • Department of MathematicsAligarh Muslim University
  • Radwan Mohammed AL-Omary
    • Department of Mathematics, Al-Naderah FacultyIbb University
  • Shuliang Huang
    • Department of MathematicsChuzhou University
Article

DOI: 10.1007/s13370-012-0075-9

Cite this article as:
Rehman, N.u., AL-Omary, R.M. & Huang, S. Afr. Mat. (2013) 24: 503. doi:10.1007/s13370-012-0075-9
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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 ringsDerivations and generalized (α, β)-derivations

Mathematics Subject Classification

16D9016W2516N6016U80
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© African Mathematical Union and Springer-Verlag 2012