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17 Apr 2012
Lie ideals and generalized (α, β)derivations of *prime rings
 Nadeem ur Rehman,
 Radwan Mohammed ALOmary,
 Shuliang Huang
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Let (R, *) be a 2torsion 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: R → R 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 *.
N. Rehman’s research is supported by UGC, India, Grant No. 368/2008(SR).
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 Title
 Lie ideals and generalized (α, β)derivations of *prime rings
 Journal

Afrika Matematika
Volume 24, Issue 4 , pp 503510
 Cover Date
 20131201
 DOI
 10.1007/s1337001200759
 Print ISSN
 10129405
 Online ISSN
 21907668
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 *ideals
 *prime rings
 Derivations and generalized (α, β)derivations
 16D90
 16W25
 16N60
 16U80
 Authors

 Nadeem ur Rehman ^{(1)}
 Radwan Mohammed ALOmary ^{(2)}
 Shuliang Huang ^{(3)}
 Author Affiliations

 1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
 2. Department of Mathematics, AlNaderah Faculty, Ibb University, Ibb, Yemen
 3. Department of Mathematics, Chuzhou University, Chuzhou, 239012, Anhui, People’s Republic of China