Rendiconti del Seminario Matematico della Università di Padova
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Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach AlgebrasFeng Wei and Zhankui Xiao (1) Department of Applied Mathematics, Beijing Institute of Technology, 100081, Beijing, China
(2) Department of Applied Mathematics, Beijing Institute of Technology, 100081, Beijing, China
We first give several polynomial identities of semiprime rings which make the additive mappings appearing in the identities to be generalized derivations. Then we study pairs of generalized Jordan derivations on prime rings. Let m,n be fixed positive integers,R be a noncommutative 2(m+n)!-torsion free prime ring with the center Z and μ, ν be a pair of generalized Jordan derivations on RR. Ifμ(xm)xn+xnν(xm) ∈ Z for all x ∈ R, then μ and ν are left (or right) multipliers.In particular, if μ, ν are a pair of derivations onR satisfying the same assumption, then μ = ν = 0. Then applying these purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.
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Wei Feng, Xiao Zhankui: Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras. Rend. Sem. Mat. Univ. Padova 122 (2009), 171-190. doi: 10.4171/RSMUP/122-11