- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
122
2009
0
Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras
Feng
Wei
Beijing Institute of Technology, BEIJING, CHINA
Zhankui
Xiao
Beijing Institute of Technology, 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. If μ(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 on R 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.
Associative rings and algebras
General
171
190
10.4171/RSMUP/122-11
http://www.ems-ph.org/doi/10.4171/RSMUP/122-11