On generalized derivations satisfying certain identities
Let R be a prime ring with char R ≠ 2 and let d be a generalized derivation on R. We study the generalized derivation d satisfying any of the following identities:
d[(x, y)] = [d(x), d(y)] for all x , y ∈ R ;
d[(x, y)] = [d(y), d(x)] for all x , y ∈ R ;
either d([x, y]) = [d(x), d(y)] or d([x, y]) = [d(y), d(x)] for all x , y ∈ R .
KeywordsPrime Ring Generalize Derivation Proper Subgroup Quotient Ring Semiprime Ring
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- 6.K. I. Beidar, W. S. Martindale, and V. Mikhalev, “Rings with generalized identities,” Pure Appl. Math. (1996).Google Scholar
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