Let R be a non-commutative prime of characteristic different from 2, C the extended centroid of R, f(x1, … , xn) a non-central polynomial over C and S= { f(r1, … , rn) : r1, … , rn∈ R}. If F and G are generalized derivations of R such that F(x) G(y) + G(y) F(x) = xy+ yx, for any x∈ S, then there exist λ, μ∈ C such that λμ= 1 and F(x) = λx, G(x) = μx, for all x∈ R.
Generalized derivations with skew-commutativity conditions on polynomials in prime rings
Rania F.
2019-01-01
Abstract
Let R be a non-commutative prime of characteristic different from 2, C the extended centroid of R, f(x1, … , xn) a non-central polynomial over C and S= { f(r1, … , rn) : r1, … , rn∈ R}. If F and G are generalized derivations of R such that F(x) G(y) + G(y) F(x) = xy+ yx, for any x∈ S, then there exist λ, μ∈ C such that λμ= 1 and F(x) = λx, G(x) = μx, for all x∈ R.File in questo prodotto:
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