Let R be a prime ring of characteristic different from 2, with right Utumi quotient ring U and extended centroid C, and let f(x1, . . . , xn) be a multilinear polynomial over C, not central valued on R. Suppose that d is a derivation of R and G is a generalized derivation of R such that G(f(r1,...,rn))d(f(r1,...,rn)) + d(f(r1,...,rn))G(f(r1,...,rn)) = 0 forall r1,...,rn ∈R. Then either d=0 or G=0, unless when d is an inner derivation of R, there exists λ ∈ C such that G(x) = λx, for all x ∈ R and f(x1,...,xn)2 is central valued on R.
A Quadratic Differential Identity with Generalized Derivations on Multilinear Polynomials in Prime Rings
RANIA F;
2014-01-01
Abstract
Let R be a prime ring of characteristic different from 2, with right Utumi quotient ring U and extended centroid C, and let f(x1, . . . , xn) be a multilinear polynomial over C, not central valued on R. Suppose that d is a derivation of R and G is a generalized derivation of R such that G(f(r1,...,rn))d(f(r1,...,rn)) + d(f(r1,...,rn))G(f(r1,...,rn)) = 0 forall r1,...,rn ∈R. Then either d=0 or G=0, unless when d is an inner derivation of R, there exists λ ∈ C such that G(x) = λx, for all x ∈ R and f(x1,...,xn)2 is central valued on R.File in questo prodotto:
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