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Generalized Derivations with Power-Central Values on Multilinear Polynomials

Yu Wang

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematical School, Jilin Normal University, Siping, Jilin 136000, China

https://doi.org/10.1142/S1005386706000344Cited by:14 (Source: Crossref)

Abstract

Let R be a prime algebra over a commutative ring K, Z and C the center and extended centroid of R, respectively, g a generalized derivation of R, and f (X₁, …,X_t) a multilinear polynomial over K. If g(f (X₁, …,X_t))ⁿ ∈ Z for all x₁, …, x_t ∈ R, then either there exists an element λ ∈ C such that g(x)= λx for all x ∈ R or f(x₁, …,x_t) is central-valued on R except when R satisfies s₄, the standard identity in four variables.

Keywords:

AMSC: primary 16W25, secondary 16N60, secondary 16U80

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