Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. Suppose that G is a non-zero generalized skew derivation of R and f(x1,...,xn) is a non-central multilinear polynomial over C with n non-commuting variables. If there exists a non-zero element a of R such that then one of the following holds: (a) there exists λ ∈ C such that G(x) = λx for all x ∈ R; (b) there exist q ∈ Qr and λ ∈ C such that G(x) = (q + λ)x + xq for all x ∈ R and f(x1,...,xn)2 is central-valued on R. © Instytut Matematyczny PAN, 2012.
Posner's second theorem and annihilator conditions with generalized skew derivations
DE FILIPPIS, Vincenzo;
2012-01-01
Abstract
Let R be a prime ring of characteristic different from 2, Qr be its right Martindale quotient ring and C be its extended centroid. Suppose that G is a non-zero generalized skew derivation of R and f(x1,...,xn) is a non-central multilinear polynomial over C with n non-commuting variables. If there exists a non-zero element a of R such that then one of the following holds: (a) there exists λ ∈ C such that G(x) = λx for all x ∈ R; (b) there exist q ∈ Qr and λ ∈ C such that G(x) = (q + λ)x + xq for all x ∈ R and f(x1,...,xn)2 is central-valued on R. © Instytut Matematyczny PAN, 2012.File in questo prodotto:
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