Posner's second theorem and annihilator conditions with generalized skew derivations

• Autorzy: Vincenzo De Filippis , Feng Wei
• Języki publikacji: EN

Abstrakty

EN

Let 𝓡 be a prime ring of characteristic different from 2, $𝒬_r$ 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 a[𝒢 (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ 𝓡, then one of the following holds:
(a) there exists λ ∈ 𝓒 such that 𝒢 (x) = λx for all x ∈ 𝓡;
(b) there exist $q ∈ 𝒬_r$ 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.

Kategorie tematyczne

• 16N60: Prime and semiprime rings
• 16W25: Derivations, actions of Lie algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 61-74

Daty

wydano

2012

Twórcy

autor

Vincenzo De Filippis

• DI.S.I.A., Faculty of Engineering, University of Messina, Contrada Di Dio, 98166 Messina, Italy

autor

Feng Wei

• School of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China

Identyfikatory

DOI

10.4064/cm129-1-4