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

Vincenzo De Filippis, and Feng Wei. "Posner's second theorem and annihilator conditions with generalized skew derivations." Colloquium Mathematicae 129.1 (2012): 61-74. <http://eudml.org/doc/283824>.

@article{VincenzoDeFilippis2012,
abstract = {Let be a prime ring of characteristic different from 2, $_r$ be its right Martindale quotient ring and be its extended centroid. Suppose that is a non-zero generalized skew derivation of and f(x₁,..., xₙ) is a non-central multilinear polynomial over with n non-commuting variables. If there exists a non-zero element a of such that a[ (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ , then one of the following holds: (a) there exists λ ∈ such that (x) = λx for all x ∈ ; (b) there exist $q ∈ _r$ and λ ∈ such that (x) = (q+λ)x + xq for all x ∈ and f(x₁, ..., xₙ)² is central-valued on .},
author = {Vincenzo De Filippis, Feng Wei},
journal = {Colloquium Mathematicae},
keywords = {generalized skew derivations; additive maps; prime rings; commutator identities; multilinear polynomials},
language = {eng},
number = {1},
pages = {61-74},
title = {Posner's second theorem and annihilator conditions with generalized skew derivations},
url = {http://eudml.org/doc/283824},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Vincenzo De Filippis
AU - Feng Wei
TI - Posner's second theorem and annihilator conditions with generalized skew derivations
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 61
EP - 74
AB - Let be a prime ring of characteristic different from 2, $_r$ be its right Martindale quotient ring and be its extended centroid. Suppose that is a non-zero generalized skew derivation of and f(x₁,..., xₙ) is a non-central multilinear polynomial over with n non-commuting variables. If there exists a non-zero element a of such that a[ (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ , then one of the following holds: (a) there exists λ ∈ such that (x) = λx for all x ∈ ; (b) there exist $q ∈ _r$ and λ ∈ such that (x) = (q+λ)x + xq for all x ∈ and f(x₁, ..., xₙ)² is central-valued on .
LA - eng
KW - generalized skew derivations; additive maps; prime rings; commutator identities; multilinear polynomials
UR - http://eudml.org/doc/283824
ER -