Let be a prime ring of characteristic different from 2, 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 and λ ∈ such that (x) = (q+λ)x + xq for all x ∈ and f(x₁, ..., xₙ)² is central-valued on .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-4,
author = {Vincenzo De Filippis and Feng Wei},
title = {Posner's second theorem and annihilator conditions with generalized skew derivations},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {61-74},
zbl = {1270.16033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-4}
}
Vincenzo De Filippis; Feng Wei. Posner's second theorem and annihilator conditions with generalized skew derivations. Colloquium Mathematicae, Tome 126 (2012) pp. 61-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-4/