We examine when the nil and prime radicals of an algebra are stable under q-skew σ-derivations. We provide an example which shows that even if q is not a root of 1 or if δ and σ commute in characteristic 0, then the nil and prime radicals need not be δ-stable. However, when certain finiteness conditions are placed on δ or σ, then the nil and prime radicals are δ-stable.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-8,
author = {Jeffrey Bergen and Piotr Grzeszczuk},
title = {Skew derivations and the nil and prime radicals},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {229-236},
zbl = {1266.16017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-8}
}
Jeffrey Bergen; Piotr Grzeszczuk. Skew derivations and the nil and prime radicals. Colloquium Mathematicae, Tome 126 (2012) pp. 229-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-8/