Skew derivations and the nil and prime radicals
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 229-236
MSC: 16N40, 16W25, 16W55.
DOI: 10.4064/cm128-2-8
Abstract
We examine when the nil and prime radicals of an algebra are stable under $q$-skew $\sigma $-derivations. We provide an example which shows that even if $q$ is not a root of $1$ or if $\delta $ and $\sigma $ commute in characteristic $0$, then the nil and prime radicals need not be $\delta $-stable. However, when certain finiteness conditions are placed on $\delta $ or $\sigma $, then the nil and prime radicals are $\delta $-stable.
