Skew derivations and the nil and prime radicals

Volume 128 / 2012

Jeffrey Bergen, Piotr Grzeszczuk Colloquium Mathematicum 128 (2012), 229-236 MSC: 16N40, 16W25, 16W55. DOI: 10.4064/cm128-2-8


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.


  • Jeffrey BergenDepartment of Mathematics
    DePaul University
    2320 N. Kenmore Avenue
    Chicago, IL 60614, U.S.A.
  • Piotr GrzeszczukFaculty of Computer Science
    Białystok University of Technology
    Wiejska 45A
    15-351 Białystok, Poland

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