Locally nilpotent skew derivations with central invariants

JOURNAL OF ALGEBRA

卷:483

Article

Bergen, Jeffrey¹  Grzeszczuk, Piotr² 

[1] Depaul Univ, Dept Math, 2320 N Kenmore Ave, Chicago, IL 60614 USA

[2] Bialystok Tech Univ, Fac Comp Sci, Wiejska 45A, PL-15351 Bialystok, Poland

关键词: Central invariants;    Skew derivations;   

DOI  :  10.1016/j.jalgebra.2017.03.040

来源: Elsevier

【 摘 要 】

Let delta be a locally nilpotent q-skew derivation of an algebra R such that the invariants are central. With some natural assumptions on the q-characteristic, we show that if R is semiprime then R is commutative. We also examine other conditions which imply, even when R is not commutative, that the commutator ideal is contained in the prime radical. These results extend previous work of the authors and of Osterburg and may shed some light on a conjecture of Herstein. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free