Abstract
A Lie algebra (over any field and of any dimension) is Noetherian if it satisfies the maximal condition on ideals. We introduce a new and more general class of quasi-Noetherian Lie algebras that possess several of the main properties of Noetherian Lie algebras. This class is shown to be closed under quotients and extensions. We obtain conditions under which a quasi-Noetherian Lie algebra is Noetherian. Next, we consider various questions about locally nilpotent and soluble radicals of quasi-Noetherian Lie algebras. We show that there exists a semisimple quasi-Noetherian Lie algebra that is not Noetherian. Finally, we consider some analogous results for groups and prove that a quasi-Noetherian group is countably recognizable.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
