Abstract
A Noetherian (Artinian) Lie algebra satisfies the maximal (minimal) condition for ideals. Generalisations include quasi-Noetherian and quasi-Artinian Lie algebras. We study conditions on prime ideals relating these properties. We prove that the radical of any ideal of a quasi-Artinian Lie algebra is the intersection of finitely many prime ideals, and an ideally finite Lie algebra is quasi-Noetherian if and only if it is quasi-Artinian. Both properties are equivalent to soluble-by-finite. We also prove a structure theorem for serially finite Artinian Lie algebras.
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.
