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- W2885267037 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." @default.
- W2885267037 created "2018-08-22" @default.
- W2885267037 creator A5004771658 @default.
- W2885267037 creator A5079169390 @default.
- W2885267037 date "2019-07-05" @default.
- W2885267037 modified "2023-09-27" @default.
- W2885267037 title "A generalized Noetherian condition for Lie algebras" @default.
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- W2885267037 doi "https://doi.org/10.1142/s0219498819501469" @default.
- W2885267037 hasPublicationYear "2019" @default.
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