Generalised Chain Conditions, Prime Ideals, and Classes of Locally Finite Lie Algebras

• 作者: Falih A.M.Aldosray Ian Stewart
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 63-86
• 页数: 24页
• 语种: 英文
• DOI: 10.1142/S1005386721000079

摘要

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 radicalof 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 qussi-Artinian.Both properties are equivalent to soluble-by-finite.We also prove a structure theorem for serially finite Artinian Lie algebras.