【摘 要】
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A Noetherian (Artinian) Lie algebra satisfies the maximal (minimal) condition for ideals.Generalisations include quasi-Noetherian and quasi-Artinian Lie algebra
【机 构】
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Department of Mathematics, Umm Al-Qura University P.O.Box 56199, Makkah, Saudi Arabia;Mathematics In
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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.
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