链条件Lie代数的结构

The Structures of Lie Algebrs with Chain Conditions

[2]中给出了模论中Krull-Schmidt定理的经典证明,本文针对Lie代数的情形,引入理想自同态这一概念,得到相应的结果(定理2.7),但唯一性命题比简单地说“不可分解因子不计同构是唯一确定的”要强。

The classical proof of Krull-Schmidt Theorem in module theory was given in 〔2〕 . The main object of this paper is to extend the above Theorem to the case of Lie algebrad by introduce the concept of ideal endomorphism of Lie algebras. We point out that the uniqueness is stronger than that we say 'The indecomposable factors are uniquely determined up to an isomorphism' simply.