We reprove the following theorem with a simpler means: theorem: let a is the solvable algebra, then a is the local nilpotent algebra.
用一种简单的方法重新证明了以下定理：定理：假设A是可解的交错代数，则A是局部幂零的交错代数。
It is theoretically important to solve the problems of decomposition of automorphisms of solvable subalgebra and nilpotent subalgebra of matrix algebra over commutative rings.
交换环上矩阵代数的可解子代数和幂零子代数的自同构分解问题是一类重要的具有理论意义的研究课题。
A class of solvable 3-lie algebras with a 5-dimensional maximal hypo-nilpotent ideal, which is a 5-dimensional simplest filiform 3-lie algebra, is constructed.
构造了一类以5维最简线状3 -李代数为极大次幂零理想的可解3 -李代数，并且对构造的3 -李代数进行了分类。
A class of solvable 3-lie algebras with a 5-dimensional maximal hypo-nilpotent ideal, which is a 5-dimensional simplest filiform 3-lie algebra, is constructed.
构造了一类以5维最简线状3 -李代数为极大次幂零理想的可解3 -李代数，并且对构造的3 -李代数进行了分类。
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