In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings.
本文研究了含幺可换环上一般线性李代数的子代数结构。
Using the notion of coefficient matrix and maximal element. We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.
利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。
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。
Subsequently, we character and study the 2-cocycles on a subalgebra of the algebra M3 (c) and obtain the necessary and sufficient conditions that a bilinear mapping is a 2-cocycle on this algebra.
接着对矩阵代数m_3 (C)的子代数上的2 -上循环进行了等价刻画，得到了其上的双线性映射是2 -上循环的充要条件。
Subsequently, we character and study the 2-cocycles on a subalgebra of the algebra M3 (c) and obtain the necessary and sufficient conditions that a bilinear mapping is a 2-cocycle on this algebra.
接着对矩阵代数m_3 (C)的子代数上的2 -上循环进行了等价刻画，得到了其上的双线性映射是2 -上循环的充要条件。
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