在有单位元的交换环上，可应用生成元和定义关系的方法给出仿型李代数的定义。
On commutative ring with the identity, the definition of affine Lie algebras was given by applying the means of generator and defining relation.
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。
It is theoretically important to solve the problems of decomposition of automorphisms of solvable subalgebra and nilpotent subalgebra of matrix algebra 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。
In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings.
第一章中，我们研究了剩余域是代数闭域的离散赋值环上的完全分次代数；
In the first chapter, we discuss the fully graded algebras over discrete valuation ring with an algebraically closed residue field of characteristic p.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
给出基于连续值逻辑上的不分明化环的概念，从一个新的方向讨论了环的某些代数性质。
In this paper, we introduce the concept of fuzzifying rings based on continuous valued logic and ivestigate some of the their algebraic properties.
给出基于连续值逻辑上的不分明化环的概念，从一个新的方向讨论了环的某些代数性质。
In this paper, we introduce the concept of fuzzifying rings based on continuous valued logic and ivestigate some of the their algebraic properties.
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