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.
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.
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.
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