对具有泛包络代数结构的量子力学控制系统，研究了泛包络代数的可扩张性和系统状态的定义域问题。

For quantum mechanical control systems with structures of universal enveloping algebras, the thesis studies the enlargability of the universal enveloping algebras and the domain problems.

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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.

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