伪代数闭扩张
Pseudo Algebraically Closed Extensions
摘要：
这个博士学位涉及域的伪代数闭（PAC）扩展的概念。它开发了一个组理论的机器，嵌入问题的推广的基础上，研究这些扩展。也许主要的结果是，虽然有许多PAC扩展，但一个适当的PAC扩展的伽罗瓦闭包是可分离的。本论文还包括以下几个方面的内容。伪代数闭扩张的群论对应物，即所谓的投射对。应用于看似无关的主题，例如，关于无限域上一元多项式环的等差数列中素数的狄利克雷定理的模拟。
英文摘要：
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
