正则环的实闭包 * 的唯一性
Uniqueness of real closure * of regular rings
摘要：
本文给出了正则环的实闭包 * 的一个刻划，它与[4]中Baer正则环的实闭包 * 的刻划十分相似.利用近开映射刻画了正则环的Baer性。本文的最后一部分将集中于利用支撑映射的连续截面对Baer环和非Baer正则环（上同构）的实闭包 * 进行分类，并在此基础上构造了Baer情形的拓扑。对于非Baer正则环的情形，为了研究Baer壳的实谱和素谱，几乎不需要关于Baer壳的环结构的信息.我们将利用T2空间的绝对性来构造正则环的Baer壳的谱。最后给出了一个非有理完备的Baer正则环的例子。
英文摘要：
In this paper we give a characterisation of real closure * of regular rings, which is quite similar to the characterisation of real closure * of Baer regular rings seen in [4]. We also characterize Baer-ness of regular rings using near-open maps. The last part of this work will concentrate on classifying the real closure * of Baer and non-Baer regular rings (upto isomorphisms) using continuous sections of the support map, we construct a topology on this set for the Baer case. For the case of non-Baer regular rings, it will be shown that almost no information of the ring structure of the Baer hull is necessary in order to study the real and prime spectra of the Baer hull. We shall make use of the absolutes of Hausdorff spaces in order to give a construction of the spectra of the Baer hulls of regular rings. Finally we give example of a Baer regular ring that is not rationally complete.
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。
