摘要翻译：
本文给出了正则环的实闭包*的一个刻划，它与文[4]中Baer正则环的实闭包*的刻划非常相似。利用近开映射刻画了正则环的Baer-ness。本文的最后一部分将集中于Baer和非Baer正则环（上同构）的实闭包*的分类，利用支撑映射的连续截面，我们在此集合上构造了一个拓扑。对于非Baer正则环，研究Baer壳的实谱和素谱几乎不需要Baer壳的环结构信息。我们将利用Hausdorff空间的绝对性来构造正则环的Baer壳的谱。最后给出了一个非理性完备的Baer正则环的例子。
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英文标题：
《Uniqueness of real closure * of regular rings》
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作者：
J. Capco
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Rings and Algebras        环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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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.
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PDF链接：
https://arxiv.org/pdf/0712.2674