由调节函数构成的环的极大谱
Maximal Spectra of rings consisting of regulated functions
摘要：
在1969年Höchster证明，对于每一个准紧T1-空间$X$，我们可以找到一个交换环$R$，使$X$同胚的最大谱$\mathrm{Specm}(R)$的$R$。这个结果暗示了交换环$R$的存在性，它允许非Hausdorff和全不连通的的极大谱$\mathrm{Specm}(R)$ .然而，还没有这样的交换环的例子。本文研究几乎允许非Hausdorff且全不连通的极大谱的环。
英文摘要：
In 1969 Höchster proved that for every quasi-compact T1-space $X$ we can find a commutative ring $R$ such that $X$ is homeomorphic to the maximal spectrum $\mathrm{Specm}(R)$ of $R$. This result implies the existence of a commutative ring $R$ that admits a non-Hausdorff and totally disconnected maximal spectrum $\mathrm{Specm}(R)$. However, there has not been an example of such a commutative ring yet. The aim of this paper is to investigate rings that almost admit a non-Hausdorff and totally disconnected maximal spectrum.
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。
