谱可数的不可数局部环的补
Completions of Uncountable Local Rings with Countable Spectra
摘要：
本文给出了完备局部（Noether）环是不可数局部（Noether）整环的完备化的充要条件。我们的研究结果表明，不可数局域可数谱比以前认为的更常见。我们还刻画了具有可数谱的不可数优秀局部域的完备化（假设完备化包含有理数）、具有可数谱的不可数局部唯一因子分解域的完备化、具有可数谱的不可数非悬链线局部域的完备化以及具有可数谱的不可数非悬链线局部唯一因子分解域的完备化.
英文摘要：
We find necessary and sufficient conditions for a complete local (Noetherian) ring to be the completion of an uncountable local (Noetherian) domain with a countable spectrum. Our results suggest that uncountable local domains with countable spectra are more common than previously thought. We also characterize completions of uncountable excellent local domains with countable spectra assuming the completion contains the rationals, completions of uncountable local unique factorization domains with countable spectra, completions of uncountable noncatenary local domains with countable spectra, and completions of uncountable noncatenary local unique factorization domains with countable spectra.
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