most recent 30 from http://mathoverflow.net 2013-05-20T03:23:04Z http://mathoverflow.net/feeds/question/103444 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103444/completion-of-commutative-rings Aurora 2012-07-29T10:58:39Z 2012-07-29T22:44:17Z

<p>Assume that $(R,\mathfrak{m})$ is a commutative local ring of equal characteristic zero. So $R$ contains the field of rationals. The well known $\mathfrak{m}$-adic completion of $R$ provides a complete ring $\hat{R}$ whose coefficient field is isomorphic to the residue field of $R$. Do there exists a topological method (completion) for providing a local Noetheiran extension $S$ of $R$ such that $S$ contains the real numbers and also contains $R$ as a dense subring.</p>