most recent 30 from http://mathoverflow.net 2013-05-19T09:12:01Z http://mathoverflow.net/feeds/user/3427 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/12508/examples-of-completions-and-algebraic-closures Willem Noorduin 2010-01-21T07:03:58Z 2010-01-21T13:18:12Z

<p>It is widely known that the algebaric closure of the $p$-adic completion $\mathbb{Q}_p$ of $\mathbb{Q}$ isn't complete anymore. It's completion is complete and known as $\mathbb{C}_p$. </p> <p>I have read in a book about non-archimedean analysis that in this case the process ends, which means that $\mathbb{C}_p$ is also algebraically closed.</p> <p>My question is: is there an example of a field K, in which the algebraic closure $K^{alg}$ isn't complete, and the completion of $K^{alg}$ isn't algebraically closed ? And how do I construct such an example.</p>