User richard - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T22:49:11Z http://mathoverflow.net/feeds/user/23424 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/124219/almost-prime-elements-in-perfect-hahn-field "almost prime" elements in perfect Hahn field Richard 2013-03-11T11:07:29Z 2013-03-11T12:10:24Z <p>Let $K$ be the field $\mathbb{F_p}^{alg}((\mathbb{Q}))$ (field of Hahn series over $\mathbb{F_p}^{alg}$ and with value group $\mathbb{Q}$).</p> <p>Is there elements $x$ of $K$ which are "almost prime" that is such that if $x=ab$ with $a, b\in K$, then $a=u(x^{1/p^k})^{p^k-n}$ and $b=u^{-1}(x^{1/p^k})^n$ where $u\in K$ ? And if so, how can such elements be recognized ?</p> <p>Thank you to anyone who could help.</p> http://mathoverflow.net/questions/95870/uniqueness-of-a-limit-of-a-pseudo-convergent-set uniqueness of a limit of a pseudo convergent set Richard 2012-05-03T14:49:18Z 2012-12-04T14:53:43Z <p>Is there an example of valued field in which any pseudo convergent set has a limit and such that this limit is unique?</p> http://mathoverflow.net/questions/115375/algebraic-maximal-extension-and-algebraic-closure Algebraic maximal extension and algebraic closure Richard 2012-12-04T08:29:42Z 2012-12-04T12:54:20Z <p>Let $K$ be a valued field. We say that $K$ is algebraic maximal if any algebraic extension of $K$ has either a bigger value group or a bigger residue field. Under which condition is an algebraic maximal valued field algebraically closed ?</p> <p>Thank you.</p> http://mathoverflow.net/questions/112545/absolute-galois-group-of-the-field-of-puiseux-series-over-overline-mathbbf/114588#114588 Answer by Richard for Absolute Galois group of the field of Puiseux series over $\overline{\mathbb{F}}_p$ Richard 2012-11-26T22:01:48Z 2012-11-26T22:01:48Z <p>I'm sorry to add an answer rather han a comment I have lost again the access to my account. @Laurent Berger Thank you very much for your answers !</p> http://mathoverflow.net/questions/115375/algebraic-maximal-extension-and-algebraic-closure/115393#115393 Comment by Richard Richard 2012-12-04T13:31:30Z 2012-12-04T13:31:30Z Thank you very much ! http://mathoverflow.net/questions/115375/algebraic-maximal-extension-and-algebraic-closure/115385#115385 Comment by Richard Richard 2012-12-04T12:14:38Z 2012-12-04T12:14:38Z Thank you! And if you consider fields whose residue fiels is algebraically closed and whose value group is divisible, when are such fields algebraically closed ?