most recent 30 from http://mathoverflow.net 2013-06-18T20:59:37Z http://mathoverflow.net/feeds/question/114227 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/114227/a-problem-about-field-extension bo.gu 2012-11-23T09:42:35Z 2012-11-23T10:06:32Z

<p>Let K and L are fields,L is a sub field of K,and L is isomorphic to K,whether can we get K=L?If true,how to prove? Thanks.</p>

http://mathoverflow.net/questions/114227/a-problem-about-field-extension/114230#114230 Aakumadula 2012-11-23T10:02:10Z 2012-11-23T10:02:10Z

<p>No. ${\mathbb C}(X^2,Y)=L$ is a subfield of $K={\mathbb C}(X,Y)$ where $X,Y$ are algebraically independent variables over $\mathbb C$. Hence $L$ is isomorphic to $K$ but not equal. </p>

http://mathoverflow.net/questions/114227/a-problem-about-field-extension/114231#114231 bo.gu 2012-11-23T10:03:58Z 2012-11-23T10:06:32Z

<p>If K and L are F-field extensions, K/F and L/F are both finite dimensional, and the isomorphism from K to L is an F-homomorphism, then the proof is easy, but the general case seems difficult. </p>