most recent 30 from http://mathoverflow.net 2013-06-20T04:34:00Z http://mathoverflow.net/feeds/question/44669 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44669/sum-of-two-free-o-submodules-in-a-vector-space-over-a-local-field Tiffy 2010-11-03T12:02:51Z 2010-11-03T12:41:13Z

<p>Let $V$ be a countably infinite dimensional $K$-vector space over a local field $K$ (nontrivially discretely valued with finite residue field). Let $o$ be the ring of integers of $K$.</p> <p>Given two free o-submodules $L_1,L_2$ in $V$, does $L_1+L_2 \subsetneqq V$ hold? (Here L_1+L_2 denotes the smallest $o$-module inside $V$ containing $L_1$ and $L_2$)</p>