Pure submodules - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T23:20:52Z http://mathoverflow.net/feeds/question/61772 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61772/pure-submodules Pure submodules Neha 2011-04-15T01:25:50Z 2011-04-15T01:30:21Z <p>Is the dual of a pure module also pure?</p> <p>Suppose $H$ is a Hopf algebra over a field $K$ and $S$ is a ring which has a right $H$-action.</p> <p>If ${}_HA$ is a pure left $H$-submodule, will $S\otimes_H A$ be a pure $S$-submodule ? If not, then what are the minimum conditions required (on $H$ or $S$) to make it so? </p>