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User:TakuyaMurata/Algebra exercises

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This is an old revision of this page, as edited by TakuyaMurata (talk | contribs) at 23:31, 11 July 2014 (Created page with '*An integral domain is a PID if and only if every submodule of a free module over it is free. *Not every module contains a maximal free submodule. (Consider ''Q'...'). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
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  • An integral domain is a PID if and only if every submodule of a free module over it is free.
  • Not every module contains a maximal free submodule. (Consider Q as a Z-module?.)