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Jun 9, 2010 at 23:42 comment added Victor Protsak The situation for noncommutative rings is substantially different (see McConnell and Robson's book). For example, every projective module of rank at least 2 over the first Weyl algebra is free. But there are (many) nonprincipal left ideals. The proofs aren't too hard.
Jun 9, 2010 at 19:33 comment added Seamus I don't think it's been published yet, but I'll see if I can get an electronic copy for you. Swan's paper is worth having a look at but it is very difficult and long so it's a rather major undertaking!
Jun 9, 2010 at 19:16 comment added Hailong Dao Hi Seamus, thanks! The result looks very interesting, do you have a reference for Frank's paper?
Jun 9, 2010 at 19:09 history answered Seamus CC BY-SA 2.5