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As far as I know, over any PID, an polynomial rings over a field, or an local ring, projective modules are always free.

This kind of results make me curious about if there are any overall characterization of a commutative ring $R$ such that all projective $R$-modules are free.

Does anyone have some thoughts on it? Any idea will be appreciated.

user26857
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Censi LI
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    Most likely not: see http://math.stackexchange.com/questions/115187/condition-for-a-ring-on-projective-and-free-modules-problem – user26857 Apr 08 '16 at 11:53
  • @user26857 Thank for offering the link. Seems that such a characterization is extremely unachievable. – Censi LI Apr 08 '16 at 14:53

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