I know that for a finitely presented commutative module $M$, if all prime localizations $M_\mathfrak{p}$ are free, then $M$ is projective. Is there a weakening or a converse of this statement? What can be said about a module if knowing its prime localizations are free implies projectivity?
2026-03-29 11:42:57.1774784577
Weakest condition on module such that free prime localizations imply projective?
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