Is it true that if $\operatorname{Ext}^{1}_{A}(P,A/I)=0$ forall $I$ then $P$ is projective?
Similar statements are true for flat and injective modules, but I'm beginning to suspect that projective modules cannot be characterized solely by ideals.
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Is it true that if $\operatorname{Ext}^{1}_{A}(P,A/I)=0 $ for all $ I$ then $P$ is projective?
ashpool
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