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edit approved Feb 15, 2016 at 7:36
user 1
edit approved Feb 15, 2016 at 7:36
user 1
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Answer is yes if A$A$ is Noetherian and P$P$ is finitely generated. Indeed, your condition implies that Ext^1(P, N)=0 $Ext^1(P, N)=0$ for any finitely generated A$A$-module N$N$, which implies that P$P$ is projective.

Answer is yes if A is Noetherian and P is finitely generated. Indeed, your condition implies that Ext^1(P, N)=0 for any finitely generated A-module N, which implies that P is projective.

Answer is yes if $A$ is Noetherian and $P$ is finitely generated. Indeed, your condition implies that $Ext^1(P, N)=0$ for any finitely generated $A$-module $N$, which implies that $P$ is projective.

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Bedini
Bedini
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Answer is yes if A is Noetherian and P is finitely generated. Indeed, your condition implies that Ext^1(P, N)=0 for any finitely generated A-module N, which implies that P is projective.