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Let $R$ be a Gorenstein (not necessarily commutative) ring and let $I$ be an injective finitely generated module over $R$. Is it true that if $\operatorname{Ext}_R^i(I, R)=0$ for $i > 0$, then $I$ is projective?

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    What definition of Gorenstein are you using? In the non-comm. case there are dozens... :P2012-02-21
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    In my definition $S$ is left and right noetherian and have finite injective dimension as left or right module over itself.2012-02-21

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