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For questions having to do with projective and injective dimensions of modules, global dimension of rings and algebras, and related concepts.

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Question on an exercise on homological algebra?

Suppose $R$ has finite global dimension $n$, $N$ is a finitely generated module, $F$ is a free module, and $\operatorname{Ext}^n(N, F) \neq 0$. Then $\operatorname{Ext}^n(N, R)$ is also non-trivial. N …
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