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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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The full linear ring is of finite projective dimension over the enevelopping algebra?
It is known that if $R=End_k(V)$, with $V$ a finite dimension $k$-vector space then $R$ is projective as $R^e$-module, thus of projective dimension $pd_{R^e}(R)=0$. If $V$ is of infinite dimension doe …