Given a finite dimensional algebra $A$ over an algebraically closed field $K$. Let $A^e=A^{op} \otimes_K A$ be the enveloping algebra of $A$. Who noted first that the global dimension of $A$ is equal to the projective dimension of $A$ as $A^e$-module? Earliest reference I can find is a paper by Happel, see https://link.springer.com/chapter/10.1007/BFb0084073 .


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