The Stacks project

Definition 46.8.8. Let $A$ be a ring and let $M$, $N$ be $A$-modules. The $i$th pure extension module $\text{Pext}^ i_ A(M, N)$ is the $i$th cohomology module of the complex $\mathop{\mathrm{Hom}}\nolimits _ A(M, I^\bullet )$ where $I^\bullet $ is a pure injective resolution of $N$.