Remark 1

If the ring $A$ is Noetherian, and if the $A$-modules $M$ and $N$ are of finite type, it follows from the proof of a) that every element of $\mathrm{Ext}_A^n(M, N)$ is the class associated with an exact sequence $0 \to N \to R_n \to \ldots \to R_1 \to M \to 0$ where the $R_i$ are of finite type.