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Let $Q$ be a local ring with maximal ideal $\mathfrak{n}$ and let $f,g\in\mathfrak{n}\smallsetminus\mathfrak{n}^2$ with $fg=0$. When $M$ is a finite$Q$-module with $fM=0$, we show that a minimal free resolution of $M$ over $Q$has a differential graded module structure over the differential graded algebra$Q\langle y,t\mid \partial(y)=f, \partial(t)=gy\rangle$. When $(f,g)$ is a pairof exact zero divisors, we use this structure to describe a minimal freeresolution of $M$ over $Q/(f)$.

DG module structures and minimal free resolutions modulo an exact zero-divisor