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