For the group of integers $\mathbb Z$, we know that we have a finite free $\mathbb Z[t^{\pm 1}]-$resolution of $\mathbb Z$:
$$0\longrightarrow \mathbb Z[t^{\pm 1}] \stackrel{t-1}{\longrightarrow} \mathbb Z[t^{\pm 1}]\stackrel{\epsilon}{\longrightarrow} \mathbb Z\longrightarrow 0 $$ Where $\epsilon$ is the augmentation map.
Now what about $\mathbb Z\times \mathbb Z$, can we find a finite free $\mathbb Z[s^{\pm 1},t^{\pm 1}]-$resolution of $\mathbb Z\times \mathbb Z$. Thank you for your help!