If $R$ is a PID and $M$ is a finitely generated $R$-module,
How do I show that M has a free resolution of length at most $1$?
So I have to show that M has a free resolution
$....\to F_2 \to F_1 \to F_0 \to 0$ with $F_i = 0$ for all $i > 1$
I know that every $R$-module $M$ admits a free resolution
$....\to F_2 \to F_1 \to F_0 \to 0$
But I don't know how to proceed from here