Let $M$ be a module over an integral domain $R$. An element $m \in M$ is said to be torsion if there exists a nonzero $r \in R$ with $\mathrm{rm}=0 ; M$ is said to be torsion-free if its only torsion element is 0 . Show that there exists a unique submodule $N$ of $M$ such that (a) all elements of $N$ are torsion and (b) the quotient module $M / N$ is torsion-free.