Solution
= Solution
The zero element is torsion. If $m,n\in T$, choose nonzero $r,s\in R$ with $rm=0$ and $sn=0$. Since $R$ is an <integral domain>, $rs\ne0$, and
$$
rs(m+n)=s(rm)+r(sn)=0.
$$
\b[Thus $m+n\in T$. If $a\in R$, then $r(am)=a(rm)=0$, so $am\in T$. Hence $T$ is closed under addition and scalar multiplication and is an <R-module>[submodule] of $M$.]