  Let $R$ be a ring, let $\mathfrak{a}\subseteq R$ be an ideal, and let $M$ be
an $R$-module. Let $\Gamma_{\mathfrak{a}}$ denote the $\mathfrak{a}$-torsion
functor. Conditions are given for the (weakly) associated primes of
$\Gamma_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$
containing $\mathfrak{a}$, and for the (weakly) associated primes of
$M/\Gamma_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ not
containing $\mathfrak{a}$.
