  Let $R$ be a commutative ring and $S$ a multiplicative subset of $R$. A ring
$R$ is called an $S$-Matlis ring if $pd_RR_S\leq 1$. In this note, we give some
new characterizations of $S$-Matlis rings in terms of $S$-strongly flat
modules, $S$-weakly cotorsion modules and $S$-$h$-divisible modules.
