  Let $M$ be an $R$-module and $S$ a semigroup. Our goal is to discuss
zero-divisors of the semigroup module $M[S]$. Particularly we show that if $M$
is an $R$-module and $S$ a commutative, cancellative and torsion-free monoid,
then the $R[S]$-module $M[S]$ has few zero-divisors of degree $n$ if and only
if the $R$-module $M$ has few zero-divisors of degree $n$ and Property (A).
