Zero-divisors of Semigroup Modules
share
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 size $n$ if and only if the $R$-module $M$ has few zero-divisors of size $n$ and Property (A).
READ FULL TEXT