  Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication
semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of
$S$ such that $N=IM$. In this paper we investigate some properties of
multiplication semimodules and generalize some results on multiplication
modules to semimodules. We show that every multiplicatively cancellative
multiplication semimodule is finitely generated and projective. Moreover, we
characterize finitely generated cancellative multiplication $S$-semimodules
when $S$ is a yoked semiring such that every maximal ideal of $S$ is
subtractive.

Commutative Algebra