Multiplication Semimodules

Abstract

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.