2019/04/26 by Rafieh Razavi Nazari, Nazari, Rafieh Razavi, Shaban Ghalandarzadeh +1 · 1 citation
Mathematics · #16Y60 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1904.11729
openalex publication_date 2019/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.