Zero-divisors of semigroup modules

Abstract

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).

arXiv commentAn important typo in one reference edited. arXiv admin note: text overlap with arXiv:0807.1835

Cited by in corpus (6)

• On the Anderson-Badawi ${\omega }_{R[X]}(I[X])={\omega }_R(I)$ conjecture
• On zero-divisors of semimodules and semialgebras
• Auslander Modules
• Algebraic properties of expectation semirings
• Eversible and reversible semigroups and semirings
• Distinguished elements in semiring extensions