We prove McCoy's property for the zero-divisors of polynomials in semirings, investigate the
zero-divisors of semimodules and prove that under suitable conditions, the monoid …

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 …

Let R be a commutative ring, I a finitely generated ideal of R, and M a zero-divisor R-module.
It is shown that the M-grade of I defined by the Koszul complex is consistent with the …

This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens
Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let R be a …