Let $ R $ be a commutative ring with an identity different from zero and $ n $ be a positive
integer. Anderson and Badawi, in their paper on $ n $-absorbing ideals, define a proper …

In the first section of this paper, we introduce the notions of fractional and invertible ideals of
semirings and characterize invertible ideals of a semidomain. In section two, we define …

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 $ M $ be an $ R $-module and $ c $ the function from $ M $ to the ideals of $ R $ defined
by $ c (x)=\cap\lbrace I\colon I\text {is an ideal of} R\text {and} x\in IM\rbrace $. $ M $ is said …

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 …

We define Dedekind semidomains as semirings in which each nonzero fractional ideal is
invertible. Then we find some equivalent condition for semirings to being Dedekind. For …