Let $R$ be a commutative ring and $mathbb{A}(R)$ be the set of all ideals with non-zero annihilators. Assume that $mathbb{A}^*(R)=mathbb{A}(R)diagdown {0}$ and $mathbb{F}(R)$ denote the set of all finitely generated ideals of $R$. In this paper, we introduce and investigate the {it finitely generated subgraph} of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_F(R)$. It is the (undi...

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2 states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

let m be an artinian module over the commutative ring a (with nonzero identity) and a p spec a be such that a is a finitely generated ideal of a and am = m. also suppose that h = h where h. = m/ (0: a )for i

The purpose of this paper is to investigate properties of subsemigroups of finitely presented semigroups, particularly with respect to the property of being finitely presented. More precisely, we will consider various instances of the following: Main Problem. Let S be a finitely presented semigroup. Ž . Ž . i Is every subsemigroup ideal, one-sided ideal of S finitely generated? Ž . Ž . ii Is ev...