A new characterization of the weakly Laskerian (FSF) modules

TL;DR

This paper characterizes weakly Laskerian modules over Noetherian rings by showing the existence of finitely generated submodules with equal associated primes and support, advancing understanding of module structure.

Contribution

It introduces a new characterization of weakly Laskerian modules, linking associated primes of quotients to finitely generated submodules in Noetherian rings.

Findings

Existence of finitely generated submodules with equal associated primes and support

New characterization of weakly Laskerian modules

Enhanced understanding of module structure over Noetherian rings

Abstract

Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that the set of associated prime ideals of the quotient module $M/L$ is finite for all submodules $L$ of $M$. In this paper, it is shown that there is a finitely generated submodule $N$ of $M$ such that the set of associated primes of $M/N$ and the support of $M/N$ are equal.