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A new characterization of the weakly Laskerian (FSF) modules
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Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that, for each submodule $L$ of $M$, the set of associated prime ideals of the quotient module $M/L$ is finite. In this paper, it is shown that $M$ admits a finitely generated submodule $N$ such that the set of associated prime ideals of $M/N$ and the support of $M/N$ are equal.
Abstract
Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that, for each submodule $L$ of $M$, the set of associated prime ideals of the quotient module $M/L$ is finite. In this paper, it is shown that $M$ admits a finitely generated submodule $N$ such that the set of associated prime ideals of $M/N$ and the support of $M/N$ are equal.
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