Associated prime submodules of finitely generated modules

Details Associated prime submodules of finitely generated modules Associated prime submodules of finitely generated modules

2004-07-28

arxiv.org/abs/math/0407492v1

Mathematics

Commutative Algebra

9 pages, to appear in Communications in Algebra

Scientific paper

Let $R$ be a commutative ring with identity. For a finitely generated $R$-module $M$, the notion of associated prime submodules of $M$ is defined. It is shown that this notion inherits most of essential properties of the usual notion of associated prime ideals. In particular, it is proved that for a Noetherian multiplication module $M$, the set of associated prime submodules of $M$ coincides with the set of $M$-radicals of primary submodules of $M$ which appear in a minimal primary decomposition of the zero submodule of $M$. Also, Anderson's theorem [{\bf 2}] is extended to minimal prime submodules in a certain type of modules.

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