Associated prime submodules of finitely generated modules

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dc.creatorDivaani-Aazar, Kamran
dc.creatorEsmkhani, Mohammad Ali
dc.date2004-07-28
dc.date.accessioned2026-07-07T05:10:47Z
dc.date.available2026-07-07T05:10:47Z
dc.descriptionLet $R$ 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.
dc.description9 pages, to appear in Communications in Algebra
dc.identifierhttps://arxiv.org/abs/math/0407492
dc.identifierhttp://arxiv.org/abs/math/0407492
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72042
dc.subjectCommutative Algebra
dc.subject13E05, 13E10, 13C99
dc.titleAssociated prime submodules of finitely generated modules
dc.typetext

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