A new characterization of commutative Artinian rings

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dc.creatorDivaani-Aazar, Kamran
dc.creatorMafi, Amir
dc.date2004-07-15
dc.date.accessioned2026-07-07T05:10:21Z
dc.date.available2026-07-07T05:10:21Z
dc.descriptionLet $R$ be a commutative Noetherian ring. It is shown that $R$ is Artinian if and only if every $R$-module is good, if and only if every $R$-module is representable. As a result, it follows that every nonzero submodule of any representable $R$-module is representable if and only if $R$ is Artinian. This provides an answer to a question which is investigated in [{\bf 1}].
dc.description5 pages. Accepted for publications in Vietnam Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0407270
dc.identifierhttp://arxiv.org/abs/math/0407270
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71905
dc.subjectCommutative Algebra
dc.subject13E10, 13C05
dc.titleA new characterization of commutative Artinian rings
dc.typetext

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