A criterion for rings which are locally valuation

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dc.creatorDivaani-Aazar, Kamran
dc.creatorEsmkhani, Mohammad Ali
dc.creatorTousi, Massoud
dc.date2007-02-13
dc.date.accessioned2026-07-07T07:46:41Z
dc.date.available2026-07-07T07:46:41Z
dc.descriptionUsing the notion of cyclically pure injective modules, a characterization for rings which are locally valuation is established. As applications, new characterizations for Prufer domains and pure semi-simple rings are provided. Namely, we show that a domain R is Prufer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semi-simple if and only if every R-module is cyclically pure injective.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0702372
dc.identifierhttp://arxiv.org/abs/math/0702372
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123908
dc.subjectCommutative Algebra
dc.subject13F05, 13F30
dc.titleA criterion for rings which are locally valuation
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