Some criteria of cyclically pure injective modules

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dc.creatorDivaani-Aazar, Kamran
dc.creatorEsmkhani, Mohammad Ali
dc.creatorTousi, Massoud
dc.date2005-10-20
dc.date.accessioned2026-07-07T06:47:42Z
dc.date.available2026-07-07T06:47:42Z
dc.descriptionThe structure of cyclically pure injective modules over a commutative ring $R$ is investigated and several characterizations for them are presented. In particular, we prove that a module $D$ is cyclically pure injective if and only if $D$ is isomorphic to a direct summand of a module of the form $\Hom_R(L,E)$ where $L$ is the direct sum of a family of finitely presented cyclic modules and $E$ is an injective module. Also, we prove that over a quasi-complete Noetherian ring $(R,\fm)$ an $R$-module $D$ is cyclically pure injective if and only if there is a family $\{C_λ\}_{λ\in Λ}$ of cocyclic modules such that $D$ is isomorphic to a direct summand of $Π_{λ\in Λ}C_λ$. Finally, we show that over a complete local ring every finitely generated module which has small cofinite irreducibles is cyclically pure injective.
dc.description18 pages, to appear in Journal of Algebra
dc.identifierhttps://arxiv.org/abs/math/0510433
dc.identifierhttp://arxiv.org/abs/math/0510433
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103743
dc.subjectCommutative Algebra
dc.subject13C11, 13H10
dc.titleSome criteria of cyclically pure injective modules
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