Remarks on reflexive modules, covers, and envelopes.

Belshoff, Richard

Displaying similar documents to “Remarks on reflexive modules, covers, and envelopes.”

On Matlis dualizing modules.

Enochs, Edgar E., López-Ramos, J.A., Torrecillas, B. (2002)

International Journal of Mathematics and Mathematical Sciences

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$k$ -torsionless modules with finite Gorenstein dimension

Maryam Salimi, Elham Tavasoli, Siamak Yassemi (2012)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative Noetherian ring. It is shown that the finitely generated $R$ -module $M$ with finite Gorenstein dimension is reflexive if and only if $M_{𝔭}$ is reflexive for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \leq 1$ , and ${G- dim}_{R_{𝔭}} (M_{𝔭}) \leq depth (R_{𝔭}) - 2$ for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \geq 2$ . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for $n \geq 2$ we give a characterization of $n$ -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally...

Minimal injective resolutions with applications to dualizing modules and Gorenstein modules

Robert Fossum, Hans-Bjorn Foxby, Phillip Griffith, Idun Reiten (1975)

Publications Mathématiques de l'IHÉS

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Indecomposable Cohen-Macaulay modules and irreducible maps

Dorin Popescu, Marko Roczen (1990)

Compositio Mathematica

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Mittag-Leffler modules, reduced products, and direct products

Alberto Facchini (1991)

Rendiconti del Seminario Matematico della Università di Padova

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On the Axiomatizability of Certain Classes of Modules.

Christian U. Jensen, Peter Vamos (1979)

Mathematische Zeitschrift

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Strongly $𝒲$ -Gorenstein modules

Husheng Qiao, Zongyang Xie (2013)

Czechoslovak Mathematical Journal

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Let $𝒲$ be a self-orthogonal class of left $R$ -modules. We introduce a class of modules, which is called strongly $𝒲$ -Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly $𝒲$ -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly $𝒲$ -Gorenstein module can be inherited by its submodules and quotient...

Displaying similar documents to “Remarks on reflexive modules, covers, and envelopes.”

On Matlis dualizing modules.

k -torsionless modules with finite Gorenstein dimension

Minimal injective resolutions with applications to dualizing modules and Gorenstein modules

Indecomposable Cohen-Macaulay modules and irreducible maps

Mittag-Leffler modules, reduced products, and direct products

On the Axiomatizability of Certain Classes of Modules.

Strongly 𝒲 -Gorenstein modules

$k$ -torsionless modules with finite Gorenstein dimension

Strongly $𝒲$ -Gorenstein modules