Displaying similar documents to “On co-Gorenstein modules, minimal flat resolutions and dual Bass numbers”

On Cohen-Macaulay rings

Edgar E. Enochs, Jenda M. G. Overtoun (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we use a characterization of R -modules N such that f d R N = p d R N to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the d t h local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R .

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 ∈ Spec ( R ) with depth ( R 𝔭 ) ≤ 1 , and G- dim R 𝔭 ( M 𝔭 ) ≤ depth ( R 𝔭 ) - 2 for 𝔭 ∈ Spec ( R ) with depth ( R 𝔭 ) ≥ 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 ≥ 2 we give a characterization of n -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally...

On torsion Gorenstein injective modules

Okyeon Yi (1998)

Archivum Mathematicum

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In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if D is a Gorenstein integral domain and M is a left D -module, then the torsion submodule t G M of Gorenstein injective envelope G M of M is also Gorenstein injective. We can also show that if M is a torsion D -module of a Gorenstein injective integral domain D , then the Gorenstein injective envelope G M of M is torsion.