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.

FC-modules with an application to cotorsion pairs

Yonghua Guo (2009)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring. A left R -module M is called an FC-module if M + = Hom ℤ ( M , ℚ / ℤ ) is a flat right R -module. In this paper, some homological properties of FC-modules are given. Let n be a nonnegative integer and ℱ𝒞 n the class of all left R -modules M such that the flat dimension of M + is less than or equal to n . It is shown that ( ⊥ ( ℱ𝒞 n ⊥ ) , ℱ𝒞 n ⊥ ) is a complete cotorsion pair and if R is a ring such that fd ( ( R R ) + ) ≤ n and ℱ𝒞 n is closed under direct sums, then ( ℱ𝒞 n , ℱ𝒞 n ⊥ ) is a perfect cotorsion pair. In particular, some known results are obtained as...

A variant theory for the Gorenstein flat dimension

Samir Bouchiba (2015)

Colloquium Mathematicae

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This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is not yet known whether the category (R) of Gorenstein flat modules over a ring R is projectively resolving or not, it appears legitimate to seek alternate ways of measuring the Gorenstein flat dimension of modules which coincide with the usual one in the case where (R) is projectively resolving, on the one hand, and present nice behavior for an arbitrary ring R, on the other. In this paper,...