Displaying similar documents to “Minimal injective resolutions with applications to dualizing modules and Gorenstein modules”

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 .

On the structure of the canonical model of the Rees algebra and the associated graded ring of an ideal.

Santiago Zarzuela (1992)

Publicacions Matemàtiques

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In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.

Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

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Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.

On co-Gorenstein modules, minimal flat resolutions and dual Bass numbers

Zahra Heidarian, Hossein Zakeri (2015)

Colloquium Mathematicae

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The dual of a Gorenstein module is called a co-Gorenstein module, defined by Lingguang Li. In this paper, we prove that if R is a local U-ring and M is an Artinian R-module, then M is a co-Gorenstein R-module if and only if the complex H o m R ̂ ( ( , R ̂ ) , M ) is a minimal flat resolution for M when we choose a suitable triangular subset on R̂. Moreover we characterize the co-Gorenstein modules over a local U-ring and Cohen-Macaulay local U-ring.