Displaying similar documents to “Cohen-Macaulay and Gorenstein finitely graded rings”

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.

Recognizing dualizing complexes

Peter Jørgensen (2003)

Fundamenta Mathematicae

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Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

Weak dimension of group-graded rings.

Angel del Río (1990)

Publicacions Matemàtiques

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We study the weak dimension of a group-graded ring using methods developed in [B1], [Q] and [R]. We prove that if R is a G-graded ring with G locally finite and the order of every subgroup of G is invertible in R, then the graded weak dimension of R is equal to the ungraded one.

Categorical methods in graded ring theory.

Angel del Río (1992)

Publicacions Matemàtiques

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Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring. ...

Some properties of graded comultiplication modules

Khaldoun Al-Zoubi, Amani Al-Qderat (2017)

Open Mathematics

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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.