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2009•Communications in AlgebraRequires access

Gorenstein Global Dimensions and Cotorsion Dimension of Rings

Driss Bennis, Najib Mahdou

Open publisher page 13 citations

Abstract

In this article, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

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What this paper is about

In this article, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this article, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

Key concepts: Mathematics, Global dimension, Dimension (graph theory), Generalization, Commutative property, Pure mathematics, Commutative algebra, Local ring

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