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arXiv · 1106.4972

G--Gorenstein modules

Mohsen Aghajani·Hossein Zakeri
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Abstract

Let $R$ be a commutative Noetherian ring. In this paper, we study those finitely generated $R$-modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a module a G-Gorenstein module. Characterizations of G-Gorenstein modules are given and a class of such modules is determined. It is shown that the class of G-Gorenstein modules strictly contains the class of Gorenstein modules. Also, we provide a Gorenstein injective resolution for a balanced big Cohen-Macaulay $R$-module. Finally, using the notion of a G-Gorenstein module, we obtain characterizations of Gorenstein and regular local rings.

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Mohsen Aghajani, Hossein Zakeri. 2011-06-24. G--Gorenstein modules. https://arxiv.org/abs/1106.4972

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