Five theorems on Gorenstein global dimensions

Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions but also the suprema of projective/injective dimensions of injective/projective modules and finitistic dimensions.

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When are the classes of Gorenstein modules (co)tilting?

Wang,

Liu,

Zhao

2024

Comptes Rendus. Mathématique

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Five theorems on Gorenstein global dimensions

Abstract: We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimension. We also include the answer to a question of Y. Xiang on Gorenstein weak global dimension of group rings.

Cited by 3 publications

References 28 publications

When do the Gorenstein Injective Modules and Strongly Cotorsion Modules Coincide?

When do the Gorenstein Injective Modules and Strongly Cotorsion Modules Coincide?

One-sided Gorenstein rings

When are the classes of Gorenstein modules (co)tilting?

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