Corrigendum to “m-Periodic Gorenstein objects” [J. Algebra 621 (2023) 1–40]

Huerta, Mindy Y.; Mendoza, Octavio; Pérez, Marco A.

doi:10.1016/j.jalgebra.2024.05.006

Journal of Algebra

2024

DOI: 10.1016/j.jalgebra.2024.05.006

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Corrigendum to “m-Periodic Gorenstein objects” [J. Algebra 621 (2023) 1–40]

Mindy Y. Huerta,

Octavio Mendoza,

Marco A. Pérez

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2024

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Model structures, n-Gorenstein flat modules and PGF dimensions

El Maaouy

2024

Proceedings of the Edinburgh Mathematical Society

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Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian model structure on the category of left R-modules where the class of cofibrant objects coincides with $\mathcal{GF}_n(R)$ the class of left R-modules with Gorenstein flat dimension at most n, the class of fibrant objects coincides with $\mathcal{F}_n(R)^\perp$ the right ${\rm Ext}$ -orthogonal class of left R-modules with flat dimension at most n, and the class of trivial objects coincides with $\mathcal{PGF}(R)^\perp$ the right ${\rm Ext}$ -orthogonal class of PGF left R-modules recently introduced by Šaroch and . The homotopy category of this model structure is triangulated equivalent to the stable category $\underline{\mathcal{GF}(R)\cap\mathcal{C}(R)}$ modulo flat-cotorsion modules and it is compactly generated when R has finite global Gorenstein projective dimension. The second part of this paper deals with the PGF dimension of modules and rings. Our results suggest that this dimension could serve as an alternative definition of the Gorenstein projective dimension. We show, among other things, that (n-)perfect rings can be characterized in terms of Gorenstein homological dimensions, similar to the classical ones, and the global Gorenstein projective dimension coincides with the global PGF dimension.

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Model structures, n-Gorenstein flat modules and PGF dimensions

El Maaouy

2024

Proceedings of the Edinburgh Mathematical Society

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Corrigendum to “m-Periodic Gorenstein objects” [J. Algebra 621 (2023) 1–40]

Cited by 1 publication

References 9 publications

Model structures, n-Gorenstein flat modules and PGF dimensions

Model structures, n-Gorenstein flat modules and PGF dimensions

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