Finitistic dimension conjectures via Gorenstein projective dimension

Moradifar, Pooyan; Šaroch, Jan

doi:10.1016/j.jalgebra.2021.10.026

Journal of Algebra

2022

DOI: 10.1016/j.jalgebra.2021.10.026

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Finitistic dimension conjectures via Gorenstein projective dimension

Pooyan Moradifar

Jan Šaroch

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Cited by 3 publications

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“…In fact, we may complement this assertion and prove the following result. Here, condition (iii) is analogous to [11,Lemma 2.17] (see also [25,Lemma 1.9]) and conditions (iv) and (v) are inspired by the Remark following [26,Theorem 4.11].…”

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Homological dimension based on a class of Gorenstein flat modules

Dalezios,

Emmanouil

2023

Comptes Rendus. Mathématique

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In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class of Gorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen [24], Gedrich and Gruenberg [17] that were originally proved in the realm of commutative Noetherian rings. Funding. Research supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the "1st Call for H.F.R.I. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant", project number 4226.

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Homological dimension based on a class of Gorenstein flat modules

Dalezios,

Emmanouil

2023

Comptes Rendus. Mathématique

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Auslander conditions and tilting-like cotorsion pairs

Wang

et al. 2023

Journal of Algebra

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Gorenstein Projective Precovers and Finitely Presented Modules

Estrada,

Iacob

2024

Rocky Mountain J. Math.

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Finitistic dimension conjectures via Gorenstein projective dimension

Cited by 3 publications

References 25 publications

Homological dimension based on a class of Gorenstein flat modules

Homological dimension based on a class of Gorenstein flat modules

Auslander conditions and tilting-like cotorsion pairs

Gorenstein Projective Precovers and Finitely Presented Modules

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