Gorenstein Cotilting and Tilting Modules

Yan, Liang; Li, Weiqing; Ouyang, Baiyu

doi:10.1080/00927872.2014.981752

Cited by 10 publications

(3 citation statements)

References 9 publications

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“…p2q By Proposition 2.6 in [5], we can obtain that pGP, GIq in Example 2.6 is an admissible balanced pair. Then the n-Gorenstein tilting modules [20] is n-GP tilting module with respect to balanced pair pGP, GIq.…”

Section: Example 32 P1qmentioning

confidence: 99%

Balanced pairs and tilting modules in recollement

Zhang¹,

Liu²,

Wei³

2022

Preprint

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In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a characterization of relative tilting modules, which similar to Bazzoni characterization of n-tilting modules [4]. Finally, we mainly consider the relationship of relative tilting modules in a recollement.

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Section: Example 32 P1qmentioning

confidence: 99%

Balanced pairs and tilting modules in recollement

Zhang¹,

Liu²,

Wei³

2022

Preprint

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“…For example, Holm gave some homological properties of Gorenstein projective, and proved that every R-module M with finite Gorenstein projective dimensions admits a surjective Gorenstein projective modules precover in [7]. Using the relative homological theory developed by Enochs and Jenda [5], the authors [17] introduced Gorenstein cotilting and tilting modules, and gave a characterization of Gorenstein tilting modules which similar to Bazzoni characterization of n-tilting modules [3], and so on.…”

Section: Introductionmentioning

confidence: 99%

Gorenstein projective objects and recollements of Abelian categories

Zhang¹,

Shu²,

Liu³

2022

Preprint

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In this paper, we study the relationship of Gorenstein projective objects among three Abelian categories in a recollement. As an application, we introduce the relation of n-Gorenstein tilting modules (and Gorenstein syzygy modules) in three Abelian categories. For a recollement RpA 1 , A , A 2 q of Abelian categories, we show that a resolving subcategory in A induce two resolving subcategories in A 1 and A 2 . On the other hand, we also prove that two resolving subcategories in A 1 and A 2 can induce a resolving subcategory in A . Moreover, we give the size relationship between the relative global dimensions of three Abelian categories.

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“…This line of thought has been followed especially in the context of "Gorenstein homological algebra"-a particular relative (co)homology theory-by several authors, e.g. [50], [52], and [22], where the theory of "infinitely generated Gorenstein tilting modules" has been developed to some extent.…”

Section: Introductionmentioning

confidence: 99%

Infinitely Generated Gorenstein Tilting Modules

Moradifar¹,

Yassemi²

2018

Preprint

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The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, and infinitely generated relative tilting modules have recently been studied by many authors in the context of Gorenstein homological algebra. In this work, we build on the theory of infinitely generated Gorenstein tilting modules by developing "Gorenstein tilting approximations" and employing these approximations to study Gorenstein tilting classes and their associated relative cotorsion pairs. As applications of our results, we discuss the problem of existence of complements to partial Gorenstein tilting modules as well as some connections between Gorenstein tilting modules and finitistic dimension conjectures.

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Gorenstein Cotilting and Tilting Modules

Cited by 10 publications

References 9 publications

Balanced pairs and tilting modules in recollement

Balanced pairs and tilting modules in recollement

Gorenstein projective objects and recollements of Abelian categories

Infinitely Generated Gorenstein Tilting Modules

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