Recollements from Ding Injective Modules

Wang, Miao; Wang, Zhanping; Peng-fei, Yang

doi:10.1007/s40840-020-01017-3

Cited by 2 publications

(1 citation statement)

References 20 publications

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“…Finally, we give some applications of our results for projectively coresolved Gorenstein flat, Ding injective and Gorenstein flat model structures. It should be noticed that the recollements of stable categories of Ding injective modules and Gorenstein flat modules over a triangular matrix ring T have been established in [28,Theorem 2.10] and [33,Theorem 4.12] respectively. Our result Theorem 4.5 gives a new criterion for the existence of these two recollements.…”

Section: Introductionmentioning

confidence: 99%

Gorenstein and duality pair over triangular matrix rings

Liu¹,

Zhu²

2022

Preprint

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Let A, B be two rings and T = A M 0 B with M an A-B-bimodule. We first construct a semi-complete duality pair D T of T -modules using duality pairs in A-Mod and B-Mod respectively. Then we characterize when a left T -module is Gorenstein D T -projective, Gorenstein D T -injective or Gorenstein D T -flat. These three class of T -modules will induce model structures on T -Mod. Finally we show that the homotopy category of each of model structures above admits a recollement relative to corresponding stable categories. Our results give new characterizations to earlier results in this direction.

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Section: Introductionmentioning

confidence: 99%

Gorenstein and duality pair over triangular matrix rings

Liu¹,

Zhu²

2022

Preprint

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Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings

Zhu,

Liu

2024

Int. J. Algebra Comput.

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Let A and B be rings and [Formula: see text] with M an A-B-bimodule. We first construct a semi-complete duality pair [Formula: see text] over T using duality pairs over A and B, respectively. Then we characterize when a left T-module is Gorenstein projective, injective or flat with respect to the duality pair [Formula: see text]. As applications, we investigate when a left T-module is projectively coresolved Gorenstein flat, Ding injective or Gorenstein flat. In addition, we give an estimate of Gorenstein flat dimension of a left T-module with respect to [Formula: see text]. Finally, we construct model structures and recollements relative to these generalized Gorenstein modules.

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Recollements from Ding Injective Modules

Cited by 2 publications

References 20 publications

Gorenstein and duality pair over triangular matrix rings

Gorenstein and duality pair over triangular matrix rings

Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings

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