Gorenstein-projective modules and symmetric recollements

This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category S and a maximal object s of S and construct a recollement of Mod-S in terms of Mod-End S (s) and Mod-(S \ {s}) in four different levels. In case S is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N -complexes.

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“…Note that, the existence of these recollements have been proved for Gorenstein algebras in [57,Theorem 3.5], but using a different approach.…”

Section: Triangular Matrix Ringsmentioning

confidence: 99%

On the Recollements of Functor Categories

Asadollahi

Hafezi

Vahed

2015

Appl Categor Struct

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“…It is clearly an interesting idea to investigate recollement situations related to these triangulated categories. Existence of recollement has been studied recently for the stable category of the Gorensteinprojective modules over a Gorenstein triangular matrix algebra [15,32] and for the stable category of vector bundles [10].…”

Section: Introductionmentioning

confidence: 99%

Recollements of Singularity Categories and Monomorphism Categories

2015

Communications in Algebra

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“…For example, Zhang [27] explicitly described the Gorenstein projective modules over a triangular matrix Artin algebra. Enochs and other authors [5] characterized when a left module over a triangular matrix ring is Gorenstein projective or Gorenstein injective under the "Gorenstein regular" condition.…”

Section: Introductionmentioning

confidence: 99%

Gorenstein flat modules and dimensions over formal triangular matrix rings

Mao

2020

Journal of Pure and Applied Algebra

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Gorenstein-projective modules and symmetric recollements

Cited by 102 publications

References 17 publications

On the Recollements of Functor Categories

On the Recollements of Functor Categories

Recollements of Singularity Categories and Monomorphism Categories

Gorenstein flat modules and dimensions over formal triangular matrix rings

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