Recollements of derived categories I: Construction from exact contexts

Chen, Haishan; Xi, Changchang

doi:10.1016/j.jpaa.2020.106648

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…The result (I) not only generalises and extends greatly the ones on triangular matrix algebras by Pu Zhang and his students, and on Morita context rings with two bimodule homomorphisms zero by Nan Gao and Chrysostomos Psaroudakis in [20,21] and [10], respectively, to a large class of Morita context algebras, but also can be applied to a class of noncommutative tensor products, see Corollary 4.2 for details. Notably, noncommutative tensor products generalize usual tensor products over commutative rings, capture many known constructions in ring theory, and are useful in constructing reollements of derived module categories (see [5,6]).…”

Section: Introductionmentioning

confidence: 99%

Gorenstein projective modules over rings of Morita contexts

Guo¹,

Xi²

2022

Preprint

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By introducing semi-weak and weak compatibility of modules, we establish sufficient and necessary conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism zero. This generalises and extends results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature, where only sufficient conditions are given under a strong assumption of compatibility of modules. An application is provided to construct Gorenstein-projective modules over noncommutative tensor products arising from Morita contexts. Moreover, we work with Noether rings and modules instead of Artin algebras and modules.

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Section: Introductionmentioning

confidence: 99%

Gorenstein projective modules over rings of Morita contexts

Guo¹,

Xi²

2022

Preprint

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“…The recollements of triangulated categories were introduced by Beilinson, Bernstein and Deligne in order to decompose derived categories of sheaves into two parts, which provided a derived version of Grothendieck's six functors on abelian categories. Recollements of triangulated categories play an important role in geometry, representation theory and ring theory; see [1,4,10,11,20,30,34,36] for instance. To produce recollements of triangulated categories is an interesting topic.…”

Section: Introductionmentioning

confidence: 99%

Recollements induced by Frobenius pairs

Ma¹,

Sun²,

Zhu³

et al. 2021

Preprint

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Let T be a right exact functor from an abelian category B into another abelian category A . Then there exists an abelian category, named comma category and denoted by (T ↓ A ). In this paper, we construct left Frobenius pairs (resp. strong left Frobenius pairs) over (T ↓ A ) using left Frobenius pairs (resp. strong left Frobenius pairs) over A and B. As a consequence, we obtain a recollement of (right) triangulated categories, generalizing the result of Xiong-Zhang-Zhang (J. Algebra 503 (2018) 21-55) about the recollement of additive (resp. triangulated) categories induced by monomorphism categories. This result is applied to the classes of flat modules and Gorenstein flat modules, the classes of Gorenstein projective modules and Gorenstein projective complexes, the class of Ding projective modules and the class of Gorenstein flat-cotorsion modules.

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Recollements of Derived Categories from Two-Term Big Tilting Complexes

2024

Algebr Represent Theor

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Recollements of derived categories I: Construction from exact contexts

Cited by 5 publications

References 17 publications

Gorenstein projective modules over rings of Morita contexts

Gorenstein projective modules over rings of Morita contexts

Recollements induced by Frobenius pairs

Recollements of Derived Categories from Two-Term Big Tilting Complexes

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