# Model structures and recollements induced by duality pairs

@inproceedings{Chen2021ModelSA, title={Model structures and recollements induced by duality pairs}, author={Wenjing Chen and Ling Li and Y. Prabhakara Rao}, year={2021} }

We give some equivalent characterizations of GP, the class of Gorenstein (L,A)projective modules, and construct some model structures associated to duality pairs and Frobenius pairs. Moreover, some rings are described by Frobenius pairs. Meanwhile, we investigate strongly Gorenstein (L,A)-projective modules and obtain some equivalent characterizations of them. Also, some model structures and recollements associated to strongly Gorenstein (L,A)-projective modules are constructed.

## References

SHOWING 1-10 OF 26 REFERENCES

Cotorsion pairs induced by duality pairs

- Mathematics
- 2009

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is “often” covering and preenveloping. As an application, we generalize a result by Enochs et al. on…

STRONGLY GORENSTEIN FLAT MODULES

- MathematicsJournal of the Australian Mathematical Society
- 2009

Abstract In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective…

Cotorsion pairs, model category structures, and representation theory

- Mathematics
- 2002

Abstract. We make a general study of Quillen model structures on abelian categories. We show that they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have been…

Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs

- Mathematics
- 2017

ABSTRACT Let (𝒳,𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜. We introduce a Gorenstein category 𝒢(𝒳) and 𝒢(𝒳)-resolution dimension of complexes with…

A new method to construct model structures from a cotorsion pair

- MathematicsCommunications in Algebra
- 2019

Abstract Let be a complete and hereditary cotorsion pair in an abelian category . We show that if is closed under kernels of epimorphisms, then is a strong left Frobenius pair, which induces a unique…

Gorenstein flat modules with respect to duality pairs

- MathematicsCommunications in Algebra
- 2019

Abstract Let be a class of left R-modules, be a class of right R-modules. In this article, we introduce and study Gorenstein -flat modules as a common generalization of some known modules such as…

The stable module category of a general ring

- Mathematics
- 2014

For any ring R we construct two triangulated categories, each admitting a functor from R-modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or Gorenstein ring,…

Approximations and Endomorphism Algebras of Modules

- Mathematics
- 2006

The category of all modules over a general associative ring is too complex to admit any reasonable classification. Thus, unless the ring is of finite representation type, one must limit attempts at…