7 papers
A note on the -quiver
Xue-Song Lu
A two-parameter hierarchy of classes of finitely generated modules over an artin algebra is described by using the -quiver. As an application, it is shown that the stable cat…
Pretriangulated categories failing (TR4)
Xiao-Wu Chen, Jian Liu, Sergei O. Ivanov +3
We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category whose stable category of cohere…
Cotorsion pairs, thick subcategories, and finitely generated Gorenstein projective modules
Souvik Dey, Jian Liu, Xue-Song Lu
Let be a noetherian algebra over a Cohen--Macaulay ring admitting a canonical module , and assume that is maximal Cohen--Macaulay over . We prove that the categor…
Claus Michael Ringel's main contributions to Gorenstein-projective modules
Nan Gao, Xue-Song Lu, Pu Zhang
In this article we try to recall Claus Michael Ringel's works on the Gorenstein-projective modules. This will involve but not limited to his fundamental contributions, such as in,…
Homotopy categories and fibrant model structures
Xue-Song Lu, Pu Zhang
The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibran…
Chains of model structures arising from modules of finite Gorenstein dimension
Nan Gao, Xue-Song Lu, Pu Zhang
For any integer and any ring , \ proves to be a complete hereditary cotorsion pair in -Mod, wh…
Model structure from one hereditary complete cortorsion pair
Jian Cui, Xue-Song Lu, Pu Zhang
In contrast with the Hovey correspondence of abelian model structures from two complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian c…