Ding projective complexes with respect to a semidualizing module

Gorenstein AC-projective complexes

Let $R$ be any ring with identity and Ch($R$) the category of chain complexes of (left) $R$-modules. We show that the Gorenstein AC-projective chain complexes are the cofibrant objects of an abelian model structure on Ch($R$). The model structure is cofibrantly generated and is projective in the sense that the trivially cofibrant objects are the categorically projective chain complexes. We show that when $R$ is a Ding-Chen ring, that is, a two-sided coherent ring with finite self FP-injective dimension, then the model structure is finitely generated, and so its homotopy category is compactly g…

Acyclic complexes and Gorenstein rings

For a given class of modules $\mathcal{A}$, we denote by $\widetilde{\mathcal{A}}$ the class of exact complexes $X$ having all cycles in $\mathcal{A}$, and by $dw(\mathcal{A})$ the class of complexes $Y$ with all components $Y_j$ in $\mathcal{A}$. We use the notations $\mathcal{GI}$ $(\mathcal{GF}, \mathcal{GP})$ for the class of Gorenstein injective (Gorenstein flat, Gorenstein projective respectively) $R$-modules, $\mathcal{DI}$ for Ding injective modules, and $\mathcal{PGF}$ for projectively coresolved Gorenstein flat modules (see section 2 for definitions). We prove that the following are …

无环复形的FP-注入模在丁-陈环上的研究

Acyclic complexes of FP-injective modules over Ding-Chen rings

本文提出了一种结合cotorsion对的方法，用于构建新的模型结构，并研究丁-陈环的稳定模块范畴，通过引入Gorenstein FP-pro-注入模块。

关于Gorenstein投射预覆盖的一些注记

Some Remarks on Gorenstein Projective Precovers

本文针对任意环上Gorenstein投射预覆盖的存在性开放问题，通过三种技术研究相对Gorenstein投射模类，获得遗传余挠对与Hovey三元组，并利用约化性质探讨了与Auslander类相关的模类。