In this article we proved that the quotient triangulated category is triangle-equivalent to the
stable category of the Frobenius category of all Gorenstein FI-flat and FI-cotorsion left R …

Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …

Recently, Hu et al. introduced the notion of Gorenstein FP-injective modules and
investigated a notion of Gorenstein FP-injective dimension for complexes. Let R be a left …

A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …

We first introduce in the paper the W_F-Gorenstein modules to establish the following Foxby
equivalence: \xymatrix@C=80ptG(F)∩A_C\ar@\lt0.5ex>r^C⊗_R-\amp\,\,\,\,G(W_F)\ar@\lt0 …

We obtain the Gorenstein flat model structure on the category Mod (R) of left R-modules
provided R is a GF-closed ring. Our approach does not rely on the coherence of the ring and …

Abstract Set 𝔊𝔉 (R) the class of all Gorenstein flat modules over R. In this paper, we
consider the double orthogonal classes⊥(𝔊𝔉 (R)⊥) and (⊥ 𝔊𝔉 (R))⊥ which clearly lies …

Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …

We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian
model structure on the category of left R-modules where the class of cofibrant objects …