We consider a two sided noetherian ring R such that the character modules of Gorenstein
injective left R-modules are Gorenstein flat right R-modules. We then prove that the class of …

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states
that “for what rings R do we have K (AC)= K (R-Inj)?”. We give an answer to such a question …

Let 𝐴 and 𝐵 be rings and 𝑈 a (B, A)-bimodule. The Gorenstein projective, injective and flat
complexes over the formal triangular matrix ring T=(A 0 UB) are explicitly described. These …

Abstract Let (A, B)(A, B) be a cotorsion pair in R-Mod. We introduce and study the notion of
Cartan–Eilenberg-A A complexes. Specifically, we establish some relationships between …

We study homological and homotopical aspects of Gorenstein flat modules over a ring with
respect to a duality pair $(\mathcal {L, A}) $. These modules are defined as cycles of exact …

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 …

We extend the cotorsion dimension of R-modules to unbounded R-complexes by applying
the flat model structure on Ch (R) proposed by J. Gillespie. This is not natural because there …

Let R be a ring such that (GP, GP⊥) forms a cotorsion pair cogenerated by a set, where GP
denotes the category of all Gorenstein projective R-modules. Recently, the first author …

For an integer N≥ 2 and three subcategories 𝒲, 𝒳, 𝒴 of modules, we study the notion of (𝒲,
𝒳, 𝒴)-Gorenstein N-complexes. We show that under certain hypotheses, an N-complex C is …

Acta Mathematica Sinica, English Series Page 1 Acta Mathematica Sinica, English Series
Nov., 2018, Vol. 34, No. 11, pp. 1718–1730 Published online: June 6, 2018 https://doi.org/10.1007/s10114-018-7461-7 …