Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions
of C-transpose and nC-torsionfree and give a criterion for a module A to be G_C-projective …

Let $ R $ be a commutative ring, and let $ S $ be a multiplicative subset of $ R $. In this
paper, we investigate the notion of $ S $-cotorsion modules. An $ R $-module $ C $ is called …

Let 𝑅 be a complete Gorenstein local domain, 𝐽 an ideal of 𝑅 of dimension one, and 𝑁• a
complex of 𝑅-modules bounded below. In this paper, we prove that 𝑁• is a 𝐽-cofinite …

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 …

We consider the perfect cotorsion pair (𝒫1, 𝒟) over a commutative ring (often over a domain)
R consisting of modules of projective dimension≤ 1 and of divisible modules, respectively …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13](however,
only a few nontrivial examples are known). Integral group rings over polycyclic-by-finite …

In this article, the concept of Gorenstein FP-injective modules and some related known
results are generalized to Gorenstein FP-injective complexes. Moreover, some new …

In this paper, we construct some model structures corresponding Gorenstein (ℒ, 𝒜)-modules
and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and …

We investigate adjoint and Frobenius pairs between categories of comodules over rather
general corings. We particularize to the case of the adjoint pair of functors associated to a …