We introduce and investigate the notion of 𝐺𝐶-projective modules over (possibly non-
Noetherian) commutative rings, where 𝐶 is a semidualizing module. This extends Holm and …

We investigate the notion of the C-projective dimension of a module, where C is a
semidualizing module. When C= R, this recovers the standard projective dimension. We …

We investigate Tate cohomology of modules over a commutative noetherian ring with
respect to semidualizing modules. We identify classes of modules admitting Tate resolutions …

Let R be an arbitrary ring and C a complex with finite Gorenstein projective dimension (that
is, the supremum of Gorenstein projective dimension of all R-modules in C is finite). For …

Let X and Y be N-complexes with N≥ 2 an integer such that X has finite Gorenstein
projective dimension and Y has finite Gorenstein injective dimension. We define the n th …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

In this paper, we prove that the Bass class with respect to a semidualizing bimodule C
contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules …

From the notion of (co) generator in relative homological algebra, we present the concept of
finite balanced system $[(\mathcal {X},\omega);(\nu,\mathcal {Y})] $ as a tool to induce …

Let 𝒜 be an abelian category with enough projectives. In the category of 𝒜-complexes, we
introduce generalized Tate cohomology with respect to subcategories, and show that there …

In this paper, we further study Tate cohomology of modules over a commutative ring with
respect to semidualizing modules using the ideals of Sather-Wagstaff et al.['Tate …