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 introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

We investigate the properties of categories of GC-flat R-modules where C is a semidualizing
module over a commutative noetherian ring R. We prove that the category of all GC-flat R …

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 C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

In this paper we further develop the theory of linkage with respect to a semidualizing module
C introduced in 2018 by Dibaei and Sadeghi. It is shown that under certain conditions a …

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 …

In their investigation of horizontal linkage of modules of finite Gorenstein dimension over a
commutative, Noetherian, semiperfect (eg, local) ring, Dibaei and Sadeghi introduced the …

Abstract We study Tate–Vogel cohomology of complexes by applying the model structure
induced by a complete hereditary cotorsion pair (A, B) of modules. Vanishing of Tate–Vogel …