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 …

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 …

Let $ R $ be a commutative noetherian ring. Denote by $\operatorname {mod} R $ the
category of finitely generated $ R $-modules, by $\operatorname {D^ b}(R) $ the bounded …

This paper aims at generalizing the notions of “Auslander dual”,“k-torsionless” and “k-th
syzygy” modules to the relative setting with respect to a semidualizing module. It is shown …