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 …

Let A be an abelian category and C an additive full subcategory of A. We provide a method
to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short …

Let W be a self-orthogonal class of left R-modules. We introduce and study W-Gorenstein
modules as a common generalization of some known modules such as Gorenstein …

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 …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

Semidualizing modules have been found to be useful for several constructions in
homological algebra. Introduced by Foxby, Vasconcelos, Golod, and Wakamatsu. Studied …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

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

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

Let A be an abelian category. A subcategory X of A is called a resolving subcategory if X is
closed under extensions and kernels of epimorphisms and contains all projective objects of …