… Are the conditions on C to be semidualizing necessary so that the relative homological
dimensions preserve their properties? If not, what are the minimum necessary conditions? …

… of projective R-module we write pd R ( M ) for the associated homological dimension and call
it the projective dimension of M… Similarly, the injective dimension of M is denoted id R ( M ) . …

… modules, one basically focuses on extending the classical notions and results of homological
… For instance, this has been done for the classical and Gorenstein homological dimensions …

… Ring homomorphisms and GC-projective dimensions In this section, the Gorenstein projective
dimension of complexes with respect to a semidualizing module is considered. First, we …

… G-perfect R-modules with respect to C. We prove several results for the new … similar to the
classical results. It is shown that for a \(G_{C}\)-perfect R-module M of grade n, the R-module \({\…

… that the class of C⊗ R S-Gorenstein flat S-modules is closed under extensions, then an R-module
M is C-Gorenstein flat if and only if the S-module S⊗ R M is C⊗ R S-Gorenstein flat. …

… is to study relative Gorenstein homological notions (w-tilting, … Gorenstein projective
modules, relative Gorenstein projective dimensions, and the relative global projective dimension) …

… C-valued derivation modules over a local ring R of low depth; if C = R and R is a three-dimensional
Gorenstein domain, we … Jørgensen, Semi-dualizing modules and related Gorenstein …

… 3, for a given semidualizing module C, we study the C-Gorenstein flat dimension for …
classes of C-Gorenstein flat R-modules. It is clear that every projective R-module is in GFC. …

… of modules for which their Gorenstein homological dimensions are finite. Since … Gorenstein
homological dimensions and Auslander Categories with respect to a semidualizing module…