We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

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 …

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 relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …

In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay
rings. Regular non-Noetherian rings were originally defined by Bertin in 1971. In 2007 …

Of the many interesting insights in the Auslander-Bridger Memoir of 1969, the theory of
Gorenstein dimension has most often been taken up by commutative algebraists. Over a …

In this paper, we introduce and investigate the notion of Gorenstein A-ſlat modules with
respect to a semidualizing module and also study the relationship between the GA-flat …