This book is intended as a reference for mathematicians working with homological dimensions
in commutative algebra and as an introduction to Gorenstein dimensions for graduate …

… →M, where G is Gorenstein projective, such that the … Gorenstein projective module Q. We
show that every module M with finite Gorenstein projective dimension admits a nice Gorenstein …

… the concepts of GC -projective module and dimension, weakening the condition of C being
… relate this new dimension with the classical Gorenstein projective dimension of a module. …

… in the theorem the left Gorenstein global dimension of R and … Gorenstein homological
dimensions of modules, Gorenstein global dimension of rings, weak Gorenstein global dimension …

… -Gorenstein projective modules to the non-Noetherian setting and generalizes projective and
Gorenstein … We then study the resulting modules of finite Geprojective dimension, showing …

… the flat dimension of the R-modules S by one on the finiteness of their Gorenstein dimension
, or G-dimension. This … For the Gorenstein dimension we have the following partial results. …

… both the Gorenstein projective dimension and the Gorenstein injective dimension which may
… 3, we prove that the finitistic dimension associated to the cover Gorenstein flat dimension of …

… Therefore, it is natural to try to establish analogous results for Gorenstein dimensions. In …
In the paper [3], we attempted to extend this result to the setting of Gorenstein dimensions as …

… known about Gorenstein projective dimension of Gorenstein flat … Gorenstein dimensions, we
address this question; see (4.2): … basic properties of Gorenstein dimensions in the generality …

… projective dimension. We also examine the class of rings that have finite Gorenstein global
and weak dimensions and compute these dimensions, in terms of certain cohomological …