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 define a notion of Gorenstein flat dimension for unbounded complexes over left GF-
closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for …

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra
assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S⊗ RM is …

It is well-known that the weak global dimension of a ring does not exceed its global
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …

We introduce and study a complete cohomology theory for complexes, which provides an
extended version of Tate–Vogel cohomology in the setting of (arbitrary) complexes over …

For any ring R, we show that, in the bounded derived category Db (Mod R) of le R-modules,
the subcategory of complexes with nite Gorenstein projective (resp. injective) dimension …

Let A be an associative ring with identity, K (FlatA) the homotopy category of flat modules
and Kp (FlatA) the full subcategory of pure complexes. The quotient category K (FlatA)/Kp …

In this paper, we study injective dimension and Gorenstein injective dimension over local
ring homomorphisms. Some well-known results are generalized. For example, the Bass …

In this paper, we first study the Gorenstein projective/flat dimension of complexes of
modules. The relation between the Gorenstein projective/flat dimension for complexes and …

In this article, we define and study a notion of strongly Gorenstein flat dimensions for
complexes of left modules over associative rings. In particular, we consider the class of …