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 …

For complexes of modules we study two new constructions which we call the pinched tensor
product and the pinched Hom. They provide new methods for computing Tate homology …

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

Auslander's depth formula for pairs of Tor-independent modules over a regular local ring,
depth (M⊗ RN)= depth M+ depth N− depth R, has been generalized in several directions; …

The main purpose of this article is to present some applications of the notion of Gorenstein
injective dimension of complexes over an associative ring. Among the applications, we give …

Let R be an arbitrary ring and C a complex with finite Gorenstein projective dimension (that
is, the supremum of Gorenstein projective dimension of all R-modules in C is finite). For …

Let X and Y be N-complexes with N≥ 2 an integer such that X has finite Gorenstein
projective dimension and Y has finite Gorenstein injective dimension. We define the n th …

Given a double complex X there are spectral sequences with the E 2 terms being either HI
(H II (X)) or H II (HI (X)). But if HI (X)= H II (X)= 0, then both spectral sequences have all their …

Gorenstein homological algebra is an important area of mathematics, with applications in
commutative and noncommutative algebra, model category theory, representation theory …

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 …