In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-
module M is called strongly Gorenstein flat if there is an exact sequence⋯→ P1→ P0→ P0→ …

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M
is called Gorenstein FP-injective if there is an exact sequence⋯→ E1→ E0→ E0→ E1→⋯ of …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

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 …

Existence of Gorenstein projective resolutions and Tate cohomology Page 1 J. Eur. Math. Soc. 9,
59–76 c European Mathematical Society 2007 Peter Jørgensen Existence of Gorenstein …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …

It is known that over an Iwanaga–Gorenstein ring the Gorenstein injective (Gorenstein
projective, Gorenstein flat) modules are simply the cycles of acyclic complexes of injective …

Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …