Let R be a ring. In this paper, FP-Gorenstein cotorsion modules are introduced and studied.
An R-module N is said to be FP-Gorenstein cotorsion if Ext1 R (F, N)= 0 for any finitely …

Over a commutative Noetherian ring R, the Bass invariants μi (p, M) were defined for any
module M and any prime p∈ Spec R by H. Bass (Math. Z. 82, 1963, 8-28). In the first part of …

In this paper, we show that if R is a local Cohen–Macaulay ring admitting a dualizing module
Ω, then Ω-Gorenstein projective and flat covers and Ω-Gorenstein injective envelopes exist …

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-
injective) modules which are special Gorenstein projective (resp. Gorenstein injective) …

Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13](however,
only a few nontrivial examples are known). Integral group rings over polycyclic-by-finite …

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein
projective, then its underlying module over the base ring is Gorenstein projective; the …

Let R be a graded ring and n⩾ 1 be an integer. We introduce and study the notions of
Gorenstein n-FP-gr-injective and Gorenstein n-gr-flat modules by using the notion of special …

Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

We study homological and homotopical aspects of Gorenstein flat modules over a ring with
respect to a duality pair $(\mathcal {L, A}) $. These modules are defined as cycles of exact …