Let R be a ring. An R-module N is called Gorenstein cotorsion module if Ext R 1 (F, N)= 0 for
any Gorenstein flat R-module F. We investigate some properties of Gorenstein cotorsion …

In this paper, we study criteria for the equality between the homological and the
cohomological dimension of a group. In particular, we obtain criteria for the freeness of …

Let R be a ring and let 𝒮𝒢ℱ be the class of strongly Gorenstein at right R-modules. We call a
right R-module M a weak Gorenstein cotorsion module if M is in the class 𝒮𝒢ℱ⊥. Properties …

We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

In basic homological algebra, the flat and injective dimensions of modules play an important
and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions …

Let R be a ring with an identity and, for a left Λ-module RM, pd (M) and ίd (M) denote the
projective and injective dimension of RM, respectively. A (left and right) noether ring R is …

The study of global dimension of pullback rings has been subject of several interesting
works and has been served to solve many open problems. In this paper, we attempt to …

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 …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

For a class of $ R $-modules $\mathcal {X} $ containing all projective $ R $-modules, the
$\mathcal {X} $-Gorenstein projective $ R $-modules vary from projective to Gorenstein …