This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is
not yet known whether the category GF (R) of Gorenstein flat modules over a ring R is …

In these expository notes I discuss several concepts and results in the theory of modules
over commutative rings, revolving around the Gorenstein dimension of modules. Some of …

We prove that if $ f: R\rightarrow S $ is a local homomorphism of noetherian local rings of
finite flat dimension and $ M $ is a non-zero finitely generated $ S $-module whose …

An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes
of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …

Let C be a semidualizing module for a commutative ring R. In this paper, we study the
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …

Let $(\mathcal {A, B}) $ be a GP-admissible pair and $(\mathcal {Z, W}) $ be a GI-admissible
pair of classes of objects in an abelian category $\mathcal {C} $, and consider the class …

The classical global and weak dimensions of rings play an important role in the theory of
rings and have a great impact on homological and commutative algebra. In this paper, we …

Let G (X) and G (Y) be Gorenstein subcategories induced by an admissible balanced pair
(X, Y) in an abelian category A. In this paper, we establish Gorenstein homological …

Let $\mathbf {k} $ be an algebraically closed field, and let $\Lambda $ be a finite
dimensional $\mathbf {k} $-algebra. We prove that if $\Lambda $ is a Gorenstein algebra …