In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

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

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …

Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

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 …

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 …