Related papers: (projectively coresolved) Gorenstein flat modules …

Let $(R, \mathfrak{m})$ be a Noetherian local ring. In this paper, we introduce a dual notion for dualizing modules, namely codualizing modules. We study the basic properties of codualizing modules and use them to establish an equivalence…

The category ${\rm gp}(\Lambda)$ of Gorenstein-projective modules over tensor algebra $\Lambda = A\otimes_kB$ can be described as the monomorphism category ${\rm mon}(B, {\rm gp}(A))$ of $B$ over ${\rm gp}(A)$. In particular,…

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…

One of the main results of this paper is the characterization of the rings over which all modules are strongly Gorenstein projective. We show that these kinds of rings are very particular cases of the well-known quasi-Frobenius rings. We…

In this paper, we study the resolving of $\mathcal{SGP}(-)$ and $\mathcal{SGF}(-)$, the classes of all strongly Gorenstein projective and flat modules respectively, over a direct product of commutative rings.

It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue…

In this paper, we examine the relation between certain subclasses of the classes of Gorenstein projective, Gorenstein flat and Gorenstein injective modules over a group algebra, which consist of the cofibrant, cofibrant-flat and fibrant…

Let $R$ be a commutative ring. An $R$-module $M$ is said to be super finitely presented if there is an exact sequence of $R$-modules $\cdots\rightarrow P_n\rightarrow\cdots \rightarrow P_1\rightarrow P_0\rightarrow M\rightarrow 0$ where…

An A-module M will be said to be semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of…

The aim of this article is to consider the spectral sequences induced by tensor-hom adjunction, and provide a number of new results. Let $R$ be a commutative Noetherian local ring of dimension $d$. In the 1st part, it is proved that $R$ is…

We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras $A$ and $B$, we use the special monomorphism category…

Let $\mathcal{X}$ be a class of left $R$-modules, $\mathcal{Y}$ be a class of right $R$-modules. In this paper, we introduce and study Gorenstein $(\mathcal{X}, \mathcal{Y})$-flat modules as a common generalization of some known modules…

(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…

For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of…

We consider the following question: Is Gorenstein homology a X-pure homology, in the sense defined by Warfield, for a class X of modules? Let GP denote the class of Gorenstein projective modules. We prove that over a commutative Noetherian…

In this paper, we are concerned with Gorenstein projective objects in homotopy categories. Specifically, we present a characterization on Gorenstein projective objects in the category of complexes. Using this result, it is proved that the…

We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting…

The principle "Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra" is given in [3]. There is a remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps one of the…

We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As…

In the paper, we investigate the lifting of recollements with respect to Gorenstein-projective modules. Specifically, a homological ring epimorphism can induce a lifting of the recollement of the stable category of finitely generated…