Related papers: Gorenstein flat and projective (pre)covers

We study Artin algebras $A$ and commutative Noetherian complete local rings $R$ in connection with the following decomposition property of Gorenstein-projective modules: $(*)$ any Gorenstein-projective module is a direct sum of finitely…

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which…

Gorenstein rings are important to mathematical areas as diverse as algebraic geometry, where they encode information about singularities of spaces, and homotopy theory, through the concept of model categories. In consequence, the study of…

Let $R$ be a ring, $\textrm{Proj}$ be the class of all projective right $R$-modules, $\mathcal K$ be the full subcategory of the homotopy category $\mathbf K(\textrm{Proj})$ whose class of objects consists of all totally acyclic complexes,…

For a compact Lie group G we show that if the representing spectrum for Borel cohomology generates its category of modules if G is connected. For a closed subgroup H of G we consider the map C^*(BG)--->C^*(BH) and establish the sense in…

Recently the author has studied rings for which products of flat modules have finite flat dimension. In this paper we extend the theory to characterize when products of modules in $\mathcal T$ have finite $\mathcal T$-projective dimension,…

The existence of the Gorenstein projective precovers over $R$ an arbitrary ring, as well as the completeness of the Gorenstein projective cotorsion pair $(\mathcal{GP},\mathcal{GP}^{\perp})$, are open questions. In this paper, we provide…

In 2004 and 2005 Enochs et al. characterized the flat and projective quiver-representations of left rooted quivers. The proofs can be understood as filtering the classes $\Phi(\operatorname{Add}\mathscr X)$ and $\Phi(\varinjlim\mathscr X)$…

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

In this paper, we mainly investigate the $\mathfrak{X}$-Gorenstein projective dimension of modules and the (left) $\mathfrak{X}$-Gorenstein global dimension of rings. Some properties of $\mathfrak{X}$-Gorenstein projective dimensions are…

A model structure on a category is a formal way of introducing a homotopy theory on that category, and if the model structure is abelian and hereditary, its homotopy category is known to be triangulated. So a good way to both build and…

We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic complexes to the stable derived category. We show that…

The main aim of this paper is to investigate rings over which all (finitely generated strongly) Gorenstein projective modules are projective. We consider this propriety under change of rings, and give various examples of rings with and…

One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class of Gorenstein injective modules, $\mathcal{GI}$, is closed…

We characterize Gorenstein modules over those local rings that admit a finite contracting endomorphism.

Let $T_R(M)$ be a tensor ring and $\mathcal{X}$, $\mathcal{Y}$ be two classes of $R$-modules. Under certain conditions, we prove that a $T_R(M)$-module $(A, u)$ is $Ind(\mathcal{X})$-Gorenstein projective if and only if $u$ is monomorphic…

We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring $R$ that coincides with the $R$-topology defined by Matlis when $R$ is commutative. (2) We…

We construct a class of Gorenstein local rings $R$ which admit minimal complete $R$-free resolutions $\bd C$ such that the sequence $\{\rank_R C_i\}$ is constant for $i< 0$, and grows exponentially for all $i>0$. Over these rings we show…

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…

Invariants with respect to recollements of the stable category of Gorenstein projective A-modules over an algebra A and stable equivalences are investigated. Specifically, the Gorenstein rigidity dimension is introduced. It is shown that…