Let R and S be rings, and let R ω S be a semidualizing bimodule. We prove that there exists
a Morita equivalence between the class of∞-ω-cotorsion-free modules and a subclass of the …

0 Introduction 611 1 Left derived extension functors 612 2 Gorenstein injective modules 616
3 Resolutions and resolvents 620 4 The existence of Gorenstein injective modules 623 5 …

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein
projective if and only if its underlying module over the base ring is Gorenstein projective. For …

In this article, we study the relation between m-strongly Gorenstein projective (resp.,
injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever …

We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove
that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that …

In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often
infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring …

We apply tilting theory to study modules of finite projective dimension. We introduce the
notion of finite and cofinite type for tilting and cotilting classes of modules, respectively …

Let $ A $ be a virtually Gorenstein algebra of finite CM-type. We establish a duality between
the subcategory of compact objects in the homotopy category of Gorenstein projective left …

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 …

Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …