We establish relations between Gorenstein projective precovers linked by Frobenius
functors. This is motivated by an open problem that how to find general classes of rings for …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein
projective, then its underlying module over the base ring is Gorenstein projective; the …

We give a sufficient condition for the class of Gorenstein injective modules be precovering: if
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …

Let $ k $ be a commutative ring, let ${\mathcal {C}} $ be a small, $ k $-linear, Hom-finite,
locally bounded category, and let ${\mathcal {B}} $ be a $ k $-linear abelian category. We …

Let $ R $ be a commutative noetherian ring. Enochs and Huang [EH] proved that over a
Gorenstein ring of Krull dimension $ d $, every Gorenstein injective module admits a …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

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 …

We first introduce and study Gorenstein cophantom objects. Let C be a full and additive
subcategory of an abelian category A which is self-orthogonal and closed under …

We prove several characterizations of Gorenstein rings in terms of vanishings of derived
functors of certain modules or complexes whose scalars are restricted via contracting …