Let $\varphi\colon R\rightarrow A $ be a ring homomorphism, where $ R $ is a commutative
noetherian ring and $ A $ is a finite $ R $-algebra. We give criteria for detecting the ascent …

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 …

In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states
that “for what rings R do we have K (AC)= K (R-Inj)?”. We give an answer to such a question …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective
preenvelopes for finite R-modules is known (it was proved using duality arguments). In the …

Throughout R is an associative ring with identity and all modules are unitary. Unless stated
otherwise, an R-module will be understood to be a left R-module. As usual, pdR (M) and idR …

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

Ascent Properties of Auslander Categories Page 1 Canad. J. Math. Vol. 61 (1), 2009 pp. 76–108
Ascent Properties of Auslander Categories Lars Winther Christensen and Henrik Holm Abstract …

In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …