Gorenstein injective modules and Auslander categories

MA Esmkhani, M Tousi - Archiv der Mathematik, 2007 - Springer
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

Auslander-Gorenstein rings

K Ajitabh, SP Smith, JJ Zhang - Communications in Algebra, 1998 - Taylor & Francis
Auslander-gorenstein rings Page 1 COMMUNICATIONS IN ALGEBRA, 26(7), 2159-2180 (1998)
AUSLANDER-GORENSTEIN RINGS K . AJITABH: DEPARTMENT OF MATHEMATICS, FLORIDA …

On relative counterpart of Auslander's conditions

D Bennis, R El Maaouy, JRG Rozas… - Journal of Algebra and …, 2023 - World Scientific
It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …

Rings without a Gorenstein analogue of the Govorov–Lazard theorem

H Holm, P Jørgensen - Quarterly journal of mathematics, 2011 - ieeexplore.ieee.org
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 …

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Y Geng - Czechoslovak mathematical journal, 2013 - Springer
Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a
transpose Tr c M of an R-module M with respect to C which unifies the Auslander transpose …

Nonvanishing cohomology and classes of Gorenstein rings

DA Jorgensen, LM Şega - Advances in Mathematics, 2004 - Elsevier
We give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

Gorenstein injective and strongly cotorsion modules

Z Huang - Israel Journal of Mathematics, 2013 - Springer
By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

On Modules M such that both M and M are Semi-Gorenstein-Projective

CM Ringel, P Zhang - Algebras and Representation Theory, 2021 - Springer
Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Ext i
(M, A)= 0 for all i≥ 1. If M is Gorenstein-projective, then both M and its A-dual M∗ are semi …

Gorenstein-projective and semi-Gorenstein-projective modules

CM Ringel, P Zhang - Algebra & Number Theory, 2020 - msp.org
Let A be an artin algebra. An A-module M will be said to be semi-Gorenstein-projective
provided that Ext i (M, A)= 0 for all i≥ 1. All Gorenstein-projective modules are semi …

Gorenstein flat covers of modules over Gorenstein rings

E Enochs, J Xu - Journal of Algebra, 1996 - Elsevier
A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …