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 …
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 …
AUSLANDER-GORENSTEIN RINGS K . AJITABH: DEPARTMENT OF MATHEMATICS, FLORIDA …
On relative counterpart of Auslander's conditions
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 …
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 …
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 …
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 …
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 …
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 …
(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 …
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 …
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …