Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings
HB Foxby, AJ Frankild - Illinois Journal of Mathematics, 2007 - projecteuclid.org
The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …
Modules with finite reducing Gorenstein dimension
T Araya, O Celikbas, J Cook, T Kobayashi - Beiträge zur Algebra und …, 2024 - Springer
If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …
[引用][C] Rings of type 1 are Gorenstein
P Roberts - Bulletin of the London Mathematical Society, 1983 - academic.oup.com
In the original paper on Gorenstein rings, Bass [1] characterizes Gorenstein rings as those
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …
[HTML][HTML] Gorenstein dimension of modules over homomorphisms
LW Christensen, S Iyengar - Journal of Pure and Applied Algebra, 2007 - Elsevier
Given a homomorphism of commutative noetherian rings R→ S and an S-module N, it is
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …
Gorenstein projective and injective dimensions over Frobenius extensions
W Ren - Communications in Algebra, 2018 - Taylor & Francis
ABSTRACT Let R⊂ A be a Frobenius extension of rings. We prove that:(1) for any left A-
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …
[PDF][PDF] The existence of finitely generated modules of finite Gorenstein injective dimension
R Takahashi - Proceedings of the American Mathematical …, 2006 - community.ams.org
THE EXISTENCE OF FINITELY GENERATED MODULES OF FINITE GORENSTEIN
INJECTIVE DIMENSION 1. Introduction Throughout this note, we as Page 1 …
INJECTIVE DIMENSION 1. Introduction Throughout this note, we as Page 1 …
Foxby duality and Gorenstein injective and projective modules
E Enochs, O Jenda, J Xu - Transactions of the American Mathematical …, 1996 - ams.org
In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …
A generalization of a theorem of Foxby
T Araya, R Takahashi - Archiv der Mathematik, 2009 - Springer
A generalization of a theorem of Foxby Page 1 Arch. Math. 93 (2009), 123–127 c© 2009
Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020123-5 published online August 6, 2009 …
Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020123-5 published online August 6, 2009 …
The Auslander-Bridger formula and the Gorenstein property for coherent rings
L Hummel, T Marley - Journal of Commutative Algebra, 2009 - JSTOR
The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely
generated modules over a Noetherian ring, is studied in the context of finitely presented …
generated modules over a Noetherian ring, is studied in the context of finitely presented …
𝑛-Gorenstein rings
HB Foxby - Proceedings of the American Mathematical Society, 1974 - ams.org
The object of this note is to study commutative noetherian n-Gorenstein rings. The first result
is: if each module satisfying Samuel's conditions $({{\text {a}} _i}) $ for some $ i\leqq n $ is an …
is: if each module satisfying Samuel's conditions $({{\text {a}} _i}) $ for some $ i\leqq n $ is an …