Testing for the Gorenstein property
O Celikbas, S Sather-Wagstaff - Collectanea mathematica, 2016 - Springer
We answer a question of Celikbas, Dao, and Takahashi by establishing the following
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …
The converse to a theorem of Sharp on Gorenstein modules
I Reiten - Proceedings of the American Mathematical Society, 1972 - ams.org
Let A be a commutative local Noetherian ring with identity of Krull dimension n, m its
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …
Modules that detect finite homological dimensions
O Celikbas, H Dao, R Takahashi - 2014 - projecteuclid.org
We study homological properties of test modules that are, in principle, modules that detect
finite homological dimensions. The main outcome of our results is a generalization of a …
finite homological dimensions. The main outcome of our results is a generalization of a …
Ideals defining Gorenstein rings are (almost) never products
C Huneke - Proceedings of the American Mathematical Society, 2007 - JSTOR
Ideals Defining Gorenstein Rings Are (Almost) Never Products Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 135, Number 7, July 2007, Pages 2003-2005 …
AMERICAN MATHEMATICAL SOCIETY Volume 135, Number 7, July 2007, Pages 2003-2005 …
[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 …
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 …
Gorenstein rings and irreducible parameter ideals
T Marley, M Rogers, H Sakurai - Proceedings of the American Mathematical …, 2008 - ams.org
Given a Noetherian local ring $(R, m) $ it is shown that there exists an integer $\ell $ such
that $ R $ is Gorenstein if and only if some system of parameters contained in $ m^{\ell} …
that $ R $ is Gorenstein if and only if some system of parameters contained in $ m^{\ell} …
On a construction of Gorenstein rings proposed by M. D'Anna
J Shapiro - Journal of Algebra, 2010 - Elsevier
On a construction of Gorenstein rings proposed by M. D'Anna Page 1 Journal of Algebra
323 (2010) 1155–1158 Contents lists available at ScienceDirect Journal of Algebra www.elsevier.com/locate/jalgebra …
323 (2010) 1155–1158 Contents lists available at ScienceDirect Journal of Algebra www.elsevier.com/locate/jalgebra …
When is 𝑅⋉ 𝐼 an almost Gorenstein local ring?
S Goto, S Kumashiro - Proceedings of the American Mathematical Society, 2018 - ams.org
Let $(R,\mathfrak {m}) $ be a Gorenstein local ring of dimension $ d> 0$ and let $ I $ be an
ideal of $ R $ such that $(0)\ne I\subsetneq R $ and $ R/I $ is a Cohen-Macaulay ring of …
ideal of $ R $ such that $(0)\ne I\subsetneq R $ and $ R/I $ is a Cohen-Macaulay ring of …
The existence of finitely generated modules of finite Gorenstein injective dimension
R Takahashi - Proceedings of the American Mathematical Society, 2006 - JSTOR
The Existence of Finitely Generated Modules of Finite Gorenstein Injective Dimension Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …