Modules of G-Dimension Zero over Local Rings with the Cube of Maximal Ideal Being Zero
By Yu Yoshino. 2003
53 citations recorded by the source corpus.
Let (R,m) be a commutative Noetherian local ring with m3 = (0). We give a condition for R to have a non-free module of G-dimension zero. We shall also construct a family of non- isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of pro- jective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over R is not necessarily a contravariantly finite subcategory in the category of finitely generated R-modules.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3078ac409ef385b0acd95d8a87d7a780960f22ad
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Xiao-Wu Chen
- Apostolos Beligiannis
- Henning Krause
- J. Št’ovíček
- Chrysostomos Psaroudakis
- Pu Zhang
- I. Reiten
- Osamu Iyama
In Geometry and Topology
- Xiao-Wu Chen
- Apostolos Beligiannis
- Henning Krause
- J. Št’ovíček
- Pu Zhang
- Chrysostomos Psaroudakis
- I. Reiten
- Greg Stevenson
Citations in the corpus
- Thick subcategories and virtually Gorenstein algebras (2006, background): “in [ 9 ] (in a more general setting) that the trivial �-module K has no right Gproj�approximation, hence Gproj� fails to be contravariantly finite in mod�.”
- Gorenstein Homological Algebra of Artin Algebras (2017, background): “Note that for an artin algebra A the categoryA-Gproj of finitely generated Gorensteinprojective modules is not necessarily contravariantly finite in A-mod; see [62, 14].”