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Erschienen in:
2003 | OriginalPaper | Buchkapitel
Modules of G-Dimension Zero over Local Rings with the Cube of Maximal Ideal Being Zero
verfasst von : Yuji Yoshino
Erschienen in: Commutative Algebra, Singularities and Computer Algebra
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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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.