Asymptotic behavior of dimensions of syzygies
| Autor: | Micah J. Leamer, Kristen A. Beck |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Noetherian
Discrete mathematics Pure mathematics Hilbert's syzygy theorem Mathematics::Commutative Algebra Betti number Applied Mathematics General Mathematics MathematicsofComputing_GENERAL Local ring Complex dimension Equidimensional Mathematics - Commutative Algebra Commutative Algebra (math.AC) Global dimension FOS: Mathematics GeneralLiterature_REFERENCE(e.g. dictionaries encyclopedias glossaries) Commutative property Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 141:2245-2252 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | Let R be a commutative noetherian local ring, and M a finitely generated R-module of infinite projective dimension. It is well-known that the depths of the syzygy modules of M eventually stabilize to the depth of R. In this paper, we investigate the conditions under which a similar statement can be made regarding dimension. In particular, we show that if R is equidimensional and the Betti numbers of M are eventually non-decreasing, then the dimension of any sufficiently high syzygy module of M coincides with the dimension of R. Comment: 8 pages; to appear in Proc. Amer. Math. Soc |
| Databáze: | OpenAIRE |
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