Hilbert-Samuel functions of modules over Cohen-Macaulay rings
| dc.creator | Iyengar, Srikanth | |
| dc.creator | Puthenpurakal, Tony J. | |
| dc.date | 2004-12-09 | |
| dc.date | 2005-07-19 | |
| dc.date.accessioned | 2026-07-07T05:15:09Z | |
| dc.date.available | 2026-07-07T05:15:09Z | |
| dc.description | For a finitely generated, non-free module $M$ over a CM local ring $(R,\fm,k)$, it is proved that for $n\gg 0$ the length of $\tor 1RM{R/\fm^{n+1}}$ is given by a polynomial of degree $\dim R-1$. The vanishing of $\tor iRM{N/\fm^{n+1}N}$ is studied, with a view towards answering the question: if there exists a finitely generated $R$-module $N$ with $\dim N\ge 1$ such that the projective dimension or the injective dimension of $N/\fm^{n+1}N$ is finite, then is $R$-regular? Upper bounds are provided for $n$ beyond which the question has an affirmative answer. | |
| dc.description | revised version. To appear in Proc. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0412194 | |
| dc.identifier | http://arxiv.org/abs/math/0412194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73540 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 13D40; Secondary 13D02, 13D07 | |
| dc.title | Hilbert-Samuel functions of modules over Cohen-Macaulay rings | |
| dc.type | text |