Hilbert-Samuel functions of modules over Cohen-Macaulay rings

dc.creatorIyengar, Srikanth
dc.creatorPuthenpurakal, Tony J.
dc.date2004-12-09
dc.date2005-07-19
dc.date.accessioned2026-07-07T05:15:09Z
dc.date.available2026-07-07T05:15:09Z
dc.descriptionFor 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.descriptionrevised version. To appear in Proc. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0412194
dc.identifierhttp://arxiv.org/abs/math/0412194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73540
dc.subjectCommutative Algebra
dc.subjectPrimary 13D40; Secondary 13D02, 13D07
dc.titleHilbert-Samuel functions of modules over Cohen-Macaulay rings
dc.typetext

Files

Collections