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Hilbert-Samuel functions of modules over Cohen-Macaulay rings

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Title Hilbert-Samuel functions of modules over Cohen-Macaulay rings
 
Creator IYENGAR, S
PUTHENPURAKAL, TJ
 
Subject local ring
powers
ideal
hilbert-samuel functions
growth and vanishing of derived functors
 
Description For a finitely generated, non-free module M over a CM local ring ( R, m, k), it is proved that for n >> 0 the length of TorR 1 ( M, R/m(n+1)) is given by a polynomial of degree dim R-1. The vanishing of Tor(i)(R) ( M, N/m(n+1)N) is studied, with a view towards answering the question: If there exists a finitely generated R-module N with dimN >= 1 such that the projective dimension or the injective dimension of N/m(n+1)N is finite, then is R regular? Upper bounds are provided for n beyond which the question has an affirmative answer.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2011-07-16T18:36:27Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
2011-07-16T18:36:27Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
2007
 
Type Article
 
Identifier PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135(3), 637-648
0002-9939
http://dx.doi.org/10.1090/S0002-9939-06-08519-4
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4497
http://hdl.handle.net/10054/4497
 
Language en