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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/4497

Title: Hilbert-Samuel functions of modules over Cohen-Macaulay rings
Authors: IYENGAR, S
PUTHENPURAKAL, TJ
Keywords: local ring
powers
ideal
Issue Date: 2007
Publisher: AMER MATHEMATICAL SOC
Citation: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135(3), 637-648
Abstract: 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.
URI: 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
ISSN: 0002-9939
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