Title : ( On the free resolutions of local cohomology modules with respect to an ideal generated by a u.s.d-sequence )
Authors: Kazem Khashyarmanesh ,
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Abstract
Let a be an almost complete intersection ideal of a commutative Noetherian local ring R and r be the number of elements of a minimal generating set of a. Suppose that the i-th local cohomology module H^i_a(R) is finitely generated for all i< r. We show that there exists a sequence x=x_1, ... ,x_r of elements in a which is both an a-filter regular and u.s.d-sequence on R and \Omega_R^{r-1}(H^{r-1}_a(R))\cong \Omega_R^{r+1}(R/(x)) where, for an R-module M, \Omega_R^{i}(M) is the i-th syzygy of M.
Keywords
, minimal free resolution, local cohomology module
@article{paperid:1022492,
author = {Khashyarmanesh, Kazem},
title = {On the free resolutions of local cohomology modules with respect to an ideal generated by a u.s.d-sequence},
journal = {Acta Universitatis Carolinae: Mathematica et Physica},
year = {2010},
volume = {51},
number = {2},
month = {January},
issn = {0001-7140},
pages = {3--8},
numpages = {5},
keywords = {minimal free resolution; local cohomology module},
}
%0 Journal Article
%T On the free resolutions of local cohomology modules with respect to an ideal generated by a u.s.d-sequence
%A Khashyarmanesh, Kazem
%J Acta Universitatis Carolinae: Mathematica et Physica
%@ 0001-7140
%D 2010
