EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES

Title & Authors
EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES
BAHMANPOUR, KAMAL;

Abstract
Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $\small{x_1,{\ldots },x_t}$ ($\small{1{\leq}t{\leq}n}$) be a sub-set of a system of parameters for M, then the R-module $\small{H^t_{(x_1,{\ldots },x_t)}}$(R) is faithful, i.e., Ann $\small{H^t_{(x_1,{\ldots },x_t)}}$(R) = 0. Also, it is shown that, if $\small{H^i_I}$ (R) = 0 for all i > dim R - dim R/I, then the R-module $\small{H^{dimR-dimR/I}_I(R)}$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $\small{H^1_I(M)}$, when $\small{H^i_I(M)=0}$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $\small{D_I(R)}$ is a flat R-algebra.
Keywords
cohomological dimension;ideal transform;local cohomology;Noetherian ring;
Language
English
Cited by
1.
Ideal Transforms with Respect to a Pair of Ideals, Acta Mathematica Vietnamica, 2017
2.
A note on Lynch’s conjecture, Communications in Algebra, 2017, 45, 6, 2738
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