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Keywords
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Annihilator, Attached primes, Cohomological dimension
Local cohomology.
Arch. Math. 102 (2014), 225–236
c
2014 The Author(s). This article is published
with open access at Springerlink.com
0003-889X/14/030225-12
published online March 19, 2014
DOI 10.1007/s00013-014-0629-1
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Abstract
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Let a be an ideal of a commutative Noetherian ring R and M
a finitely generated R-module. It is shown that AnnR(HdimM
a (M)) =
AnnR(M/TR(a,M)), where TR(a,M) is the largest submodule of M
such that cd(a, TR(a,M)) < cd(a,M). Several applications of this result
are given. Among other things, it is shown that there exists an
ideal b of R such that AnnR(HdimM
a (M)) = AnnR(M/H0b
(M)). Using
this, we show that if HdimR
a (R) = 0, then AttR HdimR−1
a (R) = {p ∈
SpecR| cd(a,R/p) = dimR − 1}. These generalize the main results of
Bahmanpour et al. (see [2, Theorem 2.6]), Hellus (see [7, Theorem 2.3]),
and Lynch (see [10, Theorem 2.4]).
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