|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Faltings' local-global principle for the in dimension $f< n$ of local cohomology modules | | Reza Naghipour
; Robabeh Maddahali
; Khadijeh Ahmadi Amoli
; | | Date: |
18 Dec 2017 | | Abstract: | The concept of Faltings’ local-global principle for the in dimension $< n$ of
local cohomology modules over a Noetherian ring $R$ is introduced, and it is
shown that this principle holds at levels 1, 2. We also establish the same
principle at all levels over an arbitrary Noetherian ring of dimension not
exceeding 3. These generalize the main results of Brodmann et al. in
cite{BRS}. Moreover, as a generalization of Raghavan’s result, we show that
the Faltings’ local-global principle for the in dimension $<n$ of local
cohomology modules holds at all levels $rin mathbb{N}$ whenever the ring $R$
is a homomorphic image of a Noetherian Gorenstein ring. Finally, it is shown
that if $M$ is a finitely generated $R$-module, $frak a$ an ideal of $R$ and
$r$ a non-negative integer such that $frak a^tH^i_{frak a}(M)$ is in
dimension $< 2$ for all $i<r$ and for some positive integer $t$, then for any
minimax submodule $N$ of $H^r_{frak a}(M)$, the $R$-module $Hom_R(R/frak a,
H^r_{frak a}(M)/N)$ is finitely generated. As a consequence, it follows that
the associated primes of $H^r_{frak a}(M)/N$ are finite. This generalizes the
main results of Brodmann-Lashgari cite{BL} and Quy cite{Qu}. | | Source: | arXiv, 1712.7580 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER