| | |
| | |
Stat |
Members: 3645 Articles: 2'504'585 Articles rated: 2609
24 April 2024 |
|
| | | |
|
Article overview
| |
|
The structure of the core of ideals | Alberto Corso
; Claudia Polini
; Bernd Ulrich
; | Date: |
4 Oct 2002 | Journal: | Math. Ann. 321 (2001), 89-105 | Subject: | Commutative Algebra | math.AC | Abstract: | The core of an $R$-ideal $I$ is the intersection of all reductions of $I$. This object was introduced by D. Rees and J. Sally and later studied by C. Huneke and I. Swanson, who showed in particular its connection to J. Lipman’s notion of adjoint of an ideal. Being an a priori infinite intersection of ideals, the core is difficult to describe explicitly. We prove in a broad setting that: ${
m core}(I)$ is a finite intersection of minimal reductions; ${
m core}(I)$ is a finite intersection of general minimal reductions; ${
m core}(I)$ is the contraction to $R$ of a `universal’ ideal; ${
m core}(I)$ behaves well under flat extensions. The proofs are based on general multiplicity estimates for certain modules. | Source: | arXiv, math.AC/0210069 | 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:
| |