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Computing the core of ideals in arbitrary characteristic
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fouli, Louiza |
| Copyright Year | 2007 |
| Abstract | Abstract Let R be a local Gorenstein ring with infinite residue field of arbitrary characteristic. Let I be an R -ideal with g = ht I > 0 , analytic spread l , and let J be a minimal reduction of I . We further assume that I satisfies G l and depth R / I j ⩾ dim R / I − j + 1 for 1 ⩽ j ⩽ l − g . The question we are interested in is whether core ( I ) = J n + 1 : ∑ b ∈ I ( J , b ) n for n ≫ 0 . In the case of analytic spread Polini and Ulrich show that this is true with even weaker assumptions [C. Polini, B. Ulrich, A formula for the core of an ideal, Math. Ann. 331 (2005) 487–503, Theorem 3.4]. We give a negative answer to this question for higher analytic spreads and suggest a formula for the core of such ideals. |
| Starting Page | 2855 |
| Ending Page | 2867 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.jalgebra.2007.10.009 |
| Volume Number | 319 |
| Alternate Webpage(s) | http://arxiv.org/pdf/0705.1808v1.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/0705.1808v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.jalgebra.2007.10.009 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
