| Title:
|
On power integral bases for certain pure number fields defined by $x^{18}-m$ (English) |
| Author:
|
El Fadil, Lhoussain |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
11-19 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K={\mathbb Q}(\alpha)$ be a number field generated by a complex root $\alpha$ of a monic irreducible polynomial $f(x)=x^{18}-m$, $m\neq \mp 1$, is a square free rational integer. We prove that if $ m \equiv 2$ or $3 {\rm(mod }{ 4})$ and $m\not\equiv \mp 1 {\rm(mod }{ 9})$, then the number field $K$ is monogenic. If $ m \equiv 1 {\rm(mod }{ 4})$ or $m\equiv 1 {\rm(mod }{ 9})$, then the number field $K$ is not monogenic. (English) |
| Keyword:
|
power integral base |
| Keyword:
|
theorem of Ore |
| Keyword:
|
prime ideal factorization |
| MSC:
|
11R04 |
| MSC:
|
11R16 |
| MSC:
|
11R21 |
| idZBL:
|
Zbl 07584110 |
| idMR:
|
MR4445734 |
| DOI:
|
10.14712/1213-7243.2022.005 |
| . |
| Date available:
|
2022-07-18T11:46:52Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150432 |
| . |
| Reference:
|
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| Reference:
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