Low degree extensions with Cyclic class group
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909592537006080 |
|---|---|
| author | Krishnamoorthy, Srilakshmi Pasupulati, Sunil Kumar |
| author_facet | Krishnamoorthy, Srilakshmi Pasupulati, Sunil Kumar |
| contents | Lenstra introduced the notion of the Euclidean ideal class, a generalization of the Euclidean domain that captures cyclic class groups. In this article, we establish the existence of Euclidean ideal classes in abelian quartic fields. As a corollary, we demonstrate that certain biquadratic fields with class number two possess a Euclidean ideal class. Additionally, we investigate the presence of Euclidean ideal classes in specific cubic and quadratic extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_00225 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Low degree extensions with Cyclic class group Krishnamoorthy, Srilakshmi Pasupulati, Sunil Kumar Number Theory Lenstra introduced the notion of the Euclidean ideal class, a generalization of the Euclidean domain that captures cyclic class groups. In this article, we establish the existence of Euclidean ideal classes in abelian quartic fields. As a corollary, we demonstrate that certain biquadratic fields with class number two possess a Euclidean ideal class. Additionally, we investigate the presence of Euclidean ideal classes in specific cubic and quadratic extensions. |
| title | Low degree extensions with Cyclic class group |
| topic | Number Theory |
| url | https://arxiv.org/abs/2110.00225 |