The classification of dp-minimal integral domains
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913793713373184 |
|---|---|
| author | d'Elbée, Christian Halevi, Yatir Johnson, Will |
| author_facet | d'Elbée, Christian Halevi, Yatir Johnson, Will |
| contents | We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral domain, then R is a field or a valuation ring or arises from the following construction: there is a dp-minimal valuation overring O extending R, a proper ideal I in O, and a finite subring S in O/I such that R is the preimage of S in O. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_21014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The classification of dp-minimal integral domains d'Elbée, Christian Halevi, Yatir Johnson, Will Logic Rings and Algebras 03C45 We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral domain, then R is a field or a valuation ring or arises from the following construction: there is a dp-minimal valuation overring O extending R, a proper ideal I in O, and a finite subring S in O/I such that R is the preimage of S in O. |
| title | The classification of dp-minimal integral domains |
| topic | Logic Rings and Algebras 03C45 |
| url | https://arxiv.org/abs/2405.21014 |