On $w$-Hilbert domains
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917354285301760 |
|---|---|
| author | Baek, Hyungtae |
| author_facet | Baek, Hyungtae |
| contents | In this paper, we introduce the notion of a $w$-Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using $D+M$ constructions. Furthermore, we establish necessary and sufficient conditions for the polynomial ring and the Anderson ring to be $w$-Hilbert domains, and compare the $w$-dimension of the polynomial ring with that of its base ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19692 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $w$-Hilbert domains Baek, Hyungtae Commutative Algebra 13A15, 13B30 In this paper, we introduce the notion of a $w$-Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using $D+M$ constructions. Furthermore, we establish necessary and sufficient conditions for the polynomial ring and the Anderson ring to be $w$-Hilbert domains, and compare the $w$-dimension of the polynomial ring with that of its base ring. |
| title | On $w$-Hilbert domains |
| topic | Commutative Algebra 13A15, 13B30 |
| url | https://arxiv.org/abs/2603.19692 |