The reciprocal complement of a polynomial ring in several variables over a field
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_ | 1866911122134663168 |
|---|---|
| author | Epstein, Neil Guerrieri, Lorenzo Loper, K. Alan |
| author_facet | Epstein, Neil Guerrieri, Lorenzo Loper, K. Alan |
| contents | The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when $D$ is a polynomial ring in $n\geq 2$ variables over a field. In particular, $R(D)$ is an $n$-dimensional, local, non-Noetherian, non-integrally closed, non-factorial, atomic G-domain, with infinitely many prime ideals at each height other than $0$ and $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The reciprocal complement of a polynomial ring in several variables over a field Epstein, Neil Guerrieri, Lorenzo Loper, K. Alan Commutative Algebra The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when $D$ is a polynomial ring in $n\geq 2$ variables over a field. In particular, $R(D)$ is an $n$-dimensional, local, non-Noetherian, non-integrally closed, non-factorial, atomic G-domain, with infinitely many prime ideals at each height other than $0$ and $n$. |
| title | The reciprocal complement of a polynomial ring in several variables over a field |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2407.15637 |