| Title:
|
Maximal non valuation domains in an integral domain (English) |
| Author:
|
Kumar, Rahul |
| Author:
|
Gaur, Atul |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1019-1032 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper subring $R$ of an integral domain $S$ is called a maximal non valuation domain in $S$ if $R$ is not a valuation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a valuation subring of $S$. For a local domain $S$, the equivalence of an integrally closed maximal non VD in $S$ and a maximal non local subring of $S$ is established. The relation between $\dim (R,S)$ and the number of rings between $R$ and $S$ is given when $R$ is a maximal non VD in $S$ and $\dim (R,S)$ is finite. For a maximal non VD $R$ in $S$ such that $R\subset R^{\prime _S} \subset S$ and $\dim (R,S)$ is finite, the equality of $\dim (R,S)$ and $\dim (R^{\prime _S},S)$ is established. (English) |
| Keyword:
|
maximal non valuation domain |
| Keyword:
|
valuation subring |
| Keyword:
|
integrally closed subring |
| MSC:
|
13B02 |
| MSC:
|
13B22 |
| MSC:
|
13B30 |
| MSC:
|
13F30 |
| MSC:
|
13G05 |
| idZBL:
|
07285976 |
| idMR:
|
MR4181793 |
| DOI:
|
10.21136/CMJ.2020.0098-19 |
| . |
| Date available:
|
2020-11-18T09:44:42Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148408 |
| . |
| Reference:
|
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