| Title:
|
On prolongations of rank one discrete valuations (English) |
| Author:
|
El Fadil, Lhoussain |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
299-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(K,\nu)$ be a valued field, where $\nu$ is a rank one discrete valuation. Let $R$ be its ring of valuation, ${\mathfrak m}$ its maximal ideal, and $L$ an extension of $K$, defined by a monic irreducible polynomial $F(X) \in R[X]$. Assume that $\overline{F}(X)$ factors as a product of $r$ distinct powers of monic irreducible polynomials. In this paper a condition which guarantees the existence of exactly $r$ distinct valuations of $K$ extending $\nu$ is given, in such a way that it generalizes the results given in the paper ``Prolongations of valuations to finite extensions" by S.\,K. Khanduja, M. Kumar (2010). (English) |
| Keyword:
|
discrete valuation |
| Keyword:
|
extension of valuation |
| Keyword:
|
prime ideal factorization |
| MSC:
|
11S05 |
| MSC:
|
13A18 |
| idZBL:
|
Zbl 07144895 |
| idMR:
|
MR4034433 |
| DOI:
|
10.14712/1213-7243.2019.017 |
| . |
| Date available:
|
2019-10-29T12:51:47Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147854 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
