| Title:
|
Some notes on the composite $G$-valuations (English) |
| Author:
|
Kontolatou, Angeliki |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
271-275 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In analogy with the notion of the composite semi-valuations, we define the composite $G$-valuation $v$ from two other $G$-valuations $w$ and $u$. We consider a lexicographically exact sequence $(a,\beta ):A_u\rightarrow B_v\rightarrow C_w$ and the composite $G$-valuation $v$ of a field $K$ with value group $B_v$. If the assigned to $v$ set $R_v=\lbrace x\in K/v(x)\ge 0$ or $v(x)$ non comparable to $0\rbrace $ is a local ring, then a $G$-valuation $w$ of $K$ into $C_w$ is defined with its assigned set $R_w$ a local ring, as well as another $G$-valuation $u$ of a residue field is defined with $G$-value group $A_u$. (English) |
| Keyword:
|
composite semi-valuation |
| Keyword:
|
ordered group |
| Keyword:
|
G-homomorphism of ordered groups |
| MSC:
|
13A18 |
| idZBL:
|
Zbl 0829.13002 |
| idMR:
|
MR1322571 |
| . |
| Date available:
|
2008-06-06T21:27:08Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107513 |
| . |
| Reference:
|
[1] Kontolatou, A., Stabakis, J.: Embedding groups into linear or lattice structures.Bull. Cal. Math. Soc. 82 (1987), 290-297. MR 1134208 |
| Reference:
|
[2] Ohm, J.: Semi-valuations and groups of divisibility.Canad. Journ. of Math. 21 (1969), 576-591. Zbl 0177.06501, MR 0242819 |
| Reference:
|
[3] Ribenboim, P.: Theorie des valuations.Les presses de l’ Universite de Montreal (1968). MR 0249425 |
| . |
