| Title:
|
Topological characterizations of ordered groups with quasi-divisor theory (English) |
| Author:
|
Močkoř, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
595-607 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For an order embedding $G\overset{h}{\rightarrow }{\rightarrow }\Gamma $ of a partly ordered group $G$ into an $l$-group $\Gamma $ a topology $\mathcal T_{\widehat{W}}$ is introduced on $\Gamma $ which is defined by a family of valuations $W$ on $G$. Some density properties of sets $h(G)$, $h(X_t)$ and $(h(X_t)\setminus \lbrace h(g_1),\dots ,h(g_n)\rbrace )$ ($X_t$ being $t$-ideals in $G$) in the topological space $(\Gamma ,\mathcal T_{\widehat{W}})$ are then investigated, each of them being equivalent to the statement that $h$ is a strong theory of quasi-divisors. (English) |
| Keyword:
|
quasi-divisor theory |
| Keyword:
|
ordered group |
| Keyword:
|
valuations |
| Keyword:
|
$t$-ideal |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
13F05 |
| MSC:
|
20F60 |
| idZBL:
|
Zbl 1019.06008 |
| idMR:
|
MR1923265 |
| . |
| Date available:
|
2009-09-24T10:54:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127747 |
| . |
| Reference:
|
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| . |
