Geodesic
Topological characterizations of ordered groups with quasi-divisor theory
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 595-607 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06F15, 06F20, 13F05, 20F60
Keywords: quasi-divisor theory; ordered group; valuations; $t$-ideal 
@article{CMJ_2002_52_3_a13,
     author = {Mo\v{c}ko\v{r}, Ji\v{r}{\'\i}},
     title = {Topological characterizations of ordered groups with quasi-divisor theory},
     journal = {Czechoslovak Mathematical Journal},
     pages = {595--607},
     year = {2002},
     volume = {52},
     number = {3},
     mrnumber = {1923265},
     zbl = {1019.06008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a13/}
}
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Močkoř, Jiří. Topological characterizations of ordered groups with quasi-divisor theory. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 595-607. http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a13/