Abstract
For an order embedding \(G\mathop \to \limits^h \;\Gamma \) of a partly ordered group G into an l-group Γ a topology ’ is introduced on Γ which is defined by a family of valuations W on G. Some density properties of sets h(G), h(X t ) and \((h(X_t )\backslash \{ h(g_1 ),\;.\;.\;.\;,h(g_n )\} )\) (X t being t-ideals in G) in the topological space ’ are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.
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Močkoř, J. Topological characterizations of ordered groups with quasi-divisor theory. Czechoslovak Mathematical Journal 52, 595–607 (2002). https://doi.org/10.1023/A:1021783914729
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DOI: https://doi.org/10.1023/A:1021783914729