Geodesic
On the distributive radical of an Archimedean lattice-ordered group
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 687-693

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Let $G$ be an Archimedean $\ell $-group. We denote by $G^d$ and $R_D(G)$ the divisible hull of $G$ and the distributive radical of $G$, respectively. In the present note we prove the relation $(R_D(G))^d=R_D(G^d)$. As an application, we show that if $G$ is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.
Classification : 06F20, 46A40
Keywords: Archimedean $\ell $-group; divisible hull; distributive radical; complete distributivity 
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     title = {On the distributive radical of an {Archimedean} lattice-ordered group},
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Jakubík, Ján. On the distributive radical of an Archimedean lattice-ordered group. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 687-693. http://geodesic.mathdoc.fr/item/CMJ_2009__59_3_a9/