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Locally conditioned radical classes of lattice-ordered groups. (English) Zbl 0767.06016
Let \(G\) be an \(\ell\)-group, \(G(x)\) be a convex \(\ell\)-subgroup of \(G\) generated by \(x\) and \(N_ x\) be the intersection of all values of \(x\) in \(G(x)\). Let \(X\) be an arbitrary class of archimedean \(\ell\)-groups and \(\text{Loc}(X)\) be the class of all \(\ell\)-groups \(G\) for which every local residue \(G(x)/N_ x\) belongs to \(X\).
In this paper, properties of \(\text{Loc}(X)\) are investigated. It is proved that for a lot of classes \(X\) of archimedean \(\ell\)-groups \(\text{Loc}(X)\) is a torsion class.

06F15 Ordered groups
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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