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On Carathéodory vector lattices. (English) Zbl 1071.06009
Summary: To each generalized Boolean algebra \(B\) there corresponds a vector lattice \(V\); this correspondence goes back to Gofman. In general, \(B\) cannot be uniquely reconstructed from \(V\). In this paper we investigate pairs of generalized Boolean algebras \(B\) and \(B'\) which generate the same vector lattice \(V\). Further, we deal with the relations between the internal direct product decompositions of \(V\) and \(B\).

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46A40 Ordered topological linear spaces, vector lattices
06E99 Boolean algebras (Boolean rings)
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