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Torsion classes and subdirect products of Carathéodory vector lattices. (English) Zbl 1164.06330
Summary: In this paper we prove that there exists a one-to-one correspondence between torsion classes of Carathéodory vector lattice and torsion classes of generalized Boolean algebras. Further, we deal with the relations between completely subdirect product decompositions of a Carathéodory vector lattice \(V\) and completely subdirect product decompositions of the generalized Boolean algebra \(B\) which generates \(V\).

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46A40 Ordered topological linear spaces, vector lattices
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