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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 \(V\).

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