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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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##### References:
 [1] BIRKHOFF G.: Lattice Theory. (3rd. Amer. Math. Soc. Colloq. Publ. 25, Amer. Math. Soc, Providence, RI, 1967. · Zbl 0153.02501 [2] CONRAD P.: Lattice Ordered Groups. Tulane Universitu, Math. Res. Libraru, New Orleans, 1970. · Zbl 0258.06011 [3] CONRAD P.: Torsion radicals of lattice-ordered groups. Sumpos. Math. 21 (1977), 479-513. · Zbl 0372.06011 [4] CONRAD P.-DARNEL M. R.: Subgroups and hulls of Specker lattice-ordered groups. Czechoslovak Math. J. · Zbl 0978.06011 [5] GOFMAN C.: Remarks on lattice ordered groups and vector lattices. I. Carathéodory functions. Trans. Amer. Math. Soc 88 (1958), 107-120. [6] JAKUBÍK J.: Cardinal properties of lattice ordered groups. Fund. Math. 74 (1972), 85-98. · Zbl 0259.06015 [7] JAKUBÍK J.: Prime selectors and torsion classes of lattice ordered groups. Czechoslovak Math. J. 31 (1981), 325-337. · Zbl 0473.06012 [8] JAKUBÍK J.: Torsion classes of Specker lattice ordered groups. Czechoslovak Math. J. 52 (2002), 469-482. · Zbl 1012.06018 [9] JAKUBÍK J.: On vector lattices of elementary Carathéodory functions. Czechoslovak Math. J. 55 (2005), 223-236. · Zbl 1081.06021 [10] JAKUBÍK J.: On Carathéodory vector lattices. Math. Slovaca 53 (2003), 479-503. · Zbl 1071.06009 [11] MARTINEZ J.: Torsion theory for lattice ordered groups. Czechoslovak Math. J. 25 (1975), 284-299. · Zbl 0321.06020 [12] MARTINEZ J.: Torsion theory for lattice ordered groups II. Czechoslovak Math. J. 26 (1976), 93-100. · Zbl 0331.06009 [13] ŠIK F.: Über subdirekte Summen geordneter Gruppen. Czechoslovak Math. J. 10 (I960), 400-424. · Zbl 0102.26501
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