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Torsion classes of Specker lattice ordered groups. (English) Zbl 1012.06018

Summary: In this paper we investigate the relations between torsion classes of Specker lattice-ordered groups and torsion classes of generalized Boolean algebras.

MSC:

06F15 Ordered groups
06E99 Boolean algebras (Boolean rings)
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References:

[1] G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967. · Zbl 0153.02501
[2] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. · Zbl 0258.06011
[3] P. Conrad and M. R. Darnel: Lattice-ordered groups whose lattices determine their additions. Trans. Amer. Math. Soc. 330 (1992), 575-598. · Zbl 0756.06009 · doi:10.2307/2153923
[4] P. F. Conrad and M. R. Darnel: Generalized Boolean algebras in lattice-ordered groups. Order 14 (1998), 295-319. · Zbl 0919.06009 · doi:10.1023/A:1006075129584
[5] P. F. Conrad and M. R. Darnel: Subgroups and hulls of Specker lattice-ordered groups. Czechoslovak Math. J 51 (2001), 395-413. · Zbl 0978.06011 · doi:10.1023/A:1013759300701
[6] P. F. Conrad and D. McAlister: The completion of an \(\ell \)-group. J. Austral. Math. Soc. 9 (1969), 182-208. · Zbl 0172.31601 · doi:10.1017/S1446788700005760
[7] P. F. Conrad and J. Martinez: Signatures and \(S\)-discrete lattice ordered groups. Algebra Universalis 29 (1992), 521-545. · Zbl 0767.06015 · doi:10.1007/BF01190779
[8] C. Gofman: Remarks on lattice ordered groups and vector lattices. I. Carathéodory functions. Trans. Amer. Math. Soc. 88 (1958), 107-120.
[9] J. Jakubík: Cardinal properties of lattice ordered groups. Fund. Math. 74 (1972), 85-98. · Zbl 0259.06015
[10] J. Jakubík: Radical mappings and radical classes of lattice ordered groups. Symposia Math. 21, Academic Press, New York-London, 1977, pp. 451-477.
[11] J. Jakubík: Radical classes of generalized Boolean algebras. Czechoslovak Math. J. 48 (1998), 253-268. · Zbl 0952.06017 · doi:10.1023/A:1022885303504
[12] J. Jakubík: Radical classes of complete lattice ordered groups. Math. Slovaca 49 (1999), 417-424. · Zbl 0948.06012
[13] J. Martinez: Torsion theory for lattice ordered groups. Czechoslovak Math. J. 25 (1975), 284-299. · Zbl 0321.06020
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