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Generalized Dedekind completion of a lattice ordered group. (English) Zbl 0391.06013


MSC:

06F15 Ordered groups
06B23 Complete lattices, completions
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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References:

[1] G. Birkhoff: Lattice theory. third edition, Providence 1967. · Zbl 0153.02501
[2] F. Conrad: Lattice ordered groups. Tulane University 1970. · Zbl 0258.06011
[3] [31 F. Conrad: Epiarchimedean lattice ordered groups. Czech. Math. J. 24 (1974), 192-218. · Zbl 0319.06009
[4] F. Conrad: Changing the scalar multiplication on a vector lattice. J. Austral. Math. Soc. 20(1975), 33 - 347. · Zbl 0317.06014
[5] Л. Фукс: Частично упорядоченные алгебраические системы. Москва, 1965. · Zbl 1099.01519
[6] J. Jakubík: Die Dedekindschen Schnitte im direkten Produkt von halbgeordneten Gruppen. Matem. fyz. casop. 16 (1966), 329-336. · Zbl 0154.02602
[7] J. Jakubík: Distributivity in lattice ordered groups. Czech. Math. J. 22 (1972), 108-125. · Zbl 0244.06014
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[9] J. Jakubík: Conditionally a-complete sublattices of a distributive lattice. Algebra univ. 2 (1972), 255-261. · Zbl 0258.06008
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[11] J. Jakubík: Radical classes and radical mappings of lattice ordered groups. Symposia Math. 31 (1977), 451-477.
[12] J. Martinez: Pairwise splitting lattice ordered groups. Czech. Math. J. 27(1977), 545-551. · Zbl 0378.06009
[13] Г. Я. Роткович: О дизъюнктно полных архимедовых полуупорядоченных группах. Czech. Math. J. 27 (1977), 523-527. · Zbl 1170.01341
[14] Б. Z. Вулих: Введение в теорию полуупорядоченных пространств. Москва 1961. · Zbl 1160.68305
[15] E. C. Weinberg: Completely distributive lattice ordered groups. Pacif. J. Math. 12 (1962), 1131-1148. · Zbl 0111.24301
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