Conrad, Paul; Harvey, John; Holland, Charles The Hahn embedding theorem for abelian lattice-ordered groups. (English) Zbl 0126.05002 Trans. Am. Math. Soc. 108, 143-169 (1963). Reviewer: Jan Jakubík (Košice) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 61 Documents MSC: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces Keywords:Hahn embedding theorem; abelian lattice-ordered groups Citations:Zbl 0021.38703; JFM 38.0501.01; Zbl 0051.01303; Zbl 0065.00803; Zbl 0099.25401 PDFBibTeX XMLCite \textit{P. Conrad} et al., Trans. Am. Math. Soc. 108, 143--169 (1963; Zbl 0126.05002) Full Text: DOI References: [1] Bernhard Banaschewski, Totalgeordnete Moduln, Arch. Math. 7 (1957), 430 – 440 (German). · Zbl 0208.03702 · doi:10.1007/BF01899022 [2] Garrett Birkhoff, Lattice, ordered groups, Ann. of Math. (2) 43 (1942), 298 – 331. · Zbl 0060.05808 · doi:10.2307/1968871 [3] -, Lattice theory, rev. ed., Amer. Math. Soc. Colloq. Publ. Vol. 25, Amer. Math. Soc., Providence, R. I., 1948. · Zbl 0033.10103 [4] A. H. Clifford, Note on Hahn’s theorem on ordered abelian groups, Proc. Amer. Math. Soc. 5 (1954), 860 – 863. · Zbl 0056.25503 [5] Paul F. Conrad, Embedding theorems for abelian groups with valuations, Amer. J. Math. 75 (1953), 1 – 29. · Zbl 0050.02303 · doi:10.2307/2372611 [6] Paul Conrad, Some structure theorems for lattice-ordered groups, Trans. Amer. Math. Soc. 99 (1961), 212 – 240. · Zbl 0099.25401 [7] K. A. H. Gravett, Valued linear spaces, Quart. J. Math., Oxford Ser. (2) 6 (1955), 309 – 315. · Zbl 0067.26605 · doi:10.1093/qmath/6.1.309 [8] K. A. H. Gravett, ”Netrics” of sets and linear spaces, Quart. J. Math. Oxford Ser. (2) 10 (1959), 9 – 16. · Zbl 0214.26504 · doi:10.1093/qmath/10.1.9 [9] H. Hahn, Über die nichtarchimedischen Grössensysteme, S.-B. Kaiserlichen Akad. Wiss. Math. Nat. Kl. IIa, 116 (1907), 601-655. · JFM 38.0501.01 [10] P. Jaffard, Contribution a l’étude des groupes ordonées, J. Math. Pure Appl. 32 (1953), 203-280. · Zbl 0051.01303 [11] Paul Jaffard, Extension des groupes réticulés et applications, Publ. Sci. Univ. Alger. Sér. A. 1 (1954), 197 – 222 (1955) (French). [12] Paul Jaffard, Sur le spectre d’un groupe réticulé et l’unicité des réalisations irréductibles, Ann. Univ. Lyon. Sect. A (3) 22 (1959), 43 – 47 (French). · Zbl 0103.01601 [13] P. Lorenzen, Abstrakte Begründung der multiplikativen Idealtheorie, Math. Z. 45 (1939), 533 – 553 (German). · JFM 65.0101.01 · doi:10.1007/BF01580299 [14] -, Über halbgeordnete Gruppen, Math. Z. 52 (1949), 484-526. · Zbl 0035.29303 [15] Tadasi Nakayama, Note on lattice-ordered groups, Proc. Imp. Acad. Tokyo 18 (1942), 1 – 4. · Zbl 0063.05897 [16] P. Ribenboim, Conjonction d’ordres dans les groupes abéliens ordonnés, An. Acad. Brasil Ci. 29 (1957), 201 – 224 (French). · Zbl 0086.25202 [17] -, Un théorème de réalisation de groupes réticulés, Pacific J. Math. 10 (1960), 305-308. · Zbl 0104.02602 [18] František Šik, Über Summen einfach geordneter Gruppen, Czechoslovak Math. J. 8(83) (1958), 22 – 53 (German, with Russian summary). [19] František Šik, Über subdirekte Summen geordneter Gruppen, Czechoslovak Math. J. 10 (85) (1960), 400 – 424 (German, with Russian summary). · Zbl 0102.26501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.