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A theorem on lattice ordered groups and its applications to the valuation theory. (English) Zbl 0121.27102


Keywords:

group theory
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References:

[1] Birkhoff, G.: Lattice Theory. Rev. ed. Am. Math. Soc. Coll. Publ., Vol. XXV. New York 1948. · Zbl 0033.10103
[2] Jaffard, P.: Solution d’un problème de Krull. Bull. Sc. Math., 2 e série,85, 127-135 (1961). · Zbl 0112.26702
[3] Krull, W.: Zur Theorie der Bewertungen mit nichtarchimedisch geordneter Wertgruppe und der nichtarchimedisch geordneten Körper. Colloque d’Algèbre Supérieure, Bruxelles 1956, 45-77.
[4] Lorenzen, P.: Über halbgeordnete Gruppen. Math. Z.52, 483-526 (1949/50). · Zbl 0035.29303
[5] Müller, D.: Verbandsgruppen und Durchschnitte endlich vieler Bewertungsringe. Math. Z.77, 45-62 (1961). · Zbl 0107.03101
[6] Nakano, T.: A generalized valuation and its value groups. To appear in Comm. Math. Univ. St. Pauli. · Zbl 0178.37101
[7] Ribenboim, P.: Le théorème d’approximation pour les valuations de Krull. Math. Z.68, 1-18 (1957). · Zbl 0102.03002
[8] Schilling, O. F. G.: The theory of Valuations. Math. Surveys Nr. IV, New York 1950. · Zbl 0037.30702
[9] Yakabe, I.: On semi-valuations II. Memoirs of Fac. Sci. Kyûshû Univ.17, 10-28 (1963). · Zbl 0168.40204
[10] Yakabe, I.: Equivalence of the Krull-Müller-Jaffard theorem and Ribenboim’s approximation theorem. (To appear.) · Zbl 0161.04201
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