Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

A theorem on lattice ordered groups and its applications to the valuation theory

  • 37 Accesses

  • 1 Citations

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Birkhoff, G.: Lattice Theory. Rev. ed. Am. Math. Soc. Coll. Publ., Vol. XXV. New York 1948.

  2. [2]

    Jaffard, P.: Solution d'un problème de Krull. Bull. Sc. Math., 2e série,85, 127–135 (1961).

  3. [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. [4]

    Lorenzen, P.: Über halbgeordnete Gruppen. Math. Z.52, 483–526 (1949/50).

  5. [5]

    Müller, D.: Verbandsgruppen und Durchschnitte endlich vieler Bewertungsringe. Math. Z.77, 45–62 (1961).

  6. [6]

    Nakano, T.: A generalized valuation and its value groups. To appear in Comm. Math. Univ. St. Pauli.

  7. [7]

    Ribenboim, P.: Le théorème d'approximation pour les valuations de Krull. Math. Z.68, 1–18 (1957).

  8. [8]

    Schilling, O. F. G.: The theory of Valuations. Math. Surveys Nr. IV, New York 1950.

  9. [9]

    Yakabe, I.: On semi-valuations II. Memoirs of Fac. Sci. Kyûshû Univ.17, 10–28 (1963).

  10. [10]

    Yakabe, I.: Equivalence of the Krull-Müller-Jaffard theorem and Ribenboim's approximation theorem. (To appear.)

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nakano, T. A theorem on lattice ordered groups and its applications to the valuation theory. Math Z 83, 140–146 (1964). https://doi.org/10.1007/BF01111251

Download citation

Keywords

  • Valuation Theory