Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Rings and partly ordered systems

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

References

  1. [1]

    Aubert, K.E.: Über Bewerungen mit halbgeordneter Wertgruppe. Math. Ann.127, 8–14 (1954).

  2. [1a]

    Benado, M.: Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier. II. Czechosl. Math. J.5, 308–344 (1955).

  3. [2]

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

  4. [3]

    Dresher, M., andO. Ore: Theory of multigroups. Am. J. Math.60, 705–733 (1938).

  5. [4]

    Eaton, J.E., andO. Ore: Remarks on multigroups. Am. J. Math.62, 67–71 (1940).

  6. [4a]

    Ellis, D.: Notes on the foundations of lattice theory. II. Arch. Math.4, 257–260 (1953).

  7. [5]

    Fuchs, L.: The generalization of the valuation theory. Duke Math. J.18, 19–26 (1951).

  8. [6]

    —: Partially ordered algebraic systems. Internat. series of monographs, vol. 28. Oxford-London-New York-Paris: Pergamon-Press 1963.

  9. [7]

    Jaffard, P.: Théorie des filets dans les groups réticulés. C. R. Acad. Sci. Paris230, 1024–1025 (1950).

  10. [8]

    —: Corps demi-valués. C. R. Acad. Sci. Paris231, 1401–1403 (1950).

  11. [9]

    Lorenz, K.: Über Strukturverbände von Verbandsgruppen. Acta Math. Acad. Sci. Hung.13, 55–67 (1962).

  12. [10]

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

  13. [11]

    —: Die Erweiterung halbgeordneter Gruppen zu Verbandsgruppen. Math. Z.58, 15–24 (1953).

  14. [12]

    Nagata, M.: Local rings. Interscience Tracts, No. 13. New York and London: Interscience Publishers 1962.

  15. [13]

    Prenowitz, W.: Projective geometries as multigroups Am. J. Math.65, 235–256 (1943).

  16. [14]

    —: Descriptive geometries as multigroups. Trans. Am. Math. Soc.59, 333–380 (1946).

  17. [15]

    —: Total lattices of convex sets and of linear spaces. Ann. Math.49, 659–688 (1948).

  18. [16]

    — Spherical geometries and multigroups. Canadian J. Math.2, 100–119 (1950).

  19. [17]

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

  20. [18]

    Sik, F.: Über subdirekte Summen geordneter Gruppen. Czechosl. Math. J.10, 400–424 (1960).

  21. [19]

    Wyler, O.: Clans. Compositio Math.17, 172–189 (1966).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nakano, T. Rings and partly ordered systems. Math Z 99, 355–376 (1967). https://doi.org/10.1007/BF01111015

Download citation