Algebra and Logic

, Volume 41, Issue 6, pp 374–390 | Cite as

Multi-Valued Fields. II

  • Yu. L. Ershov
Article

Abstract

The main model-theoretic results on multi-valued fields with near Boolean families of valuation rings obtained in [1, Ch. 4, Sec. 4.6] are generalized along two lines: we weaken the restriction on being absolutely unramified to a condition of being finite for an absolute ramification index, and we combine, through context, Theorems 4.6.2 and 4.6.4 (4.6.3 and 4.6.5).

multi-valued field Boolean family of valuation rings absolute ramification index 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Yu. L. Ershov, Multi-Valued Fields [in Russian], Nauch. Kniga, Novosibirsk (2000).Google Scholar
  2. 2.
    Yu. L. Ershov, “Multiply valued fields,” Usp. Mat. Nauk, 37, No. 3, 55-93 (1982).Google Scholar
  3. 3.
    R. Balbes and Ph. Dwinger, Distributive Lattices, Missouri Press, Columbia, MI (1974).Google Scholar
  4. 4.
    C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam (1973).Google Scholar
  5. 5.
    Yu. L. Ershov, “Immediate extensions of Prüfer rings,” Algebra Logika, 40, No. 3, 262-289 (2001).Google Scholar
  6. 6.
    A. Prestel and J. Schmid, “Decidability of the rings of real algebraic and p-adic algebraic integers,” J. Reine Ang. Math., 414, 141-148 (1991).Google Scholar
  7. 7.
    L. Darnière, “Nonsingular Hasse principle for rings,” J. Reine Ang. Math., 529, 75-100 (2000).Google Scholar
  8. 8.
    B. Green, F. Pop, and P. Roquette, “On Rumely's local-global principle,” Jahr. Deutsche Math. Ver., 97, No. 2, 43-74 (1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Yu. L. Ershov
    • 1
  1. 1.NovosibirskRussia

Personalised recommendations