Advertisement

Decidable Modules

  • Martin Ziegler
Part of the NATO ASI Series book series (ASIC, volume 496)

Abstract

Let k be a recursive field with effective factorization of polynomials. Mike Prest conjectured in [11]:

A quiver is tame iff the elementary theory of all k-representations is decidable.

Keywords

Abelian Group Direct Summand Dimension Vector Directed Cycle Quantifier Elimination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Baur, Elimination of quantifiers for modules, Israel J. Math. 25 (1976), 64–70.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    W. Baur, On the elementary theory of quadruples of vector spaces, Ann. Math. Logic 19 (1980), 243–262.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    P. Donovan and M.R. Preislich, The representation theory of finite graphs and associated algebras, Carleton Mathematical Lecture Notes, 5, Carleton University, Ottawa, Ont., 1973.zbMATHGoogle Scholar
  4. 4.
    P.C. Eklof and E.R. Fisher, The elementary theory of abelian groups, Ann. Math. Logic 4 (1972), 115–171.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    P. Gabriel, Unzerlegbare Darstellungen I, Manuscripta Math. 6 (1972), 71–103.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    P. Gabriel, Indecomposable representations II, Symposia Math., XI, Academic Press, London, 1973, pp. 81–104.Google Scholar
  7. 7.
    Gunter Geisler, Zur Modelltheorie von Moduln, Dissertation, Freiburg, 1995.Google Scholar
  8. 8.
    I.M. Gelfand and V.A. Ponomarev. Problems of linear algebra and classification of quadruples of subspaces in a finite-dimensional vector space, Hilbert Space Operators and Operator Algebras, Colloq. Math. Soc. Janos Bolyai, 5, North Holland, Amsterdam, 1972, pp. 163–237.Google Scholar
  9. 9.
    L. Kronecker, Algebraische Reduktion der Scharen bilinearer Formen. Sitz. ber. der Akad. Berlin, 1890, pp. 1225–1237.Google Scholar
  10. 10.
    F. Okoh, Indecomposable pure-injective modules over hereditary Artin algebras of tame type, Comm. Algebra 8 (1980), 1939–1941.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    M. Prest, Tame categories of modules and decidability, preprint, 1985.Google Scholar
  12. 12.
    M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, 130, Cambridge University Press, Cambridge-New York, 1988.zbMATHCrossRefGoogle Scholar
  13. 13.
    Wanda Szmielew, Elementary properties of abelian groups, Fund. Math. 41 (1954), 203–271.MathSciNetGoogle Scholar
  14. 14.
    Martin Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149–213.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    B. Zimmermann-Huisgen and W. Zimmermann, Algebraic compact rings and modules, Math. Z. 161 (1978), 81–93.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Martin Ziegler
    • 1
  1. 1.Mathematisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburgGermany

Personalised recommendations