On totally ordered groups, and K0

  • George A. Elliott
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 734)


Some results are described concerning totally ordered abelian groups. These can be interpreted, via the functor K0, as classification results for certain noncommutative rings, for which K0 as an ordered group happens to be a complete invariant.


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  1. 1.
    H. Behncke and H. Leptin, Classification of C*-algebras with a finite dual, J. Functional Analysis 16 (1974), 241–257.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234.MathSciNetzbMATHGoogle Scholar
  3. 3.
    O. Bratteli and G.A. Elliott, Structure spaces of approximately finite-dimensional C*-algebras II, J. Functional Analysis (to appear).Google Scholar
  4. 4.
    P. Conrad, The structure of a lattice-ordered group with a finite number of disjoint elements, Michigan Math. J. 7 (1960), 171–180.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    P. Conrad, Some structure theorems for lattice-ordered groups, Trans. Amer. Math. Soc. 99 (1961), 212–240.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    P. Conrad, J. Harvey and C. Holland, The Hahn embedding theorem for abelian lattice-ordered groups, Trans. Amer. Math. Soc. 108 (1963), 143–169.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. Cuntz, Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173–185.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    J. Dixmier, On some C*-algebras considered by Glimm, J. Functional Analysis 1 (1967), 182–203.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    R.G. Douglas, On the C*-algebra of a one-parameter semigroup of isometries, Acta Math. 128 (1972), 143–151.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    G.A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29–44.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    G.A. Elliott, Automorphisms determined by multipliers on ideals of a C*-algebra, J. Functional Analysis 23 (1976), 1–10.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    J. Erdös, On the structure of ordered real vector spaces, Publ. Math. Debrecen 4 (1956), 334–343.MathSciNetGoogle Scholar
  13. 13.
    L. Fuchs, Riesz groups, Ann. Scuola Norm. Pisa III 19 (1965), 1–34.MathSciNetzbMATHGoogle Scholar
  14. 14.
    J. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    O. Hölder, Die Axiome der Quantität und die Lehre vom Mass, Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math. Phys. Cl. 53 (1901), 1–64.zbMATHGoogle Scholar
  16. 16.
    P. Ribenboim, Sur les groupes totalement ordonnés et l'arithmétique des anneaux de valuation, Summa Brasil. Math. 4 (1958), 1–64.MathSciNetzbMATHGoogle Scholar
  17. 17.
    J.R. Teller, On partially ordered groups satisfying the Riesz interpolation property, Proc. Amer. Math. Soc. 16 (1965), 1392–1400.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • George A. Elliott
    • 1
  1. 1.Mathematics InstituteUniversity of CopenhagenDenmark

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