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Lower K-theory, regular rings and operator algebras — A survey

Part of the Lecture Notes in Mathematics book series (LNM,volume 734)

Keywords

  • Rank Function
  • Direct Limit
  • Regular Ring
  • Modular Lattice
  • Matrix Ring

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§7. References

  1. S. Berberian, The regular ring of a finite AW*-algebra, Annals of Math. 65 (1957), 224–240.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. _____, NxN matrices over an AW*-algebra, Amer. J. Math. 80 (1958), 37–44.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. _____, The Regular ring of a finite Baer*-ring, J. Alg. 23 (1972), 35–65.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. _____, Baer*-Rings, Grundlehren, Band 195, Springer-Verlag, (1972), New York.

    Google Scholar 

  5. J. Cuntz, The structure of multiplication and addition in simple C*-algebras, Math. Scand. 40 (1977), 215–233.

    MathSciNet  MATH  Google Scholar 

  6. ___, Dimension functions on simple C*-algebras (to appear).

    Google Scholar 

  7. G. Ehrlich, Unit regular rings, Portugal Math. 27 (1968), 209–212.

    MathSciNet  MATH  Google Scholar 

  8. G. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Alq. 38 (1976), 29–44.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. K. Goodearl, Von Neumann Regular Rings, (to appear).

    Google Scholar 

  10. K. Goodearl and D. Handelman, KO and rank functions of regular rings, J. of Pure and Applied Algebra, 7 (1976), 195–216.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. K. Goodearl, D. Handelman, and J. Lawrence, xQ-continuous rings and affine functions on a Choquet simplex, (to appear).

    Google Scholar 

  12. I. Hafner, The regular ring and the maximal ring of quotients of a finite Baer*-ring, Michgan Math. J. 21 (1974), 153–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. D. Handelman, Perspectivity and cancellation in regular rings, J. Alg. 48 (1977), 1–16.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. _____, Coordination applied to finite Baer*-rings, Trans. Amer. Math. Soc. 235 (1978), 1–34.

    MathSciNet  MATH  Google Scholar 

  15. _____, Finite Rickart C*-algebras and their properties, Advances in Math. (to appear).

    Google Scholar 

  16. _____, Finite Rickart C*-algebras and their properties II, Advances in Math. (to appear).

    Google Scholar 

  17. _____, Stable range in AW*-algebras, Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  18. _____, KO of von Neumann and AF C*-algebras, Oxford Quart. J. (to appear).

    Google Scholar 

  19. D. Handelman, D. Higgs and J. Lawrence, Directed abelian groups, X0-continuous rings and Rickart C*-algebras, (to appear).

    Google Scholar 

  20. D. Handelman and J. Lawrence, Finite Rickart C*-algebras, Bull. Amer. Math. Soc. 84 (1978), 157–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. I. Kaplansky, Projections in Banach algebras, Annals of Math. 53 (1951), 235–249.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. _____, Any orthocomplemented complete modular lattice is a continuous geometry, Annals of Math. 61 (1955), 524–541.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. _____, Rings of Operators, Benjamin (1968), New York.

    MATH  Google Scholar 

  24. F. Murray and J. von Neumann, On rings of operators, Annals of Math. 37 (1936), 116–165.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. 22 (1936), 707–713.

    CrossRef  MATH  Google Scholar 

  26. E. Pyle, The regular ring and the maximal ring of quotients of a finite Baer*-ring, Trans. Amer. Math. Soc. 203 (1975), 201–213.

    MathSciNet  MATH  Google Scholar 

  27. J.-E. Roos, Sur l'anneau maximal de fractions des AW*-algèbres et des anneaux de Baer, C. R. Acad. Sci. Paris Ser A-B, 266 (1968), A120–A133.

    MATH  Google Scholar 

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Handelman, D., Lawrence, J. (1979). Lower K-theory, regular rings and operator algebras — A survey. In: Handelman, D., Lawrence, J. (eds) Ring Theory Waterloo 1978 Proceedings, University of Waterloo, Canada, 12–16 June, 1978. Lecture Notes in Mathematics, vol 734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103158

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  • DOI: https://doi.org/10.1007/BFb0103158

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