Bulletin (New Series) of the American Mathematical Society

Von Neumann regular rings: connections with functional analysis

K. R. Goodearl

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.) Volume 4, Number 2 (1981), 125-134.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.bams/1183547995

Mathematical Reviews number (MathSciNet)
MR598680

Zentralblatt MATH identifier
0467.16020

Subjects
Primary: 16A30 06C20: Complemented modular lattices, continuous geometries 46L10: General theory of von Neumann algebras 46L05: General theory of $C^*$-algebras 46A55: Convex sets in topological linear spaces; Choquet theory [See also 52A07]

Citation

Goodearl, K. R. Von Neumann regular rings: connections with functional analysis. Bulletin (New Series) of the American Mathematical Society 4 (1981), no. 2, 125--134. http://projecteuclid.org/euclid.bams/1183547995.


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References

  • 1. R. Baer, Linear algebra and projective geometry, Academic Press, New York, 1952.
  • 2. S. K. Berberian, The regular ring of a finite AW*-algebra, Ann. of Math. (2) 65 (1957), 224-240.
  • 3. S. K. Berberian, N × N matrices over an A W*-algebra, Amer. J. Math. 80 (1958), 37-44.
  • 4. S. K. Berberian, Baer *-rings, Die Grundlehren der Math. Wissenschaften, Band 195, Springer-Verlag, Berlin and New York, 1972.
  • 5. G. Birkhoff, Combinatorial relations in projective geometries, Ann. of Math. (2) 36 (1935), 743-748.
  • 6. O. Bratteli, Inductive limits of finite-dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234.
  • 7. E. G. Effros, D. E. Handelman, and C.-L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407.
  • 8. G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29-44.
  • 9. K. R. Goodearl, Simple regular rings and rank functions, Math. Ann. 214 (1975), 267-287.
  • 10. K. R. Goodearl, Completions of regular rings, Math. Ann. 220 (1976), 229-252.
  • 11. K. R. Goodearl, Completions of regular rings. II, Pacific J. Math. 72 (1977), 423-459.
  • 12. K. R. Goodearl, Von Neumann regular rings, Pitman, London, 1979.
  • 13. K. R. Goodearl, D. E. Handelman, and J. W. Lawrence, Affine representations of Grothendieck groups and applications to Rickart $C\sp{*} $-algebras and $\aleph \sb{0}$-continuous regular rings, Mem. Amer. Math. Soc. No. 234 (1980).
  • 14. I. Halperin, Regular rank rings, Canad. J. Math. 17 (1965), 709-719.
  • 15. D. Handelman, Finite Rickart C*-algebras and their properties, Studies in Analysis, Advances in Math. Supplementary Studies, Vol. 4, 1979, pp. 171-196.
  • 16. D. Higgs, and J. Lawrence, Directed abelian groups, $C\sp{*} $-continuous rings, and Rickart C*-algebras, J. London Math. Soc. 21 (1980), 193-202.
  • 17. I. Kaplansky, Projections in Banach algebras, Ann. of Math. (2) 53 (1951), 235-249.
  • 18. K. Menger, New foundations of projective and affine geometry, Ann. of Math. (2) 37 (1936), 456-482.
  • 19. F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229.
  • 20. C. E. Rickart, Banach algebras with an adjoint operation, Ann. of Math. (2) 47 (1946), 528-550.
  • 21. O. Veblen and J. W. Young, Projective geometry. Vol. I, Ginn and Co., Boston, 1910.
  • 22. J. von Neumann, Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren, Math. Ann. 102 (1929), 370-427.
  • 23. J. von Neumann, Continuous geometry, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 92-100.
  • 24. J. von Neumann, On regular rings, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 707-713.
  • 25. J. von Neumann. Lectures on continuous geometry (Planographed notes, Institute for Advanced Study), Edwards Brothers, Ann Arbor, Michigan, 1937.