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Von Neumann regular rings: connections with functional analysis
Author(s):
K. R.
Goodearl
Journal:
Bull. Amer. Math. Soc.
4
(1981),
125-134.
MSC (1980):
Primary 16A30, 06C20, 46L10, 46L05, 46A55
MathSciNet review:
598680
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Additional information
References:
- 1.
- R. Baer, Linear algebra and projective geometry, Academic Press, New York, 1952. MR 52795
- 2.
- S. K. Berberian, The regular ring of a finite AW*-algebra, Ann. of Math. (2) 65 (1957), 224-240. MR 84743
- 3.
- S. K. Berberian, N × N matrices over an A W*-algebra, Amer. J. Math. 80 (1958), 37-44. MR 98329
- 4.
- S. K. Berberian, Baer *-rings, Die Grundlehren der Math. Wissenschaften, Band 195, Springer-Verlag, Berlin and New York, 1972. MR 429975
- 5.
- G. Birkhoff, Combinatorial relations in projective geometries, Ann. of Math. (2) 36 (1935), 743-748. MR 1503250
- 6.
- O. Bratteli, Inductive limits of finite-dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 312282
- 7.
- E. G. Effros, D. E. Handelman, and C.-L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407. MR 564479
- 8.
- G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29-44. MR 397420
- 9.
- K. R. Goodearl, Simple regular rings and rank functions, Math. Ann. 214 (1975), 267-287. MR 409541
- 10.
- K. R. Goodearl, Completions of regular rings, Math. Ann. 220 (1976), 229-252. MR 409542
- 11.
- K. R. Goodearl, Completions of regular rings. II, Pacific J. Math. 72 (1977), 423-459. MR 476800
- 12.
- K. R. Goodearl, Von Neumann regular rings, Pitman, London, 1979. MR 533669
- 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). MR 571998
- 14.
- I. Halperin, Regular rank rings, Canad. J. Math. 17 (1965), 709-719. MR 191926
- 15.
- D. Handelman, Finite Rickart C*-algebras and their properties, Studies in Analysis, Advances in Math. Supplementary Studies, Vol. 4, 1979, pp. 171-196. MR 546806
- 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. MR 575375
- 17.
- I. Kaplansky, Projections in Banach algebras, Ann. of Math. (2) 53 (1951), 235-249. MR 42067
- 18.
- K. Menger, New foundations of projective and affine geometry, Ann. of Math. (2) 37 (1936), 456-482. MR 1503293
- 19.
- F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229. MR 1503275
- 20.
- C. E. Rickart, Banach algebras with an adjoint operation, Ann. of Math. (2) 47 (1946), 528-550. MR 17474
- 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.
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Additional Information:
DOI:
10.1090/S0273-0979-1981-14865-5
PII:
S 0273-0979(1981)14865-5
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