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$ K$-theoretic triviality for Rickart $ C\sp \ast$-algebras and $ \aleph\sb 0$-continuous regular rings


Author: Claudi Busqué
Journal: Proc. Amer. Math. Soc. 101 (1987), 24-28
MSC: Primary 46L80; Secondary 16A54, 19K99, 46L05
DOI: https://doi.org/10.1090/S0002-9939-1987-0897065-3
MathSciNet review: 897065
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Abstract: In this paper we prove that if $ R$ is a purely infinite Rickart $ {C^*}$-algebra or a purely infinite right $ {\aleph _0}$-continuous regular ring, then $ R$ is an infinite sum ring and hence $ {K_i}(R) = 0$ for all $ i$.


References [Enhancements On Off] (What's this?)

  • [1] P. Ara, Aleph-Nought continuous regular rings, J. Algebra (to appear). MR 898340 (88k:16010)
  • [2] S. K. Berberian, Baer*-rings, Grundlehren Math. Wiss., Band 195, Springer-Verlag, Berlin and New York, 1972. MR 0429975 (55:2983)
  • [3] K. R. Goodearl, Von Neumann regular rings, Pitman, London, 1979. MR 533669 (80e:16011)
  • [4] P. Menal and J. Moncasi, $ {K_1}$ of Von Neumann regular rings, J. Pure Appl. Algebra 33 (1984), 295-312. MR 761635 (86i:18014)
  • [5] -, Lifting units in self-injective rings and an index theory for Rickart $ {C^ *}$-algebras, Pacific J. Math. 126 (1987), 295-329. MR 869781 (88a:18020)
  • [6] J. B. Wagoner, Delooping classifying spaces in algebraic $ K$-theory, Topology 11 (1972), 349-370. MR 0354816 (50:7293)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0897065-3
Keywords: Purely infinite Rickart $ {C^*}$-algebra, purely infinite right $ {\aleph _0}$-continuous regular ring, infinite sum ring
Article copyright: © Copyright 1987 American Mathematical Society

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