Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T04:13:17.757Z Has data issue: false hasContentIssue false
  • English
  • Français

Torsion in K0 of unit-regular rings*

Published online by Cambridge University Press:  20 January 2009

K. R. Goodearl
K. R. Goodearl
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct examples of unit-regular rings R for which K0(R) has torsion, thus answering a longstanding open question in the negative. In fact, arbitrary countable torsion abelian groups are embedded in K0 of simple unit-regular algebras over arbitrary countable fields. In contrast, in all these examples K0(R) is strictly unperforated.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 2 , June 1995 , pp. 331 - 341
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Ara, P., Aleph-nought-continuous regular rings, J. Algebra 109 (1987), 115–126.Google Scholar
2.Blackadar, B., Rational C*-algebras and non-stable K-theory, Rocky Mountain J. Math. 20 (1990), 285–316.CrossRefGoogle Scholar
3.Chuang, C.-L. and Lee, P.-H., On regular subdirect products of simple artinian rings, Pacific J.Math. 142 (1990), 17–21.CrossRefGoogle Scholar
4.Goodearl, K. R., Von Neumann Regular Rings (Pitman, London, 1979); Second Ed. (Krieger, Melbourne, FL, 1991).Google Scholar
5.Goodearl, K. R., Metrically complete regular rings, Trans. Amer. Math. Soc. 272 (1982), 275–310.CrossRefGoogle Scholar
6.Goodearl, K. R., Directly finite aleph-nought-continuous regular rings, Pacific J. Math. 100 (1982), 105–122.CrossRefGoogle Scholar
7.Goodearl, K. R., Notes on a class of simple C*-algebras with real rank zero, Publ. Mat. (Barcelona) 36 (1992), 637–654.CrossRefGoogle Scholar
8.Goodearl, K. R. and Handelman, D., Rank functions and K 0 of regular rings, J. Pure Appl. Algebra 7 (1976), 195–216.CrossRefGoogle Scholar
9.Goodearl, K. R. and Menal, P., Stable range one for rings with many units, J. Pure Appl. Algebra 54 (1988), 261–287.CrossRefGoogle Scholar
10.Goodearl, K. R., Menal, P. and Moncasi, J., Free and residually artinian regular rings, J. Algebra 156 (1993), 407–432.Google Scholar
11.Handelman, D., Higgs, D. and Lawrence, J., Directed abelian groups, countably continuous rings, and Rickart C*-algebras, J. London Math. Soc. (2) 21 (1980), 193–202.Google Scholar
12.Menal, P. and Moncasi, J., On regular rings with stable range 2, J. Pure Appl. Algebra 24 (1982), 25–40.Google Scholar
13.O'Meara, K. C., Simple regular rings satisfying weak comparability, J. Algebra 141 (1991), 162–186.CrossRefGoogle Scholar
14.Tyukavkin, D. V., Regular rings with involution (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. 39, No. 3 (1984), 29–32; English transl.: Moscow Univ. Math. Bull. 39 (1984), 38–41.Google Scholar