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Completions of Rank Rings

Published online by Cambridge University Press:  20 November 2018

David Handelman
David Handelman*
Affiliation:
Dept. of Mathematics, Mcgill UniversityP.O. Box 6070, Stn. A Montreal, P.Q. Canada H3C 3G1
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In this note, we prove three results on regular rings possessing a rank function: (a) the completion of a *-regular rank ring is a regular Baer *-ring; (b) (a) is used to construct regular Baer * factors of type IIf with centre any complex subfield closed under conjugation; (c) the units of a unit-regular rank ring form a dense topological subgroup of the units of the completion.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 199 - 205
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Ehrlich, G., Unit-regular rings, Portugal. Math. 27 (1968) 209-212.Google Scholar
2. Goodearl, K. R., Simple regular rings and rank functions. Math. Ann. 214 (1975) 267-287.Google Scholar
3. Goodearland, K. R. Handelman, D., Simple self-injective rings, Comm. Algebra 3 (9) (1975) 797-834.Google Scholar
4. Halperin, I., Complemented modular lattices, p. 51-64 of Lattice Theory, G. Birkhofl, Editor; AMS Publications (1961).Google Scholar
5. Halperin, I., Regular rank rings, Canad. J. Math. 17 (1965) 709-719.Google Scholar
6. Handelman, D., Perspectivity and cancellation in regular rings, J. of Algebra (to appear).Google Scholar
7. Handelman, D., K1 of noncommutative von Neumann regular rings, J. of Pure and App. Algebra 8 (1976) 105-118,Google Scholar
8. Henriksen, M., On a class of regular rings that are elementary divisor rings, Arch. Math. 34 (1973) 133-141.Google Scholar
9. Kaplansky, I., Any orthocomplemented complete modular lattice is a continuous geometry, Ann. Math. 15 (1955) 650-685.Google Scholar
10. Kaplansky, I., Rings of Operators, Benjamin (1968) New York.Google Scholar
11. von Neumann, J., Continuous Geometry, Princeton 25 (1960).Google Scholar
12. Utumi, Y., On continuous regular rings and semi-simple self-injective rings, Canad. J. Math. 12 (1960) 597-605.Google Scholar