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Von Neumann's Manuscript on Inductive Limits of Regular Rings

Published online by Cambridge University Press:  20 November 2018

Israel Halperin
Israel Halperin*
Affiliation:
University of Toronto
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It is now known (3) that if is a regular rank ring, then the rank function can be extended to the matrix ring in such a way that R(a) = R(a ꕕ n) ; here, a is an arbitrary element of is the n × n diagonal matrix with a for each entry on the diagonal, and R denotes rank in and also in . It is also known (2) that every regular rank ring has a rankmetric completion which is again a regular rank ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 477 - 483
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Dawkins, Brian P. and Halperin, Israel, The isomorphism of certain continuous rings, Can. J. Math., 18 (1966), 1333–1344.Google Scholar
2. Halperin, Israel, Regular rank rings, Can. J. Math., 17 (1965), 709–719.Google Scholar
3. Halperin, Israel, Extension of the rank function, Studia Math. 27 (1966), 325–335.Google Scholar
4. von Neumann, John, Continuous geometry (Princeton, 1960).Google Scholar
5. von Neumann, John, Independence of F-from the sequencey, unpublished manuscript written in 1936–37 review by I. Halperin in Vol. IV of the Collected Works of John von Neumann Pergamon, (1962).Google Scholar