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The Isomorphism of Certain Continuous Rings

Published online by Cambridge University Press:  20 November 2018

Brian P. Dawkins  and
Israel Halperin
Brian P. Dawkins
Affiliation:
Carleton University and University of Toronto
Israel Halperin
Affiliation:
Carleton University and University of Toronto
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In this paper we shall prove the following two theorems (the terminology is explained in § 2 below; all rings are assumed to be associative).

THEOREM 1. Suppose that is a division ring of finite order m over its centre Z and let μ(m) denote the factor sequence 1, m, m2, … , mn, … . Then the rings μ(w) and Zμ(m) are isomorphic.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1333 - 1344
Copyright
Copyright © Canadian Mathematical Society 1966

References

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3. von Neumann, J., Examples of continuous geometries, Proc. Nat. Acad. Sci., U.S.A., 22 (1936), 101–108.Google Scholar
4. von Neumann, J., Independence of F∞ from the sequence v (review by I. Halperin of unpublished manuscript of J. von Neumann), Collected Works of John von Neumann, Vol. IV (London, 1962).Google Scholar