Vol. 33, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On normed rings with monotone multiplication

Silvio Aurora

Vol. 33 (1970), No. 1, 15–20

It is shown that if a normed division ring has a norm which is “multiplication monotone” in the sense that N(x) < N(x) and N(y) < N(y) imply N(xy) N(xy), and if the norm is “commutative” in the sense that N(xy) = N(yx) for all x and y, then the topology of that ring is given by an absolute value. A consequence of this result is that if the norm of a connected normed ring with unity is multiplication monotone and commutative then the ring is embeddable in the system of quaternions.

Mathematical Subject Classification
Primary: 46.50
Received: 9 April 1969
Published: 1 April 1970
Silvio Aurora