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On normed rings with
monotone multiplication
Silvio Aurora |
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Vol. 33 (1970), No. 1, 15–20
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Abstract |
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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(x′y′), 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
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Milestones
Received: 9 April 1969
Published: 1 April 1970
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Authors |
| Silvio Aurora | |
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