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Order Characterization of the Complex Field
Published online by Cambridge University Press: 20 November 2018
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It is well known that the real number field can be characterized as an ordered field satisfied the “least upper bound” property.
Using the idea of n -ordered set, introduced in [3], and generalizing the notion of l.u.b. in a suitable way, it is possible to give a similar categorical definition of the complex field.
With these extended meanings, the main theorem of this paper (Theorem 7 in the text) is stated almost identically to the one for the real field. Any directly two-ordered field, in which the "supremum property" holds, is isomorphic to the complex field.
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- Copyright © Canadian Mathematical Society 1978