Order Characterization of the Complex Field
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 313-318
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Novoa, Lino Gutierrez. Order Characterization of the Complex Field. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 313-318. doi: 10.4153/CMB-1978-054-6
@article{10_4153_CMB_1978_054_6,
author = {Novoa, Lino Gutierrez},
title = {Order {Characterization} of the {Complex} {Field}},
journal = {Canadian mathematical bulletin},
pages = {313--318},
year = {1978},
volume = {21},
number = {3},
doi = {10.4153/CMB-1978-054-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-054-6/}
}
[1] [1] Birkhoff, G., Lattice Theory, Rev. edition. Am. Math. Soc. Colloquium Publications. Vol. XXV (1948). Google Scholar
[2] [2] Cohen, and Ehrlich, , The Structure of the Real Number System. A. Van Nostrand Co., Princeton, New Jersey (1963). Google Scholar
[3] [3] Novoa, L. G., On n-ordered Sets and Order Completeness. Pacific Journal of Math., 15 (1965), 1337-1345. Google Scholar
[4] [4] Novoa, L. G., Ten axioms for three dimensional Euclidean geometry. Proc. of the Am. Math. Soc. Vol. 19, No. 1 (1968), 146-152. Google Scholar
Cité par Sources :