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Order Characterization of the Complex Field
Canadian Mathematical Bulletin, 1978It 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 ...
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On the Theory of Cuts in Ordered Fields
Siberian Mathematical Journal, 2001The author studies and classifies cuts in ordered fields and proves a criterion of isomorphism for real closed ordered fields.
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1998
Let υ, η, ... be any algebraic integers whose domain of rationality is the field k l of degree m; then the set of all polynomials in ϑ, η, ... with rational integer coefficients is called an order 2. Addition, subtraction and multiplication of two numbers in an order produce again numbers in the order.
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Let υ, η, ... be any algebraic integers whose domain of rationality is the field k l of degree m; then the set of all polynomials in ϑ, η, ... with rational integer coefficients is called an order 2. Addition, subtraction and multiplication of two numbers in an order produce again numbers in the order.
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Ordered Fields, Real Closed Fields
1998The first three sections of this chapter briefly review Artin-Schreier theory: ordered fields, real fields, real closed fields and the real closure of an ordered field. The fourth section is devoted to the Tarski-Seidenberg principle, which is an essential tool for real algebraic geometry.
Jacek Bochnak +2 more
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