9. Recall from Section 2 that a field F is called an ordered field if there exists a subset P of F (called the set of positive elements) such that (a) sums and products of elements in P are in P, and (b) for each element a in F, one and only one of the following possibilities holds: a e P, a = 0, – a e P. Prove that the field of complex numbers is not an ordered field.

9. Recall from Section 2 that a field F is called an ordered field if there exists a subset P of F (called the set of positive elements) such that (a) sums and products of elements in P are in P, and (b) for each element a in F, one and only one of the following possibilities holds: a e P, a = 0, – a e P. Prove that the field of complex numbers is not an ordered field.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 25E: Suppose S is a subset of an field F that contains at least two elements and satisfies both of the...

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