An ordered field is a field F together with the order ( satisfying the conditions(i) a +b(a+cif b (c, and(ii) 0 (ab if 0 (a and 0 (b.Show that no order can be defined on the complex plane C such that C is an orderedfield. (Hint: Use the definition and the result in §1 Q4 for C.)

To prove: No order can be defined on complex plane ℂ, such that ℂ is an ordered field.

Answered: An ordered field is a field F together…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.1: The Field Of Real Numbers

Problem 22E: Prove that if F is an ordered field with F+ as its set of positive elements, then F+nen+, where e...

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An ordered field is a field F together with the order ( satisfying the conditions (i) a+b(a+cif b (c, and (ii) 0 ( ab if 0 ( a and 0 (b. Show that no order can be defined on the complex plane C such that C is an ordered field. (Hint: Use the definition and the result in §1 Q4 for C.)