Mathematics · Abstract Algebra
Which of the following statements is false regarding field extensions?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Every finite extension of a field is an algebraic extension.
- 2The top field of a finite tower of finite extensions of fields is a finite extension of the bottom field.
- 3The field of real numbers ℝ is algebraically closed.✓
- 4The field of complex numbers ℂ is algebraically closed in ℂ(x), where x is an indeterminate.
Correct answer
The field of real numbers ℝ is algebraically closed.
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