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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2025 • Question 3

Question

Math 6320 • Algebra II Summer 2025 • Question 3

Let \(F\) and \(E = F(\alpha )\) be two fields such that \([E:F]\) is odd. Prove that \(E = F(\alpha ^2)\).

Raw LaTeX

Let \(F\) and \(E = F(\alpha)\) be two fields such that \([E:F]\) is odd. Prove
that \(E = F(\alpha^2)\).

Topic Tags

Field Extensions