Rings and Fields · Algebra
Field Extensions
A field extension K of F is a bigger field containing F. The degree is the dimension of K as an F-vector space — the language for proving impossibility of classical constructions.
WHAT STUDENTS WILL LEARN
✓Define field extensions and the degree [K:F]
✓Construct simple extensions F(α)
✓Apply the tower law: [K:F] = [K:E][E:F]
✓Find the degree of √2 + √3 over ℚ
BUILDS ON
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