Fields and field extensions (intro)
General · Mathematics
Study notes
Q: What is [ℚ(√2):ℚ]? Describe ℚ(√2,√3). √2: minimal polynomial x²-2 (degree 2!): [ℚ(√2):ℚ] = 2. Basis: {1, √2}! ℚ(√2,√3): adjoin both: basis {1,√2,√3,√6}: degree 4! Tower: ℚ ⊂ ℚ(√2) ⊂ ℚ(√2,√3): 2×2 = 4 ✓!