If alpha and beta are algebraic over K then alpha+beta and alpha*beta are algebraic over K

preview_player
Показать описание
Proving that if two elements are algebraic over a field then their sum and product are also algebraic.
Рекомендации по теме
Комментарии
Автор

Is it true that [K(α, β):K(α+β)] = 1, and therefore K(α, β) = K(α+β) ? I've found several examples that point in this direction, and no counterexample (it's false for the product αβ, though; consider ℚ(√2, √3) ≠ ℚ(√6))

Risuchan