Unformatted text preview: β,F ( X ) is irreducible over F ( α )[ X ]. 2. Let E and K be extensions of a ±eld F such that E and K are both sub±elds of some ±eld J . Let τ be an embedding of J into some ±eld L over F . Show that τ ( EK ) = τ ( E ) τ ( K ). Also show that τ ( E ∩ K ) = τ ( E ) ∩ τ ( K ). 1...
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- Spring '09
- Algebra, Prime number, Rational number, Foote, deg mα,f, Algebraic closures