ps1 - β,F X is irreducible over F α X 2 Let E and K be...

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Math 5c, Spring 10 Problem Set 1 Due Tuesday, April 4pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Field extensions, Algebraic closures, embeddings over a ±eld. § 13.1 4 § 13.2 12, 13 1. Let α and β be two algebraic elements over a ±eld F . Supose deg m α,f ( X ) and deg m β,F ( X ) are relatively prime. Show that m
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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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