Recent content by dabien

My progress: For #1: I note that one equivalent condition for an extension to be Galois is that the number of automorphisms which fix the base field equals the degree of the extension. It is clear that G_1 \times G_2 is contained in the group of automorphisms of B_1 \otimes B_2 which fix F. Now...

Homework Statement Prove Suppose that B_1, B_2 are Galois extensions of F with respective Galois groups G_1, G_2, and that E=B_1 \otimes B_2 is a field. Then it is Galois over F with Galois group isomorphic to G_1 \times G_2. #2 Suppose that E is a Galois extension of F with Galois...

Homework Statement Let F be a field of characteristic p>0 and let E = F(a) where a is separable over F. Prove that E=F(a^p). Homework Equations The Attempt at a Solution I know that maybe show how mod F(a) = mod F(a^p) or something around there.