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Homework Help: Being dense about an Algebra problem

  1. Feb 27, 2008 #1
    1. The problem statement, all variables and given/known data

    I need to show that, given [itex]F \subset E \subset K \subset L[/itex] (K/F is Galois but I don't know how important that is for the part of the problem I'm having trouble with) and a homomorphism [itex]\phi:E \rightarrow L[/itex] that's the identity on F, that [itex]\phi(E) \subset K[/itex].

    Edit: Yeah, if it wasn't obvious from the context, those are all supposed to be fields.

    2. Relevant equations

    3. The attempt at a solution

    So basically all the facts about this I've been able to come up with are that, being a field homomorphism, the map is injective, and that if I have [itex]\alpha \in E-F[/itex] with [itex]\phi(\alpha) \in L-K[/itex], the additive and multiplicative inverses of both [itex]\alpha[/itex] and [itex]\phi(\alpha)[/itex] have to be in E-F and L-K respectively. I have a feeling I'm overlooking something really simple, but I just can't get my brain out of the funk to figure out what it is.
    Last edited: Feb 27, 2008
  2. jcsd
  3. Feb 27, 2008 #2
    I guess I'll give this a quick bump before I go to bed. Maybe I was wrong about missing something simple and I actually do have to use the Galois condition.
  4. Feb 28, 2008 #3
    Yeah, I hate to keep doing this, but I still haven't figured it out. So I guess I'll try one more time. Sorry to be irritating.
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