Being dense about an Algebra problem

  • Thread starter Mystic998
  • Start date
  • #1
206
0

Homework Statement



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.

Homework Equations




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:

Answers and Replies

  • #2
206
0
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.
 
  • #3
206
0
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.
 

Related Threads on Being dense about an Algebra problem

Replies
1
Views
772
Replies
2
Views
2K
Replies
2
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
2
Views
832
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
2K
Top