Results 1 to 2 of 2

Math Help - Separable extension..

  1. #1
    ynj
    ynj is offline
    Senior Member
    Joined
    Jul 2009
    Posts
    254

    Separable extension..

    Let F be a field with characteristic 0. Eis a finite field extension of F. Prove that Eis a separable extension...
    I know that for an \alpha, if the minimal polynomial f(x) splits on E, then f(x)is separable on E. But why f(x)splits?
    Last edited by ynj; September 2nd 2009 at 11:24 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by ynj View Post
    Let F be a field with characteristic 0. Eis a finite field extension of F. Prove that Eis a separable extension...
    I know that for an \alpha, if the minimal polynomial f(x) splits on E, then f(x)is separable on E. But why f(x)splits?
    You are misunderstanding what "seperable" means. An irreducible polynomial f(x)\in F[x] is "seperable" over F iff f(x) has no repeated roots in its splitting field. Now \alpha \in E is seperable iff the minimal polynomial for \alpha is seperable over F. This does not mean that the miniminal polynomial must split over E.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. extension
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 28th 2011, 08:07 AM
  2. Prove that an extension is a continuous extension
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: August 12th 2011, 06:50 AM
  3. HNN extension
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 23rd 2010, 07:46 AM
  4. Extension
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 14th 2010, 06:40 AM
  5. separable extension and separable polynomial
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: August 30th 2009, 08:22 PM

Search Tags


/mathhelpforum @mathhelpforum