Results 1 to 1 of 1

Thread: easy simple extensions question

  1. #1
    Jan 2011

    easy simple extensions question

    For a field K, we always have K(x)\subseteq K(x,y). If y\in K(x), it seems to be true that K(x,y)\subseteq K(x). My line of reasoning is this: any element h of K(x,y) is a quotient of polynomials with coefficients in K and "variables" x,y\in K(x). Each of these polynomials (in the 'numerator' and 'denominator' of h) is a polynomial in K[x]. Therefore being a field, K(x) must contain h, so K(x,y)\subseteq K(x). (i.e. we have equality in this case, so K(x) is an extension field of K(y)).

    Alternatively K(x,y)=K(x)(y) is the smallest subfield of K containing K(x) and y, which is K(x) if y\in K(x).

    Do these explanations make sense??

    Thanks in advance.
    Last edited by arlingtonbassett; Jan 22nd 2013 at 03:40 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Easy Question - Simple Interest, Simple Discount
    Posted in the Business Math Forum
    Replies: 0
    Last Post: Sep 21st 2010, 08:22 PM
  2. Easy simple regression model
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Jan 26th 2010, 06:05 AM
  3. Seemingly easy question... too easy.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Aug 23rd 2009, 09:36 PM
  4. Quick Easy Simple Task
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 6th 2009, 05:25 PM
  5. Replies: 2
    Last Post: Nov 1st 2008, 03:41 PM

Search Tags

/mathhelpforum @mathhelpforum