Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do I prove the existence of this norm?

  1. Jun 1, 2015 #1
    I am reading an article[1] that states:

    Let k be a fixed local field. Then there is an integer q=pr, where p is a fixed prime element of k and r is a positive integer, and a norm |.| on k such that for all x∈k we have |x|≥0 and for each x∈k\{0} we get |x|=qm for some integer m. This norm is non-Archimedean, that is |x+y|≤max{|x|,|y|} for all x,y∈k and |x+y|=max{|x|,|y|} whenever |x|≠|y|.

    how do i prove the existence of this norm?


    how to prove that the norm is non-Archimedean?

    [1]: http://docdro.id/11a73
    Last edited: Jun 1, 2015
  2. jcsd
  3. Jun 1, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper

  4. Jun 1, 2015 #3
    Thank you mathwonk.. I read these pages, but my question is different.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook