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How do I prove the existence of this norm?

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  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?

    and

    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

    mathwonk

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  4. Jun 1, 2015 #3
    Thank you mathwonk.. I read these pages, but my question is different.
     
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