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P-adic field

  1. Jan 25, 2009 #1

    If [tex]p \neq q[/tex] are two primes, then the p-adic fields [tex]\mathbb{Q}_p[/tex] and [tex]\mathbb{Q}_q[/tex] are non isomorphic, right?

    Actually I've read this in my book and I'm not sure, if that's obvious (which means its just me who doesn't recognize it) or a statement which has to be proven.

    The p-adic fields as I know them are defined as:
    Let [tex]\mathcal{C}_p[/tex] be the set of all rational Cauchy-Sequences, and [tex]\mathcal{N}_p[/tex] be the ideal of [tex]\mathcal{C}_p[/tex] of all sequences converging to zero. Then [tex]\mathbb{Q}_p := \mathcal{C}_p / \mathcal{N}_p[/tex]

  2. jcsd
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