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Does there exist a canonical projection from Z^p-1 to Z_p

  1. Feb 19, 2014 #1
    Okay, I thought that there would exist a projection from ##\mathbb{Z}^{p-1}## to ##\mathbb{Z}_{p}## where ##p## is a prime. Like there exist a projection from ##\mathbb{Z}## to ##\mathbb{Z}_p##
     
  2. jcsd
  3. Feb 19, 2014 #2

    jgens

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    Assuming Zp denotes the integers modulo p (and not the p-adic integers), then there is a "natural" projection Zp-1Z/p obtained simply by looking at the coproduct of the p-1 natural maps ZZ/p.
     
  4. Feb 19, 2014 #3
    okay, yeah you assumption is correct. Also, not to get to far off topic, but what does the p-adic integers look like.
     
  5. Feb 19, 2014 #4

    jgens

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    Just consider the inverse limit of the sequence ...→Z/p3Z/p2Z/p and this produces the p-adic integers. Another way is completing Q with respect to the p-adic norm and then consider all element with p-adic norm less than or equal to one.
     
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