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Im soooooo close to solving this problem (Rings)

  1. Apr 27, 2007 #1
    Question: Let R be a ring of characteristic m > 0, and let n be any
    integer. Show that if 1 < gcd(n,m) < m, then n · 1R is a zero divisor



    heres what i got out of this:

    Let gcd(n,m) = b

    1< d < m so m/d = b < m
    and d | n


    Also, m * 1_R = 0

    can someone please offer some insight?
    thanks,
    nick
     
  2. jcsd
  3. Apr 27, 2007 #2

    StatusX

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    Homework Helper

    I don't follow you at all. What is d?

    If a ring has characteristic m, then the elements n*1_R which are zero are exactly those with n a multiple of m. So to show n is a zero divisor, you need to find another integer k such that nk is a multiple of m, but k is not, ie, n*1_R k*1_R=0, but k*1_R is not 0.
     
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