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Equal additive order of all elem in simple ring

  1. May 2, 2010 #1


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    1. The problem statement, all variables and given/known data

    Let S be a simple ring. Show that all nonzero elements of S have equal additive order. Show that this order either is a prime number p or is infinite.

    3. The attempt at a solution

    All I could show is that the order of any element x in S must divide that of the unity element: if n is the order of the unity element, then nx=n(1x)=(n1)x=0x=0. By Lagrange's theorem the order of any element must also divide the number of elements in the ring.
  2. jcsd
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