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Cyclic rings

  1. Nov 17, 2011 #1
    If R is a finite ring and its additive group is cyclic, then
    R = <r> = {nr : n an integer} for some r in R.
    r^2 is in R so r^2 = kr for some integer k.
    Does k have to divide the order of R?
     
  2. jcsd
  3. Nov 17, 2011 #2

    Deveno

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    Science Advisor

    the finite field of 5 elements is a ring with a cyclic additive group.

    3 generates this ring, and 4= 32= (3)(3), is it the case that 3 divides 5?
     
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