Cyclic rings

  • Thread starter tjkubo
  • Start date
  • #1
42
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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?
 

Answers and Replies

  • #2
Deveno
Science Advisor
906
6
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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