1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Equal additive order of all elem in simple ring

  1. May 2, 2010 #1


    User Avatar

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted