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Equivalence classes in rings

  1. Jan 24, 2008 #1
    So I'm kind of confused about the definition:

    [tex] a-b\in I[/tex]

    Why a - b instead of a + b?
  2. jcsd
  3. Jan 24, 2008 #2
    Are you trying to prove that a-b is an equivalence relation? Can you be more specific?
    Last edited: Jan 24, 2008
  4. Jan 24, 2008 #3


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    It's actually natural to write a-b because I becomes zero when you quotient out by it, so a-b in I means a-b=0 or, written differently, a=b.
  5. Jan 27, 2008 #4


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    you would presumably want a equivalent to a, which follows from a-a in I, rather than a+a in I.
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