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Homework Help: Proving the identity of the field

  1. Oct 22, 2008 #1
    1. The problem statement, all variables and given/known data
    If S = {s in R such that s=/=1} is an abelian group under circle operation (Circle Operation a*b = a + b -ab for a, b in R) then R is a field

    2. Relevant equations
    The verification of the field axioms

    3. The attempt at a solution
    The field axiom that I'm struggling to verify is the existence of the identity for the multiplicative operation since s=/=1. I'm wondering if someone can help me resolve this.

  2. jcsd
  3. Oct 23, 2008 #2


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    Isn't the identity 0? Why do you think it's not?
  4. Oct 23, 2008 #3


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    If aob= a+ b- ab Then the identity, e, must satisfy a+ e+ ae= a for all a. Solve that for e.
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