1. Not finding help here? Sign up for a free 30min 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!

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


    User Avatar
    Science Advisor
    Homework Helper

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


    User Avatar
    Staff Emeritus
    Science Advisor

    If aob= a+ b- ab Then the identity, e, must satisfy a+ e+ ae= a for all a. Solve that for e.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Proving the identity of the field
  1. Proving identities (Replies: 13)

  2. Proving identities (Replies: 4)

  3. Proving Identities (Replies: 1)

  4. Prove identity (Replies: 0)

  5. Prove identity (Replies: 7)