Hello I want to solve the following problem:
Let R = Z( ) = { a+b |a,b belong to Z.
1. Prove that R is integral domain.
2. If I = ( ) is the ideal generated by , prove that R/I~=Z2 (~= means isomorphic).
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In 1. I showed that elements of R are commutative and without zero-divisors.
In 2. I understood I as all elements of R multiplied by ) . Am I correct?
How shall I prove isomorphism? I tried the following function from R to Z2: f(a+ b+I)= a mod 2. But it is only hommomorphism in my opinion, not isomorphism.
Can you help me?
Thank you in advance!