Hello I want to solve the following problem:

Let R =Z() ={ a+b |a,b belong toZ.

. Prove that R is integral domain.1

If2.I= ( ) is the ideal generated by , prove that R/I~=Z2(~= means isomorphic).

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InI showed that elements of R are commutative and without zero-divisors.1.

InI understood2.Ias all elements ofRmultiplied by ) . Am I correct?

How shall I prove isomorphism? I tried the following function fromRtoZ2: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!