(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove thatZwith the following addition and subtraction is a ring.

2. Relevant equations

a[tex]\oplus[/tex]b = a + b - 1 and a[tex]\odot[/tex]b = ab - (a + b) + 2

3. The attempt at a solutionI proved all the axioms for addition. I'm stuck on the multiplication part.

(a[tex]\odot[/tex]b)[tex]\odot[/tex]c = (ab-(a+b)+2)c - (ab-(a+b)+2+c) + 2

a[tex]\odot[/tex](b[tex]\odot[/tex]c) = a(bc-(b+c)+2) - (a+bc-(b+c)+2) + 2

How are these equal? I know it's a ring because a couple problems later, my books wants me to prove that it's an integral domain...

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# Ring proof

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