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

Show that R = {0.5(a+b(root2)) : a,b are integers} is not a domain

2. Relevant equations

A commutative ring (non trivial) is a domain iff (ab=0 => a=0 or b=0)

3. The attempt at a solution

I've try to construct a counterexample where x, y in R and xy=0 but x,y=/=0 but this has been hard to do since i realize that x and y mostly like have to be "conjugates of each other" and xy is of some form 0.25(a^2 - 2b^2) and (a^2 - 2b^2) = 0 and its impossible to do this just by using integers for a and b.

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# Homework Help: Show R is not a domain

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