Question

Show that z(sqrt-2) is non ufd

Answer 1

The given ring is $R=\Z[\sqrt{-2}]$ .

Your question is wrong , Since we known that $R$ is a Euclidean domain by defining a norm on $R$ ,i,e,$N(a+b\sqrt{-2})=a^2+2b^2$ and every Euclidean domain is PID .

Again every PID is UFD.

Hence $R$ is a UFD.