The given ring is R=Z[−2]R=\Z[\sqrt{-2}]R=Z[−2] .
Your question is wrong , Since we known that RRR is a Euclidean domain by defining a norm on RRR ,i,e,N(a+b−2)=a2+2b2N(a+b\sqrt{-2})=a^2+2b^2N(a+b−2)=a2+2b2 and every Euclidean domain is PID .
Again every PID is UFD.
Hence RRR is a UFD.
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