Mathematics

7 September, 15:43

et $R = / ZZ[/sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. Prove that $2$, $/sqrt{-n}$, and $1 + / sqrt{-n}$ are all irreducible in $R$. / item Prove that $R$ is not a UFD. [Hint: Show that either $/sqrt{-n}$ or $1+/sqrt{-n}$ is not prime.] / item Find a non-principal ideal in R.

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