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

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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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 UF…

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