et $R = \ZZ[\sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. Prove that $2$, $\sqrt{-n}$, and $1 + \sqrt{-n}$ are all irr

Question

3 years ago

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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 irr

educible 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.

Mathematics

1 answer:

melisa1 [442] · Answer 1 · 2022-03-01T21:50:31+03:00

melisa1 [442]3 years ago

7 0

What the hell is that?