query: Proving $\mathbb{Z}[\sqrt{6}]$ is a PID
positive_passages.docid: 146470
positive_passages.text: Show $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain
negative_passages.docid: 86807
negative_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 130826
negative_passages.text: Computing class group of $\mathbb Q(\sqrt{6})$
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 126503
negative_passages.text: Showing that an integral domain is a PID if it satisfies two conditions
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 134885
negative_passages.text: proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 88304
negative_passages.text: Center of $D_6$ is $\mathbb{Z}_2$
negative_passages.docid: 100892
negative_passages.text: Proving divisibility of $a^3 - a$ by $6$
negative_passages.docid: 114793
negative_passages.text: Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
negative_passages.docid: 50930
negative_passages.text: Proving the continued fraction representation of $\sqrt{2}$
negative_passages.docid: 94958
negative_passages.text: Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?
negative_passages.docid: 14447
negative_passages.text: Direct proof that $\pi$ is not constructible
negative_passages.docid: 140949
negative_passages.text: Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
negative_passages.docid: 155991
negative_passages.text: Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?