query: Why isn't $\mathbb{Z}[\sqrt{5}]$ integrally closed?
positive_passages.docid: 150677
positive_passages.text: What are the integers $n$ such that $\mathbb{Z}[\sqrt{n}]$ is integrally closed?
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 48162
negative_passages.text: Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
negative_passages.docid: 90599
negative_passages.text: Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
negative_passages.docid: 21114
negative_passages.text: $S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
negative_passages.docid: 86807
negative_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 30192
negative_passages.text: How far are the $p$-adic numbers from being algebraically closed?
negative_passages.docid: 1020
negative_passages.text: Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 95669
negative_passages.text: Solutions of $|z| = z^5$ in $\Bbb{C}$?
negative_passages.docid: 95105
negative_passages.text: Solutions in complex number field, instead of $\mathbb{N}$, to Fermat's Last Theorem
negative_passages.docid: 9794
negative_passages.text: Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 120699
negative_passages.text: Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
negative_passages.docid: 252
negative_passages.text: Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
negative_passages.docid: 136855
negative_passages.text: Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$