query: Why the ring of integers of $ \mathbb Q(\sqrt{-19}) $ is $ \mathbb Z\left[\frac{1+\sqrt{-19}}{2}\right] $?
positive_passages.docid: 19473
positive_passages.text: Why is quadratic integer ring defined in that way?
negative_passages.docid: 133775
negative_passages.text: Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
negative_passages.docid: 27704
negative_passages.text: Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
negative_passages.docid: 42875
negative_passages.text: The prime elements of the ring $ \mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right] $.
negative_passages.docid: 61292
negative_passages.text: How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
negative_passages.docid: 8087
negative_passages.text: Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
negative_passages.docid: 34668
negative_passages.text: Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$
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: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 102721
negative_passages.text: Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
negative_passages.docid: 39492
negative_passages.text: Finding $z\in \mathbb C$ with $\sin z = 2$?
negative_passages.docid: 35691
negative_passages.text: $\mathbb Z[\sqrt 3]$ contains infinitely many units
negative_passages.docid: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 132193
negative_passages.text: Why $\Bbb Z$ = (integers) is an integral domain?