query: Find the ring of algebraic integers.
positive_passages.docid: 92517
positive_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
negative_passages.docid: 69649
negative_passages.text: If an ideal contains the multiplicative identity, then it is the whole ring
negative_passages.docid: 127029
negative_passages.text: Ring of formal power series finitely generated as algebra?
negative_passages.docid: 148310
negative_passages.text: Showing rational numbers are algebraic
negative_passages.docid: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 8087
negative_passages.text: Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
negative_passages.docid: 24203
negative_passages.text: Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
negative_passages.docid: 24259
negative_passages.text: Quotient ring of $T/I$
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 138672
negative_passages.text: Finding Ideals in $\begin{bmatrix} \mathbb{Q} & \mathbb{Q}\\ 0 & 0 \end{bmatrix}$
negative_passages.docid: 127814
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$
negative_passages.docid: 135087
negative_passages.text: Find integer solutions of $xy=-1$ (using only elementary ring theory).
negative_passages.docid: 138459
negative_passages.text: Norm and Algebraic Integers
negative_passages.docid: 19112
negative_passages.text: Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
negative_passages.docid: 147671
negative_passages.text: Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$
negative_passages.docid: 102721
negative_passages.text: Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$