query: To identify field $Z[i]/(3)$
positive_passages.docid: 142212
positive_passages.text: Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements
negative_passages.docid: 82328
negative_passages.text: Constructing a Galois extension field with Galois group $S_n$
negative_passages.docid: 87467
negative_passages.text: Finding some missing subfields of a splitting field of $x^4-7$
negative_passages.docid: 92517
negative_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: 19310
negative_passages.text: Identify the ring $\mathbb{Z}[x]/(2x)$
negative_passages.docid: 124438
negative_passages.text: Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
negative_passages.docid: 103561
negative_passages.text: Residue fields of schemes of finite type (over $\mathbb{Z}$)
negative_passages.docid: 53701
negative_passages.text: Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$
negative_passages.docid: 93328
negative_passages.text: $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
negative_passages.docid: 157074
negative_passages.text: The elements in the composite field $FK$
negative_passages.docid: 46047
negative_passages.text: Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
negative_passages.docid: 114295
negative_passages.text: Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$
negative_passages.docid: 126552
negative_passages.text: Number of subfields of finite field
negative_passages.docid: 137858
negative_passages.text: Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 119052
negative_passages.text: Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
negative_passages.docid: 19525
negative_passages.text: Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8