query: The ring $\mathbb{Z}[i]/(2)$
positive_passages.docid: 41069
positive_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
negative_passages.docid: 45627
negative_passages.text: Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 86922
negative_passages.text: Ring with 10 elements is isomorphic to $\mathbb{Z}/10 \mathbb{Z} $
negative_passages.docid: 50412
negative_passages.text: Prime elements in $\mathbb{Z}/n\mathbb{Z}$
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: 33245
negative_passages.text: Show that every ideal of the ring $\mathbb Z$ is principal
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
negative_passages.docid: 146980
negative_passages.text: Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
negative_passages.docid: 22084
negative_passages.text: $\mathbb{Z}[i] / (2+3i)$ has 13 elements
negative_passages.docid: 20097
negative_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 135611
negative_passages.text: Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
negative_passages.docid: 129750
negative_passages.text: Order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?