query: Describe the rings: a) $\mathbb{Z}[x] / (x^2 - 3, 2x + 4)$, b) $\mathbb{Z}[i]/ (2 + i)$
positive_passages.docid: 20097
positive_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 77903
negative_passages.text: Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 89215
negative_passages.text: How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
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: 87617
negative_passages.text: Ring of $\mathbb{Z}_2$-valued functions
negative_passages.docid: 87160
negative_passages.text: Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
negative_passages.docid: 30401
negative_passages.text: Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
negative_passages.docid: 95863
negative_passages.text: Describe the units in $\mathbb{Z}[\sqrt{-d}]$
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 81982
negative_passages.text: Is $\mathbb{Z}[x]$ a principal ideal domain?
negative_passages.docid: 18186
negative_passages.text: Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
negative_passages.docid: 65637
negative_passages.text: Squares in Polynomial Quotient Ring $ (\mathbb{Z}/2)[x] /(x^{17} - 1) $
negative_passages.docid: 30752
negative_passages.text: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
negative_passages.docid: 73743
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$