query: The number of ideals in the quotient ring $\mathbb R[x]/\langle x^2-3x+2 \rangle$
positive_passages.docid: 147671
positive_passages.text: Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$
negative_passages.docid: 91627
negative_passages.text: What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
negative_passages.docid: 1719
negative_passages.text: Ideals in the ring of Gaussian integers
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: 3327
negative_passages.text: Height and minimal number of generators of an ideal
negative_passages.docid: 69649
negative_passages.text: If an ideal contains the multiplicative identity, then it is the whole ring
negative_passages.docid: 129438
negative_passages.text: Gaussian Integers and Quotient Rings
negative_passages.docid: 74150
negative_passages.text: Problem on the number of generators of some ideals in $k[x,y,z]$
negative_passages.docid: 50445
negative_passages.text: Explaining the product of two ideals
negative_passages.docid: 19112
negative_passages.text: Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
negative_passages.docid: 17239
negative_passages.text: Find all ideals of ${\mathbb{Z}_n}$
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 152297
negative_passages.text: Understanding quotients of $\mathbb{Q}[x]$
negative_passages.docid: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 140557
negative_passages.text: Counting ring homomorphisms from $\mathbb{Z}[x,y]/(x^3+y^2-1)$ to $\mathbb{Z_7}$
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$