query: Quotient ring $\mathbb{Z}[x]/(2x)$
positive_passages.docid: 19310
positive_passages.text: Identify the ring $\mathbb{Z}[x]/(2x)$
negative_passages.docid: 122914
negative_passages.text: An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$
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: 3203
negative_passages.text: Quotient group $\mathbb Z^n/\ \text{im}(A)$
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 129239
negative_passages.text: Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
negative_passages.docid: 135611
negative_passages.text: Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
negative_passages.docid: 50412
negative_passages.text: Prime elements in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 155991
negative_passages.text: Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
negative_passages.docid: 87617
negative_passages.text: Ring of $\mathbb{Z}_2$-valued functions
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: 54585
negative_passages.text: Order of some quotient ring of Gaussian integers
negative_passages.docid: 86922
negative_passages.text: Ring with 10 elements is isomorphic to $\mathbb{Z}/10 \mathbb{Z} $
negative_passages.docid: 93773
negative_passages.text: How many elements are in the quotient ring $\frac{\mathbb Z_3[x]}{\langle 2x^3+ x+1\rangle} $
negative_passages.docid: 74318
negative_passages.text: Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
negative_passages.docid: 24259
negative_passages.text: Quotient ring of $T/I$