query: How to calculate $ \mathbb{Z}[x] /\langle2x-1\rangle $?
positive_passages.docid: 144789
positive_passages.text: identify the ring $\mathbb{Z}[x]/(2x-1)$
negative_passages.docid: 105363
negative_passages.text: $\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
negative_passages.docid: 41069
negative_passages.text: Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
negative_passages.docid: 67772
negative_passages.text: How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
negative_passages.docid: 122312
negative_passages.text: How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
negative_passages.docid: 66313
negative_passages.text: $\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
negative_passages.docid: 68951
negative_passages.text: Normalization of the overlap $\langle x'|p'\rangle$
negative_passages.docid: 127814
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$
negative_passages.docid: 83183
negative_passages.text: Why is $\langle x| x' \rangle=\delta(x-x')$?
negative_passages.docid: 42213
negative_passages.text: Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
negative_passages.docid: 7967
negative_passages.text: Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
negative_passages.docid: 77903
negative_passages.text: Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
negative_passages.docid: 9223
negative_passages.text: Finding $\iiint_K (x^2 -z^2)\, dx\, dy \,dz$
negative_passages.docid: 134687
negative_passages.text: Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 54267
negative_passages.text: Field of fractions of $\mathbb{Q}[x,y]/\langle x^2+y^2-1\rangle$
negative_passages.docid: 147671
negative_passages.text: Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$