query: Is $\langle x⁴+1\rangle$ maximal in $\Bbb Z_7[x]$?
positive_passages.docid: 16592
positive_passages.text: Irreducible polynomial which is reducible modulo every prime
negative_passages.docid: 93169
negative_passages.text: Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
negative_passages.docid: 138572
negative_passages.text: Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 158315
negative_passages.text: Are $M_2= \langle(\sqrt{2}^{\sqrt{2}},\infty),\cdot \rangle$ , $M_1 = \langle(2,\infty),\cdot\rangle$ isomorphic structures?
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 76661
negative_passages.text: Checking the maximality of a principal ideal in $R[x]$
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 91627
negative_passages.text: What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
negative_passages.docid: 13682
negative_passages.text: Is $\langle a,b \mid a^2b^2=1 \rangle$ a semidirect product of $\mathbb{Z}^2$ and $\mathbb{Z}_2$?
negative_passages.docid: 157031
negative_passages.text: Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$
negative_passages.docid: 20296
negative_passages.text: The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
negative_passages.docid: 2907
negative_passages.text: How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 89782
negative_passages.text: To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field