query: Proving that $I+x$ is irreducible in $R/I$, where $R=k[x,y,z]$ and $I=\langle x^2-yz\rangle$
positive_passages.docid: 18484
positive_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 87101
negative_passages.text: Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
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: 93291
negative_passages.text: Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
negative_passages.docid: 8977
negative_passages.text: Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 65558
negative_passages.text: Irreducible in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 7858
negative_passages.text: Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
negative_passages.docid: 29545
negative_passages.text: $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
negative_passages.docid: 95594
negative_passages.text: Prove that a polynomial is irreducible or the field contains a $p$th root
negative_passages.docid: 66946
negative_passages.text: show that $(i+k)! > i!k!$ algebraically
negative_passages.docid: 134726
negative_passages.text: Show the polynomial is irreducible in $\textbf Z_2$
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension
negative_passages.docid: 90144
negative_passages.text: Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$