query: If $g(X)\in \Bbb Z[X]$ irreducible polynomial, then $\langle g(X) \rangle \trianglelefteq \Bbb Z[X]$ is not maximal
positive_passages.docid: 17991
positive_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 2043
negative_passages.text: $X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
negative_passages.docid: 8977
negative_passages.text: Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
negative_passages.docid: 140808
negative_passages.text: Problem on Galois theory and irreducible polynomial
negative_passages.docid: 132665
negative_passages.text: Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
negative_passages.docid: 97729
negative_passages.text: Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
negative_passages.docid: 80188
negative_passages.text: There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
negative_passages.docid: 104782
negative_passages.text: Polynomial irreducible - maximal ideal
negative_passages.docid: 63605
negative_passages.text: Irreducible polynomials and affine variety
negative_passages.docid: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
negative_passages.docid: 31303
negative_passages.text: If $p\in\Bbb Z[X]$ show that: $ \max\limits_{x\in [0,1]}\left|p(x) \right| > \frac{1}{e^{n}}. $
negative_passages.docid: 60816
negative_passages.text: Irreducibility of special cyclotomic polynomial.
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 31049
negative_passages.text: If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
negative_passages.docid: 76017
negative_passages.text: Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
negative_passages.docid: 35959
negative_passages.text: irreducibility of a polynomial over $\mathbb{F}_2$