query: Residue fields of $\mathbb Z[X_1,...,X_n]$ are always finite ?
positive_passages.docid: 29635
positive_passages.text: Fields finitely generated as $\mathbb Z$-algebras are finite?
negative_passages.docid: 65558
negative_passages.text: Irreducible in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 25471
negative_passages.text: Irreducibility of $x^n-x-1$ over $\mathbb Q$
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
negative_passages.docid: 135611
negative_passages.text: Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
negative_passages.docid: 84746
negative_passages.text: elementary proof that infinite primes quadratic residue modulo $p$
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 250
negative_passages.text: An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
negative_passages.docid: 96087
negative_passages.text: Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
negative_passages.docid: 93328
negative_passages.text: $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
negative_passages.docid: 20218
negative_passages.text: Is this field extension finite?
negative_passages.docid: 97904
negative_passages.text: Example of infinite field of characteristic $p\neq 0$
negative_passages.docid: 14918
negative_passages.text: Degree of splitting field of $X^n-1$ over some finite field
negative_passages.docid: 9129
negative_passages.text: Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements