query: Yes/No: Is $\mathbb{Q}[y]$ is field?
positive_passages.docid: 46254
positive_passages.text: Why can't the Polynomial Ring be a Field?
negative_passages.docid: 79725
negative_passages.text: Fields of arbitrary cardinality
negative_passages.docid: 118310
negative_passages.text: How to find $\operatorname{Gal}(S/\mathbb{Q})$
negative_passages.docid: 55026
negative_passages.text: $\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
negative_passages.docid: 120699
negative_passages.text: Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
negative_passages.docid: 153444
negative_passages.text: $\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 41035
negative_passages.text: Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
negative_passages.docid: 11710
negative_passages.text: How to show that $\mathbb{Q}$ is not $G_\delta$
negative_passages.docid: 29626
negative_passages.text: Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
negative_passages.docid: 53432
negative_passages.text: What is the algebraic closure of $\mathbb F_q$?
negative_passages.docid: 42213
negative_passages.text: Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 121658
negative_passages.text: $x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$