query: Constructability of algebraic elements over $\mathbb{Q}$
positive_passages.docid: 147459
positive_passages.text: Find a non-constructible algebraic number of degree $4$ over $\Bbb Q$
negative_passages.docid: 102112
negative_passages.text: Idempotents in $\mathbb Z_n$
negative_passages.docid: 53432
negative_passages.text: What is the algebraic closure of $\mathbb F_q$?
negative_passages.docid: 83595
negative_passages.text: Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
negative_passages.docid: 25139
negative_passages.text: P-adic expansion construction
negative_passages.docid: 103654
negative_passages.text: A finite field extension that is not simple
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 119052
negative_passages.text: Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
negative_passages.docid: 88301
negative_passages.text: What are all of the connected subsets of $\mathbb{Q}$?
negative_passages.docid: 43987
negative_passages.text: Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields
negative_passages.docid: 120522
negative_passages.text: Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
negative_passages.docid: 19511
negative_passages.text: Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
negative_passages.docid: 5802
negative_passages.text: Proving the universal mapping property for polynomial rings
negative_passages.docid: 4401
negative_passages.text: Constructive proof that algebraic numbers form a field
negative_passages.docid: 87451
negative_passages.text: Construction of matrices under ZFC axioms
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$