DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-26

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A radical extension is a tower obtained by adjoining one $n$ -th root at each step

Let $L / F$ be a field extension. It is a radical extension when there is a finite tower

$F = F_{0} \subseteq F_{1} \subseteq \dots \subseteq F_{r} = L$

such that for each $i$ with $1 \leq i \leq r$ there are an integer $m_{i} \geq 1$ and an element $a_{i} \in F_{i - 1}$ with

$F_{i} = F_{i - 1} (α_{i}) and α_{i}^{m_{i}} = a_{i} .$

No Galois or root-of-unity hypothesis is built into the definition. Trivial steps with $m_{i} = 1$ are allowed.

Used by

Nothing. This result depends on no other item in the library.