DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-17

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.

The inseparable degree $[K : F]_{i} = [K : F] / [K : F]_{s}$ of a finite extension

Definition

For a finite extension $K / F$ (The degree $[K : F] = \dim_{F} K$ of a finite field extension), the inseparable degree is the natural number

$[K : F]_{i} : = \frac{[K : F]}{[K : F]_{s}} .$

The quotient is an integer because The separable degree divides the degree of every finite extension proves that the separable degree divides the ordinary degree.

Depends on

Dependency tree · 2 levels

Sources