DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24

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.

Finite Galois extensions and $Gal (K / F)$

Definition

A finite extension $K / F$ is Galois when it is normal (A normal algebraic extension is one in which every minimal polynomial with a root in the extension splits there) and separable (Separable algebraic elements and separable extensions). Its Galois group is

$Gal (K / F) : = Aut (K / F),$

with the group operation supplied by Relative field automorphisms and $Aut (K / F)$ . The notation $Gal (K / F)$ is reserved here for an extension already known to be finite Galois; for an arbitrary extension the notation remains $Aut (K / F)$ .

Finite Galois extensions and $Gal (K / F)$

Definition

Depends on

Dependency tree · 2 levels

Sources

Finite Galois extensions and Gal⁡(K/F)Gal(K/F)

Definition

Depends on

Dependency tree · 2 levels

Sources

Finite Galois extensions and $Gal (K / F)$