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.

Relative field automorphisms and $Aut (K / F)$

Definition

Let $K / F$ be a field extension. An $F$ -automorphism of $K$ is an $F$ -isomorphism $K \to K$ . This is the relative-automorphism case of $F$ -homomorphisms and $F$ -embeddings of field extensions.

The set of all $F$ -automorphisms of $K$ is denoted

$Aut (K / F) : = {σ : K \to K : σ is an F -automorphism} .$

Composition is the proposed operation. That it makes this set a group, and the basic finite-extension bound on its order, are proved in $Aut (K / F)$ is a group and $∣ Aut (K / F) ∣ \leq [K : F]_{s} \leq [K : F]$ ↗.

Depends on

$F$ -homomorphisms and $F$ -embeddings of field extensions

Dependency tree · 2 levels

Sources