DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 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.

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

Definition

Let $K / F$ and $L / F$ be field extensions (Field extensions, generated subrings $F [S]$ , generated subfields $F (S)$ , and simple extensions). An $F$ -homomorphism $σ : K \to L$ is a field homomorphism (Field homomorphism and embedding) satisfying $σ (a) = a$ for every $a \in F$ . Because field homomorphisms are injective, it is also called an $F$ -embedding. A bijective $F$ -homomorphism is an $F$ -isomorphism, and an $F$ -isomorphism $K \to K$ is an $F$ -automorphism of $K$ .

Depends on

Dependency tree · 2 levels

Sources