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.

Purely inseparable algebraic extensions

Definition

Let $K / F$ be algebraic (Algebraic and transcendental elements and algebraic extensions). If $char F = p > 0$ , the extension is purely inseparable when for every $α \in K$ there is $n \in N$ such that $α^{p^{n}} \in F$ . The exponent $n = 0$ is allowed. If $char F = 0$ , the term purely inseparable is reserved for the trivial extension $K = F$ .

The powers in positive characteristic are governed by the Frobenius endomorphism of Frobenius $x \mapsto x^{p}$ is an injective endomorphism in characteristic $p$ , and an automorphism for finite fields.

Purely inseparable algebraic extensions

Definition

Depends on

Dependency tree · 2 levels

Sources