DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-13

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.

A normal algebraic extension is one in which every minimal polynomial with a root in the extension splits there

Definition

An algebraic field extension $E / F$ is normal if, for every $α \in E$ , the minimal polynomial of $α$ over $F$ splits over $E$ .

Equivalently, every irreducible polynomial $p \in F [x]$ that has one root in $E$ splits over $E$ . Indeed, the monic associate of such a $p$ is the minimal polynomial of any one of its roots in $E$ , and multiplying by a nonzero scalar does not change whether a polynomial splits.

A normal algebraic extension is one in which every minimal polynomial with a root in the extension splits there

Definition

Depends on

Dependency tree · 2 levels

Sources