DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

The relative algebraic closure of $F$ in an extension $K$

Definition

For a field extension $K / F$ , the relative algebraic closure of $F$ in $K$ is

${acl}_{K} (F) : = {a \in K : a is algebraic over F} .$

By The elements of an extension algebraic over the base field form a subfield, this set is a subfield of $K$ containing $F$ .

Depends on

The elements of an extension algebraic over the base field form a subfield

Dependency tree · 2 levels

Sources

A. W. Knapp, Basic Algebra, 2nd ed., Chapter IX, Section 1