DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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.

An algebraically closed field: every nonconstant polynomial has a root in the field

Definition

A field $F$ is algebraically closed when every nonconstant polynomial $p \in F [x]$ has a root in $F$ : there is $λ \in F$ such that $p (λ) = 0$ .

This definition concerns roots in the field itself. It does not assert here that any particular field, including $C$ , is algebraically closed.

Depends on

Used by

Every endomorphism of a nonzero finite-dimensional vector space over an algebraically closed field has an eigenvalue Corollary

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 11 results over 6 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

M. Khovanov, Linear Algebra II notes, §6 (standard reference, not scraped)
H. Pinkham, Linear Algebra, §12.1 (standard reference, not scraped)