DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Index of a central division algebra

Definition

Let $D$ be a finite-dimensional division algebra whose centre is the field $K$ . Then $[D : K]$ is a square. Its positive square root $ind (D) : = \sqrt{[D : K]}$ is the index (or degree) of $D$ . Equivalently, every maximal subfield $L$ has $[L : K] = ind (D)$ and splits $D$ . This convention applies only to central finite-dimensional division algebras.

Depends on

Used by

The Schur index equals the division-algebra index Theorem

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Gabor Wiese, Galois Representations, Theorem 2.3.5 (standard reference, not scraped)
Weizhe Zheng, Lectures on Algebra, Section 3.7 (standard reference, not scraped)