Theorem

Wedderburn's Little Theorem

Algebra

Every finite division ring is a field, meaning multiplication in a finite division ring is automatically commutative. Proved by Joseph Wedderburn, the theorem is a striking example of a finiteness condition forcing an algebraic structure into a more restrictive one.

Facts

Statement

Every finite division ring is a field; equivalently, every finite integral domain is a field, so for finite rings there is no distinction between domains, division rings and fields. 1

Proof Year

1905 1

Classification

Statement Form

Impossibility Theorem 1

Connections

Has Statement Form

Impossibility Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Algebra

Sources

1. Wedderburn's Little Theorem (Wikipedia)

Wikimedia Foundation

Lead section, opening sentence
Wedderburn's little theorem states that every finite division ring is a field; thus, every finite domain is a field.
History clause on Wedderburn's 1905 proof
The original proof was given by Joseph Wedderburn in 1905

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Wedderburn's Little Theorem

Has Statement Form

In Branch