Every semisimple ring is isomorphic to a finite direct product of matrix rings over division rings. Named for Emil Artin and Joseph Wedderburn, it is the central structure theorem of noncommutative ring theory.
Facts
StatementEvery semisimple ring is isomorphic to a finite product of matrix rings over division rings, with the matrix sizes and division rings uniquely determined up to permutation of the factors. 1 Classification
Statement Form Connections
Has Statement Form
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
Proved By
Source Wedderburn-Artin theorem (Wikipedia)
Sources
1. Artin-Wedderburn Theorem (Wikipedia)
Wikimedia FoundationLead section, opening sentenceQuote, Lead section, opening sentence
the Wedderburn-Artin theorem is a classification theorem for semisimple rings and semisimple algebras.
Wedderburn-Artin theorem (Wikipedia)
Proved By: Emil Artin, Lead paragraphQuote, Proved By: Emil Artin, Lead paragraph
In algebra, the Wedderburn-Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that a(n Artinian)
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