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
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.
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