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.
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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
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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 paragraph
In algebra, the Wedderburn-Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that a(n Artinian)
In Group: Ring Theory and Commutative Algebra, Lead section
to the product of finitely many ni-by-ni matrix rings over division rings Di, for some integers ni, both of which are
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