View source for Classical semi-simple ring

An associative right  (or, equivalently, left) [[Artinian ring]] with zero [[Jacobson radical|Jacobson radical]]. The [[Wedderburn–Artin theorem]] describes the structure of the classical semi-simple rings. The class of classical semi-simple rings can also be characterized by homological properties (see [[Homological classification of rings]]). Every [[group algebra]] of a finite group over a field of characteristic coprime with the order of the group is a classical semi-simple ring. Commutative classical semi-simple rings are finite direct sums of fields. Connected with classical semi-simple rings is Goldie's theorem, which states that a ring has a left classical ring of fractions that is a classical semi-simple ring if and only if it satisfies the maximum condition for left annihilators and does not contain any infinite direct sums of left ideals.

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[[Category:Associative rings and algebras]]