Goldie's theorem, in the context of algebra and particularly concerning semigroups and group theory, pertains to the structure of certain algebraic objects. It is often discussed in relation to goldie dimensions and the growth of modules over rings.
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A semiprime ring has a classical right ring of quotients that is a semisimple ring and Artinian exactly when it is a right Goldie ring. In particular, the theorem applies to a semiprime ring that is a right Noetherian ring. It extends the fraction-field construction from commutative domains to rings whose quotient can be a finite product of matrix rings over division rings.