= Goldie's theorem
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{title2=$R\text{ semiprime right Goldie}\iff Q_{\mathrm{cl}}^r(R)\text{ semisimple Artinian}$}
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= Goldie theorem
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{synonym}
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.
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