Theorem

Goldie's theorem on semisimple classical quotient rings

For a ring $R$, the following are equivalent: 1) the right classical ring of quotients for $R$ is semisimple; 2) $R$ is a semiprime and right Goldie ring.

Link: https://en.wikipedia.org/wiki/Goldie%27s_theorem

Reference(s)

  • (Citation needed)