Andrunakievič's theorem on subdirect representations of reduced rings

For any reduced ring $R$, $R$ is a subdirect product of (possibly noncommutative) domains. In particular, every simple reduced ring is a domain.


  • A. A. Klein. A simple proof of a theorem on reduced rings. (1980) @ main Theorem p 495
  • V. Andrunakievic. Rings without nilpotent elements and completely simple ideals. (1968) @ main theorem