Noetherian semiprime rings and distributivity

Theorem 1 is the main result of the article.
Theorem 1. The following conditions are equivalent: (1) $A$ is a right distributive right noetherian semiprime ring with finite left Goldie dimension; (2) $A$ is a left distributive left noetherian semiprime ring with finite right Goldie dimension; (3) $A$ is a finite direct product of invariant hereditary noetherian domains.