A DECOMPOSITION THEOREM FOR HEREDITARY QUASI-CONTINUOUS RINGS

Abstract

It was shown in [1, Theorem 3.1] that a right CS right hereditary ring is right noetherian. However, the structure of such a ring is unknown. In this note we give a decomposition theorem for such rings under a ”slightly” stronger hypothesis. Namely, we will prove the following theorem.
Theorem A right hereditary ring is right quasi-continuous if and only if it is a ring-direct sum of a semisimple artinian ring and finitely many right hereditary right noetherian domains.