Rings with quasi-continuous right ideals

Rings in which each right ideal is quasi-continuous (right π-rings) are shown to be a direct sum of semisimple artinian square full ring and a right square free ring. Among other results it is also shown that (i) a nonlocal right continuous indecomposable right π-ring is either simple artinian or a ring of matrices of a certain type, and (ii) an indecomposable non-local right continuous ring is both a right and a left π-ring if and only if it is a right q-ring. In particular, a non local indecomposable right q-ring is a left q-ring.