When is a quasi-p-injective module continuous? (Q1396729)

The question when a quasi-p-injective right module is continuous (i.e. satisfies both the C1 and C2 conditions) is natural, since any quasi-p-injective module is known to have the C2-condition. Of course, since any uniform module has C1, uniform quasi-p-injective modules will be continuous. It is shown that a quasi-p-injective module that is a direct sum of uniform modules and is duo, is continuous. A projective semiperfect, duo, quasi-p-injective module that is a self-generator, is also shown to be continuous.