Abstract

In this paper, the authors continue their study, [started in J. Algebra 223, No. 1, 133-153 (2000; Zbl 0955.16023)], of rings \(R\) over which every (countably generated) right module is a direct sum of a projective module and a quasi-continuous module. They obtain some additional interesting features of these rings, for example that they are in fact of finite representation type, hence are also left Artinian, but they may not satisfy the above decomposition property on left modules. A structure theorem is given for rings satisfying the above property, showing that they are precisely the rings over which every right module is a direct sum of a projective module and a quasi-injective module.