When every projective module is a direct sum of finitely generated modules (Q2456192)

The authors investigate the question of when every projective right module is a direct sum of finitely generated modules. The main result is a precise criterion for every projective right module having the aforementioned property. Using this criterion they give a new proof of a Bergman's result that ensures that every projective module over a weakly semihereditary ring is a direct sum of finitely generated modules.