On Almost Projective Modules

Abstract

In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if M is generalized N-projective for any modules M and N, then M is almost N-projective. We also show that if M is almost N-projective and N is lifting, then M is im-small N-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting.