The Study On Almost Projective Modules And AP-Alomost Projective Modules

In this thesis,we study almost projective modules and AP-almost projective modules.Some equivalent characterizations of alomst projective modules and almost projec-tive dimensions are provided,and some equivalent characterizations of AP-alomst projective modules and AP-almost projective dimensions are also provided.The following statements are proved:(1)R is a von Neumann regular ring if and only if every module of R is almost projective.(2)ApdRM≤ApdTM+ApdRT holds for any T-module M when φ:R→T is surjective.(3)R is a QF ring if and only if every module of R is AP-almost projective.(4)AFPD(R)=0 when R is a locally perfect ring.(5)R is a locally almost perfect domain if and only if Rm is an almost perfect domain,as well as m∈ Max(R).