【摘要】 设R是交换环,m∈Max(R).R-模M称为几乎投射模,是指对任意R_m-模N,都有Ext_R~1(M,N)=0.给出Rees定理对于几乎投射维数的一个应用.证明若R模A是非零模且Apd_RA<∞,则Apd_RA=Apd_RA+1其中R=R/aR,a∈R既不是单位也不是零因子.得到若环R是局部完全环,则AFPD(R)=0.还证明整环R是几乎局部完全整环,当且仅当对任何极大理想m,有R_m是几乎完全整环.更多还原

【Abstract】 Let R be a commutative ring.An R-module M is said to be almost projective if Ext_R~1(M,N)=Ofor any R_m-module,and m of R is a maximal ideal of R.In this paper,We give the change theorem of rings on the almost projective dimensions of R based on its property.The equality that Apd_RA=Apd_RA+1 is proved when A is nonzero and Apd_RA<∞.Moreover,we have we also prove that AFPD(R)=0 when R is a locally perfect ring.R is an almost locally perfect domain if and only if Rm is an almost perfect domain,where m of R is any maximal ideal of R.更多还原