设R是MFG整环,S表示R的极大理想生成的乘法系.R-模M称为几乎投射模,是指对任何无挠的ε-模N,Ext1(M,N)是S-挠模.证明了ε-有限生成模M是几乎投射模当且仅当对R的任何次极大素理想(p),M(p)是自由R(p)-模.同时证明了ε-有限生成的几乎投射模是ε-有限表现模,ε-有限生成的几乎投射的ε-模一定是自反模.
Let R be an MFG domain and S be the ideal multiplicative system generated by maximal ideals of R.An R-module M is called nearly projective if ExtR1(L(M),N) is S-torsion for every torsion-free ε-module N,where L(M) =(M/torε(M))ε.It is shown in this paper that an ε-finitely generated module M is nearly projective if and only if M(p) is free over R(p) and that ε-finitely generated nearly projective modules are ε-finitely presented.Moreover,it is also shown that ε-finitely generated nearly projective ε-modules are reflexive.