∞-余纯投射模

∞-copure Projective Modules

设R是环,F∞表示平坦维数有限的左R-模类.左R-模M称为∞-余纯投射模,指对任意N∈F∞都有Ext1R(M,N)=0.证明∞-余纯投射模M是投射模当且仅当M∈F∞,同时证明当l.FFD(R)=0时,余纯投射模是∞-余纯投射模.用∞-余纯投射模刻画QF环和CPH环,证明R是QF环当且仅当每一左R-模是∞-余纯投射模,当且仅当每一N∈F∞是内射模.也证明了R是CPH环当且仅当∞-余纯投射左R-模的子模是∞-余纯投射模,当且仅当每一N∈F∞的内射维数不超过1.

Let R be a ring and denote by F∞ the class of left R-modules with finite flat dimension. A left R-module M is called zo - copure projective if Ext^（M,N） =0 for all N∈ F∞. In this paper we prove that an ∞ -copure projective module M is projective if and only if M ∈F∞ , and that if 1. FFD（R） =0 then every copure projective left R-module is ∞-copure projective. Then we characterize QF and CPH rings in terms of ∞ -copure projective modules, and prove that R is QF ring if and only if every left R-module is ∞ -copure projective if and only if every N∈F∞ is injective. We also prove that R is CPH ring if and only if every submodule of an ∞ -copure pro- jective left R-module is ∞ -copure projective if and only if idR N≤1 for all N∈F∞ .