余纯平坦模与CFH环

Copure flat modules and CFH-rings

设R是环。称左R-模M为余纯平坦模,是指对于任意的内射右R-模E,都有TorR1(E,M)=0;称环R为左CFH(Copure-Flat-Hereditary)环,是指左余纯平坦模的子模是左余纯平坦模。证明R是左CFH环,当且仅当内射右模的平坦维数不超过1;当且仅当R的每个左理想是余纯平坦的。

Let R be a ring. A left R- module M is called copure flat if TorR1（E,M） =0 for any injective right R- module E. A ring R is said to be left CFH （Copure-Flat-Hereditary） tings if every submodule of left copure fiat modules is copure fiat. It is proved that R is a left CFH ring if and only if the fiat dimen- sion of injective right modules is at most one; if and only if every ideal of R is copure fiat.