∞-余纯平坦模

摘要

通过引入∞-余纯平坦模,证明了:R是QF环当且仅当R是左Noether环,且每个有限表现左R-模是∞-余纯平坦模;R是右IF环当且仅当每个左R-模是∞-余纯平坦模;R是左CF H环当且仅当∞-余纯平坦模对子模封闭;左凝聚环R是左半遗传环当且仅当∞-余纯平坦左R-模是平坦的.%By introducing the ∞-copure flat modules,we proved that R is a QF ring if and only if R is left Noetherian ring and every finitely presented left R-module is ∞-copure flat;R is a right IF ring if and only if every left R-module is ∞-copure flat;R is a left CFH ring if and only if ∞-copure flat modules are closed to their submodules;a left coherent ring R is a semihereditary ring if and only if∞-copure flat left R-modules are flat.