摘要
左(右)R-模A称为GFP-内射模,如果ExtR1(M,A)=0对任-2-表现R-模M成立;左(右)R-模称为G-平坦的,如果TorR1(M,A)=0(TorR1(AM)=0)对于任一2-表现右(左)R-模M成立;环R称左(右)G-半遗传环,如果投射左(右)R-模的有限表现子模是投射的;环R称为左(右)G-正则环,如果自由左(右)R-模的有限表现子模为其直和项.研究了GFP-内射模和G-平坦模的一些性质,给出了它们的一些等价刻划.并利用它们刻划了凝聚环、G-半遗传环和G-正则环.
A left (right )R-modeule A is said to be GFP-injective,if ExtR1(M,A)=0 for all 2-presented module M;A left (right) R-module A is called G-flat,if TorR1 (M,.A) = 0 (TorR1 (A,M) = 0) for all 2 -presented right (left) R-modeluele M ;A ring R is Said to be left (right) G-semihereditary ,if every finitely presented submodule of a projective left (right) R- module is protective;A ring R is called left (right). G-regular if each finitely presented submodule of a free left (right) R- module is a summand. Some properties of GFP-injective module and G -flat modules are studied,and some equivalent characterizations of them are given. Moreover,Coherent rings,G-semihereditary rings and G-regular rings are characterized by GFP -injective modules and G-flat modules.
出处
《数学理论与应用》
2002年第3期40-46,共7页
Mathematical Theory and Applications
基金
湖北省教育厅重点科研项目(99A019)