广义FP-内射模、广义平坦模与某些环

Generalized FP-injective modules、generalized flat modules and some rings

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.