摘要
设R是任何环,左R-模A叫作FP-内射模,如果对任何有限表现模F,(Ext_R)′(F,A)=0。FP-内射模成功地刻划了凝聚环的性质因而越来越受到人们的关注。众所周知,任何模均有一个内射包(in jective hull)。本文利用反向极限函子,证明了任何模A在它的内射包E_R(A)中,一定有一个包含A的最小的FP-内射子模,因而是唯一确定的,它可用来定义为A的FP-内射包。
Let R be a ring with unit element, and A a left R-module. A is called FP-injective if ExtR'(P, A)=0 for every finitely presented R-module P. Let ER(A) denote the injective hull of A. In the paper we prove by means of inverse limit functor that any module A Over coherent ring R has the minimum FP-injective submodule eR(A) in ER(A) which contains A and can be defined as the FP-injective hull of A.
基金
国家自然科学基金会资助项目.
