半局部环的同调性质及其应用

Homological properties of semi-local rings and their applications

为了探索环的同调性质,分别研究了当可交换环上可逆模的投射盖是阿丁的、J(R)是诣零根、每个正则模是有限长度的等情形下环的半局部性;得到了各情形下相应环的同调性质;给出了连通环在半局部化条件下的一个刻画,即半局部环R为连通环当且仅当R的有限生成投射模均为稳定自由模.

In order to explore the homology properties of rings,when the projective cover of an any invertible module over a commutative ring is artinian and when Jacobson radical is nil radical,and every regular module is of finite length,the semi-locality of the ring was studied,respectively.A characterization of connected rings under semi-local conditions is given,namely,a semi-local ring R is a connected ring if and only if the finite generated projective modules of R are stable free modules.