环的局部化条件及应用  

Localization of a Ring and Its Application

作　　者：李艳午[1] LI Yanwu(Basic Teaching Department,Wuhu Institute of Technology,Wuhu 241003,Anhui,China)

机构地区：[1]芜湖职业技术学院基础教学部,安徽芜湖241003

出　　处：《江汉大学学报（自然科学版）》2020年第6期38-43,共6页Journal of Jianghan University：Natural Science Edition

基　　金：安徽省教育厅2019年自然科学研究重点项目(KJ2019A0976)。

摘　　要：首先,分别从环中不可逆元的幂零性和环的理想格的链条件实现了环的局部化,在局部化的基础上研究K0群和K1群的同调性质。然后,从投射模的自由性出发,构造局部环的条件,研究了该条件下的矩阵环的行列式映射性质和幂等矩阵的可对角化问题。最后,作为应用,给出了SF环局部化条件下的若干结果。Firstly,the homological properties of K0 groups and K1 groups were studied on the basis of localization from the nilpotency of irreversible elements in rings and the chain condition of ideal lattices of rings,respectively.Then,starting from the freedom of projective modules,the conditions of constructing local rings were given,and the determinant mapping properties of matrix rings and the diagonalization of idempotent matrices were studied.Finally,as an application,some results of localization of SF ring were given.

关 键 词：局部环 不可逆元 理想格 同调性质 置换环 矩阵环 对角化 

分 类 号：O153.3[理学—数学]