Artin环局部化结构与一类商环的等价刻画  

Equivalent Characterization of Localization Structure of Artin Rings and A Class of Quotient Rings

作　　者：王玲[1] WANG Ling(Department of Data Science,College of Mathematics and Physics,Southwest University of Science and Technology,Mianyang Sichuan 621000,China)

机构地区：[1]西南科技大学数理学院数据科学系,四川绵阳621000

出　　处：《大学数学》2024年第3期1-4,共4页College Mathematics

基　　金：西南科技大学教育教学改革与研究项目(19xn0038)。

摘　　要：设R是Artin交换环,m_(i)(1≤i≤k)是R的k个极大理想.通过Artin环的Jacobson根幂零和中国剩余定理得到R到⊕R/m_(i)^(l)的同态是一种同构关系.进一步把Artin环写成有限个局部环Re_(i)的直和,发现这些直和加项与商环R/m_(i)^(l)是同构关系,并且与局部环R_(m_(i))的也是同构关系.Let R be an Artin commutative ring,and m_(i)(1≤i≤k)be the k maximal ideals of R.Through the Jacobson root nilpotent of Artin ring and chinese remainder theorem,it is obtained that the homomorphism from R to ⊕R/m_(i)^(l)is an isomorphism.Further,Artin rings are written as the direct sum of finite local rings Re i.It is found that each addition of direct sum is isomorphic to a quotient ring R/m_(i)^(l),and it is isomorphic with local ring R_(m_(i)).

关 键 词：Artin交换环 局部化 直和 同构 

分 类 号：O153.3[理学—数学]