一类三阶矩阵环的quasipolar性质（英文）  

Quasipolar Properties of a Class of 3×3 Matrix Rings

作　　者：何亚茹 陈焕艮[1] HE Yaru;CHEN Huanyin(School of Science,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学理学院

出　　处：《杭州师范大学学报（自然科学版）》2019年第3期300-304,328,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(LY17A010018)

摘　　要：环R中的元素a称为quasipolar的,如果存在p∈R使得p2=p∈comm2(a),a+p∈U(R)并且有ap∈Rqnil.环R是quasipolr的若环中每一个元素都是quasipolar的.文章证明了带有自同态σ的局部环R上的一类相对于σ的3×3阶矩阵环是quasipolar的.对于一个带有自同态σ的局部环R,若σ(J(R))■J(R),则T3(R,σ)是quasipolar的当且仅当R是唯一bleached的.An element a∈R is called quasipolar if there exists p∈R such that p 2=p∈comm 2(a),a+p∈U(R)and ap∈R qnil.A ring R is quasipolar in case every element in R is quasipolar.In this paper,it is determined that the 3×3 matrix rings on the local ring R with endomorphismσis quasipolar.Let R be a local ring,and let σ:R→R be an endomorphism of R.If σ(J(R))■J(R),it is proved that T 3(R,σ)is quasipolar if and only if R is uniquely bleached.

关 键 词：quasipolar环 矩阵环 局部环 

分 类 号：O153.3[理学—数学]