一类伪polar环（英文）  

A Class of Pseudopolar Rings

作　　者：崔建 殷晓斌 CUI Jian;YIN Xiaobin(Department of Mathematics, Anhui Normal University, Wuhu, Anhui, 241002, P. R. China)

机构地区：[1]安徽师范大学数学系,芜湖安徽241002

出　　处：《数学进展》2018年第4期543-552,共10页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11401009);the Key Natural Science Foundation of Anhui Educational Committee(No.KJ2014A082);Anhui Provincial Natural Science Foundation(No.1408085QA01)

摘　　要：受拟polar环和伪polar环概念的启发,引入根polar环的定义.称环R中的元素α是根polar元,如果存在p^2=p∈R使得p∈comm^2(α),α+p∈U(R)且ap∈J(R);称环R是根polar的,如果R中每个元素都是根polar元.本文研究了根polar环的基本性质并构造了许多例子,同时借助根polar环研究了相关环类.证明了阶数大于1的任意矩阵环都不是根polar的,因此给出局部环上2阶矩阵是根polar元的判定准则.Motivated by the concepts of quasipolar rings and pseudopolar rings, we intro- duce the notion of radpolar rings. An element a of a ring R is called radpolar if there exists p^2 = p ∈ R such that p ∈ comm^2（a）, a＋p ∈ U（R） and ap ∈ J（R）; R is radpolar if every element of R is radpolar. Basic properties and illustrative examples of this sort of rings are presented; some related rings are studied by means of radpolar rings. It is proved that any matrix ring of size greater than 1 is not radpolar. Consequently, we determine when a 2 × 2 matrix over a local ring is radpolar.

关 键 词：根polar环 伪polar环 强正则环 拟polar环 矩阵 

分 类 号：O153.3[理学—数学]