关于Primely Polar环  

On Primely Polar Rings

作　　者：李颉琛 陈焕艮[1] LI Jiechen;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,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2020年第1期76-81,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY17A010018).

摘　　要：称环R中的元素a是primely polar的,如果存在p^2=p∈comm^2(a)使得a+p∈U(R)且ap∈P(R).称环R是primely polar的,如果环R中每个元素都是primely polar的.文章将primely polar环与其他熟悉的环理论建立起联系,证明了交换的强π正则环是primely polar的,以及primely polar环是强π正则环.此外,还研究了primely polar环在Drazin逆中的特性.结论表明,一个环R是primely polar的,当且仅当对任意的a∈R,存在e^2=e∈comm(a)使得a-e∈U(R),ae∈P(R),当且仅当对任意的a∈R,存在b∈comm(a)使得b=b^2a,a-a^2b∈P(R).A element a of a ring R is called primely polar if there exists p^2=p∈comm^2(a)such that a+p∈U(R)and ap∈P(R).A ring R is said to be primely polar in case every element of R is primely polar.This paper connects the primely polar rings with other related rings,proves that a commutative stronglyπ-regular ring is primely polar and a primely polar ring is stronglyπ-regular.Furthermore,it investigates the characteristics of primely polar rings in Drazin inverses.The results show that a ring R is primely polar if and only if for any a∈R,there exists e^2=e∈comm(a)such that a-e∈U(R),ae∈P(R),if and only if for any a∈R there exists b∈comm(a)such that b=b^2a,a-a^2b∈P(R).

关 键 词：quasinilpotent quasipolar环 强幂零 primely polar环 DRAZIN逆 

分 类 号：O153.3[理学—数学]