计算Drazin逆的一个方法  

A Method of Computing Drazin Inverse

作　　者：阿布都卡的·吾甫[1] Abdukadir Obul(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院

出　　处：《新疆大学学报（自然科学版）》2019年第4期406-410,431,共6页Journal of Xinjiang University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861061)

摘　　要：有单位元的环R中的元素a称为Drazin可逆,如果存在b∈R和自然数k使得ab=ba, a^kba=a^k.满足以上等式的最小自然数k称为元素a的Drazin指数.关于Drazin逆有相似于Jacobson引理的结果:1-ab Drazin可逆当且仅当1-ba Drazin可逆.在本文,当1-ab的Drazin指数为2时,我们通过Gr?bner-Shirshov基方法用1-ab的Drazin逆计算出1-ba的Drazin逆.In a ring R with identity 1, an element a ∈ R is called Drazin invertible, if there is b ∈ R and a natural number k such that ab = ba and a^kba = a^k. The smallest natural number k with above property is called the Drazin index of a. About Drazin invertibility, there is "Jacobson’s Lemma": 1-ab is Drazin invertible if and only if 1-ba is Drazin invertible. In this paper, using Gr?bner-Shirshov basis method, we compute the Drazin inverse of 1-ba in terms of the Drazin inverse of 1-ab for k = 2.

关 键 词：环 Grobner-Shirshov基 合成 DRAZIN逆 Drazin指数 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]