摘要
称环R中的元素a为Drazin可逆的,如果存在R中的元素b使得ab=ba,bab=b,a-a2b是幂零的.上述元素b如果存在则是唯一的,并表示为aD.给出了一些环中涉及幂等元的Drazin逆的等价条件.作为应用,给出了环中幂等元的积与差的Drazin逆的公式.因此,一些关于Banach空间中有界线性算子的结果被推广到环上.
An element a of a ring R is called Drazin invertible if there exists b∈R such that ab =ba,bab =b,and a -a2 b is nilpotent.The element b above is unique if it exists and is denoted as aD .The equivalent conditions of the Drazin inverse involving idempotents in R are established.As applications, some formulae for the Drazin inverse of the difference and the product of idempotents in a ring are given.Hence,a number of results of bounded linear operators in Banach spaces are extended to the ring case.
基金
The National Natural Science Foundation of China(No.11371089)
the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)
the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13-072)
the Scientific Research Foundation of Graduate School of Southeast University
the Fundamental Research Funds for the Central Universities(No.22420135011)