New characterizations for core inverses in rings with involution  

作　　者：Sanzhang XU Jianlong CHEN Xiaoxiang ZHANG 

机构地区：[1]Department of Mathematics,Southeast University,Nanjing 210096,China

出　　处：《Frontiers of Mathematics in China》2017年第1期231-246,共16页中国高等学校学术文摘·数学(英文)

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11201063,11371089);the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020);the Jiangsu Planned Projects for Postdoctoral Research Funds(No.1501048B);the Natural Science Foundation of Jiangsu Province(No.BK20141327).

摘　　要：The core inverse for a complex matrix was introduced by O.M.Baksalary and G.Trenkler.D.S.Rakic,N.C.Dincic and D.S.Djordjevc generalized the core inverse of a complex matrix to the case of an element in a ring.They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible.It is natural to ask when a group invertible element is core invertible.In this paper,we will answer this question.Let R be a ring with involution,we will use three equations to characterize the core inverse of an element.That is,let a,b∈R.Then a∈R with a=b if and only if(ab)^(*)=ab,ba^(2)=a,and ab^(2)=b.Finally,we investigate the additive property of two core invertible elements.Moreover,the formulae of the sum of two core invertible elements are presented.

关 键 词：Core inverse dual core inverse group inverse {1 3}-inverse inverse{1 4}-inverse 

分 类 号：O153.3[理学—数学] X142[理学—基础数学]