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 ...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.展开更多
This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all gen...For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.展开更多
In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinator...In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.展开更多
基金The National Natural Science Foundation of China(No.11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)+2 种基金the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13-072)the Scientific Research Foundation of Graduate School of Southeast Universitythe Fundamental Research Funds for the Central Universities(No.22420135011)
文摘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supported by the National Natural Science Foundation of China under grant No.11171222the Doctoral Program of the Ministry of Education under grant No.20094407120001
文摘This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.
文摘For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.
文摘In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.
