Drazin Invertibility of Product and Difference of Idempotents in a Ring
نویسندگان
چکیده
In this paper, several equivalent conditions on the Drazin invertibility of product and difference of idempotents are obtained in a ring. Some results in Banach algebras are extended to the ring case.
منابع مشابه
Generalized Drazin invertibility of combinations of idempotents
The paper deals with the generalized Drazin invertibility of combinations of idempotents p, q in a Banach algebra. It proves the equivalence of the generalized Drazin invertibility of p−q and p+q, as well as the equivalence of the generalized Drazin invertibility of the commutator pq − qp and anticommutator pq + qp of p, q. It extends several results of J. Math. Anal. Appl. 359 (2009) 731–738, ...
متن کاملJacobson’s Lemma for Drazin Inverses
If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....
متن کاملCline’s formula for the generalized Drazin inverse
†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...
متن کاملRings in which elements are the sum of an idempotent and a regular element
Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents...
متن کاملElements of Rings with Equal Spectral Idempotents
In this paper we define and study a generalized Drazin inverse x for ring elements x, and give a characterization of elements a, b for which aa = bb. We apply our results to the study of EP elements in a ring with involution. 2000 Mathematics subject classification: primary 16A32, 16A28, 15A09; secondary 46H05, 46L05.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014