Turkish Journal of Mathematics
Abstract
Let R be a ring and n be a positive integer. In this paper, further results on the n-strong Drazin inverse are obtained in a ring. We prove that a ∈ R is n-strongly Drazin invertible if and only if a-an+1 is nilpotent. In terms of this characterization, the extensions of Cline's formula and Jacobson's lemma for this inverse are proved. Moreover, the n-strong Drazin invertibility for the sums of two elements is considered. We prove that a,b ∈ R are n-strongly Drazin invertible if and only if a + b is n-strongly Drazin invertible, under the condition ab = 0. As applications for the additive results, we obtain some equivalent conditions of the n-strong Drazin invertibility of matrices over a ring.
DOI
10.3906/mat-1905-50
Keywords
Strong Drazin inverse, Hirano inverse, n-strong Drazin inverse, Drazin inverse ring
First Page
2659
Last Page
2679
Recommended Citation
ZOU, HONGLIN; MOSIC, DIJANA; ZUO, KEZHENG; and CHEN, YINLAN
(2019)
"On the n-strong Drazin invertibility in rings,"
Turkish Journal of Mathematics: Vol. 43:
No.
6, Article 1.
https://doi.org/10.3906/mat-1905-50
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss6/1
