On the n-strong Drazin invertibility in rings

Honglin ZOU; Dijana MOSIC; Kezheng ZUO; Yinlan CHEN

Article Details

On the n-strong Drazin invertibility in rings

Authors:

Honglin ZOU | Dijana MOSIC | Kezheng ZUO | Yinlan CHEN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 6, pp.2659-2679

Document Type:

Article

Publication Date:

11/2019

Document Language:

English

Document ID (Org No.):

2000745489

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

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.

Article Details

On the n-strong Drazin invertibility in rings

Authors: Honglin ZOU | Dijana MOSIC | Kezheng ZUO | Yinlan CHEN

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2019 Vol.43 Issue 6, pp.2659-2679

Document Type: Article

Publication Date: 11/2019

Document Language: English

Document ID (Org No.): 2000745489

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Honglin ZOU | Dijana MOSIC | Kezheng ZUO | Yinlan CHEN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 6, pp.2659-2679

Document Type:

Article

Publication Date:

11/2019

Document Language:

English

Document ID (Org No.):

2000745489

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098