Generalized symmetric $*$-rings and Jacobson's Lemma for Moore--Penrose inverse

2017 ◽  
Vol 91 (3-4) ◽  
pp. 321-329
Author(s):  
Xiaoxiang Zhang ◽  
Jianlong Chen ◽  
Long Wang
Keyword(s):  
Jacobson’S Lemma

scholarly journals Jacobson’s lemma for the generalized Drazin inverse

2012 ◽  
Vol 436 (3) ◽  
pp. 742-746 ◽  
Author(s):  
Guifen Zhuang ◽  
Jianlong Chen ◽  
Jian Cui
Keyword(s):  
Drazin Inverse ◽  
Generalized Drazin Inverse ◽  
Jacobson’S Lemma

New extensions of Jacobson’s lemma and Cline’s formula

2017 ◽  
Vol 67 (1) ◽  
pp. 105-114
Author(s):  
V. G. Miller ◽  
H. Zguitti
Keyword(s):  
Cline’S Formula ◽  
Jacobson’S Lemma

A Generalization of Strongly Nil Clean Rings

2018 ◽  
Vol 25 (04) ◽  
pp. 585-594
Author(s):  
Jian Cui ◽  
Xiaobin Yin
Keyword(s):  
Clean Rings ◽  
Fundamental Properties ◽  
Cline’S Formula ◽  
Jacobson’S Lemma

Generalizing the notion of strongly nil clean rings, we introduce strongly quasi-nil clean rings. Some fundamental properties and equivalent characterizations of this class of rings are provided. By means of g-Drazin inverses, Cline’s formula and Jacobson’s lemma for strongly quasi-nil clean elements are investigated.

Jacobson’s lemma and Cline’s formula for generalized inverses in a ring with involution

2020 ◽  
Vol 48 (9) ◽  
pp. 3948-3961
Author(s):  
Guiqi Shi ◽  
Jianlong Chen ◽  
Tingting Li ◽  
Mengmeng Zhou
Keyword(s):  
Generalized Inverses ◽  
Cline’S Formula ◽  
Jacobson’S Lemma

Generalized Jacobson's lemma for Drazin inverses and its applications

2018 ◽  
Vol 68 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Kai Yan ◽  
Qingping Zeng ◽  
Yucan Zhu
Keyword(s):  
Jacobson’S Lemma

scholarly journals Jacobson's Lemma revisited

1980 ◽  
Vol 62 (2) ◽  
pp. 473-476 ◽  
Author(s):  
Irving Kaplansky
Keyword(s):  
Jacobson’S Lemma

On gs-Drazin inverses in a ring

2019 ◽  
Vol 19 (02) ◽  
pp. 2050029 ◽  
Author(s):  
Huanyin Chen ◽  
Mete Burak Calci
Keyword(s):  
Drazin Inverse ◽  
Cline’S Formula ◽  
Jacobson’S Lemma

An element [Formula: see text] in a ring [Formula: see text] has a gs-Drazin inverse if there exists [Formula: see text] such that [Formula: see text]. In this paper, we extend Cline’s formula and Jacobson’s Lemma for gs-Drazin inverses. Various additive properties of gs-Drazin inverses are thereby obtained.

scholarly journals Generalized Jacobson’s lemma for generalized Drazin inverses

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2267-2275
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Drazin Inverse ◽  
Multilinear Algebra ◽  
Jacobson’S Lemma

We present new generalized Jacobson?s lemma for generalized Drazin inverses. This extends the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear & Multilinear Algebra, 68(2020), 81-93).

scholarly journals On Jacobson’s lemma and Drazin invertibility

2010 ◽  
Vol 23 (4) ◽  
pp. 417-420 ◽  
Author(s):  
Dragana Cvetkovic-Ilic ◽  
Robin Harte
Keyword(s):  
Jacobson’S Lemma

scholarly journals Generalized Jacobson’s Lemma in a Banach algebra

2021 ◽  
pp. 1-13
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani Abdolyousefi
Keyword(s):  
Banach Algebra ◽  
Jacobson’S Lemma
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