5 papers · 1 filter
The higher order group inverse in a ring
Liu Dayong, Chen Huanyin
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring…
Group invertibility of the sum in rings and its applications
Huanyin Chen, Dayong Liu, Marjan Sheibani
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inv…
Perturbation for group inverse in a Banach algebra
Dayong Liu, Tugce Pekacar Calci, Handan Kose +1
We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of is thereby given. These extend the ma…
The group invertibility of matrices over Bézout domains
Dayong Liu, Aixiang Fang
Let be a Bézout domain, and let with . If and are group invertible, we prove that is similar to . Moreover, we have $(AB)^{…
The Generalized Flanders' Theorem in Unit-regular Rings
Dayong Liu, Aixiang Fang
Let R be a unit-regular ring, and let a,b,c in R satisfy aba=aca. If ac and ba are group invertible, we prove that ac is similar to ba. Furthermore, if ac and ba are Drazin inverti…