2024/06/22 by Chen, Huanyin
#15A09 #16U90 #46H05 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2406.15745
The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and prove that it coincides with its m-weak group invertibility. We present the equivalent characterization of the m-weak group inverse by using a polar-like property. The relations between m-weak group inverse and core-EP inverse are also established. These give some new properties of the weak group inverse for complex matrices and ring elements.