Weak group inverses in proper ∗-rings
Mengmeng Zhou, Jianlong Chen, Yukun Zhou · Journal of Algebra and Its Applications · 2019
In proper ∗-rings, we characterize weak group inverses by three equations. It generalizes the notion of weak group inverse, which was introduced by Wang and Chen for complex matrices in 2018. Some new equivalent characterizations for elements to be weak group invertible are presented. Furthermore, we define the group-EP decomposition. Some properties of the weak group inverse are established by the group-EP decomposition.