The group inverse and core inverse of sums of two elements in a ring
Mengmeng Zhou, Jianlong Chen, Xia Zhu · Communications in Algebra · 2019
In Dedekind-finite ring, we present the group inverse of sum of two group invertible elements under different conditions. Then, the core inverse of a sum of two core invertible elements is investigated. Furthermore, the core inverse of the difference of two core invertible elements is presented. These results generalized the corresponding results of complex matrices.