The group inverse and core inverse of sums of two elements in a ring

Abstract

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.

Keywords:

• Group inverse
• core inverse
• sum
• difference

AMS SUBJECT CLASSIFICATIONS:

• 15A09
• 16W10

Additional information

Funding

The authors thank the editor and reviewer sincerely for their constructive comments and suggestions that have improved the quality of the paper. This research is supported by the National Natural Science Foundation of China (Nos. 11771076 and 11871145), the Fundamental Research Funds for the Central Universities, the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX18_0053).