Hybrid core-EP-$(b,c)$ inverses in rings

Abstract

In this paper, we study when the core inverse in a ring coincides with its hybrid (b,c)-inverse, i.e., hybrid core-(b,c)-inverse. We present many characterizations of hybrid core-(b,c)-inverse. To establish a broader framework for this generalized inverses, we define hybrid core-EP-(b,c)-inverse that serves as a natural extension of the hybrid core-(b,c)-inverse. We characterize this new generalized inverse by combining the hybrid core-(b,c)-inverses and quasinilpotents. This generalized inverse is thereby examined through a novel limit-based approach. Its polar-like properties and image-based representations are presented.

20 pages