环中的混合core-EP-$(b,c)$逆
Hybrid core-EP-$(b,c)$ inverses in rings
AI总结：
本文研究环中core逆与混合(b,c)逆重合的条件，定义混合core-EP-(b,c)逆作为扩展，结合混合core-(b,c)逆与拟幂零元刻画该逆，给出其类极性质及基于像的表示。
AI中文摘要：
本文研究环中core逆与其混合(b,c)逆（即混合core-(b,c)逆）重合的条件，给出混合core-(b,c)逆的诸多刻画。为给这类广义逆建立更宽泛框架，定义混合core-EP-(b,c)逆作为混合core-(b,c)逆的自然扩展，结合混合core-(b,c)逆与拟幂零元刻画该新广义逆，通过新颖的基于极限的方法对其进行研究，给出其类极性质及基于像的表示。
英文摘要：
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.
