Characterizations of Generalized Inverses by Clean Elements

被引：0
|
作者：
Shi, Guiqi [1 ]
Chen, Jianlong [2 ]
Zhou, Yukun [2 ]
机构：
[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China
[2] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2025年 / 22卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Generalized inverse; inverse along an element; clean element; & lowast; -clean element; MOORE-PENROSE INVERSE; EP ELEMENTS; RINGS;
D O I：
10.1007/s00009-025-02801-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, generalized inverses are studied by using (one-sided) clean elements. On one hand, the (one-sided) invertibility along an element is characterized by a (one-sided) clean element. As its applications, the existence criteria for Moore-Penrose inverse, group inverse, core inverse and right core inverse are given. On the other hand, two elements being simultaneously (one-sided) invertible along a same element are characterized by a (one-sided) clean element. As its special cases, the characterizations of an element being both Moore-Penrose invertible and group invertible are given.
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页数：16
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