The Moore-Penrose Inverse in Rings with Involution

被引：3
|
作者：
Xu, Sanzhang [1 ]
Chen, Jianlong [2 ]
机构：
[1] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Peoples R China
[2] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China
来源：
FILOMAT | 2019年 / 33卷 / 18期
基金：
中国国家自然科学基金;
关键词：
Moore-Penrose inverse; Group inverse; EP element; Normal element; Hermitian element; Projection; ELEMENTS; EP;
D O I：
10.2298/FIL1918791X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let R be a unital ring with involution. In this paper, we first show that for an element a 2 R, a is Moore-Penrose invertible if and only if a is well-supported if and only if a is co-supported. Moreover, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring R are obtained. In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented.
引用
收藏
页码：5791 / 5802
页数：12
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