EP Elements in Rings with Involution

被引：29
作者：
Xu, Sanzhang [1 ]
Chen, Jianlong [2 ]
Benitez, Julio [3 ]
机构：
[1] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Peoples R China
[2] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
[3] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46022 Valencia, Spain
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2019年 / 42卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Core inverse; EP; bi-EP; n-EP; MOORE-PENROSE; CORE INVERSE;
D O I：
10.1007/s40840-019-00731-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let R be a unital ring with involution. We first show that the EP elements in R can be characterized by three equations. Namely, let a. R, then a is EP if and only if there exists x. R such that (xa)* = xa, xa(2) = a and ax(2) = x. Any EP element in R is core invertible and Moore-Penrose invertible. We give more equivalent conditions for a core (Moore-Penrose) invertible element to be an EP element. Finally, any EP element is characterized in terms of the n-EP property, which is a generalization of the bi-EP property.
引用
收藏
页码：3409 / 3426
页数：18
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