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EP Elements in Rings with Involution
被引:32
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
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.
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页码:3409 / 3426
页数:18
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