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
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
相关论文
共 50 条
[41]   Moore-Penrose-invertible normal and Hermitian elements in rings [J].
Mosic, Dijana ;
Djordjevic, Dragan S. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (5-7) :732-745
[42]   The one-sided EP invertibility and the related generalized inverses [J].
Wang, Long ;
Zhai, Peipei ;
Li, Tingting ;
Zou, Honglin .
COMMUNICATIONS IN ALGEBRA, 2025,
[43]   The core inverse of the sum in a ring with involution [J].
Chen, Huanyin ;
Abdolyousefi, Marjan Sheibani .
FILOMAT, 2024, 38 (26) :9203-9211
[44]   Jacobson's lemma and Cline's formula for weighted generalized inverses in a ring with involution [J].
Zhou, Yukun ;
Chen, Jianlong .
FILOMAT, 2023, 37 (16) :5313-5324
[45]   Weak group inverses in proper *-rings [J].
Zhou, Mengmeng ;
Chen, Jianlong ;
Zhou, Yukun .
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (12)
[46]   Characterizations of *-DMP matrices over rings [J].
Gao, Yuefeng ;
Chen, Jianlong .
TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (03) :786-796
[47]   Reverse Order Law for the Core Inverse in Rings [J].
Zou, Honglin ;
Chen, Jianlong ;
Patricio, Pedro .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (03)
[48]   Characterizations for the (b , c)-core inverse in rings [J].
Zhang, Qi ;
Song, Jingjing ;
Zhu, Huihui ;
Zou, Honglin .
FILOMAT, 2024, 38 (22) :7737-7742
[49]   Core-EP inverse [J].
Prasad, K. Manjunatha ;
Mohana, K. S. .
LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (06) :792-802
[50]   On forward-order law for core inverse in rings [J].
Kumar, Amit ;
Mishra, Debasisha .
AEQUATIONES MATHEMATICAE, 2023, 97 (03) :537-562