Existence Criteria and Expressions of the (b, c)-Inverse in Rings and Their Applications

被引：15

作者：

Xu, Sanzhang ^{[1
]}

Benitez, Julio ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46022 Valencia, Spain

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 01期

关键词：

(b; c)-Inverse; inner inverse; the inverse along an element; annihilator; GENERALIZED INVERSES; CORE INVERSE;

D O I：

10.1007/s00009-017-1056-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a ring. Existence criteria for the (b, c)-inverse are given. We present explicit expressions for the (b, c)-inverse by using inner inverses. We answer the question when the (b, c)-inverse of a. R is an inner inverse of a. As applications, we give a unified theory of some well-known results of the {1, 3}-inverse, the {1, 4}-inverse, the Moore-Penrose inverse, the group inverse and the core inverse.

引用

页数：11

共 35 条

[1] Existence Criteria and Expressions of the (b, c)-Inverse in Rings and Their Applications
Sanzhang Xu
Julio Benítez
Mediterranean Journal of Mathematics, 2018, 15
[2] THE EXISTENCE AND EXPRESSIONS OF THE INVERSE ALONG OPERATORS B AND C
Deng, Chunyuan
Liu, Rufang
OPERATORS AND MATRICES, 2018, 12 (04): : 1027 - 1042
[3] New characterizations for the weighted (b, c)-inverse in rings and their applications
Xu, Sanzhang
Wang, Dingguo
Benitez, Julio
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (03)
[4] Characterizations for the (b , c)-core inverse in rings
Zhang, Qi
Song, Jingjing
Zhu, Huihui
Zou, Honglin
FILOMAT, 2024, 38 (22) : 7737 - 7742
[5] Left and Right Weighted (b, c)-inverse in Rings and Its Applications
Xu, Sanzhang
FRONTIERS OF MATHEMATICS, 2024, 19 (04): : 711 - 720
[6] New characterizations for the weighted (b, c)-inverse in rings and their applications
Sanzhang Xu
Dingguo Wang
Julio Benítez
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117
[7] On the (b, c)-Inverse in Rings
Mosic, Dijana
Zou, Honglin
Chen, Jianlong
FILOMAT, 2018, 32 (04) : 1221 - 1231
[8] The (b, c)-Inverse in Rings and in the Banach Context
Boasso, Enrico
Kantun-Montiel, Gabriel D
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (03)
[9] The (b, c)-inverse in semigroups and rings with involution
Chen, Xiaofeng
Chen, Jianlong
FRONTIERS OF MATHEMATICS IN CHINA, 2020, 15 (06) : 1089 - 1104
[10] The (b, c)-inverse in semigroups and rings with involution
Xiaofeng Chen
Jianlong Chen
Frontiers of Mathematics in China, 2020, 15 : 1089 - 1104

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