Generalized inverses modulo H in semigroups and rings

被引：54

作者：

Mary, Xavier ^{[1
]}

Patricio, Pedro ^{[2
]}

机构：

[1] Univ Paris Ouest Nanterre La Def, Lab Modal X, F-92000 Nanterre, France

[2] Univ Minho, Dept Matemat & Aplicacoes, P-4710057 Braga, Portugal

来源：

LINEAR & MULTILINEAR ALGEBRA | 2013年 / 61卷 / 08期

关键词：

generalized inverses; Green's relations; semigroups; rings; 15A09; 16E50; 20M99; MOORE-PENROSE INVERSE;

D O I：

10.1080/03081087.2012.731054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The definition of the inverse along an element was very recently introduced, and it contains known generalized inverses such as the group, Drazin and Moore-Penrose inverses. In this article, we first prove a simple existence criterion for this inverse in a semigroup, and then relate the existence of such an inverse in a ring to the ring units.

引用

页码：1130 / 1135

页数：6

共 50 条

[1] A new class of generalized inverses in semigroups and rings with involution
Zhu, Huihui
Wu, Liyun
Chen, Jianlong
[J]. COMMUNICATIONS IN ALGEBRA, 2023, 51 (05) : 2098 - 2113
[2] A class of outer generalized inverses and a note on Drazin's finiteness conditions in rings and semigroups
Wu, Cang
Chen, Jianlong
[J]. COMMUNICATIONS IN ALGEBRA, 2023, 51 (12) : 5167 - 5174
[3] Outer generalized inverses in rings
Djordjevic, DS
Wei, YM
[J]. COMMUNICATIONS IN ALGEBRA, 2005, 33 (09) : 3051 - 3060
[4] Generalized Hirano inverses in rings
Chen, Huanyin
Sheibani, Marjan
[J]. COMMUNICATIONS IN ALGEBRA, 2019, 47 (07) : 2967 - 2978
[5] GENERALIZED INVERSES OF A SUM IN RINGS
Castro-Gonzalez, N.
Mendes-Araujo, C.
Patricio, Pedro
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2010, 82 (01) : 156 - 164
[6] Generalized Zhou inverses in rings
Chen, Huanyin
Abdolyousefi, Marjan Sheibani
[J]. COMMUNICATIONS IN ALGEBRA, 2021, 49 (10) : 4098 - 4108
[7] Minimal Weak Drazin Inverses in Semigroups and Rings
Xu, Shuxian
Chen, Jianlong
Wu, Cang
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2024, 21 (03)
[8] GENERALIZED INVERSES IN REGULAR RINGS
SAVAGE, TR
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1980, 87 (02) : 455 - 466
[9] Generalized Inverses of Matrices over Rings
韩瑞珠
陈建龙
[J]. Chinese Quarterly Journal of Mathematics, 1992, (04) : 40 - 47
[10] THE ABSORPTION LAWS FOR THE GENERALIZED INVERSES IN RINGS
Jin, Hongwei
Benitez, Julio
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2015, 30 : 827 - 842

← 1 2 3 4 5 →