Generalized inverses modulo H in semigroups and rings

被引：61

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 15 条

[1]

[Anonymous], 2001, GRADUATE TEXTS MATH

[2]

Azumaya G., 1954, J FS HOKKAIDO U, V13, P034

[3]

Ben-Israel A., 2003, Generalized inverses: theory and applications

[4]

Drazin M., 1958, AM MATH MONTHLY, V65, P506, DOI [DOI 10.2307/2308576.416, 10.1080/00029890.1958.11991949]