Minimal Weak Drazin Inverses in Semigroups and Rings

被引：0

作者：

Xu, Shuxian ^{[1
]}

Chen, Jianlong ^{[1
]}

Wu, Cang ^{[1
]}

机构：

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

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Drazin inverse; minimal rank weak Drazin inverse; pi-regularity; Green's preorder;

D O I：

10.1007/s00009-024-02661-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1978, Campbell and Meyer proposed the notion of minimalrank weak Drazin inverses of complex matrices. In this paper, we defineminimal weak Drazin inverses of elements in semigroups using Green'spreorde r <= R,which generalize minimal rank weak Drazin inverses ofcomplex matrices. For two elementsa, yof a semigroup, it is provedthatyis a minimal weak Drazin inverse ofaif and only if ya(k+1)=a(k) for some nonnegative integer k and ay(2)=y

引用

页数：15

共 50 条

[1] MINIMAL RANK WEIGHTED WEAK DRAZIN INVERSES
Mosic, Dijana
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2024, 40 : 714 - 728
[2] WEAK DRAZIN INVERSES
CAMPBELL, SL
MEYER, CD
LINEAR ALGEBRA AND ITS APPLICATIONS, 1978, 20 (02) : 167 - 178
[3] MINIMAL RANK WEAK DRAZIN INVERSES: A CLASS OF OUTER INVERSES WITH PRESCRIBED RANGE
Wu, Cang
Chen, Jianlong
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2023, 39 : 1 - 16
[4] A Class of Drazin Inverses in Rings
Wang, Zhou
FILOMAT, 2017, 31 (06) : 1781 - 1789
[5] A class of outer generalized inverses and a note on Drazin's finiteness conditions in rings and semigroups
Wu, Cang
Chen, Jianlong
COMMUNICATIONS IN ALGEBRA, 2023, 51 (12) : 5167 - 5174
[6] Pseudo Drazin inverses in associative rings and Banach algebras
Wang, Zhou
Chen, Jianlong
LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (06) : 1332 - 1345
[7] Generalized inverses modulo H in semigroups and rings
Mary, Xavier
Patricio, Pedro
LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (08): : 1130 - 1135
[8] The generalized and pseudo n-strong Drazin inverses in rings
Mosic, Dijana
LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (02): : 361 - 375
[9] Left and right-Drazin inverses in rings and operator algebras
Ren, Yanxun
Jiang, Lining
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (04)
[10] Weak group inverses in proper *-rings
Zhou, Mengmeng
Chen, Jianlong
Zhou, Yukun
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (12)

← 1 2 3 4 5 →