CHARACTERIZATIONS OF ANNIHILATOR (b, c)-INVERSES IN ARBITRARY RINGS

被引：0

作者：

Zhang, Chong-Quan ^{[1
]}

Chang, Fujia ^{[1
]}

Gao, Heng ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2020年 / 46卷 / 02期

基金：

中国国家自然科学基金;

关键词：

generalized inverse; one-sided inverse; bicommutant; GENERALIZED INVERSES; CORE;

D O I：

10.17654/NT046020165

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we extend the notion of annihilator (b, c)-inverses to arbitrary rings (not necessary with identity). Then we demonstrate that annihilator (b, c) -inverses of elements in arbitrary rings may behave differently in contrast to (b, c) -inverses in semigroups. Further connections between annihilator (b, c) -inverses and one-sided ones are also investigated. In addition, we obtain a new general case of bicommutant property for annihilator (b, c) -inverses. As a consequence, we show that y(2)a(1) = a(2)y(1) and y(1)a(1)(*) a(2)(*)y(2) = together imply y(1)a(1)(dagger) = a(2)(dagger)y(2), where a(dagger) is the Moore-Penrose inverse of a in a *-ring.

引用

页码：165 / 179

页数：15

共 16 条

[1] Bicommuting properties of generalized inverses [J].

Drazin, Michael P. .

LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (09) :1770-1780

[2] Left and right generalized inverses [J].

Drazin, Michael P. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 510 :64-78

[3] Generalized inverses: Uniqueness proofs and three new classes [J].

Drazin, Michael P. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 449 :402-416

[4] Commuting properties of generalized inverses [J].

Drazin, Michael P. .

LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (12) :1675-1681

[5] A class of outer generalized inverses [J].

Drazin, Michael P. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (07) :1909-1923

[6] Pseudo core inverses in rings with involution [J].

Gao, Yuefeng ;

Chen, Jianlong .

COMMUNICATIONS IN ALGEBRA, 2018, 46 (01) :38-50

[7]

Johnson R.E., 1957, Trans. Amer. Math. Soc, V84, P523, DOI DOI 10.2307/1992828

[8]

Ke Y., 2016, ARXIV160706230MATH, P1

[9] New results on (b,c)-inverses [J].

Ke, Yuanyuan ;

Cvetkovic-Ilic, Dragana S. ;

Chen, Jianlong ;

Visnjic, Jelena .

LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (03) :447-458

[10] On generalized inverses and Green's relations [J].

Mary, X. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (08) :1836-1844

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