On the (b, c)-Inverse in Rings

被引：10
作者：
Mosic, Dijana [1 ]
Zou, Honglin [2 ]
Chen, Jianlong [3 ]
机构：
[1] Univ Nis, Fac Sci & Math, POB 224, Nish 18000, Serbia
[2] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Peoples R China
[3] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
FILOMAT | 2018年 / 32卷 / 04期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
(b; c)-inverse; outer inverse; group inverse; ring; OUTER GENERALIZED INVERSES; ELEMENT;
D O I：
10.2298/FIL1804221M
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present new characterizations for the existence of the (b, c)-inverse in a ring. The set of all (b, c)-invertible elements is described too. Necessary and sufficient conditions which ensure that the (b, c)-inverse of a given element commutes with that element are investigated. As an application of these results, we obtain new characterizations for the existence of the image-kernel (p, q)-inverse.
引用
收藏
页码：1221 / 1231
页数：11
相关论文
共 10 条
  • [1] THE INVERSE ALONG AN ELEMENT IN RINGS
    Benitez, Julio
    Boasso, Enrico
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 : 572 - 592
  • [2] The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras
    Cao, Jianbing
    Xue, Yifeng
    [J]. FILOMAT, 2013, 27 (05) : 851 - 863
  • [3] Outer generalized inverses in rings
    Djordjevic, DS
    Wei, YM
    [J]. COMMUNICATIONS IN ALGEBRA, 2005, 33 (09) : 3051 - 3060
  • [4] Commuting properties of generalized inverses
    Drazin, Michael P.
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (12) : 1675 - 1681
  • [5] A class of outer generalized inverses
    Drazin, Michael P.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (07) : 1909 - 1923
  • [6] Outer generalized inverses with prescribed ideals
    Kantun-Montiel, Gabriel
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (09) : 1187 - 1196
  • [7] On generalized inverses and Green's relations
    Mary, X.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (08) : 1836 - 1844
  • [8] Mosic D, 2014, ELECTRON J LINEAR AL, V27, P272
  • [9] Characterizations of Outer Generalized Inverses
    Wang, Long
    Castro-Gonzalez, Nieves
    Chen, Jianlong
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2017, 60 (04): : 861 - 871
  • [10] Reverse order law for the inverse along an element
    Zhu, Huihui
    Chen, Jianlong
    Patricio, Pedro
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (01) : 166 - 177
1